LMFDB - Embedded newform 828.2.q.c.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [828,2,Mod(73,828)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(828, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("828.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 828 = 2^{2} \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	828.q (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:	$6.61161328736$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 276)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			73.1
Root			$-0.404188 + 2.81119i$ of defining polynomial
Character	$\chi$	$=$	828.73
Dual form			828.2.q.c.397.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.332496 + 0.213682i) q^{5} +(-0.440112 - 3.06105i) q^{7} +O(q^{10})$	$q+(0.332496 + 0.213682i) q^{5} +(-0.440112 - 3.06105i) q^{7} +(-1.09466 + 2.39697i) q^{11} +(0.315289 - 2.19288i) q^{13} +(-2.42879 - 2.80297i) q^{17} +(4.61122 - 5.32163i) q^{19} +(4.06629 + 2.54269i) q^{23} +(-2.01218 - 4.40606i) q^{25} +(-4.37075 - 5.04411i) q^{29} +(-2.22075 - 0.652070i) q^{31} +(0.507756 - 1.11183i) q^{35} +(-4.80517 + 3.08810i) q^{37} +(2.36514 + 1.51998i) q^{41} +(3.75382 - 1.10222i) q^{43} +4.37944 q^{47} +(-2.45987 + 0.722282i) q^{49} +(-1.80647 - 12.5643i) q^{53} +(-0.876162 + 0.563075i) q^{55} +(1.40772 - 9.79088i) q^{59} +(6.36499 + 1.86893i) q^{61} +(0.573412 - 0.661753i) q^{65} +(0.559732 + 1.22564i) q^{67} +(3.25308 + 7.12324i) q^{71} +(4.16279 - 4.80412i) q^{73} +(7.81903 + 2.29587i) q^{77} +(-1.05877 + 7.36392i) q^{79} +(0.579976 - 0.372728i) q^{83} +(-0.208617 - 1.45097i) q^{85} +(-5.91112 + 1.73566i) q^{89} -6.85128 q^{91} +(2.67035 - 0.784086i) q^{95} +(-4.89824 - 3.14790i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{5}+O(q^{10}) $ 20 * q + 4 * q^5	$ 20 q + 4 q^{5} - 22 q^{13} - 7 q^{17} + 19 q^{19} - 20 q^{23} + 20 q^{25} - 32 q^{29} - 3 q^{31} + 26 q^{35} - 10 q^{37} + 40 q^{41} + 8 q^{43} + 18 q^{47} - 34 q^{49} + 34 q^{53} - 17 q^{55} + 32 q^{59} + 32 q^{61} - 49 q^{65} + 35 q^{67} - 33 q^{71} - q^{73} + 50 q^{77} + 22 q^{79} + 14 q^{83} - 9 q^{85} - 10 q^{89} - 72 q^{91} + 51 q^{95} - 4 q^{97}+O(q^{100}) $ 20 * q + 4 * q^5 - 22 * q^13 - 7 * q^17 + 19 * q^19 - 20 * q^23 + 20 * q^25 - 32 * q^29 - 3 * q^31 + 26 * q^35 - 10 * q^37 + 40 * q^41 + 8 * q^43 + 18 * q^47 - 34 * q^49 + 34 * q^53 - 17 * q^55 + 32 * q^59 + 32 * q^61 - 49 * q^65 + 35 * q^67 - 33 * q^71 - q^73 + 50 * q^77 + 22 * q^79 + 14 * q^83 - 9 * q^85 - 10 * q^89 - 72 * q^91 + 51 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/828\mathbb{Z}\right)^\times$.

$n$	$415$	$461$	$649$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{11}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.332496	+	0.213682i	0.148697	+	0.0955616i	0.612874	−	0.790181i	$-0.290013\pi$
$5$	0.332496	+	0.213682i	0.148697	+	0.0955616i	−0.464177	+	0.885743i	$0.653650\pi$
$6$		0			0
$7$	−0.440112	−	3.06105i	−0.166347	−	1.15697i	−0.886356	−	0.463003i	$-0.846772\pi$
$7$	−0.440112	−	3.06105i	−0.166347	−	1.15697i	0.720010	−	0.693964i	$-0.244137\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.09466	+	2.39697i	−0.330053	+	0.722715i	−0.999803	−	0.0198719i	$-0.993674\pi$
$11$	−1.09466	+	2.39697i	−0.330053	+	0.722715i	0.669750	+	0.742587i	$0.266401\pi$
$12$		0			0
$13$	0.315289	−	2.19288i	0.0874454	−	0.608196i	−0.898228	−	0.439530i	$-0.855145\pi$
$13$	0.315289	−	2.19288i	0.0874454	−	0.608196i	0.985673	−	0.168666i	$-0.0539459\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.42879	−	2.80297i	−0.589068	−	0.679821i	0.380461	−	0.924797i	$-0.375765\pi$
$17$	−2.42879	−	2.80297i	−0.589068	−	0.679821i	−0.969529	+	0.244976i	$0.921220\pi$
$18$		0			0
$19$	4.61122	−	5.32163i	1.05789	−	1.22087i	0.0833775	−	0.996518i	$-0.473429\pi$
$19$	4.61122	−	5.32163i	1.05789	−	1.22087i	0.974509	−	0.224348i	$-0.0720253\pi$
$20$		0			0
$21$		0			0
$22$		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			0
$28$		0			0
$29$	−4.37075	−	5.04411i	−0.811627	−	0.936668i	0.187331	−	0.982297i	$-0.440016\pi$
$29$	−4.37075	−	5.04411i	−0.811627	−	0.936668i	−0.998958	+	0.0456288i	$0.985471\pi$
$30$		0			0
$31$	−2.22075	−	0.652070i	−0.398858	−	0.117115i	0.0761510	−	0.997096i	$-0.475737\pi$
$31$	−2.22075	−	0.652070i	−0.398858	−	0.117115i	−0.475009	+	0.879981i	$0.657555\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.507756	−	1.11183i	0.0858264	−	0.187934i
$36$		0			0
$37$	−4.80517	+	3.08810i	−0.789966	+	0.507680i	−0.872327	−	0.488922i	$-0.837390\pi$
$37$	−4.80517	+	3.08810i	−0.789966	+	0.507680i	0.0823615	+	0.996603i	$0.473754\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.36514	+	1.51998i	0.369372	+	0.237381i	0.712138	−	0.702040i	$-0.247727\pi$
$41$	2.36514	+	1.51998i	0.369372	+	0.237381i	−0.342765	+	0.939421i	$0.611364\pi$
$42$		0			0
$43$	3.75382	−	1.10222i	0.572451	−	0.168087i	0.0173207	−	0.999850i	$-0.494486\pi$
$43$	3.75382	−	1.10222i	0.572451	−	0.168087i	0.555131	+	0.831763i	$0.312668\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.37944			0.638808			0.319404	−	0.947619i	$-0.396517\pi$
$47$	4.37944			0.638808			0.319404	+	0.947619i	$0.396517\pi$
$48$		0			0
$49$	−2.45987	+	0.722282i	−0.351410	+	0.103183i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.80647	−	12.5643i	−0.248138	−	1.72584i	−0.608959	−	0.793202i	$-0.708413\pi$
$53$	−1.80647	−	12.5643i	−0.248138	−	1.72584i	0.360821	−	0.932635i	$-0.382496\pi$
$54$		0			0
$55$	−0.876162	+	0.563075i	−0.118142	+	0.0759250i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.40772	−	9.79088i	0.183269	−	1.27466i	−0.665699	−	0.746220i	$-0.731867\pi$
$59$	1.40772	−	9.79088i	0.183269	−	1.27466i	0.848968	−	0.528444i	$-0.177224\pi$
$60$		0			0
$61$	6.36499	+	1.86893i	0.814954	+	0.239292i	0.662542	−	0.749025i	$-0.269478\pi$
