LMFDB - Embedded newform 1512.2.j.d.323.37

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("1512.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.37
Character	$\chi$	$=$	1512.323
Dual form			1512.2.j.d.323.38

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.04493 - 0.952952i) q^{2} +(0.183763 - 1.99154i) q^{4} -2.35025 q^{5} -1.00000i q^{7} +(-1.70582 - 2.25614i) q^{8} +O(q^{10})$	\(q+(1.04493 - 0.952952i) q^{2} +(0.183763 - 1.99154i) q^{4} -2.35025 q^{5} -1.00000i q^{7} +(-1.70582 - 2.25614i) q^{8} +(-2.45584 + 2.23967i) q^{10} -1.09095i q^{11} +4.10613i q^{13} +(-0.952952 - 1.04493i) q^{14} +(-3.93246 - 0.731943i) q^{16} -4.74991i q^{17} -7.10196 q^{19} +(-0.431888 + 4.68061i) q^{20} +(-1.03962 - 1.13997i) q^{22} +3.99240 q^{23} +0.523653 q^{25} +(3.91295 + 4.29063i) q^{26} +(-1.99154 - 0.183763i) q^{28} -4.09983 q^{29} +10.8933i q^{31} +(-4.80666 + 2.98262i) q^{32} +(-4.52644 - 4.96333i) q^{34} +2.35025i q^{35} -2.27336i q^{37} +(-7.42106 + 6.76783i) q^{38} +(4.00910 + 5.30248i) q^{40} -1.29246i q^{41} -8.59200 q^{43} +(-2.17267 - 0.200477i) q^{44} +(4.17179 - 3.80457i) q^{46} -6.79438 q^{47} -1.00000 q^{49} +(0.547181 - 0.499016i) q^{50} +(8.17753 + 0.754556i) q^{52} +0.688525 q^{53} +2.56400i q^{55} +(-2.25614 + 1.70582i) q^{56} +(-4.28404 + 3.90694i) q^{58} -7.72675i q^{59} +9.70563i q^{61} +(10.3808 + 11.3827i) q^{62} +(-2.18034 + 7.69715i) q^{64} -9.65042i q^{65} +8.23313 q^{67} +(-9.45963 - 0.872858i) q^{68} +(2.23967 + 2.45584i) q^{70} -6.46122 q^{71} +8.44644 q^{73} +(-2.16640 - 2.37550i) q^{74} +(-1.30508 + 14.1438i) q^{76} -1.09095 q^{77} -5.70061i q^{79} +(9.24225 + 1.72025i) q^{80} +(-1.23165 - 1.35053i) q^{82} +10.0681i q^{83} +11.1634i q^{85} +(-8.97805 + 8.18777i) q^{86} +(-2.46134 + 1.86097i) q^{88} +2.54950i q^{89} +4.10613 q^{91} +(0.733657 - 7.95103i) q^{92} +(-7.09966 + 6.47472i) q^{94} +16.6913 q^{95} -15.6447 q^{97} +(-1.04493 + 0.952952i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4}+O(q^{10}) $ 48 * q - 4 * q^4	$ 48 q - 4 q^{4} - 12 q^{10} - 12 q^{16} + 16 q^{19} - 24 q^{22} + 48 q^{25} + 8 q^{28} + 12 q^{34} + 32 q^{40} + 64 q^{43} + 60 q^{46} - 48 q^{49} + 16 q^{52} + 36 q^{58} - 4 q^{64} + 32 q^{67} + 12 q^{70} - 32 q^{76} + 36 q^{82} + 24 q^{88} - 60 q^{94}+O(q^{100}) $ 48 * q - 4 * q^4 - 12 * q^10 - 12 * q^16 + 16 * q^19 - 24 * q^22 + 48 * q^25 + 8 * q^28 + 12 * q^34 + 32 * q^40 + 64 * q^43 + 60 * q^46 - 48 * q^49 + 16 * q^52 + 36 * q^58 - 4 * q^64 + 32 * q^67 + 12 * q^70 - 32 * q^76 + 36 * q^82 + 24 * q^88 - 60 * q^94

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.04493	−	0.952952i	0.738878	−	0.673839i
$2$	1.04493	−	0.952952i	0.738878	−	0.673839i
$3$		0			0
$3$		0			0
$4$	0.183763	−	1.99154i	0.0918816	−	0.995770i
$5$	−2.35025			−1.05106			−0.525531	−	0.850775i	$-0.676133\pi$
$5$	−2.35025			−1.05106			−0.525531	+	0.850775i	$0.676133\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−1.70582	−	2.25614i	−0.603100	−	0.797666i
$9$		0			0
$10$	−2.45584	+	2.23967i	−0.776606	+	0.708246i
$11$		−	1.09095i		−	0.328934i	−0.986383	−	0.164467i	$-0.947410\pi$
$11$		−	1.09095i		−	0.328934i	0.986383	−	0.164467i	$-0.0525904\pi$
$12$		0			0
$13$			4.10613i			1.13884i	0.822048	+	0.569418i	$0.192832\pi$
$13$			4.10613i			1.13884i	−0.822048	+	0.569418i	$0.807168\pi$
$14$	−0.952952	−	1.04493i	−0.254687	−	0.279270i
$15$		0			0
$16$	−3.93246	−	0.731943i	−0.983116	−	0.182986i
$17$		−	4.74991i		−	1.15202i	−0.817442	−	0.576011i	$-0.804609\pi$
$17$		−	4.74991i		−	1.15202i	0.817442	−	0.576011i	$-0.195391\pi$
$18$		0			0
$19$	−7.10196			−1.62930			−0.814650	−	0.579953i	$-0.803071\pi$
$19$	−7.10196			−1.62930			−0.814650	+	0.579953i	$0.803071\pi$
$20$	−0.431888	+	4.68061i	−0.0965732	+	1.04662i
$21$		0			0
$22$	−1.03962	−	1.13997i	−0.221649	−	0.243042i
$23$	3.99240			0.832474			0.416237	−	0.909256i	$-0.363349\pi$
$23$	3.99240			0.832474			0.416237	+	0.909256i	$0.363349\pi$
$24$		0			0
$25$	0.523653			0.104731
$26$	3.91295	+	4.29063i	0.767393	+	0.841461i
$27$		0			0
$28$	−1.99154	−	0.183763i	−0.376366	−	0.0347280i
$29$	−4.09983			−0.761319			−0.380660	−	0.924715i	$-0.624303\pi$
$29$	−4.09983			−0.761319			−0.380660	+	0.924715i	$0.624303\pi$
$30$		0			0
$31$			10.8933i			1.95649i	0.207454	+	0.978245i	$0.433482\pi$
$31$			10.8933i			1.95649i	−0.207454	+	0.978245i	$0.566518\pi$
$32$	−4.80666	+	2.98262i	−0.849706	+	0.527258i
$33$		0			0
$34$	−4.52644	−	4.96333i	−0.776278	−	0.851204i
$35$			2.35025i			0.397264i
$36$		0			0
$37$		−	2.27336i		−	0.373737i	−0.982385	−	0.186869i	$-0.940166\pi$
$37$		−	2.27336i		−	0.373737i	0.982385	−	0.186869i	$-0.0598339\pi$
$38$	−7.42106	+	6.76783i	−1.20385	+	1.09789i
$39$		0			0
$40$	4.00910	+	5.30248i	0.633895	+	0.838396i
$41$		−	1.29246i		−	0.201848i	−0.994894	−	0.100924i	$-0.967820\pi$
$41$		−	1.29246i		−	0.201848i	0.994894	−	0.100924i	$-0.0321799\pi$
$42$		0			0
$43$	−8.59200			−1.31027			−0.655134	−	0.755513i	$-0.727388\pi$
$43$	−8.59200			−1.31027			−0.655134	+	0.755513i	$0.727388\pi$
$44$	−2.17267	−	0.200477i	−0.327543	−	0.0302230i
$45$		0			0
$46$	4.17179	−	3.80457i	0.615097	−	0.560953i
$47$	−6.79438			−0.991062			−0.495531	−	0.868590i	$-0.665026\pi$
$47$	−6.79438			−0.991062			−0.495531	+	0.868590i	$0.665026\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	0.547181	−	0.499016i	0.0773831	−	0.0705715i
$51$		0			0
$52$	8.17753	+	0.754556i	1.13402	+	0.104638i
$53$	0.688525			0.0945762			0.0472881	−	0.998881i	$-0.484942\pi$
$53$	0.688525			0.0945762			0.0472881	+	0.998881i	$0.484942\pi$
$54$		0			0
$55$			2.56400i			0.345730i
$56$	−2.25614	+	1.70582i	−0.301489	+	0.227950i
$57$		0			0
$58$	−4.28404	+	3.90694i	−0.562522	+	0.513007i
$59$		−	7.72675i		−	1.00594i	−0.864305	−	0.502968i	$-0.832241\pi$
$59$		−	7.72675i		−	1.00594i	0.864305	−	0.502968i	$-0.167759\pi$
$60$		0			0
$61$			9.70563i			1.24268i	0.783542	+	0.621339i	$0.213411\pi$
$61$			9.70563i			1.24268i	−0.783542	+	0.621339i	$0.786589\pi$
$62$	10.3808	+	11.3827i	1.31836	+	1.44561i
$63$		0			0
$64$	−2.18034	+	7.69715i	−0.272542	+	0.962144i
$65$		−	9.65042i		−	1.19699i
$66$		0			0
$67$	8.23313			1.00584			0.502918	−	0.864334i	$-0.332260\pi$
$67$	8.23313			1.00584			0.502918	+	0.864334i	$0.332260\pi$
$68$	−9.45963	−	0.872858i	−1.14715	−	0.105850i
$69$		0			0
$70$	2.23967	+	2.45584i	0.267692	+	0.293530i
$71$	−6.46122			−0.766806			−0.383403	−	0.923581i	$-0.625248\pi$
$71$	−6.46122			−0.766806			−0.383403	+	0.923581i	$0.625248\pi$
$72$		0			0
$73$	8.44644			0.988581			0.494290	−	0.869297i	$-0.335428\pi$
