LMFDB - Embedded newform 1134.2.t.e.593.3

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			593.3
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1134.593
Dual form			1134.2.t.e.1025.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	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	$-0.551286\pi$
$5$	−0.717439			−0.320848			−0.160424	+	0.987048i	$0.551286\pi$
$6$		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	−0.764444	−	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
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.95680	+	5.12132i	0.717128	+	1.24210i	0.962133	+	0.272581i	$0.0878772\pi$
$17$	2.95680	+	5.12132i	0.717128	+	1.24210i	−0.245005	+	0.969522i	$0.578789\pi$
$18$		0			0
$19$	−5.12132	−	2.95680i	−1.17491	−	0.678335i	−0.220080	−	0.975482i	$-0.570632\pi$
$19$	−5.12132	−	2.95680i	−1.17491	−	0.678335i	−0.954832	+	0.297146i	$0.903965\pi$
$20$	−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	$-0.568097\pi$
$29$	−6.27231	−	3.62132i	−1.16474	−	0.672462i	−0.952435	+	0.304741i	$0.901430\pi$
$30$		0			0
$31$	7.86396	+	4.54026i	1.41241	+	0.815455i	0.995615	−	0.0935461i	$-0.0298203\pi$
$31$	7.86396	+	4.54026i	1.41241	+	0.815455i	0.416794	+	0.909001i	$0.363154\pi$
$32$	−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	−0.855881	−	0.517173i	$-0.826984\pi$
$37$	0.121320	−	0.210133i	0.0199449	−	0.0345457i	0.875826	+	0.482628i	$0.160318\pi$
$38$	−5.91359			−0.959311
$39$		0			0
$40$			0.717439i			0.113437i
$41$	5.91359	+	10.2426i	0.923548	+	1.59963i	0.793880	+	0.608074i	$0.208058\pi$
$41$	5.91359	+	10.2426i	0.923548	+	1.59963i	0.129668	+	0.991558i	$0.458609\pi$
$42$		0			0
$43$	0.121320	−	0.210133i	0.0185012	−	0.0320450i	−0.856627	−	0.515937i	$-0.827444\pi$
$43$	0.121320	−	0.210133i	0.0185012	−	0.0320450i	0.875128	+	0.483892i	$0.160777\pi$
$44$	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	$-0.0247242\pi$
$47$	2.95680	+	5.12132i	0.431293	+	0.747021i	−0.565692	+	0.824617i	$0.691391\pi$
$48$		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	$-0.500945\pi$
$53$	6.27231	−	3.62132i	0.861568	−	0.497427i	0.864537	+	0.502569i	$0.167612\pi$
$54$		0			0
$55$		−	2.15232i		−	0.290218i
$56$	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	0.474529	+	0.880240i	$0.342619\pi$
$59$	−4.03295	+	6.98528i	−0.525046	+	0.909406i	−0.999575	+	0.0291661i	$0.990715\pi$
$60$		0			0
$61$	−0.878680	+	0.507306i	−0.112503	+	0.0649539i	−0.555196	−	0.831720i	$-0.687357\pi$
$61$	−0.878680	+	0.507306i	−0.112503	+	0.0649539i	0.442692	+	0.896674i	$0.354023\pi$
$62$	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	−0.380251	−	0.924883i	$-0.624162\pi$
$67$	5.00000	−	8.66025i	0.610847	−	1.05802i	0.991098	−	0.133135i	$-0.0425044\pi$
$68$	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	−0.570954	−	0.820982i	$-0.693427\pi$
$73$	−1.24264	+	0.717439i	−0.145440	+	0.0839699i	0.425514	+	0.904952i	$0.360093\pi$
$74$		−	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	0.933100	−	0.359616i	$-0.117092\pi$
$79$	1.37868	+	2.38794i	0.155114	+	0.268665i	−0.777987	+	0.628281i	$0.783759\pi$
$80$	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	$-0.714770\pi$
$83$	3.31552	−	5.74264i	0.363925	−	0.630337i	0.988603	+	0.150546i	$0.0481031\pi$
$84$		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	0.447427	+	0.894321i	$0.352341\pi$
$89$	−5.19615	+	9.00000i	−0.550791	+	0.953998i	−0.998218	+	0.0596775i	$0.980993\pi$
