LMFDB - Embedded newform 784.2.x.b.557.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [784,2,Mod(165,784)] 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("784.165"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(784, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 3, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,2,-4,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	784.557
Dual form			784.2.x.b.373.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.366025 + 1.36603i) q^{2} +(-2.73205 + 0.732051i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-2.73205 - 0.732051i) q^{5} -4.00000i q^{6} +(2.00000 - 2.00000i) q^{8} +(4.33013 - 2.50000i) q^{9} +(2.00000 - 3.46410i) q^{10} +(-1.09808 - 4.09808i) q^{11} +(5.46410 + 1.46410i) q^{12} +8.00000 q^{15} +(2.00000 + 3.46410i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(1.83013 + 6.83013i) q^{18} +(1.46410 - 5.46410i) q^{19} +(4.00000 + 4.00000i) q^{20} +6.00000 q^{22} +(-1.73205 + 1.00000i) q^{23} +(-4.00000 + 6.92820i) q^{24} +(2.59808 + 1.50000i) q^{25} +(-4.00000 + 4.00000i) q^{27} +(-1.00000 - 1.00000i) q^{29} +(-2.92820 + 10.9282i) q^{30} +(2.00000 - 3.46410i) q^{31} +(-5.46410 + 1.46410i) q^{32} +(6.00000 + 10.3923i) q^{33} +(-6.00000 - 6.00000i) q^{34} -10.0000 q^{36} +(-4.09808 - 1.09808i) q^{37} +(6.92820 + 4.00000i) q^{38} +(-6.92820 + 4.00000i) q^{40} +2.00000i q^{41} +(-5.00000 + 5.00000i) q^{43} +(-2.19615 + 8.19615i) q^{44} +(-13.6603 + 3.66025i) q^{45} +(-0.732051 - 2.73205i) q^{46} +(-4.00000 - 6.92820i) q^{47} +(-8.00000 - 8.00000i) q^{48} +(-3.00000 + 3.00000i) q^{50} +(4.39230 - 16.3923i) q^{51} +(2.56218 + 9.56218i) q^{53} +(-4.00000 - 6.92820i) q^{54} +12.0000i q^{55} +16.0000i q^{57} +(1.73205 - 1.00000i) q^{58} +(-0.732051 - 2.73205i) q^{59} +(-13.8564 - 8.00000i) q^{60} +(-2.19615 + 8.19615i) q^{61} +(4.00000 + 4.00000i) q^{62} -8.00000i q^{64} +(-16.3923 + 4.39230i) q^{66} +(6.83013 - 1.83013i) q^{67} +(10.3923 - 6.00000i) q^{68} +(4.00000 - 4.00000i) q^{69} +8.00000i q^{71} +(3.66025 - 13.6603i) q^{72} +(8.66025 + 5.00000i) q^{73} +(3.00000 - 5.19615i) q^{74} +(-8.19615 - 2.19615i) q^{75} +(-8.00000 + 8.00000i) q^{76} +(7.00000 + 12.1244i) q^{79} +(-2.92820 - 10.9282i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-2.73205 - 0.732051i) q^{82} +(12.0000 - 12.0000i) q^{85} +(-5.00000 - 8.66025i) q^{86} +(3.46410 + 2.00000i) q^{87} +(-10.3923 - 6.00000i) q^{88} +(5.19615 - 3.00000i) q^{89} -20.0000i q^{90} +4.00000 q^{92} +(-2.92820 + 10.9282i) q^{93} +(10.9282 - 2.92820i) q^{94} +(-8.00000 + 13.8564i) q^{95} +(13.8564 - 8.00000i) q^{96} +6.00000 q^{97} +(-15.0000 - 15.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 4 q^{3} - 4 q^{5} + 8 q^{8} + 8 q^{10} + 6 q^{11} + 8 q^{12} + 32 q^{15} + 8 q^{16} - 12 q^{17} - 10 q^{18} - 8 q^{19} + 16 q^{20} + 24 q^{22} - 16 q^{24} - 16 q^{27} - 4 q^{29} + 16 q^{30}+ \cdots - 60 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 4 * q^3 - 4 * q^5 + 8 * q^8 + 8 * q^10 + 6 * q^11 + 8 * q^12 + 32 * q^15 + 8 * q^16 - 12 * q^17 - 10 * q^18 - 8 * q^19 + 16 * q^20 + 24 * q^22 - 16 * q^24 - 16 * q^27 - 4 * q^29 + 16 * q^30 + 8 * q^31 - 8 * q^32 + 24 * q^33 - 24 * q^34 - 40 * q^36 - 6 * q^37 - 20 * q^43 + 12 * q^44 - 20 * q^45 + 4 * q^46 - 16 * q^47 - 32 * q^48 - 12 * q^50 - 24 * q^51 - 14 * q^53 - 16 * q^54 + 4 * q^59 + 12 * q^61 + 16 * q^62 - 24 * q^66 + 10 * q^67 + 16 * q^69 - 20 * q^72 + 12 * q^74 - 12 * q^75 - 32 * q^76 + 28 * q^79 + 16 * q^80 + 2 * q^81 - 4 * q^82 + 48 * q^85 - 20 * q^86 + 16 * q^92 + 16 * q^93 + 16 * q^94 - 32 * q^95 + 24 * q^97 - 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.366025	+	1.36603i	−0.258819	+	0.965926i
$2$	−0.366025	+	1.36603i	−0.258819	+	0.965926i
$3$	−2.73205	+	0.732051i	−1.57735	+	0.422650i	−0.938104	−	0.346353i	$-0.887420\pi$
$3$	−2.73205	+	0.732051i	−1.57735	+	0.422650i	−0.639246	+	0.769002i	$0.720753\pi$
$4$	−1.73205	−	1.00000i	−0.866025	−	0.500000i
$5$	−2.73205	−	0.732051i	−1.22181	−	0.327383i	−0.410425	−	0.911894i	$-0.634620\pi$
$5$	−2.73205	−	0.732051i	−1.22181	−	0.327383i	−0.811386	+	0.584511i	$0.801286\pi$
$6$		−	4.00000i		−	1.63299i
$7$		0			0
$7$		0			0
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$	4.33013	−	2.50000i	1.44338	−	0.833333i
$10$	2.00000	−	3.46410i	0.632456	−	1.09545i
$11$	−1.09808	−	4.09808i	−0.331082	−	1.23562i	−0.908054	−	0.418852i	$-0.862432\pi$
$11$	−1.09808	−	4.09808i	−0.331082	−	1.23562i	0.576972	−	0.816764i	$-0.304234\pi$
$12$	5.46410	+	1.46410i	1.57735	+	0.422650i
$13$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$13$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$14$		0			0
$15$	8.00000			2.06559
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	0.230285	+	0.973123i	$0.426034\pi$
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	−0.957892	+	0.287129i	$0.907299\pi$
$18$	1.83013	+	6.83013i	0.431365	+	1.60988i
$19$	1.46410	−	5.46410i	0.335888	−	1.25355i	−0.567015	−	0.823707i	$-0.691902\pi$
$19$	1.46410	−	5.46410i	0.335888	−	1.25355i	0.902903	−	0.429844i	$-0.141431\pi$
$20$	4.00000	+	4.00000i	0.894427	+	0.894427i
$21$		0			0
$22$	6.00000			1.27920
$23$	−1.73205	+	1.00000i	−0.361158	+	0.208514i	−0.669588	−	0.742732i	$-0.733529\pi$
$23$	−1.73205	+	1.00000i	−0.361158	+	0.208514i	0.308431	+	0.951247i	$0.400196\pi$
$24$	−4.00000	+	6.92820i	−0.816497	+	1.41421i
$25$	2.59808	+	1.50000i	0.519615	+	0.300000i
$26$		0			0
$27$	−4.00000	+	4.00000i	−0.769800	+	0.769800i
$28$		0			0
$29$	−1.00000	−	1.00000i	−0.185695	−	0.185695i	0.608137	−	0.793832i	$-0.291917\pi$
$29$	−1.00000	−	1.00000i	−0.185695	−	0.185695i	−0.793832	+	0.608137i	$0.791917\pi$
$30$	−2.92820	+	10.9282i	−0.534614	+	1.99521i
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	−5.46410	+	1.46410i	−0.965926	+	0.258819i
$33$	6.00000	+	10.3923i	1.04447	+	1.80907i
$34$	−6.00000	−	6.00000i	−1.02899	−	1.02899i
$35$		0			0
$36$	−10.0000			−1.66667
$37$	−4.09808	−	1.09808i	−0.673720	−	0.180523i	−0.0942898	−	0.995545i	$-0.530058\pi$
$37$	−4.09808	−	1.09808i	−0.673720	−	0.180523i	−0.579430	+	0.815022i	$0.696725\pi$
$38$	6.92820	+	4.00000i	1.12390	+	0.648886i
$39$		0			0
$40$	−6.92820	+	4.00000i	−1.09545	+	0.632456i
$41$			2.00000i			0.312348i	0.987730	+	0.156174i	$0.0499160\pi$
$41$			2.00000i			0.312348i	−0.987730	+	0.156174i	$0.950084\pi$
$42$		0			0
$43$	−5.00000	+	5.00000i	−0.762493	+	0.762493i	−0.976772	−	0.214280i	$-0.931260\pi$
$43$	−5.00000	+	5.00000i	−0.762493	+	0.762493i	0.214280	+	0.976772i	$0.431260\pi$
$44$	−2.19615	+	8.19615i	−0.331082	+	1.23562i
$45$	−13.6603	+	3.66025i	−2.03635	+	0.545638i
$46$	−0.732051	−	2.73205i	−0.107935	−	0.402819i
$47$	−4.00000	−	6.92820i	−0.583460	−	1.01058i	−0.995066	−	0.0992202i	$-0.968365\pi$
$47$	−4.00000	−	6.92820i	−0.583460	−	1.01058i	0.411606	−	0.911362i	$-0.364968\pi$
$48$	−8.00000	−	8.00000i	−1.15470	−	1.15470i
$49$		0			0
$50$	−3.00000	+	3.00000i	−0.424264	+	0.424264i
$51$	4.39230	−	16.3923i	0.615046	−	2.29538i
$52$		0			0
$53$	2.56218	+	9.56218i	0.351942	+	1.31347i	0.884289	+	0.466940i	$0.154644\pi$
$53$	2.56218	+	9.56218i	0.351942	+	1.31347i	−0.532347	+	0.846526i	$0.678690\pi$
$54$	−4.00000	−	6.92820i	−0.544331	−	0.942809i
$55$			12.0000i			1.61808i
$56$		0			0
$57$			16.0000i			2.11925i
$58$	1.73205	−	1.00000i	0.227429	−	0.131306i
$59$	−0.732051	−	2.73205i	−0.0953049	−	0.355683i	0.901761	−	0.432236i	$-0.142275\pi$
$59$	−0.732051	−	2.73205i	−0.0953049	−	0.355683i	−0.997066	+	0.0765531i	$0.975609\pi$
$60$	−13.8564	−	8.00000i	−1.78885	−	1.03280i
$61$	−2.19615	+	8.19615i	−0.281189	+	1.04941i	0.670391	+	0.742008i	$0.266126\pi$
$61$	−2.19615	+	8.19615i	−0.281189	+	1.04941i	−0.951580	+	0.307402i	$0.900540\pi$
$62$	4.00000	+	4.00000i	0.508001	+	0.508001i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$		0			0
$66$	−16.3923	+	4.39230i	−2.01775	+	0.540655i
$67$	6.83013	−	1.83013i	0.834433	−	0.223586i	0.183786	−	0.982966i	$-0.441165\pi$
$67$	6.83013	−	1.83013i	0.834433	−	0.223586i	0.650647	+	0.759381i	$0.274498\pi$
