LMFDB - Embedded newform 1008.2.cc.b.209.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(209,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1, 3]))

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

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

chi := DirichletCharacter("1008.209");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cc (of order $6$, 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 $ x^16 - 6x^14 + 9x^12 + 54x^10 - 288x^8 + 486x^6 + 729x^4 - 4374*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			209.3
Root			$-1.40917 - 1.00709i$ of defining polynomial
Character	$\chi$	$=$	1008.209
Dual form			1008.2.cc.b.545.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40917 + 1.00709i) q^{3} +(1.17468 + 2.03460i) q^{5} +(-1.55364 - 2.14154i) q^{7} +(0.971521 - 2.83834i) q^{9} +O(q^{10})$	\(q+(-1.40917 + 1.00709i) q^{3} +(1.17468 + 2.03460i) q^{5} +(-1.55364 - 2.14154i) q^{7} +(0.971521 - 2.83834i) q^{9} +(4.91614 + 2.83834i) q^{11} +(1.48943 - 0.859925i) q^{13} +(-3.70436 - 1.68409i) q^{15} -1.76883 q^{17} +1.13932i q^{19} +(4.34608 + 1.45313i) q^{21} +(3.18272 - 1.83755i) q^{23} +(-0.259741 + 0.449885i) q^{25} +(1.48943 + 4.97811i) q^{27} +(3.59886 + 2.07781i) q^{29} +(7.24879 - 4.18509i) q^{31} +(-9.78615 + 0.951321i) q^{33} +(2.53215 - 5.67667i) q^{35} -9.19773 q^{37} +(-1.23284 + 2.71178i) q^{39} +(3.99709 + 6.92317i) q^{41} +(-1.76053 + 3.04933i) q^{43} +(6.91611 - 1.35747i) q^{45} +(-5.90494 + 10.2277i) q^{47} +(-2.17238 + 6.65438i) q^{49} +(2.49258 - 1.78138i) q^{51} +13.3365i q^{55} +(-1.14740 - 1.60550i) q^{57} +(-1.11483 - 1.93094i) q^{59} +(7.79396 + 4.49985i) q^{61} +(-7.58780 + 2.32921i) q^{63} +(3.49921 + 2.02027i) q^{65} +(5.43562 + 9.41477i) q^{67} +(-2.63442 + 5.79472i) q^{69} -4.52106i q^{71} +5.34234i q^{73} +(-0.0870571 - 0.895548i) q^{75} +(-1.55953 - 14.9379i) q^{77} +(-6.51422 + 11.2830i) q^{79} +(-7.11229 - 5.51501i) q^{81} +(6.27298 - 10.8651i) q^{83} +(-2.07781 - 3.59886i) q^{85} +(-7.16396 + 0.696415i) q^{87} -1.16106 q^{89} +(-4.15561 - 1.85366i) q^{91} +(-6.00000 + 13.1977i) q^{93} +(-2.31806 + 1.33834i) q^{95} +(-3.97536 - 2.29517i) q^{97} +(12.8323 - 11.1962i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{7} + 12 q^{9}+O(q^{10}) $ 16 * q - 2 * q^7 + 12 * q^9	$ 16 q - 2 q^{7} + 12 q^{9} + 12 q^{11} + 18 q^{21} + 48 q^{23} - 8 q^{25} - 12 q^{29} - 8 q^{37} + 36 q^{39} - 4 q^{43} - 8 q^{49} - 12 q^{51} + 48 q^{57} - 24 q^{63} + 84 q^{65} + 28 q^{67} + 78 q^{77} + 4 q^{79} + 36 q^{81} - 12 q^{85} - 24 q^{91} - 96 q^{93} - 12 q^{95} + 72 q^{99}+O(q^{100}) $ 16 * q - 2 * q^7 + 12 * q^9 + 12 * q^11 + 18 * q^21 + 48 * q^23 - 8 * q^25 - 12 * q^29 - 8 * q^37 + 36 * q^39 - 4 * q^43 - 8 * q^49 - 12 * q^51 + 48 * q^57 - 24 * q^63 + 84 * q^65 + 28 * q^67 + 78 * q^77 + 4 * q^79 + 36 * q^81 - 12 * q^85 - 24 * q^91 - 96 * q^93 - 12 * q^95 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.40917	+	1.00709i	−0.813585	+	0.581446i
$3$	−1.40917	+	1.00709i	−0.813585	+	0.581446i
$4$		0			0
$5$	1.17468	+	2.03460i	0.525332	+	0.909902i	0.999565	+	0.0295026i	$0.00939234\pi$
$5$	1.17468	+	2.03460i	0.525332	+	0.909902i	−0.474232	+	0.880400i	$0.657274\pi$
$6$		0			0
$7$	−1.55364	−	2.14154i	−0.587222	−	0.809426i
$7$	−1.55364	−	2.14154i	−0.587222	−	0.809426i
$8$		0			0
$9$	0.971521	−	2.83834i	0.323840	−	0.946112i
$10$		0			0
$11$	4.91614	+	2.83834i	1.48227	+	0.855790i	0.999798	−	0.0201197i	$-0.00640473\pi$
$11$	4.91614	+	2.83834i	1.48227	+	0.855790i	0.482475	+	0.875910i	$0.339738\pi$
$12$		0			0
$13$	1.48943	−	0.859925i	0.413094	−	0.238500i	−0.279024	−	0.960284i	$-0.590011\pi$
$13$	1.48943	−	0.859925i	0.413094	−	0.238500i	0.692118	+	0.721784i	$0.256678\pi$
$14$		0			0
$15$	−3.70436	−	1.68409i	−0.956462	−	0.434830i
$16$		0			0
$17$	−1.76883			−0.429004			−0.214502	−	0.976724i	$-0.568813\pi$
$17$	−1.76883			−0.429004			−0.214502	+	0.976724i	$0.568813\pi$
$18$		0			0
$19$			1.13932i			0.261378i	0.991423	+	0.130689i	$0.0417189\pi$
$19$			1.13932i			0.261378i	−0.991423	+	0.130689i	$0.958281\pi$
$20$		0			0
$21$	4.34608	+	1.45313i	0.948393	+	0.317098i
$22$		0			0
$23$	3.18272	−	1.83755i	0.663644	−	0.383155i	−0.130020	−	0.991511i	$-0.541504\pi$
$23$	3.18272	−	1.83755i	0.663644	−	0.383155i	0.793664	+	0.608356i	$0.208171\pi$
$24$		0			0
$25$	−0.259741	+	0.449885i	−0.0519482	+	0.0899769i
$26$		0			0
$27$	1.48943	+	4.97811i	0.286642	+	0.958038i
$28$		0			0
$29$	3.59886	+	2.07781i	0.668292	+	0.385839i	0.795429	−	0.606046i	$-0.207245\pi$
$29$	3.59886	+	2.07781i	0.668292	+	0.385839i	−0.127137	+	0.991885i	$0.540579\pi$
$30$		0			0
$31$	7.24879	−	4.18509i	1.30192	−	0.751665i	0.321188	−	0.947015i	$-0.395918\pi$
$31$	7.24879	−	4.18509i	1.30192	−	0.751665i	0.980734	+	0.195350i	$0.0625844\pi$
$32$		0			0
$33$	−9.78615	+	0.951321i	−1.70355	+	0.165604i
$34$		0			0
$35$	2.53215	−	5.67667i	0.428012	−	0.959532i
$36$		0			0
$37$	−9.19773			−1.51210			−0.756049	−	0.654515i	$-0.772873\pi$
$37$	−9.19773			−1.51210			−0.756049	+	0.654515i	$0.772873\pi$
$38$		0			0
$39$	−1.23284	+	2.71178i	−0.197412	+	0.434232i
$40$		0			0
$41$	3.99709	+	6.92317i	0.624241	+	1.08122i	0.988687	+	0.149993i	$0.0479251\pi$
$41$	3.99709	+	6.92317i	0.624241	+	1.08122i	−0.364446	+	0.931225i	$0.618742\pi$
$42$		0			0
$43$	−1.76053	+	3.04933i	−0.268478	+	0.465018i	−0.968469	−	0.249134i	$-0.919854\pi$
$43$	−1.76053	+	3.04933i	−0.268478	+	0.465018i	0.699991	+	0.714152i	$0.253187\pi$
$44$		0			0
$45$	6.91611	−	1.35747i	1.03099	−	0.202360i
$46$		0			0
$47$	−5.90494	+	10.2277i	−0.861324	+	1.49186i	0.00932669	+	0.999957i	$0.497031\pi$
$47$	−5.90494	+	10.2277i	−0.861324	+	1.49186i	−0.870651	+	0.491901i	$0.836302\pi$
$48$		0			0
$49$	−2.17238	+	6.65438i	−0.310340	+	0.950626i
$50$		0			0
$51$	2.49258	−	1.78138i	0.349031	−	0.249443i
$52$		0			0
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$		0			0
$55$			13.3365i			1.79830i
$56$		0			0
$57$	−1.14740	−	1.60550i	−0.151977	−	0.212653i
$58$		0			0
$59$	−1.11483	−	1.93094i	−0.145139	−	0.251387i	0.784286	−	0.620399i	$-0.213029\pi$
$59$	−1.11483	−	1.93094i	−0.145139	−	0.251387i	−0.929425	+	0.369012i	$0.879696\pi$
$60$		0			0
$61$	7.79396	+	4.49985i	0.997915	+	0.576146i	0.907631	−	0.419770i	$-0.137889\pi$
$61$	7.79396	+	4.49985i	0.997915	+	0.576146i	0.0902842	+	0.995916i	$0.471222\pi$
$62$		0			0
$63$	−7.58780	+	2.32921i	−0.955973	+	0.293453i
$64$		0			0
$65$	3.49921	+	2.02027i	0.434024	+	0.250584i
$66$		0			0
$67$	5.43562	+	9.41477i	0.664067	+	1.15020i	0.979537	+	0.201262i	$0.0645044\pi$
$67$	5.43562	+	9.41477i	0.664067	+	1.15020i	−0.315470	+	0.948935i	$0.602162\pi$
$68$		0			0
$69$	−2.63442	+	5.79472i	−0.317147	+	0.697602i
$70$		0			0
$71$		−	4.52106i		−	0.536551i	−0.963342	−	0.268276i	$-0.913546\pi$
$71$		−	4.52106i		−	0.536551i	0.963342	−	0.268276i	$-0.0864538\pi$
$72$		0			0
$73$			5.34234i			0.625274i	0.949873	+	0.312637i	$0.101212\pi$
