LMFDB - Embedded newform 378.2.m.a.125.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(125,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("378.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.m (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:	$3.01834519640$
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			125.6
Root			$1.40917 + 1.00709i$ of defining polynomial
Character	$\chi$	$=$	378.125
Dual form			378.2.m.a.251.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.17468 + 2.03460i) q^{5} +(1.55364 - 2.14154i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.17468 + 2.03460i) q^{5} +(1.55364 - 2.14154i) q^{7} -1.00000i q^{8} +2.34936i q^{10} +(4.91614 - 2.83834i) q^{11} +(1.48943 + 0.859925i) q^{13} +(0.274725 - 2.63145i) q^{14} +(-0.500000 - 0.866025i) q^{16} +1.76883 q^{17} +1.13932i q^{19} +(1.17468 + 2.03460i) q^{20} +(2.83834 - 4.91614i) q^{22} +(3.18272 + 1.83755i) q^{23} +(-0.259741 - 0.449885i) q^{25} +1.71985 q^{26} +(-1.07781 - 2.41626i) q^{28} +(-3.59886 + 2.07781i) q^{29} +(-7.24879 - 4.18509i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.53185 - 0.884414i) q^{34} +(2.53215 + 5.67667i) q^{35} -9.19773 q^{37} +(0.569660 + 0.986680i) q^{38} +(2.03460 + 1.17468i) q^{40} +(-3.99709 + 6.92317i) q^{41} +(1.76053 + 3.04933i) q^{43} -5.67667i q^{44} +3.67509 q^{46} +(-5.90494 - 10.2277i) q^{47} +(-2.17238 - 6.65438i) q^{49} +(-0.449885 - 0.259741i) q^{50} +(1.48943 - 0.859925i) q^{52} +13.3365i q^{55} +(-2.14154 - 1.55364i) q^{56} +(-2.07781 + 3.59886i) q^{58} +(-1.11483 + 1.93094i) q^{59} +(7.79396 - 4.49985i) q^{61} -8.37019 q^{62} -1.00000 q^{64} +(-3.49921 + 2.02027i) q^{65} +(-5.43562 + 9.41477i) q^{67} +(0.884414 - 1.53185i) q^{68} +(5.03124 + 3.65007i) q^{70} +4.52106i q^{71} -5.34234i q^{73} +(-7.96547 + 4.59886i) q^{74} +(0.986680 + 0.569660i) q^{76} +(1.55953 - 14.9379i) q^{77} +(6.51422 + 11.2830i) q^{79} +2.34936 q^{80} +7.99419i q^{82} +(6.27298 + 10.8651i) q^{83} +(-2.07781 + 3.59886i) q^{85} +(3.04933 + 1.76053i) q^{86} +(-2.83834 - 4.91614i) q^{88} +1.16106 q^{89} +(4.15561 - 1.85366i) q^{91} +(3.18272 - 1.83755i) q^{92} +(-10.2277 - 5.90494i) q^{94} +(-2.31806 - 1.33834i) q^{95} +(-3.97536 + 2.29517i) q^{97} +(-5.20853 - 4.67667i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 2 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 + 2 * q^7	$ 16 q + 8 q^{4} + 2 q^{7} + 12 q^{11} + 6 q^{14} - 8 q^{16} + 48 q^{23} - 8 q^{25} + 4 q^{28} + 12 q^{29} - 8 q^{37} + 4 q^{43} + 24 q^{46} - 8 q^{49} - 60 q^{50} + 6 q^{56} - 12 q^{58} - 16 q^{64} - 84 q^{65} - 28 q^{67} - 36 q^{74} - 78 q^{77} - 4 q^{79} - 12 q^{85} + 24 q^{86} + 24 q^{91} + 48 q^{92} - 12 q^{95}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^7 + 12 * q^11 + 6 * q^14 - 8 * q^16 + 48 * q^23 - 8 * q^25 + 4 * q^28 + 12 * q^29 - 8 * q^37 + 4 * q^43 + 24 * q^46 - 8 * q^49 - 60 * q^50 + 6 * q^56 - 12 * q^58 - 16 * q^64 - 84 * q^65 - 28 * q^67 - 36 * q^74 - 78 * q^77 - 4 * q^79 - 12 * q^85 + 24 * q^86 + 24 * q^91 + 48 * q^92 - 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.17468	+	2.03460i	−0.525332	+	0.909902i	0.474232	+	0.880400i	$0.342726\pi$
$5$	−1.17468	+	2.03460i	−0.525332	+	0.909902i	−0.999565	+	0.0295026i	$0.990608\pi$
$6$		0			0
$7$	1.55364	−	2.14154i	0.587222	−	0.809426i
$7$	1.55364	−	2.14154i	0.587222	−	0.809426i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$			2.34936i			0.742932i
$11$	4.91614	−	2.83834i	1.48227	−	0.855790i	0.482475	−	0.875910i	$-0.339738\pi$
$11$	4.91614	−	2.83834i	1.48227	−	0.855790i	0.999798	+	0.0201197i	$0.00640473\pi$
$12$		0			0
$13$	1.48943	+	0.859925i	0.413094	+	0.238500i	0.692118	−	0.721784i	$-0.256678\pi$
$13$	1.48943	+	0.859925i	0.413094	+	0.238500i	−0.279024	+	0.960284i	$0.590011\pi$
$14$	0.274725	−	2.63145i	0.0734234	−	0.703284i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.76883			0.429004			0.214502	−	0.976724i	$-0.431187\pi$
$17$	1.76883			0.429004			0.214502	+	0.976724i	$0.431187\pi$
$18$		0			0
$19$			1.13932i			0.261378i	0.991423	+	0.130689i	$0.0417189\pi$
$19$			1.13932i			0.261378i	−0.991423	+	0.130689i	$0.958281\pi$
$20$	1.17468	+	2.03460i	0.262666	+	0.454951i
$21$		0			0
$22$	2.83834	−	4.91614i	0.605135	−	1.04812i
$23$	3.18272	+	1.83755i	0.663644	+	0.383155i	0.793664	−	0.608356i	$-0.208171\pi$
$23$	3.18272	+	1.83755i	0.663644	+	0.383155i	−0.130020	+	0.991511i	$0.541504\pi$
$24$		0			0
$25$	−0.259741	−	0.449885i	−0.0519482	−	0.0899769i
$26$	1.71985			0.337290
$27$		0			0
$28$	−1.07781	−	2.41626i	−0.203686	−	0.456631i
$29$	−3.59886	+	2.07781i	−0.668292	+	0.385839i	−0.795429	−	0.606046i	$-0.792755\pi$
$29$	−3.59886	+	2.07781i	−0.668292	+	0.385839i	0.127137	+	0.991885i	$0.459421\pi$
$30$		0			0
$31$	−7.24879	−	4.18509i	−1.30192	−	0.751665i	−0.321188	−	0.947015i	$-0.604082\pi$
$31$	−7.24879	−	4.18509i	−1.30192	−	0.751665i	−0.980734	+	0.195350i	$0.937416\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	1.53185	−	0.884414i	0.262710	−	0.151676i
$35$	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	$0.772873\pi$
$38$	0.569660	+	0.986680i	0.0924111	+	0.160061i
$39$		0			0
$40$	2.03460	+	1.17468i	0.321699	+	0.185733i
$41$	−3.99709	+	6.92317i	−0.624241	+	1.08122i	0.364446	+	0.931225i	$0.381258\pi$
$41$	−3.99709	+	6.92317i	−0.624241	+	1.08122i	−0.988687	+	0.149993i	$0.952075\pi$
$42$		0			0
$43$	1.76053	+	3.04933i	0.268478	+	0.465018i	0.968469	−	0.249134i	$-0.0801459\pi$
$43$	1.76053	+	3.04933i	0.268478	+	0.465018i	−0.699991	+	0.714152i	$0.746813\pi$
$44$		−	5.67667i		−	0.855790i
$45$		0			0
$46$	3.67509			0.541863
$47$	−5.90494	−	10.2277i	−0.861324	−	1.49186i	−0.870651	−	0.491901i	$-0.836302\pi$
$47$	−5.90494	−	10.2277i	−0.861324	−	1.49186i	0.00932669	−	0.999957i	$-0.497031\pi$
$48$		0			0
$49$	−2.17238	−	6.65438i	−0.310340	−	0.950626i
$50$	−0.449885	−	0.259741i	−0.0636233	−	0.0367329i
$51$		0			0
$52$	1.48943	−	0.859925i	0.206547	−	0.119250i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$		0			0
$55$			13.3365i			1.79830i
$56$	−2.14154	−	1.55364i	−0.286175	−	0.207614i
$57$		0			0
$58$	−2.07781	+	3.59886i	−0.272829	+	0.472554i
$59$	−1.11483	+	1.93094i	−0.145139	+	0.251387i	−0.929425	−	0.369012i	$-0.879696\pi$
$59$	−1.11483	+	1.93094i	−0.145139	+	0.251387i	0.784286	+	0.620399i	$0.213029\pi$
$60$		0			0
$61$	7.79396	−	4.49985i	0.997915	−	0.576146i	0.0902842	−	0.995916i	$-0.471222\pi$
$61$	7.79396	−	4.49985i	0.997915	−	0.576146i	0.907631	+	0.419770i	$0.137889\pi$
$62$	−8.37019			−1.06301
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−3.49921	+	2.02027i	−0.434024	+	0.250584i
$66$		0			0
$67$	−5.43562	+	9.41477i	−0.664067	+	1.15020i	0.315470	+	0.948935i	$0.397838\pi$
$67$	−5.43562	+	9.41477i	−0.664067	+	1.15020i	−0.979537	+	0.201262i	$0.935496\pi$
$68$	0.884414	−	1.53185i	0.107251	−	0.185764i
$69$		0			0
$70$	5.03124	+	3.65007i	0.601348	+	0.436266i
$71$			4.52106i			0.536551i	0.963342	+	0.268276i	$0.0864538\pi$
$71$			4.52106i			0.536551i	−0.963342	+	0.268276i	$0.913546\pi$
$72$		0			0
$73$		−	5.34234i		−	0.625274i	−0.949873	−	0.312637i	$-0.898788\pi$
$73$		−	5.34234i		−	0.625274i	0.949873	−	0.312637i	$-0.101212\pi$
