LMFDB - Embedded newform 1323.2.h.g.802.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(226,1323)]

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, 2]))

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

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

chi := DirichletCharacter("1323.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.h (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:	$\Z[a_1, \ldots, a_{11}]$
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			802.3
Root			$1.29589 - 0.748185i$ of defining polynomial
Character	$\chi$	$=$	1323.802
Dual form			1323.2.h.g.226.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.239123 q^{2} -1.94282 q^{4} +(-1.29589 + 2.24456i) q^{5} +0.942820 q^{8} +O(q^{10})$	\(q-0.239123 q^{2} -1.94282 q^{4} +(-1.29589 + 2.24456i) q^{5} +0.942820 q^{8} +(0.309879 - 0.536725i) q^{10} +(2.09097 + 3.62167i) q^{11} +(-1.84155 - 3.18966i) q^{13} +3.66019 q^{16} +(0.855536 - 1.48183i) q^{17} +(3.57780 + 6.19694i) q^{19} +(2.51769 - 4.36077i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(-2.56238 + 4.43818i) q^{23} +(-0.858685 - 1.48729i) q^{25} +(0.440358 + 0.762722i) q^{26} +(-1.06238 + 1.84010i) q^{29} -6.53585 q^{31} -2.76088 q^{32} +(-0.204579 + 0.354341i) q^{34} +(-0.830095 - 1.43777i) q^{37} +(-0.855536 - 1.48183i) q^{38} +(-1.22180 + 2.11621i) q^{40} +(-5.10948 - 8.84988i) q^{41} +(0.830095 - 1.43777i) q^{43} +(-4.06238 - 7.03625i) q^{44} +(0.612725 - 1.06127i) q^{46} -9.33824 q^{47} +(0.205332 + 0.355645i) q^{50} +(3.57780 + 6.19694i) q^{52} +(5.32326 - 9.22015i) q^{53} -10.8387 q^{55} +(0.254040 - 0.440011i) q^{58} -6.06429 q^{59} -7.98597 q^{61} +1.56287 q^{62} -6.66019 q^{64} +9.54583 q^{65} +8.26320 q^{67} +(-1.66215 + 2.87893i) q^{68} -6.23912 q^{71} +(-3.57780 + 6.19694i) q^{73} +(0.198495 + 0.343803i) q^{74} +(-6.95103 - 12.0395i) q^{76} -9.82846 q^{79} +(-4.74322 + 8.21550i) q^{80} +(1.22180 + 2.11621i) q^{82} +(3.44733 - 5.97094i) q^{83} +(2.21737 + 3.84060i) q^{85} +(-0.198495 + 0.343803i) q^{86} +(1.97141 + 3.41458i) q^{88} +(-2.51769 - 4.36077i) q^{89} +(4.97825 - 8.62258i) q^{92} +2.23299 q^{94} -18.5458 q^{95} +(-1.53167 + 2.65294i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} + 12 q^{4} - 24 q^{8}+O(q^{10}) $ 12 * q - 4 * q^2 + 12 * q^4 - 24 * q^8	$ 12 q - 4 q^{2} + 12 q^{4} - 24 q^{8} + 8 q^{11} + 12 q^{16} - 6 q^{22} + 4 q^{23} - 12 q^{25} + 22 q^{29} - 32 q^{32} + 6 q^{37} - 6 q^{43} - 14 q^{44} - 12 q^{46} + 56 q^{50} + 28 q^{53} - 18 q^{58} - 48 q^{64} + 12 q^{65} - 76 q^{71} + 36 q^{74} - 12 q^{79} + 30 q^{85} - 36 q^{86} + 6 q^{88} + 62 q^{92} - 120 q^{95}+O(q^{100}) $ 12 * q - 4 * q^2 + 12 * q^4 - 24 * q^8 + 8 * q^11 + 12 * q^16 - 6 * q^22 + 4 * q^23 - 12 * q^25 + 22 * q^29 - 32 * q^32 + 6 * q^37 - 6 * q^43 - 14 * q^44 - 12 * q^46 + 56 * q^50 + 28 * q^53 - 18 * q^58 - 48 * q^64 + 12 * q^65 - 76 * q^71 + 36 * q^74 - 12 * q^79 + 30 * q^85 - 36 * q^86 + 6 * q^88 + 62 * q^92 - 120 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.239123			−0.169086			−0.0845428	−	0.996420i	$-0.526943\pi$
$2$	−0.239123			−0.169086			−0.0845428	+	0.996420i	$0.526943\pi$
$3$		0			0
$3$		0			0
$4$	−1.94282			−0.971410
$5$	−1.29589	+	2.24456i	−0.579542	+	1.00380i	0.415990	+	0.909369i	$0.363435\pi$
$5$	−1.29589	+	2.24456i	−0.579542	+	1.00380i	−0.995532	+	0.0944264i	$0.969898\pi$
$6$		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
$11$	2.09097	+	3.62167i	0.630452	+	1.09197i	0.987459	+	0.157873i	$0.0504636\pi$
$11$	2.09097	+	3.62167i	0.630452	+	1.09197i	−0.357008	+	0.934101i	$0.616203\pi$
$12$		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
$16$	3.66019			0.915047
$17$	0.855536	−	1.48183i	0.207498	−	0.359397i	−0.743428	−	0.668816i	$-0.766801\pi$
$17$	0.855536	−	1.48183i	0.207498	−	0.359397i	0.950926	+	0.309419i	$0.100135\pi$
$18$		0			0
$19$	3.57780	+	6.19694i	0.820805	+	1.42168i	0.905084	+	0.425233i	$0.139808\pi$
$19$	3.57780	+	6.19694i	0.820805	+	1.42168i	−0.0842790	+	0.996442i	$0.526859\pi$
$20$	2.51769	−	4.36077i	0.562973	−	0.975097i
$21$		0			0
$22$	−0.500000	−	0.866025i	−0.106600	−	0.184637i
$23$	−2.56238	+	4.43818i	−0.534294	+	0.925424i	0.464904	+	0.885361i	$0.346089\pi$
$23$	−2.56238	+	4.43818i	−0.534294	+	0.925424i	−0.999197	+	0.0400622i	$0.987244\pi$
$24$		0			0
$25$	−0.858685	−	1.48729i	−0.171737	−	0.297457i
$26$	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
$31$	−6.53585			−1.17387			−0.586937	−	0.809633i	$-0.699666\pi$
$31$	−6.53585			−1.17387			−0.586937	+	0.809633i	$0.699666\pi$
$32$	−2.76088			−0.488059
$33$		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	$0.876908\pi$
$38$	−0.855536	−	1.48183i	−0.138786	−	0.240385i
$39$		0			0
$40$	−1.22180	+	2.11621i	−0.193183	+	0.334602i
$41$	−5.10948	−	8.84988i	−0.797967	−	1.38212i	−0.920938	−	0.389708i	$-0.872576\pi$
$41$	−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
$47$	−9.33824			−1.36212			−0.681061	−	0.732226i	$-0.738481\pi$
$47$	−9.33824			−1.36212			−0.681061	+	0.732226i	$0.738481\pi$
$48$		0			0
$49$		0			0
$50$	0.205332	+	0.355645i	0.0290383	+	0.0502958i
$51$		0			0
$52$	3.57780	+	6.19694i	0.496152	+	0.859361i
$53$	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
$58$	0.254040	−	0.440011i	0.0333571	−	0.0577762i
$59$	−6.06429			−0.789504			−0.394752	−	0.918788i	$-0.629169\pi$
$59$	−6.06429			−0.789504			−0.394752	+	0.918788i	$0.629169\pi$
$60$		0			0
