LMFDB - Embedded newform 585.2.h.g.64.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(64,585)]

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, 1]))

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

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

chi := DirichletCharacter("585.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.h (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:	$12$
Coefficient field:	12.0.2593100598870016.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{10} + 9x^{8} - 16x^{6} + 36x^{4} - 64x^{2} + 64 $ x^12 - 4x^10 + 9x^8 - 16x^6 + 36x^4 - 64*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			64.9
Root			$-0.721581 - 1.21627i$ of defining polynomial
Character	$\chi$	$=$	585.64
Dual form			585.2.h.g.64.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.61036 q^{2} +0.593272 q^{4} +(-1.11567 - 1.93785i) q^{5} -4.86509 q^{7} -2.26534 q^{8} +O(q^{10})$	\(q+1.61036 q^{2} +0.593272 q^{4} +(-1.11567 - 1.93785i) q^{5} -4.86509 q^{7} -2.26534 q^{8} +(-1.79664 - 3.12065i) q^{10} -0.989386i q^{11} +(-0.822183 + 3.51056i) q^{13} -7.83457 q^{14} -4.83457 q^{16} -3.83457i q^{17} +2.88632i q^{19} +(-0.661896 - 1.14967i) q^{20} -1.59327i q^{22} -4.00000i q^{23} +(-2.51056 + 4.32401i) q^{25} +(-1.32401 + 5.65327i) q^{26} -2.88632 q^{28} +2.81346 q^{29} -6.84387i q^{31} -3.25473 q^{32} -6.17506i q^{34} +(5.42784 + 9.42784i) q^{35} -0.334405 q^{37} +4.64803i q^{38} +(2.52738 + 4.38991i) q^{40} -5.85448i q^{41} -7.83457i q^{43} -0.586975i q^{44} -6.44146i q^{46} -0.989386 q^{47} +16.6691 q^{49} +(-4.04291 + 6.96324i) q^{50} +(-0.487778 + 2.08271i) q^{52} +7.02112i q^{53} +(-1.91729 + 1.10383i) q^{55} +11.0211 q^{56} +4.53069 q^{58} +6.76203i q^{59} -6.64803 q^{61} -11.0211i q^{62} +4.42784 q^{64} +(7.72023 - 2.32335i) q^{65} -7.34901 q^{67} -2.27494i q^{68} +(8.74080 + 15.1823i) q^{70} -9.91475i q^{71} -1.64437 q^{73} -0.538514 q^{74} +1.71237i q^{76} +4.81346i q^{77} -11.8346 q^{79} +(5.39379 + 9.36870i) q^{80} -9.42784i q^{82} -13.2035 q^{83} +(-7.43084 + 4.27812i) q^{85} -12.6165i q^{86} +2.24130i q^{88} -1.89694i q^{89} +(4.00000 - 17.0792i) q^{91} -2.37309i q^{92} -1.59327 q^{94} +(5.59327 - 3.22019i) q^{95} +10.5697 q^{97} +26.8434 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{4}+O(q^{10}) $ 12 * q + 12 * q^4	$ 12 q + 12 q^{4} - 24 q^{10} - 16 q^{14} + 20 q^{16} + 4 q^{25} + 28 q^{26} + 24 q^{29} - 8 q^{35} - 16 q^{40} + 44 q^{49} + 16 q^{55} + 64 q^{56} + 8 q^{61} - 20 q^{64} - 28 q^{65} - 104 q^{74} - 64 q^{79} + 48 q^{91} - 24 q^{94} + 72 q^{95}+O(q^{100}) $ 12 * q + 12 * q^4 - 24 * q^10 - 16 * q^14 + 20 * q^16 + 4 * q^25 + 28 * q^26 + 24 * q^29 - 8 * q^35 - 16 * q^40 + 44 * q^49 + 16 * q^55 + 64 * q^56 + 8 * q^61 - 20 * q^64 - 28 * q^65 - 104 * q^74 - 64 * q^79 + 48 * q^91 - 24 * q^94 + 72 * q^95

Display 100 coefficients 10 coefficients

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 $

$2$	1.61036			1.13870			0.569350	−	0.822096i	$-0.307195\pi$
$2$	1.61036			1.13870			0.569350	+	0.822096i	$0.307195\pi$
$3$		0			0
$3$		0			0
$4$	0.593272			0.296636
$5$	−1.11567	−	1.93785i	−0.498943	−	0.866635i
$5$	−1.11567	−	1.93785i	−0.498943	−	0.866635i
$6$		0			0
$7$	−4.86509			−1.83883			−0.919416	−	0.393285i	$-0.871338\pi$
$7$	−4.86509			−1.83883			−0.919416	+	0.393285i	$0.871338\pi$
$8$	−2.26534			−0.800920
$9$		0			0
$10$	−1.79664	−	3.12065i	−0.568146	−	0.986836i
$11$		−	0.989386i		−	0.298311i	−0.988814	−	0.149156i	$-0.952344\pi$
$11$		−	0.989386i		−	0.298311i	0.988814	−	0.149156i	$-0.0476555\pi$
$12$		0			0
$13$	−0.822183	+	3.51056i	−0.228033	+	0.973653i
$13$	−0.822183	+	3.51056i	−0.228033	+	0.973653i
$14$	−7.83457			−2.09388
$15$		0			0
$16$	−4.83457			−1.20864
$17$		−	3.83457i		−	0.930020i	−0.885305	−	0.465010i	$-0.846051\pi$
$17$		−	3.83457i		−	0.930020i	0.885305	−	0.465010i	$-0.153949\pi$
$18$		0			0
$19$			2.88632i			0.662168i	0.943601	+	0.331084i	$0.107414\pi$
$19$			2.88632i			0.662168i	−0.943601	+	0.331084i	$0.892586\pi$
$20$	−0.661896	−	1.14967i	−0.148004	−	0.257075i
$21$		0			0
$22$		−	1.59327i		−	0.339687i
$23$		−	4.00000i		−	0.834058i	−0.908893	−	0.417029i	$-0.863071\pi$
$23$		−	4.00000i		−	0.834058i	0.908893	−	0.417029i	$-0.136929\pi$
$24$		0			0
$25$	−2.51056	+	4.32401i	−0.502112	+	0.864803i
$26$	−1.32401	+	5.65327i	−0.259661	+	1.10870i
$27$		0			0
$28$	−2.88632			−0.545464
$29$	2.81346			0.522446			0.261223	−	0.965279i	$-0.415874\pi$
$29$	2.81346			0.522446			0.261223	+	0.965279i	$0.415874\pi$
$30$		0			0
$31$		−	6.84387i		−	1.22919i	−0.788841	−	0.614597i	$-0.789318\pi$
$31$		−	6.84387i		−	1.22919i	0.788841	−	0.614597i	$-0.210682\pi$
$32$	−3.25473			−0.575361
$33$		0			0
$34$		−	6.17506i		−	1.05901i
$35$	5.42784	+	9.42784i	0.917473	+	1.59360i
$36$		0			0
$37$	−0.334405			−0.0549759			−0.0274880	−	0.999622i	$-0.508751\pi$
$37$	−0.334405			−0.0549759			−0.0274880	+	0.999622i	$0.508751\pi$
$38$			4.64803i			0.754010i
$39$		0			0
$40$	2.52738	+	4.38991i	0.399614	+	0.694105i
$41$		−	5.85448i		−	0.914316i	−0.889385	−	0.457158i	$-0.848867\pi$
$41$		−	5.85448i		−	0.914316i	0.889385	−	0.457158i	$-0.151133\pi$
$42$		0			0
$43$		−	7.83457i		−	1.19476i	−0.801958	−	0.597381i	$-0.796208\pi$
$43$		−	7.83457i		−	1.19476i	0.801958	−	0.597381i	$-0.203792\pi$
$44$		−	0.586975i		−	0.0884898i
$45$		0			0
$46$		−	6.44146i		−	0.949741i
$47$	−0.989386			−0.144317			−0.0721584	−	0.997393i	$-0.522989\pi$
$47$	−0.989386			−0.144317			−0.0721584	+	0.997393i	$0.522989\pi$
$48$		0			0
$49$	16.6691			2.38131
$50$	−4.04291	+	6.96324i	−0.571754	+	0.984750i
$51$		0			0
$52$	−0.487778	+	2.08271i	−0.0676426	+	0.288820i
$53$			7.02112i			0.964424i	0.876054	+	0.482212i	$0.160167\pi$
$53$			7.02112i			0.964424i	−0.876054	+	0.482212i	$0.839833\pi$
$54$		0			0
$55$	−1.91729	+	1.10383i	−0.258527	+	0.148840i
$56$	11.0211			1.47276
$57$		0			0
$58$	4.53069			0.594909
$59$			6.76203i			0.880341i	0.897914	+	0.440171i	$0.145082\pi$
$59$			6.76203i			0.880341i	−0.897914	+	0.440171i	$0.854918\pi$
$60$		0			0
$61$	−6.64803			−0.851193			−0.425596	−	0.904913i	$-0.639936\pi$
$61$	−6.64803			−0.851193			−0.425596	+	0.904913i	$0.639936\pi$
$62$		−	11.0211i		−	1.39968i
$63$		0			0
$64$	4.42784			0.553480
$65$	7.72023	−	2.32335i	0.957577	−	0.288177i
