LMFDB - Embedded newform 882.2.k.a.215.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(215,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("882.215");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.k (of order $6$, degree $2$, not 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			215.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	882.215
Dual form			882.2.k.a.521.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.358719 + 0.621320i) q^{5} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.358719 + 0.621320i) q^{5} -1.00000i q^{8} +(0.621320 - 0.358719i) q^{10} +(2.59808 - 1.50000i) q^{11} +2.44949i q^{13} +(-0.500000 + 0.866025i) q^{16} +(-2.95680 - 5.12132i) q^{17} +(5.12132 + 2.95680i) q^{19} -0.717439 q^{20} -3.00000 q^{22} +(-3.67423 - 2.12132i) q^{23} +(2.24264 + 3.88437i) q^{25} +(1.22474 - 2.12132i) q^{26} +7.24264i q^{29} +(7.86396 - 4.54026i) q^{31} +(0.866025 - 0.500000i) q^{32} +5.91359i q^{34} +(0.121320 - 0.210133i) q^{37} +(-2.95680 - 5.12132i) q^{38} +(0.621320 + 0.358719i) q^{40} +11.8272 q^{41} -0.242641 q^{43} +(2.59808 + 1.50000i) q^{44} +(2.12132 + 3.67423i) q^{46} +(-2.95680 + 5.12132i) q^{47} -4.48528i q^{50} +(-2.12132 + 1.22474i) q^{52} +(6.27231 - 3.62132i) q^{53} +2.15232i q^{55} +(3.62132 - 6.27231i) q^{58} +(4.03295 + 6.98528i) q^{59} +(-0.878680 - 0.507306i) q^{61} -9.08052 q^{62} -1.00000 q^{64} +(-1.52192 - 0.878680i) q^{65} +(5.00000 + 8.66025i) q^{67} +(2.95680 - 5.12132i) q^{68} -1.75736i q^{71} +(1.24264 - 0.717439i) q^{73} +(-0.210133 + 0.121320i) q^{74} +5.91359i q^{76} +(1.37868 - 2.38794i) q^{79} +(-0.358719 - 0.621320i) q^{80} +(-10.2426 - 5.91359i) q^{82} +6.63103 q^{83} +4.24264 q^{85} +(0.210133 + 0.121320i) q^{86} +(-1.50000 - 2.59808i) q^{88} +(5.19615 - 9.00000i) q^{89} -4.24264i q^{92} +(5.12132 - 2.95680i) q^{94} +(-3.67423 + 2.12132i) q^{95} -13.5592i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 8 q + 4 q^{4} - 12 q^{10} - 4 q^{16} + 24 q^{19} - 24 q^{22} - 16 q^{25} + 12 q^{31} - 16 q^{37} - 12 q^{40} + 32 q^{43} + 12 q^{58} - 24 q^{61} - 8 q^{64} + 40 q^{67} - 24 q^{73} + 28 q^{79} - 48 q^{82} - 12 q^{88} + 24 q^{94}+O(q^{100}) $ 8 * q + 4 * q^4 - 12 * q^10 - 4 * q^16 + 24 * q^19 - 24 * q^22 - 16 * q^25 + 12 * q^31 - 16 * q^37 - 12 * q^40 + 32 * q^43 + 12 * q^58 - 24 * q^61 - 8 * q^64 + 40 * q^67 - 24 * q^73 + 28 * q^79 - 48 * q^82 - 12 * q^88 + 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.358719	+	0.621320i	−0.160424	+	0.277863i	−0.935021	−	0.354593i	$-0.884620\pi$
$5$	−0.358719	+	0.621320i	−0.160424	+	0.277863i	0.774597	+	0.632456i	$0.217953\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	0.621320	−	0.358719i	0.196479	−	0.113437i
$11$	2.59808	−	1.50000i	0.783349	−	0.452267i	−0.0542666	−	0.998526i	$-0.517282\pi$
$11$	2.59808	−	1.50000i	0.783349	−	0.452267i	0.837616	+	0.546259i	$0.183949\pi$
$12$		0			0
$13$			2.44949i			0.679366i	0.940540	+	0.339683i	$0.110320\pi$
$13$			2.44949i			0.679366i	−0.940540	+	0.339683i	$0.889680\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.95680	−	5.12132i	−0.717128	−	1.24210i	−0.962133	−	0.272581i	$-0.912123\pi$
$17$	−2.95680	−	5.12132i	−0.717128	−	1.24210i	0.245005	−	0.969522i	$-0.421211\pi$
$18$		0			0
$19$	5.12132	+	2.95680i	1.17491	+	0.678335i	0.954832	−	0.297146i	$-0.0960350\pi$
$19$	5.12132	+	2.95680i	1.17491	+	0.678335i	0.220080	+	0.975482i	$0.429368\pi$
$20$	−0.717439			−0.160424
$21$		0			0
$22$	−3.00000			−0.639602
$23$	−3.67423	−	2.12132i	−0.766131	−	0.442326i	0.0653618	−	0.997862i	$-0.479180\pi$
$23$	−3.67423	−	2.12132i	−0.766131	−	0.442326i	−0.831493	+	0.555536i	$0.812513\pi$
$24$		0			0
$25$	2.24264	+	3.88437i	0.448528	+	0.776874i
$26$	1.22474	−	2.12132i	0.240192	−	0.416025i
$27$		0			0
$28$		0			0
$29$			7.24264i			1.34492i	0.740131	+	0.672462i	$0.234763\pi$
$29$			7.24264i			1.34492i	−0.740131	+	0.672462i	$0.765237\pi$
$30$		0			0
$31$	7.86396	−	4.54026i	1.41241	−	0.815455i	0.416794	−	0.909001i	$-0.363154\pi$
$31$	7.86396	−	4.54026i	1.41241	−	0.815455i	0.995615	+	0.0935461i	$0.0298203\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$			5.91359i			1.01417i
$35$		0			0
$36$		0			0
$37$	0.121320	−	0.210133i	0.0199449	−	0.0345457i	−0.855881	−	0.517173i	$-0.826984\pi$
$37$	0.121320	−	0.210133i	0.0199449	−	0.0345457i	0.875826	+	0.482628i	$0.160318\pi$
$38$	−2.95680	−	5.12132i	−0.479656	−	0.830788i
$39$		0			0
$40$	0.621320	+	0.358719i	0.0982394	+	0.0567185i
$41$	11.8272			1.84710			0.923548	−	0.383483i	$-0.125276\pi$
$41$	11.8272			1.84710			0.923548	+	0.383483i	$0.125276\pi$
$42$		0			0
$43$	−0.242641			−0.0370024			−0.0185012	−	0.999829i	$-0.505889\pi$
$43$	−0.242641			−0.0370024			−0.0185012	+	0.999829i	$0.505889\pi$
$44$	2.59808	+	1.50000i	0.391675	+	0.226134i
$45$		0			0
$46$	2.12132	+	3.67423i	0.312772	+	0.541736i
$47$	−2.95680	+	5.12132i	−0.431293	+	0.747021i	−0.996985	−	0.0775953i	$-0.975276\pi$
$47$	−2.95680	+	5.12132i	−0.431293	+	0.747021i	0.565692	+	0.824617i	$0.308609\pi$
$48$		0			0
$49$		0			0
$50$		−	4.48528i		−	0.634315i
$51$		0			0
$52$	−2.12132	+	1.22474i	−0.294174	+	0.169842i
$53$	6.27231	−	3.62132i	0.861568	−	0.497427i	−0.00296896	−	0.999996i	$-0.500945\pi$
$53$	6.27231	−	3.62132i	0.861568	−	0.497427i	0.864537	+	0.502569i	$0.167612\pi$
$54$		0			0
$55$			2.15232i			0.290218i
$56$		0			0
$57$		0			0
$58$	3.62132	−	6.27231i	0.475503	−	0.823595i
$59$	4.03295	+	6.98528i	0.525046	+	0.909406i	0.999575	+	0.0291661i	$0.00928518\pi$
$59$	4.03295	+	6.98528i	0.525046	+	0.909406i	−0.474529	+	0.880240i	$0.657381\pi$
$60$		0			0
$61$	−0.878680	−	0.507306i	−0.112503	−	0.0649539i	0.442692	−	0.896674i	$-0.354023\pi$
$61$	−0.878680	−	0.507306i	−0.112503	−	0.0649539i	−0.555196	+	0.831720i	$0.687357\pi$
$62$	−9.08052			−1.15323
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.52192	−	0.878680i	−0.188771	−	0.108987i
$66$		0			0
$67$	5.00000	+	8.66025i	0.610847	+	1.05802i	0.991098	+	0.133135i	$0.0425044\pi$
$67$	5.00000	+	8.66025i	0.610847	+	1.05802i	−0.380251	+	0.924883i	$0.624162\pi$
$68$	2.95680	−	5.12132i	0.358564	−	0.621051i
$69$		0			0
$70$		0			0
$71$		−	1.75736i		−	0.208560i	−0.994548	−	0.104280i	$-0.966746\pi$
$71$		−	1.75736i		−	0.208560i	0.994548	−	0.104280i	$-0.0332538\pi$
$72$		0			0
$73$	1.24264	−	0.717439i	0.145440	−	0.0839699i	−0.425514	−	0.904952i	$-0.639907\pi$
$73$	1.24264	−	0.717439i	0.145440	−	0.0839699i	0.570954	+	0.820982i	$0.306573\pi$
$74$	−0.210133	+	0.121320i	−0.0244275	+	0.0141032i
$75$		0			0
$76$			5.91359i			0.678335i
$77$		0			0
$78$		0			0
$79$	1.37868	−	2.38794i	0.155114	−	0.268665i	−0.777987	−	0.628281i	$-0.783759\pi$
$79$	1.37868	−	2.38794i	0.155114	−	0.268665i	0.933100	+	0.359616i	$0.117092\pi$
$80$	−0.358719	−	0.621320i	−0.0401061	−	0.0694657i
$81$		0			0
$82$	−10.2426	−	5.91359i	−1.13111	−	0.653047i
$83$	6.63103			0.727850			0.363925	−	0.931428i	$-0.381436\pi$