$68$	10.3923	−	6.00000i	1.26025	−	0.727607i
$69$	4.00000	−	4.00000i	0.481543	−	0.481543i
$70$		0			0
$71$			8.00000i			0.949425i	0.880141	+	0.474713i	$0.157448\pi$
$71$			8.00000i			0.949425i	−0.880141	+	0.474713i	$0.842552\pi$
$72$	3.66025	−	13.6603i	0.431365	−	1.60988i
$73$	8.66025	+	5.00000i	1.01361	+	0.585206i	0.912245	−	0.409644i	$-0.134347\pi$
$73$	8.66025	+	5.00000i	1.01361	+	0.585206i	0.101361	+	0.994850i	$0.467680\pi$
$74$	3.00000	−	5.19615i	0.348743	−	0.604040i
$75$	−8.19615	−	2.19615i	−0.946410	−	0.253590i
$76$	−8.00000	+	8.00000i	−0.917663	+	0.917663i
$77$		0			0
$78$		0			0
$79$	7.00000	+	12.1244i	0.787562	+	1.36410i	0.927457	+	0.373930i	$0.121990\pi$
$79$	7.00000	+	12.1244i	0.787562	+	1.36410i	−0.139895	+	0.990166i	$0.544677\pi$
$80$	−2.92820	−	10.9282i	−0.327383	−	1.22181i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−2.73205	−	0.732051i	−0.301705	−	0.0808415i
$83$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$83$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$84$		0			0
$85$	12.0000	−	12.0000i	1.30158	−	1.30158i
$86$	−5.00000	−	8.66025i	−0.539164	−	0.933859i
$87$	3.46410	+	2.00000i	0.371391	+	0.214423i
$88$	−10.3923	−	6.00000i	−1.10782	−	0.639602i
$89$	5.19615	−	3.00000i	0.550791	−	0.317999i	−0.198650	−	0.980071i	$-0.563656\pi$
$89$	5.19615	−	3.00000i	0.550791	−	0.317999i	0.749441	+	0.662071i	$0.230322\pi$
$90$		−	20.0000i		−	2.10819i
$91$		0			0
$92$	4.00000			0.417029
$93$	−2.92820	+	10.9282i	−0.303641	+	1.13320i
$94$	10.9282	−	2.92820i	1.12716	−	0.302021i
$95$	−8.00000	+	13.8564i	−0.820783	+	1.42164i
$96$	13.8564	−	8.00000i	1.41421	−	0.816497i
$97$	6.00000			0.609208			0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000			0.609208			0.304604	+	0.952479i	$0.401476\pi$
$98$		0			0
$99$	−15.0000	−	15.0000i	−1.50756	−	1.50756i
$100$	−3.00000	−	5.19615i	−0.300000	−	0.519615i
$101$	−0.732051	−	2.73205i	−0.0728418	−	0.271849i	0.919893	−	0.392168i	$-0.128275\pi$
$101$	−0.732051	−	2.73205i	−0.0728418	−	0.271849i	−0.992735	+	0.120319i	$0.961608\pi$
$102$	20.7846	+	12.0000i	2.05798	+	1.18818i
$103$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$103$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$104$		0			0
$105$		0			0
$106$	−14.0000			−1.35980
$107$	−6.83013	−	1.83013i	−0.660293	−	0.176925i	−0.0869149	−	0.996216i	$-0.527701\pi$
$107$	−6.83013	−	1.83013i	−0.660293	−	0.176925i	−0.573378	+	0.819291i	$0.694367\pi$
$108$	10.9282	−	2.92820i	1.05157	−	0.281766i
$109$	4.09808	−	1.09808i	0.392525	−	0.105177i	−0.0571579	−	0.998365i	$-0.518204\pi$
$109$	4.09808	−	1.09808i	0.392525	−	0.105177i	0.449682	+	0.893189i	$0.351537\pi$
$110$	−16.3923	−	4.39230i	−1.56294	−	0.418790i
$111$	12.0000			1.13899
$112$		0			0
$113$	−12.0000			−1.12887			−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000			−1.12887			−0.564433	+	0.825479i	$0.690905\pi$
$114$	−21.8564	−	5.85641i	−2.04704	−	0.548503i
$115$	5.46410	−	1.46410i	0.509530	−	0.136528i
$116$	0.732051	+	2.73205i	0.0679692	+	0.253665i
$117$		0			0
$118$	4.00000			0.368230
$119$		0			0
$120$	16.0000	−	16.0000i	1.46059	−	1.46059i
$121$	−6.06218	+	3.50000i	−0.551107	+	0.318182i
$122$	−10.3923	−	6.00000i	−0.940875	−	0.543214i
$123$	−1.46410	−	5.46410i	−0.132014	−	0.492681i
$124$	−6.92820	+	4.00000i	−0.622171	+	0.359211i
$125$	4.00000	+	4.00000i	0.357771	+	0.357771i
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	10.9282	+	2.92820i	0.965926	+	0.258819i
$129$	10.0000	−	17.3205i	0.880451	−	1.52499i
$130$		0			0
$131$	−4.39230	+	16.3923i	−0.383757	+	1.43220i	0.456359	+	0.889796i	$0.349153\pi$
$131$	−4.39230	+	16.3923i	−0.383757	+	1.43220i	−0.840116	+	0.542406i	$0.817513\pi$
$132$		−	24.0000i		−	2.08893i
$133$		0			0
$134$			10.0000i			0.863868i
$135$	13.8564	−	8.00000i	1.19257	−	0.688530i
$136$	4.39230	+	16.3923i	0.376637	+	1.40563i
$137$	10.3923	+	6.00000i	0.887875	+	0.512615i	0.873247	−	0.487278i	$-0.162010\pi$
$137$	10.3923	+	6.00000i	0.887875	+	0.512615i	0.0146279	+	0.999893i	$0.495344\pi$
$138$	4.00000	+	6.92820i	0.340503	+	0.589768i
$139$	12.0000	−	12.0000i	1.01783	−	1.01783i	0.0179885	−	0.999838i	$-0.494274\pi$
$139$	12.0000	−	12.0000i	1.01783	−	1.01783i	0.999838	−	0.0179885i	$-0.00572623\pi$
$140$		0			0
$141$	16.0000	+	16.0000i	1.34744	+	1.34744i
$142$	−10.9282	−	2.92820i	−0.917074	−	0.245729i
$143$		0			0
$144$	17.3205	+	10.0000i	1.44338	+	0.833333i
$145$	2.00000	+	3.46410i	0.166091	+	0.287678i
$146$	−10.0000	+	10.0000i	−0.827606	+	0.827606i
$147$		0			0
$148$	6.00000	+	6.00000i	0.493197	+	0.493197i
$149$	17.7583	+	4.75833i	1.45482	+	0.389818i	0.897697	−	0.440613i	$-0.145239\pi$
$149$	17.7583	+	4.75833i	1.45482	+	0.389818i	0.557122	+	0.830431i	$0.311906\pi$
$150$	6.00000	−	10.3923i	0.489898	−	0.848528i
$151$	−5.19615	−	3.00000i	−0.422857	−	0.244137i	0.273442	−	0.961888i	$-0.411838\pi$
$151$	−5.19615	−	3.00000i	−0.422857	−	0.244137i	−0.696299	+	0.717752i	$0.745171\pi$
$152$	−8.00000	−	13.8564i	−0.648886	−	1.12390i
$153$			30.0000i			2.42536i
$154$		0			0
$155$	−8.00000	+	8.00000i	−0.642575	+	0.642575i
$156$		0			0
$157$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$157$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$158$	−19.1244	+	5.12436i	−1.52145	+	0.407672i
$159$	−14.0000	−	24.2487i	−1.11027	−	1.92305i
$160$	16.0000			1.26491
$161$		0			0
$162$	1.00000	+	1.00000i	0.0785674	+	0.0785674i
$163$	−1.83013	+	6.83013i	−0.143347	+	0.534977i	0.856477	+	0.516185i	$0.172648\pi$
$163$	−1.83013	+	6.83013i	−0.143347	+	0.534977i	−0.999823	+	0.0187913i	$0.994018\pi$
$164$	2.00000	−	3.46410i	0.156174	−	0.270501i
$165$	−8.78461	−	32.7846i	−0.683881	−	2.55228i
$166$		0			0
$167$		0			0		1.00000			$0$
$167$		0			0		−1.00000			$\pi$
$168$		0			0
$169$		−	13.0000i		−	1.00000i
$170$	12.0000	+	20.7846i	0.920358	+	1.59411i
$171$	−7.32051	−	27.3205i	−0.559813	−	2.08925i
$172$	13.6603	−	3.66025i	1.04158	−	0.279092i
$173$	−5.85641	+	21.8564i	−0.445254	+	1.66171i	0.270010	+	0.962858i	$0.412973\pi$
$173$	−5.85641	+	21.8564i	−0.445254	+	1.66171i	−0.715264	+	0.698854i	$0.753694\pi$
$174$	−4.00000	+	4.00000i	−0.303239	+	0.303239i
$175$		0			0
$176$	12.0000	−	12.0000i	0.904534	−	0.904534i
$177$	4.00000	+	6.92820i	0.300658	+	0.520756i
$178$	2.19615	+	8.19615i	0.164609	+	0.614328i
$179$	−6.83013	+	1.83013i	−0.510508	+	0.136790i	−0.504872	−	0.863194i	$-0.668460\pi$
$179$	−6.83013	+	1.83013i	−0.510508	+	0.136790i	−0.00563529	+	0.999984i	$0.501794\pi$
$180$	27.3205	+	7.32051i	2.03635	+	0.545638i
$181$	−4.00000	+	4.00000i	−0.297318	+	0.297318i	−0.839962	−	0.542645i	$-0.817423\pi$
$181$	−4.00000	+	4.00000i	−0.297318	+	0.297318i	0.542645	+	0.839962i	$0.317423\pi$
$182$		0			0
$183$		−	24.0000i		−	1.77413i
$184$	−1.46410	+	5.46410i	−0.107935	+	0.402819i
$185$	10.3923	+	6.00000i	0.764057	+	0.441129i
$186$	−13.8564	−	8.00000i	−1.01600	−	0.586588i
$187$	24.5885	+	6.58846i	1.79809	+	0.481796i
$188$			16.0000i			1.16692i
$189$		0			0
$190$	−16.0000	−	16.0000i	−1.16076	−	1.16076i
$191$	−11.0000	−	19.0526i	−0.795932	−	1.37859i	−0.922246	−	0.386604i	$-0.873648\pi$
$191$	−11.0000	−	19.0526i	−0.795932	−	1.37859i	0.126314	−	0.991990i	$-0.459685\pi$
$192$	5.85641	+	21.8564i	0.422650	+	1.57735i
$193$	12.0000	−	20.7846i	0.863779	−	1.49611i	−0.00447566	−	0.999990i	$-0.501425\pi$
$193$	12.0000	−	20.7846i	0.863779	−	1.49611i	0.868255	−	0.496119i	$-0.165242\pi$
$194$	−2.19615	+	8.19615i	−0.157675	+	0.588449i
$195$		0			0
$196$		0			0
$197$	−11.0000	+	11.0000i	−0.783718	+	0.783718i	−0.980456	−	0.196738i	$-0.936965\pi$
$197$	−11.0000	+	11.0000i	−0.783718	+	0.783718i	0.196738	+	0.980456i	$0.436965\pi$
$198$	25.9808	−	15.0000i	1.84637	−	1.06600i
$199$	17.3205	+	10.0000i	1.22782	+	0.708881i	0.966573	−	0.256391i	$-0.0825336\pi$
$199$	17.3205	+	10.0000i	1.22782	+	0.708881i	0.261245	+	0.965272i	$0.415867\pi$
$200$	8.19615	−	2.19615i	0.579555	−	0.155291i
$201$	−17.3205	+	10.0000i	−1.22169	+	0.705346i
$202$	4.00000			0.281439
$203$		0			0
$204$	−24.0000	+	24.0000i	−1.68034	+	1.68034i
