LMFDB - Embedded newform 1134.2.t.f.1025.4

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 378)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1025.4
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1134.1025
Dual form			1134.2.t.f.593.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +2.44949 q^{5} +(2.62132 - 0.358719i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +2.44949 q^{5} +(2.62132 - 0.358719i) q^{7} +1.00000i q^{8} +(2.12132 + 1.22474i) q^{10} +4.24264i q^{11} +(0.621320 + 0.358719i) q^{13} +(2.44949 + 1.00000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.22474 + 2.12132i) q^{17} +(-4.24264 + 2.44949i) q^{19} +(1.22474 + 2.12132i) q^{20} +(-2.12132 + 3.67423i) q^{22} -6.00000i q^{23} +1.00000 q^{25} +(0.358719 + 0.621320i) q^{26} +(1.62132 + 2.09077i) q^{28} +(1.52192 - 0.878680i) q^{29} +(7.86396 - 4.54026i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.12132 + 1.22474i) q^{34} +(6.42090 - 0.878680i) q^{35} +(-2.62132 - 4.54026i) q^{37} -4.89898 q^{38} +2.44949i q^{40} +(1.22474 - 2.12132i) q^{41} +(-3.50000 - 6.06218i) q^{43} +(-3.67423 + 2.12132i) q^{44} +(3.00000 - 5.19615i) q^{46} +(-6.42090 + 11.1213i) q^{47} +(6.74264 - 1.88064i) q^{49} +(0.866025 + 0.500000i) q^{50} +0.717439i q^{52} +(12.5446 + 7.24264i) q^{53} +10.3923i q^{55} +(0.358719 + 2.62132i) q^{56} +1.75736 q^{58} +(1.22474 + 2.12132i) q^{59} +(-3.62132 - 2.09077i) q^{61} +9.08052 q^{62} -1.00000 q^{64} +(1.52192 + 0.878680i) q^{65} +(-6.74264 - 11.6786i) q^{67} -2.44949 q^{68} +(6.00000 + 2.44949i) q^{70} +12.7279i q^{71} +(-4.75736 - 2.74666i) q^{73} -5.24264i q^{74} +(-4.24264 - 2.44949i) q^{76} +(1.52192 + 11.1213i) q^{77} +(-0.378680 + 0.655892i) q^{79} +(-1.22474 + 2.12132i) q^{80} +(2.12132 - 1.22474i) q^{82} +(-7.64564 - 13.2426i) q^{83} +(-3.00000 + 5.19615i) q^{85} -7.00000i q^{86} -4.24264 q^{88} +(-1.52192 - 2.63604i) q^{89} +(1.75736 + 0.717439i) q^{91} +(5.19615 - 3.00000i) q^{92} +(-11.1213 + 6.42090i) q^{94} +(-10.3923 + 6.00000i) q^{95} +(2.74264 - 1.58346i) q^{97} +(6.77962 + 1.74264i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 4 q^{7}+O(q^{10}) $ 8 * q + 4 * q^4 + 4 * q^7	$ 8 q + 4 q^{4} + 4 q^{7} - 12 q^{13} - 4 q^{16} + 8 q^{25} - 4 q^{28} + 12 q^{31} - 4 q^{37} - 28 q^{43} + 24 q^{46} + 20 q^{49} + 48 q^{58} - 12 q^{61} - 8 q^{64} - 20 q^{67} + 48 q^{70} - 72 q^{73} - 20 q^{79} - 24 q^{85} + 48 q^{91} - 72 q^{94} - 12 q^{97}+O(q^{100}) $ 8 * q + 4 * q^4 + 4 * q^7 - 12 * q^13 - 4 * q^16 + 8 * q^25 - 4 * q^28 + 12 * q^31 - 4 * q^37 - 28 * q^43 + 24 * q^46 + 20 * q^49 + 48 * q^58 - 12 * q^61 - 8 * q^64 - 20 * q^67 + 48 * q^70 - 72 * q^73 - 20 * q^79 - 24 * q^85 + 48 * q^91 - 72 * q^94 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	2.44949			1.09545			0.547723	−	0.836660i	$-0.315495\pi$
$5$	2.44949			1.09545			0.547723	+	0.836660i	$0.315495\pi$
$6$		0			0
$7$	2.62132	−	0.358719i	0.990766	−	0.135583i
$7$	2.62132	−	0.358719i	0.990766	−	0.135583i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	2.12132	+	1.22474i	0.670820	+	0.387298i
$11$			4.24264i			1.27920i	0.768706	+	0.639602i	$0.220901\pi$
$11$			4.24264i			1.27920i	−0.768706	+	0.639602i	$0.779099\pi$
$12$		0			0
$13$	0.621320	+	0.358719i	0.172323	+	0.0994909i	0.583681	−	0.811983i	$-0.301612\pi$
$13$	0.621320	+	0.358719i	0.172323	+	0.0994909i	−0.411358	+	0.911474i	$0.634945\pi$
$14$	2.44949	+	1.00000i	0.654654	+	0.267261i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.22474	+	2.12132i	−0.297044	+	0.514496i	−0.975458	−	0.220184i	$-0.929334\pi$
$17$	−1.22474	+	2.12132i	−0.297044	+	0.514496i	0.678414	+	0.734680i	$0.262668\pi$
$18$		0			0
$19$	−4.24264	+	2.44949i	−0.973329	+	0.561951i	−0.900249	−	0.435375i	$-0.856616\pi$
$19$	−4.24264	+	2.44949i	−0.973329	+	0.561951i	−0.0730792	+	0.997326i	$0.523283\pi$
$20$	1.22474	+	2.12132i	0.273861	+	0.474342i
$21$		0			0
$22$	−2.12132	+	3.67423i	−0.452267	+	0.783349i
$23$		−	6.00000i		−	1.25109i	−0.780189	−	0.625543i	$-0.784877\pi$
$23$		−	6.00000i		−	1.25109i	0.780189	−	0.625543i	$-0.215123\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	0.358719	+	0.621320i	0.0703507	+	0.121851i
$27$		0			0
$28$	1.62132	+	2.09077i	0.306401	+	0.395118i
$29$	1.52192	−	0.878680i	0.282613	−	0.163167i	−0.351993	−	0.936003i	$-0.614496\pi$
$29$	1.52192	−	0.878680i	0.282613	−	0.163167i	0.634606	+	0.772836i	$0.281162\pi$
$30$		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
$34$	−2.12132	+	1.22474i	−0.363803	+	0.210042i
$35$	6.42090	−	0.878680i	1.08533	−	0.148524i
$36$		0			0
$37$	−2.62132	−	4.54026i	−0.430942	−	0.746414i	0.566012	−	0.824397i	$-0.308485\pi$
$37$	−2.62132	−	4.54026i	−0.430942	−	0.746414i	−0.996955	+	0.0779826i	$0.975152\pi$
$38$	−4.89898			−0.794719
$39$		0			0
$40$			2.44949i			0.387298i
$41$	1.22474	−	2.12132i	0.191273	−	0.331295i	−0.754399	−	0.656416i	$-0.772072\pi$
$41$	1.22474	−	2.12132i	0.191273	−	0.331295i	0.945672	+	0.325121i	$0.105405\pi$
$42$		0			0
$43$	−3.50000	−	6.06218i	−0.533745	−	0.924473i	−0.999223	−	0.0394140i	$-0.987451\pi$
$43$	−3.50000	−	6.06218i	−0.533745	−	0.924473i	0.465478	−	0.885059i	$-0.345882\pi$
$44$	−3.67423	+	2.12132i	−0.553912	+	0.319801i
$45$		0			0
$46$	3.00000	−	5.19615i	0.442326	−	0.766131i
$47$	−6.42090	+	11.1213i	−0.936584	+	1.62221i	−0.164800	+	0.986327i	$0.552698\pi$
$47$	−6.42090	+	11.1213i	−0.936584	+	1.62221i	−0.771784	+	0.635884i	$0.780636\pi$
$48$		0			0
$49$	6.74264	−	1.88064i	0.963234	−	0.268662i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$		0			0
$52$			0.717439i			0.0994909i
$53$	12.5446	+	7.24264i	1.72314	+	0.994853i	0.912231	+	0.409675i	$0.134358\pi$
$53$	12.5446	+	7.24264i	1.72314	+	0.994853i	0.810905	+	0.585178i	$0.198975\pi$
$54$		0			0
$55$			10.3923i			1.40130i
$56$	0.358719	+	2.62132i	0.0479359	+	0.350289i
$57$		0			0
$58$	1.75736			0.230753
$59$	1.22474	+	2.12132i	0.159448	+	0.276172i	0.934670	−	0.355517i	$-0.115695\pi$
$59$	1.22474	+	2.12132i	0.159448	+	0.276172i	−0.775222	+	0.631689i	$0.782362\pi$
$60$		0			0
$61$	−3.62132	−	2.09077i	−0.463663	−	0.267696i	0.249920	−	0.968266i	$-0.419596\pi$
$61$	−3.62132	−	2.09077i	−0.463663	−	0.267696i	−0.713583	+	0.700571i	$0.752929\pi$
$62$	9.08052			1.15323
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.52192	+	0.878680i	0.188771	+	0.108987i
$66$		0			0
$67$	−6.74264	−	11.6786i	−0.823745	−	1.42677i	−0.902875	−	0.429903i	$-0.858548\pi$
$67$	−6.74264	−	11.6786i	−0.823745	−	1.42677i	0.0791303	−	0.996864i	$-0.474786\pi$
$68$	−2.44949			−0.297044
$69$		0			0
$70$	6.00000	+	2.44949i	0.717137	+	0.292770i
$71$			12.7279i			1.51053i	0.655422	+	0.755263i	$0.272491\pi$
$71$			12.7279i			1.51053i	−0.655422	+	0.755263i	$0.727509\pi$
$72$		0			0
$73$	−4.75736	−	2.74666i	−0.556807	−	0.321473i	0.195056	−	0.980792i	$-0.437511\pi$
$73$	−4.75736	−	2.74666i	−0.556807	−	0.321473i	−0.751863	+	0.659320i	$0.770844\pi$
$74$		−	5.24264i		−	0.609445i
$75$		0			0
$76$	−4.24264	−	2.44949i	−0.486664	−	0.280976i
$77$	1.52192	+	11.1213i	0.173439	+	1.26739i
$78$		0			0
$79$	−0.378680	+	0.655892i	−0.0426048	+	0.0737937i	−0.886541	−	0.462649i	$-0.846899\pi$
