LMFDB - Embedded newform 276.2.i.b.73.2

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			73.2
Root			$-0.410543 - 2.85539i$ of defining polynomial
Character	$\chi$	$=$	276.73
Dual form			276.2.i.b.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 - 0.281733i) q^{3} +(2.17941 + 1.40062i) q^{5} +(-0.529416 - 3.68217i) q^{7} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(0.959493 - 0.281733i) q^{3} +(2.17941 + 1.40062i) q^{5} +(-0.529416 - 3.68217i) q^{7} +(0.841254 - 0.540641i) q^{9} +(0.659363 - 1.44380i) q^{11} +(-0.493987 + 3.43575i) q^{13} +(2.48573 + 0.729877i) q^{15} +(1.41335 + 1.63109i) q^{17} +(-2.90294 + 3.35017i) q^{19} +(-1.54536 - 3.38386i) q^{21} +(4.46678 - 1.74582i) q^{23} +(0.711016 + 1.55691i) q^{25} +(0.654861 - 0.755750i) q^{27} +(-4.64339 - 5.35876i) q^{29} +(2.96579 + 0.870835i) q^{31} +(0.225888 - 1.57108i) q^{33} +(4.00351 - 8.76647i) q^{35} +(-7.14585 + 4.59236i) q^{37} +(0.493987 + 3.43575i) q^{39} +(4.48072 + 2.87958i) q^{41} +(-9.28229 + 2.72553i) q^{43} +2.59067 q^{45} -4.62880 q^{47} +(-6.56163 + 1.92667i) q^{49} +(1.81563 + 1.16683i) q^{51} +(-0.0895406 - 0.622769i) q^{53} +(3.45925 - 2.22312i) q^{55} +(-1.84150 + 4.03232i) q^{57} +(-2.08408 + 14.4951i) q^{59} +(-3.95837 - 1.16228i) q^{61} +(-2.43610 - 2.81141i) q^{63} +(-5.88880 + 6.79603i) q^{65} +(-4.19729 - 9.19078i) q^{67} +(3.79399 - 2.93354i) q^{69} +(-1.60565 - 3.51589i) q^{71} +(-8.13034 + 9.38292i) q^{73} +(1.12085 + 1.29353i) q^{75} +(-5.66541 - 1.66351i) q^{77} +(1.98166 - 13.7828i) q^{79} +(0.415415 - 0.909632i) q^{81} +(9.08652 - 5.83955i) q^{83} +(0.795723 + 5.53438i) q^{85} +(-5.96504 - 3.83350i) q^{87} +(9.91096 - 2.91012i) q^{89} +12.9125 q^{91} +3.09100 q^{93} +(-11.0190 + 3.23548i) q^{95} +(-5.68415 - 3.65298i) q^{97} +(-0.225888 - 1.57108i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$1$	$1$

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
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$4$		0			0
$5$	2.17941	+	1.40062i	0.974663	+	0.626378i	0.928019	−	0.372534i	$-0.121511\pi$
$5$	2.17941	+	1.40062i	0.974663	+	0.626378i	0.0466440	+	0.998912i	$0.485147\pi$
$6$		0			0
$7$	−0.529416	−	3.68217i	−0.200100	−	1.39173i	−0.803981	−	0.594654i	$-0.797289\pi$
$7$	−0.529416	−	3.68217i	−0.200100	−	1.39173i	0.603881	−	0.797074i	$-0.293620\pi$
$8$		0			0
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$		0			0
$11$	0.659363	−	1.44380i	0.198805	−	0.435323i	−0.783804	−	0.621008i	$-0.786723\pi$
$11$	0.659363	−	1.44380i	0.198805	−	0.435323i	0.982609	+	0.185685i	$0.0594505\pi$
$12$		0			0
$13$	−0.493987	+	3.43575i	−0.137007	+	0.952907i	0.799102	+	0.601196i	$0.205309\pi$
$13$	−0.493987	+	3.43575i	−0.137007	+	0.952907i	−0.936109	+	0.351710i	$0.885600\pi$
$14$		0			0
$15$	2.48573	+	0.729877i	0.641813	+	0.188453i
$16$		0			0
$17$	1.41335	+	1.63109i	0.342787	+	0.395597i	0.900799	−	0.434235i	$-0.142981\pi$
$17$	1.41335	+	1.63109i	0.342787	+	0.395597i	−0.558013	+	0.829832i	$0.688436\pi$
$18$		0			0
$19$	−2.90294	+	3.35017i	−0.665980	+	0.768582i	−0.983742	−	0.179589i	$-0.942523\pi$
$19$	−2.90294	+	3.35017i	−0.665980	+	0.768582i	0.317762	+	0.948171i	$0.397069\pi$
$20$		0			0
$21$	−1.54536	−	3.38386i	−0.337225	−	0.738419i
$22$		0			0
$23$	4.46678	−	1.74582i	0.931388	−	0.364029i
$23$	4.46678	−	1.74582i	0.931388	−	0.364029i
$24$		0			0
$25$	0.711016	+	1.55691i	0.142203	+	0.311382i
$26$		0			0
$27$	0.654861	−	0.755750i	0.126028	−	0.145444i
$28$		0			0
$29$	−4.64339	−	5.35876i	−0.862256	−	0.995097i	−0.999989	−	0.00462728i	$-0.998527\pi$
$29$	−4.64339	−	5.35876i	−0.862256	−	0.995097i	0.137733	−	0.990469i	$-0.456018\pi$
$30$		0			0
$31$	2.96579	+	0.870835i	0.532672	+	0.156407i	0.536997	−	0.843584i	$-0.319559\pi$
$31$	2.96579	+	0.870835i	0.532672	+	0.156407i	−0.00432525	+	0.999991i	$0.501377\pi$
$32$		0			0
$33$	0.225888	−	1.57108i	0.0393220	−	0.273490i
$34$		0			0
$35$	4.00351	−	8.76647i	0.676717	−	1.48180i
$36$		0			0
$37$	−7.14585	+	4.59236i	−1.17477	+	0.754980i	−0.974418	−	0.224744i	$-0.927845\pi$
$37$	−7.14585	+	4.59236i	−1.17477	+	0.754980i	−0.200353	+	0.979724i	$0.564209\pi$
$38$		0			0
$39$	0.493987	+	3.43575i	0.0791012	+	0.550161i
$40$		0			0
$41$	4.48072	+	2.87958i	0.699771	+	0.449716i	0.841547	−	0.540183i	$-0.181645\pi$
$41$	4.48072	+	2.87958i	0.699771	+	0.449716i	−0.141776	+	0.989899i	$0.545281\pi$
$42$		0			0
$43$	−9.28229	+	2.72553i	−1.41554	+	0.415639i	−0.897990	−	0.440016i	$-0.854973\pi$
$43$	−9.28229	+	2.72553i	−1.41554	+	0.415639i	−0.517546	+	0.855655i	$0.673154\pi$
$44$		0			0
$45$	2.59067			0.386195
$46$		0			0
$47$	−4.62880			−0.675180			−0.337590	−	0.941293i	$-0.609612\pi$
$47$	−4.62880			−0.675180			−0.337590	+	0.941293i	$0.609612\pi$
$48$		0			0
$49$	−6.56163	+	1.92667i	−0.937376	+	0.275239i
$50$		0			0
$51$	1.81563	+	1.16683i	0.254239	+	0.163389i
$52$		0			0
$53$	−0.0895406	−	0.622769i	−0.0122993	−	0.0855438i	0.982747	−	0.184954i	$-0.0592136\pi$
$53$	−0.0895406	−	0.622769i	−0.0122993	−	0.0855438i	−0.995047	+	0.0994100i	$0.968304\pi$
$54$		0			0
$55$	3.45925	−	2.22312i	0.466445	−	0.299766i
$56$		0			0
$57$	−1.84150	+	4.03232i	−0.243912	+	0.534093i
$58$		0			0
$59$	−2.08408	+	14.4951i	−0.271324	+	1.88710i	0.163440	+	0.986553i	$0.447741\pi$
$59$	−2.08408	+	14.4951i	−0.271324	+	1.88710i	−0.434763	+	0.900545i	$0.643168\pi$
$60$		0			0
$61$	−3.95837	−	1.16228i	−0.506818	−	0.148815i	0.0183204	−	0.999832i	$-0.494168\pi$
$61$	−3.95837	−	1.16228i	−0.506818	−	0.148815i	−0.525138	+	0.851017i	$0.675986\pi$
$62$		0			0
$63$	−2.43610	−	2.81141i	−0.306920	−	0.354205i
$64$		0			0
$65$	−5.88880	+	6.79603i	−0.730415	+	0.842944i
$66$		0			0
$67$	−4.19729	−	9.19078i	−0.512781	−	1.12283i	−0.972101	−	0.234562i	$-0.924634\pi$
$67$	−4.19729	−	9.19078i	−0.512781	−	1.12283i	0.459320	−	0.888271i	$-0.348093\pi$
$68$		0			0
$69$	3.79399	−	2.93354i	0.456743	−	0.353157i
$70$		0			0
$71$	−1.60565	−	3.51589i	−0.190556	−	0.417260i	0.790105	−	0.612971i	$-0.210026\pi$
$71$	−1.60565	−	3.51589i	−0.190556	−	0.417260i	−0.980662	+	0.195711i	$0.937298\pi$
$72$		0			0
$73$	−8.13034	+	9.38292i	−0.951585	+	1.09819i	0.0434893	+	0.999054i	$0.486153\pi$
$73$	−8.13034	+	9.38292i	−0.951585	+	1.09819i	−0.995074	+	0.0991336i	$0.968393\pi$
$74$		0			0
$75$	1.12085	+	1.29353i	0.129424	+	0.149363i
$76$		0			0
$77$	−5.66541	−	1.66351i	−0.645633	−	0.189575i
$78$		0			0
$79$	1.98166	−	13.7828i	0.222955	−	1.55068i	−0.503821	−	0.863808i	$-0.668073\pi$
$79$	1.98166	−	13.7828i	0.222955	−	1.55068i	0.726775	−	0.686875i	$-0.241018\pi$
$80$		0			0
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$		0			0
$83$	9.08652	−	5.83955i	0.997375	−	0.640974i	0.0632791	−	0.997996i	$-0.479844\pi$
