LMFDB - Embedded newform 896.2.z.b.479.14

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)

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")

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);

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			479.14
Character	$\chi$	$=$	896.479
Dual form			896.2.z.b.159.14

$q$-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 $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

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	0.788405	−	0.615156i	$-0.210907\pi$
$3$	3.08091	−	0.825526i	1.77876	−	0.476618i	0.990357	+	0.138539i	$0.0442405\pi$
$4$		0			0
$5$	−0.501060	+	1.86998i	−0.224081	+	0.836281i	0.758690	+	0.651452i	$0.225840\pi$
$5$	−0.501060	+	1.86998i	−0.224081	+	0.836281i	−0.982771	+	0.184829i	$0.940827\pi$
$6$		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	−0.747376	−	0.664401i	$-0.768687\pi$
$11$	−3.52366	+	0.944161i	−1.06242	+	0.284675i	−0.315046	+	0.949076i	$0.602020\pi$
$12$		0			0
$13$	0.372046	−	0.372046i	0.103187	−	0.103187i	−0.653628	−	0.756816i	$-0.726754\pi$
$13$	0.372046	−	0.372046i	0.103187	−	0.103187i	0.756816	+	0.653628i	$0.226754\pi$
$14$		0			0
$15$			6.17487i			1.59435i
$16$		0			0
$17$	2.39966	+	1.38545i	0.582003	+	0.336020i	0.761929	−	0.647660i	$-0.224252\pi$
$17$	2.39966	+	1.38545i	0.582003	+	0.336020i	−0.179926	+	0.983680i	$0.557586\pi$
$18$		0			0
$19$	−0.431397	+	1.61000i	−0.0989693	+	0.369358i	−0.997591	−	0.0693652i	$-0.977903\pi$
$19$	−0.431397	+	1.61000i	−0.0989693	+	0.369358i	0.898622	+	0.438724i	$0.144569\pi$
$20$		0			0
$21$	7.95312	+	2.82174i	1.73551	+	0.615755i
$22$		0			0
$23$	−1.27273	−	2.20444i	−0.265383	−	0.459657i	0.702281	−	0.711900i	$-0.252165\pi$
$23$	−1.27273	−	2.20444i	−0.265383	−	0.459657i	−0.967664	+	0.252243i	$0.918832\pi$
$24$		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	0.479907	−	0.877319i	$-0.340670\pi$
$29$	−2.14013	−	2.14013i	−0.397413	−	0.397413i	−0.877319	+	0.479907i	$0.840670\pi$
$30$		0			0
$31$	2.74674	−	4.75749i	0.493329	−	0.854471i	−0.506641	−	0.862157i	$-0.669113\pi$
$31$	2.74674	−	4.75749i	0.493329	−	0.854471i	0.999970	+	0.00768582i	$0.00244650\pi$
$32$		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	−0.134000	−	0.990981i	$-0.542782\pi$
$37$	−4.53493	−	1.21513i	−0.745537	−	0.199766i	−0.611538	+	0.791215i	$0.709449\pi$
$38$		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	0.954360	−	0.298659i	$-0.0965394\pi$
$43$	4.29972	+	4.29972i	0.655701	+	0.655701i	−0.298659	+	0.954360i	$0.596539\pi$
$44$		0			0
$45$	3.59434	+	13.4143i	0.535813	+	1.99968i
$46$		0			0
$47$	−1.85655	−	3.21563i	−0.270805	−	0.469048i	0.698263	−	0.715841i	$-0.253957\pi$
$47$	−1.85655	−	3.21563i	−0.270805	−	0.469048i	−0.969068	+	0.246793i	$0.920623\pi$
$48$		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	0.976212	+	0.216819i	$0.0695681\pi$
$53$	1.74138	+	6.49892i	0.239197	+	0.892696i	−0.737015	+	0.675877i	$0.763765\pi$
$54$		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	−0.947664	−	0.319270i	$-0.896562\pi$
$59$	−2.20140	−	8.21574i	−0.286598	−	1.06960i	0.661066	−	0.750328i	$-0.270104\pi$
$60$		0			0
$61$	−0.378874	−	0.101519i	−0.0485098	−	0.0129982i	0.234483	−	0.972120i	$-0.424660\pi$
$61$	−0.378874	−	0.101519i	−0.0485098	−	0.0129982i	−0.282992	+	0.959122i	$0.591327\pi$
$62$		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	−0.688248	−	0.725476i	$-0.741620\pi$
$67$	−3.72389	−	13.8977i	−0.454946	−	1.69788i	0.233302	−	0.972404i	$-0.425047\pi$
$68$		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	−0.907379	−	0.420313i	$-0.861920\pi$
$73$	−0.766294	+	1.32726i	−0.0896879	+	0.155344i	0.817691	+	0.575657i	$0.195254\pi$
$74$		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	−0.682370	−	0.731007i	$-0.739051\pi$
$79$	−3.47070	+	2.00381i	−0.390484	+	0.225446i	0.291886	+	0.956453i	$0.405717\pi$
$80$		0			0
$81$	10.4692	−	18.1331i	1.16324	−	2.01479i
$82$		0			0
