LMFDB - Embedded newform 1512.2.c.f.757.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(757,1512)]

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([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("1512.757");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			757.14
Character	$\chi$	$=$	1512.757
Dual form			1512.2.c.f.757.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.174217 + 1.40344i) q^{2} +(-1.93930 + 0.489007i) q^{4} +1.26947i q^{5} +1.00000 q^{7} +(-1.02415 - 2.63650i) q^{8} +O(q^{10})$	\(q+(0.174217 + 1.40344i) q^{2} +(-1.93930 + 0.489007i) q^{4} +1.26947i q^{5} +1.00000 q^{7} +(-1.02415 - 2.63650i) q^{8} +(-1.78162 + 0.221163i) q^{10} -2.02805i q^{11} -4.05339i q^{13} +(0.174217 + 1.40344i) q^{14} +(3.52175 - 1.89666i) q^{16} +1.33658 q^{17} -3.28346i q^{19} +(-0.620778 - 2.46188i) q^{20} +(2.84625 - 0.353321i) q^{22} -2.25680 q^{23} +3.38845 q^{25} +(5.68870 - 0.706169i) q^{26} +(-1.93930 + 0.489007i) q^{28} -3.58798i q^{29} -0.464312 q^{31} +(3.27540 + 4.61213i) q^{32} +(0.232854 + 1.87581i) q^{34} +1.26947i q^{35} -11.8743i q^{37} +(4.60814 - 0.572034i) q^{38} +(3.34695 - 1.30013i) q^{40} +1.73758 q^{41} -1.70380i q^{43} +(0.991730 + 3.93299i) q^{44} +(-0.393173 - 3.16729i) q^{46} +8.45083 q^{47} +1.00000 q^{49} +(0.590326 + 4.75549i) q^{50} +(1.98213 + 7.86073i) q^{52} +11.7544i q^{53} +2.57454 q^{55} +(-1.02415 - 2.63650i) q^{56} +(5.03553 - 0.625087i) q^{58} +5.49489i q^{59} -6.02150i q^{61} +(-0.0808911 - 0.651635i) q^{62} +(-5.90223 + 5.40034i) q^{64} +5.14565 q^{65} -0.381481i q^{67} +(-2.59202 + 0.653595i) q^{68} +(-1.78162 + 0.221163i) q^{70} -9.47622 q^{71} -10.0336 q^{73} +(16.6648 - 2.06870i) q^{74} +(1.60563 + 6.36760i) q^{76} -2.02805i q^{77} +4.90442 q^{79} +(2.40775 + 4.47074i) q^{80} +(0.302717 + 2.43860i) q^{82} -6.95800i q^{83} +1.69674i q^{85} +(2.39118 - 0.296830i) q^{86} +(-5.34695 + 2.07703i) q^{88} +17.4322 q^{89} -4.05339i q^{91} +(4.37661 - 1.10359i) q^{92} +(1.47228 + 11.8602i) q^{94} +4.16824 q^{95} +7.62794 q^{97} +(0.174217 + 1.40344i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{7}+O(q^{10}) $ 24 * q + 24 * q^7	$ 24 q + 24 q^{7} + 20 q^{10} - 4 q^{16} + 4 q^{22} - 24 q^{25} - 16 q^{31} + 4 q^{34} + 12 q^{40} - 52 q^{46} + 24 q^{49} + 12 q^{52} - 8 q^{55} - 28 q^{58} + 24 q^{64} + 20 q^{70} - 24 q^{76} + 32 q^{79} + 44 q^{82} - 60 q^{88} + 12 q^{94}+O(q^{100}) $ 24 * q + 24 * q^7 + 20 * q^10 - 4 * q^16 + 4 * q^22 - 24 * q^25 - 16 * q^31 + 4 * q^34 + 12 * q^40 - 52 * q^46 + 24 * q^49 + 12 * q^52 - 8 * q^55 - 28 * q^58 + 24 * q^64 + 20 * q^70 - 24 * q^76 + 32 * q^79 + 44 * q^82 - 60 * q^88 + 12 * 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 $

$2$	0.174217	+	1.40344i	0.123190	+	0.992383i
$2$	0.174217	+	1.40344i	0.123190	+	0.992383i
$3$		0			0
$3$		0			0
$4$	−1.93930	+	0.489007i	−0.969648	+	0.244503i
$5$			1.26947i			0.567723i	0.958865	+	0.283862i	$0.0916156\pi$
$5$			1.26947i			0.567723i	−0.958865	+	0.283862i	$0.908384\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−1.02415	−	2.63650i	−0.362092	−	0.932142i
$9$		0			0
$10$	−1.78162	+	0.221163i	−0.563399	+	0.0699378i
$11$		−	2.02805i		−	0.611480i	−0.952115	−	0.305740i	$-0.901096\pi$
$11$		−	2.02805i		−	0.611480i	0.952115	−	0.305740i	$-0.0989039\pi$
$12$		0			0
$13$		−	4.05339i		−	1.12421i	−0.827066	−	0.562104i	$-0.809992\pi$
$13$		−	4.05339i		−	1.12421i	0.827066	−	0.562104i	$-0.190008\pi$
$14$	0.174217	+	1.40344i	0.0465614	+	0.375086i
$15$		0			0
$16$	3.52175	−	1.89666i	0.880436	−	0.474164i
$17$	1.33658			0.324167			0.162084	−	0.986777i	$-0.448179\pi$
$17$	1.33658			0.324167			0.162084	+	0.986777i	$0.448179\pi$
$18$		0			0
$19$		−	3.28346i		−	0.753277i	−0.926360	−	0.376638i	$-0.877080\pi$
$19$		−	3.28346i		−	0.753277i	0.926360	−	0.376638i	$-0.122920\pi$
$20$	−0.620778	−	2.46188i	−0.138810	−	0.550492i
$21$		0			0
$22$	2.84625	−	0.353321i	0.606823	−	0.0753282i
$23$	−2.25680			−0.470576			−0.235288	−	0.971926i	$-0.575603\pi$
$23$	−2.25680			−0.470576			−0.235288	+	0.971926i	$0.575603\pi$
$24$		0			0
$25$	3.38845			0.677690
$26$	5.68870	−	0.706169i	1.11565	−	0.138491i
$27$		0			0
$28$	−1.93930	+	0.489007i	−0.366493	+	0.0924136i
$29$		−	3.58798i		−	0.666272i	−0.942879	−	0.333136i	$-0.891893\pi$
$29$		−	3.58798i		−	0.666272i	0.942879	−	0.333136i	$-0.108107\pi$
$30$		0			0
$31$	−0.464312			−0.0833930			−0.0416965	−	0.999130i	$-0.513276\pi$
$31$	−0.464312			−0.0833930			−0.0416965	+	0.999130i	$0.513276\pi$
$32$	3.27540	+	4.61213i	0.579014	+	0.815318i
$33$		0			0
$34$	0.232854	+	1.87581i	0.0399342	+	0.321698i
$35$			1.26947i			0.214579i
$36$		0			0
$37$		−	11.8743i		−	1.95212i	−0.217507	−	0.976059i	$-0.569793\pi$
$37$		−	11.8743i		−	1.95212i	0.217507	−	0.976059i	$-0.430207\pi$
$38$	4.60814	−	0.572034i	0.747539	−	0.0927962i
$39$		0			0
$40$	3.34695	−	1.30013i	0.529199	−	0.205568i
$41$	1.73758			0.271365			0.135683	−	0.990752i	$-0.456677\pi$
$41$	1.73758			0.271365			0.135683	+	0.990752i	$0.456677\pi$
$42$		0			0
$43$		−	1.70380i		−	0.259827i	−0.991525	−	0.129913i	$-0.958530\pi$
$43$		−	1.70380i		−	0.259827i	0.991525	−	0.129913i	$-0.0414699\pi$
$44$	0.991730	+	3.93299i	0.149509	+	0.592921i
$45$		0			0
$46$	−0.393173	−	3.16729i	−0.0579702	−	0.466991i
$47$	8.45083			1.23268			0.616340	−	0.787480i	$-0.288615\pi$
$47$	8.45083			1.23268			0.616340	+	0.787480i	$0.288615\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	0.590326	+	4.75549i	0.0834846	+	0.672528i
$51$		0			0
$52$	1.98213	+	7.86073i	0.274873	+	1.09009i
$53$			11.7544i			1.61459i	0.590146	+	0.807296i	$0.299070\pi$
$53$			11.7544i			1.61459i	−0.590146	+	0.807296i	$0.700930\pi$
$54$		0			0
$55$	2.57454			0.347152
$56$	−1.02415	−	2.63650i	−0.136858	−	0.352317i
$57$		0			0
$58$	5.03553	−	0.625087i	0.661197	−	0.0820780i
$59$			5.49489i			0.715374i	0.933842	+	0.357687i	$0.116435\pi$
$59$			5.49489i			0.715374i	−0.933842	+	0.357687i	$0.883565\pi$
$60$		0			0
$61$		−	6.02150i		−	0.770975i	−0.922713	−	0.385487i	$-0.874033\pi$
$61$		−	6.02150i		−	0.770975i	0.922713	−	0.385487i	$-0.125967\pi$
$62$	−0.0808911	−	0.651635i	−0.0102732	−	0.0827578i
$63$		0			0
$64$	−5.90223	+	5.40034i	−0.737779	+	0.675042i
$65$	5.14565			0.638239
$66$		0			0
$67$		−	0.381481i		−	0.0466054i	−0.999728	−	0.0233027i	$-0.992582\pi$
$67$		−	0.381481i		−	0.0466054i	0.999728	−	0.0233027i	$-0.00741815\pi$
$68$	−2.59202	+	0.653595i	−0.314328	+	0.0792600i
$69$		0			0
$70$	−1.78162	+	0.221163i	−0.212945	+	0.0264340i
$71$	−9.47622			−1.12462			−0.562310	−	0.826926i	$-0.690087\pi$
$71$	−9.47622			−1.12462			−0.562310	+	0.826926i	$0.690087\pi$