$74$	−7.96547	+	4.59886i	−0.925967	+	0.534607i
$75$		0			0
$76$	0.986680	+	0.569660i	0.113180	+	0.0653445i
$77$	1.55953	−	14.9379i	0.177724	−	1.70233i
$78$		0			0
$79$	6.51422	+	11.2830i	0.732907	+	1.26943i	0.955636	+	0.294551i	$0.0951701\pi$
$79$	6.51422	+	11.2830i	0.732907	+	1.26943i	−0.222729	+	0.974880i	$0.571497\pi$
$80$	2.34936			0.262666
$81$		0			0
$82$			7.99419i			0.882810i
$83$	6.27298	+	10.8651i	0.688549	+	1.19260i	0.972307	+	0.233707i	$0.0750855\pi$
$83$	6.27298	+	10.8651i	0.688549	+	1.19260i	−0.283758	+	0.958896i	$0.591581\pi$
$84$		0			0
$85$	−2.07781	+	3.59886i	−0.225370	+	0.390352i
$86$	3.04933	+	1.76053i	0.328817	+	0.189843i
$87$		0			0
$88$	−2.83834	−	4.91614i	−0.302568	−	0.524062i
$89$	1.16106			0.123072			0.0615360	−	0.998105i	$-0.480400\pi$
$89$	1.16106			0.123072			0.0615360	+	0.998105i	$0.480400\pi$
$90$		0			0
$91$	4.15561	−	1.85366i	0.435626	−	0.194317i
$92$	3.18272	−	1.83755i	0.331822	−	0.191577i
$93$		0			0
$94$	−10.2277	−	5.90494i	−1.05490	−	0.609048i
$95$	−2.31806	−	1.33834i	−0.237828	−	0.137310i
$96$		0			0
$97$	−3.97536	+	2.29517i	−0.403636	+	0.233039i	−0.688052	−	0.725662i	$-0.741534\pi$
$97$	−3.97536	+	2.29517i	−0.403636	+	0.233039i	0.284416	+	0.958701i	$0.408200\pi$
$98$	−5.20853	−	4.67667i	−0.526141	−	0.472415i
$99$		0			0
$100$	−0.519482			−0.0519482
$101$	−3.31155	−	5.73577i	−0.329511	−	0.570730i	0.652904	−	0.757441i	$-0.273551\pi$
$101$	−3.31155	−	5.73577i	−0.329511	−	0.570730i	−0.982415	+	0.186711i	$0.940217\pi$
$102$		0			0
$103$	−5.07471	−	2.92989i	−0.500026	−	0.288690i	0.228698	−	0.973497i	$-0.426553\pi$
$103$	−5.07471	−	2.92989i	−0.500026	−	0.288690i	−0.728724	+	0.684807i	$0.759886\pi$
$104$	0.859925	−	1.48943i	0.0843225	−	0.146051i
$105$		0			0
$106$		0			0
$107$		−	4.71563i		−	0.455878i	−0.973675	−	0.227939i	$-0.926801\pi$
$107$		−	4.71563i		−	0.455878i	0.973675	−	0.227939i	$-0.0731986\pi$
$108$		0			0
$109$	4.23669			0.405802			0.202901	−	0.979199i	$-0.434963\pi$
$109$	4.23669			0.405802			0.202901	+	0.979199i	$0.434963\pi$
$110$	6.66826	+	11.5498i	0.635794	+	1.10123i
$111$		0			0
$112$	−2.63145	−	0.274725i	−0.248649	−	0.0259591i
$113$	−5.91693	−	3.41614i	−0.556618	−	0.321363i	0.195169	−	0.980770i	$-0.437474\pi$
$113$	−5.91693	−	3.41614i	−0.556618	−	0.321363i	−0.751787	+	0.659406i	$0.770808\pi$
$114$		0			0
$115$	−7.47736	+	4.31705i	−0.697267	+	0.402567i
$116$			4.15561i			0.385839i
$117$		0			0
$118$			2.22966i			0.205257i
$119$	2.74813	−	3.78802i	0.251921	−	0.347247i
$120$		0			0
$121$	10.6123	−	18.3810i	0.964754	−	1.67100i
$122$	4.49985	−	7.79396i	0.407397	−	0.705632i
$123$		0			0
$124$	−7.24879	+	4.18509i	−0.650961	+	0.375832i
$125$	−10.5263			−0.941504
$126$		0			0
$127$	−6.67667			−0.592459			−0.296229	−	0.955117i	$-0.595729\pi$
$127$	−6.67667			−0.592459			−0.296229	+	0.955117i	$0.595729\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−2.02027	+	3.49921i	−0.177189	+	0.306901i
$131$	−3.73653	+	6.47185i	−0.326462	+	0.565448i	−0.981807	−	0.189881i	$-0.939190\pi$
$131$	−3.73653	+	6.47185i	−0.326462	+	0.565448i	0.655345	+	0.755329i	$0.272523\pi$
$132$		0			0
$133$	2.43990	+	1.77010i	0.211566	+	0.153487i
$134$			10.8712i			0.939133i
$135$		0			0
$136$		−	1.76883i		−	0.151676i
$137$	−6.91772	+	3.99395i	−0.591021	+	0.341226i	−0.765501	−	0.643435i	$-0.777509\pi$
$137$	−6.91772	+	3.99395i	−0.591021	+	0.341226i	0.174480	+	0.984661i	$0.444175\pi$
$138$		0			0
$139$	17.9792	+	10.3803i	1.52498	+	0.880446i	0.999562	+	0.0295993i	$0.00942312\pi$
$139$	17.9792	+	10.3803i	1.52498	+	0.880446i	0.525415	+	0.850846i	$0.323910\pi$
$140$	6.18222	+	0.645428i	0.522493	+	0.0545486i
$141$		0			0
$142$	2.26053	+	3.91535i	0.189699	+	0.328569i
$143$	9.76302			0.816425
$144$		0			0
$145$		−	9.76302i		−	0.810774i
$146$	−2.67117	−	4.62660i	−0.221068	−	0.382900i
$147$		0			0
$148$	−4.59886	+	7.96547i	−0.378024	+	0.654757i
$149$	1.03726	+	0.598865i	0.0849760	+	0.0490609i	0.541886	−	0.840452i	$-0.317710\pi$
$149$	1.03726	+	0.598865i	0.0849760	+	0.0490609i	−0.456910	+	0.889513i	$0.651044\pi$
$150$		0			0
$151$	−7.61229	−	13.1849i	−0.619480	−	1.07297i	−0.989581	−	0.143979i	$-0.954010\pi$
$151$	−7.61229	−	13.1849i	−0.619480	−	1.07297i	0.370101	−	0.928991i	$-0.379323\pi$
$152$	1.13932			0.0924111
$153$		0			0
$154$	−6.11835	−	13.7163i	−0.493030	−	1.10529i
$155$	17.0300	−	9.83228i	1.36788	−	0.789748i
$156$		0			0
$157$	8.68358	+	5.01347i	0.693025	+	0.400118i	0.804744	−	0.593621i	$-0.202302\pi$
$157$	8.68358	+	5.01347i	0.693025	+	0.400118i	−0.111719	+	0.993740i	$0.535636\pi$
$158$	11.2830	+	6.51422i	0.897624	+	0.518243i
$159$		0			0
$160$	2.03460	−	1.17468i	0.160850	−	0.0928665i
$161$	8.88000	−	3.96104i	0.699842	−	0.312173i
$162$		0			0
$163$	12.0032			0.940160			0.470080	−	0.882624i	$-0.344225\pi$
$163$	12.0032			0.940160			0.470080	+	0.882624i	$0.344225\pi$
$164$	3.99709	+	6.92317i	0.312121	+	0.540609i
$165$		0			0
$166$	10.8651	+	6.27298i	0.843297	+	0.486878i
$167$	−8.57472	+	14.8518i	−0.663532	+	1.14927i	0.316150	+	0.948709i	$0.397610\pi$
$167$	−8.57472	+	14.8518i	−0.663532	+	1.14927i	−0.979681	+	0.200561i	$0.935723\pi$
$168$		0			0
$169$	−5.02106	−	8.69673i	−0.386235	−	0.668979i
$170$			4.15561i			0.318721i
$171$		0			0
$172$	3.52106			0.268478
$173$	−0.993738	−	1.72121i	−0.0755525	−	0.130861i	0.825774	−	0.564001i	$-0.190739\pi$
$173$	−0.993738	−	1.72121i	−0.0755525	−	0.130861i	−0.901326	+	0.433140i	$0.857405\pi$
$174$		0			0
$175$	−1.36699	−	0.142715i	−0.103335	−	0.0107882i
$176$	−4.91614	−	2.83834i	−0.370568	−	0.213948i
$177$		0			0
$178$	1.00551	−	0.580529i	0.0753659	−	0.0435125i
$179$		−	8.31122i		−	0.621210i	−0.950539	−	0.310605i	$-0.899468\pi$
$179$		−	8.31122i		−	0.621210i	0.950539	−	0.310605i	$-0.100532\pi$
$180$		0			0
$181$			15.4541i			1.14870i	0.818611	+	0.574348i	$0.194744\pi$
$181$			15.4541i			1.14870i	−0.818611	+	0.574348i	$0.805256\pi$
$182$	2.67203	−	3.68312i	0.198064	−	0.273011i
$183$		0			0
$184$	1.83755	−	3.18272i	0.135466	−	0.234634i
$185$	10.8044	−	18.7137i	0.794354	−	1.37586i
$186$		0			0
$187$	8.69581	−	5.02053i	0.635901	−	0.367137i
$188$	−11.8099			−0.861324
$189$		0			0
$190$	−2.67667			−0.194186
$191$	−10.6851	+	6.16904i	−0.773146	+	0.446376i	−0.833996	−	0.551771i	$-0.813952\pi$
$191$	−10.6851	+	6.16904i	−0.773146	+	0.446376i	0.0608498	+	0.998147i	$0.480619\pi$
$192$		0			0
$193$	−2.19694	+	3.80521i	−0.158139	+	0.273905i	−0.934198	−	0.356756i	$-0.883883\pi$
$193$	−2.19694	+	3.80521i	−0.158139	+	0.273905i	0.776058	+	0.630661i	$0.217216\pi$
$194$	−2.29517	+	3.97536i	−0.164784	+	0.285414i
$195$		0			0
$196$	−6.84905	−	1.44585i	−0.489218	−	0.103275i
$197$		−	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	$-0.431701\pi$
$200$	−0.449885	+	0.259741i	−0.0318116	+	0.0183665i
$201$		0			0
$202$	−5.73577	−	3.31155i	−0.403567	−	0.233000i
$203$	−1.14165	+	10.9353i	−0.0801282	+	0.767506i
$204$		0			0
$205$	−9.39060	−	16.2650i	−0.655868	−	1.13600i
$206$	−5.85977			−0.408270
$207$		0			0
$208$		−	1.71985i		−	0.119250i
$209$	3.23377	+	5.60106i	0.223685	+	0.387433i
$210$		0			0
$211$	5.15561	−	8.92978i	0.354927	−	0.614751i	−0.632179	−	0.774823i	$-0.717839\pi$
