LMFDB - Embedded newform 810.2.f.d.323.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(323,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("810.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.f (of order $4$, degree $2$, 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:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 16x^{14} + 145x^{12} - 976x^{10} + 5296x^{8} - 24400x^{6} + 90625x^{4} - 250000x^{2} + 390625 $ x^16 - 16x^14 + 145x^12 - 976x^10 + 5296x^8 - 24400x^6 + 90625x^4 - 250000*x^2 + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.1
Root			$-1.79407 - 1.33466i$ of defining polynomial
Character	$\chi$	$=$	810.323
Dual form			810.2.f.d.647.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-2.05289 + 0.886375i) q^{5} +(0.887499 - 0.887499i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.07837 + 0.824847i) q^{10} -0.918806i q^{11} +(1.40897 + 1.40897i) q^{13} -1.25511 q^{14} -1.00000 q^{16} +(-0.765342 - 0.765342i) q^{17} +2.42469i q^{19} +(-0.886375 - 2.05289i) q^{20} +(-0.649694 + 0.649694i) q^{22} +(-5.79806 + 5.79806i) q^{23} +(3.42868 - 3.63925i) q^{25} -1.99259i q^{26} +(0.887499 + 0.887499i) q^{28} +5.25752 q^{29} +8.70320 q^{31} +(0.707107 + 0.707107i) q^{32} +1.08236i q^{34} +(-1.03528 + 2.60859i) q^{35} +(-5.63527 + 5.63527i) q^{37} +(1.71452 - 1.71452i) q^{38} +(-0.824847 + 2.07837i) q^{40} +10.9973i q^{41} +(6.42469 + 6.42469i) q^{43} +0.918806 q^{44} +8.19969 q^{46} +(0.795710 + 0.795710i) q^{47} +5.42469i q^{49} +(-4.99778 + 0.148901i) q^{50} +(-1.40897 + 1.40897i) q^{52} +(8.52312 - 8.52312i) q^{53} +(0.814407 + 1.88620i) q^{55} -1.25511i q^{56} +(-3.71763 - 3.71763i) q^{58} +5.55349 q^{59} -2.83175 q^{61} +(-6.15409 - 6.15409i) q^{62} -1.00000i q^{64} +(-4.14134 - 1.64358i) q^{65} +(1.61028 - 1.61028i) q^{67} +(0.765342 - 0.765342i) q^{68} +(2.57660 - 1.11250i) q^{70} +11.1564i q^{71} +(-6.25352 - 6.25352i) q^{73} +7.96947 q^{74} -2.42469 q^{76} +(-0.815440 - 0.815440i) q^{77} +15.3020i q^{79} +(2.05289 - 0.886375i) q^{80} +(7.77629 - 7.77629i) q^{82} +(1.57331 - 1.57331i) q^{83} +(2.24954 + 0.892779i) q^{85} -9.08589i q^{86} +(-0.649694 - 0.649694i) q^{88} +4.28298 q^{89} +2.50092 q^{91} +(-5.79806 - 5.79806i) q^{92} -1.12530i q^{94} +(-2.14919 - 4.97761i) q^{95} +(0.350306 - 0.350306i) q^{97} +(3.83584 - 3.83584i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{7} - 8 q^{10} - 16 q^{16} + 8 q^{22} + 32 q^{25} - 4 q^{28} - 8 q^{31} - 12 q^{37} - 4 q^{40} + 48 q^{43} + 40 q^{46} - 24 q^{55} + 28 q^{58} - 72 q^{61} + 8 q^{67} + 4 q^{70} - 68 q^{73} + 16 q^{76}+ \cdots + 24 q^{97}+O(q^{100}) $ 16 * q - 4 * q^7 - 8 * q^10 - 16 * q^16 + 8 * q^22 + 32 * q^25 - 4 * q^28 - 8 * q^31 - 12 * q^37 - 4 * q^40 + 48 * q^43 + 40 * q^46 - 24 * q^55 + 28 * q^58 - 72 * q^61 + 8 * q^67 + 4 * q^70 - 68 * q^73 + 16 * q^76 - 4 * q^82 - 28 * q^85 + 8 * q^88 + 168 * q^91 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	−2.05289	+	0.886375i	−0.918078	+	0.396399i
$5$	−2.05289	+	0.886375i	−0.918078	+	0.396399i
$6$		0			0
$7$	0.887499	−	0.887499i	0.335443	−	0.335443i	−0.519206	−	0.854649i	$-0.673772\pi$
$7$	0.887499	−	0.887499i	0.335443	−	0.335443i	0.854649	+	0.519206i	$0.173772\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	2.07837	+	0.824847i	0.657239	+	0.260840i
$11$		−	0.918806i		−	0.277031i	−0.990360	−	0.138515i	$-0.955767\pi$
$11$		−	0.918806i		−	0.277031i	0.990360	−	0.138515i	$-0.0442330\pi$
$12$		0			0
$13$	1.40897	+	1.40897i	0.390779	+	0.390779i	0.874965	−	0.484186i	$-0.160884\pi$
$13$	1.40897	+	1.40897i	0.390779	+	0.390779i	−0.484186	+	0.874965i	$0.660884\pi$
$14$	−1.25511			−0.335443
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−0.765342	−	0.765342i	−0.185623	−	0.185623i	0.608178	−	0.793801i	$-0.291901\pi$
$17$	−0.765342	−	0.765342i	−0.185623	−	0.185623i	−0.793801	+	0.608178i	$0.791901\pi$
$18$		0			0
$19$			2.42469i			0.556262i	0.960543	+	0.278131i	$0.0897150\pi$
$19$			2.42469i			0.556262i	−0.960543	+	0.278131i	$0.910285\pi$
$20$	−0.886375	−	2.05289i	−0.198200	−	0.459039i
$21$		0			0
$22$	−0.649694	+	0.649694i	−0.138515	+	0.138515i
$23$	−5.79806	+	5.79806i	−1.20898	+	1.20898i	−0.237620	+	0.971358i	$0.576367\pi$
$23$	−5.79806	+	5.79806i	−1.20898	+	1.20898i	−0.971358	+	0.237620i	$0.923633\pi$
$24$		0			0
$25$	3.42868	−	3.63925i	0.685735	−	0.727851i
$26$		−	1.99259i		−	0.390779i
$27$		0			0
$28$	0.887499	+	0.887499i	0.167722	+	0.167722i
$29$	5.25752			0.976296			0.488148	−	0.872761i	$-0.337673\pi$
$29$	5.25752			0.976296			0.488148	+	0.872761i	$0.337673\pi$
$30$		0			0
$31$	8.70320			1.56314			0.781571	−	0.623817i	$-0.214419\pi$
$31$	8.70320			1.56314			0.781571	+	0.623817i	$0.214419\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$			1.08236i			0.185623i
$35$	−1.03528	+	2.60859i	−0.174994	+	0.440932i
$36$		0			0
$37$	−5.63527	+	5.63527i	−0.926433	+	0.926433i	−0.997473	−	0.0710409i	$-0.977368\pi$
$37$	−5.63527	+	5.63527i	−0.926433	+	0.926433i	0.0710409	+	0.997473i	$0.477368\pi$
$38$	1.71452	−	1.71452i	0.278131	−	0.278131i
$39$		0			0
$40$	−0.824847	+	2.07837i	−0.130420	+	0.328619i
$41$			10.9973i			1.71750i	0.512398	+	0.858748i	$0.328757\pi$
$41$			10.9973i			1.71750i	−0.512398	+	0.858748i	$0.671243\pi$
$42$		0			0
$43$	6.42469	+	6.42469i	0.979756	+	0.979756i	0.999799	−	0.0200428i	$-0.00638025\pi$
$43$	6.42469	+	6.42469i	0.979756	+	0.979756i	−0.0200428	+	0.999799i	$0.506380\pi$
$44$	0.918806			0.138515
$45$		0			0
$46$	8.19969			1.20898
$47$	0.795710	+	0.795710i	0.116066	+	0.116066i	0.762754	−	0.646688i	$-0.223847\pi$
$47$	0.795710	+	0.795710i	0.116066	+	0.116066i	−0.646688	+	0.762754i	$0.723847\pi$
$48$		0			0
$49$			5.42469i			0.774956i
$50$	−4.99778	+	0.148901i	−0.706793	+	0.0210577i
$51$		0			0
$52$	−1.40897	+	1.40897i	−0.195389	+	0.195389i
$53$	8.52312	−	8.52312i	1.17074	−	1.17074i	0.188707	−	0.982034i	$-0.439571\pi$
$53$	8.52312	−	8.52312i	1.17074	−	1.17074i	0.982034	−	0.188707i	$-0.0604295\pi$
$54$		0			0
$55$	0.814407	+	1.88620i	0.109815	+	0.254336i
$56$		−	1.25511i		−	0.167722i
$57$		0			0
$58$	−3.71763	−	3.71763i	−0.488148	−	0.488148i
$59$	5.55349			0.723002			0.361501	−	0.932372i	$-0.382264\pi$
$59$	5.55349			0.723002			0.361501	+	0.932372i	$0.382264\pi$
$60$		0			0
$61$	−2.83175			−0.362568			−0.181284	−	0.983431i	$-0.558025\pi$
$61$	−2.83175			−0.362568			−0.181284	+	0.983431i	$0.558025\pi$
$62$	−6.15409	−	6.15409i	−0.781571	−	0.781571i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−4.14134	−	1.64358i	−0.513670	−	0.203861i
$66$		0			0
$67$	1.61028	−	1.61028i	0.196728	−	0.196728i	−0.601868	−	0.798596i	$-0.705577\pi$
$67$	1.61028	−	1.61028i	0.196728	−	0.196728i	0.798596	+	0.601868i	$0.205577\pi$
$68$	0.765342	−	0.765342i	0.0928113	−	0.0928113i
$69$		0			0
$70$	2.57660	−	1.11250i	0.307963	−	0.132969i
$71$			11.1564i			1.32403i	0.749492	+	0.662013i	$0.230298\pi$
$71$			11.1564i			1.32403i	−0.749492	+	0.662013i	$0.769702\pi$
$72$		0			0