$61$	−7.98597			−1.02250			−0.511249	−	0.859433i	$-0.670817\pi$
$61$	−7.98597			−1.02250			−0.511249	+	0.859433i	$0.670817\pi$
$62$	1.56287			0.198485
$63$		0			0
$64$	−6.66019			−0.832524
$65$	9.54583			1.18401
$66$		0			0
$67$	8.26320			1.00951			0.504755	−	0.863262i	$-0.331583\pi$
$67$	8.26320			1.00951			0.504755	+	0.863262i	$0.331583\pi$
$68$	−1.66215	+	2.87893i	−0.201566	+	0.349122i
$69$		0			0
$70$		0			0
$71$	−6.23912			−0.740448			−0.370224	−	0.928943i	$-0.620719\pi$
$71$	−6.23912			−0.740448			−0.370224	+	0.928943i	$0.620719\pi$
$72$		0			0
$73$	−3.57780	+	6.19694i	−0.418750	+	0.725297i	−0.995814	−	0.0914022i	$-0.970865\pi$
$73$	−3.57780	+	6.19694i	−0.418750	+	0.725297i	0.577064	+	0.816699i	$0.304198\pi$
$74$	0.198495	+	0.343803i	0.0230746	+	0.0399663i
$75$		0			0
$76$	−6.95103	−	12.0395i	−0.797338	−	1.38103i
$77$		0			0
$78$		0			0
$79$	−9.82846			−1.10579			−0.552894	−	0.833252i	$-0.686477\pi$
$79$	−9.82846			−1.10579			−0.552894	+	0.833252i	$0.686477\pi$
$80$	−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
$86$	−0.198495	+	0.343803i	−0.0214043	+	0.0370733i
$87$		0			0
$88$	1.97141	+	3.41458i	0.210153	+	0.363996i
$89$	−2.51769	−	4.36077i	−0.266875	−	0.462240i	0.701178	−	0.712986i	$-0.252658\pi$
$89$	−2.51769	−	4.36077i	−0.266875	−	0.462240i	−0.968053	+	0.250745i	$0.919324\pi$
$90$		0			0
$91$		0			0
$92$	4.97825	−	8.62258i	0.519018	−	0.898966i
$93$		0			0
$94$	2.23299			0.230315
$95$	−18.5458			−1.90276
$96$		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
$101$	−5.54984	−	9.61260i	−0.552229	−	0.956489i	−0.998113	−	0.0613986i	$-0.980444\pi$
$101$	−5.54984	−	9.61260i	−0.552229	−	0.956489i	0.445884	−	0.895091i	$-0.352889\pi$
$102$		0			0
$103$	−3.99298	+	6.91605i	−0.393440	+	0.681459i	−0.992901	−	0.118946i	$-0.962049\pi$
$103$	−3.99298	+	6.91605i	−0.393440	+	0.681459i	0.599460	+	0.800404i	$0.295382\pi$
$104$	−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	$0.279753\pi$
$110$	2.59179			0.247117
$111$		0			0
$112$		0			0
$113$	3.46457	+	6.00082i	0.325920	+	0.564509i	0.981698	−	0.190444i	$-0.0609928\pi$
$113$	3.46457	+	6.00082i	0.325920	+	0.564509i	−0.655778	+	0.754953i	$0.727659\pi$
$114$		0			0
$115$	−6.64115	−	11.5028i	−0.619291	−	1.07264i
$116$	2.06402	−	3.57498i	0.191639	−	0.331929i
$117$		0			0
$118$	1.45011			0.133494
$119$		0			0
$120$		0			0
$121$	−3.24433	+	5.61934i	−0.294939	+	0.510849i
$122$	1.90963			0.172890
$123$		0			0
$124$	12.6980			1.14031
$125$	−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	$0.367536\pi$
$128$	7.11436			0.628827
$129$		0			0
$130$	−2.28263			−0.200200
$131$	−2.15143	+	3.72639i	−0.187971	+	0.325576i	−0.944574	−	0.328299i	$-0.893525\pi$
$131$	−2.15143	+	3.72639i	−0.187971	+	0.325576i	0.756602	+	0.653875i	$0.226858\pi$
$132$		0			0
$133$		0			0
$134$	−1.97592			−0.170694
$135$		0			0
$136$	0.806617	−	1.39710i	0.0691668	−	0.119800i
$137$	10.2947	+	17.8309i	0.879533	+	1.52340i	0.851854	+	0.523779i	$0.175478\pi$
$137$	10.2947	+	17.8309i	0.879533	+	1.52340i	0.0276785	+	0.999617i	$0.491189\pi$
$138$		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
$142$	1.49192			0.125199
$143$	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
$149$	3.03379	−	5.25468i	0.248538	−	0.430480i	−0.714582	−	0.699551i	$-0.753383\pi$
$149$	3.03379	−	5.25468i	0.248538	−	0.430480i	0.963120	+	0.269071i	$0.0867166\pi$
$150$		0			0
$151$	−2.24433	−	3.88728i	−0.182641	−	0.316343i	0.760138	−	0.649761i	$-0.225131\pi$
$151$	−2.24433	−	3.88728i	−0.182641	−	0.316343i	−0.942779	+	0.333418i	$0.891798\pi$
$152$	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
$157$	1.02891			0.0821163			0.0410582	−	0.999157i	$-0.486927\pi$
$157$	1.02891			0.0821163			0.0410582	+	0.999157i	$0.486927\pi$
$158$	2.35021			0.186973
$159$		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	$0.919505\pi$
$164$	9.92680	+	17.1937i	0.775153	+	1.34260i
$165$		0			0
$166$	−0.824336	+	1.42779i	−0.0639809	+	0.110818i
$167$	8.99716	+	15.5835i	0.696221	+	1.20589i	0.969767	+	0.244032i	$0.0784701\pi$
$167$	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
$173$	0.830357			0.0631309			0.0315654	−	0.999502i	$-0.489951\pi$
$173$	0.830357			0.0631309			0.0315654	+	0.999502i	$0.489951\pi$
$174$		0			0
$175$		0			0
$176$	7.65335	+	13.2560i	0.576893	+	0.999208i
$177$		0			0
$178$	0.602038	+	1.04276i	0.0451247	+	0.0781582i
$179$	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	$-0.495160\pi$
$181$	0.409157			0.0304124			0.0152062	+	0.999884i	$0.495160\pi$
$182$		0			0
$183$		0			0
$184$	−2.41586	+	4.18440i	−0.178100	+	0.308478i
$185$	4.30286			0.316353
$186$		0			0
$187$	7.15561			0.523270
$188$	18.1425			1.32318
$189$		0			0
$190$	4.43474			0.321730
$191$	−16.0241			−1.15946			−0.579731	−	0.814808i	$-0.696842\pi$
$191$	−16.0241			−1.15946			−0.579731	+	0.814808i	$0.696842\pi$
$192$		0			0
$193$	−12.3743			−0.890721			−0.445360	−	0.895351i	$-0.646924\pi$
$193$	−12.3743			−0.890721			−0.445360	+	0.895351i	$0.646924\pi$
$194$	0.366259	−	0.634379i	0.0262959	−	0.0455458i
$195$		0			0
$196$		0			0
$197$	−23.1021			−1.64595			−0.822977	−	0.568075i	$-0.807688\pi$
$197$	−23.1021			−1.64595			−0.822977	+	0.568075i	$0.807688\pi$
$198$		0			0
$199$	3.37323	−	5.84260i	0.239122	−	0.414171i	−0.721341	−	0.692580i	$-0.756474\pi$
$199$	3.37323	−	5.84260i	0.239122	−	0.414171i	0.960463	+	0.278409i	$0.0898072\pi$
$200$	−0.809585	−	1.40224i	−0.0572463	−	0.0991536i
