LMFDB - Embedded newform 1323.2.f.e.883.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1323.442");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			883.2
Root			$0.920620 - 1.59456i$ of defining polynomial
Character	$\chi$	$=$	1323.883
Dual form			1323.2.f.e.442.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.920620 + 1.59456i) q^{2} +(-0.695084 - 1.20392i) q^{4} +(0.667377 + 1.15593i) q^{5} -1.12285 q^{8} +O(q^{10})$	\(q+(-0.920620 + 1.59456i) q^{2} +(-0.695084 - 1.20392i) q^{4} +(0.667377 + 1.15593i) q^{5} -1.12285 q^{8} -2.45760 q^{10} +(0.756508 - 1.31031i) q^{11} +(-2.58800 - 4.48254i) q^{13} +(2.42388 - 4.19829i) q^{16} +1.54893 q^{17} +2.50422 q^{19} +(0.927765 - 1.60694i) q^{20} +(1.39291 + 2.41260i) q^{22} +(-3.68039 - 6.37463i) q^{23} +(1.60922 - 2.78725i) q^{25} +9.53025 q^{26} +(0.0309713 - 0.0536439i) q^{29} +(1.92388 + 3.33227i) q^{31} +(3.34011 + 5.78523i) q^{32} +(-1.42597 + 2.46986i) q^{34} +0.563216 q^{37} +(-2.30543 + 3.99313i) q^{38} +(-0.749363 - 1.29794i) q^{40} +(-4.51188 - 7.81481i) q^{41} +(5.09988 - 8.83325i) q^{43} -2.10335 q^{44} +13.5530 q^{46} +(-4.75925 + 8.24327i) q^{47} +(2.96296 + 5.13199i) q^{50} +(-3.59775 + 6.23148i) q^{52} +1.51075 q^{53} +2.01950 q^{55} +(0.0570257 + 0.0987714i) q^{58} +(-4.22166 - 7.31212i) q^{59} +(-1.61958 + 2.80520i) q^{61} -7.08467 q^{62} -2.60434 q^{64} +(3.45434 - 5.98309i) q^{65} +(-3.46670 - 6.00449i) q^{67} +(-1.07663 - 1.86478i) q^{68} +12.3304 q^{71} +2.75871 q^{73} +(-0.518508 + 0.898083i) q^{74} +(-1.74064 - 3.01488i) q^{76} +(2.95969 - 5.12633i) q^{79} +6.47058 q^{80} +16.6149 q^{82} +(-2.80111 + 4.85167i) q^{83} +(1.03372 + 1.79045i) q^{85} +(9.39010 + 16.2641i) q^{86} +(-0.849444 + 1.47128i) q^{88} +1.40657 q^{89} +(-5.11636 + 8.86180i) q^{92} +(-8.76293 - 15.1778i) q^{94} +(1.67126 + 2.89470i) q^{95} +(-6.09713 + 10.5605i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 6 q^{8}+O(q^{10}) $ 10 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 6 * q^8	$ 10 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 6 q^{8} + 14 q^{10} - 4 q^{11} - 8 q^{13} + 2 q^{16} + 24 q^{17} - 2 q^{19} - 5 q^{20} - q^{22} - 3 q^{23} - q^{25} + 22 q^{26} - 7 q^{29} - 3 q^{31} + 2 q^{32} + 3 q^{34} - 20 q^{38} - 3 q^{40} - 5 q^{41} - 7 q^{43} - 20 q^{44} - 6 q^{46} - 27 q^{47} - 19 q^{50} - 10 q^{52} - 42 q^{53} + 4 q^{55} - 10 q^{58} - 30 q^{59} - 14 q^{61} + 12 q^{62} - 50 q^{64} + 11 q^{65} - 2 q^{67} - 27 q^{68} + 6 q^{71} - 30 q^{73} + 36 q^{74} + 5 q^{76} - 4 q^{79} + 40 q^{80} + 10 q^{82} - 9 q^{83} - 6 q^{85} + 8 q^{86} - 18 q^{88} + 56 q^{89} - 27 q^{92} - 3 q^{94} + 14 q^{95} - 12 q^{97}+O(q^{100}) $ 10 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 6 * q^8 + 14 * q^10 - 4 * q^11 - 8 * q^13 + 2 * q^16 + 24 * q^17 - 2 * q^19 - 5 * q^20 - q^22 - 3 * q^23 - q^25 + 22 * q^26 - 7 * q^29 - 3 * q^31 + 2 * q^32 + 3 * q^34 - 20 * q^38 - 3 * q^40 - 5 * q^41 - 7 * q^43 - 20 * q^44 - 6 * q^46 - 27 * q^47 - 19 * q^50 - 10 * q^52 - 42 * q^53 + 4 * q^55 - 10 * q^58 - 30 * q^59 - 14 * q^61 + 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 - 27 * q^68 + 6 * q^71 - 30 * q^73 + 36 * q^74 + 5 * q^76 - 4 * q^79 + 40 * q^80 + 10 * q^82 - 9 * q^83 - 6 * q^85 + 8 * q^86 - 18 * q^88 + 56 * q^89 - 27 * q^92 - 3 * q^94 + 14 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.920620	+	1.59456i	−0.650977	+	1.12753i	0.331909	+	0.943311i	$0.392307\pi$
$2$	−0.920620	+	1.59456i	−0.650977	+	1.12753i	−0.982886	+	0.184214i	$0.941026\pi$
$3$		0			0
$3$		0			0
$4$	−0.695084	−	1.20392i	−0.347542	−	0.601960i
$5$	0.667377	+	1.15593i	0.298460	+	0.516948i	0.975784	−	0.218737i	$-0.0701937\pi$
$5$	0.667377	+	1.15593i	0.298460	+	0.516948i	−0.677324	+	0.735685i	$0.736860\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.12285			−0.396987
$9$		0			0
$10$	−2.45760			−0.777162
$11$	0.756508	−	1.31031i	0.228096	−	0.395073i	−0.729148	−	0.684356i	$-0.760083\pi$
$11$	0.756508	−	1.31031i	0.228096	−	0.395073i	0.957244	+	0.289283i	$0.0934167\pi$
$12$		0			0
$13$	−2.58800	−	4.48254i	−0.717781	−	1.24323i	−0.961877	−	0.273482i	$-0.911824\pi$
$13$	−2.58800	−	4.48254i	−0.717781	−	1.24323i	0.244096	−	0.969751i	$-0.421509\pi$
$14$		0			0
$15$		0			0
$16$	2.42388	−	4.19829i	0.605971	−	1.04957i
$17$	1.54893			0.375670			0.187835	−	0.982201i	$-0.439853\pi$
$17$	1.54893			0.375670			0.187835	+	0.982201i	$0.439853\pi$
$18$		0			0
$19$	2.50422			0.574507			0.287254	−	0.957855i	$-0.407258\pi$
$19$	2.50422			0.574507			0.287254	+	0.957855i	$0.407258\pi$
$20$	0.927765	−	1.60694i	0.207455	−	0.359322i
$21$		0			0
$22$	1.39291	+	2.41260i	0.296970	+	0.514367i
$23$	−3.68039	−	6.37463i	−0.767415	−	1.32920i	−0.938960	−	0.344025i	$-0.888209\pi$
$23$	−3.68039	−	6.37463i	−0.767415	−	1.32920i	0.171545	−	0.985176i	$-0.445124\pi$
$24$		0			0
$25$	1.60922	−	2.78725i	0.321843	−	0.557449i
$26$	9.53025			1.86904
$27$		0			0
$28$		0			0
$29$	0.0309713	−	0.0536439i	0.00575123	−	0.00996143i	−0.863135	−	0.504972i	$-0.831503\pi$
$29$	0.0309713	−	0.0536439i	0.00575123	−	0.00996143i	0.868887	+	0.495011i	$0.164836\pi$
$30$		0			0
$31$	1.92388	+	3.33227i	0.345540	+	0.598493i	0.985452	−	0.169956i	$-0.0543625\pi$
$31$	1.92388	+	3.33227i	0.345540	+	0.598493i	−0.639912	+	0.768448i	$0.721029\pi$
$32$	3.34011	+	5.78523i	0.590453	+	1.02269i
$33$		0			0
$34$	−1.42597	+	2.46986i	−0.244552	+	0.423577i
$35$		0			0
$36$		0			0
$37$	0.563216			0.0925922			0.0462961	−	0.998928i	$-0.485258\pi$
$37$	0.563216			0.0925922			0.0462961	+	0.998928i	$0.485258\pi$
$38$	−2.30543	+	3.99313i	−0.373991	+	0.647771i
$39$		0			0
$40$	−0.749363	−	1.29794i	−0.118485	−	0.205222i
$41$	−4.51188	−	7.81481i	−0.704638	−	1.22047i	−0.966822	−	0.255450i	$-0.917776\pi$
$41$	−4.51188	−	7.81481i	−0.704638	−	1.22047i	0.262185	−	0.965018i	$-0.415557\pi$
$42$		0			0
$43$	5.09988	−	8.83325i	0.777724	−	1.34706i	−0.155526	−	0.987832i	$-0.549707\pi$
$43$	5.09988	−	8.83325i	0.777724	−	1.34706i	0.933251	−	0.359226i	$-0.116959\pi$
$44$	−2.10335			−0.317091
$45$		0			0
$46$	13.5530			1.99828
$47$	−4.75925	+	8.24327i	−0.694209	+	1.20240i	0.276238	+	0.961089i	$0.410912\pi$
$47$	−4.75925	+	8.24327i	−0.694209	+	1.20240i	−0.970447	+	0.241315i	$0.922421\pi$
$48$		0			0
$49$		0			0
$50$	2.96296	+	5.13199i	0.419025	+	0.725773i
$51$		0			0
$52$	−3.59775	+	6.23148i	−0.498918	+	0.864151i
$53$	1.51075			0.207517			0.103759	−	0.994603i	$-0.466913\pi$
$53$	1.51075			0.207517			0.103759	+	0.994603i	$0.466913\pi$
$54$		0			0
$55$	2.01950			0.272310
$56$		0			0
$57$		0			0
$58$	0.0570257	+	0.0987714i	0.00748784	+	0.0129693i
$59$	−4.22166	−	7.31212i	−0.549613	−	0.951957i	−0.998301	−	0.0582689i	$-0.981442\pi$
$59$	−4.22166	−	7.31212i	−0.549613	−	0.951957i	0.448688	−	0.893688i	$-0.351891\pi$
$60$		0			0
$61$	−1.61958	+	2.80520i	−0.207367	+	0.359169i	−0.950884	−	0.309547i	$-0.899823\pi$
$61$	−1.61958	+	2.80520i	−0.207367	+	0.359169i	0.743518	+	0.668716i	$0.233156\pi$
$62$	−7.08467			−0.899754
$63$		0			0
$64$	−2.60434			−0.325543
$65$	3.45434	−	5.98309i	0.428458	−	0.742111i
$66$		0			0
$67$	−3.46670	−	6.00449i	−0.423524	−	0.733566i	0.572757	−	0.819725i	$-0.305874\pi$
