LMFDB - Embedded newform 1372.2.e.d.1353.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1372,2,Mod(361,1372)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1372.361"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1372, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1372 = 2^{2} \cdot 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1372.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,7,0,7,0,0,0,-9,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.9554751573$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 10 x^{10} - 7 x^{9} + 68 x^{8} - 44 x^{7} + 225 x^{6} - 77 x^{5} + 490 x^{4} + \cdots + 49 $ x^12 - x^11 + 10x^10 - 7x^9 + 68x^8 - 44x^7 + 225x^6 - 77x^5 + 490x^4 - 182x^3 + 343x^2 + 98x + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1353.4
Root			$-1.15344 + 1.99781i$ of defining polynomial
Character	$\chi$	$=$	1372.1353
Dual form			1372.2.e.d.361.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.02995 + 1.78392i) q^{3} +(1.41759 - 2.45533i) q^{5} +(-0.621582 + 1.07661i) q^{9} +(-3.23925 - 5.61055i) q^{11} -1.96477 q^{13} +5.84016 q^{15} +(-1.39258 - 2.41201i) q^{17} +(0.151939 - 0.263166i) q^{19} +(2.69518 - 4.66819i) q^{23} +(-1.51911 - 2.63118i) q^{25} +3.61890 q^{27} -2.13019 q^{29} +(-3.28970 - 5.69793i) q^{31} +(6.67252 - 11.5571i) q^{33} +(-3.87278 + 6.70785i) q^{37} +(-2.02361 - 3.50499i) q^{39} +6.51081 q^{41} -10.6807 q^{43} +(1.76229 + 3.05238i) q^{45} +(5.48283 - 9.49654i) q^{47} +(2.86856 - 4.96849i) q^{51} +(4.43366 + 7.67932i) q^{53} -18.3677 q^{55} +0.625956 q^{57} +(5.91250 + 10.2408i) q^{59} +(4.80658 - 8.32525i) q^{61} +(-2.78524 + 4.82417i) q^{65} +(1.02193 + 1.77003i) q^{67} +11.1036 q^{69} -5.91185 q^{71} +(1.56711 + 2.71431i) q^{73} +(3.12921 - 5.41995i) q^{75} +(-1.40716 + 2.43728i) q^{79} +(5.59202 + 9.68566i) q^{81} -0.482973 q^{83} -7.89640 q^{85} +(-2.19398 - 3.80009i) q^{87} +(-7.00477 + 12.1326i) q^{89} +(6.77644 - 11.7371i) q^{93} +(-0.430773 - 0.746121i) q^{95} +5.17392 q^{97} +8.05385 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 7 q^{3} + 7 q^{5} - 9 q^{9} - 3 q^{11} - 14 q^{13} + 22 q^{15} + 7 q^{19} - 11 q^{23} - 3 q^{25} - 56 q^{27} + 12 q^{29} + 14 q^{31} + 6 q^{37} - 5 q^{39} - 6 q^{43} + 21 q^{45} + 42 q^{47} + 17 q^{51}+ \cdots - 68 q^{99}+O(q^{100}) $ 12 * q + 7 * q^3 + 7 * q^5 - 9 * q^9 - 3 * q^11 - 14 * q^13 + 22 * q^15 + 7 * q^19 - 11 * q^23 - 3 * q^25 - 56 * q^27 + 12 * q^29 + 14 * q^31 + 6 * q^37 - 5 * q^39 - 6 * q^43 + 21 * q^45 + 42 * q^47 + 17 * q^51 + 17 * q^53 - 28 * q^55 - 12 * q^57 + 35 * q^59 + 7 * q^61 + 6 * q^65 + 14 * q^67 - 28 * q^69 - 56 * q^71 + 35 * q^75 - 6 * q^79 - 34 * q^81 - 98 * q^83 - 46 * q^85 + 21 * q^87 - 7 * q^89 + 14 * q^93 + 25 * q^95 + 42 * q^97 - 68 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1372\mathbb{Z}\right)^\times$.

$n$	$687$	$689$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.02995	+	1.78392i	0.594640	+	1.02995i	0.993598	+	0.112978i	$0.0360388\pi$
$3$	1.02995	+	1.78392i	0.594640	+	1.02995i	−0.398957	+	0.916969i	$0.630628\pi$
$4$		0			0
$5$	1.41759	−	2.45533i	0.633965	−	1.09806i	−0.352769	−	0.935711i	$-0.614760\pi$
$5$	1.41759	−	2.45533i	0.633965	−	1.09806i	0.986733	−	0.162349i	$-0.0519069\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.621582	+	1.07661i	−0.207194	+	0.358870i
$10$		0			0
$11$	−3.23925	−	5.61055i	−0.976672	−	1.69165i	−0.674303	−	0.738454i	$-0.735556\pi$
$11$	−3.23925	−	5.61055i	−0.976672	−	1.69165i	−0.302369	−	0.953191i	$-0.597777\pi$
$12$		0			0
$13$	−1.96477			−0.544929			−0.272465	−	0.962166i	$-0.587839\pi$
$13$	−1.96477			−0.544929			−0.272465	+	0.962166i	$0.587839\pi$
$14$		0			0
$15$	5.84016			1.50792
$16$		0			0
$17$	−1.39258	−	2.41201i	−0.337750	−	0.584999i	0.646260	−	0.763118i	$-0.276332\pi$
$17$	−1.39258	−	2.41201i	−0.337750	−	0.584999i	−0.984009	+	0.178118i	$0.942999\pi$
$18$		0			0
$19$	0.151939	−	0.263166i	0.0348572	−	0.0603744i	−0.848071	−	0.529883i	$-0.822236\pi$
$19$	0.151939	−	0.263166i	0.0348572	−	0.0603744i	0.882928	+	0.469509i	$0.155569\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.69518	−	4.66819i	0.561984	−	0.973385i	−0.435339	−	0.900267i	$-0.643371\pi$
$23$	2.69518	−	4.66819i	0.561984	−	0.973385i	0.997323	−	0.0731186i	$-0.0232952\pi$
$24$		0			0
$25$	−1.51911	−	2.63118i	−0.303823	−	0.526236i
$26$		0			0
$27$	3.61890			0.696457
$28$		0			0
$29$	−2.13019			−0.395566			−0.197783	−	0.980246i	$-0.563374\pi$
$29$	−2.13019			−0.395566			−0.197783	+	0.980246i	$0.563374\pi$
$30$		0			0
$31$	−3.28970	−	5.69793i	−0.590848	−	1.02338i	−0.994118	−	0.108298i	$-0.965460\pi$
$31$	−3.28970	−	5.69793i	−0.590848	−	1.02338i	0.403271	−	0.915081i	$-0.367873\pi$
$32$		0			0
$33$	6.67252	−	11.5571i	1.16154	−	2.01184i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.87278	+	6.70785i	−0.636681	+	1.10276i	0.349475	+	0.936946i	$0.386360\pi$
$37$	−3.87278	+	6.70785i	−0.636681	+	1.10276i	−0.986156	+	0.165818i	$0.946973\pi$
$38$		0			0
$39$	−2.02361	−	3.50499i	−0.324037	−	0.561248i
$40$		0			0
$41$	6.51081			1.01682			0.508409	−	0.861116i	$-0.330234\pi$
$41$	6.51081			1.01682			0.508409	+	0.861116i	$0.330234\pi$
$42$		0			0
$43$	−10.6807			−1.62880			−0.814399	−	0.580305i	$-0.802933\pi$
$43$	−10.6807			−1.62880			−0.814399	+	0.580305i	$0.802933\pi$
$44$		0			0
$45$	1.76229	+	3.05238i	0.262707	+	0.455022i
$46$		0			0
$47$	5.48283	−	9.49654i	0.799753	−	1.38521i	−0.120024	−	0.992771i	$-0.538297\pi$
$47$	5.48283	−	9.49654i	0.799753	−	1.38521i	0.919777	−	0.392441i	$-0.128369\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	2.86856	−	4.96849i	0.401679	−	0.695728i
$52$		0			0
$53$	4.43366	+	7.67932i	0.609009	+	1.05484i	0.991404	+	0.130836i	$0.0417662\pi$
$53$	4.43366	+	7.67932i	0.609009	+	1.05484i	−0.382395	+	0.923999i	$0.624901\pi$
$54$		0			0
$55$	−18.3677			−2.47670
$56$		0			0
$57$	0.625956			0.0829099
$58$		0			0
$59$	5.91250	+	10.2408i	0.769742	+	1.33323i	0.937703	+	0.347439i	$0.112949\pi$
$59$	5.91250	+	10.2408i	0.769742	+	1.33323i	−0.167960	+	0.985794i	$0.553718\pi$
$60$		0			0
$61$	4.80658	−	8.32525i	0.615420	−	1.06594i	−0.374891	−	0.927069i	$-0.622320\pi$
$61$	4.80658	−	8.32525i	0.615420	−	1.06594i	0.990311	−	0.138870i	$-0.0443470\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.78524	+	4.82417i	−0.345466	+	0.598365i
