LMFDB - Embedded newform 1512.2.j.c.323.2

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:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.2
Character	$\chi$	$=$	1512.323
Dual form			1512.2.j.c.323.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40936 + 0.117111i) q^{2} +(1.97257 - 0.330101i) q^{4} +1.17792 q^{5} -1.00000i q^{7} +(-2.74140 + 0.696239i) q^{8} +O(q^{10})$	\(q+(-1.40936 + 0.117111i) q^{2} +(1.97257 - 0.330101i) q^{4} +1.17792 q^{5} -1.00000i q^{7} +(-2.74140 + 0.696239i) q^{8} +(-1.66010 + 0.137947i) q^{10} +2.90595i q^{11} -1.05317i q^{13} +(0.117111 + 1.40936i) q^{14} +(3.78207 - 1.30230i) q^{16} +6.48837i q^{17} -3.11597 q^{19} +(2.32352 - 0.388832i) q^{20} +(-0.340317 - 4.09552i) q^{22} -0.812516 q^{23} -3.61251 q^{25} +(0.123337 + 1.48429i) q^{26} +(-0.330101 - 1.97257i) q^{28} -4.03607 q^{29} -0.108779i q^{31} +(-5.17777 + 2.27832i) q^{32} +(-0.759857 - 9.14442i) q^{34} -1.17792i q^{35} +9.97034i q^{37} +(4.39151 - 0.364913i) q^{38} +(-3.22914 + 0.820111i) q^{40} +9.44298i q^{41} +10.3446 q^{43} +(0.959257 + 5.73219i) q^{44} +(1.14512 - 0.0951542i) q^{46} -4.03126 q^{47} -1.00000 q^{49} +(5.09132 - 0.423064i) q^{50} +(-0.347652 - 2.07745i) q^{52} -2.97772 q^{53} +3.42296i q^{55} +(0.696239 + 2.74140i) q^{56} +(5.68827 - 0.472667i) q^{58} +0.868874i q^{59} -5.33629i q^{61} +(0.0127391 + 0.153308i) q^{62} +(7.03050 - 3.81733i) q^{64} -1.24054i q^{65} -3.97987 q^{67} +(2.14182 + 12.7988i) q^{68} +(0.137947 + 1.66010i) q^{70} +0.844302 q^{71} +3.59513 q^{73} +(-1.16763 - 14.0518i) q^{74} +(-6.14647 + 1.02859i) q^{76} +2.90595 q^{77} -9.48320i q^{79} +(4.45496 - 1.53400i) q^{80} +(-1.10587 - 13.3085i) q^{82} -2.71280i q^{83} +7.64276i q^{85} +(-14.5793 + 1.21146i) q^{86} +(-2.02323 - 7.96636i) q^{88} -2.22575i q^{89} -1.05317 q^{91} +(-1.60275 + 0.268212i) q^{92} +(5.68148 - 0.472103i) q^{94} -3.67035 q^{95} -3.93019 q^{97} +(1.40936 - 0.117111i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4}+O(q^{10}) $ 32 * q + 8 * q^4	$ 32 q + 8 q^{4} - 8 q^{10} - 8 q^{16} - 64 q^{19} + 24 q^{22} - 16 q^{25} - 8 q^{28} + 8 q^{34} - 24 q^{40} - 48 q^{43} - 8 q^{46} - 32 q^{49} - 24 q^{52} - 96 q^{58} - 40 q^{64} + 16 q^{67} - 16 q^{70} - 16 q^{73} + 16 q^{76} + 24 q^{82} + 72 q^{88} + 16 q^{91} - 56 q^{94} + 64 q^{97}+O(q^{100}) $ 32 * q + 8 * q^4 - 8 * q^10 - 8 * q^16 - 64 * q^19 + 24 * q^22 - 16 * q^25 - 8 * q^28 + 8 * q^34 - 24 * q^40 - 48 * q^43 - 8 * q^46 - 32 * q^49 - 24 * q^52 - 96 * q^58 - 40 * q^64 + 16 * q^67 - 16 * q^70 - 16 * q^73 + 16 * q^76 + 24 * q^82 + 72 * q^88 + 16 * q^91 - 56 * q^94 + 64 * q^97

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 $

$2$	−1.40936	+	0.117111i	−0.996565	+	0.0828097i
$2$	−1.40936	+	0.117111i	−0.996565	+	0.0828097i
$3$		0			0
$3$		0			0
$4$	1.97257	−	0.330101i	0.986285	−	0.165051i
$5$	1.17792			0.526780			0.263390	−	0.964689i	$-0.415159\pi$
$5$	1.17792			0.526780			0.263390	+	0.964689i	$0.415159\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−2.74140	+	0.696239i	−0.969230	+	0.246158i
$9$		0			0
$10$	−1.66010	+	0.137947i	−0.524971	+	0.0436225i
$11$			2.90595i			0.876176i	0.898932	+	0.438088i	$0.144344\pi$
$11$			2.90595i			0.876176i	−0.898932	+	0.438088i	$0.855656\pi$
$12$		0			0
$13$		−	1.05317i		−	0.292096i	−0.989278	−	0.146048i	$-0.953345\pi$
$13$		−	1.05317i		−	0.292096i	0.989278	−	0.146048i	$-0.0466554\pi$
$14$	0.117111	+	1.40936i	0.0312991	+	0.376666i
$15$		0			0
$16$	3.78207	−	1.30230i	0.945517	−	0.325574i
$17$			6.48837i			1.57366i	0.617169	+	0.786830i	$0.288279\pi$
$17$			6.48837i			1.57366i	−0.617169	+	0.786830i	$0.711721\pi$
$18$		0			0
$19$	−3.11597			−0.714853			−0.357426	−	0.933941i	$-0.616346\pi$
$19$	−3.11597			−0.714853			−0.357426	+	0.933941i	$0.616346\pi$
$20$	2.32352	−	0.388832i	0.519556	−	0.0869454i
$21$		0			0
$22$	−0.340317	−	4.09552i	−0.0725559	−	0.873167i
$23$	−0.812516			−0.169421			−0.0847107	−	0.996406i	$-0.526997\pi$
$23$	−0.812516			−0.169421			−0.0847107	+	0.996406i	$0.526997\pi$
$24$		0			0
$25$	−3.61251			−0.722503
$26$	0.123337	+	1.48429i	0.0241884	+	0.291093i
$27$		0			0
$28$	−0.330101	−	1.97257i	−0.0623832	−	0.372781i
$29$	−4.03607			−0.749480			−0.374740	−	0.927130i	$-0.622268\pi$
$29$	−4.03607			−0.749480			−0.374740	+	0.927130i	$0.622268\pi$
$30$		0			0
$31$		−	0.108779i		−	0.0195372i	−0.999952	−	0.00976861i	$-0.996891\pi$
$31$		−	0.108779i		−	0.0195372i	0.999952	−	0.00976861i	$-0.00310949\pi$
$32$	−5.17777	+	2.27832i	−0.915308	+	0.402754i
$33$		0			0
$34$	−0.759857	−	9.14442i	−0.130314	−	1.56826i
$35$		−	1.17792i		−	0.199104i
$36$		0			0
$37$			9.97034i			1.63911i	0.572998	+	0.819557i	$0.305780\pi$
$37$			9.97034i			1.63911i	−0.572998	+	0.819557i	$0.694220\pi$
$38$	4.39151	−	0.364913i	0.712397	−	0.0591967i
$39$		0			0
$40$	−3.22914	+	0.820111i	−0.510571	+	0.129671i
$41$			9.44298i			1.47475i	0.675486	+	0.737373i	$0.263934\pi$
$41$			9.44298i			1.47475i	−0.675486	+	0.737373i	$0.736066\pi$
$42$		0			0
$43$	10.3446			1.57754			0.788770	−	0.614688i	$-0.210718\pi$
$43$	10.3446			1.57754			0.788770	+	0.614688i	$0.210718\pi$
$44$	0.959257	+	5.73219i	0.144613	+	0.864160i
$45$		0			0
$46$	1.14512	−	0.0951542i	0.168839	−	0.0140297i
$47$	−4.03126			−0.588019			−0.294010	−	0.955802i	$-0.594990\pi$
$47$	−4.03126			−0.588019			−0.294010	+	0.955802i	$0.594990\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	5.09132	−	0.423064i	0.720021	−	0.0598302i
$51$		0			0
$52$	−0.347652	−	2.07745i	−0.0482106	−	0.288090i
$53$	−2.97772			−0.409022			−0.204511	−	0.978864i	$-0.565560\pi$
$53$	−2.97772			−0.409022			−0.204511	+	0.978864i	$0.565560\pi$
$54$		0			0
$55$			3.42296i			0.461552i
$56$	0.696239	+	2.74140i	0.0930388	+	0.366334i
$57$		0			0
$58$	5.68827	−	0.472667i	0.746906	−	0.0620642i
$59$			0.868874i			0.113118i	0.998399	+	0.0565589i	$0.0180129\pi$
$59$			0.868874i			0.113118i	−0.998399	+	0.0565589i	$0.981987\pi$
$60$		0			0
$61$		−	5.33629i		−	0.683242i	−0.939838	−	0.341621i	$-0.889024\pi$
$61$		−	5.33629i		−	0.683242i	0.939838	−	0.341621i	$-0.110976\pi$
$62$	0.0127391	+	0.153308i	0.00161787	+	0.0194701i
$63$		0			0
$64$	7.03050	−	3.81733i	0.878813	−	0.477167i
$65$		−	1.24054i		−	0.153870i
$66$		0			0
$67$	−3.97987			−0.486218			−0.243109	−	0.969999i	$-0.578167\pi$
$67$	−3.97987			−0.486218			−0.243109	+	0.969999i	$0.578167\pi$
$68$	2.14182	+	12.7988i	0.259734	+	1.55208i
$69$		0			0
$70$	0.137947	+	1.66010i	0.0164878	+	0.198420i
$71$	0.844302			0.100200			0.0501001	−	0.998744i	$-0.484046\pi$
$71$	0.844302			0.100200			0.0501001	+	0.998744i	$0.484046\pi$
$72$		0			0