$67$	−3.46670	−	6.00449i	−0.423524	−	0.733566i	−0.996281	+	0.0861595i	$0.972541\pi$
$68$	−1.07663	−	1.86478i	−0.130561	−	0.226138i
$69$		0			0
$70$		0			0
$71$	12.3304			1.46335			0.731673	−	0.681656i	$-0.238740\pi$
$71$	12.3304			1.46335			0.731673	+	0.681656i	$0.238740\pi$
$72$		0			0
$73$	2.75871			0.322883			0.161442	−	0.986882i	$-0.448386\pi$
$73$	2.75871			0.322883			0.161442	+	0.986882i	$0.448386\pi$
$74$	−0.518508	+	0.898083i	−0.0602754	+	0.104400i
$75$		0			0
$76$	−1.74064	−	3.01488i	−0.199665	−	0.345830i
$77$		0			0
$78$		0			0
$79$	2.95969	−	5.12633i	0.332991	−	0.576758i	−0.650106	−	0.759844i	$-0.725275\pi$
$79$	2.95969	−	5.12633i	0.332991	−	0.576758i	0.983097	+	0.183086i	$0.0586087\pi$
$80$	6.47058			0.723432
$81$		0			0
$82$	16.6149			1.83481
$83$	−2.80111	+	4.85167i	−0.307462	+	0.532540i	−0.977806	−	0.209510i	$-0.932813\pi$
$83$	−2.80111	+	4.85167i	−0.307462	+	0.532540i	0.670344	+	0.742050i	$0.266146\pi$
$84$		0			0
$85$	1.03372	+	1.79045i	0.112122	+	0.194202i
$86$	9.39010	+	16.2641i	1.01256	+	1.75381i
$87$		0			0
$88$	−0.849444	+	1.47128i	−0.0905511	+	0.156839i
$89$	1.40657			0.149097			0.0745483	−	0.997217i	$-0.476249\pi$
$89$	1.40657			0.149097			0.0745483	+	0.997217i	$0.476249\pi$
$90$		0			0
$91$		0			0
$92$	−5.11636	+	8.86180i	−0.533418	+	0.923906i
$93$		0			0
$94$	−8.76293	−	15.1778i	−0.903827	−	1.56548i
$95$	1.67126	+	2.89470i	0.171467	+	0.296990i
$96$		0			0
$97$	−6.09713	+	10.5605i	−0.619070	+	1.07226i	0.370586	+	0.928798i	$0.379157\pi$
$97$	−6.09713	+	10.5605i	−0.619070	+	1.07226i	−0.989656	+	0.143462i	$0.954176\pi$
$98$		0			0
$99$		0			0
$100$	−4.47416			−0.447416
$101$	0.559336	−	0.968798i	0.0556560	−	0.0963990i	−0.836855	−	0.547425i	$-0.815608\pi$
$101$	0.559336	−	0.968798i	0.0556560	−	0.0963990i	0.892511	+	0.451025i	$0.148942\pi$
$102$		0			0
$103$	−0.965224	−	1.67182i	−0.0951063	−	0.164729i	0.814547	−	0.580098i	$-0.196986\pi$
$103$	−0.965224	−	1.67182i	−0.0951063	−	0.164729i	−0.909653	+	0.415369i	$0.863652\pi$
$104$	2.90593	+	5.03322i	0.284950	+	0.493548i
$105$		0			0
$106$	−1.39082	+	2.40898i	−0.135089	+	0.233981i
$107$	5.77938			0.558714			0.279357	−	0.960187i	$-0.409879\pi$
$107$	5.77938			0.558714			0.279357	+	0.960187i	$0.409879\pi$
$108$		0			0
$109$	8.24211			0.789451			0.394726	−	0.918799i	$-0.370840\pi$
$109$	8.24211			0.789451			0.394726	+	0.918799i	$0.370840\pi$
$110$	−1.85920	+	3.22022i	−0.177267	+	0.307036i
$111$		0			0
$112$		0			0
$113$	−7.25105	−	12.5592i	−0.682121	−	1.18147i	−0.974332	−	0.225115i	$-0.927724\pi$
$113$	−7.25105	−	12.5592i	−0.682121	−	1.18147i	0.292211	−	0.956354i	$-0.405609\pi$
$114$		0			0
$115$	4.91242	−	8.50856i	0.458085	−	0.793427i
$116$	−0.0861107			−0.00799518
$117$		0			0
$118$	15.5462			1.43114
$119$		0			0
$120$		0			0
$121$	4.35539	+	7.54376i	0.395945	+	0.685796i
$122$	−2.98204	−	5.16505i	−0.269982	−	0.467622i
$123$		0			0
$124$	2.67452	−	4.63241i	0.240179	−	0.416002i
$125$	10.9696			0.981149
$126$		0			0
$127$	8.50004			0.754257			0.377128	−	0.926161i	$-0.376912\pi$
$127$	8.50004			0.754257			0.377128	+	0.926161i	$0.376912\pi$
$128$	−4.28260	+	7.41769i	−0.378532	+	0.655637i
$129$		0			0
$130$	6.36027	+	11.0163i	0.557832	+	0.966194i
$131$	−1.00673	−	1.74371i	−0.0879585	−	0.152349i	0.818690	−	0.574236i	$-0.194701\pi$
$131$	−1.00673	−	1.74371i	−0.0879585	−	0.152349i	−0.906648	+	0.421888i	$0.861368\pi$
$132$		0			0
$133$		0			0
$134$	12.7660			1.10282
$135$		0			0
$136$	−1.73921			−0.149136
$137$	1.10870	−	1.92032i	0.0947225	−	0.164064i	−0.814770	−	0.579784i	$-0.803137\pi$
$137$	1.10870	−	1.92032i	0.0947225	−	0.164064i	0.909493	+	0.415720i	$0.136470\pi$
$138$		0			0
$139$	0.377669	+	0.654143i	0.0320335	+	0.0554836i	0.881598	−	0.472002i	$-0.156468\pi$
$139$	0.377669	+	0.654143i	0.0320335	+	0.0554836i	−0.849564	+	0.527485i	$0.823135\pi$
$140$		0			0
$141$		0			0
$142$	−11.3516	+	19.6615i	−0.952604	+	1.64996i
$143$	−7.83136			−0.654891
$144$		0			0
$145$	0.0826782			0.00686605
$146$	−2.53973	+	4.39894i	−0.210189	+	0.364059i
$147$		0			0
$148$	−0.391482	−	0.678068i	−0.0321797	−	0.0557368i
$149$	3.29249	+	5.70277i	0.269732	+	0.467189i	0.968792	−	0.247873i	$-0.0797317\pi$
$149$	3.29249	+	5.70277i	0.269732	+	0.467189i	−0.699061	+	0.715062i	$0.746398\pi$
$150$		0			0
$151$	−6.33356	+	10.9700i	−0.515417	+	0.892729i	0.484422	+	0.874834i	$0.339030\pi$
$151$	−6.33356	+	10.9700i	−0.515417	+	0.892729i	−0.999840	+	0.0178950i	$0.994304\pi$
$152$	−2.81186			−0.228072
$153$		0			0
$154$		0			0
$155$	−2.56791	+	4.44775i	−0.206260	+	0.357252i
$156$		0			0
$157$	8.65372	+	14.9887i	0.690642	+	1.19623i	0.971628	+	0.236515i	$0.0760052\pi$
$157$	8.65372	+	14.9887i	0.690642	+	1.19623i	−0.280986	+	0.959712i	$0.590662\pi$
$158$	5.44950	+	9.43882i	0.433539	+	0.750912i
$159$		0			0
$160$	−4.45822	+	7.72186i	−0.352453	+	0.610467i
$161$		0			0
$162$		0			0
$163$	−12.2193			−0.957086			−0.478543	−	0.878064i	$-0.658835\pi$
$163$	−12.2193			−0.957086			−0.478543	+	0.878064i	$0.658835\pi$
$164$	−6.27227	+	10.8639i	−0.489782	+	0.848327i
$165$		0			0
$166$	−5.15752	−	8.93309i	−0.400301	−	0.693342i
$167$	−1.76248	−	3.05270i	−0.136385	−	0.236225i	0.789741	−	0.613440i	$-0.210215\pi$
$167$	−1.76248	−	3.05270i	−0.136385	−	0.236225i	−0.926126	+	0.377215i	$0.876882\pi$
$168$		0			0
$169$	−6.89546	+	11.9433i	−0.530420	+	0.918714i
$170$	−3.80665			−0.291956
$171$		0			0
$172$	−14.1794			−1.08117
$173$	5.07046	−	8.78229i	0.385500	−	0.667705i	−0.606339	−	0.795206i	$-0.707362\pi$
$173$	5.07046	−	8.78229i	0.385500	−	0.667705i	0.991838	+	0.127502i	$0.0406958\pi$
$174$		0			0
$175$		0			0
$176$	−3.66738	−	6.35208i	−0.276439	−	0.478806i
$177$		0			0
$178$	−1.29492	+	2.24287i	−0.0970584	+	0.168110i
$179$	1.70116			0.127150			0.0635752	−	0.997977i	$-0.479750\pi$
$179$	1.70116			0.127150			0.0635752	+	0.997977i	$0.479750\pi$
$180$		0			0
$181$	−16.9941			−1.26316			−0.631581	−	0.775310i	$-0.717594\pi$
$181$	−16.9941			−1.26316			−0.631581	+	0.775310i	$0.717594\pi$
$182$		0			0
$183$		0			0
$184$	4.13252	+	7.15774i	0.304654	+	0.527676i
$185$	0.375877	+	0.651039i	0.0276351	+	0.0478653i
$186$		0			0
$187$	1.17178	−	2.02957i	0.0856887	−	0.148417i
$188$	13.2323			0.965066
$189$		0			0
$190$	−6.15437			−0.446485
$191$	11.3470	−	19.6535i	0.821038	−	1.42208i	−0.0838717	−	0.996477i	$-0.526729\pi$
$191$	11.3470	−	19.6535i	0.821038	−	1.42208i	0.904910	−	0.425603i	$-0.139938\pi$
$192$		0			0
$193$	−3.09349	−	5.35808i	−0.222674	−	0.385683i	0.732945	−	0.680288i	$-0.238145\pi$
$193$	−3.09349	−	5.35808i	−0.222674	−	0.385683i	−0.955619	+	0.294605i	$0.904812\pi$
$194$	−11.2263	−	19.4445i	−0.806001	−	1.39603i
$195$		0			0
$196$		0			0
$197$	−9.77010			−0.696091			−0.348045	−	0.937478i	$-0.613154\pi$
$197$	−9.77010			−0.696091			−0.348045	+	0.937478i	$0.613154\pi$
$198$		0			0
$199$	8.67947			0.615271			0.307636	−	0.951504i	$-0.400462\pi$
$199$	8.67947			0.615271			0.307636	+	0.951504i	$0.400462\pi$
$200$	−1.80691	+	3.12965i	−0.127768	+	0.221300i
$201$		0			0
$202$	1.02987	+	1.78379i	0.0724615	+	0.125507i
$203$		0			0
$204$		0			0
$205$	6.02225	−	10.4308i	0.420612	−	0.728522i
$206$	3.55442			0.247648
$207$		0			0