$66$		0			0
$67$	1.02193	+	1.77003i	0.124848	+	0.216243i	0.921674	−	0.387966i	$-0.126822\pi$
$67$	1.02193	+	1.77003i	0.124848	+	0.216243i	−0.796825	+	0.604210i	$0.793489\pi$
$68$		0			0
$69$	11.1036			1.33671
$70$		0			0
$71$	−5.91185			−0.701608			−0.350804	−	0.936449i	$-0.614092\pi$
$71$	−5.91185			−0.701608			−0.350804	+	0.936449i	$0.614092\pi$
$72$		0			0
$73$	1.56711	+	2.71431i	0.183416	+	0.317686i	0.943042	−	0.332675i	$-0.107951\pi$
$73$	1.56711	+	2.71431i	0.183416	+	0.317686i	−0.759626	+	0.650361i	$0.774618\pi$
$74$		0			0
$75$	3.12921	−	5.41995i	0.361330	−	0.625842i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−1.40716	+	2.43728i	−0.158318	+	0.274215i	−0.934262	−	0.356586i	$-0.883941\pi$
$79$	−1.40716	+	2.43728i	−0.158318	+	0.274215i	0.775944	+	0.630802i	$0.217274\pi$
$80$		0			0
$81$	5.59202	+	9.68566i	0.621335	+	1.07618i
$82$		0			0
$83$	−0.482973			−0.0530131			−0.0265066	−	0.999649i	$-0.508438\pi$
$83$	−0.482973			−0.0530131			−0.0265066	+	0.999649i	$0.508438\pi$
$84$		0			0
$85$	−7.89640			−0.856485
$86$		0			0
$87$	−2.19398	−	3.80009i	−0.235219	−	0.407412i
$88$		0			0
$89$	−7.00477	+	12.1326i	−0.742504	+	1.28606i	0.208847	+	0.977948i	$0.433029\pi$
$89$	−7.00477	+	12.1326i	−0.742504	+	1.28606i	−0.951352	+	0.308107i	$0.900304\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	6.77644	−	11.7371i	0.702684	−	1.21708i
$94$		0			0
$95$	−0.430773	−	0.746121i	−0.0441964	−	0.0765504i
$96$		0			0
$97$	5.17392			0.525332			0.262666	−	0.964887i	$-0.415398\pi$
$97$	5.17392			0.525332			0.262666	+	0.964887i	$0.415398\pi$
$98$		0			0
$99$	8.05385			0.809442
$100$		0			0
$101$	−0.397737	−	0.688900i	−0.0395763	−	0.0685481i	0.845559	−	0.533882i	$-0.179267\pi$
$101$	−0.397737	−	0.688900i	−0.0395763	−	0.0685481i	−0.885135	+	0.465334i	$0.845934\pi$
$102$		0			0
$103$	8.05028	−	13.9435i	0.793218	−	1.37389i	−0.130747	−	0.991416i	$-0.541737\pi$
$103$	8.05028	−	13.9435i	0.793218	−	1.37389i	0.923965	−	0.382478i	$-0.124929\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.07751	−	7.06245i	0.394188	−	0.682753i	−0.598809	−	0.800892i	$-0.704359\pi$
$107$	4.07751	−	7.06245i	0.394188	−	0.682753i	0.992997	+	0.118138i	$0.0376927\pi$
$108$		0			0
$109$	6.98060	+	12.0907i	0.668620	+	1.15808i	0.978290	+	0.207240i	$0.0664480\pi$
$109$	6.98060	+	12.0907i	0.668620	+	1.15808i	−0.309670	+	0.950844i	$0.600219\pi$
$110$		0			0
$111$	−15.9550			−1.51438
$112$		0			0
$113$	5.53024			0.520241			0.260120	−	0.965576i	$-0.416238\pi$
$113$	5.53024			0.520241			0.260120	+	0.965576i	$0.416238\pi$
$114$		0			0
$115$	−7.64132	−	13.2351i	−0.712556	−	1.23418i
$116$		0			0
$117$	1.22127	−	2.11529i	0.112906	−	0.195559i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−15.4855	+	26.8217i	−1.40778	+	2.43834i
$122$		0			0
$123$	6.70579	+	11.6148i	0.604641	+	1.04727i
$124$		0			0
$125$	5.56198			0.497478
$126$		0			0
$127$	16.6326			1.47590			0.737952	−	0.674854i	$-0.235793\pi$
$127$	16.6326			1.47590			0.737952	+	0.674854i	$0.235793\pi$
$128$		0			0
$129$	−11.0006	−	19.0536i	−0.968549	−	1.67758i
$130$		0			0
$131$	8.75856	−	15.1703i	0.765239	−	1.32543i	−0.174881	−	0.984590i	$-0.555954\pi$
$131$	8.75856	−	15.1703i	0.765239	−	1.32543i	0.940120	−	0.340844i	$-0.110713\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	5.13011	−	8.88560i	0.441529	−	0.764751i
$136$		0			0
$137$	0.278941	+	0.483140i	0.0238315	+	0.0412774i	0.877695	−	0.479219i	$-0.159080\pi$
$137$	0.278941	+	0.483140i	0.0238315	+	0.0412774i	−0.853864	+	0.520497i	$0.825747\pi$
$138$		0			0
$139$	8.92595			0.757090			0.378545	−	0.925583i	$-0.376425\pi$
$139$	8.92595			0.757090			0.378545	+	0.925583i	$0.376425\pi$
$140$		0			0
$141$	22.5881			1.90226
$142$		0			0
$143$	6.36439	+	11.0234i	0.532217	+	0.921827i
$144$		0			0
$145$	−3.01973	+	5.23032i	−0.250775	+	0.434355i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	7.09490	−	12.2887i	0.581237	−	1.00673i	−0.414096	−	0.910233i	$-0.635902\pi$
$149$	7.09490	−	12.2887i	0.581237	−	1.00673i	0.995333	−	0.0964985i	$-0.0307643\pi$
$150$		0			0
$151$	3.43906	+	5.95662i	0.279866	+	0.484743i	0.971351	−	0.237648i	$-0.0763765\pi$
$151$	3.43906	+	5.95662i	0.279866	+	0.484743i	−0.691485	+	0.722391i	$0.743043\pi$
$152$		0			0
$153$	3.46240			0.279919
$154$		0			0
$155$	−18.6538			−1.49831
$156$		0			0
$157$	10.6540	+	18.4533i	0.850281	+	1.47273i	0.880954	+	0.473201i	$0.156902\pi$
$157$	10.6540	+	18.4533i	0.850281	+	1.47273i	−0.0306731	+	0.999529i	$0.509765\pi$
$158$		0			0
$159$	−9.13286	+	15.8186i	−0.724283	+	1.25449i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	1.45931	−	2.52760i	0.114302	−	0.197977i	−0.803198	−	0.595711i	$-0.796870\pi$
$163$	1.45931	−	2.52760i	0.114302	−	0.197977i	0.917501	+	0.397735i	$0.130204\pi$
$164$		0			0
$165$	−18.9178	−	32.7665i	−1.47275	−	2.55087i
$166$		0			0
$167$	−9.59517			−0.742497			−0.371248	−	0.928534i	$-0.621070\pi$
$167$	−9.59517			−0.742497			−0.371248	+	0.928534i	$0.621070\pi$
$168$		0			0
$169$	−9.13968			−0.703052
$170$		0			0
$171$	0.188885	+	0.327158i	0.0144444	+	0.0250184i
$172$		0			0
$173$	0.553059	−	0.957926i	0.0420483	−	0.0728298i	−0.844235	−	0.535973i	$-0.819945\pi$
$173$	0.553059	−	0.957926i	0.0420483	−	0.0728298i	0.886284	+	0.463143i	$0.153278\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−12.1791	+	21.0949i	−0.915439	+	1.58559i
$178$		0			0
$179$	2.14925	+	3.72262i	0.160643	+	0.278242i	0.935099	−	0.354386i	$-0.115310\pi$
$179$	2.14925	+	3.72262i	0.160643	+	0.278242i	−0.774457	+	0.632627i	$0.781977\pi$
$180$		0			0
$181$	16.0928			1.19617			0.598086	−	0.801432i	$-0.295928\pi$
$181$	16.0928			1.19617			0.598086	+	0.801432i	$0.295928\pi$
$182$		0			0
$183$	19.8021			1.46381
$184$		0			0
$185$	10.9800	+	19.0179i	0.807267	+	1.39823i
$186$		0			0
$187$	−9.02182	+	15.6263i	−0.659741	+	1.14271i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.18116	+	3.77788i	−0.157823	+	0.273358i	−0.934083	−	0.357055i	$-0.883781\pi$
$191$	−2.18116	+	3.77788i	−0.157823	+	0.273358i	0.776260	+	0.630413i	$0.217114\pi$
$192$		0			0
$193$	−10.3793	−	17.9775i	−0.747119	−	1.29405i	−0.949198	−	0.314679i	$-0.898103\pi$
$193$	−10.3793	−	17.9775i	−0.747119	−	1.29405i	0.202079	−	0.979369i	$-0.435230\pi$