$61$	6.36499	+	1.86893i	0.814954	+	0.239292i	0.152412	+	0.988317i	$0.451296\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.573412	−	0.661753i	0.0711231	−	0.0820804i
$66$		0			0
$67$	0.559732	+	1.22564i	0.0683822	+	0.149736i	0.940737	−	0.339138i	$-0.110135\pi$
$67$	0.559732	+	1.22564i	0.0683822	+	0.149736i	−0.872355	+	0.488874i	$0.837408\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.25308	+	7.12324i	0.386069	+	0.845374i	0.998495	+	0.0548454i	$0.0174666\pi$
$71$	3.25308	+	7.12324i	0.386069	+	0.845374i	−0.612426	+	0.790528i	$0.709806\pi$
$72$		0			0
$73$	4.16279	−	4.80412i	0.487218	−	0.562280i	−0.457902	−	0.889003i	$-0.651399\pi$
$73$	4.16279	−	4.80412i	0.487218	−	0.562280i	0.945120	+	0.326723i	$0.105944\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	7.81903	+	2.29587i	0.891061	+	0.261639i
$78$		0			0
$79$	−1.05877	+	7.36392i	−0.119121	+	0.828505i	0.839406	+	0.543505i	$0.182903\pi$
$79$	−1.05877	+	7.36392i	−0.119121	+	0.828505i	−0.958527	+	0.285001i	$0.908006\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.579976	−	0.372728i	0.0636606	−	0.0409122i	−0.508423	−	0.861107i	$-0.669771\pi$
$83$	0.579976	−	0.372728i	0.0636606	−	0.0409122i	0.572084	+	0.820195i	$0.306135\pi$
$84$		0			0
$85$	−0.208617	−	1.45097i	−0.0226277	−	0.157379i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.91112	+	1.73566i	−0.626578	+	0.183980i	−0.579580	−	0.814915i	$-0.696783\pi$
$89$	−5.91112	+	1.73566i	−0.626578	+	0.183980i	−0.0469975	+	0.998895i	$0.514965\pi$
$90$		0			0
$91$	−6.85128			−0.718210
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.67035	−	0.784086i	0.273972	−	0.0804455i
$96$		0			0
$97$	−4.89824	−	3.14790i	−0.497340	−	0.319621i	0.267811	−	0.963471i	$-0.413700\pi$
$97$	−4.89824	−	3.14790i	−0.497340	−	0.319621i	−0.765152	+	0.643850i	$0.777336\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.86524	+	5.05468i	−0.782620	+	0.502959i	−0.869902	−	0.493224i	$-0.835818\pi$
$101$	−7.86524	+	5.05468i	−0.782620	+	0.502959i	0.0872820	+	0.996184i	$0.472182\pi$
$102$		0			0
$103$	0.945200	−	2.06970i	0.0931334	−	0.203934i	−0.857332	−	0.514764i	$-0.827880\pi$
$103$	0.945200	−	2.06970i	0.0931334	−	0.203934i	0.950466	+	0.310830i	$0.100607\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−12.1337	−	3.56279i	−1.17301	−	0.344428i	−0.363536	−	0.931580i	$-0.618431\pi$
$107$	−12.1337	−	3.56279i	−1.17301	−	0.344428i	−0.809476	+	0.587153i	$0.800249\pi$
$108$		0			0
$109$	0.145524	+	0.167943i	0.0139387	+	0.0160861i	0.762676	−	0.646781i	$-0.223885\pi$
$109$	0.145524	+	0.167943i	0.0139387	+	0.0160861i	−0.748737	+	0.662867i	$0.769340\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.84385	−	4.03747i	−0.173455	−	0.379813i	0.802860	−	0.596167i	$-0.203311\pi$
$113$	−1.84385	−	4.03747i	−0.173455	−	0.379813i	−0.976315	+	0.216355i	$0.930583\pi$
$114$		0			0
$115$	0.808699	+	1.71433i	0.0754116	+	0.159862i
$116$		0			0
$117$		0			0
$118$		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
$123$		0			0
$124$		0			0
$125$	0.553697	−	3.85105i	0.0495241	−	0.344448i
$126$		0			0
$127$	−3.38374	+	7.40936i	−0.300258	+	0.657474i	−0.998281	−	0.0586010i	$-0.981336\pi$
$127$	−3.38374	+	7.40936i	−0.300258	+	0.657474i	0.698023	+	0.716075i	$0.254063\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.51207	+	17.4719i	0.219481	+	1.52652i	0.739961	+	0.672650i	$0.234844\pi$
$131$	2.51207	+	17.4719i	0.219481	+	1.52652i	−0.520480	+	0.853874i	$0.674247\pi$
$132$		0			0
$133$	−18.3192	−	11.7731i	−1.58848	−	1.02085i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	13.3712			1.14238			0.571191	−	0.820817i	$-0.306482\pi$
$137$	13.3712			1.14238			0.571191	+	0.820817i	$0.306482\pi$
$138$		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
$141$		0			0
$142$		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
$147$		0			0
$148$		0			0
$149$	−9.60048	+	21.0221i	−0.786502	+	1.72220i	−0.100098	+	0.994978i	$0.531916\pi$
$149$	−9.60048	+	21.0221i	−0.786502	+	1.72220i	−0.686404	+	0.727221i	$0.740812\pi$
$150$		0			0
$151$	−2.80811	+	19.5308i	−0.228520	+	1.58939i	0.475827	+	0.879539i	$0.342149\pi$
$151$	−2.80811	+	19.5308i	−0.228520	+	1.58939i	−0.704348	+	0.709855i	$0.748760\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.599053	−	0.691345i	−0.0481171	−	0.0555301i
$156$		0			0
$157$	3.08803	−	3.56377i	0.246451	−	0.284420i	−0.619023	−	0.785372i	$-0.712471\pi$
$157$	3.08803	−	3.56377i	0.246451	−	0.284420i	0.865475	+	0.500953i	$0.167017\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	5.99367	−	13.5662i	0.472367	−	1.06917i
$162$		0			0
$163$	3.18435	+	6.97275i	0.249417	+	0.546148i	0.992384	−	0.123180i	$-0.0393093\pi$
$163$	3.18435	+	6.97275i	0.249417	+	0.546148i	−0.742967	+	0.669328i	$0.766582\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	13.4153	+	15.4821i	1.03811	+	1.19804i	0.979850	+	0.199737i	$0.0640088\pi$
$167$	13.4153	+	15.4821i	1.03811	+	1.19804i	0.0582568	+	0.998302i	$0.481446\pi$
$168$		0			0
$169$	7.76408	+	2.27974i	0.597237	+	0.175365i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−6.46235	+	14.1506i	−0.491323	+	1.07585i	0.487870	+	0.872916i	$0.337774\pi$
$173$	−6.46235	+	14.1506i	−0.491323	+	1.07585i	−0.979193	+	0.202931i	$0.934953\pi$
$174$		0			0
$175$	−12.6016	+	8.09855i	−0.952590	+	0.612193i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−12.2018	−	7.84161i	−0.912004	−	0.586110i	−0.00167699	−	0.999999i	$-0.500534\pi$
$179$	−12.2018	−	7.84161i	−0.912004	−	0.586110i	−0.910327	+	0.413889i	$0.864170\pi$
$180$		0			0
$181$	−4.91748	+	1.44390i	−0.365513	+	0.107324i	−0.459331	−	0.888265i	$-0.651911\pi$
$181$	−4.91748	+	1.44390i	−0.365513	+	0.107324i	0.0938180	+	0.995589i	$0.470093\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.25757			−0.165980
