LMFDB - Embedded newform 1512.2.j.d.323.1

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			323.1
Character	$\chi$	$=$	1512.323
Dual form			1512.2.j.d.323.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41047 - 0.102782i) q^{2} +(1.97887 + 0.289943i) q^{4} -2.90802 q^{5} -1.00000i q^{7} +(-2.76135 - 0.612349i) q^{8} +O(q^{10})$	\(q+(-1.41047 - 0.102782i) q^{2} +(1.97887 + 0.289943i) q^{4} -2.90802 q^{5} -1.00000i q^{7} +(-2.76135 - 0.612349i) q^{8} +(4.10168 + 0.298892i) q^{10} +1.28828i q^{11} -1.86999i q^{13} +(-0.102782 + 1.41047i) q^{14} +(3.83187 + 1.14752i) q^{16} +3.87222i q^{17} -2.04228 q^{19} +(-5.75460 - 0.843159i) q^{20} +(0.132412 - 1.81709i) q^{22} +0.934839 q^{23} +3.45657 q^{25} +(-0.192202 + 2.63757i) q^{26} +(0.289943 - 1.97887i) q^{28} -2.98295 q^{29} +1.85691i q^{31} +(-5.28680 - 2.01239i) q^{32} +(0.397995 - 5.46166i) q^{34} +2.90802i q^{35} +3.85846i q^{37} +(2.88059 + 0.209910i) q^{38} +(8.03004 + 1.78072i) q^{40} -8.72247i q^{41} -1.19319 q^{43} +(-0.373528 + 2.54935i) q^{44} +(-1.31857 - 0.0960846i) q^{46} +11.1537 q^{47} -1.00000 q^{49} +(-4.87541 - 0.355274i) q^{50} +(0.542190 - 3.70047i) q^{52} +4.43885 q^{53} -3.74635i q^{55} +(-0.612349 + 2.76135i) q^{56} +(4.20737 + 0.306594i) q^{58} -10.9714i q^{59} -4.70930i q^{61} +(0.190857 - 2.61913i) q^{62} +(7.25006 + 3.38181i) q^{64} +5.43797i q^{65} +4.41800 q^{67} +(-1.12272 + 7.66263i) q^{68} +(0.298892 - 4.10168i) q^{70} +9.72888 q^{71} +9.40756 q^{73} +(0.396580 - 5.44225i) q^{74} +(-4.04142 - 0.592145i) q^{76} +1.28828 q^{77} +16.4660i q^{79} +(-11.1431 - 3.33701i) q^{80} +(-0.896513 + 12.3028i) q^{82} -3.72150i q^{83} -11.2605i q^{85} +(1.68296 + 0.122638i) q^{86} +(0.788879 - 3.55739i) q^{88} +12.2297i q^{89} -1.86999 q^{91} +(1.84993 + 0.271050i) q^{92} +(-15.7320 - 1.14640i) q^{94} +5.93900 q^{95} +15.8302 q^{97} +(1.41047 + 0.102782i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.725337\pi$
$5$	−2.90802			−1.30051			−0.650253	+	0.759718i	$0.725337\pi$
$6$		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	$0.0622163\pi$
$11$			1.28828i			0.388432i	−0.980959	+	0.194216i	$0.937784\pi$
$12$		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	$0.155593\pi$
$17$			3.87222i			0.939151i	−0.882892	+	0.469576i	$0.844407\pi$
$18$		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	$-0.468927\pi$
$23$	0.934839			0.194927			0.0974637	+	0.995239i	$0.468927\pi$
$24$		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	$-0.589327\pi$
$29$	−2.98295			−0.553920			−0.276960	+	0.960881i	$0.589327\pi$
$30$		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	$-0.761497\pi$
$41$		−	8.72247i		−	1.36222i	0.732181	−	0.681110i	$-0.238503\pi$
$42$		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	$-0.197577\pi$
$47$	11.1537			1.62694			0.813468	+	0.581609i	$0.197577\pi$
$48$		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	$-0.401390\pi$
$53$	4.43885			0.609723			0.304862	+	0.952397i	$0.401390\pi$
$54$		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	$-0.746801\pi$
$59$		−	10.9714i		−	1.42836i	0.699964	−	0.714178i	$-0.253199\pi$
$60$		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	$-0.304105\pi$
$71$	9.72888			1.15461			0.577303	+	0.816530i	$0.304105\pi$
$72$		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	$-0.934526\pi$
$83$		−	3.72150i		−	0.408488i	0.978920	−	0.204244i	$-0.0654736\pi$
$84$		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	$0.224467\pi$
$89$			12.2297i			1.29635i	−0.761492	+	0.648174i	$0.775533\pi$
$90$		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	$-0.488313\pi$
