LMFDB - Embedded newform 896.2.z.a.31.1

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			31.1
Character	$\chi$	$=$	896.31
Dual form			896.2.z.a.607.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.825526 - 3.08091i) q^{3} +(-1.86998 - 0.501060i) q^{5} +(-2.17953 - 1.49988i) q^{7} +(-6.21241 + 3.58674i) q^{9} +(-0.944161 - 3.52366i) q^{11} +(-0.372046 - 0.372046i) q^{13} +6.17487i q^{15} +(2.39966 + 1.38545i) q^{17} +(1.61000 + 0.431397i) q^{19} +(-2.82174 + 7.95312i) q^{21} +(1.27273 + 2.20444i) q^{23} +(-1.08436 - 0.626056i) q^{25} +(9.41278 + 9.41278i) q^{27} +(-2.14013 + 2.14013i) q^{29} +(2.74674 - 4.75749i) q^{31} +(-10.0766 + 5.81774i) q^{33} +(3.32415 + 3.89683i) q^{35} +(1.21513 - 4.53493i) q^{37} +(-0.839106 + 1.45337i) q^{39} +3.95954 q^{41} +(-4.29972 + 4.29972i) q^{43} +(13.4143 - 3.59434i) q^{45} +(-1.85655 - 3.21563i) q^{47} +(2.50070 + 6.53808i) q^{49} +(2.28744 - 8.53685i) q^{51} +(-6.49892 + 1.74138i) q^{53} +7.06225i q^{55} -5.31638i q^{57} +(8.21574 - 2.20140i) q^{59} +(-0.101519 + 0.378874i) q^{61} +(18.9198 + 1.50050i) q^{63} +(0.509302 + 0.882137i) q^{65} +(-13.8977 + 3.72389i) q^{67} +(5.74099 - 5.74099i) q^{69} +8.98576 q^{71} +(0.766294 - 1.32726i) q^{73} +(-1.03365 + 3.85764i) q^{75} +(-3.22725 + 9.09605i) q^{77} +(-3.47070 + 2.00381i) q^{79} +(10.4692 - 18.1331i) q^{81} +(-3.67570 + 3.67570i) q^{83} +(-3.79313 - 3.79313i) q^{85} +(8.36028 + 4.82681i) q^{87} +(3.35201 + 5.80586i) q^{89} +(0.252860 + 1.36891i) q^{91} +(-16.9249 - 4.53501i) q^{93} +(-2.79451 - 1.61341i) q^{95} +4.52980i q^{97} +(18.5040 + 18.5040i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.825526	−	3.08091i	−0.476618	−	1.77876i	−0.615156	−	0.788405i	$-0.710907\pi$
$3$	−0.825526	−	3.08091i	−0.476618	−	1.77876i	0.138539	−	0.990357i	$-0.455759\pi$
$4$		0			0
$5$	−1.86998	−	0.501060i	−0.836281	−	0.224081i	−0.184829	−	0.982771i	$-0.559173\pi$
$5$	−1.86998	−	0.501060i	−0.836281	−	0.224081i	−0.651452	+	0.758690i	$0.725840\pi$
$6$		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
$11$	−0.944161	−	3.52366i	−0.284675	−	1.06242i	−0.949076	−	0.315046i	$-0.897980\pi$
$11$	−0.944161	−	3.52366i	−0.284675	−	1.06242i	0.664401	−	0.747376i	$-0.268687\pi$
$12$		0			0
$13$	−0.372046	−	0.372046i	−0.103187	−	0.103187i	0.653628	−	0.756816i	$-0.273246\pi$
$13$	−0.372046	−	0.372046i	−0.103187	−	0.103187i	−0.756816	+	0.653628i	$0.773246\pi$
$14$		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
$19$	1.61000	+	0.431397i	0.369358	+	0.0989693i	0.438724	−	0.898622i	$-0.355431\pi$
$19$	1.61000	+	0.431397i	0.369358	+	0.0989693i	−0.0693652	+	0.997591i	$0.522097\pi$
$20$		0			0
$21$	−2.82174	+	7.95312i	−0.615755	+	1.73551i
$22$		0			0
$23$	1.27273	+	2.20444i	0.265383	+	0.459657i	0.967664	−	0.252243i	$-0.0811683\pi$
$23$	1.27273	+	2.20444i	0.265383	+	0.459657i	−0.702281	+	0.711900i	$0.747835\pi$
$24$		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	−0.506641	−	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
$35$	3.32415	+	3.89683i	0.561883	+	0.658684i
$36$		0			0
$37$	1.21513	−	4.53493i	0.199766	−	0.745537i	−0.791215	−	0.611538i	$-0.790551\pi$
$37$	1.21513	−	4.53493i	0.199766	−	0.745537i	0.990981	−	0.134000i	$-0.0427821\pi$
$38$		0			0
$39$	−0.839106	+	1.45337i	−0.134364	+	0.232726i
$40$		0			0
$41$	3.95954			0.618376			0.309188	−	0.951001i	$-0.399943\pi$
$41$	3.95954			0.618376			0.309188	+	0.951001i	$0.399943\pi$
$42$		0			0
$43$	−4.29972	+	4.29972i	−0.655701	+	0.655701i	−0.954360	−	0.298659i	$-0.903461\pi$
$43$	−4.29972	+	4.29972i	−0.655701	+	0.655701i	0.298659	+	0.954360i	$0.403461\pi$
$44$		0			0
$45$	13.4143	−	3.59434i	1.99968	−	0.535813i
$46$		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
$51$	2.28744	−	8.53685i	0.320306	−	1.19540i
$52$		0			0
$53$	−6.49892	+	1.74138i	−0.892696	+	0.239197i	−0.675877	−	0.737015i	$-0.736235\pi$
$53$	−6.49892	+	1.74138i	−0.892696	+	0.239197i	−0.216819	+	0.976212i	$0.569568\pi$
$54$		0			0
$55$			7.06225i			0.952274i
$56$		0			0
$57$		−	5.31638i		−	0.704171i
$58$		0			0
$59$	8.21574	−	2.20140i	1.06960	−	0.286598i	0.319270	−	0.947664i	$-0.396562\pi$
$59$	8.21574	−	2.20140i	1.06960	−	0.286598i	0.750328	+	0.661066i	$0.229896\pi$
$60$		0			0
$61$	−0.101519	+	0.378874i	−0.0129982	+	0.0485098i	−0.972120	−	0.234483i	$-0.924660\pi$
$61$	−0.101519	+	0.378874i	−0.0129982	+	0.0485098i	0.959122	+	0.282992i	$0.0913271\pi$
$62$		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