$66$		0			0
$67$	−7.34901			−0.897824			−0.448912	−	0.893576i	$-0.648188\pi$
$67$	−7.34901			−0.897824			−0.448912	+	0.893576i	$0.648188\pi$
$68$		−	2.27494i		−	0.275877i
$69$		0			0
$70$	8.74080	+	15.1823i	1.04473	+	1.81463i
$71$		−	9.91475i		−	1.17666i	−0.808619	−	0.588332i	$-0.799785\pi$
$71$		−	9.91475i		−	1.17666i	0.808619	−	0.588332i	$-0.200215\pi$
$72$		0			0
$73$	−1.64437			−0.192459			−0.0962293	−	0.995359i	$-0.530678\pi$
$73$	−1.64437			−0.192459			−0.0962293	+	0.995359i	$0.530678\pi$
$74$	−0.538514			−0.0626010
$75$		0			0
$76$			1.71237i			0.196423i
$77$			4.81346i			0.548544i
$78$		0			0
$79$	−11.8346			−1.33149			−0.665747	−	0.746178i	$-0.731887\pi$
$79$	−11.8346			−1.33149			−0.665747	+	0.746178i	$0.731887\pi$
$80$	5.39379	+	9.36870i	0.603044	+	1.04745i
$81$		0			0
$82$		−	9.42784i		−	1.04113i
$83$	−13.2035			−1.44927			−0.724635	−	0.689132i	$-0.757992\pi$
$83$	−13.2035			−1.44927			−0.724635	+	0.689132i	$0.757992\pi$
$84$		0			0
$85$	−7.43084	+	4.27812i	−0.805988	+	0.464027i
$86$		−	12.6165i		−	1.36047i
$87$		0			0
$88$			2.24130i			0.238923i
$89$		−	1.89694i		−	0.201075i	−0.994933	−	0.100537i	$-0.967944\pi$
$89$		−	1.89694i		−	0.201075i	0.994933	−	0.100537i	$-0.0320562\pi$
$90$		0			0
$91$	4.00000	−	17.0792i	0.419314	−	1.79039i
$92$		−	2.37309i		−	0.247411i
$93$		0			0
$94$	−1.59327			−0.164333
$95$	5.59327	−	3.22019i	0.573858	−	0.330384i
$96$		0			0
$97$	10.5697			1.07319			0.536597	−	0.843839i	$-0.319710\pi$
$97$	10.5697			1.07319			0.536597	+	0.843839i	$0.319710\pi$
$98$	26.8434			2.71159
$99$		0			0
$100$	−1.48944	+	2.56531i	−0.148944	+	0.256531i
$101$	−13.6691			−1.36013			−0.680065	−	0.733152i	$-0.738049\pi$
$101$	−13.6691			−1.36013			−0.680065	+	0.733152i	$0.738049\pi$
$102$		0			0
$103$			14.2077i			1.39992i	0.714181	+	0.699961i	$0.246799\pi$
$103$			14.2077i			1.39992i	−0.714181	+	0.699961i	$0.753201\pi$
$104$	1.86253	−	7.95262i	0.182636	−	0.779819i
$105$		0			0
$106$			11.3065i			1.09819i
$107$		−	14.8557i		−	1.43615i	−0.695964	−	0.718077i	$-0.745023\pi$
$107$		−	14.8557i		−	1.43615i	0.695964	−	0.718077i	$-0.254977\pi$
$108$		0			0
$109$			20.6343i			1.97641i	0.153137	+	0.988205i	$0.451063\pi$
$109$			20.6343i			1.97641i	−0.153137	+	0.988205i	$0.548937\pi$
$110$	−3.08753	+	1.77757i	−0.294384	+	0.169484i
$111$		0			0
$112$	23.5206			2.22249
$113$			13.4615i			1.26635i	0.774009	+	0.633175i	$0.218249\pi$
$113$			13.4615i			1.26635i	−0.774009	+	0.633175i	$0.781751\pi$
$114$		0			0
$115$	−7.75142	+	4.46268i	−0.722823	+	0.416147i
$116$	1.66914			0.154976
$117$		0			0
$118$			10.8893i			1.00244i
$119$			18.6556i			1.71015i
$120$		0			0
$121$	10.0211			0.911010
$122$	−10.7057			−0.969253
$123$		0			0
$124$		−	4.06027i		−	0.364623i
$125$	11.1803	+	0.0409180i	0.999993	+	0.00365982i
$126$		0			0
$127$		−	3.66914i		−	0.325584i	−0.986660	−	0.162792i	$-0.947950\pi$
$127$		−	3.66914i		−	0.325584i	0.986660	−	0.162792i	$-0.0520499\pi$
$128$	13.6399			1.20561
$129$		0			0
$130$	12.4324	−	3.74145i	1.09039	−	0.328147i
$131$	−2.37309			−0.207338			−0.103669	−	0.994612i	$-0.533058\pi$
$131$	−2.37309			−0.207338			−0.103669	+	0.994612i	$0.533058\pi$
$132$		0			0
$133$		−	14.0422i		−	1.21762i
$134$	−11.8346			−1.02235
$135$		0			0
$136$			8.68663i			0.744872i
$137$	−7.49885			−0.640670			−0.320335	−	0.947304i	$-0.603795\pi$
$137$	−7.49885			−0.640670			−0.320335	+	0.947304i	$0.603795\pi$
$138$		0			0
$139$	−2.37309			−0.201283			−0.100641	−	0.994923i	$-0.532089\pi$
$139$	−2.37309			−0.201283			−0.100641	+	0.994923i	$0.532089\pi$
$140$	3.22019	+	5.59327i	0.272155	+	0.472718i
$141$		0			0
$142$		−	15.9664i		−	1.33987i
$143$	3.47330	+	0.813457i	0.290452	+	0.0680247i
$144$		0			0
$145$	−3.13889	−	5.45207i	−0.260671	−	0.452770i
$146$	−2.64803			−0.219152
$147$		0			0
$148$	−0.198393			−0.0163078
$149$		−	3.87571i		−	0.317510i	−0.987318	−	0.158755i	$-0.949252\pi$
$149$		−	3.87571i		−	0.317510i	0.987318	−	0.158755i	$-0.0507481\pi$
$150$		0			0
$151$		−	6.84387i		−	0.556946i	−0.960444	−	0.278473i	$-0.910172\pi$
$151$		−	6.84387i		−	0.556946i	0.960444	−	0.278473i	$-0.0898283\pi$
$152$		−	6.53851i		−	0.530344i
$153$		0			0
$154$			7.75142i			0.624627i
$155$	−13.2624	+	7.63550i	−1.06526	+	0.613298i
$156$		0			0
$157$		−	8.00000i		−	0.638470i	−0.947676	−	0.319235i	$-0.896574\pi$
$157$		−	8.00000i		−	0.638470i	0.947676	−	0.319235i	$-0.103426\pi$
$158$	−19.0580			−1.51617
$159$		0			0
$160$	3.63121	+	6.30719i	0.287072	+	0.498627i
$161$			19.4604i			1.53369i
$162$		0			0
$163$	19.0580			1.49274			0.746368	−	0.665534i	$-0.231796\pi$
$163$	19.0580			1.49274			0.746368	+	0.665534i	$0.231796\pi$
$164$		−	3.47330i		−	0.271219i
$165$		0			0
$166$	−21.2624			−1.65028
$167$	−2.96816			−0.229683			−0.114841	−	0.993384i	$-0.536636\pi$
$167$	−2.96816			−0.229683			−0.114841	+	0.993384i	$0.536636\pi$
$168$		0			0
$169$	−11.6480	−	5.77264i	−0.896002	−	0.444050i
$170$	−11.9664	+	6.88933i	−0.917778	+	0.528387i
$171$		0			0
$172$		−	4.64803i		−	0.354409i
$173$		−	24.3172i		−	1.84880i	−0.381424	−	0.924400i	$-0.624566\pi$
$173$		−	24.3172i		−	1.84880i	0.381424	−	0.924400i	$-0.375434\pi$
$174$		0			0
$175$	12.2141	−	21.0367i	0.923299	−	1.59023i
$176$			4.78326i			0.360552i
$177$		0			0
$178$		−	3.05476i		−	0.228964i
$179$	16.4153			1.22694			0.613469	−	0.789719i	$-0.289773\pi$
$179$	16.4153			1.22694			0.613469	+	0.789719i	$0.289773\pi$
$180$		0			0
$181$	−6.00000			−0.445976			−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000			−0.445976			−0.222988	+	0.974821i	$0.571581\pi$
$182$	6.44146	−	27.5037i	0.477472	−	2.03871i
$183$		0			0
$184$			9.06138i			0.668014i
$185$	0.373086	+	0.648029i	0.0274298	+	0.0476440i
$186$		0			0
$187$	−3.79387			−0.277435
$188$	−0.586975			−0.0428095
$189$		0			0
$190$	9.00720	−	5.18567i	0.653451	−	0.376208i
$191$	−12.4826			−0.903209			−0.451605	−	0.892218i	$-0.649148\pi$
$191$	−12.4826			−0.903209			−0.451605	+	0.892218i	$0.649148\pi$
$192$		0			0
$193$	3.62314			0.260799			0.130400	−	0.991462i	$-0.458374\pi$
$193$	3.62314			0.260799			0.130400	+	0.991462i	$0.458374\pi$
$194$	17.0211			1.22204
$195$		0			0
$196$	9.88933			0.706381
$197$	17.2290			1.22752			0.613759	−	0.789493i	$-0.289657\pi$
$197$	17.2290			1.22752			0.613759	+	0.789493i	$0.289657\pi$
