LMFDB - Embedded newform 2646.2.f.j.1765.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(883,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("2646.883");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.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:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1765.2
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	2646.1765
Dual form			2646.2.f.j.883.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.686141 - 1.18843i) q^{5} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.686141 - 1.18843i) q^{5} +1.00000 q^{8} -1.37228 q^{10} +(2.18614 + 3.78651i) q^{11} +(1.00000 - 1.73205i) q^{13} +(-0.500000 - 0.866025i) q^{16} -4.37228 q^{17} -5.00000 q^{19} +(0.686141 + 1.18843i) q^{20} +(2.18614 - 3.78651i) q^{22} +(-3.68614 + 6.38458i) q^{23} +(1.55842 + 2.69927i) q^{25} -2.00000 q^{26} +(1.37228 + 2.37686i) q^{29} +(1.00000 - 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.18614 + 3.78651i) q^{34} +2.00000 q^{37} +(2.50000 + 4.33013i) q^{38} +(0.686141 - 1.18843i) q^{40} +(-5.18614 + 8.98266i) q^{41} +(-4.55842 - 7.89542i) q^{43} -4.37228 q^{44} +7.37228 q^{46} +(1.55842 - 2.69927i) q^{50} +(1.00000 + 1.73205i) q^{52} -2.74456 q^{53} +6.00000 q^{55} +(1.37228 - 2.37686i) q^{58} +(-3.55842 + 6.16337i) q^{59} +(-7.05842 - 12.2255i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(-1.37228 - 2.37686i) q^{65} +(-7.55842 + 13.0916i) q^{67} +(2.18614 - 3.78651i) q^{68} -10.1168 q^{71} +5.11684 q^{73} +(-1.00000 - 1.73205i) q^{74} +(2.50000 - 4.33013i) q^{76} +(-6.05842 - 10.4935i) q^{79} -1.37228 q^{80} +10.3723 q^{82} +(2.74456 + 4.75372i) q^{83} +(-3.00000 + 5.19615i) q^{85} +(-4.55842 + 7.89542i) q^{86} +(2.18614 + 3.78651i) q^{88} +3.25544 q^{89} +(-3.68614 - 6.38458i) q^{92} +(-3.43070 + 5.94215i) q^{95} +(4.55842 + 7.89542i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} - 3 q^{5} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 - 3 * q^5 + 4 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} - 3 q^{5} + 4 q^{8} + 6 q^{10} + 3 q^{11} + 4 q^{13} - 2 q^{16} - 6 q^{17} - 20 q^{19} - 3 q^{20} + 3 q^{22} - 9 q^{23} - 11 q^{25} - 8 q^{26} - 6 q^{29} + 4 q^{31} - 2 q^{32} + 3 q^{34} + 8 q^{37} + 10 q^{38} - 3 q^{40} - 15 q^{41} - q^{43} - 6 q^{44} + 18 q^{46} - 11 q^{50} + 4 q^{52} + 12 q^{53} + 24 q^{55} - 6 q^{58} + 3 q^{59} - 11 q^{61} - 8 q^{62} + 4 q^{64} + 6 q^{65} - 13 q^{67} + 3 q^{68} - 6 q^{71} - 14 q^{73} - 4 q^{74} + 10 q^{76} - 7 q^{79} + 6 q^{80} + 30 q^{82} - 12 q^{83} - 12 q^{85} - q^{86} + 3 q^{88} + 36 q^{89} - 9 q^{92} + 15 q^{95} + q^{97}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 - 3 * q^5 + 4 * q^8 + 6 * q^10 + 3 * q^11 + 4 * q^13 - 2 * q^16 - 6 * q^17 - 20 * q^19 - 3 * q^20 + 3 * q^22 - 9 * q^23 - 11 * q^25 - 8 * q^26 - 6 * q^29 + 4 * q^31 - 2 * q^32 + 3 * q^34 + 8 * q^37 + 10 * q^38 - 3 * q^40 - 15 * q^41 - q^43 - 6 * q^44 + 18 * q^46 - 11 * q^50 + 4 * q^52 + 12 * q^53 + 24 * q^55 - 6 * q^58 + 3 * q^59 - 11 * q^61 - 8 * q^62 + 4 * q^64 + 6 * q^65 - 13 * q^67 + 3 * q^68 - 6 * q^71 - 14 * q^73 - 4 * q^74 + 10 * q^76 - 7 * q^79 + 6 * q^80 + 30 * q^82 - 12 * q^83 - 12 * q^85 - q^86 + 3 * q^88 + 36 * q^89 - 9 * q^92 + 15 * q^95 + q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.686141	−	1.18843i	0.306851	−	0.531482i	−0.670820	−	0.741620i	$-0.734058\pi$
$5$	0.686141	−	1.18843i	0.306851	−	0.531482i	0.977672	+	0.210138i	$0.0673912\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.37228			−0.433953
$11$	2.18614	+	3.78651i	0.659146	+	1.14167i	0.980837	+	0.194830i	$0.0624155\pi$
$11$	2.18614	+	3.78651i	0.659146	+	1.14167i	−0.321691	+	0.946845i	$0.604251\pi$
$12$		0			0
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	0.970725	+	0.240192i	$0.0772105\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−4.37228			−1.06043			−0.530217	−	0.847862i	$-0.677890\pi$
$17$	−4.37228			−1.06043			−0.530217	+	0.847862i	$0.677890\pi$
$18$		0			0
$19$	−5.00000			−1.14708			−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000			−1.14708			−0.573539	+	0.819178i	$0.694430\pi$
$20$	0.686141	+	1.18843i	0.153426	+	0.265741i
$21$		0			0
$22$	2.18614	−	3.78651i	0.466087	−	0.807286i
$23$	−3.68614	+	6.38458i	−0.768613	+	1.33128i	0.169701	+	0.985496i	$0.445720\pi$
$23$	−3.68614	+	6.38458i	−0.768613	+	1.33128i	−0.938315	+	0.345782i	$0.887614\pi$
$24$		0			0
$25$	1.55842	+	2.69927i	0.311684	+	0.539853i
$26$	−2.00000			−0.392232
$27$		0			0
$28$		0			0
$29$	1.37228	+	2.37686i	0.254826	+	0.441372i	0.964848	−	0.262807i	$-0.0846484\pi$
$29$	1.37228	+	2.37686i	0.254826	+	0.441372i	−0.710022	+	0.704179i	$0.751315\pi$
$30$		0			0
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	−0.762140	−	0.647412i	$-0.775851\pi$
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	0.941745	+	0.336327i	$0.109185\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	2.18614	+	3.78651i	0.374920	+	0.649381i
$35$		0			0
$36$		0			0
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	2.50000	+	4.33013i	0.405554	+	0.702439i
$39$		0			0
$40$	0.686141	−	1.18843i	0.108488	−	0.187907i
$41$	−5.18614	+	8.98266i	−0.809939	+	1.40286i	0.102966	+	0.994685i	$0.467167\pi$
$41$	−5.18614	+	8.98266i	−0.809939	+	1.40286i	−0.912906	+	0.408171i	$0.866167\pi$
$42$		0			0
$43$	−4.55842	−	7.89542i	−0.695153	−	1.20404i	−0.970129	−	0.242589i	$-0.922003\pi$
$43$	−4.55842	−	7.89542i	−0.695153	−	1.20404i	0.274976	−	0.961451i	$-0.411330\pi$
$44$	−4.37228			−0.659146
$45$		0			0
$46$	7.37228			1.08698
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$		0			0
$50$	1.55842	−	2.69927i	0.220394	−	0.381734i
$51$		0			0
$52$	1.00000	+	1.73205i	0.138675	+	0.240192i
$53$	−2.74456			−0.376995			−0.188497	−	0.982074i	$-0.560362\pi$
$53$	−2.74456			−0.376995			−0.188497	+	0.982074i	$0.560362\pi$
$54$		0			0
$55$	6.00000			0.809040
$56$		0			0
$57$		0			0
$58$	1.37228	−	2.37686i	0.180189	−	0.312097i
$59$	−3.55842	+	6.16337i	−0.463267	+	0.802402i	−0.999121	−	0.0419083i	$-0.986656\pi$
$59$	−3.55842	+	6.16337i	−0.463267	+	0.802402i	0.535854	+	0.844310i	$0.319990\pi$
$60$		0			0
$61$	−7.05842	−	12.2255i	−0.903738	−	1.56532i	−0.822602	−	0.568618i	$-0.807478\pi$
$61$	−7.05842	−	12.2255i	−0.903738	−	1.56532i	−0.0811364	−	0.996703i	$-0.525855\pi$
$62$	−2.00000			−0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.37228	−	2.37686i	−0.170211	−	0.294813i
$66$		0			0
$67$	−7.55842	+	13.0916i	−0.923408	+	1.59939i	−0.129307	+	0.991605i	$0.541275\pi$
$67$	−7.55842	+	13.0916i	−0.923408	+	1.59939i	−0.794101	+	0.607785i	$0.792058\pi$
$68$	2.18614	−	3.78651i	0.265108	−	0.459181i
$69$		0			0
$70$		0			0
$71$	−10.1168			−1.20065			−0.600324	−	0.799757i	$-0.704962\pi$
$71$	−10.1168			−1.20065			−0.600324	+	0.799757i	$0.704962\pi$
$72$		0			0
$73$	5.11684			0.598881			0.299441	−	0.954115i	$-0.403200\pi$
$73$	5.11684			0.598881			0.299441	+	0.954115i	$0.403200\pi$
