LMFDB - Embedded newform 896.2.z.b.159.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [896,2,Mod(31,896)] 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("896.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(896, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [56,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			159.14
Character	$\chi$	$=$	896.159
Dual form			896.2.z.b.479.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.08091 + 0.825526i) q^{3} +(-0.501060 - 1.86998i) q^{5} +(2.17953 - 1.49988i) q^{7} +(6.21241 + 3.58674i) q^{9} +(-3.52366 - 0.944161i) q^{11} +(0.372046 + 0.372046i) q^{13} -6.17487i q^{15} +(2.39966 - 1.38545i) q^{17} +(-0.431397 - 1.61000i) q^{19} +(7.95312 - 2.82174i) q^{21} +(-1.27273 + 2.20444i) q^{23} +(1.08436 - 0.626056i) q^{25} +(9.41278 + 9.41278i) q^{27} +(-2.14013 + 2.14013i) q^{29} +(2.74674 + 4.75749i) q^{31} +(-10.0766 - 5.81774i) q^{33} +(-3.89683 - 3.32415i) q^{35} +(-4.53493 + 1.21513i) q^{37} +(0.839106 + 1.45337i) q^{39} -3.95954 q^{41} +(4.29972 - 4.29972i) q^{43} +(3.59434 - 13.4143i) q^{45} +(-1.85655 + 3.21563i) q^{47} +(2.50070 - 6.53808i) q^{49} +(8.53685 - 2.28744i) q^{51} +(1.74138 - 6.49892i) q^{53} +7.06225i q^{55} -5.31638i q^{57} +(-2.20140 + 8.21574i) q^{59} +(-0.378874 + 0.101519i) q^{61} +(18.9198 - 1.50050i) q^{63} +(0.509302 - 0.882137i) q^{65} +(-3.72389 + 13.8977i) q^{67} +(-5.74099 + 5.74099i) q^{69} -8.98576 q^{71} +(-0.766294 - 1.32726i) q^{73} +(3.85764 - 1.03365i) q^{75} +(-9.09605 + 3.22725i) q^{77} +(-3.47070 - 2.00381i) q^{79} +(10.4692 + 18.1331i) q^{81} +(-3.67570 + 3.67570i) q^{83} +(-3.79313 - 3.79313i) q^{85} +(-8.36028 + 4.82681i) q^{87} +(-3.35201 + 5.80586i) q^{89} +(1.36891 + 0.252860i) q^{91} +(4.53501 + 16.9249i) q^{93} +(-2.79451 + 1.61341i) q^{95} -4.52980i q^{97} +(-18.5040 - 18.5040i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 6 q^{3} + 6 q^{5} - 8 q^{7} - 2 q^{11} - 12 q^{17} + 6 q^{19} + 10 q^{21} - 12 q^{23} + 24 q^{29} - 12 q^{33} + 2 q^{35} - 6 q^{37} - 4 q^{39} - 12 q^{45} - 8 q^{49} + 34 q^{51} - 6 q^{53} - 42 q^{59}+ \cdots + 16 q^{99}+O(q^{100}) $ 56 * q + 6 * q^3 + 6 * q^5 - 8 * q^7 - 2 * q^11 - 12 * q^17 + 6 * q^19 + 10 * q^21 - 12 * q^23 + 24 * q^29 - 12 * q^33 + 2 * q^35 - 6 * q^37 - 4 * q^39 - 12 * q^45 - 8 * q^49 + 34 * q^51 - 6 * q^53 - 42 * q^59 + 6 * q^61 - 4 * q^65 - 6 * q^67 - 80 * q^71 - 24 * q^75 - 10 * q^77 - 8 * q^81 + 28 * q^85 - 12 * q^87 - 16 * q^91 - 10 * q^93 + 16 * q^99

Character values

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

$n$	$127$	$129$	$645$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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
$3$	3.08091	+	0.825526i	1.77876	+	0.476618i	0.990357	−	0.138539i	$-0.0442405\pi$
$3$	3.08091	+	0.825526i	1.77876	+	0.476618i	0.788405	+	0.615156i	$0.210907\pi$
$4$		0			0
$5$	−0.501060	−	1.86998i	−0.224081	−	0.836281i	−0.982771	−	0.184829i	$-0.940827\pi$
$5$	−0.501060	−	1.86998i	−0.224081	−	0.836281i	0.758690	−	0.651452i	$-0.225840\pi$
$6$		0			0
$7$	2.17953	−	1.49988i	0.823785	−	0.566903i
$7$	2.17953	−	1.49988i	0.823785	−	0.566903i
$8$		0			0
$9$	6.21241	+	3.58674i	2.07080	+	1.19558i
$10$		0			0
$11$	−3.52366	−	0.944161i	−1.06242	−	0.284675i	−0.315046	−	0.949076i	$-0.602020\pi$
$11$	−3.52366	−	0.944161i	−1.06242	−	0.284675i	−0.747376	+	0.664401i	$0.768687\pi$
$12$		0			0
$13$	0.372046	+	0.372046i	0.103187	+	0.103187i	0.756816	−	0.653628i	$-0.226754\pi$
$13$	0.372046	+	0.372046i	0.103187	+	0.103187i	−0.653628	+	0.756816i	$0.726754\pi$
$14$		0			0
$15$		−	6.17487i		−	1.59435i
$16$		0			0
$17$	2.39966	−	1.38545i	0.582003	−	0.336020i	−0.179926	−	0.983680i	$-0.557586\pi$
$17$	2.39966	−	1.38545i	0.582003	−	0.336020i	0.761929	+	0.647660i	$0.224252\pi$
$18$		0			0
$19$	−0.431397	−	1.61000i	−0.0989693	−	0.369358i	0.898622	−	0.438724i	$-0.144569\pi$
$19$	−0.431397	−	1.61000i	−0.0989693	−	0.369358i	−0.997591	+	0.0693652i	$0.977903\pi$
$20$		0			0
$21$	7.95312	−	2.82174i	1.73551	−	0.615755i
$22$		0			0
$23$	−1.27273	+	2.20444i	−0.265383	+	0.459657i	−0.967664	−	0.252243i	$-0.918832\pi$
$23$	−1.27273	+	2.20444i	−0.265383	+	0.459657i	0.702281	+	0.711900i	$0.252165\pi$
$24$		0			0
$25$	1.08436	−	0.626056i	0.216872	−	0.125211i
$26$		0			0
$27$	9.41278	+	9.41278i	1.81149	+	1.81149i
$28$		0			0
$29$	−2.14013	+	2.14013i	−0.397413	+	0.397413i	−0.877319	−	0.479907i	$-0.840670\pi$
$29$	−2.14013	+	2.14013i	−0.397413	+	0.397413i	0.479907	+	0.877319i	$0.340670\pi$
$30$		0			0
$31$	2.74674	+	4.75749i	0.493329	+	0.854471i	0.999970	−	0.00768582i	$-0.00244650\pi$
$31$	2.74674	+	4.75749i	0.493329	+	0.854471i	−0.506641	+	0.862157i	$0.669113\pi$
$32$		0			0
$33$	−10.0766	−	5.81774i	−1.75412	−	1.01274i
$34$		0			0
$35$	−3.89683	−	3.32415i	−0.658684	−	0.561883i
$36$		0			0
$37$	−4.53493	+	1.21513i	−0.745537	+	0.199766i	−0.611538	−	0.791215i	$-0.709449\pi$
$37$	−4.53493	+	1.21513i	−0.745537	+	0.199766i	−0.134000	+	0.990981i	$0.542782\pi$
$38$		0			0
$39$	0.839106	+	1.45337i	0.134364	+	0.232726i
$40$		0			0
$41$	−3.95954			−0.618376			−0.309188	−	0.951001i	$-0.600057\pi$
$41$	−3.95954			−0.618376			−0.309188	+	0.951001i	$0.600057\pi$
$42$		0			0
$43$	4.29972	−	4.29972i	0.655701	−	0.655701i	−0.298659	−	0.954360i	$-0.596539\pi$
$43$	4.29972	−	4.29972i	0.655701	−	0.655701i	0.954360	+	0.298659i	$0.0965394\pi$
$44$		0			0
$45$	3.59434	−	13.4143i	0.535813	−	1.99968i
$46$		0			0
$47$	−1.85655	+	3.21563i	−0.270805	+	0.469048i	−0.969068	−	0.246793i	$-0.920623\pi$
$47$	−1.85655	+	3.21563i	−0.270805	+	0.469048i	0.698263	+	0.715841i	$0.253957\pi$
$48$		0			0
$49$	2.50070	−	6.53808i	0.357242	−	0.934012i
$50$		0			0
$51$	8.53685	−	2.28744i	1.19540	−	0.320306i
$52$		0			0
$53$	1.74138	−	6.49892i	0.239197	−	0.892696i	−0.737015	−	0.675877i	$-0.763765\pi$
$53$	1.74138	−	6.49892i	0.239197	−	0.892696i	0.976212	−	0.216819i	$-0.0695681\pi$
$54$		0			0
$55$			7.06225i			0.952274i
$56$		0			0
$57$		−	5.31638i		−	0.704171i
$58$		0			0
$59$	−2.20140	+	8.21574i	−0.286598	+	1.06960i	0.661066	+	0.750328i	$0.270104\pi$
$59$	−2.20140	+	8.21574i	−0.286598	+	1.06960i	−0.947664	+	0.319270i	$0.896562\pi$
$60$		0			0
$61$	−0.378874	+	0.101519i	−0.0485098	+	0.0129982i	−0.282992	−	0.959122i	$-0.591327\pi$
$61$	−0.378874	+	0.101519i	−0.0485098	+	0.0129982i	0.234483	+	0.972120i	$0.424660\pi$
$62$		0			0
$63$	18.9198	−	1.50050i	2.38367	−	0.189045i
$64$		0			0
$65$	0.509302	−	0.882137i	0.0631711	−	0.109416i
$66$		0			0
$67$	−3.72389	+	13.8977i	−0.454946	+	1.69788i	0.233302	+	0.972404i	$0.425047\pi$
$67$	−3.72389	+	13.8977i	−0.454946	+	1.69788i	−0.688248	+	0.725476i	$0.741620\pi$
$68$		0			0
$69$	−5.74099	+	5.74099i	−0.691134	+	0.691134i
$70$		0			0
$71$	−8.98576			−1.06641			−0.533207	−	0.845985i	$-0.679013\pi$
$71$	−8.98576			−1.06641			−0.533207	+	0.845985i	$0.679013\pi$
$72$		0			0
$73$	−0.766294	−	1.32726i	−0.0896879	−	0.155344i	0.817691	−	0.575657i	$-0.195254\pi$
