LMFDB - Embedded newform 1134.2.k.d.971.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(647,1134)]

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([3, 1]))

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

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

chi := DirichletCharacter("1134.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.k (of order $6$, degree $2$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 796 x^{12} - 2228 x^{11} + 5254 x^{10} - 10232 x^{9} + \cdots + 225 $ x^16 - 8x^15 + 52x^14 - 224x^13 + 796x^12 - 2228x^11 + 5254x^10 - 10232x^9 + 16903x^8 - 23292x^7 + 26994x^6 - 25716x^5 + 19962x^4 - 12096x^3 + 5454x^2 - 1620*x + 225
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			971.3
Root			$0.500000 + 3.05304i$ of defining polynomial
Character	$\chi$	$=$	1134.971
Dual form			1134.2.k.d.647.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.360068 - 0.623656i) q^{5} +(1.03982 + 2.43285i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.360068 - 0.623656i) q^{5} +(1.03982 + 2.43285i) q^{7} -1.00000i q^{8} +(-0.623656 + 0.360068i) q^{10} +(3.81944 - 2.20516i) q^{11} -1.25451i q^{13} +(0.315916 - 2.62682i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.25492 - 5.63769i) q^{17} +(-4.66633 - 2.69411i) q^{19} +0.720136 q^{20} -4.41031 q^{22} +(5.95507 + 3.43816i) q^{23} +(2.24070 + 3.88101i) q^{25} +(-0.627256 + 1.08644i) q^{26} +(-1.58700 + 2.11694i) q^{28} +0.0221465i q^{29} +(3.21600 - 1.85676i) q^{31} +(0.866025 - 0.500000i) q^{32} +6.50984i q^{34} +(1.89167 + 0.227503i) q^{35} +(-1.82735 + 3.16506i) q^{37} +(2.69411 + 4.66633i) q^{38} +(-0.623656 - 0.360068i) q^{40} +1.96278 q^{41} +9.88445 q^{43} +(3.81944 + 2.20516i) q^{44} +(-3.43816 - 5.95507i) q^{46} +(4.11735 - 7.13145i) q^{47} +(-4.83755 + 5.05946i) q^{49} -4.48140i q^{50} +(1.08644 - 0.627256i) q^{52} +(2.95555 - 1.70638i) q^{53} -3.17602i q^{55} +(2.43285 - 1.03982i) q^{56} +(0.0110733 - 0.0191795i) q^{58} +(-2.09076 - 3.62130i) q^{59} +(7.08448 + 4.09023i) q^{61} -3.71351 q^{62} -1.00000 q^{64} +(-0.782383 - 0.451709i) q^{65} +(-5.60764 - 9.71272i) q^{67} +(3.25492 - 5.63769i) q^{68} +(-1.52448 - 1.14286i) q^{70} +2.47961i q^{71} +(8.54555 - 4.93377i) q^{73} +(3.16506 - 1.82735i) q^{74} -5.38821i q^{76} +(9.33635 + 6.99918i) q^{77} +(-1.23351 + 2.13650i) q^{79} +(0.360068 + 0.623656i) q^{80} +(-1.69981 - 0.981388i) q^{82} -11.3925 q^{83} -4.68797 q^{85} +(-8.56019 - 4.94223i) q^{86} +(-2.20516 - 3.81944i) q^{88} +(7.50204 - 12.9939i) q^{89} +(3.05204 - 1.30447i) q^{91} +6.87632i q^{92} +(-7.13145 + 4.11735i) q^{94} +(-3.36039 + 1.94012i) q^{95} +10.2660i q^{97} +(6.71917 - 1.96284i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 + 8 * q^7	$ 16 q + 8 q^{4} + 8 q^{7} + 12 q^{11} + 12 q^{14} - 8 q^{16} + 12 q^{23} - 8 q^{25} + 4 q^{28} + 12 q^{31} + 60 q^{35} + 4 q^{37} - 12 q^{38} - 48 q^{41} - 32 q^{43} + 12 q^{44} + 4 q^{49} - 12 q^{52} + 12 q^{56} - 12 q^{58} - 24 q^{59} - 12 q^{61} - 48 q^{62} - 16 q^{64} + 48 q^{65} - 4 q^{67} - 24 q^{70} + 36 q^{73} + 36 q^{74} + 84 q^{77} + 8 q^{79} - 72 q^{83} + 24 q^{85} + 24 q^{86} + 24 q^{89} - 12 q^{91} - 36 q^{94} + 12 q^{95} + 36 q^{98}+O(q^{100}) $ 16 * q + 8 * q^4 + 8 * q^7 + 12 * q^11 + 12 * q^14 - 8 * q^16 + 12 * q^23 - 8 * q^25 + 4 * q^28 + 12 * q^31 + 60 * q^35 + 4 * q^37 - 12 * q^38 - 48 * q^41 - 32 * q^43 + 12 * q^44 + 4 * q^49 - 12 * q^52 + 12 * q^56 - 12 * q^58 - 24 * q^59 - 12 * q^61 - 48 * q^62 - 16 * q^64 + 48 * q^65 - 4 * q^67 - 24 * q^70 + 36 * q^73 + 36 * q^74 + 84 * q^77 + 8 * q^79 - 72 * q^83 + 24 * q^85 + 24 * q^86 + 24 * q^89 - 12 * q^91 - 36 * q^94 + 12 * q^95 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.360068	−	0.623656i	0.161027	−	0.278907i	−0.774210	−	0.632929i	$-0.781853\pi$
$5$	0.360068	−	0.623656i	0.161027	−	0.278907i	0.935237	+	0.354021i	$0.115186\pi$
$6$		0			0
$7$	1.03982	+	2.43285i	0.393015	+	0.919532i
$7$	1.03982	+	2.43285i	0.393015	+	0.919532i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.623656	+	0.360068i	−0.197217	+	0.113863i
$11$	3.81944	−	2.20516i	1.15161	−	0.664880i	0.202328	−	0.979318i	$-0.435149\pi$
$11$	3.81944	−	2.20516i	1.15161	−	0.664880i	0.949278	+	0.314438i	$0.101816\pi$
$12$		0			0
$13$		−	1.25451i		−	0.347939i	−0.984751	−	0.173969i	$-0.944341\pi$
$13$		−	1.25451i		−	0.347939i	0.984751	−	0.173969i	$-0.0556594\pi$
$14$	0.315916	−	2.62682i	0.0844322	−	0.702048i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.25492	−	5.63769i	−0.789434	−	1.36734i	−0.926314	−	0.376752i	$-0.877041\pi$
$17$	−3.25492	−	5.63769i	−0.789434	−	1.36734i	0.136880	−	0.990588i	$-0.456292\pi$
$18$		0			0
$19$	−4.66633	−	2.69411i	−1.07053	−	0.618070i	−0.142203	−	0.989838i	$-0.545419\pi$
$19$	−4.66633	−	2.69411i	−1.07053	−	0.618070i	−0.928326	+	0.371767i	$0.878752\pi$
$20$	0.720136			0.161027
$21$		0			0
$22$	−4.41031			−0.940282
$23$	5.95507	+	3.43816i	1.24172	+	0.716906i	0.969444	−	0.245313i	$-0.0788909\pi$
$23$	5.95507	+	3.43816i	1.24172	+	0.716906i	0.272274	+	0.962220i	$0.412224\pi$
$24$		0			0
$25$	2.24070	+	3.88101i	0.448140	+	0.776202i
$26$	−0.627256	+	1.08644i	−0.123015	+	0.213068i
$27$		0			0
$28$	−1.58700	+	2.11694i	−0.299915	+	0.400063i
$29$			0.0221465i			0.00411251i	0.999998	+	0.00205625i	$0.000654527\pi$
$29$			0.0221465i			0.00411251i	−0.999998	+	0.00205625i	$0.999345\pi$
$30$		0			0
$31$	3.21600	−	1.85676i	0.577610	−	0.333483i	−0.182573	−	0.983192i	$-0.558443\pi$
$31$	3.21600	−	1.85676i	0.577610	−	0.333483i	0.760183	+	0.649709i	$0.225109\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$			6.50984i			1.11643i
$35$	1.89167	+	0.227503i	0.319750	+	0.0384550i
$36$		0			0
$37$	−1.82735	+	3.16506i	−0.300414	+	0.520333i	−0.976230	−	0.216738i	$-0.930458\pi$
$37$	−1.82735	+	3.16506i	−0.300414	+	0.520333i	0.675815	+	0.737071i	$0.263792\pi$
$38$	2.69411	+	4.66633i	0.437042	+	0.756978i
$39$		0			0
$40$	−0.623656	−	0.360068i	−0.0986087	−	0.0569317i
$41$	1.96278			0.306534			0.153267	−	0.988185i	$-0.451021\pi$
$41$	1.96278			0.306534			0.153267	+	0.988185i	$0.451021\pi$
$42$		0			0
$43$	9.88445			1.50736			0.753682	−	0.657239i	$-0.228276\pi$
$43$	9.88445			1.50736			0.753682	+	0.657239i	$0.228276\pi$
$44$	3.81944	+	2.20516i	0.575803	+	0.332440i
$45$		0			0
$46$	−3.43816	−	5.95507i	−0.506929	−	0.878027i
$47$	4.11735	−	7.13145i	0.600577	−	1.04023i	−0.392157	−	0.919898i	$-0.628271\pi$
$47$	4.11735	−	7.13145i	0.600577	−	1.04023i	0.992734	−	0.120331i	$-0.0383956\pi$
$48$		0			0
$49$	−4.83755	+	5.05946i	−0.691079	+	0.722780i
$50$		−	4.48140i		−	0.633766i
$51$		0			0
$52$	1.08644	−	0.627256i	0.150662	−	0.0869847i
$53$	2.95555	−	1.70638i	0.405975	−	0.234390i	−0.283084	−	0.959095i	$-0.591357\pi$
$53$	2.95555	−	1.70638i	0.405975	−	0.234390i	0.689059	+	0.724705i	$0.258024\pi$
$54$		0			0
$55$		−	3.17602i		−	0.428255i
$56$	2.43285	−	1.03982i	0.325104	−	0.138952i
$57$		0			0
$58$	0.0110733	−	0.0191795i	0.00145399	−	0.00251839i
$59$	−2.09076	−	3.62130i	−0.272193	−	0.471452i	0.697230	−	0.716848i	$-0.254416\pi$
$59$	−2.09076	−	3.62130i	−0.272193	−	0.471452i	−0.969423	+	0.245395i	$0.921082\pi$
$60$		0			0
$61$	7.08448	+	4.09023i	0.907075	+	0.523700i	0.879489	−	0.475920i	$-0.157885\pi$
$61$	7.08448	+	4.09023i	0.907075	+	0.523700i	0.0275859	+	0.999619i	$0.491218\pi$
$62$	−3.71351			−0.471616
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.782383	−	0.451709i	−0.0970427	−	0.0560276i
