LMFDB - Embedded newform 896.2.ba.b.865.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [896,2,Mod(289,896)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(896, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("896.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.ba (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-2,0,0,0,0,0,-6,0,10] 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:	$7.15459602111$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			865.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	896.865
Dual form			896.2.ba.b.289.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 1.86603i) q^{3} +(-0.866025 + 3.23205i) q^{5} +(-1.73205 - 2.00000i) q^{7} +(-0.633975 + 0.366025i) q^{9} +(4.23205 - 1.13397i) q^{11} +(-0.267949 + 0.267949i) q^{13} +6.46410 q^{15} +(0.232051 - 0.401924i) q^{17} +(-4.23205 - 1.13397i) q^{19} +(-2.86603 + 4.23205i) q^{21} +(2.13397 - 1.23205i) q^{23} +(-5.36603 - 3.09808i) q^{25} +(-3.09808 - 3.09808i) q^{27} +(3.73205 - 3.73205i) q^{29} +(-0.133975 + 0.232051i) q^{31} +(-4.23205 - 7.33013i) q^{33} +(7.96410 - 3.86603i) q^{35} +(2.86603 - 10.6962i) q^{37} +(0.633975 + 0.366025i) q^{39} -8.92820i q^{41} +(0.464102 + 0.464102i) q^{43} +(-0.633975 - 2.36603i) q^{45} +(-3.86603 - 6.69615i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(-0.866025 - 0.232051i) q^{51} +(-11.0622 + 2.96410i) q^{53} +14.6603i q^{55} +8.46410i q^{57} +(9.96410 - 2.66987i) q^{59} +(-0.133975 - 0.0358984i) q^{61} +(1.83013 + 0.633975i) q^{63} +(-0.633975 - 1.09808i) q^{65} +(-1.96410 - 7.33013i) q^{67} +(-3.36603 - 3.36603i) q^{69} -7.46410i q^{71} +(2.76795 + 1.59808i) q^{73} +(-3.09808 + 11.5622i) q^{75} +(-9.59808 - 6.50000i) q^{77} +(-0.330127 - 0.571797i) q^{79} +(-5.33013 + 9.23205i) q^{81} +(-8.46410 + 8.46410i) q^{83} +(1.09808 + 1.09808i) q^{85} +(-8.83013 - 5.09808i) q^{87} +(-4.50000 + 2.59808i) q^{89} +(1.00000 + 0.0717968i) q^{91} +(0.500000 + 0.133975i) q^{93} +(7.33013 - 12.6962i) q^{95} +10.9282 q^{97} +(-2.26795 + 2.26795i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 6 q^{9} + 10 q^{11} - 8 q^{13} + 12 q^{15} - 6 q^{17} - 10 q^{19} - 8 q^{21} + 12 q^{23} - 18 q^{25} - 2 q^{27} + 8 q^{29} - 4 q^{31} - 10 q^{33} + 18 q^{35} + 8 q^{37} + 6 q^{39} - 12 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 6 * q^9 + 10 * q^11 - 8 * q^13 + 12 * q^15 - 6 * q^17 - 10 * q^19 - 8 * q^21 + 12 * q^23 - 18 * q^25 - 2 * q^27 + 8 * q^29 - 4 * q^31 - 10 * q^33 + 18 * q^35 + 8 * q^37 + 6 * q^39 - 12 * q^43 - 6 * q^45 - 12 * q^47 - 4 * q^49 - 20 * q^53 + 26 * q^59 - 4 * q^61 - 10 * q^63 - 6 * q^65 + 6 * q^67 - 10 * q^69 + 18 * q^73 - 2 * q^75 - 28 * q^77 + 16 * q^79 - 4 * q^81 - 20 * q^83 - 6 * q^85 - 18 * q^87 - 18 * q^89 + 4 * q^91 + 2 * q^93 + 12 * q^95 + 16 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

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
$3$	−0.500000	−	1.86603i	−0.288675	−	1.07735i	−0.946112	−	0.323840i	$-0.895026\pi$
$3$	−0.500000	−	1.86603i	−0.288675	−	1.07735i	0.657437	−	0.753510i	$-0.271641\pi$
$4$		0			0
$5$	−0.866025	+	3.23205i	−0.387298	+	1.44542i	0.447214	+	0.894427i	$0.352416\pi$
$5$	−0.866025	+	3.23205i	−0.387298	+	1.44542i	−0.834512	+	0.550990i	$0.814250\pi$
$6$		0			0
$7$	−1.73205	−	2.00000i	−0.654654	−	0.755929i
$7$	−1.73205	−	2.00000i	−0.654654	−	0.755929i
$8$		0			0
$9$	−0.633975	+	0.366025i	−0.211325	+	0.122008i
$10$		0			0
$11$	4.23205	−	1.13397i	1.27601	−	0.341906i	0.443680	−	0.896185i	$-0.353673\pi$
$11$	4.23205	−	1.13397i	1.27601	−	0.341906i	0.832331	+	0.554279i	$0.187006\pi$
$12$		0			0
$13$	−0.267949	+	0.267949i	−0.0743157	+	0.0743157i	−0.743288	−	0.668972i	$-0.766735\pi$
$13$	−0.267949	+	0.267949i	−0.0743157	+	0.0743157i	0.668972	+	0.743288i	$0.266735\pi$
$14$		0			0
$15$	6.46410			1.66902
$16$		0			0
$17$	0.232051	−	0.401924i	0.0562806	−	0.0974808i	−0.836512	−	0.547948i	$-0.815409\pi$
$17$	0.232051	−	0.401924i	0.0562806	−	0.0974808i	0.892793	+	0.450467i	$0.148743\pi$
$18$		0			0
$19$	−4.23205	−	1.13397i	−0.970899	−	0.260152i	−0.261692	−	0.965152i	$-0.584280\pi$
$19$	−4.23205	−	1.13397i	−0.970899	−	0.260152i	−0.709207	+	0.705000i	$0.750947\pi$
$20$		0			0
$21$	−2.86603	+	4.23205i	−0.625418	+	0.923509i
$22$		0			0
$23$	2.13397	−	1.23205i	0.444964	−	0.256900i	−0.260737	−	0.965410i	$-0.583965\pi$
$23$	2.13397	−	1.23205i	0.444964	−	0.256900i	0.705701	+	0.708510i	$0.250632\pi$
$24$		0			0
$25$	−5.36603	−	3.09808i	−1.07321	−	0.619615i
$26$		0			0
$27$	−3.09808	−	3.09808i	−0.596225	−	0.596225i
$28$		0			0
$29$	3.73205	−	3.73205i	0.693024	−	0.693024i	−0.269872	−	0.962896i	$-0.586981\pi$
$29$	3.73205	−	3.73205i	0.693024	−	0.693024i	0.962896	+	0.269872i	$0.0869813\pi$
$30$		0			0
$31$	−0.133975	+	0.232051i	−0.0240625	+	0.0416776i	−0.877806	−	0.479016i	$-0.840993\pi$
$31$	−0.133975	+	0.232051i	−0.0240625	+	0.0416776i	0.853743	+	0.520694i	$0.174327\pi$
$32$		0			0
$33$	−4.23205	−	7.33013i	−0.736705	−	1.27601i
$34$		0			0
$35$	7.96410	−	3.86603i	1.34618	−	0.653478i
$36$		0			0
$37$	2.86603	−	10.6962i	0.471172	−	1.75844i	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	2.86603	−	10.6962i	0.471172	−	1.75844i	0.635571	−	0.772043i	$-0.280765\pi$
$38$		0			0
$39$	0.633975	+	0.366025i	0.101517	+	0.0586110i
$40$		0			0
$41$		−	8.92820i		−	1.39435i	−0.716900	−	0.697176i	$-0.754440\pi$
$41$		−	8.92820i		−	1.39435i	0.716900	−	0.697176i	$-0.245560\pi$
$42$		0			0
$43$	0.464102	+	0.464102i	0.0707748	+	0.0707748i	0.741608	−	0.670833i	$-0.234063\pi$
$43$	0.464102	+	0.464102i	0.0707748	+	0.0707748i	−0.670833	+	0.741608i	$0.734063\pi$
$44$		0			0
$45$	−0.633975	−	2.36603i	−0.0945074	−	0.352706i
$46$		0			0
$47$	−3.86603	−	6.69615i	−0.563918	−	0.976734i	−0.997149	−	0.0754516i	$-0.975960\pi$
$47$	−3.86603	−	6.69615i	−0.563918	−	0.976734i	0.433232	−	0.901283i	$-0.357373\pi$
$48$		0			0
$49$	−1.00000	+	6.92820i	−0.142857	+	0.989743i
$50$		0			0
$51$	−0.866025	−	0.232051i	−0.121268	−	0.0324936i
$52$		0			0
$53$	−11.0622	+	2.96410i	−1.51951	+	0.407151i	−0.919580	−	0.392904i	$-0.871471\pi$
$53$	−11.0622	+	2.96410i	−1.51951	+	0.407151i	−0.599927	+	0.800054i	$0.704804\pi$
$54$		0			0
$55$			14.6603i			1.97679i
$56$		0			0
$57$			8.46410i			1.12110i
$58$		0			0
$59$	9.96410	−	2.66987i	1.29722	−	0.347588i	0.456819	−	0.889560i	$-0.348989\pi$
$59$	9.96410	−	2.66987i	1.29722	−	0.347588i	0.840397	+	0.541972i	$0.182322\pi$
$60$		0			0
$61$	−0.133975	−	0.0358984i	−0.0171537	−	0.00459632i	0.250232	−	0.968186i	$-0.419493\pi$
$61$	−0.133975	−	0.0358984i	−0.0171537	−	0.00459632i	−0.267386	+	0.963590i	$0.586160\pi$
$62$		0			0
$63$	1.83013	+	0.633975i	0.230574	+	0.0798733i
$64$		0			0
$65$	−0.633975	−	1.09808i	−0.0786349	−	0.136200i
$66$		0			0
$67$	−1.96410	−	7.33013i	−0.239953	−	0.895518i	−0.975853	−	0.218427i	$-0.929907\pi$
$67$	−1.96410	−	7.33013i	−0.239953	−	0.895518i	0.735900	−	0.677090i	$-0.236759\pi$
$68$		0			0
$69$	−3.36603	−	3.36603i	−0.405222	−	0.405222i
$70$		0			0
