LMFDB - Embedded newform 1134.2.t.e.1025.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(593,1134)]

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([1, 5]))

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

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

chi := DirichletCharacter("1134.593");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.t (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:	$\Z[a_1, \ldots, a_{5}]$
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			1025.2
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1134.1025
Dual form			1134.2.t.e.593.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +0.717439 q^{5} +(-1.00000 - 2.44949i) q^{7} -1.00000i q^{8} +(-0.621320 - 0.358719i) q^{10} +3.00000i q^{11} +(-2.12132 - 1.22474i) q^{13} +(-0.358719 + 2.62132i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.95680 + 5.12132i) q^{17} +(-5.12132 + 2.95680i) q^{19} +(0.358719 + 0.621320i) q^{20} +(1.50000 - 2.59808i) q^{22} +4.24264i q^{23} -4.48528 q^{25} +(1.22474 + 2.12132i) q^{26} +(1.62132 - 2.09077i) q^{28} +(6.27231 - 3.62132i) q^{29} +(7.86396 - 4.54026i) q^{31} +(0.866025 - 0.500000i) q^{32} +(5.12132 - 2.95680i) q^{34} +(-0.717439 - 1.75736i) q^{35} +(0.121320 + 0.210133i) q^{37} +5.91359 q^{38} -0.717439i q^{40} +(-5.91359 + 10.2426i) q^{41} +(0.121320 + 0.210133i) q^{43} +(-2.59808 + 1.50000i) q^{44} +(2.12132 - 3.67423i) q^{46} +(-2.95680 + 5.12132i) q^{47} +(-5.00000 + 4.89898i) q^{49} +(3.88437 + 2.24264i) q^{50} -2.44949i q^{52} +(-6.27231 - 3.62132i) q^{53} +2.15232i q^{55} +(-2.44949 + 1.00000i) q^{56} -7.24264 q^{58} +(4.03295 + 6.98528i) q^{59} +(-0.878680 - 0.507306i) q^{61} -9.08052 q^{62} -1.00000 q^{64} +(-1.52192 - 0.878680i) q^{65} +(5.00000 + 8.66025i) q^{67} -5.91359 q^{68} +(-0.257359 + 1.88064i) q^{70} -1.75736i q^{71} +(-1.24264 - 0.717439i) q^{73} -0.242641i q^{74} +(-5.12132 - 2.95680i) q^{76} +(7.34847 - 3.00000i) q^{77} +(1.37868 - 2.38794i) q^{79} +(-0.358719 + 0.621320i) q^{80} +(10.2426 - 5.91359i) q^{82} +(-3.31552 - 5.74264i) q^{83} +(-2.12132 + 3.67423i) q^{85} -0.242641i q^{86} +3.00000 q^{88} +(5.19615 + 9.00000i) q^{89} +(-0.878680 + 6.42090i) q^{91} +(-3.67423 + 2.12132i) q^{92} +(5.12132 - 2.95680i) q^{94} +(-3.67423 + 2.12132i) q^{95} +(-11.7426 + 6.77962i) q^{97} +(6.77962 - 1.74264i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 8 q^{7} + 12 q^{10} - 4 q^{16} - 24 q^{19} + 12 q^{22} + 32 q^{25} - 4 q^{28} + 12 q^{31} + 24 q^{34} - 16 q^{37} - 16 q^{43} - 40 q^{49} - 24 q^{58} - 24 q^{61} - 8 q^{64} + 40 q^{67} - 36 q^{70}+ \cdots - 60 q^{97}+O(q^{100}) $ 8 * q + 4 * q^4 - 8 * q^7 + 12 * q^10 - 4 * q^16 - 24 * q^19 + 12 * q^22 + 32 * q^25 - 4 * q^28 + 12 * q^31 + 24 * q^34 - 16 * q^37 - 16 * q^43 - 40 * q^49 - 24 * q^58 - 24 * q^61 - 8 * q^64 + 40 * q^67 - 36 * q^70 + 24 * q^73 - 24 * q^76 + 28 * q^79 + 48 * q^82 + 24 * q^88 - 24 * q^91 + 24 * q^94 - 60 * q^97

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.717439			0.320848			0.160424	−	0.987048i	$-0.448714\pi$
$5$	0.717439			0.320848			0.160424	+	0.987048i	$0.448714\pi$
$6$		0			0
$7$	−1.00000	−	2.44949i	−0.377964	−	0.925820i
$7$	−1.00000	−	2.44949i	−0.377964	−	0.925820i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.621320	−	0.358719i	−0.196479	−	0.113437i
$11$			3.00000i			0.904534i	0.891883	+	0.452267i	$0.149385\pi$
$11$			3.00000i			0.904534i	−0.891883	+	0.452267i	$0.850615\pi$
$12$		0			0
$13$	−2.12132	−	1.22474i	−0.588348	−	0.339683i	0.176096	−	0.984373i	$-0.443653\pi$
$13$	−2.12132	−	1.22474i	−0.588348	−	0.339683i	−0.764444	+	0.644690i	$0.776986\pi$
$14$	−0.358719	+	2.62132i	−0.0958718	+	0.700577i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.95680	+	5.12132i	−0.717128	+	1.24210i	0.245005	+	0.969522i	$0.421211\pi$
$17$	−2.95680	+	5.12132i	−0.717128	+	1.24210i	−0.962133	+	0.272581i	$0.912123\pi$
$18$		0			0
$19$	−5.12132	+	2.95680i	−1.17491	+	0.678335i	−0.954832	−	0.297146i	$-0.903965\pi$
$19$	−5.12132	+	2.95680i	−1.17491	+	0.678335i	−0.220080	+	0.975482i	$0.570632\pi$
$20$	0.358719	+	0.621320i	0.0802121	+	0.138931i
$21$		0			0
$22$	1.50000	−	2.59808i	0.319801	−	0.553912i
$23$			4.24264i			0.884652i	0.896854	+	0.442326i	$0.145847\pi$
$23$			4.24264i			0.884652i	−0.896854	+	0.442326i	$0.854153\pi$
$24$		0			0
$25$	−4.48528			−0.897056
$26$	1.22474	+	2.12132i	0.240192	+	0.416025i
$27$		0			0
$28$	1.62132	−	2.09077i	0.306401	−	0.395118i
$29$	6.27231	−	3.62132i	1.16474	−	0.672462i	0.212304	−	0.977204i	$-0.431903\pi$
$29$	6.27231	−	3.62132i	1.16474	−	0.672462i	0.952435	+	0.304741i	$0.0985700\pi$
$30$		0			0
$31$	7.86396	−	4.54026i	1.41241	−	0.815455i	0.416794	−	0.909001i	$-0.363154\pi$
$31$	7.86396	−	4.54026i	1.41241	−	0.815455i	0.995615	+	0.0935461i	$0.0298203\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	5.12132	−	2.95680i	0.878299	−	0.507086i
$35$	−0.717439	−	1.75736i	−0.121269	−	0.297048i
$36$		0			0
$37$	0.121320	+	0.210133i	0.0199449	+	0.0345457i	0.875826	−	0.482628i	$-0.160318\pi$
$37$	0.121320	+	0.210133i	0.0199449	+	0.0345457i	−0.855881	+	0.517173i	$0.826984\pi$
$38$	5.91359			0.959311
$39$		0			0
$40$		−	0.717439i		−	0.113437i
$41$	−5.91359	+	10.2426i	−0.923548	+	1.59963i	−0.129668	+	0.991558i	$0.541391\pi$
$41$	−5.91359	+	10.2426i	−0.923548	+	1.59963i	−0.793880	+	0.608074i	$0.791942\pi$
$42$		0			0
$43$	0.121320	+	0.210133i	0.0185012	+	0.0320450i	0.875128	−	0.483892i	$-0.160777\pi$
$43$	0.121320	+	0.210133i	0.0185012	+	0.0320450i	−0.856627	+	0.515937i	$0.827444\pi$
$44$	−2.59808	+	1.50000i	−0.391675	+	0.226134i
$45$		0			0
$46$	2.12132	−	3.67423i	0.312772	−	0.541736i
$47$	−2.95680	+	5.12132i	−0.431293	+	0.747021i	−0.996985	−	0.0775953i	$-0.975276\pi$
$47$	−2.95680	+	5.12132i	−0.431293	+	0.747021i	0.565692	+	0.824617i	$0.308609\pi$
$48$		0			0
$49$	−5.00000	+	4.89898i	−0.714286	+	0.699854i
$50$	3.88437	+	2.24264i	0.549333	+	0.317157i
$51$		0			0
$52$		−	2.44949i		−	0.339683i
$53$	−6.27231	−	3.62132i	−0.861568	−	0.497427i	0.00296896	−	0.999996i	$-0.499055\pi$
$53$	−6.27231	−	3.62132i	−0.861568	−	0.497427i	−0.864537	+	0.502569i	$0.832388\pi$
$54$		0			0
$55$			2.15232i			0.290218i
$56$	−2.44949	+	1.00000i	−0.327327	+	0.133631i
$57$		0			0
$58$	−7.24264			−0.951005
$59$	4.03295	+	6.98528i	0.525046	+	0.909406i	0.999575	+	0.0291661i	$0.00928518\pi$
$59$	4.03295	+	6.98528i	0.525046	+	0.909406i	−0.474529	+	0.880240i	$0.657381\pi$
$60$		0			0
$61$	−0.878680	−	0.507306i	−0.112503	−	0.0649539i	0.442692	−	0.896674i	$-0.354023\pi$
$61$	−0.878680	−	0.507306i	−0.112503	−	0.0649539i	−0.555196	+	0.831720i	$0.687357\pi$
$62$	−9.08052			−1.15323
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.52192	−	0.878680i	−0.188771	−	0.108987i
$66$		0			0
$67$	5.00000	+	8.66025i	0.610847	+	1.05802i	0.991098	+	0.133135i	$0.0425044\pi$
$67$	5.00000	+	8.66025i	0.610847	+	1.05802i	−0.380251	+	0.924883i	$0.624162\pi$
$68$	−5.91359			−0.717128
$69$		0			0
$70$	−0.257359	+	1.88064i	−0.0307603	+	0.224779i
$71$		−	1.75736i		−	0.208560i	−0.994548	−	0.104280i	$-0.966746\pi$
$71$		−	1.75736i		−	0.208560i	0.994548	−	0.104280i	$-0.0332538\pi$
$72$		0			0
$73$	−1.24264	−	0.717439i	−0.145440	−	0.0839699i	0.425514	−	0.904952i	$-0.360093\pi$
$73$	−1.24264	−	0.717439i	−0.145440	−	0.0839699i	−0.570954	+	0.820982i	$0.693427\pi$
$74$		−	0.242641i		−	0.0282064i
$75$		0			0
$76$	−5.12132	−	2.95680i	−0.587456	−	0.339168i
