LMFDB - Embedded newform 276.2.i.b.169.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(13,276)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("276.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.i (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 18 x^{18} - 58 x^{17} + 169 x^{16} - 363 x^{15} + 800 x^{14} - 1682 x^{13} + \cdots + 529 $ x^20 - 4x^19 + 18x^18 - 58x^17 + 169x^16 - 363x^15 + 800x^14 - 1682x^13 + 2817x^12 - 3731x^11 + 5829x^10 - 8312x^9 + 7737x^8 + 4348x^7 - 12995x^6 - 2574x^5 + 24401x^4 + 22582x^3 + 9558x^2 + 2829*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			169.2
Root			$1.55029 + 0.996309i$ of defining polynomial
Character	$\chi$	$=$	276.169
Dual form			276.2.i.b.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 - 0.909632i) q^{3} +(0.542284 + 0.625829i) q^{5} +(3.79055 + 2.43604i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.415415 - 0.909632i) q^{3} +(0.542284 + 0.625829i) q^{5} +(3.79055 + 2.43604i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(-0.421075 - 2.92864i) q^{11} +(-2.52446 + 1.62237i) q^{13} +(0.344001 - 0.753257i) q^{15} +(5.65351 - 1.66002i) q^{17} +(5.36039 + 1.57395i) q^{19} +(0.641248 - 4.45998i) q^{21} +(4.33584 - 2.04950i) q^{23} +(0.613984 - 4.27035i) q^{25} +(0.959493 + 0.281733i) q^{27} +(-9.91333 + 2.91082i) q^{29} +(-0.0738383 + 0.161683i) q^{31} +(-2.48906 + 1.59962i) q^{33} +(0.531011 + 3.69326i) q^{35} +(-6.71602 + 7.75071i) q^{37} +(2.52446 + 1.62237i) q^{39} +(-5.72205 - 6.60360i) q^{41} +(0.230068 + 0.503778i) q^{43} -0.828090 q^{45} -4.82044 q^{47} +(5.52610 + 12.1005i) q^{49} +(-3.85856 - 4.45301i) q^{51} +(-4.70991 - 3.02688i) q^{53} +(1.60448 - 1.85167i) q^{55} +(-0.795068 - 5.52982i) q^{57} +(0.611348 - 0.392890i) q^{59} +(-1.09823 + 2.40478i) q^{61} +(-4.32332 + 1.26944i) q^{63} +(-2.38430 - 0.700093i) q^{65} +(0.100386 - 0.698201i) q^{67} +(-3.66547 - 3.09263i) q^{69} +(-1.31662 + 9.15731i) q^{71} +(0.159822 + 0.0469279i) q^{73} +(-4.13951 + 1.21547i) q^{75} +(5.53818 - 12.1269i) q^{77} +(-1.36039 + 0.874270i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(-1.81835 + 2.09849i) q^{83} +(4.10469 + 2.63792i) q^{85} +(6.76592 + 7.80829i) q^{87} +(-0.471560 - 1.03257i) q^{89} -13.5213 q^{91} +0.177746 q^{93} +(1.92183 + 4.20821i) q^{95} +(-9.45458 - 10.9112i) q^{97} +(2.48906 + 1.59962i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9}+O(q^{10}) $ 20 * q + 2 * q^3 - 4 * q^7 - 2 * q^9	$ 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9} + 14 q^{13} - 11 q^{15} + 3 q^{17} + 7 q^{19} + 4 q^{21} + 24 q^{23} + 12 q^{25} + 2 q^{27} - 26 q^{29} + 33 q^{31} - 11 q^{33} - 2 q^{35} - 18 q^{37} - 14 q^{39} + 4 q^{41} - 40 q^{43} - 54 q^{47} + 30 q^{49} - 14 q^{51} - 14 q^{53} + 11 q^{55} - 29 q^{57} + 4 q^{59} + 12 q^{61} - 4 q^{63} - 33 q^{65} + 15 q^{67} - 2 q^{69} - 33 q^{71} + 15 q^{73} + 10 q^{75} + 66 q^{77} - 42 q^{79} - 2 q^{81} - 14 q^{83} - 13 q^{85} + 4 q^{87} - 66 q^{89} - 16 q^{91} - 22 q^{93} - 31 q^{95} - 24 q^{97} + 11 q^{99}+O(q^{100}) $ 20 * q + 2 * q^3 - 4 * q^7 - 2 * q^9 + 14 * q^13 - 11 * q^15 + 3 * q^17 + 7 * q^19 + 4 * q^21 + 24 * q^23 + 12 * q^25 + 2 * q^27 - 26 * q^29 + 33 * q^31 - 11 * q^33 - 2 * q^35 - 18 * q^37 - 14 * q^39 + 4 * q^41 - 40 * q^43 - 54 * q^47 + 30 * q^49 - 14 * q^51 - 14 * q^53 + 11 * q^55 - 29 * q^57 + 4 * q^59 + 12 * q^61 - 4 * q^63 - 33 * q^65 + 15 * q^67 - 2 * q^69 - 33 * q^71 + 15 * q^73 + 10 * q^75 + 66 * q^77 - 42 * q^79 - 2 * q^81 - 14 * q^83 - 13 * q^85 + 4 * q^87 - 66 * q^89 - 16 * q^91 - 22 * q^93 - 31 * q^95 - 24 * q^97 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{3}{11}\right)$	$1$	$1$

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
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$4$		0			0
$5$	0.542284	+	0.625829i	0.242517	+	0.279879i	0.863939	−	0.503597i	$-0.167990\pi$
$5$	0.542284	+	0.625829i	0.242517	+	0.279879i	−0.621422	+	0.783476i	$0.713445\pi$
$6$		0			0
$7$	3.79055	+	2.43604i	1.43269	+	0.920737i	0.999814	+	0.0192861i	$0.00613933\pi$
$7$	3.79055	+	2.43604i	1.43269	+	0.920737i	0.432881	+	0.901451i	$0.357497\pi$
$8$		0			0
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$		0			0
$11$	−0.421075	−	2.92864i	−0.126959	−	0.883018i	−0.949378	−	0.314136i	$-0.898285\pi$
$11$	−0.421075	−	2.92864i	−0.126959	−	0.883018i	0.822419	−	0.568882i	$-0.192624\pi$
$12$		0			0
$13$	−2.52446	+	1.62237i	−0.700159	+	0.449965i	−0.841684	−	0.539970i	$-0.818436\pi$
$13$	−2.52446	+	1.62237i	−0.700159	+	0.449965i	0.141525	+	0.989935i	$0.454799\pi$
$14$		0			0
$15$	0.344001	−	0.753257i	0.0888207	−	0.194490i
$16$		0			0
$17$	5.65351	−	1.66002i	1.37118	−	0.402614i	0.488487	−	0.872571i	$-0.337549\pi$
$17$	5.65351	−	1.66002i	1.37118	−	0.402614i	0.882689	+	0.469957i	$0.155731\pi$
$18$		0			0
$19$	5.36039	+	1.57395i	1.22976	+	0.361089i	0.831158	−	0.556036i	$-0.187678\pi$
$19$	5.36039	+	1.57395i	1.22976	+	0.361089i	0.398599	+	0.917125i	$0.369497\pi$
$20$		0			0
$21$	0.641248	−	4.45998i	0.139932	−	0.973247i
$22$		0			0
$23$	4.33584	−	2.04950i	0.904086	−	0.427351i
$23$	4.33584	−	2.04950i	0.904086	−	0.427351i
$24$		0			0
$25$	0.613984	−	4.27035i	0.122797	−	0.854071i
$26$		0			0
$27$	0.959493	+	0.281733i	0.184655	+	0.0542195i
$28$		0			0
$29$	−9.91333	+	2.91082i	−1.84086	+	0.540525i	−1.00000		0.000727304i	$-0.999768\pi$
$29$	−9.91333	+	2.91082i	−1.84086	+	0.540525i	−0.840860	+	0.541253i	$0.817950\pi$
$30$		0			0
$31$	−0.0738383	+	0.161683i	−0.0132617	+	0.0290392i	−0.916147	−	0.400843i	$-0.868717\pi$
$31$	−0.0738383	+	0.161683i	−0.0132617	+	0.0290392i	0.902885	+	0.429882i	$0.141445\pi$
$32$		0			0
$33$	−2.48906	+	1.59962i	−0.433290	+	0.278459i
$34$		0			0
$35$	0.531011	+	3.69326i	0.0897572	+	0.624275i
$36$		0			0
$37$	−6.71602	+	7.75071i	−1.10411	+	1.27421i	−0.145537	+	0.989353i	$0.546491\pi$
$37$	−6.71602	+	7.75071i	−1.10411	+	1.27421i	−0.958571	+	0.284855i	$0.908054\pi$
$38$		0			0
$39$	2.52446	+	1.62237i	0.404237	+	0.259787i
$40$		0			0
$41$	−5.72205	−	6.60360i	−0.893635	−	1.03131i	−0.999319	−	0.0369095i	$-0.988249\pi$
$41$	−5.72205	−	6.60360i	−0.893635	−	1.03131i	0.105684	−	0.994400i	$-0.466297\pi$
$42$		0			0
$43$	0.230068	+	0.503778i	0.0350850	+	0.0768255i	0.926363	−	0.376632i	$-0.122918\pi$
$43$	0.230068	+	0.503778i	0.0350850	+	0.0768255i	−0.891278	+	0.453457i	$0.850190\pi$
$44$		0			0
$45$	−0.828090			−0.123444
$46$		0			0
$47$	−4.82044			−0.703133			−0.351567	−	0.936163i	$-0.614351\pi$
$47$	−4.82044			−0.703133			−0.351567	+	0.936163i	$0.614351\pi$
$48$		0			0
$49$	5.52610	+	12.1005i	0.789443	+	1.72864i
$50$		0			0
$51$	−3.85856	−	4.45301i	−0.540306	−	0.623547i
$52$		0			0
$53$	−4.70991	−	3.02688i	−0.646956	−	0.415774i	0.175596	−	0.984462i	$-0.443815\pi$
$53$	−4.70991	−	3.02688i	−0.646956	−	0.415774i	−0.822553	+	0.568689i	$0.807451\pi$
$54$		0			0
$55$	1.60448	−	1.85167i	0.216349	−	0.249680i
$56$		0			0
$57$	−0.795068	−	5.52982i	−0.105309	−	0.732443i
$58$		0			0
$59$	0.611348	−	0.392890i	0.0795908	−	0.0511499i	−0.500240	−	0.865887i	$-0.666755\pi$
$59$	0.611348	−	0.392890i	0.0795908	−	0.0511499i	0.579831	+	0.814737i	$0.303119\pi$