$73$	3.59513			0.420778			0.210389	−	0.977618i	$-0.432527\pi$
$73$	3.59513			0.420778			0.210389	+	0.977618i	$0.432527\pi$
$74$	−1.16763	−	14.0518i	−0.135734	−	1.63348i
$75$		0			0
$76$	−6.14647	+	1.02859i	−0.705048	+	0.117987i
$77$	2.90595			0.331164
$78$		0			0
$79$		−	9.48320i		−	1.06694i	−0.845818	−	0.533472i	$-0.820887\pi$
$79$		−	9.48320i		−	1.06694i	0.845818	−	0.533472i	$-0.179113\pi$
$80$	4.45496	−	1.53400i	0.498080	−	0.171506i
$81$		0			0
$82$	−1.10587	−	13.3085i	−0.122123	−	1.46968i
$83$		−	2.71280i		−	0.297769i	−0.988855	−	0.148884i	$-0.952432\pi$
$83$		−	2.71280i		−	0.297769i	0.988855	−	0.148884i	$-0.0475682\pi$
$84$		0			0
$85$			7.64276i			0.828973i
$86$	−14.5793	+	1.21146i	−1.57212	+	0.130636i
$87$		0			0
$88$	−2.02323	−	7.96636i	−0.215678	−	0.849216i
$89$		−	2.22575i		−	0.235930i	−0.993018	−	0.117965i	$-0.962363\pi$
$89$		−	2.22575i		−	0.235930i	0.993018	−	0.117965i	$-0.0376370\pi$
$90$		0			0
$91$	−1.05317			−0.110402
$92$	−1.60275	+	0.268212i	−0.167098	+	0.0279631i
$93$		0			0
$94$	5.68148	−	0.472103i	0.586000	−	0.0486937i
$95$	−3.67035			−0.376570
$96$		0			0
$97$	−3.93019			−0.399050			−0.199525	−	0.979893i	$-0.563940\pi$
$97$	−3.93019			−0.399050			−0.199525	+	0.979893i	$0.563940\pi$
$98$	1.40936	−	0.117111i	0.142366	−	0.0118300i
$99$		0			0
$100$	−7.12593	+	1.19249i	−0.712593	+	0.119249i
$101$	18.0700			1.79803			0.899016	−	0.437915i	$-0.144283\pi$
$101$	18.0700			1.79803			0.899016	+	0.437915i	$0.144283\pi$
$102$		0			0
$103$			17.8616i			1.75995i	0.475017	+	0.879977i	$0.342442\pi$
$103$			17.8616i			1.75995i	−0.475017	+	0.879977i	$0.657558\pi$
$104$	0.733256	+	2.88715i	0.0719016	+	0.283108i
$105$		0			0
$106$	4.19667	−	0.348723i	0.407617	−	0.0338709i
$107$		−	7.67720i		−	0.742183i	−0.928596	−	0.371091i	$-0.878984\pi$
$107$		−	7.67720i		−	0.742183i	0.928596	−	0.371091i	$-0.121016\pi$
$108$		0			0
$109$			12.6991i			1.21635i	0.793801	+	0.608177i	$0.208099\pi$
$109$			12.6991i			1.21635i	−0.793801	+	0.608177i	$0.791901\pi$
$110$	−0.400865	−	4.82418i	−0.0382210	−	0.459967i
$111$		0			0
$112$	−1.30230	−	3.78207i	−0.123055	−	0.357372i
$113$			15.4017i			1.44887i	0.689342	+	0.724437i	$0.257900\pi$
$113$			15.4017i			1.44887i	−0.689342	+	0.724437i	$0.742100\pi$
$114$		0			0
$115$	−0.957076			−0.0892478
$116$	−7.96144	+	1.33231i	−0.739201	+	0.123702i
$117$		0			0
$118$	−0.101754	−	1.22455i	−0.00936725	−	0.112729i
$119$	6.48837			0.594788
$120$		0			0
$121$	2.55546			0.232315
$122$	0.624936	+	7.52074i	0.0565791	+	0.680896i
$123$		0			0
$124$	−0.0359079	−	0.214573i	−0.00322463	−	0.0192693i
$125$	−10.1448			−0.907380
$126$		0			0
$127$			17.1514i			1.52194i	0.648787	+	0.760970i	$0.275276\pi$
$127$			17.1514i			1.52194i	−0.648787	+	0.760970i	$0.724724\pi$
$128$	−9.46143	+	6.20333i	−0.836280	+	0.548302i
$129$		0			0
$130$	0.145281	+	1.74837i	0.0127420	+	0.153342i
$131$		−	10.5118i		−	0.918421i	−0.888328	−	0.459210i	$-0.848132\pi$
$131$		−	10.5118i		−	0.918421i	0.888328	−	0.459210i	$-0.151868\pi$
$132$		0			0
$133$			3.11597i			0.270189i
$134$	5.60905	−	0.466084i	0.484548	−	0.0402636i
$135$		0			0
$136$	−4.51745	−	17.7872i	−0.387369	−	1.52524i
$137$			13.6268i			1.16422i	0.813110	+	0.582110i	$0.197773\pi$
$137$			13.6268i			1.16422i	−0.813110	+	0.582110i	$0.802227\pi$
$138$		0			0
$139$	−5.37620			−0.456003			−0.228002	−	0.973661i	$-0.573219\pi$
$139$	−5.37620			−0.456003			−0.228002	+	0.973661i	$0.573219\pi$
$140$	−0.388832	−	2.32352i	−0.0328623	−	0.196374i
$141$		0			0
$142$	−1.18992	+	0.0988767i	−0.0998560	+	0.00829755i
$143$	3.06045			0.255928
$144$		0			0
$145$	−4.75416			−0.394811
$146$	−5.06681	+	0.421027i	−0.419332	+	0.0348445i
$147$		0			0
$148$	3.29122	+	19.6672i	0.270537	+	1.61663i
$149$	−17.3187			−1.41880			−0.709401	−	0.704805i	$-0.751035\pi$
$149$	−17.3187			−1.41880			−0.709401	+	0.704805i	$0.751035\pi$
$150$		0			0
$151$			4.50773i			0.366834i	0.983035	+	0.183417i	$0.0587158\pi$
$151$			4.50773i			0.366834i	−0.983035	+	0.183417i	$0.941284\pi$
$152$	8.54211	−	2.16946i	0.692856	−	0.175966i
$153$		0			0
$154$	−4.09552	+	0.340317i	−0.330026	+	0.0274236i
$155$		−	0.128132i		−	0.0102918i
$156$		0			0
$157$			8.84696i			0.706064i	0.935611	+	0.353032i	$0.114849\pi$
$157$			8.84696i			0.706064i	−0.935611	+	0.353032i	$0.885151\pi$
$158$	1.11058	+	13.3652i	0.0883533	+	1.06328i
$159$		0			0
$160$	−6.09898	+	2.68367i	−0.482166	+	0.212163i
$161$			0.812516i			0.0640352i
$162$		0			0
$163$	−8.38238			−0.656558			−0.328279	−	0.944581i	$-0.606469\pi$
$163$	−8.38238			−0.656558			−0.328279	+	0.944581i	$0.606469\pi$
$164$	3.11714	+	18.6269i	0.243408	+	1.45452i
$165$		0			0
$166$	0.317698	+	3.82331i	0.0246582	+	0.296746i
$167$	8.93563			0.691460			0.345730	−	0.938334i	$-0.387631\pi$
$167$	8.93563			0.691460			0.345730	+	0.938334i	$0.387631\pi$
$168$		0			0
$169$	11.8908			0.914680
$170$	−0.895048	−	10.7714i	−0.0686470	−	0.826126i
$171$		0			0
$172$	20.4055	−	3.41477i	1.55590	−	0.260374i
$173$	−14.1612			−1.07666			−0.538328	−	0.842736i	$-0.680944\pi$
$173$	−14.1612			−1.07666			−0.538328	+	0.842736i	$0.680944\pi$
$174$		0			0
$175$			3.61251i			0.273080i
$176$	3.78440	+	10.9905i	0.285260	+	0.828439i
$177$		0			0
$178$	0.260659	+	3.13688i	0.0195373	+	0.235119i
$179$		−	20.3695i		−	1.52249i	−0.648467	−	0.761243i	$-0.724589\pi$
$179$		−	20.3695i		−	1.52249i	0.648467	−	0.761243i	$-0.275411\pi$
$180$		0			0
$181$			18.2659i			1.35770i	0.734279	+	0.678848i	$0.237520\pi$
$181$			18.2659i			1.35770i	−0.734279	+	0.678848i	$0.762480\pi$
$182$	1.48429	−	0.123337i	0.110023	−	0.00914235i
$183$		0			0
$184$	2.22743	−	0.565705i	0.164208	−	0.0417044i
$185$			11.7442i			0.863453i
$186$		0			0
$187$	−18.8549			−1.37880
$188$	−7.95194	+	1.33072i	−0.579955	+	0.0970529i
$189$		0			0
$190$	5.17283	−	0.429837i	0.375277	−	0.0311837i
$191$	−7.83849			−0.567173			−0.283587	−	0.958947i	$-0.591524\pi$
$191$	−7.83849			−0.567173			−0.283587	+	0.958947i	$0.591524\pi$
$192$		0			0
$193$	−13.0241			−0.937498			−0.468749	−	0.883331i	$-0.655295\pi$
$193$	−13.0241			−0.937498			−0.468749	+	0.883331i	$0.655295\pi$
$194$	5.53903	−	0.460266i	0.397679	−	0.0330452i
$195$		0			0
$196$	−1.97257	+	0.330101i	−0.140898	+	0.0235786i
$197$	14.9576			1.06568			0.532842	−	0.846215i	$-0.321124\pi$
$197$	14.9576			1.06568			0.532842	+	0.846215i	$0.321124\pi$
$198$		0			0
$199$			16.9147i			1.19905i	0.800356	+	0.599525i	$0.204644\pi$
$199$			16.9147i			1.19905i	−0.800356	+	0.599525i	$0.795356\pi$
$200$	9.90333	−	2.51517i	0.700271	−	0.177850i
$201$		0			0
$202$	−25.4671	+	2.11619i	−1.79186	+	0.148895i
$203$			4.03607i			0.283277i
$204$		0			0
