LMFDB - Embedded newform 585.2.c.b.469.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(469,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("585.469");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.c (of order $2$, degree $1$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			469.3
Root			$1.45161 + 1.45161i$ of defining polynomial
Character	$\chi$	$=$	585.469
Dual form			585.2.c.b.469.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.21432i q^{2} +0.525428 q^{4} +(2.21432 + 0.311108i) q^{5} -2.90321i q^{7} -3.06668i q^{8} +(0.377784 - 2.68889i) q^{10} -0.214320 q^{11} -1.00000i q^{13} -3.52543 q^{14} -2.67307 q^{16} +6.42864i q^{17} -2.21432 q^{19} +(1.16346 + 0.163465i) q^{20} +0.260253i q^{22} -4.68889i q^{23} +(4.80642 + 1.37778i) q^{25} -1.21432 q^{26} -1.52543i q^{28} +8.70964 q^{29} -5.59210 q^{31} -2.88739i q^{32} +7.80642 q^{34} +(0.903212 - 6.42864i) q^{35} -2.28100i q^{37} +2.68889i q^{38} +(0.954067 - 6.79060i) q^{40} -3.05086 q^{41} +6.36196i q^{43} -0.112610 q^{44} -5.69381 q^{46} +1.09679i q^{47} -1.42864 q^{49} +(1.67307 - 5.83654i) q^{50} -0.525428i q^{52} +6.23506i q^{53} +(-0.474572 - 0.0666765i) q^{55} -8.90321 q^{56} -10.5763i q^{58} -9.26517 q^{59} -0.280996 q^{61} +6.79060i q^{62} -8.85236 q^{64} +(0.311108 - 2.21432i) q^{65} +7.76049i q^{67} +3.37778i q^{68} +(-7.80642 - 1.09679i) q^{70} +6.08097 q^{71} -10.2810i q^{73} -2.76986 q^{74} -1.16346 q^{76} +0.622216i q^{77} +14.2351 q^{79} +(-5.91903 - 0.831613i) q^{80} +3.70471i q^{82} -9.52543i q^{83} +(-2.00000 + 14.2351i) q^{85} +7.72546 q^{86} +0.657249i q^{88} -5.61285 q^{89} -2.90321 q^{91} -2.46367i q^{92} +1.33185 q^{94} +(-4.90321 - 0.688892i) q^{95} +18.0415i q^{97} +1.73483i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 10 q^{4} + 2 q^{10} + 12 q^{11} - 8 q^{14} + 10 q^{16} + 20 q^{20} + 2 q^{25} + 6 q^{26} + 12 q^{29} - 20 q^{31} + 20 q^{34} - 8 q^{35} - 34 q^{40} + 8 q^{41} - 40 q^{44} + 32 q^{46} + 18 q^{49} - 16 q^{50}+ \cdots - 16 q^{95}+O(q^{100}) $ 6 * q - 10 * q^4 + 2 * q^10 + 12 * q^11 - 8 * q^14 + 10 * q^16 + 20 * q^20 + 2 * q^25 + 6 * q^26 + 12 * q^29 - 20 * q^31 + 20 * q^34 - 8 * q^35 - 34 * q^40 + 8 * q^41 - 40 * q^44 + 32 * q^46 + 18 * q^49 - 16 * q^50 - 16 * q^55 - 40 * q^56 - 16 * q^59 + 12 * q^61 - 66 * q^64 + 2 * q^65 - 20 * q^70 + 24 * q^71 - 4 * q^74 - 20 * q^76 + 32 * q^79 - 48 * q^80 - 12 * q^85 + 32 * q^86 + 20 * q^89 - 4 * q^91 - 32 * q^94 - 16 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.21432i		−	0.858654i	−0.903149	−	0.429327i	$-0.858751\pi$
$2$		−	1.21432i		−	0.858654i	0.903149	−	0.429327i	$-0.141249\pi$
$3$		0			0
$3$		0			0
$4$	0.525428			0.262714
$5$	2.21432	+	0.311108i	0.990274	+	0.139132i
$5$	2.21432	+	0.311108i	0.990274	+	0.139132i
$6$		0			0
$7$		−	2.90321i		−	1.09731i	−0.836049	−	0.548655i	$-0.815140\pi$
$7$		−	2.90321i		−	1.09731i	0.836049	−	0.548655i	$-0.184860\pi$
$8$		−	3.06668i		−	1.08423i
$9$		0			0
$10$	0.377784	−	2.68889i	0.119466	−	0.850302i
$11$	−0.214320			−0.0646198			−0.0323099	−	0.999478i	$-0.510286\pi$
$11$	−0.214320			−0.0646198			−0.0323099	+	0.999478i	$0.510286\pi$
$12$		0			0
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−3.52543			−0.942210
$15$		0			0
$16$	−2.67307			−0.668268
$17$			6.42864i			1.55917i	0.626294	+	0.779587i	$0.284571\pi$
$17$			6.42864i			1.55917i	−0.626294	+	0.779587i	$0.715429\pi$
$18$		0			0
$19$	−2.21432			−0.508000			−0.254000	−	0.967204i	$-0.581746\pi$
$19$	−2.21432			−0.508000			−0.254000	+	0.967204i	$0.581746\pi$
$20$	1.16346	+	0.163465i	0.260159	+	0.0365518i
$21$		0			0
$22$			0.260253i			0.0554861i
$23$		−	4.68889i		−	0.977702i	−0.872367	−	0.488851i	$-0.837416\pi$
$23$		−	4.68889i		−	0.977702i	0.872367	−	0.488851i	$-0.162584\pi$
$24$		0			0
$25$	4.80642	+	1.37778i	0.961285	+	0.275557i
$26$	−1.21432			−0.238148
$27$		0			0
$28$		−	1.52543i		−	0.288279i
$29$	8.70964			1.61734			0.808669	−	0.588263i	$-0.200188\pi$
$29$	8.70964			1.61734			0.808669	+	0.588263i	$0.200188\pi$
$30$		0			0
$31$	−5.59210			−1.00437			−0.502186	−	0.864760i	$-0.667471\pi$
$31$	−5.59210			−1.00437			−0.502186	+	0.864760i	$0.667471\pi$
$32$		−	2.88739i		−	0.510423i
$33$		0			0
$34$	7.80642			1.33879
$35$	0.903212	−	6.42864i	0.152671	−	1.08664i
$36$		0			0
$37$		−	2.28100i		−	0.374993i	−0.982265	−	0.187497i	$-0.939963\pi$
$37$		−	2.28100i		−	0.374993i	0.982265	−	0.187497i	$-0.0600374\pi$
$38$			2.68889i			0.436196i
$39$		0			0
$40$	0.954067	−	6.79060i	0.150851	−	1.07369i
$41$	−3.05086			−0.476464			−0.238232	−	0.971208i	$-0.576568\pi$
$41$	−3.05086			−0.476464			−0.238232	+	0.971208i	$0.576568\pi$
$42$		0			0
$43$			6.36196i			0.970190i	0.874461	+	0.485095i	$0.161215\pi$
$43$			6.36196i			0.970190i	−0.874461	+	0.485095i	$0.838785\pi$
$44$	−0.112610			−0.0169765
$45$		0			0
$46$	−5.69381			−0.839507
$47$			1.09679i			0.159983i	0.996796	+	0.0799915i	$0.0254893\pi$
$47$			1.09679i			0.159983i	−0.996796	+	0.0799915i	$0.974511\pi$
$48$		0			0
$49$	−1.42864			−0.204091
$50$	1.67307	−	5.83654i	0.236608	−	0.825411i
$51$		0			0
$52$		−	0.525428i		−	0.0728637i
$53$			6.23506i			0.856452i	0.903672	+	0.428226i	$0.140861\pi$
$53$			6.23506i			0.856452i	−0.903672	+	0.428226i	$0.859139\pi$
$54$		0			0
$55$	−0.474572	−	0.0666765i	−0.0639913	−	0.00899066i
$56$	−8.90321			−1.18974
$57$		0			0
$58$		−	10.5763i		−	1.38873i
$59$	−9.26517			−1.20622			−0.603112	−	0.797657i	$-0.706073\pi$
$59$	−9.26517			−1.20622			−0.603112	+	0.797657i	$0.706073\pi$
$60$		0			0
$61$	−0.280996			−0.0359779			−0.0179889	−	0.999838i	$-0.505726\pi$
$61$	−0.280996			−0.0359779			−0.0179889	+	0.999838i	$0.505726\pi$
$62$			6.79060i			0.862407i
$63$		0			0
$64$	−8.85236			−1.10654
$65$	0.311108	−	2.21432i	0.0385882	−	0.274653i
$66$		0			0
$67$			7.76049i			0.948095i	0.880499	+	0.474047i	$0.157207\pi$
$67$			7.76049i			0.948095i	−0.880499	+	0.474047i	$0.842793\pi$
$68$			3.37778i			0.409617i
$69$		0			0
$70$	−7.80642	−	1.09679i	−0.933046	−	0.131091i
$71$	6.08097			0.721678			0.360839	−	0.932628i	$-0.382490\pi$
$71$	6.08097			0.721678			0.360839	+	0.932628i	$0.382490\pi$
$72$		0			0
$73$		−	10.2810i		−	1.20330i	−0.798760	−	0.601650i	$-0.794510\pi$
$73$		−	10.2810i		−	1.20330i	0.798760	−	0.601650i	$-0.205490\pi$
$74$	−2.76986			−0.321990