$90$		0			0
$91$	−0.878680	−	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	−0.233460	−	0.972366i	$-0.575005\pi$
$97$	−11.7426	−	6.77962i	−1.19228	−	0.688366i	−0.958824	+	0.284001i	$0.908338\pi$
$98$	−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	$0.0872342\pi$
$103$			5.49333i			0.541273i	−0.962682	+	0.270637i	$0.912766\pi$
$104$	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	$-0.145990\pi$
$107$	9.94655	+	5.74264i	0.961569	+	0.555162i	0.0649133	+	0.997891i	$0.479323\pi$
$108$		0			0
$109$	−9.24264	−	16.0087i	−0.885284	−	1.53336i	−0.845387	−	0.534154i	$-0.820630\pi$
$109$	−9.24264	−	16.0087i	−0.885284	−	1.53336i	−0.0398971	−	0.999204i	$-0.512703\pi$
$110$	−1.07616	−	1.86396i	−0.102608	−	0.177722i
$111$		0			0
$112$	2.62132	−	0.358719i	0.247691	−	0.0338958i
$113$	7.34847	−	4.24264i	0.691286	−	0.399114i	−0.112808	−	0.993617i	$-0.535984\pi$
$113$	7.34847	−	4.24264i	0.691286	−	0.399114i	0.804094	+	0.594503i	$0.202651\pi$
$114$		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	$-0.572890\pi$
$131$	−5.19615			−0.453990			−0.226995	+	0.973896i	$0.572890\pi$
$132$		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	−0.521670	−	0.853147i	$-0.674691\pi$
$139$	−0.514719	+	0.297173i	−0.0436579	+	0.0252059i	0.478012	+	0.878353i	$0.341357\pi$
$140$	−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	−0.102915	−	0.994690i	$-0.532817\pi$
$157$	−12.7279	−	7.34847i	−1.01580	−	0.586472i	−0.912884	+	0.408219i	$0.866150\pi$
$158$	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	−0.818764	−	0.574130i	$-0.805341\pi$
$163$	1.12132	−	1.94218i	0.0878286	−	0.152124i	0.906593	+	0.422006i	$0.138674\pi$
$164$	11.8272			0.923548
$165$		0			0
$166$		−	6.63103i		−	0.514668i
$167$	−8.06591	−	13.9706i	−0.624159	−	1.08107i	−0.988703	−	0.149889i	$-0.952109\pi$
$167$	−8.06591	−	13.9706i	−0.624159	−	1.08107i	0.364544	−	0.931186i	$-0.381225\pi$
$168$		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	0.925897	+	0.377776i	$0.123311\pi$
$173$	10.3923	+	18.0000i	0.790112	+	1.36851i	−0.135785	+	0.990738i	$0.543356\pi$
$174$		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	−0.785966	+	0.618269i	$0.787834\pi$
$179$	−22.9369	+	13.2426i	−1.71439	+	0.989801i	−0.928420	+	0.371532i	$0.878833\pi$
$180$		0			0
$181$			11.8272i			0.879108i	0.898216	+	0.439554i	$0.144863\pi$
$181$			11.8272i			0.879108i	−0.898216	+	0.439554i	$0.855137\pi$
$182$	−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	$-0.567346\pi$
$191$	7.34847	−	4.24264i	0.531717	−	0.306987i	0.741715	+	0.670715i	$0.234013\pi$
$192$		0			0
$193$	−4.74264	+	8.21449i	−0.341383	+	0.591292i	−0.984690	−	0.174316i	$-0.944229\pi$
$193$	−4.74264	+	8.21449i	−0.341383	+	0.591292i	0.643307	+	0.765608i	$0.277562\pi$
$194$	−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	0.419761	−	0.907635i	$-0.362114\pi$
$199$	19.9706	−	11.5300i	1.41568	−	0.817341i	0.995915	+	0.0902942i	$0.0287807\pi$
$200$			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	0.870171	−	0.492749i	$-0.164008\pi$
$211$	0.121320	+	0.210133i	0.00835204	+	0.0144662i	−0.861819	+	0.507216i	$0.830675\pi$
$212$		−	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	0.436290	−	0.899806i	$-0.356292\pi$
$223$	−1.86396	−	1.07616i	−0.124820	−	0.0720649i	−0.561110	+	0.827741i	$0.689626\pi$
$224$	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	$-0.326929\pi$
$227$	15.5885			1.03464			0.517321	+	0.855791i	$0.326929\pi$
