LMFDB - Embedded newform 784.2.x.l.557.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.6
Character	$\chi$	$=$	784.557
Dual form			784.2.x.l.373.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16343 + 0.804007i) q^{2} +(-1.90046 + 0.509227i) q^{3} +(0.707146 + 1.87081i) q^{4} +(-2.95714 - 0.792364i) q^{5} +(-2.62048 - 0.935533i) q^{6} +(-0.681431 + 2.74511i) q^{8} +(0.754366 - 0.435533i) q^{9} +O(q^{10})$	\(q+(1.16343 + 0.804007i) q^{2} +(-1.90046 + 0.509227i) q^{3} +(0.707146 + 1.87081i) q^{4} +(-2.95714 - 0.792364i) q^{5} +(-2.62048 - 0.935533i) q^{6} +(-0.681431 + 2.74511i) q^{8} +(0.754366 - 0.435533i) q^{9} +(-2.80337 - 3.29942i) q^{10} +(-1.13308 - 4.22870i) q^{11} +(-2.29657 - 3.19531i) q^{12} +(1.75410 + 1.75410i) q^{13} +6.02343 q^{15} +(-2.99989 + 2.64588i) q^{16} +(2.60235 - 4.50740i) q^{17} +(1.22782 + 0.0998021i) q^{18} +(-0.311715 + 1.16333i) q^{19} +(-0.608766 - 6.09258i) q^{20} +(2.08165 - 5.83081i) q^{22} +(5.33038 - 3.07750i) q^{23} +(-0.102853 - 5.56399i) q^{24} +(3.78672 + 2.18626i) q^{25} +(0.630466 + 3.45108i) q^{26} +(2.96185 - 2.96185i) q^{27} +(-6.24096 - 6.24096i) q^{29} +(7.00784 + 4.84288i) q^{30} +(1.39123 - 2.40969i) q^{31} +(-5.61747 + 0.666365i) q^{32} +(4.30674 + 7.45950i) q^{33} +(6.65164 - 3.15175i) q^{34} +(1.34825 + 1.10329i) q^{36} +(-5.61713 - 1.50511i) q^{37} +(-1.29799 + 1.10284i) q^{38} +(-4.22683 - 2.44036i) q^{39} +(4.19022 - 7.57775i) q^{40} +6.32956i q^{41} +(3.05937 - 3.05937i) q^{43} +(7.10987 - 5.11009i) q^{44} +(-2.57587 + 0.690201i) q^{45} +(8.67586 + 0.705206i) q^{46} +(-1.80192 - 3.12101i) q^{47} +(4.35382 - 6.55601i) q^{48} +(2.64782 + 5.58812i) q^{50} +(-2.65037 + 9.89133i) q^{51} +(-2.04119 + 4.52199i) q^{52} +(1.93405 + 7.21798i) q^{53} +(5.82725 - 1.06456i) q^{54} +13.4027i q^{55} -2.36961i q^{57} +(-2.24315 - 12.2787i) q^{58} +(-2.61179 - 9.74734i) q^{59} +(4.25944 + 11.2687i) q^{60} +(0.380638 - 1.42056i) q^{61} +(3.55601 - 1.68495i) q^{62} +(-7.07130 - 3.74121i) q^{64} +(-3.79723 - 6.57700i) q^{65} +(-0.986887 + 12.1413i) q^{66} +(1.32053 - 0.353834i) q^{67} +(10.2728 + 1.68112i) q^{68} +(-8.56304 + 8.56304i) q^{69} -10.0597i q^{71} +(0.681540 + 2.36761i) q^{72} +(-13.1391 - 7.58585i) q^{73} +(-5.32503 - 6.26730i) q^{74} +(-8.30982 - 2.22661i) q^{75} +(-2.39681 + 0.239487i) q^{76} +(-2.95556 - 6.23759i) q^{78} +(3.30674 + 5.72745i) q^{79} +(10.9676 - 5.44723i) q^{80} +(-5.42722 + 9.40022i) q^{81} +(-5.08901 + 7.36400i) q^{82} +(-7.41730 - 7.41730i) q^{83} +(-11.2670 + 11.2670i) q^{85} +(6.01912 - 1.09961i) q^{86} +(15.0388 + 8.68264i) q^{87} +(12.3804 - 0.228856i) q^{88} +(2.82449 - 1.63072i) q^{89} +(-3.55177 - 1.26801i) q^{90} +(9.52678 + 7.79591i) q^{92} +(-1.41691 + 5.28798i) q^{93} +(0.412907 - 5.07983i) q^{94} +(1.84357 - 3.19315i) q^{95} +(10.3365 - 4.12697i) q^{96} -7.66352 q^{97} +(-2.69650 - 2.69650i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} - 4 q^{3} + 6 q^{4} - 4 q^{5} + 8 q^{6} - 8 q^{8}+O(q^{10}) $ 24 * q - 2 * q^2 - 4 * q^3 + 6 * q^4 - 4 * q^5 + 8 * q^6 - 8 * q^8	$ 24 q - 2 q^{2} - 4 q^{3} + 6 q^{4} - 4 q^{5} + 8 q^{6} - 8 q^{8} + 4 q^{10} - 8 q^{12} - 48 q^{15} - 10 q^{16} + 8 q^{17} - 40 q^{20} + 28 q^{22} + 8 q^{24} + 20 q^{26} + 8 q^{27} - 8 q^{29} + 28 q^{30} + 8 q^{31} - 12 q^{32} + 16 q^{34} - 32 q^{36} + 20 q^{37} - 16 q^{38} + 8 q^{40} + 32 q^{43} - 14 q^{44} - 40 q^{45} + 28 q^{46} - 16 q^{47} + 32 q^{48} + 88 q^{50} + 16 q^{51} + 16 q^{52} - 4 q^{53} - 64 q^{54} - 14 q^{58} + 16 q^{59} - 60 q^{60} + 20 q^{61} + 16 q^{62} - 36 q^{64} - 32 q^{65} - 12 q^{66} - 24 q^{67} + 28 q^{68} - 8 q^{69} - 6 q^{72} + 38 q^{74} + 40 q^{75} + 96 q^{76} - 152 q^{78} - 24 q^{79} - 24 q^{80} + 44 q^{81} + 16 q^{82} - 40 q^{83} - 16 q^{85} - 38 q^{86} + 14 q^{88} - 80 q^{90} + 64 q^{92} + 48 q^{93} + 24 q^{94} + 16 q^{96} + 96 q^{97} + 64 q^{99}+O(q^{100}) $ 24 * q - 2 * q^2 - 4 * q^3 + 6 * q^4 - 4 * q^5 + 8 * q^6 - 8 * q^8 + 4 * q^10 - 8 * q^12 - 48 * q^15 - 10 * q^16 + 8 * q^17 - 40 * q^20 + 28 * q^22 + 8 * q^24 + 20 * q^26 + 8 * q^27 - 8 * q^29 + 28 * q^30 + 8 * q^31 - 12 * q^32 + 16 * q^34 - 32 * q^36 + 20 * q^37 - 16 * q^38 + 8 * q^40 + 32 * q^43 - 14 * q^44 - 40 * q^45 + 28 * q^46 - 16 * q^47 + 32 * q^48 + 88 * q^50 + 16 * q^51 + 16 * q^52 - 4 * q^53 - 64 * q^54 - 14 * q^58 + 16 * q^59 - 60 * q^60 + 20 * q^61 + 16 * q^62 - 36 * q^64 - 32 * q^65 - 12 * q^66 - 24 * q^67 + 28 * q^68 - 8 * q^69 - 6 * q^72 + 38 * q^74 + 40 * q^75 + 96 * q^76 - 152 * q^78 - 24 * q^79 - 24 * q^80 + 44 * q^81 + 16 * q^82 - 40 * q^83 - 16 * q^85 - 38 * q^86 + 14 * q^88 - 80 * q^90 + 64 * q^92 + 48 * q^93 + 24 * q^94 + 16 * q^96 + 96 * q^97 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.16343	+	0.804007i	0.822670	+	0.568519i
$2$	1.16343	+	0.804007i	0.822670	+	0.568519i
$3$	−1.90046	+	0.509227i	−1.09723	+	0.294002i	−0.761637	−	0.648004i	$-0.775604\pi$
$3$	−1.90046	+	0.509227i	−1.09723	+	0.294002i	−0.335595	+	0.942006i	$0.608937\pi$
$4$	0.707146	+	1.87081i	0.353573	+	0.935407i
$5$	−2.95714	−	0.792364i	−1.32247	−	0.354356i	−0.472570	−	0.881293i	$-0.656674\pi$
$5$	−2.95714	−	0.792364i	−1.32247	−	0.354356i	−0.849904	+	0.526937i	$0.823340\pi$
$6$	−2.62048	−	0.935533i	−1.06981	−	0.381930i
$7$		0			0
$7$		0			0
$8$	−0.681431	+	2.74511i	−0.240922	+	0.970544i
$9$	0.754366	−	0.435533i	0.251455	−	0.145178i
$10$	−2.80337	−	3.29942i	−0.886502	−	1.04337i
$11$	−1.13308	−	4.22870i	−0.341636	−	1.27500i	−0.896493	−	0.443057i	$-0.853894\pi$
$11$	−1.13308	−	4.22870i	−0.341636	−	1.27500i	0.554858	−	0.831945i	$-0.312773\pi$
$12$	−2.29657	−	3.19531i	−0.662963	−	0.922407i
$13$	1.75410	+	1.75410i	0.486499	+	0.486499i	0.907200	−	0.420701i	$-0.138216\pi$
$13$	1.75410	+	1.75410i	0.486499	+	0.486499i	−0.420701	+	0.907200i	$0.638216\pi$
$14$		0			0
$15$	6.02343			1.55524
$16$	−2.99989	+	2.64588i	−0.749972	+	0.661469i
$17$	2.60235	−	4.50740i	0.631163	−	1.09321i	−0.356152	−	0.934428i	$-0.615911\pi$
$17$	2.60235	−	4.50740i	0.631163	−	1.09321i	0.987314	−	0.158778i	$-0.0507553\pi$
$18$	1.22782	+	0.0998021i	0.289401	+	0.0235236i
$19$	−0.311715	+	1.16333i	−0.0715122	+	0.266887i	−0.992420	−	0.122894i	$-0.960783\pi$
$19$	−0.311715	+	1.16333i	−0.0715122	+	0.266887i	0.920908	+	0.389781i	$0.127449\pi$
$20$	−0.608766	−	6.09258i	−0.136124	−	1.36234i
$21$		0			0
$22$	2.08165	−	5.83081i	0.443809	−	1.24313i
$23$	5.33038	−	3.07750i	1.11146	−	0.641703i	0.172254	−	0.985053i	$-0.444895\pi$
$23$	5.33038	−	3.07750i	1.11146	−	0.641703i	0.939208	+	0.343350i	$0.111562\pi$
$24$	−0.102853	−	5.56399i	−0.0209947	−	1.13574i
$25$	3.78672	+	2.18626i	0.757344	+	0.437253i
$26$	0.630466	+	3.45108i	0.123645	+	0.676812i
$27$	2.96185	−	2.96185i	0.570007	−	0.570007i
$28$		0			0
$29$	−6.24096	−	6.24096i	−1.15892	−	1.15892i	−0.984709	−	0.174208i	$-0.944264\pi$
$29$	−6.24096	−	6.24096i	−1.15892	−	1.15892i	−0.174208	−	0.984709i	$-0.555736\pi$
$30$	7.00784	+	4.84288i	1.27945	+	0.884184i
$31$	1.39123	−	2.40969i	0.249873	−	0.432793i	−0.713617	−	0.700536i	$-0.752944\pi$
$31$	1.39123	−	2.40969i	0.249873	−	0.432793i	0.963490	+	0.267743i	$0.0862778\pi$
$32$	−5.61747	+	0.666365i	−0.993038	+	0.117798i
$33$	4.30674	+	7.45950i	0.749708	+	1.29853i
$34$	6.65164	−	3.15175i	1.14075	−	0.540520i
$35$		0			0
$36$	1.34825	+	1.10329i	0.224708	+	0.183882i
$37$	−5.61713	−	1.50511i	−0.923450	−	0.247438i	−0.234391	−	0.972142i	$-0.575310\pi$
$37$	−5.61713	−	1.50511i	−0.923450	−	0.247438i	−0.689060	+	0.724705i	$0.741976\pi$
$38$	−1.29799	+	1.10284i	−0.210561	+	0.178904i
$39$	−4.22683	−	2.44036i	−0.676834	−	0.390770i
$40$	4.19022	−	7.57775i	0.662532	−	1.19815i
$41$			6.32956i			0.988511i	0.869317	+	0.494255i	$0.164559\pi$
$41$			6.32956i			0.988511i	−0.869317	+	0.494255i	$0.835441\pi$
$42$		0			0
$43$	3.05937	−	3.05937i	0.466549	−	0.466549i	−0.434245	−	0.900795i	$-0.642985\pi$
$43$	3.05937	−	3.05937i	0.466549	−	0.466549i	0.900795	+	0.434245i	$0.142985\pi$
$44$	7.10987	−	5.11009i	1.07185	−	0.770375i
$45$	−2.57587	+	0.690201i	−0.383988	+	0.102889i
$46$	8.67586	+	0.705206i	1.27919	+	0.103977i
$47$	−1.80192	−	3.12101i	−0.262836	−	0.455246i	0.704158	−	0.710043i	$-0.251325\pi$
$47$	−1.80192	−	3.12101i	−0.262836	−	0.455246i	−0.966994	+	0.254797i	$0.917991\pi$
$48$	4.35382	−	6.55601i	0.628420	−	0.946279i
$49$		0			0
$50$	2.64782	+	5.58812i	0.374458	+	0.790279i
$51$	−2.65037	+	9.89133i	−0.371127	+	1.38506i
$52$	−2.04119	+	4.52199i	−0.283062	+	0.627087i
$53$	1.93405	+	7.21798i	0.265662	+	0.991466i	0.961844	+	0.273600i	$0.0882144\pi$
$53$	1.93405	+	7.21798i	0.265662	+	0.991466i	−0.696181	+	0.717866i	$0.745119\pi$
$54$	5.82725	−	1.06456i	0.792988	−	0.144868i
$55$			13.4027i			1.80722i
$56$		0			0
$57$		−	2.36961i		−	0.313862i
$58$	−2.24315	−	12.2787i	−0.294541	−	1.61227i
$59$	−2.61179	−	9.74734i	−0.340026	−	1.26900i	−0.898316	−	0.439350i	$-0.855209\pi$
$59$	−2.61179	−	9.74734i	−0.340026	−	1.26900i	0.558290	−	0.829646i	$-0.311458\pi$
$60$	4.25944	+	11.2687i	0.549892	+	1.45478i
$61$	0.380638	−	1.42056i	0.0487357	−	0.181884i	−0.937267	−	0.348611i	$-0.886653\pi$