$83$	6.63103			0.727850			0.363925	+	0.931428i	$0.381436\pi$
$84$		0			0
$85$	4.24264			0.460179
$86$	0.210133	+	0.121320i	0.0226592	+	0.0130823i
$87$		0			0
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$	5.19615	−	9.00000i	0.550791	−	0.953998i	−0.447427	−	0.894321i	$-0.647659\pi$
$89$	5.19615	−	9.00000i	0.550791	−	0.953998i	0.998218	−	0.0596775i	$-0.0190072\pi$
$90$		0			0
$91$		0			0
$92$		−	4.24264i		−	0.442326i
$93$		0			0
$94$	5.12132	−	2.95680i	0.528224	−	0.304970i
$95$	−3.67423	+	2.12132i	−0.376969	+	0.217643i
$96$		0			0
$97$		−	13.5592i		−	1.37673i	−0.725364	−	0.688366i	$-0.758328\pi$
$97$		−	13.5592i		−	1.37673i	0.725364	−	0.688366i	$-0.241672\pi$
$98$		0			0
$99$		0			0
$100$	−2.24264	+	3.88437i	−0.224264	+	0.388437i
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	4.75736	+	2.74666i	0.468757	+	0.270637i	0.715719	−	0.698388i	$-0.246099\pi$
$103$	4.75736	+	2.74666i	0.468757	+	0.270637i	−0.246963	+	0.969025i	$0.579432\pi$
$104$	2.44949			0.240192
$105$		0			0
$106$	−7.24264			−0.703467
$107$	9.94655	+	5.74264i	0.961569	+	0.555162i	0.896656	−	0.442729i	$-0.145990\pi$
$107$	9.94655	+	5.74264i	0.961569	+	0.555162i	0.0649133	+	0.997891i	$0.479323\pi$
$108$		0			0
$109$	−9.24264	−	16.0087i	−0.885284	−	1.53336i	−0.845387	−	0.534154i	$-0.820630\pi$
$109$	−9.24264	−	16.0087i	−0.885284	−	1.53336i	−0.0398971	−	0.999204i	$-0.512703\pi$
$110$	1.07616	−	1.86396i	0.102608	−	0.177722i
$111$		0			0
$112$		0			0
$113$			8.48528i			0.798228i	0.916901	+	0.399114i	$0.130682\pi$
$113$			8.48528i			0.798228i	−0.916901	+	0.399114i	$0.869318\pi$
$114$		0			0
$115$	2.63604	−	1.52192i	0.245812	−	0.141920i
$116$	−6.27231	+	3.62132i	−0.582369	+	0.336231i
$117$		0			0
$118$		−	8.06591i		−	0.742527i
$119$		0			0
$120$		0			0
$121$	−1.00000	+	1.73205i	−0.0909091	+	0.157459i
$122$	0.507306	+	0.878680i	0.0459293	+	0.0795519i
$123$		0			0
$124$	7.86396	+	4.54026i	0.706205	+	0.407727i
$125$	−6.80511			−0.608668
$126$		0			0
$127$	3.24264			0.287738			0.143869	−	0.989597i	$-0.454046\pi$
$127$	3.24264			0.287738			0.143869	+	0.989597i	$0.454046\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	0.878680	+	1.52192i	0.0770653	+	0.133481i
$131$	−2.59808	+	4.50000i	−0.226995	+	0.393167i	−0.956916	−	0.290365i	$-0.906223\pi$
$131$	−2.59808	+	4.50000i	−0.226995	+	0.393167i	0.729921	+	0.683531i	$0.239557\pi$
$132$		0			0
$133$		0			0
$134$		−	10.0000i		−	0.863868i
$135$		0			0
$136$	−5.12132	+	2.95680i	−0.439150	+	0.253543i
$137$	2.15232	−	1.24264i	0.183885	−	0.106166i	−0.405232	−	0.914214i	$-0.632809\pi$
$137$	2.15232	−	1.24264i	0.183885	−	0.106166i	0.589117	+	0.808048i	$0.299476\pi$
$138$		0			0
$139$			0.594346i			0.0504118i	0.999682	+	0.0252059i	$0.00802413\pi$
$139$			0.594346i			0.0504118i	−0.999682	+	0.0252059i	$0.991976\pi$
$140$		0			0
$141$		0			0
$142$	−0.878680	+	1.52192i	−0.0737372	+	0.127717i
$143$	3.67423	+	6.36396i	0.307255	+	0.532181i
$144$		0			0
$145$	−4.50000	−	2.59808i	−0.373705	−	0.215758i
$146$	−1.43488			−0.118751
$147$		0			0
$148$	0.242641			0.0199449
$149$	3.04384	+	1.75736i	0.249361	+	0.143968i	0.619472	−	0.785019i	$-0.287347\pi$
$149$	3.04384	+	1.75736i	0.249361	+	0.143968i	−0.370111	+	0.928988i	$0.620680\pi$
$150$		0			0
$151$	−2.62132	−	4.54026i	−0.213320	−	0.369481i	0.739432	−	0.673232i	$-0.235094\pi$
$151$	−2.62132	−	4.54026i	−0.213320	−	0.369481i	−0.952752	+	0.303751i	$0.901761\pi$
$152$	2.95680	−	5.12132i	0.239828	−	0.415394i
$153$		0			0
$154$		0			0
$155$			6.51472i			0.523275i
$156$		0			0
$157$	−12.7279	+	7.34847i	−1.01580	+	0.586472i	−0.912884	−	0.408219i	$-0.866150\pi$
$157$	−12.7279	+	7.34847i	−1.01580	+	0.586472i	−0.102915	+	0.994690i	$0.532817\pi$
$158$	−2.38794	+	1.37868i	−0.189975	+	0.109682i
$159$		0			0
$160$			0.717439i			0.0567185i
$161$		0			0
$162$		0			0
$163$	1.12132	−	1.94218i	0.0878286	−	0.152124i	−0.818764	−	0.574130i	$-0.805341\pi$
$163$	1.12132	−	1.94218i	0.0878286	−	0.152124i	0.906593	+	0.422006i	$0.138674\pi$
$164$	5.91359	+	10.2426i	0.461774	+	0.799816i
$165$		0			0
$166$	−5.74264	−	3.31552i	−0.445715	−	0.257334i
$167$	−16.1318			−1.24832			−0.624159	−	0.781298i	$-0.714558\pi$
$167$	−16.1318			−1.24832			−0.624159	+	0.781298i	$0.714558\pi$
$168$		0			0
$169$	7.00000			0.538462
$170$	−3.67423	−	2.12132i	−0.281801	−	0.162698i
$171$		0			0
$172$	−0.121320	−	0.210133i	−0.00925059	−	0.0160225i
$173$	−10.3923	+	18.0000i	−0.790112	+	1.36851i	0.135785	+	0.990738i	$0.456644\pi$
$173$	−10.3923	+	18.0000i	−0.790112	+	1.36851i	−0.925897	+	0.377776i	$0.876689\pi$
$174$		0			0
$175$		0			0
$176$			3.00000i			0.226134i
$177$		0			0
$178$	−9.00000	+	5.19615i	−0.674579	+	0.389468i
$179$	−22.9369	+	13.2426i	−1.71439	+	0.989801i	−0.785966	+	0.618269i	$0.787834\pi$
$179$	−22.9369	+	13.2426i	−1.71439	+	0.989801i	−0.928420	+	0.371532i	$0.878833\pi$
$180$		0			0
$181$		−	11.8272i		−	0.879108i	−0.898216	−	0.439554i	$-0.855137\pi$
$181$		−	11.8272i		−	0.879108i	0.898216	−	0.439554i	$-0.144863\pi$
$182$		0			0
$183$		0			0
$184$	−2.12132	+	3.67423i	−0.156386	+	0.270868i
$185$	0.0870399	+	0.150758i	0.00639930	+	0.0110839i
$186$		0			0
$187$	−15.3640	−	8.87039i	−1.12352	−	0.648667i
$188$	−5.91359			−0.431293
$189$		0			0
$190$	4.24264			0.307794
$191$	−7.34847	−	4.24264i	−0.531717	−	0.306987i	0.209999	−	0.977702i	$-0.432654\pi$
$191$	−7.34847	−	4.24264i	−0.531717	−	0.306987i	−0.741715	+	0.670715i	$0.765987\pi$
$192$		0			0
$193$	−4.74264	−	8.21449i	−0.341383	−	0.591292i	0.643307	−	0.765608i	$-0.277562\pi$
$193$	−4.74264	−	8.21449i	−0.341383	−	0.591292i	−0.984690	+	0.174316i	$0.944229\pi$
$194$	−6.77962	+	11.7426i	−0.486748	+	0.843072i
$195$		0			0
$196$		0			0
$197$		−	26.4853i		−	1.88700i	−0.331375	−	0.943499i	$-0.607513\pi$
$197$		−	26.4853i		−	1.88700i	0.331375	−	0.943499i	$-0.392487\pi$
$198$		0			0
$199$	−19.9706	+	11.5300i	−1.41568	+	0.817341i	−0.995915	−	0.0902942i	$-0.971219\pi$
$199$	−19.9706	+	11.5300i	−1.41568	+	0.817341i	−0.419761	+	0.907635i	$0.637886\pi$
$200$	3.88437	−	2.24264i	0.274666	−	0.158579i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−4.24264	+	7.34847i	−0.296319	+	0.513239i
$206$	−2.74666	−	4.75736i	−0.191369	−	0.331461i
$207$		0			0
$208$	−2.12132	−	1.22474i	−0.147087	−	0.0849208i
$209$	17.7408			1.22716
$210$		0			0
$211$	−0.242641			−0.0167041			−0.00835204	−	0.999965i	$-0.502659\pi$
$211$	−0.242641			−0.0167041			−0.00835204	+	0.999965i	$0.502659\pi$
$212$	6.27231	+	3.62132i	0.430784	+	0.248713i
$213$		0			0
$214$	−5.74264	−	9.94655i	−0.392559	−	0.679932i
$215$	0.0870399	−	0.150758i	0.00593607	−	0.0102816i
$216$		0			0
$217$		0			0
$218$			18.4853i			1.25198i
$219$		0			0
$220$	−1.86396	+	1.07616i	−0.125668	+	0.0725546i
$221$	12.5446	−	7.24264i	0.843843	−	0.487193i
$222$		0			0
$223$		−	2.15232i		−	0.144130i	−0.997400	−	0.0720649i	$-0.977041\pi$
$223$		−	2.15232i		−	0.144130i	0.997400	−	0.0720649i	$-0.0229589\pi$
$224$		0			0