$205$	1.46410	−	5.46410i	0.102257	−	0.381629i
$206$		0			0
$207$	−5.00000	+	8.66025i	−0.347524	+	0.601929i
$208$		0			0
$209$	−24.0000			−1.66011
$210$		0			0
$211$	−9.00000	−	9.00000i	−0.619586	−	0.619586i	0.325840	−	0.945425i	$-0.394353\pi$
$211$	−9.00000	−	9.00000i	−0.619586	−	0.619586i	−0.945425	+	0.325840i	$0.894353\pi$
$212$	5.12436	−	19.1244i	0.351942	−	1.31347i
$213$	−5.85641	−	21.8564i	−0.401274	−	1.49758i
$214$	5.00000	−	8.66025i	0.341793	−	0.592003i
$215$	17.3205	−	10.0000i	1.18125	−	0.681994i
$216$			16.0000i			1.08866i
$217$		0			0
$218$			6.00000i			0.406371i
$219$	−27.3205	−	7.32051i	−1.84615	−	0.494674i
$220$	12.0000	−	20.7846i	0.809040	−	1.40130i
$221$		0			0
$222$	−4.39230	+	16.3923i	−0.294792	+	1.10018i
$223$	−4.00000			−0.267860			−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000			−0.267860			−0.133930	+	0.990991i	$0.542760\pi$
$224$		0			0
$225$	15.0000			1.00000
$226$	4.39230	−	16.3923i	0.292172	−	1.09040i
$227$	5.46410	−	1.46410i	0.362665	−	0.0971758i	−0.0728849	−	0.997340i	$-0.523221\pi$
$227$	5.46410	−	1.46410i	0.362665	−	0.0971758i	0.435550	+	0.900165i	$0.356554\pi$
$228$	16.0000	−	27.7128i	1.05963	−	1.83533i
$229$	16.3923	+	4.39230i	1.08323	+	0.290252i	0.755920	−	0.654664i	$-0.227190\pi$
$229$	16.3923	+	4.39230i	1.08323	+	0.290252i	0.327314	+	0.944916i	$0.393857\pi$
$230$			8.00000i			0.527504i
$231$		0			0
$232$	−4.00000			−0.262613
$233$	6.92820	−	4.00000i	0.453882	−	0.262049i	−0.255586	−	0.966786i	$-0.582269\pi$
$233$	6.92820	−	4.00000i	0.453882	−	0.262049i	0.709468	+	0.704737i	$0.248935\pi$
$234$		0			0
$235$	5.85641	+	21.8564i	0.382030	+	1.42575i
$236$	−1.46410	+	5.46410i	−0.0953049	+	0.355683i
$237$	−28.0000	−	28.0000i	−1.81880	−	1.81880i
$238$		0			0
$239$	−8.00000			−0.517477			−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000			−0.517477			−0.258738	+	0.965947i	$0.583307\pi$
$240$	16.0000	+	27.7128i	1.03280	+	1.78885i
$241$	−11.0000	+	19.0526i	−0.708572	+	1.22728i	0.256814	+	0.966461i	$0.417327\pi$
$241$	−11.0000	+	19.0526i	−0.708572	+	1.22728i	−0.965387	+	0.260822i	$0.916006\pi$
$242$	−2.56218	−	9.56218i	−0.164703	−	0.614680i
$243$	3.66025	−	13.6603i	0.234805	−	0.876306i
$244$	12.0000	−	12.0000i	0.768221	−	0.768221i
$245$		0			0
$246$	8.00000			0.510061
$247$		0			0
$248$	−2.92820	−	10.9282i	−0.185941	−	0.693942i
$249$		0			0
$250$	−6.92820	+	4.00000i	−0.438178	+	0.252982i
$251$	−4.00000	+	4.00000i	−0.252478	+	0.252478i	−0.821986	−	0.569508i	$-0.807134\pi$
$251$	−4.00000	+	4.00000i	−0.252478	+	0.252478i	0.569508	+	0.821986i	$0.307134\pi$
$252$		0			0
$253$	6.00000	+	6.00000i	0.377217	+	0.377217i
$254$	−2.92820	+	10.9282i	−0.183732	+	0.685696i
$255$	−24.0000	+	41.5692i	−1.50294	+	2.60317i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−5.00000	−	8.66025i	−0.311891	−	0.540212i	0.666880	−	0.745165i	$-0.267629\pi$
$257$	−5.00000	−	8.66025i	−0.311891	−	0.540212i	−0.978772	+	0.204953i	$0.934296\pi$
$258$	20.0000	+	20.0000i	1.24515	+	1.24515i
$259$		0			0
$260$		0			0
$261$	−6.83013	−	1.83013i	−0.422774	−	0.113282i
$262$	−20.7846	−	12.0000i	−1.28408	−	0.741362i
$263$	20.7846	+	12.0000i	1.28163	+	0.739952i	0.977147	−	0.212565i	$-0.0681817\pi$
$263$	20.7846	+	12.0000i	1.28163	+	0.739952i	0.304487	+	0.952517i	$0.401515\pi$
$264$	32.7846	+	8.78461i	2.01775	+	0.540655i
$265$		−	28.0000i		−	1.72003i
$266$		0			0
$267$	−12.0000	+	12.0000i	−0.734388	+	0.734388i
$268$	−13.6603	−	3.66025i	−0.834433	−	0.223586i
$269$	−21.8564	+	5.85641i	−1.33261	+	0.357071i	−0.853687	−	0.520786i	$-0.825639\pi$
$269$	−21.8564	+	5.85641i	−1.33261	+	0.357071i	−0.478922	+	0.877858i	$0.658972\pi$
$270$	5.85641	+	21.8564i	0.356410	+	1.33014i
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	−0.513905	+	0.857847i	$0.671801\pi$
$272$	−24.0000			−1.45521
$273$		0			0
$274$	−12.0000	+	12.0000i	−0.724947	+	0.724947i
$275$	3.29423	−	12.2942i	0.198649	−	0.741370i
$276$	−10.9282	+	2.92820i	−0.657801	+	0.176257i
$277$	0.366025	+	1.36603i	0.0219923	+	0.0820765i	0.976050	−	0.217547i	$-0.0698056\pi$
$277$	0.366025	+	1.36603i	0.0219923	+	0.0820765i	−0.954057	+	0.299624i	$0.903139\pi$
$278$	12.0000	+	20.7846i	0.719712	+	1.24658i
$279$		−	20.0000i		−	1.19737i
$280$		0			0
$281$		−	24.0000i		−	1.43172i	−0.698244	−	0.715860i	$-0.746035\pi$
$281$		−	24.0000i		−	1.43172i	0.698244	−	0.715860i	$-0.253965\pi$
$282$	−27.7128	+	16.0000i	−1.65027	+	0.952786i
$283$	2.19615	+	8.19615i	0.130548	+	0.487211i	0.999977	−	0.00684749i	$-0.00217964\pi$
$283$	2.19615	+	8.19615i	0.130548	+	0.487211i	−0.869429	+	0.494058i	$0.835513\pi$
$284$	8.00000	−	13.8564i	0.474713	−	0.822226i
$285$	11.7128	−	43.7128i	0.693807	−	2.58932i
$286$		0			0
$287$		0			0
$288$	−20.0000	+	20.0000i	−1.17851	+	1.17851i
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$	−5.46410	+	1.46410i	−0.320863	+	0.0859750i
$291$	−16.3923	+	4.39230i	−0.960934	+	0.257481i
$292$	−10.0000	−	17.3205i	−0.585206	−	1.01361i
$293$	10.0000	−	10.0000i	0.584206	−	0.584206i	−0.351850	−	0.936056i	$-0.614447\pi$
$293$	10.0000	−	10.0000i	0.584206	−	0.584206i	0.936056	+	0.351850i	$0.114447\pi$
$294$		0			0
$295$			8.00000i			0.465778i
$296$	−10.3923	+	6.00000i	−0.604040	+	0.348743i
$297$	20.7846	+	12.0000i	1.20605	+	0.696311i
$298$	−13.0000	+	22.5167i	−0.753070	+	1.30436i
$299$		0			0
$300$	12.0000	+	12.0000i	0.692820	+	0.692820i
$301$		0			0
$302$	6.00000	−	6.00000i	0.345261	−	0.345261i
$303$	4.00000	+	6.92820i	0.229794	+	0.398015i
$304$	21.8564	−	5.85641i	1.25355	−	0.335888i
$305$	12.0000	−	20.7846i	0.687118	−	1.19012i
$306$	−40.9808	−	10.9808i	−2.34271	−	0.627728i
$307$	8.00000	+	8.00000i	0.456584	+	0.456584i	0.897532	−	0.440948i	$-0.145358\pi$
$307$	8.00000	+	8.00000i	0.456584	+	0.456584i	−0.440948	+	0.897532i	$0.645358\pi$
$308$		0			0
$309$		0			0
$310$	−8.00000	−	13.8564i	−0.454369	−	0.786991i
$311$	3.46410	+	2.00000i	0.196431	+	0.113410i	0.594990	−	0.803733i	$-0.297156\pi$
$311$	3.46410	+	2.00000i	0.196431	+	0.113410i	−0.398559	+	0.917143i	$0.630489\pi$
$312$		0			0
$313$	−1.73205	+	1.00000i	−0.0979013	+	0.0565233i	−0.548151	−	0.836379i	$-0.684668\pi$
$313$	−1.73205	+	1.00000i	−0.0979013	+	0.0565233i	0.450250	+	0.892903i	$0.351335\pi$
$314$		0			0
$315$		0			0
$316$		−	28.0000i		−	1.57512i
$317$	−5.49038	+	20.4904i	−0.308371	+	1.15085i	0.621634	+	0.783307i	$0.286469\pi$
$317$	−5.49038	+	20.4904i	−0.308371	+	1.15085i	−0.930005	+	0.367547i	$0.880198\pi$
$318$	38.2487	−	10.2487i	2.14488	−	0.574719i
$319$	−3.00000	+	5.19615i	−0.167968	+	0.290929i
$320$	−5.85641	+	21.8564i	−0.327383	+	1.22181i
$321$	20.0000			1.11629
$322$		0			0
$323$	24.0000	+	24.0000i	1.33540	+	1.33540i
$324$	−1.73205	+	1.00000i	−0.0962250	+	0.0555556i
$325$		0			0
$326$	−8.66025	−	5.00000i	−0.479647	−	0.276924i
$327$	−10.3923	+	6.00000i	−0.574696	+	0.331801i
$328$	4.00000	+	4.00000i	0.220863	+	0.220863i
$329$		0			0
$330$	48.0000			2.64231
$331$	20.4904	+	5.49038i	1.12625	+	0.301779i	0.773411	−	0.633904i	$-0.218549\pi$
$331$	20.4904	+	5.49038i	1.12625	+	0.301779i	0.352842	+	0.935683i	$0.385215\pi$
$332$		0			0
$333$	−20.4904	+	5.49038i	−1.12287	+	0.300871i
$334$		0			0
$335$	−20.0000			−1.09272
$336$		0			0
$337$	−8.00000			−0.435788			−0.217894	−	0.975972i	$-0.569919\pi$
$337$	−8.00000			−0.435788			−0.217894	+	0.975972i	$0.569919\pi$
$338$	17.7583	+	4.75833i	0.965926	+	0.258819i
$339$	32.7846	−	8.78461i	1.78062	−	0.477115i
$340$	−32.7846	+	8.78461i	−1.77800	+	0.476412i
$341$	−16.3923	−	4.39230i	−0.887693	−	0.237857i
$342$	40.0000			2.16295
$343$		0			0
$344$			20.0000i			1.07833i
$345$	−13.8564	+	8.00000i	−0.746004	+	0.430706i
$346$	−27.7128	−	16.0000i	−1.48985	−	0.860165i
$347$	−4.75833	−	17.7583i	−0.255441	−	0.953317i	−0.967845	−	0.251548i	$-0.919060\pi$
$347$	−4.75833	−	17.7583i	−0.255441	−	0.953317i	0.712404	−	0.701769i	$-0.247606\pi$
$348$	−4.00000	−	6.92820i	−0.214423	−	0.371391i
$349$	−16.0000	−	16.0000i	−0.856460	−	0.856460i	0.134459	−	0.990919i	$-0.457070\pi$
$349$	−16.0000	−	16.0000i	−0.856460	−	0.856460i	−0.990919	+	0.134459i	$0.957070\pi$
