LMFDB - Embedded newform 378.2.m.a.125.7

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			125.7
Root			$-1.40917 - 1.00709i$ of defining polynomial
Character	$\chi$	$=$	378.125
Dual form			378.2.m.a.251.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.17468 - 2.03460i) q^{5} +(-2.63145 + 0.274725i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.17468 - 2.03460i) q^{5} +(-2.63145 + 0.274725i) q^{7} -1.00000i q^{8} -2.34936i q^{10} +(4.91614 - 2.83834i) q^{11} +(-1.48943 - 0.859925i) q^{13} +(-2.14154 + 1.55364i) q^{14} +(-0.500000 - 0.866025i) q^{16} -1.76883 q^{17} -1.13932i q^{19} +(-1.17468 - 2.03460i) q^{20} +(2.83834 - 4.91614i) q^{22} +(3.18272 + 1.83755i) q^{23} +(-0.259741 - 0.449885i) q^{25} -1.71985 q^{26} +(-1.07781 + 2.41626i) q^{28} +(-3.59886 + 2.07781i) q^{29} +(7.24879 + 4.18509i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.53185 + 0.884414i) q^{34} +(-2.53215 + 5.67667i) q^{35} -9.19773 q^{37} +(-0.569660 - 0.986680i) q^{38} +(-2.03460 - 1.17468i) q^{40} +(3.99709 - 6.92317i) q^{41} +(1.76053 + 3.04933i) q^{43} -5.67667i q^{44} +3.67509 q^{46} +(5.90494 + 10.2277i) q^{47} +(6.84905 - 1.44585i) q^{49} +(-0.449885 - 0.259741i) q^{50} +(-1.48943 + 0.859925i) q^{52} -13.3365i q^{55} +(0.274725 + 2.63145i) q^{56} +(-2.07781 + 3.59886i) q^{58} +(1.11483 - 1.93094i) q^{59} +(-7.79396 + 4.49985i) q^{61} +8.37019 q^{62} -1.00000 q^{64} +(-3.49921 + 2.02027i) q^{65} +(-5.43562 + 9.41477i) q^{67} +(-0.884414 + 1.53185i) q^{68} +(0.645428 + 6.18222i) q^{70} +4.52106i q^{71} +5.34234i q^{73} +(-7.96547 + 4.59886i) q^{74} +(-0.986680 - 0.569660i) q^{76} +(-12.1568 + 8.81952i) q^{77} +(6.51422 + 11.2830i) q^{79} -2.34936 q^{80} -7.99419i q^{82} +(-6.27298 - 10.8651i) q^{83} +(-2.07781 + 3.59886i) q^{85} +(3.04933 + 1.76053i) q^{86} +(-2.83834 - 4.91614i) q^{88} -1.16106 q^{89} +(4.15561 + 1.85366i) q^{91} +(3.18272 - 1.83755i) q^{92} +(10.2277 + 5.90494i) q^{94} +(-2.31806 - 1.33834i) q^{95} +(3.97536 - 2.29517i) q^{97} +(5.20853 - 4.67667i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.657274\pi$
$5$	1.17468	−	2.03460i	0.525332	−	0.909902i	0.999565	−	0.0295026i	$-0.00939234\pi$
$6$		0			0
$7$	−2.63145	+	0.274725i	−0.994594	+	0.103836i
$7$	−2.63145	+	0.274725i	−0.994594	+	0.103836i
$8$		−	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	0.279024	−	0.960284i	$-0.409989\pi$
$13$	−1.48943	−	0.859925i	−0.413094	−	0.238500i	−0.692118	+	0.721784i	$0.743322\pi$
$14$	−2.14154	+	1.55364i	−0.572350	+	0.415229i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−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	$-0.958281\pi$
$19$		−	1.13932i		−	0.261378i	0.991423	−	0.130689i	$-0.0417189\pi$
$20$	−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	0.980734	−	0.195350i	$-0.0625844\pi$
$31$	7.24879	+	4.18509i	1.30192	+	0.751665i	0.321188	+	0.947015i	$0.395918\pi$
$32$	−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	$-0.618742\pi$
$41$	3.99709	−	6.92317i	0.624241	−	1.08122i	0.988687	−	0.149993i	$-0.0479251\pi$
$42$		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	$0.163698\pi$
$47$	5.90494	+	10.2277i	0.861324	+	1.49186i	−0.00932669	+	0.999957i	$0.502969\pi$