$194$		0			0
$195$	−11.4746			−0.821712
$196$		0			0
$197$	−5.03072			−0.358424			−0.179212	−	0.983811i	$-0.557355\pi$
$197$	−5.03072			−0.358424			−0.179212	+	0.983811i	$0.557355\pi$
$198$		0			0
$199$	−1.36569	−	2.36545i	−0.0968115	−	0.167682i	0.813552	−	0.581493i	$-0.197531\pi$
$199$	−1.36569	−	2.36545i	−0.0968115	−	0.167682i	−0.910363	+	0.413810i	$0.864198\pi$
$200$		0			0
$201$	−2.10506	+	3.64607i	−0.148479	+	0.257174i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	9.22965	−	15.9862i	0.644626	−	1.11653i
$206$		0			0
$207$	3.35055	+	5.80333i	0.232879	+	0.403359i
$208$		0			0
$209$	−1.96867			−0.136176
$210$		0			0
$211$	−4.23961			−0.291867			−0.145933	−	0.989294i	$-0.546619\pi$
$211$	−4.23961			−0.291867			−0.145933	+	0.989294i	$0.546619\pi$
$212$		0			0
$213$	−6.08890	−	10.5463i	−0.417204	−	0.722619i
$214$		0			0
$215$	−15.1409	+	26.2248i	−1.03260	+	1.78852i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−3.22808	+	5.59119i	−0.218133	+	0.377818i
$220$		0			0
$221$	2.73609	+	4.73905i	0.184050	+	0.318783i
$222$		0			0
$223$	0.0535924			0.00358881			0.00179441	−	0.999998i	$-0.499429\pi$
$223$	0.0535924			0.00358881			0.00179441	+	0.999998i	$0.499429\pi$
$224$		0			0
$225$	3.77701			0.251801
$226$		0			0
$227$	7.21238	+	12.4922i	0.478702	+	0.829136i	0.999702	−	0.0244204i	$-0.00777404\pi$
$227$	7.21238	+	12.4922i	0.478702	+	0.829136i	−0.521000	+	0.853557i	$0.674441\pi$
$228$		0			0
$229$	−7.13610	+	12.3601i	−0.471567	+	0.816778i	−0.999471	−	0.0325264i	$-0.989645\pi$
$229$	−7.13610	+	12.3601i	−0.471567	+	0.816778i	0.527904	+	0.849304i	$0.322978\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.48877	−	14.7030i	0.556118	−	0.963224i	−0.441698	−	0.897164i	$-0.645624\pi$
$233$	8.48877	−	14.7030i	0.556118	−	0.963224i	0.997816	−	0.0660604i	$-0.0210430\pi$
$234$		0			0
$235$	−15.5448	−	26.9244i	−1.01403	−	1.75635i
$236$		0			0
$237$	−5.79722			−0.376570
$238$		0			0
$239$	−13.7721			−0.890846			−0.445423	−	0.895320i	$-0.646947\pi$
$239$	−13.7721			−0.890846			−0.445423	+	0.895320i	$0.646947\pi$
$240$		0			0
$241$	−12.2391	−	21.1987i	−0.788388	−	1.36553i	−0.926954	−	0.375176i	$-0.877582\pi$
$241$	−12.2391	−	21.1987i	−0.788388	−	1.36553i	0.138565	−	0.990353i	$-0.455751\pi$
$242$		0			0
$243$	−6.09062	+	10.5493i	−0.390713	+	0.676735i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.298525	+	0.517060i	−0.0189947	+	0.0328998i
$248$		0			0
$249$	−0.497436	−	0.861585i	−0.0315237	−	0.0546007i
$250$		0			0
$251$	−26.4105			−1.66702			−0.833509	−	0.552505i	$-0.813672\pi$
$251$	−26.4105			−1.66702			−0.833509	+	0.552505i	$0.813672\pi$
$252$		0			0
$253$	−34.9215			−2.19550
$254$		0			0
$255$	−8.13288	−	14.0866i	−0.509301	−	0.882134i
$256$		0			0
$257$	4.98567	−	8.63544i	0.310998	−	0.538664i	−0.667581	−	0.744537i	$-0.732670\pi$
$257$	4.98567	−	8.63544i	0.310998	−	0.538664i	0.978579	+	0.205873i	$0.0660035\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	1.32409	−	2.29338i	0.0819589	−	0.141957i
$262$		0			0
$263$	−7.37665	−	12.7767i	−0.454864	−	0.787847i	0.543817	−	0.839204i	$-0.316979\pi$
$263$	−7.37665	−	12.7767i	−0.454864	−	0.787847i	−0.998680	+	0.0513569i	$0.983645\pi$
$264$		0			0
$265$	25.1404			1.54436
$266$		0			0
$267$	−28.8582			−1.76609
$268$		0			0
$269$	10.2899	+	17.8226i	0.627384	+	1.08666i	0.988075	+	0.153976i	$0.0492078\pi$
$269$	10.2899	+	17.8226i	0.627384	+	1.08666i	−0.360690	+	0.932686i	$0.617459\pi$
$270$		0			0
$271$	−3.93814	+	6.82105i	−0.239225	+	0.414350i	−0.960492	−	0.278307i	$-0.910227\pi$
$271$	−3.93814	+	6.82105i	−0.239225	+	0.414350i	0.721267	+	0.692657i	$0.243560\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−9.84159	+	17.0461i	−0.593470	+	1.02792i
$276$		0			0
$277$	−1.01357	−	1.75556i	−0.0608998	−	0.105482i	0.833968	−	0.551813i	$-0.186064\pi$
$277$	−1.01357	−	1.75556i	−0.0608998	−	0.105482i	−0.894868	+	0.446331i	$0.852730\pi$
$278$		0			0
$279$	8.17928			0.489680
$280$		0			0
$281$	−9.12693			−0.544467			−0.272233	−	0.962231i	$-0.587762\pi$
$281$	−9.12693			−0.544467			−0.272233	+	0.962231i	$0.587762\pi$
$282$		0			0
$283$	−15.3211	−	26.5370i	−0.910746	−	1.57746i	−0.813013	−	0.582246i	$-0.802174\pi$
$283$	−15.3211	−	26.5370i	−0.910746	−	1.57746i	−0.0977331	−	0.995213i	$-0.531159\pi$
$284$		0			0
$285$	0.887348	−	1.53693i	0.0525619	−	0.0910399i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	4.62146	−	8.00460i	0.271850	−	0.470859i
$290$		0			0
$291$	5.32886	+	9.22986i	0.312383	+	0.541064i
$292$		0			0
$293$	−2.54763			−0.148834			−0.0744170	−	0.997227i	$-0.523710\pi$
$293$	−2.54763			−0.148834			−0.0744170	+	0.997227i	$0.523710\pi$
$294$		0			0
$295$	33.5260			1.95196
$296$		0			0
$297$	−11.7225	−	20.3040i	−0.680210	−	1.17816i
$298$		0			0
$299$	−5.29541	+	9.17192i	−0.306242	+	0.530426i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	0.819296	−	1.41906i	0.0470673	−	0.0815230i
$304$		0			0
$305$	−13.6275	−	23.6036i	−0.780309	−	1.35154i
$306$		0			0
$307$	−3.66780			−0.209332			−0.104666	−	0.994507i	$-0.533377\pi$
$307$	−3.66780			−0.209332			−0.104666	+	0.994507i	$0.533377\pi$
$308$		0			0
$309$	33.1655			1.88672
$310$		0			0
$311$	14.6672	+	25.4043i	0.831699	+	1.44054i	0.896690	+	0.442659i	$0.145965\pi$
$311$	14.6672	+	25.4043i	0.831699	+	1.44054i	−0.0649916	+	0.997886i	$0.520702\pi$
$312$		0			0
$313$	−5.55183	+	9.61605i	−0.313808	+	0.543531i	−0.979183	−	0.202977i	$-0.934938\pi$
$313$	−5.55183	+	9.61605i	−0.313808	+	0.543531i	0.665375	+	0.746509i	$0.268272\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.11524	+	10.5919i	−0.343466	+	0.594900i	−0.985074	−	0.172132i	$-0.944934\pi$
$317$	−6.11524	+	10.5919i	−0.343466	+	0.594900i	0.641608	+	0.767033i	$0.278268\pi$
$318$		0			0
$319$	6.90022	+	11.9515i	0.386338	+	0.669157i
$320$		0			0
$321$	16.7985			0.937599
$322$		0			0
$323$	−0.846346			−0.0470920
$324$		0			0
$325$	2.98471	+	5.16967i	0.165562	+	0.286761i
$326$		0			0
$327$	−14.3793	+	24.9057i	−0.795177	+	1.37729i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−13.4277	+	23.2574i	−0.738052	+	1.27834i	0.215320	+	0.976544i	$0.430921\pi$
$331$	−13.4277	+	23.2574i	−0.738052	+	1.27834i	−0.953371	+	0.301799i	$0.902413\pi$
$332$		0			0