$73$	−0.766294	−	1.32726i	−0.0896879	−	0.155344i	−0.907379	+	0.420313i	$0.861920\pi$
$74$		0			0
$75$	3.85764	−	1.03365i	0.445442	−	0.119356i
$76$		0			0
$77$	−9.09605	+	3.22725i	−1.03659	+	0.367779i
$78$		0			0
$79$	−3.47070	−	2.00381i	−0.390484	−	0.225446i	0.291886	−	0.956453i	$-0.405717\pi$
$79$	−3.47070	−	2.00381i	−0.390484	−	0.225446i	−0.682370	+	0.731007i	$0.739051\pi$
$80$		0			0
$81$	10.4692	+	18.1331i	1.16324	+	2.01479i
$82$		0			0
$83$	−3.67570	+	3.67570i	−0.403460	+	0.403460i	−0.879451	−	0.475990i	$-0.842090\pi$
$83$	−3.67570	+	3.67570i	−0.403460	+	0.403460i	0.475990	+	0.879451i	$0.342090\pi$
$84$		0			0
$85$	−3.79313	−	3.79313i	−0.411423	−	0.411423i
$86$		0			0
$87$	−8.36028	+	4.82681i	−0.896317	+	0.517489i
$88$		0			0
$89$	−3.35201	+	5.80586i	−0.355313	+	0.615420i	−0.987171	−	0.159664i	$-0.948959\pi$
$89$	−3.35201	+	5.80586i	−0.355313	+	0.615420i	0.631859	+	0.775084i	$0.282292\pi$
$90$		0			0
$91$	1.36891	+	0.252860i	0.143501	+	0.0265069i
$92$		0			0
$93$	4.53501	+	16.9249i	0.470259	+	1.75503i
$94$		0			0
$95$	−2.79451	+	1.61341i	−0.286710	+	0.165532i
$96$		0			0
$97$		−	4.52980i		−	0.459931i	−0.973199	−	0.229966i	$-0.926139\pi$
$97$		−	4.52980i		−	0.459931i	0.973199	−	0.229966i	$-0.0738613\pi$
$98$		0			0
$99$	−18.5040	−	18.5040i	−1.85972	−	1.85972i
$100$		0			0
$101$	13.0735	+	3.50302i	1.30086	+	0.348564i	0.841775	−	0.539829i	$-0.181511\pi$
$101$	13.0735	+	3.50302i	1.30086	+	0.348564i	0.459084	+	0.888393i	$0.348178\pi$
$102$		0			0
$103$	10.9548	+	6.32478i	1.07941	+	0.623200i	0.930738	−	0.365687i	$-0.119166\pi$
$103$	10.9548	+	6.32478i	1.07941	+	0.623200i	0.148675	+	0.988886i	$0.452499\pi$
$104$		0			0
$105$	−9.26159	−	13.4583i	−0.903839	−	1.31340i
$106$		0			0
$107$	−0.934307	−	3.48688i	−0.0903229	−	0.337090i	0.905946	−	0.423393i	$-0.139161\pi$
$107$	−0.934307	−	3.48688i	−0.0903229	−	0.337090i	−0.996269	+	0.0863036i	$0.972494\pi$
$108$		0			0
$109$	9.84896	+	2.63902i	0.943360	+	0.252772i	0.697542	−	0.716544i	$-0.254277\pi$
$109$	9.84896	+	2.63902i	0.943360	+	0.252772i	0.245817	+	0.969316i	$0.420944\pi$
$110$		0			0
$111$	−14.9748			−1.42135
$112$		0			0
$113$	−18.4361			−1.73432			−0.867160	−	0.498030i	$-0.834057\pi$
$113$	−18.4361			−1.73432			−0.867160	+	0.498030i	$0.834057\pi$
$114$		0			0
$115$	4.75997	+	1.27543i	0.443869	+	0.118934i
$116$		0			0
$117$	0.976873	+	3.64574i	0.0903119	+	0.337049i
$118$		0			0
$119$	3.15213	−	6.61883i	0.288955	−	0.606747i
$120$		0			0
$121$	1.99844	+	1.15380i	0.181676	+	0.104891i
$122$		0			0
$123$	−12.1990	−	3.26871i	−1.09994	−	0.294729i
$124$		0			0
$125$	−8.55865	−	8.55865i	−0.765509	−	0.765509i
$126$		0			0
$127$			20.5841i			1.82654i	0.407350	+	0.913272i	$0.366453\pi$
$127$			20.5841i			1.82654i	−0.407350	+	0.913272i	$0.633547\pi$
$128$		0			0
$129$	16.7966	−	9.69749i	1.47885	−	0.853817i
$130$		0			0
$131$	4.12134	+	15.3810i	0.360083	+	1.34385i	0.873966	+	0.485987i	$0.161540\pi$
$131$	4.12134	+	15.3810i	0.360083	+	1.34385i	−0.513883	+	0.857860i	$0.671793\pi$
$132$		0			0
$133$	−3.35505	−	2.86199i	−0.290920	−	0.248166i
$134$		0			0
$135$	12.8853	−	22.3181i	1.10899	−	1.92083i
$136$		0			0
$137$	−1.13536	+	0.655503i	−0.0970008	+	0.0560034i	−0.547716	−	0.836665i	$-0.684502\pi$
$137$	−1.13536	+	0.655503i	−0.0970008	+	0.0560034i	0.450715	+	0.892668i	$0.351169\pi$
$138$		0			0
$139$	−15.6775	−	15.6775i	−1.32975	−	1.32975i	−0.905583	−	0.424169i	$-0.860566\pi$
$139$	−15.6775	−	15.6775i	−1.32975	−	1.32975i	−0.424169	−	0.905583i	$-0.639434\pi$
$140$		0			0
$141$	−8.37444	+	8.37444i	−0.705255	+	0.705255i
$142$		0			0
$143$	−0.959692	−	1.66224i	−0.0802535	−	0.139003i
$144$		0			0
$145$	5.07434	+	2.92967i	0.421401	+	0.243296i
$146$		0			0
$147$	13.1018	−	18.0788i	1.08062	−	1.49112i
$148$		0			0
$149$	12.1169	−	3.24672i	0.992656	−	0.265981i	0.274290	−	0.961647i	$-0.411557\pi$
$149$	12.1169	−	3.24672i	0.992656	−	0.265981i	0.718366	+	0.695666i	$0.244891\pi$
$150$		0			0
$151$	4.56845	+	7.91278i	0.371775	+	0.643933i	0.989839	−	0.142195i	$-0.0454160\pi$
$151$	4.56845	+	7.91278i	0.371775	+	0.643933i	−0.618064	+	0.786128i	$0.712083\pi$
$152$		0			0
$153$	19.8769			1.60695
$154$		0			0
$155$	7.52014	−	7.52014i	0.604032	−	0.604032i
$156$		0			0
$157$	3.42134	−	12.7686i	0.273053	−	1.01905i	−0.684083	−	0.729405i	$-0.739797\pi$
$157$	3.42134	−	12.7686i	0.273053	−	1.01905i	0.957135	−	0.289642i	$-0.0935361\pi$
$158$		0			0
$159$	10.7301	−	18.5850i	0.850949	−	1.47389i
$160$		0			0
$161$	0.532442	+	6.71358i	0.0419623	+	0.529104i
$162$		0			0
$163$	−0.383258	+	0.102694i	−0.0300191	+	0.00804358i	−0.273797	−	0.961787i	$-0.588280\pi$
$163$	−0.383258	+	0.102694i	−0.0300191	+	0.00804358i	0.243778	+	0.969831i	$0.421613\pi$
$164$		0			0
$165$	−5.83007	+	21.7581i	−0.453871	+	1.69387i
$166$		0			0
$167$		−	23.6587i		−	1.83076i	−0.402588	−	0.915381i	$-0.631889\pi$
$167$		−	23.6587i		−	1.83076i	0.402588	−	0.915381i	$-0.368111\pi$
$168$		0			0
$169$		−	12.7232i		−	0.978705i
$170$		0			0
$171$	3.09462	−	11.5493i	0.236651	−	0.883195i
$172$		0			0
$173$	−14.8537	+	3.98004i	−1.12931	+	0.302597i	−0.774644	−	0.632398i	$-0.782071\pi$
$173$	−14.8537	+	3.98004i	−1.12931	+	0.302597i	−0.354662	+	0.934994i	$0.615404\pi$
$174$		0			0
$175$	1.42439	−	2.99092i	0.107673	−	0.226093i
$176$		0			0
$177$	−13.5646	+	23.4946i	−1.01958	+	1.76596i
$178$		0			0
$179$	0.148935	−	0.555832i	0.0111319	−	0.0415448i	−0.960136	−	0.279532i	$-0.909821\pi$
$179$	0.148935	−	0.555832i	0.0111319	−	0.0415448i	0.971268	+	0.237987i	$0.0764875\pi$
$180$		0			0
$181$	0.240422	−	0.240422i	0.0178705	−	0.0178705i	−0.698115	−	0.715986i	$-0.745978\pi$
$181$	0.240422	−	0.240422i	0.0178705	−	0.0178705i	0.715986	+	0.698115i	$0.245978\pi$
$182$		0			0
$183$	−1.25108			−0.0924826
$184$		0			0
$185$	4.54454	+	7.87137i	0.334121	+	0.578715i
$186$		0			0
$187$	−9.76367	+	2.61617i	−0.713990	+	0.191313i
$188$		0			0
$189$	34.6335	+	6.39735i	2.51922	+	0.465339i
$190$		0			0
$191$	−4.57833	−	2.64330i	−0.331277	−	0.191263i	0.325131	−	0.945669i	$-0.394592\pi$
$191$	−4.57833	−	2.64330i	−0.331277	−	0.191263i	−0.656408	+	0.754406i	$0.727925\pi$
$192$		0			0
$193$	−8.43656	−	14.6125i	−0.607277	−	1.05183i	−0.991687	−	0.128672i	$-0.958929\pi$
$193$	−8.43656	−	14.6125i	−0.607277	−	1.05183i	0.384411	−	0.923162i	$-0.374405\pi$
$194$		0			0
$195$	2.29734	−	2.29734i	0.164516	−	0.164516i
$196$		0			0
$197$	1.81729	+	1.81729i	0.129477	+	0.129477i	0.768875	−	0.639399i	$-0.220817\pi$
$197$	1.81729	+	1.81729i	0.129477	+	0.129477i	−0.639399	+	0.768875i	$0.720817\pi$
$198$		0			0
$199$	−0.631178	+	0.364411i	−0.0447430	+	0.0258324i	−0.522205	−	0.852820i	$-0.674890\pi$
$199$	−0.631178	+	0.364411i	−0.0447430	+	0.0258324i	0.477462	+	0.878653i	$0.341557\pi$
$200$		0			0
$201$	−22.9459	+	39.7435i	−1.61848	+	2.80329i
$202$		0			0
$203$	−1.45453	+	7.87443i	−0.102088	+	0.552677i
$204$		0			0
$205$	1.98397	+	7.40426i	0.138566	+	0.517136i