$48$		0			0
$49$	6.84905	−	1.44585i	0.978436	−	0.206550i
$50$	−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
$56$	0.274725	+	2.63145i	0.0367117	+	0.351642i
$57$		0			0
$58$	−2.07781	+	3.59886i	−0.272829	+	0.472554i
$59$	1.11483	−	1.93094i	0.145139	−	0.251387i	−0.784286	−	0.620399i	$-0.786971\pi$
$59$	1.11483	−	1.93094i	0.145139	−	0.251387i	0.929425	+	0.369012i	$0.120304\pi$
$60$		0			0
$61$	−7.79396	+	4.49985i	−0.997915	+	0.576146i	−0.907631	−	0.419770i	$-0.862111\pi$
$61$	−7.79396	+	4.49985i	−0.997915	+	0.576146i	−0.0902842	+	0.995916i	$0.528778\pi$
$62$	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
$70$	0.645428	+	6.18222i	0.0771434	+	0.738916i
$71$			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	$0.101212\pi$
$73$			5.34234i			0.625274i	−0.949873	+	0.312637i	$0.898788\pi$
$74$	−7.96547	+	4.59886i	−0.925967	+	0.534607i
$75$		0			0
$76$	−0.986680	−	0.569660i	−0.113180	−	0.0653445i
$77$	−12.1568	+	8.81952i	−1.38540	+	1.00508i
$78$		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	$-0.924915\pi$
$83$	−6.27298	−	10.8651i	−0.688549	−	1.19260i	0.283758	−	0.958896i	$-0.408419\pi$
$84$		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	$-0.519600\pi$
$89$	−1.16106			−0.123072			−0.0615360	+	0.998105i	$0.519600\pi$
$90$		0			0
$91$	4.15561	+	1.85366i	0.435626	+	0.194317i
$92$	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	−0.284416	−	0.958701i	$-0.591800\pi$
$97$	3.97536	−	2.29517i	0.403636	−	0.233039i	0.688052	+	0.725662i	$0.258466\pi$
$98$	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	0.982415	−	0.186711i	$-0.0597827\pi$
$101$	3.31155	+	5.73577i	0.329511	+	0.570730i	−0.652904	+	0.757441i	$0.726449\pi$
$102$		0			0
$103$	5.07471	+	2.92989i	0.500026	+	0.288690i	0.728724	−	0.684807i	$-0.240114\pi$
$103$	5.07471	+	2.92989i	0.500026	+	0.288690i	−0.228698	+	0.973497i	$0.573447\pi$
$104$	−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
$112$	1.55364	+	2.14154i	0.146806	+	0.202356i
$113$	−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
$119$	4.65458	−	0.485942i	0.426685	−	0.0445462i
$120$		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	−0.655345	−	0.755329i	$-0.727477\pi$
$131$	3.73653	−	6.47185i	0.326462	−	0.565448i	0.981807	+	0.189881i	$0.0608102\pi$
$132$		0			0
$133$	0.313000	+	2.99806i	0.0271406	+	0.259965i
$134$			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	$-0.990577\pi$
$139$	−17.9792	−	10.3803i	−1.52498	−	0.880446i	−0.525415	−	0.850846i	$-0.676090\pi$
$140$	3.65007	+	5.03124i	0.308487	+	0.425218i
$141$		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	0.111719	−	0.993740i	$-0.464364\pi$
$157$	−8.68358	−	5.01347i	−0.693025	−	0.400118i	−0.804744	+	0.593621i	$0.797698\pi$
$158$	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	$-0.602390\pi$
$167$	8.57472	−	14.8518i	0.663532	−	1.14927i	0.979681	−	0.200561i	$-0.0642765\pi$
$168$		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	0.901326	−	0.433140i	$-0.142595\pi$
$173$	0.993738	+	1.72121i	0.0755525	+	0.130861i	−0.825774	+	0.564001i	$0.809261\pi$
$174$		0			0
$175$	0.807090	+	1.11249i	0.0610103	+	0.0840964i
$176$	−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	$-0.805256\pi$
