LMFDB - Embedded newform 504.2.bk.a.19.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(19,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$504 = 2^{3} \cdot 3^{2} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	504.bk (of order $6$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.144054149089536.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{12} - 3x^{11} + x^{9} + 48x^{8} - 189x^{7} + 431x^{6} - 654x^{5} + 624x^{4} - 340x^{3} + 96x^{2} - 12x + 4$ x^12 - 3x^11 + x^9 + 48x^8 - 189x^7 + 431x^6 - 654x^5 + 624x^4 - 340x^3 + 96x^2 - 12*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$2^{2}$
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.6
Root			$-0.0263223 - 0.217464i$ of defining polynomial
Character	$\chi$	$=$	504.19
Dual form			504.2.bk.a.451.5

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30084 + 0.554812i) q^{2} +(1.38437 + 1.44344i) q^{4} +(1.03926 - 1.80005i) q^{5} +(-1.25203 + 2.33076i) q^{7} +(1.00000 + 2.64575i) q^{8} +(2.35060 - 1.76498i) q^{10} +(0.669938 + 1.16037i) q^{11} +2.50406 q^{13} +(-2.92182 + 2.33730i) q^{14} +(-0.167055 + 3.99651i) q^{16} +(2.78212 - 1.60626i) q^{17} +(3.55442 + 2.05215i) q^{19} +(4.03699 - 0.991819i) q^{20} +(0.227697 + 1.88114i) q^{22} +(-5.54952 - 3.20402i) q^{23} +(0.339877 + 0.588684i) q^{25} +(3.25737 + 1.38928i) q^{26} +(-5.09758 + 1.41939i) q^{28} -4.66151i q^{29} +(-2.21897 - 3.84337i) q^{31} +(-2.43462 + 5.10613i) q^{32} +(4.51026 - 0.545930i) q^{34} +(2.89430 + 4.67598i) q^{35} +(-5.50178 - 3.17646i) q^{37} +(3.48518 + 4.64155i) q^{38} +(5.80175 + 0.949572i) q^{40} -5.55076i q^{41} +(-0.747483 + 2.57339i) q^{44} +(-5.44141 - 7.24685i) q^{46} +(-0.565988 + 0.980320i) q^{47} +(-3.86485 - 5.83634i) q^{49} +(0.115516 + 0.954351i) q^{50} +(3.46653 + 3.61446i) q^{52} +(-7.43567 + 4.29299i) q^{53} +2.78496 q^{55} +(-7.41863 - 0.981797i) q^{56} +(2.58626 - 6.06388i) q^{58} +(-6.29193 + 3.63265i) q^{59} +(-2.57219 + 4.45517i) q^{61} +(-0.754178 - 6.23073i) q^{62} +(-6.00000 + 5.29150i) q^{64} +(2.60236 - 4.50743i) q^{65} +(3.93243 + 6.81116i) q^{67} +(6.17001 + 1.79218i) q^{68} +(1.17073 + 7.68849i) q^{70} -5.29150i q^{71} +(0.480369 - 0.277341i) q^{73} +(-5.39460 - 7.18452i) q^{74} +(1.95847 + 7.97153i) q^{76} +(-3.54332 + 0.108651i) q^{77} +(-5.26862 - 3.04184i) q^{79} +(7.02031 + 4.45412i) q^{80} +(3.07963 - 7.22064i) q^{82} +0.503175i q^{83} -6.67728i q^{85} +(-2.40011 + 2.93286i) q^{88} +(-1.50000 - 0.866025i) q^{89} +(-3.13515 + 5.83634i) q^{91} +(-3.05776 - 12.4460i) q^{92} +(-1.28015 + 0.961222i) q^{94} +(7.38794 - 4.26543i) q^{95} -17.2234i q^{97} +(-1.78948 - 9.73641i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$12 q + 12 q^{8} + 6 q^{10} + 6 q^{11} - 6 q^{14} + 6 q^{17} - 6 q^{19} + 24 q^{22} - 6 q^{26} + 6 q^{28} - 18 q^{35} + 24 q^{38} + 42 q^{40} - 6 q^{44} - 18 q^{46} - 12 q^{49} + 48 q^{50} - 24 q^{52} + 18 q^{58}+ \cdots + 6 q^{98}+O(q^{100})$ 12 * q + 12 * q^8 + 6 * q^10 + 6 * q^11 - 6 * q^14 + 6 * q^17 - 6 * q^19 + 24 * q^22 - 6 * q^26 + 6 * q^28 - 18 * q^35 + 24 * q^38 + 42 * q^40 - 6 * q^44 - 18 * q^46 - 12 * q^49 + 48 * q^50 - 24 * q^52 + 18 * q^58 - 42 * q^59 - 72 * q^64 + 12 * q^65 + 30 * q^67 + 36 * q^68 + 30 * q^70 + 18 * q^73 - 12 * q^74 - 36 * q^80 + 54 * q^82 + 6 * q^88 - 18 * q^89 - 72 * q^91 - 60 * q^92 - 12 * q^94 + 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$ .

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

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

)

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

$2$	1.30084	+	0.554812i	0.919832	+	0.392311i
$2$	1.30084	+	0.554812i	0.919832	+	0.392311i
$3$		0			0
$3$		0			0
$4$	1.38437	+	1.44344i	0.692184	+	0.721721i
$5$	1.03926	−	1.80005i	0.464771	−	0.805007i	−0.534420	−	0.845219i	$-0.679470\pi$
$5$	1.03926	−	1.80005i	0.464771	−	0.805007i	0.999191	+	0.0402117i	$0.0128032\pi$
$6$		0			0
$7$	−1.25203	+	2.33076i	−0.473222	+	0.880943i
$7$	−1.25203	+	2.33076i	−0.473222	+	0.880943i
$8$	1.00000	+	2.64575i	0.353553	+	0.935414i
$9$		0			0
$10$	2.35060	−	1.76498i	0.743325	−	0.558137i
$11$	0.669938	+	1.16037i	0.201994	+	0.349864i	0.949171	−	0.314761i	$-0.101925\pi$
$11$	0.669938	+	1.16037i	0.201994	+	0.349864i	−0.747177	+	0.664625i	$0.768591\pi$
$12$		0			0
$13$	2.50406			0.694500			0.347250	−	0.937773i	$-0.387116\pi$
$13$	2.50406			0.694500			0.347250	+	0.937773i	$0.387116\pi$
$14$	−2.92182	+	2.33730i	−0.780889	+	0.624670i
$15$		0			0
$16$	−0.167055	+	3.99651i	−0.0417638	+	0.999128i
$17$	2.78212	−	1.60626i	0.674763	−	0.389575i	−0.123116	−	0.992392i	$-0.539289\pi$
$17$	2.78212	−	1.60626i	0.674763	−	0.389575i	0.797879	+	0.602818i	$0.205955\pi$
$18$		0			0
$19$	3.55442	+	2.05215i	0.815440	+	0.470795i	0.848842	−	0.528647i	$-0.177301\pi$
$19$	3.55442	+	2.05215i	0.815440	+	0.470795i	−0.0334012	+	0.999442i	$0.510634\pi$
$20$	4.03699	−	0.991819i	0.902698	−	0.221778i
$21$		0			0
$22$	0.227697	+	1.88114i	0.0485451	+	0.401061i
$23$	−5.54952	−	3.20402i	−1.15716	−	0.668084i	−0.206535	−	0.978439i	$-0.566219\pi$
$23$	−5.54952	−	3.20402i	−1.15716	−	0.668084i	−0.950621	+	0.310355i	$0.899552\pi$
$24$		0			0
$25$	0.339877	+	0.588684i	0.0679754	+	0.117737i
$26$	3.25737	+	1.38928i	0.638824	+	0.272460i
$27$		0			0
$28$	−5.09758	+	1.41939i	−0.963352	+	0.268240i
$29$		−	4.66151i		−	0.865621i	−0.901485	−	0.432811i	$-0.857522\pi$
$29$		−	4.66151i		−	0.865621i	0.901485	−	0.432811i	$-0.142478\pi$
$30$		0			0
$31$	−2.21897	−	3.84337i	−0.398539	−	0.690290i	0.595007	−	0.803721i	$-0.297149\pi$
$31$	−2.21897	−	3.84337i	−0.398539	−	0.690290i	−0.993546	+	0.113430i	$0.963816\pi$
$32$	−2.43462	+	5.10613i	−0.430385	+	0.902646i
$33$		0			0
$34$	4.51026	−	0.545930i	0.773503	−	0.0936262i
$35$	2.89430	+	4.67598i	0.489226	+	0.790384i
$36$		0			0
$37$	−5.50178	−	3.17646i	−0.904488	−	0.522206i	−0.0258343	−	0.999666i	$-0.508224\pi$
$37$	−5.50178	−	3.17646i	−0.904488	−	0.522206i	−0.878653	+	0.477460i	$0.841558\pi$
$38$	3.48518	+	4.64155i	0.565370	+	0.752959i
$39$		0			0
$40$	5.80175	+	0.949572i	0.917337	+	0.150141i
$41$		−	5.55076i		−	0.866882i	−0.901182	−	0.433441i	$-0.857299\pi$
$41$		−	5.55076i		−	0.866882i	0.901182	−	0.433441i	$-0.142701\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$	−0.747483	+	2.57339i	−0.112687	+	0.387954i
$45$		0			0
$46$	−5.44141	−	7.24685i	−0.802292	−	1.06849i
$47$	−0.565988	+	0.980320i	−0.0825579	+	0.142994i	−0.904348	−	0.426796i	$-0.859642\pi$
$47$	−0.565988	+	0.980320i	−0.0825579	+	0.142994i	0.821790	+	0.569790i	$0.192976\pi$
$48$		0			0
$49$	−3.86485	−	5.83634i	−0.552122	−	0.833763i
$50$	0.115516	+	0.954351i	0.0163365	+	0.134966i
$51$		0			0
$52$	3.46653	+	3.61446i	0.480722	+	0.501236i
$53$	−7.43567	+	4.29299i	−1.02137	+	0.589687i	−0.914500	−	0.404586i	$-0.867416\pi$
$53$	−7.43567	+	4.29299i	−1.02137	+	0.589687i	−0.106868	+	0.994273i	$0.534082\pi$
$54$		0			0
$55$	2.78496			0.375524
$56$	−7.41863	−	0.981797i	−0.991356	−	0.131198i
$57$		0			0
$58$	2.58626	−	6.06388i	0.339593	−	0.796227i
$59$	−6.29193	+	3.63265i	−0.819140	+	0.472931i	−0.850120	−	0.526589i	$-0.823471\pi$
$59$	−6.29193	+	3.63265i	−0.819140	+	0.472931i	0.0309798	+	0.999520i	$0.490137\pi$
$60$		0			0
$61$	−2.57219	+	4.45517i	−0.329336	+	0.570426i	−0.982380	−	0.186893i	$-0.940158\pi$
$61$	−2.57219	+	4.45517i	−0.329336	+	0.570426i	0.653045	+	0.757319i	$0.273491\pi$