$101$	0.737825			0.0734163			0.0367081	+	0.999326i	$0.488313\pi$
$102$		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	$0.0230080\pi$
$107$			1.49407i			0.144438i	−0.997389	+	0.0722188i	$0.976992\pi$
$108$		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	$-0.743682\pi$
$113$		−	15.3287i		−	1.44200i	0.692934	−	0.721001i	$-0.256318\pi$
$114$		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	$0.170595\pi$
$131$			11.6893i			1.02130i	−0.859790	+	0.510648i	$0.829405\pi$
$132$		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	$-0.898214\pi$
$137$		−	7.35868i		−	0.628694i	0.949308	−	0.314347i	$-0.101786\pi$
$138$		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	$-0.260611\pi$
$149$	16.6778			1.36630			0.683148	+	0.730280i	$0.260611\pi$
$150$		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	$-0.336166\pi$
$167$	12.7232			0.984549			0.492275	+	0.870440i	$0.336166\pi$
$168$		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	$-0.359231\pi$
$173$	11.2579			0.855925			0.427963	+	0.903796i	$0.359231\pi$
$174$		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	$0.105164\pi$
$179$			8.68048i			0.648809i	−0.945918	+	0.324405i	$0.894836\pi$
$180$		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	$-0.539285\pi$
$191$	−3.40263			−0.246206			−0.123103	+	0.992394i	$0.539285\pi$
$192$		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	$-0.302033\pi$
$197$	16.3546			1.16521			0.582607	+	0.812754i	$0.302033\pi$
$198$		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	$-0.637276\pi$
$227$		−	27.3740i		−	1.81688i	0.418020	−	0.908438i	$-0.362724\pi$
$228$		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	$0.289329\pi$
$233$			24.0829i			1.57772i	−0.614571	+	0.788862i	$0.710671\pi$
$234$		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	$-0.698333\pi$
$239$	−18.0426			−1.16708			−0.583540	+	0.812085i	$0.698333\pi$
$240$		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	$0.0671025\pi$
$251$			6.63032i			0.418502i	−0.977862	+	0.209251i	$0.932897\pi$
$252$		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	$0.124678\pi$
$257$			12.2398i			0.763497i	−0.924266	+	0.381748i	$0.875322\pi$
$258$		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	$-0.528250\pi$
$263$	−2.87474			−0.177264			−0.0886320	+	0.996064i	$0.528250\pi$
$264$		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	$-0.439713\pi$
$269$	6.17565			0.376536			0.188268	+	0.982118i	$0.439713\pi$
$270$		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	$-0.652388\pi$
$281$		−	29.7569i		−	1.77515i	0.460663	−	0.887575i	$-0.347612\pi$
$282$		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	$-0.446713\pi$
$293$	5.70430			0.333249			0.166624	+	0.986020i	$0.446713\pi$
$294$		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	$-0.477896\pi$
$311$	2.44723			0.138770			0.0693848	+	0.997590i	$0.477896\pi$
$312$		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	$-0.320745\pi$
$317$	19.0098			1.06770			0.533850	+	0.845579i	$0.320745\pi$
$318$		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	$0.444610\pi$
$347$			36.6932i			1.96980i	−0.173135	+	0.984898i	$0.555390\pi$
$348$		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	$0.223997\pi$
$353$			24.3138i			1.29410i	−0.762450	+	0.647048i	$0.776003\pi$
$354$		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	$-0.483581\pi$
$359$	1.95382			0.103119			0.0515594	+	0.998670i	$0.483581\pi$
$360$		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	$-0.631708\pi$
$383$	−15.7372			−0.804132			−0.402066	+	0.915611i	$0.631708\pi$
