LMFDB - Embedded newform 1134.2.l.f.269.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(215,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1134.215");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.l (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:	$9.05503558921$
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:	$\Z[a_1, \ldots, a_{11}]$
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			269.4
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1134.269
Dual form			1134.2.l.f.215.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(2.09077 - 3.62132i) q^{5} +(2.62132 - 0.358719i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(2.09077 - 3.62132i) q^{5} +(2.62132 - 0.358719i) q^{7} -1.00000i q^{8} +(3.62132 + 2.09077i) q^{10} +(2.59808 - 1.50000i) q^{11} +(-2.12132 + 1.22474i) q^{13} +(0.358719 + 2.62132i) q^{14} +1.00000 q^{16} +(-0.507306 + 0.878680i) q^{17} +(-0.878680 + 0.507306i) q^{19} +(-2.09077 + 3.62132i) q^{20} +(1.50000 + 2.59808i) q^{22} +(3.67423 + 2.12132i) q^{23} +(-6.24264 - 10.8126i) q^{25} +(-1.22474 - 2.12132i) q^{26} +(-2.62132 + 0.358719i) q^{28} +(1.07616 + 0.621320i) q^{29} -5.61642i q^{31} +1.00000i q^{32} +(-0.878680 - 0.507306i) q^{34} +(4.18154 - 10.2426i) q^{35} +(-4.12132 - 7.13834i) q^{37} +(-0.507306 - 0.878680i) q^{38} +(-3.62132 - 2.09077i) q^{40} +(-1.01461 - 1.75736i) q^{41} +(-4.12132 + 7.13834i) q^{43} +(-2.59808 + 1.50000i) q^{44} +(-2.12132 + 3.67423i) q^{46} +1.01461 q^{47} +(6.74264 - 1.88064i) q^{49} +(10.8126 - 6.24264i) q^{50} +(2.12132 - 1.22474i) q^{52} +(1.07616 + 0.621320i) q^{53} -12.5446i q^{55} +(-0.358719 - 2.62132i) q^{56} +(-0.621320 + 1.07616i) q^{58} +11.5300 q^{59} +5.91359i q^{61} +5.61642 q^{62} -1.00000 q^{64} +10.2426i q^{65} -10.0000 q^{67} +(0.507306 - 0.878680i) q^{68} +(10.2426 + 4.18154i) q^{70} -10.2426i q^{71} +(7.24264 + 4.18154i) q^{73} +(7.13834 - 4.12132i) q^{74} +(0.878680 - 0.507306i) q^{76} +(6.27231 - 4.86396i) q^{77} -11.2426 q^{79} +(2.09077 - 3.62132i) q^{80} +(1.75736 - 1.01461i) q^{82} +(1.58346 - 2.74264i) q^{83} +(2.12132 + 3.67423i) q^{85} +(-7.13834 - 4.12132i) q^{86} +(-1.50000 - 2.59808i) q^{88} +(5.19615 + 9.00000i) q^{89} +(-5.12132 + 3.97141i) q^{91} +(-3.67423 - 2.12132i) q^{92} +1.01461i q^{94} +4.24264i q^{95} +(3.25736 + 1.88064i) q^{97} +(1.88064 + 6.74264i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 4 q^{7}+O(q^{10}) $ 8 * q - 8 * q^4 + 4 * q^7	$ 8 q - 8 q^{4} + 4 q^{7} + 12 q^{10} + 8 q^{16} - 24 q^{19} + 12 q^{22} - 16 q^{25} - 4 q^{28} - 24 q^{34} - 16 q^{37} - 12 q^{40} - 16 q^{43} + 20 q^{49} + 12 q^{58} - 8 q^{64} - 80 q^{67} + 48 q^{70} + 24 q^{73} + 24 q^{76} - 56 q^{79} + 48 q^{82} - 12 q^{88} - 24 q^{91} + 60 q^{97}+O(q^{100}) $ 8 * q - 8 * q^4 + 4 * q^7 + 12 * q^10 + 8 * q^16 - 24 * q^19 + 12 * q^22 - 16 * q^25 - 4 * q^28 - 24 * q^34 - 16 * q^37 - 12 * q^40 - 16 * q^43 + 20 * q^49 + 12 * q^58 - 8 * q^64 - 80 * q^67 + 48 * q^70 + 24 * q^73 + 24 * q^76 - 56 * q^79 + 48 * q^82 - 12 * q^88 - 24 * q^91 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	2.09077	−	3.62132i	0.935021	−	1.61950i	0.160424	−	0.987048i	$-0.448714\pi$
$5$	2.09077	−	3.62132i	0.935021	−	1.61950i	0.774597	−	0.632456i	$-0.217953\pi$
$6$		0			0
$7$	2.62132	−	0.358719i	0.990766	−	0.135583i
$7$	2.62132	−	0.358719i	0.990766	−	0.135583i
$8$		−	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	−0.0542666	−	0.998526i	$-0.517282\pi$
$11$	2.59808	−	1.50000i	0.783349	−	0.452267i	0.837616	+	0.546259i	$0.183949\pi$
$12$		0			0
$13$	−2.12132	+	1.22474i	−0.588348	+	0.339683i	−0.764444	−	0.644690i	$-0.776986\pi$
$13$	−2.12132	+	1.22474i	−0.588348	+	0.339683i	0.176096	+	0.984373i	$0.443653\pi$
$14$	0.358719	+	2.62132i	0.0958718	+	0.700577i
$15$		0			0
$16$	1.00000			0.250000
$17$	−0.507306	+	0.878680i	−0.123040	+	0.213111i	−0.920965	−	0.389645i	$-0.872598\pi$
$17$	−0.507306	+	0.878680i	−0.123040	+	0.213111i	0.797925	+	0.602756i	$0.205931\pi$
$18$		0			0
$19$	−0.878680	+	0.507306i	−0.201583	+	0.116384i	−0.597394	−	0.801948i	$-0.703797\pi$
$19$	−0.878680	+	0.507306i	−0.201583	+	0.116384i	0.395811	+	0.918332i	$0.370464\pi$
$20$	−2.09077	+	3.62132i	−0.467510	+	0.809752i
$21$		0			0
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$	3.67423	+	2.12132i	0.766131	+	0.442326i	0.831493	−	0.555536i	$-0.187487\pi$
$23$	3.67423	+	2.12132i	0.766131	+	0.442326i	−0.0653618	+	0.997862i	$0.520820\pi$
$24$		0			0
$25$	−6.24264	−	10.8126i	−1.24853	−	2.16251i
$26$	−1.22474	−	2.12132i	−0.240192	−	0.416025i
$27$		0			0
$28$	−2.62132	+	0.358719i	−0.495383	+	0.0677916i
$29$	1.07616	+	0.621320i	0.199838	+	0.115376i	0.596580	−	0.802554i	$-0.296526\pi$
$29$	1.07616	+	0.621320i	0.199838	+	0.115376i	−0.396742	+	0.917930i	$0.629859\pi$
$30$		0			0
$31$		−	5.61642i		−	1.00874i	−0.863488	−	0.504369i	$-0.831725\pi$
$31$		−	5.61642i		−	1.00874i	0.863488	−	0.504369i	$-0.168275\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−0.878680	−	0.507306i	−0.150692	−	0.0870023i
$35$	4.18154	−	10.2426i	0.706809	−	1.73132i
$36$		0			0
$37$	−4.12132	−	7.13834i	−0.677541	−	1.17354i	−0.975719	−	0.219025i	$-0.929712\pi$
$37$	−4.12132	−	7.13834i	−0.677541	−	1.17354i	0.298178	−	0.954510i	$-0.403621\pi$
$38$	−0.507306	−	0.878680i	−0.0822959	−	0.142541i
$39$		0			0
$40$	−3.62132	−	2.09077i	−0.572581	−	0.330580i
$41$	−1.01461	−	1.75736i	−0.158456	−	0.274453i	0.775856	−	0.630910i	$-0.217318\pi$
$41$	−1.01461	−	1.75736i	−0.158456	−	0.274453i	−0.934312	+	0.356456i	$0.883985\pi$
$42$		0			0
$43$	−4.12132	+	7.13834i	−0.628495	+	1.08859i	0.359358	+	0.933200i	$0.382996\pi$
$43$	−4.12132	+	7.13834i	−0.628495	+	1.08859i	−0.987854	+	0.155386i	$0.950338\pi$
$44$	−2.59808	+	1.50000i	−0.391675	+	0.226134i
$45$		0			0
$46$	−2.12132	+	3.67423i	−0.312772	+	0.541736i
$47$	1.01461			0.147996			0.0739982	−	0.997258i	$-0.476424\pi$
$47$	1.01461			0.147996			0.0739982	+	0.997258i	$0.476424\pi$
$48$		0			0
$49$	6.74264	−	1.88064i	0.963234	−	0.268662i
$50$	10.8126	−	6.24264i	1.52913	−	0.882843i
$51$		0			0
$52$	2.12132	−	1.22474i	0.294174	−	0.169842i
$53$	1.07616	+	0.621320i	0.147822	+	0.0853449i	0.572087	−	0.820193i	$-0.306134\pi$
$53$	1.07616	+	0.621320i	0.147822	+	0.0853449i	−0.424265	+	0.905538i	$0.639467\pi$
$54$		0			0
$55$		−	12.5446i		−	1.69152i
$56$	−0.358719	−	2.62132i	−0.0479359	−	0.350289i
$57$		0			0
$58$	−0.621320	+	1.07616i	−0.0815834	+	0.141307i
$59$	11.5300			1.50108			0.750540	−	0.660825i	$-0.229794\pi$
$59$	11.5300			1.50108			0.750540	+	0.660825i	$0.229794\pi$
$60$		0			0
$61$			5.91359i			0.757158i	0.925569	+	0.378579i	$0.123587\pi$