$79$	−0.378680	+	0.655892i	−0.0426048	+	0.0737937i	0.843937	+	0.536443i	$0.180232\pi$
$80$	−1.22474	+	2.12132i	−0.136931	+	0.237171i
$81$		0			0
$82$	2.12132	−	1.22474i	0.234261	−	0.135250i
$83$	−7.64564	−	13.2426i	−0.839218	−	1.45357i	−0.890549	−	0.454887i	$-0.849680\pi$
$83$	−7.64564	−	13.2426i	−0.839218	−	1.45357i	0.0513309	−	0.998682i	$-0.483654\pi$
$84$		0			0
$85$	−3.00000	+	5.19615i	−0.325396	+	0.563602i
$86$		−	7.00000i		−	0.754829i
$87$		0			0
$88$	−4.24264			−0.452267
$89$	−1.52192	−	2.63604i	−0.161323	−	0.279420i	0.774020	−	0.633161i	$-0.218243\pi$
$89$	−1.52192	−	2.63604i	−0.161323	−	0.279420i	−0.935343	+	0.353741i	$0.884909\pi$
$90$		0			0
$91$	1.75736	+	0.717439i	0.184221	+	0.0752080i
$92$	5.19615	−	3.00000i	0.541736	−	0.312772i
$93$		0			0
$94$	−11.1213	+	6.42090i	−1.14708	+	0.662265i
$95$	−10.3923	+	6.00000i	−1.06623	+	0.615587i
$96$		0			0
$97$	2.74264	−	1.58346i	0.278473	−	0.160776i	−0.354259	−	0.935147i	$-0.615267\pi$
$97$	2.74264	−	1.58346i	0.278473	−	0.160776i	0.632732	+	0.774371i	$0.281934\pi$
$98$	6.77962	+	1.74264i	0.684845	+	0.176033i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	7.34847			0.731200			0.365600	−	0.930772i	$-0.380864\pi$
$101$	7.34847			0.731200			0.365600	+	0.930772i	$0.380864\pi$
$102$		0			0
$103$			11.1097i			1.09468i	0.836912	+	0.547338i	$0.184359\pi$
$103$			11.1097i			1.09468i	−0.836912	+	0.547338i	$0.815641\pi$
$104$	−0.358719	+	0.621320i	−0.0351753	+	0.0609255i
$105$		0			0
$106$	7.24264	+	12.5446i	0.703467	+	1.21844i
$107$	2.15232	−	1.24264i	0.208072	−	0.120131i	−0.392343	−	0.919819i	$-0.628335\pi$
$107$	2.15232	−	1.24264i	0.208072	−	0.120131i	0.600415	+	0.799688i	$0.295002\pi$
$108$		0			0
$109$	8.86396	−	15.3528i	0.849013	−	1.47053i	−0.0330761	−	0.999453i	$-0.510530\pi$
$109$	8.86396	−	15.3528i	0.849013	−	1.47053i	0.882090	−	0.471082i	$-0.156136\pi$
$110$	−5.19615	+	9.00000i	−0.495434	+	0.858116i
$111$		0			0
$112$	−1.00000	+	2.44949i	−0.0944911	+	0.231455i
$113$	8.87039	+	5.12132i	0.834456	+	0.481773i	0.855376	−	0.518008i	$-0.173326\pi$
$113$	8.87039	+	5.12132i	0.834456	+	0.481773i	−0.0209200	+	0.999781i	$0.506660\pi$
$114$		0			0
$115$		−	14.6969i		−	1.37050i
$116$	1.52192	+	0.878680i	0.141307	+	0.0815834i
$117$		0			0
$118$			2.44949i			0.225494i
$119$	−2.44949	+	6.00000i	−0.224544	+	0.550019i
$120$		0			0
$121$	−7.00000			−0.636364
$122$	−2.09077	−	3.62132i	−0.189289	−	0.327859i
$123$		0			0
$124$	7.86396	+	4.54026i	0.706205	+	0.407727i
$125$	−9.79796			−0.876356
$126$		0			0
$127$	−7.72792			−0.685742			−0.342871	−	0.939382i	$-0.611399\pi$
$127$	−7.72792			−0.685742			−0.342871	+	0.939382i	$0.611399\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	0.878680	+	1.52192i	0.0770653	+	0.133481i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	−10.2426	+	7.94282i	−0.888150	+	0.688729i
$134$		−	13.4853i		−	1.16495i
$135$		0			0
$136$	−2.12132	−	1.22474i	−0.181902	−	0.105021i
$137$		−	6.00000i		−	0.512615i	−0.966595	−	0.256307i	$-0.917494\pi$
$137$		−	6.00000i		−	0.512615i	0.966595	−	0.256307i	$-0.0825059\pi$
$138$		0			0
$139$	−6.98528	−	4.03295i	−0.592484	−	0.342071i	0.173595	−	0.984817i	$-0.444462\pi$
$139$	−6.98528	−	4.03295i	−0.592484	−	0.342071i	−0.766079	+	0.642746i	$0.777795\pi$
$140$	3.97141	+	5.12132i	0.335645	+	0.432831i
$141$		0			0
$142$	−6.36396	+	11.0227i	−0.534052	+	0.925005i
$143$	−1.52192	+	2.63604i	−0.127269	+	0.220437i
$144$		0			0
$145$	3.72792	−	2.15232i	0.309587	−	0.178740i
$146$	−2.74666	−	4.75736i	−0.227315	−	0.393722i
$147$		0			0
$148$	2.62132	−	4.54026i	0.215471	−	0.373207i
$149$		−	16.2426i		−	1.33065i	−0.746554	−	0.665324i	$-0.768293\pi$
$149$		−	16.2426i		−	1.33065i	0.746554	−	0.665324i	$-0.231707\pi$
$150$		0			0
$151$	8.75736			0.712664			0.356332	−	0.934359i	$-0.384027\pi$
$151$	8.75736			0.712664			0.356332	+	0.934359i	$0.384027\pi$
$152$	−2.44949	−	4.24264i	−0.198680	−	0.344124i
$153$		0			0
$154$	−4.24264	+	10.3923i	−0.341882	+	0.837436i
$155$	19.2627	−	11.1213i	1.54722	−	0.893286i
$156$		0			0
$157$	9.00000	−	5.19615i	0.718278	−	0.414698i	−0.0958404	−	0.995397i	$-0.530554\pi$
$157$	9.00000	−	5.19615i	0.718278	−	0.414698i	0.814119	+	0.580699i	$0.197221\pi$
$158$	−0.655892	+	0.378680i	−0.0521800	+	0.0301261i
$159$		0			0
$160$	−2.12132	+	1.22474i	−0.167705	+	0.0968246i
$161$	−2.15232	−	15.7279i	−0.169626	−	1.23953i
$162$		0			0
$163$	4.74264	+	8.21449i	0.371472	+	0.643409i	0.989792	−	0.142518i	$-0.0455197\pi$
$163$	4.74264	+	8.21449i	0.371472	+	0.643409i	−0.618320	+	0.785926i	$0.712186\pi$
$164$	2.44949			0.191273
$165$		0			0
$166$		−	15.2913i		−	1.18683i
$167$	0.297173	−	0.514719i	0.0229959	−	0.0398301i	−0.854298	−	0.519783i	$-0.826013\pi$
$167$	0.297173	−	0.514719i	0.0229959	−	0.0398301i	0.877294	+	0.479953i	$0.159346\pi$
$168$		0			0
$169$	−6.24264	−	10.8126i	−0.480203	−	0.831736i
$170$	−5.19615	+	3.00000i	−0.398527	+	0.230089i
$171$		0			0
$172$	3.50000	−	6.06218i	0.266872	−	0.462237i
$173$	−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
$175$	2.62132	−	0.358719i	0.198153	−	0.0271166i
$176$	−3.67423	−	2.12132i	−0.276956	−	0.159901i
$177$		0			0
$178$		−	3.04384i		−	0.228145i
$179$	−5.82655	−	3.36396i	−0.435497	−	0.251434i	0.266189	−	0.963921i	$-0.414236\pi$
$179$	−5.82655	−	3.36396i	−0.435497	−	0.251434i	−0.701686	+	0.712487i	$0.747569\pi$
$180$		0			0
$181$		−	9.79796i		−	0.728277i	−0.931345	−	0.364138i	$-0.881364\pi$
$181$		−	9.79796i		−	0.728277i	0.931345	−	0.364138i	$-0.118636\pi$
$182$	1.16320	+	1.50000i	0.0862220	+	0.111187i
$183$		0			0
$184$	6.00000			0.442326
$185$	−6.42090	−	11.1213i	−0.472074	−	0.817656i
$186$		0			0
$187$	−9.00000	−	5.19615i	−0.658145	−	0.379980i
$188$	−12.8418			−0.936584
$189$		0			0
$190$	−12.0000			−0.870572
$191$	18.3712	+	10.6066i	1.32929	+	0.767467i	0.985190	−	0.171466i	$-0.0548503\pi$
$191$	18.3712	+	10.6066i	1.32929	+	0.767467i	0.344101	+	0.938933i	$0.388184\pi$
$192$		0			0
$193$	0.742641	+	1.28629i	0.0534564	+	0.0925893i	0.891515	−	0.452990i	$-0.149643\pi$
$193$	0.742641	+	1.28629i	0.0534564	+	0.0925893i	−0.838059	+	0.545580i	$0.816310\pi$
$194$	3.16693			0.227372
$195$		0			0
$196$	5.00000	+	4.89898i	0.357143	+	0.349927i
$197$		−	16.9706i		−	1.20910i	−0.796566	−	0.604551i	$-0.793352\pi$
$197$		−	16.9706i		−	1.20910i	0.796566	−	0.604551i	$-0.206648\pi$
$198$		0			0
$199$	−18.1066	−	10.4539i	−1.28354	−	0.741054i	−0.306049	−	0.952016i	$-0.599007\pi$
$199$	−18.1066	−	10.4539i	−1.28354	−	0.741054i	−0.977494	+	0.210962i	$0.932340\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	6.36396	+	3.67423i	0.447767	+	0.258518i
$203$	3.67423	−	2.84924i	0.257881	−	0.199978i
$204$		0			0
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$	−5.55487	+	9.62132i	−0.387026	+	0.670349i
$207$		0			0
$208$	−0.621320	+	0.358719i	−0.0430808	+	0.0248727i
$209$	−10.3923	−	18.0000i	−0.718851	−	1.24509i
$210$		0			0
$211$	−1.74264	+	3.01834i	−0.119968	+	0.207791i	−0.919755	−	0.392493i	$-0.871613\pi$
$211$	−1.74264	+	3.01834i	−0.119968	+	0.207791i	0.799787	+	0.600284i	$0.204946\pi$
$212$			14.4853i			0.994853i
$213$		0			0
$214$	2.48528			0.169890
$215$	−8.57321	−	14.8492i	−0.584688	−	1.01271i
$216$		0			0
$217$	18.9853	−	14.7224i	1.28880	−	0.999424i