$75$		0			0
$76$	−1.16346			−0.133459
$77$			0.622216i			0.0709081i
$78$		0			0
$79$	14.2351			1.60157			0.800785	−	0.598952i	$-0.204416\pi$
$79$	14.2351			1.60157			0.800785	+	0.598952i	$0.204416\pi$
$80$	−5.91903	−	0.831613i	−0.661768	−	0.0929772i
$81$		0			0
$82$			3.70471i			0.409117i
$83$		−	9.52543i		−	1.04555i	−0.852470	−	0.522776i	$-0.824897\pi$
$83$		−	9.52543i		−	1.04555i	0.852470	−	0.522776i	$-0.175103\pi$
$84$		0			0
$85$	−2.00000	+	14.2351i	−0.216930	+	1.54401i
$86$	7.72546			0.833057
$87$		0			0
$88$			0.657249i			0.0700630i
$89$	−5.61285			−0.594961			−0.297480	−	0.954728i	$-0.596146\pi$
$89$	−5.61285			−0.594961			−0.297480	+	0.954728i	$0.596146\pi$
$90$		0			0
$91$	−2.90321			−0.304339
$92$		−	2.46367i		−	0.256856i
$93$		0			0
$94$	1.33185			0.137370
$95$	−4.90321	−	0.688892i	−0.503059	−	0.0706788i
$96$		0			0
$97$			18.0415i			1.83184i	0.401366	+	0.915918i	$0.368536\pi$
$97$			18.0415i			1.83184i	−0.401366	+	0.915918i	$0.631464\pi$
$98$			1.73483i			0.175244i
$99$		0			0
$100$	2.52543	+	0.723926i	0.252543	+	0.0723926i
$101$	−3.93978			−0.392022			−0.196011	−	0.980602i	$-0.562799\pi$
$101$	−3.93978			−0.392022			−0.196011	+	0.980602i	$0.562799\pi$
$102$		0			0
$103$			2.82225i			0.278084i	0.990286	+	0.139042i	$0.0444023\pi$
$103$			2.82225i			0.278084i	−0.990286	+	0.139042i	$0.955598\pi$
$104$	−3.06668			−0.300712
$105$		0			0
$106$	7.57136			0.735396
$107$			17.1175i			1.65481i	0.561603	+	0.827407i	$0.310185\pi$
$107$			17.1175i			1.65481i	−0.561603	+	0.827407i	$0.689815\pi$
$108$		0			0
$109$	16.7239			1.60186			0.800931	−	0.598757i	$-0.204338\pi$
$109$	16.7239			1.60186			0.800931	+	0.598757i	$0.204338\pi$
$110$	−0.0809666	+	0.576283i	−0.00771987	+	0.0549464i
$111$		0			0
$112$			7.76049i			0.733297i
$113$		−	1.18421i		−	0.111401i	−0.998448	−	0.0557005i	$-0.982261\pi$
$113$		−	1.18421i		−	0.111401i	0.998448	−	0.0557005i	$-0.0177392\pi$
$114$		0			0
$115$	1.45875	−	10.3827i	0.136029	−	0.968192i
$116$	4.57628			0.424897
$117$		0			0
$118$			11.2509i			1.03573i
$119$	18.6637			1.71090
$120$		0			0
$121$	−10.9541			−0.995824
$122$			0.341219i			0.0308925i
$123$		0			0
$124$	−2.93825			−0.263862
$125$	10.2143	+	4.54617i	0.913597	+	0.406622i
$126$		0			0
$127$		−	2.30174i		−	0.204246i	−0.994772	−	0.102123i	$-0.967436\pi$
$127$		−	2.30174i		−	0.204246i	0.994772	−	0.102123i	$-0.0325636\pi$
$128$			4.97481i			0.439715i
$129$		0			0
$130$	−2.68889	−	0.377784i	−0.235831	−	0.0331339i
$131$	13.4193			1.17245			0.586224	−	0.810149i	$-0.300614\pi$
$131$	13.4193			1.17245			0.586224	+	0.810149i	$0.300614\pi$
$132$		0			0
$133$			6.42864i			0.557434i
$134$	9.42372			0.814085
$135$		0			0
$136$	19.7146			1.69051
$137$			19.1526i			1.63631i	0.574995	+	0.818157i	$0.305004\pi$
$137$			19.1526i			1.63631i	−0.574995	+	0.818157i	$0.694996\pi$
$138$		0			0
$139$	−19.0923			−1.61939			−0.809696	−	0.586850i	$-0.800368\pi$
$139$	−19.0923			−1.61939			−0.809696	+	0.586850i	$0.800368\pi$
$140$	0.474572	−	3.37778i	0.0401087	−	0.285475i
$141$		0			0
$142$		−	7.38424i		−	0.619671i
$143$			0.214320i			0.0179223i
$144$		0			0
$145$	19.2859	+	2.70964i	1.60161	+	0.225023i
$146$	−12.4844			−1.03322
$147$		0			0
$148$		−	1.19850i		−	0.0985160i
$149$	−3.57136			−0.292577			−0.146289	−	0.989242i	$-0.546733\pi$
$149$	−3.57136			−0.292577			−0.146289	+	0.989242i	$0.546733\pi$
$150$		0			0
$151$	−1.26517			−0.102958			−0.0514792	−	0.998674i	$-0.516394\pi$
$151$	−1.26517			−0.102958			−0.0514792	+	0.998674i	$0.516394\pi$
$152$			6.79060i			0.550791i
$153$		0			0
$154$	0.755569			0.0608855
$155$	−12.3827	−	1.73975i	−0.994603	−	0.139740i
$156$		0			0
$157$			5.61285i			0.447954i	0.974594	+	0.223977i	$0.0719041\pi$
$157$			5.61285i			0.447954i	−0.974594	+	0.223977i	$0.928096\pi$
$158$		−	17.2859i		−	1.37519i
$159$		0			0
$160$	0.898290	−	6.39361i	0.0710160	−	0.505459i
$161$	−13.6128			−1.07284
$162$		0			0
$163$			3.71900i			0.291295i	0.989337	+	0.145647i	$0.0465265\pi$
$163$			3.71900i			0.291295i	−0.989337	+	0.145647i	$0.953473\pi$
$164$	−1.60300			−0.125174
$165$		0			0
$166$	−11.5669			−0.897767
$167$		−	7.03657i		−	0.544506i	−0.962226	−	0.272253i	$-0.912231\pi$
$167$		−	7.03657i		−	0.544506i	0.962226	−	0.272253i	$-0.0877687\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	17.2859	+	2.42864i	1.32577	+	0.186268i
$171$		0			0
$172$			3.34275i			0.254882i
$173$		−	0.723926i		−	0.0550391i	−0.999621	−	0.0275195i	$-0.991239\pi$
$173$		−	0.723926i		−	0.0550391i	0.999621	−	0.0275195i	$-0.00876085\pi$
$174$		0			0
$175$	4.00000	−	13.9541i	0.302372	−	1.05483i
$176$	0.572892			0.0431833
$177$		0			0
$178$			6.81579i			0.510865i
$179$	−4.04149			−0.302075			−0.151037	−	0.988528i	$-0.548261\pi$
$179$	−4.04149			−0.302075			−0.151037	+	0.988528i	$0.548261\pi$
$180$		0			0
$181$	2.34122			0.174021			0.0870107	−	0.996207i	$-0.472269\pi$
$181$	2.34122			0.174021			0.0870107	+	0.996207i	$0.472269\pi$
$182$			3.52543i			0.261322i
$183$		0			0
$184$	−14.3793			−1.06006
$185$	0.709636	−	5.05086i	0.0521735	−	0.371346i
$186$		0			0
$187$		−	1.37778i		−	0.100754i
$188$			0.576283i			0.0420297i
$189$		0			0
$190$	−0.836535	+	5.95407i	−0.0606887	+	0.431953i
$191$	2.10171			0.152074			0.0760372	−	0.997105i	$-0.475773\pi$
$191$	2.10171			0.152074			0.0760372	+	0.997105i	$0.475773\pi$
$192$		0			0
$193$			13.5210i			0.973262i	0.873608	+	0.486631i	$0.161774\pi$
$193$			13.5210i			0.973262i	−0.873608	+	0.486631i	$0.838226\pi$
$194$	21.9081			1.57291
$195$		0			0
$196$	−0.750647			−0.0536176
$197$			2.00000i			0.142494i	0.997459	+	0.0712470i	$0.0226979\pi$
$197$			2.00000i			0.142494i	−0.997459	+	0.0712470i	$0.977302\pi$
$198$		0			0
$199$	−22.1432			−1.56969			−0.784845	−	0.619692i	$-0.787257\pi$
$199$	−22.1432			−1.56969			−0.784845	+	0.619692i	$0.787257\pi$
$200$	4.22522	−	14.7397i	0.298768	−	1.04226i
$201$		0			0
$202$			4.78415i			0.336612i
$203$		−	25.2859i		−	1.77472i
$204$		0			0
$205$	−6.75557	−	0.949145i	−0.471829	−	0.0662912i
$206$	3.42711			0.238778
$207$		0			0
$208$			2.67307i			0.185344i
$209$	0.474572			0.0328269
$210$		0			0
$211$	19.6543			1.35306			0.676530	−	0.736415i	$-0.263483\pi$
$211$	19.6543			1.35306			0.676530	+	0.736415i	$0.263483\pi$
$212$			3.27607i			0.225002i
$213$		0			0