$211$	5.15561	−	8.92978i	0.354927	−	0.614751i	0.987105	+	0.160071i	$0.0511724\pi$
$212$		0			0
$213$		0			0
$214$	−2.35782	−	4.08386i	−0.161177	−	0.279167i
$215$	−8.27223			−0.564161
$216$		0			0
$217$	−20.2246	+	9.02143i	−1.37293	+	0.612415i
$218$	3.66908	−	2.11835i	0.248502	−	0.143473i
$219$		0			0
$220$	11.5498	+	6.66826i	0.778686	+	0.449574i
$221$	2.63455	+	1.52106i	0.177219	+	0.102318i
$222$		0			0
$223$	−6.24329	+	3.60456i	−0.418081	+	0.241379i	−0.694256	−	0.719728i	$-0.744267\pi$
$223$	−6.24329	+	3.60456i	−0.418081	+	0.241379i	0.276175	+	0.961107i	$0.410933\pi$
$224$	−2.41626	+	1.07781i	−0.161443	+	0.0720139i
$225$		0			0
$226$	−6.83228			−0.454477
$227$	−6.37800	−	11.0470i	−0.423323	−	0.733217i	0.572939	−	0.819598i	$-0.305803\pi$
$227$	−6.37800	−	11.0470i	−0.423323	−	0.733217i	−0.996262	+	0.0863812i	$0.972470\pi$
$228$		0			0
$229$	3.89208	+	2.24709i	0.257196	+	0.148492i	0.623055	−	0.782178i	$-0.285891\pi$
$229$	3.89208	+	2.24709i	0.257196	+	0.148492i	−0.365859	+	0.930670i	$0.619225\pi$
$230$	−4.31705	+	7.47736i	−0.284658	+	0.493042i
$231$		0			0
$232$	2.07781	+	3.59886i	0.136415	+	0.236277i
$233$		−	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
$236$	1.11483	+	1.93094i	0.0725693	+	0.125694i
$237$		0			0
$238$	0.485942	−	4.65458i	0.0314989	−	0.301712i
$239$	8.78317	+	5.07096i	0.568136	+	0.328013i	0.756404	−	0.654104i	$-0.226954\pi$
$239$	8.78317	+	5.07096i	0.568136	+	0.328013i	−0.188269	+	0.982118i	$0.560288\pi$
$240$		0			0
$241$	9.13490	−	5.27404i	0.588431	−	0.339731i	−0.176046	−	0.984382i	$-0.556331\pi$
$241$	9.13490	−	5.27404i	0.588431	−	0.339731i	0.764477	+	0.644651i	$0.222997\pi$
$242$		−	21.2246i		−	1.36437i
$243$		0			0
$244$		−	8.99970i		−	0.576146i
$245$	16.0909	+	3.39682i	1.02801	+	0.217015i
$246$		0			0
$247$	−0.979729	+	1.69694i	−0.0623387	+	0.107974i
$248$	−4.18509	+	7.24879i	−0.265754	+	0.460299i
$249$		0			0
$250$	−9.11608	+	5.26317i	−0.576551	+	0.332872i
$251$	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
$254$	−5.78217	+	3.33834i	−0.362805	+	0.209466i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.81430	−	6.60656i	0.237930	−	0.412106i	−0.722190	−	0.691694i	$-0.756865\pi$
$257$	3.81430	−	6.60656i	0.237930	−	0.412106i	0.960120	+	0.279588i	$0.0901979\pi$
$258$		0			0
$259$	−14.2900	+	19.6973i	−0.887937	+	1.22393i
$260$			4.04054i			0.250584i
$261$		0			0
$262$			7.47305i			0.461687i
$263$	10.5531	−	6.09281i	0.650729	−	0.375699i	−0.138006	−	0.990431i	$-0.544069\pi$
$263$	10.5531	−	6.09281i	0.650729	−	0.375699i	0.788736	+	0.614733i	$0.210736\pi$
$264$		0			0
$265$		0			0
$266$	2.99806	+	0.313000i	0.183823	+	0.0191913i
$267$		0			0
$268$	5.43562	+	9.41477i	0.332034	+	0.575099i
$269$	−2.77433			−0.169154			−0.0845771	−	0.996417i	$-0.526954\pi$
$269$	−2.77433			−0.169154			−0.0845771	+	0.996417i	$0.526954\pi$
$270$		0			0
$271$			3.20793i			0.194868i	0.995242	+	0.0974338i	$0.0310634\pi$
$271$			3.20793i			0.194868i	−0.995242	+	0.0974338i	$0.968937\pi$
$272$	−0.884414	−	1.53185i	−0.0536255	−	0.0928821i
$273$		0			0
$274$	−3.99395	+	6.91772i	−0.241283	+	0.417915i
$275$	−2.55385	−	1.47446i	−0.154003	−	0.0889135i
$276$		0			0
$277$	−5.04054	−	8.73047i	−0.302857	−	0.524563i	0.673925	−	0.738800i	$-0.264607\pi$
$277$	−5.04054	−	8.73047i	−0.302857	−	0.524563i	−0.976782	+	0.214236i	$0.931274\pi$
$278$	20.7606			1.24514
$279$		0			0
$280$	5.67667	−	2.53215i	0.339246	−	0.151325i
$281$	−4.21999	+	2.43641i	−0.251743	+	0.145344i	−0.620562	−	0.784157i	$-0.713096\pi$
$281$	−4.21999	+	2.43641i	−0.251743	+	0.145344i	0.368819	+	0.929501i	$0.379762\pi$
$282$		0			0
$283$	−2.44030	−	1.40891i	−0.145061	−	0.0837508i	0.425713	−	0.904858i	$-0.360023\pi$
$283$	−2.44030	−	1.40891i	−0.145061	−	0.0837508i	−0.570774	+	0.821107i	$0.693357\pi$
$284$	3.91535	+	2.26053i	0.232333	+	0.134138i
$285$		0			0
$286$	8.45502	−	4.88151i	0.499956	−	0.288650i
$287$	8.61618	+	19.3161i	0.508597	+	1.14019i
$288$		0			0
$289$	−13.8712			−0.815956
$290$	−4.88151	−	8.45502i	−0.286652	−	0.496496i
$291$		0			0
$292$	−4.62660	−	2.67117i	−0.270751	−	0.156318i
$293$	4.05694	−	7.02683i	0.237009	−	0.410512i	−0.722846	−	0.691010i	$-0.757166\pi$
$293$	4.05694	−	7.02683i	0.237009	−	0.410512i	0.959855	+	0.280498i	$0.0904995\pi$
$294$		0			0
$295$	−2.61914	−	4.53648i	−0.152492	−	0.264124i
$296$			9.19773i			0.534607i
$297$		0			0
$298$	1.19773			0.0693826
$299$	3.16030	+	5.47381i	0.182765	+	0.316558i
$300$		0			0
$301$	9.26549	+	0.967324i	0.534054	+	0.0557556i
$302$	−13.1849	−	7.61229i	−0.758705	−	0.438038i
$303$		0			0
$304$	0.986680	−	0.569660i	0.0565900	−	0.0326722i
$305$			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	$-0.100676\pi$
$308$	−12.1568	−	8.81952i	−0.692699	−	0.502539i
$309$		0			0
$310$	9.83228	−	17.0300i	0.558436	−	0.967240i
$311$	−4.11819	+	7.13291i	−0.233521	+	0.404470i	−0.958842	−	0.283941i	$-0.908358\pi$
$311$	−4.11819	+	7.13291i	−0.233521	+	0.404470i	0.725321	+	0.688411i	$0.241691\pi$
$312$		0			0
$313$	−29.2736	+	16.9011i	−1.65464	+	0.955308i	−0.679516	+	0.733661i	$0.737810\pi$
$313$	−29.2736	+	16.9011i	−1.65464	+	0.955308i	−0.975127	+	0.221648i	$0.928857\pi$
$314$	10.0269			0.565853
$315$		0			0
$316$	13.0284			0.732907
$317$	−5.82913	+	3.36545i	−0.327396	+	0.189022i	−0.654685	−	0.755902i	$-0.727199\pi$
$317$	−5.82913	+	3.36545i	−0.327396	+	0.189022i	0.327288	+	0.944925i	$0.393865\pi$
$318$		0			0
$319$	−11.7950	+	20.4296i	−0.660394	+	1.14384i
$320$	1.17468	−	2.03460i	0.0656665	−	0.113738i
$321$		0			0
$322$	5.70979	−	7.87036i	0.318194	−	0.438598i
$323$			2.01526i			0.112132i
$324$		0			0
$325$		−	0.893431i		−	0.0495586i
$326$	10.3950	−	6.00158i	0.575728	−	0.332397i
$327$		0			0
$328$	6.92317	+	3.99709i	0.382268	+	0.220703i
$329$	−31.0771	−	3.24447i	−1.71334	−	0.178874i
$330$		0			0
$331$	16.0284	+	27.7621i	0.881002	+	1.52594i	0.850228	+	0.526415i	$0.176464\pi$
$331$	16.0284	+	27.7621i	0.881002	+	1.52594i	0.0307744	+	0.999526i	$0.490203\pi$
$332$	12.5460			0.688549
$333$		0			0
$334$			17.1494i			0.938375i
$335$	−12.7702	−	22.1187i	−0.697712	−	1.20847i
$336$		0			0
$337$	−12.1123	+	20.9791i	−0.659799	+	1.14280i	0.320869	+	0.947124i	$0.396025\pi$
$337$	−12.1123	+	20.9791i	−0.659799	+	1.14280i	−0.980668	+	0.195681i	$0.937308\pi$
$338$	−8.69673	−	5.02106i	−0.473040	−	0.273110i
$339$		0			0
$340$	2.07781	+	3.59886i	0.112685	+	0.195176i
$341$	−47.5148			−2.57307
$342$		0			0
$343$	−17.6257	−	5.68629i	−0.951700	−	0.307031i
$344$	3.04933	−	1.76053i	0.164409	−	0.0949214i
$345$		0			0
$346$	−1.72121	−	0.993738i	−0.0925326	−	0.0534237i
$347$	−19.7453	−	11.3999i	−1.05998	−	0.611981i	−0.134554	−	0.990906i	$-0.542960\pi$
$347$	−19.7453	−	11.3999i	−1.05998	−	0.611981i	−0.925427	+	0.378926i	$0.876294\pi$
$348$		0			0
$349$	−2.46389	+	1.42253i	−0.131889	+	0.0761461i	−0.564493	−	0.825438i	$-0.690928\pi$
$349$	−2.46389	+	1.42253i	−0.131889	+	0.0761461i	0.432604	+	0.901584i	$0.357595\pi$
$350$	−1.25521	+	0.559901i	−0.0670936	+	0.0299279i
$351$		0			0
$352$	−5.67667			−0.302568
$353$	3.57212	+	6.18709i	0.190125	+	0.329306i	0.945291	−	0.326227i	$-0.105777\pi$