$208$	−25.0920			−1.73982
$209$	1.89446	−	3.28130i	0.131043	−	0.226973i
$210$		0			0
$211$	−2.84219	−	4.92283i	−0.195665	−	0.338901i	0.751453	−	0.659786i	$-0.229353\pi$
$211$	−2.84219	−	4.92283i	−0.195665	−	0.338901i	−0.947118	+	0.320885i	$0.896020\pi$
$212$	−1.05010	−	1.81882i	−0.0721209	−	0.124917i
$213$		0			0
$214$	−5.32062	+	9.21558i	−0.363710	+	0.629964i
$215$	13.6142			0.928478
$216$		0			0
$217$		0			0
$218$	−7.58786	+	13.1426i	−0.513915	+	0.890126i
$219$		0			0
$220$	−1.40372	−	2.43132i	−0.0946390	−	0.163920i
$221$	−4.00862	−	6.94313i	−0.269649	−	0.467045i
$222$		0			0
$223$	5.86133	−	10.1521i	0.392503	−	0.679836i	−0.600276	−	0.799793i	$-0.704942\pi$
$223$	5.86133	−	10.1521i	0.392503	−	0.679836i	0.992779	+	0.119957i	$0.0382758\pi$
$224$		0			0
$225$		0			0
$226$	26.7019			1.77618
$227$	5.59154	−	9.68482i	0.371123	−	0.642804i	−0.618615	−	0.785694i	$-0.712306\pi$
$227$	5.59154	−	9.68482i	0.371123	−	0.642804i	0.989739	+	0.142890i	$0.0456394\pi$
$228$		0			0
$229$	4.82824	+	8.36275i	0.319059	+	0.552626i	0.980292	−	0.197554i	$-0.0632999\pi$
$229$	4.82824	+	8.36275i	0.319059	+	0.552626i	−0.661233	+	0.750181i	$0.729967\pi$
$230$	9.04494	+	15.6663i	0.596406	+	1.03301i
$231$		0			0
$232$	−0.0347761	+	0.0602340i	−0.00228317	+	0.00395456i
$233$	−19.2898			−1.26372			−0.631860	−	0.775083i	$-0.717708\pi$
$233$	−19.2898			−1.26372			−0.631860	+	0.775083i	$0.717708\pi$
$234$		0			0
$235$	−12.7049			−0.828774
$236$	−5.86881	+	10.1651i	−0.382027	+	0.661690i
$237$		0			0
$238$		0			0
$239$	0.194641	+	0.337128i	0.0125903	+	0.0218070i	0.872252	−	0.489057i	$-0.162659\pi$
$239$	0.194641	+	0.337128i	0.0125903	+	0.0218070i	−0.859662	+	0.510864i	$0.829326\pi$
$240$		0			0
$241$	−5.31807	+	9.21117i	−0.342567	+	0.593344i	−0.984909	−	0.173075i	$-0.944630\pi$
$241$	−5.31807	+	9.21117i	−0.342567	+	0.593344i	0.642342	+	0.766419i	$0.277963\pi$
$242$	−16.0386			−1.03100
$243$		0			0
$244$	4.50299			0.288274
$245$		0			0
$246$		0			0
$247$	−6.48091	−	11.2253i	−0.412370	−	0.714247i
$248$	−2.16023	−	3.74163i	−0.137175	−	0.237594i
$249$		0			0
$250$	−10.0988	+	17.4917i	−0.638705	+	1.10627i
$251$	3.26628			0.206166			0.103083	−	0.994673i	$-0.467129\pi$
$251$	3.26628			0.206166			0.103083	+	0.994673i	$0.467129\pi$
$252$		0			0
$253$	−11.1370			−0.700176
$254$	−7.82531	+	13.5538i	−0.491004	+	0.850443i
$255$		0			0
$256$	−10.4896	−	18.1686i	−0.655603	−	1.13554i
$257$	−2.34787	−	4.06663i	−0.146456	−	0.253669i	0.783459	−	0.621443i	$-0.213453\pi$
$257$	−2.34787	−	4.06663i	−0.146456	−	0.253669i	−0.929915	+	0.367774i	$0.880120\pi$
$258$		0			0
$259$		0			0
$260$	−9.60421			−0.595628
$261$		0			0
$262$	3.70727			0.229036
$263$	9.77491	−	16.9306i	0.602747	−	1.04399i	−0.389656	−	0.920960i	$-0.627406\pi$
$263$	9.77491	−	16.9306i	0.602747	−	1.04399i	0.992403	−	0.123028i	$-0.0392605\pi$
$264$		0			0
$265$	1.00824	+	1.74632i	0.0619355	+	0.107276i
$266$		0			0
$267$		0			0
$268$	−4.81929	+	8.34725i	−0.294385	+	0.509890i
$269$	15.7673			0.961349			0.480675	−	0.876899i	$-0.340392\pi$
$269$	15.7673			0.961349			0.480675	+	0.876899i	$0.340392\pi$
$270$		0			0
$271$	−14.7976			−0.898893			−0.449446	−	0.893307i	$-0.648379\pi$
$271$	−14.7976			−0.898893			−0.449446	+	0.893307i	$0.648379\pi$
$272$	3.75442	−	6.50285i	0.227645	−	0.394293i
$273$		0			0
$274$	2.04138	+	3.53578i	0.123324	+	0.213604i
$275$	−2.43477	−	4.21715i	−0.146822	−	0.254304i
$276$		0			0
$277$	3.72561	−	6.45295i	0.223850	−	0.387720i	−0.732124	−	0.681172i	$-0.761471\pi$
$277$	3.72561	−	6.45295i	0.223850	−	0.387720i	0.955974	+	0.293452i	$0.0948040\pi$
$278$	−1.39076			−0.0834123
$279$		0			0
$280$		0			0
$281$	12.9938	−	22.5060i	0.775146	−	1.34259i	−0.159566	−	0.987187i	$-0.551009\pi$
$281$	12.9938	−	22.5060i	0.775146	−	1.34259i	0.934712	−	0.355406i	$-0.115657\pi$
$282$		0			0
$283$	−9.37768	−	16.2426i	−0.557445	−	0.965524i	−0.997709	−	0.0676550i	$-0.978448\pi$
$283$	−9.37768	−	16.2426i	−0.557445	−	0.965524i	0.440263	−	0.897869i	$-0.354885\pi$
$284$	−8.57064	−	14.8448i	−0.508574	−	0.880876i
$285$		0			0
$286$	7.20971	−	12.4876i	0.426319	−	0.738406i
$287$		0			0
$288$		0			0
$289$	−14.6008			−0.858872
$290$	−0.0761152	+	0.131835i	−0.00446964	+	0.00774165i
$291$		0			0
$292$	−1.91754	−	3.32127i	−0.112215	−	0.194363i
$293$	1.23089	+	2.13196i	0.0719093	+	0.124551i	0.899738	−	0.436430i	$-0.143757\pi$
$293$	1.23089	+	2.13196i	0.0719093	+	0.124551i	−0.827829	+	0.560981i	$0.810424\pi$
$294$		0			0
$295$	5.63487	−	9.75988i	0.328075	−	0.568242i
$296$	−0.632407			−0.0367579
$297$		0			0
$298$	−12.1245			−0.702356
$299$	−19.0497	+	32.9950i	−1.10167	+	1.90815i
$300$		0			0
$301$		0			0
$302$	−11.6616	−	20.1985i	−0.671050	−	1.16229i
$303$		0			0
$304$	6.06994	−	10.5134i	0.348135	−	0.602987i
$305$	−4.32349			−0.247562
$306$		0			0
$307$	−4.66277			−0.266118			−0.133059	−	0.991108i	$-0.542480\pi$
$307$	−4.66277			−0.266118			−0.133059	+	0.991108i	$0.542480\pi$
$308$		0			0
$309$		0			0
$310$	−4.72814	−	8.18938i	−0.268541	−	0.465126i
$311$	13.7410	+	23.8002i	0.779183	+	1.34958i	0.932413	+	0.361393i	$0.117699\pi$
$311$	13.7410	+	23.8002i	0.779183	+	1.34958i	−0.153231	+	0.988190i	$0.548968\pi$
$312$		0			0
$313$	−2.74666	+	4.75735i	−0.155250	+	0.268901i	−0.933150	−	0.359487i	$-0.882952\pi$
$313$	−2.74666	+	4.75735i	−0.155250	+	0.268901i	0.777900	+	0.628388i	$0.216285\pi$
$314$	−31.8671			−1.79837
$315$		0			0
$316$	−8.22893			−0.462914
$317$	4.93879	−	8.55424i	0.277390	−	0.480454i	−0.693345	−	0.720606i	$-0.743864\pi$
$317$	4.93879	−	8.55424i	0.277390	−	0.480454i	0.970735	+	0.240152i	$0.0771972\pi$
$318$		0			0
$319$	−0.0468601	−	0.0811641i	−0.00262366	−	0.00454432i
$320$	−1.73808	−	3.01044i	−0.0971614	−	0.168288i
$321$		0			0
$322$		0			0
$323$	3.87885			0.215825
$324$		0			0
$325$	−16.6586			−0.924052
$326$	11.2493	−	19.4844i	0.623041	−	1.07914i
$327$		0			0
$328$	5.06616	+	8.77485i	0.279732	+	0.484510i
$329$		0			0
$330$		0			0
$331$	10.3471	−	17.9217i	0.568729	−	0.985067i	−0.427963	−	0.903796i	$-0.640769\pi$
$331$	10.3471	−	17.9217i	0.568729	−	0.985067i	0.996692	−	0.0812710i	$-0.0258979\pi$
$332$	7.78803			0.427424
$333$		0			0
$334$	6.49029			0.355133
$335$	4.62718	−	8.01452i	0.252810	−	0.437880i
$336$		0			0
$337$	0.748747	+	1.29687i	0.0407869	+	0.0706449i	0.885698	−	0.464261i	$-0.153680\pi$
$337$	0.748747	+	1.29687i	0.0407869	+	0.0706449i	−0.844911	+	0.534906i	$0.820347\pi$
$338$	−12.6962	−	21.9905i	−0.690582	−	1.19612i
$339$		0			0
$340$	1.43704	−	2.48903i	0.0779344	−	0.134986i
$341$	5.82174			0.315265
$342$		0			0
$343$		0			0
$344$	−5.72639	+	9.91840i	−0.308746	+	0.534764i
$345$		0			0
$346$	9.33593	+	16.1703i	0.501903	+	0.869321i
$347$	−14.7694	−	25.5813i	−0.792862	−	1.37328i	−0.924188	−	0.381938i	$-0.875257\pi$
$347$	−14.7694	−	25.5813i	−0.792862	−	1.37328i	0.131326	−	0.991339i	$-0.458077\pi$
$348$		0			0
$349$	18.0006	−	31.1780i	0.963551	−	1.66892i	0.250094	−	0.968222i	$-0.419539\pi$
$349$	18.0006	−	31.1780i	0.963551	−	1.66892i	0.713458	−	0.700698i	$-0.247128\pi$
$350$		0			0
$351$		0			0
$352$	10.1073			0.538719
$353$	−14.7465	+	25.5417i	−0.784877	+	1.35945i	0.144196	+	0.989549i	$0.453940\pi$