$66$		0			0
$67$	−5.60764	−	9.71272i	−0.685083	−	1.18660i	−0.973411	−	0.229066i	$-0.926433\pi$
$67$	−5.60764	−	9.71272i	−0.685083	−	1.18660i	0.288328	−	0.957532i	$-0.406901\pi$
$68$	3.25492	−	5.63769i	0.394717	−	0.683670i
$69$		0			0
$70$	−1.52448	−	1.14286i	−0.182210	−	0.136598i
$71$			2.47961i			0.294275i	0.989116	+	0.147138i	$0.0470060\pi$
$71$			2.47961i			0.294275i	−0.989116	+	0.147138i	$0.952994\pi$
$72$		0			0
$73$	8.54555	−	4.93377i	1.00018	−	0.577454i	0.0918788	−	0.995770i	$-0.470713\pi$
$73$	8.54555	−	4.93377i	1.00018	−	0.577454i	0.908302	+	0.418316i	$0.137379\pi$
$74$	3.16506	−	1.82735i	0.367931	−	0.212425i
$75$		0			0
$76$		−	5.38821i		−	0.618070i
$77$	9.33635	+	6.99918i	1.06398	+	0.797631i
$78$		0			0
$79$	−1.23351	+	2.13650i	−0.138781	+	0.240375i	−0.927035	−	0.374974i	$-0.877652\pi$
$79$	−1.23351	+	2.13650i	−0.138781	+	0.240375i	0.788255	+	0.615349i	$0.210985\pi$
$80$	0.360068	+	0.623656i	0.0402568	+	0.0697269i
$81$		0			0
$82$	−1.69981	−	0.981388i	−0.187713	−	0.108376i
$83$	−11.3925			−1.25049			−0.625244	−	0.780429i	$-0.715001\pi$
$83$	−11.3925			−1.25049			−0.625244	+	0.780429i	$0.715001\pi$
$84$		0			0
$85$	−4.68797			−0.508482
$86$	−8.56019	−	4.94223i	−0.923069	−	0.532934i
$87$		0			0
$88$	−2.20516	−	3.81944i	−0.235070	−	0.407154i
$89$	7.50204	−	12.9939i	0.795214	−	1.37735i	−0.127489	−	0.991840i	$-0.540692\pi$
$89$	7.50204	−	12.9939i	0.795214	−	1.37735i	0.922703	−	0.385512i	$-0.125975\pi$
$90$		0			0
$91$	3.05204	−	1.30447i	0.319941	−	0.136745i
$92$			6.87632i			0.716906i
$93$		0			0
$94$	−7.13145	+	4.11735i	−0.735553	+	0.424672i
$95$	−3.36039	+	1.94012i	−0.344769	+	0.199052i
$96$		0			0
$97$			10.2660i			1.04236i	0.853448	+	0.521178i	$0.174507\pi$
$97$			10.2660i			1.04236i	−0.853448	+	0.521178i	$0.825493\pi$
$98$	6.71917	−	1.96284i	0.678739	−	0.198277i
$99$		0			0
$100$	−2.24070	+	3.88101i	−0.224070	+	0.388101i
$101$	−2.27149	−	3.93433i	−0.226021	−	0.391481i	0.730604	−	0.682802i	$-0.239239\pi$
$101$	−2.27149	−	3.93433i	−0.226021	−	0.391481i	−0.956625	+	0.291321i	$0.905905\pi$
$102$		0			0
$103$	16.3043	+	9.41328i	1.60651	+	0.927518i	0.990144	+	0.140056i	$0.0447284\pi$
$103$	16.3043	+	9.41328i	1.60651	+	0.927518i	0.616364	+	0.787461i	$0.288605\pi$
$104$	−1.25451			−0.123015
$105$		0			0
$106$	−3.41277			−0.331477
$107$	0.881040	+	0.508669i	0.0851734	+	0.0491749i	0.541982	−	0.840390i	$-0.317674\pi$
$107$	0.881040	+	0.508669i	0.0851734	+	0.0491749i	−0.456808	+	0.889565i	$0.651008\pi$
$108$		0			0
$109$	−5.26044	−	9.11136i	−0.503859	−	0.872710i	−0.999990	−	0.00446195i	$-0.998580\pi$
$109$	−5.26044	−	9.11136i	−0.503859	−	0.872710i	0.496131	−	0.868248i	$-0.334754\pi$
$110$	−1.58801	+	2.75052i	−0.151411	+	0.262252i
$111$		0			0
$112$	−2.62682	−	0.315916i	−0.248211	−	0.0298513i
$113$			5.50175i			0.517562i	0.965936	+	0.258781i	$0.0833207\pi$
$113$			5.50175i			0.517562i	−0.965936	+	0.258781i	$0.916679\pi$
$114$		0			0
$115$	4.28846	−	2.47594i	0.399901	−	0.230883i
$116$	−0.0191795	+	0.0110733i	−0.00178077	+	0.00102813i
$117$		0			0
$118$			4.18151i			0.384939i
$119$	10.3311	−	13.7809i	0.947054	−	1.26329i
$120$		0			0
$121$	4.22543	−	7.31866i	0.384130	−	0.665333i
$122$	−4.09023	−	7.08448i	−0.370312	−	0.641399i
$123$		0			0
$124$	3.21600	+	1.85676i	0.288805	+	0.166742i
$125$	6.82790			0.610706
$126$		0			0
$127$	7.28997			0.646880			0.323440	−	0.946249i	$-0.395161\pi$
$127$	7.28997			0.646880			0.323440	+	0.946249i	$0.395161\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	0.451709	+	0.782383i	0.0396175	+	0.0686196i
$131$	−3.82644	+	6.62759i	−0.334318	+	0.579055i	−0.983354	−	0.181703i	$-0.941839\pi$
$131$	−3.82644	+	6.62759i	−0.334318	+	0.579055i	0.649036	+	0.760758i	$0.275172\pi$
$132$		0			0
$133$	1.70222	−	14.1539i	0.147602	−	1.22730i
$134$			11.2153i			0.968853i
$135$		0			0
$136$	−5.63769	+	3.25492i	−0.483428	+	0.279107i
$137$	2.07631	−	1.19876i	0.177391	−	0.102417i	−0.408675	−	0.912680i	$-0.634009\pi$
$137$	2.07631	−	1.19876i	0.177391	−	0.102417i	0.586066	+	0.810263i	$0.300676\pi$
$138$		0			0
$139$		−	12.9971i		−	1.10240i	−0.834372	−	0.551201i	$-0.814170\pi$
$139$		−	12.9971i		−	1.10240i	0.834372	−	0.551201i	$-0.185830\pi$
$140$	0.748811	+	1.75198i	0.0632861	+	0.148070i
$141$		0			0
$142$	1.23980	−	2.14740i	0.104042	−	0.180206i
$143$	−2.76639	−	4.79153i	−0.231337	−	0.400688i
$144$		0			0
$145$	0.0138118	+	0.00797426i	0.00114701	+	0.000662226i
$146$	−9.86755			−0.816644
$147$		0			0
$148$	−3.65470			−0.300414
$149$	−3.79969	−	2.19375i	−0.311282	−	0.179719i	0.336218	−	0.941784i	$-0.390852\pi$
$149$	−3.79969	−	2.19375i	−0.311282	−	0.179719i	−0.647500	+	0.762065i	$0.724186\pi$
$150$		0			0
$151$	−8.27064	−	14.3252i	−0.673056	−	1.16577i	−0.977033	−	0.213087i	$-0.931648\pi$
$151$	−8.27064	−	14.3252i	−0.673056	−	1.16577i	0.303978	−	0.952679i	$-0.401685\pi$
$152$	−2.69411	+	4.66633i	−0.218521	+	0.378489i
$153$		0			0
$154$	−4.58593	−	10.7296i	−0.369545	−	0.864619i
$155$		−	2.67423i		−	0.214800i
$156$		0			0
$157$	19.9547	−	11.5209i	1.59256	−	0.919465i	0.599695	−	0.800229i	$-0.295289\pi$
$157$	19.9547	−	11.5209i	1.59256	−	0.919465i	0.992866	−	0.119237i	$-0.0380448\pi$
$158$	2.13650	−	1.23351i	0.169971	−	0.0981327i
$159$		0			0
$160$		−	0.720136i		−	0.0569317i
$161$	−2.17234	+	18.0629i	−0.171205	+	1.42355i
$162$		0			0
$163$	2.68095	−	4.64354i	0.209988	−	0.363710i	−0.741722	−	0.670707i	$-0.765991\pi$
$163$	2.68095	−	4.64354i	0.209988	−	0.363710i	0.951711	+	0.306997i	$0.0993241\pi$
$164$	0.981388	+	1.69981i	0.0766335	+	0.132733i
$165$		0			0
$166$	9.86619	+	5.69625i	0.765765	+	0.442115i
$167$	−11.3689			−0.879755			−0.439877	−	0.898058i	$-0.644978\pi$
$167$	−11.3689			−0.879755			−0.439877	+	0.898058i	$0.644978\pi$
$168$		0			0
$169$	11.4262			0.878939
$170$	4.05990	+	2.34398i	0.311380	+	0.179775i
$171$		0			0
$172$	4.94223	+	8.56019i	0.376841	+	0.652708i
$173$	−11.9236	+	20.6523i	−0.906536	+	1.57017i	−0.0876944	+	0.996147i	$0.527950\pi$
$173$	−11.9236	+	20.6523i	−0.906536	+	1.57017i	−0.818842	+	0.574019i	$0.805383\pi$
$174$		0			0
$175$	−7.11200	+	9.48685i	−0.537617	+	0.717138i
$176$			4.41031i			0.332440i
$177$		0			0
$178$	−12.9939	+	7.50204i	−0.973935	+	0.562302i
$179$	−9.25956	+	5.34601i	−0.692092	+	0.399580i	−0.804395	−	0.594094i	$-0.797511\pi$
$179$	−9.25956	+	5.34601i	−0.692092	+	0.399580i	0.112303	+	0.993674i	$0.464177\pi$
$180$		0			0
$181$			22.7895i			1.69393i	0.531649	+	0.846964i	$0.321572\pi$
$181$			22.7895i			1.69393i	−0.531649	+	0.846964i	$0.678428\pi$
$182$	−3.29538	−	0.396321i	−0.244270	−	0.0293772i
$183$		0			0
$184$	3.43816	−	5.95507i	0.253465	−	0.439014i
$185$	1.31594	+	2.27928i	0.0967499	+	0.167576i
$186$		0			0
$187$	−24.8640	−	14.3552i	−1.81823	−	1.04976i
$188$	8.23469			0.600577
$189$		0			0
$190$	3.88024			0.281503
$191$	4.98861	+	2.88017i	0.360963	+	0.208402i	0.669503	−	0.742809i	$-0.266507\pi$
$191$	4.98861	+	2.88017i	0.360963	+	0.208402i	−0.308540	+	0.951211i	$0.599840\pi$
$192$		0			0
$193$	12.7218	+	22.0349i	0.915738	+	1.58610i	0.805818	+	0.592164i	$0.201726\pi$
$193$	12.7218	+	22.0349i	0.915738	+	1.58610i	0.109920	+	0.993940i	$0.464940\pi$
$194$	5.13301	−	8.89063i	0.368529	−	0.638310i
$195$		0			0
$196$	−6.80039	−	1.65971i	−0.485742	−	0.118551i
$197$		−	0.133910i		−	0.00954067i	−0.999989	−	0.00477033i	$-0.998482\pi$