$205$			11.1230i			0.776867i
$206$	−2.09178	−	25.1733i	−0.145741	−	1.75391i
$207$		0			0
$208$	−1.37153	−	3.98315i	−0.0950988	−	0.276182i
$209$		−	9.05485i		−	0.626337i
$210$		0			0
$211$	5.68386			0.391293			0.195647	−	0.980674i	$-0.437319\pi$
$211$	5.68386			0.391293			0.195647	+	0.980674i	$0.437319\pi$
$212$	−5.87376	+	0.982949i	−0.403412	+	0.0675092i
$213$		0			0
$214$	0.899081	+	10.8199i	0.0614599	+	0.739633i
$215$	12.1851			0.831017
$216$		0			0
$217$	−0.108779			−0.00738437
$218$	−1.48720	−	17.8976i	−0.100726	−	1.21218i
$219$		0			0
$220$	1.12992	+	6.75204i	0.0761795	+	0.455222i
$221$	6.83333			0.459660
$222$		0			0
$223$		−	3.43963i		−	0.230335i	−0.993346	−	0.115167i	$-0.963260\pi$
$223$		−	3.43963i		−	0.230335i	0.993346	−	0.115167i	$-0.0367404\pi$
$224$	2.27832	+	5.17777i	0.152227	+	0.345954i
$225$		0			0
$226$	−1.80371	−	21.7065i	−0.119981	−	1.44390i
$227$		−	8.86522i		−	0.588406i	−0.955743	−	0.294203i	$-0.904946\pi$
$227$		−	8.86522i		−	0.588406i	0.955743	−	0.294203i	$-0.0950541\pi$
$228$		0			0
$229$		−	17.3653i		−	1.14753i	−0.819019	−	0.573767i	$-0.805482\pi$
$229$		−	17.3653i		−	1.14753i	0.819019	−	0.573767i	$-0.194518\pi$
$230$	1.34886	−	0.112084i	0.0889413	−	0.00739058i
$231$		0			0
$232$	11.0645	−	2.81007i	0.726418	−	0.184490i
$233$			9.99149i			0.654564i	0.944927	+	0.327282i	$0.106133\pi$
$233$			9.99149i			0.654564i	−0.944927	+	0.327282i	$0.893867\pi$
$234$		0			0
$235$	−4.74848			−0.309757
$236$	0.286816	+	1.71392i	0.0186702	+	0.111566i
$237$		0			0
$238$	−9.14442	+	0.759857i	−0.592745	+	0.0492542i
$239$	−24.5708			−1.58935			−0.794677	−	0.607032i	$-0.792360\pi$
$239$	−24.5708			−1.58935			−0.794677	+	0.607032i	$0.792360\pi$
$240$		0			0
$241$	23.1786			1.49306			0.746532	−	0.665349i	$-0.231717\pi$
$241$	23.1786			1.49306			0.746532	+	0.665349i	$0.231717\pi$
$242$	−3.60156	+	0.299272i	−0.231517	+	0.0192379i
$243$		0			0
$244$	−1.76152	−	10.5262i	−0.112769	−	0.673872i
$245$	−1.17792			−0.0752543
$246$		0			0
$247$			3.28164i			0.208806i
$248$	0.0757359	+	0.298205i	0.00480924	+	0.0189361i
$249$		0			0
$250$	14.2977	−	1.18807i	0.904264	−	0.0751399i
$251$		−	21.3670i		−	1.34868i	−0.738423	−	0.674338i	$-0.764429\pi$
$251$		−	21.3670i		−	1.34868i	0.738423	−	0.674338i	$-0.235571\pi$
$252$		0			0
$253$		−	2.36113i		−	0.148443i
$254$	−2.00861	−	24.1724i	−0.126031	−	1.51671i
$255$		0			0
$256$	12.6081	−	9.85073i	0.788003	−	0.615671i
$257$			29.5594i			1.84386i	0.387352	+	0.921932i	$0.373390\pi$
$257$			29.5594i			1.84386i	−0.387352	+	0.921932i	$0.626610\pi$
$258$		0			0
$259$	9.97034			0.619527
$260$	−0.409504	−	2.44706i	−0.0253964	−	0.151760i
$261$		0			0
$262$	1.23104	+	14.8149i	0.0760542	+	0.915266i
$263$	15.8001			0.974277			0.487139	−	0.873325i	$-0.338041\pi$
$263$	15.8001			0.974277			0.487139	+	0.873325i	$0.338041\pi$
$264$		0			0
$265$	−3.50751			−0.215464
$266$	−0.364913	−	4.39151i	−0.0223743	−	0.269261i
$267$		0			0
$268$	−7.85056	+	1.31376i	−0.479550	+	0.0802505i
$269$	6.41502			0.391131			0.195565	−	0.980691i	$-0.437346\pi$
$269$	6.41502			0.391131			0.195565	+	0.980691i	$0.437346\pi$
$270$		0			0
$271$		−	0.0927686i		−	0.00563529i	−0.999996	−	0.00281765i	$-0.999103\pi$
$271$		−	0.0927686i		−	0.00563529i	0.999996	−	0.00281765i	$-0.000896886\pi$
$272$	8.44977	+	24.5394i	0.512343	+	1.48792i
$273$		0			0
$274$	−1.59585	−	19.2051i	−0.0964087	−	1.16022i
$275$		−	10.4978i		−	0.633040i
$276$		0			0
$277$		−	19.7900i		−	1.18907i	−0.804071	−	0.594534i	$-0.797337\pi$
$277$		−	19.7900i		−	1.18907i	0.804071	−	0.594534i	$-0.202663\pi$
$278$	7.57698	−	0.629610i	0.454437	−	0.0377615i
$279$		0			0
$280$	0.820111	+	3.22914i	0.0490110	+	0.192978i
$281$		−	14.4404i		−	0.861443i	−0.902485	−	0.430721i	$-0.858259\pi$
$281$		−	14.4404i		−	0.861443i	0.902485	−	0.430721i	$-0.141741\pi$
$282$		0			0
$283$	20.3759			1.21122			0.605612	−	0.795760i	$-0.292929\pi$
$283$	20.3759			1.21122			0.605612	+	0.795760i	$0.292929\pi$
$284$	1.66544	−	0.278705i	0.0988259	−	0.0165381i
$285$		0			0
$286$	−4.31326	+	0.358411i	−0.255049	+	0.0211933i
$287$	9.44298			0.557402
$288$		0			0
$289$	−25.0989			−1.47641
$290$	6.70030	−	0.556762i	0.393455	−	0.0326942i
$291$		0			0
$292$	7.09164	−	1.18675i	0.415007	−	0.0694496i
$293$	−10.2919			−0.601262			−0.300631	−	0.953741i	$-0.597197\pi$
$293$	−10.2919			−0.601262			−0.300631	+	0.953741i	$0.597197\pi$
$294$		0			0
$295$			1.02346i			0.0595882i
$296$	−6.94174	−	27.3326i	−0.403480	−	1.58868i
$297$		0			0
$298$	24.4082	−	2.02820i	1.41393	−	0.117491i
$299$			0.855715i			0.0494873i
$300$		0			0
$301$		−	10.3446i		−	0.596254i
$302$	−0.527903	−	6.35300i	−0.0303774	−	0.365574i
$303$		0			0
$304$	−11.7848	+	4.05791i	−0.675905	+	0.232737i
$305$		−	6.28571i		−	0.359919i
$306$		0			0
$307$	19.8799			1.13461			0.567304	−	0.823508i	$-0.307986\pi$
$307$	19.8799			1.13461			0.567304	+	0.823508i	$0.307986\pi$
$308$	5.73219	−	0.959257i	0.326622	−	0.0546587i
$309$		0			0
$310$	0.0150056	+	0.180584i	0.000852263	+	0.0102565i
$311$	7.94464			0.450499			0.225250	−	0.974301i	$-0.427680\pi$
$311$	7.94464			0.450499			0.225250	+	0.974301i	$0.427680\pi$
$312$		0			0
$313$	−28.2451			−1.59651			−0.798254	−	0.602321i	$-0.794243\pi$
$313$	−28.2451			−1.59651			−0.798254	+	0.602321i	$0.794243\pi$
$314$	−1.03607	−	12.4685i	−0.0584689	−	0.703639i
$315$		0			0
$316$	−3.13042	−	18.7063i	−0.176100	−	1.05231i
$317$	−13.8609			−0.778506			−0.389253	−	0.921131i	$-0.627267\pi$
$317$	−13.8609			−0.778506			−0.389253	+	0.921131i	$0.627267\pi$
$318$		0			0
$319$		−	11.7286i		−	0.656677i
$320$	8.28135	−	4.49650i	0.462941	−	0.251362i
$321$		0			0
$322$	−0.0951542	−	1.14512i	−0.00530274	−	0.0638153i
$323$		−	20.2176i		−	1.12494i
$324$		0			0
$325$			3.80458i			0.211040i
$326$	11.8138	−	0.981665i	0.654303	−	0.0543694i
$327$		0			0
$328$	−6.57457	−	25.8869i	−0.363020	−	1.42937i
$329$			4.03126i			0.222250i
$330$		0			0
$331$	−14.5450			−0.799468			−0.399734	−	0.916631i	$-0.630897\pi$
$331$	−14.5450			−0.799468			−0.399734	+	0.916631i	$0.630897\pi$
$332$	−0.895500	−	5.35120i	−0.0491469	−	0.293685i
$333$		0			0
$334$	−12.5935	+	1.04646i	−0.689085	+	0.0572596i
$335$	−4.68795			−0.256130
$336$		0			0
$337$	5.26170			0.286623			0.143312	−	0.989678i	$-0.454225\pi$
$337$	5.26170			0.286623			0.143312	+	0.989678i	$0.454225\pi$
$338$	−16.7584	+	1.39254i	−0.911538	+	0.0757444i
$339$		0			0
$340$	2.52288	+	15.0759i	0.136823	+	0.817604i
$341$	0.316105			0.0171181
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−28.3587	+	7.20233i	−1.52900	+	0.388324i
$345$		0			0
$346$	19.9582	−	1.65843i	1.07296	−	0.0891575i