$72$		0			0
$73$	−10.0336			−1.17434			−0.587171	−	0.809463i	$-0.699759\pi$
$73$	−10.0336			−1.17434			−0.587171	+	0.809463i	$0.699759\pi$
$74$	16.6648	−	2.06870i	1.93725	−	0.240481i
$75$		0			0
$76$	1.60563	+	6.36760i	0.184179	+	0.730414i
$77$		−	2.02805i		−	0.231118i
$78$		0			0
$79$	4.90442			0.551791			0.275895	−	0.961188i	$-0.411026\pi$
$79$	4.90442			0.551791			0.275895	+	0.961188i	$0.411026\pi$
$80$	2.40775	+	4.47074i	0.269194	+	0.499844i
$81$		0			0
$82$	0.302717	+	2.43860i	0.0334295	+	0.269298i
$83$		−	6.95800i		−	0.763740i	−0.924216	−	0.381870i	$-0.875280\pi$
$83$		−	6.95800i		−	0.763740i	0.924216	−	0.381870i	$-0.124720\pi$
$84$		0			0
$85$			1.69674i			0.184037i
$86$	2.39118	−	0.296830i	0.257848	−	0.0320080i
$87$		0			0
$88$	−5.34695	+	2.07703i	−0.569987	+	0.221412i
$89$	17.4322			1.84781			0.923903	−	0.382628i	$-0.124981\pi$
$89$	17.4322			1.84781			0.923903	+	0.382628i	$0.124981\pi$
$90$		0			0
$91$		−	4.05339i		−	0.424911i
$92$	4.37661	−	1.10359i	0.456293	−	0.115057i
$93$		0			0
$94$	1.47228	+	11.8602i	0.151854	+	1.22329i
$95$	4.16824			0.427653
$96$		0			0
$97$	7.62794			0.774500			0.387250	−	0.921975i	$-0.373425\pi$
$97$	7.62794			0.774500			0.387250	+	0.921975i	$0.373425\pi$
$98$	0.174217	+	1.40344i	0.0175986	+	0.141769i
$99$		0			0
$100$	−6.57121	+	1.65697i	−0.657121	+	0.165697i
$101$		−	5.27674i		−	0.525055i	−0.964924	−	0.262528i	$-0.915444\pi$
$101$		−	5.27674i		−	0.525055i	0.964924	−	0.262528i	$-0.0845561\pi$
$102$		0			0
$103$	−5.07253			−0.499812			−0.249906	−	0.968270i	$-0.580400\pi$
$103$	−5.07253			−0.499812			−0.249906	+	0.968270i	$0.580400\pi$
$104$	−10.6868	+	4.15128i	−1.04792	+	0.407067i
$105$		0			0
$106$	−16.4966	+	2.04782i	−1.60229	+	0.198902i
$107$			5.22269i			0.504896i	0.967610	+	0.252448i	$0.0812357\pi$
$107$			5.22269i			0.504896i	−0.967610	+	0.252448i	$0.918764\pi$
$108$		0			0
$109$			10.8354i			1.03784i	0.854822	+	0.518922i	$0.173667\pi$
$109$			10.8354i			1.03784i	−0.854822	+	0.518922i	$0.826333\pi$
$110$	0.448529	+	3.61322i	0.0427656	+	0.344507i
$111$		0			0
$112$	3.52175	−	1.89666i	0.332774	−	0.179217i
$113$	10.8783			1.02334			0.511672	−	0.859181i	$-0.329026\pi$
$113$	10.8783			1.02334			0.511672	+	0.859181i	$0.329026\pi$
$114$		0			0
$115$		−	2.86494i		−	0.267157i
$116$	1.75455	+	6.95817i	0.162906	+	0.646049i
$117$		0			0
$118$	−7.71176	+	0.957303i	−0.709925	+	0.0881269i
$119$	1.33658			0.122524
$120$		0			0
$121$	6.88701			0.626092
$122$	8.45083	−	1.04905i	0.765102	−	0.0949763i
$123$		0			0
$124$	0.900440	−	0.227052i	0.0808619	−	0.0203899i
$125$			10.6489i			0.952464i
$126$		0			0
$127$	1.57175			0.139471			0.0697353	−	0.997566i	$-0.477785\pi$
$127$	1.57175			0.139471			0.0697353	+	0.997566i	$0.477785\pi$
$128$	−8.60733	−	7.34261i	−0.760788	−	0.649001i
$129$		0			0
$130$	0.896459	+	7.22162i	0.0786247	+	0.633378i
$131$			11.7947i			1.03051i	0.857037	+	0.515256i	$0.172303\pi$
$131$			11.7947i			1.03051i	−0.857037	+	0.515256i	$0.827697\pi$
$132$		0			0
$133$		−	3.28346i		−	0.284712i
$134$	0.535387	−	0.0664605i	0.0462504	−	0.00574131i
$135$		0			0
$136$	−1.36886	−	3.52388i	−0.117378	−	0.302170i
$137$	18.4006			1.57207			0.786033	−	0.618184i	$-0.212131\pi$
$137$	18.4006			1.57207			0.786033	+	0.618184i	$0.212131\pi$
$138$		0			0
$139$		−	11.3851i		−	0.965674i	−0.875710	−	0.482837i	$-0.839606\pi$
$139$		−	11.3851i		−	0.965674i	0.875710	−	0.482837i	$-0.160394\pi$
$140$	−0.620778	−	2.46188i	−0.0524653	−	0.208066i
$141$		0			0
$142$	−1.65092	−	13.2993i	−0.138542	−	1.11605i
$143$	−8.22048			−0.687431
$144$		0			0
$145$	4.55483			0.378258
$146$	−1.74802	−	14.0816i	−0.144667	−	1.16540i
$147$		0			0
$148$	5.80659	+	23.0277i	0.477299	+	1.89287i
$149$		−	14.6966i		−	1.20400i	−0.798498	−	0.601998i	$-0.794372\pi$
$149$		−	14.6966i		−	1.20400i	0.798498	−	0.601998i	$-0.205628\pi$
$150$		0			0
$151$	−0.220342			−0.0179312			−0.00896559	−	0.999960i	$-0.502854\pi$
$151$	−0.220342			−0.0179312			−0.00896559	+	0.999960i	$0.502854\pi$
$152$	−8.65683	+	3.36276i	−0.702161	+	0.272755i
$153$		0			0
$154$	2.84625	−	0.353321i	0.229357	−	0.0284714i
$155$		−	0.589430i		−	0.0473441i
$156$		0			0
$157$		−	10.4367i		−	0.832941i	−0.909149	−	0.416471i	$-0.863267\pi$
$157$		−	10.4367i		−	0.832941i	0.909149	−	0.416471i	$-0.136733\pi$
$158$	0.854434	+	6.88307i	0.0679751	+	0.547588i
$159$		0			0
$160$	−5.85496	+	4.15801i	−0.462875	+	0.328720i
$161$	−2.25680			−0.177861
$162$		0			0
$163$		−	4.46955i		−	0.350082i	−0.984561	−	0.175041i	$-0.943994\pi$
$163$		−	4.46955i		−	0.350082i	0.984561	−	0.175041i	$-0.0560058\pi$
$164$	−3.36969	+	0.849690i	−0.263129	+	0.0663497i
$165$		0			0
$166$	9.76515	−	1.21220i	0.757923	−	0.0940851i
$167$	−14.0617			−1.08812			−0.544062	−	0.839045i	$-0.683114\pi$
$167$	−14.0617			−1.08812			−0.544062	+	0.839045i	$0.683114\pi$
$168$		0			0
$169$	−3.42998			−0.263844
$170$	−2.38128	+	0.295601i	−0.182636	+	0.0226716i
$171$		0			0
$172$	0.833168	+	3.30417i	0.0635284	+	0.251940i
$173$			0.334570i			0.0254369i	0.999919	+	0.0127184i	$0.00404851\pi$
$173$			0.334570i			0.0254369i	−0.999919	+	0.0127184i	$0.995951\pi$
$174$		0			0
$175$	3.38845			0.256143
$176$	−3.84652	−	7.14228i	−0.289942	−	0.538369i
$177$		0			0
$178$	3.03698	+	24.4650i	0.227631	+	1.83373i
$179$		−	1.85419i		−	0.138589i	−0.997596	−	0.0692944i	$-0.977925\pi$
$179$		−	1.85419i		−	0.138589i	0.997596	−	0.0692944i	$-0.0220748\pi$
$180$		0			0
$181$		−	11.8864i		−	0.883512i	−0.897135	−	0.441756i	$-0.854356\pi$
$181$		−	11.8864i		−	0.883512i	0.897135	−	0.441756i	$-0.145644\pi$
$182$	5.68870	−	0.706169i	0.421674	−	0.0523447i
$183$		0			0
$184$	2.31130	+	5.95005i	0.170392	+	0.438643i
$185$	15.0740			1.10826
$186$		0			0
$187$		−	2.71064i		−	0.198222i
$188$	−16.3887	+	4.13251i	−1.19527	+	0.301394i
$189$		0			0
$190$	0.726179	+	5.84989i	0.0526825	+	0.424396i
$191$	−26.4777			−1.91586			−0.957928	−	0.287008i	$-0.907339\pi$
$191$	−26.4777			−1.91586			−0.957928	+	0.287008i	$0.907339\pi$
$192$		0			0
$193$	−17.6831			−1.27285			−0.636427	−	0.771337i	$-0.719588\pi$
$193$	−17.6831			−1.27285			−0.636427	+	0.771337i	$0.719588\pi$
$194$	1.32892	+	10.7054i	0.0954106	+	0.768600i
$195$		0			0
$196$	−1.93930	+	0.489007i	−0.138521	+	0.0349290i
$197$			9.22153i			0.657007i	0.944503	+	0.328504i	$0.106544\pi$
$197$			9.22153i			0.657007i	−0.944503	+	0.328504i	$0.893456\pi$
$198$		0			0
$199$	−8.46365			−0.599973			−0.299986	−	0.953944i	$-0.596982\pi$
$199$	−8.46365			−0.599973			−0.299986	+	0.953944i	$0.596982\pi$
$200$	−3.47028	−	8.93364i	−0.245386	−	0.631704i
$201$		0			0
$202$	7.40560	−	0.919297i	0.521056	−	0.0646815i