$214$	20.7862			1.42091
$215$	−1.97926	+	14.0874i	−0.134984	+	0.960754i
$216$		0			0
$217$			16.2351i			1.10211i
$218$		−	20.3082i		−	1.37544i
$219$		0			0
$220$	−0.249353	−	0.0350337i	−0.0168114	−	0.00236197i
$221$	6.42864			0.432437
$222$		0			0
$223$		−	19.6686i		−	1.31711i	−0.752533	−	0.658554i	$-0.771168\pi$
$223$		−	19.6686i		−	1.31711i	0.752533	−	0.658554i	$-0.228832\pi$
$224$	−8.38271			−0.560093
$225$		0			0
$226$	−1.43801			−0.0956548
$227$			13.2716i			0.880869i	0.897785	+	0.440434i	$0.145176\pi$
$227$			13.2716i			0.880869i	−0.897785	+	0.440434i	$0.854824\pi$
$228$		0			0
$229$	2.42864			0.160489			0.0802445	−	0.996775i	$-0.474430\pi$
$229$	2.42864			0.160489			0.0802445	+	0.996775i	$0.474430\pi$
$230$	−12.6079	−	1.77139i	−0.831342	−	0.116802i
$231$		0			0
$232$		−	26.7096i		−	1.75357i
$233$			16.1748i			1.05965i	0.848107	+	0.529825i	$0.177742\pi$
$233$			16.1748i			1.05965i	−0.848107	+	0.529825i	$0.822258\pi$
$234$		0			0
$235$	−0.341219	+	2.42864i	−0.0222587	+	0.158427i
$236$	−4.86818			−0.316891
$237$		0			0
$238$		−	22.6637i		−	1.46907i
$239$	−12.7763			−0.826431			−0.413215	−	0.910633i	$-0.635594\pi$
$239$	−12.7763			−0.826431			−0.413215	+	0.910633i	$0.635594\pi$
$240$		0			0
$241$	−5.89829			−0.379942			−0.189971	−	0.981790i	$-0.560839\pi$
$241$	−5.89829			−0.379942			−0.189971	+	0.981790i	$0.560839\pi$
$242$			13.3017i			0.855068i
$243$		0			0
$244$	−0.147643			−0.00945189
$245$	−3.16346	−	0.444461i	−0.202106	−	0.0283956i
$246$		0			0
$247$			2.21432i			0.140894i
$248$			17.1492i			1.08897i
$249$		0			0
$250$	5.52051	−	12.4035i	0.349147	−	0.784463i
$251$	2.07313			0.130855			0.0654274	−	0.997857i	$-0.479159\pi$
$251$	2.07313			0.130855			0.0654274	+	0.997857i	$0.479159\pi$
$252$		0			0
$253$			1.00492i			0.0631789i
$254$	−2.79505			−0.175377
$255$		0			0
$256$	−11.6637			−0.728981
$257$		−	18.3970i		−	1.14757i	−0.819005	−	0.573787i	$-0.805474\pi$
$257$		−	18.3970i		−	1.14757i	0.819005	−	0.573787i	$-0.194526\pi$
$258$		0			0
$259$	−6.62222			−0.411484
$260$	0.163465	−	1.16346i	0.0101376	−	0.0721550i
$261$		0			0
$262$		−	16.2953i		−	1.00673i
$263$			11.0257i			0.679872i	0.940449	+	0.339936i	$0.110405\pi$
$263$			11.0257i			0.679872i	−0.940449	+	0.339936i	$0.889595\pi$
$264$		0			0
$265$	−1.93978	+	13.8064i	−0.119160	+	0.848122i
$266$	7.80642			0.478643
$267$		0			0
$268$			4.07758i			0.249078i
$269$	−16.1432			−0.984268			−0.492134	−	0.870519i	$-0.663783\pi$
$269$	−16.1432			−0.984268			−0.492134	+	0.870519i	$0.663783\pi$
$270$		0			0
$271$	13.0114			0.790385			0.395192	−	0.918598i	$-0.370678\pi$
$271$	13.0114			0.790385			0.395192	+	0.918598i	$0.370678\pi$
$272$		−	17.1842i		−	1.04195i
$273$		0			0
$274$	23.2573			1.40503
$275$	−1.03011	−	0.295286i	−0.0621181	−	0.0178064i
$276$		0			0
$277$			7.57136i			0.454919i	0.973788	+	0.227459i	$0.0730419\pi$
$277$			7.57136i			0.454919i	−0.973788	+	0.227459i	$0.926958\pi$
$278$			23.1842i			1.39050i
$279$		0			0
$280$	−19.7146	−	2.76986i	−1.17817	−	0.165531i
$281$	−6.75557			−0.403003			−0.201502	−	0.979488i	$-0.564582\pi$
$281$	−6.75557			−0.403003			−0.201502	+	0.979488i	$0.564582\pi$
$282$		0			0
$283$		−	19.0859i		−	1.13454i	−0.823532	−	0.567269i	$-0.808000\pi$
$283$		−	19.0859i		−	1.13454i	0.823532	−	0.567269i	$-0.192000\pi$
$284$	3.19511			0.189595
$285$		0			0
$286$	0.260253			0.0153891
$287$			8.85728i			0.522829i
$288$		0			0
$289$	−24.3274			−1.43102
$290$	3.29036	−	23.4193i	0.193217	−	1.37523i
$291$		0			0
$292$		−	5.40192i		−	0.316123i
$293$		−	8.08742i		−	0.472472i	−0.971696	−	0.236236i	$-0.924086\pi$
$293$		−	8.08742i		−	0.472472i	0.971696	−	0.236236i	$-0.0759139\pi$
$294$		0			0
$295$	−20.5161	−	2.88247i	−1.19449	−	0.167824i
$296$	−6.99508			−0.406581
$297$		0			0
$298$			4.33677i			0.251223i
$299$	−4.68889			−0.271166
$300$		0			0
$301$	18.4701			1.06460
$302$			1.53633i			0.0884057i
$303$		0			0
$304$	5.91903			0.339480
$305$	−0.622216	−	0.0874201i	−0.0356280	−	0.00500566i
$306$		0			0
$307$		−	13.4336i		−	0.766694i	−0.923604	−	0.383347i	$-0.874771\pi$
$307$		−	13.4336i		−	0.766694i	0.923604	−	0.383347i	$-0.125229\pi$
$308$			0.326929i			0.0186285i
$309$		0			0
$310$	−2.11261	+	15.0366i	−0.119988	+	0.854020i
$311$	−20.2034			−1.14563			−0.572815	−	0.819684i	$-0.694149\pi$
$311$	−20.2034			−1.14563			−0.572815	+	0.819684i	$0.694149\pi$
$312$		0			0
$313$		−	15.1111i		−	0.854129i	−0.904221	−	0.427064i	$-0.859548\pi$
$313$		−	15.1111i		−	0.854129i	0.904221	−	0.427064i	$-0.140452\pi$
$314$	6.81579			0.384637
$315$		0			0
$316$	7.47949			0.420754
$317$		−	22.2810i		−	1.25143i	−0.780054	−	0.625713i	$-0.784808\pi$
$317$		−	22.2810i		−	1.25143i	0.780054	−	0.625713i	$-0.215192\pi$
$318$		0			0
$319$	−1.86665			−0.104512
$320$	−19.6019	−	2.75404i	−1.09578	−	0.153955i
$321$		0			0
$322$			16.5303i			0.921200i
$323$		−	14.2351i		−	0.792060i
$324$		0			0
$325$	1.37778	−	4.80642i	0.0764257	−	0.266612i
$326$	4.51606			0.250121
$327$		0			0
$328$			9.35599i			0.516598i
$329$	3.18421			0.175551
$330$		0			0
$331$	8.25581			0.453780			0.226890	−	0.973920i	$-0.427144\pi$
$331$	8.25581			0.453780			0.226890	+	0.973920i	$0.427144\pi$
$332$		−	5.00492i		−	0.274681i
$333$		0			0
$334$	−8.54464			−0.467542
$335$	−2.41435	+	17.1842i	−0.131910	+	0.938874i
$336$		0			0
$337$		−	13.7462i		−	0.748803i	−0.927267	−	0.374402i	$-0.877848\pi$
$337$		−	13.7462i		−	0.748803i	0.927267	−	0.374402i	$-0.122152\pi$
$338$			1.21432i			0.0660503i
$339$		0			0
$340$	−1.05086	+	7.47949i	−0.0569906	+	0.405633i
$341$	1.19850			0.0649023
$342$		0			0
$343$		−	16.1748i		−	0.873359i
$344$	19.5101			1.05191
$345$		0			0
$346$	−0.879077			−0.0472595
$347$		−	1.21924i		−	0.0654523i	−0.999464	−	0.0327262i	$-0.989581\pi$
$347$		−	1.21924i		−	0.0654523i	0.999464	−	0.0327262i	$-0.0104189\pi$
$348$		0			0
$349$	−22.5116			−1.20502			−0.602510	−	0.798112i	$-0.705832\pi$
$349$	−22.5116			−1.20502			−0.602510	+	0.798112i	$0.705832\pi$
$350$	−16.9447	−	4.85728i	−0.905732	−	0.259632i
$351$		0			0
$352$			0.618825i			0.0329835i
$353$		−	14.2810i		−	0.760101i	−0.924966	−	0.380050i	$-0.875907\pi$
$353$		−	14.2810i		−	0.760101i	0.924966	−	0.380050i	$-0.124093\pi$
$354$		0			0
$355$	13.4652	+	1.89184i	0.714659	+	0.100408i
$356$	−2.94914			−0.156304
$357$		0			0