$350$		0			0
$351$		0			0
$352$	12.0000	+	20.7846i	0.639602	+	1.10782i
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	−0.520689	−	0.853746i	$-0.674325\pi$
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	0.999711	+	0.0240566i	$0.00765819\pi$
$354$	−10.9282	+	2.92820i	−0.580827	+	0.155632i
$355$	5.85641	−	21.8564i	0.310826	−	1.16002i
$356$	−12.0000			−0.635999
$357$		0			0
$358$		−	10.0000i		−	0.528516i
$359$	−19.0526	+	11.0000i	−1.00556	+	0.580558i	−0.909887	−	0.414855i	$-0.863832\pi$
$359$	−19.0526	+	11.0000i	−1.00556	+	0.580558i	−0.0956683	+	0.995413i	$0.530499\pi$
$360$	−20.0000	+	34.6410i	−1.05409	+	1.82574i
$361$	−11.2583	−	6.50000i	−0.592544	−	0.342105i
$362$	−4.00000	−	6.92820i	−0.210235	−	0.364138i
$363$	14.0000	−	14.0000i	0.734809	−	0.734809i
$364$		0			0
$365$	−20.0000	−	20.0000i	−1.04685	−	1.04685i
$366$	32.7846	+	8.78461i	1.71368	+	0.459179i
$367$	−8.00000	+	13.8564i	−0.417597	+	0.723299i	−0.995697	−	0.0926670i	$-0.970461\pi$
$367$	−8.00000	+	13.8564i	−0.417597	+	0.723299i	0.578101	+	0.815966i	$0.303794\pi$
$368$	−6.92820	−	4.00000i	−0.361158	−	0.208514i
$369$	5.00000	+	8.66025i	0.260290	+	0.450835i
$370$	−12.0000	+	12.0000i	−0.623850	+	0.623850i
$371$		0			0
$372$	16.0000	−	16.0000i	0.829561	−	0.829561i
$373$	−6.83013	−	1.83013i	−0.353651	−	0.0947604i	0.0776200	−	0.996983i	$-0.475268\pi$
$373$	−6.83013	−	1.83013i	−0.353651	−	0.0947604i	−0.431271	+	0.902223i	$0.641935\pi$
$374$	−18.0000	+	31.1769i	−0.930758	+	1.61212i
$375$	−13.8564	−	8.00000i	−0.715542	−	0.413118i
$376$	−21.8564	−	5.85641i	−1.12716	−	0.302021i
$377$		0			0
$378$		0			0
$379$	17.0000	−	17.0000i	0.873231	−	0.873231i	−0.119592	−	0.992823i	$-0.538159\pi$
$379$	17.0000	−	17.0000i	0.873231	−	0.873231i	0.992823	+	0.119592i	$0.0381586\pi$
$380$	27.7128	−	16.0000i	1.42164	−	0.820783i
$381$	−21.8564	+	5.85641i	−1.11974	+	0.300033i
$382$	30.0526	−	8.05256i	1.53762	−	0.412005i
$383$	−8.00000	−	13.8564i	−0.408781	−	0.708029i	0.585973	−	0.810331i	$-0.300713\pi$
$383$	−8.00000	−	13.8564i	−0.408781	−	0.708029i	−0.994753	+	0.102302i	$0.967379\pi$
$384$	−32.0000			−1.63299
$385$		0			0
$386$	24.0000	+	24.0000i	1.22157	+	1.22157i
$387$	−9.15064	+	34.1506i	−0.465153	+	1.73597i
$388$	−10.3923	−	6.00000i	−0.527589	−	0.304604i
$389$	6.95448	+	25.9545i	0.352606	+	1.31594i	0.883470	+	0.468487i	$0.155201\pi$
$389$	6.95448	+	25.9545i	0.352606	+	1.31594i	−0.530864	+	0.847457i	$0.678132\pi$
$390$		0			0
$391$		−	12.0000i		−	0.606866i
$392$		0			0
$393$		−	48.0000i		−	2.42128i
$394$	−11.0000	−	19.0526i	−0.554172	−	0.959854i
$395$	−10.2487	−	38.2487i	−0.515669	−	1.92450i
$396$	10.9808	+	40.9808i	0.551804	+	2.05936i
$397$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$397$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$398$	−20.0000	+	20.0000i	−1.00251	+	1.00251i
$399$		0			0
$400$			12.0000i			0.600000i
$401$	2.00000	+	3.46410i	0.0998752	+	0.172989i	0.911633	−	0.411005i	$-0.134822\pi$
$401$	2.00000	+	3.46410i	0.0998752	+	0.172989i	−0.811758	+	0.583994i	$0.801489\pi$
$402$	−7.32051	−	27.3205i	−0.365114	−	1.36262i
$403$		0			0
$404$	−1.46410	+	5.46410i	−0.0728418	+	0.271849i
$405$	−2.00000	+	2.00000i	−0.0993808	+	0.0993808i
$406$		0			0
$407$			18.0000i			0.892227i
$408$	−24.0000	−	41.5692i	−1.18818	−	2.05798i
$409$	−8.66025	−	5.00000i	−0.428222	−	0.247234i	0.270367	−	0.962757i	$-0.412855\pi$
$409$	−8.66025	−	5.00000i	−0.428222	−	0.247234i	−0.698589	+	0.715523i	$0.746188\pi$
$410$	6.92820	+	4.00000i	0.342160	+	0.197546i
$411$	−32.7846	−	8.78461i	−1.61715	−	0.433313i
$412$		0			0
$413$		0			0
$414$	−10.0000	−	10.0000i	−0.491473	−	0.491473i
$415$		0			0
$416$		0			0
$417$	−24.0000	+	41.5692i	−1.17529	+	2.03565i
$418$	8.78461	−	32.7846i	0.429669	−	1.60355i
$419$	10.0000	+	10.0000i	0.488532	+	0.488532i	0.907843	−	0.419311i	$-0.137728\pi$
$419$	10.0000	+	10.0000i	0.488532	+	0.488532i	−0.419311	+	0.907843i	$0.637728\pi$
$420$		0			0
$421$	−25.0000	+	25.0000i	−1.21843	+	1.21843i	−0.250242	+	0.968183i	$0.580510\pi$
$421$	−25.0000	+	25.0000i	−1.21843	+	1.21843i	−0.968183	+	0.250242i	$0.919490\pi$
$422$	15.5885	−	9.00000i	0.758834	−	0.438113i
$423$	−34.6410	−	20.0000i	−1.68430	−	0.972433i
$424$	24.2487	+	14.0000i	1.17762	+	0.679900i
$425$	−15.5885	+	9.00000i	−0.756151	+	0.436564i
$426$	32.0000			1.55041
$427$		0			0
$428$	10.0000	+	10.0000i	0.483368	+	0.483368i
$429$		0			0
$430$	7.32051	+	27.3205i	0.353026	+	1.31751i
$431$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$431$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$432$	−21.8564	−	5.85641i	−1.05157	−	0.281766i
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$		0			0
$435$	−8.00000	−	8.00000i	−0.383571	−	0.383571i
$436$	−8.19615	−	2.19615i	−0.392525	−	0.105177i
$437$	2.92820	+	10.9282i	0.140075	+	0.522767i
$438$	20.0000	−	34.6410i	0.955637	−	1.65521i
$439$	−20.7846	+	12.0000i	−0.991995	+	0.572729i	−0.905870	−	0.423556i	$-0.860782\pi$
$439$	−20.7846	+	12.0000i	−0.991995	+	0.572729i	−0.0861252	+	0.996284i	$0.527448\pi$
$440$	24.0000	+	24.0000i	1.14416	+	1.14416i
$441$		0			0
$442$		0			0
$443$	23.2224	+	6.22243i	1.10333	+	0.295637i	0.764120	−	0.645074i	$-0.223173\pi$
$443$	23.2224	+	6.22243i	1.10333	+	0.295637i	0.339211	+	0.940710i	$0.389840\pi$
$444$	−20.7846	−	12.0000i	−0.986394	−	0.569495i
$445$	−16.3923	+	4.39230i	−0.777070	+	0.208215i
$446$	1.46410	−	5.46410i	0.0693272	−	0.258733i
$447$	−52.0000			−2.45952
$448$		0			0
$449$	34.0000			1.60456			0.802280	−	0.596948i	$-0.203620\pi$
$449$	34.0000			1.60456			0.802280	+	0.596948i	$0.203620\pi$
$450$	−5.49038	+	20.4904i	−0.258819	+	0.965926i
$451$	8.19615	−	2.19615i	0.385942	−	0.103413i
$452$	20.7846	+	12.0000i	0.977626	+	0.564433i
$453$	16.3923	+	4.39230i	0.770178	+	0.206368i
$454$			8.00000i			0.375459i
$455$		0			0
$456$	32.0000	+	32.0000i	1.49854	+	1.49854i
$457$	22.5167	−	13.0000i	1.05328	−	0.608114i	0.129718	−	0.991551i	$-0.458593\pi$
$457$	22.5167	−	13.0000i	1.05328	−	0.608114i	0.923567	+	0.383437i	$0.125260\pi$
$458$	−12.0000	+	20.7846i	−0.560723	+	0.971201i
$459$	−8.78461	−	32.7846i	−0.410030	−	1.53025i
$460$	−10.9282	−	2.92820i	−0.509530	−	0.136528i
$461$	28.0000	+	28.0000i	1.30409	+	1.30409i	0.925609	+	0.378481i	$0.123553\pi$
$461$	28.0000	+	28.0000i	1.30409	+	1.30409i	0.378481	+	0.925609i	$0.376447\pi$
$462$		0			0
$463$	14.0000			0.650635			0.325318	−	0.945605i	$-0.394529\pi$
$463$	14.0000			0.650635			0.325318	+	0.945605i	$0.394529\pi$
$464$	1.46410	−	5.46410i	0.0679692	−	0.253665i
$465$	16.0000	−	27.7128i	0.741982	−	1.28515i
$466$	2.92820	+	10.9282i	0.135646	+	0.506239i
$467$	5.85641	−	21.8564i	0.271002	−	1.01139i	−0.687471	−	0.726212i	$-0.741279\pi$
$467$	5.85641	−	21.8564i	0.271002	−	1.01139i	0.958473	−	0.285182i	$-0.0920541\pi$
$468$		0			0
$469$		0			0
$470$	−32.0000			−1.47605
$471$		0			0
$472$	−6.92820	−	4.00000i	−0.318896	−	0.184115i
$473$	25.9808	+	15.0000i	1.19460	+	0.689701i
$474$	48.4974	−	28.0000i	2.22756	−	1.28608i
$475$	12.0000	−	12.0000i	0.550598	−	0.550598i
$476$		0			0
$477$	35.0000	+	35.0000i	1.60254	+	1.60254i
$478$	2.92820	−	10.9282i	0.133933	−	0.499844i
$479$	−4.00000	+	6.92820i	−0.182765	+	0.316558i	−0.942821	−	0.333300i	$-0.891838\pi$
$479$	−4.00000	+	6.92820i	−0.182765	+	0.316558i	0.760056	+	0.649857i	$0.225171\pi$
$480$	−43.7128	+	11.7128i	−1.99521	+	0.534614i
$481$		0			0
$482$	−22.0000	−	22.0000i	−1.00207	−	1.00207i
$483$		0			0
$484$	14.0000			0.636364
$485$	−16.3923	−	4.39230i	−0.744336	−	0.199444i
$486$	17.3205	+	10.0000i	0.785674	+	0.453609i
$487$	−1.73205	−	1.00000i	−0.0784867	−	0.0453143i	0.460243	−	0.887793i	$-0.347762\pi$
$487$	−1.73205	−	1.00000i	−0.0784867	−	0.0453143i	−0.538730	+	0.842479i	$0.681096\pi$
$488$	12.0000	+	20.7846i	0.543214	+	0.940875i
$489$		−	20.0000i		−	0.904431i
$490$		0			0
$491$	−11.0000	+	11.0000i	−0.496423	+	0.496423i	−0.910323	−	0.413900i	$-0.864166\pi$
$491$	−11.0000	+	11.0000i	−0.496423	+	0.496423i	0.413900	+	0.910323i	$0.364166\pi$
$492$	−2.92820	+	10.9282i	−0.132014	+	0.492681i