$74$	−1.00000	−	1.73205i	−0.116248	−	0.201347i
$75$		0			0
$76$	2.50000	−	4.33013i	0.286770	−	0.496700i
$77$		0			0
$78$		0			0
$79$	−6.05842	−	10.4935i	−0.681626	−	1.18061i	−0.974485	−	0.224455i	$-0.927940\pi$
$79$	−6.05842	−	10.4935i	−0.681626	−	1.18061i	0.292859	−	0.956156i	$-0.405393\pi$
$80$	−1.37228			−0.153426
$81$		0			0
$82$	10.3723			1.14543
$83$	2.74456	+	4.75372i	0.301255	+	0.521789i	0.976420	−	0.215877i	$-0.0692612\pi$
$83$	2.74456	+	4.75372i	0.301255	+	0.521789i	−0.675166	+	0.737666i	$0.735928\pi$
$84$		0			0
$85$	−3.00000	+	5.19615i	−0.325396	+	0.563602i
$86$	−4.55842	+	7.89542i	−0.491547	+	0.851385i
$87$		0			0
$88$	2.18614	+	3.78651i	0.233043	+	0.403643i
$89$	3.25544			0.345076			0.172538	−	0.985003i	$-0.444803\pi$
$89$	3.25544			0.345076			0.172538	+	0.985003i	$0.444803\pi$
$90$		0			0
$91$		0			0
$92$	−3.68614	−	6.38458i	−0.384307	−	0.665639i
$93$		0			0
$94$		0			0
$95$	−3.43070	+	5.94215i	−0.351983	+	0.609652i
$96$		0			0
$97$	4.55842	+	7.89542i	0.462838	+	0.801658i	0.999101	−	0.0423924i	$-0.0134980\pi$
$97$	4.55842	+	7.89542i	0.462838	+	0.801658i	−0.536263	+	0.844051i	$0.680165\pi$
$98$		0			0
$99$		0			0
$100$	−3.11684			−0.311684
$101$	−3.68614	−	6.38458i	−0.366785	−	0.635290i	0.622276	−	0.782798i	$-0.286208\pi$
$101$	−3.68614	−	6.38458i	−0.366785	−	0.635290i	−0.989061	+	0.147508i	$0.952875\pi$
$102$		0			0
$103$	−5.00000	+	8.66025i	−0.492665	+	0.853320i	−0.999964	−	0.00844953i	$-0.997310\pi$
$103$	−5.00000	+	8.66025i	−0.492665	+	0.853320i	0.507300	+	0.861770i	$0.330644\pi$
$104$	1.00000	−	1.73205i	0.0980581	−	0.169842i
$105$		0			0
$106$	1.37228	+	2.37686i	0.133288	+	0.230861i
$107$	1.62772			0.157358			0.0786788	−	0.996900i	$-0.474930\pi$
$107$	1.62772			0.157358			0.0786788	+	0.996900i	$0.474930\pi$
$108$		0			0
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$	−3.00000	−	5.19615i	−0.286039	−	0.495434i
$111$		0			0
$112$		0			0
$113$	0.686141	−	1.18843i	0.0645467	−	0.111798i	−0.831946	−	0.554856i	$-0.812773\pi$
$113$	0.686141	−	1.18843i	0.0645467	−	0.111798i	0.896493	+	0.443058i	$0.146107\pi$
$114$		0			0
$115$	5.05842	+	8.76144i	0.471700	+	0.817009i
$116$	−2.74456			−0.254826
$117$		0			0
$118$	7.11684			0.655159
$119$		0			0
$120$		0			0
$121$	−4.05842	+	7.02939i	−0.368947	+	0.639036i
$122$	−7.05842	+	12.2255i	−0.639040	+	1.10685i
$123$		0			0
$124$	1.00000	+	1.73205i	0.0898027	+	0.155543i
$125$	11.1386			0.996266
$126$		0			0
$127$	−14.1168			−1.25267			−0.626334	−	0.779555i	$-0.715445\pi$
$127$	−14.1168			−1.25267			−0.626334	+	0.779555i	$0.715445\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−1.37228	+	2.37686i	−0.120357	+	0.208464i
$131$	3.68614	−	6.38458i	0.322060	−	0.557824i	−0.658853	−	0.752271i	$-0.728958\pi$
$131$	3.68614	−	6.38458i	0.322060	−	0.557824i	0.980913	+	0.194448i	$0.0622915\pi$
$132$		0			0
$133$		0			0
$134$	15.1168			1.30590
$135$		0			0
$136$	−4.37228			−0.374920
$137$	8.18614	+	14.1788i	0.699389	+	1.21138i	0.968678	+	0.248318i	$0.0798779\pi$
$137$	8.18614	+	14.1788i	0.699389	+	1.21138i	−0.269289	+	0.963059i	$0.586789\pi$
$138$		0			0
$139$	−10.6168	+	18.3889i	−0.900509	+	1.55973i	−0.0736742	+	0.997282i	$0.523472\pi$
$139$	−10.6168	+	18.3889i	−0.900509	+	1.55973i	−0.826835	+	0.562445i	$0.809861\pi$
$140$		0			0
$141$		0			0
$142$	5.05842	+	8.76144i	0.424493	+	0.735244i
$143$	8.74456			0.731257
$144$		0			0
$145$	3.76631			0.312775
$146$	−2.55842	−	4.43132i	−0.211737	−	0.366738i
$147$		0			0
$148$	−1.00000	+	1.73205i	−0.0821995	+	0.142374i
$149$	7.37228	−	12.7692i	0.603961	−	1.04609i	−0.388254	−	0.921552i	$-0.626922\pi$
$149$	7.37228	−	12.7692i	0.603961	−	1.04609i	0.992215	−	0.124538i	$-0.0397450\pi$
$150$		0			0
$151$	4.05842	+	7.02939i	0.330270	+	0.572044i	0.982565	−	0.185921i	$-0.0595270\pi$
$151$	4.05842	+	7.02939i	0.330270	+	0.572044i	−0.652295	+	0.757965i	$0.726194\pi$
$152$	−5.00000			−0.405554
$153$		0			0
$154$		0			0
$155$	−1.37228	−	2.37686i	−0.110224	−	0.190914i
$156$		0			0
$157$	−4.05842	+	7.02939i	−0.323897	+	0.561007i	−0.981289	−	0.192543i	$-0.938327\pi$
$157$	−4.05842	+	7.02939i	−0.323897	+	0.561007i	0.657391	+	0.753549i	$0.271660\pi$
$158$	−6.05842	+	10.4935i	−0.481982	+	0.834818i
$159$		0			0
$160$	0.686141	+	1.18843i	0.0542442	+	0.0939537i
$161$		0			0
$162$		0			0
$163$	16.2337			1.27152			0.635760	−	0.771887i	$-0.280687\pi$
$163$	16.2337			1.27152			0.635760	+	0.771887i	$0.280687\pi$
$164$	−5.18614	−	8.98266i	−0.404970	−	0.701428i
$165$		0			0
$166$	2.74456	−	4.75372i	0.213019	−	0.368960i
$167$	−8.74456	+	15.1460i	−0.676675	+	1.17203i	0.299302	+	0.954158i	$0.403246\pi$
$167$	−8.74456	+	15.1460i	−0.676675	+	1.17203i	−0.975976	+	0.217876i	$0.930087\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	6.00000			0.460179
$171$		0			0
$172$	9.11684			0.695153
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$		0			0
$175$		0			0
$176$	2.18614	−	3.78651i	0.164787	−	0.285419i
$177$		0			0
$178$	−1.62772	−	2.81929i	−0.122003	−	0.211315i
$179$	−14.7446			−1.10206			−0.551030	−	0.834485i	$-0.685765\pi$
$179$	−14.7446			−1.10206			−0.551030	+	0.834485i	$0.685765\pi$
$180$		0			0
$181$	−18.1168			−1.34661			−0.673307	−	0.739363i	$-0.735127\pi$
$181$	−18.1168			−1.34661			−0.673307	+	0.739363i	$0.735127\pi$
$182$		0			0
$183$		0			0
$184$	−3.68614	+	6.38458i	−0.271746	+	0.470678i
$185$	1.37228	−	2.37686i	0.100892	−	0.174750i
$186$		0			0
$187$	−9.55842	−	16.5557i	−0.698981	−	1.21067i
$188$		0			0
$189$		0			0
$190$	6.86141			0.497779
$191$	−0.941578	−	1.63086i	−0.0681302	−	0.118005i	0.829948	−	0.557841i	$-0.188370\pi$
$191$	−0.941578	−	1.63086i	−0.0681302	−	0.118005i	−0.898078	+	0.439836i	$0.855037\pi$
$192$		0			0
$193$	3.50000	−	6.06218i	0.251936	−	0.436365i	−0.712123	−	0.702055i	$-0.752266\pi$
$193$	3.50000	−	6.06218i	0.251936	−	0.436365i	0.964059	+	0.265689i	$0.0855996\pi$
$194$	4.55842	−	7.89542i	0.327276	−	0.566858i
$195$		0			0
$196$		0			0
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$	10.0000			0.708881			0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000			0.708881			0.354441	+	0.935079i	$0.384671\pi$
$200$	1.55842	+	2.69927i	0.110197	+	0.190867i
$201$		0			0
$202$	−3.68614	+	6.38458i	−0.259356	+	0.449218i
$203$		0			0
$204$		0			0
$205$	7.11684	+	12.3267i	0.497062	+	0.860937i
$206$	10.0000			0.696733
$207$		0			0
$208$	−2.00000			−0.138675
$209$	−10.9307	−	18.9325i	−0.756093	−	1.30959i
$210$		0			0
$211$	8.00000	−	13.8564i	0.550743	−	0.953914i	−0.447478	−	0.894295i	$-0.647678\pi$
$211$	8.00000	−	13.8564i	0.550743	−	0.953914i	0.998221	−	0.0596196i	$-0.0189888\pi$
$212$	1.37228	−	2.37686i	0.0942487	−	0.163243i
$213$		0			0
$214$	−0.813859	−	1.40965i	−0.0556343	−	0.0963614i
$215$	−12.5109			−0.853235
$216$		0			0
$217$		0			0
$218$	−7.00000	−	12.1244i	−0.474100	−	0.821165i
$219$		0			0
$220$	−3.00000	+	5.19615i	−0.202260	+	0.350325i
