LMFDB - Embedded newform 2016.2.cp.b.17.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2016,2,Mod(17,2016)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2016, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2016.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2016 = 2^{5} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2016.cp (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$16.0978410475$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	2016.17
Dual form			2016.2.cp.b.593.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.16007 + 1.82447i) q^{5} +(1.64838 - 2.06951i) q^{7} +(-0.200123 + 0.346624i) q^{11} +0.581419 q^{13} +(-2.27603 + 3.94220i) q^{17} +(-2.43222 - 4.21272i) q^{19} +(6.21119 - 3.58603i) q^{23} +(4.15738 - 7.20080i) q^{25} -6.69007 q^{29} +(2.85749 + 1.64978i) q^{31} +(-1.43324 + 9.54721i) q^{35} +(1.93278 - 1.11589i) q^{37} +4.51491 q^{41} +4.09678i q^{43} +(2.86389 + 4.96040i) q^{47} +(-1.56571 - 6.82265i) q^{49} +(6.74170 - 11.6770i) q^{53} -1.46048i q^{55} +(7.72158 + 4.45806i) q^{59} +(6.42386 + 11.1265i) q^{61} +(-1.83733 + 1.06078i) q^{65} +(8.30513 + 4.79497i) q^{67} -6.42019i q^{71} +(-6.18408 - 3.57038i) q^{73} +(0.387462 + 0.985523i) q^{77} +(-4.15037 - 7.18866i) q^{79} -10.3852i q^{83} -16.6102i q^{85} +(5.25986 + 9.11034i) q^{89} +(0.958396 - 1.20325i) q^{91} +(15.3720 + 8.87501i) q^{95} -4.00635i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 20 q^{7} + 8 q^{25} + 36 q^{31} - 28 q^{49} + 72 q^{73} + 12 q^{79}+O(q^{100}) $ 56 * q + 20 * q^7 + 8 * q^25 + 36 * q^31 - 28 * q^49 + 72 * q^73 + 12 * q^79

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$1765$	$1793$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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			0
$3$		0			0
$4$		0			0
$5$	−3.16007	+	1.82447i	−1.41323	+	0.815928i	−0.995691	−	0.0927320i	$-0.970440\pi$
$5$	−3.16007	+	1.82447i	−1.41323	+	0.815928i	−0.417537	+	0.908660i	$0.637107\pi$
$6$		0			0
$7$	1.64838	−	2.06951i	0.623028	−	0.782200i
$7$	1.64838	−	2.06951i	0.623028	−	0.782200i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.200123	+	0.346624i	−0.0603394	+	0.104511i	−0.894617	−	0.446833i	$-0.852552\pi$
$11$	−0.200123	+	0.346624i	−0.0603394	+	0.104511i	0.834278	+	0.551344i	$0.185885\pi$
$12$		0			0
$13$	0.581419			0.161256			0.0806282	−	0.996744i	$-0.474307\pi$
$13$	0.581419			0.161256			0.0806282	+	0.996744i	$0.474307\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.27603	+	3.94220i	−0.552019	+	0.956124i	0.446110	+	0.894978i	$0.352809\pi$
$17$	−2.27603	+	3.94220i	−0.552019	+	0.956124i	−0.998129	+	0.0611464i	$0.980524\pi$
$18$		0			0
$19$	−2.43222	−	4.21272i	−0.557989	−	0.966465i	−0.997664	−	0.0683081i	$-0.978240\pi$
$19$	−2.43222	−	4.21272i	−0.557989	−	0.966465i	0.439676	−	0.898157i	$-0.355093\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	6.21119	−	3.58603i	1.29512	−	0.747739i	0.315565	−	0.948904i	$-0.397806\pi$
$23$	6.21119	−	3.58603i	1.29512	−	0.747739i	0.979557	+	0.201165i	$0.0644728\pi$
$24$		0			0
$25$	4.15738	−	7.20080i	0.831476	−	1.44016i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−6.69007			−1.24232			−0.621158	−	0.783686i	$-0.713337\pi$
$29$	−6.69007			−1.24232			−0.621158	+	0.783686i	$0.713337\pi$
$30$		0			0
$31$	2.85749	+	1.64978i	0.513221	+	0.296308i	0.734157	−	0.678980i	$-0.237578\pi$
$31$	2.85749	+	1.64978i	0.513221	+	0.296308i	−0.220936	+	0.975288i	$0.570911\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.43324	+	9.54721i	−0.242262	+	1.61377i
$36$		0			0
$37$	1.93278	−	1.11589i	0.317747	−	0.183451i	−0.332641	−	0.943054i	$-0.607940\pi$
$37$	1.93278	−	1.11589i	0.317747	−	0.183451i	0.650388	+	0.759602i	$0.274606\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.51491			0.705111			0.352556	−	0.935791i	$-0.385313\pi$
$41$	4.51491			0.705111			0.352556	+	0.935791i	$0.385313\pi$
$42$		0			0
$43$			4.09678i			0.624754i	0.949958	+	0.312377i	$0.101125\pi$
$43$			4.09678i			0.624754i	−0.949958	+	0.312377i	$0.898875\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.86389	+	4.96040i	0.417741	+	0.723549i	0.995712	−	0.0925088i	$-0.0294886\pi$
$47$	2.86389	+	4.96040i	0.417741	+	0.723549i	−0.577971	+	0.816057i	$0.696155\pi$
$48$		0			0
$49$	−1.56571	−	6.82265i	−0.223673	−	0.974664i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.74170	−	11.6770i	0.926043	−	1.60395i	0.136169	−	0.990686i	$-0.456521\pi$
$53$	6.74170	−	11.6770i	0.926043	−	1.60395i	0.789875	−	0.613268i	$-0.210146\pi$
$54$		0			0
$55$		−	1.46048i		−	0.196931i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	7.72158	+	4.45806i	1.00526	+	0.580390i	0.909802	−	0.415043i	$-0.136234\pi$
$59$	7.72158	+	4.45806i	1.00526	+	0.580390i	0.0954627	+	0.995433i	$0.469567\pi$
$60$		0			0
$61$	6.42386	+	11.1265i	0.822491	+	1.42460i	0.903822	+	0.427910i	$0.140750\pi$
$61$	6.42386	+	11.1265i	0.822491	+	1.42460i	−0.0813302	+	0.996687i	$0.525917\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.83733	+	1.06078i	−0.227892	+	0.131574i
$66$		0			0
$67$	8.30513	+	4.79497i	1.01463	+	0.585798i	0.912545	−	0.408977i	$-0.134114\pi$
$67$	8.30513	+	4.79497i	1.01463	+	0.585798i	0.102088	+	0.994775i	$0.467448\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	6.42019i		−	0.761937i	−0.924588	−	0.380968i	$-0.875591\pi$
$71$		−	6.42019i		−	0.761937i	0.924588	−	0.380968i	$-0.124409\pi$
$72$		0			0
$73$	−6.18408	−	3.57038i	−0.723791	−	0.417881i	0.0923551	−	0.995726i	$-0.470561\pi$
$73$	−6.18408	−	3.57038i	−0.723791	−	0.417881i	−0.816147	+	0.577845i	$0.803894\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.387462	+	0.985523i	0.0441553	+	0.112311i
$78$		0			0
$79$	−4.15037	−	7.18866i	−0.466953	−	0.808787i	0.532334	−	0.846535i	$-0.321315\pi$
$79$	−4.15037	−	7.18866i	−0.466953	−	0.808787i	−0.999287	+	0.0377474i	$0.987982\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	10.3852i		−	1.13992i	−0.821673	−	0.569959i	$-0.806959\pi$