$218$	15.3528	−	8.86396i	1.03982	−	0.600343i
$219$		0			0
$220$	−9.00000	+	5.19615i	−0.606780	+	0.350325i
$221$	−1.52192	+	0.878680i	−0.102375	+	0.0591064i
$222$		0			0
$223$	−9.00000	+	5.19615i	−0.602685	+	0.347960i	−0.770097	−	0.637927i	$-0.779792\pi$
$223$	−9.00000	+	5.19615i	−0.602685	+	0.347960i	0.167412	+	0.985887i	$0.446459\pi$
$224$	−2.09077	+	1.62132i	−0.139695	+	0.108329i
$225$		0			0
$226$	5.12132	+	8.87039i	0.340665	+	0.590049i
$227$	−25.0892			−1.66523			−0.832616	−	0.553851i	$-0.813158\pi$
$227$	−25.0892			−1.66523			−0.832616	+	0.553851i	$0.813158\pi$
$228$		0			0
$229$		−	5.61642i		−	0.371143i	−0.982631	−	0.185572i	$-0.940586\pi$
$229$		−	5.61642i		−	0.371143i	0.982631	−	0.185572i	$-0.0594137\pi$
$230$	7.34847	−	12.7279i	0.484544	−	0.839254i
$231$		0			0
$232$	0.878680	+	1.52192i	0.0576881	+	0.0999188i
$233$	−17.7408	+	10.2426i	−1.16224	+	0.671018i	−0.951839	−	0.306598i	$-0.900809\pi$
$233$	−17.7408	+	10.2426i	−1.16224	+	0.671018i	−0.210398	+	0.977616i	$0.567476\pi$
$234$		0			0
$235$	−15.7279	+	27.2416i	−1.02598	+	1.77704i
$236$	−1.22474	+	2.12132i	−0.0797241	+	0.138086i
$237$		0			0
$238$	−5.12132	+	3.97141i	−0.331966	+	0.257428i
$239$	14.0665	+	8.12132i	0.909889	+	0.525325i	0.880395	−	0.474240i	$-0.157277\pi$
$239$	14.0665	+	8.12132i	0.909889	+	0.525325i	0.0294934	+	0.999565i	$0.490611\pi$
$240$		0			0
$241$			1.13770i			0.0732860i	0.999328	+	0.0366430i	$0.0116664\pi$
$241$			1.13770i			0.0732860i	−0.999328	+	0.0366430i	$0.988334\pi$
$242$	−6.06218	−	3.50000i	−0.389692	−	0.224989i
$243$		0			0
$244$		−	4.18154i		−	0.267696i
$245$	16.5160	−	4.60660i	1.05517	−	0.294305i
$246$		0			0
$247$	−3.51472			−0.223636
$248$	4.54026	+	7.86396i	0.288307	+	0.499362i
$249$		0			0
$250$	−8.48528	−	4.89898i	−0.536656	−	0.309839i
$251$	−15.2913			−0.965177			−0.482589	−	0.875847i	$-0.660303\pi$
$251$	−15.2913			−0.965177			−0.482589	+	0.875847i	$0.660303\pi$
$252$		0			0
$253$	25.4558			1.60040
$254$	−6.69258	−	3.86396i	−0.419930	−	0.242446i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−25.0892			−1.56502			−0.782512	−	0.622636i	$-0.786062\pi$
$257$	−25.0892			−1.56502			−0.782512	+	0.622636i	$0.786062\pi$
$258$		0			0
$259$	−8.50000	−	10.9612i	−0.528164	−	0.681093i
$260$			1.75736i			0.108987i
$261$		0			0
$262$		0			0
$263$		−	6.72792i		−	0.414861i	−0.978250	−	0.207431i	$-0.933490\pi$
$263$		−	6.72792i		−	0.414861i	0.978250	−	0.207431i	$-0.0665102\pi$
$264$		0			0
$265$	30.7279	+	17.7408i	1.88760	+	1.08981i
$266$	−12.8418	+	1.75736i	−0.787381	+	0.107751i
$267$		0			0
$268$	6.74264	−	11.6786i	0.411872	−	0.713384i
$269$	4.89898	−	8.48528i	0.298696	−	0.517357i	−0.677142	−	0.735853i	$-0.736782\pi$
$269$	4.89898	−	8.48528i	0.298696	−	0.517357i	0.975838	+	0.218496i	$0.0701150\pi$
$270$		0			0
$271$	−16.3492	+	9.43924i	−0.993146	+	0.573393i	−0.906213	−	0.422821i	$-0.861040\pi$
$271$	−16.3492	+	9.43924i	−0.993146	+	0.573393i	−0.0869326	+	0.996214i	$0.527706\pi$
$272$	−1.22474	−	2.12132i	−0.0742611	−	0.128624i
$273$		0			0
$274$	3.00000	−	5.19615i	0.181237	−	0.313911i
$275$			4.24264i			0.255841i
$276$		0			0
$277$	23.7279			1.42567			0.712836	−	0.701330i	$-0.247410\pi$
$277$	23.7279			1.42567			0.712836	+	0.701330i	$0.247410\pi$
$278$	−4.03295	−	6.98528i	−0.241881	−	0.418949i
$279$		0			0
$280$	0.878680	+	6.42090i	0.0525112	+	0.383722i
$281$	11.9142	−	6.87868i	0.710743	−	0.410348i	−0.100593	−	0.994928i	$-0.532074\pi$
$281$	11.9142	−	6.87868i	0.710743	−	0.410348i	0.811336	+	0.584580i	$0.198741\pi$
$282$		0			0
$283$	−5.22792	+	3.01834i	−0.310768	+	0.179422i	−0.647270	−	0.762261i	$-0.724089\pi$
$283$	−5.22792	+	3.01834i	−0.310768	+	0.179422i	0.336502	+	0.941683i	$0.390756\pi$
$284$	−11.0227	+	6.36396i	−0.654077	+	0.377632i
$285$		0			0
$286$	−2.63604	+	1.52192i	−0.155872	+	0.0899929i
$287$	2.44949	−	6.00000i	0.144589	−	0.354169i
$288$		0			0
$289$	5.50000	+	9.52628i	0.323529	+	0.560369i
$290$	4.30463			0.252777
$291$		0			0
$292$		−	5.49333i		−	0.321473i
$293$	6.42090	−	11.1213i	0.375113	−	0.649714i	−0.615231	−	0.788347i	$-0.710937\pi$
$293$	6.42090	−	11.1213i	0.375113	−	0.649714i	0.990344	+	0.138632i	$0.0442706\pi$
$294$		0			0
$295$	3.00000	+	5.19615i	0.174667	+	0.302532i
$296$	4.54026	−	2.62132i	0.263897	−	0.152361i
$297$		0			0
$298$	8.12132	−	14.0665i	0.470455	−	0.814853i
$299$	2.15232	−	3.72792i	0.124472	−	0.215591i
$300$		0			0
$301$	−11.3492	−	14.6354i	−0.654159	−	0.843570i
$302$	7.58410	+	4.37868i	0.436416	+	0.251965i
$303$		0			0
$304$		−	4.89898i		−	0.280976i
$305$	−8.87039	−	5.12132i	−0.507917	−	0.293246i
$306$		0			0
$307$			26.8213i			1.53077i	0.643571	+	0.765386i	$0.277452\pi$
$307$			26.8213i			1.53077i	−0.643571	+	0.765386i	$0.722548\pi$
$308$	−8.87039	+	6.87868i	−0.505437	+	0.391949i
$309$		0			0
$310$	22.2426			1.26330
$311$	−8.57321	−	14.8492i	−0.486142	−	0.842023i	0.513731	−	0.857951i	$-0.328263\pi$
$311$	−8.57321	−	14.8492i	−0.486142	−	0.842023i	−0.999873	+	0.0159282i	$0.994930\pi$
$312$		0			0
$313$	17.4853	+	10.0951i	0.988327	+	0.570611i	0.904774	−	0.425893i	$-0.140040\pi$
$313$	17.4853	+	10.0951i	0.988327	+	0.570611i	0.0835529	+	0.996503i	$0.473373\pi$
$314$	10.3923			0.586472
$315$		0			0
$316$	−0.757359			−0.0426048
$317$	−19.2627	−	11.1213i	−1.08190	−	0.624636i	−0.150492	−	0.988611i	$-0.548086\pi$
$317$	−19.2627	−	11.1213i	−1.08190	−	0.624636i	−0.931408	+	0.363976i	$0.881419\pi$
$318$		0			0
$319$	3.72792	+	6.45695i	0.208724	+	0.361520i
$320$	−2.44949			−0.136931
$321$		0			0
$322$	6.00000	−	14.6969i	0.334367	−	0.819028i
$323$		−	12.0000i		−	0.667698i
$324$		0			0
$325$	0.621320	+	0.358719i	0.0344647	+	0.0198982i
$326$			9.48528i			0.525341i
$327$		0			0
$328$	2.12132	+	1.22474i	0.117130	+	0.0676252i
$329$	−12.8418	+	31.4558i	−0.707991	+	1.73422i
$330$		0			0
$331$	−5.00000	+	8.66025i	−0.274825	+	0.476011i	−0.970091	−	0.242742i	$-0.921953\pi$
$331$	−5.00000	+	8.66025i	−0.274825	+	0.476011i	0.695266	+	0.718752i	$0.255287\pi$
$332$	7.64564	−	13.2426i	0.419609	−	0.726784i
$333$		0			0
$334$	0.514719	−	0.297173i	0.0281642	−	0.0162606i
$335$	−16.5160	−	28.6066i	−0.902367	−	1.56295i
$336$		0			0
$337$	10.7279	−	18.5813i	0.584387	−	1.01219i	−0.410564	−	0.911832i	$-0.634668\pi$
$337$	10.7279	−	18.5813i	0.584387	−	1.01219i	0.994952	−	0.100357i	$-0.0319984\pi$
$338$		−	12.4853i		−	0.679110i
$339$		0			0
$340$	−6.00000			−0.325396
$341$	19.2627	+	33.3640i	1.04313	+	1.80676i
$342$		0			0
$343$	17.0000	−	7.34847i	0.917914	−	0.396780i
$344$	6.06218	−	3.50000i	0.326851	−	0.188707i
$345$		0			0
$346$	−18.0000	+	10.3923i	−0.967686	+	0.558694i
$347$	−4.30463	+	2.48528i	−0.231085	+	0.133417i	−0.611072	−	0.791575i	$-0.709262\pi$
$347$	−4.30463	+	2.48528i	−0.231085	+	0.133417i	0.379988	+	0.924992i	$0.375928\pi$
$348$		0			0
$349$	−0.106602	+	0.0615465i	−0.00570626	+	0.00329451i	−0.502850	−	0.864373i	$-0.667715\pi$
$349$	−0.106602	+	0.0615465i	−0.00570626	+	0.00329451i	0.497144	+	0.867668i	$0.334382\pi$
$350$	2.44949	+	1.00000i	0.130931	+	0.0534522i
$351$		0			0
$352$	−2.12132	−	3.67423i	−0.113067	−	0.195837i
$353$	−10.9867			−0.584760			−0.292380	−	0.956302i	$-0.594447\pi$