$221$	−4.37228	+	7.57301i	−0.294111	+	0.509416i
$222$		0			0
$223$	−2.00000	−	3.46410i	−0.133930	−	0.231973i	0.791258	−	0.611482i	$-0.209426\pi$
$223$	−2.00000	−	3.46410i	−0.133930	−	0.231973i	−0.925188	+	0.379509i	$0.876093\pi$
$224$		0			0
$225$		0			0
$226$	−1.37228			−0.0912828
$227$	11.8723	+	20.5634i	0.787991	+	1.36484i	0.927196	+	0.374577i	$0.122212\pi$
$227$	11.8723	+	20.5634i	0.787991	+	1.36484i	−0.139205	+	0.990264i	$0.544455\pi$
$228$		0			0
$229$	−10.0584	+	17.4217i	−0.664679	+	1.15126i	0.314693	+	0.949194i	$0.398098\pi$
$229$	−10.0584	+	17.4217i	−0.664679	+	1.15126i	−0.979372	+	0.202065i	$0.935235\pi$
$230$	5.05842	−	8.76144i	0.333542	−	0.577713i
$231$		0			0
$232$	1.37228	+	2.37686i	0.0900947	+	0.156049i
$233$	11.7446			0.769412			0.384706	−	0.923039i	$-0.374303\pi$
$233$	11.7446			0.769412			0.384706	+	0.923039i	$0.374303\pi$
$234$		0			0
$235$		0			0
$236$	−3.55842	−	6.16337i	−0.231634	−	0.401201i
$237$		0			0
$238$		0			0
$239$	−9.43070	+	16.3345i	−0.610021	+	1.05659i	0.381215	+	0.924487i	$0.375506\pi$
$239$	−9.43070	+	16.3345i	−0.610021	+	1.05659i	−0.991236	+	0.132102i	$0.957827\pi$
$240$		0			0
$241$	0.441578	+	0.764836i	0.0284445	+	0.0492674i	0.879897	−	0.475164i	$-0.157611\pi$
$241$	0.441578	+	0.764836i	0.0284445	+	0.0492674i	−0.851453	+	0.524431i	$0.824278\pi$
$242$	8.11684			0.521770
$243$		0			0
$244$	14.1168			0.903738
$245$		0			0
$246$		0			0
$247$	−5.00000	+	8.66025i	−0.318142	+	0.551039i
$248$	1.00000	−	1.73205i	0.0635001	−	0.109985i
$249$		0			0
$250$	−5.56930	−	9.64630i	−0.352233	−	0.610086i
$251$	−9.00000			−0.568075			−0.284037	−	0.958813i	$-0.591674\pi$
$251$	−9.00000			−0.568075			−0.284037	+	0.958813i	$0.591674\pi$
$252$		0			0
$253$	−32.2337			−2.02651
$254$	7.05842	+	12.2255i	0.442885	+	0.767099i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.9307	+	18.9325i	−0.681839	+	1.18098i	0.292581	+	0.956241i	$0.405486\pi$
$257$	−10.9307	+	18.9325i	−0.681839	+	1.18098i	−0.974419	+	0.224738i	$0.927847\pi$
$258$		0			0
$259$		0			0
$260$	2.74456			0.170211
$261$		0			0
$262$	−7.37228			−0.455461
$263$	6.68614	+	11.5807i	0.412285	+	0.714099i	0.995139	−	0.0984781i	$-0.0313974\pi$
$263$	6.68614	+	11.5807i	0.412285	+	0.714099i	−0.582854	+	0.812577i	$0.698064\pi$
$264$		0			0
$265$	−1.88316	+	3.26172i	−0.115681	+	0.200366i
$266$		0			0
$267$		0			0
$268$	−7.55842	−	13.0916i	−0.461704	−	0.799695i
$269$	−7.37228			−0.449496			−0.224748	−	0.974417i	$-0.572156\pi$
$269$	−7.37228			−0.449496			−0.224748	+	0.974417i	$0.572156\pi$
$270$		0			0
$271$	18.2337			1.10762			0.553809	−	0.832644i	$-0.313174\pi$
$271$	18.2337			1.10762			0.553809	+	0.832644i	$0.313174\pi$
$272$	2.18614	+	3.78651i	0.132554	+	0.229591i
$273$		0			0
$274$	8.18614	−	14.1788i	0.494543	−	0.856573i
$275$	−6.81386	+	11.8020i	−0.410891	+	0.711684i
$276$		0			0
$277$	−11.1168	−	19.2549i	−0.667946	−	1.15692i	−0.978477	−	0.206354i	$-0.933840\pi$
$277$	−11.1168	−	19.2549i	−0.667946	−	1.15692i	0.310531	−	0.950563i	$-0.399493\pi$
$278$	21.2337			1.27351
$279$		0			0
$280$		0			0
$281$	5.31386	+	9.20387i	0.316998	+	0.549057i	0.979860	−	0.199685i	$-0.0639917\pi$
$281$	5.31386	+	9.20387i	0.316998	+	0.549057i	−0.662862	+	0.748742i	$0.730658\pi$
$282$		0			0
$283$	4.94158	−	8.55906i	0.293746	−	0.508784i	−0.680946	−	0.732333i	$-0.738431\pi$
$283$	4.94158	−	8.55906i	0.293746	−	0.508784i	0.974692	+	0.223550i	$0.0717646\pi$
$284$	5.05842	−	8.76144i	0.300162	−	0.519896i
$285$		0			0
$286$	−4.37228	−	7.57301i	−0.258538	−	0.447802i
$287$		0			0
$288$		0			0
$289$	2.11684			0.124520
$290$	−1.88316	−	3.26172i	−0.110583	−	0.191535i
$291$		0			0
$292$	−2.55842	+	4.43132i	−0.149720	+	0.259323i
$293$	2.31386	−	4.00772i	0.135177	−	0.234134i	−0.790488	−	0.612478i	$-0.790173\pi$
$293$	2.31386	−	4.00772i	0.135177	−	0.234134i	0.925665	+	0.378344i	$0.123506\pi$
$294$		0			0
$295$	4.88316	+	8.45787i	0.284308	+	0.492436i
$296$	2.00000			0.116248
$297$		0			0
$298$	−14.7446			−0.854130
$299$	7.37228	+	12.7692i	0.426350	+	0.738460i
$300$		0			0
$301$		0			0
$302$	4.05842	−	7.02939i	0.233536	−	0.404496i
$303$		0			0
$304$	2.50000	+	4.33013i	0.143385	+	0.248350i
$305$	−19.3723			−1.10925
$306$		0			0
$307$	13.0000			0.741949			0.370975	−	0.928643i	$-0.379024\pi$
$307$	13.0000			0.741949			0.370975	+	0.928643i	$0.379024\pi$
$308$		0			0
$309$		0			0
$310$	−1.37228	+	2.37686i	−0.0779403	+	0.134997i
$311$	13.1168	−	22.7190i	0.743788	−	1.28828i	−0.206971	−	0.978347i	$-0.566361\pi$
$311$	13.1168	−	22.7190i	0.743788	−	1.28828i	0.950759	−	0.309931i	$-0.100306\pi$
$312$		0			0
$313$	−1.44158	−	2.49689i	−0.0814828	−	0.141132i	0.822404	−	0.568904i	$-0.192632\pi$
$313$	−1.44158	−	2.49689i	−0.0814828	−	0.141132i	−0.903887	+	0.427771i	$0.859299\pi$
$314$	8.11684			0.458060
$315$		0			0
$316$	12.1168			0.681626
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	0.769395	−	0.638774i	$-0.220558\pi$
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	−0.937892	+	0.346929i	$0.887225\pi$
$318$		0			0
$319$	−6.00000	+	10.3923i	−0.335936	+	0.581857i
$320$	0.686141	−	1.18843i	0.0383564	−	0.0664353i
$321$		0			0
$322$		0			0
$323$	21.8614			1.21640
$324$		0			0
$325$	6.23369			0.345783
$326$	−8.11684	−	14.0588i	−0.449550	−	0.778644i
$327$		0			0
$328$	−5.18614	+	8.98266i	−0.286357	+	0.495984i
$329$		0			0
$330$		0			0
$331$	6.11684	+	10.5947i	0.336212	+	0.582337i	0.983717	−	0.179725i	$-0.0575207\pi$
$331$	6.11684	+	10.5947i	0.336212	+	0.582337i	−0.647505	+	0.762061i	$0.724187\pi$
$332$	−5.48913			−0.301255
$333$		0			0
$334$	17.4891			0.956962
$335$	10.3723	+	17.9653i	0.566698	+	0.981550i
$336$		0			0
$337$	−4.55842	+	7.89542i	−0.248313	+	0.430091i	−0.963058	−	0.269294i	$-0.913210\pi$
$337$	−4.55842	+	7.89542i	−0.248313	+	0.430091i	0.714745	+	0.699385i	$0.246543\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$		0			0
$340$	−3.00000	−	5.19615i	−0.162698	−	0.281801i
$341$	8.74456			0.473545
$342$		0			0
$343$		0			0
$344$	−4.55842	−	7.89542i	−0.245774	−	0.425692i
$345$		0			0
$346$	3.00000	−	5.19615i	0.161281	−	0.279347i
$347$	3.55842	−	6.16337i	0.191026	−	0.330867i	−0.754564	−	0.656226i	$-0.772152\pi$
$347$	3.55842	−	6.16337i	0.191026	−	0.330867i	0.945591	+	0.325359i	$0.105485\pi$
$348$		0			0
$349$	−11.0000	−	19.0526i	−0.588817	−	1.01986i	−0.994388	−	0.105797i	$-0.966261\pi$
$349$	−11.0000	−	19.0526i	−0.588817	−	1.01986i	0.405571	−	0.914063i	$-0.367073\pi$
$350$		0			0
$351$		0			0
$352$	−4.37228			−0.233043
$353$	3.81386	+	6.60580i	0.202991	+	0.351591i	0.949491	−	0.313795i	$-0.101600\pi$
$353$	3.81386	+	6.60580i	0.202991	+	0.351591i	−0.746500	+	0.665386i	$0.768267\pi$
$354$		0			0
$355$	−6.94158	+	12.0232i	−0.368421	+	0.638123i
$356$	−1.62772	+	2.81929i	−0.0862689	+	0.149422i
$357$		0			0
$358$	7.37228	+	12.7692i	0.389637	+	0.674871i
$359$	6.86141			0.362131			0.181066	−	0.983471i	$-0.442045\pi$