$71$		−	7.46410i		−	0.885826i	−0.896565	−	0.442913i	$-0.853945\pi$
$71$		−	7.46410i		−	0.885826i	0.896565	−	0.442913i	$-0.146055\pi$
$72$		0			0
$73$	2.76795	+	1.59808i	0.323964	+	0.187041i	0.653158	−	0.757222i	$-0.273444\pi$
$73$	2.76795	+	1.59808i	0.323964	+	0.187041i	−0.329194	+	0.944262i	$0.606777\pi$
$74$		0			0
$75$	−3.09808	+	11.5622i	−0.357735	+	1.33509i
$76$		0			0
$77$	−9.59808	−	6.50000i	−1.09380	−	0.740744i
$78$		0			0
$79$	−0.330127	−	0.571797i	−0.0371422	−	0.0643322i	0.846857	−	0.531821i	$-0.178492\pi$
$79$	−0.330127	−	0.571797i	−0.0371422	−	0.0643322i	−0.883999	+	0.467489i	$0.845159\pi$
$80$		0			0
$81$	−5.33013	+	9.23205i	−0.592236	+	1.02578i
$82$		0			0
$83$	−8.46410	+	8.46410i	−0.929056	+	0.929056i	−0.997645	−	0.0685891i	$-0.978150\pi$
$83$	−8.46410	+	8.46410i	−0.929056	+	0.929056i	0.0685891	+	0.997645i	$0.478150\pi$
$84$		0			0
$85$	1.09808	+	1.09808i	0.119103	+	0.119103i
$86$		0			0
$87$	−8.83013	−	5.09808i	−0.946689	−	0.546571i
$88$		0			0
$89$	−4.50000	+	2.59808i	−0.476999	+	0.275396i	−0.719165	−	0.694839i	$-0.755475\pi$
$89$	−4.50000	+	2.59808i	−0.476999	+	0.275396i	0.242166	+	0.970235i	$0.422142\pi$
$90$		0			0
$91$	1.00000	+	0.0717968i	0.104828	+	0.00752635i
$92$		0			0
$93$	0.500000	+	0.133975i	0.0518476	+	0.0138925i
$94$		0			0
$95$	7.33013	−	12.6962i	0.752055	−	1.30260i
$96$		0			0
$97$	10.9282			1.10959			0.554795	−	0.831987i	$-0.312797\pi$
$97$	10.9282			1.10959			0.554795	+	0.831987i	$0.312797\pi$
$98$		0			0
$99$	−2.26795	+	2.26795i	−0.227937	+	0.227937i
$100$		0			0
$101$	7.06218	−	1.89230i	0.702713	−	0.188291i	0.110268	−	0.993902i	$-0.464829\pi$
$101$	7.06218	−	1.89230i	0.702713	−	0.188291i	0.592445	+	0.805611i	$0.298163\pi$
$102$		0			0
$103$	−0.401924	+	0.232051i	−0.0396027	+	0.0228646i	−0.519671	−	0.854367i	$-0.673945\pi$
$103$	−0.401924	+	0.232051i	−0.0396027	+	0.0228646i	0.480068	+	0.877231i	$0.340612\pi$
$104$		0			0
$105$	−11.1962	−	12.9282i	−1.09263	−	1.26166i
$106$		0			0
$107$	0.232051	−	0.866025i	0.0224332	−	0.0837218i	−0.953802	−	0.300437i	$-0.902868\pi$
$107$	0.232051	−	0.866025i	0.0224332	−	0.0837218i	0.976235	+	0.216715i	$0.0695342\pi$
$108$		0			0
$109$	3.86603	+	14.4282i	0.370298	+	1.38197i	0.860095	+	0.510134i	$0.170404\pi$
$109$	3.86603	+	14.4282i	0.370298	+	1.38197i	−0.489797	+	0.871837i	$0.662929\pi$
$110$		0			0
$111$	−21.3923			−2.03047
$112$		0			0
$113$	5.46410			0.514019			0.257010	−	0.966409i	$-0.417263\pi$
$113$	5.46410			0.514019			0.257010	+	0.966409i	$0.417263\pi$
$114$		0			0
$115$	2.13397	+	7.96410i	0.198994	+	0.742656i
$116$		0			0
$117$	0.0717968	−	0.267949i	0.00663761	−	0.0247719i
$118$		0			0
$119$	−1.20577	+	0.232051i	−0.110533	+	0.0212721i
$120$		0			0
$121$	7.09808	−	4.09808i	0.645280	−	0.372552i
$122$		0			0
$123$	−16.6603	+	4.46410i	−1.50220	+	0.402514i
$124$		0			0
$125$	2.83013	−	2.83013i	0.253134	−	0.253134i
$126$		0			0
$127$	2.53590			0.225025			0.112512	−	0.993650i	$-0.464110\pi$
$127$	2.53590			0.225025			0.112512	+	0.993650i	$0.464110\pi$
$128$		0			0
$129$	0.633975	−	1.09808i	0.0558184	−	0.0966802i
$130$		0			0
$131$	8.96410	+	2.40192i	0.783197	+	0.209857i	0.628194	−	0.778057i	$-0.283794\pi$
$131$	8.96410	+	2.40192i	0.783197	+	0.209857i	0.155003	+	0.987914i	$0.450461\pi$
$132$		0			0
$133$	5.06218	+	10.4282i	0.438946	+	0.904240i
$134$		0			0
$135$	12.6962	−	7.33013i	1.09271	−	0.630877i
$136$		0			0
$137$	11.7679	+	6.79423i	1.00540	+	0.580470i	0.909843	−	0.414953i	$-0.136202\pi$
$137$	11.7679	+	6.79423i	1.00540	+	0.580470i	0.0955611	+	0.995424i	$0.469535\pi$
$138$		0			0
$139$	−1.92820	−	1.92820i	−0.163548	−	0.163548i	0.620588	−	0.784136i	$-0.286894\pi$
$139$	−1.92820	−	1.92820i	−0.163548	−	0.163548i	−0.784136	+	0.620588i	$0.786894\pi$
$140$		0			0
$141$	−10.5622	+	10.5622i	−0.889496	+	0.889496i
$142$		0			0
$143$	−0.830127	+	1.43782i	−0.0694187	+	0.120237i
$144$		0			0
$145$	8.83013	+	15.2942i	0.733302	+	1.27012i
$146$		0			0
$147$	13.4282	−	1.59808i	1.10754	−	0.131807i
$148$		0			0
$149$	2.40192	−	8.96410i	0.196773	−	0.734368i	−0.795027	−	0.606573i	$-0.792544\pi$
$149$	2.40192	−	8.96410i	0.196773	−	0.734368i	0.991801	−	0.127794i	$-0.0407897\pi$
$150$		0			0
$151$	8.13397	+	4.69615i	0.661933	+	0.382167i	0.793013	−	0.609204i	$-0.208511\pi$
$151$	8.13397	+	4.69615i	0.661933	+	0.382167i	−0.131080	+	0.991372i	$0.541844\pi$
$152$		0			0
$153$			0.339746i			0.0274668i
$154$		0			0
$155$	−0.633975	−	0.633975i	−0.0509221	−	0.0509221i
$156$		0			0
$157$	−4.25833	−	15.8923i	−0.339852	−	1.26834i	−0.898513	−	0.438948i	$-0.855351\pi$
$157$	−4.25833	−	15.8923i	−0.339852	−	1.26834i	0.558661	−	0.829396i	$-0.311315\pi$
$158$		0			0
$159$	11.0622	+	19.1603i	0.877288	+	1.51951i
$160$		0			0
$161$	−6.16025	−	2.13397i	−0.485496	−	0.168181i
$162$		0			0
$163$	0.232051	+	0.0621778i	0.0181756	+	0.00487014i	0.267895	−	0.963448i	$-0.413672\pi$
$163$	0.232051	+	0.0621778i	0.0181756	+	0.00487014i	−0.249720	+	0.968318i	$0.580339\pi$
$164$		0			0
$165$	27.3564	−	7.33013i	2.12969	−	0.570650i
$166$		0			0
$167$		−	5.85641i		−	0.453182i	−0.973990	−	0.226591i	$-0.927242\pi$
$167$		−	5.85641i		−	0.453182i	0.973990	−	0.226591i	$-0.0727581\pi$
$168$		0			0
$169$			12.8564i			0.988954i
$170$		0			0
$171$	3.09808	−	0.830127i	0.236916	−	0.0634814i
$172$		0			0
$173$	4.59808	+	1.23205i	0.349585	+	0.0936711i	0.429339	−	0.903144i	$-0.358747\pi$
$173$	4.59808	+	1.23205i	0.349585	+	0.0936711i	−0.0797535	+	0.996815i	$0.525413\pi$
$174$		0			0
$175$	3.09808	+	16.0981i	0.234193	+	1.21690i
$176$		0			0
$177$	−9.96410	−	17.2583i	−0.748948	−	1.29722i
$178$		0			0
$179$	−2.03590	−	7.59808i	−0.152170	−	0.567907i	−0.999331	−	0.0365704i	$-0.988357\pi$
$179$	−2.03590	−	7.59808i	−0.152170	−	0.567907i	0.847161	−	0.531336i	$-0.178310\pi$
$180$		0			0
$181$	7.39230	+	7.39230i	0.549466	+	0.549466i	0.926286	−	0.376821i	$-0.122983\pi$
$181$	7.39230	+	7.39230i	0.549466	+	0.549466i	−0.376821	+	0.926286i	$0.622983\pi$
$182$		0			0
$183$			0.267949i			0.0198074i
$184$		0			0
$185$	32.0885	+	18.5263i	2.35919	+	1.36208i
$186$		0			0
$187$	0.526279	−	1.96410i	0.0384854	−	0.143629i
$188$		0			0
$189$	−0.830127	+	11.5622i	−0.0603829	+	0.841025i
$190$		0			0
$191$	4.33013	+	7.50000i	0.313317	+	0.542681i	0.979078	−	0.203484i	$-0.0652264\pi$
$191$	4.33013	+	7.50000i	0.313317	+	0.542681i	−0.665761	+	0.746165i	$0.731893\pi$
$192$		0			0
$193$	11.5000	−	19.9186i	0.827788	−	1.43377i	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	11.5000	−	19.9186i	0.827788	−	1.43377i	0.899770	−	0.436365i	$-0.143734\pi$
$194$		0			0
$195$	−1.73205	+	1.73205i	−0.124035	+	0.124035i
$196$		0			0
$197$	−0.660254	−	0.660254i	−0.0470412	−	0.0470412i	0.683195	−	0.730236i	$-0.260590\pi$
$197$	−0.660254	−	0.660254i	−0.0470412	−	0.0470412i	−0.730236	+	0.683195i	$0.760590\pi$
$198$		0			0
$199$	−1.66987	−	0.964102i	−0.118374	−	0.0683434i	0.439644	−	0.898172i	$-0.355105\pi$
$199$	−1.66987	−	0.964102i	−0.118374	−	0.0683434i	−0.558018	+	0.829829i	$0.688438\pi$
$200$		0			0