$83$	9.08652	−	5.83955i	0.997375	−	0.640974i	0.934096	+	0.357022i	$0.116208\pi$
$84$		0			0
$85$	0.795723	+	5.53438i	0.0863083	+	0.600287i
$86$		0			0
$87$	−5.96504	−	3.83350i	−0.639519	−	0.410994i
$88$		0			0
$89$	9.91096	−	2.91012i	1.05056	−	0.308472i	0.289516	−	0.957173i	$-0.406506\pi$
$89$	9.91096	−	2.91012i	1.05056	−	0.308472i	0.761043	+	0.648701i	$0.224687\pi$
$90$		0			0
$91$	12.9125			1.35360
$92$		0			0
$93$	3.09100			0.320522
$94$		0			0
$95$	−11.0190	+	3.23548i	−1.13053	+	0.331953i
$96$		0			0
$97$	−5.68415	−	3.65298i	−0.577138	−	0.370904i	0.219270	−	0.975664i	$-0.429633\pi$
$97$	−5.68415	−	3.65298i	−0.577138	−	0.370904i	−0.796408	+	0.604760i	$0.793269\pi$
$98$		0			0
$99$	−0.225888	−	1.57108i	−0.0227026	−	0.157900i
$100$		0			0
$101$	−9.55211	+	6.13877i	−0.950470	+	0.610830i	−0.921345	−	0.388746i	$-0.872908\pi$
$101$	−9.55211	+	6.13877i	−0.950470	+	0.610830i	−0.0291251	+	0.999576i	$0.509272\pi$
$102$		0			0
$103$	−0.443373	+	0.970851i	−0.0436868	+	0.0956608i	−0.930217	−	0.367010i	$-0.880381\pi$
$103$	−0.443373	+	0.970851i	−0.0436868	+	0.0956608i	0.886530	+	0.462671i	$0.153109\pi$
$104$		0			0
$105$	1.37154	−	9.53929i	0.133849	−	0.930939i
$106$		0			0
$107$	−8.34422	−	2.45008i	−0.806666	−	0.236858i	−0.147701	−	0.989032i	$-0.547187\pi$
$107$	−8.34422	−	2.45008i	−0.806666	−	0.236858i	−0.658965	+	0.752174i	$0.729005\pi$
$108$		0			0
$109$	8.65373	+	9.98693i	0.828877	+	0.956575i	0.999587	−	0.0287465i	$-0.00915154\pi$
$109$	8.65373	+	9.98693i	0.828877	+	0.956575i	−0.170710	+	0.985321i	$0.554606\pi$
$110$		0			0
$111$	−5.56258	+	6.41956i	−0.527977	+	0.609318i
$112$		0			0
$113$	1.89327	+	4.14568i	0.178104	+	0.389992i	0.977537	−	0.210762i	$-0.0675944\pi$
$113$	1.89327	+	4.14568i	0.178104	+	0.389992i	−0.799434	+	0.600754i	$0.794867\pi$
$114$		0			0
$115$	12.1802	+	2.45141i	1.13581	+	0.228595i
$116$		0			0
$117$	1.44194	+	3.15741i	0.133307	+	0.291903i
$118$		0			0
$119$	5.25769	−	6.06770i	0.481972	−	0.556225i
$120$		0			0
$121$	5.55366	+	6.40926i	0.504878	+	0.582660i
$122$		0			0
$123$	5.11049	+	1.50058i	0.460798	+	0.135302i
$124$		0			0
$125$	1.21241	−	8.43250i	0.108441	−	0.754226i
$126$		0			0
$127$	2.14495	−	4.69679i	0.190334	−	0.416773i	−0.790274	−	0.612754i	$-0.790062\pi$
$127$	2.14495	−	4.69679i	0.190334	−	0.416773i	0.980608	+	0.195981i	$0.0627891\pi$
$128$		0			0
$129$	−8.13842	+	5.23025i	−0.716548	+	0.460498i
$130$		0			0
$131$	1.98462	+	13.8033i	0.173397	+	1.20600i	0.871641	+	0.490144i	$0.163056\pi$
$131$	1.98462	+	13.8033i	0.173397	+	1.20600i	−0.698244	+	0.715860i	$0.746035\pi$
$132$		0			0
$133$	13.8728	+	8.91548i	1.20292	+	0.773070i
$134$		0			0
$135$	2.48573	−	0.729877i	0.213938	−	0.0628178i
$136$		0			0
$137$	17.4372			1.48976			0.744882	−	0.667196i	$-0.232506\pi$
$137$	17.4372			1.48976			0.744882	+	0.667196i	$0.232506\pi$
$138$		0			0
$139$	−1.34955			−0.114467			−0.0572336	−	0.998361i	$-0.518228\pi$
$139$	−1.34955			−0.114467			−0.0572336	+	0.998361i	$0.518228\pi$
$140$		0			0
$141$	−4.44130	+	1.30408i	−0.374025	+	0.109824i
$142$		0			0
$143$	4.63484	+	2.97863i	0.387584	+	0.249085i
$144$		0			0
$145$	−2.61426	−	18.1826i	−0.217103	−	1.50998i
$146$		0			0
$147$	−5.75304	+	3.69725i	−0.474502	+	0.304944i
$148$		0			0
$149$	9.31811	−	20.4038i	0.763369	−	1.67155i	0.0226384	−	0.999744i	$-0.492793\pi$
$149$	9.31811	−	20.4038i	0.763369	−	1.67155i	0.740731	−	0.671802i	$-0.234479\pi$
$150$		0			0
$151$	3.12068	−	21.7048i	0.253957	−	1.76631i	−0.319991	−	0.947420i	$-0.603680\pi$
$151$	3.12068	−	21.7048i	0.253957	−	1.76631i	0.573949	−	0.818891i	$-0.305411\pi$
$152$		0			0
$153$	2.07082	+	0.608046i	0.167415	+	0.0491576i
$154$		0			0
$155$	5.24397	+	6.05186i	0.421206	+	0.486097i
$156$		0			0
$157$	13.4301	−	15.4991i	1.07184	−	1.23697i	0.101595	−	0.994826i	$-0.467605\pi$
$157$	13.4301	−	15.4991i	1.07184	−	1.23697i	0.970241	−	0.242140i	$-0.0778493\pi$
$158$		0			0
$159$	−0.261368	−	0.572316i	−0.0207278	−	0.0453876i
$160$		0			0
$161$	−8.79319	−	15.5232i	−0.693000	−	1.22340i
$162$		0			0
$163$	4.53354	+	9.92708i	0.355095	+	0.777549i	0.999913	+	0.0132127i	$0.00420586\pi$
$163$	4.53354	+	9.92708i	0.355095	+	0.777549i	−0.644818	+	0.764336i	$0.723067\pi$
$164$		0			0
$165$	2.69280	−	3.10765i	0.209634	−	0.241931i
$166$		0			0
$167$	−2.65410	−	3.06300i	−0.205381	−	0.237022i	0.643709	−	0.765270i	$-0.277395\pi$
$167$	−2.65410	−	3.06300i	−0.205381	−	0.237022i	−0.849090	+	0.528248i	$0.822849\pi$
$168$		0			0
$169$	0.913030	+	0.268090i	0.0702330	+	0.0206223i
$170$		0			0
$171$	−0.630869	+	4.38779i	−0.0482437	+	0.335543i
$172$		0			0
$173$	−4.06943	+	8.91082i	−0.309393	+	0.677477i	−0.998904	−	0.0467984i	$-0.985098\pi$
$173$	−4.06943	+	8.91082i	−0.309393	+	0.677477i	0.689511	+	0.724275i	$0.257825\pi$
$174$		0			0
$175$	5.35637	−	3.44233i	0.404904	−	0.260216i
$176$		0			0
$177$	2.08408	+	14.4951i	0.156649	+	1.08952i
$178$		0			0
$179$	19.3373	+	12.4273i	1.44533	+	0.928860i	0.999429	+	0.0337793i	$0.0107543\pi$
$179$	19.3373	+	12.4273i	1.44533	+	0.928860i	0.445905	+	0.895080i	$0.352882\pi$
$180$		0			0
$181$	5.96883	−	1.75261i	0.443660	−	0.130270i	−0.0522698	−	0.998633i	$-0.516646\pi$
$181$	5.96883	−	1.75261i	0.443660	−	0.130270i	0.495930	+	0.868363i	$0.334827\pi$
$182$		0			0
$183$	−4.12548			−0.304964
$184$		0			0
$185$	−22.0059			−1.61791
$186$		0			0
$187$	3.28688	−	0.965115i	0.240360	−	0.0705762i
$188$		0			0
$189$	−3.12949	−	2.01120i	−0.227637	−	0.146293i
$190$		0			0
$191$	1.99594	+	13.8820i	0.144421	+	1.00447i	0.925151	+	0.379600i	$0.123939\pi$
$191$	1.99594	+	13.8820i	0.144421	+	1.00447i	−0.780730	+	0.624869i	$0.785152\pi$
$192$		0			0
$193$	−5.74051	+	3.68920i	−0.413211	+	0.265555i	−0.730688	−	0.682711i	$-0.760801\pi$
$193$	−5.74051	+	3.68920i	−0.413211	+	0.265555i	0.317477	+	0.948266i	$0.397164\pi$
$194$		0			0
$195$	−3.73559	+	8.17981i	−0.267511	+	0.585768i
$196$		0			0
$197$	3.10243	−	21.5779i	0.221039	−	1.53736i	−0.513081	−	0.858340i	$-0.671496\pi$
$197$	3.10243	−	21.5779i	0.221039	−	1.53736i	0.734120	−	0.679020i	$-0.237595\pi$
$198$		0			0
$199$	−11.1539	−	3.27509i	−0.790682	−	0.232165i	−0.138635	−	0.990344i	$-0.544271\pi$
$199$	−11.1539	−	3.27509i	−0.790682	−	0.232165i	−0.652047	+	0.758178i	$0.726090\pi$
$200$		0			0
$201$	−6.61661	−	7.63598i	−0.466700	−	0.538600i
$202$		0			0
$203$	−17.2736	+	19.9348i	−1.21237	+	1.39915i
$204$		0			0
$205$	5.73212	+	12.5516i	0.400349	+	0.876642i
$206$		0			0
$207$	2.81383	−	3.88360i	0.195575	−	0.269929i
$208$		0			0
$209$	2.92290	+	6.40025i	0.202181	+	0.442715i
$210$		0			0
$211$	−6.94953	+	8.02018i	−0.478425	+	0.552132i	−0.942736	−	0.333540i	$-0.891757\pi$
$211$	−6.94953	+	8.02018i	−0.478425	+	0.552132i	0.464311	+	0.885672i	$0.346302\pi$
$212$		0			0
