LMFDB - Embedded newform 448.2.z.a.271.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [448,2,Mod(47,448)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(448, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("448.47"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.z (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.57729801055$
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			271.14
Character	$\chi$	$=$	448.271
Dual form			448.2.z.a.367.14

$q$-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 $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	3.08091	+	0.825526i	1.77876	+	0.476618i	0.990357	−	0.138539i	$-0.0442405\pi$
$3$	3.08091	+	0.825526i	1.77876	+	0.476618i	0.788405	+	0.615156i	$0.210907\pi$
$4$		0			0
$5$	0.501060	+	1.86998i	0.224081	+	0.836281i	0.982771	+	0.184829i	$0.0591731\pi$
$5$	0.501060	+	1.86998i	0.224081	+	0.836281i	−0.758690	+	0.651452i	$0.774160\pi$
$6$		0			0
$7$	−2.17953	+	1.49988i	−0.823785	+	0.566903i
$7$	−2.17953	+	1.49988i	−0.823785	+	0.566903i
$8$		0			0
$9$	6.21241	+	3.58674i	2.07080	+	1.19558i
$10$		0			0
$11$	−3.52366	−	0.944161i	−1.06242	−	0.284675i	−0.315046	−	0.949076i	$-0.602020\pi$
$11$	−3.52366	−	0.944161i	−1.06242	−	0.284675i	−0.747376	+	0.664401i	$0.768687\pi$
$12$		0			0
$13$	−0.372046	−	0.372046i	−0.103187	−	0.103187i	0.653628	−	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	−0.179926	−	0.983680i	$-0.557586\pi$
$17$	2.39966	−	1.38545i	0.582003	−	0.336020i	0.761929	+	0.647660i	$0.224252\pi$
$18$		0			0
$19$	−0.431397	−	1.61000i	−0.0989693	−	0.369358i	0.898622	−	0.438724i	$-0.144569\pi$
$19$	−0.431397	−	1.61000i	−0.0989693	−	0.369358i	−0.997591	+	0.0693652i	$0.977903\pi$
$20$		0			0
$21$	−7.95312	+	2.82174i	−1.73551	+	0.615755i
$22$		0			0
$23$	1.27273	−	2.20444i	0.265383	−	0.459657i	−0.702281	−	0.711900i	$-0.747835\pi$
$23$	1.27273	−	2.20444i	0.265383	−	0.459657i	0.967664	+	0.252243i	$0.0811683\pi$
$24$		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	$-0.659330\pi$
$29$	2.14013	−	2.14013i	0.397413	−	0.397413i	0.877319	+	0.479907i	$0.159330\pi$
$30$		0			0
$31$	−2.74674	−	4.75749i	−0.493329	−	0.854471i	0.506641	−	0.862157i	$-0.330887\pi$
$31$	−2.74674	−	4.75749i	−0.493329	−	0.854471i	−0.999970	+	0.00768582i	$0.997554\pi$
$32$		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	$-0.457218\pi$
$37$	4.53493	−	1.21513i	0.745537	−	0.199766i	0.611538	+	0.791215i	$0.290551\pi$
$38$		0			0
$39$	−0.839106	−	1.45337i	−0.134364	−	0.232726i
$40$		0			0
$41$	−3.95954			−0.618376			−0.309188	−	0.951001i	$-0.600057\pi$
$41$	−3.95954			−0.618376			−0.309188	+	0.951001i	$0.600057\pi$
$42$		0			0
$43$	4.29972	−	4.29972i	0.655701	−	0.655701i	−0.298659	−	0.954360i	$-0.596539\pi$
$43$	4.29972	−	4.29972i	0.655701	−	0.655701i	0.954360	+	0.298659i	$0.0965394\pi$
$44$		0			0
$45$	−3.59434	+	13.4143i	−0.535813	+	1.99968i
$46$		0			0
$47$	1.85655	−	3.21563i	0.270805	−	0.469048i	−0.698263	−	0.715841i	$-0.746043\pi$
$47$	1.85655	−	3.21563i	0.270805	−	0.469048i	0.969068	+	0.246793i	$0.0793767\pi$
$48$		0			0
$49$	2.50070	−	6.53808i	0.357242	−	0.934012i
$50$		0			0
$51$	8.53685	−	2.28744i	1.19540	−	0.320306i
$52$		0			0
$53$	−1.74138	+	6.49892i	−0.239197	+	0.892696i	0.737015	+	0.675877i	$0.236235\pi$
$53$	−1.74138	+	6.49892i	−0.239197	+	0.892696i	−0.976212	+	0.216819i	$0.930432\pi$
$54$		0			0
$55$		−	7.06225i		−	0.952274i
$56$		0			0
$57$		−	5.31638i		−	0.704171i
$58$		0			0
$59$	−2.20140	+	8.21574i	−0.286598	+	1.06960i	0.661066	+	0.750328i	$0.270104\pi$
$59$	−2.20140	+	8.21574i	−0.286598	+	1.06960i	−0.947664	+	0.319270i	$0.896562\pi$
$60$		0			0
$61$	0.378874	−	0.101519i	0.0485098	−	0.0129982i	−0.234483	−	0.972120i	$-0.575340\pi$
$61$	0.378874	−	0.101519i	0.0485098	−	0.0129982i	0.282992	+	0.959122i	$0.408673\pi$
$62$		0			0
$63$	−18.9198	+	1.50050i	−2.38367	+	0.189045i
$64$		0			0
$65$	0.509302	−	0.882137i	0.0631711	−	0.109416i
$66$		0			0
$67$	−3.72389	+	13.8977i	−0.454946	+	1.69788i	0.233302	+	0.972404i	$0.425047\pi$
$67$	−3.72389	+	13.8977i	−0.454946	+	1.69788i	−0.688248	+	0.725476i	$0.741620\pi$
$68$		0			0
$69$	5.74099	−	5.74099i	0.691134	−	0.691134i
$70$		0			0
$71$	8.98576			1.06641			0.533207	−	0.845985i	$-0.320987\pi$
$71$	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	$-0.195254\pi$
$73$	−0.766294	−	1.32726i	−0.0896879	−	0.155344i	−0.907379	+	0.420313i	$0.861920\pi$
$74$		0			0
$75$	3.85764	−	1.03365i	0.445442	−	0.119356i
$76$		0			0
$77$	9.09605	−	3.22725i	1.03659	−	0.367779i
$78$		0			0
$79$	3.47070	+	2.00381i	0.390484	+	0.225446i	0.682370	−	0.731007i	$-0.260949\pi$
$79$	3.47070	+	2.00381i	0.390484	+	0.225446i	−0.291886	+	0.956453i	$0.594283\pi$
$80$		0			0
$81$	10.4692	+	18.1331i	1.16324	+	2.01479i
$82$		0			0
$83$	−3.67570	+	3.67570i	−0.403460	+	0.403460i	−0.879451	−	0.475990i	$-0.842090\pi$
$83$	−3.67570	+	3.67570i	−0.403460	+	0.403460i	0.475990	+	0.879451i	$0.342090\pi$
$84$		0			0
$85$	3.79313	+	3.79313i	0.411423	+	0.411423i
$86$		0			0
$87$	8.36028	−	4.82681i	0.896317	−	0.517489i
$88$		0			0
$89$	−3.35201	+	5.80586i	−0.355313	+	0.615420i	−0.987171	−	0.159664i	$-0.948959\pi$
$89$	−3.35201	+	5.80586i	−0.355313	+	0.615420i	0.631859	+	0.775084i	$0.282292\pi$
$90$		0			0
$91$	1.36891	+	0.252860i	0.143501	+	0.0265069i
$92$		0			0
$93$	−4.53501	−	16.9249i	−0.470259	−	1.75503i
$94$		0			0
$95$	2.79451	−	1.61341i	0.286710	−	0.165532i
$96$		0			0
$97$		−	4.52980i		−	0.459931i	−0.973199	−	0.229966i	$-0.926139\pi$