$77$	7.34847	−	3.00000i	0.837436	−	0.341882i
$78$		0			0
$79$	1.37868	−	2.38794i	0.155114	−	0.268665i	−0.777987	−	0.628281i	$-0.783759\pi$
$79$	1.37868	−	2.38794i	0.155114	−	0.268665i	0.933100	+	0.359616i	$0.117092\pi$
$80$	−0.358719	+	0.621320i	−0.0401061	+	0.0694657i
$81$		0			0
$82$	10.2426	−	5.91359i	1.13111	−	0.653047i
$83$	−3.31552	−	5.74264i	−0.363925	−	0.630337i	0.624678	−	0.780882i	$-0.285230\pi$
$83$	−3.31552	−	5.74264i	−0.363925	−	0.630337i	−0.988603	+	0.150546i	$0.951897\pi$
$84$		0			0
$85$	−2.12132	+	3.67423i	−0.230089	+	0.398527i
$86$		−	0.242641i		−	0.0261646i
$87$		0			0
$88$	3.00000			0.319801
$89$	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
$91$	−0.878680	+	6.42090i	−0.0921107	+	0.673093i
$92$	−3.67423	+	2.12132i	−0.383065	+	0.221163i
$93$		0			0
$94$	5.12132	−	2.95680i	0.528224	−	0.304970i
$95$	−3.67423	+	2.12132i	−0.376969	+	0.217643i
$96$		0			0
$97$	−11.7426	+	6.77962i	−1.19228	+	0.688366i	−0.958824	−	0.284001i	$-0.908338\pi$
$97$	−11.7426	+	6.77962i	−1.19228	+	0.688366i	−0.233460	+	0.972366i	$0.575005\pi$
$98$	6.77962	−	1.74264i	0.684845	−	0.176033i
$99$		0			0
$100$	−2.24264	−	3.88437i	−0.224264	−	0.388437i
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$		0			0
$103$		−	5.49333i		−	0.541273i	−0.962682	−	0.270637i	$-0.912766\pi$
$103$		−	5.49333i		−	0.541273i	0.962682	−	0.270637i	$-0.0872342\pi$
$104$	−1.22474	+	2.12132i	−0.120096	+	0.208013i
$105$		0			0
$106$	3.62132	+	6.27231i	0.351734	+	0.609221i
$107$	−9.94655	+	5.74264i	−0.961569	+	0.555162i	−0.896656	−	0.442729i	$-0.854010\pi$
$107$	−9.94655	+	5.74264i	−0.961569	+	0.555162i	−0.0649133	+	0.997891i	$0.520677\pi$
$108$		0			0
$109$	−9.24264	+	16.0087i	−0.885284	+	1.53336i	−0.0398971	+	0.999204i	$0.512703\pi$
$109$	−9.24264	+	16.0087i	−0.885284	+	1.53336i	−0.845387	+	0.534154i	$0.820630\pi$
$110$	1.07616	−	1.86396i	0.102608	−	0.177722i
$111$		0			0
$112$	2.62132	+	0.358719i	0.247691	+	0.0338958i
$113$	−7.34847	−	4.24264i	−0.691286	−	0.399114i	0.112808	−	0.993617i	$-0.464016\pi$
$113$	−7.34847	−	4.24264i	−0.691286	−	0.399114i	−0.804094	+	0.594503i	$0.797349\pi$
$114$		0			0
$115$			3.04384i			0.283839i
$116$	6.27231	+	3.62132i	0.582369	+	0.336231i
$117$		0			0
$118$		−	8.06591i		−	0.742527i
$119$	15.5014	+	2.12132i	1.42101	+	0.194461i
$120$		0			0
$121$	2.00000			0.181818
$122$	0.507306	+	0.878680i	0.0459293	+	0.0795519i
$123$		0			0
$124$	7.86396	+	4.54026i	0.706205	+	0.407727i
$125$	−6.80511			−0.608668
$126$		0			0
$127$	3.24264			0.287738			0.143869	−	0.989597i	$-0.454046\pi$
$127$	3.24264			0.287738			0.143869	+	0.989597i	$0.454046\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	0.878680	+	1.52192i	0.0770653	+	0.133481i
$131$	5.19615			0.453990			0.226995	−	0.973896i	$-0.427110\pi$
$131$	5.19615			0.453990			0.226995	+	0.973896i	$0.427110\pi$
$132$		0			0
$133$	12.3640	+	9.58783i	1.07209	+	0.831370i
$134$		−	10.0000i		−	0.863868i
$135$		0			0
$136$	5.12132	+	2.95680i	0.439150	+	0.253543i
$137$			2.48528i			0.212332i	0.994348	+	0.106166i	$0.0338575\pi$
$137$			2.48528i			0.212332i	−0.994348	+	0.106166i	$0.966143\pi$
$138$		0			0
$139$	−0.514719	−	0.297173i	−0.0436579	−	0.0252059i	0.478012	−	0.878353i	$-0.341357\pi$
$139$	−0.514719	−	0.297173i	−0.0436579	−	0.0252059i	−0.521670	+	0.853147i	$0.674691\pi$
$140$	1.16320	−	1.50000i	0.0983082	−	0.126773i
$141$		0			0
$142$	−0.878680	+	1.52192i	−0.0737372	+	0.127717i
$143$	3.67423	−	6.36396i	0.307255	−	0.532181i
$144$		0			0
$145$	4.50000	−	2.59808i	0.373705	−	0.215758i
$146$	0.717439	+	1.24264i	0.0593757	+	0.102842i
$147$		0			0
$148$	−0.121320	+	0.210133i	−0.00997247	+	0.0172728i
$149$		−	3.51472i		−	0.287937i	−0.989582	−	0.143968i	$-0.954014\pi$
$149$		−	3.51472i		−	0.287937i	0.989582	−	0.143968i	$-0.0459864\pi$
$150$		0			0
$151$	5.24264			0.426640			0.213320	−	0.976982i	$-0.431572\pi$
$151$	5.24264			0.426640			0.213320	+	0.976982i	$0.431572\pi$
$152$	2.95680	+	5.12132i	0.239828	+	0.415394i
$153$		0			0
$154$	−7.86396	−	1.07616i	−0.633696	−	0.0867193i
$155$	5.64191	−	3.25736i	0.453169	−	0.261637i
$156$		0			0
$157$	−12.7279	+	7.34847i	−1.01580	+	0.586472i	−0.912884	−	0.408219i	$-0.866150\pi$
$157$	−12.7279	+	7.34847i	−1.01580	+	0.586472i	−0.102915	+	0.994690i	$0.532817\pi$
$158$	−2.38794	+	1.37868i	−0.189975	+	0.109682i
$159$		0			0
$160$	0.621320	−	0.358719i	0.0491197	−	0.0283593i
$161$	10.3923	−	4.24264i	0.819028	−	0.334367i
$162$		0			0
$163$	1.12132	+	1.94218i	0.0878286	+	0.152124i	0.906593	−	0.422006i	$-0.138674\pi$
$163$	1.12132	+	1.94218i	0.0878286	+	0.152124i	−0.818764	+	0.574130i	$0.805341\pi$
$164$	−11.8272			−0.923548
$165$		0			0
$166$			6.63103i			0.514668i
$167$	8.06591	−	13.9706i	0.624159	−	1.08107i	−0.364544	−	0.931186i	$-0.618775\pi$
$167$	8.06591	−	13.9706i	0.624159	−	1.08107i	0.988703	−	0.149889i	$-0.0478915\pi$
$168$		0			0
$169$	−3.50000	−	6.06218i	−0.269231	−	0.466321i
$170$	3.67423	−	2.12132i	0.281801	−	0.162698i
$171$		0			0
$172$	−0.121320	+	0.210133i	−0.00925059	+	0.0160225i
$173$	−10.3923	+	18.0000i	−0.790112	+	1.36851i	0.135785	+	0.990738i	$0.456644\pi$
$173$	−10.3923	+	18.0000i	−0.790112	+	1.36851i	−0.925897	+	0.377776i	$0.876689\pi$
$174$		0			0
$175$	4.48528	+	10.9867i	0.339055	+	0.830513i
$176$	−2.59808	−	1.50000i	−0.195837	−	0.113067i
$177$		0			0
$178$		−	10.3923i		−	0.778936i
$179$	22.9369	+	13.2426i	1.71439	+	0.989801i	0.928420	+	0.371532i	$0.121167\pi$
$179$	22.9369	+	13.2426i	1.71439	+	0.989801i	0.785966	+	0.618269i	$0.212166\pi$
$180$		0			0
$181$		−	11.8272i		−	0.879108i	−0.898216	−	0.439554i	$-0.855137\pi$
$181$		−	11.8272i		−	0.879108i	0.898216	−	0.439554i	$-0.144863\pi$
$182$	3.97141	−	5.12132i	0.294380	−	0.379618i
$183$		0			0
$184$	4.24264			0.312772
$185$	0.0870399	+	0.150758i	0.00639930	+	0.0110839i
$186$		0			0
$187$	−15.3640	−	8.87039i	−1.12352	−	0.648667i
$188$	−5.91359			−0.431293
$189$		0			0
$190$	4.24264			0.307794
$191$	−7.34847	−	4.24264i	−0.531717	−	0.306987i	0.209999	−	0.977702i	$-0.432654\pi$
$191$	−7.34847	−	4.24264i	−0.531717	−	0.306987i	−0.741715	+	0.670715i	$0.765987\pi$
$192$		0			0
$193$	−4.74264	−	8.21449i	−0.341383	−	0.591292i	0.643307	−	0.765608i	$-0.277562\pi$
$193$	−4.74264	−	8.21449i	−0.341383	−	0.591292i	−0.984690	+	0.174316i	$0.944229\pi$
$194$	13.5592			0.973496
$195$		0			0
$196$	−6.74264	−	1.88064i	−0.481617	−	0.134331i
$197$		−	26.4853i		−	1.88700i	−0.331375	−	0.943499i	$-0.607513\pi$
$197$		−	26.4853i		−	1.88700i	0.331375	−	0.943499i	$-0.392487\pi$
$198$		0			0
$199$	19.9706	+	11.5300i	1.41568	+	0.817341i	0.995915	−	0.0902942i	$-0.0287807\pi$
$199$	19.9706	+	11.5300i	1.41568	+	0.817341i	0.419761	+	0.907635i	$0.362114\pi$
$200$			4.48528i			0.317157i
$201$		0			0
$202$		0			0
$203$	−15.1427	−	11.7426i	−1.06281	−	0.824172i
$204$		0			0
$205$	−4.24264	+	7.34847i	−0.296319	+	0.513239i
$206$	−2.74666	+	4.75736i	−0.191369	+	0.331461i
$207$		0			0
$208$	2.12132	−	1.22474i	0.147087	−	0.0849208i
$209$	−8.87039	−	15.3640i	−0.613578	−	1.06275i
$210$		0			0
$211$	0.121320	−	0.210133i	0.00835204	−	0.0144662i	−0.861819	−	0.507216i	$-0.830675\pi$
$211$	0.121320	−	0.210133i	0.00835204	−	0.0144662i	0.870171	+	0.492749i	$0.164008\pi$
$212$		−	7.24264i		−	0.497427i
$213$		0			0
$214$	11.4853			0.785118
$215$	0.0870399	+	0.150758i	0.00593607	+	0.0102816i
$216$		0			0
$217$	−18.9853	−	14.7224i	−1.28880	−	0.999424i
$218$	16.0087	−	9.24264i	1.08425	−	0.625991i
