LMFDB - Embedded newform 882.2.k.a.215.3

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			215.3
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	882.215
Dual form			882.2.k.a.521.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.09077 + 3.62132i) q^{5} +1.00000i q^{8} +(-3.62132 + 2.09077i) q^{10} +(-2.59808 + 1.50000i) q^{11} -2.44949i q^{13} +(-0.500000 + 0.866025i) q^{16} +(0.507306 + 0.878680i) q^{17} +(0.878680 + 0.507306i) q^{19} -4.18154 q^{20} -3.00000 q^{22} +(-3.67423 - 2.12132i) q^{23} +(-6.24264 - 10.8126i) q^{25} +(1.22474 - 2.12132i) q^{26} +1.24264i q^{29} +(-4.86396 + 2.80821i) q^{31} +(-0.866025 + 0.500000i) q^{32} +1.01461i q^{34} +(-4.12132 + 7.13834i) q^{37} +(0.507306 + 0.878680i) q^{38} +(-3.62132 - 2.09077i) q^{40} -2.02922 q^{41} +8.24264 q^{43} +(-2.59808 - 1.50000i) q^{44} +(-2.12132 - 3.67423i) q^{46} +(0.507306 - 0.878680i) q^{47} -12.4853i q^{50} +(2.12132 - 1.22474i) q^{52} +(1.07616 - 0.621320i) q^{53} -12.5446i q^{55} +(-0.621320 + 1.07616i) q^{58} +(5.76500 + 9.98528i) q^{59} +(-5.12132 - 2.95680i) q^{61} -5.61642 q^{62} -1.00000 q^{64} +(8.87039 + 5.12132i) q^{65} +(5.00000 + 8.66025i) q^{67} +(-0.507306 + 0.878680i) q^{68} +10.2426i q^{71} +(-7.24264 + 4.18154i) q^{73} +(-7.13834 + 4.12132i) q^{74} +1.01461i q^{76} +(5.62132 - 9.73641i) q^{79} +(-2.09077 - 3.62132i) q^{80} +(-1.75736 - 1.01461i) q^{82} +3.16693 q^{83} -4.24264 q^{85} +(7.13834 + 4.12132i) q^{86} +(-1.50000 - 2.59808i) q^{88} +(-5.19615 + 9.00000i) q^{89} -4.24264i q^{92} +(0.878680 - 0.507306i) q^{94} +(-3.67423 + 2.12132i) q^{95} -3.76127i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots + 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

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
$5$	−2.09077	+	3.62132i	−0.935021	+	1.61950i	−0.160424	+	0.987048i	$0.551286\pi$
$5$	−2.09077	+	3.62132i	−0.935021	+	1.61950i	−0.774597	+	0.632456i	$0.782047\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−3.62132	+	2.09077i	−1.14516	+	0.661160i
$11$	−2.59808	+	1.50000i	−0.783349	+	0.452267i	−0.837616	−	0.546259i	$-0.816051\pi$
$11$	−2.59808	+	1.50000i	−0.783349	+	0.452267i	0.0542666	+	0.998526i	$0.482718\pi$
$12$		0			0
$13$		−	2.44949i		−	0.679366i	−0.940540	−	0.339683i	$-0.889680\pi$
$13$		−	2.44949i		−	0.679366i	0.940540	−	0.339683i	$-0.110320\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.507306	+	0.878680i	0.123040	+	0.213111i	0.920965	−	0.389645i	$-0.127402\pi$
$17$	0.507306	+	0.878680i	0.123040	+	0.213111i	−0.797925	+	0.602756i	$0.794069\pi$
$18$		0			0
$19$	0.878680	+	0.507306i	0.201583	+	0.116384i	0.597394	−	0.801948i	$-0.296203\pi$
$19$	0.878680	+	0.507306i	0.201583	+	0.116384i	−0.395811	+	0.918332i	$0.629536\pi$
$20$	−4.18154			−0.935021
$21$		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
$25$	−6.24264	−	10.8126i	−1.24853	−	2.16251i
$26$	1.22474	−	2.12132i	0.240192	−	0.416025i
$27$		0			0
$28$		0			0
$29$			1.24264i			0.230753i	0.993322	+	0.115376i	$0.0368074\pi$
$29$			1.24264i			0.230753i	−0.993322	+	0.115376i	$0.963193\pi$
$30$		0			0
$31$	−4.86396	+	2.80821i	−0.873593	+	0.504369i	−0.868541	−	0.495618i	$-0.834942\pi$
$31$	−4.86396	+	2.80821i	−0.873593	+	0.504369i	−0.00505256	+	0.999987i	$0.501608\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$			1.01461i			0.174005i
$35$		0			0
$36$		0			0
$37$	−4.12132	+	7.13834i	−0.677541	+	1.17354i	0.298178	+	0.954510i	$0.403621\pi$
$37$	−4.12132	+	7.13834i	−0.677541	+	1.17354i	−0.975719	+	0.219025i	$0.929712\pi$
$38$	0.507306	+	0.878680i	0.0822959	+	0.142541i
$39$		0			0
$40$	−3.62132	−	2.09077i	−0.572581	−	0.330580i
$41$	−2.02922			−0.316912			−0.158456	−	0.987366i	$-0.550652\pi$
$41$	−2.02922			−0.316912			−0.158456	+	0.987366i	$0.550652\pi$
$42$		0			0
$43$	8.24264			1.25699			0.628495	−	0.777813i	$-0.283671\pi$
$43$	8.24264			1.25699			0.628495	+	0.777813i	$0.283671\pi$
$44$	−2.59808	−	1.50000i	−0.391675	−	0.226134i
$45$		0			0
$46$	−2.12132	−	3.67423i	−0.312772	−	0.541736i
$47$	0.507306	−	0.878680i	0.0739982	−	0.128169i	−0.826652	−	0.562713i	$-0.809757\pi$
$47$	0.507306	−	0.878680i	0.0739982	−	0.128169i	0.900650	+	0.434545i	$0.143091\pi$
$48$		0			0
$49$		0			0
$50$		−	12.4853i		−	1.76569i
$51$		0			0
$52$	2.12132	−	1.22474i	0.294174	−	0.169842i
$53$	1.07616	−	0.621320i	0.147822	−	0.0853449i	−0.424265	−	0.905538i	$-0.639467\pi$
$53$	1.07616	−	0.621320i	0.147822	−	0.0853449i	0.572087	+	0.820193i	$0.306134\pi$
$54$		0			0
$55$		−	12.5446i		−	1.69152i
$56$		0			0
$57$		0			0
$58$	−0.621320	+	1.07616i	−0.0815834	+	0.141307i
$59$	5.76500	+	9.98528i	0.750540	+	1.29997i	0.947561	+	0.319574i	$0.103540\pi$
$59$	5.76500	+	9.98528i	0.750540	+	1.29997i	−0.197022	+	0.980399i	$0.563127\pi$
$60$		0			0
$61$	−5.12132	−	2.95680i	−0.655718	−	0.378579i	0.134926	−	0.990856i	$-0.456920\pi$
$61$	−5.12132	−	2.95680i	−0.655718	−	0.378579i	−0.790643	+	0.612277i	$0.790254\pi$
$62$	−5.61642			−0.713286
$63$		0			0
$64$	−1.00000			−0.125000
$65$	8.87039	+	5.12132i	1.10024	+	0.635222i
$66$		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	$0.624162\pi$
$68$	−0.507306	+	0.878680i	−0.0615199	+	0.106556i
$69$		0			0
$70$		0			0
$71$			10.2426i			1.21558i	0.794099	+	0.607789i	$0.207943\pi$
$71$			10.2426i			1.21558i	−0.794099	+	0.607789i	$0.792057\pi$
$72$		0			0
$73$	−7.24264	+	4.18154i	−0.847687	+	0.489412i	−0.859870	−	0.510513i	$-0.829455\pi$
$73$	−7.24264	+	4.18154i	−0.847687	+	0.489412i	0.0121828	+	0.999926i	$0.496122\pi$
$74$	−7.13834	+	4.12132i	−0.829815	+	0.479094i
$75$		0			0
$76$			1.01461i			0.116384i
$77$		0			0
$78$		0			0
$79$	5.62132	−	9.73641i	0.632448	−	1.09543i	−0.354602	−	0.935017i	$-0.615384\pi$
$79$	5.62132	−	9.73641i	0.632448	−	1.09543i	0.987050	−	0.160415i	$-0.0512831\pi$
$80$	−2.09077	−	3.62132i	−0.233755	−	0.404876i
$81$		0			0
$82$	−1.75736	−	1.01461i	−0.194068	−	0.112045i
$83$	3.16693			0.347616			0.173808	−	0.984780i	$-0.444393\pi$
$83$	3.16693			0.347616			0.173808	+	0.984780i	$0.444393\pi$
$84$		0			0
$85$	−4.24264			−0.460179
$86$	7.13834	+	4.12132i	0.769747	+	0.444413i
$87$		0			0
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$	−5.19615	+	9.00000i	−0.550791	+	0.953998i	0.447427	+	0.894321i	$0.352341\pi$
$89$	−5.19615	+	9.00000i	−0.550791	+	0.953998i	−0.998218	+	0.0596775i	$0.980993\pi$
$90$		0			0
$91$		0			0
$92$		−	4.24264i		−	0.442326i
$93$		0			0
$94$	0.878680	−	0.507306i	0.0906289	−	0.0523246i
$95$	−3.67423	+	2.12132i	−0.376969	+	0.217643i
$96$		0			0
$97$		−	3.76127i		−	0.381900i	−0.981600	−	0.190950i	$-0.938843\pi$
