LMFDB - Embedded newform 1134.2.t.f.593.4

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			593.4
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1134.593
Dual form			1134.2.t.f.1025.4

$q$-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 $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

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

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
$5$	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	$-0.779099\pi$
$11$		−	4.24264i		−	1.27920i	0.768706	−	0.639602i	$-0.220901\pi$
$12$		0			0
$13$	0.621320	−	0.358719i	0.172323	−	0.0994909i	−0.411358	−	0.911474i	$-0.634945\pi$
$13$	0.621320	−	0.358719i	0.172323	−	0.0994909i	0.583681	+	0.811983i	$0.301612\pi$
$14$	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	0.678414	−	0.734680i	$-0.262668\pi$
$17$	−1.22474	−	2.12132i	−0.297044	−	0.514496i	−0.975458	+	0.220184i	$0.929334\pi$
$18$		0			0
$19$	−4.24264	−	2.44949i	−0.973329	−	0.561951i	−0.0730792	−	0.997326i	$-0.523283\pi$
$19$	−4.24264	−	2.44949i	−0.973329	−	0.561951i	−0.900249	+	0.435375i	$0.856616\pi$
$20$	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	$0.215123\pi$
$23$			6.00000i			1.25109i	−0.780189	+	0.625543i	$0.784877\pi$
$24$		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	0.634606	−	0.772836i	$-0.281162\pi$
$29$	1.52192	+	0.878680i	0.282613	+	0.163167i	−0.351993	+	0.936003i	$0.614496\pi$
$30$		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
$34$	−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	−0.996955	−	0.0779826i	$-0.975152\pi$
$37$	−2.62132	+	4.54026i	−0.430942	+	0.746414i	0.566012	+	0.824397i	$0.308485\pi$
$38$	−4.89898			−0.794719
$39$		0			0
$40$		−	2.44949i		−	0.387298i
$41$	1.22474	+	2.12132i	0.191273	+	0.331295i	0.945672	−	0.325121i	$-0.105405\pi$
$41$	1.22474	+	2.12132i	0.191273	+	0.331295i	−0.754399	+	0.656416i	$0.772072\pi$
$42$		0			0
$43$	−3.50000	+	6.06218i	−0.533745	+	0.924473i	0.465478	+	0.885059i	$0.345882\pi$
$43$	−3.50000	+	6.06218i	−0.533745	+	0.924473i	−0.999223	+	0.0394140i	$0.987451\pi$
$44$	−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	−0.771784	−	0.635884i	$-0.780636\pi$
$47$	−6.42090	−	11.1213i	−0.936584	−	1.62221i	−0.164800	−	0.986327i	$-0.552698\pi$
$48$		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	0.810905	−	0.585178i	$-0.198975\pi$
$53$	12.5446	−	7.24264i	1.72314	−	0.994853i	0.912231	−	0.409675i	$-0.134358\pi$
$54$		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	−0.775222	−	0.631689i	$-0.782362\pi$
$59$	1.22474	−	2.12132i	0.159448	−	0.276172i	0.934670	+	0.355517i	$0.115695\pi$
$60$		0			0
$61$	−3.62132	+	2.09077i	−0.463663	+	0.267696i	−0.713583	−	0.700571i	$-0.752929\pi$
$61$	−3.62132	+	2.09077i	−0.463663	+	0.267696i	0.249920	+	0.968266i	$0.419596\pi$
$62$	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	0.0791303	+	0.996864i	$0.474786\pi$
$67$	−6.74264	+	11.6786i	−0.823745	+	1.42677i	−0.902875	+	0.429903i	$0.858548\pi$
$68$	−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	$-0.727509\pi$
$71$		−	12.7279i		−	1.51053i	0.655422	−	0.755263i	$-0.272491\pi$
$72$		0			0
$73$	−4.75736	+	2.74666i	−0.556807	+	0.321473i	−0.751863	−	0.659320i	$-0.770844\pi$