$219$		0			0
$220$	−1.86396	+	1.07616i	−0.125668	+	0.0725546i
$221$	12.5446	−	7.24264i	0.843843	−	0.487193i
$222$		0			0
$223$	−1.86396	+	1.07616i	−0.124820	+	0.0720649i	−0.561110	−	0.827741i	$-0.689626\pi$
$223$	−1.86396	+	1.07616i	−0.124820	+	0.0720649i	0.436290	+	0.899806i	$0.356292\pi$
$224$	−2.09077	−	1.62132i	−0.139695	−	0.108329i
$225$		0			0
$226$	4.24264	+	7.34847i	0.282216	+	0.488813i
$227$	−15.5885			−1.03464			−0.517321	−	0.855791i	$-0.673071\pi$
$227$	−15.5885			−1.03464			−0.517321	+	0.855791i	$0.673071\pi$
$228$		0			0
$229$		−	13.8564i		−	0.915657i	−0.889041	−	0.457829i	$-0.848627\pi$
$229$		−	13.8564i		−	0.915657i	0.889041	−	0.457829i	$-0.151373\pi$
$230$	1.52192	−	2.63604i	0.100352	−	0.173815i
$231$		0			0
$232$	−3.62132	−	6.27231i	−0.237751	−	0.411797i
$233$	16.2189	−	9.36396i	1.06253	−	0.613453i	0.136401	−	0.990654i	$-0.456446\pi$
$233$	16.2189	−	9.36396i	1.06253	−	0.613453i	0.926132	+	0.377200i	$0.123113\pi$
$234$		0			0
$235$	−2.12132	+	3.67423i	−0.138380	+	0.239681i
$236$	−4.03295	+	6.98528i	−0.262523	+	0.454703i
$237$		0			0
$238$	−12.3640	−	9.58783i	−0.801437	−	0.621486i
$239$	−11.0227	−	6.36396i	−0.712999	−	0.411650i	0.0991712	−	0.995070i	$-0.468381\pi$
$239$	−11.0227	−	6.36396i	−0.712999	−	0.411650i	−0.812171	+	0.583420i	$0.801714\pi$
$240$		0			0
$241$		−	7.22538i		−	0.465427i	−0.972545	−	0.232714i	$-0.925239\pi$
$241$		−	7.22538i		−	0.465427i	0.972545	−	0.232714i	$-0.0747605\pi$
$242$	−1.73205	−	1.00000i	−0.111340	−	0.0642824i
$243$		0			0
$244$		−	1.01461i		−	0.0649539i
$245$	−3.58719	+	3.51472i	−0.229177	+	0.224547i
$246$		0			0
$247$	14.4853			0.921676
$248$	−4.54026	−	7.86396i	−0.288307	−	0.499362i
$249$		0			0
$250$	5.89340	+	3.40256i	0.372731	+	0.215196i
$251$	−27.4156			−1.73046			−0.865230	−	0.501375i	$-0.832828\pi$
$251$	−27.4156			−1.73046			−0.865230	+	0.501375i	$0.832828\pi$
$252$		0			0
$253$	−12.7279			−0.800198
$254$	−2.80821	−	1.62132i	−0.176203	−	0.101731i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.30463			−0.268516			−0.134258	−	0.990946i	$-0.542865\pi$
$257$	−4.30463			−0.268516			−0.134258	+	0.990946i	$0.542865\pi$
$258$		0			0
$259$	0.393398	−	0.507306i	0.0244446	−	0.0315225i
$260$		−	1.75736i		−	0.108987i
$261$		0			0
$262$	−4.50000	−	2.59808i	−0.278011	−	0.160510i
$263$		−	15.2132i		−	0.938086i	−0.883175	−	0.469043i	$-0.844599\pi$
$263$		−	15.2132i		−	0.938086i	0.883175	−	0.469043i	$-0.155401\pi$
$264$		0			0
$265$	−4.50000	−	2.59808i	−0.276433	−	0.159599i
$266$	−5.91359	−	14.4853i	−0.362586	−	0.888150i
$267$		0			0
$268$	−5.00000	+	8.66025i	−0.305424	+	0.529009i
$269$	−6.98975	+	12.1066i	−0.426173	+	0.738153i	−0.996529	−	0.0832447i	$-0.973472\pi$
$269$	−6.98975	+	12.1066i	−0.426173	+	0.738153i	0.570357	+	0.821397i	$0.306805\pi$
$270$		0			0
$271$	−5.37868	+	3.10538i	−0.326732	+	0.188639i	−0.654389	−	0.756158i	$-0.727074\pi$
$271$	−5.37868	+	3.10538i	−0.326732	+	0.188639i	0.327658	+	0.944797i	$0.393741\pi$
$272$	−2.95680	−	5.12132i	−0.179282	−	0.310526i
$273$		0			0
$274$	1.24264	−	2.15232i	0.0750707	−	0.130026i
$275$		−	13.4558i		−	0.811418i
$276$		0			0
$277$	12.9706			0.779326			0.389663	−	0.920958i	$-0.372592\pi$
$277$	12.9706			0.779326			0.389663	+	0.920958i	$0.372592\pi$
$278$	0.297173	+	0.514719i	0.0178232	+	0.0308708i
$279$		0			0
$280$	−1.75736	+	0.717439i	−0.105022	+	0.0428752i
$281$	5.19615	−	3.00000i	0.309976	−	0.178965i	−0.336939	−	0.941526i	$-0.609392\pi$
$281$	5.19615	−	3.00000i	0.309976	−	0.178965i	0.646916	+	0.762561i	$0.276058\pi$
$282$		0			0
$283$	18.3640	−	10.6024i	1.09162	−	0.630250i	0.157616	−	0.987501i	$-0.449619\pi$
$283$	18.3640	−	10.6024i	1.09162	−	0.630250i	0.934008	+	0.357251i	$0.116286\pi$
$284$	1.52192	−	0.878680i	0.0903092	−	0.0521400i
$285$		0			0
$286$	−6.36396	+	3.67423i	−0.376309	+	0.217262i
$287$	31.0028	+	4.24264i	1.83004	+	0.250435i
$288$		0			0
$289$	−8.98528	−	15.5630i	−0.528546	−	0.915468i
$290$	−5.19615			−0.305129
$291$		0			0
$292$		−	1.43488i		−	0.0839699i
$293$	0.358719	−	0.621320i	0.0209566	−	0.0362979i	−0.855357	−	0.518039i	$-0.826662\pi$
$293$	0.358719	−	0.621320i	0.0209566	−	0.0362979i	0.876314	+	0.481741i	$0.159995\pi$
$294$		0			0
$295$	2.89340	+	5.01151i	0.168460	+	0.291782i
$296$	0.210133	−	0.121320i	0.0122137	−	0.00705160i
$297$		0			0
$298$	−1.75736	+	3.04384i	−0.101801	+	0.176325i
$299$	5.19615	−	9.00000i	0.300501	−	0.520483i
$300$		0			0
$301$	0.393398	−	0.507306i	0.0226751	−	0.0292406i
$302$	−4.54026	−	2.62132i	−0.261263	−	0.150840i
$303$		0			0
$304$		−	5.91359i		−	0.339168i
$305$	−0.630399	−	0.363961i	−0.0360965	−	0.0208403i
$306$		0			0
$307$			9.97204i			0.569134i	0.958656	+	0.284567i	$0.0918499\pi$
$307$			9.97204i			0.569134i	−0.958656	+	0.284567i	$0.908150\pi$
$308$	6.27231	+	4.86396i	0.357398	+	0.277150i
$309$		0			0
$310$	−6.51472			−0.370011
$311$	−4.47871	−	7.75736i	−0.253965	−	0.439879i	0.710649	−	0.703547i	$-0.248401\pi$
$311$	−4.47871	−	7.75736i	−0.253965	−	0.439879i	−0.964614	+	0.263667i	$0.915068\pi$
$312$		0			0
$313$	−15.9853	−	9.22911i	−0.903542	−	0.521660i	−0.0251940	−	0.999683i	$-0.508020\pi$
$313$	−15.9853	−	9.22911i	−0.903542	−	0.521660i	−0.878348	+	0.478023i	$0.841354\pi$
$314$	14.6969			0.829396
$315$		0			0
$316$	2.75736			0.155114
$317$	−1.07616	−	0.621320i	−0.0604431	−	0.0348968i	0.469474	−	0.882946i	$-0.344444\pi$
$317$	−1.07616	−	0.621320i	−0.0604431	−	0.0348968i	−0.529917	+	0.848050i	$0.677777\pi$
$318$		0			0
$319$	10.8640	+	18.8169i	0.608265	+	1.05355i
$320$	−0.717439			−0.0401061
$321$		0			0
$322$	−11.1213	−	1.52192i	−0.619767	−	0.0848132i
$323$		−	34.9706i		−	1.94581i
$324$		0			0
$325$	9.51472	+	5.49333i	0.527782	+	0.304715i
$326$		−	2.24264i		−	0.124208i
$327$		0			0
$328$	10.2426	+	5.91359i	0.565555	+	0.326523i
$329$	15.5014	+	2.12132i	0.854621	+	0.116952i
$330$		0			0
$331$	16.7279	−	28.9736i	0.919450	−	1.59253i	0.119197	−	0.992871i	$-0.461968\pi$
$331$	16.7279	−	28.9736i	0.919450	−	1.59253i	0.800253	−	0.599663i	$-0.204699\pi$
$332$	3.31552	−	5.74264i	0.181963	−	0.315168i
$333$		0			0
$334$	−13.9706	+	8.06591i	−0.764435	+	0.441347i
$335$	3.58719	+	6.21320i	0.195989	+	0.339464i
$336$		0			0
$337$	2.50000	−	4.33013i	0.136184	−	0.235877i	−0.789865	−	0.613280i	$-0.789850\pi$
$337$	2.50000	−	4.33013i	0.136184	−	0.235877i	0.926049	+	0.377403i	$0.123183\pi$
$338$			7.00000i			0.380750i
$339$		0			0
$340$	−4.24264			−0.230089
$341$	13.6208	+	23.5919i	0.737607	+	1.27757i
$342$		0			0
$343$	17.0000	+	7.34847i	0.917914	+	0.396780i
$344$	0.210133	−	0.121320i	0.0113296	−	0.00654115i
$345$		0			0
$346$	18.0000	−	10.3923i	0.967686	−	0.558694i
$347$	−2.15232	+	1.24264i	−0.115542	+	0.0667084i	−0.556657	−	0.830742i	$-0.687916\pi$
$347$	−2.15232	+	1.24264i	−0.115542	+	0.0667084i	0.441115	+	0.897451i	$0.354583\pi$
$348$		0			0
$349$	1.97056	−	1.13770i	0.105482	−	0.0608999i	−0.446331	−	0.894868i	$-0.647270\pi$
$349$	1.97056	−	1.13770i	0.105482	−	0.0608999i	0.551813	+	0.833968i	$0.313936\pi$
$350$	1.60896	−	11.7574i	0.0860024	−	0.628457i
$351$		0			0
$352$	1.50000	+	2.59808i	0.0799503	+	0.138478i
$353$	8.95743			0.476756			0.238378	−	0.971172i	$-0.423384\pi$
$353$	8.95743			0.476756			0.238378	+	0.971172i	$0.423384\pi$
$354$		0			0
$355$		−	1.26080i		−	0.0669162i
$356$	−5.19615	+	9.00000i	−0.275396	+	0.476999i
$357$		0			0
$358$	−13.2426	−	22.9369i	−0.699895	−	1.21225i
$359$	−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