$384$		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	$-0.696024\pi$
$389$	−22.7854			−1.15527			−0.577634	+	0.816296i	$0.696024\pi$
$390$		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	$-0.987994\pi$
$401$		−	1.51029i		−	0.0754204i	0.999289	−	0.0377102i	$-0.0120064\pi$
$402$		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	$0.169807\pi$
$419$			20.8183i			1.01704i	−0.861050	+	0.508520i	$0.830193\pi$
$420$		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	$-0.550278\pi$
$431$	−6.53111			−0.314593			−0.157296	+	0.987551i	$0.550278\pi$
$432$		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	$-0.877581\pi$
$443$		−	15.7932i		−	0.750359i	0.926952	−	0.375179i	$-0.122419\pi$
$444$		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	$-0.780267\pi$
$449$		−	26.9861i		−	1.27355i	0.771049	−	0.636776i	$-0.219733\pi$
$450$		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	$-0.562362\pi$
$461$	−8.35921			−0.389327			−0.194664	+	0.980870i	$0.562362\pi$
$462$		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	$-0.967979\pi$
$467$		−	4.34051i		−	0.200855i	0.994944	−	0.100427i	$-0.0320210\pi$
$468$		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	$-0.780025\pi$
$479$	−33.7292			−1.54113			−0.770564	+	0.637363i	$0.780025\pi$
$480$		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	$0.201995\pi$
$491$			26.2731i			1.18569i	−0.805318	+	0.592844i	$0.798005\pi$
$492$		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	$-0.614411\pi$
$503$	−15.7775			−0.703485			−0.351743	+	0.936097i	$0.614411\pi$
$504$		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	$-0.543095\pi$
$509$	−6.09029			−0.269947			−0.134974	+	0.990849i	$0.543095\pi$
$510$		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	$0.129934\pi$
$521$			18.1215i			0.793916i	−0.917837	+	0.396958i	$0.870066\pi$
$522$		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	$-0.397600\pi$
$557$	14.9242			0.632360			0.316180	+	0.948699i	$0.397600\pi$
$558$		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	$0.00105887\pi$
$563$			0.157861i			0.00665305i	−0.999994	+	0.00332653i	$0.998941\pi$
$564$		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	$0.0801864\pi$
$569$			11.8914i			0.498514i	−0.968437	+	0.249257i	$0.919814\pi$
$570$		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	$-0.937360\pi$
$587$		−	9.47422i		−	0.391043i	0.980699	−	0.195521i	$-0.0626399\pi$
$588$		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	$0.127143\pi$
$593$			18.9405i			0.777792i	−0.921282	+	0.388896i	$0.872857\pi$
$594$		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	$-0.247171\pi$
$599$	34.9184			1.42673			0.713364	+	0.700794i	$0.247171\pi$
$600$		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	$-0.798697\pi$
$617$		−	29.3648i		−	1.18218i	0.806605	−	0.591091i	$-0.201303\pi$
$618$		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	$0.285670\pi$
$641$			39.5844i			1.56349i	−0.623597	+	0.781746i	$0.714330\pi$
$642$		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	$-0.217583\pi$
$647$	39.4430			1.55066			0.775331	+	0.631555i	$0.217583\pi$
$648$		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	$-0.823846\pi$
$653$	−43.4794			−1.70148			−0.850741	+	0.525585i	$0.823846\pi$
$654$		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	$-0.824715\pi$
$659$		−	26.8653i		−	1.04652i	0.852172	−	0.523262i	$-0.175285\pi$
$660$		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	$-0.314166\pi$
$677$	28.6841			1.10242			0.551211	+	0.834366i	$0.314166\pi$
$678$		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	$0.143414\pi$
