LMFDB - Embedded newform 276.2.i.a.121.2

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} - 8 x^{19} + 43 x^{18} - 165 x^{17} + 538 x^{16} - 1433 x^{15} + 3444 x^{14} - 7370 x^{13} + \cdots + 529 $ x^20 - 8x^19 + 43x^18 - 165x^17 + 538x^16 - 1433x^15 + 3444x^14 - 7370x^13 + 15500x^12 - 28190x^11 + 41920x^10 - 33520x^9 - 13837x^8 + 78980x^7 - 92652x^6 - 52852x^5 + 177374x^4 + 151360x^3 + 115323x^2 + 12834*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			121.2
Root			$-0.404188 + 2.81119i$ of defining polynomial
Character	$\chi$	$=$	276.121
Dual form			276.2.i.a.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 - 0.281733i) q^{3} +(-0.332496 + 0.213682i) q^{5} +(-0.440112 + 3.06105i) q^{7} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.959493 - 0.281733i) q^{3} +(-0.332496 + 0.213682i) q^{5} +(-0.440112 + 3.06105i) q^{7} +(0.841254 + 0.540641i) q^{9} +(1.09466 + 2.39697i) q^{11} +(0.315289 + 2.19288i) q^{13} +(0.379229 - 0.111352i) q^{15} +(2.42879 - 2.80297i) q^{17} +(4.61122 + 5.32163i) q^{19} +(1.28468 - 2.81306i) q^{21} +(-4.06629 + 2.54269i) q^{23} +(-2.01218 + 4.40606i) q^{25} +(-0.654861 - 0.755750i) q^{27} +(4.37075 - 5.04411i) q^{29} +(-2.22075 + 0.652070i) q^{31} +(-0.375014 - 2.60828i) q^{33} +(-0.507756 - 1.11183i) q^{35} +(-4.80517 - 3.08810i) q^{37} +(0.315289 - 2.19288i) q^{39} +(-2.36514 + 1.51998i) q^{41} +(3.75382 + 1.10222i) q^{43} -0.395239 q^{45} -4.37944 q^{47} +(-2.45987 - 0.722282i) q^{49} +(-3.12009 + 2.00516i) q^{51} +(1.80647 - 12.5643i) q^{53} +(-0.876162 - 0.563075i) q^{55} +(-2.92516 - 6.40520i) q^{57} +(-1.40772 - 9.79088i) q^{59} +(6.36499 - 1.86893i) q^{61} +(-2.02517 + 2.33718i) q^{63} +(-0.573412 - 0.661753i) q^{65} +(0.559732 - 1.22564i) q^{67} +(4.61794 - 1.29408i) q^{69} +(-3.25308 + 7.12324i) q^{71} +(4.16279 + 4.80412i) q^{73} +(3.17201 - 3.66069i) q^{75} +(-7.81903 + 2.29587i) q^{77} +(-1.05877 - 7.36392i) q^{79} +(0.415415 + 0.909632i) q^{81} +(-0.579976 - 0.372728i) q^{83} +(-0.208617 + 1.45097i) q^{85} +(-5.61479 + 3.60841i) q^{87} +(5.91112 + 1.73566i) q^{89} -6.85128 q^{91} +2.31450 q^{93} +(-2.67035 - 0.784086i) q^{95} +(-4.89824 + 3.14790i) q^{97} +(-0.375014 + 2.60828i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9	$ 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9} - 22 q^{13} + 7 q^{15} + 7 q^{17} + 19 q^{19} + 20 q^{23} + 20 q^{25} - 2 q^{27} + 32 q^{29} - 3 q^{31} + 11 q^{33} - 26 q^{35} - 10 q^{37} - 22 q^{39} - 40 q^{41} + 8 q^{43} - 4 q^{45} - 18 q^{47} - 34 q^{49} - 26 q^{51} - 34 q^{53} - 17 q^{55} - 3 q^{57} - 32 q^{59} + 32 q^{61} + 49 q^{65} + 35 q^{67} - 2 q^{69} + 33 q^{71} - q^{73} - 2 q^{75} - 50 q^{77} + 22 q^{79} - 2 q^{81} - 14 q^{83} - 9 q^{85} - 12 q^{87} + 10 q^{89} - 72 q^{91} + 30 q^{93} - 51 q^{95} - 4 q^{97} + 11 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9 - 22 * q^13 + 7 * q^15 + 7 * q^17 + 19 * q^19 + 20 * q^23 + 20 * q^25 - 2 * q^27 + 32 * q^29 - 3 * q^31 + 11 * q^33 - 26 * q^35 - 10 * q^37 - 22 * q^39 - 40 * q^41 + 8 * q^43 - 4 * q^45 - 18 * q^47 - 34 * q^49 - 26 * q^51 - 34 * q^53 - 17 * q^55 - 3 * q^57 - 32 * q^59 + 32 * q^61 + 49 * q^65 + 35 * q^67 - 2 * q^69 + 33 * q^71 - q^73 - 2 * q^75 - 50 * q^77 + 22 * q^79 - 2 * q^81 - 14 * q^83 - 9 * q^85 - 12 * q^87 + 10 * q^89 - 72 * q^91 + 30 * q^93 - 51 * q^95 - 4 * q^97 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{9}{11}\right)$	$1$	$1$

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
$5$	−0.332496	+	0.213682i	−0.148697	+	0.0955616i	−0.612874	−	0.790181i	$-0.709987\pi$
$5$	−0.332496	+	0.213682i	−0.148697	+	0.0955616i	0.464177	+	0.885743i	$0.346350\pi$
$6$		0			0
$7$	−0.440112	+	3.06105i	−0.166347	+	1.15697i	0.720010	+	0.693964i	$0.244137\pi$
$7$	−0.440112	+	3.06105i	−0.166347	+	1.15697i	−0.886356	+	0.463003i	$0.846772\pi$
$8$		0			0
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$		0			0
$11$	1.09466	+	2.39697i	0.330053	+	0.722715i	0.999803	−	0.0198719i	$-0.00632584\pi$
$11$	1.09466	+	2.39697i	0.330053	+	0.722715i	−0.669750	+	0.742587i	$0.733599\pi$
$12$		0			0
$13$	0.315289	+	2.19288i	0.0874454	+	0.608196i	0.985673	+	0.168666i	$0.0539459\pi$
$13$	0.315289	+	2.19288i	0.0874454	+	0.608196i	−0.898228	+	0.439530i	$0.855145\pi$
$14$		0			0
$15$	0.379229	−	0.111352i	0.0979165	−	0.0287509i
$16$		0			0
$17$	2.42879	−	2.80297i	0.589068	−	0.679821i	−0.380461	−	0.924797i	$-0.624235\pi$
$17$	2.42879	−	2.80297i	0.589068	−	0.679821i	0.969529	+	0.244976i	$0.0787802\pi$
$18$		0			0
$19$	4.61122	+	5.32163i	1.05789	+	1.22087i	0.974509	+	0.224348i	$0.0720253\pi$
$19$	4.61122	+	5.32163i	1.05789	+	1.22087i	0.0833775	+	0.996518i	$0.473429\pi$
$20$		0			0
$21$	1.28468	−	2.81306i	0.280341	−	0.613860i
$22$		0			0
$23$	−4.06629	+	2.54269i	−0.847881	+	0.530187i
$23$	−4.06629	+	2.54269i	−0.847881	+	0.530187i
$24$		0			0
$25$	−2.01218	+	4.40606i	−0.402436	+	0.881213i
$26$		0			0
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$		0			0
$29$	4.37075	−	5.04411i	0.811627	−	0.936668i	−0.187331	−	0.982297i	$-0.559984\pi$
$29$	4.37075	−	5.04411i	0.811627	−	0.936668i	0.998958	+	0.0456288i	$0.0145291\pi$
$30$		0			0
$31$	−2.22075	+	0.652070i	−0.398858	+	0.117115i	−0.475009	−	0.879981i	$-0.657555\pi$
$31$	−2.22075	+	0.652070i	−0.398858	+	0.117115i	0.0761510	+	0.997096i	$0.475737\pi$
$32$		0			0
$33$	−0.375014	−	2.60828i	−0.0652816	−	0.454044i
$34$		0			0
$35$	−0.507756	−	1.11183i	−0.0858264	−	0.187934i
$36$		0			0
$37$	−4.80517	−	3.08810i	−0.789966	−	0.507680i	0.0823615	−	0.996603i	$-0.473754\pi$
$37$	−4.80517	−	3.08810i	−0.789966	−	0.507680i	−0.872327	+	0.488922i	$0.837390\pi$
$38$		0			0
$39$	0.315289	−	2.19288i	0.0504866	−	0.351142i
$40$		0			0
$41$	−2.36514	+	1.51998i	−0.369372	+	0.237381i	−0.712138	−	0.702040i	$-0.752273\pi$
$41$	−2.36514	+	1.51998i	−0.369372	+	0.237381i	0.342765	+	0.939421i	$0.388636\pi$
$42$		0			0
$43$	3.75382	+	1.10222i	0.572451	+	0.168087i	0.555131	−	0.831763i	$-0.312668\pi$
$43$	3.75382	+	1.10222i	0.572451	+	0.168087i	0.0173207	+	0.999850i	$0.494486\pi$
$44$		0			0
$45$	−0.395239			−0.0589187
$46$		0			0
$47$	−4.37944			−0.638808			−0.319404	−	0.947619i	$-0.603483\pi$
$47$	−4.37944			−0.638808			−0.319404	+	0.947619i	$0.603483\pi$
$48$		0			0
$49$	−2.45987	−	0.722282i	−0.351410	−	0.103183i
$50$		0			0
$51$	−3.12009	+	2.00516i	−0.436901	+	0.280779i
$52$		0			0
$53$	1.80647	−	12.5643i	0.248138	−	1.72584i	−0.360821	−	0.932635i	$-0.617504\pi$
$53$	1.80647	−	12.5643i	0.248138	−	1.72584i	0.608959	−	0.793202i	$-0.291587\pi$
$54$		0			0
$55$	−0.876162	−	0.563075i	−0.118142	−	0.0759250i
$56$		0			0
$57$	−2.92516	−	6.40520i	−0.387446	−	0.848389i
$58$		0			0
$59$	−1.40772	−	9.79088i	−0.183269	−	1.27466i	−0.848968	−	0.528444i	$-0.822776\pi$
$59$	−1.40772	−	9.79088i	−0.183269	−	1.27466i	0.665699	−	0.746220i	$-0.268133\pi$
$60$		0			0
$61$	6.36499	−	1.86893i	0.814954	−	0.239292i	0.152412	−	0.988317i	$-0.451296\pi$
$61$	6.36499	−	1.86893i	0.814954	−	0.239292i	0.662542	+	0.749025i	$0.269478\pi$
$62$		0			0
$63$	−2.02517	+	2.33718i	−0.255148	+	0.294456i