$197$		−	0.133910i		−	0.00954067i	0.999989	−	0.00477033i	$-0.00151845\pi$
$198$		0			0
$199$	−3.89988	+	2.25160i	−0.276455	+	0.159612i	−0.631818	−	0.775117i	$-0.717691\pi$
$199$	−3.89988	+	2.25160i	−0.276455	+	0.159612i	0.355362	+	0.934729i	$0.384358\pi$
$200$	3.88101	−	2.24070i	0.274429	−	0.158442i
$201$		0			0
$202$			4.54298i			0.319643i
$203$	−0.0538793	+	0.0230284i	−0.00378158	+	0.00161628i
$204$		0			0
$205$	0.706733	−	1.22410i	0.0493604	−	0.0854947i
$206$	−9.41328	−	16.3043i	−0.655854	−	1.13597i
$207$		0			0
$208$	1.08644	+	0.627256i	0.0753309	+	0.0434923i
$209$	−23.7637			−1.64377
$210$		0			0
$211$	−25.7693			−1.77403			−0.887016	−	0.461738i	$-0.847226\pi$
$211$	−25.7693			−1.77403			−0.887016	+	0.461738i	$0.847226\pi$
$212$	2.95555	+	1.70638i	0.202988	+	0.117195i
$213$		0			0
$214$	−0.508669	−	0.881040i	−0.0347719	−	0.0602267i
$215$	3.55907	−	6.16450i	0.242727	−	0.420415i
$216$		0			0
$217$	7.86127	+	5.89335i	0.533658	+	0.400067i
$218$			10.5209i			0.712564i
$219$		0			0
$220$	2.75052	−	1.58801i	0.185440	−	0.107064i
$221$	−7.07254	+	4.08333i	−0.475751	+	0.274675i
$222$		0			0
$223$			1.10783i			0.0741861i	0.999312	+	0.0370930i	$0.0118098\pi$
$223$			1.10783i			0.0741861i	−0.999312	+	0.0370930i	$0.988190\pi$
$224$	2.11694	+	1.58700i	0.141444	+	0.106036i
$225$		0			0
$226$	2.75088	−	4.76466i	0.182986	−	0.316940i
$227$	2.19998	+	3.81048i	0.146018	+	0.252911i	0.929752	−	0.368186i	$-0.120021\pi$
$227$	2.19998	+	3.81048i	0.146018	+	0.252911i	−0.783734	+	0.621096i	$0.786688\pi$
$228$		0			0
$229$	3.39374	+	1.95937i	0.224264	+	0.129479i	0.607923	−	0.793996i	$-0.292003\pi$
$229$	3.39374	+	1.95937i	0.224264	+	0.129479i	−0.383659	+	0.923475i	$0.625336\pi$
$230$	−4.95189			−0.326518
$231$		0			0
$232$	0.0221465			0.00145399
$233$	−18.1850	−	10.4991i	−1.19134	−	0.687819i	−0.232727	−	0.972542i	$-0.574765\pi$
$233$	−18.1850	−	10.4991i	−1.19134	−	0.687819i	−0.958610	+	0.284723i	$0.908098\pi$
$234$		0			0
$235$	−2.96505	−	5.13561i	−0.193418	−	0.335011i
$236$	2.09076	−	3.62130i	0.136097	−	0.235726i
$237$		0			0
$238$	−15.8375	+	6.76906i	−1.02659	+	0.438773i
$239$			26.2305i			1.69671i	0.529429	+	0.848354i	$0.322406\pi$
$239$			26.2305i			1.69671i	−0.529429	+	0.848354i	$0.677594\pi$
$240$		0			0
$241$	−4.24909	+	2.45321i	−0.273708	+	0.158025i	−0.630572	−	0.776131i	$-0.717179\pi$
$241$	−4.24909	+	2.45321i	−0.273708	+	0.158025i	0.356864	+	0.934157i	$0.383846\pi$
$242$	−7.31866	+	4.22543i	−0.470461	+	0.271621i
$243$		0			0
$244$			8.18045i			0.523700i
$245$	1.41351	+	4.83872i	0.0903061	+	0.309134i
$246$		0			0
$247$	−3.37979	+	5.85396i	−0.215051	+	0.372479i
$248$	−1.85676	−	3.21600i	−0.117904	−	0.204216i
$249$		0			0
$250$	−5.91313	−	3.41395i	−0.373979	−	0.215917i
$251$	−28.3990			−1.79253			−0.896264	−	0.443521i	$-0.853729\pi$
$251$	−28.3990			−1.79253			−0.896264	+	0.443521i	$0.853729\pi$
$252$		0			0
$253$	30.3267			1.90663
$254$	−6.31330	−	3.64498i	−0.396132	−	0.228707i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.4625	−	18.1215i	0.652630	−	1.13039i	−0.329852	−	0.944032i	$-0.606999\pi$
$257$	10.4625	−	18.1215i	0.652630	−	1.13039i	0.982482	−	0.186356i	$-0.0596677\pi$
$258$		0			0
$259$	−9.60025	−	1.15458i	−0.596530	−	0.0717421i
$260$		−	0.903418i		−	0.0560276i
$261$		0			0
$262$	6.62759	−	3.82644i	0.409454	−	0.236398i
$263$	19.5793	−	11.3041i	1.20731	−	0.697040i	0.245138	−	0.969488i	$-0.421167\pi$
$263$	19.5793	−	11.3041i	1.20731	−	0.697040i	0.962171	+	0.272448i	$0.0878333\pi$
$264$		0			0
$265$		−	2.45766i		−	0.150973i
$266$	−8.55111	+	11.4065i	−0.524302	+	0.699378i
$267$		0			0
$268$	5.60764	−	9.71272i	0.342541	−	0.593299i
$269$	10.0754	+	17.4511i	0.614309	+	1.06401i	0.990505	+	0.137474i	$0.0438985\pi$
$269$	10.0754	+	17.4511i	0.614309	+	1.06401i	−0.376196	+	0.926540i	$0.622768\pi$
$270$		0			0
$271$	−0.753738	−	0.435171i	−0.0457863	−	0.0264347i	0.476932	−	0.878940i	$-0.341749\pi$
$271$	−0.753738	−	0.435171i	−0.0457863	−	0.0264347i	−0.522718	+	0.852505i	$0.675082\pi$
$272$	6.50984			0.394717
$273$		0			0
$274$	−2.39751			−0.144839
$275$	17.1165	+	9.88220i	1.03216	+	0.595919i
$276$		0			0
$277$	−8.63594	−	14.9579i	−0.518884	−	0.898733i	−0.999759	−	0.0219439i	$-0.993014\pi$
$277$	−8.63594	−	14.9579i	−0.518884	−	0.898733i	0.480876	−	0.876789i	$-0.340319\pi$
$278$	−6.49857	+	11.2559i	−0.389758	+	0.675081i
$279$		0			0
$280$	0.227503	−	1.89167i	0.0135959	−	0.113049i
$281$			30.3053i			1.80786i	0.427678	+	0.903931i	$0.359332\pi$
$281$			30.3053i			1.80786i	−0.427678	+	0.903931i	$0.640668\pi$
$282$		0			0
$283$	5.02502	−	2.90119i	0.298706	−	0.172458i	−0.343155	−	0.939279i	$-0.611496\pi$
$283$	5.02502	−	2.90119i	0.298706	−	0.172458i	0.641862	+	0.766821i	$0.278162\pi$
$284$	−2.14740	+	1.23980i	−0.127425	+	0.0735688i
$285$		0			0
$286$			5.53279i			0.327161i
$287$	2.04093	+	4.77515i	0.120473	+	0.281868i
$288$		0			0
$289$	−12.6890	+	21.9780i	−0.746412	+	1.29282i
$290$	−0.00797426	−	0.0138118i	−0.000468265	−	0.000811058i
$291$		0			0
$292$	8.54555	+	4.93377i	0.500090	+	0.288727i
$293$	−17.2563			−1.00813			−0.504063	−	0.863667i	$-0.668162\pi$
$293$	−17.2563			−1.00813			−0.504063	+	0.863667i	$0.668162\pi$
$294$		0			0
$295$	−3.01126			−0.175322
$296$	3.16506	+	1.82735i	0.183966	+	0.106213i
$297$		0			0
$298$	2.19375	+	3.79969i	0.127081	+	0.220110i
$299$	4.31321	−	7.47070i	0.249439	−	0.432042i
$300$		0			0
$301$	10.2780	+	24.0474i	0.592417	+	1.38607i
$302$			16.5413i			0.951844i
$303$		0			0
$304$	4.66633	−	2.69411i	0.267632	−	0.154518i
$305$	5.10179	−	2.94552i	0.292128	−	0.168660i
$306$		0			0
$307$			13.5843i			0.775300i	0.921807	+	0.387650i	$0.126713\pi$
$307$			13.5843i			0.775300i	−0.921807	+	0.387650i	$0.873287\pi$
$308$	−1.39329	+	11.5851i	−0.0793901	+	0.660123i
$309$		0			0
$310$	−1.33712	+	2.31595i	−0.0759431	+	0.131537i
$311$	−9.38959	−	16.2632i	−0.532435	−	0.922204i	−0.999283	−	0.0378663i	$-0.987944\pi$
$311$	−9.38959	−	16.2632i	−0.532435	−	0.922204i	0.466848	−	0.884337i	$-0.345389\pi$
$312$		0			0
$313$	−10.7766	−	6.22185i	−0.609127	−	0.351680i	0.163497	−	0.986544i	$-0.447723\pi$
$313$	−10.7766	−	6.22185i	−0.609127	−	0.351680i	−0.772624	+	0.634864i	$0.781056\pi$
$314$	−23.0417			−1.30032
$315$		0			0
$316$	−2.46702			−0.138781
$317$	−24.2326	−	13.9907i	−1.36104	−	0.785795i	−0.371275	−	0.928523i	$-0.621079\pi$
$317$	−24.2326	−	13.9907i	−1.36104	−	0.785795i	−0.989762	+	0.142728i	$0.954413\pi$
$318$		0			0
$319$	0.0488366	+	0.0845875i	0.00273432	+	0.00473599i
$320$	−0.360068	+	0.623656i	−0.0201284	+	0.0348634i
$321$		0			0
$322$	10.9127	−	14.5567i	0.608144	−	0.811216i
$323$			35.0764i			1.95170i
$324$		0			0
$325$	4.86877	−	2.81099i	0.270071	−	0.155925i
$326$	−4.64354	+	2.68095i	−0.257182	+	0.148484i
$327$		0			0
$328$		−	1.96278i		−	0.108376i
$329$	21.6311	+	2.60147i	1.19256	+	0.143424i
$330$		0			0
$331$	−12.9738	+	22.4713i	−0.713106	+	1.23514i	0.250579	+	0.968096i	$0.419379\pi$
$331$	−12.9738	+	22.4713i	−0.713106	+	1.23514i	−0.963685	+	0.267040i	$0.913954\pi$
$332$	−5.69625	−	9.86619i	−0.312622	−	0.541478i
$333$		0			0
$334$	9.84579	+	5.68447i	0.538738	+	0.311040i
$335$	−8.07653			−0.441268
$336$		0			0
$337$	−2.98199			−0.162439			−0.0812197	−	0.996696i	$-0.525882\pi$
$337$	−2.98199			−0.162439			−0.0812197	+	0.996696i	$0.525882\pi$
$338$	−9.89538	−	5.71310i	−0.538238	−	0.310752i
$339$		0			0
$340$	−2.34398	−	4.05990i	−0.127120	−	0.220179i
$341$	8.18888	−	14.1835i	0.443452	−	0.768082i