$97$		−	3.76127i		−	0.381900i	0.981600	−	0.190950i	$-0.0611568\pi$
$98$		0			0
$99$		0			0
$100$	6.24264	−	10.8126i	0.624264	−	1.08126i
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	13.2426	+	7.64564i	1.30484	+	0.753348i	0.981229	−	0.192844i	$-0.0617712\pi$
$103$	13.2426	+	7.64564i	1.30484	+	0.753348i	0.323607	+	0.946192i	$0.395105\pi$
$104$	2.44949			0.240192
$105$		0			0
$106$	1.24264			0.120696
$107$	4.75039	+	2.74264i	0.459238	+	0.265141i	0.711724	−	0.702459i	$-0.247915\pi$
$107$	4.75039	+	2.74264i	0.459238	+	0.265141i	−0.252486	+	0.967601i	$0.581248\pi$
$108$		0			0
$109$	−0.757359	−	1.31178i	−0.0725419	−	0.125646i	0.827473	−	0.561506i	$-0.189778\pi$
$109$	−0.757359	−	1.31178i	−0.0725419	−	0.125646i	−0.900015	+	0.435860i	$0.856444\pi$
$110$	6.27231	−	10.8640i	0.598041	−	1.03584i
$111$		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
$115$	15.3640	−	8.87039i	1.43270	−	0.827168i
$116$	−1.07616	+	0.621320i	−0.0999188	+	0.0576881i
$117$		0			0
$118$			11.5300i			1.06142i
$119$		0			0
$120$		0			0
$121$	−1.00000	+	1.73205i	−0.0909091	+	0.157459i
$122$	−2.95680	−	5.12132i	−0.267696	−	0.463663i
$123$		0			0
$124$	−4.86396	−	2.80821i	−0.436797	−	0.252185i
$125$	31.3000			2.79956
$126$		0			0
$127$	−5.24264			−0.465209			−0.232605	−	0.972571i	$-0.574725\pi$
$127$	−5.24264			−0.465209			−0.232605	+	0.972571i	$0.574725\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	5.12132	+	8.87039i	0.449170	+	0.777984i
$131$	2.59808	−	4.50000i	0.226995	−	0.393167i	−0.729921	−	0.683531i	$-0.760443\pi$
$131$	2.59808	−	4.50000i	0.226995	−	0.393167i	0.956916	+	0.290365i	$0.0937766\pi$
$132$		0			0
$133$		0			0
$134$			10.0000i			0.863868i
$135$		0			0
$136$	−0.878680	+	0.507306i	−0.0753462	+	0.0435011i
$137$	12.5446	−	7.24264i	1.07176	−	0.618781i	0.143098	−	0.989709i	$-0.454294\pi$
$137$	12.5446	−	7.24264i	1.07176	−	0.618781i	0.928662	+	0.370928i	$0.120960\pi$
$138$		0			0
$139$			20.1903i			1.71252i	0.516549	+	0.856258i	$0.327217\pi$
$139$			20.1903i			1.71252i	−0.516549	+	0.856258i	$0.672783\pi$
$140$		0			0
$141$		0			0
$142$	−5.12132	+	8.87039i	−0.429772	+	0.744386i
$143$	3.67423	+	6.36396i	0.307255	+	0.532181i
$144$		0			0
$145$	−4.50000	−	2.59808i	−0.373705	−	0.215758i
$146$	−8.36308			−0.692134
$147$		0			0
$148$	−8.24264			−0.677541
$149$	−17.7408	−	10.2426i	−1.45338	−	0.839110i	−0.454709	−	0.890640i	$-0.650257\pi$
$149$	−17.7408	−	10.2426i	−1.45338	−	0.839110i	−0.998671	+	0.0515300i	$0.983590\pi$
$150$		0			0
$151$	1.62132	+	2.80821i	0.131941	+	0.228529i	0.924425	−	0.381364i	$-0.124546\pi$
$151$	1.62132	+	2.80821i	0.131941	+	0.228529i	−0.792484	+	0.609893i	$0.791212\pi$
$152$	−0.507306	+	0.878680i	−0.0411479	+	0.0712703i
$153$		0			0
$154$		0			0
$155$		−	23.4853i		−	1.88638i
$156$		0			0
$157$	12.7279	−	7.34847i	1.01580	−	0.586472i	0.102915	−	0.994690i	$-0.467183\pi$
$157$	12.7279	−	7.34847i	1.01580	−	0.586472i	0.912884	+	0.408219i	$0.133850\pi$
$158$	9.73641	−	5.62132i	0.774587	−	0.447208i
$159$		0			0
$160$		−	4.18154i		−	0.330580i
$161$		0			0
$162$		0			0
$163$	−3.12132	+	5.40629i	−0.244481	+	0.423453i	−0.961985	−	0.273101i	$-0.911951\pi$
$163$	−3.12132	+	5.40629i	−0.244481	+	0.423453i	0.717505	+	0.696554i	$0.245284\pi$
$164$	−1.01461	−	1.75736i	−0.0792279	−	0.137227i
$165$		0			0
$166$	2.74264	+	1.58346i	0.212870	+	0.122901i
$167$	−23.0600			−1.78444			−0.892219	−	0.451603i	$-0.850852\pi$
$167$	−23.0600			−1.78444			−0.892219	+	0.451603i	$0.850852\pi$
$168$		0			0
$169$	7.00000			0.538462
$170$	−3.67423	−	2.12132i	−0.281801	−	0.162698i
$171$		0			0
$172$	4.12132	+	7.13834i	0.314248	+	0.544293i
$173$	10.3923	−	18.0000i	0.790112	−	1.36851i	−0.135785	−	0.990738i	$-0.543356\pi$
$173$	10.3923	−	18.0000i	0.790112	−	1.36851i	0.925897	−	0.377776i	$-0.123311\pi$
$174$		0			0
$175$		0			0
$176$		−	3.00000i		−	0.226134i
$177$		0			0
$178$	−9.00000	+	5.19615i	−0.674579	+	0.389468i
$179$	8.23999	−	4.75736i	0.615886	−	0.355582i	−0.159380	−	0.987217i	$-0.550949\pi$
$179$	8.23999	−	4.75736i	0.615886	−	0.355582i	0.775265	+	0.631636i	$0.217616\pi$
$180$		0			0
$181$		−	2.02922i		−	0.150831i	−0.997152	−	0.0754155i	$-0.975972\pi$
$181$		−	2.02922i		−	0.150831i	0.997152	−	0.0754155i	$-0.0240283\pi$
$182$		0			0
$183$		0			0
$184$	2.12132	−	3.67423i	0.156386	−	0.270868i
$185$	−17.2335	−	29.8492i	−1.26703	−	2.19456i
$186$		0			0
$187$	−2.63604	−	1.52192i	−0.192766	−	0.111294i
$188$	1.01461			0.0739982
$189$		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
$193$	3.74264	+	6.48244i	0.269401	+	0.466617i	0.968707	−	0.248206i	$-0.0798409\pi$
$193$	3.74264	+	6.48244i	0.269401	+	0.466617i	−0.699306	+	0.714822i	$0.746508\pi$
$194$	1.88064	−	3.25736i	0.135022	−	0.233865i
$195$		0			0
$196$		0			0
$197$			9.51472i			0.677896i	0.940805	+	0.338948i	$0.110071\pi$
$197$			9.51472i			0.677896i	−0.940805	+	0.338948i	$0.889929\pi$
$198$		0			0
$199$	13.9706	−	8.06591i	0.990347	−	0.571777i	0.0849690	−	0.996384i	$-0.472921\pi$
$199$	13.9706	−	8.06591i	0.990347	−	0.571777i	0.905378	+	0.424607i	$0.139588\pi$
$200$	10.8126	−	6.24264i	0.764564	−	0.441421i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	4.24264	−	7.34847i	0.296319	−	0.513239i
$206$	7.64564	+	13.2426i	0.532697	+	0.922658i
$207$		0			0
$208$	2.12132	+	1.22474i	0.147087	+	0.0849208i
$209$	−3.04384			−0.210547
$210$		0			0
$211$	8.24264			0.567447			0.283723	−	0.958906i	$-0.408430\pi$
$211$	8.24264			0.567447			0.283723	+	0.958906i	$0.408430\pi$
$212$	1.07616	+	0.621320i	0.0739109	+	0.0426725i
$213$		0			0
$214$	2.74264	+	4.75039i	0.187483	+	0.324730i
$215$	−17.2335	+	29.8492i	−1.17531	+	2.03570i
$216$		0			0
$217$		0			0
$218$		−	1.51472i		−	0.102590i
$219$		0			0
$220$	10.8640	−	6.27231i	0.732448	−	0.422879i
$221$	2.15232	−	1.24264i	0.144780	−	0.0835891i
$222$		0			0
$223$			12.5446i			0.840050i	0.907513	+	0.420025i	$0.137979\pi$
$223$			12.5446i			0.840050i	−0.907513	+	0.420025i	$0.862021\pi$
$224$		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	$-0.993596\pi$
$227$	−7.79423	−	13.5000i	−0.517321	−	0.896026i	0.482476	−	0.875909i	$-0.339737\pi$
$228$		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	$0.515294\pi$
$230$	17.7408			1.16979
$231$		0			0
$232$	−1.24264			−0.0815834
$233$	−5.82655	−	3.36396i	−0.381710	−	0.220380i	0.296852	−	0.954924i	$-0.404063\pi$
$233$	−5.82655	−	3.36396i	−0.381710	−	0.220380i	−0.678562	+	0.734543i	$0.737397\pi$
$234$		0			0
$235$	2.12132	+	3.67423i	0.138380	+	0.239681i
$236$	−5.76500	+	9.98528i	−0.375270	+	0.649986i