$61$	0.380638	−	1.42056i	0.0487357	−	0.181884i	0.986003	+	0.166727i	$0.0533200\pi$
$62$	3.55601	−	1.68495i	0.451614	−	0.213988i
$63$		0			0
$64$	−7.07130	−	3.74121i	−0.883913	−	0.467652i
$65$	−3.79723	−	6.57700i	−0.470988	−	0.815776i
$66$	−0.986887	+	12.1413i	−0.121477	+	1.49449i
$67$	1.32053	−	0.353834i	0.161328	−	0.0432277i	−0.177251	−	0.984166i	$-0.556720\pi$
$67$	1.32053	−	0.353834i	0.161328	−	0.0432277i	0.338579	+	0.940938i	$0.390054\pi$
$68$	10.2728	+	1.68112i	1.24575	+	0.203866i
$69$	−8.56304	+	8.56304i	−1.03087	+	1.03087i
$70$		0			0
$71$		−	10.0597i		−	1.19386i	−0.802291	−	0.596932i	$-0.796386\pi$
$71$		−	10.0597i		−	1.19386i	0.802291	−	0.596932i	$-0.203614\pi$
$72$	0.681540	+	2.36761i	0.0803203	+	0.279025i
$73$	−13.1391	−	7.58585i	−1.53781	−	0.887857i	−0.998966	−	0.0454536i	$-0.985527\pi$
$73$	−13.1391	−	7.58585i	−1.53781	−	0.887857i	−0.538847	−	0.842404i	$-0.681140\pi$
$74$	−5.32503	−	6.26730i	−0.619022	−	0.728559i
$75$	−8.30982	−	2.22661i	−0.959535	−	0.257107i
$76$	−2.39681	+	0.239487i	−0.274933	+	0.0274711i
$77$		0			0
$78$	−2.95556	−	6.23759i	−0.334651	−	0.706268i
$79$	3.30674	+	5.72745i	0.372038	+	0.644388i	0.989879	−	0.141915i	$-0.0453259\pi$
$79$	3.30674	+	5.72745i	0.372038	+	0.644388i	−0.617841	+	0.786303i	$0.711993\pi$
$80$	10.9676	−	5.44723i	1.22621	−	0.609019i
$81$	−5.42722	+	9.40022i	−0.603025	+	1.04447i
$82$	−5.08901	+	7.36400i	−0.561987	+	0.813218i
$83$	−7.41730	−	7.41730i	−0.814154	−	0.814154i	0.171100	−	0.985254i	$-0.445268\pi$
$83$	−7.41730	−	7.41730i	−0.814154	−	0.814154i	−0.985254	+	0.171100i	$0.945268\pi$
$84$		0			0
$85$	−11.2670	+	11.2670i	−1.22208	+	1.22208i
$86$	6.01912	−	1.09961i	0.649058	−	0.118574i
$87$	15.0388	+	8.68264i	1.61232	+	0.930876i
$88$	12.3804	−	0.228856i	1.31975	−	0.0243962i
$89$	2.82449	−	1.63072i	0.299396	−	0.172856i	−0.342776	−	0.939417i	$-0.611367\pi$
$89$	2.82449	−	1.63072i	0.299396	−	0.172856i	0.642171	+	0.766561i	$0.278034\pi$
$90$	−3.55177	−	1.26801i	−0.374390	−	0.133660i
$91$		0			0
$92$	9.52678	+	7.79591i	0.993236	+	0.812780i
$93$	−1.41691	+	5.28798i	−0.146927	+	0.548337i
$94$	0.412907	−	5.07983i	0.0425881	−	0.523945i
$95$	1.84357	−	3.19315i	0.189146	−	0.327611i
$96$	10.3365	−	4.12697i	1.05496	−	0.421207i
$97$	−7.66352			−0.778112			−0.389056	−	0.921214i	$-0.627199\pi$
$97$	−7.66352			−0.778112			−0.389056	+	0.921214i	$0.627199\pi$
$98$		0			0
$99$	−2.69650	−	2.69650i	−0.271008	−	0.271008i
$100$	−1.41233	+	8.63025i	−0.141233	+	0.863025i
$101$	3.63555	+	13.5681i	0.361751	+	1.35007i	0.871772	+	0.489912i	$0.162971\pi$
$101$	3.63555	+	13.5681i	0.361751	+	1.35007i	−0.510021	+	0.860162i	$0.670362\pi$
$102$	−11.0362	+	9.37697i	−1.09275	+	0.928458i
$103$	−1.39602	+	0.805993i	−0.137554	+	0.0794169i	−0.567198	−	0.823582i	$-0.691972\pi$
$103$	−1.39602	+	0.805993i	−0.137554	+	0.0794169i	0.429644	+	0.902998i	$0.358639\pi$
$104$	−6.01049	+	3.61990i	−0.589377	+	0.354960i
$105$		0			0
$106$	−3.55317	+	9.95262i	−0.345114	+	0.966684i
$107$	−10.8240	−	2.90028i	−1.04640	−	0.280381i	−0.305634	−	0.952149i	$-0.598869\pi$
$107$	−10.8240	−	2.90028i	−1.04640	−	0.280381i	−0.740762	+	0.671768i	$0.765535\pi$
$108$	7.63552	+	3.44660i	0.734728	+	0.331650i
$109$	−7.77240	+	2.08261i	−0.744461	+	0.199478i	−0.611060	−	0.791584i	$-0.709257\pi$
$109$	−7.77240	+	2.08261i	−0.744461	+	0.199478i	−0.133401	+	0.991062i	$0.542590\pi$
$110$	−10.7759	+	15.5931i	−1.02744	+	1.48674i
$111$	11.4416			1.08599
$112$		0			0
$113$	15.2609			1.43563			0.717813	−	0.696235i	$-0.245143\pi$
$113$	15.2609			1.43563			0.717813	+	0.696235i	$0.245143\pi$
$114$	1.90518	−	2.75688i	0.178436	−	0.258205i
$115$	−18.2012	+	4.87699i	−1.69727	+	0.454782i
$116$	7.26240	−	16.0889i	0.674297	−	1.49382i
$117$	2.08720	+	0.559263i	0.192962	+	0.0517039i
$118$	4.79829	−	13.4403i	0.441718	−	1.23728i
$119$		0			0
$120$	−4.10455	+	16.5350i	−0.374693	+	1.50943i
$121$	−7.07180	+	4.08290i	−0.642891	+	0.371173i
$122$	1.58499	−	1.34669i	0.143498	−	0.121924i
$123$	−3.22318	−	12.0291i	−0.290624	−	1.08463i
$124$	5.49188	+	0.898739i	0.493186	+	0.0807092i
$125$	1.35834	+	1.35834i	0.121494	+	0.121494i
$126$		0			0
$127$	−1.80529			−0.160193			−0.0800966	−	0.996787i	$-0.525523\pi$
$127$	−1.80529			−0.160193			−0.0800966	+	0.996787i	$0.525523\pi$
$128$	−5.21902	−	10.0380i	−0.461300	−	0.887244i
$129$	−4.25630	+	7.37213i	−0.374746	+	0.649080i
$130$	0.870132	−	10.7049i	0.0763157	−	0.938880i
$131$	3.39881	−	12.6845i	0.296956	−	1.10825i	−0.642696	−	0.766121i	$-0.722184\pi$
$131$	3.39881	−	12.6845i	0.296956	−	1.10825i	0.939652	−	0.342132i	$-0.111149\pi$
$132$	−10.9098	+	13.3321i	−0.949579	+	1.16041i
$133$		0			0
$134$	1.82083	+	0.650051i	0.157296	+	0.0561559i
$135$	−11.1055	+	6.41174i	−0.955805	+	0.551835i
$136$	10.6000	+	10.2152i	0.908943	+	0.875949i
$137$	−6.87323	−	3.96826i	−0.587220	−	0.339031i	0.176778	−	0.984251i	$-0.443433\pi$
$137$	−6.87323	−	3.96826i	−0.587220	−	0.339031i	−0.763997	+	0.645219i	$0.776766\pi$
$138$	−16.8473	+	3.07777i	−1.43413	+	0.261997i
$139$	−2.06915	+	2.06915i	−0.175503	+	0.175503i	−0.789392	−	0.613889i	$-0.789604\pi$
$139$	−2.06915	+	2.06915i	−0.175503	+	0.175503i	0.613889	+	0.789392i	$0.289604\pi$
$140$		0			0
$141$	5.01377	+	5.01377i	0.422236	+	0.422236i
$142$	8.08806	−	11.7038i	0.678735	−	0.982157i
$143$	5.43003	−	9.40509i	0.454082	−	0.786493i
$144$	−1.11065	+	3.30251i	−0.0925539	+	0.275209i
$145$	13.5103	+	23.4005i	1.12197	+	1.94331i
$146$	−9.18735	−	19.3895i	−0.760350	−	1.60469i
$147$		0			0
$148$	−1.15636	−	11.5729i	−0.0950521	−	0.951289i
$149$	−12.5060	−	3.35096i	−1.02453	−	0.274521i	−0.292840	−	0.956161i	$-0.594600\pi$
$149$	−12.5060	−	3.35096i	−1.02453	−	0.274521i	−0.731688	+	0.681640i	$0.761267\pi$
$150$	−7.87770	−	9.27166i	−0.643211	−	0.757028i
$151$	−2.42743	−	1.40148i	−0.197541	−	0.114051i	0.397967	−	0.917400i	$-0.369716\pi$
$151$	−2.42743	−	1.40148i	−0.197541	−	0.114051i	−0.595508	+	0.803349i	$0.703049\pi$
$152$	−2.98107	−	1.64842i	−0.241797	−	0.133705i
$153$		−	4.53364i		−	0.366523i
$154$		0			0
$155$	−6.02343	+	6.02343i	−0.483813	+	0.483813i
$156$	1.57648	−	9.63330i	0.126219	−	0.771281i
$157$	−1.30974	+	0.350944i	−0.104529	+	0.0280084i	−0.310704	−	0.950507i	$-0.600565\pi$
$157$	−1.30974	+	0.350944i	−0.104529	+	0.0280084i	0.206176	+	0.978515i	$0.433898\pi$
$158$	−0.757737	+	9.32213i	−0.0602823	+	0.741629i
$159$	−7.35118	−	12.7326i	−0.582987	−	1.00976i
$160$	17.1397	+	2.48054i	1.35501	+	0.196104i
$161$		0			0
$162$	−13.8720	+	6.57299i	−1.08989	+	0.516423i
$163$	4.72925	−	17.6498i	0.370423	−	1.38244i	−0.489495	−	0.872006i	$-0.662819\pi$
$163$	4.72925	−	17.6498i	0.370423	−	1.38244i	0.859918	−	0.510432i	$-0.170515\pi$
$164$	−11.8414	+	4.47592i	−0.924660	+	0.349511i
$165$	−6.82501	−	25.4713i	−0.531326	−	1.98294i
$166$	−2.66596	−	14.5931i	−0.206919	−	1.13264i
$167$		−	1.96111i		−	0.151755i	−0.997117	−	0.0758775i	$-0.975824\pi$
$167$		−	1.96111i		−	0.151755i	0.997117	−	0.0758775i	$-0.0241758\pi$
$168$		0			0
$169$		−	6.84629i		−	0.526637i
$170$	−22.1672	+	4.04964i	−1.70014	+	0.310594i
$171$	0.271524	+	1.01334i	0.0207640	+	0.0774922i
$172$	7.88693	+	3.56009i	0.601373	+	0.271454i
$173$	−1.51549	+	5.65589i	−0.115221	+	0.430009i	−0.999303	−	0.0373213i	$-0.988117\pi$
$173$	−1.51549	+	5.65589i	−0.115221	+	0.430009i	0.884083	+	0.467330i	$0.154784\pi$
$174$	10.5157	+	22.1929i	0.797191	+	1.68244i
$175$		0			0
$176$	14.5877	+	9.68766i	1.09959	+	0.730235i
$177$	9.92722	+	17.1945i	0.746176	+	1.29241i
$178$	4.59722	+	0.373679i	0.344576	+	0.0280084i
$179$	12.9980	−	3.48281i	0.971519	−	0.260318i	0.262050	−	0.965054i	$-0.415602\pi$
$179$	12.9980	−	3.48281i	0.971519	−	0.260318i	0.709469	+	0.704737i	$0.248935\pi$
$180$	−3.11275	−	4.33089i	−0.232011	−	0.322806i
$181$	7.60424	−	7.60424i	0.565219	−	0.565219i	−0.365566	−	0.930785i	$-0.619125\pi$
$181$	7.60424	−	7.60424i	0.565219	−	0.565219i	0.930785	+	0.365566i	$0.119125\pi$
$182$		0			0
$183$			2.89355i			0.213897i
$184$	4.81579	+	16.7296i	0.355025	+	1.23332i
$185$	15.4181	+	8.90162i	1.13356	+	0.654460i
$186$	−5.90004	+	5.01299i	−0.432612	+	0.367570i
$187$	−22.0091	−	5.89733i	−1.60947	−	0.431256i
$188$	4.56461	−	5.57806i	0.332908	−	0.406822i
$189$		0			0
$190$	4.71218	−	2.23277i	0.341858	−	0.161982i
$191$	10.2439	+	17.7430i	0.741223	+	1.28384i	0.951939	+	0.306289i	$0.0990873\pi$
$191$	10.2439	+	17.7430i	0.741223	+	1.28384i	−0.210715	+	0.977547i	$0.567579\pi$
$192$	15.3439	+	3.50913i	1.10735	+	0.253250i
$193$	−6.35776	+	11.0120i	−0.457642	+	0.792659i	−0.998836	−	0.0482388i	$-0.984639\pi$
$193$	−6.35776	+	11.0120i	−0.457642	+	0.792659i	0.541194	+	0.840898i	$0.317972\pi$
$194$	−8.91598	−	6.16152i	−0.640130	−	0.442371i
$195$	10.5657	+	10.5657i	0.756624	+	0.756624i
$196$		0			0
$197$	−12.8638	+	12.8638i	−0.916509	+	0.916509i	−0.996774	−	0.0802649i	$-0.974423\pi$
$197$	−12.8638	+	12.8638i	−0.916509	+	0.916509i	0.0802649	+	0.996774i	$0.474423\pi$
$198$	−0.969187	−	5.30519i	−0.0688771	−	0.377023i
$199$	1.27174	+	0.734237i	0.0901510	+	0.0520487i	0.544398	−	0.838827i	$-0.316758\pi$