$73$	−4.75736	+	2.74666i	−0.556807	+	0.321473i	0.195056	+	0.980792i	$0.437511\pi$
$74$			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	0.843937	−	0.536443i	$-0.180232\pi$
$79$	−0.378680	−	0.655892i	−0.0426048	−	0.0737937i	−0.886541	+	0.462649i	$0.846899\pi$
$80$	−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	0.0513309	+	0.998682i	$0.483654\pi$
$83$	−7.64564	+	13.2426i	−0.839218	+	1.45357i	−0.890549	+	0.454887i	$0.849680\pi$
$84$		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	−0.935343	−	0.353741i	$-0.884909\pi$
$89$	−1.52192	+	2.63604i	−0.161323	+	0.279420i	0.774020	+	0.633161i	$0.218243\pi$
$90$		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	0.632732	−	0.774371i	$-0.281934\pi$
$97$	2.74264	+	1.58346i	0.278473	+	0.160776i	−0.354259	+	0.935147i	$0.615267\pi$
$98$	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	$-0.815641\pi$
$103$		−	11.1097i		−	1.09468i	0.836912	−	0.547338i	$-0.184359\pi$
$104$	−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	0.600415	−	0.799688i	$-0.295002\pi$
$107$	2.15232	+	1.24264i	0.208072	+	0.120131i	−0.392343	+	0.919819i	$0.628335\pi$
$108$		0			0
$109$	8.86396	+	15.3528i	0.849013	+	1.47053i	0.882090	+	0.471082i	$0.156136\pi$
$109$	8.86396	+	15.3528i	0.849013	+	1.47053i	−0.0330761	+	0.999453i	$0.510530\pi$
$110$	−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	−0.0209200	−	0.999781i	$-0.506660\pi$
$113$	8.87039	−	5.12132i	0.834456	−	0.481773i	0.855376	+	0.518008i	$0.173326\pi$
$114$		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	$0.0825059\pi$
$137$			6.00000i			0.512615i	−0.966595	+	0.256307i	$0.917494\pi$
$138$		0			0
$139$	−6.98528	+	4.03295i	−0.592484	+	0.342071i	−0.766079	−	0.642746i	$-0.777795\pi$
$139$	−6.98528	+	4.03295i	−0.592484	+	0.342071i	0.173595	+	0.984817i	$0.444462\pi$
$140$	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	$0.231707\pi$
$149$			16.2426i			1.33065i	−0.746554	+	0.665324i	$0.768293\pi$
$150$		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	0.814119	−	0.580699i	$-0.197221\pi$
$157$	9.00000	+	5.19615i	0.718278	+	0.414698i	−0.0958404	+	0.995397i	$0.530554\pi$
$158$	−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	−0.618320	−	0.785926i	$-0.712186\pi$
$163$	4.74264	−	8.21449i	0.371472	−	0.643409i	0.989792	+	0.142518i	$0.0455197\pi$
$164$	2.44949			0.191273
$165$		0			0
$166$			15.2913i			1.18683i
$167$	0.297173	+	0.514719i	0.0229959	+	0.0398301i	0.877294	−	0.479953i	$-0.159346\pi$
$167$	0.297173	+	0.514719i	0.0229959	+	0.0398301i	−0.854298	+	0.519783i	$0.826013\pi$
$168$		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	−0.925897	−	0.377776i	$-0.876689\pi$
$173$	−10.3923	−	18.0000i	−0.790112	−	1.36851i	0.135785	−	0.990738i	$-0.456644\pi$
$174$		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	−0.701686	−	0.712487i	$-0.747569\pi$
$179$	−5.82655	+	3.36396i	−0.435497	+	0.251434i	0.266189	+	0.963921i	$0.414236\pi$
$180$		0			0
$181$			9.79796i			0.728277i	0.931345	+	0.364138i	$0.118636\pi$
$181$			9.79796i			0.728277i	−0.931345	+	0.364138i	$0.881364\pi$
$182$	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	0.344101	−	0.938933i	$-0.388184\pi$