$493$	8.19615	−	2.19615i	0.369136	−	0.0989097i
$494$		0			0
$495$	30.0000	+	51.9615i	1.34840	+	2.33550i
$496$	16.0000			0.718421
$497$		0			0
$498$		0			0
$499$	−5.49038	+	20.4904i	−0.245783	+	0.917275i	0.727205	+	0.686420i	$0.240819\pi$
$499$	−5.49038	+	20.4904i	−0.245783	+	0.917275i	−0.972988	+	0.230855i	$0.925848\pi$
$500$	−2.92820	−	10.9282i	−0.130953	−	0.488724i
$501$		0			0
$502$	−4.00000	−	6.92820i	−0.178529	−	0.309221i
$503$			8.00000i			0.356702i	0.983967	+	0.178351i	$0.0570763\pi$
$503$			8.00000i			0.356702i	−0.983967	+	0.178351i	$0.942924\pi$
$504$		0			0
$505$			8.00000i			0.355995i
$506$	−10.3923	+	6.00000i	−0.461994	+	0.266733i
$507$	9.51666	+	35.5167i	0.422650	+	1.57735i
$508$	−13.8564	−	8.00000i	−0.614779	−	0.354943i
$509$	4.39230	−	16.3923i	0.194685	−	0.726576i	−0.797663	−	0.603104i	$-0.793930\pi$
$509$	4.39230	−	16.3923i	0.194685	−	0.726576i	0.992348	−	0.123472i	$-0.0394030\pi$
$510$	−48.0000	−	48.0000i	−2.12548	−	2.12548i
$511$		0			0
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$	16.0000	+	27.7128i	0.706417	+	1.22355i
$514$	13.6603	−	3.66025i	0.602528	−	0.161447i
$515$		0			0
$516$	−34.6410	+	20.0000i	−1.52499	+	0.880451i
$517$	−24.0000	+	24.0000i	−1.05552	+	1.05552i
$518$		0			0
$519$		−	64.0000i		−	2.80929i
$520$		0			0
$521$	−5.19615	−	3.00000i	−0.227648	−	0.131432i	0.381839	−	0.924229i	$-0.375291\pi$
$521$	−5.19615	−	3.00000i	−0.227648	−	0.131432i	−0.609486	+	0.792797i	$0.708624\pi$
$522$	5.00000	−	8.66025i	0.218844	−	0.379049i
$523$	35.5167	+	9.51666i	1.55304	+	0.416135i	0.930450	−	0.366418i	$-0.119416\pi$
$523$	35.5167	+	9.51666i	1.55304	+	0.416135i	0.622585	+	0.782552i	$0.286083\pi$
$524$	24.0000	−	24.0000i	1.04844	−	1.04844i
$525$		0			0
$526$	−24.0000	+	24.0000i	−1.04645	+	1.04645i
$527$	12.0000	+	20.7846i	0.522728	+	0.905392i
$528$	−24.0000	+	41.5692i	−1.04447	+	1.80907i
$529$	−9.50000	+	16.4545i	−0.413043	+	0.715412i
$530$	38.2487	+	10.2487i	1.66142	+	0.445176i
$531$	−10.0000	−	10.0000i	−0.433963	−	0.433963i
$532$		0			0
$533$		0			0
$534$	−12.0000	−	20.7846i	−0.519291	−	0.899438i
$535$	17.3205	+	10.0000i	0.748831	+	0.432338i
$536$	10.0000	−	17.3205i	0.431934	−	0.748132i
$537$	17.3205	−	10.0000i	0.747435	−	0.431532i
$538$		−	32.0000i		−	1.37962i
$539$		0			0
$540$	−32.0000			−1.37706
$541$	−10.6147	+	39.6147i	−0.456363	+	1.70317i	0.227686	+	0.973735i	$0.426884\pi$
$541$	−10.6147	+	39.6147i	−0.456363	+	1.70317i	−0.684049	+	0.729436i	$0.739783\pi$
$542$	−21.8564	+	5.85641i	−0.938813	+	0.251554i
$543$	8.00000	−	13.8564i	0.343313	−	0.594635i
$544$	8.78461	−	32.7846i	0.376637	−	1.40563i
$545$	−12.0000			−0.514024
$546$		0			0
$547$	19.0000	+	19.0000i	0.812381	+	0.812381i	0.984990	−	0.172609i	$-0.0552197\pi$
$547$	19.0000	+	19.0000i	0.812381	+	0.812381i	−0.172609	+	0.984990i	$0.555220\pi$
$548$	−12.0000	−	20.7846i	−0.512615	−	0.887875i
$549$	10.9808	+	40.9808i	0.468648	+	1.74902i
$550$	15.5885	+	9.00000i	0.664694	+	0.383761i
$551$	−6.92820	+	4.00000i	−0.295151	+	0.170406i
$552$		−	16.0000i		−	0.681005i
$553$		0			0
$554$	−2.00000			−0.0849719
$555$	−32.7846	−	8.78461i	−1.39163	−	0.372886i
$556$	−32.7846	+	8.78461i	−1.39038	+	0.372550i
$557$	−20.4904	+	5.49038i	−0.868205	+	0.232635i	−0.665312	−	0.746566i	$-0.731701\pi$
$557$	−20.4904	+	5.49038i	−0.868205	+	0.232635i	−0.202894	+	0.979201i	$0.565035\pi$
$558$	27.3205	+	7.32051i	1.15657	+	0.309902i
$559$		0			0
$560$		0			0
$561$	−72.0000			−3.03984
$562$	32.7846	+	8.78461i	1.38294	+	0.370556i
$563$	−30.0526	+	8.05256i	−1.26656	+	0.339375i	−0.828714	−	0.559673i	$-0.810927\pi$
$563$	−30.0526	+	8.05256i	−1.26656	+	0.339375i	−0.437851	+	0.899048i	$0.644260\pi$
$564$	−11.7128	−	43.7128i	−0.493198	−	1.84064i
$565$	32.7846	+	8.78461i	1.37926	+	0.369571i
$566$	−12.0000			−0.504398
$567$		0			0
$568$	16.0000	+	16.0000i	0.671345	+	0.671345i
$569$	39.8372	−	23.0000i	1.67006	−	0.964210i	0.702461	−	0.711722i	$-0.252085\pi$
$569$	39.8372	−	23.0000i	1.67006	−	0.964210i	0.967600	−	0.252488i	$-0.0812488\pi$
$570$	55.4256	+	32.0000i	2.32152	+	1.34033i
$571$	−7.68653	−	28.6865i	−0.321671	−	1.20049i	−0.917616	−	0.397468i	$-0.869889\pi$
$571$	−7.68653	−	28.6865i	−0.321671	−	1.20049i	0.595944	−	0.803026i	$-0.296778\pi$
$572$		0			0
$573$	44.0000	+	44.0000i	1.83813	+	1.83813i
$574$		0			0
$575$	−6.00000			−0.250217
$576$	−20.0000	−	34.6410i	−0.833333	−	1.44338i
$577$	−13.0000	+	22.5167i	−0.541197	+	0.937381i	0.457639	+	0.889138i	$0.348695\pi$
$577$	−13.0000	+	22.5167i	−0.541197	+	0.937381i	−0.998836	+	0.0482425i	$0.984638\pi$
$578$	25.9545	−	6.95448i	1.07956	−	0.289268i
$579$	−17.5692	+	65.5692i	−0.730152	+	2.72496i
$580$		−	8.00000i		−	0.332182i
$581$		0			0
$582$		−	24.0000i		−	0.994832i
$583$	36.3731	−	21.0000i	1.50642	−	0.869731i
$584$	27.3205	−	7.32051i	1.13053	−	0.302925i
$585$		0			0
$586$	10.0000	+	17.3205i	0.413096	+	0.715504i
$587$	−8.00000	+	8.00000i	−0.330195	+	0.330195i	−0.852661	−	0.522465i	$-0.825012\pi$
$587$	−8.00000	+	8.00000i	−0.330195	+	0.330195i	0.522465	+	0.852661i	$0.325012\pi$
$588$		0			0
$589$	−16.0000	−	16.0000i	−0.659269	−	0.659269i
$590$	−10.9282	−	2.92820i	−0.449907	−	0.120552i
$591$	22.0000	−	38.1051i	0.904959	−	1.56744i
$592$	−4.39230	−	16.3923i	−0.180523	−	0.673720i
$593$	−11.0000	−	19.0526i	−0.451716	−	0.782395i	0.546777	−	0.837278i	$-0.315855\pi$
$593$	−11.0000	−	19.0526i	−0.451716	−	0.782395i	−0.998493	+	0.0548835i	$0.982521\pi$
$594$	−24.0000	+	24.0000i	−0.984732	+	0.984732i
$595$		0			0
$596$	−26.0000	−	26.0000i	−1.06500	−	1.06500i
$597$	−54.6410	−	14.6410i	−2.23631	−	0.599217i
$598$		0			0
$599$	−6.92820	−	4.00000i	−0.283079	−	0.163436i	0.351738	−	0.936099i	$-0.385591\pi$
$599$	−6.92820	−	4.00000i	−0.283079	−	0.163436i	−0.634816	+	0.772663i	$0.718924\pi$
$600$	−20.7846	+	12.0000i	−0.848528	+	0.489898i
$601$		−	10.0000i		−	0.407909i	−0.978980	−	0.203954i	$-0.934621\pi$
$601$		−	10.0000i		−	0.407909i	0.978980	−	0.203954i	$-0.0653794\pi$
$602$		0			0
$603$	25.0000	−	25.0000i	1.01808	−	1.01808i
$604$	6.00000	+	10.3923i	0.244137	+	0.422857i
$605$	19.1244	−	5.12436i	0.777516	−	0.208335i
$606$	−10.9282	+	2.92820i	−0.443928	+	0.118950i
$607$	10.0000	+	17.3205i	0.405887	+	0.703018i	0.994424	−	0.105453i	$-0.0336291\pi$
$607$	10.0000	+	17.3205i	0.405887	+	0.703018i	−0.588537	+	0.808470i	$0.700296\pi$
$608$			32.0000i			1.29777i
$609$		0			0
$610$	24.0000	+	24.0000i	0.971732	+	0.971732i
$611$		0			0
$612$	30.0000	−	51.9615i	1.21268	−	2.10042i
$613$	−5.49038	−	20.4904i	−0.221754	−	0.827599i	−0.983679	−	0.179933i	$-0.942412\pi$
$613$	−5.49038	−	20.4904i	−0.221754	−	0.827599i	0.761924	−	0.647666i	$-0.224255\pi$
$614$	−13.8564	+	8.00000i	−0.559199	+	0.322854i
$615$			16.0000i			0.645182i
$616$		0			0
$617$			6.00000i			0.241551i	0.992680	+	0.120775i	$0.0385381\pi$
$617$			6.00000i			0.241551i	−0.992680	+	0.120775i	$0.961462\pi$
$618$		0			0
$619$	−6.58846	−	24.5885i	−0.264812	−	0.988294i	−0.962365	−	0.271760i	$-0.912394\pi$
$619$	−6.58846	−	24.5885i	−0.264812	−	0.988294i	0.697553	−	0.716534i	$-0.254272\pi$
$620$	21.8564	−	5.85641i	0.877774	−	0.235199i
$621$	2.92820	−	10.9282i	0.117505	−	0.438534i
$622$	−4.00000	+	4.00000i	−0.160385	+	0.160385i
$623$		0			0
$624$		0			0
$625$	−15.5000	−	26.8468i	−0.620000	−	1.07387i
$626$	−0.732051	−	2.73205i	−0.0292586	−	0.109195i
$627$	65.5692	−	17.5692i	2.61858	−	0.701647i
$628$		0			0
$629$	18.0000	−	18.0000i	0.717707	−	0.717707i
$630$		0			0
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$	38.2487	+	10.2487i	1.52145	+	0.407672i
$633$	31.1769	+	18.0000i	1.23917	+	0.715436i
$634$	−25.9808	−	15.0000i	−1.03183	−	0.595726i
$635$	−21.8564	−	5.85641i	−0.867345	−	0.232404i
$636$			56.0000i			2.22054i
$637$		0			0
$638$	−6.00000	−	6.00000i	−0.237542	−	0.237542i
$639$	20.0000	+	34.6410i	0.791188	+	1.37038i
$640$	−27.7128	−	16.0000i	−1.09545	−	0.632456i
$641$	−22.0000	+	38.1051i	−0.868948	+	1.50506i	−0.00587459	+	0.999983i	$0.501870\pi$
$641$	−22.0000	+	38.1051i	−0.868948	+	1.50506i	−0.863073	+	0.505079i	$0.831463\pi$