$83$	−3.67570	−	3.67570i	−0.403460	−	0.403460i	0.475990	−	0.879451i	$-0.342090\pi$
$83$	−3.67570	−	3.67570i	−0.403460	−	0.403460i	−0.879451	+	0.475990i	$0.842090\pi$
$84$		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	0.631859	−	0.775084i	$-0.282292\pi$
$89$	−3.35201	−	5.80586i	−0.355313	−	0.615420i	−0.987171	+	0.159664i	$0.948959\pi$
$90$		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	$0.0738613\pi$
$97$			4.52980i			0.459931i	−0.973199	+	0.229966i	$0.926139\pi$
$98$		0			0
$99$	−18.5040	+	18.5040i	−1.85972	+	1.85972i
$100$		0			0
$101$	13.0735	−	3.50302i	1.30086	−	0.348564i	0.459084	−	0.888393i	$-0.348178\pi$
$101$	13.0735	−	3.50302i	1.30086	−	0.348564i	0.841775	+	0.539829i	$0.181511\pi$
$102$		0			0
$103$	10.9548	−	6.32478i	1.07941	−	0.623200i	0.148675	−	0.988886i	$-0.452499\pi$
$103$	10.9548	−	6.32478i	1.07941	−	0.623200i	0.930738	+	0.365687i	$0.119166\pi$
$104$		0			0
$105$	−9.26159	+	13.4583i	−0.903839	+	1.31340i
$106$		0			0
$107$	−0.934307	+	3.48688i	−0.0903229	+	0.337090i	−0.996269	−	0.0863036i	$-0.972494\pi$
$107$	−0.934307	+	3.48688i	−0.0903229	+	0.337090i	0.905946	+	0.423393i	$0.139161\pi$
$108$		0			0
$109$	9.84896	−	2.63902i	0.943360	−	0.252772i	0.245817	−	0.969316i	$-0.420944\pi$
$109$	9.84896	−	2.63902i	0.943360	−	0.252772i	0.697542	+	0.716544i	$0.254277\pi$
$110$		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	$-0.633547\pi$
$127$		−	20.5841i		−	1.82654i	0.407350	−	0.913272i	$-0.366453\pi$
$128$		0			0
$129$	16.7966	+	9.69749i	1.47885	+	0.853817i
$130$		0			0
$131$	4.12134	−	15.3810i	0.360083	−	1.34385i	−0.513883	−	0.857860i	$-0.671793\pi$
$131$	4.12134	−	15.3810i	0.360083	−	1.34385i	0.873966	−	0.485987i	$-0.161540\pi$
$132$		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	0.450715	−	0.892668i	$-0.351169\pi$
$137$	−1.13536	−	0.655503i	−0.0970008	−	0.0560034i	−0.547716	+	0.836665i	$0.684502\pi$
$138$		0			0
$139$	−15.6775	+	15.6775i	−1.32975	+	1.32975i	−0.424169	+	0.905583i	$0.639434\pi$
$139$	−15.6775	+	15.6775i	−1.32975	+	1.32975i	−0.905583	+	0.424169i	$0.860566\pi$
$140$		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	0.718366	−	0.695666i	$-0.244891\pi$
$149$	12.1169	+	3.24672i	0.992656	+	0.265981i	0.274290	+	0.961647i	$0.411557\pi$
$150$		0			0
$151$	4.56845	−	7.91278i	0.371775	−	0.643933i	−0.618064	−	0.786128i	$-0.712083\pi$
$151$	4.56845	−	7.91278i	0.371775	−	0.643933i	0.989839	+	0.142195i	$0.0454160\pi$
$152$		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	0.957135	+	0.289642i	$0.0935361\pi$
$157$	3.42134	+	12.7686i	0.273053	+	1.01905i	−0.684083	+	0.729405i	$0.739797\pi$
$158$		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	0.243778	−	0.969831i	$-0.421613\pi$
$163$	−0.383258	−	0.102694i	−0.0300191	−	0.00804358i	−0.273797	+	0.961787i	$0.588280\pi$
$164$		0			0
$165$	−5.83007	−	21.7581i	−0.453871	−	1.69387i
$166$		0			0
$167$			23.6587i			1.83076i	0.402588	+	0.915381i	$0.368111\pi$
$167$			23.6587i			1.83076i	−0.402588	+	0.915381i	$0.631889\pi$
$168$		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	−0.354662	−	0.934994i	$-0.615404\pi$
$173$	−14.8537	−	3.98004i	−1.12931	−	0.302597i	−0.774644	+	0.632398i	$0.782071\pi$
$174$		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	0.971268	−	0.237987i	$-0.0764875\pi$
$179$	0.148935	+	0.555832i	0.0111319	+	0.0415448i	−0.960136	+	0.279532i	$0.909821\pi$
$180$		0			0
$181$	0.240422	+	0.240422i	0.0178705	+	0.0178705i	0.715986	−	0.698115i	$-0.245978\pi$
$181$	0.240422	+	0.240422i	0.0178705	+	0.0178705i	−0.698115	+	0.715986i	$0.745978\pi$
$182$		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	−0.656408	−	0.754406i	$-0.727925\pi$
$191$	−4.57833	+	2.64330i	−0.331277	+	0.191263i	0.325131	+	0.945669i	$0.394592\pi$
$192$		0			0
$193$	−8.43656	+	14.6125i	−0.607277	+	1.05183i	0.384411	+	0.923162i	$0.374405\pi$
$193$	−8.43656	+	14.6125i	−0.607277	+	1.05183i	−0.991687	+	0.128672i	$0.958929\pi$
$194$		0			0
$195$	2.29734	+	2.29734i	0.164516	+	0.164516i