$191$	18.3712	−	10.6066i	1.32929	−	0.767467i	0.985190	+	0.171466i	$0.0548503\pi$
$192$		0			0
$193$	0.742641	−	1.28629i	0.0534564	−	0.0925893i	−0.838059	−	0.545580i	$-0.816310\pi$
$193$	0.742641	−	1.28629i	0.0534564	−	0.0925893i	0.891515	+	0.452990i	$0.149643\pi$
$194$	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	$0.206648\pi$
$197$			16.9706i			1.20910i	−0.796566	+	0.604551i	$0.793352\pi$
$198$		0			0
$199$	−18.1066	+	10.4539i	−1.28354	+	0.741054i	−0.977494	−	0.210962i	$-0.932340\pi$
$199$	−18.1066	+	10.4539i	−1.28354	+	0.741054i	−0.306049	+	0.952016i	$0.599007\pi$
$200$		−	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	0.799787	−	0.600284i	$-0.204946\pi$
$211$	−1.74264	−	3.01834i	−0.119968	−	0.207791i	−0.919755	+	0.392493i	$0.871613\pi$
$212$		−	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	0.167412	−	0.985887i	$-0.446459\pi$
$223$	−9.00000	−	5.19615i	−0.602685	−	0.347960i	−0.770097	+	0.637927i	$0.779792\pi$
$224$	−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	$0.0594137\pi$
$229$			5.61642i			0.371143i	−0.982631	+	0.185572i	$0.940586\pi$
$230$	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	−0.210398	−	0.977616i	$-0.567476\pi$
$233$	−17.7408	−	10.2426i	−1.16224	−	0.671018i	−0.951839	+	0.306598i	$0.900809\pi$
$234$		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	0.0294934	−	0.999565i	$-0.490611\pi$
$239$	14.0665	−	8.12132i	0.909889	−	0.525325i	0.880395	+	0.474240i	$0.157277\pi$
$240$		0			0
$241$		−	1.13770i		−	0.0732860i	−0.999328	−	0.0366430i	$-0.988334\pi$
$241$		−	1.13770i		−	0.0732860i	0.999328	−	0.0366430i	$-0.0116664\pi$
$242$	−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	$0.0665102\pi$
$263$			6.72792i			0.414861i	−0.978250	+	0.207431i	$0.933490\pi$
$264$		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	0.975838	−	0.218496i	$-0.0701150\pi$
$269$	4.89898	+	8.48528i	0.298696	+	0.517357i	−0.677142	+	0.735853i	$0.736782\pi$
$270$		0			0
$271$	−16.3492	−	9.43924i	−0.993146	−	0.573393i	−0.0869326	−	0.996214i	$-0.527706\pi$
$271$	−16.3492	−	9.43924i	−0.993146	−	0.573393i	−0.906213	+	0.422821i	$0.861040\pi$
$272$	−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	0.811336	−	0.584580i	$-0.198741\pi$
$281$	11.9142	+	6.87868i	0.710743	+	0.410348i	−0.100593	+	0.994928i	$0.532074\pi$
$282$		0			0
$283$	−5.22792	−	3.01834i	−0.310768	−	0.179422i	0.336502	−	0.941683i	$-0.390756\pi$
$283$	−5.22792	−	3.01834i	−0.310768	−	0.179422i	−0.647270	+	0.762261i	$0.724089\pi$
$284$	−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	0.990344	−	0.138632i	$-0.0442706\pi$
$293$	6.42090	+	11.1213i	0.375113	+	0.649714i	−0.615231	+	0.788347i	$0.710937\pi$
$294$		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	$-0.722548\pi$
$307$		−	26.8213i		−	1.53077i	0.643571	−	0.765386i	$-0.277452\pi$
$308$	−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	−0.999873	−	0.0159282i	$-0.994930\pi$
$311$	−8.57321	+	14.8492i	−0.486142	+	0.842023i	0.513731	+	0.857951i	$0.328263\pi$
$312$		0			0
$313$	17.4853	−	10.0951i	0.988327	−	0.570611i	0.0835529	−	0.996503i	$-0.473373\pi$
$313$	17.4853	−	10.0951i	0.988327	−	0.570611i	0.904774	+	0.425893i	$0.140040\pi$
$314$	10.3923			0.586472