$203$		−	3.58798i		−	0.251827i
$204$		0			0
$205$			2.20581i			0.154060i
$206$	−0.883721	−	7.11900i	−0.0615718	−	0.496005i
$207$		0			0
$208$	−7.68790	−	14.2750i	−0.533060	−	0.989794i
$209$	−6.65902			−0.460614
$210$		0			0
$211$		−	4.66745i		−	0.321321i	−0.987010	−	0.160660i	$-0.948638\pi$
$211$		−	4.66745i		−	0.321321i	0.987010	−	0.160660i	$-0.0513624\pi$
$212$	−5.74798	−	22.7953i	−0.394773	−	1.56559i
$213$		0			0
$214$	−7.32974	+	0.909880i	−0.501050	+	0.0621981i
$215$	2.16292			0.147510
$216$		0			0
$217$	−0.464312			−0.0315196
$218$	−15.2069	+	1.88771i	−1.02994	+	0.127852i
$219$		0			0
$220$	−4.99281	+	1.25897i	−0.336615	+	0.0848797i
$221$		−	5.41767i		−	0.364432i
$222$		0			0
$223$	7.85009			0.525681			0.262841	−	0.964839i	$-0.415341\pi$
$223$	7.85009			0.525681			0.262841	+	0.964839i	$0.415341\pi$
$224$	3.27540	+	4.61213i	0.218847	+	0.308161i
$225$		0			0
$226$	1.89518	+	15.2670i	0.126066	+	1.01555i
$227$		−	19.2857i		−	1.28004i	−0.768360	−	0.640018i	$-0.778927\pi$
$227$		−	19.2857i		−	1.28004i	0.768360	−	0.640018i	$-0.221073\pi$
$228$		0			0
$229$			1.71588i			0.113389i	0.998392	+	0.0566944i	$0.0180561\pi$
$229$			1.71588i			0.113389i	−0.998392	+	0.0566944i	$0.981944\pi$
$230$	4.02077	−	0.499120i	0.265122	−	0.0329110i
$231$		0			0
$232$	−9.45971	+	3.67464i	−0.621060	+	0.241252i
$233$	−23.8734			−1.56400			−0.781999	−	0.623280i	$-0.785800\pi$
$233$	−23.8734			−1.56400			−0.781999	+	0.623280i	$0.785800\pi$
$234$		0			0
$235$			10.7281i			0.699821i
$236$	−2.68704	−	10.6562i	−0.174911	−	0.693661i
$237$		0			0
$238$	0.232854	+	1.87581i	0.0150937	+	0.121591i
$239$	−21.6697			−1.40170			−0.700848	−	0.713310i	$-0.747195\pi$
$239$	−21.6697			−1.40170			−0.700848	+	0.713310i	$0.747195\pi$
$240$		0			0
$241$	27.8432			1.79354			0.896770	−	0.442497i	$-0.145907\pi$
$241$	27.8432			1.79354			0.896770	+	0.442497i	$0.145907\pi$
$242$	1.19983	+	9.66552i	0.0771283	+	0.621323i
$243$		0			0
$244$	2.94455	+	11.6775i	0.188506	+	0.747574i
$245$			1.26947i			0.0811033i
$246$		0			0
$247$	−13.3091			−0.846840
$248$	0.475526	+	1.22416i	0.0301959	+	0.0777341i
$249$		0			0
$250$	−14.9451	+	1.85521i	−0.945209	+	0.117334i
$251$		−	27.7106i		−	1.74908i	−0.484957	−	0.874538i	$-0.661165\pi$
$251$		−	27.7106i		−	1.74908i	0.484957	−	0.874538i	$-0.338835\pi$
$252$		0			0
$253$			4.57691i			0.287748i
$254$	0.273826	+	2.20586i	0.0171814	+	0.138408i
$255$		0			0
$256$	8.80538	−	13.3591i	0.550336	−	0.834943i
$257$	1.90462			0.118807			0.0594035	−	0.998234i	$-0.481080\pi$
$257$	1.90462			0.118807			0.0594035	+	0.998234i	$0.481080\pi$
$258$		0			0
$259$		−	11.8743i		−	0.737831i
$260$	−9.97894	+	2.51626i	−0.618868	+	0.156052i
$261$		0			0
$262$	−16.5532	+	2.05484i	−1.02266	+	0.126949i
$263$	−19.2186			−1.18507			−0.592534	−	0.805545i	$-0.701872\pi$
$263$	−19.2186			−1.18507			−0.592534	+	0.805545i	$0.701872\pi$
$264$		0			0
$265$	−14.9218			−0.916642
$266$	4.60814	−	0.572034i	0.282543	−	0.0350737i
$267$		0			0
$268$	0.186547	+	0.739806i	0.0113952	+	0.0451908i
$269$			18.2931i			1.11535i	0.830059	+	0.557676i	$0.188307\pi$
$269$			18.2931i			1.11535i	−0.830059	+	0.557676i	$0.811693\pi$
$270$		0			0
$271$	19.1450			1.16297			0.581487	−	0.813555i	$-0.302471\pi$
$271$	19.1450			1.16297			0.581487	+	0.813555i	$0.302471\pi$
$272$	4.70708	−	2.53503i	0.285409	−	0.153709i
$273$		0			0
$274$	3.20569	+	25.8241i	0.193663	+	1.56009i
$275$		−	6.87195i		−	0.414394i
$276$		0			0
$277$			17.6288i			1.05921i	0.848244	+	0.529606i	$0.177660\pi$
$277$			17.6288i			1.05921i	−0.848244	+	0.529606i	$0.822340\pi$
$278$	15.9784	−	1.98348i	0.958318	−	0.118961i
$279$		0			0
$280$	3.34695	−	1.30013i	0.200018	−	0.0776974i
$281$	12.3772			0.738362			0.369181	−	0.929358i	$-0.379638\pi$
$281$	12.3772			0.738362			0.369181	+	0.929358i	$0.379638\pi$
$282$		0			0
$283$			2.56225i			0.152310i	0.997096	+	0.0761550i	$0.0242644\pi$
$283$			2.56225i			0.152310i	−0.997096	+	0.0761550i	$0.975736\pi$
$284$	18.3772	−	4.63394i	1.09049	−	0.274973i
$285$		0			0
$286$	−1.43215	−	11.5370i	−0.0846846	−	0.682195i
$287$	1.73758			0.102566
$288$		0			0
$289$	−15.2136			−0.894916
$290$	0.793528	+	6.39244i	0.0465976	+	0.375377i
$291$		0			0
$292$	19.4581	−	4.90649i	1.13870	−	0.287131i
$293$			1.12608i			0.0657866i	0.999459	+	0.0328933i	$0.0104721\pi$
$293$			1.12608i			0.0657866i	−0.999459	+	0.0328933i	$0.989528\pi$
$294$		0			0
$295$	−6.97559			−0.406135
$296$	−31.3065	+	12.1610i	−1.81965	+	0.706846i
$297$		0			0
$298$	20.6259	−	2.56040i	1.19483	−	0.148320i
$299$			9.14770i			0.529025i
$300$		0			0
$301$		−	1.70380i		−	0.0982052i
$302$	−0.0383873	−	0.309237i	−0.00220894	−	0.0177946i
$303$		0			0
$304$	−6.22760	−	11.5635i	−0.357177	−	0.663212i
$305$	7.64411			0.437700
$306$		0			0
$307$		−	24.9543i		−	1.42422i	−0.702070	−	0.712108i	$-0.747741\pi$
$307$		−	24.9543i		−	1.42422i	0.702070	−	0.712108i	$-0.252259\pi$
$308$	0.991730	+	3.93299i	0.0565091	+	0.224103i
$309$		0			0
$310$	0.827230	−	0.102689i	0.0469835	−	0.00583232i
$311$	−20.4110			−1.15740			−0.578701	−	0.815540i	$-0.696440\pi$
$311$	−20.4110			−1.15740			−0.578701	+	0.815540i	$0.696440\pi$
$312$		0			0
$313$	18.5902			1.05078			0.525389	−	0.850862i	$-0.323920\pi$
$313$	18.5902			1.05078			0.525389	+	0.850862i	$0.323920\pi$
$314$	14.6473	−	1.81825i	0.826597	−	0.102610i
$315$		0			0
$316$	−9.51113	+	2.39830i	−0.535043	+	0.134915i
$317$		−	1.68959i		−	0.0948970i	−0.998874	−	0.0474485i	$-0.984891\pi$
$317$		−	1.68959i		−	0.0948970i	0.998874	−	0.0474485i	$-0.0151090\pi$
$318$		0			0
$319$	−7.27661			−0.407412
$320$	−6.85556	−	7.49269i	−0.383237	−	0.418854i
$321$		0			0
$322$	−0.393173	−	3.16729i	−0.0219107	−	0.176506i
$323$		−	4.38859i		−	0.244188i
$324$		0			0
$325$		−	13.7347i		−	0.761865i
$326$	6.27275	−	0.778671i	0.347416	−	0.0431266i
$327$		0			0
$328$	−1.77955	−	4.58114i	−0.0982591	−	0.252951i
$329$	8.45083			0.465909
$330$		0			0
$331$			25.4187i			1.39714i	0.715542	+	0.698570i	$0.246180\pi$
$331$			25.4187i			1.39714i	−0.715542	+	0.698570i	$0.753820\pi$
$332$	3.40251	+	13.4936i	0.186737	+	0.740559i
$333$		0			0
$334$	−2.44978	−	19.7347i	−0.134046	−	1.07984i
$335$	0.484278			0.0264590
$336$		0			0
$337$	−10.5368			−0.573979			−0.286989	−	0.957934i	$-0.592654\pi$
$337$	−10.5368			−0.573979			−0.286989	+	0.957934i	$0.592654\pi$
$338$	−0.597560	−	4.81377i	−0.0325030	−	0.261835i
$339$		0			0
$340$	−0.829717	−	3.29048i	−0.0449977	−	0.178452i
$341$			0.941649i			0.0509932i
$342$		0			0
$343$	1.00000			0.0539949
$344$	−4.49206	+	1.74494i	−0.242195	+	0.0940811i
$345$		0			0
$346$	−0.469549	+	0.0582877i	−0.0252431	+	0.00313356i