$353$	3.57212	+	6.18709i	0.190125	+	0.329306i	−0.755167	+	0.655533i	$0.772444\pi$
$354$		0			0
$355$	−9.19856	−	5.31079i	−0.488209	−	0.281868i
$356$	0.580529	−	1.00551i	0.0307680	−	0.0532917i
$357$		0			0
$358$	−4.15561	−	7.19773i	−0.219631	−	0.380412i
$359$		−	11.6037i		−	0.612421i	−0.951964	−	0.306210i	$-0.900939\pi$
$359$		−	11.6037i		−	0.612421i	0.951964	−	0.306210i	$-0.0990611\pi$
$360$		0			0
$361$	17.7019			0.931682
$362$	7.72706	+	13.3837i	0.406125	+	0.703429i
$363$		0			0
$364$	0.472486	−	4.52570i	0.0247650	−	0.237211i
$365$	10.8695	+	6.27554i	0.568938	+	0.328477i
$366$		0			0
$367$	6.78525	−	3.91747i	0.354187	−	0.204490i	−0.312341	−	0.949970i	$-0.601113\pi$
$367$	6.78525	−	3.91747i	0.354187	−	0.204490i	0.666528	+	0.745480i	$0.267780\pi$
$368$		−	3.67509i		−	0.191577i
$369$		0			0
$370$		−	21.6088i		−	1.12339i
$371$		0			0
$372$		0			0
$373$	−12.8339	+	22.2289i	−0.664512	+	1.15097i	0.314905	+	0.949123i	$0.398027\pi$
$373$	−12.8339	+	22.2289i	−0.664512	+	1.15097i	−0.979417	+	0.201845i	$0.935306\pi$
$374$	5.02053	−	8.69581i	0.259605	−	0.449650i
$375$		0			0
$376$	−10.2277	+	5.90494i	−0.527451	+	0.304524i
$377$	−7.14702			−0.368091
$378$		0			0
$379$	−15.1045			−0.775868			−0.387934	−	0.921687i	$-0.626811\pi$
$379$	−15.1045			−0.775868			−0.387934	+	0.921687i	$0.626811\pi$
$380$	−2.31806	+	1.33834i	−0.118914	+	0.0686551i
$381$		0			0
$382$	−6.16904	+	10.6851i	−0.315636	+	0.546697i
$383$	−0.763322	+	1.32211i	−0.0390040	+	0.0675568i	−0.884868	−	0.465841i	$-0.845752\pi$
$383$	−0.763322	+	1.32211i	−0.0390040	+	0.0675568i	0.845864	+	0.533398i	$0.179085\pi$
$384$		0			0
$385$	28.5607	+	20.7202i	1.45559	+	1.05600i
$386$			4.39388i			0.223643i
$387$		0			0
$388$			4.59035i			0.233039i
$389$	−12.8948	+	7.44483i	−0.653794	+	0.377468i	−0.789908	−	0.613225i	$-0.789872\pi$
$389$	−12.8948	+	7.44483i	−0.653794	+	0.377468i	0.136115	+	0.990693i	$0.456538\pi$
$390$		0			0
$391$	5.62969	+	3.25030i	0.284706	+	0.164375i
$392$	−6.65438	+	2.17238i	−0.336097	+	0.109722i
$393$		0			0
$394$	−5.44325	−	9.42799i	−0.274227	−	0.474975i
$395$	−30.6085			−1.54008
$396$		0			0
$397$		−	28.7869i		−	1.44478i	−0.691488	−	0.722388i	$-0.743045\pi$
$397$		−	28.7869i		−	1.44478i	0.691488	−	0.722388i	$-0.256955\pi$
$398$	−13.7832	−	23.8733i	−0.690892	−	1.19666i
$399$		0			0
$400$	−0.259741	+	0.449885i	−0.0129871	+	0.0224942i
$401$	33.0592	+	19.0868i	1.65090	+	0.953147i	0.976703	+	0.214595i	$0.0688431\pi$
$401$	33.0592	+	19.0868i	1.65090	+	0.953147i	0.674196	+	0.738552i	$0.264490\pi$
$402$		0			0
$403$	−7.19773	−	12.4668i	−0.358544	−	0.621017i
$404$	−6.62310			−0.329511
$405$		0			0
$406$	4.47894	+	10.0411i	0.222286	+	0.498329i
$407$	−45.2173	+	26.1062i	−2.24134	+	1.29404i
$408$		0			0
$409$	6.03355	+	3.48347i	0.298340	+	0.172247i	0.641697	−	0.766958i	$-0.278231\pi$
$409$	6.03355	+	3.48347i	0.298340	+	0.172247i	−0.343357	+	0.939205i	$0.611564\pi$
$410$	−16.2650	−	9.39060i	−0.803271	−	0.463769i
$411$		0			0
$412$	−5.07471	+	2.92989i	−0.250013	+	0.144345i
$413$	2.40314	+	5.38745i	0.118251	+	0.265099i
$414$		0			0
$415$	−29.4750			−1.44687
$416$	−0.859925	−	1.48943i	−0.0421613	−	0.0730255i
$417$		0			0
$418$	5.60106	+	3.23377i	0.273957	+	0.158169i
$419$	17.4232	−	30.1778i	0.851177	−	1.47428i	−0.0289690	−	0.999580i	$-0.509222\pi$
$419$	17.4232	−	30.1778i	0.851177	−	1.47428i	0.880146	−	0.474702i	$-0.157444\pi$
$420$		0			0
$421$	2.84597	+	4.92936i	0.138704	+	0.240242i	0.927006	−	0.375046i	$-0.122373\pi$
$421$	2.84597	+	4.92936i	0.138704	+	0.240242i	−0.788302	+	0.615288i	$0.789040\pi$
$422$		−	10.3112i		−	0.501942i
$423$		0			0
$424$		0			0
$425$	−0.459437	−	0.795769i	−0.0222860	−	0.0386005i
$426$		0			0
$427$	2.47244	−	23.6822i	0.119650	−	1.14606i
$428$	−4.08386	−	2.35782i	−0.197401	−	0.113969i
$429$		0			0
$430$	−7.16396	+	4.13611i	−0.345477	+	0.199461i
$431$			30.2936i			1.45919i	0.683880	+	0.729595i	$0.260291\pi$
$431$			30.2936i			1.45919i	−0.683880	+	0.729595i	$0.739709\pi$
$432$		0			0
$433$		−	23.6094i		−	1.13459i	−0.823513	−	0.567297i	$-0.807989\pi$
$433$		−	23.6094i		−	1.13459i	0.823513	−	0.567297i	$-0.192011\pi$
$434$	−13.0043	+	17.9251i	−0.624226	+	0.860432i
$435$		0			0
$436$	2.11835	−	3.66908i	0.101450	−	0.175717i
$437$	−2.09355	+	3.62614i	−0.100148	+	0.173462i
$438$		0			0
$439$	21.6681	−	12.5101i	1.03416	−	0.597075i	0.115989	−	0.993250i	$-0.462996\pi$
$439$	21.6681	−	12.5101i	1.03416	−	0.597075i	0.918175	+	0.396175i	$0.129663\pi$
$440$	13.3365			0.635794
$441$		0			0
$442$	3.04212			0.144699
$443$	19.9446	−	11.5150i	0.947595	−	0.547094i	0.0552622	−	0.998472i	$-0.482401\pi$
$443$	19.9446	−	11.5150i	0.947595	−	0.547094i	0.892333	+	0.451377i	$0.149067\pi$
$444$		0			0
$445$	−1.36387	+	2.36229i	−0.0646537	+	0.111983i
$446$	−3.60456	+	6.24329i	−0.170681	+	0.295628i
$447$		0			0
$448$	−1.55364	+	2.14154i	−0.0734028	+	0.101178i
$449$		−	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
$452$	−5.91693	+	3.41614i	−0.278309	+	0.160682i
$453$		0			0
$454$	−11.0470	−	6.37800i	−0.518462	−	0.299334i
$455$	−1.11004	+	10.6325i	−0.0520394	+	0.498458i
$456$		0			0
$457$	2.83307	+	4.90702i	0.132525	+	0.229541i	0.924649	−	0.380819i	$-0.124358\pi$
$457$	2.83307	+	4.90702i	0.132525	+	0.229541i	−0.792124	+	0.610360i	$0.791025\pi$
$458$	4.49418			0.209999
$459$		0			0
$460$			8.63411i			0.402567i
$461$	15.7292	+	27.2438i	0.732582	+	1.26887i	0.955776	+	0.294095i	$0.0950183\pi$
$461$	15.7292	+	27.2438i	0.732582	+	1.26887i	−0.223194	+	0.974774i	$0.571648\pi$
$462$		0			0
$463$	4.55148	−	7.88340i	0.211525	−	0.366373i	−0.740667	−	0.671873i	$-0.765490\pi$
$463$	4.55148	−	7.88340i	0.211525	−	0.366373i	0.952192	+	0.305500i	$0.0988236\pi$
$464$	3.59886	+	2.07781i	0.167073	+	0.0964597i
$465$		0			0
$466$	−1.07702	−	1.86545i	−0.0498918	−	0.0864152i
$467$	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
$470$	24.0284	−	13.8728i	1.10835	−	0.639906i
$471$		0			0
$472$	1.93094	+	1.11483i	0.0888788	+	0.0513142i
$473$	17.3100	+	9.99395i	0.795916	+	0.459522i
$474$		0			0
$475$	0.512563	−	0.295928i	0.0235180	−	0.0135781i
$476$	−1.90645	−	4.27396i	−0.0873821	−	0.195897i
$477$		0			0
$478$	10.1419			0.463881
$479$	2.33143	+	4.03816i	0.106526	+	0.184508i	0.914361	−	0.404901i	$-0.132694\pi$
$479$	2.33143	+	4.03816i	0.106526	+	0.184508i	−0.807835	+	0.589409i	$0.799361\pi$
$480$		0			0
$481$	−13.6994	−	7.90935i	−0.624639	−	0.360636i
$482$	5.27404	−	9.13490i	0.240226	−	0.416083i
$483$		0			0
$484$	−10.6123	−	18.3810i	−0.482377	−	0.835501i
$485$		−	10.7844i		−	0.489693i
$486$		0			0
$487$	−19.4821			−0.882818			−0.441409	−	0.897306i	$-0.645521\pi$
$487$	−19.4821			−0.882818			−0.441409	+	0.897306i	$0.645521\pi$
$488$	−4.49985	−	7.79396i	−0.203699	−	0.352816i
$489$		0			0
$490$	15.6335	−	5.10370i	0.706250	−	0.230562i
$491$	17.7437	+	10.2443i	0.800762	+	0.462320i	0.843737	−	0.536756i	$-0.180351\pi$
$491$	17.7437	+	10.2443i	0.800762	+	0.462320i	−0.0429758	+	0.999076i	$0.513684\pi$
$492$		0			0
$493$	−6.36577	+	3.67528i	−0.286700	+	0.165526i
$494$			1.95946i			0.0881602i
$495$		0			0
$496$			8.37019i			0.375832i
$497$	9.68203	+	7.02412i	0.434298	+	0.315075i