$199$	1.27174	+	0.734237i	0.0901510	+	0.0520487i	−0.454247	+	0.890876i	$0.650092\pi$
$200$	−8.58193	+	8.90519i	−0.606834	+	0.629692i
$201$	−2.32943	+	1.34490i	−0.164305	+	0.0948617i
$202$	−6.67911	+	18.7085i	−0.469940	+	1.31633i
$203$		0			0
$204$	−20.3790	+	2.03626i	−1.42682	+	0.142567i
$205$	5.01531	−	18.7174i	0.350284	−	1.30728i
$206$	−2.27220	−	0.184693i	−0.158312	−	0.0128681i
$207$	2.68070	−	4.64312i	0.186322	−	0.322719i
$208$	−9.90322	−	0.620972i	−0.686665	−	0.0430567i
$209$	5.27260			0.364713
$210$		0			0
$211$	0.534767	+	0.534767i	0.0368149	+	0.0368149i	0.725275	−	0.688460i	$-0.241713\pi$
$211$	0.534767	+	0.534767i	0.0368149	+	0.0368149i	−0.688460	+	0.725275i	$0.741713\pi$
$212$	−12.1358	+	8.72242i	−0.833493	+	0.599058i
$213$	5.12266	+	19.1180i	0.350999	+	1.30995i
$214$	−10.2611	−	12.0769i	−0.701437	−	0.825557i
$215$	−11.4711	+	6.62285i	−0.782324	+	0.451675i
$216$	6.11231	+	10.1489i	0.415890	+	0.690545i
$217$		0			0
$218$	−10.7171	−	3.82609i	−0.725853	−	0.259136i
$219$	28.8333	+	7.72585i	1.94837	+	0.522064i
$220$	−25.0739	+	9.47766i	−1.69048	+	0.638983i
$221$	12.4712	−	3.34165i	0.838903	−	0.224784i
$222$	13.3115	+	9.19911i	0.893409	+	0.617404i
$223$	−7.83775			−0.524855			−0.262427	−	0.964952i	$-0.584523\pi$
$223$	−7.83775			−0.524855			−0.262427	+	0.964952i	$0.584523\pi$
$224$		0			0
$225$	3.80876			0.253917
$226$	17.7550	+	12.2699i	1.18105	+	0.816181i
$227$	−0.338192	+	0.0906182i	−0.0224466	+	0.00601454i	−0.270025	−	0.962853i	$-0.587032\pi$
$227$	−0.338192	+	0.0906182i	−0.0224466	+	0.00601454i	0.247578	+	0.968868i	$0.420365\pi$
$228$	4.43309	−	1.67566i	0.293589	−	0.110973i
$229$	21.3140	+	5.71108i	1.40847	+	0.377399i	0.881379	−	0.472409i	$-0.156616\pi$
$229$	21.3140	+	5.71108i	1.40847	+	0.377399i	0.527092	+	0.849808i	$0.323282\pi$
$230$	−25.0970	−	8.95983i	−1.65485	−	0.590794i
$231$		0			0
$232$	21.3849	−	12.8794i	1.40399	−	0.845571i
$233$	8.24017	−	4.75746i	0.539831	−	0.311672i	−0.205179	−	0.978724i	$-0.565778\pi$
$233$	8.24017	−	4.75746i	0.539831	−	0.311672i	0.745011	+	0.667053i	$0.232444\pi$
$234$	1.97866	+	2.32879i	0.129349	+	0.152238i
$235$	2.85554	+	10.6570i	0.186275	+	0.695188i
$236$	16.3885	−	11.7790i	1.06680	−	0.766746i
$237$	−9.20091	−	9.20091i	−0.597663	−	0.597663i
$238$		0			0
$239$	18.8469			1.21910			0.609552	−	0.792746i	$-0.291349\pi$
$239$	18.8469			1.21910			0.609552	+	0.792746i	$0.291349\pi$
$240$	−18.0696	+	15.9372i	−1.16639	+	1.02874i
$241$	3.19914	−	5.54108i	0.206075	−	0.356932i	−0.744400	−	0.667734i	$-0.767264\pi$
$241$	3.19914	−	5.54108i	0.206075	−	0.356932i	0.950475	+	0.310802i	$0.100598\pi$
$242$	−11.5102	−	0.935594i	−0.739906	−	0.0601423i
$243$	2.27504	−	8.49058i	0.145944	−	0.544671i
$244$	2.92677	−	0.292441i	0.187367	−	0.0187216i
$245$		0			0
$246$	5.92151	−	16.5865i	0.377542	−	1.05751i
$247$	−2.58738	+	1.49382i	−0.164631	+	0.0950498i
$248$	5.66684	+	5.46113i	0.359845	+	0.346782i
$249$	17.8734	+	10.3192i	1.13268	+	0.653953i
$250$	0.488221	+	2.67245i	0.0308778	+	0.169021i
$251$	−2.93159	+	2.93159i	−0.185040	+	0.185040i	−0.793548	−	0.608508i	$-0.791768\pi$
$251$	−2.93159	+	2.93159i	−0.185040	+	0.185040i	0.608508	+	0.793548i	$0.291768\pi$
$252$		0			0
$253$	−19.0536	−	19.0536i	−1.19789	−	1.19789i
$254$	−2.10033	−	1.45146i	−0.131786	−	0.0910728i
$255$	15.6751	−	27.1500i	0.981611	−	1.70020i
$256$	1.99867	−	15.8747i	0.124917	−	0.992167i
$257$	−14.4838	−	25.0867i	−0.903475	−	1.56487i	−0.822951	−	0.568113i	$-0.807674\pi$
$257$	−14.4838	−	25.0867i	−0.903475	−	1.56487i	−0.0805246	−	0.996753i	$-0.525660\pi$
$258$	−10.8792	+	5.15487i	−0.677306	+	0.320928i
$259$		0			0
$260$	9.61914	−	11.7548i	0.596554	−	0.729002i
$261$	−7.42611	−	1.98982i	−0.459665	−	0.123167i
$262$	14.1527	−	12.0249i	0.874359	−	0.742902i
$263$	−0.298299	−	0.172223i	−0.0183939	−	0.0106197i	0.490775	−	0.871286i	$-0.336714\pi$
$263$	−0.298299	−	0.172223i	−0.0183939	−	0.0106197i	−0.509169	+	0.860667i	$0.670047\pi$
$264$	−23.4119	+	6.73936i	−1.44090	+	0.414779i
$265$		−	22.8771i		−	1.40533i
$266$		0			0
$267$	−4.53743	+	4.53743i	−0.277686	+	0.277686i
$268$	1.59576	+	2.22025i	0.0974768	+	0.135623i
$269$	13.4946	−	3.61587i	0.822781	−	0.220463i	0.177219	−	0.984171i	$-0.443290\pi$
$269$	13.4946	−	3.61587i	0.822781	−	0.220463i	0.645562	+	0.763708i	$0.276623\pi$
$270$	−18.0755	−	1.46924i	−1.10004	−	0.0894154i
$271$	6.24843	+	10.8226i	0.379565	+	0.657426i	0.990999	−	0.133869i	$-0.0427403\pi$
$271$	6.24843	+	10.8226i	0.379565	+	0.657426i	−0.611434	+	0.791296i	$0.709407\pi$
$272$	4.11927	+	20.4072i	0.249767	+	1.23737i
$273$		0			0
$274$	−4.80602	−	10.1429i	−0.290342	−	0.612756i
$275$	4.95441	−	18.4901i	0.298762	−	1.11500i
$276$	−22.0752	−	9.96454i	−1.32877	−	0.599795i
$277$	−2.19595	−	8.19541i	−0.131942	−	0.492415i	0.868050	−	0.496477i	$-0.165373\pi$
$277$	−2.19595	−	8.19541i	−0.131942	−	0.492415i	−0.999992	+	0.00406280i	$0.998707\pi$
$278$	−4.07093	+	0.743704i	−0.244158	+	0.0446044i
$279$		−	2.42372i		−	0.145104i
$280$		0			0
$281$		−	9.56494i		−	0.570596i	−0.958439	−	0.285298i	$-0.907907\pi$
$281$		−	9.56494i		−	0.570596i	0.958439	−	0.285298i	$-0.0920926\pi$
$282$	1.80207	+	9.86429i	0.107312	+	0.587410i
$283$	4.27803	+	15.9658i	0.254303	+	0.949070i	0.968477	+	0.249102i	$0.0801356\pi$
$283$	4.27803	+	15.9658i	0.254303	+	0.949070i	−0.714175	+	0.699968i	$0.753198\pi$
$284$	18.8198	−	7.11367i	1.11675	−	0.422118i
$285$	−1.87759	+	7.00726i	−0.111219	+	0.415074i
$286$	13.8792	−	6.57639i	0.820696	−	0.388870i
$287$		0			0
$288$	−3.94740	+	2.94928i	−0.232603	+	0.173788i
$289$	−5.04445	−	8.73725i	−0.296732	−	0.513956i
$290$	−3.09587	+	38.0873i	−0.181796	+	2.23656i
$291$	14.5642	−	3.90247i	0.853769	−	0.228767i
$292$	4.90047	−	29.9451i	0.286778	−	1.75240i
$293$	−15.2913	+	15.2913i	−0.893328	+	0.893328i	−0.994835	−	0.101507i	$-0.967634\pi$
$293$	−15.2913	+	15.2913i	−0.893328	+	0.893328i	0.101507	+	0.994835i	$0.467634\pi$
$294$		0			0
$295$			30.8938i			1.79870i
$296$	7.95937	−	14.3940i	0.462629	−	0.836636i
$297$	−15.8808	−	9.16877i	−0.921496	−	0.532026i
$298$	−11.8556	−	13.9535i	−0.686778	−	0.808304i
$299$	14.7482	+	3.95178i	0.852913	+	0.228537i
$300$	−1.71068	−	17.1207i	−0.0987663	−	0.988462i
$301$		0			0
$302$	−1.69735	−	3.58219i	−0.0976716	−	0.206132i
$303$	−13.8185	−	23.9343i	−0.793850	−	1.37499i
$304$	−2.14293	−	4.31463i	−0.122906	−	0.247461i
$305$	−2.25120	+	3.89919i	−0.128903	+	0.223267i
$306$	3.64508	−	5.27458i	0.208375	−	0.301528i
$307$	−4.16259	−	4.16259i	−0.237571	−	0.237571i	0.578272	−	0.815844i	$-0.303727\pi$
$307$	−4.16259	−	4.16259i	−0.237571	−	0.237571i	−0.815844	+	0.578272i	$0.803727\pi$
$308$		0			0
$309$	2.24265	−	2.24265i	0.127580	−	0.127580i
$310$	−11.8507	+	2.16497i	−0.673076	+	0.122962i
$311$	−0.695092	−	0.401312i	−0.0394151	−	0.0227563i	0.480163	−	0.877179i	$-0.340578\pi$
$311$	−0.695092	−	0.401312i	−0.0394151	−	0.0227563i	−0.519578	+	0.854423i	$0.673911\pi$
$312$	9.57936	−	9.94019i	0.542325	−	0.562752i
$313$	15.3533	−	8.86423i	0.867819	−	0.501036i	0.00119626	−	0.999999i	$-0.499619\pi$
$313$	15.3533	−	8.86423i	0.867819	−	0.501036i	0.866623	+	0.498964i	$0.166286\pi$
$314$	−1.80596	−	0.644742i	−0.101916	−	0.0363849i
$315$		0			0
$316$	−8.37664	+	10.2364i	−0.471223	+	0.575845i
$317$	3.79534	−	14.1644i	0.213168	−	0.795552i	−0.773636	−	0.633630i	$-0.781564\pi$
$317$	3.79534	−	14.1644i	0.213168	−	0.795552i	0.986804	−	0.161922i	$-0.0517693\pi$
$318$	1.68452	−	20.7239i	0.0944631	−	1.16214i
$319$	−19.3197	+	33.4627i	−1.08169	+	1.87355i
$320$	17.9464	+	16.6663i	1.00324	+	0.931677i
$321$	22.0475			1.23057
$322$		0			0
$323$	4.43243	+	4.43243i	0.246627	+	0.246627i
$324$	−21.4239	−	3.50599i	−1.19022	−	0.194777i
$325$	2.80735	+	10.4772i	0.155724	+	0.581170i
$326$	19.6927	−	16.7320i	1.09068	−	0.926699i
$327$	13.7106	−	7.91584i	0.758200	−	0.437747i
$328$	−17.3754	−	4.31316i	−0.959393	−	0.238154i
$329$		0			0
$330$	12.5387	−	35.1215i	0.690230	−	1.93337i
$331$	0.304708	+	0.0816464i	0.0167483	+	0.00448769i	0.267183	−	0.963646i	$-0.413907\pi$
$331$	0.304708	+	0.0816464i	0.0167483	+	0.00448769i	−0.250435	+	0.968133i	$0.580574\pi$
$332$	8.63127	−	19.1215i	0.473702	−	1.04943i
$333$	−4.89289	+	1.31105i	−0.268129	+	0.0718449i
$334$	1.57674	−	2.28161i	0.0862756	−	0.124844i
$335$	−4.18535			−0.228670
$336$		0			0
$337$	−26.7633			−1.45789			−0.728944	−	0.684573i	$-0.759989\pi$
$337$	−26.7633			−1.45789			−0.728944	+	0.684573i	$0.759989\pi$
$338$	5.50446	−	7.96519i	0.299403	−	0.433249i
$339$	−29.0028	+	7.77128i	−1.57522	+	0.422078i
$340$	−29.0459	−	13.1111i	−1.57524	−	0.711048i
$341$	−11.7662	−	3.15275i	−0.637178	−	0.170731i
$342$	−0.498834	+	1.39726i	−0.0269739	+	0.0755552i
$343$		0			0
$344$	6.31357	+	10.4831i	0.340405	+	0.565209i
$345$	32.1072	−	18.5371i	1.72859	−	0.998003i
$346$	−6.31054	+	5.36177i	−0.339257	+	0.288251i
$347$	9.00704	+	33.6147i	0.483523	+	1.80453i	0.586621	+	0.809861i	$0.300458\pi$
$347$	9.00704	+	33.6147i	0.483523	+	1.80453i	−0.103098	+	0.994671i	$0.532876\pi$
$348$	−5.60899	+	34.2746i	−0.300674	+	1.83731i