$67$	−13.8977	+	3.72389i	−1.69788	+	0.454946i	−0.972404	−	0.233302i	$-0.925047\pi$
$67$	−13.8977	+	3.72389i	−1.69788	+	0.454946i	−0.725476	+	0.688248i	$0.758380\pi$
$68$		0			0
$69$	5.74099	−	5.74099i	0.691134	−	0.691134i
$70$		0			0
$71$	8.98576			1.06641			0.533207	−	0.845985i	$-0.320987\pi$
$71$	8.98576			1.06641			0.533207	+	0.845985i	$0.320987\pi$
$72$		0			0
$73$	0.766294	−	1.32726i	0.0896879	−	0.155344i	−0.817691	−	0.575657i	$-0.804746\pi$
$73$	0.766294	−	1.32726i	0.0896879	−	0.155344i	0.907379	+	0.420313i	$0.138080\pi$
$74$		0			0
$75$	−1.03365	+	3.85764i	−0.119356	+	0.445442i
$76$		0			0
$77$	−3.22725	+	9.09605i	−0.367779	+	1.03659i
$78$		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	−0.879451	−	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	$-0.0510410\pi$
$89$	3.35201	+	5.80586i	0.355313	+	0.615420i	−0.631859	+	0.775084i	$0.717708\pi$
$90$		0			0
$91$	0.252860	+	1.36891i	0.0265069	+	0.143501i
$92$		0			0
$93$	−16.9249	−	4.53501i	−1.75503	−	0.470259i
$94$		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
$101$	3.50302	+	13.0735i	0.348564	+	1.30086i	0.888393	+	0.459084i	$0.151822\pi$
$101$	3.50302	+	13.0735i	0.348564	+	1.30086i	−0.539829	+	0.841775i	$0.681511\pi$
$102$		0			0
$103$	−10.9548	+	6.32478i	−1.07941	+	0.623200i	−0.930738	−	0.365687i	$-0.880834\pi$
$103$	−10.9548	+	6.32478i	−1.07941	+	0.623200i	−0.148675	+	0.988886i	$0.547501\pi$
$104$		0			0
$105$	9.26159	−	13.4583i	0.903839	−	1.31340i
$106$		0			0
$107$	−3.48688	−	0.934307i	−0.337090	−	0.0903229i	0.0863036	−	0.996269i	$-0.472494\pi$
$107$	−3.48688	−	0.934307i	−0.337090	−	0.0903229i	−0.423393	+	0.905946i	$0.639161\pi$
$108$		0			0
$109$	−2.63902	−	9.84896i	−0.252772	−	0.943360i	−0.969316	−	0.245817i	$-0.920944\pi$
$109$	−2.63902	−	9.84896i	−0.252772	−	0.943360i	0.716544	−	0.697542i	$-0.245723\pi$
$110$		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
$115$	−1.27543	−	4.75997i	−0.118934	−	0.443869i
$116$		0			0
$117$	3.64574	+	0.976873i	0.337049	+	0.0903119i
$118$		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
$123$	−3.26871	−	12.1990i	−0.294729	−	1.09994i
$124$		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
$131$	−15.3810	−	4.12134i	−1.34385	−	0.360083i	−0.485987	−	0.873966i	$-0.661540\pi$
$131$	−15.3810	−	4.12134i	−1.34385	−	0.360083i	−0.857860	+	0.513883i	$0.828207\pi$
$132$		0			0
$133$	−2.86199	−	3.35505i	−0.248166	−	0.290920i
$134$		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	$-0.315498\pi$
$137$	1.13536	+	0.655503i	0.0970008	+	0.0560034i	−0.450715	+	0.892668i	$0.648831\pi$
$138$		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
$147$	18.0788	−	13.1018i	1.49112	−	1.08062i
$148$		0			0
$149$	−3.24672	+	12.1169i	−0.265981	+	0.992656i	0.695666	+	0.718366i	$0.255109\pi$
$149$	−3.24672	+	12.1169i	−0.265981	+	0.992656i	−0.961647	+	0.274290i	$0.911557\pi$
$150$		0			0
$151$	−4.56845	+	7.91278i	−0.371775	+	0.643933i	−0.989839	−	0.142195i	$-0.954584\pi$
$151$	−4.56845	+	7.91278i	−0.371775	+	0.643933i	0.618064	+	0.786128i	$0.287917\pi$
$152$		0			0
$153$	−19.8769			−1.60695
$154$		0			0
$155$	−7.52014	+	7.52014i	−0.604032	+	0.604032i
$156$		0			0
$157$	12.7686	−	3.42134i	1.01905	−	0.273053i	0.289642	−	0.957135i	$-0.406464\pi$
$157$	12.7686	−	3.42134i	1.01905	−	0.273053i	0.729405	+	0.684083i	$0.239797\pi$
$158$		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
$163$	−0.102694	+	0.383258i	−0.00804358	+	0.0300191i	−0.969831	−	0.243778i	$-0.921613\pi$
$163$	−0.102694	+	0.383258i	−0.00804358	+	0.0300191i	0.961787	+	0.273797i	$0.0882798\pi$
$164$		0			0
$165$	21.7581	−	5.83007i	1.69387	−	0.453871i
$166$		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
$171$	−11.5493	+	3.09462i	−0.883195	+	0.236651i
$172$		0			0
$173$	−3.98004	+	14.8537i	−0.302597	+	1.12931i	0.632398	+	0.774644i	$0.282071\pi$
$173$	−3.98004	+	14.8537i	−0.302597	+	1.12931i	−0.934994	+	0.354662i	$0.884596\pi$
$174$		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
$179$	0.555832	−	0.148935i	0.0415448	−	0.0111319i	−0.237987	−	0.971268i	$-0.576487\pi$
$179$	0.555832	−	0.148935i	0.0415448	−	0.0111319i	0.279532	+	0.960136i	$0.409821\pi$
$180$		0			0
$181$	−0.240422	+	0.240422i	−0.0178705	+	0.0178705i	−0.715986	−	0.698115i	$-0.754022\pi$
$181$	−0.240422	+	0.240422i	−0.0178705	+	0.0178705i	0.698115	+	0.715986i	$0.254022\pi$
$182$		0			0
$183$	1.25108			0.0924826
$184$		0			0
$185$	−4.54454	+	7.87137i	−0.334121	+	0.578715i
$186$		0			0
$187$	2.61617	−	9.76367i	0.191313	−	0.713990i