$237$		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
$241$	−14.7426	+	8.51167i	−0.949657	+	0.548285i	−0.892974	−	0.450108i	$-0.851386\pi$
$241$	−14.7426	+	8.51167i	−0.949657	+	0.548285i	−0.0566826	+	0.998392i	$0.518052\pi$
$242$	−1.73205	+	1.00000i	−0.111340	+	0.0642824i
$243$		0			0
$244$		−	5.91359i		−	0.378579i
$245$		0			0
$246$		0			0
$247$	1.24264	−	2.15232i	0.0790673	−	0.136949i
$248$	−2.80821	−	4.86396i	−0.178321	−	0.308862i
$249$		0			0
$250$	27.1066	+	15.6500i	1.71437	+	0.989793i
$251$	17.6177			1.11202			0.556009	−	0.831176i	$-0.312332\pi$
$251$	17.6177			1.11202			0.556009	+	0.831176i	$0.312332\pi$
$252$		0			0
$253$	12.7279			0.800198
$254$	−4.54026	−	2.62132i	−0.284881	−	0.164476i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.5446	−	21.7279i	0.782512	−	1.35535i	−0.147962	−	0.988993i	$-0.547271\pi$
$257$	12.5446	−	21.7279i	0.782512	−	1.35535i	0.930474	−	0.366358i	$-0.119395\pi$
$258$		0			0
$259$		0			0
$260$			10.2426i			0.635222i
$261$		0			0
$262$	4.50000	−	2.59808i	0.278011	−	0.160510i
$263$	−23.5673	+	13.6066i	−1.45322	+	0.839019i	−0.998663	−	0.0516967i	$-0.983537\pi$
$263$	−23.5673	+	13.6066i	−1.45322	+	0.839019i	−0.454561	+	0.890716i	$0.650204\pi$
$264$		0			0
$265$			5.19615i			0.319197i
$266$		0			0
$267$		0			0
$268$	−5.00000	+	8.66025i	−0.305424	+	0.529009i
$269$	−5.25770	−	9.10660i	−0.320568	−	0.555239i	0.660038	−	0.751232i	$-0.270540\pi$
$269$	−5.25770	−	9.10660i	−0.320568	−	0.555239i	−0.980605	+	0.195993i	$0.937207\pi$
$270$		0			0
$271$	9.62132	+	5.55487i	0.584454	+	0.337434i	0.762901	−	0.646515i	$-0.223774\pi$
$271$	9.62132	+	5.55487i	0.584454	+	0.337434i	−0.178448	+	0.983949i	$0.557108\pi$
$272$	−1.01461			−0.0615199
$273$		0			0
$274$	14.4853			0.875088
$275$	32.4377	+	18.7279i	1.95607	+	1.12934i
$276$		0			0
$277$	10.4853	+	18.1610i	0.630000	+	1.09119i	0.987551	+	0.157298i	$0.0502783\pi$
$277$	10.4853	+	18.1610i	0.630000	+	1.09119i	−0.357552	+	0.933893i	$0.616388\pi$
$278$	−10.0951	+	17.4853i	−0.605466	+	1.04870i
$279$		0			0
$280$		0			0
$281$		−	6.00000i		−	0.357930i	−0.983855	−	0.178965i	$-0.942725\pi$
$281$		−	6.00000i		−	0.357930i	0.983855	−	0.178965i	$-0.0572749\pi$
$282$		0			0
$283$	5.63604	−	3.25397i	0.335028	−	0.193428i	−0.323043	−	0.946384i	$-0.604706\pi$
$283$	5.63604	−	3.25397i	0.335028	−	0.193428i	0.658071	+	0.752956i	$0.271373\pi$
$284$	−8.87039	+	5.12132i	−0.526361	+	0.303894i
$285$		0			0
$286$			7.34847i			0.434524i
$287$		0			0
$288$		0			0
$289$	7.98528	−	13.8309i	0.469722	−	0.813583i
$290$	−2.59808	−	4.50000i	−0.152564	−	0.264249i
$291$		0			0
$292$	−7.24264	−	4.18154i	−0.423843	−	0.244706i
$293$	−4.18154			−0.244288			−0.122144	−	0.992512i	$-0.538977\pi$
$293$	−4.18154			−0.244288			−0.122144	+	0.992512i	$0.538977\pi$
$294$		0			0
$295$	−48.2132			−2.80708
$296$	−7.13834	−	4.12132i	−0.414907	−	0.239547i
$297$		0			0
$298$	−10.2426	−	17.7408i	−0.593340	−	1.02770i
$299$	−5.19615	+	9.00000i	−0.300501	+	0.520483i
$300$		0			0
$301$		0			0
$302$			3.24264i			0.186593i
$303$		0			0
$304$	−0.878680	+	0.507306i	−0.0503957	+	0.0290960i
$305$	21.4150	−	12.3640i	1.22622	−	0.707958i
$306$		0			0
$307$			24.6690i			1.40793i	0.710233	+	0.703966i	$0.248589\pi$
$307$			24.6690i			1.40793i	−0.710233	+	0.703966i	$0.751411\pi$
$308$		0			0
$309$		0			0
$310$	11.7426	−	20.3389i	0.666937	−	1.15517i
$311$	9.37769	+	16.2426i	0.531760	+	0.921036i	0.999313	+	0.0370703i	$0.0118026\pi$
$311$	9.37769	+	16.2426i	0.531760	+	0.921036i	−0.467552	+	0.883965i	$0.654864\pi$
$312$		0			0
$313$	0.985281	+	0.568852i	0.0556914	+	0.0321534i	0.527587	−	0.849501i	$-0.323097\pi$
$313$	0.985281	+	0.568852i	0.0556914	+	0.0321534i	−0.471896	+	0.881654i	$0.656430\pi$
$314$	14.6969			0.829396
$315$		0			0
$316$	11.2426			0.632448
$317$	−6.27231	−	3.62132i	−0.352288	−	0.203394i	0.313404	−	0.949620i	$-0.398530\pi$
$317$	−6.27231	−	3.62132i	−0.352288	−	0.203394i	−0.665693	+	0.746226i	$0.731864\pi$
$318$		0			0
$319$	−1.86396	−	3.22848i	−0.104362	−	0.180760i
$320$	2.09077	−	3.62132i	0.116878	−	0.202438i
$321$		0			0
$322$		0			0
$323$			1.02944i			0.0572794i
$324$		0			0
$325$	−26.4853	+	15.2913i	−1.46914	+	0.848208i
$326$	−5.40629	+	3.12132i	−0.299426	+	0.172874i
$327$		0			0
$328$		−	2.02922i		−	0.112045i
$329$		0			0
$330$		0			0
$331$	−8.72792	+	15.1172i	−0.479730	+	0.830917i	−0.999730	−	0.0232497i	$-0.992599\pi$
$331$	−8.72792	+	15.1172i	−0.479730	+	0.830917i	0.520000	+	0.854166i	$0.325932\pi$
$332$	1.58346	+	2.74264i	0.0869039	+	0.150522i
$333$		0			0
$334$	−19.9706	−	11.5300i	−1.09274	−	0.630894i
$335$	−41.8154			−2.28462
$336$		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
$341$	8.42463	−	14.5919i	0.456219	−	0.790195i
$342$		0			0
$343$		0			0
$344$			8.24264i			0.444413i
$345$		0			0
$346$	18.0000	−	10.3923i	0.967686	−	0.558694i
$347$	−12.5446	+	7.24264i	−0.673431	+	0.388805i	−0.797375	−	0.603484i	$-0.793779\pi$
$347$	−12.5446	+	7.24264i	−0.673431	+	0.388805i	0.123945	+	0.992289i	$0.460445\pi$
$348$		0			0
$349$		−	36.9164i		−	1.97609i	−0.154163	−	0.988045i	$-0.549268\pi$
$349$		−	36.9164i		−	1.97609i	0.154163	−	0.988045i	$-0.450732\pi$
$350$		0			0
$351$		0			0
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	9.37769	+	16.2426i	0.499124	+	0.864509i	0.999999	−	0.00101095i	$-0.000321796\pi$
$353$	9.37769	+	16.2426i	0.499124	+	0.864509i	−0.500875	+	0.865519i	$0.666988\pi$
$354$		0			0
$355$	−37.0919	−	21.4150i	−1.96863	−	1.13659i
$356$	−10.3923			−0.550791
$357$		0			0
$358$	9.51472			0.502869
$359$	−15.5885	−	9.00000i	−0.822727	−	0.475002i	0.0286287	−	0.999590i	$-0.490886\pi$
$359$	−15.5885	−	9.00000i	−0.822727	−	0.475002i	−0.851356	+	0.524588i	$0.824219\pi$
$360$		0			0
$361$	−8.98528	−	15.5630i	−0.472910	−	0.819103i
$362$	1.01461	−	1.75736i	0.0533268	−	0.0923648i
$363$		0			0
$364$		0			0
$365$		−	34.9706i		−	1.83044i
$366$		0			0
$367$	−16.3492	+	9.43924i	−0.853424	+	0.492724i	−0.861804	−	0.507241i	$-0.830666\pi$
$367$	−16.3492	+	9.43924i	−0.853424	+	0.492724i	0.00838099	+	0.999965i	$0.497332\pi$
$368$	3.67423	−	2.12132i	0.191533	−	0.110581i
$369$		0			0
$370$		−	34.4669i		−	1.79185i
$371$		0			0
$372$		0			0
$373$	−10.7279	+	18.5813i	−0.555471	+	0.962104i	0.442396	+	0.896820i	$0.354129\pi$
$373$	−10.7279	+	18.5813i	−0.555471	+	0.962104i	−0.997867	+	0.0652837i	$0.979205\pi$
$374$	−1.52192	−	2.63604i	−0.0786965	−	0.136306i
$375$		0			0
$376$	0.878680	+	0.507306i	0.0453144	+	0.0261623i
$377$	3.04384			0.156766
$378$		0			0
$379$	−4.48528			−0.230393			−0.115197	−	0.993343i	$-0.536750\pi$