$228$		0			0
$229$			13.8564i			0.915657i	0.889041	+	0.457829i	$0.151373\pi$
$229$			13.8564i			0.915657i	−0.889041	+	0.457829i	$0.848627\pi$
$230$	−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	$-0.543554\pi$
$233$	−16.2189	−	9.36396i	−1.06253	−	0.613453i	−0.926132	+	0.377200i	$0.876887\pi$
$234$		0			0
$235$	−2.12132	−	3.67423i	−0.138380	−	0.239681i
$236$	4.03295	+	6.98528i	0.262523	+	0.454703i
$237$		0			0
$238$	−12.3640	+	9.58783i	−0.801437	+	0.621486i
$239$	11.0227	−	6.36396i	0.712999	−	0.411650i	−0.0991712	−	0.995070i	$-0.531619\pi$
$239$	11.0227	−	6.36396i	0.712999	−	0.411650i	0.812171	+	0.583420i	$0.198286\pi$
$240$		0			0
$241$			7.22538i			0.465427i	0.972545	+	0.232714i	$0.0747605\pi$
$241$			7.22538i			0.465427i	−0.972545	+	0.232714i	$0.925239\pi$
$242$	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	$-0.167172\pi$
$251$	27.4156			1.73046			0.865230	+	0.501375i	$0.167172\pi$
$252$		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	$-0.457135\pi$
$257$	4.30463			0.268516			0.134258	+	0.990946i	$0.457135\pi$
$258$		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	$-0.0265283\pi$
$269$	6.98975	+	12.1066i	0.426173	+	0.738153i	−0.570357	+	0.821397i	$0.693195\pi$
$270$		0			0
$271$	−5.37868	−	3.10538i	−0.326732	−	0.188639i	0.327658	−	0.944797i	$-0.393741\pi$
$271$	−5.37868	−	3.10538i	−0.326732	−	0.188639i	−0.654389	+	0.756158i	$0.727074\pi$
$272$	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	$-0.390608\pi$
$281$	−5.19615	−	3.00000i	−0.309976	−	0.178965i	−0.646916	+	0.762561i	$0.723942\pi$
$282$		0			0
$283$	18.3640	+	10.6024i	1.09162	+	0.630250i	0.934008	−	0.357251i	$-0.116286\pi$
$283$	18.3640	+	10.6024i	1.09162	+	0.630250i	0.157616	+	0.987501i	$0.449619\pi$
$284$	−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	$-0.173338\pi$
$293$	−0.358719	−	0.621320i	−0.0209566	−	0.0362979i	−0.876314	+	0.481741i	$0.840005\pi$
$294$		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	$-0.908150\pi$
$307$		−	9.97204i		−	0.569134i	0.958656	−	0.284567i	$-0.0918499\pi$
$308$	−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	$-0.751599\pi$
$311$	4.47871	−	7.75736i	0.253965	−	0.439879i	0.964614	+	0.263667i	$0.0849320\pi$
$312$		0			0
$313$	−15.9853	+	9.22911i	−0.903542	+	0.521660i	−0.878348	−	0.478023i	$-0.841354\pi$
$313$	−15.9853	+	9.22911i	−0.903542	+	0.521660i	−0.0251940	+	0.999683i	$0.508020\pi$
$314$	−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	$-0.655556\pi$
$317$	1.07616	−	0.621320i	0.0604431	−	0.0348968i	0.529917	+	0.848050i	$0.322223\pi$
$318$		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	0.800253	+	0.599663i	$0.204699\pi$
$331$	16.7279	+	28.9736i	0.919450	+	1.59253i	0.119197	+	0.992871i	$0.461968\pi$
$332$	−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	0.926049	−	0.377403i	$-0.123183\pi$
$337$	2.50000	+	4.33013i	0.136184	+	0.235877i	−0.789865	+	0.613280i	$0.789850\pi$
$338$			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	$-0.312084\pi$
$347$	2.15232	+	1.24264i	0.115542	+	0.0667084i	−0.441115	+	0.897451i	$0.645417\pi$
$348$		0			0
$349$	1.97056	+	1.13770i	0.105482	+	0.0608999i	0.551813	−	0.833968i	$-0.313936\pi$
$349$	1.97056	+	1.13770i	0.105482	+	0.0608999i	−0.446331	+	0.894868i	$0.647270\pi$
$350$	−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	$-0.576616\pi$
$353$	−8.95743			−0.476756			−0.238378	+	0.971172i	$0.576616\pi$