$347$		−	15.5549i		−	0.835029i	−0.908670	−	0.417514i	$-0.862901\pi$
$347$		−	15.5549i		−	0.835029i	0.908670	−	0.417514i	$-0.137099\pi$
$348$		0			0
$349$		−	17.1607i		−	0.918594i	−0.888283	−	0.459297i	$-0.848101\pi$
$349$		−	17.1607i		−	0.918594i	0.888283	−	0.459297i	$-0.151899\pi$
$350$	−0.423064	−	5.09132i	−0.0226137	−	0.272142i
$351$		0			0
$352$	−6.62067	−	15.0463i	−0.352883	−	0.801972i
$353$		−	15.5438i		−	0.827314i	−0.910433	−	0.413657i	$-0.864251\pi$
$353$		−	15.5438i		−	0.827314i	0.910433	−	0.413657i	$-0.135749\pi$
$354$		0			0
$355$	0.994517			0.0527835
$356$	−0.734724	−	4.39046i	−0.0389403	−	0.232694i
$357$		0			0
$358$	2.38548	+	28.7078i	0.126077	+	1.51726i
$359$	−14.9471			−0.788876			−0.394438	−	0.918923i	$-0.629061\pi$
$359$	−14.9471			−0.788876			−0.394438	+	0.918923i	$0.629061\pi$
$360$		0			0
$361$	−9.29073			−0.488986
$362$	−2.13913	−	25.7432i	−0.112430	−	1.35303i
$363$		0			0
$364$	−2.07745	+	0.347652i	−0.108888	+	0.0182219i
$365$	4.23476			0.221657
$366$		0			0
$367$			2.86184i			0.149387i	0.997207	+	0.0746934i	$0.0237978\pi$
$367$			2.86184i			0.149387i	−0.997207	+	0.0746934i	$0.976202\pi$
$368$	−3.07299	+	1.05814i	−0.160191	+	0.0551591i
$369$		0			0
$370$	−1.37537	−	16.5518i	−0.0715023	−	0.860487i
$371$			2.97772i			0.154596i
$372$		0			0
$373$		−	20.7327i		−	1.07350i	−0.843743	−	0.536748i	$-0.819653\pi$
$373$		−	20.7327i		−	1.07350i	0.843743	−	0.536748i	$-0.180347\pi$
$374$	26.5732	−	2.20810i	1.37407	−	0.114178i
$375$		0			0
$376$	11.0513	−	2.80672i	0.569926	−	0.144745i
$377$			4.25066i			0.218920i
$378$		0			0
$379$	28.1561			1.44628			0.723141	−	0.690700i	$-0.242698\pi$
$379$	28.1561			1.44628			0.723141	+	0.690700i	$0.242698\pi$
$380$	−7.24003	+	1.21159i	−0.371406	+	0.0621531i
$381$		0			0
$382$	11.0472	−	0.917970i	0.565225	−	0.0469675i
$383$	29.9733			1.53156			0.765781	−	0.643101i	$-0.222352\pi$
$383$	29.9733			1.53156			0.765781	+	0.643101i	$0.222352\pi$
$384$		0			0
$385$	3.42296			0.174450
$386$	18.3556	−	1.52526i	0.934278	−	0.0776339i
$387$		0			0
$388$	−7.75257	+	1.29736i	−0.393577	+	0.0658634i
$389$	29.4931			1.49536			0.747679	−	0.664060i	$-0.231168\pi$
$389$	29.4931			1.49536			0.747679	+	0.664060i	$0.231168\pi$
$390$		0			0
$391$		−	5.27190i		−	0.266612i
$392$	2.74140	−	0.696239i	0.138461	−	0.0351654i
$393$		0			0
$394$	−21.0806	+	1.75169i	−1.06202	+	0.0882489i
$395$		−	11.1704i		−	0.562045i
$396$		0			0
$397$			22.0845i			1.10839i	0.832386	+	0.554196i	$0.186974\pi$
$397$			22.0845i			1.10839i	−0.832386	+	0.554196i	$0.813026\pi$
$398$	−1.98089	−	23.8388i	−0.0992930	−	1.19493i
$399$		0			0
$400$	−13.6628	+	4.70456i	−0.683138	+	0.235228i
$401$			7.42054i			0.370564i	0.982685	+	0.185282i	$0.0593198\pi$
$401$			7.42054i			0.370564i	−0.982685	+	0.185282i	$0.940680\pi$
$402$		0			0
$403$	−0.114562			−0.00570674
$404$	35.6443	−	5.96493i	1.77337	−	0.296766i
$405$		0			0
$406$	−0.472667	−	5.68827i	−0.0234581	−	0.282304i
$407$	−28.9733			−1.43615
$408$		0			0
$409$	37.3983			1.84923			0.924615	−	0.380904i	$-0.124387\pi$
$409$	37.3983			1.84923			0.924615	+	0.380904i	$0.124387\pi$
$410$	−1.30263	−	15.6763i	−0.0643321	−	0.774199i
$411$		0			0
$412$	5.89612	+	35.2332i	0.290481	+	1.73582i
$413$	0.868874			0.0427545
$414$		0			0
$415$		−	3.19546i		−	0.156859i
$416$	2.39945	+	5.45305i	0.117643	+	0.267358i
$417$		0			0
$418$	1.06042	+	12.7615i	0.0518668	+	0.624186i
$419$		−	8.55960i		−	0.418164i	−0.977898	−	0.209082i	$-0.932952\pi$
$419$		−	8.55960i		−	0.418164i	0.977898	−	0.209082i	$-0.0670475\pi$
$420$		0			0
$421$			6.56688i			0.320050i	0.987113	+	0.160025i	$0.0511575\pi$
$421$			6.56688i			0.320050i	−0.987113	+	0.160025i	$0.948842\pi$
$422$	−8.01059	+	0.665640i	−0.389949	+	0.0324029i
$423$		0			0
$424$	8.16311	−	2.07321i	0.396436	−	0.100684i
$425$		−	23.4393i		−	1.13697i
$426$		0			0
$427$	−5.33629			−0.258241
$428$	−2.53425	−	15.1438i	−0.122498	−	0.732004i
$429$		0			0
$430$	−17.1731	+	1.42700i	−0.828163	+	0.0688163i
$431$	5.61014			0.270231			0.135116	−	0.990830i	$-0.456859\pi$
$431$	5.61014			0.270231			0.135116	+	0.990830i	$0.456859\pi$
$432$		0			0
$433$	7.96675			0.382857			0.191429	−	0.981507i	$-0.438688\pi$
$433$	7.96675			0.382857			0.191429	+	0.981507i	$0.438688\pi$
$434$	0.153308	−	0.0127391i	0.00735901	−	0.000611498i
$435$		0			0
$436$	4.19199	+	25.0499i	0.200760	+	1.19967i
$437$	2.53178			0.121111
$438$		0			0
$439$		−	33.9176i		−	1.61880i	−0.587258	−	0.809400i	$-0.699792\pi$
$439$		−	33.9176i		−	1.61880i	0.587258	−	0.809400i	$-0.300208\pi$
$440$	−2.38320	−	9.38370i	−0.113615	−	0.447350i
$441$		0			0
$442$	−9.63060	+	0.800256i	−0.458081	+	0.0380643i
$443$		−	6.31862i		−	0.300207i	−0.988670	−	0.150103i	$-0.952039\pi$
$443$		−	6.31862i		−	0.300207i	0.988670	−	0.150103i	$-0.0479606\pi$
$444$		0			0
$445$		−	2.62175i		−	0.124283i
$446$	0.402817	+	4.84767i	0.0190740	+	0.229544i
$447$		0			0
$448$	−3.81733	−	7.03050i	−0.180352	−	0.332160i
$449$			11.9562i			0.564246i	0.959378	+	0.282123i	$0.0910387\pi$
$449$			11.9562i			0.564246i	−0.959378	+	0.282123i	$0.908961\pi$
$450$		0			0
$451$	−27.4408			−1.29214
$452$	5.08413	+	30.3810i	0.239137	+	1.42900i
$453$		0			0
$454$	1.03821	+	12.4943i	0.0487257	+	0.586385i
$455$	−1.24054			−0.0581575
$456$		0			0
$457$	10.7774			0.504144			0.252072	−	0.967708i	$-0.418888\pi$
$457$	10.7774			0.504144			0.252072	+	0.967708i	$0.418888\pi$
$458$	2.03366	+	24.4739i	0.0950269	+	1.14359i
$459$		0			0
$460$	−1.88790	+	0.315932i	−0.0880238	+	0.0147304i
$461$	−2.36887			−0.110329			−0.0551647	−	0.998477i	$-0.517568\pi$
$461$	−2.36887			−0.110329			−0.0551647	+	0.998477i	$0.517568\pi$
$462$		0			0
$463$		−	38.4537i		−	1.78709i	−0.448969	−	0.893547i	$-0.648209\pi$
$463$		−	38.4537i		−	1.78709i	0.448969	−	0.893547i	$-0.351791\pi$
$464$	−15.2647	+	5.25616i	−0.708646	+	0.244011i
$465$		0			0
$466$	−1.17011	−	14.0816i	−0.0542043	−	0.652316i
$467$		−	5.09381i		−	0.235713i	−0.993031	−	0.117857i	$-0.962398\pi$
$467$		−	5.09381i		−	0.235713i	0.993031	−	0.117857i	$-0.0376023\pi$
$468$		0			0
$469$			3.97987i			0.183773i
$470$	6.69231	−	0.556098i	0.308693	−	0.0256509i
$471$		0			0
$472$	−0.604944	−	2.38193i	−0.0278448	−	0.109637i
$473$			30.0609i			1.38220i
$474$		0			0
$475$	11.2565			0.516483
$476$	12.7988	−	2.14182i	0.586630	−	0.0981701i
$477$		0			0
$478$	34.6291	−	2.87750i	1.58390	−	0.131614i
$479$	20.8166			0.951137			0.475568	−	0.879679i	$-0.342242\pi$
$479$	20.8166			0.951137			0.475568	+	0.879679i	$0.342242\pi$
$480$		0			0
$481$	10.5004			0.478778
$482$	−32.6669	+	2.71446i	−1.48794	+	0.123640i
$483$		0			0
$484$	5.04083	−	0.843561i	0.229129	−	0.0383437i