$213$	−2.53116	−	2.92111i	−0.173432	−	0.200151i
$214$		0			0
$215$	−24.0474	−	7.06094i	−1.64002	−	0.481552i
$216$		0			0
$217$	1.63642	−	11.3816i	0.111088	−	0.772632i
$218$		0			0
$219$	−5.15754	+	11.2934i	−0.348514	+	0.763139i
$220$		0			0
$221$	−6.30219	+	4.05017i	−0.423931	+	0.272444i
$222$		0			0
$223$	−0.530780	−	3.69165i	−0.0355436	−	0.247211i	0.964302	−	0.264807i	$-0.0853081\pi$
$223$	−0.530780	−	3.69165i	−0.0355436	−	0.247211i	−0.999845	+	0.0175952i	$0.994399\pi$
$224$		0			0
$225$	1.43987	+	0.925350i	0.0959915	+	0.0616900i
$226$		0			0
$227$	−11.6873	+	3.43169i	−0.775710	+	0.227769i	−0.645544	−	0.763723i	$-0.723369\pi$
$227$	−11.6873	+	3.43169i	−0.775710	+	0.227769i	−0.130166	+	0.991492i	$0.541551\pi$
$228$		0			0
$229$	16.9557			1.12046			0.560232	−	0.828336i	$-0.310712\pi$
$229$	16.9557			1.12046			0.560232	+	0.828336i	$0.310712\pi$
$230$		0			0
$231$	−5.90458			−0.388493
$232$		0			0
$233$	25.9786	−	7.62800i	1.70191	−	0.499727i	0.720798	−	0.693145i	$-0.243776\pi$
$233$	25.9786	−	7.62800i	1.70191	−	0.499727i	0.981116	+	0.193418i	$0.0619574\pi$
$234$		0			0
$235$	−10.0881	−	6.48320i	−0.658073	−	0.422918i
$236$		0			0
$237$	−1.98166	−	13.7828i	−0.128723	−	0.895288i
$238$		0			0
$239$	−20.1566	+	12.9539i	−1.30382	+	0.837917i	−0.993623	−	0.112754i	$-0.964033\pi$
$239$	−20.1566	+	12.9539i	−1.30382	+	0.837917i	−0.310201	+	0.950671i	$0.600396\pi$
$240$		0			0
$241$	−2.72191	+	5.96015i	−0.175333	+	0.383927i	−0.976813	−	0.214096i	$-0.931319\pi$
$241$	−2.72191	+	5.96015i	−0.175333	+	0.383927i	0.801479	+	0.598023i	$0.204047\pi$
$242$		0			0
$243$	0.142315	−	0.989821i	0.00912950	−	0.0634971i
$244$		0			0
$245$	−16.9990	−	4.99137i	−1.08603	−	0.318887i
$246$		0			0
$247$	−10.0763	−	11.6287i	−0.641142	−	0.739918i
$248$		0			0
$249$	7.07326	−	8.16298i	0.448250	−	0.517308i
$250$		0			0
$251$	−0.298445	−	0.653503i	−0.0188377	−	0.0412487i	0.899979	−	0.435933i	$-0.143581\pi$
$251$	−0.298445	−	0.653503i	−0.0188377	−	0.0412487i	−0.918817	+	0.394684i	$0.870854\pi$
$252$		0			0
$253$	0.424608	−	7.60028i	0.0266949	−	0.477825i
$254$		0			0
$255$	2.32271	+	5.08601i	0.145453	+	0.318499i
$256$		0			0
$257$	−2.88138	+	3.32529i	−0.179735	+	0.207426i	−0.838467	−	0.544952i	$-0.816548\pi$
$257$	−2.88138	+	3.32529i	−0.179735	+	0.207426i	0.658732	+	0.752378i	$0.271093\pi$
$258$		0			0
$259$	20.6930	+	23.8810i	1.28580	+	1.48389i
$260$		0			0
$261$	−6.80343	−	1.99767i	−0.421122	−	0.123653i
$262$		0			0
$263$	0.634779	−	4.41498i	0.0391421	−	0.272240i	−0.960846	−	0.277082i	$-0.910632\pi$
$263$	0.634779	−	4.41498i	0.0391421	−	0.272240i	0.999988	+	0.00484293i	$0.00154156\pi$
$264$		0			0
$265$	0.677118	−	1.48268i	0.0415950	−	0.0910804i
$266$		0			0
$267$	8.68962	−	5.58448i	0.531796	−	0.341765i
$268$		0			0
$269$	3.24712	+	22.5842i	0.197980	+	1.37698i	0.810134	+	0.586245i	$0.199394\pi$
$269$	3.24712	+	22.5842i	0.197980	+	1.37698i	−0.612154	+	0.790739i	$0.709697\pi$
$270$		0			0
$271$	5.19526	+	3.33879i	0.315590	+	0.202817i	0.688840	−	0.724914i	$-0.258120\pi$
$271$	5.19526	+	3.33879i	0.315590	+	0.202817i	−0.373250	+	0.927731i	$0.621757\pi$
$272$		0			0
$273$	12.3895	−	3.63789i	0.749847	−	0.220175i
$274$		0			0
$275$	2.71669			0.163822
$276$		0			0
$277$	−27.5242			−1.65377			−0.826885	−	0.562371i	$-0.809889\pi$
$277$	−27.5242			−1.65377			−0.826885	+	0.562371i	$0.809889\pi$
$278$		0			0
$279$	2.96579	−	0.870835i	0.177557	−	0.0521355i
$280$		0			0
$281$	2.30384	+	1.48059i	0.137436	+	0.0883246i	0.607552	−	0.794280i	$-0.292152\pi$
$281$	2.30384	+	1.48059i	0.137436	+	0.0883246i	−0.470116	+	0.882605i	$0.655788\pi$
$282$		0			0
$283$	−3.16275	−	21.9974i	−0.188006	−	1.30761i	−0.837162	−	0.546955i	$-0.815787\pi$
$283$	−3.16275	−	21.9974i	−0.188006	−	1.30761i	0.649156	−	0.760655i	$-0.275122\pi$
$284$		0			0
$285$	−9.66114	+	6.20883i	−0.572276	+	0.367780i
$286$		0			0
$287$	8.23095	−	18.0233i	0.485858	−	1.06388i
$288$		0			0
$289$	1.75645	−	12.2164i	0.103321	−	0.718611i
$290$		0			0
$291$	−6.48307	−	1.90360i	−0.380044	−	0.111591i
$292$		0			0
$293$	−1.68141	−	1.94045i	−0.0982291	−	0.113362i	0.704507	−	0.709698i	$-0.251168\pi$
$293$	−1.68141	−	1.94045i	−0.0982291	−	0.113362i	−0.802736	+	0.596335i	$0.796623\pi$
$294$		0			0
$295$	−24.8442	+	28.6717i	−1.44648	+	1.66933i
$296$		0			0
$297$	−0.659363	−	1.44380i	−0.0382601	−	0.0837780i
$298$		0			0
$299$	3.79168	+	16.2092i	0.219278	+	0.937400i
$300$		0			0
$301$	14.9500	+	32.7360i	0.861706	+	1.88687i
$302$		0			0
$303$	−7.43569	+	8.58124i	−0.427169	+	0.492980i
$304$		0			0
$305$	−6.99900	−	8.07728i	−0.400762	−	0.462504i
$306$		0			0
$307$	7.50756	+	2.20442i	0.428479	+	0.125813i	0.488859	−	0.872363i	$-0.337413\pi$
$307$	7.50756	+	2.20442i	0.428479	+	0.125813i	−0.0603801	+	0.998175i	$0.519231\pi$
$308$		0			0
$309$	−0.151893	+	1.05644i	−0.00864088	+	0.0600986i
$310$		0			0
$311$	7.73790	−	16.9436i	0.438776	−	0.960786i	−0.553045	−	0.833151i	$-0.686534\pi$
$311$	7.73790	−	16.9436i	0.438776	−	0.960786i	0.991821	−	0.127635i	$-0.0407385\pi$
$312$		0			0
$313$	13.5185	−	8.68782i	0.764111	−	0.491065i	−0.0996148	−	0.995026i	$-0.531761\pi$
$313$	13.5185	−	8.68782i	0.764111	−	0.491065i	0.863726	+	0.503962i	$0.168125\pi$
$314$		0			0
$315$	−1.37154	−	9.53929i	−0.0772777	−	0.537478i
$316$		0			0
$317$	−0.248534	−	0.159723i	−0.0139591	−	0.00897095i	0.533643	−	0.845710i	$-0.320823\pi$
$317$	−0.248534	−	0.159723i	−0.0139591	−	0.00897095i	−0.547602	+	0.836739i	$0.684459\pi$
$318$		0			0
$319$	−10.7987	+	3.17078i	−0.604610	+	0.177529i
$320$		0			0
$321$	−8.69649			−0.485390
$322$		0			0
$323$	−9.56728			−0.532338
$324$		0			0
$325$	−5.70038	+	1.67378i	−0.316200	+	0.0928448i
$326$		0			0
$327$	11.1168	+	7.14436i	0.614762	+	0.395084i
$328$		0			0
$329$	2.45056	+	17.0440i	0.135104	+	0.939667i
$330$		0			0
$331$	3.03028	−	1.94744i	0.166559	−	0.107041i	−0.454706	−	0.890642i	$-0.650256\pi$
$331$	3.03028	−	1.94744i	0.166559	−	0.107041i	0.621265	+	0.783601i	$0.286619\pi$
$332$		0			0
$333$	−3.52866	+	7.72668i	−0.193369	+	0.423419i
$334$		0			0
$335$	3.72520	−	25.9093i	0.203529	−	1.41558i
$336$		0			0
$337$	−32.1873	−	9.45104i	−1.75335	−	0.514831i	−0.762175	−	0.647371i	$-0.775869\pi$
$337$	−32.1873	−	9.45104i	−1.75335	−	0.514831i	−0.991178	+	0.132540i	$0.957687\pi$
$338$		0			0
$339$	2.98455	+	3.44435i	0.162098	+	0.187072i
$340$		0			0
$341$	3.21285	−	3.70782i	0.173985	−	0.200790i
$342$		0			0
$343$	−0.249347	−	0.545995i	−0.0134635	−	0.0294809i
$344$		0			0
$345$	12.3774	−	1.07944i	0.666379	−	0.0581152i
$346$		0			0
$347$	5.54358	+	12.1387i	0.297595	+	0.651642i	0.998074	−	0.0620310i	$-0.0197578\pi$
$347$	5.54358	+	12.1387i	0.297595	+	0.651642i	−0.700479	+	0.713673i	$0.747030\pi$
$348$		0			0