$60$		0			0
$61$	−1.09823	+	2.40478i	−0.140614	+	0.307901i	−0.966816	−	0.255472i	$-0.917769\pi$
$61$	−1.09823	+	2.40478i	−0.140614	+	0.307901i	0.826203	+	0.563373i	$0.190496\pi$
$62$		0			0
$63$	−4.32332	+	1.26944i	−0.544687	+	0.159935i
$64$		0			0
$65$	−2.38430	−	0.700093i	−0.295736	−	0.0868359i
$66$		0			0
$67$	0.100386	−	0.698201i	0.0122641	−	0.0852988i	−0.982770	−	0.184832i	$-0.940826\pi$
$67$	0.100386	−	0.698201i	0.0122641	−	0.0852988i	0.995034	+	0.0995333i	$0.0317350\pi$
$68$		0			0
$69$	−3.66547	−	3.09263i	−0.441271	−	0.372309i
$70$		0			0
$71$	−1.31662	+	9.15731i	−0.156254	+	1.08677i	0.749204	+	0.662339i	$0.230436\pi$
$71$	−1.31662	+	9.15731i	−0.156254	+	1.08677i	−0.905459	+	0.424434i	$0.860473\pi$
$72$		0			0
$73$	0.159822	+	0.0469279i	0.0187057	+	0.00549249i	0.291072	−	0.956701i	$-0.405988\pi$
$73$	0.159822	+	0.0469279i	0.0187057	+	0.00549249i	−0.272366	+	0.962194i	$0.587806\pi$
$74$		0			0
$75$	−4.13951	+	1.21547i	−0.477989	+	0.140350i
$76$		0			0
$77$	5.53818	−	12.1269i	0.631134	−	1.38199i
$78$		0			0
$79$	−1.36039	+	0.874270i	−0.153056	+	0.0983630i	−0.614927	−	0.788584i	$-0.710815\pi$
$79$	−1.36039	+	0.874270i	−0.153056	+	0.0983630i	0.461871	+	0.886947i	$0.347178\pi$
$80$		0			0
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$		0			0
$83$	−1.81835	+	2.09849i	−0.199590	+	0.230339i	−0.846718	−	0.532043i	$-0.821425\pi$
$83$	−1.81835	+	2.09849i	−0.199590	+	0.230339i	0.647128	+	0.762382i	$0.275970\pi$
$84$		0			0
$85$	4.10469	+	2.63792i	0.445216	+	0.286123i
$86$		0			0
$87$	6.76592	+	7.80829i	0.725383	+	0.837136i
$88$		0			0
$89$	−0.471560	−	1.03257i	−0.0499852	−	0.109452i	0.882992	−	0.469389i	$-0.155526\pi$
$89$	−0.471560	−	1.03257i	−0.0499852	−	0.109452i	−0.932977	+	0.359936i	$0.882798\pi$
$90$		0			0
$91$	−13.5213			−1.41741
$92$		0			0
$93$	0.177746			0.0184314
$94$		0			0
$95$	1.92183	+	4.20821i	0.197175	+	0.431753i
$96$		0			0
$97$	−9.45458	−	10.9112i	−0.959968	−	1.10786i	−0.994103	−	0.108444i	$-0.965413\pi$
$97$	−9.45458	−	10.9112i	−0.959968	−	1.10786i	0.0341350	−	0.999417i	$-0.489132\pi$
$98$		0			0
$99$	2.48906	+	1.59962i	0.250160	+	0.160768i
$100$		0			0
$101$	−0.420509	+	0.485294i	−0.0418422	+	0.0482885i	−0.776285	−	0.630382i	$-0.782898\pi$
$101$	−0.420509	+	0.485294i	−0.0418422	+	0.0482885i	0.734443	+	0.678671i	$0.237444\pi$
$102$		0			0
$103$	−2.39482	−	16.6563i	−0.235968	−	1.64119i	−0.671488	−	0.741015i	$-0.734345\pi$
$103$	−2.39482	−	16.6563i	−0.235968	−	1.64119i	0.435520	−	0.900179i	$-0.356565\pi$
$104$		0			0
$105$	3.13892	−	2.01726i	0.306327	−	0.196865i
$106$		0			0
$107$	4.76174	−	10.4268i	0.460335	−	1.00799i	−0.527076	−	0.849818i	$-0.676712\pi$
$107$	4.76174	−	10.4268i	0.460335	−	1.00799i	0.987411	−	0.158175i	$-0.0505609\pi$
$108$		0			0
$109$	8.91080	−	2.61645i	0.853500	−	0.250610i	0.174417	−	0.984672i	$-0.444196\pi$
$109$	8.91080	−	2.61645i	0.853500	−	0.250610i	0.679083	+	0.734062i	$0.262378\pi$
$110$		0			0
$111$	9.84023	+	2.88935i	0.933993	+	0.274245i
$112$		0			0
$113$	−2.83632	+	19.7270i	−0.266818	+	1.85576i	0.211240	+	0.977434i	$0.432250\pi$
$113$	−2.83632	+	19.7270i	−0.266818	+	1.85576i	−0.478058	+	0.878328i	$0.658659\pi$
$114$		0			0
$115$	3.63389	+	1.60208i	0.338862	+	0.149395i
$116$		0			0
$117$	0.427063	−	2.97029i	0.0394820	−	0.274603i
$118$		0			0
$119$	25.4738	+	7.47978i	2.33518	+	0.685670i
$120$		0			0
$121$	2.15480	−	0.632707i	0.195891	−	0.0575188i
$122$		0			0
$123$	−3.62982	+	7.94820i	−0.327290	+	0.716665i
$124$		0			0
$125$	6.48863	−	4.16999i	0.580361	−	0.372975i
$126$		0			0
$127$	−0.910659	−	6.33377i	−0.0808079	−	0.562031i	−0.989497	−	0.144557i	$-0.953824\pi$
$127$	−0.910659	−	6.33377i	−0.0808079	−	0.562031i	0.908689	−	0.417475i	$-0.137085\pi$
$128$		0			0
$129$	0.362679	−	0.418554i	0.0319321	−	0.0368516i
$130$		0			0
$131$	−10.2919	−	6.61419i	−0.899206	−	0.577885i	0.00734861	−	0.999973i	$-0.497661\pi$
$131$	−10.2919	−	6.61419i	−0.899206	−	0.577885i	−0.906555	+	0.422088i	$0.861297\pi$
$132$		0			0
$133$	16.4846	+	19.0243i	1.42940	+	1.64961i
$134$		0			0
$135$	0.344001	+	0.753257i	0.0296069	+	0.0648300i
$136$		0			0
$137$	−9.14602			−0.781397			−0.390699	−	0.920519i	$-0.627767\pi$
$137$	−9.14602			−0.781397			−0.390699	+	0.920519i	$0.627767\pi$
$138$		0			0
$139$	−10.2038			−0.865479			−0.432739	−	0.901519i	$-0.642453\pi$
$139$	−10.2038			−0.865479			−0.432739	+	0.901519i	$0.642453\pi$
$140$		0			0
$141$	2.00248	+	4.38482i	0.168639	+	0.369269i
$142$		0			0
$143$	5.81433	+	6.71009i	0.486218	+	0.561126i
$144$		0			0
$145$	−7.19751	−	4.62556i	−0.597721	−	0.384132i
$146$		0			0
$147$	8.71135	−	10.0534i	0.718500	−	0.829193i
$148$		0			0
$149$	−0.0873799	−	0.607741i	−0.00715844	−	0.0497881i	0.985929	−	0.167164i	$-0.0534609\pi$
$149$	−0.0873799	−	0.607741i	−0.00715844	−	0.0497881i	−0.993088	+	0.117376i	$0.962552\pi$
$150$		0			0
$151$	5.92585	−	3.80831i	0.482239	−	0.309916i	−0.276838	−	0.960916i	$-0.589287\pi$
$151$	5.92585	−	3.80831i	0.482239	−	0.309916i	0.759078	+	0.651000i	$0.225650\pi$
$152$		0			0
$153$	−2.44770	+	5.35972i	−0.197885	+	0.433307i
$154$		0			0
$155$	−0.141227	+	0.0414681i	−0.0113436	+	0.00333079i
$156$		0			0
$157$	−6.94423	−	2.03901i	−0.554210	−	0.162731i	−0.00737765	−	0.999973i	$-0.502348\pi$
$157$	−6.94423	−	2.03901i	−0.554210	−	0.162731i	−0.546833	+	0.837242i	$0.684167\pi$
$158$		0			0
$159$	−0.796776	+	5.54170i	−0.0631885	+	0.439485i
$160$		0			0
$161$	21.4279	+	2.79354i	1.68876	+	0.220162i
$162$		0			0
$163$	2.48595	−	17.2901i	0.194714	−	1.35427i	−0.624609	−	0.780937i	$-0.714742\pi$
$163$	2.48595	−	17.2901i	0.194714	−	1.35427i	0.819324	−	0.573331i	$-0.194349\pi$
$164$		0			0
$165$	−2.35087	−	0.690277i	−0.183015	−	0.0537380i
$166$		0			0
$167$	−12.4943	+	3.66865i	−0.966835	+	0.283888i	−0.726779	−	0.686871i	$-0.758984\pi$
$167$	−12.4943	+	3.66865i	−0.966835	+	0.283888i	−0.240055	+	0.970759i	$0.577166\pi$
$168$		0			0
$169$	−1.65959	+	3.63399i	−0.127661	+	0.279538i
$170$		0			0
$171$	−4.69982	+	3.02039i	−0.359404	+	0.230975i
$172$		0			0
$173$	−1.34335	−	9.34321i	−0.102133	−	0.710351i	−0.974970	−	0.222338i	$-0.928631\pi$
$173$	−1.34335	−	9.34321i	−0.102133	−	0.710351i	0.872837	−	0.488013i	$-0.162278\pi$
$174$		0			0
$175$	12.7301	−	14.6913i	0.962305	−	1.11056i
$176$		0			0
$177$	−0.611348	−	0.392890i	−0.0459518	−	0.0295314i
$178$		0			0
$179$	12.7023	+	14.6592i	0.949414	+	1.09568i	0.995310	+	0.0967365i	$0.0308404\pi$
$179$	12.7023	+	14.6592i	0.949414	+	1.09568i	−0.0458956	+	0.998946i	$0.514614\pi$
$180$		0			0
$181$	7.93827	+	17.3824i	0.590047	+	1.29202i	0.935414	+	0.353555i	$0.115027\pi$
$181$	7.93827	+	17.3824i	0.590047	+	1.29202i	−0.345367	+	0.938468i	$0.612246\pi$
$182$		0			0
$183$	2.64369			0.195427
$184$		0			0
$185$	−8.49260			−0.624389
$186$		0			0
$187$	−7.24214	−	15.8581i	−0.529598	−	1.15966i
$188$		0			0
$189$	2.95070	+	3.40529i	0.214632	+	0.247698i
$190$		0			0
$191$	15.9106	+	10.2251i	1.15125	+	0.739862i	0.969887	−	0.243555i	$-0.0783137\pi$
$191$	15.9106	+	10.2251i	1.15125	+	0.739862i	0.181360	+	0.983417i	$0.441950\pi$
$192$		0			0