$188$		0			0
$189$	−6.39735	−	34.6335i	−0.465339	−	2.51922i
$190$		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	0.768875	−	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	$-0.325110\pi$
$199$	0.631178	+	0.364411i	0.0447430	+	0.0258324i	−0.477462	+	0.878653i	$0.658443\pi$
$200$		0			0
$201$	22.9459	+	39.7435i	1.61848	+	2.80329i
$202$		0			0
$203$	7.87443	−	1.45453i	0.552677	−	0.102088i
$204$		0			0
$205$	−7.40426	−	1.98397i	−0.517136	−	0.138566i
$206$		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	$-0.381440\pi$
$211$	−8.24367	−	8.24367i	−0.567518	−	0.567518i	−0.931432	+	0.363915i	$0.881440\pi$
$212$		0			0
$213$	−7.41798	−	27.6843i	−0.508272	−	1.89690i
$214$		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
$219$	−4.72176	−	1.26519i	−0.319067	−	0.0854937i
$220$		0			0
$221$	−0.377335	−	1.40824i	−0.0253823	−	0.0947281i
$222$		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
$227$	1.67563	+	6.25352i	0.111215	+	0.415061i	0.998976	−	0.0452445i	$-0.0144067\pi$
$227$	1.67563	+	6.25352i	0.111215	+	0.415061i	−0.887761	+	0.460305i	$0.847740\pi$
$228$		0			0
$229$	−7.68701	−	2.05973i	−0.507972	−	0.136111i	−0.00427468	−	0.999991i	$-0.501361\pi$
$229$	−7.68701	−	2.05973i	−0.507972	−	0.136111i	−0.503697	+	0.863880i	$0.668027\pi$
$230$		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	$-0.668585\pi$
$233$	−0.159304	+	0.0919739i	−0.0104363	+	0.00602541i	0.494773	+	0.869022i	$0.335251\pi$
$234$		0			0
$235$	1.86048	+	6.94341i	0.121364	+	0.452938i
$236$		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
$243$	−25.9348	−	6.94921i	−1.66372	−	0.445792i
$244$		0			0
$245$	−1.40028	−	13.4791i	−0.0894608	−	0.861147i
$246$		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	−0.230313	−	0.973117i	$-0.573975\pi$
$257$	7.97191	−	4.60259i	0.497274	−	0.287101i	0.727587	+	0.686015i	$0.240642\pi$
$258$		0			0
$259$	−9.45028	+	8.06145i	−0.587212	+	0.500914i
$260$		0			0
$261$	5.61929	−	20.9715i	0.347825	−	1.29810i
$262$		0			0
$263$	−1.54283	+	2.67226i	−0.0951349	+	0.164778i	−0.909665	−	0.415343i	$-0.863662\pi$
$263$	−1.54283	+	2.67226i	−0.0951349	+	0.164778i	0.814530	+	0.580121i	$0.196995\pi$
$264$		0			0
$265$	13.0254			0.800143
$266$		0			0
$267$	15.1201	−	15.1201i	0.925337	−	0.925337i
$268$		0			0
$269$	23.3503	−	6.25670i	1.42369	−	0.381478i	0.536902	−	0.843645i	$-0.319595\pi$
$269$	23.3503	−	6.25670i	1.42369	−	0.381478i	0.886793	+	0.462167i	$0.152928\pi$
$270$		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
$275$	−1.18220	+	4.41202i	−0.0712891	+	0.266055i
$276$		0			0
$277$	6.42687	−	1.72208i	0.386153	−	0.103469i	−0.0605191	−	0.998167i	$-0.519276\pi$
$277$	6.42687	−	1.72208i	0.386153	−	0.103469i	0.446672	+	0.894698i	$0.352609\pi$
$278$		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
$283$	23.1624	−	6.20636i	1.37686	−	0.368930i	0.506883	−	0.862015i	$-0.330798\pi$
$283$	23.1624	−	6.20636i	1.37686	−	0.368930i	0.869981	+	0.493085i	$0.164131\pi$
$284$		0			0
$285$	−2.66382	+	9.94152i	−0.157791	+	0.588885i
$286$		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
$291$	13.9559	−	3.73947i	0.818108	−	0.219211i
$292$		0			0
$293$	15.5002	−	15.5002i	0.905534	−	0.905534i	−0.0903743	−	0.995908i	$-0.528806\pi$
$293$	15.5002	−	15.5002i	0.905534	−	0.905534i	0.995908	+	0.0903743i	$0.0288063\pi$
$294$		0			0
$295$	−16.4663			−0.958705
$296$		0			0
$297$	24.2802	−	42.0546i	1.40888	−	2.44025i
$298$		0			0
$299$	0.346637	−	1.29367i	0.0200465	−	0.0748147i
$300$		0			0
$301$	15.8204	−	2.92228i	0.911875	−	0.168438i
$302$		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	$-0.414020\pi$
$311$	−7.66004	−	4.42252i	−0.434361	−	0.250778i	−0.701203	+	0.712962i	$0.747353\pi$
$312$		0			0
$313$	−12.5112	−	21.6700i	−0.707174	−	1.22486i	−0.965901	−	0.258911i	$-0.916636\pi$
$313$	−12.5112	−	21.6700i	−0.707174	−	1.22486i	0.258727	−	0.965951i	$-0.416697\pi$
$314$		0			0
$315$	−34.6279	−	12.2859i	−1.95106	−	0.692230i
$316$		0			0
$317$	3.08904	+	0.827705i	0.173498	+	0.0464885i	0.344522	−	0.938778i	$-0.388041\pi$
$317$	3.08904	+	0.827705i	0.173498	+	0.0464885i	−0.171024	+	0.985267i	$0.554708\pi$
$318$		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
$325$	0.170511	+	0.636355i	0.00945823	+	0.0352986i
$326$		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
$331$	13.2504	+	3.55043i	0.728306	+	0.195149i	0.603875	−	0.797079i	$-0.293623\pi$
$331$	13.2504	+	3.55043i	0.728306	+	0.195149i	0.124431	+	0.992228i	$0.460289\pi$