$73$			5.34234i			0.625274i	−0.949873	+	0.312637i	$0.898788\pi$
$74$		0			0
$75$	−0.0870571	−	0.895548i	−0.0100525	−	0.103409i
$76$		0			0
$77$	−1.55953	−	14.9379i	−0.177724	−	1.70233i
$78$		0			0
$79$	−6.51422	+	11.2830i	−0.732907	+	1.26943i	0.222729	+	0.974880i	$0.428503\pi$
$79$	−6.51422	+	11.2830i	−0.732907	+	1.26943i	−0.955636	+	0.294551i	$0.904830\pi$
$80$		0			0
$81$	−7.11229	−	5.51501i	−0.790255	−	0.612778i
$82$		0			0
$83$	6.27298	−	10.8651i	0.688549	−	1.19260i	−0.283758	−	0.958896i	$-0.591581\pi$
$83$	6.27298	−	10.8651i	0.688549	−	1.19260i	0.972307	−	0.233707i	$-0.0750855\pi$
$84$		0			0
$85$	−2.07781	−	3.59886i	−0.225370	−	0.390352i
$86$		0			0
$87$	−7.16396	+	0.696415i	−0.768057	+	0.0746636i
$88$		0			0
$89$	−1.16106			−0.123072			−0.0615360	−	0.998105i	$-0.519600\pi$
$89$	−1.16106			−0.123072			−0.0615360	+	0.998105i	$0.519600\pi$
$90$		0			0
$91$	−4.15561	−	1.85366i	−0.435626	−	0.194317i
$92$		0			0
$93$	−6.00000	+	13.1977i	−0.622171	+	1.36854i
$94$		0			0
$95$	−2.31806	+	1.33834i	−0.237828	+	0.137310i
$96$		0			0
$97$	−3.97536	−	2.29517i	−0.403636	−	0.233039i	0.284416	−	0.958701i	$-0.408200\pi$
$97$	−3.97536	−	2.29517i	−0.403636	−	0.233039i	−0.688052	+	0.725662i	$0.741534\pi$
$98$		0			0
$99$	12.8323	−	11.1962i	1.28969	−	1.12526i
$100$		0			0
$101$	3.31155	−	5.73577i	0.329511	−	0.570730i	−0.652904	−	0.757441i	$-0.726449\pi$
$101$	3.31155	−	5.73577i	0.329511	−	0.570730i	0.982415	+	0.186711i	$0.0597827\pi$
$102$		0			0
$103$	5.07471	−	2.92989i	0.500026	−	0.288690i	−0.228698	−	0.973497i	$-0.573447\pi$
$103$	5.07471	−	2.92989i	0.500026	−	0.288690i	0.728724	+	0.684807i	$0.240114\pi$
$104$		0			0
$105$	2.14871	+	10.5495i	0.209693	+	1.02953i
$106$		0			0
$107$			4.71563i			0.455878i	0.973675	+	0.227939i	$0.0731986\pi$
$107$			4.71563i			0.455878i	−0.973675	+	0.227939i	$0.926801\pi$
$108$		0			0
$109$	4.23669			0.405802			0.202901	−	0.979199i	$-0.434963\pi$
$109$	4.23669			0.405802			0.202901	+	0.979199i	$0.434963\pi$
$110$		0			0
$111$	12.9612	−	9.26298i	1.23022	−	0.879203i
$112$		0			0
$113$	5.91693	−	3.41614i	0.556618	−	0.321363i	−0.195169	−	0.980770i	$-0.562526\pi$
$113$	5.91693	−	3.41614i	0.556618	−	0.321363i	0.751787	+	0.659406i	$0.229192\pi$
$114$		0			0
$115$	7.47736	+	4.31705i	0.697267	+	0.402567i
$116$		0			0
$117$	−0.993738	−	5.06295i	−0.0918712	−	0.468069i
$118$		0			0
$119$	2.74813	+	3.78802i	0.251921	+	0.347247i
$120$		0			0
$121$	10.6123	+	18.3810i	0.964754	+	1.67100i
$122$		0			0
$123$	−12.6049	−	5.73047i	−1.13654	−	0.516699i
$124$		0			0
$125$	10.5263			0.941504
$126$		0			0
$127$	6.67667			0.592459			0.296229	−	0.955117i	$-0.404271\pi$
$127$	6.67667			0.592459			0.296229	+	0.955117i	$0.404271\pi$
$128$		0			0
$129$	−0.590074	−	6.07004i	−0.0519532	−	0.534437i
$130$		0			0
$131$	−3.73653	−	6.47185i	−0.326462	−	0.565448i	0.655345	−	0.755329i	$-0.272523\pi$
$131$	−3.73653	−	6.47185i	−0.326462	−	0.565448i	−0.981807	+	0.189881i	$0.939190\pi$
$132$		0			0
$133$	2.43990	−	1.77010i	0.211566	−	0.153487i
$134$		0			0
$135$	−8.37888	+	8.87809i	−0.721139	+	0.764104i
$136$		0			0
$137$	6.91772	+	3.99395i	0.591021	+	0.341226i	0.765501	−	0.643435i	$-0.222491\pi$
$137$	6.91772	+	3.99395i	0.591021	+	0.341226i	−0.174480	+	0.984661i	$0.555825\pi$
$138$		0			0
$139$	−17.9792	+	10.3803i	−1.52498	+	0.880446i	−0.525415	+	0.850846i	$0.676090\pi$
$139$	−17.9792	+	10.3803i	−1.52498	+	0.880446i	−0.999562	+	0.0295993i	$0.990577\pi$
$140$		0			0
$141$	−1.97915	−	20.3593i	−0.166675	−	1.71457i
$142$		0			0
$143$	9.76302			0.816425
$144$		0			0
$145$			9.76302i			0.810774i
$146$		0			0
$147$	−3.64033	−	11.5649i	−0.300250	−	0.953861i
$148$		0			0
$149$	−1.03726	+	0.598865i	−0.0849760	+	0.0490609i	−0.541886	−	0.840452i	$-0.682290\pi$
$149$	−1.03726	+	0.598865i	−0.0849760	+	0.0490609i	0.456910	+	0.889513i	$0.348956\pi$
$150$		0			0
$151$	7.61229	−	13.1849i	0.619480	−	1.07297i	−0.370101	−	0.928991i	$-0.620677\pi$
$151$	7.61229	−	13.1849i	0.619480	−	1.07297i	0.989581	−	0.143979i	$-0.0459897\pi$
$152$		0			0
$153$	−1.71845	+	5.02053i	−0.138929	+	0.405886i
$154$		0			0
$155$	17.0300	+	9.83228i	1.36788	+	0.789748i
$156$		0			0
$157$	8.68358	−	5.01347i	0.693025	−	0.400118i	−0.111719	−	0.993740i	$-0.535636\pi$
$157$	8.68358	−	5.01347i	0.693025	−	0.400118i	0.804744	+	0.593621i	$0.202302\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−8.88000	−	3.96104i	−0.699842	−	0.312173i
$162$		0			0
$163$	−12.0032			−0.940160			−0.470080	−	0.882624i	$-0.655775\pi$
$163$	−12.0032			−0.940160			−0.470080	+	0.882624i	$0.655775\pi$
$164$		0			0
$165$	−13.4311	−	18.7934i	−1.04561	−	1.46307i
$166$		0			0
$167$	−8.57472	−	14.8518i	−0.663532	−	1.14927i	−0.979681	−	0.200561i	$-0.935723\pi$
$167$	−8.57472	−	14.8518i	−0.663532	−	1.14927i	0.316150	−	0.948709i	$-0.397610\pi$
$168$		0			0
$169$	−5.02106	+	8.69673i	−0.386235	+	0.668979i
$170$		0			0
$171$	3.23377	+	1.10687i	0.247293	+	0.0846447i
$172$		0			0
$173$	0.993738	−	1.72121i	0.0755525	−	0.130861i	−0.825774	−	0.564001i	$-0.809261\pi$
$173$	0.993738	−	1.72121i	0.0755525	−	0.130861i	0.901326	+	0.433140i	$0.142595\pi$
$174$		0			0
$175$	1.36699	−	0.142715i	0.103335	−	0.0107882i
$176$		0			0
$177$	3.51563	+	1.59829i	0.264251	+	0.120135i
$178$		0			0
$179$			8.31122i			0.621210i	0.950539	+	0.310605i	$0.100532\pi$
$179$			8.31122i			0.621210i	−0.950539	+	0.310605i	$0.899468\pi$
$180$		0			0
$181$		−	15.4541i		−	1.14870i	−0.818611	−	0.574348i	$-0.805256\pi$
$181$		−	15.4541i		−	1.14870i	0.818611	−	0.574348i	$-0.194744\pi$
$182$		0			0
$183$	−15.5148	+	1.50821i	−1.14689	+	0.111490i
$184$		0			0
$185$	−10.8044	−	18.7137i	−0.794354	−	1.37586i
$186$		0			0
$187$	−8.69581	−	5.02053i	−0.635901	−	0.367137i
$188$		0			0
$189$	8.34677	−	10.9239i	0.607138	−	0.794596i
$190$		0			0
$191$	−10.6851	−	6.16904i	−0.773146	−	0.446376i	0.0608498	−	0.998147i	$-0.480619\pi$
$191$	−10.6851	−	6.16904i	−0.773146	−	0.446376i	−0.833996	+	0.551771i	$0.813952\pi$
$192$		0			0
$193$	−2.19694	−	3.80521i	−0.158139	−	0.273905i	0.776058	−	0.630661i	$-0.217216\pi$
$193$	−2.19694	−	3.80521i	−0.158139	−	0.273905i	−0.934198	+	0.356756i	$0.883883\pi$
$194$		0			0
$195$	−6.96559	+	0.677132i	−0.498816	+	0.0484904i
$196$		0			0
$197$		−	10.8865i		−	0.775632i	−0.921737	−	0.387816i	$-0.873230\pi$
$197$		−	10.8865i		−	0.775632i	0.921737	−	0.387816i	$-0.126770\pi$
$198$		0			0
$199$		−	27.5665i		−	1.95414i	−0.212926	−	0.977068i	$-0.568299\pi$
$199$		−	27.5665i		−	1.95414i	0.212926	−	0.977068i	$-0.431701\pi$
$200$		0			0
$201$	−17.1413	−	7.79283i	−1.20905	−	0.549664i
$202$		0			0
$203$	−1.14165	−	10.9353i	−0.0801282	−	0.767506i
$204$		0			0
$205$	−9.39060	+	16.2650i	−0.655868	+	1.13600i
$206$		0			0
$207$	−2.12349	−	10.8189i	−0.147593	−	0.751962i
$208$		0			0
$209$	−3.23377	+	5.60106i	−0.223685	+	0.387433i
$210$		0			0
$211$	−5.15561	−	8.92978i	−0.354927	−	0.614751i	0.632179	−	0.774823i	$-0.282161\pi$