$353$	−10.9867			−0.584760			−0.292380	+	0.956302i	$0.594447\pi$
$354$		0			0
$355$			31.1769i			1.65470i
$356$	1.52192	−	2.63604i	0.0806615	−	0.139710i
$357$		0			0
$358$	−3.36396	−	5.82655i	−0.177791	−	0.307943i
$359$	12.5446	−	7.24264i	0.662080	−	0.382252i	−0.130989	−	0.991384i	$-0.541815\pi$
$359$	12.5446	−	7.24264i	0.662080	−	0.382252i	0.793069	+	0.609132i	$0.208482\pi$
$360$		0			0
$361$	2.50000	−	4.33013i	0.131579	−	0.227901i
$362$	4.89898	−	8.48528i	0.257485	−	0.445976i
$363$		0			0
$364$	0.257359	+	1.88064i	0.0134893	+	0.0985722i
$365$	−11.6531	−	6.72792i	−0.609951	−	0.352156i
$366$		0			0
$367$			29.9882i			1.56537i	0.622416	+	0.782686i	$0.286151\pi$
$367$			29.9882i			1.56537i	−0.622416	+	0.782686i	$0.713849\pi$
$368$	5.19615	+	3.00000i	0.270868	+	0.156386i
$369$		0			0
$370$		−	12.8418i		−	0.667613i
$371$	35.4815	+	14.4853i	1.84211	+	0.752038i
$372$		0			0
$373$	−22.0000			−1.13912			−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000			−1.13912			−0.569558	+	0.821951i	$0.692886\pi$
$374$	−5.19615	−	9.00000i	−0.268687	−	0.465379i
$375$		0			0
$376$	−11.1213	−	6.42090i	−0.573538	−	0.331132i
$377$	1.26080			0.0649344
$378$		0			0
$379$	−7.48528			−0.384493			−0.192247	−	0.981347i	$-0.561577\pi$
$379$	−7.48528			−0.384493			−0.192247	+	0.981347i	$0.561577\pi$
$380$	−10.3923	−	6.00000i	−0.533114	−	0.307794i
$381$		0			0
$382$	10.6066	+	18.3712i	0.542681	+	0.939951i
$383$	−5.49333			−0.280696			−0.140348	−	0.990102i	$-0.544822\pi$
$383$	−5.49333			−0.280696			−0.140348	+	0.990102i	$0.544822\pi$
$384$		0			0
$385$	3.72792	+	27.2416i	0.189993	+	1.38836i
$386$			1.48528i			0.0755988i
$387$		0			0
$388$	2.74264	+	1.58346i	0.139236	+	0.0803882i
$389$			15.5147i			0.786627i	0.919404	+	0.393314i	$0.128671\pi$
$389$			15.5147i			0.786627i	−0.919404	+	0.393314i	$0.871329\pi$
$390$		0			0
$391$	12.7279	+	7.34847i	0.643679	+	0.371628i
$392$	1.88064	+	6.74264i	0.0949865	+	0.340555i
$393$		0			0
$394$	8.48528	−	14.6969i	0.427482	−	0.740421i
$395$	−0.927572	+	1.60660i	−0.0466712	+	0.0808369i
$396$		0			0
$397$	−13.1360	+	7.58410i	−0.659279	+	0.380635i	−0.792002	−	0.610518i	$-0.790961\pi$
$397$	−13.1360	+	7.58410i	−0.659279	+	0.380635i	0.132723	+	0.991153i	$0.457628\pi$
$398$	−10.4539	−	18.1066i	−0.524004	−	0.907602i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$			19.7574i			0.986635i	0.869849	+	0.493318i	$0.164216\pi$
$401$			19.7574i			0.986635i	−0.869849	+	0.493318i	$0.835784\pi$
$402$		0			0
$403$	6.51472			0.324521
$404$	3.67423	+	6.36396i	0.182800	+	0.316619i
$405$		0			0
$406$	4.60660	−	0.630399i	0.228622	−	0.0312862i
$407$	19.2627	−	11.1213i	0.954816	−	0.551263i
$408$		0			0
$409$	3.25736	−	1.88064i	0.161066	−	0.0929915i	−0.417300	−	0.908769i	$-0.637024\pi$
$409$	3.25736	−	1.88064i	0.161066	−	0.0929915i	0.578366	+	0.815777i	$0.303690\pi$
$410$	5.19615	−	3.00000i	0.256620	−	0.148159i
$411$		0			0
$412$	−9.62132	+	5.55487i	−0.474008	+	0.273669i
$413$	3.97141	+	5.12132i	0.195420	+	0.252004i
$414$		0			0
$415$	−18.7279	−	32.4377i	−0.919318	−	1.59230i
$416$	−0.717439			−0.0351753
$417$		0			0
$418$		−	20.7846i		−	1.01661i
$419$	3.97141	−	6.87868i	0.194016	−	0.336045i	−0.752562	−	0.658522i	$-0.771182\pi$
$419$	3.97141	−	6.87868i	0.194016	−	0.336045i	0.946577	+	0.322476i	$0.104515\pi$
$420$		0			0
$421$	11.7279	+	20.3134i	0.571584	+	0.990012i	0.996404	+	0.0847344i	$0.0270042\pi$
$421$	11.7279	+	20.3134i	0.571584	+	0.990012i	−0.424820	+	0.905278i	$0.639662\pi$
$422$	−3.01834	+	1.74264i	−0.146931	+	0.0848304i
$423$		0			0
$424$	−7.24264	+	12.5446i	−0.351734	+	0.609221i
$425$	−1.22474	+	2.12132i	−0.0594089	+	0.102899i
$426$		0			0
$427$	−10.2426	−	4.18154i	−0.495676	−	0.202359i
$428$	2.15232	+	1.24264i	0.104036	+	0.0600653i
$429$		0			0
$430$		−	17.1464i		−	0.826874i
$431$	−1.52192	−	0.878680i	−0.0733082	−	0.0423245i	0.462898	−	0.886412i	$-0.346810\pi$
$431$	−1.52192	−	0.878680i	−0.0733082	−	0.0423245i	−0.536206	+	0.844087i	$0.680143\pi$
$432$		0			0
$433$			2.57258i			0.123630i	0.998088	+	0.0618152i	$0.0196889\pi$
$433$			2.57258i			0.123630i	−0.998088	+	0.0618152i	$0.980311\pi$
$434$	23.8030	−	3.25736i	1.14258	−	0.156358i
$435$		0			0
$436$	17.7279			0.849013
$437$	14.6969	+	25.4558i	0.703050	+	1.21772i
$438$		0			0
$439$	−3.72792	−	2.15232i	−0.177924	−	0.102724i	0.408393	−	0.912806i	$-0.366089\pi$
$439$	−3.72792	−	2.15232i	−0.177924	−	0.102724i	−0.586317	+	0.810082i	$0.699423\pi$
$440$	−10.3923			−0.495434
$441$		0			0
$442$	−1.75736			−0.0835891
$443$	−22.0454	−	12.7279i	−1.04741	−	0.604722i	−0.125486	−	0.992095i	$-0.540049\pi$
$443$	−22.0454	−	12.7279i	−1.04741	−	0.604722i	−0.921923	+	0.387374i	$0.873382\pi$
$444$		0			0
$445$	−3.72792	−	6.45695i	−0.176720	−	0.306089i
$446$	−10.3923			−0.492090
$447$		0			0
$448$	−2.62132	+	0.358719i	−0.123846	+	0.0169479i
$449$		−	5.27208i		−	0.248805i	−0.992232	−	0.124402i	$-0.960299\pi$
$449$		−	5.27208i		−	0.248805i	0.992232	−	0.124402i	$-0.0397014\pi$
$450$		0			0
$451$	9.00000	+	5.19615i	0.423793	+	0.244677i
$452$			10.2426i			0.481773i
$453$		0			0
$454$	−21.7279	−	12.5446i	−1.01974	−	0.588748i
$455$	4.30463	+	1.75736i	0.201804	+	0.0823863i
$456$		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	$-0.0141334\pi$
$458$	2.80821	−	4.86396i	0.131219	−	0.227278i
$459$		0			0
$460$	12.7279	−	7.34847i	0.593442	−	0.342624i
$461$	10.7255	+	18.5772i	0.499538	+	0.865225i	1.00000		0.000533648i	$-0.000169865\pi$
$461$	10.7255	+	18.5772i	0.499538	+	0.865225i	−0.500462	+	0.865758i	$0.666837\pi$
$462$		0			0
$463$	11.0000	−	19.0526i	0.511213	−	0.885448i	−0.488702	−	0.872451i	$-0.662530\pi$
$463$	11.0000	−	19.0526i	0.511213	−	0.885448i	0.999916	−	0.0129968i	$-0.00413714\pi$
$464$			1.75736i			0.0815834i
$465$		0			0
$466$	−20.4853			−0.948962
$467$	8.87039	+	15.3640i	0.410473	+	0.710959i	0.994941	−	0.100457i	$-0.0320304\pi$
$467$	8.87039	+	15.3640i	0.410473	+	0.710959i	−0.584469	+	0.811416i	$0.698697\pi$
$468$		0			0
$469$	−21.8640	−	28.1946i	−1.00958	−	1.30191i
$470$	−27.2416	+	15.7279i	−1.25656	+	0.725475i
$471$		0			0
$472$	−2.12132	+	1.22474i	−0.0976417	+	0.0563735i
$473$	25.7196	−	14.8492i	1.18259	−	0.682769i
$474$		0			0
$475$	−4.24264	+	2.44949i	−0.194666	+	0.112390i
$476$	−6.42090	+	0.878680i	−0.294301	+	0.0402742i
$477$		0			0
$478$	8.12132	+	14.0665i	0.371461	+	0.643389i
$479$	−2.44949			−0.111920			−0.0559600	−	0.998433i	$-0.517822\pi$
$479$	−2.44949			−0.111920			−0.0559600	+	0.998433i	$0.517822\pi$
$480$		0			0
$481$		−	3.76127i		−	0.171499i
$482$	−0.568852	+	0.985281i	−0.0259105	+	0.0448783i
$483$		0			0
$484$	−3.50000	−	6.06218i	−0.159091	−	0.275554i
$485$	6.71807	−	3.87868i	0.305052	−	0.176122i
$486$		0			0
$487$	−11.0000	+	19.0526i	−0.498458	+	0.863354i	−0.999998	−	0.00178012i	$-0.999433\pi$
$487$	−11.0000	+	19.0526i	−0.498458	+	0.863354i	0.501541	+	0.865134i	$0.332767\pi$
$488$	2.09077	−	3.62132i	0.0946447	−	0.163929i
$489$		0			0
$490$	16.6066	+	4.26858i	0.750210	+	0.192835i
$491$	30.2854	+	17.4853i	1.36676	+	0.789100i	0.990513	−	0.137419i	$-0.0438808\pi$
$491$	30.2854	+	17.4853i	1.36676	+	0.789100i	0.376248	+	0.926519i	$0.377214\pi$
$492$		0			0
$493$			4.30463i			0.193871i