$196$		0			0
$197$	1.81729	−	1.81729i	0.129477	−	0.129477i	−0.639399	−	0.768875i	$-0.720817\pi$
$197$	1.81729	−	1.81729i	0.129477	−	0.129477i	0.768875	+	0.639399i	$0.220817\pi$
$198$		0			0
$199$	−0.631178	−	0.364411i	−0.0447430	−	0.0258324i	0.477462	−	0.878653i	$-0.341557\pi$
$199$	−0.631178	−	0.364411i	−0.0447430	−	0.0258324i	−0.522205	+	0.852820i	$0.674890\pi$
$200$		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	−0.363915	−	0.931432i	$-0.618560\pi$
$211$	8.24367	−	8.24367i	0.567518	−	0.567518i	0.931432	+	0.363915i	$0.118560\pi$
$212$		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	−0.460305	−	0.887761i	$-0.652260\pi$
$227$	−6.25352	+	1.67563i	−0.415061	+	0.111215i	0.0452445	+	0.998976i	$0.485593\pi$
$228$		0			0
$229$	−2.05973	+	7.68701i	−0.136111	+	0.507972i	0.863880	+	0.503697i	$0.168027\pi$
$229$	−2.05973	+	7.68701i	−0.136111	+	0.507972i	−0.999991	+	0.00427468i	$0.998639\pi$
$230$		0			0
$231$	−30.6882	−	2.43383i	−2.01914	−	0.160134i
$232$		0			0
$233$	0.159304	−	0.0919739i	0.0104363	−	0.00602541i	−0.494773	−	0.869022i	$-0.664749\pi$
$233$	0.159304	−	0.0919739i	0.0104363	−	0.00602541i	0.505209	+	0.862997i	$0.331415\pi$
$234$		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	$0.219444\pi$
$239$			19.6670i			1.27215i	−0.771626	+	0.636077i	$0.780556\pi$
$240$		0			0
$241$	−3.10397	−	1.79208i	−0.199944	−	0.115438i	0.396685	−	0.917955i	$-0.370160\pi$
$241$	−3.10397	−	1.79208i	−0.199944	−	0.115438i	−0.596630	+	0.802517i	$0.703494\pi$
$242$		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	−0.259547	−	0.965731i	$-0.583573\pi$
$251$	11.1881	−	11.1881i	0.706184	−	0.706184i	0.965731	+	0.259547i	$0.0835731\pi$
$252$		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	−0.230313	−	0.973117i	$-0.573975\pi$
$257$	7.97191	−	4.60259i	0.497274	−	0.287101i	0.727587	+	0.686015i	$0.240642\pi$
$258$		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	−0.814530	−	0.580121i	$-0.803005\pi$
$263$	1.54283	−	2.67226i	0.0951349	−	0.164778i	0.909665	+	0.415343i	$0.136338\pi$
$264$		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	0.843645	+	0.536902i	$0.180405\pi$
$269$	6.25670	+	23.3503i	0.381478	+	1.42369i	−0.462167	+	0.886793i	$0.652928\pi$
$270$		0			0
$271$	−5.80261	−	10.0504i	−0.352484	−	0.610520i	0.634200	−	0.773169i	$-0.281329\pi$
$271$	−5.80261	−	10.0504i	−0.352484	−	0.610520i	−0.986684	+	0.162649i	$0.947996\pi$
$272$		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	0.894698	−	0.446672i	$-0.147391\pi$
$277$	−1.72208	−	6.42687i	−0.103469	−	0.386153i	−0.998167	+	0.0605191i	$0.980724\pi$
$278$		0			0
$279$		−	39.4074i		−	2.35926i
$280$		0			0
$281$			16.2605i			0.970022i	0.874508	+	0.485011i	$0.161184\pi$
$281$			16.2605i			0.970022i	−0.874508	+	0.485011i	$0.838816\pi$
$282$		0			0
$283$	−6.20636	−	23.1624i	−0.368930	−	1.37686i	−0.862015	−	0.506883i	$-0.830798\pi$
$283$	−6.20636	−	23.1624i	−0.368930	−	1.37686i	0.493085	−	0.869981i	$-0.335869\pi$
$284$		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	0.0903743	−	0.995908i	$-0.471194\pi$
$293$	−15.5002	−	15.5002i	−0.905534	−	0.905534i	−0.995908	+	0.0903743i	$0.971194\pi$
$294$		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	0.903189	−	0.429243i	$-0.141220\pi$
$307$	8.30421	+	8.30421i	0.473946	+	0.473946i	−0.429243	+	0.903189i	$0.641220\pi$
$308$		0			0
$309$	28.5296	−	28.5296i	1.62299	−	1.62299i
$310$		0			0
$311$	7.66004	+	4.42252i	0.434361	+	0.250778i	0.701203	−	0.712962i	$-0.252647\pi$
$311$	7.66004	+	4.42252i	0.434361	+	0.250778i	−0.266842	+	0.963740i	$0.585980\pi$
$312$		0			0
$313$	12.5112	+	21.6700i	0.707174	+	1.22486i	0.965901	+	0.258911i	$0.0833637\pi$
$313$	12.5112	+	21.6700i	0.707174	+	1.22486i	−0.258727	+	0.965951i	$0.583303\pi$
$314$		0			0
$315$	−12.2859	+	34.6279i	−0.692230	+	1.95106i
$316$		0			0
$317$	−0.827705	+	3.08904i	−0.0464885	+	0.173498i	−0.985267	−	0.171024i	$-0.945292\pi$