$211$	−5.15561	−	8.92978i	−0.354927	−	0.614751i	−0.987105	+	0.160071i	$0.948828\pi$
$212$		0			0
$213$	4.55313	+	6.37094i	0.311976	+	0.436530i
$214$		0			0
$215$	−8.27223			−0.564161
$216$		0			0
$217$	−20.2246	−	9.02143i	−1.37293	−	0.612415i
$218$		0			0
$219$	−5.38024	−	7.52827i	−0.363563	−	0.508713i
$220$		0			0
$221$	−2.63455	+	1.52106i	−0.177219	+	0.102318i
$222$		0			0
$223$	6.24329	+	3.60456i	0.418081	+	0.241379i	0.694256	−	0.719728i	$-0.255733\pi$
$223$	6.24329	+	3.60456i	0.418081	+	0.241379i	−0.276175	+	0.961107i	$0.589067\pi$
$224$		0			0
$225$	1.02458	+	1.17430i	0.0683053	+	0.0782870i
$226$		0			0
$227$	−6.37800	+	11.0470i	−0.423323	+	0.733217i	−0.996262	−	0.0863812i	$-0.972470\pi$
$227$	−6.37800	+	11.0470i	−0.423323	+	0.733217i	0.572939	+	0.819598i	$0.305803\pi$
$228$		0			0
$229$	3.89208	−	2.24709i	0.257196	−	0.148492i	−0.365859	−	0.930670i	$-0.619225\pi$
$229$	3.89208	−	2.24709i	0.257196	−	0.148492i	0.623055	+	0.782178i	$0.285891\pi$
$230$		0			0
$231$	17.2415	+	19.4794i	1.13441	+	1.28165i
$232$		0			0
$233$		−	2.15403i		−	0.141115i	−0.997508	−	0.0705577i	$-0.977522\pi$
$233$		−	2.15403i		−	0.141115i	0.997508	−	0.0705577i	$-0.0224779\pi$
$234$		0			0
$235$	−27.7456			−1.80993
$236$		0			0
$237$	−2.18336	−	22.4600i	−0.141825	−	1.45894i
$238$		0			0
$239$	8.78317	−	5.07096i	0.568136	−	0.328013i	−0.188269	−	0.982118i	$-0.560288\pi$
$239$	8.78317	−	5.07096i	0.568136	−	0.328013i	0.756404	+	0.654104i	$0.226954\pi$
$240$		0			0
$241$	9.13490	+	5.27404i	0.588431	+	0.339731i	0.764477	−	0.644651i	$-0.222997\pi$
$241$	9.13490	+	5.27404i	0.588431	+	0.339731i	−0.176046	+	0.984382i	$0.556331\pi$
$242$		0			0
$243$	15.5766	+	0.608830i	0.999237	+	0.0390564i
$244$		0			0
$245$	−16.0909	+	3.39682i	−1.02801	+	0.217015i
$246$		0			0
$247$	0.979729	+	1.69694i	0.0623387	+	0.107974i
$248$		0			0
$249$	2.10251	+	21.6283i	0.133241	+	1.37064i
$250$		0			0
$251$	29.3005			1.84943			0.924714	−	0.380662i	$-0.124304\pi$
$251$	29.3005			1.84943			0.924714	+	0.380662i	$0.124304\pi$
$252$		0			0
$253$	20.8623			1.31160
$254$		0			0
$255$	6.55238	+	2.97887i	0.410326	+	0.186544i
$256$		0			0
$257$	−3.81430	−	6.60656i	−0.237930	−	0.412106i	0.722190	−	0.691694i	$-0.243135\pi$
$257$	−3.81430	−	6.60656i	−0.237930	−	0.412106i	−0.960120	+	0.279588i	$0.909802\pi$
$258$		0			0
$259$	14.2900	+	19.6973i	0.887937	+	1.22393i
$260$		0			0
$261$	9.39388	−	8.19615i	0.581467	−	0.507329i
$262$		0			0
$263$	10.5531	+	6.09281i	0.650729	+	0.375699i	0.788736	−	0.614733i	$-0.210736\pi$
$263$	10.5531	+	6.09281i	0.650729	+	0.375699i	−0.138006	+	0.990431i	$0.544069\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.63613	−	1.16930i	0.100129	−	0.0715597i
$268$		0			0
$269$	2.77433			0.169154			0.0845771	−	0.996417i	$-0.473046\pi$
$269$	2.77433			0.169154			0.0845771	+	0.996417i	$0.473046\pi$
$270$		0			0
$271$			3.20793i			0.194868i	0.995242	+	0.0974338i	$0.0310634\pi$
$271$			3.20793i			0.194868i	−0.995242	+	0.0974338i	$0.968937\pi$
$272$		0			0
$273$	7.72278	−	1.57297i	0.467404	−	0.0952003i
$274$		0			0
$275$	−2.55385	+	1.47446i	−0.154003	+	0.0889135i
$276$		0			0
$277$	−5.04054	+	8.73047i	−0.302857	+	0.524563i	−0.976782	−	0.214236i	$-0.931274\pi$
$277$	−5.04054	+	8.73047i	−0.302857	+	0.524563i	0.673925	+	0.738800i	$0.264607\pi$
$278$		0			0
$279$	−4.83634	−	24.6404i	−0.289544	−	1.47518i
$280$		0			0
$281$	4.21999	+	2.43641i	0.251743	+	0.145344i	0.620562	−	0.784157i	$-0.286904\pi$
$281$	4.21999	+	2.43641i	0.251743	+	0.145344i	−0.368819	+	0.929501i	$0.620238\pi$
$282$		0			0
$283$	2.44030	−	1.40891i	0.145061	−	0.0837508i	−0.425713	−	0.904858i	$-0.639977\pi$
$283$	2.44030	−	1.40891i	0.145061	−	0.0837508i	0.570774	+	0.821107i	$0.306643\pi$
$284$		0			0
$285$	1.91872	−	4.22045i	0.113655	−	0.249998i
$286$		0			0
$287$	8.61618	−	19.3161i	0.508597	−	1.14019i
$288$		0			0
$289$	−13.8712			−0.815956
$290$		0			0
$291$	7.91341	−	0.769270i	0.463892	−	0.0450954i
$292$		0			0
$293$	−4.05694	−	7.02683i	−0.237009	−	0.410512i	0.722846	−	0.691010i	$-0.242834\pi$
$293$	−4.05694	−	7.02683i	−0.237009	−	0.410512i	−0.959855	+	0.280498i	$0.909500\pi$
$294$		0			0
$295$	2.61914	−	4.53648i	0.152492	−	0.264124i
$296$		0			0
$297$	−6.80728	+	28.7006i	−0.394999	+	1.66538i
$298$		0			0
$299$	3.16030	−	5.47381i	0.182765	−	0.316558i
$300$		0			0
$301$	9.26549	−	0.967324i	0.534054	−	0.0557556i
$302$		0			0
$303$	1.10993	+	11.4177i	0.0637637	+	0.655931i
$304$		0			0
$305$			21.1435i			1.21067i
$306$		0			0
$307$		−	10.8996i		−	0.622074i	−0.950398	−	0.311037i	$-0.899324\pi$
$307$		−	10.8996i		−	0.622074i	0.950398	−	0.311037i	$-0.100676\pi$
$308$		0			0
$309$	−4.20046	+	9.23943i	−0.238956	+	0.525613i
$310$		0			0
$311$	−4.11819	−	7.13291i	−0.233521	−	0.404470i	0.725321	−	0.688411i	$-0.241691\pi$
$311$	−4.11819	−	7.13291i	−0.233521	−	0.404470i	−0.958842	+	0.283941i	$0.908358\pi$
$312$		0			0
$313$	−29.2736	−	16.9011i	−1.65464	−	0.955308i	−0.975127	−	0.221648i	$-0.928857\pi$
$313$	−29.2736	−	16.9011i	−1.65464	−	0.955308i	−0.679516	−	0.733661i	$-0.737810\pi$
$314$		0			0
$315$	−13.6523	−	12.7021i	−0.769217	−	0.715682i
$316$		0			0
$317$	5.82913	+	3.36545i	0.327396	+	0.189022i	0.654685	−	0.755902i	$-0.272801\pi$
$317$	5.82913	+	3.36545i	0.327396	+	0.189022i	−0.327288	+	0.944925i	$0.606135\pi$
$318$		0			0
$319$	11.7950	+	20.4296i	0.660394	+	1.14384i
$320$		0			0
$321$	−4.74909	−	6.64513i	−0.265068	−	0.370895i
$322$		0			0
$323$		−	2.01526i		−	0.112132i
$324$		0			0
$325$			0.893431i			0.0495586i
$326$		0			0
$327$	−5.97022	+	4.26675i	−0.330154	+	0.235952i
$328$		0			0
$329$	31.0771	−	3.24447i	1.71334	−	0.178874i
$330$		0			0
$331$	−16.0284	+	27.7621i	−0.881002	+	1.52594i	−0.0307744	+	0.999526i	$0.509797\pi$
$331$	−16.0284	+	27.7621i	−0.881002	+	1.52594i	−0.850228	+	0.526415i	$0.823536\pi$
$332$		0			0
$333$	−8.93579	+	26.1062i	−0.489678	+	1.43061i
$334$		0			0
$335$	−12.7702	+	22.1187i	−0.697712	+	1.20847i
$336$		0			0
$337$	−12.1123	−	20.9791i	−0.659799	−	1.14280i	−0.980668	−	0.195681i	$-0.937308\pi$
$337$	−12.1123	−	20.9791i	−0.659799	−	1.14280i	0.320869	−	0.947124i	$-0.396025\pi$
$338$		0			0
$339$	−4.89758	+	10.7728i	−0.266000	+	0.585100i
$340$		0			0
$341$	47.5148			2.57307
$342$		0			0
$343$	17.6257	−	5.68629i	0.951700	−	0.307031i
$344$		0			0
$345$	−14.8846	+	1.44694i	−0.801357	+	0.0779007i
$346$		0			0
$347$	−19.7453	+	11.3999i	−1.05998	+	0.611981i	−0.925427	−	0.378926i	$-0.876294\pi$
$347$	−19.7453	+	11.3999i	−1.05998	+	0.611981i	−0.134554	+	0.990906i	$0.542960\pi$
$348$		0			0
$349$	−2.46389	−	1.42253i	−0.131889	−	0.0761461i	0.432604	−	0.901584i	$-0.357595\pi$
$349$	−2.46389	−	1.42253i	−0.131889	−	0.0761461i	−0.564493	+	0.825438i	$0.690928\pi$
$350$		0			0
$351$	6.49921	+	6.13376i	0.346902	+	0.327396i
$352$		0			0
$353$	−3.57212	+	6.18709i	−0.190125	+	0.329306i	−0.945291	−	0.326227i	$-0.894223\pi$
