LMFDB - Embedded newform 1512.2.c.f.757.13

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

$q$-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	$-0.908384\pi$
$5$		−	1.26947i		−	0.567723i	0.958865	−	0.283862i	$-0.0916156\pi$
$6$		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	$0.0989039\pi$
$11$			2.02805i			0.611480i	−0.952115	+	0.305740i	$0.901096\pi$
$12$		0			0
$13$			4.05339i			1.12421i	0.827066	+	0.562104i	$0.190008\pi$
$13$			4.05339i			1.12421i	−0.827066	+	0.562104i	$0.809992\pi$
$14$	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	$0.122920\pi$
$19$			3.28346i			0.753277i	−0.926360	+	0.376638i	$0.877080\pi$
$20$	−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	$0.108107\pi$
$29$			3.58798i			0.666272i	−0.942879	+	0.333136i	$0.891893\pi$
$30$		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	$0.430207\pi$
$37$			11.8743i			1.95212i	−0.217507	+	0.976059i	$0.569793\pi$
$38$	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	$0.0414699\pi$
$43$			1.70380i			0.259827i	−0.991525	+	0.129913i	$0.958530\pi$
$44$	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	$-0.700930\pi$
$53$		−	11.7544i		−	1.61459i	0.590146	−	0.807296i	$-0.299070\pi$
$54$		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	$-0.883565\pi$
$59$		−	5.49489i		−	0.715374i	0.933842	−	0.357687i	$-0.116435\pi$
$60$		0			0
$61$			6.02150i			0.770975i	0.922713	+	0.385487i	$0.125967\pi$
$61$			6.02150i			0.770975i	−0.922713	+	0.385487i	$0.874033\pi$
$62$	−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	$0.00741815\pi$
$67$			0.381481i			0.0466054i	−0.999728	+	0.0233027i	$0.992582\pi$
$68$	−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	$0.124720\pi$
$83$			6.95800i			0.763740i	−0.924216	+	0.381870i	$0.875280\pi$
$84$		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	$0.0845561\pi$
$101$			5.27674i			0.525055i	−0.964924	+	0.262528i	$0.915444\pi$
$102$		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	$-0.918764\pi$
$107$		−	5.22269i		−	0.504896i	0.967610	−	0.252448i	$-0.0812357\pi$
$108$		0			0
$109$		−	10.8354i		−	1.03784i	−0.854822	−	0.518922i	$-0.826333\pi$
$109$		−	10.8354i		−	1.03784i	0.854822	−	0.518922i	$-0.173667\pi$
$110$	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	$-0.827697\pi$
$131$		−	11.7947i		−	1.03051i	0.857037	−	0.515256i	$-0.172303\pi$
$132$		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	$0.160394\pi$
$139$			11.3851i			0.965674i	−0.875710	+	0.482837i	$0.839606\pi$
$140$	−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	$0.205628\pi$
$149$			14.6966i			1.20400i	−0.798498	+	0.601998i	$0.794372\pi$
$150$		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	$0.136733\pi$
$157$			10.4367i			0.832941i	−0.909149	+	0.416471i	$0.863267\pi$
$158$	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	$0.0560058\pi$
$163$			4.46955i			0.350082i	−0.984561	+	0.175041i	$0.943994\pi$
$164$	−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	$-0.995951\pi$
$173$		−	0.334570i		−	0.0254369i	0.999919	−	0.0127184i	$-0.00404851\pi$
$174$		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	$0.0220748\pi$
$179$			1.85419i			0.138589i	−0.997596	+	0.0692944i	$0.977925\pi$
$180$		0			0
$181$			11.8864i			0.883512i	0.897135	+	0.441756i	$0.145644\pi$
$181$			11.8864i			0.883512i	−0.897135	+	0.441756i	$0.854356\pi$
$182$	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	$-0.893456\pi$
$197$		−	9.22153i		−	0.657007i	0.944503	−	0.328504i	$-0.106544\pi$
$198$		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	$0.0513624\pi$
$211$			4.66745i			0.321321i	−0.987010	+	0.160660i	$0.948638\pi$
$212$	−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	$0.221073\pi$
$227$			19.2857i			1.28004i	−0.768360	+	0.640018i	$0.778927\pi$
$228$		0			0
$229$		−	1.71588i		−	0.113389i	−0.998392	−	0.0566944i	$-0.981944\pi$
$229$		−	1.71588i		−	0.113389i	0.998392	−	0.0566944i	$-0.0180561\pi$
$230$	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	$0.338835\pi$
$251$			27.7106i			1.74908i	−0.484957	+	0.874538i	$0.661165\pi$
$252$		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	$-0.811693\pi$
$269$		−	18.2931i		−	1.11535i	0.830059	−	0.557676i	$-0.188307\pi$
$270$		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	$-0.822340\pi$