$181$		−	15.4541i		−	1.14870i	0.818611	−	0.574348i	$-0.194744\pi$
$182$	4.52570	−	0.472486i	0.335467	−	0.0350230i
$183$		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
$196$	2.17238	−	6.65438i	0.155170	−	0.475313i
$197$		−	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	$0.431701\pi$
$199$			27.5665i			1.95414i	−0.212926	+	0.977068i	$0.568299\pi$
$200$	−0.449885	+	0.259741i	−0.0318116	+	0.0183665i
$201$		0			0
$202$	5.73577	+	3.31155i	0.403567	+	0.233000i
$203$	8.89940	−	6.45634i	0.624616	−	0.453146i
$204$		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	−0.276175	−	0.961107i	$-0.589067\pi$
$223$	6.24329	−	3.60456i	0.418081	−	0.241379i	0.694256	+	0.719728i	$0.255733\pi$
$224$	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	0.996262	−	0.0863812i	$-0.0275303\pi$
$227$	6.37800	+	11.0470i	0.423323	+	0.733217i	−0.572939	+	0.819598i	$0.694197\pi$
$228$		0			0
$229$	−3.89208	−	2.24709i	−0.257196	−	0.148492i	0.365859	−	0.930670i	$-0.380775\pi$
$229$	−3.89208	−	2.24709i	−0.257196	−	0.148492i	−0.623055	+	0.782178i	$0.714109\pi$
$230$	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
$238$	3.78802	−	2.74813i	0.245541	−	0.178135i
$239$	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	−0.764477	−	0.644651i	$-0.777003\pi$
$241$	−9.13490	+	5.27404i	−0.588431	+	0.339731i	0.176046	+	0.984382i	$0.443669\pi$
$242$		−	21.2246i		−	1.36437i
$243$		0			0
$244$			8.99970i			0.576146i
$245$	5.10370	−	15.6335i	0.326064	−	0.998789i
$246$		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	$-0.875696\pi$
$251$	−29.3005			−1.84943			−0.924714	+	0.380662i	$0.875696\pi$
$252$		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	−0.960120	−	0.279588i	$-0.909802\pi$
$257$	−3.81430	+	6.60656i	−0.237930	+	0.412106i	0.722190	+	0.691694i	$0.243135\pi$
$258$		0			0
$259$	24.2034	−	2.52685i	1.50392	−	0.157011i
$260$			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
$266$	1.77010	+	2.43990i	0.108532	+	0.149600i
$267$		0			0
$268$	5.43562	+	9.41477i	0.332034	+	0.575099i
$269$	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	$-0.968937\pi$
$271$		−	3.20793i		−	0.194868i	0.995242	−	0.0974338i	$-0.0310634\pi$
$272$	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	0.570774	−	0.821107i	$-0.306643\pi$
$283$	2.44030	+	1.40891i	0.145061	+	0.0837508i	−0.425713	+	0.904858i	$0.639977\pi$
$284$	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	−0.959855	−	0.280498i	$-0.909500\pi$
$293$	−4.05694	+	7.02683i	−0.237009	+	0.410512i	0.722846	+	0.691010i	$0.242834\pi$
$294$		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
$301$	−5.47047	−	7.54049i	−0.315313	−	0.434626i
$302$	−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	$0.100676\pi$
$307$			10.8996i			0.622074i	−0.950398	+	0.311037i	$0.899324\pi$
$308$	1.55953	+	14.9379i	0.0888622	+	0.851164i
$309$		0			0
$310$	9.83228	−	17.0300i	0.558436	−	0.967240i
$311$	4.11819	−	7.13291i	0.233521	−	0.404470i	−0.725321	−	0.688411i	$-0.758309\pi$
$311$	4.11819	−	7.13291i	0.233521	−	0.404470i	0.958842	+	0.283941i	$0.0916419\pi$
$312$		0			0
$313$	29.2736	−	16.9011i	1.65464	−	0.955308i	0.679516	−	0.733661i	$-0.262190\pi$