$201$		0			0
$202$	1.32710	+	2.29860i	0.0933741	+	0.161729i
$203$		0			0
$204$		0			0
$205$	26.4854			1.84982
$206$	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	$-0.364094\pi$
$212$	−10.3421	+	17.9131i	−0.710301	+	1.23028i
$213$		0			0
$214$	−0.473045	−	0.819338i	−0.0323367	−	0.0560088i
$215$	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
$220$	21.0577			1.41971
$221$	−6.30206			−0.423922
$222$		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
$227$	−3.03215	−	5.25183i	−0.201251	−	0.348576i	0.747681	−	0.664058i	$-0.231167\pi$
$227$	−3.03215	−	5.25183i	−0.201251	−	0.348576i	−0.948932	+	0.315482i	$0.897834\pi$
$228$		0			0
$229$	5.52466	−	9.56899i	0.365080	−	0.632336i	−0.623709	−	0.781656i	$-0.714375\pi$
$229$	5.52466	−	9.56899i	0.365080	−	0.632336i	0.988789	+	0.149320i	$0.0477084\pi$
$230$	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
$236$	11.7818			0.766932
$237$		0			0
$238$		0			0
$239$	10.5813	+	18.3273i	0.684445	+	1.18549i	0.973611	+	0.228214i	$0.0732886\pi$
$239$	10.5813	+	18.3273i	0.684445	+	1.18549i	−0.289166	+	0.957279i	$0.593378\pi$
$240$		0			0
$241$	−6.84573	−	11.8572i	−0.440972	−	0.763786i	0.556790	−	0.830654i	$-0.312033\pi$
$241$	−6.84573	−	11.8572i	−0.440972	−	0.763786i	−0.997762	+	0.0668671i	$0.978700\pi$
$242$	0.775794	−	1.34371i	0.0498699	−	0.0863772i
$243$		0			0
$244$	15.5153			0.993265
$245$		0			0
$246$		0			0
$247$	13.1774	−	22.8240i	0.838460	−	1.45225i
$248$	−6.16213			−0.391296
$249$		0			0
$250$	2.03443			0.128669
$251$	−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
$254$	−2.17867			−0.136702
$255$		0			0
$256$	11.6192			0.726198
$257$	12.8107	−	22.1889i	0.799112	−	1.38410i	−0.121082	−	0.992642i	$-0.538637\pi$
$257$	12.8107	−	22.1889i	0.799112	−	1.38410i	0.920195	−	0.391461i	$-0.128030\pi$
$258$		0			0
$259$		0			0
$260$	−18.5458			−1.15016
$261$		0			0
$262$	0.514457	−	0.891066i	0.0317833	−	0.0550502i
$263$	3.55034	+	6.14938i	0.218924	+	0.379187i	0.954479	−	0.298278i	$-0.0964121\pi$
$263$	3.55034	+	6.14938i	0.218924	+	0.379187i	−0.735556	+	0.677464i	$0.763079\pi$
$264$		0			0
$265$	13.7968	+	23.8967i	0.847528	+	1.46796i
$266$		0			0
$267$		0			0
$268$	−16.0539			−0.980649
$269$	−8.21572	+	14.2301i	−0.500922	+	0.867622i	0.499078	+	0.866557i	$0.333672\pi$
$269$	−8.21572	+	14.2301i	−0.500922	+	0.867622i	−0.999999	+	0.00106448i	$0.999661\pi$
$270$		0			0
$271$	−6.34899	−	10.9968i	−0.385674	−	0.668007i	0.606189	−	0.795321i	$-0.292698\pi$
$271$	−6.34899	−	10.9968i	−0.385674	−	0.668007i	−0.991862	+	0.127314i	$0.959364\pi$
$272$	3.13143	−	5.42379i	0.189871	−	0.328865i
$273$		0			0
$274$	−2.46169	−	4.26378i	−0.148716	−	0.257584i
$275$	3.59097	−	6.21975i	0.216544	−	0.375065i
$276$		0			0
$277$	0.414230	+	0.717468i	0.0248887	+	0.0431084i	0.878201	−	0.478291i	$-0.158744\pi$
$277$	0.414230	+	0.717468i	0.0248887	+	0.0431084i	−0.853313	+	0.521399i	$0.825410\pi$
$278$	−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
$283$	−7.35417			−0.437160			−0.218580	−	0.975819i	$-0.570142\pi$
$283$	−7.35417			−0.437160			−0.218580	+	0.975819i	$0.570142\pi$
$284$	12.1215			0.719278
$285$		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
$290$	0.658419	+	1.14041i	0.0386637	+	0.0669674i
$291$		0			0
$292$	6.95103	−	12.0395i	0.406778	−	0.704561i
$293$	3.91286	+	6.77728i	0.228592	+	0.395933i	0.957391	−	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
$299$	18.8750			1.09157
$300$		0			0
$301$		0			0
$302$	0.536670	+	0.929540i	0.0308819	+	0.0534890i
$303$		0			0
$304$	13.0954	+	22.6820i	0.751075	+	1.30090i
$305$	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
$310$	−2.02532	+	3.50796i	−0.115030	+	0.199239i
$311$	32.3176			1.83256			0.916281	−	0.400536i	$-0.131176\pi$
$311$	32.3176			1.83256			0.916281	+	0.400536i	$0.131176\pi$
$312$		0			0
$313$	−24.3196			−1.37462			−0.687312	−	0.726362i	$-0.741209\pi$
$313$	−24.3196			−1.37462			−0.687312	+	0.726362i	$0.741209\pi$
$314$	−0.246037			−0.0138847
$315$		0			0
$316$	19.0949			1.07417
$317$	−5.13844			−0.288603			−0.144302	−	0.989534i	$-0.546094\pi$
$317$	−5.13844			−0.288603			−0.144302	+	0.989534i	$0.546094\pi$
$318$		0			0
$319$	−8.88564			−0.497500
$320$	8.63090	−	14.9492i	0.482482	−	0.835684i
$321$		0			0
$322$		0			0
$323$	12.2438			0.681262
$324$		0			0
$325$	−3.16263	+	5.47783i	−0.175431	+	0.303855i
$326$	0.816422	+	1.41408i	0.0452174	+	0.0783189i
$327$		0			0
$328$	−4.81732	−	8.34384i	−0.265992	−	0.460712i
$329$		0			0
$330$		0			0
$331$	−11.6979			−0.642977			−0.321488	−	0.946913i	$-0.604183\pi$
$331$	−11.6979			−0.642977			−0.321488	+	0.946913i	$0.604183\pi$
$332$	−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	$0.463351\pi$
$338$	0.0675835	−	0.117058i	0.00367606	−	0.00636711i
$339$		0			0
$340$	−4.30795	−	7.46159i	−0.233631	−	0.404661i
$341$	−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
$346$	−0.198558			−0.0106745
$347$	−27.3114			−1.46615			−0.733075	−	0.680148i	$-0.761916\pi$
$347$	−27.3114			−1.46615			−0.733075	+	0.680148i	$0.761916\pi$
$348$		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
$353$	5.13466	+	8.89349i	0.273290	+	0.473353i	0.969702	−	0.244289i	$-0.0785547\pi$
$353$	5.13466	+	8.89349i	0.273290	+	0.473353i	−0.696412	+	0.717642i	$0.745221\pi$
$354$		0			0
$355$	8.08525	−	14.0041i	0.429120	−	0.743258i
$356$	4.89142	+	8.47218i	0.259245	+	0.449025i
$357$		0			0