$225$		0			0
$226$	4.24264	−	7.34847i	0.282216	−	0.488813i
$227$	7.79423	+	13.5000i	0.517321	+	0.896026i	0.999798	+	0.0201176i	$0.00640405\pi$
$227$	7.79423	+	13.5000i	0.517321	+	0.896026i	−0.482476	+	0.875909i	$0.660263\pi$
$228$		0			0
$229$	12.0000	+	6.92820i	0.792982	+	0.457829i	0.841011	−	0.541017i	$-0.181961\pi$
$229$	12.0000	+	6.92820i	0.792982	+	0.457829i	−0.0480291	+	0.998846i	$0.515294\pi$
$230$	−3.04384			−0.200705
$231$		0			0
$232$	7.24264			0.475503
$233$	−16.2189	−	9.36396i	−1.06253	−	0.613453i	−0.136401	−	0.990654i	$-0.543554\pi$
$233$	−16.2189	−	9.36396i	−1.06253	−	0.613453i	−0.926132	+	0.377200i	$0.876887\pi$
$234$		0			0
$235$	−2.12132	−	3.67423i	−0.138380	−	0.239681i
$236$	−4.03295	+	6.98528i	−0.262523	+	0.454703i
$237$		0			0
$238$		0			0
$239$			12.7279i			0.823301i	0.911342	+	0.411650i	$0.135048\pi$
$239$			12.7279i			0.823301i	−0.911342	+	0.411650i	$0.864952\pi$
$240$		0			0
$241$	−6.25736	+	3.61269i	−0.403072	+	0.232714i	−0.687809	−	0.725892i	$-0.741427\pi$
$241$	−6.25736	+	3.61269i	−0.403072	+	0.232714i	0.284737	+	0.958606i	$0.408094\pi$
$242$	1.73205	−	1.00000i	0.111340	−	0.0642824i
$243$		0			0
$244$		−	1.01461i		−	0.0649539i
$245$		0			0
$246$		0			0
$247$	−7.24264	+	12.5446i	−0.460838	+	0.798195i
$248$	−4.54026	−	7.86396i	−0.288307	−	0.499362i
$249$		0			0
$250$	5.89340	+	3.40256i	0.372731	+	0.215196i
$251$	−27.4156			−1.73046			−0.865230	−	0.501375i	$-0.832828\pi$
$251$	−27.4156			−1.73046			−0.865230	+	0.501375i	$0.832828\pi$
$252$		0			0
$253$	−12.7279			−0.800198
$254$	−2.80821	−	1.62132i	−0.176203	−	0.101731i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.15232	−	3.72792i	0.134258	−	0.232541i	−0.791056	−	0.611744i	$-0.790468\pi$
$257$	2.15232	−	3.72792i	0.134258	−	0.232541i	0.925314	+	0.379203i	$0.123802\pi$
$258$		0			0
$259$		0			0
$260$		−	1.75736i		−	0.108987i
$261$		0			0
$262$	4.50000	−	2.59808i	0.278011	−	0.160510i
$263$	−13.1750	+	7.60660i	−0.812407	+	0.469043i	−0.847791	−	0.530331i	$-0.822068\pi$
$263$	−13.1750	+	7.60660i	−0.812407	+	0.469043i	0.0353843	+	0.999374i	$0.488734\pi$
$264$		0			0
$265$			5.19615i			0.319197i
$266$		0			0
$267$		0			0
$268$	−5.00000	+	8.66025i	−0.305424	+	0.529009i
$269$	−6.98975	−	12.1066i	−0.426173	−	0.738153i	0.570357	−	0.821397i	$-0.306805\pi$
$269$	−6.98975	−	12.1066i	−0.426173	−	0.738153i	−0.996529	+	0.0832447i	$0.973472\pi$
$270$		0			0
$271$	5.37868	+	3.10538i	0.326732	+	0.188639i	0.654389	−	0.756158i	$-0.272926\pi$
$271$	5.37868	+	3.10538i	0.326732	+	0.188639i	−0.327658	+	0.944797i	$0.606259\pi$
$272$	5.91359			0.358564
$273$		0			0
$274$	−2.48528			−0.150141
$275$	11.6531	+	6.72792i	0.702709	+	0.405709i
$276$		0			0
$277$	−6.48528	−	11.2328i	−0.389663	−	0.674916i	0.602741	−	0.797937i	$-0.294075\pi$
$277$	−6.48528	−	11.2328i	−0.389663	−	0.674916i	−0.992404	+	0.123021i	$0.960742\pi$
$278$	0.297173	−	0.514719i	0.0178232	−	0.0308708i
$279$		0			0
$280$		0			0
$281$			6.00000i			0.357930i	0.983855	+	0.178965i	$0.0572749\pi$
$281$			6.00000i			0.357930i	−0.983855	+	0.178965i	$0.942725\pi$
$282$		0			0
$283$	18.3640	−	10.6024i	1.09162	−	0.630250i	0.157616	−	0.987501i	$-0.449619\pi$
$283$	18.3640	−	10.6024i	1.09162	−	0.630250i	0.934008	+	0.357251i	$0.116286\pi$
$284$	1.52192	−	0.878680i	0.0903092	−	0.0521400i
$285$		0			0
$286$		−	7.34847i		−	0.434524i
$287$		0			0
$288$		0			0
$289$	−8.98528	+	15.5630i	−0.528546	+	0.915468i
$290$	2.59808	+	4.50000i	0.152564	+	0.264249i
$291$		0			0
$292$	1.24264	+	0.717439i	0.0727200	+	0.0419849i
$293$	−0.717439			−0.0419132			−0.0209566	−	0.999780i	$-0.506671\pi$
$293$	−0.717439			−0.0419132			−0.0209566	+	0.999780i	$0.506671\pi$
$294$		0			0
$295$	−5.78680			−0.336920
$296$	−0.210133	−	0.121320i	−0.0122137	−	0.00705160i
$297$		0			0
$298$	−1.75736	−	3.04384i	−0.101801	−	0.176325i
$299$	5.19615	−	9.00000i	0.300501	−	0.520483i
$300$		0			0
$301$		0			0
$302$			5.24264i			0.301680i
$303$		0			0
$304$	−5.12132	+	2.95680i	−0.293728	+	0.169584i
$305$	0.630399	−	0.363961i	0.0360965	−	0.0208403i
$306$		0			0
$307$			9.97204i			0.569134i	0.958656	+	0.284567i	$0.0918499\pi$
$307$			9.97204i			0.569134i	−0.958656	+	0.284567i	$0.908150\pi$
$308$		0			0
$309$		0			0
$310$	3.25736	−	5.64191i	0.185006	−	0.320439i
$311$	−4.47871	−	7.75736i	−0.253965	−	0.439879i	0.710649	−	0.703547i	$-0.248401\pi$
$311$	−4.47871	−	7.75736i	−0.253965	−	0.439879i	−0.964614	+	0.263667i	$0.915068\pi$
$312$		0			0
$313$	−15.9853	−	9.22911i	−0.903542	−	0.521660i	−0.0251940	−	0.999683i	$-0.508020\pi$
$313$	−15.9853	−	9.22911i	−0.903542	−	0.521660i	−0.878348	+	0.478023i	$0.841354\pi$
$314$	14.6969			0.829396
$315$		0			0
$316$	2.75736			0.155114
$317$	−1.07616	−	0.621320i	−0.0604431	−	0.0348968i	0.469474	−	0.882946i	$-0.344444\pi$
$317$	−1.07616	−	0.621320i	−0.0604431	−	0.0348968i	−0.529917	+	0.848050i	$0.677777\pi$
$318$		0			0
$319$	10.8640	+	18.8169i	0.608265	+	1.05355i
$320$	0.358719	−	0.621320i	0.0200530	−	0.0347329i
$321$		0			0
$322$		0			0
$323$		−	34.9706i		−	1.94581i
$324$		0			0
$325$	−9.51472	+	5.49333i	−0.527782	+	0.304715i
$326$	−1.94218	+	1.12132i	−0.107568	+	0.0621042i
$327$		0			0
$328$		−	11.8272i		−	0.653047i
$329$		0			0
$330$		0			0
$331$	16.7279	−	28.9736i	0.919450	−	1.59253i	0.119197	−	0.992871i	$-0.461968\pi$
$331$	16.7279	−	28.9736i	0.919450	−	1.59253i	0.800253	−	0.599663i	$-0.204699\pi$
$332$	3.31552	+	5.74264i	0.181963	+	0.315168i
$333$		0			0
$334$	13.9706	+	8.06591i	0.764435	+	0.441347i
$335$	−7.17439			−0.391979
$336$		0			0
$337$	−5.00000			−0.272367			−0.136184	−	0.990684i	$-0.543484\pi$
$337$	−5.00000			−0.272367			−0.136184	+	0.990684i	$0.543484\pi$
$338$	−6.06218	−	3.50000i	−0.329739	−	0.190375i
$339$		0			0
$340$	2.12132	+	3.67423i	0.115045	+	0.199263i
$341$	13.6208	−	23.5919i	0.737607	−	1.27757i
$342$		0			0
$343$		0			0
$344$			0.242641i			0.0130823i
$345$		0			0
$346$	18.0000	−	10.3923i	0.967686	−	0.558694i
$347$	−2.15232	+	1.24264i	−0.115542	+	0.0667084i	−0.556657	−	0.830742i	$-0.687916\pi$
$347$	−2.15232	+	1.24264i	−0.115542	+	0.0667084i	0.441115	+	0.897451i	$0.354583\pi$
$348$		0			0
$349$			2.27541i			0.121800i	0.998144	+	0.0608999i	$0.0193971\pi$
$349$			2.27541i			0.121800i	−0.998144	+	0.0608999i	$0.980603\pi$
$350$		0			0
$351$		0			0
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	−4.47871	−	7.75736i	−0.238378	−	0.412883i	0.721871	−	0.692028i	$-0.243282\pi$
$353$	−4.47871	−	7.75736i	−0.238378	−	0.412883i	−0.960249	+	0.279145i	$0.909949\pi$
$354$		0			0
$355$	1.09188	+	0.630399i	0.0579511	+	0.0334581i
$356$	10.3923			0.550791
$357$		0			0
$358$	26.4853			1.39979
$359$	15.5885	+	9.00000i	0.822727	+	0.475002i	0.851356	−	0.524588i	$-0.175781\pi$
$359$	15.5885	+	9.00000i	0.822727	+	0.475002i	−0.0286287	+	0.999590i	$0.509114\pi$
$360$		0			0
$361$	7.98528	+	13.8309i	0.420278	+	0.727943i
$362$	−5.91359	+	10.2426i	−0.310811	+	0.538341i
$363$		0			0
$364$		0			0