$198$		0			0
$199$	−9.87680			−0.700148			−0.350074	−	0.936722i	$-0.613844\pi$
$199$	−9.87680			−0.700148			−0.350074	+	0.936722i	$0.613844\pi$
$200$	5.68728	−	9.79538i	0.402151	−	0.692638i
$201$		0			0
$202$	−22.0123			−1.54878
$203$	−13.6877			−0.960691
$204$		0			0
$205$	−11.3451	+	6.53167i	−0.792378	+	0.456192i
$206$			22.8795i			1.59409i
$207$		0			0
$208$	3.97490	−	16.9720i	0.275610	−	1.17680i
$209$	2.85569			0.197532
$210$		0			0
$211$	21.8768			1.50606			0.753031	−	0.657986i	$-0.228591\pi$
$211$	21.8768			1.50606			0.753031	+	0.657986i	$0.228591\pi$
$212$			4.16543i			0.286083i
$213$		0			0
$214$		−	23.9231i		−	1.63535i
$215$	−15.1823	+	8.74080i	−1.03542	+	0.596118i
$216$		0			0
$217$			33.2961i			2.26028i
$218$			33.2288i			2.25054i
$219$		0			0
$220$	−1.13747	+	0.654870i	−0.0766883	+	0.0441514i
$221$	13.4615	+	3.15272i	0.905518	+	0.212075i
$222$		0			0
$223$	−18.3892			−1.23143			−0.615714	−	0.787969i	$-0.711133\pi$
$223$	−18.3892			−1.23143			−0.615714	+	0.787969i	$0.711133\pi$
$224$	15.8346			1.05799
$225$		0			0
$226$			21.6779i			1.44199i
$227$	−12.0295			−0.798428			−0.399214	−	0.916858i	$-0.630717\pi$
$227$	−12.0295			−0.798428			−0.399214	+	0.916858i	$0.630717\pi$
$228$		0			0
$229$		−	1.17395i		−	0.0775768i	−0.999247	−	0.0387884i	$-0.987650\pi$
$229$		−	1.17395i		−	0.0775768i	0.999247	−	0.0387884i	$-0.0123498\pi$
$230$	−12.4826	+	7.18654i	−0.823078	+	0.473867i
$231$		0			0
$232$	−6.37345			−0.418437
$233$		−	15.0211i		−	0.984066i	−0.870577	−	0.492033i	$-0.836254\pi$
$233$		−	15.0211i		−	0.984066i	0.870577	−	0.492033i	$-0.163746\pi$
$234$		0			0
$235$	1.10383	+	1.91729i	0.0720059	+	0.125070i
$236$			4.01172i			0.261141i
$237$		0			0
$238$			30.0422i			1.94735i
$239$		−	18.4710i		−	1.19479i	−0.801947	−	0.597395i	$-0.796203\pi$
$239$		−	18.4710i		−	1.19479i	0.801947	−	0.597395i	$-0.203797\pi$
$240$		0			0
$241$			10.9041i			0.702397i	0.936301	+	0.351199i	$0.114226\pi$
$241$			10.9041i			0.702397i	−0.936301	+	0.351199i	$0.885774\pi$
$242$	16.1376			1.03737
$243$		0			0
$244$	−3.94409			−0.252494
$245$	−18.5973	−	32.3024i	−1.18814	−	2.06372i
$246$		0			0
$247$	−10.1326	−	2.37309i	−0.644722	−	0.150996i
$248$			15.5037i			0.984487i
$249$		0			0
$250$	18.0043	+	0.0658929i	1.13869	+	0.00416744i
$251$	16.8135			1.06126			0.530628	−	0.847605i	$-0.321956\pi$
$251$	16.8135			1.06126			0.530628	+	0.847605i	$0.321956\pi$
$252$		0			0
$253$	−3.95754			−0.248809
$254$		−	5.90866i		−	0.370742i
$255$		0			0
$256$	13.1095			0.819345
$257$		−	8.64803i		−	0.539449i	−0.962938	−	0.269725i	$-0.913067\pi$
$257$		−	8.64803i		−	0.539449i	0.962938	−	0.269725i	$-0.0869327\pi$
$258$		0			0
$259$	1.62691			0.101091
$260$	4.58020	−	1.37838i	0.284052	−	0.0854835i
$261$		0			0
$262$	−3.82153			−0.236095
$263$			0.813457i			0.0501599i	0.999685	+	0.0250799i	$0.00798403\pi$
$263$			0.813457i			0.0501599i	−0.999685	+	0.0250799i	$0.992016\pi$
$264$		0			0
$265$	13.6059	−	7.83325i	0.835804	−	0.481193i
$266$		−	22.6131i		−	1.38650i
$267$		0			0
$268$	−4.35996			−0.266327
$269$	−23.2288			−1.41628			−0.708142	−	0.706070i	$-0.750466\pi$
$269$	−23.2288			−1.41628			−0.708142	+	0.706070i	$0.750466\pi$
$270$		0			0
$271$		−	14.5953i		−	0.886600i	−0.896373	−	0.443300i	$-0.853808\pi$
$271$		−	14.5953i		−	0.886600i	0.896373	−	0.443300i	$-0.146192\pi$
$272$			18.5385i			1.12406i
$273$		0			0
$274$	−12.0759			−0.729530
$275$	4.27812	+	2.48391i	0.257980	+	0.149785i
$276$		0			0
$277$		−	17.6269i		−	1.05910i	−0.848279	−	0.529549i	$-0.822361\pi$
$277$		−	17.6269i		−	1.05910i	0.848279	−	0.529549i	$-0.177639\pi$
$278$	−3.82153			−0.229200
$279$		0			0
$280$	−12.2959	−	21.3573i	−0.734823	−	1.27634i
$281$			9.64835i			0.575572i	0.957695	+	0.287786i	$0.0929193\pi$
$281$			9.64835i			0.575572i	−0.957695	+	0.287786i	$0.907081\pi$
$282$		0			0
$283$		−	4.00000i		−	0.237775i	−0.992908	−	0.118888i	$-0.962067\pi$
$283$		−	4.00000i		−	0.237775i	0.992908	−	0.118888i	$-0.0379328\pi$
$284$		−	5.88214i		−	0.349041i
$285$		0			0
$286$	5.59327	+	1.30996i	0.330737	+	0.0774596i
$287$			28.4826i			1.68127i
$288$		0			0
$289$	2.29606			0.135062
$290$	−5.05476	−	8.77981i	−0.296826	−	0.515568i
$291$		0			0
$292$	−0.975556			−0.0570901
$293$	17.8978			1.04560			0.522802	−	0.852454i	$-0.324887\pi$
$293$	17.8978			1.04560			0.522802	+	0.852454i	$0.324887\pi$
$294$		0			0
$295$	13.1038	−	7.54420i	0.762934	−	0.439240i
$296$	0.757543			0.0440313
$297$		0			0
$298$		−	6.24130i		−	0.361549i
$299$	14.0422	+	3.28873i	0.812083	+	0.190192i
$300$		0			0
$301$			38.1159i			2.19697i
$302$		−	11.0211i		−	0.634194i
$303$		0			0
$304$		−	13.9541i		−	0.800324i
$305$	7.41701	+	12.8829i	0.424697	+	0.737673i
$306$		0			0
$307$	−9.49145			−0.541706			−0.270853	−	0.962621i	$-0.587306\pi$
$307$	−9.49145			−0.541706			−0.270853	+	0.962621i	$0.587306\pi$
$308$			2.85569i			0.162718i
$309$		0			0
$310$	−21.3573	+	12.2959i	−1.21301	+	0.698362i
$311$	−34.5248			−1.95772			−0.978862	−	0.204523i	$-0.934436\pi$
$311$	−34.5248			−1.95772			−0.978862	+	0.204523i	$0.934436\pi$
$312$		0			0
$313$		−	5.39420i		−	0.304898i	−0.988311	−	0.152449i	$-0.951284\pi$
$313$		−	5.39420i		−	0.304898i	0.988311	−	0.152449i	$-0.0487160\pi$
$314$		−	12.8829i		−	0.727025i
$315$		0			0
$316$	−7.02112			−0.394969
$317$	5.01494			0.281667			0.140833	−	0.990033i	$-0.455022\pi$
$317$	5.01494			0.281667			0.140833	+	0.990033i	$0.455022\pi$
$318$		0			0
$319$		−	2.78360i		−	0.155851i
$320$	−4.94002	−	8.58052i	−0.276155	−	0.479665i
$321$		0			0
$322$			31.3383i			1.74641i
$323$	11.0678			0.615829
$324$		0			0
$325$	−13.1156	−	12.3686i	−0.727521	−	0.686086i
$326$	30.6903			1.69978
$327$		0			0
$328$			13.2624i			0.732294i
$329$	4.81346			0.265374
$330$		0			0
$331$			17.7480i			0.975519i	0.872978	+	0.487759i	$0.162186\pi$
$331$			17.7480i			0.975519i	−0.872978	+	0.487759i	$0.837814\pi$
$332$	−7.83325			−0.429906
$333$		0			0
$334$	−4.77981			−0.261540
$335$	8.19907	+	14.2413i	0.447963	+	0.778085i
$336$		0			0
$337$		−	18.2749i		−	0.995500i	−0.867321	−	0.497750i	$-0.834160\pi$
$337$		−	18.2749i		−	0.995500i	0.867321	−	0.497750i	$-0.165840\pi$
$338$	−18.7576	−	9.29606i	−1.02028	−	0.505639i
$339$		0			0
$340$	−4.40851	+	2.53809i	−0.239085	+	0.137647i