$64$		0			0
$65$	−0.573412	−	0.661753i	−0.0711231	−	0.0820804i
$66$		0			0
$67$	0.559732	−	1.22564i	0.0683822	−	0.149736i	−0.872355	−	0.488874i	$-0.837408\pi$
$67$	0.559732	−	1.22564i	0.0683822	−	0.149736i	0.940737	+	0.339138i	$0.110135\pi$
$68$		0			0
$69$	4.61794	−	1.29408i	0.555934	−	0.155790i
$70$		0			0
$71$	−3.25308	+	7.12324i	−0.386069	+	0.845374i	0.612426	+	0.790528i	$0.290194\pi$
$71$	−3.25308	+	7.12324i	−0.386069	+	0.845374i	−0.998495	+	0.0548454i	$0.982533\pi$
$72$		0			0
$73$	4.16279	+	4.80412i	0.487218	+	0.562280i	0.945120	−	0.326723i	$-0.105944\pi$
$73$	4.16279	+	4.80412i	0.487218	+	0.562280i	−0.457902	+	0.889003i	$0.651399\pi$
$74$		0			0
$75$	3.17201	−	3.66069i	0.366272	−	0.422700i
$76$		0			0
$77$	−7.81903	+	2.29587i	−0.891061	+	0.261639i
$78$		0			0
$79$	−1.05877	−	7.36392i	−0.119121	−	0.828505i	−0.958527	−	0.285001i	$-0.908006\pi$
$79$	−1.05877	−	7.36392i	−0.119121	−	0.828505i	0.839406	−	0.543505i	$-0.182903\pi$
$80$		0			0
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$		0			0
$83$	−0.579976	−	0.372728i	−0.0636606	−	0.0409122i	0.508423	−	0.861107i	$-0.330229\pi$
$83$	−0.579976	−	0.372728i	−0.0636606	−	0.0409122i	−0.572084	+	0.820195i	$0.693865\pi$
$84$		0			0
$85$	−0.208617	+	1.45097i	−0.0226277	+	0.157379i
$86$		0			0
$87$	−5.61479	+	3.60841i	−0.601969	+	0.386862i
$88$		0			0
$89$	5.91112	+	1.73566i	0.626578	+	0.183980i	0.579580	−	0.814915i	$-0.303217\pi$
$89$	5.91112	+	1.73566i	0.626578	+	0.183980i	0.0469975	+	0.998895i	$0.485035\pi$
$90$		0			0
$91$	−6.85128			−0.718210
$92$		0			0
$93$	2.31450			0.240002
$94$		0			0
$95$	−2.67035	−	0.784086i	−0.273972	−	0.0804455i
$96$		0			0
$97$	−4.89824	+	3.14790i	−0.497340	+	0.319621i	−0.765152	−	0.643850i	$-0.777336\pi$
$97$	−4.89824	+	3.14790i	−0.497340	+	0.319621i	0.267811	+	0.963471i	$0.413700\pi$
$98$		0			0
$99$	−0.375014	+	2.60828i	−0.0376904	+	0.262142i
$100$		0			0
$101$	7.86524	+	5.05468i	0.782620	+	0.502959i	0.869902	−	0.493224i	$-0.164182\pi$
$101$	7.86524	+	5.05468i	0.782620	+	0.502959i	−0.0872820	+	0.996184i	$0.527818\pi$
$102$		0			0
$103$	0.945200	+	2.06970i	0.0931334	+	0.203934i	0.950466	−	0.310830i	$-0.100607\pi$
$103$	0.945200	+	2.06970i	0.0931334	+	0.203934i	−0.857332	+	0.514764i	$0.827880\pi$
$104$		0			0
$105$	0.173949	+	1.20985i	0.0169757	+	0.118069i
$106$		0			0
$107$	12.1337	−	3.56279i	1.17301	−	0.344428i	0.363536	−	0.931580i	$-0.381569\pi$
$107$	12.1337	−	3.56279i	1.17301	−	0.344428i	0.809476	+	0.587153i	$0.199751\pi$
$108$		0			0
$109$	0.145524	−	0.167943i	0.0139387	−	0.0160861i	−0.748737	−	0.662867i	$-0.769340\pi$
$109$	0.145524	−	0.167943i	0.0139387	−	0.0160861i	0.762676	+	0.646781i	$0.223885\pi$
$110$		0			0
$111$	3.74051	+	4.31678i	0.355034	+	0.409731i
$112$		0			0
$113$	1.84385	−	4.03747i	0.173455	−	0.379813i	−0.802860	−	0.596167i	$-0.796689\pi$
$113$	1.84385	−	4.03747i	0.173455	−	0.379813i	0.976315	+	0.216355i	$0.0694167\pi$
$114$		0			0
$115$	0.808699	−	1.71433i	0.0754116	−	0.159862i
$116$		0			0
$117$	−0.920324	+	2.01523i	−0.0850840	+	0.186308i
$118$		0			0
$119$	7.51109	+	8.66826i	0.688541	+	0.794618i
$120$		0			0
$121$	2.65626	−	3.06549i	0.241479	−	0.278681i
$122$		0			0
$123$	2.69756	−	0.792075i	0.243231	−	0.0714190i
$124$		0			0
$125$	−0.553697	−	3.85105i	−0.0495241	−	0.344448i
$126$		0			0
$127$	−3.38374	−	7.40936i	−0.300258	−	0.657474i	0.698023	−	0.716075i	$-0.254063\pi$
$127$	−3.38374	−	7.40936i	−0.300258	−	0.657474i	−0.998281	+	0.0586010i	$0.981336\pi$
$128$		0			0
$129$	−3.29123	−	2.11514i	−0.289776	−	0.186228i
$130$		0			0
$131$	−2.51207	+	17.4719i	−0.219481	+	1.52652i	0.520480	+	0.853874i	$0.325753\pi$
$131$	−2.51207	+	17.4719i	−0.219481	+	1.52652i	−0.739961	+	0.672650i	$0.765156\pi$
$132$		0			0
$133$	−18.3192	+	11.7731i	−1.58848	+	1.02085i
$134$		0			0
$135$	0.379229	+	0.111352i	0.0326388	+	0.00958362i
$136$		0			0
$137$	−13.3712			−1.14238			−0.571191	−	0.820817i	$-0.693518\pi$
$137$	−13.3712			−1.14238			−0.571191	+	0.820817i	$0.693518\pi$
$138$		0			0
$139$	23.4118			1.98576			0.992881	−	0.119108i	$-0.0380034\pi$
$139$	23.4118			1.98576			0.992881	+	0.119108i	$0.0380034\pi$
$140$		0			0
$141$	4.20205	+	1.23383i	0.353876	+	0.103907i
$142$		0			0
$143$	−4.91115	+	3.15620i	−0.410691	+	0.263935i
$144$		0			0
$145$	−0.375419	+	2.61110i	−0.0311769	+	0.216840i
$146$		0			0
$147$	2.15673	+	1.38605i	0.177884	+	0.114319i
$148$		0			0
$149$	9.60048	+	21.0221i	0.786502	+	1.72220i	0.686404	+	0.727221i	$0.259188\pi$
$149$	9.60048	+	21.0221i	0.786502	+	1.72220i	0.100098	+	0.994978i	$0.468084\pi$
$150$		0			0
$151$	−2.80811	−	19.5308i	−0.228520	−	1.58939i	−0.704348	−	0.709855i	$-0.748760\pi$
$151$	−2.80811	−	19.5308i	−0.228520	−	1.58939i	0.475827	−	0.879539i	$-0.342149\pi$
$152$		0			0
$153$	3.55863	−	1.04491i	0.287698	−	0.0844758i
$154$		0			0
$155$	0.599053	−	0.691345i	0.0481171	−	0.0555301i
$156$		0			0
$157$	3.08803	+	3.56377i	0.246451	+	0.284420i	0.865475	−	0.500953i	$-0.167017\pi$
$157$	3.08803	+	3.56377i	0.246451	+	0.284420i	−0.619023	+	0.785372i	$0.712471\pi$
$158$		0			0
$159$	−5.27306	+	11.5464i	−0.418181	+	0.915689i
$160$		0			0
$161$	−5.99367	−	13.5662i	−0.472367	−	1.06917i
$162$		0			0
$163$	3.18435	−	6.97275i	0.249417	−	0.546148i	−0.742967	−	0.669328i	$-0.766582\pi$
$163$	3.18435	−	6.97275i	0.249417	−	0.546148i	0.992384	+	0.123180i	$0.0393093\pi$
$164$		0			0
$165$	0.682034	+	0.787110i	0.0530963	+	0.0612764i
$166$		0			0
$167$	−13.4153	+	15.4821i	−1.03811	+	1.19804i	−0.0582568	+	0.998302i	$0.518554\pi$
$167$	−13.4153	+	15.4821i	−1.03811	+	1.19804i	−0.979850	+	0.199737i	$0.935991\pi$
$168$		0			0
$169$	7.76408	−	2.27974i	0.597237	−	0.175365i
$170$		0			0
$171$	1.00211	+	6.96986i	0.0766336	+	0.532998i
$172$		0			0
$173$	6.46235	+	14.1506i	0.491323	+	1.07585i	0.979193	+	0.202931i	$0.0650468\pi$
$173$	6.46235	+	14.1506i	0.491323	+	1.07585i	−0.487870	+	0.872916i	$0.662226\pi$
$174$		0			0
$175$	−12.6016	−	8.09855i	−0.952590	−	0.612193i
$176$		0			0
$177$	−1.40772	+	9.79088i	−0.105810	+	0.735927i
$178$		0			0
$179$	12.2018	−	7.84161i	0.912004	−	0.586110i	0.00167699	−	0.999999i	$-0.499466\pi$
$179$	12.2018	−	7.84161i	0.912004	−	0.586110i	0.910327	+	0.413889i	$0.135830\pi$
$180$		0			0
$181$	−4.91748	−	1.44390i	−0.365513	−	0.107324i	0.0938180	−	0.995589i	$-0.470093\pi$
$181$	−4.91748	−	1.44390i	−0.365513	−	0.107324i	−0.459331	+	0.888265i	$0.651911\pi$
$182$		0			0
$183$	−6.63370			−0.490378
$184$		0			0
$185$	2.25757			0.165980
$186$		0			0
$187$	9.37736	+	2.75344i	0.685740	+	0.201352i
$188$		0			0
$189$	2.60160	−	1.67195i	0.189238	−	0.121616i
$190$		0			0
$191$	1.24708	−	8.67363i	0.0902355	−	0.627602i	−0.893645	−	0.448775i	$-0.851861\pi$
$191$	1.24708	−	8.67363i	0.0902355	−	0.627602i	0.983881	−	0.178827i	$-0.0572303\pi$
$192$		0			0
$193$	6.40555	+	4.11659i	0.461081	+	0.296319i	0.750484	−	0.660888i	$-0.229820\pi$
$193$	6.40555	+	4.11659i	0.461081	+	0.296319i	−0.289403	+	0.957207i	$0.593457\pi$
$194$		0			0
$195$	0.363748	+	0.796496i	0.0260485	+	0.0570383i
$196$		0			0
