LMFDB - Embedded newform 784.2.x.l.165.6

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			165.6
Character	$\chi$	$=$	784.165
Dual form			784.2.x.l.765.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37745 - 0.320359i) q^{2} +(0.811002 + 3.02670i) q^{3} +(1.79474 - 0.882557i) q^{4} +(-0.143894 + 0.537019i) q^{5} +(2.08675 + 3.90932i) q^{6} +(2.18943 - 1.79064i) q^{8} +(-5.90511 + 3.40932i) q^{9} +O(q^{10})$	\(q+(1.37745 - 0.320359i) q^{2} +(0.811002 + 3.02670i) q^{3} +(1.79474 - 0.882557i) q^{4} +(-0.143894 + 0.537019i) q^{5} +(2.08675 + 3.90932i) q^{6} +(2.18943 - 1.79064i) q^{8} +(-5.90511 + 3.40932i) q^{9} +(-0.0261678 + 0.785815i) q^{10} +(-3.04081 + 0.814781i) q^{11} +(4.12677 + 4.71638i) q^{12} +(-3.16316 + 3.16316i) q^{13} -1.74209 q^{15} +(2.44219 - 3.16792i) q^{16} +(-0.490475 + 0.849528i) q^{17} +(-7.04179 + 6.58792i) q^{18} +(7.19116 + 1.92687i) q^{19} +(0.215698 + 1.09080i) q^{20} +(-3.92754 + 2.09647i) q^{22} +(1.09077 - 0.629754i) q^{23} +(7.19536 + 5.17454i) q^{24} +(4.06244 + 2.34545i) q^{25} +(-3.34375 + 5.37045i) q^{26} +(-8.46094 - 8.46094i) q^{27} +(3.17349 - 3.17349i) q^{29} +(-2.39965 + 0.558095i) q^{30} +(2.21570 - 3.83770i) q^{31} +(2.34912 - 5.14603i) q^{32} +(-4.93220 - 8.54282i) q^{33} +(-0.403452 + 1.32731i) q^{34} +(-7.58922 + 11.3304i) q^{36} +(0.236140 - 0.881285i) q^{37} +(10.5228 + 0.350410i) q^{38} +(-12.1393 - 7.00862i) q^{39} +(0.646562 + 1.43343i) q^{40} -1.21375i q^{41} +(0.966515 + 0.966515i) q^{43} +(-4.73837 + 4.14601i) q^{44} +(-0.981160 - 3.66174i) q^{45} +(1.30073 - 1.21689i) q^{46} +(-4.98574 - 8.63555i) q^{47} +(11.5690 + 4.82257i) q^{48} +(6.34720 + 1.92931i) q^{50} +(-2.96904 - 0.795553i) q^{51} +(-2.88539 + 8.46873i) q^{52} +(11.0350 - 2.95681i) q^{53} +(-14.3651 - 8.94399i) q^{54} -1.75021i q^{55} +23.3282i q^{57} +(3.35467 - 5.38798i) q^{58} +(-2.47776 + 0.663915i) q^{59} +(-3.12661 + 1.53750i) q^{60} +(3.53504 + 0.947210i) q^{61} +(1.82257 - 5.99606i) q^{62} +(1.58722 - 7.84097i) q^{64} +(-1.24352 - 2.15384i) q^{65} +(-9.53063 - 10.1872i) q^{66} +(-0.582936 - 2.17555i) q^{67} +(-0.130519 + 1.95755i) q^{68} +(2.79069 + 2.79069i) q^{69} -0.934634i q^{71} +(-6.82397 + 18.0384i) q^{72} +(0.615321 + 0.355256i) q^{73} +(0.0429431 - 1.28958i) q^{74} +(-3.80433 + 14.1980i) q^{75} +(14.6068 - 2.88839i) q^{76} +(-18.9665 - 5.76510i) q^{78} +(-5.93220 - 10.2749i) q^{79} +(1.34982 + 1.76735i) q^{80} +(8.51894 - 14.7552i) q^{81} +(-0.388835 - 1.67188i) q^{82} +(-6.77482 + 6.77482i) q^{83} +(-0.385637 - 0.385637i) q^{85} +(1.64096 + 1.02170i) q^{86} +(12.1789 + 7.03150i) q^{87} +(-5.19865 + 7.22890i) q^{88} +(-8.84053 + 5.10408i) q^{89} +(-2.52457 - 4.72954i) q^{90} +(1.40185 - 2.09291i) q^{92} +(13.4125 + 3.59387i) q^{93} +(-9.63408 - 10.2978i) q^{94} +(-2.06953 + 3.58453i) q^{95} +(17.4806 + 2.93663i) q^{96} -3.03684 q^{97} +(15.1784 - 15.1784i) 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 $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.37745	−	0.320359i	0.974005	−	0.226528i
$2$	1.37745	−	0.320359i	0.974005	−	0.226528i
$3$	0.811002	+	3.02670i	0.468232	+	1.74747i	0.645945	+	0.763384i	$0.276463\pi$
$3$	0.811002	+	3.02670i	0.468232	+	1.74747i	−0.177713	+	0.984082i	$0.556870\pi$
$4$	1.79474	−	0.882557i	0.897370	−	0.441279i
$5$	−0.143894	+	0.537019i	−0.0643513	+	0.240162i	−0.990608	−	0.136730i	$-0.956341\pi$
$5$	−0.143894	+	0.537019i	−0.0643513	+	0.240162i	0.926257	+	0.376892i	$0.123007\pi$
$6$	2.08675	+	3.90932i	0.851910	+	1.59597i
$7$		0			0
$7$		0			0
$8$	2.18943	−	1.79064i	0.774081	−	0.633087i
$9$	−5.90511	+	3.40932i	−1.96837	+	1.13644i
$10$	−0.0261678	+	0.785815i	−0.00827498	+	0.248497i
$11$	−3.04081	+	0.814781i	−0.916837	+	0.245666i	−0.686233	−	0.727382i	$-0.740737\pi$
$11$	−3.04081	+	0.814781i	−0.916837	+	0.245666i	−0.230604	+	0.973048i	$0.574070\pi$
$12$	4.12677	+	4.71638i	1.19130	+	1.36150i
$13$	−3.16316	+	3.16316i	−0.877304	+	0.877304i	−0.993255	−	0.115951i	$-0.963008\pi$
$13$	−3.16316	+	3.16316i	−0.877304	+	0.877304i	0.115951	+	0.993255i	$0.463008\pi$
$14$		0			0
$15$	−1.74209			−0.449807
$16$	2.44219	−	3.16792i	0.610546	−	0.791980i
$17$	−0.490475	+	0.849528i	−0.118958	+	0.206041i	−0.919355	−	0.393429i	$-0.871289\pi$
$17$	−0.490475	+	0.849528i	−0.118958	+	0.206041i	0.800397	+	0.599470i	$0.204622\pi$
$18$	−7.04179	+	6.58792i	−1.65977	+	1.55279i
$19$	7.19116	+	1.92687i	1.64977	+	0.442053i	0.959547	−	0.281548i	$-0.0908478\pi$
$19$	7.19116	+	1.92687i	1.64977	+	0.442053i	0.690218	+	0.723601i	$0.257515\pi$
$20$	0.215698	+	1.09080i	0.0482315	+	0.243911i
$21$		0			0
$22$	−3.92754	+	2.09647i	−0.837354	+	0.446969i
$23$	1.09077	−	0.629754i	0.227441	−	0.131313i	−0.381950	−	0.924183i	$-0.624747\pi$
$23$	1.09077	−	0.629754i	0.227441	−	0.131313i	0.609391	+	0.792870i	$0.291414\pi$
$24$	7.19536	+	5.17454i	1.46875	+	1.05625i
$25$	4.06244	+	2.34545i	0.812489	+	0.469090i
$26$	−3.34375	+	5.37045i	−0.655764	+	1.05323i
$27$	−8.46094	−	8.46094i	−1.62831	−	1.62831i
$28$		0			0
$29$	3.17349	−	3.17349i	0.589302	−	0.589302i	−0.348140	−	0.937443i	$-0.613187\pi$
$29$	3.17349	−	3.17349i	0.589302	−	0.589302i	0.937443	+	0.348140i	$0.113187\pi$
$30$	−2.39965	+	0.558095i	−0.438114	+	0.101894i
$31$	2.21570	−	3.83770i	0.397951	−	0.689272i	−0.595522	−	0.803339i	$-0.703055\pi$
$31$	2.21570	−	3.83770i	0.397951	−	0.689272i	0.993473	+	0.114068i	$0.0363880\pi$
$32$	2.34912	−	5.14603i	0.415269	−	0.909699i
$33$	−4.93220	−	8.54282i	−0.858585	−	1.48711i
$34$	−0.403452	+	1.32731i	−0.0691914	+	0.227632i
$35$		0			0
$36$	−7.58922	+	11.3304i	−1.26487	+	1.88841i
$37$	0.236140	−	0.881285i	0.0388211	−	0.144882i	−0.943795	−	0.330531i	$-0.892772\pi$
$37$	0.236140	−	0.881285i	0.0388211	−	0.144882i	0.982616	+	0.185649i	$0.0594387\pi$
$38$	10.5228	+	0.350410i	1.70702	+	0.0568440i
$39$	−12.1393	−	7.00862i	−1.94384	−	1.12228i
$40$	0.646562	+	1.43343i	0.102230	+	0.226645i
$41$		−	1.21375i		−	0.189556i	−0.995498	−	0.0947779i	$-0.969786\pi$
$41$		−	1.21375i		−	0.189556i	0.995498	−	0.0947779i	$-0.0302141\pi$
$42$		0			0
$43$	0.966515	+	0.966515i	0.147392	+	0.147392i	0.776952	−	0.629560i	$-0.216765\pi$
$43$	0.966515	+	0.966515i	0.147392	+	0.147392i	−0.629560	+	0.776952i	$0.716765\pi$
$44$	−4.73837	+	4.14601i	−0.714335	+	0.625034i
$45$	−0.981160	−	3.66174i	−0.146263	−	0.545860i
$46$	1.30073	−	1.21689i	0.191782	−	0.179421i
$47$	−4.98574	−	8.63555i	−0.727244	−	1.25962i	−0.958043	−	0.286623i	$-0.907467\pi$
$47$	−4.98574	−	8.63555i	−0.727244	−	1.25962i	0.230799	−	0.973001i	$-0.425866\pi$
$48$	11.5690	+	4.82257i	1.66984	+	0.696078i
$49$		0			0
$50$	6.34720	+	1.92931i	0.897630	+	0.272845i
$51$	−2.96904	−	0.795553i	−0.415749	−	0.111400i
$52$	−2.88539	+	8.46873i	−0.400131	+	1.17440i
$53$	11.0350	−	2.95681i	1.51577	−	0.406149i	0.597421	−	0.801928i	$-0.296192\pi$
$53$	11.0350	−	2.95681i	1.51577	−	0.406149i	0.918346	+	0.395779i	$0.129525\pi$
$54$	−14.3651	−	8.94399i	−1.95484	−	1.21712i
$55$		−	1.75021i		−	0.235999i
$56$		0			0
$57$			23.3282i			3.08989i
$58$	3.35467	−	5.38798i	0.440490	−	0.707477i
$59$	−2.47776	+	0.663915i	−0.322577	+	0.0864344i	−0.416474	−	0.909148i	$-0.636734\pi$
$59$	−2.47776	+	0.663915i	−0.322577	+	0.0864344i	0.0938966	+	0.995582i	$0.470068\pi$
$60$	−3.12661	+	1.53750i	−0.403643	+	0.198490i
$61$	3.53504	+	0.947210i	0.452615	+	0.121278i	0.477923	−	0.878402i	$-0.341390\pi$
$61$	3.53504	+	0.947210i	0.452615	+	0.121278i	−0.0253078	+	0.999680i	$0.508057\pi$
$62$	1.82257	−	5.99606i	0.231467	−	0.761501i
$63$		0			0
$64$	1.58722	−	7.84097i	0.198402	−	0.980121i
$65$	−1.24352	−	2.15384i	−0.154240	−	0.267151i
$66$	−9.53063	−	10.1872i	−1.17314	−	1.25396i
$67$	−0.582936	−	2.17555i	−0.0712170	−	0.265785i	0.921132	−	0.389251i	$-0.127266\pi$
$67$	−0.582936	−	2.17555i	−0.0712170	−	0.265785i	−0.992349	+	0.123465i	$0.960599\pi$
$68$	−0.130519	+	1.95755i	−0.0158277	+	0.237388i
$69$	2.79069	+	2.79069i	0.335960	+	0.335960i
$70$		0			0
$71$		−	0.934634i		−	0.110921i	−0.998461	−	0.0554603i	$-0.982337\pi$
$71$		−	0.934634i		−	0.110921i	0.998461	−	0.0554603i	$-0.0176626\pi$
$72$	−6.82397	+	18.0384i	−0.804213	+	2.12585i
$73$	0.615321	+	0.355256i	0.0720179	+	0.0415795i	0.535577	−	0.844487i	$-0.320094\pi$
$73$	0.615321	+	0.355256i	0.0720179	+	0.0415795i	−0.463559	+	0.886066i	$0.653428\pi$
$74$	0.0429431	−	1.28958i	0.00499204	−	0.149910i
$75$	−3.80433	+	14.1980i	−0.439286	+	1.63944i
$76$	14.6068	−	2.88839i	1.67552	−	0.331321i
$77$		0			0
$78$	−18.9665	−	5.76510i	−2.14754	−	0.652769i
$79$	−5.93220	−	10.2749i	−0.667424	−	1.15601i	−0.978622	−	0.205668i	$-0.934063\pi$