$341$	−6.77123			−0.366682
$342$		0			0
$343$	−47.0413			−2.53999
$344$			17.7480i			0.956908i
$345$		0			0
$346$		−	39.1595i		−	2.10523i
$347$		−	21.6269i		−	1.16099i	−0.814263	−	0.580497i	$-0.802858\pi$
$347$		−	21.6269i		−	1.16099i	0.814263	−	0.580497i	$-0.197142\pi$
$348$		0			0
$349$			12.8829i			0.689606i	0.938675	+	0.344803i	$0.112054\pi$
$349$			12.8829i			0.689606i	−0.938675	+	0.344803i	$0.887946\pi$
$350$	19.6691	−	33.8768i	1.05136	−	1.81079i
$351$		0			0
$352$			3.22019i			0.171636i
$353$	−10.7876			−0.574165			−0.287083	−	0.957906i	$-0.592685\pi$
$353$	−10.7876			−0.574165			−0.287083	+	0.957906i	$0.592685\pi$
$354$		0			0
$355$	−19.2133	+	11.0616i	−1.01974	+	0.587089i
$356$		−	1.12540i		−	0.0596460i
$357$		0			0
$358$	26.4346			1.39711
$359$		−	15.3183i		−	0.808467i	−0.914656	−	0.404234i	$-0.867538\pi$
$359$		−	15.3183i		−	0.808467i	0.914656	−	0.404234i	$-0.132462\pi$
$360$		0			0
$361$	10.6691			0.561534
$362$	−9.66218			−0.507833
$363$		0			0
$364$	2.37309	−	10.1326i	0.124384	−	0.531093i
$365$	1.83457	+	3.18654i	0.0960259	+	0.166791i
$366$		0			0
$367$			0.165428i			0.00863527i	0.999991	+	0.00431764i	$0.00137435\pi$
$367$			0.165428i			0.00863527i	−0.999991	+	0.00431764i	$0.998626\pi$
$368$			19.3383i			1.00808i
$369$		0			0
$370$	0.600805	+	1.04356i	0.0312343	+	0.0542522i
$371$		−	34.1584i		−	1.77342i
$372$		0			0
$373$		−	1.30974i		−	0.0678158i	−0.999425	−	0.0339079i	$-0.989205\pi$
$373$		−	1.30974i		−	0.0678158i	0.999425	−	0.0339079i	$-0.0107953\pi$
$374$	−6.10951			−0.315915
$375$		0			0
$376$	2.24130			0.115586
$377$	−2.31318	+	9.87680i	−0.119135	+	0.508681i
$378$		0			0
$379$		−	0.266399i		−	0.0136840i	−0.999977	−	0.00684201i	$-0.997822\pi$
$379$		−	0.266399i		−	0.0136840i	0.999977	−	0.00684201i	$-0.00217790\pi$
$380$	3.31833	−	1.91044i	0.170227	−	0.0980037i
$381$		0			0
$382$	−20.1015			−1.02848
$383$	9.91475			0.506620			0.253310	−	0.967385i	$-0.418481\pi$
$383$	9.91475			0.506620			0.253310	+	0.967385i	$0.418481\pi$
$384$		0			0
$385$	9.32778	−	5.37023i	0.475388	−	0.273692i
$386$	5.83457			0.296972
$387$		0			0
$388$	6.27072			0.318348
$389$	−15.2288			−0.772129			−0.386065	−	0.922472i	$-0.626166\pi$
$389$	−15.2288			−0.772129			−0.386065	+	0.922472i	$0.626166\pi$
$390$		0			0
$391$	−15.3383			−0.775691
$392$	−37.7614			−1.90724
$393$		0			0
$394$	27.7450			1.39777
$395$	13.2035	+	22.9337i	0.664339	+	1.15392i
$396$		0			0
$397$	13.3533			0.670184			0.335092	−	0.942185i	$-0.391233\pi$
$397$	13.3533			0.670184			0.335092	+	0.942185i	$0.391233\pi$
$398$	−15.9052			−0.797258
$399$		0			0
$400$	12.1375	−	20.9048i	0.606874	−	1.04524i
$401$			33.0663i			1.65125i	0.564219	+	0.825625i	$0.309178\pi$
$401$			33.0663i			1.65125i	−0.564219	+	0.825625i	$0.690822\pi$
$402$		0			0
$403$	24.0258	+	5.62691i	1.19681	+	0.280297i
$404$	−8.10951			−0.403463
$405$		0			0
$406$	−22.0422			−1.09394
$407$			0.330856i			0.0163999i
$408$		0			0
$409$		−	19.2967i		−	0.954161i	−0.878860	−	0.477080i	$-0.841695\pi$
$409$		−	19.2967i		−	0.954161i	0.878860	−	0.477080i	$-0.158305\pi$
$410$	−18.2698	+	10.5184i	−0.902280	+	0.519465i
$411$		0			0
$412$			8.42900i			0.415267i
$413$		−	32.8979i		−	1.61880i
$414$		0			0
$415$	14.7307	+	25.5864i	0.723104	+	1.25599i
$416$	2.67599	−	11.4259i	0.131201	−	0.560202i
$417$		0			0
$418$	4.59870			0.224930
$419$	−16.4153			−0.801941			−0.400970	−	0.916091i	$-0.631327\pi$
$419$	−16.4153			−0.801941			−0.400970	+	0.916091i	$0.631327\pi$
$420$		0			0
$421$			2.78360i			0.135664i	0.997697	+	0.0678321i	$0.0216082\pi$
$421$			2.78360i			0.135664i	−0.997697	+	0.0678321i	$0.978392\pi$
$422$	35.2296			1.71495
$423$		0			0
$424$		−	15.9052i		−	0.772427i
$425$	16.5807	+	9.62691i	0.804284	+	0.466974i
$426$		0			0
$427$	32.3433			1.56520
$428$		−	8.81346i		−	0.426015i
$429$		0			0
$430$	−24.4490	+	14.0759i	−1.17903	+	0.678799i
$431$			8.74080i			0.421030i	0.977591	+	0.210515i	$0.0675140\pi$
$431$			8.74080i			0.421030i	−0.977591	+	0.210515i	$0.932486\pi$
$432$		0			0
$433$		−	22.6903i		−	1.09042i	−0.838298	−	0.545212i	$-0.816449\pi$
$433$		−	22.6903i		−	1.09042i	0.838298	−	0.545212i	$-0.183551\pi$
$434$			53.6188i			2.57378i
$435$		0			0
$436$			12.2418i			0.586274i
$437$	11.5453			0.552286
$438$		0			0
$439$	−9.62691			−0.459468			−0.229734	−	0.973254i	$-0.573786\pi$
$439$	−9.62691			−0.459468			−0.229734	+	0.973254i	$0.573786\pi$
$440$	4.34331	−	2.50055i	0.207059	−	0.119209i
$441$		0			0
$442$	21.6779	+	5.07703i	1.03111	+	0.241490i
$443$		−	28.8979i		−	1.37298i	−0.727139	−	0.686491i	$-0.759150\pi$
$443$		−	28.8979i		−	1.37298i	0.727139	−	0.686491i	$-0.240850\pi$
$444$		0			0
$445$	−3.67599	+	2.11636i	−0.174258	+	0.100325i
$446$	−29.6132			−1.40223
$447$		0			0
$448$	−21.5419			−1.01776
$449$		−	11.9963i		−	0.566138i	−0.959100	−	0.283069i	$-0.908647\pi$
$449$		−	11.9963i		−	0.566138i	0.959100	−	0.283069i	$-0.0913526\pi$
$450$		0			0
$451$	−5.79234			−0.272751
$452$			7.98632i			0.375645i
$453$		0			0
$454$	−19.3719			−0.909170
$455$	−37.5597	+	11.3033i	−1.76082	+	0.529909i
$456$		0			0
$457$	2.44919			0.114568			0.0572841	−	0.998358i	$-0.481756\pi$
$457$	2.44919			0.114568			0.0572841	+	0.998358i	$0.481756\pi$
$458$		−	1.89049i		−	0.0883366i
$459$		0			0
$460$	−4.59870	+	2.64758i	−0.214415	+	0.123444i
$461$		−	15.5847i		−	0.725850i	−0.931818	−	0.362925i	$-0.881778\pi$
$461$		−	15.5847i		−	0.725850i	0.931818	−	0.362925i	$-0.118222\pi$
$462$		0			0
$463$	−14.5953			−0.678300			−0.339150	−	0.940732i	$-0.610139\pi$
$463$	−14.5953			−0.678300			−0.339150	+	0.940732i	$0.610139\pi$
$464$	−13.6019			−0.631450
$465$		0			0
$466$		−	24.1895i		−	1.12056i
$467$			21.2961i			0.985464i	0.870181	+	0.492732i	$0.164002\pi$
$467$			21.2961i			0.985464i	−0.870181	+	0.492732i	$0.835998\pi$
$468$		0			0
$469$	35.7536			1.65095
$470$	1.77757	+	3.08753i	0.0819930	+	0.142417i
$471$		0			0
$472$		−	15.3183i		−	0.705083i
$473$	−7.75142			−0.356411
$474$		0			0
$475$	−12.4805	−	7.24628i	−0.572645	−	0.332482i
$476$			11.0678i			0.507292i
$477$		0			0
$478$		−	29.7450i		−	1.36051i
$479$			15.8511i			0.724254i	0.932129	+	0.362127i	$0.117949\pi$
$479$			15.8511i			0.724254i	−0.932129	+	0.362127i	$0.882051\pi$
$480$		0			0
$481$	0.274943	−	1.17395i	0.0125363	−	0.0535275i