$333$	−4.81450	−	8.33896i	−0.263833	−	0.456972i
$334$		0			0
$335$	5.79468			0.316597
$336$		0			0
$337$	−23.9447			−1.30435			−0.652177	−	0.758067i	$-0.726144\pi$
$337$	−23.9447			−1.30435			−0.652177	+	0.758067i	$0.726144\pi$
$338$		0			0
$339$	5.69585	+	9.86550i	0.309356	+	0.535821i
$340$		0			0
$341$	−21.3124	+	36.9141i	−1.15413	+	1.99901i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	15.7403	−	27.2630i	0.847429	−	1.46779i
$346$		0			0
$347$	16.2626	+	28.1677i	0.873022	+	1.51212i	0.858855	+	0.512219i	$0.171176\pi$
$347$	16.2626	+	28.1677i	0.873022	+	1.51212i	0.0141675	+	0.999900i	$0.495490\pi$
$348$		0			0
$349$	29.3997			1.57373			0.786864	−	0.617126i	$-0.211703\pi$
$349$	29.3997			1.57373			0.786864	+	0.617126i	$0.211703\pi$
$350$		0			0
$351$	−7.11030			−0.379520
$352$		0			0
$353$	−3.32940	−	5.76669i	−0.177206	−	0.306930i	0.763716	−	0.645552i	$-0.223373\pi$
$353$	−3.32940	−	5.76669i	−0.177206	−	0.306930i	−0.940923	+	0.338622i	$0.890039\pi$
$354$		0			0
$355$	−8.38057	+	14.5156i	−0.444795	+	0.770407i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−9.52828	+	16.5035i	−0.502883	+	0.871019i	0.497111	+	0.867687i	$0.334394\pi$
$359$	−9.52828	+	16.5035i	−0.502883	+	0.871019i	−0.999994	+	0.00333235i	$0.998939\pi$
$360$		0			0
$361$	9.45383	+	16.3745i	0.497570	+	0.861816i
$362$		0			0
$363$	−63.7971			−3.34848
$364$		0			0
$365$	8.88606			0.465117
$366$		0			0
$367$	8.17563	+	14.1606i	0.426765	+	0.739178i	0.996583	−	0.0825925i	$-0.0263200\pi$
$367$	8.17563	+	14.1606i	0.426765	+	0.739178i	−0.569819	+	0.821770i	$0.692987\pi$
$368$		0			0
$369$	−4.04700	+	7.00961i	−0.210678	+	0.364906i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	14.9845	−	25.9540i	0.775870	−	1.34385i	−0.158434	−	0.987370i	$-0.550645\pi$
$373$	14.9845	−	25.9540i	0.775870	−	1.34385i	0.934304	−	0.356477i	$-0.116022\pi$
$374$		0			0
$375$	5.72854	+	9.92212i	0.295821	+	0.512376i
$376$		0			0
$377$	4.18533			0.215555
$378$		0			0
$379$	−12.4996			−0.642062			−0.321031	−	0.947069i	$-0.604029\pi$
$379$	−12.4996			−0.642062			−0.321031	+	0.947069i	$0.604029\pi$
$380$		0			0
$381$	17.1307	+	29.6712i	0.877631	+	1.52010i
$382$		0			0
$383$	11.1435	−	19.3011i	0.569405	−	0.986238i	−0.427220	−	0.904148i	$-0.640507\pi$
$383$	11.1435	−	19.3011i	0.569405	−	0.986238i	0.996625	−	0.0820906i	$-0.0261597\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	6.63896	−	11.4990i	0.337477	−	0.584528i
$388$		0			0
$389$	0.289492	+	0.501416i	0.0146779	+	0.0254228i	0.873271	−	0.487235i	$-0.161994\pi$
$389$	0.289492	+	0.501416i	0.0146779	+	0.0254228i	−0.858593	+	0.512658i	$0.828661\pi$
$390$		0			0
$391$	−15.0130			−0.759240
$392$		0			0
$393$	36.0834			1.82017
$394$		0			0
$395$	3.98956	+	6.91012i	0.200736	+	0.347686i
$396$		0			0
$397$	−0.551375	+	0.955009i	−0.0276727	+	0.0479305i	−0.879530	−	0.475843i	$-0.842143\pi$
$397$	−0.551375	+	0.955009i	−0.0276727	+	0.0479305i	0.851857	+	0.523774i	$0.175476\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−4.70956	+	8.15720i	−0.235184	+	0.407351i	−0.959326	−	0.282300i	$-0.908903\pi$
$401$	−4.70956	+	8.15720i	−0.235184	+	0.407351i	0.724142	+	0.689651i	$0.242236\pi$
$402$		0			0
$403$	6.46351	+	11.1951i	0.321970	+	0.557669i
$404$		0			0
$405$	31.7087			1.57562
$406$		0			0
$407$	50.1797			2.48731
$408$		0			0
$409$	−6.97808	−	12.0864i	−0.345044	−	0.597633i	0.640318	−	0.768110i	$-0.278803\pi$
$409$	−6.97808	−	12.0864i	−0.345044	−	0.597633i	−0.985362	+	0.170477i	$0.945469\pi$
$410$		0			0
$411$	−0.574589	+	0.995217i	−0.0283424	+	0.0490904i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−0.684656	+	1.18586i	−0.0336085	+	0.0582116i
$416$		0			0
$417$	9.19326	+	15.9232i	0.450196	+	0.779762i
$418$		0			0
$419$	8.82670			0.431212			0.215606	−	0.976480i	$-0.430827\pi$
$419$	8.82670			0.431212			0.215606	+	0.976480i	$0.430827\pi$
$420$		0			0
$421$	15.4458			0.752783			0.376392	−	0.926461i	$-0.377165\pi$
$421$	15.4458			0.752783			0.376392	+	0.926461i	$0.377165\pi$
$422$		0			0
$423$	6.81605	+	11.8058i	0.331408	+	0.574015i
$424$		0			0
$425$	−4.23096	+	7.32824i	−0.205232	+	0.355472i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−13.1100	+	22.7071i	−0.632955	+	1.09631i
$430$		0			0
$431$	−5.50396	−	9.53315i	−0.265117	−	0.459195i	0.702478	−	0.711706i	$-0.252077\pi$
$431$	−5.50396	−	9.53315i	−0.265117	−	0.459195i	−0.967594	+	0.252510i	$0.918744\pi$
$432$		0			0
$433$	−32.2767			−1.55112			−0.775559	−	0.631274i	$-0.782532\pi$
$433$	−32.2767			−1.55112			−0.775559	+	0.631274i	$0.782532\pi$
$434$		0			0
$435$	−12.4406			−0.596483
$436$		0			0
$437$	−0.819006	−	1.41856i	−0.0391783	−	0.0678589i
$438$		0			0
$439$	14.6753	−	25.4184i	0.700415	−	1.21315i	−0.267906	−	0.963445i	$-0.586332\pi$
$439$	14.6753	−	25.4184i	0.700415	−	1.21315i	0.968321	−	0.249710i	$-0.0803351\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	12.1070	−	20.9699i	0.575221	−	0.996311i	−0.420797	−	0.907155i	$-0.638250\pi$
$443$	12.1070	−	20.9699i	0.575221	−	0.996311i	0.996018	−	0.0891564i	$-0.0284171\pi$
$444$		0			0
$445$	19.8598	+	34.3981i	0.941443	+	1.63063i
$446$		0			0
$447$	29.2295			1.38251
$448$		0			0
$449$	10.1820			0.480517			0.240259	−	0.970709i	$-0.422768\pi$
$449$	10.1820			0.480517			0.240259	+	0.970709i	$0.422768\pi$
$450$		0			0
$451$	−21.0902	−	36.5292i	−0.993097	−	1.72009i
$452$		0			0
$453$	−7.08409	+	12.2700i	−0.332840	+	0.576495i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	6.63503	−	11.4922i	0.310373	−	0.537583i	−0.668070	−	0.744099i	$-0.732879\pi$
$457$	6.63503	−	11.4922i	0.310373	−	0.537583i	0.978443	+	0.206516i	$0.0662126\pi$
$458$		0			0
$459$	−5.03959	−	8.72883i	−0.235228	−	0.407427i
$460$		0			0
$461$	−0.360129			−0.0167729			−0.00838643	−	0.999965i	$-0.502670\pi$
$461$	−0.360129			−0.0167729			−0.00838643	+	0.999965i	$0.502670\pi$
$462$		0			0
$463$	−4.44765			−0.206700			−0.103350	−	0.994645i	$-0.532956\pi$
$463$	−4.44765			−0.206700			−0.103350	+	0.994645i	$0.532956\pi$
$464$		0			0
$465$	−19.2124	−	33.2768i	−0.890954	−	1.54318i
$466$		0			0
$467$	8.52427	−	14.7645i	0.394456	−	0.683218i	−0.598576	−	0.801066i	$-0.704266\pi$
$467$	8.52427	−	14.7645i	0.394456	−	0.683218i	0.993032	+	0.117849i	$0.0375997\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−21.9461	+	38.0118i	−1.01122	+	1.75149i