$79$	−5.93220	−	10.2749i	−0.667424	−	1.15601i	0.311198	−	0.950345i	$-0.399270\pi$
$80$	1.34982	+	1.76735i	0.150914	+	0.197595i
$81$	8.51894	−	14.7552i	0.946549	−	1.63947i
$82$	−0.388835	−	1.67188i	−0.0429397	−	0.184628i
$83$	−6.77482	+	6.77482i	−0.743634	+	0.743634i	−0.973275	−	0.229642i	$-0.926245\pi$
$83$	−6.77482	+	6.77482i	−0.743634	+	0.743634i	0.229642	+	0.973275i	$0.426245\pi$
$84$		0			0
$85$	−0.385637	−	0.385637i	−0.0418282	−	0.0418282i
$86$	1.64096	+	1.02170i	0.176949	+	0.110172i
$87$	12.1789	+	7.03150i	1.30572	+	0.753856i
$88$	−5.19865	+	7.22890i	−0.554178	+	0.770603i
$89$	−8.84053	+	5.10408i	−0.937095	+	0.541032i	−0.889048	−	0.457813i	$-0.848633\pi$
$89$	−8.84053	+	5.10408i	−0.937095	+	0.541032i	−0.0480464	+	0.998845i	$0.515300\pi$
$90$	−2.52457	−	4.72954i	−0.266113	−	0.498537i
$91$		0			0
$92$	1.40185	−	2.09291i	0.146153	−	0.218201i
$93$	13.4125	+	3.59387i	1.39081	+	0.372667i
$94$	−9.63408	−	10.2978i	−0.993680	−	1.06214i
$95$	−2.06953	+	3.58453i	−0.212329	+	0.367765i
$96$	17.4806	+	2.93663i	1.78411	+	0.299719i
$97$	−3.03684			−0.308344			−0.154172	−	0.988044i	$-0.549271\pi$
$97$	−3.03684			−0.308344			−0.154172	+	0.988044i	$0.549271\pi$
$98$		0			0
$99$	15.1784	−	15.1784i	1.52549	−	1.52549i
$100$	9.36103	+	0.624140i	0.936103	+	0.0624140i
$101$	13.8853	−	3.72056i	1.38164	−	0.370210i	0.509925	−	0.860219i	$-0.329673\pi$
$101$	13.8853	−	3.72056i	1.38164	−	0.370210i	0.871717	+	0.490009i	$0.163007\pi$
$102$	−4.34457	−	0.144675i	−0.430177	−	0.0143250i
$103$	−5.24395	+	3.02760i	−0.516702	+	0.298318i	−0.735584	−	0.677433i	$-0.763092\pi$
$103$	−5.24395	+	3.02760i	−0.516702	+	0.298318i	0.218882	+	0.975751i	$0.429759\pi$
$104$	−1.26144	+	12.5896i	−0.123695	+	1.23451i
$105$		0			0
$106$	14.2529	−	7.60800i	1.38436	−	0.738954i
$107$	4.57432	−	17.0716i	0.442216	−	1.65037i	−0.280968	−	0.959717i	$-0.590656\pi$
$107$	4.57432	−	17.0716i	0.442216	−	1.65037i	0.723184	−	0.690655i	$-0.242678\pi$
$108$	−22.6525	−	7.71793i	−2.17973	−	0.742658i
$109$	3.68130	+	13.7388i	0.352604	+	1.31594i	0.883473	+	0.468483i	$0.155199\pi$
$109$	3.68130	+	13.7388i	0.352604	+	1.31594i	−0.530868	+	0.847454i	$0.678134\pi$
$110$	−0.560696	−	2.41083i	−0.0534603	−	0.229864i
$111$	2.85889			0.271354
$112$		0			0
$113$	5.01929			0.472175			0.236088	−	0.971732i	$-0.424135\pi$
$113$	5.01929			0.472175			0.236088	+	0.971732i	$0.424135\pi$
$114$	7.47339	+	32.1334i	0.699947	+	3.00957i
$115$	0.181236	+	0.676380i	0.0169003	+	0.0630728i
$116$	2.89480	−	8.49638i	0.268776	−	0.788869i
$117$	7.89461	−	29.4631i	0.729857	−	2.72386i
$118$	−3.20031	+	1.70828i	−0.294612	+	0.157260i
$119$		0			0
$120$	−3.81420	+	3.11946i	−0.348187	+	0.284767i
$121$	−0.943649	+	0.544816i	−0.0857863	+	0.0495287i
$122$	5.17278	+	0.172255i	0.468322	+	0.0155952i
$123$	3.67365	−	0.984353i	0.331242	−	0.0887561i
$124$	0.589612	−	8.84316i	0.0529487	−	0.794139i
$125$	−3.80974	+	3.80974i	−0.340754	+	0.340754i
$126$		0			0
$127$	−19.3869			−1.72031			−0.860156	−	0.510031i	$-0.829634\pi$
$127$	−19.3869			−1.72031			−0.860156	+	0.510031i	$0.829634\pi$
$128$	−0.325610	−	11.3090i	−0.0287802	−	0.999586i
$129$	−2.14151	+	3.70920i	−0.188549	+	0.326577i
$130$	−2.40289	−	2.56844i	−0.210747	−	0.225267i
$131$	−11.3274	−	3.03517i	−0.989680	−	0.265184i	−0.272564	−	0.962138i	$-0.587872\pi$
$131$	−11.3274	−	3.03517i	−0.989680	−	0.265184i	−0.717116	+	0.696954i	$0.754538\pi$
$132$	−16.3915	−	10.9792i	−1.42670	−	0.955616i
$133$		0			0
$134$	−1.49992	−	2.80996i	−0.129574	−	0.242744i
$135$	5.76117	−	3.32621i	0.495842	−	0.286275i
$136$	0.447337	+	2.73825i	0.0383588	+	0.234803i
$137$	−8.98270	−	5.18617i	−0.767444	−	0.443084i	0.0645179	−	0.997917i	$-0.479449\pi$
$137$	−8.98270	−	5.18617i	−0.767444	−	0.443084i	−0.831962	+	0.554832i	$0.812782\pi$
$138$	4.73806	+	2.95002i	0.403331	+	0.251122i
$139$	−4.83290	−	4.83290i	−0.409921	−	0.409921i	0.471790	−	0.881711i	$-0.343608\pi$
$139$	−4.83290	−	4.83290i	−0.409921	−	0.409921i	−0.881711	+	0.471790i	$0.843608\pi$
$140$		0			0
$141$	22.0938	−	22.0938i	1.86063	−	1.86063i
$142$	−0.299418	−	1.28741i	−0.0251266	−	0.108037i
$143$	7.04128	−	12.1959i	0.588821	−	1.01987i
$144$	−3.62093	+	27.0331i	−0.301744	+	2.25276i
$145$	1.24758	+	2.16087i	0.103606	+	0.179451i
$146$	0.961384	+	0.292224i	0.0795647	+	0.0241846i
$147$		0			0
$148$	−0.353975	−	1.79008i	−0.0290966	−	0.147144i
$149$	0.637064	−	2.37756i	0.0521903	−	0.194777i	−0.934909	−	0.354889i	$-0.884519\pi$
$149$	0.637064	−	2.37756i	0.0521903	−	0.194777i	0.987099	+	0.160112i	$0.0511854\pi$
$150$	−0.691836	+	20.7757i	−0.0564882	+	1.69633i
$151$	18.0246	+	10.4065i	1.46682	+	0.846871i	0.999311	−	0.0371149i	$-0.0118168\pi$
$151$	18.0246	+	10.4065i	1.46682	+	0.846871i	0.467513	+	0.883986i	$0.345150\pi$
$152$	19.1949	−	8.65804i	1.55691	−	0.702260i
$153$		−	6.68874i		−	0.540753i
$154$		0			0
$155$	1.74209	+	1.74209i	0.139928	+	0.139928i
$156$	−27.9724	−	1.86504i	−2.23958	−	0.149323i
$157$	−3.71300	−	13.8571i	−0.296330	−	1.10592i	−0.940155	−	0.340746i	$-0.889320\pi$
$157$	−3.71300	−	13.8571i	−0.296330	−	1.10592i	0.643825	−	0.765172i	$-0.277346\pi$
$158$	−11.4630	−	12.2527i	−0.911944	−	0.974772i
$159$	17.8987	+	31.0015i	1.41946	+	2.45858i
$160$	2.42549	+	2.00200i	0.191752	+	0.158272i
$161$		0			0
$162$	7.00745	−	23.0537i	0.550557	−	1.81127i
$163$	16.2395	+	4.35137i	1.27198	+	0.340825i	0.830788	−	0.556589i	$-0.187890\pi$
$163$	16.2395	+	4.35137i	1.27198	+	0.340825i	0.441190	+	0.897414i	$0.354557\pi$
$164$	−1.07120	−	2.17836i	−0.0836469	−	0.170102i
$165$	5.29737	−	1.41943i	0.412400	−	0.110502i
$166$	−7.16161	+	11.5024i	−0.555849	+	0.892756i
$167$		−	1.10868i		−	0.0857923i	−0.999080	−	0.0428962i	$-0.986342\pi$
$167$		−	1.10868i		−	0.0857923i	0.999080	−	0.0428962i	$-0.0136585\pi$
$168$		0			0
$169$		−	7.01121i		−	0.539324i
$170$	−0.654737	−	0.407653i	−0.0502161	−	0.0312656i
$171$	−49.0339	+	13.1386i	−3.74972	+	1.00473i
$172$	2.58765	+	0.881639i	0.197306	+	0.0672244i
$173$	9.88962	+	2.64992i	0.751894	+	0.201469i	0.614358	−	0.789027i	$-0.289415\pi$
$173$	9.88962	+	2.64992i	0.751894	+	0.201469i	0.137536	+	0.990497i	$0.456082\pi$
$174$	19.0284	+	5.78392i	1.44254	+	0.438478i
$175$		0			0
$176$	−4.84505	+	11.6229i	−0.365209	+	0.876108i
$177$	−4.01894	−	6.96101i	−0.302082	−	0.523222i
$178$	−10.5423	+	9.86277i	−0.790176	+	0.739246i
$179$	3.63814	+	13.5777i	0.271928	+	1.01485i	0.957872	+	0.287194i	$0.0927225\pi$
$179$	3.63814	+	13.5777i	0.271928	+	1.01485i	−0.685945	+	0.727654i	$0.740611\pi$
$180$	−4.99262	−	5.70594i	−0.372128	−	0.425296i
$181$	7.35342	+	7.35342i	0.546576	+	0.546576i	0.925449	−	0.378873i	$-0.123688\pi$
$181$	7.35342	+	7.35342i	0.546576	+	0.546576i	−0.378873	+	0.925449i	$0.623688\pi$
$182$		0			0
$183$			11.4677i			0.847715i
$184$	1.26049	−	3.33197i	0.0929249	−	0.245636i
$185$	0.439288	+	0.253623i	0.0322971	+	0.0186467i
$186$	19.6264	+	0.653563i	1.43908	+	0.0479215i
$187$	0.799260	−	2.98288i	0.0584477	−	0.218130i
$188$	−16.5695	−	11.0984i	−1.20845	−	0.809432i
$189$		0			0
$190$	−1.70234	+	5.60050i	−0.123501	+	0.406303i
$191$	−1.77342	−	3.07165i	−0.128320	−	0.222257i	0.794706	−	0.606995i	$-0.207625\pi$
$191$	−1.77342	−	3.07165i	−0.128320	−	0.222257i	−0.923026	+	0.384738i	$0.874292\pi$
$192$	25.0195	−	1.55501i	1.80563	−	0.112223i
$193$	−1.49697	+	2.59283i	−0.107754	+	0.186636i	−0.914860	−	0.403771i	$-0.867699\pi$
$193$	−1.49697	+	2.59283i	−0.107754	+	0.186636i	0.807106	+	0.590407i	$0.201033\pi$
$194$	−4.18310	+	0.972879i	−0.300329	+	0.0698486i
$195$	5.51053	−	5.51053i	0.394617	−	0.394617i
$196$		0			0
$197$	3.55345	+	3.55345i	0.253173	+	0.253173i	0.822270	−	0.569097i	$-0.192707\pi$
$197$	3.55345	+	3.55345i	0.253173	+	0.253173i	−0.569097	+	0.822270i	$0.692707\pi$
$198$	16.0450	−	25.7701i	1.14027	−	1.83140i
$199$	−1.55979	−	0.900545i	−0.110571	−	0.0638380i	0.443695	−	0.896178i	$-0.353667\pi$
$199$	−1.55979	−	0.900545i	−0.110571	−	0.0638380i	−0.554265	+	0.832340i	$0.687001\pi$
$200$	13.0943	−	2.13917i	0.925907	−	0.151262i
$201$	6.11197	−	3.52875i	0.431105	−	0.248899i
$202$	17.9344	−	9.57318i	1.26186	−	0.673567i
$203$		0			0
$204$	−6.03078	+	1.19254i	−0.422239	+	0.0834945i
$205$	0.651807	+	0.174651i	0.0455242	+	0.0121982i
$206$	−6.25337	+	5.85032i	−0.435693	+	0.407611i
$207$	−4.29407	+	7.43754i	−0.298458	+	0.516945i
$208$	2.29562	+	17.7457i	0.159173	+	1.23044i
$209$	−23.4369			−1.62116
$210$		0			0
$211$	−15.1022	+	15.1022i	−1.03968	+	1.03968i	−0.0404953	+	0.999180i	$0.512894\pi$
$211$	−15.1022	+	15.1022i	−1.03968	+	1.03968i	−0.999180	+	0.0404953i	$0.987106\pi$
$212$	17.1953	−	15.0457i	1.18098	−	1.03334i
$213$	2.82886	−	0.757990i	0.193830	−	0.0519366i