$73$	8.44644			0.988581			0.494290	+	0.869297i	$0.335428\pi$
$74$	−2.16640	−	2.37550i	−0.251839	−	0.276146i
$75$		0			0
$76$	−1.30508	+	14.1438i	−0.149703	+	1.62241i
$77$	−1.09095			−0.124325
$78$		0			0
$79$		−	5.70061i		−	0.641369i	−0.947186	−	0.320684i	$-0.896087\pi$
$79$		−	5.70061i		−	0.641369i	0.947186	−	0.320684i	$-0.103913\pi$
$80$	9.24225	+	1.72025i	1.03332	+	0.192329i
$81$		0			0
$82$	−1.23165	−	1.35053i	−0.136013	−	0.149141i
$83$			10.0681i			1.10512i	0.833474	+	0.552558i	$0.186348\pi$
$83$			10.0681i			1.10512i	−0.833474	+	0.552558i	$0.813652\pi$
$84$		0			0
$85$			11.1634i			1.21085i
$86$	−8.97805	+	8.18777i	−0.968128	+	0.882910i
$87$		0			0
$88$	−2.46134	+	1.86097i	−0.262380	+	0.198380i
$89$			2.54950i			0.270246i	0.990829	+	0.135123i	$0.0431430\pi$
$89$			2.54950i			0.270246i	−0.990829	+	0.135123i	$0.956857\pi$
$90$		0			0
$91$	4.10613			0.430440
$92$	0.733657	−	7.95103i	0.0764890	−	0.828952i
$93$		0			0
$94$	−7.09966	+	6.47472i	−0.732274	+	0.667816i
$95$	16.6913			1.71250
$96$		0			0
$97$	−15.6447			−1.58847			−0.794237	−	0.607607i	$-0.792129\pi$
$97$	−15.6447			−1.58847			−0.794237	+	0.607607i	$0.792129\pi$
$98$	−1.04493	+	0.952952i	−0.105554	+	0.0962627i
$99$		0			0
$100$	0.0962281	−	1.04288i	0.00962281	−	0.104288i
$101$	−12.3962			−1.23347			−0.616736	−	0.787170i	$-0.711546\pi$
$101$	−12.3962			−1.23347			−0.616736	+	0.787170i	$0.711546\pi$
$102$		0			0
$103$		−	13.2234i		−	1.30294i	−0.758673	−	0.651472i	$-0.774152\pi$
$103$		−	13.2234i		−	1.30294i	0.758673	−	0.651472i	$-0.225848\pi$
$104$	9.26401	−	7.00434i	0.908411	−	0.686832i
$105$		0			0
$106$	0.719461	−	0.656131i	0.0698802	−	0.0637291i
$107$		−	5.44530i		−	0.526417i	−0.964739	−	0.263209i	$-0.915219\pi$
$107$		−	5.44530i		−	0.526417i	0.964739	−	0.263209i	$-0.0847808\pi$
$108$		0			0
$109$		−	0.947776i		−	0.0907805i	−0.998969	−	0.0453902i	$-0.985547\pi$
$109$		−	0.947776i		−	0.0907805i	0.998969	−	0.0453902i	$-0.0144531\pi$
$110$	2.44337	+	2.67921i	0.232967	+	0.255452i
$111$		0			0
$112$	−0.731943	+	3.93246i	−0.0691621	+	0.371583i
$113$		−	16.8819i		−	1.58812i	−0.607840	−	0.794059i	$-0.707964\pi$
$113$		−	16.8819i		−	1.58812i	0.607840	−	0.794059i	$-0.292036\pi$
$114$		0			0
$115$	−9.38313			−0.874981
$116$	−0.753398	+	8.16497i	−0.0699512	+	0.758099i
$117$		0			0
$118$	−7.36322	−	8.07392i	−0.677839	−	0.743264i
$119$	−4.74991			−0.435423
$120$		0			0
$121$	9.80982			0.891802
$122$	9.24900	+	10.1417i	0.837365	+	0.918188i
$123$		0			0
$124$	21.6944	+	2.00178i	1.94821	+	0.179765i
$125$	10.5205			0.940983
$126$		0			0
$127$		−	10.2310i		−	0.907852i	−0.891039	−	0.453926i	$-0.850023\pi$
$127$		−	10.2310i		−	0.907852i	0.891039	−	0.453926i	$-0.149977\pi$
$128$	5.05672	+	10.1208i	0.446955	+	0.894556i
$129$		0			0
$130$	−9.19639	−	10.0840i	−0.806577	−	0.884428i
$131$		−	15.9013i		−	1.38930i	−0.719346	−	0.694651i	$-0.755559\pi$
$131$		−	15.9013i		−	1.38930i	0.719346	−	0.694651i	$-0.244441\pi$
$132$		0			0
$133$			7.10196i			0.615818i
$134$	8.60306	−	7.84578i	0.743191	−	0.677772i
$135$		0			0
$136$	−10.7165	+	8.10250i	−0.918929	+	0.694784i
$137$		−	10.0619i		−	0.859647i	−0.902913	−	0.429823i	$-0.858576\pi$
$137$		−	10.0619i		−	0.859647i	0.902913	−	0.429823i	$-0.141424\pi$
$138$		0			0
$139$	−4.44750			−0.377232			−0.188616	−	0.982051i	$-0.560400\pi$
$139$	−4.44750			−0.377232			−0.188616	+	0.982051i	$0.560400\pi$
$140$	4.68061	+	0.431888i	0.395584	+	0.0365012i
$141$		0			0
$142$	−6.75153	+	6.15724i	−0.566576	+	0.516704i
$143$	4.47959			0.374602
$144$		0			0
$145$	9.63561			0.800193
$146$	8.82595	−	8.04905i	0.730440	−	0.666144i
$147$		0			0
$148$	−4.52748	−	0.417759i	−0.372156	−	0.0343396i
$149$	−12.3264			−1.00981			−0.504907	−	0.863174i	$-0.668473\pi$
$149$	−12.3264			−1.00981			−0.504907	+	0.863174i	$0.668473\pi$
$150$		0			0
$151$		−	9.25492i		−	0.753154i	−0.926385	−	0.376577i	$-0.877101\pi$
$151$		−	9.25492i		−	0.753154i	0.926385	−	0.376577i	$-0.122899\pi$
$152$	12.1147	+	16.0230i	0.982630	+	1.29964i
$153$		0			0
$154$	−1.13997	+	1.03962i	−0.0918614	+	0.0837754i
$155$		−	25.6019i		−	2.05639i
$156$		0			0
$157$			4.19774i			0.335016i	0.985871	+	0.167508i	$0.0535720\pi$
$157$			4.19774i			0.335016i	−0.985871	+	0.167508i	$0.946428\pi$
$158$	−5.43241	−	5.95674i	−0.432179	−	0.473893i
$159$		0			0
$160$	11.2968	−	7.00989i	0.893093	−	0.554180i
$161$		−	3.99240i		−	0.314645i
$162$		0			0
$163$	−23.6952			−1.85595			−0.927977	−	0.372639i	$-0.878453\pi$
$163$	−23.6952			−1.85595			−0.927977	+	0.372639i	$0.878453\pi$
$164$	−2.57398	−	0.237506i	−0.200994	−	0.0185461i
$165$		0			0
$166$	9.59441	+	10.5205i	0.744670	+	0.816546i
$167$	−4.79250			−0.370855			−0.185427	−	0.982658i	$-0.559367\pi$
$167$	−4.79250			−0.370855			−0.185427	+	0.982658i	$0.559367\pi$
$168$		0			0
$169$	−3.86033			−0.296949
$170$	10.6382	+	11.6650i	0.815915	+	0.894668i
$171$		0			0
$172$	−1.57889	+	17.1113i	−0.120389	+	1.30473i
$173$	18.2897			1.39054			0.695271	−	0.718747i	$-0.255284\pi$
$173$	18.2897			1.39054			0.695271	+	0.718747i	$0.255284\pi$
$174$		0			0
$175$		−	0.523653i		−	0.0395844i
$176$	−0.798515	+	4.29013i	−0.0601903	+	0.323380i
$177$		0			0
$178$	2.42955	+	2.66405i	0.182103	+	0.199679i
$179$			6.64806i			0.496899i	0.968645	+	0.248450i	$0.0799210\pi$
$179$			6.64806i			0.496899i	−0.968645	+	0.248450i	$0.920079\pi$
$180$		0			0
$181$		−	2.46631i		−	0.183320i	−0.995790	−	0.0916598i	$-0.970783\pi$
$181$		−	2.46631i		−	0.183320i	0.995790	−	0.0916598i	$-0.0292172\pi$
$182$	4.29063	−	3.91295i	0.318043	−	0.290047i
$183$		0			0
$184$	−6.81033	−	9.00742i	−0.502064	−	0.664036i
$185$			5.34294i			0.392821i
$186$		0			0
$187$	−5.18192			−0.378939
$188$	−1.24856	+	13.5313i	−0.0910603	+	0.986869i
$189$		0			0
$190$	17.4413	−	15.9061i	1.26533	−	1.15395i
$191$	12.9048			0.933760			0.466880	−	0.884321i	$-0.345378\pi$
$191$	12.9048			0.933760			0.466880	+	0.884321i	$0.345378\pi$
$192$		0			0
$193$	18.3689			1.32222			0.661112	−	0.750287i	$-0.270085\pi$
$193$	18.3689			1.32222			0.661112	+	0.750287i	$0.270085\pi$
$194$	−16.3476	+	14.9086i	−1.17369	+	1.07038i
$195$		0			0
$196$	−0.183763	+	1.99154i	−0.0131259	+	0.142253i
$197$	15.0957			1.07552			0.537761	−	0.843098i	$-0.319270\pi$
$197$	15.0957			1.07552			0.537761	+	0.843098i	$0.319270\pi$
$198$		0			0
$199$		−	3.51621i		−	0.249258i	−0.992203	−	0.124629i	$-0.960226\pi$
$199$		−	3.51621i		−	0.249258i	0.992203	−	0.124629i	$-0.0397740\pi$
$200$	−0.893259	−	1.18143i	−0.0631629	−	0.0835400i
$201$		0			0
$202$	−12.9532	+	11.8130i	−0.911386	+	0.831162i
$203$			4.09983i			0.287752i
$204$		0			0
$205$			3.03759i			0.212155i