$186$		0			0
$187$	9.37736	−	2.75344i	0.685740	−	0.201352i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.24708	−	8.67363i	−0.0902355	−	0.627602i	−0.983881	−	0.178827i	$-0.942770\pi$
$191$	−1.24708	−	8.67363i	−0.0902355	−	0.627602i	0.893645	−	0.448775i	$-0.148139\pi$
$192$		0			0
$193$	6.40555	−	4.11659i	0.461081	−	0.296319i	−0.289403	−	0.957207i	$-0.593457\pi$
$193$	6.40555	−	4.11659i	0.461081	−	0.296319i	0.750484	+	0.660888i	$0.229820\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	3.03344	−	21.0981i	0.216124	−	1.50318i	−0.536036	−	0.844195i	$-0.680079\pi$
$197$	3.03344	−	21.0981i	0.216124	−	1.50318i	0.752160	−	0.658980i	$-0.229012\pi$
$198$		0			0
$199$	24.3686	+	7.15526i	1.72744	+	0.507223i	0.986418	−	0.164255i	$-0.0525220\pi$
$199$	24.3686	+	7.15526i	1.72744	+	0.507223i	0.741025	+	0.671478i	$0.234340\pi$
$200$		0			0
$201$		0			0
$202$		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
$207$		0			0
$208$		0			0
$209$	7.70809	+	16.8784i	0.533180	+	1.16750i
$210$		0			0
$211$	−12.8102	+	14.7838i	−0.881891	+	1.01776i	0.117803	+	0.993037i	$0.462415\pi$
$211$	−12.8102	+	14.7838i	−0.881891	+	1.01776i	−0.999694	+	0.0247197i	$0.992131\pi$
$212$		0			0
$213$		0			0
$214$		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
$219$		0			0
$220$		0			0
$221$	−6.91236	+	4.44230i	−0.464976	+	0.298822i
$222$		0			0
$223$	−1.00285	−	6.97494i	−0.0671555	−	0.467077i	−0.995454	−	0.0952414i	$-0.969638\pi$
$223$	−1.00285	−	6.97494i	−0.0671555	−	0.467077i	0.928299	−	0.371835i	$-0.121271\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	22.6593	−	6.65336i	1.50395	−	0.441599i	0.576986	−	0.816754i	$-0.304229\pi$
$227$	22.6593	−	6.65336i	1.50395	−	0.441599i	0.926962	+	0.375156i	$0.122411\pi$
$228$		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
$231$		0			0
$232$		0			0
$233$	−0.683723	+	0.200759i	−0.0447922	+	0.0131522i	−0.304052	−	0.952655i	$-0.598340\pi$
$233$	−0.683723	+	0.200759i	−0.0447922	+	0.0131522i	0.259260	+	0.965808i	$0.416521\pi$
$234$		0			0
$235$	1.45615	+	0.935810i	0.0949886	+	0.0610455i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.28510	−	0.825882i	0.0831261	−	0.0534219i	−0.498418	−	0.866937i	$-0.666085\pi$
$239$	1.28510	−	0.825882i	0.0831261	−	0.0534219i	0.581544	+	0.813515i	$0.302449\pi$
$240$		0			0
$241$	−11.3499	+	24.8528i	−0.731111	+	1.60091i	0.0665361	+	0.997784i	$0.478805\pi$
$241$	−11.3499	+	24.8528i	−0.731111	+	1.60091i	−0.797647	+	0.603125i	$0.793922\pi$
$242$		0			0
$243$		0			0
$244$		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			0
$250$		0			0
$251$	−9.87995	−	21.6341i	−0.623617	−	1.36553i	−0.912859	−	0.408274i	$-0.866131\pi$
$251$	−9.87995	−	21.6341i	−0.623617	−	1.36553i	0.289243	−	0.957256i	$-0.406597\pi$
$252$		0			0
$253$	−10.5460	+	6.96342i	−0.663020	+	0.437786i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−10.4861	+	12.1017i	−0.654108	+	0.754880i	−0.981803	−	0.189903i	$-0.939183\pi$
$257$	−10.4861	+	12.1017i	−0.654108	+	0.754880i	0.327695	+	0.944783i	$0.393728\pi$
$258$		0			0
$259$	11.5676	+	13.3498i	0.718778	+	0.829514i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	3.96549	−	27.5806i	0.244522	−	1.70069i	−0.384354	−	0.923186i	$-0.625576\pi$
$263$	3.96549	−	27.5806i	0.244522	−	1.70069i	0.628877	−	0.777505i	$-0.283515\pi$
$264$		0			0
$265$	2.08412	−	4.56358i	0.128026	−	0.280339i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.678639	−	4.72004i	−0.0413774	−	0.287786i	−0.999995	−	0.00308994i	$-0.999016\pi$
$269$	−0.678639	−	4.72004i	−0.0413774	−	0.287786i	0.958618	−	0.284696i	$-0.0918927\pi$
$270$		0			0
$271$	−10.5864	−	6.80348i	−0.643080	−	0.413282i	0.178052	−	0.984021i	$-0.443020\pi$
$271$	−10.5864	−	6.80348i	−0.643080	−	0.413282i	−0.821132	+	0.570739i	$0.806657\pi$
$272$		0			0
$273$		0			0
$274$		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
$279$		0			0
$280$		0			0
$281$	−2.56835	−	1.65058i	−0.153215	−	0.0984653i	0.461787	−	0.886991i	$-0.347208\pi$
$281$	−2.56835	−	1.65058i	−0.153215	−	0.0984653i	−0.615002	+	0.788526i	$0.710845\pi$
$282$		0			0
$283$	4.33156	+	30.1266i	0.257484	+	1.79084i	0.550603	+	0.834767i	$0.314398\pi$
$283$	4.33156	+	30.1266i	0.257484	+	1.79084i	−0.293119	+	0.956076i	$0.594693\pi$
$284$		0			0
$285$		0			0
$286$		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
$291$		0			0
$292$		0			0
$293$	−5.30169	−	6.11848i	−0.309728	−	0.357445i	0.579449	−	0.815009i	$-0.303268\pi$
$293$	−5.30169	−	6.11848i	−0.309728	−	0.357445i	−0.889177	+	0.457563i	$0.848722\pi$
$294$		0			0
$295$	2.56020	−	2.95462i	0.149060	−	0.172025i
$296$		0			0
$297$		0			0
$298$		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
$303$		0			0
$304$		0			0
$305$	1.71698	+	1.98150i	0.0983139	+	0.113460i
$306$		0			0
$307$	7.75969	+	2.27845i	0.442869	+	0.130038i	0.495562	−	0.868573i	$-0.334962\pi$
$307$	7.75969	+	2.27845i	0.442869	+	0.130038i	−0.0526927	+	0.998611i	$0.516780\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.338709	−	0.741670i	0.0192064	−	0.0420562i	−0.899786	−	0.436332i	$-0.856277\pi$
$311$	0.338709	−	0.741670i	0.0192064	−	0.0420562i	0.918992	+	0.394276i	$0.129005\pi$
$312$		0			0
$313$	24.3434	−	15.6445i	1.37597	−	0.884281i	0.376850	−	0.926274i	$-0.377007\pi$
$313$	24.3434	−	15.6445i	1.37597	−	0.884281i	0.999118	+	0.0419935i	$0.0133709\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	29.1679	+	18.7451i	1.63823	+	1.05283i	0.942328	+	0.334692i	$0.108632\pi$
$317$	29.1679	+	18.7451i	1.63823	+	1.05283i	0.695903	+	0.718135i	$0.255004\pi$
$318$		0			0
$319$	16.8751	−	4.95498i	0.944824	−	0.277425i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−26.1161			−1.45314
$324$		0			0