$206$		0			0
$207$	−15.8135	+	9.12991i	−1.09911	+	0.634573i
$208$		0			0
$209$			6.08038i			0.420589i
$210$		0			0
$211$	8.24367	+	8.24367i	0.567518	+	0.567518i	0.931432	−	0.363915i	$-0.118560\pi$
$211$	8.24367	+	8.24367i	0.567518	+	0.567518i	−0.363915	+	0.931432i	$0.618560\pi$
$212$		0			0
$213$	−27.6843	−	7.41798i	−1.89690	−	0.508272i
$214$		0			0
$215$	−10.1948	−	5.88597i	−0.695280	−	0.401420i
$216$		0			0
$217$	13.1223	+	6.24931i	0.890799	+	0.424230i
$218$		0			0
$219$	−1.26519	−	4.72176i	−0.0854937	−	0.319067i
$220$		0			0
$221$	1.40824	+	0.377335i	0.0947281	+	0.0253823i
$222$		0			0
$223$	−28.3640			−1.89940			−0.949698	−	0.313166i	$-0.898610\pi$
$223$	−28.3640			−1.89940			−0.949698	+	0.313166i	$0.898610\pi$
$224$		0			0
$225$	8.98200			0.598800
$226$		0			0
$227$	−6.25352	−	1.67563i	−0.415061	−	0.111215i	0.0452445	−	0.998976i	$-0.485593\pi$
$227$	−6.25352	−	1.67563i	−0.415061	−	0.111215i	−0.460305	+	0.887761i	$0.652260\pi$
$228$		0			0
$229$	−2.05973	−	7.68701i	−0.136111	−	0.507972i	−0.999991	−	0.00427468i	$-0.998639\pi$
$229$	−2.05973	−	7.68701i	−0.136111	−	0.507972i	0.863880	−	0.503697i	$-0.168027\pi$
$230$		0			0
$231$	−30.6882	+	2.43383i	−2.01914	+	0.160134i
$232$		0			0
$233$	0.159304	+	0.0919739i	0.0104363	+	0.00602541i	0.505209	−	0.862997i	$-0.331415\pi$
$233$	0.159304	+	0.0919739i	0.0104363	+	0.00602541i	−0.494773	+	0.869022i	$0.664749\pi$
$234$		0			0
$235$	6.94341	+	1.86048i	0.452938	+	0.121364i
$236$		0			0
$237$	−9.03870	−	9.03870i	−0.587127	−	0.587127i
$238$		0			0
$239$		−	19.6670i		−	1.27215i	−0.771626	−	0.636077i	$-0.780556\pi$
$239$		−	19.6670i		−	1.27215i	0.771626	−	0.636077i	$-0.219444\pi$
$240$		0			0
$241$	−3.10397	+	1.79208i	−0.199944	+	0.115438i	−0.596630	−	0.802517i	$-0.703494\pi$
$241$	−3.10397	+	1.79208i	−0.199944	+	0.115438i	0.396685	+	0.917955i	$0.370160\pi$
$242$		0			0
$243$	6.94921	+	25.9348i	0.445792	+	1.66372i
$244$		0			0
$245$	−13.4791	−	1.40028i	−0.861147	−	0.0894608i
$246$		0			0
$247$	0.438493	−	0.759493i	0.0279007	−	0.0483254i
$248$		0			0
$249$	−14.3589	+	8.29010i	−0.909957	+	0.525364i
$250$		0			0
$251$	11.1881	+	11.1881i	0.706184	+	0.706184i	0.965731	−	0.259547i	$-0.0835731\pi$
$251$	11.1881	+	11.1881i	0.706184	+	0.706184i	−0.259547	+	0.965731i	$0.583573\pi$
$252$		0			0
$253$	6.56601	−	6.56601i	0.412802	−	0.412802i
$254$		0			0
$255$	−8.55495	−	14.8176i	−0.535732	−	0.927914i
$256$		0			0
$257$	7.97191	+	4.60259i	0.497274	+	0.287101i	0.727587	−	0.686015i	$-0.240642\pi$
$257$	7.97191	+	4.60259i	0.497274	+	0.287101i	−0.230313	+	0.973117i	$0.573975\pi$
$258$		0			0
$259$	−8.06145	+	9.45028i	−0.500914	+	0.587212i
$260$		0			0
$261$	−20.9715	+	5.61929i	−1.29810	+	0.347825i
$262$		0			0
$263$	1.54283	+	2.67226i	0.0951349	+	0.164778i	0.909665	−	0.415343i	$-0.136338\pi$
$263$	1.54283	+	2.67226i	0.0951349	+	0.164778i	−0.814530	+	0.580121i	$0.803005\pi$
$264$		0			0
$265$	−13.0254			−0.800143
$266$		0			0
$267$	−15.1201	+	15.1201i	−0.925337	+	0.925337i
$268$		0			0
$269$	6.25670	−	23.3503i	0.381478	−	1.42369i	−0.462167	−	0.886793i	$-0.652928\pi$
$269$	6.25670	−	23.3503i	0.381478	−	1.42369i	0.843645	−	0.536902i	$-0.180405\pi$
$270$		0			0
$271$	−5.80261	+	10.0504i	−0.352484	+	0.610520i	−0.986684	−	0.162649i	$-0.947996\pi$
$271$	−5.80261	+	10.0504i	−0.352484	+	0.610520i	0.634200	+	0.773169i	$0.281329\pi$
$272$		0			0
$273$	4.00875	+	1.90911i	0.242620	+	0.115545i
$274$		0			0
$275$	−4.41202	+	1.18220i	−0.266055	+	0.0712891i
$276$		0			0
$277$	−1.72208	+	6.42687i	−0.103469	+	0.386153i	−0.998167	−	0.0605191i	$-0.980724\pi$
$277$	−1.72208	+	6.42687i	−0.103469	+	0.386153i	0.894698	+	0.446672i	$0.147391\pi$
$278$		0			0
$279$			39.4074i			2.35926i
$280$		0			0
$281$		−	16.2605i		−	0.970022i	−0.874508	−	0.485011i	$-0.838816\pi$
$281$		−	16.2605i		−	0.970022i	0.874508	−	0.485011i	$-0.161184\pi$
$282$		0			0
$283$	−6.20636	+	23.1624i	−0.368930	+	1.37686i	0.493085	+	0.869981i	$0.335869\pi$
$283$	−6.20636	+	23.1624i	−0.368930	+	1.37686i	−0.862015	+	0.506883i	$0.830798\pi$
$284$		0			0
$285$	−9.94152	+	2.66382i	−0.588885	+	0.157791i
$286$		0			0
$287$	−8.62993	+	5.93885i	−0.509409	+	0.350559i
$288$		0			0
$289$	−4.66108	+	8.07323i	−0.274181	+	0.474896i
$290$		0			0
$291$	3.73947	−	13.9559i	0.219211	−	0.818108i
$292$		0			0
$293$	−15.5002	+	15.5002i	−0.905534	+	0.905534i	−0.995908	−	0.0903743i	$-0.971194\pi$
$293$	−15.5002	+	15.5002i	−0.905534	+	0.905534i	0.0903743	+	0.995908i	$0.471194\pi$
$294$		0			0
$295$	16.4663			0.958705
$296$		0			0
$297$	−24.2802	−	42.0546i	−1.40888	−	2.44025i
$298$		0			0
$299$	−1.29367	+	0.346637i	−0.0748147	+	0.0200465i
$300$		0			0
$301$	2.92228	−	15.8204i	0.168438	−	0.911875i
$302$		0			0
$303$	37.3863	+	21.5850i	2.14779	+	1.24002i
$304$		0			0
$305$	0.379677	+	0.657620i	0.0217402	+	0.0376552i
$306$		0			0
$307$	8.30421	−	8.30421i	0.473946	−	0.473946i	−0.429243	−	0.903189i	$-0.641220\pi$
$307$	8.30421	−	8.30421i	0.473946	−	0.473946i	0.903189	+	0.429243i	$0.141220\pi$
$308$		0			0
$309$	28.5296	+	28.5296i	1.62299	+	1.62299i
$310$		0			0
$311$	7.66004	−	4.42252i	0.434361	−	0.250778i	−0.266842	−	0.963740i	$-0.585980\pi$
$311$	7.66004	−	4.42252i	0.434361	−	0.250778i	0.701203	+	0.712962i	$0.252647\pi$
$312$		0			0
$313$	12.5112	−	21.6700i	0.707174	−	1.22486i	−0.258727	−	0.965951i	$-0.583303\pi$
$313$	12.5112	−	21.6700i	0.707174	−	1.22486i	0.965901	−	0.258911i	$-0.0833637\pi$
$314$		0			0
$315$	−12.2859	−	34.6279i	−0.692230	−	1.95106i
$316$		0			0
$317$	−0.827705	−	3.08904i	−0.0464885	−	0.173498i	0.938778	−	0.344522i	$-0.111959\pi$
$317$	−0.827705	−	3.08904i	−0.0464885	−	0.173498i	−0.985267	+	0.171024i	$0.945292\pi$
$318$		0			0
$319$	9.56172	−	5.52046i	0.535354	−	0.309087i
$320$		0			0
$321$		−	11.5141i		−	0.642652i
$322$		0			0
$323$	−3.26577	−	3.26577i	−0.181712	−	0.181712i
$324$		0			0
$325$	0.636355	+	0.170511i	0.0352986	+	0.00945823i
$326$		0			0
$327$	28.1652	+	16.2612i	1.55754	+	0.899244i
$328$		0			0
$329$	0.776679	+	9.79317i	0.0428197	+	0.539915i
$330$		0			0
$331$	3.55043	+	13.2504i	0.195149	+	0.728306i	0.992228	+	0.124431i	$0.0397107\pi$
$331$	3.55043	+	13.2504i	0.195149	+	0.728306i	−0.797079	+	0.603875i	$0.793623\pi$
$332$		0			0
$333$	−32.5312	−	8.71671i	−1.78270	−	0.477673i
$334$		0			0
$335$	27.8544			1.52185
$336$		0			0
$337$	30.3580			1.65371			0.826854	−	0.562417i	$-0.190128\pi$
$337$	30.3580			1.65371			0.826854	+	0.562417i	$0.190128\pi$
$338$		0			0
$339$	−56.7998	−	15.2195i	−3.08494	−	0.826608i
$340$		0			0
$341$	−5.18673	−	19.3571i	−0.280877	−	1.04825i
$342$		0			0
$343$	−4.35602	−	18.0007i	−0.235203	−	0.971946i
$344$		0			0
$345$	13.6121	+	7.85895i	0.732851	+	0.423112i
$346$		0			0
$347$	13.0551	+	3.49811i	0.700836	+	0.187788i	0.591605	−	0.806228i	$-0.298494\pi$
$347$	13.0551	+	3.49811i	0.700836	+	0.187788i	0.109231	+	0.994016i	$0.465161\pi$
$348$		0			0
$349$	12.6593	+	12.6593i	0.677639	+	0.677639i	0.959465	−	0.281826i	$-0.0909402\pi$