$62$	−0.754178	−	6.23073i	−0.0957807	−	0.791303i
$63$		0			0
$64$	−6.00000	+	5.29150i	−0.750000	+	0.661438i
$65$	2.60236	−	4.50743i	0.322784	−	0.559078i
$66$		0			0
$67$	3.93243	+	6.81116i	0.480422	+	0.832116i	0.999748	−	0.0224607i	$-0.00715005\pi$
$67$	3.93243	+	6.81116i	0.480422	+	0.832116i	−0.519325	+	0.854577i	$0.673817\pi$
$68$	6.17001	+	1.79218i	0.748224	+	0.217334i
$69$		0			0
$70$	1.17073	+	7.68849i	0.139929	+	0.918950i
$71$		−	5.29150i		−	0.627986i	−0.949425	−	0.313993i	$-0.898333\pi$
$71$		−	5.29150i		−	0.627986i	0.949425	−	0.313993i	$-0.101667\pi$
$72$		0			0
$73$	0.480369	−	0.277341i	0.0562230	−	0.0324604i	−0.471625	−	0.881799i	$-0.656332\pi$
$73$	0.480369	−	0.277341i	0.0562230	−	0.0324604i	0.527848	+	0.849339i	$0.322999\pi$
$74$	−5.39460	−	7.18452i	−0.627110	−	0.835183i
$75$		0			0
$76$	1.95847	+	7.97153i	0.224652	+	0.914397i
$77$	−3.54332	+	0.108651i	−0.403798	+	0.0123820i
$78$		0			0
$79$	−5.26862	−	3.04184i	−0.592766	−	0.342233i	0.173425	−	0.984847i	$-0.444517\pi$
$79$	−5.26862	−	3.04184i	−0.592766	−	0.342233i	−0.766190	+	0.642614i	$0.777850\pi$
$80$	7.02031	+	4.45412i	0.784894	+	0.497986i
$81$		0			0
$82$	3.07963	−	7.22064i	0.340088	−	0.797386i
$83$			0.503175i			0.0552307i	0.999619	+	0.0276153i	$0.00879135\pi$
$83$			0.503175i			0.0552307i	−0.999619	+	0.0276153i	$0.991209\pi$
$84$		0			0
$85$		−	6.67728i		−	0.724252i
$86$		0			0
$87$		0			0
$88$	−2.40011	+	2.93286i	−0.255852	+	0.312644i
$89$	−1.50000	−	0.866025i	−0.159000	−	0.0917985i	0.418389	−	0.908268i	$-0.362595\pi$
$89$	−1.50000	−	0.866025i	−0.159000	−	0.0917985i	−0.577389	+	0.816469i	$0.695928\pi$
$90$		0			0
$91$	−3.13515	+	5.83634i	−0.328653	+	0.611815i
$92$	−3.05776	−	12.4460i	−0.318793	−	1.29758i
$93$		0			0
$94$	−1.28015	+	0.961222i	−0.132038	+	0.0991425i
$95$	7.38794	−	4.26543i	0.757986	−	0.437624i
$96$		0			0
$97$		−	17.2234i		−	1.74878i	−0.485228	−	0.874388i	$-0.661263\pi$
$97$		−	17.2234i		−	1.74878i	0.485228	−	0.874388i	$-0.338737\pi$
$98$	−1.78948	−	9.73641i	−0.180765	−	0.983526i
$99$		0			0
$100$	−0.379217	+	1.30555i	−0.0379217	+	0.130555i
$101$	−0.613725	−	1.06300i	−0.0610679	−	0.105773i	0.833875	−	0.551953i	$-0.186117\pi$
$101$	−0.613725	−	1.06300i	−0.0610679	−	0.105773i	−0.894943	+	0.446180i	$0.852784\pi$
$102$		0			0
$103$	7.62804	−	13.2122i	0.751613	−	1.30183i	−0.195427	−	0.980718i	$-0.562609\pi$
$103$	7.62804	−	13.2122i	0.751613	−	1.30183i	0.947041	−	0.321114i	$-0.104057\pi$
$104$	2.50406	+	6.62511i	0.245543	+	0.649645i
$105$		0			0
$106$	−12.0544	+	1.45909i	−1.17083	+	0.141719i
$107$	5.55442	−	9.62054i	0.536966	−	0.930053i	−0.462099	−	0.886828i	$-0.652904\pi$
$107$	5.55442	−	9.62054i	0.536966	−	0.930053i	0.999065	−	0.0432246i	$-0.0137631\pi$
$108$		0			0
$109$	10.9109	−	6.29938i	1.04507	−	0.603372i	0.123805	−	0.992307i	$-0.460490\pi$
$109$	10.9109	−	6.29938i	1.04507	−	0.603372i	0.921265	+	0.388935i	$0.127157\pi$
$110$	3.62279	+	1.54513i	0.345419	+	0.147322i
$111$		0			0
$112$	−9.10573	−	5.39311i	−0.860411	−	0.509601i
$113$	−20.0629			−1.88736			−0.943680	−	0.330860i	$-0.892661\pi$
$113$	−20.0629			−1.88736			−0.943680	+	0.330860i	$0.892661\pi$
$114$		0			0
$115$	−11.5348	+	6.65961i	−1.07562	+	0.621012i
$116$	6.72863	−	6.45325i	0.624737	−	0.599169i
$117$		0			0
$118$	−10.2002	+	1.23465i	−0.939008	+	0.113659i
$119$	0.260504	+	8.49552i	0.0238804	+	0.778783i
$120$		0			0
$121$	4.60236	−	7.97153i	0.418397	−	0.724685i
$122$	−5.81779	+	4.36838i	−0.526718	+	0.395494i
$123$		0			0
$124$	2.47582	−	8.52360i	0.222335	−	0.765442i
$125$	11.8055			1.05591
$126$		0			0
$127$			14.6145i			1.29683i	0.761287	+	0.648415i	$0.224568\pi$
$127$			14.6145i			1.29683i	−0.761287	+	0.648415i	$0.775432\pi$
$128$	−10.7408	+	3.55452i	−0.949364	+	0.314178i
$129$		0			0
$130$	5.88603	−	4.41962i	0.516239	−	0.387626i
$131$	5.27230	+	3.04397i	0.460643	+	0.265953i	0.712315	−	0.701860i	$-0.247647\pi$
$131$	5.27230	+	3.04397i	0.460643	+	0.265953i	−0.251671	+	0.967813i	$0.580980\pi$
$132$		0			0
$133$	−9.23329	+	5.71515i	−0.800628	+	0.495566i
$134$	1.33654	+	11.0420i	0.115460	+	0.953882i
$135$		0			0
$136$	7.03188	+	5.75454i	0.602978	+	0.493448i
$137$	6.98685	+	12.1016i	0.596927	+	1.03391i	0.993272	+	0.115806i	$0.0369451\pi$
$137$	6.98685	+	12.1016i	0.596927	+	1.03391i	−0.396345	+	0.918102i	$0.629722\pi$
$138$		0			0
$139$			0.503175i			0.0426788i	0.999772	+	0.0213394i	$0.00679305\pi$
$139$			0.503175i			0.0426788i	−0.999772	+	0.0213394i	$0.993207\pi$
$140$	−2.74273	+	10.6510i	−0.231803	+	0.900176i
$141$		0			0
$142$	2.93579	−	6.88340i	0.246366	−	0.577642i
$143$	1.67756	+	2.90562i	0.140285	+	0.242981i
$144$		0			0
$145$	−8.39096	−	4.84452i	−0.696832	−	0.402316i
$146$	0.778756	−	0.0942619i	0.0644503	−	0.00780117i
$147$		0			0
$148$	−3.03146	−	12.3389i	−0.249184	−	1.01425i
$149$	4.77077	+	2.75440i	0.390836	+	0.225649i	0.682522	−	0.730865i	$-0.260883\pi$
$149$	4.77077	+	2.75440i	0.390836	+	0.225649i	−0.291686	+	0.956514i	$0.594216\pi$
$150$		0			0
$151$	−6.09511	+	3.51901i	−0.496013	+	0.286373i	−0.727066	−	0.686568i	$-0.759116\pi$
$151$	−6.09511	+	3.51901i	−0.496013	+	0.286373i	0.231053	+	0.972941i	$0.425783\pi$
$152$	−1.87505	+	11.4563i	−0.152086	+	0.929226i
$153$		0			0
$154$	−4.66957	−	1.82454i	−0.376284	−	0.147025i
$155$	−9.22436			−0.740918
$156$		0			0
$157$	7.15477	+	12.3924i	0.571013	+	0.989023i	0.996462	+	0.0840409i	$0.0267827\pi$
$157$	7.15477	+	12.3924i	0.571013	+	0.989023i	−0.425450	+	0.904982i	$0.639884\pi$
$158$	−5.16598	−	6.88003i	−0.410983	−	0.547346i
$159$		0			0
$160$	6.66110	+	9.68905i	0.526606	+	0.765987i
$161$	14.4159	−	8.92306i	1.13614	−	0.703236i
$162$		0			0
$163$	−4.15679	+	7.19977i	−0.325585	+	0.563929i	−0.981631	−	0.190792i	$-0.938894\pi$
$163$	−4.15679	+	7.19977i	−0.325585	+	0.563929i	0.656046	+	0.754721i	$0.272228\pi$
$164$	8.01220	−	7.68428i	0.625648	−	0.600042i
$165$		0			0
$166$	−0.279168	+	0.654550i	−0.0216676	+	0.0508030i
$167$	−2.50406			−0.193770			−0.0968848	−	0.995296i	$-0.530888\pi$
$167$	−2.50406			−0.193770			−0.0968848	+	0.995296i	$0.530888\pi$
$168$		0			0
$169$	−6.72971			−0.517670
$170$	3.70463	−	8.68606i	0.284132	−	0.666191i
$171$		0			0
$172$		0			0
$173$	2.71682	−	4.70568i	0.206556	−	0.357766i	−0.744071	−	0.668100i	$-0.767108\pi$
$173$	2.71682	−	4.70568i	0.206556	−	0.357766i	0.950627	+	0.310334i	$0.100441\pi$
$174$		0			0
$175$	−1.79761	+	0.0551216i	−0.135887	+	0.00416680i
$176$	−4.74934	+	2.48357i	−0.357995	+	0.187206i
$177$		0			0
$178$	−1.47078	−	1.95878i	−0.110239	−	0.146817i
$179$	1.75915	+	3.04694i	0.131485	+	0.227739i	0.924249	−	0.381790i	$-0.124692\pi$
$179$	1.75915	+	3.04694i	0.131485	+	0.227739i	−0.792764	+	0.609529i	$0.791359\pi$
$180$		0			0
$181$	22.1981			1.64997			0.824985	−	0.565154i	$-0.191183\pi$
$181$	22.1981			1.64997			0.824985	+	0.565154i	$0.191183\pi$
$182$	−7.31640	+	5.85273i	−0.542327	+	0.433833i
$183$		0			0
$184$	2.92751	−	17.8867i	0.215819	−	1.31862i
$185$	−11.4356	+	6.60233i	−0.840760	+	0.485413i
$186$		0			0
$187$	3.72770	+	2.15219i	0.272596	+	0.157383i
$188$	−2.19857	+	0.540152i	−0.160347	+	0.0393946i
$189$		0			0
$190$	11.9770	−	1.44972i	0.868905	−	0.105174i
$191$	−1.13615	−	0.655958i	−0.0822091	−	0.0474635i	0.458332	−	0.888781i	$-0.348447\pi$
$191$	−1.13615	−	0.655958i	−0.0822091	−	0.0474635i	−0.540541	+	0.841318i	$0.681780\pi$
$192$		0			0
$193$	5.64697	+	9.78084i	0.406478	+	0.704040i	0.994492	−	0.104810i	$-0.0334235\pi$