$313$	29.2736	−	16.9011i	1.65464	−	0.955308i	0.975127	−	0.221648i	$-0.0711435\pi$
$314$	−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
$322$	−9.67082	+	1.00964i	−0.538934	+	0.0562651i
$323$			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
$329$	−18.3484	−	25.2913i	−1.01158	−	1.39436i
$330$		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	−0.432604	−	0.901584i	$-0.642405\pi$
$349$	2.46389	−	1.42253i	0.131889	−	0.0761461i	0.564493	+	0.825438i	$0.309072\pi$
$350$	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	0.755167	−	0.655533i	$-0.227556\pi$
$353$	−3.57212	−	6.18709i	−0.190125	−	0.329306i	−0.945291	+	0.326227i	$0.894223\pi$
$354$		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
$364$	3.68312	−	2.67203i	0.193048	−	0.140053i
$365$	10.8695	+	6.27554i	0.568938	+	0.328477i
$366$		0			0
$367$	−6.78525	+	3.91747i	−0.354187	+	0.204490i	−0.666528	−	0.745480i	$-0.732220\pi$
$367$	−6.78525	+	3.91747i	−0.354187	+	0.204490i	0.312341	+	0.949970i	$0.398887\pi$
$368$		−	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	−0.845864	−	0.533398i	$-0.820915\pi$
$383$	0.763322	−	1.32211i	0.0390040	−	0.0675568i	0.884868	+	0.465841i	$0.154248\pi$
$384$		0			0
$385$	3.66388	+	35.0944i	0.186729	+	1.78858i
$386$			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
$392$	−1.44585	−	6.84905i	−0.0730265	−	0.345929i
$393$		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	$0.256955\pi$
$397$			28.7869i			1.44478i	−0.691488	+	0.722388i	$0.743045\pi$
$398$	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	0.343357	−	0.939205i	$-0.388436\pi$
$409$	−6.03355	−	3.48347i	−0.298340	−	0.172247i	−0.641697	+	0.766958i	$0.721769\pi$
$410$	−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	$0.490778\pi$
$419$	−17.4232	+	30.1778i	−0.851177	+	1.47428i	−0.880146	+	0.474702i	$0.842556\pi$
$420$		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
$427$	19.2732	−	13.9823i	0.932696	−	0.676652i
$428$	−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	$0.192011\pi$
$433$			23.6094i			1.13459i	−0.823513	+	0.567297i	$0.807989\pi$
$434$	−22.0257	+	2.29950i	−1.05727	+	0.110380i
$435$		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	−0.918175	−	0.396175i	$-0.870337\pi$
$439$	−21.6681	+	12.5101i	−1.03416	+	0.597075i	−0.115989	+	0.993250i	$0.537004\pi$
$440$	−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
$448$	2.63145	−	0.274725i	0.124324	−	0.0129796i
$449$		−	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
$455$	8.65298	−	6.27756i	0.405658	−	0.294297i
$456$		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	$-0.904982\pi$
$461$	−15.7292	−	27.2438i	−0.732582	−	1.26887i	0.223194	−	0.974774i	$-0.428352\pi$
$462$		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	$-0.747322\pi$
$467$	−30.3032			−1.40226			−0.701132	+	0.713032i	$0.747322\pi$
$468$		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	0.807835	−	0.589409i	$-0.200639\pi$
$479$	−2.33143	−	4.03816i	−0.106526	−	0.184508i	−0.914361	+	0.404901i	$0.867306\pi$
$480$		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
$490$	−3.39682	−	16.0909i	−0.153453	−	0.726912i
$491$	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