$379$	−4.48528			−0.230393			−0.115197	+	0.993343i	$0.536750\pi$
$380$	−3.67423	−	2.12132i	−0.188484	−	0.108821i
$381$		0			0
$382$	−4.24264	−	7.34847i	−0.217072	−	0.375980i
$383$	6.21076	−	10.7574i	0.317355	−	0.549675i	−0.662580	−	0.748991i	$-0.730539\pi$
$383$	6.21076	−	10.7574i	0.317355	−	0.549675i	0.979935	+	0.199316i	$0.0638719\pi$
$384$		0			0
$385$		0			0
$386$			7.48528i			0.380991i
$387$		0			0
$388$	3.25736	−	1.88064i	0.165367	−	0.0954749i
$389$	16.8493	−	9.72792i	0.854291	−	0.493225i	−0.00780525	−	0.999970i	$-0.502485\pi$
$389$	16.8493	−	9.72792i	0.854291	−	0.493225i	0.862096	+	0.506744i	$0.169151\pi$
$390$		0			0
$391$		−	4.30463i		−	0.217695i
$392$		0			0
$393$		0			0
$394$	−4.75736	+	8.23999i	−0.239672	+	0.415125i
$395$	23.5058	+	40.7132i	1.18270	+	2.04850i
$396$		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	$0.779710\pi$
$398$	16.1318			0.808615
$399$		0			0
$400$	12.4853			0.624264
$401$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$401$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$402$		0			0
$403$	6.87868	+	11.9142i	0.342651	+	0.593490i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	24.7279i		−	1.22572i
$408$		0			0
$409$	3.98528	−	2.30090i	0.197059	−	0.113772i	−0.398224	−	0.917288i	$-0.630373\pi$
$409$	3.98528	−	2.30090i	0.197059	−	0.113772i	0.595283	+	0.803516i	$0.297040\pi$
$410$	7.34847	−	4.24264i	0.362915	−	0.209529i
$411$		0			0
$412$			15.2913i			0.753348i
$413$		0			0
$414$		0			0
$415$	−6.62132	+	11.4685i	−0.325028	+	0.562965i
$416$	1.22474	+	2.12132i	0.0600481	+	0.104006i
$417$		0			0
$418$	−2.63604	−	1.52192i	−0.128933	−	0.0744394i
$419$	−4.05845			−0.198268			−0.0991341	−	0.995074i	$-0.531607\pi$
$419$	−4.05845			−0.198268			−0.0991341	+	0.995074i	$0.531607\pi$
$420$		0			0
$421$	−5.75736			−0.280597			−0.140298	−	0.990109i	$-0.544806\pi$
$421$	−5.75736			−0.280597			−0.140298	+	0.990109i	$0.544806\pi$
$422$	7.13834	+	4.12132i	0.347489	+	0.200623i
$423$		0			0
$424$	0.621320	+	1.07616i	0.0301740	+	0.0522629i
$425$	6.33386	−	10.9706i	0.307237	−	0.532150i
$426$		0			0
$427$		0			0
$428$			5.48528i			0.265141i
$429$		0			0
$430$	−29.8492	+	17.2335i	−1.43946	+	0.831072i
$431$	−17.7408	+	10.2426i	−0.854543	+	0.493371i	−0.862181	−	0.506600i	$-0.830902\pi$
$431$	−17.7408	+	10.2426i	−0.854543	+	0.493371i	0.00763808	+	0.999971i	$0.497569\pi$
$432$		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
$436$	0.757359	−	1.31178i	0.0362709	−	0.0628231i
$437$	−2.15232	−	3.72792i	−0.102959	−	0.178331i
$438$		0			0
$439$	−23.5919	−	13.6208i	−1.12598	−	0.650084i	−0.183059	−	0.983102i	$-0.558600\pi$
$439$	−23.5919	−	13.6208i	−1.12598	−	0.650084i	−0.942921	+	0.333018i	$0.891933\pi$
$440$	12.5446			0.598041
$441$		0			0
$442$	2.48528			0.118213
$443$	29.8396	+	17.2279i	1.41772	+	0.818523i	0.996099	−	0.0882469i	$-0.0281264\pi$
$443$	29.8396	+	17.2279i	1.41772	+	0.818523i	0.421625	+	0.906770i	$0.361460\pi$
$444$		0			0
$445$	−21.7279	−	37.6339i	−1.03000	−	1.78402i
$446$	−6.27231	+	10.8640i	−0.297003	+	0.514423i
$447$		0			0
$448$		0			0
$449$			10.2426i			0.483380i	0.970354	+	0.241690i	$0.0777017\pi$
$449$			10.2426i			0.483380i	−0.970354	+	0.241690i	$0.922298\pi$
$450$		0			0
$451$	5.27208	−	3.04384i	0.248252	−	0.143329i
$452$	−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
$460$	15.3640	+	8.87039i	0.716348	+	0.413584i
$461$	−22.8138			−1.06255			−0.531273	−	0.847201i	$-0.678286\pi$
$461$	−22.8138			−1.06255			−0.531273	+	0.847201i	$0.678286\pi$
$462$		0			0
$463$	21.4558			0.997138			0.498569	−	0.866850i	$-0.333859\pi$
$463$	21.4558			0.997138			0.498569	+	0.866850i	$0.333859\pi$
$464$	−1.07616	−	0.621320i	−0.0499594	−	0.0288441i
$465$		0			0
$466$	−3.36396	−	5.82655i	−0.155832	−	0.269910i
$467$	9.50079	−	16.4558i	0.439644	−	0.761486i	−0.558018	−	0.829829i	$-0.688438\pi$
$467$	9.50079	−	16.4558i	0.439644	−	0.761486i	0.997662	+	0.0683432i	$0.0217713\pi$
$468$		0			0
$469$		0			0
$470$			4.24264i			0.195698i
$471$		0			0
$472$	−9.98528	+	5.76500i	−0.459610	+	0.265356i
$473$	−21.4150	+	12.3640i	−0.984663	+	0.568496i
$474$		0			0
$475$		−	12.6677i		−	0.581235i
$476$		0			0
$477$		0			0
$478$	−6.36396	+	11.0227i	−0.291081	+	0.504167i
$479$	−18.2481	−	31.6066i	−0.833776	−	1.44414i	−0.895023	−	0.446020i	$-0.852841\pi$
$479$	−18.2481	−	31.6066i	−0.833776	−	1.44414i	0.0612470	−	0.998123i	$-0.480492\pi$
$480$		0			0
$481$	17.4853	+	10.0951i	0.797260	+	0.460298i
$482$	−17.0233			−0.775392
$483$		0			0
$484$	−2.00000			−0.0909091
$485$	13.6208	+	7.86396i	0.618488	+	0.357084i
$486$		0			0
$487$	−14.1066	−	24.4334i	−0.639231	−	1.10718i	−0.985602	−	0.169083i	$-0.945919\pi$
$487$	−14.1066	−	24.4334i	−0.639231	−	1.10718i	0.346371	−	0.938098i	$-0.387414\pi$
$488$	2.95680	−	5.12132i	0.133848	−	0.231831i
$489$		0			0
$490$		0			0
$491$		−	19.9706i		−	0.901259i	−0.892711	−	0.450629i	$-0.851200\pi$
$491$		−	19.9706i		−	0.901259i	0.892711	−	0.450629i	$-0.148800\pi$
$492$		0			0
$493$	−1.09188	+	0.630399i	−0.0491759	+	0.0283917i
$494$	2.15232	−	1.24264i	0.0968373	−	0.0559090i
$495$		0			0
$496$		−	5.61642i		−	0.252185i
$497$		0			0
$498$		0			0
$499$	17.9706	−	31.1259i	0.804473	−	1.39339i	−0.112173	−	0.993689i	$-0.535781\pi$
$499$	17.9706	−	31.1259i	0.804473	−	1.39339i	0.916646	−	0.399699i	$-0.130885\pi$
$500$	15.6500	+	27.1066i	0.699889	+	1.21224i
$501$		0			0
$502$	15.2574	+	8.80884i	0.680969	+	0.393158i
$503$	−3.29002			−0.146695			−0.0733474	−	0.997306i	$-0.523368\pi$
$503$	−3.29002			−0.146695			−0.0733474	+	0.997306i	$0.523368\pi$
$504$		0			0
$505$		0			0
$506$	11.0227	+	6.36396i	0.490019	+	0.282913i
$507$		0			0
$508$	−2.62132	−	4.54026i	−0.116302	−	0.201441i
$509$	−20.8462	+	36.1066i	−0.923990	+	1.60040i	−0.130812	+	0.991407i	$0.541758\pi$
$509$	−20.8462	+	36.1066i	−0.923990	+	1.60040i	−0.793178	+	0.608990i	$0.791575\pi$
$510$		0			0
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	21.7279	−	12.5446i	0.958378	−	0.553320i
$515$	−55.3746	+	31.9706i	−2.44010	+	1.40879i
$516$		0			0
$517$			3.04384i			0.133868i
$518$		0			0
$519$		0			0
$520$	−5.12132	+	8.87039i	−0.224585	+	0.388992i
$521$	−10.0081	−	17.3345i	−0.438462	−	0.759439i	0.559109	−	0.829094i	$-0.311143\pi$
$521$	−10.0081	−	17.3345i	−0.438462	−	0.759439i	−0.997571	+	0.0696551i	$0.977810\pi$
$522$		0			0
$523$	23.8492	+	13.7694i	1.04285	+	0.602092i	0.920641	−	0.390411i	$-0.127667\pi$
$523$	23.8492	+	13.7694i	1.04285	+	0.602092i	0.122214	+	0.992504i	$0.461001\pi$
$524$	5.19615			0.226995
$525$		0			0
$526$	−27.2132			−1.18655