$349$	−5.10012	+	5.88585i	−0.273003	+	0.315062i	−0.875651	−	0.482945i	$-0.839567\pi$
$349$	−5.10012	+	5.88585i	−0.273003	+	0.315062i	0.602648	+	0.798007i	$0.294112\pi$
$350$		0			0
$351$	2.27308	+	2.62327i	0.121328	+	0.140020i
$352$		0			0
$353$	10.4904	+	3.08026i	0.558348	+	0.163946i	0.548718	−	0.836008i	$-0.315116\pi$
$353$	10.4904	+	3.08026i	0.558348	+	0.163946i	0.00963074	+	0.999954i	$0.496934\pi$
$354$		0			0
$355$	1.42506	−	9.91150i	0.0756342	−	0.526048i
$356$		0			0
$357$	3.33525	−	7.30318i	0.176520	−	0.386525i
$358$		0			0
$359$	19.3813	−	12.4556i	1.02291	−	0.657382i	0.0822044	−	0.996615i	$-0.473804\pi$
$359$	19.3813	−	12.4556i	1.02291	−	0.657382i	0.940702	+	0.339233i	$0.110168\pi$
$360$		0			0
$361$	−0.0926025	−	0.644065i	−0.00487382	−	0.0338981i
$362$		0			0
$363$	7.13440	+	4.58500i	0.374459	+	0.240650i
$364$		0			0
$365$	−30.8613	+	9.06169i	−1.61535	+	0.474311i
$366$		0			0
$367$	−17.3258			−0.904402			−0.452201	−	0.891916i	$-0.649361\pi$
$367$	−17.3258			−0.904402			−0.452201	+	0.891916i	$0.649361\pi$
$368$		0			0
$369$	5.32624			0.277273
$370$		0			0
$371$	−2.24573	+	0.659407i	−0.116593	+	0.0342347i
$372$		0			0
$373$	−1.06292	−	0.683095i	−0.0550357	−	0.0353693i	0.512834	−	0.858488i	$-0.328596\pi$
$373$	−1.06292	−	0.683095i	−0.0550357	−	0.0353693i	−0.567869	+	0.823119i	$0.692232\pi$
$374$		0			0
$375$	−1.21241	−	8.43250i	−0.0626086	−	0.435453i
$376$		0			0
$377$	20.7052	−	13.3064i	1.06637	−	0.685314i
$378$		0			0
$379$	−1.60552	+	3.51561i	−0.0824702	+	0.180585i	−0.946375	−	0.323071i	$-0.895285\pi$
$379$	−1.60552	+	3.51561i	−0.0824702	+	0.180585i	0.863904	+	0.503656i	$0.168012\pi$
$380$		0			0
$381$	0.734828	−	5.11084i	0.0376464	−	0.261836i
$382$		0			0
$383$	14.5125	+	4.26125i	0.741554	+	0.217740i	0.630624	−	0.776088i	$-0.282799\pi$
$383$	14.5125	+	4.26125i	0.741554	+	0.217740i	0.110930	+	0.993828i	$0.464617\pi$
$384$		0			0
$385$	−10.0173	−	11.5606i	−0.510529	−	0.589181i
$386$		0			0
$387$	−6.33523	+	7.31124i	−0.322038	+	0.371651i
$388$		0			0
$389$	−2.01459	−	4.41134i	−0.102144	−	0.223664i	0.851659	−	0.524096i	$-0.175597\pi$
$389$	−2.01459	−	4.41134i	−0.102144	−	0.223664i	−0.953803	+	0.300432i	$0.902869\pi$
$390$		0			0
$391$	9.16069	+	4.81826i	0.463276	+	0.243670i
$392$		0			0
$393$	5.79308	+	12.6851i	0.292222	+	0.639878i
$394$		0			0
$395$	23.6233	−	27.2628i	1.18862	−	1.37174i
$396$		0			0
$397$	−20.9128	−	24.1346i	−1.04958	−	1.21128i	−0.976849	−	0.213932i	$-0.931373\pi$
$397$	−20.9128	−	24.1346i	−1.04958	−	1.21128i	−0.0727343	−	0.997351i	$-0.523173\pi$
$398$		0			0
$399$	15.8226	+	4.64593i	0.792120	+	0.232587i
$400$		0			0
$401$	2.57964	−	17.9418i	0.128821	−	0.895969i	−0.818231	−	0.574889i	$-0.805045\pi$
$401$	2.57964	−	17.9418i	0.128821	−	0.895969i	0.947052	−	0.321080i	$-0.104046\pi$
$402$		0			0
$403$	−4.45704	+	9.75955i	−0.222021	+	0.486158i
$404$		0			0
$405$	2.17941	−	1.40062i	0.108296	−	0.0695975i
$406$		0			0
$407$	1.91876	+	13.3452i	0.0951092	+	0.661499i
$408$		0			0
$409$	18.2181	+	11.7080i	0.900825	+	0.578925i	0.907035	−	0.421055i	$-0.138340\pi$
$409$	18.2181	+	11.7080i	0.900825	+	0.578925i	−0.00620948	+	0.999981i	$0.501977\pi$
$410$		0			0
$411$	16.7309	−	4.91264i	0.825275	−	0.242323i
$412$		0			0
$413$	54.4767			2.68062
$414$		0			0
$415$	27.9823			1.37360
$416$		0			0
$417$	−1.29488	+	0.380212i	−0.0634107	+	0.0186191i
$418$		0			0
$419$	0.637534	+	0.409718i	0.0311456	+	0.0200160i	0.556121	−	0.831101i	$-0.312289\pi$
$419$	0.637534	+	0.409718i	0.0311456	+	0.0200160i	−0.524975	+	0.851117i	$0.675925\pi$
$420$		0			0
$421$	4.25716	+	29.6092i	0.207481	+	1.44306i	0.781338	+	0.624108i	$0.214537\pi$
$421$	4.25716	+	29.6092i	0.207481	+	1.44306i	−0.573857	+	0.818956i	$0.694553\pi$
$422$		0			0
$423$	−3.89399	+	2.50252i	−0.189332	+	0.121677i
$424$		0			0
$425$	−1.53454	+	3.36018i	−0.0744362	+	0.162993i
$426$		0			0
$427$	−2.18410	+	15.1907i	−0.105696	+	0.735131i
$428$		0			0
$429$	5.28627	+	1.55219i	0.255223	+	0.0749404i
$430$		0			0
$431$	−3.93173	−	4.53745i	−0.189385	−	0.218561i	0.653115	−	0.757259i	$-0.273462\pi$
$431$	−3.93173	−	4.53745i	−0.189385	−	0.218561i	−0.842499	+	0.538698i	$0.818917\pi$
$432$		0			0
$433$	−5.28581	+	6.10015i	−0.254020	+	0.293155i	−0.868409	−	0.495849i	$-0.834857\pi$
$433$	−5.28581	+	6.10015i	−0.254020	+	0.293155i	0.614389	+	0.789003i	$0.289403\pi$
$434$		0			0
$435$	−7.63099	−	16.7095i	−0.365878	−	0.801161i
$436$		0			0
$437$	−7.11799	+	20.0325i	−0.340500	+	0.958283i
$438$		0			0
$439$	−1.24942	−	2.73585i	−0.0596315	−	0.130575i	0.877470	−	0.479631i	$-0.159229\pi$
$439$	−1.24942	−	2.73585i	−0.0596315	−	0.130575i	−0.937102	+	0.349056i	$0.886502\pi$
$440$		0			0
$441$	−4.47836	+	5.16830i	−0.213255	+	0.246110i
$442$		0			0
$443$	−24.7584	−	28.5727i	−1.17631	−	1.35753i	−0.920472	−	0.390809i	$-0.872195\pi$
$443$	−24.7584	−	28.5727i	−1.17631	−	1.35753i	−0.255834	−	0.966721i	$-0.582350\pi$
$444$		0			0
$445$	25.6760	+	7.53917i	1.21716	+	0.357391i
$446$		0			0
$447$	3.19224	−	22.2025i	0.150988	−	1.05014i
$448$		0			0
$449$	−3.79485	+	8.30956i	−0.179090	+	0.392152i	−0.977793	−	0.209573i	$-0.932793\pi$
$449$	−3.79485	+	8.30956i	−0.179090	+	0.392152i	0.798703	+	0.601725i	$0.205520\pi$
$450$		0			0
$451$	7.11197	−	4.57059i	0.334890	−	0.215221i
$452$		0			0
$453$	−3.12068	−	21.7048i	−0.146622	−	1.01978i
$454$		0			0
$455$	28.1418	+	18.0856i	1.31931	+	0.847866i
$456$		0			0
$457$	19.6774	−	5.77780i	0.920469	−	0.270274i	0.213028	−	0.977046i	$-0.431667\pi$
$457$	19.6774	−	5.77780i	0.920469	−	0.270274i	0.707441	+	0.706772i	$0.249849\pi$
$458$		0			0
$459$	2.15824			0.100738
$460$		0			0
$461$	32.8341			1.52924			0.764618	−	0.644484i	$-0.222928\pi$
$461$	32.8341			1.52924			0.764618	+	0.644484i	$0.222928\pi$
$462$		0			0
$463$	−1.00582	+	0.295337i	−0.0467446	+	0.0137255i	−0.305021	−	0.952346i	$-0.598664\pi$
$463$	−1.00582	+	0.295337i	−0.0467446	+	0.0137255i	0.258277	+	0.966071i	$0.416845\pi$
$464$		0			0
$465$	6.73656	+	4.32932i	0.312400	+	0.200768i
$466$		0			0
$467$	−4.01976	−	27.9580i	−0.186012	−	1.29374i	−0.842208	−	0.539152i	$-0.818745\pi$
$467$	−4.01976	−	27.9580i	−0.186012	−	1.29374i	0.656196	−	0.754590i	$-0.272164\pi$
$468$		0			0
$469$	−31.6199	+	20.3209i	−1.46007	+	0.938331i
$470$		0			0
$471$	8.51945	−	18.6550i	0.392556	−	0.859577i
$472$		0			0
$473$	−2.18527	+	15.1989i	−0.100479	+	0.698847i
$474$		0			0
$475$	−7.27994	−	2.13758i	−0.334027	−	0.0980790i
$476$		0			0
$477$	−0.412020	−	0.475497i	−0.0188651	−	0.0217715i
$478$		0			0
$479$	−8.88661	+	10.2557i	−0.406040	+	0.468595i	−0.921534	−	0.388299i	$-0.873063\pi$
$479$	−8.88661	+	10.2557i	−0.406040	+	0.468595i	0.515494	+	0.856893i	$0.327608\pi$
$480$		0			0
$481$	−12.2483	−	26.8200i	−0.558473	−	1.22288i
