LMFDB - Embedded newform 1512.2.j.d.323.48

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(323,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 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("1512.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.j (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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.48
Character	$\chi$	$=$	1512.323
Dual form			1512.2.j.d.323.47

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41047 + 0.102782i) q^{2} +(1.97887 + 0.289943i) q^{4} +2.90802 q^{5} -1.00000i q^{7} +(2.76135 + 0.612349i) q^{8} +O(q^{10})$	\(q+(1.41047 + 0.102782i) q^{2} +(1.97887 + 0.289943i) q^{4} +2.90802 q^{5} -1.00000i q^{7} +(2.76135 + 0.612349i) q^{8} +(4.10168 + 0.298892i) q^{10} -1.28828i q^{11} -1.86999i q^{13} +(0.102782 - 1.41047i) q^{14} +(3.83187 + 1.14752i) q^{16} -3.87222i q^{17} -2.04228 q^{19} +(5.75460 + 0.843159i) q^{20} +(0.132412 - 1.81709i) q^{22} -0.934839 q^{23} +3.45657 q^{25} +(0.192202 - 2.63757i) q^{26} +(0.289943 - 1.97887i) q^{28} +2.98295 q^{29} +1.85691i q^{31} +(5.28680 + 2.01239i) q^{32} +(0.397995 - 5.46166i) q^{34} -2.90802i q^{35} +3.85846i q^{37} +(-2.88059 - 0.209910i) q^{38} +(8.03004 + 1.78072i) q^{40} +8.72247i q^{41} -1.19319 q^{43} +(0.373528 - 2.54935i) q^{44} +(-1.31857 - 0.0960846i) q^{46} -11.1537 q^{47} -1.00000 q^{49} +(4.87541 + 0.355274i) q^{50} +(0.542190 - 3.70047i) q^{52} -4.43885 q^{53} -3.74635i q^{55} +(0.612349 - 2.76135i) q^{56} +(4.20737 + 0.306594i) q^{58} +10.9714i q^{59} -4.70930i q^{61} +(-0.190857 + 2.61913i) q^{62} +(7.25006 + 3.38181i) q^{64} -5.43797i q^{65} +4.41800 q^{67} +(1.12272 - 7.66263i) q^{68} +(0.298892 - 4.10168i) q^{70} -9.72888 q^{71} +9.40756 q^{73} +(-0.396580 + 5.44225i) q^{74} +(-4.04142 - 0.592145i) q^{76} -1.28828 q^{77} +16.4660i q^{79} +(11.1431 + 3.33701i) q^{80} +(-0.896513 + 12.3028i) q^{82} +3.72150i q^{83} -11.2605i q^{85} +(-1.68296 - 0.122638i) q^{86} +(0.788879 - 3.55739i) q^{88} -12.2297i q^{89} -1.86999 q^{91} +(-1.84993 - 0.271050i) q^{92} +(-15.7320 - 1.14640i) q^{94} -5.93900 q^{95} +15.8302 q^{97} +(-1.41047 - 0.102782i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4}+O(q^{10}) $ 48 * q - 4 * q^4	$ 48 q - 4 q^{4} - 12 q^{10} - 12 q^{16} + 16 q^{19} - 24 q^{22} + 48 q^{25} + 8 q^{28} + 12 q^{34} + 32 q^{40} + 64 q^{43} + 60 q^{46} - 48 q^{49} + 16 q^{52} + 36 q^{58} - 4 q^{64} + 32 q^{67} + 12 q^{70} - 32 q^{76} + 36 q^{82} + 24 q^{88} - 60 q^{94}+O(q^{100}) $ 48 * q - 4 * q^4 - 12 * q^10 - 12 * q^16 + 16 * q^19 - 24 * q^22 + 48 * q^25 + 8 * q^28 + 12 * q^34 + 32 * q^40 + 64 * q^43 + 60 * q^46 - 48 * q^49 + 16 * q^52 + 36 * q^58 - 4 * q^64 + 32 * q^67 + 12 * q^70 - 32 * q^76 + 36 * q^82 + 24 * q^88 - 60 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	1.41047	+	0.102782i	0.997355	+	0.0726779i
$2$	1.41047	+	0.102782i	0.997355	+	0.0726779i
$3$		0			0
$3$		0			0
$4$	1.97887	+	0.289943i	0.989436	+	0.144971i
$5$	2.90802			1.30051			0.650253	−	0.759718i	$-0.274663\pi$
$5$	2.90802			1.30051			0.650253	+	0.759718i	$0.274663\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	2.76135	+	0.612349i	0.976283	+	0.216498i
$9$		0			0
$10$	4.10168	+	0.298892i	1.29707	+	0.0945180i
$11$		−	1.28828i		−	0.388432i	−0.980959	−	0.194216i	$-0.937784\pi$
$11$		−	1.28828i		−	0.388432i	0.980959	−	0.194216i	$-0.0622163\pi$
$12$		0			0
$13$		−	1.86999i		−	0.518642i	−0.965791	−	0.259321i	$-0.916501\pi$
$13$		−	1.86999i		−	0.518642i	0.965791	−	0.259321i	$-0.0834988\pi$
$14$	0.102782	−	1.41047i	0.0274697	−	0.376965i
$15$		0			0
$16$	3.83187	+	1.14752i	0.957967	+	0.286880i
$17$		−	3.87222i		−	0.939151i	−0.882892	−	0.469576i	$-0.844407\pi$
$17$		−	3.87222i		−	0.939151i	0.882892	−	0.469576i	$-0.155593\pi$
$18$		0			0
$19$	−2.04228			−0.468532			−0.234266	−	0.972173i	$-0.575269\pi$
$19$	−2.04228			−0.468532			−0.234266	+	0.972173i	$0.575269\pi$
$20$	5.75460	+	0.843159i	1.28677	+	0.188536i
$21$		0			0
$22$	0.132412	−	1.81709i	0.0282304	−	0.387405i
$23$	−0.934839			−0.194927			−0.0974637	−	0.995239i	$-0.531073\pi$
$23$	−0.934839			−0.194927			−0.0974637	+	0.995239i	$0.531073\pi$
$24$		0			0
$25$	3.45657			0.691315
$26$	0.192202	−	2.63757i	0.0376938	−	0.517271i
$27$		0			0
$28$	0.289943	−	1.97887i	0.0547940	−	0.373972i
$29$	2.98295			0.553920			0.276960	−	0.960881i	$-0.410673\pi$
$29$	2.98295			0.553920			0.276960	+	0.960881i	$0.410673\pi$
$30$		0			0
$31$			1.85691i			0.333511i	0.985998	+	0.166756i	$0.0533291\pi$
$31$			1.85691i			0.333511i	−0.985998	+	0.166756i	$0.946671\pi$
$32$	5.28680	+	2.01239i	0.934583	+	0.355744i
$33$		0			0
$34$	0.397995	−	5.46166i	0.0682555	−	0.936668i
$35$		−	2.90802i		−	0.491545i
$36$		0			0
$37$			3.85846i			0.634327i	0.948371	+	0.317163i	$0.102730\pi$
$37$			3.85846i			0.634327i	−0.948371	+	0.317163i	$0.897270\pi$
$38$	−2.88059	−	0.209910i	−0.467293	−	0.0340519i
$39$		0			0
$40$	8.03004	+	1.78072i	1.26966	+	0.281557i
$41$			8.72247i			1.36222i	0.732181	+	0.681110i	$0.238503\pi$
$41$			8.72247i			1.36222i	−0.732181	+	0.681110i	$0.761497\pi$
$42$		0			0
$43$	−1.19319			−0.181959			−0.0909796	−	0.995853i	$-0.529000\pi$
$43$	−1.19319			−0.181959			−0.0909796	+	0.995853i	$0.529000\pi$
$44$	0.373528	−	2.54935i	0.0563115	−	0.384329i
$45$		0			0
$46$	−1.31857	−	0.0960846i	−0.194412	−	0.0141669i
$47$	−11.1537			−1.62694			−0.813468	−	0.581609i	$-0.802423\pi$
$47$	−11.1537			−1.62694			−0.813468	+	0.581609i	$0.802423\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	4.87541	+	0.355274i	0.689487	+	0.0502433i
$51$		0			0
$52$	0.542190	−	3.70047i	0.0751883	−	0.513163i
$53$	−4.43885			−0.609723			−0.304862	−	0.952397i	$-0.598610\pi$
$53$	−4.43885			−0.609723			−0.304862	+	0.952397i	$0.598610\pi$
$54$		0			0
$55$		−	3.74635i		−	0.505158i
$56$	0.612349	−	2.76135i	0.0818286	−	0.369000i
$57$		0			0
$58$	4.20737	+	0.306594i	0.552455	+	0.0402577i
$59$			10.9714i			1.42836i	0.699964	+	0.714178i	$0.253199\pi$
$59$			10.9714i			1.42836i	−0.699964	+	0.714178i	$0.746801\pi$
$60$		0			0
$61$		−	4.70930i		−	0.602964i	−0.953472	−	0.301482i	$-0.902519\pi$
$61$		−	4.70930i		−	0.602964i	0.953472	−	0.301482i	$-0.0974813\pi$
$62$	−0.190857	+	2.61913i	−0.0242389	+	0.332629i
$63$		0			0
$64$	7.25006	+	3.38181i	0.906257	+	0.422727i
$65$		−	5.43797i		−	0.674497i
$66$		0			0
$67$	4.41800			0.539745			0.269872	−	0.962896i	$-0.413019\pi$
$67$	4.41800			0.539745			0.269872	+	0.962896i	$0.413019\pi$
$68$	1.12272	−	7.66263i	0.136150	−	0.929230i
$69$		0			0
$70$	0.298892	−	4.10168i	0.0357244	−	0.490245i
$71$	−9.72888			−1.15461			−0.577303	−	0.816530i	$-0.695895\pi$