$349$	13.7818	+	13.7818i	0.737725	+	0.737725i	0.972137	−	0.234412i	$-0.0753166\pi$
$349$	13.7818	+	13.7818i	0.737725	+	0.737725i	−0.234412	+	0.972137i	$0.575317\pi$
$350$		0			0
$351$	10.3907			0.554616
$352$	9.18289	+	22.9996i	0.489450	+	1.22588i
$353$	13.0221	−	22.5550i	0.693099	−	1.20048i	−0.277718	−	0.960663i	$-0.589578\pi$
$353$	13.0221	−	22.5550i	0.693099	−	1.20048i	0.970817	−	0.239820i	$-0.0770884\pi$
$354$	−2.27481	+	27.9861i	−0.120905	+	1.48745i
$355$	−7.97093	+	29.7479i	−0.423053	+	1.57886i
$356$	5.04811	+	4.13094i	0.267549	+	0.218940i
$357$		0			0
$358$	17.9225	+	6.39850i	0.947235	+	0.338171i
$359$	−18.2196	+	10.5191i	−0.961593	+	0.555176i	−0.896663	−	0.442714i	$-0.854016\pi$
$359$	−18.2196	+	10.5191i	−0.961593	+	0.555176i	−0.0649297	+	0.997890i	$0.520682\pi$
$360$	−0.139405	−	7.54137i	−0.00734730	−	0.397465i
$361$	15.1983	+	8.77474i	0.799911	+	0.461829i
$362$	14.9609	−	2.73315i	0.786326	−	0.143651i
$363$	11.3606	−	11.3606i	0.596274	−	0.596274i
$364$		0			0
$365$	32.8434	+	32.8434i	1.71910	+	1.71910i
$366$	−2.32644	+	3.36645i	−0.121605	+	0.175967i
$367$	−3.70670	+	6.42020i	−0.193488	+	0.335132i	−0.946404	−	0.322986i	$-0.895313\pi$
$367$	−3.70670	+	6.42020i	−0.193488	+	0.335132i	0.752916	+	0.658117i	$0.228647\pi$
$368$	−7.84788	+	23.3357i	−0.409099	+	1.21646i
$369$	2.75673	+	4.77480i	0.143510	+	0.248566i
$370$	10.7809	+	22.7526i	0.560472	+	1.18285i
$371$		0			0
$372$	−10.8948	+	1.08860i	−0.564868	+	0.0564412i
$373$	−5.12662	−	1.37367i	−0.265446	−	0.0711261i	0.123641	−	0.992327i	$-0.460543\pi$
$373$	−5.12662	−	1.37367i	−0.265446	−	0.0711261i	−0.389087	+	0.921201i	$0.627210\pi$
$374$	−20.8646	−	24.5566i	−1.07888	−	1.26979i
$375$	−3.27318	−	1.88977i	−0.169026	−	0.0975873i
$376$	9.79541	−	2.81971i	0.505160	−	0.145415i
$377$		−	21.8945i		−	1.12762i
$378$		0			0
$379$	18.8387	−	18.8387i	0.967677	−	0.967677i	−0.0318167	−	0.999494i	$-0.510129\pi$
$379$	18.8387	−	18.8387i	0.967677	−	0.967677i	0.999494	+	0.0318167i	$0.0101293\pi$
$380$	7.27747	+	1.19095i	0.373326	+	0.0610943i
$381$	3.43087	−	0.919300i	0.175769	−	0.0470972i
$382$	−2.34738	+	28.8789i	−0.120103	+	1.47757i
$383$	2.47310	+	4.28353i	0.126369	+	0.218878i	0.922267	−	0.386553i	$-0.126334\pi$
$383$	2.47310	+	4.28353i	0.126369	+	0.218878i	−0.795898	+	0.605431i	$0.793001\pi$
$384$	15.0302	+	16.4192i	0.767005	+	0.837889i
$385$		0			0
$386$	−16.2505	+	7.69999i	−0.827130	+	0.391919i
$387$	0.975426	−	3.64034i	0.0495837	−	0.185049i
$388$	−5.41922	−	14.3370i	−0.275119	−	0.727851i
$389$	5.13412	+	19.1608i	0.260310	+	0.971491i	0.965059	+	0.262034i	$0.0843932\pi$
$389$	5.13412	+	19.1608i	0.260310	+	0.971491i	−0.704748	+	0.709457i	$0.748940\pi$
$390$	3.79756	+	20.7873i	0.192297	+	1.05261i
$391$		−	32.0349i		−	1.62007i
$392$		0			0
$393$			25.8372i			1.30332i
$394$	−25.3088	+	4.62357i	−1.27504	+	0.232932i
$395$	−5.24028	−	19.5570i	−0.263667	−	0.984020i
$396$	3.13783	−	6.95146i	0.157682	−	0.349324i
$397$	−0.0233859	+	0.0872772i	−0.00117370	+	0.00438032i	−0.966510	−	0.256628i	$-0.917388\pi$
$397$	−0.0233859	+	0.0872772i	−0.00117370	+	0.00438032i	0.965336	+	0.261009i	$0.0840551\pi$
$398$	0.889246	+	1.87672i	0.0445739	+	0.0940714i
$399$		0			0
$400$	−17.1443	+	3.46064i	−0.857216	+	0.173032i
$401$	12.7052	+	22.0060i	0.634466	+	1.09893i	0.986628	+	0.162988i	$0.0521133\pi$
$401$	12.7052	+	22.0060i	0.634466	+	1.09893i	−0.352162	+	0.935939i	$0.614553\pi$
$402$	−3.79144	−	0.308182i	−0.189100	−	0.0153707i
$403$	6.66719	−	1.78647i	0.332116	−	0.0889903i
$404$	−22.8125	+	16.3961i	−1.13496	+	0.815734i
$405$	23.4975	−	23.4975i	1.16760	−	1.16760i
$406$		0			0
$407$			25.4586i			1.26194i
$408$	−25.3468	−	14.0158i	−1.25485	−	0.693888i
$409$	−19.4037	−	11.2027i	−0.959450	−	0.553939i	−0.0634462	−	0.997985i	$-0.520209\pi$
$409$	−19.4037	−	11.2027i	−0.959450	−	0.553939i	−0.896004	+	0.444047i	$0.853542\pi$
$410$	20.8839	−	17.7441i	1.03138	−	0.876317i
$411$	15.0831	+	4.04149i	0.743992	+	0.199352i
$412$	−2.49505	−	2.04174i	−0.122922	−	0.100589i
$413$		0			0
$414$	6.85191	−	3.24664i	0.336753	−	0.159564i
$415$	16.0568	+	27.8112i	0.788197	+	1.36520i
$416$	−11.0225	−	8.68472i	−0.540420	−	0.425803i
$417$	2.87867	−	4.98601i	0.140969	−	0.244166i
$418$	6.13430	+	4.23920i	0.300039	+	0.207346i
$419$	−24.2758	−	24.2758i	−1.18595	−	1.18595i	−0.978177	−	0.207775i	$-0.933378\pi$
$419$	−24.2758	−	24.2758i	−1.18595	−	1.18595i	−0.207775	−	0.978177i	$-0.566622\pi$
$420$		0			0
$421$	16.0270	−	16.0270i	0.781108	−	0.781108i	−0.198910	−	0.980018i	$-0.563740\pi$
$421$	16.0270	−	16.0270i	0.781108	−	0.781108i	0.980018	+	0.198910i	$0.0637400\pi$
$422$	0.192208	+	1.05212i	0.00935656	+	0.0512164i
$423$	−2.71861	−	1.56959i	−0.132183	−	0.0763160i
$424$	−21.1321	+	0.390635i	−1.02627	+	0.0189709i
$425$	19.7087	−	11.3788i	0.956014	−	0.551955i
$426$	−9.41117	+	26.3612i	−0.455973	+	1.27720i
$427$		0			0
$428$	−2.22826	−	22.3006i	−0.107707	−	1.07794i
$429$	−5.53024	+	20.6391i	−0.267002	+	0.996466i
$430$	−18.6707	−	1.51762i	−0.900380	−	0.0731862i
$431$	15.8307	−	27.4196i	0.762540	−	1.32076i	−0.178998	−	0.983849i	$-0.557285\pi$
$431$	15.8307	−	27.4196i	0.762540	−	1.32076i	0.941538	−	0.336908i	$-0.109381\pi$
$432$	−1.04853	+	16.7219i	−0.0504474	+	0.804532i
$433$	−11.6823			−0.561413			−0.280707	−	0.959794i	$-0.590569\pi$
$433$	−11.6823			−0.561413			−0.280707	+	0.959794i	$0.590569\pi$
$434$		0			0
$435$	−37.5920	−	37.5920i	−1.80240	−	1.80240i
$436$	−9.39240	−	13.0680i	−0.449814	−	0.625844i
$437$	1.91860	+	7.16032i	0.0917792	+	0.342525i
$438$	27.3339	+	32.1706i	1.30606	+	1.53717i
$439$	−11.3637	+	6.56086i	−0.542362	+	0.313133i	−0.746036	−	0.665906i	$-0.768045\pi$
$439$	−11.3637	+	6.56086i	−0.542362	+	0.313133i	0.203674	+	0.979039i	$0.434712\pi$
$440$	−36.7919	−	9.13301i	−1.75399	−	0.435399i
$441$		0			0
$442$	17.1961	+	6.13915i	0.817935	+	0.292010i
$443$	22.1569	+	5.93692i	1.05271	+	0.282071i	0.743369	−	0.668881i	$-0.233227\pi$
$443$	22.1569	+	5.93692i	1.05271	+	0.282071i	0.309336	+	0.950953i	$0.399893\pi$
$444$	8.09087	+	21.4051i	0.383976	+	1.01584i
$445$	−9.64455	+	2.58425i	−0.457196	+	0.122505i
$446$	−9.11869	−	6.30160i	−0.431782	−	0.298390i
$447$	25.4735			1.20485
$448$		0			0
$449$	−15.6396			−0.738077			−0.369038	−	0.929414i	$-0.620313\pi$
$449$	−15.6396			−0.738077			−0.369038	+	0.929414i	$0.620313\pi$
$450$	4.43123	+	3.06227i	0.208890	+	0.144357i
$451$	26.7658	−	7.17188i	1.26035	−	0.337711i
$452$	10.7917	+	28.5503i	0.507599	+	1.34290i
$453$	5.32691	+	1.42734i	0.250280	+	0.0670623i
$454$	−0.466321	−	0.166480i	−0.0218855	−	0.00781331i
$455$		0			0
$456$	6.50484	+	1.61472i	0.304617	+	0.0756164i
$457$	−10.5919	+	6.11523i	−0.495468	+	0.286058i	−0.726840	−	0.686807i	$-0.759012\pi$
$457$	−10.5919	+	6.11523i	−0.495468	+	0.286058i	0.231372	+	0.972865i	$0.425678\pi$
$458$	20.2057	+	23.7811i	0.944150	+	1.11122i
$459$	−5.64247	−	21.0580i	−0.263368	−	0.982903i
$460$	−21.9948	−	30.6023i	−1.02552	−	1.42684i
$461$	−13.4658	−	13.4658i	−0.627163	−	0.627163i	0.320191	−	0.947353i	$-0.396253\pi$
$461$	−13.4658	−	13.4658i	−0.627163	−	0.627163i	−0.947353	+	0.320191i	$0.896253\pi$
$462$		0			0
$463$	−24.7807			−1.15166			−0.575829	−	0.817570i	$-0.695321\pi$
$463$	−24.7807			−1.15166			−0.575829	+	0.817570i	$0.695321\pi$
$464$	35.2350	+	2.20938i	1.63574	+	0.102568i
$465$	8.38000	−	14.5146i	0.388613	−	0.673098i
$466$	13.4119	+	1.09017i	0.621295	+	0.0505011i
$467$	8.48020	−	31.6485i	0.392417	−	1.46452i	−0.433718	−	0.901048i	$-0.642799\pi$
$467$	8.48020	−	31.6485i	0.392417	−	1.46452i	0.826135	−	0.563472i	$-0.190535\pi$
$468$	0.429677	+	4.30024i	0.0198618	+	0.198779i
$469$		0			0
$470$	−5.24610	+	14.6946i	−0.241985	+	0.677812i
$471$	2.31040	−	1.33391i	0.106458	−	0.0614634i
$472$	28.5373	−	0.527524i	1.31354	−	0.0242812i
$473$	−16.4037	−	9.47066i	−0.754242	−	0.435462i
$474$	−3.30703	−	18.1022i	−0.151897	−	0.831462i
$475$	−3.72373	+	3.72373i	−0.170857	+	0.170857i
$476$		0			0
$477$	4.60265	+	4.60265i	0.210741	+	0.210741i
$478$	21.9271	+	15.1530i	1.00292	+	0.693084i
$479$	−17.6824	+	30.6268i	−0.807930	+	1.39938i	0.106365	+	0.994327i	$0.466079\pi$
$479$	−17.6824	+	30.6268i	−0.807930	+	1.39938i	−0.914295	+	0.405049i	$0.867254\pi$
$480$	−33.8364	+	4.01380i	−1.54441	+	0.183204i
$481$	−7.21289	−	12.4931i	−0.328879	−	0.569636i
$482$	8.17705	−	3.87453i	0.372454	−	0.176480i
$483$		0			0
$484$	−12.6391	−	10.3428i	−0.574507	−	0.470128i
$485$	22.6621	+	6.07229i	1.02903	+	0.275729i
$486$	9.47334	−	8.04906i	0.429720	−	0.365113i
$487$	−14.4850	−	8.36292i	−0.656378	−	0.378960i	0.134517	−	0.990911i	$-0.457052\pi$
$487$	−14.4850	−	8.36292i	−0.656378	−	0.378960i	−0.790896	+	0.611951i	$0.790385\pi$
$488$	3.64022	+	2.01291i	0.164785	+	0.0911201i
$489$			35.9510i			1.62576i
$490$		0			0
$491$	5.93243	−	5.93243i	0.267727	−	0.267727i	−0.560457	−	0.828184i	$-0.689374\pi$
$491$	5.93243	−	5.93243i	0.267727	−	0.267727i	0.828184	+	0.560457i	$0.189374\pi$
$492$	20.2249	−	14.5363i	0.911809	−	0.655346i
$493$	−44.3717	+	11.8894i	−1.99840	+	0.535470i