$325$	−10.2964	+	3.02330i	−0.571141	+	0.167702i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.92745	−	13.4057i	−0.106264	−	0.739080i
$330$		0			0
$331$	11.7815	−	7.57152i	0.647570	−	0.416168i	−0.175207	−	0.984532i	$-0.556060\pi$
$331$	11.7815	−	7.57152i	0.647570	−	0.416168i	0.822778	+	0.568363i	$0.192423\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.0757893	+	0.527126i	−0.00414081	+	0.0288000i
$336$		0			0
$337$	11.2111	+	3.29189i	0.610710	+	0.179321i	0.572440	−	0.819947i	$-0.305997\pi$
$337$	11.2111	+	3.29189i	0.610710	+	0.179321i	0.0382703	+	0.999267i	$0.487815\pi$
$338$		0			0
$339$		0			0
$340$		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
$345$		0			0
$346$		0			0
$347$	12.7515	+	27.9220i	0.684538	+	1.49893i	0.857762	+	0.514048i	$0.171855\pi$
$347$	12.7515	+	27.9220i	0.684538	+	1.49893i	−0.173223	+	0.984883i	$0.555418\pi$
$348$		0			0
$349$	18.4824	−	21.3299i	0.989342	−	1.14176i	−0.000558286	−	1.00000i	$-0.500178\pi$
$349$	18.4824	−	21.3299i	0.989342	−	1.14176i	0.989901	−	0.141762i	$-0.0452768\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	15.1718	+	4.45484i	0.807514	+	0.237107i	0.659331	−	0.751853i	$-0.270839\pi$
$353$	15.1718	+	4.45484i	0.807514	+	0.237107i	0.148183	+	0.988960i	$0.452658\pi$
$354$		0			0
$355$	−0.440476	+	3.06358i	−0.0233780	+	0.162598i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.567977	+	0.365017i	−0.0299767	+	0.0192648i	−0.555543	−	0.831488i	$-0.687490\pi$
$359$	−0.567977	+	0.365017i	−0.0299767	+	0.0192648i	0.525567	+	0.850752i	$0.323853\pi$
$360$		0			0
$361$	−4.35243	−	30.2718i	−0.229075	−	1.59325i
$362$		0			0
$363$		0			0
$364$		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
$369$		0			0
$370$		0			0
$371$	−37.6648	+	11.0594i	−1.95546	+	0.574175i
$372$		0			0
$373$	5.57634	+	3.58369i	0.288732	+	0.185557i	0.676986	−	0.735995i	$-0.263286\pi$
$373$	5.57634	+	3.58369i	0.288732	+	0.185557i	−0.388255	+	0.921552i	$0.626922\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−12.4392	+	7.99418i	−0.640651	+	0.411721i
$378$		0			0
$379$	1.67512	−	3.66799i	0.0860449	−	0.188412i	−0.861718	−	0.507387i	$-0.830611\pi$
$379$	1.67512	−	3.66799i	0.0860449	−	0.188412i	0.947763	+	0.318975i	$0.103339\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	8.86688	+	2.60355i	0.453076	+	0.133035i	0.500306	−	0.865849i	$-0.333221\pi$
$383$	8.86688	+	2.60355i	0.453076	+	0.133035i	−0.0472294	+	0.998884i	$0.515039\pi$
$384$		0			0
$385$	2.10921	+	2.43416i	0.107495	+	0.124056i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−6.71406	−	14.7017i	−0.340416	−	0.745407i	0.659564	−	0.751648i	$-0.270741\pi$
$389$	−6.71406	−	14.7017i	−0.340416	−	0.745407i	−0.999981	+	0.00624068i	$0.998014\pi$
$390$		0			0
$391$	−2.74908	−	17.5734i	−0.139027	−	0.888723i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−1.92558	+	2.22223i	−0.0968862	+	0.111813i
$396$		0			0
$397$	0.206863	+	0.238733i	0.0103822	+	0.0119817i	0.760917	−	0.648849i	$-0.224749\pi$
$397$	0.206863	+	0.238733i	0.0103822	+	0.0119817i	−0.750535	+	0.660831i	$0.770204\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−0.204711	+	1.42380i	−0.0102228	+	0.0711011i	−0.994294	−	0.106672i	$-0.965980\pi$
$401$	−0.204711	+	1.42380i	−0.0102228	+	0.0711011i	0.984071	+	0.177774i	$0.0568895\pi$
$402$		0			0
$403$	−2.13009	+	4.66424i	−0.106107	+	0.232343i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.14205	−	14.8983i	−0.106178	−	0.738482i
$408$		0			0
$409$	−1.86910	−	1.20120i	−0.0924211	−	0.0593954i	0.493614	−	0.869681i	$-0.335676\pi$
$409$	−1.86910	−	1.20120i	−0.0924211	−	0.0593954i	−0.586035	+	0.810286i	$0.699312\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−30.5899			−1.50523
$414$		0			0
$415$	0.272485			0.0133758
$416$		0			0
$417$		0			0
$418$		0			0
$419$	8.96288	+	5.76010i	0.437866	+	0.281399i	0.740944	−	0.671566i	$-0.234378\pi$
$419$	8.96288	+	5.76010i	0.437866	+	0.281399i	−0.303079	+	0.952965i	$0.598015\pi$
$420$		0			0
$421$	−2.54761	−	17.7190i	−0.124163	−	0.863572i	−0.952759	−	0.303726i	$-0.901769\pi$
$421$	−2.54761	−	17.7190i	−0.124163	−	0.863572i	0.828596	−	0.559846i	$-0.189140\pi$
$422$		0			0
$423$		0			0
$424$		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
$429$		0			0
$430$		0			0
$431$	1.11016	+	1.28119i	0.0534744	+	0.0617128i	0.781857	−	0.623458i	$-0.214273\pi$
$431$	1.11016	+	1.28119i	0.0534744	+	0.0617128i	−0.728382	+	0.685171i	$0.759727\pi$
$432$		0			0
$433$	20.1428	−	23.2460i	0.968001	−	1.11713i	−0.0250786	−	0.999685i	$-0.507984\pi$
$433$	20.1428	−	23.2460i	0.968001	−	1.11713i	0.993079	−	0.117447i	$-0.0374709\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	32.2818	−	9.91442i	1.54425	−	0.474271i
$438$		0			0
$439$	−11.6426	−	25.4938i	−0.555672	−	1.21675i	−0.954082	−	0.299544i	$-0.903165\pi$
$439$	−11.6426	−	25.4938i	−0.555672	−	1.21675i	0.398411	−	0.917207i	$-0.369562\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5.96931	+	6.88895i	0.283611	+	0.327304i	0.879623	−	0.475671i	$-0.157795\pi$
$443$	5.96931	+	6.88895i	0.283611	+	0.327304i	−0.596013	+	0.802975i	$0.703249\pi$
$444$		0			0
$445$	−2.33630	−	0.686001i	−0.110751	−	0.0325196i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	16.2833	−	35.6554i	0.768456	−	1.68268i	0.0384319	−	0.999261i	$-0.487764\pi$
$449$	16.2833	−	35.6554i	0.768456	−	1.68268i	0.730024	−	0.683422i	$-0.239509\pi$
$450$		0			0
$451$	−6.23238	+	4.00531i	−0.293471	+	0.188602i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.27802	−	1.46400i	−0.106795	−	0.0686333i
$456$		0			0
$457$	29.8827	−	8.77435i	1.39785	−	0.410447i	0.505907	−	0.862588i	$-0.331158\pi$
$457$	29.8827	−	8.77435i	1.39785	−	0.410447i	0.891946	+	0.452141i	$0.149340\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−19.9022			−0.926939			−0.463469	−	0.886113i	$-0.653396\pi$