$353$	−3.57212	+	6.18709i	−0.190125	+	0.329306i	0.755167	+	0.655533i	$0.227556\pi$
$354$		0			0
$355$	9.19856	−	5.31079i	0.488209	−	0.281868i
$356$		0			0
$357$	−7.68747	−	2.57033i	−0.406864	−	0.136036i
$358$		0			0
$359$			11.6037i			0.612421i	0.951964	+	0.306210i	$0.0990611\pi$
$359$			11.6037i			0.612421i	−0.951964	+	0.306210i	$0.900939\pi$
$360$		0			0
$361$	17.7019			0.931682
$362$		0			0
$363$	−33.4660	−	15.2144i	−1.75651	−	0.798550i
$364$		0			0
$365$	−10.8695	+	6.27554i	−0.568938	+	0.328477i
$366$		0			0
$367$	−6.78525	−	3.91747i	−0.354187	−	0.204490i	0.312341	−	0.949970i	$-0.398887\pi$
$367$	−6.78525	−	3.91747i	−0.354187	−	0.204490i	−0.666528	+	0.745480i	$0.732220\pi$
$368$		0			0
$369$	23.5335	−	4.61909i	1.22511	−	0.240460i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−12.8339	−	22.2289i	−0.664512	−	1.15097i	−0.979417	−	0.201845i	$-0.935306\pi$
$373$	−12.8339	−	22.2289i	−0.664512	−	1.15097i	0.314905	−	0.949123i	$-0.398027\pi$
$374$		0			0
$375$	−14.8334	+	10.6010i	−0.765994	+	0.547434i
$376$		0			0
$377$	7.14702			0.368091
$378$		0			0
$379$	15.1045			0.775868			0.387934	−	0.921687i	$-0.373189\pi$
$379$	15.1045			0.775868			0.387934	+	0.921687i	$0.373189\pi$
$380$		0			0
$381$	−9.40856	+	6.72404i	−0.482015	+	0.344483i
$382$		0			0
$383$	−0.763322	−	1.32211i	−0.0390040	−	0.0675568i	0.845864	−	0.533398i	$-0.179085\pi$
$383$	−0.763322	−	1.32211i	−0.0390040	−	0.0675568i	−0.884868	+	0.465841i	$0.845752\pi$
$384$		0			0
$385$	28.5607	−	20.7202i	1.45559	−	1.05600i
$386$		0			0
$387$	6.94462	+	7.95946i	0.353015	+	0.404602i
$388$		0			0
$389$	12.8948	+	7.44483i	0.653794	+	0.377468i	0.789908	−	0.613225i	$-0.210128\pi$
$389$	12.8948	+	7.44483i	0.653794	+	0.377468i	−0.136115	+	0.990693i	$0.543462\pi$
$390$		0			0
$391$	−5.62969	+	3.25030i	−0.284706	+	0.164375i
$392$		0			0
$393$	11.7832	+	5.35691i	0.594382	+	0.270220i
$394$		0			0
$395$	−30.6085			−1.54008
$396$		0			0
$397$			28.7869i			1.44478i	0.691488	+	0.722388i	$0.256955\pi$
$397$			28.7869i			1.44478i	−0.691488	+	0.722388i	$0.743045\pi$
$398$		0			0
$399$	−1.65558	+	4.95158i	−0.0828825	+	0.247889i
$400$		0			0
$401$	−33.0592	+	19.0868i	−1.65090	+	0.953147i	−0.674196	+	0.738552i	$0.735510\pi$
$401$	−33.0592	+	19.0868i	−1.65090	+	0.953147i	−0.976703	+	0.214595i	$0.931157\pi$
$402$		0			0
$403$	7.19773	−	12.4668i	0.358544	−	0.621017i
$404$		0			0
$405$	2.86619	−	20.9491i	0.142422	−	1.04097i
$406$		0			0
$407$	−45.2173	−	26.1062i	−2.24134	−	1.29404i
$408$		0			0
$409$	6.03355	−	3.48347i	0.298340	−	0.172247i	−0.343357	−	0.939205i	$-0.611564\pi$
$409$	6.03355	−	3.48347i	0.298340	−	0.172247i	0.641697	+	0.766958i	$0.278231\pi$
$410$		0			0
$411$	−13.7705	+	1.33865i	−0.679250	+	0.0660305i
$412$		0			0
$413$	−2.40314	+	5.38745i	−0.118251	+	0.265099i
$414$		0			0
$415$	29.4750			1.44687
$416$		0			0
$417$	14.8818	−	32.7344i	0.728766	−	1.60301i
$418$		0			0
$419$	17.4232	+	30.1778i	0.851177	+	1.47428i	0.880146	+	0.474702i	$0.157444\pi$
$419$	17.4232	+	30.1778i	0.851177	+	1.47428i	−0.0289690	+	0.999580i	$0.509222\pi$
$420$		0			0
$421$	2.84597	−	4.92936i	0.138704	−	0.240242i	−0.788302	−	0.615288i	$-0.789040\pi$
$421$	2.84597	−	4.92936i	0.138704	−	0.240242i	0.927006	+	0.375046i	$0.122373\pi$
$422$		0			0
$423$	23.2928	+	26.6966i	1.13253	+	1.29803i
$424$		0			0
$425$	0.459437	−	0.795769i	0.0222860	−	0.0386005i
$426$		0			0
$427$	−2.47244	−	23.6822i	−0.119650	−	1.14606i
$428$		0			0
$429$	−13.7578	+	9.83228i	−0.664231	+	0.474707i
$430$		0			0
$431$		−	30.2936i		−	1.45919i	−0.683880	−	0.729595i	$-0.739709\pi$
$431$		−	30.2936i		−	1.45919i	0.683880	−	0.729595i	$-0.260291\pi$
$432$		0			0
$433$			23.6094i			1.13459i	0.823513	+	0.567297i	$0.192011\pi$
$433$			23.6094i			1.13459i	−0.823513	+	0.567297i	$0.807989\pi$
$434$		0			0
$435$	−9.83228	−	13.7578i	−0.471422	−	0.659634i
$436$		0			0
$437$	2.09355	+	3.62614i	0.100148	+	0.173462i
$438$		0			0
$439$	−21.6681	−	12.5101i	−1.03416	−	0.597075i	−0.115989	−	0.993250i	$-0.537004\pi$
$439$	−21.6681	−	12.5101i	−1.03416	−	0.597075i	−0.918175	+	0.396175i	$0.870337\pi$
$440$		0			0
$441$	16.7768	+	12.6308i	0.798897	+	0.601467i
$442$		0			0
$443$	19.9446	+	11.5150i	0.947595	+	0.547094i	0.892333	−	0.451377i	$-0.149067\pi$
$443$	19.9446	+	11.5150i	0.947595	+	0.547094i	0.0552622	+	0.998472i	$0.482401\pi$
$444$		0			0
$445$	−1.36387	−	2.36229i	−0.0646537	−	0.111983i
$446$		0			0
$447$	0.858568	−	1.88853i	0.0406089	−	0.0893242i
$448$		0			0
$449$		−	15.9028i		−	0.750501i	−0.926923	−	0.375251i	$-0.877557\pi$
$449$		−	15.9028i		−	0.750501i	0.926923	−	0.375251i	$-0.122443\pi$
$450$		0			0
$451$			45.3804i			2.13688i
$452$		0			0
$453$	2.55140	+	26.2460i	0.119875	+	1.23315i
$454$		0			0
$455$	−1.11004	−	10.6325i	−0.0520394	−	0.498458i
$456$		0			0
$457$	2.83307	−	4.90702i	0.132525	−	0.229541i	−0.792124	−	0.610360i	$-0.791025\pi$
$457$	2.83307	−	4.90702i	0.132525	−	0.229541i	0.924649	+	0.380819i	$0.124358\pi$
$458$		0			0
$459$	−2.63455	−	8.80542i	−0.122970	−	0.411002i
$460$		0			0
$461$	−15.7292	+	27.2438i	−0.732582	+	1.26887i	0.223194	+	0.974774i	$0.428352\pi$
$461$	−15.7292	+	27.2438i	−0.732582	+	1.26887i	−0.955776	+	0.294095i	$0.904982\pi$
$462$		0			0
$463$	−4.55148	−	7.88340i	−0.211525	−	0.366373i	0.740667	−	0.671873i	$-0.234510\pi$
$463$	−4.55148	−	7.88340i	−0.211525	−	0.366373i	−0.952192	+	0.305500i	$0.901176\pi$
$464$		0			0
$465$	−33.9002	+	3.29547i	−1.57209	+	0.152824i
$466$		0			0
$467$	30.3032			1.40226			0.701132	−	0.713032i	$-0.252678\pi$
$467$	30.3032			1.40226			0.701132	+	0.713032i	$0.252678\pi$
$468$		0			0
$469$	11.7171	−	26.2678i	0.541045	−	1.21293i
$470$		0			0
$471$	−7.18761	+	15.8100i	−0.331188	+	0.728487i
$472$		0			0
$473$	−17.3100	+	9.99395i	−0.795916	+	0.459522i
$474$		0			0
$475$	−0.512563	−	0.295928i	−0.0235180	−	0.0135781i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	2.33143	−	4.03816i	0.106526	−	0.184508i	−0.807835	−	0.589409i	$-0.799361\pi$
$479$	2.33143	−	4.03816i	0.106526	−	0.184508i	0.914361	+	0.404901i	$0.132694\pi$
$480$		0			0
$481$	−13.6994	+	7.90935i	−0.624639	+	0.360636i
$482$		0			0
$483$	16.5026	−	3.36122i	0.750893	−	0.152941i
$484$		0			0
$485$		−	10.7844i		−	0.489693i
$486$		0			0
$487$	19.4821			0.882818			0.441409	−	0.897306i	$-0.354479\pi$
$487$	19.4821			0.882818			0.441409	+	0.897306i	$0.354479\pi$
$488$		0			0
$489$	16.9145	−	12.0883i	0.764900	−	0.546652i
$490$		0			0
$491$	17.7437	−	10.2443i	0.800762	−	0.462320i	−0.0429758	−	0.999076i	$-0.513684\pi$
$491$	17.7437	−	10.2443i	0.800762	−	0.462320i	0.843737	+	0.536756i	$0.180351\pi$
$492$		0			0
$493$	−6.36577	−	3.67528i	−0.286700	−	0.165526i
$494$		0			0
$495$	37.8535	+	12.9567i	1.70139	+	0.582361i
$496$		0			0
$497$	−9.68203	+	7.02412i	−0.434298	+	0.315075i
$498$		0			0
$499$	−5.12598	−	8.87845i	−0.229470	−	0.397454i	0.728181	−	0.685385i	$-0.240366\pi$
$499$	−5.12598	−	8.87845i	−0.229470	−	0.397454i	−0.957651	+	0.287931i	$0.907033\pi$