$197$	−3.03344	−	21.0981i	−0.216124	−	1.50318i	−0.752160	−	0.658980i	$-0.770988\pi$
$197$	−3.03344	−	21.0981i	−0.216124	−	1.50318i	0.536036	−	0.844195i	$-0.319921\pi$
$198$		0			0
$199$	24.3686	−	7.15526i	1.72744	−	0.507223i	0.741025	−	0.671478i	$-0.234340\pi$
$199$	24.3686	−	7.15526i	1.72744	−	0.507223i	0.986418	+	0.164255i	$0.0525220\pi$
$200$		0			0
$201$	−0.882362	+	1.01830i	−0.0622370	+	0.0718254i
$202$		0			0
$203$	13.5167	+	15.5990i	0.948683	+	1.09484i
$204$		0			0
$205$	0.461605	−	1.01077i	0.0322399	−	0.0705956i
$206$		0			0
$207$	−4.79546	−	0.0593580i	−0.333308	−	0.00412567i
$208$		0			0
$209$	−7.70809	+	16.8784i	−0.533180	+	1.16750i
$210$		0			0
$211$	−12.8102	−	14.7838i	−0.881891	−	1.01776i	−0.999694	−	0.0247197i	$-0.992131\pi$
$211$	−12.8102	−	14.7838i	−0.881891	−	1.01776i	0.117803	−	0.993037i	$-0.462415\pi$
$212$		0			0
$213$	5.12815	−	5.91821i	0.351375	−	0.405509i
$214$		0			0
$215$	−1.48365	+	0.435640i	−0.101184	+	0.0297104i
$216$		0			0
$217$	−1.01864	−	7.08479i	−0.0691498	−	0.480947i
$218$		0			0
$219$	−2.64069	−	5.78231i	−0.178442	−	0.390733i
$220$		0			0
$221$	6.91236	+	4.44230i	0.464976	+	0.298822i
$222$		0			0
$223$	−1.00285	+	6.97494i	−0.0671555	+	0.467077i	0.928299	+	0.371835i	$0.121271\pi$
$223$	−1.00285	+	6.97494i	−0.0671555	+	0.467077i	−0.995454	+	0.0952414i	$0.969638\pi$
$224$		0			0
$225$	−4.07485	+	2.61875i	−0.271657	+	0.174583i
$226$		0			0
$227$	−22.6593	−	6.65336i	−1.50395	−	0.441599i	−0.576986	−	0.816754i	$-0.695771\pi$
$227$	−22.6593	−	6.65336i	−1.50395	−	0.441599i	−0.926962	+	0.375156i	$0.877589\pi$
$228$		0			0
$229$	−24.5083			−1.61956			−0.809778	−	0.586736i	$-0.800412\pi$
$229$	−24.5083			−1.61956			−0.809778	+	0.586736i	$0.800412\pi$
$230$		0			0
$231$	8.14913			0.536173
$232$		0			0
$233$	0.683723	+	0.200759i	0.0447922	+	0.0131522i	0.304052	−	0.952655i	$-0.401660\pi$
$233$	0.683723	+	0.200759i	0.0447922	+	0.0131522i	−0.259260	+	0.965808i	$0.583479\pi$
$234$		0			0
$235$	1.45615	−	0.935810i	0.0949886	−	0.0610455i
$236$		0			0
$237$	−1.05877	+	7.36392i	−0.0687746	+	0.478338i
$238$		0			0
$239$	−1.28510	−	0.825882i	−0.0831261	−	0.0534219i	0.498418	−	0.866937i	$-0.333915\pi$
$239$	−1.28510	−	0.825882i	−0.0831261	−	0.0534219i	−0.581544	+	0.813515i	$0.697551\pi$
$240$		0			0
$241$	−11.3499	−	24.8528i	−0.731111	−	1.60091i	−0.797647	−	0.603125i	$-0.793922\pi$
$241$	−11.3499	−	24.8528i	−0.731111	−	1.60091i	0.0665361	−	0.997784i	$-0.478805\pi$
$242$		0			0
$243$	−0.142315	−	0.989821i	−0.00912950	−	0.0634971i
$244$		0			0
$245$	0.972235	−	0.285474i	0.0621138	−	0.0182383i
$246$		0			0
$247$	−10.2158	+	11.7897i	−0.650019	+	0.750162i
$248$		0			0
$249$	0.451473	+	0.521028i	0.0286109	+	0.0330188i
$250$		0			0
$251$	9.87995	−	21.6341i	0.623617	−	1.36553i	−0.289243	−	0.957256i	$-0.593403\pi$
$251$	9.87995	−	21.6341i	0.623617	−	1.36553i	0.912859	−	0.408274i	$-0.133869\pi$
$252$		0			0
$253$	−10.5460	−	6.96342i	−0.663020	−	0.437786i
$254$		0			0
$255$	0.608951	−	1.33342i	0.0381340	−	0.0835019i
$256$		0			0
$257$	10.4861	+	12.1017i	0.654108	+	0.754880i	0.981803	−	0.189903i	$-0.0608174\pi$
$257$	10.4861	+	12.1017i	0.654108	+	0.754880i	−0.327695	+	0.944783i	$0.606272\pi$
$258$		0			0
$259$	11.5676	−	13.3498i	0.718778	−	0.829514i
$260$		0			0
$261$	6.40396	−	1.88037i	0.396395	−	0.116392i
$262$		0			0
$263$	−3.96549	−	27.5806i	−0.244522	−	1.70069i	−0.628877	−	0.777505i	$-0.716485\pi$
$263$	−3.96549	−	27.5806i	−0.244522	−	1.70069i	0.384354	−	0.923186i	$-0.374424\pi$
$264$		0			0
$265$	2.08412	+	4.56358i	0.128026	+	0.280339i
$266$		0			0
$267$	−5.18269	−	3.33071i	−0.317175	−	0.203836i
$268$		0			0
$269$	0.678639	−	4.72004i	0.0413774	−	0.287786i	−0.958618	−	0.284696i	$-0.908107\pi$
$269$	0.678639	−	4.72004i	0.0413774	−	0.287786i	0.999995	−	0.00308994i	$-0.000983561\pi$
$270$		0			0
$271$	−10.5864	+	6.80348i	−0.643080	+	0.413282i	−0.821132	−	0.570739i	$-0.806657\pi$
$271$	−10.5864	+	6.80348i	−0.643080	+	0.413282i	0.178052	+	0.984021i	$0.443020\pi$
$272$		0			0
$273$	6.57376	+	1.93023i	0.397862	+	0.116823i
$274$		0			0
$275$	−12.7639			−0.769691
$276$		0			0
$277$	−19.2855			−1.15875			−0.579376	−	0.815060i	$-0.696704\pi$
$277$	−19.2855			−1.15875			−0.579376	+	0.815060i	$0.696704\pi$
$278$		0			0
$279$	−2.22075	−	0.652070i	−0.132953	−	0.0390384i
$280$		0			0
$281$	2.56835	−	1.65058i	0.153215	−	0.0984653i	−0.461787	−	0.886991i	$-0.652792\pi$
$281$	2.56835	−	1.65058i	0.153215	−	0.0984653i	0.615002	+	0.788526i	$0.289155\pi$
$282$		0			0
$283$	4.33156	−	30.1266i	0.257484	−	1.79084i	−0.293119	−	0.956076i	$-0.594693\pi$
$283$	4.33156	−	30.1266i	0.257484	−	1.79084i	0.550603	−	0.834767i	$-0.314398\pi$
$284$		0			0
$285$	2.34128	+	1.50465i	0.138685	+	0.0891277i
$286$		0			0
$287$	−3.61181	−	7.90876i	−0.213198	−	0.466839i
$288$		0			0
$289$	0.461716	+	3.21131i	0.0271598	+	0.188900i
$290$		0			0
$291$	5.58669	−	1.64040i	0.327498	−	0.0961620i
$292$		0			0
$293$	5.30169	−	6.11848i	0.309728	−	0.357445i	−0.579449	−	0.815009i	$-0.696732\pi$
$293$	5.30169	−	6.11848i	0.309728	−	0.357445i	0.889177	+	0.457563i	$0.151278\pi$
$294$		0			0
$295$	2.56020	+	2.95462i	0.149060	+	0.172025i
$296$		0			0
$297$	1.09466	−	2.39697i	0.0635187	−	0.139087i
$298$		0			0
$299$	−6.85787	−	8.11522i	−0.396601	−	0.469315i
$300$		0			0
$301$	−5.02605	+	11.0055i	−0.289697	+	0.634347i
$302$		0			0
$303$	−6.12257	−	7.06582i	−0.351732	−	0.405921i
$304$		0			0
$305$	−1.71698	+	1.98150i	−0.0983139	+	0.113460i
$306$		0			0
$307$	7.75969	−	2.27845i	0.442869	−	0.130038i	−0.0526927	−	0.998611i	$-0.516780\pi$
$307$	7.75969	−	2.27845i	0.442869	−	0.130038i	0.495562	+	0.868573i	$0.334962\pi$
$308$		0			0
$309$	−0.323811	−	2.25216i	−0.0184210	−	0.128121i
$310$		0			0
$311$	−0.338709	−	0.741670i	−0.0192064	−	0.0420562i	0.899786	−	0.436332i	$-0.143723\pi$
$311$	−0.338709	−	0.741670i	−0.0192064	−	0.0420562i	−0.918992	+	0.394276i	$0.870995\pi$
$312$		0			0
$313$	24.3434	+	15.6445i	1.37597	+	0.884281i	0.999118	−	0.0419935i	$-0.0133709\pi$
$313$	24.3434	+	15.6445i	1.37597	+	0.884281i	0.376850	+	0.926274i	$0.377007\pi$
$314$		0			0
$315$	0.173949	−	1.20985i	0.00980094	−	0.0681671i
$316$		0			0
$317$	−29.1679	+	18.7451i	−1.63823	+	1.05283i	−0.695903	+	0.718135i	$0.744996\pi$
$317$	−29.1679	+	18.7451i	−1.63823	+	1.05283i	−0.942328	+	0.334692i	$0.891368\pi$
$318$		0			0
$319$	16.8751	+	4.95498i	0.944824	+	0.277425i
$320$		0			0
$321$	−12.6460			−0.705830
$322$		0			0
$323$	26.1161			1.45314
$324$		0			0
$325$	−10.2964	−	3.02330i	−0.571141	−	0.167702i
$326$		0			0
$327$	−0.186944	+	0.120142i	−0.0103380	+	0.00664386i
$328$		0			0
$329$	1.92745	−	13.4057i	0.106264	−	0.739080i
$330$		0			0
$331$	11.7815	+	7.57152i	0.647570	+	0.416168i	0.822778	−	0.568363i	$-0.192423\pi$
$331$	11.7815	+	7.57152i	0.647570	+	0.416168i	−0.175207	+	0.984532i	$0.556060\pi$
$332$		0			0
$333$	−2.37282	−	5.19575i	−0.130030	−	0.284725i
$334$		0			0
$335$	0.0757893	+	0.527126i	0.00414081	+	0.0288000i
$336$		0			0
$337$	11.2111	−	3.29189i	0.610710	−	0.179321i	0.0382703	−	0.999267i	$-0.487815\pi$