$342$		0			0
$343$	−17.3391	−	6.50813i	−0.936223	−	0.351406i
$344$		−	9.88445i		−	0.532934i
$345$		0			0
$346$	20.6523	−	11.9236i	1.11028	−	0.641018i
$347$	0.960504	−	0.554547i	0.0515625	−	0.0297696i	−0.473997	−	0.880526i	$-0.657189\pi$
$347$	0.960504	−	0.554547i	0.0515625	−	0.0297696i	0.525560	+	0.850757i	$0.323856\pi$
$348$		0			0
$349$			20.5877i			1.10203i	0.834494	+	0.551017i	$0.185760\pi$
$349$			20.5877i			1.10203i	−0.834494	+	0.551017i	$0.814240\pi$
$350$	10.9026	−	4.65985i	0.582768	−	0.249080i
$351$		0			0
$352$	2.20516	−	3.81944i	0.117535	−	0.203577i
$353$	12.4002	+	21.4777i	0.659994	+	1.14314i	0.980617	+	0.195936i	$0.0627746\pi$
$353$	12.4002	+	21.4777i	0.659994	+	1.14314i	−0.320623	+	0.947207i	$0.603892\pi$
$354$		0			0
$355$	1.54642	+	0.892827i	0.0820756	+	0.0473864i
$356$	15.0041			0.795214
$357$		0			0
$358$	10.6920			0.565091
$359$	−16.5875	−	9.57681i	−0.875456	−	0.505445i	−0.00629854	−	0.999980i	$-0.502005\pi$
$359$	−16.5875	−	9.57681i	−0.875456	−	0.505445i	−0.869157	+	0.494535i	$0.835338\pi$
$360$		0			0
$361$	5.01641	+	8.68868i	0.264022	+	0.457299i
$362$	11.3947	−	19.7363i	0.598894	−	1.03732i
$363$		0			0
$364$	2.65572	+	1.99091i	0.139198	+	0.104352i
$365$		−	7.10597i		−	0.371944i
$366$		0			0
$367$	14.5233	−	8.38501i	0.758108	−	0.437694i	−0.0705081	−	0.997511i	$-0.522462\pi$
$367$	14.5233	−	8.38501i	0.758108	−	0.437694i	0.828616	+	0.559817i	$0.189129\pi$
$368$	−5.95507	+	3.43816i	−0.310430	+	0.179227i
$369$		0			0
$370$		−	2.63188i		−	0.136825i
$371$	7.22462	+	5.41608i	0.375083	+	0.281189i
$372$		0			0
$373$	−13.2507	+	22.9509i	−0.686094	+	1.18835i	0.286997	+	0.957931i	$0.407343\pi$
$373$	−13.2507	+	22.9509i	−0.686094	+	1.18835i	−0.973092	+	0.230419i	$0.925990\pi$
$374$	14.3552	+	24.8640i	0.742291	+	1.28568i
$375$		0			0
$376$	−7.13145	−	4.11735i	−0.367777	−	0.212336i
$377$	0.0277831			0.00143090
$378$		0			0
$379$	−16.7747			−0.861657			−0.430829	−	0.902434i	$-0.641779\pi$
$379$	−16.7747			−0.861657			−0.430829	+	0.902434i	$0.641779\pi$
$380$	−3.36039	−	1.94012i	−0.172384	−	0.0995262i
$381$		0			0
$382$	−2.88017	−	4.98861i	−0.147363	−	0.255239i
$383$	−8.36992	+	14.4971i	−0.427683	+	0.740769i	−0.996667	−	0.0815798i	$-0.974003\pi$
$383$	−8.36992	+	14.4971i	−0.427683	+	0.740769i	0.568984	+	0.822349i	$0.307337\pi$
$384$		0			0
$385$	7.72680	−	3.30249i	0.393794	−	0.168311i
$386$		−	25.4437i		−	1.29505i
$387$		0			0
$388$	−8.89063	+	5.13301i	−0.451353	+	0.260589i
$389$	−7.82510	+	4.51783i	−0.396749	+	0.229063i	−0.685080	−	0.728468i	$-0.740233\pi$
$389$	−7.82510	+	4.51783i	−0.396749	+	0.229063i	0.288332	+	0.957531i	$0.406899\pi$
$390$		0			0
$391$		−	44.7638i		−	2.26380i
$392$	5.05946	+	4.83755i	0.255541	+	0.244333i
$393$		0			0
$394$	−0.0669548	+	0.115969i	−0.00337314	+	0.00584244i
$395$	0.888294	+	1.53857i	0.0446949	+	0.0774139i
$396$		0			0
$397$	−13.4999	−	7.79420i	−0.677543	−	0.391180i	0.121386	−	0.992605i	$-0.461266\pi$
$397$	−13.4999	−	7.79420i	−0.677543	−	0.391180i	−0.798929	+	0.601426i	$0.794600\pi$
$398$	4.50320			0.225725
$399$		0			0
$400$	−4.48140			−0.224070
$401$	−10.7706	−	6.21840i	−0.537857	−	0.310532i	0.206353	−	0.978478i	$-0.433840\pi$
$401$	−10.7706	−	6.21840i	−0.537857	−	0.310532i	−0.744210	+	0.667946i	$0.767174\pi$
$402$		0			0
$403$	−2.32932	−	4.03450i	−0.116032	−	0.200973i
$404$	2.27149	−	3.93433i	0.113011	−	0.195740i
$405$		0			0
$406$	0.0581750	+	0.00699646i	0.00288718	+	0.000347228i
$407$			16.1184i			0.798958i
$408$		0			0
$409$	1.18775	−	0.685749i	0.0587306	−	0.0339081i	−0.470347	−	0.882481i	$-0.655871\pi$
$409$	1.18775	−	0.685749i	0.0587306	−	0.0339081i	0.529078	+	0.848573i	$0.322538\pi$
$410$	−1.22410	+	0.706733i	−0.0604539	+	0.0349030i
$411$		0			0
$412$			18.8266i			0.927518i
$413$	6.63607	−	8.85200i	0.326540	−	0.435578i
$414$		0			0
$415$	−4.10207	+	7.10500i	−0.201363	+	0.348771i
$416$	−0.627256	−	1.08644i	−0.0307537	−	0.0532670i
$417$		0			0
$418$	20.5800	+	11.8819i	1.00660	+	0.581160i
$419$	−15.2548			−0.745248			−0.372624	−	0.927983i	$-0.621542\pi$
$419$	−15.2548			−0.745248			−0.372624	+	0.927983i	$0.621542\pi$
$420$		0			0
$421$	9.37509			0.456914			0.228457	−	0.973554i	$-0.426632\pi$
$421$	9.37509			0.456914			0.228457	+	0.973554i	$0.426632\pi$
$422$	22.3169	+	12.8847i	1.08637	+	0.627215i
$423$		0			0
$424$	−1.70638	−	2.95555i	−0.0828694	−	0.143534i
$425$	14.5866	−	25.2648i	0.707555	−	1.22552i
$426$		0			0
$427$	−2.58434	+	21.4886i	−0.125065	+	1.03991i
$428$			1.01734i			0.0491749i
$429$		0			0
$430$	−6.16450	+	3.55907i	−0.297278	+	0.171634i
$431$	−6.44133	+	3.71890i	−0.310268	+	0.179133i	−0.647046	−	0.762451i	$-0.723996\pi$
$431$	−6.44133	+	3.71890i	−0.310268	+	0.179133i	0.336779	+	0.941584i	$0.390663\pi$
$432$		0			0
$433$		−	6.40343i		−	0.307729i	−0.988092	−	0.153865i	$-0.950828\pi$
$433$		−	6.40343i		−	0.307729i	0.988092	−	0.153865i	$-0.0491720\pi$
$434$	−3.86138	−	9.03443i	−0.185352	−	0.433666i
$435$		0			0
$436$	5.26044	−	9.11136i	0.251930	−	0.436355i
$437$	−18.5255	−	32.0872i	−0.886197	−	1.53494i
$438$		0			0
$439$	−17.7661	−	10.2573i	−0.847930	−	0.489553i	0.0120217	−	0.999928i	$-0.496173\pi$
$439$	−17.7661	−	10.2573i	−0.847930	−	0.489553i	−0.859952	+	0.510375i	$0.829507\pi$
$440$	−3.17602			−0.151411
$441$		0			0
$442$	8.16667			0.388449
$443$	22.4927	+	12.9861i	1.06866	+	0.616990i	0.927815	−	0.373041i	$-0.121685\pi$
$443$	22.4927	+	12.9861i	1.06866	+	0.616990i	0.140844	+	0.990032i	$0.455018\pi$
$444$		0			0
$445$	−5.40249	−	9.35738i	−0.256102	−	0.443582i
$446$	0.553917	−	0.959412i	0.0262287	−	0.0454295i
$447$		0			0
$448$	−1.03982	−	2.43285i	−0.0491269	−	0.114942i
$449$			2.44022i			0.115161i	0.998341	+	0.0575805i	$0.0183386\pi$
$449$			2.44022i			0.115161i	−0.998341	+	0.0575805i	$0.981661\pi$
$450$		0			0
$451$	7.49671	−	4.32823i	0.353006	−	0.203808i
$452$	−4.76466	+	2.75088i	−0.224111	+	0.129390i
$453$		0			0
$454$		−	4.39997i		−	0.206501i
$455$	0.285405	−	2.37312i	0.0133800	−	0.111254i
$456$		0			0
$457$	−13.6605	+	23.6607i	−0.639011	+	1.10680i	0.346639	+	0.937998i	$0.387323\pi$
$457$	−13.6605	+	23.6607i	−0.639011	+	1.10680i	−0.985650	+	0.168801i	$0.946011\pi$
$458$	−1.95937	−	3.39374i	−0.0915555	−	0.158579i
$459$		0			0
$460$	4.28846	+	2.47594i	0.199950	+	0.115441i
$461$	−12.7947			−0.595910			−0.297955	−	0.954580i	$-0.596304\pi$
$461$	−12.7947			−0.595910			−0.297955	+	0.954580i	$0.596304\pi$
$462$		0			0
$463$	−27.4026			−1.27350			−0.636752	−	0.771068i	$-0.719723\pi$
$463$	−27.4026			−1.27350			−0.636752	+	0.771068i	$0.719723\pi$
$464$	−0.0191795	−	0.0110733i	−0.000890384	−	0.000514064i
$465$		0			0
$466$	10.4991	+	18.1850i	0.486361	+	0.842403i
$467$	12.8190	−	22.2031i	0.593191	−	1.02744i	−0.400609	−	0.916249i	$-0.631201\pi$
$467$	12.8190	−	22.2031i	0.593191	−	1.02744i	0.993799	−	0.111187i	$-0.0354653\pi$
$468$		0			0
$469$	17.7987	−	23.7421i	0.821867	−	1.09631i
$470$			5.93010i			0.273535i
$471$		0			0
$472$	−3.62130	+	2.09076i	−0.166684	+	0.0962348i
$473$	37.7531	−	21.7968i	1.73589	−	1.00222i
$474$		0			0
$475$		−	24.1468i		−	1.10793i
$476$	17.1002	+	2.05657i	0.783786	+	0.0942625i
$477$		0			0
$478$	13.1152	−	22.7163i	0.599877	−	1.03902i
$479$	−17.8762	−	30.9625i	−0.816784	−	1.41471i	−0.908040	−	0.418883i	$-0.862422\pi$
$479$	−17.8762	−	30.9625i	−0.816784	−	1.41471i	0.0912565	−	0.995827i	$-0.470912\pi$
$480$		0			0
$481$	3.97061	+	2.29243i	0.181044	+	0.104526i