$361$	7.98528	−	13.8309i	0.420278	−	0.727943i
$362$	−5.91359	+	10.2426i	−0.310811	+	0.538341i
$363$		0			0
$364$	−6.00000	+	2.44949i	−0.314485	+	0.128388i
$365$	−0.891519	−	0.514719i	−0.0466642	−	0.0269416i
$366$		0			0
$367$			15.4144i			0.804624i	0.915503	+	0.402312i	$0.131793\pi$
$367$			15.4144i			0.804624i	−0.915503	+	0.402312i	$0.868207\pi$
$368$	−3.67423	−	2.12132i	−0.191533	−	0.110581i
$369$		0			0
$370$		−	0.174080i		−	0.00904998i
$371$	−2.59808	+	18.9853i	−0.134885	+	0.985667i
$372$		0			0
$373$	−29.4558			−1.52517			−0.762583	−	0.646891i	$-0.776069\pi$
$373$	−29.4558			−1.52517			−0.762583	+	0.646891i	$0.776069\pi$
$374$	8.87039	+	15.3640i	0.458677	+	0.794452i
$375$		0			0
$376$	5.12132	+	2.95680i	0.264112	+	0.152485i
$377$	−17.7408			−0.913696
$378$		0			0
$379$	12.4853			0.641326			0.320663	−	0.947193i	$-0.396094\pi$
$379$	12.4853			0.641326			0.320663	+	0.947193i	$0.396094\pi$
$380$	−3.67423	−	2.12132i	−0.188484	−	0.108821i
$381$		0			0
$382$	4.24264	+	7.34847i	0.217072	+	0.375980i
$383$	22.2195			1.13536			0.567681	−	0.823248i	$-0.307841\pi$
$383$	22.2195			1.13536			0.567681	+	0.823248i	$0.307841\pi$
$384$		0			0
$385$	5.27208	−	2.15232i	0.268690	−	0.109692i
$386$			9.48528i			0.482788i
$387$		0			0
$388$	−11.7426	−	6.77962i	−0.596142	−	0.344183i
$389$			31.4558i			1.59487i	0.603402	+	0.797437i	$0.293812\pi$
$389$			31.4558i			1.59487i	−0.603402	+	0.797437i	$0.706188\pi$
$390$		0			0
$391$	−21.7279	−	12.5446i	−1.09883	−	0.634409i
$392$	4.89898	+	5.00000i	0.247436	+	0.252538i
$393$		0			0
$394$	−13.2426	+	22.9369i	−0.667155	+	1.15555i
$395$	0.989118	−	1.71320i	0.0497680	−	0.0862006i
$396$		0			0
$397$	12.0000	−	6.92820i	0.602263	−	0.347717i	−0.167668	−	0.985843i	$-0.553624\pi$
$397$	12.0000	−	6.92820i	0.602263	−	0.347717i	0.769931	+	0.638127i	$0.220290\pi$
$398$	−11.5300	−	19.9706i	−0.577947	−	1.00103i
$399$		0			0
$400$	2.24264	−	3.88437i	0.112132	−	0.194218i
$401$		0			0		1.00000			$0$
$401$		0			0		−1.00000			$\pi$
$402$		0			0
$403$	−22.2426			−1.10798
$404$		0			0
$405$		0			0
$406$	7.24264	+	17.7408i	0.359446	+	0.880460i
$407$	−0.630399	+	0.363961i	−0.0312477	+	0.0180409i
$408$		0			0
$409$	−12.9853	+	7.49706i	−0.642081	+	0.370706i	−0.785416	−	0.618969i	$-0.787551\pi$
$409$	−12.9853	+	7.49706i	−0.642081	+	0.370706i	0.143335	+	0.989674i	$0.454217\pi$
$410$	7.34847	−	4.24264i	0.362915	−	0.209529i
$411$		0			0
$412$	4.75736	−	2.74666i	0.234378	−	0.135318i
$413$	13.0774	−	16.8640i	0.643498	−	0.829821i
$414$		0			0
$415$	−2.37868	−	4.11999i	−0.116765	−	0.202243i
$416$	−2.44949			−0.120096
$417$		0			0
$418$			17.7408i			0.867730i
$419$	−11.8272	+	20.4853i	−0.577796	+	1.00077i	0.417936	+	0.908476i	$0.362754\pi$
$419$	−11.8272	+	20.4853i	−0.577796	+	1.00077i	−0.995732	+	0.0922950i	$0.970580\pi$
$420$		0			0
$421$	7.12132	+	12.3345i	0.347072	+	0.601146i	0.985728	−	0.168346i	$-0.0538426\pi$
$421$	7.12132	+	12.3345i	0.347072	+	0.601146i	−0.638656	+	0.769492i	$0.720509\pi$
$422$	−0.210133	+	0.121320i	−0.0102291	+	0.00590578i
$423$		0			0
$424$	−3.62132	+	6.27231i	−0.175867	+	0.304610i
$425$	13.2621	−	22.9706i	0.643304	−	1.11424i
$426$		0			0
$427$	−0.363961	+	2.65962i	−0.0176133	+	0.128708i
$428$	−9.94655	−	5.74264i	−0.480784	−	0.277581i
$429$		0			0
$430$		−	0.174080i		−	0.00839488i
$431$	−3.04384	−	1.75736i	−0.146616	−	0.0846490i	0.424897	−	0.905242i	$-0.360310\pi$
$431$	−3.04384	−	1.75736i	−0.146616	−	0.0846490i	−0.571514	+	0.820593i	$0.693644\pi$
$432$		0			0
$433$			3.46410i			0.166474i	0.996530	+	0.0832370i	$0.0265259\pi$
$433$			3.46410i			0.166474i	−0.996530	+	0.0832370i	$0.973474\pi$
$434$	9.08052	+	22.2426i	0.435879	+	1.06768i
$435$		0			0
$436$	−18.4853			−0.885284
$437$	−12.5446	−	21.7279i	−0.600091	−	1.03939i
$438$		0			0
$439$	14.5919	+	8.42463i	0.696433	+	0.402086i	0.806017	−	0.591892i	$-0.201619\pi$
$439$	14.5919	+	8.42463i	0.696433	+	0.402086i	−0.109585	+	0.993977i	$0.534952\pi$
$440$	2.15232			0.102608
$441$		0			0
$442$	−14.4853			−0.688995
$443$	14.2512	+	8.22792i	0.677094	+	0.390920i	0.798759	−	0.601651i	$-0.205490\pi$
$443$	14.2512	+	8.22792i	0.677094	+	0.390920i	−0.121665	+	0.992571i	$0.538823\pi$
$444$		0			0
$445$	3.72792	+	6.45695i	0.176720	+	0.306089i
$446$	2.15232			0.101915
$447$		0			0
$448$	1.00000	+	2.44949i	0.0472456	+	0.115728i
$449$		−	1.75736i		−	0.0829349i	−0.999140	−	0.0414675i	$-0.986797\pi$
$449$		−	1.75736i		−	0.0829349i	0.999140	−	0.0414675i	$-0.0132033\pi$
$450$		0			0
$451$	−30.7279	−	17.7408i	−1.44692	−	0.835380i
$452$		−	8.48528i		−	0.399114i
$453$		0			0
$454$	13.5000	+	7.79423i	0.633586	+	0.365801i
$455$	−0.630399	+	4.60660i	−0.0295536	+	0.215961i
$456$		0			0
$457$	11.5000	−	19.9186i	0.537947	−	0.931752i	−0.461067	−	0.887365i	$-0.652533\pi$
$457$	11.5000	−	19.9186i	0.537947	−	0.931752i	0.999014	−	0.0443868i	$-0.0141334\pi$
$458$	−6.92820	+	12.0000i	−0.323734	+	0.560723i
$459$		0			0
$460$	−2.63604	+	1.52192i	−0.122906	+	0.0709598i
$461$	−16.3059	−	28.2426i	−0.759441	−	1.31539i	−0.943136	−	0.332408i	$-0.892139\pi$
$461$	−16.3059	−	28.2426i	−0.759441	−	1.31539i	0.183695	−	0.982983i	$-0.441194\pi$
$462$		0			0
$463$	14.7279	−	25.5095i	0.684465	−	1.18553i	−0.289140	−	0.957287i	$-0.593369\pi$
$463$	14.7279	−	25.5095i	0.684465	−	1.18553i	0.973605	−	0.228241i	$-0.0732973\pi$
$464$			7.24264i			0.336231i
$465$		0			0
$466$	−18.7279			−0.867554
$467$	19.8931	+	34.4558i	0.920542	+	1.59443i	0.798578	+	0.601892i	$0.205586\pi$
$467$	19.8931	+	34.4558i	0.920542	+	1.59443i	0.121965	+	0.992534i	$0.461080\pi$
$468$		0			0
$469$	16.2132	−	20.9077i	0.748656	−	0.965428i
$470$	3.67423	−	2.12132i	0.169480	−	0.0978492i
$471$		0			0
$472$	6.98528	−	4.03295i	0.321524	−	0.185632i
$473$	−0.630399	+	0.363961i	−0.0289858	+	0.0167349i
$474$		0			0
$475$	22.9706	−	13.2621i	1.05396	−	0.608505i
$476$	5.91359	+	14.4853i	0.271049	+	0.663932i
$477$		0			0
$478$	6.36396	+	11.0227i	0.291081	+	0.504167i
$479$	−12.0013			−0.548352			−0.274176	−	0.961680i	$-0.588405\pi$
$479$	−12.0013			−0.548352			−0.274176	+	0.961680i	$0.588405\pi$
$480$		0			0
$481$		−	0.594346i		−	0.0270998i
$482$	−3.61269	+	6.25736i	−0.164553	+	0.285015i
$483$		0			0
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	−8.42463	+	4.86396i	−0.382543	+	0.220861i
$486$		0			0
$487$	7.10660	−	12.3090i	0.322031	−	0.557774i	−0.658876	−	0.752251i	$-0.728968\pi$
$487$	7.10660	−	12.3090i	0.322031	−	0.557774i	0.980907	+	0.194478i	$0.0623012\pi$
$488$	−0.507306	+	0.878680i	−0.0229647	+	0.0397760i
$489$		0			0
$490$	4.86396	−	1.25024i	0.219731	−	0.0564800i
$491$	12.0989	+	6.98528i	0.546014	+	0.315241i	0.747513	−	0.664247i	$-0.231248\pi$
$491$	12.0989	+	6.98528i	0.546014	+	0.315241i	−0.201499	+	0.979489i	$0.564581\pi$
$492$		0			0
$493$			42.8300i			1.92897i
$494$	−12.5446	−	7.24264i	−0.564409	−	0.325862i
$495$		0			0
$496$			9.08052i			0.407727i
$497$	−4.30463	+	1.75736i	−0.193089	+	0.0788283i
$498$		0			0
$499$	31.9411			1.42988			0.714941	−	0.699185i	$-0.246454\pi$
$499$	31.9411			1.42988			0.714941	+	0.699185i	$0.246454\pi$
$500$	−3.40256	−	5.89340i	−0.152167	−	0.263561i
$501$		0			0
$502$	23.7426	+	13.7078i	1.05969	+	0.611810i
$503$	−31.0028			−1.38235			−0.691174	−	0.722688i	$-0.742906\pi$
$503$	−31.0028			−1.38235			−0.691174	+	0.722688i	$0.742906\pi$
$504$		0			0
$505$		0			0
$506$	11.0227	+	6.36396i	0.490019	+	0.282913i
$507$		0			0
$508$	1.62132	+	2.80821i	0.0719345	+	0.124594i