$485$	−4.62943			−0.210212
$486$		0			0
$487$			26.1716i			1.18595i	0.805222	+	0.592973i	$0.202046\pi$
$487$			26.1716i			1.18595i	−0.805222	+	0.592973i	$0.797954\pi$
$488$	3.71533	+	14.6289i	0.168185	+	0.662219i
$489$		0			0
$490$	1.66010	−	0.137947i	0.0749959	−	0.00623179i
$491$		−	27.7686i		−	1.25318i	−0.779349	−	0.626590i	$-0.784450\pi$
$491$		−	27.7686i		−	1.25318i	0.779349	−	0.626590i	$-0.215550\pi$
$492$		0			0
$493$		−	26.1875i		−	1.17943i
$494$	−0.384314	−	4.62499i	−0.0172911	−	0.208088i
$495$		0			0
$496$	−0.141662	−	0.411408i	−0.00636081	−	0.0184728i
$497$		−	0.844302i		−	0.0378721i
$498$		0			0
$499$	−13.7781			−0.616791			−0.308395	−	0.951258i	$-0.599792\pi$
$499$	−13.7781			−0.616791			−0.308395	+	0.951258i	$0.599792\pi$
$500$	−20.0114	+	3.34882i	−0.894936	+	0.149764i
$501$		0			0
$502$	2.50231	+	30.1138i	0.111683	+	1.34404i
$503$	−32.5875			−1.45300			−0.726502	−	0.687165i	$-0.758855\pi$
$503$	−32.5875			−1.45300			−0.726502	+	0.687165i	$0.758855\pi$
$504$		0			0
$505$	21.2850			0.947168
$506$	0.276513	+	3.32767i	0.0122925	+	0.147933i
$507$		0			0
$508$	5.66169	+	33.8323i	0.251197	+	1.50107i
$509$	17.1161			0.758657			0.379328	−	0.925262i	$-0.376155\pi$
$509$	17.1161			0.758657			0.379328	+	0.925262i	$0.376155\pi$
$510$		0			0
$511$		−	3.59513i		−	0.159039i
$512$	−16.6156	+	15.3597i	−0.734313	+	0.678811i
$513$		0			0
$514$	−3.46172	−	41.6597i	−0.152690	−	1.83753i
$515$			21.0394i			0.927109i
$516$		0			0
$517$		−	11.7146i		−	0.515209i
$518$	−14.0518	+	1.16763i	−0.617399	+	0.0513028i
$519$		0			0
$520$	0.863714	+	3.40082i	0.0378764	+	0.149136i
$521$			22.6308i			0.991471i	0.868473	+	0.495736i	$0.165102\pi$
$521$			22.6308i			0.991471i	−0.868473	+	0.495736i	$0.834898\pi$
$522$		0			0
$523$	−19.0252			−0.831914			−0.415957	−	0.909384i	$-0.636553\pi$
$523$	−19.0252			−0.831914			−0.415957	+	0.909384i	$0.636553\pi$
$524$	−3.46996	−	20.7353i	−0.151586	−	0.905825i
$525$		0			0
$526$	−22.2680	+	1.85036i	−0.970931	+	0.0806796i
$527$	0.705796			0.0307450
$528$		0			0
$529$	−22.3398			−0.971296
$530$	4.94333	−	0.410766i	0.214724	−	0.0178425i
$531$		0			0
$532$	1.02859	+	6.14647i	0.0445948	+	0.266483i
$533$	9.94503			0.430767
$534$		0			0
$535$		−	9.04310i		−	0.390967i
$536$	10.9104	−	2.77094i	0.471257	−	0.119686i
$537$		0			0
$538$	−9.04105	+	0.751267i	−0.389787	+	0.0323894i
$539$		−	2.90595i		−	0.125168i
$540$		0			0
$541$		−	17.3996i		−	0.748066i	−0.927415	−	0.374033i	$-0.877975\pi$
$541$		−	17.3996i		−	0.748066i	0.927415	−	0.374033i	$-0.122025\pi$
$542$	0.0108642	+	0.130744i	0.000466657	+	0.00561594i
$543$		0			0
$544$	−14.7826	−	33.5953i	−0.633797	−	1.44038i
$545$			14.9585i			0.640751i
$546$		0			0
$547$	4.96571			0.212318			0.106159	−	0.994349i	$-0.466145\pi$
$547$	4.96571			0.212318			0.106159	+	0.994349i	$0.466145\pi$
$548$	4.49824	+	26.8799i	0.192155	+	1.14825i
$549$		0			0
$550$	1.22940	+	14.7951i	0.0524218	+	0.630865i
$551$	12.5763			0.535768
$552$		0			0
$553$	−9.48320			−0.403267
$554$	2.31762	+	27.8912i	0.0984663	+	1.18498i
$555$		0			0
$556$	−10.6049	+	1.77469i	−0.449749	+	0.0752635i
$557$	5.67400			0.240415			0.120208	−	0.992749i	$-0.461644\pi$
$557$	5.67400			0.240415			0.120208	+	0.992749i	$0.461644\pi$
$558$		0			0
$559$		−	10.8946i		−	0.460793i
$560$	−1.53400	−	4.45496i	−0.0648231	−	0.188256i
$561$		0			0
$562$	1.69113	+	20.3517i	0.0713358	+	0.858484i
$563$		−	25.4752i		−	1.07365i	−0.843693	−	0.536826i	$-0.819623\pi$
$563$		−	25.4752i		−	1.07365i	0.843693	−	0.536826i	$-0.180377\pi$
$564$		0			0
$565$			18.1420i			0.763238i
$566$	−28.7169	+	2.38624i	−1.20706	+	0.100301i
$567$		0			0
$568$	−2.31457	+	0.587836i	−0.0971170	+	0.0246650i
$569$		−	19.5120i		−	0.817986i	−0.912537	−	0.408993i	$-0.865880\pi$
$569$		−	19.5120i		−	0.817986i	0.912537	−	0.408993i	$-0.134120\pi$
$570$		0			0
$571$	−38.0268			−1.59137			−0.795686	−	0.605709i	$-0.792889\pi$
$571$	−38.0268			−1.59137			−0.795686	+	0.605709i	$0.792889\pi$
$572$	6.03695	−	1.01026i	0.252418	−	0.0422410i
$573$		0			0
$574$	−13.3085	+	1.10587i	−0.555487	+	0.0461582i
$575$	2.93522			0.122407
$576$		0			0
$577$	5.32632			0.221738			0.110869	−	0.993835i	$-0.464637\pi$
$577$	5.32632			0.221738			0.110869	+	0.993835i	$0.464637\pi$
$578$	35.3733	−	2.93935i	1.47134	−	0.122261i
$579$		0			0
$580$	−9.37791	+	1.56935i	−0.389397	+	0.0651638i
$581$	−2.71280			−0.112546
$582$		0			0
$583$		−	8.65311i		−	0.358375i
$584$	−9.85566	+	2.50307i	−0.407830	+	0.103578i
$585$		0			0
$586$	14.5050	−	1.20530i	0.599197	−	0.0497903i
$587$			25.6946i			1.06053i	0.847832	+	0.530265i	$0.177908\pi$
$587$			25.6946i			1.06053i	−0.847832	+	0.530265i	$0.822092\pi$
$588$		0			0
$589$			0.338951i			0.0139662i
$590$	−0.119858	−	1.44242i	−0.00493448	−	0.0593836i
$591$		0			0
$592$	12.9843	+	37.7085i	0.533652	+	1.54981i
$593$			35.9249i			1.47526i	0.675205	+	0.737630i	$0.264055\pi$
$593$			35.9249i			1.47526i	−0.675205	+	0.737630i	$0.735945\pi$
$594$		0			0
$595$	7.64276			0.313322
$596$	−34.1623	+	5.71692i	−1.39934	+	0.234174i
$597$		0			0
$598$	−0.100213	−	1.20601i	−0.00409803	−	0.0493173i
$599$	−8.08090			−0.330177			−0.165088	−	0.986279i	$-0.552791\pi$
$599$	−8.08090			−0.330177			−0.165088	+	0.986279i	$0.552791\pi$
$600$		0			0
$601$	39.0492			1.59285			0.796425	−	0.604738i	$-0.206722\pi$
$601$	39.0492			1.59285			0.796425	+	0.604738i	$0.206722\pi$
$602$	1.21146	+	14.5793i	0.0493756	+	0.594206i
$603$		0			0
$604$	1.48801	+	8.89181i	0.0605461	+	0.361803i
$605$	3.01012			0.122379
$606$		0			0
$607$		−	39.0636i		−	1.58554i	−0.609519	−	0.792772i	$-0.708637\pi$
$607$		−	39.0636i		−	1.58554i	0.609519	−	0.792772i	$-0.291363\pi$
$608$	16.1338	−	7.09917i	0.654311	−	0.287909i
$609$		0			0
$610$	0.736123	+	8.85880i	0.0298047	+	0.358682i
$611$			4.24559i			0.171758i
$612$		0			0
$613$		−	27.0877i		−	1.09406i	−0.837112	−	0.547031i	$-0.815758\pi$
$613$		−	27.0877i		−	1.09406i	0.837112	−	0.547031i	$-0.184242\pi$
$614$	−28.0179	+	2.32815i	−1.13071	+	0.0939566i
$615$		0			0
$616$	−7.96636	+	2.02323i	−0.320974	+	0.0815184i
$617$		−	10.2143i		−	0.411213i	−0.978635	−	0.205607i	$-0.934083\pi$
$617$		−	10.2143i		−	0.411213i	0.978635	−	0.205607i	$-0.0659167\pi$
$618$		0			0
$619$	28.5400			1.14712			0.573560	−	0.819164i	$-0.305562\pi$
$619$	28.5400			1.14712			0.573560	+	0.819164i	$0.305562\pi$
$620$	−0.0422966	−	0.252750i	−0.00169867	−	0.0101507i
$621$		0			0
$622$	−11.1968	+	0.930401i	−0.448952	+	0.0373057i
$623$	−2.22575			−0.0891730
$624$		0			0
$625$	6.11281			0.244512
$626$	39.8074	−	3.30780i	1.59102	−	0.132206i
$627$		0			0
$628$	2.92039	+	17.4512i	0.116536	+	0.696380i