$193$	5.64697	+	9.78084i	0.406478	+	0.704040i	−0.588014	+	0.808851i	$0.700090\pi$
$194$	9.55577	−	22.4049i	0.686065	−	1.60858i
$195$		0			0
$196$	3.07405	−	13.6583i	0.219575	−	0.975596i
$197$			5.92149i			0.421889i	0.977498	+	0.210944i	$0.0676539\pi$
$197$			5.92149i			0.421889i	−0.977498	+	0.210944i	$0.932346\pi$
$198$		0			0
$199$	9.30560	+	16.1178i	0.659657	+	1.14256i	0.980704	+	0.195496i	$0.0626317\pi$
$199$	9.30560	+	16.1178i	0.659657	+	1.14256i	−0.321048	+	0.947063i	$0.604035\pi$
$200$	−1.21763	+	1.48791i	−0.0860998	+	0.105211i
$201$		0			0
$202$	−0.208591	−	1.72330i	−0.0146764	−	0.121251i
$203$	10.8649	+	5.83634i	0.762563	+	0.409631i
$204$		0			0
$205$	−9.99164	−	5.76868i	−0.697847	−	0.402902i
$206$	17.2531	−	12.9548i	1.20208	−	0.902601i
$207$		0			0
$208$	−0.418315	+	10.0075i	−0.0290050	+	0.693894i
$209$			5.49925i			0.380391i
$210$		0			0
$211$	5.72971			0.394449			0.197225	−	0.980358i	$-0.436807\pi$
$211$	5.72971			0.394449			0.197225	+	0.980358i	$0.436807\pi$
$212$	−16.4904	−	4.78990i	−1.13256	−	0.328972i
$213$		0			0
$214$	12.5630	−	9.43312i	0.858789	−	0.644835i
$215$		0			0
$216$		0			0
$217$	11.7362	−	0.359875i	0.796704	−	0.0244299i
$218$	17.6882	−	2.14101i	1.19800	−	0.145008i
$219$		0			0
$220$	3.85541	+	4.01993i	0.259932	+	0.271024i
$221$	6.96658	−	4.02216i	0.468623	−	0.270560i
$222$		0			0
$223$	−20.8668			−1.39734			−0.698672	−	0.715442i	$-0.746225\pi$
$223$	−20.8668			−1.39734			−0.698672	+	0.715442i	$0.746225\pi$
$224$	−8.85294	−	12.0675i	−0.591512	−	0.806296i
$225$		0			0
$226$	−26.0986	−	11.1311i	−1.73605	−	0.740433i
$227$	−14.2775	+	8.24309i	−0.947628	+	0.547113i	−0.892343	−	0.451357i	$-0.850940\pi$
$227$	−14.2775	+	8.24309i	−0.947628	+	0.547113i	−0.0552847	+	0.998471i	$0.517607\pi$
$228$		0			0
$229$	−4.24976	+	7.36079i	−0.280832	+	0.486415i	−0.971590	−	0.236671i	$-0.923944\pi$
$229$	−4.24976	+	7.36079i	−0.280832	+	0.486415i	0.690758	+	0.723086i	$0.257277\pi$
$230$	−18.6997	+	2.26345i	−1.23302	+	0.149247i
$231$		0			0
$232$	12.3332	−	4.66151i	0.809715	−	0.306043i
$233$	2.23751	−	3.87548i	0.146584	−	0.253891i	−0.783379	−	0.621545i	$-0.786505\pi$
$233$	2.23751	−	3.87548i	0.146584	−	0.253891i	0.929963	+	0.367653i	$0.119839\pi$
$234$		0			0
$235$	1.17642	+	2.03762i	0.0767410	+	0.132919i
$236$	−13.9539	−	4.05313i	−0.908320	−	0.263836i
$237$		0			0
$238$	−4.37454	+	11.1958i	−0.283559	+	0.725718i
$239$			24.5675i			1.58914i	0.607171	+	0.794571i	$0.292304\pi$
$239$			24.5675i			1.58914i	−0.607171	+	0.794571i	$0.707696\pi$
$240$		0			0
$241$	−5.02498	+	2.90117i	−0.323687	+	0.186881i	−0.653035	−	0.757328i	$-0.726505\pi$
$241$	−5.02498	+	2.90117i	−0.323687	+	0.186881i	0.329348	+	0.944209i	$0.393171\pi$
$242$	10.4096	−	7.81623i	0.669157	−	0.502447i
$243$		0			0
$244$	−9.99164	+	2.45478i	−0.639649	+	0.157151i
$245$	−14.5223	+	0.891454i	−0.927796	+	0.0569529i
$246$		0			0
$247$	8.90047	+	5.13869i	0.566323	+	0.326967i
$248$	7.94964	−	9.71422i	0.504803	−	0.616854i
$249$		0			0
$250$	15.3570	+	6.54982i	0.971264	+	0.414247i
$251$		−	18.8010i		−	1.18671i	−0.804942	−	0.593353i	$-0.797804\pi$
$251$		−	18.8010i		−	1.18671i	0.804942	−	0.593353i	$-0.202196\pi$
$252$		0			0
$253$		−	8.58598i		−	0.539796i
$254$	−8.10832	+	19.0112i	−0.508761	+	1.19287i
$255$		0			0
$256$	−15.9442	−	1.33528i	−0.996512	−	0.0834547i
$257$	−10.9106	−	6.29923i	−0.680584	−	0.392935i	0.119491	−	0.992835i	$-0.461874\pi$
$257$	−10.9106	−	6.29923i	−0.680584	−	0.392935i	−0.800075	+	0.599900i	$0.795207\pi$
$258$		0			0
$259$	14.2919	−	8.84631i	0.888058	−	0.549683i
$260$	10.1088	−	2.48357i	0.626924	−	0.154024i
$261$		0			0
$262$	5.16959	+	6.88485i	0.319378	+	0.425347i
$263$	−4.27292	+	2.46697i	−0.263479	+	0.152120i	−0.625921	−	0.779887i	$-0.715277\pi$
$263$	−4.27292	+	2.46697i	−0.263479	+	0.152120i	0.362441	+	0.932007i	$0.381943\pi$
$264$		0			0
$265$			17.8461i			1.09628i
$266$	−15.1819	+	2.31175i	−0.930860	+	0.141743i
$267$		0			0
$268$	−4.38760	+	15.1054i	−0.268015	+	0.922708i
$269$	13.1502	+	22.7769i	0.801783	+	1.38873i	0.918441	+	0.395558i	$0.129449\pi$
$269$	13.1502	+	22.7769i	0.801783	+	1.38873i	−0.116658	+	0.993172i	$0.537218\pi$
$270$		0			0
$271$	14.0490	−	24.3336i	0.853418	−	1.47816i	−0.0246868	−	0.999695i	$-0.507859\pi$
$271$	14.0490	−	24.3336i	0.853418	−	1.47816i	0.878105	−	0.478468i	$-0.158808\pi$
$272$	5.95465	+	11.3871i	0.361054	+	0.690444i
$273$		0			0
$274$	2.37467	+	19.6186i	0.143459	+	1.18520i
$275$	−0.455393	+	0.788764i	−0.0274612	+	0.0475643i
$276$		0			0
$277$	−23.3982	+	13.5090i	−1.40586	+	0.811675i	−0.994986	−	0.100017i	$-0.968110\pi$
$277$	−23.3982	+	13.5090i	−1.40586	+	0.811675i	−0.410876	+	0.911691i	$0.634777\pi$
$278$	−0.279168	+	0.654550i	−0.0167434	+	0.0392573i
$279$		0			0
$280$	−9.47717	+	12.3336i	−0.566369	+	0.737072i
$281$	20.0629			1.19685			0.598426	−	0.801178i	$-0.295793\pi$
$281$	20.0629			1.19685			0.598426	+	0.801178i	$0.295793\pi$
$282$		0			0
$283$	−4.75248	+	2.74385i	−0.282506	+	0.163105i	−0.634557	−	0.772876i	$-0.718817\pi$
$283$	−4.75248	+	2.74385i	−0.282506	+	0.163105i	0.352052	+	0.935981i	$0.385484\pi$
$284$	7.63798	−	7.32538i	0.453231	−	0.434681i
$285$		0			0
$286$	0.570165	+	4.71048i	0.0337146	+	0.278537i
$287$	12.9375	+	6.94970i	0.763674	+	0.410228i
$288$		0			0
$289$	−3.33988	+	5.78484i	−0.196463	+	0.340284i
$290$	−8.22750	−	10.9574i	−0.483135	−	0.643438i
$291$		0			0
$292$	1.06533	+	0.309443i	0.0623440	+	0.0181088i
$293$	−13.6931			−0.799957			−0.399978	−	0.916525i	$-0.630982\pi$
$293$	−13.6931			−0.799957			−0.399978	+	0.916525i	$0.630982\pi$
$294$		0			0
$295$			15.1011i			0.879218i
$296$	2.90233	−	17.7328i	0.168695	−	1.03070i
$297$		0			0
$298$	4.67782	+	6.22991i	0.270979	+	0.360889i
$299$	−13.8963	−	8.02304i	−0.803644	−	0.463984i
$300$		0			0
$301$		0			0
$302$	−9.88115	+	1.19603i	−0.568596	+	0.0688238i
$303$		0			0
$304$	−8.79521	+	13.8625i	−0.504440	+	0.795067i
$305$	5.34636	+	9.26016i	0.306131	+	0.530235i
$306$		0			0
$307$		−	24.4197i		−	1.39371i	−0.717213	−	0.696854i	$-0.754583\pi$
$307$		−	24.4197i		−	1.39371i	0.717213	−	0.696854i	$-0.245417\pi$
$308$	−5.06208	−	4.96416i	−0.288439	−	0.282859i
$309$		0			0
$310$	−11.9994	−	5.11779i	−0.681521	−	0.290671i
$311$	−8.61539	−	14.9223i	−0.488534	−	0.846165i	0.511379	−	0.859355i	$-0.329135\pi$
$311$	−8.61539	−	14.9223i	−0.488534	−	0.846165i	−0.999913	+	0.0131898i	$0.995801\pi$
$312$		0			0
$313$	15.0446	+	8.68601i	0.850371	+	0.490962i	0.860776	−	0.508984i	$-0.169979\pi$
$313$	15.0446	+	8.68601i	0.850371	+	0.490962i	−0.0104047	+	0.999946i	$0.503312\pi$
$314$	2.43174	+	20.0901i	0.137231	+	1.13375i
$315$		0			0
$316$	−2.90298	−	11.8160i	−0.163305	−	0.664700i
$317$	16.7863	+	9.69155i	0.942810	+	0.544332i	0.890840	−	0.454317i	$-0.150117\pi$
$317$	16.7863	+	9.69155i	0.942810	+	0.544332i	0.0519701	+	0.998649i	$0.483450\pi$
$318$		0			0
$319$	5.40907	−	3.12293i	0.302850	−	0.174850i
$320$	3.28942	+	16.2996i	0.183884	+	0.911173i
$321$		0			0
$322$	23.7034	−	3.60934i	1.32094	−	0.201141i
$323$	13.1851			0.733639
$324$		0			0
$325$	0.851071	+	1.47410i	0.0472089	+	0.0817682i
$326$	−9.40183	+	7.05951i	−0.520719	+	0.390990i
$327$		0			0
$328$	14.6859	−	5.55076i	0.810894	−	0.306489i
$329$	−1.57625	−	2.54657i	−0.0869018	−	0.140397i
$330$		0			0
$331$	10.4008	−	18.0147i	0.571678	−	0.990176i	−0.424715	−	0.905327i	$-0.639626\pi$