$494$	−4.21128	−	0.342309i	−0.189475	−	0.0154012i
$495$	5.83732	+	10.1105i	0.262368	+	0.454434i
$496$	2.20219	+	10.9098i	0.0988813	+	0.489866i
$497$		0			0
$498$	12.4977	+	26.3760i	0.560037	+	1.18194i
$499$	−2.03391	+	7.59066i	−0.0910504	+	0.339805i	−0.996391	−	0.0848814i	$-0.972949\pi$
$499$	−2.03391	+	7.59066i	−0.0910504	+	0.339805i	0.905341	+	0.424686i	$0.139616\pi$
$500$	−1.58066	+	3.50175i	−0.0706892	+	0.156603i
$501$	0.998649	+	3.72701i	0.0446164	+	0.166510i
$502$	−5.76772	+	1.05368i	−0.257426	+	0.0470282i
$503$		−	6.99765i		−	0.312010i	−0.987756	−	0.156005i	$-0.950138\pi$
$503$		−	6.99765i		−	0.312010i	0.987756	−	0.156005i	$-0.0498616\pi$
$504$		0			0
$505$		−	43.0034i		−	1.91363i
$506$	−6.84832	−	37.4867i	−0.304445	−	1.66649i
$507$	3.48631	+	13.0111i	0.154833	+	0.577843i
$508$	−1.27660	−	3.37735i	−0.0566400	−	0.149846i
$509$	1.30940	−	4.88676i	0.0580383	−	0.216602i	−0.930816	−	0.365488i	$-0.880902\pi$
$509$	1.30940	−	4.88676i	0.0580383	−	0.216602i	0.988854	+	0.148886i	$0.0475688\pi$
$510$	40.0657	−	18.9843i	1.77414	−	0.840640i
$511$		0			0
$512$	15.0887	−	16.8622i	0.666831	−	0.745209i
$513$	2.52237	+	4.36887i	0.111365	+	0.192890i
$514$	3.31895	−	40.8317i	0.146393	−	1.80101i
$515$	4.76687	−	1.27728i	0.210053	−	0.0562837i
$516$	−16.8017	−	2.74957i	−0.739654	−	0.121043i
$517$	−11.1561	+	11.1561i	−0.490645	+	0.490645i
$518$		0			0
$519$		−	11.5205i		−	0.505695i
$520$	20.6422	−	5.94206i	0.905218	−	0.260577i
$521$	−15.0383	−	8.68234i	−0.658838	−	0.380380i	0.132996	−	0.991117i	$-0.457540\pi$
$521$	−15.0383	−	8.68234i	−0.658838	−	0.380380i	−0.791834	+	0.610736i	$0.790874\pi$
$522$	−7.03994	−	8.28566i	−0.308130	−	0.362654i
$523$	35.4526	+	9.49950i	1.55023	+	0.415384i	0.929556	−	0.368681i	$-0.120190\pi$
$523$	35.4526	+	9.49950i	1.55023	+	0.415384i	0.620679	+	0.784065i	$0.286857\pi$
$524$	26.1339	−	2.61128i	1.14166	−	0.114074i
$525$		0			0
$526$	−0.208582	−	0.440204i	−0.00909461	−	0.0191938i
$527$	−7.24096	−	12.5417i	−0.315421	−	0.546325i
$528$	−32.6567	−	10.9826i	−1.42120	−	0.477954i
$529$	7.44198	−	12.8899i	0.323564	−	0.560430i
$530$	18.3933	−	26.6159i	0.798955	−	1.15612i
$531$	−6.21554	−	6.21554i	−0.269731	−	0.269731i
$532$		0			0
$533$	−11.1027	+	11.1027i	−0.480909	+	0.480909i
$534$	−8.92712	+	1.63087i	−0.386314	+	0.0705744i
$535$	29.7100	+	17.1531i	1.28448	+	0.741593i
$536$	0.0714666	+	3.86611i	0.00308689	+	0.166991i
$537$	−22.9287	+	13.2379i	−0.989448	+	0.571258i
$538$	18.6072	+	6.64294i	0.802215	+	0.286397i
$539$		0			0
$540$	−19.8483	−	16.2422i	−0.854137	−	0.698953i
$541$	−4.14648	+	15.4749i	−0.178271	+	0.665317i	0.817700	+	0.575644i	$0.195249\pi$
$541$	−4.14648	+	15.4749i	−0.178271	+	0.665317i	−0.995971	+	0.0896726i	$0.971418\pi$
$542$	−1.43182	+	17.6151i	−0.0615021	+	0.756635i
$543$	−10.5793	+	18.3239i	−0.454001	+	0.786352i
$544$	−11.6150	+	27.0543i	−0.497991	+	1.15994i
$545$	24.6343			1.05522
$546$		0			0
$547$	−10.8422	−	10.8422i	−0.463578	−	0.463578i	0.436248	−	0.899826i	$-0.356307\pi$
$547$	−10.8422	−	10.8422i	−0.463578	−	0.463578i	−0.899826	+	0.436248i	$0.856307\pi$
$548$	2.56350	−	15.6647i	0.109507	−	0.669162i
$549$	−0.331561	−	1.23740i	−0.0141507	−	0.0528111i
$550$	20.6303	−	17.5286i	0.879679	−	0.747422i
$551$	9.20572	−	5.31493i	0.392177	−	0.226423i
$552$	−17.6714	−	29.3416i	−0.752145	−	1.24886i
$553$		0			0
$554$	4.03433	−	11.3004i	0.171402	−	0.480106i
$555$	−33.8344	−	9.06589i	−1.43619	−	0.384826i
$556$	−5.33419	−	2.40781i	−0.226220	−	0.102114i
$557$	21.5541	−	5.77540i	0.913275	−	0.244711i	0.228567	−	0.973528i	$-0.426596\pi$
$557$	21.5541	−	5.77540i	0.913275	−	0.244711i	0.684709	+	0.728817i	$0.259929\pi$
$558$	1.94868	−	2.81983i	0.0824944	−	0.119373i
$559$	10.7329			0.453952
$560$		0			0
$561$	44.8306			1.89275
$562$	7.69028	−	11.1282i	0.324395	−	0.469413i
$563$	−20.1711	+	5.40483i	−0.850110	+	0.227786i	−0.657468	−	0.753483i	$-0.728372\pi$
$563$	−20.1711	+	5.40483i	−0.850110	+	0.227786i	−0.192643	+	0.981269i	$0.561706\pi$
$564$	−5.83437	+	12.9253i	−0.245671	+	0.544254i
$565$	−45.1287	−	12.0922i	−1.89858	−	0.508723i
$566$	−7.85944	+	22.0147i	−0.330357	+	0.925348i
$567$		0			0
$568$	27.6150	+	6.85498i	1.15870	+	0.287629i
$569$	−15.2567	+	8.80848i	−0.639596	+	0.369271i	−0.784459	−	0.620181i	$-0.787059\pi$
$569$	−15.2567	+	8.80848i	−0.639596	+	0.369271i	0.144863	+	0.989452i	$0.453726\pi$
$570$	−7.81833	+	6.64287i	−0.327474	+	0.278239i
$571$	−2.22250	−	8.29448i	−0.0930087	−	0.347113i	0.903701	−	0.428164i	$-0.140839\pi$
$571$	−2.22250	−	8.29448i	−0.0930087	−	0.347113i	−0.996710	+	0.0810502i	$0.974173\pi$
$572$	21.4350	+	3.50781i	0.896242	+	0.146669i
$573$	−28.5034	−	28.5034i	−1.19074	−	1.19074i
$574$		0			0
$575$	26.9129			1.12234
$576$	−6.96377	+	0.257544i	−0.290157	+	0.0107310i
$577$	17.6514	−	30.5732i	0.734838	−	1.27278i	−0.219956	−	0.975510i	$-0.570591\pi$
$577$	17.6514	−	30.5732i	0.734838	−	1.27278i	0.954794	−	0.297268i	$-0.0960753\pi$
$578$	1.15593	−	14.2210i	0.0480804	−	0.591514i
$579$	6.47509	−	24.1654i	0.269096	−	1.00428i
$580$	−34.2242	+	41.8228i	−1.42108	+	1.73660i
$581$		0			0
$582$	20.0821	+	7.16947i	0.832429	+	0.297184i
$583$	28.3313	−	16.3571i	1.17336	−	0.677441i
$584$	29.7774	−	30.8991i	1.23220	−	1.27861i
$585$	−5.72900	−	3.30764i	−0.236865	−	0.136754i
$586$	−30.0847	+	5.49608i	−1.24279	+	0.227041i
$587$	−2.38838	+	2.38838i	−0.0985791	+	0.0985791i	−0.754676	−	0.656097i	$-0.772206\pi$
$587$	−2.38838	+	2.38838i	−0.0985791	+	0.0985791i	0.656097	+	0.754676i	$0.272206\pi$
$588$		0			0
$589$	2.36961	+	2.36961i	0.0976379	+	0.0976379i
$590$	−24.8388	+	35.9428i	−1.02260	+	1.47974i
$591$	17.8966	−	30.9978i	0.736167	−	1.27508i
$592$	20.8331	−	10.3471i	0.856235	−	0.425263i
$593$	−5.78207	−	10.0148i	−0.237441	−	0.411260i	0.722538	−	0.691331i	$-0.242975\pi$
$593$	−5.78207	−	10.0148i	−0.237441	−	0.411260i	−0.959979	+	0.280071i	$0.909642\pi$
$594$	−11.1044	−	23.4355i	−0.455621	−	0.961570i
$595$		0			0
$596$	−2.57451	−	25.7659i	−0.105456	−	1.05541i
$597$	−2.79078	−	0.747787i	−0.114219	−	0.0306049i
$598$	13.9813	+	16.4553i	0.571738	+	0.672908i
$599$	−10.6273	−	6.13567i	−0.434219	−	0.250697i	0.266923	−	0.963718i	$-0.413993\pi$
$599$	−10.6273	−	6.13567i	−0.434219	−	0.250697i	−0.701142	+	0.713021i	$0.747326\pi$
$600$	11.7749	−	21.2941i	0.480707	−	0.869329i
$601$			14.1538i			0.577347i	0.957428	+	0.288674i	$0.0932143\pi$
$601$			14.1538i			0.577347i	−0.957428	+	0.288674i	$0.906786\pi$
$602$		0			0
$603$	0.842054	−	0.842054i	0.0342911	−	0.0342911i
$604$	0.905356	−	5.53232i	0.0368384	−	0.225107i
$605$	24.1474	−	6.47029i	0.981733	−	0.263055i
$606$	3.16649	−	38.9560i	0.128630	−	1.58248i
$607$	12.8174	+	22.2005i	0.520244	+	0.901089i	0.999723	+	0.0235358i	$0.00749237\pi$
$607$	12.8174	+	22.2005i	0.520244	+	0.901089i	−0.479479	+	0.877553i	$0.659174\pi$
$608$	0.975842	−	6.74271i	0.0395756	−	0.273453i
$609$		0			0
$610$	−5.75410	+	2.72646i	−0.232977	+	0.110391i
$611$	2.31382	−	8.63529i	0.0936071	−	0.349346i
$612$	8.48160	−	3.20594i	0.342848	−	0.129593i
$613$	2.49198	+	9.30020i	0.100650	+	0.375632i	0.997815	−	0.0660634i	$-0.0210440\pi$
$613$	2.49198	+	9.30020i	0.100650	+	0.375632i	−0.897165	+	0.441695i	$0.854377\pi$
$614$	−1.49614	−	8.18963i	−0.0603792	−	0.330507i
$615$			38.1256i			1.53737i
$616$		0			0
$617$			23.1951i			0.933800i	0.884310	+	0.466900i	$0.154629\pi$
$617$			23.1951i			0.933800i	−0.884310	+	0.466900i	$0.845371\pi$
$618$	4.41228	−	0.806064i	0.177488	−	0.0324247i
$619$	8.68871	+	32.4267i	0.349229	+	1.30334i	0.887594	+	0.460627i	$0.152375\pi$
$619$	8.68871	+	32.4267i	0.349229	+	1.30334i	−0.538365	+	0.842712i	$0.680958\pi$
$620$	−15.5282	−	7.00927i	−0.623626	−	0.281499i
$621$	6.67270	−	24.9028i	0.267766	−	0.999317i
$622$	−0.486035	−	1.02576i	−0.0194882	−	0.0411291i
$623$		0			0
$624$	19.1369	−	3.86286i	0.766089	−	0.154638i
$625$	−13.8718	−	24.0267i	−0.554873	−	0.961068i
$626$	24.9894	+	2.03123i	0.998777	+	0.0811843i
$627$	−10.0204	+	2.68495i	−0.400175	+	0.107227i
$628$	−1.58273	−	2.20211i	−0.0631578	−	0.0878739i
$629$	−21.4019	+	21.4019i	−0.853348	+	0.853348i
$630$		0			0
$631$			30.2574i			1.20453i	0.798296	+	0.602265i	$0.205735\pi$
$631$			30.2574i			1.20453i	−0.798296	+	0.602265i	$0.794265\pi$
$632$	−17.9758	+	5.17452i	−0.715039	+	0.205832i
$633$	−1.28862	−	0.743986i	−0.0512181	−	0.0295708i
$634$	15.8039	−	13.4278i	0.627653	−	0.533287i
$635$	5.33848	+	1.43044i	0.211851	+	0.0567654i
$636$	18.6220	−	22.7565i	0.738411	−	0.902355i
$637$		0			0
$638$	−49.3813	+	23.3984i	−1.95503	+	0.926350i
$639$	−4.38133	−	7.58868i	−0.173323	−	0.300204i
$640$	7.47960	+	33.8192i	0.295657	+	1.33682i
$641$	3.34695	−	5.79709i	0.132197	−	0.228971i	−0.792326	−	0.610097i	$-0.791130\pi$
$641$	3.34695	−	5.79709i	0.132197	−	0.228971i	0.924523	+	0.381126i	$0.124464\pi$
$642$	25.6508	+	17.7263i	1.01236	+	0.699603i
$643$	24.7491	+	24.7491i	0.976007	+	0.976007i	0.999719	−	0.0237114i	$-0.00754828\pi$
$643$	24.7491	+	24.7491i	0.976007	+	0.976007i	−0.0237114	+	0.999719i	$0.507548\pi$
$644$		0			0
$645$	18.4279	−	18.4279i	0.725597	−	0.725597i