$494$	−3.04384	−	1.75736i	−0.136949	−	0.0790673i
$495$		0			0
$496$			9.08052i			0.407727i
$497$	4.56575	+	33.3640i	0.204802	+	1.49658i
$498$		0			0
$499$	−24.4558			−1.09479			−0.547397	−	0.836873i	$-0.684381\pi$
$499$	−24.4558			−1.09479			−0.547397	+	0.836873i	$0.684381\pi$
$500$	−4.89898	−	8.48528i	−0.219089	−	0.379473i
$501$		0			0
$502$	−13.2426	−	7.64564i	−0.591048	−	0.341242i
$503$	0.594346			0.0265006			0.0132503	−	0.999912i	$-0.495782\pi$
$503$	0.594346			0.0265006			0.0132503	+	0.999912i	$0.495782\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$	22.0454	+	12.7279i	0.980038	+	0.565825i
$507$		0			0
$508$	−3.86396	−	6.69258i	−0.171436	−	0.296935i
$509$	9.20361			0.407943			0.203971	−	0.978977i	$-0.434615\pi$
$509$	9.20361			0.407943			0.203971	+	0.978977i	$0.434615\pi$
$510$		0			0
$511$	−13.4558	−	5.49333i	−0.595251	−	0.243010i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−21.7279	−	12.5446i	−0.958378	−	0.553320i
$515$			27.2132i			1.19916i
$516$		0			0
$517$	−47.1838	−	27.2416i	−2.07514	−	1.19808i
$518$	−1.88064	−	13.7426i	−0.0826305	−	0.603817i
$519$		0			0
$520$	−0.878680	+	1.52192i	−0.0385327	+	0.0667405i
$521$	−14.9941	+	25.9706i	−0.656904	+	1.13779i	0.324509	+	0.945883i	$0.394801\pi$
$521$	−14.9941	+	25.9706i	−0.656904	+	1.13779i	−0.981413	+	0.191908i	$0.938532\pi$
$522$		0			0
$523$	23.7426	−	13.7078i	1.03819	−	0.599401i	0.118872	−	0.992910i	$-0.462072\pi$
$523$	23.7426	−	13.7078i	1.03819	−	0.599401i	0.919321	+	0.393508i	$0.128739\pi$
$524$		0			0
$525$		0			0
$526$	3.36396	−	5.82655i	0.146676	−	0.254050i
$527$			22.2426i			0.968905i
$528$		0			0
$529$	−13.0000			−0.565217
$530$	17.7408	+	30.7279i	0.770610	+	1.33474i
$531$		0			0
$532$	−12.0000	−	4.89898i	−0.520266	−	0.212398i
$533$	1.52192	−	0.878680i	0.0659216	−	0.0380598i
$534$		0			0
$535$	5.27208	−	3.04384i	0.227932	−	0.131596i
$536$	11.6786	−	6.74264i	0.504439	−	0.291238i
$537$		0			0
$538$	8.48528	−	4.89898i	0.365826	−	0.211210i
$539$	7.97887	+	28.6066i	0.343674	+	1.23217i
$540$		0			0
$541$	2.72792	+	4.72490i	0.117283	+	0.203139i	0.918690	−	0.394980i	$-0.129248\pi$
$541$	2.72792	+	4.72490i	0.117283	+	0.203139i	−0.801407	+	0.598119i	$0.795915\pi$
$542$	−18.8785			−0.810900
$543$		0			0
$544$		−	2.44949i		−	0.105021i
$545$	21.7122	−	37.6066i	0.930048	−	1.61089i
$546$		0			0
$547$	−19.9853	−	34.6155i	−0.854509	−	1.48005i	−0.877100	−	0.480308i	$-0.840525\pi$
$547$	−19.9853	−	34.6155i	−0.854509	−	1.48005i	0.0225909	−	0.999745i	$-0.492808\pi$
$548$	5.19615	−	3.00000i	0.221969	−	0.128154i
$549$		0			0
$550$	−2.12132	+	3.67423i	−0.0904534	+	0.156670i
$551$	−4.30463	+	7.45584i	−0.183384	+	0.317630i
$552$		0			0
$553$	−0.757359	+	1.85514i	−0.0322062	+	0.0788887i
$554$	20.5490	+	11.8640i	0.873043	+	0.504051i
$555$		0			0
$556$		−	8.06591i		−	0.342071i
$557$	18.3712	+	10.6066i	0.778412	+	0.449416i	0.835867	−	0.548932i	$-0.184965\pi$
$557$	18.3712	+	10.6066i	0.778412	+	0.449416i	−0.0574555	+	0.998348i	$0.518299\pi$
$558$		0			0
$559$		−	5.02207i		−	0.212411i
$560$	−2.44949	+	6.00000i	−0.103510	+	0.253546i
$561$		0			0
$562$	13.7574			0.580319
$563$	−22.9369	−	39.7279i	−0.966676	−	1.67433i	−0.705043	−	0.709165i	$-0.749072\pi$
$563$	−22.9369	−	39.7279i	−0.966676	−	1.67433i	−0.261634	−	0.965167i	$-0.584261\pi$
$564$		0			0
$565$	21.7279	+	12.5446i	0.914101	+	0.527756i
$566$	−6.03668			−0.253741
$567$		0			0
$568$	−12.7279			−0.534052
$569$	−8.87039	−	5.12132i	−0.371866	−	0.214697i	0.302407	−	0.953179i	$-0.402210\pi$
$569$	−8.87039	−	5.12132i	−0.371866	−	0.214697i	−0.674273	+	0.738482i	$0.735543\pi$
$570$		0			0
$571$	11.0000	+	19.0526i	0.460336	+	0.797325i	0.998978	−	0.0452101i	$-0.0143957\pi$
$571$	11.0000	+	19.0526i	0.460336	+	0.797325i	−0.538642	+	0.842535i	$0.681062\pi$
$572$	−3.04384			−0.127269
$573$		0			0
$574$	5.12132	−	3.97141i	0.213760	−	0.165763i
$575$		−	6.00000i		−	0.250217i
$576$		0			0
$577$	23.7426	+	13.7078i	0.988419	+	0.570664i	0.904801	−	0.425834i	$-0.140019\pi$
$577$	23.7426	+	13.7078i	0.988419	+	0.570664i	0.0836177	+	0.996498i	$0.473353\pi$
$578$			11.0000i			0.457540i
$579$		0			0
$580$	3.72792	+	2.15232i	0.154794	+	0.0893701i
$581$	−24.7921	−	31.9706i	−1.02855	−	1.32636i
$582$		0			0
$583$	−30.7279	+	53.2223i	−1.27262	+	2.20424i
$584$	2.74666	−	4.75736i	0.113658	−	0.196861i
$585$		0			0
$586$	11.1213	−	6.42090i	0.459418	−	0.265245i
$587$	16.2189	+	28.0919i	0.669424	+	1.15948i	0.978065	+	0.208298i	$0.0667923\pi$
$587$	16.2189	+	28.0919i	0.669424	+	1.15948i	−0.308642	+	0.951178i	$0.599874\pi$
$588$		0			0
$589$	−22.2426	+	38.5254i	−0.916492	+	1.58741i
$590$			6.00000i			0.247016i
$591$		0			0
$592$	5.24264			0.215471
$593$	−0.927572	−	1.60660i	−0.0380908	−	0.0659752i	0.846352	−	0.532625i	$-0.178794\pi$
$593$	−0.927572	−	1.60660i	−0.0380908	−	0.0659752i	−0.884442	+	0.466650i	$0.845461\pi$
$594$		0			0
$595$	−6.00000	+	14.6969i	−0.245976	+	0.602516i
$596$	14.0665	−	8.12132i	0.576188	−	0.332662i
$597$		0			0
$598$	3.72792	−	2.15232i	0.152446	−	0.0880148i
$599$	3.04384	−	1.75736i	0.124368	−	0.0718038i	−0.436526	−	0.899692i	$-0.643791\pi$
$599$	3.04384	−	1.75736i	0.124368	−	0.0718038i	0.560893	+	0.827888i	$0.310458\pi$
$600$		0			0
$601$	35.9558	−	20.7591i	1.46667	−	0.846782i	0.467365	−	0.884065i	$-0.345204\pi$
$601$	35.9558	−	20.7591i	1.46667	−	0.846782i	0.999305	+	0.0372826i	$0.0118702\pi$
$602$	−2.51104	−	18.3492i	−0.102342	−	0.747859i
$603$		0			0
$604$	4.37868	+	7.58410i	0.178166	+	0.308592i
$605$	−17.1464			−0.697101
$606$		0			0
$607$			36.0759i			1.46428i	0.681157	+	0.732138i	$0.261477\pi$
$607$			36.0759i			1.46428i	−0.681157	+	0.732138i	$0.738523\pi$
$608$	2.44949	−	4.24264i	0.0993399	−	0.172062i
$609$		0			0
$610$	−5.12132	−	8.87039i	−0.207356	−	0.359151i
$611$	−7.97887	+	4.60660i	−0.322790	+	0.186363i
$612$		0			0
$613$	14.1066	−	24.4334i	0.569760	−	0.986854i	−0.426829	−	0.904332i	$-0.640369\pi$
$613$	14.1066	−	24.4334i	0.569760	−	0.986854i	0.996589	−	0.0825214i	$-0.0262973\pi$
$614$	−13.4106	+	23.2279i	−0.541210	+	0.937403i
$615$		0			0
$616$	−11.1213	+	1.52192i	−0.448091	+	0.0613198i
$617$	3.67423	+	2.12132i	0.147919	+	0.0854011i	0.572133	−	0.820161i	$-0.306116\pi$
$617$	3.67423	+	2.12132i	0.147919	+	0.0854011i	−0.424214	+	0.905562i	$0.639449\pi$
$618$		0			0
$619$			12.7187i			0.511208i	0.966782	+	0.255604i	$0.0822743\pi$
$619$			12.7187i			0.511208i	−0.966782	+	0.255604i	$0.917726\pi$
$620$	19.2627	+	11.1213i	0.773608	+	0.446643i
$621$		0			0
$622$		−	17.1464i		−	0.687509i
$623$	−4.93503	−	6.36396i	−0.197718	−	0.254967i
$624$		0			0
$625$	−29.0000			−1.16000
$626$	10.0951	+	17.4853i	0.403483	+	0.698852i
$627$		0			0
$628$	9.00000	+	5.19615i	0.359139	+	0.207349i
$629$	12.8418			0.512036
$630$		0			0
$631$	−14.7574			−0.587481			−0.293741	−	0.955885i	$-0.594900\pi$
$631$	−14.7574			−0.587481			−0.293741	+	0.955885i	$0.594900\pi$
$632$	−0.655892	−	0.378680i	−0.0260900	−	0.0150631i
$633$		0			0
$634$	−11.1213	−	19.2627i	−0.441684	−	0.765019i
$635$	−18.9295			−0.751193
$636$		0			0
$637$	4.86396	+	1.25024i	0.192717	+	0.0495362i
$638$			7.45584i			0.295180i
$639$		0			0
$640$	−2.12132	−	1.22474i	−0.0838525	−	0.0484123i