$359$	6.86141			0.362131			0.181066	+	0.983471i	$0.442045\pi$
$360$		0			0
$361$	6.00000			0.315789
$362$	9.05842	+	15.6896i	0.476100	+	0.824630i
$363$		0			0
$364$		0			0
$365$	3.51087	−	6.08101i	0.183768	−	0.318295i
$366$		0			0
$367$	11.1168	+	19.2549i	0.580295	+	1.00510i	0.995444	+	0.0953465i	$0.0303959\pi$
$367$	11.1168	+	19.2549i	0.580295	+	1.00510i	−0.415150	+	0.909753i	$0.636271\pi$
$368$	7.37228			0.384307
$369$		0			0
$370$	−2.74456			−0.142683
$371$		0			0
$372$		0			0
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	−0.707055	−	0.707159i	$-0.749977\pi$
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	0.965945	+	0.258748i	$0.0833099\pi$
$374$	−9.55842	+	16.5557i	−0.494254	+	0.856073i
$375$		0			0
$376$		0			0
$377$	5.48913			0.282704
$378$		0			0
$379$	9.11684			0.468301			0.234150	−	0.972200i	$-0.424769\pi$
$379$	9.11684			0.468301			0.234150	+	0.972200i	$0.424769\pi$
$380$	−3.43070	−	5.94215i	−0.175991	−	0.304826i
$381$		0			0
$382$	−0.941578	+	1.63086i	−0.0481753	+	0.0834421i
$383$	10.6277	−	18.4077i	0.543051	−	0.940592i	−0.455676	−	0.890146i	$-0.650602\pi$
$383$	10.6277	−	18.4077i	0.543051	−	0.940592i	0.998727	−	0.0504462i	$-0.0160643\pi$
$384$		0			0
$385$		0			0
$386$	−7.00000			−0.356291
$387$		0			0
$388$	−9.11684			−0.462838
$389$	−17.4891	−	30.2921i	−0.886734	−	1.53587i	−0.843713	−	0.536794i	$-0.819635\pi$
$389$	−17.4891	−	30.2921i	−0.886734	−	1.53587i	−0.0430204	−	0.999074i	$-0.513698\pi$
$390$		0			0
$391$	16.1168	−	27.9152i	0.815064	−	1.41173i
$392$		0			0
$393$		0			0
$394$	−3.00000	−	5.19615i	−0.151138	−	0.261778i
$395$	−16.6277			−0.836631
$396$		0			0
$397$	22.0000			1.10415			0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000			1.10415			0.552074	+	0.833795i	$0.313837\pi$
$398$	−5.00000	−	8.66025i	−0.250627	−	0.434099i
$399$		0			0
$400$	1.55842	−	2.69927i	0.0779211	−	0.134963i
$401$	−0.127719	+	0.221215i	−0.00637797	+	0.0110470i	−0.869197	−	0.494466i	$-0.835364\pi$
$401$	−0.127719	+	0.221215i	−0.00637797	+	0.0110470i	0.862819	+	0.505513i	$0.168697\pi$
$402$		0			0
$403$	−2.00000	−	3.46410i	−0.0996271	−	0.172559i
$404$	7.37228			0.366785
$405$		0			0
$406$		0			0
$407$	4.37228	+	7.57301i	0.216726	+	0.375380i
$408$		0			0
$409$	14.6753	−	25.4183i	0.725645	−	1.25685i	−0.233063	−	0.972462i	$-0.574875\pi$
$409$	14.6753	−	25.4183i	0.725645	−	1.25685i	0.958708	−	0.284393i	$-0.0917919\pi$
$410$	7.11684	−	12.3267i	0.351476	−	0.608774i
$411$		0			0
$412$	−5.00000	−	8.66025i	−0.246332	−	0.426660i
$413$		0			0
$414$		0			0
$415$	7.53262			0.369762
$416$	1.00000	+	1.73205i	0.0490290	+	0.0849208i
$417$		0			0
$418$	−10.9307	+	18.9325i	−0.534638	+	0.926020i
$419$	−13.8030	+	23.9075i	−0.674320	+	1.16796i	0.302347	+	0.953198i	$0.402230\pi$
$419$	−13.8030	+	23.9075i	−0.674320	+	1.16796i	−0.976667	+	0.214759i	$0.931104\pi$
$420$		0			0
$421$	0.116844	+	0.202380i	0.00569463	+	0.00986338i	0.868859	−	0.495060i	$-0.164854\pi$
$421$	0.116844	+	0.202380i	0.00569463	+	0.00986338i	−0.863164	+	0.504924i	$0.831521\pi$
$422$	−16.0000			−0.778868
$423$		0			0
$424$	−2.74456			−0.133288
$425$	−6.81386	−	11.8020i	−0.330521	−	0.572479i
$426$		0			0
$427$		0			0
$428$	−0.813859	+	1.40965i	−0.0393394	+	0.0681378i
$429$		0			0
$430$	6.25544	+	10.8347i	0.301664	+	0.522497i
$431$	29.4891			1.42044			0.710221	−	0.703979i	$-0.248595\pi$
$431$	29.4891			1.42044			0.710221	+	0.703979i	$0.248595\pi$
$432$		0			0
$433$	2.88316			0.138556			0.0692778	−	0.997597i	$-0.477931\pi$
$433$	2.88316			0.138556			0.0692778	+	0.997597i	$0.477931\pi$
$434$		0			0
$435$		0			0
$436$	−7.00000	+	12.1244i	−0.335239	+	0.580651i
$437$	18.4307	−	31.9229i	0.881660	−	1.52708i
$438$		0			0
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	0.945552	−	0.325471i	$-0.105523\pi$
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	−0.754642	+	0.656136i	$0.772190\pi$
$440$	6.00000			0.286039
$441$		0			0
$442$	8.74456			0.415936
$443$	−11.4416	−	19.8174i	−0.543606	−	0.941553i	−0.998693	−	0.0511061i	$-0.983725\pi$
$443$	−11.4416	−	19.8174i	−0.543606	−	0.941553i	0.455087	−	0.890447i	$-0.349608\pi$
$444$		0			0
$445$	2.23369	−	3.86886i	0.105887	−	0.183402i
$446$	−2.00000	+	3.46410i	−0.0947027	+	0.164030i
$447$		0			0
$448$		0			0
$449$	−33.0000			−1.55737			−0.778683	−	0.627417i	$-0.784112\pi$
$449$	−33.0000			−1.55737			−0.778683	+	0.627417i	$0.784112\pi$
$450$		0			0
$451$	−45.3505			−2.13547
$452$	0.686141	+	1.18843i	0.0322733	+	0.0558991i
$453$		0			0
$454$	11.8723	−	20.5634i	0.557194	−	0.965088i
$455$		0			0
$456$		0			0
$457$	−16.7337	−	28.9836i	−0.782769	−	1.35580i	−0.930323	−	0.366742i	$-0.880473\pi$
$457$	−16.7337	−	28.9836i	−0.782769	−	1.35580i	0.147554	−	0.989054i	$-0.452860\pi$
$458$	20.1168			0.939998
$459$		0			0
$460$	−10.1168			−0.471700
$461$	−15.4307	−	26.7268i	−0.718680	−	1.24479i	−0.961523	−	0.274724i	$-0.911414\pi$
$461$	−15.4307	−	26.7268i	−0.718680	−	1.24479i	0.242844	−	0.970065i	$-0.421920\pi$
$462$		0			0
$463$	2.94158	−	5.09496i	0.136707	−	0.236783i	−0.789541	−	0.613697i	$-0.789682\pi$
$463$	2.94158	−	5.09496i	0.136707	−	0.236783i	0.926248	+	0.376914i	$0.123015\pi$
$464$	1.37228	−	2.37686i	0.0637066	−	0.110343i
$465$		0			0
$466$	−5.87228	−	10.1711i	−0.272028	−	0.471167i
$467$	−30.0951			−1.39263			−0.696317	−	0.717734i	$-0.745179\pi$
$467$	−30.0951			−1.39263			−0.696317	+	0.717734i	$0.745179\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−3.55842	+	6.16337i	−0.163790	+	0.283692i
$473$	19.9307	−	34.5210i	0.916415	−	1.58728i
$474$		0			0
$475$	−7.79211	−	13.4963i	−0.357527	−	0.619254i
$476$		0			0
$477$		0			0
$478$	18.8614			0.862701
$479$	−10.6277	−	18.4077i	−0.485593	−	0.841072i	0.514270	−	0.857628i	$-0.328063\pi$
$479$	−10.6277	−	18.4077i	−0.485593	−	0.841072i	−0.999863	+	0.0165568i	$0.994730\pi$
$480$		0			0
$481$	2.00000	−	3.46410i	0.0911922	−	0.157949i
$482$	0.441578	−	0.764836i	0.0201133	−	0.0348373i
$483$		0			0
$484$	−4.05842	−	7.02939i	−0.184474	−	0.319518i
$485$	12.5109			0.568090
$486$		0			0
$487$	−16.3505			−0.740913			−0.370457	−	0.928850i	$-0.620799\pi$
$487$	−16.3505			−0.740913			−0.370457	+	0.928850i	$0.620799\pi$
$488$	−7.05842	−	12.2255i	−0.319520	−	0.553424i
$489$		0			0
$490$		0			0
$491$	−9.81386	+	16.9981i	−0.442893	+	0.767114i	−0.997903	−	0.0647303i	$-0.979381\pi$
$491$	−9.81386	+	16.9981i	−0.442893	+	0.767114i	0.555010	+	0.831844i	$0.312715\pi$
$492$		0			0
$493$	−6.00000	−	10.3923i	−0.270226	−	0.468046i
$494$	10.0000			0.449921
$495$		0			0
$496$	−2.00000			−0.0898027
$497$		0			0
$498$		0			0
$499$	−0.441578	+	0.764836i	−0.0197677	+	0.0342387i	−0.875740	−	0.482783i	$-0.839626\pi$
$499$	−0.441578	+	0.764836i	−0.0197677	+	0.0342387i	0.855972	+	0.517022i	$0.172959\pi$
$500$	−5.56930	+	9.64630i	−0.249067	+	0.431396i
$501$		0			0
$502$	4.50000	+	7.79423i	0.200845	+	0.347873i
$503$	2.23369			0.0995952			0.0497976	−	0.998759i	$-0.484142\pi$