$201$	−12.6962	+	7.33013i	−0.895518	+	0.517027i
$202$		0			0
$203$	−13.9282	−	1.00000i	−0.977568	−	0.0701862i
$204$		0			0
$205$	28.8564	+	7.73205i	2.01542	+	0.540030i
$206$		0			0
$207$	−0.901924	+	1.56218i	−0.0626880	+	0.108579i
$208$		0			0
$209$	−19.1962			−1.32783
$210$		0			0
$211$	2.07180	−	2.07180i	0.142628	−	0.142628i	−0.632187	−	0.774816i	$-0.717843\pi$
$211$	2.07180	−	2.07180i	0.142628	−	0.142628i	0.774816	+	0.632187i	$0.217843\pi$
$212$		0			0
$213$	−13.9282	+	3.73205i	−0.954345	+	0.255716i
$214$		0			0
$215$	−1.90192	+	1.09808i	−0.129710	+	0.0748882i
$216$		0			0
$217$	0.696152	−	0.133975i	0.0472579	−	0.00909479i
$218$		0			0
$219$	1.59808	−	5.96410i	0.107988	−	0.403017i
$220$		0			0
$221$	0.0455173	+	0.169873i	0.00306183	+	0.0114269i
$222$		0			0
$223$	−17.8564			−1.19575			−0.597877	−	0.801588i	$-0.703989\pi$
$223$	−17.8564			−1.19575			−0.597877	+	0.801588i	$0.703989\pi$
$224$		0			0
$225$	4.53590			0.302393
$226$		0			0
$227$	6.16025	+	22.9904i	0.408870	+	1.52593i	0.796804	+	0.604238i	$0.206522\pi$
$227$	6.16025	+	22.9904i	0.408870	+	1.52593i	−0.387934	+	0.921687i	$0.626811\pi$
$228$		0			0
$229$	−4.66987	+	17.4282i	−0.308594	+	1.15169i	0.621213	+	0.783641i	$0.286640\pi$
$229$	−4.66987	+	17.4282i	−0.308594	+	1.15169i	−0.929807	+	0.368047i	$0.880027\pi$
$230$		0			0
$231$	−7.33013	+	21.1603i	−0.482287	+	1.39224i
$232$		0			0
$233$	−9.69615	+	5.59808i	−0.635216	+	0.366742i	−0.782769	−	0.622312i	$-0.786194\pi$
$233$	−9.69615	+	5.59808i	−0.635216	+	0.366742i	0.147553	+	0.989054i	$0.452860\pi$
$234$		0			0
$235$	24.9904	−	6.69615i	1.63019	−	0.436809i
$236$		0			0
$237$	−0.901924	+	0.901924i	−0.0585862	+	0.0585862i
$238$		0			0
$239$	−15.4641			−1.00029			−0.500145	−	0.865942i	$-0.666720\pi$
$239$	−15.4641			−1.00029			−0.500145	+	0.865942i	$0.666720\pi$
$240$		0			0
$241$	−0.0358984	+	0.0621778i	−0.00231242	+	0.00400523i	−0.867179	−	0.497996i	$-0.834069\pi$
$241$	−0.0358984	+	0.0621778i	−0.00231242	+	0.00400523i	0.864867	+	0.502001i	$0.167403\pi$
$242$		0			0
$243$	7.19615	+	1.92820i	0.461633	+	0.123694i
$244$		0			0
$245$	−21.5263	−	9.23205i	−1.37526	−	0.589814i
$246$		0			0
$247$	1.43782	−	0.830127i	0.0914864	−	0.0528197i
$248$		0			0
$249$	20.0263	+	11.5622i	1.26911	+	0.732723i
$250$		0			0
$251$	−13.5885	−	13.5885i	−0.857696	−	0.857696i	0.133370	−	0.991066i	$-0.457420\pi$
$251$	−13.5885	−	13.5885i	−0.857696	−	0.857696i	−0.991066	+	0.133370i	$0.957420\pi$
$252$		0			0
$253$	7.63397	−	7.63397i	0.479944	−	0.479944i
$254$		0			0
$255$	1.50000	−	2.59808i	0.0939336	−	0.162698i
$256$		0			0
$257$	−0.696152	−	1.20577i	−0.0434248	−	0.0752140i	0.843496	−	0.537135i	$-0.180494\pi$
$257$	−0.696152	−	1.20577i	−0.0434248	−	0.0752140i	−0.886921	+	0.461921i	$0.847160\pi$
$258$		0			0
$259$	−26.3564	+	12.7942i	−1.63771	+	0.794995i
$260$		0			0
$261$	−1.00000	+	3.73205i	−0.0618984	+	0.231008i
$262$		0			0
$263$	−21.9904	−	12.6962i	−1.35598	−	0.782878i	−0.366905	−	0.930258i	$-0.619583\pi$
$263$	−21.9904	−	12.6962i	−1.35598	−	0.782878i	−0.989080	+	0.147380i	$0.952916\pi$
$264$		0			0
$265$		−	38.3205i		−	2.35401i
$266$		0			0
$267$	7.09808	+	7.09808i	0.434395	+	0.434395i
$268$		0			0
$269$	5.79423	+	21.6244i	0.353280	+	1.31846i	0.882635	+	0.470059i	$0.155768\pi$
$269$	5.79423	+	21.6244i	0.353280	+	1.31846i	−0.529354	+	0.848401i	$0.677566\pi$
$270$		0			0
$271$	6.06218	+	10.5000i	0.368251	+	0.637830i	0.989292	−	0.145948i	$-0.0466233\pi$
$271$	6.06218	+	10.5000i	0.368251	+	0.637830i	−0.621041	+	0.783778i	$0.713290\pi$
$272$		0			0
$273$	−0.366025	−	1.90192i	−0.0221529	−	0.115110i
$274$		0			0
$275$	−26.2224	−	7.02628i	−1.58127	−	0.423701i
$276$		0			0
$277$	16.7942	−	4.50000i	1.00907	−	0.270379i	0.283828	−	0.958875i	$-0.408396\pi$
$277$	16.7942	−	4.50000i	1.00907	−	0.270379i	0.725240	+	0.688496i	$0.241729\pi$
$278$		0			0
$279$		−	0.196152i		−	0.0117433i
$280$		0			0
$281$		−	12.9282i		−	0.771232i	−0.922659	−	0.385616i	$-0.873989\pi$
$281$		−	12.9282i		−	0.771232i	0.922659	−	0.385616i	$-0.126011\pi$
$282$		0			0
$283$	−16.8923	+	4.52628i	−1.00414	+	0.269059i	−0.723180	−	0.690659i	$-0.757320\pi$
$283$	−16.8923	+	4.52628i	−1.00414	+	0.269059i	−0.280963	+	0.959719i	$0.590654\pi$
$284$		0			0
$285$	−27.3564	−	7.33013i	−1.62045	−	0.434199i
$286$		0			0
$287$	−17.8564	+	15.4641i	−1.05403	+	0.912817i
$288$		0			0
$289$	8.39230	+	14.5359i	0.493665	+	0.855053i
$290$		0			0
$291$	−5.46410	−	20.3923i	−0.320311	−	1.19542i
$292$		0			0
$293$	−5.92820	−	5.92820i	−0.346329	−	0.346329i	0.512411	−	0.858740i	$-0.328752\pi$
$293$	−5.92820	−	5.92820i	−0.346329	−	0.346329i	−0.858740	+	0.512411i	$0.828752\pi$
$294$		0			0
$295$			34.5167i			2.00964i
$296$		0			0
$297$	−16.6244	−	9.59808i	−0.964643	−	0.556937i
$298$		0			0
$299$	−0.241670	+	0.901924i	−0.0139761	+	0.0521596i
$300$		0			0
$301$	0.124356	−	1.73205i	0.00716774	−	0.0998337i
$302$		0			0
$303$	−7.06218	−	12.2321i	−0.405712	−	0.702713i
$304$		0			0
$305$	0.232051	−	0.401924i	0.0132872	−	0.0230141i
$306$		0			0
$307$	−9.00000	+	9.00000i	−0.513657	+	0.513657i	−0.915645	−	0.401988i	$-0.868319\pi$
$307$	−9.00000	+	9.00000i	−0.513657	+	0.513657i	0.401988	+	0.915645i	$0.368319\pi$
$308$		0			0
$309$	0.633975	+	0.633975i	0.0360656	+	0.0360656i
$310$		0			0
$311$	0.401924	+	0.232051i	0.0227910	+	0.0131584i	0.511352	−	0.859371i	$-0.329145\pi$
$311$	0.401924	+	0.232051i	0.0227910	+	0.0131584i	−0.488561	+	0.872530i	$0.662478\pi$
$312$		0			0
$313$	−8.30385	+	4.79423i	−0.469361	+	0.270986i	−0.715972	−	0.698129i	$-0.754016\pi$
$313$	−8.30385	+	4.79423i	−0.469361	+	0.270986i	0.246611	+	0.969115i	$0.420683\pi$
$314$		0			0
$315$	−3.63397	+	5.36603i	−0.204751	+	0.302341i
$316$		0			0
$317$	−11.7942	−	3.16025i	−0.662430	−	0.177498i	−0.0880875	−	0.996113i	$-0.528076\pi$
$317$	−11.7942	−	3.16025i	−0.662430	−	0.177498i	−0.574342	+	0.818615i	$0.694742\pi$
$318$		0			0
$319$	11.5622	−	20.0263i	0.647358	−	1.12126i
$320$		0			0
$321$	−1.73205			−0.0966736
$322$		0			0
$323$	−1.43782	+	1.43782i	−0.0800026	+	0.0800026i
$324$		0			0
$325$	2.26795	−	0.607695i	0.125803	−	0.0337089i
$326$		0			0
$327$	24.9904	−	14.4282i	1.38197	−	0.797881i
$328$		0			0
$329$	−6.69615	+	19.3301i	−0.369171	+	1.06570i
$330$		0			0
$331$	−4.62436	+	17.2583i	−0.254178	+	0.948604i	0.714369	+	0.699770i	$0.246714\pi$
$331$	−4.62436	+	17.2583i	−0.254178	+	0.948604i	−0.968546	+	0.248834i	$0.919953\pi$
$332$		0			0
$333$	2.09808	+	7.83013i	0.114974	+	0.429088i
$334$		0			0
$335$	25.3923			1.38733
$336$		0			0
$337$	−33.8564			−1.84428			−0.922138	−	0.386861i	$-0.873559\pi$
$337$	−33.8564			−1.84428			−0.922138	+	0.386861i	$0.873559\pi$
$338$		0			0
$339$	−2.73205	−	10.1962i	−0.148385	−	0.553779i
$340$		0			0
$341$	−0.303848	+	1.13397i	−0.0164543	+	0.0614082i
$342$		0			0
$343$	15.5885	−	10.0000i	0.841698	−	0.539949i
$344$		0			0
$345$	13.7942	−	7.96410i	0.742656	−	0.428773i
$346$		0			0
$347$	16.6962	−	4.47372i	0.896296	−	0.240162i	0.218871	−	0.975754i	$-0.429762\pi$