$641$			33.2132i			1.31184i	0.754829	+	0.655921i	$0.227720\pi$
$641$			33.2132i			1.31184i	−0.754829	+	0.655921i	$0.772280\pi$
$642$		0			0
$643$	1.50000	+	0.866025i	0.0591542	+	0.0341527i	0.529285	−	0.848444i	$-0.322460\pi$
$643$	1.50000	+	0.866025i	0.0591542	+	0.0341527i	−0.470131	+	0.882597i	$0.655793\pi$
$644$	12.5446	−	9.72792i	0.494327	−	0.383334i
$645$		0			0
$646$	6.00000	−	10.3923i	0.236067	−	0.408880i
$647$	10.3923	−	18.0000i	0.408564	−	0.707653i	−0.586165	−	0.810191i	$-0.699363\pi$
$647$	10.3923	−	18.0000i	0.408564	−	0.707653i	0.994729	+	0.102538i	$0.0326965\pi$
$648$		0			0
$649$	−9.00000	+	5.19615i	−0.353281	+	0.203967i
$650$	0.358719	+	0.621320i	0.0140701	+	0.0243702i
$651$		0			0
$652$	−4.74264	+	8.21449i	−0.185736	+	0.321704i
$653$			2.48528i			0.0972566i	0.998817	+	0.0486283i	$0.0154850\pi$
$653$			2.48528i			0.0972566i	−0.998817	+	0.0486283i	$0.984515\pi$
$654$		0			0
$655$		0			0
$656$	1.22474	+	2.12132i	0.0478183	+	0.0828236i
$657$		0			0
$658$	−26.8492	+	20.8207i	−1.04669	+	0.811674i
$659$	−19.2627	+	11.1213i	−0.750368	+	0.433225i	−0.825827	−	0.563924i	$-0.809291\pi$
$659$	−19.2627	+	11.1213i	−0.750368	+	0.433225i	0.0754589	+	0.997149i	$0.475958\pi$
$660$		0			0
$661$	4.24264	−	2.44949i	0.165020	−	0.0952741i	−0.415216	−	0.909723i	$-0.636294\pi$
$661$	4.24264	−	2.44949i	0.165020	−	0.0952741i	0.580235	+	0.814449i	$0.302961\pi$
$662$	−8.66025	+	5.00000i	−0.336590	+	0.194331i
$663$		0			0
$664$	13.2426	−	7.64564i	0.513914	−	0.296708i
$665$	−25.0892	+	19.4558i	−0.972919	+	0.754465i
$666$		0			0
$667$	−5.27208	−	9.13151i	−0.204136	−	0.353573i
$668$	0.594346			0.0229959
$669$		0			0
$670$		−	33.0321i		−	1.27614i
$671$	8.87039	−	15.3640i	0.342437	−	0.593119i
$672$		0			0
$673$	22.7279	+	39.3659i	0.876097	+	1.51744i	0.855590	+	0.517655i	$0.173195\pi$
$673$	22.7279	+	39.3659i	0.876097	+	1.51744i	0.0205075	+	0.999790i	$0.493472\pi$
$674$	18.5813	−	10.7279i	0.715725	−	0.413224i
$675$		0			0
$676$	6.24264	−	10.8126i	0.240102	−	0.415868i
$677$	−7.34847	+	12.7279i	−0.282425	+	0.489174i	−0.971981	−	0.235058i	$-0.924472\pi$
$677$	−7.34847	+	12.7279i	−0.282425	+	0.489174i	0.689557	+	0.724232i	$0.257805\pi$
$678$		0			0
$679$	6.62132	−	5.13461i	0.254103	−	0.197048i
$680$	−5.19615	−	3.00000i	−0.199263	−	0.115045i
$681$		0			0
$682$			38.5254i			1.47521i
$683$	−8.87039	−	5.12132i	−0.339416	−	0.195962i	0.320598	−	0.947215i	$-0.396116\pi$
$683$	−8.87039	−	5.12132i	−0.339416	−	0.195962i	−0.660014	+	0.751254i	$0.729450\pi$
$684$		0			0
$685$		−	14.6969i		−	0.561541i
$686$	18.3967	+	2.13604i	0.702388	+	0.0815543i
$687$		0			0
$688$	7.00000			0.266872
$689$	5.19615	+	9.00000i	0.197958	+	0.342873i
$690$		0			0
$691$	−2.22792	−	1.28629i	−0.0847541	−	0.0489328i	0.457024	−	0.889454i	$-0.348915\pi$
$691$	−2.22792	−	1.28629i	−0.0847541	−	0.0489328i	−0.541778	+	0.840522i	$0.682249\pi$
$692$	−20.7846			−0.790112
$693$		0			0
$694$	−4.97056			−0.188680
$695$	−17.1104	−	9.87868i	−0.649034	−	0.374720i
$696$		0			0
$697$	3.00000	+	5.19615i	0.113633	+	0.196818i
$698$	−0.123093			−0.00465914
$699$		0			0
$700$	1.62132	+	2.09077i	0.0612801	+	0.0790237i
$701$		−	20.4853i		−	0.773718i	−0.922139	−	0.386859i	$-0.873560\pi$
$701$		−	20.4853i		−	0.773718i	0.922139	−	0.386859i	$-0.126440\pi$
$702$		0			0
$703$	22.2426	+	12.8418i	0.838897	+	0.484337i
$704$		−	4.24264i		−	0.159901i
$705$		0			0
$706$	−9.51472	−	5.49333i	−0.358091	−	0.206744i
$707$	19.2627	−	2.63604i	0.724448	−	0.0991384i
$708$		0			0
$709$	−8.10660	+	14.0410i	−0.304450	+	0.527323i	−0.977139	−	0.212603i	$-0.931806\pi$
$709$	−8.10660	+	14.0410i	−0.304450	+	0.527323i	0.672689	+	0.739925i	$0.265139\pi$
$710$	−15.5885	+	27.0000i	−0.585024	+	1.01329i
$711$		0			0
$712$	2.63604	−	1.52192i	0.0987897	−	0.0570363i
$713$	−27.2416	−	47.1838i	−1.02020	−	1.76705i
$714$		0			0
$715$	−3.72792	+	6.45695i	−0.139416	+	0.241476i
$716$		−	6.72792i		−	0.251434i
$717$		0			0
$718$	14.4853			0.540586
$719$	26.3140	+	45.5772i	0.981346	+	1.69974i	0.657166	+	0.753746i	$0.271755\pi$
$719$	26.3140	+	45.5772i	0.981346	+	1.69974i	0.324181	+	0.945995i	$0.394911\pi$
$720$		0			0
$721$	3.98528	+	29.1222i	0.148420	+	1.08457i
$722$	4.33013	−	2.50000i	0.161151	−	0.0930404i
$723$		0			0
$724$	8.48528	−	4.89898i	0.315353	−	0.182069i
$725$	1.52192	−	0.878680i	0.0565226	−	0.0326333i
$726$		0			0
$727$	−24.3198	+	14.0410i	−0.901972	+	0.520754i	−0.877839	−	0.478955i	$-0.841016\pi$
$727$	−24.3198	+	14.0410i	−0.901972	+	0.520754i	−0.0241323	+	0.999709i	$0.507682\pi$
$728$	−0.717439	+	1.75736i	−0.0265901	+	0.0651321i
$729$		0			0
$730$	−6.72792	−	11.6531i	−0.249012	−	0.431301i
$731$	17.1464			0.634184
$732$		0			0
$733$			1.31178i			0.0484519i	0.999707	+	0.0242259i	$0.00771211\pi$
$733$			1.31178i			0.0484519i	−0.999707	+	0.0242259i	$0.992288\pi$
$734$	−14.9941	+	25.9706i	−0.553443	+	0.958591i
$735$		0			0
$736$	3.00000	+	5.19615i	0.110581	+	0.191533i
$737$	49.5481	−	28.6066i	1.82513	−	1.05374i
$738$		0			0
$739$	4.22792	−	7.32298i	0.155527	−	0.269380i	−0.777724	−	0.628606i	$-0.783626\pi$
$739$	4.22792	−	7.32298i	0.155527	−	0.269380i	0.933251	+	0.359226i	$0.116959\pi$
$740$	6.42090	−	11.1213i	0.236037	−	0.408828i
$741$		0			0
$742$	23.4853	+	30.2854i	0.862172	+	1.11181i
$743$	16.2189	+	9.36396i	0.595012	+	0.343530i	0.767077	−	0.641555i	$-0.221710\pi$
$743$	16.2189	+	9.36396i	0.595012	+	0.343530i	−0.172065	+	0.985086i	$0.555044\pi$
$744$		0			0
$745$		−	39.7862i		−	1.45765i
$746$	−19.0526	−	11.0000i	−0.697564	−	0.402739i
$747$		0			0
$748$		−	10.3923i		−	0.379980i
$749$	5.19615	−	4.02944i	0.189863	−	0.147232i
$750$		0			0
$751$	53.4558			1.95063			0.975316	−	0.220815i	$-0.0708717\pi$
$751$	53.4558			1.95063			0.975316	+	0.220815i	$0.0708717\pi$
$752$	−6.42090	−	11.1213i	−0.234146	−	0.405553i
$753$		0			0
$754$	1.09188	+	0.630399i	0.0397640	+	0.0229578i
$755$	21.4511			0.780684
$756$		0			0
$757$	32.7574			1.19059			0.595293	−	0.803509i	$-0.297036\pi$
$757$	32.7574			1.19059			0.595293	+	0.803509i	$0.297036\pi$
$758$	−6.48244	−	3.74264i	−0.235453	−	0.135939i
$759$		0			0
$760$	−6.00000	−	10.3923i	−0.217643	−	0.376969i
$761$	−24.4949			−0.887939			−0.443970	−	0.896042i	$-0.646430\pi$
$761$	−24.4949			−0.887939			−0.443970	+	0.896042i	$0.646430\pi$
$762$		0			0
$763$	17.7279	−	43.4244i	0.641794	−	1.57207i
$764$			21.2132i			0.767467i
$765$		0			0
$766$	−4.75736	−	2.74666i	−0.171890	−	0.0992410i
$767$			1.75736i			0.0634546i
$768$		0			0
$769$	34.9706	+	20.1903i	1.26107	+	0.728080i	0.973282	−	0.229614i	$-0.0737465\pi$
$769$	34.9706	+	20.1903i	1.26107	+	0.728080i	0.287789	+	0.957694i	$0.407080\pi$
$770$	−10.3923	+	25.4558i	−0.374513	+	0.917365i
$771$		0			0
$772$	−0.742641	+	1.28629i	−0.0267282	+	0.0462946i
$773$	−4.89898	+	8.48528i	−0.176204	+	0.305194i	−0.940577	−	0.339580i	$-0.889715\pi$
$773$	−4.89898	+	8.48528i	−0.176204	+	0.305194i	0.764373	+	0.644774i	$0.223049\pi$
$774$		0			0
$775$	7.86396	−	4.54026i	0.282482	−	0.163091i
$776$	1.58346	+	2.74264i	0.0568431	+	0.0984551i
$777$		0			0
$778$	−7.75736	+	13.4361i	−0.278115	+	0.481709i
$779$			12.0000i			0.429945i
$780$		0			0
$781$	−54.0000			−1.93227
$782$	7.34847	+	12.7279i	0.262781	+	0.455150i