$646$	1.59312	+	8.72053i	0.0626806	+	0.343105i
$647$	−37.7857	−	21.8156i	−1.48551	−	0.857659i	−0.485645	−	0.874156i	$-0.661415\pi$
$647$	−37.7857	−	21.8156i	−1.48551	−	0.857659i	−0.999864	+	0.0164976i	$0.994748\pi$
$648$	−22.1064	−	21.3039i	−0.868422	−	0.836898i
$649$	−38.2593	+	22.0890i	−1.50181	+	0.867069i
$650$	−5.15757	+	14.4466i	−0.202296	+	0.566643i
$651$		0			0
$652$	36.3637	−	3.63344i	1.42411	−	0.142296i
$653$	−6.54748	+	24.4355i	−0.256223	+	0.956236i	0.711184	+	0.703006i	$0.248159\pi$
$653$	−6.54748	+	24.4355i	−0.256223	+	0.956236i	−0.967406	+	0.253230i	$0.918507\pi$
$654$	22.3158	+	1.81391i	0.872616	+	0.0709294i
$655$	−20.1015	+	34.8169i	−0.785432	+	1.36041i
$656$	−16.7472	−	18.9880i	−0.653869	−	0.741356i
$657$	−13.2156			−0.515588
$658$		0			0
$659$	−16.0357	−	16.0357i	−0.624662	−	0.624662i	0.322058	−	0.946720i	$-0.395626\pi$
$659$	−16.0357	−	16.0357i	−0.624662	−	0.624662i	−0.946720	+	0.322058i	$0.895626\pi$
$660$	42.8258	−	30.7802i	1.66699	−	1.19812i
$661$	2.82150	+	10.5300i	0.109743	+	0.409568i	0.998840	−	0.0481514i	$-0.0153330\pi$
$661$	2.82150	+	10.5300i	0.109743	+	0.409568i	−0.889097	+	0.457720i	$0.848666\pi$
$662$	0.288863	+	0.339978i	0.0112270	+	0.0132136i
$663$	−21.9994	+	12.7013i	−0.854385	+	0.493279i
$664$	25.4157	−	15.3069i	0.986321	−	0.594025i
$665$		0			0
$666$	−6.74664	−	2.40861i	−0.261427	−	0.0933316i
$667$	−52.4732	−	14.0602i	−2.03177	−	0.544412i
$668$	3.66887	−	1.38679i	0.141953	−	0.0536565i
$669$	14.8953	−	3.99120i	0.575887	−	0.154309i
$670$	−4.86937	−	3.36505i	−0.188120	−	0.130003i
$671$	−6.43842			−0.248553
$672$		0			0
$673$	1.82580			0.0703795			0.0351897	−	0.999381i	$-0.488796\pi$
$673$	1.82580			0.0703795			0.0351897	+	0.999381i	$0.488796\pi$
$674$	−31.1372	−	21.5178i	−1.19936	−	0.828837i
$675$	17.6911	−	4.74030i	0.680929	−	0.182454i
$676$	12.8081	−	4.84132i	0.492620	−	0.186205i
$677$	−26.1437	−	7.00518i	−1.00478	−	0.269231i	−0.281335	−	0.959610i	$-0.590777\pi$
$677$	−26.1437	−	7.00518i	−1.00478	−	0.269231i	−0.723448	+	0.690379i	$0.757444\pi$
$678$	−39.9909	−	14.2771i	−1.53584	−	0.548309i
$679$		0			0
$680$	−23.2516	−	38.6070i	−0.891656	−	1.48051i
$681$	0.596575	−	0.344433i	0.0228608	−	0.0131987i
$682$	−11.1544	−	13.1282i	−0.427123	−	0.502703i
$683$	−5.18175	−	19.3386i	−0.198274	−	0.739970i	−0.991395	−	0.130905i	$-0.958212\pi$
$683$	−5.18175	−	19.3386i	−0.198274	−	0.739970i	0.793121	−	0.609065i	$-0.208455\pi$
$684$	−1.70377	+	1.22455i	−0.0651452	+	0.0468219i
$685$	17.1808	+	17.1808i	0.656445	+	0.656445i
$686$		0			0
$687$	−43.4148			−1.65638
$688$	−1.08305	+	17.2725i	−0.0412911	+	0.658507i
$689$	−9.26852	+	16.0536i	−0.353103	+	0.611592i
$690$	52.2584	+	4.24776i	1.98944	+	0.161709i
$691$	−3.95994	+	14.7787i	−0.150643	+	0.562208i	0.848796	+	0.528720i	$0.177328\pi$
$691$	−3.95994	+	14.7787i	−0.150643	+	0.562208i	−0.999439	+	0.0334874i	$0.989339\pi$
$692$	−11.6528	+	1.16434i	−0.442972	+	0.0442614i
$693$		0			0
$694$	−16.5474	+	46.3501i	−0.628130	+	1.75943i
$695$	7.75829	−	4.47925i	0.294289	−	0.169908i
$696$	−34.0827	+	35.3665i	−1.29190	+	1.34056i
$697$	28.5299	+	16.4717i	1.08065	+	0.623911i
$698$	4.95353	+	27.1149i	0.187494	+	1.02631i
$699$	−13.2375	+	13.2375i	−0.500688	+	0.500688i
$700$		0			0
$701$	2.64009	+	2.64009i	0.0997148	+	0.0997148i	0.755204	−	0.655490i	$-0.227538\pi$
$701$	2.64009	+	2.64009i	0.0997148	+	0.0997148i	−0.655490	+	0.755204i	$0.727538\pi$
$702$	12.0889	+	8.35422i	0.456266	+	0.315310i
$703$	3.50188	−	6.06544i	0.132076	−	0.228762i
$704$	−7.80815	+	34.1415i	−0.294281	+	1.28676i
$705$	−10.8537	−	18.7992i	−0.408774	−	0.708018i
$706$	33.2848	−	15.7713i	1.25269	−	0.593562i
$707$		0			0
$708$	−25.1476	+	30.7310i	−0.945106	+	1.15494i
$709$	27.6926	+	7.42020i	1.04002	+	0.278671i	0.738120	−	0.674669i	$-0.235714\pi$
$709$	27.6926	+	7.42020i	1.04002	+	0.278671i	0.301896	+	0.953341i	$0.402380\pi$
$710$	−33.1912	+	28.2010i	−1.24564	+	1.05836i
$711$	4.98899	+	2.88039i	0.187102	+	0.108023i
$712$	2.55182	+	8.86478i	0.0956335	+	0.332222i
$713$		−	17.1261i		−	0.641377i
$714$		0			0
$715$	−23.5096	+	23.5096i	−0.879210	+	0.879210i
$716$	15.7072	+	21.8541i	0.587006	+	0.816724i
$717$	−35.8178	+	9.59735i	−1.33764	+	0.358420i
$718$	−29.6546	−	2.41044i	−1.10670	−	0.0899568i
$719$	−10.0679	−	17.4381i	−0.375468	−	0.650330i	0.614929	−	0.788583i	$-0.289185\pi$
$719$	−10.0679	−	17.4381i	−0.375468	−	0.650330i	−0.990397	+	0.138253i	$0.955851\pi$
$720$	5.90113	−	8.88595i	0.219922	−	0.331160i
$721$		0			0
$722$	10.6272	+	22.4284i	0.395505	+	0.834697i
$723$	−3.25818	+	12.1597i	−0.121173	+	0.452224i
$724$	19.6034	+	8.84882i	0.728556	+	0.328864i
$725$	−9.98838	−	37.2771i	−0.370959	−	1.38444i
$726$	22.3512	−	4.08326i	0.829530	−	0.151544i
$727$			30.0313i			1.11380i	0.830580	+	0.556900i	$0.188009\pi$
$727$			30.0313i			1.11380i	−0.830580	+	0.556900i	$0.811991\pi$
$728$		0			0
$729$		−	15.2688i		−	0.565511i
$730$	11.8047	+	64.6173i	0.436912	+	2.39159i
$731$	−5.82826	−	21.7514i	−0.215566	−	0.804503i
$732$	−5.41330	+	2.04616i	−0.200081	+	0.0756284i
$733$	−3.31347	+	12.3660i	−0.122386	+	0.456750i	−0.999733	−	0.0231062i	$-0.992644\pi$
$733$	−3.31347	+	12.3660i	−0.122386	+	0.456750i	0.877347	+	0.479856i	$0.159311\pi$
$734$	−9.47438	+	4.48925i	−0.349706	+	0.165701i
$735$		0			0
$736$	−27.8925	+	20.8397i	−1.02813	+	0.768163i
$737$	−2.99252	−	5.18320i	−0.110231	−	0.190926i
$738$	−0.631703	+	7.77158i	−0.0232533	+	0.286076i
$739$	−27.5947	+	7.39398i	−1.01509	+	0.271992i	−0.727754	−	0.685839i	$-0.759436\pi$
$739$	−27.5947	+	7.39398i	−1.01509	+	0.271992i	−0.287334	+	0.957831i	$0.592769\pi$
$740$	−5.75046	+	35.1391i	−0.211391	+	1.29174i
$741$	4.15652	−	4.15652i	0.152694	−	0.152694i
$742$		0			0
$743$		−	32.8469i		−	1.20504i	−0.798106	−	0.602518i	$-0.794164\pi$
$743$		−	32.8469i		−	1.20504i	0.798106	−	0.602518i	$-0.205836\pi$
$744$	−13.5506	−	7.49297i	−0.496788	−	0.274706i
$745$	34.3267	+	19.8185i	1.25763	+	0.726095i
$746$	−4.86003	−	5.72001i	−0.177938	−	0.209424i
$747$	−8.82583	−	2.36487i	−0.322920	−	0.0865262i
$748$	−4.53086	−	45.3453i	−0.165665	−	1.65799i
$749$		0			0
$750$	−2.28873	−	4.83028i	−0.0835726	−	0.176377i
$751$	−8.80060	−	15.2431i	−0.321138	−	0.556228i	0.659585	−	0.751630i	$-0.270732\pi$
$751$	−8.80060	−	15.2431i	−0.321138	−	0.556228i	−0.980723	+	0.195402i	$0.937399\pi$
$752$	13.6634	+	4.59503i	0.498251	+	0.167564i
$753$	4.07852	−	7.06421i	0.148630	−	0.257434i
$754$	17.6033	−	25.4727i	0.641075	−	0.927663i
$755$	6.06777	+	6.06777i	0.220829	+	0.220829i
$756$		0			0
$757$	−10.8261	+	10.8261i	−0.393480	+	0.393480i	−0.875926	−	0.482446i	$-0.839749\pi$
$757$	−10.8261	+	10.8261i	−0.393480	+	0.393480i	0.482446	+	0.875926i	$0.339749\pi$
$758$	37.0639	−	6.77108i	1.34622	−	0.245937i
$759$	45.9132	+	26.5080i	1.66654	+	0.962179i
$760$	7.50931	+	7.23672i	0.272391	+	0.262503i
$761$	−1.13395	+	0.654687i	−0.0411057	+	0.0237324i	−0.520412	−	0.853915i	$-0.674222\pi$
$761$	−1.13395	+	0.654687i	−0.0411057	+	0.0237324i	0.479306	+	0.877648i	$0.340888\pi$
$762$	4.73071	+	1.68890i	0.171376	+	0.0611825i
$763$		0			0
$764$	−25.9499	+	31.7113i	−0.938833	+	1.14728i
$765$	−3.59229	+	13.4066i	−0.129880	+	0.484717i
$766$	−0.566708	+	6.97198i	−0.0204760	+	0.251908i
$767$	12.5164	−	21.6791i	0.451943	−	0.782788i
$768$	4.28542	+	31.1870i	0.154637	+	1.12536i
$769$	22.6761			0.817720			0.408860	−	0.912597i	$-0.365926\pi$
$769$	22.6761			0.817720			0.408860	+	0.912597i	$0.365926\pi$
$770$		0			0
$771$	40.3008	+	40.3008i	1.45140	+	1.45140i
$772$	−25.0972	−	4.10712i	−0.903269	−	0.147819i
$773$	−1.01468	−	3.78685i	−0.0364956	−	0.136203i	0.945274	−	0.326277i	$-0.105794\pi$
$773$	−1.01468	−	3.78685i	−0.0364956	−	0.136203i	−0.981770	+	0.190073i	$0.939127\pi$
$774$	4.06170	−	3.45104i	0.145995	−	0.124045i
$775$	10.5364	−	6.08321i	0.378480	−	0.218515i
$776$	5.22216	−	21.0372i	0.187465	−	0.755192i
$777$		0			0
$778$	−9.43222	+	26.4201i	−0.338161	+	0.947208i
$779$	−7.36339	−	1.97301i	−0.263821	−	0.0706906i
$780$	−12.2949	+	27.2379i	−0.440229	+	0.975273i
$781$	−42.5394	+	11.3984i	−1.52218	+	0.407867i
$782$	25.7563	−	37.2704i	0.921043	−	1.33279i
$783$	−36.9695			−1.32118
$784$		0			0
$785$	4.15117			0.148161
$786$	−20.7733	+	30.0599i	−0.740960	+	1.07220i
$787$	−30.0204	+	8.04395i	−1.07011	+	0.286736i	−0.750539	−	0.660826i	$-0.770206\pi$
$787$	−30.0204	+	8.04395i	−1.07011	+	0.286736i	−0.319573	+	0.947562i	$0.603540\pi$
$788$	−33.1624	−	14.9692i	−1.18136	−	0.533256i
$789$	0.654607	+	0.175401i	0.0233046	+	0.00624445i
$790$	9.62726	−	26.9665i	0.342522	−	0.959424i
$791$		0			0
$792$	9.23967	−	5.56471i	0.328317	−	0.197733i
$793$	3.15948	−	1.82412i	0.112196	−	0.0647766i
$794$	−0.0973794	+	0.0827387i	−0.00345586	+	0.00293629i
$795$	11.6496	+	43.4770i	0.413170	+	1.54197i
$796$	−0.474318	+	2.89839i	−0.0168118	+	0.102731i
$797$	27.7986	+	27.7986i	0.984679	+	0.984679i	0.999884	−	0.0152058i	$-0.00484033\pi$
$797$	27.7986	+	27.7986i	0.984679	+	0.984679i	−0.0152058	+	0.999884i	$0.504840\pi$
$798$		0			0
$799$	−18.7569			−0.663570