$482$	4.90643			0.223482
$483$		0			0
$484$	8.45086			0.384130
$485$	6.40246	+	3.69646i	0.290721	+	0.167848i
$486$		0			0
$487$	−4.94736	−	8.56907i	−0.224186	−	0.388302i	0.731889	−	0.681424i	$-0.238639\pi$
$487$	−4.94736	−	8.56907i	−0.224186	−	0.388302i	−0.956075	+	0.293122i	$0.905306\pi$
$488$	4.09023	−	7.08448i	0.185156	−	0.320699i
$489$		0			0
$490$	1.19522	−	4.89721i	0.0539945	−	0.221233i
$491$		−	38.7331i		−	1.74800i	−0.485924	−	0.874001i	$-0.661517\pi$
$491$		−	38.7331i		−	1.74800i	0.485924	−	0.874001i	$-0.338483\pi$
$492$		0			0
$493$	0.124855	−	0.0720852i	0.00562320	−	0.00324655i
$494$	5.85396	−	3.37979i	0.263382	−	0.152064i
$495$		0			0
$496$			3.71351i			0.166742i
$497$	−6.03252	+	2.57835i	−0.270596	+	0.115655i
$498$		0			0
$499$	5.72202	−	9.91083i	0.256153	−	0.443670i	−0.709055	−	0.705153i	$-0.750878\pi$
$499$	5.72202	−	9.91083i	0.256153	−	0.443670i	0.965208	+	0.261483i	$0.0842116\pi$
$500$	3.41395	+	5.91313i	0.152676	+	0.264443i
$501$		0			0
$502$	24.5942	+	14.1995i	1.09769	+	0.633754i
$503$	23.3446			1.04088			0.520442	−	0.853897i	$-0.325767\pi$
$503$	23.3446			1.04088			0.520442	+	0.853897i	$0.325767\pi$
$504$		0			0
$505$	−3.27156			−0.145582
$506$	−26.2637	−	15.1634i	−1.16757	−	0.674094i
$507$		0			0
$508$	3.64498	+	6.31330i	0.161720	+	0.280107i
$509$	10.0656	−	17.4341i	0.446149	−	0.772753i	−0.551983	−	0.833856i	$-0.686129\pi$
$509$	10.0656	−	17.4341i	0.446149	−	0.772753i	0.998131	+	0.0611031i	$0.0194619\pi$
$510$		0			0
$511$	20.8890	+	15.6598i	0.924074	+	0.692750i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−18.1215	+	10.4625i	−0.799305	+	0.461479i
$515$	11.7413	−	6.77884i	0.517383	−	0.298711i
$516$		0			0
$517$		−	36.3176i		−	1.59724i
$518$	7.73677	+	5.80002i	0.339934	+	0.254838i
$519$		0			0
$520$	−0.451709	+	0.782383i	−0.0198088	+	0.0343098i
$521$	2.27906	+	3.94745i	0.0998474	+	0.172941i	0.911621	−	0.411031i	$-0.134831\pi$
$521$	2.27906	+	3.94745i	0.0998474	+	0.172941i	−0.811774	+	0.583972i	$0.801498\pi$
$522$		0			0
$523$	−24.2504	−	14.0009i	−1.06039	−	0.612219i	−0.134853	−	0.990866i	$-0.543056\pi$
$523$	−24.2504	−	14.0009i	−1.06039	−	0.612219i	−0.925541	+	0.378647i	$0.876389\pi$
$524$	−7.65288			−0.334318
$525$		0			0
$526$	−22.6082			−0.985764
$527$	−20.9356	−	12.0872i	−0.911970	−	0.526526i
$528$		0			0
$529$	12.1419	+	21.0304i	0.527909	+	0.914366i
$530$	−1.22883	+	2.12839i	−0.0533769	+	0.0924515i
$531$		0			0
$532$	13.1087	−	5.60277i	0.568335	−	0.242911i
$533$		−	2.46232i		−	0.106655i
$534$		0			0
$535$	0.634469	−	0.366311i	0.0274305	−	0.0158370i
$536$	−9.71272	+	5.60764i	−0.419526	+	0.242213i
$537$		0			0
$538$		−	20.1508i		−	0.868764i
$539$	−7.31985	+	29.9919i	−0.315288	+	1.29184i
$540$		0			0
$541$	4.70552	−	8.15020i	0.202306	−	0.350405i	−0.746965	−	0.664863i	$-0.768490\pi$
$541$	4.70552	−	8.15020i	0.202306	−	0.350405i	0.949271	+	0.314459i	$0.101823\pi$
$542$	0.435171	+	0.753738i	0.0186922	+	0.0323758i
$543$		0			0
$544$	−5.63769	−	3.25492i	−0.241714	−	0.139554i
$545$	−7.57647			−0.324540
$546$		0			0
$547$	21.4285			0.916216			0.458108	−	0.888896i	$-0.348527\pi$
$547$	21.4285			0.916216			0.458108	+	0.888896i	$0.348527\pi$
$548$	2.07631	+	1.19876i	0.0886954	+	0.0512083i
$549$		0			0
$550$	−9.88220	−	17.1165i	−0.421378	−	0.729849i
$551$	0.0596651	−	0.103343i	0.00254182	−	0.00440256i
$552$		0			0
$553$	−6.48042	−	0.779371i	−0.275575	−	0.0331422i
$554$			17.2719i			0.733812i
$555$		0			0
$556$	11.2559	−	6.49857i	0.477354	−	0.275601i
$557$	27.3775	−	15.8064i	1.16002	−	0.669740i	0.208714	−	0.977977i	$-0.433072\pi$
$557$	27.3775	−	15.8064i	1.16002	−	0.669740i	0.951310	+	0.308237i	$0.0997390\pi$
$558$		0			0
$559$		−	12.4002i		−	0.524471i
$560$	−1.14286	+	1.52448i	−0.0482946	+	0.0644211i
$561$		0			0
$562$	15.1526	−	26.2452i	0.639176	−	1.10709i
$563$	5.37125	+	9.30328i	0.226371	+	0.392087i	0.956730	−	0.290977i	$-0.0939804\pi$
$563$	5.37125	+	9.30328i	0.226371	+	0.392087i	−0.730359	+	0.683064i	$0.760647\pi$
$564$		0			0
$565$	3.43120	+	1.98101i	0.144352	+	0.0833415i
$566$	−5.80239			−0.243893
$567$		0			0
$568$	2.47961			0.104042
$569$	26.0909	+	15.0636i	1.09379	+	0.631499i	0.934582	−	0.355747i	$-0.115773\pi$
$569$	26.0909	+	15.0636i	1.09379	+	0.631499i	0.159205	+	0.987245i	$0.449107\pi$
$570$		0			0
$571$	4.77343	+	8.26783i	0.199762	+	0.345998i	0.948451	−	0.316923i	$-0.102650\pi$
$571$	4.77343	+	8.26783i	0.199762	+	0.345998i	−0.748689	+	0.662921i	$0.769316\pi$
$572$	2.76639	−	4.79153i	0.115669	−	0.200344i
$573$		0			0
$574$	0.620073	−	5.15587i	0.0258814	−	0.215202i
$575$			30.8156i			1.28510i
$576$		0			0
$577$	−32.3763	+	18.6925i	−1.34784	+	0.778178i	−0.987944	−	0.154813i	$-0.950523\pi$
$577$	−32.3763	+	18.6925i	−1.34784	+	0.778178i	−0.359900	+	0.932991i	$0.617189\pi$
$578$	21.9780	−	12.6890i	0.914164	−	0.527793i
$579$		0			0
$580$			0.0159485i			0.000662226i
$581$	−11.8461	−	27.7163i	−0.491461	−	1.14986i
$582$		0			0
$583$	7.52569	−	13.0349i	0.311682	−	0.539850i
$584$	−4.93377	−	8.54555i	−0.204161	−	0.353617i
$585$		0			0
$586$	14.9444	+	8.62817i	0.617348	+	0.356426i
$587$	21.7523			0.897813			0.448906	−	0.893579i	$-0.351814\pi$
$587$	21.7523			0.897813			0.448906	+	0.893579i	$0.351814\pi$
$588$		0			0
$589$	−20.0092			−0.824464
$590$	2.60782	+	1.50563i	0.107362	+	0.0619857i
$591$		0			0
$592$	−1.82735	−	3.16506i	−0.0751036	−	0.130083i
$593$	15.0439	−	26.0569i	0.617780	−	1.07003i	−0.372110	−	0.928189i	$-0.621365\pi$
$593$	15.0439	−	26.0569i	0.617780	−	1.07003i	0.989890	−	0.141838i	$-0.0453012\pi$
$594$		0			0
$595$	−4.87464	−	11.4051i	−0.199841	−	0.467565i
$596$		−	4.38750i		−	0.179719i
$597$		0			0
$598$	−7.47070	+	4.31321i	−0.305500	+	0.176380i
$599$	−9.96294	+	5.75211i	−0.407075	+	0.235025i	−0.689532	−	0.724255i	$-0.742184\pi$
$599$	−9.96294	+	5.75211i	−0.407075	+	0.235025i	0.282457	+	0.959280i	$0.408850\pi$
$600$		0			0
$601$			36.9294i			1.50638i	0.657801	+	0.753191i	$0.271487\pi$
$601$			36.9294i			1.50638i	−0.657801	+	0.753191i	$0.728513\pi$
$602$	3.12266	−	25.9647i	0.127270	−	1.05824i
$603$		0			0
$604$	8.27064	−	14.3252i	0.336528	−	0.582883i
$605$	−3.04288	−	5.27043i	−0.123711	−	0.214274i
$606$		0			0
$607$	−22.4941	−	12.9870i	−0.913008	−	0.527125i	−0.0316101	−	0.999500i	$-0.510063\pi$
$607$	−22.4941	−	12.9870i	−0.913008	−	0.527125i	−0.881398	+	0.472375i	$0.843397\pi$
$608$	−5.38821			−0.218521
$609$		0			0
$610$	−5.89104			−0.238521
$611$	−8.94648	−	5.16526i	−0.361936	−	0.208964i
$612$		0			0
$613$	−2.92902	−	5.07322i	−0.118302	−	0.204905i	0.800793	−	0.598941i	$-0.204412\pi$
$613$	−2.92902	−	5.07322i	−0.118302	−	0.204905i	−0.919095	+	0.394036i	$0.871078\pi$
$614$	6.79217	−	11.7644i	0.274110	−	0.474772i
$615$		0			0
$616$	6.99918	−	9.33635i	0.282005	−	0.376172i
$617$			42.9297i			1.72828i	0.503248	+	0.864142i	$0.332138\pi$
$617$			42.9297i			1.72828i	−0.503248	+	0.864142i	$0.667862\pi$
$618$		0			0
$619$	−24.5874	+	14.1955i	−0.988251	+	0.570567i	−0.904751	−	0.425941i	$-0.859943\pi$
$619$	−24.5874	+	14.1955i	−0.988251	+	0.570567i	−0.0835001	+	0.996508i	$0.526610\pi$
$620$	2.31595	−	1.33712i	0.0930109	−	0.0536999i
$621$		0			0
$622$			18.7792i			0.752976i
$623$	39.4130	+	4.74003i	1.57905	+	0.189905i
$624$		0			0
$625$	−8.74500	+	15.1468i	−0.349800	+	0.605872i
$626$	6.22185	+	10.7766i	0.248675	+	0.430718i
$627$		0			0
$628$	19.9547	+	11.5209i	0.796280	+	0.459733i
$629$	23.7915			0.948630