$317$	−0.827705	+	3.08904i	−0.0464885	+	0.173498i	0.938778	+	0.344522i	$0.111959\pi$
$318$		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	−0.797079	−	0.603875i	$-0.793623\pi$
$331$	3.55043	−	13.2504i	0.195149	−	0.728306i	0.992228	−	0.124431i	$-0.0397107\pi$
$332$		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	0.109231	−	0.994016i	$-0.465161\pi$
$347$	13.0551	−	3.49811i	0.700836	−	0.187788i	0.591605	+	0.806228i	$0.298494\pi$
$348$		0			0
$349$	12.6593	−	12.6593i	0.677639	−	0.677639i	−0.281826	−	0.959465i	$-0.590940\pi$
$349$	12.6593	−	12.6593i	0.677639	−	0.677639i	0.959465	+	0.281826i	$0.0909402\pi$
$350$		0			0
$351$		−	7.00398i		−	0.373845i
$352$		0			0
$353$	−26.7828	−	15.4631i	−1.42550	−	0.823016i	−0.428743	−	0.903426i	$-0.641043\pi$
$353$	−26.7828	−	15.4631i	−1.42550	−	0.823016i	−0.996762	+	0.0804108i	$0.974377\pi$
$354$		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	0.512787	−	0.858516i	$-0.328613\pi$
$359$	−9.22928	−	15.9856i	−0.487103	−	0.843687i	−0.999890	+	0.0148287i	$0.995280\pi$
$360$		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	−0.996237	−	0.0866738i	$-0.972376\pi$
$367$	−8.10460	+	14.0376i	−0.423057	+	0.732756i	0.573180	+	0.819429i	$0.305710\pi$
$368$		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	0.994109	−	0.108381i	$-0.0345666\pi$
$373$	34.7801	+	9.31929i	1.80084	+	0.482534i	0.806734	+	0.590915i	$0.201233\pi$
$374$		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	0.999708	−	0.0241768i	$-0.00769645\pi$
$379$	18.9916	+	18.9916i	0.975531	+	0.975531i	−0.0241768	+	0.999708i	$0.507696\pi$
$380$		0			0
$381$	−16.9927	−	63.4177i	−0.870564	−	3.24899i
$382$		0			0
$383$	−11.8784	−	20.5740i	−0.606957	−	1.05128i	−0.991739	−	0.128273i	$-0.959057\pi$
$383$	−11.8784	−	20.5740i	−0.606957	−	1.05128i	0.384782	−	0.923007i	$-0.374277\pi$
$384$		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	0.996145	+	0.0877254i	$0.0279598\pi$
$389$	3.49731	+	13.0521i	0.177321	+	0.661770i	−0.818824	+	0.574045i	$0.805374\pi$
$390$		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	0.369040	−	0.929413i	$-0.379687\pi$
$397$	4.46180	+	1.19554i	0.223931	+	0.0600022i	−0.145109	+	0.989416i	$0.546353\pi$
$398$		0			0
$399$	−7.97395	+	11.5872i	−0.399197	+	0.580086i
$400$		0			0
$401$	11.1566	+	19.3238i	0.557135	+	0.964986i	0.997734	+	0.0672821i	$0.0214327\pi$
$401$	11.1566	+	19.3238i	0.557135	+	0.964986i	−0.440599	+	0.897704i	$0.645234\pi$
$402$		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	−0.787433	−	0.616401i	$-0.788590\pi$
$409$	2.83340	−	4.90759i	0.140102	−	0.242665i	0.927535	+	0.373736i	$0.121923\pi$
$410$		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	0.769431	−	0.638730i	$-0.220540\pi$
$419$	2.67538	+	2.67538i	0.130701	+	0.130701i	−0.638730	+	0.769431i	$0.720540\pi$
$420$		0			0
$421$	−17.2159	+	17.2159i	−0.839052	+	0.839052i	−0.988734	−	0.149682i	$-0.952175\pi$
$421$	−17.2159	+	17.2159i	−0.839052	+	0.839052i	0.149682	+	0.988734i	$0.452175\pi$
$422$		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	0.986582	−	0.163264i	$-0.0522021\pi$
$431$	27.7876	+	16.0432i	1.33848	+	0.772774i	0.351901	+	0.936037i	$0.385535\pi$
$432$		0			0
$433$		−	15.7783i		−	0.758258i	−0.925344	−	0.379129i	$-0.876224\pi$
$433$		−	15.7783i		−	0.758258i	0.925344	−	0.379129i	$-0.123776\pi$
$434$		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	−0.454188	−	0.890906i	$-0.650070\pi$
$439$	1.89128	−	1.09193i	0.0902658	−	0.0521150i	0.544453	+	0.838791i	$0.316737\pi$
$440$		0			0
$441$	38.9857	+	31.6479i	1.85646	+	1.50704i
$442$		0			0
$443$	−5.35487	+	19.9847i	−0.254418	+	0.949500i	0.713996	+	0.700150i	$0.246884\pi$
$443$	−5.35487	+	19.9847i	−0.254418	+	0.949500i	−0.968413	+	0.249350i	$0.919783\pi$
$444$		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	−0.281262	−	0.959631i	$-0.590753\pi$
$457$	8.74709	−	5.05014i	0.409172	−	0.236235i	0.690434	+	0.723396i	$0.257420\pi$
$458$		0			0
$459$	35.6284	−	9.54659i	1.66299	−	0.445597i