$277$		−	17.6288i		−	1.05921i	0.848244	−	0.529606i	$-0.177660\pi$
$278$	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	$-0.975736\pi$
$283$		−	2.56225i		−	0.152310i	0.997096	−	0.0761550i	$-0.0242644\pi$
$284$	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	$-0.989528\pi$
$293$		−	1.12608i		−	0.0657866i	0.999459	−	0.0328933i	$-0.0104721\pi$
$294$		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	$0.252259\pi$
$307$			24.9543i			1.42422i	−0.702070	+	0.712108i	$0.747741\pi$
$308$	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	$0.0151090\pi$
$317$			1.68959i			0.0948970i	−0.998874	+	0.0474485i	$0.984891\pi$
$318$		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	$-0.753820\pi$
$331$		−	25.4187i		−	1.39714i	0.715542	−	0.698570i	$-0.246180\pi$
$332$	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	$-0.890092\pi$
$347$		−	12.6098i		−	0.676930i	0.940979	−	0.338465i	$-0.109908\pi$
$348$		0			0
$349$			10.3681i			0.554990i	0.960727	+	0.277495i	$0.0895043\pi$
$349$			10.3681i			0.554990i	−0.960727	+	0.277495i	$0.910496\pi$
$350$	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	$0.0986260\pi$
$373$			11.7775i			0.609818i	−0.952382	+	0.304909i	$0.901374\pi$
$374$	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	$-0.879362\pi$
$379$		−	14.4058i		−	0.739975i	0.929037	−	0.369988i	$-0.120638\pi$
$380$	−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	$0.136158\pi$
$389$			16.3633i			0.829655i	−0.909900	+	0.414827i	$0.863842\pi$
$390$		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	$-0.913359\pi$
$397$		−	10.7133i		−	0.537685i	0.963184	−	0.268843i	$-0.0866411\pi$
$398$	−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	$-0.691065\pi$
$419$		−	33.7826i		−	1.65039i	0.564849	−	0.825194i	$-0.308935\pi$
$420$		0			0
$421$		−	10.6036i		−	0.516788i	−0.966040	−	0.258394i	$-0.916807\pi$
$421$		−	10.6036i		−	0.516788i	0.966040	−	0.258394i	$-0.0831933\pi$
$422$	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	$0.0976254\pi$
$443$			12.7091i			0.603827i	−0.953335	+	0.301914i	$0.902375\pi$
$444$		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	$0.249516\pi$
$461$			30.3182i			1.41206i	−0.708181	+	0.706030i	$0.750484\pi$
$462$		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	$0.273915\pi$
$467$			32.7692i			1.51638i	−0.652036	+	0.758188i	$0.726085\pi$
$468$		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	$0.0271408\pi$
$491$			3.77413i			0.170324i	−0.996367	+	0.0851621i	$0.972859\pi$
$492$		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	$-0.945087\pi$
$499$		−	7.66921i		−	0.343321i	0.985156	−	0.171661i	$-0.0549132\pi$
$500$	−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	$0.0518841\pi$
$509$			7.32231i			0.324556i	−0.986745	+	0.162278i	$0.948116\pi$
$510$		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	$-0.694433\pi$
$523$		−	37.4676i		−	1.63835i	0.573547	−	0.819173i	$-0.305567\pi$
$524$	−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	$-0.836053\pi$
$541$		−	22.9143i		−	0.985164i	0.870266	−	0.492582i	$-0.163947\pi$
$542$	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	$0.0969798\pi$
$547$			14.0319i			0.599959i	−0.953946	+	0.299979i	$0.903020\pi$
$548$	−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	$-0.787728\pi$
$557$		−	29.1958i		−	1.23706i	0.785760	−	0.618532i	$-0.212272\pi$
$558$		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	$-0.785925\pi$
$563$		−	29.5633i		−	1.24594i	0.782245	−	0.622971i	$-0.214075\pi$
$564$		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	$-0.680040\pi$
$571$		−	40.3483i		−	1.68852i	0.535932	−	0.844261i	$-0.319960\pi$
$572$	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	$-0.843136\pi$
$587$		−	22.9245i		−	0.946195i	0.881010	−	0.473098i	$-0.156864\pi$
$588$		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	$-0.739149\pi$
$613$		−	36.1874i		−	1.46159i	0.682595	−	0.730797i	$-0.260851\pi$
$614$	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	$-0.793861\pi$
$619$		−	30.0187i		−	1.20656i	0.797531	−	0.603278i	$-0.206139\pi$
$620$	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	$0.0749774\pi$
$643$			11.8356i			0.466752i	−0.972387	+	0.233376i	$0.925023\pi$