$503$	2.23369			0.0995952			0.0497976	+	0.998759i	$0.484142\pi$
$504$		0			0
$505$	−10.1168			−0.450194
$506$	16.1168	+	27.9152i	0.716481	+	1.24098i
$507$		0			0
$508$	7.05842	−	12.2255i	0.313167	−	0.542421i
$509$	−8.48913	+	14.7036i	−0.376274	+	0.651725i	−0.990517	−	0.137392i	$-0.956128\pi$
$509$	−8.48913	+	14.7036i	−0.376274	+	0.651725i	0.614243	+	0.789117i	$0.289461\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	21.8614			0.964265
$515$	6.86141	+	11.8843i	0.302350	+	0.523685i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−1.37228	−	2.37686i	−0.0601785	−	0.104232i
$521$	3.86141			0.169171			0.0845856	−	0.996416i	$-0.473043\pi$
$521$	3.86141			0.169171			0.0845856	+	0.996416i	$0.473043\pi$
$522$		0			0
$523$	17.8832			0.781976			0.390988	−	0.920396i	$-0.372133\pi$
$523$	17.8832			0.781976			0.390988	+	0.920396i	$0.372133\pi$
$524$	3.68614	+	6.38458i	0.161030	+	0.278912i
$525$		0			0
$526$	6.68614	−	11.5807i	0.291530	−	0.504944i
$527$	−4.37228	+	7.57301i	−0.190460	+	0.329886i
$528$		0			0
$529$	−15.6753	−	27.1504i	−0.681533	−	1.18045i
$530$	3.76631			0.163598
$531$		0			0
$532$		0			0
$533$	10.3723	+	17.9653i	0.449273	+	0.778164i
$534$		0			0
$535$	1.11684	−	1.93443i	0.0482854	−	0.0836327i
$536$	−7.55842	+	13.0916i	−0.326474	+	0.565470i
$537$		0			0
$538$	3.68614	+	6.38458i	0.158921	+	0.275259i
$539$		0			0
$540$		0			0
$541$	28.2337			1.21386			0.606931	−	0.794755i	$-0.292401\pi$
$541$	28.2337			1.21386			0.606931	+	0.794755i	$0.292401\pi$
$542$	−9.11684	−	15.7908i	−0.391602	−	0.678275i
$543$		0			0
$544$	2.18614	−	3.78651i	0.0937300	−	0.162345i
$545$	9.60597	−	16.6380i	0.411475	−	0.712695i
$546$		0			0
$547$	−0.441578	−	0.764836i	−0.0188805	−	0.0327020i	0.856431	−	0.516262i	$-0.172677\pi$
$547$	−0.441578	−	0.764836i	−0.0188805	−	0.0327020i	−0.875311	+	0.483560i	$0.839344\pi$
$548$	−16.3723			−0.699389
$549$		0			0
$550$	13.6277			0.581088
$551$	−6.86141	−	11.8843i	−0.292306	−	0.506288i
$552$		0			0
$553$		0			0
$554$	−11.1168	+	19.2549i	−0.472309	+	0.818064i
$555$		0			0
$556$	−10.6168	−	18.3889i	−0.450254	−	0.779864i
$557$	−6.51087			−0.275875			−0.137937	−	0.990441i	$-0.544047\pi$
$557$	−6.51087			−0.275875			−0.137937	+	0.990441i	$0.544047\pi$
$558$		0			0
$559$	−18.2337			−0.771203
$560$		0			0
$561$		0			0
$562$	5.31386	−	9.20387i	0.224152	−	0.388242i
$563$	−1.50000	+	2.59808i	−0.0632175	+	0.109496i	−0.895902	−	0.444252i	$-0.853470\pi$
$563$	−1.50000	+	2.59808i	−0.0632175	+	0.109496i	0.832684	+	0.553748i	$0.186803\pi$
$564$		0			0
$565$	−0.941578	−	1.63086i	−0.0396125	−	0.0686108i
$566$	−9.88316			−0.415420
$567$		0			0
$568$	−10.1168			−0.424493
$569$	−0.558422	−	0.967215i	−0.0234103	−	0.0405478i	0.854083	−	0.520137i	$-0.174119\pi$
$569$	−0.558422	−	0.967215i	−0.0234103	−	0.0405478i	−0.877493	+	0.479589i	$0.840786\pi$
$570$		0			0
$571$	−14.6753	+	25.4183i	−0.614141	+	1.06372i	0.376394	+	0.926460i	$0.377164\pi$
$571$	−14.6753	+	25.4183i	−0.614141	+	1.06372i	−0.990535	+	0.137263i	$0.956169\pi$
$572$	−4.37228	+	7.57301i	−0.182814	+	0.316644i
$573$		0			0
$574$		0			0
$575$	−22.9783			−0.958259
$576$		0			0
$577$	−27.1168			−1.12889			−0.564444	−	0.825471i	$-0.690910\pi$
$577$	−27.1168			−1.12889			−0.564444	+	0.825471i	$0.690910\pi$
$578$	−1.05842	−	1.83324i	−0.0440246	−	0.0762528i
$579$		0			0
$580$	−1.88316	+	3.26172i	−0.0781938	+	0.135436i
$581$		0			0
$582$		0			0
$583$	−6.00000	−	10.3923i	−0.248495	−	0.430405i
$584$	5.11684			0.211737
$585$		0			0
$586$	−4.62772			−0.191169
$587$	4.24456	+	7.35180i	0.175192	+	0.303441i	0.940228	−	0.340547i	$-0.110612\pi$
$587$	4.24456	+	7.35180i	0.175192	+	0.303441i	−0.765036	+	0.643988i	$0.777279\pi$
$588$		0			0
$589$	−5.00000	+	8.66025i	−0.206021	+	0.356840i
$590$	4.88316	−	8.45787i	0.201036	−	0.348205i
$591$		0			0
$592$	−1.00000	−	1.73205i	−0.0410997	−	0.0711868i
$593$	3.25544			0.133685			0.0668424	−	0.997764i	$-0.478708\pi$
$593$	3.25544			0.133685			0.0668424	+	0.997764i	$0.478708\pi$
$594$		0			0
$595$		0			0
$596$	7.37228	+	12.7692i	0.301980	+	0.523045i
$597$		0			0
$598$	7.37228	−	12.7692i	0.301475	−	0.522170i
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	−0.509631	−	0.860393i	$-0.670218\pi$
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	0.999938	+	0.0111569i	$0.00355143\pi$
$600$		0			0
$601$	3.44158	+	5.96099i	0.140385	+	0.243154i	0.927642	−	0.373472i	$-0.121833\pi$
$601$	3.44158	+	5.96099i	0.140385	+	0.243154i	−0.787257	+	0.616625i	$0.788499\pi$
$602$		0			0
$603$		0			0
$604$	−8.11684			−0.330270
$605$	5.56930	+	9.64630i	0.226424	+	0.392178i
$606$		0			0
$607$	−6.11684	+	10.5947i	−0.248275	+	0.430025i	−0.963047	−	0.269332i	$-0.913197\pi$
$607$	−6.11684	+	10.5947i	−0.248275	+	0.430025i	0.714772	+	0.699357i	$0.246530\pi$
$608$	2.50000	−	4.33013i	0.101388	−	0.175610i
$609$		0			0
$610$	9.68614	+	16.7769i	0.392180	+	0.679276i
$611$		0			0
$612$		0			0
$613$	−1.76631			−0.0713407			−0.0356703	−	0.999364i	$-0.511357\pi$
$613$	−1.76631			−0.0713407			−0.0356703	+	0.999364i	$0.511357\pi$
$614$	−6.50000	−	11.2583i	−0.262319	−	0.454349i
$615$		0			0
$616$		0			0
$617$	−4.93070	+	8.54023i	−0.198503	+	0.343817i	−0.948043	−	0.318142i	$-0.896941\pi$
$617$	−4.93070	+	8.54023i	−0.198503	+	0.343817i	0.749540	+	0.661959i	$0.230275\pi$
$618$		0			0
$619$	−11.7337	−	20.3233i	−0.471617	−	0.816864i	0.527856	−	0.849334i	$-0.322996\pi$
$619$	−11.7337	−	20.3233i	−0.471617	−	0.816864i	−0.999473	+	0.0324697i	$0.989663\pi$
$620$	2.74456			0.110224
$621$		0			0
$622$	−26.2337			−1.05188
$623$		0			0
$624$		0			0
$625$	−0.149468	+	0.258886i	−0.00597872	+	0.0103555i
$626$	−1.44158	+	2.49689i	−0.0576170	+	0.0997956i
$627$		0			0
$628$	−4.05842	−	7.02939i	−0.161949	−	0.280503i
$629$	−8.74456			−0.348669
$630$		0			0
$631$	14.3505			0.571286			0.285643	−	0.958336i	$-0.407793\pi$
$631$	14.3505			0.571286			0.285643	+	0.958336i	$0.407793\pi$
$632$	−6.05842	−	10.4935i	−0.240991	−	0.417409i
$633$		0			0
$634$	−3.00000	+	5.19615i	−0.119145	+	0.206366i
$635$	−9.68614	+	16.7769i	−0.384383	+	0.665770i
$636$		0			0
$637$		0			0
$638$	12.0000			0.475085
$639$		0			0
$640$	−1.37228			−0.0542442
$641$	−23.1060	−	40.0207i	−0.912631	−	1.58072i	−0.810333	−	0.585969i	$-0.800714\pi$
$641$	−23.1060	−	40.0207i	−0.912631	−	1.58072i	−0.102298	−	0.994754i	$-0.532619\pi$
$642$		0			0
$643$	−12.6753	+	21.9542i	−0.499864	+	0.865789i	−1.00000		0.000157386i	$-0.999950\pi$
$643$	−12.6753	+	21.9542i	−0.499864	+	0.865789i	0.500136	+	0.865947i	$0.333283\pi$
$644$		0			0
$645$		0			0
$646$	−10.9307	−	18.9325i	−0.430063	−	0.744891i
$647$	−17.4891			−0.687568			−0.343784	−	0.939049i	$-0.611709\pi$
$647$	−17.4891			−0.687568			−0.343784	+	0.939049i	$0.611709\pi$
$648$		0			0
$649$	−31.1168			−1.22144
$650$	−3.11684	−	5.39853i	−0.122253	−	0.211748i
$651$		0			0
$652$	−8.11684	+	14.0588i	−0.317880	+	0.550585i
$653$	−7.62772	+	13.2116i	−0.298496	+	0.517010i	−0.975792	−	0.218701i	$-0.929818\pi$