$498$		0			0
$499$	5.12598	−	8.87845i	0.229470	−	0.397454i	−0.728181	−	0.685385i	$-0.759634\pi$
$499$	5.12598	−	8.87845i	0.229470	−	0.397454i	0.957651	+	0.287931i	$0.0929673\pi$
$500$	−5.26317	+	9.11608i	−0.235376	+	0.407683i
$501$		0			0
$502$	25.3749	−	14.6502i	1.13254	−	0.653872i
$503$	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
$506$	18.0673	−	10.4311i	0.803188	−	0.463721i
$507$		0			0
$508$	−3.33834	+	5.78217i	−0.148115	+	0.256542i
$509$	16.6617	−	28.8589i	0.738517	−	1.27915i	−0.214646	−	0.976692i	$-0.568860\pi$
$509$	16.6617	−	28.8589i	0.738517	−	1.27915i	0.953163	−	0.302457i	$-0.0978068\pi$
$510$		0			0
$511$	−11.4408	−	8.30010i	−0.506113	−	0.367175i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$		−	7.62860i		−	0.336483i
$515$	11.9223	−	6.88335i	0.525360	−	0.303317i
$516$		0			0
$517$	−58.0591	−	33.5204i	−2.55343	−	1.47423i
$518$	−2.52685	+	24.2034i	−0.111023	+	1.06343i
$519$		0			0
$520$	2.02027	+	3.49921i	0.0885947	+	0.153451i
$521$	6.53925			0.286490			0.143245	−	0.989687i	$-0.454246\pi$
$521$	6.53925			0.286490			0.143245	+	0.989687i	$0.454246\pi$
$522$		0			0
$523$			0.786858i			0.0344069i	0.999852	+	0.0172034i	$0.00547630\pi$
$523$			0.786858i			0.0344069i	−0.999852	+	0.0172034i	$0.994524\pi$
$524$	3.73653	+	6.47185i	0.163231	+	0.282724i
$525$		0			0
$526$	6.09281	−	10.5531i	0.265659	−	0.460135i
$527$	−12.8219	−	7.40271i	−0.558530	−	0.322467i
$528$		0			0
$529$	−4.74685	−	8.22178i	−0.206385	−	0.357469i
$530$		0			0
$531$		0			0
$532$	2.75290	−	1.22797i	0.119353	−	0.0532391i
$533$	−11.9068	+	6.87440i	−0.515741	+	0.297763i
$534$		0			0
$535$	9.59445	+	5.53936i	0.414804	+	0.239487i
$536$	9.41477	+	5.43562i	0.406656	+	0.234783i
$537$		0			0
$538$	−2.40264	+	1.38717i	−0.103585	+	0.0598050i
$539$	−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	$0.461557\pi$
$542$	1.60396	+	2.77815i	0.0688961	+	0.119332i
$543$		0			0
$544$	−1.53185	−	0.884414i	−0.0656775	−	0.0379189i
$545$	−4.97675	+	8.61999i	−0.213181	+	0.369240i
$546$		0			0
$547$	−6.91456	−	11.9764i	−0.295645	−	0.512073i	0.679489	−	0.733685i	$-0.262201\pi$
$547$	−6.91456	−	11.9764i	−0.295645	−	0.512073i	−0.975135	+	0.221612i	$0.928868\pi$
$548$			7.98789i			0.341226i
$549$		0			0
$550$	−2.94893			−0.125743
$551$	−2.36729	−	4.10026i	−0.100850	−	0.174677i
$552$		0			0
$553$	34.2837	+	3.57924i	1.45789	+	0.152205i
$554$	−8.73047	−	5.04054i	−0.370922	−	0.214152i
$555$		0			0
$556$	17.9792	−	10.3803i	0.762488	−	0.440223i
$557$		−	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
$560$	3.65007	−	5.03124i	0.154243	−	0.212609i
$561$		0			0
$562$	−2.43641	+	4.21999i	−0.102774	+	0.178009i
$563$	−12.2650	+	21.2436i	−0.516909	+	0.895312i	0.482898	+	0.875676i	$0.339584\pi$
$563$	−12.2650	+	21.2436i	−0.516909	+	0.895312i	−0.999807	+	0.0196359i	$0.993749\pi$
$564$		0			0
$565$	13.9010	−	8.02574i	0.584819	−	0.337645i
$566$	−2.81781			−0.118441
$567$		0			0
$568$	4.52106			0.189699
$569$	23.4762	−	13.5540i	0.984172	−	0.568212i	0.0806449	−	0.996743i	$-0.474302\pi$
$569$	23.4762	−	13.5540i	0.984172	−	0.568212i	0.903527	+	0.428531i	$0.140969\pi$
$570$		0			0
$571$	14.9177	−	25.8382i	0.624287	−	1.08130i	−0.364391	−	0.931246i	$-0.618723\pi$
$571$	14.9177	−	25.8382i	0.624287	−	1.08130i	0.988678	−	0.150051i	$-0.0479438\pi$
$572$	4.88151	−	8.45502i	0.204106	−	0.353522i
$573$		0			0
$574$	17.1199	+	12.4201i	0.714570	+	0.518406i
$575$		−	1.90915i		−	0.0796169i
$576$		0			0
$577$			28.1666i			1.17259i	0.810097	+	0.586296i	$0.199415\pi$
$577$			28.1666i			1.17259i	−0.810097	+	0.586296i	$0.800585\pi$
$578$	−12.0129	+	6.93562i	−0.499669	+	0.288484i
$579$		0			0
$580$	−8.45502	−	4.88151i	−0.351076	−	0.202694i
$581$	33.0141	+	3.44670i	1.36965	+	0.142993i
$582$		0			0
$583$		0			0
$584$	−5.34234			−0.221068
$585$		0			0
$586$		−	8.11389i		−	0.335182i
$587$	−4.95928	−	8.58973i	−0.204692	−	0.354536i	0.745343	−	0.666681i	$-0.232286\pi$
$587$	−4.95928	−	8.58973i	−0.204692	−	0.354536i	−0.950034	+	0.312145i	$0.898952\pi$
$588$		0			0
$589$	4.76816	−	8.25870i	0.196469	−	0.340294i
$590$	−4.53648	−	2.61914i	−0.186764	−	0.107828i
$591$		0			0
$592$	4.59886	+	7.96547i	0.189012	+	0.327379i
$593$	4.69872			0.192953			0.0964766	−	0.995335i	$-0.469243\pi$
$593$	4.69872			0.192953			0.0964766	+	0.995335i	$0.469243\pi$
$594$		0			0
$595$	4.47894	+	10.0411i	0.183619	+	0.411643i
$596$	1.03726	−	0.598865i	0.0424880	−	0.0245305i
$597$		0			0
$598$	5.47381	+	3.16030i	0.223841	+	0.129234i
$599$	−12.7309	−	7.35019i	−0.520170	−	0.300320i	0.216834	−	0.976208i	$-0.430427\pi$
$599$	−12.7309	−	7.35019i	−0.520170	−	0.300320i	−0.737004	+	0.675888i	$0.763760\pi$
$600$		0			0
$601$	16.2923	−	9.40634i	0.664575	−	0.383693i	−0.129443	−	0.991587i	$-0.541319\pi$
$601$	16.2923	−	9.40634i	0.664575	−	0.383693i	0.794018	+	0.607894i	$0.207986\pi$
$602$	8.50781	−	3.79502i	0.346752	−	0.154673i
$603$		0			0
$604$	−15.2246			−0.619480
$605$	24.9321	+	43.1836i	1.01363	+	1.75566i
$606$		0			0
$607$	10.9051	+	6.29608i	0.442625	+	0.255550i	0.704711	−	0.709495i	$-0.251077\pi$
$607$	10.9051	+	6.29608i	0.442625	+	0.255550i	−0.262085	+	0.965045i	$0.584410\pi$
$608$	0.569660	−	0.986680i	0.0231028	−	0.0400152i
$609$		0			0
$610$	10.5718	+	18.3108i	0.428038	+	0.741383i
$611$		−	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	$0.563547\pi$
$614$	−5.44981	−	9.43935i	−0.219937	−	0.380941i
$615$		0			0
$616$	−14.9379	−	1.55953i	−0.601864	−	0.0628351i
$617$	3.25158	+	1.87730i	0.130904	+	0.0755772i	0.564022	−	0.825760i	$-0.309253\pi$
$617$	3.25158	+	1.87730i	0.130904	+	0.0755772i	−0.433118	+	0.901337i	$0.642587\pi$
$618$		0			0
$619$	9.56902	−	5.52468i	0.384611	−	0.222055i	−0.295211	−	0.955432i	$-0.595390\pi$
$619$	9.56902	−	5.52468i	0.384611	−	0.222055i	0.679823	+	0.733376i	$0.262057\pi$
$620$		−	19.6646i		−	0.789748i
$621$		0			0
$622$			8.23637i			0.330248i
$623$	1.80387	−	2.48645i	0.0722706	−	0.0996176i
$624$		0			0
$625$	13.6638	−	23.6664i	0.546551	−	0.946654i
$626$	−16.9011	+	29.2736i	−0.675505	+	1.17001i
$627$		0			0
$628$	8.68358	−	5.01347i	0.346513	−	0.200059i
$629$	−16.2692			−0.648696
$630$		0			0
$631$	19.4921			0.775969			0.387984	−	0.921666i	$-0.373171\pi$
$631$	19.4921			0.775969			0.387984	+	0.921666i	$0.373171\pi$
$632$	11.2830	−	6.51422i	0.448812	−	0.259122i
$633$		0			0
$634$	−3.36545	+	5.82913i	−0.133659	+	0.231504i
$635$	7.84294	−	13.5844i	0.311238	−	0.539080i
$636$		0			0
$637$	2.48665	−	11.7793i	0.0985245	−	0.466714i
$638$			23.5900i			0.933938i
$639$		0			0
$640$		−	2.34936i		−	0.0928665i
$641$	22.6669	−	13.0868i	0.895290	−	0.516896i	0.0196208	−	0.999807i	$-0.493754\pi$
$641$	22.6669	−	13.0868i	0.895290	−	0.516896i	0.875669	+	0.482912i	$0.160421\pi$
$642$		0			0
$643$	9.50955	+	5.49034i	0.375020	+	0.216518i	0.675649	−	0.737223i	$-0.263863\pi$
$643$	9.50955	+	5.49034i	0.375020	+	0.216518i	−0.300629	+	0.953741i	$0.597197\pi$
$644$	1.00964	−	9.67082i	0.0397854	−	0.381084i
$645$		0			0
$646$	1.00763	+	1.74527i	0.0396447	+	0.0686666i
$647$	−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
$650$	−0.446715	−	0.773734i	−0.0175216	−	0.0303483i
$651$		0			0