$214$	0.831862	−	24.9807i	0.0568649	−	1.70764i
$215$	−0.658113	+	0.379962i	−0.0448829	+	0.0259132i
$216$	−33.6752	−	3.37415i	−2.29130	−	0.229582i
$217$		0			0
$218$	9.47215	+	17.7452i	0.641535	+	1.20185i
$219$	−0.576226	+	2.15050i	−0.0389377	+	0.145318i
$220$	−1.54466	−	3.14118i	−0.104141	−	0.211778i
$221$	−1.13574	−	4.23865i	−0.0763983	−	0.285123i
$222$	3.93799	−	0.915872i	0.264300	−	0.0614693i
$223$	7.11258			0.476294			0.238147	−	0.971229i	$-0.423460\pi$
$223$	7.11258			0.476294			0.238147	+	0.971229i	$0.423460\pi$
$224$		0			0
$225$	−31.9856			−2.13237
$226$	6.91383	−	1.60798i	0.459901	−	0.106961i
$227$	−4.45405	−	16.6228i	−0.295626	−	1.10329i	−0.940719	−	0.339187i	$-0.889848\pi$
$227$	−4.45405	−	16.6228i	−0.295626	−	1.10329i	0.645093	−	0.764104i	$-0.276819\pi$
$228$	20.5884	+	41.8680i	1.36350	+	2.77278i
$229$	−0.227479	+	0.848962i	−0.0150322	+	0.0561010i	−0.973035	−	0.230659i	$-0.925912\pi$
$229$	−0.227479	+	0.848962i	−0.0150322	+	0.0561010i	0.958002	+	0.286760i	$0.0925784\pi$
$230$	0.466328	+	0.873620i	0.0307487	+	0.0576048i
$231$		0			0
$232$	1.26556	−	12.6307i	0.0830881	−	0.829247i
$233$	−4.20619	+	2.42844i	−0.275556	+	0.159093i	−0.631410	−	0.775449i	$-0.717523\pi$
$233$	−4.20619	+	2.42844i	−0.275556	+	0.159093i	0.355854	+	0.934542i	$0.384190\pi$
$234$	1.43567	−	43.1130i	0.0938528	−	2.81839i
$235$	5.35487	−	1.43483i	0.349313	−	0.0935982i
$236$	−3.86100	+	3.37832i	−0.251330	+	0.219910i
$237$	26.2879	−	26.2879i	1.70758	−	1.70758i
$238$		0			0
$239$	4.91033			0.317623			0.158811	−	0.987309i	$-0.449234\pi$
$239$	4.91033			0.317623			0.158811	+	0.987309i	$0.449234\pi$
$240$	−4.25452	+	5.51882i	−0.274628	+	0.356238i
$241$	−5.42956	+	9.40428i	−0.349749	+	0.605783i	−0.986205	−	0.165530i	$-0.947066\pi$
$241$	−5.42956	+	9.40428i	−0.349749	+	0.605783i	0.636456	+	0.771313i	$0.280400\pi$
$242$	−1.12529	+	1.05276i	−0.0723366	+	0.0676742i
$243$	16.8950	+	4.52699i	1.08381	+	0.290407i
$244$	7.18044	−	1.41987i	0.459680	−	0.0908982i
$245$		0			0
$246$	4.74493	−	2.53279i	0.302526	−	0.161484i
$247$	−28.8418	+	16.6518i	−1.83516	+	1.05953i
$248$	−2.02082	−	12.3699i	−0.128322	−	0.785489i
$249$	−25.9998	−	15.0110i	−1.64767	−	0.951281i
$250$	−4.02725	+	6.46821i	−0.254705	+	0.409086i
$251$	8.18516	+	8.18516i	0.516643	+	0.516643i	0.916554	−	0.399911i	$-0.130959\pi$
$251$	8.18516	+	8.18516i	0.516643	+	0.516643i	−0.399911	+	0.916554i	$0.630959\pi$
$252$		0			0
$253$	−2.80370	+	2.80370i	−0.176267	+	0.176267i
$254$	−26.7045	+	6.21078i	−1.67559	+	0.389699i
$255$	0.854454	−	1.47996i	0.0535080	−	0.0926786i
$256$	−4.07146	−	15.4733i	−0.254466	−	0.967082i
$257$	−10.3065	−	17.8514i	−0.642902	−	1.11354i	−0.984782	−	0.173795i	$-0.944397\pi$
$257$	−10.3065	−	17.8514i	−0.642902	−	1.11354i	0.341880	−	0.939744i	$-0.388936\pi$
$258$	−1.76154	+	5.79529i	−0.109669	+	0.360799i
$259$		0			0
$260$	−4.13268	−	2.76811i	−0.256298	−	0.171671i
$261$	−7.92038	+	29.5593i	−0.490259	+	1.82967i
$262$	−16.5753	−	0.551960i	−1.02402	−	0.0341002i
$263$	−11.8037	−	6.81485i	−0.727846	−	0.420222i	0.0897878	−	0.995961i	$-0.471381\pi$
$263$	−11.8037	−	6.81485i	−0.727846	−	0.420222i	−0.817634	+	0.575739i	$0.804714\pi$
$264$	−26.0958	−	9.87212i	−1.60609	−	0.607587i
$265$			6.35145i			0.390166i
$266$		0			0
$267$	−22.6182	−	22.6182i	−1.38421	−	1.38421i
$268$	−2.96626	−	3.39007i	−0.181193	−	0.207081i
$269$	1.62149	+	6.05148i	0.0988639	+	0.368965i	0.997577	−	0.0695721i	$-0.0221634\pi$
$269$	1.62149	+	6.05148i	0.0988639	+	0.368965i	−0.898713	+	0.438537i	$0.855497\pi$
$270$	6.87014	−	6.42733i	0.418104	−	0.391155i
$271$	−6.34254	−	10.9856i	−0.385282	−	0.667328i	0.606526	−	0.795063i	$-0.292562\pi$
$271$	−6.34254	−	10.9856i	−0.385282	−	0.667328i	−0.991808	+	0.127736i	$0.959229\pi$
$272$	1.49341	+	3.62849i	0.0905511	+	0.220010i
$273$		0			0
$274$	−14.0347	−	4.26600i	−0.847865	−	0.257718i
$275$	−14.2641	−	3.82206i	−0.860159	−	0.230479i
$276$	7.47151	+	2.54562i	0.449732	+	0.153228i
$277$	−23.3375	+	6.25325i	−1.40221	+	0.375721i	−0.879139	−	0.476566i	$-0.841881\pi$
$277$	−23.3375	+	6.25325i	−1.40221	+	0.375721i	−0.523073	+	0.852288i	$0.675215\pi$
$278$	−8.20534	−	5.10882i	−0.492124	−	0.306406i
$279$			30.2161i			1.80899i
$280$		0			0
$281$			12.8628i			0.767330i	0.923472	+	0.383665i	$0.125338\pi$
$281$			12.8628i			0.767330i	−0.923472	+	0.383665i	$0.874662\pi$
$282$	23.3551	−	37.5110i	1.39078	−	2.23375i
$283$	1.20086	−	0.321770i	0.0713837	−	0.0191272i	−0.222950	−	0.974830i	$-0.571569\pi$
$283$	1.20086	−	0.321770i	0.0713837	−	0.0191272i	0.294334	+	0.955703i	$0.404902\pi$
$284$	−0.824868	−	1.67743i	−0.0489469	−	0.0995369i
$285$	−12.5277	−	3.35678i	−0.742076	−	0.198839i
$286$	5.79196	−	19.0549i	0.342486	−	1.12674i
$287$		0			0
$288$	3.67265	+	38.3968i	0.216413	+	2.26255i
$289$	8.01887	+	13.8891i	0.471698	+	0.817005i
$290$	2.41073	+	2.57682i	0.141563	+	0.151316i
$291$	−2.46288	−	9.19160i	−0.144377	−	0.538821i
$292$	1.41787	+	0.0945358i	0.0829748	+	0.00553229i
$293$	−17.9935	−	17.9935i	−1.05119	−	1.05119i	−0.998617	−	0.0525765i	$-0.983257\pi$
$293$	−17.9935	−	17.9935i	−1.05119	−	1.05119i	−0.0525765	−	0.998617i	$-0.516743\pi$
$294$		0			0
$295$		−	1.42614i		−	0.0830331i
$296$	−1.06105	−	2.35235i	−0.0616724	−	0.136728i
$297$	32.6219	+	18.8343i	1.89291	+	1.09287i
$298$	0.115853	−	3.47905i	0.00671119	−	0.201536i
$299$	−1.45826	+	5.44229i	−0.0843332	+	0.314736i
$300$	5.70272	+	28.8392i	0.329247	+	1.66503i
$301$		0			0
$302$	28.1619	+	8.56013i	1.62053	+	0.492580i
$303$	22.5221	+	39.0093i	1.29386	+	2.24103i
$304$	23.6663	−	18.0753i	1.35736	−	1.03669i
$305$	−1.01734	+	1.76208i	−0.0582527	+	0.100897i
$306$	−2.14280	−	9.21342i	−0.122496	−	0.526696i
$307$	−1.74987	+	1.74987i	−0.0998702	+	0.0998702i	−0.755277	−	0.655406i	$-0.772497\pi$
$307$	−1.74987	+	1.74987i	−0.0998702	+	0.0998702i	0.655406	+	0.755277i	$0.272497\pi$
$308$		0			0
$309$	−13.4165	−	13.4165i	−0.763237	−	0.763237i
$310$	2.95774	+	1.84155i	0.167989	+	0.104593i
$311$	−15.0938	−	8.71439i	−0.855889	−	0.494148i	0.00674419	−	0.999977i	$-0.497853\pi$
$311$	−15.0938	−	8.71439i	−0.855889	−	0.494148i	−0.862634	+	0.505829i	$0.831187\pi$
$312$	−39.1280	+	6.39220i	−2.21519	+	0.361887i
$313$	24.5458	−	14.1715i	1.38741	−	0.801021i	0.394386	−	0.918945i	$-0.370957\pi$
$313$	24.5458	−	14.1715i	1.38741	−	0.801021i	0.993023	+	0.117924i	$0.0376240\pi$
$314$	−9.55373	−	17.8980i	−0.539148	−	1.01004i
$315$		0			0
$316$	−19.7149	−	13.2052i	−1.10905	−	0.742851i
$317$	−11.2615	−	3.01750i	−0.632508	−	0.169480i	−0.0717003	−	0.997426i	$-0.522843\pi$
$317$	−11.2615	−	3.01750i	−0.632508	−	0.169480i	−0.560807	+	0.827946i	$0.689509\pi$
$318$	34.5862	+	36.9690i	1.93950	+	2.07312i
$319$	−7.06427	+	12.2357i	−0.395523	+	0.685066i
$320$	3.98236	+	1.98063i	0.222621	+	0.110721i
$321$	55.3803			3.09103
$322$		0			0
$323$	−5.16401	+	5.16401i	−0.287333	+	0.287333i
$324$	2.26695	−	34.0003i	0.125941	−	1.88890i
$325$	−20.2692	+	5.43112i	−1.12433	+	0.301264i
$326$	23.7631	+	0.791317i	1.31612	+	0.0438270i
$327$	−38.5977	+	22.2844i	−2.13446	+	1.23233i
$328$	−2.17339	−	2.65742i	−0.120005	−	0.146731i
$329$		0			0
$330$	6.84214	−	3.65225i	0.376647	−	0.201050i
$331$	0.0861852	−	0.321647i	0.00473716	−	0.0176793i	−0.963517	−	0.267648i	$-0.913754\pi$
$331$	0.0861852	−	0.321647i	0.00473716	−	0.0176793i	0.968254	+	0.249969i	$0.0804203\pi$
$332$	−6.17988	+	18.1382i	−0.339165	+	0.995464i
$333$	1.61015	+	6.00916i	0.0882357	+	0.329300i
$334$	−0.355176	−	1.52715i	−0.0194344	−	0.0835621i
$335$	1.25219			0.0684146
$336$		0			0
$337$	9.22099			0.502299			0.251150	−	0.967948i	$-0.419191\pi$
$337$	9.22099			0.502299			0.251150	+	0.967948i	$0.419191\pi$
$338$	−2.24611	−	9.65760i	−0.122172	−	0.525304i
$339$	4.07066	+	15.1919i	0.221088	+	0.825111i
$340$	−1.03246	−	0.351771i	−0.0559932	−	0.0190775i
$341$	−3.61062	+	13.4750i	−0.195526	+	0.729713i
$342$	−63.3327	+	33.8062i	−3.42464	+	1.82803i
$343$		0			0
$344$	3.84680	+	0.385438i	0.207406	+	0.0207814i
$345$	−1.90022	+	1.09709i	−0.102304	+	0.0590654i
$346$	14.4714	+	0.481900i	0.777987	+	0.0259071i
$347$	10.9654	−	2.93816i	0.588652	−	0.157729i	0.0478151	−	0.998856i	$-0.484774\pi$
$347$	10.9654	−	2.93816i	0.588652	−	0.157729i	0.540837	+	0.841127i	$0.318108\pi$
$348$	28.0637	+	1.87113i	1.50437	+	0.100303i
$349$	11.5879	−	11.5879i	0.620287	−	0.620287i	−0.325318	−	0.945605i	$-0.605471\pi$
$349$	11.5879	−	11.5879i	0.620287	−	0.620287i	0.945605	+	0.325318i	$0.105471\pi$
$350$		0			0
$351$	53.5267			2.85704
$352$	−2.95032	+	17.5621i	−0.157253	+	0.936063i
$353$	−9.47403	+	16.4095i	−0.504252	+	0.873390i	0.495736	+	0.868473i	$0.334898\pi$