$61$			5.91359i			0.757158i	−0.925569	+	0.378579i	$0.876413\pi$
$62$	5.61642			0.713286
$63$		0			0
$64$	−1.00000			−0.125000
$65$			10.2426i			1.27044i
$66$		0			0
$67$	−10.0000			−1.22169			−0.610847	−	0.791748i	$-0.709171\pi$
$67$	−10.0000			−1.22169			−0.610847	+	0.791748i	$0.709171\pi$
$68$	0.507306	−	0.878680i	0.0615199	−	0.106556i
$69$		0			0
$70$	10.2426	+	4.18154i	1.22423	+	0.499790i
$71$		−	10.2426i		−	1.21558i	−0.794099	−	0.607789i	$-0.792057\pi$
$71$		−	10.2426i		−	1.21558i	0.794099	−	0.607789i	$-0.207943\pi$
$72$		0			0
$73$	7.24264	+	4.18154i	0.847687	+	0.489412i	0.859870	−	0.510513i	$-0.170545\pi$
$73$	7.24264	+	4.18154i	0.847687	+	0.489412i	−0.0121828	+	0.999926i	$0.503878\pi$
$74$	7.13834	−	4.12132i	0.829815	−	0.479094i
$75$		0			0
$76$	0.878680	−	0.507306i	0.100791	−	0.0581920i
$77$	6.27231	−	4.86396i	0.714796	−	0.554300i
$78$		0			0
$79$	−11.2426			−1.26490			−0.632448	−	0.774603i	$-0.717950\pi$
$79$	−11.2426			−1.26490			−0.632448	+	0.774603i	$0.717950\pi$
$80$	2.09077	−	3.62132i	0.233755	−	0.404876i
$81$		0			0
$82$	1.75736	−	1.01461i	0.194068	−	0.112045i
$83$	1.58346	−	2.74264i	0.173808	−	0.301044i	−0.765940	−	0.642912i	$-0.777726\pi$
$83$	1.58346	−	2.74264i	0.173808	−	0.301044i	0.939748	+	0.341868i	$0.111060\pi$
$84$		0			0
$85$	2.12132	+	3.67423i	0.230089	+	0.398527i
$86$	−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	0.998218	+	0.0596775i	$0.0190072\pi$
$89$	5.19615	+	9.00000i	0.550791	+	0.953998i	−0.447427	+	0.894321i	$0.647659\pi$
$90$		0			0
$91$	−5.12132	+	3.97141i	−0.536860	+	0.416317i
$92$	−3.67423	−	2.12132i	−0.383065	−	0.221163i
$93$		0			0
$94$			1.01461i			0.104649i
$95$			4.24264i			0.435286i
$96$		0			0
$97$	3.25736	+	1.88064i	0.330735	+	0.190950i	0.656167	−	0.754615i	$-0.272177\pi$
$97$	3.25736	+	1.88064i	0.330735	+	0.190950i	−0.325433	+	0.945565i	$0.605510\pi$
$98$	1.88064	+	6.74264i	0.189973	+	0.681110i
$99$		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	$0.395105\pi$
$104$	1.22474	+	2.12132i	0.120096	+	0.208013i
$105$		0			0
$106$	−0.621320	+	1.07616i	−0.0603480	+	0.104526i
$107$	4.75039	−	2.74264i	0.459238	−	0.265141i	−0.252486	−	0.967601i	$-0.581248\pi$
$107$	4.75039	−	2.74264i	0.459238	−	0.265141i	0.711724	+	0.702459i	$0.247915\pi$
$108$		0			0
$109$	−0.757359	+	1.31178i	−0.0725419	+	0.125646i	−0.900015	−	0.435860i	$-0.856444\pi$
$109$	−0.757359	+	1.31178i	−0.0725419	+	0.125646i	0.827473	+	0.561506i	$0.189778\pi$
$110$	12.5446			1.19608
$111$		0			0
$112$	2.62132	−	0.358719i	0.247691	−	0.0338958i
$113$	−7.34847	+	4.24264i	−0.691286	+	0.399114i	−0.804094	−	0.594503i	$-0.797349\pi$
$113$	−7.34847	+	4.24264i	−0.691286	+	0.399114i	0.112808	+	0.993617i	$0.464016\pi$
$114$		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
$119$	−1.01461	+	2.48528i	−0.0930093	+	0.227825i
$120$		0			0
$121$	−1.00000	+	1.73205i	−0.0909091	+	0.157459i
$122$	−5.91359			−0.535391
$123$		0			0
$124$			5.61642i			0.504369i
$125$	−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	$0.574725\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−10.2426			−0.898339
$131$	−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
$133$	−2.12132	+	1.64501i	−0.183942	+	0.142641i
$134$		−	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	−0.928662	−	0.370928i	$-0.879040\pi$
$137$	−12.5446	+	7.24264i	−1.07176	+	0.618781i	−0.143098	+	0.989709i	$0.545706\pi$
$138$		0			0
$139$	17.4853	−	10.0951i	1.48308	−	0.856258i	0.483267	−	0.875473i	$-0.339450\pi$
$139$	17.4853	−	10.0951i	1.48308	−	0.856258i	0.999815	+	0.0192152i	$0.00611676\pi$
$140$	−4.18154	+	10.2426i	−0.353405	+	0.865661i
$141$		0			0
$142$	10.2426			0.859543
$143$	−3.67423	+	6.36396i	−0.307255	+	0.532181i
$144$		0			0
$145$	4.50000	−	2.59808i	0.373705	−	0.215758i
$146$	−4.18154	+	7.24264i	−0.346067	+	0.599405i
$147$		0			0
$148$	4.12132	+	7.13834i	0.338770	+	0.586768i
$149$	17.7408	+	10.2426i	1.45338	+	0.839110i	0.998671	−	0.0515300i	$-0.0164098\pi$
$149$	17.7408	+	10.2426i	1.45338	+	0.839110i	0.454709	+	0.890640i	$0.349743\pi$
$150$		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
$154$	4.86396	+	6.27231i	0.391949	+	0.505437i
$155$	−20.3389	−	11.7426i	−1.63366	−	0.943192i
$156$		0			0
$157$			14.6969i			1.17294i	0.809970	+	0.586472i	$0.199483\pi$
$157$			14.6969i			1.17294i	−0.809970	+	0.586472i	$0.800517\pi$
$158$		−	11.2426i		−	0.894416i
$159$		0			0
$160$	3.62132	+	2.09077i	0.286291	+	0.165290i
$161$	10.3923	+	4.24264i	0.819028	+	0.334367i
$162$		0			0
$163$	−3.12132	−	5.40629i	−0.244481	−	0.423453i	0.717505	−	0.696554i	$-0.245284\pi$
$163$	−3.12132	−	5.40629i	−0.244481	−	0.423453i	−0.961985	+	0.273101i	$0.911951\pi$
$164$	1.01461	+	1.75736i	0.0792279	+	0.137227i
$165$		0			0
$166$	2.74264	+	1.58346i	0.212870	+	0.122901i
$167$	−11.5300	−	19.9706i	−0.892219	−	1.54537i	−0.837209	−	0.546883i	$-0.815814\pi$
$167$	−11.5300	−	19.9706i	−0.892219	−	1.54537i	−0.0550097	−	0.998486i	$-0.517519\pi$
$168$		0			0
$169$	−3.50000	+	6.06218i	−0.269231	+	0.466321i
$170$	−3.67423	+	2.12132i	−0.281801	+	0.162698i
$171$		0			0
$172$	4.12132	−	7.13834i	0.314248	−	0.544293i
$173$	20.7846			1.58022			0.790112	−	0.612962i	$-0.210022\pi$
$173$	20.7846			1.58022			0.790112	+	0.612962i	$0.210022\pi$
$174$		0			0
$175$	−20.2426	−	26.1039i	−1.53020	−	1.97327i
$176$	2.59808	−	1.50000i	0.195837	−	0.113067i
$177$		0			0
$178$	−9.00000	+	5.19615i	−0.674579	+	0.389468i
$179$	8.23999	+	4.75736i	0.615886	+	0.355582i	0.775265	−	0.631636i	$-0.217616\pi$
$179$	8.23999	+	4.75736i	0.615886	+	0.355582i	−0.159380	+	0.987217i	$0.550949\pi$
$180$		0			0
$181$		−	2.02922i		−	0.150831i	−0.997152	−	0.0754155i	$-0.975972\pi$
$181$		−	2.02922i		−	0.150831i	0.997152	−	0.0754155i	$-0.0240283\pi$
$182$	−3.97141	−	5.12132i	−0.294380	−	0.379618i
$183$		0			0
$184$	2.12132	−	3.67423i	0.156386	−	0.270868i
$185$	−34.4669			−2.53406
$186$		0			0
$187$			3.04384i			0.222587i
$188$	−1.01461			−0.0739982
$189$		0			0
$190$	−4.24264			−0.307794
$191$		−	8.48528i		−	0.613973i	−0.951714	−	0.306987i	$-0.900679\pi$
$191$		−	8.48528i		−	0.613973i	0.951714	−	0.306987i	$-0.0993207\pi$
$192$		0			0
$193$	−7.48528			−0.538802			−0.269401	−	0.963028i	$-0.586826\pi$
$193$	−7.48528			−0.538802			−0.269401	+	0.963028i	$0.586826\pi$
$194$	−1.88064	+	3.25736i	−0.135022	+	0.233865i
$195$		0			0
$196$	−6.74264	+	1.88064i	−0.481617	+	0.134331i
$197$		−	9.51472i		−	0.677896i	−0.940805	−	0.338948i	$-0.889929\pi$
$197$		−	9.51472i		−	0.677896i	0.940805	−	0.338948i	$-0.110071\pi$
$198$		0			0
$199$	−13.9706	−	8.06591i	−0.990347	−	0.571777i	−0.0849690	−	0.996384i	$-0.527079\pi$
$199$	−13.9706	−	8.06591i	−0.990347	−	0.571777i	−0.905378	+	0.424607i	$0.860412\pi$