$653$	−7.62772	+	13.2116i	−0.298496	+	0.517010i	0.677296	+	0.735710i	$0.263152\pi$
$654$		0			0
$655$	−5.05842	−	8.76144i	−0.197649	−	0.342338i
$656$	10.3723			0.404970
$657$		0			0
$658$		0			0
$659$	−4.62772	−	8.01544i	−0.180270	−	0.312237i	0.761702	−	0.647927i	$-0.224364\pi$
$659$	−4.62772	−	8.01544i	−0.180270	−	0.312237i	−0.941973	+	0.335690i	$0.891031\pi$
$660$		0			0
$661$	4.94158	−	8.55906i	0.192205	−	0.332909i	−0.753776	−	0.657132i	$-0.771769\pi$
$661$	4.94158	−	8.55906i	0.192205	−	0.332909i	0.945981	+	0.324223i	$0.105103\pi$
$662$	6.11684	−	10.5947i	0.237738	−	0.411774i
$663$		0			0
$664$	2.74456	+	4.75372i	0.106510	+	0.184480i
$665$		0			0
$666$		0			0
$667$	−20.2337			−0.783452
$668$	−8.74456	−	15.1460i	−0.338337	−	0.586017i
$669$		0			0
$670$	10.3723	−	17.9653i	0.400716	−	0.694061i
$671$	30.8614	−	53.4535i	1.19139	−	2.06355i
$672$		0			0
$673$	10.0584	+	17.4217i	0.387724	+	0.671557i	0.992143	−	0.125109i	$-0.0399281\pi$
$673$	10.0584	+	17.4217i	0.387724	+	0.671557i	−0.604419	+	0.796666i	$0.706595\pi$
$674$	9.11684			0.351168
$675$		0			0
$676$	−9.00000			−0.346154
$677$	17.2337	+	29.8496i	0.662344	+	1.14721i	0.979998	+	0.199007i	$0.0637718\pi$
$677$	17.2337	+	29.8496i	0.662344	+	1.14721i	−0.317654	+	0.948207i	$0.602895\pi$
$678$		0			0
$679$		0			0
$680$	−3.00000	+	5.19615i	−0.115045	+	0.199263i
$681$		0			0
$682$	−4.37228	−	7.57301i	−0.167423	−	0.289986i
$683$	44.8397			1.71574			0.857871	−	0.513865i	$-0.171787\pi$
$683$	44.8397			1.71574			0.857871	+	0.513865i	$0.171787\pi$
$684$		0			0
$685$	22.4674			0.858434
$686$		0			0
$687$		0			0
$688$	−4.55842	+	7.89542i	−0.173788	+	0.301010i
$689$	−2.74456	+	4.75372i	−0.104560	+	0.181102i
$690$		0			0
$691$	−2.94158	−	5.09496i	−0.111903	−	0.193822i	0.804635	−	0.593770i	$-0.202361\pi$
$691$	−2.94158	−	5.09496i	−0.111903	−	0.193822i	−0.916537	+	0.399949i	$0.869028\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−7.11684			−0.270152
$695$	14.5693	+	25.2348i	0.552645	+	0.957209i
$696$		0			0
$697$	22.6753	−	39.2747i	0.858887	−	1.48764i
$698$	−11.0000	+	19.0526i	−0.416356	+	0.721150i
$699$		0			0
$700$		0			0
$701$	3.76631			0.142252			0.0711258	−	0.997467i	$-0.477341\pi$
$701$	3.76631			0.142252			0.0711258	+	0.997467i	$0.477341\pi$
$702$		0			0
$703$	−10.0000			−0.377157
$704$	2.18614	+	3.78651i	0.0823933	+	0.142709i
$705$		0			0
$706$	3.81386	−	6.60580i	0.143536	−	0.248612i
$707$		0			0
$708$		0			0
$709$	−22.0000	−	38.1051i	−0.826227	−	1.43107i	−0.900978	−	0.433865i	$-0.857149\pi$
$709$	−22.0000	−	38.1051i	−0.826227	−	1.43107i	0.0747503	−	0.997202i	$-0.476184\pi$
$710$	13.8832			0.521026
$711$		0			0
$712$	3.25544			0.122003
$713$	7.37228	+	12.7692i	0.276094	+	0.478209i
$714$		0			0
$715$	6.00000	−	10.3923i	0.224387	−	0.388650i
$716$	7.37228	−	12.7692i	0.275515	−	0.477206i
$717$		0			0
$718$	−3.43070	−	5.94215i	−0.128033	−	0.221759i
$719$	−8.74456			−0.326117			−0.163059	−	0.986616i	$-0.552136\pi$
$719$	−8.74456			−0.326117			−0.163059	+	0.986616i	$0.552136\pi$
$720$		0			0
$721$		0			0
$722$	−3.00000	−	5.19615i	−0.111648	−	0.193381i
$723$		0			0
$724$	9.05842	−	15.6896i	0.336654	−	0.583101i
$725$	−4.27719	+	7.40830i	−0.158851	+	0.275138i
$726$		0			0
$727$	−0.883156	−	1.52967i	−0.0327544	−	0.0567324i	0.849183	−	0.528098i	$-0.177095\pi$
$727$	−0.883156	−	1.52967i	−0.0327544	−	0.0567324i	−0.881938	+	0.471366i	$0.843761\pi$
$728$		0			0
$729$		0			0
$730$	−7.02175			−0.259887
$731$	19.9307	+	34.5210i	0.737164	+	1.27680i
$732$		0			0
$733$	−11.9416	+	20.6834i	−0.441072	+	0.763960i	−0.997769	−	0.0667560i	$-0.978735\pi$
$733$	−11.9416	+	20.6834i	−0.441072	+	0.763960i	0.556697	+	0.830716i	$0.312068\pi$
$734$	11.1168	−	19.2549i	0.410330	−	0.710713i
$735$		0			0
$736$	−3.68614	−	6.38458i	−0.135873	−	0.235339i
$737$	−66.0951			−2.43464
$738$		0			0
$739$	9.11684			0.335369			0.167684	−	0.985841i	$-0.446371\pi$
$739$	9.11684			0.335369			0.167684	+	0.985841i	$0.446371\pi$
$740$	1.37228	+	2.37686i	0.0504461	+	0.0873751i
$741$		0			0
$742$		0			0
$743$	21.8614	−	37.8651i	0.802017	−	1.38913i	−0.116269	−	0.993218i	$-0.537094\pi$
$743$	21.8614	−	37.8651i	0.802017	−	1.38913i	0.918286	−	0.395917i	$-0.129573\pi$
$744$		0			0
$745$	−10.1168	−	17.5229i	−0.370652	−	0.641989i
$746$	−10.0000			−0.366126
$747$		0			0
$748$	19.1168			0.698981
$749$		0			0
$750$		0			0
$751$	−0.0584220	+	0.101190i	−0.00213185	+	0.00369247i	−0.867089	−	0.498153i	$-0.834012\pi$
$751$	−0.0584220	+	0.101190i	−0.00213185	+	0.00369247i	0.864958	+	0.501845i	$0.167345\pi$
$752$		0			0
$753$		0			0
$754$	−2.74456	−	4.75372i	−0.0999511	−	0.173120i
$755$	11.1386			0.405375
$756$		0			0
$757$	11.7663			0.427654			0.213827	−	0.976872i	$-0.431407\pi$
$757$	11.7663			0.427654			0.213827	+	0.976872i	$0.431407\pi$
$758$	−4.55842	−	7.89542i	−0.165569	−	0.286775i
$759$		0			0
$760$	−3.43070	+	5.94215i	−0.124445	+	0.215545i
$761$	−6.25544	+	10.8347i	−0.226759	+	0.392759i	−0.956846	−	0.290596i	$-0.906146\pi$
$761$	−6.25544	+	10.8347i	−0.226759	+	0.392759i	0.730086	+	0.683355i	$0.239480\pi$
$762$		0			0
$763$		0			0
$764$	1.88316			0.0681302
$765$		0			0
$766$	−21.2554			−0.767990
$767$	7.11684	+	12.3267i	0.256974	+	0.445093i
$768$		0			0
$769$	−5.00000	+	8.66025i	−0.180305	+	0.312297i	−0.941984	−	0.335657i	$-0.891042\pi$
$769$	−5.00000	+	8.66025i	−0.180305	+	0.312297i	0.761680	+	0.647954i	$0.224375\pi$
$770$		0			0
$771$		0			0
$772$	3.50000	+	6.06218i	0.125968	+	0.218183i
$773$	−11.1386			−0.400627			−0.200314	−	0.979732i	$-0.564196\pi$
$773$	−11.1386			−0.400627			−0.200314	+	0.979732i	$0.564196\pi$
$774$		0			0
$775$	6.23369			0.223921
$776$	4.55842	+	7.89542i	0.163638	+	0.283429i
$777$		0			0
$778$	−17.4891	+	30.2921i	−0.627016	+	1.08602i
$779$	25.9307	−	44.9133i	0.929064	−	1.60919i
$780$		0			0
$781$	−22.1168	−	38.3075i	−0.791403	−	1.37075i
$782$	−32.2337			−1.15267
$783$		0			0
$784$		0			0
$785$	5.56930	+	9.64630i	0.198777	+	0.344291i
$786$		0			0
$787$	−2.00000	+	3.46410i	−0.0712923	+	0.123482i	−0.899468	−	0.436987i	$-0.856046\pi$
$787$	−2.00000	+	3.46410i	−0.0712923	+	0.123482i	0.828176	+	0.560469i	$0.189379\pi$
$788$	−3.00000	+	5.19615i	−0.106871	+	0.185105i
$789$		0			0
$790$	8.31386	+	14.4000i	0.295794	+	0.512330i
$791$		0			0
$792$		0			0
$793$	−28.2337			−1.00261
$794$	−11.0000	−	19.0526i	−0.390375	−	0.676150i
$795$		0			0
$796$	−5.00000	+	8.66025i	−0.177220	+	0.306955i
$797$	18.4307	−	31.9229i	0.652849	−	1.13077i	−0.329579	−	0.944128i	$-0.606907\pi$
$797$	18.4307	−	31.9229i	0.652849	−	1.13077i	0.982428	−	0.186640i	$-0.0597597\pi$
$798$		0			0
$799$		0			0
$800$	−3.11684			−0.110197
$801$		0			0
$802$	0.255437			0.00901981
$803$	11.1861	+	19.3750i	0.394750	+	0.683728i
$804$		0			0
$805$		0			0
$806$	−2.00000	+	3.46410i	−0.0704470	+	0.122018i
$807$		0			0
$808$	−3.68614	−	6.38458i	−0.129678	−	0.224609i