$331$	10.4008	−	18.0147i	0.571678	−	0.990176i	0.996394	−	0.0848492i	$-0.0270409\pi$
$332$	−0.726305	+	0.696579i	−0.0398612	+	0.0382298i
$333$		0			0
$334$	−3.25737	−	1.38928i	−0.178236	−	0.0760180i
$335$	16.3473			0.893146
$336$		0			0
$337$	10.3332			0.562886			0.281443	−	0.959578i	$-0.409187\pi$
$337$	10.3332			0.562886			0.281443	+	0.959578i	$0.409187\pi$
$338$	−8.75427	−	3.73372i	−0.476169	−	0.203088i
$339$		0			0
$340$	9.63827	−	9.24380i	0.522708	−	0.501315i
$341$	2.97315	−	5.14965i	0.161005	−	0.278869i
$342$		0			0
$343$	18.4420	−	1.70077i	0.995774	−	0.0918328i
$344$		0			0
$345$		0			0
$346$	6.14492	−	4.61400i	0.330353	−	0.248050i
$347$	16.8169	+	29.1277i	0.902779	+	1.56366i	0.823871	+	0.566777i	$0.191810\pi$
$347$	16.8169	+	29.1277i	0.902779	+	1.56366i	0.0789080	+	0.996882i	$0.474857\pi$
$348$		0			0
$349$	13.3546			0.714858			0.357429	−	0.933940i	$-0.383653\pi$
$349$	13.3546			0.714858			0.357429	+	0.933940i	$0.383653\pi$
$350$	−2.36899	−	0.925634i	−0.126628	−	0.0494772i
$351$		0			0
$352$	−7.55604	+	0.595737i	−0.402738	+	0.0317529i
$353$	−6.80175	+	3.92699i	−0.362021	+	0.209013i	−0.669967	−	0.742391i	$-0.733692\pi$
$353$	−6.80175	+	3.92699i	−0.362021	+	0.209013i	0.307946	+	0.951404i	$0.400358\pi$
$354$		0			0
$355$	−9.52498	−	5.49925i	−0.505533	−	0.291870i
$356$	−0.826492	−	3.36406i	−0.0438040	−	0.178295i
$357$		0			0
$358$	0.597895	+	4.93958i	0.0315997	+	0.261065i
$359$	−0.140453	−	0.0810905i	−0.00741282	−	0.00427979i	0.496289	−	0.868157i	$-0.334696\pi$
$359$	−0.140453	−	0.0810905i	−0.00741282	−	0.00427979i	−0.503702	+	0.863878i	$0.668029\pi$
$360$		0			0
$361$	−1.07739	−	1.86609i	−0.0567047	−	0.0982154i
$362$	28.8761	+	12.3158i	1.51770	+	0.647302i
$363$		0			0
$364$	−12.7646	+	3.55424i	−0.669048	+	0.186293i
$365$		−	1.15292i		−	0.0603466i
$366$		0			0
$367$	−10.1321	−	17.5493i	−0.528891	−	0.916066i	−0.999432	−	0.0336883i	$-0.989275\pi$
$367$	−10.1321	−	17.5493i	−0.528891	−	0.916066i	0.470541	−	0.882378i	$-0.344059\pi$
$368$	13.7320	−	21.6435i	0.715828	−	1.12824i
$369$		0			0
$370$	−18.5389	+	2.24398i	−0.963791	+	0.116659i
$371$	−0.696241	−	22.7057i	−0.0361470	−	1.17882i
$372$		0			0
$373$	5.78269	+	3.33864i	0.299416	+	0.172868i	0.642181	−	0.766553i	$-0.278030\pi$
$373$	5.78269	+	3.33864i	0.299416	+	0.172868i	−0.342764	+	0.939421i	$0.611363\pi$
$374$	3.65508	+	4.86782i	0.188999	+	0.251709i
$375$		0			0
$376$	−3.15967	−	0.517144i	−0.162948	−	0.0266696i
$377$		−	11.6727i		−	0.601174i
$378$		0			0
$379$	−4.60350			−0.236466			−0.118233	−	0.992986i	$-0.537723\pi$
$379$	−4.60350			−0.236466			−0.118233	+	0.992986i	$0.537723\pi$
$380$	16.3845	+	4.75915i	0.840508	+	0.244139i
$381$		0			0
$382$	−1.11402	−	1.48365i	−0.0569982	−	0.0759100i
$383$	5.71038	−	9.89066i	0.291787	−	0.505389i	−0.682446	−	0.730936i	$-0.739084\pi$
$383$	5.71038	−	9.89066i	0.291787	−	0.505389i	0.974232	+	0.225547i	$0.0724170\pi$
$384$		0			0
$385$	−3.48685	+	6.49107i	−0.177706	+	0.330815i
$386$	1.91928	+	15.8563i	0.0976885	+	0.807065i
$387$		0			0
$388$	24.8611	−	23.8436i	1.26213	−	1.21047i
$389$	−26.0307	+	15.0288i	−1.31981	+	0.761991i	−0.983697	−	0.179832i	$-0.942445\pi$
$389$	−26.0307	+	15.0288i	−1.31981	+	0.761991i	−0.336109	+	0.941823i	$0.609111\pi$
$390$		0			0
$391$	−20.5859			−1.04107
$392$	11.5767	−	16.0618i	0.584710	−	0.811243i
$393$		0			0
$394$	−3.28532	+	7.70291i	−0.165512	+	0.388067i
$395$	−10.9509	+	6.32252i	−0.551001	+	0.318120i
$396$		0			0
$397$	2.17124	−	3.76069i	0.108971	−	0.188744i	−0.806383	−	0.591394i	$-0.798578\pi$
$397$	2.17124	−	3.76069i	0.108971	−	0.188744i	0.915354	+	0.402651i	$0.131911\pi$
$398$	3.16276	+	26.1295i	0.158535	+	1.30975i
$399$		0			0
$400$	−2.40946	+	1.25998i	−0.120473	+	0.0629989i
$401$	−9.98685	+	17.2977i	−0.498719	+	0.863807i	−0.999999	−	0.00147805i	$-0.999530\pi$
$401$	−9.98685	+	17.2977i	−0.498719	+	0.863807i	0.501279	+	0.865285i	$0.332863\pi$
$402$		0			0
$403$	−5.55643	−	9.62402i	−0.276786	−	0.479407i
$404$	0.684763	−	2.35746i	0.0340682	−	0.117288i
$405$		0			0
$406$	10.8954	+	13.6201i	0.540727	+	0.675954i
$407$		−	8.51212i		−	0.421930i
$408$		0			0
$409$	−26.4356	+	15.2626i	−1.30715	+	0.754686i	−0.981620	−	0.190844i	$-0.938878\pi$
$409$	−26.4356	+	15.2626i	−1.30715	+	0.754686i	−0.325534	+	0.945530i	$0.605544\pi$
$410$	−9.79699	−	13.0476i	−0.483839	−	0.644376i
$411$		0			0
$412$	29.6310	−	7.27983i	1.45981	−	0.358652i
$413$	−0.589147	−	19.2131i	−0.0289900	−	0.945417i
$414$		0			0
$415$	0.905741	+	0.522930i	0.0444611	+	0.0256696i
$416$	−6.09643	+	12.7860i	−0.298902	+	0.626887i
$417$		0			0
$418$	−3.05105	+	7.15364i	−0.149232	+	0.349896i
$419$			2.08070i			0.101649i	0.998708	+	0.0508245i	$0.0161849\pi$
$419$			2.08070i			0.101649i	−0.998708	+	0.0508245i	$0.983815\pi$
$420$		0			0
$421$		−	30.4039i		−	1.48180i	−0.671618	−	0.740898i	$-0.734400\pi$
$421$		−	30.4039i		−	1.48180i	0.671618	−	0.740898i	$-0.265600\pi$
$422$	7.45343	+	3.17891i	0.362827	+	0.154747i
$423$		0			0
$424$	−18.7939	−	15.3800i	−0.912710	−	0.746917i
$425$	1.89116	+	1.09186i	0.0917345	+	0.0529630i
$426$		0			0
$427$	−7.16346	−	11.5732i	−0.346664	−	0.560064i
$428$	21.5761	−	5.30087i	1.04292	−	0.256227i
$429$		0			0
$430$		0			0
$431$	2.32280	−	1.34107i	0.111885	−	0.0645970i	−0.443013	−	0.896515i	$-0.646090\pi$
$431$	2.32280	−	1.34107i	0.111885	−	0.0645970i	0.554898	+	0.831918i	$0.312757\pi$
$432$		0			0
$433$			29.4673i			1.41611i	0.706158	+	0.708054i	$0.250427\pi$
$433$			29.4673i			1.41611i	−0.706158	+	0.708054i	$0.749573\pi$
$434$	15.4666	+	6.04324i	0.742419	+	0.290085i
$435$		0			0
$436$	24.1974	+	7.02853i	1.15885	+	0.336606i
$437$	−13.1502	−	22.7769i	−0.629061	−	1.08957i
$438$		0			0
$439$	3.77648	−	6.54106i	0.180242	−	0.312188i	−0.761721	−	0.647905i	$-0.775645\pi$
$439$	3.77648	−	6.54106i	0.180242	−	0.312188i	0.941963	+	0.335717i	$0.108979\pi$
$440$	2.78496	+	7.36831i	0.132768	+	0.351271i
$441$		0			0
$442$	11.2939	−	1.36704i	0.537198	−	0.0650234i
$443$	−3.75915	+	6.51104i	−0.178603	+	0.309349i	−0.941402	−	0.337286i	$-0.890491\pi$
$443$	−3.75915	+	6.51104i	−0.178603	+	0.309349i	0.762799	+	0.646635i	$0.223824\pi$
$444$		0			0
$445$	−3.11778	+	1.80005i	−0.147797	+	0.0853306i
$446$	−27.1444	−	11.5772i	−1.28532	−	0.548194i
$447$		0			0
$448$	−4.82104	−	20.6096i	−0.227773	−	0.973714i
$449$	14.3332			0.676426			0.338213	−	0.941070i	$-0.390178\pi$
$449$	14.3332			0.676426			0.338213	+	0.941070i	$0.390178\pi$
$450$		0			0
$451$	6.44092	−	3.71866i	0.303291	−	0.175105i
$452$	−27.7744	−	28.9597i	−1.30640	−	1.36215i
$453$		0			0
$454$	−23.1460	+	2.80164i	−1.08630	+	0.131487i
$455$	7.24749	+	11.7089i	0.339767	+	0.548922i
$456$		0			0
$457$	−6.48037	+	11.2243i	−0.303139	+	0.525052i	−0.976845	−	0.213947i	$-0.931368\pi$
$457$	−6.48037	+	11.2243i	−0.303139	+	0.525052i	0.673706	+	0.738999i	$0.264701\pi$
$458$	−9.61211	+	7.21740i	−0.449144	+	0.337247i
$459$		0			0
$460$	−25.5812	−	7.43046i	−1.19273	−	0.346447i
$461$	33.3871			1.55499			0.777496	−	0.628888i	$-0.216490\pi$
$461$	33.3871			1.55499			0.777496	+	0.628888i	$0.216490\pi$
$462$		0			0
$463$			29.7739i			1.38371i	0.722036	+	0.691855i	$0.243206\pi$
$463$			29.7739i			1.38371i	−0.722036	+	0.691855i	$0.756794\pi$
$464$	18.6298	+	0.778730i	0.864866	+	0.0361516i
$465$		0			0
$466$	5.06081	−	3.79998i	0.234437	−	0.176031i
$467$	−23.5399	−	13.5908i	−1.08930	−	0.628907i	−0.155909	−	0.987771i	$-0.549831\pi$