$642$	−7.32051	+	27.3205i	−0.288917	+	1.07825i
$643$	−26.0000	−	26.0000i	−1.02534	−	1.02534i	−0.999670	−	0.0256694i	$-0.991828\pi$
$643$	−26.0000	−	26.0000i	−1.02534	−	1.02534i	−0.0256694	−	0.999670i	$-0.508172\pi$
$644$		0			0
$645$	−40.0000	+	40.0000i	−1.57500	+	1.57500i
$646$	−41.5692	+	24.0000i	−1.63552	+	0.944267i
$647$	20.7846	+	12.0000i	0.817127	+	0.471769i	0.849425	−	0.527710i	$-0.176949\pi$
$647$	20.7846	+	12.0000i	0.817127	+	0.471769i	−0.0322975	+	0.999478i	$0.510282\pi$
$648$	−0.732051	−	2.73205i	−0.0287577	−	0.107325i
$649$	−10.3923	+	6.00000i	−0.407934	+	0.235521i
$650$		0			0
$651$		0			0
$652$	10.0000	−	10.0000i	0.391630	−	0.391630i
$653$	9.15064	−	34.1506i	0.358092	−	1.33642i	−0.518456	−	0.855104i	$-0.673493\pi$
$653$	9.15064	−	34.1506i	0.358092	−	1.33642i	0.876548	−	0.481314i	$-0.159840\pi$
$654$	−4.39230	−	16.3923i	−0.171753	−	0.640990i
$655$	24.0000	−	41.5692i	0.937758	−	1.62424i
$656$	−6.92820	+	4.00000i	−0.270501	+	0.156174i
$657$	50.0000			1.95069
$658$		0			0
$659$	17.0000	+	17.0000i	0.662226	+	0.662226i	0.955904	−	0.293678i	$-0.0948794\pi$
$659$	17.0000	+	17.0000i	0.662226	+	0.662226i	−0.293678	+	0.955904i	$0.594879\pi$
$660$	−17.5692	+	65.5692i	−0.683881	+	2.55228i
$661$	−10.9808	−	40.9808i	−0.427102	−	1.59397i	−0.759289	−	0.650753i	$-0.774453\pi$
$661$	−10.9808	−	40.9808i	−0.427102	−	1.59397i	0.332187	−	0.943214i	$-0.392213\pi$
$662$	−15.0000	+	25.9808i	−0.582992	+	1.00977i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		−	30.0000i		−	1.16248i
$667$	2.73205	+	0.732051i	0.105785	+	0.0283451i
$668$		0			0
$669$	10.9282	−	2.92820i	0.422509	−	0.113211i
$670$	7.32051	−	27.3205i	0.282816	−	1.05548i
$671$	36.0000			1.38976
$672$		0			0
$673$	26.0000			1.00223			0.501113	−	0.865382i	$-0.332924\pi$
$673$	26.0000			1.00223			0.501113	+	0.865382i	$0.332924\pi$
$674$	2.92820	−	10.9282i	0.112790	−	0.420939i
$675$	−16.3923	+	4.39230i	−0.630940	+	0.169060i
$676$	−13.0000	+	22.5167i	−0.500000	+	0.866025i
$677$	10.9282	+	2.92820i	0.420005	+	0.112540i	0.462631	−	0.886551i	$-0.346906\pi$
$677$	10.9282	+	2.92820i	0.420005	+	0.112540i	−0.0426257	+	0.999091i	$0.513572\pi$
$678$			48.0000i			1.84343i
$679$		0			0
$680$		−	48.0000i		−	1.84072i
$681$	−13.8564	+	8.00000i	−0.530979	+	0.306561i
$682$	12.0000	−	20.7846i	0.459504	−	0.795884i
$683$	1.83013	+	6.83013i	0.0700279	+	0.261348i	0.992060	−	0.125766i	$-0.0401388\pi$
$683$	1.83013	+	6.83013i	0.0700279	+	0.261348i	−0.922032	+	0.387113i	$0.873472\pi$
$684$	−14.6410	+	54.6410i	−0.559813	+	2.08925i
$685$	−24.0000	−	24.0000i	−0.916993	−	0.916993i
$686$		0			0
$687$	−48.0000			−1.83131
$688$	−27.3205	−	7.32051i	−1.04158	−	0.279092i
$689$		0			0
$690$	−5.85641	−	21.8564i	−0.222950	−	0.832059i
$691$	−4.39230	+	16.3923i	−0.167091	+	0.623593i	0.830673	+	0.556760i	$0.187956\pi$
$691$	−4.39230	+	16.3923i	−0.167091	+	0.623593i	−0.997764	+	0.0668322i	$0.978711\pi$
$692$	32.0000	−	32.0000i	1.21646	−	1.21646i
$693$		0			0
$694$	26.0000			0.986947
$695$	−41.5692	+	24.0000i	−1.57681	+	0.910372i
$696$	10.9282	−	2.92820i	0.414232	−	0.110993i
$697$	−10.3923	−	6.00000i	−0.393637	−	0.227266i
$698$	27.7128	−	16.0000i	1.04895	−	0.605609i
$699$	−16.0000	+	16.0000i	−0.605176	+	0.605176i
$700$		0			0
$701$	13.0000	+	13.0000i	0.491003	+	0.491003i	0.908622	−	0.417619i	$-0.137135\pi$
$701$	13.0000	+	13.0000i	0.491003	+	0.491003i	−0.417619	+	0.908622i	$0.637135\pi$
$702$		0			0
$703$	−12.0000	+	20.7846i	−0.452589	+	0.783906i
$704$	−32.7846	+	8.78461i	−1.23562	+	0.331082i
$705$	−32.0000	−	55.4256i	−1.20519	−	2.08745i
$706$	18.0000	+	18.0000i	0.677439	+	0.677439i
$707$		0			0
$708$		−	16.0000i		−	0.601317i
$709$	42.3468	+	11.3468i	1.59037	+	0.426138i	0.942115	−	0.335289i	$-0.108834\pi$
$709$	42.3468	+	11.3468i	1.59037	+	0.426138i	0.648252	+	0.761426i	$0.275501\pi$
$710$	27.7128	+	16.0000i	1.04004	+	0.600469i
$711$	60.6218	+	35.0000i	2.27349	+	1.31260i
$712$	4.39230	−	16.3923i	0.164609	−	0.614328i
$713$			8.00000i			0.299602i
$714$		0			0
$715$		0			0
$716$	13.6603	+	3.66025i	0.510508	+	0.136790i
$717$	21.8564	−	5.85641i	0.816242	−	0.218712i
$718$	−8.05256	−	30.0526i	−0.300519	−	1.12155i
$719$	−4.00000	−	6.92820i	−0.149175	−	0.258378i	0.781748	−	0.623595i	$-0.214328\pi$
$719$	−4.00000	−	6.92820i	−0.149175	−	0.258378i	−0.930923	+	0.365216i	$0.880995\pi$
$720$	−40.0000	−	40.0000i	−1.49071	−	1.49071i
$721$		0			0
$722$	13.0000	−	13.0000i	0.483810	−	0.483810i
$723$	16.1051	−	60.1051i	0.598956	−	2.23533i
$724$	10.9282	−	2.92820i	0.406143	−	0.108826i
$725$	−1.09808	−	4.09808i	−0.0407815	−	0.152199i
$726$	14.0000	+	24.2487i	0.519589	+	0.899954i
$727$			44.0000i			1.63187i	0.578144	+	0.815935i	$0.303777\pi$
$727$			44.0000i			1.63187i	−0.578144	+	0.815935i	$0.696223\pi$
$728$		0			0
$729$			43.0000i			1.59259i
$730$	34.6410	−	20.0000i	1.28212	−	0.740233i
$731$	−10.9808	−	40.9808i	−0.406138	−	1.51573i
$732$	−24.0000	+	41.5692i	−0.887066	+	1.53644i
$733$	0.732051	−	2.73205i	0.0270389	−	0.100911i	−0.951088	−	0.308921i	$-0.900032\pi$
$733$	0.732051	−	2.73205i	0.0270389	−	0.100911i	0.978127	+	0.208010i	$0.0666988\pi$
$734$	−16.0000	−	16.0000i	−0.590571	−	0.590571i
$735$		0			0
$736$	8.00000	−	8.00000i	0.294884	−	0.294884i
$737$	−15.0000	−	25.9808i	−0.552532	−	0.957014i
$738$	−13.6603	+	3.66025i	−0.502841	+	0.134736i
$739$	6.83013	−	1.83013i	0.251250	−	0.0673223i	−0.130996	−	0.991383i	$-0.541817\pi$
$739$	6.83013	−	1.83013i	0.251250	−	0.0673223i	0.382246	+	0.924061i	$0.375151\pi$
$740$	−12.0000	−	20.7846i	−0.441129	−	0.764057i
$741$		0			0
$742$		0			0
$743$			6.00000i			0.220119i	0.993925	+	0.110059i	$0.0351041\pi$
$743$			6.00000i			0.220119i	−0.993925	+	0.110059i	$0.964896\pi$
$744$	16.0000	+	27.7128i	0.586588	+	1.01600i
$745$	−45.0333	−	26.0000i	−1.64989	−	0.952566i
$746$	5.00000	−	8.66025i	0.183063	−	0.317074i
$747$		0			0
$748$	−36.0000	−	36.0000i	−1.31629	−	1.31629i
$749$		0			0
$750$	16.0000	−	16.0000i	0.584237	−	0.584237i
$751$	−20.0000	−	34.6410i	−0.729810	−	1.26407i	−0.956963	−	0.290209i	$-0.906275\pi$
$751$	−20.0000	−	34.6410i	−0.729810	−	1.26407i	0.227153	−	0.973859i	$-0.427058\pi$
$752$	16.0000	−	27.7128i	0.583460	−	1.01058i
$753$	8.00000	−	13.8564i	0.291536	−	0.504956i
$754$		0			0
$755$	12.0000	+	12.0000i	0.436725	+	0.436725i
$756$		0			0
$757$	33.0000	−	33.0000i	1.19941	−	1.19941i	0.225061	−	0.974345i	$-0.427742\pi$
$757$	33.0000	−	33.0000i	1.19941	−	1.19941i	0.974345	−	0.225061i	$-0.0722580\pi$
$758$	17.0000	+	29.4449i	0.617468	+	1.06949i
$759$	−20.7846	−	12.0000i	−0.754434	−	0.435572i
$760$	11.7128	+	43.7128i	0.424868	+	1.58563i
$761$	15.5885	−	9.00000i	0.565081	−	0.326250i	−0.190101	−	0.981764i	$-0.560882\pi$
$761$	15.5885	−	9.00000i	0.565081	−	0.326250i	0.755182	+	0.655515i	$0.227548\pi$
$762$		−	32.0000i		−	1.15924i
$763$		0			0
$764$			44.0000i			1.59186i
$765$	21.9615	−	81.9615i	0.794021	−	2.96333i
$766$	21.8564	−	5.85641i	0.789704	−	0.211601i
$767$		0			0
$768$	11.7128	−	43.7128i	0.422650	−	1.57735i
$769$	30.0000			1.08183			0.540914	−	0.841078i	$-0.318079\pi$
$769$	30.0000			1.08183			0.540914	+	0.841078i	$0.318079\pi$
$770$		0			0
$771$	20.0000	+	20.0000i	0.720282	+	0.720282i
$772$	−41.5692	+	24.0000i	−1.49611	+	0.863779i
$773$	10.9808	+	40.9808i	0.394951	+	1.47398i	0.821864	+	0.569683i	$0.192934\pi$
$773$	10.9808	+	40.9808i	0.394951	+	1.47398i	−0.426914	+	0.904292i	$0.640399\pi$
$774$	−43.3013	−	25.0000i	−1.55643	−	0.898606i
$775$	10.3923	−	6.00000i	0.373303	−	0.215526i
$776$	12.0000	−	12.0000i	0.430775	−	0.430775i
$777$		0			0
$778$	−38.0000			−1.36237
$779$	10.9282	+	2.92820i	0.391544	+	0.104914i
$780$		0			0
$781$	32.7846	−	8.78461i	1.17313	−	0.314338i
$782$	16.3923	+	4.39230i	0.586188	+	0.157069i
$783$	8.00000			0.285897
$784$		0			0
$785$		0			0
$786$	65.5692	+	17.5692i	2.33878	+	0.626673i
$787$	−16.3923	+	4.39230i	−0.584323	+	0.156569i	−0.538857	−	0.842397i	$-0.681144\pi$
$787$	−16.3923	+	4.39230i	−0.584323	+	0.156569i	−0.0454654	+	0.998966i	$0.514477\pi$
$788$	30.0526	−	8.05256i	1.07058	−	0.286861i