$353$	−14.7465	+	25.5417i	−0.784877	+	1.35945i	−0.929073	+	0.369897i	$0.879393\pi$
$354$		0			0
$355$	8.22900	+	14.2530i	0.436750	+	0.756473i
$356$	−0.977687	−	1.69340i	−0.0518173	−	0.0897502i
$357$		0			0
$358$	−1.56612	+	2.71260i	−0.0827720	+	0.143365i
$359$	5.41069			0.285566			0.142783	−	0.989754i	$-0.454395\pi$
$359$	5.41069			0.285566			0.142783	+	0.989754i	$0.454395\pi$
$360$		0			0
$361$	−12.7289			−0.669942
$362$	15.6451	−	27.0981i	0.822289	−	1.42425i
$363$		0			0
$364$		0			0
$365$	1.84110	+	3.18888i	0.0963676	+	0.166914i
$366$		0			0
$367$	11.5422	−	19.9916i	0.602496	−	1.04355i	−0.389946	−	0.920838i	$-0.627506\pi$
$367$	11.5422	−	19.9916i	0.602496	−	1.04355i	0.992442	−	0.122715i	$-0.0391602\pi$
$368$	−35.6834			−1.86013
$369$		0			0
$370$	−1.38416			−0.0719591
$371$		0			0
$372$		0			0
$373$	−10.7515	−	18.6222i	−0.556692	−	0.964219i	−0.997770	−	0.0667498i	$-0.978737\pi$
$373$	−10.7515	−	18.6222i	−0.556692	−	0.964219i	0.441078	−	0.897469i	$-0.354596\pi$
$374$	2.15752	+	3.73694i	0.111563	+	0.193232i
$375$		0			0
$376$	5.34392	−	9.25595i	0.275592	−	0.477339i
$377$	−0.320615			−0.0165125
$378$		0			0
$379$	5.72168			0.293903			0.146952	−	0.989144i	$-0.453054\pi$
$379$	5.72168			0.293903			0.146952	+	0.989144i	$0.453054\pi$
$380$	2.32333	−	4.02412i	0.119184	−	0.206433i
$381$		0			0
$382$	20.8925	+	36.1869i	1.06895	+	1.85148i
$383$	−17.4604	−	30.2424i	−0.892187	−	1.54531i	−0.837248	−	0.546823i	$-0.815837\pi$
$383$	−17.4604	−	30.2424i	−0.892187	−	1.54531i	−0.0549390	−	0.998490i	$-0.517496\pi$
$384$		0			0
$385$		0			0
$386$	11.3917			0.579823
$387$		0			0
$388$	16.9521			0.860611
$389$	−14.4411	+	25.0127i	−0.732192	+	1.26819i	0.223752	+	0.974646i	$0.428169\pi$
$389$	−14.4411	+	25.0127i	−0.732192	+	1.26819i	−0.955944	+	0.293548i	$0.905164\pi$
$390$		0			0
$391$	−5.70066	−	9.87383i	−0.288295	−	0.499341i
$392$		0			0
$393$		0			0
$394$	8.99455	−	15.5790i	0.453139	−	0.784860i
$395$	7.90091			0.397538
$396$		0			0
$397$	−11.1845			−0.561335			−0.280667	−	0.959805i	$-0.590556\pi$
$397$	−11.1845			−0.561335			−0.280667	+	0.959805i	$0.590556\pi$
$398$	−7.99049	+	13.8399i	−0.400527	+	0.693734i
$399$		0			0
$400$	−7.80111	−	13.5119i	−0.390056	−	0.675596i
$401$	−0.541061	−	0.937146i	−0.0270193	−	0.0467988i	0.852200	−	0.523217i	$-0.175268\pi$
$401$	−0.541061	−	0.937146i	−0.0270193	−	0.0467988i	−0.879219	+	0.476418i	$0.841935\pi$
$402$		0			0
$403$	9.95802	−	17.2478i	0.496044	−	0.859174i
$404$	−1.55514			−0.0773711
$405$		0			0
$406$		0			0
$407$	0.426078	−	0.737988i	0.0211199	−	0.0365807i
$408$		0			0
$409$	10.8674	+	18.8229i	0.537360	+	0.930735i	0.999045	+	0.0436908i	$0.0139116\pi$
$409$	10.8674	+	18.8229i	0.537360	+	0.930735i	−0.461685	+	0.887044i	$0.652755\pi$
$410$	11.0884	+	19.2057i	0.547618	+	0.948501i
$411$		0			0
$412$	−1.34182	+	2.32410i	−0.0661069	+	0.114500i
$413$		0			0
$414$		0			0
$415$	−7.47759			−0.367060
$416$	17.2884	−	29.9443i	0.847632	−	1.46814i
$417$		0			0
$418$	3.48816	+	6.04167i	0.170611	+	0.295508i
$419$	−12.5906	−	21.8075i	−0.615090	−	1.06537i	−0.990369	−	0.138455i	$-0.955787\pi$
$419$	−12.5906	−	21.8075i	−0.615090	−	1.06537i	0.375279	−	0.926912i	$-0.377547\pi$
$420$		0			0
$421$	−14.8304	+	25.6869i	−0.722788	+	1.25191i	0.237090	+	0.971488i	$0.423806\pi$
$421$	−14.8304	+	25.6869i	−0.722788	+	1.25191i	−0.959878	+	0.280418i	$0.909527\pi$
$422$	10.4663			0.509493
$423$		0			0
$424$	−1.69634			−0.0823816
$425$	2.49256	−	4.31724i	0.120907	−	0.209417i
$426$		0			0
$427$		0			0
$428$	−4.01715	−	6.95791i	−0.194176	−	0.336323i
$429$		0			0
$430$	−12.5335	+	21.7086i	−0.604418	+	1.04688i
$431$	4.89034			0.235559			0.117780	−	0.993040i	$-0.462422\pi$
$431$	4.89034			0.235559			0.117780	+	0.993040i	$0.462422\pi$
$432$		0			0
$433$	9.71430			0.466839			0.233420	−	0.972376i	$-0.425008\pi$
$433$	9.71430			0.466839			0.233420	+	0.972376i	$0.425008\pi$
$434$		0			0
$435$		0			0
$436$	−5.72896	−	9.92285i	−0.274367	−	0.475218i
$437$	−9.21651	−	15.9635i	−0.440885	−	0.763636i
$438$		0			0
$439$	7.41176	−	12.8375i	0.353744	−	0.612703i	−0.633158	−	0.774022i	$-0.718242\pi$
$439$	7.41176	−	12.8375i	0.353744	−	0.612703i	0.986902	+	0.161320i	$0.0515751\pi$
$440$	−2.26760			−0.108103
$441$		0			0
$442$	14.7617			0.702141
$443$	−10.9510	+	18.9676i	−0.520297	+	0.901180i	0.479425	+	0.877583i	$0.340845\pi$
$443$	−10.9510	+	18.9676i	−0.520297	+	0.901180i	−0.999722	+	0.0235972i	$0.992488\pi$
$444$		0			0
$445$	0.938715	+	1.62590i	0.0444994	+	0.0770751i
$446$	10.7921	+	18.6925i	0.511021	+	0.885115i
$447$		0			0
$448$		0			0
$449$	−21.4952			−1.01442			−0.507212	−	0.861822i	$-0.669324\pi$
$449$	−21.4952			−1.01442			−0.507212	+	0.861822i	$0.669324\pi$
$450$		0			0
$451$	−13.6531			−0.642899
$452$	−10.0802	+	17.4594i	−0.474131	+	0.821220i
$453$		0			0
$454$	10.2954	+	17.8321i	0.483185	+	0.836902i
$455$		0			0
$456$		0			0
$457$	−20.3128	+	35.1827i	−0.950190	+	1.64578i	−0.205181	+	0.978724i	$0.565778\pi$
$457$	−20.3128	+	35.1827i	−0.950190	+	1.64578i	−0.745009	+	0.667054i	$0.767555\pi$
$458$	−17.7799			−0.830800
$459$		0			0
$460$	−13.6582			−0.636815
$461$	−1.41541	+	2.45155i	−0.0659220	+	0.114180i	−0.897103	−	0.441822i	$-0.854332\pi$
$461$	−1.41541	+	2.45155i	−0.0659220	+	0.114180i	0.831181	+	0.556003i	$0.187666\pi$
$462$		0			0
$463$	−13.9324	−	24.1317i	−0.647494	−	1.12149i	−0.983719	−	0.179711i	$-0.942484\pi$
$463$	−13.9324	−	24.1317i	−0.647494	−	1.12149i	0.336225	−	0.941782i	$-0.390850\pi$
$464$	−0.150142	−	0.260053i	−0.00697016	−	0.0120727i
$465$		0			0
$466$	17.7586	−	30.7588i	0.822653	−	1.42488i
$467$	−26.6438			−1.23293			−0.616464	−	0.787383i	$-0.711436\pi$
$467$	−26.6438			−1.23293			−0.616464	+	0.787383i	$0.711436\pi$
$468$		0			0
$469$		0			0
$470$	11.6964	−	20.2587i	0.539513	−	0.934463i
$471$		0			0
$472$	4.74028	+	8.21041i	0.218189	+	0.377915i
$473$	−7.71620	−	13.3648i	−0.354791	−	0.614516i
$474$		0			0
$475$	4.02983	−	6.97987i	0.184901	−	0.320258i
$476$		0			0
$477$		0			0
$478$	−0.716762			−0.0327839
$479$	−15.7895	+	27.3483i	−0.721443	+	1.24958i	0.238979	+	0.971025i	$0.423187\pi$
$479$	−15.7895	+	27.3483i	−0.721443	+	1.24958i	−0.960422	+	0.278551i	$0.910146\pi$
$480$		0			0
$481$	−1.45760	−	2.52464i	−0.0664609	−	0.115114i
$482$	−9.79185	−	16.9600i	−0.446007	−	0.772506i
$483$		0			0
$484$	6.05472	−	10.4871i	0.275215	−	0.476686i
$485$	−16.2763			−0.739070
$486$		0			0
$487$	0.306174			0.0138741			0.00693703	−	0.999976i	$-0.497792\pi$
$487$	0.306174			0.0138741			0.00693703	+	0.999976i	$0.497792\pi$
$488$	1.81855	−	3.14982i	0.0823218	−	0.142586i
$489$		0			0
$490$		0			0
$491$	9.06981	+	15.7094i	0.409315	+	0.708954i	0.994813	−	0.101720i	$-0.0324345\pi$
$491$	9.06981	+	15.7094i	0.409315	+	0.708954i	−0.585498	+	0.810674i	$0.699101\pi$
$492$		0			0
$493$	0.0479723	−	0.0830905i	0.00216057	−	0.00374221i
$494$	23.8658			1.07377
$495$		0			0
$496$	18.6531			0.837549
$497$		0			0
$498$		0			0
$499$	10.6546	+	18.4543i	0.476964	+	0.826126i	0.999652	−	0.0263983i	$-0.00840381\pi$
$499$	10.6546	+	18.4543i	0.476964	+	0.826126i	−0.522687	+	0.852524i	$0.675070\pi$
$500$	−7.62478	−	13.2065i	−0.340990	−	0.590613i
$501$		0			0