$337$	11.2111	−	3.29189i	0.610710	−	0.179321i	0.572440	+	0.819947i	$0.305997\pi$
$338$		0			0
$339$	−2.90665	+	3.35445i	−0.157867	+	0.182189i
$340$		0			0
$341$	−3.99396	−	4.60928i	−0.216285	−	0.249606i
$342$		0			0
$343$	−5.69921	+	12.4795i	−0.307729	+	0.673832i
$344$		0			0
$345$	−1.25892	+	1.41705i	−0.0677781	+	0.0762914i
$346$		0			0
$347$	−12.7515	+	27.9220i	−0.684538	+	1.49893i	0.173223	+	0.984883i	$0.444582\pi$
$347$	−12.7515	+	27.9220i	−0.684538	+	1.49893i	−0.857762	+	0.514048i	$0.828145\pi$
$348$		0			0
$349$	18.4824	+	21.3299i	0.989342	+	1.14176i	0.989901	+	0.141762i	$0.0452768\pi$
$349$	18.4824	+	21.3299i	0.989342	+	1.14176i	−0.000558286		1.00000i	$0.500178\pi$
$350$		0			0
$351$	1.45080	−	1.67431i	0.0774380	−	0.0893682i
$352$		0			0
$353$	−15.1718	+	4.45484i	−0.807514	+	0.237107i	−0.659331	−	0.751853i	$-0.729161\pi$
$353$	−15.1718	+	4.45484i	−0.807514	+	0.237107i	−0.148183	+	0.988960i	$0.547342\pi$
$354$		0			0
$355$	−0.440476	−	3.06358i	−0.0233780	−	0.162598i
$356$		0			0
$357$	−4.76471	−	10.4333i	−0.252175	−	0.552187i
$358$		0			0
$359$	0.567977	+	0.365017i	0.0299767	+	0.0192648i	0.555543	−	0.831488i	$-0.312510\pi$
$359$	0.567977	+	0.365017i	0.0299767	+	0.0192648i	−0.525567	+	0.850752i	$0.676147\pi$
$360$		0			0
$361$	−4.35243	+	30.2718i	−0.229075	+	1.59325i
$362$		0			0
$363$	−3.41232	+	2.19296i	−0.179100	+	0.115101i
$364$		0			0
$365$	−2.41067	−	0.707836i	−0.126180	−	0.0370498i
$366$		0			0
$367$	−14.9235			−0.778998			−0.389499	−	0.921027i	$-0.627352\pi$
$367$	−14.9235			−0.778998			−0.389499	+	0.921027i	$0.627352\pi$
$368$		0			0
$369$	−2.81144			−0.146358
$370$		0			0
$371$	37.6648	+	11.0594i	1.95546	+	0.574175i
$372$		0			0
$373$	5.57634	−	3.58369i	0.288732	−	0.185557i	−0.388255	−	0.921552i	$-0.626922\pi$
$373$	5.57634	−	3.58369i	0.288732	−	0.185557i	0.676986	+	0.735995i	$0.263286\pi$
$374$		0			0
$375$	−0.553697	+	3.85105i	−0.0285928	+	0.198867i
$376$		0			0
$377$	12.4392	+	7.99418i	0.640651	+	0.411721i
$378$		0			0
$379$	1.67512	+	3.66799i	0.0860449	+	0.188412i	0.947763	−	0.318975i	$-0.103339\pi$
$379$	1.67512	+	3.66799i	0.0860449	+	0.188412i	−0.861718	+	0.507387i	$0.830611\pi$
$380$		0			0
$381$	1.15922	+	8.06254i	0.0593885	+	0.413056i
$382$		0			0
$383$	−8.86688	+	2.60355i	−0.453076	+	0.133035i	−0.500306	−	0.865849i	$-0.666779\pi$
$383$	−8.86688	+	2.60355i	−0.453076	+	0.133035i	0.0472294	+	0.998884i	$0.484961\pi$
$384$		0			0
$385$	2.10921	−	2.43416i	0.107495	−	0.124056i
$386$		0			0
$387$	2.56201	+	2.95671i	0.130234	+	0.150298i
$388$		0			0
$389$	6.71406	−	14.7017i	0.340416	−	0.745407i	−0.659564	−	0.751648i	$-0.729259\pi$
$389$	6.71406	−	14.7017i	0.340416	−	0.745407i	0.999981	+	0.00624068i	$0.00198648\pi$
$390$		0			0
$391$	−2.74908	+	17.5734i	−0.139027	+	0.888723i
$392$		0			0
$393$	7.33271	−	16.0564i	0.369886	−	0.809938i
$394$		0			0
$395$	1.92558	+	2.22223i	0.0968862	+	0.111813i
$396$		0			0
$397$	0.206863	−	0.238733i	0.0103822	−	0.0119817i	−0.750535	−	0.660831i	$-0.770204\pi$
$397$	0.206863	−	0.238733i	0.0103822	−	0.0119817i	0.760917	+	0.648849i	$0.224749\pi$
$398$		0			0
$399$	20.8940	−	6.13504i	1.04601	−	0.307136i
$400$		0			0
$401$	0.204711	+	1.42380i	0.0102228	+	0.0711011i	0.994294	−	0.106672i	$-0.0340196\pi$
$401$	0.204711	+	1.42380i	0.0102228	+	0.0711011i	−0.984071	+	0.177774i	$0.943111\pi$
$402$		0			0
$403$	−2.13009	−	4.66424i	−0.106107	−	0.232343i
$404$		0			0
$405$	−0.332496	−	0.213682i	−0.0165219	−	0.0106180i
$406$		0			0
$407$	2.14205	−	14.8983i	0.106178	−	0.738482i
$408$		0			0
$409$	−1.86910	+	1.20120i	−0.0924211	+	0.0593954i	−0.586035	−	0.810286i	$-0.699312\pi$
$409$	−1.86910	+	1.20120i	−0.0924211	+	0.0593954i	0.493614	+	0.869681i	$0.335676\pi$
$410$		0			0
$411$	12.8296	+	3.76711i	0.632838	+	0.185818i
$412$		0			0
$413$	30.5899			1.50523
$414$		0			0
$415$	0.272485			0.0133758
$416$		0			0
$417$	−22.4635	−	6.59587i	−1.10004	−	0.323001i
$418$		0			0
$419$	−8.96288	+	5.76010i	−0.437866	+	0.281399i	−0.740944	−	0.671566i	$-0.765622\pi$
$419$	−8.96288	+	5.76010i	−0.437866	+	0.281399i	0.303079	+	0.952965i	$0.401985\pi$
$420$		0			0
$421$	−2.54761	+	17.7190i	−0.124163	+	0.863572i	0.828596	+	0.559846i	$0.189140\pi$
$421$	−2.54761	+	17.7190i	−0.124163	+	0.863572i	−0.952759	+	0.303726i	$0.901769\pi$
$422$		0			0
$423$	−3.68422	−	2.36771i	−0.179133	−	0.115122i
$424$		0			0
$425$	7.46291	+	16.3415i	0.362004	+	0.792679i
$426$		0			0
$427$	2.91957	+	20.3061i	0.141288	+	0.982681i
$428$		0			0
$429$	5.60142	−	1.64473i	0.270439	−	0.0794081i
$430$		0			0
$431$	−1.11016	+	1.28119i	−0.0534744	+	0.0617128i	−0.781857	−	0.623458i	$-0.785727\pi$
$431$	−1.11016	+	1.28119i	−0.0534744	+	0.0617128i	0.728382	+	0.685171i	$0.240273\pi$
$432$		0			0
$433$	20.1428	+	23.2460i	0.968001	+	1.11713i	0.993079	+	0.117447i	$0.0374709\pi$
$433$	20.1428	+	23.2460i	0.968001	+	1.11713i	−0.0250786	+	0.999685i	$0.507984\pi$
$434$		0			0
$435$	1.09584	−	2.39956i	0.0525417	−	0.115050i
$436$		0			0
$437$	−32.2818	−	9.91442i	−1.54425	−	0.474271i
$438$		0			0
$439$	−11.6426	+	25.4938i	−0.555672	+	1.21675i	0.398411	+	0.917207i	$0.369562\pi$
$439$	−11.6426	+	25.4938i	−0.555672	+	1.21675i	−0.954082	+	0.299544i	$0.903165\pi$
$440$		0			0
$441$	−1.67888	−	1.93753i	−0.0799465	−	0.0922632i
$442$		0			0
$443$	−5.96931	+	6.88895i	−0.283611	+	0.327304i	−0.879623	−	0.475671i	$-0.842205\pi$
$443$	−5.96931	+	6.88895i	−0.283611	+	0.327304i	0.596013	+	0.802975i	$0.296751\pi$
$444$		0			0
$445$	−2.33630	+	0.686001i	−0.110751	+	0.0325196i
$446$		0			0
$447$	−3.28898	−	22.8753i	−0.155563	−	1.08197i
$448$		0			0
$449$	−16.2833	−	35.6554i	−0.768456	−	1.68268i	−0.730024	−	0.683422i	$-0.760491\pi$
$449$	−16.2833	−	35.6554i	−0.768456	−	1.68268i	−0.0384319	−	0.999261i	$-0.512236\pi$
$450$		0			0
$451$	−6.23238	−	4.00531i	−0.293471	−	0.188602i
$452$		0			0
$453$	−2.80811	+	19.5308i	−0.131936	+	0.917637i
$454$		0			0
$455$	2.27802	−	1.46400i	0.106795	−	0.0686333i
$456$		0			0
$457$	29.8827	+	8.77435i	1.39785	+	0.410447i	0.891946	−	0.452141i	$-0.149340\pi$
$457$	29.8827	+	8.77435i	1.39785	+	0.410447i	0.505907	+	0.862588i	$0.331158\pi$
$458$		0			0
$459$	−3.70886			−0.173115
$460$		0			0
$461$	19.9022			0.926939			0.463469	−	0.886113i	$-0.346604\pi$
$461$	19.9022			0.926939			0.463469	+	0.886113i	$0.346604\pi$
$462$		0			0
$463$	2.03576	+	0.597752i	0.0946097	+	0.0277799i	0.328695	−	0.944436i	$-0.393391\pi$
$463$	2.03576	+	0.597752i	0.0946097	+	0.0277799i	−0.234085	+	0.972216i	$0.575209\pi$
$464$		0			0
$465$	−0.769562	+	0.494567i	−0.0356876	+	0.0229350i
$466$		0			0
$467$	4.25711	−	29.6089i	0.196996	−	1.37013i	−0.615946	−	0.787789i	$-0.711226\pi$
$467$	4.25711	−	29.6089i	0.196996	−	1.37013i	0.812941	−	0.582346i	$-0.197865\pi$
$468$		0			0
$469$	3.50541	+	2.25279i	0.161865	+	0.104024i
$470$		0			0
$471$	−1.95891	−	4.28941i	−0.0902617	−	0.197646i
$472$		0			0
$473$	1.46717	+	10.2044i	0.0674603	+	0.469197i
$474$		0			0
$475$	−32.7261	+	9.60924i	−1.50157	+	0.440902i
$476$		0			0
$477$	8.31246	−	9.59309i	0.380601	−	0.439238i
$478$		0			0