$800$	−22.7286	−	9.75793i	−0.803578	−	0.344995i
$801$	1.42047	−	2.46032i	0.0501897	−	0.0869312i
$802$	−2.91138	+	35.8175i	−0.102804	+	1.26476i
$803$	−17.1907	+	64.1567i	−0.606648	+	2.26404i
$804$	−4.16330	−	3.40689i	−0.146828	−	0.120152i
$805$		0			0
$806$	9.19315	+	3.28203i	0.323815	+	0.115605i
$807$	−23.8047	+	13.7436i	−0.837964	+	0.483799i
$808$	−39.7233	+	0.734301i	−1.39746	+	0.0258326i
$809$	−42.7813	−	24.6998i	−1.50411	−	0.868398i	−0.999989	−	0.00476483i	$-0.998483\pi$
$809$	−42.7813	−	24.6998i	−1.50411	−	0.868398i	−0.504121	−	0.863633i	$-0.668183\pi$
$810$	46.2298	−	8.44557i	1.62435	−	0.296747i
$811$	−13.1428	+	13.1428i	−0.461506	+	0.461506i	−0.899149	−	0.437643i	$-0.855813\pi$
$811$	−13.1428	+	13.1428i	−0.461506	+	0.461506i	0.437643	+	0.899149i	$0.355813\pi$
$812$		0			0
$813$	−17.3861	−	17.3861i	−0.609756	−	0.609756i
$814$	−20.4689	+	29.6193i	−0.717434	+	1.03816i
$815$	−27.9701	+	48.4457i	−0.979750	+	1.69698i
$816$	−18.2204	−	36.6855i	−0.637842	−	1.28425i
$817$	2.60542	+	4.51272i	0.0911521	+	0.157880i
$818$	−13.5678	−	28.6343i	−0.474386	−	1.00117i
$819$		0			0
$820$	38.5633	−	3.85322i	1.34669	−	0.134560i
$821$	−1.03860	−	0.278293i	−0.0362475	−	0.00971248i	0.240650	−	0.970612i	$-0.422639\pi$
$821$	−1.03860	−	0.278293i	−0.0362475	−	0.00971248i	−0.276897	+	0.960900i	$0.589306\pi$
$822$	14.2987	+	16.8289i	0.498725	+	0.586975i
$823$	17.3926	+	10.0416i	0.606268	+	0.350029i	0.771504	−	0.636225i	$-0.219505\pi$
$823$	17.3926	+	10.0416i	0.606268	+	0.350029i	−0.165235	+	0.986254i	$0.552838\pi$
$824$	−1.26125	−	4.38147i	−0.0439377	−	0.152636i
$825$			37.6627i			1.31125i
$826$		0			0
$827$	6.99770	−	6.99770i	0.243334	−	0.243334i	−0.574894	−	0.818228i	$-0.694957\pi$
$827$	6.99770	−	6.99770i	0.243334	−	0.243334i	0.818228	+	0.574894i	$0.194957\pi$
$828$	10.5821	+	1.73174i	0.367752	+	0.0601821i
$829$	44.6990	−	11.9771i	1.55246	−	0.415980i	0.622193	−	0.782864i	$-0.286242\pi$
$829$	44.6990	−	11.9771i	1.55246	−	0.415980i	0.930267	+	0.366884i	$0.119575\pi$
$830$	−3.67940	+	45.2662i	−0.127714	+	1.57121i
$831$	8.34665	+	14.4568i	0.289542	+	0.501502i
$832$	−5.84130	−	18.9662i	−0.202511	−	0.657535i
$833$		0			0
$834$	7.35793	−	3.48641i	0.254784	−	0.120724i
$835$	−1.55391	+	5.79927i	−0.0537753	+	0.200692i
$836$	3.72849	+	9.86405i	0.128953	+	0.341155i
$837$	−3.01650	−	11.2577i	−0.104266	−	0.389125i
$838$	−8.72533	−	47.7612i	−0.301411	−	1.64988i
$839$		−	11.1872i		−	0.386225i	−0.981177	−	0.193113i	$-0.938142\pi$
$839$		−	11.1872i		−	0.386225i	0.981177	−	0.193113i	$-0.0618583\pi$
$840$		0			0
$841$			48.8991i			1.68618i
$842$	31.5321	−	5.76050i	1.08667	−	0.198520i
$843$	4.87073	+	18.1778i	0.167757	+	0.626077i
$844$	−0.622291	+	1.37861i	−0.0214201	+	0.0474536i
$845$	−5.42475	+	20.2454i	−0.186617	+	0.696464i
$846$	−1.90095	−	4.01189i	−0.0653561	−	0.137931i
$847$		0			0
$848$	−24.8998	−	16.5359i	−0.855064	−	0.567844i
$849$	−16.2605	−	28.1640i	−0.558058	−	0.966585i
$850$	32.0784	+	2.60745i	1.10028	+	0.0894349i
$851$	−34.5734	+	9.26392i	−1.18516	+	0.317563i
$852$	−32.1438	+	23.1028i	−1.10123	+	0.791489i
$853$	−25.4369	+	25.4369i	−0.870944	+	0.870944i	−0.992575	−	0.121632i	$-0.961187\pi$
$853$	−25.4369	+	25.4369i	−0.870944	+	0.870944i	0.121632	+	0.992575i	$0.461187\pi$
$854$		0			0
$855$		−	3.21174i		−	0.109839i
$856$	15.3374	−	27.7368i	0.524222	−	0.948024i
$857$	28.5281	+	16.4707i	0.974500	+	0.562628i	0.900605	−	0.434638i	$-0.143124\pi$
$857$	28.5281	+	16.4707i	0.974500	+	0.562628i	0.0738951	+	0.997266i	$0.476457\pi$
$858$	−23.0281	+	19.5659i	−0.786165	+	0.667967i
$859$	40.8704	+	10.9512i	1.39448	+	0.373649i	0.876359	−	0.481659i	$-0.159966\pi$
$859$	40.8704	+	10.9512i	1.39448	+	0.373649i	0.518120	+	0.855308i	$0.326632\pi$
$860$	−20.5019	−	16.7770i	−0.699108	−	0.572091i
$861$		0			0
$862$	40.4636	−	19.1729i	1.37819	−	0.653030i
$863$	−10.9071	−	18.8916i	−0.371281	−	0.643078i	0.618482	−	0.785799i	$-0.287748\pi$
$863$	−10.9071	−	18.8916i	−0.371281	−	0.643078i	−0.989763	+	0.142721i	$0.954415\pi$
$864$	−14.6644	+	18.6117i	−0.498893	+	0.633184i
$865$	8.96304	−	15.5244i	0.304752	−	0.527847i
$866$	−13.5915	−	9.39261i	−0.461858	−	0.319174i
$867$	14.0360	+	14.0360i	0.476689	+	0.476689i
$868$		0			0
$869$	20.4729	−	20.4729i	0.694495	−	0.694495i
$870$	−13.5115	−	73.9599i	−0.458082	−	2.50747i
$871$	2.93699	+	1.69567i	0.0995162	+	0.0574557i
$872$	−0.420640	−	22.7553i	−0.0142447	−	0.770591i
$873$	−5.78109	+	3.33772i	−0.195660	+	0.112965i
$874$	−3.52478	+	9.87311i	−0.119228	+	0.333963i
$875$		0			0
$876$	5.93570	+	59.4049i	0.200549	+	2.00711i
$877$	3.62186	−	13.5170i	0.122302	−	0.456435i	−0.877428	−	0.479709i	$-0.840742\pi$
$877$	3.62186	−	13.5170i	0.122302	−	0.456435i	0.999729	+	0.0232736i	$0.00740889\pi$
$878$	−18.4959	−	1.50342i	−0.624207	−	0.0507378i
$879$	21.2738	−	36.8473i	0.717548	−	1.24283i
$880$	−35.4619	−	40.2066i	−1.19542	−	1.35536i
$881$	−12.3319			−0.415471			−0.207735	−	0.978185i	$-0.566609\pi$
$881$	−12.3319			−0.415471			−0.207735	+	0.978185i	$0.566609\pi$
$882$		0			0
$883$	24.3508	+	24.3508i	0.819469	+	0.819469i	0.986031	−	0.166562i	$-0.0532667\pi$
$883$	24.3508	+	24.3508i	0.819469	+	0.819469i	−0.166562	+	0.986031i	$0.553267\pi$
$884$	15.0706	+	20.9683i	0.506878	+	0.705239i
$885$	−15.7319	−	58.7124i	−0.528823	−	1.97360i
$886$	21.0047	+	24.7215i	0.705666	+	0.830534i
$887$	−3.69725	+	2.13461i	−0.124141	+	0.0716731i	−0.560785	−	0.827962i	$-0.689500\pi$
$887$	−3.69725	+	2.13461i	−0.124141	+	0.0716731i	0.436643	+	0.899635i	$0.356167\pi$
$888$	−7.79665	+	31.4084i	−0.261638	+	1.05400i
$889$		0			0
$890$	−13.2985	−	4.74769i	−0.445768	−	0.159143i
$891$	45.9002	+	12.2989i	1.53772	+	0.412030i
$892$	−5.54243	−	14.6630i	−0.185574	−	0.490953i
$893$	4.19246	−	1.12337i	0.140295	−	0.0375920i
$894$	29.6367	+	20.4809i	0.991198	+	0.684982i
$895$	−41.1967			−1.37705
$896$		0			0
$897$	−30.0408			−1.00303
$898$	−18.1956	−	12.5743i	−0.607194	−	0.419610i
$899$	−23.7214	+	6.35613i	−0.791153	+	0.211989i
$900$	2.69335	+	7.12548i	0.0897783	+	0.237516i
$901$	37.5674	+	10.0662i	1.25155	+	0.335352i
$902$	36.9064	+	13.1759i	1.22885	+	0.438710i
$903$		0			0
$904$	−10.3993	+	41.8930i	−0.345875	+	1.39334i
$905$	−28.5122	+	16.4615i	−0.947776	+	0.547199i
$906$	5.04990	+	5.94348i	0.167772	+	0.197459i
$907$	−8.71495	−	32.5246i	−0.289375	−	1.07996i	−0.945583	−	0.325382i	$-0.894507\pi$
$907$	−8.71495	−	32.5246i	−0.289375	−	1.07996i	0.656208	−	0.754580i	$-0.272160\pi$
$908$	−0.408681	−	0.568613i	−0.0135625	−	0.0188701i
$909$	8.65188	+	8.65188i	0.286965	+	0.286965i
$910$		0			0
$911$	4.22749			0.140063			0.0700315	−	0.997545i	$-0.477690\pi$
$911$	4.22749			0.140063			0.0700315	+	0.997545i	$0.477690\pi$
$912$	6.26969	+	7.10856i	0.207610	+	0.235388i
$913$	−22.9612	+	39.7699i	−0.759904	+	1.31619i
$914$	−17.2396	−	1.40130i	−0.570236	−	0.0463509i
$915$	2.29275	−	8.55664i	0.0757958	−	0.282874i
$916$	4.38777	+	43.9132i	0.144976	+	1.45093i
$917$		0			0
$918$	10.3661	−	29.0361i	0.342134	−	0.958335i
$919$	−18.8641	+	10.8912i	−0.622270	+	0.359268i	−0.777752	−	0.628571i	$-0.783640\pi$
$919$	−18.8641	+	10.8912i	−0.622270	+	0.359268i	0.155482	+	0.987839i	$0.450307\pi$
$920$	−0.985044	−	53.2877i	−0.0324759	−	1.75684i
$921$	10.0305	+	5.79113i	0.330517	+	0.190824i
$922$	−4.83992	−	26.4930i	−0.159394	−	0.872502i
$923$	17.6457	−	17.6457i	0.580814	−	0.580814i
$924$		0			0
$925$	−17.9799	−	17.9799i	−0.591177	−	0.591177i
$926$	−28.8307	−	19.9239i	−0.947435	−	0.654739i
$927$	−0.702074	+	1.21603i	−0.0230591	+	0.0399396i
$928$	39.2171	+	30.8996i	1.28737	+	1.01433i
$929$	15.6683	+	27.1384i	0.514062	+	0.890381i	0.999867	+	0.0163141i	$0.00519316\pi$
$929$	15.6683	+	27.1384i	0.514062	+	0.890381i	−0.485805	+	0.874067i	$0.661474\pi$
$930$	21.4194	−	10.1491i	0.702369	−	0.332804i
$931$		0			0
$932$	14.7273	+	12.0516i	0.482410	+	0.394763i
$933$	1.52535	+	0.408718i	0.0499379	+	0.0133808i
$934$	35.3118	−	30.0028i	1.15544	−	0.981721i
$935$	60.4113	+	34.8785i	1.97566	+	1.14065i
$936$	−2.95752	+	5.34850i	−0.0966697	+	0.174821i
$937$		−	53.9341i		−	1.76195i	−0.473162	−	0.880975i	$-0.656887\pi$
$937$		−	53.9341i		−	1.76195i	0.473162	−	0.880975i	$-0.343113\pi$
$938$		0			0
$939$	−24.6644	+	24.6644i	−0.804893	+	0.804893i
$940$	−17.9180	+	12.8783i	−0.584422	+	0.420043i
$941$	47.8941	−	12.8332i	1.56130	−	0.418350i	0.628227	−	0.778030i	$-0.283781\pi$
$941$	47.8941	−	12.8332i	1.56130	−	0.418350i	0.933076	+	0.359680i	$0.117114\pi$
$942$	3.76047	+	0.305665i	0.122523	+	0.00995910i
$943$	19.4792	+	33.7390i	0.634330	+	1.09869i
$944$	33.6254	+	22.3305i	1.09441	+	0.726795i
$945$		0			0
$946$	−11.4701	−	24.2071i	−0.372924	−	0.787042i
$947$	0.0235259	−	0.0877997i	0.000764488	−	0.00285311i	−0.965543	−	0.260245i	$-0.916197\pi$
$947$	0.0235259	−	0.0877997i	0.000764488	−	0.00285311i	0.966307	+	0.257392i	$0.0828632\pi$
$948$	10.7068	−	23.7196i	0.347741	−	0.770376i
$949$	−9.74091	−	36.3536i	−0.316203	−	1.18009i
$950$	−7.32621	+	1.33840i	−0.237694	+	0.0434235i
$951$			28.8516i			0.935577i
$952$		0			0