$332$		0			0
$333$	8.71671	+	32.5312i	0.477673	+	1.78270i
$334$		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
$339$	15.2195	+	56.7998i	0.826608	+	3.08494i
$340$		0			0
$341$	−19.3571	−	5.18673i	−1.04825	−	0.280877i
$342$		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
$347$	3.49811	+	13.0551i	0.187788	+	0.700836i	0.994016	+	0.109231i	$0.0348389\pi$
$347$	3.49811	+	13.0551i	0.187788	+	0.700836i	−0.806228	+	0.591605i	$0.798494\pi$
$348$		0			0
$349$	−12.6593	−	12.6593i	−0.677639	−	0.677639i	0.281826	−	0.959465i	$-0.409060\pi$
$349$	−12.6593	−	12.6593i	−0.677639	−	0.677639i	−0.959465	+	0.281826i	$0.909060\pi$
$350$		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
$355$	−16.8032	−	4.50240i	−0.891821	−	0.238963i
$356$		0			0
$357$	−17.7898	+	15.1754i	−0.941538	+	0.803169i
$358$		0			0
$359$	9.22928	+	15.9856i	0.487103	+	0.843687i	0.999890	−	0.0148287i	$-0.00472029\pi$
$359$	9.22928	+	15.9856i	0.487103	+	0.843687i	−0.512787	+	0.858516i	$0.671387\pi$
$360$		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
$371$	16.7765	+	5.95224i	0.870990	+	0.309025i
$372$		0			0
$373$	−9.31929	+	34.7801i	−0.482534	+	1.80084i	0.108381	+	0.994109i	$0.465433\pi$
$373$	−9.31929	+	34.7801i	−0.482534	+	1.80084i	−0.590915	+	0.806734i	$0.701233\pi$
$374$		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	$-0.992304\pi$
$379$	−18.9916	+	18.9916i	−0.975531	+	0.975531i	0.0241768	+	0.999708i	$0.492304\pi$
$380$		0			0
$381$	−63.4177	+	16.9927i	−3.24899	+	0.870564i
$382$		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
$387$	11.2897	−	42.1336i	0.573886	−	2.14177i
$388$		0			0
$389$	−13.0521	+	3.49731i	−0.661770	+	0.177321i	−0.574045	−	0.818824i	$-0.694626\pi$
$389$	−13.0521	+	3.49731i	−0.661770	+	0.177321i	−0.0877254	+	0.996145i	$0.527960\pi$
$390$		0			0
$391$			7.05320i			0.356696i
$392$		0			0
$393$			50.7898i			2.56201i
$394$		0			0
$395$	7.49417	−	2.00806i	0.377073	−	0.101036i
$396$		0			0
$397$	1.19554	−	4.46180i	0.0600022	−	0.223931i	−0.929413	−	0.369040i	$-0.879687\pi$
$397$	1.19554	−	4.46180i	0.0600022	−	0.223931i	0.989416	+	0.145109i	$0.0463532\pi$
$398$		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
$403$	−2.79192	+	0.748093i	−0.139076	+	0.0372652i
$404$		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	$-0.878077\pi$
$409$	−2.83340	+	4.90759i	−0.140102	+	0.242665i	0.787433	+	0.616401i	$0.211410\pi$
$410$		0			0
$411$	1.08227	−	4.03909i	0.0533845	−	0.199234i
$412$		0			0
$413$	−21.2083	−	7.52464i	−1.04359	−	0.370263i
$414$		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
$427$	0.789530	−	0.673500i	0.0382081	−	0.0325930i
$428$		0			0
$429$	5.91344	+	1.58450i	0.285504	+	0.0765005i
$430$		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
$437$	1.09811	+	4.09819i	0.0525295	+	0.196043i
$438$		0			0
$439$	−1.89128	+	1.09193i	−0.0902658	+	0.0521150i	−0.544453	−	0.838791i	$-0.683263\pi$
$439$	−1.89128	+	1.09193i	−0.0902658	+	0.0521150i	0.454188	+	0.890906i	$0.349930\pi$
$440$		0			0
$441$	−38.9857	−	31.6479i	−1.85646	−	1.50704i
$442$		0			0
$443$	−19.9847	−	5.35487i	−0.949500	−	0.254418i	−0.249350	−	0.968413i	$-0.580217\pi$
$443$	−19.9847	−	5.35487i	−0.949500	−	0.254418i	−0.700150	+	0.713996i	$0.746884\pi$
$444$		0			0
$445$	−3.35912	−	12.5364i	−0.159237	−	0.594282i
$446$		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
$451$	−3.73844	−	13.9521i	−0.176036	−	0.656977i
$452$		0			0
$453$	28.1499	+	7.54275i	1.32260	+	0.354389i
$454$		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	$-0.742580\pi$
$457$	−8.74709	+	5.05014i	−0.409172	+	0.236235i	0.281262	+	0.959631i	$0.409247\pi$
$458$		0			0
$459$	9.54659	+	35.6284i	0.445597	+	1.66299i
$460$		0			0
$461$	14.0523	+	14.0523i	0.654479	+	0.654479i	0.954068	−	0.299589i	$-0.0968497\pi$
$461$	14.0523	+	14.0523i	0.654479	+	0.654479i	−0.299589	+	0.954068i	$0.596850\pi$
$462$		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
$467$	13.2103	+	3.53968i	0.611298	+	0.163797i	0.551169	−	0.834394i	$-0.314182\pi$
$467$	13.2103	+	3.53968i	0.611298	+	0.163797i	0.0601291	+	0.998191i	$0.480849\pi$
$468$		0			0
$469$	35.8760	+	12.7287i	1.65660	+	0.587756i
$470$		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
$483$	−21.1235	+	3.90183i	−0.961151	+	0.177540i
$484$		0			0
$485$	2.26970	−	8.47063i	0.103062	−	0.384631i
$486$		0			0
$487$	−16.0930	+	27.8738i	−0.729242	+	1.26308i	0.227962	+	0.973670i	$0.426794\pi$