$482$		0			0
$483$	−12.8104	−	12.4170i	−0.582893	−	0.564995i
$484$		0			0
$485$	−7.27165	−	15.9227i	−0.330189	−	0.723013i
$486$		0			0
$487$	−22.4260	+	25.8810i	−1.01622	+	1.17278i	−0.0313458	+	0.999509i	$0.509979\pi$
$487$	−22.4260	+	25.8810i	−1.01622	+	1.17278i	−0.984874	+	0.173272i	$0.944566\pi$
$488$		0			0
$489$	7.14669	+	8.24772i	0.323184	+	0.372975i
$490$		0			0
$491$	−8.89193	−	2.61091i	−0.401287	−	0.117829i	0.0748602	−	0.997194i	$-0.476149\pi$
$491$	−8.89193	−	2.61091i	−0.401287	−	0.117829i	−0.476147	+	0.879365i	$0.657967\pi$
$492$		0			0
$493$	2.17789	−	15.1476i	0.0980873	−	0.682212i
$494$		0			0
$495$	1.70819	−	3.74042i	0.0767776	−	0.168119i
$496$		0			0
$497$	−12.0961	+	7.77366i	−0.542582	+	0.348696i
$498$		0			0
$499$	0.825311	+	5.74016i	0.0369460	+	0.256965i	0.999920	−	0.0126283i	$-0.00401983\pi$
$499$	0.825311	+	5.74016i	0.0369460	+	0.256965i	−0.962974	+	0.269593i	$0.913111\pi$
$500$		0			0
$501$	−3.40954	−	2.19118i	−0.152327	−	0.0978946i
$502$		0			0
$503$	−39.6723	+	11.6488i	−1.76890	+	0.519396i	−0.993676	−	0.112288i	$-0.964182\pi$
$503$	−39.6723	+	11.6488i	−1.76890	+	0.519396i	−0.775226	+	0.631684i	$0.782364\pi$
$504$		0			0
$505$	−29.4161			−1.30900
$506$		0			0
$507$	0.951575			0.0422609
$508$		0			0
$509$	26.9051	−	7.90004i	1.19255	−	0.350163i	0.375548	−	0.926803i	$-0.377455\pi$
$509$	26.9051	−	7.90004i	1.19255	−	0.350163i	0.816999	+	0.576640i	$0.195636\pi$
$510$		0			0
$511$	38.8538	+	24.9698i	1.71879	+	1.10460i
$512$		0			0
$513$	0.630869	+	4.38779i	0.0278535	+	0.193726i
$514$		0			0
$515$	−2.32609	+	1.49489i	−0.102500	+	0.0658725i
$516$		0			0
$517$	−3.05206	+	6.68308i	−0.134229	+	0.293921i
$518$		0			0
$519$	−1.39413	+	9.69636i	−0.0611953	+	0.425623i
$520$		0			0
$521$	−23.1820	−	6.80686i	−1.01562	−	0.298214i	−0.268771	−	0.963204i	$-0.586618\pi$
$521$	−23.1820	−	6.80686i	−1.01562	−	0.298214i	−0.746852	+	0.664990i	$0.768436\pi$
$522$		0			0
$523$	17.4354	+	20.1215i	0.762397	+	0.879853i	0.995708	−	0.0925491i	$-0.0295015\pi$
$523$	17.4354	+	20.1215i	0.762397	+	0.879853i	−0.233311	+	0.972402i	$0.574956\pi$
$524$		0			0
$525$	4.16959	−	4.81196i	0.181976	−	0.210011i
$526$		0			0
$527$	2.77128	+	6.06826i	0.120719	+	0.264337i
$528$		0			0
$529$	16.9042	−	15.5964i	0.734966	−	0.678103i
$530$		0			0
$531$	6.08339	+	13.3208i	0.263997	+	0.578072i
$532$		0			0
$533$	−12.1070	+	13.9722i	−0.524411	+	0.605202i
$534$		0			0
$535$	−14.7538	−	17.0268i	−0.637864	−	0.736135i
$536$		0			0
$537$	22.0551	+	6.47597i	0.951749	+	0.279459i
$538$		0			0
$539$	−1.54477	+	10.7441i	−0.0665378	+	0.462780i
$540$		0			0
$541$	1.46879	−	3.21620i	0.0631483	−	0.138275i	−0.875427	−	0.483351i	$-0.839419\pi$
$541$	1.46879	−	3.21620i	0.0631483	−	0.138275i	0.938575	+	0.345076i	$0.112147\pi$
$542$		0			0
$543$	5.23328	−	3.36323i	0.224582	−	0.144330i
$544$		0			0
$545$	4.87211	+	33.8863i	0.208698	+	1.45153i
$546$		0			0
$547$	−36.2867	−	23.3201i	−1.55151	−	0.997094i	−0.984904	−	0.173104i	$-0.944620\pi$
$547$	−36.2867	−	23.3201i	−1.55151	−	0.997094i	−0.566604	−	0.823990i	$-0.691743\pi$
$548$		0			0
$549$	−3.95837	+	1.16228i	−0.168939	+	0.0496050i
$550$		0			0
$551$	31.4322			1.33906
$552$		0			0
$553$	−51.7996			−2.20274
$554$		0			0
$555$	−21.1145	+	6.19979i	−0.896262	+	0.263166i
$556$		0			0
$557$	−6.53427	−	4.19932i	−0.276866	−	0.177931i	0.394838	−	0.918751i	$-0.370801\pi$
$557$	−6.53427	−	4.19932i	−0.276866	−	0.177931i	−0.671704	+	0.740820i	$0.734437\pi$
$558$		0			0
$559$	−4.77891	−	33.2380i	−0.202126	−	1.40582i
$560$		0			0
$561$	2.88183	−	1.85204i	0.121671	−	0.0781933i
$562$		0			0
$563$	−11.3549	+	24.8638i	−0.478554	+	1.04789i	0.504305	+	0.863526i	$0.331749\pi$
$563$	−11.3549	+	24.8638i	−0.478554	+	1.04789i	−0.982859	+	0.184361i	$0.940979\pi$
$564$		0			0
$565$	−1.68032	+	11.6869i	−0.0706916	+	0.491671i
$566$		0			0
$567$	−3.56935	−	1.04805i	−0.149898	−	0.0440142i
$568$		0			0
$569$	−5.11269	−	5.90036i	−0.214335	−	0.247356i	0.638393	−	0.769710i	$-0.279599\pi$
$569$	−5.11269	−	5.90036i	−0.214335	−	0.247356i	−0.852729	+	0.522354i	$0.825054\pi$
$570$		0			0
$571$	−4.04773	+	4.67133i	−0.169392	+	0.195489i	−0.834098	−	0.551616i	$-0.814011\pi$
$571$	−4.04773	+	4.67133i	−0.169392	+	0.195489i	0.664706	+	0.747105i	$0.268557\pi$
$572$		0			0
$573$	5.82611	+	12.7574i	0.243389	+	0.532948i
$574$		0			0
$575$	5.89403	+	5.71306i	0.245798	+	0.238251i
$576$		0			0
$577$	−2.85223	−	6.24552i	−0.118740	−	0.260005i	0.840924	−	0.541153i	$-0.182012\pi$
$577$	−2.85223	−	6.24552i	−0.118740	−	0.260005i	−0.959664	+	0.281148i	$0.909285\pi$
$578$		0			0
$579$	−4.46861	+	5.15705i	−0.185709	+	0.214320i
$580$		0			0
$581$	−26.3128	−	30.3665i	−1.09164	−	1.25982i
$582$		0			0
$583$	−0.958195	−	0.281351i	−0.0396844	−	0.0116524i
$584$		0			0
$585$	−1.27976	+	8.90091i	−0.0529115	+	0.368007i
$586$		0			0
$587$	14.1029	−	30.8811i	0.582090	−	1.27460i	−0.358016	−	0.933716i	$-0.616547\pi$
$587$	14.1029	−	30.8811i	0.582090	−	1.27460i	0.940106	−	0.340883i	$-0.110726\pi$
$588$		0			0
$589$	−11.5270	+	7.40792i	−0.474960	+	0.305238i
$590$		0			0
$591$	−3.10243	−	21.5779i	−0.127617	−	0.887595i
$592$		0			0
$593$	−22.6893	−	14.5815i	−0.931739	−	0.598792i	−0.0156978	−	0.999877i	$-0.504997\pi$
$593$	−22.6893	−	14.5815i	−0.931739	−	0.598792i	−0.916041	+	0.401085i	$0.868633\pi$
$594$		0			0
$595$	19.9572	−	5.85997i	0.818167	−	0.240236i
$596$		0			0
$597$	−11.6248			−0.475773
$598$		0			0
$599$	30.9426			1.26428			0.632140	−	0.774854i	$-0.282177\pi$
$599$	30.9426			1.26428			0.632140	+	0.774854i	$0.282177\pi$
$600$		0			0
$601$	−21.1453	+	6.20881i	−0.862534	+	0.253263i	−0.682937	−	0.730478i	$-0.739298\pi$
$601$	−21.1453	+	6.20881i	−0.862534	+	0.253263i	−0.179597	+	0.983740i	$0.557479\pi$
$602$		0			0
$603$	−8.49990	−	5.46255i	−0.346143	−	0.222452i
$604$		0			0
$605$	3.12675	+	21.7470i	0.127120	+	0.884142i
$606$		0			0
$607$	−4.15222	+	2.66847i	−0.168533	+	0.108310i	−0.622188	−	0.782868i	$-0.713756\pi$
$607$	−4.15222	+	2.66847i	−0.168533	+	0.108310i	0.453655	+	0.891177i	$0.350120\pi$
$608$		0			0
$609$	−10.9576	+	23.9938i	−0.444024	+	0.972278i
$610$		0			0
$611$	2.28657	−	15.9034i	0.0925046	−	0.643383i
$612$		0			0
$613$	32.9884	+	9.68626i	1.33239	+	0.391224i	0.868948	−	0.494904i	$-0.164797\pi$
$613$	32.9884	+	9.68626i	1.33239	+	0.391224i	0.463440	+	0.886128i	$0.346615\pi$
$614$		0			0
$615$	9.03613	+	10.4282i	0.364372	+	0.420507i
$616$		0			0
$617$	−19.5951	+	22.6139i	−0.788868	+	0.910402i	−0.997716	−	0.0675457i	$-0.978483\pi$
$617$	−19.5951	+	22.6139i	−0.788868	+	0.910402i	0.208848	+	0.977948i	$0.433029\pi$
$618$		0			0
$619$	−15.3090	−	33.5219i	−0.615319	−	1.34736i	−0.918876	−	0.394547i	$-0.870901\pi$
