LMFDB - Embedded newform 2646.2.e.n.1549.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(1549,2646)]

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([2, 2]))

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

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

chi := DirichletCharacter("2646.1549");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.e (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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1549.1
Root			$-1.18614 - 1.26217i$ of defining polynomial
Character	$\chi$	$=$	2646.1549
Dual form			2646.2.e.n.2125.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(-0.686141 - 1.18843i) q^{5} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.686141 - 1.18843i) q^{5} +1.00000 q^{8} +(-0.686141 - 1.18843i) q^{10} +(2.18614 - 3.78651i) q^{11} +(-1.00000 + 1.73205i) q^{13} +1.00000 q^{16} +(-2.18614 - 3.78651i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(-0.686141 - 1.18843i) q^{20} +(2.18614 - 3.78651i) q^{22} +(-3.68614 - 6.38458i) q^{23} +(1.55842 - 2.69927i) q^{25} +(-1.00000 + 1.73205i) q^{26} +(1.37228 + 2.37686i) q^{29} +2.00000 q^{31} +1.00000 q^{32} +(-2.18614 - 3.78651i) q^{34} +(-1.00000 + 1.73205i) q^{37} +(-2.50000 + 4.33013i) q^{38} +(-0.686141 - 1.18843i) q^{40} +(5.18614 - 8.98266i) q^{41} +(-4.55842 - 7.89542i) q^{43} +(2.18614 - 3.78651i) q^{44} +(-3.68614 - 6.38458i) q^{46} +(1.55842 - 2.69927i) q^{50} +(-1.00000 + 1.73205i) q^{52} +(1.37228 + 2.37686i) q^{53} -6.00000 q^{55} +(1.37228 + 2.37686i) q^{58} -7.11684 q^{59} -14.1168 q^{61} +2.00000 q^{62} +1.00000 q^{64} +2.74456 q^{65} +15.1168 q^{67} +(-2.18614 - 3.78651i) q^{68} -10.1168 q^{71} +(2.55842 + 4.43132i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(-2.50000 + 4.33013i) q^{76} +12.1168 q^{79} +(-0.686141 - 1.18843i) q^{80} +(5.18614 - 8.98266i) q^{82} +(-2.74456 - 4.75372i) q^{83} +(-3.00000 + 5.19615i) q^{85} +(-4.55842 - 7.89542i) q^{86} +(2.18614 - 3.78651i) q^{88} +(1.62772 - 2.81929i) q^{89} +(-3.68614 - 6.38458i) q^{92} +6.86141 q^{95} +(-4.55842 - 7.89542i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{4} + 3 q^{5} + 4 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^4 + 3 * q^5 + 4 * q^8	$ 4 q + 4 q^{2} + 4 q^{4} + 3 q^{5} + 4 q^{8} + 3 q^{10} + 3 q^{11} - 4 q^{13} + 4 q^{16} - 3 q^{17} - 10 q^{19} + 3 q^{20} + 3 q^{22} - 9 q^{23} - 11 q^{25} - 4 q^{26} - 6 q^{29} + 8 q^{31} + 4 q^{32} - 3 q^{34} - 4 q^{37} - 10 q^{38} + 3 q^{40} + 15 q^{41} - q^{43} + 3 q^{44} - 9 q^{46} - 11 q^{50} - 4 q^{52} - 6 q^{53} - 24 q^{55} - 6 q^{58} + 6 q^{59} - 22 q^{61} + 8 q^{62} + 4 q^{64} - 12 q^{65} + 26 q^{67} - 3 q^{68} - 6 q^{71} - 7 q^{73} - 4 q^{74} - 10 q^{76} + 14 q^{79} + 3 q^{80} + 15 q^{82} + 12 q^{83} - 12 q^{85} - q^{86} + 3 q^{88} + 18 q^{89} - 9 q^{92} - 30 q^{95} - q^{97}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^4 + 3 * q^5 + 4 * q^8 + 3 * q^10 + 3 * q^11 - 4 * q^13 + 4 * q^16 - 3 * q^17 - 10 * q^19 + 3 * q^20 + 3 * q^22 - 9 * q^23 - 11 * q^25 - 4 * q^26 - 6 * q^29 + 8 * q^31 + 4 * q^32 - 3 * q^34 - 4 * q^37 - 10 * q^38 + 3 * q^40 + 15 * q^41 - q^43 + 3 * q^44 - 9 * q^46 - 11 * q^50 - 4 * q^52 - 6 * q^53 - 24 * q^55 - 6 * q^58 + 6 * q^59 - 22 * q^61 + 8 * q^62 + 4 * q^64 - 12 * q^65 + 26 * q^67 - 3 * q^68 - 6 * q^71 - 7 * q^73 - 4 * q^74 - 10 * q^76 + 14 * q^79 + 3 * q^80 + 15 * q^82 + 12 * q^83 - 12 * q^85 - q^86 + 3 * q^88 + 18 * q^89 - 9 * q^92 - 30 * q^95 - q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−0.686141	−	1.18843i	−0.306851	−	0.531482i	0.670820	−	0.741620i	$-0.265942\pi$
$5$	−0.686141	−	1.18843i	−0.306851	−	0.531482i	−0.977672	+	0.210138i	$0.932609\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.686141	−	1.18843i	−0.216977	−	0.375815i
$11$	2.18614	−	3.78651i	0.659146	−	1.14167i	−0.321691	−	0.946845i	$-0.604251\pi$
$11$	2.18614	−	3.78651i	0.659146	−	1.14167i	0.980837	−	0.194830i	$-0.0624155\pi$
$12$		0			0
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$	−2.18614	−	3.78651i	−0.530217	−	0.918363i	−0.999379	−	0.0352504i	$-0.988777\pi$
$17$	−2.18614	−	3.78651i	−0.530217	−	0.918363i	0.469162	−	0.883112i	$-0.344556\pi$
$18$		0			0
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	0.422659	+	0.906289i	$0.361097\pi$
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	−0.996199	+	0.0871106i	$0.972237\pi$
$20$	−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	−0.938315	−	0.345782i	$-0.887614\pi$
$23$	−3.68614	−	6.38458i	−0.768613	−	1.33128i	0.169701	−	0.985496i	$-0.445720\pi$
$24$		0			0
$25$	1.55842	−	2.69927i	0.311684	−	0.539853i
$26$	−1.00000	+	1.73205i	−0.196116	+	0.339683i
$27$		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
$31$	2.00000			0.359211			0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000			0.359211			0.179605	+	0.983739i	$0.442518\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−2.18614	−	3.78651i	−0.374920	−	0.649381i
$35$		0			0
$36$		0			0
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$	−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	$-0.532833\pi$
$41$	5.18614	−	8.98266i	0.809939	−	1.40286i	0.912906	−	0.408171i	$-0.133833\pi$
$42$		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	$-0.411330\pi$
$44$	2.18614	−	3.78651i	0.329573	−	0.570837i
$45$		0			0
$46$	−3.68614	−	6.38458i	−0.543492	−	0.941355i
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		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
$53$	1.37228	+	2.37686i	0.188497	+	0.326487i	0.944749	−	0.327793i	$-0.106305\pi$
$53$	1.37228	+	2.37686i	0.188497	+	0.326487i	−0.756252	+	0.654280i	$0.772972\pi$
$54$		0			0
$55$	−6.00000			−0.809040
$56$		0			0
$57$		0			0
$58$	1.37228	+	2.37686i	0.180189	+	0.312097i