$347$			12.6098i			0.676930i	0.940979	+	0.338465i	$0.109908\pi$
$347$			12.6098i			0.676930i	−0.940979	+	0.338465i	$0.890092\pi$
$348$		0			0
$349$		−	10.3681i		−	0.554990i	−0.960727	−	0.277495i	$-0.910496\pi$
$349$		−	10.3681i		−	0.554990i	0.960727	−	0.277495i	$-0.0895043\pi$
$350$	0.590326	+	4.75549i	0.0315542	+	0.254192i
$351$		0			0
$352$	9.35364	−	6.64267i	0.498551	−	0.354055i
$353$	21.4319			1.14071			0.570353	−	0.821399i	$-0.306806\pi$
$353$	21.4319			1.14071			0.570353	+	0.821399i	$0.306806\pi$
$354$		0			0
$355$		−	12.0298i		−	0.638473i
$356$	−33.8061	+	8.52444i	−1.79172	+	0.451794i
$357$		0			0
$358$	2.60225	−	0.323031i	0.137533	−	0.0170727i
$359$	−17.5414			−0.925798			−0.462899	−	0.886411i	$-0.653191\pi$
$359$	−17.5414			−0.925798			−0.462899	+	0.886411i	$0.653191\pi$
$360$		0			0
$361$	8.21890			0.432574
$362$	16.6819	−	2.07082i	0.876783	−	0.108840i
$363$		0			0
$364$	1.98213	+	7.86073i	0.103892	+	0.412014i
$365$		−	12.7373i		−	0.666702i
$366$		0			0
$367$	28.4730			1.48628			0.743140	−	0.669136i	$-0.233335\pi$
$367$	28.4730			1.48628			0.743140	+	0.669136i	$0.233335\pi$
$368$	−7.94788	+	4.28038i	−0.414312	+	0.223130i
$369$		0			0
$370$	2.62615	+	21.1555i	0.136527	+	1.09982i
$371$			11.7544i			0.610259i
$372$		0			0
$373$		−	11.7775i		−	0.609818i	−0.952382	−	0.304909i	$-0.901374\pi$
$373$		−	11.7775i		−	0.609818i	0.952382	−	0.304909i	$-0.0986260\pi$
$374$	3.80423	−	0.472240i	0.196712	−	0.0244190i
$375$		0			0
$376$	−8.65492	−	22.2806i	−0.446343	−	1.14903i
$377$	−14.5435			−0.749028
$378$		0			0
$379$			14.4058i			0.739975i	0.929037	+	0.369988i	$0.120638\pi$
$379$			14.4058i			0.739975i	−0.929037	+	0.369988i	$0.879362\pi$
$380$	−8.08346	+	2.03830i	−0.414673	+	0.104563i
$381$		0			0
$382$	−4.61286	−	37.1599i	−0.236014	−	1.90126i
$383$	11.8612			0.606078			0.303039	−	0.952978i	$-0.401999\pi$
$383$	11.8612			0.606078			0.303039	+	0.952978i	$0.401999\pi$
$384$		0			0
$385$	2.57454			0.131211
$386$	−3.08069	−	24.8171i	−0.156803	−	1.26316i
$387$		0			0
$388$	−14.7928	+	3.73011i	−0.750992	+	0.189368i
$389$		−	16.3633i		−	0.829655i	−0.909900	−	0.414827i	$-0.863842\pi$
$389$		−	16.3633i		−	0.829655i	0.909900	−	0.414827i	$-0.136158\pi$
$390$		0			0
$391$	−3.01639			−0.152545
$392$	−1.02415	−	2.63650i	−0.0517274	−	0.133163i
$393$		0			0
$394$	−12.9419	+	1.60655i	−0.652003	+	0.0809367i
$395$			6.22601i			0.313265i
$396$		0			0
$397$			10.7133i			0.537685i	0.963184	+	0.268843i	$0.0866411\pi$
$397$			10.7133i			0.537685i	−0.963184	+	0.268843i	$0.913359\pi$
$398$	−1.47451	−	11.8782i	−0.0739106	−	0.595403i
$399$		0			0
$400$	11.9333	−	6.42673i	0.596663	−	0.321337i
$401$	−21.7286			−1.08507			−0.542536	−	0.840032i	$-0.682536\pi$
$401$	−21.7286			−1.08507			−0.542536	+	0.840032i	$0.682536\pi$
$402$		0			0
$403$			1.88204i			0.0937511i
$404$	2.58036	+	10.2332i	0.128378	+	0.509119i
$405$		0			0
$406$	5.03553	−	0.625087i	0.249909	−	0.0310226i
$407$	−24.0816			−1.19368
$408$		0			0
$409$	−14.3607			−0.710092			−0.355046	−	0.934849i	$-0.615535\pi$
$409$	−14.3607			−0.710092			−0.355046	+	0.934849i	$0.615535\pi$
$410$	−3.09572	+	0.384289i	−0.152887	+	0.0189787i
$411$		0			0
$412$	9.83715	−	2.48050i	0.484642	−	0.122206i
$413$			5.49489i			0.270386i
$414$		0			0
$415$	8.83296			0.433593
$416$	18.6948	−	13.2765i	0.916587	−	0.650932i
$417$		0			0
$418$	−1.16011	−	9.34554i	−0.0567430	−	0.457105i
$419$			33.7826i			1.65039i	0.564849	+	0.825194i	$0.308935\pi$
$419$			33.7826i			1.65039i	−0.564849	+	0.825194i	$0.691065\pi$
$420$		0			0
$421$			10.6036i			0.516788i	0.966040	+	0.258394i	$0.0831933\pi$
$421$			10.6036i			0.516788i	−0.966040	+	0.258394i	$0.916807\pi$
$422$	6.55050	−	0.813149i	0.318873	−	0.0395835i
$423$		0			0
$424$	30.9905	−	12.0383i	1.50503	−	0.584631i
$425$	4.52892			0.219685
$426$		0			0
$427$		−	6.02150i		−	0.291401i
$428$	−2.55393	−	10.1283i	−0.123449	−	0.489572i
$429$		0			0
$430$	0.376816	+	3.03553i	0.0181717	+	0.146386i
$431$	−19.2155			−0.925577			−0.462788	−	0.886469i	$-0.653151\pi$
$431$	−19.2155			−0.925577			−0.462788	+	0.886469i	$0.653151\pi$
$432$		0			0
$433$	39.8723			1.91614			0.958070	−	0.286534i	$-0.0925030\pi$
$433$	39.8723			1.91614			0.958070	+	0.286534i	$0.0925030\pi$
$434$	−0.0808911	−	0.651635i	−0.00388290	−	0.0312795i
$435$		0			0
$436$	−5.29859	−	21.0131i	−0.253756	−	1.00634i
$437$			7.41011i			0.354474i
$438$		0			0
$439$	2.96048			0.141296			0.0706481	−	0.997501i	$-0.477493\pi$
$439$	2.96048			0.141296			0.0706481	+	0.997501i	$0.477493\pi$
$440$	−2.63672	−	6.78778i	−0.125701	−	0.323595i
$441$		0			0
$442$	7.60338	−	0.943849i	0.361656	−	0.0448943i
$443$		−	12.7091i		−	0.603827i	−0.953335	−	0.301914i	$-0.902375\pi$
$443$		−	12.7091i		−	0.603827i	0.953335	−	0.301914i	$-0.0976254\pi$
$444$		0			0
$445$			22.1296i			1.04904i
$446$	1.36762	+	11.0171i	0.0647586	+	0.521677i
$447$		0			0
$448$	−5.90223	+	5.40034i	−0.278854	+	0.255142i
$449$	27.4353			1.29475			0.647375	−	0.762171i	$-0.275867\pi$
$449$	27.4353			1.29475			0.647375	+	0.762171i	$0.275867\pi$
$450$		0			0
$451$		−	3.52391i		−	0.165934i
$452$	−21.0962	+	5.31955i	−0.992283	+	0.250211i
$453$		0			0
$454$	27.0663	−	3.35989i	1.27029	−	0.157688i
$455$	5.14565			0.241232
$456$		0			0
$457$	18.9049			0.884335			0.442168	−	0.896932i	$-0.354210\pi$
$457$	18.9049			0.884335			0.442168	+	0.896932i	$0.354210\pi$
$458$	−2.40814	+	0.298936i	−0.112525	+	0.0139684i
$459$		0			0
$460$	1.40097	+	5.55596i	0.0653207	+	0.259048i
$461$		−	30.3182i		−	1.41206i	−0.708181	−	0.706030i	$-0.750484\pi$
$461$		−	30.3182i		−	1.41206i	0.708181	−	0.706030i	$-0.249516\pi$
$462$		0			0
$463$	−29.2518			−1.35944			−0.679722	−	0.733470i	$-0.737900\pi$
$463$	−29.2518			−1.35944			−0.679722	+	0.733470i	$0.737900\pi$
$464$	−6.80518	−	12.6360i	−0.315922	−	0.586610i
$465$		0			0
$466$	−4.15915	−	33.5049i	−0.192669	−	1.55208i
$467$		−	32.7692i		−	1.51638i	−0.652036	−	0.758188i	$-0.726085\pi$
$467$		−	32.7692i		−	1.51638i	0.652036	−	0.758188i	$-0.273915\pi$
$468$		0			0
$469$		−	0.381481i		−	0.0176152i
$470$	−15.0562	+	1.86901i	−0.694491	+	0.0862109i
$471$		0			0
$472$	14.4873	−	5.62760i	0.666831	−	0.259031i
$473$	−3.45539			−0.158879
$474$		0			0
$475$		−	11.1258i		−	0.510488i
$476$	−2.59202	+	0.653595i	−0.118805	+	0.0299575i
$477$		0			0
$478$	−3.77523	−	30.4122i	−0.172675	−	1.39102i
$479$	25.8900			1.18294			0.591472	−	0.806326i	$-0.298547\pi$
$479$	25.8900			1.18294			0.591472	+	0.806326i	$0.298547\pi$
$480$		0			0
$481$	−48.1310			−2.19459
$482$	4.85076	+	39.0763i	0.220946	+	1.77988i
$483$		0			0
$484$	−13.3560	+	3.36779i	−0.607089	+	0.153082i