$347$	16.6962	−	4.47372i	0.896296	−	0.240162i	0.677425	+	0.735592i	$0.263096\pi$
$348$		0			0
$349$	18.1244	−	18.1244i	0.970175	−	0.970175i	−0.0293934	−	0.999568i	$-0.509358\pi$
$349$	18.1244	−	18.1244i	0.970175	−	0.970175i	0.999568	+	0.0293934i	$0.00935756\pi$
$350$		0			0
$351$	1.66025			0.0886178
$352$		0			0
$353$	−6.89230	+	11.9378i	−0.366840	+	0.635386i	−0.989070	−	0.147449i	$-0.952894\pi$
$353$	−6.89230	+	11.9378i	−0.366840	+	0.635386i	0.622229	+	0.782835i	$0.286227\pi$
$354$		0			0
$355$	24.1244	+	6.46410i	1.28039	+	0.343079i
$356$		0			0
$357$	1.03590	+	2.13397i	0.0548256	+	0.112942i
$358$		0			0
$359$	−2.13397	+	1.23205i	−0.112627	+	0.0650252i	−0.555255	−	0.831680i	$-0.687379\pi$
$359$	−2.13397	+	1.23205i	−0.112627	+	0.0650252i	0.442628	+	0.896705i	$0.354046\pi$
$360$		0			0
$361$	0.169873	+	0.0980762i	0.00894068	+	0.00516191i
$362$		0			0
$363$	−11.1962	−	11.1962i	−0.587646	−	0.587646i
$364$		0			0
$365$	−7.56218	+	7.56218i	−0.395822	+	0.395822i
$366$		0			0
$367$	9.06218	−	15.6962i	0.473042	−	0.819332i	−0.526482	−	0.850186i	$-0.676489\pi$
$367$	9.06218	−	15.6962i	0.473042	−	0.819332i	0.999524	+	0.0308537i	$0.00982261\pi$
$368$		0			0
$369$	3.26795	+	5.66025i	0.170123	+	0.294661i
$370$		0			0
$371$	25.0885	+	16.9904i	1.30253	+	0.882097i
$372$		0			0
$373$	0.866025	−	3.23205i	0.0448411	−	0.167349i	−0.939874	−	0.341521i	$-0.889058\pi$
$373$	0.866025	−	3.23205i	0.0448411	−	0.167349i	0.984715	+	0.174171i	$0.0557247\pi$
$374$		0			0
$375$	−6.69615	−	3.86603i	−0.345788	−	0.199641i
$376$		0			0
$377$			2.00000i			0.103005i
$378$		0			0
$379$	24.1244	+	24.1244i	1.23918	+	1.23918i	0.960335	+	0.278850i	$0.0899533\pi$
$379$	24.1244	+	24.1244i	1.23918	+	1.23918i	0.278850	+	0.960335i	$0.410047\pi$
$380$		0			0
$381$	−1.26795	−	4.73205i	−0.0649590	−	0.242430i
$382$		0			0
$383$	7.40192	+	12.8205i	0.378221	+	0.655097i	0.990803	−	0.135309i	$-0.0432027\pi$
$383$	7.40192	+	12.8205i	0.378221	+	0.655097i	−0.612583	+	0.790406i	$0.709869\pi$
$384$		0			0
$385$	29.3205	−	25.3923i	1.49431	−	1.29411i
$386$		0			0
$387$	−0.464102	−	0.124356i	−0.0235916	−	0.00632135i
$388$		0			0
$389$	19.9904	−	5.35641i	1.01355	−	0.271581i	0.286440	−	0.958098i	$-0.407528\pi$
$389$	19.9904	−	5.35641i	1.01355	−	0.271581i	0.727113	+	0.686518i	$0.240862\pi$
$390$		0			0
$391$		−	1.14359i		−	0.0578340i
$392$		0			0
$393$		−	17.9282i		−	0.904358i
$394$		0			0
$395$	2.13397	−	0.571797i	0.107372	−	0.0287702i
$396$		0			0
$397$	−5.13397	−	1.37564i	−0.257667	−	0.0690416i	0.127673	−	0.991816i	$-0.459249\pi$
$397$	−5.13397	−	1.37564i	−0.257667	−	0.0690416i	−0.385340	+	0.922775i	$0.625916\pi$
$398$		0			0
$399$	16.9282	−	14.6603i	0.847470	−	0.733931i
$400$		0			0
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	0.990257	−	0.139253i	$-0.0444700\pi$
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	−0.615725	+	0.787961i	$0.711137\pi$
$402$		0			0
$403$	−0.0262794	−	0.0980762i	−0.00130907	−	0.00488552i
$404$		0			0
$405$	−25.2224	−	25.2224i	−1.25331	−	1.25331i
$406$		0			0
$407$		−	48.5167i		−	2.40488i
$408$		0			0
$409$	−7.50000	−	4.33013i	−0.370851	−	0.214111i	0.302979	−	0.952997i	$-0.402019\pi$
$409$	−7.50000	−	4.33013i	−0.370851	−	0.214111i	−0.673830	+	0.738886i	$0.735352\pi$
$410$		0			0
$411$	6.79423	−	25.3564i	0.335135	−	1.25074i
$412$		0			0
$413$	−22.5981	−	15.3038i	−1.11198	−	0.753053i
$414$		0			0
$415$	−20.0263	−	34.6865i	−0.983051	−	1.70269i
$416$		0			0
$417$	−2.63397	+	4.56218i	−0.128986	+	0.223411i
$418$		0			0
$419$	19.0000	−	19.0000i	0.928211	−	0.928211i	−0.0693796	−	0.997590i	$-0.522102\pi$
$419$	19.0000	−	19.0000i	0.928211	−	0.928211i	0.997590	+	0.0693796i	$0.0221020\pi$
$420$		0			0
$421$	8.66025	+	8.66025i	0.422075	+	0.422075i	0.885918	−	0.463843i	$-0.153530\pi$
$421$	8.66025	+	8.66025i	0.422075	+	0.422075i	−0.463843	+	0.885918i	$0.653530\pi$
$422$		0			0
$423$	4.90192	+	2.83013i	0.238340	+	0.137605i
$424$		0			0
$425$	−2.49038	+	1.43782i	−0.120801	+	0.0697446i
$426$		0			0
$427$	0.160254	+	0.330127i	0.00775524	+	0.0159760i
$428$		0			0
$429$	3.09808	+	0.830127i	0.149577	+	0.0400789i
$430$		0			0
$431$	−6.66987	+	11.5526i	−0.321276	+	0.556467i	−0.980752	−	0.195259i	$-0.937445\pi$
$431$	−6.66987	+	11.5526i	−0.321276	+	0.556467i	0.659475	+	0.751726i	$0.270779\pi$
$432$		0			0
$433$	29.1769			1.40215			0.701077	−	0.713086i	$-0.252703\pi$
$433$	29.1769			1.40215			0.701077	+	0.713086i	$0.252703\pi$
$434$		0			0
$435$	24.1244	−	24.1244i	1.15667	−	1.15667i
$436$		0			0
$437$	−10.4282	+	2.79423i	−0.498849	+	0.133666i
$438$		0			0
$439$	−12.5263	+	7.23205i	−0.597847	+	0.345167i	−0.768194	−	0.640217i	$-0.778844\pi$
$439$	−12.5263	+	7.23205i	−0.597847	+	0.345167i	0.170347	+	0.985384i	$0.445511\pi$
$440$		0			0
$441$	−1.90192	−	4.75833i	−0.0905678	−	0.226587i
$442$		0			0
$443$	−3.42820	+	12.7942i	−0.162879	+	0.607872i	0.835422	+	0.549608i	$0.185223\pi$
$443$	−3.42820	+	12.7942i	−0.162879	+	0.607872i	−0.998301	+	0.0582637i	$0.981444\pi$
$444$		0			0
$445$	−4.50000	−	16.7942i	−0.213320	−	0.796123i
$446$		0			0
$447$	−17.9282			−0.847975
$448$		0			0
$449$	11.3205			0.534248			0.267124	−	0.963662i	$-0.413927\pi$
$449$	11.3205			0.534248			0.267124	+	0.963662i	$0.413927\pi$
$450$		0			0
$451$	−10.1244	−	37.7846i	−0.476737	−	1.77921i
$452$		0			0
$453$	4.69615	−	17.5263i	0.220644	−	0.823456i
$454$		0			0
$455$	−1.09808	+	3.16987i	−0.0514786	+	0.148606i
$456$		0			0
$457$	−25.2846	+	14.5981i	−1.18276	+	0.682869i	−0.956652	−	0.291232i	$-0.905935\pi$
$457$	−25.2846	+	14.5981i	−1.18276	+	0.682869i	−0.226112	+	0.974101i	$0.572601\pi$
$458$		0			0
$459$	−1.96410	+	0.526279i	−0.0916764	+	0.0245646i
$460$		0			0
$461$	−1.33975	+	1.33975i	−0.0623982	+	0.0623982i	−0.737617	−	0.675219i	$-0.764049\pi$
$461$	−1.33975	+	1.33975i	−0.0623982	+	0.0623982i	0.675219	+	0.737617i	$0.264049\pi$
$462$		0			0
$463$	29.8564			1.38754			0.693772	−	0.720194i	$-0.255947\pi$
$463$	29.8564			1.38754			0.693772	+	0.720194i	$0.255947\pi$
$464$		0			0
$465$	−0.866025	+	1.50000i	−0.0401610	+	0.0695608i
$466$		0			0
$467$	0.0358984	+	0.00961894i	0.00166118	+	0.000445112i	0.259650	−	0.965703i	$-0.416393\pi$
$467$	0.0358984	+	0.00961894i	0.00166118	+	0.000445112i	−0.257988	+	0.966148i	$0.583060\pi$
$468$		0			0
$469$	−11.2583	+	16.6244i	−0.519861	+	0.767641i
$470$		0			0
$471$	−27.5263	+	15.8923i	−1.26834	+	0.732279i
$472$		0			0
$473$	2.49038	+	1.43782i	0.114508	+	0.0661111i
$474$		0			0
$475$	19.1962	+	19.1962i	0.880780	+	0.880780i
$476$		0			0
$477$	5.92820	−	5.92820i	0.271434	−	0.271434i
$478$		0			0
$479$	7.79423	−	13.5000i	0.356127	−	0.616831i	−0.631183	−	0.775634i	$-0.717430\pi$
$479$	7.79423	−	13.5000i	0.356127	−	0.616831i	0.987310	+	0.158803i	$0.0507636\pi$
$480$		0			0
$481$	2.09808	+	3.63397i	0.0956640	+	0.165695i
$482$		0			0
$483$	−0.901924	+	12.5622i	−0.0410390	+	0.571599i
$484$		0			0
$485$	−9.46410	+	35.3205i	−0.429743	+	1.60382i
$486$		0			0
$487$	19.3301	+	11.1603i	0.875932	+	0.505719i	0.869315	−	0.494259i	$-0.164560\pi$