$487$	−16.0930	+	27.8738i	−0.729242	+	1.26308i	−0.957204	+	0.289414i	$0.906540\pi$
$488$		0			0
$489$	1.26556			0.0572305
$490$		0			0
$491$	−2.25713	+	2.25713i	−0.101863	+	0.101863i	−0.756202	−	0.654339i	$-0.772947\pi$
$491$	−2.25713	+	2.25713i	−0.101863	+	0.101863i	0.654339	+	0.756202i	$0.272947\pi$
$492$		0			0
$493$	−8.10063	+	2.17056i	−0.364834	+	0.0977570i
$494$		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
$499$	5.90659	−	22.0437i	0.264415	−	0.986811i	−0.698192	−	0.715910i	$-0.746012\pi$
$499$	5.90659	−	22.0437i	0.264415	−	0.986811i	0.962607	−	0.270900i	$-0.0873214\pi$
$500$		0			0
$501$	−72.8901	+	19.5309i	−3.25649	+	0.872574i
$502$		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
$507$	−39.1989	+	10.5033i	−1.74088	+	0.466468i
$508$		0			0
$509$	−2.84236	+	10.6078i	−0.125986	+	0.470185i	−0.999873	−	0.0159440i	$-0.994925\pi$
$509$	−2.84236	+	10.6078i	−0.125986	+	0.470185i	0.873887	+	0.486129i	$0.161591\pi$
$510$		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
$515$	23.6544	−	6.33819i	1.04234	−	0.279294i
$516$		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	$-0.895379\pi$
$521$	−4.42108	+	7.65754i	−0.193691	+	0.335483i	0.752780	+	0.658273i	$0.228713\pi$
$522$		0			0
$523$	−4.92948	+	18.3971i	−0.215551	+	0.804448i	0.770420	+	0.637536i	$0.220046\pi$
$523$	−4.92948	+	18.3971i	−0.215551	+	0.804448i	−0.985972	+	0.166912i	$0.946620\pi$
$524$		0			0
$525$	8.03889	−	6.85749i	0.350846	−	0.299285i
$526$		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
$539$	20.6769	−	14.9846i	0.890617	−	0.645432i
$540$		0			0
$541$	2.32628	+	0.623324i	0.100014	+	0.0267988i	0.308479	−	0.951231i	$-0.400180\pi$
$541$	2.32628	+	0.623324i	0.100014	+	0.0267988i	−0.208465	+	0.978030i	$0.566847\pi$
$542$		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	$-0.368151\pi$
$547$	−11.9972	−	11.9972i	−0.512962	−	0.512962i	−0.915433	+	0.402471i	$0.868151\pi$
$548$		0			0
$549$	−0.728244	−	2.71784i	−0.0310807	−	0.115995i
$550$		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
$555$	28.0026	+	7.50327i	1.18864	+	0.318496i
$556$		0			0
$557$	−5.28493	−	19.7236i	−0.223930	−	0.835716i	−0.982831	−	0.184510i	$-0.940930\pi$
$557$	−5.28493	−	19.7236i	−0.223930	−	0.835716i	0.758901	−	0.651206i	$-0.225737\pi$
$558$		0			0
$559$	3.19939			0.135320
$560$		0			0
$561$	−32.2407			−1.36120
$562$		0			0
$563$	4.13466	+	15.4308i	0.174255	+	0.650330i	0.996677	+	0.0814517i	$0.0259556\pi$
$563$	4.13466	+	15.4308i	0.174255	+	0.650330i	−0.822422	+	0.568878i	$0.807378\pi$
$564$		0			0
$565$	34.4751	+	9.23757i	1.45038	+	0.388628i
$566$		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	$-0.804962\pi$
$569$	−17.3910	+	10.0407i	−0.729068	+	0.420928i	0.0890129	+	0.996030i	$0.471629\pi$
$570$		0			0
$571$	4.66153	+	17.3971i	0.195079	+	0.728045i	0.992246	+	0.124286i	$0.0396641\pi$
$571$	4.66153	+	17.3971i	0.195079	+	0.728045i	−0.797167	+	0.603758i	$0.793669\pi$
$572$		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
$579$	51.9845	+	13.9292i	2.16040	+	0.578878i
$580$		0			0
$581$	13.5244	−	2.49817i	0.561087	−	0.103642i
$582$		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	−0.472119	−	0.881535i	$-0.656511\pi$
$593$	1.34548	−	0.776813i	0.0552522	−	0.0318999i	0.527372	+	0.849635i	$0.323178\pi$
$594$		0			0
$595$	2.57798	+	13.9565i	0.105687	+	0.572160i
$596$		0			0
$597$	0.601662	−	2.24543i	0.0246244	−	0.0918994i
$598$		0			0
$599$	−0.821999	+	1.42374i	−0.0335860	+	0.0581726i	−0.882330	−	0.470632i	$-0.844026\pi$
$599$	−0.821999	+	1.42374i	−0.0335860	+	0.0581726i	0.848744	+	0.528804i	$0.177359\pi$
$600$		0			0
$601$	35.9484			1.46637			0.733183	−	0.680031i	$-0.238034\pi$
$601$	35.9484			1.46637			0.733183	+	0.680031i	$0.238034\pi$
$602$		0			0
$603$	72.9819	−	72.9819i	2.97205	−	2.97205i
$604$		0			0
$605$	4.31517	−	1.15625i	0.175437	−	0.0470081i
$606$		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
$611$	−0.505643	+	1.88709i	−0.0204561	+	0.0763433i
$612$		0			0
$613$	27.9559	−	7.49076i	1.12913	−	0.302549i	0.354556	−	0.935035i	$-0.384632\pi$
$613$	27.9559	−	7.49076i	1.12913	−	0.302549i	0.774572	+	0.632485i	$0.217965\pi$
$614$		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
$619$	8.86168	−	2.37448i	0.356181	−	0.0954384i	−0.0762915	−	0.997086i	$-0.524308\pi$
$619$	8.86168	−	2.37448i	0.356181	−	0.0954384i	0.432472	+	0.901647i	$0.357641\pi$
$620$		0			0
$621$	−8.76992	+	32.7298i	−0.351925	+	1.31340i
$622$		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