$59$	−7.11684			−0.926534			−0.463267	−	0.886219i	$-0.653323\pi$
$59$	−7.11684			−0.926534			−0.463267	+	0.886219i	$0.653323\pi$
$60$		0			0
$61$	−14.1168			−1.80748			−0.903738	−	0.428085i	$-0.859188\pi$
$61$	−14.1168			−1.80748			−0.903738	+	0.428085i	$0.859188\pi$
$62$	2.00000			0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	2.74456			0.340421
$66$		0			0
$67$	15.1168			1.84682			0.923408	−	0.383819i	$-0.125391\pi$
$67$	15.1168			1.84682			0.923408	+	0.383819i	$0.125391\pi$
$68$	−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
$73$	2.55842	+	4.43132i	0.299441	+	0.518646i	0.976008	−	0.217734i	$-0.0698666\pi$
$73$	2.55842	+	4.43132i	0.299441	+	0.518646i	−0.676567	+	0.736381i	$0.736533\pi$
$74$	−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
$79$	12.1168			1.36325			0.681626	−	0.731701i	$-0.261273\pi$
$79$	12.1168			1.36325			0.681626	+	0.731701i	$0.261273\pi$
$80$	−0.686141	−	1.18843i	−0.0767129	−	0.132871i
$81$		0			0
$82$	5.18614	−	8.98266i	0.572713	−	0.991969i
$83$	−2.74456	−	4.75372i	−0.301255	−	0.521789i	0.675166	−	0.737666i	$-0.264072\pi$
$83$	−2.74456	−	4.75372i	−0.301255	−	0.521789i	−0.976420	+	0.215877i	$0.930739\pi$
$84$		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
$89$	1.62772	−	2.81929i	0.172538	−	0.298844i	−0.766769	−	0.641924i	$-0.778137\pi$
$89$	1.62772	−	2.81929i	0.172538	−	0.298844i	0.939306	+	0.343079i	$0.111470\pi$
$90$		0			0
$91$		0			0
$92$	−3.68614	−	6.38458i	−0.384307	−	0.665639i
$93$		0			0
$94$		0			0
$95$	6.86141			0.703965
$96$		0			0
$97$	−4.55842	−	7.89542i	−0.462838	−	0.801658i	0.536263	−	0.844051i	$-0.319835\pi$
$97$	−4.55842	−	7.89542i	−0.462838	−	0.801658i	−0.999101	+	0.0423924i	$0.986502\pi$
$98$		0			0
$99$		0			0
$100$	1.55842	−	2.69927i	0.155842	−	0.269927i
$101$	3.68614	−	6.38458i	0.366785	−	0.635290i	−0.622276	−	0.782798i	$-0.713792\pi$
$101$	3.68614	−	6.38458i	0.366785	−	0.635290i	0.989061	+	0.147508i	$0.0471252\pi$
$102$		0			0
$103$	5.00000	+	8.66025i	0.492665	+	0.853320i	0.999964	−	0.00844953i	$-0.00268960\pi$
$103$	5.00000	+	8.66025i	0.492665	+	0.853320i	−0.507300	+	0.861770i	$0.669356\pi$
$104$	−1.00000	+	1.73205i	−0.0980581	+	0.169842i
$105$		0			0
$106$	1.37228	+	2.37686i	0.133288	+	0.230861i
$107$	−0.813859	+	1.40965i	−0.0786788	+	0.136276i	−0.902680	−	0.430312i	$-0.858403\pi$
$107$	−0.813859	+	1.40965i	−0.0786788	+	0.136276i	0.824001	+	0.566588i	$0.191737\pi$
$108$		0			0
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	−0.977769	−	0.209687i	$-0.932756\pi$
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	0.307290	−	0.951616i	$-0.400578\pi$
$110$	−6.00000			−0.572078
$111$		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
$116$	1.37228	+	2.37686i	0.127413	+	0.220686i
$117$		0			0
$118$	−7.11684			−0.655159
$119$		0			0
$120$		0			0
$121$	−4.05842	−	7.02939i	−0.368947	−	0.639036i
$122$	−14.1168			−1.27808
$123$		0			0
$124$	2.00000			0.179605
$125$	−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	$0.715445\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	2.74456			0.240714
$131$	−3.68614	−	6.38458i	−0.322060	−	0.557824i	0.658853	−	0.752271i	$-0.271042\pi$
$131$	−3.68614	−	6.38458i	−0.322060	−	0.557824i	−0.980913	+	0.194448i	$0.937708\pi$
$132$		0			0
$133$		0			0
$134$	15.1168			1.30590
$135$		0			0
$136$	−2.18614	−	3.78651i	−0.187460	−	0.324690i
$137$	8.18614	−	14.1788i	0.699389	−	1.21138i	−0.269289	−	0.963059i	$-0.586789\pi$
$137$	8.18614	−	14.1788i	0.699389	−	1.21138i	0.968678	−	0.248318i	$-0.0798779\pi$
$138$		0			0
$139$	10.6168	−	18.3889i	0.900509	−	1.55973i	0.0736742	−	0.997282i	$-0.476528\pi$
$139$	10.6168	−	18.3889i	0.900509	−	1.55973i	0.826835	−	0.562445i	$-0.190139\pi$
$140$		0			0
$141$		0			0
$142$	−10.1168			−0.848987
$143$	4.37228	+	7.57301i	0.365629	+	0.633287i
$144$		0			0
$145$	1.88316	−	3.26172i	0.156388	−	0.270871i
$146$	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	0.992215	+	0.124538i	$0.0397450\pi$
$149$	7.37228	+	12.7692i	0.603961	+	1.04609i	−0.388254	+	0.921552i	$0.626922\pi$
$150$		0			0
$151$	4.05842	−	7.02939i	0.330270	−	0.572044i	−0.652295	−	0.757965i	$-0.726194\pi$
$151$	4.05842	−	7.02939i	0.330270	−	0.572044i	0.982565	+	0.185921i	$0.0595270\pi$
$152$	−2.50000	+	4.33013i	−0.202777	+	0.351220i
$153$		0			0
$154$		0			0
$155$	−1.37228	−	2.37686i	−0.110224	−	0.190914i
$156$		0			0
$157$	−8.11684			−0.647795			−0.323897	−	0.946092i	$-0.604993\pi$
$157$	−8.11684			−0.647795			−0.323897	+	0.946092i	$0.604993\pi$
$158$	12.1168			0.963964
$159$		0			0
$160$	−0.686141	−	1.18843i	−0.0542442	−	0.0939537i
$161$		0			0
$162$		0			0
$163$	−8.11684	+	14.0588i	−0.635760	+	1.10117i	0.350593	+	0.936528i	$0.385980\pi$
$163$	−8.11684	+	14.0588i	−0.635760	+	1.10117i	−0.986354	+	0.164641i	$0.947353\pi$
$164$	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	$-0.596754\pi$
$167$	8.74456	−	15.1460i	0.676675	−	1.17203i	0.975976	−	0.217876i	$-0.0699129\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	−3.00000	+	5.19615i	−0.230089	+	0.398527i
$171$		0			0
$172$	−4.55842	−	7.89542i	−0.347576	−	0.602020i
$173$	6.00000			0.456172			0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000			0.456172			0.228086	+	0.973641i	$0.426753\pi$
$174$		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
$179$	7.37228	+	12.7692i	0.551030	+	0.954412i	0.998201	+	0.0599635i	$0.0190984\pi$
$179$	7.37228	+	12.7692i	0.551030	+	0.954412i	−0.447170	+	0.894449i	$0.647568\pi$
$180$		0			0
$181$	18.1168			1.34661			0.673307	−	0.739363i	$-0.264873\pi$
$181$	18.1168			1.34661			0.673307	+	0.739363i	$0.264873\pi$
$182$		0			0
$183$		0			0
$184$	−3.68614	−	6.38458i	−0.271746	−	0.470678i
$185$	2.74456			0.201784
$186$		0			0
$187$	−19.1168			−1.39796