$71$	−9.72888			−1.15461			−0.577303	+	0.816530i	$0.695895\pi$
$72$		0			0
$73$	9.40756			1.10107			0.550536	−	0.834812i	$-0.314423\pi$
$73$	9.40756			1.10107			0.550536	+	0.834812i	$0.314423\pi$
$74$	−0.396580	+	5.44225i	−0.0461015	+	0.632649i
$75$		0			0
$76$	−4.04142	−	0.592145i	−0.463582	−	0.0679237i
$77$	−1.28828			−0.146813
$78$		0			0
$79$			16.4660i			1.85257i	0.376822	+	0.926286i	$0.377017\pi$
$79$			16.4660i			1.85257i	−0.376822	+	0.926286i	$0.622983\pi$
$80$	11.1431	+	3.33701i	1.24584	+	0.373089i
$81$		0			0
$82$	−0.896513	+	12.3028i	−0.0990033	+	1.35862i
$83$			3.72150i			0.408488i	0.978920	+	0.204244i	$0.0654736\pi$
$83$			3.72150i			0.408488i	−0.978920	+	0.204244i	$0.934526\pi$
$84$		0			0
$85$		−	11.2605i		−	1.22137i
$86$	−1.68296	−	0.122638i	−0.181478	−	0.0132244i
$87$		0			0
$88$	0.788879	−	3.55739i	0.0840948	−	0.379220i
$89$		−	12.2297i		−	1.29635i	−0.761492	−	0.648174i	$-0.775533\pi$
$89$		−	12.2297i		−	1.29635i	0.761492	−	0.648174i	$-0.224467\pi$
$90$		0			0
$91$	−1.86999			−0.196028
$92$	−1.84993	−	0.271050i	−0.192868	−	0.0282589i
$93$		0			0
$94$	−15.7320	−	1.14640i	−1.62263	−	0.118242i
$95$	−5.93900			−0.609329
$96$		0			0
$97$	15.8302			1.60731			0.803657	−	0.595093i	$-0.202885\pi$
$97$	15.8302			1.60731			0.803657	+	0.595093i	$0.202885\pi$
$98$	−1.41047	−	0.102782i	−0.142479	−	0.0103826i
$99$		0			0
$100$	6.84012	+	1.00221i	0.684012	+	0.100221i
$101$	−0.737825			−0.0734163			−0.0367081	−	0.999326i	$-0.511687\pi$
$101$	−0.737825			−0.0734163			−0.0367081	+	0.999326i	$0.511687\pi$
$102$		0			0
$103$		−	16.2518i		−	1.60134i	−0.599109	−	0.800668i	$-0.704478\pi$
$103$		−	16.2518i		−	1.60134i	0.599109	−	0.800668i	$-0.295522\pi$
$104$	1.14509	−	5.16369i	0.112285	−	0.506342i
$105$		0			0
$106$	−6.26088	−	0.456234i	−0.608111	−	0.0443134i
$107$		−	1.49407i		−	0.144438i	−0.997389	−	0.0722188i	$-0.976992\pi$
$107$		−	1.49407i		−	0.144438i	0.997389	−	0.0722188i	$-0.0230080\pi$
$108$		0			0
$109$			11.8362i			1.13370i	0.823821	+	0.566850i	$0.191838\pi$
$109$			11.8362i			1.13370i	−0.823821	+	0.566850i	$0.808162\pi$
$110$	0.385058	−	5.28413i	0.0367138	−	0.503822i
$111$		0			0
$112$	1.14752	−	3.83187i	0.108430	−	0.362077i
$113$			15.3287i			1.44200i	0.692934	+	0.721001i	$0.256318\pi$
$113$			15.3287i			1.44200i	−0.692934	+	0.721001i	$0.743682\pi$
$114$		0			0
$115$	−2.71853			−0.253504
$116$	5.90288	+	0.864885i	0.548068	+	0.0803026i
$117$		0			0
$118$	−1.12766	+	15.4749i	−0.103810	+	1.42458i
$119$	−3.87222			−0.354966
$120$		0			0
$121$	9.34033			0.849121
$122$	0.484032	−	6.64234i	0.0438222	−	0.601370i
$123$		0			0
$124$	−0.538398	+	3.67459i	−0.0483496	+	0.329988i
$125$	−4.48831			−0.401447
$126$		0			0
$127$		−	6.55275i		−	0.581462i	−0.956805	−	0.290731i	$-0.906101\pi$
$127$		−	6.55275i		−	0.581462i	0.956805	−	0.290731i	$-0.0938985\pi$
$128$	9.87842	+	5.51514i	0.873138	+	0.487474i
$129$		0			0
$130$	0.558926	−	7.67011i	0.0490210	−	0.672713i
$131$		−	11.6893i		−	1.02130i	−0.859790	−	0.510648i	$-0.829405\pi$
$131$		−	11.6893i		−	1.02130i	0.859790	−	0.510648i	$-0.170595\pi$
$132$		0			0
$133$			2.04228i			0.177088i
$134$	6.23147	+	0.454091i	0.538317	+	0.0392275i
$135$		0			0
$136$	2.37115	−	10.6925i	0.203324	−	0.916877i
$137$			7.35868i			0.628694i	0.949308	+	0.314347i	$0.101786\pi$
$137$			7.35868i			0.628694i	−0.949308	+	0.314347i	$0.898214\pi$
$138$		0			0
$139$	−15.2683			−1.29504			−0.647520	−	0.762048i	$-0.724194\pi$
$139$	−15.2683			−1.29504			−0.647520	+	0.762048i	$0.724194\pi$
$140$	0.843159	−	5.75460i	0.0712599	−	0.486352i
$141$		0			0
$142$	−13.7223	−	0.999955i	−1.15155	−	0.0839143i
$143$	−2.40908			−0.201457
$144$		0			0
$145$	8.67448			0.720376
$146$	13.2691	+	0.966928i	1.09816	+	0.0800235i
$147$		0			0
$148$	−1.11873	+	7.63540i	−0.0919592	+	0.627626i
$149$	−16.6778			−1.36630			−0.683148	−	0.730280i	$-0.739389\pi$
$149$	−16.6778			−1.36630			−0.683148	+	0.730280i	$0.739389\pi$
$150$		0			0
$151$			16.4838i			1.34143i	0.741714	+	0.670716i	$0.234013\pi$
$151$			16.4838i			1.34143i	−0.741714	+	0.670716i	$0.765987\pi$
$152$	−5.63945	−	1.25059i	−0.457420	−	0.101436i
$153$		0			0
$154$	−1.81709	−	0.132412i	−0.146425	−	0.0106701i
$155$			5.39994i			0.433733i
$156$		0			0
$157$		−	16.0196i		−	1.27851i	−0.768997	−	0.639253i	$-0.779244\pi$
$157$		−	16.0196i		−	1.27851i	0.768997	−	0.639253i	$-0.220756\pi$
$158$	−1.69241	+	23.2249i	−0.134641	+	1.84767i
$159$		0			0
$160$	15.3741	+	5.85208i	1.21543	+	0.462647i
$161$			0.934839i			0.0736756i
$162$		0			0
$163$	6.18368			0.484343			0.242172	−	0.970233i	$-0.422140\pi$
$163$	6.18368			0.484343			0.242172	+	0.970233i	$0.422140\pi$
$164$	−2.52902	+	17.2606i	−0.197483	+	1.34783i
$165$		0			0
$166$	−0.382504	+	5.24908i	−0.0296881	+	0.407408i
$167$	−12.7232			−0.984549			−0.492275	−	0.870440i	$-0.663834\pi$
$167$	−12.7232			−0.984549			−0.492275	+	0.870440i	$0.663834\pi$
$168$		0			0
$169$	9.50313			0.731010
$170$	1.15738	−	15.8826i	0.0887667	−	1.21814i
$171$		0			0
$172$	−2.36116	−	0.345956i	−0.180037	−	0.0263789i
$173$	−11.2579			−0.855925			−0.427963	−	0.903796i	$-0.640769\pi$
$173$	−11.2579			−0.855925			−0.427963	+	0.903796i	$0.640769\pi$
$174$		0			0
$175$		−	3.45657i		−	0.261292i
$176$	1.47833	−	4.93653i	0.111433	−	0.372105i
$177$		0			0
$178$	1.25700	−	17.2497i	0.0942159	−	1.29292i
$179$		−	8.68048i		−	0.648809i	−0.945918	−	0.324405i	$-0.894836\pi$
$179$		−	8.68048i		−	0.648809i	0.945918	−	0.324405i	$-0.105164\pi$
$180$		0			0
$181$			2.48587i			0.184773i	0.995723	+	0.0923866i	$0.0294496\pi$
$181$			2.48587i			0.184773i	−0.995723	+	0.0923866i	$0.970550\pi$
$182$	−2.63757	−	0.192202i	−0.195510	−	0.0142469i
$183$		0			0
$184$	−2.58141	−	0.572448i	−0.190304	−	0.0422014i
$185$			11.2205i			0.824945i
$186$		0			0
$187$	−4.98851			−0.364796
$188$	−22.0718	−	3.23394i	−1.60975	−	0.235859i
$189$		0			0
$190$	−8.37680	−	0.610423i	−0.607717	−	0.0442847i
$191$	3.40263			0.246206			0.123103	−	0.992394i	$-0.460715\pi$
$191$	3.40263			0.246206			0.123103	+	0.992394i	$0.460715\pi$
$192$		0			0
$193$	20.7031			1.49024			0.745121	−	0.666929i	$-0.232392\pi$
$193$	20.7031			1.49024			0.745121	+	0.666929i	$0.232392\pi$
$194$	22.3281	+	1.62706i	1.60306	+	0.116816i
$195$		0			0
$196$	−1.97887	−	0.289943i	−0.141348	−	0.0207102i
$197$	−16.3546			−1.16521			−0.582607	−	0.812754i	$-0.697967\pi$
$197$	−16.3546			−1.16521			−0.582607	+	0.812754i	$0.697967\pi$
$198$		0			0
$199$		−	11.3717i		−	0.806121i	−0.915173	−	0.403061i	$-0.867946\pi$
$199$		−	11.3717i		−	0.806121i	0.915173	−	0.403061i	$-0.132054\pi$
$200$	9.54480	+	2.11663i	0.674919	+	0.149668i
$201$		0			0