$200$	−10.8126	+	6.24264i	−0.764564	+	0.441421i
$201$		0			0
$202$		0			0
$203$	3.04384	+	1.24264i	0.213635	+	0.0872163i
$204$		0			0
$205$	−8.48528			−0.592638
$206$	−7.64564	+	13.2426i	−0.532697	+	0.922658i
$207$		0			0
$208$	−2.12132	+	1.22474i	−0.147087	+	0.0849208i
$209$	−1.52192	+	2.63604i	−0.105273	+	0.182339i
$210$		0			0
$211$	−4.12132	−	7.13834i	−0.283723	−	0.491423i	0.688575	−	0.725165i	$-0.258236\pi$
$211$	−4.12132	−	7.13834i	−0.283723	−	0.491423i	−0.972299	+	0.233741i	$0.924903\pi$
$212$	−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
$217$	−2.01472	−	14.7224i	−0.136768	−	0.999424i
$218$	−1.31178	−	0.757359i	−0.0888453	−	0.0512948i
$219$		0			0
$220$			12.5446i			0.845758i
$221$		−	2.48528i		−	0.167178i
$222$		0			0
$223$	−10.8640	−	6.27231i	−0.727505	−	0.420025i	0.0900039	−	0.995941i	$-0.471312\pi$
$223$	−10.8640	−	6.27231i	−0.727505	−	0.420025i	−0.817509	+	0.575916i	$0.804645\pi$
$224$	0.358719	+	2.62132i	0.0239680	+	0.175144i
$225$		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	$0.515294\pi$
$230$	8.87039	+	15.3640i	0.584896	+	1.01307i
$231$		0			0
$232$	0.621320	−	1.07616i	0.0407917	−	0.0706533i
$233$	−5.82655	+	3.36396i	−0.381710	+	0.220380i	−0.678562	−	0.734543i	$-0.737397\pi$
$233$	−5.82655	+	3.36396i	−0.381710	+	0.220380i	0.296852	+	0.954924i	$0.404063\pi$
$234$		0			0
$235$	2.12132	−	3.67423i	0.138380	−	0.239681i
$236$	−11.5300			−0.750540
$237$		0			0
$238$	−2.48528	−	1.01461i	−0.161097	−	0.0657675i
$239$	−11.0227	+	6.36396i	−0.712999	+	0.411650i	−0.812171	−	0.583420i	$-0.801714\pi$
$239$	−11.0227	+	6.36396i	−0.712999	+	0.411650i	0.0991712	+	0.995070i	$0.468381\pi$
$240$		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
$245$	7.28692	−	28.3492i	0.465544	−	1.81117i
$246$		0			0
$247$	1.24264	−	2.15232i	0.0790673	−	0.136949i
$248$	−5.61642			−0.356643
$249$		0			0
$250$		−	31.3000i		−	1.97959i
$251$	−17.6177			−1.11202			−0.556009	−	0.831176i	$-0.687668\pi$
$251$	−17.6177			−1.11202			−0.556009	+	0.831176i	$0.687668\pi$
$252$		0			0
$253$	12.7279			0.800198
$254$		−	5.24264i		−	0.328953i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−12.5446	+	21.7279i	−0.782512	+	1.35535i	0.147962	+	0.988993i	$0.452729\pi$
$257$	−12.5446	+	21.7279i	−0.782512	+	1.35535i	−0.930474	+	0.366358i	$0.880605\pi$
$258$		0			0
$259$	−13.3640	−	17.2335i	−0.830396	−	1.07084i
$260$		−	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	0.454561	−	0.890716i	$-0.349796\pi$
$263$	23.5673	−	13.6066i	1.45322	−	0.839019i	0.998663	+	0.0516967i	$0.0164629\pi$
$264$		0			0
$265$	4.50000	−	2.59808i	0.276433	−	0.159599i
$266$	−1.64501	−	2.12132i	−0.100862	−	0.130066i
$267$		0			0
$268$	10.0000			0.610847
$269$	5.25770	−	9.10660i	0.320568	−	0.555239i	−0.660038	−	0.751232i	$-0.729460\pi$
$269$	5.25770	−	9.10660i	0.320568	−	0.555239i	0.980605	+	0.195993i	$0.0627930\pi$
$270$		0			0
$271$	−9.62132	+	5.55487i	−0.584454	+	0.337434i	−0.762901	−	0.646515i	$-0.776226\pi$
$271$	−9.62132	+	5.55487i	−0.584454	+	0.337434i	0.178448	+	0.983949i	$0.442892\pi$
$272$	−0.507306	+	0.878680i	−0.0307599	+	0.0532778i
$273$		0			0
$274$	−7.24264	−	12.5446i	−0.437544	−	0.757848i
$275$	−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
$280$	−10.2426	−	4.18154i	−0.612115	−	0.249895i
$281$	−5.19615	−	3.00000i	−0.309976	−	0.178965i	0.336939	−	0.941526i	$-0.390608\pi$
$281$	−5.19615	−	3.00000i	−0.309976	−	0.178965i	−0.646916	+	0.762561i	$0.723942\pi$
$282$		0			0
$283$			6.50794i			0.386857i	0.981114	+	0.193428i	$0.0619607\pi$
$283$			6.50794i			0.386857i	−0.981114	+	0.193428i	$0.938039\pi$
$284$			10.2426i			0.607789i
$285$		0			0
$286$	−6.36396	−	3.67423i	−0.376309	−	0.217262i
$287$	−3.29002	−	4.24264i	−0.194204	−	0.250435i
$288$		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
$293$	−2.09077	−	3.62132i	−0.122144	−	0.211560i	0.798469	−	0.602036i	$-0.205644\pi$
$293$	−2.09077	−	3.62132i	−0.122144	−	0.211560i	−0.920613	+	0.390476i	$0.872310\pi$
$294$		0			0
$295$	24.1066	−	41.7539i	1.40354	−	2.43100i
$296$	−7.13834	+	4.12132i	−0.414907	+	0.239547i
$297$		0			0
$298$	−10.2426	+	17.7408i	−0.593340	+	1.02770i
$299$	−10.3923			−0.601003
$300$		0			0
$301$	−8.24264	+	20.1903i	−0.475098	+	1.16375i
$302$	−2.80821	+	1.62132i	−0.161594	+	0.0932965i
$303$		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	$0.751411\pi$
$308$	−6.27231	+	4.86396i	−0.357398	+	0.277150i
$309$		0			0
$310$	11.7426	−	20.3389i	0.666937	−	1.15517i
$311$	18.7554			1.06352			0.531760	−	0.846895i	$-0.321531\pi$
$311$	18.7554			1.06352			0.531760	+	0.846895i	$0.321531\pi$
$312$		0			0
$313$		−	1.13770i		−	0.0643069i	−0.999483	−	0.0321534i	$-0.989763\pi$
$313$		−	1.13770i		−	0.0643069i	0.999483	−	0.0321534i	$-0.0102365\pi$
$314$	−14.6969			−0.829396
$315$		0			0
$316$	11.2426			0.632448
$317$		−	7.24264i		−	0.406787i	−0.979097	−	0.203394i	$-0.934803\pi$
$317$		−	7.24264i		−	0.406787i	0.979097	−	0.203394i	$-0.0651971\pi$
$318$		0			0
$319$	3.72792			0.208724
$320$	−2.09077	+	3.62132i	−0.116878	+	0.202438i
$321$		0			0
$322$	−4.24264	+	10.3923i	−0.236433	+	0.579141i
$323$		−	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
$328$	−1.75736	+	1.01461i	−0.0970339	+	0.0560226i
$329$	2.65962	−	0.363961i	0.146630	−	0.0200658i
$330$		0			0
$331$	17.4558			0.959460			0.479730	−	0.877416i	$-0.340735\pi$
$331$	17.4558			0.959460			0.479730	+	0.877416i	$0.340735\pi$
$332$	−1.58346	+	2.74264i	−0.0869039	+	0.150522i
$333$		0			0
$334$	19.9706	−	11.5300i	1.09274	−	0.630894i
$335$	−20.9077	+	36.2132i	−1.14231	+	1.97854i
$336$		0			0
$337$	2.50000	+	4.33013i	0.136184	+	0.235877i	0.926049	−	0.377403i	$-0.123183\pi$
$337$	2.50000	+	4.33013i	0.136184	+	0.235877i	−0.789865	+	0.613280i	$0.789850\pi$
$338$	−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
$343$	17.0000	−	7.34847i	0.917914	−	0.396780i
$344$	7.13834	+	4.12132i	0.384873	+	0.222207i
$345$		0			0
$346$			20.7846i			1.11739i
$347$			14.4853i			0.777611i	0.921320	+	0.388805i	$0.127112\pi$
$347$			14.4853i			0.777611i	−0.921320	+	0.388805i	$0.872888\pi$
$348$		0			0
$349$	31.9706	+	18.4582i	1.71134	+	0.988045i	0.932754	+	0.360514i	$0.117399\pi$
$349$	31.9706	+	18.4582i	1.71134	+	0.988045i	0.778591	+	0.627531i	$0.215935\pi$
$350$	26.1039	−	20.2426i	1.39531	−	1.08201i
$351$		0			0
$352$	1.50000	+	2.59808i	0.0799503	+	0.138478i
$353$	−9.37769	−	16.2426i	−0.499124	−	0.864509i	0.500875	−	0.865519i	$-0.333012\pi$
$353$	−9.37769	−	16.2426i	−0.499124	−	0.864509i	−0.999999	+	0.00101095i	$0.999678\pi$
$354$		0			0
$355$	−37.0919	−	21.4150i	−1.96863	−	1.13659i
$356$	−5.19615	−	9.00000i	−0.275396	−	0.476999i
$357$		0			0