$527$	−4.93503	−	2.84924i	−0.214973	−	0.124115i
$528$		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
$533$			4.97056i			0.215299i
$534$		0			0
$535$	−19.8640	+	11.4685i	−0.858794	+	0.495825i
$536$	−8.66025	+	5.00000i	−0.374066	+	0.215967i
$537$		0			0
$538$		−	10.5154i		−	0.453351i
$539$		0			0
$540$		0			0
$541$	5.36396	−	9.29065i	0.230615	−	0.399436i	−0.727374	−	0.686241i	$-0.759260\pi$
$541$	5.36396	−	9.29065i	0.230615	−	0.399436i	0.957989	+	0.286804i	$0.0925930\pi$
$542$	5.55487	+	9.62132i	0.238602	+	0.413271i
$543$		0			0
$544$	−0.878680	−	0.507306i	−0.0376731	−	0.0217506i
$545$	6.33386			0.271313
$546$		0			0
$547$	19.6985			0.842246			0.421123	−	0.907003i	$-0.361636\pi$
$547$	19.6985			0.842246			0.421123	+	0.907003i	$0.361636\pi$
$548$	12.5446	+	7.24264i	0.535880	+	0.309390i
$549$		0			0
$550$	18.7279	+	32.4377i	0.798561	+	1.38315i
$551$	−0.630399	+	1.09188i	−0.0268559	+	0.0465158i
$552$		0			0
$553$		0			0
$554$			20.9706i			0.890954i
$555$		0			0
$556$	−17.4853	+	10.0951i	−0.741541	+	0.428129i
$557$	−13.6208	+	7.86396i	−0.577131	+	0.333207i	−0.759992	−	0.649932i	$-0.774797\pi$
$557$	−13.6208	+	7.86396i	−0.577131	+	0.333207i	0.182861	+	0.983139i	$0.441464\pi$
$558$		0			0
$559$		−	20.1903i		−	0.853957i
$560$		0			0
$561$		0			0
$562$	3.00000	−	5.19615i	0.126547	−	0.219186i
$563$	12.0989	+	20.9558i	0.509906	+	0.883184i	0.999934	+	0.0114768i	$0.00365325\pi$
$563$	12.0989	+	20.9558i	0.509906	+	0.883184i	−0.490028	+	0.871707i	$0.663013\pi$
$564$		0			0
$565$	−30.7279	−	17.7408i	−1.29273	−	0.746360i
$566$	6.50794			0.273549
$567$		0			0
$568$	−10.2426			−0.429772
$569$	−1.52192	−	0.878680i	−0.0638021	−	0.0368362i	0.467760	−	0.883856i	$-0.345061\pi$
$569$	−1.52192	−	0.878680i	−0.0638021	−	0.0368362i	−0.531562	+	0.847020i	$0.678395\pi$
$570$		0			0
$571$	8.36396	+	14.4868i	0.350021	+	0.606254i	0.986253	−	0.165244i	$-0.0528412\pi$
$571$	8.36396	+	14.4868i	0.350021	+	0.606254i	−0.636232	+	0.771498i	$0.719508\pi$
$572$	−3.67423	+	6.36396i	−0.153627	+	0.266091i
$573$		0			0
$574$		0			0
$575$			52.9706i			2.20903i
$576$		0			0
$577$	−17.7426	+	10.2437i	−0.738636	+	0.426452i	−0.821573	−	0.570103i	$-0.806903\pi$
$577$	−17.7426	+	10.2437i	−0.738636	+	0.426452i	0.0829373	+	0.996555i	$0.473570\pi$
$578$	13.8309	−	7.98528i	0.575290	−	0.332144i
$579$		0			0
$580$		−	5.19615i		−	0.215758i
$581$		0			0
$582$		0			0
$583$	−1.86396	+	3.22848i	−0.0771974	+	0.133710i
$584$	−4.18154	−	7.24264i	−0.173033	−	0.299703i
$585$		0			0
$586$	−3.62132	−	2.09077i	−0.149595	−	0.0863689i
$587$	−5.19615			−0.214468			−0.107234	−	0.994234i	$-0.534199\pi$
$587$	−5.19615			−0.214468			−0.107234	+	0.994234i	$0.534199\pi$
$588$		0			0
$589$	−5.69848			−0.234802
$590$	−41.7539	−	24.1066i	−1.71898	−	0.992453i
$591$		0			0
$592$	−4.12132	−	7.13834i	−0.169385	−	0.293384i
$593$	−15.2042	+	26.3345i	−0.624363	+	1.08143i	0.364300	+	0.931282i	$0.381308\pi$
$593$	−15.2042	+	26.3345i	−0.624363	+	1.08143i	−0.988664	+	0.150148i	$0.952025\pi$
$594$		0			0
$595$		0			0
$596$		−	20.4853i		−	0.839110i
$597$		0			0
$598$	−9.00000	+	5.19615i	−0.368037	+	0.212486i
$599$	37.6339	−	21.7279i	1.53768	−	0.887779i	0.538704	−	0.842495i	$-0.318914\pi$
$599$	37.6339	−	21.7279i	1.53768	−	0.887779i	0.998974	−	0.0452836i	$-0.0144192\pi$
$600$		0			0
$601$			6.03668i			0.246241i	0.992392	+	0.123121i	$0.0392902\pi$
$601$			6.03668i			0.246241i	−0.992392	+	0.123121i	$0.960710\pi$
$602$		0			0
$603$		0			0
$604$	−1.62132	+	2.80821i	−0.0659706	+	0.114264i
$605$	−4.18154	−	7.24264i	−0.170004	−	0.294455i
$606$		0			0
$607$	21.6213	+	12.4831i	0.877582	+	0.506672i	0.869860	−	0.493298i	$-0.164209\pi$
$607$	21.6213	+	12.4831i	0.877582	+	0.506672i	0.00772182	+	0.999970i	$0.497542\pi$
$608$	−1.01461			−0.0411479
$609$		0			0
$610$	24.7279			1.00120
$611$	−2.15232	−	1.24264i	−0.0870734	−	0.0502719i
$612$		0			0
$613$	−2.60660	−	4.51477i	−0.105280	−	0.182350i	0.808573	−	0.588396i	$-0.200240\pi$
$613$	−2.60660	−	4.51477i	−0.105280	−	0.182350i	−0.913852	+	0.406046i	$0.866907\pi$
$614$	−12.3345	+	21.3640i	−0.497779	+	0.862179i
$615$		0			0
$616$		0			0
$617$		−	41.6985i		−	1.67872i	−0.543578	−	0.839359i	$-0.682931\pi$
$617$		−	41.6985i		−	1.67872i	0.543578	−	0.839359i	$-0.317069\pi$
$618$		0			0
$619$	41.3345	−	23.8645i	1.66137	−	0.959195i	0.689315	−	0.724462i	$-0.257912\pi$
$619$	41.3345	−	23.8645i	1.66137	−	0.959195i	0.972060	−	0.234733i	$-0.0754217\pi$
$620$	20.3389	−	11.7426i	0.816828	−	0.471596i
$621$		0			0
$622$			18.7554i			0.752022i
$623$		0			0
$624$		0			0
$625$	−34.2279	+	59.2845i	−1.36912	+	2.37138i
$626$	0.568852	+	0.985281i	0.0227359	+	0.0393798i
$627$		0			0
$628$	12.7279	+	7.34847i	0.507899	+	0.293236i
$629$	−8.36308			−0.333458
$630$		0			0
$631$	33.2426			1.32337			0.661684	−	0.749783i	$-0.269842\pi$
$631$	33.2426			1.32337			0.661684	+	0.749783i	$0.269842\pi$
$632$	9.73641	+	5.62132i	0.387294	+	0.223604i
$633$		0			0
$634$	−3.62132	−	6.27231i	−0.143821	−	0.249105i
$635$	10.9612	−	18.9853i	0.434980	−	0.753408i
$636$		0			0
$637$		0			0
$638$		−	3.72792i		−	0.147590i
$639$		0			0
$640$	3.62132	−	2.09077i	0.143145	−	0.0826450i
$641$	36.1119	−	20.8492i	1.42634	−	0.823496i	0.429507	−	0.903064i	$-0.358687\pi$
$641$	36.1119	−	20.8492i	1.42634	−	0.823496i	0.996829	+	0.0795681i	$0.0253541\pi$
$642$		0			0
$643$		−	2.62357i		−	0.103463i	−0.998661	−	0.0517317i	$-0.983526\pi$
$643$		−	2.62357i		−	0.103463i	0.998661	−	0.0517317i	$-0.0164741\pi$
$644$		0			0
$645$		0			0
$646$	−0.514719	+	0.891519i	−0.0202513	+	0.0350763i
$647$	−5.82655	−	10.0919i	−0.229065	−	0.396753i	0.728466	−	0.685082i	$-0.240234\pi$
$647$	−5.82655	−	10.0919i	−0.229065	−	0.396753i	−0.957531	+	0.288329i	$0.906900\pi$
$648$		0			0
$649$	−29.9558	−	17.2950i	−1.17587	−	0.678889i
$650$	−30.5826			−1.19955
$651$		0			0
$652$	−6.24264			−0.244481
$653$	9.31615	+	5.37868i	0.364569	+	0.210484i	0.671083	−	0.741382i	$-0.265829\pi$
$653$	9.31615	+	5.37868i	0.364569	+	0.210484i	−0.306514	+	0.951866i	$0.599163\pi$
$654$		0			0
$655$	10.8640	+	18.8169i	0.424490	+	0.735238i
$656$	1.01461	−	1.75736i	0.0396139	−	0.0686134i
$657$		0			0
$658$		0			0
$659$		−	6.00000i		−	0.233727i	−0.993148	−	0.116863i	$-0.962716\pi$
$659$		−	6.00000i		−	0.233727i	0.993148	−	0.116863i	$-0.0372840\pi$
$660$		0			0
$661$	−35.1213	+	20.2773i	−1.36606	+	0.788696i	−0.990422	−	0.138071i	$-0.955910\pi$
$661$	−35.1213	+	20.2773i	−1.36606	+	0.788696i	−0.375639	+	0.926766i	$0.622577\pi$
$662$	−15.1172	+	8.72792i	−0.587547	+	0.339220i
$663$		0			0
$664$			3.16693i			0.122901i