$354$		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	$-0.175781\pi$
$359$	15.5885	+	9.00000i	0.822727	+	0.475002i	−0.0286287	+	0.999590i	$0.509114\pi$
$360$		0			0
$361$	7.98528	+	13.8309i	0.420278	+	0.727943i
$362$	5.91359	+	10.2426i	0.310811	+	0.538341i
$363$		0			0
$364$	−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	$-0.868207\pi$
$367$		−	15.4144i		−	0.804624i	0.915503	−	0.402312i	$-0.131793\pi$
$368$	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	$-0.692159\pi$
$383$	−22.2195			−1.13536			−0.567681	+	0.823248i	$0.692159\pi$
$384$		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	0.769931	−	0.638127i	$-0.220290\pi$
$397$	12.0000	+	6.92820i	0.602263	+	0.347717i	−0.167668	+	0.985843i	$0.553624\pi$
$398$	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	0.143335	−	0.989674i	$-0.454217\pi$
$409$	−12.9853	−	7.49706i	−0.642081	−	0.370706i	−0.785416	+	0.618969i	$0.787551\pi$
$410$	−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	0.995732	+	0.0922950i	$0.0294203\pi$
$419$	11.8272	+	20.4853i	0.577796	+	1.00077i	−0.417936	+	0.908476i	$0.637246\pi$
$420$		0			0
$421$	7.12132	−	12.3345i	0.347072	−	0.601146i	−0.638656	−	0.769492i	$-0.720509\pi$
$421$	7.12132	−	12.3345i	0.347072	−	0.601146i	0.985728	+	0.168346i	$0.0538426\pi$
$422$	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	$-0.639690\pi$
$431$	3.04384	−	1.75736i	0.146616	−	0.0846490i	0.571514	+	0.820593i	$0.306356\pi$
$432$		0			0
$433$		−	3.46410i		−	0.166474i	−0.996530	−	0.0832370i	$-0.973474\pi$
$433$		−	3.46410i		−	0.166474i	0.996530	−	0.0832370i	$-0.0265259\pi$
$434$	−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	−0.109585	−	0.993977i	$-0.534952\pi$
$439$	14.5919	−	8.42463i	0.696433	−	0.402086i	0.806017	+	0.591892i	$0.201619\pi$
$440$	−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	$-0.794510\pi$
$443$	−14.2512	+	8.22792i	−0.677094	+	0.390920i	0.121665	+	0.992571i	$0.461177\pi$
$444$		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	0.999014	+	0.0443868i	$0.0141334\pi$
$457$	11.5000	+	19.9186i	0.537947	+	0.931752i	−0.461067	+	0.887365i	$0.652533\pi$
$458$	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	−0.183695	−	0.982983i	$-0.558806\pi$
$461$	16.3059	−	28.2426i	0.759441	−	1.31539i	0.943136	−	0.332408i	$-0.107861\pi$
$462$		0			0
$463$	14.7279	+	25.5095i	0.684465	+	1.18553i	0.973605	+	0.228241i	$0.0732973\pi$
$463$	14.7279	+	25.5095i	0.684465	+	1.18553i	−0.289140	+	0.957287i	$0.593369\pi$
$464$			7.24264i			0.336231i
$465$		0			0
$466$	−18.7279			−0.867554
$467$	−19.8931	+	34.4558i	−0.920542	+	1.59443i	−0.121965	+	0.992534i	$0.538920\pi$
$467$	−19.8931	+	34.4558i	−0.920542	+	1.59443i	−0.798578	+	0.601892i	$0.794414\pi$
$468$		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	$-0.411595\pi$
$479$	12.0013			0.548352			0.274176	+	0.961680i	$0.411595\pi$
$480$		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	0.980907	−	0.194478i	$-0.0623012\pi$
$487$	7.10660	+	12.3090i	0.322031	+	0.557774i	−0.658876	+	0.752251i	$0.728968\pi$
$488$	0.507306	+	0.878680i	0.0229647	+	0.0397760i
$489$		0			0
$490$	4.86396	+	1.25024i	0.219731	+	0.0564800i
$491$	−12.0989	+	6.98528i	−0.546014	+	0.315241i	−0.747513	−	0.664247i	$-0.768752\pi$
$491$	−12.0989	+	6.98528i	−0.546014	+	0.315241i	0.201499	+	0.979489i	$0.435419\pi$
$492$		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	$-0.257094\pi$