$358$	−4.75736	+	8.23999i	−0.251434	+	0.435497i
$359$	−15.5885	+	9.00000i	−0.822727	+	0.475002i	−0.851356	−	0.524588i	$-0.824219\pi$
$359$	−15.5885	+	9.00000i	−0.822727	+	0.475002i	0.0286287	+	0.999590i	$0.490886\pi$
$360$		0			0
$361$	−8.98528	+	15.5630i	−0.472910	+	0.819103i
$362$	2.02922			0.106654
$363$		0			0
$364$	5.12132	−	3.97141i	0.268430	−	0.208158i
$365$	30.2854	−	17.4853i	1.58521	−	0.915221i
$366$		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
$371$	3.04384	+	1.24264i	0.158028	+	0.0645147i
$372$		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	$0.979205\pi$
$374$	−3.04384			−0.157393
$375$		0			0
$376$		−	1.01461i		−	0.0523246i
$377$	−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	$0.536750\pi$
$380$		−	4.24264i		−	0.217643i
$381$		0			0
$382$	8.48528			0.434145
$383$	−6.21076	+	10.7574i	−0.317355	+	0.549675i	−0.979935	−	0.199316i	$-0.936128\pi$
$383$	−6.21076	+	10.7574i	−0.317355	+	0.549675i	0.662580	+	0.748991i	$0.269461\pi$
$384$		0			0
$385$	−4.50000	−	32.8835i	−0.229341	−	1.67590i
$386$		−	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	−0.862096	−	0.506744i	$-0.830849\pi$
$389$	−16.8493	+	9.72792i	−0.854291	+	0.493225i	0.00780525	+	0.999970i	$0.497515\pi$
$390$		0			0
$391$	−3.72792	+	2.15232i	−0.188529	+	0.108847i
$392$	−1.88064	−	6.74264i	−0.0949865	−	0.340555i
$393$		0			0
$394$	9.51472			0.479345
$395$	−23.5058	+	40.7132i	−1.18270	+	2.04850i
$396$		0			0
$397$	12.0000	−	6.92820i	0.602263	−	0.347717i	−0.167668	−	0.985843i	$-0.553624\pi$
$397$	12.0000	−	6.92820i	0.602263	−	0.347717i	0.769931	+	0.638127i	$0.220290\pi$
$398$	8.06591	−	13.9706i	0.404307	−	0.700281i
$399$		0			0
$400$	−6.24264	−	10.8126i	−0.312132	−	0.540629i
$401$		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
$406$	−1.24264	+	3.04384i	−0.0616712	+	0.151063i
$407$	−21.4150	−	12.3640i	−1.06150	−	0.612859i
$408$		0			0
$409$			4.60181i			0.227545i	0.993507	+	0.113772i	$0.0362934\pi$
$409$			4.60181i			0.227545i	−0.993507	+	0.113772i	$0.963707\pi$
$410$		−	8.48528i		−	0.419058i
$411$		0			0
$412$	−13.2426	−	7.64564i	−0.652418	−	0.376674i
$413$	30.2238	−	4.13604i	1.48722	−	0.203521i
$414$		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
$419$	−2.02922	−	3.51472i	−0.0991341	−	0.171705i	0.812192	−	0.583390i	$-0.198274\pi$
$419$	−2.02922	−	3.51472i	−0.0991341	−	0.171705i	−0.911326	+	0.411684i	$0.864941\pi$
$420$		0			0
$421$	2.87868	−	4.98602i	0.140298	−	0.243004i	−0.787311	−	0.616557i	$-0.788527\pi$
$421$	2.87868	−	4.98602i	0.140298	−	0.243004i	0.927609	+	0.373553i	$0.121861\pi$
$422$	7.13834	−	4.12132i	0.347489	−	0.200623i
$423$		0			0
$424$	0.621320	−	1.07616i	0.0301740	−	0.0522629i
$425$	12.6677			0.614474
$426$		0			0
$427$	2.12132	+	15.5014i	0.102658	+	0.750166i
$428$	−4.75039	+	2.74264i	−0.229619	+	0.132571i
$429$		0			0
$430$	−29.8492	+	17.2335i	−1.43946	+	0.831072i
$431$	−17.7408	−	10.2426i	−0.854543	−	0.493371i	0.00763808	−	0.999971i	$-0.497569\pi$
$431$	−17.7408	−	10.2426i	−0.854543	−	0.493371i	−0.862181	+	0.506600i	$0.830902\pi$
$432$		0			0
$433$			3.46410i			0.166474i	0.996530	+	0.0832370i	$0.0265259\pi$
$433$			3.46410i			0.166474i	−0.996530	+	0.0832370i	$0.973474\pi$
$434$	14.7224	−	2.01472i	0.706699	−	0.0967096i
$435$		0			0
$436$	0.757359	−	1.31178i	0.0362709	−	0.0628231i
$437$	−4.30463			−0.205919
$438$		0			0
$439$			27.2416i			1.30017i	0.759862	+	0.650084i	$0.225266\pi$
$439$			27.2416i			1.30017i	−0.759862	+	0.650084i	$0.774734\pi$
$440$	−12.5446			−0.598041
$441$		0			0
$442$	2.48528			0.118213
$443$			34.4558i			1.63705i	0.574473	+	0.818523i	$0.305207\pi$
$443$			34.4558i			1.63705i	−0.574473	+	0.818523i	$0.694793\pi$
$444$		0			0
$445$	43.4558			2.06000
$446$	6.27231	−	10.8640i	0.297003	−	0.514423i
$447$		0			0
$448$	−2.62132	+	0.358719i	−0.123846	+	0.0169479i
$449$		−	10.2426i		−	0.483380i	−0.970354	−	0.241690i	$-0.922298\pi$
$449$		−	10.2426i		−	0.483380i	0.970354	−	0.241690i	$-0.0777017\pi$
$450$		0			0
$451$	−5.27208	−	3.04384i	−0.248252	−	0.143329i
$452$	7.34847	−	4.24264i	0.345643	−	0.199557i
$453$		0			0
$454$	−13.5000	+	7.79423i	−0.633586	+	0.365801i
$455$	3.67423	+	26.8492i	0.172251	+	1.25871i
$456$		0			0
$457$	−23.0000			−1.07589			−0.537947	−	0.842978i	$-0.680800\pi$
$457$	−23.0000			−1.07589			−0.537947	+	0.842978i	$0.680800\pi$
$458$	−6.92820	+	12.0000i	−0.323734	+	0.560723i
$459$		0			0
$460$	−15.3640	+	8.87039i	−0.716348	+	0.413584i
$461$	−11.4069	+	19.7574i	−0.531273	+	0.920192i	0.468061	+	0.883696i	$0.344953\pi$
$461$	−11.4069	+	19.7574i	−0.531273	+	0.920192i	−0.999334	+	0.0364957i	$0.988380\pi$
$462$		0			0
$463$	−10.7279	−	18.5813i	−0.498569	−	0.863547i	0.501430	−	0.865198i	$-0.332808\pi$
$463$	−10.7279	−	18.5813i	−0.498569	−	0.863547i	−0.999999	+	0.00165180i	$0.999474\pi$
$464$	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	$-0.311562\pi$
$467$	−9.50079	−	16.4558i	−0.439644	−	0.761486i	−0.997662	+	0.0683432i	$0.978229\pi$
$468$		0			0
$469$	−26.2132	+	3.58719i	−1.21041	+	0.165641i
$470$	3.67423	+	2.12132i	0.169480	+	0.0978492i
$471$		0			0
$472$		−	11.5300i		−	0.530712i
$473$			24.7279i			1.13699i
$474$		0			0
$475$	10.9706	+	6.33386i	0.503364	+	0.290617i
$476$	1.01461	−	2.48528i	0.0465047	−	0.113913i
$477$		0			0
$478$	−6.36396	−	11.0227i	−0.291081	−	0.504167i
$479$	18.2481	+	31.6066i	0.833776	+	1.44414i	0.895023	+	0.446020i	$0.147159\pi$
$479$	18.2481	+	31.6066i	0.833776	+	1.44414i	−0.0612470	+	0.998123i	$0.519508\pi$
$480$		0			0
$481$	17.4853	+	10.0951i	0.797260	+	0.460298i
$482$	−8.51167	−	14.7426i	−0.387696	−	0.671509i
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	13.6208	−	7.86396i	0.618488	−	0.357084i
$486$		0			0
$487$	−14.1066	+	24.4334i	−0.639231	+	1.10718i	0.346371	+	0.938098i	$0.387414\pi$
$487$	−14.1066	+	24.4334i	−0.639231	+	1.10718i	−0.985602	+	0.169083i	$0.945919\pi$
$488$	5.91359			0.267696
$489$		0			0
$490$	28.3492	+	7.28692i	1.28069	+	0.329190i
$491$	17.2950	−	9.98528i	0.780513	−	0.450629i	−0.0560990	−	0.998425i	$-0.517866\pi$
$491$	17.2950	−	9.98528i	0.780513	−	0.450629i	0.836612	+	0.547796i	$0.184533\pi$
$492$		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
$497$	−3.67423	−	26.8492i	−0.164812	−	1.20435i
$498$		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	$-0.130885\pi$
$500$	31.3000			1.39978
$501$		0			0
$502$		−	17.6177i		−	0.786316i
$503$	3.29002			0.146695			0.0733474	−	0.997306i	$-0.476632\pi$
$503$	3.29002			0.146695			0.0733474	+	0.997306i	$0.476632\pi$
$504$		0			0
$505$		0			0
$506$			12.7279i			0.565825i
$507$		0			0
$508$	5.24264			0.232605
$509$	20.8462	−	36.1066i	0.923990	−	1.60040i	0.130812	−	0.991407i	$-0.458242\pi$