$482$			17.5596i			0.799819i
$483$		0			0
$484$	5.94524			0.270238
$485$	−11.7923	−	20.4826i	−0.535463	−	0.930067i
$486$		0			0
$487$	6.03904			0.273655			0.136828	−	0.990595i	$-0.456309\pi$
$487$	6.03904			0.273655			0.136828	+	0.990595i	$0.456309\pi$
$488$	15.0601			0.681738
$489$		0			0
$490$	−29.9484	−	52.0186i	−1.35293	−	2.34996i
$491$	4.89792			0.221040			0.110520	−	0.993874i	$-0.464748\pi$
$491$	4.89792			0.221040			0.110520	+	0.993874i	$0.464748\pi$
$492$		0			0
$493$		−	10.7884i		−	0.485885i
$494$	−16.3172	−	3.82153i	−0.734144	−	0.171939i
$495$		0			0
$496$			33.0872i			1.48566i
$497$			48.2362i			2.16369i
$498$		0			0
$499$			38.0132i			1.70170i	0.525405	+	0.850852i	$0.323914\pi$
$499$			38.0132i			1.70170i	−0.525405	+	0.850852i	$0.676086\pi$
$500$	6.63293	+	0.0242755i	0.296634	+	0.00108563i
$501$		0			0
$502$	27.0758			1.20845
$503$		−	8.15174i		−	0.363468i	−0.983348	−	0.181734i	$-0.941829\pi$
$503$		−	8.15174i		−	0.363468i	0.983348	−	0.181734i	$-0.0581710\pi$
$504$		0			0
$505$	15.2503	+	26.4888i	0.678628	+	1.17874i
$506$	−6.37309			−0.283318
$507$		0			0
$508$		−	2.17680i		−	0.0965798i
$509$			19.5422i			0.866193i	0.901347	+	0.433097i	$0.142579\pi$
$509$			19.5422i			0.866193i	−0.901347	+	0.433097i	$0.857421\pi$
$510$		0			0
$511$	8.00000			0.353899
$512$	−6.16871			−0.272621
$513$		0			0
$514$		−	13.9265i		−	0.614270i
$515$	27.5324	−	15.8511i	1.21322	−	0.698482i
$516$		0			0
$517$			0.978885i			0.0430513i
$518$	2.61992			0.115113
$519$		0			0
$520$	−17.4890	+	5.26320i	−0.766943	+	0.230807i
$521$	−6.89792			−0.302203			−0.151102	−	0.988518i	$-0.548282\pi$
$521$	−6.89792			−0.302203			−0.151102	+	0.988518i	$0.548282\pi$
$522$		0			0
$523$			21.5459i			0.942138i	0.882096	+	0.471069i	$0.156132\pi$
$523$			21.5459i			0.942138i	−0.882096	+	0.471069i	$0.843868\pi$
$524$	−1.40788			−0.0615037
$525$		0			0
$526$			1.30996i			0.0571170i
$527$	−26.2433			−1.14318
$528$		0			0
$529$	7.00000			0.304348
$530$	21.9104	−	12.6144i	0.951729	−	0.547934i
$531$		0			0
$532$		−	8.33086i		−	0.361188i
$533$	20.5525	+	4.81346i	0.890227	+	0.208494i
$534$		0			0
$535$	−28.7882	+	16.5741i	−1.24462	+	0.716559i
$536$	16.6480			0.719085
$537$		0			0
$538$	−37.4068			−1.61272
$539$		−	16.4922i		−	0.710370i
$540$		0			0
$541$		−	0.369126i		−	0.0158700i	−0.999969	−	0.00793499i	$-0.997474\pi$
$541$		−	0.369126i		−	0.0158700i	0.999969	−	0.00793499i	$-0.00252581\pi$
$542$		−	23.5037i		−	1.00957i
$543$		0			0
$544$			12.4805i			0.535097i
$545$	39.9863	−	23.0211i	1.71283	−	0.986116i
$546$		0			0
$547$			21.5459i			0.921238i	0.887598	+	0.460619i	$0.152373\pi$
$547$			21.5459i			0.921238i	−0.887598	+	0.460619i	$0.847627\pi$
$548$	−4.44885			−0.190046
$549$		0			0
$550$	6.88933	+	4.00000i	0.293762	+	0.170561i
$551$			8.12054i			0.345947i
$552$		0			0
$553$	57.5763			2.44839
$554$		−	28.3857i		−	1.20599i
$555$		0			0
$556$	−1.40788			−0.0597076
$557$	1.22106			0.0517382			0.0258691	−	0.999665i	$-0.491765\pi$
$557$	1.22106			0.0517382			0.0258691	+	0.999665i	$0.491765\pi$
$558$		0			0
$559$	27.5037	+	6.44146i	1.16328	+	0.272445i
$560$	−26.2413	−	45.5796i	−1.10890	−	1.92609i
$561$		0			0
$562$			15.5374i			0.655404i
$563$		−	8.48260i		−	0.357499i	−0.983895	−	0.178750i	$-0.942795\pi$
$563$		−	8.48260i		−	0.357499i	0.983895	−	0.178750i	$-0.0572052\pi$
$564$		0			0
$565$	26.0864	−	15.0186i	1.09746	−	0.631837i
$566$		−	6.44146i		−	0.270755i
$567$		0			0
$568$			22.4603i			0.942414i
$569$	2.33086			0.0977146			0.0488573	−	0.998806i	$-0.484442\pi$
$569$	2.33086			0.0977146			0.0488573	+	0.998806i	$0.484442\pi$
$570$		0			0
$571$	−29.8768			−1.25031			−0.625153	−	0.780503i	$-0.714963\pi$
$571$	−29.8768			−1.25031			−0.625153	+	0.780503i	$0.714963\pi$
$572$	2.06061	+	0.482601i	0.0861584	+	0.0201786i
$573$		0			0
$574$			45.8673i			1.91447i
$575$	17.2961	+	10.0422i	0.721295	+	0.418790i
$576$		0			0
$577$	36.1024			1.50296			0.751482	−	0.659753i	$-0.229339\pi$
$577$	36.1024			1.50296			0.751482	+	0.659753i	$0.229339\pi$
$578$	3.69749			0.153795
$579$		0			0
$580$	−1.86222	−	3.23456i	−0.0773243	−	0.134308i
$581$	64.2362			2.66497
$582$		0			0
$583$	6.94659			0.287699
$584$	3.72506			0.154144
$585$		0			0
$586$	28.8220			1.19063
$587$	8.87681			0.366385			0.183193	−	0.983077i	$-0.441357\pi$
$587$	8.87681			0.366385			0.183193	+	0.983077i	$0.441357\pi$
$588$		0			0
$589$	19.7536			0.813933
$590$	21.1019	−	12.1489i	0.868753	−	0.500163i
$591$		0			0
$592$	1.61671			0.0664462
$593$	26.2904			1.07962			0.539809	−	0.841788i	$-0.318496\pi$
$593$	26.2904			1.07962			0.539809	+	0.841788i	$0.318496\pi$
$594$		0			0
$595$	36.1517	−	20.8135i	1.48208	−	0.853269i
$596$		−	2.29935i		−	0.0941849i
$597$		0			0
$598$	22.6131	+	5.29606i	0.924718	+	0.216572i
$599$	12.4153			0.507276			0.253638	−	0.967299i	$-0.418373\pi$
$599$	12.4153			0.507276			0.253638	+	0.967299i	$0.418373\pi$
$600$		0			0
$601$	−5.02112			−0.204816			−0.102408	−	0.994743i	$-0.532655\pi$
$601$	−5.02112			−0.204816			−0.102408	+	0.994743i	$0.532655\pi$
$602$			61.3805i			2.50168i
$603$		0			0
$604$		−	4.06027i		−	0.165210i
$605$	−11.1803	−	19.4195i	−0.454542	−	0.789513i
$606$		0			0
$607$		−	13.8768i		−	0.563242i	−0.959526	−	0.281621i	$-0.909128\pi$
$607$		−	13.8768i		−	0.563242i	0.959526	−	0.281621i	$-0.0908721\pi$
$608$		−	9.39420i		−	0.380985i
$609$		0			0
$610$	11.9441	+	20.7462i	0.483602	+	0.839988i
$611$	0.813457	−	3.47330i	0.0329089	−	0.140515i
$612$		0			0
$613$	34.4928			1.39315			0.696575	−	0.717484i	$-0.254706\pi$
$613$	34.4928			1.39315			0.696575	+	0.717484i	$0.254706\pi$
$614$	−15.2847			−0.616840
$615$		0			0
$616$		−	10.9041i		−	0.439340i
$617$	23.5068			0.946349			0.473174	−	0.880969i	$-0.343108\pi$
$617$	23.5068			0.946349			0.473174	+	0.880969i	$0.343108\pi$
$618$		0			0
$619$		−	8.01782i		−	0.322263i	−0.986933	−	0.161132i	$-0.948486\pi$
$619$		−	8.01782i		−	0.322263i	0.986933	−	0.161132i	$-0.0515144\pi$
$620$	−7.86821	+	4.52993i	−0.315995	+	0.181926i
$621$		0			0
$622$	−55.5975			−2.22926
$623$			9.22877i			0.369743i
$624$		0			0
$625$	−12.3942	−	21.7114i	−0.495768	−	0.868455i
$626$		−	8.68663i		−	0.347187i
$627$		0			0
$628$		−	4.74617i		−	0.189393i
$629$			1.28230i			0.0511287i
$630$		0			0
$631$			28.1193i			1.11941i	0.828691	+	0.559707i	$0.189086\pi$