$461$	−19.9022			−0.926939			−0.463469	+	0.886113i	$0.653396\pi$
$462$		0			0
$463$	2.03576	−	0.597752i	0.0946097	−	0.0277799i	−0.234085	−	0.972216i	$-0.575209\pi$
$463$	2.03576	−	0.597752i	0.0946097	−	0.0277799i	0.328695	+	0.944436i	$0.393391\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4.25711	−	29.6089i	−0.196996	−	1.37013i	−0.812941	−	0.582346i	$-0.802135\pi$
$467$	−4.25711	−	29.6089i	−0.196996	−	1.37013i	0.615946	−	0.787789i	$-0.288774\pi$
$468$		0			0
$469$	3.50541	−	2.25279i	0.161865	−	0.104024i
$470$		0			0
$471$		0			0
$472$		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
$477$		0			0
$478$		0			0
$479$	−20.4583	+	23.6101i	−0.934764	+	1.07877i	0.0619749	+	0.998078i	$0.480260\pi$
$479$	−20.4583	+	23.6101i	−0.934764	+	1.07877i	−0.996739	+	0.0806972i	$0.974285\pi$
$480$		0			0
$481$	5.25682	+	11.5108i	0.239690	+	0.524848i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.955993	−	2.09333i	−0.0434094	−	0.0950533i
$486$		0			0
$487$	1.50158	−	1.73291i	0.0680429	−	0.0785257i	−0.720708	−	0.693239i	$-0.756183\pi$
$487$	1.50158	−	1.73291i	0.0680429	−	0.0785257i	0.788750	+	0.614714i	$0.210728\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	30.7180	+	9.01961i	1.38628	+	0.407049i	0.887951	−	0.459938i	$-0.152128\pi$
$491$	30.7180	+	9.01961i	1.38628	+	0.407049i	0.498331	+	0.866987i	$0.333947\pi$
$492$		0			0
$493$	−3.52288	+	24.5022i	−0.158663	+	1.10352i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	20.3729	−	13.0929i	0.913848	−	0.587295i
$498$		0			0
$499$	−4.53308	−	31.5283i	−0.202929	−	1.41140i	−0.795535	−	0.605907i	$-0.792810\pi$
$499$	−4.53308	−	31.5283i	−0.202929	−	1.41140i	0.592607	−	0.805492i	$-0.298099\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	21.5336	−	6.32282i	0.960134	−	0.281921i	0.236134	−	0.971721i	$-0.424120\pi$
$503$	21.5336	−	6.32282i	0.960134	−	0.281921i	0.724000	+	0.689800i	$0.242301\pi$
$504$		0			0
$505$	−3.69526			−0.164437
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−16.2921	+	4.78378i	−0.722133	+	0.212037i	−0.622090	−	0.782946i	$-0.713716\pi$
$509$	−16.2921	+	4.78378i	−0.722133	+	0.212037i	−0.100043	+	0.994983i	$0.531898\pi$
$510$		0			0
$511$	−16.5377	−	10.6282i	−0.731586	−	0.470162i
$512$		0			0
$513$		0			0
$514$		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
$519$		0			0
$520$		0			0
$521$	−12.8096	−	3.76125i	−0.561200	−	0.164783i	−0.0111844	−	0.999937i	$-0.503560\pi$
$521$	−12.8096	−	3.76125i	−0.561200	−	0.164783i	−0.550016	+	0.835154i	$0.685378\pi$
$522$		0			0
$523$	−4.27548	−	4.93417i	−0.186954	−	0.215756i	0.654534	−	0.756033i	$-0.272865\pi$
$523$	−4.27548	−	4.93417i	−0.186954	−	0.215756i	−0.841487	+	0.540277i	$0.818320\pi$
$524$		0			0
$525$		0			0
$526$		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
$531$		0			0
$532$		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
$537$		0			0
$538$		0			0
$539$	0.961430	−	6.68689i	0.0414117	−	0.288025i
$540$		0			0
$541$	−9.25561	+	20.2670i	−0.397930	+	0.871345i	0.599546	+	0.800340i	$0.295348\pi$
$541$	−9.25561	+	20.2670i	−0.397930	+	0.871345i	−0.997476	+	0.0710046i	$0.977379\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.0124996	+	0.0869364i	0.000535423	+	0.00372395i
$546$		0			0
$547$	3.96660	+	2.54918i	0.169600	+	0.108995i	0.622687	−	0.782471i	$-0.286041\pi$
$547$	3.96660	+	2.54918i	0.169600	+	0.108995i	−0.453087	+	0.891466i	$0.649677\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−46.9974			−2.00216
$552$		0			0
$553$	23.0073			0.978369
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−13.4469	−	8.64180i	−0.569764	−	0.366165i	0.223816	−	0.974631i	$-0.428149\pi$
$557$	−13.4469	−	8.64180i	−0.569764	−	0.366165i	−0.793580	+	0.608467i	$0.791785\pi$
$558$		0			0
$559$	−1.23350	−	8.57919i	−0.0521716	−	0.362861i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	2.59556	−	5.68349i	0.109390	−	0.239531i	−0.847018	−	0.531564i	$-0.821605\pi$
$563$	2.59556	−	5.68349i	0.109390	−	0.239531i	0.956408	+	0.292033i	$0.0943318\pi$
$564$		0			0
$565$	0.249662	−	1.73644i	0.0105034	−	0.0730526i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−8.55803	−	9.87649i	−0.358771	−	0.414044i	0.547456	−	0.836834i	$-0.315596\pi$
$569$	−8.55803	−	9.87649i	−0.358771	−	0.414044i	−0.906228	+	0.422790i	$0.861051\pi$
$570$		0			0
$571$	4.06617	−	4.69261i	0.170164	−	0.196380i	−0.664262	−	0.747500i	$-0.731254\pi$
$571$	4.06617	−	4.69261i	0.170164	−	0.196380i	0.834426	+	0.551120i	$0.185799\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	3.02113	−	23.0327i	0.125990	−	0.960530i
$576$		0			0
$577$	18.8091	+	41.1861i	0.783031	+	1.71460i	0.695601	+	0.718429i	$0.255138\pi$
$577$	18.8091	+	41.1861i	0.783031	+	1.71460i	0.0874304	+	0.996171i	$0.472134\pi$
$578$		0			0
$579$		0			0
$580$		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			0
$586$		0			0
$587$	−6.87091	+	15.0452i	−0.283593	+	0.620982i	−0.996797	−	0.0799747i	$-0.974516\pi$
$587$	−6.87091	+	15.0452i	−0.283593	+	0.620982i	0.713204	+	0.700957i	$0.247243\pi$
$588$		0			0
$589$	−13.7104	+	8.81115i	−0.564928	+	0.363057i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	28.4481	+	18.2825i	1.16822	+	0.750772i	0.973185	−	0.230023i	$-0.0738801\pi$
$593$	28.4481	+	18.2825i	1.16822	+	0.750772i	0.195039	+	0.980795i	$0.437517\pi$
$594$		0			0
$595$	−4.34966	+	1.27718i	−0.178319	+	0.0523591i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	28.1009			1.14817			0.574085	−	0.818796i	$-0.305358\pi$
$599$	28.1009			1.14817			0.574085	+	0.818796i	$0.305358\pi$
$600$		0			0
$601$	−24.6957	+	7.25132i	−1.00736	+	0.295788i	−0.743473	−	0.668766i	$-0.766823\pi$
$601$	−24.6957	+	7.25132i	−1.00736	+	0.295788i	−0.263887	+	0.964554i	$0.585005\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.228156	+	1.58686i	0.00927586	+	0.0645151i