$630$		0			0
$631$	−12.6791			−0.504749			−0.252374	−	0.967630i	$-0.581211\pi$
$631$	−12.6791			−0.504749			−0.252374	+	0.967630i	$0.581211\pi$
$632$	2.13650	+	1.23351i	0.0849854	+	0.0490663i
$633$		0			0
$634$	13.9907	+	24.2326i	0.555641	+	0.962399i
$635$	2.62488	−	4.54643i	0.104165	−	0.180420i
$636$		0			0
$637$	6.34714	+	6.06876i	0.251483	+	0.240453i
$638$		−	0.0976732i		−	0.00386692i
$639$		0			0
$640$	0.623656	−	0.360068i	0.0246522	−	0.0142329i
$641$	−30.5826	+	17.6569i	−1.20794	+	0.697406i	−0.962309	−	0.271957i	$-0.912329\pi$
$641$	−30.5826	+	17.6569i	−1.20794	+	0.697406i	−0.245633	+	0.969363i	$0.578996\pi$
$642$		0			0
$643$		−	9.07091i		−	0.357722i	−0.983874	−	0.178861i	$-0.942759\pi$
$643$		−	9.07091i		−	0.357722i	0.983874	−	0.178861i	$-0.0572412\pi$
$644$	−16.7291	+	7.15014i	−0.659218	+	0.281755i
$645$		0			0
$646$	17.5382	−	30.3770i	0.690031	−	1.19517i
$647$	12.5913	+	21.8088i	0.495017	+	0.857394i	0.999983	−	0.00574473i	$-0.00182861\pi$
$647$	12.5913	+	21.8088i	0.495017	+	0.857394i	−0.504967	+	0.863139i	$0.668495\pi$
$648$		0			0
$649$	−15.9710	−	9.22089i	−0.626918	−	0.361952i
$650$	−5.62197			−0.220512
$651$		0			0
$652$	5.36190			0.209988
$653$	30.9107	+	17.8463i	1.20963	+	0.698380i	0.962679	−	0.270648i	$-0.0872378\pi$
$653$	30.9107	+	17.8463i	1.20963	+	0.698380i	0.246952	+	0.969028i	$0.420571\pi$
$654$		0			0
$655$	2.75556	+	4.77276i	0.107669	+	0.186487i
$656$	−0.981388	+	1.69981i	−0.0383168	+	0.0663666i
$657$		0			0
$658$	−17.4323	−	13.0685i	−0.679583	−	0.509462i
$659$		−	8.24284i		−	0.321096i	−0.987028	−	0.160548i	$-0.948674\pi$
$659$		−	8.24284i		−	0.321096i	0.987028	−	0.160548i	$-0.0513261\pi$
$660$		0			0
$661$	22.2734	−	12.8596i	0.866336	−	0.500179i	0.000207182	−	1.00000i	$-0.499934\pi$
$661$	22.2734	−	12.8596i	0.866336	−	0.500179i	0.866129	+	0.499821i	$0.166601\pi$
$662$	22.4713	−	12.9738i	0.873373	−	0.504242i
$663$		0			0
$664$			11.3925i			0.442115i
$665$	−8.21423	−	6.15796i	−0.318534	−	0.238795i
$666$		0			0
$667$	−0.0761434	+	0.131884i	−0.00294828	+	0.00510658i
$668$	−5.68447	−	9.84579i	−0.219939	−	0.380945i
$669$		0			0
$670$	6.99448	+	4.03826i	0.270220	+	0.156012i
$671$	36.0784			1.39279
$672$		0			0
$673$	40.0224			1.54275			0.771374	−	0.636382i	$-0.219570\pi$
$673$	40.0224			1.54275			0.771374	+	0.636382i	$0.219570\pi$
$674$	2.58248	+	1.49100i	0.0994735	+	0.0574310i
$675$		0			0
$676$	5.71310	+	9.89538i	0.219735	+	0.380592i
$677$	−24.5616	+	42.5420i	−0.943979	+	1.63502i	−0.186197	+	0.982512i	$0.559616\pi$
$677$	−24.5616	+	42.5420i	−0.943979	+	1.63502i	−0.757782	+	0.652508i	$0.773717\pi$
$678$		0			0
$679$	−24.9757	+	10.6748i	−0.958480	+	0.409661i
$680$			4.68797i			0.179775i
$681$		0			0
$682$	−14.1835	+	8.18888i	−0.543116	+	0.313568i
$683$	36.2000	−	20.9001i	1.38516	−	0.799720i	0.392391	−	0.919798i	$-0.371648\pi$
$683$	36.2000	−	20.9001i	1.38516	−	0.799720i	0.992764	+	0.120079i	$0.0383147\pi$
$684$		0			0
$685$		−	1.72653i		−	0.0659675i
$686$	11.7620	+	14.3058i	0.449077	+	0.546196i
$687$		0			0
$688$	−4.94223	+	8.56019i	−0.188421	+	0.326354i
$689$	−2.14068	−	3.70776i	−0.0815534	−	0.141255i
$690$		0			0
$691$	14.8071	+	8.54891i	0.563290	+	0.325216i	0.754465	−	0.656340i	$-0.227896\pi$
$691$	14.8071	+	8.54891i	0.563290	+	0.325216i	−0.191175	+	0.981556i	$0.561230\pi$
$692$	−23.8472			−0.906536
$693$		0			0
$694$	−1.10909			−0.0421006
$695$	−8.10574	−	4.67985i	−0.307468	−	0.177517i
$696$		0			0
$697$	−6.38868	−	11.0655i	−0.241989	−	0.419136i
$698$	10.2939	−	17.8295i	0.389628	−	0.674856i
$699$		0			0
$700$	−11.7719	−	1.41575i	−0.444934	−	0.0535103i
$701$			0.310638i			0.0117326i	0.999983	+	0.00586632i	$0.00186732\pi$
$701$			0.310638i			0.0117326i	−0.999983	+	0.00586632i	$0.998133\pi$
$702$		0			0
$703$	17.0540	−	9.84615i	0.643205	−	0.371355i
$704$	−3.81944	+	2.20516i	−0.143951	+	0.0831100i
$705$		0			0
$706$		−	24.8003i		−	0.933373i
$707$	7.20972	−	9.61719i	0.271149	−	0.361692i
$708$		0			0
$709$	7.44666	−	12.8980i	0.279665	−	0.484394i	−0.691636	−	0.722246i	$-0.743110\pi$
$709$	7.44666	−	12.8980i	0.279665	−	0.484394i	0.971302	+	0.237852i	$0.0764432\pi$
$710$	−0.892827	−	1.54642i	−0.0335072	−	0.0580362i
$711$		0			0
$712$	−12.9939	−	7.50204i	−0.486967	−	0.281151i
$713$	25.5353			0.956305
$714$		0			0
$715$	−3.98436			−0.149007
$716$	−9.25956	−	5.34601i	−0.346046	−	0.199790i
$717$		0			0
$718$	9.57681	+	16.5875i	0.357403	+	0.619041i
$719$	−3.97677	+	6.88798i	−0.148309	+	0.256878i	−0.930602	−	0.366031i	$-0.880716\pi$
$719$	−3.97677	+	6.88798i	−0.148309	+	0.256878i	0.782294	+	0.622910i	$0.214050\pi$
$720$		0			0
$721$	−5.94762	+	49.4540i	−0.221501	+	1.84176i
$722$		−	10.0328i		−	0.373383i
$723$		0			0
$724$	−19.7363	+	11.3947i	−0.733493	+	0.423482i
$725$	−0.0859510	+	0.0496238i	−0.00319214	+	0.00184298i
$726$		0			0
$727$			36.3509i			1.34818i	0.738649	+	0.674091i	$0.235464\pi$
$727$			36.3509i			1.34818i	−0.738649	+	0.674091i	$0.764536\pi$
$728$	−1.30447	−	3.05204i	−0.0483467	−	0.113116i
$729$		0			0
$730$	−3.55299	+	6.15395i	−0.131502	+	0.227768i
$731$	−32.1731	−	55.7254i	−1.18997	−	2.06108i
$732$		0			0
$733$	9.31396	+	5.37741i	0.344019	+	0.198619i	0.662048	−	0.749462i	$-0.269688\pi$
$733$	9.31396	+	5.37741i	0.344019	+	0.198619i	−0.318029	+	0.948081i	$0.603021\pi$
$734$	−16.7700			−0.618992
$735$		0			0
$736$	6.87632			0.253465
$737$	−42.8362	−	24.7315i	−1.57789	−	0.910995i
$738$		0			0
$739$	1.32601	+	2.29671i	0.0487779	+	0.0844858i	0.889383	−	0.457162i	$-0.151134\pi$
$739$	1.32601	+	2.29671i	0.0487779	+	0.0844858i	−0.840606	+	0.541648i	$0.817801\pi$
$740$	−1.31594	+	2.27928i	−0.0483749	+	0.0837878i
$741$		0			0
$742$	−3.54866	−	8.30277i	−0.130276	−	0.304804i
$743$		−	31.1629i		−	1.14325i	−0.820513	−	0.571627i	$-0.806312\pi$
$743$		−	31.1629i		−	1.14325i	0.820513	−	0.571627i	$-0.193688\pi$
$744$		0			0
$745$	−2.73629	+	1.57980i	−0.100250	+	0.0578793i
$746$	22.9509	−	13.2507i	0.840291	−	0.485142i
$747$		0			0
$748$		−	28.7104i		−	1.04976i
$749$	−0.321394	+	2.67237i	−0.0117435	+	0.0976461i
$750$		0			0
$751$	13.6273	−	23.6031i	0.497267	−	0.861291i	−0.502728	−	0.864444i	$-0.667670\pi$
$751$	13.6273	−	23.6031i	0.497267	−	0.861291i	0.999995	+	0.00315345i	$0.00100378\pi$
$752$	4.11735	+	7.13145i	0.150144	+	0.260057i
$753$		0			0
$754$	−0.0240609	−	0.0138915i	−0.000876245	−	0.000505900i
$755$	−11.9120			−0.433521
$756$		0			0
$757$	18.1863			0.660993			0.330496	−	0.943807i	$-0.392784\pi$
$757$	18.1863			0.660993			0.330496	+	0.943807i	$0.392784\pi$
$758$	14.5273	+	8.38734i	0.527655	+	0.304642i
$759$		0			0
$760$	1.94012	+	3.36039i	0.0703756	+	0.121894i
$761$	4.08064	−	7.06787i	0.147923	−	0.256210i	−0.782537	−	0.622605i	$-0.786075\pi$
$761$	4.08064	−	7.06787i	0.147923	−	0.256210i	0.930460	+	0.366394i	$0.119408\pi$
$762$		0			0
$763$	16.6967	−	22.2721i	0.604460	−	0.806303i
$764$			5.76035i			0.208402i
$765$		0			0
$766$	14.4971	−	8.36992i	0.523803	−	0.302418i
$767$	−4.54295	+	2.62288i	−0.164037	+	0.0947066i
$768$		0			0
$769$			49.7465i			1.79391i	0.442127	+	0.896953i	$0.354224\pi$
$769$			49.7465i			1.79391i	−0.442127	+	0.896953i	$0.645776\pi$
$770$	−8.34285	−	1.00336i	−0.300656	−	0.0361585i
$771$		0			0
$772$	−12.7218	+	22.0349i	−0.457869	+	0.793052i
$773$	9.09567	+	15.7542i	0.327148	+	0.566638i	0.981945	−	0.189168i	$-0.0605790\pi$
$773$	9.09567	+	15.7542i	0.327148	+	0.566638i	−0.654796	+	0.755805i	$0.727246\pi$