$485$			9.68342i			0.439701i
$486$		0			0
$487$	−5.94127			−0.269225			−0.134612	−	0.990898i	$-0.542979\pi$
$487$	−5.94127			−0.269225			−0.134612	+	0.990898i	$0.542979\pi$
$488$	−15.8757	+	6.16693i	−0.718658	+	0.279164i
$489$		0			0
$490$	−1.78162	+	0.221163i	−0.0804856	+	0.00999112i
$491$		−	3.77413i		−	0.170324i	−0.996367	−	0.0851621i	$-0.972859\pi$
$491$		−	3.77413i		−	0.170324i	0.996367	−	0.0851621i	$-0.0271408\pi$
$492$		0			0
$493$		−	4.79561i		−	0.215984i
$494$	−2.31868	−	18.6786i	−0.104322	−	0.840390i
$495$		0			0
$496$	−1.63519	+	0.880642i	−0.0734222	+	0.0395420i
$497$	−9.47622			−0.425067
$498$		0			0
$499$			7.66921i			0.343321i	0.985156	+	0.171661i	$0.0549132\pi$
$499$			7.66921i			0.343321i	−0.985156	+	0.171661i	$0.945087\pi$
$500$	−5.20737	−	20.6513i	−0.232881	−	0.923555i
$501$		0			0
$502$	38.8902	−	4.82765i	1.73575	−	0.215469i
$503$	7.29637			0.325329			0.162664	−	0.986681i	$-0.447991\pi$
$503$	7.29637			0.325329			0.162664	+	0.986681i	$0.447991\pi$
$504$		0			0
$505$	6.69865			0.298086
$506$	−6.42342	+	0.797374i	−0.285556	+	0.0354476i
$507$		0			0
$508$	−3.04810	+	0.768597i	−0.135237	+	0.0341010i
$509$		−	7.32231i		−	0.324556i	−0.986745	−	0.162278i	$-0.948116\pi$
$509$		−	7.32231i		−	0.324556i	0.986745	−	0.162278i	$-0.0518841\pi$
$510$		0			0
$511$	−10.0336			−0.443860
$512$	20.2828	+	10.0305i	0.896379	+	0.443288i
$513$		0			0
$514$	0.331817	+	2.67302i	0.0146358	+	0.117902i
$515$		−	6.43942i		−	0.283755i
$516$		0			0
$517$		−	17.1387i		−	0.753759i
$518$	16.6648	−	2.06870i	0.732211	−	0.0908934i
$519$		0			0
$520$	−5.26992	−	13.5665i	−0.231101	−	0.594930i
$521$	29.2300			1.28059			0.640295	−	0.768129i	$-0.278812\pi$
$521$	29.2300			1.28059			0.640295	+	0.768129i	$0.278812\pi$
$522$		0			0
$523$			37.4676i			1.63835i	0.573547	+	0.819173i	$0.305567\pi$
$523$			37.4676i			1.63835i	−0.573547	+	0.819173i	$0.694433\pi$
$524$	−5.76770	−	22.8735i	−0.251963	−	0.999234i
$525$		0			0
$526$	−3.34820	−	26.9721i	−0.145988	−	1.17604i
$527$	−0.620589			−0.0270333
$528$		0			0
$529$	−17.9068			−0.778559
$530$	−2.59964	−	20.9419i	−0.112921	−	0.909660i
$531$		0			0
$532$	1.60563	+	6.36760i	0.0696130	+	0.276070i
$533$		−	7.04311i		−	0.305071i
$534$		0			0
$535$	−6.63003			−0.286641
$536$	−1.00577	+	0.390694i	−0.0434428	+	0.0168754i
$537$		0			0
$538$	−25.6733	+	3.18697i	−1.10686	+	0.137400i
$539$		−	2.02805i		−	0.0873543i
$540$		0			0
$541$			22.9143i			0.985164i	0.870266	+	0.492582i	$0.163947\pi$
$541$			22.9143i			0.985164i	−0.870266	+	0.492582i	$0.836053\pi$
$542$	3.33538	+	26.8689i	0.143267	+	1.15412i
$543$		0			0
$544$	4.37782	+	6.16447i	0.187697	+	0.264299i
$545$	−13.7552			−0.589208
$546$		0			0
$547$		−	14.0319i		−	0.599959i	−0.953946	−	0.299979i	$-0.903020\pi$
$547$		−	14.0319i		−	0.599959i	0.953946	−	0.299979i	$-0.0969798\pi$
$548$	−35.6842	+	8.99800i	−1.52435	+	0.384375i
$549$		0			0
$550$	9.64438	−	1.19721i	0.411238	−	0.0510492i
$551$	−11.7810			−0.501887
$552$		0			0
$553$	4.90442			0.208557
$554$	−24.7410	+	3.07123i	−1.05114	+	0.130484i
$555$		0			0
$556$	5.56740	+	22.0791i	0.236110	+	0.936364i
$557$			29.1958i			1.23706i	0.785760	+	0.618532i	$0.212272\pi$
$557$			29.1958i			1.23706i	−0.785760	+	0.618532i	$0.787728\pi$
$558$		0			0
$559$	−6.90615			−0.292099
$560$	2.40775	+	4.47074i	0.101746	+	0.188923i
$561$		0			0
$562$	2.15632	+	17.3707i	0.0909587	+	0.732738i
$563$			29.5633i			1.24594i	0.782245	+	0.622971i	$0.214075\pi$
$563$			29.5633i			1.24594i	−0.782245	+	0.622971i	$0.785925\pi$
$564$		0			0
$565$			13.8096i			0.580976i
$566$	−3.59597	+	0.446387i	−0.151150	+	0.0187631i
$567$		0			0
$568$	9.70508	+	24.9840i	0.407216	+	1.04831i
$569$	−28.2748			−1.18534			−0.592672	−	0.805444i	$-0.701927\pi$
$569$	−28.2748			−1.18534			−0.592672	+	0.805444i	$0.701927\pi$
$570$		0			0
$571$			40.3483i			1.68852i	0.535932	+	0.844261i	$0.319960\pi$
$571$			40.3483i			1.68852i	−0.535932	+	0.844261i	$0.680040\pi$
$572$	15.9420	−	4.01987i	0.666567	−	0.168079i
$573$		0			0
$574$	0.302717	+	2.43860i	0.0126351	+	0.101785i
$575$	−7.64706			−0.318904
$576$		0			0
$577$	−0.0318593			−0.00132632			−0.000663161	−	1.00000i	$-0.500211\pi$
$577$	−0.0318593			−0.00132632			−0.000663161		1.00000i	$0.500211\pi$
$578$	−2.65046	−	21.3513i	−0.110245	−	0.888099i
$579$		0			0
$580$	−8.83317	+	2.22734i	−0.366777	+	0.0924853i
$581$		−	6.95800i		−	0.288667i
$582$		0			0
$583$	23.8385			0.987291
$584$	10.2759	+	26.4535i	0.425220	+	1.09465i
$585$		0			0
$586$	−1.58039	+	0.196183i	−0.0652855	+	0.00810424i
$587$			22.9245i			0.946195i	0.881010	+	0.473098i	$0.156864\pi$
$587$			22.9245i			0.946195i	−0.881010	+	0.473098i	$0.843136\pi$
$588$		0			0
$589$			1.52455i			0.0628180i
$590$	−1.21527	−	9.78983i	−0.0500317	−	0.403041i
$591$		0			0
$592$	−22.5214	−	41.8181i	−0.925625	−	1.71872i
$593$	−19.8895			−0.816764			−0.408382	−	0.912811i	$-0.633907\pi$
$593$	−19.8895			−0.816764			−0.408382	+	0.912811i	$0.633907\pi$
$594$		0			0
$595$			1.69674i			0.0695596i
$596$	7.18675	+	28.5012i	0.294381	+	1.16745i
$597$		0			0
$598$	−12.8383	+	1.59368i	−0.524995	+	0.0651706i
$599$	9.01493			0.368340			0.184170	−	0.982894i	$-0.441040\pi$
$599$	9.01493			0.368340			0.184170	+	0.982894i	$0.441040\pi$
$600$		0			0
$601$	−30.3934			−1.23977			−0.619886	−	0.784692i	$-0.712821\pi$
$601$	−30.3934			−1.23977			−0.619886	+	0.784692i	$0.712821\pi$
$602$	2.39118	−	0.296830i	0.0974572	−	0.0120979i
$603$		0			0
$604$	0.427308	−	0.107749i	0.0173869	−	0.00438423i
$605$			8.74284i			0.355447i
$606$		0			0
$607$	−35.5668			−1.44361			−0.721807	−	0.692095i	$-0.756688\pi$
$607$	−35.5668			−1.44361			−0.721807	+	0.692095i	$0.756688\pi$
$608$	15.1437	−	10.7546i	0.614160	−	0.436158i
$609$		0			0
$610$	1.33173	+	10.7281i	0.0539203	+	0.434366i
$611$		−	34.2545i		−	1.38579i
$612$		0			0
$613$			36.1874i			1.46159i	0.682595	+	0.730797i	$0.260851\pi$
$613$			36.1874i			1.46159i	−0.682595	+	0.730797i	$0.739149\pi$
$614$	35.0219	−	4.34746i	1.41337	−	0.175449i
$615$		0			0
$616$	−5.34695	+	2.07703i	−0.215435	+	0.0836859i
$617$	27.7558			1.11741			0.558704	−	0.829367i	$-0.311299\pi$
$617$	27.7558			1.11741			0.558704	+	0.829367i	$0.311299\pi$
$618$		0			0
$619$			30.0187i			1.20656i	0.797531	+	0.603278i	$0.206139\pi$
$619$			30.0187i			1.20656i	−0.797531	+	0.603278i	$0.793861\pi$
$620$	0.288235	+	1.14308i	0.0115758	+	0.0459072i
$621$		0			0
$622$	−3.55594	−	28.6457i	−0.142580	−	1.14859i
$623$	17.4322			0.698405
$624$		0			0
$625$	3.42386			0.136954
$626$	3.23872	+	26.0902i	0.129445	+	1.04277i
$627$		0			0
$628$	5.10363	+	20.2399i	0.203657	+	0.807660i