$467$	−23.5399	−	13.5908i	−1.08930	−	0.628907i	−0.933390	+	0.358865i	$0.883164\pi$
$468$		0			0
$469$	−20.7987	+	0.637765i	−0.960393	+	0.0294492i
$470$	0.399837	+	3.30330i	0.0184431	+	0.152370i
$471$		0			0
$472$	−15.9030	−	13.0142i	−0.731996	−	0.599029i
$473$		0			0
$474$		0			0
$475$			2.78991i			0.128010i
$476$	−11.9022	+	12.1369i	−0.545535	+	0.556296i
$477$		0			0
$478$	−13.6304	+	31.9584i	−0.623439	+	1.46174i
$479$	−17.2187	−	29.8237i	−0.786744	−	1.36268i	−0.927952	−	0.372700i	$-0.878432\pi$
$479$	−17.2187	−	29.8237i	−0.786744	−	1.36268i	0.141208	−	0.989980i	$-0.454901\pi$
$480$		0			0
$481$	−13.7768	−	7.95402i	−0.628167	−	0.362672i
$482$	−8.14629	+	0.986041i	−0.371053	+	0.0449129i
$483$		0			0
$484$	17.8778	−	4.39227i	0.812628	−	0.199649i
$485$	−31.0031	−	17.8996i	−1.40778	−	0.812781i
$486$		0			0
$487$	6.82613	−	3.94107i	0.309321	−	0.178587i	−0.337301	−	0.941397i	$-0.609514\pi$
$487$	6.82613	−	3.94107i	0.309321	−	0.178587i	0.646623	+	0.762810i	$0.276181\pi$
$488$	−14.3595	−	2.35021i	−0.650022	−	0.106389i
$489$		0			0
$490$	−19.3858	−	6.89751i	−0.875760	−	0.311598i
$491$	8.06291			0.363874			0.181937	−	0.983310i	$-0.441763\pi$
$491$	8.06291			0.363874			0.181937	+	0.983310i	$0.441763\pi$
$492$		0			0
$493$	−7.48759	−	12.9689i	−0.337224	−	0.584089i
$494$	8.72708	+	11.6227i	0.392650	+	0.522930i
$495$		0			0
$496$	15.7308	−	8.22609i	0.706333	−	0.369362i
$497$	12.3332	+	6.62511i	0.553220	+	0.297177i
$498$		0			0
$499$	12.0216	−	20.8221i	0.538163	−	0.932125i	−0.460841	−	0.887483i	$-0.652452\pi$
$499$	12.0216	−	20.8221i	0.538163	−	0.932125i	0.999003	−	0.0446419i	$-0.0142147\pi$
$500$	16.3431	+	17.0405i	0.730887	+	0.762076i
$501$		0			0
$502$	10.4310	−	24.4570i	0.465559	−	1.09157i
$503$	−40.8993			−1.82361			−0.911804	−	0.410626i	$-0.865310\pi$
$503$	−40.8993			−1.82361			−0.911804	+	0.410626i	$0.865310\pi$
$504$		0			0
$505$	−2.55128			−0.113530
$506$	4.76360	−	11.1690i	0.211768	−	0.496522i
$507$		0			0
$508$	−21.0952	+	20.2319i	−0.935950	+	0.897644i
$509$	−2.02661	+	3.51019i	−0.0898278	+	0.155586i	−0.907438	−	0.420186i	$-0.861965\pi$
$509$	−2.02661	+	3.51019i	−0.0898278	+	0.155586i	0.817610	+	0.575772i	$0.195298\pi$
$510$		0			0
$511$	0.0449795	+	1.46686i	0.00198978	+	0.0648902i
$512$	−20.0000	−	10.5830i	−0.883883	−	0.467707i
$513$		0			0
$514$	−10.6980	−	14.2476i	−0.471870	−	0.628436i
$515$	−15.8550	−	27.4617i	−0.698656	−	1.21011i
$516$		0			0
$517$	−1.51671			−0.0667048
$518$	23.4996	−	3.57829i	1.03251	−	0.157221i
$519$		0			0
$520$	14.5279	+	2.37778i	0.637091	+	0.104273i
$521$	−27.1927	+	15.6997i	−1.19133	+	0.687817i	−0.958609	−	0.284725i	$-0.908098\pi$
$521$	−27.1927	+	15.6997i	−1.19133	+	0.687817i	−0.232725	+	0.972543i	$0.574764\pi$
$522$		0			0
$523$	−11.7132	−	6.76263i	−0.512183	−	0.295709i	0.221547	−	0.975150i	$-0.428889\pi$
$523$	−11.7132	−	6.76263i	−0.512183	−	0.295709i	−0.733731	+	0.679440i	$0.762223\pi$
$524$	2.90501	+	11.8242i	0.126906	+	0.516544i
$525$		0			0
$526$	−6.92708	+	0.838466i	−0.302035	+	0.0365588i
$527$	−12.3469	−	7.12848i	−0.537839	−	0.310522i
$528$		0			0
$529$	9.03146	+	15.6429i	0.392672	+	0.680128i
$530$	−9.90125	+	23.2149i	−0.430083	+	1.00839i
$531$		0			0
$532$	−21.0318	−	5.41586i	−0.911842	−	0.234807i
$533$		−	13.8994i		−	0.602050i
$534$		0			0
$535$	−11.5450	−	19.9965i	−0.499133	−	0.864524i
$536$	−14.0882	+	17.2154i	−0.608518	+	0.743591i
$537$		0			0
$538$	4.46946	+	36.9249i	0.192692	+	1.59195i
$539$	4.18309	−	8.39464i	0.180178	−	0.361583i
$540$		0			0
$541$	27.1543	+	15.6775i	1.16745	+	0.674030i	0.953079	−	0.302722i	$-0.0978953\pi$
$541$	27.1543	+	15.6775i	1.16745	+	0.674030i	0.214375	+	0.976751i	$0.431229\pi$
$542$	31.7761	−	23.8596i	1.36490	−	1.02486i
$543$		0			0
$544$	1.42835	+	18.1165i	0.0612400	+	0.776739i
$545$		−	26.1868i		−	1.12172i
$546$		0			0
$547$	−44.7293			−1.91249			−0.956244	−	0.292571i	$-0.905489\pi$
$547$	−44.7293			−1.91249			−0.956244	+	0.292571i	$0.905489\pi$
$548$	−7.79557	+	26.8381i	−0.333010	+	1.14647i
$549$		0			0
$550$	−1.03001	+	0.773398i	−0.0439197	+	0.0329778i
$551$	9.56611	−	16.5690i	0.407530	−	0.705863i
$552$		0			0
$553$	13.6862	−	8.47140i	0.581998	−	0.360240i
$554$	−37.9322	+	4.59138i	−1.61159	+	0.195069i
$555$		0			0
$556$	−0.726305	+	0.696579i	−0.0308022	+	0.0295415i
$557$	10.5345	−	6.08208i	0.446360	−	0.257706i	−0.259932	−	0.965627i	$-0.583700\pi$
$557$	10.5345	−	6.08208i	0.446360	−	0.257706i	0.706292	+	0.707921i	$0.250367\pi$
$558$		0			0
$559$		0			0
$560$	−19.1711	+	10.7859i	−0.810127	+	0.455790i
$561$		0			0
$562$	26.0986	+	11.1311i	1.10090	+	0.469539i
$563$	31.4311	−	18.1468i	1.32466	−	0.764794i	0.340194	−	0.940355i	$-0.389507\pi$
$563$	31.4311	−	18.1468i	1.32466	−	0.764794i	0.984469	+	0.175561i	$0.0561738\pi$
$564$		0			0
$565$	−20.8506	+	36.1143i	−0.877191	+	1.51934i
$566$	−7.70453	+	0.932570i	−0.323846	+	0.0391988i
$567$		0			0
$568$	14.0000	−	5.29150i	0.587427	−	0.222027i
$569$	6.01830	−	10.4240i	0.252300	−	0.436997i	−0.711858	−	0.702323i	$-0.752146\pi$
$569$	6.01830	−	10.4240i	0.252300	−	0.436997i	0.964159	+	0.265326i	$0.0854795\pi$
$570$		0			0
$571$	−4.10570	−	7.11128i	−0.171818	−	0.297598i	0.767237	−	0.641363i	$-0.221631\pi$
$571$	−4.10570	−	7.11128i	−0.171818	−	0.297598i	−0.939056	+	0.343765i	$0.888298\pi$
$572$	−1.87174	+	6.44392i	−0.0782614	+	0.269434i
$573$		0			0
$574$	12.9738	+	16.2183i	0.541515	+	0.676939i
$575$		−	4.35589i		−	0.181653i
$576$		0			0
$577$	14.5500	−	8.40042i	0.605722	−	0.349714i	−0.165567	−	0.986199i	$-0.552945\pi$
$577$	14.5500	−	8.40042i	0.605722	−	0.349714i	0.771289	+	0.636485i	$0.219612\pi$
$578$	−7.55414	+	5.67214i	−0.314211	+	0.235930i
$579$		0			0
$580$	−4.62338	−	18.8185i	−0.191975	−	0.781395i
$581$	−1.17278	−	0.629989i	−0.0486551	−	0.0261364i
$582$		0			0
$583$	−9.96289	−	5.75208i	−0.412621	−	0.238227i
$584$	1.21415	+	0.993596i	0.0502417	+	0.0411153i
$585$		0			0
$586$	−17.8125	−	7.59707i	−0.735826	−	0.313832i
$587$		−	25.4261i		−	1.04945i	−0.851273	−	0.524723i	$-0.824169\pi$
$587$		−	25.4261i		−	1.04945i	0.851273	−	0.524723i	$-0.175831\pi$
$588$		0			0
$589$		−	18.2146i		−	0.750521i
$590$	−8.37826	+	19.6441i	−0.344927	+	0.808734i
$591$		0			0
$592$	13.6138	−	21.4573i	0.559525	−	0.881889i
$593$	19.0694	+	11.0097i	0.783086	+	0.452115i	0.837523	−	0.546402i	$-0.184003\pi$
$593$	19.0694	+	11.0097i	0.783086	+	0.452115i	−0.0544368	+	0.998517i	$0.517336\pi$
$594$		0			0
$595$	15.5631	+	8.36013i	0.638025	+	0.342732i
$596$	2.62867	+	10.6994i	0.107674	+	0.438266i
$597$		0			0
$598$	−13.6256	−	18.1465i	−0.557192	−	0.742067i
$599$	−0.500607	+	0.289026i	−0.0204543	+	0.0118093i	−0.510192	−	0.860060i	$-0.670426\pi$
$599$	−0.500607	+	0.289026i	−0.0204543	+	0.0118093i	0.489738	+	0.871870i	$0.337092\pi$
$600$		0			0
$601$		−	27.3186i		−	1.11435i	−0.830395	−	0.557175i	$-0.811885\pi$
$601$		−	27.3186i		−	1.11435i	0.830395	−	0.557175i	$-0.188115\pi$
$602$		0			0
$603$		0			0
$604$	−13.5174	−	3.92634i	−0.550014	−	0.159760i
$605$	−9.56611	−	16.5690i	−0.388918	−	0.673625i
$606$		0			0
$607$	−5.99963	+	10.3917i	−0.243518	+	0.421785i	−0.961714	−	0.274056i	$-0.911635\pi$
$607$	−5.99963	+	10.3917i	−0.243518	+	0.421785i	0.718196	+	0.695841i	$0.244968\pi$
$608$	−19.1322	+	13.1532i	−0.775914	+	0.533431i
$609$		0			0
$610$	1.81710	+	15.0122i	0.0735723	+	0.607826i
$611$	−1.41727	+	2.45478i	−0.0573364	+	0.0993096i
$612$		0			0
$613$	3.96050	−	2.28659i	0.159963	−	0.0923547i	−0.417882	−	0.908501i	$-0.637227\pi$