$619$	−15.3090	−	33.5219i	−0.615319	−	1.34736i	0.303557	−	0.952813i	$-0.401826\pi$
$620$		0			0
$621$	1.60572	−	4.51903i	0.0644352	−	0.181343i
$622$		0			0
$623$	−15.9626	−	34.9532i	−0.639527	−	1.40037i
$624$		0			0
$625$	20.0573	−	23.1474i	0.802293	−	0.925896i
$626$		0			0
$627$	4.60766	+	5.31752i	0.184012	+	0.212361i
$628$		0			0
$629$	−17.5901	−	5.16492i	−0.701364	−	0.205939i
$630$		0			0
$631$	−4.66746	+	32.4629i	−0.185809	+	1.29233i	0.656908	+	0.753971i	$0.271864\pi$
$631$	−4.66746	+	32.4629i	−0.185809	+	1.29233i	−0.842717	+	0.538357i	$0.819045\pi$
$632$		0			0
$633$	−4.40848	+	9.65322i	−0.175221	+	0.383681i
$634$		0			0
$635$	11.2532	−	7.23197i	0.446568	−	0.286992i
$636$		0			0
$637$	−3.37820	−	23.4959i	−0.133849	−	0.930942i
$638$		0			0
$639$	−3.25160	−	2.08968i	−0.128631	−	0.0826663i
$640$		0			0
$641$	−42.5763	+	12.5015i	−1.68166	+	0.493780i	−0.976545	−	0.215311i	$-0.930923\pi$
$641$	−42.5763	+	12.5015i	−1.68166	+	0.493780i	−0.705116	+	0.709092i	$0.749105\pi$
$642$		0			0
$643$	16.1473			0.636787			0.318394	−	0.947959i	$-0.396857\pi$
$643$	16.1473			0.636787			0.318394	+	0.947959i	$0.396857\pi$
$644$		0			0
$645$	−25.0626			−0.986838
$646$		0			0
$647$	−11.8522	+	3.48011i	−0.465957	+	0.136817i	−0.506279	−	0.862370i	$-0.668980\pi$
$647$	−11.8522	+	3.48011i	−0.465957	+	0.136817i	0.0403228	+	0.999187i	$0.487161\pi$
$648$		0			0
$649$	19.5539	+	12.5665i	0.767557	+	0.493279i
$650$		0			0
$651$	−1.63642	−	11.3816i	−0.0641365	−	0.446079i
$652$		0			0
$653$	24.8630	−	15.9785i	0.972963	−	0.625286i	0.0454069	−	0.998969i	$-0.485542\pi$
$653$	24.8630	−	15.9785i	0.972963	−	0.625286i	0.927556	+	0.373683i	$0.121905\pi$
$654$		0			0
$655$	−15.0080	+	32.8629i	−0.586410	+	1.28406i
$656$		0			0
$657$	−1.76689	+	12.2890i	−0.0689331	+	0.479440i
$658$		0			0
$659$	−14.1142	−	4.14431i	−0.549812	−	0.161439i	−0.00498478	−	0.999988i	$-0.501587\pi$
$659$	−14.1142	−	4.14431i	−0.549812	−	0.161439i	−0.544828	+	0.838548i	$0.683405\pi$
$660$		0			0
$661$	−2.96487	−	3.42164i	−0.115320	−	0.133087i	0.695154	−	0.718861i	$-0.255336\pi$
$661$	−2.96487	−	3.42164i	−0.115320	−	0.133087i	−0.810474	+	0.585774i	$0.800791\pi$
$662$		0			0
$663$	−4.90584	+	5.66164i	−0.190527	+	0.219880i
$664$		0			0
$665$	17.7472	+	38.8610i	0.688208	+	1.50696i
$666$		0			0
$667$	−30.0964	−	15.8299i	−1.16534	−	0.612935i
$668$		0			0
$669$	−1.54934	−	3.39258i	−0.0599009	−	0.131165i
$670$		0			0
$671$	−4.28811	+	4.94874i	−0.165541	+	0.191044i
$672$		0			0
$673$	9.92426	+	11.4532i	0.382552	+	0.441489i	0.914069	−	0.405559i	$-0.132923\pi$
$673$	9.92426	+	11.4532i	0.382552	+	0.441489i	−0.531517	+	0.847048i	$0.678378\pi$
$674$		0			0
$675$	1.64225	+	0.482208i	0.0632102	+	0.0185602i
$676$		0			0
$677$	−0.576021	+	4.00632i	−0.0221383	+	0.153975i	−0.997892	−	0.0648961i	$-0.979328\pi$
$677$	−0.576021	+	4.00632i	−0.0221383	+	0.153975i	0.975754	+	0.218871i	$0.0702375\pi$
$678$		0			0
$679$	−10.4416	+	22.8639i	−0.400712	+	0.877438i
$680$		0			0
$681$	−10.2470	+	6.58536i	−0.392667	+	0.252352i
$682$		0			0
$683$	−0.374266	−	2.60308i	−0.0143209	−	0.0996040i	0.981407	−	0.191937i	$-0.0614768\pi$
$683$	−0.374266	−	2.60308i	−0.0143209	−	0.0996040i	−0.995728	+	0.0923326i	$0.970568\pi$
$684$		0			0
$685$	38.0029	+	24.4230i	1.45202	+	0.933155i
$686$		0			0
$687$	16.2689	−	4.77697i	0.620697	−	0.182253i
$688$		0			0
$689$	2.18391			0.0832004
$690$		0			0
$691$	11.3624			0.432246			0.216123	−	0.976366i	$-0.430659\pi$
$691$	11.3624			0.432246			0.216123	+	0.976366i	$0.430659\pi$
$692$		0			0
$693$	−5.66541	+	1.66351i	−0.215211	+	0.0631916i
$694$		0			0
$695$	−2.94122	−	1.89021i	−0.111567	−	0.0716997i
$696$		0			0
$697$	1.63595	+	11.3783i	0.0619661	+	0.430984i
$698$		0			0
$699$	22.7772	−	14.6380i	0.861514	−	0.553661i
$700$		0			0
$701$	6.66194	−	14.5876i	0.251618	−	0.550966i	−0.741105	−	0.671389i	$-0.765698\pi$
$701$	6.66194	−	14.5876i	0.251618	−	0.550966i	0.992723	+	0.120423i	$0.0384251\pi$
$702$		0			0
$703$	5.35878	−	37.2712i	0.202110	−	1.40571i
$704$		0			0
$705$	−11.5060	−	3.37845i	−0.433339	−	0.127240i
$706$		0			0
$707$	27.6610	+	31.9225i	1.04030	+	1.20057i
$708$		0			0
$709$	−7.01258	+	8.09295i	−0.263363	+	0.303937i	−0.871994	−	0.489516i	$-0.837173\pi$
$709$	−7.01258	+	8.09295i	−0.263363	+	0.303937i	0.608631	+	0.793453i	$0.291719\pi$
$710$		0			0
$711$	−5.78445	−	12.6662i	−0.216934	−	0.475019i
$712$		0			0
$713$	14.7679	−	1.28791i	0.553061	−	0.0482326i
$714$		0			0
$715$	5.92928	+	12.9833i	0.221743	+	0.485548i
$716$		0			0
$717$	−15.6906	+	18.1079i	−0.585977	+	0.676253i
$718$		0			0
$719$	19.8822	+	22.9453i	0.741480	+	0.855713i	0.993714	−	0.111953i	$-0.0357106\pi$
$719$	19.8822	+	22.9453i	0.741480	+	0.855713i	−0.252234	+	0.967666i	$0.581165\pi$
$720$		0			0
$721$	3.80957	+	1.11859i	0.141876	+	0.0416584i
$722$		0			0
$723$	−0.932484	+	6.48557i	−0.0346795	+	0.241201i
$724$		0			0
$725$	5.04157	−	11.0395i	0.187239	−	0.409997i
$726$		0			0
$727$	7.41734	−	4.76683i	0.275094	−	0.176792i	−0.395818	−	0.918329i	$-0.629539\pi$
$727$	7.41734	−	4.76683i	0.275094	−	0.176792i	0.670912	+	0.741537i	$0.265903\pi$
$728$		0			0
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$		0			0
$731$	−17.5647	−	11.2881i	−0.649652	−	0.417506i
$732$		0			0
$733$	42.8671	−	12.5869i	1.58333	−	0.464908i	0.632485	−	0.774572i	$-0.282035\pi$
$733$	42.8671	−	12.5869i	1.58333	−	0.464908i	0.950846	+	0.309665i	$0.100217\pi$
$734$		0			0
$735$	−17.7167			−0.653490
$736$		0			0
$737$	−16.0372			−0.590739
$738$		0			0
$739$	−15.8447	+	4.65242i	−0.582856	+	0.171142i	−0.559851	−	0.828593i	$-0.689142\pi$
$739$	−15.8447	+	4.65242i	−0.582856	+	0.171142i	−0.0230053	+	0.999735i	$0.507323\pi$
$740$		0			0
$741$	−12.9444	−	8.31884i	−0.475523	−	0.305600i
$742$		0			0
$743$	−0.365858	−	2.54460i	−0.0134220	−	0.0933521i	0.982009	−	0.188833i	$-0.0604704\pi$
$743$	−0.365858	−	2.54460i	−0.0134220	−	0.0933521i	−0.995431	+	0.0954804i	$0.969561\pi$
$744$		0			0
$745$	48.8860	−	31.4172i	1.79105	−	1.15104i
$746$		0			0
$747$	4.48697	−	9.82509i	0.164170	−	0.359481i
$748$		0			0
$749$	−4.60406	+	32.0219i	−0.168229	+	1.17006i
$750$		0			0
$751$	35.3396	+	10.3766i	1.28956	+	0.378649i	0.853417	−	0.521229i	$-0.174526\pi$
$751$	35.3396	+	10.3766i	1.28956	+	0.378649i	0.436142	+	0.899878i	$0.356344\pi$
$752$		0			0
$753$	−0.470469	−	0.542950i	−0.0171448	−	0.0197862i
$754$		0			0
$755$	37.2015	−	42.9328i	1.35390	−	1.56248i
$756$		0			0
$757$	−3.59137	−	7.86399i	−0.130530	−	0.285822i	0.833070	−	0.553167i	$-0.186581\pi$
$757$	−3.59137	−	7.86399i	−0.130530	−	0.285822i	−0.963601	+	0.267345i	$0.913854\pi$
$758$		0			0
$759$	−1.73384	−	7.41204i	−0.0629343	−	0.269040i
$760$		0			0
$761$	−18.5471	−	40.6124i	−0.672330	−	1.47220i	−0.870570	−	0.492044i	$-0.836250\pi$