$349$	12.6593	+	12.6593i	0.677639	+	0.677639i	−0.281826	+	0.959465i	$0.590940\pi$
$350$		0			0
$351$			7.00398i			0.373845i
$352$		0			0
$353$	−26.7828	+	15.4631i	−1.42550	+	0.823016i	−0.996762	−	0.0804108i	$-0.974377\pi$
$353$	−26.7828	+	15.4631i	−1.42550	+	0.823016i	−0.428743	+	0.903426i	$0.641043\pi$
$354$		0			0
$355$	4.50240	+	16.8032i	0.238963	+	0.891821i
$356$		0			0
$357$	15.1754	−	17.7898i	0.803169	−	0.941538i
$358$		0			0
$359$	−9.22928	+	15.9856i	−0.487103	+	0.843687i	−0.999890	−	0.0148287i	$-0.995280\pi$
$359$	−9.22928	+	15.9856i	−0.487103	+	0.843687i	0.512787	+	0.858516i	$0.328613\pi$
$360$		0			0
$361$	14.0485	−	8.11090i	0.739395	−	0.426890i
$362$		0			0
$363$	5.20452	+	5.20452i	0.273166	+	0.273166i
$364$		0			0
$365$	−2.09799	+	2.09799i	−0.109814	+	0.109814i
$366$		0			0
$367$	−8.10460	−	14.0376i	−0.423057	−	0.732756i	0.573180	−	0.819429i	$-0.305710\pi$
$367$	−8.10460	−	14.0376i	−0.423057	−	0.732756i	−0.996237	+	0.0866738i	$0.972376\pi$
$368$		0			0
$369$	−24.5983	−	14.2018i	−1.28054	−	0.739318i
$370$		0			0
$371$	−5.95224	−	16.7765i	−0.309025	−	0.870990i
$372$		0			0
$373$	34.7801	−	9.31929i	1.80084	−	0.482534i	0.806734	−	0.590915i	$-0.201233\pi$
$373$	34.7801	−	9.31929i	1.80084	−	0.482534i	0.994109	+	0.108381i	$0.0345666\pi$
$374$		0			0
$375$	−19.3030	−	33.4338i	−0.996803	−	1.72651i
$376$		0			0
$377$	−1.59246			−0.0820157
$378$		0			0
$379$	18.9916	−	18.9916i	0.975531	−	0.975531i	−0.0241768	−	0.999708i	$-0.507696\pi$
$379$	18.9916	−	18.9916i	0.975531	−	0.975531i	0.999708	+	0.0241768i	$0.00769645\pi$
$380$		0			0
$381$	−16.9927	+	63.4177i	−0.870564	+	3.24899i
$382$		0			0
$383$	−11.8784	+	20.5740i	−0.606957	+	1.05128i	0.384782	+	0.923007i	$0.374277\pi$
$383$	−11.8784	+	20.5740i	−0.606957	+	1.05128i	−0.991739	+	0.128273i	$0.959057\pi$
$384$		0			0
$385$	10.5926	+	15.3924i	0.539847	+	0.784468i
$386$		0			0
$387$	42.1336	−	11.2897i	2.14177	−	0.573886i
$388$		0			0
$389$	3.49731	−	13.0521i	0.177321	−	0.661770i	−0.818824	−	0.574045i	$-0.805374\pi$
$389$	3.49731	−	13.0521i	0.177321	−	0.661770i	0.996145	−	0.0877254i	$-0.0279598\pi$
$390$		0			0
$391$			7.05320i			0.356696i
$392$		0			0
$393$			50.7898i			2.56201i
$394$		0			0
$395$	−2.00806	+	7.49417i	−0.101036	+	0.377073i
$396$		0			0
$397$	4.46180	−	1.19554i	0.223931	−	0.0600022i	−0.145109	−	0.989416i	$-0.546353\pi$
$397$	4.46180	−	1.19554i	0.223931	−	0.0600022i	0.369040	+	0.929413i	$0.379687\pi$
$398$		0			0
$399$	−7.97395	−	11.5872i	−0.399197	−	0.580086i
$400$		0			0
$401$	11.1566	−	19.3238i	0.557135	−	0.964986i	−0.440599	−	0.897704i	$-0.645234\pi$
$401$	11.1566	−	19.3238i	0.557135	−	0.964986i	0.997734	−	0.0672821i	$-0.0214327\pi$
$402$		0			0
$403$	−0.748093	+	2.79192i	−0.0372652	+	0.139076i
$404$		0			0
$405$	28.6629	−	28.6629i	1.42427	−	1.42427i
$406$		0			0
$407$	17.1268			0.848944
$408$		0			0
$409$	2.83340	+	4.90759i	0.140102	+	0.242665i	0.927535	−	0.373736i	$-0.121923\pi$
$409$	2.83340	+	4.90759i	0.140102	+	0.242665i	−0.787433	+	0.616401i	$0.788590\pi$
$410$		0			0
$411$	−4.03909	+	1.08227i	−0.199234	+	0.0533845i
$412$		0			0
$413$	7.52464	+	21.2083i	0.370263	+	1.04359i
$414$		0			0
$415$	8.71523	+	5.03174i	0.427814	+	0.246998i
$416$		0			0
$417$	−35.3588	−	61.2433i	−1.73153	−	2.99910i
$418$		0			0
$419$	2.67538	−	2.67538i	0.130701	−	0.130701i	−0.638730	−	0.769431i	$-0.720540\pi$
$419$	2.67538	−	2.67538i	0.130701	−	0.130701i	0.769431	+	0.638730i	$0.220540\pi$
$420$		0			0
$421$	−17.2159	−	17.2159i	−0.839052	−	0.839052i	0.149682	−	0.988734i	$-0.452175\pi$
$421$	−17.2159	−	17.2159i	−0.839052	−	0.839052i	−0.988734	+	0.149682i	$0.952175\pi$
$422$		0			0
$423$	−23.0673	+	13.3179i	−1.12157	+	0.647538i
$424$		0			0
$425$	1.73473	−	3.00465i	0.0841470	−	0.145747i
$426$		0			0
$427$	−0.673500	+	0.789530i	−0.0325930	+	0.0382081i
$428$		0			0
$429$	−1.58450	−	5.91344i	−0.0765005	−	0.285504i
$430$		0			0
$431$	27.7876	−	16.0432i	1.33848	−	0.772774i	0.351901	−	0.936037i	$-0.385535\pi$
$431$	27.7876	−	16.0432i	1.33848	−	0.772774i	0.986582	+	0.163264i	$0.0522021\pi$
$432$		0			0
$433$			15.7783i			0.758258i	0.925344	+	0.379129i	$0.123776\pi$
$433$			15.7783i			0.758258i	−0.925344	+	0.379129i	$0.876224\pi$
$434$		0			0
$435$	13.2150	+	13.2150i	0.633613	+	0.633613i
$436$		0			0
$437$	4.09819	+	1.09811i	0.196043	+	0.0525295i
$438$		0			0
$439$	1.89128	+	1.09193i	0.0902658	+	0.0521150i	0.544453	−	0.838791i	$-0.316737\pi$
$439$	1.89128	+	1.09193i	0.0902658	+	0.0521150i	−0.454188	+	0.890906i	$0.650070\pi$
$440$		0			0
$441$	38.9857	−	31.6479i	1.85646	−	1.50704i
$442$		0			0
$443$	−5.35487	−	19.9847i	−0.254418	−	0.949500i	−0.968413	−	0.249350i	$-0.919783\pi$
$443$	−5.35487	−	19.9847i	−0.254418	−	0.949500i	0.713996	−	0.700150i	$-0.246884\pi$
$444$		0			0
$445$	12.5364	+	3.35912i	0.594282	+	0.159237i
$446$		0			0
$447$	40.0113			1.89247
$448$		0			0
$449$	31.8400			1.50262			0.751311	−	0.659949i	$-0.229422\pi$
$449$	31.8400			1.50262			0.751311	+	0.659949i	$0.229422\pi$
$450$		0			0
$451$	13.9521	+	3.73844i	0.656977	+	0.176036i
$452$		0			0
$453$	7.54275	+	28.1499i	0.354389	+	1.32260i
$454$		0			0
$455$	−0.213064	−	2.68654i	−0.00998861	−	0.125947i
$456$		0			0
$457$	8.74709	+	5.05014i	0.409172	+	0.236235i	0.690434	−	0.723396i	$-0.257420\pi$
$457$	8.74709	+	5.05014i	0.409172	+	0.236235i	−0.281262	+	0.959631i	$0.590753\pi$
$458$		0			0
$459$	35.6284	+	9.54659i	1.66299	+	0.445597i
$460$		0			0
$461$	−14.0523	−	14.0523i	−0.654479	−	0.654479i	0.299589	−	0.954068i	$-0.403150\pi$
$461$	−14.0523	−	14.0523i	−0.654479	−	0.654479i	−0.954068	+	0.299589i	$0.903150\pi$
$462$		0			0
$463$			9.31917i			0.433099i	0.976272	+	0.216549i	$0.0694802\pi$
$463$			9.31917i			0.433099i	−0.976272	+	0.216549i	$0.930520\pi$
$464$		0			0
$465$	29.3769	−	16.9608i	1.36232	−	0.786537i
$466$		0			0
$467$	−3.53968	−	13.2103i	−0.163797	−	0.611298i	−0.998191	−	0.0601291i	$-0.980849\pi$
$467$	−3.53968	−	13.2103i	−0.163797	−	0.611298i	0.834394	−	0.551169i	$-0.185818\pi$
$468$		0			0
$469$	12.7287	+	35.8760i	0.587756	+	1.65660i
$470$		0			0
$471$	21.0817	−	36.5145i	0.971391	−	1.68250i
$472$		0			0
$473$	−19.2104	+	11.0911i	−0.883293	+	0.509969i
$474$		0			0
$475$	−1.47574	−	1.47574i	−0.0677116	−	0.0677116i
$476$		0			0
$477$	34.1281	−	34.1281i	1.56262	−	1.56262i
$478$		0			0
$479$	−13.2090	−	22.8786i	−0.603534	−	1.04535i	−0.992281	−	0.124007i	$-0.960426\pi$
$479$	−13.2090	−	22.8786i	−0.603534	−	1.04535i	0.388748	−	0.921344i	$-0.372908\pi$
$480$		0			0
$481$	−2.13929	−	1.23512i	−0.0975431	−	0.0563165i
$482$		0			0
$483$	−3.90183	+	21.1235i	−0.177540	+	0.961151i
$484$		0			0
$485$	−8.47063	+	2.26970i	−0.384631	+	0.103062i
$486$		0			0
$487$	16.0930	+	27.8738i	0.729242	+	1.26308i	0.957204	+	0.289414i	$0.0934604\pi$
$487$	16.0930	+	27.8738i	0.729242	+	1.26308i	−0.227962	+	0.973670i	$0.573206\pi$
$488$		0			0
$489$	−1.26556			−0.0572305