$353$	−9.47403	+	16.4095i	−0.504252	+	0.873390i	−0.999988	+	0.00491672i	$0.998435\pi$
$354$	−7.76592	−	8.30095i	−0.412754	−	0.441190i
$355$	0.501916	+	0.134488i	0.0266390	+	0.00713789i
$356$	−11.3618	+	16.9628i	−0.602175	+	0.899026i
$357$		0			0
$358$	9.36111	+	17.5371i	0.494750	+	0.926867i
$359$	−3.06722	+	1.77086i	−0.161882	+	0.0934624i	−0.578752	−	0.815503i	$-0.696460\pi$
$359$	−3.06722	+	1.77086i	−0.161882	+	0.0934624i	0.416871	+	0.908966i	$0.363127\pi$
$360$	−8.70504	−	6.26022i	−0.458796	−	0.329943i
$361$	31.5455	+	18.2128i	1.66029	+	0.958569i
$362$	12.4847	+	7.77324i	0.656182	+	0.408553i
$363$	−2.41430	−	2.41430i	−0.126718	−	0.126718i
$364$		0			0
$365$	−0.279320	+	0.279320i	−0.0146203	+	0.0146203i
$366$	3.67377	+	15.7962i	0.192031	+	0.825679i
$367$	−5.59371	+	9.68859i	−0.291989	+	0.505740i	−0.974280	−	0.225341i	$-0.927651\pi$
$367$	−5.59371	+	9.68859i	−0.291989	+	0.505740i	0.682291	+	0.731081i	$0.260984\pi$
$368$	0.668842	−	4.99344i	0.0348658	−	0.260301i
$369$	4.13806	+	7.16732i	0.215419	+	0.373116i
$370$	0.686348	+	0.208623i	0.0356815	+	0.0108458i
$371$		0			0
$372$	27.2438	−	5.38724i	1.41252	−	0.279315i
$373$	5.05377	−	18.8609i	0.261674	−	0.976581i	−0.702581	−	0.711604i	$-0.747969\pi$
$373$	5.05377	−	18.8609i	0.261674	−	0.976581i	0.964255	−	0.264977i	$-0.0853644\pi$
$374$	0.145349	−	4.36482i	0.00751584	−	0.225699i
$375$	−14.6206	−	8.44123i	−0.755007	−	0.435903i
$376$	−26.3791	−	9.97928i	−1.36040	−	0.514642i
$377$			20.0765i			1.03399i
$378$		0			0
$379$	−10.9875	−	10.9875i	−0.564391	−	0.564391i	0.366161	−	0.930552i	$-0.380672\pi$
$379$	−10.9875	−	10.9875i	−0.564391	−	0.564391i	−0.930552	+	0.366161i	$0.880672\pi$
$380$	−0.550715	+	8.25977i	−0.0282511	+	0.423717i
$381$	−15.7228	−	58.6784i	−0.805505	−	3.00619i
$382$	−3.42683	−	3.66292i	−0.175332	−	0.187411i
$383$	2.41973	+	4.19109i	0.123642	+	0.214155i	0.921201	−	0.389086i	$-0.127209\pi$
$383$	2.41973	+	4.19109i	0.123642	+	0.214155i	−0.797559	+	0.603241i	$0.793876\pi$
$384$	33.9649	−	10.1572i	1.73327	−	0.518330i
$385$		0			0
$386$	−1.23137	+	4.05106i	−0.0626750	+	0.206194i
$387$	−9.00254	−	2.41222i	−0.457625	−	0.122620i
$388$	−5.45034	+	2.68018i	−0.276699	+	0.136066i
$389$	−17.0489	+	4.56824i	−0.864414	+	0.231619i	−0.663671	−	0.748025i	$-0.731002\pi$
$389$	−17.0489	+	4.56824i	−0.864414	+	0.231619i	−0.200743	+	0.979644i	$0.564336\pi$
$390$	5.82514	−	9.35583i	0.294967	−	0.473751i
$391$			1.23552i			0.0624827i
$392$		0			0
$393$		−	36.7462i		−	1.85360i
$394$	6.03308	+	3.75632i	0.303942	+	0.189241i
$395$	6.37141	−	1.70721i	0.320580	−	0.0858992i
$396$	13.8455	−	40.6372i	0.695764	−	2.04210i
$397$	16.0566	+	4.30237i	0.805860	+	0.215930i	0.638155	−	0.769908i	$-0.279698\pi$
$397$	16.0566	+	4.30237i	0.805860	+	0.215930i	0.167705	+	0.985837i	$0.446364\pi$
$398$	−2.43703	−	0.740764i	−0.122157	−	0.0371311i
$399$		0			0
$400$	17.3514	−	7.14147i	0.867572	−	0.357074i
$401$	12.7912	+	22.1549i	0.638760	+	1.10636i	0.985705	+	0.168479i	$0.0538857\pi$
$401$	12.7912	+	22.1549i	0.638760	+	1.10636i	−0.346945	+	0.937885i	$0.612781\pi$
$402$	7.28847	−	6.81870i	0.363516	−	0.340086i
$403$	5.13066	+	19.1479i	0.255577	+	0.953825i
$404$	21.6370	−	18.9320i	1.07648	−	0.941904i
$405$	6.69803	+	6.69803i	0.332828	+	0.332828i
$406$		0			0
$407$			2.87222i			0.142371i
$408$	−7.92506	+	3.57468i	−0.392349	+	0.176973i
$409$	16.6386	+	9.60629i	0.822725	+	0.475001i	0.851355	−	0.524589i	$-0.175781\pi$
$409$	16.6386	+	9.60629i	0.822725	+	0.475001i	−0.0286301	+	0.999590i	$0.509115\pi$
$410$	0.953783	+	0.0317611i	0.0471040	+	0.00156857i
$411$	8.41198	−	31.3939i	0.414932	−	1.54855i
$412$	−6.73951	+	10.0618i	−0.332032	+	0.495711i
$413$		0			0
$414$	−3.53218	+	11.6205i	−0.173597	+	0.571116i
$415$	−2.66336	−	4.61307i	−0.130739	−	0.226447i
$416$	8.84710	+	23.7084i	0.433765	+	1.16240i
$417$	10.7082	−	18.5472i	0.524385	−	0.908261i
$418$	−32.2832	+	7.50822i	−1.57902	+	0.367239i
$419$	11.2764	−	11.2764i	0.550888	−	0.550888i	−0.375809	−	0.926697i	$-0.622635\pi$
$419$	11.2764	−	11.2764i	0.550888	−	0.550888i	0.926697	+	0.375809i	$0.122635\pi$
$420$		0			0
$421$	27.1033	+	27.1033i	1.32094	+	1.32094i	0.913019	+	0.407918i	$0.133745\pi$
$421$	27.1033	+	27.1033i	1.32094	+	1.32094i	0.407918	+	0.913019i	$0.366255\pi$
$422$	−15.9644	+	25.6406i	−0.777133	+	1.24816i
$423$	58.8827	+	33.9959i	2.86297	+	1.65294i
$424$	18.8657	−	26.2333i	0.916199	−	1.27400i
$425$	−3.98506	+	2.30077i	−0.193304	+	0.111604i
$426$	3.65378	−	1.95034i	0.177026	−	0.0944944i
$427$		0			0
$428$	−6.85694	−	34.6762i	−0.331443	−	1.67614i
$429$	42.6237	+	11.4210i	2.05789	+	0.551410i
$430$	−0.784794	+	0.734211i	−0.0378461	+	0.0354068i
$431$	7.38092	−	12.7841i	0.355526	−	0.615790i	−0.631682	−	0.775228i	$-0.717635\pi$
$431$	7.38092	−	12.7841i	0.355526	−	0.615790i	0.987208	+	0.159438i	$0.0509683\pi$
$432$	−47.4668	+	6.14041i	−2.28375	+	0.295431i
$433$	−30.0057			−1.44198			−0.720991	−	0.692944i	$-0.756313\pi$
$433$	−30.0057			−1.44198			−0.720991	+	0.692944i	$0.756313\pi$
$434$		0			0
$435$	−5.52852	+	5.52852i	−0.265072	+	0.265072i
$436$	18.7322	+	21.4086i	0.897112	+	1.02529i
$437$	9.05733	−	2.42690i	0.433271	−	0.116095i
$438$	−0.104789	+	3.14681i	−0.00500704	+	0.150361i
$439$	29.2303	−	16.8761i	1.39509	−	0.805454i	0.401214	−	0.915984i	$-0.368588\pi$
$439$	29.2303	−	16.8761i	1.39509	−	0.805454i	0.993873	+	0.110531i	$0.0352551\pi$
$440$	−3.13400	−	3.83197i	−0.149408	−	0.182682i
$441$		0			0
$442$	−2.92232	−	5.47469i	−0.139001	−	0.260404i
$443$	1.91073	−	7.13093i	0.0907813	−	0.338800i	−0.905565	−	0.424208i	$-0.860553\pi$
$443$	1.91073	−	7.13093i	0.0907813	−	0.338800i	0.996346	+	0.0854075i	$0.0272192\pi$
$444$	5.13097	−	2.52314i	0.243505	−	0.119743i
$445$	−1.46889	−	5.48198i	−0.0696322	−	0.259871i
$446$	9.79723	−	2.27858i	0.463912	−	0.107894i
$447$	7.71281			0.364803
$448$		0			0
$449$	−1.59006			−0.0750395			−0.0375197	−	0.999296i	$-0.511946\pi$
$449$	−1.59006			−0.0750395			−0.0375197	+	0.999296i	$0.511946\pi$
$450$	−44.0585	+	10.2469i	−2.07694	+	0.483042i
$451$	0.988940	+	3.69078i	0.0465674	+	0.173792i
$452$	9.00833	−	4.42981i	0.423716	−	0.208361i
$453$	−16.8794	+	62.9949i	−0.793065	+	2.95976i
$454$	−11.4605	−	21.4701i	−0.537867	−	1.00764i
$455$		0			0
$456$	41.7724	+	51.0754i	1.95617	+	2.39183i
$457$	−1.86124	+	1.07459i	−0.0870651	+	0.0502671i	−0.542900	−	0.839797i	$-0.682674\pi$
$457$	−1.86124	+	1.07459i	−0.0870651	+	0.0502671i	0.455835	+	0.890064i	$0.349341\pi$
$458$	−0.0413681	+	1.24228i	−0.00193301	+	0.0580479i
$459$	11.3377	−	3.03793i	0.529198	−	0.141798i
$460$	0.922215	+	1.05398i	0.0429985	+	0.0491419i
$461$	−26.7406	+	26.7406i	−1.24543	+	1.24543i	−0.287719	+	0.957715i	$0.592897\pi$
$461$	−26.7406	+	26.7406i	−1.24543	+	1.24543i	−0.957715	+	0.287719i	$0.907103\pi$
$462$		0			0
$463$	16.2686			0.756065			0.378033	−	0.925792i	$-0.376601\pi$
$463$	16.2686			0.756065			0.378033	+	0.925792i	$0.376601\pi$
$464$	−2.30312	−	17.8036i	−0.106920	−	0.826512i
$465$	−3.85995	+	6.68564i	−0.179001	+	0.310039i
$466$	−5.01584	+	4.69255i	−0.232354	+	0.217378i
$467$	−24.4908	−	6.56228i	−1.13330	−	0.303666i	−0.357044	−	0.934087i	$-0.616216\pi$
$467$	−24.4908	−	6.56228i	−1.13330	−	0.303666i	−0.776253	+	0.630421i	$0.782882\pi$
$468$	−11.8341	−	59.8460i	−0.547030	−	2.76638i
$469$		0			0
$470$	6.91641	−	3.69189i	0.319030	−	0.170294i
$471$	38.9301	−	22.4763i	1.79380	−	1.03565i
$472$	−4.23606	+	5.89038i	−0.194981	+	0.271127i
$473$	−3.72648	−	2.15149i	−0.171344	−	0.0989255i
$474$	27.7887	−	44.6319i	1.27638	−	2.05001i
$475$	24.6943	+	24.6943i	1.13305	+	1.13305i
$476$		0			0
$477$	−55.0819	+	55.0819i	−2.52203	+	2.52203i
$478$	6.76374	−	1.57307i	0.309366	−	0.0719504i
$479$	8.49302	−	14.7103i	0.388056	−	0.672133i	−0.604132	−	0.796884i	$-0.706480\pi$
$479$	8.49302	−	14.7103i	0.388056	−	0.672133i	0.992188	+	0.124751i	$0.0398134\pi$
$480$	−4.09239	+	8.96487i	−0.186791	+	0.409189i
$481$	2.04070	+	3.53460i	0.0930479	+	0.161164i
$482$	−4.46621	+	14.6933i	−0.203430	+	0.669263i
$483$		0			0
$484$	−1.21277	+	1.81063i	−0.0551261	+	0.0823012i
$485$	0.436983	−	1.63084i	0.0198424	−	0.0740527i
$486$	24.7223	+	0.823256i	1.12142	+	0.0373436i
$487$	−33.8046	−	19.5171i	−1.53183	−	0.884404i	−0.999277	−	0.0380089i	$-0.987898\pi$
$487$	−33.8046	−	19.5171i	−1.53183	−	0.884404i	−0.532555	−	0.846395i	$-0.678768\pi$
$488$	9.43583	−	4.25612i	0.427140	−	0.192666i
$489$			52.6811i			2.38232i
$490$		0			0
$491$	−26.8828	−	26.8828i	−1.21320	−	1.21320i	−0.969967	−	0.243238i	$-0.921790\pi$
$491$	−26.8828	−	26.8828i	−1.21320	−	1.21320i	−0.243238	−	0.969967i	$-0.578210\pi$