$73$	−6.25352	−	6.25352i	−0.731920	−	0.731920i	0.239080	−	0.971000i	$-0.423154\pi$
$73$	−6.25352	−	6.25352i	−0.731920	−	0.731920i	−0.971000	+	0.239080i	$0.923154\pi$
$74$	7.96947			0.926433
$75$		0			0
$76$	−2.42469			−0.278131
$77$	−0.815440	−	0.815440i	−0.0929280	−	0.0929280i
$78$		0			0
$79$			15.3020i			1.72161i	0.508937	+	0.860803i	$0.330038\pi$
$79$			15.3020i			1.72161i	−0.508937	+	0.860803i	$0.669962\pi$
$80$	2.05289	−	0.886375i	0.229520	−	0.0990998i
$81$		0			0
$82$	7.77629	−	7.77629i	0.858748	−	0.858748i
$83$	1.57331	−	1.57331i	0.172694	−	0.172694i	−0.615468	−	0.788162i	$-0.711033\pi$
$83$	1.57331	−	1.57331i	0.172694	−	0.172694i	0.788162	+	0.615468i	$0.211033\pi$
$84$		0			0
$85$	2.24954	+	0.892779i	0.243997	+	0.0968354i
$86$		−	9.08589i		−	0.979756i
$87$		0			0
$88$	−0.649694	−	0.649694i	−0.0692576	−	0.0692576i
$89$	4.28298			0.453995			0.226997	−	0.973895i	$-0.427109\pi$
$89$	4.28298			0.453995			0.226997	+	0.973895i	$0.427109\pi$
$90$		0			0
$91$	2.50092			0.262168
$92$	−5.79806	−	5.79806i	−0.604489	−	0.604489i
$93$		0			0
$94$		−	1.12530i		−	0.116066i
$95$	−2.14919	−	4.97761i	−0.220502	−	0.510692i
$96$		0			0
$97$	0.350306	−	0.350306i	0.0355682	−	0.0355682i	−0.689099	−	0.724667i	$-0.741994\pi$
$97$	0.350306	−	0.350306i	0.0355682	−	0.0355682i	0.724667	+	0.689099i	$0.241994\pi$
$98$	3.83584	−	3.83584i	0.387478	−	0.387478i
$99$		0			0
$100$	3.63925	+	3.42868i	0.363925	+	0.342868i
$101$			5.32238i			0.529596i	0.964304	+	0.264798i	$0.0853054\pi$
$101$			5.32238i			0.529596i	−0.964304	+	0.264798i	$0.914695\pi$
$102$		0			0
$103$	−8.94101	−	8.94101i	−0.880983	−	0.880983i	0.112651	−	0.993635i	$-0.464066\pi$
$103$	−8.94101	−	8.94101i	−0.880983	−	0.880983i	−0.993635	+	0.112651i	$0.964066\pi$
$104$	1.99259			0.195389
$105$		0			0
$106$	−12.0535			−1.17074
$107$	−2.49212	−	2.49212i	−0.240922	−	0.240922i	0.576309	−	0.817232i	$-0.304492\pi$
$107$	−2.49212	−	2.49212i	−0.240922	−	0.240922i	−0.817232	+	0.576309i	$0.804492\pi$
$108$		0			0
$109$		−	13.5420i		−	1.29709i	−0.761176	−	0.648545i	$-0.775378\pi$
$109$		−	13.5420i		−	1.29709i	0.761176	−	0.648545i	$-0.224622\pi$
$110$	0.757875	−	1.90962i	0.0722605	−	0.182075i
$111$		0			0
$112$	−0.887499	+	0.887499i	−0.0838608	+	0.0838608i
$113$	5.42909	−	5.42909i	0.510725	−	0.510725i	−0.404023	−	0.914749i	$-0.632389\pi$
$113$	5.42909	−	5.42909i	0.510725	−	0.510725i	0.914749	+	0.404023i	$0.132389\pi$
$114$		0			0
$115$	6.76349	−	17.0420i	0.630699	−	1.58917i
$116$			5.25752i			0.488148i
$117$		0			0
$118$	−3.92691	−	3.92691i	−0.361501	−	0.361501i
$119$	−1.35848			−0.124532
$120$		0			0
$121$	10.1558			0.923254
$122$	2.00235	+	2.00235i	0.181284	+	0.181284i
$123$		0			0
$124$			8.70320i			0.781571i
$125$	−3.81294	+	10.5101i	−0.341039	+	0.940049i
$126$		0			0
$127$	−9.70191	+	9.70191i	−0.860905	+	0.860905i	−0.991443	−	0.130538i	$-0.958329\pi$
$127$	−9.70191	+	9.70191i	−0.860905	+	0.860905i	0.130538	+	0.991443i	$0.458329\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	1.76618	+	4.09055i	0.154904	+	0.358765i
$131$			5.11381i			0.446796i	0.974727	+	0.223398i	$0.0717150\pi$
$131$			5.11381i			0.446796i	−0.974727	+	0.223398i	$0.928285\pi$
$132$		0			0
$133$	2.15191	+	2.15191i	0.186594	+	0.186594i
$134$	−2.27729			−0.196728
$135$		0			0
$136$	−1.08236			−0.0928113
$137$	10.4115	+	10.4115i	0.889514	+	0.889514i	0.994476	−	0.104962i	$-0.0334721\pi$
$137$	10.4115	+	10.4115i	0.889514	+	0.889514i	−0.104962	+	0.994476i	$0.533472\pi$
$138$		0			0
$139$		−	17.7267i		−	1.50356i	−0.659416	−	0.751778i	$-0.729196\pi$
$139$		−	17.7267i		−	1.50356i	0.659416	−	0.751778i	$-0.270804\pi$
$140$	−2.60859	−	1.03528i	−0.220466	−	0.0874968i
$141$		0			0
$142$	7.88879	−	7.88879i	0.662013	−	0.662013i
$143$	1.29457	−	1.29457i	0.108258	−	0.108258i
$144$		0			0
$145$	−10.7931	+	4.66013i	−0.896316	+	0.387003i
$146$			8.84382i			0.731920i
$147$		0			0
$148$	−5.63527	−	5.63527i	−0.463216	−	0.463216i
$149$	19.5049			1.59790			0.798950	−	0.601398i	$-0.205389\pi$
$149$	19.5049			1.59790			0.798950	+	0.601398i	$0.205389\pi$
$150$		0			0
$151$	−14.9538			−1.21692			−0.608462	−	0.793583i	$-0.708213\pi$
$151$	−14.9538			−1.21692			−0.608462	+	0.793583i	$0.708213\pi$
$152$	1.71452	+	1.71452i	0.139066	+	0.139066i
$153$		0			0
$154$			1.15321i			0.0929280i
$155$	−17.8667	+	7.71430i	−1.43509	+	0.619628i
$156$		0			0
$157$	−15.3004	+	15.3004i	−1.22110	+	1.22110i	−0.253860	+	0.967241i	$0.581700\pi$
$157$	−15.3004	+	15.3004i	−1.22110	+	1.22110i	−0.967241	+	0.253860i	$0.918300\pi$
$158$	10.8201	−	10.8201i	0.860803	−	0.860803i
$159$		0			0
$160$	−2.07837	−	0.824847i	−0.164310	−	0.0652099i
$161$			10.2915i			0.811087i
$162$		0			0
$163$	−9.29939	−	9.29939i	−0.728384	−	0.728384i	0.241914	−	0.970298i	$-0.422225\pi$
$163$	−9.29939	−	9.29939i	−0.728384	−	0.728384i	−0.970298	+	0.241914i	$0.922225\pi$
$164$	−10.9973			−0.858748
$165$		0			0
$166$	−2.22500			−0.172694
$167$	−11.4746	−	11.4746i	−0.887934	−	0.887934i	0.106390	−	0.994324i	$-0.466071\pi$
$167$	−11.4746	−	11.4746i	−0.887934	−	0.887934i	−0.994324	+	0.106390i	$0.966071\pi$
$168$		0			0
$169$		−	9.02959i		−	0.694584i
$170$	−0.959374	−	2.22195i	−0.0735807	−	0.170416i
$171$		0			0
$172$	−6.42469	+	6.42469i	−0.489878	+	0.489878i
$173$	2.45763	−	2.45763i	0.186850	−	0.186850i	−0.607483	−	0.794333i	$-0.707821\pi$
$173$	2.45763	−	2.45763i	0.186850	−	0.186850i	0.794333	+	0.607483i	$0.207821\pi$
$174$		0			0
$175$	−0.186887	−	6.27278i	−0.0141273	−	0.474178i
$176$			0.918806i			0.0692576i
$177$		0			0
$178$	−3.02852	−	3.02852i	−0.226997	−	0.226997i
$179$	−16.2803			−1.21684			−0.608422	−	0.793614i	$-0.708197\pi$
$179$	−16.2803			−1.21684			−0.608422	+	0.793614i	$0.708197\pi$
$180$		0			0
$181$	7.97440			0.592732			0.296366	−	0.955074i	$-0.404225\pi$
$181$	7.97440			0.592732			0.296366	+	0.955074i	$0.404225\pi$
$182$	−1.76842	−	1.76842i	−0.131084	−	0.131084i
$183$		0			0
$184$			8.19969i			0.604489i
$185$	6.57360	−	16.5635i	0.483301	−	1.21777i
$186$		0			0
$187$	−0.703201	+	0.703201i	−0.0514231	+	0.0514231i
$188$	−0.795710	+	0.795710i	−0.0580331	+	0.0580331i
$189$		0			0
$190$	−2.00000	+	5.03941i	−0.145095	+	0.365597i
$191$			17.8078i			1.28852i	0.764804	+	0.644262i	$0.222836\pi$
$191$			17.8078i			1.28852i	−0.764804	+	0.644262i	$0.777164\pi$
$192$		0			0
$193$	4.60383	+	4.60383i	0.331391	+	0.331391i	0.853115	−	0.521724i	$-0.174711\pi$
$193$	4.60383	+	4.60383i	0.331391	+	0.331391i	−0.521724	+	0.853115i	$0.674711\pi$
$194$	−0.495407			−0.0355682
$195$		0			0
$196$	−5.42469			−0.387478
$197$	−0.969574	−	0.969574i	−0.0690793	−	0.0690793i	0.671723	−	0.740802i	$-0.265554\pi$
$197$	−0.969574	−	0.969574i	−0.0690793	−	0.0690793i	−0.740802	+	0.671723i	$0.765554\pi$
$198$		0			0
$199$			5.55258i			0.393612i	0.980442	+	0.196806i	$0.0630570\pi$
$199$			5.55258i			0.393612i	−0.980442	+	0.196806i	$0.936943\pi$
$200$	−0.148901	−	4.99778i	−0.0105289	−	0.353397i
$201$		0			0
$202$	3.76349	−	3.76349i	0.264798	−	0.264798i
$203$	4.66604	−	4.66604i	0.327492	−	0.327492i
$204$		0			0