$503$	31.0028			1.38235			0.691174	+	0.722688i	$0.257094\pi$
$504$		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	$-0.375535\pi$
$509$	17.1974			0.762262			0.381131	+	0.924521i	$0.375535\pi$
$510$		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	0.951587	+	0.307380i	$0.0994524\pi$
$521$	16.9363	+	29.3345i	0.741993	+	1.28517i	−0.209594	+	0.977788i	$0.567214\pi$
$522$		0			0
$523$	5.84924	+	3.37706i	0.255770	+	0.147669i	0.622403	−	0.782697i	$-0.286156\pi$
$523$	5.84924	+	3.37706i	0.255770	+	0.147669i	−0.366634	+	0.930365i	$0.619490\pi$
$524$	−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	−0.979777	−	0.200094i	$-0.935875\pi$
$541$	−7.36396	+	12.7548i	−0.316601	+	0.548370i	0.663175	+	0.748464i	$0.269208\pi$
$542$	−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	−0.0336833	−	0.999433i	$-0.510724\pi$
$547$	19.8492	−	34.3799i	0.848692	−	1.46998i	0.882376	−	0.470546i	$-0.155943\pi$
$548$	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	$-0.732741\pi$
$557$	−8.42463	+	4.86396i	−0.356963	+	0.206093i	0.310785	+	0.950480i	$0.399408\pi$
$558$		0			0
$559$			0.594346i			0.0251382i
$560$	−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	0.228451	+	0.973555i	$0.426634\pi$
$563$	−17.2950	+	29.9558i	−0.728898	+	1.26249i	−0.957349	+	0.288933i	$0.906700\pi$
$564$		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	$-0.735543\pi$
$569$	−8.87039	+	5.12132i	−0.371866	+	0.214697i	0.302407	+	0.953179i	$0.402210\pi$
$570$		0			0
$571$	−4.36396	+	7.55860i	−0.182626	+	0.316318i	−0.942774	−	0.333432i	$-0.891793\pi$
$571$	−4.36396	+	7.55860i	−0.182626	+	0.316318i	0.760148	+	0.649750i	$0.225126\pi$
$572$	−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	−0.294771	−	0.955568i	$-0.595243\pi$
$577$	9.25736	−	5.34474i	0.385389	−	0.222504i	0.680160	+	0.733063i	$0.261910\pi$
$578$			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	$-0.799134\pi$
$587$	2.59808	−	4.50000i	0.107234	−	0.185735i	0.914649	+	0.404249i	$0.132467\pi$
$588$		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	$-0.673204\pi$
$593$	11.7401	−	20.3345i	0.482110	−	0.835039i	0.999789	+	0.0205360i	$0.00653726\pi$
$594$		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	$-0.382007\pi$
$599$	−6.45695	−	3.72792i	−0.263824	−	0.152319i	−0.626078	+	0.779761i	$0.715341\pi$
$600$		0			0
$601$	−20.2279	−	11.6786i	−0.825114	−	0.476380i	0.0270627	−	0.999634i	$-0.491385\pi$
$601$	−20.2279	−	11.6786i	−0.825114	−	0.476380i	−0.852177	+	0.523254i	$0.824718\pi$
$602$	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	$0.133512\pi$
$607$			20.0672i			0.814501i	−0.913316	+	0.407251i	$0.866488\pi$
$608$	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	0.947089	+	0.320971i	$0.104009\pi$
$613$	18.6066	+	32.2276i	0.751514	+	1.30166i	−0.195575	+	0.980689i	$0.562657\pi$
$614$	−4.98602	−	8.63604i	−0.201219	−	0.348522i
$615$		0			0
$616$	−3.00000	+	7.34847i	−0.120873	+	0.296078i
$617$	−15.3273	+	8.84924i	−0.617055	+	0.356257i	−0.775722	−	0.631075i	$-0.782614\pi$
$617$	−15.3273	+	8.84924i	−0.617055	+	0.356257i	0.158666	+	0.987332i	$0.449281\pi$
$618$		0			0
$619$			6.15978i			0.247582i	0.992308	+	0.123791i	$0.0395053\pi$
$619$			6.15978i			0.247582i	−0.992308	+	0.123791i	$0.960495\pi$
$620$	−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	0.158981	−	0.987282i	$-0.449179\pi$
$643$	27.7279	−	16.0087i	1.09348	−	0.631322i	0.934501	+	0.355959i	$0.115846\pi$