$193$	9.28557	−	10.7161i	0.668390	−	0.771363i	−0.315734	−	0.948848i	$-0.602251\pi$
$193$	9.28557	−	10.7161i	0.668390	−	0.771363i	0.984124	+	0.177485i	$0.0567961\pi$
$194$		0			0
$195$	0.353646	+	2.45966i	0.0253251	+	0.176140i
$196$		0			0
$197$	19.5129	−	12.5402i	1.39024	−	0.893453i	0.390607	−	0.920558i	$-0.372265\pi$
$197$	19.5129	−	12.5402i	1.39024	−	0.893453i	0.999633	+	0.0271049i	$0.00862881\pi$
$198$		0			0
$199$	−4.56281	+	9.99117i	−0.323449	+	0.708255i	−0.999593	−	0.0285142i	$-0.990922\pi$
$199$	−4.56281	+	9.99117i	−0.323449	+	0.708255i	0.676144	+	0.736769i	$0.263650\pi$
$200$		0			0
$201$	−0.676807	+	0.198729i	−0.0477383	+	0.0140172i
$202$		0			0
$203$	−44.6679	−	13.1157i	−3.13507	−	0.920540i
$204$		0			0
$205$	1.02975	−	7.16205i	0.0719207	−	0.500219i
$206$		0			0
$207$	−1.29046	+	4.61895i	−0.0896933	+	0.321039i
$208$		0			0
$209$	2.35241	−	16.3614i	0.162720	−	1.13174i
$210$		0			0
$211$	2.12810	+	0.624868i	0.146505	+	0.0430177i	0.354163	−	0.935184i	$-0.384766\pi$
$211$	2.12810	+	0.624868i	0.146505	+	0.0430177i	−0.207658	+	0.978202i	$0.566584\pi$
$212$		0			0
$213$	8.87673	−	2.60644i	0.608224	−	0.178591i
$214$		0			0
$215$	−0.190517	+	0.417174i	−0.0129931	+	0.0284510i
$216$		0			0
$217$	−0.673755	+	0.432996i	−0.0457375	+	0.0293937i
$218$		0			0
$219$	−0.0237052	−	0.164873i	−0.00160185	−	0.0111411i
$220$		0			0
$221$	−11.5789	+	13.3627i	−0.778880	+	0.898875i
$222$		0			0
$223$	−10.6113	−	6.81948i	−0.710586	−	0.456666i	0.134764	−	0.990878i	$-0.456972\pi$
$223$	−10.6113	−	6.81948i	−0.710586	−	0.456666i	−0.845351	+	0.534211i	$0.820609\pi$
$224$		0			0
$225$	2.82524	+	3.26051i	0.188350	+	0.217367i
$226$		0			0
$227$	−3.03348	−	6.64239i	−0.201339	−	0.440871i	0.781849	−	0.623468i	$-0.214277\pi$
$227$	−3.03348	−	6.64239i	−0.201339	−	0.440871i	−0.983188	+	0.182597i	$0.941550\pi$
$228$		0			0
$229$	−25.2689			−1.66981			−0.834907	−	0.550390i	$-0.814479\pi$
$229$	−25.2689			−1.66981			−0.834907	+	0.550390i	$0.814479\pi$
$230$		0			0
$231$	−13.3317			−0.877160
$232$		0			0
$233$	9.88098	+	21.6363i	0.647325	+	1.41744i	0.893876	+	0.448314i	$0.147975\pi$
$233$	9.88098	+	21.6363i	0.647325	+	1.41744i	−0.246552	+	0.969130i	$0.579298\pi$
$234$		0			0
$235$	−2.61404	−	3.01677i	−0.170521	−	0.196792i
$236$		0			0
$237$	1.36039	+	0.874270i	0.0883668	+	0.0567899i
$238$		0			0
$239$	−10.1465	+	11.7097i	−0.656323	+	0.757437i	−0.982172	−	0.187985i	$-0.939804\pi$
$239$	−10.1465	+	11.7097i	−0.656323	+	0.757437i	0.325849	+	0.945422i	$0.394350\pi$
$240$		0			0
$241$	−0.226356	−	1.57434i	−0.0145809	−	0.101412i	0.981231	−	0.192834i	$-0.0617679\pi$
$241$	−0.226356	−	1.57434i	−0.0145809	−	0.101412i	−0.995812	+	0.0914219i	$0.970859\pi$
$242$		0			0
$243$	−0.841254	+	0.540641i	−0.0539664	+	0.0346821i
$244$		0			0
$245$	−4.57611	+	10.0203i	−0.292357	+	0.640172i
$246$		0			0
$247$	−16.0856	+	4.72316i	−1.02350	+	0.300528i
$248$		0			0
$249$	2.66422	+	0.782287i	0.168838	+	0.0495754i
$250$		0			0
$251$	−2.03282	+	14.1386i	−0.128310	+	0.892418i	0.819385	+	0.573243i	$0.194315\pi$
$251$	−2.03282	+	14.1386i	−0.128310	+	0.892418i	−0.947696	+	0.319175i	$0.896594\pi$
$252$		0			0
$253$	−7.82797	−	11.8351i	−0.492140	−	0.744068i
$254$		0			0
$255$	0.694390	−	4.82959i	0.0434844	−	0.302441i
$256$		0			0
$257$	10.0748	+	2.95822i	0.628446	+	0.184529i	0.580420	−	0.814318i	$-0.302889\pi$
$257$	10.0748	+	2.95822i	0.628446	+	0.184529i	0.0480268	+	0.998846i	$0.484707\pi$
$258$		0			0
$259$	−44.3385	+	13.0190i	−2.75506	+	0.808959i
$260$		0			0
$261$	4.29200	−	9.39818i	0.265668	−	0.581733i
$262$		0			0
$263$	11.8388	−	7.60834i	0.730012	−	0.469151i	−0.122094	−	0.992519i	$-0.538961\pi$
$263$	11.8388	−	7.60834i	0.730012	−	0.469151i	0.852107	+	0.523368i	$0.175325\pi$
$264$		0			0
$265$	−0.659802	−	4.58902i	−0.0405313	−	0.281902i
$266$		0			0
$267$	−0.743368	+	0.857892i	−0.0454934	+	0.0525021i
$268$		0			0
$269$	13.9943	+	8.99361i	0.853250	+	0.548350i	0.892587	−	0.450876i	$-0.148888\pi$
$269$	13.9943	+	8.99361i	0.853250	+	0.548350i	−0.0393371	+	0.999226i	$0.512525\pi$
$270$		0			0
$271$	4.18143	+	4.82562i	0.254004	+	0.293136i	0.868403	−	0.495860i	$-0.165147\pi$
$271$	4.18143	+	4.82562i	0.254004	+	0.293136i	−0.614399	+	0.788995i	$0.710602\pi$
$272$		0			0
$273$	5.61694	+	12.2994i	0.339952	+	0.744392i
$274$		0			0
$275$	−12.7649			−0.769750
$276$		0			0
$277$	−1.46019			−0.0877344			−0.0438672	−	0.999037i	$-0.513968\pi$
$277$	−1.46019			−0.0877344			−0.0438672	+	0.999037i	$0.513968\pi$
$278$		0			0
$279$	−0.0738383	−	0.161683i	−0.00442058	−	0.00967972i
$280$		0			0
$281$	−1.84938	−	2.13430i	−0.110325	−	0.127322i	0.697901	−	0.716194i	$-0.254118\pi$
$281$	−1.84938	−	2.13430i	−0.110325	−	0.127322i	−0.808226	+	0.588872i	$0.799572\pi$
$282$		0			0
$283$	9.96004	+	6.40093i	0.592063	+	0.380496i	0.802093	−	0.597199i	$-0.203720\pi$
$283$	9.96004	+	6.40093i	0.592063	+	0.380496i	−0.210030	+	0.977695i	$0.567356\pi$
$284$		0			0
$285$	3.02957	−	3.49631i	0.179456	−	0.207103i
$286$		0			0
$287$	−5.60311	−	38.9705i	−0.330741	−	2.30035i
$288$		0			0
$289$	14.9052	−	9.57896i	0.876774	−	0.563468i
$290$		0			0
$291$	−5.99757	+	13.1329i	−0.351584	+	0.769862i
$292$		0			0
$293$	−5.13925	+	1.50902i	−0.300238	+	0.0881578i	−0.428382	−	0.903598i	$-0.640916\pi$
$293$	−5.13925	+	1.50902i	−0.300238	+	0.0881578i	0.128144	+	0.991756i	$0.459098\pi$
$294$		0			0
$295$	0.577406	+	0.169542i	0.0336179	+	0.00987109i
$296$		0			0
$297$	0.421075	−	2.92864i	0.0244332	−	0.169937i
$298$		0			0
$299$	−7.62060	+	12.2082i	−0.440711	+	0.706021i
$300$		0			0
$301$	−0.355140	+	2.47005i	−0.0204699	+	0.142372i
$302$		0			0
$303$	0.616124	+	0.180910i	0.0353954	+	0.0103930i
$304$		0			0
$305$	−2.10053	+	0.616772i	−0.120276	+	0.0353162i
$306$		0			0
$307$	9.68010	−	21.1965i	0.552473	−	1.20975i	−0.403145	−	0.915136i	$-0.632083\pi$
$307$	9.68010	−	21.1965i	0.552473	−	1.20975i	0.955618	−	0.294610i	$-0.0951898\pi$
$308$		0			0
$309$	−14.1563	+	9.09768i	−0.805322	+	0.517549i
$310$		0			0
$311$	−2.66511	−	18.5362i	−0.151124	−	1.05109i	−0.914340	−	0.404948i	$-0.867289\pi$
$311$	−2.66511	−	18.5362i	−0.151124	−	1.05109i	0.763215	−	0.646144i	$-0.223620\pi$
$312$		0			0
$313$	−8.47071	+	9.77572i	−0.478793	+	0.552557i	−0.942836	−	0.333256i	$-0.891853\pi$
$313$	−8.47071	+	9.77572i	−0.478793	+	0.552557i	0.464043	+	0.885812i	$0.346398\pi$
$314$		0			0
$315$	−3.13892	−	2.01726i	−0.176858	−	0.113660i
$316$		0			0
$317$	−12.1782	−	14.0544i	−0.683997	−	0.789375i	0.302500	−	0.953149i	$-0.402179\pi$
$317$	−12.1782	−	14.0544i	−0.683997	−	0.789375i	−0.986498	+	0.163774i	$0.947633\pi$
$318$		0			0
$319$	12.6990	+	27.8069i	0.711007	+	1.55689i
$320$		0			0
$321$	−11.4626			−0.639781
$322$		0			0
$323$	32.9178			1.83159
$324$		0			0
$325$	5.37812	+	11.7764i	0.298325	+	0.653240i
$326$		0			0
$327$	−6.08168	−	7.01863i	−0.336318	−	0.388131i
$328$		0			0
$329$	−18.2721	−	11.7428i	−1.00738	−	0.647401i
$330$		0			0
$331$	14.7075	−	16.9733i	0.808396	−	0.932939i	−0.190414	−	0.981704i	$-0.560983\pi$
$331$	14.7075	−	16.9733i	0.808396	−	0.932939i	0.998810	+	0.0487650i	$0.0155286\pi$
$332$		0			0