$205$	−9.74777	−	22.5763i	−0.680814	−	1.57680i
$206$			12.6445i			0.880983i
$207$		0			0
$208$	−1.40897	−	1.40897i	−0.0976946	−	0.0976946i
$209$	2.22782			0.154102
$210$		0			0
$211$	−8.82148			−0.607296			−0.303648	−	0.952784i	$-0.598205\pi$
$211$	−8.82148			−0.607296			−0.303648	+	0.952784i	$0.598205\pi$
$212$	8.52312	+	8.52312i	0.585370	+	0.585370i
$213$		0			0
$214$			3.52439i			0.240922i
$215$	−18.8838	−	7.49447i	−1.28787	−	0.511118i
$216$		0			0
$217$	7.72408	−	7.72408i	0.524345	−	0.524345i
$218$	−9.57566	+	9.57566i	−0.648545	+	0.648545i
$219$		0			0
$220$	−1.88620	+	0.814407i	−0.127168	+	0.0549073i
$221$		−	2.15669i		−	0.145075i
$222$		0			0
$223$	0.503511	+	0.503511i	0.0337176	+	0.0337176i	0.723765	−	0.690047i	$-0.242410\pi$
$223$	0.503511	+	0.503511i	0.0337176	+	0.0337176i	−0.690047	+	0.723765i	$0.742410\pi$
$224$	1.25511			0.0838608
$225$		0			0
$226$	−7.67789			−0.510725
$227$	−12.0933	−	12.0933i	−0.802664	−	0.802664i	0.180847	−	0.983511i	$-0.442116\pi$
$227$	−12.0933	−	12.0933i	−0.802664	−	0.802664i	−0.983511	+	0.180847i	$0.942116\pi$
$228$		0			0
$229$		−	6.65672i		−	0.439888i	−0.975512	−	0.219944i	$-0.929412\pi$
$229$		−	6.65672i		−	0.439888i	0.975512	−	0.219944i	$-0.0705875\pi$
$230$	−16.8330	+	7.26800i	−1.10994	+	0.479238i
$231$		0			0
$232$	3.71763	−	3.71763i	0.244074	−	0.244074i
$233$	3.86934	−	3.86934i	0.253489	−	0.253489i	−0.568911	−	0.822399i	$-0.692635\pi$
$233$	3.86934	−	3.86934i	0.253489	−	0.253489i	0.822399	+	0.568911i	$0.192635\pi$
$234$		0			0
$235$	−2.33880	−	0.928203i	−0.152566	−	0.0605493i
$236$			5.55349i			0.361501i
$237$		0			0
$238$	0.960590	+	0.960590i	0.0622658	+	0.0622658i
$239$	−3.58630			−0.231979			−0.115989	−	0.993250i	$-0.537004\pi$
$239$	−3.58630			−0.231979			−0.115989	+	0.993250i	$0.537004\pi$
$240$		0			0
$241$	−22.1279			−1.42538			−0.712691	−	0.701478i	$-0.752524\pi$
$241$	−22.1279			−1.42538			−0.712691	+	0.701478i	$0.752524\pi$
$242$	−7.18123	−	7.18123i	−0.461627	−	0.461627i
$243$		0			0
$244$		−	2.83175i		−	0.181284i
$245$	−4.80831	−	11.1363i	−0.307192	−	0.711470i
$246$		0			0
$247$	−3.41632	+	3.41632i	−0.217375	+	0.217375i
$248$	6.15409	−	6.15409i	0.390785	−	0.390785i
$249$		0			0
$250$	10.1279	−	4.73559i	0.640544	−	0.299505i
$251$		−	8.90685i		−	0.562195i	−0.959679	−	0.281098i	$-0.909302\pi$
$251$		−	8.90685i		−	0.562195i	0.959679	−	0.281098i	$-0.0906985\pi$
$252$		0			0
$253$	5.32729	+	5.32729i	0.334924	+	0.334924i
$254$	13.7206			0.860905
$255$		0			0
$256$	1.00000			0.0625000
$257$	−8.47052	−	8.47052i	−0.528376	−	0.528376i	0.391712	−	0.920088i	$-0.371883\pi$
$257$	−8.47052	−	8.47052i	−0.528376	−	0.528376i	−0.920088	+	0.391712i	$0.871883\pi$
$258$		0			0
$259$			10.0026i			0.621531i
$260$	1.64358	−	4.14134i	0.101931	−	0.256835i
$261$		0			0
$262$	3.61601	−	3.61601i	0.223398	−	0.223398i
$263$	4.75778	−	4.75778i	0.293377	−	0.293377i	−0.545036	−	0.838413i	$-0.683484\pi$
$263$	4.75778	−	4.75778i	0.293377	−	0.293377i	0.838413	+	0.545036i	$0.183484\pi$
$264$		0			0
$265$	−9.94230	+	25.0517i	−0.610751	+	1.53891i
$266$		−	3.04326i		−	0.186594i
$267$		0			0
$268$	1.61028	+	1.61028i	0.0983638	+	0.0983638i
$269$	8.45361			0.515426			0.257713	−	0.966222i	$-0.417031\pi$
$269$	8.45361			0.515426			0.257713	+	0.966222i	$0.417031\pi$
$270$		0			0
$271$	30.6552			1.86217			0.931084	−	0.364804i	$-0.118864\pi$
$271$	30.6552			1.86217			0.931084	+	0.364804i	$0.118864\pi$
$272$	0.765342	+	0.765342i	0.0464057	+	0.0464057i
$273$		0			0
$274$		−	14.7241i		−	0.889514i
$275$	−3.34377	−	3.15029i	−0.201637	−	0.189970i
$276$		0			0
$277$	11.1895	−	11.1895i	0.672310	−	0.672310i	−0.285938	−	0.958248i	$-0.592305\pi$
$277$	11.1895	−	11.1895i	0.672310	−	0.672310i	0.958248	+	0.285938i	$0.0923050\pi$
$278$	−12.5346	+	12.5346i	−0.751778	+	0.751778i
$279$		0			0
$280$	1.11250	+	2.57660i	0.0664847	+	0.153981i
$281$		−	8.02838i		−	0.478933i	−0.970905	−	0.239466i	$-0.923027\pi$
$281$		−	8.02838i		−	0.478933i	0.970905	−	0.239466i	$-0.0769725\pi$
$282$		0			0
$283$	−10.9632	−	10.9632i	−0.651693	−	0.651693i	0.301707	−	0.953401i	$-0.402443\pi$
$283$	−10.9632	−	10.9632i	−0.651693	−	0.651693i	−0.953401	+	0.301707i	$0.902443\pi$
$284$	−11.1564			−0.662013
$285$		0			0
$286$	−1.83080			−0.108258
$287$	9.76012	+	9.76012i	0.576122	+	0.576122i
$288$		0			0
$289$		−	15.8285i		−	0.931088i
$290$	10.9271	+	4.33665i	0.641660	+	0.254657i
$291$		0			0
$292$	6.25352	−	6.25352i	0.365960	−	0.365960i
$293$	4.26388	−	4.26388i	0.249099	−	0.249099i	−0.571502	−	0.820601i	$-0.693639\pi$
$293$	4.26388	−	4.26388i	0.249099	−	0.249099i	0.820601	+	0.571502i	$0.193639\pi$
$294$		0			0
$295$	−11.4007	+	4.92247i	−0.663773	+	0.286598i
$296$			7.96947i			0.463216i
$297$		0			0
$298$	−13.7920	−	13.7920i	−0.798950	−	0.798950i
$299$	−16.3386			−0.944886
$300$		0			0
$301$	11.4038			0.657305
$302$	10.5739	+	10.5739i	0.608462	+	0.608462i
$303$		0			0
$304$		−	2.42469i		−	0.139066i
$305$	5.81326	−	2.50999i	0.332866	−	0.143722i
$306$		0			0
$307$	−14.4876	+	14.4876i	−0.826849	+	0.826849i	−0.987080	−	0.160230i	$-0.948776\pi$
$307$	−14.4876	+	14.4876i	−0.826849	+	0.826849i	0.160230	+	0.987080i	$0.448776\pi$
$308$	0.815440	−	0.815440i	0.0464640	−	0.0464640i
$309$		0			0
$310$	18.0885	+	7.17881i	1.02736	+	0.407729i
$311$			21.7843i			1.23527i	0.786464	+	0.617637i	$0.211910\pi$
$311$			21.7843i			1.23527i	−0.786464	+	0.617637i	$0.788090\pi$
$312$		0			0
$313$	17.9961	+	17.9961i	1.01720	+	1.01720i	0.999849	+	0.0173522i	$0.00552367\pi$
$313$	17.9961	+	17.9961i	1.01720	+	1.01720i	0.0173522	+	0.999849i	$0.494476\pi$
$314$	21.6380			1.22110
$315$		0			0
$316$	−15.3020			−0.860803
$317$	0.788243	+	0.788243i	0.0442721	+	0.0442721i	0.728896	−	0.684624i	$-0.240034\pi$
$317$	0.788243	+	0.788243i	0.0442721	+	0.0442721i	−0.684624	+	0.728896i	$0.740034\pi$
$318$		0			0
$319$		−	4.83064i		−	0.270464i
$320$	0.886375	+	2.05289i	0.0495499	+	0.114760i
$321$		0			0
$322$	7.27721	−	7.27721i	0.405543	−	0.405543i
$323$	1.85572	−	1.85572i	0.103255	−	0.103255i
$324$		0			0
$325$	9.95852	−	0.296698i	0.552399	−	0.0164578i
$326$			13.1513i			0.728384i
$327$		0			0
$328$	7.77629	+	7.77629i	0.429374	+	0.429374i
$329$	1.41238			0.0778672
$330$		0			0
$331$	20.1770			1.10903			0.554513	−	0.832175i	$-0.312905\pi$
$331$	20.1770			1.10903			0.554513	+	0.832175i	$0.312905\pi$
$332$	1.57331	+	1.57331i	0.0863468	+	0.0863468i
$333$		0			0
$334$			16.2276i			0.887934i
$335$	−1.87841	+	4.73305i	−0.102629	+	0.258594i
$336$		0			0
$337$	−2.29939	+	2.29939i	−0.125256	+	0.125256i	−0.766956	−	0.641700i	$-0.778229\pi$
$337$	−2.29939	+	2.29939i	−0.125256	+	0.125256i	0.641700	+	0.766956i	$0.278229\pi$
$338$	−6.38489	+	6.38489i	−0.347292	+	0.347292i
$339$		0			0
$340$	−0.892779	+	2.24954i	−0.0484177	+	0.121998i
$341$		−	7.99656i		−	0.433038i
$342$		0			0
$343$	11.0269	+	11.0269i	0.595397	+	0.595397i
$344$	9.08589			0.489878
$345$		0			0
$346$	−3.47561			−0.186850
$347$	−9.44030	−	9.44030i	−0.506782	−	0.506782i	0.406755	−	0.913537i	$-0.366660\pi$