$206$	−12.6013	−	13.8176i	−0.877975	−	0.962717i
$207$		0			0
$208$	3.00546	−	16.1472i	0.208391	−	1.11961i
$209$			7.74789i			0.535933i
$210$		0			0
$211$	−20.2502			−1.39408			−0.697041	−	0.717031i	$-0.745500\pi$
$211$	−20.2502			−1.39408			−0.697041	+	0.717031i	$0.745500\pi$
$212$	0.126525	−	1.37122i	0.00868981	−	0.0941761i
$213$		0			0
$214$	−5.18912	−	5.68997i	−0.354721	−	0.388958i
$215$	20.1933			1.37717
$216$		0			0
$217$	10.8933			0.739484
$218$	−0.903185	−	0.990361i	−0.0611714	−	0.0670757i
$219$		0			0
$220$	5.10632	+	0.471169i	0.344268	+	0.0317662i
$221$	19.5038			1.31196
$222$		0			0
$223$		−	12.9963i		−	0.870295i	−0.900359	−	0.435148i	$-0.856696\pi$
$223$		−	12.9963i		−	0.870295i	0.900359	−	0.435148i	$-0.143304\pi$
$224$	2.98262	+	4.80666i	0.199285	+	0.321158i
$225$		0			0
$226$	−16.0877	−	17.6405i	−1.07014	−	1.17343i
$227$		−	28.8974i		−	1.91799i	−0.283430	−	0.958993i	$-0.591473\pi$
$227$		−	28.8974i		−	1.91799i	0.283430	−	0.958993i	$-0.408527\pi$
$228$		0			0
$229$		−	3.65438i		−	0.241488i	−0.992684	−	0.120744i	$-0.961472\pi$
$229$		−	3.65438i		−	0.241488i	0.992684	−	0.120744i	$-0.0385281\pi$
$230$	−9.80472	+	8.94167i	−0.646504	+	0.589597i
$231$		0			0
$232$	6.99358	+	9.24979i	0.459151	+	0.607278i
$233$			13.7096i			0.898143i	0.893496	+	0.449071i	$0.148245\pi$
$233$			13.7096i			0.898143i	−0.893496	+	0.449071i	$0.851755\pi$
$234$		0			0
$235$	15.9685			1.04167
$236$	−15.3881	−	1.41989i	−1.00168	−	0.0924270i
$237$		0			0
$238$	−4.96333	+	4.52644i	−0.321725	+	0.293405i
$239$	−20.5360			−1.32836			−0.664181	−	0.747572i	$-0.731220\pi$
$239$	−20.5360			−1.32836			−0.664181	+	0.747572i	$0.731220\pi$
$240$		0			0
$241$	22.1694			1.42806			0.714030	−	0.700116i	$-0.246868\pi$
$241$	22.1694			1.42806			0.714030	+	0.700116i	$0.246868\pi$
$242$	10.2506	−	9.34830i	0.658933	−	0.600931i
$243$		0			0
$244$	19.3291	+	1.78354i	1.23742	+	0.114179i
$245$	2.35025			0.150152
$246$		0			0
$247$		−	29.1616i		−	1.85551i
$248$	24.5767	−	18.5820i	1.56063	−	1.17996i
$249$		0			0
$250$	10.9932	−	10.0255i	0.695272	−	0.634071i
$251$		−	2.82901i		−	0.178565i	−0.996006	−	0.0892827i	$-0.971543\pi$
$251$		−	2.82901i		−	0.178565i	0.996006	−	0.0892827i	$-0.0284575\pi$
$252$		0			0
$253$		−	4.35552i		−	0.273829i
$254$	−9.74963	−	10.6907i	−0.611746	−	0.670792i
$255$		0			0
$256$	14.9285	+	5.75668i	0.933032	+	0.359792i
$257$			19.2158i			1.19865i	0.800505	+	0.599325i	$0.204564\pi$
$257$			19.2158i			1.19865i	−0.800505	+	0.599325i	$0.795436\pi$
$258$		0			0
$259$	−2.27336			−0.141259
$260$	−19.2192	−	1.77339i	−1.19192	−	0.109981i
$261$		0			0
$262$	−15.1532	−	16.6158i	−0.936167	−	1.02653i
$263$	−26.5713			−1.63846			−0.819230	−	0.573465i	$-0.805599\pi$
$263$	−26.5713			−1.63846			−0.819230	+	0.573465i	$0.805599\pi$
$264$		0			0
$265$	−1.61820			−0.0994054
$266$	6.76783	+	7.42106i	0.414962	+	0.455014i
$267$		0			0
$268$	1.51295	−	16.3966i	0.0924179	−	1.00158i
$269$	−7.88420			−0.480708			−0.240354	−	0.970685i	$-0.577264\pi$
$269$	−7.88420			−0.480708			−0.240354	+	0.970685i	$0.577264\pi$
$270$		0			0
$271$			15.1206i			0.918513i	0.888304	+	0.459256i	$0.151884\pi$
$271$			15.1206i			0.918513i	−0.888304	+	0.459256i	$0.848116\pi$
$272$	−3.47666	+	18.6788i	−0.210804	+	1.13257i
$273$		0			0
$274$	−9.58852	−	10.5140i	−0.579264	−	0.635174i
$275$		−	0.571280i		−	0.0344495i
$276$		0			0
$277$			10.1215i			0.608141i	0.952650	+	0.304071i	$0.0983459\pi$
$277$			10.1215i			0.608141i	−0.952650	+	0.304071i	$0.901654\pi$
$278$	−4.64733	+	4.23825i	−0.278728	+	0.254194i
$279$		0			0
$280$	5.30248	−	4.00910i	0.316884	−	0.239590i
$281$		−	23.6645i		−	1.41170i	−0.708359	−	0.705852i	$-0.750564\pi$
$281$		−	23.6645i		−	1.41170i	0.708359	−	0.705852i	$-0.249436\pi$
$282$		0			0
$283$	18.1838			1.08091			0.540457	−	0.841371i	$-0.318251\pi$
$283$	18.1838			1.08091			0.540457	+	0.841371i	$0.318251\pi$
$284$	−1.18733	+	12.8678i	−0.0704554	+	0.763562i
$285$		0			0
$286$	4.68087	−	4.26884i	0.276785	−	0.252422i
$287$	−1.29246			−0.0762914
$288$		0			0
$289$	−5.56163			−0.327155
$290$	10.0685	−	9.18227i	0.591245	−	0.539202i
$291$		0			0
$292$	1.55214	−	16.8214i	0.0908323	−	0.984399i
$293$	−20.8327			−1.21706			−0.608529	−	0.793532i	$-0.708240\pi$
$293$	−20.8327			−1.21706			−0.608529	+	0.793532i	$0.708240\pi$
$294$		0			0
$295$			18.1597i			1.05730i
$296$	−5.12901	+	3.87794i	−0.298118	+	0.225401i
$297$		0			0
$298$	−12.8802	+	11.7464i	−0.746130	+	0.680453i
$299$			16.3933i			0.948052i
$300$		0			0
$301$			8.59200i			0.495235i
$302$	−8.81949	−	9.67075i	−0.507505	−	0.556489i
$303$		0			0
$304$	27.9282	+	5.19823i	1.60179	+	0.298139i
$305$		−	22.8106i		−	1.30613i
$306$		0			0
$307$	−4.57939			−0.261360			−0.130680	−	0.991425i	$-0.541716\pi$
$307$	−4.57939			−0.261360			−0.130680	+	0.991425i	$0.541716\pi$
$308$	−0.200477	+	2.17267i	−0.0114232	+	0.123800i
$309$		0			0
$310$	−24.3974	−	26.7522i	−1.38568	−	1.51942i
$311$	−6.20035			−0.351589			−0.175795	−	0.984427i	$-0.556249\pi$
$311$	−6.20035			−0.351589			−0.175795	+	0.984427i	$0.556249\pi$
$312$		0			0
$313$	−22.0230			−1.24481			−0.622406	−	0.782695i	$-0.713845\pi$
$313$	−22.0230			−1.24481			−0.622406	+	0.782695i	$0.713845\pi$
$314$	4.00024	+	4.38635i	0.225747	+	0.247536i
$315$		0			0
$316$	−11.3530	−	1.04756i	−0.638656	−	0.0589299i
$317$	−2.35768			−0.132420			−0.0662102	−	0.997806i	$-0.521091\pi$
$317$	−2.35768			−0.132420			−0.0662102	+	0.997806i	$0.521091\pi$
$318$		0			0
$319$			4.47272i			0.250424i
$320$	5.12432	−	18.0902i	0.286458	−	1.01127i
$321$		0			0
$322$	−3.80457	−	4.17179i	−0.212020	−	0.232485i
$323$			33.7336i			1.87699i
$324$		0			0
$325$			2.15019i			0.119271i
$326$	−24.7599	+	22.5804i	−1.37132	+	1.25061i
$327$		0			0
$328$	−2.91597	+	2.20470i	−0.161007	+	0.121734i
$329$			6.79438i			0.374586i
$330$		0			0
$331$	2.15331			0.118357			0.0591784	−	0.998247i	$-0.481152\pi$
$331$	2.15331			0.118357			0.0591784	+	0.998247i	$0.481152\pi$
$332$	20.0510	+	1.85014i	1.10044	+	0.101540i
$333$		0			0
$334$	−5.00783	+	4.56702i	−0.274016	+	0.249896i
$335$	−19.3499			−1.05720
$336$		0			0
$337$	23.2469			1.26634			0.633169	−	0.774014i	$-0.281754\pi$
$337$	23.2469			1.26634			0.633169	+	0.774014i	$0.281754\pi$
$338$	−4.03378	+	3.67872i	−0.219409	+	0.200096i
$339$		0			0
$340$	22.2325	+	2.05143i	1.20572	+	0.111254i
$341$	11.8840			0.643556
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	14.6564	+	19.3848i	0.790222	+	1.04516i
$345$		0			0
$346$	19.1115	−	17.4292i	1.02744	−	0.937002i
$347$		−	26.1260i		−	1.40252i	−0.712906	−	0.701260i	$-0.752621\pi$