$472$		0			0
$473$	34.5977	+	59.9249i	1.59080	+	2.75535i
$474$		0			0
$475$	−0.923249			−0.0423616
$476$		0			0
$477$	−11.0235			−0.504732
$478$		0			0
$479$	−2.55713	−	4.42908i	−0.116838	−	0.202370i	0.801675	−	0.597760i	$-0.203943\pi$
$479$	−2.55713	−	4.42908i	−0.116838	−	0.202370i	−0.918513	+	0.395390i	$0.870609\pi$
$480$		0			0
$481$	7.60912	−	13.1794i	0.346946	−	0.600928i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	7.33449	−	12.7037i	0.333042	−	0.576845i
$486$		0			0
$487$	−10.4819	−	18.1552i	−0.474982	−	0.822693i	0.524608	−	0.851344i	$-0.324212\pi$
$487$	−10.4819	−	18.1552i	−0.474982	−	0.822693i	−0.999589	+	0.0286516i	$0.990879\pi$
$488$		0			0
$489$	6.01205			0.271874
$490$		0			0
$491$	−25.0780			−1.13175			−0.565877	−	0.824489i	$-0.691462\pi$
$491$	−25.0780			−1.13175			−0.565877	+	0.824489i	$0.691462\pi$
$492$		0			0
$493$	2.96645	+	5.13804i	0.133602	+	0.231406i
$494$		0			0
$495$	11.4170	−	19.7749i	0.513158	−	0.888815i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	9.40055	−	16.2822i	0.420827	−	0.728893i	−0.575194	−	0.818017i	$-0.695073\pi$
$499$	9.40055	−	16.2822i	0.420827	−	0.728893i	0.996021	+	0.0891241i	$0.0284068\pi$
$500$		0			0
$501$	−9.88252	−	17.1170i	−0.441519	−	0.764732i
$502$		0			0
$503$	7.64963			0.341080			0.170540	−	0.985351i	$-0.445449\pi$
$503$	7.64963			0.341080			0.170540	+	0.985351i	$0.445449\pi$
$504$		0			0
$505$	−2.25531			−0.100360
$506$		0			0
$507$	−9.41338	−	16.3045i	−0.418063	−	0.724106i
$508$		0			0
$509$	10.9032	−	18.8849i	0.483276	−	0.837058i	−0.516540	−	0.856263i	$-0.672780\pi$
$509$	10.9032	−	18.8849i	0.483276	−	0.837058i	0.999816	+	0.0192050i	$0.00611353\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	0.549851	−	0.952370i	0.0242765	−	0.0420482i
$514$		0			0
$515$	−22.8240	−	39.5323i	−1.00574	−	1.74200i
$516$		0			0
$517$	−71.0411			−3.12438
$518$		0			0
$519$	2.27849			0.100014
$520$		0			0
$521$	12.2898	+	21.2866i	0.538427	+	0.932582i	0.998989	+	0.0449550i	$0.0143144\pi$
$521$	12.2898	+	21.2866i	0.538427	+	0.932582i	−0.460562	+	0.887627i	$0.652352\pi$
$522$		0			0
$523$	−15.6689	+	27.1393i	−0.685153	+	1.18672i	0.288235	+	0.957560i	$0.406932\pi$
$523$	−15.6689	+	27.1393i	−0.685153	+	1.18672i	−0.973389	+	0.229161i	$0.926402\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−9.16233	+	15.8696i	−0.399117	+	0.691291i
$528$		0			0
$529$	−3.02801	−	5.24466i	−0.131652	−	0.228029i
$530$		0			0
$531$	−14.7004			−0.637944
$532$		0			0
$533$	−12.7922			−0.554094
$534$		0			0
$535$	−11.5605	−	20.0233i	−0.499802	−	0.865683i
$536$		0			0
$537$	−4.42724	+	7.66820i	−0.191049	+	0.330907i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	11.0575	−	19.1522i	0.475400	−	0.823417i	−0.524203	−	0.851593i	$-0.675637\pi$
$541$	11.0575	−	19.1522i	0.475400	−	0.823417i	0.999603	+	0.0281764i	$0.00897001\pi$
$542$		0			0
$543$	16.5748	+	28.7084i	0.711292	+	1.23199i
$544$		0			0
$545$	39.5824			1.69553
$546$		0			0
$547$	15.7584			0.673783			0.336891	−	0.941544i	$-0.390625\pi$
$547$	15.7584			0.673783			0.336891	+	0.941544i	$0.390625\pi$
$548$		0			0
$549$	5.97537	+	10.3496i	0.255023	+	0.441712i
$550$		0			0
$551$	−0.323658	+	0.560592i	−0.0137883	+	0.0238820i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−22.6177	+	39.1750i	−0.960067	+	1.66288i
$556$		0			0
$557$	−6.73065	−	11.6578i	−0.285187	−	0.493958i	0.687468	−	0.726215i	$-0.258722\pi$
$557$	−6.73065	−	11.6578i	−0.285187	−	0.493958i	−0.972654	+	0.232257i	$0.925389\pi$
$558$		0			0
$559$	20.9852			0.887580
$560$		0			0
$561$	−37.1680			−1.56923
$562$		0			0
$563$	14.2863	+	24.7447i	0.602097	+	1.04286i	0.992503	+	0.122220i	$0.0390013\pi$
$563$	14.2863	+	24.7447i	0.602097	+	1.04286i	−0.390406	+	0.920643i	$0.627665\pi$
$564$		0			0
$565$	7.83960	−	13.5786i	0.329814	−	0.571255i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−13.8357	+	23.9641i	−0.580023	+	1.00463i	0.415453	+	0.909615i	$0.363623\pi$
$569$	−13.8357	+	23.9641i	−0.580023	+	1.00463i	−0.995476	+	0.0950142i	$0.969710\pi$
$570$		0			0
$571$	−5.35461	−	9.27446i	−0.224083	−	0.388124i	0.731961	−	0.681347i	$-0.238605\pi$
$571$	−5.35461	−	9.27446i	−0.224083	−	0.388124i	−0.956044	+	0.293223i	$0.905272\pi$
$572$		0			0
$573$	−8.98593			−0.375392
$574$		0			0
$575$	−16.3771			−0.682974
$576$		0			0
$577$	−12.3328	−	21.3610i	−0.513420	−	0.889269i	−0.999879	−	0.0155655i	$-0.995045\pi$
$577$	−12.3328	−	21.3610i	−0.513420	−	0.889269i	0.486459	−	0.873703i	$-0.338288\pi$
$578$		0			0
$579$	21.3803	−	37.0317i	0.888534	−	1.53899i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	28.7235	−	49.7505i	1.18960	−	2.06046i
$584$		0			0
$585$	−3.46250	−	5.99723i	−0.143157	−	0.247955i
$586$		0			0
$587$	20.7654			0.857081			0.428541	−	0.903523i	$-0.359028\pi$
$587$	20.7654			0.857081			0.428541	+	0.903523i	$0.359028\pi$
$588$		0			0
$589$	−1.99933			−0.0823811
$590$		0			0
$591$	−5.18137	−	8.97440i	−0.213133	−	0.369158i
$592$		0			0
$593$	−20.1928	+	34.9750i	−0.829220	+	1.43625i	0.0694313	+	0.997587i	$0.477882\pi$
$593$	−20.1928	+	34.9750i	−0.829220	+	1.43625i	−0.898651	+	0.438664i	$0.855452\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2.81318	−	4.87258i	0.115136	−	0.199421i
$598$		0			0
$599$	3.82876	+	6.63161i	0.156439	+	0.270960i	0.933582	−	0.358364i	$-0.116665\pi$
$599$	3.82876	+	6.63161i	0.156439	+	0.270960i	−0.777143	+	0.629324i	$0.783332\pi$
$600$		0			0
$601$	−7.76541			−0.316758			−0.158379	−	0.987378i	$-0.550627\pi$
$601$	−7.76541			−0.316758			−0.158379	+	0.987378i	$0.550627\pi$
$602$		0			0
$603$	−2.54084			−0.103471
$604$		0			0
$605$	43.9042	+	76.0444i	1.78496	+	3.09164i
$606$		0			0
$607$	10.7797	−	18.6710i	0.437535	−	0.757832i	−0.559964	−	0.828517i	$-0.689185\pi$
$607$	10.7797	−	18.6710i	0.437535	−	0.757832i	0.997499	+	0.0706846i	$0.0225184\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−10.7725	+	18.6585i	−0.435809	+	0.754843i
$612$		0			0
$613$	7.12534	+	12.3415i	0.287790	+	0.498467i	0.973282	−	0.229613i	$-0.0737462\pi$
$613$	7.12534	+	12.3415i	0.287790	+	0.498467i	−0.685492	+	0.728080i	$0.740413\pi$
$614$		0			0
$615$	38.0242			1.53328
$616$		0			0
$617$	−2.37248			−0.0955126			−0.0477563	−	0.998859i	$-0.515207\pi$