$606$		0			0
$607$	7.02454	−	4.51439i	0.285117	−	0.183234i	−0.390263	−	0.920703i	$-0.627616\pi$
$607$	7.02454	−	4.51439i	0.285117	−	0.183234i	0.675380	+	0.737470i	$0.263980\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.38079	−	9.60361i	0.0558608	−	0.388520i
$612$		0			0
$613$	−2.17393	−	0.638325i	−0.0878044	−	0.0257817i	0.237535	−	0.971379i	$-0.423660\pi$
$613$	−2.17393	−	0.638325i	−0.0878044	−	0.0257817i	−0.325340	+	0.945597i	$0.605479\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	27.7560	−	32.0322i	1.11742	−	1.28957i	0.164484	−	0.986380i	$-0.447404\pi$
$617$	27.7560	−	32.0322i	1.11742	−	1.28957i	0.952931	−	0.303186i	$-0.0980504\pi$
$618$		0			0
$619$	−1.39428	−	3.05306i	−0.0560410	−	0.122713i	0.879540	−	0.475825i	$-0.157851\pi$
$619$	−1.39428	−	3.05306i	−0.0560410	−	0.122713i	−0.935581	+	0.353113i	$0.885123\pi$
$620$		0			0
$621$		0			0
$622$		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
$627$		0			0
$628$		0			0
$629$	20.3266	+	5.96843i	0.810475	+	0.237977i
$630$		0			0
$631$	−0.265066	+	1.84358i	−0.0105521	+	0.0733916i	−0.994417	−	0.105521i	$-0.966349\pi$
$631$	−0.265066	+	1.84358i	−0.0105521	+	0.0733916i	0.983865	+	0.178913i	$0.0572580\pi$
$632$		0			0
$633$		0			0
$634$		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
$639$		0			0
$640$		0			0
$641$	42.9732	−	12.6181i	1.69734	−	0.498384i	0.717229	−	0.696837i	$-0.245410\pi$
$641$	42.9732	−	12.6181i	1.69734	−	0.498384i	0.980110	+	0.198454i	$0.0635919\pi$
$642$		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
$645$		0			0
$646$		0			0
$647$	−22.7754	+	6.68747i	−0.895394	+	0.262911i	−0.696881	−	0.717187i	$-0.745429\pi$
$647$	−22.7754	+	6.68747i	−0.895394	+	0.262911i	−0.198513	+	0.980098i	$0.563611\pi$
$648$		0			0
$649$	21.9275	+	14.0920i	0.860730	+	0.553158i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−26.4780	+	17.0164i	−1.03616	+	0.665902i	−0.944035	−	0.329846i	$-0.893003\pi$
$653$	−26.4780	+	17.0164i	−1.03616	+	0.665902i	−0.0921282	+	0.995747i	$0.529367\pi$
$654$		0			0
$655$	−2.89817	+	6.34611i	−0.113241	+	0.247963i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	7.87364	+	2.31191i	0.306714	+	0.0900592i	0.431468	−	0.902128i	$-0.357996\pi$
$659$	7.87364	+	2.31191i	0.306714	+	0.0900592i	−0.124754	+	0.992188i	$0.539814\pi$
$660$		0			0
$661$	12.5124	+	14.4401i	0.486677	+	0.561656i	0.944975	−	0.327143i	$-0.106086\pi$
$661$	12.5124	+	14.4401i	0.486677	+	0.561656i	−0.458297	+	0.888799i	$0.651541\pi$
$662$		0			0
$663$		0			0
$664$		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
$669$		0			0
$670$		0			0
$671$	−11.4473	+	13.2109i	−0.441918	+	0.510000i
$672$		0			0
$673$	22.6217	+	26.1068i	0.872003	+	1.00634i	0.999894	+	0.0145567i	$0.00463371\pi$
$673$	22.6217	+	26.1068i	0.872003	+	1.00634i	−0.127891	+	0.991788i	$0.540821\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	0.808364	−	5.62230i	0.0310680	−	0.216082i	−0.968373	−	0.249506i	$-0.919732\pi$
$677$	0.808364	−	5.62230i	0.0310680	−	0.216082i	0.999441	+	0.0334233i	$0.0106409\pi$
$678$		0			0
$679$	−7.48011	+	16.3792i	−0.287060	+	0.628575i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−6.17313	−	42.9350i	−0.236208	−	1.64286i	−0.670369	−	0.742028i	$-0.733864\pi$
$683$	−6.17313	−	42.9350i	−0.236208	−	1.64286i	0.434161	−	0.900835i	$-0.357045\pi$
$684$		0			0
$685$	4.44588	+	2.85720i	0.169869	+	0.109168i
$686$		0			0
$687$		0			0
$688$		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
$693$		0			0
$694$		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			0
$700$		0			0
$701$	−9.63854	+	21.1055i	−0.364043	+	0.797142i	0.635641	+	0.771985i	$0.280736\pi$
$701$	−9.63854	+	21.1055i	−0.364043	+	0.797142i	−0.999684	+	0.0251573i	$0.991991\pi$
$702$		0			0
$703$	−5.72400	+	39.8113i	−0.215885	+	1.50151i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	18.9342	+	21.8512i	0.712094	+	0.821800i
$708$		0			0
$709$	−27.3462	+	31.5591i	−1.02701	+	1.18523i	−0.0444980	+	0.999009i	$0.514169\pi$
$709$	−27.3462	+	31.5591i	−1.02701	+	1.18523i	−0.982508	+	0.186219i	$0.940377\pi$
$710$		0			0
$711$		0			0
$712$		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
$717$		0			0
$718$		0			0
$719$	17.9557	+	20.7220i	0.669635	+	0.772800i	0.984319	−	0.176396i	$-0.0564440\pi$
$719$	17.9557	+	20.7220i	0.669635	+	0.772800i	−0.314684	+	0.949196i	$0.601899\pi$
$720$		0			0
$721$	−6.75145	−	1.98240i	−0.251437	−	0.0738286i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−13.4299	+	29.4075i	−0.498775	+	1.09217i
$726$		0			0
$727$	19.3465	−	12.4333i	0.717523	−	0.461124i	−0.130252	−	0.991481i	$-0.541578\pi$
$727$	19.3465	−	12.4333i	0.717523	−	0.461124i	0.847774	+	0.530357i	$0.177942\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−12.2067	−	7.84478i	−0.451482	−	0.290150i
$732$		0			0
$733$	8.58286	−	2.52016i	0.317015	−	0.0930841i	−0.119354	−	0.992852i	$-0.538082\pi$
$733$	8.58286	−	2.52016i	0.317015	−	0.0930841i	0.436369	+	0.899768i	$0.356264\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.55055			−0.130786
$738$		0			0
$739$	−6.20386	+	1.82162i	−0.228213	+	0.0670093i	−0.393840	−	0.919179i	$-0.628853\pi$
$739$	−6.20386	+	1.82162i	−0.228213	+	0.0670093i	0.165627	+	0.986188i	$0.447035\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−5.68094	−	39.5118i	−0.208414	−	1.44955i	−0.778335	−	0.627849i	$-0.783935\pi$
$743$	−5.68094	−	39.5118i	−0.208414	−	1.44955i	0.569921	−	0.821699i	$-0.306974\pi$
$744$		0			0
$745$	−7.68417	+	4.93832i	−0.281526	+	0.180926i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−5.56565	+	38.7100i	−0.203365	+	1.41443i
$750$		0			0
$751$	−1.95344	−	0.573581i	−0.0712819	−	0.0209303i	0.245897	−	0.969296i	$-0.420917\pi$