$497$	−1.24205	−	11.8969i	−0.0557135	−	0.533651i
$498$		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	$-0.605170\pi$
$503$	−14.5521			−0.648845			−0.324422	+	0.945912i	$0.605170\pi$
$504$		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	$0.431140\pi$
$509$	−16.6617	+	28.8589i	−0.738517	+	1.27915i	−0.953163	+	0.302457i	$0.902193\pi$
$510$		0			0
$511$	−1.46768	−	14.0581i	−0.0649262	−	0.621894i
$512$			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
$518$	19.6973	−	14.2900i	0.865450	−	0.627866i
$519$		0			0
$520$	2.02027	+	3.49921i	0.0885947	+	0.153451i
$521$	−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	$-0.994524\pi$
$523$		−	0.786858i		−	0.0344069i	0.999852	−	0.0172034i	$-0.00547630\pi$
$524$	−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
$553$	−20.2415	−	27.9009i	−0.860758	−	1.18647i
$554$	−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
$560$	6.18222	−	0.645428i	0.261246	−	0.0272743i
$561$		0			0
$562$	−2.43641	+	4.21999i	−0.102774	+	0.178009i
$563$	12.2650	−	21.2436i	0.516909	−	0.895312i	−0.482898	−	0.875676i	$-0.660416\pi$
$563$	12.2650	−	21.2436i	0.516909	−	0.895312i	0.999807	−	0.0196359i	$-0.00625069\pi$
$564$		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
$574$	2.19621	+	21.0363i	0.0916679	+	0.878038i
$575$		−	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	$-0.199415\pi$
$578$	−12.0129	+	6.93562i	−0.499669	+	0.288484i
$579$		0			0
$580$	8.45502	+	4.88151i	0.351076	+	0.202694i
$581$	19.4920	+	26.8677i	0.808663	+	1.11466i
$582$		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	0.950034	−	0.312145i	$-0.101048\pi$
$587$	4.95928	+	8.58973i	0.204692	+	0.354536i	−0.745343	+	0.666681i	$0.767714\pi$
$588$		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	$-0.530757\pi$
$593$	−4.69872			−0.192953			−0.0964766	+	0.995335i	$0.530757\pi$
$594$		0			0
$595$	4.47894	−	10.0411i	0.183619	−	0.411643i
$596$	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	−0.794018	−	0.607894i	$-0.792014\pi$
$601$	−16.2923	+	9.40634i	−0.664575	+	0.383693i	0.129443	+	0.991587i	$0.458681\pi$
$602$	−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	0.262085	−	0.965045i	$-0.415590\pi$
$607$	−10.9051	−	6.29608i	−0.442625	−	0.255550i	−0.704711	+	0.709495i	$0.748923\pi$
$608$	−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
$616$	8.81952	+	12.1568i	0.355349	+	0.489812i
$617$	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	−0.679823	−	0.733376i	$-0.737943\pi$
$619$	−9.56902	+	5.52468i	−0.384611	+	0.222055i	0.295211	+	0.955432i	$0.404610\pi$
$620$		−	19.6646i		−	0.789748i
$621$		0			0
$622$		−	8.23637i		−	0.330248i
$623$	3.05527	−	0.318972i	0.122407	−	0.0127794i
$624$		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
$637$	−11.4445	−	3.73617i	−0.453449	−	0.148032i
$638$			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	0.300629	−	0.953741i	$-0.402803\pi$
$643$	−9.50955	−	5.49034i	−0.375020	−	0.216518i	−0.675649	+	0.737223i	$0.736137\pi$
$644$	−7.87036	+	5.70979i	−0.310136	+	0.224997i
$645$		0			0
$646$	1.00763	+	1.74527i	0.0396447	+	0.0686666i
$647$	32.0126			1.25855			0.629273	−	0.777185i	$-0.283353\pi$
$647$	32.0126			1.25855			0.629273	+	0.777185i	$0.283353\pi$