$83$		−	10.3852i		−	1.13992i	0.821673	−	0.569959i	$-0.193041\pi$
$84$		0			0
$85$		−	16.6102i		−	1.80163i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.25986	+	9.11034i	0.557544	+	0.965694i	0.997701	+	0.0677734i	$0.0215895\pi$
$89$	5.25986	+	9.11034i	0.557544	+	0.965694i	−0.440157	+	0.897921i	$0.645077\pi$
$90$		0			0
$91$	0.958396	−	1.20325i	0.100467	−	0.126135i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	15.3720	+	8.87501i	1.57713	+	0.910557i
$96$		0			0
$97$		−	4.00635i		−	0.406783i	−0.979097	−	0.203392i	$-0.934804\pi$
$97$		−	4.00635i		−	0.406783i	0.979097	−	0.203392i	$-0.0651964\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	12.1877	+	7.03656i	1.21272	+	0.700164i	0.963351	−	0.268245i	$-0.0864437\pi$
$101$	12.1877	+	7.03656i	1.21272	+	0.700164i	0.249368	+	0.968409i	$0.419777\pi$
$102$		0			0
$103$	17.4850	−	10.0950i	1.72285	−	0.994686i	0.809943	−	0.586508i	$-0.199498\pi$
$103$	17.4850	−	10.0950i	1.72285	−	0.994686i	0.912903	−	0.408177i	$-0.133835\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.09913	−	3.63581i	−0.202931	−	0.351487i	0.746541	−	0.665340i	$-0.231713\pi$
$107$	−2.09913	−	3.63581i	−0.202931	−	0.351487i	−0.949472	+	0.313853i	$0.898380\pi$
$108$		0			0
$109$	16.0796	+	9.28357i	1.54015	+	0.889205i	0.998829	+	0.0483874i	$0.0154082\pi$
$109$	16.0796	+	9.28357i	1.54015	+	0.889205i	0.541319	+	0.840817i	$0.317925\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	3.44494i		−	0.324073i	−0.986785	−	0.162037i	$-0.948194\pi$
$113$		−	3.44494i		−	0.324073i	0.986785	−	0.162037i	$-0.0518063\pi$
$114$		0			0
$115$	−13.0852	+	22.6642i	−1.22020	+	2.11345i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	4.40666	+	11.2085i	0.403958	+	1.02748i
$120$		0			0
$121$	5.41990	+	9.38754i	0.492718	+	0.853413i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			12.0954i			1.08184i
$126$		0			0
$127$	3.82179			0.339129			0.169565	−	0.985519i	$-0.445764\pi$
$127$	3.82179			0.339129			0.169565	+	0.985519i	$0.445764\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.160576	+	0.0927085i	−0.0140296	+	0.00809998i	−0.506998	−	0.861947i	$-0.669245\pi$
$131$	−0.160576	+	0.0927085i	−0.0140296	+	0.00809998i	0.492969	+	0.870047i	$0.335912\pi$
$132$		0			0
$133$	−12.7275	−	1.91066i	−1.10361	−	0.165676i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	13.2672	+	7.65983i	1.13350	+	0.654424i	0.944812	−	0.327614i	$-0.106245\pi$
$137$	13.2672	+	7.65983i	1.13350	+	0.654424i	0.188684	+	0.982038i	$0.439578\pi$
$138$		0			0
$139$	10.5472			0.894602			0.447301	−	0.894383i	$-0.352385\pi$
$139$	10.5472			0.894602			0.447301	+	0.894383i	$0.352385\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.116355	+	0.201533i	−0.00973013	+	0.0168531i
$144$		0			0
$145$	21.1411	−	12.2058i	1.75567	−	1.01364i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−4.59117	−	7.95213i	−0.376123	−	0.651464i	0.614371	−	0.789017i	$-0.289410\pi$
$149$	−4.59117	−	7.95213i	−0.376123	−	0.651464i	−0.990494	+	0.137553i	$0.956076\pi$
$150$		0			0
$151$	−1.79999	+	3.11768i	−0.146481	+	0.253713i	−0.929925	−	0.367750i	$-0.880128\pi$
$151$	−1.79999	+	3.11768i	−0.146481	+	0.253713i	0.783443	+	0.621463i	$0.213461\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−12.0399			−0.967065
$156$		0			0
$157$	0.359090	−	0.621963i	0.0286585	−	0.0496380i	−0.851340	−	0.524614i	$-0.824210\pi$
$157$	0.359090	−	0.621963i	0.0286585	−	0.0496380i	0.879999	+	0.474976i	$0.157543\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.81706	−	18.7652i	0.222015	−	1.47891i
$162$		0			0
$163$	19.1125	−	11.0346i	1.49700	−	0.864296i	0.497011	−	0.867744i	$-0.334431\pi$
$163$	19.1125	−	11.0346i	1.49700	−	0.864296i	0.999994	+	0.00344810i	$0.00109757\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−13.4882			−1.04375			−0.521875	−	0.853022i	$-0.674767\pi$
$167$	−13.4882			−1.04375			−0.521875	+	0.853022i	$0.674767\pi$
$168$		0			0
$169$	−12.6620			−0.973996
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−14.0098	+	8.08856i	−1.06514	+	0.614962i	−0.926851	−	0.375430i	$-0.877495\pi$
$173$	−14.0098	+	8.08856i	−1.06514	+	0.614962i	−0.138294	+	0.990391i	$0.544162\pi$
$174$		0			0
$175$	−8.04917	−	20.4733i	−0.608460	−	1.54764i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.872025	+	1.51039i	−0.0651782	+	0.112892i	−0.896773	−	0.442491i	$-0.854095\pi$
$179$	−0.872025	+	1.51039i	−0.0651782	+	0.112892i	0.831595	+	0.555383i	$0.187428\pi$
$180$		0			0
$181$	−9.44875			−0.702320			−0.351160	−	0.936315i	$-0.614213\pi$
$181$	−9.44875			−0.702320			−0.351160	+	0.936315i	$0.614213\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−4.07182	+	7.05260i	−0.299366	+	0.518517i
$186$		0			0
$187$	−0.910974	−	1.57785i	−0.0666170	−	0.115384i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−16.4118	+	9.47537i	−1.18752	+	0.685614i	−0.957742	−	0.287630i	$-0.907133\pi$
$191$	−16.4118	+	9.47537i	−1.18752	+	0.685614i	−0.229776	+	0.973244i	$0.573799\pi$
$192$		0			0
$193$	2.66715	−	4.61965i	0.191986	−	0.332529i	−0.753922	−	0.656964i	$-0.771841\pi$
$193$	2.66715	−	4.61965i	0.191986	−	0.332529i	0.945908	+	0.324434i	$0.105174\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.80474			−0.199829			−0.0999147	−	0.994996i	$-0.531857\pi$
$197$	−2.80474			−0.199829			−0.0999147	+	0.994996i	$0.531857\pi$
$198$		0			0
$199$	6.44198	+	3.71928i	0.456660	+	0.263653i	0.710639	−	0.703557i	$-0.248406\pi$
$199$	6.44198	+	3.71928i	0.456660	+	0.263653i	−0.253979	+	0.967210i	$0.581739\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−11.0278	+	13.8451i	−0.773997	+	0.971739i
$204$		0			0
$205$	−14.2675	+	8.23733i	−0.996483	+	0.575320i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.94697			0.134675
$210$		0			0
$211$		−	24.6986i		−	1.70032i	−0.526521	−	0.850162i	$-0.676504\pi$