$487$	19.3301	+	11.1603i	0.875932	+	0.505719i	0.00661681	+	0.999978i	$0.497894\pi$
$488$		0			0
$489$		−	0.464102i		−	0.0209874i
$490$		0			0
$491$	−27.5885	−	27.5885i	−1.24505	−	1.24505i	−0.957880	−	0.287170i	$-0.907286\pi$
$491$	−27.5885	−	27.5885i	−1.24505	−	1.24505i	−0.287170	−	0.957880i	$-0.592714\pi$
$492$		0			0
$493$	−0.633975	−	2.36603i	−0.0285528	−	0.106560i
$494$		0			0
$495$	−5.36603	−	9.29423i	−0.241185	−	0.417745i
$496$		0			0
$497$	−14.9282	+	12.9282i	−0.669621	+	0.579909i
$498$		0			0
$499$	3.69615	+	0.990381i	0.165463	+	0.0443355i	0.340599	−	0.940209i	$-0.389370\pi$
$499$	3.69615	+	0.990381i	0.165463	+	0.0443355i	−0.175137	+	0.984544i	$0.556037\pi$
$500$		0			0
$501$	−10.9282	+	2.92820i	−0.488236	+	0.130822i
$502$		0			0
$503$			4.14359i			0.184754i	0.995724	+	0.0923769i	$0.0294464\pi$
$503$			4.14359i			0.184754i	−0.995724	+	0.0923769i	$0.970554\pi$
$504$		0			0
$505$			24.4641i			1.08864i
$506$		0			0
$507$	23.9904	−	6.42820i	1.06545	−	0.285487i
$508$		0			0
$509$	16.5263	+	4.42820i	0.732514	+	0.196277i	0.605749	−	0.795656i	$-0.292874\pi$
$509$	16.5263	+	4.42820i	0.732514	+	0.196277i	0.126766	+	0.991933i	$0.459540\pi$
$510$		0			0
$511$	−1.59808	−	8.30385i	−0.0706947	−	0.367341i
$512$		0			0
$513$	9.59808	+	16.6244i	0.423765	+	0.733983i
$514$		0			0
$515$	−0.401924	−	1.50000i	−0.0177109	−	0.0660979i
$516$		0			0
$517$	−23.9545	−	23.9545i	−1.05352	−	1.05352i
$518$		0			0
$519$		−	9.19615i		−	0.403666i
$520$		0			0
$521$	−37.6244	−	21.7224i	−1.64835	−	0.951677i	−0.977727	−	0.209881i	$-0.932692\pi$
$521$	−37.6244	−	21.7224i	−1.64835	−	0.951677i	−0.670626	−	0.741796i	$-0.733974\pi$
$522$		0			0
$523$	−9.28461	+	34.6506i	−0.405988	+	1.51517i	0.396239	+	0.918147i	$0.370315\pi$
$523$	−9.28461	+	34.6506i	−0.405988	+	1.51517i	−0.802227	+	0.597019i	$0.796352\pi$
$524$		0			0
$525$	28.4904	−	13.8301i	1.24342	−	0.603596i
$526$		0			0
$527$	0.0621778	+	0.107695i	0.00270851	+	0.00469127i
$528$		0			0
$529$	−8.46410	+	14.6603i	−0.368004	+	0.637402i
$530$		0			0
$531$	−5.33975	+	5.33975i	−0.231725	+	0.231725i
$532$		0			0
$533$	2.39230	+	2.39230i	0.103622	+	0.103622i
$534$		0			0
$535$	2.59808	+	1.50000i	0.112325	+	0.0648507i
$536$		0			0
$537$	−13.1603	+	7.59808i	−0.567907	+	0.327881i
$538$		0			0
$539$	3.62436	+	30.4545i	0.156112	+	1.31177i
$540$		0			0
$541$	−21.5263	−	5.76795i	−0.925487	−	0.247984i	−0.235558	−	0.971860i	$-0.575692\pi$
$541$	−21.5263	−	5.76795i	−0.925487	−	0.247984i	−0.689929	+	0.723877i	$0.742358\pi$
$542$		0			0
$543$	10.0981	−	17.4904i	0.433350	−	0.750584i
$544$		0			0
$545$	−49.9808			−2.14094
$546$		0			0
$547$	−15.0526	+	15.0526i	−0.643601	+	0.643601i	−0.951439	−	0.307838i	$-0.900395\pi$
$547$	−15.0526	+	15.0526i	−0.643601	+	0.643601i	0.307838	+	0.951439i	$0.400395\pi$
$548$		0			0
$549$	0.0980762	−	0.0262794i	0.00418579	−	0.00112158i
$550$		0			0
$551$	−20.0263	+	11.5622i	−0.853148	+	0.492565i
$552$		0			0
$553$	−0.571797	+	1.65064i	−0.0243153	+	0.0701921i
$554$		0			0
$555$	18.5263	−	69.1410i	0.786397	−	2.93487i
$556$		0			0
$557$	−1.40192	−	5.23205i	−0.0594014	−	0.221689i	0.929844	−	0.367954i	$-0.119942\pi$
$557$	−1.40192	−	5.23205i	−0.0594014	−	0.221689i	−0.989245	+	0.146265i	$0.953275\pi$
$558$		0			0
$559$	−0.248711			−0.0105194
$560$		0			0
$561$	−3.92820			−0.165849
$562$		0			0
$563$	−11.4282	−	42.6506i	−0.481641	−	1.79751i	−0.594731	−	0.803925i	$-0.702741\pi$
$563$	−11.4282	−	42.6506i	−0.481641	−	1.79751i	0.113089	−	0.993585i	$-0.463925\pi$
$564$		0			0
$565$	−4.73205	+	17.6603i	−0.199079	+	0.742972i
$566$		0			0
$567$	27.6962	−	5.33013i	1.16313	−	0.223844i
$568$		0			0
$569$	26.0885	−	15.0622i	1.09369	−	0.631439i	0.159130	−	0.987258i	$-0.449131\pi$
$569$	26.0885	−	15.0622i	1.09369	−	0.631439i	0.934555	+	0.355818i	$0.115798\pi$
$570$		0			0
$571$	−10.1603	+	2.72243i	−0.425193	+	0.113930i	−0.465069	−	0.885274i	$-0.653970\pi$
$571$	−10.1603	+	2.72243i	−0.425193	+	0.113930i	0.0398756	+	0.999205i	$0.487304\pi$
$572$		0			0
$573$	11.8301	−	11.8301i	0.494211	−	0.494211i
$574$		0			0
$575$	−15.2679			−0.636717
$576$		0			0
$577$	17.6244	−	30.5263i	0.733712	−	1.27083i	−0.221575	−	0.975143i	$-0.571120\pi$
$577$	17.6244	−	30.5263i	0.733712	−	1.27083i	0.955286	−	0.295682i	$-0.0955470\pi$
$578$		0			0
$579$	−42.9186	−	11.5000i	−1.78364	−	0.477924i
$580$		0			0
$581$	31.5885	+	2.26795i	1.31051	+	0.0940904i
$582$		0			0
$583$	−43.4545	+	25.0885i	−1.79970	+	1.03906i
$584$		0			0
$585$	0.803848	+	0.464102i	0.0332350	+	0.0191882i
$586$		0			0
$587$	−8.07180	−	8.07180i	−0.333159	−	0.333159i	0.520626	−	0.853785i	$-0.325699\pi$
$587$	−8.07180	−	8.07180i	−0.333159	−	0.333159i	−0.853785	+	0.520626i	$0.825699\pi$
$588$		0			0
$589$	0.830127	−	0.830127i	0.0342048	−	0.0342048i
$590$		0			0
$591$	−0.901924	+	1.56218i	−0.0371002	+	0.0642594i
$592$		0			0
$593$	−4.69615	−	8.13397i	−0.192848	−	0.334022i	0.753345	−	0.657625i	$-0.228439\pi$
$593$	−4.69615	−	8.13397i	−0.192848	−	0.334022i	−0.946193	+	0.323603i	$0.895106\pi$
$594$		0			0
$595$	0.294229	−	4.09808i	0.0120622	−	0.168005i
$596$		0			0
$597$	−0.964102	+	3.59808i	−0.0394581	+	0.147259i
$598$		0			0
$599$	25.3301	+	14.6244i	1.03496	+	0.597535i	0.918402	−	0.395649i	$-0.129480\pi$
$599$	25.3301	+	14.6244i	1.03496	+	0.597535i	0.116559	+	0.993184i	$0.462814\pi$
$600$		0			0
$601$		−	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
$603$	3.92820	+	3.92820i	0.159969	+	0.159969i
$604$		0			0
$605$	7.09808	+	26.4904i	0.288578	+	1.07699i
$606$		0			0
$607$	10.5263	+	18.2321i	0.427249	+	0.740016i	0.996627	−	0.0820591i	$-0.0261496\pi$
$607$	10.5263	+	18.2321i	0.427249	+	0.740016i	−0.569379	+	0.822075i	$0.692816\pi$
$608$		0			0
$609$	5.09808	+	26.4904i	0.206584	+	1.07344i
$610$		0			0
$611$	2.83013	+	0.758330i	0.114495	+	0.0306788i
$612$		0			0
$613$	−21.5263	+	5.76795i	−0.869438	+	0.232965i	−0.665845	−	0.746090i	$-0.731929\pi$
$613$	−21.5263	+	5.76795i	−0.869438	+	0.232965i	−0.203593	+	0.979056i	$0.565262\pi$
$614$		0			0
$615$		−	57.7128i		−	2.32721i
$616$		0			0
$617$		−	7.46410i		−	0.300493i	−0.988649	−	0.150247i	$-0.951993\pi$
$617$		−	7.46410i		−	0.300493i	0.988649	−	0.150247i	$-0.0480068\pi$
$618$		0			0
$619$	−25.8923	+	6.93782i	−1.04070	+	0.278855i	−0.738403	−	0.674359i	$-0.764420\pi$
$619$	−25.8923	+	6.93782i	−1.04070	+	0.278855i	−0.302296	+	0.953214i	$0.597753\pi$
$620$		0			0
$621$	−10.4282	−	2.79423i	−0.418469	−	0.112129i
$622$		0			0
$623$	12.9904	+	4.50000i	0.520449	+	0.180289i
$624$		0			0
$625$	−8.79423	−	15.2321i	−0.351769	−	0.609282i
$626$		0			0
$627$	9.59808	+	35.8205i	0.383310	+	1.43053i
$628$		0			0
$629$	−3.63397	−	3.63397i	−0.144896	−	0.144896i
$630$		0			0
$631$			16.2487i			0.646851i	0.946254	+	0.323425i	$0.104835\pi$
$631$			16.2487i			0.646851i	−0.946254	+	0.323425i	$0.895165\pi$
$632$		0			0
$633$	−4.90192	−	2.83013i	−0.194834	−	0.112487i
$634$		0			0
$635$	−2.19615	+	8.19615i	−0.0871517	+	0.325254i
$636$		0			0
$637$	−1.58846	−	2.12436i	−0.0629370	−	0.0841700i
$638$		0			0