$502$	−3.00701	+	5.20829i	−0.134209	+	0.232457i
$503$	17.0738			0.761285			0.380642	−	0.924722i	$-0.375703\pi$
$503$	17.0738			0.761285			0.380642	+	0.924722i	$0.375703\pi$
$504$		0			0
$505$	1.49315			0.0664443
$506$	10.2529	−	17.7586i	0.455799	−	0.789466i
$507$		0			0
$508$	−5.90824	−	10.2334i	−0.262136	−	0.454032i
$509$	18.3868	+	31.8468i	0.814979	+	1.41159i	0.909343	+	0.416048i	$0.136585\pi$
$509$	18.3868	+	31.8468i	0.814979	+	1.41159i	−0.0943635	+	0.995538i	$0.530082\pi$
$510$		0			0
$511$		0			0
$512$	21.4975			0.950065
$513$		0			0
$514$	8.64598			0.381358
$515$	1.28834	−	2.23146i	0.0567709	−	0.0983300i
$516$		0			0
$517$	7.20083	+	12.4722i	0.316692	+	0.548527i
$518$		0			0
$519$		0			0
$520$	−3.87870	+	6.71810i	−0.170092	+	0.294608i
$521$	−19.1507			−0.839008			−0.419504	−	0.907754i	$-0.637796\pi$
$521$	−19.1507			−0.839008			−0.419504	+	0.907754i	$0.637796\pi$
$522$		0			0
$523$	41.9429			1.83404			0.917018	−	0.398847i	$-0.130589\pi$
$523$	41.9429			1.83404			0.917018	+	0.398847i	$0.130589\pi$
$524$	−1.39952	+	2.42405i	−0.0611385	+	0.105895i
$525$		0			0
$526$	17.9980	+	31.1734i	0.784749	+	1.35922i
$527$	2.97996	+	5.16144i	0.129809	+	0.224836i
$528$		0			0
$529$	−15.5906	+	27.0037i	−0.677851	+	1.17407i
$530$	−3.71282			−0.161274
$531$		0			0
$532$		0			0
$533$	−23.3535	+	40.4494i	−1.01155	+	1.75206i
$534$		0			0
$535$	3.85702	+	6.68056i	0.166754	+	0.288826i
$536$	3.89258	+	6.74214i	0.168134	+	0.291216i
$537$		0			0
$538$	−14.5157	+	25.1419i	−0.625816	+	1.08395i
$539$		0			0
$540$		0			0
$541$	2.88544			0.124055			0.0620273	−	0.998074i	$-0.480243\pi$
$541$	2.88544			0.124055			0.0620273	+	0.998074i	$0.480243\pi$
$542$	13.6230	−	23.5957i	0.585158	−	1.01352i
$543$		0			0
$544$	5.17358	+	8.96090i	0.221815	+	0.384196i
$545$	5.50059	+	9.52731i	0.235620	+	0.408105i
$546$		0			0
$547$	1.38738	−	2.40301i	0.0593201	−	0.102745i	−0.834840	−	0.550492i	$-0.814440\pi$
$547$	1.38738	−	2.40301i	0.0593201	−	0.102745i	0.894160	+	0.447747i	$0.147773\pi$
$548$	−3.08255			−0.131680
$549$		0			0
$550$	8.96600			0.382311
$551$	0.0775590	−	0.134336i	0.00330413	−	0.00572291i
$552$		0			0
$553$		0			0
$554$	6.85975	+	11.8814i	0.291443	+	0.504794i
$555$		0			0
$556$	0.525024	−	0.909368i	0.0222660	−	0.0385658i
$557$	31.0688			1.31643			0.658214	−	0.752831i	$-0.271312\pi$
$557$	31.0688			1.31643			0.658214	+	0.752831i	$0.271312\pi$
$558$		0			0
$559$	−52.7939			−2.23294
$560$		0			0
$561$		0			0
$562$	23.9248	+	41.4389i	1.00920	+	1.74799i
$563$	0.144020	+	0.249451i	0.00606973	+	0.0105131i	0.869044	−	0.494734i	$-0.164735\pi$
$563$	0.144020	+	0.249451i	0.00606973	+	0.0105131i	−0.862975	+	0.505247i	$0.831401\pi$
$564$		0			0
$565$	9.67836	−	16.7634i	0.407172	−	0.705242i
$566$	34.5331			1.45154
$567$		0			0
$568$	−13.8451			−0.580929
$569$	−8.04004	+	13.9258i	−0.337056	+	0.583798i	−0.983878	−	0.178843i	$-0.942765\pi$
$569$	−8.04004	+	13.9258i	−0.337056	+	0.583798i	0.646821	+	0.762641i	$0.276098\pi$
$570$		0			0
$571$	7.64289	+	13.2379i	0.319845	+	0.553988i	0.980456	−	0.196741i	$-0.0630358\pi$
$571$	7.64289	+	13.2379i	0.319845	+	0.553988i	−0.660610	+	0.750729i	$0.729702\pi$
$572$	5.44345	+	9.42834i	0.227602	+	0.394218i
$573$		0			0
$574$		0			0
$575$	−23.6902			−0.987950
$576$		0			0
$577$	−24.1625			−1.00590			−0.502949	−	0.864316i	$-0.667752\pi$
$577$	−24.1625			−1.00590			−0.502949	+	0.864316i	$0.667752\pi$
$578$	13.4418	−	23.2819i	0.559106	−	0.968400i
$579$		0			0
$580$	−0.0574683	−	0.0995380i	−0.00238624	−	0.00413309i
$581$		0			0
$582$		0			0
$583$	1.14289	−	1.97955i	0.0473338	−	0.0819845i
$584$	−3.09762			−0.128180
$585$		0			0
$586$	−4.53273			−0.187245
$587$	−18.0145	+	31.2020i	−0.743537	+	1.28784i	0.207339	+	0.978269i	$0.433520\pi$
$587$	−18.0145	+	31.2020i	−0.743537	+	1.28784i	−0.950875	+	0.309574i	$0.899814\pi$
$588$		0			0
$589$	4.81783	+	8.34472i	0.198515	+	0.343838i
$590$	10.3752	+	17.9703i	0.427138	+	0.739825i
$591$		0			0
$592$	1.36517	−	2.36455i	0.0561082	−	0.0971823i
$593$	24.9337			1.02390			0.511951	−	0.859014i	$-0.328923\pi$
$593$	24.9337			1.02390			0.511951	+	0.859014i	$0.328923\pi$
$594$		0			0
$595$		0			0
$596$	4.57712	−	7.92780i	0.187486	−	0.324735i
$597$		0			0
$598$	−35.0751	−	60.7518i	−1.43433	−	2.48433i
$599$	19.7642	+	34.2325i	0.807542	+	1.39870i	0.914561	+	0.404447i	$0.132536\pi$
$599$	19.7642	+	34.2325i	0.807542	+	1.39870i	−0.107019	+	0.994257i	$0.534131\pi$
$600$		0			0
$601$	1.86447	−	3.22936i	0.0760534	−	0.131728i	−0.825490	−	0.564416i	$-0.809101\pi$
$601$	1.86447	−	3.22936i	0.0760534	−	0.131728i	0.901544	+	0.432688i	$0.142435\pi$
$602$		0			0
$603$		0			0
$604$	17.6094			0.716516
$605$	−5.81337	+	10.0691i	−0.236347	+	0.409365i
$606$		0			0
$607$	−11.8264	−	20.4839i	−0.480018	−	0.831415i	0.519719	−	0.854337i	$-0.326036\pi$
$607$	−11.8264	−	20.4839i	−0.480018	−	0.831415i	−0.999737	+	0.0229218i	$0.992703\pi$
$608$	8.36436	+	14.4875i	0.339219	+	0.587545i
$609$		0			0
$610$	3.98029	−	6.89407i	0.161157	−	0.279133i
$611$	49.2677			1.99316
$612$		0			0
$613$	−3.79903			−0.153442			−0.0767208	−	0.997053i	$-0.524445\pi$
$613$	−3.79903			−0.153442			−0.0767208	+	0.997053i	$0.524445\pi$
$614$	4.29264	−	7.43507i	0.173237	−	0.300055i
$615$		0			0
$616$		0			0
$617$	17.5615	+	30.4174i	0.706999	+	1.22456i	0.965965	+	0.258672i	$0.0832849\pi$
$617$	17.5615	+	30.4174i	0.706999	+	1.22456i	−0.258966	+	0.965886i	$0.583382\pi$
$618$		0			0
$619$	10.5816	−	18.3279i	0.425311	−	0.736660i	−0.571138	−	0.820854i	$-0.693498\pi$
$619$	10.5816	−	18.3279i	0.425311	−	0.736660i	0.996449	+	0.0841934i	$0.0268314\pi$
$620$	7.13965			0.286735
$621$		0			0
$622$	−50.6011			−2.02892
$623$		0			0
$624$		0			0
$625$	−0.725240	−	1.25615i	−0.0290096	−	0.0502461i
$626$	−5.05726	−	8.75943i	−0.202129	−	0.350097i
$627$		0			0
$628$	12.0301	−	20.8368i	0.480054	−	0.831477i
$629$	0.872381			0.0347841
$630$		0			0
$631$	4.74845			0.189033			0.0945164	−	0.995523i	$-0.469870\pi$
$631$	4.74845			0.189033			0.0945164	+	0.995523i	$0.469870\pi$
$632$	−3.32329	+	5.75610i	−0.132193	+	0.228965i
$633$		0			0
$634$	9.09350	+	15.7504i	0.361149	+	0.625529i
$635$	5.67273	+	9.82546i	0.225115	+	0.389911i
$636$		0			0
$637$		0			0
$638$	0.172562			0.00683178
$639$		0			0
$640$	−11.4324			−0.451907
$641$	−4.93735	+	8.55174i	−0.195013	+	0.337773i	−0.946905	−	0.321514i	$-0.895808\pi$
$641$	−4.93735	+	8.55174i	−0.195013	+	0.337773i	0.751891	+	0.659287i	$0.229142\pi$
$642$		0			0
$643$	21.9748	+	38.0615i	0.866602	+	1.50100i	0.865448	+	0.501000i	$0.167034\pi$
$643$	21.9748	+	38.0615i	0.866602	+	1.50100i	0.00115462	+	0.999999i	$0.499632\pi$
$644$		0			0
$645$		0			0
$646$	−3.57095	+	6.18507i	−0.140497	+	0.243348i
$647$	44.3872			1.74504			0.872521	−	0.488577i	$-0.162484\pi$
$647$	44.3872			1.74504			0.872521	+	0.488577i	$0.162484\pi$
$648$		0			0
$649$	−12.7749			−0.501457
$650$	15.3362	−	26.5631i	0.601537	−	1.04189i
$651$		0			0
$652$	8.49341	+	14.7110i	0.332628	+	0.576128i
$653$	20.9956	+	36.3655i	0.821622	+	1.42309i	0.904474	+	0.426529i	$0.140264\pi$
$653$	20.9956	+	36.3655i	0.821622	+	1.42309i	−0.0828523	+	0.996562i	$0.526403\pi$
$654$		0			0