$211$		−	24.6986i		−	1.70032i	0.526521	−	0.850162i	$-0.323496\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−7.47446	−	12.9461i	−0.509754	−	0.882920i
$216$		0			0
$217$	8.12445	−	3.19415i	0.551523	−	0.216833i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.32333	+	2.29207i	−0.0890166	+	0.154181i
$222$		0			0
$223$			7.98964i			0.535026i	0.963554	+	0.267513i	$0.0862019\pi$
$223$			7.98964i			0.535026i	−0.963554	+	0.267513i	$0.913798\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.04318	−	1.17963i	−0.135610	−	0.0782947i	0.430660	−	0.902514i	$-0.358281\pi$
$227$	−2.04318	−	1.17963i	−0.135610	−	0.0782947i	−0.566270	+	0.824220i	$0.691614\pi$
$228$		0			0
$229$	−5.32512	−	9.22338i	−0.351894	−	0.609498i	0.634687	−	0.772769i	$-0.281129\pi$
$229$	−5.32512	−	9.22338i	−0.351894	−	0.609498i	−0.986581	+	0.163271i	$0.947796\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	12.6645	−	7.31188i	0.829682	−	0.479017i	−0.0240618	−	0.999710i	$-0.507660\pi$
$233$	12.6645	−	7.31188i	0.829682	−	0.479017i	0.853744	+	0.520693i	$0.174327\pi$
$234$		0			0
$235$	−18.1002	−	10.4502i	−1.18073	−	0.681693i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	11.5819i		−	0.749168i	−0.927193	−	0.374584i	$-0.877786\pi$
$239$		−	11.5819i		−	0.749168i	0.927193	−	0.374584i	$-0.122214\pi$
$240$		0			0
$241$	1.36690	+	0.789180i	0.0880498	+	0.0508356i	0.543378	−	0.839488i	$-0.317145\pi$
$241$	1.36690	+	0.789180i	0.0880498	+	0.0508356i	−0.455329	+	0.890323i	$0.650478\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	17.3955	+	18.7035i	1.11136	+	1.19492i
$246$		0			0
$247$	−1.41414	−	2.44935i	−0.0899793	−	0.155849i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	17.9769i		−	1.13469i	−0.823480	−	0.567345i	$-0.807971\pi$
$251$		−	17.9769i		−	1.13469i	0.823480	−	0.567345i	$-0.192029\pi$
$252$		0			0
$253$			2.87059i			0.180473i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.71744	+	6.43879i	0.231887	+	0.401640i	0.958363	−	0.285551i	$-0.0921766\pi$
$257$	3.71744	+	6.43879i	0.231887	+	0.401640i	−0.726476	+	0.687192i	$0.758843\pi$
$258$		0			0
$259$	0.876604	−	5.83931i	0.0544695	−	0.362837i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	7.28419	+	4.20553i	0.449162	+	0.259324i	0.707476	−	0.706737i	$-0.249834\pi$
$263$	7.28419	+	4.20553i	0.449162	+	0.259324i	−0.258314	+	0.966061i	$0.583167\pi$
$264$		0			0
$265$			49.2001i			3.02234i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−11.9259	−	6.88541i	−0.727134	−	0.419811i	0.0902390	−	0.995920i	$-0.471237\pi$
$269$	−11.9259	−	6.88541i	−0.727134	−	0.419811i	−0.817373	+	0.576109i	$0.804570\pi$
$270$		0			0
$271$	−16.0976	+	9.29397i	−0.977861	+	0.564568i	−0.901624	−	0.432521i	$-0.857624\pi$
$271$	−16.0976	+	9.29397i	−0.977861	+	0.564568i	−0.0762374	+	0.997090i	$0.524291\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.66398	+	2.88209i	0.100342	+	0.173797i
$276$		0			0
$277$	15.1885	+	8.76910i	0.912590	+	0.526884i	0.881264	−	0.472625i	$-0.156693\pi$
$277$	15.1885	+	8.76910i	0.912590	+	0.526884i	0.0313266	+	0.999509i	$0.490027\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	14.8388i		−	0.885208i	−0.896717	−	0.442604i	$-0.854055\pi$
$281$		−	14.8388i		−	0.885208i	0.896717	−	0.442604i	$-0.145945\pi$
$282$		0			0
$283$	0.293271	−	0.507960i	0.0174331	−	0.0301951i	−0.857177	−	0.515022i	$-0.827784\pi$
$283$	0.293271	−	0.507960i	0.0174331	−	0.0301951i	0.874610	+	0.484826i	$0.161117\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	7.44228	−	9.34364i	0.439304	−	0.551538i
$288$		0			0
$289$	−1.86064	−	3.22272i	−0.109449	−	0.189572i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	6.07405i		−	0.354850i	−0.984134	−	0.177425i	$-0.943223\pi$
$293$		−	6.07405i		−	0.354850i	0.984134	−	0.177425i	$-0.0567767\pi$
$294$		0			0
$295$	−32.5344			−1.89422
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.61130	−	2.08498i	0.208847	−	0.120578i
$300$		0			0
$301$	8.47832	+	6.75304i	0.488682	+	0.389239i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−40.5998	−	23.4403i	−2.32474	−	1.34219i
$306$		0			0
$307$	−19.0443			−1.08691			−0.543457	−	0.839437i	$-0.682885\pi$
$307$	−19.0443			−1.08691			−0.543457	+	0.839437i	$0.682885\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.52301	+	7.83409i	−0.256476	+	0.444230i	−0.965295	−	0.261160i	$-0.915895\pi$
$311$	−4.52301	+	7.83409i	−0.256476	+	0.444230i	0.708819	+	0.705390i	$0.249228\pi$
$312$		0			0
$313$	−6.45654	+	3.72768i	−0.364945	+	0.210701i	−0.671248	−	0.741233i	$-0.734241\pi$
$313$	−6.45654	+	3.72768i	−0.364945	+	0.210701i	0.306303	+	0.951934i	$0.400908\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.40732	−	4.16961i	−0.135209	−	0.234188i	0.790468	−	0.612503i	$-0.209837\pi$
$317$	−2.40732	−	4.16961i	−0.135209	−	0.234188i	−0.925677	+	0.378314i	$0.876504\pi$
$318$		0			0
$319$	1.33884	−	2.31894i	0.0749606	−	0.129836i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	22.1432			1.23208
$324$		0			0
$325$	2.41718	−	4.18668i	0.134081	−	0.232235i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	14.9863	+	2.24977i	0.826224	+	0.124034i
$330$		0			0
$331$	5.43500	−	3.13790i	0.298735	−	0.172475i	−0.343140	−	0.939284i	$-0.611490\pi$
$331$	5.43500	−	3.13790i	0.298735	−	0.172475i	0.641874	+	0.766810i	$0.278157\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−34.9931			−1.91188
$336$		0			0
$337$	−20.1329			−1.09671			−0.548353	−	0.836247i	$-0.684745\pi$
$337$	−20.1329			−1.09671			−0.548353	+	0.836247i	$0.684745\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.14370	+	0.660317i	−0.0619350	+	0.0357582i
$342$		0			0
$343$	−16.7004	−	8.00604i	−0.901737	−	0.432285i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	9.04269	−	15.6624i	0.485437	−	0.840802i	−0.514423	−	0.857537i	$-0.671994\pi$
$347$	9.04269	−	15.6624i	0.485437	−	0.840802i	0.999860	+	0.0167350i	$0.00532716\pi$