$631$			28.1193i			1.11941i	−0.828691	+	0.559707i	$0.810914\pi$
$632$	26.8094			1.06642
$633$		0			0
$634$	8.07587			0.320734
$635$	−7.11027	+	4.09356i	−0.282162	+	0.162448i
$636$		0			0
$637$	−13.7051	+	58.5180i	−0.543016	+	2.31857i
$638$		−	4.48260i		−	0.177468i
$639$		0			0
$640$	−15.2176	−	26.4321i	−0.601530	−	1.04482i
$641$	40.5248			1.60063			0.800317	−	0.599577i	$-0.204664\pi$
$641$	40.5248			1.60063			0.800317	+	0.599577i	$0.204664\pi$
$642$		0			0
$643$	−24.1895			−0.953939			−0.476970	−	0.878920i	$-0.658265\pi$
$643$	−24.1895			−0.953939			−0.476970	+	0.878920i	$0.658265\pi$
$644$			11.5453i			0.454948i
$645$		0			0
$646$	17.8232			0.701244
$647$		−	26.1095i		−	1.02647i	−0.858248	−	0.513235i	$-0.828447\pi$
$647$		−	26.1095i		−	1.02647i	0.858248	−	0.513235i	$-0.171553\pi$
$648$		0			0
$649$	6.69026			0.262616
$650$	−21.1208	−	19.9179i	−0.828427	−	0.781245i
$651$		0			0
$652$	11.3065			0.442799
$653$			24.7153i			0.967185i	0.875293	+	0.483592i	$0.160668\pi$
$653$			24.7153i			0.967185i	−0.875293	+	0.483592i	$0.839332\pi$
$654$		0			0
$655$	2.64758	+	4.59870i	0.103450	+	0.179686i
$656$			28.3039i			1.10508i
$657$		0			0
$658$	7.75142			0.302182
$659$	33.7787			1.31583			0.657915	−	0.753092i	$-0.271439\pi$
$659$	33.7787			1.31583			0.657915	+	0.753092i	$0.271439\pi$
$660$		0			0
$661$			4.96782i			0.193226i	0.995322	+	0.0966129i	$0.0308009\pi$
$661$			4.96782i			0.193226i	−0.995322	+	0.0966129i	$0.969199\pi$
$662$			28.5807i			1.11082i
$663$		0			0
$664$	29.9104			1.16075
$665$	−27.2118	+	15.6665i	−1.05523	+	0.607521i
$666$		0			0
$667$		−	11.2538i		−	0.435750i
$668$	−1.76092			−0.0681322
$669$		0			0
$670$	13.2035	+	22.9337i	0.510095	+	0.886005i
$671$			6.57747i			0.253920i
$672$		0			0
$673$			8.33086i			0.321131i	0.987025	+	0.160565i	$0.0513318\pi$
$673$			8.33086i			0.321131i	−0.987025	+	0.160565i	$0.948668\pi$
$674$		−	29.4293i		−	1.13357i
$675$		0			0
$676$	−6.91044	−	3.42475i	−0.265786	−	0.131721i
$677$		−	12.2327i		−	0.470141i	−0.971978	−	0.235071i	$-0.924468\pi$
$677$		−	12.2327i		−	0.470141i	0.971978	−	0.235071i	$-0.0755322\pi$
$678$		0			0
$679$	−51.4227			−1.97342
$680$	16.8334	−	9.69142i	0.645532	−	0.371649i
$681$		0			0
$682$	−10.9041			−0.417541
$683$	−30.8488			−1.18040			−0.590198	−	0.807259i	$-0.700950\pi$
$683$	−30.8488			−1.18040			−0.590198	+	0.807259i	$0.700950\pi$
$684$		0			0
$685$	8.36624	+	14.5317i	0.319658	+	0.555227i
$686$	−75.7536			−2.89229
$687$		0			0
$688$			37.8768i			1.44404i
$689$	−24.6480	−	5.77264i	−0.939015	−	0.219920i
$690$		0			0
$691$		−	39.0235i		−	1.48452i	−0.670110	−	0.742262i	$-0.733753\pi$
$691$		−	39.0235i		−	1.48452i	0.670110	−	0.742262i	$-0.266247\pi$
$692$		−	14.4267i		−	0.548420i
$693$		0			0
$694$		−	34.8272i		−	1.32202i
$695$	2.64758	+	4.59870i	0.100429	+	0.174438i
$696$		0			0
$697$	−22.4494			−0.850333
$698$			20.7462i			0.785254i
$699$		0			0
$700$	7.24628	−	12.4805i	0.273884	−	0.471719i
$701$	1.60186			0.0605014			0.0302507	−	0.999542i	$-0.490369\pi$
$701$	1.60186			0.0605014			0.0302507	+	0.999542i	$0.490369\pi$
$702$		0			0
$703$		−	0.965202i		−	0.0364033i
$704$		−	4.38085i		−	0.165109i
$705$		0			0
$706$	−17.3719			−0.653801
$707$	66.5017			2.50105
$708$		0			0
$709$			39.2899i			1.47556i	0.675040	+	0.737781i	$0.264126\pi$
$709$			39.2899i			1.47556i	−0.675040	+	0.737781i	$0.735874\pi$
$710$	−30.9405	+	17.8132i	−1.16118	+	0.668517i
$711$		0			0
$712$			4.29721i			0.161045i
$713$	−27.3755			−1.02522
$714$		0			0
$715$	−2.29869	−	7.63829i	−0.0859663	−	0.285656i
$716$	9.73874			0.363954
$717$		0			0
$718$		−	24.6680i		−	0.920601i
$719$	−4.48260			−0.167173			−0.0835864	−	0.996501i	$-0.526637\pi$
$719$	−4.48260			−0.167173			−0.0835864	+	0.996501i	$0.526637\pi$
$720$		0			0
$721$		−	69.1216i		−	2.57422i
$722$	17.1812			0.639418
$723$		0			0
$724$	−3.55963			−0.132293
$725$	−7.06335	+	12.1654i	−0.262326	+	0.451813i
$726$		0			0
$727$		−	7.58468i		−	0.281300i	−0.990059	−	0.140650i	$-0.955081\pi$
$727$		−	7.58468i		−	0.281300i	0.990059	−	0.140650i	$-0.0449193\pi$
$728$	−9.06138	+	38.6903i	−0.335837	+	1.43396i
$729$		0			0
$730$	2.95433	+	5.13149i	0.109345	+	0.189925i
$731$	−30.0422			−1.11115
$732$		0			0
$733$	−34.9979			−1.29268			−0.646339	−	0.763050i	$-0.723701\pi$
$733$	−34.9979			−1.29268			−0.646339	+	0.763050i	$0.723701\pi$
$734$			0.266399i			0.00983298i
$735$		0			0
$736$			13.0189i			0.479884i
$737$			7.27100i			0.267831i
$738$		0			0
$739$		−	26.6734i		−	0.981196i	−0.871386	−	0.490598i	$-0.836778\pi$
$739$		−	26.6734i		−	0.981196i	0.871386	−	0.490598i	$-0.163222\pi$
$740$	0.221341	+	0.384457i	0.00813667	+	0.0141329i
$741$		0			0
$742$		−	55.0074i		−	2.01939i
$743$	28.2012			1.03460			0.517300	−	0.855804i	$-0.326937\pi$
$743$	28.2012			1.03460			0.517300	+	0.855804i	$0.326937\pi$
$744$		0			0
$745$	−7.51056	+	4.32401i	−0.275166	+	0.158420i
$746$		−	2.10916i		−	0.0772218i
$747$		0			0
$748$	−2.25080			−0.0822973
$749$			72.2743i			2.64085i
$750$		0			0
$751$	4.74617			0.173190			0.0865951	−	0.996244i	$-0.472401\pi$
$751$	4.74617			0.173190			0.0865951	+	0.996244i	$0.472401\pi$
$752$	4.78326			0.174427
$753$		0			0
$754$	−3.72506	+	15.9052i	−0.135659	+	0.579235i
$755$	−13.2624	+	7.63550i	−0.482669	+	0.277884i
$756$		0			0
$757$			31.9863i			1.16256i	0.813703	+	0.581281i	$0.197448\pi$
$757$			31.9863i			1.16256i	−0.813703	+	0.581281i	$0.802552\pi$
$758$		−	0.429000i		−	0.0155820i
$759$		0			0
$760$	−12.6707	+	7.29483i	−0.459614	+	0.264611i
$761$			37.0238i			1.34211i	0.741406	+	0.671056i	$0.234159\pi$
$761$			37.0238i			1.34211i	−0.741406	+	0.671056i	$0.765841\pi$
$762$		0			0
$763$		−	100.388i		−	3.63429i
$764$	−7.40557			−0.267924
$765$		0			0
$766$	15.9664			0.576888
$767$	−23.7385	−	5.55963i	−0.857147	−	0.200747i
$768$		0			0
$769$		−	35.7680i		−	1.28983i	−0.764255	−	0.644914i	$-0.776893\pi$
$769$		−	35.7680i		−	1.28983i	0.764255	−	0.644914i	$-0.223107\pi$
$770$	15.0211	−	8.64803i	0.541323	−	0.311653i
$771$		0			0
$772$	2.14951			0.0773624
$773$	−40.4833			−1.45608			−0.728041	−	0.685533i	$-0.759569\pi$
$773$	−40.4833			−1.45608			−0.728041	+	0.685533i	$0.759569\pi$
$774$		0			0
$775$	29.5930	+	17.1819i	1.06301	+	0.617193i
$776$	−23.9441			−0.859543
$777$		0			0