$629$	−64.6912			−2.57941
$630$		0			0
$631$			17.9037i			0.712734i	0.934346	+	0.356367i	$0.115985\pi$
$631$			17.9037i			0.712734i	−0.934346	+	0.356367i	$0.884015\pi$
$632$	6.60258	+	25.9972i	0.262636	+	1.03411i
$633$		0			0
$634$	19.5350	−	1.62326i	0.775832	−	0.0644679i
$635$			20.2029i			0.801728i
$636$		0			0
$637$			1.05317i			0.0417280i
$638$	1.37355	+	16.5298i	0.0543792	+	0.654421i
$639$		0			0
$640$	−11.1448	+	7.30700i	−0.440536	+	0.288835i
$641$		−	36.5576i		−	1.44394i	−0.691925	−	0.721969i	$-0.743237\pi$
$641$		−	36.5576i		−	1.44394i	0.691925	−	0.721969i	$-0.256763\pi$
$642$		0			0
$643$	28.5306			1.12514			0.562568	−	0.826751i	$-0.309813\pi$
$643$	28.5306			1.12514			0.562568	+	0.826751i	$0.309813\pi$
$644$	0.268212	+	1.60275i	0.0105691	+	0.0631570i
$645$		0			0
$646$	2.36769	+	28.4938i	0.0931556	+	1.12107i
$647$	−25.0326			−0.984134			−0.492067	−	0.870557i	$-0.663758\pi$
$647$	−25.0326			−0.984134			−0.492067	+	0.870557i	$0.663758\pi$
$648$		0			0
$649$	−2.52490			−0.0991112
$650$	−0.445556	−	5.36201i	−0.0174762	−	0.210315i
$651$		0			0
$652$	−16.5348	+	2.76703i	−0.647554	+	0.108365i
$653$	−43.1196			−1.68740			−0.843699	−	0.536816i	$-0.819627\pi$
$653$	−43.1196			−1.68740			−0.843699	+	0.536816i	$0.819627\pi$
$654$		0			0
$655$		−	12.3820i		−	0.483806i
$656$	12.2975	+	35.7140i	0.480139	+	1.39440i
$657$		0			0
$658$	−0.472103	−	5.68148i	−0.0184045	−	0.221487i
$659$			8.36352i			0.325796i	0.986643	+	0.162898i	$0.0520842\pi$
$659$			8.36352i			0.325796i	−0.986643	+	0.162898i	$0.947916\pi$
$660$		0			0
$661$			8.48754i			0.330127i	0.986283	+	0.165064i	$0.0527829\pi$
$661$			8.48754i			0.330127i	−0.986283	+	0.165064i	$0.947217\pi$
$662$	20.4991	−	1.70338i	0.796722	−	0.0662037i
$663$		0			0
$664$	1.88876	+	7.43687i	0.0732981	+	0.288607i
$665$			3.67035i			0.142330i
$666$		0			0
$667$	3.27937			0.126978
$668$	17.6262	−	2.94966i	0.681977	−	0.114126i
$669$		0			0
$670$	6.60699	−	0.549009i	0.255250	−	0.0212100i
$671$	15.5070			0.598641
$672$		0			0
$673$	−25.4287			−0.980206			−0.490103	−	0.871664i	$-0.663041\pi$
$673$	−25.4287			−0.980206			−0.490103	+	0.871664i	$0.663041\pi$
$674$	−7.41562	+	0.616201i	−0.285639	+	0.0237352i
$675$		0			0
$676$	23.4555	−	3.92518i	0.902135	−	0.150968i
$677$	−17.0820			−0.656515			−0.328258	−	0.944588i	$-0.606461\pi$
$677$	−17.0820			−0.656515			−0.328258	+	0.944588i	$0.606461\pi$
$678$		0			0
$679$			3.93019i			0.150827i
$680$	−5.32118	−	20.9518i	−0.204058	−	0.803466i
$681$		0			0
$682$	−0.445505	+	0.0370193i	−0.0170593	+	0.00141754i
$683$			44.0552i			1.68573i	0.538128	+	0.842863i	$0.319132\pi$
$683$			44.0552i			1.68573i	−0.538128	+	0.842863i	$0.680868\pi$
$684$		0			0
$685$			16.0513i			0.613288i
$686$	−0.117111	−	1.40936i	−0.00447130	−	0.0538095i
$687$		0			0
$688$	39.1240	−	13.4718i	1.49159	−	0.513606i
$689$			3.13604i			0.119474i
$690$		0			0
$691$	−18.3483			−0.698002			−0.349001	−	0.937122i	$-0.613479\pi$
$691$	−18.3483			−0.698002			−0.349001	+	0.937122i	$0.613479\pi$
$692$	−27.9339	+	4.67462i	−1.06189	+	0.177703i
$693$		0			0
$694$	1.82164	+	21.9223i	0.0691485	+	0.832161i
$695$	−6.33271			−0.240213
$696$		0			0
$697$	−61.2695			−2.32075
$698$	2.00971	+	24.1856i	0.0760685	+	0.915439i
$699$		0			0
$700$	1.19249	+	7.12593i	0.0450721	+	0.269335i
$701$	33.6724			1.27179			0.635894	−	0.771777i	$-0.280632\pi$
$701$	33.6724			1.27179			0.635894	+	0.771777i	$0.280632\pi$
$702$		0			0
$703$		−	31.0673i		−	1.17172i
$704$	11.0930	+	20.4303i	0.418082	+	0.769995i
$705$		0			0
$706$	1.82035	+	21.9068i	0.0685096	+	0.824472i
$707$		−	18.0700i		−	0.679592i
$708$		0			0
$709$		−	15.9147i		−	0.597689i	−0.954302	−	0.298845i	$-0.903399\pi$
$709$		−	15.9147i		−	0.597689i	0.954302	−	0.298845i	$-0.0966013\pi$
$710$	−1.40163	+	0.116468i	−0.0526022	+	0.00437098i
$711$		0			0
$712$	1.54966	+	6.10168i	0.0580759	+	0.228670i
$713$			0.0883844i			0.00331002i
$714$		0			0
$715$	3.60495			0.134818
$716$	−6.72399	−	40.1802i	−0.251287	−	1.50161i
$717$		0			0
$718$	21.0657	−	1.75046i	0.786167	−	0.0653266i
$719$	34.6441			1.29201			0.646004	−	0.763334i	$-0.276439\pi$
$719$	34.6441			1.29201			0.646004	+	0.763334i	$0.276439\pi$
$720$		0			0
$721$	17.8616			0.665200
$722$	13.0939	−	1.08804i	0.487306	−	0.0404928i
$723$		0			0
$724$	6.02960	+	36.0308i	0.224088	+	1.33907i
$725$	14.5804			0.541501
$726$		0			0
$727$			38.6477i			1.43336i	0.697400	+	0.716682i	$0.254340\pi$
$727$			38.6477i			1.43336i	−0.697400	+	0.716682i	$0.745660\pi$
$728$	2.88715	−	0.733256i	0.107005	−	0.0271763i
$729$		0			0
$730$	−5.96828	+	0.495935i	−0.220896	+	0.0183554i
$731$			67.1197i			2.48251i
$732$		0			0
$733$			4.45768i			0.164648i	0.996606	+	0.0823240i	$0.0262342\pi$
$733$			4.45768i			0.164648i	−0.996606	+	0.0823240i	$0.973766\pi$
$734$	−0.335152	−	4.03335i	−0.0123707	−	0.148874i
$735$		0			0
$736$	4.20702	−	1.85117i	0.155073	−	0.0682350i
$737$		−	11.5653i		−	0.426013i
$738$		0			0
$739$	−32.0619			−1.17942			−0.589709	−	0.807616i	$-0.700757\pi$
$739$	−32.0619			−1.17942			−0.589709	+	0.807616i	$0.700757\pi$
$740$	3.87678	+	23.1663i	0.142513	+	0.851611i
$741$		0			0
$742$	−0.348723	−	4.19667i	−0.0128020	−	0.154065i
$743$	−44.9201			−1.64796			−0.823979	−	0.566620i	$-0.808251\pi$
$743$	−44.9201			−1.64796			−0.823979	+	0.566620i	$0.808251\pi$
$744$		0			0
$745$	−20.4000			−0.747397
$746$	2.42801	+	29.2197i	0.0888959	+	1.06981i
$747$		0			0
$748$	−37.1925	+	6.22401i	−1.35989	+	0.227572i
$749$	−7.67720			−0.280519
$750$		0			0
$751$			20.4697i			0.746951i	0.927640	+	0.373475i	$0.121834\pi$
$751$			20.4697i			0.746951i	−0.927640	+	0.373475i	$0.878166\pi$
$752$	−15.2465	+	5.24989i	−0.555982	+	0.191444i
$753$		0			0
$754$	−0.497797	−	5.99069i	−0.0181287	−	0.218168i
$755$			5.30973i			0.193241i
$756$		0			0
$757$			11.4003i			0.414352i	0.978304	+	0.207176i	$0.0664273\pi$
$757$			11.4003i			0.414352i	−0.978304	+	0.207176i	$0.933573\pi$
$758$	−39.6820	+	3.29738i	−1.44131	+	0.119766i
$759$		0			0
$760$	10.0619	−	2.55544i	0.364983	−	0.0926956i
$761$		−	32.5142i		−	1.17864i	−0.807901	−	0.589319i	$-0.799396\pi$
$761$		−	32.5142i		−	1.17864i	0.807901	−	0.589319i	$-0.200604\pi$
$762$		0			0
$763$	12.6991			0.459739
$764$	−15.4620	+	2.58749i	−0.559395	+	0.0936123i
$765$		0			0
$766$	−42.2430	+	3.51019i	−1.52630	+	0.126828i
$767$	0.915070			0.0330413
$768$		0			0
$769$	25.1134			0.905614			0.452807	−	0.891609i	$-0.350423\pi$
$769$	25.1134			0.905614			0.452807	+	0.891609i	$0.350423\pi$
$770$	−4.82418	+	0.400865i	−0.173851	+	0.0144462i
$771$		0			0
$772$	−25.6910	+	4.29928i	−0.924640	+	0.154735i