$644$	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	$0.136018\pi$
$653$			21.1804i			0.828851i	−0.910083	+	0.414426i	$0.863982\pi$
$654$		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	$-0.881830\pi$
$659$		−	18.6255i		−	0.725548i	0.931877	−	0.362774i	$-0.118170\pi$
$660$		0			0
$661$			8.43660i			0.328146i	0.986448	+	0.164073i	$0.0524632\pi$
$661$			8.43660i			0.328146i	−0.986448	+	0.164073i	$0.947537\pi$
$662$	−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	$-0.696592\pi$
$677$		−	42.4251i		−	1.63053i	0.579089	−	0.815264i	$-0.303408\pi$
$678$		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	$0.171548\pi$
$683$			26.8253i			1.02644i	−0.858257	+	0.513221i	$0.828452\pi$
$684$		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	$-0.601829\pi$
$691$		−	49.9065i		−	1.89853i	0.314476	−	0.949265i	$-0.398171\pi$
$692$	−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	$-0.643843\pi$
$701$		−	47.6375i		−	1.79924i	0.436671	−	0.899621i	$-0.356157\pi$
$702$		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	$-0.850699\pi$
$709$		−	24.0726i		−	0.904064i	0.892002	−	0.452032i	$-0.149301\pi$
$710$	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	$-0.985032\pi$
$733$		−	2.54526i		−	0.0940114i	0.998895	−	0.0470057i	$-0.0149679\pi$
$734$	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	$-0.763441\pi$
$739$		−	36.7876i		−	1.35326i	0.736325	−	0.676628i	$-0.236559\pi$
$740$	−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	$-0.998031\pi$
$757$		−	0.340328i		−	0.0123694i	0.999981	−	0.00618471i	$-0.00196867\pi$
$758$	−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	$0.0188929\pi$
$773$			3.29847i			0.118638i	−0.998239	+	0.0593188i	$0.981107\pi$
$774$		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	$0.0841506\pi$
$787$			14.6607i			0.522597i	−0.965258	+	0.261298i	$0.915849\pi$
$788$	−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	$-0.939311\pi$
$797$		−	10.7001i		−	0.379016i	0.981879	−	0.189508i	$-0.0606892\pi$
$798$		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	$-0.824677\pi$
$811$		−	29.8088i		−	1.04673i	0.852109	−	0.523364i	$-0.175323\pi$
$812$	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	$-0.766995\pi$
$821$		−	38.3014i		−	1.33673i	0.743834	−	0.668364i	$-0.233005\pi$
$822$		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	$0.282074\pi$
$827$			44.5542i			1.54930i	−0.632390	+	0.774650i	$0.717926\pi$
$828$		0			0
$829$			48.8761i			1.69754i	0.528765	+	0.848768i	$0.322655\pi$
$829$			48.8761i			1.69754i	−0.528765	+	0.848768i	$0.677345\pi$
$830$	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	$0.126642\pi$
$853$			22.6315i			0.774887i	−0.921893	+	0.387444i	$0.873358\pi$
$854$	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	$-0.717455\pi$
$859$		−	45.4628i		−	1.55117i	0.631244	−	0.775585i	$-0.282545\pi$
$860$	−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	$-0.798812\pi$
$877$		−	34.9922i		−	1.18160i	0.806817	−	0.590802i	$-0.201188\pi$
$878$	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	$0.286082\pi$
$883$			46.5075i			1.56510i	−0.622586	+	0.782551i	$0.713918\pi$
$884$	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	$-0.691184\pi$
$907$		−	49.6912i		−	1.64997i	0.565156	−	0.824984i	$-0.308816\pi$
$908$	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	$0.195199\pi$
$941$			35.3088i			1.15103i	−0.817790	+	0.575517i	$0.804801\pi$
$942$		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	$-0.765832\pi$
$947$		−	41.3026i		−	1.34215i	0.741388	−	0.671077i	$-0.234168\pi$
$948$		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	$-0.953667\pi$
$971$		−	9.03959i		−	0.290094i	0.989425	−	0.145047i	$-0.0463334\pi$
$972$		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	$-0.951677\pi$
$997$		−	9.55023i		−	0.302459i	0.988499	−	0.151229i	$-0.0483232\pi$
$998$	−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.757.13	yes	24
3.2	odd	2	inner	1512.2.c.f.757.12	yes	24
4.3	odd	2		6048.2.c.g.3025.12		24
8.3	odd	2		6048.2.c.g.3025.13		24
8.5	even	2	inner	1512.2.c.f.757.14	yes	24
12.11	even	2		6048.2.c.g.3025.14		24
24.5	odd	2	inner	1512.2.c.f.757.11	✓	24
24.11	even	2		6048.2.c.g.3025.11		24

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