$347$	−9.44030	−	9.44030i	−0.506782	−	0.506782i	−0.913537	+	0.406755i	$0.866660\pi$
$348$		0			0
$349$			9.47118i			0.506980i	0.967338	+	0.253490i	$0.0815786\pi$
$349$			9.47118i			0.506980i	−0.967338	+	0.253490i	$0.918421\pi$
$350$	−4.30338	+	4.56768i	−0.230025	+	0.244152i
$351$		0			0
$352$	0.649694	−	0.649694i	0.0346288	−	0.0346288i
$353$	16.7594	−	16.7594i	0.892012	−	0.892012i	−0.102700	−	0.994712i	$-0.532748\pi$
$353$	16.7594	−	16.7594i	0.892012	−	0.892012i	0.994712	+	0.102700i	$0.0327482\pi$
$354$		0			0
$355$	−9.88879	−	22.9029i	−0.524843	−	1.21556i
$356$			4.28298i			0.226997i
$357$		0			0
$358$	11.5119	+	11.5119i	0.608422	+	0.608422i
$359$	22.6274			1.19423			0.597115	−	0.802156i	$-0.296314\pi$
$359$	22.6274			1.19423			0.597115	+	0.802156i	$0.296314\pi$
$360$		0			0
$361$	13.1209			0.690572
$362$	−5.63875	−	5.63875i	−0.296366	−	0.296366i
$363$		0			0
$364$			2.50092i			0.131084i
$365$	18.3807	+	7.29480i	0.962092	+	0.381827i
$366$		0			0
$367$	−22.6779	+	22.6779i	−1.18378	+	1.18378i	−0.205018	+	0.978758i	$0.565725\pi$
$367$	−22.6779	+	22.6779i	−1.18378	+	1.18378i	−0.978758	+	0.205018i	$0.934275\pi$
$368$	5.79806	−	5.79806i	0.302245	−	0.302245i
$369$		0			0
$370$	−16.3604	+	7.06395i	−0.850538	+	0.367237i
$371$		−	15.1285i		−	0.785433i
$372$		0			0
$373$	23.5411	+	23.5411i	1.21891	+	1.21891i	0.968014	+	0.250897i	$0.0807255\pi$
$373$	23.5411	+	23.5411i	1.21891	+	1.21891i	0.250897	+	0.968014i	$0.419274\pi$
$374$	0.994476			0.0514231
$375$		0			0
$376$	1.12530			0.0580331
$377$	7.40769	+	7.40769i	0.381516	+	0.381516i
$378$		0			0
$379$		−	7.80549i		−	0.400941i	−0.979700	−	0.200471i	$-0.935753\pi$
$379$		−	7.80549i		−	0.400941i	0.979700	−	0.200471i	$-0.0642471\pi$
$380$	4.97761	−	2.14919i	0.255346	−	0.110251i
$381$		0			0
$382$	12.5920	−	12.5920i	0.644262	−	0.644262i
$383$	−25.1791	+	25.1791i	−1.28659	+	1.28659i	−0.349751	+	0.936843i	$0.613734\pi$
$383$	−25.1791	+	25.1791i	−1.28659	+	1.28659i	−0.936843	+	0.349751i	$0.886266\pi$
$384$		0			0
$385$	2.39679	+	0.951218i	0.122152	+	0.0484786i
$386$		−	6.51080i		−	0.331391i
$387$		0			0
$388$	0.350306	+	0.350306i	0.0177841	+	0.0177841i
$389$	29.5054			1.49598			0.747992	−	0.663708i	$-0.231018\pi$
$389$	29.5054			1.49598			0.747992	+	0.663708i	$0.231018\pi$
$390$		0			0
$391$	8.87499			0.448827
$392$	3.83584	+	3.83584i	0.193739	+	0.193739i
$393$		0			0
$394$			1.37119i			0.0690793i
$395$	−13.5633	−	31.4132i	−0.682444	−	1.58057i
$396$		0			0
$397$	8.04262	−	8.04262i	0.403647	−	0.403647i	−0.475869	−	0.879516i	$-0.657866\pi$
$397$	8.04262	−	8.04262i	0.403647	−	0.403647i	0.879516	+	0.475869i	$0.157866\pi$
$398$	3.92627	−	3.92627i	0.196806	−	0.196806i
$399$		0			0
$400$	−3.42868	+	3.63925i	−0.171434	+	0.181963i
$401$			23.9673i			1.19687i	0.801171	+	0.598436i	$0.204211\pi$
$401$			23.9673i			1.19687i	−0.801171	+	0.598436i	$0.795789\pi$
$402$		0			0
$403$	12.2626	+	12.2626i	0.610842	+	0.610842i
$404$	−5.32238			−0.264798
$405$		0			0
$406$	−6.59878			−0.327492
$407$	5.17772	+	5.17772i	0.256650	+	0.256650i
$408$		0			0
$409$			5.42823i			0.268409i	0.990954	+	0.134204i	$0.0428478\pi$
$409$			5.42823i			0.268409i	−0.990954	+	0.134204i	$0.957152\pi$
$410$	−9.07112	+	22.8566i	−0.447991	+	1.12880i
$411$		0			0
$412$	8.94101	−	8.94101i	0.440492	−	0.440492i
$413$	4.92871	−	4.92871i	0.242526	−	0.242526i
$414$		0			0
$415$	−1.83529	+	4.62438i	−0.0900907	+	0.227002i
$416$			1.99259i			0.0976946i
$417$		0			0
$418$	−1.57531	−	1.57531i	−0.0770508	−	0.0770508i
$419$	0.712073			0.0347870			0.0173935	−	0.999849i	$-0.494463\pi$
$419$	0.712073			0.0347870			0.0173935	+	0.999849i	$0.494463\pi$
$420$		0			0
$421$	0.0553510			0.00269764			0.00134882	−	0.999999i	$-0.499571\pi$
$421$	0.0553510			0.00269764			0.00134882	+	0.999999i	$0.499571\pi$
$422$	6.23773	+	6.23773i	0.303648	+	0.303648i
$423$		0			0
$424$		−	12.0535i		−	0.585370i
$425$	−5.40938	+	0.161164i	−0.262394	+	0.00781759i
$426$		0			0
$427$	−2.51317	+	2.51317i	−0.121621	+	0.121621i
$428$	2.49212	−	2.49212i	0.120461	−	0.120461i
$429$		0			0
$430$	8.05351	+	18.6523i	0.388375	+	0.899493i
$431$		−	17.8078i		−	0.857770i	−0.903359	−	0.428885i	$-0.858907\pi$
$431$		−	17.8078i		−	0.857770i	0.903359	−	0.428885i	$-0.141093\pi$
$432$		0			0
$433$	15.6599	+	15.6599i	0.752568	+	0.752568i	0.974958	−	0.222390i	$-0.0713858\pi$
$433$	15.6599	+	15.6599i	0.752568	+	0.752568i	−0.222390	+	0.974958i	$0.571386\pi$
$434$	−10.9235			−0.524345
$435$		0			0
$436$	13.5420			0.648545
$437$	−14.0585	−	14.0585i	−0.672509	−	0.672509i
$438$		0			0
$439$			4.87499i			0.232670i	0.993210	+	0.116335i	$0.0371147\pi$
$439$			4.87499i			0.232670i	−0.993210	+	0.116335i	$0.962885\pi$
$440$	1.90962	+	0.757875i	0.0910376	+	0.0361303i
$441$		0			0
$442$	−1.52501	+	1.52501i	−0.0725373	+	0.0725373i
$443$	22.1914	−	22.1914i	1.05435	−	1.05435i	0.0559097	−	0.998436i	$-0.482194\pi$
$443$	22.1914	−	22.1914i	1.05435	−	1.05435i	0.998436	−	0.0559097i	$-0.0178059\pi$
$444$		0			0
$445$	−8.79246	+	3.79633i	−0.416803	+	0.179963i
$446$		−	0.712073i		−	0.0337176i
$447$		0			0
$448$	−0.887499	−	0.887499i	−0.0419304	−	0.0419304i
$449$	−2.54785			−0.120241			−0.0601203	−	0.998191i	$-0.519148\pi$
$449$	−2.54785			−0.120241			−0.0601203	+	0.998191i	$0.519148\pi$
$450$		0			0
$451$	10.1044			0.475799
$452$	5.42909	+	5.42909i	0.255363	+	0.255363i
$453$		0			0
$454$			17.1026i			0.802664i
$455$	−5.13411	+	2.21676i	−0.240691	+	0.103923i
$456$		0			0
$457$	1.73710	−	1.73710i	0.0812583	−	0.0812583i	−0.665309	−	0.746568i	$-0.731700\pi$
$457$	1.73710	−	1.73710i	0.0812583	−	0.0812583i	0.746568	+	0.665309i	$0.231700\pi$
$458$	−4.70701	+	4.70701i	−0.219944	+	0.219944i
$459$		0			0
$460$	17.0420	+	6.76349i	0.794587	+	0.315349i
$461$		−	31.7007i		−	1.47645i	−0.674555	−	0.738224i	$-0.735665\pi$
$461$		−	31.7007i		−	1.47645i	0.674555	−	0.738224i	$-0.264335\pi$
$462$		0			0
$463$	−1.87599	−	1.87599i	−0.0871847	−	0.0871847i	0.662169	−	0.749354i	$-0.269636\pi$
$463$	−1.87599	−	1.87599i	−0.0871847	−	0.0871847i	−0.749354	+	0.662169i	$0.769636\pi$
$464$	−5.25752			−0.244074
$465$		0			0
$466$	−5.47207			−0.253489
$467$	−8.83969	−	8.83969i	−0.409052	−	0.409052i	0.472356	−	0.881408i	$-0.343404\pi$
$467$	−8.83969	−	8.83969i	−0.409052	−	0.409052i	−0.881408	+	0.472356i	$0.843404\pi$
$468$		0			0
$469$		−	2.85825i		−	0.131982i
$470$	0.997441	+	2.31012i	0.0460085	+	0.106558i
$471$		0			0
$472$	3.92691	−	3.92691i	0.180751	−	0.180751i
$473$	5.90305	−	5.90305i	0.271422	−	0.271422i
$474$		0			0
$475$	8.82407	+	8.31349i	0.404876	+	0.381449i
$476$		−	1.35848i		−	0.0622658i
$477$		0			0
$478$	2.53590	+	2.53590i	0.115989	+	0.115989i
$479$	−16.7055			−0.763293			−0.381647	−	0.924308i	$-0.624643\pi$
$479$	−16.7055			−0.763293			−0.381647	+	0.924308i	$0.624643\pi$
$480$		0			0
$481$	−15.8799			−0.724060
$482$	15.6468	+	15.6468i	0.712691	+	0.712691i
$483$		0			0
$484$			10.1558i			0.461627i
$485$	−0.408635	+	1.02964i	−0.0185552	+	0.0467535i
$486$		0			0