$665$		0			0
$666$		0			0
$667$	2.63604	−	4.56575i	0.102068	−	0.176787i
$668$	−11.5300	−	19.9706i	−0.446109	−	0.772684i
$669$		0			0
$670$	−36.2132	−	20.9077i	−1.39904	−	0.807735i
$671$	17.7408			0.684875
$672$		0			0
$673$	−15.9706			−0.615620			−0.307810	−	0.951448i	$-0.599596\pi$
$673$	−15.9706			−0.615620			−0.307810	+	0.951448i	$0.599596\pi$
$674$	−4.33013	−	2.50000i	−0.166790	−	0.0962964i
$675$		0			0
$676$	3.50000	+	6.06218i	0.134615	+	0.233161i
$677$	6.27231	−	10.8640i	0.241064	−	0.417536i	−0.719953	−	0.694023i	$-0.755837\pi$
$677$	6.27231	−	10.8640i	0.241064	−	0.417536i	0.961018	+	0.276487i	$0.0891701\pi$
$678$		0			0
$679$		0			0
$680$		−	4.24264i		−	0.162698i
$681$		0			0
$682$	14.5919	−	8.42463i	0.558752	−	0.322596i
$683$	22.4912	−	12.9853i	0.860601	−	0.496868i	−0.00361277	−	0.999993i	$-0.501150\pi$
$683$	22.4912	−	12.9853i	0.860601	−	0.496868i	0.864213	+	0.503125i	$0.167817\pi$
$684$		0			0
$685$			60.5708i			2.31429i
$686$		0			0
$687$		0			0
$688$	−4.12132	+	7.13834i	−0.157124	+	0.272147i
$689$	−1.52192	−	2.63604i	−0.0579805	−	0.100425i
$690$		0			0
$691$	0.727922	+	0.420266i	0.0276915	+	0.0159877i	0.513782	−	0.857921i	$-0.328244\pi$
$691$	0.727922	+	0.420266i	0.0276915	+	0.0159877i	−0.486090	+	0.873909i	$0.661577\pi$
$692$	20.7846			0.790112
$693$		0			0
$694$	−14.4853			−0.549854
$695$	−73.1154	−	42.2132i	−2.77343	−	1.60124i
$696$		0			0
$697$	−1.02944	−	1.78304i	−0.0389927	−	0.0675374i
$698$	18.4582	−	31.9706i	0.698654	−	1.21010i
$699$		0			0
$700$		0			0
$701$			38.6985i			1.46162i	0.682580	+	0.730811i	$0.260858\pi$
$701$			38.6985i			1.46162i	−0.682580	+	0.730811i	$0.739142\pi$
$702$		0			0
$703$	−7.24264	+	4.18154i	−0.273161	+	0.157710i
$704$	2.59808	−	1.50000i	0.0979187	−	0.0565334i
$705$		0			0
$706$			18.7554i			0.705868i
$707$		0			0
$708$		0			0
$709$	3.48528	−	6.03668i	0.130892	−	0.226712i	−0.793128	−	0.609055i	$-0.791549\pi$
$709$	3.48528	−	6.03668i	0.130892	−	0.226712i	0.924021	+	0.382342i	$0.124882\pi$
$710$	−21.4150	−	37.0919i	−0.803691	−	1.39203i
$711$		0			0
$712$	−9.00000	−	5.19615i	−0.337289	−	0.194734i
$713$	23.8284			0.892382
$714$		0			0
$715$	−30.7279			−1.14916
$716$	8.23999	+	4.75736i	0.307943	+	0.177791i
$717$		0			0
$718$	−9.00000	−	15.5885i	−0.335877	−	0.581756i
$719$	−11.5300	+	19.9706i	−0.429997	+	0.744776i	−0.996872	−	0.0790270i	$-0.974819\pi$
$719$	−11.5300	+	19.9706i	−0.429997	+	0.744776i	0.566876	+	0.823803i	$0.308152\pi$
$720$		0			0
$721$		0			0
$722$		−	17.9706i		−	0.668795i
$723$		0			0
$724$	1.75736	−	1.01461i	0.0653117	−	0.0377078i
$725$	13.4361	−	7.75736i	0.499006	−	0.288101i
$726$		0			0
$727$			26.4010i			0.979160i	0.871958	+	0.489580i	$0.162850\pi$
$727$			26.4010i			0.979160i	−0.871958	+	0.489580i	$0.837150\pi$
$728$		0			0
$729$		0			0
$730$	17.4853	−	30.2854i	0.647159	−	1.12091i
$731$	4.18154	+	7.24264i	0.154660	+	0.267879i
$732$		0			0
$733$	34.0919	+	19.6830i	1.25921	+	0.727007i	0.972921	−	0.231136i	$-0.0742443\pi$
$733$	34.0919	+	19.6830i	1.25921	+	0.727007i	0.286291	+	0.958143i	$0.407578\pi$
$734$	−18.8785			−0.696817
$735$		0			0
$736$	4.24264			0.156386
$737$	−25.9808	−	15.0000i	−0.957014	−	0.552532i
$738$		0			0
$739$	17.7279	+	30.7057i	0.652132	+	1.12953i	0.982605	+	0.185710i	$0.0594586\pi$
$739$	17.7279	+	30.7057i	0.652132	+	1.12953i	−0.330472	+	0.943816i	$0.607208\pi$
$740$	17.2335	−	29.8492i	0.633515	−	1.09728i
$741$		0			0
$742$		0			0
$743$		−	21.5147i		−	0.789298i	−0.918832	−	0.394649i	$-0.870866\pi$
$743$		−	21.5147i		−	0.789298i	0.918832	−	0.394649i	$-0.129134\pi$
$744$		0			0
$745$	74.1838	−	42.8300i	2.71788	−	1.56917i
$746$	−18.5813	+	10.7279i	−0.680310	+	0.392777i
$747$		0			0
$748$		−	3.04384i		−	0.111294i
$749$		0			0
$750$		0			0
$751$	−13.3787	+	23.1726i	−0.488195	+	0.845578i	−0.999908	−	0.0135781i	$-0.995678\pi$
$751$	−13.3787	+	23.1726i	−0.488195	+	0.845578i	0.511713	+	0.859157i	$0.329011\pi$
$752$	0.507306	+	0.878680i	0.0184995	+	0.0320422i
$753$		0			0
$754$	2.63604	+	1.52192i	0.0959989	+	0.0554250i
$755$	−13.5592			−0.493471
$756$		0			0
$757$	−42.2426			−1.53533			−0.767667	−	0.640848i	$-0.778583\pi$
$757$	−42.2426			−1.53533			−0.767667	+	0.640848i	$0.778583\pi$
$758$	−3.88437	−	2.24264i	−0.141087	−	0.0814564i
$759$		0			0
$760$	−2.12132	−	3.67423i	−0.0769484	−	0.133278i
$761$	2.53653	−	4.39340i	0.0919491	−	0.159261i	−0.816382	−	0.577512i	$-0.804024\pi$
$761$	2.53653	−	4.39340i	0.0919491	−	0.159261i	0.908331	+	0.418252i	$0.137357\pi$
$762$		0			0
$763$		0			0
$764$		−	8.48528i		−	0.306987i
$765$		0			0
$766$	10.7574	−	6.21076i	0.388679	−	0.224404i
$767$	24.4588	−	14.1213i	0.883158	−	0.509891i
$768$		0			0
$769$		−	49.0408i		−	1.76846i	−0.467056	−	0.884228i	$-0.654685\pi$
$769$		−	49.0408i		−	1.76846i	0.467056	−	0.884228i	$-0.345315\pi$
$770$		0			0
$771$		0			0
$772$	−3.74264	+	6.48244i	−0.134701	+	0.233308i
$773$	11.5300	+	19.9706i	0.414706	+	0.718291i	0.995398	−	0.0958322i	$-0.0305512\pi$
$773$	11.5300	+	19.9706i	0.414706	+	0.718291i	−0.580692	+	0.814123i	$0.697218\pi$
$774$		0			0
$775$	60.7279	+	35.0613i	2.18141	+	1.25944i
$776$	3.76127			0.135022
$777$		0			0
$778$	19.4558			0.697526
$779$	−1.78304	−	1.02944i	−0.0638840	−	0.0368834i
$780$		0			0
$781$	−15.3640	−	26.6112i	−0.549766	−	0.952222i
$782$	2.15232	−	3.72792i	0.0769667	−	0.133310i
$783$		0			0
$784$		0			0
$785$			61.4558i			2.19345i
$786$		0			0
$787$	−32.1213	+	18.5453i	−1.14500	+	0.661067i	−0.947664	−	0.319269i	$-0.896563\pi$
$787$	−32.1213	+	18.5453i	−1.14500	+	0.661067i	−0.197337	+	0.980336i	$0.563229\pi$
$788$	−8.23999	+	4.75736i	−0.293537	+	0.169474i
$789$		0			0
$790$			47.0116i			1.67260i
$791$		0			0
$792$		0			0
$793$	−7.24264	+	12.5446i	−0.257194	+	0.445473i
$794$	−6.92820	−	12.0000i	−0.245873	−	0.425864i
$795$		0			0
$796$	13.9706	+	8.06591i	0.495173	+	0.285889i
$797$	37.6339			1.33306			0.666530	−	0.745478i	$-0.267779\pi$
$797$	37.6339			1.33306			0.666530	+	0.745478i	$0.267779\pi$
$798$		0			0
$799$	1.02944			0.0364189
$800$	10.8126	+	6.24264i	0.382282	+	0.220711i
$801$		0			0
$802$		0			0
$803$	12.5446	−	21.7279i	0.442690	−	0.766762i
$804$		0			0
$805$		0			0
$806$			13.7574i			0.484582i
$807$		0			0
$808$		0			0
$809$	−35.4815	+	20.4853i	−1.24746	+	0.720224i	−0.970603	−	0.240686i	$-0.922628\pi$
$809$	−35.4815	+	20.4853i	−1.24746	+	0.720224i	−0.276862	+	0.960910i	$0.589294\pi$
$810$		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
$814$	12.3640	−	21.4150i	0.433357	−	0.750596i
$815$	−13.0519	−	22.6066i	−0.457189	−	0.791875i
$816$		0			0