$683$			22.7609i			0.870921i	−0.900208	+	0.435460i	$0.856586\pi$
$684$		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	$-0.345029\pi$
$701$	24.7739			0.935699			0.467849	+	0.883808i	$0.345029\pi$
$702$		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	$-0.751429\pi$
$719$	−38.0908			−1.42055			−0.710274	+	0.703926i	$0.751429\pi$
$720$		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	$-0.542372\pi$
$743$	−7.23548			−0.265444			−0.132722	+	0.991153i	$0.542372\pi$
$744$		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	$-0.872183\pi$
$761$		−	21.5639i		−	0.781689i	0.920457	−	0.390845i	$-0.127817\pi$
$762$		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	$-0.642397\pi$
$773$	−24.0539			−0.865160			−0.432580	+	0.901596i	$0.642397\pi$
$774$		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	$-0.459401\pi$
$797$	7.18205			0.254401			0.127201	+	0.991877i	$0.459401\pi$
$798$		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	$0.322516\pi$
$809$			48.2698i			1.69707i	−0.529136	+	0.848537i	$0.677484\pi$
$810$		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	$-0.290343\pi$
$821$	35.0745			1.22411			0.612055	+	0.790815i	$0.290343\pi$
$822$		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	$-0.840960\pi$
$827$		−	27.5561i		−	0.958218i	0.877755	−	0.479109i	$-0.159040\pi$
$828$		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	$-0.514008\pi$
$839$	−2.54853			−0.0879849			−0.0439925	+	0.999032i	$0.514008\pi$
$840$		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	$-0.891510\pi$
$857$		−	19.5713i		−	0.668544i	0.942477	−	0.334272i	$-0.108490\pi$
$858$		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	$-0.731854\pi$
$863$	−39.1106			−1.33134			−0.665671	+	0.746246i	$0.731854\pi$
$864$		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	$-0.688761\pi$
$881$		−	49.2277i		−	1.65852i	0.558860	−	0.829262i	$-0.311239\pi$
$882$		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	$-0.463387\pi$
$887$	6.83633			0.229542			0.114771	+	0.993392i	$0.463387\pi$
$888$		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	$-0.464293\pi$
$911$	6.75748			0.223885			0.111943	+	0.993715i	$0.464293\pi$
$912$		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	$0.0809587\pi$
$929$			15.3376i			0.503212i	−0.967830	+	0.251606i	$0.919041\pi$
$930$		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	$-0.310404\pi$
$941$	34.4202			1.12207			0.561034	+	0.827793i	$0.310404\pi$
$942$		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	$0.149411\pi$
$947$			27.8402i			0.904684i	−0.891844	+	0.452342i	$0.850589\pi$
$948$		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	$0.120064\pi$
$953$			22.7401i			0.736624i	−0.929702	+	0.368312i	$0.879936\pi$
$954$		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	$0.0517790\pi$
$971$			10.0931i			0.323904i	−0.986799	+	0.161952i	$0.948221\pi$
$972$		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	$-0.990144\pi$
$977$		−	1.93536i		−	0.0619176i	0.999521	−	0.0309588i	$-0.00985607\pi$
$978$		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	$-0.761150\pi$
$983$	−45.8652			−1.46287			−0.731436	+	0.681910i	$0.761150\pi$
$984$		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.323.1	✓	48
3.2	odd	2	inner	1512.2.j.d.323.48	yes	48
4.3	odd	2		6048.2.j.d.5615.7		48
8.3	odd	2	inner	1512.2.j.d.323.47	yes	48
8.5	even	2		6048.2.j.d.5615.41		48
12.11	even	2		6048.2.j.d.5615.42		48
24.5	odd	2		6048.2.j.d.5615.8		48
24.11	even	2	inner	1512.2.j.d.323.2	yes	48

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