$509$	20.8462	−	36.1066i	0.923990	−	1.60040i	0.793178	−	0.608990i	$-0.208425\pi$
$510$		0			0
$511$	20.4853	+	8.36308i	0.906215	+	0.369961i
$512$			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
$517$	2.63604	−	1.52192i	0.115933	−	0.0669339i
$518$	17.2335	−	13.3640i	0.757195	−	0.587179i
$519$		0			0
$520$	10.2426			0.449170
$521$	10.0081	−	17.3345i	0.438462	−	0.759439i	−0.559109	−	0.829094i	$-0.688857\pi$
$521$	10.0081	−	17.3345i	0.438462	−	0.759439i	0.997571	+	0.0696551i	$0.0221899\pi$
$522$		0			0
$523$	−23.8492	+	13.7694i	−1.04285	+	0.602092i	−0.920641	−	0.390411i	$-0.872333\pi$
$523$	−23.8492	+	13.7694i	−1.04285	+	0.602092i	−0.122214	+	0.992504i	$0.538999\pi$
$524$	2.59808	−	4.50000i	0.113497	−	0.196583i
$525$		0			0
$526$	13.6066	+	23.5673i	0.593276	+	1.02758i
$527$	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
$532$	2.12132	−	1.64501i	0.0919709	−	0.0713203i
$533$	4.30463	+	2.48528i	0.186454	+	0.107649i
$534$		0			0
$535$		−	22.9369i		−	0.991650i
$536$			10.0000i			0.431934i
$537$		0			0
$538$	9.10660	+	5.25770i	0.392613	+	0.226675i
$539$	14.6969	−	15.0000i	0.633042	−	0.646096i
$540$		0			0
$541$	5.36396	+	9.29065i	0.230615	+	0.399436i	0.957989	−	0.286804i	$-0.0925930\pi$
$541$	5.36396	+	9.29065i	0.230615	+	0.399436i	−0.727374	+	0.686241i	$0.759260\pi$
$542$	−5.55487	−	9.62132i	−0.238602	−	0.413271i
$543$		0			0
$544$	−0.878680	−	0.507306i	−0.0376731	−	0.0217506i
$545$	3.16693	+	5.48528i	0.135656	+	0.234964i
$546$		0			0
$547$	−9.84924	+	17.0594i	−0.421123	+	0.729407i	−0.996050	−	0.0887983i	$-0.971697\pi$
$547$	−9.84924	+	17.0594i	−0.421123	+	0.729407i	0.574926	+	0.818205i	$0.305031\pi$
$548$	12.5446	−	7.24264i	0.535880	−	0.309390i
$549$		0			0
$550$	18.7279	−	32.4377i	0.798561	−	1.38315i
$551$	−1.26080			−0.0537118
$552$		0			0
$553$	−29.4706	+	4.03295i	−1.25322	+	0.171499i
$554$	−18.1610	+	10.4853i	−0.771589	+	0.445477i
$555$		0			0
$556$	−17.4853	+	10.0951i	−0.741541	+	0.428129i
$557$	−13.6208	−	7.86396i	−0.577131	−	0.333207i	0.182861	−	0.983139i	$-0.441464\pi$
$557$	−13.6208	−	7.86396i	−0.577131	−	0.333207i	−0.759992	+	0.649932i	$0.774797\pi$
$558$		0			0
$559$		−	20.1903i		−	0.853957i
$560$	4.18154	−	10.2426i	0.176702	−	0.432831i
$561$		0			0
$562$	3.00000	−	5.19615i	0.126547	−	0.219186i
$563$	24.1977			1.01981			0.509906	−	0.860230i	$-0.329680\pi$
$563$	24.1977			1.01981			0.509906	+	0.860230i	$0.329680\pi$
$564$		0			0
$565$			35.4815i			1.49272i
$566$	−6.50794			−0.273549
$567$		0			0
$568$	−10.2426			−0.429772
$569$		−	1.75736i		−	0.0736723i	−0.999321	−	0.0368362i	$-0.988272\pi$
$569$		−	1.75736i		−	0.0736723i	0.999321	−	0.0368362i	$-0.0117280\pi$
$570$		0			0
$571$	−16.7279			−0.700042			−0.350021	−	0.936742i	$-0.613826\pi$
$571$	−16.7279			−0.700042			−0.350021	+	0.936742i	$0.613826\pi$
$572$	3.67423	−	6.36396i	0.153627	−	0.266091i
$573$		0			0
$574$	4.24264	−	3.29002i	0.177084	−	0.137323i
$575$		−	52.9706i		−	2.20903i
$576$		0			0
$577$	17.7426	+	10.2437i	0.738636	+	0.426452i	0.821573	−	0.570103i	$-0.193097\pi$
$577$	17.7426	+	10.2437i	0.738636	+	0.426452i	−0.0829373	+	0.996555i	$0.526430\pi$
$578$	−13.8309	+	7.98528i	−0.575290	+	0.332144i
$579$		0			0
$580$	−4.50000	+	2.59808i	−0.186852	+	0.107879i
$581$	3.16693	−	7.75736i	0.131386	−	0.321829i
$582$		0			0
$583$	3.72792			0.154395
$584$	4.18154	−	7.24264i	0.173033	−	0.299703i
$585$		0			0
$586$	3.62132	−	2.09077i	0.149595	−	0.0863689i
$587$	−2.59808	+	4.50000i	−0.107234	+	0.185735i	−0.914649	−	0.404249i	$-0.867533\pi$
$587$	−2.59808	+	4.50000i	−0.107234	+	0.185735i	0.807415	+	0.589984i	$0.200866\pi$
$588$		0			0
$589$	2.84924	+	4.93503i	0.117401	+	0.203344i
$590$	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	0.988664	+	0.150148i	$0.0479749\pi$
$593$	15.2042	+	26.3345i	0.624363	+	1.08143i	−0.364300	+	0.931282i	$0.618692\pi$
$594$		0			0
$595$	6.87868	+	8.87039i	0.281998	+	0.363650i
$596$	−17.7408	−	10.2426i	−0.726690	−	0.419555i
$597$		0			0
$598$		−	10.3923i		−	0.424973i
$599$		−	43.4558i		−	1.77556i	−0.460270	−	0.887779i	$-0.652248\pi$
$599$		−	43.4558i		−	1.77556i	0.460270	−	0.887779i	$-0.347752\pi$
$600$		0			0
$601$	−5.22792	−	3.01834i	−0.213251	−	0.123121i	0.389570	−	0.920997i	$-0.372624\pi$
$601$	−5.22792	−	3.01834i	−0.213251	−	0.123121i	−0.602822	+	0.797876i	$0.705957\pi$
$602$	−20.1903	−	8.24264i	−0.822894	−	0.335945i
$603$		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	$0.497542\pi$
$608$	−0.507306	−	0.878680i	−0.0205740	−	0.0356352i
$609$		0			0
$610$	−12.3640	+	21.4150i	−0.500602	+	0.867068i
$611$	−2.15232	+	1.24264i	−0.0870734	+	0.0502719i
$612$		0			0
$613$	−2.60660	+	4.51477i	−0.105280	+	0.182350i	−0.913852	−	0.406046i	$-0.866907\pi$
$613$	−2.60660	+	4.51477i	−0.105280	+	0.182350i	0.808573	+	0.588396i	$0.200240\pi$
$614$	−24.6690			−0.995559
$615$		0			0
$616$	−4.86396	−	6.27231i	−0.195975	−	0.252719i
$617$	36.1119	−	20.8492i	1.45381	−	0.839359i	0.455117	−	0.890431i	$-0.349597\pi$
$617$	36.1119	−	20.8492i	1.45381	−	0.839359i	0.998695	+	0.0510726i	$0.0162640\pi$
$618$		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
$623$	16.8493	+	21.7279i	0.675051	+	0.870511i
$624$		0			0
$625$	−34.2279	+	59.2845i	−1.36912	+	2.37138i
$626$	1.13770			0.0454718
$627$		0			0
$628$		−	14.6969i		−	0.586472i
$629$	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	$0.269842\pi$
$632$			11.2426i			0.447208i
$633$		0			0
$634$	7.24264			0.287642
$635$	−10.9612	+	18.9853i	−0.434980	+	0.753408i
$636$		0			0
$637$	−12.0000	+	12.2474i	−0.475457	+	0.485262i
$638$			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	−0.996829	−	0.0795681i	$-0.974646\pi$
$641$	−36.1119	+	20.8492i	−1.42634	+	0.823496i	−0.429507	+	0.903064i	$0.641313\pi$
$642$		0			0
$643$	−2.27208	+	1.31178i	−0.0896020	+	0.0517317i	−0.544132	−	0.839000i	$-0.683141\pi$
$643$	−2.27208	+	1.31178i	−0.0896020	+	0.0517317i	0.454530	+	0.890732i	$0.349807\pi$
$644$	−10.3923	−	4.24264i	−0.409514	−	0.167183i
$645$		0			0
$646$	1.02944			0.0405027
$647$	5.82655	−	10.0919i	0.229065	−	0.396753i	−0.728466	−	0.685082i	$-0.759766\pi$
$647$	5.82655	−	10.0919i	0.229065	−	0.396753i	0.957531	+	0.288329i	$0.0930997\pi$
$648$		0			0
$649$	29.9558	−	17.2950i	1.17587	−	0.678889i
$650$	−15.2913	+	26.4853i	−0.599774	+	1.03884i
$651$		0			0
$652$	3.12132	+	5.40629i	0.122240	+	0.211726i
$653$	−9.31615	−	5.37868i	−0.364569	−	0.210484i	0.306514	−	0.951866i	$-0.400837\pi$
$653$	−9.31615	−	5.37868i	−0.364569	−	0.210484i	−0.671083	+	0.741382i	$0.734171\pi$
$654$		0			0
$655$	10.8640	+	18.8169i	0.424490	+	0.735238i
$656$	−1.01461	−	1.75736i	−0.0396139	−	0.0686134i
$657$		0			0