$774$		0			0
$775$	14.4122	+	8.32087i	0.517701	+	0.298895i
$776$	10.2660			0.368529
$777$		0			0
$778$	9.03565			0.323944
$779$	−9.15896	−	5.28793i	−0.328154	−	0.189460i
$780$		0			0
$781$	5.46792	+	9.47072i	0.195658	+	0.338889i
$782$	−22.3819	+	38.7666i	−0.800374	+	1.38629i
$783$		0			0
$784$	−1.96284	−	6.71917i	−0.0701015	−	0.239970i
$785$		−	16.5932i		−	0.592236i
$786$		0			0
$787$	1.42794	−	0.824423i	0.0509006	−	0.0293875i	−0.474334	−	0.880345i	$-0.657311\pi$
$787$	1.42794	−	0.824423i	0.0509006	−	0.0293875i	0.525234	+	0.850958i	$0.323978\pi$
$788$	0.115969	−	0.0669548i	0.00413123	−	0.00238517i
$789$		0			0
$790$		−	1.77659i		−	0.0632082i
$791$	−13.3850	+	5.72083i	−0.475914	+	0.203409i
$792$		0			0
$793$	5.13123	−	8.88756i	0.182215	−	0.315606i
$794$	7.79420	+	13.4999i	0.276606	+	0.479095i
$795$		0			0
$796$	−3.89988	−	2.25160i	−0.138228	−	0.0798058i
$797$	−36.4437			−1.29090			−0.645451	−	0.763802i	$-0.723330\pi$
$797$	−36.4437			−1.29090			−0.645451	+	0.763802i	$0.723330\pi$
$798$		0			0
$799$	−53.6065			−1.89646
$800$	3.88101	+	2.24070i	0.137214	+	0.0792208i
$801$		0			0
$802$	6.21840	+	10.7706i	0.219579	+	0.380322i
$803$	21.7595	−	37.6885i	0.767876	−	1.33000i
$804$		0			0
$805$	10.4828	+	7.85866i	0.369471	+	0.276981i
$806$			4.65864i			0.164094i
$807$		0			0
$808$	−3.93433	+	2.27149i	−0.138409	+	0.0799107i
$809$	−13.6983	+	7.90874i	−0.481608	+	0.278057i	−0.721086	−	0.692845i	$-0.756357\pi$
$809$	−13.6983	+	7.90874i	−0.481608	+	0.278057i	0.239478	+	0.970902i	$0.423024\pi$
$810$		0			0
$811$		−	19.4667i		−	0.683567i	−0.939779	−	0.341783i	$-0.888969\pi$
$811$		−	19.4667i		−	0.683567i	0.939779	−	0.341783i	$-0.111031\pi$
$812$	−0.0468828	−	0.0351466i	−0.00164526	−	0.00123340i
$813$		0			0
$814$	8.05919	−	13.9589i	0.282474	−	0.489260i
$815$	−1.93065	−	3.34398i	−0.0676276	−	0.117135i
$816$		0			0
$817$	−46.1241	−	26.6298i	−1.61368	−	0.931657i
$818$	−1.37150			−0.0479533
$819$		0			0
$820$	1.41347			0.0493604
$821$	18.4672	+	10.6620i	0.644508	+	0.372107i	0.786349	−	0.617783i	$-0.211969\pi$
$821$	18.4672	+	10.6620i	0.644508	+	0.372107i	−0.141841	+	0.989889i	$0.545302\pi$
$822$		0			0
$823$	6.97099	+	12.0741i	0.242993	+	0.420877i	0.961566	−	0.274575i	$-0.0885373\pi$
$823$	6.97099	+	12.0741i	0.242993	+	0.420877i	−0.718572	+	0.695452i	$0.755204\pi$
$824$	9.41328	−	16.3043i	0.327927	−	0.567986i
$825$		0			0
$826$	−10.1730	+	4.34802i	−0.353964	+	0.151287i
$827$		−	27.2974i		−	0.949224i	−0.880195	−	0.474612i	$-0.842588\pi$
$827$		−	27.2974i		−	0.949224i	0.880195	−	0.474612i	$-0.157412\pi$
$828$		0			0
$829$	−33.1694	+	19.1504i	−1.15202	+	0.665119i	−0.949379	−	0.314134i	$-0.898286\pi$
$829$	−33.1694	+	19.1504i	−1.15202	+	0.665119i	−0.202642	+	0.979253i	$0.564953\pi$
$830$	7.10500	−	4.10207i	0.246618	−	0.142385i
$831$		0			0
$832$			1.25451i			0.0434923i
$833$	44.2695	+	10.8045i	1.53385	+	0.374352i
$834$		0			0
$835$	−4.09359	+	7.09031i	−0.141665	+	0.245370i
$836$	−11.8819	−	20.5800i	−0.410942	−	0.711773i
$837$		0			0
$838$	13.2111	+	7.62742i	0.456369	+	0.263485i
$839$	−5.81634			−0.200803			−0.100401	−	0.994947i	$-0.532013\pi$
$839$	−5.81634			−0.200803			−0.100401	+	0.994947i	$0.532013\pi$
$840$		0			0
$841$	28.9995			0.999983
$842$	−8.11907	−	4.68755i	−0.279802	−	0.161544i
$843$		0			0
$844$	−12.8847	−	22.3169i	−0.443508	−	0.768179i
$845$	4.11421	−	7.12602i	0.141533	−	0.245143i
$846$		0			0
$847$	22.1989	+	2.66977i	0.762764	+	0.0917343i
$848$			3.41277i			0.117195i
$849$		0			0
$850$	−25.2648	+	14.5866i	−0.866574	+	0.500317i
$851$	−21.7640	+	12.5654i	−0.746060	+	0.430738i
$852$		0			0
$853$		−	51.7422i		−	1.77162i	−0.464047	−	0.885810i	$-0.653603\pi$
$853$		−	51.7422i		−	1.77162i	0.464047	−	0.885810i	$-0.346397\pi$
$854$	12.9824	−	17.3175i	0.444249	−	0.592593i
$855$		0			0
$856$	0.508669	−	0.881040i	0.0173859	−	0.0301133i
$857$	0.717546	+	1.24283i	0.0245109	+	0.0424542i	0.878021	−	0.478623i	$-0.158864\pi$
$857$	0.717546	+	1.24283i	0.0245109	+	0.0424542i	−0.853510	+	0.521077i	$0.825530\pi$
$858$		0			0
$859$	−2.35458	−	1.35942i	−0.0803372	−	0.0463827i	0.459293	−	0.888285i	$-0.348103\pi$
$859$	−2.35458	−	1.35942i	−0.0803372	−	0.0463827i	−0.539630	+	0.841902i	$0.681436\pi$
$860$	7.11815			0.242727
$861$		0			0
$862$	7.43780			0.253333
$863$	−29.2938	−	16.9128i	−0.997171	−	0.575717i	−0.0897610	−	0.995963i	$-0.528610\pi$
$863$	−29.2938	−	16.9128i	−0.997171	−	0.575717i	−0.907410	+	0.420246i	$0.861944\pi$
$864$		0			0
$865$	8.58663	+	14.8725i	0.291954	+	0.505679i
$866$	−3.20172	+	5.54553i	−0.108799	+	0.188445i
$867$		0			0
$868$	−1.17316	+	9.75474i	−0.0398196	+	0.331097i
$869$			10.8803i			0.369090i
$870$		0			0
$871$	−12.1847	+	7.03485i	−0.412863	+	0.238367i
$872$	−9.11136	+	5.26044i	−0.308549	+	0.178141i
$873$		0			0
$874$			37.0511i			1.25327i
$875$	7.09978	+	16.6113i	0.240016	+	0.561564i
$876$		0			0
$877$	−1.10648	+	1.91648i	−0.0373632	+	0.0647150i	−0.884102	−	0.467293i	$-0.845229\pi$
$877$	−1.10648	+	1.91648i	−0.0373632	+	0.0647150i	0.846739	+	0.532008i	$0.178563\pi$
$878$	10.2573	+	17.7661i	0.346166	+	0.599577i
$879$		0			0
$880$	2.75052	+	1.58801i	0.0927199	+	0.0535319i
$881$	−48.6451			−1.63890			−0.819448	−	0.573153i	$-0.805720\pi$
$881$	−48.6451			−1.63890			−0.819448	+	0.573153i	$0.805720\pi$
$882$		0			0
$883$	1.22677			0.0412841			0.0206420	−	0.999787i	$-0.493429\pi$
$883$	1.22677			0.0412841			0.0206420	+	0.999787i	$0.493429\pi$
$884$	−7.07254	−	4.08333i	−0.237875	−	0.137337i
$885$		0			0
$886$	−12.9861	−	22.4927i	−0.436278	−	0.755656i
$887$	−15.4263	+	26.7192i	−0.517966	+	0.897143i	0.481816	+	0.876272i	$0.339977\pi$
$887$	−15.4263	+	26.7192i	−0.517966	+	0.897143i	−0.999782	+	0.0208707i	$0.993356\pi$
$888$		0			0
$889$	7.58025	+	17.7354i	0.254234	+	0.594827i
$890$			10.8050i			0.362184i
$891$		0			0
$892$	−0.959412	+	0.553917i	−0.0321235	+	0.0185465i
$893$	−38.4258	+	22.1851i	−1.28587	+	0.742397i
$894$		0			0
$895$			7.69971i			0.257373i
$896$	−0.315916	+	2.62682i	−0.0105540	+	0.0877560i
$897$		0			0
$898$	1.22011	−	2.11329i	0.0407156	−	0.0705215i
$899$	0.0411207	+	0.0712232i	0.00137145	+	0.00237543i
$900$		0			0
$901$	−19.2401	−	11.1083i	−0.640981	−	0.370071i
$902$	−8.65646			−0.288229
$903$		0			0
$904$	5.50175			0.182986
$905$	14.2128	+	8.20576i	0.472449	+	0.272769i
$906$		0			0
$907$	8.23138	+	14.2572i	0.273318	+	0.473401i	0.969709	−	0.244261i	$-0.0785454\pi$
$907$	8.23138	+	14.2572i	0.273318	+	0.473401i	−0.696391	+	0.717662i	$0.745212\pi$
$908$	−2.19998	+	3.81048i	−0.0730090	+	0.126455i
$909$		0			0
$910$	−1.43373	+	1.91248i	−0.0475276	+	0.0633981i
$911$			13.8920i			0.460264i	0.973159	+	0.230132i	$0.0739158\pi$
$911$			13.8920i			0.460264i	−0.973159	+	0.230132i	$0.926084\pi$
$912$		0			0
$913$	−43.5130	+	25.1222i	−1.44007	+	0.831425i
$914$	23.6607	−	13.6605i	0.782625	−	0.451849i
$915$		0			0
$916$			3.91875i			0.129479i
$917$	−20.1028	−	2.41767i	−0.663852	−	0.0798385i
$918$		0			0
$919$	−17.8502	+	30.9174i	−0.588822	+	1.01987i	0.405565	+	0.914066i	$0.367075\pi$
$919$	−17.8502	+	30.9174i	−0.588822	+	1.01987i	−0.994387	+	0.105804i	$0.966258\pi$
$920$	−2.47594	−	4.28846i	−0.0816294	−	0.141386i
$921$		0			0
$922$	11.0806	+	6.39736i	0.364919	+	0.210686i
$923$	3.11070			0.102390
$924$		0			0
$925$	−16.3782			−0.538512
$926$	23.7313	+	13.7013i	0.779859	+	0.450252i
$927$		0			0
$928$	0.0110733	+	0.0191795i	0.000363498	+	0.000629597i