$358$	−0.906150	+	1.56950i	−0.0478915	+	0.0829505i
$359$	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
$362$	−0.0978390			−0.00514231
$363$		0			0
$364$		0			0
$365$	−9.27292	−	16.0612i	−0.485367	−	0.840680i
$366$		0			0
$367$	3.88768	+	6.73367i	0.202935	+	0.351494i	0.949473	−	0.313849i	$-0.101619\pi$
$367$	3.88768	+	6.73367i	0.202935	+	0.351494i	−0.746538	+	0.665343i	$0.768285\pi$
$368$	−9.37880	+	16.2446i	−0.488904	+	0.846806i
$369$		0			0
$370$	−1.02891			−0.0534907
$371$		0			0
$372$		0			0
$373$	−12.0555	+	20.8808i	−0.624212	+	1.08117i	0.364480	+	0.931211i	$0.381247\pi$
$373$	−12.0555	+	20.8808i	−0.624212	+	1.08117i	−0.988693	+	0.149957i	$0.952087\pi$
$374$	−1.71107			−0.0884775
$375$		0			0
$376$	−8.80428			−0.454046
$377$	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	$0.611470\pi$
$380$	36.0312			1.84836
$381$		0			0
$382$	3.83173			0.196048
$383$	−4.62020	+	8.00242i	−0.236081	+	0.408905i	−0.959586	−	0.281414i	$-0.909196\pi$
$383$	−4.62020	+	8.00242i	−0.236081	+	0.408905i	0.723505	+	0.690319i	$0.242530\pi$
$384$		0			0
$385$		0			0
$386$	2.95898			0.150608
$387$		0			0
$388$	2.97577	−	5.15418i	0.151072	−	0.261664i
$389$	5.22421	+	9.04859i	0.264878	+	0.458782i	0.967532	−	0.252750i	$-0.0813351\pi$
$389$	5.22421	+	9.04859i	0.264878	+	0.458782i	−0.702654	+	0.711532i	$0.748002\pi$
$390$		0			0
$391$	4.38442	+	7.59404i	0.221730	+	0.384047i
$392$		0			0
$393$		0			0
$394$	5.52424			0.278307
$395$	12.7366	−	22.0605i	0.640850	−	1.10999i
$396$		0			0
$397$	0.204579	+	0.354341i	0.0102675	+	0.0177838i	0.871114	−	0.491082i	$-0.163398\pi$
$397$	0.204579	+	0.354341i	0.0102675	+	0.0177838i	−0.860846	+	0.508866i	$0.830065\pi$
$398$	−0.806617	+	1.39710i	−0.0404321	+	0.0700304i
$399$		0			0
$400$	−3.14295	−	5.44375i	−0.157147	−	0.272187i
$401$	7.62640	−	13.2093i	0.380844	−	0.659641i	−0.610339	−	0.792140i	$-0.708967\pi$
$401$	7.62640	−	13.2093i	0.380844	−	0.659641i	0.991183	+	0.132499i	$0.0423001\pi$
$402$		0			0
$403$	12.0361	+	20.8472i	0.599562	+	1.03847i
$404$	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
$409$	−6.12670			−0.302946			−0.151473	−	0.988461i	$-0.548402\pi$
$409$	−6.12670			−0.302946			−0.151473	+	0.988461i	$0.548402\pi$
$410$	−6.33327			−0.312778
$411$		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
$416$	5.08430	+	8.80626i	0.249278	+	0.431763i
$417$		0			0
$418$	3.57780	−	6.19694i	0.174996	−	0.303102i
$419$	0.781437	+	1.35349i	0.0381757	+	0.0661223i	0.884482	−	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
$425$	−2.93854			−0.142540
$426$		0			0
$427$		0			0
$428$	−3.84338	−	6.65692i	−0.185777	−	0.321775i
$429$		0			0
$430$	−0.514457	−	0.891066i	−0.0248093	−	0.0429710i
$431$	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	$-0.398014\pi$
$433$	13.1071			0.629889			0.314945	+	0.949110i	$0.398014\pi$
$434$		0			0
$435$		0			0
$436$	7.05555	−	12.2206i	0.337899	−	0.585259i
$437$	−36.6708			−1.75420
$438$		0			0
$439$	18.6141			0.888402			0.444201	−	0.895927i	$-0.353488\pi$
$439$	18.6141			0.888402			0.444201	+	0.895927i	$0.353488\pi$
$440$	−10.2190			−0.487170
$441$		0			0
$442$	1.50697			0.0716792
$443$	1.11901			0.0531656			0.0265828	−	0.999647i	$-0.491537\pi$
$443$	1.11901			0.0531656			0.0265828	+	0.999647i	$0.491537\pi$
$444$		0			0
$445$	13.0506			0.618660
$446$	−0.538197	+	0.932185i	−0.0254844	+	0.0441402i
$447$		0			0
$448$		0			0
$449$	39.4419			1.86138			0.930689	−	0.365813i	$-0.119209\pi$
$449$	39.4419			1.86138			0.930689	+	0.365813i	$0.119209\pi$
$450$		0			0
$451$	21.3676	−	37.0097i	1.00616	−	1.74272i
$452$	−6.73104	−	11.6585i	−0.316602	−	0.548370i
$453$		0			0
$454$	0.725057	+	1.25584i	0.0340286	+	0.0589393i
$455$		0			0
$456$		0			0
$457$	−34.2405			−1.60170			−0.800852	−	0.598863i	$-0.795619\pi$
$457$	−34.2405			−1.60170			−0.800852	+	0.598863i	$0.795619\pi$
$458$	−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	$0.883909\pi$
$464$	−3.88852	+	6.73511i	−0.180520	+	0.312670i
$465$		0			0
$466$	0.973045	+	1.68536i	0.0450754	+	0.0780729i
$467$	12.3956	+	21.4698i	0.573598	+	0.993502i	0.996192	+	0.0871825i	$0.0277863\pi$
$467$	12.3956	+	21.4698i	0.573598	+	0.993502i	−0.422594	+	0.906319i	$0.638880\pi$
$468$		0			0
$469$		0			0
$470$	−2.89372	+	5.01207i	−0.133477	+	0.231190i
$471$		0			0
$472$	−5.71754			−0.263171
$473$	6.94282			0.319231
$474$		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
$479$	−5.54984	−	9.61260i	−0.253579	−	0.439211i	0.710930	−	0.703263i	$-0.248274\pi$
$479$	−5.54984	−	9.61260i	−0.253579	−	0.439211i	−0.964508	+	0.264052i	$0.914941\pi$
$480$		0			0
$481$	−3.05733	+	5.29545i	−0.139402	+	0.241452i
$482$	1.63697	+	2.83532i	0.0745621	+	0.129145i
$483$		0			0
$484$	6.30314	−	10.9174i	0.286506	−	0.496244i
$485$	−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	$0.0936354\pi$
$488$	−7.52933			−0.340837
$489$		0			0
$490$		0			0
$491$	−6.19398	−	10.7283i	−0.279530	−	0.484161i	0.691738	−	0.722149i	$-0.256845\pi$
$491$	−6.19398	−	10.7283i	−0.279530	−	0.484161i	−0.971268	+	0.237988i	$0.923512\pi$
$492$		0			0
$493$	1.81781	+	3.14854i	0.0818702	+	0.141803i
$494$	−3.15103	+	5.45774i	−0.141772	+	0.245556i
$495$		0			0
$496$	−23.9225			−1.07415
$497$		0			0
$498$		0			0
$499$	−5.11109	+	8.85267i	−0.228804	+	0.396300i	−0.957454	−	0.288586i	$-0.906815\pi$
$499$	−5.11109	+	8.85267i	−0.228804	+	0.396300i	0.728650	+	0.684886i	$0.240148\pi$
$500$	16.5293			0.739212
$501$		0			0