$479$	20.4583	+	23.6101i	0.934764	+	1.07877i	0.996739	+	0.0806972i	$0.0257147\pi$
$479$	20.4583	+	23.6101i	0.934764	+	1.07877i	−0.0619749	+	0.998078i	$0.519740\pi$
$480$		0			0
$481$	5.25682	−	11.5108i	0.239690	−	0.524848i
$482$		0			0
$483$	1.92885	+	14.7053i	0.0877655	+	0.669113i
$484$		0			0
$485$	0.955993	−	2.09333i	0.0434094	−	0.0950533i
$486$		0			0
$487$	1.50158	+	1.73291i	0.0680429	+	0.0785257i	0.788750	−	0.614714i	$-0.210728\pi$
$487$	1.50158	+	1.73291i	0.0680429	+	0.0785257i	−0.720708	+	0.693239i	$0.756183\pi$
$488$		0			0
$489$	−5.01981	+	5.79317i	−0.227004	+	0.261976i
$490$		0			0
$491$	−30.7180	+	9.01961i	−1.38628	+	0.407049i	−0.887951	−	0.459938i	$-0.847872\pi$
$491$	−30.7180	+	9.01961i	−1.38628	+	0.407049i	−0.498331	+	0.866987i	$0.666053\pi$
$492$		0			0
$493$	−3.52288	−	24.5022i	−0.158663	−	1.10352i
$494$		0			0
$495$	−0.432653	−	0.947378i	−0.0194463	−	0.0425815i
$496$		0			0
$497$	−20.3729	−	13.0929i	−0.913848	−	0.587295i
$498$		0			0
$499$	−4.53308	+	31.5283i	−0.202929	+	1.41140i	0.592607	+	0.805492i	$0.298099\pi$
$499$	−4.53308	+	31.5283i	−0.202929	+	1.41140i	−0.795535	+	0.605907i	$0.792810\pi$
$500$		0			0
$501$	17.2337	−	11.0754i	0.769944	−	0.494813i
$502$		0			0
$503$	−21.5336	−	6.32282i	−0.960134	−	0.281921i	−0.236134	−	0.971721i	$-0.575880\pi$
$503$	−21.5336	−	6.32282i	−0.960134	−	0.281921i	−0.724000	+	0.689800i	$0.757699\pi$
$504$		0			0
$505$	−3.69526			−0.164437
$506$		0			0
$507$	−8.09186			−0.359372
$508$		0			0
$509$	16.2921	+	4.78378i	0.722133	+	0.212037i	0.622090	−	0.782946i	$-0.286284\pi$
$509$	16.2921	+	4.78378i	0.722133	+	0.212037i	0.100043	+	0.994983i	$0.468102\pi$
$510$		0			0
$511$	−16.5377	+	10.6282i	−0.731586	+	0.470162i
$512$		0			0
$513$	1.00211	−	6.96986i	0.0442444	−	0.307727i
$514$		0			0
$515$	−0.756534	−	0.486195i	−0.0333369	−	0.0214243i
$516$		0			0
$517$	−4.79401	−	10.4974i	−0.210840	−	0.461676i
$518$		0			0
$519$	−2.21390	−	15.3980i	−0.0971795	−	0.675898i
$520$		0			0
$521$	12.8096	−	3.76125i	0.561200	−	0.164783i	0.0111844	−	0.999937i	$-0.496440\pi$
$521$	12.8096	−	3.76125i	0.561200	−	0.164783i	0.550016	+	0.835154i	$0.314622\pi$
$522$		0			0
$523$	−4.27548	+	4.93417i	−0.186954	+	0.215756i	−0.841487	−	0.540277i	$-0.818320\pi$
$523$	−4.27548	+	4.93417i	−0.186954	+	0.215756i	0.654534	+	0.756033i	$0.272865\pi$
$524$		0			0
$525$	9.80951	+	11.3208i	0.428122	+	0.494079i
$526$		0			0
$527$	−3.56599	+	7.80843i	−0.155337	+	0.340140i
$528$		0			0
$529$	10.0695	−	20.6786i	0.437803	−	0.899071i
$530$		0			0
$531$	4.10910	−	8.99768i	0.178320	−	0.390466i
$532$		0			0
$533$	−4.07884	−	4.70723i	−0.176674	−	0.203893i
$534$		0			0
$535$	−3.27311	+	3.77738i	−0.141509	+	0.163310i
$536$		0			0
$537$	−13.9168	+	4.08633i	−0.600553	+	0.176338i
$538$		0			0
$539$	−0.961430	−	6.68689i	−0.0414117	−	0.288025i
$540$		0			0
$541$	−9.25561	−	20.2670i	−0.397930	−	0.871345i	−0.997476	−	0.0710046i	$-0.977379\pi$
$541$	−9.25561	−	20.2670i	−0.397930	−	0.871345i	0.599546	−	0.800340i	$-0.295348\pi$
$542$		0			0
$543$	4.31149	+	2.77083i	0.185024	+	0.118908i
$544$		0			0
$545$	−0.0124996	+	0.0869364i	−0.000535423	+	0.00372395i
$546$		0			0
$547$	3.96660	−	2.54918i	0.169600	−	0.108995i	−0.453087	−	0.891466i	$-0.649677\pi$
$547$	3.96660	−	2.54918i	0.169600	−	0.108995i	0.622687	+	0.782471i	$0.286041\pi$
$548$		0			0
$549$	6.36499	+	1.86893i	0.271651	+	0.0797640i
$550$		0			0
$551$	46.9974			2.00216
$552$		0			0
$553$	23.0073			0.978369
$554$		0			0
$555$	−2.16613	−	0.636032i	−0.0919469	−	0.0269980i
$556$		0			0
$557$	13.4469	−	8.64180i	0.569764	−	0.366165i	−0.223816	−	0.974631i	$-0.571851\pi$
$557$	13.4469	−	8.64180i	0.569764	−	0.366165i	0.793580	+	0.608467i	$0.208215\pi$
$558$		0			0
$559$	−1.23350	+	8.57919i	−0.0521716	+	0.362861i
$560$		0			0
$561$	−8.22177	−	5.28381i	−0.347124	−	0.223083i
$562$		0			0
$563$	−2.59556	−	5.68349i	−0.109390	−	0.239531i	0.847018	−	0.531564i	$-0.178395\pi$
$563$	−2.59556	−	5.68349i	−0.109390	−	0.239531i	−0.956408	+	0.292033i	$0.905668\pi$
$564$		0			0
$565$	0.249662	+	1.73644i	0.0105034	+	0.0730526i
$566$		0			0
$567$	−2.96726	+	0.871265i	−0.124613	+	0.0365897i
$568$		0			0
$569$	8.55803	−	9.87649i	0.358771	−	0.414044i	−0.547456	−	0.836834i	$-0.684404\pi$
$569$	8.55803	−	9.87649i	0.358771	−	0.414044i	0.906228	+	0.422790i	$0.138949\pi$
$570$		0			0
$571$	4.06617	+	4.69261i	0.170164	+	0.196380i	0.834426	−	0.551120i	$-0.185799\pi$
$571$	4.06617	+	4.69261i	0.170164	+	0.196380i	−0.664262	+	0.747500i	$0.731254\pi$
$572$		0			0
$573$	−3.64021	+	7.97094i	−0.152072	+	0.332991i
$574$		0			0
$575$	−3.02113	−	23.0327i	−0.125990	−	0.960530i
$576$		0			0
$577$	18.8091	−	41.1861i	0.783031	−	1.71460i	0.0874304	−	0.996171i	$-0.472134\pi$
$577$	18.8091	−	41.1861i	0.783031	−	1.71460i	0.695601	−	0.718429i	$-0.255138\pi$
$578$		0			0
$579$	−4.98630	−	5.75449i	−0.207223	−	0.239149i
$580$		0			0
$581$	1.39619	−	1.61129i	0.0579238	−	0.0668477i
$582$		0			0
$583$	32.0937	−	9.42357i	1.32919	−	0.390284i
$584$		0			0
$585$	−0.124614	−	0.866712i	−0.00515217	−	0.0358341i
$586$		0			0
$587$	6.87091	+	15.0452i	0.283593	+	0.620982i	0.996797	−	0.0799747i	$-0.0254840\pi$
$587$	6.87091	+	15.0452i	0.283593	+	0.620982i	−0.713204	+	0.700957i	$0.752757\pi$
$588$		0			0
$589$	−13.7104	−	8.81115i	−0.564928	−	0.363057i
$590$		0			0
$591$	−3.03344	+	21.0981i	−0.124779	+	0.867859i
$592$		0			0
$593$	−28.4481	+	18.2825i	−1.16822	+	0.750772i	−0.973185	−	0.230023i	$-0.926120\pi$
$593$	−28.4481	+	18.2825i	−1.16822	+	0.750772i	−0.195039	+	0.980795i	$0.562483\pi$
$594$		0			0
$595$	−4.34966	−	1.27718i	−0.178319	−	0.0523591i
$596$		0			0
$597$	−25.3973			−1.03944
$598$		0			0
$599$	−28.1009			−1.14817			−0.574085	−	0.818796i	$-0.694642\pi$
$599$	−28.1009			−1.14817			−0.574085	+	0.818796i	$0.694642\pi$
$600$		0			0
$601$	−24.6957	−	7.25132i	−1.00736	−	0.295788i	−0.263887	−	0.964554i	$-0.585005\pi$
$601$	−24.6957	−	7.25132i	−1.00736	−	0.295788i	−0.743473	+	0.668766i	$0.766823\pi$
$602$		0			0
$603$	1.13351	−	0.728462i	0.0461600	−	0.0296653i
$604$		0			0
$605$	−0.228156	+	1.58686i	−0.00927586	+	0.0645151i
$606$		0			0
$607$	7.02454	+	4.51439i	0.285117	+	0.183234i	0.675380	−	0.737470i	$-0.263980\pi$
$607$	7.02454	+	4.51439i	0.285117	+	0.183234i	−0.390263	+	0.920703i	$0.627616\pi$
$608$		0			0
$609$	−8.57437	−	18.7753i	−0.347451	−	0.760812i
$610$		0			0
$611$	−1.38079	−	9.60361i	−0.0558608	−	0.388520i
$612$		0			0
$613$	−2.17393	+	0.638325i	−0.0878044	+	0.0257817i	−0.325340	−	0.945597i	$-0.605479\pi$
$613$	−2.17393	+	0.638325i	−0.0878044	+	0.0257817i	0.237535	+	0.971379i	$0.423660\pi$
$614$		0			0
$615$	−0.727675	+	0.839782i	−0.0293427	+	0.0338633i
$616$		0			0
$617$	−27.7560	−	32.0322i	−1.11742	−	1.28957i	−0.952931	−	0.303186i	$-0.901950\pi$
$617$	−27.7560	−	32.0322i	−1.11742	−	1.28957i	−0.164484	−	0.986380i	$-0.552596\pi$
$618$		0			0
$619$	−1.39428	+	3.05306i	−0.0560410	+	0.122713i	−0.935581	−	0.353113i	$-0.885123\pi$
$619$	−1.39428	+	3.05306i	−0.0560410	+	0.122713i	0.879540	+	0.475825i	$0.157851\pi$
$620$		0			0