$655$	1.34374	−	2.32742i	0.0525042	−	0.0909399i
$656$	−43.7451			−1.70796
$657$		0			0
$658$		0			0
$659$	19.6365	−	34.0114i	0.764928	−	1.32489i	−0.175356	−	0.984505i	$-0.556108\pi$
$659$	19.6365	−	34.0114i	0.764928	−	1.32489i	0.940284	−	0.340390i	$-0.110559\pi$
$660$		0			0
$661$	0.0933694	+	0.161721i	0.00363165	+	0.00629020i	0.867836	−	0.496852i	$-0.165511\pi$
$661$	0.0933694	+	0.161721i	0.00363165	+	0.00629020i	−0.864204	+	0.503142i	$0.832177\pi$
$662$	19.0515	+	32.9982i	0.740459	+	1.28251i
$663$		0			0
$664$	3.14522	−	5.44769i	0.122058	−	0.211411i
$665$		0			0
$666$		0			0
$667$	−0.455947			−0.0176543
$668$	−2.45014	+	4.24376i	−0.0947987	+	0.164196i
$669$		0			0
$670$	8.51976	+	14.7567i	0.329147	+	0.570099i
$671$	2.45046	+	4.24432i	0.0945989	+	0.163850i
$672$		0			0
$673$	−5.43382	+	9.41166i	−0.209458	+	0.362793i	−0.951544	−	0.307512i	$-0.900503\pi$
$673$	−5.43382	+	9.41166i	−0.209458	+	0.362793i	0.742086	+	0.670305i	$0.233837\pi$
$674$	−2.75725			−0.106205
$675$		0			0
$676$	19.1717			0.737372
$677$	14.1950	−	24.5865i	0.545560	−	0.944937i	−0.453012	−	0.891505i	$-0.649650\pi$
$677$	14.1950	−	24.5865i	0.545560	−	0.944937i	0.998571	−	0.0534326i	$-0.0170162\pi$
$678$		0			0
$679$		0			0
$680$	−1.16071	−	2.01041i	−0.0445111	−	0.0770956i
$681$		0			0
$682$	−5.35961	+	9.28312i	−0.205230	+	0.355469i
$683$	11.8407			0.453071			0.226536	−	0.974003i	$-0.427260\pi$
$683$	11.8407			0.453071			0.226536	+	0.974003i	$0.427260\pi$
$684$		0			0
$685$	2.95968			0.113083
$686$		0			0
$687$		0			0
$688$	−24.7230	−	42.8216i	−0.942557	−	1.63256i
$689$	−3.90981	−	6.77199i	−0.148952	−	0.257992i
$690$		0			0
$691$	−5.95416	+	10.3129i	−0.226507	+	0.392321i	−0.956770	−	0.290844i	$-0.906064\pi$
$691$	−5.95416	+	10.3129i	−0.226507	+	0.392321i	0.730264	+	0.683165i	$0.239397\pi$
$692$	−14.0976			−0.535909
$693$		0			0
$694$	54.3880			2.06454
$695$	−0.504096	+	0.873119i	−0.0191214	+	0.0331193i
$696$		0			0
$697$	−6.98857	−	12.1046i	−0.264711	−	0.458493i
$698$	33.1435	+	57.4062i	1.25450	+	2.17286i
$699$		0			0
$700$		0			0
$701$	31.3902			1.18559			0.592795	−	0.805353i	$-0.298024\pi$
$701$	31.3902			1.18559			0.592795	+	0.805353i	$0.298024\pi$
$702$		0			0
$703$	1.41042			0.0531949
$704$	−1.97020	+	3.41249i	−0.0742549	+	0.128613i
$705$		0			0
$706$	−27.1518	−	47.0284i	−1.02187	−	1.76994i
$707$		0			0
$708$		0			0
$709$	−0.312609	+	0.541455i	−0.0117403	+	0.0203348i	−0.871836	−	0.489798i	$-0.837070\pi$
$709$	−0.312609	+	0.541455i	−0.0117403	+	0.0203348i	0.860096	+	0.510133i	$0.170404\pi$
$710$	−30.3031			−1.13726
$711$		0			0
$712$	−1.57937			−0.0591894
$713$	14.1613	−	24.5281i	0.530345	−	0.918584i
$714$		0			0
$715$	−5.22647	−	9.05251i	−0.195459	−	0.338545i
$716$	−1.18245	−	2.04806i	−0.0441901	−	0.0765395i
$717$		0			0
$718$	−4.98119	+	8.62768i	−0.185897	+	0.321982i
$719$	24.3939			0.909739			0.454869	−	0.890558i	$-0.349686\pi$
$719$	24.3939			0.909739			0.454869	+	0.890558i	$0.349686\pi$
$720$		0			0
$721$		0			0
$722$	11.7185	−	20.2970i	0.436116	−	0.755376i
$723$		0			0
$724$	11.8123	+	20.4595i	0.439002	+	0.760373i
$725$	−0.0996792	−	0.172649i	−0.00370199	−	0.00641204i
$726$		0			0
$727$	−18.9253	+	32.7796i	−0.701900	+	1.21573i	0.265899	+	0.964001i	$0.414331\pi$
$727$	−18.9253	+	32.7796i	−0.701900	+	1.21573i	−0.967799	+	0.251726i	$0.919002\pi$
$728$		0			0
$729$		0			0
$730$	−6.77982			−0.250932
$731$	7.89934	−	13.6821i	0.292168	−	0.506049i
$732$		0			0
$733$	−1.20077	−	2.07980i	−0.0443516	−	0.0768193i	0.842997	−	0.537918i	$-0.180789\pi$
$733$	−1.20077	−	2.07980i	−0.0443516	−	0.0768193i	−0.887349	+	0.461098i	$0.847456\pi$
$734$	21.2519	+	36.8093i	0.784421	+	1.35866i
$735$		0			0
$736$	24.5858	−	42.5839i	0.906245	−	1.56966i
$737$	−10.4903			−0.386416
$738$		0			0
$739$	30.3880			1.11784			0.558920	−	0.829222i	$-0.311216\pi$
$739$	30.3880			1.11784			0.558920	+	0.829222i	$0.311216\pi$
$740$	0.522533	−	0.905053i	0.0192087	−	0.0332704i
$741$		0			0
$742$		0			0
$743$	2.54785	+	4.41300i	0.0934715	+	0.161897i	0.908970	−	0.416862i	$-0.136870\pi$
$743$	2.54785	+	4.41300i	0.0934715	+	0.161897i	−0.815498	+	0.578760i	$0.803537\pi$
$744$		0			0
$745$	−4.39467	+	7.61179i	−0.161008	+	0.278874i
$746$	39.5922			1.44957
$747$		0			0
$748$	−3.25793			−0.119122
$749$		0			0
$750$		0			0
$751$	0.487506	+	0.844384i	0.0177893	+	0.0308120i	0.874783	−	0.484515i	$-0.161004\pi$
$751$	0.487506	+	0.844384i	0.0177893	+	0.0308120i	−0.856994	+	0.515327i	$0.827671\pi$
$752$	23.0718	+	39.9615i	0.841341	+	1.45724i
$753$		0			0
$754$	0.295165	−	0.511240i	0.0107493	−	0.0186183i
$755$	−16.9075			−0.615326
$756$		0			0
$757$	11.6346			0.422865			0.211433	−	0.977393i	$-0.432187\pi$
$757$	11.6346			0.422865			0.211433	+	0.977393i	$0.432187\pi$
$758$	−5.26750	+	9.12357i	−0.191324	+	0.331383i
$759$		0			0
$760$	−1.87657	−	3.25031i	−0.0680703	−	0.117901i
$761$	−27.0875	−	46.9169i	−0.981920	−	1.70073i	−0.654897	−	0.755718i	$-0.727288\pi$
$761$	−27.0875	−	46.9169i	−0.981920	−	1.70073i	−0.327023	−	0.945016i	$-0.606045\pi$
$762$		0			0
$763$		0			0
$764$	−31.5484			−1.14138
$765$		0			0
$766$	64.2978			2.32317
$767$	−21.8513	+	37.8475i	−0.789004	+	1.36659i
$768$		0			0
$769$	−10.4326	−	18.0698i	−0.376208	−	0.651612i	0.614299	−	0.789074i	$-0.289439\pi$
$769$	−10.4326	−	18.0698i	−0.376208	−	0.651612i	−0.990507	+	0.137462i	$0.956106\pi$
$770$		0			0
$771$		0			0
$772$	−4.30047	+	7.44863i	−0.154777	+	0.268082i
$773$	−54.9945			−1.97801			−0.989007	−	0.147868i	$-0.952759\pi$
$773$	−54.9945			−1.97801			−0.989007	+	0.147868i	$0.952759\pi$
$774$		0			0
$775$	12.3838			0.444839
$776$	6.84616	−	11.8579i	0.245763	−	0.425674i
$777$		0			0
$778$	−26.5895	−	46.0544i	−0.953281	−	1.65113i
$779$	−11.2987	−	19.5700i	−0.404819	−	0.701168i
$780$		0			0
$781$	9.32802	−	16.1566i	0.333783	−	0.578129i
$782$	20.9926			0.750693
$783$		0			0
$784$		0			0
$785$	−11.5506	+	20.0062i	−0.412258	+	0.714051i
$786$		0			0
$787$	−4.59475	−	7.95833i	−0.163785	−	0.283684i	0.772438	−	0.635090i	$-0.219037\pi$
$787$	−4.59475	−	7.95833i	−0.163785	−	0.283684i	−0.936223	+	0.351406i	$0.885704\pi$
$788$	6.79103	+	11.7624i	0.241921	+	0.419019i
$789$		0			0
$790$	−7.27374	+	12.5985i	−0.258788	+	0.448234i
$791$		0			0
$792$		0			0
$793$	16.7659			0.595375
$794$	10.2967	−	17.8344i	0.365416	−	0.632919i
$795$		0			0
$796$	−6.03296	−	10.4494i	−0.213832	−	0.370369i
$797$	−3.53774	−	6.12754i	−0.125313	−	0.217049i	0.796542	−	0.604583i	$-0.206660\pi$
$797$	−3.53774	−	6.12754i	−0.125313	−	0.217049i	−0.921855	+	0.387534i	$0.873327\pi$
$798$		0			0
$799$	−7.37174	+	12.7682i	−0.260793	+	0.451707i
$800$	21.4998			0.760133
$801$		0			0
$802$	1.99245			0.0703558
$803$	2.08699	−	3.61477i	0.0736483	−	0.127563i
$804$		0			0
$805$		0			0
$806$	18.3351	+	31.7573i	0.645827	+	1.11860i
$807$		0			0
$808$	−0.628050	+	1.08781i	−0.0220947	+	0.0382692i
$809$	−5.94119			−0.208881			−0.104441	−	0.994531i	$-0.533305\pi$
$809$	−5.94119			−0.208881			−0.104441	+	0.994531i	$0.533305\pi$
$810$		0			0
$811$	44.4139			1.55958			0.779791	−	0.626039i	$-0.215325\pi$
$811$	44.4139			1.55958			0.779791	+	0.626039i	$0.215325\pi$
$812$		0			0
$813$		0			0
$814$	0.784512	+	1.35881i	0.0274971	+	0.0476264i