$188$		0			0
$189$		0			0
$190$	6.86141			0.497779
$191$	1.88316			0.136260			0.0681302	−	0.997676i	$-0.478297\pi$
$191$	1.88316			0.136260			0.0681302	+	0.997676i	$0.478297\pi$
$192$		0			0
$193$	−7.00000			−0.503871			−0.251936	−	0.967744i	$-0.581067\pi$
$193$	−7.00000			−0.503871			−0.251936	+	0.967744i	$0.581067\pi$
$194$	−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
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	0.987022	−	0.160585i	$-0.0513380\pi$
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	−0.632581	+	0.774494i	$0.718005\pi$
$200$	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
$205$	−14.2337			−0.994124
$206$	5.00000	+	8.66025i	0.348367	+	0.603388i
$207$		0			0
$208$	−1.00000	+	1.73205i	−0.0693375	+	0.120096i
$209$	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
$215$	−6.25544	+	10.8347i	−0.426617	+	0.738923i
$216$		0			0
$217$		0			0
$218$	−7.00000	−	12.1244i	−0.474100	−	0.821165i
$219$		0			0
$220$	−6.00000			−0.404520
$221$	8.74456			0.588223
$222$		0			0
$223$	2.00000	+	3.46410i	0.133930	+	0.231973i	0.925188	−	0.379509i	$-0.123907\pi$
$223$	2.00000	+	3.46410i	0.133930	+	0.231973i	−0.791258	+	0.611482i	$0.790574\pi$
$224$		0			0
$225$		0			0
$226$	0.686141	−	1.18843i	0.0456414	−	0.0790532i
$227$	−11.8723	+	20.5634i	−0.787991	+	1.36484i	0.139205	+	0.990264i	$0.455545\pi$
$227$	−11.8723	+	20.5634i	−0.787991	+	1.36484i	−0.927196	+	0.374577i	$0.877788\pi$
$228$		0			0
$229$	10.0584	+	17.4217i	0.664679	+	1.15126i	0.979372	+	0.202065i	$0.0647651\pi$
$229$	10.0584	+	17.4217i	0.664679	+	1.15126i	−0.314693	+	0.949194i	$0.601902\pi$
$230$	−5.05842	+	8.76144i	−0.333542	+	0.577713i
$231$		0			0
$232$	1.37228	+	2.37686i	0.0900947	+	0.156049i
$233$	−5.87228	+	10.1711i	−0.384706	+	0.666330i	−0.991728	−	0.128354i	$-0.959030\pi$
$233$	−5.87228	+	10.1711i	−0.384706	+	0.666330i	0.607022	+	0.794685i	$0.292364\pi$
$234$		0			0
$235$		0			0
$236$	−7.11684			−0.463267
$237$		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	$-0.842389\pi$
$241$	−0.441578	+	0.764836i	−0.0284445	+	0.0492674i	0.851453	+	0.524431i	$0.175722\pi$
$242$	−4.05842	−	7.02939i	−0.260885	−	0.451867i
$243$		0			0
$244$	−14.1168			−0.903738
$245$		0			0
$246$		0			0
$247$	−5.00000	−	8.66025i	−0.318142	−	0.551039i
$248$	2.00000			0.127000
$249$		0			0
$250$	−11.1386			−0.704467
$251$	9.00000			0.568075			0.284037	−	0.958813i	$-0.408326\pi$
$251$	9.00000			0.568075			0.284037	+	0.958813i	$0.408326\pi$
$252$		0			0
$253$	−32.2337			−2.02651
$254$	−14.1168			−0.885770
$255$		0			0
$256$	1.00000			0.0625000
$257$	10.9307	+	18.9325i	0.681839	+	1.18098i	0.974419	+	0.224738i	$0.0721527\pi$
$257$	10.9307	+	18.9325i	0.681839	+	1.18098i	−0.292581	+	0.956241i	$0.594514\pi$
$258$		0			0
$259$		0			0
$260$	2.74456			0.170211
$261$		0			0
$262$	−3.68614	−	6.38458i	−0.227731	−	0.394441i
$263$	6.68614	−	11.5807i	0.412285	−	0.714099i	−0.582854	−	0.812577i	$-0.698064\pi$
$263$	6.68614	−	11.5807i	0.412285	−	0.714099i	0.995139	+	0.0984781i	$0.0313974\pi$
$264$		0			0
$265$	1.88316	−	3.26172i	0.115681	−	0.200366i
$266$		0			0
$267$		0			0
$268$	15.1168			0.923408
$269$	−3.68614	−	6.38458i	−0.224748	−	0.389275i	0.731496	−	0.681846i	$-0.238823\pi$
$269$	−3.68614	−	6.38458i	−0.224748	−	0.389275i	−0.956244	+	0.292571i	$0.905489\pi$
$270$		0			0
$271$	9.11684	−	15.7908i	0.553809	−	0.959225i	−0.444186	−	0.895934i	$-0.646507\pi$
$271$	9.11684	−	15.7908i	0.553809	−	0.959225i	0.997995	−	0.0632906i	$-0.0201595\pi$
$272$	−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	0.310531	+	0.950563i	$0.399493\pi$
$277$	−11.1168	+	19.2549i	−0.667946	+	1.15692i	−0.978477	+	0.206354i	$0.933840\pi$
$278$	10.6168	−	18.3889i	0.636756	−	1.10289i
$279$		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
$283$	9.88316			0.587493			0.293746	−	0.955883i	$-0.405098\pi$
$283$	9.88316			0.587493			0.293746	+	0.955883i	$0.405098\pi$
$284$	−10.1168			−0.600324
$285$		0			0
$286$	4.37228	+	7.57301i	0.258538	+	0.447802i
$287$		0			0
$288$		0			0
$289$	−1.05842	+	1.83324i	−0.0622601	+	0.107838i
$290$	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	−0.925665	−	0.378344i	$-0.876494\pi$
$293$	−2.31386	+	4.00772i	−0.135177	+	0.234134i	0.790488	+	0.612478i	$0.209827\pi$
$294$		0			0
$295$	4.88316	+	8.45787i	0.284308	+	0.492436i
$296$	−1.00000	+	1.73205i	−0.0581238	+	0.100673i
$297$		0			0
$298$	7.37228	+	12.7692i	0.427065	+	0.739698i
$299$	14.7446			0.852700
$300$		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
$305$	9.68614	+	16.7769i	0.554627	+	0.960642i
$306$		0			0
$307$	−13.0000			−0.741949			−0.370975	−	0.928643i	$-0.620976\pi$
$307$	−13.0000			−0.741949			−0.370975	+	0.928643i	$0.620976\pi$
$308$		0			0
$309$		0			0
$310$	−1.37228	−	2.37686i	−0.0779403	−	0.134997i
$311$	26.2337			1.48758			0.743788	−	0.668416i	$-0.233027\pi$
$311$	26.2337			1.48758			0.743788	+	0.668416i	$0.233027\pi$
$312$		0			0
$313$	−2.88316			−0.162966			−0.0814828	−	0.996675i	$-0.525966\pi$
$313$	−2.88316			−0.162966			−0.0814828	+	0.996675i	$0.525966\pi$
$314$	−8.11684			−0.458060
$315$		0			0
$316$	12.1168			0.681626
$317$	6.00000			0.336994			0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000			0.336994			0.168497	+	0.985702i	$0.446109\pi$
$318$		0			0
$319$	12.0000			0.671871
$320$	−0.686141	−	1.18843i	−0.0383564	−	0.0664353i
$321$		0			0
$322$		0			0
$323$	21.8614			1.21640
$324$		0			0
$325$	3.11684	+	5.39853i	0.172891	+	0.299457i
$326$	−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
$331$	−12.2337			−0.672424			−0.336212	−	0.941786i	$-0.609146\pi$
$331$	−12.2337			−0.672424			−0.336212	+	0.941786i	$0.609146\pi$
$332$	−2.74456	−	4.75372i	−0.150627	−	0.260894i
$333$		0			0