$348$		0			0
$349$	−3.24549			−0.173727			−0.0868635	−	0.996220i	$-0.527684\pi$
$349$	−3.24549			−0.173727			−0.0868635	+	0.996220i	$0.527684\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−14.6032	+	25.2934i	−0.777248	+	1.34623i	0.156274	+	0.987714i	$0.450052\pi$
$353$	−14.6032	+	25.2934i	−0.777248	+	1.34623i	−0.933522	+	0.358519i	$0.883282\pi$
$354$		0			0
$355$	11.7135	+	20.2883i	0.621685	+	1.07679i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	8.87600	−	5.12456i	0.468457	−	0.270464i	−0.247136	−	0.968981i	$-0.579490\pi$
$359$	8.87600	−	5.12456i	0.468457	−	0.270464i	0.715594	+	0.698517i	$0.246156\pi$
$360$		0			0
$361$	−2.33135	+	4.03802i	−0.122703	+	0.212528i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	26.0562			1.36384
$366$		0			0
$367$	26.6034	+	15.3595i	1.38869	+	0.801758i	0.993167	−	0.116700i	$-0.0372317\pi$
$367$	26.6034	+	15.3595i	1.38869	+	0.801758i	0.395518	+	0.918458i	$0.370565\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−13.0527	−	33.2000i	−0.677662	−	1.72366i
$372$		0			0
$373$	−17.5313	+	10.1217i	−0.907737	+	0.524082i	−0.879702	−	0.475525i	$-0.842258\pi$
$373$	−17.5313	+	10.1217i	−0.907737	+	0.524082i	−0.0280346	+	0.999607i	$0.508925\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−3.88973			−0.200331
$378$		0			0
$379$			15.4020i			0.791146i	0.918435	+	0.395573i	$0.129454\pi$
$379$			15.4020i			0.791146i	−0.918435	+	0.395573i	$0.870546\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.96494	+	3.40338i	0.100404	+	0.173905i	0.911851	−	0.410521i	$-0.134653\pi$
$383$	1.96494	+	3.40338i	0.100404	+	0.173905i	−0.811447	+	0.584426i	$0.801320\pi$
$384$		0			0
$385$	−3.02246	−	2.40741i	−0.154039	−	0.122693i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	6.94490	−	12.0289i	0.352121	−	0.609891i	−0.634500	−	0.772923i	$-0.718794\pi$
$389$	6.94490	−	12.0289i	0.352121	−	0.609891i	0.986621	+	0.163032i	$0.0521273\pi$
$390$		0			0
$391$			32.6477i			1.65106i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	26.2310	+	15.1445i	1.31982	+	0.762001i
$396$		0			0
$397$	−4.40738	−	7.63380i	−0.221200	−	0.383129i	0.733973	−	0.679179i	$-0.237664\pi$
$397$	−4.40738	−	7.63380i	−0.221200	−	0.383129i	−0.955173	+	0.296050i	$0.904331\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−13.0887	+	7.55674i	−0.653616	+	0.377365i	−0.789840	−	0.613313i	$-0.789837\pi$
$401$	−13.0887	+	7.55674i	−0.653616	+	0.377365i	0.136224	+	0.990678i	$0.456503\pi$
$402$		0			0
$403$	1.66140	+	0.959210i	0.0827602	+	0.0477816i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			0.893263i			0.0442774i
$408$		0			0
$409$	−5.85435	−	3.38001i	−0.289479	−	0.167131i	0.348228	−	0.937410i	$-0.386784\pi$
$409$	−5.85435	−	3.38001i	−0.289479	−	0.167131i	−0.637707	+	0.770279i	$0.720117\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	21.9540	−	8.63131i	1.08029	−	0.424719i
$414$		0			0
$415$	18.9474	+	32.8179i	0.930091	+	1.61097i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			11.1005i			0.542293i	0.962538	+	0.271147i	$0.0874029\pi$
$419$			11.1005i			0.542293i	−0.962538	+	0.271147i	$0.912597\pi$
$420$		0			0
$421$			6.72143i			0.327582i	0.986495	+	0.163791i	$0.0523723\pi$
$421$			6.72143i			0.327582i	−0.986495	+	0.163791i	$0.947628\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	18.9247	+	32.7785i	0.917981	+	1.58999i
$426$		0			0
$427$	33.6152	+	5.04636i	1.62675	+	0.244210i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.32418	+	0.764518i	0.0637837	+	0.0368255i	0.531553	−	0.847025i	$-0.321609\pi$
$431$	1.32418	+	0.764518i	0.0637837	+	0.0368255i	−0.467769	+	0.883851i	$0.654942\pi$
$432$		0			0
$433$			19.9225i			0.957416i	0.877974	+	0.478708i	$0.158895\pi$
$433$			19.9225i			0.957416i	−0.877974	+	0.478708i	$0.841105\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−30.2139	−	17.4440i	−1.44533	−	0.834460i
$438$		0			0
$439$	14.9668	−	8.64107i	0.714325	−	0.412416i	−0.0983355	−	0.995153i	$-0.531352\pi$
$439$	14.9668	−	8.64107i	0.714325	−	0.412416i	0.812660	+	0.582738i	$0.198018\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	0.666057	+	1.15364i	0.0316453	+	0.0548113i	0.881414	−	0.472344i	$-0.156592\pi$
$443$	0.666057	+	1.15364i	0.0316453	+	0.0548113i	−0.849769	+	0.527155i	$0.823259\pi$
$444$		0			0
$445$	−33.2431	−	19.1929i	−1.57587	−	0.909831i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	38.5884i		−	1.82110i	−0.413397	−	0.910551i	$-0.635658\pi$
$449$		−	38.5884i		−	1.82110i	0.413397	−	0.910551i	$-0.364342\pi$
$450$		0			0
$451$	−0.903540	+	1.56498i	−0.0425460	+	0.0736919i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.833312	+	5.55092i	−0.0390663	+	0.260231i
$456$		0			0
$457$	7.80133	+	13.5123i	0.364931	+	0.632079i	0.988765	−	0.149478i	$-0.0477593\pi$
$457$	7.80133	+	13.5123i	0.364931	+	0.632079i	−0.623834	+	0.781557i	$0.714426\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	17.6616i		−	0.822583i	−0.911504	−	0.411291i	$-0.865078\pi$
$461$		−	17.6616i		−	0.822583i	0.911504	−	0.411291i	$-0.134922\pi$
$462$		0			0
$463$	−15.1430			−0.703753			−0.351877	−	0.936046i	$-0.614456\pi$
$463$	−15.1430			−0.703753			−0.351877	+	0.936046i	$0.614456\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	12.0392	−	6.95086i	0.557110	−	0.321647i	−0.194875	−	0.980828i	$-0.562430\pi$
$467$	12.0392	−	6.95086i	0.557110	−	0.321647i	0.751985	+	0.659181i	$0.229097\pi$
$468$		0			0
$469$	23.6132	−	9.28360i	1.09036	−	0.428677i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.42004	−	0.819862i	−0.0652936	−	0.0376973i
$474$		0			0
$475$	−40.4466			−1.85582
$476$		0			0
$477$		0			0
$478$		0			0
$479$	15.2782	−	26.4626i	0.698077	−	1.20911i	−0.271055	−	0.962564i	$-0.587373\pi$
$479$	15.2782	−	26.4626i	0.698077	−	1.20911i	0.969132	−	0.246541i	$-0.0792941\pi$
$480$		0			0
$481$	1.12375	−	0.648799i	0.0512388	−	0.0295827i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	7.30946	+	12.6604i	0.331906	+	0.574877i
