LMFDB - Embedded newform 784.2.x.j.165.1

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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 4 x^{14} + 4 x^{13} - 13 x^{12} + 32 x^{11} - 4 x^{10} - 34 x^{9} + 121 x^{8} + \cdots + 256 $ x^16 - 2x^15 + 4x^14 + 4x^13 - 13x^12 + 32x^11 - 4x^10 - 34x^9 + 121x^8 - 68x^7 - 16x^6 + 256x^5 - 208x^4 + 128x^3 + 256x^2 - 256*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			165.1
Root			$-1.33068 - 0.478848i$ of defining polynomial
Character	$\chi$	$=$	784.165
Dual form			784.2.x.j.765.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19412 + 0.757684i) q^{2} +(-0.538823 - 2.01092i) q^{3} +(0.851831 - 1.80953i) q^{4} +(-0.129523 + 0.483385i) q^{5} +(2.16706 + 1.99301i) q^{6} +(0.353863 + 2.80620i) q^{8} +(-1.15537 + 0.667056i) q^{9} +O(q^{10})$	\(q+(-1.19412 + 0.757684i) q^{2} +(-0.538823 - 2.01092i) q^{3} +(0.851831 - 1.80953i) q^{4} +(-0.129523 + 0.483385i) q^{5} +(2.16706 + 1.99301i) q^{6} +(0.353863 + 2.80620i) q^{8} +(-1.15537 + 0.667056i) q^{9} +(-0.211588 - 0.675356i) q^{10} +(-0.456405 + 0.122293i) q^{11} +(-4.09779 - 0.737945i) q^{12} +(3.17982 - 3.17982i) q^{13} +1.04184 q^{15} +(-2.54877 - 3.08282i) q^{16} +(0.646137 - 1.11914i) q^{17} +(0.874235 - 1.67195i) q^{18} +(3.59560 + 0.963437i) q^{19} +(0.764367 + 0.646137i) q^{20} +(0.452341 - 0.491843i) q^{22} +(2.26039 - 1.30504i) q^{23} +(5.45237 - 2.22364i) q^{24} +(4.11324 + 2.37478i) q^{25} +(-1.38778 + 6.20637i) q^{26} +(-2.45234 - 2.45234i) q^{27} +(-6.98602 + 6.98602i) q^{29} +(-1.24408 + 0.789383i) q^{30} +(4.17982 - 7.23966i) q^{31} +(5.37933 + 1.75009i) q^{32} +(0.491843 + 0.851898i) q^{33} +(0.0763926 + 1.82596i) q^{34} +(0.222871 + 2.65890i) q^{36} +(-1.21525 + 4.53539i) q^{37} +(-5.02354 + 1.57387i) q^{38} +(-8.10770 - 4.68099i) q^{39} +(-1.40231 - 0.192415i) q^{40} -9.93254i q^{41} +(-7.61241 - 7.61241i) q^{43} +(-0.167487 + 0.930050i) q^{44} +(-0.172798 - 0.644890i) q^{45} +(-1.71036 + 3.27103i) q^{46} +(-2.29805 - 3.98033i) q^{47} +(-4.82596 + 6.78645i) q^{48} +(-6.71102 + 0.280770i) q^{50} +(-2.59866 - 0.696308i) q^{51} +(-3.04530 - 8.46263i) q^{52} +(5.38786 - 1.44367i) q^{53} +(4.78648 + 1.07028i) q^{54} -0.236459i q^{55} -7.74956i q^{57} +(3.04893 - 13.6353i) q^{58} +(-8.73669 + 2.34099i) q^{59} +(0.887469 - 1.88523i) q^{60} +(5.94749 + 1.59362i) q^{61} +(0.494178 + 11.8120i) q^{62} +(-7.74956 + 1.98602i) q^{64} +(1.12522 + 1.94894i) q^{65} +(-1.23279 - 0.644604i) q^{66} +(-3.65002 - 13.6221i) q^{67} +(-1.47472 - 2.12252i) q^{68} +(-3.84227 - 3.84227i) q^{69} -7.62395i q^{71} +(-2.28074 - 3.00617i) q^{72} +(-0.482023 - 0.278296i) q^{73} +(-1.98523 - 6.33656i) q^{74} +(2.55917 - 9.55097i) q^{75} +(4.80620 - 5.68564i) q^{76} +(13.2283 - 0.553431i) q^{78} +(0.744616 + 1.28971i) q^{79} +(1.82031 - 0.832742i) q^{80} +(-5.61124 + 9.71895i) q^{81} +(7.52572 + 11.8606i) q^{82} +(-1.47209 + 1.47209i) q^{83} +(0.457288 + 