$783$		0			0
$784$	−1.74264	+	6.77962i	−0.0622372	+	0.242129i
$785$	22.0454	−	12.7279i	0.786834	−	0.454279i
$786$		0			0
$787$	24.4706	−	14.1281i	0.872281	−	0.503612i	0.00417567	−	0.999991i	$-0.498671\pi$
$787$	24.4706	−	14.1281i	0.872281	−	0.503612i	0.868106	+	0.496379i	$0.165338\pi$
$788$	14.6969	−	8.48528i	0.523557	−	0.302276i
$789$		0			0
$790$	−1.60660	+	0.927572i	−0.0571603	+	0.0330015i
$791$	25.0892	+	10.2426i	0.892071	+	0.364186i
$792$		0			0
$793$	−1.50000	−	2.59808i	−0.0532666	−	0.0922604i
$794$	−15.1682			−0.538299
$795$		0			0
$796$		−	20.9077i		−	0.741054i
$797$	−8.87039	+	15.3640i	−0.314205	+	0.544219i	−0.979268	−	0.202568i	$-0.935071\pi$
$797$	−8.87039	+	15.3640i	−0.314205	+	0.544219i	0.665063	+	0.746787i	$0.268405\pi$
$798$		0			0
$799$	−15.7279	−	27.2416i	−0.556414	−	0.963737i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$		0			0
$802$	−9.87868	+	17.1104i	−0.348828	+	0.604188i
$803$	11.6531	−	20.1838i	0.411229	−	0.712270i
$804$		0			0
$805$	−5.27208	−	38.5254i	−0.185816	−	1.35784i
$806$	5.64191	+	3.25736i	0.198728	+	0.114736i
$807$		0			0
$808$			7.34847i			0.258518i
$809$	−12.5446	−	7.24264i	−0.441045	−	0.254638i	0.262996	−	0.964797i	$-0.415290\pi$
$809$	−12.5446	−	7.24264i	−0.441045	−	0.254638i	−0.704041	+	0.710159i	$0.748623\pi$
$810$		0			0
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	4.30463	+	1.75736i	0.151063	+	0.0616712i
$813$		0			0
$814$	22.2426			0.779604
$815$	11.6170	+	20.1213i	0.406928	+	0.704819i
$816$		0			0
$817$	29.6985	+	17.1464i	1.03902	+	0.599878i
$818$	3.76127			0.131510
$819$		0			0
$820$	6.00000			0.209529
$821$	19.8931	+	11.4853i	0.694274	+	0.400839i	0.805211	−	0.592988i	$-0.202052\pi$
$821$	19.8931	+	11.4853i	0.694274	+	0.400839i	−0.110937	+	0.993827i	$0.535385\pi$
$822$		0			0
$823$	1.37868	+	2.38794i	0.0480578	+	0.0832385i	0.889054	−	0.457803i	$-0.151364\pi$
$823$	1.37868	+	2.38794i	0.0480578	+	0.0832385i	−0.840996	+	0.541042i	$0.818030\pi$
$824$	−11.1097			−0.387026
$825$		0			0
$826$	0.878680	+	6.42090i	0.0305732	+	0.223412i
$827$			3.51472i			0.122219i	0.998131	+	0.0611094i	$0.0194638\pi$
$827$			3.51472i			0.122219i	−0.998131	+	0.0611094i	$0.980536\pi$
$828$		0			0
$829$	8.48528	+	4.89898i	0.294706	+	0.170149i	0.640062	−	0.768323i	$-0.278909\pi$
$829$	8.48528	+	4.89898i	0.294706	+	0.170149i	−0.345356	+	0.938472i	$0.612242\pi$
$830$		−	37.4558i		−	1.30011i
$831$		0			0
$832$	−0.621320	−	0.358719i	−0.0215404	−	0.0124364i
$833$	−4.26858	+	16.6066i	−0.147898	+	0.575385i
$834$		0			0
$835$	0.727922	−	1.26080i	0.0251908	−	0.0436317i
$836$	10.3923	−	18.0000i	0.359425	−	0.622543i
$837$		0			0
$838$	6.87868	−	3.97141i	0.237620	−	0.137190i
$839$	7.64564	+	13.2426i	0.263957	+	0.457187i	0.967290	−	0.253674i	$-0.0816390\pi$
$839$	7.64564	+	13.2426i	0.263957	+	0.457187i	−0.703333	+	0.710861i	$0.748306\pi$
$840$		0			0
$841$	−12.9558	+	22.4402i	−0.446753	+	0.773799i
$842$			23.4558i			0.808342i
$843$		0			0
$844$	−3.48528			−0.119968
$845$	−15.2913	−	26.4853i	−0.526036	−	0.911121i
$846$		0			0
$847$	−18.3492	+	2.51104i	−0.630487	+	0.0862802i
$848$	−12.5446	+	7.24264i	−0.430784	+	0.248713i
$849$		0			0
$850$	−2.12132	+	1.22474i	−0.0727607	+	0.0420084i
$851$	−27.2416	+	15.7279i	−0.933829	+	0.539146i
$852$		0			0
$853$	27.5147	−	15.8856i	0.942086	−	0.543914i	0.0514724	−	0.998674i	$-0.483609\pi$
$853$	27.5147	−	15.8856i	0.942086	−	0.543914i	0.890614	+	0.454761i	$0.150275\pi$
$854$	−6.77962	−	8.74264i	−0.231994	−	0.299167i
$855$		0			0
$856$	1.24264	+	2.15232i	0.0424726	+	0.0735647i
$857$	27.5387			0.940705			0.470353	−	0.882479i	$-0.344127\pi$
$857$	27.5387			0.940705			0.470353	+	0.882479i	$0.344127\pi$
$858$		0			0
$859$			28.2562i			0.964088i	0.876147	+	0.482044i	$0.160105\pi$
$859$			28.2562i			0.964088i	−0.876147	+	0.482044i	$0.839895\pi$
$860$	8.57321	−	14.8492i	0.292344	−	0.506355i
$861$		0			0
$862$	−0.878680	−	1.52192i	−0.0299279	−	0.0518367i
$863$	−32.4377	+	18.7279i	−1.10419	+	0.637506i	−0.937319	−	0.348472i	$-0.886700\pi$
$863$	−32.4377	+	18.7279i	−1.10419	+	0.637506i	−0.166874	+	0.985978i	$0.553367\pi$
$864$		0			0
$865$	−25.4558	+	44.0908i	−0.865525	+	1.49913i
$866$	−1.28629	+	2.22792i	−0.0437100	+	0.0757079i
$867$		0			0
$868$	22.2426	+	9.08052i	0.754964	+	0.308213i
$869$	−2.78272	−	1.60660i	−0.0943972	−	0.0545002i
$870$		0			0
$871$		−	9.67487i		−	0.327820i
$872$	15.3528	+	8.86396i	0.519912	+	0.300172i
$873$		0			0
$874$			29.3939i			0.994263i
$875$	−25.6836	+	3.51472i	−0.868264	+	0.118819i
$876$		0			0
$877$	−46.2132			−1.56051			−0.780254	−	0.625462i	$-0.784910\pi$
$877$	−46.2132			−1.56051			−0.780254	+	0.625462i	$0.784910\pi$
$878$	−2.15232	−	3.72792i	−0.0726372	−	0.125811i
$879$		0			0
$880$	−9.00000	−	5.19615i	−0.303390	−	0.175162i
$881$	25.0892			0.845278			0.422639	−	0.906298i	$-0.361104\pi$
$881$	25.0892			0.845278			0.422639	+	0.906298i	$0.361104\pi$
$882$		0			0
$883$	−2.00000			−0.0673054			−0.0336527	−	0.999434i	$-0.510714\pi$
$883$	−2.00000			−0.0673054			−0.0336527	+	0.999434i	$0.510714\pi$
$884$	−1.52192	−	0.878680i	−0.0511876	−	0.0295532i
$885$		0			0
$886$	−12.7279	−	22.0454i	−0.427603	−	0.740630i
$887$	−9.20361			−0.309027			−0.154514	−	0.987991i	$-0.549381\pi$
$887$	−9.20361			−0.309027			−0.154514	+	0.987991i	$0.549381\pi$
$888$		0			0
$889$	−20.2574	+	2.77216i	−0.679410	+	0.0929751i
$890$		−	7.45584i		−	0.249920i
$891$		0			0
$892$	−9.00000	−	5.19615i	−0.301342	−	0.173980i
$893$		−	62.9117i		−	2.10526i
$894$		0			0
$895$	−14.2721	−	8.23999i	−0.477063	−	0.275432i
$896$	−2.44949	−	1.00000i	−0.0818317	−	0.0334077i
$897$		0			0
$898$	2.63604	−	4.56575i	0.0879658	−	0.152361i
$899$	7.97887	−	13.8198i	0.266110	−	0.460916i
$900$		0			0
$901$	−30.7279	+	17.7408i	−1.02370	+	0.591031i
$902$	5.19615	+	9.00000i	0.173013	+	0.299667i
$903$		0			0
$904$	−5.12132	+	8.87039i	−0.170333	+	0.295025i
$905$		−	24.0000i		−	0.797787i
$906$		0			0
$907$	−13.4853			−0.447771			−0.223886	−	0.974615i	$-0.571874\pi$
$907$	−13.4853			−0.447771			−0.223886	+	0.974615i	$0.571874\pi$
$908$	−12.5446	−	21.7279i	−0.416308	−	0.721066i
$909$		0			0
$910$	2.84924	+	3.67423i	0.0944515	+	0.121800i
$911$	8.87039	−	5.12132i	0.293889	−	0.169677i	−0.345805	−	0.938306i	$-0.612394\pi$
$911$	8.87039	−	5.12132i	0.293889	−	0.169677i	0.639694	+	0.768629i	$0.279061\pi$
$912$		0			0
$913$	56.1838	−	32.4377i	1.85941	−	1.07353i
$914$	19.9186	−	11.5000i	0.658848	−	0.380386i
$915$		0			0
$916$	4.86396	−	2.80821i	0.160710	−	0.0927858i
$917$		0			0
$918$		0			0
$919$	−12.8640	−	22.2810i	−0.424343	−	0.734983i	0.572016	−	0.820243i	$-0.306162\pi$
$919$	−12.8640	−	22.2810i	−0.424343	−	0.734983i	−0.996359	+	0.0852590i	$0.972828\pi$
$920$	14.6969			0.484544
$921$		0			0
$922$			21.4511i			0.706453i
$923$	−4.56575	+	7.90812i	−0.150284	+	0.260299i
$924$		0			0
$925$	−2.62132	−	4.54026i	−0.0861885	−	0.149283i
$926$	19.0526	−	11.0000i	0.626106	−	0.361482i
$927$		0			0
$928$	−0.878680	+	1.52192i	−0.0288441	+	0.0499594i
$929$	14.3637	−	24.8787i	0.471258	−	0.816243i	−0.528201	−	0.849119i	$-0.677133\pi$
$929$	14.3637	−	24.8787i	0.471258	−	0.816243i	0.999459	+	0.0328762i	$0.0104667\pi$
$930$		0			0