$617$	−2.37248			−0.0955126			−0.0477563	+	0.998859i	$0.515207\pi$
$618$		0			0
$619$	16.5349	+	28.6392i	0.664593	+	1.15111i	0.979396	+	0.201951i	$0.0647283\pi$
$619$	16.5349	+	28.6392i	0.664593	+	1.15111i	−0.314803	+	0.949157i	$0.601938\pi$
$620$		0			0
$621$	9.75358	−	16.8937i	0.391398	−	0.677921i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	15.4802	−	26.8124i	0.619206	−	1.07250i
$626$		0			0
$627$	−2.02763	−	3.51196i	−0.0809758	−	0.140254i
$628$		0			0
$629$	21.5726			0.860155
$630$		0			0
$631$	20.6627			0.822568			0.411284	−	0.911507i	$-0.365080\pi$
$631$	20.6627			0.822568			0.411284	+	0.911507i	$0.365080\pi$
$632$		0			0
$633$	−4.36657	−	7.56313i	−0.173556	−	0.300607i
$634$		0			0
$635$	23.5782	−	40.8386i	0.935671	−	1.62063i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	3.67470	−	6.36477i	0.145369	−	0.251786i
$640$		0			0
$641$	−17.5858	−	30.4595i	−0.694597	−	1.20308i	−0.970316	−	0.241839i	$-0.922249\pi$
$641$	−17.5858	−	30.4595i	−0.694597	−	1.20308i	0.275719	−	0.961238i	$-0.411084\pi$
$642$		0			0
$643$	−17.9112			−0.706348			−0.353174	−	0.935558i	$-0.614898\pi$
$643$	−17.9112			−0.706348			−0.353174	+	0.935558i	$0.614898\pi$
$644$		0			0
$645$	−62.3773			−2.45610
$646$		0			0
$647$	2.20859	+	3.82539i	0.0868287	+	0.150392i	0.906169	−	0.422916i	$-0.138993\pi$
$647$	2.20859	+	3.82539i	0.0868287	+	0.150392i	−0.819340	+	0.573308i	$0.805660\pi$
$648$		0			0
$649$	38.3042	−	66.3448i	1.50357	−	2.60426i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−0.790743	+	1.36961i	−0.0309442	+	0.0535969i	−0.881083	−	0.472962i	$-0.843185\pi$
$653$	−0.790743	+	1.36961i	−0.0309442	+	0.0535969i	0.850139	+	0.526559i	$0.176518\pi$
$654$		0			0
$655$	−24.8321	−	43.0104i	−0.970269	−	1.68056i
$656$		0			0
$657$	−3.89634			−0.152011
$658$		0			0
$659$	−27.5009			−1.07128			−0.535641	−	0.844446i	$-0.679930\pi$
$659$	−27.5009			−1.07128			−0.535641	+	0.844446i	$0.679930\pi$
$660$		0			0
$661$	−10.7157	−	18.5602i	−0.416794	−	0.721908i	0.578821	−	0.815454i	$-0.303513\pi$
$661$	−10.7157	−	18.5602i	−0.416794	−	0.721908i	−0.995615	+	0.0935468i	$0.970180\pi$
$662$		0			0
$663$	−5.63606	+	9.76195i	−0.218887	+	0.379123i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−5.74124	+	9.94412i	−0.222302	+	0.385038i
$668$		0			0
$669$	0.0551973	+	0.0956046i	0.00213405	+	0.00369629i
$670$		0			0
$671$	−62.2790			−2.40425
$672$		0			0
$673$	22.6801			0.874254			0.437127	−	0.899400i	$-0.355996\pi$
$673$	22.6801			0.874254			0.437127	+	0.899400i	$0.355996\pi$
$674$		0			0
$675$	−5.49751	−	9.52197i	−0.211599	−	0.366501i
$676$		0			0
$677$	12.9637	−	22.4538i	0.498235	−	0.862968i	−0.501763	−	0.865005i	$-0.667315\pi$
$677$	12.9637	−	22.4538i	0.498235	−	0.862968i	0.999998	+	0.00203722i	$0.000648466\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−14.8567	+	25.7326i	−0.569311	+	0.986076i
$682$		0			0
$683$	−17.8640	−	30.9414i	−0.683548	−	1.18394i	−0.973891	−	0.227018i	$-0.927102\pi$
$683$	−17.8640	−	30.9414i	−0.683548	−	1.18394i	0.290342	−	0.956923i	$-0.406231\pi$
$684$		0			0
$685$	1.58169			0.0604334
$686$		0			0
$687$	−29.3992			−1.12165
$688$		0			0
$689$	−8.71111	−	15.0881i	−0.331867	−	0.574811i
$690$		0			0
$691$	−11.5790	+	20.0555i	−0.440488	+	0.762947i	−0.997726	−	0.0674059i	$-0.978528\pi$
$691$	−11.5790	+	20.0555i	−0.440488	+	0.762947i	0.557238	+	0.830353i	$0.311861\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	12.6533	−	21.9162i	0.479968	−	0.831329i
$696$		0			0
$697$	−9.06680	−	15.7042i	−0.343430	−	0.594838i
$698$		0			0
$699$	34.9719			1.32276
$700$		0			0
$701$	30.0408			1.13462			0.567312	−	0.823503i	$-0.307983\pi$
$701$	30.0408			1.13462			0.567312	+	0.823503i	$0.307983\pi$
$702$		0			0
$703$	1.17685	+	2.03837i	0.0443858	+	0.0768785i
$704$		0			0
$705$	32.0206	−	55.4613i	1.20597	−	2.08879i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−22.4038	+	38.8044i	−0.841391	+	1.45733i	0.0473285	+	0.998879i	$0.484929\pi$
$709$	−22.4038	+	38.8044i	−0.841391	+	1.45733i	−0.888719	+	0.458452i	$0.848404\pi$
$710$		0			0
$711$	−1.74934	−	3.02994i	−0.0656052	−	0.113632i
$712$		0			0
$713$	−35.4654			−1.32819
$714$		0			0
$715$	36.0883			1.34963
$716$		0			0
$717$	−14.1846	−	24.5684i	−0.529733	−	0.917525i
$718$		0			0
$719$	5.62326	−	9.73978i	0.209712	−	0.363233i	−0.741912	−	0.670498i	$-0.766081\pi$
$719$	5.62326	−	9.73978i	0.209712	−	0.363233i	0.951624	+	0.307265i	$0.0994139\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	25.2112	−	43.6671i	0.937615	−	1.62400i
$724$		0			0
$725$	3.23599	+	5.60491i	0.120182	+	0.208161i
$726$		0			0
$727$	−0.171318			−0.00635382			−0.00317691	−	0.999995i	$-0.501011\pi$
$727$	−0.171318			−0.00635382			−0.00317691	+	0.999995i	$0.501011\pi$
$728$		0			0
$729$	8.46004			0.313335
$730$		0			0
$731$	14.8738	+	25.7621i	0.550126	+	0.952846i
$732$		0			0
$733$	2.80436	−	4.85729i	0.103581	−	0.179408i	−0.809576	−	0.587015i	$-0.800303\pi$
$733$	2.80436	−	4.85729i	0.103581	−	0.179408i	0.913158	+	0.407606i	$0.133636\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.62055	−	11.4671i	0.243871	−	0.422397i
$738$		0			0
$739$	−3.96790	−	6.87261i	−0.145962	−	0.252813i	0.783770	−	0.621052i	$-0.213294\pi$
$739$	−3.96790	−	6.87261i	−0.145962	−	0.252813i	−0.929731	+	0.368239i	$0.879961\pi$
$740$		0			0
$741$	−1.22986			−0.0451800
$742$		0			0
$743$	17.9533			0.658644			0.329322	−	0.944218i	$-0.393180\pi$
$743$	17.9533			0.658644			0.329322	+	0.944218i	$0.393180\pi$
$744$		0			0
$745$	−20.1153	−	34.8407i	−0.736967	−	1.27646i
$746$		0			0
$747$	0.300207	−	0.519974i	0.0109840	−	0.0190249i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	1.54137	−	2.66973i	0.0562454	−	0.0974199i	−0.836532	−	0.547918i	$-0.815420\pi$
$751$	1.54137	−	2.66973i	0.0562454	−	0.0974199i	0.892777	+	0.450499i	$0.148754\pi$
$752$		0			0
$753$	−27.2015	−	47.1143i	−0.991276	−	1.71694i
$754$		0			0
$755$	19.5007			0.709702
$756$		0			0
$757$	21.9791			0.798844			0.399422	−	0.916767i	$-0.369211\pi$
$757$	21.9791			0.798844			0.399422	+	0.916767i	$0.369211\pi$
$758$		0			0
$759$	−35.9673	−	62.2972i	−1.30553	−	2.26125i
$760$		0			0
$761$	5.91924	−	10.2524i	0.214572	−	0.371650i	−0.738568	−	0.674179i	$-0.764498\pi$