$490$		0			0
$491$	2.25713	−	2.25713i	0.101863	−	0.101863i	−0.654339	−	0.756202i	$-0.727053\pi$
$491$	2.25713	−	2.25713i	0.101863	−	0.101863i	0.756202	+	0.654339i	$0.227053\pi$
$492$		0			0
$493$	−2.17056	+	8.10063i	−0.0977570	+	0.364834i
$494$		0			0
$495$	−25.3304	+	43.8736i	−1.13852	+	1.97197i
$496$		0			0
$497$	−19.5847	+	13.4776i	−0.878495	+	0.604553i
$498$		0			0
$499$	22.0437	−	5.90659i	0.986811	−	0.264415i	0.270900	−	0.962607i	$-0.412679\pi$
$499$	22.0437	−	5.90659i	0.986811	−	0.264415i	0.715910	+	0.698192i	$0.246012\pi$
$500$		0			0
$501$	19.5309	−	72.8901i	0.872574	−	3.25649i
$502$		0			0
$503$		−	23.1194i		−	1.03084i	−0.856937	−	0.515422i	$-0.827635\pi$
$503$		−	23.1194i		−	1.03084i	0.856937	−	0.515422i	$-0.172365\pi$
$504$		0			0
$505$		−	26.2023i		−	1.16599i
$506$		0			0
$507$	10.5033	−	39.1989i	0.466468	−	1.74088i
$508$		0			0
$509$	−10.6078	+	2.84236i	−0.470185	+	0.125986i	−0.486129	−	0.873887i	$-0.661591\pi$
$509$	−10.6078	+	2.84236i	−0.470185	+	0.125986i	0.0159440	+	0.999873i	$0.494925\pi$
$510$		0			0
$511$	−3.66089	−	1.74345i	−0.161948	−	0.0771257i
$512$		0			0
$513$	11.0939	−	19.2152i	0.489807	−	0.848371i
$514$		0			0
$515$	6.33819	−	23.6544i	0.279294	−	1.04234i
$516$		0			0
$517$	9.57791	−	9.57791i	0.421236	−	0.421236i
$518$		0			0
$519$	−49.0485			−2.15299
$520$		0			0
$521$	4.42108	+	7.65754i	0.193691	+	0.335483i	0.946471	−	0.322790i	$-0.104621\pi$
$521$	4.42108	+	7.65754i	0.193691	+	0.335483i	−0.752780	+	0.658273i	$0.771287\pi$
$522$		0			0
$523$	18.3971	−	4.92948i	0.804448	−	0.215551i	0.166912	−	0.985972i	$-0.446620\pi$
$523$	18.3971	−	4.92948i	0.804448	−	0.215551i	0.637536	+	0.770420i	$0.279954\pi$
$524$		0			0
$525$	6.85749	−	8.03889i	0.299285	−	0.350846i
$526$		0			0
$527$	13.1825	+	7.61092i	0.574239	+	0.331537i
$528$		0			0
$529$	8.26031	+	14.3073i	0.359144	+	0.622055i
$530$		0			0
$531$	−43.1437	+	43.1437i	−1.87228	+	1.87228i
$532$		0			0
$533$	−1.47313	−	1.47313i	−0.0638085	−	0.0638085i
$534$		0			0
$535$	−6.05226	+	3.49427i	−0.261662	+	0.151071i
$536$		0			0
$537$	0.917707	−	1.58952i	0.0396020	−	0.0685927i
$538$		0			0
$539$	−14.9846	+	20.6769i	−0.645432	+	0.890617i
$540$		0			0
$541$	−0.623324	−	2.32628i	−0.0267988	−	0.100014i	0.951231	−	0.308479i	$-0.0998200\pi$
$541$	−0.623324	−	2.32628i	−0.0267988	−	0.100014i	−0.978030	+	0.208465i	$0.933153\pi$
$542$		0			0
$543$	0.939194	−	0.542244i	0.0403047	−	0.0232699i
$544$		0			0
$545$		−	19.7397i		−	0.845555i
$546$		0			0
$547$	11.9972	+	11.9972i	0.512962	+	0.512962i	0.915433	−	0.402471i	$-0.131849\pi$
$547$	11.9972	+	11.9972i	0.512962	+	0.512962i	−0.402471	+	0.915433i	$0.631849\pi$
$548$		0			0
$549$	−2.71784	−	0.728244i	−0.115995	−	0.0310807i
$550$		0			0
$551$	4.36885	+	2.52236i	0.186119	+	0.107456i
$552$		0			0
$553$	−10.5700	+	0.838286i	−0.449481	+	0.0356475i
$554$		0			0
$555$	7.50327	+	28.0026i	0.318496	+	1.18864i
$556$		0			0
$557$	19.7236	+	5.28493i	0.835716	+	0.223930i	0.651206	−	0.758901i	$-0.274263\pi$
$557$	19.7236	+	5.28493i	0.835716	+	0.223930i	0.184510	+	0.982831i	$0.440930\pi$
$558$		0			0
$559$	3.19939			0.135320
$560$		0			0
$561$	−32.2407			−1.36120
$562$		0			0
$563$	−15.4308	−	4.13466i	−0.650330	−	0.174255i	−0.0814517	−	0.996677i	$-0.525956\pi$
$563$	−15.4308	−	4.13466i	−0.650330	−	0.174255i	−0.568878	+	0.822422i	$0.692622\pi$
$564$		0			0
$565$	9.23757	+	34.4751i	0.388628	+	1.45038i
$566$		0			0
$567$	50.0155	+	23.8192i	2.10045	+	1.00031i
$568$		0			0
$569$	17.3910	+	10.0407i	0.729068	+	0.420928i	0.818081	−	0.575103i	$-0.195038\pi$
$569$	17.3910	+	10.0407i	0.729068	+	0.420928i	−0.0890129	+	0.996030i	$0.528371\pi$
$570$		0			0
$571$	17.3971	+	4.66153i	0.728045	+	0.195079i	0.603758	−	0.797167i	$-0.293669\pi$
$571$	17.3971	+	4.66153i	0.728045	+	0.195079i	0.124286	+	0.992246i	$0.460336\pi$
$572$		0			0
$573$	−11.9233	−	11.9233i	−0.498103	−	0.498103i
$574$		0			0
$575$			3.18721i			0.132916i
$576$		0			0
$577$	−16.2314	+	9.37123i	−0.675724	+	0.390129i	−0.798242	−	0.602337i	$-0.794236\pi$
$577$	−16.2314	+	9.37123i	−0.675724	+	0.390129i	0.122518	+	0.992466i	$0.460903\pi$
$578$		0			0
$579$	−13.9292	−	51.9845i	−0.578878	−	2.16040i
$580$		0			0
$581$	−2.49817	+	13.5244i	−0.103642	+	0.561087i
$582$		0			0
$583$	−12.2721	+	21.2558i	−0.508257	+	0.880327i
$584$		0			0
$585$	6.32799	−	3.65347i	0.261630	−	0.151052i
$586$		0			0
$587$	−16.4500	−	16.4500i	−0.678963	−	0.678963i	0.280802	−	0.959766i	$-0.409399\pi$
$587$	−16.4500	−	16.4500i	−0.678963	−	0.678963i	−0.959766	+	0.280802i	$0.909399\pi$
$588$		0			0
$589$	6.47461	−	6.47461i	0.266782	−	0.266782i
$590$		0			0
$591$	4.09868	+	7.09912i	0.168597	+	0.292019i
$592$		0			0
$593$	1.34548	+	0.776813i	0.0552522	+	0.0318999i	0.527372	−	0.849635i	$-0.323178\pi$
$593$	1.34548	+	0.776813i	0.0552522	+	0.0318999i	−0.472119	+	0.881535i	$0.656511\pi$
$594$		0			0
$595$	−13.9565	−	2.57798i	−0.572160	−	0.105687i
$596$		0			0
$597$	−2.24543	+	0.601662i	−0.0918994	+	0.0246244i
$598$		0			0
$599$	0.821999	+	1.42374i	0.0335860	+	0.0581726i	0.882330	−	0.470632i	$-0.155974\pi$
$599$	0.821999	+	1.42374i	0.0335860	+	0.0581726i	−0.848744	+	0.528804i	$0.822641\pi$
$600$		0			0
$601$	−35.9484			−1.46637			−0.733183	−	0.680031i	$-0.761966\pi$
$601$	−35.9484			−1.46637			−0.733183	+	0.680031i	$0.761966\pi$
$602$		0			0
$603$	−72.9819	+	72.9819i	−2.97205	+	2.97205i
$604$		0			0
$605$	1.15625	−	4.31517i	0.0470081	−	0.175437i
$606$		0			0
$607$	12.3075	−	21.3172i	0.499545	−	0.865237i	−0.500455	−	0.865763i	$-0.666834\pi$
$607$	12.3075	−	21.3172i	0.499545	−	0.865237i	1.00000		0.000525205i	$0.000167178\pi$
$608$		0			0
$609$	−10.9818	+	23.0596i	−0.445006	+	0.934424i
$610$		0			0
$611$	−1.88709	+	0.505643i	−0.0763433	+	0.0204561i
$612$		0			0
$613$	−7.49076	+	27.9559i	−0.302549	+	1.12913i	0.632485	+	0.774572i	$0.282035\pi$
$613$	−7.49076	+	27.9559i	−0.302549	+	1.12913i	−0.935035	+	0.354556i	$0.884632\pi$
$614$		0			0
$615$			24.4497i			0.985905i
$616$		0			0
$617$		−	10.2299i		−	0.411839i	−0.978569	−	0.205920i	$-0.933981\pi$
$617$		−	10.2299i		−	0.411839i	0.978569	−	0.205920i	$-0.0660186\pi$
$618$		0			0
$619$	−2.37448	+	8.86168i	−0.0954384	+	0.356181i	−0.997086	−	0.0762915i	$-0.975692\pi$
$619$	−2.37448	+	8.86168i	−0.0954384	+	0.356181i	0.901647	+	0.432472i	$0.142359\pi$
$620$		0			0
$621$	−32.7298	+	8.76992i	−1.31340	+	0.351925i
$622$		0			0
$623$	1.40230	+	17.6817i	0.0561820	+	0.708401i
$624$		0			0
$625$	−8.58582	+	14.8711i	−0.343433	+	0.594843i
$626$		0			0
$627$	−5.01952	+	18.7331i	−0.200460	+	0.748128i
$628$		0			0
$629$	−9.19880	+	9.19880i	−0.366780	+	0.366780i
$630$		0			0
$631$	−2.48179			−0.0987983			−0.0493992	−	0.998779i	$-0.515731\pi$
$631$	−2.48179			−0.0987983			−0.0493992	+	0.998779i	$0.515731\pi$
$632$		0			0
$633$	18.5926	+	32.2033i	0.738990	+	1.27997i
$634$		0			0
$635$	38.4919	−	10.3139i	1.52750	−	0.409293i
$636$		0			0
$637$	3.36284	−	1.50209i	0.133241	−	0.0595152i