$509$	−17.1974			−0.762262			−0.381131	−	0.924521i	$-0.624465\pi$
$509$	−17.1974			−0.762262			−0.381131	+	0.924521i	$0.624465\pi$
$510$		0			0
$511$	−0.514719	+	3.76127i	−0.0227698	+	0.166389i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	3.72792	+	2.15232i	0.164432	+	0.0949346i
$515$		−	3.94113i		−	0.173667i
$516$		0			0
$517$	−15.3640	−	8.87039i	−0.675706	−	0.390119i
$518$	−0.594346	+	0.242641i	−0.0261141	+	0.0106610i
$519$		0			0
$520$	−0.878680	+	1.52192i	−0.0385327	+	0.0667405i
$521$	−16.9363	+	29.3345i	−0.741993	+	1.28517i	0.209594	+	0.977788i	$0.432786\pi$
$521$	−16.9363	+	29.3345i	−0.741993	+	1.28517i	−0.951587	+	0.307380i	$0.900548\pi$
$522$		0			0
$523$	5.84924	−	3.37706i	0.255770	−	0.147669i	−0.366634	−	0.930365i	$-0.619490\pi$
$523$	5.84924	−	3.37706i	0.255770	−	0.147669i	0.622403	+	0.782697i	$0.286156\pi$
$524$	2.59808	+	4.50000i	0.113497	+	0.196583i
$525$		0			0
$526$	−7.60660	+	13.1750i	−0.331664	+	0.574458i
$527$			53.6985i			2.33914i
$528$		0			0
$529$	5.00000			0.217391
$530$	2.59808	+	4.50000i	0.112853	+	0.195468i
$531$		0			0
$532$	−2.12132	+	15.5014i	−0.0919709	+	0.672072i
$533$	25.0892	−	14.4853i	1.08674	−	0.627427i
$534$		0			0
$535$	−7.13604	+	4.11999i	−0.308518	+	0.178123i
$536$	8.66025	−	5.00000i	0.374066	−	0.215967i
$537$		0			0
$538$	12.1066	−	6.98975i	0.521953	−	0.301350i
$539$	−14.6969	−	15.0000i	−0.633042	−	0.646096i
$540$		0			0
$541$	−7.36396	−	12.7548i	−0.316601	−	0.548370i	0.663175	−	0.748464i	$-0.269208\pi$
$541$	−7.36396	−	12.7548i	−0.316601	−	0.548370i	−0.979777	+	0.200094i	$0.935875\pi$
$542$	6.21076			0.266775
$543$		0			0
$544$			5.91359i			0.253543i
$545$	−6.63103	+	11.4853i	−0.284042	+	0.491975i
$546$		0			0
$547$	19.8492	+	34.3799i	0.848692	+	1.46998i	0.882376	+	0.470546i	$0.155943\pi$
$547$	19.8492	+	34.3799i	0.848692	+	1.46998i	−0.0336833	+	0.999433i	$0.510724\pi$
$548$	−2.15232	+	1.24264i	−0.0919424	+	0.0530830i
$549$		0			0
$550$	−6.72792	+	11.6531i	−0.286880	+	0.496890i
$551$	−21.4150	+	37.0919i	−0.912310	+	1.58017i
$552$		0			0
$553$	−7.22792	−	0.989118i	−0.307363	−	0.0420616i
$554$	−11.2328	−	6.48528i	−0.477238	−	0.275533i
$555$		0			0
$556$		−	0.594346i		−	0.0252059i
$557$	8.42463	+	4.86396i	0.356963	+	0.206093i	0.667748	−	0.744388i	$-0.267259\pi$
$557$	8.42463	+	4.86396i	0.356963	+	0.206093i	−0.310785	+	0.950480i	$0.600592\pi$
$558$		0			0
$559$		−	0.594346i		−	0.0251382i
$560$	1.88064	+	0.257359i	0.0794714	+	0.0108754i
$561$		0			0
$562$	−6.00000			−0.253095
$563$	17.2950	+	29.9558i	0.728898	+	1.26249i	0.957349	+	0.288933i	$0.0933005\pi$
$563$	17.2950	+	29.9558i	0.728898	+	1.26249i	−0.228451	+	0.973555i	$0.573366\pi$
$564$		0			0
$565$	−5.27208	−	3.04384i	−0.221798	−	0.128055i
$566$	−21.2049			−0.891307
$567$		0			0
$568$	−1.75736			−0.0737372
$569$	8.87039	+	5.12132i	0.371866	+	0.214697i	0.674273	−	0.738482i	$-0.264457\pi$
$569$	8.87039	+	5.12132i	0.371866	+	0.214697i	−0.302407	+	0.953179i	$0.597790\pi$
$570$		0			0
$571$	−4.36396	−	7.55860i	−0.182626	−	0.316318i	0.760148	−	0.649750i	$-0.225126\pi$
$571$	−4.36396	−	7.55860i	−0.182626	−	0.316318i	−0.942774	+	0.333432i	$0.891793\pi$
$572$	7.34847			0.307255
$573$		0			0
$574$	−24.7279	−	19.1757i	−1.03212	−	0.800376i
$575$		−	19.0294i		−	0.793582i
$576$		0			0
$577$	9.25736	+	5.34474i	0.385389	+	0.222504i	0.680160	−	0.733063i	$-0.261910\pi$
$577$	9.25736	+	5.34474i	0.385389	+	0.222504i	−0.294771	+	0.955568i	$0.595243\pi$
$578$			17.9706i			0.747477i
$579$		0			0
$580$	4.50000	+	2.59808i	0.186852	+	0.107879i
$581$	−10.7510	+	13.8640i	−0.446028	+	0.575174i
$582$		0			0
$583$	10.8640	−	18.8169i	0.449939	−	0.779318i
$584$	−0.717439	+	1.24264i	−0.0296878	+	0.0514208i
$585$		0			0
$586$	−0.621320	+	0.358719i	−0.0256665	+	0.0148186i
$587$	−2.59808	−	4.50000i	−0.107234	−	0.185735i	0.807415	−	0.589984i	$-0.200866\pi$
$587$	−2.59808	−	4.50000i	−0.107234	−	0.185735i	−0.914649	+	0.404249i	$0.867533\pi$
$588$		0			0
$589$	−26.8492	+	46.5043i	−1.10630	+	1.91617i
$590$		−	5.78680i		−	0.238239i
$591$		0			0
$592$	−0.242641			−0.00997247
$593$	−11.7401	−	20.3345i	−0.482110	−	0.835039i	0.517679	−	0.855575i	$-0.326796\pi$
$593$	−11.7401	−	20.3345i	−0.482110	−	0.835039i	−0.999789	+	0.0205360i	$0.993463\pi$
$594$		0			0
$595$	11.1213	+	1.52192i	0.455930	+	0.0623925i
$596$	3.04384	−	1.75736i	0.124680	−	0.0719842i
$597$		0			0
$598$	−9.00000	+	5.19615i	−0.368037	+	0.212486i
$599$	6.45695	−	3.72792i	0.263824	−	0.152319i	−0.362254	−	0.932079i	$-0.617993\pi$
$599$	6.45695	−	3.72792i	0.263824	−	0.152319i	0.626078	+	0.779761i	$0.284659\pi$
$600$		0			0
$601$	−20.2279	+	11.6786i	−0.825114	+	0.476380i	−0.852177	−	0.523254i	$-0.824718\pi$
$601$	−20.2279	+	11.6786i	−0.825114	+	0.476380i	0.0270627	+	0.999634i	$0.491385\pi$
$602$	−0.594346	+	0.242641i	−0.0242237	+	0.00988930i
$603$		0			0
$604$	2.62132	+	4.54026i	0.106660	+	0.184741i
$605$	1.43488			0.0583361
$606$		0			0
$607$		−	20.0672i		−	0.814501i	−0.913316	−	0.407251i	$-0.866488\pi$
$607$		−	20.0672i		−	0.814501i	0.913316	−	0.407251i	$-0.133512\pi$
$608$	−2.95680	+	5.12132i	−0.119914	+	0.207697i
$609$		0			0
$610$	0.363961	+	0.630399i	0.0147364	+	0.0255241i
$611$	12.5446	−	7.24264i	0.507501	−	0.293006i
$612$		0			0
$613$	18.6066	−	32.2276i	0.751514	−	1.30166i	−0.195575	−	0.980689i	$-0.562657\pi$
$613$	18.6066	−	32.2276i	0.751514	−	1.30166i	0.947089	−	0.320971i	$-0.104009\pi$
$614$	4.98602	−	8.63604i	0.201219	−	0.348522i
$615$		0			0
$616$	−3.00000	−	7.34847i	−0.120873	−	0.296078i
$617$	15.3273	+	8.84924i	0.617055	+	0.356257i	0.775722	−	0.631075i	$-0.217386\pi$
$617$	15.3273	+	8.84924i	0.617055	+	0.356257i	−0.158666	+	0.987332i	$0.550719\pi$
$618$		0			0
$619$		−	6.15978i		−	0.247582i	−0.992308	−	0.123791i	$-0.960495\pi$
$619$		−	6.15978i		−	0.247582i	0.992308	−	0.123791i	$-0.0395053\pi$
$620$	5.64191	+	3.25736i	0.226585	+	0.130819i
$621$		0			0
$622$			8.95743i			0.359160i
$623$	16.8493	−	21.7279i	0.675051	−	0.870511i
$624$		0			0
$625$	17.5442			0.701766
$626$	9.22911	+	15.9853i	0.368869	+	0.638900i
$627$		0			0
$628$	−12.7279	−	7.34847i	−0.507899	−	0.293236i
$629$	−1.43488			−0.0572123
$630$		0			0
$631$	24.7574			0.985575			0.492787	−	0.870150i	$-0.335978\pi$
$631$	24.7574			0.985575			0.492787	+	0.870150i	$0.335978\pi$
$632$	−2.38794	−	1.37868i	−0.0949873	−	0.0548409i
$633$		0			0
$634$	0.621320	+	1.07616i	0.0246758	+	0.0427397i
$635$	2.32640			0.0923202
$636$		0			0
$637$	16.6066	−	4.26858i	0.657978	−	0.169127i
$638$		−	21.7279i		−	0.860217i
$639$		0			0
$640$	0.621320	+	0.358719i	0.0245598	+	0.0141796i
$641$			17.6985i			0.699048i	0.936927	+	0.349524i	$0.113657\pi$
$641$			17.6985i			0.699048i	−0.936927	+	0.349524i	$0.886343\pi$
$642$		0			0
$643$	27.7279	+	16.0087i	1.09348	+	0.631322i	0.934501	−	0.355959i	$-0.115846\pi$
$643$	27.7279	+	16.0087i	1.09348	+	0.631322i	0.158981	+	0.987282i	$0.449179\pi$
$644$	8.87039	+	6.87868i	0.349542	+	0.271058i
$645$		0			0
$646$	−17.4853	+	30.2854i	−0.687949	+	1.19156i
$647$	−16.2189	+	28.0919i	−0.637629	+	1.10441i	0.348323	+	0.937375i	$0.386751\pi$
$647$	−16.2189	+	28.0919i	−0.637629	+	1.10441i	−0.985952	+	0.167031i	$0.946582\pi$
$648$		0			0
$649$	−20.9558	+	12.0989i	−0.822589	+	0.474922i
$650$	−5.49333	−	9.51472i	−0.215466	−	0.373198i
$651$		0			0
$652$	−1.12132	+	1.94218i	−0.0439143	+	0.0760618i
$653$			19.2426i			0.753023i	0.926412	+	0.376511i	$0.122876\pi$