$761$	5.91924	−	10.2524i	0.214572	−	0.371650i	0.953140	+	0.302529i	$0.0978309\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	4.90826	−	8.50136i	0.177459	−	0.307367i
$766$		0			0
$767$	−11.6167	−	20.1207i	−0.419455	−	0.726518i
$768$		0			0
$769$	10.6729			0.384875			0.192437	−	0.981309i	$-0.438361\pi$
$769$	10.6729			0.384875			0.192437	+	0.981309i	$0.438361\pi$
$770$		0			0
$771$	20.5399			0.739727
$772$		0			0
$773$	12.4934	+	21.6392i	0.449357	+	0.778310i	0.998344	−	0.0575213i	$-0.0183197\pi$
$773$	12.4934	+	21.6392i	0.449357	+	0.778310i	−0.548987	+	0.835831i	$0.684986\pi$
$774$		0			0
$775$	−9.99486	+	17.3116i	−0.359026	+	0.621851i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.989245	−	1.71342i	0.0354434	−	0.0613897i
$780$		0			0
$781$	19.1500	+	33.1688i	0.685241	+	1.18687i
$782$		0			0
$783$	−7.70893			−0.275495
$784$		0			0
$785$	60.4119			2.15619
$786$		0			0
$787$	27.0865	+	46.9153i	0.965531	+	1.67235i	0.708182	+	0.706030i	$0.249516\pi$
$787$	27.0865	+	46.9153i	0.965531	+	1.67235i	0.257349	+	0.966319i	$0.417151\pi$
$788$		0			0
$789$	15.1951	−	26.3187i	0.540961	−	0.936971i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−9.44384	+	16.3572i	−0.335360	+	0.580861i
$794$		0			0
$795$	25.8933	+	44.8485i	0.918340	+	1.59061i
$796$		0			0
$797$	−3.11643			−0.110390			−0.0551948	−	0.998476i	$-0.517578\pi$
$797$	−3.11643			−0.110390			−0.0551948	+	0.998476i	$0.517578\pi$
$798$		0			0
$799$	−30.5410			−1.08046
$800$		0			0
$801$	−8.70808	−	15.0828i	−0.307685	−	0.532926i
$802$		0			0
$803$	10.1525	−	17.5847i	0.358275	−	0.620550i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−21.1960	+	36.7126i	−0.746136	+	1.29234i
$808$		0			0
$809$	22.6387	+	39.2113i	0.795933	+	1.37860i	0.922245	+	0.386605i	$0.126352\pi$
$809$	22.6387	+	39.2113i	0.795933	+	1.37860i	−0.126313	+	0.991990i	$0.540314\pi$
$810$		0			0
$811$	−12.8719			−0.451993			−0.225997	−	0.974128i	$-0.572564\pi$
$811$	−12.8719			−0.451993			−0.225997	+	0.974128i	$0.572564\pi$
$812$		0			0
$813$	−16.2243			−0.569011
$814$		0			0
$815$	−4.13740	−	7.16619i	−0.144927	−	0.251021i
$816$		0			0
$817$	−1.62282	+	2.81081i	−0.0567753	+	0.0983377i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−28.2576	+	48.9436i	−0.986197	+	1.70814i	−0.349707	+	0.936859i	$0.613719\pi$
$821$	−28.2576	+	48.9436i	−0.986197	+	1.70814i	−0.636491	+	0.771284i	$0.719615\pi$
$822$		0			0
$823$	−12.6190	−	21.8568i	−0.439872	−	0.761881i	0.557807	−	0.829971i	$-0.311643\pi$
$823$	−12.6190	−	21.8568i	−0.439872	−	0.761881i	−0.997679	+	0.0680898i	$0.978310\pi$
$824$		0			0
$825$	−40.5453			−1.41160
$826$		0			0
$827$	13.9362			0.484608			0.242304	−	0.970200i	$-0.422097\pi$
$827$	13.9362			0.484608			0.242304	+	0.970200i	$0.422097\pi$
$828$		0			0
$829$	−4.34080	−	7.51849i	−0.150762	−	0.261128i	0.780746	−	0.624849i	$-0.214839\pi$
$829$	−4.34080	−	7.51849i	−0.150762	−	0.261128i	−0.931508	+	0.363721i	$0.881506\pi$
$830$		0			0
$831$	2.08786	−	3.61627i	0.0724270	−	0.125447i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−13.6020	+	23.5594i	−0.470717	+	0.815305i
$836$		0			0
$837$	−11.9051	−	20.6202i	−0.411500	−	0.712739i
$838$		0			0
$839$	20.5609			0.709843			0.354921	−	0.934896i	$-0.384508\pi$
$839$	20.5609			0.709843			0.354921	+	0.934896i	$0.384508\pi$
$840$		0			0
$841$	−24.4623			−0.843528
$842$		0			0
$843$	−9.40025	−	16.2817i	−0.323762	−	0.560772i
$844$		0			0
$845$	−12.9563	+	22.4410i	−0.445710	+	0.771993i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	31.5599	−	54.6633i	1.08313	−	1.87604i
$850$		0			0
$851$	20.8757	+	36.1578i	0.715610	+	1.23947i
$852$		0			0
$853$	29.1377			0.997655			0.498828	−	0.866701i	$-0.333764\pi$
$853$	29.1377			0.997655			0.498828	+	0.866701i	$0.333764\pi$
$854$		0			0
$855$	1.07104			0.0366289
$856$		0			0
$857$	−8.60008	−	14.8958i	−0.293773	−	0.508830i	0.680926	−	0.732353i	$-0.261578\pi$
$857$	−8.60008	−	14.8958i	−0.293773	−	0.508830i	−0.974699	+	0.223522i	$0.928244\pi$
$858$		0			0
$859$	−16.7681	+	29.0432i	−0.572121	+	0.990942i	0.424227	+	0.905556i	$0.360546\pi$
$859$	−16.7681	+	29.0432i	−0.572121	+	0.990942i	−0.996348	+	0.0853863i	$0.972788\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	9.06279	−	15.6972i	0.308501	−	0.534339i	−0.669534	−	0.742782i	$-0.733506\pi$
$863$	9.06279	−	15.6972i	0.308501	−	0.534339i	0.978035	+	0.208442i	$0.0668394\pi$
$864$		0			0
$865$	−1.56802	−	2.71589i	−0.0533143	−	0.0923430i
$866$		0			0
$867$	19.0394			0.646613
$868$		0			0
$869$	18.2326			0.618500
$870$		0			0
$871$	−2.00785	−	3.47770i	−0.0680334	−	0.117837i
$872$		0			0
$873$	−3.21601	+	5.57030i	−0.108846	+	0.188526i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−15.4502	+	26.7605i	−0.521716	+	0.903639i	0.477965	+	0.878379i	$0.341375\pi$
$877$	−15.4502	+	26.7605i	−0.521716	+	0.903639i	−0.999681	+	0.0252598i	$0.991959\pi$
$878$		0			0
$879$	−2.62392	−	4.54476i	−0.0885026	−	0.153291i
$880$		0			0
$881$	6.51958			0.219650			0.109825	−	0.993951i	$-0.464971\pi$
$881$	6.51958			0.219650			0.109825	+	0.993951i	$0.464971\pi$
$882$		0			0
$883$	32.8703			1.10617			0.553086	−	0.833124i	$-0.313450\pi$
$883$	32.8703			1.10617			0.553086	+	0.833124i	$0.313450\pi$
$884$		0			0
$885$	34.5300	+	59.8077i	1.16071	+	2.01041i
$886$		0			0
$887$	−3.66798	+	6.35312i	−0.123159	+	0.213317i	−0.921012	−	0.389535i	$-0.872636\pi$
$887$	−3.66798	+	6.35312i	−0.123159	+	0.213317i	0.797853	+	0.602852i	$0.205969\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	36.2279	−	62.7486i	1.21368	−	2.10216i
$892$		0			0
$893$	−1.66611	−	2.88579i	−0.0557542	−	0.0965691i
$894$		0			0
$895$	12.1870			0.407368
$896$		0			0
$897$	−21.8160			−0.728414
$898$		0			0
$899$	7.00768	+	12.1377i	0.233719	+	0.404814i
$900$		0			0
$901$	12.3484	−	21.3881i	0.411385	−	0.712540i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	22.8130	−	39.5133i	0.758331	−	1.31347i
$906$		0			0
$907$	15.7381	+	27.2592i	0.522575	+	0.905126i	0.999655	+	0.0262662i	$0.00836177\pi$
$907$	15.7381	+	27.2592i	0.522575	+	0.905126i	−0.477080	+	0.878860i	$0.658305\pi$
$908$		0			0
$909$	0.988904			0.0327999
$910$		0			0
$911$	17.1627			0.568626			0.284313	−	0.958732i	$-0.408235\pi$
$911$	17.1627			0.568626			0.284313	+	0.958732i	$0.408235\pi$
$912$		0			0
$913$	1.56447	+	2.70974i	0.0517765	+	0.0896794i