$202$	−1.04068	−	0.0758351i	−0.0732221	−	0.00533574i
$203$		−	2.98295i		−	0.209362i
$204$		0			0
$205$			25.3651i			1.77158i
$206$	1.67039	−	22.9227i	0.116382	−	1.59710i
$207$		0			0
$208$	2.14585	−	7.16556i	0.148788	−	0.496842i
$209$			2.63104i			0.181993i
$210$		0			0
$211$	−2.56405			−0.176517			−0.0882583	−	0.996098i	$-0.528130\pi$
$211$	−2.56405			−0.176517			−0.0882583	+	0.996098i	$0.528130\pi$
$212$	−8.78392	−	1.28701i	−0.603282	−	0.0883924i
$213$		0			0
$214$	0.153564	−	2.10735i	0.0104974	−	0.144056i
$215$	−3.46981			−0.236639
$216$		0			0
$217$	1.85691			0.126055
$218$	−1.21655	+	16.6946i	−0.0823950	+	1.13070i
$219$		0			0
$220$	1.08623	−	7.41355i	0.0732334	−	0.499821i
$221$	−7.24102			−0.487083
$222$		0			0
$223$		−	1.37584i		−	0.0921329i	−0.998938	−	0.0460665i	$-0.985331\pi$
$223$		−	1.37584i		−	0.0921329i	0.998938	−	0.0460665i	$-0.0146686\pi$
$224$	2.01239	−	5.28680i	0.134459	−	0.353239i
$225$		0			0
$226$	−1.57551	+	21.6207i	−0.104802	+	1.43819i
$227$			27.3740i			1.81688i	0.418020	+	0.908438i	$0.362724\pi$
$227$			27.3740i			1.81688i	−0.418020	+	0.908438i	$0.637276\pi$
$228$		0			0
$229$		−	12.3066i		−	0.813243i	−0.913597	−	0.406621i	$-0.866707\pi$
$229$		−	12.3066i		−	0.813243i	0.913597	−	0.406621i	$-0.133293\pi$
$230$	−3.83441	−	0.279416i	−0.252834	−	0.0184241i
$231$		0			0
$232$	8.23696	+	1.82661i	0.540783	+	0.119923i
$233$		−	24.0829i		−	1.57772i	−0.614571	−	0.788862i	$-0.710671\pi$
$233$		−	24.0829i		−	1.57772i	0.614571	−	0.788862i	$-0.289329\pi$
$234$		0			0
$235$	−32.4352			−2.11584
$236$	−3.18108	+	21.7110i	−0.207071	+	1.41327i
$237$		0			0
$238$	−5.46166	−	0.397995i	−0.354027	−	0.0257982i
$239$	18.0426			1.16708			0.583540	−	0.812085i	$-0.301667\pi$
$239$	18.0426			1.16708			0.583540	+	0.812085i	$0.301667\pi$
$240$		0			0
$241$	−10.8541			−0.699174			−0.349587	−	0.936904i	$-0.613678\pi$
$241$	−10.8541			−0.699174			−0.349587	+	0.936904i	$0.613678\pi$
$242$	13.1743	+	0.960018i	0.846875	+	0.0617123i
$243$		0			0
$244$	1.36543	−	9.31910i	0.0874125	−	0.596594i
$245$	−2.90802			−0.185787
$246$		0			0
$247$			3.81905i			0.243001i
$248$	−1.13708	+	5.12758i	−0.0722046	+	0.325601i
$249$		0			0
$250$	−6.33065	−	0.461318i	−0.400385	−	0.0291763i
$251$		−	6.63032i		−	0.418502i	−0.977862	−	0.209251i	$-0.932897\pi$
$251$		−	6.63032i		−	0.418502i	0.977862	−	0.209251i	$-0.0671025\pi$
$252$		0			0
$253$			1.20434i			0.0757160i
$254$	0.673505	−	9.24248i	0.0422595	−	0.579925i
$255$		0			0
$256$	13.3664	+	8.79428i	0.835400	+	0.549642i
$257$		−	12.2398i		−	0.763497i	−0.924266	−	0.381748i	$-0.875322\pi$
$257$		−	12.2398i		−	0.763497i	0.924266	−	0.381748i	$-0.124678\pi$
$258$		0			0
$259$	3.85846			0.239753
$260$	1.57670	−	10.7610i	0.0977828	−	0.667372i
$261$		0			0
$262$	1.20145	−	16.4874i	0.0742257	−	1.01860i
$263$	2.87474			0.177264			0.0886320	−	0.996064i	$-0.471750\pi$
$263$	2.87474			0.177264			0.0886320	+	0.996064i	$0.471750\pi$
$264$		0			0
$265$	−12.9083			−0.792948
$266$	−0.209910	+	2.88059i	−0.0128704	+	0.176620i
$267$		0			0
$268$	8.74265	+	1.28097i	0.534043	+	0.0782475i
$269$	−6.17565			−0.376536			−0.188268	−	0.982118i	$-0.560287\pi$
$269$	−6.17565			−0.376536			−0.188268	+	0.982118i	$0.560287\pi$
$270$		0			0
$271$		−	19.5103i		−	1.18517i	−0.805510	−	0.592583i	$-0.798108\pi$
$271$		−	19.5103i		−	1.18517i	0.805510	−	0.592583i	$-0.201892\pi$
$272$	4.44345	−	14.8378i	0.269423	−	0.899675i
$273$		0			0
$274$	−0.756340	+	10.3792i	−0.0456922	+	0.627031i
$275$		−	4.45305i		−	0.268529i
$276$		0			0
$277$		−	2.82757i		−	0.169892i	−0.996386	−	0.0849460i	$-0.972928\pi$
$277$		−	2.82757i		−	0.169892i	0.996386	−	0.0849460i	$-0.0270718\pi$
$278$	−21.5355	−	1.56931i	−1.29162	−	0.0941208i
$279$		0			0
$280$	1.78072	−	8.03004i	0.106419	−	0.479887i
$281$			29.7569i			1.77515i	0.460663	+	0.887575i	$0.347612\pi$
$281$			29.7569i			1.77515i	−0.460663	+	0.887575i	$0.652388\pi$
$282$		0			0
$283$	−30.7427			−1.82746			−0.913731	−	0.406319i	$-0.866812\pi$
$283$	−30.7427			−1.82746			−0.913731	+	0.406319i	$0.866812\pi$
$284$	−19.2522	−	2.82082i	−1.14241	−	0.167385i
$285$		0			0
$286$	−3.39794	−	0.247610i	−0.200924	−	0.0146415i
$287$	8.72247			0.514871
$288$		0			0
$289$	2.00592			0.117995
$290$	12.2351	+	0.891581i	0.718471	+	0.0523554i
$291$		0			0
$292$	18.6164	+	2.72765i	1.08944	+	0.159624i
$293$	−5.70430			−0.333249			−0.166624	−	0.986020i	$-0.553287\pi$
$293$	−5.70430			−0.333249			−0.166624	+	0.986020i	$0.553287\pi$
$294$		0			0
$295$			31.9051i			1.85758i
$296$	−2.36272	+	10.6545i	−0.137331	+	0.619282i
$297$		0			0
$298$	−23.5235	−	1.71417i	−1.36268	−	0.0992995i
$299$			1.74814i			0.101098i
$300$		0			0
$301$			1.19319i			0.0687741i
$302$	−1.69424	+	23.2499i	−0.0974924	+	1.33788i
$303$		0			0
$304$	−7.82576	−	2.34356i	−0.448838	−	0.134412i
$305$		−	13.6947i		−	0.784158i
$306$		0			0
$307$	−6.47411			−0.369497			−0.184748	−	0.982786i	$-0.559147\pi$
$307$	−6.47411			−0.369497			−0.184748	+	0.982786i	$0.559147\pi$
$308$	−2.54935	−	0.373528i	−0.145263	−	0.0212838i
$309$		0			0
$310$	−0.555016	+	7.61647i	−0.0315228	+	0.432586i
$311$	−2.44723			−0.138770			−0.0693848	−	0.997590i	$-0.522104\pi$
$311$	−2.44723			−0.138770			−0.0693848	+	0.997590i	$0.522104\pi$
$312$		0			0
$313$	−8.03434			−0.454128			−0.227064	−	0.973880i	$-0.572913\pi$
$313$	−8.03434			−0.454128			−0.227064	+	0.973880i	$0.572913\pi$
$314$	1.64653	−	22.5953i	0.0929191	−	1.27512i
$315$		0			0
$316$	−4.77420	+	32.5841i	−0.268570	+	1.83300i
$317$	−19.0098			−1.06770			−0.533850	−	0.845579i	$-0.679255\pi$
$317$	−19.0098			−1.06770			−0.533850	+	0.845579i	$0.679255\pi$
$318$		0			0
$319$		−	3.84289i		−	0.215160i
$320$	21.0833	+	9.83438i	1.17859	+	0.549759i
$321$		0			0
$322$	−0.0960846	+	1.31857i	−0.00535459	+	0.0734808i
$323$			7.90817i			0.440022i
$324$		0			0
$325$		−	6.46376i		−	0.358545i
$326$	8.72192	+	0.635571i	0.483062	+	0.0352010i
$327$		0			0
$328$	−5.34119	+	24.0857i	−0.294918	+	1.32991i
$329$			11.1537i			0.614924i
$330$		0			0
$331$	−35.8597			−1.97103			−0.985515	−	0.169588i	$-0.945756\pi$
$331$	−35.8597			−1.97103			−0.985515	+	0.169588i	$0.945756\pi$
$332$	−1.07902	+	7.36438i	−0.0592191	+	0.404173i
$333$		0			0
$334$	−17.9457	−	1.30771i	−0.981946	−	0.0715550i
$335$	12.8476			0.701941
$336$		0			0
$337$	−6.90274			−0.376016			−0.188008	−	0.982168i	$-0.560203\pi$
$337$	−6.90274			−0.376016			−0.188008	+	0.982168i	$0.560203\pi$
$338$	13.4039	+	0.976751i	0.729077	+	0.0531283i
$339$		0			0
$340$	3.26490	−	22.2831i	0.177064	−	1.20847i
$341$	2.39223			0.129546
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−3.29480	−	0.730646i	−0.177644	−	0.0393938i