$502$	3.63562			0.162266
$503$	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
$506$	5.12476			0.227824
$507$		0			0
$508$	−17.7012			−0.785364
$509$	−5.28286	+	9.15018i	−0.234159	+	0.405574i	−0.959028	−	0.283312i	$-0.908567\pi$
$509$	−5.28286	+	9.15018i	−0.234159	+	0.405574i	0.724869	+	0.688886i	$0.241900\pi$
$510$		0			0
$511$		0			0
$512$	−17.0071			−0.751616
$513$		0			0
$514$	−3.06335	+	5.30587i	−0.135118	+	0.234032i
$515$	−10.3490	−	17.9249i	−0.456030	−	0.789867i
$516$		0			0
$517$	−19.5260	−	33.8200i	−0.858752	−	1.48740i
$518$		0			0
$519$		0			0
$520$	9.00000			0.394676
$521$	9.87788	−	17.1090i	0.432758	−	0.749558i	−0.564352	−	0.825534i	$-0.690874\pi$
$521$	9.87788	−	17.1090i	0.432758	−	0.749558i	0.997110	+	0.0759760i	$0.0242072\pi$
$522$		0			0
$523$	16.2641	+	28.1702i	0.711179	+	1.23180i	0.964415	+	0.264394i	$0.0851718\pi$
$523$	16.2641	+	28.1702i	0.711179	+	1.23180i	−0.253236	+	0.967405i	$0.581495\pi$
$524$	4.17984	−	7.23970i	0.182597	−	0.316268i
$525$		0			0
$526$	−0.848970	−	1.47046i	−0.0370168	−	0.0641150i
$527$	−5.59166	+	9.68504i	−0.243577	+	0.421887i
$528$		0			0
$529$	−1.63160	−	2.82601i	−0.0709391	−	0.122870i
$530$	−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
$535$	−10.2544			−0.443336
$536$	7.79071			0.336507
$537$		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	$0.939447\pi$
$542$	1.51819	+	2.62959i	0.0652119	+	0.112950i
$543$		0			0
$544$	−2.36203	+	4.09116i	−0.101271	+	0.175407i
$545$	−9.41234	−	16.3027i	−0.403180	−	0.698329i
$546$		0			0
$547$	−11.6871	+	20.2427i	−0.499706	+	0.865517i	−1.00000		0.000339172i	$-0.999892\pi$
$547$	−11.6871	+	20.2427i	−0.499706	+	0.865517i	0.500294	+	0.865856i	$0.333225\pi$
$548$	−20.0007	−	34.6422i	−0.854387	−	1.47984i
$549$		0			0
$550$	−0.858685	+	1.48729i	−0.0366144	+	0.0634181i
$551$	−15.2040			−0.647711
$552$		0			0
$553$		0			0
$554$	−0.0990521	−	0.171563i	−0.00420832	−	0.00728902i
$555$		0			0
$556$	−15.3107	−	26.5189i	−0.649319	−	1.12465i
$557$	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
$562$	−0.624075	+	1.08093i	−0.0263250	+	0.0455963i
$563$	8.55824			0.360687			0.180343	−	0.983604i	$-0.442279\pi$
$563$	8.55824			0.360687			0.180343	+	0.983604i	$0.442279\pi$
$564$		0			0
$565$	−17.9589			−0.755536
$566$	1.75855			0.0739175
$567$		0			0
$568$	−5.88237			−0.246819
$569$	−13.7278			−0.575498			−0.287749	−	0.957706i	$-0.592907\pi$
$569$	−13.7278			−0.575498			−0.287749	+	0.957706i	$0.592907\pi$
$570$		0			0
$571$	10.7174			0.448508			0.224254	−	0.974531i	$-0.428005\pi$
$571$	10.7174			0.448508			0.224254	+	0.974531i	$0.428005\pi$
$572$	−14.9622	+	25.9153i	−0.625600	+	1.08357i
$573$		0			0
$574$		0			0
$575$	8.80111			0.367032
$576$		0			0
$577$	−22.8177	+	39.5214i	−0.949912	+	1.64530i	−0.204307	+	0.978907i	$0.565494\pi$
$577$	−22.8177	+	39.5214i	−0.949912	+	1.64530i	−0.745605	+	0.666389i	$0.767839\pi$
$578$	−1.68250	−	2.91417i	−0.0699827	−	0.121214i
$579$		0			0
$580$	5.34950	+	9.26560i	0.222126	+	0.384733i
$581$		0			0
$582$		0			0
$583$	44.5231			1.84396
$584$	−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
$590$	−1.87919	+	3.25486i	−0.0773652	+	0.134000i
$591$		0			0
$592$	−3.03831	−	5.26250i	−0.124874	−	0.216287i
$593$	−5.69804	−	9.86929i	−0.233990	−	0.405283i	0.724988	−	0.688761i	$-0.241845\pi$
$593$	−5.69804	−	9.86929i	−0.233990	−	0.405283i	−0.958979	+	0.283478i	$0.908512\pi$
$594$		0			0
$595$		0			0
$596$	−5.89411	+	10.2089i	−0.241432	+	0.418173i
$597$		0			0
$598$	−4.51346			−0.184569
$599$	34.5746			1.41268			0.706339	−	0.707874i	$-0.250345\pi$
$599$	34.5746			1.41268			0.706339	+	0.707874i	$0.250345\pi$
$600$		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
$605$	−8.40861	−	14.5641i	−0.341858	−	0.592116i
$606$		0			0
$607$	−20.6662	+	35.7950i	−0.838817	+	1.45287i	0.0520683	+	0.998644i	$0.483419\pi$
$607$	−20.6662	+	35.7950i	−0.838817	+	1.45287i	−0.890885	+	0.454229i	$0.849915\pi$
$608$	−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	$-0.0297813\pi$
$614$	−5.42114			−0.218779
$615$		0			0
$616$		0			0
$617$	−16.8518	−	29.1883i	−0.678430	−	1.17508i	−0.975454	−	0.220205i	$-0.929327\pi$
$617$	−16.8518	−	29.1883i	−0.678430	−	1.17508i	0.297024	−	0.954870i	$-0.404006\pi$
$618$		0			0
$619$	0.719036	+	1.24541i	0.0289005	+	0.0500571i	0.880114	−	0.474763i	$-0.157466\pi$
$619$	0.719036	+	1.24541i	0.0289005	+	0.0500571i	−0.851213	+	0.524820i	$0.824133\pi$
$620$	−16.4552	+	28.5013i	−0.660859	+	1.14464i
$621$		0			0
$622$	−7.72789			−0.309860
$623$		0			0
$624$		0			0
$625$	15.3187	−	26.5328i	0.612750	−	1.06131i
$626$	5.81538			0.232429
$627$		0			0
$628$	−1.99900			−0.0797686
$629$	−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	$0.709807\pi$
$632$	−9.26647			−0.368600
$633$		0			0
$634$	1.22872			0.0487987
$635$	−11.8070	+	20.4503i	−0.468547	+	0.811547i
$636$		0			0
$637$		0			0
$638$	2.12476			0.0841202
$639$		0			0
$640$	−9.21946	+	15.9686i	−0.364431	+	0.631213i
$641$	4.61956	+	8.00132i	0.182462	+	0.316033i	0.942718	−	0.333590i	$-0.108260\pi$
$641$	4.61956	+	8.00132i	0.182462	+	0.316033i	−0.760257	+	0.649623i	$0.774927\pi$
$642$		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
$646$	−2.92777			−0.115192
$647$	−14.1556	+	24.5181i	−0.556512	+	0.963908i	0.441272	+	0.897374i	$0.354528\pi$
$647$	−14.1556	+	24.5181i	−0.556512	+	0.963908i	−0.997784	+	0.0665343i	$0.978806\pi$
$648$		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