$347$		−	26.1260i		−	1.40252i	0.712906	−	0.701260i	$-0.247379\pi$
$348$		0			0
$349$		−	3.68463i		−	0.197234i	−0.995125	−	0.0986169i	$-0.968558\pi$
$349$		−	3.68463i		−	0.197234i	0.995125	−	0.0986169i	$-0.0314418\pi$
$350$	−0.499016	−	0.547181i	−0.0266735	−	0.0292481i
$351$		0			0
$352$	3.25389	+	5.24383i	0.173433	+	0.279497i
$353$			15.5433i			0.827285i	0.910439	+	0.413642i	$0.135744\pi$
$353$			15.5433i			0.827285i	−0.910439	+	0.413642i	$0.864256\pi$
$354$		0			0
$355$	15.1855			0.805960
$356$	5.07743	+	0.468504i	0.269103	+	0.0248307i
$357$		0			0
$358$	6.33528	+	6.94676i	0.334830	+	0.367148i
$359$	−23.0367			−1.21583			−0.607914	−	0.794003i	$-0.707994\pi$
$359$	−23.0367			−1.21583			−0.607914	+	0.794003i	$0.707994\pi$
$360$		0			0
$361$	31.4378			1.65462
$362$	−2.35028	−	2.57713i	−0.123528	−	0.135451i
$363$		0			0
$364$	0.754556	−	8.17753i	0.0395495	−	0.428619i
$365$	−19.8512			−1.03906
$366$		0			0
$367$		−	16.1135i		−	0.841116i	−0.907266	−	0.420558i	$-0.861834\pi$
$367$		−	16.1135i		−	0.841116i	0.907266	−	0.420558i	$-0.138166\pi$
$368$	−15.7000	−	2.92221i	−0.818418	−	0.152331i
$369$		0			0
$370$	5.09157	+	5.58301i	0.264698	+	0.290247i
$371$		−	0.688525i		−	0.0357464i
$372$		0			0
$373$			8.37018i			0.433392i	0.976239	+	0.216696i	$0.0695280\pi$
$373$			8.37018i			0.433392i	−0.976239	+	0.216696i	$0.930472\pi$
$374$	−5.41475	+	4.93812i	−0.279990	+	0.255344i
$375$		0			0
$376$	11.5900	+	15.3291i	0.597709	+	0.790536i
$377$		−	16.8344i		−	0.867018i
$378$		0			0
$379$	−4.66739			−0.239748			−0.119874	−	0.992789i	$-0.538249\pi$
$379$	−4.66739			−0.239748			−0.119874	+	0.992789i	$0.538249\pi$
$380$	3.06725	−	33.2415i	0.157347	−	1.70525i
$381$		0			0
$382$	13.4846	−	12.2977i	0.689935	−	0.629204i
$383$	11.1113			0.567761			0.283880	−	0.958860i	$-0.408378\pi$
$383$	11.1113			0.567761			0.283880	+	0.958860i	$0.408378\pi$
$384$		0			0
$385$	2.56400			0.130674
$386$	19.1943	−	17.5047i	0.976963	−	0.890967i
$387$		0			0
$388$	−2.87491	+	31.1570i	−0.145952	+	1.58176i
$389$	33.8483			1.71618			0.858090	−	0.513500i	$-0.171651\pi$
$389$	33.8483			1.71618			0.858090	+	0.513500i	$0.171651\pi$
$390$		0			0
$391$		−	18.9636i		−	0.959028i
$392$	1.70582	+	2.25614i	0.0861571	+	0.113952i
$393$		0			0
$394$	15.7739	−	14.3854i	0.794679	−	0.724728i
$395$			13.3978i			0.674118i
$396$		0			0
$397$			30.2554i			1.51848i	0.650813	+	0.759238i	$0.274428\pi$
$397$			30.2554i			1.51848i	−0.650813	+	0.759238i	$0.725572\pi$
$398$	−3.35078	−	3.67420i	−0.167960	−	0.184171i
$399$		0			0
$400$	−2.05924	−	0.383284i	−0.102962	−	0.0191642i
$401$			35.7603i			1.78578i	0.450272	+	0.892891i	$0.351327\pi$
$401$			35.7603i			1.78578i	−0.450272	+	0.892891i	$0.648673\pi$
$402$		0			0
$403$	−44.7292			−2.22812
$404$	−2.27797	+	24.6876i	−0.113333	+	1.22826i
$405$		0			0
$406$	3.90694	+	4.28404i	0.193898	+	0.212613i
$407$	−2.48012			−0.122935
$408$		0			0
$409$	25.9283			1.28207			0.641036	−	0.767511i	$-0.278505\pi$
$409$	25.9283			1.28207			0.641036	+	0.767511i	$0.278505\pi$
$410$	2.89468	+	3.17408i	0.142958	+	0.156756i
$411$		0			0
$412$	−26.3350	−	2.42998i	−1.29743	−	0.119717i
$413$	−7.72675			−0.380208
$414$		0			0
$415$		−	23.6625i		−	1.16155i
$416$	−12.2470	−	19.7368i	−0.600460	−	0.967676i
$417$		0			0
$418$	7.38337	+	8.09601i	0.361132	+	0.395989i
$419$		−	6.32586i		−	0.309038i	−0.987990	−	0.154519i	$-0.950617\pi$
$419$		−	6.32586i		−	0.309038i	0.987990	−	0.154519i	$-0.0493829\pi$
$420$		0			0
$421$		−	27.3586i		−	1.33338i	−0.745336	−	0.666689i	$-0.767711\pi$
$421$		−	27.3586i		−	1.33338i	0.745336	−	0.666689i	$-0.232289\pi$
$422$	−21.1601	+	19.2975i	−1.03006	+	0.939387i
$423$		0			0
$424$	−1.17450	−	1.55341i	−0.0570388	−	0.0754402i
$425$		−	2.48730i		−	0.120652i
$426$		0			0
$427$	9.70563			0.469688
$428$	−10.8445	−	1.00065i	−0.524191	−	0.0483681i
$429$		0			0
$430$	21.1006	−	19.2433i	1.01756	−	0.927992i
$431$	27.5526			1.32716			0.663582	−	0.748104i	$-0.269035\pi$
$431$	27.5526			1.32716			0.663582	+	0.748104i	$0.269035\pi$
$432$		0			0
$433$	13.0479			0.627040			0.313520	−	0.949582i	$-0.398492\pi$
$433$	13.0479			0.627040			0.313520	+	0.949582i	$0.398492\pi$
$434$	11.3827	−	10.3808i	0.546388	−	0.498293i
$435$		0			0
$436$	−1.88753	−	0.174166i	−0.0903964	−	0.00834105i
$437$	−28.3539			−1.35635
$438$		0			0
$439$		−	6.42338i		−	0.306571i	−0.988182	−	0.153286i	$-0.951015\pi$
$439$		−	6.42338i		−	0.306571i	0.988182	−	0.153286i	$-0.0489854\pi$
$440$	5.78475	−	4.37374i	0.275777	−	0.208510i
$441$		0			0
$442$	20.3801	−	18.5862i	0.969382	−	0.884053i
$443$			22.1824i			1.05392i	0.849891	+	0.526959i	$0.176668\pi$
$443$			22.1824i			1.05392i	−0.849891	+	0.526959i	$0.823332\pi$
$444$		0			0
$445$		−	5.99195i		−	0.284046i
$446$	−12.3848	−	13.5802i	−0.586439	−	0.643042i
$447$		0			0
$448$	7.69715	+	2.18034i	0.363656	+	0.103011i
$449$		−	1.86593i		−	0.0880586i	−0.999030	−	0.0440293i	$-0.985981\pi$
$449$		−	1.86593i		−	0.0880586i	0.999030	−	0.0440293i	$-0.0140195\pi$
$450$		0			0
$451$	−1.41001			−0.0663947
$452$	−33.6210	−	3.10228i	−1.58140	−	0.145919i
$453$		0			0
$454$	−27.5378	−	30.1958i	−1.29241	−	1.41716i
$455$	−9.65042			−0.452419
$456$		0			0
$457$	−28.3835			−1.32773			−0.663863	−	0.747854i	$-0.731084\pi$
$457$	−28.3835			−1.32773			−0.663863	+	0.747854i	$0.731084\pi$
$458$	−3.48245	−	3.81858i	−0.162724	−	0.178430i
$459$		0			0
$460$	−1.72427	+	18.6869i	−0.0803946	+	0.871280i
$461$	−33.2364			−1.54797			−0.773986	−	0.633202i	$-0.781740\pi$
$461$	−33.2364			−1.54797			−0.773986	+	0.633202i	$0.781740\pi$
$462$		0			0
$463$		−	2.11779i		−	0.0984219i	−0.998788	−	0.0492110i	$-0.984329\pi$
$463$		−	2.11779i		−	0.0984219i	0.998788	−	0.0492110i	$-0.0156707\pi$
$464$	16.1224	+	3.00084i	0.748465	+	0.139311i
$465$		0			0
$466$	13.0646	+	14.3255i	0.605204	+	0.663618i
$467$			13.7416i			0.635884i	0.948110	+	0.317942i	$0.102992\pi$
$467$			13.7416i			0.635884i	−0.948110	+	0.317942i	$0.897008\pi$
$468$		0			0
$469$		−	8.23313i		−	0.380171i
$470$	16.6859	−	15.2172i	0.769665	−	0.701916i
$471$		0			0
$472$	−17.4326	+	13.1805i	−0.802401	+	0.606680i
$473$			9.37345i			0.430992i
$474$		0			0
$475$	−3.71896			−0.170638
$476$	−0.872858	+	9.45963i	−0.0400074	+	0.433582i
$477$		0			0
$478$	−21.4587	+	19.5698i	−0.981498	+	0.895103i
$479$	8.78287			0.401299			0.200650	−	0.979663i	$-0.435695\pi$
$479$	8.78287			0.401299			0.200650	+	0.979663i	$0.435695\pi$
$480$		0			0
$481$	9.33470			0.425626
$482$	23.1655	−	21.1264i	1.05516	−	0.962282i
$483$		0			0
$484$	1.80268	−	19.5367i	0.0819402	−	0.888030i
$485$	36.7688			1.66959
$486$		0			0