$486$		0			0
$487$	−10.9031	+	18.8848i	−0.494068	+	0.855751i	−0.999977	−	0.00683637i	$-0.997824\pi$
$487$	−10.9031	+	18.8848i	−0.494068	+	0.855751i	0.505909	+	0.862587i	$0.331157\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−3.38847			−0.152919			−0.0764597	−	0.997073i	$-0.524362\pi$
$491$	−3.38847			−0.152919			−0.0764597	+	0.997073i	$0.524362\pi$
$492$		0			0
$493$	15.2268	−	26.3736i	0.685781	−	1.18781i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−13.2866	−	10.5829i	−0.595987	−	0.474708i
$498$		0			0
$499$	−35.9490	+	20.7552i	−1.60930	+	0.929128i	−0.619770	+	0.784784i	$0.712774\pi$
$499$	−35.9490	+	20.7552i	−1.60930	+	0.929128i	−0.989528	+	0.144344i	$0.953893\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−18.4870			−0.824295			−0.412147	−	0.911117i	$-0.635221\pi$
$503$	−18.4870			−0.824295			−0.412147	+	0.911117i	$0.635221\pi$
$504$		0			0
$505$	−51.3519			−2.28513
$506$		0			0
$507$		0			0
$508$		0			0
$509$	5.71745	−	3.30097i	0.253422	−	0.146313i	−0.367908	−	0.929862i	$-0.619926\pi$
$509$	5.71745	−	3.30097i	0.253422	−	0.146313i	0.621330	+	0.783549i	$0.286593\pi$
$510$		0			0
$511$	−17.5826	+	6.91266i	−0.777809	+	0.305798i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−36.8359	+	63.8016i	−1.62318	+	2.81144i
$516$		0			0
$517$	−2.29252			−0.100825
$518$		0			0
$519$		0			0
$520$		0			0
$521$	3.54303	−	6.13671i	0.155223	−	0.268854i	−0.777917	−	0.628367i	$-0.783724\pi$
$521$	3.54303	−	6.13671i	0.155223	−	0.268854i	0.933140	+	0.359513i	$0.117057\pi$
$522$		0			0
$523$	12.3169	+	21.3336i	0.538583	+	0.932852i	0.998981	+	0.0451399i	$0.0143733\pi$
$523$	12.3169	+	21.3336i	0.538583	+	0.932852i	−0.460398	+	0.887713i	$0.652293\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−13.0075	+	7.50988i	−0.566615	+	0.327136i
$528$		0			0
$529$	14.2192	−	24.6284i	0.618227	−	1.07080i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	2.62505			0.113704
$534$		0			0
$535$	13.2668	+	7.65962i	0.573576	+	0.331154i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	2.67823	+	0.822658i	0.115359	+	0.0354344i
$540$		0			0
$541$	20.3549	−	11.7519i	0.875125	−	0.505254i	0.00607698	−	0.999982i	$-0.498066\pi$
$541$	20.3549	−	11.7519i	0.875125	−	0.505254i	0.869048	+	0.494728i	$0.164732\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−67.7504			−2.90211
$546$		0			0
$547$		−	16.9894i		−	0.726412i	−0.931709	−	0.363206i	$-0.881682\pi$
$547$		−	16.9894i		−	0.726412i	0.931709	−	0.363206i	$-0.118318\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	16.2717	+	28.1834i	0.693198	+	1.20065i
$552$		0			0
$553$	−21.7183	−	3.26039i	−0.923558	−	0.138646i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−2.69847	+	4.67389i	−0.114338	+	0.198039i	−0.917515	−	0.397701i	$-0.869808\pi$
$557$	−2.69847	+	4.67389i	−0.114338	+	0.198039i	0.803177	+	0.595740i	$0.203141\pi$
$558$		0			0
$559$			2.38195i			0.100746i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−29.2646	−	16.8959i	−1.23336	−	0.712078i	−0.265628	−	0.964076i	$-0.585579\pi$
$563$	−29.2646	−	16.8959i	−1.23336	−	0.712078i	−0.967728	+	0.251997i	$0.918913\pi$
$564$		0			0
$565$	6.28520	+	10.8863i	0.264420	+	0.457989i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−14.2390	+	8.22089i	−0.596930	+	0.344638i	−0.767833	−	0.640650i	$-0.778665\pi$
$569$	−14.2390	+	8.22089i	−0.596930	+	0.344638i	0.170903	+	0.985288i	$0.445332\pi$
$570$		0			0
$571$	−33.2026	−	19.1696i	−1.38949	−	0.802221i	−0.396230	−	0.918151i	$-0.629682\pi$
$571$	−33.2026	−	19.1696i	−1.38949	−	0.802221i	−0.993257	+	0.115931i	$0.963015\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	59.6340i		−	2.48691i
$576$		0			0
$577$	19.2194	+	11.0963i	0.800113	+	0.461946i	0.843511	−	0.537112i	$-0.180485\pi$
$577$	19.2194	+	11.0963i	0.800113	+	0.461946i	−0.0433975	+	0.999058i	$0.513818\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−21.4921	−	17.1186i	−0.891644	−	0.710201i
$582$		0			0
$583$	2.69834	+	4.67366i	0.111754	+	0.193563i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	3.25736i		−	0.134445i	−0.997738	−	0.0672227i	$-0.978586\pi$
$587$		−	3.25736i		−	0.134445i	0.997738	−	0.0672227i	$-0.0214138\pi$
$588$		0			0
$589$		−	16.0504i		−	0.661347i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−19.4634	−	33.7116i	−0.799267	−	1.38437i	−0.920094	−	0.391697i	$-0.871888\pi$
$593$	−19.4634	−	33.7116i	−0.799267	−	1.38437i	0.120827	−	0.992674i	$-0.461445\pi$
$594$		0			0
$595$	−34.3749	−	27.3799i	−1.40923	−	1.12246i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−8.92743	−	5.15425i	−0.364765	−	0.210597i	0.306404	−	0.951902i	$-0.400874\pi$
$599$	−8.92743	−	5.15425i	−0.364765	−	0.210597i	−0.671169	+	0.741304i	$0.734207\pi$
$600$		0			0
$601$			16.1379i			0.658277i	0.944282	+	0.329139i	$0.106758\pi$
$601$			16.1379i			0.658277i	−0.944282	+	0.329139i	$0.893242\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−34.2546	−	19.7769i	−1.39265	−	0.804045i
$606$		0			0
$607$	31.3010	−	18.0717i	1.27047	−	0.733506i	0.295393	−	0.955376i	$-0.404549\pi$
$607$	31.3010	−	18.0717i	1.27047	−	0.733506i	0.975076	+	0.221870i	$0.0712159\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.66512	+	2.88407i	0.0673634	+	0.116677i
$612$		0			0
$613$	−1.33431	−	0.770363i	−0.0538922	−	0.0311147i	0.472812	−	0.881163i	$-0.343239\pi$
$613$	−1.33431	−	0.770363i	−0.0538922	−	0.0311147i	−0.526704	+	0.850049i	$0.676572\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			40.1412i			1.61602i	0.589165	+	0.808012i	$0.299457\pi$
$617$			40.1412i			1.61602i	−0.589165	+	0.808012i	$0.700543\pi$
$618$		0			0
$619$	18.4948	−	32.0339i	0.743368	−	1.28755i	−0.207586	−	0.978217i	$-0.566561\pi$
$619$	18.4948	−	32.0339i	0.743368	−	1.28755i	0.950953	−	0.309334i	$-0.100106\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	27.5241	+	4.13196i	1.10273	+	0.165543i