$97$		−	4.52980i		−	0.459931i	0.973199	−	0.229966i	$-0.0738613\pi$
$98$		0			0
$99$	−18.5040	−	18.5040i	−1.85972	−	1.85972i
$100$		0			0
$101$	−13.0735	−	3.50302i	−1.30086	−	0.348564i	−0.459084	−	0.888393i	$-0.651822\pi$
$101$	−13.0735	−	3.50302i	−1.30086	−	0.348564i	−0.841775	+	0.539829i	$0.818489\pi$
$102$		0			0
$103$	−10.9548	−	6.32478i	−1.07941	−	0.623200i	−0.148675	−	0.988886i	$-0.547501\pi$
$103$	−10.9548	−	6.32478i	−1.07941	−	0.623200i	−0.930738	+	0.365687i	$0.880834\pi$
$104$		0			0
$105$	−9.26159	−	13.4583i	−0.903839	−	1.31340i
$106$		0			0
$107$	−0.934307	−	3.48688i	−0.0903229	−	0.337090i	0.905946	−	0.423393i	$-0.139161\pi$
$107$	−0.934307	−	3.48688i	−0.0903229	−	0.337090i	−0.996269	+	0.0863036i	$0.972494\pi$
$108$		0			0
$109$	−9.84896	−	2.63902i	−0.943360	−	0.252772i	−0.245817	−	0.969316i	$-0.579056\pi$
$109$	−9.84896	−	2.63902i	−0.943360	−	0.252772i	−0.697542	+	0.716544i	$0.745723\pi$
$110$		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	0.873966	+	0.485987i	$0.161540\pi$
$131$	4.12134	+	15.3810i	0.360083	+	1.34385i	−0.513883	+	0.857860i	$0.671793\pi$
$132$		0			0
$133$	3.35505	+	2.86199i	0.290920	+	0.248166i
$134$		0			0
$135$	−12.8853	+	22.3181i	−1.10899	+	1.92083i
$136$		0			0
$137$	−1.13536	+	0.655503i	−0.0970008	+	0.0560034i	−0.547716	−	0.836665i	$-0.684502\pi$
$137$	−1.13536	+	0.655503i	−0.0970008	+	0.0560034i	0.450715	+	0.892668i	$0.351169\pi$
$138$		0			0
$139$	−15.6775	−	15.6775i	−1.32975	−	1.32975i	−0.905583	−	0.424169i	$-0.860566\pi$
$139$	−15.6775	−	15.6775i	−1.32975	−	1.32975i	−0.424169	−	0.905583i	$-0.639434\pi$
$140$		0			0
$141$	8.37444	−	8.37444i	0.705255	−	0.705255i
$142$		0			0
$143$	0.959692	+	1.66224i	0.0802535	+	0.139003i
$144$		0			0
$145$	5.07434	+	2.92967i	0.421401	+	0.243296i
$146$		0			0
$147$	13.1018	−	18.0788i	1.08062	−	1.49112i
$148$		0			0
$149$	−12.1169	+	3.24672i	−0.992656	+	0.265981i	−0.718366	−	0.695666i	$-0.755109\pi$
$149$	−12.1169	+	3.24672i	−0.992656	+	0.265981i	−0.274290	+	0.961647i	$0.588443\pi$
$150$		0			0
$151$	−4.56845	−	7.91278i	−0.371775	−	0.643933i	0.618064	−	0.786128i	$-0.287917\pi$
$151$	−4.56845	−	7.91278i	−0.371775	−	0.643933i	−0.989839	+	0.142195i	$0.954584\pi$
$152$		0			0
$153$	19.8769			1.60695
$154$		0			0
$155$	7.52014	−	7.52014i	0.604032	−	0.604032i
$156$		0			0
$157$	−3.42134	+	12.7686i	−0.273053	+	1.01905i	0.684083	+	0.729405i	$0.260203\pi$
$157$	−3.42134	+	12.7686i	−0.273053	+	1.01905i	−0.957135	+	0.289642i	$0.906464\pi$
$158$		0			0
$159$	−10.7301	+	18.5850i	−0.850949	+	1.47389i
$160$		0			0
$161$	0.532442	+	6.71358i	0.0419623	+	0.529104i
$162$		0			0
$163$	−0.383258	+	0.102694i	−0.0300191	+	0.00804358i	−0.273797	−	0.961787i	$-0.588280\pi$
$163$	−0.383258	+	0.102694i	−0.0300191	+	0.00804358i	0.243778	+	0.969831i	$0.421613\pi$
$164$		0			0
$165$	5.83007	−	21.7581i	0.453871	−	1.69387i
$166$		0			0
$167$			23.6587i			1.83076i	0.402588	+	0.915381i	$0.368111\pi$
$167$			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	$-0.384596\pi$
$173$	14.8537	−	3.98004i	1.12931	−	0.302597i	0.774644	+	0.632398i	$0.217929\pi$
$174$		0			0
$175$	−1.42439	+	2.99092i	−0.107673	+	0.226093i
$176$		0			0
$177$	−13.5646	+	23.4946i	−1.01958	+	1.76596i
$178$		0			0
$179$	0.148935	−	0.555832i	0.0111319	−	0.0415448i	−0.960136	−	0.279532i	$-0.909821\pi$
$179$	0.148935	−	0.555832i	0.0111319	−	0.0415448i	0.971268	+	0.237987i	$0.0764875\pi$
$180$		0			0
$181$	−0.240422	+	0.240422i	−0.0178705	+	0.0178705i	−0.715986	−	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
$187$	−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	$-0.272075\pi$
$191$	4.57833	+	2.64330i	0.331277	+	0.191263i	−0.325131	+	0.945669i	$0.605408\pi$
$192$		0			0
$193$	−8.43656	−	14.6125i	−0.607277	−	1.05183i	−0.991687	−	0.128672i	$-0.958929\pi$
$193$	−8.43656	−	14.6125i	−0.607277	−	1.05183i	0.384411	−	0.923162i	$-0.374405\pi$
$194$		0			0
$195$	2.29734	−	2.29734i	0.164516	−	0.164516i
$196$		0			0
$197$	−1.81729	−	1.81729i	−0.129477	−	0.129477i	0.639399	−	0.768875i	$-0.279183\pi$
$197$	−1.81729	−	1.81729i	−0.129477	−	0.129477i	−0.768875	+	0.639399i	$0.779183\pi$
$198$		0			0
$199$	0.631178	−	0.364411i	0.0447430	−	0.0258324i	−0.477462	−	0.878653i	$-0.658443\pi$
$199$	0.631178	−	0.364411i	0.0447430	−	0.0258324i	0.522205	+	0.852820i	$0.325110\pi$
$200$		0			0
$201$	−22.9459	+	39.7435i	−1.61848	+	2.80329i
$202$		0			0
$203$	−1.45453	+	7.87443i	−0.102088	+	0.552677i
$204$		0			0
$205$	−1.98397	−	7.40426i	−0.138566	−	0.517136i
$206$		0			0
$207$	15.8135	−	9.12991i	1.09911	−	0.634573i
$208$		0			0
$209$			6.08038i			0.420589i
$210$		0			0
$211$	8.24367	+	8.24367i	0.567518	+	0.567518i	0.931432	−	0.363915i	$-0.118560\pi$
$211$	8.24367	+	8.24367i	0.567518	+	0.567518i	−0.363915	+	0.931432i	$0.618560\pi$
$212$		0			0
$213$	27.6843	+	7.41798i	1.89690	+	0.508272i
$214$		0			0
$215$	10.1948	+	5.88597i	0.695280	+	0.401420i
$216$		0			0
$217$	13.1223	+	6.24931i	0.890799	+	0.424230i
$218$		0			0
$219$	−1.26519	−	4.72176i	−0.0854937	−	0.319067i
$220$		0			0
$221$	−1.40824	−	0.377335i	−0.0947281	−	0.0253823i
$222$		0			0
$223$	28.3640			1.89940			0.949698	−	0.313166i	$-0.101390\pi$
$223$	28.3640			1.89940			0.949698	+	0.313166i	$0.101390\pi$
$224$		0			0
$225$	8.98200			0.598800
$226$		0			0
$227$	−6.25352	−	1.67563i	−0.415061	−	0.111215i	0.0452445	−	0.998976i	$-0.485593\pi$
$227$	−6.25352	−	1.67563i	−0.415061	−	0.111215i	−0.460305	+	0.887761i	$0.652260\pi$