$315$		0			0
$316$	−0.757359			−0.0426048
$317$	−19.2627	+	11.1213i	−1.08190	+	0.624636i	−0.931408	−	0.363976i	$-0.881419\pi$
$317$	−19.2627	+	11.1213i	−1.08190	+	0.624636i	−0.150492	+	0.988611i	$0.548086\pi$
$318$		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	0.695266	−	0.718752i	$-0.255287\pi$
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	−0.970091	+	0.242742i	$0.921953\pi$
$332$	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	0.994952	+	0.100357i	$0.0319984\pi$
$337$	10.7279	+	18.5813i	0.584387	+	1.01219i	−0.410564	+	0.911832i	$0.634668\pi$
$338$			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	0.379988	−	0.924992i	$-0.375928\pi$
$347$	−4.30463	−	2.48528i	−0.231085	−	0.133417i	−0.611072	+	0.791575i	$0.709262\pi$
$348$		0			0
$349$	−0.106602	−	0.0615465i	−0.00570626	−	0.00329451i	0.497144	−	0.867668i	$-0.334382\pi$
$349$	−0.106602	−	0.0615465i	−0.00570626	−	0.00329451i	−0.502850	+	0.864373i	$0.667715\pi$
$350$	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	0.793069	−	0.609132i	$-0.208482\pi$
$359$	12.5446	+	7.24264i	0.662080	+	0.382252i	−0.130989	+	0.991384i	$0.541815\pi$
$360$		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	$-0.713849\pi$
$367$		−	29.9882i		−	1.56537i	0.622416	−	0.782686i	$-0.286151\pi$
$368$	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	$-0.871329\pi$
$389$		−	15.5147i		−	0.786627i	0.919404	−	0.393314i	$-0.128671\pi$
$390$		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	0.132723	−	0.991153i	$-0.457628\pi$
$397$	−13.1360	−	7.58410i	−0.659279	−	0.380635i	−0.792002	+	0.610518i	$0.790961\pi$
$398$	−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	$-0.835784\pi$
$401$		−	19.7574i		−	0.986635i	0.869849	−	0.493318i	$-0.164216\pi$
$402$		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	0.578366	−	0.815777i	$-0.303690\pi$
$409$	3.25736	+	1.88064i	0.161066	+	0.0929915i	−0.417300	+	0.908769i	$0.637024\pi$
$410$	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	0.946577	−	0.322476i	$-0.104515\pi$
$419$	3.97141	+	6.87868i	0.194016	+	0.336045i	−0.752562	+	0.658522i	$0.771182\pi$
$420$		0			0
$421$	11.7279	−	20.3134i	0.571584	−	0.990012i	−0.424820	−	0.905278i	$-0.639662\pi$
$421$	11.7279	−	20.3134i	0.571584	−	0.990012i	0.996404	−	0.0847344i	$-0.0270042\pi$
$422$	−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	−0.536206	−	0.844087i	$-0.680143\pi$
$431$	−1.52192	+	0.878680i	−0.0733082	+	0.0423245i	0.462898	+	0.886412i	$0.346810\pi$
$432$		0			0
$433$		−	2.57258i		−	0.123630i	−0.998088	−	0.0618152i	$-0.980311\pi$
$433$		−	2.57258i		−	0.123630i	0.998088	−	0.0618152i	$-0.0196889\pi$
$434$	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	−0.586317	−	0.810082i	$-0.699423\pi$
$439$	−3.72792	+	2.15232i	−0.177924	+	0.102724i	0.408393	+	0.912806i	$0.366089\pi$
$440$	−10.3923			−0.495434
$441$		0			0
$442$	−1.75736			−0.0835891
$443$	−22.0454	+	12.7279i	−1.04741	+	0.604722i	−0.921923	−	0.387374i	$-0.873382\pi$
$443$	−22.0454	+	12.7279i	−1.04741	+	0.604722i	−0.125486	+	0.992095i	$0.540049\pi$
$444$		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	$0.0397014\pi$
$449$			5.27208i			0.248805i	−0.992232	+	0.124402i	$0.960299\pi$