$487$			4.42586i			0.200555i	0.994960	+	0.100277i	$0.0319730\pi$
$487$			4.42586i			0.200555i	−0.994960	+	0.100277i	$0.968027\pi$
$488$	21.8973	−	16.5561i	0.991242	−	0.749459i
$489$		0			0
$490$	2.45584	−	2.23967i	0.110944	−	0.101178i
$491$		−	18.5511i		−	0.837199i	−0.908171	−	0.418599i	$-0.862521\pi$
$491$		−	18.5511i		−	0.837199i	0.908171	−	0.418599i	$-0.137479\pi$
$492$		0			0
$493$			19.4738i			0.877056i
$494$	−27.7896	−	30.4719i	−1.25031	−	1.37099i
$495$		0			0
$496$	7.97326	−	42.8374i	0.358010	−	1.92346i
$497$			6.46122i			0.289825i
$498$		0			0
$499$	5.23350			0.234284			0.117142	−	0.993115i	$-0.462627\pi$
$499$	5.23350			0.234284			0.117142	+	0.993115i	$0.462627\pi$
$500$	1.93328	−	20.9520i	0.0864590	−	0.937003i
$501$		0			0
$502$	−2.69591	−	2.95612i	−0.120324	−	0.131938i
$503$	−27.2800			−1.21635			−0.608177	−	0.793802i	$-0.708099\pi$
$503$	−27.2800			−1.21635			−0.608177	+	0.793802i	$0.708099\pi$
$504$		0			0
$505$	29.1342			1.29646
$506$	−4.15060	−	4.55122i	−0.184517	−	0.202326i
$507$		0			0
$508$	−20.3754	−	1.88008i	−0.904012	−	0.0834149i
$509$	−34.0131			−1.50761			−0.753803	−	0.657101i	$-0.771783\pi$
$509$	−34.0131			−1.50761			−0.753803	+	0.657101i	$0.771783\pi$
$510$		0			0
$511$		−	8.44644i		−	0.373648i
$512$	21.0851	−	8.21083i	0.931839	−	0.362871i
$513$		0			0
$514$	18.3118	+	20.0792i	0.807698	+	0.885657i
$515$			31.0783i			1.36947i
$516$		0			0
$517$			7.41234i			0.325994i
$518$	−2.37550	+	2.16640i	−0.104374	+	0.0951861i
$519$		0			0
$520$	−21.7727	+	16.4619i	−0.954796	+	0.721903i
$521$			34.1052i			1.49417i	0.664726	+	0.747087i	$0.268548\pi$
$521$			34.1052i			1.49417i	−0.664726	+	0.747087i	$0.731452\pi$
$522$		0			0
$523$	24.7371			1.08168			0.540840	−	0.841126i	$-0.318106\pi$
$523$	24.7371			1.08168			0.540840	+	0.841126i	$0.318106\pi$
$524$	−31.6681	−	2.92207i	−1.38343	−	0.127651i
$525$		0			0
$526$	−27.7652	+	25.3212i	−1.21062	+	1.10406i
$527$	51.7420			2.25392
$528$		0			0
$529$	−7.06071			−0.306987
$530$	−1.69091	+	1.54207i	−0.0734484	+	0.0669832i
$531$		0			0
$532$	14.1438	+	1.30508i	0.613213	+	0.0565823i
$533$	5.30700			0.229872
$534$		0			0
$535$			12.7978i			0.553297i
$536$	−14.0443	−	18.5751i	−0.606620	−	0.802322i
$537$		0			0
$538$	−8.23845	+	7.51327i	−0.355185	+	0.323920i
$539$			1.09095i			0.0469906i
$540$		0			0
$541$			1.11043i			0.0477412i	0.999715	+	0.0238706i	$0.00759897\pi$
$541$			1.11043i			0.0477412i	−0.999715	+	0.0238706i	$0.992401\pi$
$542$	14.4092	+	15.8000i	0.618930	+	0.678669i
$543$		0			0
$544$	14.1672	+	22.8312i	0.607412	+	0.978879i
$545$			2.22751i			0.0954159i
$546$		0			0
$547$	−43.6930			−1.86818			−0.934089	−	0.357040i	$-0.883786\pi$
$547$	−43.6930			−1.86818			−0.934089	+	0.357040i	$0.883786\pi$
$548$	−20.0387	−	1.84901i	−0.856011	−	0.0789857i
$549$		0			0
$550$	−0.544402	−	0.596948i	−0.0232134	−	0.0254539i
$551$	29.1168			1.24042
$552$		0			0
$553$	−5.70061			−0.242415
$554$	9.64529	+	10.5763i	0.409789	+	0.449342i
$555$		0			0
$556$	−0.817286	+	8.85737i	−0.0346606	+	0.375636i
$557$	33.0536			1.40053			0.700263	−	0.713884i	$-0.253066\pi$
$557$	33.0536			1.40053			0.700263	+	0.713884i	$0.253066\pi$
$558$		0			0
$559$		−	35.2799i		−	1.49218i
$560$	1.72025	−	9.24225i	0.0726937	−	0.390556i
$561$		0			0
$562$	−22.5511	−	24.7278i	−0.951262	−	1.04308i
$563$		−	17.6097i		−	0.742159i	−0.928601	−	0.371080i	$-0.878988\pi$
$563$		−	17.6097i		−	0.742159i	0.928601	−	0.371080i	$-0.121012\pi$
$564$		0			0
$565$			39.6767i			1.66921i
$566$	19.0008	−	17.3283i	0.798664	−	0.728363i
$567$		0			0
$568$	11.0217	+	14.5774i	0.462460	+	0.611655i
$569$		−	12.0355i		−	0.504555i	−0.967655	−	0.252277i	$-0.918820\pi$
$569$		−	12.0355i		−	0.504555i	0.967655	−	0.252277i	$-0.0811795\pi$
$570$		0			0
$571$	−6.04104			−0.252810			−0.126405	−	0.991979i	$-0.540344\pi$
$571$	−6.04104			−0.252810			−0.126405	+	0.991979i	$0.540344\pi$
$572$	0.823184	−	8.92129i	0.0344191	−	0.373018i
$573$		0			0
$574$	−1.35053	+	1.23165i	−0.0563700	+	0.0514081i
$575$	2.09063			0.0871854
$576$		0			0
$577$	−31.2605			−1.30139			−0.650696	−	0.759339i	$-0.725523\pi$
$577$	−31.2605			−1.30139			−0.650696	+	0.759339i	$0.725523\pi$
$578$	−5.81152	+	5.29997i	−0.241727	+	0.220450i
$579$		0			0
$580$	1.77067	−	19.1897i	0.0735230	−	0.796809i
$581$	10.0681			0.417695
$582$		0			0
$583$		−	0.751147i		−	0.0311093i
$584$	−14.4081	−	19.0563i	−0.596212	−	0.788557i
$585$		0			0
$586$	−21.7687	+	19.8525i	−0.899257	+	0.820101i
$587$			29.7168i			1.22654i	0.789872	+	0.613272i	$0.210147\pi$
$587$			29.7168i			1.22654i	−0.789872	+	0.613272i	$0.789853\pi$
$588$		0			0
$589$		−	77.3635i		−	3.18771i
$590$	17.3054	+	18.9757i	0.712451	+	0.781217i
$591$		0			0
$592$	−1.66397	+	8.93989i	−0.0683886	+	0.367427i
$593$		−	19.9618i		−	0.819732i	−0.912146	−	0.409866i	$-0.865575\pi$
$593$		−	19.9618i		−	0.819732i	0.912146	−	0.409866i	$-0.134425\pi$
$594$		0			0
$595$	11.1634			0.457657
$596$	−2.26513	+	24.5484i	−0.0927834	+	1.00554i
$597$		0			0
$598$	15.6221	+	17.1299i	0.638834	+	0.700494i
$599$	26.5569			1.08509			0.542543	−	0.840028i	$-0.317461\pi$
$599$	26.5569			1.08509			0.542543	+	0.840028i	$0.317461\pi$
$600$		0			0
$601$	−19.6439			−0.801289			−0.400645	−	0.916233i	$-0.631214\pi$
$601$	−19.6439			−0.801289			−0.400645	+	0.916233i	$0.631214\pi$
$602$	8.18777	+	8.97805i	0.333708	+	0.365918i
$603$		0			0
$604$	−18.4315	−	1.70071i	−0.749968	−	0.0692010i
$605$	−23.0555			−0.937339
$606$		0			0
$607$		−	29.0877i		−	1.18063i	−0.807172	−	0.590316i	$-0.799003\pi$
$607$		−	29.0877i		−	1.18063i	0.807172	−	0.590316i	$-0.200997\pi$
$608$	34.1367	−	21.1824i	1.38443	−	0.859061i
$609$		0			0
$610$	−21.7374	−	23.8355i	−0.880123	−	0.965072i
$611$		−	27.8986i		−	1.12866i
$612$		0			0
$613$			9.44223i			0.381368i	0.981651	+	0.190684i	$0.0610706\pi$
$613$			9.44223i			0.381368i	−0.981651	+	0.190684i	$0.938929\pi$
$614$	−4.78515	+	4.36394i	−0.193113	+	0.176114i
$615$		0			0
$616$	1.86097	+	2.46134i	0.0749806	+	0.0991702i
$617$			29.4177i			1.18431i	0.805823	+	0.592157i	$0.201723\pi$
$617$			29.4177i			1.18431i	−0.805823	+	0.592157i	$0.798277\pi$
$618$		0			0
$619$	4.45956			0.179245			0.0896225	−	0.995976i	$-0.471434\pi$
$619$	4.45956			0.179245			0.0896225	+	0.995976i	$0.471434\pi$
$620$	−50.9871	−	4.70468i	−2.04769	−	0.188944i
$621$		0			0
$622$	−6.47894	+	5.90864i	−0.259782	+	0.236915i
$623$	2.54950			0.102144
$624$		0			0
$625$	−27.3441			−1.09376
$626$	−23.0125	+	20.9868i	−0.919764	+	0.838803i
$627$		0			0
$628$	8.35996	+	0.771389i	0.333599	+	0.0307818i
$629$	−10.7982			−0.430554
$630$		0			0