$228$		0			0
$229$	2.05973	+	7.68701i	0.136111	+	0.507972i	0.999991	+	0.00427468i	$0.00136068\pi$
$229$	2.05973	+	7.68701i	0.136111	+	0.507972i	−0.863880	+	0.503697i	$0.831973\pi$
$230$		0			0
$231$	30.6882	−	2.43383i	2.01914	−	0.160134i
$232$		0			0
$233$	0.159304	+	0.0919739i	0.0104363	+	0.00602541i	0.505209	−	0.862997i	$-0.331415\pi$
$233$	0.159304	+	0.0919739i	0.0104363	+	0.00602541i	−0.494773	+	0.869022i	$0.664749\pi$
$234$		0			0
$235$	6.94341	+	1.86048i	0.452938	+	0.121364i
$236$		0			0
$237$	9.03870	+	9.03870i	0.587127	+	0.587127i
$238$		0			0
$239$			19.6670i			1.27215i	0.771626	+	0.636077i	$0.219444\pi$
$239$			19.6670i			1.27215i	−0.771626	+	0.636077i	$0.780556\pi$
$240$		0			0
$241$	−3.10397	+	1.79208i	−0.199944	+	0.115438i	−0.596630	−	0.802517i	$-0.703494\pi$
$241$	−3.10397	+	1.79208i	−0.199944	+	0.115438i	0.396685	+	0.917955i	$0.370160\pi$
$242$		0			0
$243$	6.94921	+	25.9348i	0.445792	+	1.66372i
$244$		0			0
$245$	13.4791	+	1.40028i	0.861147	+	0.0894608i
$246$		0			0
$247$	−0.438493	+	0.759493i	−0.0279007	+	0.0483254i
$248$		0			0
$249$	−14.3589	+	8.29010i	−0.909957	+	0.525364i
$250$		0			0
$251$	11.1881	+	11.1881i	0.706184	+	0.706184i	0.965731	−	0.259547i	$-0.0835731\pi$
$251$	11.1881	+	11.1881i	0.706184	+	0.706184i	−0.259547	+	0.965731i	$0.583573\pi$
$252$		0			0
$253$	−6.56601	+	6.56601i	−0.412802	+	0.412802i
$254$		0			0
$255$	8.55495	+	14.8176i	0.535732	+	0.927914i
$256$		0			0
$257$	7.97191	+	4.60259i	0.497274	+	0.287101i	0.727587	−	0.686015i	$-0.240642\pi$
$257$	7.97191	+	4.60259i	0.497274	+	0.287101i	−0.230313	+	0.973117i	$0.573975\pi$
$258$		0			0
$259$	−8.06145	+	9.45028i	−0.500914	+	0.587212i
$260$		0			0
$261$	20.9715	−	5.61929i	1.29810	−	0.347825i
$262$		0			0
$263$	−1.54283	−	2.67226i	−0.0951349	−	0.164778i	0.814530	−	0.580121i	$-0.196995\pi$
$263$	−1.54283	−	2.67226i	−0.0951349	−	0.164778i	−0.909665	+	0.415343i	$0.863662\pi$
$264$		0			0
$265$	−13.0254			−0.800143
$266$		0			0
$267$	−15.1201	+	15.1201i	−0.925337	+	0.925337i
$268$		0			0
$269$	−6.25670	+	23.3503i	−0.381478	+	1.42369i	0.462167	+	0.886793i	$0.347072\pi$
$269$	−6.25670	+	23.3503i	−0.381478	+	1.42369i	−0.843645	+	0.536902i	$0.819595\pi$
$270$		0			0
$271$	5.80261	−	10.0504i	0.352484	−	0.610520i	−0.634200	−	0.773169i	$-0.718671\pi$
$271$	5.80261	−	10.0504i	0.352484	−	0.610520i	0.986684	+	0.162649i	$0.0520039\pi$
$272$		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	$-0.852609\pi$
$277$	1.72208	−	6.42687i	0.103469	−	0.386153i	0.998167	+	0.0605191i	$0.0192756\pi$
$278$		0			0
$279$		−	39.4074i		−	2.35926i
$280$		0			0
$281$		−	16.2605i		−	0.970022i	−0.874508	−	0.485011i	$-0.838816\pi$
$281$		−	16.2605i		−	0.970022i	0.874508	−	0.485011i	$-0.161184\pi$
$282$		0			0
$283$	−6.20636	+	23.1624i	−0.368930	+	1.37686i	0.493085	+	0.869981i	$0.335869\pi$
$283$	−6.20636	+	23.1624i	−0.368930	+	1.37686i	−0.862015	+	0.506883i	$0.830798\pi$
$284$		0			0
$285$	9.94152	−	2.66382i	0.588885	−	0.157791i
$286$		0			0
$287$	8.62993	−	5.93885i	0.509409	−	0.350559i
$288$		0			0
$289$	−4.66108	+	8.07323i	−0.274181	+	0.474896i
$290$		0			0
$291$	3.73947	−	13.9559i	0.219211	−	0.818108i
$292$		0			0
$293$	15.5002	−	15.5002i	0.905534	−	0.905534i	−0.0903743	−	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
$299$	−1.29367	+	0.346637i	−0.0748147	+	0.0200465i
$300$		0			0
$301$	−2.92228	+	15.8204i	−0.168438	+	0.911875i
$302$		0			0
$303$	−37.3863	−	21.5850i	−2.14779	−	1.24002i
$304$		0			0
$305$	0.379677	+	0.657620i	0.0217402	+	0.0376552i
$306$		0			0
$307$	8.30421	−	8.30421i	0.473946	−	0.473946i	−0.429243	−	0.903189i	$-0.641220\pi$
$307$	8.30421	−	8.30421i	0.473946	−	0.473946i	0.903189	+	0.429243i	$0.141220\pi$
$308$		0			0
$309$	−28.5296	−	28.5296i	−1.62299	−	1.62299i
$310$		0			0
$311$	−7.66004	+	4.42252i	−0.434361	+	0.250778i	−0.701203	−	0.712962i	$-0.747353\pi$
$311$	−7.66004	+	4.42252i	−0.434361	+	0.250778i	0.266842	+	0.963740i	$0.414020\pi$
$312$		0			0
$313$	12.5112	−	21.6700i	0.707174	−	1.22486i	−0.258727	−	0.965951i	$-0.583303\pi$
$313$	12.5112	−	21.6700i	0.707174	−	1.22486i	0.965901	−	0.258911i	$-0.0833637\pi$
$314$		0			0
$315$	−12.2859	−	34.6279i	−0.692230	−	1.95106i
$316$		0			0
$317$	0.827705	+	3.08904i	0.0464885	+	0.173498i	0.985267	−	0.171024i	$-0.0547077\pi$
$317$	0.827705	+	3.08904i	0.0464885	+	0.173498i	−0.938778	+	0.344522i	$0.888041\pi$
$318$		0			0
$319$	−9.56172	+	5.52046i	−0.535354	+	0.309087i
$320$		0			0
$321$		−	11.5141i		−	0.642652i
$322$		0			0
$323$	−3.26577	−	3.26577i	−0.181712	−	0.181712i
$324$		0			0
$325$	−0.636355	−	0.170511i	−0.0352986	−	0.00945823i
$326$		0			0
$327$	−28.1652	−	16.2612i	−1.55754	−	0.899244i
$328$		0			0
$329$	0.776679	+	9.79317i	0.0428197	+	0.539915i
$330$		0			0
$331$	3.55043	+	13.2504i	0.195149	+	0.728306i	0.992228	+	0.124431i	$0.0397107\pi$
$331$	3.55043	+	13.2504i	0.195149	+	0.728306i	−0.797079	+	0.603875i	$0.793623\pi$
$332$		0			0
$333$	32.5312	+	8.71671i	1.78270	+	0.477673i
$334$		0			0
$335$	−27.8544			−1.52185
$336$		0			0
$337$	30.3580			1.65371			0.826854	−	0.562417i	$-0.190128\pi$
$337$	30.3580			1.65371			0.826854	+	0.562417i	$0.190128\pi$
$338$		0			0
$339$	−56.7998	−	15.2195i	−3.08494	−	0.826608i
$340$		0			0
$341$	5.18673	+	19.3571i	0.280877	+	1.04825i
$342$		0			0
$343$	4.35602	+	18.0007i	0.235203	+	0.971946i
$344$		0			0
$345$	13.6121	+	7.85895i	0.732851	+	0.423112i
$346$		0			0