$334$	8.74456	−	15.1460i	0.478481	−	0.828754i
$335$	−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
$341$	4.37228	−	7.57301i	0.236772	−	0.410102i
$342$		0			0
$343$		0			0
$344$	−4.55842	−	7.89542i	−0.245774	−	0.425692i
$345$		0			0
$346$	6.00000			0.322562
$347$	−7.11684			−0.382052			−0.191026	−	0.981585i	$-0.561182\pi$
$347$	−7.11684			−0.382052			−0.191026	+	0.981585i	$0.561182\pi$
$348$		0			0
$349$	11.0000	+	19.0526i	0.588817	+	1.01986i	0.994388	+	0.105797i	$0.0337393\pi$
$349$	11.0000	+	19.0526i	0.588817	+	1.01986i	−0.405571	+	0.914063i	$0.632927\pi$
$350$		0			0
$351$		0			0
$352$	2.18614	−	3.78651i	0.116522	−	0.201821i
$353$	−3.81386	+	6.60580i	−0.202991	+	0.351591i	−0.949491	−	0.313795i	$-0.898400\pi$
$353$	−3.81386	+	6.60580i	−0.202991	+	0.351591i	0.746500	+	0.665386i	$0.231733\pi$
$354$		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
$359$	−3.43070	+	5.94215i	−0.181066	+	0.313615i	−0.942244	−	0.334928i	$-0.891288\pi$
$359$	−3.43070	+	5.94215i	−0.181066	+	0.313615i	0.761178	+	0.648543i	$0.224621\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$	18.1168			0.952200
$363$		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	0.415150	+	0.909753i	$0.363729\pi$
$367$	−11.1168	+	19.2549i	−0.580295	+	1.00510i	−0.995444	+	0.0953465i	$0.969604\pi$
$368$	−3.68614	−	6.38458i	−0.192153	−	0.332819i
$369$		0			0
$370$	2.74456			0.142683
$371$		0			0
$372$		0			0
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	0.965945	−	0.258748i	$-0.0833099\pi$
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	−0.707055	+	0.707159i	$0.749977\pi$
$374$	−19.1168			−0.988508
$375$		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	$0.424769\pi$
$380$	6.86141			0.351983
$381$		0			0
$382$	1.88316			0.0963506
$383$	−10.6277	−	18.4077i	−0.543051	−	0.940592i	−0.998727	−	0.0504462i	$-0.983936\pi$
$383$	−10.6277	−	18.4077i	−0.543051	−	0.940592i	0.455676	−	0.890146i	$-0.349398\pi$
$384$		0			0
$385$		0			0
$386$	−7.00000			−0.356291
$387$		0			0
$388$	−4.55842	−	7.89542i	−0.231419	−	0.400829i
$389$	−17.4891	+	30.2921i	−0.886734	+	1.53587i	−0.0430204	+	0.999074i	$0.513698\pi$
$389$	−17.4891	+	30.2921i	−0.886734	+	1.53587i	−0.843713	+	0.536794i	$0.819635\pi$
$390$		0			0
$391$	−16.1168	+	27.9152i	−0.815064	+	1.41173i
$392$		0			0
$393$		0			0
$394$	6.00000			0.302276
$395$	−8.31386	−	14.4000i	−0.418316	−	0.724544i
$396$		0			0
$397$	11.0000	−	19.0526i	0.552074	−	0.956221i	−0.446051	−	0.895008i	$-0.647170\pi$
$397$	11.0000	−	19.0526i	0.552074	−	0.956221i	0.998125	−	0.0612128i	$-0.0194968\pi$
$398$	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	0.862819	−	0.505513i	$-0.168697\pi$
$401$	−0.127719	−	0.221215i	−0.00637797	−	0.0110470i	−0.869197	+	0.494466i	$0.835364\pi$
$402$		0			0
$403$	−2.00000	+	3.46410i	−0.0996271	+	0.172559i
$404$	3.68614	−	6.38458i	0.183392	−	0.317645i
$405$		0			0
$406$		0			0
$407$	4.37228	+	7.57301i	0.216726	+	0.375380i
$408$		0			0
$409$	29.3505			1.45129			0.725645	−	0.688069i	$-0.241541\pi$
$409$	29.3505			1.45129			0.725645	+	0.688069i	$0.241541\pi$
$410$	−14.2337			−0.702952
$411$		0			0
$412$	5.00000	+	8.66025i	0.246332	+	0.426660i
$413$		0			0
$414$		0			0
$415$	−3.76631	+	6.52344i	−0.184881	+	0.320223i
$416$	−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	$-0.597770\pi$
$419$	13.8030	−	23.9075i	0.674320	−	1.16796i	0.976667	−	0.214759i	$-0.0688964\pi$
$420$		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	$0.831521\pi$
$422$	8.00000	−	13.8564i	0.389434	−	0.674519i
$423$		0			0
$424$	1.37228	+	2.37686i	0.0666439	+	0.115431i
$425$	−13.6277			−0.661041
$426$		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
$431$	−14.7446	−	25.5383i	−0.710221	−	1.23014i	−0.964774	−	0.263079i	$-0.915262\pi$
$431$	−14.7446	−	25.5383i	−0.710221	−	1.23014i	0.254554	−	0.967059i	$-0.418071\pi$
$432$		0			0
$433$	−2.88316			−0.138556			−0.0692778	−	0.997597i	$-0.522069\pi$
$433$	−2.88316			−0.138556			−0.0692778	+	0.997597i	$0.522069\pi$
$434$		0			0
$435$		0			0
$436$	−7.00000	−	12.1244i	−0.335239	−	0.580651i
$437$	36.8614			1.76332
$438$		0			0
$439$	8.00000			0.381819			0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000			0.381819			0.190910	+	0.981608i	$0.438856\pi$
$440$	−6.00000			−0.286039
$441$		0			0
$442$	8.74456			0.415936
$443$	22.8832			1.08721			0.543606	−	0.839341i	$-0.317059\pi$
$443$	22.8832			1.08721			0.543606	+	0.839341i	$0.317059\pi$
$444$		0			0
$445$	−4.46738			−0.211774
$446$	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
$451$	−22.6753	−	39.2747i	−1.06774	−	1.84937i
$452$	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
$457$	33.4674			1.56554			0.782769	−	0.622312i	$-0.213807\pi$
$457$	33.4674			1.56554			0.782769	+	0.622312i	$0.213807\pi$
$458$	10.0584	+	17.4217i	0.469999	+	0.814062i
$459$		0			0
$460$	−5.05842	+	8.76144i	−0.235850	+	0.408504i
$461$	15.4307	+	26.7268i	0.718680	+	1.24479i	0.961523	+	0.274724i	$0.0885865\pi$
$461$	15.4307	+	26.7268i	0.718680	+	1.24479i	−0.242844	+	0.970065i	$0.578080\pi$
$462$		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
$467$	−15.0475	+	26.0631i	−0.696317	+	1.20606i	0.273417	+	0.961896i	$0.411846\pi$
$467$	−15.0475	+	26.0631i	−0.696317	+	1.20606i	−0.969735	+	0.244162i	$0.921487\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−7.11684			−0.327579
$473$	−39.8614			−1.83283
$474$		0			0
$475$	7.79211	+	13.4963i	0.357527	+	0.619254i
$476$		0			0
$477$		0			0
$478$	−9.43070	+	16.3345i	−0.431350	+	0.747121i
$479$	10.6277	−	18.4077i	0.485593	−	0.841072i	−0.514270	−	0.857628i	$-0.671937\pi$
$479$	10.6277	−	18.4077i	0.485593	−	0.841072i	0.999863	+	0.0165568i	$0.00527043\pi$
$480$		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