$492$	5.72451	−	5.00887i	0.258081	−	0.225817i
$493$	1.13945	+	4.25249i	0.0513183	+	0.191522i
$494$	−34.3936	+	32.1768i	−1.54744	+	1.44770i
$495$	5.96703	+	10.3352i	0.268198	+	0.464533i
$496$	−6.74639	−	16.3915i	−0.302922	−	0.736002i
$497$		0			0
$498$	−40.6223	−	12.3476i	−1.82033	−	0.553310i
$499$	−6.18767	−	1.65798i	−0.276998	−	0.0742214i	0.117646	−	0.993056i	$-0.462465\pi$
$499$	−6.18767	−	1.65798i	−0.276998	−	0.0742214i	−0.394644	+	0.918834i	$0.629132\pi$
$500$	−3.47518	+	10.1998i	−0.155415	+	0.456149i
$501$	3.35565	−	0.899143i	0.149919	−	0.0401707i
$502$	13.8968	+	8.65247i	0.620247	+	0.386178i
$503$		−	35.6215i		−	1.58829i	−0.607731	−	0.794143i	$-0.707920\pi$
$503$		−	35.6215i		−	1.58829i	0.607731	−	0.794143i	$-0.292080\pi$
$504$		0			0
$505$			7.99206i			0.355642i
$506$	−2.96376	+	4.76014i	−0.131755	+	0.211614i
$507$	21.2208	−	5.68611i	0.942451	−	0.252529i
$508$	−34.7945	+	17.1101i	−1.54376	+	0.759137i
$509$	−24.6300	−	6.59958i	−1.09170	−	0.292521i	−0.332322	−	0.943166i	$-0.607832\pi$
$509$	−24.6300	−	6.59958i	−1.09170	−	0.292521i	−0.759382	+	0.650645i	$0.774499\pi$
$510$	0.702851	−	2.31230i	0.0311228	−	0.102390i
$511$		0			0
$512$	−10.5652	−	20.0094i	−0.466922	−	0.884298i
$513$	−44.5409	−	77.1471i	−1.96653	−	3.40613i
$514$	−19.9155	−	21.2876i	−0.878437	−	0.938957i
$515$	−0.871306	−	3.25176i	−0.0383943	−	0.143290i
$516$	−0.569869	+	8.54705i	−0.0250871	+	0.376263i
$517$	22.1967	+	22.1967i	0.976212	+	0.976212i
$518$		0			0
$519$			32.0820i			1.40824i
$520$	−6.57935	−	2.48899i	−0.288524	−	0.109149i
$521$	13.4493	+	7.76498i	0.589226	+	0.340190i	0.764792	−	0.644278i	$-0.222842\pi$
$521$	13.4493	+	7.76498i	0.589226	+	0.340190i	−0.175565	+	0.984468i	$0.556175\pi$
$522$	−1.44036	+	43.2538i	−0.0630428	+	1.89317i
$523$	2.77474	−	10.3555i	0.121331	−	0.452814i	−0.878351	−	0.478016i	$-0.841356\pi$
$523$	2.77474	−	10.3555i	0.121331	−	0.452814i	0.999682	+	0.0252020i	$0.00802290\pi$
$524$	−23.0085	+	4.54974i	−1.00513	+	0.198756i
$525$		0			0
$526$	−18.4422	−	5.60571i	−0.804117	−	0.244421i
$527$	2.17349	+	3.76460i	0.0946787	+	0.163988i
$528$	−39.1083	−	5.23833i	−1.70197	−	0.227969i
$529$	−10.7068	+	18.5448i	−0.465514	+	0.806294i
$530$	2.03474	+	8.74880i	0.0883836	+	0.380024i
$531$	12.3680	−	12.3680i	0.536725	−	0.536725i
$532$		0			0
$533$	3.83929	+	3.83929i	0.166298	+	0.166298i
$534$	−38.4014	−	23.9095i	−1.66179	−	1.03467i
$535$	8.50955	+	4.91299i	0.367900	+	0.212407i
$536$	−5.17192	−	3.71938i	−0.223393	−	0.160653i
$537$	−38.1452	+	22.0231i	−1.64609	+	0.950368i
$538$	4.17217	+	7.81615i	0.179875	+	0.336978i
$539$		0			0
$540$	7.40423	−	11.0542i	0.318627	−	0.475699i
$541$	−22.9383	−	6.14630i	−0.986194	−	0.264250i	−0.270543	−	0.962708i	$-0.587203\pi$
$541$	−22.9383	−	6.14630i	−0.986194	−	0.264250i	−0.715651	+	0.698458i	$0.753870\pi$
$542$	−12.2559	−	13.1002i	−0.526435	−	0.562703i
$543$	−16.2930	+	28.2202i	−0.699198	+	1.21105i
$544$	3.21951	+	4.51964i	0.138036	+	0.193778i
$545$	−7.90771			−0.338729
$546$		0			0
$547$	−28.9159	+	28.9159i	−1.23636	+	1.23636i	−0.274875	+	0.961480i	$0.588637\pi$
$547$	−28.9159	+	28.9159i	−1.23636	+	1.23636i	−0.961480	+	0.274875i	$0.911363\pi$
$548$	−20.6987	−	1.38007i	−0.884205	−	0.0589538i
$549$	−24.1041	+	6.45868i	−1.02874	+	0.275650i
$550$	−20.8726	−	0.695061i	−0.890009	−	0.0296375i
$551$	28.9360	−	16.7062i	1.23271	−	0.711708i
$552$	11.1071	+	1.11290i	0.472752	+	0.0473683i
$553$		0			0
$554$	−30.1429	+	16.0899i	−1.28065	+	0.683595i
$555$	−0.411377	+	1.53528i	−0.0174620	+	0.0651691i
$556$	−12.9391	−	4.40849i	−0.548740	−	0.186962i
$557$	4.34676	+	16.2223i	0.184178	+	0.687362i	0.994805	+	0.101799i	$0.0324599\pi$
$557$	4.34676	+	16.2223i	0.184178	+	0.687362i	−0.810627	+	0.585563i	$0.800873\pi$
$558$	9.67999	+	41.6212i	0.409787	+	1.76196i
$559$	−6.11449			−0.258616
$560$		0			0
$561$	9.67648			0.408541
$562$	4.12071	+	17.7179i	0.173822	+	0.747383i
$563$	−0.922146	−	3.44149i	−0.0388638	−	0.145042i	0.943768	−	0.330609i	$-0.107254\pi$
$563$	−0.922146	−	3.44149i	−0.0388638	−	0.145042i	−0.982631	+	0.185568i	$0.940588\pi$
$564$	20.1536	−	59.1516i	0.848618	−	2.49073i
$565$	−0.722246	+	2.69546i	−0.0303851	+	0.113399i
$566$	1.55104	−	0.827928i	0.0651952	−	0.0348004i
$567$		0			0
$568$	−1.67359	−	2.04632i	−0.0702224	−	0.0858615i
$569$	−1.64887	+	0.951974i	−0.0691241	+	0.0399088i	−0.534164	−	0.845381i	$-0.679373\pi$
$569$	−1.64887	+	0.951974i	−0.0691241	+	0.0399088i	0.465040	+	0.885290i	$0.346040\pi$
$570$	−18.3316	−	0.610447i	−0.767828	−	0.0255688i
$571$	−2.65754	+	0.712086i	−0.111215	+	0.0297999i	−0.313997	−	0.949424i	$-0.601668\pi$
$571$	−2.65754	+	0.712086i	−0.111215	+	0.0297999i	0.202782	+	0.979224i	$0.435002\pi$
$572$	1.87373	−	28.1027i	0.0783446	−	1.17503i
$573$	7.85872	−	7.85872i	0.328303	−	0.328303i
$574$		0			0
$575$	5.90824			0.246390
$576$	17.3597	+	51.7131i	0.723319	+	2.15471i
$577$	0.135023	−	0.233867i	0.00562108	−	0.00973599i	−0.863201	−	0.504860i	$-0.831544\pi$
$577$	0.135023	−	0.233867i	0.00562108	−	0.00973599i	0.868822	+	0.495124i	$0.164877\pi$
$578$	15.4951	+	16.5626i	0.644511	+	0.688914i
$579$	−9.06176	−	2.42809i	−0.376594	−	0.100908i
$580$	4.14617	+	2.77714i	0.172160	+	0.115315i
$581$		0			0
$582$	−6.33711	−	11.8720i	−0.262682	−	0.492109i
$583$	−31.1460	+	17.9821i	−1.28994	+	0.744744i
$584$	1.98334	−	0.324010i	0.0820711	−	0.0134076i
$585$	14.6862	+	8.47911i	0.607202	+	0.350568i
$586$	−30.5496	−	19.0208i	−1.26199	−	0.785743i
$587$	−22.4556	−	22.4556i	−0.926842	−	0.926842i	0.0706582	−	0.997501i	$-0.477490\pi$
$587$	−22.4556	−	22.4556i	−0.926842	−	0.926842i	−0.997501	+	0.0706582i	$0.977490\pi$
$588$		0			0
$589$	23.3282	−	23.3282i	0.961221	−	0.961221i
$590$	−0.456877	−	1.96444i	−0.0188093	−	0.0808746i
$591$	−7.87338	+	13.6371i	−0.323867	+	0.560955i
$592$	−2.21515	−	2.90033i	−0.0910419	−	0.119203i
$593$	18.0313	+	31.2311i	0.740456	+	1.28251i	0.952288	+	0.305201i	$0.0987238\pi$
$593$	18.0313	+	31.2311i	0.740456	+	1.28251i	−0.211832	+	0.977306i	$0.567943\pi$
$594$	50.9688	+	15.4926i	2.09127	+	0.635667i
$595$		0			0
$596$	−0.954964	−	4.82934i	−0.0391168	−	0.197817i
$597$	1.46069	−	5.45136i	0.0597820	−	0.223109i
$598$	−0.265191	+	7.96365i	−0.0108445	+	0.325658i
$599$	9.29172	+	5.36458i	0.379649	+	0.219191i	0.677666	−	0.735370i	$-0.262992\pi$
$599$	9.29172	+	5.36458i	0.379649	+	0.219191i	−0.298016	+	0.954561i	$0.596325\pi$
$600$	17.0941	+	37.8976i	0.697864	+	1.54716i
$601$		−	36.0677i		−	1.47123i	−0.677399	−	0.735616i	$-0.736893\pi$
$601$		−	36.0677i		−	1.47123i	0.677399	−	0.735616i	$-0.263107\pi$
$602$		0			0
$603$	10.8594	+	10.8594i	0.442230	+	0.442230i
$604$	41.5339	+	2.76924i	1.68999	+	0.112679i
$605$	−0.156791	−	0.585153i	−0.00637448	−	0.0237899i
$606$	43.5200	+	46.5183i	1.76788	+	1.88968i
$607$	−3.49308	−	6.05020i	−0.141780	−	0.245570i	0.786387	−	0.617734i	$-0.211949\pi$
$607$	−3.49308	−	6.05020i	−0.141780	−	0.245570i	−0.928167	+	0.372164i	$0.878616\pi$
$608$	26.8086	−	32.4795i	1.08723	−	1.31722i
$609$		0			0
$610$	−0.836836	+	2.75310i	−0.0338825	+	0.111470i
$611$	43.0864	+	11.5450i	1.74309	+	0.467059i
$612$	−5.90320	−	12.0046i	−0.238623	−	0.485256i
$613$	31.9049	−	8.54889i	1.28863	−	0.345286i	0.451488	−	0.892277i	$-0.350893\pi$
$613$	31.9049	−	8.54889i	1.28863	−	0.345286i	0.837138	+	0.546991i	$0.184227\pi$
$614$	−1.84977	+	2.97094i	−0.0746507	+	0.119897i
$615$			2.11447i			0.0852635i
$616$		0			0
$617$		−	41.5107i		−	1.67116i	−0.549370	−	0.835579i	$-0.685132\pi$
$617$		−	41.5107i		−	1.67116i	0.549370	−	0.835579i	$-0.314868\pi$
$618$	−22.7786	−	14.1825i	−0.916291	−	0.570502i
$619$	26.4389	−	7.08429i	1.06267	−	0.284742i	0.315192	−	0.949028i	$-0.397931\pi$
$619$	26.4389	−	7.08429i	1.06267	−	0.284742i	0.747478	+	0.664286i	$0.231264\pi$
$620$	4.66410	+	1.58911i	0.187315	+	0.0638202i
$621$	−14.5572	−	3.90060i	−0.584162	−	0.156526i
$622$	−23.5827	−	7.16822i	−0.945579	−	0.287420i
$623$		0			0
$624$	−51.8491	+	21.3399i	−2.07563	+	0.854282i
$625$	10.2296	+	17.7181i	0.409182	+	0.708724i
$626$	29.2706	−	27.3840i	1.16989	−	1.09448i
$627$	−19.0074	−	70.9365i	−0.759081	−	2.83293i
$628$	−18.8936	−	21.5930i	−0.753936	−	0.861654i
$629$	0.632856	+	0.632856i	0.0252336	+	0.0252336i
$630$		0			0
$631$			2.56032i			0.101925i	0.998701	+	0.0509624i	$0.0162289\pi$
$631$			2.56032i			0.101925i	−0.998701	+	0.0509624i	$0.983771\pi$
$632$	−31.3867	−	11.8737i	−1.24850	−	0.472310i
$633$	−57.9576	−	33.4618i	−2.30361	−	1.32999i
$634$	−16.4788	−	0.548748i	−0.654457	−	0.0217936i
$635$	2.78966	−	10.4112i	0.110704	−	0.413154i
$636$	59.4842	+	39.8430i	2.35870	+	1.57988i
$637$		0			0
$638$	−5.81087	+	19.1171i	−0.230055	+	0.756854i