$333$	−1.45953	−	10.1513i	−0.0799818	−	0.556286i
$334$		0			0
$335$	0.491392	−	0.315798i	0.0268476	−	0.0172539i
$336$		0			0
$337$	−2.97618	+	6.51693i	−0.162123	+	0.355000i	−0.973207	−	0.229929i	$-0.926150\pi$
$337$	−2.97618	+	6.51693i	−0.162123	+	0.355000i	0.811084	+	0.584929i	$0.198878\pi$
$338$		0			0
$339$	19.1226	−	5.61490i	1.03860	−	0.304959i
$340$		0			0
$341$	0.504603	+	0.148165i	0.0273258	+	0.00802358i
$342$		0			0
$343$	−4.04153	+	28.1095i	−0.218222	+	1.51777i
$344$		0			0
$345$	−0.0522686	−	3.97104i	−0.00281404	−	0.213793i
$346$		0			0
$347$	−2.52766	+	17.5802i	−0.135692	+	0.943757i	0.802256	+	0.596980i	$0.203633\pi$
$347$	−2.52766	+	17.5802i	−0.135692	+	0.943757i	−0.937948	+	0.346776i	$0.887276\pi$
$348$		0			0
$349$	14.4592	+	4.24560i	0.773982	+	0.227261i	0.644792	−	0.764358i	$-0.276944\pi$
$349$	14.4592	+	4.24560i	0.773982	+	0.227261i	0.129190	+	0.991620i	$0.458762\pi$
$350$		0			0
$351$	−2.87928	+	0.845432i	−0.153684	+	0.0451258i
$352$		0			0
$353$	−13.9571	+	30.5618i	−0.742862	+	1.62664i	0.0359270	+	0.999354i	$0.488562\pi$
$353$	−13.9571	+	30.5618i	−0.742862	+	1.62664i	−0.778789	+	0.627286i	$0.784166\pi$
$354$		0			0
$355$	−6.44489	+	4.14188i	−0.342059	+	0.219828i
$356$		0			0
$357$	−3.77835	−	26.2790i	−0.199971	−	1.39083i
$358$		0			0
$359$	−19.1864	+	22.1423i	−1.01262	+	1.16863i	−0.0270037	+	0.999635i	$0.508597\pi$
$359$	−19.1864	+	22.1423i	−1.01262	+	1.16863i	−0.985617	+	0.168992i	$0.945949\pi$
$360$		0			0
$361$	10.2726	+	6.60180i	0.540663	+	0.347463i
$362$		0			0
$363$	−1.47067	−	1.69724i	−0.0771900	−	0.0890820i
$364$		0			0
$365$	0.0572998	+	0.125469i	0.00299921	+	0.00656735i
$366$		0			0
$367$	30.9079			1.61338			0.806689	−	0.590976i	$-0.201257\pi$
$367$	30.9079			1.61338			0.806689	+	0.590976i	$0.201257\pi$
$368$		0			0
$369$	8.73782			0.454873
$370$		0			0
$371$	−10.4796	−	22.9471i	−0.544073	−	1.19135i
$372$		0			0
$373$	9.24171	+	10.6655i	0.478518	+	0.552239i	0.942761	−	0.333469i	$-0.108219\pi$
$373$	9.24171	+	10.6655i	0.478518	+	0.552239i	−0.464243	+	0.885708i	$0.653674\pi$
$374$		0			0
$375$	−6.48863	−	4.16999i	−0.335071	−	0.215337i
$376$		0			0
$377$	20.3034	−	23.4314i	1.04568	−	1.20678i
$378$		0			0
$379$	−1.16386	−	8.09482i	−0.0597835	−	0.415803i	−0.997633	−	0.0687614i	$-0.978095\pi$
$379$	−1.16386	−	8.09482i	−0.0597835	−	0.415803i	0.937850	−	0.347042i	$-0.112814\pi$
$380$		0			0
$381$	−5.38310	+	3.45951i	−0.275785	+	0.177236i
$382$		0			0
$383$	3.45298	−	7.56097i	0.176439	−	0.386348i	−0.800664	−	0.599113i	$-0.795520\pi$
$383$	3.45298	−	7.56097i	0.176439	−	0.386348i	0.977103	+	0.212766i	$0.0682471\pi$
$384$		0			0
$385$	10.5926	−	3.11028i	0.539851	−	0.158514i
$386$		0			0
$387$	−0.531393	−	0.156031i	−0.0270122	−	0.00793150i
$388$		0			0
$389$	3.67786	−	25.5801i	0.186475	−	1.29696i	−0.654572	−	0.756000i	$-0.727151\pi$
$389$	3.67786	−	25.5801i	0.186475	−	1.29696i	0.841047	−	0.540962i	$-0.181940\pi$
$390$		0			0
$391$	21.1105	−	18.7845i	1.06760	−	0.949971i
$392$		0			0
$393$	−1.74108	+	12.1095i	−0.0878258	+	0.610842i
$394$		0			0
$395$	−1.28486	−	0.377269i	−0.0646483	−	0.0189825i
$396$		0			0
$397$	4.78437	−	1.40482i	0.240121	−	0.0705057i	−0.159458	−	0.987205i	$-0.550975\pi$
$397$	4.78437	−	1.40482i	0.240121	−	0.0705057i	0.399579	+	0.916699i	$0.369156\pi$
$398$		0			0
$399$	10.4571	−	22.8979i	0.523511	−	1.14633i
$400$		0			0
$401$	17.3941	−	11.1785i	0.868621	−	0.558229i	−0.0287098	−	0.999588i	$-0.509140\pi$
$401$	17.3941	−	11.1785i	0.868621	−	0.558229i	0.897331	+	0.441359i	$0.145503\pi$
$402$		0			0
$403$	−0.0759086	−	0.527956i	−0.00378128	−	0.0262994i
$404$		0			0
$405$	0.542284	−	0.625829i	0.0269463	−	0.0310977i
$406$		0			0
$407$	25.5270	+	16.4052i	1.26532	+	0.813175i
$408$		0			0
$409$	4.43051	+	5.11309i	0.219075	+	0.252826i	0.854640	−	0.519222i	$-0.173778\pi$
$409$	4.43051	+	5.11309i	0.219075	+	0.252826i	−0.635565	+	0.772048i	$0.719233\pi$
$410$		0			0
$411$	3.79940	+	8.31952i	0.187410	+	0.410371i
$412$		0			0
$413$	3.27444			0.161125
$414$		0			0
$415$	−2.29936			−0.112871
$416$		0			0
$417$	4.23883	+	9.28174i	0.207576	+	0.454529i
$418$		0			0
$419$	−11.0627	−	12.7670i	−0.540447	−	0.623709i	0.418183	−	0.908363i	$-0.362667\pi$
$419$	−11.0627	−	12.7670i	−0.540447	−	0.623709i	−0.958631	+	0.284653i	$0.908122\pi$
$420$		0			0
$421$	33.6785	+	21.6438i	1.64139	+	1.05486i	0.939489	+	0.342579i	$0.111301\pi$
$421$	33.6785	+	21.6438i	1.64139	+	1.05486i	0.701899	+	0.712276i	$0.252336\pi$
$422$		0			0
$423$	3.15672	−	3.64304i	0.153485	−	0.177131i
$424$		0			0
$425$	−3.61771	−	25.1617i	−0.175485	−	1.22052i
$426$		0			0
$427$	−10.0210	+	6.44013i	−0.484952	+	0.311660i
$428$		0			0
$429$	3.68835	−	8.07637i	0.178075	−	0.389931i
$430$		0			0
$431$	−2.05180	+	0.602462i	−0.0988316	+	0.0290196i	−0.330774	−	0.943710i	$-0.607310\pi$
$431$	−2.05180	+	0.602462i	−0.0988316	+	0.0290196i	0.231943	+	0.972729i	$0.425492\pi$
$432$		0			0
$433$	−12.0704	−	3.54419i	−0.580066	−	0.170323i	−0.0214801	−	0.999769i	$-0.506838\pi$
$433$	−12.0704	−	3.54419i	−0.580066	−	0.170323i	−0.558586	+	0.829446i	$0.688656\pi$
$434$		0			0
$435$	−1.21760	+	8.46861i	−0.0583796	+	0.406039i
$436$		0			0
$437$	26.4676	−	4.16172i	1.26612	−	0.199082i
$438$		0			0
$439$	−4.55290	+	31.6661i	−0.217298	+	1.51134i	0.530654	+	0.847589i	$0.321947\pi$
$439$	−4.55290	+	31.6661i	−0.217298	+	1.51134i	−0.747952	+	0.663753i	$0.768963\pi$
$440$		0			0
$441$	−12.7638	−	3.74778i	−0.607798	−	0.178466i
$442$		0			0
$443$	12.6415	−	3.71189i	0.600618	−	0.176357i	0.0327313	−	0.999464i	$-0.489579\pi$
$443$	12.6415	−	3.71189i	0.600618	−	0.176357i	0.567886	+	0.823107i	$0.307761\pi$
$444$		0			0
$445$	0.390494	−	0.855063i	0.0185112	−	0.0405338i
$446$		0			0
$447$	−0.516522	+	0.331948i	−0.0244306	+	0.0157006i
$448$		0			0
$449$	5.43277	+	37.7858i	0.256388	+	1.78322i	0.558052	+	0.829806i	$0.311549\pi$
$449$	5.43277	+	37.7858i	0.256388	+	1.78322i	−0.301664	+	0.953414i	$0.597542\pi$
$450$		0			0
$451$	−16.9302	+	19.5384i	−0.797210	+	0.920029i
$452$		0			0
$453$	−5.92585	−	3.80831i	−0.278421	−	0.178930i
$454$		0			0
$455$	−7.33236	−	8.46199i	−0.343746	−	0.396704i
$456$		0			0
$457$	−6.77403	−	14.8330i	−0.316876	−	0.693861i	0.682437	−	0.730945i	$-0.260920\pi$
$457$	−6.77403	−	14.8330i	−0.316876	−	0.693861i	−0.999312	+	0.0370841i	$0.988193\pi$
$458$		0			0
$459$	5.89218			0.275023
$460$		0			0
$461$	−29.1351			−1.35696			−0.678479	−	0.734620i	$-0.737361\pi$
$461$	−29.1351			−1.35696			−0.678479	+	0.734620i	$0.737361\pi$
$462$		0			0
$463$	15.9787	+	34.9885i	0.742594	+	1.62605i	0.779241	+	0.626725i	$0.215605\pi$
$463$	15.9787	+	34.9885i	0.742594	+	1.62605i	−0.0366471	+	0.999328i	$0.511668\pi$
$464$		0			0
$465$	0.0963886	+	0.111238i	0.00446991	+	0.00515856i
$466$		0			0
$467$	20.1121	+	12.9252i	0.930676	+	0.598109i	0.915737	−	0.401779i	$-0.131608\pi$
$467$	20.1121	+	12.9252i	0.930676	+	0.598109i	0.0149395	+	0.999888i	$0.495244\pi$
$468$		0			0
$469$	2.08136	−	2.40202i	0.0961085	−	0.110915i
$470$		0			0
$471$	1.02999	+	7.16373i	0.0474594	+	0.330087i
$472$		0			0
$473$	1.37851	−	0.885914i	0.0633839	−	0.0407344i
$474$		0			0