$365$			1.02944i			0.0538832i
$366$		0			0
$367$	13.3492	−	7.70719i	0.696825	−	0.402312i	−0.109339	−	0.994005i	$-0.534873\pi$
$367$	13.3492	−	7.70719i	0.696825	−	0.402312i	0.806164	+	0.591693i	$0.201540\pi$
$368$	3.67423	−	2.12132i	0.191533	−	0.110581i
$369$		0			0
$370$		−	0.174080i		−	0.00904998i
$371$		0			0
$372$		0			0
$373$	14.7279	−	25.5095i	0.762583	−	1.32083i	−0.178932	−	0.983861i	$-0.557264\pi$
$373$	14.7279	−	25.5095i	0.762583	−	1.32083i	0.941515	−	0.336971i	$-0.109402\pi$
$374$	8.87039	+	15.3640i	0.458677	+	0.794452i
$375$		0			0
$376$	5.12132	+	2.95680i	0.264112	+	0.152485i
$377$	−17.7408			−0.913696
$378$		0			0
$379$	12.4853			0.641326			0.320663	−	0.947193i	$-0.396094\pi$
$379$	12.4853			0.641326			0.320663	+	0.947193i	$0.396094\pi$
$380$	−3.67423	−	2.12132i	−0.188484	−	0.108821i
$381$		0			0
$382$	4.24264	+	7.34847i	0.217072	+	0.375980i
$383$	−11.1097	+	19.2426i	−0.567681	+	0.983253i	0.429113	+	0.903251i	$0.358826\pi$
$383$	−11.1097	+	19.2426i	−0.567681	+	0.983253i	−0.996795	+	0.0800023i	$0.974507\pi$
$384$		0			0
$385$		0			0
$386$			9.48528i			0.482788i
$387$		0			0
$388$	11.7426	−	6.77962i	0.596142	−	0.344183i
$389$	27.2416	−	15.7279i	1.38120	−	0.797437i	0.388900	−	0.921280i	$-0.372855\pi$
$389$	27.2416	−	15.7279i	1.38120	−	0.797437i	0.992302	+	0.123843i	$0.0395218\pi$
$390$		0			0
$391$			25.0892i			1.26882i
$392$		0			0
$393$		0			0
$394$	−13.2426	+	22.9369i	−0.667155	+	1.15555i
$395$	0.989118	+	1.71320i	0.0497680	+	0.0862006i
$396$		0			0
$397$	−12.0000	−	6.92820i	−0.602263	−	0.347717i	0.167668	−	0.985843i	$-0.446376\pi$
$397$	−12.0000	−	6.92820i	−0.602263	−	0.347717i	−0.769931	+	0.638127i	$0.779710\pi$
$398$	23.0600			1.15589
$399$		0			0
$400$	−4.48528			−0.224264
$401$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$401$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$402$		0			0
$403$	11.1213	+	19.2627i	0.553992	+	0.959543i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	0.727922i		−	0.0360818i
$408$		0			0
$409$	−12.9853	+	7.49706i	−0.642081	+	0.370706i	−0.785416	−	0.618969i	$-0.787551\pi$
$409$	−12.9853	+	7.49706i	−0.642081	+	0.370706i	0.143335	+	0.989674i	$0.454217\pi$
$410$	7.34847	−	4.24264i	0.362915	−	0.209529i
$411$		0			0
$412$			5.49333i			0.270637i
$413$		0			0
$414$		0			0
$415$	−2.37868	+	4.11999i	−0.116765	+	0.202243i
$416$	1.22474	+	2.12132i	0.0600481	+	0.104006i
$417$		0			0
$418$	−15.3640	−	8.87039i	−0.751476	−	0.433865i
$419$	23.6544			1.15559			0.577796	−	0.816181i	$-0.303913\pi$
$419$	23.6544			1.15559			0.577796	+	0.816181i	$0.303913\pi$
$420$		0			0
$421$	−14.2426			−0.694144			−0.347072	−	0.937839i	$-0.612824\pi$
$421$	−14.2426			−0.694144			−0.347072	+	0.937839i	$0.612824\pi$
$422$	0.210133	+	0.121320i	0.0102291	+	0.00590578i
$423$		0			0
$424$	−3.62132	−	6.27231i	−0.175867	−	0.304610i
$425$	13.2621	−	22.9706i	0.643304	−	1.11424i
$426$		0			0
$427$		0			0
$428$			11.4853i			0.555162i
$429$		0			0
$430$	−0.150758	+	0.0870399i	−0.00727018	+	0.00419744i
$431$	3.04384	−	1.75736i	0.146616	−	0.0846490i	−0.424897	−	0.905242i	$-0.639690\pi$
$431$	3.04384	−	1.75736i	0.146616	−	0.0846490i	0.571514	+	0.820593i	$0.306356\pi$
$432$		0			0
$433$			3.46410i			0.166474i	0.996530	+	0.0832370i	$0.0265259\pi$
$433$			3.46410i			0.166474i	−0.996530	+	0.0832370i	$0.973474\pi$
$434$		0			0
$435$		0			0
$436$	9.24264	−	16.0087i	0.442642	−	0.766679i
$437$	−12.5446	−	21.7279i	−0.600091	−	1.03939i
$438$		0			0
$439$	14.5919	+	8.42463i	0.696433	+	0.402086i	0.806017	−	0.591892i	$-0.201619\pi$
$439$	14.5919	+	8.42463i	0.696433	+	0.402086i	−0.109585	+	0.993977i	$0.534952\pi$
$440$	2.15232			0.102608
$441$		0			0
$442$	−14.4853			−0.688995
$443$	14.2512	+	8.22792i	0.677094	+	0.390920i	0.798759	−	0.601651i	$-0.205490\pi$
$443$	14.2512	+	8.22792i	0.677094	+	0.390920i	−0.121665	+	0.992571i	$0.538823\pi$
$444$		0			0
$445$	3.72792	+	6.45695i	0.176720	+	0.306089i
$446$	−1.07616	+	1.86396i	−0.0509576	+	0.0882611i
$447$		0			0
$448$		0			0
$449$		−	1.75736i		−	0.0829349i	−0.999140	−	0.0414675i	$-0.986797\pi$
$449$		−	1.75736i		−	0.0829349i	0.999140	−	0.0414675i	$-0.0132033\pi$
$450$		0			0
$451$	30.7279	−	17.7408i	1.44692	−	0.835380i
$452$	−7.34847	+	4.24264i	−0.345643	+	0.199557i
$453$		0			0
$454$		−	15.5885i		−	0.731603i
$455$		0			0
$456$		0			0
$457$	11.5000	−	19.9186i	0.537947	−	0.931752i	−0.461067	−	0.887365i	$-0.652533\pi$
$457$	11.5000	−	19.9186i	0.537947	−	0.931752i	0.999014	−	0.0443868i	$-0.0141334\pi$
$458$	−6.92820	−	12.0000i	−0.323734	−	0.560723i
$459$		0			0
$460$	2.63604	+	1.52192i	0.122906	+	0.0709598i
$461$	32.6118			1.51888			0.759441	−	0.650576i	$-0.225472\pi$
$461$	32.6118			1.51888			0.759441	+	0.650576i	$0.225472\pi$
$462$		0			0
$463$	−29.4558			−1.36893			−0.684465	−	0.729046i	$-0.739964\pi$
$463$	−29.4558			−1.36893			−0.684465	+	0.729046i	$0.739964\pi$
$464$	−6.27231	−	3.62132i	−0.291185	−	0.168116i
$465$		0			0
$466$	9.36396	+	16.2189i	0.433777	+	0.751324i
$467$	19.8931	−	34.4558i	0.920542	−	1.59443i	0.121965	−	0.992534i	$-0.461080\pi$
$467$	19.8931	−	34.4558i	0.920542	−	1.59443i	0.798578	−	0.601892i	$-0.205586\pi$
$468$		0			0
$469$		0			0
$470$			4.24264i			0.195698i
$471$		0			0
$472$	6.98528	−	4.03295i	0.321524	−	0.185632i
$473$	−0.630399	+	0.363961i	−0.0289858	+	0.0167349i
$474$		0			0
$475$			26.5241i			1.21701i
$476$		0			0
$477$		0			0
$478$	6.36396	−	11.0227i	0.291081	−	0.504167i
$479$	6.00063	+	10.3934i	0.274176	+	0.474886i	0.969927	−	0.243397i	$-0.0782616\pi$
$479$	6.00063	+	10.3934i	0.274176	+	0.474886i	−0.695751	+	0.718283i	$0.744928\pi$
$480$		0			0
$481$	0.514719	+	0.297173i	0.0234691	+	0.0135499i
$482$	7.22538			0.329107
$483$		0			0
$484$	−2.00000			−0.0909091
$485$	8.42463	+	4.86396i	0.382543	+	0.220861i
$486$		0			0
$487$	7.10660	+	12.3090i	0.322031	+	0.557774i	0.980907	−	0.194478i	$-0.0623012\pi$
$487$	7.10660	+	12.3090i	0.322031	+	0.557774i	−0.658876	+	0.752251i	$0.728968\pi$
$488$	−0.507306	+	0.878680i	−0.0229647	+	0.0397760i
$489$		0			0
$490$		0			0
$491$		−	13.9706i		−	0.630483i	−0.949012	−	0.315241i	$-0.897915\pi$
$491$		−	13.9706i		−	0.630483i	0.949012	−	0.315241i	$-0.102085\pi$
$492$		0			0
$493$	37.0919	−	21.4150i	1.67053	−	0.964483i
$494$	12.5446	−	7.24264i	0.564409	−	0.325862i
$495$		0			0
$496$			9.08052i			0.407727i
$497$		0			0
$498$		0			0
$499$	−15.9706	+	27.6618i	−0.714941	+	1.23831i	0.248042	+	0.968749i	$0.420213\pi$
$499$	−15.9706	+	27.6618i	−0.714941	+	1.23831i	−0.962982	+	0.269564i	$0.913120\pi$
$500$	−3.40256	−	5.89340i	−0.152167	−	0.263561i
$501$		0			0
$502$	23.7426	+	13.7078i	1.05969	+	0.611810i
$503$	−31.0028			−1.38235			−0.691174	−	0.722688i	$-0.742906\pi$
$503$	−31.0028			−1.38235			−0.691174	+	0.722688i	$0.742906\pi$
$504$		0			0
$505$		0			0
$506$	11.0227	+	6.36396i	0.490019	+	0.282913i
$507$		0			0
$508$	1.62132	+	2.80821i	0.0719345	+	0.124594i