$658$	0.363961	+	2.65962i	0.0141887	+	0.103683i
$659$	−5.19615	−	3.00000i	−0.202413	−	0.116863i	0.395367	−	0.918523i	$-0.370617\pi$
$659$	−5.19615	−	3.00000i	−0.202413	−	0.116863i	−0.597781	+	0.801660i	$0.703951\pi$
$660$		0			0
$661$		−	40.5546i		−	1.57739i	−0.614784	−	0.788696i	$-0.710757\pi$
$661$		−	40.5546i		−	1.57739i	0.614784	−	0.788696i	$-0.289243\pi$
$662$			17.4558i			0.678441i
$663$		0			0
$664$	−2.74264	−	1.58346i	−0.106435	−	0.0614503i
$665$	1.52192	+	11.1213i	0.0590174	+	0.431266i
$666$		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
$671$	8.87039	+	15.3640i	0.342437	+	0.593119i
$672$		0			0
$673$	7.98528	−	13.8309i	0.307810	−	0.533143i	−0.670073	−	0.742295i	$-0.733737\pi$
$673$	7.98528	−	13.8309i	0.307810	−	0.533143i	0.977883	+	0.209153i	$0.0670706\pi$
$674$	−4.33013	+	2.50000i	−0.166790	+	0.0962964i
$675$		0			0
$676$	3.50000	−	6.06218i	0.134615	−	0.233161i
$677$	12.5446			0.482129			0.241064	−	0.970509i	$-0.422503\pi$
$677$	12.5446			0.482129			0.241064	+	0.970509i	$0.422503\pi$
$678$		0			0
$679$	9.21320	+	3.76127i	0.353570	+	0.144344i
$680$	3.67423	−	2.12132i	0.140900	−	0.0813489i
$681$		0			0
$682$	14.5919	−	8.42463i	0.558752	−	0.322596i
$683$	22.4912	+	12.9853i	0.860601	+	0.496868i	0.864213	−	0.503125i	$-0.167817\pi$
$683$	22.4912	+	12.9853i	0.860601	+	0.496868i	−0.00361277	+	0.999993i	$0.501150\pi$
$684$		0			0
$685$			60.5708i			2.31429i
$686$	7.34847	+	17.0000i	0.280566	+	0.649063i
$687$		0			0
$688$	−4.12132	+	7.13834i	−0.157124	+	0.272147i
$689$	−3.04384			−0.115961
$690$		0			0
$691$		−	0.840532i		−	0.0319753i	−0.999872	−	0.0159877i	$-0.994911\pi$
$691$		−	0.840532i		−	0.0319753i	0.999872	−	0.0159877i	$-0.00508925\pi$
$692$	−20.7846			−0.790112
$693$		0			0
$694$	−14.4853			−0.549854
$695$		−	84.4264i		−	3.20248i
$696$		0			0
$697$	2.05887			0.0779854
$698$	−18.4582	+	31.9706i	−0.698654	+	1.21010i
$699$		0			0
$700$	20.2426	+	26.1039i	0.765100	+	0.986633i
$701$		−	38.6985i		−	1.46162i	−0.682580	−	0.730811i	$-0.739142\pi$
$701$		−	38.6985i		−	1.46162i	0.682580	−	0.730811i	$-0.260858\pi$
$702$		0			0
$703$	7.24264	+	4.18154i	0.273161	+	0.157710i
$704$	−2.59808	+	1.50000i	−0.0979187	+	0.0565334i
$705$		0			0
$706$	16.2426	−	9.37769i	0.611300	−	0.352934i
$707$		0			0
$708$		0			0
$709$	−6.97056			−0.261785			−0.130892	−	0.991397i	$-0.541784\pi$
$709$	−6.97056			−0.261785			−0.130892	+	0.991397i	$0.541784\pi$
$710$	21.4150	−	37.0919i	0.803691	−	1.39203i
$711$		0			0
$712$	9.00000	−	5.19615i	0.337289	−	0.194734i
$713$	11.9142	−	20.6360i	0.446191	−	0.772826i
$714$		0			0
$715$	15.3640	+	26.6112i	0.574580	+	0.995201i
$716$	−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	$-0.0251813\pi$
$719$	11.5300	+	19.9706i	0.429997	+	0.744776i	−0.566876	+	0.823803i	$0.691848\pi$
$720$		0			0
$721$	37.4558	+	15.2913i	1.39493	+	0.569477i
$722$	−15.5630	−	8.98528i	−0.579194	−	0.334398i
$723$		0			0
$724$			2.02922i			0.0754155i
$725$		−	15.5147i		−	0.576202i
$726$		0			0
$727$	−22.8640	−	13.2005i	−0.847977	−	0.489580i	0.0119905	−	0.999928i	$-0.496183\pi$
$727$	−22.8640	−	13.2005i	−0.847977	−	0.489580i	−0.859968	+	0.510348i	$0.829517\pi$
$728$	3.97141	+	5.12132i	0.147190	+	0.189809i
$729$		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	$0.407578\pi$
$734$	−9.43924	−	16.3492i	−0.348409	−	0.603462i
$735$		0			0
$736$	−2.12132	+	3.67423i	−0.0781929	+	0.135434i
$737$	−25.9808	+	15.0000i	−0.957014	+	0.552532i
$738$		0			0
$739$	17.7279	−	30.7057i	0.652132	−	1.12953i	−0.330472	−	0.943816i	$-0.607208\pi$
$739$	17.7279	−	30.7057i	0.652132	−	1.12953i	0.982605	−	0.185710i	$-0.0594586\pi$
$740$	34.4669			1.26703
$741$		0			0
$742$	−1.24264	+	3.04384i	−0.0456188	+	0.111743i
$743$	18.6323	−	10.7574i	0.683553	−	0.394649i	−0.117640	−	0.993056i	$-0.537533\pi$
$743$	18.6323	−	10.7574i	0.683553	−	0.394649i	0.801192	+	0.598407i	$0.204199\pi$
$744$		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
$749$	11.4685	−	8.89340i	0.419049	−	0.324958i
$750$		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	$0.329011\pi$
$752$	1.01461			0.0369991
$753$		0			0
$754$		−	3.04384i		−	0.110850i
$755$	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	$0.778583\pi$
$758$		−	4.48528i		−	0.162913i
$759$		0			0
$760$	4.24264			0.153897
$761$	−2.53653	+	4.39340i	−0.0919491	+	0.159261i	−0.908331	−	0.418252i	$-0.862643\pi$
$761$	−2.53653	+	4.39340i	−0.0919491	+	0.159261i	0.816382	+	0.577512i	$0.195976\pi$
$762$		0			0
$763$	−1.51472	+	3.71029i	−0.0548365	+	0.134321i
$764$			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
$769$	−42.4706	+	24.5204i	−1.53153	+	0.884228i	−0.532236	+	0.846596i	$0.678648\pi$
$769$	−42.4706	+	24.5204i	−1.53153	+	0.884228i	−0.999292	+	0.0376319i	$0.988019\pi$
$770$	32.8835	−	4.50000i	1.18504	−	0.162169i
$771$		0			0
$772$	7.48528			0.269401
$773$	−11.5300	+	19.9706i	−0.414706	+	0.718291i	−0.995398	−	0.0958322i	$-0.969449\pi$
$773$	−11.5300	+	19.9706i	−0.414706	+	0.718291i	0.580692	+	0.814123i	$0.302782\pi$
$774$		0			0
$775$	−60.7279	+	35.0613i	−2.18141	+	1.25944i
$776$	1.88064	−	3.25736i	0.0675109	−	0.116932i
$777$		0			0
$778$	−9.72792	−	16.8493i	−0.348763	−	0.604075i
$779$	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
$784$	6.74264	−	1.88064i	0.240809	−	0.0671656i
$785$	53.2223	+	30.7279i	1.89959	+	1.09673i
$786$		0			0
$787$		−	37.0905i		−	1.32213i	−0.750327	−	0.661067i	$-0.770104\pi$
$787$		−	37.0905i		−	1.32213i	0.750327	−	0.661067i	$-0.229896\pi$
$788$			9.51472i			0.338948i
$789$		0			0
$790$	−40.7132	−	23.5058i	−1.44851	−	0.836298i
$791$	−17.7408	+	13.7574i	−0.630789	+	0.489155i
$792$		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
$797$	18.8169	+	32.5919i	0.666530	+	1.15446i	0.978868	+	0.204493i	$0.0655545\pi$
$797$	18.8169	+	32.5919i	0.666530	+	1.15446i	−0.312338	+	0.949971i	$0.601112\pi$
$798$		0			0
$799$	−0.514719	+	0.891519i	−0.0182094	+	0.0315397i
$800$	10.8126	−	6.24264i	0.382282	−	0.220711i
$801$		0			0
$802$		0			0
$803$	25.0892			0.885380
$804$		0			0
$805$	37.0919	−	28.7635i	1.30732	−	1.01378i
$806$	−11.9142	+	6.87868i	−0.419661	+	0.242291i
$807$		0			0
$808$		0			0
$809$	−35.4815	−	20.4853i	−1.24746	−	0.720224i	−0.276862	−	0.960910i	$-0.589294\pi$
$809$	−35.4815	−	20.4853i	−1.24746	−	0.720224i	−0.970603	+	0.240686i	$0.922628\pi$
$810$		0			0
$811$		−	31.1769i		−	1.09477i	−0.836881	−	0.547385i	$-0.815623\pi$
$811$		−	31.1769i		−	1.09477i	0.836881	−	0.547385i	$-0.184377\pi$
$812$	−3.04384	−	1.24264i	−0.106818	−	0.0436081i
$813$		0			0
$814$	12.3640	−	21.4150i	0.433357	−	0.750596i
$815$	−26.1039			−0.914378
$816$		0			0
$817$		−	8.36308i		−	0.292587i
$818$	−4.60181			−0.160898