$627$	−18.7331	+	5.01952i	−0.748128	+	0.200460i
$628$		0			0
$629$	9.19880	−	9.19880i	0.366780	−	0.366780i
$630$		0			0
$631$	2.48179			0.0987983			0.0493992	−	0.998779i	$-0.484269\pi$
$631$	2.48179			0.0987983			0.0493992	+	0.998779i	$0.484269\pi$
$632$		0			0
$633$	−18.5926	+	32.2033i	−0.738990	+	1.27997i
$634$		0			0
$635$	−10.3139	+	38.4919i	−0.409293	+	1.52750i
$636$		0			0
$637$	1.50209	−	3.36284i	0.0595152	−	0.133241i
$638$		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	−0.539652	−	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	$-0.280456\pi$
$647$	7.28511	+	4.20606i	0.286407	+	0.165357i	−0.349913	+	0.936782i	$0.613789\pi$
$648$		0			0
$649$	−15.5140	−	26.8710i	−0.608976	−	1.05478i
$650$		0			0
$651$	30.0863	+	35.2696i	1.17918	+	1.38232i
$652$		0			0
$653$	−47.4173	−	12.7054i	−1.85558	−	0.497201i	−0.855783	−	0.517335i	$-0.826924\pi$
$653$	−47.4173	−	12.7054i	−1.85558	−	0.497201i	−0.999797	+	0.0201333i	$0.993591\pi$
$654$		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	$-0.290233\pi$
$659$	−4.57653	−	4.57653i	−0.178276	−	0.178276i	−0.790604	+	0.612328i	$0.790233\pi$
$660$		0			0
$661$	−9.70671	−	36.2259i	−0.377547	−	1.40903i	−0.849587	−	0.527448i	$-0.823149\pi$
$661$	−9.70671	−	36.2259i	−0.377547	−	1.40903i	0.472040	−	0.881577i	$-0.343518\pi$
$662$		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
$667$	−7.44160	−	1.99397i	−0.288140	−	0.0772068i
$668$		0			0
$669$	23.4153	+	87.3870i	0.905286	+	3.37858i
$670$		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
$675$	−4.31392	−	16.0998i	−0.166043	−	0.619681i
$676$		0			0
$677$	10.2182	+	2.73796i	0.392717	+	0.105228i	0.449774	−	0.893143i	$-0.351505\pi$
$677$	10.2182	+	2.73796i	0.392717	+	0.105228i	−0.0570560	+	0.998371i	$0.518171\pi$
$678$		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
$683$	−8.66885	−	32.3526i	−0.331705	−	1.23794i	−0.907398	−	0.420272i	$-0.861935\pi$
$683$	−8.66885	−	32.3526i	−0.331705	−	1.23794i	0.575693	−	0.817666i	$-0.304732\pi$
$684$		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
$691$	−14.3264	−	3.83874i	−0.545001	−	0.146033i	−0.0241943	−	0.999707i	$-0.507702\pi$
$691$	−14.3264	−	3.83874i	−0.545001	−	0.146033i	−0.520807	+	0.853675i	$0.674369\pi$
$692$		0			0
$693$	−12.5761	−	68.0837i	−0.477728	−	2.58629i
$694$		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
$707$	11.9737	−	33.7481i	0.450319	−	1.26923i
$708$		0			0
$709$	−3.36966	+	12.5757i	−0.126550	+	0.472291i	−0.999890	−	0.0148195i	$-0.995283\pi$
$709$	−3.36966	+	12.5757i	−0.126550	+	0.472291i	0.873340	+	0.487111i	$0.161949\pi$
$710$		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
$717$	60.5923	−	16.2356i	2.26286	−	0.606331i
$718$		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
$723$	−2.95882	+	11.0425i	−0.110040	+	0.410673i
$724$		0			0
$725$	3.66052	−	0.980834i	0.135948	−	0.0364272i
$726$		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
$731$	−16.2749	+	4.36084i	−0.601948	+	0.161292i
$732$		0			0
$733$	12.9875	−	48.4699i	0.479703	−	1.79028i	−0.123110	−	0.992393i	$-0.539287\pi$
$733$	12.9875	−	48.4699i	0.479703	−	1.79028i	0.602813	−	0.797882i	$-0.294046\pi$
$734$		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
$739$	−7.12602	+	1.90941i	−0.262135	+	0.0702388i	−0.387493	−	0.921873i	$-0.626659\pi$
$739$	−7.12602	+	1.90941i	−0.262135	+	0.0702388i	0.125358	+	0.992112i	$0.459992\pi$
$740$		0			0
$741$	−1.97794	+	1.97794i	−0.0726614	+	0.0726614i
$742$		0			0
$743$	−13.2937			−0.487698			−0.243849	−	0.969813i	$-0.578410\pi$
$743$	−13.2937			−0.487698			−0.243849	+	0.969813i	$0.578410\pi$
$744$		0			0
$745$	12.1426	−	21.0316i	0.444870	−	0.770537i
$746$		0			0
$747$	9.65119	−	36.0187i	0.353119	−	1.31786i
$748$		0			0
$749$	6.19841	+	7.26627i	0.226485	+	0.265504i
$750$		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	0.00914525	−	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	$-0.0467550\pi$
$761$	10.1480	+	17.5769i	0.367867	+	0.637164i	−0.621365	+	0.783521i	$0.713422\pi$
$762$		0			0
$763$	−9.02048	+	25.4243i	−0.326563	+	0.920423i
$764$		0			0
$765$	37.1695	+	9.95952i	1.34386	+	0.360087i
$766$		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
$773$	12.6902	+	47.3606i	0.456436	+	1.70344i	0.683832	+	0.729639i	$0.260312\pi$
$773$	12.6902	+	47.3606i	0.456436	+	1.70344i	−0.227397	+	0.973802i	$0.573021\pi$
$774$		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
$779$	6.37485	+	1.70813i	0.228403	+	0.0612003i
$780$		0			0