$653$	−4.17511	+	7.23150i	−0.163385	+	0.282990i	−0.936080	−	0.351786i	$-0.885574\pi$
$653$	−4.17511	+	7.23150i	−0.163385	+	0.282990i	0.772696	+	0.634776i	$0.218908\pi$
$654$		0			0
$655$	−5.57605	−	9.65801i	−0.217874	−	0.377370i
$656$	−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
$661$	16.9534			0.659410			0.329705	−	0.944084i	$-0.393051\pi$
$661$	16.9534			0.659410			0.329705	+	0.944084i	$0.393051\pi$
$662$	2.79725			0.108718
$663$		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
$668$	−17.4799	−	30.2760i	−0.676316	−	1.17141i
$669$		0			0
$670$	2.56059	−	4.43507i	0.0989242	−	0.171342i
$671$	−16.6984	−	28.9225i	−0.644636	−	1.11654i
$672$		0			0
$673$	22.2157	−	38.4788i	0.856354	−	1.48325i	−0.0190299	−	0.999819i	$-0.506058\pi$
$673$	22.2157	−	38.4788i	0.856354	−	1.48325i	0.875384	−	0.483429i	$-0.160609\pi$
$674$	−4.02859	−	6.97772i	−0.155175	−	0.268772i
$675$		0			0
$676$	0.549100	−	0.951068i	0.0211192	−	0.0365796i
$677$	−14.3736			−0.552423			−0.276212	−	0.961097i	$-0.589079\pi$
$677$	−14.3736			−0.552423			−0.276212	+	0.961097i	$0.589079\pi$
$678$		0			0
$679$		0			0
$680$	2.09058	+	3.62099i	0.0801701	+	0.138859i
$681$		0			0
$682$	3.26793	+	5.66021i	0.125135	+	0.216741i
$683$	−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
$688$	3.03831	−	5.26250i	0.115834	−	0.200631i
$689$	−39.2122			−1.49387
$690$		0			0
$691$	28.9962			1.10307			0.551533	−	0.834153i	$-0.314043\pi$
$691$	28.9962			1.10307			0.551533	+	0.834153i	$0.314043\pi$
$692$	−1.61323			−0.0613259
$693$		0			0
$694$	6.53078			0.247905
$695$	−40.8500			−1.54953
$696$		0			0
$697$	−17.4854			−0.662306
$698$	2.73999	−	4.74580i	0.103710	−	0.179631i
$699$		0			0
$700$		0			0
$701$	26.3912			0.996783			0.498392	−	0.866952i	$-0.333924\pi$
$701$	26.3912			0.996783			0.498392	+	0.866952i	$0.333924\pi$
$702$		0			0
$703$	5.93984	−	10.2881i	0.224025	−	0.388023i
$704$	−13.9263	−	24.1210i	−0.524866	−	0.909095i
$705$		0			0
$706$	−1.22782	−	2.12664i	−0.0462095	−	0.0800372i
$707$		0			0
$708$		0			0
$709$	−7.88564			−0.296151			−0.148076	−	0.988976i	$-0.547308\pi$
$709$	−7.88564			−0.296151			−0.148076	+	0.988976i	$0.547308\pi$
$710$	−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
$716$	−7.36225	+	12.7518i	−0.275140	+	0.476557i
$717$		0			0
$718$	−1.20765	−	2.09172i	−0.0450693	−	0.0780623i
$719$	16.5754	+	28.7095i	0.618159	+	1.07068i	0.989822	+	0.142314i	$0.0454544\pi$
$719$	16.5754	+	28.7095i	0.618159	+	1.07068i	−0.371663	+	0.928368i	$0.621212\pi$
$720$		0			0
$721$		0			0
$722$	3.85021	−	6.66877i	0.143290	−	0.248186i
$723$		0			0
$724$	−0.794919			−0.0295429
$725$	3.64900			0.135521
$726$		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
$731$	−1.42035	−	2.46012i	−0.0525337	−	0.0909910i
$732$		0			0
$733$	−22.2795	+	38.5892i	−0.822911	+	1.42532i	0.0805946	+	0.996747i	$0.474318\pi$
$733$	−22.2795	+	38.5892i	−0.822911	+	1.42532i	−0.903505	+	0.428577i	$0.859015\pi$
$734$	−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	$0.905161\pi$
$740$	−8.35969			−0.307308
$741$		0			0
$742$		0			0
$743$	5.37072	+	9.30237i	0.197033	+	0.341271i	0.947565	−	0.319563i	$-0.103536\pi$
$743$	5.37072	+	9.30237i	0.197033	+	0.341271i	−0.750532	+	0.660834i	$0.770203\pi$
$744$		0			0
$745$	7.86295	+	13.6190i	0.288076	+	0.498962i
$746$	2.88276	−	4.99309i	0.105545	−	0.182810i
$747$		0			0
$748$	−13.9021			−0.508310
$749$		0			0
$750$		0			0
$751$	−9.85705	+	17.0729i	−0.359689	+	0.622999i	−0.987909	−	0.155036i	$-0.950450\pi$
$751$	−9.85705	+	17.0729i	−0.359689	+	0.622999i	0.628220	+	0.778036i	$0.283784\pi$
$752$	−34.1797			−1.24641
$753$		0			0
$754$	−1.87131			−0.0681492
$755$	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	$0.277898\pi$
$758$	3.19424			0.116020
$759$		0			0
$760$	−17.4854			−0.634261
$761$	19.5572	−	33.8741i	0.708948	−	1.22793i	−0.256300	−	0.966597i	$-0.582503\pi$
$761$	19.5572	−	33.8741i	0.708948	−	1.22793i	0.965248	−	0.261336i	$-0.0841632\pi$
$762$		0			0
$763$		0			0
$764$	31.1319			1.12631
$765$		0			0
$766$	1.10480	−	1.91357i	0.0399180	−	0.0691399i
$767$	11.1677	+	19.3430i	0.403243	+	0.698437i
$768$		0			0
$769$	−18.9240	−	32.7773i	−0.682415	−	1.18198i	−0.974242	−	0.225507i	$-0.927596\pi$
$769$	−18.9240	−	32.7773i	−0.682415	−	1.18198i	0.291826	−	0.956471i	$-0.405737\pi$
$770$		0			0
$771$		0			0
$772$	24.0410			0.865255
$773$	−14.9133	+	25.8305i	−0.536393	+	0.929059i	0.462702	+	0.886514i	$0.346880\pi$
$773$	−14.9133	+	25.8305i	−0.536393	+	0.929059i	−0.999095	+	0.0425453i	$0.986453\pi$
$774$		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
$779$	36.5614	−	63.3263i	1.30995	−	2.26890i
$780$		0			0
$781$	−13.0458	−	22.5960i	−0.466817	−	0.808550i
$782$	−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
$787$	−17.6206			−0.628107			−0.314053	−	0.949405i	$-0.601687\pi$
$787$	−17.6206			−0.628107			−0.314053	+	0.949405i	$0.601687\pi$
$788$	44.8832			1.59890
$789$		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
$794$	−0.0489195	−	0.0847311i	−0.00173609	−	0.00300699i
$795$		0			0
$796$	−6.55357	+	11.3511i	−0.232285	+	0.402330i
$797$	−5.06056	−	8.76515i	−0.179254	−	0.310477i	0.762371	−	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
$803$	−29.9244			−1.05601
$804$		0			0
$805$		0			0
$806$	−2.87812	−	4.98504i	−0.101377	−	0.175591i
$807$		0			0
$808$	−5.23250	−	9.06295i	−0.184079	−	0.318834i