$817$	7.24264	+	4.18154i	0.253388	+	0.146294i
$818$	4.60181			0.160898
$819$		0			0
$820$	8.48528			0.296319
$821$	42.6454	+	24.6213i	1.48833	+	0.859290i	0.999911	−	0.0133172i	$-0.00423912\pi$
$821$	42.6454	+	24.6213i	1.48833	+	0.859290i	0.488423	+	0.872607i	$0.337572\pi$
$822$		0			0
$823$	18.9706	+	32.8580i	0.661272	+	1.14536i	0.980282	+	0.197606i	$0.0633165\pi$
$823$	18.9706	+	32.8580i	0.661272	+	1.14536i	−0.319009	+	0.947752i	$0.603350\pi$
$824$	−7.64564	+	13.2426i	−0.266349	+	0.461329i
$825$		0			0
$826$		0			0
$827$		−	4.02944i		−	0.140117i	−0.997543	−	0.0700586i	$-0.977681\pi$
$827$		−	4.02944i		−	0.140117i	0.997543	−	0.0700586i	$-0.0223186\pi$
$828$		0			0
$829$	35.3345	−	20.4004i	1.22722	−	0.708535i	0.260772	−	0.965401i	$-0.416023\pi$
$829$	35.3345	−	20.4004i	1.22722	−	0.708535i	0.966447	+	0.256865i	$0.0826897\pi$
$830$	−11.4685	+	6.62132i	−0.398076	+	0.229829i
$831$		0			0
$832$			2.44949i			0.0849208i
$833$		0			0
$834$		0			0
$835$	48.2132	−	83.5077i	1.66849	−	2.88990i
$836$	−1.52192	−	2.63604i	−0.0526366	−	0.0911693i
$837$		0			0
$838$	−3.51472	−	2.02922i	−0.121414	−	0.0700984i
$839$	24.0746			0.831149			0.415574	−	0.909559i	$-0.363581\pi$
$839$	24.0746			0.831149			0.415574	+	0.909559i	$0.363581\pi$
$840$		0			0
$841$	27.4558			0.946753
$842$	−4.98602	−	2.87868i	−0.171830	−	0.0992059i
$843$		0			0
$844$	4.12132	+	7.13834i	0.141862	+	0.245712i
$845$	−14.6354	+	25.3492i	−0.503473	+	0.872040i
$846$		0			0
$847$		0			0
$848$			1.24264i			0.0426725i
$849$		0			0
$850$	10.9706	−	6.33386i	0.376287	−	0.217250i
$851$	30.2854	−	17.4853i	1.03817	−	0.599388i
$852$		0			0
$853$			2.27541i			0.0779085i	0.999241	+	0.0389543i	$0.0124027\pi$
$853$			2.27541i			0.0779085i	−0.999241	+	0.0389543i	$0.987597\pi$
$854$		0			0
$855$		0			0
$856$	−2.74264	+	4.75039i	−0.0937415	+	0.162365i
$857$	10.0081	+	17.3345i	0.341870	+	0.592136i	0.984780	−	0.173806i	$-0.0556064\pi$
$857$	10.0081	+	17.3345i	0.341870	+	0.592136i	−0.642910	+	0.765942i	$0.722273\pi$
$858$		0			0
$859$	−3.87868	−	2.23936i	−0.132339	−	0.0764059i	0.432369	−	0.901697i	$-0.357678\pi$
$859$	−3.87868	−	2.23936i	−0.132339	−	0.0764059i	−0.564708	+	0.825291i	$0.691011\pi$
$860$	−34.4669			−1.17531
$861$		0			0
$862$	−20.4853			−0.697731
$863$	43.7215	+	25.2426i	1.48830	+	0.859269i	0.999911	−	0.0133573i	$-0.00425189\pi$
$863$	43.7215	+	25.2426i	1.48830	+	0.859269i	0.488388	+	0.872627i	$0.337585\pi$
$864$		0			0
$865$	43.4558	+	75.2677i	1.47754	+	2.55918i
$866$	−1.73205	+	3.00000i	−0.0588575	+	0.101944i
$867$		0			0
$868$		0			0
$869$			33.7279i			1.14414i
$870$		0			0
$871$	21.2132	−	12.2474i	0.718782	−	0.414989i
$872$	1.31178	−	0.757359i	0.0444226	−	0.0256474i
$873$		0			0
$874$		−	4.30463i		−	0.145606i
$875$		0			0
$876$		0			0
$877$	6.24264	−	10.8126i	0.210799	−	0.365115i	−0.741166	−	0.671322i	$-0.765727\pi$
$877$	6.24264	−	10.8126i	0.210799	−	0.365115i	0.951965	+	0.306207i	$0.0990601\pi$
$878$	−13.6208	−	23.5919i	−0.459679	−	0.796187i
$879$		0			0
$880$	10.8640	+	6.27231i	0.366224	+	0.211440i
$881$	39.7862			1.34043			0.670215	−	0.742167i	$-0.266202\pi$
$881$	39.7862			1.34043			0.670215	+	0.742167i	$0.266202\pi$
$882$		0			0
$883$	−9.45584			−0.318214			−0.159107	−	0.987261i	$-0.550862\pi$
$883$	−9.45584			−0.318214			−0.159107	+	0.987261i	$0.550862\pi$
$884$	2.15232	+	1.24264i	0.0723902	+	0.0417945i
$885$		0			0
$886$	17.2279	+	29.8396i	0.578783	+	1.00248i
$887$	−22.4296	+	38.8492i	−0.753113	+	1.30443i	0.193194	+	0.981161i	$0.438115\pi$
$887$	−22.4296	+	38.8492i	−0.753113	+	1.30443i	−0.946307	+	0.323269i	$0.895218\pi$
$888$		0			0
$889$		0			0
$890$		−	43.4558i		−	1.45664i
$891$		0			0
$892$	−10.8640	+	6.27231i	−0.363752	+	0.210012i
$893$	0.891519	−	0.514719i	0.0298335	−	0.0172244i
$894$		0			0
$895$			39.7862i			1.32991i
$896$		0			0
$897$		0			0
$898$	−5.12132	+	8.87039i	−0.170901	+	0.296009i
$899$	−3.48960	−	6.04416i	−0.116385	−	0.201584i
$900$		0			0
$901$	1.09188	+	0.630399i	0.0363759	+	0.0210016i
$902$	6.08767			0.202697
$903$		0			0
$904$	−8.48528			−0.282216
$905$	7.34847	+	4.24264i	0.244271	+	0.141030i
$906$		0			0
$907$	−13.8492	−	23.9876i	−0.459857	−	0.796495i	0.539096	−	0.842244i	$-0.318766\pi$
$907$	−13.8492	−	23.9876i	−0.459857	−	0.796495i	−0.998953	+	0.0457492i	$0.985433\pi$
$908$	7.79423	−	13.5000i	0.258661	−	0.448013i
$909$		0			0
$910$		0			0
$911$		−	18.7279i		−	0.620484i	−0.950658	−	0.310242i	$-0.899590\pi$
$911$		−	18.7279i		−	0.620484i	0.950658	−	0.310242i	$-0.100410\pi$
$912$		0			0
$913$	−8.22792	+	4.75039i	−0.272304	+	0.157215i
$914$	19.9186	−	11.5000i	0.658848	−	0.380386i
$915$		0			0
$916$			13.8564i			0.457829i
$917$		0			0
$918$		0			0
$919$	−9.75736	+	16.9002i	−0.321866	+	0.557488i	−0.980873	−	0.194649i	$-0.937643\pi$
$919$	−9.75736	+	16.9002i	−0.321866	+	0.557488i	0.659007	+	0.752136i	$0.270977\pi$
$920$	8.87039	+	15.3640i	0.292448	+	0.506535i
$921$		0			0
$922$	−19.7574	−	11.4069i	−0.650674	−	0.375667i
$923$	25.0892			0.825823
$924$		0			0
$925$	102.912			3.38372
$926$	18.5813	+	10.7279i	0.610620	+	0.352541i
$927$		0			0
$928$	−0.621320	−	1.07616i	−0.0203958	−	0.0353266i
$929$	−1.64501	+	2.84924i	−0.0539711	+	0.0934806i	−0.891749	−	0.452531i	$-0.850521\pi$
$929$	−1.64501	+	2.84924i	−0.0539711	+	0.0934806i	0.837778	+	0.546012i	$0.183855\pi$
$930$		0			0
$931$		0			0
$932$		−	6.72792i		−	0.220380i
$933$		0			0
$934$	16.4558	−	9.50079i	0.538452	−	0.310875i
$935$	11.0227	−	6.36396i	0.360481	−	0.208124i
$936$		0			0
$937$		−	4.00746i		−	0.130918i	−0.997855	−	0.0654590i	$-0.979149\pi$
$937$		−	4.00746i		−	0.130918i	0.997855	−	0.0654590i	$-0.0208512\pi$
$938$		0			0
$939$		0			0
$940$	−2.12132	+	3.67423i	−0.0691898	+	0.119840i
$941$	−26.0423	−	45.1066i	−0.848955	−	1.47043i	−0.882142	−	0.470984i	$-0.843899\pi$
$941$	−26.0423	−	45.1066i	−0.848955	−	1.47043i	0.0331867	−	0.999449i	$-0.489434\pi$
$942$		0			0
$943$	7.45584	+	4.30463i	0.242796	+	0.140178i
$944$	−11.5300			−0.375270
$945$		0			0
$946$	−24.7279			−0.803974
$947$	19.8931	+	11.4853i	0.646439	+	0.373221i	0.787090	−	0.616838i	$-0.211586\pi$
$947$	19.8931	+	11.4853i	0.646439	+	0.373221i	−0.140652	+	0.990059i	$0.544920\pi$
$948$		0			0
$949$	10.2426	+	17.7408i	0.332490	+	0.575890i
$950$	6.33386	−	10.9706i	0.205497	−	0.355932i
$951$		0			0
$952$		0			0
$953$		−	41.6985i		−	1.35075i	−0.737476	−	0.675373i	$-0.763983\pi$
$953$		−	41.6985i		−	1.35075i	0.737476	−	0.675373i	$-0.236017\pi$
$954$		0			0
$955$	30.7279	−	17.7408i	0.994332	−	0.574078i
$956$	−11.0227	+	6.36396i	−0.356500	+	0.205825i
$957$		0			0