$773$	42.4890			1.52822			0.764112	−	0.645083i	$-0.223177\pi$
$773$	42.4890			1.52822			0.764112	+	0.645083i	$0.223177\pi$
$774$		0			0
$775$			0.392964i			0.0141157i
$776$	10.7742	−	2.73635i	0.386771	−	0.0982292i
$777$		0			0
$778$	−41.5663	+	3.45395i	−1.49022	+	0.123830i
$779$		−	29.4240i		−	1.05423i
$780$		0			0
$781$			2.45350i			0.0877930i
$782$	0.617396	+	7.42999i	0.0220780	+	0.265696i
$783$		0			0
$784$	−3.78207	+	1.30230i	−0.135074	+	0.0465105i
$785$			10.4210i			0.371941i
$786$		0			0
$787$	19.1415			0.682322			0.341161	−	0.940005i	$-0.389180\pi$
$787$	19.1415			0.682322			0.341161	+	0.940005i	$0.389180\pi$
$788$	29.5049	−	4.93751i	1.05107	−	0.175892i
$789$		0			0
$790$	1.30817	+	15.7431i	0.0465428	+	0.560115i
$791$	15.4017			0.547623
$792$		0			0
$793$	−5.62001			−0.199572
$794$	−2.58633	−	31.1250i	−0.0917856	−	1.10458i
$795$		0			0
$796$	5.58356	+	33.3654i	0.197904	+	1.18261i
$797$	14.9802			0.530625			0.265312	−	0.964162i	$-0.414525\pi$
$797$	14.9802			0.530625			0.265312	+	0.964162i	$0.414525\pi$
$798$		0			0
$799$		−	26.1563i		−	0.925343i
$800$	18.7047	−	8.23045i	0.661313	−	0.290990i
$801$		0			0
$802$	−0.869023	−	10.4582i	−0.0306863	−	0.369291i
$803$			10.4473i			0.368675i
$804$		0			0
$805$			0.957076i			0.0337325i
$806$	0.161459	−	0.0134164i	0.00568714	−	0.000472574i
$807$		0			0
$808$	−49.5370	+	12.5810i	−1.74271	+	0.442599i
$809$			20.4899i			0.720388i	0.932877	+	0.360194i	$0.117289\pi$
$809$			20.4899i			0.720388i	−0.932877	+	0.360194i	$0.882711\pi$
$810$		0			0
$811$	19.0258			0.668087			0.334043	−	0.942558i	$-0.391587\pi$
$811$	19.0258			0.668087			0.334043	+	0.942558i	$0.391587\pi$
$812$	1.33231	+	7.96144i	0.0467550	+	0.279392i
$813$		0			0
$814$	40.8337	−	3.39308i	1.43122	−	0.118927i
$815$	−9.87374			−0.345862
$816$		0			0
$817$	−32.2335			−1.12771
$818$	−52.7076	+	4.37974i	−1.84288	+	0.153134i
$819$		0			0
$820$	3.67173	+	21.9410i	0.128222	+	0.766212i
$821$	−39.0750			−1.36373			−0.681863	−	0.731480i	$-0.738830\pi$
$821$	−39.0750			−1.36373			−0.681863	+	0.731480i	$0.738830\pi$
$822$		0			0
$823$		−	38.1369i		−	1.32937i	−0.747124	−	0.664684i	$-0.768566\pi$
$823$		−	38.1369i		−	1.32937i	0.747124	−	0.664684i	$-0.231434\pi$
$824$	−12.4359	−	48.9656i	−0.433226	−	1.70580i
$825$		0			0
$826$	−1.22455	+	0.101754i	−0.0426077	+	0.00354049i
$827$			13.8842i			0.482802i	0.970425	+	0.241401i	$0.0776070\pi$
$827$			13.8842i			0.482802i	−0.970425	+	0.241401i	$0.922393\pi$
$828$		0			0
$829$		−	0.705296i		−	0.0244960i	−0.999925	−	0.0122480i	$-0.996101\pi$
$829$		−	0.705296i		−	0.0244960i	0.999925	−	0.0122480i	$-0.00389875\pi$
$830$	0.374222	+	4.50354i	0.0129894	+	0.156320i
$831$		0			0
$832$	−4.02029	−	7.40429i	−0.139378	−	0.256698i
$833$		−	6.48837i		−	0.224809i
$834$		0			0
$835$	10.5254			0.364248
$836$	−2.98902	−	17.8613i	−0.103377	−	0.617747i
$837$		0			0
$838$	1.00242	+	12.0635i	0.0346280	+	0.416728i
$839$	50.4627			1.74217			0.871083	−	0.491136i	$-0.163418\pi$
$839$	50.4627			1.74217			0.871083	+	0.491136i	$0.163418\pi$
$840$		0			0
$841$	−12.7101			−0.438280
$842$	−0.769051	−	9.25507i	−0.0265033	−	0.318951i
$843$		0			0
$844$	11.2118	−	1.87625i	0.385927	−	0.0645832i
$845$	14.0064			0.481835
$846$		0			0
$847$		−	2.55546i		−	0.0878068i
$848$	−11.2619	+	3.87787i	−0.386737	+	0.133167i
$849$		0			0
$850$	2.74499	+	33.0343i	0.0941524	+	1.13307i
$851$		−	8.10106i		−	0.277701i
$852$		0			0
$853$		−	10.7370i		−	0.367628i	−0.982961	−	0.183814i	$-0.941156\pi$
$853$		−	10.7370i		−	0.367628i	0.982961	−	0.183814i	$-0.0588444\pi$
$854$	7.52074	−	0.624936i	0.257354	−	0.0213849i
$855$		0			0
$856$	5.34516	+	21.0462i	0.182694	+	0.719345i
$857$			9.75153i			0.333106i	0.986033	+	0.166553i	$0.0532637\pi$
$857$			9.75153i			0.333106i	−0.986033	+	0.166553i	$0.946736\pi$
$858$		0			0
$859$	28.9169			0.986630			0.493315	−	0.869851i	$-0.335785\pi$
$859$	28.9169			0.986630			0.493315	+	0.869851i	$0.335785\pi$
$860$	24.0360	−	4.02232i	0.819620	−	0.137160i
$861$		0			0
$862$	−7.90669	+	0.657007i	−0.269303	+	0.0223777i
$863$	16.0259			0.545528			0.272764	−	0.962081i	$-0.412062\pi$
$863$	16.0259			0.545528			0.272764	+	0.962081i	$0.412062\pi$
$864$		0			0
$865$	−16.6807			−0.567161
$866$	−11.2280	+	0.932990i	−0.381542	+	0.0317043i
$867$		0			0
$868$	−0.214573	+	0.0359079i	−0.00728310	+	0.00121880i
$869$	27.5577			0.934831
$870$		0			0
$871$			4.19146i			0.142022i
$872$	−8.84161	−	34.8133i	−0.299415	−	1.17893i
$873$		0			0
$874$	−3.56817	+	0.296498i	−0.120695	+	0.0100292i
$875$			10.1448i			0.342958i
$876$		0			0
$877$		−	2.24225i		−	0.0757154i	−0.999283	−	0.0378577i	$-0.987947\pi$
$877$		−	2.24225i		−	0.0757154i	0.999283	−	0.0378577i	$-0.0120534\pi$
$878$	3.97211	+	47.8020i	0.134052	+	1.61324i
$879$		0			0
$880$	4.45771	+	12.9459i	0.150269	+	0.436406i
$881$		−	9.97799i		−	0.336167i	−0.985773	−	0.168083i	$-0.946242\pi$
$881$		−	9.97799i		−	0.336167i	0.985773	−	0.168083i	$-0.0537578\pi$
$882$		0			0
$883$	19.8382			0.667609			0.333805	−	0.942642i	$-0.391667\pi$
$883$	19.8382			0.667609			0.333805	+	0.942642i	$0.391667\pi$
$884$	13.4792	−	2.25569i	0.453356	−	0.0758671i
$885$		0			0
$886$	0.739977	+	8.90518i	0.0248600	+	0.299176i
$887$	34.8500			1.17015			0.585074	−	0.810980i	$-0.301065\pi$
$887$	34.8500			1.17015			0.585074	+	0.810980i	$0.301065\pi$
$888$		0			0
$889$	17.1514			0.575239
$890$	0.307035	+	3.69498i	0.0102918	+	0.123856i
$891$		0			0
$892$	−1.13543	−	6.78492i	−0.0380169	−	0.227176i
$893$	12.5613			0.420347
$894$		0			0
$895$		−	23.9935i		−	0.802016i
$896$	6.20333	+	9.46143i	0.207239	+	0.316084i
$897$		0			0
$898$	−1.40019	−	16.8505i	−0.0467251	−	0.562308i
$899$			0.439039i			0.0146428i
$900$		0			0
$901$		−	19.3206i		−	0.643661i
$902$	38.6739	−	3.21361i	1.28770	−	0.107002i
$903$		0			0
$904$	−10.7233	−	42.2222i	−0.356651	−	1.40429i
$905$			21.5157i			0.715207i
$906$		0			0
$907$	−3.69626			−0.122732			−0.0613662	−	0.998115i	$-0.519546\pi$
$907$	−3.69626			−0.122732			−0.0613662	+	0.998115i	$0.519546\pi$
$908$	−2.92642	−	17.4873i	−0.0971167	−	0.580336i
$909$		0			0
$910$	1.74837	−	0.145281i	0.0579578	−	0.00481601i
$911$	−51.1975			−1.69625			−0.848125	−	0.529796i	$-0.822268\pi$
$911$	−51.1975			−1.69625			−0.848125	+	0.529796i	$0.822268\pi$
$912$		0			0
$913$	7.88327			0.260898
$914$	−15.1892	+	1.26214i	−0.502413	+	0.0417480i
$915$		0			0
$916$	−5.73232	−	34.2543i	−0.189401	−	1.13180i
$917$	−10.5118			−0.347130
$918$		0			0
$919$			50.4632i			1.66463i	0.554306	+	0.832313i	$0.312984\pi$
$919$			50.4632i			1.66463i	−0.554306	+	0.832313i	$0.687016\pi$
$920$	2.62372	−	0.666354i	0.0865016	−	0.0219690i