$358$			4.90766i			0.259378i
$359$	−12.1541			−0.641469			−0.320734	−	0.947169i	$-0.603930\pi$
$359$	−12.1541			−0.641469			−0.320734	+	0.947169i	$0.603930\pi$
$360$		0			0
$361$	−14.0968			−0.741936
$362$		−	2.84299i		−	0.149424i
$363$		0			0
$364$	−1.52543			−0.0799541
$365$	3.19850	−	22.7654i	0.167417	−	1.19160i
$366$		0			0
$367$		−	4.65725i		−	0.243106i	−0.992585	−	0.121553i	$-0.961212\pi$
$367$		−	4.65725i		−	0.243106i	0.992585	−	0.121553i	$-0.0387875\pi$
$368$			12.5337i			0.653366i
$369$		0			0
$370$	−6.13335	−	0.861725i	−0.318858	−	0.0447989i
$371$	18.1017			0.939794
$372$		0			0
$373$		−	34.9403i		−	1.80914i	−0.426328	−	0.904569i	$-0.640193\pi$
$373$		−	34.9403i		−	1.80914i	0.426328	−	0.904569i	$-0.359807\pi$
$374$	−1.67307			−0.0865124
$375$		0			0
$376$	3.36349			0.173459
$377$		−	8.70964i		−	0.448569i
$378$		0			0
$379$	17.4717			0.897459			0.448729	−	0.893668i	$-0.351877\pi$
$379$	17.4717			0.897459			0.448729	+	0.893668i	$0.351877\pi$
$380$	−2.57628	−	0.361963i	−0.132161	−	0.0185683i
$381$		0			0
$382$		−	2.55215i		−	0.130579i
$383$		−	18.6780i		−	0.954401i	−0.878794	−	0.477200i	$-0.841652\pi$
$383$		−	18.6780i		−	0.954401i	0.878794	−	0.477200i	$-0.158348\pi$
$384$		0			0
$385$	−0.193576	+	1.37778i	−0.00986555	+	0.0702184i
$386$	16.4188			0.835695
$387$		0			0
$388$			9.47949i			0.481248i
$389$	1.61285			0.0817746			0.0408873	−	0.999164i	$-0.486982\pi$
$389$	1.61285			0.0817746			0.0408873	+	0.999164i	$0.486982\pi$
$390$		0			0
$391$	30.1432			1.52441
$392$			4.38118i			0.221283i
$393$		0			0
$394$	2.42864			0.122353
$395$	31.5210	+	4.42864i	1.58599	+	0.222829i
$396$		0			0
$397$			6.57628i			0.330054i	0.986289	+	0.165027i	$0.0527712\pi$
$397$			6.57628i			0.330054i	−0.986289	+	0.165027i	$0.947229\pi$
$398$			26.8889i			1.34782i
$399$		0			0
$400$	−12.8479	−	3.68292i	−0.642396	−	0.184146i
$401$	21.9081			1.09404			0.547020	−	0.837120i	$-0.315762\pi$
$401$	21.9081			1.09404			0.547020	+	0.837120i	$0.315762\pi$
$402$		0			0
$403$			5.59210i			0.278563i
$404$	−2.07007			−0.102990
$405$		0			0
$406$	−30.7052			−1.52387
$407$			0.488863i			0.0242320i
$408$		0			0
$409$	10.1936			0.504040			0.252020	−	0.967722i	$-0.418905\pi$
$409$	10.1936			0.504040			0.252020	+	0.967722i	$0.418905\pi$
$410$	−1.15257	+	8.20342i	−0.0569211	+	0.405138i
$411$		0			0
$412$			1.48289i			0.0730565i
$413$			26.8988i			1.32360i
$414$		0			0
$415$	2.96343	−	21.0923i	0.145469	−	1.03538i
$416$	−2.88739			−0.141566
$417$		0			0
$418$		−	0.576283i		−	0.0281869i
$419$	7.31756			0.357486			0.178743	−	0.983896i	$-0.442797\pi$
$419$	7.31756			0.357486			0.178743	+	0.983896i	$0.442797\pi$
$420$		0			0
$421$	−7.86665			−0.383397			−0.191698	−	0.981454i	$-0.561400\pi$
$421$	−7.86665			−0.383397			−0.191698	+	0.981454i	$0.561400\pi$
$422$		−	23.8666i		−	1.16181i
$423$		0			0
$424$	19.1209			0.928594
$425$	−8.85728	+	30.8988i	−0.429641	+	1.49881i
$426$		0			0
$427$			0.815792i			0.0394789i
$428$			8.99402i			0.434743i
$429$		0			0
$430$	17.1066	+	2.40345i	0.824955	+	0.115905i
$431$	38.9195			1.87469			0.937343	−	0.348407i	$-0.113277\pi$
$431$	38.9195			1.87469			0.937343	+	0.348407i	$0.113277\pi$
$432$		0			0
$433$			20.2034i			0.970914i	0.874260	+	0.485457i	$0.161347\pi$
$433$			20.2034i			0.970914i	−0.874260	+	0.485457i	$0.838653\pi$
$434$	19.7146			0.946329
$435$		0			0
$436$	8.78721			0.420831
$437$			10.3827i			0.496672i
$438$		0			0
$439$	−10.8889			−0.519700			−0.259850	−	0.965649i	$-0.583673\pi$
$439$	−10.8889			−0.519700			−0.259850	+	0.965649i	$0.583673\pi$
$440$	−0.204475	+	1.45536i	−0.00974798	+	0.0693816i
$441$		0			0
$442$		−	7.80642i		−	0.371314i
$443$		−	28.6287i		−	1.36019i	−0.733124	−	0.680095i	$-0.761939\pi$
$443$		−	28.6287i		−	1.36019i	0.733124	−	0.680095i	$-0.238061\pi$
$444$		0			0
$445$	−12.4286	−	1.74620i	−0.589174	−	0.0827779i
$446$	−23.8840			−1.13094
$447$		0			0
$448$			25.7003i			1.21422i
$449$	−10.9304			−0.515838			−0.257919	−	0.966167i	$-0.583037\pi$
$449$	−10.9304			−0.515838			−0.257919	+	0.966167i	$0.583037\pi$
$450$		0			0
$451$	0.653858			0.0307890
$452$		−	0.622216i		−	0.0292666i
$453$		0			0
$454$	16.1160			0.756361
$455$	−6.42864	−	0.903212i	−0.301379	−	0.0423432i
$456$		0			0
$457$		−	11.4064i		−	0.533567i	−0.963756	−	0.266784i	$-0.914039\pi$
$457$		−	11.4064i		−	0.533567i	0.963756	−	0.266784i	$-0.0859609\pi$
$458$		−	2.94914i		−	0.137804i
$459$		0			0
$460$	0.766468	−	5.45536i	0.0357368	−	0.254357i
$461$	26.1334			1.21715			0.608576	−	0.793496i	$-0.291741\pi$
$461$	26.1334			1.21715			0.608576	+	0.793496i	$0.291741\pi$
$462$		0			0
$463$			7.92242i			0.368186i	0.982909	+	0.184093i	$0.0589348\pi$
$463$			7.92242i			0.368186i	−0.982909	+	0.184093i	$0.941065\pi$
$464$	−23.2815			−1.08082
$465$		0			0
$466$	19.6414			0.909872
$467$		−	10.8923i		−	0.504036i	−0.967723	−	0.252018i	$-0.918906\pi$
$467$		−	10.8923i		−	0.504036i	0.967723	−	0.252018i	$-0.0810942\pi$
$468$		0			0
$469$	22.5303			1.04035
$470$	2.94914	+	0.414349i	0.136034	+	0.0191125i
$471$		0			0
$472$			28.4133i			1.30783i
$473$		−	1.36349i		−	0.0626935i
$474$		0			0
$475$	−10.6430	−	3.05086i	−0.488332	−	0.139983i
$476$	9.80642			0.449477
$477$		0			0
$478$			15.5145i			0.709618i
$479$	−9.13182			−0.417244			−0.208622	−	0.977996i	$-0.566898\pi$
$479$	−9.13182			−0.417244			−0.208622	+	0.977996i	$0.566898\pi$
$480$		0			0
$481$	−2.28100			−0.104004
$482$			7.16241i			0.326239i
$483$		0			0
$484$	−5.75557			−0.261617
$485$	−5.61285	+	39.9496i	−0.254866	+	1.81402i
$486$		0			0
$487$		−	16.1891i		−	0.733600i	−0.930300	−	0.366800i	$-0.880453\pi$
$487$		−	16.1891i		−	0.733600i	0.930300	−	0.366800i	$-0.119547\pi$
$488$			0.861725i			0.0390084i
$489$		0			0
$490$	−0.539718	+	3.84146i	−0.0243820	+	0.173539i
$491$	−26.2636			−1.18526			−0.592631	−	0.805474i	$-0.701911\pi$
$491$	−26.2636			−1.18526			−0.592631	+	0.805474i	$0.701911\pi$
$492$		0			0
$493$			55.9911i			2.52171i
$494$	2.68889			0.120979
$495$		0			0
$496$	14.9481			0.671189
$497$		−	17.6543i		−	0.791905i
$498$		0			0
$499$	−30.0306			−1.34435			−0.672177	−	0.740391i	$-0.734641\pi$
$499$	−30.0306			−1.34435			−0.672177	+	0.740391i	$0.734641\pi$
$500$	5.36689	+	2.38868i	0.240014	+	0.106825i
$501$		0			0
$502$		−	2.51744i		−	0.112359i