$819$		0			0
$820$	8.48528			0.296319
$821$			49.2426i			1.71858i	0.511489	+	0.859290i	$0.329094\pi$
$821$			49.2426i			1.71858i	−0.511489	+	0.859290i	$0.670906\pi$
$822$		0			0
$823$	−37.9411			−1.32254			−0.661272	−	0.750146i	$-0.729983\pi$
$823$	−37.9411			−1.32254			−0.661272	+	0.750146i	$0.729983\pi$
$824$	7.64564	−	13.2426i	0.266349	−	0.461329i
$825$		0			0
$826$	4.13604	+	30.2238i	0.143911	+	1.05162i
$827$			4.02944i			0.140117i	0.997543	+	0.0700586i	$0.0223186\pi$
$827$			4.02944i			0.140117i	−0.997543	+	0.0700586i	$0.977681\pi$
$828$		0			0
$829$	−35.3345	−	20.4004i	−1.22722	−	0.708535i	−0.260772	−	0.965401i	$-0.583977\pi$
$829$	−35.3345	−	20.4004i	−1.22722	−	0.708535i	−0.966447	+	0.256865i	$0.917310\pi$
$830$	11.4685	−	6.62132i	0.398076	−	0.229829i
$831$		0			0
$832$	2.12132	−	1.22474i	0.0735436	−	0.0424604i
$833$	−1.76810	+	6.87868i	−0.0612612	+	0.238332i
$834$		0			0
$835$	−96.4264			−3.33697
$836$	1.52192	−	2.63604i	0.0526366	−	0.0911693i
$837$		0			0
$838$	3.51472	−	2.02922i	0.121414	−	0.0700984i
$839$	12.0373	−	20.8492i	0.415574	−	0.719796i	−0.579914	−	0.814678i	$-0.696914\pi$
$839$	12.0373	−	20.8492i	0.415574	−	0.719796i	0.995489	+	0.0948817i	$0.0302473\pi$
$840$		0			0
$841$	−13.7279	−	23.7775i	−0.473377	−	0.819912i
$842$	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
$847$	−2.00000	+	4.89898i	−0.0687208	+	0.168331i
$848$	1.07616	+	0.621320i	0.0369554	+	0.0213362i
$849$		0			0
$850$			12.6677i			0.434499i
$851$		−	34.9706i		−	1.19878i
$852$		0			0
$853$	−1.97056	−	1.13770i	−0.0674708	−	0.0389543i	0.465885	−	0.884845i	$-0.345736\pi$
$853$	−1.97056	−	1.13770i	−0.0674708	−	0.0389543i	−0.533356	+	0.845891i	$0.679069\pi$
$854$	−15.5014	+	2.12132i	−0.530448	+	0.0725901i
$855$		0			0
$856$	−2.74264	−	4.75039i	−0.0937415	−	0.162365i
$857$	−10.0081	−	17.3345i	−0.341870	−	0.592136i	0.642910	−	0.765942i	$-0.277727\pi$
$857$	−10.0081	−	17.3345i	−0.341870	−	0.592136i	−0.984780	+	0.173806i	$0.944394\pi$
$858$		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	$0.691011\pi$
$860$	−17.2335	−	29.8492i	−0.587656	−	1.01785i
$861$		0			0
$862$	10.2426	−	17.7408i	0.348866	−	0.604253i
$863$	43.7215	−	25.2426i	1.48830	−	0.859269i	0.488388	−	0.872627i	$-0.337585\pi$
$863$	43.7215	−	25.2426i	1.48830	−	0.859269i	0.999911	+	0.0133573i	$0.00425189\pi$
$864$		0			0
$865$	43.4558	−	75.2677i	1.47754	−	2.55918i
$866$	−3.46410			−0.117715
$867$		0			0
$868$	2.01472	+	14.7224i	0.0683840	+	0.499712i
$869$	−29.2092	+	16.8640i	−0.990856	+	0.572071i
$870$		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
$875$	−82.0473	+	11.2279i	−2.77371	+	0.379573i
$876$		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	$0.0990601\pi$
$878$	−27.2416			−0.919358
$879$		0			0
$880$		−	12.5446i		−	0.422879i
$881$	−39.7862			−1.34043			−0.670215	−	0.742167i	$-0.733798\pi$
$881$	−39.7862			−1.34043			−0.670215	+	0.742167i	$0.733798\pi$
$882$		0			0
$883$	−9.45584			−0.318214			−0.159107	−	0.987261i	$-0.550862\pi$
$883$	−9.45584			−0.318214			−0.159107	+	0.987261i	$0.550862\pi$
$884$			2.48528i			0.0835891i
$885$		0			0
$886$	−34.4558			−1.15757
$887$	22.4296	−	38.8492i	0.753113	−	1.30443i	−0.193194	−	0.981161i	$-0.561885\pi$
$887$	22.4296	−	38.8492i	0.753113	−	1.30443i	0.946307	−	0.323269i	$-0.104782\pi$
$888$		0			0
$889$	−13.7426	+	1.88064i	−0.460913	+	0.0630745i
$890$			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
$895$	34.4558	−	19.8931i	1.15173	−	0.664953i
$896$	−0.358719	−	2.62132i	−0.0119840	−	0.0875722i
$897$		0			0
$898$	10.2426			0.341801
$899$	3.48960	−	6.04416i	0.116385	−	0.201584i
$900$		0			0
$901$	−1.09188	+	0.630399i	−0.0363759	+	0.0210016i
$902$	3.04384	−	5.27208i	0.101349	−	0.175541i
$903$		0			0
$904$	4.24264	+	7.34847i	0.141108	+	0.244406i
$905$	−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
$910$	−26.8492	+	3.67423i	−0.890044	+	0.121800i
$911$	−16.2189	−	9.36396i	−0.537355	−	0.310242i	0.206651	−	0.978415i	$-0.433743\pi$
$911$	−16.2189	−	9.36396i	−0.537355	−	0.310242i	−0.744006	+	0.668173i	$0.767077\pi$
$912$		0			0
$913$		−	9.50079i		−	0.314430i
$914$		−	23.0000i		−	0.760772i
$915$		0			0
$916$	−12.0000	−	6.92820i	−0.396491	−	0.228914i
$917$	−5.19615	+	12.7279i	−0.171592	+	0.420313i
$918$		0			0
$919$	−9.75736	−	16.9002i	−0.321866	−	0.557488i	0.659007	−	0.752136i	$-0.270977\pi$
$919$	−9.75736	−	16.9002i	−0.321866	−	0.557488i	−0.980873	+	0.194649i	$0.937643\pi$
$920$	−8.87039	−	15.3640i	−0.292448	−	0.506535i
$921$		0			0
$922$	−19.7574	−	11.4069i	−0.650674	−	0.375667i
$923$	12.5446	+	21.7279i	0.412911	+	0.715183i
$924$		0			0
$925$	−51.4558	+	89.1241i	−1.69186	+	2.93038i
$926$	18.5813	−	10.7279i	0.610620	−	0.352541i
$927$		0			0
$928$	−0.621320	+	1.07616i	−0.0203958	+	0.0353266i
$929$	−3.29002			−0.107942			−0.0539711	−	0.998543i	$-0.517188\pi$
$929$	−3.29002			−0.107942			−0.0539711	+	0.998543i	$0.517188\pi$
$930$		0			0
$931$	−4.97056	+	5.07306i	−0.162904	+	0.166263i
$932$	5.82655	−	3.36396i	0.190855	−	0.110190i
$933$		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	$-0.0208512\pi$
$938$	−3.58719	−	26.2132i	−0.117126	−	0.855891i
$939$		0			0
$940$	−2.12132	+	3.67423i	−0.0691898	+	0.119840i
$941$	−52.0846			−1.69791			−0.848955	−	0.528465i	$-0.822768\pi$
$941$	−52.0846			−1.69791			−0.848955	+	0.528465i	$0.822768\pi$
$942$		0			0
$943$		−	8.60927i		−	0.280356i
$944$	11.5300			0.375270
$945$		0			0
$946$	−24.7279			−0.803974
$947$			22.9706i			0.746443i	0.927742	+	0.373221i	$0.121747\pi$
$947$			22.9706i			0.746443i	−0.927742	+	0.373221i	$0.878253\pi$
$948$		0			0
$949$	−20.4853			−0.664980
$950$	−6.33386	+	10.9706i	−0.205497	+	0.355932i
$951$		0			0
$952$	2.48528	+	1.01461i	0.0805484	+	0.0328838i
$953$			41.6985i			1.35075i	0.737476	+	0.675373i	$0.236017\pi$
$953$			41.6985i			1.35075i	−0.737476	+	0.675373i	$0.763983\pi$
$954$		0			0
$955$	−30.7279	−	17.7408i	−0.994332	−	0.574078i
$956$	11.0227	−	6.36396i	0.356500	−	0.205825i
$957$		0			0
$958$	−31.6066	+	18.2481i	−1.02116	+	0.589569i
$959$	−30.2854	+	23.4853i	−0.977966	+	0.758379i
$960$		0			0
$961$	−0.544156			−0.0175534
$962$	−10.0951	+	17.4853i	−0.325480	+	0.563748i
$963$		0			0
$964$	14.7426	−	8.51167i	0.474828	−	0.274142i
$965$	−15.6500	+	27.1066i	−0.503791	+	0.872592i
$966$		0			0
$967$	−11.1360	−	19.2882i	−0.358111	−	0.620266i	0.629534	−	0.776973i	$-0.283246\pi$
$967$	−11.1360	−	19.2882i	−0.358111	−	0.620266i	−0.987645	+	0.156706i	$0.949912\pi$
$968$	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	−0.903130	−	0.429367i	$-0.858737\pi$
$971$	−25.6581	−	44.4411i	−0.823407	−	1.42618i	0.0797229	−	0.996817i	$-0.474596\pi$
$972$		0			0