$500$		0			0
$501$	27.0405	+	12.2932i	1.20808	+	0.549221i
$502$		0			0
$503$	14.5521			0.648845			0.324422	−	0.945912i	$-0.394830\pi$
$503$	14.5521			0.648845			0.324422	+	0.945912i	$0.394830\pi$
$504$		0			0
$505$	15.5600			0.692412
$506$		0			0
$507$	−1.68290	−	17.3119i	−0.0747403	−	0.768846i
$508$		0			0
$509$	−16.6617	−	28.8589i	−0.738517	−	1.27915i	−0.953163	−	0.302457i	$-0.902193\pi$
$509$	−16.6617	−	28.8589i	−0.738517	−	1.27915i	0.214646	−	0.976692i	$-0.431140\pi$
$510$		0			0
$511$	11.4408	−	8.30010i	0.506113	−	0.367175i
$512$		0			0
$513$	−5.67166	+	1.69694i	−0.250410	+	0.0749218i
$514$		0			0
$515$	11.9223	+	6.88335i	0.525360	+	0.303317i
$516$		0			0
$517$	−58.0591	+	33.5204i	−2.55343	+	1.47423i
$518$		0			0
$519$	0.333070	+	3.42626i	0.0146202	+	0.150396i
$520$		0			0
$521$	−6.53925			−0.286490			−0.143245	−	0.989687i	$-0.545754\pi$
$521$	−6.53925			−0.286490			−0.143245	+	0.989687i	$0.545754\pi$
$522$		0			0
$523$			0.786858i			0.0344069i	0.999852	+	0.0172034i	$0.00547630\pi$
$523$			0.786858i			0.0344069i	−0.999852	+	0.0172034i	$0.994524\pi$
$524$		0			0
$525$	−1.78260	+	1.57780i	−0.0777988	+	0.0688608i
$526$		0			0
$527$	−12.8219	+	7.40271i	−0.558530	+	0.322467i
$528$		0			0
$529$	−4.74685	+	8.22178i	−0.206385	+	0.357469i
$530$		0			0
$531$	−6.56374	+	1.28831i	−0.284842	+	0.0559079i
$532$		0			0
$533$	11.9068	+	6.87440i	0.515741	+	0.297763i
$534$		0			0
$535$	−9.59445	+	5.53936i	−0.414804	+	0.239487i
$536$		0			0
$537$	−8.37019	−	11.7119i	−0.361200	−	0.505407i
$538$		0			0
$539$	−29.5671	+	26.5479i	−1.27354	+	1.14350i
$540$		0			0
$541$	5.60454			0.240958			0.120479	−	0.992716i	$-0.461557\pi$
$541$	5.60454			0.240958			0.120479	+	0.992716i	$0.461557\pi$
$542$		0			0
$543$	15.5638	+	21.7775i	0.667905	+	0.934561i
$544$		0			0
$545$	4.97675	+	8.61999i	0.213181	+	0.369240i
$546$		0			0
$547$	6.91456	−	11.9764i	0.295645	−	0.512073i	−0.679489	−	0.733685i	$-0.737799\pi$
$547$	6.91456	−	11.9764i	0.295645	−	0.512073i	0.975135	+	0.221612i	$0.0711320\pi$
$548$		0			0
$549$	20.3441	−	17.7502i	0.868264	−	0.757559i
$550$		0			0
$551$	−2.36729	+	4.10026i	−0.100850	+	0.174677i
$552$		0			0
$553$	34.2837	−	3.57924i	1.45789	−	0.152205i
$554$		0			0
$555$	34.0717	+	15.4898i	1.44626	+	0.657506i
$556$		0			0
$557$		−	27.8233i		−	1.17891i	−0.807800	−	0.589456i	$-0.799342\pi$
$557$		−	27.8233i		−	1.17891i	0.807800	−	0.589456i	$-0.200658\pi$
$558$		0			0
$559$			6.05569i			0.256128i
$560$		0			0
$561$	17.3100	−	1.68272i	0.730830	−	0.0710447i
$562$		0			0
$563$	−12.2650	−	21.2436i	−0.516909	−	0.895312i	−0.999807	−	0.0196359i	$-0.993749\pi$
$563$	−12.2650	−	21.2436i	−0.516909	−	0.895312i	0.482898	−	0.875676i	$-0.339584\pi$
$564$		0			0
$565$	13.9010	+	8.02574i	0.584819	+	0.337645i
$566$		0			0
$567$	−0.760631	+	23.7996i	−0.0319435	+	0.999490i
$568$		0			0
$569$	−23.4762	−	13.5540i	−0.984172	−	0.568212i	−0.0806449	−	0.996743i	$-0.525698\pi$
$569$	−23.4762	−	13.5540i	−0.984172	−	0.568212i	−0.903527	+	0.428531i	$0.859031\pi$
$570$		0			0
$571$	−14.9177	−	25.8382i	−0.624287	−	1.08130i	−0.988678	−	0.150051i	$-0.952056\pi$
$571$	−14.9177	−	25.8382i	−0.624287	−	1.08130i	0.364391	−	0.931246i	$-0.381277\pi$
$572$		0			0
$573$	21.2699	−	2.06767i	0.888563	−	0.0863781i
$574$		0			0
$575$			1.90915i			0.0796169i
$576$		0			0
$577$		−	28.1666i		−	1.17259i	−0.810097	−	0.586296i	$-0.800585\pi$
$577$		−	28.1666i		−	1.17259i	0.810097	−	0.586296i	$-0.199415\pi$
$578$		0			0
$579$	6.92807	+	3.14967i	0.287921	+	0.130896i
$580$		0			0
$581$	−33.0141	+	3.44670i	−1.36965	+	0.142993i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	9.13376	−	7.96920i	0.377635	−	0.329486i
$586$		0			0
$587$	−4.95928	+	8.58973i	−0.204692	+	0.354536i	−0.950034	−	0.312145i	$-0.898952\pi$
$587$	−4.95928	+	8.58973i	−0.204692	+	0.354536i	0.745343	+	0.666681i	$0.232286\pi$
$588$		0			0
$589$	4.76816	+	8.25870i	0.196469	+	0.340294i
$590$		0			0
$591$	10.9637	+	15.3409i	0.450988	+	0.631042i
$592$		0			0
$593$	−4.69872			−0.192953			−0.0964766	−	0.995335i	$-0.530757\pi$
$593$	−4.69872			−0.192953			−0.0964766	+	0.995335i	$0.530757\pi$
$594$		0			0
$595$	−4.47894	+	10.0411i	−0.183619	+	0.411643i
$596$		0			0
$597$	27.7621	+	38.8459i	1.13623	+	1.58986i
$598$		0			0
$599$	−12.7309	+	7.35019i	−0.520170	+	0.300320i	−0.737004	−	0.675888i	$-0.763760\pi$
$599$	−12.7309	+	7.35019i	−0.520170	+	0.300320i	0.216834	+	0.976208i	$0.430427\pi$
$600$		0			0
$601$	16.2923	+	9.40634i	0.664575	+	0.383693i	0.794018	−	0.607894i	$-0.207986\pi$
$601$	16.2923	+	9.40634i	0.664575	+	0.383693i	−0.129443	+	0.991587i	$0.541319\pi$
$602$		0			0
$603$	32.0031	−	6.28147i	1.30327	−	0.255801i
$604$		0			0
$605$	−24.9321	+	43.1836i	−1.01363	+	1.75566i
$606$		0			0
$607$	−10.9051	+	6.29608i	−0.442625	+	0.255550i	−0.704711	−	0.709495i	$-0.748923\pi$
$607$	−10.9051	+	6.29608i	−0.442625	+	0.255550i	0.262085	+	0.965045i	$0.415590\pi$
$608$		0			0
$609$	12.6216	+	14.2599i	0.511455	+	0.577841i
$610$		0			0
$611$			20.3112i			0.821704i
$612$		0			0
$613$	−9.82017			−0.396633			−0.198317	−	0.980138i	$-0.563547\pi$
$613$	−9.82017			−0.396633			−0.198317	+	0.980138i	$0.563547\pi$
$614$		0			0
$615$	−3.14744	−	32.3774i	−0.126917	−	1.30558i
$616$		0			0
$617$	−3.25158	+	1.87730i	−0.130904	+	0.0755772i	−0.564022	−	0.825760i	$-0.690747\pi$
$617$	−3.25158	+	1.87730i	−0.130904	+	0.0755772i	0.433118	+	0.901337i	$0.357413\pi$
$618$		0			0
$619$	−9.56902	−	5.52468i	−0.384611	−	0.222055i	0.295211	−	0.955432i	$-0.404610\pi$
$619$	−9.56902	−	5.52468i	−0.384611	−	0.222055i	−0.679823	+	0.733376i	$0.737943\pi$
$620$		0			0
$621$	13.8880	+	13.1071i	0.557305	+	0.525968i
$622$		0			0
$623$	1.80387	+	2.48645i	0.0722706	+	0.0996176i
$624$		0			0
$625$	13.6638	+	23.6664i	0.546551	+	0.946654i
$626$		0			0
$627$	−1.08386	−	11.1496i	−0.0432852	−	0.445270i
$628$		0			0
$629$	16.2692			0.648696
$630$		0			0
$631$	−19.4921			−0.775969			−0.387984	−	0.921666i	$-0.626829\pi$
$631$	−19.4921			−0.775969			−0.387984	+	0.921666i	$0.626829\pi$
$632$		0			0
$633$	16.2583	+	7.39139i	0.646208	+	0.293781i
$634$		0			0
$635$	7.84294	+	13.5844i	0.311238	+	0.539080i
$636$		0			0
$637$	2.48665	+	11.7793i	0.0985245	+	0.466714i
$638$		0			0
$639$	−12.8323	−	4.39230i	−0.507637	−	0.173757i
$640$		0			0
$641$	−22.6669	−	13.0868i	−0.895290	−	0.516896i	−0.0196208	−	0.999807i	$-0.506246\pi$
$641$	−22.6669	−	13.0868i	−0.895290	−	0.516896i	−0.875669	+	0.482912i	$0.839579\pi$
$642$		0			0
$643$	−9.50955	+	5.49034i	−0.375020	+	0.216518i	−0.675649	−	0.737223i	$-0.736137\pi$
$643$	−9.50955	+	5.49034i	−0.375020	+	0.216518i	0.300629	+	0.953741i	$0.402803\pi$
$644$		0			0
$645$	11.6570	−	8.33092i	0.458993	−	0.328029i
$646$		0			0
$647$	−32.0126			−1.25855			−0.629273	−	0.777185i	$-0.716647\pi$
$647$	−32.0126			−1.25855			−0.629273	+	0.777185i	$0.716647\pi$
$648$		0			0
$649$		−	12.6570i		−	0.496833i
$650$		0			0