$450$		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	0.999014	+	0.0443868i	$0.0141334\pi$
$457$	11.5000	+	19.9186i	0.537947	+	0.931752i	−0.461067	+	0.887365i	$0.652533\pi$
$458$	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	−0.500462	−	0.865758i	$-0.666837\pi$
$461$	10.7255	−	18.5772i	0.499538	−	0.865225i	1.00000		0.000533648i	$0.000169865\pi$
$462$		0			0
$463$	11.0000	+	19.0526i	0.511213	+	0.885448i	0.999916	+	0.0129968i	$0.00413714\pi$
$463$	11.0000	+	19.0526i	0.511213	+	0.885448i	−0.488702	+	0.872451i	$0.662530\pi$
$464$		−	1.75736i		−	0.0815834i
$465$		0			0
$466$	−20.4853			−0.948962
$467$	8.87039	−	15.3640i	0.410473	−	0.710959i	−0.584469	−	0.811416i	$-0.698697\pi$
$467$	8.87039	−	15.3640i	0.410473	−	0.710959i	0.994941	+	0.100457i	$0.0320304\pi$
$468$		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	0.501541	−	0.865134i	$-0.332767\pi$
$487$	−11.0000	−	19.0526i	−0.498458	−	0.863354i	−0.999998	+	0.00178012i	$0.999433\pi$
$488$	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	0.376248	−	0.926519i	$-0.377214\pi$
$491$	30.2854	−	17.4853i	1.36676	−	0.789100i	0.990513	+	0.137419i	$0.0438808\pi$
$492$		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	−0.981413	−	0.191908i	$-0.938532\pi$
$521$	−14.9941	−	25.9706i	−0.656904	−	1.13779i	0.324509	−	0.945883i	$-0.394801\pi$
$522$		0			0
$523$	23.7426	+	13.7078i	1.03819	+	0.599401i	0.919321	−	0.393508i	$-0.128739\pi$
$523$	23.7426	+	13.7078i	1.03819	+	0.599401i	0.118872	+	0.992910i	$0.462072\pi$
$524$		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	−0.801407	−	0.598119i	$-0.795915\pi$
$541$	2.72792	−	4.72490i	0.117283	−	0.203139i	0.918690	+	0.394980i	$0.129248\pi$
$542$	−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	0.0225909	+	0.999745i	$0.492808\pi$
$547$	−19.9853	+	34.6155i	−0.854509	+	1.48005i	−0.877100	+	0.480308i	$0.840525\pi$
$548$	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	−0.0574555	−	0.998348i	$-0.518299\pi$
$557$	18.3712	−	10.6066i	0.778412	−	0.449416i	0.835867	+	0.548932i	$0.184965\pi$
$558$		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	−0.261634	+	0.965167i	$0.584261\pi$
$563$	−22.9369	+	39.7279i	−0.966676	+	1.67433i	−0.705043	+	0.709165i	$0.749072\pi$
$564$		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	−0.674273	−	0.738482i	$-0.735543\pi$
$569$	−8.87039	+	5.12132i	−0.371866	+	0.214697i	0.302407	+	0.953179i	$0.402210\pi$
$570$		0			0
$571$	11.0000	−	19.0526i	0.460336	−	0.797325i	−0.538642	−	0.842535i	$-0.681062\pi$
$571$	11.0000	−	19.0526i	0.460336	−	0.797325i	0.998978	+	0.0452101i	$0.0143957\pi$
$572$	−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	0.0836177	−	0.996498i	$-0.473353\pi$
$577$	23.7426	−	13.7078i	0.988419	−	0.570664i	0.904801	+	0.425834i	$0.140019\pi$
$578$		−	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	−0.308642	−	0.951178i	$-0.599874\pi$
$587$	16.2189	−	28.0919i	0.669424	−	1.15948i	0.978065	−	0.208298i	$-0.0667923\pi$
$588$		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	−0.884442	−	0.466650i	$-0.845461\pi$
$593$	−0.927572	+	1.60660i	−0.0380908	+	0.0659752i	0.846352	+	0.532625i	$0.178794\pi$