$809$	−21.8614			−0.768606			−0.384303	−	0.923207i	$-0.625558\pi$
$809$	−21.8614			−0.768606			−0.384303	+	0.923207i	$0.625558\pi$
$810$		0			0
$811$	−24.8832			−0.873766			−0.436883	−	0.899518i	$-0.643918\pi$
$811$	−24.8832			−0.873766			−0.436883	+	0.899518i	$0.643918\pi$
$812$		0			0
$813$		0			0
$814$	4.37228	−	7.57301i	0.153248	−	0.265434i
$815$	11.1386	−	19.2926i	0.390168	−	0.675791i
$816$		0			0
$817$	22.7921	+	39.4771i	0.797395	+	1.38113i
$818$	−29.3505			−1.02622
$819$		0			0
$820$	−14.2337			−0.497062
$821$	−19.1168	−	33.1113i	−0.667182	−	1.15559i	−0.978689	−	0.205350i	$-0.934167\pi$
$821$	−19.1168	−	33.1113i	−0.667182	−	1.15559i	0.311506	−	0.950244i	$-0.399167\pi$
$822$		0			0
$823$	−11.1168	+	19.2549i	−0.387509	+	0.671185i	−0.992114	−	0.125341i	$-0.959998\pi$
$823$	−11.1168	+	19.2549i	−0.387509	+	0.671185i	0.604605	+	0.796525i	$0.293331\pi$
$824$	−5.00000	+	8.66025i	−0.174183	+	0.301694i
$825$		0			0
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		0			0
$829$	48.2337			1.67523			0.837613	−	0.546265i	$-0.183951\pi$
$829$	48.2337			1.67523			0.837613	+	0.546265i	$0.183951\pi$
$830$	−3.76631	−	6.52344i	−0.130731	−	0.226432i
$831$		0			0
$832$	1.00000	−	1.73205i	0.0346688	−	0.0600481i
$833$		0			0
$834$		0			0
$835$	12.0000	+	20.7846i	0.415277	+	0.719281i
$836$	21.8614			0.756093
$837$		0			0
$838$	27.6060			0.953632
$839$	8.74456	+	15.1460i	0.301896	+	0.522899i	0.976565	−	0.215221i	$-0.0690472\pi$
$839$	8.74456	+	15.1460i	0.301896	+	0.522899i	−0.674670	+	0.738120i	$0.735714\pi$
$840$		0			0
$841$	10.7337	−	18.5913i	0.370127	−	0.641079i
$842$	0.116844	−	0.202380i	0.00402671	−	0.00697446i
$843$		0			0
$844$	8.00000	+	13.8564i	0.275371	+	0.476957i
$845$	12.3505			0.424871
$846$		0			0
$847$		0			0
$848$	1.37228	+	2.37686i	0.0471243	+	0.0816217i
$849$		0			0
$850$	−6.81386	+	11.8020i	−0.233713	+	0.404804i
$851$	−7.37228	+	12.7692i	−0.252719	+	0.437721i
$852$		0			0
$853$	−8.94158	−	15.4873i	−0.306154	−	0.530274i	0.671364	−	0.741128i	$-0.265709\pi$
$853$	−8.94158	−	15.4873i	−0.306154	−	0.530274i	−0.977518	+	0.210854i	$0.932376\pi$
$854$		0			0
$855$		0			0
$856$	1.62772			0.0556343
$857$	−25.9783	−	44.9956i	−0.887400	−	1.53702i	−0.842938	−	0.538011i	$-0.819176\pi$
$857$	−25.9783	−	44.9956i	−0.887400	−	1.53702i	−0.0444624	−	0.999011i	$-0.514157\pi$
$858$		0			0
$859$	25.5584	−	44.2685i	0.872042	−	1.51042i	0.0121615	−	0.999926i	$-0.496129\pi$
$859$	25.5584	−	44.2685i	0.872042	−	1.51042i	0.859881	−	0.510495i	$-0.170538\pi$
$860$	6.25544	−	10.8347i	0.213309	−	0.369461i
$861$		0			0
$862$	−14.7446	−	25.5383i	−0.502202	−	0.869839i
$863$	18.8614			0.642050			0.321025	−	0.947071i	$-0.395973\pi$
$863$	18.8614			0.642050			0.321025	+	0.947071i	$0.395973\pi$
$864$		0			0
$865$	8.23369			0.279954
$866$	−1.44158	−	2.49689i	−0.0489868	−	0.0848477i
$867$		0			0
$868$		0			0
$869$	26.4891	−	45.8805i	0.898582	−	1.55639i
$870$		0			0
$871$	15.1168	+	26.1831i	0.512215	+	0.887182i
$872$	14.0000			0.474100
$873$		0			0
$874$	−36.8614			−1.24686
$875$		0			0
$876$		0			0
$877$	−22.3505	+	38.7123i	−0.754724	+	1.30722i	0.190788	+	0.981631i	$0.438896\pi$
$877$	−22.3505	+	38.7123i	−0.754724	+	1.30722i	−0.945512	+	0.325589i	$0.894438\pi$
$878$	4.00000	−	6.92820i	0.134993	−	0.233816i
$879$		0			0
$880$	−3.00000	−	5.19615i	−0.101130	−	0.175162i
$881$	14.2337			0.479545			0.239773	−	0.970829i	$-0.422927\pi$
$881$	14.2337			0.479545			0.239773	+	0.970829i	$0.422927\pi$
$882$		0			0
$883$	11.3505			0.381976			0.190988	−	0.981592i	$-0.438831\pi$
$883$	11.3505			0.381976			0.190988	+	0.981592i	$0.438831\pi$
$884$	−4.37228	−	7.57301i	−0.147056	−	0.254708i
$885$		0			0
$886$	−11.4416	+	19.8174i	−0.384387	+	0.665778i
$887$	15.8614	−	27.4728i	0.532574	−	0.922445i	−0.466703	−	0.884414i	$-0.654558\pi$
$887$	15.8614	−	27.4728i	0.532574	−	0.922445i	0.999277	−	0.0380308i	$-0.0121085\pi$
$888$		0			0
$889$		0			0
$890$	−4.46738			−0.149747
$891$		0			0
$892$	4.00000			0.133930
$893$		0			0
$894$		0			0
$895$	−10.1168	+	17.5229i	−0.338169	+	0.585726i
$896$		0			0
$897$		0			0
$898$	16.5000	+	28.5788i	0.550612	+	0.953688i
$899$	5.48913			0.183073
$900$		0			0
$901$	12.0000			0.399778
$902$	22.6753	+	39.2747i	0.755004	+	1.30770i
$903$		0			0
$904$	0.686141	−	1.18843i	0.0228207	−	0.0395266i
$905$	−12.4307	+	21.5306i	−0.413211	+	0.715702i
$906$		0			0
$907$	4.44158	+	7.69304i	0.147480	+	0.255443i	0.930296	−	0.366811i	$-0.119550\pi$
$907$	4.44158	+	7.69304i	0.147480	+	0.255443i	−0.782815	+	0.622254i	$0.786217\pi$
$908$	−23.7446			−0.787991
$909$		0			0
$910$		0			0
$911$	−21.6861	−	37.5615i	−0.718494	−	1.24447i	−0.961596	−	0.274467i	$-0.911498\pi$
$911$	−21.6861	−	37.5615i	−0.718494	−	1.24447i	0.243103	−	0.970001i	$-0.421835\pi$
$912$		0			0
$913$	−12.0000	+	20.7846i	−0.397142	+	0.687870i
$914$	−16.7337	+	28.9836i	−0.553501	+	0.958692i
$915$		0			0
$916$	−10.0584	−	17.4217i	−0.332340	−	0.575629i
$917$		0			0
$918$		0			0
$919$	−29.8832			−0.985754			−0.492877	−	0.870099i	$-0.664055\pi$
$919$	−29.8832			−0.985754			−0.492877	+	0.870099i	$0.664055\pi$
$920$	5.05842	+	8.76144i	0.166771	+	0.288856i
$921$		0			0
$922$	−15.4307	+	26.7268i	−0.508183	+	0.880199i
$923$	−10.1168	+	17.5229i	−0.333000	+	0.576773i
$924$		0			0
$925$	3.11684	+	5.39853i	0.102481	+	0.177503i
$926$	−5.88316			−0.193333
$927$		0			0
$928$	−2.74456			−0.0900947
$929$	−4.88316	−	8.45787i	−0.160211	−	0.277494i	0.774733	−	0.632288i	$-0.217884\pi$
$929$	−4.88316	−	8.45787i	−0.160211	−	0.277494i	−0.934944	+	0.354794i	$0.884551\pi$
$930$		0			0
$931$		0			0
$932$	−5.87228	+	10.1711i	−0.192353	+	0.333165i
$933$		0			0
$934$	15.0475	+	26.0631i	0.492371	+	0.852811i
$935$	−26.2337			−0.857933
$936$		0			0
$937$	38.4674			1.25667			0.628337	−	0.777941i	$-0.283736\pi$
$937$	38.4674			1.25667			0.628337	+	0.777941i	$0.283736\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.941578	+	1.63086i	−0.0306946	+	0.0531645i	−0.880965	−	0.473182i	$-0.843105\pi$
$941$	−0.941578	+	1.63086i	−0.0306946	+	0.0531645i	0.850270	+	0.526347i	$0.176439\pi$
$942$		0			0
$943$	−38.2337	−	66.2227i	−1.24506	−	2.15651i
$944$	7.11684			0.231634
$945$		0			0
$946$	−39.8614			−1.29601
$947$	8.44158	+	14.6212i	0.274314	+	0.475127i	0.969962	−	0.243257i	$-0.0782158\pi$
$947$	8.44158	+	14.6212i	0.274314	+	0.475127i	−0.695648	+	0.718383i	$0.744882\pi$
$948$		0			0
$949$	5.11684	−	8.86263i	0.166100	−	0.287693i
$950$	−7.79211	+	13.4963i	−0.252809	+	0.437879i
$951$		0			0
$952$		0			0
$953$	−10.8832			−0.352540			−0.176270	−	0.984342i	$-0.556403\pi$
$953$	−10.8832			−0.352540			−0.176270	+	0.984342i	$0.556403\pi$
$954$		0			0
$955$	−2.58422			−0.0836234
$956$	−9.43070	−	16.3345i	−0.305011	−	0.528294i
$957$		0			0
$958$	−10.6277	+	18.4077i	−0.343366	+	0.594727i
$959$		0			0
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$	−4.00000			−0.128965
$963$		0			0
$964$	−0.883156			−0.0284445