$781$	−8.48400	−	31.6627i	−0.303581	−	1.13298i
$782$		0			0
$783$	−40.2892			−1.43982
$784$		0			0
$785$	−25.5913			−0.913394
$786$		0			0
$787$	−0.740742	−	2.76449i	−0.0264046	−	0.0985433i	0.951466	−	0.307754i	$-0.0995773\pi$
$787$	−0.740742	−	2.76449i	−0.0264046	−	0.0985433i	−0.977871	+	0.209210i	$0.932911\pi$
$788$		0			0
$789$	9.50662	+	2.54729i	0.338445	+	0.0906860i
$790$		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
$795$	−10.7528	−	40.1300i	−0.381363	−	1.42326i
$796$		0			0
$797$	−39.0301	−	39.0301i	−1.38252	−	1.38252i	−0.840129	−	0.542386i	$-0.817521\pi$
$797$	−39.0301	−	39.0301i	−1.38252	−	1.38252i	−0.542386	−	0.840129i	$-0.682479\pi$
$798$		0			0
$799$		−	10.2886i		−	0.363984i
$800$		0			0
$801$	−41.6482	−	24.0456i	−1.47157	−	0.849609i
$802$		0			0
$803$	−5.40031	−	1.44701i	−0.190573	−	0.0510639i
$804$		0			0
$805$	−4.35956	+	12.2875i	−0.153654	+	0.433077i
$806$		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	$-0.594872\pi$
$809$	−36.0749	−	20.8279i	−1.26833	−	0.732269i	−0.974671	+	0.223642i	$0.928205\pi$
$810$		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
$819$	−6.48080	−	7.59731i	−0.226457	−	0.265471i
$820$		0			0
$821$	11.0196	−	41.1258i	0.384588	−	1.43530i	−0.454228	−	0.890886i	$-0.650085\pi$
$821$	11.0196	−	41.1258i	0.384588	−	1.43530i	0.838816	−	0.544416i	$-0.183249\pi$
$822$		0			0
$823$	−0.688665	+	1.19280i	−0.0240054	+	0.0415785i	−0.877779	−	0.479067i	$-0.840975\pi$
$823$	−0.688665	+	1.19280i	−0.0240054	+	0.0415785i	0.853773	+	0.520645i	$0.174309\pi$
$824$		0			0
$825$	14.5689			0.507225
$826$		0			0
$827$	−14.2870	+	14.2870i	−0.496807	+	0.496807i	−0.910443	−	0.413636i	$-0.864259\pi$
$827$	−14.2870	+	14.2870i	−0.496807	+	0.496807i	0.413636	+	0.910443i	$0.364259\pi$
$828$		0			0
$829$	−20.0887	+	5.38274i	−0.697708	+	0.186950i	−0.590204	−	0.807254i	$-0.700953\pi$
$829$	−20.0887	+	5.38274i	−0.697708	+	0.186950i	−0.107504	+	0.994205i	$0.534286\pi$
$830$		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
$835$	−11.8544	+	44.2412i	−0.410239	+	1.53103i
$836$		0			0
$837$	70.6357	−	18.9268i	2.44153	−	0.654205i
$838$		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
$843$	−50.0972	+	13.4235i	−1.72544	+	0.462330i
$844$		0			0
$845$	−6.37506	+	23.7921i	−0.219309	+	0.818472i
$846$		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
$851$	11.5435	−	3.09307i	0.395706	−	0.106029i
$852$		0			0
$853$	−17.4577	+	17.4577i	−0.597741	+	0.597741i	−0.939711	−	0.341970i	$-0.888906\pi$
$853$	−17.4577	+	17.4577i	−0.597741	+	0.597741i	0.341970	+	0.939711i	$0.388906\pi$
$854$		0			0
$855$	23.1475			0.791628
$856$		0			0
$857$	−1.56865	+	2.71698i	−0.0535840	+	0.0928102i	−0.891573	−	0.452877i	$-0.850398\pi$
$857$	−1.56865	+	2.71698i	−0.0535840	+	0.0928102i	0.837989	+	0.545687i	$0.183731\pi$
$858$		0			0
$859$	−0.462421	+	1.72578i	−0.0157776	+	0.0588828i	−0.973366	−	0.229257i	$-0.926370\pi$
$859$	−0.462421	+	1.72578i	−0.0157776	+	0.0588828i	0.957588	+	0.288140i	$0.0930369\pi$
$860$		0			0
$861$	−11.1728	+	31.4907i	−0.380768	+	1.07320i
$862$		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
$875$	−5.81684	−	31.4908i	−0.196645	−	1.06458i
$876$		0			0
$877$	−4.01542	−	1.07593i	−0.135591	−	0.0363316i	0.190385	−	0.981709i	$-0.439026\pi$
$877$	−4.01542	−	1.07593i	−0.135591	−	0.0363316i	−0.325976	+	0.945378i	$0.605693\pi$
$878$		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	0.995158	+	0.0982911i	$0.0313376\pi$
$883$	32.4922	+	32.4922i	1.09345	+	1.09345i	0.0982911	+	0.995158i	$0.468662\pi$
$884$		0			0
$885$	13.5934	+	50.7311i	0.456936	+	1.70531i
$886$		0			0
$887$	32.4376	−	18.7278i	1.08915	−	0.628820i	0.155798	−	0.987789i	$-0.450205\pi$
$887$	32.4376	−	18.7278i	1.08915	−	0.628820i	0.933349	+	0.358969i	$0.116872\pi$
$888$		0			0
$889$	−30.8738	+	44.8637i	−1.03547	+	1.50468i
$890$		0			0
$891$	−73.7795	−	19.7692i	−2.47171	−	0.662292i
$892$		0			0
$893$	−1.60182	−	5.97807i	−0.0536028	−	0.200048i
$894$		0			0
$895$	−1.11402			−0.0372376
$896$		0			0
$897$	−4.27183			−0.142632
$898$		0			0
$899$	4.30328	+	16.0601i	0.143522	+	0.535633i
$900$		0			0
$901$	−18.0078	−	4.82518i	−0.599927	−	0.160750i
$902$		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
$907$	−8.94245	−	33.3737i	−0.296929	−	1.10815i	−0.939673	−	0.342074i	$-0.888871\pi$
$907$	−8.94245	−	33.3737i	−0.296929	−	1.10815i	0.642744	−	0.766081i	$-0.277796\pi$
$908$		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
$915$	−2.33950	−	0.626867i	−0.0773414	−	0.0207236i