$653$			19.2426i			0.753023i	−0.926412	+	0.376511i	$0.877124\pi$
$654$		0			0
$655$	3.72792			0.145662
$656$	−5.91359	−	10.2426i	−0.230887	−	0.399908i
$657$		0			0
$658$	−12.3640	−	9.58783i	−0.481997	−	0.373772i
$659$	5.19615	−	3.00000i	0.202413	−	0.116863i	−0.395367	−	0.918523i	$-0.629383\pi$
$659$	5.19615	−	3.00000i	0.202413	−	0.116863i	0.597781	+	0.801660i	$0.296049\pi$
$660$		0			0
$661$	−30.8787	+	17.8278i	−1.20104	+	0.693422i	−0.960787	−	0.277288i	$-0.910564\pi$
$661$	−30.8787	+	17.8278i	−1.20104	+	0.693422i	−0.240255	+	0.970710i	$0.577231\pi$
$662$	−28.9736	+	16.7279i	−1.12609	+	0.650149i
$663$		0			0
$664$	−5.74264	+	3.31552i	−0.222858	+	0.128667i
$665$	8.87039	+	6.87868i	0.343979	+	0.266744i
$666$		0			0
$667$	15.3640	+	26.6112i	0.594895	+	1.03039i
$668$	16.1318			0.624159
$669$		0			0
$670$		−	7.17439i		−	0.277171i
$671$	1.52192	−	2.63604i	0.0587530	−	0.101763i
$672$		0			0
$673$	−8.98528	−	15.5630i	−0.346357	−	0.599908i	0.639242	−	0.769005i	$-0.279248\pi$
$673$	−8.98528	−	15.5630i	−0.346357	−	0.599908i	−0.985599	+	0.169097i	$0.945915\pi$
$674$	−4.33013	+	2.50000i	−0.166790	+	0.0962964i
$675$		0			0
$676$	3.50000	−	6.06218i	0.134615	−	0.233161i
$677$	1.07616	−	1.86396i	0.0413601	−	0.0716378i	−0.844604	−	0.535391i	$-0.820164\pi$
$677$	1.07616	−	1.86396i	0.0413601	−	0.0716378i	0.885964	+	0.463753i	$0.153498\pi$
$678$		0			0
$679$	28.3492	+	21.9839i	1.08794	+	0.843663i
$680$	3.67423	+	2.12132i	0.140900	+	0.0813489i
$681$		0			0
$682$		−	27.2416i		−	1.04313i
$683$	−6.90271	−	3.98528i	−0.264125	−	0.152493i	0.362090	−	0.932143i	$-0.382063\pi$
$683$	−6.90271	−	3.98528i	−0.264125	−	0.152493i	−0.626215	+	0.779651i	$0.715397\pi$
$684$		0			0
$685$			1.78304i			0.0681264i
$686$	−11.0482	−	14.8640i	−0.421822	−	0.567509i
$687$		0			0
$688$	−0.242641			−0.00925059
$689$	8.87039	+	15.3640i	0.337935	+	0.585320i
$690$		0			0
$691$	−24.7279	−	14.2767i	−0.940694	−	0.543110i	−0.0505165	−	0.998723i	$-0.516087\pi$
$691$	−24.7279	−	14.2767i	−0.940694	−	0.543110i	−0.890178	+	0.455613i	$0.849420\pi$
$692$	−20.7846			−0.790112
$693$		0			0
$694$	2.48528			0.0943400
$695$	−0.369279	−	0.213203i	−0.0140076	−	0.00808727i
$696$		0			0
$697$	−34.9706	−	60.5708i	−1.32460	−	2.29428i
$698$	−2.27541			−0.0861255
$699$		0			0
$700$	−7.27208	+	9.37769i	−0.274859	+	0.354443i
$701$			20.6985i			0.781771i	0.920439	+	0.390885i	$0.127831\pi$
$701$			20.6985i			0.781771i	−0.920439	+	0.390885i	$0.872169\pi$
$702$		0			0
$703$	−1.24264	−	0.717439i	−0.0468671	−	0.0270587i
$704$		−	3.00000i		−	0.113067i
$705$		0			0
$706$	−7.75736	−	4.47871i	−0.291952	−	0.168559i
$707$		0			0
$708$		0			0
$709$	−13.4853	+	23.3572i	−0.506450	+	0.877198i	0.493522	+	0.869733i	$0.335709\pi$
$709$	−13.4853	+	23.3572i	−0.506450	+	0.877198i	−0.999972	+	0.00746433i	$0.997624\pi$
$710$	−0.630399	+	1.09188i	−0.0236585	+	0.0409776i
$711$		0			0
$712$	9.00000	−	5.19615i	0.337289	−	0.194734i
$713$	19.2627	+	33.3640i	0.721393	+	1.24949i
$714$		0			0
$715$	2.63604	−	4.56575i	0.0985823	−	0.170749i
$716$			26.4853i			0.989801i
$717$		0			0
$718$	18.0000			0.671754
$719$	−8.06591	−	13.9706i	−0.300808	−	0.521014i	0.675511	−	0.737349i	$-0.263923\pi$
$719$	−8.06591	−	13.9706i	−0.300808	−	0.521014i	−0.976319	+	0.216335i	$0.930590\pi$
$720$		0			0
$721$	−13.4558	+	5.49333i	−0.501122	+	0.204582i
$722$	−13.8309	+	7.98528i	−0.514733	+	0.297181i
$723$		0			0
$724$	10.2426	−	5.91359i	0.380665	−	0.219777i
$725$	−28.1331	+	16.2426i	−1.04484	+	0.603237i
$726$		0			0
$727$	10.1360	−	5.85204i	0.375925	−	0.217040i	−0.300119	−	0.953902i	$-0.597026\pi$
$727$	10.1360	−	5.85204i	0.375925	−	0.217040i	0.676044	+	0.736861i	$0.263693\pi$
$728$	6.42090	+	0.878680i	0.237974	+	0.0325660i
$729$		0			0
$730$	0.514719	+	0.891519i	0.0190506	+	0.0329966i
$731$	−1.43488			−0.0530709
$732$		0			0
$733$			4.72490i			0.174518i	0.996186	+	0.0872591i	$0.0278108\pi$
$733$			4.72490i			0.174518i	−0.996186	+	0.0872591i	$0.972189\pi$
$734$	7.70719	−	13.3492i	0.284478	−	0.492730i
$735$		0			0
$736$	2.12132	+	3.67423i	0.0781929	+	0.135434i
$737$	−25.9808	+	15.0000i	−0.957014	+	0.552532i
$738$		0			0
$739$	−7.72792	+	13.3852i	−0.284276	+	0.492381i	−0.972433	−	0.233181i	$-0.925087\pi$
$739$	−7.72792	+	13.3852i	−0.284276	+	0.492381i	0.688157	+	0.725562i	$0.258420\pi$
$740$	−0.0870399	+	0.150758i	−0.00319965	+	0.00554196i
$741$		0			0
$742$	11.7426	−	15.1427i	0.431086	−	0.555906i
$743$	−33.3292	−	19.2426i	−1.22273	−	0.705944i	−0.257232	−	0.966350i	$-0.582810\pi$
$743$	−33.3292	−	19.2426i	−1.22273	−	0.705944i	−0.965499	+	0.260406i	$0.916144\pi$
$744$		0			0
$745$		−	2.52160i		−	0.0923841i
$746$	25.5095	+	14.7279i	0.933969	+	0.539228i
$747$		0			0
$748$		−	17.7408i		−	0.648667i
$749$	24.0131	+	18.6213i	0.877419	+	0.680408i
$750$		0			0
$751$	35.2426			1.28602			0.643011	−	0.765857i	$-0.277685\pi$
$751$	35.2426			1.28602			0.643011	+	0.765857i	$0.277685\pi$
$752$	−2.95680	−	5.12132i	−0.107823	−	0.186755i
$753$		0			0
$754$	15.3640	+	8.87039i	0.559522	+	0.323040i
$755$	3.76127			0.136887
$756$		0			0
$757$	−33.7574			−1.22693			−0.613466	−	0.789721i	$-0.710225\pi$
$757$	−33.7574			−1.22693			−0.613466	+	0.789721i	$0.710225\pi$
$758$	−10.8126	−	6.24264i	−0.392730	−	0.226743i
$759$		0			0
$760$	2.12132	+	3.67423i	0.0769484	+	0.133278i
$761$	29.5680			1.07184			0.535919	−	0.844270i	$-0.319965\pi$
$761$	29.5680			1.07184			0.535919	+	0.844270i	$0.319965\pi$
$762$		0			0
$763$	48.4558	+	6.63103i	1.75422	+	0.240059i
$764$		−	8.48528i		−	0.306987i
$765$		0			0
$766$	−19.2426	−	11.1097i	−0.695265	−	0.401411i
$767$		−	19.7574i		−	0.713397i
$768$		0			0
$769$	8.52944	+	4.92447i	0.307579	+	0.177581i	0.645843	−	0.763470i	$-0.276506\pi$
$769$	8.52944	+	4.92447i	0.307579	+	0.177581i	−0.338263	+	0.941051i	$0.609839\pi$
$770$	−5.64191	−	0.772078i	−0.203320	−	0.0278238i
$771$		0			0
$772$	4.74264	−	8.21449i	0.170691	−	0.295646i
$773$	8.06591	−	13.9706i	0.290111	−	0.502486i	−0.683725	−	0.729740i	$-0.739641\pi$
$773$	8.06591	−	13.9706i	0.290111	−	0.502486i	0.973836	+	0.227253i	$0.0729746\pi$
$774$		0			0
$775$	−35.2721	+	20.3643i	−1.26701	+	0.731509i
$776$	6.77962	+	11.7426i	0.243374	+	0.421536i
$777$		0			0
$778$	15.7279	−	27.2416i	0.563873	−	0.976657i
$779$		−	69.9411i		−	2.50590i
$780$		0			0
$781$	5.27208			0.188650
$782$	12.5446	+	21.7279i	0.448595	+	0.776989i
$783$		0			0
$784$	−1.74264	−	6.77962i	−0.0622372	−	0.242129i
$785$	−9.13151	+	5.27208i	−0.325917	+	0.188169i
$786$		0			0
$787$	−27.8787	+	16.0958i	−0.993768	+	0.573752i	−0.906398	−	0.422424i	$-0.861179\pi$
$787$	−27.8787	+	16.0958i	−0.993768	+	0.573752i	−0.0873693	+	0.996176i	$0.527846\pi$
$788$	22.9369	−	13.2426i	0.817094	−	0.471750i
$789$		0			0
$790$	−1.71320	+	0.989118i	−0.0609530	+	0.0351913i
$791$	−3.04384	+	22.2426i	−0.108226	+	0.790857i
$792$		0			0
$793$	1.24264	+	2.15232i	0.0441275	+	0.0764310i
$794$	−13.8564			−0.491745
$795$		0			0
$796$			23.0600i			0.817341i
$797$	−3.22848	+	5.59188i	−0.114358	+	0.198075i	−0.917523	−	0.397682i	$-0.869815\pi$
$797$	−3.22848	+	5.59188i	−0.114358	+	0.198075i	0.803165	+	0.595757i	$0.203148\pi$
$798$		0			0
$799$	−17.4853	−	30.2854i	−0.618585	−	1.07142i
$800$	−3.88437	+	2.24264i	−0.137333	+	0.0792893i
$801$		0			0
$802$		0			0
$803$	2.15232	−	3.72792i	0.0759536	−	0.131556i
$804$		0			0
$805$	7.45584	−	3.04384i	0.262784	−	0.107281i
$806$	19.2627	+	11.1213i	0.678499	+	0.391732i
$807$		0			0
$808$		0			0