$345$		0			0
$346$	−15.8790	−	1.15711i	−0.853662	−	0.0622068i
$347$		−	36.6932i		−	1.96980i	−0.173135	−	0.984898i	$-0.555390\pi$
$347$		−	36.6932i		−	1.96980i	0.173135	−	0.984898i	$-0.444610\pi$
$348$		0			0
$349$			28.2560i			1.51251i	0.654278	+	0.756254i	$0.272973\pi$
$349$			28.2560i			1.51251i	−0.654278	+	0.756254i	$0.727027\pi$
$350$	0.355274	−	4.87541i	0.0189902	−	0.260601i
$351$		0			0
$352$	2.59253	−	6.81090i	0.138182	−	0.363022i
$353$		−	24.3138i		−	1.29410i	−0.762450	−	0.647048i	$-0.776003\pi$
$353$		−	24.3138i		−	1.29410i	0.762450	−	0.647048i	$-0.223997\pi$
$354$		0			0
$355$	−28.2918			−1.50157
$356$	3.54592	−	24.2011i	0.187933	−	1.28265i
$357$		0			0
$358$	0.892197	−	12.2436i	0.0471541	−	0.647094i
$359$	−1.95382			−0.103119			−0.0515594	−	0.998670i	$-0.516419\pi$
$359$	−1.95382			−0.103119			−0.0515594	+	0.998670i	$0.516419\pi$
$360$		0			0
$361$	−14.8291			−0.780478
$362$	−0.255503	+	3.50625i	−0.0134289	+	0.184284i
$363$		0			0
$364$	−3.70047	−	0.542190i	−0.193957	−	0.0284185i
$365$	27.3574			1.43195
$366$		0			0
$367$			21.3819i			1.11613i	0.829798	+	0.558064i	$0.188456\pi$
$367$			21.3819i			1.11613i	−0.829798	+	0.558064i	$0.811544\pi$
$368$	−3.58218	−	1.07275i	−0.186734	−	0.0559207i
$369$		0			0
$370$	−1.15326	+	15.8262i	−0.0599553	+	0.822764i
$371$			4.43885i			0.230454i
$372$		0			0
$373$			33.0682i			1.71221i	0.516804	+	0.856104i	$0.327122\pi$
$373$			33.0682i			1.71221i	−0.516804	+	0.856104i	$0.672878\pi$
$374$	−7.03617	−	0.512730i	−0.363832	−	0.0265126i
$375$		0			0
$376$	−30.7993	−	6.82997i	−1.58835	−	0.352229i
$377$		−	5.57809i		−	0.287286i
$378$		0			0
$379$	−17.0331			−0.874934			−0.437467	−	0.899235i	$-0.644124\pi$
$379$	−17.0331			−0.874934			−0.437467	+	0.899235i	$0.644124\pi$
$380$	−11.7525	−	1.72197i	−0.602892	−	0.0883352i
$381$		0			0
$382$	4.79932	+	0.349729i	0.245555	+	0.0178937i
$383$	15.7372			0.804132			0.402066	−	0.915611i	$-0.368292\pi$
$383$	15.7372			0.804132			0.402066	+	0.915611i	$0.368292\pi$
$384$		0			0
$385$	−3.74635			−0.190932
$386$	29.2012	+	2.12791i	1.48630	+	0.108308i
$387$		0			0
$388$	31.3259	+	4.58985i	1.59033	+	0.233015i
$389$	22.7854			1.15527			0.577634	−	0.816296i	$-0.303976\pi$
$389$	22.7854			1.15527			0.577634	+	0.816296i	$0.303976\pi$
$390$		0			0
$391$			3.61990i			0.183066i
$392$	−2.76135	−	0.612349i	−0.139469	−	0.0309283i
$393$		0			0
$394$	−23.0677	−	1.68096i	−1.16213	−	0.0846853i
$395$			47.8835i			2.40928i
$396$		0			0
$397$		−	23.6829i		−	1.18861i	−0.804239	−	0.594306i	$-0.797427\pi$
$397$		−	23.6829i		−	1.18861i	0.804239	−	0.594306i	$-0.202573\pi$
$398$	1.16881	−	16.0395i	0.0585872	−	0.803990i
$399$		0			0
$400$	13.2451	+	3.96648i	0.662257	+	0.198324i
$401$			1.51029i			0.0754204i	0.999289	+	0.0377102i	$0.0120064\pi$
$401$			1.51029i			0.0754204i	−0.999289	+	0.0377102i	$0.987994\pi$
$402$		0			0
$403$	3.47241			0.172973
$404$	−1.46006	−	0.213927i	−0.0726407	−	0.0106433i
$405$		0			0
$406$	0.306594	−	4.20737i	0.0152160	−	0.208808i
$407$	4.97079			0.246393
$408$		0			0
$409$	9.86160			0.487625			0.243812	−	0.969822i	$-0.421602\pi$
$409$	9.86160			0.487625			0.243812	+	0.969822i	$0.421602\pi$
$410$	−2.60708	+	35.7768i	−0.128754	+	1.76689i
$411$		0			0
$412$	4.71209	−	32.1602i	0.232148	−	1.58442i
$413$	10.9714			0.539868
$414$		0			0
$415$			10.8222i			0.531241i
$416$	3.76316	−	9.88627i	0.184504	−	0.484714i
$417$		0			0
$418$	−0.270424	+	3.71101i	−0.0132269	+	0.181512i
$419$		−	20.8183i		−	1.01704i	−0.861050	−	0.508520i	$-0.830193\pi$
$419$		−	20.8183i		−	1.01704i	0.861050	−	0.508520i	$-0.169807\pi$
$420$		0			0
$421$		−	28.5459i		−	1.39124i	−0.718409	−	0.695621i	$-0.755129\pi$
$421$		−	28.5459i		−	1.39124i	0.718409	−	0.695621i	$-0.244871\pi$
$422$	−3.61653	−	0.263538i	−0.176050	−	0.0128288i
$423$		0			0
$424$	−12.2572	−	2.71813i	−0.595262	−	0.132004i
$425$		−	13.3846i		−	0.649249i
$426$		0			0
$427$	−4.70930			−0.227899
$428$	0.433196	−	2.95658i	0.0209393	−	0.142912i
$429$		0			0
$430$	−4.89407	−	0.356634i	−0.236013	−	0.0171984i
$431$	6.53111			0.314593			0.157296	−	0.987551i	$-0.449722\pi$
$431$	6.53111			0.314593			0.157296	+	0.987551i	$0.449722\pi$
$432$		0			0
$433$	14.2151			0.683136			0.341568	−	0.939857i	$-0.389042\pi$
$433$	14.2151			0.683136			0.341568	+	0.939857i	$0.389042\pi$
$434$	2.61913	+	0.190857i	0.125722	+	0.00916144i
$435$		0			0
$436$	−3.43182	+	23.4223i	−0.164354	+	1.12172i
$437$	1.90921			0.0913297
$438$		0			0
$439$		−	22.5811i		−	1.07773i	−0.842391	−	0.538867i	$-0.818852\pi$
$439$		−	22.5811i		−	1.07773i	0.842391	−	0.538867i	$-0.181148\pi$
$440$	2.29408	−	10.3450i	0.109366	−	0.493177i
$441$		0			0
$442$	−10.2133	−	0.744247i	−0.485795	−	0.0354002i
$443$			15.7932i			0.750359i	0.926952	+	0.375179i	$0.122419\pi$
$443$			15.7932i			0.750359i	−0.926952	+	0.375179i	$0.877581\pi$
$444$		0			0
$445$		−	35.5643i		−	1.68591i
$446$	0.141411	−	1.94058i	0.00669603	−	0.0918893i
$447$		0			0
$448$	3.38181	−	7.25006i	0.159776	−	0.342533i
$449$			26.9861i			1.27355i	0.771049	+	0.636776i	$0.219733\pi$
$449$			26.9861i			1.27355i	−0.771049	+	0.636776i	$0.780267\pi$
$450$		0			0
$451$	11.2370			0.529130
$452$	−4.44444	+	30.3335i	−0.209049	+	1.42677i
$453$		0			0
$454$	−2.81356	+	38.6103i	−0.132047	+	1.81207i
$455$	−5.43797			−0.254936
$456$		0			0
$457$	37.9588			1.77564			0.887818	−	0.460195i	$-0.152220\pi$
$457$	37.9588			1.77564			0.887818	+	0.460195i	$0.152220\pi$
$458$	1.26490	−	17.3581i	0.0591048	−	0.811092i
$459$		0			0
$460$	−5.37962	−	0.788218i	−0.250826	−	0.0367508i
$461$	8.35921			0.389327			0.194664	−	0.980870i	$-0.437638\pi$
$461$	8.35921			0.389327			0.194664	+	0.980870i	$0.437638\pi$
$462$		0			0
$463$			18.4723i			0.858483i	0.903190	+	0.429241i	$0.141219\pi$
$463$			18.4723i			0.858483i	−0.903190	+	0.429241i	$0.858781\pi$
$464$	11.4303	+	3.42299i	0.530637	+	0.158908i
$465$		0			0
$466$	2.47529	−	33.9683i	0.114666	−	1.57355i
$467$			4.34051i			0.200855i	0.994944	+	0.100427i	$0.0320210\pi$
$467$			4.34051i			0.200855i	−0.994944	+	0.100427i	$0.967979\pi$
$468$		0			0
$469$		−	4.41800i		−	0.204004i
$470$	−45.7490	−	3.33376i	−2.11024	−	0.153775i
$471$		0			0
$472$	−6.71833	+	30.2958i	−0.309236	+	1.39448i
$473$			1.53716i			0.0706788i
$474$		0			0
$475$	−7.05931			−0.323903
$476$	−7.66263	−	1.12272i	−0.351216	−	0.0514599i
$477$		0			0
$478$	25.4486	+	1.85446i	1.16399	+	0.0848209i
$479$	33.7292			1.54113			0.770564	−	0.637363i	$-0.219975\pi$
$479$	33.7292			1.54113			0.770564	+	0.637363i	$0.219975\pi$
$480$		0			0
$481$	7.21528			0.328989
$482$	−15.3094	−	1.11561i	−0.697325	−	0.0508145i
$483$		0			0