$624$		0			0
$625$	−1.28074	−	2.21830i	−0.0512295	−	0.0887321i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			10.1592i			0.405074i
$630$		0			0
$631$	−31.1044			−1.23825			−0.619123	−	0.785294i	$-0.712512\pi$
$631$	−31.1044			−1.23825			−0.619123	+	0.785294i	$0.712512\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−12.0771	+	6.97274i	−0.479267	+	0.276705i
$636$		0			0
$637$	−0.910334	−	3.96681i	−0.0360688	−	0.157171i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−3.44022	−	1.98621i	−0.135881	−	0.0784507i	0.430519	−	0.902582i	$-0.358331\pi$
$641$	−3.44022	−	1.98621i	−0.135881	−	0.0784507i	−0.566399	+	0.824131i	$0.691664\pi$
$642$		0			0
$643$	47.5503			1.87520			0.937600	−	0.347717i	$-0.113043\pi$
$643$	47.5503			1.87520			0.937600	+	0.347717i	$0.113043\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	20.9097	−	36.2166i	0.822044	−	1.42382i	−0.0821142	−	0.996623i	$-0.526167\pi$
$647$	20.9097	−	36.2166i	0.822044	−	1.42382i	0.904158	−	0.427199i	$-0.140499\pi$
$648$		0			0
$649$	−3.09054	+	1.78432i	−0.121314	+	0.0700408i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	10.6456	+	18.4388i	0.416596	+	0.721565i	0.995595	−	0.0937632i	$-0.0298896\pi$
$653$	10.6456	+	18.4388i	0.416596	+	0.721565i	−0.578999	+	0.815329i	$0.696556\pi$
$654$		0			0
$655$	0.338288	−	0.585932i	0.0132180	−	0.0228943i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	50.0936			1.95137			0.975685	−	0.219179i	$-0.0703378\pi$
$659$	50.0936			1.95137			0.975685	+	0.219179i	$0.0703378\pi$
$660$		0			0
$661$	−11.9756	+	20.7423i	−0.465797	+	0.806784i	−0.999237	−	0.0390540i	$-0.987566\pi$
$661$	−11.9756	+	20.7423i	−0.465797	+	0.806784i	0.533440	+	0.845838i	$0.320899\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	43.7057	−	17.1830i	1.69483	−	0.666330i
$666$		0			0
$667$	−41.5533	+	23.9908i	−1.60895	+	0.928927i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−5.14226			−0.198515
$672$		0			0
$673$	−2.60756			−0.100514			−0.0502570	−	0.998736i	$-0.516004\pi$
$673$	−2.60756			−0.100514			−0.0502570	+	0.998736i	$0.516004\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−13.5947	+	7.84890i	−0.522486	+	0.301658i	−0.737951	−	0.674854i	$-0.764207\pi$
$677$	−13.5947	+	7.84890i	−0.522486	+	0.301658i	0.215465	+	0.976512i	$0.430873\pi$
$678$		0			0
$679$	−8.29116	−	6.60397i	−0.318186	−	0.253437i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−10.7229	+	18.5726i	−0.410300	+	0.710661i	−0.994922	−	0.100645i	$-0.967909\pi$
$683$	−10.7229	+	18.5726i	−0.410300	+	0.710661i	0.584622	+	0.811306i	$0.301243\pi$
$684$		0			0
$685$	−55.9005			−2.13585
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3.91975	−	6.78920i	0.149330	−	0.258648i
$690$		0			0
$691$	−12.6075	−	21.8368i	−0.479611	−	0.830710i	0.520116	−	0.854096i	$-0.325889\pi$
$691$	−12.6075	−	21.8368i	−0.479611	−	0.830710i	−0.999727	+	0.0233857i	$0.992555\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−33.3300	+	19.2431i	−1.26428	+	0.729931i
$696$		0			0
$697$	−10.2761	+	17.7987i	−0.389235	+	0.674174i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	33.6820			1.27215			0.636076	−	0.771626i	$-0.280556\pi$
$701$	33.6820			1.27215			0.636076	+	0.771626i	$0.280556\pi$
$702$		0			0
$703$	−9.40187	−	5.42818i	−0.354598	−	0.204727i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	34.6521	−	13.6236i	1.30323	−	0.512367i
$708$		0			0
$709$	33.1687	−	19.1499i	1.24568	−	0.719191i	0.275431	−	0.961321i	$-0.411179\pi$
$709$	33.1687	−	19.1499i	1.24568	−	0.719191i	0.970244	+	0.242130i	$0.0778460\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	23.6646			0.886245
$714$		0			0
$715$		−	0.849148i		−	0.0317563i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−3.40747	−	5.90191i	−0.127077	−	0.220104i	0.795466	−	0.605998i	$-0.207226\pi$
$719$	−3.40747	−	5.90191i	−0.127077	−	0.220104i	−0.922543	+	0.385894i	$0.873893\pi$
$720$		0			0
$721$	7.93024	−	52.8256i	0.295338	−	1.96733i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−27.8132	+	48.1738i	−1.03296	+	1.78913i
$726$		0			0
$727$			44.3315i			1.64416i	0.569369	+	0.822082i	$0.307188\pi$
$727$			44.3315i			1.64416i	−0.569369	+	0.822082i	$0.692812\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−16.1504	−	9.32441i	−0.597342	−	0.344876i
$732$		0			0
$733$	−4.98689	−	8.63755i	−0.184195	−	0.319035i	0.759110	−	0.650962i	$-0.225634\pi$
$733$	−4.98689	−	8.63755i	−0.184195	−	0.319035i	−0.943305	+	0.331927i	$0.892301\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.32410	+	1.91917i	−0.122445	+	0.0706935i
$738$		0			0
$739$	37.1489	+	21.4480i	1.36655	+	0.788976i	0.990485	−	0.137619i	$-0.0439450\pi$
$739$	37.1489	+	21.4480i	1.36655	+	0.788976i	0.376061	+	0.926595i	$0.377278\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			11.2075i			0.411165i	0.978640	+	0.205582i	$0.0659088\pi$
$743$			11.2075i			0.411165i	−0.978640	+	0.205582i	$0.934091\pi$
$744$		0			0
$745$	29.0169	+	16.7529i	1.06310	+	0.613778i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−10.9845	−	1.64901i	−0.401365	−	0.0602534i
$750$		0			0
$751$	−18.5560	−	32.1399i	−0.677117	−	1.17280i	−0.975845	−	0.218462i	$-0.929896\pi$
$751$	−18.5560	−	32.1399i	−0.677117	−	1.17280i	0.298729	−	0.954338i	$-0.403437\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	13.1361i		−	0.478073i
$756$		0			0
$757$			20.8257i			0.756924i	0.925617	+	0.378462i	$0.123547\pi$
$757$			20.8257i			0.756924i	−0.925617	+	0.378462i	$0.876453\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	7.26978	+	12.5916i	0.263529	+	0.456446i	0.967177	−	0.254103i	$-0.0817801\pi$
$761$	7.26978	+	12.5916i	0.263529	+	0.456446i	−0.703648	+	0.710549i	$0.748447\pi$
$762$		0			0
$763$	45.7177	−	17.9740i	1.65509	−	0.650704i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	4.48947	+	2.59200i	0.162105	+	0.0935916i
$768$		0			0