$347$	13.0551	+	3.49811i	0.700836	+	0.187788i	0.591605	−	0.806228i	$-0.298494\pi$
$347$	13.0551	+	3.49811i	0.700836	+	0.187788i	0.109231	+	0.994016i	$0.465161\pi$
$348$		0			0
$349$	−12.6593	−	12.6593i	−0.677639	−	0.677639i	0.281826	−	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	−0.996762	−	0.0804108i	$-0.974377\pi$
$353$	−26.7828	+	15.4631i	−1.42550	+	0.823016i	−0.428743	+	0.903426i	$0.641043\pi$
$354$		0			0
$355$	4.50240	+	16.8032i	0.238963	+	0.891821i
$356$		0			0
$357$	−15.1754	+	17.7898i	−0.803169	+	0.941538i
$358$		0			0
$359$	9.22928	−	15.9856i	0.487103	−	0.843687i	−0.512787	−	0.858516i	$-0.671387\pi$
$359$	9.22928	−	15.9856i	0.487103	−	0.843687i	0.999890	+	0.0148287i	$0.00472029\pi$
$360$		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	$-0.0276238\pi$
$367$	8.10460	+	14.0376i	0.423057	+	0.732756i	−0.573180	+	0.819429i	$0.694290\pi$
$368$		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	$-0.965433\pi$
$373$	−34.7801	+	9.31929i	−1.80084	+	0.482534i	−0.806734	+	0.590915i	$0.798767\pi$
$374$		0			0
$375$	19.3030	+	33.4338i	0.996803	+	1.72651i
$376$		0			0
$377$	−1.59246			−0.0820157
$378$		0			0
$379$	18.9916	−	18.9916i	0.975531	−	0.975531i	−0.0241768	−	0.999708i	$-0.507696\pi$
$379$	18.9916	−	18.9916i	0.975531	−	0.975531i	0.999708	+	0.0241768i	$0.00769645\pi$
$380$		0			0
$381$	16.9927	−	63.4177i	0.870564	−	3.24899i
$382$		0			0
$383$	11.8784	−	20.5740i	0.606957	−	1.05128i	−0.384782	−	0.923007i	$-0.625723\pi$
$383$	11.8784	−	20.5740i	0.606957	−	1.05128i	0.991739	−	0.128273i	$-0.0409433\pi$
$384$		0			0
$385$	10.5926	+	15.3924i	0.539847	+	0.784468i
$386$		0			0
$387$	42.1336	−	11.2897i	2.14177	−	0.573886i
$388$		0			0
$389$	−3.49731	+	13.0521i	−0.177321	+	0.661770i	0.818824	+	0.574045i	$0.194626\pi$
$389$	−3.49731	+	13.0521i	−0.177321	+	0.661770i	−0.996145	+	0.0877254i	$0.972040\pi$
$390$		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	$-0.620313\pi$
$397$	−4.46180	+	1.19554i	−0.223931	+	0.0600022i	0.145109	+	0.989416i	$0.453647\pi$
$398$		0			0
$399$	7.97395	+	11.5872i	0.399197	+	0.580086i
$400$		0			0
$401$	11.1566	−	19.3238i	0.557135	−	0.964986i	−0.440599	−	0.897704i	$-0.645234\pi$
$401$	11.1566	−	19.3238i	0.557135	−	0.964986i	0.997734	−	0.0672821i	$-0.0214327\pi$
$402$		0			0
$403$	−0.748093	+	2.79192i	−0.0372652	+	0.139076i
$404$		0			0
$405$	−28.6629	+	28.6629i	−1.42427	+	1.42427i
$406$		0			0
$407$	−17.1268			−0.848944
$408$		0			0
$409$	2.83340	+	4.90759i	0.140102	+	0.242665i	0.927535	−	0.373736i	$-0.121923\pi$
$409$	2.83340	+	4.90759i	0.140102	+	0.242665i	−0.787433	+	0.616401i	$0.788590\pi$
$410$		0			0
$411$	−4.03909	+	1.08227i	−0.199234	+	0.0533845i
$412$		0			0
$413$	−7.52464	−	21.2083i	−0.370263	−	1.04359i
$414$		0			0
$415$	−8.71523	−	5.03174i	−0.427814	−	0.246998i
$416$		0			0
$417$	−35.3588	−	61.2433i	−1.73153	−	2.99910i
$418$		0			0
$419$	2.67538	−	2.67538i	0.130701	−	0.130701i	−0.638730	−	0.769431i	$-0.720540\pi$
$419$	2.67538	−	2.67538i	0.130701	−	0.130701i	0.769431	+	0.638730i	$0.220540\pi$
$420$		0			0
$421$	17.2159	+	17.2159i	0.839052	+	0.839052i	0.988734	−	0.149682i	$-0.0478251\pi$
$421$	17.2159	+	17.2159i	0.839052	+	0.839052i	−0.149682	+	0.988734i	$0.547825\pi$
$422$		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	$-0.947798\pi$
$431$	−27.7876	+	16.0432i	−1.33848	+	0.772774i	−0.351901	+	0.936037i	$0.614465\pi$
$432$		0			0
$433$			15.7783i			0.758258i	0.925344	+	0.379129i	$0.123776\pi$
$433$			15.7783i			0.758258i	−0.925344	+	0.379129i	$0.876224\pi$
$434$		0			0
$435$	13.2150	+	13.2150i	0.633613	+	0.633613i
$436$		0			0
$437$	−4.09819	−	1.09811i	−0.196043	−	0.0525295i
$438$		0			0
$439$	−1.89128	−	1.09193i	−0.0902658	−	0.0521150i	0.454188	−	0.890906i	$-0.349930\pi$
$439$	−1.89128	−	1.09193i	−0.0902658	−	0.0521150i	−0.544453	+	0.838791i	$0.683263\pi$
$440$		0			0
$441$	38.9857	−	31.6479i	1.85646	−	1.50704i
$442$		0			0
$443$	−5.35487	−	19.9847i	−0.254418	−	0.949500i	−0.968413	−	0.249350i	$-0.919783\pi$
$443$	−5.35487	−	19.9847i	−0.254418	−	0.949500i	0.713996	−	0.700150i	$-0.246884\pi$
$444$		0			0
$445$	−12.5364	−	3.35912i	−0.594282	−	0.159237i
$446$		0			0
$447$	−40.0113			−1.89247
$448$		0			0
$449$	31.8400			1.50262			0.751311	−	0.659949i	$-0.229422\pi$
$449$	31.8400			1.50262			0.751311	+	0.659949i	$0.229422\pi$
$450$		0			0
$451$	13.9521	+	3.73844i	0.656977	+	0.176036i
$452$		0			0
$453$	−7.54275	−	28.1499i	−0.354389	−	1.32260i
$454$		0			0
$455$	0.213064	+	2.68654i	0.00998861	+	0.125947i
$456$		0			0
$457$	8.74709	+	5.05014i	0.409172	+	0.236235i	0.690434	−	0.723396i	$-0.257420\pi$
$457$	8.74709	+	5.05014i	0.409172	+	0.236235i	−0.281262	+	0.959631i	$0.590753\pi$
$458$		0			0
$459$	35.6284	+	9.54659i	1.66299	+	0.445597i
$460$		0			0
$461$	14.0523	+	14.0523i	0.654479	+	0.654479i	0.954068	−	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
$467$	−3.53968	−	13.2103i	−0.163797	−	0.611298i	−0.998191	−	0.0601291i	$-0.980849\pi$
$467$	−3.53968	−	13.2103i	−0.163797	−	0.611298i	0.834394	−	0.551169i	$-0.185818\pi$
$468$		0			0
$469$	−12.7287	−	35.8760i	−0.587756	−	1.65660i
$470$		0			0
$471$	−21.0817	+	36.5145i	−0.971391	+	1.68250i
$472$		0			0
$473$	−19.2104	+	11.0911i	−0.883293	+	0.509969i
$474$		0			0
$475$	−1.47574	−	1.47574i	−0.0677116	−	0.0677116i
$476$		0			0
$477$	−34.1281	+	34.1281i	−1.56262	+	1.56262i
$478$		0			0
$479$	13.2090	+	22.8786i	0.603534	+	1.04535i	0.992281	+	0.124007i	$0.0395745\pi$