$965$	−4.80298	−	8.31901i	−0.154614	−	0.267799i
$966$		0			0
$967$	−24.0584	+	41.6704i	−0.773667	+	1.34003i	0.161874	+	0.986811i	$0.448246\pi$
$967$	−24.0584	+	41.6704i	−0.773667	+	1.34003i	−0.935541	+	0.353219i	$0.885087\pi$
$968$	−4.05842	+	7.02939i	−0.130443	+	0.225933i
$969$		0			0
$970$	−6.25544	−	10.8347i	−0.200850	−	0.347882i
$971$	7.37228			0.236588			0.118294	−	0.992979i	$-0.462258\pi$
$971$	7.37228			0.236588			0.118294	+	0.992979i	$0.462258\pi$
$972$		0			0
$973$		0			0
$974$	8.17527	+	14.1600i	0.261952	+	0.453715i
$975$		0			0
$976$	−7.05842	+	12.2255i	−0.225935	+	0.391330i
$977$	11.4416	−	19.8174i	0.366049	−	0.634015i	−0.622895	−	0.782305i	$-0.714044\pi$
$977$	11.4416	−	19.8174i	0.366049	−	0.634015i	0.988944	+	0.148291i	$0.0473771\pi$
$978$		0			0
$979$	7.11684	+	12.3267i	0.227455	+	0.393964i
$980$		0			0
$981$		0			0
$982$	19.6277			0.626346
$983$	25.3723	+	43.9461i	0.809250	+	1.40166i	0.913384	+	0.407099i	$0.133460\pi$
$983$	25.3723	+	43.9461i	0.809250	+	1.40166i	−0.104134	+	0.994563i	$0.533207\pi$
$984$		0			0
$985$	4.11684	−	7.13058i	0.131174	−	0.227199i
$986$	−6.00000	+	10.3923i	−0.191079	+	0.330958i
$987$		0			0
$988$	−5.00000	−	8.66025i	−0.159071	−	0.275519i
$989$	67.2119			2.13722
$990$		0			0
$991$	−20.4674			−0.650168			−0.325084	−	0.945685i	$-0.605393\pi$
$991$	−20.4674			−0.650168			−0.325084	+	0.945685i	$0.605393\pi$
$992$	1.00000	+	1.73205i	0.0317500	+	0.0549927i
$993$		0			0
$994$		0			0
$995$	6.86141	−	11.8843i	0.217521	−	0.376758i
$996$		0			0
$997$	6.05842	+	10.4935i	0.191872	+	0.332332i	0.945871	−	0.324544i	$-0.105211\pi$
$997$	6.05842	+	10.4935i	0.191872	+	0.332332i	−0.753999	+	0.656876i	$0.771877\pi$
$998$	0.883156			0.0279558
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.f.j.1765.2		4
3.2	odd	2		882.2.f.k.589.1		4
7.2	even	3		2646.2.h.l.361.1		4
7.3	odd	6		2646.2.e.n.1549.1		4
7.4	even	3		2646.2.e.m.1549.2		4
7.5	odd	6		2646.2.h.k.361.2		4
7.6	odd	2		378.2.f.c.253.1		4
9.2	odd	6		882.2.f.k.295.1		4
9.4	even	3		7938.2.a.bs.1.1		2
9.5	odd	6		7938.2.a.bh.1.2		2
9.7	even	3	inner	2646.2.f.j.883.2		4
21.2	odd	6		882.2.h.n.67.2		4
21.5	even	6		882.2.h.m.67.1		4
21.11	odd	6		882.2.e.k.373.2		4
21.17	even	6		882.2.e.l.373.1		4
21.20	even	2		126.2.f.d.85.2	yes	4
28.27	even	2		3024.2.r.f.1009.1		4
63.2	odd	6		882.2.e.k.655.1		4
63.11	odd	6		882.2.h.n.79.2		4
63.13	odd	6		1134.2.a.n.1.2		2
63.16	even	3		2646.2.e.m.2125.2		4
63.20	even	6		126.2.f.d.43.2	✓	4
63.25	even	3		2646.2.h.l.667.1		4
63.34	odd	6		378.2.f.c.127.1		4
63.38	even	6		882.2.h.m.79.1		4
63.41	even	6		1134.2.a.k.1.1		2
63.47	even	6		882.2.e.l.655.2		4
63.52	odd	6		2646.2.h.k.667.2		4
63.61	odd	6		2646.2.e.n.2125.1		4
84.83	odd	2		1008.2.r.f.337.1		4
252.83	odd	6		1008.2.r.f.673.1		4
252.139	even	6		9072.2.a.bb.1.2		2
252.167	odd	6		9072.2.a.bm.1.1		2
252.223	even	6		3024.2.r.f.2017.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.d.43.2	✓	4	63.20	even	6
126.2.f.d.85.2	yes	4	21.20	even	2
378.2.f.c.127.1		4	63.34	odd	6
378.2.f.c.253.1		4	7.6	odd	2
882.2.e.k.373.2		4	21.11	odd	6
882.2.e.k.655.1		4	63.2	odd	6
882.2.e.l.373.1		4	21.17	even	6
882.2.e.l.655.2		4	63.47	even	6
882.2.f.k.295.1		4	9.2	odd	6
882.2.f.k.589.1		4	3.2	odd	2
882.2.h.m.67.1		4	21.5	even	6
882.2.h.m.79.1		4	63.38	even	6
882.2.h.n.67.2		4	21.2	odd	6
882.2.h.n.79.2		4	63.11	odd	6
1008.2.r.f.337.1		4	84.83	odd	2
1008.2.r.f.673.1		4	252.83	odd	6
1134.2.a.k.1.1		2	63.41	even	6
1134.2.a.n.1.2		2	63.13	odd	6
2646.2.e.m.1549.2		4	7.4	even	3
2646.2.e.m.2125.2		4	63.16	even	3
2646.2.e.n.1549.1		4	7.3	odd	6
2646.2.e.n.2125.1		4	63.61	odd	6
2646.2.f.j.883.2		4	9.7	even	3	inner
2646.2.f.j.1765.2		4	1.1	even	1	trivial
2646.2.h.k.361.2		4	7.5	odd	6
2646.2.h.k.667.2		4	63.52	odd	6
2646.2.h.l.361.1		4	7.2	even	3
2646.2.h.l.667.1		4	63.25	even	3
3024.2.r.f.1009.1		4	28.27	even	2
3024.2.r.f.2017.1		4	252.223	even	6
7938.2.a.bh.1.2		2	9.5	odd	6
7938.2.a.bs.1.1		2	9.4	even	3
9072.2.a.bb.1.2		2	252.139	even	6
9072.2.a.bm.1.1		2	252.167	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.686141 - 1.18843i) q^{5} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.686141 - 1.18843i) q^{5} +1.00000 q^{8} -1.37228 q^{10} +(2.18614 + 3.78651i) q^{11} +(1.00000 - 1.73205i) q^{13} +(-0.500000 - 0.866025i) q^{16} -4.37228 q^{17} -5.00000 q^{19} +(0.686141 + 1.18843i) q^{20} +(2.18614 - 3.78651i) q^{22} +(-3.68614 + 6.38458i) q^{23} +(1.55842 + 2.69927i) q^{25} -2.00000 q^{26} +(1.37228 + 2.37686i) q^{29} +(1.00000 - 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.18614 + 3.78651i) q^{34} +2.00000 q^{37} +(2.50000 + 4.33013i) q^{38} +(0.686141 - 1.18843i) q^{40} +(-5.18614 + 8.98266i) q^{41} +(-4.55842 - 7.89542i) q^{43} -4.37228 q^{44} +7.37228 q^{46} +(1.55842 - 2.69927i) q^{50} +(1.00000 + 1.73205i) q^{52} -2.74456 q^{53} +6.00000 q^{55} +(1.37228 - 2.37686i) q^{58} +(-3.55842 + 6.16337i) q^{59} +(-7.05842 - 12.2255i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(-1.37228 - 2.37686i) q^{65} +(-7.55842 + 13.0916i) q^{67} +(2.18614 - 3.78651i) q^{68} -10.1168 q^{71} +5.11684 q^{73} +(-1.00000 - 1.73205i) q^{74} +(2.50000 - 4.33013i) q^{76} +(-6.05842 - 10.4935i) q^{79} -1.37228 q^{80} +10.3723 q^{82} +(2.74456 + 4.75372i) q^{83} +(-3.00000 + 5.19615i) q^{85} +(-4.55842 + 7.89542i) q^{86} +(2.18614 + 3.78651i) q^{88} +3.25544 q^{89} +(-3.68614 - 6.38458i) q^{92} +(-3.43070 + 5.94215i) q^{95} +(4.55842 + 7.89542i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} - 3 q^{5} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 - 3 * q^5 + 4 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} - 3 q^{5} + 4 q^{8} + 6 q^{10} + 3 q^{11} + 4 q^{13} - 2 q^{16} - 6 q^{17} - 20 q^{19} - 3 q^{20} + 3 q^{22} - 9 q^{23} - 11 q^{25} - 8 q^{26} - 6 q^{29} + 4 q^{31} - 2 q^{32} + 3 q^{34} + 8 q^{37} + 10 q^{38} - 3 q^{40} - 15 q^{41} - q^{43} - 6 q^{44} + 18 q^{46} - 11 q^{50} + 4 q^{52} + 12 q^{53} + 24 q^{55} - 6 q^{58} + 3 q^{59} - 11 q^{61} - 8 q^{62} + 4 q^{64} + 6 q^{65} - 13 q^{67} + 3 q^{68} - 6 q^{71} - 14 q^{73} - 4 q^{74} + 10 q^{76} - 7 q^{79} + 6 q^{80} + 30 q^{82} - 12 q^{83} - 12 q^{85} - q^{86} + 3 q^{88} + 36 q^{89} - 9 q^{92} + 15 q^{95} + q^{97}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 - 3 * q^5 + 4 * q^8 + 6 * q^10 + 3 * q^11 + 4 * q^13 - 2 * q^16 - 6 * q^17 - 20 * q^19 - 3 * q^20 + 3 * q^22 - 9 * q^23 - 11 * q^25 - 8 * q^26 - 6 * q^29 + 4 * q^31 - 2 * q^32 + 3 * q^34 + 8 * q^37 + 10 * q^38 - 3 * q^40 - 15 * q^41 - q^43 - 6 * q^44 + 18 * q^46 - 11 * q^50 + 4 * q^52 + 12 * q^53 + 24 * q^55 - 6 * q^58 + 3 * q^59 - 11 * q^61 - 8 * q^62 + 4 * q^64 + 6 * q^65 - 13 * q^67 + 3 * q^68 - 6 * q^71 - 14 * q^73 - 4 * q^74 + 10 * q^76 - 7 * q^79 + 6 * q^80 + 30 * q^82 - 12 * q^83 - 12 * q^85 - q^86 + 3 * q^88 + 36 * q^89 - 9 * q^92 + 15 * q^95 + q^97

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