$789$	−65.5692	−	17.5692i	−2.33433	−	0.625481i
$790$	56.0000			1.99239
$791$		0			0
$792$	−60.0000			−2.13201
$793$		0			0
$794$		0			0
$795$	20.4974	+	76.4974i	0.726969	+	2.71308i
$796$	−20.0000	−	34.6410i	−0.708881	−	1.22782i
$797$	−8.00000	−	8.00000i	−0.283375	−	0.283375i	0.551079	−	0.834453i	$-0.314216\pi$
$797$	−8.00000	−	8.00000i	−0.283375	−	0.283375i	−0.834453	+	0.551079i	$0.814216\pi$
$798$		0			0
$799$	48.0000			1.69812
$800$	−16.3923	−	4.39230i	−0.579555	−	0.155291i
$801$	15.0000	−	25.9808i	0.529999	−	0.917985i
$802$	−5.46410	+	1.46410i	−0.192944	+	0.0516992i
$803$	10.9808	−	40.9808i	0.387503	−	1.44618i
$804$	40.0000			1.41069
$805$		0			0
$806$		0			0
$807$	55.4256	−	32.0000i	1.95107	−	1.12645i
$808$	−6.92820	−	4.00000i	−0.243733	−	0.140720i
$809$	32.9090	+	19.0000i	1.15702	+	0.668004i	0.950587	−	0.310457i	$-0.100482\pi$
$809$	32.9090	+	19.0000i	1.15702	+	0.668004i	0.206430	+	0.978461i	$0.433815\pi$
$810$	−2.00000	−	3.46410i	−0.0702728	−	0.121716i
$811$	−30.0000	+	30.0000i	−1.05344	+	1.05344i	−0.0549536	+	0.998489i	$0.517501\pi$
$811$	−30.0000	+	30.0000i	−1.05344	+	1.05344i	−0.998489	+	0.0549536i	$0.982499\pi$
$812$		0			0
$813$	−32.0000	−	32.0000i	−1.12229	−	1.12229i
$814$	−24.5885	−	6.58846i	−0.861825	−	0.230925i
$815$	10.0000	−	17.3205i	0.350285	−	0.606711i
$816$	65.5692	−	17.5692i	2.29538	−	0.615046i
$817$	20.0000	+	34.6410i	0.699711	+	1.21194i
$818$	10.0000	−	10.0000i	0.349642	−	0.349642i
$819$		0			0
$820$	−8.00000	+	8.00000i	−0.279372	+	0.279372i
$821$	9.56218	+	2.56218i	0.333722	+	0.0894206i	0.421789	−	0.906694i	$-0.361402\pi$
$821$	9.56218	+	2.56218i	0.333722	+	0.0894206i	−0.0880668	+	0.996115i	$0.528069\pi$
$822$	24.0000	−	41.5692i	0.837096	−	1.44989i
$823$	−34.6410	−	20.0000i	−1.20751	−	0.697156i	−0.245295	−	0.969448i	$-0.578885\pi$
$823$	−34.6410	−	20.0000i	−1.20751	−	0.697156i	−0.962215	+	0.272292i	$0.912218\pi$
$824$		0			0
$825$			36.0000i			1.25336i
$826$		0			0
$827$	−13.0000	+	13.0000i	−0.452054	+	0.452054i	−0.896036	−	0.443982i	$-0.853566\pi$
$827$	−13.0000	+	13.0000i	−0.452054	+	0.452054i	0.443982	+	0.896036i	$0.353566\pi$
$828$	17.3205	−	10.0000i	0.601929	−	0.347524i
$829$	−2.73205	+	0.732051i	−0.0948880	+	0.0254252i	−0.305951	−	0.952047i	$-0.598974\pi$
$829$	−2.73205	+	0.732051i	−0.0948880	+	0.0254252i	0.211063	+	0.977473i	$0.432308\pi$
$830$		0			0
$831$	−2.00000	−	3.46410i	−0.0693792	−	0.120168i
$832$		0			0
$833$		0			0
$834$	−48.0000	−	48.0000i	−1.66210	−	1.66210i
$835$		0			0
$836$	41.5692	+	24.0000i	1.43770	+	0.830057i
$837$	5.85641	+	21.8564i	0.202427	+	0.755468i
$838$	−17.3205	+	10.0000i	−0.598327	+	0.345444i
$839$		−	24.0000i		−	0.828572i	−0.910147	−	0.414286i	$-0.864031\pi$
$839$		−	24.0000i		−	0.828572i	0.910147	−	0.414286i	$-0.135969\pi$
$840$		0			0
$841$		−	27.0000i		−	0.931034i
$842$	−25.0000	−	43.3013i	−0.861557	−	1.49226i
$843$	17.5692	+	65.5692i	0.605116	+	2.25832i
$844$	6.58846	+	24.5885i	0.226784	+	0.846370i
$845$	−9.51666	+	35.5167i	−0.327383	+	1.22181i
$846$	40.0000	−	40.0000i	1.37523	−	1.37523i
$847$		0			0
$848$	−28.0000	+	28.0000i	−0.961524	+	0.961524i
$849$	−12.0000	−	20.7846i	−0.411839	−	0.713326i
$850$	−6.58846	−	24.5885i	−0.225982	−	0.843377i
$851$	8.19615	−	2.19615i	0.280960	−	0.0752831i
$852$	−11.7128	+	43.7128i	−0.401274	+	1.49758i
$853$	4.00000	−	4.00000i	0.136957	−	0.136957i	−0.635304	−	0.772262i	$-0.719125\pi$
$853$	4.00000	−	4.00000i	0.136957	−	0.136957i	0.772262	+	0.635304i	$0.219125\pi$
$854$		0			0
$855$			80.0000i			2.73594i
$856$	−17.3205	+	10.0000i	−0.592003	+	0.341793i
$857$	15.5885	+	9.00000i	0.532492	+	0.307434i	0.742030	−	0.670366i	$-0.233863\pi$
$857$	15.5885	+	9.00000i	0.532492	+	0.307434i	−0.209539	+	0.977800i	$0.567196\pi$
$858$		0			0
$859$	−5.46410	−	1.46410i	−0.186433	−	0.0499545i	0.164395	−	0.986395i	$-0.447433\pi$
$859$	−5.46410	−	1.46410i	−0.186433	−	0.0499545i	−0.350827	+	0.936440i	$0.614100\pi$
$860$	−40.0000			−1.36399
$861$		0			0
$862$		0			0
$863$	−3.00000	−	5.19615i	−0.102121	−	0.176879i	0.810437	−	0.585826i	$-0.199230\pi$
$863$	−3.00000	−	5.19615i	−0.102121	−	0.176879i	−0.912558	+	0.408946i	$0.865896\pi$
$864$	16.0000	−	27.7128i	0.544331	−	0.942809i
$865$	32.0000	−	55.4256i	1.08803	−	1.88453i
$866$	−0.732051	+	2.73205i	−0.0248761	+	0.0928389i
$867$	38.0000	+	38.0000i	1.29055	+	1.29055i
$868$		0			0
$869$	42.0000	−	42.0000i	1.42475	−	1.42475i
$870$	13.8564	−	8.00000i	0.469776	−	0.271225i
$871$		0			0
$872$	6.00000	−	10.3923i	0.203186	−	0.351928i
$873$	25.9808	−	15.0000i	0.879316	−	0.507673i
$874$	−16.0000			−0.541208
$875$		0			0
$876$	40.0000	+	40.0000i	1.35147	+	1.35147i
$877$	−7.68653	+	28.6865i	−0.259556	+	0.968675i	0.705943	+	0.708268i	$0.250523\pi$
$877$	−7.68653	+	28.6865i	−0.259556	+	0.968675i	−0.965499	+	0.260407i	$0.916143\pi$
$878$	−8.78461	−	32.7846i	−0.296466	−	1.10643i
$879$	−20.0000	+	34.6410i	−0.674583	+	1.16841i
$880$	−41.5692	+	24.0000i	−1.40130	+	0.809040i
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$		0			0
$883$	−17.0000	−	17.0000i	−0.572096	−	0.572096i	0.360618	−	0.932714i	$-0.382566\pi$
$883$	−17.0000	−	17.0000i	−0.572096	−	0.572096i	−0.932714	+	0.360618i	$0.882566\pi$
$884$		0			0
$885$	−5.85641	−	21.8564i	−0.196861	−	0.734695i
$886$	−17.0000	+	29.4449i	−0.571126	+	0.989220i
$887$	−20.7846	+	12.0000i	−0.697879	+	0.402921i	−0.806557	−	0.591156i	$-0.798672\pi$
$887$	−20.7846	+	12.0000i	−0.697879	+	0.402921i	0.108678	+	0.994077i	$0.465338\pi$
$888$	24.0000	−	24.0000i	0.805387	−	0.805387i
$889$		0			0
$890$		−	24.0000i		−	0.804482i
$891$	−4.09808	−	1.09808i	−0.137291	−	0.0367869i
$892$	6.92820	+	4.00000i	0.231973	+	0.133930i
$893$	−43.7128	+	11.7128i	−1.46279	+	0.391954i
$894$	19.0333	−	71.0333i	0.636569	−	2.37571i
$895$	20.0000			0.668526
$896$		0			0
$897$		0			0
$898$	−12.4449	+	46.4449i	−0.415290	+	1.54989i
$899$	−5.46410	+	1.46410i	−0.182238	+	0.0488305i
$900$	−25.9808	−	15.0000i	−0.866025	−	0.500000i
$901$	−57.3731	−	15.3731i	−1.91137	−	0.512151i
$902$			12.0000i			0.399556i
$903$		0			0
$904$	−24.0000	+	24.0000i	−0.798228	+	0.798228i
$905$	13.8564	−	8.00000i	0.460603	−	0.265929i
$906$	−12.0000	+	20.7846i	−0.398673	+	0.690522i
$907$	−3.29423	−	12.2942i	−0.109383	−	0.408223i	0.889422	−	0.457086i	$-0.151107\pi$
$907$	−3.29423	−	12.2942i	−0.109383	−	0.408223i	−0.998805	+	0.0488630i	$0.984440\pi$
$908$	−10.9282	−	2.92820i	−0.362665	−	0.0971758i
$909$	−10.0000	−	10.0000i	−0.331679	−	0.331679i
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$	−55.4256	+	32.0000i	−1.83533	+	1.05963i
$913$		0			0
$914$	9.51666	+	35.5167i	0.314783	+	1.17479i
$915$	−17.5692	+	65.5692i	−0.580820	+	2.16765i
$916$	−24.0000	−	24.0000i	−0.792982	−	0.792982i
$917$		0			0
$918$	48.0000			1.58424
$919$	−48.4974	+	28.0000i	−1.59978	+	0.923635i	−0.608254	+	0.793742i	$0.708130\pi$
$919$	−48.4974	+	28.0000i	−1.59978	+	0.923635i	−0.991528	+	0.129893i	$0.958537\pi$
$920$	8.00000	−	13.8564i	0.263752	−	0.456832i
$921$	−27.7128	−	16.0000i	−0.913168	−	0.527218i
$922$	−48.4974	+	28.0000i	−1.59718	+	0.922131i
$923$		0			0
$924$		0			0
$925$	−9.00000	−	9.00000i	−0.295918	−	0.295918i
$926$	−5.12436	+	19.1244i	−0.168397	+	0.628465i
$927$		0			0
$928$	6.92820	+	4.00000i	0.227429	+	0.131306i
$929$	−15.0000	−	25.9808i	−0.492134	−	0.852401i	0.507825	−	0.861460i	$-0.330450\pi$
$929$	−15.0000	−	25.9808i	−0.492134	−	0.852401i	−0.999959	+	0.00905914i	$0.997116\pi$
$930$	32.0000	+	32.0000i	1.04932	+	1.04932i
$931$		0			0
$932$	−16.0000			−0.524097
$933$	−10.9282	−	2.92820i	−0.357773	−	0.0958651i
$934$	27.7128	+	16.0000i	0.906791	+	0.523536i
$935$	−62.3538	−	36.0000i	−2.03919	−	1.17733i
$936$		0			0
$937$			50.0000i			1.63343i	0.577042	+	0.816714i	$0.304207\pi$
$937$			50.0000i			1.63343i	−0.577042	+	0.816714i	$0.695793\pi$
$938$		0			0
$939$	4.00000	−	4.00000i	0.130535	−	0.130535i
$940$	11.7128	−	43.7128i	0.382030	−	1.42575i
$941$	35.5167	−	9.51666i	1.15781	−	0.310234i	0.371719	−	0.928345i	$-0.378768\pi$
$941$	35.5167	−	9.51666i	1.15781	−	0.310234i	0.786091	+	0.618111i	$0.212102\pi$