$503$		−	16.7304i		−	0.745971i	−0.927837	−	0.372985i	$-0.878334\pi$
$503$		−	16.7304i		−	0.745971i	0.927837	−	0.372985i	$-0.121666\pi$
$504$		0			0
$505$	−8.72393	−	1.22570i	−0.388210	−	0.0545427i
$506$	1.22030			0.0542488
$507$		0			0
$508$		−	1.20940i		−	0.0536583i
$509$	−11.9684			−0.530488			−0.265244	−	0.964181i	$-0.585453\pi$
$509$	−11.9684			−0.530488			−0.265244	+	0.964181i	$0.585453\pi$
$510$		0			0
$511$	−29.8479			−1.32039
$512$			24.1131i			1.06566i
$513$		0			0
$514$	−22.3398			−0.985368
$515$	−0.878023	+	6.24935i	−0.0386903	+	0.275379i
$516$		0			0
$517$		−	0.235063i		−	0.0103381i
$518$			8.04149i			0.353323i
$519$		0			0
$520$	−6.79060	−	0.954067i	−0.297788	−	0.0418386i
$521$	−5.75065			−0.251940			−0.125970	−	0.992034i	$-0.540204\pi$
$521$	−5.75065			−0.251940			−0.125970	+	0.992034i	$0.540204\pi$
$522$		0			0
$523$			20.8035i			0.909674i	0.890575	+	0.454837i	$0.150302\pi$
$523$			20.8035i			0.909674i	−0.890575	+	0.454837i	$0.849698\pi$
$524$	7.05086			0.308018
$525$		0			0
$526$	13.3887			0.583774
$527$		−	35.9496i		−	1.56599i
$528$		0			0
$529$	1.01429			0.0440996
$530$	16.7654	+	2.35551i	0.728243	+	0.102317i
$531$		0			0
$532$			3.37778i			0.146446i
$533$			3.05086i			0.132147i
$534$		0			0
$535$	−5.32540	+	37.9037i	−0.230237	+	1.63872i
$536$	23.7989			1.02796
$537$		0			0
$538$			19.6030i			0.845145i
$539$	0.306186			0.0131883
$540$		0			0
$541$	16.6222			0.714645			0.357322	−	0.933981i	$-0.383690\pi$
$541$	16.6222			0.714645			0.357322	+	0.933981i	$0.383690\pi$
$542$		−	15.8000i		−	0.678667i
$543$		0			0
$544$	18.5620			0.795839
$545$	37.0321	+	5.20294i	1.58628	+	0.222870i
$546$		0			0
$547$		−	29.9748i		−	1.28163i	−0.767695	−	0.640815i	$-0.778596\pi$
$547$		−	29.9748i		−	1.28163i	0.767695	−	0.640815i	$-0.221404\pi$
$548$			10.0633i			0.429882i
$549$		0			0
$550$	−0.358572	+	1.25088i	−0.0152896	+	0.0533379i
$551$	−19.2859			−0.821608
$552$		0			0
$553$		−	41.3274i		−	1.75742i
$554$	9.19405			0.390618
$555$		0			0
$556$	−10.0316			−0.425436
$557$			5.03657i			0.213406i	0.994291	+	0.106703i	$0.0340294\pi$
$557$			5.03657i			0.213406i	−0.994291	+	0.106703i	$0.965971\pi$
$558$		0			0
$559$	6.36196			0.269082
$560$	−2.41435	+	17.1842i	−0.102025	+	0.726165i
$561$		0			0
$562$			8.20342i			0.346040i
$563$			2.88247i			0.121482i	0.998154	+	0.0607408i	$0.0193463\pi$
$563$			2.88247i			0.121482i	−0.998154	+	0.0607408i	$0.980654\pi$
$564$		0			0
$565$	0.368416	−	2.62222i	0.0154994	−	0.110317i
$566$	−23.1764			−0.974176
$567$		0			0
$568$		−	18.6484i		−	0.782468i
$569$	−4.37286			−0.183320			−0.0916600	−	0.995790i	$-0.529217\pi$
$569$	−4.37286			−0.183320			−0.0916600	+	0.995790i	$0.529217\pi$
$570$		0			0
$571$	−1.58120			−0.0661714			−0.0330857	−	0.999453i	$-0.510533\pi$
$571$	−1.58120			−0.0661714			−0.0330857	+	0.999453i	$0.510533\pi$
$572$			0.112610i			0.00470844i
$573$		0			0
$574$	10.7556			0.448929
$575$	6.46028	−	22.5368i	0.269412	−	0.939850i
$576$		0			0
$577$		−	7.61729i		−	0.317112i	−0.987350	−	0.158556i	$-0.949316\pi$
$577$		−	7.61729i		−	0.317112i	0.987350	−	0.158556i	$-0.0506839\pi$
$578$			29.5412i			1.22875i
$579$		0			0
$580$	10.1334	+	1.42372i	0.420765	+	0.0591166i
$581$	−27.6543			−1.14730
$582$		0			0
$583$		−	1.33630i		−	0.0553438i
$584$	−31.5285			−1.30466
$585$		0			0
$586$	−9.82071			−0.405690
$587$			46.8243i			1.93264i	0.257336	+	0.966322i	$0.417155\pi$
$587$			46.8243i			1.93264i	−0.257336	+	0.966322i	$0.582845\pi$
$588$		0			0
$589$	12.3827			0.510221
$590$	−3.50024	+	24.9131i	−0.144103	+	1.02565i
$591$		0			0
$592$			6.09726i			0.250596i
$593$		−	15.9398i		−	0.654568i	−0.944926	−	0.327284i	$-0.893867\pi$
$593$		−	15.9398i		−	0.654568i	0.944926	−	0.327284i	$-0.106133\pi$
$594$		0			0
$595$	41.3274	+	5.80642i	1.69426	+	0.238040i
$596$	−1.87649			−0.0768641
$597$		0			0
$598$			5.69381i			0.232837i
$599$	18.4889			0.755434			0.377717	−	0.925921i	$-0.376709\pi$
$599$	18.4889			0.755434			0.377717	+	0.925921i	$0.376709\pi$
$600$		0			0
$601$	20.7556			0.846637			0.423319	−	0.905981i	$-0.360865\pi$
$601$	20.7556			0.846637			0.423319	+	0.905981i	$0.360865\pi$
$602$		−	22.4286i		−	0.914123i
$603$		0			0
$604$	−0.664758			−0.0270486
$605$	−24.2558	−	3.40790i	−0.986139	−	0.138551i
$606$		0			0
$607$			36.0765i			1.46430i	0.681143	+	0.732150i	$0.261483\pi$
$607$			36.0765i			1.46430i	−0.681143	+	0.732150i	$0.738517\pi$
$608$			6.39361i			0.259295i
$609$		0			0
$610$	−0.106156	+	0.755569i	−0.00429813	+	0.0305921i
$611$	1.09679			0.0443713
$612$		0			0
$613$		−	9.94962i		−	0.401861i	−0.979605	−	0.200931i	$-0.935603\pi$
$613$		−	9.94962i		−	0.401861i	0.979605	−	0.200931i	$-0.0643966\pi$
$614$	−16.3126			−0.658325
$615$		0			0
$616$	1.90813			0.0768809
$617$		−	2.09187i		−	0.0842154i	−0.999113	−	0.0421077i	$-0.986593\pi$
$617$		−	2.09187i		−	0.0842154i	0.999113	−	0.0421077i	$-0.0134073\pi$
$618$		0			0
$619$	−18.4681			−0.742296			−0.371148	−	0.928574i	$-0.621036\pi$
$619$	−18.4681			−0.742296			−0.371148	+	0.928574i	$0.621036\pi$
$620$	−6.50622	−	0.914111i	−0.261296	−	0.0367116i
$621$		0			0
$622$			24.5334i			0.983700i
$623$			16.2953i			0.652857i
$624$		0			0
$625$	21.2034	+	13.2444i	0.848137	+	0.529777i
$626$	−18.3497			−0.733401
$627$		0			0
$628$			2.94914i			0.117684i
$629$	14.6637			0.584680
$630$		0			0
$631$	−38.6657			−1.53926			−0.769629	−	0.638492i	$-0.779559\pi$
$631$	−38.6657			−1.53926			−0.769629	+	0.638492i	$0.779559\pi$
$632$		−	43.6543i		−	1.73648i
$633$		0			0
$634$	−27.0563			−1.07454
$635$	0.716089	−	5.09679i	0.0284171	−	0.202260i
$636$		0			0
$637$			1.42864i			0.0566048i
$638$			2.26671i			0.0897398i
$639$		0			0
$640$	−1.54770	+	11.0158i	−0.0611783	+	0.435439i
$641$	−24.5718			−0.970529			−0.485265	−	0.874367i	$-0.661277\pi$
$641$	−24.5718			−0.970529			−0.485265	+	0.874367i	$0.661277\pi$
$642$		0			0
$643$		−	27.4938i		−	1.08425i	−0.840298	−	0.542125i	$-0.817620\pi$
$643$		−	27.4938i		−	1.08425i	0.840298	−	0.542125i	$-0.182380\pi$
$644$	−7.15257			−0.281851
$645$		0			0
$646$	−17.2859			−0.680105
$647$		−	13.7812i		−	0.541796i	−0.962608	−	0.270898i	$-0.912679\pi$
$647$		−	13.7812i		−	0.541796i	0.962608	−	0.270898i	$-0.0873207\pi$
$648$		0			0
$649$	1.98571			0.0779459
$650$	−5.83654	−	1.67307i	−0.228928	−	0.0656232i
$651$		0			0