$479$	13.2090	+	22.8786i	0.603534	+	1.04535i	−0.388748	+	0.921344i	$0.627092\pi$
$480$		0			0
$481$	−2.13929	−	1.23512i	−0.0975431	−	0.0563165i
$482$		0			0
$483$	−3.90183	+	21.1235i	−0.177540	+	0.961151i
$484$		0			0
$485$	8.47063	−	2.26970i	0.384631	−	0.103062i
$486$		0			0
$487$	−16.0930	−	27.8738i	−0.729242	−	1.26308i	−0.957204	−	0.289414i	$-0.906540\pi$
$487$	−16.0930	−	27.8738i	−0.729242	−	1.26308i	0.227962	−	0.973670i	$-0.426794\pi$
$488$		0			0
$489$	−1.26556			−0.0572305
$490$		0			0
$491$	2.25713	−	2.25713i	0.101863	−	0.101863i	−0.654339	−	0.756202i	$-0.727053\pi$
$491$	2.25713	−	2.25713i	0.101863	−	0.101863i	0.756202	+	0.654339i	$0.227053\pi$
$492$		0			0
$493$	2.17056	−	8.10063i	0.0977570	−	0.364834i
$494$		0			0
$495$	25.3304	−	43.8736i	1.13852	−	1.97197i
$496$		0			0
$497$	−19.5847	+	13.4776i	−0.878495	+	0.604553i
$498$		0			0
$499$	22.0437	−	5.90659i	0.986811	−	0.264415i	0.270900	−	0.962607i	$-0.412679\pi$
$499$	22.0437	−	5.90659i	0.986811	−	0.264415i	0.715910	+	0.698192i	$0.246012\pi$
$500$		0			0
$501$	−19.5309	+	72.8901i	−0.872574	+	3.25649i
$502$		0			0
$503$			23.1194i			1.03084i	0.856937	+	0.515422i	$0.172365\pi$
$503$			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	$-0.505075\pi$
$509$	10.6078	−	2.84236i	0.470185	−	0.125986i	0.486129	+	0.873887i	$0.338409\pi$
$510$		0			0
$511$	3.66089	+	1.74345i	0.161948	+	0.0771257i
$512$		0			0
$513$	11.0939	−	19.2152i	0.489807	−	0.848371i
$514$		0			0
$515$	6.33819	−	23.6544i	0.279294	−	1.04234i
$516$		0			0
$517$	−9.57791	+	9.57791i	−0.421236	+	0.421236i
$518$		0			0
$519$	49.0485			2.15299
$520$		0			0
$521$	4.42108	+	7.65754i	0.193691	+	0.335483i	0.946471	−	0.322790i	$-0.104621\pi$
$521$	4.42108	+	7.65754i	0.193691	+	0.335483i	−0.752780	+	0.658273i	$0.771287\pi$
$522$		0			0
$523$	18.3971	−	4.92948i	0.804448	−	0.215551i	0.166912	−	0.985972i	$-0.446620\pi$
$523$	18.3971	−	4.92948i	0.804448	−	0.215551i	0.637536	+	0.770420i	$0.279954\pi$
$524$		0			0
$525$	−6.85749	+	8.03889i	−0.299285	+	0.350846i
$526$		0			0
$527$	−13.1825	−	7.61092i	−0.574239	−	0.331537i
$528$		0			0
$529$	8.26031	+	14.3073i	0.359144	+	0.622055i
$530$		0			0
$531$	−43.1437	+	43.1437i	−1.87228	+	1.87228i
$532$		0			0
$533$	1.47313	+	1.47313i	0.0638085	+	0.0638085i
$534$		0			0
$535$	6.05226	−	3.49427i	0.261662	−	0.151071i
$536$		0			0
$537$	0.917707	−	1.58952i	0.0396020	−	0.0685927i
$538$		0			0
$539$	−14.9846	+	20.6769i	−0.645432	+	0.890617i
$540$		0			0
$541$	0.623324	+	2.32628i	0.0267988	+	0.100014i	0.978030	−	0.208465i	$-0.0668467\pi$
$541$	0.623324	+	2.32628i	0.0267988	+	0.100014i	−0.951231	+	0.308479i	$0.900180\pi$
$542$		0			0
$543$	−0.939194	+	0.542244i	−0.0403047	+	0.0232699i
$544$		0			0
$545$		−	19.7397i		−	0.845555i
$546$		0			0
$547$	11.9972	+	11.9972i	0.512962	+	0.512962i	0.915433	−	0.402471i	$-0.131849\pi$
$547$	11.9972	+	11.9972i	0.512962	+	0.512962i	−0.402471	+	0.915433i	$0.631849\pi$
$548$		0			0
$549$	2.71784	+	0.728244i	0.115995	+	0.0310807i
$550$		0			0
$551$	−4.36885	−	2.52236i	−0.186119	−	0.107456i
$552$		0			0
$553$	−10.5700	+	0.838286i	−0.449481	+	0.0356475i
$554$		0			0
$555$	7.50327	+	28.0026i	0.318496	+	1.18864i
$556$		0			0
$557$	−19.7236	−	5.28493i	−0.835716	−	0.223930i	−0.184510	−	0.982831i	$-0.559070\pi$
$557$	−19.7236	−	5.28493i	−0.835716	−	0.223930i	−0.651206	+	0.758901i	$0.725737\pi$
$558$		0			0
$559$	−3.19939			−0.135320
$560$		0			0
$561$	−32.2407			−1.36120
$562$		0			0
$563$	−15.4308	−	4.13466i	−0.650330	−	0.174255i	−0.0814517	−	0.996677i	$-0.525956\pi$
$563$	−15.4308	−	4.13466i	−0.650330	−	0.174255i	−0.568878	+	0.822422i	$0.692622\pi$
$564$		0			0
$565$	−9.23757	−	34.4751i	−0.388628	−	1.45038i
$566$		0			0
$567$	−50.0155	−	23.8192i	−2.10045	−	1.00031i
$568$		0			0
$569$	17.3910	+	10.0407i	0.729068	+	0.420928i	0.818081	−	0.575103i	$-0.195038\pi$
$569$	17.3910	+	10.0407i	0.729068	+	0.420928i	−0.0890129	+	0.996030i	$0.528371\pi$
$570$		0			0
$571$	17.3971	+	4.66153i	0.728045	+	0.195079i	0.603758	−	0.797167i	$-0.293669\pi$
$571$	17.3971	+	4.66153i	0.728045	+	0.195079i	0.124286	+	0.992246i	$0.460336\pi$
$572$		0			0
$573$	11.9233	+	11.9233i	0.498103	+	0.498103i
$574$		0			0
$575$		−	3.18721i		−	0.132916i
$576$		0			0
$577$	−16.2314	+	9.37123i	−0.675724	+	0.390129i	−0.798242	−	0.602337i	$-0.794236\pi$
$577$	−16.2314	+	9.37123i	−0.675724	+	0.390129i	0.122518	+	0.992466i	$0.460903\pi$
$578$		0			0
$579$	−13.9292	−	51.9845i	−0.578878	−	2.16040i
$580$		0			0
$581$	2.49817	−	13.5244i	0.103642	−	0.561087i
$582$		0			0
$583$	12.2721	−	21.2558i	0.508257	−	0.880327i
$584$		0			0
$585$	6.32799	−	3.65347i	0.261630	−	0.151052i
$586$		0			0
$587$	−16.4500	−	16.4500i	−0.678963	−	0.678963i	0.280802	−	0.959766i	$-0.409399\pi$
$587$	−16.4500	−	16.4500i	−0.678963	−	0.678963i	−0.959766	+	0.280802i	$0.909399\pi$
$588$		0			0
$589$	−6.47461	+	6.47461i	−0.266782	+	0.266782i
$590$		0			0
$591$	−4.09868	−	7.09912i	−0.168597	−	0.292019i
$592$		0			0
$593$	1.34548	+	0.776813i	0.0552522	+	0.0318999i	0.527372	−	0.849635i	$-0.323178\pi$
$593$	1.34548	+	0.776813i	0.0552522	+	0.0318999i	−0.472119	+	0.881535i	$0.656511\pi$
$594$		0			0
$595$	−13.9565	−	2.57798i	−0.572160	−	0.105687i
$596$		0			0
$597$	2.24543	−	0.601662i	0.0918994	−	0.0246244i
$598$		0			0
$599$	−0.821999	−	1.42374i	−0.0335860	−	0.0581726i	0.848744	−	0.528804i	$-0.177359\pi$
$599$	−0.821999	−	1.42374i	−0.0335860	−	0.0581726i	−0.882330	+	0.470632i	$0.844026\pi$