$761$	−18.5471	−	40.6124i	−0.672330	−	1.47220i	0.198240	−	0.980154i	$-0.436477\pi$
$762$		0			0
$763$	32.1922	−	37.1517i	1.16543	−	1.34498i
$764$		0			0
$765$	3.66152	+	4.22561i	0.132382	+	0.152777i
$766$		0			0
$767$	−48.7720	−	14.3208i	−1.76105	−	0.517092i
$768$		0			0
$769$	−1.50669	+	10.4793i	−0.0543327	+	0.377892i	0.944454	+	0.328644i	$0.106592\pi$
$769$	−1.50669	+	10.4793i	−0.0543327	+	0.377892i	−0.998787	+	0.0492483i	$0.984317\pi$
$770$		0			0
$771$	−1.82782	+	4.00237i	−0.0658273	+	0.144142i
$772$		0			0
$773$	−28.4622	+	18.2915i	−1.02371	+	0.657900i	−0.940907	−	0.338665i	$-0.890025\pi$
$773$	−28.4622	+	18.2915i	−1.02371	+	0.657900i	−0.0828059	+	0.996566i	$0.526388\pi$
$774$		0			0
$775$	0.752915	+	5.23664i	0.0270455	+	0.188106i
$776$		0			0
$777$	26.5828	+	17.0837i	0.953653	+	0.612876i
$778$		0			0
$779$	−22.6544	+	6.65192i	−0.811676	+	0.238330i
$780$		0			0
$781$	−6.13497			−0.219526
$782$		0			0
$783$	−7.09066			−0.253399
$784$		0			0
$785$	50.9781	−	14.9685i	1.81949	−	0.534249i
$786$		0			0
$787$	9.42814	+	6.05910i	0.336077	+	0.215984i	0.697784	−	0.716308i	$-0.254170\pi$
$787$	9.42814	+	6.05910i	0.336077	+	0.215984i	−0.361707	+	0.932292i	$0.617806\pi$
$788$		0			0
$789$	−0.634779	−	4.41498i	−0.0225987	−	0.157178i
$790$		0			0
$791$	14.2628	−	9.16612i	0.507125	−	0.325910i
$792$		0			0
$793$	5.94870	−	13.0258i	0.211245	−	0.462561i
$794$		0			0
$795$	0.231970	−	1.61339i	0.00822714	−	0.0572210i
$796$		0			0
$797$	−35.9817	−	10.5652i	−1.27454	−	0.374238i	−0.426652	−	0.904416i	$-0.640307\pi$
$797$	−35.9817	−	10.5652i	−1.27454	−	0.374238i	−0.847886	+	0.530178i	$0.822125\pi$
$798$		0			0
$799$	−6.54210	−	7.54998i	−0.231443	−	0.267099i
$800$		0			0
$801$	6.76430	−	7.80642i	0.239005	−	0.275826i
$802$		0			0
$803$	8.18624	+	17.9254i	0.288886	+	0.632572i
$804$		0			0
$805$	2.57813	−	46.1473i	0.0908672	−	1.62648i
$806$		0			0
$807$	9.47829	+	20.7546i	0.333652	+	0.730595i
$808$		0			0
$809$	−4.37192	+	5.04547i	−0.153709	+	0.177389i	−0.827381	−	0.561641i	$-0.810170\pi$
$809$	−4.37192	+	5.04547i	−0.153709	+	0.177389i	0.673673	+	0.739030i	$0.264716\pi$
$810$		0			0
$811$	16.8632	+	19.4612i	0.592148	+	0.683375i	0.970171	−	0.242421i	$-0.0779414\pi$
$811$	16.8632	+	19.4612i	0.592148	+	0.683375i	−0.378023	+	0.925796i	$0.623396\pi$
$812$		0			0
$813$	5.92546	+	1.73987i	0.207815	+	0.0610200i
$814$		0			0
$815$	−4.02363	+	27.9850i	−0.140942	+	0.980271i
$816$		0			0
$817$	17.8149	−	39.0093i	0.623266	−	1.36476i
$818$		0			0
$819$	10.8627	−	6.98105i	0.379574	−	0.243938i
$820$		0			0
$821$	6.48842	+	45.1279i	0.226447	+	1.57498i	0.712898	+	0.701268i	$0.247382\pi$
$821$	6.48842	+	45.1279i	0.226447	+	1.57498i	−0.486451	+	0.873708i	$0.661709\pi$
$822$		0			0
$823$	−21.8743	−	14.0578i	−0.762490	−	0.490023i	0.100691	−	0.994918i	$-0.467895\pi$
$823$	−21.8743	−	14.0578i	−0.762490	−	0.490023i	−0.863181	+	0.504895i	$0.831531\pi$
$824$		0			0
$825$	2.60664	−	0.765379i	0.0907516	−	0.0266471i
$826$		0			0
$827$	50.7176			1.76363			0.881813	−	0.471600i	$-0.156323\pi$
$827$	50.7176			1.76363			0.881813	+	0.471600i	$0.156323\pi$
$828$		0			0
$829$	40.5584			1.40865			0.704326	−	0.709876i	$-0.251249\pi$
$829$	40.5584			1.40865			0.704326	+	0.709876i	$0.251249\pi$
$830$		0			0
$831$	−26.4093	+	7.75447i	−0.916129	+	0.269000i
$832$		0			0
$833$	−12.4164	−	7.97955i	−0.430204	−	0.276475i
$834$		0			0
$835$	−1.49428	−	10.3929i	−0.0517116	−	0.359662i
$836$		0			0
$837$	2.60031	−	1.67112i	0.0898800	−	0.0577624i
$838$		0			0
$839$	14.8144	−	32.4390i	0.511449	−	1.11992i	−0.461127	−	0.887334i	$-0.652555\pi$
$839$	14.8144	−	32.4390i	0.511449	−	1.11992i	0.972576	−	0.232584i	$-0.0747179\pi$
$840$		0			0
$841$	−3.02809	+	21.0608i	−0.104417	+	0.726235i
$842$		0			0
$843$	2.62765	+	0.771548i	0.0905011	+	0.0265735i
$844$		0			0
$845$	1.61437	+	1.86309i	0.0555362	+	0.0640922i
$846$		0			0
$847$	20.6598	−	23.8427i	0.709879	−	0.819244i
$848$		0			0
$849$	−9.23202	−	20.2153i	−0.316842	−	0.693788i
$850$		0			0
$851$	−23.9015	+	32.9884i	−0.819333	+	1.13083i
$852$		0			0
$853$	−12.1597	−	26.6261i	−0.416342	−	0.911662i	−0.995349	−	0.0963388i	$-0.969287\pi$
$853$	−12.1597	−	26.6261i	−0.416342	−	0.911662i	0.579007	−	0.815323i	$-0.303440\pi$
$854$		0			0
$855$	−7.52056	+	8.67919i	−0.257198	+	0.296822i
$856$		0			0
$857$	26.4447	+	30.5188i	0.903335	+	1.04250i	0.998891	+	0.0470796i	$0.0149914\pi$
$857$	26.4447	+	30.5188i	0.903335	+	1.04250i	−0.0955566	+	0.995424i	$0.530463\pi$
$858$		0			0
$859$	−3.70737	−	1.08858i	−0.126494	−	0.0371419i	0.217873	−	0.975977i	$-0.430088\pi$
$859$	−3.70737	−	1.08858i	−0.126494	−	0.0371419i	−0.344367	+	0.938835i	$0.611906\pi$
$860$		0			0
$861$	2.81980	−	19.6121i	0.0960985	−	0.668379i
$862$		0			0
$863$	−18.6771	+	40.8971i	−0.635775	+	1.39215i	0.267696	+	0.963503i	$0.413738\pi$
$863$	−18.6771	+	40.8971i	−0.635775	+	1.39215i	−0.903471	+	0.428649i	$0.858990\pi$
$864$		0			0
$865$	−21.3497	+	13.7206i	−0.725910	+	0.466514i
$866$		0			0
$867$	−1.75645	−	12.2164i	−0.0596522	−	0.414890i
$868$		0			0
$869$	−18.5930	−	11.9490i	−0.630724	−	0.405342i
$870$		0			0
$871$	33.6507	−	9.88073i	1.14021	−	0.334796i
$872$		0			0
$873$	−6.75676			−0.228682
$874$		0			0
$875$	−31.6918			−1.07138
$876$		0			0
$877$	30.4639	−	8.94500i	1.02869	−	0.302051i	0.276513	−	0.961010i	$-0.410821\pi$
$877$	30.4639	−	8.94500i	1.02869	−	0.302051i	0.752179	+	0.658959i	$0.229003\pi$
$878$		0			0
$879$	−2.15999	−	1.38814i	−0.0728547	−	0.0468208i
$880$		0			0
$881$	6.46781	+	44.9846i	0.217906	+	1.51557i	0.745749	+	0.666227i	$0.232092\pi$
$881$	6.46781	+	44.9846i	0.217906	+	1.51557i	−0.527843	+	0.849342i	$0.676999\pi$
$882$		0			0
$883$	−43.8199	+	28.1613i	−1.47466	+	0.947704i	−0.477026	+	0.878889i	$0.658285\pi$
$883$	−43.8199	+	28.1613i	−1.47466	+	0.947704i	−0.997629	+	0.0688143i	$0.978078\pi$
$884$		0			0
$885$	−15.7601	+	34.5097i	−0.529769	+	1.16003i
$886$		0			0
$887$	−2.34422	+	16.3044i	−0.0787113	+	0.547449i	0.911865	+	0.410490i	$0.134642\pi$
$887$	−2.34422	+	16.3044i	−0.0787113	+	0.547449i	−0.990577	+	0.136960i	$0.956267\pi$
$888$		0			0
$889$	−18.4299	−	5.41152i	−0.618121	−	0.181497i
$890$		0			0
$891$	−1.03942	−	1.19956i	−0.0348219	−	0.0401866i
$892$		0			0
$893$	13.4371	−	15.5073i	0.449656	−	0.518931i
$894$		0			0
$895$	24.7379	+	54.1684i	0.826896	+	1.81065i
$896$		0			0
$897$	8.20474	+	14.4843i	0.273948	+	0.483618i
$898$		0			0
$899$	−9.10474	−	19.9366i	−0.303660	−	0.664923i
$900$		0			0
$901$	0.889239	−	1.02624i	0.0296248	−	0.0341889i
$902$		0			0
$903$	23.5673	+	27.1981i	0.784269	+	0.905095i
$904$		0			0
$905$	15.4633	+	4.54043i	0.514017	+	0.150929i
$906$		0			0
$907$	−3.83361	+	26.6633i	−0.127293	+	0.885341i	0.821672	+	0.569960i	$0.193041\pi$