$638$		0			0
$639$	−55.8232	−	32.2296i	−2.20833	−	1.27498i
$640$		0			0
$641$	7.96198	+	13.7906i	0.314479	+	0.544694i	0.979327	−	0.202285i	$-0.0648367\pi$
$641$	7.96198	+	13.7906i	0.314479	+	0.544694i	−0.664847	+	0.746979i	$0.731503\pi$
$642$		0			0
$643$	7.66392	−	7.66392i	0.302236	−	0.302236i	−0.539652	−	0.841888i	$-0.681444\pi$
$643$	7.66392	−	7.66392i	0.302236	−	0.302236i	0.841888	+	0.539652i	$0.181444\pi$
$644$		0			0
$645$	−26.5502	−	26.5502i	−1.04541	−	1.04541i
$646$		0			0
$647$	−7.28511	+	4.20606i	−0.286407	+	0.165357i	−0.636320	−	0.771425i	$-0.719544\pi$
$647$	−7.28511	+	4.20606i	−0.286407	+	0.165357i	0.349913	+	0.936782i	$0.386211\pi$
$648$		0			0
$649$	15.5140	−	26.8710i	0.608976	−	1.05478i
$650$		0			0
$651$	35.2696	+	30.0863i	1.38232	+	1.17918i
$652$		0			0
$653$	12.7054	+	47.4173i	0.497201	+	1.85558i	0.517335	+	0.855783i	$0.326924\pi$
$653$	12.7054	+	47.4173i	0.497201	+	1.85558i	−0.0201333	+	0.999797i	$0.506409\pi$
$654$		0			0
$655$	26.6972	−	15.4136i	1.04315	−	0.602261i
$656$		0			0
$657$		−	10.9940i		−	0.428916i
$658$		0			0
$659$	4.57653	+	4.57653i	0.178276	+	0.178276i	0.790604	−	0.612328i	$-0.209767\pi$
$659$	4.57653	+	4.57653i	0.178276	+	0.178276i	−0.612328	+	0.790604i	$0.709767\pi$
$660$		0			0
$661$	−36.2259	−	9.70671i	−1.40903	−	0.377547i	−0.527448	−	0.849587i	$-0.676851\pi$
$661$	−36.2259	−	9.70671i	−1.40903	−	0.377547i	−0.881577	+	0.472040i	$0.843518\pi$
$662$		0			0
$663$	4.02714	+	2.32507i	0.156401	+	0.0902983i
$664$		0			0
$665$	−3.67078	+	7.70791i	−0.142347	+	0.298900i
$666$		0			0
$667$	−1.99397	−	7.44160i	−0.0772068	−	0.288140i
$668$		0			0
$669$	−87.3870	−	23.4153i	−3.37858	−	0.905286i
$670$		0			0
$671$	1.43087			0.0552382
$672$		0			0
$673$	1.25969			0.0485576			0.0242788	−	0.999705i	$-0.492271\pi$
$673$	1.25969			0.0485576			0.0242788	+	0.999705i	$0.492271\pi$
$674$		0			0
$675$	16.0998	+	4.31392i	0.619681	+	0.166043i
$676$		0			0
$677$	2.73796	+	10.2182i	0.105228	+	0.392717i	0.998371	−	0.0570560i	$-0.0181714\pi$
$677$	2.73796	+	10.2182i	0.105228	+	0.392717i	−0.893143	+	0.449774i	$0.851505\pi$
$678$		0			0
$679$	−6.79417	−	9.87282i	−0.260736	−	0.378884i
$680$		0			0
$681$	−17.8832	−	10.3249i	−0.685287	−	0.395651i
$682$		0			0
$683$	−32.3526	−	8.66885i	−1.23794	−	0.331705i	−0.420272	−	0.907398i	$-0.638065\pi$
$683$	−32.3526	−	8.66885i	−1.23794	−	0.331705i	−0.817666	+	0.575693i	$0.804732\pi$
$684$		0			0
$685$	1.79466	+	1.79466i	0.0685706	+	0.0685706i
$686$		0			0
$687$		−	25.3833i		−	0.968434i
$688$		0			0
$689$	3.06577	−	1.77003i	0.116797	−	0.0674326i
$690$		0			0
$691$	3.83874	+	14.3264i	0.146033	+	0.545001i	0.999707	+	0.0241943i	$0.00770204\pi$
$691$	3.83874	+	14.3264i	0.146033	+	0.545001i	−0.853675	+	0.520807i	$0.825631\pi$
$692$		0			0
$693$	−68.0837	−	12.5761i	−2.58629	−	0.477728i
$694$		0			0
$695$	−21.4613	+	37.1721i	−0.814074	+	1.41002i
$696$		0			0
$697$	−9.50156	+	5.48573i	−0.359897	+	0.207787i
$698$		0			0
$699$	0.414872	+	0.414872i	0.0156919	+	0.0156919i
$700$		0			0
$701$	14.0698	−	14.0698i	0.531408	−	0.531408i	−0.389583	−	0.920991i	$-0.627381\pi$
$701$	14.0698	−	14.0698i	0.531408	−	0.531408i	0.920991	+	0.389583i	$0.127381\pi$
$702$		0			0
$703$	3.91271	+	6.77701i	0.147571	+	0.255600i
$704$		0			0
$705$	19.8561	+	11.4639i	0.747825	+	0.431757i
$706$		0			0
$707$	33.7481	−	11.9737i	1.26923	−	0.450319i
$708$		0			0
$709$	12.5757	−	3.36966i	0.472291	−	0.126550i	−0.0148195	−	0.999890i	$-0.504717\pi$
$709$	12.5757	−	3.36966i	0.472291	−	0.126550i	0.487111	+	0.873340i	$0.338051\pi$
$710$		0			0
$711$	−14.3743	−	24.8970i	−0.539078	−	0.933710i
$712$		0			0
$713$	−13.9835			−0.523684
$714$		0			0
$715$	−2.62748	+	2.62748i	−0.0982623	+	0.0982623i
$716$		0			0
$717$	16.2356	−	60.5923i	0.606331	−	2.26286i
$718$		0			0
$719$	10.1472	−	17.5754i	0.378425	−	0.655452i	−0.612408	−	0.790542i	$-0.709799\pi$
$719$	10.1472	−	17.5754i	0.378425	−	0.655452i	0.990833	+	0.135090i	$0.0431324\pi$
$720$		0			0
$721$	33.3629	−	2.64595i	1.24250	−	0.0985403i
$722$		0			0
$723$	−11.0425	+	2.95882i	−0.410673	+	0.110040i
$724$		0			0
$725$	−0.980834	+	3.66052i	−0.0364272	+	0.135948i
$726$		0			0
$727$		−	38.4308i		−	1.42532i	−0.701510	−	0.712660i	$-0.747490\pi$
$727$		−	38.4308i		−	1.42532i	0.701510	−	0.712660i	$-0.252510\pi$
$728$		0			0
$729$			22.8244i			0.845348i
$730$		0			0
$731$	4.36084	−	16.2749i	0.161292	−	0.601948i
$732$		0			0
$733$	48.4699	−	12.9875i	1.79028	−	0.479703i	0.797882	−	0.602813i	$-0.205954\pi$
$733$	48.4699	−	12.9875i	1.79028	−	0.479703i	0.992393	+	0.123110i	$0.0392870\pi$
$734$		0			0
$735$	−40.3718	−	15.4415i	−1.48914	−	0.569567i
$736$		0			0
$737$	26.2434	−	45.4549i	0.966689	−	1.67435i
$738$		0			0
$739$	−1.90941	+	7.12602i	−0.0702388	+	0.262135i	−0.992112	−	0.125358i	$-0.959992\pi$
$739$	−1.90941	+	7.12602i	−0.0702388	+	0.262135i	0.921873	+	0.387493i	$0.126659\pi$
$740$		0			0
$741$	1.97794	−	1.97794i	0.0726614	−	0.0726614i
$742$		0			0
$743$	13.2937			0.487698			0.243849	−	0.969813i	$-0.421590\pi$
$743$	13.2937			0.487698			0.243849	+	0.969813i	$0.421590\pi$
$744$		0			0
$745$	−12.1426	−	21.0316i	−0.444870	−	0.770537i
$746$		0			0
$747$	−36.0187	+	9.65119i	−1.31786	+	0.353119i
$748$		0			0
$749$	−7.26627	−	6.19841i	−0.265504	−	0.226485i
$750$		0			0
$751$	10.6206	+	6.13182i	0.387552	+	0.223753i	0.681099	−	0.732191i	$-0.261502\pi$
$751$	10.6206	+	6.13182i	0.387552	+	0.223753i	−0.293547	+	0.955945i	$0.594836\pi$
$752$		0			0
$753$	25.2333	+	43.7054i	0.919553	+	1.59271i
$754$		0			0
$755$	12.5077	−	12.5077i	0.455201	−	0.455201i
$756$		0			0
$757$	−27.2609	−	27.2609i	−0.990813	−	0.990813i	0.00914525	−	0.999958i	$-0.497089\pi$
$757$	−27.2609	−	27.2609i	−0.990813	−	0.990813i	−0.999958	+	0.00914525i	$0.997089\pi$
$758$		0			0
$759$	25.6497	−	14.8089i	0.931025	−	0.537527i
$760$		0			0
$761$	−10.1480	+	17.5769i	−0.367867	+	0.637164i	−0.989232	−	0.146358i	$-0.953245\pi$
$761$	−10.1480	+	17.5769i	−0.367867	+	0.637164i	0.621365	+	0.783521i	$0.286578\pi$
$762$		0			0
$763$	25.4243	−	9.02048i	0.920423	−	0.326563i
$764$		0			0
$765$	−9.95952	−	37.1695i	−0.360087	−	1.34386i
$766$		0			0
$767$	−3.87566	+	2.23761i	−0.139942	+	0.0807955i
$768$		0			0
$769$		−	19.6449i		−	0.708412i	−0.935167	−	0.354206i	$-0.884751\pi$
$769$		−	19.6449i		−	0.708412i	0.935167	−	0.354206i	$-0.115249\pi$
$770$		0			0
$771$	20.7612	+	20.7612i	0.747695	+	0.747695i
$772$		0			0
$773$	47.3606	+	12.6902i	1.70344	+	0.456436i	0.973802	−	0.227397i	$-0.0730214\pi$
$773$	47.3606	+	12.6902i	1.70344	+	0.456436i	0.729639	+	0.683832i	$0.239688\pi$
$774$		0			0
$775$	5.95692	+	3.43923i	0.213979	+	0.123541i
$776$		0			0
$777$	−32.6380	+	22.4605i	−1.17088	+	0.805765i
$778$		0			0
$779$	1.70813	+	6.37485i	0.0612003	+	0.228403i
$780$		0			0
$781$	31.6627	+	8.48400i	1.13298	+	0.303581i
$782$		0			0
$783$	−40.2892			−1.43982
$784$		0			0
$785$	−25.5913			−0.913394
$786$		0			0