$487$	27.7395	−	27.7395i	1.25700	−	1.25700i	0.304475	−	0.952520i	$-0.401519\pi$
$487$	27.7395	−	27.7395i	1.25700	−	1.25700i	0.952520	−	0.304475i	$-0.0984811\pi$
$488$	−2.00235	+	2.00235i	−0.0906421	+	0.0906421i
$489$		0			0
$490$	−4.47454	+	11.2745i	−0.202139	+	0.509331i
$491$		−	5.94370i		−	0.268235i	−0.990965	−	0.134118i	$-0.957180\pi$
$491$		−	5.94370i		−	0.268235i	0.990965	−	0.134118i	$-0.0428200\pi$
$492$		0			0
$493$	−4.02380	−	4.02380i	−0.181223	−	0.181223i
$494$	4.83141			0.217375
$495$		0			0
$496$	−8.70320			−0.390785
$497$	9.90133	+	9.90133i	0.444135	+	0.444135i
$498$		0			0
$499$			0.605346i			0.0270990i	0.999908	+	0.0135495i	$0.00431307\pi$
$499$			0.605346i			0.0270990i	−0.999908	+	0.0135495i	$0.995687\pi$
$500$	−10.5101	−	3.81294i	−0.470025	−	0.170520i
$501$		0			0
$502$	−6.29809	+	6.29809i	−0.281098	+	0.281098i
$503$	−17.7321	+	17.7321i	−0.790635	+	0.790635i	−0.981597	−	0.190962i	$-0.938839\pi$
$503$	−17.7321	+	17.7321i	−0.790635	+	0.790635i	0.190962	+	0.981597i	$0.438839\pi$
$504$		0			0
$505$	−4.71763	−	10.9262i	−0.209932	−	0.486211i
$506$		−	7.53393i		−	0.334924i
$507$		0			0
$508$	−9.70191	−	9.70191i	−0.430452	−	0.430452i
$509$	−35.1623			−1.55854			−0.779270	−	0.626688i	$-0.784410\pi$
$509$	−35.1623			−1.55854			−0.779270	+	0.626688i	$0.784410\pi$
$510$		0			0
$511$	−11.1000			−0.491035
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$			11.9791i			0.528376i
$515$	26.2799	+	10.4298i	1.15803	+	0.459591i
$516$		0			0
$517$	0.731103	−	0.731103i	0.0321539	−	0.0321539i
$518$	7.07290	−	7.07290i	0.310765	−	0.310765i
$519$		0			0
$520$	−4.09055	+	1.76618i	−0.179383	+	0.0774521i
$521$		−	28.9982i		−	1.27043i	−0.772334	−	0.635217i	$-0.780911\pi$
$521$		−	28.9982i		−	1.27043i	0.772334	−	0.635217i	$-0.219089\pi$
$522$		0			0
$523$	14.5709	+	14.5709i	0.637140	+	0.637140i	0.949849	−	0.312709i	$-0.101236\pi$
$523$	14.5709	+	14.5709i	0.637140	+	0.637140i	−0.312709	+	0.949849i	$0.601236\pi$
$524$	−5.11381			−0.223398
$525$		0			0
$526$	−6.72851			−0.293377
$527$	−6.66092	−	6.66092i	−0.290154	−	0.290154i
$528$		0			0
$529$		−	44.2349i		−	1.92326i
$530$	24.7445	−	10.6839i	1.07483	−	0.464080i
$531$		0			0
$532$	−2.15191	+	2.15191i	−0.0932972	+	0.0932972i
$533$	−15.4949	+	15.4949i	−0.671160	+	0.671160i
$534$		0			0
$535$	7.32499	+	2.90708i	0.316687	+	0.125684i
$536$		−	2.27729i		−	0.0983638i
$537$		0			0
$538$	−5.97760	−	5.97760i	−0.257713	−	0.257713i
$539$	4.98424			0.214686
$540$		0			0
$541$	−27.1708			−1.16817			−0.584083	−	0.811694i	$-0.698546\pi$
$541$	−27.1708			−1.16817			−0.584083	+	0.811694i	$0.698546\pi$
$542$	−21.6765	−	21.6765i	−0.931084	−	0.931084i
$543$		0			0
$544$		−	1.08236i		−	0.0464057i
$545$	12.0033	+	27.8002i	0.514166	+	1.19083i
$546$		0			0
$547$	7.58497	−	7.58497i	0.324310	−	0.324310i	−0.526108	−	0.850418i	$-0.676349\pi$
$547$	7.58497	−	7.58497i	0.324310	−	0.324310i	0.850418	+	0.526108i	$0.176349\pi$
$548$	−10.4115	+	10.4115i	−0.444757	+	0.444757i
$549$		0			0
$550$	0.136811	+	4.59199i	0.00583364	+	0.195803i
$551$			12.7479i			0.543077i
$552$		0			0
$553$	13.5805	+	13.5805i	0.577501	+	0.577501i
$554$	−15.8243			−0.672310
$555$		0			0
$556$	17.7267			0.751778
$557$	−2.13228	−	2.13228i	−0.0903476	−	0.0903476i	0.660489	−	0.750836i	$-0.270349\pi$
$557$	−2.13228	−	2.13228i	−0.0903476	−	0.0903476i	−0.750836	+	0.660489i	$0.770349\pi$
$558$		0			0
$559$			18.1044i			0.765736i
$560$	1.03528	−	2.60859i	0.0437484	−	0.110233i
$561$		0			0
$562$	−5.67692	+	5.67692i	−0.239466	+	0.239466i
$563$	−5.17138	+	5.17138i	−0.217948	+	0.217948i	−0.807633	−	0.589685i	$-0.799252\pi$
$563$	−5.17138	+	5.17138i	−0.217948	+	0.217948i	0.589685	+	0.807633i	$0.299252\pi$
$564$		0			0
$565$	−6.33308	+	15.9575i	−0.266435	+	0.671337i
$566$			15.5043i			0.651693i
$567$		0			0
$568$	7.88879	+	7.88879i	0.331006	+	0.331006i
$569$	−7.01763			−0.294194			−0.147097	−	0.989122i	$-0.546993\pi$
$569$	−7.01763			−0.294194			−0.147097	+	0.989122i	$0.546993\pi$
$570$		0			0
$571$	17.9770			0.752313			0.376157	−	0.926556i	$-0.377245\pi$
$571$	17.9770			0.752313			0.376157	+	0.926556i	$0.377245\pi$
$572$	1.29457	+	1.29457i	0.0541288	+	0.0541288i
$573$		0			0
$574$		−	13.8029i		−	0.576122i
$575$	1.22094	+	40.9803i	0.0509167	+	1.70900i
$576$		0			0
$577$	−12.5461	+	12.5461i	−0.522302	+	0.522302i	−0.918266	−	0.395964i	$-0.870411\pi$
$577$	−12.5461	+	12.5461i	−0.522302	+	0.522302i	0.395964	+	0.918266i	$0.370411\pi$
$578$	−11.1924	+	11.1924i	−0.465544	+	0.465544i
$579$		0			0
$580$	−4.66013	−	10.7931i	−0.193502	−	0.448158i
$581$		−	2.79263i		−	0.115858i
$582$		0			0
$583$	−7.83109	−	7.83109i	−0.324331	−	0.324331i
$584$	−8.84382			−0.365960
$585$		0			0
$586$	−6.03004			−0.249099
$587$	−23.0889	−	23.0889i	−0.952979	−	0.952979i	0.0459640	−	0.998943i	$-0.485364\pi$
$587$	−23.0889	−	23.0889i	−0.952979	−	0.952979i	−0.998943	+	0.0459640i	$0.985364\pi$
$588$		0			0
$589$			21.1026i			0.869517i
$590$	11.5422	+	4.58078i	0.475185	+	0.188588i
$591$		0			0
$592$	5.63527	−	5.63527i	0.231608	−	0.231608i
$593$	5.88645	−	5.88645i	0.241728	−	0.241728i	−0.575837	−	0.817565i	$-0.695324\pi$
$593$	5.88645	−	5.88645i	0.241728	−	0.241728i	0.817565	+	0.575837i	$0.195324\pi$
$594$		0			0
$595$	2.78880	−	1.20412i	0.114330	−	0.0493642i
$596$			19.5049i			0.798950i
$597$		0			0
$598$	11.5531	+	11.5531i	0.472443	+	0.472443i
$599$	23.4284			0.957259			0.478630	−	0.878017i	$-0.341134\pi$
$599$	23.4284			0.957259			0.478630	+	0.878017i	$0.341134\pi$
$600$		0			0
$601$	22.8090			0.930400			0.465200	−	0.885206i	$-0.345982\pi$
$601$	22.8090			0.930400			0.465200	+	0.885206i	$0.345982\pi$
$602$	−8.06371	−	8.06371i	−0.328652	−	0.328652i
$603$		0			0
$604$		−	14.9538i		−	0.608462i
$605$	−20.8487	+	9.00185i	−0.847620	+	0.365977i
$606$		0			0
$607$	15.9144	−	15.9144i	0.645945	−	0.645945i	−0.306065	−	0.952011i	$-0.599013\pi$
$607$	15.9144	−	15.9144i	0.645945	−	0.645945i	0.952011	+	0.306065i	$0.0990125\pi$
$608$	−1.71452	+	1.71452i	−0.0695328	+	0.0695328i
$609$		0			0
$610$	−5.88543	−	2.33576i	−0.238294	−	0.0945722i
$611$			2.24227i			0.0907124i
$612$		0			0
$613$	6.98979	+	6.98979i	0.282315	+	0.282315i	0.834032	−	0.551717i	$-0.186027\pi$
$613$	6.98979	+	6.98979i	0.282315	+	0.282315i	−0.551717	+	0.834032i	$0.686027\pi$
$614$	20.4885			0.826849
$615$		0			0
$616$	−1.15321			−0.0464640
$617$	−4.51624	−	4.51624i	−0.181817	−	0.181817i	0.610330	−	0.792147i	$-0.291037\pi$
$617$	−4.51624	−	4.51624i	−0.181817	−	0.181817i	−0.792147	+	0.610330i	$0.791037\pi$
$618$		0			0
$619$		−	17.2767i		−	0.694408i	−0.937790	−	0.347204i	$-0.887131\pi$
$619$		−	17.2767i		−	0.694408i	0.937790	−	0.347204i	$-0.112869\pi$
$620$	−7.71430	−	17.8667i	−0.309814	−	0.717543i
$621$		0			0
$622$	15.4038	−	15.4038i	0.617637	−	0.617637i
$623$	3.80114	−	3.80114i	0.152289	−	0.152289i
$624$		0			0
$625$	−1.48835	−	24.9557i	−0.0595339	−	0.998226i
$626$		−	25.4504i		−	1.01720i
$627$		0			0
$628$	−15.3004	−	15.3004i	−0.610551	−	0.610551i
$629$	8.62581			0.343934