$460$		0			0
$461$	−14.0523	+	14.0523i	−0.654479	+	0.654479i	−0.954068	−	0.299589i	$-0.903150\pi$
$461$	−14.0523	+	14.0523i	−0.654479	+	0.654479i	0.299589	+	0.954068i	$0.403150\pi$
$462$		0			0
$463$		−	9.31917i		−	0.433099i	−0.976272	−	0.216549i	$-0.930520\pi$
$463$		−	9.31917i		−	0.433099i	0.976272	−	0.216549i	$-0.0694802\pi$
$464$		0			0
$465$	29.3769	+	16.9608i	1.36232	+	0.786537i
$466$		0			0
$467$	−3.53968	+	13.2103i	−0.163797	+	0.611298i	0.834394	+	0.551169i	$0.185818\pi$
$467$	−3.53968	+	13.2103i	−0.163797	+	0.611298i	−0.998191	+	0.0601291i	$0.980849\pi$
$468$		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	0.388748	+	0.921344i	$0.372908\pi$
$479$	−13.2090	+	22.8786i	−0.603534	+	1.04535i	−0.992281	+	0.124007i	$0.960426\pi$
$480$		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	−0.227962	−	0.973670i	$-0.573206\pi$
$487$	16.0930	−	27.8738i	0.729242	−	1.26308i	0.957204	−	0.289414i	$-0.0934604\pi$
$488$		0			0
$489$	−1.26556			−0.0572305
$490$		0			0
$491$	2.25713	+	2.25713i	0.101863	+	0.101863i	0.756202	−	0.654339i	$-0.227053\pi$
$491$	2.25713	+	2.25713i	0.101863	+	0.101863i	−0.654339	+	0.756202i	$0.727053\pi$
$492$		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	0.715910	−	0.698192i	$-0.246012\pi$
$499$	22.0437	+	5.90659i	0.986811	+	0.264415i	0.270900	+	0.962607i	$0.412679\pi$
$500$		0			0
$501$	19.5309	+	72.8901i	0.872574	+	3.25649i
$502$		0			0
$503$			23.1194i			1.03084i	0.856937	+	0.515422i	$0.172365\pi$
$503$			23.1194i			1.03084i	−0.856937	+	0.515422i	$0.827635\pi$
$504$		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	0.0159440	−	0.999873i	$-0.494925\pi$
$509$	−10.6078	−	2.84236i	−0.470185	−	0.125986i	−0.486129	+	0.873887i	$0.661591\pi$
$510$		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	−0.752780	−	0.658273i	$-0.771287\pi$
$521$	4.42108	−	7.65754i	0.193691	−	0.335483i	0.946471	+	0.322790i	$0.104621\pi$
$522$		0			0
$523$	18.3971	+	4.92948i	0.804448	+	0.215551i	0.637536	−	0.770420i	$-0.279954\pi$
$523$	18.3971	+	4.92948i	0.804448	+	0.215551i	0.166912	+	0.985972i	$0.446620\pi$
$524$		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	−0.978030	−	0.208465i	$-0.933153\pi$
$541$	−0.623324	+	2.32628i	−0.0267988	+	0.100014i	0.951231	+	0.308479i	$0.0998200\pi$
$542$		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	−0.402471	−	0.915433i	$-0.631849\pi$
$547$	11.9972	−	11.9972i	0.512962	−	0.512962i	0.915433	+	0.402471i	$0.131849\pi$
$548$		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	0.184510	−	0.982831i	$-0.440930\pi$
$557$	19.7236	−	5.28493i	0.835716	−	0.223930i	0.651206	+	0.758901i	$0.274263\pi$
$558$		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	−0.568878	−	0.822422i	$-0.692622\pi$
$563$	−15.4308	+	4.13466i	−0.650330	+	0.174255i	−0.0814517	+	0.996677i	$0.525956\pi$
$564$		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	−0.0890129	−	0.996030i	$-0.528371\pi$
$569$	17.3910	−	10.0407i	0.729068	−	0.420928i	0.818081	+	0.575103i	$0.195038\pi$
$570$		0			0
$571$	17.3971	−	4.66153i	0.728045	−	0.195079i	0.124286	−	0.992246i	$-0.460336\pi$
$571$	17.3971	−	4.66153i	0.728045	−	0.195079i	0.603758	+	0.797167i	$0.293669\pi$
$572$		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	0.122518	−	0.992466i	$-0.460903\pi$
$577$	−16.2314	−	9.37123i	−0.675724	−	0.390129i	−0.798242	+	0.602337i	$0.794236\pi$
$578$		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	−0.959766	−	0.280802i	$-0.909399\pi$
$587$	−16.4500	+	16.4500i	−0.678963	+	0.678963i	0.280802	+	0.959766i	$0.409399\pi$
$588$		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	−0.472119	−	0.881535i	$-0.656511\pi$
$593$	1.34548	−	0.776813i	0.0552522	−	0.0318999i	0.527372	+	0.849635i	$0.323178\pi$
$594$		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	−0.848744	−	0.528804i	$-0.822641\pi$
$599$	0.821999	−	1.42374i	0.0335860	−	0.0581726i	0.882330	+	0.470632i	$0.155974\pi$