$613$	3.96050	−	2.28659i	0.159963	−	0.0923547i	0.577845	+	0.816147i	$0.303894\pi$
$614$	13.5484	−	31.7661i	0.546767	−	1.28198i
$615$		0			0
$616$	−3.83078	−	9.26608i	−0.154347	−	0.373341i
$617$	−5.12621			−0.206373			−0.103187	−	0.994662i	$-0.532904\pi$
$617$	−5.12621			−0.206373			−0.103187	+	0.994662i	$0.532904\pi$
$618$		0			0
$619$	39.5293	−	22.8222i	1.58881	−	0.917303i	0.595312	−	0.803495i	$-0.297028\pi$
$619$	39.5293	−	22.8222i	1.58881	−	0.917303i	0.993503	−	0.113808i	$-0.0363049\pi$
$620$	−12.7699	−	13.3148i	−0.512852	−	0.534737i
$621$		0			0
$622$	−2.92817	−	24.1914i	−0.117409	−	0.969988i
$623$	3.89654	−	2.41185i	0.156111	−	0.0966286i
$624$		0			0
$625$	10.5696	−	18.3071i	0.422783	−	0.732282i
$626$	14.7515	+	19.6460i	0.589589	+	0.785213i
$627$		0			0
$628$	−7.98293	+	27.4832i	−0.318554	+	1.09670i
$629$	−20.4088			−0.813753
$630$		0			0
$631$		−	17.1345i		−	0.682113i	−0.940043	−	0.341057i	$-0.889215\pi$
$631$		−	17.1345i		−	0.682113i	0.940043	−	0.341057i	$-0.110785\pi$
$632$	2.77933	−	16.9813i	0.110556	−	0.675479i
$633$		0			0
$634$	16.4592	+	21.9204i	0.653680	+	0.870569i
$635$	26.3069	+	15.1883i	1.04396	+	0.602729i
$636$		0			0
$637$	−9.67781	−	14.6145i	−0.383449	−	0.579049i
$638$	8.76897	−	1.06141i	0.347167	−	0.0420217i
$639$		0			0
$640$	−4.76419	+	23.0281i	−0.188321	+	0.910266i
$641$	4.02498	+	6.97146i	0.158977	+	0.275356i	0.934500	−	0.355963i	$-0.115847\pi$
$641$	4.02498	+	6.97146i	0.158977	+	0.275356i	−0.775523	+	0.631319i	$0.782514\pi$
$642$		0			0
$643$			22.2710i			0.878283i	0.898418	+	0.439142i	$0.144717\pi$
$643$			22.2710i			0.878283i	−0.898418	+	0.439142i	$0.855283\pi$
$644$	32.8369	+	8.45579i	1.29395	+	0.333205i
$645$		0			0
$646$	17.1517	+	7.31525i	0.674825	+	0.287815i
$647$	18.9125	+	32.7574i	0.743528	+	1.28783i	0.950879	+	0.309561i	$0.100182\pi$
$647$	18.9125	+	32.7574i	0.743528	+	1.28783i	−0.207352	+	0.978266i	$0.566484\pi$
$648$		0			0
$649$	−8.43042	−	4.86730i	−0.330923	−	0.191058i
$650$	0.289259	+	2.38975i	0.0113457	+	0.0937337i
$651$		0			0
$652$	−16.1470	+	3.96704i	−0.632364	+	0.155361i
$653$	25.6130	+	14.7877i	1.00231	+	0.578686i	0.908932	−	0.416944i	$-0.136899\pi$
$653$	25.6130	+	14.7877i	1.00231	+	0.578686i	0.0933818	+	0.995630i	$0.470232\pi$
$654$		0			0
$655$	10.9586	−	6.32694i	0.428188	−	0.247214i
$656$	22.1836	+	0.927282i	0.866126	+	0.0362043i
$657$		0			0
$658$	−0.637588	−	4.18720i	−0.0248558	−	0.163234i
$659$	−18.3961			−0.716611			−0.358305	−	0.933604i	$-0.616645\pi$
$659$	−18.3961			−0.716611			−0.358305	+	0.933604i	$0.616645\pi$
$660$		0			0
$661$	−5.92732	−	10.2664i	−0.230546	−	0.399317i	0.727423	−	0.686189i	$-0.240718\pi$
$661$	−5.92732	−	10.2664i	−0.230546	−	0.399317i	−0.957969	+	0.286872i	$0.907385\pi$
$662$	23.5245	−	17.6637i	0.914306	−	0.686520i
$663$		0			0
$664$	−1.33128	+	0.503175i	−0.0516635	+	0.0195270i
$665$	0.691771	+	22.5599i	0.0268257	+	0.874836i
$666$		0			0
$667$	−14.9356	+	25.8692i	−0.578308	+	1.00166i
$668$	−3.46653	−	3.61446i	−0.134124	−	0.139848i
$669$		0			0
$670$	21.2652	+	9.06965i	0.821545	+	0.350391i
$671$	−6.89285			−0.266095
$672$		0			0
$673$	10.8738			0.419154			0.209577	−	0.977792i	$-0.432791\pi$
$673$	10.8738			0.419154			0.209577	+	0.977792i	$0.432791\pi$
$674$	13.4418	+	5.73299i	0.517760	+	0.220826i
$675$		0			0
$676$	−9.31638	−	9.71395i	−0.358322	−	0.373613i
$677$	−22.7163	+	39.3458i	−0.873060	+	1.51218i	−0.0142443	+	0.999899i	$0.504534\pi$
$677$	−22.7163	+	39.3458i	−0.873060	+	1.51218i	−0.858815	+	0.512285i	$0.828799\pi$
$678$		0			0
$679$	40.1437	+	21.5642i	1.54057	+	0.827559i
$680$	17.6664	−	6.67728i	0.677476	−	0.256062i
$681$		0			0
$682$	6.72468	−	5.04933i	0.257501	−	0.193349i
$683$	12.3693	+	21.4243i	0.473299	+	0.819778i	0.999533	−	0.0305620i	$-0.00972970\pi$
$683$	12.3693	+	21.4243i	0.473299	+	0.819778i	−0.526234	+	0.850340i	$0.676396\pi$
$684$		0			0
$685$	29.0446			1.10974
$686$	24.9337	+	8.01942i	0.951973	+	0.306183i
$687$		0			0
$688$		0			0
$689$	−18.6193	+	10.7499i	−0.709340	+	0.409538i
$690$		0			0
$691$	−4.10457	−	2.36977i	−0.156145	−	0.0901504i	0.419892	−	0.907574i	$-0.362068\pi$
$691$	−4.10457	−	2.36977i	−0.156145	−	0.0901504i	−0.576037	+	0.817424i	$0.695401\pi$
$692$	10.5535	−	2.59280i	0.401182	−	0.0985636i
$693$		0			0
$694$	5.71568	+	47.2207i	0.216964	+	1.79247i
$695$	0.905741	+	0.522930i	0.0343567	+	0.0198359i
$696$		0			0
$697$	−8.91594	−	15.4429i	−0.337715	−	0.584940i
$698$	17.3722	+	7.40932i	0.657549	+	0.280447i
$699$		0			0
$700$	−2.56812	−	2.51845i	−0.0970659	−	0.0951883i
$701$		−	39.8121i		−	1.50368i	−0.659345	−	0.751840i	$-0.729166\pi$
$701$		−	39.8121i		−	1.50368i	0.659345	−	0.751840i	$-0.270834\pi$
$702$		0			0
$703$	−13.0371	−	22.5809i	−0.491704	−	0.851656i
$704$	−10.1597	−	3.41722i	−0.382909	−	0.128791i
$705$		0			0
$706$	−11.0267	+	1.33469i	−0.414996	+	0.0502319i
$707$	3.24600	−	0.0995345i	0.122078	−	0.00374338i
$708$		0			0
$709$	−4.97242	−	2.87083i	−0.186743	−	0.107816i	0.403714	−	0.914885i	$-0.367719\pi$
$709$	−4.97242	−	2.87083i	−0.186743	−	0.107816i	−0.590457	+	0.807069i	$0.701052\pi$
$710$	−9.33942	−	12.4382i	−0.350502	−	0.466798i
$711$		0			0
$712$	0.791288	−	4.83465i	0.0296548	−	0.181186i
$713$			28.4385i			1.06503i
$714$		0			0
$715$	6.97370			0.260801
$716$	−1.96277	+	6.75732i	−0.0733523	+	0.252533i
$717$		0			0
$718$	−0.137717	−	0.183411i	−0.00513954	−	0.00684482i
$719$	−7.62804	+	13.2122i	−0.284478	+	0.492730i	−0.972482	−	0.232976i	$-0.925154\pi$
$719$	−7.62804	+	13.2122i	−0.284478	+	0.492730i	0.688005	+	0.725706i	$0.258487\pi$
$720$		0			0
$721$	21.2438	+	34.3211i	0.791160	+	1.27818i
$722$	−0.366180	−	3.02523i	−0.0136278	−	0.112588i
$723$		0			0
$724$	30.7303	+	32.0417i	1.14208	+	1.19082i
$725$	2.74416	−	1.58434i	0.101915	−	0.0588409i
$726$		0			0
$727$	−40.8993			−1.51687			−0.758435	−	0.651749i	$-0.774036\pi$
$727$	−40.8993			−1.51687			−0.758435	+	0.651749i	$0.774036\pi$
$728$	−18.5767	−	2.45848i	−0.688497	−	0.0911172i
$729$		0			0
$730$	0.639654	−	1.49976i	0.0236746	−	0.0555087i
$731$		0			0
$732$		0			0
$733$	−12.2037	+	21.1374i	−0.450753	+	0.780728i	−0.998433	−	0.0559605i	$-0.982178\pi$
$733$	−12.2037	+	21.1374i	−0.450753	+	0.780728i	0.547680	+	0.836688i	$0.315511\pi$
$734$	−3.44367	−	28.4502i	−0.127108	−	1.05012i
$735$		0			0
$736$	29.8711	−	20.5360i	1.10106	−	0.756968i
$737$	−5.26897	+	9.12612i	−0.194085	+	0.336165i
$738$		0			0
$739$	15.3996	+	26.6730i	0.566485	+	0.981181i	0.996910	+	0.0785545i	$0.0250305\pi$
$739$	15.3996	+	26.6730i	0.566485	+	0.981181i	−0.430425	+	0.902626i	$0.641636\pi$
$740$	−25.3611	−	7.36654i	−0.932293	−	0.270800i
$741$		0			0
$742$	11.6917	−	29.9227i	0.429216	−	1.09850i
$743$			23.9376i			0.878184i	0.898442	+	0.439092i	$0.144700\pi$
$743$			23.9376i			0.878184i	−0.898442	+	0.439092i	$0.855300\pi$
$744$		0			0
$745$	9.91613	−	5.72508i	0.363299	−	0.209751i
$746$	5.67004	+	7.55134i	0.207595	+	0.276474i
$747$		0			0
$748$	2.05394	+	8.36013i	0.0750996	+	0.305677i
$749$	15.4689	+	24.9912i	0.565219	+	0.913158i
$750$		0			0
$751$	11.9543	+	6.90181i	0.436218	+	0.251851i	0.701992	−	0.712185i	$-0.252294\pi$
$751$	11.9543	+	6.90181i	0.436218	+	0.251851i	−0.265774	+	0.964035i	$0.585627\pi$
$752$	−3.82331	−	2.42574i	−0.139422	−	0.0884578i
$753$		0			0
$754$	6.47615	−	15.1843i	0.235847	−	0.552979i
$755$			14.6287i			0.532392i
$756$		0			0