$639$	3.18646	+	5.51912i	0.126055	+	0.218333i
$640$	6.12002	+	1.45244i	0.241915	+	0.0574127i
$641$	0.327094	−	0.566544i	0.0129195	−	0.0223771i	−0.859493	−	0.511147i	$-0.829221\pi$
$641$	0.327094	−	0.566544i	0.0129195	−	0.0223771i	0.872413	+	0.488770i	$0.162554\pi$
$642$	76.2837	−	17.7416i	3.01068	−	0.700204i
$643$	3.21708	−	3.21708i	0.126869	−	0.126869i	−0.640821	−	0.767690i	$-0.721406\pi$
$643$	3.21708	−	3.21708i	0.126869	−	0.126869i	0.767690	+	0.640821i	$0.221406\pi$
$644$		0			0
$645$	−1.68376	−	1.68376i	−0.0662980	−	0.0662980i
$646$	−5.45884	+	8.76751i	−0.214775	+	0.344953i
$647$	−34.1274	−	19.7035i	−1.34169	−	0.774623i	−0.354632	−	0.935006i	$-0.615394\pi$
$647$	−34.1274	−	19.7035i	−1.34169	−	0.774623i	−0.987055	+	0.160382i	$0.948727\pi$
$648$	−7.76969	−	47.5599i	−0.305222	−	1.86833i
$649$	6.99345	−	4.03767i	0.274517	−	0.158493i
$650$	−26.1799	+	13.9745i	−1.02686	+	0.548126i
$651$		0			0
$652$	32.9861	−	6.52273i	1.29183	−	0.255450i
$653$	−34.7339	−	9.30692i	−1.35924	−	0.364208i	−0.495704	−	0.868491i	$-0.665090\pi$
$653$	−34.7339	−	9.30692i	−1.35924	−	0.364208i	−0.863538	+	0.504284i	$0.831757\pi$
$654$	−46.0274	+	43.0607i	−1.79981	+	1.68381i
$655$	3.25989	−	5.64629i	0.127374	−	0.220619i
$656$	−3.84506	−	2.96420i	−0.150124	−	0.115733i
$657$	−4.84472			−0.189010
$658$		0			0
$659$	31.8006	−	31.8006i	1.23877	−	1.23877i	0.278272	−	0.960502i	$-0.410238\pi$
$659$	31.8006	−	31.8006i	1.23877	−	1.23877i	0.960502	−	0.278272i	$-0.0897616\pi$
$660$	8.25468	−	7.22273i	0.321313	−	0.281145i
$661$	7.45175	−	1.99669i	0.289839	−	0.0776622i	−0.110970	−	0.993824i	$-0.535396\pi$
$661$	7.45175	−	1.99669i	0.289839	−	0.0776622i	0.400809	+	0.916162i	$0.368729\pi$
$662$	0.0156732	−	0.470664i	0.000609156	−	0.0182929i
$663$	11.9080	−	6.87511i	0.462470	−	0.267007i
$664$	−2.70174	+	26.9643i	−0.104848	+	1.04642i
$665$		0			0
$666$	4.14299	+	7.76150i	0.160538	+	0.300752i
$667$	1.46302	−	5.46006i	0.0566483	−	0.211414i
$668$	−0.978475	−	1.98980i	−0.0378583	−	0.0769875i
$669$	5.76831	+	21.5276i	0.223016	+	0.832307i
$670$	1.72483	−	0.401151i	0.0666361	−	0.0154978i
$671$	−11.5211			−0.444768
$672$		0			0
$673$	−28.3929			−1.09446			−0.547232	−	0.836981i	$-0.684319\pi$
$673$	−28.3929			−1.09446			−0.547232	+	0.836981i	$0.684319\pi$
$674$	12.7015	−	2.95403i	0.489242	−	0.113785i
$675$	−14.5274	−	54.2168i	−0.559158	−	2.08681i
$676$	−6.18780	−	12.5833i	−0.237992	−	0.483973i
$677$	2.77675	−	10.3630i	0.106719	−	0.398281i	−0.891815	−	0.452400i	$-0.850568\pi$
$677$	2.77675	−	10.3630i	0.106719	−	0.398281i	0.998535	+	0.0541182i	$0.0172348\pi$
$678$	10.4740	+	19.6220i	0.402251	+	0.753579i
$679$		0			0
$680$	−1.53486	−	0.153788i	−0.0588592	−	0.00589752i
$681$	46.6999	−	26.9622i	1.78954	−	1.03319i
$682$	−0.656609	+	19.7179i	−0.0251428	+	0.755036i
$683$	14.5472	−	3.89792i	0.556634	−	0.149150i	0.0304747	−	0.999536i	$-0.490298\pi$
$683$	14.5472	−	3.89792i	0.556634	−	0.149150i	0.526160	+	0.850386i	$0.323631\pi$
$684$	−76.4076	+	66.8556i	−2.92152	+	2.55629i
$685$	4.07763	−	4.07763i	0.155798	−	0.155798i
$686$		0			0
$687$	−2.75404			−0.105073
$688$	5.42226	−	0.701435i	0.206722	−	0.0267420i
$689$	−25.5525	+	44.2582i	−0.973473	+	1.68610i
$690$	−2.26599	+	2.11994i	−0.0862649	+	0.0807048i
$691$	−1.80049	−	0.482439i	−0.0684938	−	0.0183529i	0.224409	−	0.974495i	$-0.427955\pi$
$691$	−1.80049	−	0.482439i	−0.0684938	−	0.0183529i	−0.292903	+	0.956142i	$0.594621\pi$
$692$	20.0880	−	3.97225i	0.763631	−	0.151002i
$693$		0			0
$694$	14.1630	−	7.56003i	0.537620	−	0.286975i
$695$	3.29078	−	1.89994i	0.124827	−	0.0720686i
$696$	39.2558	−	6.41306i	1.48799	−	0.243087i
$697$	1.03111	+	0.595314i	0.0390562	+	0.0225491i
$698$	12.2495	−	19.6741i	0.463650	−	0.744675i
$699$	−10.7614	−	10.7614i	−0.407033	−	0.407033i
$700$		0			0
$701$	5.77893	−	5.77893i	0.218267	−	0.218267i	−0.589501	−	0.807768i	$-0.700675\pi$
$701$	5.77893	−	5.77893i	0.218267	−	0.218267i	0.807768	+	0.589501i	$0.200675\pi$
$702$	73.7304	−	17.1478i	2.78277	−	0.647200i
$703$	3.39624	−	5.88245i	0.128091	−	0.221861i
$704$	1.56225	+	25.1361i	0.0588797	+	0.947352i
$705$	8.68562	+	15.0439i	0.327119	+	0.566588i
$706$	−7.79308	+	25.6384i	−0.293296	+	0.964913i
$707$		0			0
$708$	−13.3565	−	8.94626i	−0.501966	−	0.336221i
$709$	−10.0800	+	37.6192i	−0.378564	+	1.41282i	0.469503	+	0.882931i	$0.344433\pi$
$709$	−10.0800	+	37.6192i	−0.378564	+	1.41282i	−0.848067	+	0.529889i	$0.822233\pi$
$710$	0.734450	+	0.0244573i	0.0275634	+	0.000917867i
$711$	70.0606	+	40.4495i	2.62748	+	1.51697i
$712$	−10.2162	+	27.0053i	−0.382867	+	1.01206i
$713$		−	5.58138i		−	0.209024i
$714$		0			0
$715$	5.53621	+	5.53621i	0.207043	+	0.207043i
$716$	18.5126	+	21.1576i	0.691850	+	0.790698i
$717$	3.98229	+	14.8621i	0.148721	+	0.555035i
$718$	−3.65763	+	3.42188i	−0.136502	+	0.127704i
$719$	1.89904	+	3.28924i	0.0708223	+	0.122668i	0.899262	−	0.437411i	$-0.144104\pi$
$719$	1.89904	+	3.28924i	0.0708223	+	0.122668i	−0.828440	+	0.560078i	$0.810771\pi$
$720$	−13.9963	−	5.83441i	−0.521610	−	0.217436i
$721$		0			0
$722$	49.2870	+	14.9814i	1.83427	+	0.557548i
$723$	−32.8673	−	8.80677i	−1.22235	−	0.327527i
$724$	19.6873	+	6.70767i	0.731673	+	0.249289i
$725$	20.3354	−	5.44885i	0.755238	−	0.202365i
$726$	−4.09901	−	2.55213i	−0.152129	−	0.0947185i
$727$			25.5053i			0.945937i	0.881079	+	0.472969i	$0.156818\pi$
$727$			25.5053i			0.945937i	−0.881079	+	0.472969i	$0.843182\pi$
$728$		0			0
$729$			3.69376i			0.136806i
$730$	−0.295267	+	0.474232i	−0.0109283	+	0.0175521i
$731$	−1.29513	+	0.347030i	−0.0479023	+	0.0128354i
$732$	10.1209	+	20.5815i	0.374079	+	0.760714i
$733$	39.6348	+	10.6201i	1.46395	+	0.392263i	0.900851	−	0.434129i	$-0.142944\pi$
$733$	39.6348	+	10.6201i	1.46395	+	0.392263i	0.563095	+	0.826392i	$0.309611\pi$
$734$	−4.60123	+	15.1376i	−0.169835	+	0.558737i
$735$		0			0
$736$	−0.678397	−	7.09249i	−0.0250060	−	0.261433i
$737$	3.54519	+	6.14045i	0.130589	+	0.226186i
$738$	7.99609	+	8.54697i	0.294340	+	0.314618i
$739$	0.611156	+	2.28087i	0.0224817	+	0.0839030i	0.976255	−	0.216623i	$-0.0695043\pi$
$739$	0.611156	+	2.28087i	0.0224817	+	0.0839030i	−0.953774	+	0.300526i	$0.902838\pi$
$740$	1.01224	+	0.0674907i	0.0372109	+	0.00248101i
$741$	−73.7909	−	73.7909i	−2.71077	−	2.71077i
$742$		0			0
$743$		−	24.1373i		−	0.885513i	−0.896642	−	0.442756i	$-0.854001\pi$
$743$		−	24.1373i		−	0.885513i	0.896642	−	0.442756i	$-0.145999\pi$
$744$	35.8011	−	16.1484i	1.31253	−	0.592030i
$745$	1.18512	+	0.684231i	0.0434196	+	0.0250683i
$746$	0.919052	−	27.5990i	0.0336489	−	1.01047i
$747$	16.9086	−	63.1036i	0.618652	−	2.30884i
$748$	−1.19810	−	6.05889i	−0.0438068	−	0.221535i
$749$		0			0
$750$	−22.8434	−	6.94353i	−0.834125	−	0.253542i
$751$	−8.83513	−	15.3029i	−0.322398	−	0.558410i	0.658584	−	0.752507i	$-0.271156\pi$
$751$	−8.83513	−	15.3029i	−0.322398	−	0.558410i	−0.980982	+	0.194097i	$0.937822\pi$
$752$	−39.5328	−	5.29519i	−1.44161	−	0.193096i
$753$	−18.1358	+	31.4122i	−0.660907	+	1.14472i
$754$	6.43170	+	27.6544i	0.234229	+	1.00712i
$755$	−8.18214	+	8.18214i	−0.297779	+	0.297779i
$756$		0			0
$757$	−14.3436	−	14.3436i	−0.521327	−	0.521327i	0.396645	−	0.917972i	$-0.370174\pi$
$757$	−14.3436	−	14.3436i	−0.521327	−	0.521327i	−0.917972	+	0.396645i	$0.870174\pi$
$758$	−18.6547	−	11.6148i	−0.677569	−	0.421869i
$759$	−10.7598	−	6.21215i	−0.390554	−	0.225487i
$760$	1.88751	+	11.5539i	0.0684672	+	0.419102i
$761$	−11.6399	+	6.72028i	−0.421945	+	0.243610i	−0.695909	−	0.718130i	$-0.744998\pi$
$761$	−11.6399	+	6.72028i	−0.421945	+	0.243610i	0.273964	+	0.961740i	$0.411665\pi$
$762$	−40.4556	−	75.7897i	−1.46555	−	2.74557i
$763$		0			0
$764$	−5.89373	−	3.94767i	−0.213228	−	0.142822i
$765$	3.59198	+	0.962469i	0.129868	+	0.0347982i
$766$	4.67570	+	4.99783i	0.168940	+	0.180579i
$767$	5.73750	−	9.93765i	0.207169	−	0.358828i
$768$	43.5311	−	24.8720i	1.57079	−	0.897490i
$769$	−42.7134			−1.54029			−0.770143	−	0.637871i	$-0.779815\pi$
$769$	−42.7134			−1.54029			−0.770143	+	0.637871i	$0.779815\pi$
$770$		0			0
$771$	45.6722	−	45.6722i	1.64484	−	1.64484i
$772$	−0.398354	+	5.97462i	−0.0143371	+	0.215031i
$773$	−24.0746	+	6.45078i	−0.865905	+	0.232018i	−0.664316	−	0.747452i	$-0.731277\pi$
$773$	−24.0746	+	6.45078i	−0.865905	+	0.232018i	−0.201589	+	0.979470i	$0.564610\pi$
$774$	−13.1733	−	0.438675i	−0.473506	−	0.0157678i
$775$	18.0023	−	10.3936i	0.646661	−	0.373350i
$776$	−6.64895	+	5.43789i	−0.238683	+	0.195209i
$777$		0			0
$778$	−22.0206	+	11.7543i	−0.789475	+	0.421412i
$779$	2.33873	−	8.72827i	0.0837938	−	0.312723i
$780$	5.02661	−	14.7533i	0.179982	−	0.528254i
$781$	0.761522	+	2.84204i	0.0272494	+	0.101696i