$648$		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	0.667047	−	0.745016i	$-0.267558\pi$
$661$	9.13646	+	5.27494i	0.355367	+	0.205171i	−0.311679	+	0.950187i	$0.600892\pi$
$662$	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	0.671405	−	0.741090i	$-0.265691\pi$
$677$	−7.96449	−	13.7949i	−0.306100	−	0.530181i	−0.977506	+	0.210909i	$0.932358\pi$
$678$		0			0
$679$	−9.83041	+	7.13176i	−0.377256	+	0.273692i
$680$	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
$686$	−12.4212	+	13.7373i	−0.474243	+	0.524494i
$687$		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	−0.502651	−	0.864490i	$-0.667642\pi$
$691$	−0.139477	+	0.0805273i	−0.00530597	+	0.00306340i	0.497345	+	0.867553i	$0.334308\pi$
$692$	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
$700$	1.36699	−	0.142715i	0.0516674	−	0.00539412i
$701$		−	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
$707$	−10.2899	−	14.1836i	−0.386993	−	0.533430i
$708$		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	$-0.598112\pi$
$719$	−16.2692			−0.606739			−0.303370	+	0.952873i	$0.598112\pi$
$720$		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	−0.831566	−	0.555427i	$-0.812555\pi$
$727$	−20.6626	+	11.9296i	−0.766335	+	0.442444i	0.0652306	+	0.997870i	$0.479222\pi$
$728$	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	0.290756	−	0.956797i	$-0.406093\pi$
$733$	−10.6259	−	6.13486i	−0.392476	−	0.226596i	−0.683233	+	0.730201i	$0.739426\pi$
$734$	−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
$749$	1.29550	+	12.4090i	0.0473367	+	0.453413i
$750$		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	$-0.542323\pi$
$761$	21.8509	−	37.8469i	0.792096	−	1.37195i	0.924667	−	0.380777i	$-0.124343\pi$
$762$		0			0
$763$	−11.1486	+	1.16393i	−0.403608	+	0.0421370i
$764$			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	0.986417	−	0.164262i	$-0.0525242\pi$
$769$	37.0864	+	21.4118i	1.33737	+	0.772131i	0.350953	+	0.936393i	$0.385858\pi$
$770$	20.7202	+	28.5607i	0.746705	+	1.02926i
$771$		0			0
$772$	2.19694	+	3.80521i	0.0790696	+	0.136953i
$773$	−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
$776$	−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	$0.0340020\pi$
$787$	44.4307	+	25.6521i	1.58378	+	0.914398i	0.589484	+	0.807780i	$0.299331\pi$
$788$	−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	−0.881510	−	0.472166i	$-0.843472\pi$
$797$	−0.899094	+	1.55728i	−0.0318476	+	0.0551616i	0.849662	+	0.527327i	$0.176806\pi$
$798$		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
$805$	−18.4903	+	13.4143i	−0.651697	+	0.472793i
$806$	−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	$-0.997883\pi$
$811$		−	0.378710i		−	0.0132983i	0.999978	−	0.00664916i	$-0.00211651\pi$
$812$	−1.14165	−	10.9353i	−0.0400641	−	0.383753i
$813$		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
$826$	0.612544	+	5.86724i	0.0213131	+	0.204147i
$827$		−	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	$-0.733810\pi$
$829$		−	42.7361i		−	1.48429i	0.670242	−	0.742143i	$-0.266190\pi$
$830$	−25.5261	+	14.7375i	−0.886023	+	0.511545i
$831$		0			0
$832$	1.48943	+	0.859925i	0.0516368	+	0.0298125i