$475$	10.0125	−	21.9244i	0.459406	−	1.00596i
$476$		0			0
$477$	5.37190	−	1.57733i	0.245962	−	0.0722211i
$478$		0			0
$479$	13.2010	+	3.87616i	0.603169	+	0.177106i	0.569038	−	0.822311i	$-0.307316\pi$
$479$	13.2010	+	3.87616i	0.603169	+	0.177106i	0.0341305	+	0.999417i	$0.489134\pi$
$480$		0			0
$481$	4.37981	−	30.4622i	0.199702	−	1.38896i
$482$		0			0
$483$	−6.36039	−	20.6520i	−0.289408	−	0.939699i
$484$		0			0
$485$	1.70146	−	11.8339i	0.0772592	−	0.537350i
$486$		0			0
$487$	−21.4617	−	6.30173i	−0.972523	−	0.285558i	−0.243388	−	0.969929i	$-0.578259\pi$
$487$	−21.4617	−	6.30173i	−0.972523	−	0.285558i	−0.729134	+	0.684370i	$0.760077\pi$
$488$		0			0
$489$	−16.7604	+	4.92129i	−0.757930	+	0.222548i
$490$		0			0
$491$	−8.15086	+	17.8479i	−0.367843	+	0.805464i	0.631699	+	0.775214i	$0.282358\pi$
$491$	−8.15086	+	17.8479i	−0.367843	+	0.805464i	−0.999542	+	0.0302508i	$0.990369\pi$
$492$		0			0
$493$	−51.2131	+	32.9126i	−2.30652	+	1.48231i
$494$		0			0
$495$	0.348688	+	2.42518i	0.0156723	+	0.109004i
$496$		0			0
$497$	−27.2983	+	31.5040i	−1.22450	+	1.41315i
$498$		0			0
$499$	−13.4103	−	8.61829i	−0.600328	−	0.385808i	0.204891	−	0.978785i	$-0.434316\pi$
$499$	−13.4103	−	8.61829i	−0.600328	−	0.385808i	−0.805219	+	0.592977i	$0.797952\pi$
$500$		0			0
$501$	8.52742	+	9.84117i	0.380977	+	0.439671i
$502$		0			0
$503$	−1.25887	−	2.75655i	−0.0561304	−	0.122908i	0.879489	−	0.475920i	$-0.157885\pi$
$503$	−1.25887	−	2.75655i	−0.0561304	−	0.122908i	−0.935619	+	0.353012i	$0.885158\pi$
$504$		0			0
$505$	−0.531746			−0.0236624
$506$		0			0
$507$	3.99501			0.177425
$508$		0			0
$509$	−5.30767	−	11.6222i	−0.235258	−	0.515144i	0.754774	−	0.655985i	$-0.227747\pi$
$509$	−5.30767	−	11.6222i	−0.235258	−	0.515144i	−0.990032	+	0.140841i	$0.955019\pi$
$510$		0			0
$511$	0.491494	+	0.567215i	0.0217424	+	0.0250921i
$512$		0			0
$513$	4.69982	+	3.02039i	0.207502	+	0.133353i
$514$		0			0
$515$	9.12532	−	10.5312i	0.402110	−	0.464059i
$516$		0			0
$517$	2.02976	+	14.1173i	0.0892689	+	0.620879i
$518$		0			0
$519$	−7.94083	+	5.10326i	−0.348564	+	0.224008i
$520$		0			0
$521$	0.138293	−	0.302819i	0.00605872	−	0.0132667i	−0.906578	−	0.422037i	$-0.861315\pi$
$521$	0.138293	−	0.302819i	0.00605872	−	0.0132667i	0.912637	+	0.408771i	$0.134042\pi$
$522$		0			0
$523$	37.8325	−	11.1086i	1.65430	−	0.485746i	0.684370	−	0.729135i	$-0.260078\pi$
$523$	37.8325	−	11.1086i	1.65430	−	0.485746i	0.969929	+	0.243390i	$0.0782593\pi$
$524$		0			0
$525$	−18.6520	−	5.47671i	−0.814039	−	0.239023i
$526$		0			0
$527$	−0.149048	+	1.03665i	−0.00649262	+	0.0451572i
$528$		0			0
$529$	14.5991	−	17.7726i	0.634742	−	0.772724i
$530$		0			0
$531$	−0.103422	+	0.719314i	−0.00448812	+	0.0312156i
$532$		0			0
$533$	25.1586	+	7.38723i	1.08974	+	0.319976i
$534$		0			0
$535$	9.10758	−	2.67423i	0.393755	−	0.115617i
$536$		0			0
$537$	8.05778	−	17.6441i	0.347719	−	0.761398i
$538$		0			0
$539$	33.1110	−	21.2792i	1.42619	−	0.916558i
$540$		0			0
$541$	−2.18165	−	15.1737i	−0.0937962	−	0.652367i	−0.981430	−	0.191818i	$-0.938562\pi$
$541$	−2.18165	−	15.1737i	−0.0937962	−	0.652367i	0.887634	−	0.460549i	$-0.152347\pi$
$542$		0			0
$543$	12.5139	−	14.4418i	0.537023	−	0.619757i
$544$		0			0
$545$	6.46962	+	4.15778i	0.277128	+	0.178100i
$546$		0			0
$547$	15.9108	+	18.3621i	0.680299	+	0.785106i	0.985951	−	0.167037i	$-0.0534199\pi$
$547$	15.9108	+	18.3621i	0.680299	+	0.785106i	−0.305652	+	0.952143i	$0.598874\pi$
$548$		0			0
$549$	−1.09823	−	2.40478i	−0.0468712	−	0.102634i
$550$		0			0
$551$	−57.7208			−2.45899
$552$		0			0
$553$	−7.28639			−0.309849
$554$		0			0
$555$	3.52795	+	7.72514i	0.149753	+	0.327914i
$556$		0			0
$557$	−18.1037	−	20.8928i	−0.767077	−	0.885254i	0.229029	−	0.973420i	$-0.426445\pi$
$557$	−18.1037	−	20.8928i	−0.767077	−	0.885254i	−0.996106	+	0.0881653i	$0.971900\pi$
$558$		0			0
$559$	−1.39811	−	0.898512i	−0.0591339	−	0.0380030i
$560$		0			0
$561$	−11.4165	+	13.1754i	−0.482006	+	0.556265i
$562$		0			0
$563$	−4.27805	−	29.7545i	−0.180299	−	1.25400i	−0.856057	−	0.516881i	$-0.827093\pi$
$563$	−4.27805	−	29.7545i	−0.180299	−	1.25400i	0.675759	−	0.737123i	$-0.263816\pi$
$564$		0			0
$565$	−13.8838	+	8.92259i	−0.584097	+	0.375376i
$566$		0			0
$567$	1.87179	−	4.09866i	0.0786080	−	0.172127i
$568$		0			0
$569$	−43.7146	+	12.8358i	−1.83261	+	0.538104i	−0.999879	−	0.0155702i	$-0.995044\pi$
$569$	−43.7146	+	12.8358i	−1.83261	+	0.538104i	−0.832734	+	0.553674i	$0.813225\pi$
$570$		0			0
$571$	13.0634	+	3.83576i	0.546686	+	0.160521i	0.543401	−	0.839473i	$-0.317136\pi$
$571$	13.0634	+	3.83576i	0.546686	+	0.160521i	0.00328468	+	0.999995i	$0.498954\pi$
$572$		0			0
$573$	2.69159	−	18.7204i	0.112443	−	0.782056i
$574$		0			0
$575$	−6.08997	−	19.7739i	−0.253969	−	0.824631i
$576$		0			0
$577$	−1.72569	+	12.0024i	−0.0718414	+	0.499668i	0.921853	+	0.387541i	$0.126675\pi$
$577$	−1.72569	+	12.0024i	−0.0718414	+	0.499668i	−0.993694	+	0.112127i	$0.964234\pi$
$578$		0			0
$579$	−13.6051	−	3.99481i	−0.565408	−	0.166019i
$580$		0			0
$581$	−12.0046	+	3.52486i	−0.498033	+	0.146236i
$582$		0			0
$583$	−6.88141	+	15.0682i	−0.284999	+	0.624060i
$584$		0			0
$585$	2.09048	−	1.34347i	0.0864307	−	0.0555456i
$586$		0			0
$587$	4.05237	+	28.1849i	0.167259	+	1.16331i	0.884518	+	0.466507i	$0.154488\pi$
$587$	4.05237	+	28.1849i	0.167259	+	1.16331i	−0.717258	+	0.696807i	$0.754603\pi$
$588$		0			0
$589$	−0.650283	+	0.750467i	−0.0267944	+	0.0309224i
$590$		0			0
$591$	−19.5129	−	12.5402i	−0.802655	−	0.515835i
$592$		0			0
$593$	−20.1174	−	23.2167i	−0.826121	−	0.953395i	0.173384	−	0.984854i	$-0.444530\pi$
$593$	−20.1174	−	23.2167i	−0.826121	−	0.953395i	−0.999505	+	0.0314595i	$0.989984\pi$
$594$		0			0
$595$	9.13296	+	19.9984i	0.374415	+	0.819854i
$596$		0			0
$597$	10.9837			0.449535
$598$		0			0
$599$	13.5349			0.553019			0.276510	−	0.961011i	$-0.410822\pi$
$599$	13.5349			0.553019			0.276510	+	0.961011i	$0.410822\pi$
$600$		0			0
$601$	−17.9035	−	39.2033i	−0.730300	−	1.59913i	−0.798881	−	0.601489i	$-0.794574\pi$
$601$	−17.9035	−	39.2033i	−0.730300	−	1.59913i	0.0685812	−	0.997646i	$-0.478153\pi$
$602$		0			0
$603$	0.461926	+	0.533091i	0.0188111	+	0.0217091i
$604$		0			0
$605$	1.56448	+	1.00543i	0.0636051	+	0.0408765i
$606$		0			0
$607$	−4.13846	+	4.77604i	−0.167975	+	0.193853i	−0.833496	−	0.552526i	$-0.813664\pi$
$607$	−4.13846	+	4.77604i	−0.167975	+	0.193853i	0.665521	+	0.746379i	$0.268209\pi$
$608$		0			0
$609$	6.62528	+	46.0798i	0.268470	+	1.86725i
$610$		0			0
$611$	12.1690	−	7.82054i	0.492305	−	0.316385i
$612$		0			0
$613$	−8.95406	+	19.6067i	−0.361651	+	0.791906i	0.638108	+	0.769947i	$0.279717\pi$
$613$	−8.95406	+	19.6067i	−0.361651	+	0.791906i	−0.999759	+	0.0219586i	$0.993010\pi$
$614$		0			0
$615$	−6.94260	+	2.03853i	−0.279953	+	0.0822015i
$616$		0			0
$617$	−17.8308	−	5.23559i	−0.717840	−	0.210777i	−0.0976416	−	0.995222i	$-0.531130\pi$
$617$	−17.8308	−	5.23559i	−0.717840	−	0.210777i	−0.620199	+	0.784445i	$0.712948\pi$
$618$		0			0
$619$	−2.85642	+	19.8669i	−0.114809	+	0.798516i	0.848321	+	0.529482i	$0.177614\pi$
$619$	−2.85642	+	19.8669i	−0.114809	+	0.798516i	−0.963131	+	0.269034i	$0.913295\pi$