$631$			23.6013i			0.939553i	0.882786	+	0.469776i	$0.155665\pi$
$631$			23.6013i			0.939553i	−0.882786	+	0.469776i	$0.844335\pi$
$632$	−12.8614	+	9.72423i	−0.511598	+	0.386809i
$633$		0			0
$634$	−2.46361	+	2.24675i	−0.0978425	+	0.0892300i
$635$			24.0453i			0.954208i
$636$		0			0
$637$		−	4.10613i		−	0.162691i
$638$	4.26229	+	4.67368i	0.168745	+	0.185033i
$639$		0			0
$640$	−11.8845	−	23.7862i	−0.469777	−	0.940234i
$641$		−	6.81316i		−	0.269104i	−0.990907	−	0.134552i	$-0.957041\pi$
$641$		−	6.81316i		−	0.269104i	0.990907	−	0.134552i	$-0.0429595\pi$
$642$		0			0
$643$	−15.8069			−0.623361			−0.311681	−	0.950187i	$-0.600892\pi$
$643$	−15.8069			−0.623361			−0.311681	+	0.950187i	$0.600892\pi$
$644$	−7.95103	−	0.733657i	−0.313315	−	0.0289101i
$645$		0			0
$646$	32.1466	+	35.2493i	1.26479	+	1.38687i
$647$	−42.5205			−1.67165			−0.835827	−	0.548992i	$-0.815012\pi$
$647$	−42.5205			−1.67165			−0.835827	+	0.548992i	$0.815012\pi$
$648$		0			0
$649$	−8.42950			−0.330887
$650$	2.04903	+	2.24680i	0.0803694	+	0.0881267i
$651$		0			0
$652$	−4.35431	+	47.1900i	−0.170528	+	1.84810i
$653$	−2.40359			−0.0940597			−0.0470298	−	0.998893i	$-0.514976\pi$
$653$	−2.40359			−0.0940597			−0.0470298	+	0.998893i	$0.514976\pi$
$654$		0			0
$655$			37.3720i			1.46024i
$656$	−0.946006	+	5.08254i	−0.0369353	+	0.198440i
$657$		0			0
$658$	6.47472	+	7.09966i	0.252411	+	0.276773i
$659$			26.3292i			1.02564i	0.858497	+	0.512819i	$0.171399\pi$
$659$			26.3292i			1.02564i	−0.858497	+	0.512819i	$0.828601\pi$
$660$		0			0
$661$		−	8.09353i		−	0.314802i	−0.987535	−	0.157401i	$-0.949689\pi$
$661$		−	8.09353i		−	0.314802i	0.987535	−	0.157401i	$-0.0503115\pi$
$662$	2.25007	−	2.05201i	0.0874513	−	0.0797535i
$663$		0			0
$664$	22.7150	−	17.1744i	0.881513	−	0.666495i
$665$		−	16.6913i		−	0.647262i
$666$		0			0
$667$	−16.3682			−0.633778
$668$	−0.880685	+	9.54445i	−0.0340747	+	0.369286i
$669$		0			0
$670$	−20.2193	+	18.4395i	−0.781139	+	0.712380i
$671$	10.5884			0.408759
$672$		0			0
$673$	3.41009			0.131449			0.0657246	−	0.997838i	$-0.479064\pi$
$673$	3.41009			0.131449			0.0657246	+	0.997838i	$0.479064\pi$
$674$	24.2914	−	22.1532i	0.935669	−	0.853308i
$675$		0			0
$676$	−0.709387	+	7.68801i	−0.0272841	+	0.295693i
$677$	12.4265			0.477589			0.238794	−	0.971070i	$-0.423248\pi$
$677$	12.4265			0.477589			0.238794	+	0.971070i	$0.423248\pi$
$678$		0			0
$679$			15.6447i			0.600387i
$680$	25.1863	−	19.0429i	0.965851	−	0.730261i
$681$		0			0
$682$	12.4180	−	11.3249i	0.475510	−	0.433654i
$683$			19.4879i			0.745682i	0.927895	+	0.372841i	$0.121616\pi$
$683$			19.4879i			0.745682i	−0.927895	+	0.372841i	$0.878384\pi$
$684$		0			0
$685$			23.6480i			0.903542i
$686$	0.952952	+	1.04493i	0.0363839	+	0.0398957i
$687$		0			0
$688$	33.7877	+	6.28886i	1.28814	+	0.239760i
$689$			2.82717i			0.107707i
$690$		0			0
$691$	2.44853			0.0931464			0.0465732	−	0.998915i	$-0.485170\pi$
$691$	2.44853			0.0931464			0.0465732	+	0.998915i	$0.485170\pi$
$692$	3.36098	−	36.4247i	0.127765	−	1.38466i
$693$		0			0
$694$	−24.8969	−	27.2999i	−0.945073	−	1.03629i
$695$	10.4527			0.396494
$696$		0			0
$697$	−6.13906			−0.232533
$698$	−3.51128	−	3.85019i	−0.132904	−	0.145732i
$699$		0			0
$700$	−1.04288	−	0.0962281i	−0.0394170	−	0.00363708i
$701$	−21.8472			−0.825157			−0.412578	−	0.910922i	$-0.635372\pi$
$701$	−21.8472			−0.825157			−0.412578	+	0.910922i	$0.635372\pi$
$702$		0			0
$703$			16.1453i			0.608930i
$704$	8.39722	+	2.37864i	0.316482	+	0.0896484i
$705$		0			0
$706$	14.8120	+	16.2417i	0.557457	+	0.611263i
$707$			12.3962i			0.466209i
$708$		0			0
$709$		−	50.4998i		−	1.89656i	−0.317437	−	0.948279i	$-0.602822\pi$
$709$		−	50.4998i		−	1.89656i	0.317437	−	0.948279i	$-0.397178\pi$
$710$	15.8678	−	14.4710i	0.595507	−	0.543088i
$711$		0			0
$712$	5.75203	−	4.34900i	0.215566	−	0.162986i
$713$			43.4903i			1.62873i
$714$		0			0
$715$	−10.5281			−0.393730
$716$	13.2399	+	1.22167i	0.494797	+	0.0456559i
$717$		0			0
$718$	−24.0717	+	21.9528i	−0.898349	+	0.819273i
$719$	−13.7799			−0.513904			−0.256952	−	0.966424i	$-0.582718\pi$
$719$	−13.7799			−0.513904			−0.256952	+	0.966424i	$0.582718\pi$
$720$		0			0
$721$	−13.2234			−0.492467
$722$	32.8503	−	29.9587i	1.22256	−	1.11495i
$723$		0			0
$724$	−4.91176	−	0.453218i	−0.182544	−	0.0168437i
$725$	−2.14689			−0.0797334
$726$		0			0
$727$			12.5617i			0.465888i	0.972490	+	0.232944i	$0.0748358\pi$
$727$			12.5617i			0.465888i	−0.972490	+	0.232944i	$0.925164\pi$
$728$	−7.00434	−	9.26401i	−0.259598	−	0.343347i
$729$		0			0
$730$	−20.7431	+	18.9172i	−0.767738	+	0.700159i
$731$			40.8112i			1.50946i
$732$		0			0
$733$			1.04203i			0.0384883i	0.999815	+	0.0192442i	$0.00612599\pi$
$733$			1.04203i			0.0384883i	−0.999815	+	0.0192442i	$0.993874\pi$
$734$	−15.3554	−	16.8375i	−0.566777	−	0.621482i
$735$		0			0
$736$	−19.1901	+	11.9078i	−0.707358	+	0.438928i
$737$		−	8.98195i		−	0.330854i
$738$		0			0
$739$	3.73631			0.137442			0.0687212	−	0.997636i	$-0.478108\pi$
$739$	3.73631			0.137442			0.0687212	+	0.997636i	$0.478108\pi$
$740$	10.6407	+	0.981836i	0.391159	+	0.0360930i
$741$		0			0
$742$	−0.656131	−	0.719461i	−0.0240873	−	0.0264122i
$743$	4.44956			0.163239			0.0816193	−	0.996664i	$-0.473991\pi$
$743$	4.44956			0.163239			0.0816193	+	0.996664i	$0.473991\pi$
$744$		0			0
$745$	28.9700			1.06138
$746$	7.97639	+	8.74627i	0.292036	+	0.320224i
$747$		0			0
$748$	−0.952246	+	10.3200i	−0.0348176	+	0.377337i
$749$	−5.44530			−0.198967
$750$		0			0
$751$			23.5520i			0.859426i	0.902965	+	0.429713i	$0.141385\pi$
$751$			23.5520i			0.859426i	−0.902965	+	0.429713i	$0.858615\pi$
$752$	26.7186	+	4.97310i	0.974328	+	0.181350i
$753$		0			0
$754$	−16.0424	−	17.5908i	−0.584231	−	0.640621i
$755$			21.7513i			0.791612i
$756$		0			0
$757$			16.5240i			0.600576i	0.953849	+	0.300288i	$0.0970829\pi$
$757$			16.5240i			0.600576i	−0.953849	+	0.300288i	$0.902917\pi$
$758$	−4.87710	+	4.44780i	−0.177144	+	0.161551i
$759$		0			0
$760$	−28.4725	−	37.6580i	−1.03281	−	1.36600i
$761$			9.27488i			0.336214i	0.985769	+	0.168107i	$0.0537655\pi$
$761$			9.27488i			0.336214i	−0.985769	+	0.168107i	$0.946235\pi$
$762$		0			0
$763$	−0.947776			−0.0343118
$764$	2.37143	−	25.7005i	0.0857953	−	0.929810i
$765$		0			0
$766$	11.6105	−	10.5885i	0.419506	−	0.382579i
$767$	31.7270			1.14560
$768$		0			0
$769$	18.2106			0.656690			0.328345	−	0.944558i	$-0.393509\pi$
$769$	18.2106			0.656690			0.328345	+	0.944558i	$0.393509\pi$
$770$	2.67921	−	2.44337i	0.0965519	−	0.0880531i
$771$		0			0
$772$	3.37553	−	36.5825i	0.121488	−	1.31663i