$815$	−8.15485	−	14.1246i	−0.285652	−	0.494764i
$816$		0			0
$817$	12.7712	−	22.1204i	0.446808	−	0.773894i
$818$	−40.0191			−1.39924
$819$		0			0
$820$	−16.7439			−0.584721
$821$	3.17761	−	5.50378i	0.110899	−	0.192083i	−0.805234	−	0.592958i	$-0.797960\pi$
$821$	3.17761	−	5.50378i	0.110899	−	0.192083i	0.916133	+	0.400874i	$0.131294\pi$
$822$		0			0
$823$	4.73216	+	8.19635i	0.164953	+	0.285707i	0.936639	−	0.350297i	$-0.113919\pi$
$823$	4.73216	+	8.19635i	0.164953	+	0.285707i	−0.771686	+	0.636004i	$0.780586\pi$
$824$	1.08380	+	1.87720i	0.0377560	+	0.0653953i
$825$		0			0
$826$		0			0
$827$	4.86261			0.169090			0.0845448	−	0.996420i	$-0.473056\pi$
$827$	4.86261			0.169090			0.0845448	+	0.996420i	$0.473056\pi$
$828$		0			0
$829$	−40.7853			−1.41653			−0.708266	−	0.705946i	$-0.750522\pi$
$829$	−40.7853			−1.41653			−0.708266	+	0.705946i	$0.750522\pi$
$830$	6.88402	−	11.9235i	0.238948	−	0.413870i
$831$		0			0
$832$	6.74003	+	11.6741i	0.233668	+	0.404725i
$833$		0			0
$834$		0			0
$835$	2.35247	−	4.07460i	0.0814107	−	0.141007i
$836$	−5.26724			−0.182171
$837$		0			0
$838$	46.3645			1.60164
$839$	−9.60171	+	16.6307i	−0.331488	+	0.574154i	−0.982804	−	0.184653i	$-0.940884\pi$
$839$	−9.60171	+	16.6307i	−0.331488	+	0.574154i	0.651316	+	0.758807i	$0.274217\pi$
$840$		0			0
$841$	14.4981	+	25.1114i	0.499934	+	0.865911i
$842$	−27.3063	−	47.2959i	−0.941036	−	1.62992i
$843$		0			0
$844$	−3.95113	+	6.84355i	−0.136003	+	0.235565i
$845$	−18.4075			−0.633236
$846$		0			0
$847$		0			0
$848$	3.66188	−	6.34256i	0.125749	−	0.217804i
$849$		0			0
$850$	4.58940	+	7.94907i	0.157415	+	0.272651i
$851$	−2.07286	−	3.59029i	−0.0710566	−	0.123074i
$852$		0			0
$853$	−6.95055	+	12.0387i	−0.237982	+	0.412198i	−0.960135	−	0.279536i	$-0.909819\pi$
$853$	−6.95055	+	12.0387i	−0.237982	+	0.412198i	0.722153	+	0.691734i	$0.243153\pi$
$854$		0			0
$855$		0			0
$856$	−6.48937			−0.221802
$857$	28.4919	−	49.3494i	0.973265	−	1.68574i	0.287718	−	0.957715i	$-0.407103\pi$
$857$	28.4919	−	49.3494i	0.973265	−	1.68574i	0.685547	−	0.728029i	$-0.259563\pi$
$858$		0			0
$859$	10.0501	+	17.4073i	0.342905	+	0.593929i	0.984971	−	0.172721i	$-0.0552557\pi$
$859$	10.0501	+	17.4073i	0.342905	+	0.593929i	−0.642066	+	0.766650i	$0.721922\pi$
$860$	−9.46298	−	16.3904i	−0.322685	−	0.558907i
$861$		0			0
$862$	−4.50214	+	7.79794i	−0.153344	+	0.265599i
$863$	−6.17786			−0.210297			−0.105148	−	0.994457i	$-0.533532\pi$
$863$	−6.17786			−0.210297			−0.105148	+	0.994457i	$0.533532\pi$
$864$		0			0
$865$	13.5356			0.460225
$866$	−8.94318	+	15.4900i	−0.303902	+	0.526373i
$867$		0			0
$868$		0			0
$869$	−4.47806	−	7.75623i	−0.151908	−	0.263112i
$870$		0			0
$871$	−17.9436	+	31.0792i	−0.607996	+	1.05308i
$872$	−9.25465			−0.313402
$873$		0			0
$874$	33.9396			1.14802
$875$		0			0
$876$		0			0
$877$	18.6287	+	32.2658i	0.629046	+	1.08954i	0.987743	+	0.156086i	$0.0498877\pi$
$877$	18.6287	+	32.2658i	0.629046	+	1.08954i	−0.358697	+	0.933454i	$0.616779\pi$
$878$	13.6468	+	23.6370i	0.460558	+	0.797710i
$879$		0			0
$880$	4.89504	−	8.47846i	0.165012	−	0.285809i
$881$	11.7848			0.397041			0.198520	−	0.980097i	$-0.436386\pi$
$881$	11.7848			0.397041			0.198520	+	0.980097i	$0.436386\pi$
$882$		0			0
$883$	−29.2308			−0.983693			−0.491847	−	0.870682i	$-0.663678\pi$
$883$	−29.2308			−0.983693			−0.491847	+	0.870682i	$0.663678\pi$
$884$	−5.57265	+	9.65211i	−0.187428	+	0.324636i
$885$		0			0
$886$	−20.1634	−	34.9240i	−0.677402	−	1.17329i
$887$	14.2581	+	24.6957i	0.478739	+	0.829201i	0.999703	−	0.0243782i	$-0.00776058\pi$
$887$	14.2581	+	24.6957i	0.478739	+	0.829201i	−0.520964	+	0.853579i	$0.674427\pi$
$888$		0			0
$889$		0			0
$890$	−3.45680			−0.115872
$891$		0			0
$892$	−16.2964			−0.545645
$893$	−11.9182	+	20.6430i	−0.398828	+	0.690790i
$894$		0			0
$895$	1.13531	+	1.96642i	0.0379493	+	0.0657301i
$896$		0			0
$897$		0			0
$898$	19.7890	−	34.2755i	0.660366	−	1.14379i
$899$	0.238341			0.00794912
$900$		0			0
$901$	2.34004			0.0779579
$902$	12.5693	−	21.7707i	0.418513	−	0.724885i
$903$		0			0
$904$	8.14183	+	14.1021i	0.270793	+	0.469028i
$905$	−11.3415	−	19.6440i	−0.377003	−	0.652989i
$906$		0			0
$907$	3.94577	−	6.83428i	0.131017	−	0.226929i	−0.793052	−	0.609154i	$-0.791509\pi$
$907$	3.94577	−	6.83428i	0.131017	−	0.226929i	0.924069	+	0.382226i	$0.124842\pi$
$908$	−15.5463			−0.515923
$909$		0			0
$910$		0			0
$911$	14.2206	−	24.6308i	0.471150	−	0.816055i	−0.528306	−	0.849054i	$-0.677173\pi$
$911$	14.2206	−	24.6308i	0.471150	−	0.816055i	0.999455	+	0.0329991i	$0.0105058\pi$
$912$		0			0
$913$	4.23813	+	7.34065i	0.140262	+	0.242940i
$914$	−37.4007	−	64.7798i	−1.23710	−	2.14273i
$915$		0			0
$916$	6.71206	−	11.6256i	0.221773	−	0.384121i
$917$		0			0
$918$		0			0
$919$	−7.98542			−0.263415			−0.131707	−	0.991289i	$-0.542046\pi$
$919$	−7.98542			−0.263415			−0.131707	+	0.991289i	$0.542046\pi$
$920$	−5.51590	+	9.55382i	−0.181854	+	0.314980i
$921$		0			0
$922$	−2.60610	−	4.51390i	−0.0858274	−	0.148657i
$923$	−31.9110	−	55.2714i	−1.05036	−	1.81928i
$924$		0			0
$925$	0.906337	−	1.56982i	0.0298002	−	0.0516154i
$926$	51.3059			1.68602
$927$		0			0
$928$	0.413790			0.0135833
$929$	9.40031	−	16.2818i	0.308414	−	0.534189i	−0.669601	−	0.742721i	$-0.733535\pi$
$929$	9.40031	−	16.2818i	0.308414	−	0.534189i	0.978016	+	0.208531i	$0.0668684\pi$
$930$		0			0
$931$		0			0
$932$	13.4081	+	23.2234i	0.439196	+	0.760709i
$933$		0			0
$934$	24.5288	−	42.4852i	0.802608	−	1.39016i
$935$	3.12806			0.102299
$936$		0			0
$937$	48.5788			1.58700			0.793500	−	0.608570i	$-0.208256\pi$
$937$	48.5788			1.58700			0.793500	+	0.608570i	$0.208256\pi$
$938$		0			0
$939$		0			0
$940$	8.83094	+	15.2956i	0.288034	+	0.498889i
$941$	10.2425	+	17.7406i	0.333898	+	0.578328i	0.983272	−	0.182141i	$-0.0583027\pi$
$941$	10.2425	+	17.7406i	0.333898	+	0.578328i	−0.649375	+	0.760468i	$0.724969\pi$
$942$		0			0
$943$	−33.2110	+	57.5231i	−1.08150	+	1.87321i
$944$	−40.9312			−1.33220
$945$		0			0
$946$	28.4148			0.923843
$947$	−7.42524	+	12.8609i	−0.241288	+	0.417923i	−0.961081	−	0.276265i	$-0.910903\pi$
$947$	−7.42524	+	12.8609i	−0.241288	+	0.417923i	0.719793	+	0.694188i	$0.244236\pi$
$948$		0			0
$949$	−7.13954	−	12.3661i	−0.231759	−	0.401419i
$950$	7.41989	+	12.8516i	0.240733	+	0.416962i
$951$		0			0
$952$		0			0
$953$	−46.4678			−1.50524			−0.752620	−	0.658456i	$-0.771210\pi$
$953$	−46.4678			−1.50524			−0.752620	+	0.658456i	$0.771210\pi$
$954$		0			0
$955$	30.2908			0.980188
$956$	0.270584	−	0.468665i	0.00875130	−	0.0151577i
$957$		0			0
$958$	−29.0724	−	50.3548i	−0.939285	−	1.62689i
$959$		0			0
$960$		0			0
$961$	8.09733	−	14.0250i	0.261204	−	0.452419i
$962$	5.36759			0.173058
$963$		0			0
$964$	14.7860			0.476226
$965$	4.12905	−	7.15172i	0.132919	−	0.230222i
$966$		0			0
$967$	0.863670	+	1.49592i	0.0277738	+	0.0481056i	0.879578	−	0.475754i	$-0.157825\pi$
$967$	0.863670	+	1.49592i	0.0277738	+	0.0481056i	−0.851804	+	0.523860i	$0.824492\pi$
$968$	−4.89045	−	8.47050i	−0.157185	−	0.272252i
$969$		0			0
$970$	14.9843	−	25.9536i	0.481118	−	0.833320i
$971$	−7.56171			−0.242667			−0.121333	−	0.992612i	$-0.538717\pi$