$809$	−6.08767	−	3.51472i	−0.214031	−	0.123571i	0.389152	−	0.921173i	$-0.372768\pi$
$809$	−6.08767	−	3.51472i	−0.214031	−	0.123571i	−0.603183	+	0.797602i	$0.706101\pi$
$810$		0			0
$811$		−	31.1769i		−	1.09477i	−0.836881	−	0.547385i	$-0.815623\pi$
$811$		−	31.1769i		−	1.09477i	0.836881	−	0.547385i	$-0.184377\pi$
$812$	2.59808	−	18.9853i	0.0911746	−	0.666253i
$813$		0			0
$814$	0.727922			0.0255137
$815$	0.804479	+	1.39340i	0.0281797	+	0.0488086i
$816$		0			0
$817$	−1.24264	−	0.717439i	−0.0434745	−	0.0251000i
$818$	14.9941			0.524257
$819$		0			0
$820$	−8.48528			−0.296319
$821$	−35.2969	−	20.3787i	−1.23187	−	0.711221i	−0.264451	−	0.964399i	$-0.585191\pi$
$821$	−35.2969	−	20.3787i	−1.23187	−	0.711221i	−0.967420	+	0.253178i	$0.918524\pi$
$822$		0			0
$823$	−14.9706	−	25.9298i	−0.521841	−	0.903855i	−0.999677	−	0.0254062i	$-0.991912\pi$
$823$	−14.9706	−	25.9298i	−0.521841	−	0.903855i	0.477836	−	0.878449i	$-0.341421\pi$
$824$	−5.49333			−0.191369
$825$		0			0
$826$	−19.7574	+	8.06591i	−0.687446	+	0.280649i
$827$			37.9706i			1.32037i	0.751105	+	0.660183i	$0.229521\pi$
$827$			37.9706i			1.32037i	−0.751105	+	0.660183i	$0.770479\pi$
$828$		0			0
$829$	11.3345	+	6.54399i	0.393664	+	0.227282i	0.683747	−	0.729720i	$-0.260349\pi$
$829$	11.3345	+	6.54399i	0.393664	+	0.227282i	−0.290082	+	0.957002i	$0.593683\pi$
$830$			4.75736i			0.165130i
$831$		0			0
$832$	2.12132	+	1.22474i	0.0735436	+	0.0424604i
$833$	−10.3053	−	40.0919i	−0.357056	−	1.38910i
$834$		0			0
$835$	5.78680	−	10.0230i	0.200260	−	0.346861i
$836$	8.87039	−	15.3640i	0.306789	−	0.531374i
$837$		0			0
$838$	20.4853	−	11.8272i	0.707652	−	0.408563i
$839$	−5.10911	−	8.84924i	−0.176386	−	0.305510i	0.764254	−	0.644915i	$-0.223107\pi$
$839$	−5.10911	−	8.84924i	−0.176386	−	0.305510i	−0.940640	+	0.339406i	$0.889774\pi$
$840$		0			0
$841$	11.7279	−	20.3134i	0.404411	−	0.700461i
$842$		−	14.2426i		−	0.490834i
$843$		0			0
$844$	0.242641			0.00835204
$845$	−2.51104	−	4.34924i	−0.0863823	−	0.149618i
$846$		0			0
$847$	−2.00000	−	4.89898i	−0.0687208	−	0.168331i
$848$	6.27231	−	3.62132i	0.215392	−	0.124357i
$849$		0			0
$850$	−22.9706	+	13.2621i	−0.787884	+	0.454885i
$851$	−0.891519	+	0.514719i	−0.0305609	+	0.0176443i
$852$		0			0
$853$	−31.9706	+	18.4582i	−1.09465	+	0.631997i	−0.934811	−	0.355146i	$-0.884431\pi$
$853$	−31.9706	+	18.4582i	−1.09465	+	0.631997i	−0.159840	+	0.987143i	$0.551098\pi$
$854$	1.64501	−	2.12132i	0.0562911	−	0.0725901i
$855$		0			0
$856$	5.74264	+	9.94655i	0.196279	+	0.339966i
$857$	−33.8726			−1.15707			−0.578533	−	0.815659i	$-0.696375\pi$
$857$	−33.8726			−1.15707			−0.578533	+	0.815659i	$0.696375\pi$
$858$		0			0
$859$			9.37769i			0.319963i	0.987120	+	0.159981i	$0.0511434\pi$
$859$			9.37769i			0.319963i	−0.987120	+	0.159981i	$0.948857\pi$
$860$	−0.0870399	+	0.150758i	−0.00296804	+	0.00514079i
$861$		0			0
$862$	1.75736	+	3.04384i	0.0598559	+	0.103673i
$863$	29.0246	−	16.7574i	0.988009	−	0.570427i	0.0833303	−	0.996522i	$-0.473444\pi$
$863$	29.0246	−	16.7574i	0.988009	−	0.570427i	0.904679	+	0.426095i	$0.140111\pi$
$864$		0			0
$865$	−7.45584	+	12.9139i	−0.253506	+	0.439086i
$866$	1.73205	−	3.00000i	0.0588575	−	0.101944i
$867$		0			0
$868$	3.25736	−	23.8030i	0.110562	−	0.807925i
$869$	7.16383	+	4.13604i	0.243016	+	0.140306i
$870$		0			0
$871$		−	24.4949i		−	0.829978i
$872$	16.0087	+	9.24264i	0.542124	+	0.312995i
$873$		0			0
$874$			25.0892i			0.848656i
$875$	6.80511	+	16.6690i	0.230055	+	0.563517i
$876$		0			0
$877$	4.48528			0.151457			0.0757286	−	0.997128i	$-0.475872\pi$
$877$	4.48528			0.151457			0.0757286	+	0.997128i	$0.475872\pi$
$878$	−8.42463	−	14.5919i	−0.284317	−	0.492452i
$879$		0			0
$880$	−1.86396	−	1.07616i	−0.0628341	−	0.0362773i
$881$	19.0016			0.640179			0.320090	−	0.947387i	$-0.396287\pi$
$881$	19.0016			0.640179			0.320090	+	0.947387i	$0.396287\pi$
$882$		0			0
$883$	41.4558			1.39510			0.697550	−	0.716536i	$-0.254273\pi$
$883$	41.4558			1.39510			0.697550	+	0.716536i	$0.254273\pi$
$884$	12.5446	+	7.24264i	0.421921	+	0.243596i
$885$		0			0
$886$	−8.22792	−	14.2512i	−0.276422	−	0.478778i
$887$	−10.5664			−0.354784			−0.177392	−	0.984140i	$-0.556766\pi$
$887$	−10.5664			−0.354784			−0.177392	+	0.984140i	$0.556766\pi$
$888$		0			0
$889$	−3.24264	−	7.94282i	−0.108755	−	0.266393i
$890$		−	7.45584i		−	0.249920i
$891$		0			0
$892$	−1.86396	−	1.07616i	−0.0624100	−	0.0360324i
$893$		−	34.9706i		−	1.17025i
$894$		0			0
$895$	16.4558	+	9.50079i	0.550058	+	0.317576i
$896$	0.358719	−	2.62132i	0.0119840	−	0.0875722i
$897$		0			0
$898$	−0.878680	+	1.52192i	−0.0293219	+	0.0507871i
$899$	32.8835	−	56.9558i	1.09673	−	1.89958i
$900$		0			0
$901$	37.0919	−	21.4150i	1.23571	−	0.713437i
$902$	17.7408	+	30.7279i	0.590703	+	1.02313i
$903$		0			0
$904$	−4.24264	+	7.34847i	−0.141108	+	0.244406i
$905$		−	8.48528i		−	0.282060i
$906$		0			0
$907$	−31.6985			−1.05253			−0.526265	−	0.850320i	$-0.676408\pi$
$907$	−31.6985			−1.05253			−0.526265	+	0.850320i	$0.676408\pi$
$908$	−7.79423	−	13.5000i	−0.258661	−	0.448013i
$909$		0			0
$910$	2.84924	−	3.67423i	0.0944515	−	0.121800i
$911$	−5.82655	+	3.36396i	−0.193042	+	0.111453i	−0.593406	−	0.804903i	$-0.702217\pi$
$911$	−5.82655	+	3.36396i	−0.193042	+	0.111453i	0.400364	+	0.916356i	$0.368884\pi$
$912$		0			0
$913$	17.2279	−	9.94655i	0.570161	−	0.329183i
$914$	−19.9186	+	11.5000i	−0.658848	+	0.380386i
$915$		0			0
$916$	12.0000	−	6.92820i	0.396491	−	0.228914i
$917$	−5.19615	−	12.7279i	−0.171592	−	0.420313i
$918$		0			0
$919$	−18.2426	−	31.5972i	−0.601769	−	1.04229i	−0.992553	−	0.121812i	$-0.961129\pi$
$919$	−18.2426	−	31.5972i	−0.601769	−	1.04229i	0.390784	−	0.920482i	$-0.372204\pi$
$920$	3.04384			0.100352
$921$		0			0
$922$			32.6118i			1.07401i
$923$	−2.15232	+	3.72792i	−0.0708444	+	0.122706i
$924$		0			0
$925$	−0.544156	−	0.942506i	−0.0178917	−	0.0309894i
$926$	−25.5095	+	14.7279i	−0.838294	+	0.483990i
$927$		0			0
$928$	3.62132	−	6.27231i	0.118876	−	0.205899i
$929$	−15.5014	+	26.8492i	−0.508585	+	0.880895i	0.491366	+	0.870953i	$0.336498\pi$
$929$	−15.5014	+	26.8492i	−0.508585	+	0.880895i	−0.999951	+	0.00994164i	$0.996835\pi$
$930$		0			0
$931$	11.1213	−	39.8732i	0.364487	−	1.30679i
$932$	16.2189	+	9.36396i	0.531266	+	0.306727i
$933$		0			0
$934$		−	39.7862i		−	1.30184i
$935$	−11.0227	−	6.36396i	−0.360481	−	0.208124i
$936$		0			0
$937$			35.1844i			1.14942i	0.818356	+	0.574712i	$0.194886\pi$
$937$			35.1844i			1.14942i	−0.818356	+	0.574712i	$0.805114\pi$
$938$	−24.4949	+	10.0000i	−0.799787	+	0.326512i
$939$		0			0
$940$	−4.24264			−0.138380
$941$	13.7949	+	23.8934i	0.449700	+	0.778903i	0.998366	−	0.0571387i	$-0.0181977\pi$
$941$	13.7949	+	23.8934i	0.449700	+	0.778903i	−0.548667	+	0.836041i	$0.684864\pi$
$942$		0			0
$943$	−43.4558	−	25.0892i	−1.41512	−	0.817018i
$944$	−8.06591			−0.262523
$945$		0			0
$946$	0.727922			0.0236668
$947$	9.50079	+	5.48528i	0.308734	+	0.178248i	0.646360	−	0.763033i	$-0.276291\pi$
$947$	9.50079	+	5.48528i	0.308734	+	0.178248i	−0.337626	+	0.941280i	$0.609624\pi$
$948$		0			0
$949$	1.75736	+	3.04384i	0.0570463	+	0.0988071i
$950$	−26.5241			−0.860556
$951$		0			0
$952$	2.12132	−	15.5014i	0.0687524	−	0.502404i
$953$		−	17.6985i		−	0.573310i	−0.958034	−	0.286655i	$-0.907457\pi$
$953$		−	17.6985i		−	0.573310i	0.958034	−	0.286655i	$-0.0925434\pi$
$954$		0			0
$955$	−5.27208	−	3.04384i	−0.170600	−	0.0984962i
$956$		−	12.7279i		−	0.411650i
$957$		0			0