$485$	−6.25544	+	10.8347i	−0.284045	+	0.491980i
$486$		0			0
$487$	8.17527	+	14.1600i	0.370457	+	0.641650i	0.989636	−	0.143600i	$-0.0458679\pi$
$487$	8.17527	+	14.1600i	0.370457	+	0.641650i	−0.619179	+	0.785250i	$0.712535\pi$
$488$	−14.1168			−0.639040
$489$		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
$494$	−5.00000	−	8.66025i	−0.224961	−	0.389643i
$495$		0			0
$496$	2.00000			0.0898027
$497$		0			0
$498$		0			0
$499$	−0.441578	−	0.764836i	−0.0197677	−	0.0342387i	0.855972	−	0.517022i	$-0.172959\pi$
$499$	−0.441578	−	0.764836i	−0.0197677	−	0.0342387i	−0.875740	+	0.482783i	$0.839626\pi$
$500$	−11.1386			−0.498133
$501$		0			0
$502$	9.00000			0.401690
$503$	−2.23369			−0.0995952			−0.0497976	−	0.998759i	$-0.515858\pi$
$503$	−2.23369			−0.0995952			−0.0497976	+	0.998759i	$0.515858\pi$
$504$		0			0
$505$	−10.1168			−0.450194
$506$	−32.2337			−1.43296
$507$		0			0
$508$	−14.1168			−0.626334
$509$	8.48913	+	14.7036i	0.376274	+	0.651725i	0.990517	−	0.137392i	$-0.0438718\pi$
$509$	8.48913	+	14.7036i	0.376274	+	0.651725i	−0.614243	+	0.789117i	$0.710539\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	10.9307	+	18.9325i	0.482133	+	0.835078i
$515$	6.86141	−	11.8843i	0.302350	−	0.523685i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	2.74456			0.120357
$521$	1.93070	+	3.34408i	0.0845856	+	0.146507i	0.905215	−	0.424955i	$-0.139710\pi$
$521$	1.93070	+	3.34408i	0.0845856	+	0.146507i	−0.820629	+	0.571461i	$0.806377\pi$
$522$		0			0
$523$	8.94158	−	15.4873i	0.390988	−	0.677211i	−0.601592	−	0.798803i	$-0.705467\pi$
$523$	8.94158	−	15.4873i	0.390988	−	0.677211i	0.992580	+	0.121592i	$0.0388001\pi$
$524$	−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
$530$	1.88316	−	3.26172i	0.0817991	−	0.141680i
$531$		0			0
$532$		0			0
$533$	10.3723	+	17.9653i	0.449273	+	0.778164i
$534$		0			0
$535$	2.23369			0.0965708
$536$	15.1168			0.652948
$537$		0			0
$538$	−3.68614	−	6.38458i	−0.158921	−	0.275259i
$539$		0			0
$540$		0			0
$541$	−14.1168	+	24.4511i	−0.606931	+	1.05123i	0.384813	+	0.922995i	$0.374266\pi$
$541$	−14.1168	+	24.4511i	−0.606931	+	1.05123i	−0.991743	+	0.128240i	$0.959067\pi$
$542$	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	$0.839344\pi$
$548$	8.18614	−	14.1788i	0.349695	−	0.605689i
$549$		0			0
$550$	−6.81386	−	11.8020i	−0.290544	−	0.503237i
$551$	−13.7228			−0.584611
$552$		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
$557$	3.25544	+	5.63858i	0.137937	+	0.238914i	0.926716	−	0.375763i	$-0.122619\pi$
$557$	3.25544	+	5.63858i	0.137937	+	0.238914i	−0.788778	+	0.614678i	$0.789286\pi$
$558$		0			0
$559$	18.2337			0.771203
$560$		0			0
$561$		0			0
$562$	5.31386	+	9.20387i	0.224152	+	0.388242i
$563$	−3.00000			−0.126435			−0.0632175	−	0.998000i	$-0.520136\pi$
$563$	−3.00000			−0.126435			−0.0632175	+	0.998000i	$0.520136\pi$
$564$		0			0
$565$	−1.88316			−0.0792250
$566$	9.88316			0.415420
$567$		0			0
$568$	−10.1168			−0.424493
$569$	1.11684			0.0468205			0.0234103	−	0.999726i	$-0.492548\pi$
$569$	1.11684			0.0468205			0.0234103	+	0.999726i	$0.492548\pi$
$570$		0			0
$571$	29.3505			1.22828			0.614141	−	0.789197i	$-0.289503\pi$
$571$	29.3505			1.22828			0.614141	+	0.789197i	$0.289503\pi$
$572$	4.37228	+	7.57301i	0.182814	+	0.316644i
$573$		0			0
$574$		0			0
$575$	−22.9783			−0.958259
$576$		0			0
$577$	−13.5584	−	23.4839i	−0.564444	−	0.977647i	−0.997101	−	0.0760878i	$-0.975757\pi$
$577$	−13.5584	−	23.4839i	−0.564444	−	0.977647i	0.432657	−	0.901559i	$-0.357576\pi$
$578$	−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
$583$	12.0000			0.496989
$584$	2.55842	+	4.43132i	0.105868	+	0.183369i
$585$		0			0
$586$	−2.31386	+	4.00772i	−0.0955846	+	0.165557i
$587$	−4.24456	−	7.35180i	−0.175192	−	0.303441i	0.765036	−	0.643988i	$-0.222721\pi$
$587$	−4.24456	−	7.35180i	−0.175192	−	0.303441i	−0.940228	+	0.340547i	$0.889388\pi$
$588$		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
$593$	1.62772	−	2.81929i	0.0668424	−	0.115774i	−0.830667	−	0.556769i	$-0.812041\pi$
$593$	1.62772	−	2.81929i	0.0668424	−	0.115774i	0.897510	+	0.440995i	$0.145374\pi$
$594$		0			0
$595$		0			0
$596$	7.37228	+	12.7692i	0.301980	+	0.523045i
$597$		0			0
$598$	14.7446			0.602950
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$		0			0
$601$	−3.44158	−	5.96099i	−0.140385	−	0.243154i	0.787257	−	0.616625i	$-0.211501\pi$
$601$	−3.44158	−	5.96099i	−0.140385	−	0.243154i	−0.927642	+	0.373472i	$0.878167\pi$
$602$		0			0
$603$		0			0
$604$	4.05842	−	7.02939i	0.165135	−	0.286022i
$605$	−5.56930	+	9.64630i	−0.226424	+	0.392178i
$606$		0			0
$607$	6.11684	+	10.5947i	0.248275	+	0.430025i	0.963047	−	0.269332i	$-0.0868030\pi$
$607$	6.11684	+	10.5947i	0.248275	+	0.430025i	−0.714772	+	0.699357i	$0.753470\pi$
$608$	−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
$613$	0.883156	+	1.52967i	0.0356703	+	0.0617828i	0.883309	−	0.468790i	$-0.155310\pi$
$613$	0.883156	+	1.52967i	0.0356703	+	0.0617828i	−0.847639	+	0.530573i	$0.821977\pi$
$614$	−13.0000			−0.524637
$615$		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	$-0.677004\pi$
$619$	11.7337	−	20.3233i	0.471617	−	0.816864i	0.999473	+	0.0324697i	$0.0103373\pi$
$620$	−1.37228	−	2.37686i	−0.0551121	−	0.0954570i
$621$		0			0
$622$	26.2337			1.05188
$623$		0			0
$624$		0			0
$625$	−0.149468	−	0.258886i	−0.00597872	−	0.0103555i
$626$	−2.88316			−0.115234
$627$		0			0
$628$	−8.11684			−0.323897
$629$	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	$0.407793\pi$
$632$	12.1168			0.481982
$633$		0			0
$634$	6.00000			0.238290
$635$	9.68614	+	16.7769i	0.384383	+	0.665770i
$636$		0			0
$637$		0			0
$638$	12.0000			0.475085
$639$		0			0
$640$	−0.686141	−	1.18843i	−0.0271221	−	0.0469768i
$641$	−23.1060	+	40.0207i	−0.912631	+	1.58072i	−0.102298	+	0.994754i	$0.532619\pi$