$630$		0			0
$631$	−25.3506			−1.00919			−0.504596	−	0.863356i	$-0.668358\pi$
$631$	−25.3506			−1.00919			−0.504596	+	0.863356i	$0.668358\pi$
$632$	10.8201	+	10.8201i	0.430402	+	0.430402i
$633$		0			0
$634$		−	1.11474i		−	0.0442721i
$635$	11.3174	−	28.5164i	0.449116	−	1.13164i
$636$		0			0
$637$	−7.64324	+	7.64324i	−0.302836	+	0.302836i
$638$	−3.41578	+	3.41578i	−0.135232	+	0.135232i
$639$		0			0
$640$	0.824847	−	2.07837i	0.0326049	−	0.0821548i
$641$		−	6.69427i		−	0.264408i	−0.991223	−	0.132204i	$-0.957795\pi$
$641$		−	6.69427i		−	0.264408i	0.991223	−	0.132204i	$-0.0422054\pi$
$642$		0			0
$643$	−5.10677	−	5.10677i	−0.201391	−	0.201391i	0.599205	−	0.800596i	$-0.295484\pi$
$643$	−5.10677	−	5.10677i	−0.201391	−	0.201391i	−0.800596	+	0.599205i	$0.795484\pi$
$644$	−10.2915			−0.405543
$645$		0			0
$646$	−2.62438			−0.103255
$647$	27.8350	+	27.8350i	1.09431	+	1.09431i	0.995063	+	0.0992439i	$0.0316424\pi$
$647$	27.8350	+	27.8350i	1.09431	+	1.09431i	0.0992439	+	0.995063i	$0.468358\pi$
$648$		0			0
$649$		−	5.10258i		−	0.200294i
$650$	−7.25153	−	6.83194i	−0.284429	−	0.267971i
$651$		0			0
$652$	9.29939	−	9.29939i	0.364192	−	0.364192i
$653$	−8.92495	+	8.92495i	−0.349260	+	0.349260i	−0.859834	−	0.510574i	$-0.829433\pi$
$653$	−8.92495	+	8.92495i	−0.349260	+	0.349260i	0.510574	+	0.859834i	$0.329433\pi$
$654$		0			0
$655$	−4.53276	−	10.4981i	−0.177110	−	0.410194i
$656$		−	10.9973i		−	0.429374i
$657$		0			0
$658$	−0.998705	−	0.998705i	−0.0389336	−	0.0389336i
$659$	−33.4416			−1.30270			−0.651350	−	0.758777i	$-0.725797\pi$
$659$	−33.4416			−1.30270			−0.651350	+	0.758777i	$0.725797\pi$
$660$		0			0
$661$	−29.9369			−1.16441			−0.582206	−	0.813042i	$-0.697810\pi$
$661$	−29.9369			−1.16441			−0.582206	+	0.813042i	$0.697810\pi$
$662$	−14.2673	−	14.2673i	−0.554513	−	0.554513i
$663$		0			0
$664$		−	2.22500i		−	0.0863468i
$665$	−6.32503	−	2.51023i	−0.245274	−	0.0973424i
$666$		0			0
$667$	−30.4834	+	30.4834i	−1.18032	+	1.18032i
$668$	11.4746	−	11.4746i	0.443967	−	0.443967i
$669$		0			0
$670$	4.67501	−	2.01853i	0.180611	−	0.0779826i
$671$			2.60183i			0.100443i
$672$		0			0
$673$	−19.8718	−	19.8718i	−0.766001	−	0.766001i	0.211399	−	0.977400i	$-0.432198\pi$
$673$	−19.8718	−	19.8718i	−0.766001	−	0.766001i	−0.977400	+	0.211399i	$0.932198\pi$
$674$	3.25183			0.125256
$675$		0			0
$676$	9.02959			0.347292
$677$	28.8193	+	28.8193i	1.10762	+	1.10762i	0.993463	+	0.114154i	$0.0364158\pi$
$677$	28.8193	+	28.8193i	1.10762	+	1.10762i	0.114154	+	0.993463i	$0.463584\pi$
$678$		0			0
$679$		−	0.621792i		−	0.0238622i
$680$	2.22195	−	0.959374i	0.0852080	−	0.0367903i
$681$		0			0
$682$	−5.65442	+	5.65442i	−0.216519	+	0.216519i
$683$	−30.5158	+	30.5158i	−1.16765	+	1.16765i	−0.184895	+	0.982758i	$0.559194\pi$
$683$	−30.5158	+	30.5158i	−1.16765	+	1.16765i	−0.982758	+	0.184895i	$0.940806\pi$
$684$		0			0
$685$	−30.6021	−	12.1451i	−1.16925	−	0.464041i
$686$		−	15.5944i		−	0.595397i
$687$		0			0
$688$	−6.42469	−	6.42469i	−0.244939	−	0.244939i
$689$	24.0177			0.915000
$690$		0			0
$691$	46.7593			1.77881			0.889404	−	0.457123i	$-0.151120\pi$
$691$	46.7593			1.77881			0.889404	+	0.457123i	$0.151120\pi$
$692$	2.45763	+	2.45763i	0.0934250	+	0.0934250i
$693$		0			0
$694$			13.3506i			0.506782i
$695$	15.7125	+	36.3908i	0.596009	+	1.38038i
$696$		0			0
$697$	8.41672	−	8.41672i	0.318806	−	0.318806i
$698$	6.69713	−	6.69713i	0.253490	−	0.253490i
$699$		0			0
$700$	6.27278	−	0.186887i	0.237089	−	0.00706367i
$701$			24.2121i			0.914478i	0.889344	+	0.457239i	$0.151162\pi$
$701$			24.2121i			0.914478i	−0.889344	+	0.457239i	$0.848838\pi$
$702$		0			0
$703$	−13.6638	−	13.6638i	−0.515340	−	0.515340i
$704$	−0.918806			−0.0346288
$705$		0			0
$706$	−23.7014			−0.892012
$707$	4.72360	+	4.72360i	0.177649	+	0.177649i
$708$		0			0
$709$		−	19.5547i		−	0.734393i	−0.930143	−	0.367196i	$-0.880318\pi$
$709$		−	19.5547i		−	0.734393i	0.930143	−	0.367196i	$-0.119682\pi$
$710$	−9.20236	+	23.1872i	−0.345358	+	0.870201i
$711$		0			0
$712$	3.02852	−	3.02852i	0.113499	−	0.113499i
$713$	−50.4616	+	50.4616i	−1.88980	+	1.88980i
$714$		0			0
$715$	−1.51013	+	3.80509i	−0.0564757	+	0.142302i
$716$		−	16.2803i		−	0.608422i
$717$		0			0
$718$	−16.0000	−	16.0000i	−0.597115	−	0.597115i
$719$	−46.1448			−1.72091			−0.860454	−	0.509527i	$-0.829820\pi$
$719$	−46.1448			−1.72091			−0.860454	+	0.509527i	$0.829820\pi$
$720$		0			0
$721$	−15.8703			−0.591039
$722$	−9.27786	−	9.27786i	−0.345286	−	0.345286i
$723$		0			0
$724$			7.97440i			0.296366i
$725$	18.0263	−	19.1334i	0.669481	−	0.710598i
$726$		0			0
$727$	−20.2151	+	20.2151i	−0.749736	+	0.749736i	−0.974429	−	0.224694i	$-0.927862\pi$
$727$	−20.2151	+	20.2151i	−0.749736	+	0.749736i	0.224694	+	0.974429i	$0.427862\pi$
$728$	1.76842	−	1.76842i	0.0655420	−	0.0655420i
$729$		0			0
$730$	−7.83894	−	18.1553i	−0.290132	−	0.671960i
$731$		−	9.83417i		−	0.363730i
$732$		0			0
$733$	−5.08330	−	5.08330i	−0.187756	−	0.187756i	0.606969	−	0.794725i	$-0.292385\pi$
$733$	−5.08330	−	5.08330i	−0.187756	−	0.187756i	−0.794725	+	0.606969i	$0.792385\pi$
$734$	32.0714			1.18378
$735$		0			0
$736$	−8.19969			−0.302245
$737$	−1.47954	−	1.47954i	−0.0544995	−	0.0544995i
$738$		0			0
$739$		−	1.12301i		−	0.0413104i	−0.999787	−	0.0206552i	$-0.993425\pi$
$739$		−	1.12301i		−	0.0413104i	0.999787	−	0.0206552i	$-0.00657523\pi$
$740$	16.5635	+	6.57360i	0.608887	+	0.241650i
$741$		0			0
$742$	−10.6975	+	10.6975i	−0.392717	+	0.392717i
$743$	17.4501	−	17.4501i	0.640182	−	0.640182i	−0.310418	−	0.950600i	$-0.600469\pi$
$743$	17.4501	−	17.4501i	0.640182	−	0.640182i	0.950600	+	0.310418i	$0.100469\pi$
$744$		0			0
$745$	−40.0412	+	17.2886i	−1.46700	+	0.633406i
$746$		−	33.2921i		−	1.21891i
$747$		0			0
$748$	−0.703201	−	0.703201i	−0.0257116	−	0.0257116i
$749$	−4.42351			−0.161631
$750$		0			0
$751$	−3.03004			−0.110568			−0.0552838	−	0.998471i	$-0.517606\pi$
$751$	−3.03004			−0.110568			−0.0552838	+	0.998471i	$0.517606\pi$
$752$	−0.795710	−	0.795710i	−0.0290165	−	0.0290165i
$753$		0			0
$754$		−	10.4761i		−	0.381516i
$755$	30.6985	−	13.2547i	1.11723	−	0.482387i
$756$		0			0
$757$	2.13781	−	2.13781i	0.0777002	−	0.0777002i	−0.667189	−	0.744889i	$-0.732503\pi$
$757$	2.13781	−	2.13781i	0.0777002	−	0.0777002i	0.744889	+	0.667189i	$0.232503\pi$
$758$	−5.51931	+	5.51931i	−0.200471	+	0.200471i
$759$		0			0
$760$	−5.03941	−	2.00000i	−0.182799	−	0.0725476i
$761$		−	31.6191i		−	1.14619i	−0.819489	−	0.573095i	$-0.805743\pi$
$761$		−	31.6191i		−	1.14619i	0.819489	−	0.573095i	$-0.194257\pi$
$762$		0			0
$763$	−12.0185	−	12.0185i	−0.435100	−	0.435100i
$764$	−17.8078			−0.644262
$765$		0			0
$766$	35.6087			1.28659
$767$	7.82471	+	7.82471i	0.282534	+	0.282534i
$768$		0			0
$769$		−	19.8273i		−	0.714991i	−0.933915	−	0.357496i	$-0.883631\pi$
$769$		−	19.8273i		−	0.714991i	0.933915	−	0.357496i	$-0.116369\pi$
$770$	−1.02217	−	2.36740i	−0.0368366	−	0.0853151i
$771$		0			0
$772$	−4.60383	+	4.60383i	−0.165695	+	0.165695i
$773$	8.31371	−	8.31371i	0.299023	−	0.299023i	−0.541608	−	0.840631i	$-0.682184\pi$