$652$			1.95407i			0.0765272i
$653$		−	2.12045i		−	0.0829795i	−0.999139	−	0.0414897i	$-0.986790\pi$
$653$		−	2.12045i		−	0.0829795i	0.999139	−	0.0414897i	$-0.0132104\pi$
$654$		0			0
$655$	29.7146	+	4.17484i	1.16104	+	0.163125i
$656$	8.15515			0.318405
$657$		0			0
$658$		−	3.86665i		−	0.150738i
$659$	33.8894			1.32014			0.660072	−	0.751203i	$-0.270526\pi$
$659$	33.8894			1.32014			0.660072	+	0.751203i	$0.270526\pi$
$660$		0			0
$661$	−37.3689			−1.45348			−0.726741	−	0.686912i	$-0.758966\pi$
$661$	−37.3689			−1.45348			−0.726741	+	0.686912i	$0.758966\pi$
$662$		−	10.0252i		−	0.389640i
$663$		0			0
$664$	−29.2114			−1.13362
$665$	−2.00000	+	14.2351i	−0.0775567	+	0.552012i
$666$		0			0
$667$		−	40.8385i		−	1.58127i
$668$		−	3.69721i		−	0.143049i
$669$		0			0
$670$	20.8671	+	2.93179i	0.806167	+	0.113265i
$671$	0.0602231			0.00232489
$672$		0			0
$673$			35.4608i			1.36691i	0.729992	+	0.683456i	$0.239524\pi$
$673$			35.4608i			1.36691i	−0.729992	+	0.683456i	$0.760476\pi$
$674$	−16.6923			−0.642963
$675$		0			0
$676$	−0.525428			−0.0202088
$677$		−	15.3047i		−	0.588206i	−0.955774	−	0.294103i	$-0.904979\pi$
$677$		−	15.3047i		−	0.588206i	0.955774	−	0.294103i	$-0.0950208\pi$
$678$		0			0
$679$	52.3783			2.01009
$680$	43.6543	+	6.13335i	1.67407	+	0.235203i
$681$		0			0
$682$		−	1.45536i		−	0.0557286i
$683$		−	13.0968i		−	0.501135i	−0.968099	−	0.250567i	$-0.919383\pi$
$683$		−	13.0968i		−	0.501135i	0.968099	−	0.250567i	$-0.0806171\pi$
$684$		0			0
$685$	−5.95851	+	42.4099i	−0.227663	+	1.62040i
$686$	−19.6414			−0.749913
$687$		0			0
$688$		−	17.0060i		−	0.648347i
$689$	6.23506			0.237537
$690$		0			0
$691$	−18.4079			−0.700269			−0.350135	−	0.936699i	$-0.613864\pi$
$691$	−18.4079			−0.700269			−0.350135	+	0.936699i	$0.613864\pi$
$692$		−	0.380371i		−	0.0144595i
$693$		0			0
$694$	−1.48055			−0.0562009
$695$	−42.2766	−	5.93978i	−1.60364	−	0.225309i
$696$		0			0
$697$		−	19.6128i		−	0.742890i
$698$			27.3363i			1.03469i
$699$		0			0
$700$	2.10171	−	7.33185i	0.0794372	−	0.277118i
$701$	31.3689			1.18479			0.592393	−	0.805649i	$-0.298183\pi$
$701$	31.3689			1.18479			0.592393	+	0.805649i	$0.298183\pi$
$702$		0			0
$703$			5.05086i			0.190497i
$704$	1.89723			0.0715047
$705$		0			0
$706$	−17.3417			−0.652663
$707$			11.4380i			0.430171i
$708$		0			0
$709$	−9.47949			−0.356010			−0.178005	−	0.984030i	$-0.556964\pi$
$709$	−9.47949			−0.356010			−0.178005	+	0.984030i	$0.556964\pi$
$710$	2.29729	−	16.3511i	0.0862159	−	0.613644i
$711$		0			0
$712$			17.2128i			0.645077i
$713$			26.2208i			0.981976i
$714$		0			0
$715$	−0.0666765	+	0.474572i	−0.00249356	+	0.0177480i
$716$	−2.12351			−0.0793592
$717$		0			0
$718$			14.7590i			0.550799i
$719$	−29.6227			−1.10474			−0.552370	−	0.833599i	$-0.686276\pi$
$719$	−29.6227			−1.10474			−0.552370	+	0.833599i	$0.686276\pi$
$720$		0			0
$721$	8.19358			0.305145
$722$			17.1180i			0.637066i
$723$		0			0
$724$	1.23014			0.0457178
$725$	41.8622	+	12.0000i	1.55472	+	0.445669i
$726$		0			0
$727$			42.6702i			1.58255i	0.611461	+	0.791274i	$0.290582\pi$
$727$			42.6702i			1.58255i	−0.611461	+	0.791274i	$0.709418\pi$
$728$			8.90321i			0.329975i
$729$		0			0
$730$	−27.6445	−	3.88400i	−1.02317	−	0.143753i
$731$	−40.8988			−1.51270
$732$		0			0
$733$		−	26.0830i		−	0.963397i	−0.876337	−	0.481698i	$-0.840020\pi$
$733$		−	26.0830i		−	0.963397i	0.876337	−	0.481698i	$-0.159980\pi$
$734$	−5.65539			−0.208744
$735$		0			0
$736$	−13.5387			−0.499042
$737$		−	1.66323i		−	0.0612657i
$738$		0			0
$739$	28.2687			1.03988			0.519941	−	0.854202i	$-0.325954\pi$
$739$	28.2687			1.03988			0.519941	+	0.854202i	$0.325954\pi$
$740$	0.372862	−	2.65386i	0.0137067	−	0.0975578i
$741$		0			0
$742$		−	21.9813i		−	0.806958i
$743$			20.6681i			0.758241i	0.925347	+	0.379120i	$0.123773\pi$
$743$			20.6681i			0.758241i	−0.925347	+	0.379120i	$0.876227\pi$
$744$		0			0
$745$	−7.90813	−	1.11108i	−0.289732	−	0.0407068i
$746$	−42.4286			−1.55342
$747$		0			0
$748$		−	0.723926i		−	0.0264694i
$749$	49.6958			1.81585
$750$		0			0
$751$	2.46028			0.0897770			0.0448885	−	0.998992i	$-0.485707\pi$
$751$	2.46028			0.0897770			0.0448885	+	0.998992i	$0.485707\pi$
$752$		−	2.93179i		−	0.106911i
$753$		0			0
$754$	−10.5763			−0.385165
$755$	−2.80150	−	0.393606i	−0.101957	−	0.0143248i
$756$		0			0
$757$		−	48.6035i		−	1.76652i	−0.468880	−	0.883262i	$-0.655342\pi$
$757$		−	48.6035i		−	1.76652i	0.468880	−	0.883262i	$-0.344658\pi$
$758$		−	21.2162i		−	0.770606i
$759$		0			0
$760$	−2.11261	+	15.0366i	−0.0766324	+	0.545434i
$761$	13.8252			0.501162			0.250581	−	0.968096i	$-0.419378\pi$
$761$	13.8252			0.501162			0.250581	+	0.968096i	$0.419378\pi$
$762$		0			0
$763$		−	48.5531i		−	1.75774i
$764$	1.10430			0.0399520
$765$		0			0
$766$	−22.6811			−0.819500
$767$			9.26517i			0.334546i
$768$		0			0
$769$	38.9688			1.40525			0.702626	−	0.711559i	$-0.252011\pi$
$769$	38.9688			1.40525			0.702626	+	0.711559i	$0.252011\pi$
$770$	1.67307	+	0.235063i	0.0602933	+	0.00847109i
$771$		0			0
$772$			7.10430i			0.255689i
$773$		−	0.445992i		−	0.0160412i	−0.999968	−	0.00802061i	$-0.997447\pi$
$773$		−	0.445992i		−	0.0160412i	0.999968	−	0.00802061i	$-0.00255307\pi$
$774$		0			0
$775$	−26.8780	−	7.70471i	−0.965487	−	0.276761i
$776$	55.3274			1.98614
$777$		0			0
$778$		−	1.95851i		−	0.0702161i
$779$	6.75557			0.242043
$780$		0			0
$781$	−1.30327			−0.0466347
$782$		−	36.6035i		−	1.30894i
$783$		0			0
$784$	3.81885			0.136388
$785$	−1.74620	+	12.4286i	−0.0623246	+	0.443597i
$786$		0			0
$787$		−	33.9037i		−	1.20854i	−0.796781	−	0.604268i	$-0.793466\pi$
$787$		−	33.9037i		−	1.20854i	0.796781	−	0.604268i	$-0.206534\pi$
$788$			1.05086i			0.0374352i
$789$		0			0
$790$	5.37778	−	38.2766i	0.191333	−	1.36182i
$791$	−3.43801			−0.122241
$792$		0			0
$793$			0.280996i			0.00997847i
$794$	7.98571			0.283402
$795$		0			0
$796$	−11.6346			−0.412379
$797$		−	10.2953i		−	0.364678i	−0.983236	−	0.182339i	$-0.941633\pi$
$797$		−	10.2953i		−	0.364678i	0.983236	−	0.182339i	$-0.0583668\pi$
$798$		0			0
$799$	−7.05086			−0.249441
$800$	3.97820	−	13.8780i	0.140651	−	0.490662i
$801$		0			0
$802$		−	26.6035i		−	0.939402i
$803$			2.20342i			0.0777570i
$804$		0			0
$805$	−30.1432	−	4.23506i	−1.06241	−	0.149266i
$806$	6.79060			0.239189
$807$		0			0