$600$		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	$-0.999833\pi$
$607$	−12.3075	+	21.3172i	−0.499545	+	0.865237i	0.500455	+	0.865763i	$0.333166\pi$
$608$		0			0
$609$	−10.9818	+	23.0596i	−0.445006	+	0.934424i
$610$		0			0
$611$	−1.88709	+	0.505643i	−0.0763433	+	0.0204561i
$612$		0			0
$613$	7.49076	−	27.9559i	0.302549	−	1.12913i	−0.632485	−	0.774572i	$-0.717965\pi$
$613$	7.49076	−	27.9559i	0.302549	−	1.12913i	0.935035	−	0.354556i	$-0.115368\pi$
$614$		0			0
$615$		−	24.4497i		−	0.985905i
$616$		0			0
$617$		−	10.2299i		−	0.411839i	−0.978569	−	0.205920i	$-0.933981\pi$
$617$		−	10.2299i		−	0.411839i	0.978569	−	0.205920i	$-0.0660186\pi$
$618$		0			0
$619$	−2.37448	+	8.86168i	−0.0954384	+	0.356181i	−0.997086	−	0.0762915i	$-0.975692\pi$
$619$	−2.37448	+	8.86168i	−0.0954384	+	0.356181i	0.901647	+	0.432472i	$0.142359\pi$
$620$		0			0
$621$	32.7298	−	8.76992i	1.31340	−	0.351925i
$622$		0			0
$623$	−1.40230	−	17.6817i	−0.0561820	−	0.708401i
$624$		0			0
$625$	−8.58582	+	14.8711i	−0.343433	+	0.594843i
$626$		0			0
$627$	−5.01952	+	18.7331i	−0.200460	+	0.748128i
$628$		0			0
$629$	9.19880	−	9.19880i	0.366780	−	0.366780i
$630$		0			0
$631$	2.48179			0.0987983			0.0493992	−	0.998779i	$-0.484269\pi$
$631$	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
$635$	38.4919	−	10.3139i	1.52750	−	0.409293i
$636$		0			0
$637$	−3.36284	+	1.50209i	−0.133241	+	0.0595152i
$638$		0			0
$639$	55.8232	+	32.2296i	2.20833	+	1.27498i
$640$		0			0
$641$	7.96198	+	13.7906i	0.314479	+	0.544694i	0.979327	−	0.202285i	$-0.0648367\pi$
$641$	7.96198	+	13.7906i	0.314479	+	0.544694i	−0.664847	+	0.746979i	$0.731503\pi$
$642$		0			0
$643$	7.66392	−	7.66392i	0.302236	−	0.302236i	−0.539652	−	0.841888i	$-0.681444\pi$
$643$	7.66392	−	7.66392i	0.302236	−	0.302236i	0.841888	+	0.539652i	$0.181444\pi$
$644$		0			0
$645$	26.5502	+	26.5502i	1.04541	+	1.04541i
$646$		0			0
$647$	7.28511	−	4.20606i	0.286407	−	0.165357i	−0.349913	−	0.936782i	$-0.613789\pi$
$647$	7.28511	−	4.20606i	0.286407	−	0.165357i	0.636320	+	0.771425i	$0.280456\pi$
$648$		0			0
$649$	15.5140	−	26.8710i	0.608976	−	1.05478i
$650$		0			0
$651$	35.2696	+	30.0863i	1.38232	+	1.17918i
$652$		0			0
$653$	−12.7054	−	47.4173i	−0.497201	−	1.85558i	−0.517335	−	0.855783i	$-0.673076\pi$
$653$	−12.7054	−	47.4173i	−0.497201	−	1.85558i	0.0201333	−	0.999797i	$-0.493591\pi$
$654$		0			0
$655$	−26.6972	+	15.4136i	−1.04315	+	0.602261i
$656$		0			0
$657$		−	10.9940i		−	0.428916i
$658$		0			0
$659$	4.57653	+	4.57653i	0.178276	+	0.178276i	0.790604	−	0.612328i	$-0.209767\pi$
$659$	4.57653	+	4.57653i	0.178276	+	0.178276i	−0.612328	+	0.790604i	$0.709767\pi$
$660$		0			0
$661$	36.2259	+	9.70671i	1.40903	+	0.377547i	0.881577	−	0.472040i	$-0.156482\pi$
$661$	36.2259	+	9.70671i	1.40903	+	0.377547i	0.527448	+	0.849587i	$0.323149\pi$
$662$		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	$-0.148495\pi$
$677$	−2.73796	−	10.2182i	−0.105228	−	0.392717i	−0.998371	+	0.0570560i	$0.981829\pi$
$678$		0			0
$679$	6.79417	+	9.87282i	0.260736	+	0.378884i
$680$		0			0
$681$	−17.8832	−	10.3249i	−0.685287	−	0.395651i
$682$		0			0
$683$	−32.3526	−	8.66885i	−1.23794	−	0.331705i	−0.420272	−	0.907398i	$-0.638065\pi$
$683$	−32.3526	−	8.66885i	−1.23794	−	0.331705i	−0.817666	+	0.575693i	$0.804732\pi$
$684$		0			0
$685$	−1.79466	−	1.79466i	−0.0685706	−	0.0685706i
$686$		0			0
$687$			25.3833i			0.968434i
$688$		0			0
$689$	3.06577	−	1.77003i	0.116797	−	0.0674326i
$690$		0			0
$691$	3.83874	+	14.3264i	0.146033	+	0.545001i	0.999707	+	0.0241943i	$0.00770204\pi$
$691$	3.83874	+	14.3264i	0.146033	+	0.545001i	−0.853675	+	0.520807i	$0.825631\pi$
$692$		0			0
$693$	68.0837	+	12.5761i	2.58629	+	0.477728i
$694$		0			0
$695$	21.4613	−	37.1721i	0.814074	−	1.41002i
$696$		0			0
$697$	−9.50156	+	5.48573i	−0.359897	+	0.207787i
$698$		0			0
$699$	0.414872	+	0.414872i	0.0156919	+	0.0156919i
$700$		0			0
$701$	−14.0698	+	14.0698i	−0.531408	+	0.531408i	−0.920991	−	0.389583i	$-0.872619\pi$
$701$	−14.0698	+	14.0698i	−0.531408	+	0.531408i	0.389583	+	0.920991i	$0.372619\pi$
$702$		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	$-0.661949\pi$
$709$	−12.5757	+	3.36966i	−0.472291	+	0.126550i	0.0148195	+	0.999890i	$0.495283\pi$
$710$		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	$-0.956868\pi$
$719$	−10.1472	+	17.5754i	−0.378425	+	0.655452i	0.612408	+	0.790542i	$0.290201\pi$
$720$		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	$-0.960713\pi$
$733$	−48.4699	+	12.9875i	−1.79028	+	0.479703i	−0.797882	+	0.602813i	$0.794046\pi$
$734$		0			0
$735$	40.3718	+	15.4415i	1.48914	+	0.569567i
$736$		0			0
$737$	26.2434	−	45.4549i	0.966689	−	1.67435i
$738$		0			0
$739$	−1.90941	+	7.12602i	−0.0702388	+	0.262135i	−0.992112	−	0.125358i	$-0.959992\pi$
$739$	−1.90941	+	7.12602i	−0.0702388	+	0.262135i	0.921873	+	0.387493i	$0.126659\pi$
$740$		0			0
$741$	−1.97794	+	1.97794i	−0.0726614	+	0.0726614i
$742$		0			0
$743$	−13.2937			−0.487698			−0.243849	−	0.969813i	$-0.578410\pi$
$743$	−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
$747$	−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	$-0.405164\pi$
$751$	−10.6206	−	6.13182i	−0.387552	−	0.223753i	−0.681099	+	0.732191i	$0.738498\pi$
$752$		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	$-0.00291107\pi$
$757$	27.2609	+	27.2609i	0.990813	+	0.990813i	−0.00914525	+	0.999958i	$0.502911\pi$
$758$		0			0
$759$	−25.6497	+	14.8089i	−0.931025	+	0.537527i