$971$	−7.56171			−0.242667			−0.121333	+	0.992612i	$0.538717\pi$
$972$		0			0
$973$		0			0
$974$	−0.281870	+	0.488213i	−0.00903169	+	0.0156434i
$975$		0			0
$976$	7.85137	+	13.5990i	0.251316	+	0.435293i
$977$	−28.3101	−	49.0345i	−0.905721	−	1.56875i	−0.819947	−	0.572440i	$-0.805997\pi$
$977$	−28.3101	−	49.0345i	−0.905721	−	1.56875i	−0.0857737	−	0.996315i	$-0.527336\pi$
$978$		0			0
$979$	1.06408	−	1.84305i	0.0340083	−	0.0589041i
$980$		0			0
$981$		0			0
$982$	−33.3994			−1.06582
$983$	16.1486	−	27.9702i	0.515061	−	0.892112i	−0.484786	−	0.874633i	$-0.661103\pi$
$983$	16.1486	−	27.9702i	0.515061	−	0.892112i	0.999847	−	0.0174790i	$-0.00556402\pi$
$984$		0			0
$985$	−6.52033	−	11.2936i	−0.207755	−	0.359842i
$986$	0.0883286	+	0.152990i	0.00281296	+	0.00487218i
$987$		0			0
$988$	−9.00955	+	15.6050i	−0.286632	+	0.496461i
$989$	−75.0782			−2.38735
$990$		0			0
$991$	14.3100			0.454573			0.227287	−	0.973828i	$-0.427015\pi$
$991$	14.3100			0.454573			0.227287	+	0.973828i	$0.427015\pi$
$992$	−12.8520	+	22.2602i	−0.408050	+	0.706764i
$993$		0			0
$994$		0			0
$995$	5.79247	+	10.0329i	0.183634	+	0.318063i
$996$		0			0
$997$	−28.1262	+	48.7160i	−0.890765	+	1.54285i	−0.0518058	+	0.998657i	$0.516498\pi$
$997$	−28.1262	+	48.7160i	−0.890765	+	1.54285i	−0.838960	+	0.544194i	$0.816836\pi$
$998$	−39.2353			−1.24197
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.f.e.883.2		10
3.2	odd	2		441.2.f.e.295.4		10
7.2	even	3		189.2.h.b.46.4		10
7.3	odd	6		1323.2.g.f.667.2		10
7.4	even	3		189.2.g.b.100.2		10
7.5	odd	6		1323.2.h.f.802.4		10
7.6	odd	2		1323.2.f.f.883.2		10
9.2	odd	6		3969.2.a.z.1.2		5
9.4	even	3	inner	1323.2.f.e.442.2		10
9.5	odd	6		441.2.f.e.148.4		10
9.7	even	3		3969.2.a.bc.1.4		5
21.2	odd	6		63.2.h.b.25.2	yes	10
21.5	even	6		441.2.h.f.214.2		10
21.11	odd	6		63.2.g.b.16.4	yes	10
21.17	even	6		441.2.g.f.79.4		10
21.20	even	2		441.2.f.f.295.4		10
28.11	odd	6		3024.2.t.i.289.2		10
28.23	odd	6		3024.2.q.i.2881.4		10
63.2	odd	6		567.2.e.f.487.4		10
63.4	even	3		189.2.h.b.37.4		10
63.5	even	6		441.2.g.f.67.4		10
63.11	odd	6		567.2.e.f.163.4		10
63.13	odd	6		1323.2.f.f.442.2		10
63.16	even	3		567.2.e.e.487.2		10
63.20	even	6		3969.2.a.ba.1.2		5
63.23	odd	6		63.2.g.b.4.4	✓	10
63.25	even	3		567.2.e.e.163.2		10
63.31	odd	6		1323.2.h.f.226.4		10
63.32	odd	6		63.2.h.b.58.2	yes	10
63.34	odd	6		3969.2.a.bb.1.4		5
63.40	odd	6		1323.2.g.f.361.2		10
63.41	even	6		441.2.f.f.148.4		10
63.58	even	3		189.2.g.b.172.2		10
63.59	even	6		441.2.h.f.373.2		10
84.11	even	6		1008.2.t.i.961.5		10
84.23	even	6		1008.2.q.i.529.2		10
252.23	even	6		1008.2.t.i.193.5		10
252.67	odd	6		3024.2.q.i.2305.4		10
252.95	even	6		1008.2.q.i.625.2		10
252.247	odd	6		3024.2.t.i.1873.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.4	✓	10	63.23	odd	6
63.2.g.b.16.4	yes	10	21.11	odd	6
63.2.h.b.25.2	yes	10	21.2	odd	6
63.2.h.b.58.2	yes	10	63.32	odd	6
189.2.g.b.100.2		10	7.4	even	3
189.2.g.b.172.2		10	63.58	even	3
189.2.h.b.37.4		10	63.4	even	3
189.2.h.b.46.4		10	7.2	even	3
441.2.f.e.148.4		10	9.5	odd	6
441.2.f.e.295.4		10	3.2	odd	2
441.2.f.f.148.4		10	63.41	even	6
441.2.f.f.295.4		10	21.20	even	2
441.2.g.f.67.4		10	63.5	even	6
441.2.g.f.79.4		10	21.17	even	6
441.2.h.f.214.2		10	21.5	even	6
441.2.h.f.373.2		10	63.59	even	6
567.2.e.e.163.2		10	63.25	even	3
567.2.e.e.487.2		10	63.16	even	3
567.2.e.f.163.4		10	63.11	odd	6
567.2.e.f.487.4		10	63.2	odd	6
1008.2.q.i.529.2		10	84.23	even	6
1008.2.q.i.625.2		10	252.95	even	6
1008.2.t.i.193.5		10	252.23	even	6
1008.2.t.i.961.5		10	84.11	even	6
1323.2.f.e.442.2		10	9.4	even	3	inner
1323.2.f.e.883.2		10	1.1	even	1	trivial
1323.2.f.f.442.2		10	63.13	odd	6
1323.2.f.f.883.2		10	7.6	odd	2
1323.2.g.f.361.2		10	63.40	odd	6
1323.2.g.f.667.2		10	7.3	odd	6
1323.2.h.f.226.4		10	63.31	odd	6
1323.2.h.f.802.4		10	7.5	odd	6
3024.2.q.i.2305.4		10	252.67	odd	6
3024.2.q.i.2881.4		10	28.23	odd	6
3024.2.t.i.289.2		10	28.11	odd	6
3024.2.t.i.1873.2		10	252.247	odd	6
3969.2.a.z.1.2		5	9.2	odd	6
3969.2.a.ba.1.2		5	63.20	even	6
3969.2.a.bb.1.4		5	63.34	odd	6
3969.2.a.bc.1.4		5	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.920620 + 1.59456i) q^{2} +(-0.695084 - 1.20392i) q^{4} +(0.667377 + 1.15593i) q^{5} -1.12285 q^{8} +O(q^{10})\)	\(q+(-0.920620 + 1.59456i) q^{2} +(-0.695084 - 1.20392i) q^{4} +(0.667377 + 1.15593i) q^{5} -1.12285 q^{8} -2.45760 q^{10} +(0.756508 - 1.31031i) q^{11} +(-2.58800 - 4.48254i) q^{13} +(2.42388 - 4.19829i) q^{16} +1.54893 q^{17} +2.50422 q^{19} +(0.927765 - 1.60694i) q^{20} +(1.39291 + 2.41260i) q^{22} +(-3.68039 - 6.37463i) q^{23} +(1.60922 - 2.78725i) q^{25} +9.53025 q^{26} +(0.0309713 - 0.0536439i) q^{29} +(1.92388 + 3.33227i) q^{31} +(3.34011 + 5.78523i) q^{32} +(-1.42597 + 2.46986i) q^{34} +0.563216 q^{37} +(-2.30543 + 3.99313i) q^{38} +(-0.749363 - 1.29794i) q^{40} +(-4.51188 - 7.81481i) q^{41} +(5.09988 - 8.83325i) q^{43} -2.10335 q^{44} +13.5530 q^{46} +(-4.75925 + 8.24327i) q^{47} +(2.96296 + 5.13199i) q^{50} +(-3.59775 + 6.23148i) q^{52} +1.51075 q^{53} +2.01950 q^{55} +(0.0570257 + 0.0987714i) q^{58} +(-4.22166 - 7.31212i) q^{59} +(-1.61958 + 2.80520i) q^{61} -7.08467 q^{62} -2.60434 q^{64} +(3.45434 - 5.98309i) q^{65} +(-3.46670 - 6.00449i) q^{67} +(-1.07663 - 1.86478i) q^{68} +12.3304 q^{71} +2.75871 q^{73} +(-0.518508 + 0.898083i) q^{74} +(-1.74064 - 3.01488i) q^{76} +(2.95969 - 5.12633i) q^{79} +6.47058 q^{80} +16.6149 q^{82} +(-2.80111 + 4.85167i) q^{83} +(1.03372 + 1.79045i) q^{85} +(9.39010 + 16.2641i) q^{86} +(-0.849444 + 1.47128i) q^{88} +1.40657 q^{89} +(-5.11636 + 8.86180i) q^{92} +(-8.76293 - 15.1778i) q^{94} +(1.67126 + 2.89470i) q^{95} +(-6.09713 + 10.5605i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 6 q^{8}+O(q^{10}) \) 10 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 6 * q^8	\( 10 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 6 q^{8} + 14 q^{10} - 4 q^{11} - 8 q^{13} + 2 q^{16} + 24 q^{17} - 2 q^{19} - 5 q^{20} - q^{22} - 3 q^{23} - q^{25} + 22 q^{26} - 7 q^{29} - 3 q^{31} + 2 q^{32} + 3 q^{34} - 20 q^{38} - 3 q^{40} - 5 q^{41} - 7 q^{43} - 20 q^{44} - 6 q^{46} - 27 q^{47} - 19 q^{50} - 10 q^{52} - 42 q^{53} + 4 q^{55} - 10 q^{58} - 30 q^{59} - 14 q^{61} + 12 q^{62} - 50 q^{64} + 11 q^{65} - 2 q^{67} - 27 q^{68} + 6 q^{71} - 30 q^{73} + 36 q^{74} + 5 q^{76} - 4 q^{79} + 40 q^{80} + 10 q^{82} - 9 q^{83} - 6 q^{85} + 8 q^{86} - 18 q^{88} + 56 q^{89} - 27 q^{92} - 3 q^{94} + 14 q^{95} - 12 q^{97}+O(q^{100}) \) 10 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 6 * q^8 + 14 * q^10 - 4 * q^11 - 8 * q^13 + 2 * q^16 + 24 * q^17 - 2 * q^19 - 5 * q^20 - q^22 - 3 * q^23 - q^25 + 22 * q^26 - 7 * q^29 - 3 * q^31 + 2 * q^32 + 3 * q^34 - 20 * q^38 - 3 * q^40 - 5 * q^41 - 7 * q^43 - 20 * q^44 - 6 * q^46 - 27 * q^47 - 19 * q^50 - 10 * q^52 - 42 * q^53 + 4 * q^55 - 10 * q^58 - 30 * q^59 - 14 * q^61 + 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 - 27 * q^68 + 6 * q^71 - 30 * q^73 + 36 * q^74 + 5 * q^76 - 4 * q^79 + 40 * q^80 + 10 * q^82 - 9 * q^83 - 6 * q^85 + 8 * q^86 - 18 * q^88 + 56 * q^89 - 27 * q^92 - 3 * q^94 + 14 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more