$787$	2.76449	+	0.740742i	0.0985433	+	0.0264046i	0.307754	−	0.951466i	$-0.400423\pi$
$787$	2.76449	+	0.740742i	0.0985433	+	0.0264046i	−0.209210	+	0.977871i	$0.567089\pi$
$788$		0			0
$789$	2.54729	+	9.50662i	0.0906860	+	0.338445i
$790$		0			0
$791$	−40.1820	+	27.6520i	−1.42871	+	0.983191i
$792$		0			0
$793$	−0.178728	−	0.103189i	−0.00634683	−	0.00366434i
$794$		0			0
$795$	−40.1300	−	10.7528i	−1.42326	−	0.381363i
$796$		0			0
$797$	39.0301	+	39.0301i	1.38252	+	1.38252i	0.840129	+	0.542386i	$0.182479\pi$
$797$	39.0301	+	39.0301i	1.38252	+	1.38252i	0.542386	+	0.840129i	$0.317521\pi$
$798$		0			0
$799$			10.2886i			0.363984i
$800$		0			0
$801$	−41.6482	+	24.0456i	−1.47157	+	0.849609i
$802$		0			0
$803$	1.44701	+	5.40031i	0.0510639	+	0.190573i
$804$		0			0
$805$	12.2875	−	4.35956i	0.433077	−	0.153654i
$806$		0			0
$807$	38.5526	−	66.7751i	1.35712	−	2.35059i
$808$		0			0
$809$	36.0749	−	20.8279i	1.26833	−	0.732269i	0.293656	−	0.955911i	$-0.405128\pi$
$809$	36.0749	−	20.8279i	1.26833	−	0.732269i	0.974671	+	0.223642i	$0.0717946\pi$
$810$		0			0
$811$	−6.24833	−	6.24833i	−0.219409	−	0.219409i	0.588841	−	0.808249i	$-0.299585\pi$
$811$	−6.24833	−	6.24833i	−0.219409	−	0.219409i	−0.808249	+	0.588841i	$0.799585\pi$
$812$		0			0
$813$	−26.1742	+	26.1742i	−0.917969	+	0.917969i
$814$		0			0
$815$	0.384070	+	0.665229i	0.0134534	+	0.0233019i
$816$		0			0
$817$	−8.77741	−	5.06764i	−0.307083	−	0.177294i
$818$		0			0
$819$	7.59731	+	6.48080i	0.265471	+	0.226457i
$820$		0			0
$821$	−41.1258	+	11.0196i	−1.43530	+	0.384588i	−0.890886	−	0.454228i	$-0.849915\pi$
$821$	−41.1258	+	11.0196i	−1.43530	+	0.384588i	−0.544416	+	0.838816i	$0.683249\pi$
$822$		0			0
$823$	0.688665	+	1.19280i	0.0240054	+	0.0415785i	0.877779	−	0.479067i	$-0.159025\pi$
$823$	0.688665	+	1.19280i	0.0240054	+	0.0415785i	−0.853773	+	0.520645i	$0.825691\pi$
$824$		0			0
$825$	−14.5689			−0.507225
$826$		0			0
$827$	14.2870	−	14.2870i	0.496807	−	0.496807i	−0.413636	−	0.910443i	$-0.635741\pi$
$827$	14.2870	−	14.2870i	0.496807	−	0.496807i	0.910443	+	0.413636i	$0.135741\pi$
$828$		0			0
$829$	−5.38274	+	20.0887i	−0.186950	+	0.697708i	0.807254	+	0.590204i	$0.200953\pi$
$829$	−5.38274	+	20.0887i	−0.186950	+	0.697708i	−0.994205	+	0.107504i	$0.965714\pi$
$830$		0			0
$831$	−10.6111	+	18.3790i	−0.368095	+	0.637560i
$832$		0			0
$833$	−3.05733	−	19.1538i	−0.105930	−	0.663639i
$834$		0			0
$835$	−44.2412	+	11.8544i	−1.53103	+	0.410239i
$836$		0			0
$837$	−18.9268	+	70.6357i	−0.654205	+	2.44153i
$838$		0			0
$839$			12.7357i			0.439684i	0.975535	+	0.219842i	$0.0705542\pi$
$839$			12.7357i			0.439684i	−0.975535	+	0.219842i	$0.929446\pi$
$840$		0			0
$841$			19.8397i			0.684126i
$842$		0			0
$843$	13.4235	−	50.0972i	0.462330	−	1.72544i
$844$		0			0
$845$	−23.7921	+	6.37506i	−0.818472	+	0.219309i
$846$		0			0
$847$	6.08623	−	0.482688i	0.209125	−	0.0165854i
$848$		0			0
$849$	−38.2424	+	66.2378i	−1.31248	+	2.27328i
$850$		0			0
$851$	3.09307	−	11.5435i	0.106029	−	0.395706i
$852$		0			0
$853$	17.4577	−	17.4577i	0.597741	−	0.597741i	−0.341970	−	0.939711i	$-0.611094\pi$
$853$	17.4577	−	17.4577i	0.597741	−	0.597741i	0.939711	+	0.341970i	$0.111094\pi$
$854$		0			0
$855$	−23.1475			−0.791628
$856$		0			0
$857$	1.56865	+	2.71698i	0.0535840	+	0.0928102i	0.891573	−	0.452877i	$-0.149602\pi$
$857$	1.56865	+	2.71698i	0.0535840	+	0.0928102i	−0.837989	+	0.545687i	$0.816269\pi$
$858$		0			0
$859$	1.72578	−	0.462421i	0.0588828	−	0.0157776i	−0.229257	−	0.973366i	$-0.573630\pi$
$859$	1.72578	−	0.462421i	0.0588828	−	0.0157776i	0.288140	+	0.957588i	$0.406963\pi$
$860$		0			0
$861$	−31.4907	+	11.1728i	−1.07320	+	0.380768i
$862$		0			0
$863$	4.43745	+	2.56196i	0.151052	+	0.0872101i	0.573621	−	0.819121i	$-0.305538\pi$
$863$	4.43745	+	2.56196i	0.151052	+	0.0872101i	−0.422569	+	0.906331i	$0.638872\pi$
$864$		0			0
$865$	14.8852	+	25.7819i	0.506112	+	0.876611i
$866$		0			0
$867$	−21.0250	+	21.0250i	−0.714047	+	0.714047i
$868$		0			0
$869$	10.3376	+	10.3376i	0.350680	+	0.350680i
$870$		0			0
$871$	−6.55607	+	3.78515i	−0.222144	+	0.128255i
$872$		0			0
$873$	16.2472	−	28.1410i	0.549884	−	0.952427i
$874$		0			0
$875$	−31.4908	−	5.81684i	−1.06458	−	0.196645i
$876$		0			0
$877$	1.07593	+	4.01542i	0.0363316	+	0.135591i	0.981709	−	0.190385i	$-0.0609737\pi$
$877$	1.07593	+	4.01542i	0.0363316	+	0.135591i	−0.945378	+	0.325976i	$0.894307\pi$
$878$		0			0
$879$	−60.5506	+	34.9589i	−2.04232	+	1.17914i
$880$		0			0
$881$			27.5375i			0.927761i	0.885898	+	0.463880i	$0.153543\pi$
$881$			27.5375i			0.927761i	−0.885898	+	0.463880i	$0.846457\pi$
$882$		0			0
$883$	−32.4922	−	32.4922i	−1.09345	−	1.09345i	−0.995158	−	0.0982911i	$-0.968662\pi$
$883$	−32.4922	−	32.4922i	−1.09345	−	1.09345i	−0.0982911	−	0.995158i	$-0.531338\pi$
$884$		0			0
$885$	50.7311	+	13.5934i	1.70531	+	0.456936i
$886$		0			0
$887$	−32.4376	−	18.7278i	−1.08915	−	0.628820i	−0.155798	−	0.987789i	$-0.549795\pi$
$887$	−32.4376	−	18.7278i	−1.08915	−	0.628820i	−0.933349	+	0.358969i	$0.883128\pi$
$888$		0			0
$889$	30.8738	+	44.8637i	1.03547	+	1.50468i
$890$		0			0
$891$	−19.7692	−	73.7795i	−0.662292	−	2.47171i
$892$		0			0
$893$	5.97807	+	1.60182i	0.200048	+	0.0536028i
$894$		0			0
$895$	−1.11402			−0.0372376
$896$		0			0
$897$	−4.27183			−0.142632
$898$		0			0
$899$	−16.0601	−	4.30328i	−0.535633	−	0.143522i
$900$		0			0
$901$	−4.82518	−	18.0078i	−0.160750	−	0.599927i
$902$		0			0
$903$	22.0635	−	46.3289i	0.734226	−	1.54173i
$904$		0			0
$905$	−0.570051	−	0.329119i	−0.0189491	−	0.0109403i
$906$		0			0
$907$	−33.3737	−	8.94245i	−1.10815	−	0.296929i	−0.342074	−	0.939673i	$-0.611129\pi$
$907$	−33.3737	−	8.94245i	−1.10815	−	0.296929i	−0.766081	+	0.642744i	$0.777796\pi$
$908$		0			0
$909$	68.6533	+	68.6533i	2.27709	+	2.27709i
$910$		0			0
$911$		−	22.9373i		−	0.759946i	−0.924998	−	0.379973i	$-0.875933\pi$
$911$		−	22.9373i		−	0.759946i	0.924998	−	0.379973i	$-0.124067\pi$
$912$		0			0
$913$	16.4224	−	9.48145i	0.543501	−	0.313790i
$914$		0			0
$915$	0.626867	+	2.33950i	0.0207236	+	0.0773414i
$916$		0			0
$917$	32.0523	+	27.3419i	1.05846	+	0.902909i
$918$		0			0
$919$	13.8963	−	24.0691i	0.458396	−	0.793966i	−0.540480	−	0.841357i	$-0.681757\pi$
$919$	13.8963	−	24.0691i	0.458396	−	0.793966i	0.998876	+	0.0473912i	$0.0150907\pi$
$920$		0			0
$921$	32.4398	−	18.7291i	1.06893	−	0.617146i
$922$		0			0
$923$	−3.34312	−	3.34312i	−0.110040	−	0.110040i
$924$		0			0
$925$	−4.15676	+	4.15676i	−0.136673	+	0.136673i
$926$		0			0
$927$	45.3707	+	78.5844i	1.49017	+	2.58105i
$928$		0			0
$929$	13.2279	+	7.63716i	0.433995	+	0.250567i	0.701047	−	0.713115i	$-0.252716\pi$
$929$	13.2279	+	7.63716i	0.433995	+	0.250567i	−0.267052	+	0.963682i	$0.586050\pi$
$930$		0			0
$931$	−11.6051	−	1.20560i	−0.380341	−	0.0395120i
$932$		0			0
$933$	27.2508	−	7.30182i	0.892150	−	0.239051i
$934$		0			0
$935$	9.78436	+	16.9470i	0.319983	+	0.554227i
$936$		0			0
$937$	18.1308			0.592307			0.296154	−	0.955140i	$-0.404296\pi$