$757$		−	2.14156i		−	0.0778362i	−0.999242	−	0.0389181i	$-0.987609\pi$
$757$		−	2.14156i		−	0.0778362i	0.999242	−	0.0389181i	$-0.0123911\pi$
$758$	−5.98841	−	2.55408i	−0.217509	−	0.0927682i
$759$		0			0
$760$	18.6732	+	15.2812i	0.677348	+	0.554308i
$761$	−36.8321	−	21.2650i	−1.33516	−	0.770856i	−0.349076	−	0.937094i	$-0.613504\pi$
$761$	−36.8321	−	21.2650i	−1.33516	−	0.770856i	−0.986086	+	0.166239i	$0.946838\pi$
$762$		0			0
$763$	1.02164	+	33.3175i	0.0369859	+	1.20618i
$764$	−0.626015	−	2.54806i	−0.0226484	−	0.0921855i
$765$		0			0
$766$	12.9157	−	9.69798i	0.466665	−	0.350402i
$767$	−15.7554	+	9.09636i	−0.568893	+	0.328450i
$768$		0			0
$769$			15.6459i			0.564206i	0.959384	+	0.282103i	$0.0910320\pi$
$769$			15.6459i			0.564206i	−0.959384	+	0.282103i	$0.908968\pi$
$770$	−8.13715	+	6.50929i	−0.293243	+	0.234579i
$771$		0			0
$772$	−6.30061	+	21.6914i	−0.226764	+	0.780689i
$773$	15.2125	+	26.3489i	0.547156	+	0.947703i	0.998468	+	0.0553362i	$0.0176230\pi$
$773$	15.2125	+	26.3489i	0.547156	+	0.947703i	−0.451311	+	0.892367i	$0.649044\pi$
$774$		0			0
$775$	1.50836	−	2.61255i	0.0541817	−	0.0938455i
$776$	45.5689	−	17.2234i	1.63583	−	0.618286i
$777$		0			0
$778$	−42.1999	+	5.10794i	−1.51294	+	0.183129i
$779$	11.3910	−	19.7297i	0.408124	−	0.706891i
$780$		0			0
$781$	6.14009	−	3.54498i	0.219710	−	0.126849i
$782$	−26.7790	−	11.4213i	−0.957613	−	0.408425i
$783$		0			0
$784$	23.9707	−	14.4709i	0.856095	−	0.516819i
$785$	29.7427			1.06156
$786$		0			0
$787$	−28.3722	+	16.3807i	−1.01136	+	0.583909i	−0.911590	−	0.411102i	$-0.865144\pi$
$787$	−28.3722	+	16.3807i	−1.01136	+	0.583909i	−0.0997704	+	0.995010i	$0.531811\pi$
$788$	−8.54734	+	8.19752i	−0.304486	+	0.292025i
$789$		0			0
$790$	−17.7532	+	2.14888i	−0.631631	+	0.0764536i
$791$	25.1193	−	46.7618i	0.893140	−	1.66266i
$792$		0			0
$793$	−6.44092	+	11.1560i	−0.228724	+	0.396161i
$794$	4.91091	−	3.68743i	0.174282	−	0.130862i
$795$		0			0
$796$	−10.3827	+	35.7450i	−0.368006	+	1.26695i
$797$	28.3790			1.00523			0.502617	−	0.864509i	$-0.332370\pi$
$797$	28.3790			1.00523			0.502617	+	0.864509i	$0.332370\pi$
$798$		0			0
$799$			3.63649i			0.128650i
$800$	−3.83337	+	0.302233i	−0.135530	+	0.0106855i
$801$		0			0
$802$	−22.5883	+	16.9607i	−0.797620	+	0.598905i
$803$	0.643636	+	0.371603i	0.0227134	+	0.0131136i
$804$		0			0
$805$	−1.08006	−	35.2228i	−0.0380672	−	1.24144i
$806$	−1.88850	−	15.6021i	−0.0665197	−	0.549560i
$807$		0			0
$808$	2.19872	−	2.68677i	0.0773505	−	0.0945201i
$809$	−4.08387	−	7.07347i	−0.143581	−	0.248690i	0.785262	−	0.619164i	$-0.212528\pi$
$809$	−4.08387	−	7.07347i	−0.143581	−	0.248690i	−0.928843	+	0.370474i	$0.879195\pi$
$810$		0			0
$811$		−	22.2710i		−	0.782041i	−0.920382	−	0.391021i	$-0.872122\pi$
$811$		−	22.2710i		−	0.782041i	0.920382	−	0.391021i	$-0.127878\pi$
$812$	6.61652	+	23.7624i	0.232194	+	0.833898i
$813$		0			0
$814$	4.72263	−	11.0729i	0.165528	−	0.388105i
$815$	8.63997	+	14.9649i	0.302645	+	0.524196i
$816$		0			0
$817$		0			0
$818$	−42.8563	+	5.18740i	−1.49844	+	0.181373i
$819$		0			0
$820$	−5.50535	−	22.4083i	−0.192255	−	0.782533i
$821$	−4.52231	−	2.61096i	−0.157830	−	0.0911230i	0.419005	−	0.907984i	$-0.362379\pi$
$821$	−4.52231	−	2.61096i	−0.157830	−	0.0911230i	−0.576835	+	0.816861i	$0.695712\pi$
$822$		0			0
$823$	−8.29368	+	4.78836i	−0.289099	+	0.166912i	−0.637536	−	0.770421i	$-0.720046\pi$
$823$	−8.29368	+	4.78836i	−0.289099	+	0.166912i	0.348436	+	0.937333i	$0.386713\pi$
$824$	42.5841	+	6.96975i	1.48349	+	0.242803i
$825$		0			0
$826$	9.89330	−	25.3201i	0.344232	−	0.880998i
$827$	−40.6664			−1.41411			−0.707055	−	0.707159i	$-0.749977\pi$
$827$	−40.6664			−1.41411			−0.707055	+	0.707159i	$0.749977\pi$
$828$		0			0
$829$	16.6171	+	28.7816i	0.577134	+	0.999625i	0.995806	+	0.0914880i	$0.0291623\pi$
$829$	16.6171	+	28.7816i	0.577134	+	0.999625i	−0.418672	+	0.908137i	$0.637504\pi$
$830$	0.888096	+	1.18276i	0.0308263	+	0.0410543i
$831$		0			0
$832$	−15.0243	+	13.2502i	−0.520875	+	0.459369i
$833$	−20.1271	−	10.0295i	−0.697364	−	0.347500i
$834$		0			0
$835$	−2.60236	+	4.50743i	−0.0900586	+	0.155986i
$836$	−7.93785	+	7.61298i	−0.274536	+	0.263300i
$837$		0			0
$838$	−1.15440	+	2.70666i	−0.0398781	+	0.0935001i
$839$	15.0243			0.518698			0.259349	−	0.965784i	$-0.416492\pi$
$839$	15.0243			0.518698			0.259349	+	0.965784i	$0.416492\pi$
$840$		0			0
$841$	7.27029			0.250700
$842$	16.8684	−	39.5506i	0.581325	−	1.36300i
$843$		0			0
$844$	7.93202	+	8.27050i	0.273031	+	0.284682i
$845$	−6.99392	+	12.1138i	−0.240598	+	0.416728i
$846$		0			0
$847$	12.8174	+	20.7076i	0.440411	+	0.711521i
$848$	−15.9148	−	30.4339i	−0.546517	−	1.04510i
$849$		0			0
$850$	1.85431	+	2.46957i	0.0636024	+	0.0847055i
$851$	20.3548	+	35.2556i	0.697755	+	1.20855i
$852$		0			0
$853$	−12.5203			−0.428686			−0.214343	−	0.976758i	$-0.568761\pi$
$853$	−12.5203			−0.428686			−0.214343	+	0.976758i	$0.568761\pi$
$854$	−2.89759	−	19.0292i	−0.0991533	−	0.651165i
$855$		0			0
$856$	31.0080	+	5.07508i	1.05983	+	0.173463i
$857$	46.8265	−	27.0353i	1.59956	−	0.923509i	0.607993	−	0.793942i	$-0.291975\pi$
$857$	46.8265	−	27.0353i	1.59956	−	0.923509i	0.991571	−	0.129566i	$-0.0413585\pi$
$858$		0			0
$859$	17.0990	+	9.87213i	0.583411	+	0.336833i	0.762488	−	0.647002i	$-0.223978\pi$
$859$	17.0990	+	9.87213i	0.583411	+	0.336833i	−0.179077	+	0.983835i	$0.557311\pi$
$860$		0			0
$861$		0			0
$862$	3.76563	−	0.455798i	0.128258	−	0.0155246i
$863$	26.3755	+	15.2279i	0.897833	+	0.518364i	0.876497	−	0.481408i	$-0.159874\pi$
$863$	26.3755	+	15.2279i	0.897833	+	0.518364i	0.0213367	+	0.999772i	$0.493208\pi$
$864$		0			0
$865$	−5.64697	−	9.78084i	−0.192003	−	0.332559i
$866$	−16.3488	+	38.3322i	−0.555555	+	1.30258i
$867$		0			0
$868$	16.7666	+	16.4423i	0.569097	+	0.558089i
$869$		−	8.15137i		−	0.276516i
$870$		0			0
$871$	9.84701	+	17.0555i	0.333653	+	0.577905i
$872$	27.5775	+	22.5680i	0.933890	+	0.764250i
$873$		0			0
$874$	−4.46946	−	36.9249i	−0.151182	−	1.24900i
$875$	−14.7808	+	27.5157i	−0.499682	+	0.930201i
$876$		0			0
$877$	18.3275	+	10.5814i	0.618877	+	0.357309i	0.776432	−	0.630201i	$-0.217028\pi$
$877$	18.3275	+	10.5814i	0.618877	+	0.357309i	−0.157555	+	0.987510i	$0.550361\pi$
$878$	8.54166	−	6.41363i	0.288267	−	0.216450i
$879$		0			0
$880$	−0.465242	+	11.1301i	−0.0156833	+	0.375196i
$881$		−	11.5367i		−	0.388681i	−0.980934	−	0.194340i	$-0.937743\pi$
$881$		−	11.5367i		−	0.388681i	0.980934	−	0.194340i	$-0.0622566\pi$
$882$		0			0
$883$	49.8555			1.67777			0.838886	−	0.544307i	$-0.183207\pi$
$883$	49.8555			1.67777			0.838886	+	0.544307i	$0.183207\pi$
$884$	15.4501	+	4.48772i	0.519642	+	0.150938i
$885$		0			0
$886$	−8.50246	+	6.38420i	−0.285646	+	0.214481i
$887$	5.56575	−	9.64015i	0.186879	−	0.323685i	−0.757329	−	0.653034i	$-0.773496\pi$
$887$	5.56575	−	9.64015i	0.186879	−	0.323685i	0.944208	+	0.329349i	$0.106829\pi$
$888$		0			0
$889$	−34.0629	−	18.2978i	−1.14243	−	0.613688i
$890$	−5.05442	+	0.611796i	−0.169425	+	0.0205074i
$891$		0			0
$892$	−28.8873	−	30.1200i	−0.967219	−	1.00849i
$893$	−4.02352	+	2.32298i	−0.134642	+	0.0777356i
$894$		0			0
$895$	7.31287			0.244442
$896$	5.16308	−	29.4846i	0.172487	−	0.985012i
$897$		0			0
$898$	18.6452	+	7.95223i	0.622198	+	0.265370i
$899$	−17.9159	+	10.3438i	−0.597530	+	0.344984i
$900$		0			0
$901$	−13.7913	+	23.8872i	−0.459454	+	0.795798i
$902$	10.4418	−	1.26389i	0.347672	−	0.0420829i
$903$		0			0