$778$	−24.5239			−0.879223
$779$	16.8979			0.605431
$780$		0			0
$781$	−9.80952			−0.351012
$782$	−24.7002			−0.883278
$783$		0			0
$784$	−80.5882			−2.87815
$785$	−15.5028	+	8.92537i	−0.553320	+	0.318560i
$786$		0			0
$787$	−5.53391			−0.197262			−0.0986312	−	0.995124i	$-0.531446\pi$
$787$	−5.53391			−0.197262			−0.0986312	+	0.995124i	$0.531446\pi$
$788$	10.2215			0.364126
$789$		0			0
$790$	21.2624	+	36.9316i	0.756483	+	1.31397i
$791$		−	65.4914i		−	2.32861i
$792$		0			0
$793$	5.46590	−	23.3383i	0.194100	−	0.828767i
$794$	21.5037			0.763138
$795$		0			0
$796$	−5.85963			−0.207689
$797$			50.8420i			1.80092i	0.434943	+	0.900458i	$0.356769\pi$
$797$			50.8420i			1.80092i	−0.434943	+	0.900458i	$0.643231\pi$
$798$		0			0
$799$			3.79387i			0.134218i
$800$	8.17119	−	14.0735i	0.288895	−	0.497573i
$801$		0			0
$802$			53.2487i			1.88028i
$803$			1.62691i			0.0574125i
$804$		0			0
$805$	37.7114	−	21.7114i	1.32915	−	0.765225i
$806$	38.6903	+	9.06138i	1.36281	+	0.319173i
$807$		0			0
$808$	30.9653			1.08936
$809$	−15.2288			−0.535415			−0.267708	−	0.963500i	$-0.586266\pi$
$809$	−15.2288			−0.535415			−0.267708	+	0.963500i	$0.586266\pi$
$810$		0			0
$811$		−	23.6843i		−	0.831669i	−0.909440	−	0.415835i	$-0.863490\pi$
$811$		−	23.6843i		−	0.831669i	0.909440	−	0.415835i	$-0.136510\pi$
$812$	−8.12054			−0.284975
$813$		0			0
$814$			0.532799i			0.0186746i
$815$	−21.2624	−	36.9316i	−0.744790	−	1.29366i
$816$		0			0
$817$	22.6131			0.791132
$818$		−	31.0747i		−	1.08650i
$819$		0			0
$820$	−6.73074	+	3.87506i	−0.235048	+	0.135323i
$821$		−	42.7965i		−	1.49361i	−0.665045	−	0.746803i	$-0.731588\pi$
$821$		−	42.7965i		−	1.49361i	0.665045	−	0.746803i	$-0.268412\pi$
$822$		0			0
$823$			46.8420i			1.63281i	0.577480	+	0.816405i	$0.304036\pi$
$823$			46.8420i			1.63281i	−0.577480	+	0.816405i	$0.695964\pi$
$824$		−	32.1852i		−	1.12123i
$825$		0			0
$826$		−	52.9776i		−	1.84333i
$827$	−49.9818			−1.73804			−0.869019	−	0.494779i	$-0.835249\pi$
$827$	−49.9818			−1.73804			−0.869019	+	0.494779i	$0.835249\pi$
$828$		0			0
$829$	−20.0285			−0.695620			−0.347810	−	0.937565i	$-0.613075\pi$
$829$	−20.0285			−0.695620			−0.347810	+	0.937565i	$0.613075\pi$
$830$	23.7219	+	41.2035i	0.823398	+	1.43019i
$831$		0			0
$832$	−3.64050	+	15.5442i	−0.126212	+	0.538898i
$833$		−	63.9190i		−	2.21466i
$834$		0			0
$835$	3.31149	+	5.75186i	0.114599	+	0.199051i
$836$	1.69420			0.0585951
$837$		0			0
$838$	−26.4346			−0.913169
$839$			1.63054i			0.0562924i	0.999604	+	0.0281462i	$0.00896039\pi$
$839$			1.63054i			0.0562924i	−0.999604	+	0.0281462i	$0.991040\pi$
$840$		0			0
$841$	−21.0845			−0.727050
$842$			4.48260i			0.154481i
$843$		0			0
$844$	12.9789			0.446752
$845$	1.80882	+	29.0126i	0.0622254	+	0.998062i
$846$		0			0
$847$	−48.7537			−1.67520
$848$		−	33.9441i		−	1.16564i
$849$		0			0
$850$	26.7010	+	15.5028i	0.915838	+	0.531743i
$851$			1.33762i			0.0458531i
$852$		0			0
$853$	−15.0324			−0.514700			−0.257350	−	0.966318i	$-0.582849\pi$
$853$	−15.0324			−0.514700			−0.257350	+	0.966318i	$0.582849\pi$
$854$	52.0845			1.78229
$855$		0			0
$856$			33.6532i			1.15024i
$857$			26.6058i			0.908837i	0.890788	+	0.454418i	$0.150153\pi$
$857$			26.6058i			0.908837i	−0.890788	+	0.454418i	$0.849847\pi$
$858$		0			0
$859$	−4.58074			−0.156293			−0.0781465	−	0.996942i	$-0.524900\pi$
$859$	−4.58074			−0.156293			−0.0781465	+	0.996942i	$0.524900\pi$
$860$	−9.00720	+	5.18567i	−0.307143	+	0.176830i
$861$		0			0
$862$			14.0759i			0.479426i
$863$	−21.7874			−0.741651			−0.370826	−	0.928703i	$-0.620925\pi$
$863$	−21.7874			−0.741651			−0.370826	+	0.928703i	$0.620925\pi$
$864$		0			0
$865$	−47.1231	+	27.1300i	−1.60223	+	0.922446i
$866$		−	36.5396i		−	1.24167i
$867$		0			0
$868$			19.7536i			0.670481i
$869$			11.7090i			0.397199i
$870$		0			0
$871$	6.04223	−	25.7991i	0.204733	−	0.874169i
$872$		−	46.7439i		−	1.58295i
$873$		0			0
$874$	18.5921			0.628888
$875$	−54.3930	−	0.199070i	−1.83882	−	0.00672980i
$876$		0			0
$877$	23.9578			0.808997			0.404498	−	0.914539i	$-0.367446\pi$
$877$	23.9578			0.808997			0.404498	+	0.914539i	$0.367446\pi$
$878$	−15.5028			−0.523195
$879$		0			0
$880$	9.26926	−	5.33654i	0.312467	−	0.179895i
$881$	−24.9230			−0.839676			−0.419838	−	0.907599i	$-0.637913\pi$
$881$	−24.9230			−0.839676			−0.419838	+	0.907599i	$0.637913\pi$
$882$		0			0
$883$			8.88074i			0.298861i	0.988772	+	0.149430i	$0.0477440\pi$
$883$			8.88074i			0.298861i	−0.988772	+	0.149430i	$0.952256\pi$
$884$	7.98632	+	1.87042i	0.268609	+	0.0629090i
$885$		0			0
$886$		−	46.5362i		−	1.56341i
$887$			10.0422i			0.337185i	0.985686	+	0.168593i	$0.0539222\pi$
$887$			10.0422i			0.337185i	−0.985686	+	0.168593i	$0.946078\pi$
$888$		0			0
$889$			17.8507i			0.598694i
$890$	−5.91967	+	3.40810i	−0.198428	+	0.114240i
$891$		0			0
$892$	−10.9098			−0.365286
$893$		−	2.85569i		−	0.0955619i
$894$		0			0
$895$	−18.3141	−	31.8105i	−0.612172	−	1.06331i
$896$	−66.3594			−2.21691
$897$		0			0
$898$		−	19.3183i		−	0.644661i
$899$		−	19.2549i		−	0.642188i
$900$		0			0
$901$	26.9230			0.896934
$902$	−9.32778			−0.310581
$903$		0			0
$904$		−	30.4949i		−	1.01425i
$905$	6.69402	+	11.6271i	0.222517	+	0.386499i
$906$		0			0
$907$			36.9652i			1.22741i	0.789536	+	0.613705i	$0.210321\pi$
$907$			36.9652i			1.22741i	−0.789536	+	0.613705i	$0.789679\pi$
$908$	−7.13678			−0.236842
$909$		0			0
$910$	−60.4847	+	18.2025i	−2.00505	+	0.603407i
$911$	44.4826			1.47377			0.736887	−	0.676016i	$-0.236295\pi$
$911$	44.4826			1.47377			0.736887	+	0.676016i	$0.236295\pi$
$912$		0			0
$913$			13.0633i			0.432334i
$914$	3.94409			0.130459
$915$		0			0
$916$		−	0.696471i		−	0.0230120i
$917$	11.5453			0.381259
$918$		0			0
$919$	−11.8346			−0.390387			−0.195193	−	0.980765i	$-0.562533\pi$
$919$	−11.8346			−0.390387			−0.195193	+	0.980765i	$0.562533\pi$
$920$	17.5596	−	10.1095i	0.578924	−	0.333301i
$921$		0			0
$922$		−	25.0970i		−	0.826525i
$923$	34.8063	+	8.15174i	1.14566	+	0.268318i
$924$		0			0
$925$	0.839544	−	1.44597i	0.0276040	−	0.0475433i
$926$	−23.5037			−0.772380
$927$		0			0
$928$	−9.15704			−0.300595
$929$			5.69081i			0.186709i	0.995633	+	0.0933547i	$0.0297591\pi$
$929$			5.69081i			0.186709i	−0.995633	+	0.0933547i	$0.970241\pi$
$930$		0			0
$931$			48.1125i			1.57682i