$639$	2.73205	+	4.73205i	0.108078	+	0.187197i
$640$		0			0
$641$	19.4282	−	33.6506i	0.767368	−	1.32912i	−0.171618	−	0.985164i	$-0.554899\pi$
$641$	19.4282	−	33.6506i	0.767368	−	1.32912i	0.938986	−	0.343957i	$-0.111767\pi$
$642$		0			0
$643$	−15.3923	+	15.3923i	−0.607013	+	0.607013i	−0.942164	−	0.335151i	$-0.891213\pi$
$643$	−15.3923	+	15.3923i	−0.607013	+	0.607013i	0.335151	+	0.942164i	$0.391213\pi$
$644$		0			0
$645$	3.00000	+	3.00000i	0.118125	+	0.118125i
$646$		0			0
$647$	29.1340	+	16.8205i	1.14537	+	0.661282i	0.947756	−	0.318997i	$-0.103346\pi$
$647$	29.1340	+	16.8205i	1.14537	+	0.661282i	0.197619	+	0.980279i	$0.436679\pi$
$648$		0			0
$649$	39.1410	−	22.5981i	1.53642	−	0.887052i
$650$		0			0
$651$	−0.598076	−	1.23205i	−0.0234405	−	0.0482879i
$652$		0			0
$653$	−20.7224	−	5.55256i	−0.810931	−	0.217288i	−0.170554	−	0.985348i	$-0.554556\pi$
$653$	−20.7224	−	5.55256i	−0.810931	−	0.217288i	−0.640378	+	0.768060i	$0.721222\pi$
$654$		0			0
$655$	−15.5263	+	26.8923i	−0.606662	+	1.05077i
$656$		0			0
$657$	−2.33975			−0.0912822
$658$		0			0
$659$	8.85641	−	8.85641i	0.344997	−	0.344997i	−0.513245	−	0.858242i	$-0.671557\pi$
$659$	8.85641	−	8.85641i	0.344997	−	0.344997i	0.858242	+	0.513245i	$0.171557\pi$
$660$		0			0
$661$	18.0622	−	4.83975i	0.702537	−	0.188244i	0.110170	−	0.993913i	$-0.464860\pi$
$661$	18.0622	−	4.83975i	0.702537	−	0.188244i	0.592367	+	0.805668i	$0.298194\pi$
$662$		0			0
$663$	0.294229	−	0.169873i	0.0114269	−	0.00659732i
$664$		0			0
$665$	−38.0885	+	7.33013i	−1.47701	+	0.284250i
$666$		0			0
$667$	3.36603	−	12.5622i	0.130333	−	0.486409i
$668$		0			0
$669$	8.92820	+	33.3205i	0.345184	+	1.28825i
$670$		0			0
$671$	−0.607695			−0.0234598
$672$		0			0
$673$	−0.784610			−0.0302445			−0.0151222	−	0.999886i	$-0.504814\pi$
$673$	−0.784610			−0.0302445			−0.0151222	+	0.999886i	$0.504814\pi$
$674$		0			0
$675$	7.02628	+	26.2224i	0.270442	+	1.00930i
$676$		0			0
$677$	13.2776	−	49.5526i	0.510298	−	1.90446i	0.0930654	−	0.995660i	$-0.470333\pi$
$677$	13.2776	−	49.5526i	0.510298	−	1.90446i	0.417233	−	0.908800i	$-0.363000\pi$
$678$		0			0
$679$	−18.9282	−	21.8564i	−0.726398	−	0.838772i
$680$		0			0
$681$	39.8205	−	22.9904i	1.52593	−	0.880993i
$682$		0			0
$683$	43.2128	−	11.5788i	1.65349	−	0.443052i	0.692905	−	0.721029i	$-0.256331\pi$
$683$	43.2128	−	11.5788i	1.65349	−	0.443052i	0.960588	+	0.277977i	$0.0896640\pi$
$684$		0			0
$685$	−32.1506	+	32.1506i	−1.22841	+	1.22841i
$686$		0			0
$687$	34.8564			1.32985
$688$		0			0
$689$	2.16987	−	3.75833i	0.0826656	−	0.143181i
$690$		0			0
$691$	11.1603	+	2.99038i	0.424556	+	0.113759i	0.464770	−	0.885432i	$-0.346137\pi$
$691$	11.1603	+	2.99038i	0.424556	+	0.113759i	−0.0402135	+	0.999191i	$0.512804\pi$
$692$		0			0
$693$	8.46410	+	0.607695i	0.321525	+	0.0230844i
$694$		0			0
$695$	7.90192	−	4.56218i	0.299737	−	0.173053i
$696$		0			0
$697$	−3.58846	−	2.07180i	−0.135923	−	0.0784749i
$698$		0			0
$699$	15.2942	+	15.2942i	0.578481	+	0.578481i
$700$		0			0
$701$	−7.39230	+	7.39230i	−0.279204	+	0.279204i	−0.832791	−	0.553588i	$-0.813258\pi$
$701$	−7.39230	+	7.39230i	−0.279204	+	0.279204i	0.553588	+	0.832791i	$0.313258\pi$
$702$		0			0
$703$	−24.2583	+	42.0167i	−0.914920	+	1.58469i
$704$		0			0
$705$	−24.9904	−	43.2846i	−0.941192	−	1.63019i
$706$		0			0
$707$	−16.0167	−	10.8468i	−0.602369	−	0.407935i
$708$		0			0
$709$	−2.34936	+	8.76795i	−0.0882323	+	0.329287i	−0.995907	−	0.0903879i	$-0.971189\pi$
$709$	−2.34936	+	8.76795i	−0.0882323	+	0.329287i	0.907674	+	0.419675i	$0.137856\pi$
$710$		0			0
$711$	0.418584	+	0.241670i	0.0156981	+	0.00906332i
$712$		0			0
$713$			0.660254i			0.0247267i
$714$		0			0
$715$	−3.92820	−	3.92820i	−0.146906	−	0.146906i
$716$		0			0
$717$	7.73205	+	28.8564i	0.288759	+	1.07766i
$718$		0			0
$719$	−15.7942	−	27.3564i	−0.589025	−	1.02022i	−0.994360	−	0.106054i	$-0.966178\pi$
$719$	−15.7942	−	27.3564i	−0.589025	−	1.02022i	0.405335	−	0.914168i	$-0.367155\pi$
$720$		0			0
$721$	1.16025	+	0.401924i	0.0432101	+	0.0149684i
$722$		0			0
$723$	0.133975	+	0.0358984i	0.00498257	+	0.00133508i
$724$		0			0
$725$	−31.5885	+	8.46410i	−1.17317	+	0.314349i
$726$		0			0
$727$			6.67949i			0.247729i	0.992299	+	0.123864i	$0.0395288\pi$
$727$			6.67949i			0.247729i	−0.992299	+	0.123864i	$0.960471\pi$
$728$		0			0
$729$			17.5885i			0.651424i
$730$		0			0
$731$	0.294229	−	0.0788383i	0.0108824	−	0.00291594i
$732$		0			0
$733$	45.1865	+	12.1077i	1.66900	+	0.447208i	0.964842	−	0.262832i	$-0.0846566\pi$
$733$	45.1865	+	12.1077i	1.66900	+	0.447208i	0.704161	+	0.710040i	$0.251323\pi$
$734$		0			0
$735$	−6.46410	+	44.7846i	−0.238432	+	1.65191i
$736$		0			0
$737$	−16.6244	−	28.7942i	−0.612366	−	1.06065i
$738$		0			0
$739$	13.4808	+	50.3109i	0.495898	+	1.85072i	0.524942	+	0.851138i	$0.324087\pi$
$739$	13.4808	+	50.3109i	0.495898	+	1.85072i	−0.0290444	+	0.999578i	$0.509246\pi$
$740$		0			0
$741$	−2.26795	−	2.26795i	−0.0833152	−	0.0833152i
$742$		0			0
$743$			24.9282i			0.914527i	0.889331	+	0.457264i	$0.151170\pi$
$743$			24.9282i			0.914527i	−0.889331	+	0.457264i	$0.848830\pi$
$744$		0			0
$745$	26.8923	+	15.5263i	0.985258	+	0.568839i
$746$		0			0
$747$	2.26795	−	8.46410i	0.0829799	−	0.309685i
$748$		0			0
$749$	−2.13397	+	1.03590i	−0.0779737	+	0.0378509i
$750$		0			0
$751$	12.5263	+	21.6962i	0.457090	+	0.791704i	0.998806	−	0.0488582i	$-0.0155582\pi$
$751$	12.5263	+	21.6962i	0.457090	+	0.791704i	−0.541715	+	0.840562i	$0.682225\pi$
$752$		0			0
$753$	−18.5622	+	32.1506i	−0.676443	+	1.17163i
$754$		0			0
$755$	−22.2224	+	22.2224i	−0.808757	+	0.808757i
$756$		0			0
$757$	1.33975	+	1.33975i	0.0486939	+	0.0486939i	0.731034	−	0.682341i	$-0.239038\pi$
$757$	1.33975	+	1.33975i	0.0486939	+	0.0486939i	−0.682341	+	0.731034i	$0.739038\pi$
$758$		0			0
$759$	−18.0622	−	10.4282i	−0.655616	−	0.378520i
$760$		0			0
$761$	15.2321	−	8.79423i	0.552161	−	0.318791i	−0.197832	−	0.980236i	$-0.563390\pi$
$761$	15.2321	−	8.79423i	0.552161	−	0.318791i	0.749993	+	0.661445i	$0.230057\pi$
$762$		0			0
$763$	22.1603	−	32.7224i	0.802255	−	1.18463i
$764$		0			0
$765$	−1.09808	−	0.294229i	−0.0397010	−	0.0106379i
$766$		0			0
$767$	−1.95448	+	3.38526i	−0.0705723	+	0.122235i
$768$		0			0
$769$	−17.8564			−0.643918			−0.321959	−	0.946754i	$-0.604341\pi$
$769$	−17.8564			−0.643918			−0.321959	+	0.946754i	$0.604341\pi$
$770$		0			0
$771$	−1.90192	+	1.90192i	−0.0684961	+	0.0684961i
$772$		0			0
$773$	15.0622	−	4.03590i	0.541749	−	0.145161i	0.0224406	−	0.999748i	$-0.492856\pi$
$773$	15.0622	−	4.03590i	0.541749	−	0.145161i	0.519308	+	0.854587i	$0.326190\pi$
$774$		0			0
$775$	1.43782	−	0.830127i	0.0516481	−	0.0298190i
$776$		0			0
$777$	37.0526	+	42.7846i	1.32925	+	1.53489i
$778$		0			0
$779$	−10.1244	+	37.7846i	−0.362743	+	1.35377i
$780$		0			0
$781$	−8.46410	−	31.5885i	−0.302869	−	1.13032i
$782$		0			0
$783$	−23.1244			−0.826397
$784$		0			0
$785$	55.0526			1.96491
$786$		0			0
$787$	−4.16025	−	15.5263i	−0.148297	−	0.553452i	−0.999586	−	0.0287557i	$-0.990846\pi$