$782$	0.395809	+	1.70186i	0.0141541	+	0.0608585i
$783$	−53.7014			−1.91913
$784$		0			0
$785$	7.97582			0.284669
$786$	−11.7720	−	50.6161i	−0.419892	−	1.80542i
$787$	10.0507	+	37.5097i	0.358268	+	1.33708i	0.876321	+	0.481727i	$0.159990\pi$
$787$	10.0507	+	37.5097i	0.358268	+	1.33708i	−0.518053	+	0.855349i	$0.673343\pi$
$788$	9.51365	+	3.24140i	0.338910	+	0.115470i
$789$	11.0537	−	41.2530i	0.393523	−	1.46865i
$790$	8.22938	−	4.39274i	0.292788	−	0.156287i
$791$		0			0
$792$	6.05303	−	60.4113i	0.215085	−	2.14662i
$793$	−14.1781	+	8.18572i	−0.503478	+	0.290683i
$794$	23.4955	+	0.782406i	0.833826	+	0.0277666i
$795$	−19.2239	+	5.15103i	−0.681802	+	0.182688i
$796$	−3.59420	−	0.239641i	−0.127393	−	0.00849385i
$797$	37.2933	−	37.2933i	1.32100	−	1.32100i	0.408024	−	0.912971i	$-0.366218\pi$
$797$	37.2933	−	37.2933i	1.32100	−	1.32100i	0.912971	−	0.408024i	$-0.133782\pi$
$798$		0			0
$799$	9.78152			0.346045
$800$	21.6129	−	15.3957i	0.764133	−	0.544321i
$801$	34.8029	−	60.2804i	1.22970	−	2.12990i
$802$	24.7167	+	26.4196i	0.872778	+	0.932907i
$803$	−2.16053	−	0.578911i	−0.0762433	−	0.0204293i
$804$	7.85507	−	11.7273i	0.277027	−	0.413592i
$805$		0			0
$806$	13.2014	+	24.7316i	0.465001	+	0.871134i
$807$	−17.0010	+	9.81552i	−0.598463	+	0.345523i
$808$	23.7388	−	33.0095i	0.835128	−	1.16127i
$809$	−38.3756	−	22.1562i	−1.34922	−	0.778970i	−0.361077	−	0.932536i	$-0.617591\pi$
$809$	−38.3756	−	22.1562i	−1.34922	−	0.778970i	−0.988138	+	0.153566i	$0.950924\pi$
$810$	11.3720	+	7.08043i	0.399570	+	0.248781i
$811$	9.44442	+	9.44442i	0.331639	+	0.331639i	0.853209	−	0.521570i	$-0.174653\pi$
$811$	9.44442	+	9.44442i	0.331639	+	0.331639i	−0.521570	+	0.853209i	$0.674653\pi$
$812$		0			0
$813$	28.1063	−	28.1063i	0.985731	−	0.985731i
$814$	0.920141	+	3.95634i	0.0322509	+	0.138670i
$815$	−4.67354	+	8.09480i	−0.163707	+	0.283549i
$816$	−9.77120	+	7.46281i	−0.342061	+	0.261251i
$817$	5.08802	+	8.81271i	0.178007	+	0.308318i
$818$	25.9963	+	7.90187i	0.908939	+	0.276283i
$819$		0			0
$820$	1.32396	−	0.261803i	0.0462348	−	0.00914257i
$821$	12.9355	−	48.2759i	0.451451	−	1.68484i	−0.246865	−	0.969050i	$-0.579400\pi$
$821$	12.9355	−	48.2759i	0.451451	−	1.68484i	0.698316	−	0.715789i	$-0.253933\pi$
$822$	1.52976	−	45.9385i	0.0533565	−	1.60229i
$823$	−20.5366	−	11.8568i	−0.715861	−	0.413302i	0.0973664	−	0.995249i	$-0.468958\pi$
$823$	−20.5366	−	11.8568i	−0.715861	−	0.413302i	−0.813227	+	0.581946i	$0.802291\pi$
$824$	−6.05994	+	16.0188i	−0.211108	+	0.558040i
$825$		−	46.2729i		−	1.61102i
$826$		0			0
$827$	34.8453	+	34.8453i	1.21169	+	1.21169i	0.970471	+	0.241218i	$0.0775470\pi$
$827$	34.8453	+	34.8453i	1.21169	+	1.21169i	0.241218	+	0.970471i	$0.422453\pi$
$828$	−1.14268	+	17.1382i	−0.0397108	+	0.595594i
$829$	4.38741	+	16.3740i	0.152381	+	0.568694i	0.999315	+	0.0369962i	$0.0117790\pi$
$829$	4.38741	+	16.3740i	0.152381	+	0.568694i	−0.846934	+	0.531697i	$0.821554\pi$
$830$	−5.14648	−	5.50104i	−0.178637	−	0.190944i
$831$	−37.8534	−	65.5641i	−1.31312	−	2.27439i
$832$	19.7816	+	29.8229i	0.685805	+	1.03392i
$833$		0			0
$834$	8.80831	−	28.9784i	0.305007	−	1.00344i
$835$	0.595383	+	0.159532i	0.0206041	+	0.00552085i
$836$	−42.0631	+	20.6844i	−1.45478	+	0.715385i
$837$	−51.2175	+	13.7237i	−1.77033	+	0.474360i
$838$	11.9202	−	19.1452i	0.411776	−	0.661359i
$839$			1.32175i			0.0456320i	0.999740	+	0.0228160i	$0.00726318\pi$
$839$			1.32175i			0.0456320i	−0.999740	+	0.0228160i	$0.992737\pi$
$840$		0			0
$841$			8.85792i			0.305445i
$842$	46.0163	+	28.6507i	1.58583	+	0.987369i
$843$	−38.9318	+	10.4317i	−1.34088	+	0.359288i
$844$	−13.7759	+	40.4330i	−0.474187	+	1.39176i
$845$	3.76516	+	1.00887i	0.129525	+	0.0347062i
$846$	91.9989	+	27.9641i	3.16299	+	0.961426i
$847$		0			0
$848$	17.5825	−	42.1789i	0.603784	−	1.44843i
$849$	1.94780	+	3.37369i	0.0668483	+	0.115785i
$850$	−4.75214	+	4.44585i	−0.162997	+	0.152491i
$851$	−0.297420	−	1.10999i	−0.0101954	−	0.0380498i
$852$	4.40809	−	3.85702i	0.151019	−	0.132139i
$853$	33.7981	+	33.7981i	1.15722	+	1.15722i	0.985070	+	0.172153i	$0.0550725\pi$
$853$	33.7981	+	33.7981i	1.15722	+	1.15722i	0.172153	+	0.985070i	$0.444928\pi$
$854$		0			0
$855$		−	28.2227i		−	0.965196i
$856$	−20.5539	−	45.5680i	−0.702518	−	1.55748i
$857$	−10.5676	−	6.10119i	−0.360982	−	0.208413i	0.308530	−	0.951215i	$-0.400163\pi$
$857$	−10.5676	−	6.10119i	−0.360982	−	0.208413i	−0.669511	+	0.742802i	$0.733496\pi$
$858$	62.3708	+	2.07696i	2.12931	+	0.0709063i
$859$	−3.52139	+	13.1420i	−0.120148	+	0.448400i	−0.999620	−	0.0275506i	$-0.991229\pi$
$859$	−3.52139	+	13.1420i	−0.120148	+	0.448400i	0.879472	+	0.475951i	$0.157896\pi$
$860$	−0.845804	+	1.26276i	−0.0288417	+	0.0430596i
$861$		0			0
$862$	6.07134	−	19.9740i	0.206791	−	0.680319i
$863$	24.2546	+	42.0102i	0.825636	+	1.43004i	0.901433	+	0.432920i	$0.142517\pi$
$863$	24.2546	+	42.0102i	0.825636	+	1.43004i	−0.0757970	+	0.997123i	$0.524150\pi$
$864$	−63.4160	+	23.6645i	−2.15746	+	0.805084i
$865$	−2.84611	+	4.92961i	−0.0967707	+	0.167612i
$866$	−41.3314	+	9.61260i	−1.40450	+	0.326649i
$867$	−35.5348	+	35.5348i	−1.20682	+	1.20682i
$868$		0			0
$869$	26.4104	+	26.4104i	0.895913	+	0.895913i
$870$	−5.84415	+	9.38637i	−0.198135	+	0.318228i
$871$	8.72554	+	5.03769i	0.295654	+	0.170696i
$872$	32.6612	+	23.4883i	1.10605	+	0.795413i
$873$	17.9329	−	10.3536i	0.606936	−	0.350415i
$874$	11.6985	−	6.24454i	0.395709	−	0.211225i
$875$		0			0
$876$	0.863767	+	4.36815i	0.0291840	+	0.147586i
$877$	21.3388	+	5.71771i	0.720560	+	0.193073i	0.600422	−	0.799684i	$-0.294999\pi$
$877$	21.3388	+	5.71771i	0.720560	+	0.193073i	0.120138	+	0.992757i	$0.461666\pi$
$878$	34.8569	−	32.6102i	1.17636	−	1.10054i
$879$	39.8682	−	69.0538i	1.34472	−	2.32913i
$880$	−5.54454	−	4.27435i	−0.186906	−	0.144088i
$881$	22.7269			0.765688			0.382844	−	0.923813i	$-0.374945\pi$
$881$	22.7269			0.765688			0.382844	+	0.923813i	$0.374945\pi$
$882$		0			0
$883$	−30.2833	+	30.2833i	−1.01912	+	1.01912i	−0.0193019	+	0.999814i	$0.506144\pi$
$883$	−30.2833	+	30.2833i	−1.01912	+	1.01912i	−0.999814	+	0.0193019i	$0.993856\pi$
$884$	−5.77922	−	6.60492i	−0.194376	−	0.222147i
$885$	4.31650	−	1.15660i	0.145098	−	0.0388788i
$886$	0.347475	−	10.4346i	0.0116736	−	0.350558i
$887$	−33.5292	+	19.3581i	−1.12580	+	0.649980i	−0.942875	−	0.333147i	$-0.891890\pi$
$887$	−33.5292	+	19.3581i	−1.12580	+	0.649980i	−0.182924	+	0.983127i	$0.558556\pi$
$888$	6.25935	−	5.11925i	0.210050	−	0.171791i
$889$		0			0
$890$	−3.77953	−	7.08059i	−0.126690	−	0.237342i
$891$	−13.8822	+	51.8089i	−0.465070	+	1.73566i
$892$	12.7652	−	6.27726i	0.427412	−	0.210178i
$893$	−19.2137	−	71.7065i	−0.642962	−	2.39957i
$894$	10.6240	−	2.47087i	0.355320	−	0.0826381i
$895$	−7.81501			−0.261227
$896$		0			0
$897$	−17.6548			−0.589478
$898$	−2.19023	+	0.509389i	−0.0730888	+	0.0169985i
$899$	−5.14741	−	19.2104i	−0.171676	−	0.640703i
$900$	−57.4058	+	28.2291i	−1.91353	+	0.940970i
$901$	−2.90048	+	10.8247i	−0.0966290	+	0.360624i
$902$	2.54459	+	4.76705i	0.0847256	+	0.158725i
$903$		0			0
$904$	10.9894	−	8.98775i	0.365502	−	0.298928i
$905$	−5.00704	+	2.89082i	−0.166440	+	0.0960940i
$906$	−3.06961	+	92.1798i	−0.101981	+	3.06247i
$907$	34.7960	−	9.32356i	1.15538	−	0.309584i	0.370262	−	0.928927i	$-0.379268\pi$
$907$	34.7960	−	9.32356i	1.15538	−	0.309584i	0.785120	+	0.619344i	$0.212601\pi$
$908$	−22.6644	−	25.9026i	−0.752145	−	0.859607i
$909$	−69.3098	+	69.3098i	−2.29886	+	2.29886i
$910$		0			0
$911$	−52.6922			−1.74577			−0.872886	−	0.487924i	$-0.837754\pi$
$911$	−52.6922			−1.74577			−0.872886	+	0.487924i	$0.837754\pi$
$912$	73.9018	+	56.9717i	2.44713	+	1.88652i
$913$	15.0809	−	26.1209i	0.499106	−	0.864477i
$914$	−2.21951	+	2.07645i	−0.0734149	+	0.0686830i
$915$	−6.15836	−	1.65013i	−0.203589	−	0.0545516i
$916$	0.340992	+	1.72443i	0.0112667	+	0.0569768i
$917$		0			0
$918$	14.6439	−	7.81672i	0.483320	−	0.257990i
$919$	−22.0937	+	12.7558i	−0.728803	+	0.420775i	−0.817984	−	0.575241i	$-0.804908\pi$
$919$	−22.0937	+	12.7558i	−0.728803	+	0.420775i	0.0891810	+	0.996015i	$0.471575\pi$
$920$	1.60796	+	1.15636i	0.0530128	+	0.0381241i
$921$	−6.71547	−	3.87718i	−0.221282	−	0.127757i
$922$	−28.2673	+	45.4004i	−0.930933	+	1.49518i
$923$	2.95640	+	2.95640i	0.0973111	+	0.0973111i
$924$		0			0
$925$	3.02632	−	3.02632i	0.0995046	−	0.0995046i
$926$	22.4092	−	5.21179i	0.736411	−	0.171270i
$927$	20.6441	−	35.7566i	0.678041	−	1.17440i
$928$	−8.87598	−	23.7858i	−0.291368	−	0.780807i
$929$	−24.5999	−	42.6083i	−0.807097	−	1.39793i	−0.914866	−	0.403757i	$-0.867704\pi$
$929$	−24.5999	−	42.6083i	−0.807097	−	1.39793i	0.107770	−	0.994176i	$-0.465629\pi$