$600$		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	1.00000		0.000525205i	$-0.000167178\pi$
$607$	12.3075	+	21.3172i	0.499545	+	0.865237i	−0.500455	+	0.865763i	$0.666834\pi$
$608$		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	−0.935035	−	0.354556i	$-0.884632\pi$
$613$	−7.49076	−	27.9559i	−0.302549	−	1.12913i	0.632485	−	0.774572i	$-0.282035\pi$
$614$		0			0
$615$		−	24.4497i		−	0.985905i
$616$		0			0
$617$			10.2299i			0.411839i	0.978569	+	0.205920i	$0.0660186\pi$
$617$			10.2299i			0.411839i	−0.978569	+	0.205920i	$0.933981\pi$
$618$		0			0
$619$	−2.37448	−	8.86168i	−0.0954384	−	0.356181i	0.901647	−	0.432472i	$-0.142359\pi$
$619$	−2.37448	−	8.86168i	−0.0954384	−	0.356181i	−0.997086	+	0.0762915i	$0.975692\pi$
$620$		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	−0.664847	−	0.746979i	$-0.731503\pi$
$641$	7.96198	−	13.7906i	0.314479	−	0.544694i	0.979327	+	0.202285i	$0.0648367\pi$
$642$		0			0
$643$	7.66392	+	7.66392i	0.302236	+	0.302236i	0.841888	−	0.539652i	$-0.181444\pi$
$643$	7.66392	+	7.66392i	0.302236	+	0.302236i	−0.539652	+	0.841888i	$0.681444\pi$
$644$		0			0
$645$	−26.5502	+	26.5502i	−1.04541	+	1.04541i
$646$		0			0
$647$	−7.28511	−	4.20606i	−0.286407	−	0.165357i	0.349913	−	0.936782i	$-0.386211\pi$
$647$	−7.28511	−	4.20606i	−0.286407	−	0.165357i	−0.636320	+	0.771425i	$0.719544\pi$
$648$		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	−0.0201333	−	0.999797i	$-0.506409\pi$
$653$	12.7054	−	47.4173i	0.497201	−	1.85558i	0.517335	−	0.855783i	$-0.326924\pi$
$654$		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	−0.612328	−	0.790604i	$-0.709767\pi$
$659$	4.57653	−	4.57653i	0.178276	−	0.178276i	0.790604	+	0.612328i	$0.209767\pi$
$660$		0			0
$661$	−36.2259	+	9.70671i	−1.40903	+	0.377547i	−0.881577	−	0.472040i	$-0.843518\pi$
$661$	−36.2259	+	9.70671i	−1.40903	+	0.377547i	−0.527448	+	0.849587i	$0.676851\pi$
$662$		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	−0.893143	−	0.449774i	$-0.851505\pi$
$677$	2.73796	−	10.2182i	0.105228	−	0.392717i	0.998371	+	0.0570560i	$0.0181714\pi$
$678$		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	−0.817666	−	0.575693i	$-0.804732\pi$
$683$	−32.3526	+	8.66885i	−1.23794	+	0.331705i	−0.420272	+	0.907398i	$0.638065\pi$
$684$		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	−0.853675	−	0.520807i	$-0.825631\pi$
$691$	3.83874	−	14.3264i	0.146033	−	0.545001i	0.999707	−	0.0241943i	$-0.00770204\pi$
$692$		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	0.920991	−	0.389583i	$-0.127381\pi$
$701$	14.0698	+	14.0698i	0.531408	+	0.531408i	−0.389583	+	0.920991i	$0.627381\pi$
$702$		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	0.487111	−	0.873340i	$-0.338051\pi$
$709$	12.5757	+	3.36966i	0.472291	+	0.126550i	−0.0148195	+	0.999890i	$0.504717\pi$
$710$		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	0.990833	−	0.135090i	$-0.0431324\pi$
$719$	10.1472	+	17.5754i	0.378425	+	0.655452i	−0.612408	+	0.790542i	$0.709799\pi$
$720$		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	$0.252510\pi$
$727$			38.4308i			1.42532i	−0.701510	+	0.712660i	$0.747490\pi$
$728$		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	0.992393	−	0.123110i	$-0.0392870\pi$
$733$	48.4699	+	12.9875i	1.79028	+	0.479703i	0.797882	+	0.602813i	$0.205954\pi$
$734$		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	0.921873	−	0.387493i	$-0.126659\pi$
$739$	−1.90941	−	7.12602i	−0.0702388	−	0.262135i	−0.992112	+	0.125358i	$0.959992\pi$
$740$		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	−0.293547	−	0.955945i	$-0.594836\pi$
$751$	10.6206	−	6.13182i	0.387552	−	0.223753i	0.681099	+	0.732191i	$0.261502\pi$
$752$		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	−0.999958	−	0.00914525i	$-0.997089\pi$
$757$	−27.2609	+	27.2609i	−0.990813	+	0.990813i	0.00914525	+	0.999958i	$0.497089\pi$
$758$		0			0
$759$	25.6497	+	14.8089i	0.931025	+	0.537527i
$760$		0			0