$769$			2.11604i			0.0763063i	0.999272	+	0.0381532i	$0.0121475\pi$
$769$			2.11604i			0.0763063i	−0.999272	+	0.0381532i	$0.987853\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−18.3194	−	10.5767i	−0.658902	−	0.380417i	0.132957	−	0.991122i	$-0.457553\pi$
$773$	−18.3194	−	10.5767i	−0.658902	−	0.380417i	−0.791858	+	0.610705i	$0.790886\pi$
$774$		0			0
$775$	23.7594	−	13.7175i	0.853462	−	0.492747i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−10.9812	−	19.0201i	−0.393444	−	0.681465i
$780$		0			0
$781$	2.22539	+	1.28483i	0.0796308	+	0.0459748i
$782$		0			0
$783$		0			0
$784$		0			0
$785$			2.62060i			0.0935331i
$786$		0			0
$787$	−15.1516	+	26.2433i	−0.540096	+	0.935473i	0.458802	+	0.888538i	$0.348279\pi$
$787$	−15.1516	+	26.2433i	−0.540096	+	0.935473i	−0.998898	+	0.0469348i	$0.985055\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−7.12933	−	5.67856i	−0.253490	−	0.201906i
$792$		0			0
$793$	3.73495	+	6.46913i	0.132632	+	0.229725i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	12.8964i		−	0.456812i	−0.973566	−	0.228406i	$-0.926649\pi$
$797$		−	12.8964i		−	0.456812i	0.973566	−	0.228406i	$-0.0733514\pi$
$798$		0			0
$799$	−26.0732			−0.922403
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.47516	−	1.42903i	0.0873463	−	0.0504294i
$804$		0			0
$805$	25.3345	+	64.4391i	0.892922	+	2.27118i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	31.3922	+	18.1243i	1.10369	+	0.637216i	0.937188	−	0.348825i	$-0.113419\pi$
$809$	31.3922	+	18.1243i	1.10369	+	0.637216i	0.166502	+	0.986041i	$0.446753\pi$
$810$		0			0
$811$	5.48133			0.192475			0.0962377	−	0.995358i	$-0.469319\pi$
$811$	5.48133			0.192475			0.0962377	+	0.995358i	$0.469319\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−40.2646	+	69.7403i	−1.41041	+	2.44290i
$816$		0			0
$817$	17.2586	−	9.96427i	0.603803	−	0.348606i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	5.95824	+	10.3200i	0.207944	+	0.360169i	0.951067	−	0.308986i	$-0.0999895\pi$
$821$	5.95824	+	10.3200i	0.207944	+	0.360169i	−0.743123	+	0.669155i	$0.766656\pi$
$822$		0			0
$823$	20.9931	−	36.3612i	0.731775	−	1.26747i	−0.224349	−	0.974509i	$-0.572025\pi$
$823$	20.9931	−	36.3612i	0.731775	−	1.26747i	0.956124	−	0.292963i	$-0.0946412\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	18.7749			0.652869			0.326434	−	0.945220i	$-0.394153\pi$
$827$	18.7749			0.652869			0.326434	+	0.945220i	$0.394153\pi$
$828$		0			0
$829$	−7.45588	+	12.9140i	−0.258953	+	0.448520i	−0.965962	−	0.258685i	$-0.916711\pi$
$829$	−7.45588	+	12.9140i	−0.258953	+	0.448520i	0.707009	+	0.707205i	$0.250044\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	30.4599	+	9.35621i	1.05537	+	0.324173i
$834$		0			0
$835$	42.6238	−	24.6089i	1.47506	−	0.851625i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	28.4322			0.981587			0.490794	−	0.871276i	$-0.336707\pi$
$839$	28.4322			0.981587			0.490794	+	0.871276i	$0.336707\pi$
$840$		0			0
$841$	15.7571			0.543347
$842$		0			0
$843$		0			0
$844$		0			0
$845$	40.0127	−	23.1014i	1.37648	−	0.794711i
$846$		0			0
$847$	28.3616	+	4.25768i	0.974517	+	0.146296i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	8.00324	−	13.8620i	0.274347	−	0.475184i
$852$		0			0
$853$	−9.45822			−0.323843			−0.161922	−	0.986804i	$-0.551769\pi$
$853$	−9.45822			−0.323843			−0.161922	+	0.986804i	$0.551769\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−19.8068	+	34.3064i	−0.676588	+	1.17188i	0.299415	+	0.954123i	$0.403209\pi$
$857$	−19.8068	+	34.3064i	−0.676588	+	1.17188i	−0.976002	+	0.217761i	$0.930125\pi$
$858$		0			0
$859$	17.1446	+	29.6953i	0.584965	+	1.01319i	0.994880	+	0.101066i	$0.0322253\pi$
$859$	17.1446	+	29.6953i	0.584965	+	1.01319i	−0.409914	+	0.912124i	$0.634441\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	30.9385	−	17.8623i	1.05316	−	0.608041i	0.129627	−	0.991563i	$-0.458622\pi$
$863$	30.9385	−	17.8623i	1.05316	−	0.608041i	0.923532	+	0.383522i	$0.125289\pi$
$864$		0			0
$865$	29.5147	−	51.1209i	1.00353	−	1.73816i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	3.32235			0.112703
$870$		0			0
$871$	4.82875	+	2.78788i	0.163616	+	0.0944638i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	25.0315	+	19.9377i	0.846218	+	0.674018i
$876$		0			0
$877$	−13.3688	+	7.71847i	−0.451431	+	0.260634i	−0.708435	−	0.705777i	$-0.750598\pi$
$877$	−13.3688	+	7.71847i	−0.451431	+	0.260634i	0.257003	+	0.966411i	$0.417265\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−2.47237			−0.0832962			−0.0416481	−	0.999132i	$-0.513261\pi$
$881$	−2.47237			−0.0832962			−0.0416481	+	0.999132i	$0.513261\pi$
$882$		0			0
$883$			22.3515i			0.752187i	0.926582	+	0.376094i	$0.122733\pi$
$883$			22.3515i			0.752187i	−0.926582	+	0.376094i	$0.877267\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	11.2912	+	19.5570i	0.379122	+	0.656658i	0.990935	−	0.134344i	$-0.0428928\pi$
$887$	11.2912	+	19.5570i	0.379122	+	0.656658i	−0.611813	+	0.791003i	$0.709559\pi$
$888$		0			0
$889$	6.29975	−	7.90922i	0.211287	−	0.265267i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	13.9312	−	24.1295i	0.466189	−	0.807464i
$894$		0			0
$895$		−	6.36394i		−	0.212723i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−19.1168	−	11.0371i	−0.637582	−	0.368108i
$900$		0			0
$901$	30.6886	+	53.1543i	1.02239	+	1.77083i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	29.8588	−	17.2390i	0.992539	−	0.573042i
$906$		0			0
$907$	−8.75724	−	5.05599i	−0.290779	−	0.167882i	0.347514	−	0.937675i	$-0.387026\pi$
$907$	−8.75724	−	5.05599i	−0.290779	−	0.167882i	−0.638293	+	0.769793i	$0.720359\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			28.5297i			0.945230i	0.881269	+	0.472615i	$0.156690\pi$
$911$			28.5297i			0.945230i	−0.881269	+	0.472615i	$0.843310\pi$
$912$		0			0
$913$	3.59974	+	2.07831i	0.119134	+	0.0687820i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.0728286	+	0.485131i	−0.00240501	+	0.0160204i