$484$	18.4833	+	2.70816i	0.840150	+	0.123098i
$485$	46.0345			2.09032
$486$		0			0
$487$		−	6.00662i		−	0.272186i	−0.990696	−	0.136093i	$-0.956545\pi$
$487$		−	6.00662i		−	0.272186i	0.990696	−	0.136093i	$-0.0434546\pi$
$488$	2.88374	−	13.0040i	0.130541	−	0.588664i
$489$		0			0
$490$	−4.10168	−	0.298892i	−0.185295	−	0.0135026i
$491$		−	26.2731i		−	1.18569i	−0.805318	−	0.592844i	$-0.798005\pi$
$491$		−	26.2731i		−	1.18569i	0.805318	−	0.592844i	$-0.201995\pi$
$492$		0			0
$493$		−	11.5506i		−	0.520215i
$494$	−0.392530	+	5.38667i	−0.0176608	+	0.242358i
$495$		0			0
$496$	−2.13084	+	7.11544i	−0.0956776	+	0.319493i
$497$			9.72888i			0.436400i
$498$		0			0
$499$	35.9974			1.61147			0.805733	−	0.592279i	$-0.201772\pi$
$499$	35.9974			1.61147			0.805733	+	0.592279i	$0.201772\pi$
$500$	−8.88179	−	1.30135i	−0.397206	−	0.0581983i
$501$		0			0
$502$	0.681478	−	9.35189i	0.0304158	−	0.417395i
$503$	15.7775			0.703485			0.351743	−	0.936097i	$-0.385589\pi$
$503$	15.7775			0.703485			0.351743	+	0.936097i	$0.385589\pi$
$504$		0			0
$505$	−2.14561			−0.0954783
$506$	−0.123784	+	1.69869i	−0.00550288	+	0.0755158i
$507$		0			0
$508$	1.89992	−	12.9670i	0.0842954	−	0.575320i
$509$	6.09029			0.269947			0.134974	−	0.990849i	$-0.456905\pi$
$509$	6.09029			0.269947			0.134974	+	0.990849i	$0.456905\pi$
$510$		0			0
$511$		−	9.40756i		−	0.416166i
$512$	17.9491	+	13.7779i	0.793244	+	0.608904i
$513$		0			0
$514$	1.25803	−	17.2639i	0.0554893	−	0.761478i
$515$		−	47.2605i		−	2.08255i
$516$		0			0
$517$			14.3691i			0.631954i
$518$	5.44225	+	0.396580i	0.239119	+	0.0174247i
$519$		0			0
$520$	3.32994	−	15.0161i	0.146027	−	0.658500i
$521$		−	18.1215i		−	0.793916i	−0.917837	−	0.396958i	$-0.870066\pi$
$521$		−	18.1215i		−	0.793916i	0.917837	−	0.396958i	$-0.129934\pi$
$522$		0			0
$523$	4.00317			0.175046			0.0875232	−	0.996162i	$-0.472105\pi$
$523$	4.00317			0.175046			0.0875232	+	0.996162i	$0.472105\pi$
$524$	3.38922	−	23.1316i	0.148059	−	1.01051i
$525$		0			0
$526$	4.05474	+	0.295472i	0.176795	+	0.0128832i
$527$	7.19037			0.313217
$528$		0			0
$529$	−22.1261			−0.962003
$530$	−18.2068	−	1.32674i	−0.790851	−	0.0576298i
$531$		0			0
$532$	−0.592145	+	4.04142i	−0.0256728	+	0.175218i
$533$	16.3109			0.706505
$534$		0			0
$535$		−	4.34480i		−	0.187842i
$536$	12.1996	+	2.70536i	0.526943	+	0.116854i
$537$		0			0
$538$	−8.71059	−	0.634746i	−0.375540	−	0.0273658i
$539$			1.28828i			0.0554903i
$540$		0			0
$541$			4.52777i			0.194664i	0.995252	+	0.0973320i	$0.0310309\pi$
$541$			4.52777i			0.194664i	−0.995252	+	0.0973320i	$0.968969\pi$
$542$	2.00531	−	27.5187i	0.0861353	−	1.18203i
$543$		0			0
$544$	7.79243	−	20.4717i	0.334097	−	0.877715i
$545$			34.4198i			1.47438i
$546$		0			0
$547$	1.99785			0.0854218			0.0427109	−	0.999087i	$-0.486401\pi$
$547$	1.99785			0.0854218			0.0427109	+	0.999087i	$0.486401\pi$
$548$	−2.13359	+	14.5619i	−0.0911426	+	0.622052i
$549$		0			0
$550$	0.457693	−	6.28090i	0.0195161	−	0.267819i
$551$	−6.09203			−0.259529
$552$		0			0
$553$	16.4660			0.700206
$554$	0.290623	−	3.98821i	0.0123474	−	0.169443i
$555$		0			0
$556$	−30.2140	−	4.42693i	−1.28136	−	0.187744i
$557$	−14.9242			−0.632360			−0.316180	−	0.948699i	$-0.602400\pi$
$557$	−14.9242			−0.632360			−0.316180	+	0.948699i	$0.602400\pi$
$558$		0			0
$559$			2.23125i			0.0943717i
$560$	3.33701	−	11.1431i	0.141014	−	0.470884i
$561$		0			0
$562$	−3.05848	+	41.9714i	−0.129014	+	1.77046i
$563$		−	0.157861i		−	0.00665305i	−0.999994	−	0.00332653i	$-0.998941\pi$
$563$		−	0.157861i		−	0.00665305i	0.999994	−	0.00332653i	$-0.00105887\pi$
$564$		0			0
$565$			44.5761i			1.87533i
$566$	−43.3617	−	3.15980i	−1.82263	−	0.132816i
$567$		0			0
$568$	−26.8648	−	5.95747i	−1.12722	−	0.249970i
$569$		−	11.8914i		−	0.498514i	−0.968437	−	0.249257i	$-0.919814\pi$
$569$		−	11.8914i		−	0.498514i	0.968437	−	0.249257i	$-0.0801864\pi$
$570$		0			0
$571$	14.0748			0.589013			0.294507	−	0.955649i	$-0.404845\pi$
$571$	14.0748			0.589013			0.294507	+	0.955649i	$0.404845\pi$
$572$	−4.76726	−	0.698495i	−0.199329	−	0.0292055i
$573$		0			0
$574$	12.3028	+	0.896513i	0.513509	+	0.0374197i
$575$	−3.23134			−0.134756
$576$		0			0
$577$	25.5261			1.06267			0.531333	−	0.847163i	$-0.321691\pi$
$577$	25.5261			1.06267			0.531333	+	0.847163i	$0.321691\pi$
$578$	2.82929	+	0.206172i	0.117683	+	0.00857564i
$579$		0			0
$580$	17.1657	+	2.51510i	0.712766	+	0.104434i
$581$	3.72150			0.154394
$582$		0			0
$583$			5.71850i			0.236836i
$584$	25.9775	+	5.76071i	1.07496	+	0.238380i
$585$		0			0
$586$	−8.04576	−	0.586299i	−0.332367	−	0.0242198i
$587$			9.47422i			0.391043i	0.980699	+	0.195521i	$0.0626399\pi$
$587$			9.47422i			0.391043i	−0.980699	+	0.195521i	$0.937360\pi$
$588$		0			0
$589$		−	3.79234i		−	0.156261i
$590$	−3.27927	+	45.0012i	−0.135005	+	1.85267i
$591$		0			0
$592$	−4.42766	+	14.7851i	−0.181976	+	0.607664i
$593$		−	18.9405i		−	0.777792i	−0.921282	−	0.388896i	$-0.872857\pi$
$593$		−	18.9405i		−	0.777792i	0.921282	−	0.388896i	$-0.127143\pi$
$594$		0			0
$595$	−11.2605			−0.461635
$596$	−33.0031	−	4.83560i	−1.35186	−	0.198074i
$597$		0			0
$598$	−0.179677	+	2.46571i	−0.00734756	+	0.100830i
$599$	−34.9184			−1.42673			−0.713364	−	0.700794i	$-0.752829\pi$
$599$	−34.9184			−1.42673			−0.713364	+	0.700794i	$0.752829\pi$
$600$		0			0
$601$	25.8342			1.05380			0.526899	−	0.849928i	$-0.323355\pi$
$601$	25.8342			1.05380			0.526899	+	0.849928i	$0.323355\pi$
$602$	−0.122638	+	1.68296i	−0.00499836	+	0.0685922i
$603$		0			0
$604$	−4.77935	+	32.6193i	−0.194469	+	1.32726i
$605$	27.1618			1.10429
$606$		0			0
$607$		−	14.4361i		−	0.585943i	−0.956121	−	0.292972i	$-0.905356\pi$
$607$		−	14.4361i		−	0.585943i	0.956121	−	0.292972i	$-0.0946442\pi$
$608$	−10.7972	−	4.10988i	−0.437882	−	0.166678i
$609$		0			0
$610$	1.40757	−	19.3161i	0.0569910	−	0.782085i
$611$			20.8574i			0.843798i
$612$		0			0
$613$		−	46.3647i		−	1.87265i	−0.351133	−	0.936325i	$-0.614204\pi$
$613$		−	46.3647i		−	1.87265i	0.351133	−	0.936325i	$-0.385796\pi$
$614$	−9.13156	−	0.665422i	−0.368520	−	0.0268543i
$615$		0			0
$616$	−3.55739	−	0.788879i	−0.143332	−	0.0317848i
$617$			29.3648i			1.18218i	0.806605	+	0.591091i	$0.201303\pi$
$617$			29.3648i			1.18218i	−0.806605	+	0.591091i	$0.798697\pi$
$618$		0			0
$619$	13.7590			0.553021			0.276510	−	0.961011i	$-0.410822\pi$
$619$	13.7590			0.553021			0.276510	+	0.961011i	$0.410822\pi$
$620$	−1.56567	+	10.6858i	−0.0628789	+	0.429151i
$621$		0			0
$622$	−3.45175	−	0.251531i	−0.138403	−	0.0100855i
$623$	−12.2297			−0.489974
$624$		0			0
$625$	−30.3350			−1.21340
$626$	−11.3322	−	0.825786i	−0.452927	−	0.0330050i
$627$		0			0