$773$	8.31371	−	8.31371i	0.299023	−	0.299023i	0.840631	+	0.541608i	$0.182184\pi$
$774$		0			0
$775$	29.8405	−	31.6732i	1.07190	−	1.13773i
$776$		−	0.495407i		−	0.0177841i
$777$		0			0
$778$	−20.8635	−	20.8635i	−0.747992	−	0.747992i
$779$	−26.6652			−0.955378
$780$		0			0
$781$	10.2506			0.366796
$782$	−6.27556	−	6.27556i	−0.224414	−	0.224414i
$783$		0			0
$784$		−	5.42469i		−	0.193739i
$785$	17.8480	−	44.9717i	0.637023	−	1.60511i
$786$		0			0
$787$	−39.4573	+	39.4573i	−1.40650	+	1.40650i	−0.629505	+	0.776996i	$0.716742\pi$
$787$	−39.4573	+	39.4573i	−1.40650	+	1.40650i	−0.776996	+	0.629505i	$0.783258\pi$
$788$	0.969574	−	0.969574i	0.0345397	−	0.0345397i
$789$		0			0
$790$	−12.6218	+	31.8032i	−0.449063	+	1.13151i
$791$		−	9.63662i		−	0.342639i
$792$		0			0
$793$	−3.98986	−	3.98986i	−0.141684	−	0.141684i
$794$	−11.3740			−0.403647
$795$		0			0
$796$	−5.55258			−0.196806
$797$	26.1668	+	26.1668i	0.926876	+	0.926876i	0.997503	−	0.0706266i	$-0.0224999\pi$
$797$	26.1668	+	26.1668i	0.926876	+	0.926876i	−0.0706266	+	0.997503i	$0.522500\pi$
$798$		0			0
$799$		−	1.21798i		−	0.0430890i
$800$	4.99778	−	0.148901i	0.176698	−	0.00526444i
$801$		0			0
$802$	16.9475	−	16.9475i	0.598436	−	0.598436i
$803$	−5.74578	+	5.74578i	−0.202764	+	0.202764i
$804$		0			0
$805$	−9.12216	−	21.1273i	−0.321514	−	0.744641i
$806$		−	17.3419i		−	0.610842i
$807$		0			0
$808$	3.76349	+	3.76349i	0.132399	+	0.132399i
$809$	−27.1027			−0.952880			−0.476440	−	0.879207i	$-0.658073\pi$
$809$	−27.1027			−0.952880			−0.476440	+	0.879207i	$0.658073\pi$
$810$		0			0
$811$	−56.2469			−1.97510			−0.987548	−	0.157317i	$-0.949716\pi$
$811$	−56.2469			−1.97510			−0.987548	+	0.157317i	$0.949716\pi$
$812$	4.66604	+	4.66604i	0.163746	+	0.163746i
$813$		0			0
$814$		−	7.32240i		−	0.256650i
$815$	27.3333	+	10.8478i	0.957445	+	0.379983i
$816$		0			0
$817$	−15.5779	+	15.5779i	−0.545002	+	0.545002i
$818$	3.83834	−	3.83834i	0.134204	−	0.134204i
$819$		0			0
$820$	22.5763	−	9.74777i	0.788398	−	0.340407i
$821$			21.8316i			0.761928i	0.924590	+	0.380964i	$0.124408\pi$
$821$			21.8316i			0.761928i	−0.924590	+	0.380964i	$0.875592\pi$
$822$		0			0
$823$	12.4850	+	12.4850i	0.435199	+	0.435199i	0.890393	−	0.455193i	$-0.150430\pi$
$823$	12.4850	+	12.4850i	0.435199	+	0.435199i	−0.455193	+	0.890393i	$0.650430\pi$
$824$	−12.6445			−0.440492
$825$		0			0
$826$	−6.97025			−0.242526
$827$	0.260637	+	0.260637i	0.00906323	+	0.00906323i	0.711624	−	0.702561i	$-0.247960\pi$
$827$	0.260637	+	0.260637i	0.00906323	+	0.00906323i	−0.702561	+	0.711624i	$0.747960\pi$
$828$		0			0
$829$			6.87240i			0.238688i	0.992853	+	0.119344i	$0.0380792\pi$
$829$			6.87240i			0.238688i	−0.992853	+	0.119344i	$0.961921\pi$
$830$	4.56768	−	1.97219i	0.158546	−	0.0684556i
$831$		0			0
$832$	1.40897	−	1.40897i	0.0488473	−	0.0488473i
$833$	4.15174	−	4.15174i	0.143849	−	0.143849i
$834$		0			0
$835$	33.7270	+	13.3853i	1.16717	+	0.463217i
$836$			2.22782i			0.0770508i
$837$		0			0
$838$	−0.503511	−	0.503511i	−0.0173935	−	0.0173935i
$839$	−23.9364			−0.826377			−0.413189	−	0.910645i	$-0.635585\pi$
$839$	−23.9364			−0.826377			−0.413189	+	0.910645i	$0.635585\pi$
$840$		0			0
$841$	−1.35852			−0.0468454
$842$	−0.0391391	−	0.0391391i	−0.00134882	−	0.00134882i
$843$		0			0
$844$		−	8.82148i		−	0.303648i
$845$	8.00361	+	18.5367i	0.275333	+	0.637683i
$846$		0			0
$847$	9.01326	−	9.01326i	0.309699	−	0.309699i
$848$	−8.52312	+	8.52312i	−0.292685	+	0.292685i
$849$		0			0
$850$	3.93897	+	3.71105i	0.135106	+	0.127288i
$851$		−	65.3472i		−	2.24007i
$852$		0			0
$853$	11.9097	+	11.9097i	0.407779	+	0.407779i	0.880964	−	0.473184i	$-0.156895\pi$
$853$	11.9097	+	11.9097i	0.407779	+	0.407779i	−0.473184	+	0.880964i	$0.656895\pi$
$854$	3.55417			0.121621
$855$		0			0
$856$	−3.52439			−0.120461
$857$	0.540503	+	0.540503i	0.0184632	+	0.0184632i	0.716278	−	0.697815i	$-0.245844\pi$
$857$	0.540503	+	0.540503i	0.0184632	+	0.0184632i	−0.697815	+	0.716278i	$0.745844\pi$
$858$		0			0
$859$			8.26465i			0.281986i	0.990011	+	0.140993i	$0.0450296\pi$
$859$			8.26465i			0.281986i	−0.990011	+	0.140993i	$0.954970\pi$
$860$	7.49447	−	18.8838i	0.255559	−	0.643934i
$861$		0			0
$862$	−12.5920	+	12.5920i	−0.428885	+	0.428885i
$863$	−8.99415	+	8.99415i	−0.306164	+	0.306164i	−0.843420	−	0.537255i	$-0.819461\pi$
$863$	−8.99415	+	8.99415i	−0.306164	+	0.306164i	0.537255	+	0.843420i	$0.319461\pi$
$864$		0			0
$865$	−2.86685	+	7.22361i	−0.0974757	+	0.245610i
$866$		−	22.1465i		−	0.752568i
$867$		0			0
$868$	7.72408	+	7.72408i	0.262172	+	0.262172i
$869$	14.0596			0.476938
$870$		0			0
$871$	4.53769			0.153754
$872$	−9.57566	−	9.57566i	−0.324273	−	0.324273i
$873$		0			0
$874$			19.8817i			0.672509i
$875$	5.94370	+	12.7116i	0.200934	+	0.429732i
$876$		0			0
$877$	35.7424	−	35.7424i	1.20693	−	1.20693i	0.234920	−	0.972015i	$-0.424517\pi$
$877$	35.7424	−	35.7424i	1.20693	−	1.20693i	0.972015	−	0.234920i	$-0.0754828\pi$
$878$	3.44714	−	3.44714i	0.116335	−	0.116335i
$879$		0			0
$880$	−0.814407	−	1.88620i	−0.0274537	−	0.0635839i
$881$			20.5731i			0.693127i	0.938027	+	0.346563i	$0.112651\pi$
$881$			20.5731i			0.693127i	−0.938027	+	0.346563i	$0.887349\pi$
$882$		0			0
$883$	−26.9661	−	26.9661i	−0.907480	−	0.907480i	0.0885882	−	0.996068i	$-0.471764\pi$
$883$	−26.9661	−	26.9661i	−0.907480	−	0.907480i	−0.996068	+	0.0885882i	$0.971764\pi$
$884$	2.15669			0.0725373
$885$		0			0
$886$	−31.3834			−1.05435
$887$	35.8383	+	35.8383i	1.20333	+	1.20333i	0.973146	+	0.230187i	$0.0739339\pi$
$887$	35.8383	+	35.8383i	1.20333	+	1.20333i	0.230187	+	0.973146i	$0.426066\pi$
$888$		0			0
$889$			17.2209i			0.577569i
$890$	8.90162	+	3.53280i	0.298383	+	0.118420i
$891$		0			0
$892$	−0.503511	+	0.503511i	−0.0168588	+	0.0168588i
$893$	−1.92935	+	1.92935i	−0.0645633	+	0.0645633i
$894$		0			0
$895$	33.4215	−	14.4304i	1.11716	−	0.482356i
$896$			1.25511i			0.0419304i
$897$		0			0
$898$	1.80161	+	1.80161i	0.0601203	+	0.0601203i
$899$	45.7572			1.52609
$900$		0			0
$901$	−13.0462			−0.434632
$902$	−7.14491	−	7.14491i	−0.237899	−	0.237899i
$903$		0			0
$904$		−	7.67789i		−	0.255363i
$905$	−16.3705	+	7.06831i	−0.544175	+	0.234959i
$906$		0			0
$907$	6.59648	−	6.59648i	0.219032	−	0.219032i	−0.589058	−	0.808091i	$-0.700501\pi$
$907$	6.59648	−	6.59648i	0.219032	−	0.219032i	0.808091	+	0.589058i	$0.200501\pi$
$908$	12.0933	−	12.0933i	0.401332	−	0.401332i
$909$		0			0
$910$	5.19784	+	2.06288i	0.172307	+	0.0683838i
$911$		−	2.06055i		−	0.0682690i	−0.999417	−	0.0341345i	$-0.989133\pi$
$911$		−	2.06055i		−	0.0682690i	0.999417	−	0.0341345i	$-0.0108675\pi$
$912$		0			0
$913$	−1.44557	−	1.44557i	−0.0478414	−	0.0478414i
$914$	−2.45664			−0.0812583
$915$		0			0
$916$	6.65672			0.219944
$917$	4.53850	+	4.53850i	0.149875	+	0.149875i
$918$		0			0
$919$			27.0352i			0.891810i	0.895080	+	0.445905i	$0.147118\pi$
$919$			27.0352i			0.891810i	−0.895080	+	0.445905i	$0.852882\pi$
$920$	−7.26800	−	16.8330i	−0.239619	−	0.554968i
$921$		0			0