$914$		0			0
$915$	28.0712	−	48.6208i	0.928007	−	1.60735i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	18.6177	−	32.2468i	0.614141	−	1.06372i	−0.376394	−	0.926460i	$-0.622836\pi$
$919$	18.6177	−	32.2468i	0.614141	−	1.06372i	0.990535	−	0.137263i	$-0.0438306\pi$
$920$		0			0
$921$	−3.77764	−	6.54306i	−0.124477	−	0.215601i
$922$		0			0
$923$	11.6154			0.382327
$924$		0			0
$925$	23.5328			0.773752
$926$		0			0
$927$	10.0078	+	17.3341i	0.328700	+	0.569325i
$928$		0			0
$929$	14.7570	−	25.5599i	0.484162	−	0.838593i	−0.515672	−	0.856786i	$-0.672458\pi$
$929$	14.7570	−	25.5599i	0.484162	−	0.838593i	0.999835	+	0.0181925i	$0.00579117\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−30.2128	+	52.3301i	−0.989123	+	1.71321i
$934$		0			0
$935$	25.5785	+	44.3032i	0.836505	+	1.44887i
$936$		0			0
$937$	−20.2805			−0.662535			−0.331267	−	0.943537i	$-0.607476\pi$
$937$	−20.2805			−0.662535			−0.331267	+	0.943537i	$0.607476\pi$
$938$		0			0
$939$	−22.8724			−0.746412
$940$		0			0
$941$	29.0043	+	50.2369i	0.945513	+	1.63768i	0.754721	+	0.656046i	$0.227772\pi$
$941$	29.0043	+	50.2369i	0.945513	+	1.63768i	0.190792	+	0.981630i	$0.438894\pi$
$942$		0			0
$943$	17.5478	−	30.3937i	0.571435	−	0.989755i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−3.86313	+	6.69113i	−0.125535	+	0.217433i	−0.921942	−	0.387328i	$-0.873398\pi$
$947$	−3.86313	+	6.69113i	−0.125535	+	0.217433i	0.796407	+	0.604761i	$0.206731\pi$
$948$		0			0
$949$	−3.07901	−	5.33300i	−0.0999488	−	0.173116i
$950$		0			0
$951$	−25.1935			−0.816955
$952$		0			0
$953$	9.24776			0.299564			0.149782	−	0.988719i	$-0.452143\pi$
$953$	9.24776			0.299564			0.149782	+	0.988719i	$0.452143\pi$
$954$		0			0
$955$	6.18398	+	10.7110i	0.200109	+	0.346599i
$956$		0			0
$957$	−14.2137	+	24.6189i	−0.459464	+	0.795816i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−6.14428	+	10.6422i	−0.198203	+	0.343297i
$962$		0			0
$963$	5.06901	+	8.77979i	0.163347	+	0.282925i
$964$		0			0
$965$	−58.8544			−1.89459
$966$		0			0
$967$	10.5604			0.339600			0.169800	−	0.985479i	$-0.445688\pi$
$967$	10.5604			0.339600			0.169800	+	0.985479i	$0.445688\pi$
$968$		0			0
$969$	−0.871692	−	1.50981i	−0.0280028	−	0.0485022i
$970$		0			0
$971$	8.18252	−	14.1725i	0.262590	−	0.454819i	−0.704340	−	0.709863i	$-0.748757\pi$
$971$	8.18252	−	14.1725i	0.262590	−	0.454819i	0.966929	+	0.255044i	$0.0820901\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−6.14818	+	10.6490i	−0.196899	+	0.341040i
$976$		0			0
$977$	13.9943	+	24.2389i	0.447719	+	0.775471i	0.998237	−	0.0593516i	$-0.0189033\pi$
$977$	13.9943	+	24.2389i	0.447719	+	0.775471i	−0.550519	+	0.834823i	$0.685570\pi$
$978$		0			0
$979$	90.7610			2.90073
$980$		0			0
$981$	−17.3560			−0.554136
$982$		0			0
$983$	6.38258	+	11.0550i	0.203573	+	0.352598i	0.949677	−	0.313231i	$-0.101411\pi$
$983$	6.38258	+	11.0550i	0.203573	+	0.352598i	−0.746104	+	0.665829i	$0.768078\pi$
$984$		0			0
$985$	−7.13149	+	12.3521i	−0.227228	+	0.393570i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−28.7865	+	49.8598i	−0.915359	+	1.58545i
$990$		0			0
$991$	22.0561	+	38.2022i	0.700634	+	1.21353i	0.968244	+	0.250007i	$0.0804329\pi$
$991$	22.0561	+	38.2022i	0.700634	+	1.21353i	−0.267610	+	0.963527i	$0.586234\pi$
$992$		0			0
$993$	−55.3192			−1.75550
$994$		0			0
$995$	−7.74397			−0.245500
$996$		0			0
$997$	−1.29448	−	2.24211i	−0.0409966	−	0.0710082i	0.844799	−	0.535084i	$-0.179720\pi$
$997$	−1.29448	−	2.24211i	−0.0409966	−	0.0710082i	−0.885796	+	0.464076i	$0.846387\pi$
$998$		0			0
$999$	−14.0152	+	24.2750i	−0.443421	+	0.768028i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1372.2.e.d.1353.4		12
7.2	even	3		1372.2.a.a.1.3	✓	6
7.3	odd	6		1372.2.e.a.361.3		12
7.4	even	3	inner	1372.2.e.d.361.4		12
7.5	odd	6		1372.2.a.d.1.4	yes	6
7.6	odd	2		1372.2.e.a.1353.3		12
28.19	even	6		5488.2.a.g.1.3		6
28.23	odd	6		5488.2.a.q.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1372.2.a.a.1.3	✓	6	7.2	even	3
1372.2.a.d.1.4	yes	6	7.5	odd	6
1372.2.e.a.361.3		12	7.3	odd	6
1372.2.e.a.1353.3		12	7.6	odd	2
1372.2.e.d.361.4		12	7.4	even	3	inner
1372.2.e.d.1353.4		12	1.1	even	1	trivial
5488.2.a.g.1.3		6	28.19	even	6
5488.2.a.q.1.4		6	28.23	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1372 = 2^{2} \cdot 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1372.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.02995 + 1.78392i) q^{3} +(1.41759 - 2.45533i) q^{5} +(-0.621582 + 1.07661i) q^{9} +(-3.23925 - 5.61055i) q^{11} -1.96477 q^{13} +5.84016 q^{15} +(-1.39258 - 2.41201i) q^{17} +(0.151939 - 0.263166i) q^{19} +(2.69518 - 4.66819i) q^{23} +(-1.51911 - 2.63118i) q^{25} +3.61890 q^{27} -2.13019 q^{29} +(-3.28970 - 5.69793i) q^{31} +(6.67252 - 11.5571i) q^{33} +(-3.87278 + 6.70785i) q^{37} +(-2.02361 - 3.50499i) q^{39} +6.51081 q^{41} -10.6807 q^{43} +(1.76229 + 3.05238i) q^{45} +(5.48283 - 9.49654i) q^{47} +(2.86856 - 4.96849i) q^{51} +(4.43366 + 7.67932i) q^{53} -18.3677 q^{55} +0.625956 q^{57} +(5.91250 + 10.2408i) q^{59} +(4.80658 - 8.32525i) q^{61} +(-2.78524 + 4.82417i) q^{65} +(1.02193 + 1.77003i) q^{67} +11.1036 q^{69} -5.91185 q^{71} +(1.56711 + 2.71431i) q^{73} +(3.12921 - 5.41995i) q^{75} +(-1.40716 + 2.43728i) q^{79} +(5.59202 + 9.68566i) q^{81} -0.482973 q^{83} -7.89640 q^{85} +(-2.19398 - 3.80009i) q^{87} +(-7.00477 + 12.1326i) q^{89} +(6.77644 - 11.7371i) q^{93} +(-0.430773 - 0.746121i) q^{95} +5.17392 q^{97} +8.05385 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 7 q^{3} + 7 q^{5} - 9 q^{9} - 3 q^{11} - 14 q^{13} + 22 q^{15} + 7 q^{19} - 11 q^{23} - 3 q^{25} - 56 q^{27} + 12 q^{29} + 14 q^{31} + 6 q^{37} - 5 q^{39} - 6 q^{43} + 21 q^{45} + 42 q^{47} + 17 q^{51}+ \cdots - 68 q^{99}+O(q^{100}) \) 12 * q + 7 * q^3 + 7 * q^5 - 9 * q^9 - 3 * q^11 - 14 * q^13 + 22 * q^15 + 7 * q^19 - 11 * q^23 - 3 * q^25 - 56 * q^27 + 12 * q^29 + 14 * q^31 + 6 * q^37 - 5 * q^39 - 6 * q^43 + 21 * q^45 + 42 * q^47 + 17 * q^51 + 17 * q^53 - 28 * q^55 - 12 * q^57 + 35 * q^59 + 7 * q^61 + 6 * q^65 + 14 * q^67 - 28 * q^69 - 56 * q^71 + 35 * q^75 - 6 * q^79 - 34 * q^81 - 98 * q^83 - 46 * q^85 + 21 * q^87 - 7 * q^89 + 14 * q^93 + 25 * q^95 + 42 * q^97 - 68 * q^99

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