$808$			12.0820i			0.425044i
$809$	7.94422			0.279304			0.139652	−	0.990201i	$-0.455402\pi$
$809$	7.94422			0.279304			0.139652	+	0.990201i	$0.455402\pi$
$810$		0			0
$811$	−8.12245			−0.285218			−0.142609	−	0.989779i	$-0.545549\pi$
$811$	−8.12245			−0.285218			−0.142609	+	0.989779i	$0.545549\pi$
$812$		−	13.2859i		−	0.466244i
$813$		0			0
$814$	0.593635			0.0208069
$815$	−1.15701	+	8.23506i	−0.0405283	+	0.288462i
$816$		0			0
$817$		−	14.0874i		−	0.492856i
$818$		−	12.3783i		−	0.432796i
$819$		0			0
$820$	−3.54956	−	0.498707i	−0.123956	−	0.0174156i
$821$	22.2065			0.775012			0.387506	−	0.921867i	$-0.373337\pi$
$821$	22.2065			0.775012			0.387506	+	0.921867i	$0.373337\pi$
$822$		0			0
$823$			11.1175i			0.387533i	0.981048	+	0.193766i	$0.0620704\pi$
$823$			11.1175i			0.387533i	−0.981048	+	0.193766i	$0.937930\pi$
$824$	8.65491			0.301508
$825$		0			0
$826$	32.6637			1.13652
$827$			23.1570i			0.805248i	0.915365	+	0.402624i	$0.131902\pi$
$827$			23.1570i			0.805248i	−0.915365	+	0.402624i	$0.868098\pi$
$828$		0			0
$829$	27.1195			0.941901			0.470950	−	0.882160i	$-0.343911\pi$
$829$	27.1195			0.941901			0.470950	+	0.882160i	$0.343911\pi$
$830$	−25.6128	−	3.59856i	−0.889035	−	0.124908i
$831$		0			0
$832$			8.85236i			0.306900i
$833$		−	9.18421i		−	0.318214i
$834$		0			0
$835$	2.18913	−	15.5812i	0.0757580	−	0.539210i
$836$	0.249353			0.00862407
$837$		0			0
$838$		−	8.88586i		−	0.306957i
$839$	25.3955			0.876749			0.438374	−	0.898792i	$-0.355554\pi$
$839$	25.3955			0.876749			0.438374	+	0.898792i	$0.355554\pi$
$840$		0			0
$841$	46.8578			1.61578
$842$			9.55262i			0.329205i
$843$		0			0
$844$	10.3269			0.355468
$845$	−2.21432	−	0.311108i	−0.0761749	−	0.0107024i
$846$		0			0
$847$			31.8020i			1.09273i
$848$		−	16.6668i		−	0.572339i
$849$		0			0
$850$	37.5210	+	10.7556i	1.28696	+	0.368913i
$851$	−10.6953			−0.366632
$852$		0			0
$853$			25.0651i			0.858214i	0.903254	+	0.429107i	$0.141172\pi$
$853$			25.0651i			0.858214i	−0.903254	+	0.429107i	$0.858828\pi$
$854$	0.990632			0.0338987
$855$		0			0
$856$	52.4939			1.79421
$857$			7.61285i			0.260050i	0.991511	+	0.130025i	$0.0415057\pi$
$857$			7.61285i			0.260050i	−0.991511	+	0.130025i	$0.958494\pi$
$858$		0			0
$859$	−42.1432			−1.43791			−0.718954	−	0.695058i	$-0.755379\pi$
$859$	−42.1432			−1.43791			−0.718954	+	0.695058i	$0.755379\pi$
$860$	−1.03996	+	7.40192i	−0.0354622	+	0.252403i
$861$		0			0
$862$		−	47.2607i		−	1.60971i
$863$		−	51.5768i		−	1.75569i	−0.478942	−	0.877847i	$-0.658980\pi$
$863$		−	51.5768i		−	1.75569i	0.478942	−	0.877847i	$-0.341020\pi$
$864$		0			0
$865$	0.225219	−	1.60300i	0.00765768	−	0.0545037i
$866$	24.5334			0.833679
$867$		0			0
$868$			8.53035i			0.289539i
$869$	−3.05086			−0.103493
$870$		0			0
$871$	7.76049			0.262954
$872$		−	51.2869i		−	1.73679i
$873$		0			0
$874$	12.6079			0.426469
$875$	13.1985	−	29.6543i	0.446191	−	1.00250i
$876$		0			0
$877$			34.0701i			1.15046i	0.817990	+	0.575232i	$0.195088\pi$
$877$			34.0701i			1.15046i	−0.817990	+	0.575232i	$0.804912\pi$
$878$			13.2226i			0.446242i
$879$		0			0
$880$	1.26857	+	0.178231i	0.0427633	+	0.00600817i
$881$	−3.71900			−0.125296			−0.0626482	−	0.998036i	$-0.519955\pi$
$881$	−3.71900			−0.125296			−0.0626482	+	0.998036i	$0.519955\pi$
$882$		0			0
$883$		−	42.0163i		−	1.41396i	−0.707233	−	0.706981i	$-0.750057\pi$
$883$		−	42.0163i		−	1.41396i	0.707233	−	0.706981i	$-0.249943\pi$
$884$	3.37778			0.113607
$885$		0			0
$886$	−34.7644			−1.16793
$887$		−	40.3116i		−	1.35353i	−0.736199	−	0.676765i	$-0.763381\pi$
$887$		−	40.3116i		−	1.35353i	0.736199	−	0.676765i	$-0.236619\pi$
$888$		0			0
$889$	−6.68244			−0.224122
$890$	−2.12045	+	15.0923i	−0.0710775	+	0.505896i
$891$		0			0
$892$		−	10.3344i		−	0.346023i
$893$		−	2.42864i		−	0.0812713i
$894$		0			0
$895$	−8.94914	−	1.25734i	−0.299137	−	0.0420282i
$896$	14.4429			0.482504
$897$		0			0
$898$			13.2730i			0.442926i
$899$	−48.7052			−1.62441
$900$		0			0
$901$	−40.0830			−1.33536
$902$		−	0.793993i		−	0.0264371i
$903$		0			0
$904$	−3.63158			−0.120785
$905$	5.18421	+	0.728372i	0.172329	+	0.0242119i
$906$		0			0
$907$		−	34.8419i		−	1.15691i	−0.815715	−	0.578454i	$-0.803656\pi$
$907$		−	34.8419i		−	1.15691i	0.815715	−	0.578454i	$-0.196344\pi$
$908$			6.97328i			0.231416i
$909$		0			0
$910$	−1.09679	+	7.80642i	−0.0363582	+	0.258780i
$911$	−23.2672			−0.770876			−0.385438	−	0.922734i	$-0.625950\pi$
$911$	−23.2672			−0.770876			−0.385438	+	0.922734i	$0.625950\pi$
$912$		0			0
$913$			2.04149i			0.0675634i
$914$	−13.8510			−0.458149
$915$		0			0
$916$	1.27607			0.0421627
$917$		−	38.9590i		−	1.28654i
$918$		0			0
$919$	3.22570			0.106406			0.0532029	−	0.998584i	$-0.483057\pi$
$919$	3.22570			0.106406			0.0532029	+	0.998584i	$0.483057\pi$
$920$	−31.8404	−	4.47352i	−1.04975	−	0.147488i
$921$		0			0
$922$		−	31.7342i		−	1.04511i
$923$		−	6.08097i		−	0.200157i
$924$		0			0
$925$	3.14272	−	10.9634i	0.103332	−	0.360476i
$926$	9.62036			0.316145
$927$		0			0
$928$		−	25.1481i		−	0.825527i
$929$	−39.3461			−1.29091			−0.645453	−	0.763800i	$-0.723331\pi$
$929$	−39.3461			−1.29091			−0.645453	+	0.763800i	$0.723331\pi$
$930$		0			0
$931$	3.16346			0.103678
$932$			8.49871i			0.278384i
$933$		0			0
$934$	−13.2268			−0.432792
$935$	0.428639	−	3.05086i	0.0140180	−	0.0997736i
$936$		0			0
$937$			51.6040i			1.68583i	0.538048	+	0.842914i	$0.319162\pi$
$937$			51.6040i			1.68583i	−0.538048	+	0.842914i	$0.680838\pi$
$938$		−	27.3590i		−	0.893305i
$939$		0			0
$940$	−0.179286	+	1.27607i	−0.00584767	+	0.0416209i
$941$	−37.5081			−1.22273			−0.611364	−	0.791349i	$-0.709379\pi$
$941$	−37.5081			−1.22273			−0.611364	+	0.791349i	$0.709379\pi$
$942$		0			0
$943$			14.3051i			0.465839i
$944$	24.7665			0.806080
$945$		0			0
$946$	−1.65572			−0.0538320
$947$			38.1160i			1.23860i	0.785153	+	0.619302i	$0.212584\pi$
$947$			38.1160i			1.23860i	−0.785153	+	0.619302i	$0.787416\pi$
$948$		0			0
$949$	−10.2810			−0.333735
$950$	−3.70471	+	12.9240i	−0.120197	+	0.419308i
$951$		0			0
$952$		−	57.2355i		−	1.85501i
$953$		−	28.7368i		−	0.930877i	−0.885080	−	0.465439i	$-0.845897\pi$
$953$		−	28.7368i		−	0.930877i	0.885080	−	0.465439i	$-0.154103\pi$
$954$		0			0
$955$	4.65386	+	0.653858i	0.150595	+	0.0211584i
$956$	−6.71303			−0.217115
$957$		0			0