$751$	−1.95344	−	0.573581i	−0.0712819	−	0.0209303i	−0.317179	+	0.948366i	$0.602736\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−5.10707	+	5.89387i	−0.185865	+	0.214500i
$756$		0			0
$757$	−2.37358	−	5.19741i	−0.0862692	−	0.188903i	0.861580	−	0.507621i	$-0.169475\pi$
$757$	−2.37358	−	5.19741i	−0.0862692	−	0.188903i	−0.947850	+	0.318718i	$0.896748\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	13.9068	+	30.4517i	0.504122	+	1.10387i	0.975108	+	0.221732i	$0.0711710\pi$
$761$	13.9068	+	30.4517i	0.504122	+	1.10387i	−0.470986	+	0.882141i	$0.656102\pi$
$762$		0			0
$763$	0.450036	−	0.519370i	0.0162924	−	0.0188024i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−21.0264	−	6.17391i	−0.759219	−	0.222927i
$768$		0			0
$769$	3.10383	−	21.5876i	0.111927	−	0.778470i	−0.854115	−	0.520085i	$-0.825900\pi$
$769$	3.10383	−	21.5876i	0.111927	−	0.778470i	0.966042	−	0.258386i	$-0.0831905\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−16.3238	+	10.4907i	−0.587127	+	0.377324i	−0.800219	−	0.599709i	$-0.795283\pi$
$773$	−16.3238	+	10.4907i	−0.587127	+	0.377324i	0.213091	+	0.977032i	$0.431647\pi$
$774$		0			0
$775$	1.59548	+	11.0968i	0.0573114	+	0.398610i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	18.9949	−	5.57742i	0.680564	−	0.199832i
$780$		0			0
$781$	−20.6353			−0.738388
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1.78827	−	0.525084i	0.0638261	−	0.0187410i
$786$		0			0
$787$	2.19114	+	1.40816i	0.0781055	+	0.0501954i	0.579111	−	0.815249i	$-0.303400\pi$
$787$	2.19114	+	1.40816i	0.0781055	+	0.0501954i	−0.501005	+	0.865444i	$0.667036\pi$
$788$		0			0
$789$		0			0
$790$		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			0
$796$		0			0
$797$	−10.5547	−	3.09913i	−0.373866	−	0.109777i	0.0894012	−	0.995996i	$-0.471505\pi$
$797$	−10.5547	−	3.09913i	−0.373866	−	0.109777i	−0.463267	+	0.886219i	$0.653323\pi$
$798$		0			0
$799$	−10.6367	−	12.2755i	−0.376301	−	0.434275i
$800$		0			0
$801$		0			0
$802$		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
$807$		0			0
$808$		0			0
$809$	−25.4667	+	29.3901i	−0.895361	+	1.03330i	0.103889	+	0.994589i	$0.466871\pi$
$809$	−25.4667	+	29.3901i	−0.895361	+	1.03330i	−0.999250	+	0.0387128i	$0.987674\pi$
$810$		0			0
$811$	−18.2544	−	21.0667i	−0.640998	−	0.739751i	0.338553	−	0.940947i	$-0.390063\pi$
$811$	−18.2544	−	21.0667i	−0.640998	−	0.739751i	−0.979551	+	0.201196i	$0.935517\pi$
$812$		0			0
$813$		0			0
$814$		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
$819$		0			0
$820$		0			0
$821$	−2.69369	−	18.7350i	−0.0940105	−	0.653857i	−0.981277	−	0.192601i	$-0.938308\pi$
$821$	−2.69369	−	18.7350i	−0.0940105	−	0.653857i	0.887267	−	0.461257i	$-0.152601\pi$
$822$		0			0
$823$	28.6887	+	18.4371i	1.00003	+	0.642677i	0.934793	−	0.355193i	$-0.115585\pi$
$823$	28.6887	+	18.4371i	1.00003	+	0.642677i	0.0652322	+	0.997870i	$0.479221\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	6.79980			0.236452			0.118226	−	0.992987i	$-0.462279\pi$
$827$	6.79980			0.236452			0.118226	+	0.992987i	$0.462279\pi$
$828$		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
$831$		0			0
$832$		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
$837$		0			0
$838$		0			0
$839$	−4.50925	+	9.87387i	−0.155677	+	0.340884i	−0.971359	−	0.237615i	$-0.923634\pi$
$839$	−4.50925	+	9.87387i	−0.155677	+	0.340884i	0.815683	+	0.578499i	$0.196361\pi$
$840$		0			0
$841$	−2.21250	+	15.3883i	−0.0762930	+	0.530630i
$842$		0			0
$843$		0			0
$844$		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
$849$		0			0
$850$		0			0
$851$	−27.3913	+	0.339048i	−0.938962	+	0.0116224i
$852$		0			0
$853$	11.6788	+	25.5730i	0.399874	+	0.875602i	0.997283	+	0.0736653i	$0.0234696\pi$
$853$	11.6788	+	25.5730i	0.399874	+	0.875602i	−0.597409	+	0.801937i	$0.703803\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	28.1207	+	32.4530i	0.960585	+	1.10857i	0.994027	+	0.109133i	$0.0348075\pi$
$857$	28.1207	+	32.4530i	0.960585	+	1.10857i	−0.0334425	+	0.999441i	$0.510647\pi$
$858$		0			0
$859$	30.5555	+	8.97190i	1.04254	+	0.306117i	0.757800	−	0.652487i	$-0.226274\pi$
$859$	30.5555	+	8.97190i	1.04254	+	0.306117i	0.284740	+	0.958605i	$0.408093\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−18.8967	+	41.3781i	−0.643252	+	1.40853i	0.254086	+	0.967182i	$0.418225\pi$
$863$	−18.8967	+	41.3781i	−0.643252	+	1.40853i	−0.897338	+	0.441344i	$0.854502\pi$
$864$		0			0
$865$	−5.17243	+	3.32412i	−0.175868	+	0.113023i
$866$		0			0
$867$		0			0
$868$		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
$873$		0			0
$874$		0			0
$875$	−12.0319			−0.406753
$876$		0			0
$877$	10.8598	−	3.18874i	0.366711	−	0.107676i	−0.0931853	−	0.995649i	$-0.529705\pi$
$877$	10.8598	−	3.18874i	0.366711	−	0.107676i	0.459896	+	0.887973i	$0.347887\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	6.31790	+	43.9419i	0.212855	+	1.48044i	0.763558	+	0.645740i	$0.223451\pi$
$881$	6.31790	+	43.9419i	0.212855	+	1.48044i	−0.550702	+	0.834702i	$0.685640\pi$
$882$		0			0
$883$	−40.1828	+	25.8239i	−1.35226	+	0.869045i	−0.997817	−	0.0660331i	$-0.978966\pi$
$883$	−40.1828	+	25.8239i	−1.35226	+	0.869045i	−0.354442	+	0.935078i	$0.615329\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.58184	−	11.0020i	0.0531131	−	0.369410i	−0.945879	−	0.324520i	$-0.894797\pi$
$887$	1.58184	−	11.0020i	0.0531131	−	0.369410i	0.998992	−	0.0448898i	$-0.0142937\pi$
$888$		0			0
$889$	24.1696	+	7.09684i	0.810623	+	0.238021i
$890$		0			0
$891$		0			0
$892$		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
$897$		0			0
$898$		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
$903$		0			0
$904$		0			0
$905$	−1.94358	−	0.570686i	−0.0646068	−	0.0189703i
$906$		0			0
$907$	6.30586	−	43.8582i	0.209383	−	1.45629i	−0.565795	−	0.824546i	$-0.691431\pi$