$621$	4.58449	+	1.40799i	0.183969	+	0.0565008i
$622$		0			0
$623$	−7.91450	+	17.3303i	−0.317088	+	0.694326i
$624$		0			0
$625$	−14.8530	−	17.1413i	−0.594121	−	0.685652i
$626$		0			0
$627$	12.1510	−	14.0231i	0.485266	−	0.560027i
$628$		0			0
$629$	−20.3266	+	5.96843i	−0.810475	+	0.237977i
$630$		0			0
$631$	−0.265066	−	1.84358i	−0.0105521	−	0.0733916i	0.983865	−	0.178913i	$-0.0572580\pi$
$631$	−0.265066	−	1.84358i	−0.0105521	−	0.0733916i	−0.994417	+	0.105521i	$0.966349\pi$
$632$		0			0
$633$	8.12624	+	17.7940i	0.322989	+	0.707247i
$634$		0			0
$635$	2.70833	+	1.74054i	0.107477	+	0.0690711i
$636$		0			0
$637$	0.808311	−	5.62193i	0.0320265	−	0.222749i
$638$		0			0
$639$	−6.58778	+	4.23371i	−0.260608	+	0.167483i
$640$		0			0
$641$	−42.9732	−	12.6181i	−1.69734	−	0.498384i	−0.717229	−	0.696837i	$-0.754590\pi$
$641$	−42.9732	−	12.6181i	−1.69734	−	0.498384i	−0.980110	+	0.198454i	$0.936408\pi$
$642$		0			0
$643$	−31.1652			−1.22904			−0.614518	−	0.788903i	$-0.710650\pi$
$643$	−31.1652			−1.22904			−0.614518	+	0.788903i	$0.710650\pi$
$644$		0			0
$645$	1.54629			0.0608851
$646$		0			0
$647$	22.7754	+	6.68747i	0.895394	+	0.262911i	0.696881	−	0.717187i	$-0.254571\pi$
$647$	22.7754	+	6.68747i	0.895394	+	0.262911i	0.198513	+	0.980098i	$0.436389\pi$
$648$		0			0
$649$	21.9275	−	14.0920i	0.860730	−	0.553158i
$650$		0			0
$651$	−1.01864	+	7.08479i	−0.0399236	+	0.277675i
$652$		0			0
$653$	26.4780	+	17.0164i	1.03616	+	0.665902i	0.944035	−	0.329846i	$-0.106997\pi$
$653$	26.4780	+	17.0164i	1.03616	+	0.665902i	0.0921282	+	0.995747i	$0.470633\pi$
$654$		0			0
$655$	−2.89817	−	6.34611i	−0.113241	−	0.247963i
$656$		0			0
$657$	0.904661	+	6.29206i	0.0352942	+	0.245477i
$658$		0			0
$659$	−7.87364	+	2.31191i	−0.306714	+	0.0900592i	−0.431468	−	0.902128i	$-0.642004\pi$
$659$	−7.87364	+	2.31191i	−0.306714	+	0.0900592i	0.124754	+	0.992188i	$0.460186\pi$
$660$		0			0
$661$	12.5124	−	14.4401i	0.486677	−	0.561656i	−0.458297	−	0.888799i	$-0.651541\pi$
$661$	12.5124	−	14.4401i	0.486677	−	0.561656i	0.944975	+	0.327143i	$0.106086\pi$
$662$		0			0
$663$	−5.38082	−	6.20980i	−0.208974	−	0.241168i
$664$		0			0
$665$	3.57538	−	7.82899i	0.138647	−	0.303595i
$666$		0			0
$667$	−4.94713	+	31.6243i	−0.191554	+	1.22450i
$668$		0			0
$669$	2.92729	−	6.40987i	0.113176	−	0.247820i
$670$		0			0
$671$	11.4473	+	13.2109i	0.441918	+	0.510000i
$672$		0			0
$673$	22.6217	−	26.1068i	0.872003	−	1.00634i	−0.127891	−	0.991788i	$-0.540821\pi$
$673$	22.6217	−	26.1068i	0.872003	−	1.00634i	0.999894	−	0.0145567i	$-0.00463371\pi$
$674$		0			0
$675$	4.64758	−	1.36465i	0.178885	−	0.0525255i
$676$		0			0
$677$	−0.808364	−	5.62230i	−0.0310680	−	0.216082i	0.968373	−	0.249506i	$-0.0802681\pi$
$677$	−0.808364	−	5.62230i	−0.0310680	−	0.216082i	−0.999441	+	0.0334233i	$0.989359\pi$
$678$		0			0
$679$	−7.48011	−	16.3792i	−0.287060	−	0.628575i
$680$		0			0
$681$	19.8669	+	12.7677i	0.761302	+	0.489259i
$682$		0			0
$683$	6.17313	−	42.9350i	0.236208	−	1.64286i	−0.434161	−	0.900835i	$-0.642955\pi$
$683$	6.17313	−	42.9350i	0.236208	−	1.64286i	0.670369	−	0.742028i	$-0.266136\pi$
$684$		0			0
$685$	4.44588	−	2.85720i	0.169869	−	0.109168i
$686$		0			0
$687$	23.5156	+	6.90479i	0.897175	+	0.263434i
$688$		0			0
$689$	28.1215			1.07135
$690$		0			0
$691$	−29.6785			−1.12902			−0.564511	−	0.825425i	$-0.690935\pi$
$691$	−29.6785			−1.12902			−0.564511	+	0.825425i	$0.690935\pi$
$692$		0			0
$693$	−7.81903	−	2.29587i	−0.297020	−	0.0872131i
$694$		0			0
$695$	−7.78433	+	5.00269i	−0.295276	+	0.189763i
$696$		0			0
$697$	−1.48395	+	10.3211i	−0.0562087	+	0.390940i
$698$		0			0
$699$	−0.599467	−	0.385254i	−0.0226739	−	0.0145716i
$700$		0			0
$701$	9.63854	+	21.1055i	0.364043	+	0.797142i	0.999684	+	0.0251573i	$0.00800866\pi$
$701$	9.63854	+	21.1055i	0.364043	+	0.797142i	−0.635641	+	0.771985i	$0.719264\pi$
$702$		0			0
$703$	−5.72400	−	39.8113i	−0.215885	−	1.50151i
$704$		0			0
$705$	−1.66081	+	0.487658i	−0.0625498	+	0.0183663i
$706$		0			0
$707$	−18.9342	+	21.8512i	−0.712094	+	0.821800i
$708$		0			0
$709$	−27.3462	−	31.5591i	−1.02701	−	1.18523i	−0.982508	−	0.186219i	$-0.940377\pi$
$709$	−27.3462	−	31.5591i	−1.02701	−	1.18523i	−0.0444980	−	0.999009i	$-0.514169\pi$
$710$		0			0
$711$	3.09054	−	6.76734i	0.115904	−	0.253795i
$712$		0			0
$713$	7.37219	−	8.29817i	0.276091	−	0.310769i
$714$		0			0
$715$	0.958513	−	2.09885i	0.0358464	−	0.0784926i
$716$		0			0
$717$	1.00036	+	1.15448i	0.0373593	+	0.0431149i
$718$		0			0
$719$	−17.9557	+	20.7220i	−0.669635	+	0.772800i	−0.984319	−	0.176396i	$-0.943556\pi$
$719$	−17.9557	+	20.7220i	−0.669635	+	0.772800i	0.314684	+	0.949196i	$0.398101\pi$
$720$		0			0
$721$	−6.75145	+	1.98240i	−0.251437	+	0.0738286i
$722$		0			0
$723$	3.88830	+	27.0437i	0.144607	+	1.00577i
$724$		0			0
$725$	13.4299	+	29.4075i	0.498775	+	1.09217i
$726$		0			0
$727$	19.3465	+	12.4333i	0.717523	+	0.461124i	0.847774	−	0.530357i	$-0.177942\pi$
$727$	19.3465	+	12.4333i	0.717523	+	0.461124i	−0.130252	+	0.991481i	$0.541578\pi$
$728$		0			0
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$		0			0
$731$	12.2067	−	7.84478i	0.451482	−	0.290150i
$732$		0			0
$733$	8.58286	+	2.52016i	0.317015	+	0.0930841i	0.436369	−	0.899768i	$-0.356264\pi$
$733$	8.58286	+	2.52016i	0.317015	+	0.0930841i	−0.119354	+	0.992852i	$0.538082\pi$
$734$		0			0
$735$	−1.01328			−0.0373754
$736$		0			0
$737$	3.55055			0.130786
$738$		0			0
$739$	−6.20386	−	1.82162i	−0.228213	−	0.0670093i	0.165627	−	0.986188i	$-0.447035\pi$
$739$	−6.20386	−	1.82162i	−0.228213	−	0.0670093i	−0.393840	+	0.919179i	$0.628853\pi$
$740$		0			0
$741$	13.1236	−	8.43401i	0.482107	−	0.309831i
$742$		0			0
$743$	5.68094	−	39.5118i	0.208414	−	1.44955i	−0.569921	−	0.821699i	$-0.693026\pi$
$743$	5.68094	−	39.5118i	0.208414	−	1.44955i	0.778335	−	0.627849i	$-0.216065\pi$
$744$		0			0
$745$	−7.68417	−	4.93832i	−0.281526	−	0.180926i
$746$		0			0
$747$	−0.286395	−	0.627117i	−0.0104786	−	0.0229450i
$748$		0			0
$749$	5.56565	+	38.7100i	0.203365	+	1.41443i
$750$		0			0
$751$	−1.95344	+	0.573581i	−0.0712819	+	0.0209303i	−0.317179	−	0.948366i	$-0.602736\pi$
$751$	−1.95344	+	0.573581i	−0.0712819	+	0.0209303i	0.245897	+	0.969296i	$0.420917\pi$
$752$		0			0
$753$	−15.5748	+	17.9742i	−0.567576	+	0.655017i
$754$		0			0
$755$	5.10707	+	5.89387i	0.185865	+	0.214500i
$756$		0			0
$757$	−2.37358	+	5.19741i	−0.0862692	+	0.188903i	−0.947850	−	0.318718i	$-0.896748\pi$
$757$	−2.37358	+	5.19741i	−0.0862692	+	0.188903i	0.861580	+	0.507621i	$0.169475\pi$
$758$		0			0
$759$	8.15697	+	9.65249i	0.296079	+	0.350363i
$760$		0			0
$761$	−13.9068	+	30.4517i	−0.504122	+	1.10387i	0.470986	+	0.882141i	$0.343898\pi$
$761$	−13.9068	+	30.4517i	−0.504122	+	1.10387i	−0.975108	+	0.221732i	$0.928829\pi$
$762$		0			0
$763$	0.450036	+	0.519370i	0.0162924	+	0.0188024i
$764$		0			0
$765$	−0.959952	+	1.10784i	−0.0347071	+	0.0400542i
$766$		0			0
$767$	21.0264	−	6.17391i	0.759219	−	0.222927i
$768$		0			0
$769$	3.10383	+	21.5876i	0.111927	+	0.778470i	0.966042	+	0.258386i	$0.0831905\pi$