$644$	−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	0.985952	+	0.167031i	$0.0534180\pi$
$647$	16.2189	+	28.0919i	0.637629	+	1.10441i	−0.348323	+	0.937375i	$0.613249\pi$
$648$		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	$-0.370617\pi$
$659$	−5.19615	−	3.00000i	−0.202413	−	0.116863i	−0.597781	+	0.801660i	$0.703951\pi$
$660$		0			0
$661$	−30.8787	−	17.8278i	−1.20104	−	0.693422i	−0.240255	−	0.970710i	$-0.577231\pi$
$661$	−30.8787	−	17.8278i	−1.20104	−	0.693422i	−0.960787	+	0.277288i	$0.910564\pi$
$662$	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	−0.985599	−	0.169097i	$-0.945915\pi$
$673$	−8.98528	+	15.5630i	−0.346357	+	0.599908i	0.639242	+	0.769005i	$0.279248\pi$
$674$	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	$-0.179836\pi$
$677$	−1.07616	−	1.86396i	−0.0413601	−	0.0716378i	−0.885964	+	0.463753i	$0.846502\pi$
$678$		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	$-0.617937\pi$
$683$	6.90271	−	3.98528i	0.264125	−	0.152493i	0.626215	+	0.779651i	$0.284603\pi$
$684$		0			0
$685$		−	1.78304i		−	0.0681264i
$686$	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	−0.890178	−	0.455613i	$-0.849420\pi$
$691$	−24.7279	+	14.2767i	−0.940694	+	0.543110i	−0.0505165	+	0.998723i	$0.516087\pi$
$692$	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	−0.999972	−	0.00746433i	$-0.997624\pi$
$709$	−13.4853	−	23.3572i	−0.506450	−	0.877198i	0.493522	−	0.869733i	$-0.335709\pi$
$710$	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	$-0.736077\pi$
$719$	8.06591	−	13.9706i	0.300808	−	0.521014i	0.976319	+	0.216335i	$0.0694105\pi$
$720$		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	0.676044	−	0.736861i	$-0.263693\pi$
$727$	10.1360	+	5.85204i	0.375925	+	0.217040i	−0.300119	+	0.953902i	$0.597026\pi$
$728$	−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	$-0.972189\pi$
$733$		−	4.72490i		−	0.174518i	0.996186	−	0.0872591i	$-0.0278108\pi$
$734$	−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	0.688157	−	0.725562i	$-0.258420\pi$
$739$	−7.72792	−	13.3852i	−0.284276	−	0.492381i	−0.972433	+	0.233181i	$0.925087\pi$
$740$	0.0870399	+	0.150758i	0.00319965	+	0.00554196i
$741$		0			0
$742$	11.7426	+	15.1427i	0.431086	+	0.555906i
$743$	33.3292	−	19.2426i	1.22273	−	0.705944i	0.257232	−	0.966350i	$-0.417190\pi$
$743$	33.3292	−	19.2426i	1.22273	−	0.705944i	0.965499	+	0.260406i	$0.0838563\pi$
$744$		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	$-0.680035\pi$
$761$	−29.5680			−1.07184			−0.535919	+	0.844270i	$0.680035\pi$
$762$		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	−0.338263	−	0.941051i	$-0.609839\pi$
$769$	8.52944	−	4.92447i	0.307579	−	0.177581i	0.645843	+	0.763470i	$0.276506\pi$
$770$	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	$-0.260359\pi$
$773$	−8.06591	−	13.9706i	−0.290111	−	0.502486i	−0.973836	+	0.227253i	$0.927025\pi$
$774$		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	−0.0873693	−	0.996176i	$-0.527846\pi$
$787$	−27.8787	−	16.0958i	−0.993768	−	0.573752i	−0.906398	+	0.422424i	$0.861179\pi$
$788$	−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	$-0.130185\pi$
$797$	3.22848	+	5.59188i	0.114358	+	0.198075i	−0.803165	+	0.595757i	$0.796852\pi$
$798$		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	$-0.627232\pi$
$809$	6.08767	−	3.51472i	0.214031	−	0.123571i	0.603183	+	0.797602i	$0.293899\pi$
$810$		0			0
$811$			31.1769i			1.09477i	0.836881	+	0.547385i	$0.184377\pi$