$921$		0			0
$922$	3.33858	−	0.277420i	0.109950	−	0.00913634i
$923$		−	0.889190i		−	0.0292681i
$924$		0			0
$925$		−	36.0180i		−	1.18426i
$926$	4.50334	+	54.1950i	0.147989	+	1.78096i
$927$		0			0
$928$	20.8978	−	9.19546i	0.686005	−	0.301856i
$929$			8.22557i			0.269872i	0.990854	+	0.134936i	$0.0430829\pi$
$929$			8.22557i			0.269872i	−0.990854	+	0.134936i	$0.956917\pi$
$930$		0			0
$931$	3.11597			0.102122
$932$	3.29820	+	19.7089i	0.108036	+	0.645587i
$933$		0			0
$934$	0.596539	+	7.17899i	0.0195194	+	0.234904i
$935$	−22.2095			−0.726327
$936$		0			0
$937$	0.968784			0.0316488			0.0158244	−	0.999875i	$-0.494963\pi$
$937$	0.968784			0.0316488			0.0158244	+	0.999875i	$0.494963\pi$
$938$	−0.466084	−	5.60905i	−0.0152182	−	0.183142i
$939$		0			0
$940$	−9.36672	+	1.56748i	−0.305509	+	0.0511256i
$941$	−11.2805			−0.367734			−0.183867	−	0.982951i	$-0.558862\pi$
$941$	−11.2805			−0.367734			−0.183867	+	0.982951i	$0.558862\pi$
$942$		0			0
$943$		−	7.67257i		−	0.249853i
$944$	1.13153	+	3.28614i	0.0368282	+	0.106955i
$945$		0			0
$946$	−3.52045	−	42.3666i	−0.114460	−	1.37746i
$947$			57.8442i			1.87968i	0.341609	+	0.939842i	$0.389028\pi$
$947$			57.8442i			1.87968i	−0.341609	+	0.939842i	$0.610972\pi$
$948$		0			0
$949$		−	3.78627i		−	0.122907i
$950$	−15.8644	+	1.31825i	−0.514709	+	0.0427698i
$951$		0			0
$952$	−17.7872	+	4.51745i	−0.576486	+	0.146412i
$953$			23.4368i			0.759193i	0.925152	+	0.379596i	$0.123937\pi$
$953$			23.4368i			0.759193i	−0.925152	+	0.379596i	$0.876063\pi$
$954$		0			0
$955$	−9.23309			−0.298776
$956$	−48.4677	+	8.11086i	−1.56756	+	0.262324i
$957$		0			0
$958$	−29.3381	+	2.43785i	−0.947870	+	0.0787633i
$959$	13.6268			0.440034
$960$		0			0
$961$	30.9882			0.999618
$962$	−14.7988	+	1.22971i	−0.477134	+	0.0396475i
$963$		0			0
$964$	45.7214	−	7.65128i	1.47259	−	0.246431i
$965$	−15.3413			−0.493855
$966$		0			0
$967$			44.8294i			1.44162i	0.693135	+	0.720808i	$0.256229\pi$
$967$			44.8294i			1.44162i	−0.693135	+	0.720808i	$0.743771\pi$
$968$	−7.00554	+	1.77921i	−0.225166	+	0.0571861i
$969$		0			0
$970$	6.52452	−	0.542155i	0.209490	−	0.0174076i
$971$			13.3436i			0.428216i	0.976810	+	0.214108i	$0.0686844\pi$
$971$			13.3436i			0.428216i	−0.976810	+	0.214108i	$0.931316\pi$
$972$		0			0
$973$			5.37620i			0.172353i
$974$	−3.06497	−	36.8850i	−0.0982079	−	1.18187i
$975$		0			0
$976$	−6.94943	−	20.1822i	−0.222446	−	0.646017i
$977$			11.0654i			0.354015i	0.984210	+	0.177007i	$0.0566416\pi$
$977$			11.0654i			0.354015i	−0.984210	+	0.177007i	$0.943358\pi$
$978$		0			0
$979$	6.46793			0.206716
$980$	−2.32352	+	0.388832i	−0.0742222	+	0.0124208i
$981$		0			0
$982$	3.25200	+	39.1359i	0.103775	+	1.24888i
$983$	−48.7128			−1.55370			−0.776849	−	0.629687i	$-0.783183\pi$
$983$	−48.7128			−1.55370			−0.776849	+	0.629687i	$0.783183\pi$
$984$		0			0
$985$	17.6188			0.561381
$986$	3.06684	+	36.9076i	0.0976680	+	1.17538i
$987$		0			0
$988$	1.08327	+	6.47326i	0.0344635	+	0.205942i
$989$	−8.40517			−0.267269
$990$		0			0
$991$		−	44.6581i		−	1.41861i	−0.704901	−	0.709306i	$-0.749009\pi$
$991$		−	44.6581i		−	1.41861i	0.704901	−	0.709306i	$-0.250991\pi$
$992$	0.247832	+	0.563230i	0.00786868	+	0.0178826i
$993$		0			0
$994$	0.0988767	+	1.18992i	0.00313618	+	0.0377420i
$995$			19.9241i			0.631636i
$996$		0			0
$997$			20.5408i			0.650534i	0.945622	+	0.325267i	$0.105454\pi$
$997$			20.5408i			0.650534i	−0.945622	+	0.325267i	$0.894546\pi$
$998$	19.4182	−	1.61356i	0.614672	−	0.0510762i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.j.c.323.2	yes	32
3.2	odd	2	inner	1512.2.j.c.323.31	yes	32
4.3	odd	2		6048.2.j.c.5615.23		32
8.3	odd	2	inner	1512.2.j.c.323.32	yes	32
8.5	even	2		6048.2.j.c.5615.9		32
12.11	even	2		6048.2.j.c.5615.10		32
24.5	odd	2		6048.2.j.c.5615.24		32
24.11	even	2	inner	1512.2.j.c.323.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.j.c.323.1	✓	32	24.11	even	2	inner
1512.2.j.c.323.2	yes	32	1.1	even	1	trivial
1512.2.j.c.323.31	yes	32	3.2	odd	2	inner
1512.2.j.c.323.32	yes	32	8.3	odd	2	inner
6048.2.j.c.5615.9		32	8.5	even	2
6048.2.j.c.5615.10		32	12.11	even	2
6048.2.j.c.5615.23		32	4.3	odd	2
6048.2.j.c.5615.24		32	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.40936 + 0.117111i) q^{2} +(1.97257 - 0.330101i) q^{4} +1.17792 q^{5} -1.00000i q^{7} +(-2.74140 + 0.696239i) q^{8} +O(q^{10})\)	\(q+(-1.40936 + 0.117111i) q^{2} +(1.97257 - 0.330101i) q^{4} +1.17792 q^{5} -1.00000i q^{7} +(-2.74140 + 0.696239i) q^{8} +(-1.66010 + 0.137947i) q^{10} +2.90595i q^{11} -1.05317i q^{13} +(0.117111 + 1.40936i) q^{14} +(3.78207 - 1.30230i) q^{16} +6.48837i q^{17} -3.11597 q^{19} +(2.32352 - 0.388832i) q^{20} +(-0.340317 - 4.09552i) q^{22} -0.812516 q^{23} -3.61251 q^{25} +(0.123337 + 1.48429i) q^{26} +(-0.330101 - 1.97257i) q^{28} -4.03607 q^{29} -0.108779i q^{31} +(-5.17777 + 2.27832i) q^{32} +(-0.759857 - 9.14442i) q^{34} -1.17792i q^{35} +9.97034i q^{37} +(4.39151 - 0.364913i) q^{38} +(-3.22914 + 0.820111i) q^{40} +9.44298i q^{41} +10.3446 q^{43} +(0.959257 + 5.73219i) q^{44} +(1.14512 - 0.0951542i) q^{46} -4.03126 q^{47} -1.00000 q^{49} +(5.09132 - 0.423064i) q^{50} +(-0.347652 - 2.07745i) q^{52} -2.97772 q^{53} +3.42296i q^{55} +(0.696239 + 2.74140i) q^{56} +(5.68827 - 0.472667i) q^{58} +0.868874i q^{59} -5.33629i q^{61} +(0.0127391 + 0.153308i) q^{62} +(7.03050 - 3.81733i) q^{64} -1.24054i q^{65} -3.97987 q^{67} +(2.14182 + 12.7988i) q^{68} +(0.137947 + 1.66010i) q^{70} +0.844302 q^{71} +3.59513 q^{73} +(-1.16763 - 14.0518i) q^{74} +(-6.14647 + 1.02859i) q^{76} +2.90595 q^{77} -9.48320i q^{79} +(4.45496 - 1.53400i) q^{80} +(-1.10587 - 13.3085i) q^{82} -2.71280i q^{83} +7.64276i q^{85} +(-14.5793 + 1.21146i) q^{86} +(-2.02323 - 7.96636i) q^{88} -2.22575i q^{89} -1.05317 q^{91} +(-1.60275 + 0.268212i) q^{92} +(5.68148 - 0.472103i) q^{94} -3.67035 q^{95} -3.93019 q^{97} +(1.40936 - 0.117111i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4}+O(q^{10}) \) 32 * q + 8 * q^4	\( 32 q + 8 q^{4} - 8 q^{10} - 8 q^{16} - 64 q^{19} + 24 q^{22} - 16 q^{25} - 8 q^{28} + 8 q^{34} - 24 q^{40} - 48 q^{43} - 8 q^{46} - 32 q^{49} - 24 q^{52} - 96 q^{58} - 40 q^{64} + 16 q^{67} - 16 q^{70} - 16 q^{73} + 16 q^{76} + 24 q^{82} + 72 q^{88} + 16 q^{91} - 56 q^{94} + 64 q^{97}+O(q^{100}) \) 32 * q + 8 * q^4 - 8 * q^10 - 8 * q^16 - 64 * q^19 + 24 * q^22 - 16 * q^25 - 8 * q^28 + 8 * q^34 - 24 * q^40 - 48 * q^43 - 8 * q^46 - 32 * q^49 - 24 * q^52 - 96 * q^58 - 40 * q^64 + 16 * q^67 - 16 * q^70 - 16 * q^73 + 16 * q^76 + 24 * q^82 + 72 * q^88 + 16 * q^91 - 56 * q^94 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more