$651$	37.5853	−	7.65534i	1.47308	−	0.300036i
$652$		0			0
$653$	19.3686	−	11.1825i	0.757952	−	0.437604i	−0.0706080	−	0.997504i	$-0.522494\pi$
$653$	19.3686	−	11.1825i	0.757952	−	0.437604i	0.828560	+	0.559900i	$0.189161\pi$
$654$		0			0
$655$	8.77843	−	15.2047i	0.343002	−	0.594097i
$656$		0			0
$657$	15.1634	+	5.19020i	0.591579	+	0.202489i
$658$		0			0
$659$	19.2546	+	11.1166i	0.750053	+	0.433043i	0.825713	−	0.564091i	$-0.190773\pi$
$659$	19.2546	+	11.1166i	0.750053	+	0.433043i	−0.0756603	+	0.997134i	$0.524106\pi$
$660$		0			0
$661$	−9.13646	+	5.27494i	−0.355367	+	0.205171i	−0.667047	−	0.745016i	$-0.732442\pi$
$661$	−9.13646	+	5.27494i	−0.355367	+	0.205171i	0.311679	+	0.950187i	$0.399108\pi$
$662$		0			0
$663$	2.18068	−	4.79667i	0.0846907	−	0.186287i
$664$		0			0
$665$	6.46754	+	2.88493i	0.250801	+	0.111873i
$666$		0			0
$667$	15.2723			0.591344
$668$		0			0
$669$	−12.4280	+	1.20814i	−0.480494	+	0.0467093i
$670$		0			0
$671$	25.5442	+	44.2438i	0.986121	+	1.70801i
$672$		0			0
$673$	9.93562	−	17.2090i	0.382990	−	0.663358i	−0.608498	−	0.793555i	$-0.708228\pi$
$673$	9.93562	−	17.2090i	0.382990	−	0.663358i	0.991488	+	0.130197i	$0.0415610\pi$
$674$		0			0
$675$	−2.62644	−	0.622947i	−0.101092	−	0.0239772i
$676$		0			0
$677$	−7.96449	+	13.7949i	−0.306100	+	0.530181i	−0.977506	−	0.210909i	$-0.932358\pi$
$677$	−7.96449	+	13.7949i	−0.306100	+	0.530181i	0.671405	+	0.741090i	$0.265691\pi$
$678$		0			0
$679$	1.26108	+	12.0793i	0.0483960	+	0.463560i
$680$		0			0
$681$	−2.13771	−	21.9904i	−0.0819171	−	0.842673i
$682$		0			0
$683$		−	19.0269i		−	0.728042i	−0.931391	−	0.364021i	$-0.881404\pi$
$683$		−	19.0269i		−	0.728042i	0.931391	−	0.364021i	$-0.118596\pi$
$684$		0			0
$685$			18.7664i			0.717028i
$686$		0			0
$687$	−3.22157	+	7.08623i	−0.122910	+	0.270356i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−0.139477	−	0.0805273i	−0.00530597	−	0.00306340i	0.497345	−	0.867553i	$-0.334308\pi$
$691$	−0.139477	−	0.0805273i	−0.00530597	−	0.00306340i	−0.502651	+	0.864490i	$0.667642\pi$
$692$		0			0
$693$	−43.9138	−	10.0860i	−1.66815	−	0.383136i
$694$		0			0
$695$	−42.2396	−	24.3870i	−1.60224	−	0.925053i
$696$		0			0
$697$	−7.07017	−	12.2459i	−0.267802	−	0.463847i
$698$		0			0
$699$	2.16932	+	3.03540i	0.0820511	+	0.114809i
$700$		0			0
$701$		−	9.98234i		−	0.377028i	−0.982071	−	0.188514i	$-0.939633\pi$
$701$		−	9.98234i		−	0.377028i	0.982071	−	0.188514i	$-0.0603670\pi$
$702$		0			0
$703$		−	10.4792i		−	0.395229i
$704$		0			0
$705$	39.0983	−	27.9425i	1.47253	−	1.05237i
$706$		0			0
$707$	−17.4283	+	1.81953i	−0.655460	+	0.0684306i
$708$		0			0
$709$	12.1962	−	21.1244i	0.458036	−	0.793342i	−0.540821	−	0.841138i	$-0.681886\pi$
$709$	12.1962	−	21.1244i	0.458036	−	0.793342i	0.998857	+	0.0477959i	$0.0152197\pi$
$710$		0			0
$711$	25.6961	+	29.4512i	0.963679	+	1.10450i
$712$		0			0
$713$	15.3806	−	26.6400i	0.576008	−	0.997676i
$714$		0			0
$715$	11.4684	+	19.8639i	0.428894	+	0.742867i
$716$		0			0
$717$	−7.27004	+	15.9913i	−0.271504	+	0.597207i
$718$		0			0
$719$	16.2692			0.606739			0.303370	−	0.952873i	$-0.401888\pi$
$719$	16.2692			0.606739			0.303370	+	0.952873i	$0.401888\pi$
$720$		0			0
$721$	−14.1588	−	6.31570i	−0.527300	−	0.235209i
$722$		0			0
$723$	−18.1841	+	1.76769i	−0.676274	+	0.0657412i
$724$		0			0
$725$	−1.86955	+	1.07938i	−0.0694332	+	0.0400873i
$726$		0			0
$727$	−20.6626	−	11.9296i	−0.766335	−	0.442444i	0.0652306	−	0.997870i	$-0.479222\pi$
$727$	−20.6626	−	11.9296i	−0.766335	−	0.442444i	−0.831566	+	0.555427i	$0.812555\pi$
$728$		0			0
$729$	−22.5632	+	14.8291i	−0.835673	+	0.549227i
$730$		0			0
$731$	3.11408	−	5.39374i	0.115178	−	0.199495i
$732$		0			0
$733$	10.6259	−	6.13486i	0.392476	−	0.226596i	−0.290756	−	0.956797i	$-0.593907\pi$
$733$	10.6259	−	6.13486i	0.392476	−	0.226596i	0.683233	+	0.730201i	$0.260574\pi$
$734$		0			0
$735$	19.2539	−	20.9917i	0.710189	−	0.774292i
$736$		0			0
$737$			61.7125i			2.27321i
$738$		0			0
$739$	−41.8891			−1.54092			−0.770459	−	0.637490i	$-0.779973\pi$
$739$	−41.8891			−1.54092			−0.770459	+	0.637490i	$0.779973\pi$
$740$		0			0
$741$	−3.08959	−	1.40460i	−0.113499	−	0.0515992i
$742$		0			0
$743$	−43.9160	+	25.3549i	−1.61112	+	0.930182i	−0.622011	+	0.783008i	$0.713684\pi$
$743$	−43.9160	+	25.3549i	−1.61112	+	0.930182i	−0.989111	+	0.147173i	$0.952982\pi$
$744$		0			0
$745$	−2.43690	−	1.40695i	−0.0892813	−	0.0515466i
$746$		0			0
$747$	−24.7445	−	28.3605i	−0.905355	−	1.03766i
$748$		0			0
$749$	10.0987	−	7.32642i	0.368999	−	0.267701i
$750$		0			0
$751$	−16.3683	−	28.3508i	−0.597289	−	1.03454i	−0.993219	−	0.116255i	$-0.962911\pi$
$751$	−16.3683	−	28.3508i	−0.597289	−	1.03454i	0.395930	−	0.918281i	$-0.370422\pi$
$752$		0			0
$753$	−41.2893	+	29.5083i	−1.50467	+	1.07534i
$754$		0			0
$755$	35.7680			1.30173
$756$		0			0
$757$	−17.9255			−0.651512			−0.325756	−	0.945454i	$-0.605619\pi$
$757$	−17.9255			−0.651512			−0.325756	+	0.945454i	$0.605619\pi$
$758$		0			0
$759$	−29.3985	+	21.0103i	−1.06710	+	0.762626i
$760$		0			0
$761$	21.8509	+	37.8469i	0.792096	+	1.37195i	0.924667	+	0.380777i	$0.124343\pi$
$761$	21.8509	+	37.8469i	0.792096	+	1.37195i	−0.132571	+	0.991174i	$0.542323\pi$
$762$		0			0
$763$	−6.58231	−	9.07305i	−0.238296	−	0.328466i
$764$		0			0
$765$	−12.2334	+	2.40114i	−0.442300	+	0.0868132i
$766$		0			0
$767$	−3.32093	−	1.91734i	−0.119912	−	0.0692311i
$768$		0			0
$769$	−37.0864	+	21.4118i	−1.33737	+	0.772131i	−0.986417	−	0.164262i	$-0.947476\pi$
$769$	−37.0864	+	21.4118i	−1.33737	+	0.772131i	−0.350953	+	0.936393i	$0.614142\pi$
$770$		0			0
$771$	12.0284	+	5.46841i	0.433193	+	0.196940i
$772$		0			0
$773$	−21.6051			−0.777080			−0.388540	−	0.921432i	$-0.627020\pi$
$773$	−21.6051			−0.777080			−0.388540	+	0.921432i	$0.627020\pi$
$774$		0			0
$775$			4.34816i			0.156191i
$776$		0			0
$777$	−39.9741	−	13.3655i	−1.43406	−	0.479484i
$778$		0			0
$779$	−7.88771	+	4.55397i	−0.282606	+	0.163163i
$780$		0			0
$781$	12.8323	−	22.2262i	0.459175	−	0.795315i
$782$		0			0
$783$	−4.98328	+	21.0103i	−0.178088	+	0.750847i
$784$		0			0
$785$	20.4008	+	11.7784i	0.728137	+	0.420390i
$786$		0			0
$787$	44.4307	−	25.6521i	1.58378	−	0.914398i	0.589484	−	0.807780i	$-0.299331\pi$
$787$	44.4307	−	25.6521i	1.58378	−	0.914398i	0.994300	−	0.106618i	$-0.0340020\pi$
$788$		0			0
$789$	−21.0071	+	2.04212i	−0.747872	+	0.0727014i
$790$		0			0
$791$	−16.5086	−	7.36387i	−0.586978	−	0.261829i
$792$		0			0
$793$	15.4781			0.549644
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−0.899094	−	1.55728i	−0.0318476	−	0.0551616i	0.849662	−	0.527327i	$-0.176806\pi$
$797$	−0.899094	−	1.55728i	−0.0318476	−	0.0551616i	−0.881510	+	0.472166i	$0.843472\pi$
$798$		0			0
$799$	10.4448	−	18.0910i	0.369512	−	0.640013i
$800$		0			0
$801$	−1.12799	+	3.29547i	−0.0398557	+	0.116440i
$802$		0			0
$803$	−15.1634	+	26.2637i	−0.535103	+	0.926826i
$804$		0			0
$805$	−2.37201	−	22.7202i	−0.0836023	−	0.800783i
$806$		0			0