$628$	4.64478	−	31.7008i	0.185347	−	1.26500i
$629$	14.9408			0.595729
$630$		0			0
$631$			32.9228i			1.31064i	0.755352	+	0.655319i	$0.227466\pi$
$631$			32.9228i			1.31064i	−0.755352	+	0.655319i	$0.772534\pi$
$632$	−10.0830	+	45.4684i	−0.401078	+	1.80863i
$633$		0			0
$634$	−26.8129	−	1.95387i	−1.06488	−	0.0775981i
$635$		−	19.0555i		−	0.756195i
$636$		0			0
$637$			1.86999i			0.0740918i
$638$	0.394980	−	5.42029i	0.0156374	−	0.214591i
$639$		0			0
$640$	28.7266	+	16.0381i	1.13552	+	0.633962i
$641$		−	39.5844i		−	1.56349i	−0.623597	−	0.781746i	$-0.714330\pi$
$641$		−	39.5844i		−	1.56349i	0.623597	−	0.781746i	$-0.285670\pi$
$642$		0			0
$643$	44.0571			1.73744			0.868720	−	0.495303i	$-0.164943\pi$
$643$	44.0571			1.73744			0.868720	+	0.495303i	$0.164943\pi$
$644$	−0.271050	+	1.84993i	−0.0106809	+	0.0728973i
$645$		0			0
$646$	−0.812818	+	11.1543i	−0.0319799	+	0.438859i
$647$	−39.4430			−1.55066			−0.775331	−	0.631555i	$-0.782417\pi$
$647$	−39.4430			−1.55066			−0.775331	+	0.631555i	$0.782417\pi$
$648$		0			0
$649$	14.1343			0.554819
$650$	0.664359	−	9.11697i	0.0260583	−	0.357597i
$651$		0			0
$652$	12.2367	+	1.79291i	0.479227	+	0.0702159i
$653$	43.4794			1.70148			0.850741	−	0.525585i	$-0.176154\pi$
$653$	43.4794			1.70148			0.850741	+	0.525585i	$0.176154\pi$
$654$		0			0
$655$		−	33.9926i		−	1.32820i
$656$	−10.0092	+	33.4233i	−0.390793	+	1.30496i
$657$		0			0
$658$	−1.14640	+	15.7320i	−0.0446914	+	0.613298i
$659$			26.8653i			1.04652i	0.852172	+	0.523262i	$0.175285\pi$
$659$			26.8653i			1.04652i	−0.852172	+	0.523262i	$0.824715\pi$
$660$		0			0
$661$		−	0.365746i		−	0.0142259i	−0.999975	−	0.00711293i	$-0.997736\pi$
$661$		−	0.365746i		−	0.0142259i	0.999975	−	0.00711293i	$-0.00226414\pi$
$662$	−50.5792	−	3.68574i	−1.96582	−	0.143250i
$663$		0			0
$664$	−2.27886	+	10.2764i	−0.0884369	+	0.398800i
$665$			5.93900i			0.230305i
$666$		0			0
$667$	−2.78858			−0.107974
$668$	−25.1775	−	3.68899i	−0.974148	−	0.142731i
$669$		0			0
$670$	18.1212	+	1.32051i	0.700085	+	0.0510156i
$671$	−6.06691			−0.234211
$672$		0			0
$673$	35.2522			1.35887			0.679435	−	0.733735i	$-0.262225\pi$
$673$	35.2522			1.35887			0.679435	+	0.733735i	$0.262225\pi$
$674$	−9.73613	−	0.709477i	−0.375022	−	0.0273280i
$675$		0			0
$676$	18.8055	+	2.75536i	0.723288	+	0.105976i
$677$	−28.6841			−1.10242			−0.551211	−	0.834366i	$-0.685834\pi$
$677$	−28.6841			−1.10242			−0.551211	+	0.834366i	$0.685834\pi$
$678$		0			0
$679$		−	15.8302i		−	0.607508i
$680$	6.89535	−	31.0941i	0.264425	−	1.19240i
$681$		0			0
$682$	3.37418	+	0.245878i	0.129204	+	0.00941516i
$683$		−	22.7609i		−	0.870921i	−0.900208	−	0.435460i	$-0.856586\pi$
$683$		−	22.7609i		−	0.870921i	0.900208	−	0.435460i	$-0.143414\pi$
$684$		0			0
$685$			21.3992i			0.817620i
$686$	−0.102782	+	1.41047i	−0.00392424	+	0.0538521i
$687$		0			0
$688$	−4.57213	−	1.36920i	−0.174311	−	0.0522004i
$689$			8.30061i			0.316228i
$690$		0			0
$691$	36.1270			1.37434			0.687168	−	0.726499i	$-0.258854\pi$
$691$	36.1270			1.37434			0.687168	+	0.726499i	$0.258854\pi$
$692$	−22.2780	−	3.26416i	−0.846883	−	0.124085i
$693$		0			0
$694$	3.77141	−	51.7548i	0.143161	−	1.96459i
$695$	−44.4005			−1.68421
$696$		0			0
$697$	33.7753			1.27933
$698$	−2.90421	+	39.8543i	−0.109926	+	1.50851i
$699$		0			0
$700$	1.00221	−	6.84012i	0.0378799	−	0.258532i
$701$	−24.7739			−0.935699			−0.467849	−	0.883808i	$-0.654971\pi$
$701$	−24.7739			−0.935699			−0.467849	+	0.883808i	$0.654971\pi$
$702$		0			0
$703$		−	7.88007i		−	0.297202i
$704$	4.35673	−	9.34013i	0.164201	−	0.352019i
$705$		0			0
$706$	2.49903	−	34.2940i	0.0940521	−	1.29067i
$707$			0.737825i			0.0277487i
$708$		0			0
$709$			23.4819i			0.881881i	0.897536	+	0.440941i	$0.145355\pi$
$709$			23.4819i			0.881881i	−0.897536	+	0.440941i	$0.854645\pi$
$710$	−39.9048	−	2.90789i	−1.49760	−	0.109131i
$711$		0			0
$712$	7.48886	−	33.7705i	0.280657	−	1.26560i
$713$		−	1.73591i		−	0.0650105i
$714$		0			0
$715$	−7.00564			−0.261996
$716$	2.51684	−	17.1776i	0.0940588	−	0.641955i
$717$		0			0
$718$	−2.75581	−	0.200818i	−0.102846	−	0.00749446i
$719$	38.0908			1.42055			0.710274	−	0.703926i	$-0.248571\pi$
$719$	38.0908			1.42055			0.710274	+	0.703926i	$0.248571\pi$
$720$		0			0
$721$	−16.2518			−0.605248
$722$	−20.9160	−	1.52416i	−0.778414	−	0.0567235i
$723$		0			0
$724$	−0.720759	+	4.91921i	−0.0267868	+	0.182821i
$725$	10.3108			0.382933
$726$		0			0
$727$			6.53603i			0.242408i	0.992628	+	0.121204i	$0.0386755\pi$
$727$			6.53603i			0.242408i	−0.992628	+	0.121204i	$0.961324\pi$
$728$	−5.16369	−	1.14509i	−0.191379	−	0.0424398i
$729$		0			0
$730$	38.5868	+	2.81185i	1.42816	+	0.104071i
$731$			4.62028i			0.170887i
$732$		0			0
$733$			32.5549i			1.20244i	0.799082	+	0.601222i	$0.205319\pi$
$733$			32.5549i			1.20244i	−0.799082	+	0.601222i	$0.794681\pi$
$734$	−2.19768	+	30.1587i	−0.0811178	+	1.11318i
$735$		0			0
$736$	−4.94231	−	1.88126i	−0.182176	−	0.0693442i
$737$		−	5.69163i		−	0.209654i
$738$		0			0
$739$	−5.47095			−0.201252			−0.100626	−	0.994924i	$-0.532085\pi$
$739$	−5.47095			−0.201252			−0.100626	+	0.994924i	$0.532085\pi$
$740$	−3.25329	+	22.2039i	−0.119593	+	0.816231i
$741$		0			0
$742$	−0.456234	+	6.26088i	−0.0167489	+	0.229844i
$743$	7.23548			0.265444			0.132722	−	0.991153i	$-0.457628\pi$
$743$	7.23548			0.265444			0.132722	+	0.991153i	$0.457628\pi$
$744$		0			0
$745$	−48.4992			−1.77687
$746$	−3.39882	+	46.6419i	−0.124440	+	1.70768i
$747$		0			0
$748$	−9.87163	−	1.44638i	−0.360943	−	0.0528850i
$749$	−1.49407			−0.0545923
$750$		0			0
$751$		−	24.5924i		−	0.897391i	−0.893685	−	0.448695i	$-0.851889\pi$
$751$		−	24.5924i		−	0.897391i	0.893685	−	0.448695i	$-0.148111\pi$
$752$	−42.7396	−	12.7991i	−1.55855	−	0.466735i
$753$		0			0
$754$	0.573328	−	7.86775i	0.0208794	−	0.286527i
$755$			47.9352i			1.74454i
$756$		0			0
$757$		−	32.5168i		−	1.18184i	−0.806728	−	0.590922i	$-0.798764\pi$
$757$		−	32.5168i		−	1.18184i	0.806728	−	0.590922i	$-0.201236\pi$
$758$	−24.0248	−	1.75070i	−0.872620	−	0.0635883i
$759$		0			0
$760$	−16.3996	−	3.63674i	−0.594877	−	0.131918i
$761$			21.5639i			0.781689i	0.920457	+	0.390845i	$0.127817\pi$
$761$			21.5639i			0.781689i	−0.920457	+	0.390845i	$0.872183\pi$
$762$		0			0
$763$	11.8362			0.428499
$764$	6.73337	+	0.986568i	0.243605	+	0.0356928i
$765$		0			0
$766$	22.1969	+	1.61750i	0.802005	+	0.0584426i
$767$	20.5164			0.740806
$768$		0			0
$769$	−1.56057			−0.0562756			−0.0281378	−	0.999604i	$-0.508958\pi$
$769$	−1.56057			−0.0562756			−0.0281378	+	0.999604i	$0.508958\pi$
$770$	−5.28413	−	0.385058i	−0.190427	−	0.0138765i
$771$		0			0
$772$	40.9688	+	6.00271i	1.47450	+	0.216042i