$594$		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	0.560893	−	0.827888i	$-0.310458\pi$
$599$	3.04384	+	1.75736i	0.124368	+	0.0718038i	−0.436526	+	0.899692i	$0.643791\pi$
$600$		0			0
$601$	35.9558	+	20.7591i	1.46667	+	0.846782i	0.999305	−	0.0372826i	$-0.0118702\pi$
$601$	35.9558	+	20.7591i	1.46667	+	0.846782i	0.467365	+	0.884065i	$0.345204\pi$
$602$	−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	$-0.738523\pi$
$607$		−	36.0759i		−	1.46428i	0.681157	−	0.732138i	$-0.261477\pi$
$608$	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	0.996589	+	0.0825214i	$0.0262973\pi$
$613$	14.1066	+	24.4334i	0.569760	+	0.986854i	−0.426829	+	0.904332i	$0.640369\pi$
$614$	−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	−0.424214	−	0.905562i	$-0.639449\pi$
$617$	3.67423	−	2.12132i	0.147919	−	0.0854011i	0.572133	+	0.820161i	$0.306116\pi$
$618$		0			0
$619$		−	12.7187i		−	0.511208i	−0.966782	−	0.255604i	$-0.917726\pi$
$619$		−	12.7187i		−	0.511208i	0.966782	−	0.255604i	$-0.0822743\pi$
$620$	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	$-0.772280\pi$
$641$		−	33.2132i		−	1.31184i	0.754829	−	0.655921i	$-0.227720\pi$
$642$		0			0
$643$	1.50000	−	0.866025i	0.0591542	−	0.0341527i	−0.470131	−	0.882597i	$-0.655793\pi$
$643$	1.50000	−	0.866025i	0.0591542	−	0.0341527i	0.529285	+	0.848444i	$0.322460\pi$
$644$	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	0.994729	−	0.102538i	$-0.0326965\pi$
$647$	10.3923	+	18.0000i	0.408564	+	0.707653i	−0.586165	+	0.810191i	$0.699363\pi$
$648$		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	$-0.984515\pi$
$653$		−	2.48528i		−	0.0972566i	0.998817	−	0.0486283i	$-0.0154850\pi$
$654$		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	0.0754589	−	0.997149i	$-0.475958\pi$
$659$	−19.2627	−	11.1213i	−0.750368	−	0.433225i	−0.825827	+	0.563924i	$0.809291\pi$
$660$		0			0
$661$	4.24264	+	2.44949i	0.165020	+	0.0952741i	0.580235	−	0.814449i	$-0.302961\pi$
$661$	4.24264	+	2.44949i	0.165020	+	0.0952741i	−0.415216	+	0.909723i	$0.636294\pi$
$662$	−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	0.0205075	−	0.999790i	$-0.493472\pi$
$673$	22.7279	−	39.3659i	0.876097	−	1.51744i	0.855590	−	0.517655i	$-0.173195\pi$
$674$	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	0.689557	−	0.724232i	$-0.257805\pi$
$677$	−7.34847	−	12.7279i	−0.282425	−	0.489174i	−0.971981	+	0.235058i	$0.924472\pi$
$678$		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	−0.660014	−	0.751254i	$-0.729450\pi$
$683$	−8.87039	+	5.12132i	−0.339416	+	0.195962i	0.320598	+	0.947215i	$0.396116\pi$
$684$		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	−0.541778	−	0.840522i	$-0.682249\pi$
$691$	−2.22792	+	1.28629i	−0.0847541	+	0.0489328i	0.457024	+	0.889454i	$0.348915\pi$
$692$	−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	$0.126440\pi$
$701$			20.4853i			0.773718i	−0.922139	+	0.386859i	$0.873560\pi$
$702$		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	0.672689	−	0.739925i	$-0.265139\pi$
$709$	−8.10660	−	14.0410i	−0.304450	−	0.527323i	−0.977139	+	0.212603i	$0.931806\pi$
$710$	−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	0.324181	−	0.945995i	$-0.394911\pi$
$719$	26.3140	−	45.5772i	0.981346	−	1.69974i	0.657166	−	0.753746i	$-0.271755\pi$