$509$	8.59871	−	14.8934i	0.381131	−	0.660138i	−0.610093	−	0.792330i	$-0.708868\pi$
$509$	8.59871	−	14.8934i	0.381131	−	0.660138i	0.991224	+	0.132191i	$0.0422013\pi$
$510$		0			0
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−3.72792	+	2.15232i	−0.164432	+	0.0949346i
$515$	−3.41311	+	1.97056i	−0.150400	+	0.0868334i
$516$		0			0
$517$			17.7408i			0.780238i
$518$		0			0
$519$		0			0
$520$	−0.878680	+	1.52192i	−0.0385327	+	0.0667405i
$521$	−16.9363	−	29.3345i	−0.741993	−	1.28517i	−0.951587	−	0.307380i	$-0.900548\pi$
$521$	−16.9363	−	29.3345i	−0.741993	−	1.28517i	0.209594	−	0.977788i	$-0.432786\pi$
$522$		0			0
$523$	−5.84924	−	3.37706i	−0.255770	−	0.147669i	0.366634	−	0.930365i	$-0.380510\pi$
$523$	−5.84924	−	3.37706i	−0.255770	−	0.147669i	−0.622403	+	0.782697i	$0.713844\pi$
$524$	−5.19615			−0.226995
$525$		0			0
$526$	15.2132			0.663327
$527$	−46.5043	−	26.8492i	−2.02576	−	1.16957i
$528$		0			0
$529$	−2.50000	−	4.33013i	−0.108696	−	0.188266i
$530$	2.59808	−	4.50000i	0.112853	−	0.195468i
$531$		0			0
$532$		0			0
$533$			28.9706i			1.25485i
$534$		0			0
$535$	−7.13604	+	4.11999i	−0.308518	+	0.178123i
$536$	8.66025	−	5.00000i	0.374066	−	0.215967i
$537$		0			0
$538$			13.9795i			0.602699i
$539$		0			0
$540$		0			0
$541$	−7.36396	+	12.7548i	−0.316601	+	0.548370i	−0.979777	−	0.200094i	$-0.935875\pi$
$541$	−7.36396	+	12.7548i	−0.316601	+	0.548370i	0.663175	+	0.748464i	$0.269208\pi$
$542$	−3.10538	−	5.37868i	−0.133388	−	0.231034i
$543$		0			0
$544$	−5.12132	−	2.95680i	−0.219575	−	0.126772i
$545$	13.2621			0.568084
$546$		0			0
$547$	−39.6985			−1.69738			−0.848692	−	0.528887i	$-0.822610\pi$
$547$	−39.6985			−1.69738			−0.848692	+	0.528887i	$0.822610\pi$
$548$	2.15232	+	1.24264i	0.0919424	+	0.0530830i
$549$		0			0
$550$	−6.72792	−	11.6531i	−0.286880	−	0.496890i
$551$	−21.4150	+	37.0919i	−0.912310	+	1.58017i
$552$		0			0
$553$		0			0
$554$			12.9706i			0.551066i
$555$		0			0
$556$	−0.514719	+	0.297173i	−0.0218289	+	0.0126029i
$557$	−8.42463	+	4.86396i	−0.356963	+	0.206093i	−0.667748	−	0.744388i	$-0.732741\pi$
$557$	−8.42463	+	4.86396i	−0.356963	+	0.206093i	0.310785	+	0.950480i	$0.399408\pi$
$558$		0			0
$559$		−	0.594346i		−	0.0251382i
$560$		0			0
$561$		0			0
$562$	3.00000	−	5.19615i	0.126547	−	0.219186i
$563$	17.2950	+	29.9558i	0.728898	+	1.26249i	0.957349	+	0.288933i	$0.0933005\pi$
$563$	17.2950	+	29.9558i	0.728898	+	1.26249i	−0.228451	+	0.973555i	$0.573366\pi$
$564$		0			0
$565$	−5.27208	−	3.04384i	−0.221798	−	0.128055i
$566$	−21.2049			−0.891307
$567$		0			0
$568$	−1.75736			−0.0737372
$569$	8.87039	+	5.12132i	0.371866	+	0.214697i	0.674273	−	0.738482i	$-0.264457\pi$
$569$	8.87039	+	5.12132i	0.371866	+	0.214697i	−0.302407	+	0.953179i	$0.597790\pi$
$570$		0			0
$571$	−4.36396	−	7.55860i	−0.182626	−	0.316318i	0.760148	−	0.649750i	$-0.225126\pi$
$571$	−4.36396	−	7.55860i	−0.182626	−	0.316318i	−0.942774	+	0.333432i	$0.891793\pi$
$572$	−3.67423	+	6.36396i	−0.153627	+	0.266091i
$573$		0			0
$574$		0			0
$575$		−	19.0294i		−	0.793582i
$576$		0			0
$577$	−9.25736	+	5.34474i	−0.385389	+	0.222504i	−0.680160	−	0.733063i	$-0.738090\pi$
$577$	−9.25736	+	5.34474i	−0.385389	+	0.222504i	0.294771	+	0.955568i	$0.404757\pi$
$578$	15.5630	−	8.98528i	0.647334	−	0.373738i
$579$		0			0
$580$		−	5.19615i		−	0.215758i
$581$		0			0
$582$		0			0
$583$	10.8640	−	18.8169i	0.449939	−	0.779318i
$584$	−0.717439	−	1.24264i	−0.0296878	−	0.0514208i
$585$		0			0
$586$	0.621320	+	0.358719i	0.0256665	+	0.0148186i
$587$	5.19615			0.214468			0.107234	−	0.994234i	$-0.465801\pi$
$587$	5.19615			0.214468			0.107234	+	0.994234i	$0.465801\pi$
$588$		0			0
$589$	53.6985			2.21261
$590$	5.01151	+	2.89340i	0.206321	+	0.119119i
$591$		0			0
$592$	0.121320	+	0.210133i	0.00498624	+	0.00863641i
$593$	−11.7401	+	20.3345i	−0.482110	+	0.835039i	−0.999789	−	0.0205360i	$-0.993463\pi$
$593$	−11.7401	+	20.3345i	−0.482110	+	0.835039i	0.517679	+	0.855575i	$0.326796\pi$
$594$		0			0
$595$		0			0
$596$			3.51472i			0.143968i
$597$		0			0
$598$	−9.00000	+	5.19615i	−0.368037	+	0.212486i
$599$	6.45695	−	3.72792i	0.263824	−	0.152319i	−0.362254	−	0.932079i	$-0.617993\pi$
$599$	6.45695	−	3.72792i	0.263824	−	0.152319i	0.626078	+	0.779761i	$0.284659\pi$
$600$		0			0
$601$		−	23.3572i		−	0.952760i	−0.879240	−	0.476380i	$-0.841949\pi$
$601$		−	23.3572i		−	0.952760i	0.879240	−	0.476380i	$-0.158051\pi$
$602$		0			0
$603$		0			0
$604$	2.62132	−	4.54026i	0.106660	−	0.184741i
$605$	−0.717439	−	1.24264i	−0.0291680	−	0.0505205i
$606$		0			0
$607$	17.3787	+	10.0336i	0.705379	+	0.407251i	0.809348	−	0.587330i	$-0.199821\pi$
$607$	17.3787	+	10.0336i	0.705379	+	0.407251i	−0.103969	+	0.994581i	$0.533154\pi$
$608$	5.91359			0.239828
$609$		0			0
$610$	−0.727922			−0.0294727
$611$	−12.5446	−	7.24264i	−0.507501	−	0.293006i
$612$		0			0
$613$	18.6066	+	32.2276i	0.751514	+	1.30166i	0.947089	+	0.320971i	$0.104009\pi$
$613$	18.6066	+	32.2276i	0.751514	+	1.30166i	−0.195575	+	0.980689i	$0.562657\pi$
$614$	4.98602	−	8.63604i	0.201219	−	0.348522i
$615$		0			0
$616$		0			0
$617$		−	17.6985i		−	0.712514i	−0.934388	−	0.356257i	$-0.884053\pi$
$617$		−	17.6985i		−	0.712514i	0.934388	−	0.356257i	$-0.115947\pi$
$618$		0			0
$619$	−5.33452	+	3.07989i	−0.214413	+	0.123791i	−0.603360	−	0.797469i	$-0.706172\pi$
$619$	−5.33452	+	3.07989i	−0.214413	+	0.123791i	0.388948	+	0.921260i	$0.372839\pi$
$620$	−5.64191	+	3.25736i	−0.226585	+	0.130819i
$621$		0			0
$622$			8.95743i			0.359160i
$623$		0			0
$624$		0			0
$625$	−8.77208	+	15.1937i	−0.350883	+	0.607747i
$626$	9.22911	+	15.9853i	0.368869	+	0.638900i
$627$		0			0
$628$	−12.7279	−	7.34847i	−0.507899	−	0.293236i
$629$	−1.43488			−0.0572123
$630$		0			0
$631$	24.7574			0.985575			0.492787	−	0.870150i	$-0.335978\pi$
$631$	24.7574			0.985575			0.492787	+	0.870150i	$0.335978\pi$
$632$	−2.38794	−	1.37868i	−0.0949873	−	0.0548409i
$633$		0			0
$634$	0.621320	+	1.07616i	0.0246758	+	0.0427397i
$635$	−1.16320	+	2.01472i	−0.0461601	+	0.0799517i
$636$		0			0
$637$		0			0
$638$		−	21.7279i		−	0.860217i
$639$		0			0
$640$	−0.621320	+	0.358719i	−0.0245598	+	0.0141796i
$641$	15.3273	−	8.84924i	0.605393	−	0.349524i	−0.165767	−	0.986165i	$-0.553010\pi$
$641$	15.3273	−	8.84924i	0.605393	−	0.349524i	0.771160	+	0.636641i	$0.219677\pi$
$642$		0			0
$643$		−	32.0174i		−	1.26264i	−0.775520	−	0.631322i	$-0.782512\pi$
$643$		−	32.0174i		−	1.26264i	0.775520	−	0.631322i	$-0.217488\pi$
$644$		0			0
$645$		0			0
$646$	−17.4853	+	30.2854i	−0.687949	+	1.19156i
$647$	−16.2189	−	28.0919i	−0.637629	−	1.10441i	−0.985952	−	0.167031i	$-0.946582\pi$
$647$	−16.2189	−	28.0919i	−0.637629	−	1.10441i	0.348323	−	0.937375i	$-0.386751\pi$
$648$		0			0
$649$	20.9558	+	12.0989i	0.822589	+	0.474922i
$650$	10.9867			0.430932
$651$		0			0
$652$	2.24264			0.0878286
$653$	−16.6646	−	9.62132i	−0.652137	−	0.376511i	0.137138	−	0.990552i	$-0.456210\pi$
$653$	−16.6646	−	9.62132i	−0.652137	−	0.376511i	−0.789274	+	0.614041i	$0.789543\pi$