$760$		0			0
$761$	−10.1480	+	17.5769i	−0.367867	+	0.637164i	−0.989232	−	0.146358i	$-0.953245\pi$
$761$	−10.1480	+	17.5769i	−0.367867	+	0.637164i	0.621365	+	0.783521i	$0.286578\pi$
$762$		0			0
$763$	25.4243	−	9.02048i	0.920423	−	0.326563i
$764$		0			0
$765$	9.95952	+	37.1695i	0.360087	+	1.34386i
$766$		0			0
$767$	3.87566	−	2.23761i	0.139942	−	0.0807955i
$768$		0			0
$769$		−	19.6449i		−	0.708412i	−0.935167	−	0.354206i	$-0.884751\pi$
$769$		−	19.6449i		−	0.708412i	0.935167	−	0.354206i	$-0.115249\pi$
$770$		0			0
$771$	20.7612	+	20.7612i	0.747695	+	0.747695i
$772$		0			0
$773$	−47.3606	−	12.6902i	−1.70344	−	0.456436i	−0.729639	−	0.683832i	$-0.760312\pi$
$773$	−47.3606	−	12.6902i	−1.70344	−	0.456436i	−0.973802	+	0.227397i	$0.926979\pi$
$774$		0			0
$775$	−5.95692	−	3.43923i	−0.213979	−	0.123541i
$776$		0			0
$777$	−32.6380	+	22.4605i	−1.17088	+	0.805765i
$778$		0			0
$779$	1.70813	+	6.37485i	0.0612003	+	0.228403i
$780$		0			0
$781$	−31.6627	−	8.48400i	−1.13298	−	0.303581i
$782$		0			0
$783$	40.2892			1.43982
$784$		0			0
$785$	−25.5913			−0.913394
$786$		0			0
$787$	2.76449	+	0.740742i	0.0985433	+	0.0264046i	0.307754	−	0.951466i	$-0.400423\pi$
$787$	2.76449	+	0.740742i	0.0985433	+	0.0264046i	−0.209210	+	0.977871i	$0.567089\pi$
$788$		0			0
$789$	−2.54729	−	9.50662i	−0.0906860	−	0.338445i
$790$		0			0
$791$	40.1820	−	27.6520i	1.42871	−	0.983191i
$792$		0			0
$793$	−0.178728	−	0.103189i	−0.00634683	−	0.00366434i
$794$		0			0
$795$	−40.1300	−	10.7528i	−1.42326	−	0.381363i
$796$		0			0
$797$	−39.0301	−	39.0301i	−1.38252	−	1.38252i	−0.840129	−	0.542386i	$-0.817521\pi$
$797$	−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
$803$	1.44701	+	5.40031i	0.0510639	+	0.190573i
$804$		0			0
$805$	−12.2875	+	4.35956i	−0.433077	+	0.153654i
$806$		0			0
$807$	−38.5526	+	66.7751i	−1.35712	+	2.35059i
$808$		0			0
$809$	36.0749	−	20.8279i	1.26833	−	0.732269i	0.293656	−	0.955911i	$-0.405128\pi$
$809$	36.0749	−	20.8279i	1.26833	−	0.732269i	0.974671	+	0.223642i	$0.0717946\pi$
$810$		0			0
$811$	−6.24833	−	6.24833i	−0.219409	−	0.219409i	0.588841	−	0.808249i	$-0.299585\pi$
$811$	−6.24833	−	6.24833i	−0.219409	−	0.219409i	−0.808249	+	0.588841i	$0.799585\pi$
$812$		0			0
$813$	26.1742	−	26.1742i	0.917969	−	0.917969i
$814$		0			0
$815$	−0.384070	−	0.665229i	−0.0134534	−	0.0233019i
$816$		0			0
$817$	−8.77741	−	5.06764i	−0.307083	−	0.177294i
$818$		0			0
$819$	7.59731	+	6.48080i	0.265471	+	0.226457i
$820$		0			0
$821$	41.1258	−	11.0196i	1.43530	−	0.384588i	0.544416	−	0.838816i	$-0.316751\pi$
$821$	41.1258	−	11.0196i	1.43530	−	0.384588i	0.890886	+	0.454228i	$0.150085\pi$
$822$		0			0
$823$	−0.688665	−	1.19280i	−0.0240054	−	0.0415785i	0.853773	−	0.520645i	$-0.174309\pi$
$823$	−0.688665	−	1.19280i	−0.0240054	−	0.0415785i	−0.877779	+	0.479067i	$0.840975\pi$
$824$		0			0
$825$	−14.5689			−0.507225
$826$		0			0
$827$	14.2870	−	14.2870i	0.496807	−	0.496807i	−0.413636	−	0.910443i	$-0.635741\pi$
$827$	14.2870	−	14.2870i	0.496807	−	0.496807i	0.910443	+	0.413636i	$0.135741\pi$
$828$		0			0
$829$	5.38274	−	20.0887i	0.186950	−	0.697708i	−0.807254	−	0.590204i	$-0.799047\pi$
$829$	5.38274	−	20.0887i	0.186950	−	0.697708i	0.994205	−	0.107504i	$-0.0342859\pi$
$830$		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	$-0.888906\pi$
$853$	−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	$-0.149602\pi$
$857$	1.56865	+	2.71698i	0.0535840	+	0.0928102i	−0.837989	+	0.545687i	$0.816269\pi$
$858$		0			0
$859$	1.72578	−	0.462421i	0.0588828	−	0.0157776i	−0.229257	−	0.973366i	$-0.573630\pi$
$859$	1.72578	−	0.462421i	0.0588828	−	0.0157776i	0.288140	+	0.957588i	$0.406963\pi$
$860$		0			0
$861$	31.4907	−	11.1728i	1.07320	−	0.380768i
$862$		0			0
$863$	−4.43745	−	2.56196i	−0.151052	−	0.0872101i	0.422569	−	0.906331i	$-0.361128\pi$
$863$	−4.43745	−	2.56196i	−0.151052	−	0.0872101i	−0.573621	+	0.819121i	$0.694462\pi$
$864$		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	$-0.105693\pi$
$877$	−1.07593	−	4.01542i	−0.0363316	−	0.135591i	−0.981709	+	0.190385i	$0.939026\pi$
$878$		0			0
$879$	60.5506	−	34.9589i	2.04232	−	1.17914i
$880$		0			0
$881$			27.5375i			0.927761i	0.885898	+	0.463880i	$0.153543\pi$
$881$			27.5375i			0.927761i	−0.885898	+	0.463880i	$0.846457\pi$
$882$		0			0
$883$	−32.4922	−	32.4922i	−1.09345	−	1.09345i	−0.995158	−	0.0982911i	$-0.968662\pi$
$883$	−32.4922	−	32.4922i	−1.09345	−	1.09345i	−0.0982911	−	0.995158i	$-0.531338\pi$
$884$		0			0
$885$	−50.7311	−	13.5934i	−1.70531	−	0.456936i
$886$		0			0
$887$	32.4376	+	18.7278i	1.08915	+	0.628820i	0.933349	−	0.358969i	$-0.116872\pi$
$887$	32.4376	+	18.7278i	1.08915	+	0.628820i	0.155798	+	0.987789i	$0.450205\pi$
$888$		0			0
$889$	30.8738	+	44.8637i	1.03547	+	1.50468i
$890$		0			0
$891$	−19.7692	−	73.7795i	−0.662292	−	2.47171i
$892$		0			0
$893$	−5.97807	−	1.60182i	−0.200048	−	0.0536028i
$894$		0			0
$895$	1.11402			0.0372376
$896$		0			0
$897$	−4.27183			−0.142632
$898$		0			0
$899$	−16.0601	−	4.30328i	−0.535633	−	0.143522i
$900$		0			0
$901$	4.82518	+	18.0078i	0.160750	+	0.599927i
$902$		0			0
$903$	−22.0635	+	46.3289i	−0.734226	+	1.54173i
$904$		0			0
$905$	−0.570051	−	0.329119i	−0.0189491	−	0.0109403i
$906$		0			0
$907$	−33.3737	−	8.94245i	−1.10815	−	0.296929i	−0.342074	−	0.939673i	$-0.611129\pi$
$907$	−33.3737	−	8.94245i	−1.10815	−	0.296929i	−0.766081	+	0.642744i	$0.777796\pi$
$908$		0			0
$909$	−68.6533	−	68.6533i	−2.27709	−	2.27709i