$773$	24.0539			0.865160			0.432580	−	0.901596i	$-0.357603\pi$
$773$	24.0539			0.865160			0.432580	+	0.901596i	$0.357603\pi$
$774$		0			0
$775$			6.41855i			0.230561i
$776$	43.7127	+	9.69361i	1.56919	+	0.347980i
$777$		0			0
$778$	32.1383	+	2.34193i	1.15221	+	0.0839624i
$779$		−	17.8138i		−	0.638244i
$780$		0			0
$781$			12.5336i			0.448486i
$782$	−0.372061	+	5.10577i	−0.0133049	+	0.182582i
$783$		0			0
$784$	−3.83187	−	1.14752i	−0.136852	−	0.0409828i
$785$		−	46.5854i		−	1.66270i
$786$		0			0
$787$	3.99996			0.142583			0.0712916	−	0.997456i	$-0.477288\pi$
$787$	3.99996			0.142583			0.0712916	+	0.997456i	$0.477288\pi$
$788$	−32.3636	−	4.74189i	−1.15290	−	0.168923i
$789$		0			0
$790$	−4.92156	+	67.5384i	−0.175101	+	2.40291i
$791$	15.3287			0.545025
$792$		0			0
$793$	−8.80635			−0.312723
$794$	2.43418	−	33.4041i	0.0863858	−	1.18547i
$795$		0			0
$796$	3.29715	−	22.5032i	0.116865	−	0.797605i
$797$	−7.18205			−0.254401			−0.127201	−	0.991877i	$-0.540599\pi$
$797$	−7.18205			−0.254401			−0.127201	+	0.991877i	$0.540599\pi$
$798$		0			0
$799$			43.1896i			1.52794i
$800$	18.2742	+	6.95598i	0.646091	+	0.245931i
$801$		0			0
$802$	−0.155231	+	2.13023i	−0.00548139	+	0.0752209i
$803$		−	12.1196i		−	0.427691i
$804$		0			0
$805$			2.71853i			0.0958155i
$806$	4.89774	+	0.356901i	0.172516	+	0.0125713i
$807$		0			0
$808$	−2.03739	−	0.451806i	−0.0716751	−	0.0158945i
$809$		−	48.2698i		−	1.69707i	−0.529136	−	0.848537i	$-0.677484\pi$
$809$		−	48.2698i		−	1.69707i	0.529136	−	0.848537i	$-0.322516\pi$
$810$		0			0
$811$	20.3182			0.713469			0.356735	−	0.934206i	$-0.383890\pi$
$811$	20.3182			0.713469			0.356735	+	0.934206i	$0.383890\pi$
$812$	0.864885	−	5.90288i	0.0303515	−	0.207150i
$813$		0			0
$814$	7.01116	+	0.510908i	0.245741	+	0.0179073i
$815$	17.9823			0.629891
$816$		0			0
$817$	2.43682			0.0852537
$818$	13.9095	+	1.01360i	0.486335	+	0.0354395i
$819$		0			0
$820$	−7.35443	+	50.1943i	−0.256828	+	1.75286i
$821$	−35.0745			−1.22411			−0.612055	−	0.790815i	$-0.709657\pi$
$821$	−35.0745			−1.22411			−0.612055	+	0.790815i	$0.709657\pi$
$822$		0			0
$823$		−	15.4211i		−	0.537544i	−0.963204	−	0.268772i	$-0.913382\pi$
$823$		−	15.4211i		−	0.537544i	0.963204	−	0.268772i	$-0.0866179\pi$
$824$	9.95176	−	44.8768i	0.346686	−	1.56336i
$825$		0			0
$826$	15.4749	+	1.12766i	0.538440	+	0.0392364i
$827$			27.5561i			0.958218i	0.877755	+	0.479109i	$0.159040\pi$
$827$			27.5561i			0.958218i	−0.877755	+	0.479109i	$0.840960\pi$
$828$		0			0
$829$		−	56.9495i		−	1.97794i	−0.148124	−	0.988969i	$-0.547323\pi$
$829$		−	56.9495i		−	1.97794i	0.148124	−	0.988969i	$-0.452677\pi$
$830$	−1.11233	+	15.2644i	−0.0386095	+	0.529836i
$831$		0			0
$832$	6.32396	−	13.5575i	0.219244	−	0.470023i
$833$			3.87222i			0.134164i
$834$		0			0
$835$	−36.9992			−1.28041
$836$	−0.762851	+	5.20649i	−0.0263838	+	0.180070i
$837$		0			0
$838$	2.13975	−	29.3636i	0.0739163	−	1.01435i
$839$	2.54853			0.0879849			0.0439925	−	0.999032i	$-0.485992\pi$
$839$	2.54853			0.0879849			0.0439925	+	0.999032i	$0.485992\pi$
$840$		0			0
$841$	−20.1020			−0.693173
$842$	2.93401	−	40.2632i	0.101113	−	1.38756i
$843$		0			0
$844$	−5.07393	−	0.743428i	−0.174652	−	0.0255898i
$845$	27.6353			0.950683
$846$		0			0
$847$		−	9.34033i		−	0.320937i
$848$	−17.0091	−	5.09367i	−0.584094	−	0.174917i
$849$		0			0
$850$	1.37570	−	18.8786i	0.0471861	−	0.647532i
$851$		−	3.60704i		−	0.123648i
$852$		0			0
$853$			23.1990i			0.794319i	0.917750	+	0.397159i	$0.130004\pi$
$853$			23.1990i			0.794319i	−0.917750	+	0.397159i	$0.869996\pi$
$854$	−6.64234	−	0.484032i	−0.227296	−	0.0165632i
$855$		0			0
$856$	0.914895	−	4.12566i	0.0312705	−	0.141012i
$857$			19.5713i			0.668544i	0.942477	+	0.334272i	$0.108490\pi$
$857$			19.5713i			0.668544i	−0.942477	+	0.334272i	$0.891510\pi$
$858$		0			0
$859$	−50.8322			−1.73437			−0.867186	−	0.497985i	$-0.834073\pi$
$859$	−50.8322			−1.73437			−0.867186	+	0.497985i	$0.834073\pi$
$860$	−6.86630	−	1.00605i	−0.234139	−	0.0343059i
$861$		0			0
$862$	9.21196	+	0.671281i	0.313761	+	0.0228639i
$863$	39.1106			1.33134			0.665671	−	0.746246i	$-0.268146\pi$
$863$	39.1106			1.33134			0.665671	+	0.746246i	$0.268146\pi$
$864$		0			0
$865$	−32.7383			−1.11314
$866$	20.0501	+	1.46106i	0.681330	+	0.0496489i
$867$		0			0
$868$	3.67459	+	0.538398i	0.124724	+	0.0182744i
$869$	21.2129			0.719598
$870$		0			0
$871$		−	8.26162i		−	0.279934i
$872$	−7.24788	+	32.6838i	−0.245444	+	1.10681i
$873$		0			0
$874$	2.69288	+	0.196232i	0.0910882	+	0.00663765i
$875$			4.48831i			0.151733i
$876$		0			0
$877$		−	26.1514i		−	0.883070i	−0.897244	−	0.441535i	$-0.854434\pi$
$877$		−	26.1514i		−	0.883070i	0.897244	−	0.441535i	$-0.145566\pi$
$878$	2.32093	−	31.8500i	0.0783275	−	1.07488i
$879$		0			0
$880$	4.29901	−	14.3555i	0.144920	−	0.483924i
$881$			49.2277i			1.65852i	0.558860	+	0.829262i	$0.311239\pi$
$881$			49.2277i			1.65852i	−0.558860	+	0.829262i	$0.688761\pi$
$882$		0			0
$883$	44.3014			1.49086			0.745430	−	0.666584i	$-0.232244\pi$
$883$	44.3014			1.49086			0.745430	+	0.666584i	$0.232244\pi$
$884$	−14.3290	−	2.09948i	−0.481938	−	0.0706132i
$885$		0			0
$886$	−1.62326	+	22.2759i	−0.0545345	+	0.748374i
$887$	−6.83633			−0.229542			−0.114771	−	0.993392i	$-0.536613\pi$
$887$	−6.83633			−0.229542			−0.114771	+	0.993392i	$0.536613\pi$
$888$		0			0
$889$	−6.55275			−0.219772
$890$	3.65537	−	50.1625i	0.122528	−	1.68145i
$891$		0			0
$892$	0.398914	−	2.72261i	0.0133566	−	0.0911596i
$893$	22.7791			0.762272
$894$		0			0
$895$		−	25.2430i		−	0.843780i
$896$	5.51514	−	9.87842i	0.184248	−	0.330015i
$897$		0			0
$898$	−2.77369	+	38.0632i	−0.0925591	+	1.27018i
$899$			5.53908i			0.184739i
$900$		0			0
$901$			17.1882i			0.572622i
$902$	15.8495	+	1.15496i	0.527731	+	0.0384560i
$903$		0			0
$904$	−9.38651	+	42.3278i	−0.312191	+	1.40780i
$905$			7.22895i			0.240298i
$906$		0			0
$907$	24.2295			0.804528			0.402264	−	0.915524i	$-0.368223\pi$
$907$	24.2295			0.804528			0.402264	+	0.915524i	$0.368223\pi$
$908$	−7.93689	+	54.1696i	−0.263395	+	1.79768i
$909$		0			0
$910$	−7.67011	−	0.558926i	−0.254262	−	0.0185282i
$911$	−6.75748			−0.223885			−0.111943	−	0.993715i	$-0.535707\pi$
$911$	−6.75748			−0.223885			−0.111943	+	0.993715i	$0.535707\pi$
$912$		0			0
$913$	4.79435			0.158670
$914$	53.5398	+	3.90148i	1.77094	+	0.129049i
$915$		0			0
$916$	3.56821	−	24.3532i	0.117897	−	0.804652i
$917$	−11.6893			−0.386014
$918$		0			0
$919$			1.77205i			0.0584546i	0.999573	+	0.0292273i	$0.00930466\pi$
$919$			1.77205i			0.0584546i	−0.999573	+	0.0292273i	$0.990695\pi$
$920$	−7.50680	−	1.66469i	−0.247492	−	0.0548832i
$921$		0			0