$809$	−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	$-0.620546\pi$
$811$	−21.0577			−0.739435			−0.369717	+	0.929144i	$0.620546\pi$
$812$		0			0
$813$		0			0
$814$	−0.830095	+	1.43777i	−0.0290948	+	0.0503937i
$815$	17.6979			0.619931
$816$		0			0
$817$	11.8797			0.415617
$818$	1.46504			0.0512238
$819$		0			0
$820$	−51.4563			−1.79693
$821$	−11.1604			−0.389499			−0.194750	−	0.980853i	$-0.562389\pi$
$821$	−11.1604			−0.389499			−0.194750	+	0.980853i	$0.562389\pi$
$822$		0			0
$823$	9.43474			0.328874			0.164437	−	0.986388i	$-0.447419\pi$
$823$	9.43474			0.328874			0.164437	+	0.986388i	$0.447419\pi$
$824$	−3.76466	+	6.52059i	−0.131148	+	0.227156i
$825$		0			0
$826$		0			0
$827$	−17.2646			−0.600348			−0.300174	−	0.953884i	$-0.597045\pi$
$827$	−17.2646			−0.600348			−0.300174	+	0.953884i	$0.597045\pi$
$828$		0			0
$829$	−24.2263	+	41.9612i	−0.841415	+	1.45737i	0.0472838	+	0.998881i	$0.484943\pi$
$829$	−24.2263	+	41.9612i	−0.841415	+	1.45737i	−0.888699	+	0.458492i	$0.848390\pi$
$830$	−2.13650	−	3.70053i	−0.0741591	−	0.128447i
$831$		0			0
$832$	12.2651	+	21.2438i	0.425215	+	0.736495i
$833$		0			0
$834$		0			0
$835$	−46.6375			−1.61396
$836$	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
$842$	2.78139	−	4.81750i	0.0958529	−	0.166022i
$843$		0			0
$844$	16.4029	+	28.4106i	0.564610	+	0.977934i
$845$	−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
$850$	0.702674			0.0241015
$851$	8.50808			0.291653
$852$		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
$857$	21.5661	+	37.3536i	0.736684	+	1.27597i	0.953980	+	0.299869i	$0.0969429\pi$
$857$	21.5661	+	37.3536i	0.736684	+	1.27597i	−0.217296	+	0.976106i	$0.569724\pi$
$858$		0			0
$859$	−1.22180	+	2.11621i	−0.0416871	+	0.0722042i	−0.886116	−	0.463463i	$-0.846607\pi$
$859$	−1.22180	+	2.11621i	−0.0416871	+	0.0722042i	0.844429	+	0.535667i	$0.179940\pi$
$860$	−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
$866$	−3.13422			−0.106505
$867$		0			0
$868$		0			0
$869$	−20.5510	−	35.5954i	−0.697146	−	1.20749i
$870$		0			0
$871$	−15.2171	−	26.3568i	−0.515612	−	0.893067i
$872$	−3.42395	+	5.93045i	−0.115949	+	0.200830i
$873$		0			0
$874$	8.76884			0.296611
$875$		0			0
$876$		0			0
$877$	10.9795	−	19.0170i	0.370751	−	0.642160i	−0.618930	−	0.785446i	$-0.712434\pi$
$877$	10.9795	−	19.0170i	0.370751	−	0.642160i	0.989681	+	0.143286i	$0.0457670\pi$
$878$	−4.45106			−0.150216
$879$		0			0
$880$	−39.6718			−1.33733
$881$	−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	$0.354074\pi$
$884$	12.2438			0.411803
$885$		0			0
$886$	−0.267580			−0.00898954
$887$	−23.9090	+	41.4116i	−0.802785	+	1.39046i	0.114991	+	0.993366i	$0.463316\pi$
$887$	−23.9090	+	41.4116i	−0.802785	+	1.39046i	−0.917776	+	0.397098i	$0.870017\pi$
$888$		0			0
$889$		0			0
$890$	−3.12071			−0.104607
$891$		0			0
$892$	−4.37272	+	7.57378i	−0.146410	+	0.253589i
$893$	−33.4104	−	57.8685i	−1.11804	−	1.93650i
$894$		0			0
$895$	9.82150	+	17.0113i	0.328296	+	0.568626i
$896$		0			0
$897$		0			0
$898$	−9.43147			−0.314732
$899$	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
$905$	−0.530225	+	0.918376i	−0.0176253	+	0.0305279i
$906$		0			0
$907$	9.55718	+	16.5535i	0.317341	+	0.549651i	0.979932	−	0.199330i	$-0.0638767\pi$
$907$	9.55718	+	16.5535i	0.317341	+	0.549651i	−0.662591	+	0.748981i	$0.730543\pi$
$908$	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
$913$	28.8330			0.954234
$914$	8.18770			0.270825
$915$		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	$0.919481\pi$
$920$	−6.26141	−	10.8451i	−0.206433	−	0.357552i
$921$		0			0
$922$	−2.43757	+	4.22199i	−0.0802771	+	0.139044i
$923$	11.4897	+	19.9007i	0.378187	+	0.655039i
$924$		0			0
$925$	−1.42558	+	2.46918i	−0.0468728	+	0.0811860i
$926$	0.814099	+	1.41006i	0.0267529	+	0.0463375i
$927$		0			0
$928$	2.93310	−	5.08029i	0.0962839	−	0.166769i
$929$	22.6829			0.744203			0.372102	−	0.928192i	$-0.378637\pi$
$929$	22.6829			0.744203			0.372102	+	0.928192i	$0.378637\pi$
$930$		0			0
$931$		0			0
$932$	7.90576	+	13.6932i	0.258962	+	0.448535i
$933$		0			0
$934$	−2.96407	−	5.13392i	−0.0969873	−	0.167987i
$935$	−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
$940$	−23.5108	+	40.7219i	−0.766838	+	1.32820i
$941$	31.9318			1.04095			0.520474	−	0.853878i	$-0.325755\pi$
$941$	31.9318			1.04095			0.520474	+	0.853878i	$0.325755\pi$
$942$		0			0
$943$	52.3697			1.70539
$944$	−22.1965			−0.722433
$945$		0			0
$946$	−1.66019			−0.0539774
$947$	4.49330			0.146013			0.0730063	−	0.997331i	$-0.476741\pi$
$947$	4.49330			0.146013			0.0730063	+	0.997331i	$0.476741\pi$
$948$		0			0
$949$	26.3549			0.855515
$950$	−1.46927	+	2.54485i	−0.0476695	+	0.0825660i
$951$		0			0
$952$		0			0
$953$	−1.14635			−0.0371340			−0.0185670	−	0.999828i	$-0.505910\pi$
$953$	−1.14635			−0.0371340			−0.0185670	+	0.999828i	$0.505910\pi$
$954$		0			0
$955$	20.7655	−	35.9669i	0.671956	−	1.16386i
$956$	−20.5575	−	35.6066i	−0.664876	−	1.15160i
$957$		0			0
$958$	1.32710	+	2.29860i	0.0428765	+	0.0742643i
$959$		0			0
$960$		0			0
$961$	11.7174			0.377980
$962$	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	$-0.460654\pi$
$968$	−3.05881	+	5.29802i	−0.0983140	+	0.170285i
$969$		0			0
$970$	0.949266	+	1.64418i	0.0304791	+	0.0527913i
$971$	−2.56661	−	4.44550i	−0.0823664	−	0.142663i	0.821900	−	0.569632i	$-0.192914\pi$
$971$	−2.56661	−	4.44550i	−0.0823664	−	0.142663i	−0.904266	+	0.426970i	$0.859581\pi$
$972$		0			0
$973$		0			0