$652$	6.00158	−	10.3950i	0.235040	−	0.407101i
$653$	−19.3686	−	11.1825i	−0.757952	−	0.437604i	0.0706080	−	0.997504i	$-0.477506\pi$
$653$	−19.3686	−	11.1825i	−0.757952	−	0.437604i	−0.828560	+	0.559900i	$0.810839\pi$
$654$		0			0
$655$	−8.77843	−	15.2047i	−0.343002	−	0.594097i
$656$	7.99419			0.312121
$657$		0			0
$658$	−28.5358	+	12.7288i	−1.11244	+	0.496219i
$659$	19.2546	−	11.1166i	0.750053	−	0.433043i	−0.0756603	−	0.997134i	$-0.524106\pi$
$659$	19.2546	−	11.1166i	0.750053	−	0.433043i	0.825713	+	0.564091i	$0.190773\pi$
$660$		0			0
$661$	−9.13646	−	5.27494i	−0.355367	−	0.205171i	0.311679	−	0.950187i	$-0.399108\pi$
$661$	−9.13646	−	5.27494i	−0.355367	−	0.205171i	−0.667047	+	0.745016i	$0.732442\pi$
$662$	27.7621	+	16.0284i	1.07900	+	0.622963i
$663$		0			0
$664$	10.8651	−	6.27298i	0.421649	−	0.243439i
$665$	−6.46754	+	2.88493i	−0.250801	+	0.111873i
$666$		0			0
$667$	−15.2723			−0.591344
$668$	8.57472	+	14.8518i	0.331766	+	0.574635i
$669$		0			0
$670$	−22.1187	−	12.7702i	−0.854519	−	0.493357i
$671$	25.5442	−	44.2438i	0.986121	−	1.70801i
$672$		0			0
$673$	9.93562	+	17.2090i	0.382990	+	0.663358i	0.991488	−	0.130197i	$-0.0415610\pi$
$673$	9.93562	+	17.2090i	0.382990	+	0.663358i	−0.608498	+	0.793555i	$0.708228\pi$
$674$			24.2246i			0.933096i
$675$		0			0
$676$	−10.0421			−0.386235
$677$	7.96449	+	13.7949i	0.306100	+	0.530181i	0.977506	−	0.210909i	$-0.0676424\pi$
$677$	7.96449	+	13.7949i	0.306100	+	0.530181i	−0.671405	+	0.741090i	$0.734309\pi$
$678$		0			0
$679$	−1.26108	+	12.0793i	−0.0483960	+	0.463560i
$680$	3.59886	+	2.07781i	0.138010	+	0.0796802i
$681$		0			0
$682$	−41.1490	+	23.7574i	−1.57568	+	0.909718i
$683$			19.0269i			0.728042i	0.931391	+	0.364021i	$0.118596\pi$
$683$			19.0269i			0.728042i	−0.931391	+	0.364021i	$0.881404\pi$
$684$		0			0
$685$		−	18.7664i		−	0.717028i
$686$	−18.1075	+	3.88839i	−0.691346	+	0.148459i
$687$		0			0
$688$	1.76053	−	3.04933i	0.0671196	−	0.116254i
$689$		0			0
$690$		0			0
$691$	0.139477	−	0.0805273i	0.00530597	−	0.00306340i	−0.497345	−	0.867553i	$-0.665692\pi$
$691$	0.139477	−	0.0805273i	0.00530597	−	0.00306340i	0.502651	+	0.864490i	$0.332358\pi$
$692$	−1.98748			−0.0755525
$693$		0			0
$694$	−22.7999			−0.865471
$695$	−42.2396	+	24.3870i	−1.60224	+	0.925053i
$696$		0			0
$697$	−7.07017	+	12.2459i	−0.267802	+	0.463847i
$698$	−1.42253	+	2.46389i	−0.0538434	+	0.0932595i
$699$		0			0
$700$	−0.807090	+	1.11249i	−0.0305051	+	0.0420482i
$701$		−	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
$704$	−4.91614	+	2.83834i	−0.185284	+	0.106974i
$705$		0			0
$706$	6.18709	+	3.57212i	0.232854	+	0.134438i
$707$	−17.4283	−	1.81953i	−0.655460	−	0.0684306i
$708$		0			0
$709$	12.1962	+	21.1244i	0.458036	+	0.793342i	0.998857	−	0.0477959i	$-0.0152197\pi$
$709$	12.1962	+	21.1244i	0.458036	+	0.793342i	−0.540821	+	0.841138i	$0.681886\pi$
$710$	−10.6216			−0.398621
$711$		0			0
$712$		−	1.16106i		−	0.0435125i
$713$	−15.3806	−	26.6400i	−0.576008	−	0.997676i
$714$		0			0
$715$	−11.4684	+	19.8639i	−0.428894	+	0.742867i
$716$	−7.19773	−	4.15561i	−0.268992	−	0.155302i
$717$		0			0
$718$	−5.80186	−	10.0491i	−0.216523	−	0.375030i
$719$	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
$722$	15.3303	−	8.85097i	0.570536	−	0.329399i
$723$		0			0
$724$	13.3837	+	7.72706i	0.497400	+	0.287174i
$725$	1.86955	+	1.07938i	0.0694332	+	0.0400873i
$726$		0			0
$727$	20.6626	−	11.9296i	0.766335	−	0.442444i	−0.0652306	−	0.997870i	$-0.520778\pi$
$727$	20.6626	−	11.9296i	0.766335	−	0.442444i	0.831566	+	0.555427i	$0.187445\pi$
$728$	−1.85366	−	4.15561i	−0.0687013	−	0.154017i
$729$		0			0
$730$	12.5511			0.464536
$731$	3.11408	+	5.39374i	0.115178	+	0.199495i
$732$		0			0
$733$	10.6259	+	6.13486i	0.392476	+	0.226596i	0.683233	−	0.730201i	$-0.260574\pi$
$733$	10.6259	+	6.13486i	0.392476	+	0.226596i	−0.290756	+	0.956797i	$0.593907\pi$
$734$	3.91747	−	6.78525i	0.144596	−	0.250448i
$735$		0			0
$736$	−1.83755	−	3.18272i	−0.0677329	−	0.117317i
$737$			61.7125i			2.27321i
$738$		0			0
$739$	41.8891			1.54092			0.770459	−	0.637490i	$-0.220027\pi$
$739$	41.8891			1.54092			0.770459	+	0.637490i	$0.220027\pi$
$740$	−10.8044	−	18.7137i	−0.397177	−	0.687931i
$741$		0			0
$742$		0			0
$743$	−43.9160	−	25.3549i	−1.61112	−	0.930182i	−0.989111	−	0.147173i	$-0.952982\pi$
$743$	−43.9160	−	25.3549i	−1.61112	−	0.930182i	−0.622011	−	0.783008i	$-0.713684\pi$
$744$		0			0
$745$	−2.43690	+	1.40695i	−0.0892813	+	0.0515466i
$746$			25.6677i			0.939762i
$747$		0			0
$748$		−	10.0411i		−	0.367137i
$749$	−10.0987	−	7.32642i	−0.368999	−	0.267701i
$750$		0			0
$751$	16.3683	−	28.3508i	0.597289	−	1.03454i	−0.395930	−	0.918281i	$-0.629578\pi$
$751$	16.3683	−	28.3508i	0.597289	−	1.03454i	0.993219	−	0.116255i	$-0.0370890\pi$
$752$	−5.90494	+	10.2277i	−0.215331	+	0.372964i
$753$		0			0
$754$	−6.18951	+	3.57351i	−0.225408	+	0.130140i
$755$	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	$0.605619\pi$
$758$	−13.0809	+	7.55227i	−0.475120	+	0.274311i
$759$		0			0
$760$	−1.33834	+	2.31806i	−0.0485465	+	0.0840850i
$761$	−21.8509	+	37.8469i	−0.792096	+	1.37195i	0.132571	+	0.991174i	$0.457677\pi$
$761$	−21.8509	+	37.8469i	−0.792096	+	1.37195i	−0.924667	+	0.380777i	$0.875657\pi$
$762$		0			0
$763$	6.58231	−	9.07305i	0.238296	−	0.328466i
$764$			12.3381i			0.446376i
$765$		0			0
$766$			1.52664i			0.0551599i
$767$	−3.32093	+	1.91734i	−0.119912	+	0.0692311i
$768$		0			0
$769$	−37.0864	−	21.4118i	−1.33737	−	0.772131i	−0.350953	−	0.936393i	$-0.614142\pi$
$769$	−37.0864	−	21.4118i	−1.33737	−	0.772131i	−0.986417	+	0.164262i	$0.947476\pi$
$770$	35.0944	+	3.66388i	1.26471	+	0.132037i
$771$		0			0
$772$	2.19694	+	3.80521i	0.0790696	+	0.136953i
$773$	21.6051			0.777080			0.388540	−	0.921432i	$-0.372980\pi$
$773$	21.6051			0.777080			0.388540	+	0.921432i	$0.372980\pi$
$774$		0			0
$775$			4.34816i			0.156191i
$776$	2.29517	+	3.97536i	0.0823919	+	0.142707i
$777$		0			0
$778$	−7.44483	+	12.8948i	−0.266910	+	0.462302i
$779$	−7.88771	−	4.55397i	−0.282606	−	0.163163i
$780$		0			0
$781$	12.8323	+	22.2262i	0.459175	+	0.795315i
$782$	6.50061			0.232461
$783$		0			0
$784$	−4.67667	+	5.20853i	−0.167024	+	0.186019i
$785$	−20.4008	+	11.7784i	−0.728137	+	0.420390i
$786$		0			0
$787$	−44.4307	−	25.6521i	−1.58378	−	0.914398i	−0.994300	−	0.106618i	$-0.965998\pi$
$787$	−44.4307	−	25.6521i	−1.58378	−	0.914398i	−0.589484	−	0.807780i	$-0.700669\pi$
$788$	−9.42799	−	5.44325i	−0.335858	−	0.193908i
$789$		0			0
$790$	−26.5077	+	15.3042i	−0.943102	+	0.544500i
$791$	−16.5086	+	7.36387i	−0.586978	+	0.261829i
$792$		0			0
$793$	15.4781			0.549644
$794$	−14.3935	−	24.9302i	−0.510805	−	0.884740i
$795$		0			0
$796$	−23.8733	−	13.7832i	−0.846166	−	0.488534i
$797$	0.899094	−	1.55728i	0.0318476	−	0.0551616i	−0.849662	−	0.527327i	$-0.823194\pi$
$797$	0.899094	−	1.55728i	0.0318476	−	0.0551616i	0.881510	+	0.472166i	$0.156528\pi$
$798$		0			0
$799$	−10.4448	−	18.0910i	−0.369512	−	0.640013i
$800$			0.519482i			0.0183665i
$801$		0			0
$802$	38.1735			1.34795
$803$	−15.1634	−	26.2637i	−0.535103	−	0.926826i
$804$		0			0
$805$	−2.37201	+	22.7202i	−0.0836023	+	0.800783i
$806$	−12.4668	−	7.19773i	−0.439125	−	0.253529i