$922$	−22.4158	+	22.4158i	−0.738224	+	0.738224i
$923$	−15.7191	+	15.7191i	−0.517401	+	0.517401i
$924$		0			0
$925$	1.18666	+	39.8297i	0.0390172	+	1.30959i
$926$			2.65305i			0.0871847i
$927$		0			0
$928$	3.71763	+	3.71763i	0.122037	+	0.122037i
$929$	45.3678			1.48847			0.744235	−	0.667918i	$-0.232814\pi$
$929$	45.3678			1.48847			0.744235	+	0.667918i	$0.232814\pi$
$930$		0			0
$931$	−13.1532			−0.431079
$932$	3.86934	+	3.86934i	0.126744	+	0.126744i
$933$		0			0
$934$			12.5012i			0.409052i
$935$	0.820291	−	2.06689i	0.0268264	−	0.0675946i
$936$		0			0
$937$	3.90670	−	3.90670i	0.127626	−	0.127626i	−0.640408	−	0.768035i	$-0.721235\pi$
$937$	3.90670	−	3.90670i	0.127626	−	0.127626i	0.768035	+	0.640408i	$0.221235\pi$
$938$	−2.02109	+	2.02109i	−0.0659909	+	0.0659909i
$939$		0			0
$940$	0.928203	−	2.33880i	0.0302747	−	0.0762832i
$941$			9.62122i			0.313643i	0.987627	+	0.156821i	$0.0501247\pi$
$941$			9.62122i			0.313643i	−0.987627	+	0.156821i	$0.949875\pi$
$942$		0			0
$943$	−63.7632	−	63.7632i	−2.07641	−	2.07641i
$944$	−5.55349			−0.180751
$945$		0			0
$946$	−8.34817			−0.271422
$947$	36.6735	+	36.6735i	1.19173	+	1.19173i	0.976582	+	0.215147i	$0.0690232\pi$
$947$	36.6735	+	36.6735i	1.19173	+	1.19173i	0.215147	+	0.976582i	$0.430977\pi$
$948$		0			0
$949$		−	17.6221i		−	0.572037i
$950$	−0.361038	−	12.1181i	−0.0117136	−	0.393162i
$951$		0			0
$952$	−0.960590	+	0.960590i	−0.0311329	+	0.0311329i
$953$	10.4115	−	10.4115i	0.337261	−	0.337261i	−0.518074	−	0.855336i	$-0.673351\pi$
$953$	10.4115	−	10.4115i	0.337261	−	0.337261i	0.855336	+	0.518074i	$0.173351\pi$
$954$		0			0
$955$	−15.7844	−	36.5573i	−0.510770	−	1.18297i
$956$		−	3.58630i		−	0.115989i
$957$		0			0
$958$	11.8126	+	11.8126i	0.381647	+	0.381647i
$959$	18.4804			0.596763
$960$		0			0
$961$	44.7457			1.44341
$962$	11.2288	+	11.2288i	0.362030	+	0.362030i
$963$		0			0
$964$		−	22.1279i		−	0.712691i
$965$	−13.5319	−	5.37041i	−0.435606	−	0.172880i
$966$		0			0
$967$	25.3714	−	25.3714i	0.815890	−	0.815890i	−0.169620	−	0.985510i	$-0.554254\pi$
$967$	25.3714	−	25.3714i	0.815890	−	0.815890i	0.985510	+	0.169620i	$0.0542539\pi$
$968$	7.18123	−	7.18123i	0.230814	−	0.230814i
$969$		0			0
$970$	1.01701	−	0.439117i	0.0326544	−	0.0140992i
$971$		−	15.1153i		−	0.485072i	−0.970142	−	0.242536i	$-0.922021\pi$
$971$		−	15.1153i		−	0.485072i	0.970142	−	0.242536i	$-0.0779792\pi$
$972$		0			0
$973$	−15.7324	−	15.7324i	−0.504358	−	0.504358i
$974$	−39.2295			−1.25700
$975$		0			0
$976$	2.83175			0.0906421
$977$	−18.2080	−	18.2080i	−0.582525	−	0.582525i	0.353071	−	0.935596i	$-0.385137\pi$
$977$	−18.2080	−	18.2080i	−0.582525	−	0.582525i	−0.935596	+	0.353071i	$0.885137\pi$
$978$		0			0
$979$		−	3.93523i		−	0.125770i
$980$	11.1363	−	4.80831i	0.355735	−	0.153596i
$981$		0			0
$982$	−4.20283	+	4.20283i	−0.134118	+	0.134118i
$983$	4.30838	−	4.30838i	0.137416	−	0.137416i	−0.635053	−	0.772469i	$-0.719022\pi$
$983$	4.30838	−	4.30838i	0.137416	−	0.137416i	0.772469	+	0.635053i	$0.219022\pi$
$984$		0			0
$985$	2.84983	+	1.13102i	0.0908032	+	0.0360372i
$986$			5.69051i			0.181223i
$987$		0			0
$988$	−3.41632	−	3.41632i	−0.108688	−	0.108688i
$989$	−74.5014			−2.36901
$990$		0			0
$991$	22.4463			0.713031			0.356515	−	0.934289i	$-0.383965\pi$
$991$	22.4463			0.713031			0.356515	+	0.934289i	$0.383965\pi$
$992$	6.15409	+	6.15409i	0.195393	+	0.195393i
$993$		0			0
$994$		−	14.0026i		−	0.444135i
$995$	−4.92167	−	11.3988i	−0.156028	−	0.361367i
$996$		0			0
$997$	21.4010	−	21.4010i	0.677777	−	0.677777i	−0.281720	−	0.959497i	$-0.590905\pi$
$997$	21.4010	−	21.4010i	0.677777	−	0.677777i	0.959497	+	0.281720i	$0.0909050\pi$
$998$	0.428044	−	0.428044i	0.0135495	−	0.0135495i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.f.d.323.1	✓	16
3.2	odd	2	inner	810.2.f.d.323.8	yes	16
5.2	odd	4	inner	810.2.f.d.647.8	yes	16
9.2	odd	6		810.2.m.j.53.4		16
9.4	even	3		810.2.m.i.593.4		16
9.5	odd	6		810.2.m.i.593.1		16
9.7	even	3		810.2.m.j.53.1		16
15.2	even	4	inner	810.2.f.d.647.1	yes	16
45.2	even	12		810.2.m.i.377.4		16
45.7	odd	12		810.2.m.i.377.1		16
45.22	odd	12		810.2.m.j.107.3		16
45.32	even	12		810.2.m.j.107.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
810.2.f.d.323.1	✓	16	1.1	even	1	trivial
810.2.f.d.323.8	yes	16	3.2	odd	2	inner
810.2.f.d.647.1	yes	16	15.2	even	4	inner
810.2.f.d.647.8	yes	16	5.2	odd	4	inner
810.2.m.i.377.1		16	45.7	odd	12
810.2.m.i.377.4		16	45.2	even	12
810.2.m.i.593.1		16	9.5	odd	6
810.2.m.i.593.4		16	9.4	even	3
810.2.m.j.53.1		16	9.7	even	3
810.2.m.j.53.4		16	9.2	odd	6
810.2.m.j.107.2		16	45.32	even	12
810.2.m.j.107.3		16	45.22	odd	12

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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-2.05289 + 0.886375i) q^{5} +(0.887499 - 0.887499i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.07837 + 0.824847i) q^{10} -0.918806i q^{11} +(1.40897 + 1.40897i) q^{13} -1.25511 q^{14} -1.00000 q^{16} +(-0.765342 - 0.765342i) q^{17} +2.42469i q^{19} +(-0.886375 - 2.05289i) q^{20} +(-0.649694 + 0.649694i) q^{22} +(-5.79806 + 5.79806i) q^{23} +(3.42868 - 3.63925i) q^{25} -1.99259i q^{26} +(0.887499 + 0.887499i) q^{28} +5.25752 q^{29} +8.70320 q^{31} +(0.707107 + 0.707107i) q^{32} +1.08236i q^{34} +(-1.03528 + 2.60859i) q^{35} +(-5.63527 + 5.63527i) q^{37} +(1.71452 - 1.71452i) q^{38} +(-0.824847 + 2.07837i) q^{40} +10.9973i q^{41} +(6.42469 + 6.42469i) q^{43} +0.918806 q^{44} +8.19969 q^{46} +(0.795710 + 0.795710i) q^{47} +5.42469i q^{49} +(-4.99778 + 0.148901i) q^{50} +(-1.40897 + 1.40897i) q^{52} +(8.52312 - 8.52312i) q^{53} +(0.814407 + 1.88620i) q^{55} -1.25511i q^{56} +(-3.71763 - 3.71763i) q^{58} +5.55349 q^{59} -2.83175 q^{61} +(-6.15409 - 6.15409i) q^{62} -1.00000i q^{64} +(-4.14134 - 1.64358i) q^{65} +(1.61028 - 1.61028i) q^{67} +(0.765342 - 0.765342i) q^{68} +(2.57660 - 1.11250i) q^{70} +11.1564i q^{71} +(-6.25352 - 6.25352i) q^{73} +7.96947 q^{74} -2.42469 q^{76} +(-0.815440 - 0.815440i) q^{77} +15.3020i q^{79} +(2.05289 - 0.886375i) q^{80} +(7.77629 - 7.77629i) q^{82} +(1.57331 - 1.57331i) q^{83} +(2.24954 + 0.892779i) q^{85} -9.08589i q^{86} +(-0.649694 - 0.649694i) q^{88} +4.28298 q^{89} +2.50092 q^{91} +(-5.79806 - 5.79806i) q^{92} -1.12530i q^{94} +(-2.14919 - 4.97761i) q^{95} +(0.350306 - 0.350306i) q^{97} +(3.83584 - 3.83584i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{7} - 8 q^{10} - 16 q^{16} + 8 q^{22} + 32 q^{25} - 4 q^{28} - 8 q^{31} - 12 q^{37} - 4 q^{40} + 48 q^{43} + 40 q^{46} - 24 q^{55} + 28 q^{58} - 72 q^{61} + 8 q^{67} + 4 q^{70} - 68 q^{73} + 16 q^{76}+ \cdots + 24 q^{97}+O(q^{100}) \) 16 * q - 4 * q^7 - 8 * q^10 - 16 * q^16 + 8 * q^22 + 32 * q^25 - 4 * q^28 - 8 * q^31 - 12 * q^37 - 4 * q^40 + 48 * q^43 + 40 * q^46 - 24 * q^55 + 28 * q^58 - 72 * q^61 + 8 * q^67 + 4 * q^70 - 68 * q^73 + 16 * q^76 - 4 * q^82 - 28 * q^85 + 8 * q^88 + 168 * q^91 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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