$811$			31.1769i			1.09477i	−0.836881	+	0.547385i	$0.815623\pi$
$812$	−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	$-0.414809\pi$
$821$	35.2969	−	20.3787i	1.23187	−	0.711221i	0.967420	+	0.253178i	$0.0814759\pi$
$822$		0			0
$823$	−14.9706	+	25.9298i	−0.521841	+	0.903855i	0.477836	+	0.878449i	$0.341421\pi$
$823$	−14.9706	+	25.9298i	−0.521841	+	0.903855i	−0.999677	+	0.0254062i	$0.991912\pi$
$824$	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	−0.290082	−	0.957002i	$-0.593683\pi$
$829$	11.3345	−	6.54399i	0.393664	−	0.227282i	0.683747	+	0.729720i	$0.260349\pi$
$830$			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	$-0.776893\pi$
$839$	5.10911	−	8.84924i	0.176386	−	0.305510i	0.940640	+	0.339406i	$0.110226\pi$
$840$		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	−0.159840	−	0.987143i	$-0.551098\pi$
$853$	−31.9706	−	18.4582i	−1.09465	−	0.631997i	−0.934811	+	0.355146i	$0.884431\pi$
$854$	−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	$-0.303625\pi$
$857$	33.8726			1.15707			0.578533	+	0.815659i	$0.303625\pi$
$858$		0			0
$859$		−	9.37769i		−	0.319963i	−0.987120	−	0.159981i	$-0.948857\pi$
$859$		−	9.37769i		−	0.319963i	0.987120	−	0.159981i	$-0.0511434\pi$
$860$	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	$-0.526556\pi$
$863$	−29.0246	−	16.7574i	−0.988009	−	0.570427i	−0.904679	+	0.426095i	$0.859889\pi$
$864$		0			0
$865$	−7.45584	−	12.9139i	−0.253506	−	0.439086i
$866$	−1.73205	−	3.00000i	−0.0588575	−	0.101944i
$867$		0			0
$868$	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	$-0.603713\pi$
$881$	−19.0016			−0.640179			−0.320090	+	0.947387i	$0.603713\pi$
$882$		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	$-0.443234\pi$
$887$	10.5664			0.354784			0.177392	+	0.984140i	$0.443234\pi$
$888$		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	$-0.297783\pi$
$911$	5.82655	+	3.36396i	0.193042	+	0.111453i	−0.400364	+	0.916356i	$0.631116\pi$
$912$		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	0.390784	+	0.920482i	$0.372204\pi$
$919$	−18.2426	+	31.5972i	−0.601769	+	1.04229i	−0.992553	+	0.121812i	$0.961129\pi$
$920$	−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	0.999951	+	0.00994164i	$0.00316458\pi$
$929$	15.5014	+	26.8492i	0.508585	+	0.880895i	−0.491366	+	0.870953i	$0.663502\pi$
$930$		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	$-0.805114\pi$
$937$		−	35.1844i		−	1.14942i	0.818356	−	0.574712i	$-0.194886\pi$
$938$	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	$-0.981802\pi$
$941$	−13.7949	+	23.8934i	−0.449700	+	0.778903i	0.548667	+	0.836041i	$0.315136\pi$
$942$		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	$-0.723709\pi$
$947$	−9.50079	+	5.48528i	−0.308734	+	0.178248i	0.337626	+	0.941280i	$0.390376\pi$
$948$		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	−0.938961	−	0.344023i	$-0.888210\pi$
$967$	−23.8640	−	41.3336i	−0.767413	−	1.32920i	0.171548	−	0.985176i	$-0.445123\pi$
$968$		−	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	$-0.976344\pi$
$971$	−13.5337	+	23.4411i	−0.434318	+	0.752262i	0.562921	+	0.826510i	$0.309677\pi$
$972$		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	$-0.555951\pi$
$977$	−34.8511	−	20.1213i	−1.11499	−	0.643738i	−0.940116	+	0.340853i	$0.889284\pi$
$978$		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	$-0.772100\pi$