$932$		−	8.91160i		−	0.291909i
$933$		0			0
$934$			34.2944i			1.12215i
$935$	4.23271	+	7.35197i	0.138424	+	0.240435i
$936$		0			0
$937$		−	25.9441i		−	0.847556i	−0.905766	−	0.423778i	$-0.860704\pi$
$937$		−	25.9441i		−	0.847556i	0.905766	−	0.423778i	$-0.139296\pi$
$938$	57.5763			1.87993
$939$		0			0
$940$	0.654870	+	1.13747i	0.0213595	+	0.0371002i
$941$		−	15.2573i		−	0.497375i	−0.968584	−	0.248687i	$-0.920001\pi$
$941$		−	15.2573i		−	0.497375i	0.968584	−	0.248687i	$-0.0799991\pi$
$942$		0			0
$943$	−23.4179			−0.762592
$944$		−	32.6915i		−	1.06402i
$945$		0			0
$946$	−12.4826			−0.405844
$947$	19.5089			0.633955			0.316978	−	0.948433i	$-0.397332\pi$
$947$	19.5089			0.633955			0.316978	+	0.948433i	$0.397332\pi$
$948$		0			0
$949$	1.35197	−	5.77264i	0.0438868	−	0.187388i
$950$	−20.0981	−	11.6691i	−0.652070	−	0.378597i
$951$		0			0
$952$		−	42.2613i		−	1.36970i
$953$		−	5.39420i		−	0.174735i	−0.996176	−	0.0873677i	$-0.972155\pi$
$953$		−	5.39420i		−	0.174735i	0.996176	−	0.0873677i	$-0.0278455\pi$
$954$		0			0
$955$	13.9265	+	24.1895i	0.450650	+	0.782753i
$956$		−	10.9583i		−	0.354417i
$957$		0			0
$958$			25.5260i			0.824707i
$959$	36.4826			1.17808
$960$		0			0
$961$	−15.8385			−0.510920
$962$	0.442758	−	1.89049i	0.0142751	−	0.0609517i
$963$		0			0
$964$			6.46912i			0.208356i
$965$	−4.04223	−	7.02112i	−0.130124	−	0.226018i
$966$		0			0
$967$	−14.7590			−0.474616			−0.237308	−	0.971434i	$-0.576265\pi$
$967$	−14.7590			−0.474616			−0.237308	+	0.971434i	$0.576265\pi$
$968$	−22.7013			−0.729647
$969$		0			0
$970$	−18.9900	−	32.9844i	−0.609731	−	1.05907i
$971$	−14.1940			−0.455506			−0.227753	−	0.973719i	$-0.573138\pi$
$971$	−14.1940			−0.455506			−0.227753	+	0.973719i	$0.573138\pi$
$972$		0			0
$973$	11.5453			0.370125
$974$	9.72506			0.311611
$975$		0			0
$976$	32.1404			1.02879
$977$	−1.42652			−0.0456384			−0.0228192	−	0.999740i	$-0.507264\pi$
$977$	−1.42652			−0.0456384			−0.0228192	+	0.999740i	$0.507264\pi$
$978$		0			0
$979$	−1.87680			−0.0599829
$980$	−11.0332	−	19.1641i	−0.352444	−	0.612174i
$981$		0			0
$982$	7.88743			0.251698
$983$	−27.8738			−0.889037			−0.444519	−	0.895770i	$-0.646625\pi$
$983$	−27.8738			−0.889037			−0.444519	+	0.895770i	$0.646625\pi$
$984$		0			0
$985$	−19.2219	−	33.3874i	−0.612462	−	1.06381i
$986$		−	17.3733i		−	0.553277i
$987$		0			0
$988$	−6.01138	−	1.40788i	−0.191248	−	0.0447908i
$989$	−31.3383			−0.996500
$990$		0			0
$991$	−36.0845			−1.14626			−0.573130	−	0.819464i	$-0.694271\pi$
$991$	−36.0845			−1.14626			−0.573130	+	0.819464i	$0.694271\pi$
$992$			22.2749i			0.707230i
$993$		0			0
$994$			77.6778i			2.46379i
$995$	11.0193	+	19.1398i	0.349334	+	0.606773i
$996$		0			0
$997$		−	2.92297i		−	0.0925714i	−0.998928	−	0.0462857i	$-0.985262\pi$
$997$		−	2.92297i		−	0.0925714i	0.998928	−	0.0462857i	$-0.0147385\pi$
$998$			61.2151i			1.93773i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.h.g.64.9		12
3.2	odd	2		195.2.h.c.64.3	✓	12
5.4	even	2	inner	585.2.h.g.64.3		12
12.11	even	2		3120.2.r.n.2209.10		12
13.12	even	2	inner	585.2.h.g.64.4		12
15.2	even	4		975.2.b.j.376.2		6
15.8	even	4		975.2.b.l.376.5		6
15.14	odd	2		195.2.h.c.64.10	yes	12
39.38	odd	2		195.2.h.c.64.9	yes	12
60.59	even	2		3120.2.r.n.2209.3		12
65.64	even	2	inner	585.2.h.g.64.10		12
156.155	even	2		3120.2.r.n.2209.9		12
195.38	even	4		975.2.b.l.376.2		6
195.77	even	4		975.2.b.j.376.5		6
195.194	odd	2		195.2.h.c.64.4	yes	12
780.779	even	2		3120.2.r.n.2209.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.h.c.64.3	✓	12	3.2	odd	2
195.2.h.c.64.4	yes	12	195.194	odd	2
195.2.h.c.64.9	yes	12	39.38	odd	2
195.2.h.c.64.10	yes	12	15.14	odd	2
585.2.h.g.64.3		12	5.4	even	2	inner
585.2.h.g.64.4		12	13.12	even	2	inner
585.2.h.g.64.9		12	1.1	even	1	trivial
585.2.h.g.64.10		12	65.64	even	2	inner
975.2.b.j.376.2		6	15.2	even	4
975.2.b.j.376.5		6	195.77	even	4
975.2.b.l.376.2		6	195.38	even	4
975.2.b.l.376.5		6	15.8	even	4
3120.2.r.n.2209.3		12	60.59	even	2
3120.2.r.n.2209.4		12	780.779	even	2
3120.2.r.n.2209.9		12	156.155	even	2
3120.2.r.n.2209.10		12	12.11	even	2

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.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.61036 q^{2} +0.593272 q^{4} +(-1.11567 - 1.93785i) q^{5} -4.86509 q^{7} -2.26534 q^{8} +O(q^{10})\)	\(q+1.61036 q^{2} +0.593272 q^{4} +(-1.11567 - 1.93785i) q^{5} -4.86509 q^{7} -2.26534 q^{8} +(-1.79664 - 3.12065i) q^{10} -0.989386i q^{11} +(-0.822183 + 3.51056i) q^{13} -7.83457 q^{14} -4.83457 q^{16} -3.83457i q^{17} +2.88632i q^{19} +(-0.661896 - 1.14967i) q^{20} -1.59327i q^{22} -4.00000i q^{23} +(-2.51056 + 4.32401i) q^{25} +(-1.32401 + 5.65327i) q^{26} -2.88632 q^{28} +2.81346 q^{29} -6.84387i q^{31} -3.25473 q^{32} -6.17506i q^{34} +(5.42784 + 9.42784i) q^{35} -0.334405 q^{37} +4.64803i q^{38} +(2.52738 + 4.38991i) q^{40} -5.85448i q^{41} -7.83457i q^{43} -0.586975i q^{44} -6.44146i q^{46} -0.989386 q^{47} +16.6691 q^{49} +(-4.04291 + 6.96324i) q^{50} +(-0.487778 + 2.08271i) q^{52} +7.02112i q^{53} +(-1.91729 + 1.10383i) q^{55} +11.0211 q^{56} +4.53069 q^{58} +6.76203i q^{59} -6.64803 q^{61} -11.0211i q^{62} +4.42784 q^{64} +(7.72023 - 2.32335i) q^{65} -7.34901 q^{67} -2.27494i q^{68} +(8.74080 + 15.1823i) q^{70} -9.91475i q^{71} -1.64437 q^{73} -0.538514 q^{74} +1.71237i q^{76} +4.81346i q^{77} -11.8346 q^{79} +(5.39379 + 9.36870i) q^{80} -9.42784i q^{82} -13.2035 q^{83} +(-7.43084 + 4.27812i) q^{85} -12.6165i q^{86} +2.24130i q^{88} -1.89694i q^{89} +(4.00000 - 17.0792i) q^{91} -2.37309i q^{92} -1.59327 q^{94} +(5.59327 - 3.22019i) q^{95} +10.5697 q^{97} +26.8434 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{4}+O(q^{10}) \) 12 * q + 12 * q^4	\( 12 q + 12 q^{4} - 24 q^{10} - 16 q^{14} + 20 q^{16} + 4 q^{25} + 28 q^{26} + 24 q^{29} - 8 q^{35} - 16 q^{40} + 44 q^{49} + 16 q^{55} + 64 q^{56} + 8 q^{61} - 20 q^{64} - 28 q^{65} - 104 q^{74} - 64 q^{79} + 48 q^{91} - 24 q^{94} + 72 q^{95}+O(q^{100}) \) 12 * q + 12 * q^4 - 24 * q^10 - 16 * q^14 + 20 * q^16 + 4 * q^25 + 28 * q^26 + 24 * q^29 - 8 * q^35 - 16 * q^40 + 44 * q^49 + 16 * q^55 + 64 * q^56 + 8 * q^61 - 20 * q^64 - 28 * q^65 - 104 * q^74 - 64 * q^79 + 48 * q^91 - 24 * q^94 + 72 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more