$907$	6.30586	−	43.8582i	0.209383	−	1.45629i	0.775178	−	0.631743i	$-0.217660\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	12.3349	−	7.92715i	0.408673	−	0.262638i	−0.320113	−	0.947379i	$-0.603721\pi$
$911$	12.3349	−	7.92715i	0.408673	−	0.262638i	0.728787	+	0.684741i	$0.240085\pi$
$912$		0			0
$913$	0.258542	+	1.79820i	0.00855649	+	0.0595117i
$914$		0			0
$915$		0			0
$916$		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
$921$		0			0
$922$		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			0
$928$		0			0
$929$	38.6126	−	24.8148i	1.26684	−	0.814148i	0.277634	−	0.960687i	$-0.410450\pi$
$929$	38.6126	−	24.8148i	1.26684	−	0.814148i	0.989205	+	0.146539i	$0.0468135\pi$
$930$		0			0
$931$	−7.49927	+	16.4211i	−0.245779	+	0.538180i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	3.70630	+	1.08827i	0.121209	+	0.0355901i
$936$		0			0
$937$	25.1513	+	29.0262i	0.821658	+	0.948244i	0.999358	−	0.0358409i	$-0.0114109\pi$
$937$	25.1513	+	29.0262i	0.821658	+	0.948244i	−0.177699	+	0.984085i	$0.556865\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−18.8427	−	41.2597i	−0.614253	−	1.34503i	−0.919626	−	0.392794i	$-0.871509\pi$
$941$	−18.8427	−	41.2597i	−0.614253	−	1.34503i	0.305373	−	0.952233i	$-0.401219\pi$
$942$		0			0
$943$	5.75250	+	12.1945i	0.187327	+	0.397107i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−12.3370	+	14.2377i	−0.400899	+	0.462663i	−0.919924	−	0.392097i	$-0.871750\pi$
$947$	−12.3370	+	14.2377i	−0.400899	+	0.462663i	0.519025	+	0.854759i	$0.326295\pi$
$948$		0			0
$949$	−9.22239	−	10.6432i	−0.299371	−	0.345493i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−5.03248	+	35.0017i	−0.163018	+	1.13382i	0.729886	+	0.683569i	$0.239573\pi$
$953$	−5.03248	+	35.0017i	−0.163018	+	1.13382i	−0.892904	+	0.450247i	$0.851336\pi$
$954$		0			0
$955$	1.43875	−	3.15043i	0.0465569	−	0.101945i
$956$		0			0
$957$		0			0
$958$		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
$963$		0			0
$964$		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
$969$		0			0
$970$		0			0
$971$	−0.785865	−	0.505045i	−0.0252196	−	0.0162077i	0.527970	−	0.849263i	$-0.322953\pi$
$971$	−0.785865	−	0.505045i	−0.0252196	−	0.0162077i	−0.553190	+	0.833055i	$0.686590\pi$
$972$		0			0
$973$	−10.3038	−	71.6646i	−0.330325	−	2.29746i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−15.3389	+	33.5876i	−0.490736	+	1.07456i	0.488635	+	0.872488i	$0.337495\pi$
$977$	−15.3389	+	33.5876i	−0.490736	+	1.07456i	−0.979371	+	0.202073i	$0.935232\pi$
$978$		0			0
$979$	2.31034	−	16.0688i	0.0738388	−	0.513560i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−9.46173	−	10.9194i	−0.301782	−	0.348276i	0.584523	−	0.811377i	$-0.301282\pi$
$983$	−9.46173	−	10.9194i	−0.301782	−	0.348276i	−0.886305	+	0.463102i	$0.846736\pi$
$984$		0			0
$985$	5.51689	−	6.36683i	0.175783	−	0.202864i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	18.0667	+	5.06284i	0.574488	+	0.160989i
$990$		0			0
$991$	11.8065	+	25.8527i	0.375047	+	0.821238i	0.999202	+	0.0399374i	$0.0127159\pi$
$991$	11.8065	+	25.8527i	0.375047	+	0.821238i	−0.624156	+	0.781300i	$0.714557\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	6.57350	+	7.58623i	0.208394	+	0.240500i
$996$		0			0
$997$	−28.7175	−	8.43221i	−0.909491	−	0.267051i	−0.206665	−	0.978412i	$-0.566261\pi$
$997$	−28.7175	−	8.43221i	−0.909491	−	0.267051i	−0.702827	+	0.711361i	$0.748079\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.i.a.73.2	✓	20	3.2	odd	2
276.2.i.a.121.2	yes	20	69.29	odd	22
828.2.q.c.73.1		20	1.1	even	1	trivial
828.2.q.c.397.1		20	23.6	even	11	inner
6348.2.a.s.1.6		10	69.35	odd	22
6348.2.a.t.1.5		10	69.11	even	22

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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:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	828.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.332496 + 0.213682i) q^{5} +(-0.440112 - 3.06105i) q^{7} +O(q^{10})\)	\(q+(0.332496 + 0.213682i) q^{5} +(-0.440112 - 3.06105i) q^{7} +(-1.09466 + 2.39697i) q^{11} +(0.315289 - 2.19288i) q^{13} +(-2.42879 - 2.80297i) q^{17} +(4.61122 - 5.32163i) q^{19} +(4.06629 + 2.54269i) q^{23} +(-2.01218 - 4.40606i) q^{25} +(-4.37075 - 5.04411i) q^{29} +(-2.22075 - 0.652070i) q^{31} +(0.507756 - 1.11183i) q^{35} +(-4.80517 + 3.08810i) q^{37} +(2.36514 + 1.51998i) q^{41} +(3.75382 - 1.10222i) q^{43} +4.37944 q^{47} +(-2.45987 + 0.722282i) q^{49} +(-1.80647 - 12.5643i) q^{53} +(-0.876162 + 0.563075i) q^{55} +(1.40772 - 9.79088i) q^{59} +(6.36499 + 1.86893i) q^{61} +(0.573412 - 0.661753i) q^{65} +(0.559732 + 1.22564i) q^{67} +(3.25308 + 7.12324i) q^{71} +(4.16279 - 4.80412i) q^{73} +(7.81903 + 2.29587i) q^{77} +(-1.05877 + 7.36392i) q^{79} +(0.579976 - 0.372728i) q^{83} +(-0.208617 - 1.45097i) q^{85} +(-5.91112 + 1.73566i) q^{89} -6.85128 q^{91} +(2.67035 - 0.784086i) q^{95} +(-4.89824 - 3.14790i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{5}+O(q^{10}) \) 20 * q + 4 * q^5	\( 20 q + 4 q^{5} - 22 q^{13} - 7 q^{17} + 19 q^{19} - 20 q^{23} + 20 q^{25} - 32 q^{29} - 3 q^{31} + 26 q^{35} - 10 q^{37} + 40 q^{41} + 8 q^{43} + 18 q^{47} - 34 q^{49} + 34 q^{53} - 17 q^{55} + 32 q^{59} + 32 q^{61} - 49 q^{65} + 35 q^{67} - 33 q^{71} - q^{73} + 50 q^{77} + 22 q^{79} + 14 q^{83} - 9 q^{85} - 10 q^{89} - 72 q^{91} + 51 q^{95} - 4 q^{97}+O(q^{100}) \) 20 * q + 4 * q^5 - 22 * q^13 - 7 * q^17 + 19 * q^19 - 20 * q^23 + 20 * q^25 - 32 * q^29 - 3 * q^31 + 26 * q^35 - 10 * q^37 + 40 * q^41 + 8 * q^43 + 18 * q^47 - 34 * q^49 + 34 * q^53 - 17 * q^55 + 32 * q^59 + 32 * q^61 - 49 * q^65 + 35 * q^67 - 33 * q^71 - q^73 + 50 * q^77 + 22 * q^79 + 14 * q^83 - 9 * q^85 - 10 * q^89 - 72 * q^91 + 51 * q^95 - 4 * q^97

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