$833$	−12.1148	+	2.55746i	−0.419753	+	0.0886109i
$834$		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	0.830894	−	0.556431i	$-0.187830\pi$
$839$	−1.92438	−	3.33313i	−0.0664370	−	0.115072i	−0.897331	+	0.441359i	$0.854496\pi$
$840$		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	0.0242213	−	0.999707i	$-0.492289\pi$
$853$	26.3470	−	15.2114i	0.902103	−	0.520830i	0.877882	+	0.478877i	$0.158956\pi$
$854$	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	$0.0648748\pi$
$857$	19.4657	+	33.7156i	0.664937	+	1.15170i	−0.314366	+	0.949302i	$0.601792\pi$
$858$		0			0
$859$	−11.5922	−	6.69275i	−0.395520	−	0.228354i	0.289029	−	0.957320i	$-0.406668\pi$
$859$	−11.5922	−	6.69275i	−0.395520	−	0.228354i	−0.684549	+	0.728967i	$0.740001\pi$
$860$	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
$868$	−17.9251	+	13.0043i	−0.608417	+	0.441394i
$869$	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
$875$	−27.6995	+	2.89185i	−0.936415	+	0.0977625i
$876$		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	$-0.239511\pi$
$881$	43.3363			1.46004			0.730018	+	0.683427i	$0.239511\pi$
$882$		0			0
$883$	2.17403			0.0731618			0.0365809	−	0.999331i	$-0.488353\pi$
$883$	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	−0.945956	−	0.324294i	$-0.894873\pi$
$887$	−5.72215	+	9.91105i	−0.192131	+	0.332781i	0.753825	+	0.657075i	$0.228207\pi$
$888$		0			0
$889$	17.5693	−	1.83425i	0.589256	−	0.0615188i
$890$			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
$896$	2.14154	−	1.55364i	0.0715438	−	0.0519036i
$897$		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	0.941205	−	0.337837i	$-0.109695\pi$
$929$	5.42618	+	9.39842i	0.178027	+	0.308352i	−0.763177	+	0.646189i	$0.776362\pi$
$930$		0			0
$931$	−1.64729	−	7.80326i	−0.0539877	−	0.255742i
$932$	−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	$-0.997618\pi$
$937$		−	0.458120i		−	0.0149661i	0.999972	−	0.00748306i	$-0.00238195\pi$
$938$	−2.98661	−	28.6071i	−0.0975162	−	0.934056i
$939$		0			0
$940$	13.8728	−	24.0284i	0.452482	−	0.783721i
$941$	−3.68890	+	6.38937i	−0.120255	+	0.208287i	−0.919868	−	0.392228i	$-0.871704\pi$
$941$	−3.68890	+	6.38937i	−0.120255	+	0.208287i	0.799613	+	0.600515i	$0.205038\pi$
$942$		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
$952$	−0.485942	−	4.65458i	−0.0157495	−	0.150856i
$953$		−	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
$959$	17.1064	−	12.4103i	0.552394	−	0.400751i
$960$		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	$-0.532783\pi$
$971$	−6.40724			−0.205618			−0.102809	+	0.994701i	$0.532783\pi$
$972$		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	0.988473	−	0.151398i	$-0.0483774\pi$
$983$	11.3849	+	19.7192i	0.363122	+	0.628946i	−0.625351	+	0.780344i	$0.715044\pi$
$984$		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
$994$	−7.02412	−	9.68203i	−0.222791	−	0.307095i
$995$	56.0869	+	32.3818i	1.77807	+	1.02657i
$996$		0			0
$997$	16.7263	−	9.65694i	0.529728	−	0.305838i	−0.211178	−	0.977448i	$-0.567730\pi$
$997$	16.7263	−	9.65694i	0.529728	−	0.305838i	0.740906	+	0.671609i	$0.234397\pi$
$998$		−	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.125.7		16
3.2	odd	2		126.2.m.a.41.2	✓	16