$918$		0			0
$919$	−13.4674	−	23.3263i	−0.444249	−	0.769463i	0.553750	−	0.832683i	$-0.313196\pi$
$919$	−13.4674	−	23.3263i	−0.444249	−	0.769463i	−0.998000	+	0.0632203i	$0.979863\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	3.73282i		−	0.122867i
$924$		0			0
$925$		−	18.5567i		−	0.610142i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	11.2786	+	19.5350i	0.370038	+	0.640924i	0.989571	−	0.144046i	$-0.0460114\pi$
$929$	11.2786	+	19.5350i	0.370038	+	0.640924i	−0.619533	+	0.784970i	$0.712678\pi$
$930$		0			0
$931$	−24.9338	+	23.1901i	−0.817171	+	0.760024i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	5.75749	+	3.32409i	0.188290	+	0.108709i
$936$		0			0
$937$			25.6419i			0.837684i	0.908059	+	0.418842i	$0.137564\pi$
$937$			25.6419i			0.837684i	−0.908059	+	0.418842i	$0.862436\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	49.1787	+	28.3933i	1.60318	+	0.925596i	0.990846	+	0.134996i	$0.0431022\pi$
$941$	49.1787	+	28.3933i	1.60318	+	0.925596i	0.612333	+	0.790600i	$0.290231\pi$
$942$		0			0
$943$	28.0430	−	16.1906i	0.913205	−	0.527239i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−5.32282	−	9.21939i	−0.172968	−	0.299590i	0.766488	−	0.642259i	$-0.222002\pi$
$947$	−5.32282	−	9.21939i	−0.172968	−	0.299590i	−0.939456	+	0.342669i	$0.888669\pi$
$948$		0			0
$949$	−3.59554	−	2.07588i	−0.116716	−	0.0673861i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	31.4456i		−	1.01862i	−0.860582	−	0.509312i	$-0.829900\pi$
$953$		−	31.4456i		−	1.01862i	0.860582	−	0.509312i	$-0.170100\pi$
$954$		0			0
$955$	34.5750	−	59.8857i	1.11882	−	1.93786i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	37.7214	−	14.8303i	1.21809	−	0.478896i
$960$		0			0
$961$	−10.0565	−	17.4183i	−0.324403	−	0.561882i
$962$		0			0
$963$		0			0
$964$		0			0
$965$			19.4646i			0.626587i
$966$		0			0
$967$	−2.45245			−0.0788655			−0.0394327	−	0.999222i	$-0.512555\pi$
$967$	−2.45245			−0.0788655			−0.0394327	+	0.999222i	$0.512555\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−28.2257	+	16.2961i	−0.905807	+	0.522968i	−0.879080	−	0.476675i	$-0.841842\pi$
$971$	−28.2257	+	16.2961i	−0.905807	+	0.522968i	−0.0267274	+	0.999643i	$0.508509\pi$
$972$		0			0
$973$	17.3858	−	21.8275i	0.557362	−	0.699758i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	8.83921	+	5.10332i	0.282791	+	0.163270i	0.634686	−	0.772770i	$-0.281129\pi$
$977$	8.83921	+	5.10332i	0.282791	+	0.163270i	−0.351895	+	0.936039i	$0.614463\pi$
$978$		0			0
$979$	−4.21048			−0.134568
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−2.76849	+	4.79516i	−0.0883010	+	0.152942i	−0.906793	−	0.421576i	$-0.861477\pi$
$983$	−2.76849	+	4.79516i	−0.0883010	+	0.152942i	0.818492	+	0.574518i	$0.194810\pi$
$984$		0			0
$985$	8.86318	−	5.11716i	0.282405	−	0.163046i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	14.6912	+	25.4459i	0.467153	+	0.809132i
$990$		0			0
$991$	6.53951	−	11.3268i	0.207734	−	0.359806i	−0.743266	−	0.668996i	$-0.766724\pi$
$991$	6.53951	−	11.3268i	0.207734	−	0.359806i	0.951000	+	0.309189i	$0.100058\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−27.1429			−0.860487
$996$		0			0
$997$	3.01429	−	5.22091i	0.0954636	−	0.165348i	−0.814338	−	0.580390i	$-0.802900\pi$
$997$	3.01429	−	5.22091i	0.0954636	−	0.165348i	0.909802	+	0.415043i	$0.136233\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2016.2.cp.b.17.4		56
3.2	odd	2	inner	2016.2.cp.b.17.26		56
4.3	odd	2		504.2.ch.b.269.21	yes	56
7.5	odd	6	inner	2016.2.cp.b.593.3		56
8.3	odd	2		504.2.ch.b.269.26	yes	56
8.5	even	2	inner	2016.2.cp.b.17.25		56
12.11	even	2		504.2.ch.b.269.8	yes	56
21.5	even	6	inner	2016.2.cp.b.593.25		56
24.5	odd	2	inner	2016.2.cp.b.17.3		56
24.11	even	2		504.2.ch.b.269.3	✓	56
28.19	even	6		504.2.ch.b.341.3	yes	56
56.5	odd	6	inner	2016.2.cp.b.593.26		56
56.19	even	6		504.2.ch.b.341.8	yes	56
84.47	odd	6		504.2.ch.b.341.26	yes	56
168.5	even	6	inner	2016.2.cp.b.593.4		56
168.131	odd	6		504.2.ch.b.341.21	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.ch.b.269.3	✓	56	24.11	even	2
504.2.ch.b.269.8	yes	56	12.11	even	2
504.2.ch.b.269.21	yes	56	4.3	odd	2
504.2.ch.b.269.26	yes	56	8.3	odd	2
504.2.ch.b.341.3	yes	56	28.19	even	6
504.2.ch.b.341.8	yes	56	56.19	even	6
504.2.ch.b.341.21	yes	56	168.131	odd	6
504.2.ch.b.341.26	yes	56	84.47	odd	6
2016.2.cp.b.17.3		56	24.5	odd	2	inner
2016.2.cp.b.17.4		56	1.1	even	1	trivial
2016.2.cp.b.17.25		56	8.5	even	2	inner
2016.2.cp.b.17.26		56	3.2	odd	2	inner
2016.2.cp.b.593.3		56	7.5	odd	6	inner
2016.2.cp.b.593.4		56	168.5	even	6	inner
2016.2.cp.b.593.25		56	21.5	even	6	inner
2016.2.cp.b.593.26		56	56.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2016.cp (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.16007 + 1.82447i) q^{5} +(1.64838 - 2.06951i) q^{7} +(-0.200123 + 0.346624i) q^{11} +0.581419 q^{13} +(-2.27603 + 3.94220i) q^{17} +(-2.43222 - 4.21272i) q^{19} +(6.21119 - 3.58603i) q^{23} +(4.15738 - 7.20080i) q^{25} -6.69007 q^{29} +(2.85749 + 1.64978i) q^{31} +(-1.43324 + 9.54721i) q^{35} +(1.93278 - 1.11589i) q^{37} +4.51491 q^{41} +4.09678i q^{43} +(2.86389 + 4.96040i) q^{47} +(-1.56571 - 6.82265i) q^{49} +(6.74170 - 11.6770i) q^{53} -1.46048i q^{55} +(7.72158 + 4.45806i) q^{59} +(6.42386 + 11.1265i) q^{61} +(-1.83733 + 1.06078i) q^{65} +(8.30513 + 4.79497i) q^{67} -6.42019i q^{71} +(-6.18408 - 3.57038i) q^{73} +(0.387462 + 0.985523i) q^{77} +(-4.15037 - 7.18866i) q^{79} -10.3852i q^{83} -16.6102i q^{85} +(5.25986 + 9.11034i) q^{89} +(0.958396 - 1.20325i) q^{91} +(15.3720 + 8.87501i) q^{95} -4.00635i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 20 q^{7} + 8 q^{25} + 36 q^{31} - 28 q^{49} + 72 q^{73} + 12 q^{79}+O(q^{100}) \) 56 * q + 20 * q^7 + 8 * q^25 + 36 * q^31 - 28 * q^49 + 72 * q^73 + 12 * q^79

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