$807$		0			0
$808$	−5.73577	+	3.31155i	−0.201784	+	0.116500i
$809$		−	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	$0.997883\pi$
$812$	8.89940	+	6.45634i	0.312308	+	0.226573i
$813$		0			0
$814$	−26.1062	+	45.2173i	−0.915023	+	1.58487i
$815$	−14.0999	+	24.4217i	−0.493896	+	0.855453i
$816$		0			0
$817$	−3.47416	+	2.00581i	−0.121545	+	0.0701743i
$818$	6.96694			0.243593
$819$		0			0
$820$	−18.7812			−0.655868
$821$	−11.4968	+	6.63771i	−0.401243	+	0.231658i	−0.687020	−	0.726638i	$-0.741082\pi$
$821$	−11.4968	+	6.63771i	−0.401243	+	0.231658i	0.285777	+	0.958296i	$0.407748\pi$
$822$		0			0
$823$	−13.8711	+	24.0255i	−0.483517	+	0.837476i	−0.999821	−	0.0189295i	$-0.993974\pi$
$823$	−13.8711	+	24.0255i	−0.483517	+	0.837476i	0.516304	+	0.856405i	$0.327308\pi$
$824$	−2.92989	+	5.07471i	−0.102067	+	0.176786i
$825$		0			0
$826$	4.77491	+	3.46410i	0.166140	+	0.120531i
$827$		−	27.7183i		−	0.963859i	−0.876210	−	0.481929i	$-0.839936\pi$
$827$		−	27.7183i		−	0.963859i	0.876210	−	0.481929i	$-0.160064\pi$
$828$		0			0
$829$			42.7361i			1.48429i	0.670242	+	0.742143i	$0.266190\pi$
$829$			42.7361i			1.48429i	−0.670242	+	0.742143i	$0.733810\pi$
$830$	−25.5261	+	14.7375i	−0.886023	+	0.511545i
$831$		0			0
$832$	−1.48943	−	0.859925i	−0.0516368	−	0.0298125i
$833$	−3.84257	−	11.7705i	−0.133137	−	0.407822i
$834$		0			0
$835$	−20.1451	−	34.8923i	−0.697149	−	1.20750i
$836$	6.46754			0.223685
$837$		0			0
$838$		−	34.8463i		−	1.20375i
$839$	1.92438	+	3.33313i	0.0664370	+	0.115072i	0.897331	−	0.441359i	$-0.145504\pi$
$839$	1.92438	+	3.33313i	0.0664370	+	0.115072i	−0.830894	+	0.556431i	$0.812170\pi$
$840$		0			0
$841$	−5.86545	+	10.1593i	−0.202257	+	0.350319i
$842$	4.92936	+	2.84597i	0.169877	+	0.0980785i
$843$		0			0
$844$	−5.15561	−	8.92978i	−0.177463	−	0.307376i
$845$	23.5925			0.811608
$846$		0			0
$847$	−22.8760	−	51.2842i	−0.786028	−	1.76215i
$848$		0			0
$849$		0			0
$850$	−0.795769	−	0.459437i	−0.0272946	−	0.0157586i
$851$	−29.2738	−	16.9013i	−1.00349	−	0.579368i
$852$		0			0
$853$	−26.3470	+	15.2114i	−0.902103	+	0.520830i	−0.877882	−	0.478877i	$-0.841044\pi$
$853$	−26.3470	+	15.2114i	−0.902103	+	0.520830i	−0.0242213	+	0.999707i	$0.507711\pi$
$854$	−9.69992	−	21.7456i	−0.331924	−	0.744121i
$855$		0			0
$856$	−4.71563			−0.161177
$857$	−19.4657	−	33.7156i	−0.664937	−	1.15170i	−0.979303	−	0.202402i	$-0.935125\pi$
$857$	−19.4657	−	33.7156i	−0.664937	−	1.15170i	0.314366	−	0.949302i	$-0.398208\pi$
$858$		0			0
$859$	11.5922	+	6.69275i	0.395520	+	0.228354i	0.684549	−	0.728967i	$-0.259999\pi$
$859$	11.5922	+	6.69275i	0.395520	+	0.228354i	−0.289029	+	0.957320i	$0.593332\pi$
$860$	−4.13611	+	7.16396i	−0.141040	+	0.244289i
$861$		0			0
$862$	15.1468	+	26.2350i	0.515901	+	0.893567i
$863$			21.7219i			0.739424i	0.929146	+	0.369712i	$0.120544\pi$
$863$			21.7219i			0.739424i	−0.929146	+	0.369712i	$0.879456\pi$
$864$		0			0
$865$	4.66929			0.158761
$866$	−11.8047	−	20.4463i	−0.401139	−	0.694794i
$867$		0			0
$868$	−2.29950	+	22.0257i	−0.0780502	+	0.747602i
$869$	64.0496	+	36.9791i	2.17273	+	1.25443i
$870$		0			0
$871$	−16.1920	+	9.34845i	−0.548645	+	0.316760i
$872$		−	4.23669i		−	0.143473i
$873$		0			0
$874$			4.18711i			0.141631i
$875$	−16.3542	+	22.5426i	−0.552872	+	0.762078i
$876$		0			0
$877$	−0.196152	+	0.339746i	−0.00662360	+	0.0114724i	−0.869318	−	0.494253i	$-0.835442\pi$
$877$	−0.196152	+	0.339746i	−0.00662360	+	0.0114724i	0.862695	+	0.505725i	$0.168775\pi$
$878$	12.5101	−	21.6681i	0.422196	−	0.731265i
$879$		0			0
$880$	11.5498	−	6.66826i	0.389343	−	0.224787i
$881$	−43.3363			−1.46004			−0.730018	−	0.683427i	$-0.760489\pi$
$881$	−43.3363			−1.46004			−0.730018	+	0.683427i	$0.760489\pi$
$882$		0			0
$883$	2.17403			0.0731618			0.0365809	−	0.999331i	$-0.488353\pi$
$883$	2.17403			0.0731618			0.0365809	+	0.999331i	$0.488353\pi$
$884$	2.63455	−	1.52106i	0.0886096	−	0.0511588i
$885$		0			0
$886$	11.5150	−	19.9446i	0.386854	−	0.670051i
$887$	5.72215	−	9.91105i	0.192131	−	0.332781i	−0.753825	−	0.657075i	$-0.771793\pi$
$887$	5.72215	−	9.91105i	0.192131	−	0.332781i	0.945956	+	0.324294i	$0.105127\pi$
$888$		0			0
$889$	−10.3732	+	14.2984i	−0.347905	+	0.479551i
$890$			2.72774i			0.0914341i
$891$		0			0
$892$			7.20913i			0.241379i
$893$	11.6526	−	6.72762i	0.389939	−	0.225131i
$894$		0			0
$895$	16.9100	+	9.76302i	0.565240	+	0.326342i
$896$	−0.274725	+	2.63145i	−0.00917793	+	0.0879106i
$897$		0			0
$898$	−7.95142	−	13.7723i	−0.265342	−	0.459586i
$899$	34.7832			1.16009
$900$		0			0
$901$		0			0
$902$	22.6902	+	39.3006i	0.755501	+	1.30857i
$903$		0			0
$904$	−3.41614	+	5.91693i	−0.113619	+	0.196794i
$905$	−31.4430	−	18.1536i	−1.04520	−	0.603447i
$906$		0			0
$907$	26.9446	+	46.6694i	0.894680	+	1.54963i	0.834200	+	0.551462i	$0.185930\pi$
$907$	26.9446	+	46.6694i	0.894680	+	1.54963i	0.0604797	+	0.998169i	$0.480737\pi$
$908$	−12.7560			−0.423323
$909$		0			0
$910$	4.35492	+	9.76302i	0.144364	+	0.323641i
$911$	7.00460	−	4.04411i	0.232073	−	0.133987i	−0.379455	−	0.925210i	$-0.623889\pi$
$911$	7.00460	−	4.04411i	0.232073	−	0.133987i	0.611528	+	0.791223i	$0.290555\pi$
$912$		0			0
$913$	61.6777	+	35.6097i	2.04124	+	1.17851i
$914$	4.90702	+	2.83307i	0.162310	+	0.0937096i
$915$		0			0
$916$	3.89208	−	2.24709i	0.128598	−	0.0742460i
$917$	8.05450	+	18.0569i	0.265983	+	0.596290i
$918$		0			0
$919$	25.6751			0.846943			0.423472	−	0.905909i	$-0.360811\pi$
$919$	25.6751			0.846943			0.423472	+	0.905909i	$0.360811\pi$
$920$	4.31705	+	7.47736i	0.142329	+	0.246521i
$921$		0			0
$922$	27.2438	+	15.7292i	0.897226	+	0.518014i
$923$	−3.88777	+	6.73382i	−0.127968	+	0.221646i
$924$		0			0
$925$	2.38903	+	4.13792i	0.0785507	+	0.136054i
$926$		−	9.10296i		−	0.299142i
$927$		0			0
$928$	4.15561			0.136415
$929$	−5.42618	−	9.39842i	−0.178027	−	0.308352i	0.763177	−	0.646189i	$-0.223638\pi$
$929$	−5.42618	−	9.39842i	−0.178027	−	0.308352i	−0.941205	+	0.337837i	$0.890305\pi$
$930$		0			0
$931$	7.58147	−	2.47504i	0.248473	−	0.0811161i
$932$	−1.86545	−	1.07702i	−0.0611048	−	0.0352789i
$933$		0			0
$934$	26.2433	−	15.1516i	0.858708	−	0.495775i
$935$			23.5900i			0.771477i
$936$		0			0
$937$			0.458120i			0.0149661i	0.999972	+	0.00748306i	$0.00238195\pi$
$937$			0.458120i			0.0149661i	−0.999972	+	0.00748306i	$0.997618\pi$
$938$	23.2812	+	16.8900i	0.760158	+	0.551479i
$939$		0			0
$940$	13.8728	−	24.0284i	0.452482	−	0.783721i
$941$	3.68890	−	6.38937i	0.120255	−	0.208287i	−0.799613	−	0.600515i	$-0.794962\pi$
$941$	3.68890	−	6.38937i	0.120255	−	0.208287i	0.919868	+	0.392228i	$0.128296\pi$
$942$		0			0
$943$	−25.4433	+	14.6897i	−0.828548	+	0.478362i
$944$	2.22966			0.0725693
$945$		0			0
$946$	19.9879			0.649862
$947$	10.3846	−	5.99552i	0.337453	−	0.194828i	−0.321692	−	0.946844i	$-0.604252\pi$
$947$	10.3846	−	5.99552i	0.337453	−	0.194828i	0.659145	+	0.752016i	$0.270918\pi$
$948$		0			0
$949$	4.59401	−	7.95706i	0.149128	−	0.258297i
$950$	0.295928	−	0.512563i	0.00960118	−	0.0166297i
$951$		0			0
$952$	−3.78802	−	2.74813i	−0.122770	−	0.0890674i
$953$		−	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
$956$	8.78317	−	5.07096i	0.284068	−	0.164007i