$953$		−	45.4195i		−	1.47128i	−0.677371	−	0.735641i	$-0.736881\pi$
$953$		−	45.4195i		−	1.47128i	0.677371	−	0.735641i	$-0.263119\pi$
$954$	1.65431	+	9.05544i	0.0535602	+	0.293181i
$955$	−16.2338	−	60.5854i	−0.525314	−	1.96050i
$956$	13.3275	+	35.2590i	0.431042	+	1.14036i
$957$	19.6762	−	73.4326i	0.636041	−	2.37374i
$958$	−45.1965	+	21.4155i	−1.46023	+	0.691902i
$959$		0			0
$960$	−42.5935	−	22.5349i	−1.37470	−	0.727312i
$961$	11.6289	+	20.1419i	0.375127	+	0.649739i
$962$	1.65283	−	20.3341i	0.0532893	−	0.655597i
$963$	−9.42843	+	2.52634i	−0.303827	+	0.0814102i
$964$	12.6286	+	2.06665i	0.406739	+	0.0665623i
$965$	27.5263	−	27.5263i	0.886103	−	0.886103i
$966$		0			0
$967$		−	60.1289i		−	1.93362i	−0.255506	−	0.966808i	$-0.582242\pi$
$967$		−	60.1289i		−	1.93362i	0.255506	−	0.966808i	$-0.417758\pi$
$968$	−6.38909	−	22.1951i	−0.205353	−	0.713378i
$969$	−10.6808	−	6.16655i	−0.343116	−	0.198098i
$970$	21.4836	+	25.2852i	0.689798	+	0.811858i
$971$	−36.4130	−	9.75682i	−1.16855	−	0.313111i	−0.378173	−	0.925735i	$-0.623448\pi$
$971$	−36.4130	−	9.75682i	−1.16855	−	0.313111i	−0.790375	+	0.612624i	$0.790114\pi$
$972$	17.4931	−	1.74790i	0.561091	−	0.0560638i
$973$		0			0
$974$	−10.1285	−	21.3757i	−0.324537	−	0.684923i
$975$	−10.6705	−	18.4819i	−0.341731	−	0.591895i
$976$	2.61676	+	5.26865i	0.0837603	+	0.168645i
$977$	12.3444	−	21.3811i	0.394932	−	0.684042i	−0.598161	−	0.801376i	$-0.704102\pi$
$977$	12.3444	−	21.3811i	0.394932	−	0.684042i	0.993092	+	0.117334i	$0.0374349\pi$
$978$	−28.9049	+	41.8265i	−0.924276	+	1.33747i
$979$	−10.0962	−	10.0962i	−0.322676	−	0.322676i
$980$		0			0
$981$	−4.95619	+	4.95619i	−0.158239	+	0.158239i
$982$	11.6717	−	2.13226i	0.372459	−	0.0680433i
$983$	−4.43148	−	2.55852i	−0.141342	−	0.0816041i	0.427661	−	0.903939i	$-0.359338\pi$
$983$	−4.43148	−	2.55852i	−0.141342	−	0.0816041i	−0.569004	+	0.822335i	$0.692671\pi$
$984$	35.2176	−	0.651011i	1.12270	−	0.0207535i
$985$	48.2329	−	27.8473i	1.53683	−	0.887289i
$986$	−61.1825	−	21.8427i	−1.94845	−	0.695613i
$987$		0			0
$988$	−4.62432	−	3.78415i	−0.147119	−	0.120390i
$989$	6.89240	−	25.7228i	0.219166	−	0.817938i
$990$	−1.33762	+	16.4561i	−0.0425122	+	0.523011i
$991$	2.71965	−	4.71056i	0.0863924	−	0.149636i	−0.819591	−	0.572949i	$-0.805799\pi$
$991$	2.71965	−	4.71056i	0.0863924	−	0.149636i	0.905984	+	0.423313i	$0.139133\pi$
$992$	−6.20948	+	14.4634i	−0.197151	+	0.459214i
$993$	−0.620663			−0.0196961
$994$		0			0
$995$	−3.17892	−	3.17892i	−0.100779	−	0.100779i
$996$	−6.66621	+	40.7349i	−0.211227	+	1.29074i
$997$	−3.12961	−	11.6799i	−0.0991157	−	0.369905i	0.898496	−	0.438983i	$-0.144661\pi$
$997$	−3.12961	−	11.6799i	−0.0991157	−	0.369905i	−0.997611	+	0.0690777i	$0.977994\pi$
$998$	−8.46926	+	7.19594i	−0.268090	+	0.227783i
$999$	−21.0950	+	12.1792i	−0.667415	+	0.385332i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.l.557.6		24
7.2	even	3	inner	784.2.x.l.765.4		24
7.3	odd	6		784.2.m.h.589.1		12
7.4	even	3		112.2.m.d.29.1	✓	12
7.5	odd	6		784.2.x.m.765.4		24
7.6	odd	2		784.2.x.m.557.6		24
16.5	even	4	inner	784.2.x.l.165.4		24
28.11	odd	6		448.2.m.d.337.2		12
56.11	odd	6		896.2.m.h.673.5		12
56.53	even	6		896.2.m.g.673.2		12
112.5	odd	12		784.2.x.m.373.6		24
112.11	odd	12		448.2.m.d.113.2		12
112.37	even	12	inner	784.2.x.l.373.6		24
112.53	even	12		112.2.m.d.85.1	yes	12
112.67	odd	12		896.2.m.h.225.5		12
112.69	odd	4		784.2.x.m.165.4		24
112.101	odd	12		784.2.m.h.197.1		12
112.109	even	12		896.2.m.g.225.2		12
224.11	odd	24		7168.2.a.bi.1.3		12
224.53	even	24		7168.2.a.bj.1.10		12
224.123	odd	24		7168.2.a.bi.1.10		12
224.165	even	24		7168.2.a.bj.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.d.29.1	✓	12	7.4	even	3
112.2.m.d.85.1	yes	12	112.53	even	12
448.2.m.d.113.2		12	112.11	odd	12
448.2.m.d.337.2		12	28.11	odd	6
784.2.m.h.197.1		12	112.101	odd	12
784.2.m.h.589.1		12	7.3	odd	6
784.2.x.l.165.4		24	16.5	even	4	inner
784.2.x.l.373.6		24	112.37	even	12	inner
784.2.x.l.557.6		24	1.1	even	1	trivial
784.2.x.l.765.4		24	7.2	even	3	inner
784.2.x.m.165.4		24	112.69	odd	4
784.2.x.m.373.6		24	112.5	odd	12
784.2.x.m.557.6		24	7.6	odd	2
784.2.x.m.765.4		24	7.5	odd	6
896.2.m.g.225.2		12	112.109	even	12
896.2.m.g.673.2		12	56.53	even	6
896.2.m.h.225.5		12	112.67	odd	12
896.2.m.h.673.5		12	56.11	odd	6
7168.2.a.bi.1.3		12	224.11	odd	24
7168.2.a.bi.1.10		12	224.123	odd	24
7168.2.a.bj.1.3		12	224.165	even	24
7168.2.a.bj.1.10		12	224.53	even	24

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.16343 + 0.804007i) q^{2} +(-1.90046 + 0.509227i) q^{3} +(0.707146 + 1.87081i) q^{4} +(-2.95714 - 0.792364i) q^{5} +(-2.62048 - 0.935533i) q^{6} +(-0.681431 + 2.74511i) q^{8} +(0.754366 - 0.435533i) q^{9} +O(q^{10})\)	\(q+(1.16343 + 0.804007i) q^{2} +(-1.90046 + 0.509227i) q^{3} +(0.707146 + 1.87081i) q^{4} +(-2.95714 - 0.792364i) q^{5} +(-2.62048 - 0.935533i) q^{6} +(-0.681431 + 2.74511i) q^{8} +(0.754366 - 0.435533i) q^{9} +(-2.80337 - 3.29942i) q^{10} +(-1.13308 - 4.22870i) q^{11} +(-2.29657 - 3.19531i) q^{12} +(1.75410 + 1.75410i) q^{13} +6.02343 q^{15} +(-2.99989 + 2.64588i) q^{16} +(2.60235 - 4.50740i) q^{17} +(1.22782 + 0.0998021i) q^{18} +(-0.311715 + 1.16333i) q^{19} +(-0.608766 - 6.09258i) q^{20} +(2.08165 - 5.83081i) q^{22} +(5.33038 - 3.07750i) q^{23} +(-0.102853 - 5.56399i) q^{24} +(3.78672 + 2.18626i) q^{25} +(0.630466 + 3.45108i) q^{26} +(2.96185 - 2.96185i) q^{27} +(-6.24096 - 6.24096i) q^{29} +(7.00784 + 4.84288i) q^{30} +(1.39123 - 2.40969i) q^{31} +(-5.61747 + 0.666365i) q^{32} +(4.30674 + 7.45950i) q^{33} +(6.65164 - 3.15175i) q^{34} +(1.34825 + 1.10329i) q^{36} +(-5.61713 - 1.50511i) q^{37} +(-1.29799 + 1.10284i) q^{38} +(-4.22683 - 2.44036i) q^{39} +(4.19022 - 7.57775i) q^{40} +6.32956i q^{41} +(3.05937 - 3.05937i) q^{43} +(7.10987 - 5.11009i) q^{44} +(-2.57587 + 0.690201i) q^{45} +(8.67586 + 0.705206i) q^{46} +(-1.80192 - 3.12101i) q^{47} +(4.35382 - 6.55601i) q^{48} +(2.64782 + 5.58812i) q^{50} +(-2.65037 + 9.89133i) q^{51} +(-2.04119 + 4.52199i) q^{52} +(1.93405 + 7.21798i) q^{53} +(5.82725 - 1.06456i) q^{54} +13.4027i q^{55} -2.36961i q^{57} +(-2.24315 - 12.2787i) q^{58} +(-2.61179 - 9.74734i) q^{59} +(4.25944 + 11.2687i) q^{60} +(0.380638 - 1.42056i) q^{61} +(3.55601 - 1.68495i) q^{62} +(-7.07130 - 3.74121i) q^{64} +(-3.79723 - 6.57700i) q^{65} +(-0.986887 + 12.1413i) q^{66} +(1.32053 - 0.353834i) q^{67} +(10.2728 + 1.68112i) q^{68} +(-8.56304 + 8.56304i) q^{69} -10.0597i q^{71} +(0.681540 + 2.36761i) q^{72} +(-13.1391 - 7.58585i) q^{73} +(-5.32503 - 6.26730i) q^{74} +(-8.30982 - 2.22661i) q^{75} +(-2.39681 + 0.239487i) q^{76} +(-2.95556 - 6.23759i) q^{78} +(3.30674 + 5.72745i) q^{79} +(10.9676 - 5.44723i) q^{80} +(-5.42722 + 9.40022i) q^{81} +(-5.08901 + 7.36400i) q^{82} +(-7.41730 - 7.41730i) q^{83} +(-11.2670 + 11.2670i) q^{85} +(6.01912 - 1.09961i) q^{86} +(15.0388 + 8.68264i) q^{87} +(12.3804 - 0.228856i) q^{88} +(2.82449 - 1.63072i) q^{89} +(-3.55177 - 1.26801i) q^{90} +(9.52678 + 7.79591i) q^{92} +(-1.41691 + 5.28798i) q^{93} +(0.412907 - 5.07983i) q^{94} +(1.84357 - 3.19315i) q^{95} +(10.3365 - 4.12697i) q^{96} -7.66352 q^{97} +(-2.69650 - 2.69650i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} - 4 q^{3} + 6 q^{4} - 4 q^{5} + 8 q^{6} - 8 q^{8}+O(q^{10}) \) 24 * q - 2 * q^2 - 4 * q^3 + 6 * q^4 - 4 * q^5 + 8 * q^6 - 8 * q^8	\( 24 q - 2 q^{2} - 4 q^{3} + 6 q^{4} - 4 q^{5} + 8 q^{6} - 8 q^{8} + 4 q^{10} - 8 q^{12} - 48 q^{15} - 10 q^{16} + 8 q^{17} - 40 q^{20} + 28 q^{22} + 8 q^{24} + 20 q^{26} + 8 q^{27} - 8 q^{29} + 28 q^{30} + 8 q^{31} - 12 q^{32} + 16 q^{34} - 32 q^{36} + 20 q^{37} - 16 q^{38} + 8 q^{40} + 32 q^{43} - 14 q^{44} - 40 q^{45} + 28 q^{46} - 16 q^{47} + 32 q^{48} + 88 q^{50} + 16 q^{51} + 16 q^{52} - 4 q^{53} - 64 q^{54} - 14 q^{58} + 16 q^{59} - 60 q^{60} + 20 q^{61} + 16 q^{62} - 36 q^{64} - 32 q^{65} - 12 q^{66} - 24 q^{67} + 28 q^{68} - 8 q^{69} - 6 q^{72} + 38 q^{74} + 40 q^{75} + 96 q^{76} - 152 q^{78} - 24 q^{79} - 24 q^{80} + 44 q^{81} + 16 q^{82} - 40 q^{83} - 16 q^{85} - 38 q^{86} + 14 q^{88} - 80 q^{90} + 64 q^{92} + 48 q^{93} + 24 q^{94} + 16 q^{96} + 96 q^{97} + 64 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 - 4 * q^3 + 6 * q^4 - 4 * q^5 + 8 * q^6 - 8 * q^8 + 4 * q^10 - 8 * q^12 - 48 * q^15 - 10 * q^16 + 8 * q^17 - 40 * q^20 + 28 * q^22 + 8 * q^24 + 20 * q^26 + 8 * q^27 - 8 * q^29 + 28 * q^30 + 8 * q^31 - 12 * q^32 + 16 * q^34 - 32 * q^36 + 20 * q^37 - 16 * q^38 + 8 * q^40 + 32 * q^43 - 14 * q^44 - 40 * q^45 + 28 * q^46 - 16 * q^47 + 32 * q^48 + 88 * q^50 + 16 * q^51 + 16 * q^52 - 4 * q^53 - 64 * q^54 - 14 * q^58 + 16 * q^59 - 60 * q^60 + 20 * q^61 + 16 * q^62 - 36 * q^64 - 32 * q^65 - 12 * q^66 - 24 * q^67 + 28 * q^68 - 8 * q^69 - 6 * q^72 + 38 * q^74 + 40 * q^75 + 96 * q^76 - 152 * q^78 - 24 * q^79 - 24 * q^80 + 44 * q^81 + 16 * q^82 - 40 * q^83 - 16 * q^85 - 38 * q^86 + 14 * q^88 - 80 * q^90 + 64 * q^92 + 48 * q^93 + 24 * q^94 + 16 * q^96 + 96 * q^97 + 64 * q^99

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