$930$	−3.17509	+	10.4457i	−0.104115	+	0.342528i
$931$		0			0
$932$	−5.40577	+	8.07062i	−0.177072	+	0.264362i
$933$	14.1348	−	52.7517i	0.462752	−	1.72701i
$934$	−35.8371	−	1.19338i	−1.17263	−	0.0390487i
$935$	1.48686	+	0.858436i	0.0486254	+	0.0280739i
$936$	−35.4731	−	78.6438i	−1.15947	−	2.57055i
$937$		−	44.3522i		−	1.44892i	−0.689315	−	0.724462i	$-0.742088\pi$
$937$		−	44.3522i		−	1.44892i	0.689315	−	0.724462i	$-0.257912\pi$
$938$		0			0
$939$	62.7995	+	62.7995i	2.04939	+	2.04939i
$940$	8.34428	−	7.30114i	0.272161	−	0.238137i
$941$	5.14910	+	19.2167i	0.167856	+	0.626447i	0.997659	+	0.0683899i	$0.0217862\pi$
$941$	5.14910	+	19.2167i	0.167856	+	0.626447i	−0.829803	+	0.558057i	$0.811547\pi$
$942$	46.4238	−	43.4316i	1.51257	−	1.41508i
$943$	−0.764364	−	1.32392i	−0.0248911	−	0.0431127i
$944$	−3.94793	+	9.47077i	−0.128494	+	0.308247i
$945$		0			0
$946$	−5.82230	−	1.76975i	−0.189299	−	0.0575397i
$947$	30.4390	+	8.15611i	0.989136	+	0.265038i	0.716887	−	0.697189i	$-0.245566\pi$
$947$	30.4390	+	8.15611i	0.989136	+	0.265038i	0.272248	+	0.962227i	$0.412233\pi$
$948$	23.9794	−	70.3806i	0.778815	−	2.28585i
$949$	−3.07009	+	0.822629i	−0.0996594	+	0.0267037i
$950$	41.9262	+	26.1041i	1.36027	+	0.846930i
$951$		−	36.5323i		−	1.18464i
$952$		0			0
$953$			52.5006i			1.70066i	0.526250	+	0.850330i	$0.323598\pi$
$953$			52.5006i			1.70066i	−0.526250	+	0.850330i	$0.676402\pi$
$954$	−58.2266	+	93.5186i	−1.88516	+	3.02778i
$955$	1.90472	−	0.510368i	0.0616353	−	0.0165151i
$956$	8.81277	−	4.33365i	0.285025	−	0.140160i
$957$	−42.7628	−	11.4583i	−1.38233	−	0.370393i
$958$	6.98613	−	22.9836i	0.225712	−	0.742566i
$959$		0			0
$960$	−2.76508	+	13.6597i	−0.0892426	+	0.440865i
$961$	5.68136	+	9.84041i	0.183270	+	0.317433i
$962$	3.94330	+	4.21498i	0.127137	+	0.135896i
$963$	31.1906	+	116.405i	1.00510	+	3.75110i
$964$	−1.44484	+	21.6701i	−0.0465352	+	0.697948i
$965$	−1.17699	−	1.17699i	−0.0378888	−	0.0378888i
$966$		0			0
$967$			22.7183i			0.730572i	0.930895	+	0.365286i	$0.119029\pi$
$967$			22.7183i			0.730572i	−0.930895	+	0.365286i	$0.880971\pi$
$968$	−1.09049	+	2.88257i	−0.0350495	+	0.0926494i
$969$	−19.8179	−	11.4419i	−0.636644	−	0.367567i
$970$	0.0794674	−	2.38639i	0.00255154	−	0.0766225i
$971$	−3.11622	+	11.6299i	−0.100004	+	0.373221i	−0.997731	−	0.0673325i	$-0.978551\pi$
$971$	−3.11622	+	11.6299i	−0.100004	+	0.373221i	0.897726	+	0.440554i	$0.145218\pi$
$972$	34.3174	−	6.78600i	1.10073	−	0.217661i
$973$		0			0
$974$	−52.8166	−	16.0542i	−1.69235	−	0.514411i
$975$	−32.8768	−	56.9442i	−1.05290	−	1.82367i
$976$	11.6339	−	8.88545i	0.372392	−	0.284416i
$977$	18.8637	−	32.6729i	0.603503	−	1.04530i	−0.388783	−	0.921329i	$-0.627104\pi$
$977$	18.8637	−	32.6729i	0.603503	−	1.04530i	0.992286	−	0.123969i	$-0.0395622\pi$
$978$	16.8769	+	72.5657i	0.539663	+	2.32039i
$979$	22.7236	−	22.7236i	0.726250	−	0.726250i
$980$		0			0
$981$	−68.5784	−	68.5784i	−2.18954	−	2.18954i
$982$	−45.6419	−	28.4176i	−1.45649	−	0.906842i
$983$	−39.1070	−	22.5785i	−1.24732	−	0.720141i	−0.276747	−	0.960943i	$-0.589256\pi$
$983$	−39.1070	−	22.5785i	−1.24732	−	0.720141i	−0.970574	+	0.240802i	$0.922590\pi$
$984$	6.28059	−	8.73337i	0.200218	−	0.278410i
$985$	−2.41959	+	1.39695i	−0.0770946	+	0.0445106i
$986$	2.93186	+	5.49256i	0.0933694	+	0.174919i
$987$		0			0
$988$	−37.0674	+	55.3403i	−1.17927	+	1.76061i
$989$	1.66291	+	0.445575i	0.0528775	+	0.0141685i
$990$	11.5303	+	12.3246i	0.366456	+	0.391703i
$991$	23.1140	−	40.0346i	0.734240	−	1.27174i	−0.220815	−	0.975316i	$-0.570872\pi$
$991$	23.1140	−	40.0346i	0.734240	−	1.27174i	0.955056	−	0.296426i	$-0.0957949\pi$
$992$	−14.5440	−	20.4173i	−0.461772	−	0.648249i
$993$	1.04343			0.0331121
$994$		0			0
$995$	0.708054	−	0.708054i	0.0224468	−	0.0224468i
$996$	−59.9108	−	3.99452i	−1.89835	−	0.126571i
$997$	37.2185	−	9.97267i	1.17872	−	0.315838i	0.384303	−	0.923207i	$-0.374442\pi$
$997$	37.2185	−	9.97267i	1.17872	−	0.315838i	0.794419	+	0.607369i	$0.207775\pi$
$998$	−9.05436	−	0.301512i	−0.286611	−	0.00954419i
$999$	−9.45447	+	5.45854i	−0.299126	+	0.172701i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.l.165.6		24
7.2	even	3	inner	784.2.x.l.373.3		24
7.3	odd	6		784.2.m.h.197.2		12
7.4	even	3		112.2.m.d.85.2	yes	12
7.5	odd	6		784.2.x.m.373.3		24
7.6	odd	2		784.2.x.m.165.6		24
16.13	even	4	inner	784.2.x.l.557.3		24
28.11	odd	6		448.2.m.d.113.1		12
56.11	odd	6		896.2.m.h.225.6		12
56.53	even	6		896.2.m.g.225.1		12
112.11	odd	12		896.2.m.h.673.6		12
112.13	odd	4		784.2.x.m.557.3		24
112.45	odd	12		784.2.m.h.589.2		12
112.53	even	12		896.2.m.g.673.1		12
112.61	odd	12		784.2.x.m.765.6		24
112.67	odd	12		448.2.m.d.337.1		12
112.93	even	12	inner	784.2.x.l.765.6		24
112.109	even	12		112.2.m.d.29.2	✓	12
224.67	odd	24		7168.2.a.bi.1.1		12
224.109	even	24		7168.2.a.bj.1.1		12
224.179	odd	24		7168.2.a.bi.1.12		12
224.221	even	24		7168.2.a.bj.1.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.d.29.2	✓	12	112.109	even	12
112.2.m.d.85.2	yes	12	7.4	even	3
448.2.m.d.113.1		12	28.11	odd	6
448.2.m.d.337.1		12	112.67	odd	12
784.2.m.h.197.2		12	7.3	odd	6
784.2.m.h.589.2		12	112.45	odd	12
784.2.x.l.165.6		24	1.1	even	1	trivial
784.2.x.l.373.3		24	7.2	even	3	inner
784.2.x.l.557.3		24	16.13	even	4	inner
784.2.x.l.765.6		24	112.93	even	12	inner
784.2.x.m.165.6		24	7.6	odd	2
784.2.x.m.373.3		24	7.5	odd	6
784.2.x.m.557.3		24	112.13	odd	4
784.2.x.m.765.6		24	112.61	odd	12
896.2.m.g.225.1		12	56.53	even	6
896.2.m.g.673.1		12	112.53	even	12
896.2.m.h.225.6		12	56.11	odd	6
896.2.m.h.673.6		12	112.11	odd	12
7168.2.a.bi.1.1		12	224.67	odd	24
7168.2.a.bi.1.12		12	224.179	odd	24
7168.2.a.bj.1.1		12	224.109	even	24
7168.2.a.bj.1.12		12	224.221	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)

\(f(q)\)	\(=\)	\(q+(1.37745 - 0.320359i) q^{2} +(0.811002 + 3.02670i) q^{3} +(1.79474 - 0.882557i) q^{4} +(-0.143894 + 0.537019i) q^{5} +(2.08675 + 3.90932i) q^{6} +(2.18943 - 1.79064i) q^{8} +(-5.90511 + 3.40932i) q^{9} +O(q^{10})\)	\(q+(1.37745 - 0.320359i) q^{2} +(0.811002 + 3.02670i) q^{3} +(1.79474 - 0.882557i) q^{4} +(-0.143894 + 0.537019i) q^{5} +(2.08675 + 3.90932i) q^{6} +(2.18943 - 1.79064i) q^{8} +(-5.90511 + 3.40932i) q^{9} +(-0.0261678 + 0.785815i) q^{10} +(-3.04081 + 0.814781i) q^{11} +(4.12677 + 4.71638i) q^{12} +(-3.16316 + 3.16316i) q^{13} -1.74209 q^{15} +(2.44219 - 3.16792i) q^{16} +(-0.490475 + 0.849528i) q^{17} +(-7.04179 + 6.58792i) q^{18} +(7.19116 + 1.92687i) q^{19} +(0.215698 + 1.09080i) q^{20} +(-3.92754 + 2.09647i) q^{22} +(1.09077 - 0.629754i) q^{23} +(7.19536 + 5.17454i) q^{24} +(4.06244 + 2.34545i) q^{25} +(-3.34375 + 5.37045i) q^{26} +(-8.46094 - 8.46094i) q^{27} +(3.17349 - 3.17349i) q^{29} +(-2.39965 + 0.558095i) q^{30} +(2.21570 - 3.83770i) q^{31} +(2.34912 - 5.14603i) q^{32} +(-4.93220 - 8.54282i) q^{33} +(-0.403452 + 1.32731i) q^{34} +(-7.58922 + 11.3304i) q^{36} +(0.236140 - 0.881285i) q^{37} +(10.5228 + 0.350410i) q^{38} +(-12.1393 - 7.00862i) q^{39} +(0.646562 + 1.43343i) q^{40} -1.21375i q^{41} +(0.966515 + 0.966515i) q^{43} +(-4.73837 + 4.14601i) q^{44} +(-0.981160 - 3.66174i) q^{45} +(1.30073 - 1.21689i) q^{46} +(-4.98574 - 8.63555i) q^{47} +(11.5690 + 4.82257i) q^{48} +(6.34720 + 1.92931i) q^{50} +(-2.96904 - 0.795553i) q^{51} +(-2.88539 + 8.46873i) q^{52} +(11.0350 - 2.95681i) q^{53} +(-14.3651 - 8.94399i) q^{54} -1.75021i q^{55} +23.3282i q^{57} +(3.35467 - 5.38798i) q^{58} +(-2.47776 + 0.663915i) q^{59} +(-3.12661 + 1.53750i) q^{60} +(3.53504 + 0.947210i) q^{61} +(1.82257 - 5.99606i) q^{62} +(1.58722 - 7.84097i) q^{64} +(-1.24352 - 2.15384i) q^{65} +(-9.53063 - 10.1872i) q^{66} +(-0.582936 - 2.17555i) q^{67} +(-0.130519 + 1.95755i) q^{68} +(2.79069 + 2.79069i) q^{69} -0.934634i q^{71} +(-6.82397 + 18.0384i) q^{72} +(0.615321 + 0.355256i) q^{73} +(0.0429431 - 1.28958i) q^{74} +(-3.80433 + 14.1980i) q^{75} +(14.6068 - 2.88839i) q^{76} +(-18.9665 - 5.76510i) q^{78} +(-5.93220 - 10.2749i) q^{79} +(1.34982 + 1.76735i) q^{80} +(8.51894 - 14.7552i) q^{81} +(-0.388835 - 1.67188i) q^{82} +(-6.77482 + 6.77482i) q^{83} +(-0.385637 - 0.385637i) q^{85} +(1.64096 + 1.02170i) q^{86} +(12.1789 + 7.03150i) q^{87} +(-5.19865 + 7.22890i) q^{88} +(-8.84053 + 5.10408i) q^{89} +(-2.52457 - 4.72954i) q^{90} +(1.40185 - 2.09291i) q^{92} +(13.4125 + 3.59387i) q^{93} +(-9.63408 - 10.2978i) q^{94} +(-2.06953 + 3.58453i) q^{95} +(17.4806 + 2.93663i) q^{96} -3.03684 q^{97} +(15.1784 - 15.1784i) 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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