$907$	−3.83361	+	26.6633i	−0.127293	+	0.885341i	−0.948965	+	0.315381i	$0.897868\pi$
$908$		0			0
$909$	−4.71688	+	10.3285i	−0.156449	+	0.342575i
$910$		0			0
$911$	−19.9051	+	12.7922i	−0.659485	+	0.423826i	−0.827121	−	0.562023i	$-0.810023\pi$
$911$	−19.9051	+	12.7922i	−0.659485	+	0.423826i	0.167636	+	0.985849i	$0.446387\pi$
$912$		0			0
$913$	−2.43985	−	16.9695i	−0.0807473	−	0.561610i
$914$		0			0
$915$	−8.99112	−	5.77825i	−0.297237	−	0.191023i
$916$		0			0
$917$	49.7755	−	14.6154i	1.64373	−	0.482644i
$918$		0			0
$919$	10.2767			0.338997			0.169499	−	0.985530i	$-0.445785\pi$
$919$	10.2767			0.338997			0.169499	+	0.985530i	$0.445785\pi$
$920$		0			0
$921$	7.82451			0.257826
$922$		0			0
$923$	12.8729	−	3.77983i	0.423717	−	0.124415i
$924$		0			0
$925$	−12.2307	−	7.86019i	−0.402143	−	0.258442i
$926$		0			0
$927$	0.151893	+	1.05644i	0.00498881	+	0.0346979i
$928$		0			0
$929$	6.10906	−	3.92606i	0.200432	−	0.128810i	−0.436575	−	0.899668i	$-0.643809\pi$
$929$	6.10906	−	3.92606i	0.200432	−	0.128810i	0.637007	+	0.770858i	$0.280172\pi$
$930$		0			0
$931$	12.5934	−	27.5756i	0.412730	−	0.903753i
$932$		0			0
$933$	2.65089	−	18.4373i	0.0867862	−	0.603611i
$934$		0			0
$935$	8.51522	+	2.50030i	0.278478	+	0.0817684i
$936$		0			0
$937$	−15.1100	−	17.4379i	−0.493622	−	0.569670i	0.453208	−	0.891405i	$-0.350279\pi$
$937$	−15.1100	−	17.4379i	−0.493622	−	0.569670i	−0.946830	+	0.321735i	$0.895734\pi$
$938$		0			0
$939$	10.5233	−	12.1445i	0.343414	−	0.396321i
$940$		0			0
$941$	−12.1923	−	26.6975i	−0.397459	−	0.870313i	−0.997522	−	0.0703606i	$-0.977585\pi$
$941$	−12.1923	−	26.6975i	−0.397459	−	0.870313i	0.600063	−	0.799953i	$-0.295142\pi$
$942$		0			0
$943$	25.0416	+	5.03994i	0.815467	+	0.164123i
$944$		0			0
$945$	−4.00351	−	8.76647i	−0.130234	−	0.285173i
$946$		0			0
$947$	22.2530	−	25.6813i	0.723126	−	0.834532i	−0.268554	−	0.963265i	$-0.586546\pi$
$947$	22.2530	−	25.6813i	0.723126	−	0.834532i	0.991679	+	0.128733i	$0.0410911\pi$
$948$		0			0
$949$	−28.2211	−	32.5689i	−0.916096	−	1.05723i
$950$		0			0
$951$	−0.283466	−	0.0832332i	−0.00919202	−	0.00269902i
$952$		0			0
$953$	−0.377093	+	2.62274i	−0.0122152	+	0.0849589i	−0.995017	−	0.0997043i	$-0.968210\pi$
$953$	−0.377093	+	2.62274i	−0.0122152	+	0.0849589i	0.982802	+	0.184663i	$0.0591194\pi$
$954$		0			0
$955$	−15.0935	+	33.0502i	−0.488415	+	1.06948i
$956$		0			0
$957$	−9.46794	+	6.08468i	−0.306055	+	0.196690i
$958$		0			0
$959$	−9.23156	−	64.2069i	−0.298103	−	2.07335i
$960$		0			0
$961$	−18.0413	−	11.5944i	−0.581977	−	0.374014i
$962$		0			0
$963$	−8.34422	+	2.45008i	−0.268889	+	0.0789528i
$964$		0			0
$965$	−17.6781			−0.569079
$966$		0			0
$967$	22.0652			0.709568			0.354784	−	0.934948i	$-0.384554\pi$
$967$	22.0652			0.709568			0.354784	+	0.934948i	$0.384554\pi$
$968$		0			0
$969$	−9.17974	+	2.69541i	−0.294896	+	0.0865892i
$970$		0			0
$971$	−4.18795	−	2.69143i	−0.134398	−	0.0863721i	0.471714	−	0.881751i	$-0.343635\pi$
$971$	−4.18795	−	2.69143i	−0.134398	−	0.0863721i	−0.606112	+	0.795379i	$0.707272\pi$
$972$		0			0
$973$	0.714473	+	4.96927i	0.0229049	+	0.159307i
$974$		0			0
$975$	−4.99792	+	3.21197i	−0.160061	+	0.102865i
$976$		0			0
$977$	14.7947	−	32.3958i	0.473324	−	1.03643i	−0.510922	−	0.859627i	$-0.670696\pi$
$977$	14.7947	−	32.3958i	0.473324	−	1.03643i	0.984245	−	0.176807i	$-0.0565770\pi$
$978$		0			0
$979$	2.33328	−	16.2283i	0.0745719	−	0.518659i
$980$		0			0
$981$	12.6793	+	3.72299i	0.404820	+	0.118866i
$982$		0			0
$983$	24.1006	+	27.8136i	0.768690	+	0.887115i	0.996239	−	0.0866515i	$-0.0276167\pi$
$983$	24.1006	+	27.8136i	0.768690	+	0.887115i	−0.227549	+	0.973767i	$0.573071\pi$
$984$		0			0
$985$	36.9839	−	42.6817i	1.17841	−	1.35995i
$986$		0			0
$987$	7.15315	+	15.6632i	0.227687	+	0.498566i
$988$		0			0
$989$	−36.7037	+	28.3795i	−1.16711	+	0.902416i
$990$		0			0
$991$	23.9778	+	52.5040i	0.761679	+	1.66784i	0.744163	+	0.667998i	$0.232848\pi$
$991$	23.9778	+	52.5040i	0.761679	+	1.66784i	0.0175156	+	0.999847i	$0.494424\pi$
$992$		0			0
$993$	2.35887	−	2.72228i	0.0748565	−	0.0863890i
$994$		0			0
$995$	−19.7219	−	22.7602i	−0.625225	−	0.721548i
$996$		0			0
$997$	−0.419408	−	0.123149i	−0.0132828	−	0.00390017i	0.275084	−	0.961420i	$-0.411294\pi$
$997$	−0.419408	−	0.123149i	−0.0132828	−	0.00390017i	−0.288367	+	0.957520i	$0.593112\pi$
$998$		0			0
$999$	−1.20886	+	8.40783i	−0.0382468	+	0.266012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.i.b.73.2	✓	20
3.2	odd	2		828.2.q.b.73.1		20
23.6	even	11	inner	276.2.i.b.121.2	yes	20
23.11	odd	22		6348.2.a.q.1.2		10
23.12	even	11		6348.2.a.r.1.9		10
69.29	odd	22		828.2.q.b.397.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.i.b.73.2	✓	20	1.1	even	1	trivial
276.2.i.b.121.2	yes	20	23.6	even	11	inner
828.2.q.b.73.1		20	3.2	odd	2
828.2.q.b.397.1		20	69.29	odd	22
6348.2.a.q.1.2		10	23.11	odd	22
6348.2.a.r.1.9		10	23.12	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)

\(f(q)\)	\(=\)	\(q+(0.959493 - 0.281733i) q^{3} +(2.17941 + 1.40062i) q^{5} +(-0.529416 - 3.68217i) q^{7} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.959493 - 0.281733i) q^{3} +(2.17941 + 1.40062i) q^{5} +(-0.529416 - 3.68217i) q^{7} +(0.841254 - 0.540641i) q^{9} +(0.659363 - 1.44380i) q^{11} +(-0.493987 + 3.43575i) q^{13} +(2.48573 + 0.729877i) q^{15} +(1.41335 + 1.63109i) q^{17} +(-2.90294 + 3.35017i) q^{19} +(-1.54536 - 3.38386i) q^{21} +(4.46678 - 1.74582i) q^{23} +(0.711016 + 1.55691i) q^{25} +(0.654861 - 0.755750i) q^{27} +(-4.64339 - 5.35876i) q^{29} +(2.96579 + 0.870835i) q^{31} +(0.225888 - 1.57108i) q^{33} +(4.00351 - 8.76647i) q^{35} +(-7.14585 + 4.59236i) q^{37} +(0.493987 + 3.43575i) q^{39} +(4.48072 + 2.87958i) q^{41} +(-9.28229 + 2.72553i) q^{43} +2.59067 q^{45} -4.62880 q^{47} +(-6.56163 + 1.92667i) q^{49} +(1.81563 + 1.16683i) q^{51} +(-0.0895406 - 0.622769i) q^{53} +(3.45925 - 2.22312i) q^{55} +(-1.84150 + 4.03232i) q^{57} +(-2.08408 + 14.4951i) q^{59} +(-3.95837 - 1.16228i) q^{61} +(-2.43610 - 2.81141i) q^{63} +(-5.88880 + 6.79603i) q^{65} +(-4.19729 - 9.19078i) q^{67} +(3.79399 - 2.93354i) q^{69} +(-1.60565 - 3.51589i) q^{71} +(-8.13034 + 9.38292i) q^{73} +(1.12085 + 1.29353i) q^{75} +(-5.66541 - 1.66351i) q^{77} +(1.98166 - 13.7828i) q^{79} +(0.415415 - 0.909632i) q^{81} +(9.08652 - 5.83955i) q^{83} +(0.795723 + 5.53438i) q^{85} +(-5.96504 - 3.83350i) q^{87} +(9.91096 - 2.91012i) q^{89} +12.9125 q^{91} +3.09100 q^{93} +(-11.0190 + 3.23548i) q^{95} +(-5.68415 - 3.65298i) q^{97} +(-0.225888 - 1.57108i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9}+O(q^{10}) \) 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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