$620$		0			0
$621$	4.73762	−	0.744936i	0.190114	−	0.0298932i
$622$		0			0
$623$	0.727915	−	5.06276i	0.0291633	−	0.202835i
$624$		0			0
$625$	−14.5692	−	4.27789i	−0.582767	−	0.171116i
$626$		0			0
$627$	−15.8601	+	4.65694i	−0.633390	+	0.185980i
$628$		0			0
$629$	−25.1028	+	54.9674i	−1.00091	+	2.19169i
$630$		0			0
$631$	35.7270	−	22.9604i	1.42227	−	0.914037i	0.422299	−	0.906457i	$-0.361223\pi$
$631$	35.7270	−	22.9604i	1.42227	−	0.914037i	0.999971	−	0.00758072i	$-0.00241304\pi$
$632$		0			0
$633$	−0.315647	−	2.19537i	−0.0125458	−	0.0872582i
$634$		0			0
$635$	3.47002	−	4.00462i	0.137704	−	0.158918i
$636$		0			0
$637$	−33.5819	−	21.5818i	−1.33056	−	0.855101i
$638$		0			0
$639$	−6.05843	−	6.99180i	−0.239668	−	0.276591i
$640$		0			0
$641$	2.78005	+	6.08746i	0.109805	+	0.240440i	0.956555	−	0.291551i	$-0.0941713\pi$
$641$	2.78005	+	6.08746i	0.109805	+	0.240440i	−0.846750	+	0.531991i	$0.821444\pi$
$642$		0			0
$643$	0.819942			0.0323353			0.0161677	−	0.999869i	$-0.494853\pi$
$643$	0.819942			0.0323353			0.0161677	+	0.999869i	$0.494853\pi$
$644$		0			0
$645$	0.458618			0.0180581
$646$		0			0
$647$	−5.42011	−	11.8684i	−0.213087	−	0.466594i	0.772662	−	0.634817i	$-0.218925\pi$
$647$	−5.42011	−	11.8684i	−0.213087	−	0.466594i	−0.985749	+	0.168223i	$0.946197\pi$
$648$		0			0
$649$	−1.40806	−	1.62498i	−0.0552710	−	0.0637861i
$650$		0			0
$651$	0.673755	+	0.432996i	0.0264065	+	0.0169705i
$652$		0			0
$653$	−1.13276	+	1.30727i	−0.0443282	+	0.0511574i	−0.777481	−	0.628907i	$-0.783503\pi$
$653$	−1.13276	+	1.30727i	−0.0443282	+	0.0511574i	0.733152	+	0.680064i	$0.238048\pi$
$654$		0			0
$655$	−1.44177	−	10.0277i	−0.0563346	−	0.391816i
$656$		0			0
$657$	−0.140127	+	0.0900539i	−0.00546686	+	0.00351334i
$658$		0			0
$659$	−12.2402	+	26.8023i	−0.476810	+	1.04407i	0.506518	+	0.862229i	$0.330932\pi$
$659$	−12.2402	+	26.8023i	−0.476810	+	1.04407i	−0.983328	+	0.181840i	$0.941795\pi$
$660$		0			0
$661$	16.1514	−	4.74247i	0.628215	−	0.184461i	0.0478995	−	0.998852i	$-0.484747\pi$
$661$	16.1514	−	4.74247i	0.628215	−	0.184461i	0.580316	+	0.814391i	$0.302929\pi$
$662$		0			0
$663$	16.9652	+	4.98144i	0.658874	+	0.193463i
$664$		0			0
$665$	−2.96659	+	20.6331i	−0.115039	+	0.800117i
$666$		0			0
$667$	−37.0169	+	32.9383i	−1.43330	+	1.27537i
$668$		0			0
$669$	−1.79512	+	12.4853i	−0.0694032	+	0.482710i
$670$		0			0
$671$	7.50517	+	2.20372i	0.289734	+	0.0850736i
$672$		0			0
$673$	−6.33891	+	1.86127i	−0.244347	+	0.0717468i	−0.401613	−	0.915810i	$-0.631550\pi$
$673$	−6.33891	+	1.86127i	−0.244347	+	0.0717468i	0.157266	+	0.987556i	$0.449732\pi$
$674$		0			0
$675$	1.79221	−	3.92440i	0.0689822	−	0.151050i
$676$		0			0
$677$	11.8557	−	7.61923i	0.455653	−	0.292831i	−0.292611	−	0.956232i	$-0.594524\pi$
$677$	11.8557	−	7.61923i	0.455653	−	0.292831i	0.748264	+	0.663401i	$0.230888\pi$
$678$		0			0
$679$	−9.25805	−	64.3912i	−0.355291	−	2.47111i
$680$		0			0
$681$	−4.78198	+	5.51870i	−0.183246	+	0.211477i
$682$		0			0
$683$	33.8287	+	21.7404i	1.29442	+	0.831873i	0.992593	−	0.121489i	$-0.0387669\pi$
$683$	33.8287	+	21.7404i	1.29442	+	0.831873i	0.301828	+	0.953363i	$0.402403\pi$
$684$		0			0
$685$	−4.95974	−	5.72384i	−0.189502	−	0.218697i
$686$		0			0
$687$	10.4971	+	22.9854i	0.400488	+	0.876947i
$688$		0			0
$689$	16.8007			0.640056
$690$		0			0
$691$	9.52244			0.362251			0.181125	−	0.983460i	$-0.442026\pi$
$691$	9.52244			0.362251			0.181125	+	0.983460i	$0.442026\pi$
$692$		0			0
$693$	5.53818	+	12.1269i	0.210378	+	0.460664i
$694$		0			0
$695$	−5.53338	−	6.38586i	−0.209893	−	0.242229i
$696$		0			0
$697$	−43.3118	−	27.8348i	−1.64055	−	1.05432i
$698$		0			0
$699$	15.5764	−	17.9761i	0.589153	−	0.679919i
$700$		0			0
$701$	1.65345	+	11.5000i	0.0624500	+	0.434350i	0.996928	+	0.0783277i	$0.0249580\pi$
$701$	1.65345	+	11.5000i	0.0624500	+	0.434350i	−0.934478	+	0.356022i	$0.884133\pi$
$702$		0			0
$703$	−48.1997	+	30.9761i	−1.81789	+	1.16828i
$704$		0			0
$705$	−1.65824	+	3.63103i	−0.0624527	+	0.136752i
$706$		0			0
$707$	−2.77616	+	0.815154i	−0.104408	+	0.0306570i
$708$		0			0
$709$	−11.7383	−	3.44668i	−0.440841	−	0.129443i	0.0537770	−	0.998553i	$-0.482874\pi$
$709$	−11.7383	−	3.44668i	−0.440841	−	0.129443i	−0.494618	+	0.869110i	$0.664692\pi$
$710$		0			0
$711$	0.230137	−	1.60064i	0.00863082	−	0.0600287i
$712$		0			0
$713$	0.0112192	+	0.852365i	0.000420163	+	0.0319213i
$714$		0			0
$715$	−1.04635	+	7.27754i	−0.0391314	+	0.272165i
$716$		0			0
$717$	14.8665	+	4.36520i	0.555200	+	0.163022i
$718$		0			0
$719$	37.5018	−	11.0115i	1.39858	−	0.410661i	0.506385	−	0.862308i	$-0.330982\pi$
$719$	37.5018	−	11.0115i	1.39858	−	0.410661i	0.892197	+	0.451647i	$0.149163\pi$
$720$		0			0
$721$	31.4978	−	68.9705i	1.17304	−	2.56860i
$722$		0			0
$723$	−1.33804	+	0.859905i	−0.0497622	+	0.0319802i
$724$		0			0
$725$	6.34359	+	44.1206i	0.235595	+	1.63860i
$726$		0			0
$727$	30.0886	−	34.7240i	1.11592	−	1.28784i	0.162333	−	0.986736i	$-0.448098\pi$
$727$	30.0886	−	34.7240i	1.11592	−	1.28784i	0.953590	−	0.301108i	$-0.0973563\pi$
$728$		0			0
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$		0			0
$731$	2.13697	+	2.46620i	0.0790387	+	0.0912156i
$732$		0			0
$733$	−10.8717	−	23.8058i	−0.401557	−	0.879287i	−0.997110	−	0.0759712i	$-0.975794\pi$
$733$	−10.8717	−	23.8058i	−0.401557	−	0.879287i	0.595553	−	0.803316i	$-0.296933\pi$
$734$		0			0
$735$	11.0158			0.406322
$736$		0			0
$737$	−2.08705			−0.0768774
$738$		0			0
$739$	13.4854	+	29.5289i	0.496069	+	1.08624i	0.977727	+	0.209880i	$0.0673074\pi$
$739$	13.4854	+	29.5289i	0.496069	+	1.08624i	−0.481658	+	0.876359i	$0.659965\pi$
$740$		0			0
$741$	10.9785	+	12.6699i	0.403307	+	0.465441i
$742$		0			0
$743$	2.33598	+	1.50124i	0.0856987	+	0.0550752i	0.582788	−	0.812624i	$-0.301962\pi$
$743$	2.33598	+	1.50124i	0.0856987	+	0.0550752i	−0.497090	+	0.867699i	$0.665598\pi$
$744$		0			0
$745$	0.332957	−	0.384253i	0.0121986	−	0.0140779i
$746$		0			0
$747$	−0.395166	−	2.74844i	−0.0144583	−	0.100560i
$748$		0			0
$749$	43.4497	−	27.9234i	1.58762	−	1.02030i
$750$		0			0
$751$	−14.8223	+	32.4563i	−0.540873	+	1.18435i	0.420042	+	0.907505i	$0.362015\pi$
$751$	−14.8223	+	32.4563i	−0.540873	+	1.18435i	−0.960915	+	0.276842i	$0.910712\pi$
$752$		0			0
$753$	13.7053	−	4.02425i	0.499451	−	0.146652i
$754$		0			0
$755$	5.59684	+	1.64338i	0.203690	+	0.0598088i
$756$		0			0
$757$	2.40640	−	16.7369i	0.0874622	−	0.608313i	−0.898201	−	0.439586i	$-0.855125\pi$
$757$	2.40640	−	16.7369i	0.0874622	−	0.608313i	0.985663	−	0.168727i	$-0.0539656\pi$
$758$		0			0
$759$	−7.51375	+	12.0371i	−0.272732	+	0.436918i
$760$		0			0
$761$	3.72501	−	25.9080i	0.135032	−	0.939166i	−0.803827	−	0.594863i	$-0.797206\pi$
$761$	3.72501	−	25.9080i	0.135032	−	0.939166i	0.938859	−	0.344303i	$-0.111885\pi$
$762$		0			0
$763$	40.1506	+	11.7893i	1.45355	+	0.426801i
$764$		0			0
$765$	−4.68161	+	1.37464i	−0.169264	+	0.0497004i
$766$		0			0
$767$	−0.905911	+	1.98367i	−0.0327105	+	0.0716261i
$768$		0			0
$769$	−19.6508	+	12.6288i	−0.708626	+	0.455406i	−0.844664	−	0.535298i	$-0.820199\pi$
$769$	−19.6508	+	12.6288i	−0.708626	+	0.455406i	0.136038	+	0.990704i	$0.456563\pi$