$641$	−23.1060	+	40.0207i	−0.912631	+	1.58072i	−0.810333	+	0.585969i	$0.800714\pi$
$642$		0			0
$643$	12.6753	−	21.9542i	0.499864	−	0.865789i	−0.500136	−	0.865947i	$-0.666717\pi$
$643$	12.6753	−	21.9542i	0.499864	−	0.865789i	1.00000		0.000157386i	$5.00974e-5\pi$
$644$		0			0
$645$		0			0
$646$	21.8614			0.860126
$647$	−8.74456	−	15.1460i	−0.343784	−	0.595452i	0.641348	−	0.767250i	$-0.278376\pi$
$647$	−8.74456	−	15.1460i	−0.343784	−	0.595452i	−0.985132	+	0.171798i	$0.945042\pi$
$648$		0			0
$649$	−15.5584	+	26.9480i	−0.610721	+	1.05780i
$650$	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	0.677296	−	0.735710i	$-0.263152\pi$
$653$	−7.62772	−	13.2116i	−0.298496	−	0.517010i	−0.975792	+	0.218701i	$0.929818\pi$
$654$		0			0
$655$	−5.05842	+	8.76144i	−0.197649	+	0.342338i
$656$	5.18614	−	8.98266i	0.202485	−	0.350714i
$657$		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
$661$	9.88316			0.384410			0.192205	−	0.981355i	$-0.438436\pi$
$661$	9.88316			0.384410			0.192205	+	0.981355i	$0.438436\pi$
$662$	−12.2337			−0.475476
$663$		0			0
$664$	−2.74456	−	4.75372i	−0.106510	−	0.184480i
$665$		0			0
$666$		0			0
$667$	10.1168	−	17.5229i	0.391726	−	0.678489i
$668$	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	$0.706595\pi$
$674$	−4.55842	+	7.89542i	−0.175584	+	0.304120i
$675$		0			0
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	34.4674			1.32469			0.662344	−	0.749199i	$-0.269562\pi$
$677$	34.4674			1.32469			0.662344	+	0.749199i	$0.269562\pi$
$678$		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
$683$	−22.4198	−	38.8323i	−0.857871	−	1.48588i	−0.873956	−	0.486005i	$-0.838454\pi$
$683$	−22.4198	−	38.8323i	−0.857871	−	1.48588i	0.0160849	−	0.999871i	$-0.494880\pi$
$684$		0			0
$685$	−22.4674			−0.858434
$686$		0			0
$687$		0			0
$688$	−4.55842	−	7.89542i	−0.173788	−	0.301010i
$689$	−5.48913			−0.209119
$690$		0			0
$691$	−5.88316			−0.223806			−0.111903	−	0.993719i	$-0.535695\pi$
$691$	−5.88316			−0.223806			−0.111903	+	0.993719i	$0.535695\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	−7.11684			−0.270152
$695$	−29.1386			−1.10529
$696$		0			0
$697$	−45.3505			−1.71777
$698$	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
$703$	−5.00000	−	8.66025i	−0.188579	−	0.326628i
$704$	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
$709$	44.0000			1.65245			0.826227	−	0.563337i	$-0.190483\pi$
$709$	44.0000			1.65245			0.826227	+	0.563337i	$0.190483\pi$
$710$	6.94158	+	12.0232i	0.260513	+	0.451221i
$711$		0			0
$712$	1.62772	−	2.81929i	0.0610013	−	0.105657i
$713$	−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
$719$	−4.37228	+	7.57301i	−0.163059	+	0.282426i	−0.935964	−	0.352095i	$-0.885469\pi$
$719$	−4.37228	+	7.57301i	−0.163059	+	0.282426i	0.772906	+	0.634521i	$0.218803\pi$
$720$		0			0
$721$		0			0
$722$	−3.00000	−	5.19615i	−0.111648	−	0.193381i
$723$		0			0
$724$	18.1168			0.673307
$725$	8.55437			0.317701
$726$		0			0
$727$	0.883156	+	1.52967i	0.0327544	+	0.0567324i	0.881938	−	0.471366i	$-0.156239\pi$
$727$	0.883156	+	1.52967i	0.0327544	+	0.0567324i	−0.849183	+	0.528098i	$0.822905\pi$
$728$		0			0
$729$		0			0
$730$	3.51087	−	6.08101i	0.129943	−	0.225068i
$731$	−19.9307	+	34.5210i	−0.737164	+	1.27680i
$732$		0			0
$733$	11.9416	+	20.6834i	0.441072	+	0.763960i	0.997769	−	0.0667560i	$-0.0212649\pi$
$733$	11.9416	+	20.6834i	0.441072	+	0.763960i	−0.556697	+	0.830716i	$0.687932\pi$
$734$	−11.1168	+	19.2549i	−0.410330	+	0.710713i
$735$		0			0
$736$	−3.68614	−	6.38458i	−0.135873	−	0.235339i
$737$	33.0475	−	57.2400i	1.21732	−	2.10846i
$738$		0			0
$739$	−4.55842	−	7.89542i	−0.167684	−	0.290438i	0.769921	−	0.638139i	$-0.220296\pi$
$739$	−4.55842	−	7.89542i	−0.167684	−	0.290438i	−0.937605	+	0.347702i	$0.886962\pi$
$740$	2.74456			0.100892
$741$		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
$746$	5.00000	+	8.66025i	0.183063	+	0.317074i
$747$		0			0
$748$	−19.1168			−0.698981
$749$		0			0
$750$		0			0
$751$	−0.0584220	−	0.101190i	−0.00213185	−	0.00369247i	0.864958	−	0.501845i	$-0.167345\pi$
$751$	−0.0584220	−	0.101190i	−0.00213185	−	0.00369247i	−0.867089	+	0.498153i	$0.834012\pi$
$752$		0			0
$753$		0			0
$754$	−5.48913			−0.199902
$755$	−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	$0.431407\pi$
$758$	9.11684			0.331139
$759$		0			0
$760$	6.86141			0.248889
$761$	6.25544	+	10.8347i	0.226759	+	0.392759i	0.956846	−	0.290596i	$-0.0938536\pi$
$761$	6.25544	+	10.8347i	0.226759	+	0.392759i	−0.730086	+	0.683355i	$0.760520\pi$
$762$		0			0
$763$		0			0
$764$	1.88316			0.0681302
$765$		0			0
$766$	−10.6277	−	18.4077i	−0.383995	−	0.665099i
$767$	7.11684	−	12.3267i	0.256974	−	0.445093i
$768$		0			0
$769$	5.00000	−	8.66025i	0.180305	−	0.312297i	−0.761680	−	0.647954i	$-0.775625\pi$
$769$	5.00000	−	8.66025i	0.180305	−	0.312297i	0.941984	+	0.335657i	$0.108958\pi$
$770$		0			0
$771$		0			0
$772$	−7.00000			−0.251936
$773$	−5.56930	−	9.64630i	−0.200314	−	0.346953i	0.748316	−	0.663343i	$-0.230863\pi$
$773$	−5.56930	−	9.64630i	−0.200314	−	0.346953i	−0.948629	+	0.316389i	$0.897529\pi$
$774$		0			0
$775$	3.11684	−	5.39853i	0.111960	−	0.193921i
$776$	−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
$782$	−16.1168	+	27.9152i	−0.576337	+	0.998245i
$783$		0			0
$784$		0			0
$785$	5.56930	+	9.64630i	0.198777	+	0.344291i
$786$		0			0
$787$	−4.00000			−0.142585			−0.0712923	−	0.997455i	$-0.522712\pi$
$787$	−4.00000			−0.142585			−0.0712923	+	0.997455i	$0.522712\pi$
$788$	6.00000			0.213741
$789$		0			0
$790$	−8.31386	−	14.4000i	−0.295794	−	0.512330i
$791$		0			0
$792$		0			0
$793$	14.1168	−	24.4511i	0.501304	−	0.868284i
$794$	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	$0.393093\pi$