$983$	−47.3087			−1.50891			−0.754457	+	0.656349i	$0.772100\pi$
$984$		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	−0.898585	−	0.438799i	$-0.855404\pi$
$991$	−26.1066	−	45.2180i	−0.829304	−	1.43640i	0.0692818	−	0.997597i	$-0.477929\pi$
$992$	−4.54026	−	7.86396i	−0.144153	−	0.249681i
$993$		0			0
$994$	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	$-0.788465\pi$
$997$		−	38.9456i		−	1.23342i	0.787190	−	0.616711i	$-0.211535\pi$
$998$	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.593.3		8
3.2	odd	2	inner	1134.2.t.e.593.2		8
7.3	odd	6		1134.2.l.f.269.3		8
9.2	odd	6		126.2.k.a.89.3	yes	8
9.4	even	3		1134.2.l.f.215.4		8
9.5	odd	6		1134.2.l.f.215.1		8
9.7	even	3		126.2.k.a.89.2	yes	8
21.17	even	6		1134.2.l.f.269.2		8
36.7	odd	6		1008.2.bt.c.593.3		8
36.11	even	6		1008.2.bt.c.593.2		8
45.2	even	12		3150.2.bp.b.1349.3		8
45.7	odd	12		3150.2.bp.e.1349.3		8
45.29	odd	6		3150.2.bf.a.1601.1		8
45.34	even	6		3150.2.bf.a.1601.3		8
45.38	even	12		3150.2.bp.e.1349.2		8
45.43	odd	12		3150.2.bp.b.1349.2		8
63.2	odd	6		882.2.d.a.881.3		8
63.11	odd	6		882.2.k.a.521.1		8
63.16	even	3		882.2.d.a.881.6		8
63.20	even	6		882.2.k.a.215.4		8
63.25	even	3		882.2.k.a.521.4		8
63.31	odd	6	inner	1134.2.t.e.1025.2		8
63.34	odd	6		882.2.k.a.215.1		8
63.38	even	6		126.2.k.a.17.2	✓	8
63.47	even	6		882.2.d.a.881.2		8
63.52	odd	6		126.2.k.a.17.3	yes	8
63.59	even	6	inner	1134.2.t.e.1025.3		8
63.61	odd	6		882.2.d.a.881.7		8
252.47	odd	6		7056.2.k.f.881.4		8
252.79	odd	6		7056.2.k.f.881.3		8
252.115	even	6		1008.2.bt.c.17.2		8
252.187	even	6		7056.2.k.f.881.5		8
252.191	even	6		7056.2.k.f.881.6		8
252.227	odd	6		1008.2.bt.c.17.3		8
315.38	odd	12		3150.2.bp.e.899.3		8
315.52	even	12		3150.2.bp.e.899.2		8
315.164	even	6		3150.2.bf.a.1151.3		8
315.178	even	12		3150.2.bp.b.899.3		8
315.227	odd	12		3150.2.bp.b.899.2		8
315.304	odd	6		3150.2.bf.a.1151.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.k.a.17.2	✓	8	63.38	even	6
126.2.k.a.17.3	yes	8	63.52	odd	6
126.2.k.a.89.2	yes	8	9.7	even	3
126.2.k.a.89.3	yes	8	9.2	odd	6
882.2.d.a.881.2		8	63.47	even	6
882.2.d.a.881.3		8	63.2	odd	6
882.2.d.a.881.6		8	63.16	even	3
882.2.d.a.881.7		8	63.61	odd	6
882.2.k.a.215.1		8	63.34	odd	6
882.2.k.a.215.4		8	63.20	even	6
882.2.k.a.521.1		8	63.11	odd	6
882.2.k.a.521.4		8	63.25	even	3
1008.2.bt.c.17.2		8	252.115	even	6
1008.2.bt.c.17.3		8	252.227	odd	6
1008.2.bt.c.593.2		8	36.11	even	6
1008.2.bt.c.593.3		8	36.7	odd	6
1134.2.l.f.215.1		8	9.5	odd	6
1134.2.l.f.215.4		8	9.4	even	3
1134.2.l.f.269.2		8	21.17	even	6
1134.2.l.f.269.3		8	7.3	odd	6
1134.2.t.e.593.2		8	3.2	odd	2	inner
1134.2.t.e.593.3		8	1.1	even	1	trivial
1134.2.t.e.1025.2		8	63.31	odd	6	inner
1134.2.t.e.1025.3		8	63.59	even	6	inner
3150.2.bf.a.1151.1		8	315.304	odd	6
3150.2.bf.a.1151.3		8	315.164	even	6
3150.2.bf.a.1601.1		8	45.29	odd	6
3150.2.bf.a.1601.3		8	45.34	even	6
3150.2.bp.b.899.2		8	315.227	odd	12
3150.2.bp.b.899.3		8	315.178	even	12
3150.2.bp.b.1349.2		8	45.43	odd	12
3150.2.bp.b.1349.3		8	45.2	even	12
3150.2.bp.e.899.2		8	315.52	even	12
3150.2.bp.e.899.3		8	315.38	odd	12
3150.2.bp.e.1349.2		8	45.38	even	12
3150.2.bp.e.1349.3		8	45.7	odd	12
7056.2.k.f.881.3		8	252.79	odd	6
7056.2.k.f.881.4		8	252.47	odd	6
7056.2.k.f.881.5		8	252.187	even	6
7056.2.k.f.881.6		8	252.191	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.t (of order \(6\), degree \(2\), not minimal)

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