$807$	−3.90951	+	2.79402i	−0.137621	+	0.0983541i
$808$		0			0
$809$		−	40.6883i		−	1.43052i	−0.698857	−	0.715262i	$-0.746308\pi$
$809$		−	40.6883i		−	1.43052i	0.698857	−	0.715262i	$-0.253692\pi$
$810$		0			0
$811$			0.378710i			0.0132983i	0.999978	+	0.00664916i	$0.00211651\pi$
$811$			0.378710i			0.0132983i	−0.999978	+	0.00664916i	$0.997883\pi$
$812$		0			0
$813$	−3.23068	−	4.52051i	−0.113305	−	0.158541i
$814$		0			0
$815$	−14.0999	−	24.4217i	−0.493896	−	0.855453i
$816$		0			0
$817$	−3.47416	−	2.00581i	−0.121545	−	0.0701743i
$818$		0			0
$819$	−9.29858	+	9.99414i	−0.324919	+	0.349224i
$820$		0			0
$821$	11.4968	+	6.63771i	0.401243	+	0.231658i	0.687020	−	0.726638i	$-0.258918\pi$
$821$	11.4968	+	6.63771i	0.401243	+	0.231658i	−0.285777	+	0.958296i	$0.592252\pi$
$822$		0			0
$823$	13.8711	+	24.0255i	0.483517	+	0.837476i	0.999821	−	0.0189295i	$-0.00602582\pi$
$823$	13.8711	+	24.0255i	0.483517	+	0.837476i	−0.516304	+	0.856405i	$0.672692\pi$
$824$		0			0
$825$	2.11388	−	4.64974i	0.0735959	−	0.161883i
$826$		0			0
$827$			27.7183i			0.963859i	0.876210	+	0.481929i	$0.160064\pi$
$827$			27.7183i			0.963859i	−0.876210	+	0.481929i	$0.839936\pi$
$828$		0			0
$829$		−	42.7361i		−	1.48429i	−0.670242	−	0.742143i	$-0.733810\pi$
$829$		−	42.7361i		−	1.48429i	0.670242	−	0.742143i	$-0.266190\pi$
$830$		0			0
$831$	−1.68943	−	17.3790i	−0.0586057	−	0.602872i
$832$		0			0
$833$	3.84257	−	11.7705i	0.133137	−	0.407822i
$834$		0			0
$835$	20.1451	−	34.8923i	0.697149	−	1.20750i
$836$		0			0
$837$	31.6305	+	29.8519i	1.09331	+	1.03183i
$838$		0			0
$839$	1.92438	−	3.33313i	0.0664370	−	0.115072i	−0.830894	−	0.556431i	$-0.812170\pi$
$839$	1.92438	−	3.33313i	0.0664370	−	0.115072i	0.897331	+	0.441359i	$0.145504\pi$
$840$		0			0
$841$	−5.86545	−	10.1593i	−0.202257	−	0.350319i
$842$		0			0
$843$	−8.40038	+	0.816609i	−0.289324	+	0.0281255i
$844$		0			0
$845$	−23.5925			−0.811608
$846$		0			0
$847$	22.8760	−	51.2842i	0.786028	−	1.76215i
$848$		0			0
$849$	−2.01989	+	4.44300i	−0.0693225	+	0.152483i
$850$		0			0
$851$	−29.2738	+	16.9013i	−1.00349	+	0.579368i
$852$		0			0
$853$	−26.3470	−	15.2114i	−0.902103	−	0.520830i	−0.0242213	−	0.999707i	$-0.507711\pi$
$853$	−26.3470	−	15.2114i	−0.902103	−	0.520830i	−0.877882	+	0.478877i	$0.841044\pi$
$854$		0			0
$855$	1.54660	+	7.87967i	0.0528924	+	0.269479i
$856$		0			0
$857$	19.4657	−	33.7156i	0.664937	−	1.15170i	−0.314366	−	0.949302i	$-0.601792\pi$
$857$	19.4657	−	33.7156i	0.664937	−	1.15170i	0.979303	−	0.202402i	$-0.0648748\pi$
$858$		0			0
$859$	−11.5922	+	6.69275i	−0.395520	+	0.228354i	−0.684549	−	0.728967i	$-0.740001\pi$
$859$	−11.5922	+	6.69275i	−0.395520	+	0.228354i	0.289029	+	0.957320i	$0.406668\pi$
$860$		0			0
$861$	7.31145	+	35.8969i	0.249174	+	1.22336i
$862$		0			0
$863$		−	21.7219i		−	0.739424i	−0.929146	−	0.369712i	$-0.879456\pi$
$863$		−	21.7219i		−	0.739424i	0.929146	−	0.369712i	$-0.120544\pi$
$864$		0			0
$865$	4.66929			0.158761
$866$		0			0
$867$	19.5469	−	13.9697i	0.663849	−	0.474434i
$868$		0			0
$869$	−64.0496	+	36.9791i	−2.17273	+	1.25443i
$870$		0			0
$871$	16.1920	+	9.34845i	0.548645	+	0.316760i
$872$		0			0
$873$	−10.3766	+	9.05358i	−0.351195	+	0.306417i
$874$		0			0
$875$	−16.3542	−	22.5426i	−0.552872	−	0.762078i
$876$		0			0
$877$	−0.196152	−	0.339746i	−0.00662360	−	0.0114724i	0.862695	−	0.505725i	$-0.168775\pi$
$877$	−0.196152	−	0.339746i	−0.00662360	−	0.0114724i	−0.869318	+	0.494253i	$0.835442\pi$
$878$		0			0
$879$	12.7936	+	5.81628i	0.431518	+	0.196178i
$880$		0			0
$881$	43.3363			1.46004			0.730018	−	0.683427i	$-0.239511\pi$
$881$	43.3363			1.46004			0.730018	+	0.683427i	$0.239511\pi$
$882$		0			0
$883$	−2.17403			−0.0731618			−0.0365809	−	0.999331i	$-0.511647\pi$
$883$	−2.17403			−0.0731618			−0.0365809	+	0.999331i	$0.511647\pi$
$884$		0			0
$885$	0.877852	+	9.03038i	0.0295087	+	0.303553i
$886$		0			0
$887$	5.72215	+	9.91105i	0.192131	+	0.332781i	0.945956	−	0.324294i	$-0.105127\pi$
$887$	5.72215	+	9.91105i	0.192131	+	0.332781i	−0.753825	+	0.657075i	$0.771793\pi$
$888$		0			0
$889$	−10.3732	−	14.2984i	−0.347905	−	0.479551i
$890$		0			0
$891$	−19.3116	−	47.2996i	−0.646963	−	1.58460i
$892$		0			0
$893$	−11.6526	−	6.72762i	−0.389939	−	0.225131i
$894$		0			0
$895$	−16.9100	+	9.76302i	−0.565240	+	0.326342i
$896$		0			0
$897$	1.05923	+	10.8962i	0.0353668	+	0.363815i
$898$		0			0
$899$	34.7832			1.16009
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−12.0825	+	10.6943i	−0.402079	+	0.355886i
$904$		0			0
$905$	31.4430	−	18.1536i	1.04520	−	0.603447i
$906$		0			0
$907$	−26.9446	+	46.6694i	−0.894680	+	1.54963i	−0.0604797	+	0.998169i	$0.519263\pi$
$907$	−26.9446	+	46.6694i	−0.894680	+	1.54963i	−0.834200	+	0.551462i	$0.814070\pi$
$908$		0			0
$909$	−13.0628	−	14.9717i	−0.433266	−	0.496580i
$910$		0			0
$911$	7.00460	+	4.04411i	0.232073	+	0.133987i	0.611528	−	0.791223i	$-0.290555\pi$
$911$	7.00460	+	4.04411i	0.232073	+	0.133987i	−0.379455	+	0.925210i	$0.623889\pi$
$912$		0			0
$913$	61.6777	−	35.6097i	2.04124	−	1.17851i
$914$		0			0
$915$	−21.2935	−	29.7948i	−0.703942	−	0.984986i
$916$		0			0
$917$	−8.05450	+	18.0569i	−0.265983	+	0.596290i
$918$		0			0
$919$	−25.6751			−0.846943			−0.423472	−	0.905909i	$-0.639189\pi$
$919$	−25.6751			−0.846943			−0.423472	+	0.905909i	$0.639189\pi$
$920$		0			0
$921$	10.9770	+	15.3594i	0.361703	+	0.506110i
$922$		0			0
$923$	−3.88777	−	6.73382i	−0.127968	−	0.221646i
$924$		0			0
$925$	2.38903	−	4.13792i	0.0785507	−	0.136054i
$926$		0			0
$927$	−3.38581	−	17.2502i	−0.111205	−	0.566570i
$928$		0			0
$929$	5.42618	−	9.39842i	0.178027	−	0.308352i	−0.763177	−	0.646189i	$-0.776362\pi$
$929$	5.42618	−	9.39842i	0.178027	−	0.308352i	0.941205	+	0.337837i	$0.109695\pi$
$930$		0			0
$931$	−7.58147	−	2.47504i	−0.248473	−	0.0811161i
$932$		0			0
$933$	12.9867	+	5.90408i	0.425167	+	0.193291i
$934$		0			0
$935$		−	23.5900i		−	0.771477i
$936$		0			0
$937$		−	0.458120i		−	0.0149661i	−0.999972	−	0.00748306i	$-0.997618\pi$
$937$		−	0.458120i		−	0.0149661i	0.999972	−	0.00748306i	$-0.00238195\pi$
$938$		0			0
$939$	58.2725	−	5.66473i	1.90165	−	0.184861i
$940$		0			0
$941$	−3.68890	−	6.38937i	−0.120255	−	0.208287i	0.799613	−	0.600515i	$-0.205038\pi$
$941$	−3.68890	−	6.38937i	−0.120255	−	0.208287i	−0.919868	+	0.392228i	$0.871704\pi$
$942$		0			0
$943$	25.4433	+	14.6897i	0.828548	+	0.478362i
$944$		0			0
$945$	32.0306	+	4.15031i	1.04195	+	0.135009i
$946$		0			0
$947$	10.3846	+	5.99552i	0.337453	+	0.194828i	0.659145	−	0.752016i	$-0.270918\pi$
$947$	10.3846	+	5.99552i	0.337453	+	0.194828i	−0.321692	+	0.946844i	$0.604252\pi$
$948$		0			0
$949$	4.59401	+	7.95706i	0.149128	+	0.258297i
$950$		0			0
$951$	−11.6036	+	1.12799i	−0.376271	+	0.0365777i
$952$		0			0
$953$		−	58.6883i		−	1.90110i	−0.310572	−	0.950550i	$-0.600521\pi$
$953$		−	58.6883i		−	1.90110i	0.310572	−	0.950550i	$-0.399479\pi$
$954$		0			0
$955$		−	28.9866i		−	0.937983i
$956$		0			0