$629$		−	15.8709i		−	0.632813i
$630$		0			0
$631$	46.3724			1.84606			0.923028	−	0.384732i	$-0.125706\pi$
$631$	46.3724			1.84606			0.923028	+	0.384732i	$0.125706\pi$
$632$	−5.02287	−	12.9305i	−0.199799	−	0.514348i
$633$		0			0
$634$	2.37124	−	0.294356i	0.0941741	−	0.0116904i
$635$			1.99529i			0.0791807i
$636$		0			0
$637$		−	4.05339i		−	0.160601i
$638$	−1.26771	−	10.2123i	−0.0501891	−	0.404309i
$639$		0			0
$640$	9.32120	−	10.9267i	0.368453	−	0.431917i
$641$	16.0590			0.634294			0.317147	−	0.948376i	$-0.397275\pi$
$641$	16.0590			0.634294			0.317147	+	0.948376i	$0.397275\pi$
$642$		0			0
$643$		−	11.8356i		−	0.466752i	−0.972387	−	0.233376i	$-0.925023\pi$
$643$		−	11.8356i		−	0.466752i	0.972387	−	0.233376i	$-0.0749774\pi$
$644$	4.37661	−	1.10359i	0.172462	−	0.0434876i
$645$		0			0
$646$	6.15913	−	0.764567i	0.242328	−	0.0300815i
$647$	5.05582			0.198765			0.0993824	−	0.995049i	$-0.468313\pi$
$647$	5.05582			0.198765			0.0993824	+	0.995049i	$0.468313\pi$
$648$		0			0
$649$	11.1439			0.437437
$650$	19.2759	−	2.39282i	0.756062	−	0.0938541i
$651$		0			0
$652$	2.18564	+	8.66779i	0.0855963	+	0.339457i
$653$		−	21.1804i		−	0.828851i	−0.910083	−	0.414426i	$-0.863982\pi$
$653$		−	21.1804i		−	0.828851i	0.910083	−	0.414426i	$-0.136018\pi$
$654$		0			0
$655$	−14.9730			−0.585045
$656$	6.11933	−	3.29560i	0.238920	−	0.128672i
$657$		0			0
$658$	1.47228	+	11.8602i	0.0573953	+	0.462360i
$659$			18.6255i			0.725548i	0.931877	+	0.362774i	$0.118170\pi$
$659$			18.6255i			0.725548i	−0.931877	+	0.362774i	$0.881830\pi$
$660$		0			0
$661$		−	8.43660i		−	0.328146i	−0.986448	−	0.164073i	$-0.947537\pi$
$661$		−	8.43660i		−	0.328146i	0.986448	−	0.164073i	$-0.0524632\pi$
$662$	−35.6737	+	4.42837i	−1.38650	+	0.172114i
$663$		0			0
$664$	−18.3448	+	7.12604i	−0.711915	+	0.276544i
$665$	4.16824			0.161638
$666$		0			0
$667$			8.09736i			0.313531i
$668$	27.2697	−	6.87624i	1.05510	−	0.266050i
$669$		0			0
$670$	0.0843695	+	0.679657i	0.00325948	+	0.0262574i
$671$	−12.2119			−0.471436
$672$		0			0
$673$	−11.6372			−0.448581			−0.224291	−	0.974522i	$-0.572006\pi$
$673$	−11.6372			−0.448581			−0.224291	+	0.974522i	$0.572006\pi$
$674$	−1.83570	−	14.7878i	−0.0707084	−	0.569607i
$675$		0			0
$676$	6.65175	−	1.67728i	0.255836	−	0.0645108i
$677$			42.4251i			1.63053i	0.579089	+	0.815264i	$0.303408\pi$
$677$			42.4251i			1.63053i	−0.579089	+	0.815264i	$0.696592\pi$
$678$		0			0
$679$	7.62794			0.292733
$680$	4.47345	−	1.73772i	0.171549	−	0.0666384i
$681$		0			0
$682$	−1.32155	+	0.164051i	−0.0506047	+	0.00628184i
$683$		−	26.8253i		−	1.02644i	−0.858257	−	0.513221i	$-0.828452\pi$
$683$		−	26.8253i		−	1.02644i	0.858257	−	0.513221i	$-0.171548\pi$
$684$		0			0
$685$			23.3589i			0.892499i
$686$	0.174217	+	1.40344i	0.00665163	+	0.0535837i
$687$		0			0
$688$	−3.23152	−	6.00034i	−0.123201	−	0.228761i
$689$	47.6452			1.81514
$690$		0			0
$691$			49.9065i			1.89853i	0.314476	+	0.949265i	$0.398171\pi$
$691$			49.9065i			1.89853i	−0.314476	+	0.949265i	$0.601829\pi$
$692$	−0.163607	−	0.648830i	−0.00621939	−	0.0246648i
$693$		0			0
$694$	−17.6971	+	2.19684i	−0.671774	+	0.0833910i
$695$	14.4530			0.548235
$696$		0			0
$697$	2.32241			0.0879677
$698$	14.5510	−	1.80629i	0.550763	−	0.0683693i
$699$		0			0
$700$	−6.57121	+	1.65697i	−0.248369	+	0.0626278i
$701$			47.6375i			1.79924i	0.436671	+	0.899621i	$0.356157\pi$
$701$			47.6375i			1.79924i	−0.436671	+	0.899621i	$0.643843\pi$
$702$		0			0
$703$	−38.9887			−1.47049
$704$	10.9522	+	11.9700i	0.412775	+	0.451137i
$705$		0			0
$706$	3.73381	+	30.0785i	0.140524	+	1.13202i
$707$		−	5.27674i		−	0.198452i
$708$		0			0
$709$			24.0726i			0.904064i	0.892002	+	0.452032i	$0.149301\pi$
$709$			24.0726i			0.904064i	−0.892002	+	0.452032i	$0.850699\pi$
$710$	16.8831	−	2.09579i	0.633610	−	0.0786535i
$711$		0			0
$712$	−17.8532	−	45.9598i	−0.669075	−	1.72242i
$713$	1.04786			0.0392427
$714$		0			0
$715$		−	10.4356i		−	0.390271i
$716$	0.906712	+	3.59583i	0.0338854	+	0.134382i
$717$		0			0
$718$	−3.05600	−	24.6183i	−0.114049	−	0.918746i
$719$	49.0237			1.82827			0.914137	−	0.405406i	$-0.132870\pi$
$719$	49.0237			1.82827			0.914137	+	0.405406i	$0.132870\pi$
$720$		0			0
$721$	−5.07253			−0.188911
$722$	1.43187	+	11.5347i	0.0532887	+	0.429279i
$723$		0			0
$724$	5.81255	+	23.0513i	0.216022	+	0.856696i
$725$		−	12.1577i		−	0.451526i
$726$		0			0
$727$	18.0843			0.670710			0.335355	−	0.942092i	$-0.391144\pi$
$727$	18.0843			0.670710			0.335355	+	0.942092i	$0.391144\pi$
$728$	−10.6868	+	4.15128i	−0.396077	+	0.153857i
$729$		0			0
$730$	17.8761	−	2.21906i	0.661624	−	0.0821310i
$731$		−	2.27725i		−	0.0842273i
$732$		0			0
$733$			2.54526i			0.0940114i	0.998895	+	0.0470057i	$0.0149679\pi$
$733$			2.54526i			0.0940114i	−0.998895	+	0.0470057i	$0.985032\pi$
$734$	4.96049	+	39.9603i	0.183095	+	1.47496i
$735$		0			0
$736$	−7.39192	−	10.4087i	−0.272470	−	0.383669i
$737$	−0.773664			−0.0284983
$738$		0			0
$739$			36.7876i			1.35326i	0.736325	+	0.676628i	$0.236559\pi$
$739$			36.7876i			1.35326i	−0.736325	+	0.676628i	$0.763441\pi$
$740$	−29.2330	+	7.37129i	−1.07463	+	0.270974i
$741$		0			0
$742$	−16.4966	+	2.04782i	−0.605610	+	0.0751777i
$743$	−27.1051			−0.994391			−0.497196	−	0.867638i	$-0.665637\pi$
$743$	−27.1051			−0.994391			−0.497196	+	0.867638i	$0.665637\pi$
$744$		0			0
$745$	18.6569			0.683537
$746$	16.5291	−	2.05185i	0.605173	−	0.0751234i
$747$		0			0
$748$	1.32552	+	5.25674i	0.0484659	+	0.192206i
$749$			5.22269i			0.190833i
$750$		0			0
$751$	−35.3786			−1.29098			−0.645491	−	0.763768i	$-0.723347\pi$
$751$	−35.3786			−1.29098			−0.645491	+	0.763768i	$0.723347\pi$
$752$	29.7617	−	16.0283i	1.08530	−	0.584493i
$753$		0			0
$754$	−2.53372	−	20.4110i	−0.0922728	−	0.743323i
$755$		−	0.279717i		−	0.0101799i
$756$		0			0
$757$			0.340328i			0.0123694i	0.999981	+	0.00618471i	$0.00196867\pi$
$757$			0.340328i			0.0123694i	−0.999981	+	0.00618471i	$0.998031\pi$
$758$	−20.2177	+	2.50973i	−0.734339	+	0.0911575i
$759$		0			0
$760$	−4.26891	−	10.9896i	−0.154850	−	0.398633i
$761$	−30.2601			−1.09693			−0.548464	−	0.836174i	$-0.684787\pi$
$761$	−30.2601			−1.09693			−0.548464	+	0.836174i	$0.684787\pi$
$762$		0			0
$763$			10.8354i			0.392268i
$764$	51.3480	−	12.9477i	1.85771	−	0.468433i
$765$		0			0
$766$	2.06642	+	16.6465i	0.0746627	+	0.601461i
$767$	22.2729			0.804230
$768$		0			0
$769$	18.0636			0.651389			0.325695	−	0.945475i	$-0.394402\pi$
$769$	18.0636			0.651389			0.325695	+	0.945475i	$0.394402\pi$
$770$	0.448529	+	3.61322i	0.0161639	+	0.130212i
$771$		0			0
$772$	34.2927	−	8.64713i	1.23422	−	0.311217i
$773$		−	3.29847i		−	0.118638i	−0.998239	−	0.0593188i	$-0.981107\pi$