$654$		0			0
$655$	−1.86396	−	3.22848i	−0.0728310	−	0.126147i
$656$	−5.91359	+	10.2426i	−0.230887	+	0.399908i
$657$		0			0
$658$		0			0
$659$			6.00000i			0.233727i	0.993148	+	0.116863i	$0.0372840\pi$
$659$			6.00000i			0.233727i	−0.993148	+	0.116863i	$0.962716\pi$
$660$		0			0
$661$	−30.8787	+	17.8278i	−1.20104	+	0.693422i	−0.960787	−	0.277288i	$-0.910564\pi$
$661$	−30.8787	+	17.8278i	−1.20104	+	0.693422i	−0.240255	+	0.970710i	$0.577231\pi$
$662$	−28.9736	+	16.7279i	−1.12609	+	0.650149i
$663$		0			0
$664$		−	6.63103i		−	0.257334i
$665$		0			0
$666$		0			0
$667$	15.3640	−	26.6112i	0.594895	−	1.03039i
$668$	−8.06591	−	13.9706i	−0.312079	−	0.540537i
$669$		0			0
$670$	6.21320	+	3.58719i	0.240037	+	0.138585i
$671$	−3.04384			−0.117506
$672$		0			0
$673$	17.9706			0.692714			0.346357	−	0.938103i	$-0.387419\pi$
$673$	17.9706			0.692714			0.346357	+	0.938103i	$0.387419\pi$
$674$	4.33013	+	2.50000i	0.166790	+	0.0962964i
$675$		0			0
$676$	3.50000	+	6.06218i	0.134615	+	0.233161i
$677$	1.07616	−	1.86396i	0.0413601	−	0.0716378i	−0.844604	−	0.535391i	$-0.820164\pi$
$677$	1.07616	−	1.86396i	0.0413601	−	0.0716378i	0.885964	+	0.463753i	$0.153498\pi$
$678$		0			0
$679$		0			0
$680$		−	4.24264i		−	0.162698i
$681$		0			0
$682$	−23.5919	+	13.6208i	−0.903380	+	0.521567i
$683$	6.90271	−	3.98528i	0.264125	−	0.152493i	−0.362090	−	0.932143i	$-0.617937\pi$
$683$	6.90271	−	3.98528i	0.264125	−	0.152493i	0.626215	+	0.779651i	$0.284603\pi$
$684$		0			0
$685$			1.78304i			0.0681264i
$686$		0			0
$687$		0			0
$688$	0.121320	−	0.210133i	0.00462529	−	0.00801125i
$689$	8.87039	+	15.3640i	0.337935	+	0.585320i
$690$		0			0
$691$	−24.7279	−	14.2767i	−0.940694	−	0.543110i	−0.0505165	−	0.998723i	$-0.516087\pi$
$691$	−24.7279	−	14.2767i	−0.940694	−	0.543110i	−0.890178	+	0.455613i	$0.849420\pi$
$692$	−20.7846			−0.790112
$693$		0			0
$694$	2.48528			0.0943400
$695$	−0.369279	−	0.213203i	−0.0140076	−	0.00808727i
$696$		0			0
$697$	−34.9706	−	60.5708i	−1.32460	−	2.29428i
$698$	1.13770	−	1.97056i	0.0430628	−	0.0745869i
$699$		0			0
$700$		0			0
$701$			20.6985i			0.781771i	0.920439	+	0.390885i	$0.127831\pi$
$701$			20.6985i			0.781771i	−0.920439	+	0.390885i	$0.872169\pi$
$702$		0			0
$703$	1.24264	−	0.717439i	0.0468671	−	0.0270587i
$704$	−2.59808	+	1.50000i	−0.0979187	+	0.0565334i
$705$		0			0
$706$			8.95743i			0.337117i
$707$		0			0
$708$		0			0
$709$	−13.4853	+	23.3572i	−0.506450	+	0.877198i	0.493522	+	0.869733i	$0.335709\pi$
$709$	−13.4853	+	23.3572i	−0.506450	+	0.877198i	−0.999972	+	0.00746433i	$0.997624\pi$
$710$	−0.630399	−	1.09188i	−0.0236585	−	0.0409776i
$711$		0			0
$712$	−9.00000	−	5.19615i	−0.337289	−	0.194734i
$713$	−38.5254			−1.44279
$714$		0			0
$715$	−5.27208			−0.197165
$716$	−22.9369	−	13.2426i	−0.857193	−	0.494901i
$717$		0			0
$718$	−9.00000	−	15.5885i	−0.335877	−	0.581756i
$719$	−8.06591	+	13.9706i	−0.300808	+	0.521014i	−0.976319	−	0.216335i	$-0.930590\pi$
$719$	−8.06591	+	13.9706i	−0.300808	+	0.521014i	0.675511	+	0.737349i	$0.263923\pi$
$720$		0			0
$721$		0			0
$722$		−	15.9706i		−	0.594363i
$723$		0			0
$724$	10.2426	−	5.91359i	0.380665	−	0.219777i
$725$	−28.1331	+	16.2426i	−1.04484	+	0.603237i
$726$		0			0
$727$			11.7041i			0.434081i	0.976163	+	0.217040i	$0.0696403\pi$
$727$			11.7041i			0.434081i	−0.976163	+	0.217040i	$0.930360\pi$
$728$		0			0
$729$		0			0
$730$	0.514719	−	0.891519i	0.0190506	−	0.0329966i
$731$	0.717439	+	1.24264i	0.0265354	+	0.0459607i
$732$		0			0
$733$	−4.09188	−	2.36245i	−0.151137	−	0.0872591i	0.422524	−	0.906352i	$-0.361144\pi$
$733$	−4.09188	−	2.36245i	−0.151137	−	0.0872591i	−0.573661	+	0.819093i	$0.694477\pi$
$734$	−15.4144			−0.568955
$735$		0			0
$736$	−4.24264			−0.156386
$737$	25.9808	+	15.0000i	0.957014	+	0.552532i
$738$		0			0
$739$	−7.72792	−	13.3852i	−0.284276	−	0.492381i	0.688157	−	0.725562i	$-0.258420\pi$
$739$	−7.72792	−	13.3852i	−0.284276	−	0.492381i	−0.972433	+	0.233181i	$0.925087\pi$
$740$	−0.0870399	+	0.150758i	−0.00319965	+	0.00554196i
$741$		0			0
$742$		0			0
$743$			38.4853i			1.41189i	0.708268	+	0.705944i	$0.249477\pi$
$743$			38.4853i			1.41189i	−0.708268	+	0.705944i	$0.750523\pi$
$744$		0			0
$745$	−2.18377	+	1.26080i	−0.0800070	+	0.0461921i
$746$	−25.5095	+	14.7279i	−0.933969	+	0.539228i
$747$		0			0
$748$		−	17.7408i		−	0.648667i
$749$		0			0
$750$		0			0
$751$	−17.6213	+	30.5210i	−0.643011	+	1.11373i	0.341746	+	0.939792i	$0.388982\pi$
$751$	−17.6213	+	30.5210i	−0.643011	+	1.11373i	−0.984757	+	0.173936i	$0.944352\pi$
$752$	−2.95680	−	5.12132i	−0.107823	−	0.186755i
$753$		0			0
$754$	15.3640	+	8.87039i	0.559522	+	0.323040i
$755$	3.76127			0.136887
$756$		0			0
$757$	−33.7574			−1.22693			−0.613466	−	0.789721i	$-0.710225\pi$
$757$	−33.7574			−1.22693			−0.613466	+	0.789721i	$0.710225\pi$
$758$	−10.8126	−	6.24264i	−0.392730	−	0.226743i
$759$		0			0
$760$	2.12132	+	3.67423i	0.0769484	+	0.133278i
$761$	−14.7840	+	25.6066i	−0.535919	+	0.928239i	0.463199	+	0.886254i	$0.346701\pi$
$761$	−14.7840	+	25.6066i	−0.535919	+	0.928239i	−0.999118	+	0.0419845i	$0.986632\pi$
$762$		0			0
$763$		0			0
$764$		−	8.48528i		−	0.306987i
$765$		0			0
$766$	19.2426	−	11.1097i	0.695265	−	0.401411i
$767$	−17.1104	+	9.87868i	−0.617820	+	0.356698i
$768$		0			0
$769$		−	9.84895i		−	0.355162i	−0.984106	−	0.177581i	$-0.943173\pi$
$769$		−	9.84895i		−	0.355162i	0.984106	−	0.177581i	$-0.0568272\pi$
$770$		0			0
$771$		0			0
$772$	4.74264	−	8.21449i	0.170691	−	0.295646i
$773$	8.06591	+	13.9706i	0.290111	+	0.502486i	0.973836	−	0.227253i	$-0.0729746\pi$
$773$	8.06591	+	13.9706i	0.290111	+	0.502486i	−0.683725	+	0.729740i	$0.739641\pi$
$774$		0			0
$775$	35.2721	+	20.3643i	1.26701	+	0.731509i
$776$	−13.5592			−0.486748
$777$		0			0
$778$	−31.4558			−1.12775
$779$	60.5708	+	34.9706i	2.17017	+	1.25295i
$780$		0			0
$781$	−2.63604	−	4.56575i	−0.0943249	−	0.163376i
$782$	12.5446	−	21.7279i	0.448595	−	0.776989i
$783$		0			0
$784$		0			0
$785$		−	10.5442i		−	0.376337i
$786$		0			0
$787$	−27.8787	+	16.0958i	−0.993768	+	0.573752i	−0.906398	−	0.422424i	$-0.861179\pi$
$787$	−27.8787	+	16.0958i	−0.993768	+	0.573752i	−0.0873693	+	0.996176i	$0.527846\pi$
$788$	22.9369	−	13.2426i	0.817094	−	0.471750i
$789$		0			0
$790$		−	1.97824i		−	0.0703825i
$791$		0			0
$792$		0			0
$793$	1.24264	−	2.15232i	0.0441275	−	0.0764310i
$794$	6.92820	+	12.0000i	0.245873	+	0.425864i
$795$		0			0
$796$	−19.9706	−	11.5300i	−0.707838	−	0.408670i
$797$	6.45695			0.228717			0.114358	−	0.993440i	$-0.463519\pi$
$797$	6.45695			0.228717			0.114358	+	0.993440i	$0.463519\pi$
$798$		0			0
$799$	34.9706			1.23717
$800$	3.88437	+	2.24264i	0.137333	+	0.0792893i
$801$		0			0
$802$		0			0
$803$	2.15232	−	3.72792i	0.0759536	−	0.131556i
$804$		0			0
$805$		0			0
$806$		−	22.2426i		−	0.783464i
$807$		0			0
$808$		0			0
$809$	6.08767	−	3.51472i	0.214031	−	0.123571i	−0.389152	−	0.921173i	$-0.627232\pi$