$958$	10.3934	+	6.00063i	0.335795	+	0.193872i
$959$	6.08767	−	2.48528i	0.196581	−	0.0802539i
$960$		0			0
$961$	25.7279	−	44.5621i	0.829933	−	1.43749i
$962$	−0.297173	+	0.514719i	−0.00958124	+	0.0165952i
$963$		0			0
$964$	6.25736	−	3.61269i	0.201536	−	0.116357i
$965$	−3.40256	−	5.89340i	−0.109532	−	0.189715i
$966$		0			0
$967$	−23.8640	+	41.3336i	−0.767413	+	1.32920i	0.171548	+	0.985176i	$0.445123\pi$
$967$	−23.8640	+	41.3336i	−0.767413	+	1.32920i	−0.938961	+	0.344023i	$0.888210\pi$
$968$		−	2.00000i		−	0.0642824i
$969$		0			0
$970$	9.72792			0.312345
$971$	13.5337	+	23.4411i	0.434318	+	0.752262i	0.997240	−	0.0742490i	$-0.0236559\pi$
$971$	13.5337	+	23.4411i	0.434318	+	0.752262i	−0.562921	+	0.826510i	$0.690323\pi$
$972$		0			0
$973$	−0.213203	+	1.55797i	−0.00683499	+	0.0499463i
$974$	−12.3090	+	7.10660i	−0.394406	+	0.227710i
$975$		0			0
$976$	0.878680	−	0.507306i	0.0281259	−	0.0162385i
$977$	34.8511	−	20.1213i	1.11499	−	0.643738i	0.174871	−	0.984591i	$-0.444049\pi$
$977$	34.8511	−	20.1213i	1.11499	−	0.643738i	0.940116	+	0.340853i	$0.110716\pi$
$978$		0			0
$979$	−27.0000	+	15.5885i	−0.862924	+	0.498209i
$980$	−4.83743	−	1.34924i	−0.154526	−	0.0431000i
$981$		0			0
$982$	−6.98528	−	12.0989i	−0.222909	−	0.386090i
$983$	47.3087			1.50891			0.754457	−	0.656349i	$-0.227900\pi$
$983$	47.3087			1.50891			0.754457	+	0.656349i	$0.227900\pi$
$984$		0			0
$985$		−	19.0016i		−	0.605440i
$986$	21.4150	−	37.0919i	0.681993	−	1.18125i
$987$		0			0
$988$	7.24264	+	12.5446i	0.230419	+	0.399098i
$989$	−0.891519	+	0.514719i	−0.0283486	+	0.0163671i
$990$		0			0
$991$	−26.1066	+	45.2180i	−0.829304	+	1.43640i	0.0692818	+	0.997597i	$0.477929\pi$
$991$	−26.1066	+	45.2180i	−0.829304	+	1.43640i	−0.898585	+	0.438799i	$0.855404\pi$
$992$	4.54026	−	7.86396i	0.144153	−	0.249681i
$993$		0			0
$994$	4.60660	+	0.630399i	0.146113	+	0.0199950i
$995$	14.3277	+	8.27208i	0.454217	+	0.262243i
$996$		0			0
$997$			38.9456i			1.23342i	0.787190	+	0.616711i	$0.211535\pi$
$997$			38.9456i			1.23342i	−0.787190	+	0.616711i	$0.788465\pi$
$998$	−27.6618	−	15.9706i	−0.875620	−	0.505539i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.t.e.1025.2		8
3.2	odd	2	inner	1134.2.t.e.1025.3		8
7.5	odd	6		1134.2.l.f.215.4		8
9.2	odd	6		1134.2.l.f.269.2		8
9.4	even	3		126.2.k.a.17.3	yes	8
9.5	odd	6		126.2.k.a.17.2	✓	8
9.7	even	3		1134.2.l.f.269.3		8
21.5	even	6		1134.2.l.f.215.1		8
36.23	even	6		1008.2.bt.c.17.3		8
36.31	odd	6		1008.2.bt.c.17.2		8
45.4	even	6		3150.2.bf.a.1151.1		8
45.13	odd	12		3150.2.bp.b.899.3		8
45.14	odd	6		3150.2.bf.a.1151.3		8
45.22	odd	12		3150.2.bp.e.899.2		8
45.23	even	12		3150.2.bp.e.899.3		8
45.32	even	12		3150.2.bp.b.899.2		8
63.4	even	3		882.2.d.a.881.7		8
63.5	even	6		126.2.k.a.89.3	yes	8
63.13	odd	6		882.2.k.a.521.4		8
63.23	odd	6		882.2.k.a.215.4		8
63.31	odd	6		882.2.d.a.881.6		8
63.32	odd	6		882.2.d.a.881.2		8
63.40	odd	6		126.2.k.a.89.2	yes	8
63.41	even	6		882.2.k.a.521.1		8
63.47	even	6	inner	1134.2.t.e.593.2		8
63.58	even	3		882.2.k.a.215.1		8
63.59	even	6		882.2.d.a.881.3		8
63.61	odd	6	inner	1134.2.t.e.593.3		8
252.31	even	6		7056.2.k.f.881.3		8
252.59	odd	6		7056.2.k.f.881.6		8
252.67	odd	6		7056.2.k.f.881.5		8
252.95	even	6		7056.2.k.f.881.4		8
252.103	even	6		1008.2.bt.c.593.3		8
252.131	odd	6		1008.2.bt.c.593.2		8
315.68	odd	12		3150.2.bp.e.1349.2		8
315.103	even	12		3150.2.bp.b.1349.2		8
315.194	even	6		3150.2.bf.a.1601.1		8
315.229	odd	6		3150.2.bf.a.1601.3		8
315.257	odd	12		3150.2.bp.b.1349.3		8
315.292	even	12		3150.2.bp.e.1349.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.k.a.17.2	✓	8	9.5	odd	6
126.2.k.a.17.3	yes	8	9.4	even	3
126.2.k.a.89.2	yes	8	63.40	odd	6
126.2.k.a.89.3	yes	8	63.5	even	6
882.2.d.a.881.2		8	63.32	odd	6
882.2.d.a.881.3		8	63.59	even	6
882.2.d.a.881.6		8	63.31	odd	6
882.2.d.a.881.7		8	63.4	even	3
882.2.k.a.215.1		8	63.58	even	3
882.2.k.a.215.4		8	63.23	odd	6
882.2.k.a.521.1		8	63.41	even	6
882.2.k.a.521.4		8	63.13	odd	6
1008.2.bt.c.17.2		8	36.31	odd	6
1008.2.bt.c.17.3		8	36.23	even	6
1008.2.bt.c.593.2		8	252.131	odd	6
1008.2.bt.c.593.3		8	252.103	even	6
1134.2.l.f.215.1		8	21.5	even	6
1134.2.l.f.215.4		8	7.5	odd	6
1134.2.l.f.269.2		8	9.2	odd	6
1134.2.l.f.269.3		8	9.7	even	3
1134.2.t.e.593.2		8	63.47	even	6	inner
1134.2.t.e.593.3		8	63.61	odd	6	inner
1134.2.t.e.1025.2		8	1.1	even	1	trivial
1134.2.t.e.1025.3		8	3.2	odd	2	inner
3150.2.bf.a.1151.1		8	45.4	even	6
3150.2.bf.a.1151.3		8	45.14	odd	6
3150.2.bf.a.1601.1		8	315.194	even	6
3150.2.bf.a.1601.3		8	315.229	odd	6
3150.2.bp.b.899.2		8	45.32	even	12
3150.2.bp.b.899.3		8	45.13	odd	12
3150.2.bp.b.1349.2		8	315.103	even	12
3150.2.bp.b.1349.3		8	315.257	odd	12
3150.2.bp.e.899.2		8	45.22	odd	12
3150.2.bp.e.899.3		8	45.23	even	12
3150.2.bp.e.1349.2		8	315.68	odd	12
3150.2.bp.e.1349.3		8	315.292	even	12
7056.2.k.f.881.3		8	252.31	even	6
7056.2.k.f.881.4		8	252.95	even	6
7056.2.k.f.881.5		8	252.67	odd	6
7056.2.k.f.881.6		8	252.59	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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +0.717439 q^{5} +(-1.00000 - 2.44949i) q^{7} -1.00000i q^{8} +(-0.621320 - 0.358719i) q^{10} +3.00000i q^{11} +(-2.12132 - 1.22474i) q^{13} +(-0.358719 + 2.62132i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.95680 + 5.12132i) q^{17} +(-5.12132 + 2.95680i) q^{19} +(0.358719 + 0.621320i) q^{20} +(1.50000 - 2.59808i) q^{22} +4.24264i q^{23} -4.48528 q^{25} +(1.22474 + 2.12132i) q^{26} +(1.62132 - 2.09077i) q^{28} +(6.27231 - 3.62132i) q^{29} +(7.86396 - 4.54026i) q^{31} +(0.866025 - 0.500000i) q^{32} +(5.12132 - 2.95680i) q^{34} +(-0.717439 - 1.75736i) q^{35} +(0.121320 + 0.210133i) q^{37} +5.91359 q^{38} -0.717439i q^{40} +(-5.91359 + 10.2426i) q^{41} +(0.121320 + 0.210133i) q^{43} +(-2.59808 + 1.50000i) q^{44} +(2.12132 - 3.67423i) q^{46} +(-2.95680 + 5.12132i) q^{47} +(-5.00000 + 4.89898i) q^{49} +(3.88437 + 2.24264i) q^{50} -2.44949i q^{52} +(-6.27231 - 3.62132i) q^{53} +2.15232i q^{55} +(-2.44949 + 1.00000i) q^{56} -7.24264 q^{58} +(4.03295 + 6.98528i) q^{59} +(-0.878680 - 0.507306i) q^{61} -9.08052 q^{62} -1.00000 q^{64} +(-1.52192 - 0.878680i) q^{65} +(5.00000 + 8.66025i) q^{67} -5.91359 q^{68} +(-0.257359 + 1.88064i) q^{70} -1.75736i q^{71} +(-1.24264 - 0.717439i) q^{73} -0.242641i q^{74} +(-5.12132 - 2.95680i) q^{76} +(7.34847 - 3.00000i) q^{77} +(1.37868 - 2.38794i) q^{79} +(-0.358719 + 0.621320i) q^{80} +(10.2426 - 5.91359i) q^{82} +(-3.31552 - 5.74264i) q^{83} +(-2.12132 + 3.67423i) q^{85} -0.242641i q^{86} +3.00000 q^{88} +(5.19615 + 9.00000i) q^{89} +(-0.878680 + 6.42090i) q^{91} +(-3.67423 + 2.12132i) q^{92} +(5.12132 - 2.95680i) q^{94} +(-3.67423 + 2.12132i) q^{95} +(-11.7426 + 6.77962i) q^{97} +(6.77962 - 1.74264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 8 q^{7} + 12 q^{10} - 4 q^{16} - 24 q^{19} + 12 q^{22} + 32 q^{25} - 4 q^{28} + 12 q^{31} + 24 q^{34} - 16 q^{37} - 16 q^{43} - 40 q^{49} - 24 q^{58} - 24 q^{61} - 8 q^{64} + 40 q^{67} - 36 q^{70}+ \cdots - 60 q^{97}+O(q^{100}) \) 8 * q + 4 * q^4 - 8 * q^7 + 12 * q^10 - 4 * q^16 - 24 * q^19 + 12 * q^22 + 32 * q^25 - 4 * q^28 + 12 * q^31 + 24 * q^34 - 16 * q^37 - 16 * q^43 - 40 * q^49 - 24 * q^58 - 24 * q^61 - 8 * q^64 + 40 * q^67 - 36 * q^70 + 24 * q^73 - 24 * q^76 + 28 * q^79 + 48 * q^82 + 24 * q^88 - 24 * q^91 + 24 * q^94 - 60 * q^97

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