$787$	−4.16025	−	15.5263i	−0.148297	−	0.553452i	0.851289	−	0.524696i	$-0.175821\pi$
$788$		0			0
$789$	−12.6962	+	47.3827i	−0.451995	+	1.68687i
$790$		0			0
$791$	−9.46410	−	10.9282i	−0.336505	−	0.388562i
$792$		0			0
$793$	0.0455173	−	0.0262794i	0.00161637	−	0.000933210i
$794$		0			0
$795$	−71.5070	+	19.1603i	−2.53609	+	0.679544i
$796$		0			0
$797$	30.6603	−	30.6603i	1.08604	−	1.08604i	0.0901101	−	0.995932i	$-0.471278\pi$
$797$	30.6603	−	30.6603i	1.08604	−	1.08604i	0.995932	−	0.0901101i	$-0.0287219\pi$
$798$		0			0
$799$	−3.58846			−0.126950
$800$		0			0
$801$	1.90192	−	3.29423i	0.0672012	−	0.116396i
$802$		0			0
$803$	13.5263	+	3.62436i	0.477332	+	0.127901i
$804$		0			0
$805$	12.2321	−	18.0622i	0.431123	−	0.636608i
$806$		0			0
$807$	37.4545	−	21.6244i	1.31846	−	0.761213i
$808$		0			0
$809$	−15.5718	−	8.99038i	−0.547475	−	0.316085i	0.200628	−	0.979668i	$-0.435702\pi$
$809$	−15.5718	−	8.99038i	−0.547475	−	0.316085i	−0.748103	+	0.663583i	$0.769035\pi$
$810$		0			0
$811$	10.3205	+	10.3205i	0.362402	+	0.362402i	0.864697	−	0.502295i	$-0.167511\pi$
$811$	10.3205	+	10.3205i	0.362402	+	0.362402i	−0.502295	+	0.864697i	$0.667511\pi$
$812$		0			0
$813$	16.5622	−	16.5622i	0.580861	−	0.580861i
$814$		0			0
$815$	−0.401924	+	0.696152i	−0.0140788	+	0.0243852i
$816$		0			0
$817$	−1.43782	−	2.49038i	−0.0503030	−	0.0871274i
$818$		0			0
$819$	−0.660254	+	0.320508i	−0.0230711	+	0.0111995i
$820$		0			0
$821$	4.59808	−	17.1603i	0.160474	−	0.598897i	−0.838100	−	0.545516i	$-0.816334\pi$
$821$	4.59808	−	17.1603i	0.160474	−	0.598897i	0.998574	−	0.0533808i	$-0.0169997\pi$
$822$		0			0
$823$	−27.0622	−	15.6244i	−0.943328	−	0.544631i	−0.0523262	−	0.998630i	$-0.516664\pi$
$823$	−27.0622	−	15.6244i	−0.943328	−	0.544631i	−0.891002	+	0.453999i	$0.849997\pi$
$824$		0			0
$825$			52.4449i			1.82590i
$826$		0			0
$827$	−37.7846	−	37.7846i	−1.31390	−	1.31390i	−0.918516	−	0.395383i	$-0.870612\pi$
$827$	−37.7846	−	37.7846i	−1.31390	−	1.31390i	−0.395383	−	0.918516i	$-0.629388\pi$
$828$		0			0
$829$	−9.06218	−	33.8205i	−0.314742	−	1.17463i	−0.924229	−	0.381838i	$-0.875291\pi$
$829$	−9.06218	−	33.8205i	−0.314742	−	1.17463i	0.609487	−	0.792796i	$-0.291376\pi$
$830$		0			0
$831$	−16.7942	−	29.0885i	−0.582585	−	1.00907i
$832$		0			0
$833$	2.55256	+	2.00962i	0.0884409	+	0.0696292i
$834$		0			0
$835$	18.9282	+	5.07180i	0.655037	+	0.175517i
$836$		0			0
$837$	1.13397	−	0.303848i	0.0391959	−	0.0105025i
$838$		0			0
$839$			37.7128i			1.30199i	0.759082	+	0.650995i	$0.225648\pi$
$839$			37.7128i			1.30199i	−0.759082	+	0.650995i	$0.774352\pi$
$840$		0			0
$841$			1.14359i			0.0394343i
$842$		0			0
$843$	−24.1244	+	6.46410i	−0.830887	+	0.222635i
$844$		0			0
$845$	−41.5526	−	11.1340i	−1.42945	−	0.383020i
$846$		0			0
$847$	−20.4904	−	7.09808i	−0.704058	−	0.243893i
$848$		0			0
$849$	16.8923	+	29.2583i	0.579742	+	1.00414i
$850$		0			0
$851$	−7.06218	−	26.3564i	−0.242088	−	0.903486i
$852$		0			0
$853$	36.1244	+	36.1244i	1.23687	+	1.23687i	0.961272	+	0.275603i	$0.0888774\pi$
$853$	36.1244	+	36.1244i	1.23687	+	1.23687i	0.275603	+	0.961272i	$0.411123\pi$
$854$		0			0
$855$			10.7321i			0.367028i
$856$		0			0
$857$	−8.89230	−	5.13397i	−0.303755	−	0.175373i	0.340373	−	0.940290i	$-0.389447\pi$
$857$	−8.89230	−	5.13397i	−0.303755	−	0.175373i	−0.644129	+	0.764917i	$0.722780\pi$
$858$		0			0
$859$	10.6244	−	39.6506i	0.362498	−	1.35286i	−0.508282	−	0.861191i	$-0.669719\pi$
$859$	10.6244	−	39.6506i	0.362498	−	1.35286i	0.870781	−	0.491672i	$-0.163614\pi$
$860$		0			0
$861$	37.7846	+	25.5885i	1.28770	+	0.872052i
$862$		0			0
$863$	7.66987	+	13.2846i	0.261086	+	0.452213i	0.966531	−	0.256551i	$-0.0825862\pi$
$863$	7.66987	+	13.2846i	0.261086	+	0.452213i	−0.705445	+	0.708765i	$0.749253\pi$
$864$		0			0
$865$	−7.96410	+	13.7942i	−0.270788	+	0.469018i
$866$		0			0
$867$	22.9282	−	22.9282i	0.778683	−	0.778683i
$868$		0			0
$869$	−2.04552	−	2.04552i	−0.0693894	−	0.0693894i
$870$		0			0
$871$	2.49038	+	1.43782i	0.0843833	+	0.0487187i
$872$		0			0
$873$	−6.92820	+	4.00000i	−0.234484	+	0.135379i
$874$		0			0
$875$	−10.5622	−	0.758330i	−0.357067	−	0.0256362i
$876$		0			0
$877$	28.1865	+	7.55256i	0.951792	+	0.255032i	0.701122	−	0.713041i	$-0.252683\pi$
$877$	28.1865	+	7.55256i	0.951792	+	0.255032i	0.250669	+	0.968073i	$0.419349\pi$
$878$		0			0
$879$	−8.09808	+	14.0263i	−0.273141	+	0.473095i
$880$		0			0
$881$	50.0000			1.68454			0.842271	−	0.539054i	$-0.181218\pi$
$881$	50.0000			1.68454			0.842271	+	0.539054i	$0.181218\pi$
$882$		0			0
$883$	5.00000	−	5.00000i	0.168263	−	0.168263i	−0.617952	−	0.786216i	$-0.712037\pi$
$883$	5.00000	−	5.00000i	0.168263	−	0.168263i	0.786216	+	0.617952i	$0.212037\pi$
$884$		0			0
$885$	64.4090	−	17.2583i	2.16508	−	0.580132i
$886$		0			0
$887$	27.7750	−	16.0359i	0.932593	−	0.538433i	0.0449622	−	0.998989i	$-0.485683\pi$
$887$	27.7750	−	16.0359i	0.932593	−	0.538433i	0.887631	+	0.460556i	$0.152350\pi$
$888$		0			0
$889$	−4.39230	−	5.07180i	−0.147313	−	0.170103i
$890$		0			0
$891$	−12.0885	+	45.1147i	−0.404979	+	1.51140i
$892$		0			0
$893$	8.76795	+	32.7224i	0.293408	+	1.09501i
$894$		0			0
$895$	26.3205			0.879798
$896$		0			0
$897$	1.80385			0.0602287
$898$		0			0
$899$	0.366025	+	1.36603i	0.0122076	+	0.0455595i
$900$		0			0
$901$	−1.37564	+	5.13397i	−0.0458294	+	0.171037i
$902$		0			0
$903$	−3.29423	+	0.633975i	−0.109625	+	0.0210974i
$904$		0			0
$905$	−30.2942	+	17.4904i	−1.00701	+	0.581400i
$906$		0			0
$907$	10.1603	−	2.72243i	0.337366	−	0.0903969i	−0.0861591	−	0.996281i	$-0.527459\pi$
$907$	10.1603	−	2.72243i	0.337366	−	0.0903969i	0.423525	+	0.905885i	$0.360793\pi$
$908$		0			0
$909$	−3.78461	+	3.78461i	−0.125528	+	0.125528i
$910$		0			0
$911$	−27.3205			−0.905169			−0.452584	−	0.891722i	$-0.649498\pi$
$911$	−27.3205			−0.905169			−0.452584	+	0.891722i	$0.649498\pi$
$912$		0			0
$913$	−26.2224	+	45.4186i	−0.867836	+	1.50314i
$914$		0			0
$915$	−0.866025	−	0.232051i	−0.0286299	−	0.00767136i
$916$		0			0
$917$	−10.7224	−	22.0885i	−0.354086	−	0.729425i
$918$		0			0
$919$	−14.1340	+	8.16025i	−0.466237	+	0.269182i	−0.714663	−	0.699469i	$-0.753420\pi$
$919$	−14.1340	+	8.16025i	−0.466237	+	0.269182i	0.248426	+	0.968651i	$0.420087\pi$
$920$		0			0
$921$	21.2942	+	12.2942i	0.701669	+	0.405109i
$922$		0			0
$923$	2.00000	+	2.00000i	0.0658308	+	0.0658308i
$924$		0			0
$925$	−48.5167	+	48.5167i	−1.59522	+	1.59522i
$926$		0			0
$927$	0.169873	−	0.294229i	0.00557936	−	0.00966374i
$928$		0			0
$929$	20.0167	+	34.6699i	0.656725	+	1.13748i	0.981458	+	0.191676i	$0.0613922\pi$
$929$	20.0167	+	34.6699i	0.656725	+	1.13748i	−0.324733	+	0.945806i	$0.605274\pi$
$930$		0			0
$931$	12.0885	−	28.1865i	0.396183	−	0.923776i
$932$		0			0
$933$	0.232051	−	0.866025i	0.00759700	−	0.0283524i
$934$		0			0
$935$	5.89230	+	3.40192i	0.192699	+	0.111255i
$936$		0			0
$937$			42.9282i			1.40240i	0.712963	+	0.701202i	$0.247353\pi$
$937$			42.9282i			1.40240i	−0.712963	+	0.701202i	$0.752647\pi$
$938$		0			0
$939$	13.0981	+	13.0981i	0.427440	+	0.427440i
$940$		0			0