$770$		0			0
$771$	−1.49432	−	10.3932i	−0.0538166	−	0.374302i
$772$		0			0
$773$	20.5825	−	23.7535i	0.740301	−	0.854353i	−0.253290	−	0.967390i	$-0.581513\pi$
$773$	20.5825	−	23.7535i	0.740301	−	0.854353i	0.993591	+	0.113038i	$0.0360580\pi$
$774$		0			0
$775$	0.645109	+	0.414586i	0.0231730	+	0.0148924i
$776$		0			0
$777$	30.2613	+	34.9234i	1.08562	+	1.25287i
$778$		0			0
$779$	−20.2787	−	44.4041i	−0.726559	−	1.59094i
$780$		0			0
$781$	27.3729			0.979478
$782$		0			0
$783$	−10.3318			−0.369230
$784$		0			0
$785$	−2.48967	−	5.45162i	−0.0888602	−	0.194577i
$786$		0			0
$787$	−12.7129	−	14.6715i	−0.453167	−	0.522983i	0.482486	−	0.875904i	$-0.339734\pi$
$787$	−12.7129	−	14.6715i	−0.453167	−	0.522983i	−0.935653	+	0.352921i	$0.885189\pi$
$788$		0			0
$789$	−11.8388	−	7.60834i	−0.421473	−	0.270864i
$790$		0			0
$791$	−58.8071	+	67.8670i	−2.09094	+	2.41307i
$792$		0			0
$793$	−1.12902	−	7.85251i	−0.0400927	−	0.278851i
$794$		0			0
$795$	−3.90023	+	2.50653i	−0.138327	+	0.0888973i
$796$		0			0
$797$	0.354933	−	0.777195i	0.0125724	−	0.0275296i	−0.903242	−	0.429132i	$-0.858819\pi$
$797$	0.354933	−	0.777195i	0.0125724	−	0.0275296i	0.915814	+	0.401603i	$0.131547\pi$
$798$		0			0
$799$	−27.2524	+	8.00202i	−0.964120	+	0.283091i
$800$		0			0
$801$	1.08917	+	0.319810i	0.0384840	+	0.0112999i
$802$		0			0
$803$	0.0701379	−	0.487820i	0.00247511	−	0.0172148i
$804$		0			0
$805$	9.87173	+	14.9251i	0.347933	+	0.526041i
$806$		0			0
$807$	2.36742	−	16.4658i	0.0833372	−	0.579623i
$808$		0			0
$809$	13.1285	+	3.85488i	0.461574	+	0.135530i	0.504248	−	0.863559i	$-0.331770\pi$
$809$	13.1285	+	3.85488i	0.461574	+	0.135530i	−0.0426744	+	0.999089i	$0.513588\pi$
$810$		0			0
$811$	16.2587	−	4.77399i	0.570920	−	0.167637i	0.0164849	−	0.999864i	$-0.494752\pi$
$811$	16.2587	−	4.77399i	0.570920	−	0.167637i	0.554435	+	0.832227i	$0.312934\pi$
$812$		0			0
$813$	2.65251	−	5.80819i	0.0930277	−	0.203702i
$814$		0			0
$815$	12.1688	−	7.82038i	0.426253	−	0.273936i
$816$		0			0
$817$	0.440330	+	3.06256i	0.0154052	+	0.107145i
$818$		0			0
$819$	8.85455	−	10.2187i	0.309403	−	0.357070i
$820$		0			0
$821$	1.14569	+	0.736288i	0.0399847	+	0.0256966i	0.560480	−	0.828168i	$-0.310616\pi$
$821$	1.14569	+	0.736288i	0.0399847	+	0.0256966i	−0.520496	+	0.853864i	$0.674253\pi$
$822$		0			0
$823$	−14.4519	−	16.6784i	−0.503761	−	0.581371i	0.445729	−	0.895168i	$-0.352944\pi$
$823$	−14.4519	−	16.6784i	−0.503761	−	0.581371i	−0.949490	+	0.313797i	$0.898399\pi$
$824$		0			0
$825$	5.30271	+	11.6113i	0.184617	+	0.404254i
$826$		0			0
$827$	−0.551517			−0.0191781			−0.00958907	−	0.999954i	$-0.503052\pi$
$827$	−0.551517			−0.0191781			−0.00958907	+	0.999954i	$0.503052\pi$
$828$		0			0
$829$	−11.1339			−0.386696			−0.193348	−	0.981130i	$-0.561935\pi$
$829$	−11.1339			−0.386696			−0.193348	+	0.981130i	$0.561935\pi$
$830$		0			0
$831$	0.606585	+	1.32824i	0.0210422	+	0.0460760i
$832$		0			0
$833$	51.3289	+	59.2367i	1.77844	+	2.05243i
$834$		0			0
$835$	−9.07137	−	5.82982i	−0.313928	−	0.201749i
$836$		0			0
$837$	−0.116399	+	0.134331i	−0.00402333	+	0.00464317i
$838$		0			0
$839$	−3.23153	−	22.4758i	−0.111565	−	0.775950i	−0.966399	−	0.257048i	$-0.917250\pi$
$839$	−3.23153	−	22.4758i	−0.111565	−	0.775950i	0.854834	−	0.518902i	$-0.173659\pi$
$840$		0			0
$841$	65.4050	−	42.0332i	2.25534	−	1.44942i
$842$		0			0
$843$	−1.17317	+	2.56888i	−0.0404061	+	0.0884769i
$844$		0			0
$845$	−3.17422	+	0.932036i	−0.109197	+	0.0320630i
$846$		0			0
$847$	9.70919	+	2.85088i	0.333612	+	0.0979573i
$848$		0			0
$849$	1.68494	−	11.7190i	0.0578270	−	0.402196i
$850$		0			0
$851$	−13.2345	+	47.3704i	−0.453674	+	1.62383i
$852$		0			0
$853$	5.93774	−	41.2979i	0.203304	−	1.41401i	−0.591088	−	0.806607i	$-0.701301\pi$
$853$	5.93774	−	41.2979i	0.203304	−	1.41401i	0.794392	−	0.607405i	$-0.207790\pi$
$854$		0			0
$855$	−4.43888	−	1.30337i	−0.151807	−	0.0445744i
$856$		0			0
$857$	55.4366	−	16.2776i	1.89368	−	0.556034i	0.901233	−	0.433335i	$-0.142663\pi$
$857$	55.4366	−	16.2776i	1.89368	−	0.556034i	0.992444	−	0.122699i	$-0.0391549\pi$
$858$		0			0
$859$	8.20325	−	17.9626i	0.279891	−	0.612877i	−0.716516	−	0.697571i	$-0.754264\pi$
$859$	8.20325	−	17.9626i	0.279891	−	0.612877i	0.996407	+	0.0846944i	$0.0269914\pi$
$860$		0			0
$861$	−33.1212	+	21.2857i	−1.12877	+	0.725414i
$862$		0			0
$863$	−1.34345	−	9.34387i	−0.0457314	−	0.318069i	−0.999828	−	0.0185686i	$-0.994089\pi$
$863$	−1.34345	−	9.34387i	−0.0457314	−	0.318069i	0.954096	−	0.299500i	$-0.0968200\pi$
$864$		0			0
$865$	5.11877	−	5.90737i	0.174043	−	0.200857i
$866$		0			0
$867$	−14.9052	−	9.57896i	−0.506206	−	0.325319i
$868$		0			0
$869$	3.13325	+	3.61596i	0.106288	+	0.122663i
$870$		0			0
$871$	0.879320	+	1.92544i	0.0297946	+	0.0652411i
$872$		0			0
$873$	14.4375			0.488637
$874$		0			0
$875$	34.7538			1.17489
$876$		0			0
$877$	8.82500	+	19.3241i	0.297999	+	0.652527i	0.998106	−	0.0615105i	$-0.0195918\pi$
$877$	8.82500	+	19.3241i	0.297999	+	0.652527i	−0.700107	+	0.714038i	$0.746865\pi$
$878$		0			0
$879$	3.50757	+	4.04795i	0.118307	+	0.136534i
$880$		0			0
$881$	13.2797	+	8.53438i	0.447406	+	0.287530i	0.744879	−	0.667200i	$-0.232507\pi$
$881$	13.2797	+	8.53438i	0.447406	+	0.287530i	−0.297473	+	0.954730i	$0.596144\pi$
$882$		0			0
$883$	15.6731	−	18.0878i	0.527443	−	0.608702i	−0.428035	−	0.903762i	$-0.640794\pi$
$883$	15.6731	−	18.0878i	0.527443	−	0.608702i	0.955479	+	0.295060i	$0.0953396\pi$
$884$		0			0
$885$	−0.0856425	−	0.595657i	−0.00287884	−	0.0200228i
$886$		0			0
$887$	13.2269	−	8.50040i	0.444115	−	0.285415i	−0.299409	−	0.954125i	$-0.596789\pi$
$887$	13.2269	−	8.50040i	0.444115	−	0.285415i	0.743524	+	0.668710i	$0.233153\pi$
$888$		0			0
$889$	11.9774	−	26.2269i	0.401710	−	0.879622i
$890$		0			0
$891$	−2.83890	+	0.833577i	−0.0951069	+	0.0279259i
$892$		0			0
$893$	−25.8394	−	7.58713i	−0.864683	−	0.253894i
$894$		0			0
$895$	−2.28592	+	15.8989i	−0.0764099	+	0.531442i
$896$		0			0
$897$	14.2707	+	1.86046i	0.476485	+	0.0621190i
$898$		0			0
$899$	0.261353	−	1.81775i	0.00871661	−	0.0606253i
$900$		0			0
$901$	−31.6522	−	9.29392i	−1.05449	−	0.309626i
$902$		0			0
$903$	2.39437	−	0.703051i	0.0796797	−	0.0233961i
$904$		0			0
$905$	−6.57360	+	14.3942i	−0.218514	+	0.478478i
$906$		0			0
$907$	−2.07160	+	1.33134i	−0.0687865	+	0.0442064i	−0.574582	−	0.818447i	$-0.694835\pi$
$907$	−2.07160	+	1.33134i	−0.0687865	+	0.0442064i	0.505796	+	0.862653i	$0.331199\pi$
$908$		0			0
$909$	−0.0913854	−	0.635599i	−0.00303106	−	0.0210815i
$910$		0			0
$911$	−1.45112	+	1.67468i	−0.0480776	+	0.0554846i	−0.779279	−	0.626677i	$-0.784415\pi$
$911$	−1.45112	+	1.67468i	−0.0480776	+	0.0554846i	0.731201	+	0.682162i	$0.238960\pi$
$912$		0			0
$913$	6.91138	+	4.44167i	0.228733	+	0.146998i
$914$		0			0
$915$	1.43363	+	1.65449i	0.0473943	+	0.0546959i
$916$		0			0
$917$	−22.8995	−	50.1429i	−0.756208	−	1.65586i
$918$		0			0
$919$	1.37891			0.0454859			0.0227430	−	0.999741i	$-0.492760\pi$
$919$	1.37891			0.0454859			0.0227430	+	0.999741i	$0.492760\pi$
$920$		0			0
$921$	−23.3022			−0.767835
$922$		0			0