$773$	1.51105			0.0543486			0.0271743	−	0.999631i	$-0.491349\pi$
$773$	1.51105			0.0543486			0.0271743	+	0.999631i	$0.491349\pi$
$774$		0			0
$775$			5.70429i			0.204904i
$776$	26.6870	+	35.2966i	0.958008	+	1.26707i
$777$		0			0
$778$	35.3692	−	32.2559i	1.26805	−	1.15643i
$779$			9.17898i			0.328871i
$780$		0			0
$781$			7.04888i			0.252229i
$782$	−18.0714	−	19.8156i	−0.646231	−	0.708605i
$783$		0			0
$784$	3.93246	+	0.731943i	0.140445	+	0.0261408i
$785$		−	9.86571i		−	0.352122i
$786$		0			0
$787$	−3.25985			−0.116201			−0.0581005	−	0.998311i	$-0.518504\pi$
$787$	−3.25985			−0.116201			−0.0581005	+	0.998311i	$0.518504\pi$
$788$	2.77403	−	30.0636i	0.0988206	−	1.07097i
$789$		0			0
$790$	12.7675	+	13.9998i	0.454247	+	0.498091i
$791$	−16.8819			−0.600252
$792$		0			0
$793$	−39.8526			−1.41521
$794$	28.8320	+	31.6148i	1.02321	+	1.12197i
$795$		0			0
$796$	−7.00268	−	0.646150i	−0.248203	−	0.0229022i
$797$	50.5236			1.78964			0.894819	−	0.446428i	$-0.147304\pi$
$797$	50.5236			1.78964			0.894819	+	0.446428i	$0.147304\pi$
$798$		0			0
$799$			32.2727i			1.14172i
$800$	−2.51702	+	1.56186i	−0.0889901	+	0.0552200i
$801$		0			0
$802$	34.0778	+	37.3670i	1.20333	+	1.31948i
$803$		−	9.21465i		−	0.325178i
$804$		0			0
$805$			9.38313i			0.330712i
$806$	−46.7390	+	42.6248i	−1.64631	+	1.50140i
$807$		0			0
$808$	21.1458	+	27.9677i	0.743907	+	0.983899i
$809$			17.9908i			0.632523i	0.948672	+	0.316261i	$0.102428\pi$
$809$			17.9908i			0.632523i	−0.948672	+	0.316261i	$0.897572\pi$
$810$		0			0
$811$	22.2314			0.780650			0.390325	−	0.920677i	$-0.372363\pi$
$811$	22.2314			0.780650			0.390325	+	0.920677i	$0.372363\pi$
$812$	8.16497	+	0.753398i	0.286534	+	0.0264391i
$813$		0			0
$814$	−2.59156	+	2.36344i	−0.0908340	+	0.0828384i
$815$	55.6896			1.95072
$816$		0			0
$817$	61.0200			2.13482
$818$	27.0933	−	24.7084i	0.947295	−	0.863911i
$819$		0			0
$820$	6.04949	+	0.558198i	0.211257	+	0.0194931i
$821$	28.7163			1.00221			0.501103	−	0.865388i	$-0.332928\pi$
$821$	28.7163			1.00221			0.501103	+	0.865388i	$0.332928\pi$
$822$		0			0
$823$			46.1721i			1.60946i	0.593641	+	0.804730i	$0.297690\pi$
$823$			46.1721i			1.60946i	−0.593641	+	0.804730i	$0.702310\pi$
$824$	−29.8339	+	22.5568i	−1.03931	+	0.785805i
$825$		0			0
$826$	−8.07392	+	7.36322i	−0.280928	+	0.256199i
$827$			55.5900i			1.93305i	0.256568	+	0.966526i	$0.417408\pi$
$827$			55.5900i			1.93305i	−0.256568	+	0.966526i	$0.582592\pi$
$828$		0			0
$829$			7.13019i			0.247642i	0.992305	+	0.123821i	$0.0395148\pi$
$829$			7.13019i			0.247642i	−0.992305	+	0.123821i	$0.960485\pi$
$830$	−22.5492	−	24.7257i	−0.782695	−	0.858240i
$831$		0			0
$832$	−31.6055	−	8.95275i	−1.09572	−	0.310381i
$833$			4.74991i			0.164575i
$834$		0			0
$835$	11.2636			0.389791
$836$	15.4302	+	1.42378i	0.533666	+	0.0492423i
$837$		0			0
$838$	−6.02824	−	6.61009i	−0.208242	−	0.228342i
$839$	−33.3725			−1.15215			−0.576073	−	0.817399i	$-0.695415\pi$
$839$	−33.3725			−1.15215			−0.576073	+	0.817399i	$0.695415\pi$
$840$		0			0
$841$	−12.1914			−0.420393
$842$	−26.0715	−	28.5879i	−0.898482	−	0.985204i
$843$		0			0
$844$	−3.72124	+	40.3291i	−0.128090	+	1.38818i
$845$	9.07273			0.312111
$846$		0			0
$847$		−	9.80982i		−	0.337070i
$848$	−2.70760	−	0.503961i	−0.0929793	−	0.0173061i
$849$		0			0
$850$	−2.37028	−	2.59906i	−0.0813000	−	0.0891470i
$851$		−	9.07615i		−	0.311127i
$852$		0			0
$853$			34.4031i			1.17794i	0.808155	+	0.588969i	$0.200466\pi$
$853$			34.4031i			1.17794i	−0.808155	+	0.588969i	$0.799534\pi$
$854$	10.1417	−	9.24900i	0.347042	−	0.316494i
$855$		0			0
$856$	−12.2854	+	9.28872i	−0.419905	+	0.317482i
$857$		−	24.5369i		−	0.838164i	−0.907948	−	0.419082i	$-0.862352\pi$
$857$		−	24.5369i		−	0.838164i	0.907948	−	0.419082i	$-0.137648\pi$
$858$		0			0
$859$	49.8496			1.70085			0.850424	−	0.526098i	$-0.176345\pi$
$859$	49.8496			1.70085			0.850424	+	0.526098i	$0.176345\pi$
$860$	3.71079	−	40.2158i	0.126537	−	1.37135i
$861$		0			0
$862$	28.7906	−	26.2564i	0.980612	−	0.894295i
$863$	−1.18405			−0.0403055			−0.0201528	−	0.999797i	$-0.506415\pi$
$863$	−1.18405			−0.0403055			−0.0201528	+	0.999797i	$0.506415\pi$
$864$		0			0
$865$	−42.9854			−1.46155
$866$	13.6341	−	12.4340i	0.463306	−	0.422524i
$867$		0			0
$868$	2.00178	−	21.6944i	0.0679449	−	0.736355i
$869$	−6.21909			−0.210968
$870$		0			0
$871$			33.8063i			1.14548i
$872$	−2.13831	+	1.61674i	−0.0724125	+	0.0547496i
$873$		0			0
$874$	−29.6279	+	27.0199i	−1.00218	+	0.913962i
$875$		−	10.5205i		−	0.355658i
$876$		0			0
$877$			52.6756i			1.77873i	0.457200	+	0.889364i	$0.348853\pi$
$877$			52.6756i			1.77873i	−0.457200	+	0.889364i	$0.651147\pi$
$878$	−6.12117	−	6.71199i	−0.206580	−	0.226519i
$879$		0			0
$880$	1.87671	−	10.0828i	0.0632637	−	0.339893i
$881$		−	48.5193i		−	1.63466i	−0.576172	−	0.817329i	$-0.695454\pi$
$881$		−	48.5193i		−	1.63466i	0.576172	−	0.817329i	$-0.304546\pi$
$882$		0			0
$883$	36.3496			1.22326			0.611630	−	0.791144i	$-0.290514\pi$
$883$	36.3496			1.22326			0.611630	+	0.791144i	$0.290514\pi$
$884$	3.58407	−	38.8425i	0.120545	−	1.30642i
$885$		0			0
$886$	21.1388	+	23.1791i	0.710171	+	0.778717i
$887$	14.5979			0.490149			0.245075	−	0.969504i	$-0.421188\pi$
$887$	14.5979			0.490149			0.245075	+	0.969504i	$0.421188\pi$
$888$		0			0
$889$	−10.2310			−0.343136
$890$	−5.71004	−	6.26118i	−0.191401	−	0.209875i
$891$		0			0
$892$	−25.8826	−	2.38824i	−0.866614	−	0.0799641i
$893$	48.2534			1.61474
$894$		0			0
$895$		−	15.6246i		−	0.522272i
$896$	10.1208	−	5.05672i	0.338111	−	0.168933i
$897$		0			0
$898$	−1.77814	−	1.94977i	−0.0593374	−	0.0650646i
$899$		−	44.6606i		−	1.48951i
$900$		0			0
$901$		−	3.27043i		−	0.108954i
$902$	−1.47336	+	1.34367i	−0.0490576	+	0.0447394i
$903$		0			0
$904$	−38.0880	+	28.7976i	−1.26679	+	0.957793i
$905$			5.79644i			0.192680i
$906$		0			0
$907$	3.77723			0.125421			0.0627104	−	0.998032i	$-0.480026\pi$
$907$	3.77723			0.125421			0.0627104	+	0.998032i	$0.480026\pi$
$908$	−57.5503	−	5.31027i	−1.90987	−	0.176228i
$909$		0			0
$910$	−10.0840	+	9.19639i	−0.334282	+	0.304857i
$911$	−20.5255			−0.680040			−0.340020	−	0.940418i	$-0.610434\pi$
$911$	−20.5255			−0.680040			−0.340020	+	0.940418i	$0.610434\pi$
$912$		0			0
$913$	10.9838			0.363511
$914$	−29.6588	+	27.0482i	−0.981027	+	0.894674i
$915$		0			0
$916$	−7.27784	−	0.671540i	−0.240467	−	0.0221883i
$917$	−15.9013			−0.525107
$918$		0			0
$919$		−	19.8082i		−	0.653413i	−0.945126	−	0.326706i	$-0.894061\pi$
$919$		−	19.8082i		−	0.653413i	0.945126	−	0.326706i	$-0.105939\pi$
$920$	16.0060	+	21.1697i	0.527701	+	0.697943i
$921$		0			0