$916$		0			0
$917$	27.3419	+	32.0523i	0.902909	+	1.05846i
$918$		0			0
$919$	−13.8963	−	24.0691i	−0.458396	−	0.793966i	0.540480	−	0.841357i	$-0.318243\pi$
$919$	−13.8963	−	24.0691i	−0.458396	−	0.793966i	−0.998876	+	0.0473912i	$0.984909\pi$
$920$		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
$931$	1.20560	+	11.6051i	0.0395120	+	0.380341i
$932$		0			0
$933$	−7.30182	+	27.2508i	−0.239051	+	0.892150i
$934$		0			0
$935$	−9.78436	+	16.9470i	−0.319983	+	0.554227i
$936$		0			0
$937$	−18.1308			−0.592307			−0.296154	−	0.955140i	$-0.595704\pi$
$937$	−18.1308			−0.592307			−0.296154	+	0.955140i	$0.595704\pi$
$938$		0			0
$939$	−56.4350	+	56.4350i	−1.84169	+	1.84169i
$940$		0			0
$941$	−8.37369	+	2.24372i	−0.272974	+	0.0731433i	−0.392709	−	0.919663i	$-0.628462\pi$
$941$	−8.37369	+	2.24372i	−0.272974	+	0.0731433i	0.119735	+	0.992806i	$0.461796\pi$
$942$		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
$947$	3.98857	−	14.8856i	0.129611	−	0.483716i	−0.870351	−	0.492432i	$-0.836108\pi$
$947$	3.98857	−	14.8856i	0.129611	−	0.483716i	0.999962	+	0.00871655i	$0.00277460\pi$
$948$		0			0
$949$	−0.778899	+	0.208705i	−0.0252841	+	0.00677486i
$950$		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
$955$	9.88585	−	2.64890i	0.319899	−	0.0857165i
$956$		0			0
$957$	9.11458	−	34.0161i	0.294632	−	1.09958i
$958$		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
$963$	25.0131	−	6.70223i	0.806035	−	0.215976i
$964$		0			0
$965$	23.0980	−	23.0980i	0.743549	−	0.743549i
$966$		0			0
$967$	−53.4246			−1.71802			−0.859010	−	0.511958i	$-0.828920\pi$
$967$	−53.4246			−1.71802			−0.859010	+	0.511958i	$0.828920\pi$
$968$		0			0
$969$	7.36555	−	12.7575i	0.236616	−	0.409830i
$970$		0			0
$971$	5.56119	−	20.7547i	0.178467	−	0.666048i	−0.817468	−	0.575974i	$-0.804623\pi$
$971$	5.56119	−	20.7547i	0.178467	−	0.666048i	0.995935	−	0.0900743i	$-0.0287105\pi$
$972$		0			0
$973$	10.6552	+	57.6842i	0.341589	+	1.84927i
$974$		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	−0.0845448	−	0.996420i	$-0.526944\pi$
$983$	−31.0312	−	17.9159i	−0.989742	−	0.571428i	−0.905197	+	0.424992i	$0.860277\pi$
$984$		0			0
$985$	−2.48773	−	4.30887i	−0.0792655	−	0.137292i
$986$		0			0
$987$	30.8130	−	5.69165i	0.980789	−	0.181167i
$988$		0			0
$989$	−14.9508	−	4.00606i	−0.475409	−	0.127385i
$990$		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
$997$	−7.00832	−	26.1554i	−0.221956	−	0.828351i	−0.983601	−	0.180357i	$-0.942275\pi$
$997$	−7.00832	−	26.1554i	−0.221956	−	0.828351i	0.761645	−	0.647994i	$-0.224392\pi$
$998$		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.a.31.1		56
4.3	odd	2		896.2.z.b.31.14		56
7.5	odd	6	inner	896.2.z.a.159.1		56
8.3	odd	2		112.2.v.a.59.8	yes	56
8.5	even	2		448.2.z.a.143.14		56
16.3	odd	4	inner	896.2.z.a.479.1		56
16.5	even	4		112.2.v.a.3.2	✓	56
16.11	odd	4		448.2.z.a.367.14		56
16.13	even	4		896.2.z.b.479.14		56
28.19	even	6		896.2.z.b.159.14		56
56.3	even	6		784.2.j.a.587.24		56
56.5	odd	6		448.2.z.a.271.14		56
56.11	odd	6		784.2.j.a.587.23		56
56.19	even	6		112.2.v.a.75.2	yes	56
56.27	even	2		784.2.w.f.619.8		56
56.51	odd	6		784.2.w.f.411.2		56
112.5	odd	12		112.2.v.a.19.8	yes	56
112.19	even	12	inner	896.2.z.a.607.1		56
112.37	even	12		784.2.w.f.19.8		56
112.53	even	12		784.2.j.a.195.24		56
112.61	odd	12		896.2.z.b.607.14		56
112.69	odd	4		784.2.w.f.227.2		56
112.75	even	12		448.2.z.a.47.14		56
112.101	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	16.5	even	4
112.2.v.a.19.8	yes	56	112.5	odd	12
112.2.v.a.59.8	yes	56	8.3	odd	2
112.2.v.a.75.2	yes	56	56.19	even	6
448.2.z.a.47.14		56	112.75	even	12
448.2.z.a.143.14		56	8.5	even	2
448.2.z.a.271.14		56	56.5	odd	6
448.2.z.a.367.14		56	16.11	odd	4
784.2.j.a.195.23		56	112.101	odd	12
784.2.j.a.195.24		56	112.53	even	12
784.2.j.a.587.23		56	56.11	odd	6
784.2.j.a.587.24		56	56.3	even	6
784.2.w.f.19.8		56	112.37	even	12
784.2.w.f.227.2		56	112.69	odd	4
784.2.w.f.411.2		56	56.51	odd	6
784.2.w.f.619.8		56	56.27	even	2
896.2.z.a.31.1		56	1.1	even	1	trivial
896.2.z.a.159.1		56	7.5	odd	6	inner
896.2.z.a.479.1		56	16.3	odd	4	inner
896.2.z.a.607.1		56	112.19	even	12	inner
896.2.z.b.31.14		56	4.3	odd	2
896.2.z.b.159.14		56	28.19	even	6
896.2.z.b.479.14		56	16.13	even	4
896.2.z.b.607.14		56	112.61	odd	12

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)

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

Properties

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