$958$			11.0890i			0.358268i
$959$	55.6040			1.79555
$960$		0			0
$961$	0.271628			0.00876221
$962$			2.76986i			0.0893038i
$963$		0			0
$964$	−3.09912			−0.0998161
$965$	−4.20648	+	29.9398i	−0.135411	+	0.963796i
$966$		0			0
$967$			29.0593i			0.934485i	0.884129	+	0.467242i	$0.154752\pi$
$967$			29.0593i			0.934485i	−0.884129	+	0.467242i	$0.845248\pi$
$968$			33.5926i			1.07971i
$969$		0			0
$970$	48.5116	+	6.81579i	1.55761	+	0.218842i
$971$	39.8578			1.27910			0.639548	−	0.768751i	$-0.279121\pi$
$971$	39.8578			1.27910			0.639548	+	0.768751i	$0.279121\pi$
$972$		0			0
$973$			55.4291i			1.77698i
$974$	−19.6588			−0.629908
$975$		0			0
$976$	0.751123			0.0240429
$977$			12.8617i			0.411483i	0.978606	+	0.205742i	$0.0659606\pi$
$977$			12.8617i			0.411483i	−0.978606	+	0.205742i	$0.934039\pi$
$978$		0			0
$979$	1.20294			0.0384463
$980$	−1.66217	−	0.233532i	−0.0530961	−	0.00745991i
$981$		0			0
$982$			31.8925i			1.01773i
$983$			45.4880i			1.45084i	0.688306	+	0.725420i	$0.258355\pi$
$983$			45.4880i			1.45084i	−0.688306	+	0.725420i	$0.741645\pi$
$984$		0			0
$985$	−0.622216	+	4.42864i	−0.0198254	+	0.141108i
$986$	67.9911			2.16528
$987$		0			0
$988$			1.16346i			0.0370147i
$989$	29.8306			0.948557
$990$		0			0
$991$	8.07007			0.256354			0.128177	−	0.991751i	$-0.459087\pi$
$991$	8.07007			0.256354			0.128177	+	0.991751i	$0.459087\pi$
$992$			16.1466i			0.512655i
$993$		0			0
$994$	−21.4380			−0.679972
$995$	−49.0321	−	6.88892i	−1.55442	−	0.218394i
$996$		0			0
$997$		−	32.8158i		−	1.03929i	−0.854383	−	0.519643i	$-0.826065\pi$
$997$		−	32.8158i		−	1.03929i	0.854383	−	0.519643i	$-0.173935\pi$
$998$			36.4667i			1.15433i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.c.b.469.3		6
3.2	odd	2		65.2.b.a.14.4	yes	6
5.2	odd	4		2925.2.a.bf.1.3		3
5.3	odd	4		2925.2.a.bj.1.1		3
5.4	even	2	inner	585.2.c.b.469.4		6
12.11	even	2		1040.2.d.c.209.2		6
15.2	even	4		325.2.a.k.1.1		3
15.8	even	4		325.2.a.j.1.3		3
15.14	odd	2		65.2.b.a.14.3	✓	6
39.2	even	12		845.2.l.e.654.1		12
39.5	even	4		845.2.d.a.844.6		6
39.8	even	4		845.2.d.b.844.2		6
39.11	even	12		845.2.l.d.654.5		12
39.17	odd	6		845.2.n.g.484.3		12
39.20	even	12		845.2.l.d.699.6		12
39.23	odd	6		845.2.n.g.529.4		12
39.29	odd	6		845.2.n.f.529.3		12
39.32	even	12		845.2.l.e.699.2		12
39.35	odd	6		845.2.n.f.484.4		12
39.38	odd	2		845.2.b.c.339.3		6
60.23	odd	4		5200.2.a.cj.1.2		3
60.47	odd	4		5200.2.a.cb.1.2		3
60.59	even	2		1040.2.d.c.209.5		6
195.29	odd	6		845.2.n.f.529.4		12
195.38	even	4		4225.2.a.bh.1.1		3
195.44	even	4		845.2.d.b.844.1		6
195.59	even	12		845.2.l.e.699.1		12
195.74	odd	6		845.2.n.f.484.3		12
195.77	even	4		4225.2.a.ba.1.3		3
195.89	even	12		845.2.l.e.654.2		12
195.119	even	12		845.2.l.d.654.6		12
195.134	odd	6		845.2.n.g.484.4		12
195.149	even	12		845.2.l.d.699.5		12
195.164	even	4		845.2.d.a.844.5		6
195.179	odd	6		845.2.n.g.529.3		12
195.194	odd	2		845.2.b.c.339.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.b.a.14.3	✓	6	15.14	odd	2
65.2.b.a.14.4	yes	6	3.2	odd	2
325.2.a.j.1.3		3	15.8	even	4
325.2.a.k.1.1		3	15.2	even	4
585.2.c.b.469.3		6	1.1	even	1	trivial
585.2.c.b.469.4		6	5.4	even	2	inner
845.2.b.c.339.3		6	39.38	odd	2
845.2.b.c.339.4		6	195.194	odd	2
845.2.d.a.844.5		6	195.164	even	4
845.2.d.a.844.6		6	39.5	even	4
845.2.d.b.844.1		6	195.44	even	4
845.2.d.b.844.2		6	39.8	even	4
845.2.l.d.654.5		12	39.11	even	12
845.2.l.d.654.6		12	195.119	even	12
845.2.l.d.699.5		12	195.149	even	12
845.2.l.d.699.6		12	39.20	even	12
845.2.l.e.654.1		12	39.2	even	12
845.2.l.e.654.2		12	195.89	even	12
845.2.l.e.699.1		12	195.59	even	12
845.2.l.e.699.2		12	39.32	even	12
845.2.n.f.484.3		12	195.74	odd	6
845.2.n.f.484.4		12	39.35	odd	6
845.2.n.f.529.3		12	39.29	odd	6
845.2.n.f.529.4		12	195.29	odd	6
845.2.n.g.484.3		12	39.17	odd	6
845.2.n.g.484.4		12	195.134	odd	6
845.2.n.g.529.3		12	195.179	odd	6
845.2.n.g.529.4		12	39.23	odd	6
1040.2.d.c.209.2		6	12.11	even	2
1040.2.d.c.209.5		6	60.59	even	2
2925.2.a.bf.1.3		3	5.2	odd	4
2925.2.a.bj.1.1		3	5.3	odd	4
4225.2.a.ba.1.3		3	195.77	even	4
4225.2.a.bh.1.1		3	195.38	even	4
5200.2.a.cb.1.2		3	60.47	odd	4
5200.2.a.cj.1.2		3	60.23	odd	4

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.21432i q^{2} +0.525428 q^{4} +(2.21432 + 0.311108i) q^{5} -2.90321i q^{7} -3.06668i q^{8} +(0.377784 - 2.68889i) q^{10} -0.214320 q^{11} -1.00000i q^{13} -3.52543 q^{14} -2.67307 q^{16} +6.42864i q^{17} -2.21432 q^{19} +(1.16346 + 0.163465i) q^{20} +0.260253i q^{22} -4.68889i q^{23} +(4.80642 + 1.37778i) q^{25} -1.21432 q^{26} -1.52543i q^{28} +8.70964 q^{29} -5.59210 q^{31} -2.88739i q^{32} +7.80642 q^{34} +(0.903212 - 6.42864i) q^{35} -2.28100i q^{37} +2.68889i q^{38} +(0.954067 - 6.79060i) q^{40} -3.05086 q^{41} +6.36196i q^{43} -0.112610 q^{44} -5.69381 q^{46} +1.09679i q^{47} -1.42864 q^{49} +(1.67307 - 5.83654i) q^{50} -0.525428i q^{52} +6.23506i q^{53} +(-0.474572 - 0.0666765i) q^{55} -8.90321 q^{56} -10.5763i q^{58} -9.26517 q^{59} -0.280996 q^{61} +6.79060i q^{62} -8.85236 q^{64} +(0.311108 - 2.21432i) q^{65} +7.76049i q^{67} +3.37778i q^{68} +(-7.80642 - 1.09679i) q^{70} +6.08097 q^{71} -10.2810i q^{73} -2.76986 q^{74} -1.16346 q^{76} +0.622216i q^{77} +14.2351 q^{79} +(-5.91903 - 0.831613i) q^{80} +3.70471i q^{82} -9.52543i q^{83} +(-2.00000 + 14.2351i) q^{85} +7.72546 q^{86} +0.657249i q^{88} -5.61285 q^{89} -2.90321 q^{91} -2.46367i q^{92} +1.33185 q^{94} +(-4.90321 - 0.688892i) q^{95} +18.0415i q^{97} +1.73483i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 10 q^{4} + 2 q^{10} + 12 q^{11} - 8 q^{14} + 10 q^{16} + 20 q^{20} + 2 q^{25} + 6 q^{26} + 12 q^{29} - 20 q^{31} + 20 q^{34} - 8 q^{35} - 34 q^{40} + 8 q^{41} - 40 q^{44} + 32 q^{46} + 18 q^{49} - 16 q^{50}+ \cdots - 16 q^{95}+O(q^{100}) \) 6 * q - 10 * q^4 + 2 * q^10 + 12 * q^11 - 8 * q^14 + 10 * q^16 + 20 * q^20 + 2 * q^25 + 6 * q^26 + 12 * q^29 - 20 * q^31 + 20 * q^34 - 8 * q^35 - 34 * q^40 + 8 * q^41 - 40 * q^44 + 32 * q^46 + 18 * q^49 - 16 * q^50 - 16 * q^55 - 40 * q^56 - 16 * q^59 + 12 * q^61 - 66 * q^64 + 2 * q^65 - 20 * q^70 + 24 * q^71 - 4 * q^74 - 20 * q^76 + 32 * q^79 - 48 * q^80 - 12 * q^85 + 32 * q^86 + 20 * q^89 - 4 * q^91 - 32 * q^94 - 16 * q^95

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