$929$	−2.66526	+	4.61636i	−0.0874443	+	0.151458i	−0.906430	−	0.422356i	$-0.861203\pi$
$929$	−2.66526	+	4.61636i	−0.0874443	+	0.151458i	0.818986	+	0.573814i	$0.194537\pi$
$930$		0			0
$931$	36.2043	−	10.5762i	1.18655	−	0.346621i
$932$		−	20.9982i		−	0.687819i
$933$		0			0
$934$	−22.2031	+	12.8190i	−0.726507	+	0.419449i
$935$	−17.9054	+	10.3377i	−0.585570	+	0.338079i
$936$		0			0
$937$			0.645033i			0.0210723i	0.999944	+	0.0105362i	$0.00335383\pi$
$937$			0.645033i			0.0210723i	−0.999944	+	0.0105362i	$0.996646\pi$
$938$	−27.2851	+	11.6619i	−0.890892	+	0.380774i
$939$		0			0
$940$	2.96505	−	5.13561i	0.0967092	−	0.167505i
$941$	5.14487	+	8.91117i	0.167718	+	0.290496i	0.937617	−	0.347670i	$-0.113027\pi$
$941$	5.14487	+	8.91117i	0.167718	+	0.290496i	−0.769899	+	0.638165i	$0.779694\pi$
$942$		0			0
$943$	11.6885	+	6.74834i	0.380629	+	0.219756i
$944$	4.18151			0.136097
$945$		0			0
$946$	−43.5935			−1.41735
$947$	4.26637	+	2.46319i	0.138638	+	0.0800429i	0.567715	−	0.823225i	$-0.307828\pi$
$947$	4.26637	+	2.46319i	0.138638	+	0.0800429i	−0.429077	+	0.903268i	$0.641161\pi$
$948$		0			0
$949$	−6.18947	−	10.7205i	−0.200919	−	0.348002i
$950$	−12.0734	+	20.9117i	−0.391712	+	0.678465i
$951$		0			0
$952$	−13.7809	−	10.3311i	−0.446642	−	0.334834i
$953$		−	6.13857i		−	0.198848i	−0.995045	−	0.0994239i	$-0.968300\pi$
$953$		−	6.13857i		−	0.198848i	0.995045	−	0.0994239i	$-0.0317000\pi$
$954$		0			0
$955$	3.59248	−	2.07412i	0.116250	−	0.0671168i
$956$	−22.7163	+	13.1152i	−0.734696	+	0.424177i
$957$		0			0
$958$			35.7524i			1.15511i
$959$	5.07538	+	3.80486i	0.163893	+	0.122865i
$960$		0			0
$961$	−8.60492	+	14.9042i	−0.277578	+	0.480779i
$962$	−2.29243	−	3.97061i	−0.0739109	−	0.128017i
$963$		0			0
$964$	−4.24909	−	2.45321i	−0.136854	−	0.0790127i
$965$	18.3229			0.589835
$966$		0			0
$967$	14.7940			0.475744			0.237872	−	0.971296i	$-0.423550\pi$
$967$	14.7940			0.475744			0.237872	+	0.971296i	$0.423550\pi$
$968$	−7.31866	−	4.22543i	−0.235231	−	0.135811i
$969$		0			0
$970$	−3.69646	−	6.40246i	−0.118686	−	0.205571i
$971$	3.00256	−	5.20059i	0.0963569	−	0.166895i	−0.813817	−	0.581121i	$-0.802614\pi$
$971$	3.00256	−	5.20059i	0.0963569	−	0.166895i	0.910174	+	0.414226i	$0.135948\pi$
$972$		0			0
$973$	31.6201	−	13.5147i	1.01369	−	0.433261i
$974$			9.89471i			0.317047i
$975$		0			0
$976$	−7.08448	+	4.09023i	−0.226769	+	0.130925i
$977$	−7.64962	+	4.41651i	−0.244733	+	0.141297i	−0.617350	−	0.786688i	$-0.711794\pi$
$977$	−7.64962	+	4.41651i	−0.244733	+	0.141297i	0.372617	+	0.927985i	$0.378460\pi$
$978$		0			0
$979$		−	66.1727i		−	2.11489i
$980$	−3.48369	+	3.64350i	−0.111283	+	0.116387i
$981$		0			0
$982$	−19.3666	+	33.5439i	−0.618012	+	1.07043i
$983$	21.0094	+	36.3893i	0.670094	+	1.16064i	0.977877	+	0.209181i	$0.0670797\pi$
$983$	21.0094	+	36.3893i	0.670094	+	1.16064i	−0.307783	+	0.951457i	$0.599587\pi$
$984$		0			0
$985$	−0.0835136	−	0.0482166i	−0.00266096	−	0.00153631i
$986$	−0.144170			−0.00459132
$987$		0			0
$988$	−6.75957			−0.215051
$989$	58.8626	+	33.9843i	1.87172	+	1.08064i
$990$		0			0
$991$	7.95731	+	13.7825i	0.252772	+	0.437815i	0.964288	−	0.264856i	$-0.0853243\pi$
$991$	7.95731	+	13.7825i	0.252772	+	0.437815i	−0.711516	+	0.702670i	$0.751991\pi$
$992$	1.85676	−	3.21600i	0.0589521	−	0.102108i
$993$		0			0
$994$	6.51349	+	0.783349i	0.206595	+	0.0248463i
$995$			3.24291i			0.102807i
$996$		0			0
$997$	24.7367	−	14.2817i	0.783419	−	0.452307i	−0.0542215	−	0.998529i	$-0.517268\pi$
$997$	24.7367	−	14.2817i	0.783419	−	0.452307i	0.837641	+	0.546222i	$0.183934\pi$
$998$	−9.91083	+	5.72202i	−0.313722	+	0.181127i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.k.d.971.3	yes	16
3.2	odd	2		1134.2.k.c.971.6	yes	16
7.3	odd	6		1134.2.k.c.647.6	✓	16
9.2	odd	6		1134.2.l.h.215.2		16
9.4	even	3		1134.2.t.g.593.6		16
9.5	odd	6		1134.2.t.h.593.3		16
9.7	even	3		1134.2.l.g.215.7		16
21.17	even	6	inner	1134.2.k.d.647.3	yes	16
63.31	odd	6		1134.2.l.h.269.6		16
63.38	even	6		1134.2.t.g.1025.6		16
63.52	odd	6		1134.2.t.h.1025.3		16
63.59	even	6		1134.2.l.g.269.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.k.c.647.6	✓	16	7.3	odd	6
1134.2.k.c.971.6	yes	16	3.2	odd	2
1134.2.k.d.647.3	yes	16	21.17	even	6	inner
1134.2.k.d.971.3	yes	16	1.1	even	1	trivial
1134.2.l.g.215.7		16	9.7	even	3
1134.2.l.g.269.3		16	63.59	even	6
1134.2.l.h.215.2		16	9.2	odd	6
1134.2.l.h.269.6		16	63.31	odd	6
1134.2.t.g.593.6		16	9.4	even	3
1134.2.t.g.1025.6		16	63.38	even	6
1134.2.t.h.593.3		16	9.5	odd	6
1134.2.t.h.1025.3		16	63.52	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.360068 - 0.623656i) q^{5} +(1.03982 + 2.43285i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.360068 - 0.623656i) q^{5} +(1.03982 + 2.43285i) q^{7} -1.00000i q^{8} +(-0.623656 + 0.360068i) q^{10} +(3.81944 - 2.20516i) q^{11} -1.25451i q^{13} +(0.315916 - 2.62682i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.25492 - 5.63769i) q^{17} +(-4.66633 - 2.69411i) q^{19} +0.720136 q^{20} -4.41031 q^{22} +(5.95507 + 3.43816i) q^{23} +(2.24070 + 3.88101i) q^{25} +(-0.627256 + 1.08644i) q^{26} +(-1.58700 + 2.11694i) q^{28} +0.0221465i q^{29} +(3.21600 - 1.85676i) q^{31} +(0.866025 - 0.500000i) q^{32} +6.50984i q^{34} +(1.89167 + 0.227503i) q^{35} +(-1.82735 + 3.16506i) q^{37} +(2.69411 + 4.66633i) q^{38} +(-0.623656 - 0.360068i) q^{40} +1.96278 q^{41} +9.88445 q^{43} +(3.81944 + 2.20516i) q^{44} +(-3.43816 - 5.95507i) q^{46} +(4.11735 - 7.13145i) q^{47} +(-4.83755 + 5.05946i) q^{49} -4.48140i q^{50} +(1.08644 - 0.627256i) q^{52} +(2.95555 - 1.70638i) q^{53} -3.17602i q^{55} +(2.43285 - 1.03982i) q^{56} +(0.0110733 - 0.0191795i) q^{58} +(-2.09076 - 3.62130i) q^{59} +(7.08448 + 4.09023i) q^{61} -3.71351 q^{62} -1.00000 q^{64} +(-0.782383 - 0.451709i) q^{65} +(-5.60764 - 9.71272i) q^{67} +(3.25492 - 5.63769i) q^{68} +(-1.52448 - 1.14286i) q^{70} +2.47961i q^{71} +(8.54555 - 4.93377i) q^{73} +(3.16506 - 1.82735i) q^{74} -5.38821i q^{76} +(9.33635 + 6.99918i) q^{77} +(-1.23351 + 2.13650i) q^{79} +(0.360068 + 0.623656i) q^{80} +(-1.69981 - 0.981388i) q^{82} -11.3925 q^{83} -4.68797 q^{85} +(-8.56019 - 4.94223i) q^{86} +(-2.20516 - 3.81944i) q^{88} +(7.50204 - 12.9939i) q^{89} +(3.05204 - 1.30447i) q^{91} +6.87632i q^{92} +(-7.13145 + 4.11735i) q^{94} +(-3.36039 + 1.94012i) q^{95} +10.2660i q^{97} +(6.71917 - 1.96284i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 + 8 * q^7	\( 16 q + 8 q^{4} + 8 q^{7} + 12 q^{11} + 12 q^{14} - 8 q^{16} + 12 q^{23} - 8 q^{25} + 4 q^{28} + 12 q^{31} + 60 q^{35} + 4 q^{37} - 12 q^{38} - 48 q^{41} - 32 q^{43} + 12 q^{44} + 4 q^{49} - 12 q^{52} + 12 q^{56} - 12 q^{58} - 24 q^{59} - 12 q^{61} - 48 q^{62} - 16 q^{64} + 48 q^{65} - 4 q^{67} - 24 q^{70} + 36 q^{73} + 36 q^{74} + 84 q^{77} + 8 q^{79} - 72 q^{83} + 24 q^{85} + 24 q^{86} + 24 q^{89} - 12 q^{91} - 36 q^{94} + 12 q^{95} + 36 q^{98}+O(q^{100}) \) 16 * q + 8 * q^4 + 8 * q^7 + 12 * q^11 + 12 * q^14 - 8 * q^16 + 12 * q^23 - 8 * q^25 + 4 * q^28 + 12 * q^31 + 60 * q^35 + 4 * q^37 - 12 * q^38 - 48 * q^41 - 32 * q^43 + 12 * q^44 + 4 * q^49 - 12 * q^52 + 12 * q^56 - 12 * q^58 - 24 * q^59 - 12 * q^61 - 48 * q^62 - 16 * q^64 + 48 * q^65 - 4 * q^67 - 24 * q^70 + 36 * q^73 + 36 * q^74 + 84 * q^77 + 8 * q^79 - 72 * q^83 + 24 * q^85 + 24 * q^86 + 24 * q^89 - 12 * q^91 - 36 * q^94 + 12 * q^95 + 36 * q^98

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