$773$		−	3.29847i		−	0.118638i	0.998239	−	0.0593188i	$-0.0188929\pi$
$774$		0			0
$775$	−1.57330			−0.0565146
$776$	−7.81215	−	20.1110i	−0.280440	−	0.721944i
$777$		0			0
$778$	22.9650	−	2.85077i	0.823335	−	0.102205i
$779$		−	5.70529i		−	0.204413i
$780$		0			0
$781$			19.2183i			0.687683i
$782$	−0.525506	−	4.23332i	−0.0187920	−	0.151383i
$783$		0			0
$784$	3.52175	−	1.89666i	0.125777	−	0.0677378i
$785$	13.2491			0.472880
$786$		0			0
$787$		−	14.6607i		−	0.522597i	−0.965258	−	0.261298i	$-0.915849\pi$
$787$		−	14.6607i		−	0.522597i	0.965258	−	0.261298i	$-0.0841506\pi$
$788$	−4.50939	−	17.8833i	−0.160640	−	0.637066i
$789$		0			0
$790$	−8.73784	+	1.08468i	−0.310878	+	0.0385910i
$791$	10.8783			0.386787
$792$		0			0
$793$	−24.4075			−0.866736
$794$	−15.0355	+	1.86644i	−0.533590	+	0.0662374i
$795$		0			0
$796$	16.4135	−	4.13878i	0.581762	−	0.146695i
$797$			10.7001i			0.379016i	0.981879	+	0.189508i	$0.0606892\pi$
$797$			10.7001i			0.379016i	−0.981879	+	0.189508i	$0.939311\pi$
$798$		0			0
$799$	11.2952			0.399595
$800$	11.0985	+	15.6280i	0.392392	+	0.552533i
$801$		0			0
$802$	−3.78548	−	30.4948i	−0.133670	−	1.07681i
$803$			20.3486i			0.718087i
$804$		0			0
$805$		−	2.86494i		−	0.100976i
$806$	−2.64133	+	0.327883i	−0.0930370	+	0.0115492i
$807$		0			0
$808$	−13.9121	+	5.40418i	−0.489426	+	0.190118i
$809$	19.7701			0.695078			0.347539	−	0.937666i	$-0.387017\pi$
$809$	19.7701			0.695078			0.347539	+	0.937666i	$0.387017\pi$
$810$		0			0
$811$			29.8088i			1.04673i	0.852109	+	0.523364i	$0.175323\pi$
$811$			29.8088i			1.04673i	−0.852109	+	0.523364i	$0.824677\pi$
$812$	1.75455	+	6.95817i	0.0615725	+	0.244184i
$813$		0			0
$814$	−4.19542	−	33.7971i	−0.147050	−	1.18459i
$815$	5.67395			0.198750
$816$		0			0
$817$	−5.59435			−0.195721
$818$	−2.50188	−	20.1544i	−0.0874762	−	0.704683i
$819$		0			0
$820$	−1.07865	−	4.27772i	−0.0376683	−	0.149384i
$821$			38.3014i			1.33673i	0.743834	+	0.668364i	$0.233005\pi$
$821$			38.3014i			1.33673i	−0.743834	+	0.668364i	$0.766995\pi$
$822$		0			0
$823$	26.3640			0.918990			0.459495	−	0.888180i	$-0.348030\pi$
$823$	26.3640			0.918990			0.459495	+	0.888180i	$0.348030\pi$
$824$	5.19504	+	13.3737i	0.180978	+	0.465896i
$825$		0			0
$826$	−7.71176	+	0.957303i	−0.268327	+	0.0333088i
$827$		−	44.5542i		−	1.54930i	−0.632390	−	0.774650i	$-0.717926\pi$
$827$		−	44.5542i		−	1.54930i	0.632390	−	0.774650i	$-0.282074\pi$
$828$		0			0
$829$		−	48.8761i		−	1.69754i	−0.528765	−	0.848768i	$-0.677345\pi$
$829$		−	48.8761i		−	1.69754i	0.528765	−	0.848768i	$-0.322655\pi$
$830$	1.53885	+	12.3965i	0.0534143	+	0.430290i
$831$		0			0
$832$	21.8897	+	23.9241i	0.758888	+	0.829417i
$833$	1.33658			0.0463096
$834$		0			0
$835$		−	17.8508i		−	0.617753i
$836$	12.9138	−	3.25630i	0.446634	−	0.112622i
$837$		0			0
$838$	−47.4119	+	5.88550i	−1.63782	+	0.203311i
$839$	39.1944			1.35314			0.676571	−	0.736377i	$-0.263465\pi$
$839$	39.1944			1.35314			0.676571	+	0.736377i	$0.263465\pi$
$840$		0			0
$841$	16.1264			0.556082
$842$	−14.8816	+	1.84733i	−0.512852	+	0.0636631i
$843$		0			0
$844$	2.28241	+	9.05157i	0.0785639	+	0.311568i
$845$		−	4.35425i		−	0.149791i
$846$		0			0
$847$	6.88701			0.236641
$848$	22.2941	+	41.3960i	0.765582	+	1.42155i
$849$		0			0
$850$	0.789015	+	6.35608i	0.0270630	+	0.218012i
$851$			26.7979i			0.918619i
$852$		0			0
$853$		−	22.6315i		−	0.774887i	−0.921893	−	0.387444i	$-0.873358\pi$
$853$		−	22.6315i		−	0.774887i	0.921893	−	0.387444i	$-0.126642\pi$
$854$	8.45083	−	1.04905i	0.289181	−	0.0358977i
$855$		0			0
$856$	13.7696	−	5.34882i	0.470635	−	0.182819i
$857$	−25.6866			−0.877436			−0.438718	−	0.898625i	$-0.644567\pi$
$857$	−25.6866			−0.877436			−0.438718	+	0.898625i	$0.644567\pi$
$858$		0			0
$859$			45.4628i			1.55117i	0.631244	+	0.775585i	$0.282545\pi$
$859$			45.4628i			1.55117i	−0.631244	+	0.775585i	$0.717455\pi$
$860$	−4.19454	+	1.05768i	−0.143032	+	0.0360666i
$861$		0			0
$862$	−3.34766	−	26.9678i	−0.114022	−	0.918527i
$863$	6.81159			0.231869			0.115935	−	0.993257i	$-0.463014\pi$
$863$	6.81159			0.231869			0.115935	+	0.993257i	$0.463014\pi$
$864$		0			0
$865$	−0.424725			−0.0144411
$866$	6.94643	+	55.9584i	0.236049	+	1.90155i
$867$		0			0
$868$	0.900440	−	0.227052i	0.0305629	−	0.00770664i
$869$		−	9.94642i		−	0.337409i
$870$		0			0
$871$	−1.54629			−0.0523942
$872$	28.5675	−	11.0971i	0.967418	−	0.375795i
$873$		0			0
$874$	−10.3997	+	1.29097i	−0.351774	+	0.0436676i
$875$			10.6489i			0.359997i
$876$		0			0
$877$			34.9922i			1.18160i	0.806817	+	0.590802i	$0.201188\pi$
$877$			34.9922i			1.18160i	−0.806817	+	0.590802i	$0.798812\pi$
$878$	0.515766	+	4.15487i	0.0174063	+	0.140220i
$879$		0			0
$880$	9.06689	−	4.88303i	0.305645	−	0.164607i
$881$	−16.1155			−0.542946			−0.271473	−	0.962446i	$-0.587511\pi$
$881$	−16.1155			−0.542946			−0.271473	+	0.962446i	$0.587511\pi$
$882$		0			0
$883$		−	46.5075i		−	1.56510i	−0.622586	−	0.782551i	$-0.713918\pi$
$883$		−	46.5075i		−	1.56510i	0.622586	−	0.782551i	$-0.286082\pi$
$884$	2.64927	+	10.5065i	0.0891047	+	0.353371i
$885$		0			0
$886$	17.8365	−	2.21414i	0.599228	−	0.0743855i
$887$	43.0256			1.44466			0.722328	−	0.691550i	$-0.243072\pi$
$887$	43.0256			1.44466			0.722328	+	0.691550i	$0.243072\pi$
$888$		0			0
$889$	1.57175			0.0527149
$890$	−31.0576	+	3.85534i	−1.04105	+	0.129231i
$891$		0			0
$892$	−15.2237	+	3.83875i	−0.509726	+	0.128531i
$893$		−	27.7479i		−	0.928550i
$894$		0			0
$895$	2.35384			0.0786801
$896$	−8.60733	−	7.34261i	−0.287551	−	0.245299i
$897$		0			0
$898$	4.77969	+	38.5038i	0.159500	+	1.28489i
$899$			1.66595i			0.0555624i
$900$		0			0
$901$			15.7107i			0.523398i
$902$	4.94560	−	0.613925i	0.164671	−	0.0204415i
$903$		0			0
$904$	−11.1410	−	28.6806i	−0.370544	−	0.953902i
$905$	15.0895			0.501590
$906$		0			0
$907$			49.6912i			1.64997i	0.565156	+	0.824984i	$0.308816\pi$
$907$			49.6912i			1.64997i	−0.565156	+	0.824984i	$0.691184\pi$
$908$	9.43082	+	37.4007i	0.312973	+	1.24118i
$909$		0			0
$910$	0.896459	+	7.22162i	0.0297173	+	0.239394i
$911$	−44.6723			−1.48006			−0.740029	−	0.672575i	$-0.765188\pi$
$911$	−44.6723			−1.48006			−0.740029	+	0.672575i	$0.765188\pi$
$912$		0			0
$913$	−14.1112			−0.467012
$914$	3.29356	+	26.5320i	0.108941	+	0.877599i
$915$		0			0
$916$	−0.839078	−	3.32761i	−0.0277239	−	0.109947i
$917$			11.7947i			0.389497i
$918$		0			0
$919$	−51.7662			−1.70761			−0.853804	−	0.520594i	$-0.825710\pi$
$919$	−51.7662			−1.70761			−0.853804	+	0.520594i	$0.825710\pi$
$920$	−7.55340	+	2.93413i	−0.249028	+	0.0967353i
$921$		0			0
$922$	42.5499	−	5.28195i	1.40131	−	0.173952i