$923$	−11.5328	−	25.2533i	−0.379607	−	0.831223i
$924$		0			0
$925$	28.9747	+	33.4386i	0.952683	+	1.09945i
$926$		0			0
$927$	14.1563	+	9.09768i	0.464953	+	0.298807i
$928$		0			0
$929$	−6.03848	+	6.96877i	−0.198116	+	0.228638i	−0.846111	−	0.533006i	$-0.821062\pi$
$929$	−6.03848	+	6.96877i	−0.198116	+	0.228638i	0.647995	+	0.761644i	$0.275608\pi$
$930$		0			0
$931$	10.5765	+	73.5610i	0.346630	+	2.41086i
$932$		0			0
$933$	−15.7540	+	10.1245i	−0.515763	+	0.331461i
$934$		0			0
$935$	5.99715	−	13.1319i	0.196128	−	0.429460i
$936$		0			0
$937$	−46.6897	+	13.7093i	−1.52529	+	0.447865i	−0.933604	−	0.358306i	$-0.883354\pi$
$937$	−46.6897	+	13.7093i	−1.52529	+	0.447865i	−0.591683	+	0.806171i	$0.701536\pi$
$938$		0			0
$939$	12.4112	+	3.64425i	0.405023	+	0.118926i
$940$		0			0
$941$	−3.33626	+	23.2042i	−0.108759	+	0.756436i	0.860332	+	0.509734i	$0.170256\pi$
$941$	−3.33626	+	23.2042i	−0.108759	+	0.756436i	−0.969091	+	0.246702i	$0.920653\pi$
$942$		0			0
$943$	−38.3440	−	16.9048i	−1.24865	−	0.550496i
$944$		0			0
$945$	−0.531011	+	3.69326i	−0.0172738	+	0.120142i
$946$		0			0
$947$	3.59734	+	1.05628i	0.116898	+	0.0343243i	0.339658	−	0.940549i	$-0.389689\pi$
$947$	3.59734	+	1.05628i	0.116898	+	0.0343243i	−0.222760	+	0.974873i	$0.571507\pi$
$948$		0			0
$949$	−0.479598	+	0.140823i	−0.0155684	+	0.00457129i
$950$		0			0
$951$	−7.72533	+	16.9161i	−0.250511	+	0.548543i
$952$		0			0
$953$	−12.6884	+	8.15434i	−0.411018	+	0.264145i	−0.729770	−	0.683693i	$-0.760373\pi$
$953$	−12.6884	+	8.15434i	−0.411018	+	0.264145i	0.318752	+	0.947838i	$0.396736\pi$
$954$		0			0
$955$	2.22888	+	15.5022i	0.0721248	+	0.501639i
$956$		0			0
$957$	20.0187	−	23.1028i	0.647113	−	0.746808i
$958$		0			0
$959$	−34.6685	−	22.2801i	−1.11950	−	0.719462i
$960$		0			0
$961$	20.2800	+	23.4044i	0.654193	+	0.754979i
$962$		0			0
$963$	4.76174	+	10.4268i	0.153445	+	0.335998i
$964$		0			0
$965$	11.7419			0.377984
$966$		0			0
$967$	1.92418			0.0618776			0.0309388	−	0.999521i	$-0.490150\pi$
$967$	1.92418			0.0618776			0.0309388	+	0.999521i	$0.490150\pi$
$968$		0			0
$969$	−13.6745	−	29.9430i	−0.439289	−	0.961909i
$970$		0			0
$971$	2.95890	+	3.41475i	0.0949556	+	0.109585i	0.801239	−	0.598345i	$-0.204175\pi$
$971$	2.95890	+	3.41475i	0.0949556	+	0.109585i	−0.706283	+	0.707930i	$0.749629\pi$
$972$		0			0
$973$	−38.6782	−	24.8570i	−1.23997	−	0.796878i
$974$		0			0
$975$	8.47808	−	9.78423i	0.271516	−	0.313346i
$976$		0			0
$977$	4.04755	+	28.1513i	0.129493	+	0.900640i	0.946199	+	0.323586i	$0.104889\pi$
$977$	4.04755	+	28.1513i	0.129493	+	0.900640i	−0.816706	+	0.577054i	$0.804202\pi$
$978$		0			0
$979$	−2.82547	+	1.81582i	−0.0903024	+	0.0580338i
$980$		0			0
$981$	−3.85795	+	8.44774i	−0.123175	+	0.269716i
$982$		0			0
$983$	−21.4262	+	6.29130i	−0.683390	+	0.200661i	−0.604957	−	0.796258i	$-0.706810\pi$
$983$	−21.4262	+	6.29130i	−0.683390	+	0.200661i	−0.0784326	+	0.996919i	$0.524992\pi$
$984$		0			0
$985$	18.4296	+	5.41141i	0.587215	+	0.172422i
$986$		0			0
$987$	−3.09110	+	21.4990i	−0.0983907	+	0.684322i
$988$		0			0
$989$	2.03003	+	1.71278i	0.0645513	+	0.0544632i
$990$		0			0
$991$	4.29904	−	29.9005i	0.136564	−	0.949820i	−0.800169	−	0.599774i	$-0.795257\pi$
$991$	4.29904	−	29.9005i	0.136564	−	0.949820i	0.936733	−	0.350046i	$-0.113834\pi$
$992$		0			0
$993$	−21.5492	−	6.32741i	−0.683843	−	0.200794i
$994$		0			0
$995$	−8.72710	+	2.56251i	−0.276668	+	0.0812369i
$996$		0			0
$997$	−17.3513	+	37.9939i	−0.549520	+	1.20328i	0.407486	+	0.913211i	$0.366405\pi$
$997$	−17.3513	+	37.9939i	−0.549520	+	1.20328i	−0.957006	+	0.290069i	$0.906322\pi$
$998$		0			0
$999$	−8.62760	+	5.54462i	−0.272965	+	0.175424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.i.b.169.2	yes	20
3.2	odd	2		828.2.q.b.721.1		20
23.3	even	11	inner	276.2.i.b.49.2	✓	20
23.7	odd	22		6348.2.a.q.1.7		10
23.16	even	11		6348.2.a.r.1.4		10
69.26	odd	22		828.2.q.b.325.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.i.b.49.2	✓	20	23.3	even	11	inner
276.2.i.b.169.2	yes	20	1.1	even	1	trivial
828.2.q.b.325.1		20	69.26	odd	22
828.2.q.b.721.1		20	3.2	odd	2
6348.2.a.q.1.7		10	23.7	odd	22
6348.2.a.r.1.4		10	23.16	even	11

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{3} +(0.542284 + 0.625829i) q^{5} +(3.79055 + 2.43604i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.415415 - 0.909632i) q^{3} +(0.542284 + 0.625829i) q^{5} +(3.79055 + 2.43604i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(-0.421075 - 2.92864i) q^{11} +(-2.52446 + 1.62237i) q^{13} +(0.344001 - 0.753257i) q^{15} +(5.65351 - 1.66002i) q^{17} +(5.36039 + 1.57395i) q^{19} +(0.641248 - 4.45998i) q^{21} +(4.33584 - 2.04950i) q^{23} +(0.613984 - 4.27035i) q^{25} +(0.959493 + 0.281733i) q^{27} +(-9.91333 + 2.91082i) q^{29} +(-0.0738383 + 0.161683i) q^{31} +(-2.48906 + 1.59962i) q^{33} +(0.531011 + 3.69326i) q^{35} +(-6.71602 + 7.75071i) q^{37} +(2.52446 + 1.62237i) q^{39} +(-5.72205 - 6.60360i) q^{41} +(0.230068 + 0.503778i) q^{43} -0.828090 q^{45} -4.82044 q^{47} +(5.52610 + 12.1005i) q^{49} +(-3.85856 - 4.45301i) q^{51} +(-4.70991 - 3.02688i) q^{53} +(1.60448 - 1.85167i) q^{55} +(-0.795068 - 5.52982i) q^{57} +(0.611348 - 0.392890i) q^{59} +(-1.09823 + 2.40478i) q^{61} +(-4.32332 + 1.26944i) q^{63} +(-2.38430 - 0.700093i) q^{65} +(0.100386 - 0.698201i) q^{67} +(-3.66547 - 3.09263i) q^{69} +(-1.31662 + 9.15731i) q^{71} +(0.159822 + 0.0469279i) q^{73} +(-4.13951 + 1.21547i) q^{75} +(5.53818 - 12.1269i) q^{77} +(-1.36039 + 0.874270i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(-1.81835 + 2.09849i) q^{83} +(4.10469 + 2.63792i) q^{85} +(6.76592 + 7.80829i) q^{87} +(-0.471560 - 1.03257i) q^{89} -13.5213 q^{91} +0.177746 q^{93} +(1.92183 + 4.20821i) q^{95} +(-9.45458 - 10.9112i) q^{97} +(2.48906 + 1.59962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9}+O(q^{10}) \) 20 * q + 2 * q^3 - 4 * q^7 - 2 * q^9	\( 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9} + 14 q^{13} - 11 q^{15} + 3 q^{17} + 7 q^{19} + 4 q^{21} + 24 q^{23} + 12 q^{25} + 2 q^{27} - 26 q^{29} + 33 q^{31} - 11 q^{33} - 2 q^{35} - 18 q^{37} - 14 q^{39} + 4 q^{41} - 40 q^{43} - 54 q^{47} + 30 q^{49} - 14 q^{51} - 14 q^{53} + 11 q^{55} - 29 q^{57} + 4 q^{59} + 12 q^{61} - 4 q^{63} - 33 q^{65} + 15 q^{67} - 2 q^{69} - 33 q^{71} + 15 q^{73} + 10 q^{75} + 66 q^{77} - 42 q^{79} - 2 q^{81} - 14 q^{83} - 13 q^{85} + 4 q^{87} - 66 q^{89} - 16 q^{91} - 22 q^{93} - 31 q^{95} - 24 q^{97} + 11 q^{99}+O(q^{100}) \) 20 * q + 2 * q^3 - 4 * q^7 - 2 * q^9 + 14 * q^13 - 11 * q^15 + 3 * q^17 + 7 * q^19 + 4 * q^21 + 24 * q^23 + 12 * q^25 + 2 * q^27 - 26 * q^29 + 33 * q^31 - 11 * q^33 - 2 * q^35 - 18 * q^37 - 14 * q^39 + 4 * q^41 - 40 * q^43 - 54 * q^47 + 30 * q^49 - 14 * q^51 - 14 * q^53 + 11 * q^55 - 29 * q^57 + 4 * q^59 + 12 * q^61 - 4 * q^63 - 33 * q^65 + 15 * q^67 - 2 * q^69 - 33 * q^71 + 15 * q^73 + 10 * q^75 + 66 * q^77 - 42 * q^79 - 2 * q^81 - 14 * q^83 - 13 * q^85 + 4 * q^87 - 66 * q^89 - 16 * q^91 - 22 * q^93 - 31 * q^95 - 24 * q^97 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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