$797$	−18.4307	+	31.9229i	−0.652849	+	1.13077i	−0.982428	+	0.186640i	$0.940240\pi$
$798$		0			0
$799$		0			0
$800$	1.55842	−	2.69927i	0.0550985	−	0.0954335i
$801$		0			0
$802$	−0.127719	−	0.221215i	−0.00450990	−	0.00781138i
$803$	22.3723			0.789501
$804$		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
$809$	10.9307	+	18.9325i	0.384303	+	0.665632i	0.991672	−	0.128787i	$-0.0411084\pi$
$809$	10.9307	+	18.9325i	0.384303	+	0.665632i	−0.607369	+	0.794420i	$0.707775\pi$
$810$		0			0
$811$	24.8832			0.873766			0.436883	−	0.899518i	$-0.356082\pi$
$811$	24.8832			0.873766			0.436883	+	0.899518i	$0.356082\pi$
$812$		0			0
$813$		0			0
$814$	4.37228	+	7.57301i	0.153248	+	0.265434i
$815$	22.2772			0.780336
$816$		0			0
$817$	45.5842			1.59479
$818$	29.3505			1.02622
$819$		0			0
$820$	−14.2337			−0.497062
$821$	38.2337			1.33436			0.667182	−	0.744894i	$-0.267500\pi$
$821$	38.2337			1.33436			0.667182	+	0.744894i	$0.267500\pi$
$822$		0			0
$823$	22.2337			0.775018			0.387509	−	0.921866i	$-0.373336\pi$
$823$	22.2337			0.775018			0.387509	+	0.921866i	$0.373336\pi$
$824$	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
$829$	24.1168	+	41.7716i	0.837613	+	1.45079i	0.891885	+	0.452261i	$0.149383\pi$
$829$	24.1168	+	41.7716i	0.837613	+	1.45079i	−0.0542728	+	0.998526i	$0.517284\pi$
$830$	−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
$835$	−24.0000			−0.830554
$836$	10.9307	+	18.9325i	0.378046	+	0.654795i
$837$		0			0
$838$	13.8030	−	23.9075i	0.476816	−	0.825870i
$839$	−8.74456	−	15.1460i	−0.301896	−	0.522899i	0.674670	−	0.738120i	$-0.264286\pi$
$839$	−8.74456	−	15.1460i	−0.301896	−	0.522899i	−0.976565	+	0.215221i	$0.930953\pi$
$840$		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
$845$	6.17527	−	10.6959i	0.212436	−	0.367949i
$846$		0			0
$847$		0			0
$848$	1.37228	+	2.37686i	0.0471243	+	0.0816217i
$849$		0			0
$850$	−13.6277			−0.467427
$851$	14.7446			0.505437
$852$		0			0
$853$	8.94158	+	15.4873i	0.306154	+	0.530274i	0.977518	−	0.210854i	$-0.0676245\pi$
$853$	8.94158	+	15.4873i	0.306154	+	0.530274i	−0.671364	+	0.741128i	$0.734291\pi$
$854$		0			0
$855$		0			0
$856$	−0.813859	+	1.40965i	−0.0278171	+	0.0481807i
$857$	25.9783	−	44.9956i	0.887400	−	1.53702i	0.0444624	−	0.999011i	$-0.485843\pi$
$857$	25.9783	−	44.9956i	0.887400	−	1.53702i	0.842938	−	0.538011i	$-0.180824\pi$
$858$		0			0
$859$	−25.5584	−	44.2685i	−0.872042	−	1.51042i	−0.859881	−	0.510495i	$-0.829462\pi$
$859$	−25.5584	−	44.2685i	−0.872042	−	1.51042i	−0.0121615	−	0.999926i	$-0.503871\pi$
$860$	−6.25544	+	10.8347i	−0.213309	+	0.369461i
$861$		0			0
$862$	−14.7446	−	25.5383i	−0.502202	−	0.869839i
$863$	−9.43070	+	16.3345i	−0.321025	+	0.556031i	−0.980700	−	0.195520i	$-0.937361\pi$
$863$	−9.43070	+	16.3345i	−0.321025	+	0.556031i	0.659675	+	0.751551i	$0.270694\pi$
$864$		0			0
$865$	−4.11684	−	7.13058i	−0.139977	−	0.242447i
$866$	−2.88316			−0.0979736
$867$		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
$872$	−7.00000	−	12.1244i	−0.237050	−	0.410582i
$873$		0			0
$874$	36.8614			1.24686
$875$		0			0
$876$		0			0
$877$	−22.3505	−	38.7123i	−0.754724	−	1.30722i	−0.945512	−	0.325589i	$-0.894438\pi$
$877$	−22.3505	−	38.7123i	−0.754724	−	1.30722i	0.190788	−	0.981631i	$-0.438896\pi$
$878$	8.00000			0.269987
$879$		0			0
$880$	−6.00000			−0.202260
$881$	−14.2337			−0.479545			−0.239773	−	0.970829i	$-0.577073\pi$
$881$	−14.2337			−0.479545			−0.239773	+	0.970829i	$0.577073\pi$
$882$		0			0
$883$	11.3505			0.381976			0.190988	−	0.981592i	$-0.438831\pi$
$883$	11.3505			0.381976			0.190988	+	0.981592i	$0.438831\pi$
$884$	8.74456			0.294111
$885$		0			0
$886$	22.8832			0.768775
$887$	−15.8614	−	27.4728i	−0.532574	−	0.922445i	−0.999277	−	0.0380308i	$-0.987892\pi$
$887$	−15.8614	−	27.4728i	−0.532574	−	0.922445i	0.466703	−	0.884414i	$-0.345442\pi$
$888$		0			0
$889$		0			0
$890$	−4.46738			−0.149747
$891$		0			0
$892$	2.00000	+	3.46410i	0.0669650	+	0.115987i
$893$		0			0
$894$		0			0
$895$	10.1168	−	17.5229i	0.338169	−	0.585726i
$896$		0			0
$897$		0			0
$898$	−33.0000			−1.10122
$899$	2.74456	+	4.75372i	0.0915363	+	0.158546i
$900$		0			0
$901$	6.00000	−	10.3923i	0.199889	−	0.346218i
$902$	−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	−0.782815	−	0.622254i	$-0.786217\pi$
$907$	4.44158	−	7.69304i	0.147480	−	0.255443i	0.930296	+	0.366811i	$0.119550\pi$
$908$	−11.8723	+	20.5634i	−0.393995	+	0.682420i
$909$		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
$913$	−24.0000			−0.794284
$914$	33.4674			1.10700
$915$		0			0
$916$	10.0584	+	17.4217i	0.332340	+	0.575629i
$917$		0			0
$918$		0			0
$919$	14.9416	−	25.8796i	0.492877	−	0.853688i	−0.507089	−	0.861894i	$-0.669279\pi$
$919$	14.9416	−	25.8796i	0.492877	−	0.853688i	0.999966	+	0.00820529i	$0.00261185\pi$
$920$	−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
$926$	2.94158	−	5.09496i	0.0966663	−	0.167431i
$927$		0			0
$928$	1.37228	+	2.37686i	0.0450473	+	0.0780243i
$929$	−9.76631			−0.320422			−0.160211	−	0.987083i	$-0.551218\pi$
$929$	−9.76631			−0.320422			−0.160211	+	0.987083i	$0.551218\pi$
$930$		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
$935$	13.1168	+	22.7190i	0.428967	+	0.742992i
$936$		0			0
$937$	−38.4674			−1.25667			−0.628337	−	0.777941i	$-0.716264\pi$
$937$	−38.4674			−1.25667			−0.628337	+	0.777941i	$0.716264\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.88316			−0.0613891			−0.0306946	−	0.999529i	$-0.509772\pi$
$941$	−1.88316			−0.0613891			−0.0306946	+	0.999529i	$0.509772\pi$
$942$		0			0
$943$	−76.4674			−2.49012
$944$	−7.11684			−0.231634
$945$		0			0
$946$	−39.8614			−1.29601
$947$	−16.8832			−0.548629			−0.274314	−	0.961640i	$-0.588451\pi$
$947$	−16.8832			−0.548629			−0.274314	+	0.961640i	$0.588451\pi$