$974$	−1.20013	+	2.07869i	−0.0384546	+	0.0666054i
$975$		0			0
$976$	−29.2302			−0.935634
$977$	−31.1948			−0.998011			−0.499006	−	0.866599i	$-0.666301\pi$
$977$	−31.1948			−0.998011			−0.499006	+	0.866599i	$0.666301\pi$
$978$		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
$983$	10.1700	+	17.6150i	0.324374	+	0.561832i	0.981385	−	0.192049i	$-0.0615131\pi$
$983$	10.1700	+	17.6150i	0.324374	+	0.561832i	−0.657012	+	0.753880i	$0.728180\pi$
$984$		0			0
$985$	29.9378	−	51.8539i	0.953899	−	1.65220i
$986$	−0.434681	−	0.752890i	−0.0138431	−	0.0239769i
$987$		0			0
$988$	−25.6014	+	44.3429i	−0.814488	+	1.41074i
$989$	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	$0.100644\pi$
$992$	18.0447			0.572919
$993$		0			0
$994$		0			0
$995$	8.74269	+	15.1428i	0.277162	+	0.480059i
$996$		0			0
$997$	24.7408	+	42.8523i	0.783548	+	1.35715i	0.929863	+	0.367907i	$0.119926\pi$
$997$	24.7408	+	42.8523i	0.783548	+	1.35715i	−0.146314	+	0.989238i	$0.546741\pi$
$998$	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.h.g.802.3		12
3.2	odd	2		441.2.h.g.214.4		12
7.2	even	3		1323.2.g.g.667.4		12
7.3	odd	6		1323.2.f.g.883.4		12
7.4	even	3		1323.2.f.g.883.3		12
7.5	odd	6		1323.2.g.g.667.3		12
7.6	odd	2	inner	1323.2.h.g.802.4		12
9.4	even	3		1323.2.g.g.361.4		12
9.5	odd	6		441.2.g.g.67.3		12
21.2	odd	6		441.2.g.g.79.3		12
21.5	even	6		441.2.g.g.79.4		12
21.11	odd	6		441.2.f.g.295.3	yes	12
21.17	even	6		441.2.f.g.295.4	yes	12
21.20	even	2		441.2.h.g.214.3		12
63.4	even	3		1323.2.f.g.442.3		12
63.5	even	6		441.2.h.g.373.3		12
63.11	odd	6		3969.2.a.be.1.3		6
63.13	odd	6		1323.2.g.g.361.3		12
63.23	odd	6		441.2.h.g.373.4		12
63.25	even	3		3969.2.a.bd.1.4		6
63.31	odd	6		1323.2.f.g.442.4		12
63.32	odd	6		441.2.f.g.148.3	✓	12
63.38	even	6		3969.2.a.be.1.4		6
63.40	odd	6	inner	1323.2.h.g.226.4		12
63.41	even	6		441.2.g.g.67.4		12
63.52	odd	6		3969.2.a.bd.1.3		6
63.58	even	3	inner	1323.2.h.g.226.3		12
63.59	even	6		441.2.f.g.148.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.g.148.3	✓	12	63.32	odd	6
441.2.f.g.148.4	yes	12	63.59	even	6
441.2.f.g.295.3	yes	12	21.11	odd	6
441.2.f.g.295.4	yes	12	21.17	even	6
441.2.g.g.67.3		12	9.5	odd	6
441.2.g.g.67.4		12	63.41	even	6
441.2.g.g.79.3		12	21.2	odd	6
441.2.g.g.79.4		12	21.5	even	6
441.2.h.g.214.3		12	21.20	even	2
441.2.h.g.214.4		12	3.2	odd	2
441.2.h.g.373.3		12	63.5	even	6
441.2.h.g.373.4		12	63.23	odd	6
1323.2.f.g.442.3		12	63.4	even	3
1323.2.f.g.442.4		12	63.31	odd	6
1323.2.f.g.883.3		12	7.4	even	3
1323.2.f.g.883.4		12	7.3	odd	6
1323.2.g.g.361.3		12	63.13	odd	6
1323.2.g.g.361.4		12	9.4	even	3
1323.2.g.g.667.3		12	7.5	odd	6
1323.2.g.g.667.4		12	7.2	even	3
1323.2.h.g.226.3		12	63.58	even	3	inner
1323.2.h.g.226.4		12	63.40	odd	6	inner
1323.2.h.g.802.3		12	1.1	even	1	trivial
1323.2.h.g.802.4		12	7.6	odd	2	inner
3969.2.a.bd.1.3		6	63.52	odd	6
3969.2.a.bd.1.4		6	63.25	even	3
3969.2.a.be.1.3		6	63.11	odd	6
3969.2.a.be.1.4		6	63.38	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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.239123 q^{2} -1.94282 q^{4} +(-1.29589 + 2.24456i) q^{5} +0.942820 q^{8} +O(q^{10})\)	\(q-0.239123 q^{2} -1.94282 q^{4} +(-1.29589 + 2.24456i) q^{5} +0.942820 q^{8} +(0.309879 - 0.536725i) q^{10} +(2.09097 + 3.62167i) q^{11} +(-1.84155 - 3.18966i) q^{13} +3.66019 q^{16} +(0.855536 - 1.48183i) q^{17} +(3.57780 + 6.19694i) q^{19} +(2.51769 - 4.36077i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(-2.56238 + 4.43818i) q^{23} +(-0.858685 - 1.48729i) q^{25} +(0.440358 + 0.762722i) q^{26} +(-1.06238 + 1.84010i) q^{29} -6.53585 q^{31} -2.76088 q^{32} +(-0.204579 + 0.354341i) q^{34} +(-0.830095 - 1.43777i) q^{37} +(-0.855536 - 1.48183i) q^{38} +(-1.22180 + 2.11621i) q^{40} +(-5.10948 - 8.84988i) q^{41} +(0.830095 - 1.43777i) q^{43} +(-4.06238 - 7.03625i) q^{44} +(0.612725 - 1.06127i) q^{46} -9.33824 q^{47} +(0.205332 + 0.355645i) q^{50} +(3.57780 + 6.19694i) q^{52} +(5.32326 - 9.22015i) q^{53} -10.8387 q^{55} +(0.254040 - 0.440011i) q^{58} -6.06429 q^{59} -7.98597 q^{61} +1.56287 q^{62} -6.66019 q^{64} +9.54583 q^{65} +8.26320 q^{67} +(-1.66215 + 2.87893i) q^{68} -6.23912 q^{71} +(-3.57780 + 6.19694i) q^{73} +(0.198495 + 0.343803i) q^{74} +(-6.95103 - 12.0395i) q^{76} -9.82846 q^{79} +(-4.74322 + 8.21550i) q^{80} +(1.22180 + 2.11621i) q^{82} +(3.44733 - 5.97094i) q^{83} +(2.21737 + 3.84060i) q^{85} +(-0.198495 + 0.343803i) q^{86} +(1.97141 + 3.41458i) q^{88} +(-2.51769 - 4.36077i) q^{89} +(4.97825 - 8.62258i) q^{92} +2.23299 q^{94} -18.5458 q^{95} +(-1.53167 + 2.65294i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + 12 q^{4} - 24 q^{8}+O(q^{10}) \) 12 * q - 4 * q^2 + 12 * q^4 - 24 * q^8	\( 12 q - 4 q^{2} + 12 q^{4} - 24 q^{8} + 8 q^{11} + 12 q^{16} - 6 q^{22} + 4 q^{23} - 12 q^{25} + 22 q^{29} - 32 q^{32} + 6 q^{37} - 6 q^{43} - 14 q^{44} - 12 q^{46} + 56 q^{50} + 28 q^{53} - 18 q^{58} - 48 q^{64} + 12 q^{65} - 76 q^{71} + 36 q^{74} - 12 q^{79} + 30 q^{85} - 36 q^{86} + 6 q^{88} + 62 q^{92} - 120 q^{95}+O(q^{100}) \) 12 * q - 4 * q^2 + 12 * q^4 - 24 * q^8 + 8 * q^11 + 12 * q^16 - 6 * q^22 + 4 * q^23 - 12 * q^25 + 22 * q^29 - 32 * q^32 + 6 * q^37 - 6 * q^43 - 14 * q^44 - 12 * q^46 + 56 * q^50 + 28 * q^53 - 18 * q^58 - 48 * q^64 + 12 * q^65 - 76 * q^71 + 36 * q^74 - 12 * q^79 + 30 * q^85 - 36 * q^86 + 6 * q^88 + 62 * q^92 - 120 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more