$761$	−10.1480	−	17.5769i	−0.367867	−	0.637164i	0.621365	−	0.783521i	$-0.286578\pi$
$761$	−10.1480	−	17.5769i	−0.367867	−	0.637164i	−0.989232	+	0.146358i	$0.953245\pi$
$762$		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	$0.115249\pi$
$769$			19.6449i			0.708412i	−0.935167	+	0.354206i	$0.884751\pi$
$770$		0			0
$771$	20.7612	−	20.7612i	0.747695	−	0.747695i
$772$		0			0
$773$	47.3606	−	12.6902i	1.70344	−	0.456436i	0.729639	−	0.683832i	$-0.239688\pi$
$773$	47.3606	−	12.6902i	1.70344	−	0.456436i	0.973802	+	0.227397i	$0.0730214\pi$
$774$		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	−0.209210	−	0.977871i	$-0.567089\pi$
$787$	2.76449	−	0.740742i	0.0985433	−	0.0264046i	0.307754	+	0.951466i	$0.400423\pi$
$788$		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	0.542386	−	0.840129i	$-0.317521\pi$
$797$	39.0301	−	39.0301i	1.38252	−	1.38252i	0.840129	−	0.542386i	$-0.182479\pi$
$798$		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	0.974671	−	0.223642i	$-0.0717946\pi$
$809$	36.0749	+	20.8279i	1.26833	+	0.732269i	0.293656	+	0.955911i	$0.405128\pi$
$810$		0			0
$811$	−6.24833	+	6.24833i	−0.219409	+	0.219409i	−0.808249	−	0.588841i	$-0.799585\pi$
$811$	−6.24833	+	6.24833i	−0.219409	+	0.219409i	0.588841	+	0.808249i	$0.299585\pi$
$812$		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	−0.544416	−	0.838816i	$-0.683249\pi$
$821$	−41.1258	−	11.0196i	−1.43530	−	0.384588i	−0.890886	+	0.454228i	$0.849915\pi$
$822$		0			0
$823$	0.688665	−	1.19280i	0.0240054	−	0.0415785i	−0.853773	−	0.520645i	$-0.825691\pi$
$823$	0.688665	−	1.19280i	0.0240054	−	0.0415785i	0.877779	+	0.479067i	$0.159025\pi$
$824$		0			0
$825$	−14.5689			−0.507225
$826$		0			0
$827$	14.2870	+	14.2870i	0.496807	+	0.496807i	0.910443	−	0.413636i	$-0.135741\pi$
$827$	14.2870	+	14.2870i	0.496807	+	0.496807i	−0.413636	+	0.910443i	$0.635741\pi$
$828$		0			0
$829$	−5.38274	−	20.0887i	−0.186950	−	0.697708i	−0.994205	−	0.107504i	$-0.965714\pi$
$829$	−5.38274	−	20.0887i	−0.186950	−	0.697708i	0.807254	−	0.590204i	$-0.200953\pi$
$830$		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	$-0.929446\pi$
$839$		−	12.7357i		−	0.439684i	0.975535	−	0.219842i	$-0.0705542\pi$
$840$		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	0.939711	−	0.341970i	$-0.111094\pi$
$853$	17.4577	+	17.4577i	0.597741	+	0.597741i	−0.341970	+	0.939711i	$0.611094\pi$
$854$		0			0
$855$	−23.1475			−0.791628
$856$		0			0
$857$	1.56865	−	2.71698i	0.0535840	−	0.0928102i	−0.837989	−	0.545687i	$-0.816269\pi$
$857$	1.56865	−	2.71698i	0.0535840	−	0.0928102i	0.891573	+	0.452877i	$0.149602\pi$
$858$		0			0
$859$	1.72578	+	0.462421i	0.0588828	+	0.0157776i	0.288140	−	0.957588i	$-0.406963\pi$
$859$	1.72578	+	0.462421i	0.0588828	+	0.0157776i	−0.229257	+	0.973366i	$0.573630\pi$
$860$		0			0
$861$	−31.4907	−	11.1728i	−1.07320	−	0.380768i
$862$		0			0
$863$	4.43745	−	2.56196i	0.151052	−	0.0872101i	−0.422569	−	0.906331i	$-0.638872\pi$
$863$	4.43745	−	2.56196i	0.151052	−	0.0872101i	0.573621	+	0.819121i	$0.305538\pi$
$864$		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	−0.945378	−	0.325976i	$-0.894307\pi$
$877$	1.07593	−	4.01542i	0.0363316	−	0.135591i	0.981709	+	0.190385i	$0.0609737\pi$
$878$		0			0
$879$	−60.5506	−	34.9589i	−2.04232	−	1.17914i
$880$		0			0
$881$		−	27.5375i		−	0.927761i	−0.885898	−	0.463880i	$-0.846457\pi$
$881$		−	27.5375i		−	0.927761i	0.885898	−	0.463880i	$-0.153543\pi$
$882$		0			0
$883$	−32.4922	+	32.4922i	−1.09345	+	1.09345i	−0.0982911	+	0.995158i	$0.531338\pi$
$883$	−32.4922	+	32.4922i	−1.09345	+	1.09345i	−0.995158	+	0.0982911i	$0.968662\pi$
$884$		0			0
$885$	50.7311	−	13.5934i	1.70531	−	0.456936i
$886$		0			0
$887$	−32.4376	+	18.7278i	−1.08915	+	0.628820i	−0.933349	−	0.358969i	$-0.883128\pi$
$887$	−32.4376	+	18.7278i	−1.08915	+	0.628820i	−0.155798	+	0.987789i	$0.549795\pi$
$888$		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	−0.766081	−	0.642744i	$-0.777796\pi$
$907$	−33.3737	+	8.94245i	−1.10815	+	0.296929i	−0.342074	+	0.939673i	$0.611129\pi$