$910$		0			0
$911$			22.9373i			0.759946i	0.924998	+	0.379973i	$0.124067\pi$
$911$			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	$-0.984909\pi$
$919$	−13.8963	+	24.0691i	−0.458396	+	0.793966i	0.540480	+	0.841357i	$0.318243\pi$
$920$		0			0
$921$	32.4398	−	18.7291i	1.06893	−	0.617146i
$922$		0			0
$923$	−3.34312	−	3.34312i	−0.110040	−	0.110040i
$924$		0			0
$925$	4.15676	−	4.15676i	0.136673	−	0.136673i
$926$		0			0
$927$	−45.3707	−	78.5844i	−1.49017	−	2.58105i
$928$		0			0
$929$	13.2279	+	7.63716i	0.433995	+	0.250567i	0.701047	−	0.713115i	$-0.252716\pi$
$929$	13.2279	+	7.63716i	0.433995	+	0.250567i	−0.267052	+	0.963682i	$0.586050\pi$
$930$		0			0
$931$	−11.6051	−	1.20560i	−0.380341	−	0.0395120i
$932$		0			0
$933$	−27.2508	+	7.30182i	−0.892150	+	0.239051i
$934$		0			0
$935$	−9.78436	−	16.9470i	−0.319983	−	0.554227i
$936$		0			0
$937$	18.1308			0.592307			0.296154	−	0.955140i	$-0.404296\pi$
$937$	18.1308			0.592307			0.296154	+	0.955140i	$0.404296\pi$
$938$		0			0
$939$	56.4350	−	56.4350i	1.84169	−	1.84169i
$940$		0			0
$941$	2.24372	−	8.37369i	0.0731433	−	0.272974i	−0.919663	−	0.392709i	$-0.871538\pi$
$941$	2.24372	−	8.37369i	0.0731433	−	0.272974i	0.992806	+	0.119735i	$0.0382045\pi$
$942$		0			0
$943$	−5.03943	+	8.72855i	−0.164106	+	0.284241i
$944$		0			0
$945$	−5.39053	−	67.9694i	−0.175354	−	2.21105i
$946$		0			0
$947$	14.8856	−	3.98857i	0.483716	−	0.129611i	−0.00871655	−	0.999962i	$-0.502775\pi$
$947$	14.8856	−	3.98857i	0.483716	−	0.129611i	0.492432	+	0.870351i	$0.336108\pi$
$948$		0			0
$949$	−0.208705	+	0.778899i	−0.00677486	+	0.0252841i
$950$		0			0
$951$			10.2003i			0.330768i
$952$		0			0
$953$		−	14.4644i		−	0.468547i	−0.972171	−	0.234273i	$-0.924729\pi$
$953$		−	14.4644i		−	0.468547i	0.972171	−	0.234273i	$-0.0752711\pi$
$954$		0			0
$955$	−2.64890	+	9.88585i	−0.0857165	+	0.319899i
$956$		0			0
$957$	−34.0161	+	9.11458i	−1.09958	+	0.294632i
$958$		0			0
$959$	1.49138	−	3.13160i	0.0481592	−	0.101125i
$960$		0			0
$961$	0.410836	−	0.711589i	0.0132528	−	0.0229545i
$962$		0			0
$963$	6.70223	−	25.0131i	0.215976	−	0.806035i
$964$		0			0
$965$	23.0980	−	23.0980i	0.743549	−	0.743549i
$966$		0			0
$967$	−53.4246			−1.71802			−0.859010	−	0.511958i	$-0.828920\pi$
$967$	−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
$971$	−20.7547	+	5.56119i	−0.666048	+	0.178467i	−0.575974	−	0.817468i	$-0.695377\pi$
$971$	−20.7547	+	5.56119i	−0.666048	+	0.178467i	−0.0900743	+	0.995935i	$0.528710\pi$
$972$		0			0
$973$	57.6842	+	10.6552i	1.84927	+	0.341589i
$974$		0			0
$975$	−1.81979	−	1.05066i	−0.0582799	−	0.0336479i
$976$		0			0
$977$	−18.0960	−	31.3432i	−0.578942	−	1.00276i	−0.995601	−	0.0936944i	$-0.970132\pi$
$977$	−18.0960	−	31.3432i	−0.578942	−	1.00276i	0.416659	−	0.909063i	$-0.363201\pi$
$978$		0			0
$979$	17.2930	−	17.2930i	0.552687	−	0.552687i
$980$		0			0
$981$	−51.7204	−	51.7204i	−1.65130	−	1.65130i
$982$		0			0
$983$	−31.0312	+	17.9159i	−0.989742	+	0.571428i	−0.905197	−	0.424992i	$-0.860277\pi$
$983$	−31.0312	+	17.9159i	−0.989742	+	0.571428i	−0.0845448	+	0.996420i	$0.526944\pi$
$984$		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	$-0.388728\pi$
$991$	41.7865	−	24.1254i	1.32739	−	0.766370i	0.984896	+	0.173149i	$0.0553944\pi$
$992$		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	$-0.275608\pi$
$997$	26.1554	+	7.00832i	0.828351	+	0.221956i	0.180357	+	0.983601i	$0.442275\pi$
$998$		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	448.2.z.a.271.14		56
4.3	odd	2		112.2.v.a.75.2	yes	56
7.3	odd	6	inner	448.2.z.a.143.14		56
8.3	odd	2		896.2.z.b.159.14		56
8.5	even	2		896.2.z.a.159.1		56
16.3	odd	4	inner	448.2.z.a.47.14		56
16.5	even	4		896.2.z.b.607.14		56
16.11	odd	4		896.2.z.a.607.1		56
16.13	even	4		112.2.v.a.19.8	yes	56
28.3	even	6		112.2.v.a.59.8	yes	56
28.11	odd	6		784.2.w.f.619.8		56
28.19	even	6		784.2.j.a.587.23		56
28.23	odd	6		784.2.j.a.587.24		56
28.27	even	2		784.2.w.f.411.2		56
56.3	even	6		896.2.z.b.31.14		56
56.45	odd	6		896.2.z.a.31.1		56
112.3	even	12	inner	448.2.z.a.367.14		56
112.13	odd	4		784.2.w.f.19.8		56
112.45	odd	12		112.2.v.a.3.2	✓	56
112.59	even	12		896.2.z.a.479.1		56
112.61	odd	12		784.2.j.a.195.24		56
112.93	even	12		784.2.j.a.195.23		56
112.101	odd	12		896.2.z.b.479.14		56
112.109	even	12		784.2.w.f.227.2		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.2	✓	56	112.45	odd	12
112.2.v.a.19.8	yes	56	16.13	even	4
112.2.v.a.59.8	yes	56	28.3	even	6
112.2.v.a.75.2	yes	56	4.3	odd	2
448.2.z.a.47.14		56	16.3	odd	4	inner
448.2.z.a.143.14		56	7.3	odd	6	inner
448.2.z.a.271.14		56	1.1	even	1	trivial
448.2.z.a.367.14		56	112.3	even	12	inner
784.2.j.a.195.23		56	112.93	even	12
784.2.j.a.195.24		56	112.61	odd	12
784.2.j.a.587.23		56	28.19	even	6
784.2.j.a.587.24		56	28.23	odd	6
784.2.w.f.19.8		56	112.13	odd	4
784.2.w.f.227.2		56	112.109	even	12
784.2.w.f.411.2		56	28.27	even	2
784.2.w.f.619.8		56	28.11	odd	6
896.2.z.a.31.1		56	56.45	odd	6
896.2.z.a.159.1		56	8.5	even	2
896.2.z.a.479.1		56	112.59	even	12
896.2.z.a.607.1		56	16.11	odd	4
896.2.z.b.31.14		56	56.3	even	6
896.2.z.b.159.14		56	8.3	odd	2
896.2.z.b.479.14		56	112.101	odd	12
896.2.z.b.607.14		56	16.5	even	4

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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.z (of order \(12\), degree \(4\), not minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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