$931$	−24.0000	+	24.4949i	−0.786568	+	0.802788i
$932$	−17.7408	−	10.2426i	−0.581118	−	0.335509i
$933$		0			0
$934$			17.7408i			0.580496i
$935$	−22.0454	−	12.7279i	−0.720962	−	0.416248i
$936$		0			0
$937$		−	33.5033i		−	1.09451i	−0.836967	−	0.547253i	$-0.815674\pi$
$937$		−	33.5033i		−	1.09451i	0.836967	−	0.547253i	$-0.184326\pi$
$938$	−4.83743	−	35.3492i	−0.157948	−	1.15419i
$939$		0			0
$940$	−31.4558			−1.02598
$941$	21.1178	+	36.5772i	0.688422	+	1.19238i	0.972348	+	0.233535i	$0.0750295\pi$
$941$	21.1178	+	36.5772i	0.688422	+	1.19238i	−0.283927	+	0.958846i	$0.591637\pi$
$942$		0			0
$943$	−12.7279	−	7.34847i	−0.414478	−	0.239299i
$944$	−2.44949			−0.0797241
$945$		0			0
$946$	29.6985			0.965581
$947$	−14.0665	−	8.12132i	−0.457101	−	0.263907i	0.253723	−	0.967277i	$-0.418345\pi$
$947$	−14.0665	−	8.12132i	−0.457101	−	0.263907i	−0.710825	+	0.703369i	$0.751678\pi$
$948$		0			0
$949$	−1.97056	−	3.41311i	−0.0639672	−	0.110794i
$950$	−4.89898			−0.158944
$951$		0			0
$952$	−6.00000	−	2.44949i	−0.194461	−	0.0793884i
$953$			1.02944i			0.0333467i	0.999861	+	0.0166734i	$0.00530755\pi$
$953$			1.02944i			0.0333467i	−0.999861	+	0.0166734i	$0.994692\pi$
$954$		0			0
$955$	45.0000	+	25.9808i	1.45617	+	0.840718i
$956$			16.2426i			0.525325i
$957$		0			0
$958$	−2.12132	−	1.22474i	−0.0685367	−	0.0395697i
$959$	−2.15232	−	15.7279i	−0.0695019	−	0.507881i
$960$		0			0
$961$	25.7279	−	44.5621i	0.829933	−	1.43749i
$962$	1.88064	−	3.25736i	0.0606342	−	0.105021i
$963$		0			0
$964$	−0.985281	+	0.568852i	−0.0317338	+	0.0183215i
$965$	1.81909	+	3.15076i	0.0585586	+	0.101426i
$966$		0			0
$967$	21.3492	−	36.9780i	0.686545	−	1.18913i	−0.286403	−	0.958109i	$-0.592460\pi$
$967$	21.3492	−	36.9780i	0.686545	−	1.18913i	0.972948	−	0.231022i	$-0.0742070\pi$
$968$		−	7.00000i		−	0.224989i
$969$		0			0
$970$	7.75736			0.249074
$971$	−20.1903	−	34.9706i	−0.647936	−	1.12226i	−0.983615	−	0.180282i	$-0.942299\pi$
$971$	−20.1903	−	34.9706i	−0.647936	−	1.12226i	0.335679	−	0.941977i	$-0.391034\pi$
$972$		0			0
$973$	−19.7574	−	8.06591i	−0.633392	−	0.258581i
$974$	−19.0526	+	11.0000i	−0.610483	+	0.352463i
$975$		0			0
$976$	3.62132	−	2.09077i	0.115916	−	0.0669239i
$977$	−5.19615	+	3.00000i	−0.166240	+	0.0959785i	−0.580812	−	0.814038i	$-0.697265\pi$
$977$	−5.19615	+	3.00000i	−0.166240	+	0.0959785i	0.414572	+	0.910017i	$0.363931\pi$
$978$		0			0
$979$	11.1838	−	6.45695i	0.357435	−	0.206365i
$980$	12.2474	+	12.0000i	0.391230	+	0.383326i
$981$		0			0
$982$	17.4853	+	30.2854i	0.557978	+	0.966446i
$983$	−23.2341			−0.741053			−0.370526	−	0.928822i	$-0.620823\pi$
$983$	−23.2341			−0.741053			−0.370526	+	0.928822i	$0.620823\pi$
$984$		0			0
$985$		−	41.5692i		−	1.32451i
$986$	−2.15232	+	3.72792i	−0.0685437	+	0.118721i
$987$		0			0
$988$	−1.75736	−	3.04384i	−0.0559090	−	0.0968373i
$989$	−36.3731	+	21.0000i	−1.15660	+	0.667761i
$990$		0			0
$991$	10.1066	−	17.5051i	0.321047	−	0.556069i	−0.659658	−	0.751566i	$-0.729299\pi$
$991$	10.1066	−	17.5051i	0.321047	−	0.556069i	0.980704	+	0.195497i	$0.0626320\pi$
$992$	−4.54026	+	7.86396i	−0.144153	+	0.249681i
$993$		0			0
$994$	−12.7279	+	31.1769i	−0.403705	+	0.988872i
$995$	−44.3519	−	25.6066i	−1.40605	−	0.811784i
$996$		0			0
$997$		−	19.4728i		−	0.616711i	−0.951271	−	0.308355i	$-0.900221\pi$
$997$		−	19.4728i		−	0.616711i	0.951271	−	0.308355i	$-0.0997786\pi$
$998$	−21.1794	−	12.2279i	−0.670422	−	0.387068i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.t.f.1025.4		8
3.2	odd	2	inner	1134.2.t.f.1025.1		8
7.5	odd	6		1134.2.l.e.215.2		8
9.2	odd	6		1134.2.l.e.269.4		8
9.4	even	3		378.2.k.d.269.1	yes	8
9.5	odd	6		378.2.k.d.269.4	yes	8
9.7	even	3		1134.2.l.e.269.1		8
21.5	even	6		1134.2.l.e.215.3		8
63.4	even	3		2646.2.d.d.2645.4		8
63.5	even	6		378.2.k.d.215.1	✓	8
63.31	odd	6		2646.2.d.d.2645.2		8
63.32	odd	6		2646.2.d.d.2645.5		8
63.40	odd	6		378.2.k.d.215.4	yes	8
63.47	even	6	inner	1134.2.t.f.593.4		8
63.59	even	6		2646.2.d.d.2645.7		8
63.61	odd	6	inner	1134.2.t.f.593.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.k.d.215.1	✓	8	63.5	even	6
378.2.k.d.215.4	yes	8	63.40	odd	6
378.2.k.d.269.1	yes	8	9.4	even	3
378.2.k.d.269.4	yes	8	9.5	odd	6
1134.2.l.e.215.2		8	7.5	odd	6
1134.2.l.e.215.3		8	21.5	even	6
1134.2.l.e.269.1		8	9.7	even	3
1134.2.l.e.269.4		8	9.2	odd	6
1134.2.t.f.593.1		8	63.61	odd	6	inner
1134.2.t.f.593.4		8	63.47	even	6	inner
1134.2.t.f.1025.1		8	3.2	odd	2	inner
1134.2.t.f.1025.4		8	1.1	even	1	trivial
2646.2.d.d.2645.2		8	63.31	odd	6
2646.2.d.d.2645.4		8	63.4	even	3
2646.2.d.d.2645.5		8	63.32	odd	6
2646.2.d.d.2645.7		8	63.59	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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +2.44949 q^{5} +(2.62132 - 0.358719i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +2.44949 q^{5} +(2.62132 - 0.358719i) q^{7} +1.00000i q^{8} +(2.12132 + 1.22474i) q^{10} +4.24264i q^{11} +(0.621320 + 0.358719i) q^{13} +(2.44949 + 1.00000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.22474 + 2.12132i) q^{17} +(-4.24264 + 2.44949i) q^{19} +(1.22474 + 2.12132i) q^{20} +(-2.12132 + 3.67423i) q^{22} -6.00000i q^{23} +1.00000 q^{25} +(0.358719 + 0.621320i) q^{26} +(1.62132 + 2.09077i) q^{28} +(1.52192 - 0.878680i) q^{29} +(7.86396 - 4.54026i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.12132 + 1.22474i) q^{34} +(6.42090 - 0.878680i) q^{35} +(-2.62132 - 4.54026i) q^{37} -4.89898 q^{38} +2.44949i q^{40} +(1.22474 - 2.12132i) q^{41} +(-3.50000 - 6.06218i) q^{43} +(-3.67423 + 2.12132i) q^{44} +(3.00000 - 5.19615i) q^{46} +(-6.42090 + 11.1213i) q^{47} +(6.74264 - 1.88064i) q^{49} +(0.866025 + 0.500000i) q^{50} +0.717439i q^{52} +(12.5446 + 7.24264i) q^{53} +10.3923i q^{55} +(0.358719 + 2.62132i) q^{56} +1.75736 q^{58} +(1.22474 + 2.12132i) q^{59} +(-3.62132 - 2.09077i) q^{61} +9.08052 q^{62} -1.00000 q^{64} +(1.52192 + 0.878680i) q^{65} +(-6.74264 - 11.6786i) q^{67} -2.44949 q^{68} +(6.00000 + 2.44949i) q^{70} +12.7279i q^{71} +(-4.75736 - 2.74666i) q^{73} -5.24264i q^{74} +(-4.24264 - 2.44949i) q^{76} +(1.52192 + 11.1213i) q^{77} +(-0.378680 + 0.655892i) q^{79} +(-1.22474 + 2.12132i) q^{80} +(2.12132 - 1.22474i) q^{82} +(-7.64564 - 13.2426i) q^{83} +(-3.00000 + 5.19615i) q^{85} -7.00000i q^{86} -4.24264 q^{88} +(-1.52192 - 2.63604i) q^{89} +(1.75736 + 0.717439i) q^{91} +(5.19615 - 3.00000i) q^{92} +(-11.1213 + 6.42090i) q^{94} +(-10.3923 + 6.00000i) q^{95} +(2.74264 - 1.58346i) q^{97} +(6.77962 + 1.74264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 4 q^{7}+O(q^{10}) \) 8 * q + 4 * q^4 + 4 * q^7	\( 8 q + 4 q^{4} + 4 q^{7} - 12 q^{13} - 4 q^{16} + 8 q^{25} - 4 q^{28} + 12 q^{31} - 4 q^{37} - 28 q^{43} + 24 q^{46} + 20 q^{49} + 48 q^{58} - 12 q^{61} - 8 q^{64} - 20 q^{67} + 48 q^{70} - 72 q^{73} - 20 q^{79} - 24 q^{85} + 48 q^{91} - 72 q^{94} - 12 q^{97}+O(q^{100}) \) 8 * q + 4 * q^4 + 4 * q^7 - 12 * q^13 - 4 * q^16 + 8 * q^25 - 4 * q^28 + 12 * q^31 - 4 * q^37 - 28 * q^43 + 24 * q^46 + 20 * q^49 + 48 * q^58 - 12 * q^61 - 8 * q^64 - 20 * q^67 + 48 * q^70 - 72 * q^73 - 20 * q^79 - 24 * q^85 + 48 * q^91 - 72 * q^94 - 12 * q^97

Introduction

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