$908$		0			0
$909$	68.6533	−	68.6533i	2.27709	−	2.27709i
$910$		0			0
$911$			22.9373i			0.759946i	0.924998	+	0.379973i	$0.124067\pi$
$911$			22.9373i			0.759946i	−0.924998	+	0.379973i	$0.875933\pi$
$912$		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	0.998876	−	0.0473912i	$-0.0150907\pi$
$919$	13.8963	+	24.0691i	0.458396	+	0.793966i	−0.540480	+	0.841357i	$0.681757\pi$
$920$		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	−0.267052	−	0.963682i	$-0.586050\pi$
$929$	13.2279	−	7.63716i	0.433995	−	0.250567i	0.701047	+	0.713115i	$0.252716\pi$
$930$		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	0.919663	−	0.392709i	$-0.128462\pi$
$941$	−2.24372	−	8.37369i	−0.0731433	−	0.272974i	−0.992806	+	0.119735i	$0.961796\pi$
$942$		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	0.492432	−	0.870351i	$-0.336108\pi$
$947$	14.8856	+	3.98857i	0.483716	+	0.129611i	−0.00871655	+	0.999962i	$0.502775\pi$
$948$		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	$0.0752711\pi$
$953$			14.4644i			0.468547i	−0.972171	+	0.234273i	$0.924729\pi$
$954$		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	−0.0900743	−	0.995935i	$-0.528710\pi$
$971$	−20.7547	−	5.56119i	−0.666048	−	0.178467i	−0.575974	+	0.817468i	$0.695377\pi$
$972$		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	0.416659	+	0.909063i	$0.363201\pi$
$977$	−18.0960	+	31.3432i	−0.578942	+	1.00276i	−0.995601	+	0.0936944i	$0.970132\pi$
$978$		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	0.905197	−	0.424992i	$-0.139723\pi$
$983$	31.0312	+	17.9159i	0.989742	+	0.571428i	0.0845448	+	0.996420i	$0.473056\pi$
$984$		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	−0.342496	−	0.939519i	$-0.611272\pi$
$991$	−41.7865	−	24.1254i	−1.32739	−	0.766370i	−0.984896	+	0.173149i	$0.944606\pi$
$992$		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	−0.647994	−	0.761645i	$-0.724392\pi$
$997$	−26.1554	+	7.00832i	−0.828351	+	0.221956i	−0.180357	+	0.983601i	$0.557725\pi$
$998$		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.479.14		56
4.3	odd	2		896.2.z.a.479.1		56
7.5	odd	6	inner	896.2.z.b.607.14		56
8.3	odd	2		448.2.z.a.367.14		56
8.5	even	2		112.2.v.a.3.2	✓	56
16.3	odd	4		112.2.v.a.59.8	yes	56
16.5	even	4		896.2.z.a.31.1		56
16.11	odd	4	inner	896.2.z.b.31.14		56
16.13	even	4		448.2.z.a.143.14		56
28.19	even	6		896.2.z.a.607.1		56
56.5	odd	6		112.2.v.a.19.8	yes	56
56.13	odd	2		784.2.w.f.227.2		56
56.19	even	6		448.2.z.a.47.14		56
56.37	even	6		784.2.w.f.19.8		56
56.45	odd	6		784.2.j.a.195.23		56
56.53	even	6		784.2.j.a.195.24		56
112.3	even	12		784.2.j.a.587.24		56
112.5	odd	12		896.2.z.a.159.1		56
112.19	even	12		112.2.v.a.75.2	yes	56
112.51	odd	12		784.2.w.f.411.2		56
112.61	odd	12		448.2.z.a.271.14		56
112.67	odd	12		784.2.j.a.587.23		56
112.75	even	12	inner	896.2.z.b.159.14		56
112.83	even	4		784.2.w.f.619.8		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.2	✓	56	8.5	even	2
112.2.v.a.19.8	yes	56	56.5	odd	6
112.2.v.a.59.8	yes	56	16.3	odd	4
112.2.v.a.75.2	yes	56	112.19	even	12
448.2.z.a.47.14		56	56.19	even	6
448.2.z.a.143.14		56	16.13	even	4
448.2.z.a.271.14		56	112.61	odd	12
448.2.z.a.367.14		56	8.3	odd	2
784.2.j.a.195.23		56	56.45	odd	6
784.2.j.a.195.24		56	56.53	even	6
784.2.j.a.587.23		56	112.67	odd	12
784.2.j.a.587.24		56	112.3	even	12
784.2.w.f.19.8		56	56.37	even	6
784.2.w.f.227.2		56	56.13	odd	2
784.2.w.f.411.2		56	112.51	odd	12
784.2.w.f.619.8		56	112.83	even	4
896.2.z.a.31.1		56	16.5	even	4
896.2.z.a.159.1		56	112.5	odd	12
896.2.z.a.479.1		56	4.3	odd	2
896.2.z.a.607.1		56	28.19	even	6
896.2.z.b.31.14		56	16.11	odd	4	inner
896.2.z.b.159.14		56	112.75	even	12	inner
896.2.z.b.479.14		56	1.1	even	1	trivial
896.2.z.b.607.14		56	7.5	odd	6	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

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Database

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