$769$	3.10383	+	21.5876i	0.111927	+	0.778470i	−0.854115	+	0.520085i	$0.825900\pi$
$770$		0			0
$771$	−6.65195	−	14.5657i	−0.239564	−	0.524572i
$772$		0			0
$773$	16.3238	+	10.4907i	0.587127	+	0.377324i	0.800219	−	0.599709i	$-0.204717\pi$
$773$	16.3238	+	10.4907i	0.587127	+	0.377324i	−0.213091	+	0.977032i	$0.568353\pi$
$774$		0			0
$775$	1.59548	−	11.0968i	0.0573114	−	0.398610i
$776$		0			0
$777$	−14.8601	+	9.55002i	−0.533104	+	0.342605i
$778$		0			0
$779$	−18.9949	−	5.57742i	−0.680564	−	0.199832i
$780$		0			0
$781$	−20.6353			−0.738388
$782$		0			0
$783$	−6.67432			−0.238521
$784$		0			0
$785$	−1.78827	−	0.525084i	−0.0638261	−	0.0187410i
$786$		0			0
$787$	2.19114	−	1.40816i	0.0781055	−	0.0501954i	−0.501005	−	0.865444i	$-0.667036\pi$
$787$	2.19114	−	1.40816i	0.0781055	−	0.0501954i	0.579111	+	0.815249i	$0.303400\pi$
$788$		0			0
$789$	−3.96549	+	27.5806i	−0.141175	+	0.981894i
$790$		0			0
$791$	11.5474	+	7.42105i	0.410578	+	0.263862i
$792$		0			0
$793$	6.10516	+	13.3684i	0.216800	+	0.474727i
$794$		0			0
$795$	−0.713987	−	4.96589i	−0.0253225	−	0.176122i
$796$		0			0
$797$	10.5547	−	3.09913i	0.373866	−	0.109777i	−0.0894012	−	0.995996i	$-0.528495\pi$
$797$	10.5547	−	3.09913i	0.373866	−	0.109777i	0.463267	+	0.886219i	$0.346677\pi$
$798$		0			0
$799$	−10.6367	+	12.2755i	−0.376301	+	0.434275i
$800$		0			0
$801$	4.03438	+	4.65593i	0.142548	+	0.164509i
$802$		0			0
$803$	−6.95850	+	15.2370i	−0.245560	+	0.537702i
$804$		0			0
$805$	4.89172	+	3.22996i	0.172411	+	0.113841i
$806$		0			0
$807$	−1.98094	+	4.33765i	−0.0697323	+	0.152693i
$808$		0			0
$809$	25.4667	+	29.3901i	0.895361	+	1.03330i	0.999250	+	0.0387128i	$0.0123257\pi$
$809$	25.4667	+	29.3901i	0.895361	+	1.03330i	−0.103889	+	0.994589i	$0.533129\pi$
$810$		0			0
$811$	−18.2544	+	21.0667i	−0.640998	+	0.739751i	−0.979551	−	0.201196i	$-0.935517\pi$
$811$	−18.2544	+	21.0667i	−0.640998	+	0.739751i	0.338553	+	0.940947i	$0.390063\pi$
$812$		0			0
$813$	12.0744	−	3.54535i	0.423466	−	0.124341i
$814$		0			0
$815$	0.431170	+	2.99885i	0.0151032	+	0.105045i
$816$		0			0
$817$	11.4441	+	25.0590i	0.400377	+	0.876703i
$818$		0			0
$819$	−5.76367	−	3.70408i	−0.201399	−	0.129431i
$820$		0			0
$821$	2.69369	−	18.7350i	0.0940105	−	0.653857i	−0.887267	−	0.461257i	$-0.847399\pi$
$821$	2.69369	−	18.7350i	0.0940105	−	0.653857i	0.981277	−	0.192601i	$-0.0616922\pi$
$822$		0			0
$823$	28.6887	−	18.4371i	1.00003	−	0.642677i	0.0652322	−	0.997870i	$-0.479221\pi$
$823$	28.6887	−	18.4371i	1.00003	−	0.642677i	0.934793	+	0.355193i	$0.115585\pi$
$824$		0			0
$825$	12.2469	+	3.59600i	0.426381	+	0.125197i
$826$		0			0
$827$	−6.79980			−0.236452			−0.118226	−	0.992987i	$-0.537721\pi$
$827$	−6.79980			−0.236452			−0.118226	+	0.992987i	$0.537721\pi$
$828$		0			0
$829$	29.0129			1.00766			0.503829	−	0.863803i	$-0.331924\pi$
$829$	29.0129			1.00766			0.503829	+	0.863803i	$0.331924\pi$
$830$		0			0
$831$	18.5043	+	5.43335i	0.641906	+	0.188481i
$832$		0			0
$833$	−7.99904	+	5.14067i	−0.277150	+	0.178114i
$834$		0			0
$835$	1.15229	−	8.01434i	0.0398766	−	0.277348i
$836$		0			0
$837$	1.94708	+	1.25131i	0.0673009	+	0.0432517i
$838$		0			0
$839$	4.50925	+	9.87387i	0.155677	+	0.340884i	0.971359	−	0.237615i	$-0.0763658\pi$
$839$	4.50925	+	9.87387i	0.155677	+	0.340884i	−0.815683	+	0.578499i	$0.803639\pi$
$840$		0			0
$841$	−2.21250	−	15.3883i	−0.0762930	−	0.530630i
$842$		0			0
$843$	−2.92934	+	0.860131i	−0.100892	+	0.0296245i
$844$		0			0
$845$	−2.09439	+	2.41705i	−0.0720491	+	0.0831491i
$846$		0			0
$847$	8.21456	+	9.48011i	0.282256	+	0.325741i
$848$		0			0
$849$	−12.6438	+	27.6860i	−0.433933	+	0.950180i
$850$		0			0
$851$	27.3913	+	0.339048i	0.938962	+	0.0116224i
$852$		0			0
$853$	11.6788	−	25.5730i	0.399874	−	0.875602i	−0.597409	−	0.801937i	$-0.703803\pi$
$853$	11.6788	−	25.5730i	0.399874	−	0.875602i	0.997283	−	0.0736653i	$-0.0234696\pi$
$854$		0			0
$855$	−1.82253	−	2.10332i	−0.0623293	−	0.0719319i
$856$		0			0
$857$	−28.1207	+	32.4530i	−0.960585	+	1.10857i	0.0334425	+	0.999441i	$0.489353\pi$
$857$	−28.1207	+	32.4530i	−0.960585	+	1.10857i	−0.994027	+	0.109133i	$0.965193\pi$
$858$		0			0
$859$	30.5555	−	8.97190i	1.04254	−	0.306117i	0.284740	−	0.958605i	$-0.408093\pi$
$859$	30.5555	−	8.97190i	1.04254	−	0.306117i	0.757800	+	0.652487i	$0.226274\pi$
$860$		0			0
$861$	1.23735	+	8.60596i	0.0421688	+	0.293290i
$862$		0			0
$863$	18.8967	+	41.3781i	0.643252	+	1.40853i	0.897338	+	0.441344i	$0.145498\pi$
$863$	18.8967	+	41.3781i	0.643252	+	1.40853i	−0.254086	+	0.967182i	$0.581775\pi$
$864$		0			0
$865$	−5.17243	−	3.32412i	−0.175868	−	0.113023i
$866$		0			0
$867$	0.461716	−	3.21131i	0.0156807	−	0.109062i
$868$		0			0
$869$	16.4921	−	10.5988i	0.559457	−	0.359541i
$870$		0			0
$871$	2.86417	+	0.840995i	0.0970486	+	0.0284960i
$872$		0			0
$873$	−5.82254			−0.197063
$874$		0			0
$875$	12.0319			0.406753
$876$		0			0
$877$	10.8598	+	3.18874i	0.366711	+	0.107676i	0.459896	−	0.887973i	$-0.347887\pi$
$877$	10.8598	+	3.18874i	0.366711	+	0.107676i	−0.0931853	+	0.995649i	$0.529705\pi$
$878$		0			0
$879$	−6.81071	+	4.37698i	−0.229720	+	0.147632i
$880$		0			0
$881$	−6.31790	+	43.9419i	−0.212855	+	1.48044i	0.550702	+	0.834702i	$0.314360\pi$
$881$	−6.31790	+	43.9419i	−0.212855	+	1.48044i	−0.763558	+	0.645740i	$0.776549\pi$
$882$		0			0
$883$	−40.1828	−	25.8239i	−1.35226	−	0.869045i	−0.354442	−	0.935078i	$-0.615329\pi$
$883$	−40.1828	−	25.8239i	−1.35226	−	0.869045i	−0.997817	+	0.0660331i	$0.978966\pi$
$884$		0			0
$885$	−1.62408	−	3.55623i	−0.0545927	−	0.119541i
$886$		0			0
$887$	−1.58184	−	11.0020i	−0.0531131	−	0.369410i	−0.998992	−	0.0448898i	$-0.985706\pi$
$887$	−1.58184	−	11.0020i	−0.0531131	−	0.369410i	0.945879	−	0.324520i	$-0.105203\pi$
$888$		0			0
$889$	24.1696	−	7.09684i	0.810623	−	0.238021i
$890$		0			0
$891$	−1.72563	+	1.99148i	−0.0578106	+	0.0667170i
$892$		0			0
$893$	−20.1946	−	23.3058i	−0.675786	−	0.779899i
$894$		0			0
$895$	−2.38143	+	5.21461i	−0.0796025	+	0.174305i
$896$		0			0
$897$	4.29376	+	9.71858i	0.143364	+	0.324494i
$898$		0			0
$899$	−6.41721	+	14.0517i	−0.214026	+	0.468651i
$900$		0			0
$901$	−30.8298	−	35.5795i	−1.02709	−	1.18532i
$902$		0			0
$903$	7.92307	−	9.14371i	0.263663	−	0.304284i
$904$		0			0
$905$	1.94358	−	0.570686i	0.0646068	−	0.0189703i
$906$		0			0
$907$	6.30586	+	43.8582i	0.209383	+	1.45629i	0.775178	+	0.631743i	$0.217660\pi$
$907$	6.30586	+	43.8582i	0.209383	+	1.45629i	−0.565795	+	0.824546i	$0.691431\pi$
$908$		0			0
$909$	3.88389	+	8.50454i	0.128821	+	0.282078i
$910$		0			0
$911$	−12.3349	−	7.92715i	−0.408673	−	0.262638i	0.320113	−	0.947379i	$-0.396279\pi$
$911$	−12.3349	−	7.92715i	−0.408673	−	0.262638i	−0.728787	+	0.684741i	$0.759915\pi$
$912$		0			0
$913$	0.258542	−	1.79820i	0.00855649	−	0.0595117i
$914$		0			0
$915$	2.20568	−	1.41750i	0.0729175	−	0.0468613i
$916$		0			0
$917$	−52.3766	−	15.3792i	−1.72963	−	0.507865i
$918$		0			0
$919$	33.2726			1.09756			0.548781	−	0.835966i	$-0.315092\pi$
$919$	33.2726			1.09756			0.548781	+	0.835966i	$0.315092\pi$
$920$		0			0
$921$	−8.08728			−0.266485
$922$		0			0