$922$	11.7904	+	0.859177i	0.388298	+	0.0282955i
$923$			18.1929i			0.598827i
$924$		0			0
$925$			13.3370i			0.438519i
$926$	−1.89863	+	26.0548i	−0.0623927	+	0.856212i
$927$		0			0
$928$	15.7703	+	6.00287i	0.517685	+	0.197054i
$929$		−	15.3376i		−	0.503212i	−0.967830	−	0.251606i	$-0.919041\pi$
$929$		−	15.3376i		−	0.503212i	0.967830	−	0.251606i	$-0.0809587\pi$
$930$		0			0
$931$	2.04228			0.0669332
$932$	6.98266	−	47.6570i	0.228725	−	1.56106i
$933$		0			0
$934$	−0.446126	+	6.12217i	−0.0145977	+	0.200324i
$935$	−14.5067			−0.474420
$936$		0			0
$937$	−48.6373			−1.58891			−0.794456	−	0.607322i	$-0.792244\pi$
$937$	−48.6373			−1.58891			−0.794456	+	0.607322i	$0.792244\pi$
$938$	0.454091	−	6.23147i	0.0148266	−	0.203465i
$939$		0			0
$940$	−64.1851	−	9.40436i	−2.09349	−	0.306736i
$941$	−34.4202			−1.12207			−0.561034	−	0.827793i	$-0.689596\pi$
$941$	−34.4202			−1.12207			−0.561034	+	0.827793i	$0.689596\pi$
$942$		0			0
$943$		−	8.15410i		−	0.265534i
$944$	−12.5899	+	42.0410i	−0.409766	+	1.36832i
$945$		0			0
$946$	−0.157993	+	2.16813i	−0.00513678	+	0.0704918i
$947$		−	27.8402i		−	0.904684i	−0.891844	−	0.452342i	$-0.850589\pi$
$947$		−	27.8402i		−	0.904684i	0.891844	−	0.452342i	$-0.149411\pi$
$948$		0			0
$949$		−	17.5921i		−	0.571062i
$950$	−9.95697	−	0.725570i	−0.323047	−	0.0235406i
$951$		0			0
$952$	−10.6925	−	2.37115i	−0.346547	−	0.0768494i
$953$		−	22.7401i		−	0.736624i	−0.929702	−	0.368312i	$-0.879936\pi$
$953$		−	22.7401i		−	0.736624i	0.929702	−	0.368312i	$-0.120064\pi$
$954$		0			0
$955$	9.89491			0.320192
$956$	35.7040	+	5.23132i	1.15475	+	0.169193i
$957$		0			0
$958$	47.5742	+	3.46676i	1.53705	+	0.112006i
$959$	7.35868			0.237624
$960$		0			0
$961$	27.5519			0.888770
$962$	10.1770	+	0.741602i	0.328119	+	0.0239102i
$963$		0			0
$964$	−21.4789	−	3.14707i	−0.691787	−	0.101360i
$965$	60.2050			1.93807
$966$		0			0
$967$			28.0470i			0.901931i	0.892541	+	0.450965i	$0.148920\pi$
$967$			28.0470i			0.901931i	−0.892541	+	0.450965i	$0.851080\pi$
$968$	25.7919	+	5.71954i	0.828982	+	0.183833i
$969$		0			0
$970$	64.9305	+	4.73152i	2.08479	+	0.151920i
$971$		−	10.0931i		−	0.323904i	−0.986799	−	0.161952i	$-0.948221\pi$
$971$		−	10.0931i		−	0.323904i	0.986799	−	0.161952i	$-0.0517790\pi$
$972$		0			0
$973$			15.2683i			0.489479i
$974$	0.617373	−	8.47218i	0.0197819	−	0.271466i
$975$		0			0
$976$	5.40401	−	18.0454i	0.172978	−	0.577620i
$977$			1.93536i			0.0619176i	0.999521	+	0.0309588i	$0.00985607\pi$
$977$			1.93536i			0.0619176i	−0.999521	+	0.0309588i	$0.990144\pi$
$978$		0			0
$979$	−15.7553			−0.503543
$980$	−5.75460	−	0.843159i	−0.183824	−	0.0269337i
$981$		0			0
$982$	2.70040	−	37.0575i	0.0861733	−	1.18255i
$983$	45.8652			1.46287			0.731436	−	0.681910i	$-0.238850\pi$
$983$	45.8652			1.46287			0.731436	+	0.681910i	$0.238850\pi$
$984$		0			0
$985$	−47.5594			−1.51537
$986$	1.18720	−	16.2919i	0.0378081	−	0.518839i
$987$		0			0
$988$	−1.10731	+	7.55742i	−0.0352281	+	0.240433i
$989$	1.11544			0.0354688
$990$		0			0
$991$			20.5946i			0.654209i	0.944988	+	0.327105i	$0.106073\pi$
$991$			20.5946i			0.654209i	−0.944988	+	0.327105i	$0.893927\pi$
$992$	−3.73684	+	9.81713i	−0.118645	+	0.311694i
$993$		0			0
$994$	−0.999955	+	13.7223i	−0.0317166	+	0.435246i
$995$		−	33.0692i		−	1.04837i
$996$		0			0
$997$			11.0478i			0.349889i	0.984578	+	0.174944i	$0.0559745\pi$
$997$			11.0478i			0.349889i	−0.984578	+	0.174944i	$0.944025\pi$
$998$	50.7734	+	3.69989i	1.60720	+	0.117118i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.j.d.323.48	yes	48
3.2	odd	2	inner	1512.2.j.d.323.1	✓	48
4.3	odd	2		6048.2.j.d.5615.42		48
8.3	odd	2	inner	1512.2.j.d.323.2	yes	48
8.5	even	2		6048.2.j.d.5615.8		48
12.11	even	2		6048.2.j.d.5615.7		48
24.5	odd	2		6048.2.j.d.5615.41		48
24.11	even	2	inner	1512.2.j.d.323.47	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.j.d.323.1	✓	48	3.2	odd	2	inner
1512.2.j.d.323.2	yes	48	8.3	odd	2	inner
1512.2.j.d.323.47	yes	48	24.11	even	2	inner
1512.2.j.d.323.48	yes	48	1.1	even	1	trivial
6048.2.j.d.5615.7		48	12.11	even	2
6048.2.j.d.5615.8		48	8.5	even	2
6048.2.j.d.5615.41		48	24.5	odd	2
6048.2.j.d.5615.42		48	4.3	odd	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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41047 + 0.102782i) q^{2} +(1.97887 + 0.289943i) q^{4} +2.90802 q^{5} -1.00000i q^{7} +(2.76135 + 0.612349i) q^{8} +O(q^{10})\)	\(q+(1.41047 + 0.102782i) q^{2} +(1.97887 + 0.289943i) q^{4} +2.90802 q^{5} -1.00000i q^{7} +(2.76135 + 0.612349i) q^{8} +(4.10168 + 0.298892i) q^{10} -1.28828i q^{11} -1.86999i q^{13} +(0.102782 - 1.41047i) q^{14} +(3.83187 + 1.14752i) q^{16} -3.87222i q^{17} -2.04228 q^{19} +(5.75460 + 0.843159i) q^{20} +(0.132412 - 1.81709i) q^{22} -0.934839 q^{23} +3.45657 q^{25} +(0.192202 - 2.63757i) q^{26} +(0.289943 - 1.97887i) q^{28} +2.98295 q^{29} +1.85691i q^{31} +(5.28680 + 2.01239i) q^{32} +(0.397995 - 5.46166i) q^{34} -2.90802i q^{35} +3.85846i q^{37} +(-2.88059 - 0.209910i) q^{38} +(8.03004 + 1.78072i) q^{40} +8.72247i q^{41} -1.19319 q^{43} +(0.373528 - 2.54935i) q^{44} +(-1.31857 - 0.0960846i) q^{46} -11.1537 q^{47} -1.00000 q^{49} +(4.87541 + 0.355274i) q^{50} +(0.542190 - 3.70047i) q^{52} -4.43885 q^{53} -3.74635i q^{55} +(0.612349 - 2.76135i) q^{56} +(4.20737 + 0.306594i) q^{58} +10.9714i q^{59} -4.70930i q^{61} +(-0.190857 + 2.61913i) q^{62} +(7.25006 + 3.38181i) q^{64} -5.43797i q^{65} +4.41800 q^{67} +(1.12272 - 7.66263i) q^{68} +(0.298892 - 4.10168i) q^{70} -9.72888 q^{71} +9.40756 q^{73} +(-0.396580 + 5.44225i) q^{74} +(-4.04142 - 0.592145i) q^{76} -1.28828 q^{77} +16.4660i q^{79} +(11.1431 + 3.33701i) q^{80} +(-0.896513 + 12.3028i) q^{82} +3.72150i q^{83} -11.2605i q^{85} +(-1.68296 - 0.122638i) q^{86} +(0.788879 - 3.55739i) q^{88} -12.2297i q^{89} -1.86999 q^{91} +(-1.84993 - 0.271050i) q^{92} +(-15.7320 - 1.14640i) q^{94} -5.93900 q^{95} +15.8302 q^{97} +(-1.41047 - 0.102782i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4}+O(q^{10}) \) 48 * q - 4 * q^4	\( 48 q - 4 q^{4} - 12 q^{10} - 12 q^{16} + 16 q^{19} - 24 q^{22} + 48 q^{25} + 8 q^{28} + 12 q^{34} + 32 q^{40} + 64 q^{43} + 60 q^{46} - 48 q^{49} + 16 q^{52} + 36 q^{58} - 4 q^{64} + 32 q^{67} + 12 q^{70} - 32 q^{76} + 36 q^{82} + 24 q^{88} - 60 q^{94}+O(q^{100}) \) 48 * q - 4 * q^4 - 12 * q^10 - 12 * q^16 + 16 * q^19 - 24 * q^22 + 48 * q^25 + 8 * q^28 + 12 * q^34 + 32 * q^40 + 64 * q^43 + 60 * q^46 - 48 * q^49 + 16 * q^52 + 36 * q^58 - 4 * q^64 + 32 * q^67 + 12 * q^70 - 32 * q^76 + 36 * q^82 + 24 * q^88 - 60 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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