$957$	−37.1957	−	16.9100i	−1.20237	−	0.546624i
$958$		0			0
$959$	−2.19448	−	21.0197i	−0.0708633	−	0.678763i
$960$		0			0
$961$	19.5300	−	33.8270i	0.630000	−	1.09119i
$962$		0			0
$963$	13.3846	+	4.58134i	0.431311	+	0.147632i
$964$		0			0
$965$	5.16140	−	8.93981i	0.166151	−	0.287783i
$966$		0			0
$967$	3.37560	+	5.84671i	0.108552	+	0.188018i	0.915184	−	0.403037i	$-0.132045\pi$
$967$	3.37560	+	5.84671i	0.108552	+	0.188018i	−0.806632	+	0.591054i	$0.798712\pi$
$968$		0			0
$969$	2.02956	+	2.83985i	0.0651988	+	0.0912290i
$970$		0			0
$971$	6.40724			0.205618			0.102809	−	0.994701i	$-0.467217\pi$
$971$	6.40724			0.205618			0.102809	+	0.994701i	$0.467217\pi$
$972$		0			0
$973$	50.1631	+	22.3759i	1.60816	+	0.717338i
$974$		0			0
$975$	−0.899769	−	1.25900i	−0.0288157	−	0.0403201i
$976$		0			0
$977$	11.7769	−	6.79937i	0.376775	−	0.217531i	−0.299639	−	0.954053i	$-0.596866\pi$
$977$	11.7769	−	6.79937i	0.376775	−	0.217531i	0.676414	+	0.736521i	$0.263533\pi$
$978$		0			0
$979$	−5.70793	−	3.29547i	−0.182426	−	0.105324i
$980$		0			0
$981$	4.11604	−	12.0252i	0.131415	−	0.383934i
$982$		0			0
$983$	−11.3849	+	19.7192i	−0.363122	+	0.628946i	−0.988473	−	0.151398i	$-0.951623\pi$
$983$	−11.3849	+	19.7192i	−0.363122	+	0.628946i	0.625351	+	0.780344i	$0.284956\pi$
$984$		0			0
$985$	22.1497	−	12.7882i	0.705749	−	0.407464i
$986$		0			0
$987$	−40.5255	+	35.8696i	−1.28994	+	1.14174i
$988$		0			0
$989$			12.9402i			0.411475i
$990$		0			0
$991$	26.9905			0.857383			0.428691	−	0.903451i	$-0.358975\pi$
$991$	26.9905			0.857383			0.428691	+	0.903451i	$0.358975\pi$
$992$		0			0
$993$	−5.37223	−	55.2636i	−0.170483	−	1.75374i
$994$		0			0
$995$	56.0869	−	32.3818i	1.77807	−	1.02657i
$996$		0			0
$997$	−16.7263	−	9.65694i	−0.529728	−	0.305838i	0.211178	−	0.977448i	$-0.432270\pi$
$997$	−16.7263	−	9.65694i	−0.529728	−	0.305838i	−0.740906	+	0.671609i	$0.765603\pi$
$998$		0			0
$999$	−13.6994	−	45.7873i	−0.433430	−	1.44865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cc.b.209.3		16
3.2	odd	2		3024.2.cc.b.2897.2		16
4.3	odd	2		126.2.m.a.83.3	yes	16
7.6	odd	2	inner	1008.2.cc.b.209.6		16
9.4	even	3		3024.2.cc.b.881.7		16
9.5	odd	6	inner	1008.2.cc.b.545.6		16
12.11	even	2		378.2.m.a.251.6		16
21.20	even	2		3024.2.cc.b.2897.7		16
28.3	even	6		882.2.t.b.803.8		16
28.11	odd	6		882.2.t.b.803.5		16
28.19	even	6		882.2.l.a.227.6		16
28.23	odd	6		882.2.l.a.227.7		16
28.27	even	2		126.2.m.a.83.2	yes	16
36.7	odd	6		1134.2.d.a.1133.10		16
36.11	even	6		1134.2.d.a.1133.7		16
36.23	even	6		126.2.m.a.41.2	✓	16
36.31	odd	6		378.2.m.a.125.7		16
63.13	odd	6		3024.2.cc.b.881.2		16
63.41	even	6	inner	1008.2.cc.b.545.3		16
84.11	even	6		2646.2.t.a.1979.3		16
84.23	even	6		2646.2.l.b.521.2		16
84.47	odd	6		2646.2.l.b.521.3		16
84.59	odd	6		2646.2.t.a.1979.2		16
84.83	odd	2		378.2.m.a.251.7		16
252.23	even	6		882.2.t.b.815.8		16
252.31	even	6		2646.2.l.b.1097.6		16
252.59	odd	6		882.2.l.a.509.3		16
252.67	odd	6		2646.2.l.b.1097.7		16
252.83	odd	6		1134.2.d.a.1133.2		16
252.95	even	6		882.2.l.a.509.2		16
252.103	even	6		2646.2.t.a.2285.3		16
252.131	odd	6		882.2.t.b.815.5		16
252.139	even	6		378.2.m.a.125.6		16
252.167	odd	6		126.2.m.a.41.3	yes	16
252.223	even	6		1134.2.d.a.1133.15		16
252.247	odd	6		2646.2.t.a.2285.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.2	✓	16	36.23	even	6
126.2.m.a.41.3	yes	16	252.167	odd	6
126.2.m.a.83.2	yes	16	28.27	even	2
126.2.m.a.83.3	yes	16	4.3	odd	2
378.2.m.a.125.6		16	252.139	even	6
378.2.m.a.125.7		16	36.31	odd	6
378.2.m.a.251.6		16	12.11	even	2
378.2.m.a.251.7		16	84.83	odd	2
882.2.l.a.227.6		16	28.19	even	6
882.2.l.a.227.7		16	28.23	odd	6
882.2.l.a.509.2		16	252.95	even	6
882.2.l.a.509.3		16	252.59	odd	6
882.2.t.b.803.5		16	28.11	odd	6
882.2.t.b.803.8		16	28.3	even	6
882.2.t.b.815.5		16	252.131	odd	6
882.2.t.b.815.8		16	252.23	even	6
1008.2.cc.b.209.3		16	1.1	even	1	trivial
1008.2.cc.b.209.6		16	7.6	odd	2	inner
1008.2.cc.b.545.3		16	63.41	even	6	inner
1008.2.cc.b.545.6		16	9.5	odd	6	inner
1134.2.d.a.1133.2		16	252.83	odd	6
1134.2.d.a.1133.7		16	36.11	even	6
1134.2.d.a.1133.10		16	36.7	odd	6
1134.2.d.a.1133.15		16	252.223	even	6
2646.2.l.b.521.2		16	84.23	even	6
2646.2.l.b.521.3		16	84.47	odd	6
2646.2.l.b.1097.6		16	252.31	even	6
2646.2.l.b.1097.7		16	252.67	odd	6
2646.2.t.a.1979.2		16	84.59	odd	6
2646.2.t.a.1979.3		16	84.11	even	6
2646.2.t.a.2285.2		16	252.247	odd	6
2646.2.t.a.2285.3		16	252.103	even	6
3024.2.cc.b.881.2		16	63.13	odd	6
3024.2.cc.b.881.7		16	9.4	even	3
3024.2.cc.b.2897.2		16	3.2	odd	2
3024.2.cc.b.2897.7		16	21.20	even	2

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.40917 + 1.00709i) q^{3} +(1.17468 + 2.03460i) q^{5} +(-1.55364 - 2.14154i) q^{7} +(0.971521 - 2.83834i) q^{9} +O(q^{10})\)	\(q+(-1.40917 + 1.00709i) q^{3} +(1.17468 + 2.03460i) q^{5} +(-1.55364 - 2.14154i) q^{7} +(0.971521 - 2.83834i) q^{9} +(4.91614 + 2.83834i) q^{11} +(1.48943 - 0.859925i) q^{13} +(-3.70436 - 1.68409i) q^{15} -1.76883 q^{17} +1.13932i q^{19} +(4.34608 + 1.45313i) q^{21} +(3.18272 - 1.83755i) q^{23} +(-0.259741 + 0.449885i) q^{25} +(1.48943 + 4.97811i) q^{27} +(3.59886 + 2.07781i) q^{29} +(7.24879 - 4.18509i) q^{31} +(-9.78615 + 0.951321i) q^{33} +(2.53215 - 5.67667i) q^{35} -9.19773 q^{37} +(-1.23284 + 2.71178i) q^{39} +(3.99709 + 6.92317i) q^{41} +(-1.76053 + 3.04933i) q^{43} +(6.91611 - 1.35747i) q^{45} +(-5.90494 + 10.2277i) q^{47} +(-2.17238 + 6.65438i) q^{49} +(2.49258 - 1.78138i) q^{51} +13.3365i q^{55} +(-1.14740 - 1.60550i) q^{57} +(-1.11483 - 1.93094i) q^{59} +(7.79396 + 4.49985i) q^{61} +(-7.58780 + 2.32921i) q^{63} +(3.49921 + 2.02027i) q^{65} +(5.43562 + 9.41477i) q^{67} +(-2.63442 + 5.79472i) q^{69} -4.52106i q^{71} +5.34234i q^{73} +(-0.0870571 - 0.895548i) q^{75} +(-1.55953 - 14.9379i) q^{77} +(-6.51422 + 11.2830i) q^{79} +(-7.11229 - 5.51501i) q^{81} +(6.27298 - 10.8651i) q^{83} +(-2.07781 - 3.59886i) q^{85} +(-7.16396 + 0.696415i) q^{87} -1.16106 q^{89} +(-4.15561 - 1.85366i) q^{91} +(-6.00000 + 13.1977i) q^{93} +(-2.31806 + 1.33834i) q^{95} +(-3.97536 - 2.29517i) q^{97} +(12.8323 - 11.1962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{7} + 12 q^{9}+O(q^{10}) \) 16 * q - 2 * q^7 + 12 * q^9	\( 16 q - 2 q^{7} + 12 q^{9} + 12 q^{11} + 18 q^{21} + 48 q^{23} - 8 q^{25} - 12 q^{29} - 8 q^{37} + 36 q^{39} - 4 q^{43} - 8 q^{49} - 12 q^{51} + 48 q^{57} - 24 q^{63} + 84 q^{65} + 28 q^{67} + 78 q^{77} + 4 q^{79} + 36 q^{81} - 12 q^{85} - 24 q^{91} - 96 q^{93} - 12 q^{95} + 72 q^{99}+O(q^{100}) \) 16 * q - 2 * q^7 + 12 * q^9 + 12 * q^11 + 18 * q^21 + 48 * q^23 - 8 * q^25 - 12 * q^29 - 8 * q^37 + 36 * q^39 - 4 * q^43 - 8 * q^49 - 12 * q^51 + 48 * q^57 - 24 * q^63 + 84 * q^65 + 28 * q^67 + 78 * q^77 + 4 * q^79 + 36 * q^81 - 12 * q^85 - 24 * q^91 - 96 * q^93 - 12 * q^95 + 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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