$923$	−16.6461	−	4.88774i	−0.547913	−	0.160882i
$924$		0			0
$925$	23.2752	−	14.9581i	0.765285	−	0.491819i
$926$		0			0
$927$	−0.323811	+	2.25216i	−0.0106354	+	0.0739705i
$928$		0			0
$929$	−38.6126	−	24.8148i	−1.26684	−	0.814148i	−0.277634	−	0.960687i	$-0.589550\pi$
$929$	−38.6126	−	24.8148i	−1.26684	−	0.814148i	−0.989205	+	0.146539i	$0.953187\pi$
$930$		0			0
$931$	−7.49927	−	16.4211i	−0.245779	−	0.538180i
$932$		0			0
$933$	0.116037	+	0.807052i	0.00379887	+	0.0264217i
$934$		0			0
$935$	−3.70630	+	1.08827i	−0.121209	+	0.0355901i
$936$		0			0
$937$	25.1513	−	29.0262i	0.821658	−	0.948244i	−0.177699	−	0.984085i	$-0.556865\pi$
$937$	25.1513	−	29.0262i	0.821658	−	0.948244i	0.999358	+	0.0358409i	$0.0114109\pi$
$938$		0			0
$939$	−18.9497	−	21.8691i	−0.618400	−	0.713672i
$940$		0			0
$941$	18.8427	−	41.2597i	0.614253	−	1.34503i	−0.305373	−	0.952233i	$-0.598781\pi$
$941$	18.8427	−	41.2597i	0.614253	−	1.34503i	0.919626	−	0.392794i	$-0.128491\pi$
$942$		0			0
$943$	5.75250	−	12.1945i	0.187327	−	0.397107i
$944$		0			0
$945$	−0.507756	+	1.11183i	−0.0165173	+	0.0361679i
$946$		0			0
$947$	12.3370	+	14.2377i	0.400899	+	0.462663i	0.919924	−	0.392097i	$-0.128250\pi$
$947$	12.3370	+	14.2377i	0.400899	+	0.462663i	−0.519025	+	0.854759i	$0.673705\pi$
$948$		0			0
$949$	−9.22239	+	10.6432i	−0.299371	+	0.345493i
$950$		0			0
$951$	33.2675	−	9.76821i	1.07877	−	0.316756i
$952$		0			0
$953$	5.03248	+	35.0017i	0.163018	+	1.13382i	0.892904	+	0.450247i	$0.148664\pi$
$953$	5.03248	+	35.0017i	0.163018	+	1.13382i	−0.729886	+	0.683569i	$0.760427\pi$
$954$		0			0
$955$	1.43875	+	3.15043i	0.0465569	+	0.101945i
$956$		0			0
$957$	−14.7956	−	9.50853i	−0.478273	−	0.307367i
$958$		0			0
$959$	5.88485	−	40.9300i	0.190032	−	1.32170i
$960$		0			0
$961$	−21.5723	+	13.8637i	−0.695882	+	0.447216i
$962$		0			0
$963$	12.1337	+	3.56279i	0.391004	+	0.114809i
$964$		0			0
$965$	−3.00946			−0.0968780
$966$		0			0
$967$	−29.7227			−0.955817			−0.477908	−	0.878410i	$-0.658605\pi$
$967$	−29.7227			−0.955817			−0.477908	+	0.878410i	$0.658605\pi$
$968$		0			0
$969$	−25.0582	−	7.35775i	−0.804985	−	0.236365i
$970$		0			0
$971$	0.785865	−	0.505045i	0.0252196	−	0.0162077i	−0.527970	−	0.849263i	$-0.677047\pi$
$971$	0.785865	−	0.505045i	0.0252196	−	0.0162077i	0.553190	+	0.833055i	$0.313410\pi$
$972$		0			0
$973$	−10.3038	+	71.6646i	−0.330325	+	2.29746i
$974$		0			0
$975$	9.02756	+	5.80166i	0.289113	+	0.185802i
$976$		0			0
$977$	15.3389	+	33.5876i	0.490736	+	1.07456i	0.979371	+	0.202073i	$0.0647677\pi$
$977$	15.3389	+	33.5876i	0.490736	+	1.07456i	−0.488635	+	0.872488i	$0.662505\pi$
$978$		0			0
$979$	2.31034	+	16.0688i	0.0738388	+	0.513560i
$980$		0			0
$981$	0.213220	−	0.0626069i	0.00680758	−	0.00199888i
$982$		0			0
$983$	9.46173	−	10.9194i	0.301782	−	0.348276i	−0.584523	−	0.811377i	$-0.698718\pi$
$983$	9.46173	−	10.9194i	0.301782	−	0.348276i	0.886305	+	0.463102i	$0.153264\pi$
$984$		0			0
$985$	5.51689	+	6.36683i	0.175783	+	0.202864i
$986$		0			0
$987$	−5.62619	+	12.3196i	−0.179084	+	0.392139i
$988$		0			0
$989$	−18.0667	+	5.06284i	−0.574488	+	0.160989i
$990$		0			0
$991$	11.8065	−	25.8527i	0.375047	−	0.821238i	−0.624156	−	0.781300i	$-0.714557\pi$
$991$	11.8065	−	25.8527i	0.375047	−	0.821238i	0.999202	−	0.0399374i	$-0.0127159\pi$
$992$		0			0
$993$	−9.17114	−	10.5841i	−0.291037	−	0.335875i
$994$		0			0
$995$	−6.57350	+	7.58623i	−0.208394	+	0.240500i
$996$		0			0
$997$	−28.7175	+	8.43221i	−0.909491	+	0.267051i	−0.702827	−	0.711361i	$-0.748079\pi$
$997$	−28.7175	+	8.43221i	−0.909491	+	0.267051i	−0.206665	+	0.978412i	$0.566261\pi$
$998$		0			0
$999$	0.812891	+	5.65378i	0.0257187	+	0.178878i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.i.a.121.2	yes	20
3.2	odd	2		828.2.q.c.397.1		20
23.2	even	11		6348.2.a.s.1.6		10
23.4	even	11	inner	276.2.i.a.73.2	✓	20
23.21	odd	22		6348.2.a.t.1.5		10
69.50	odd	22		828.2.q.c.73.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.i.a.73.2	✓	20	23.4	even	11	inner
276.2.i.a.121.2	yes	20	1.1	even	1	trivial
828.2.q.c.73.1		20	69.50	odd	22
828.2.q.c.397.1		20	3.2	odd	2
6348.2.a.s.1.6		10	23.2	even	11
6348.2.a.t.1.5		10	23.21	odd	22

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)

\(f(q)\)	\(=\)	\(q+(-0.959493 - 0.281733i) q^{3} +(-0.332496 + 0.213682i) q^{5} +(-0.440112 + 3.06105i) q^{7} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.959493 - 0.281733i) q^{3} +(-0.332496 + 0.213682i) q^{5} +(-0.440112 + 3.06105i) q^{7} +(0.841254 + 0.540641i) q^{9} +(1.09466 + 2.39697i) q^{11} +(0.315289 + 2.19288i) q^{13} +(0.379229 - 0.111352i) q^{15} +(2.42879 - 2.80297i) q^{17} +(4.61122 + 5.32163i) q^{19} +(1.28468 - 2.81306i) q^{21} +(-4.06629 + 2.54269i) q^{23} +(-2.01218 + 4.40606i) q^{25} +(-0.654861 - 0.755750i) q^{27} +(4.37075 - 5.04411i) q^{29} +(-2.22075 + 0.652070i) q^{31} +(-0.375014 - 2.60828i) q^{33} +(-0.507756 - 1.11183i) q^{35} +(-4.80517 - 3.08810i) q^{37} +(0.315289 - 2.19288i) q^{39} +(-2.36514 + 1.51998i) q^{41} +(3.75382 + 1.10222i) q^{43} -0.395239 q^{45} -4.37944 q^{47} +(-2.45987 - 0.722282i) q^{49} +(-3.12009 + 2.00516i) q^{51} +(1.80647 - 12.5643i) q^{53} +(-0.876162 - 0.563075i) q^{55} +(-2.92516 - 6.40520i) q^{57} +(-1.40772 - 9.79088i) q^{59} +(6.36499 - 1.86893i) q^{61} +(-2.02517 + 2.33718i) q^{63} +(-0.573412 - 0.661753i) q^{65} +(0.559732 - 1.22564i) q^{67} +(4.61794 - 1.29408i) q^{69} +(-3.25308 + 7.12324i) q^{71} +(4.16279 + 4.80412i) q^{73} +(3.17201 - 3.66069i) q^{75} +(-7.81903 + 2.29587i) q^{77} +(-1.05877 - 7.36392i) q^{79} +(0.415415 + 0.909632i) q^{81} +(-0.579976 - 0.372728i) q^{83} +(-0.208617 + 1.45097i) q^{85} +(-5.61479 + 3.60841i) q^{87} +(5.91112 + 1.73566i) q^{89} -6.85128 q^{91} +2.31450 q^{93} +(-2.67035 - 0.784086i) q^{95} +(-4.89824 + 3.14790i) q^{97} +(-0.375014 + 2.60828i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9	\( 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9} - 22 q^{13} + 7 q^{15} + 7 q^{17} + 19 q^{19} + 20 q^{23} + 20 q^{25} - 2 q^{27} + 32 q^{29} - 3 q^{31} + 11 q^{33} - 26 q^{35} - 10 q^{37} - 22 q^{39} - 40 q^{41} + 8 q^{43} - 4 q^{45} - 18 q^{47} - 34 q^{49} - 26 q^{51} - 34 q^{53} - 17 q^{55} - 3 q^{57} - 32 q^{59} + 32 q^{61} + 49 q^{65} + 35 q^{67} - 2 q^{69} + 33 q^{71} - q^{73} - 2 q^{75} - 50 q^{77} + 22 q^{79} - 2 q^{81} - 14 q^{83} - 9 q^{85} - 12 q^{87} + 10 q^{89} - 72 q^{91} + 30 q^{93} - 51 q^{95} - 4 q^{97} + 11 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9 - 22 * q^13 + 7 * q^15 + 7 * q^17 + 19 * q^19 + 20 * q^23 + 20 * q^25 - 2 * q^27 + 32 * q^29 - 3 * q^31 + 11 * q^33 - 26 * q^35 - 10 * q^37 - 22 * q^39 - 40 * q^41 + 8 * q^43 - 4 * q^45 - 18 * q^47 - 34 * q^49 - 26 * q^51 - 34 * q^53 - 17 * q^55 - 3 * q^57 - 32 * q^59 + 32 * q^61 + 49 * q^65 + 35 * q^67 - 2 * q^69 + 33 * q^71 - q^73 - 2 * q^75 - 50 * q^77 + 22 * q^79 - 2 * q^81 - 14 * q^83 - 9 * q^85 - 12 * q^87 + 10 * q^89 - 72 * q^91 + 30 * q^93 - 51 * q^95 - 4 * q^97 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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