$809$	6.08767	−	3.51472i	0.214031	−	0.123571i	0.603183	+	0.797602i	$0.293899\pi$
$810$		0			0
$811$		−	31.1769i		−	1.09477i	−0.836881	−	0.547385i	$-0.815623\pi$
$811$		−	31.1769i		−	1.09477i	0.836881	−	0.547385i	$-0.184377\pi$
$812$		0			0
$813$		0			0
$814$	−0.363961	+	0.630399i	−0.0127568	+	0.0220955i
$815$	0.804479	+	1.39340i	0.0281797	+	0.0488086i
$816$		0			0
$817$	−1.24264	−	0.717439i	−0.0434745	−	0.0251000i
$818$	14.9941			0.524257
$819$		0			0
$820$	−8.48528			−0.296319
$821$	−35.2969	−	20.3787i	−1.23187	−	0.711221i	−0.264451	−	0.964399i	$-0.585191\pi$
$821$	−35.2969	−	20.3787i	−1.23187	−	0.711221i	−0.967420	+	0.253178i	$0.918524\pi$
$822$		0			0
$823$	−14.9706	−	25.9298i	−0.521841	−	0.903855i	−0.999677	−	0.0254062i	$-0.991912\pi$
$823$	−14.9706	−	25.9298i	−0.521841	−	0.903855i	0.477836	−	0.878449i	$-0.341421\pi$
$824$	2.74666	−	4.75736i	0.0956845	−	0.165730i
$825$		0			0
$826$		0			0
$827$			37.9706i			1.32037i	0.751105	+	0.660183i	$0.229521\pi$
$827$			37.9706i			1.32037i	−0.751105	+	0.660183i	$0.770479\pi$
$828$		0			0
$829$	−11.3345	+	6.54399i	−0.393664	+	0.227282i	−0.683747	−	0.729720i	$-0.739651\pi$
$829$	−11.3345	+	6.54399i	−0.393664	+	0.227282i	0.290082	+	0.957002i	$0.406317\pi$
$830$	4.11999	−	2.37868i	0.143007	−	0.0825652i
$831$		0			0
$832$		−	2.44949i		−	0.0849208i
$833$		0			0
$834$		0			0
$835$	5.78680	−	10.0230i	0.200260	−	0.346861i
$836$	8.87039	+	15.3640i	0.306789	+	0.531374i
$837$		0			0
$838$	−20.4853	−	11.8272i	−0.707652	−	0.408563i
$839$	10.2182			0.352772			0.176386	−	0.984321i	$-0.443559\pi$
$839$	10.2182			0.352772			0.176386	+	0.984321i	$0.443559\pi$
$840$		0			0
$841$	−23.4558			−0.808822
$842$	12.3345	+	7.12132i	0.425075	+	0.245417i
$843$		0			0
$844$	−0.121320	−	0.210133i	−0.00417602	−	0.00723308i
$845$	−2.51104	+	4.34924i	−0.0863823	+	0.149618i
$846$		0			0
$847$		0			0
$848$			7.24264i			0.248713i
$849$		0			0
$850$	−22.9706	+	13.2621i	−0.787884	+	0.454885i
$851$	−0.891519	+	0.514719i	−0.0305609	+	0.0176443i
$852$		0			0
$853$		−	36.9164i		−	1.26399i	−0.774971	−	0.631997i	$-0.782235\pi$
$853$		−	36.9164i		−	1.26399i	0.774971	−	0.631997i	$-0.217765\pi$
$854$		0			0
$855$		0			0
$856$	5.74264	−	9.94655i	0.196279	−	0.339966i
$857$	16.9363	+	29.3345i	0.578533	+	1.00205i	0.995648	+	0.0931946i	$0.0297079\pi$
$857$	16.9363	+	29.3345i	0.578533	+	1.00205i	−0.417115	+	0.908854i	$0.636959\pi$
$858$		0			0
$859$	−8.12132	−	4.68885i	−0.277096	−	0.159981i	0.355012	−	0.934862i	$-0.384477\pi$
$859$	−8.12132	−	4.68885i	−0.277096	−	0.159981i	−0.632108	+	0.774880i	$0.717810\pi$
$860$	0.174080			0.00593607
$861$		0			0
$862$	−3.51472			−0.119712
$863$	−29.0246	−	16.7574i	−0.988009	−	0.570427i	−0.0833303	−	0.996522i	$-0.526556\pi$
$863$	−29.0246	−	16.7574i	−0.988009	−	0.570427i	−0.904679	+	0.426095i	$0.859889\pi$
$864$		0			0
$865$	−7.45584	−	12.9139i	−0.253506	−	0.439086i
$866$	1.73205	−	3.00000i	0.0588575	−	0.101944i
$867$		0			0
$868$		0			0
$869$		−	8.27208i		−	0.280611i
$870$		0			0
$871$	−21.2132	+	12.2474i	−0.718782	+	0.414989i
$872$	−16.0087	+	9.24264i	−0.542124	+	0.312995i
$873$		0			0
$874$			25.0892i			0.848656i
$875$		0			0
$876$		0			0
$877$	−2.24264	+	3.88437i	−0.0757286	+	0.131166i	−0.901403	−	0.432981i	$-0.857462\pi$
$877$	−2.24264	+	3.88437i	−0.0757286	+	0.131166i	0.825674	+	0.564147i	$0.190795\pi$
$878$	−8.42463	−	14.5919i	−0.284317	−	0.492452i
$879$		0			0
$880$	−1.86396	−	1.07616i	−0.0628341	−	0.0362773i
$881$	19.0016			0.640179			0.320090	−	0.947387i	$-0.396287\pi$
$881$	19.0016			0.640179			0.320090	+	0.947387i	$0.396287\pi$
$882$		0			0
$883$	41.4558			1.39510			0.697550	−	0.716536i	$-0.254273\pi$
$883$	41.4558			1.39510			0.697550	+	0.716536i	$0.254273\pi$
$884$	12.5446	+	7.24264i	0.421921	+	0.243596i
$885$		0			0
$886$	−8.22792	−	14.2512i	−0.276422	−	0.478778i
$887$	5.28319	−	9.15076i	0.177392	−	0.307252i	−0.763594	−	0.645696i	$-0.776567\pi$
$887$	5.28319	−	9.15076i	0.177392	−	0.307252i	0.940987	+	0.338444i	$0.109901\pi$
$888$		0			0
$889$		0			0
$890$		−	7.45584i		−	0.249920i
$891$		0			0
$892$	1.86396	−	1.07616i	0.0624100	−	0.0360324i
$893$	−30.2854	+	17.4853i	−1.01346	+	0.585123i
$894$		0			0
$895$		−	19.0016i		−	0.635153i
$896$		0			0
$897$		0			0
$898$	−0.878680	+	1.52192i	−0.0293219	+	0.0507871i
$899$	32.8835	+	56.9558i	1.09673	+	1.89958i
$900$		0			0
$901$	−37.0919	−	21.4150i	−1.23571	−	0.713437i
$902$	−35.4815			−1.18141
$903$		0			0
$904$	8.48528			0.282216
$905$	7.34847	+	4.24264i	0.244271	+	0.141030i
$906$		0			0
$907$	15.8492	+	27.4517i	0.526265	+	0.911519i	0.999532	+	0.0305991i	$0.00974151\pi$
$907$	15.8492	+	27.4517i	0.526265	+	0.911519i	−0.473266	+	0.880919i	$0.656925\pi$
$908$	−7.79423	+	13.5000i	−0.258661	+	0.448013i
$909$		0			0
$910$		0			0
$911$		−	6.72792i		−	0.222906i	−0.993770	−	0.111453i	$-0.964450\pi$
$911$		−	6.72792i		−	0.222906i	0.993770	−	0.111453i	$-0.0355505\pi$
$912$		0			0
$913$	17.2279	−	9.94655i	0.570161	−	0.329183i
$914$	−19.9186	+	11.5000i	−0.658848	+	0.380386i
$915$		0			0
$916$			13.8564i			0.457829i
$917$		0			0
$918$		0			0
$919$	−18.2426	+	31.5972i	−0.601769	+	1.04229i	0.390784	+	0.920482i	$0.372204\pi$
$919$	−18.2426	+	31.5972i	−0.601769	+	1.04229i	−0.992553	+	0.121812i	$0.961129\pi$
$920$	−1.52192	−	2.63604i	−0.0501761	−	0.0869076i
$921$		0			0
$922$	−28.2426	−	16.3059i	−0.930122	−	0.537006i
$923$	4.30463			0.141689
$924$		0			0
$925$	1.08831			0.0357835
$926$	25.5095	+	14.7279i	0.838294	+	0.483990i
$927$		0			0
$928$	3.62132	+	6.27231i	0.118876	+	0.205899i
$929$	−15.5014	+	26.8492i	−0.508585	+	0.880895i	0.491366	+	0.870953i	$0.336498\pi$
$929$	−15.5014	+	26.8492i	−0.508585	+	0.880895i	−0.999951	+	0.00994164i	$0.996835\pi$
$930$		0			0
$931$		0			0
$932$		−	18.7279i		−	0.613453i
$933$		0			0
$934$	−34.4558	+	19.8931i	−1.12743	+	0.650922i
$935$	11.0227	−	6.36396i	0.360481	−	0.208124i
$936$		0			0
$937$			35.1844i			1.14942i	0.818356	+	0.574712i	$0.194886\pi$
$937$			35.1844i			1.14942i	−0.818356	+	0.574712i	$0.805114\pi$
$938$		0			0
$939$		0			0
$940$	2.12132	−	3.67423i	0.0691898	−	0.119840i
$941$	13.7949	+	23.8934i	0.449700	+	0.778903i	0.998366	−	0.0571387i	$-0.0181977\pi$
$941$	13.7949	+	23.8934i	0.449700	+	0.778903i	−0.548667	+	0.836041i	$0.684864\pi$
$942$		0			0
$943$	−43.4558	−	25.0892i	−1.41512	−	0.817018i
$944$	−8.06591			−0.262523
$945$		0			0
$946$	0.727922			0.0236668
$947$	9.50079	+	5.48528i	0.308734	+	0.178248i	0.646360	−	0.763033i	$-0.276291\pi$
$947$	9.50079	+	5.48528i	0.308734	+	0.178248i	−0.337626	+	0.941280i	$0.609624\pi$
$948$		0			0
$949$	1.75736	+	3.04384i	0.0570463	+	0.0988071i
$950$	13.2621	−	22.9706i	0.430278	−	0.745263i
$951$		0			0
$952$		0			0
$953$		−	17.6985i		−	0.573310i	−0.958034	−	0.286655i	$-0.907457\pi$
$953$		−	17.6985i		−	0.573310i	0.958034	−	0.286655i	$-0.0925434\pi$
$954$		0			0
$955$	5.27208	−	3.04384i	0.170600	−	0.0984962i