$904$	−20.0629	−	53.0815i	−0.667282	−	1.76546i
$905$	23.0696	−	39.9577i	0.766859	−	1.32824i
$906$		0			0
$907$	7.20674	+	12.4824i	0.239296	+	0.414473i	0.960512	−	0.278237i	$-0.0897501\pi$
$907$	7.20674	+	12.4824i	0.239296	+	0.414473i	−0.721217	+	0.692710i	$0.756417\pi$
$908$	−31.6637	−	9.19723i	−1.05080	−	0.305221i
$909$		0			0
$910$	2.93157	+	19.2524i	0.0971807	+	0.638211i
$911$			19.1909i			0.635823i	0.948120	+	0.317911i	$0.102981\pi$
$911$			19.1909i			0.635823i	−0.948120	+	0.317911i	$0.897019\pi$
$912$		0			0
$913$	−0.583868	+	0.337096i	−0.0193232	+	0.0111563i
$914$	−14.6573	+	11.0057i	−0.484821	+	0.364035i
$915$		0			0
$916$	−16.5081	+	4.05576i	−0.545443	+	0.134006i
$917$	−13.6958	+	8.47733i	−0.452276	+	0.279946i
$918$		0			0
$919$	−22.4285	−	12.9491i	−0.739848	−	0.427151i	0.0821662	−	0.996619i	$-0.473816\pi$
$919$	−22.4285	−	12.9491i	−0.739848	−	0.427151i	−0.822014	+	0.569467i	$0.807150\pi$
$920$	−29.1545	−	23.8586i	−0.961195	−	0.786594i
$921$		0			0
$922$	43.4312	+	18.5236i	1.43033	+	0.610041i
$923$		−	13.2502i		−	0.436136i
$924$		0			0
$925$		−	4.31842i		−	0.141989i
$926$	−16.5189	+	38.7311i	−0.542845	+	1.27278i
$927$		0			0
$928$	23.8023	+	11.3490i	0.781349	+	0.372550i
$929$	36.7480	+	21.2165i	1.20566	+	0.696090i	0.961809	−	0.273722i	$-0.0882548\pi$
$929$	36.7480	+	21.2165i	1.20566	+	0.696090i	0.243854	+	0.969812i	$0.421588\pi$
$930$		0			0
$931$	−1.76029	−	28.6761i	−0.0576910	−	0.939820i
$932$	8.69158	−	2.13537i	0.284702	−	0.0699464i
$933$		0			0
$934$	−23.0814	−	30.7397i	−0.755245	−	1.00583i
$935$	7.74809	−	4.47336i	0.253390	−	0.146295i
$936$		0			0
$937$		−	46.5547i		−	1.52088i	−0.649410	−	0.760439i	$-0.724984\pi$
$937$		−	46.5547i		−	1.52088i	0.649410	−	0.760439i	$-0.275016\pi$
$938$	−27.4096	−	10.7097i	−0.894954	−	0.349685i
$939$		0			0
$940$	−1.31259	+	4.51890i	−0.0428119	+	0.147390i
$941$	−1.48937	−	2.57967i	−0.0485522	−	0.0840949i	0.840728	−	0.541458i	$-0.182127\pi$
$941$	−1.48937	−	2.57967i	−0.0485522	−	0.0840949i	−0.889280	+	0.457363i	$0.848794\pi$
$942$		0			0
$943$	−17.7847	+	30.8040i	−0.579150	+	1.00312i
$944$	−13.4668	−	25.7526i	−0.438308	−	0.838177i
$945$		0			0
$946$		0			0
$947$	−13.5270	+	23.4294i	−0.439568	+	0.761354i	−0.997656	−	0.0684276i	$-0.978202\pi$
$947$	−13.5270	+	23.4294i	−0.439568	+	0.761354i	0.558088	+	0.829782i	$0.311535\pi$
$948$		0			0
$949$	1.20287	−	0.694478i	0.0390469	−	0.0225437i
$950$	−1.54788	+	3.62922i	−0.0502197	+	0.117748i
$951$		0			0
$952$	−22.2165	+	9.18475i	−0.720042	+	0.297679i
$953$	−28.7293			−0.930634			−0.465317	−	0.885144i	$-0.654060\pi$
$953$	−28.7293			−0.930634			−0.465317	+	0.885144i	$0.654060\pi$
$954$		0			0
$955$	−2.36152	+	1.36342i	−0.0764169	+	0.0441193i
$956$	−35.4619	+	34.0105i	−1.14692	+	1.09998i
$957$		0			0
$958$	−5.85225	−	48.3490i	−0.189078	−	1.56209i
$959$	−36.9536	+	1.13313i	−1.19329	+	0.0365908i
$960$		0			0
$961$	5.65232	−	9.79010i	0.182333	−	0.315810i
$962$	−13.5084	−	17.9904i	−0.435528	−	0.580035i
$963$		0			0
$964$	−11.1441	−	3.23698i	−0.358927	−	0.104256i
$965$	23.4747			0.755677
$966$		0			0
$967$			13.3546i			0.429453i	0.976674	+	0.214727i	$0.0688861\pi$
$967$			13.3546i			0.429453i	−0.976674	+	0.214727i	$0.931114\pi$
$968$	25.6931	+	4.20518i	0.825806	+	0.135160i
$969$		0			0
$970$	−30.3991	−	40.4854i	−0.976056	−	1.29991i
$971$	1.71876	+	0.992325i	0.0551575	+	0.0318452i	0.527325	−	0.849664i	$-0.323195\pi$
$971$	1.71876	+	0.992325i	0.0551575	+	0.0318452i	−0.472168	+	0.881509i	$0.656528\pi$
$972$		0			0
$973$	−1.17278	−	0.629989i	−0.0375976	−	0.0201965i
$974$	11.0662	−	1.33948i	0.354585	−	0.0429196i
$975$		0			0
$976$	−17.3754	−	11.0241i	−0.556174	−	0.352871i
$977$	−31.2242	−	54.0818i	−0.998950	−	1.73023i	−0.539158	−	0.842205i	$-0.681257\pi$
$977$	−31.2242	−	54.0818i	−0.998950	−	1.73023i	−0.459792	−	0.888027i	$-0.652076\pi$
$978$		0			0
$979$		−	2.32073i		−	0.0741710i
$980$	−21.3910	−	19.7280i	−0.683309	−	0.630188i
$981$		0			0
$982$	10.4886	+	4.47340i	0.334703	+	0.142752i
$983$	−3.64021	−	6.30503i	−0.116105	−	0.201099i	0.802116	−	0.597168i	$-0.203707\pi$
$983$	−3.64021	−	6.30503i	−0.116105	−	0.201099i	−0.918221	+	0.396069i	$0.870374\pi$
$984$		0			0
$985$	10.6590	+	6.15397i	0.339624	+	0.196082i
$986$	−2.54486	−	21.0246i	−0.0810448	−	0.669561i
$987$		0			0
$988$	4.90411	+	19.9612i	0.156021	+	0.635049i
$989$		0			0
$990$		0			0
$991$	31.3345	−	18.0910i	0.995373	−	0.574679i	0.0884967	−	0.996076i	$-0.471794\pi$
$991$	31.3345	−	18.0910i	0.995373	−	0.574679i	0.906876	+	0.421398i	$0.138460\pi$
$992$	25.0271	−	1.97320i	0.794613	−	0.0626493i
$993$		0			0
$994$	12.3678	+	15.4608i	0.392284	+	0.490387i
$995$	38.6838			1.22636
$996$		0			0
$997$	17.1218	+	29.6559i	0.542254	+	0.939211i	0.998774	+	0.0494984i	$0.0157623\pi$
$997$	17.1218	+	29.6559i	0.542254	+	0.939211i	−0.456520	+	0.889713i	$0.650904\pi$
$998$	27.1906	−	20.4164i	0.860703	−	0.646271i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bk.a.19.6		12
3.2	odd	2		56.2.m.a.19.1	yes	12
4.3	odd	2		2016.2.bs.a.271.5		12
7.3	odd	6	inner	504.2.bk.a.451.2		12
8.3	odd	2	inner	504.2.bk.a.19.1		12
8.5	even	2		2016.2.bs.a.271.2		12
12.11	even	2		224.2.q.a.47.5		12
21.2	odd	6		392.2.e.e.195.7		12
21.5	even	6		392.2.e.e.195.8		12
21.11	odd	6		392.2.m.g.227.5		12
21.17	even	6		56.2.m.a.3.5	yes	12
21.20	even	2		392.2.m.g.19.1		12
24.5	odd	2		224.2.q.a.47.6		12
24.11	even	2		56.2.m.a.19.6	yes	12
28.3	even	6		2016.2.bs.a.1711.2		12
56.3	even	6	inner	504.2.bk.a.451.5		12
56.45	odd	6		2016.2.bs.a.1711.5		12
84.11	even	6		1568.2.q.g.815.1		12
84.23	even	6		1568.2.e.e.783.12		12
84.47	odd	6		1568.2.e.e.783.1		12
84.59	odd	6		224.2.q.a.143.6		12
84.83	odd	2		1568.2.q.g.1391.2		12
168.5	even	6		1568.2.e.e.783.2		12
168.11	even	6		392.2.m.g.227.2		12
168.53	odd	6		1568.2.q.g.815.2		12
168.59	odd	6		56.2.m.a.3.2	✓	12
168.83	odd	2		392.2.m.g.19.6		12
168.101	even	6		224.2.q.a.143.5		12
168.107	even	6		392.2.e.e.195.5		12
168.125	even	2		1568.2.q.g.1391.1		12
168.131	odd	6		392.2.e.e.195.6		12
168.149	odd	6		1568.2.e.e.783.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.m.a.3.2	✓	12	168.59	odd	6
56.2.m.a.3.5	yes	12	21.17	even	6
56.2.m.a.19.1	yes	12	3.2	odd	2
56.2.m.a.19.6	yes	12	24.11	even	2
224.2.q.a.47.5		12	12.11	even	2
224.2.q.a.47.6		12	24.5	odd	2
224.2.q.a.143.5		12	168.101	even	6
224.2.q.a.143.6		12	84.59	odd	6
392.2.e.e.195.5		12	168.107	even	6
392.2.e.e.195.6		12	168.131	odd	6
392.2.e.e.195.7		12	21.2	odd	6
392.2.e.e.195.8		12	21.5	even	6
392.2.m.g.19.1		12	21.20	even	2
392.2.m.g.19.6		12	168.83	odd	2
392.2.m.g.227.2		12	168.11	even	6
392.2.m.g.227.5		12	21.11	odd	6
504.2.bk.a.19.1		12	8.3	odd	2	inner
504.2.bk.a.19.6		12	1.1	even	1	trivial
504.2.bk.a.451.2		12	7.3	odd	6	inner
504.2.bk.a.451.5		12	56.3	even	6	inner
1568.2.e.e.783.1		12	84.47	odd	6
1568.2.e.e.783.2		12	168.5	even	6
1568.2.e.e.783.11		12	168.149	odd	6
1568.2.e.e.783.12		12	84.23	even	6
1568.2.q.g.815.1		12	84.11	even	6
1568.2.q.g.815.2		12	168.53	odd	6
1568.2.q.g.1391.1		12	168.125	even	2
1568.2.q.g.1391.2		12	84.83	odd	2
2016.2.bs.a.271.2		12	8.5	even	2
2016.2.bs.a.271.5		12	4.3	odd	2
2016.2.bs.a.1711.2		12	28.3	even	6
2016.2.bs.a.1711.5		12	56.45	odd	6

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	504.2.bk.a.19.6

Level	$504$
Weight	$2$
Character	504.19
Analytic conductor	$4.024$
Analytic rank	$0$
Dimension	$12$
Inner twists	$4$