$948$		0			0
$949$	−10.2337			−0.332200
$950$	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
$955$	−1.29211	−	2.23800i	−0.0418117	−	0.0724200i
$956$	−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
$961$	−27.0000			−0.870968
$962$	−2.00000	−	3.46410i	−0.0644826	−	0.111687i
$963$		0			0
$964$	−0.441578	+	0.764836i	−0.0142223	+	0.0246337i
$965$	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
$971$	3.68614	−	6.38458i	0.118294	−	0.204891i	−0.800798	−	0.598935i	$-0.795591\pi$
$971$	3.68614	−	6.38458i	0.118294	−	0.204891i	0.919092	+	0.394044i	$0.128924\pi$
$972$		0			0
$973$		0			0
$974$	8.17527	+	14.1600i	0.261952	+	0.453715i
$975$		0			0
$976$	−14.1168			−0.451869
$977$	−22.8832			−0.732097			−0.366049	−	0.930596i	$-0.619290\pi$
$977$	−22.8832			−0.732097			−0.366049	+	0.930596i	$0.619290\pi$
$978$		0			0
$979$	−7.11684	−	12.3267i	−0.227455	−	0.393964i
$980$		0			0
$981$		0			0
$982$	−9.81386	+	16.9981i	−0.313173	+	0.542431i
$983$	−25.3723	+	43.9461i	−0.809250	+	1.40166i	0.104134	+	0.994563i	$0.466793\pi$
$983$	−25.3723	+	43.9461i	−0.809250	+	1.40166i	−0.913384	+	0.407099i	$0.866540\pi$
$984$		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
$989$	−33.6060	+	58.2072i	−1.06861	+	1.85088i
$990$		0			0
$991$	10.2337	+	17.7253i	0.325084	+	0.563062i	0.981529	−	0.191312i	$-0.0612742\pi$
$991$	10.2337	+	17.7253i	0.325084	+	0.563062i	−0.656446	+	0.754373i	$0.727941\pi$
$992$	2.00000			0.0635001
$993$		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	$-0.894789\pi$
$997$	−6.05842	+	10.4935i	−0.191872	+	0.332332i	0.753999	+	0.656876i	$0.228123\pi$
$998$	−0.441578	−	0.764836i	−0.0139779	−	0.0242104i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.d.43.2	✓	4	63.2	odd	6
126.2.f.d.85.2	yes	4	21.2	odd	6
378.2.f.c.127.1		4	63.16	even	3
378.2.f.c.253.1		4	7.2	even	3
882.2.e.k.373.2		4	21.20	even	2
882.2.e.k.655.1		4	63.38	even	6
882.2.e.l.373.1		4	3.2	odd	2
882.2.e.l.655.2		4	63.11	odd	6
882.2.f.k.295.1		4	63.47	even	6
882.2.f.k.589.1		4	21.5	even	6
882.2.h.m.67.1		4	21.11	odd	6
882.2.h.m.79.1		4	9.2	odd	6
882.2.h.n.67.2		4	21.17	even	6
882.2.h.n.79.2		4	63.20	even	6
1008.2.r.f.337.1		4	84.23	even	6
1008.2.r.f.673.1		4	252.191	even	6
1134.2.a.k.1.1		2	63.23	odd	6
1134.2.a.n.1.2		2	63.58	even	3
2646.2.e.m.1549.2		4	7.6	odd	2
2646.2.e.m.2125.2		4	63.52	odd	6
2646.2.e.n.1549.1		4	1.1	even	1	trivial
2646.2.e.n.2125.1		4	63.25	even	3	inner
2646.2.f.j.883.2		4	63.61	odd	6
2646.2.f.j.1765.2		4	7.5	odd	6
2646.2.h.k.361.2		4	7.4	even	3
2646.2.h.k.667.2		4	9.7	even	3
2646.2.h.l.361.1		4	7.3	odd	6
2646.2.h.l.667.1		4	63.34	odd	6
3024.2.r.f.1009.1		4	28.23	odd	6
3024.2.r.f.2017.1		4	252.79	odd	6
7938.2.a.bh.1.2		2	63.5	even	6
7938.2.a.bs.1.1		2	63.40	odd	6
9072.2.a.bb.1.2		2	252.247	odd	6
9072.2.a.bm.1.1		2	252.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.686141 - 1.18843i) q^{5} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.686141 - 1.18843i) q^{5} +1.00000 q^{8} +(-0.686141 - 1.18843i) q^{10} +(2.18614 - 3.78651i) q^{11} +(-1.00000 + 1.73205i) q^{13} +1.00000 q^{16} +(-2.18614 - 3.78651i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(-0.686141 - 1.18843i) q^{20} +(2.18614 - 3.78651i) q^{22} +(-3.68614 - 6.38458i) q^{23} +(1.55842 - 2.69927i) q^{25} +(-1.00000 + 1.73205i) q^{26} +(1.37228 + 2.37686i) q^{29} +2.00000 q^{31} +1.00000 q^{32} +(-2.18614 - 3.78651i) q^{34} +(-1.00000 + 1.73205i) q^{37} +(-2.50000 + 4.33013i) q^{38} +(-0.686141 - 1.18843i) q^{40} +(5.18614 - 8.98266i) q^{41} +(-4.55842 - 7.89542i) q^{43} +(2.18614 - 3.78651i) q^{44} +(-3.68614 - 6.38458i) q^{46} +(1.55842 - 2.69927i) q^{50} +(-1.00000 + 1.73205i) q^{52} +(1.37228 + 2.37686i) q^{53} -6.00000 q^{55} +(1.37228 + 2.37686i) q^{58} -7.11684 q^{59} -14.1168 q^{61} +2.00000 q^{62} +1.00000 q^{64} +2.74456 q^{65} +15.1168 q^{67} +(-2.18614 - 3.78651i) q^{68} -10.1168 q^{71} +(2.55842 + 4.43132i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(-2.50000 + 4.33013i) q^{76} +12.1168 q^{79} +(-0.686141 - 1.18843i) q^{80} +(5.18614 - 8.98266i) q^{82} +(-2.74456 - 4.75372i) q^{83} +(-3.00000 + 5.19615i) q^{85} +(-4.55842 - 7.89542i) q^{86} +(2.18614 - 3.78651i) q^{88} +(1.62772 - 2.81929i) q^{89} +(-3.68614 - 6.38458i) q^{92} +6.86141 q^{95} +(-4.55842 - 7.89542i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{4} + 3 q^{5} + 4 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^4 + 3 * q^5 + 4 * q^8	\( 4 q + 4 q^{2} + 4 q^{4} + 3 q^{5} + 4 q^{8} + 3 q^{10} + 3 q^{11} - 4 q^{13} + 4 q^{16} - 3 q^{17} - 10 q^{19} + 3 q^{20} + 3 q^{22} - 9 q^{23} - 11 q^{25} - 4 q^{26} - 6 q^{29} + 8 q^{31} + 4 q^{32} - 3 q^{34} - 4 q^{37} - 10 q^{38} + 3 q^{40} + 15 q^{41} - q^{43} + 3 q^{44} - 9 q^{46} - 11 q^{50} - 4 q^{52} - 6 q^{53} - 24 q^{55} - 6 q^{58} + 6 q^{59} - 22 q^{61} + 8 q^{62} + 4 q^{64} - 12 q^{65} + 26 q^{67} - 3 q^{68} - 6 q^{71} - 7 q^{73} - 4 q^{74} - 10 q^{76} + 14 q^{79} + 3 q^{80} + 15 q^{82} + 12 q^{83} - 12 q^{85} - q^{86} + 3 q^{88} + 18 q^{89} - 9 q^{92} - 30 q^{95} - q^{97}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^4 + 3 * q^5 + 4 * q^8 + 3 * q^10 + 3 * q^11 - 4 * q^13 + 4 * q^16 - 3 * q^17 - 10 * q^19 + 3 * q^20 + 3 * q^22 - 9 * q^23 - 11 * q^25 - 4 * q^26 - 6 * q^29 + 8 * q^31 + 4 * q^32 - 3 * q^34 - 4 * q^37 - 10 * q^38 + 3 * q^40 + 15 * q^41 - q^43 + 3 * q^44 - 9 * q^46 - 11 * q^50 - 4 * q^52 - 6 * q^53 - 24 * q^55 - 6 * q^58 + 6 * q^59 - 22 * q^61 + 8 * q^62 + 4 * q^64 - 12 * q^65 + 26 * q^67 - 3 * q^68 - 6 * q^71 - 7 * q^73 - 4 * q^74 - 10 * q^76 + 14 * q^79 + 3 * q^80 + 15 * q^82 + 12 * q^83 - 12 * q^85 - q^86 + 3 * q^88 + 18 * q^89 - 9 * q^92 - 30 * q^95 - q^97

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