$973$	42.2132	−	32.7349i	1.35329	−	1.04943i
$974$	−24.4334	−	14.1066i	−0.782895	−	0.452005i
$975$		0			0
$976$			5.91359i			0.189289i
$977$			31.7574i			1.01601i	0.861355	+	0.508004i	$0.169616\pi$
$977$			31.7574i			1.01601i	−0.861355	+	0.508004i	$0.830384\pi$
$978$		0			0
$979$	27.0000	+	15.5885i	0.862924	+	0.498209i
$980$	−7.28692	+	28.3492i	−0.232772	+	0.905583i
$981$		0			0
$982$	9.98528	+	17.2950i	0.318643	+	0.551906i
$983$	−4.05845	−	7.02944i	−0.129444	−	0.224204i	0.794017	−	0.607895i	$-0.207986\pi$
$983$	−4.05845	−	7.02944i	−0.129444	−	0.224204i	−0.923461	+	0.383691i	$0.874653\pi$
$984$		0			0
$985$	−34.4558	−	19.8931i	−1.09785	−	0.633847i
$986$	−0.630399	−	1.09188i	−0.0200760	−	0.0347726i
$987$		0			0
$988$	−1.24264	+	2.15232i	−0.0395337	+	0.0684743i
$989$	−30.2854	+	17.4853i	−0.963020	+	0.556000i
$990$		0			0
$991$	−4.89340	+	8.47561i	−0.155444	+	0.269237i	−0.933221	−	0.359304i	$-0.883014\pi$
$991$	−4.89340	+	8.47561i	−0.155444	+	0.269237i	0.777777	+	0.628541i	$0.216347\pi$
$992$	5.61642			0.178321
$993$		0			0
$994$	26.8492	−	3.67423i	0.851606	−	0.116540i
$995$	−58.4185	+	33.7279i	−1.85199	+	1.06925i
$996$		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	1134.2.l.f.269.4		8
3.2	odd	2	inner	1134.2.l.f.269.1		8
7.5	odd	6		1134.2.t.e.593.4		8
9.2	odd	6		126.2.k.a.17.1	✓	8
9.4	even	3		1134.2.t.e.1025.1		8
9.5	odd	6		1134.2.t.e.1025.4		8
9.7	even	3		126.2.k.a.17.4	yes	8
21.5	even	6		1134.2.t.e.593.1		8
36.7	odd	6		1008.2.bt.c.17.4		8
36.11	even	6		1008.2.bt.c.17.1		8
45.2	even	12		3150.2.bp.b.899.4		8
45.7	odd	12		3150.2.bp.e.899.4		8
45.29	odd	6		3150.2.bf.a.1151.4		8
45.34	even	6		3150.2.bf.a.1151.2		8
45.38	even	12		3150.2.bp.e.899.1		8
45.43	odd	12		3150.2.bp.b.899.1		8
63.2	odd	6		882.2.k.a.215.3		8
63.5	even	6	inner	1134.2.l.f.215.2		8
63.11	odd	6		882.2.d.a.881.4		8
63.16	even	3		882.2.k.a.215.2		8
63.20	even	6		882.2.k.a.521.2		8
63.25	even	3		882.2.d.a.881.5		8
63.34	odd	6		882.2.k.a.521.3		8
63.38	even	6		882.2.d.a.881.1		8
63.40	odd	6	inner	1134.2.l.f.215.3		8
63.47	even	6		126.2.k.a.89.4	yes	8
63.52	odd	6		882.2.d.a.881.8		8
63.61	odd	6		126.2.k.a.89.1	yes	8
252.11	even	6		7056.2.k.f.881.8		8
252.47	odd	6		1008.2.bt.c.593.4		8
252.115	even	6		7056.2.k.f.881.7		8
252.151	odd	6		7056.2.k.f.881.1		8
252.187	even	6		1008.2.bt.c.593.1		8
252.227	odd	6		7056.2.k.f.881.2		8
315.47	odd	12		3150.2.bp.b.1349.1		8
315.124	odd	6		3150.2.bf.a.1601.4		8
315.173	odd	12		3150.2.bp.e.1349.4		8
315.187	even	12		3150.2.bp.e.1349.1		8
315.299	even	6		3150.2.bf.a.1601.2		8
315.313	even	12		3150.2.bp.b.1349.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.k.a.17.1	✓	8	9.2	odd	6
126.2.k.a.17.4	yes	8	9.7	even	3
126.2.k.a.89.1	yes	8	63.61	odd	6
126.2.k.a.89.4	yes	8	63.47	even	6
882.2.d.a.881.1		8	63.38	even	6
882.2.d.a.881.4		8	63.11	odd	6
882.2.d.a.881.5		8	63.25	even	3
882.2.d.a.881.8		8	63.52	odd	6
882.2.k.a.215.2		8	63.16	even	3
882.2.k.a.215.3		8	63.2	odd	6
882.2.k.a.521.2		8	63.20	even	6
882.2.k.a.521.3		8	63.34	odd	6
1008.2.bt.c.17.1		8	36.11	even	6
1008.2.bt.c.17.4		8	36.7	odd	6
1008.2.bt.c.593.1		8	252.187	even	6
1008.2.bt.c.593.4		8	252.47	odd	6
1134.2.l.f.215.2		8	63.5	even	6	inner
1134.2.l.f.215.3		8	63.40	odd	6	inner
1134.2.l.f.269.1		8	3.2	odd	2	inner
1134.2.l.f.269.4		8	1.1	even	1	trivial
1134.2.t.e.593.1		8	21.5	even	6
1134.2.t.e.593.4		8	7.5	odd	6
1134.2.t.e.1025.1		8	9.4	even	3
1134.2.t.e.1025.4		8	9.5	odd	6
3150.2.bf.a.1151.2		8	45.34	even	6
3150.2.bf.a.1151.4		8	45.29	odd	6
3150.2.bf.a.1601.2		8	315.299	even	6
3150.2.bf.a.1601.4		8	315.124	odd	6
3150.2.bp.b.899.1		8	45.43	odd	12
3150.2.bp.b.899.4		8	45.2	even	12
3150.2.bp.b.1349.1		8	315.47	odd	12
3150.2.bp.b.1349.4		8	315.313	even	12
3150.2.bp.e.899.1		8	45.38	even	12
3150.2.bp.e.899.4		8	45.7	odd	12
3150.2.bp.e.1349.1		8	315.187	even	12
3150.2.bp.e.1349.4		8	315.173	odd	12
7056.2.k.f.881.1		8	252.151	odd	6
7056.2.k.f.881.2		8	252.227	odd	6
7056.2.k.f.881.7		8	252.115	even	6
7056.2.k.f.881.8		8	252.11	even	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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(2.09077 - 3.62132i) q^{5} +(2.62132 - 0.358719i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(2.09077 - 3.62132i) q^{5} +(2.62132 - 0.358719i) q^{7} -1.00000i q^{8} +(3.62132 + 2.09077i) q^{10} +(2.59808 - 1.50000i) q^{11} +(-2.12132 + 1.22474i) q^{13} +(0.358719 + 2.62132i) q^{14} +1.00000 q^{16} +(-0.507306 + 0.878680i) q^{17} +(-0.878680 + 0.507306i) q^{19} +(-2.09077 + 3.62132i) q^{20} +(1.50000 + 2.59808i) q^{22} +(3.67423 + 2.12132i) q^{23} +(-6.24264 - 10.8126i) q^{25} +(-1.22474 - 2.12132i) q^{26} +(-2.62132 + 0.358719i) q^{28} +(1.07616 + 0.621320i) q^{29} -5.61642i q^{31} +1.00000i q^{32} +(-0.878680 - 0.507306i) q^{34} +(4.18154 - 10.2426i) q^{35} +(-4.12132 - 7.13834i) q^{37} +(-0.507306 - 0.878680i) q^{38} +(-3.62132 - 2.09077i) q^{40} +(-1.01461 - 1.75736i) q^{41} +(-4.12132 + 7.13834i) q^{43} +(-2.59808 + 1.50000i) q^{44} +(-2.12132 + 3.67423i) q^{46} +1.01461 q^{47} +(6.74264 - 1.88064i) q^{49} +(10.8126 - 6.24264i) q^{50} +(2.12132 - 1.22474i) q^{52} +(1.07616 + 0.621320i) q^{53} -12.5446i q^{55} +(-0.358719 - 2.62132i) q^{56} +(-0.621320 + 1.07616i) q^{58} +11.5300 q^{59} +5.91359i q^{61} +5.61642 q^{62} -1.00000 q^{64} +10.2426i q^{65} -10.0000 q^{67} +(0.507306 - 0.878680i) q^{68} +(10.2426 + 4.18154i) q^{70} -10.2426i q^{71} +(7.24264 + 4.18154i) q^{73} +(7.13834 - 4.12132i) q^{74} +(0.878680 - 0.507306i) q^{76} +(6.27231 - 4.86396i) q^{77} -11.2426 q^{79} +(2.09077 - 3.62132i) q^{80} +(1.75736 - 1.01461i) q^{82} +(1.58346 - 2.74264i) q^{83} +(2.12132 + 3.67423i) q^{85} +(-7.13834 - 4.12132i) q^{86} +(-1.50000 - 2.59808i) q^{88} +(5.19615 + 9.00000i) q^{89} +(-5.12132 + 3.97141i) q^{91} +(-3.67423 - 2.12132i) q^{92} +1.01461i q^{94} +4.24264i q^{95} +(3.25736 + 1.88064i) q^{97} +(1.88064 + 6.74264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 4 q^{7}+O(q^{10}) \) 8 * q - 8 * q^4 + 4 * q^7	\( 8 q - 8 q^{4} + 4 q^{7} + 12 q^{10} + 8 q^{16} - 24 q^{19} + 12 q^{22} - 16 q^{25} - 4 q^{28} - 24 q^{34} - 16 q^{37} - 12 q^{40} - 16 q^{43} + 20 q^{49} + 12 q^{58} - 8 q^{64} - 80 q^{67} + 48 q^{70} + 24 q^{73} + 24 q^{76} - 56 q^{79} + 48 q^{82} - 12 q^{88} - 24 q^{91} + 60 q^{97}+O(q^{100}) \) 8 * q - 8 * q^4 + 4 * q^7 + 12 * q^10 + 8 * q^16 - 24 * q^19 + 12 * q^22 - 16 * q^25 - 4 * q^28 - 24 * q^34 - 16 * q^37 - 12 * q^40 - 16 * q^43 + 20 * q^49 + 12 * q^58 - 8 * q^64 - 80 * q^67 + 48 * q^70 + 24 * q^73 + 24 * q^76 - 56 * q^79 + 48 * q^82 - 12 * q^88 - 24 * q^91 + 60 * q^97

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