4.3	odd	2		3024.2.cc.b.881.7		16
7.2	even	3		2646.2.t.a.2285.2		16
7.3	odd	6		2646.2.l.b.1097.6		16
7.4	even	3		2646.2.l.b.1097.7		16
7.5	odd	6		2646.2.t.a.2285.3		16
7.6	odd	2	inner	378.2.m.a.125.6		16
9.2	odd	6	inner	378.2.m.a.251.6		16
9.4	even	3		1134.2.d.a.1133.10		16
9.5	odd	6		1134.2.d.a.1133.7		16
9.7	even	3		126.2.m.a.83.3	yes	16
12.11	even	2		1008.2.cc.b.545.6		16
21.2	odd	6		882.2.t.b.815.8		16
21.5	even	6		882.2.t.b.815.5		16
21.11	odd	6		882.2.l.a.509.2		16
21.17	even	6		882.2.l.a.509.3		16
21.20	even	2		126.2.m.a.41.3	yes	16
28.27	even	2		3024.2.cc.b.881.2		16
36.7	odd	6		1008.2.cc.b.209.3		16
36.11	even	6		3024.2.cc.b.2897.2		16
63.2	odd	6		2646.2.l.b.521.2		16
63.11	odd	6		2646.2.t.a.1979.3		16
63.13	odd	6		1134.2.d.a.1133.15		16
63.16	even	3		882.2.l.a.227.7		16
63.20	even	6	inner	378.2.m.a.251.7		16
63.25	even	3		882.2.t.b.803.5		16
63.34	odd	6		126.2.m.a.83.2	yes	16
63.38	even	6		2646.2.t.a.1979.2		16
63.41	even	6		1134.2.d.a.1133.2		16
63.47	even	6		2646.2.l.b.521.3		16
63.52	odd	6		882.2.t.b.803.8		16
63.61	odd	6		882.2.l.a.227.6		16
84.83	odd	2		1008.2.cc.b.545.3		16
252.83	odd	6		3024.2.cc.b.2897.7		16
252.223	even	6		1008.2.cc.b.209.6		16

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.17468 - 2.03460i) q^{5} +(-2.63145 + 0.274725i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.17468 - 2.03460i) q^{5} +(-2.63145 + 0.274725i) q^{7} -1.00000i q^{8} -2.34936i q^{10} +(4.91614 - 2.83834i) q^{11} +(-1.48943 - 0.859925i) q^{13} +(-2.14154 + 1.55364i) q^{14} +(-0.500000 - 0.866025i) q^{16} -1.76883 q^{17} -1.13932i q^{19} +(-1.17468 - 2.03460i) q^{20} +(2.83834 - 4.91614i) q^{22} +(3.18272 + 1.83755i) q^{23} +(-0.259741 - 0.449885i) q^{25} -1.71985 q^{26} +(-1.07781 + 2.41626i) q^{28} +(-3.59886 + 2.07781i) q^{29} +(7.24879 + 4.18509i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.53185 + 0.884414i) q^{34} +(-2.53215 + 5.67667i) q^{35} -9.19773 q^{37} +(-0.569660 - 0.986680i) q^{38} +(-2.03460 - 1.17468i) q^{40} +(3.99709 - 6.92317i) q^{41} +(1.76053 + 3.04933i) q^{43} -5.67667i q^{44} +3.67509 q^{46} +(5.90494 + 10.2277i) q^{47} +(6.84905 - 1.44585i) q^{49} +(-0.449885 - 0.259741i) q^{50} +(-1.48943 + 0.859925i) q^{52} -13.3365i q^{55} +(0.274725 + 2.63145i) q^{56} +(-2.07781 + 3.59886i) q^{58} +(1.11483 - 1.93094i) q^{59} +(-7.79396 + 4.49985i) q^{61} +8.37019 q^{62} -1.00000 q^{64} +(-3.49921 + 2.02027i) q^{65} +(-5.43562 + 9.41477i) q^{67} +(-0.884414 + 1.53185i) q^{68} +(0.645428 + 6.18222i) q^{70} +4.52106i q^{71} +5.34234i q^{73} +(-7.96547 + 4.59886i) q^{74} +(-0.986680 - 0.569660i) q^{76} +(-12.1568 + 8.81952i) q^{77} +(6.51422 + 11.2830i) q^{79} -2.34936 q^{80} -7.99419i q^{82} +(-6.27298 - 10.8651i) q^{83} +(-2.07781 + 3.59886i) q^{85} +(3.04933 + 1.76053i) q^{86} +(-2.83834 - 4.91614i) q^{88} -1.16106 q^{89} +(4.15561 + 1.85366i) q^{91} +(3.18272 - 1.83755i) q^{92} +(10.2277 + 5.90494i) q^{94} +(-2.31806 - 1.33834i) q^{95} +(3.97536 - 2.29517i) q^{97} +(5.20853 - 4.67667i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{7}+O(q^{10}) \) 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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