$937$	18.1308			0.592307			0.296154	+	0.955140i	$0.404296\pi$
$938$		0			0
$939$	56.4350	−	56.4350i	1.84169	−	1.84169i
$940$		0			0
$941$	−2.24372	+	8.37369i	−0.0731433	+	0.272974i	−0.992806	−	0.119735i	$-0.961796\pi$
$941$	−2.24372	+	8.37369i	−0.0731433	+	0.272974i	0.919663	+	0.392709i	$0.128462\pi$
$942$		0			0
$943$	5.03943	−	8.72855i	0.164106	−	0.284241i
$944$		0			0
$945$	−5.39053	−	67.9694i	−0.175354	−	2.21105i
$946$		0			0
$947$	14.8856	−	3.98857i	0.483716	−	0.129611i	−0.00871655	−	0.999962i	$-0.502775\pi$
$947$	14.8856	−	3.98857i	0.483716	−	0.129611i	0.492432	+	0.870351i	$0.336108\pi$
$948$		0			0
$949$	0.208705	−	0.778899i	0.00677486	−	0.0252841i
$950$		0			0
$951$		−	10.2003i		−	0.330768i
$952$		0			0
$953$		−	14.4644i		−	0.468547i	−0.972171	−	0.234273i	$-0.924729\pi$
$953$		−	14.4644i		−	0.468547i	0.972171	−	0.234273i	$-0.0752711\pi$
$954$		0			0
$955$	−2.64890	+	9.88585i	−0.0857165	+	0.319899i
$956$		0			0
$957$	34.0161	−	9.11458i	1.09958	−	0.294632i
$958$		0			0
$959$	−1.49138	+	3.13160i	−0.0481592	+	0.101125i
$960$		0			0
$961$	0.410836	−	0.711589i	0.0132528	−	0.0229545i
$962$		0			0
$963$	6.70223	−	25.0131i	0.215976	−	0.806035i
$964$		0			0
$965$	−23.0980	+	23.0980i	−0.743549	+	0.743549i
$966$		0			0
$967$	53.4246			1.71802			0.859010	−	0.511958i	$-0.171080\pi$
$967$	53.4246			1.71802			0.859010	+	0.511958i	$0.171080\pi$
$968$		0			0
$969$	−7.36555	−	12.7575i	−0.236616	−	0.409830i
$970$		0			0
$971$	−20.7547	+	5.56119i	−0.666048	+	0.178467i	−0.575974	−	0.817468i	$-0.695377\pi$
$971$	−20.7547	+	5.56119i	−0.666048	+	0.178467i	−0.0900743	+	0.995935i	$0.528710\pi$
$972$		0			0
$973$	−57.6842	−	10.6552i	−1.84927	−	0.341589i
$974$		0			0
$975$	1.81979	+	1.05066i	0.0582799	+	0.0336479i
$976$		0			0
$977$	−18.0960	−	31.3432i	−0.578942	−	1.00276i	−0.995601	−	0.0936944i	$-0.970132\pi$
$977$	−18.0960	−	31.3432i	−0.578942	−	1.00276i	0.416659	−	0.909063i	$-0.363201\pi$
$978$		0			0
$979$	17.2930	−	17.2930i	0.552687	−	0.552687i
$980$		0			0
$981$	51.7204	+	51.7204i	1.65130	+	1.65130i
$982$		0			0
$983$	31.0312	−	17.9159i	0.989742	−	0.571428i	0.0845448	−	0.996420i	$-0.473056\pi$
$983$	31.0312	−	17.9159i	0.989742	−	0.571428i	0.905197	+	0.424992i	$0.139723\pi$
$984$		0			0
$985$	2.48773	−	4.30887i	0.0792655	−	0.137292i
$986$		0			0
$987$	−5.69165	+	30.8130i	−0.181167	+	0.980789i
$988$		0			0
$989$	4.00606	+	14.9508i	0.127385	+	0.475409i
$990$		0			0
$991$	−41.7865	+	24.1254i	−1.32739	+	0.766370i	−0.984896	−	0.173149i	$-0.944606\pi$
$991$	−41.7865	+	24.1254i	−1.32739	+	0.766370i	−0.342496	+	0.939519i	$0.611272\pi$
$992$		0			0
$993$			43.7541i			1.38850i
$994$		0			0
$995$	0.997699	+	0.997699i	0.0316292	+	0.0316292i
$996$		0			0
$997$	−26.1554	−	7.00832i	−0.828351	−	0.221956i	−0.180357	−	0.983601i	$-0.557725\pi$
$997$	−26.1554	−	7.00832i	−0.828351	−	0.221956i	−0.647994	+	0.761645i	$0.724392\pi$
$998$		0			0
$999$	−54.1240	−	31.2485i	−1.71241	−	0.988659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.z.b.159.14		56
4.3	odd	2		896.2.z.a.159.1		56
7.3	odd	6	inner	896.2.z.b.31.14		56
8.3	odd	2		448.2.z.a.271.14		56
8.5	even	2		112.2.v.a.75.2	yes	56
16.3	odd	4	inner	896.2.z.b.607.14		56
16.5	even	4		448.2.z.a.47.14		56
16.11	odd	4		112.2.v.a.19.8	yes	56
16.13	even	4		896.2.z.a.607.1		56
28.3	even	6		896.2.z.a.31.1		56
56.3	even	6		448.2.z.a.143.14		56
56.5	odd	6		784.2.j.a.587.23		56
56.13	odd	2		784.2.w.f.411.2		56
56.37	even	6		784.2.j.a.587.24		56
56.45	odd	6		112.2.v.a.59.8	yes	56
56.53	even	6		784.2.w.f.619.8		56
112.3	even	12	inner	896.2.z.b.479.14		56
112.11	odd	12		784.2.w.f.227.2		56
112.27	even	4		784.2.w.f.19.8		56
112.45	odd	12		896.2.z.a.479.1		56
112.59	even	12		112.2.v.a.3.2	✓	56
112.75	even	12		784.2.j.a.195.24		56
112.101	odd	12		448.2.z.a.367.14		56
112.107	odd	12		784.2.j.a.195.23		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.2	✓	56	112.59	even	12
112.2.v.a.19.8	yes	56	16.11	odd	4
112.2.v.a.59.8	yes	56	56.45	odd	6
112.2.v.a.75.2	yes	56	8.5	even	2
448.2.z.a.47.14		56	16.5	even	4
448.2.z.a.143.14		56	56.3	even	6
448.2.z.a.271.14		56	8.3	odd	2
448.2.z.a.367.14		56	112.101	odd	12
784.2.j.a.195.23		56	112.107	odd	12
784.2.j.a.195.24		56	112.75	even	12
784.2.j.a.587.23		56	56.5	odd	6
784.2.j.a.587.24		56	56.37	even	6
784.2.w.f.19.8		56	112.27	even	4
784.2.w.f.227.2		56	112.11	odd	12
784.2.w.f.411.2		56	56.13	odd	2
784.2.w.f.619.8		56	56.53	even	6
896.2.z.a.31.1		56	28.3	even	6
896.2.z.a.159.1		56	4.3	odd	2
896.2.z.a.479.1		56	112.45	odd	12
896.2.z.a.607.1		56	16.13	even	4
896.2.z.b.31.14		56	7.3	odd	6	inner
896.2.z.b.159.14		56	1.1	even	1	trivial
896.2.z.b.479.14		56	112.3	even	12	inner
896.2.z.b.607.14		56	16.3	odd	4	inner

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.z (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.08091 + 0.825526i) q^{3} +(-0.501060 - 1.86998i) q^{5} +(2.17953 - 1.49988i) q^{7} +(6.21241 + 3.58674i) q^{9} +(-3.52366 - 0.944161i) q^{11} +(0.372046 + 0.372046i) q^{13} -6.17487i q^{15} +(2.39966 - 1.38545i) q^{17} +(-0.431397 - 1.61000i) q^{19} +(7.95312 - 2.82174i) q^{21} +(-1.27273 + 2.20444i) q^{23} +(1.08436 - 0.626056i) q^{25} +(9.41278 + 9.41278i) q^{27} +(-2.14013 + 2.14013i) q^{29} +(2.74674 + 4.75749i) q^{31} +(-10.0766 - 5.81774i) q^{33} +(-3.89683 - 3.32415i) q^{35} +(-4.53493 + 1.21513i) q^{37} +(0.839106 + 1.45337i) q^{39} -3.95954 q^{41} +(4.29972 - 4.29972i) q^{43} +(3.59434 - 13.4143i) q^{45} +(-1.85655 + 3.21563i) q^{47} +(2.50070 - 6.53808i) q^{49} +(8.53685 - 2.28744i) q^{51} +(1.74138 - 6.49892i) q^{53} +7.06225i q^{55} -5.31638i q^{57} +(-2.20140 + 8.21574i) q^{59} +(-0.378874 + 0.101519i) q^{61} +(18.9198 - 1.50050i) q^{63} +(0.509302 - 0.882137i) q^{65} +(-3.72389 + 13.8977i) q^{67} +(-5.74099 + 5.74099i) q^{69} -8.98576 q^{71} +(-0.766294 - 1.32726i) q^{73} +(3.85764 - 1.03365i) q^{75} +(-9.09605 + 3.22725i) q^{77} +(-3.47070 - 2.00381i) q^{79} +(10.4692 + 18.1331i) q^{81} +(-3.67570 + 3.67570i) q^{83} +(-3.79313 - 3.79313i) q^{85} +(-8.36028 + 4.82681i) q^{87} +(-3.35201 + 5.80586i) q^{89} +(1.36891 + 0.252860i) q^{91} +(4.53501 + 16.9249i) q^{93} +(-2.79451 + 1.61341i) q^{95} -4.52980i q^{97} +(-18.5040 - 18.5040i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 6 q^{3} + 6 q^{5} - 8 q^{7} - 2 q^{11} - 12 q^{17} + 6 q^{19} + 10 q^{21} - 12 q^{23} + 24 q^{29} - 12 q^{33} + 2 q^{35} - 6 q^{37} - 4 q^{39} - 12 q^{45} - 8 q^{49} + 34 q^{51} - 6 q^{53} - 42 q^{59}+ \cdots + 16 q^{99}+O(q^{100}) \) 56 * q + 6 * q^3 + 6 * q^5 - 8 * q^7 - 2 * q^11 - 12 * q^17 + 6 * q^19 + 10 * q^21 - 12 * q^23 + 24 * q^29 - 12 * q^33 + 2 * q^35 - 6 * q^37 - 4 * q^39 - 12 * q^45 - 8 * q^49 + 34 * q^51 - 6 * q^53 - 42 * q^59 + 6 * q^61 - 4 * q^65 - 6 * q^67 - 80 * q^71 - 24 * q^75 - 10 * q^77 - 8 * q^81 + 28 * q^85 - 12 * q^87 - 16 * q^91 - 10 * q^93 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more