$958$		−	36.4962i		−	1.17914i
$959$		0			0
$960$		0			0
$961$	0.272078	−	0.471253i	0.00877671	−	0.0152017i
$962$	10.0951	+	17.4853i	0.325480	+	0.563748i
$963$		0			0
$964$	−14.7426	−	8.51167i	−0.474828	−	0.274142i
$965$	−31.3000			−1.00758
$966$		0			0
$967$	22.2721			0.716222			0.358111	−	0.933679i	$-0.383421\pi$
$967$	22.2721			0.716222			0.358111	+	0.933679i	$0.383421\pi$
$968$	−1.73205	−	1.00000i	−0.0556702	−	0.0321412i
$969$		0			0
$970$	7.86396	+	13.6208i	0.252497	+	0.437337i
$971$	25.6581	−	44.4411i	0.823407	−	1.42618i	−0.0797229	−	0.996817i	$-0.525404\pi$
$971$	25.6581	−	44.4411i	0.823407	−	1.42618i	0.903130	−	0.429367i	$-0.141263\pi$
$972$		0			0
$973$		0			0
$974$		−	28.2132i		−	0.904009i
$975$		0			0
$976$	5.12132	−	2.95680i	0.163929	−	0.0946447i
$977$	−27.5027	+	15.8787i	−0.879889	+	0.508004i	−0.870622	−	0.491953i	$-0.836283\pi$
$977$	−27.5027	+	15.8787i	−0.879889	+	0.508004i	−0.00926698	+	0.999957i	$0.502950\pi$
$978$		0			0
$979$		−	31.1769i		−	0.996419i
$980$		0			0
$981$		0			0
$982$	9.98528	−	17.2950i	0.318643	−	0.551906i
$983$	4.05845	+	7.02944i	0.129444	+	0.224204i	0.923461	−	0.383691i	$-0.125347\pi$
$983$	4.05845	+	7.02944i	0.129444	+	0.224204i	−0.794017	+	0.607895i	$0.792014\pi$
$984$		0			0
$985$	−34.4558	−	19.8931i	−1.09785	−	0.633847i
$986$	−1.26080			−0.0401520
$987$		0			0
$988$	2.48528			0.0790673
$989$	−30.2854	−	17.4853i	−0.963020	−	0.556000i
$990$		0			0
$991$	−4.89340	−	8.47561i	−0.155444	−	0.269237i	0.777777	−	0.628541i	$-0.216347\pi$
$991$	−4.89340	−	8.47561i	−0.155444	−	0.269237i	−0.933221	+	0.359304i	$0.883014\pi$
$992$	2.80821	−	4.86396i	0.0891607	−	0.154431i
$993$		0			0
$994$		0			0
$995$			67.4558i			2.13849i
$996$		0			0
$997$	8.27208	−	4.77589i	0.261979	−	0.151254i	−0.363258	−	0.931689i	$-0.618336\pi$
$997$	8.27208	−	4.77589i	0.261979	−	0.151254i	0.625237	+	0.780435i	$0.285002\pi$
$998$	31.1259	−	17.9706i	0.985274	−	0.568848i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.k.a.215.3		8
3.2	odd	2	inner	882.2.k.a.215.2		8
7.2	even	3		882.2.d.a.881.4		8
7.3	odd	6	inner	882.2.k.a.521.2		8
7.4	even	3		126.2.k.a.17.1	✓	8
7.5	odd	6		882.2.d.a.881.1		8
7.6	odd	2		126.2.k.a.89.4	yes	8
21.2	odd	6		882.2.d.a.881.5		8
21.5	even	6		882.2.d.a.881.8		8
21.11	odd	6		126.2.k.a.17.4	yes	8
21.17	even	6	inner	882.2.k.a.521.3		8
21.20	even	2		126.2.k.a.89.1	yes	8
28.11	odd	6		1008.2.bt.c.17.1		8
28.19	even	6		7056.2.k.f.881.2		8
28.23	odd	6		7056.2.k.f.881.8		8
28.27	even	2		1008.2.bt.c.593.4		8
35.4	even	6		3150.2.bf.a.1151.4		8
35.13	even	4		3150.2.bp.e.1349.4		8
35.18	odd	12		3150.2.bp.e.899.1		8
35.27	even	4		3150.2.bp.b.1349.1		8
35.32	odd	12		3150.2.bp.b.899.4		8
35.34	odd	2		3150.2.bf.a.1601.2		8
63.4	even	3		1134.2.l.f.269.1		8
63.11	odd	6		1134.2.t.e.1025.1		8
63.13	odd	6		1134.2.t.e.593.1		8
63.20	even	6		1134.2.l.f.215.3		8
63.25	even	3		1134.2.t.e.1025.4		8
63.32	odd	6		1134.2.l.f.269.4		8
63.34	odd	6		1134.2.l.f.215.2		8
63.41	even	6		1134.2.t.e.593.4		8
84.11	even	6		1008.2.bt.c.17.4		8
84.23	even	6		7056.2.k.f.881.1		8
84.47	odd	6		7056.2.k.f.881.7		8
84.83	odd	2		1008.2.bt.c.593.1		8
105.32	even	12		3150.2.bp.e.899.4		8
105.53	even	12		3150.2.bp.b.899.1		8
105.62	odd	4		3150.2.bp.e.1349.1		8
105.74	odd	6		3150.2.bf.a.1151.2		8
105.83	odd	4		3150.2.bp.b.1349.4		8
105.104	even	2		3150.2.bf.a.1601.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.k.a.17.1	✓	8	7.4	even	3
126.2.k.a.17.4	yes	8	21.11	odd	6
126.2.k.a.89.1	yes	8	21.20	even	2
126.2.k.a.89.4	yes	8	7.6	odd	2
882.2.d.a.881.1		8	7.5	odd	6
882.2.d.a.881.4		8	7.2	even	3
882.2.d.a.881.5		8	21.2	odd	6
882.2.d.a.881.8		8	21.5	even	6
882.2.k.a.215.2		8	3.2	odd	2	inner
882.2.k.a.215.3		8	1.1	even	1	trivial
882.2.k.a.521.2		8	7.3	odd	6	inner
882.2.k.a.521.3		8	21.17	even	6	inner
1008.2.bt.c.17.1		8	28.11	odd	6
1008.2.bt.c.17.4		8	84.11	even	6
1008.2.bt.c.593.1		8	84.83	odd	2
1008.2.bt.c.593.4		8	28.27	even	2
1134.2.l.f.215.2		8	63.34	odd	6
1134.2.l.f.215.3		8	63.20	even	6
1134.2.l.f.269.1		8	63.4	even	3
1134.2.l.f.269.4		8	63.32	odd	6
1134.2.t.e.593.1		8	63.13	odd	6
1134.2.t.e.593.4		8	63.41	even	6
1134.2.t.e.1025.1		8	63.11	odd	6
1134.2.t.e.1025.4		8	63.25	even	3
3150.2.bf.a.1151.2		8	105.74	odd	6
3150.2.bf.a.1151.4		8	35.4	even	6
3150.2.bf.a.1601.2		8	35.34	odd	2
3150.2.bf.a.1601.4		8	105.104	even	2
3150.2.bp.b.899.1		8	105.53	even	12
3150.2.bp.b.899.4		8	35.32	odd	12
3150.2.bp.b.1349.1		8	35.27	even	4
3150.2.bp.b.1349.4		8	105.83	odd	4
3150.2.bp.e.899.1		8	35.18	odd	12
3150.2.bp.e.899.4		8	105.32	even	12
3150.2.bp.e.1349.1		8	105.62	odd	4
3150.2.bp.e.1349.4		8	35.13	even	4
7056.2.k.f.881.1		8	84.23	even	6
7056.2.k.f.881.2		8	28.19	even	6
7056.2.k.f.881.7		8	84.47	odd	6
7056.2.k.f.881.8		8	28.23	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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.09077 + 3.62132i) q^{5} +1.00000i q^{8} +(-3.62132 + 2.09077i) q^{10} +(-2.59808 + 1.50000i) q^{11} -2.44949i q^{13} +(-0.500000 + 0.866025i) q^{16} +(0.507306 + 0.878680i) q^{17} +(0.878680 + 0.507306i) q^{19} -4.18154 q^{20} -3.00000 q^{22} +(-3.67423 - 2.12132i) q^{23} +(-6.24264 - 10.8126i) q^{25} +(1.22474 - 2.12132i) q^{26} +1.24264i q^{29} +(-4.86396 + 2.80821i) q^{31} +(-0.866025 + 0.500000i) q^{32} +1.01461i q^{34} +(-4.12132 + 7.13834i) q^{37} +(0.507306 + 0.878680i) q^{38} +(-3.62132 - 2.09077i) q^{40} -2.02922 q^{41} +8.24264 q^{43} +(-2.59808 - 1.50000i) q^{44} +(-2.12132 - 3.67423i) q^{46} +(0.507306 - 0.878680i) q^{47} -12.4853i q^{50} +(2.12132 - 1.22474i) q^{52} +(1.07616 - 0.621320i) q^{53} -12.5446i q^{55} +(-0.621320 + 1.07616i) q^{58} +(5.76500 + 9.98528i) q^{59} +(-5.12132 - 2.95680i) q^{61} -5.61642 q^{62} -1.00000 q^{64} +(8.87039 + 5.12132i) q^{65} +(5.00000 + 8.66025i) q^{67} +(-0.507306 + 0.878680i) q^{68} +10.2426i q^{71} +(-7.24264 + 4.18154i) q^{73} +(-7.13834 + 4.12132i) q^{74} +1.01461i q^{76} +(5.62132 - 9.73641i) q^{79} +(-2.09077 - 3.62132i) q^{80} +(-1.75736 - 1.01461i) q^{82} +3.16693 q^{83} -4.24264 q^{85} +(7.13834 + 4.12132i) q^{86} +(-1.50000 - 2.59808i) q^{88} +(-5.19615 + 9.00000i) q^{89} -4.24264i q^{92} +(0.878680 - 0.507306i) q^{94} +(-3.67423 + 2.12132i) q^{95} -3.76127i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 12 q^{10} - 4 q^{16} + 24 q^{19} - 24 q^{22} - 16 q^{25} + 12 q^{31} - 16 q^{37} - 12 q^{40} + 32 q^{43} + 12 q^{58} - 24 q^{61} - 8 q^{64} + 40 q^{67} - 24 q^{73} + 28 q^{79} - 48 q^{82}+ \cdots + 24 q^{94}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more