$942$		0			0
$943$	−2.00000	−	3.46410i	−0.0651290	−	0.112807i
$944$	8.00000	−	8.00000i	0.260378	−	0.260378i
$945$		0			0
$946$	−30.0000	+	30.0000i	−0.975384	+	0.975384i
$947$	4.75833	−	17.7583i	0.154625	−	0.577068i	−0.844512	−	0.535536i	$-0.820110\pi$
$947$	4.75833	−	17.7583i	0.154625	−	0.577068i	0.999137	−	0.0415319i	$-0.0132238\pi$
$948$	20.4974	+	76.4974i	0.665725	+	2.48452i
$949$		0			0
$950$	12.0000	+	20.7846i	0.389331	+	0.674342i
$951$		−	60.0000i		−	1.94563i
$952$		0			0
$953$			16.0000i			0.518291i	0.965838	+	0.259145i	$0.0834409\pi$
$953$			16.0000i			0.518291i	−0.965838	+	0.259145i	$0.916559\pi$
$954$	−60.6218	+	35.0000i	−1.96270	+	1.13317i
$955$	16.1051	+	60.1051i	0.521149	+	1.94496i
$956$	13.8564	+	8.00000i	0.448148	+	0.258738i
$957$	4.39230	−	16.3923i	0.141983	−	0.529888i
$958$	−8.00000	−	8.00000i	−0.258468	−	0.258468i
$959$		0			0
$960$		−	64.0000i		−	2.06559i
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		0			0
$963$	−34.1506	+	9.15064i	−1.10049	+	0.294875i
$964$	38.1051	−	22.0000i	1.22728	−	0.708572i
$965$	−48.0000	+	48.0000i	−1.54517	+	1.54517i
$966$		0			0
$967$			38.0000i			1.22200i	0.791632	+	0.610999i	$0.209232\pi$
$967$			38.0000i			1.22200i	−0.791632	+	0.610999i	$0.790768\pi$
$968$	−5.12436	+	19.1244i	−0.164703	+	0.614680i
$969$	−83.1384	−	48.0000i	−2.67079	−	1.54198i
$970$	12.0000	−	20.7846i	0.385297	−	0.667354i
$971$	35.5167	+	9.51666i	1.13978	+	0.305404i	0.778864	−	0.627193i	$-0.215796\pi$
$971$	35.5167	+	9.51666i	1.13978	+	0.305404i	0.360920	+	0.932597i	$0.382463\pi$
$972$	−20.0000	+	20.0000i	−0.641500	+	0.641500i
$973$		0			0
$974$	2.00000	−	2.00000i	0.0640841	−	0.0640841i
$975$		0			0
$976$	−32.7846	+	8.78461i	−1.04941	+	0.281189i
$977$	17.0000	−	29.4449i	0.543878	−	0.942025i	−0.454798	−	0.890594i	$-0.650289\pi$
$977$	17.0000	−	29.4449i	0.543878	−	0.942025i	0.998677	−	0.0514302i	$-0.0163780\pi$
$978$	27.3205	+	7.32051i	0.873614	+	0.234084i
$979$	−18.0000	−	18.0000i	−0.575282	−	0.575282i
$980$		0			0
$981$	15.0000	−	15.0000i	0.478913	−	0.478913i
$982$	−11.0000	−	19.0526i	−0.351024	−	0.607992i
$983$	−41.5692	−	24.0000i	−1.32585	−	0.765481i	−0.341197	−	0.939992i	$-0.610832\pi$
$983$	−41.5692	−	24.0000i	−1.32585	−	0.765481i	−0.984655	+	0.174511i	$0.944166\pi$
$984$	−13.8564	−	8.00000i	−0.441726	−	0.255031i
$985$	38.1051	−	22.0000i	1.21413	−	0.700978i
$986$			12.0000i			0.382158i
$987$		0			0
$988$		0			0
$989$	3.66025	−	13.6603i	0.116389	−	0.434371i
$990$	−81.9615	+	21.9615i	−2.60491	+	0.697983i
$991$	5.00000	−	8.66025i	0.158830	−	0.275102i	−0.775617	−	0.631204i	$-0.782561\pi$
$991$	5.00000	−	8.66025i	0.158830	−	0.275102i	0.934447	+	0.356102i	$0.115894\pi$
$992$	−5.85641	+	21.8564i	−0.185941	+	0.693942i
$993$	−60.0000			−1.90404
$994$		0			0
$995$	−40.0000	−	40.0000i	−1.26809	−	1.26809i
$996$		0			0
$997$	−10.9808	−	40.9808i	−0.347764	−	1.29787i	−0.889350	−	0.457228i	$-0.848842\pi$
$997$	−10.9808	−	40.9808i	−0.347764	−	1.29787i	0.541585	−	0.840646i	$-0.317824\pi$
$998$	−25.9808	−	15.0000i	−0.822407	−	0.474817i
$999$	20.7846	−	12.0000i	0.657596	−	0.379663i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.b.557.1		4
7.2	even	3	inner	784.2.x.b.765.1		4
7.3	odd	6		112.2.m.a.29.1	✓	2
7.4	even	3		784.2.m.c.589.1		2
7.5	odd	6		784.2.x.g.765.1		4
7.6	odd	2		784.2.x.g.557.1		4
16.5	even	4	inner	784.2.x.b.165.1		4
28.3	even	6		448.2.m.b.337.1		2
56.3	even	6		896.2.m.a.673.1		2
56.45	odd	6		896.2.m.d.673.1		2
112.3	even	12		896.2.m.a.225.1		2
112.5	odd	12		784.2.x.g.373.1		4
112.37	even	12	inner	784.2.x.b.373.1		4
112.45	odd	12		896.2.m.d.225.1		2
112.53	even	12		784.2.m.c.197.1		2
112.59	even	12		448.2.m.b.113.1		2
112.69	odd	4		784.2.x.g.165.1		4
112.101	odd	12		112.2.m.a.85.1	yes	2
224.59	even	24		7168.2.a.i.1.1		2
224.101	odd	24		7168.2.a.q.1.2		2
224.171	even	24		7168.2.a.i.1.2		2
224.213	odd	24		7168.2.a.q.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.a.29.1	✓	2	7.3	odd	6
112.2.m.a.85.1	yes	2	112.101	odd	12
448.2.m.b.113.1		2	112.59	even	12
448.2.m.b.337.1		2	28.3	even	6
784.2.m.c.197.1		2	112.53	even	12
784.2.m.c.589.1		2	7.4	even	3
784.2.x.b.165.1		4	16.5	even	4	inner
784.2.x.b.373.1		4	112.37	even	12	inner
784.2.x.b.557.1		4	1.1	even	1	trivial
784.2.x.b.765.1		4	7.2	even	3	inner
784.2.x.g.165.1		4	112.69	odd	4
784.2.x.g.373.1		4	112.5	odd	12
784.2.x.g.557.1		4	7.6	odd	2
784.2.x.g.765.1		4	7.5	odd	6
896.2.m.a.225.1		2	112.3	even	12
896.2.m.a.673.1		2	56.3	even	6
896.2.m.d.225.1		2	112.45	odd	12
896.2.m.d.673.1		2	56.45	odd	6
7168.2.a.i.1.1		2	224.59	even	24
7168.2.a.i.1.2		2	224.171	even	24
7168.2.a.q.1.1		2	224.213	odd	24
7168.2.a.q.1.2		2	224.101	odd	24

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 + 1.36603i) q^{2} +(-2.73205 + 0.732051i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-2.73205 - 0.732051i) q^{5} -4.00000i q^{6} +(2.00000 - 2.00000i) q^{8} +(4.33013 - 2.50000i) q^{9} +(2.00000 - 3.46410i) q^{10} +(-1.09808 - 4.09808i) q^{11} +(5.46410 + 1.46410i) q^{12} +8.00000 q^{15} +(2.00000 + 3.46410i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(1.83013 + 6.83013i) q^{18} +(1.46410 - 5.46410i) q^{19} +(4.00000 + 4.00000i) q^{20} +6.00000 q^{22} +(-1.73205 + 1.00000i) q^{23} +(-4.00000 + 6.92820i) q^{24} +(2.59808 + 1.50000i) q^{25} +(-4.00000 + 4.00000i) q^{27} +(-1.00000 - 1.00000i) q^{29} +(-2.92820 + 10.9282i) q^{30} +(2.00000 - 3.46410i) q^{31} +(-5.46410 + 1.46410i) q^{32} +(6.00000 + 10.3923i) q^{33} +(-6.00000 - 6.00000i) q^{34} -10.0000 q^{36} +(-4.09808 - 1.09808i) q^{37} +(6.92820 + 4.00000i) q^{38} +(-6.92820 + 4.00000i) q^{40} +2.00000i q^{41} +(-5.00000 + 5.00000i) q^{43} +(-2.19615 + 8.19615i) q^{44} +(-13.6603 + 3.66025i) q^{45} +(-0.732051 - 2.73205i) q^{46} +(-4.00000 - 6.92820i) q^{47} +(-8.00000 - 8.00000i) q^{48} +(-3.00000 + 3.00000i) q^{50} +(4.39230 - 16.3923i) q^{51} +(2.56218 + 9.56218i) q^{53} +(-4.00000 - 6.92820i) q^{54} +12.0000i q^{55} +16.0000i q^{57} +(1.73205 - 1.00000i) q^{58} +(-0.732051 - 2.73205i) q^{59} +(-13.8564 - 8.00000i) q^{60} +(-2.19615 + 8.19615i) q^{61} +(4.00000 + 4.00000i) q^{62} -8.00000i q^{64} +(-16.3923 + 4.39230i) q^{66} +(6.83013 - 1.83013i) q^{67} +(10.3923 - 6.00000i) q^{68} +(4.00000 - 4.00000i) q^{69} +8.00000i q^{71} +(3.66025 - 13.6603i) q^{72} +(8.66025 + 5.00000i) q^{73} +(3.00000 - 5.19615i) q^{74} +(-8.19615 - 2.19615i) q^{75} +(-8.00000 + 8.00000i) q^{76} +(7.00000 + 12.1244i) q^{79} +(-2.92820 - 10.9282i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-2.73205 - 0.732051i) q^{82} +(12.0000 - 12.0000i) q^{85} +(-5.00000 - 8.66025i) q^{86} +(3.46410 + 2.00000i) q^{87} +(-10.3923 - 6.00000i) q^{88} +(5.19615 - 3.00000i) q^{89} -20.0000i q^{90} +4.00000 q^{92} +(-2.92820 + 10.9282i) q^{93} +(10.9282 - 2.92820i) q^{94} +(-8.00000 + 13.8564i) q^{95} +(13.8564 - 8.00000i) q^{96} +6.00000 q^{97} +(-15.0000 - 15.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 4 q^{3} - 4 q^{5} + 8 q^{8} + 8 q^{10} + 6 q^{11} + 8 q^{12} + 32 q^{15} + 8 q^{16} - 12 q^{17} - 10 q^{18} - 8 q^{19} + 16 q^{20} + 24 q^{22} - 16 q^{24} - 16 q^{27} - 4 q^{29} + 16 q^{30}+ \cdots - 60 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 4 * q^3 - 4 * q^5 + 8 * q^8 + 8 * q^10 + 6 * q^11 + 8 * q^12 + 32 * q^15 + 8 * q^16 - 12 * q^17 - 10 * q^18 - 8 * q^19 + 16 * q^20 + 24 * q^22 - 16 * q^24 - 16 * q^27 - 4 * q^29 + 16 * q^30 + 8 * q^31 - 8 * q^32 + 24 * q^33 - 24 * q^34 - 40 * q^36 - 6 * q^37 - 20 * q^43 + 12 * q^44 - 20 * q^45 + 4 * q^46 - 16 * q^47 - 32 * q^48 - 12 * q^50 - 24 * q^51 - 14 * q^53 - 16 * q^54 + 4 * q^59 + 12 * q^61 + 16 * q^62 - 24 * q^66 + 10 * q^67 + 16 * q^69 - 20 * q^72 + 12 * q^74 - 12 * q^75 - 32 * q^76 + 28 * q^79 + 16 * q^80 + 2 * q^81 - 4 * q^82 + 48 * q^85 - 20 * q^86 + 16 * q^92 + 16 * q^93 + 16 * q^94 - 32 * q^95 + 24 * q^97 - 60 * q^99

Introduction

L-functions

Modular forms

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Database

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