$922$	−34.7297	+	31.6727i	−1.14376	+	1.04308i
$923$		−	26.5306i		−	0.873267i
$924$		0			0
$925$		−	1.19045i		−	0.0391417i
$926$	−2.01815	−	2.21294i	−0.0663206	−	0.0727218i
$927$		0			0
$928$	19.7065	−	12.2282i	0.646897	−	0.401411i
$929$		−	2.90178i		−	0.0952044i	−0.998866	−	0.0476022i	$-0.984842\pi$
$929$		−	2.90178i		−	0.0952044i	0.998866	−	0.0476022i	$-0.0151580\pi$
$930$		0			0
$931$	7.10196			0.232757
$932$	27.3031	+	2.51931i	0.894343	+	0.0825228i
$933$		0			0
$934$	13.0951	+	14.3590i	0.428484	+	0.469841i
$935$	12.1788			0.398289
$936$		0			0
$937$	−9.02197			−0.294735			−0.147368	−	0.989082i	$-0.547080\pi$
$937$	−9.02197			−0.294735			−0.147368	+	0.989082i	$0.547080\pi$
$938$	−7.84578	−	8.60306i	−0.256174	−	0.280900i
$939$		0			0
$940$	2.93441	−	31.8018i	0.0957100	−	1.03726i
$941$	−26.0744			−0.850000			−0.425000	−	0.905193i	$-0.639726\pi$
$941$	−26.0744			−0.850000			−0.425000	+	0.905193i	$0.639726\pi$
$942$		0			0
$943$		−	5.16001i		−	0.168033i
$944$	−5.65554	+	30.3851i	−0.184072	+	0.988952i
$945$		0			0
$946$	8.93246	+	9.79462i	0.290419	+	0.318450i
$947$		−	46.0960i		−	1.49792i	−0.662616	−	0.748960i	$-0.730554\pi$
$947$		−	46.0960i		−	1.49792i	0.662616	−	0.748960i	$-0.269446\pi$
$948$		0			0
$949$			34.6822i			1.12583i
$950$	−3.88606	+	3.54399i	−0.126080	+	0.114982i
$951$		0			0
$952$	8.10250	+	10.7165i	0.262604	+	0.347322i
$953$			43.0803i			1.39551i	0.716338	+	0.697754i	$0.245817\pi$
$953$			43.0803i			1.39551i	−0.716338	+	0.697754i	$0.754183\pi$
$954$		0			0
$955$	−30.3295			−0.981439
$956$	−3.77376	+	40.8982i	−0.122052	+	1.32274i
$957$		0			0
$958$	9.17749	−	8.36966i	0.296511	−	0.270411i
$959$	−10.0619			−0.324916
$960$		0			0
$961$	−87.6634			−2.82785
$962$	9.75412	−	8.89553i	0.314486	−	0.286803i
$963$		0			0
$964$	4.07393	−	44.1513i	0.131212	−	1.42202i
$965$	−43.1715			−1.38974
$966$		0			0
$967$		−	0.389484i		−	0.0125249i	−0.999980	−	0.00626247i	$-0.998007\pi$
$967$		−	0.389484i		−	0.0125249i	0.999980	−	0.00626247i	$-0.00199342\pi$
$968$	−16.7338	−	22.1323i	−0.537845	−	0.711360i
$969$		0			0
$970$	38.4209	−	35.0389i	1.23362	−	1.12503i
$971$		−	41.1601i		−	1.32089i	−0.750875	−	0.660445i	$-0.770368\pi$
$971$		−	41.1601i		−	1.32089i	0.750875	−	0.660445i	$-0.229632\pi$
$972$		0			0
$973$			4.44750i			0.142580i
$974$	4.21763	+	4.62472i	0.135142	+	0.148186i
$975$		0			0
$976$	7.10397	−	38.1670i	0.227393	−	1.22170i
$977$			46.9292i			1.50140i	0.660644	+	0.750699i	$0.270283\pi$
$977$			46.9292i			1.50140i	−0.660644	+	0.750699i	$0.729717\pi$
$978$		0			0
$979$	2.78138			0.0888933
$980$	0.431888	−	4.68061i	0.0137962	−	0.149517i
$981$		0			0
$982$	−17.6783	−	19.3846i	−0.564137	−	0.618588i
$983$	−39.0802			−1.24646			−0.623232	−	0.782037i	$-0.714181\pi$
$983$	−39.0802			−1.24646			−0.623232	+	0.782037i	$0.714181\pi$
$984$		0			0
$985$	−35.4785			−1.13044
$986$	18.5576	+	20.3488i	0.590995	+	0.648038i
$987$		0			0
$988$	−58.0765	−	5.35882i	−1.84766	−	0.170487i
$989$	−34.3027			−1.09076
$990$		0			0
$991$		−	23.1043i		−	0.733932i	−0.930234	−	0.366966i	$-0.880397\pi$
$991$		−	23.1043i		−	0.733932i	0.930234	−	0.366966i	$-0.119603\pi$
$992$	−32.4905	−	52.3603i	−1.03157	−	1.66244i
$993$		0			0
$994$	6.15724	+	6.75153i	0.195296	+	0.214146i
$995$			8.26396i			0.261985i
$996$		0			0
$997$		−	47.9056i		−	1.51719i	−0.651565	−	0.758593i	$-0.725887\pi$
$997$		−	47.9056i		−	1.51719i	0.651565	−	0.758593i	$-0.274113\pi$
$998$	5.46865	−	4.98728i	0.173107	−	0.157869i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.j.d.323.37	yes	48
3.2	odd	2	inner	1512.2.j.d.323.12	yes	48
4.3	odd	2		6048.2.j.d.5615.11		48
8.3	odd	2	inner	1512.2.j.d.323.11	✓	48
8.5	even	2		6048.2.j.d.5615.37		48
12.11	even	2		6048.2.j.d.5615.38		48
24.5	odd	2		6048.2.j.d.5615.12		48
24.11	even	2	inner	1512.2.j.d.323.38	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.j.d.323.11	✓	48	8.3	odd	2	inner
1512.2.j.d.323.12	yes	48	3.2	odd	2	inner
1512.2.j.d.323.37	yes	48	1.1	even	1	trivial
1512.2.j.d.323.38	yes	48	24.11	even	2	inner
6048.2.j.d.5615.11		48	4.3	odd	2
6048.2.j.d.5615.12		48	24.5	odd	2
6048.2.j.d.5615.37		48	8.5	even	2
6048.2.j.d.5615.38		48	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.04493 - 0.952952i) q^{2} +(0.183763 - 1.99154i) q^{4} -2.35025 q^{5} -1.00000i q^{7} +(-1.70582 - 2.25614i) q^{8} +O(q^{10})\)	\(q+(1.04493 - 0.952952i) q^{2} +(0.183763 - 1.99154i) q^{4} -2.35025 q^{5} -1.00000i q^{7} +(-1.70582 - 2.25614i) q^{8} +(-2.45584 + 2.23967i) q^{10} -1.09095i q^{11} +4.10613i q^{13} +(-0.952952 - 1.04493i) q^{14} +(-3.93246 - 0.731943i) q^{16} -4.74991i q^{17} -7.10196 q^{19} +(-0.431888 + 4.68061i) q^{20} +(-1.03962 - 1.13997i) q^{22} +3.99240 q^{23} +0.523653 q^{25} +(3.91295 + 4.29063i) q^{26} +(-1.99154 - 0.183763i) q^{28} -4.09983 q^{29} +10.8933i q^{31} +(-4.80666 + 2.98262i) q^{32} +(-4.52644 - 4.96333i) q^{34} +2.35025i q^{35} -2.27336i q^{37} +(-7.42106 + 6.76783i) q^{38} +(4.00910 + 5.30248i) q^{40} -1.29246i q^{41} -8.59200 q^{43} +(-2.17267 - 0.200477i) q^{44} +(4.17179 - 3.80457i) q^{46} -6.79438 q^{47} -1.00000 q^{49} +(0.547181 - 0.499016i) q^{50} +(8.17753 + 0.754556i) q^{52} +0.688525 q^{53} +2.56400i q^{55} +(-2.25614 + 1.70582i) q^{56} +(-4.28404 + 3.90694i) q^{58} -7.72675i q^{59} +9.70563i q^{61} +(10.3808 + 11.3827i) q^{62} +(-2.18034 + 7.69715i) q^{64} -9.65042i q^{65} +8.23313 q^{67} +(-9.45963 - 0.872858i) q^{68} +(2.23967 + 2.45584i) q^{70} -6.46122 q^{71} +8.44644 q^{73} +(-2.16640 - 2.37550i) q^{74} +(-1.30508 + 14.1438i) q^{76} -1.09095 q^{77} -5.70061i q^{79} +(9.24225 + 1.72025i) q^{80} +(-1.23165 - 1.35053i) q^{82} +10.0681i q^{83} +11.1634i q^{85} +(-8.97805 + 8.18777i) q^{86} +(-2.46134 + 1.86097i) q^{88} +2.54950i q^{89} +4.10613 q^{91} +(0.733657 - 7.95103i) q^{92} +(-7.09966 + 6.47472i) q^{94} +16.6913 q^{95} -15.6447 q^{97} +(-1.04493 + 0.952952i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4}+O(q^{10}) \) 48 * q - 4 * q^4	\( 48 q - 4 q^{4} - 12 q^{10} - 12 q^{16} + 16 q^{19} - 24 q^{22} + 48 q^{25} + 8 q^{28} + 12 q^{34} + 32 q^{40} + 64 q^{43} + 60 q^{46} - 48 q^{49} + 16 q^{52} + 36 q^{58} - 4 q^{64} + 32 q^{67} + 12 q^{70} - 32 q^{76} + 36 q^{82} + 24 q^{88} - 60 q^{94}+O(q^{100}) \) 48 * q - 4 * q^4 - 12 * q^10 - 12 * q^16 + 16 * q^19 - 24 * q^22 + 48 * q^25 + 8 * q^28 + 12 * q^34 + 32 * q^40 + 64 * q^43 + 60 * q^46 - 48 * q^49 + 16 * q^52 + 36 * q^58 - 4 * q^64 + 32 * q^67 + 12 * q^70 - 32 * q^76 + 36 * q^82 + 24 * q^88 - 60 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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