$957$		0			0
$958$	4.03816	+	2.33143i	0.130467	+	0.0753251i
$959$	−2.19448	+	21.0197i	−0.0708633	+	0.678763i
$960$		0			0
$961$	19.5300	+	33.8270i	0.630000	+	1.09119i
$962$	−15.8187			−0.510016
$963$		0			0
$964$		−	10.5481i		−	0.339731i
$965$	−5.16140	−	8.93981i	−0.166151	−	0.287783i
$966$		0			0
$967$	−3.37560	+	5.84671i	−0.108552	+	0.188018i	−0.915184	−	0.403037i	$-0.867955\pi$
$967$	−3.37560	+	5.84671i	−0.108552	+	0.188018i	0.806632	+	0.591054i	$0.201288\pi$
$968$	−18.3810	−	10.6123i	−0.590789	−	0.341092i
$969$		0			0
$970$	−5.39218	−	9.33953i	−0.173133	−	0.299874i
$971$	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
$974$	−16.8720	+	9.74105i	−0.540613	+	0.312123i
$975$		0			0
$976$	−7.79396	−	4.49985i	−0.249479	−	0.144037i
$977$	−11.7769	−	6.79937i	−0.376775	−	0.217531i	0.299639	−	0.954053i	$-0.403134\pi$
$977$	−11.7769	−	6.79937i	−0.376775	−	0.217531i	−0.676414	+	0.736521i	$0.736467\pi$
$978$		0			0
$979$	5.70793	−	3.29547i	0.182426	−	0.105324i
$980$	10.9872	−	12.2367i	0.350972	−	0.390887i
$981$		0			0
$982$	20.4886			0.653819
$983$	−11.3849	−	19.7192i	−0.363122	−	0.628946i	0.625351	−	0.780344i	$-0.284956\pi$
$983$	−11.3849	−	19.7192i	−0.363122	−	0.628946i	−0.988473	+	0.151398i	$0.951623\pi$
$984$		0			0
$985$	22.1497	+	12.7882i	0.705749	+	0.407464i
$986$	−3.67528	+	6.36577i	−0.117045	+	0.202728i
$987$		0			0
$988$	0.979729	+	1.69694i	0.0311693	+	0.0539869i
$989$			12.9402i			0.411475i
$990$		0			0
$991$	−26.9905			−0.857383			−0.428691	−	0.903451i	$-0.641025\pi$
$991$	−26.9905			−0.857383			−0.428691	+	0.903451i	$0.641025\pi$
$992$	4.18509	+	7.24879i	0.132877	+	0.230149i
$993$		0			0
$994$	11.8969	+	1.24205i	0.377348	+	0.0393954i
$995$	56.0869	+	32.3818i	1.77807	+	1.02657i
$996$		0			0
$997$	−16.7263	+	9.65694i	−0.529728	+	0.305838i	−0.740906	−	0.671609i	$-0.765603\pi$
$997$	−16.7263	+	9.65694i	−0.529728	+	0.305838i	0.211178	+	0.977448i	$0.432270\pi$
$998$		−	10.2520i		−	0.324520i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.m.a.125.6		16
3.2	odd	2		126.2.m.a.41.3	yes	16
4.3	odd	2		3024.2.cc.b.881.2		16
7.2	even	3		2646.2.t.a.2285.3		16
7.3	odd	6		2646.2.l.b.1097.7		16
7.4	even	3		2646.2.l.b.1097.6		16
7.5	odd	6		2646.2.t.a.2285.2		16
7.6	odd	2	inner	378.2.m.a.125.7		16
9.2	odd	6	inner	378.2.m.a.251.7		16
9.4	even	3		1134.2.d.a.1133.15		16
9.5	odd	6		1134.2.d.a.1133.2		16
9.7	even	3		126.2.m.a.83.2	yes	16
12.11	even	2		1008.2.cc.b.545.3		16
21.2	odd	6		882.2.t.b.815.5		16
21.5	even	6		882.2.t.b.815.8		16
21.11	odd	6		882.2.l.a.509.3		16
21.17	even	6		882.2.l.a.509.2		16
21.20	even	2		126.2.m.a.41.2	✓	16
28.27	even	2		3024.2.cc.b.881.7		16
36.7	odd	6		1008.2.cc.b.209.6		16
36.11	even	6		3024.2.cc.b.2897.7		16
63.2	odd	6		2646.2.l.b.521.3		16
63.11	odd	6		2646.2.t.a.1979.2		16
63.13	odd	6		1134.2.d.a.1133.10		16
63.16	even	3		882.2.l.a.227.6		16
63.20	even	6	inner	378.2.m.a.251.6		16
63.25	even	3		882.2.t.b.803.8		16
63.34	odd	6		126.2.m.a.83.3	yes	16
63.38	even	6		2646.2.t.a.1979.3		16
63.41	even	6		1134.2.d.a.1133.7		16
63.47	even	6		2646.2.l.b.521.2		16
63.52	odd	6		882.2.t.b.803.5		16
63.61	odd	6		882.2.l.a.227.7		16
84.83	odd	2		1008.2.cc.b.545.6		16
252.83	odd	6		3024.2.cc.b.2897.2		16
252.223	even	6		1008.2.cc.b.209.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.2	✓	16	21.20	even	2
126.2.m.a.41.3	yes	16	3.2	odd	2
126.2.m.a.83.2	yes	16	9.7	even	3
126.2.m.a.83.3	yes	16	63.34	odd	6
378.2.m.a.125.6		16	1.1	even	1	trivial
378.2.m.a.125.7		16	7.6	odd	2	inner
378.2.m.a.251.6		16	63.20	even	6	inner
378.2.m.a.251.7		16	9.2	odd	6	inner
882.2.l.a.227.6		16	63.16	even	3
882.2.l.a.227.7		16	63.61	odd	6
882.2.l.a.509.2		16	21.17	even	6
882.2.l.a.509.3		16	21.11	odd	6
882.2.t.b.803.5		16	63.52	odd	6
882.2.t.b.803.8		16	63.25	even	3
882.2.t.b.815.5		16	21.2	odd	6
882.2.t.b.815.8		16	21.5	even	6
1008.2.cc.b.209.3		16	252.223	even	6
1008.2.cc.b.209.6		16	36.7	odd	6
1008.2.cc.b.545.3		16	12.11	even	2
1008.2.cc.b.545.6		16	84.83	odd	2
1134.2.d.a.1133.2		16	9.5	odd	6
1134.2.d.a.1133.7		16	63.41	even	6
1134.2.d.a.1133.10		16	63.13	odd	6
1134.2.d.a.1133.15		16	9.4	even	3
2646.2.l.b.521.2		16	63.47	even	6
2646.2.l.b.521.3		16	63.2	odd	6
2646.2.l.b.1097.6		16	7.4	even	3
2646.2.l.b.1097.7		16	7.3	odd	6
2646.2.t.a.1979.2		16	63.11	odd	6
2646.2.t.a.1979.3		16	63.38	even	6
2646.2.t.a.2285.2		16	7.5	odd	6
2646.2.t.a.2285.3		16	7.2	even	3
3024.2.cc.b.881.2		16	4.3	odd	2
3024.2.cc.b.881.7		16	28.27	even	2
3024.2.cc.b.2897.2		16	252.83	odd	6
3024.2.cc.b.2897.7		16	36.11	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.17468 + 2.03460i) q^{5} +(1.55364 - 2.14154i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.17468 + 2.03460i) q^{5} +(1.55364 - 2.14154i) q^{7} -1.00000i q^{8} +2.34936i q^{10} +(4.91614 - 2.83834i) q^{11} +(1.48943 + 0.859925i) q^{13} +(0.274725 - 2.63145i) q^{14} +(-0.500000 - 0.866025i) q^{16} +1.76883 q^{17} +1.13932i q^{19} +(1.17468 + 2.03460i) q^{20} +(2.83834 - 4.91614i) q^{22} +(3.18272 + 1.83755i) q^{23} +(-0.259741 - 0.449885i) q^{25} +1.71985 q^{26} +(-1.07781 - 2.41626i) q^{28} +(-3.59886 + 2.07781i) q^{29} +(-7.24879 - 4.18509i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.53185 - 0.884414i) q^{34} +(2.53215 + 5.67667i) q^{35} -9.19773 q^{37} +(0.569660 + 0.986680i) q^{38} +(2.03460 + 1.17468i) q^{40} +(-3.99709 + 6.92317i) q^{41} +(1.76053 + 3.04933i) q^{43} -5.67667i q^{44} +3.67509 q^{46} +(-5.90494 - 10.2277i) q^{47} +(-2.17238 - 6.65438i) q^{49} +(-0.449885 - 0.259741i) q^{50} +(1.48943 - 0.859925i) q^{52} +13.3365i q^{55} +(-2.14154 - 1.55364i) q^{56} +(-2.07781 + 3.59886i) q^{58} +(-1.11483 + 1.93094i) q^{59} +(7.79396 - 4.49985i) q^{61} -8.37019 q^{62} -1.00000 q^{64} +(-3.49921 + 2.02027i) q^{65} +(-5.43562 + 9.41477i) q^{67} +(0.884414 - 1.53185i) q^{68} +(5.03124 + 3.65007i) q^{70} +4.52106i q^{71} -5.34234i q^{73} +(-7.96547 + 4.59886i) q^{74} +(0.986680 + 0.569660i) q^{76} +(1.55953 - 14.9379i) q^{77} +(6.51422 + 11.2830i) q^{79} +2.34936 q^{80} +7.99419i q^{82} +(6.27298 + 10.8651i) q^{83} +(-2.07781 + 3.59886i) q^{85} +(3.04933 + 1.76053i) q^{86} +(-2.83834 - 4.91614i) q^{88} +1.16106 q^{89} +(4.15561 - 1.85366i) q^{91} +(3.18272 - 1.83755i) q^{92} +(-10.2277 - 5.90494i) q^{94} +(-2.31806 - 1.33834i) q^{95} +(-3.97536 + 2.29517i) q^{97} +(-5.20853 - 4.67667i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 + 2 * q^7	\( 16 q + 8 q^{4} + 2 q^{7} + 12 q^{11} + 6 q^{14} - 8 q^{16} + 48 q^{23} - 8 q^{25} + 4 q^{28} + 12 q^{29} - 8 q^{37} + 4 q^{43} + 24 q^{46} - 8 q^{49} - 60 q^{50} + 6 q^{56} - 12 q^{58} - 16 q^{64} - 84 q^{65} - 28 q^{67} - 36 q^{74} - 78 q^{77} - 4 q^{79} - 12 q^{85} + 24 q^{86} + 24 q^{91} + 48 q^{92} - 12 q^{95}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^7 + 12 * q^11 + 6 * q^14 - 8 * q^16 + 48 * q^23 - 8 * q^25 + 4 * q^28 + 12 * q^29 - 8 * q^37 + 4 * q^43 + 24 * q^46 - 8 * q^49 - 60 * q^50 + 6 * q^56 - 12 * q^58 - 16 * q^64 - 84 * q^65 - 28 * q^67 - 36 * q^74 - 78 * q^77 - 4 * q^79 - 12 * q^85 + 24 * q^86 + 24 * q^91 + 48 * q^92 - 12 * q^95

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