$956$	−11.0227	+	6.36396i	−0.356500	+	0.205825i
$957$		0			0
$958$		−	12.0013i		−	0.387743i
$959$		0			0
$960$		0			0
$961$	25.7279	−	44.5621i	0.829933	−	1.43749i
$962$	−0.297173	−	0.514719i	−0.00958124	−	0.0165952i
$963$		0			0
$964$	−6.25736	−	3.61269i	−0.201536	−	0.116357i
$965$	6.80511			0.219064
$966$		0			0
$967$	47.7279			1.53483			0.767413	−	0.641153i	$-0.221544\pi$
$967$	47.7279			1.53483			0.767413	+	0.641153i	$0.221544\pi$
$968$	1.73205	+	1.00000i	0.0556702	+	0.0321412i
$969$		0			0
$970$	−4.86396	−	8.42463i	−0.156172	−	0.270498i
$971$	13.5337	−	23.4411i	0.434318	−	0.752262i	−0.562921	−	0.826510i	$-0.690323\pi$
$971$	13.5337	−	23.4411i	0.434318	−	0.752262i	0.997240	+	0.0742490i	$0.0236559\pi$
$972$		0			0
$973$		0			0
$974$		−	14.2132i		−	0.455420i
$975$		0			0
$976$	0.878680	−	0.507306i	0.0281259	−	0.0162385i
$977$	34.8511	−	20.1213i	1.11499	−	0.643738i	0.174871	−	0.984591i	$-0.444049\pi$
$977$	34.8511	−	20.1213i	1.11499	−	0.643738i	0.940116	+	0.340853i	$0.110716\pi$
$978$		0			0
$979$		−	31.1769i		−	0.996419i
$980$		0			0
$981$		0			0
$982$	−6.98528	+	12.0989i	−0.222909	+	0.386090i
$983$	−23.6544	−	40.9706i	−0.754457	−	1.30676i	−0.945644	−	0.325204i	$-0.894567\pi$
$983$	−23.6544	−	40.9706i	−0.754457	−	1.30676i	0.191187	−	0.981554i	$-0.438766\pi$
$984$		0			0
$985$	16.4558	+	9.50079i	0.524327	+	0.302720i
$986$	−42.8300			−1.36399
$987$		0			0
$988$	−14.4853			−0.460838
$989$	0.891519	+	0.514719i	0.0283486	+	0.0163671i
$990$		0			0
$991$	−26.1066	−	45.2180i	−0.829304	−	1.43640i	−0.898585	−	0.438799i	$-0.855404\pi$
$991$	−26.1066	−	45.2180i	−0.829304	−	1.43640i	0.0692818	−	0.997597i	$-0.477929\pi$
$992$	4.54026	−	7.86396i	0.144153	−	0.249681i
$993$		0			0
$994$		0			0
$995$		−	16.5442i		−	0.524485i
$996$		0			0
$997$	33.7279	−	19.4728i	1.06817	−	0.616711i	0.140492	−	0.990082i	$-0.455132\pi$
$997$	33.7279	−	19.4728i	1.06817	−	0.616711i	0.927682	+	0.373371i	$0.121798\pi$
$998$	27.6618	−	15.9706i	0.875620	−	0.505539i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.k.a.215.1		8
3.2	odd	2	inner	882.2.k.a.215.4		8
7.2	even	3		882.2.d.a.881.7		8
7.3	odd	6	inner	882.2.k.a.521.4		8
7.4	even	3		126.2.k.a.17.3	yes	8
7.5	odd	6		882.2.d.a.881.6		8
7.6	odd	2		126.2.k.a.89.2	yes	8
21.2	odd	6		882.2.d.a.881.2		8
21.5	even	6		882.2.d.a.881.3		8
21.11	odd	6		126.2.k.a.17.2	✓	8
21.17	even	6	inner	882.2.k.a.521.1		8
21.20	even	2		126.2.k.a.89.3	yes	8
28.11	odd	6		1008.2.bt.c.17.2		8
28.19	even	6		7056.2.k.f.881.3		8
28.23	odd	6		7056.2.k.f.881.5		8
28.27	even	2		1008.2.bt.c.593.3		8
35.4	even	6		3150.2.bf.a.1151.1		8
35.13	even	4		3150.2.bp.b.1349.2		8
35.18	odd	12		3150.2.bp.b.899.3		8
35.27	even	4		3150.2.bp.e.1349.3		8
35.32	odd	12		3150.2.bp.e.899.2		8
35.34	odd	2		3150.2.bf.a.1601.3		8
63.4	even	3		1134.2.l.f.269.3		8
63.11	odd	6		1134.2.t.e.1025.3		8
63.13	odd	6		1134.2.t.e.593.3		8
63.20	even	6		1134.2.l.f.215.1		8
63.25	even	3		1134.2.t.e.1025.2		8
63.32	odd	6		1134.2.l.f.269.2		8
63.34	odd	6		1134.2.l.f.215.4		8
63.41	even	6		1134.2.t.e.593.2		8
84.11	even	6		1008.2.bt.c.17.3		8
84.23	even	6		7056.2.k.f.881.4		8
84.47	odd	6		7056.2.k.f.881.6		8
84.83	odd	2		1008.2.bt.c.593.2		8
105.32	even	12		3150.2.bp.b.899.2		8
105.53	even	12		3150.2.bp.e.899.3		8
105.62	odd	4		3150.2.bp.b.1349.3		8
105.74	odd	6		3150.2.bf.a.1151.3		8
105.83	odd	4		3150.2.bp.e.1349.2		8
105.104	even	2		3150.2.bf.a.1601.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.k.a.17.2	✓	8	21.11	odd	6
126.2.k.a.17.3	yes	8	7.4	even	3
126.2.k.a.89.2	yes	8	7.6	odd	2
126.2.k.a.89.3	yes	8	21.20	even	2
882.2.d.a.881.2		8	21.2	odd	6
882.2.d.a.881.3		8	21.5	even	6
882.2.d.a.881.6		8	7.5	odd	6
882.2.d.a.881.7		8	7.2	even	3
882.2.k.a.215.1		8	1.1	even	1	trivial
882.2.k.a.215.4		8	3.2	odd	2	inner
882.2.k.a.521.1		8	21.17	even	6	inner
882.2.k.a.521.4		8	7.3	odd	6	inner
1008.2.bt.c.17.2		8	28.11	odd	6
1008.2.bt.c.17.3		8	84.11	even	6
1008.2.bt.c.593.2		8	84.83	odd	2
1008.2.bt.c.593.3		8	28.27	even	2
1134.2.l.f.215.1		8	63.20	even	6
1134.2.l.f.215.4		8	63.34	odd	6
1134.2.l.f.269.2		8	63.32	odd	6
1134.2.l.f.269.3		8	63.4	even	3
1134.2.t.e.593.2		8	63.41	even	6
1134.2.t.e.593.3		8	63.13	odd	6
1134.2.t.e.1025.2		8	63.25	even	3
1134.2.t.e.1025.3		8	63.11	odd	6
3150.2.bf.a.1151.1		8	35.4	even	6
3150.2.bf.a.1151.3		8	105.74	odd	6
3150.2.bf.a.1601.1		8	105.104	even	2
3150.2.bf.a.1601.3		8	35.34	odd	2
3150.2.bp.b.899.2		8	105.32	even	12
3150.2.bp.b.899.3		8	35.18	odd	12
3150.2.bp.b.1349.2		8	35.13	even	4
3150.2.bp.b.1349.3		8	105.62	odd	4
3150.2.bp.e.899.2		8	35.32	odd	12
3150.2.bp.e.899.3		8	105.53	even	12
3150.2.bp.e.1349.2		8	105.83	odd	4
3150.2.bp.e.1349.3		8	35.27	even	4
7056.2.k.f.881.3		8	28.19	even	6
7056.2.k.f.881.4		8	84.23	even	6
7056.2.k.f.881.5		8	28.23	odd	6
7056.2.k.f.881.6		8	84.47	odd	6

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.358719 + 0.621320i) q^{5} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.358719 + 0.621320i) q^{5} -1.00000i q^{8} +(0.621320 - 0.358719i) q^{10} +(2.59808 - 1.50000i) q^{11} +2.44949i q^{13} +(-0.500000 + 0.866025i) q^{16} +(-2.95680 - 5.12132i) q^{17} +(5.12132 + 2.95680i) q^{19} -0.717439 q^{20} -3.00000 q^{22} +(-3.67423 - 2.12132i) q^{23} +(2.24264 + 3.88437i) q^{25} +(1.22474 - 2.12132i) q^{26} +7.24264i q^{29} +(7.86396 - 4.54026i) q^{31} +(0.866025 - 0.500000i) q^{32} +5.91359i q^{34} +(0.121320 - 0.210133i) q^{37} +(-2.95680 - 5.12132i) q^{38} +(0.621320 + 0.358719i) q^{40} +11.8272 q^{41} -0.242641 q^{43} +(2.59808 + 1.50000i) q^{44} +(2.12132 + 3.67423i) q^{46} +(-2.95680 + 5.12132i) q^{47} -4.48528i q^{50} +(-2.12132 + 1.22474i) q^{52} +(6.27231 - 3.62132i) q^{53} +2.15232i q^{55} +(3.62132 - 6.27231i) q^{58} +(4.03295 + 6.98528i) q^{59} +(-0.878680 - 0.507306i) q^{61} -9.08052 q^{62} -1.00000 q^{64} +(-1.52192 - 0.878680i) q^{65} +(5.00000 + 8.66025i) q^{67} +(2.95680 - 5.12132i) q^{68} -1.75736i q^{71} +(1.24264 - 0.717439i) q^{73} +(-0.210133 + 0.121320i) q^{74} +5.91359i q^{76} +(1.37868 - 2.38794i) q^{79} +(-0.358719 - 0.621320i) q^{80} +(-10.2426 - 5.91359i) q^{82} +6.63103 q^{83} +4.24264 q^{85} +(0.210133 + 0.121320i) q^{86} +(-1.50000 - 2.59808i) q^{88} +(5.19615 - 9.00000i) q^{89} -4.24264i q^{92} +(5.12132 - 2.95680i) q^{94} +(-3.67423 + 2.12132i) q^{95} -13.5592i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 8 * q + 4 * q^4	\( 8 q + 4 q^{4} - 12 q^{10} - 4 q^{16} + 24 q^{19} - 24 q^{22} - 16 q^{25} + 12 q^{31} - 16 q^{37} - 12 q^{40} + 32 q^{43} + 12 q^{58} - 24 q^{61} - 8 q^{64} + 40 q^{67} - 24 q^{73} + 28 q^{79} - 48 q^{82} - 12 q^{88} + 24 q^{94}+O(q^{100}) \) 8 * q + 4 * q^4 - 12 * q^10 - 4 * q^16 + 24 * q^19 - 24 * q^22 - 16 * q^25 + 12 * q^31 - 16 * q^37 - 12 * q^40 + 32 * q^43 + 12 * q^58 - 24 * q^61 - 8 * q^64 + 40 * q^67 - 24 * q^73 + 28 * q^79 - 48 * q^82 - 12 * q^88 + 24 * q^94

Introduction

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