$941$	4.47372	+	16.6962i	0.145839	+	0.544279i	0.999717	+	0.0238050i	$0.00757808\pi$
$941$	4.47372	+	16.6962i	0.145839	+	0.544279i	−0.853877	+	0.520474i	$0.825755\pi$
$942$		0			0
$943$	−11.0000	−	19.0526i	−0.358209	−	0.620437i
$944$		0			0
$945$	−36.6506	−	12.6962i	−1.19225	−	0.413006i
$946$		0			0
$947$	39.5526	+	10.5981i	1.28529	+	0.344391i	0.835868	−	0.548931i	$-0.184965\pi$
$947$	39.5526	+	10.5981i	1.28529	+	0.344391i	0.449418	+	0.893322i	$0.351632\pi$
$948$		0			0
$949$	−1.16987	+	0.313467i	−0.0379757	+	0.0101756i
$950$		0			0
$951$			23.5885i			0.764908i
$952$		0			0
$953$		−	23.4641i		−	0.760077i	−0.924971	−	0.380038i	$-0.875911\pi$
$953$		−	23.4641i		−	0.760077i	0.924971	−	0.380038i	$-0.124089\pi$
$954$		0			0
$955$	−27.9904	+	7.50000i	−0.905747	+	0.242694i
$956$		0			0
$957$	−43.1506	−	11.5622i	−1.39486	−	0.373752i
$958$		0			0
$959$	−6.79423	−	35.3038i	−0.219397	−	1.14002i
$960$		0			0
$961$	15.4641	+	26.7846i	0.498842	+	0.864020i
$962$		0			0
$963$	0.169873	+	0.633975i	0.00547408	+	0.0204295i
$964$		0			0
$965$	54.4186	+	54.4186i	1.75180	+	1.75180i
$966$		0			0
$967$			11.7513i			0.377896i	0.981987	+	0.188948i	$0.0605078\pi$
$967$			11.7513i			0.377896i	−0.981987	+	0.188948i	$0.939492\pi$
$968$		0			0
$969$	3.40192	+	1.96410i	0.109286	+	0.0630960i
$970$		0			0
$971$	−13.4090	+	50.0429i	−0.430314	+	1.60595i	0.321723	+	0.946834i	$0.395738\pi$
$971$	−13.4090	+	50.0429i	−0.430314	+	1.60595i	−0.752037	+	0.659121i	$0.770929\pi$
$972$		0			0
$973$	−0.516660	+	7.19615i	−0.0165634	+	0.230698i
$974$		0			0
$975$	−2.26795	−	3.92820i	−0.0726325	−	0.125803i
$976$		0			0
$977$	22.4282	−	38.8468i	0.717542	−	1.24282i	−0.244429	−	0.969667i	$-0.578601\pi$
$977$	22.4282	−	38.8468i	0.717542	−	1.24282i	0.961971	−	0.273152i	$-0.0880661\pi$
$978$		0			0
$979$	−16.0981	+	16.0981i	−0.514497	+	0.514497i
$980$		0			0
$981$	−7.73205	−	7.73205i	−0.246865	−	0.246865i
$982$		0			0
$983$	18.8660	+	10.8923i	0.601733	+	0.347411i	0.769723	−	0.638378i	$-0.220394\pi$
$983$	18.8660	+	10.8923i	0.601733	+	0.347411i	−0.167990	+	0.985789i	$0.553728\pi$
$984$		0			0
$985$	2.70577	−	1.56218i	0.0862130	−	0.0497751i
$986$		0			0
$987$	39.4186	+	2.83013i	1.25471	+	0.0900839i
$988$		0			0
$989$	1.56218	+	0.418584i	0.0496744	+	0.0133102i
$990$		0			0
$991$	19.7942	−	34.2846i	0.628784	−	1.08909i	−0.359012	−	0.933333i	$-0.616886\pi$
$991$	19.7942	−	34.2846i	0.628784	−	1.08909i	0.987796	−	0.155753i	$-0.0497805\pi$
$992$		0			0
$993$	34.5167			1.09535
$994$		0			0
$995$	4.56218	−	4.56218i	0.144631	−	0.144631i
$996$		0			0
$997$	−5.59808	+	1.50000i	−0.177293	+	0.0475055i	−0.346373	−	0.938097i	$-0.612587\pi$
$997$	−5.59808	+	1.50000i	−0.177293	+	0.0475055i	0.169080	+	0.985602i	$0.445920\pi$
$998$		0			0
$999$	−42.0167	+	24.2583i	−1.32935	+	0.767500i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.ba.b.865.1		4
4.3	odd	2		896.2.ba.c.865.1		4
7.2	even	3		896.2.ba.d.737.1		4
8.3	odd	2		448.2.ba.a.305.1		4
8.5	even	2		112.2.w.b.53.1	yes	4
16.3	odd	4		896.2.ba.a.417.1		4
16.5	even	4		112.2.w.a.109.1	yes	4
16.11	odd	4		448.2.ba.b.81.1		4
16.13	even	4		896.2.ba.d.417.1		4
28.23	odd	6		896.2.ba.a.737.1		4
56.5	odd	6		784.2.x.a.373.1		4
56.13	odd	2		784.2.x.h.165.1		4
56.37	even	6		112.2.w.a.37.1	✓	4
56.45	odd	6		784.2.m.d.197.1		4
56.51	odd	6		448.2.ba.b.177.1		4
56.53	even	6		784.2.m.e.197.1		4
112.5	odd	12		784.2.x.h.765.1		4
112.37	even	12		112.2.w.b.93.1	yes	4
112.51	odd	12		896.2.ba.c.289.1		4
112.53	even	12		784.2.m.e.589.1		4
112.69	odd	4		784.2.x.a.557.1		4
112.93	even	12	inner	896.2.ba.b.289.1		4
112.101	odd	12		784.2.m.d.589.1		4
112.107	odd	12		448.2.ba.a.401.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.a.37.1	✓	4	56.37	even	6
112.2.w.a.109.1	yes	4	16.5	even	4
112.2.w.b.53.1	yes	4	8.5	even	2
112.2.w.b.93.1	yes	4	112.37	even	12
448.2.ba.a.305.1		4	8.3	odd	2
448.2.ba.a.401.1		4	112.107	odd	12
448.2.ba.b.81.1		4	16.11	odd	4
448.2.ba.b.177.1		4	56.51	odd	6
784.2.m.d.197.1		4	56.45	odd	6
784.2.m.d.589.1		4	112.101	odd	12
784.2.m.e.197.1		4	56.53	even	6
784.2.m.e.589.1		4	112.53	even	12
784.2.x.a.373.1		4	56.5	odd	6
784.2.x.a.557.1		4	112.69	odd	4
784.2.x.h.165.1		4	56.13	odd	2
784.2.x.h.765.1		4	112.5	odd	12
896.2.ba.a.417.1		4	16.3	odd	4
896.2.ba.a.737.1		4	28.23	odd	6
896.2.ba.b.289.1		4	112.93	even	12	inner
896.2.ba.b.865.1		4	1.1	even	1	trivial
896.2.ba.c.289.1		4	112.51	odd	12
896.2.ba.c.865.1		4	4.3	odd	2
896.2.ba.d.417.1		4	16.13	even	4
896.2.ba.d.737.1		4	7.2	even	3

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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.ba (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 1.86603i) q^{3} +(-0.866025 + 3.23205i) q^{5} +(-1.73205 - 2.00000i) q^{7} +(-0.633975 + 0.366025i) q^{9} +(4.23205 - 1.13397i) q^{11} +(-0.267949 + 0.267949i) q^{13} +6.46410 q^{15} +(0.232051 - 0.401924i) q^{17} +(-4.23205 - 1.13397i) q^{19} +(-2.86603 + 4.23205i) q^{21} +(2.13397 - 1.23205i) q^{23} +(-5.36603 - 3.09808i) q^{25} +(-3.09808 - 3.09808i) q^{27} +(3.73205 - 3.73205i) q^{29} +(-0.133975 + 0.232051i) q^{31} +(-4.23205 - 7.33013i) q^{33} +(7.96410 - 3.86603i) q^{35} +(2.86603 - 10.6962i) q^{37} +(0.633975 + 0.366025i) q^{39} -8.92820i q^{41} +(0.464102 + 0.464102i) q^{43} +(-0.633975 - 2.36603i) q^{45} +(-3.86603 - 6.69615i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(-0.866025 - 0.232051i) q^{51} +(-11.0622 + 2.96410i) q^{53} +14.6603i q^{55} +8.46410i q^{57} +(9.96410 - 2.66987i) q^{59} +(-0.133975 - 0.0358984i) q^{61} +(1.83013 + 0.633975i) q^{63} +(-0.633975 - 1.09808i) q^{65} +(-1.96410 - 7.33013i) q^{67} +(-3.36603 - 3.36603i) q^{69} -7.46410i q^{71} +(2.76795 + 1.59808i) q^{73} +(-3.09808 + 11.5622i) q^{75} +(-9.59808 - 6.50000i) q^{77} +(-0.330127 - 0.571797i) q^{79} +(-5.33013 + 9.23205i) q^{81} +(-8.46410 + 8.46410i) q^{83} +(1.09808 + 1.09808i) q^{85} +(-8.83013 - 5.09808i) q^{87} +(-4.50000 + 2.59808i) q^{89} +(1.00000 + 0.0717968i) q^{91} +(0.500000 + 0.133975i) q^{93} +(7.33013 - 12.6962i) q^{95} +10.9282 q^{97} +(-2.26795 + 2.26795i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 6 q^{9} + 10 q^{11} - 8 q^{13} + 12 q^{15} - 6 q^{17} - 10 q^{19} - 8 q^{21} + 12 q^{23} - 18 q^{25} - 2 q^{27} + 8 q^{29} - 4 q^{31} - 10 q^{33} + 18 q^{35} + 8 q^{37} + 6 q^{39} - 12 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 6 * q^9 + 10 * q^11 - 8 * q^13 + 12 * q^15 - 6 * q^17 - 10 * q^19 - 8 * q^21 + 12 * q^23 - 18 * q^25 - 2 * q^27 + 8 * q^29 - 4 * q^31 - 10 * q^33 + 18 * q^35 + 8 * q^37 + 6 * q^39 - 12 * q^43 - 6 * q^45 - 12 * q^47 - 4 * q^49 - 20 * q^53 + 26 * q^59 - 4 * q^61 - 10 * q^63 - 6 * q^65 + 6 * q^67 - 10 * q^69 + 18 * q^73 - 2 * q^75 - 28 * q^77 + 16 * q^79 - 4 * q^81 - 20 * q^83 - 6 * q^85 - 18 * q^87 - 18 * q^89 + 4 * q^91 + 2 * q^93 + 12 * q^95 + 16 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

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Database

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