$720$		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	−0.0241323	−	0.999709i	$-0.507682\pi$
$727$	−24.3198	−	14.0410i	−0.901972	−	0.520754i	−0.877839	+	0.478955i	$0.841016\pi$
$728$	−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	$-0.992288\pi$
$733$		−	1.31178i		−	0.0484519i	0.999707	−	0.0242259i	$-0.00771211\pi$
$734$	−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	0.933251	−	0.359226i	$-0.116959\pi$
$739$	4.22792	+	7.32298i	0.155527	+	0.269380i	−0.777724	+	0.628606i	$0.783626\pi$
$740$	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	−0.172065	−	0.985086i	$-0.555044\pi$
$743$	16.2189	−	9.36396i	0.595012	−	0.343530i	0.767077	+	0.641555i	$0.221710\pi$
$744$		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	0.287789	−	0.957694i	$-0.407080\pi$
$769$	34.9706	−	20.1903i	1.26107	−	0.728080i	0.973282	+	0.229614i	$0.0737465\pi$
$770$	−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	0.764373	−	0.644774i	$-0.223049\pi$
$773$	−4.89898	−	8.48528i	−0.176204	−	0.305194i	−0.940577	+	0.339580i	$0.889715\pi$
$774$		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	0.868106	−	0.496379i	$-0.165338\pi$
$787$	24.4706	+	14.1281i	0.872281	+	0.503612i	0.00417567	+	0.999991i	$0.498671\pi$
$788$	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	0.665063	−	0.746787i	$-0.268405\pi$
$797$	−8.87039	−	15.3640i	−0.314205	−	0.544219i	−0.979268	+	0.202568i	$0.935071\pi$
$798$		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	−0.704041	−	0.710159i	$-0.748623\pi$
$809$	−12.5446	+	7.24264i	−0.441045	+	0.254638i	0.262996	+	0.964797i	$0.415290\pi$
$810$		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	−0.110937	−	0.993827i	$-0.535385\pi$
$821$	19.8931	−	11.4853i	0.694274	−	0.400839i	0.805211	+	0.592988i	$0.202052\pi$
$822$		0			0
$823$	1.37868	−	2.38794i	0.0480578	−	0.0832385i	−0.840996	−	0.541042i	$-0.818030\pi$
$823$	1.37868	−	2.38794i	0.0480578	−	0.0832385i	0.889054	+	0.457803i	$0.151364\pi$
$824$	−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	$-0.980536\pi$
$827$		−	3.51472i		−	0.122219i	0.998131	−	0.0611094i	$-0.0194638\pi$
$828$		0			0
$829$	8.48528	−	4.89898i	0.294706	−	0.170149i	−0.345356	−	0.938472i	$-0.612242\pi$
$829$	8.48528	−	4.89898i	0.294706	−	0.170149i	0.640062	+	0.768323i	$0.278909\pi$
$830$			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	−0.703333	−	0.710861i	$-0.748306\pi$
$839$	7.64564	−	13.2426i	0.263957	−	0.457187i	0.967290	+	0.253674i	$0.0816390\pi$
$840$		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	0.890614	−	0.454761i	$-0.150275\pi$
$853$	27.5147	+	15.8856i	0.942086	+	0.543914i	0.0514724	+	0.998674i	$0.483609\pi$
$854$	−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	$-0.839895\pi$
$859$		−	28.2562i		−	0.964088i	0.876147	−	0.482044i	$-0.160105\pi$
$860$	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	−0.166874	−	0.985978i	$-0.553367\pi$
$863$	−32.4377	−	18.7279i	−1.10419	−	0.637506i	−0.937319	+	0.348472i	$0.886700\pi$
$864$		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	0.639694	−	0.768629i	$-0.279061\pi$
$911$	8.87039	+	5.12132i	0.293889	+	0.169677i	−0.345805	+	0.938306i	$0.612394\pi$