$923$			38.4108i			1.26431i
$924$		0			0
$925$		−	40.2354i		−	1.32293i
$926$	−5.09615	−	41.0531i	−0.167470	−	1.34909i
$927$		0			0
$928$	16.5483	−	11.7521i	0.543223	−	0.385781i
$929$	−16.4271			−0.538956			−0.269478	−	0.963006i	$-0.586851\pi$
$929$	−16.4271			−0.538956			−0.269478	+	0.963006i	$0.586851\pi$
$930$		0			0
$931$		−	3.28346i		−	0.107611i
$932$	46.2976	−	11.6742i	1.51653	−	0.382403i
$933$		0			0
$934$	45.9896	−	5.70894i	1.50483	−	0.186802i
$935$	3.44108			0.112535
$936$		0			0
$937$	−24.9154			−0.813951			−0.406976	−	0.913439i	$-0.633417\pi$
$937$	−24.9154			−0.813951			−0.406976	+	0.913439i	$0.633417\pi$
$938$	0.535387	−	0.0664605i	0.0174810	−	0.00217001i
$939$		0			0
$940$	−5.24609	−	20.8049i	−0.171109	−	0.678581i
$941$		−	35.3088i		−	1.15103i	−0.817790	−	0.575517i	$-0.804801\pi$
$941$		−	35.3088i		−	1.15103i	0.817790	−	0.575517i	$-0.195199\pi$
$942$		0			0
$943$	−3.92138			−0.127698
$944$	10.4219	+	19.3516i	0.339205	+	0.629841i
$945$		0			0
$946$	−0.601987	−	4.84943i	−0.0195723	−	0.157669i
$947$			41.3026i			1.34215i	0.741388	+	0.671077i	$0.234168\pi$
$947$			41.3026i			1.34215i	−0.741388	+	0.671077i	$0.765832\pi$
$948$		0			0
$949$			40.6701i			1.32021i
$950$	15.6145	−	1.93831i	0.506600	−	0.0628871i
$951$		0			0
$952$	−1.36886	−	3.52388i	−0.0443649	−	0.114210i
$953$	−11.2564			−0.364630			−0.182315	−	0.983240i	$-0.558359\pi$
$953$	−11.2564			−0.364630			−0.182315	+	0.983240i	$0.558359\pi$
$954$		0			0
$955$		−	33.6125i		−	1.08768i
$956$	42.0240	−	10.5966i	1.35915	−	0.342719i
$957$		0			0
$958$	4.51047	+	36.3351i	0.145727	+	1.17393i
$959$	18.4006			0.594185
$960$		0			0
$961$	−30.7844			−0.993046
$962$	−8.38524	−	67.5491i	−0.270351	−	2.17787i
$963$		0			0
$964$	−53.9963	+	13.6155i	−1.73910	+	0.438526i
$965$		−	22.4481i		−	0.722629i
$966$		0			0
$967$	−1.51158			−0.0486093			−0.0243046	−	0.999705i	$-0.507737\pi$
$967$	−1.51158			−0.0486093			−0.0243046	+	0.999705i	$0.507737\pi$
$968$	−7.05334	−	18.1576i	−0.226703	−	0.583607i
$969$		0			0
$970$	−13.5901	+	1.68702i	−0.436352	+	0.0541668i
$971$			9.03959i			0.290094i	0.989425	+	0.145047i	$0.0463334\pi$
$971$			9.03959i			0.290094i	−0.989425	+	0.145047i	$0.953667\pi$
$972$		0			0
$973$		−	11.3851i		−	0.364990i
$974$	−1.03507	−	8.33823i	−0.0331658	−	0.267174i
$975$		0			0
$976$	−11.4207	−	21.2062i	−0.365569	−	0.678794i
$977$	−2.32341			−0.0743325			−0.0371662	−	0.999309i	$-0.511833\pi$
$977$	−2.32341			−0.0743325			−0.0371662	+	0.999309i	$0.511833\pi$
$978$		0			0
$979$		−	35.3533i		−	1.12990i
$980$	−0.620778	−	2.46188i	−0.0198300	−	0.0786417i
$981$		0			0
$982$	5.29678	−	0.657518i	0.169027	−	0.0209822i
$983$	−18.8206			−0.600284			−0.300142	−	0.953894i	$-0.597034\pi$
$983$	−18.8206			−0.600284			−0.300142	+	0.953894i	$0.597034\pi$
$984$		0			0
$985$	−11.7064			−0.372998
$986$	6.73036	−	0.835477i	0.214338	−	0.0266070i
$987$		0			0
$988$	25.8104	−	6.50826i	0.821137	−	0.207055i
$989$			3.84513i			0.122268i
$990$		0			0
$991$	−37.9699			−1.20615			−0.603077	−	0.797683i	$-0.706059\pi$
$991$	−37.9699			−1.20615			−0.603077	+	0.797683i	$0.706059\pi$
$992$	−1.52081	−	2.14147i	−0.0482857	−	0.0679918i
$993$		0			0
$994$	−1.65092	−	13.2993i	−0.0523640	−	0.421829i
$995$		−	10.7443i		−	0.340618i
$996$		0			0
$997$			9.55023i			0.302459i	0.988499	+	0.151229i	$0.0483232\pi$
$997$			9.55023i			0.302459i	−0.988499	+	0.151229i	$0.951677\pi$
$998$	−10.7633	+	1.33611i	−0.340706	+	0.0422937i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.c.f.757.14	yes	24
3.2	odd	2	inner	1512.2.c.f.757.11	✓	24
4.3	odd	2		6048.2.c.g.3025.13		24
8.3	odd	2		6048.2.c.g.3025.12		24
8.5	even	2	inner	1512.2.c.f.757.13	yes	24
12.11	even	2		6048.2.c.g.3025.11		24
24.5	odd	2	inner	1512.2.c.f.757.12	yes	24
24.11	even	2		6048.2.c.g.3025.14		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.c.f.757.11	✓	24	3.2	odd	2	inner
1512.2.c.f.757.12	yes	24	24.5	odd	2	inner
1512.2.c.f.757.13	yes	24	8.5	even	2	inner
1512.2.c.f.757.14	yes	24	1.1	even	1	trivial
6048.2.c.g.3025.11		24	12.11	even	2
6048.2.c.g.3025.12		24	8.3	odd	2
6048.2.c.g.3025.13		24	4.3	odd	2
6048.2.c.g.3025.14		24	24.11	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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.174217 + 1.40344i) q^{2} +(-1.93930 + 0.489007i) q^{4} +1.26947i q^{5} +1.00000 q^{7} +(-1.02415 - 2.63650i) q^{8} +O(q^{10})\)	\(q+(0.174217 + 1.40344i) q^{2} +(-1.93930 + 0.489007i) q^{4} +1.26947i q^{5} +1.00000 q^{7} +(-1.02415 - 2.63650i) q^{8} +(-1.78162 + 0.221163i) q^{10} -2.02805i q^{11} -4.05339i q^{13} +(0.174217 + 1.40344i) q^{14} +(3.52175 - 1.89666i) q^{16} +1.33658 q^{17} -3.28346i q^{19} +(-0.620778 - 2.46188i) q^{20} +(2.84625 - 0.353321i) q^{22} -2.25680 q^{23} +3.38845 q^{25} +(5.68870 - 0.706169i) q^{26} +(-1.93930 + 0.489007i) q^{28} -3.58798i q^{29} -0.464312 q^{31} +(3.27540 + 4.61213i) q^{32} +(0.232854 + 1.87581i) q^{34} +1.26947i q^{35} -11.8743i q^{37} +(4.60814 - 0.572034i) q^{38} +(3.34695 - 1.30013i) q^{40} +1.73758 q^{41} -1.70380i q^{43} +(0.991730 + 3.93299i) q^{44} +(-0.393173 - 3.16729i) q^{46} +8.45083 q^{47} +1.00000 q^{49} +(0.590326 + 4.75549i) q^{50} +(1.98213 + 7.86073i) q^{52} +11.7544i q^{53} +2.57454 q^{55} +(-1.02415 - 2.63650i) q^{56} +(5.03553 - 0.625087i) q^{58} +5.49489i q^{59} -6.02150i q^{61} +(-0.0808911 - 0.651635i) q^{62} +(-5.90223 + 5.40034i) q^{64} +5.14565 q^{65} -0.381481i q^{67} +(-2.59202 + 0.653595i) q^{68} +(-1.78162 + 0.221163i) q^{70} -9.47622 q^{71} -10.0336 q^{73} +(16.6648 - 2.06870i) q^{74} +(1.60563 + 6.36760i) q^{76} -2.02805i q^{77} +4.90442 q^{79} +(2.40775 + 4.47074i) q^{80} +(0.302717 + 2.43860i) q^{82} -6.95800i q^{83} +1.69674i q^{85} +(2.39118 - 0.296830i) q^{86} +(-5.34695 + 2.07703i) q^{88} +17.4322 q^{89} -4.05339i q^{91} +(4.37661 - 1.10359i) q^{92} +(1.47228 + 11.8602i) q^{94} +4.16824 q^{95} +7.62794 q^{97} +(0.174217 + 1.40344i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{7}+O(q^{10}) \) 24 * q + 24 * q^7	\( 24 q + 24 q^{7} + 20 q^{10} - 4 q^{16} + 4 q^{22} - 24 q^{25} - 16 q^{31} + 4 q^{34} + 12 q^{40} - 52 q^{46} + 24 q^{49} + 12 q^{52} - 8 q^{55} - 28 q^{58} + 24 q^{64} + 20 q^{70} - 24 q^{76} + 32 q^{79} + 44 q^{82} - 60 q^{88} + 12 q^{94}+O(q^{100}) \) 24 * q + 24 * q^7 + 20 * q^10 - 4 * q^16 + 4 * q^22 - 24 * q^25 - 16 * q^31 + 4 * q^34 + 12 * q^40 - 52 * q^46 + 24 * q^49 + 12 * q^52 - 8 * q^55 - 28 * q^58 + 24 * q^64 + 20 * q^70 - 24 * q^76 + 32 * q^79 + 44 * q^82 - 60 * q^88 + 12 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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