$912$		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	−0.996359	−	0.0852590i	$-0.972828\pi$
$919$	−12.8640	+	22.2810i	−0.424343	+	0.734983i	0.572016	+	0.820243i	$0.306162\pi$
$920$	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	0.999459	−	0.0328762i	$-0.0104667\pi$
$929$	14.3637	+	24.8787i	0.471258	+	0.816243i	−0.528201	+	0.849119i	$0.677133\pi$
$930$		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	$0.184326\pi$
$937$			33.5033i			1.09451i	−0.836967	+	0.547253i	$0.815674\pi$
$938$	−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	−0.283927	−	0.958846i	$-0.591637\pi$
$941$	21.1178	−	36.5772i	0.688422	−	1.19238i	0.972348	−	0.233535i	$-0.0750295\pi$
$942$		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	−0.710825	−	0.703369i	$-0.751678\pi$
$947$	−14.0665	+	8.12132i	−0.457101	+	0.263907i	0.253723	+	0.967277i	$0.418345\pi$
$948$		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	$-0.994692\pi$
$953$		−	1.02944i		−	0.0333467i	0.999861	−	0.0166734i	$-0.00530755\pi$
$954$		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	0.972948	+	0.231022i	$0.0742070\pi$
$967$	21.3492	+	36.9780i	0.686545	+	1.18913i	−0.286403	+	0.958109i	$0.592460\pi$
$968$			7.00000i			0.224989i
$969$		0			0
$970$	7.75736			0.249074
$971$	−20.1903	+	34.9706i	−0.647936	+	1.12226i	0.335679	+	0.941977i	$0.391034\pi$
$971$	−20.1903	+	34.9706i	−0.647936	+	1.12226i	−0.983615	+	0.180282i	$0.942299\pi$
$972$		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	0.414572	−	0.910017i	$-0.363931\pi$
$977$	−5.19615	−	3.00000i	−0.166240	−	0.0959785i	−0.580812	+	0.814038i	$0.697265\pi$
$978$		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	0.980704	−	0.195497i	$-0.0626320\pi$
$991$	10.1066	+	17.5051i	0.321047	+	0.556069i	−0.659658	+	0.751566i	$0.729299\pi$
$992$	−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	$0.0997786\pi$
$997$			19.4728i			0.616711i	−0.951271	+	0.308355i	$0.900221\pi$
$998$	−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.593.4		8
3.2	odd	2	inner	1134.2.t.f.593.1		8
7.3	odd	6		1134.2.l.e.269.4		8
9.2	odd	6		378.2.k.d.215.4	yes	8
9.4	even	3		1134.2.l.e.215.3		8
9.5	odd	6		1134.2.l.e.215.2		8
9.7	even	3		378.2.k.d.215.1	✓	8
21.17	even	6		1134.2.l.e.269.1		8
63.2	odd	6		2646.2.d.d.2645.2		8
63.16	even	3		2646.2.d.d.2645.7		8
63.31	odd	6	inner	1134.2.t.f.1025.1		8
63.38	even	6		378.2.k.d.269.1	yes	8
63.47	even	6		2646.2.d.d.2645.4		8
63.52	odd	6		378.2.k.d.269.4	yes	8
63.59	even	6	inner	1134.2.t.f.1025.4		8
63.61	odd	6		2646.2.d.d.2645.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.k.d.215.1	✓	8	9.7	even	3
378.2.k.d.215.4	yes	8	9.2	odd	6
378.2.k.d.269.1	yes	8	63.38	even	6
378.2.k.d.269.4	yes	8	63.52	odd	6
1134.2.l.e.215.2		8	9.5	odd	6
1134.2.l.e.215.3		8	9.4	even	3
1134.2.l.e.269.1		8	21.17	even	6
1134.2.l.e.269.4		8	7.3	odd	6
1134.2.t.f.593.1		8	3.2	odd	2	inner
1134.2.t.f.593.4		8	1.1	even	1	trivial
1134.2.t.f.1025.1		8	63.31	odd	6	inner
1134.2.t.f.1025.4		8	63.59	even	6	inner
2646.2.d.d.2645.2		8	63.2	odd	6
2646.2.d.d.2645.4		8	63.47	even	6
2646.2.d.d.2645.5		8	63.61	odd	6
2646.2.d.d.2645.7		8	63.16	even	3

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more