0.457288i) q^{85} +(14.8579 + 3.32231i) q^{86} +(17.8125 + 10.2841i) q^{87} +(-0.504685 - 1.23749i) q^{88} +(-10.6453 + 6.14609i) q^{89} +(0.694964 + 0.639148i) q^{90} +(-0.436028 - 5.20190i) q^{92} +(-16.8105 - 4.50437i) q^{93} +(5.75997 + 3.01179i) q^{94} +(-0.931423 + 1.61327i) q^{95} +(0.620770 - 11.7604i) q^{96} -5.50078 q^{97} +(0.445742 - 0.445742i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 32 q^{6} - 8 q^{8}+O(q^{10}) $ 16 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 32 * q^6 - 8 * q^8	$ 16 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 32 q^{6} - 8 q^{8} + 12 q^{10} - 12 q^{12} - 16 q^{15} - 8 q^{16} + 24 q^{17} - 6 q^{18} - 12 q^{19} + 16 q^{20} - 8 q^{22} + 8 q^{26} - 24 q^{27} - 32 q^{29} - 20 q^{30} + 16 q^{31} + 28 q^{32} - 24 q^{33} + 24 q^{34} + 48 q^{36} - 16 q^{37} - 16 q^{38} + 28 q^{40} - 64 q^{43} + 32 q^{44} - 8 q^{45} - 20 q^{46} + 24 q^{47} - 40 q^{48} - 28 q^{50} - 8 q^{51} + 32 q^{52} + 8 q^{53} - 16 q^{54} - 12 q^{58} - 28 q^{59} + 28 q^{60} + 28 q^{61} - 40 q^{62} - 64 q^{64} + 48 q^{65} - 16 q^{66} + 28 q^{68} - 88 q^{69} - 44 q^{72} + 4 q^{74} + 28 q^{75} + 48 q^{76} + 24 q^{78} + 24 q^{79} - 12 q^{80} - 40 q^{81} + 4 q^{82} - 80 q^{85} + 40 q^{88} + 32 q^{90} + 72 q^{92} - 16 q^{93} + 28 q^{94} - 16 q^{95} + 8 q^{96} + 64 q^{97} + 96 q^{99}+O(q^{100}) $ 16 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 32 * q^6 - 8 * q^8 + 12 * q^10 - 12 * q^12 - 16 * q^15 - 8 * q^16 + 24 * q^17 - 6 * q^18 - 12 * q^19 + 16 * q^20 - 8 * q^22 + 8 * q^26 - 24 * q^27 - 32 * q^29 - 20 * q^30 + 16 * q^31 + 28 * q^32 - 24 * q^33 + 24 * q^34 + 48 * q^36 - 16 * q^37 - 16 * q^38 + 28 * q^40 - 64 * q^43 + 32 * q^44 - 8 * q^45 - 20 * q^46 + 24 * q^47 - 40 * q^48 - 28 * q^50 - 8 * q^51 + 32 * q^52 + 8 * q^53 - 16 * q^54 - 12 * q^58 - 28 * q^59 + 28 * q^60 + 28 * q^61 - 40 * q^62 - 64 * q^64 + 48 * q^65 - 16 * q^66 + 28 * q^68 - 88 * q^69 - 44 * q^72 + 4 * q^74 + 28 * q^75 + 48 * q^76 + 24 * q^78 + 24 * q^79 - 12 * q^80 - 40 * q^81 + 4 * q^82 - 80 * q^85 + 40 * q^88 + 32 * q^90 + 72 * q^92 - 16 * q^93 + 28 * q^94 - 16 * q^95 + 8 * q^96 + 64 * q^97 + 96 * 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 $

$2$	−1.19412	+	0.757684i	−0.844368	+	0.535763i
$2$	−1.19412	+	0.757684i	−0.844368	+	0.535763i
$3$	−0.538823	−	2.01092i	−0.311090	−	1.16100i	−0.927575	−	0.373636i	$-0.878111\pi$
$3$	−0.538823	−	2.01092i	−0.311090	−	1.16100i	0.616486	−	0.787366i	$-0.288556\pi$
$4$	0.851831	−	1.80953i	0.425915	−	0.904763i
$5$	−0.129523	+	0.483385i	−0.0579243	+	0.216177i	−0.988821	−	0.149105i	$-0.952361\pi$
$5$	−0.129523	+	0.483385i	−0.0579243	+	0.216177i	0.930897	+	0.365282i	$0.119027\pi$
$6$	2.16706	+	1.99301i	0.884697	+	0.813643i
$7$		0			0
$7$		0			0
$8$	0.353863	+	2.80620i	0.125109	+	0.992143i
$9$	−1.15537	+	0.667056i	−0.385125	+	0.222352i
$10$	−0.211588	−	0.675356i	−0.0669100	−	0.213566i
$11$	−0.456405	+	0.122293i	−0.137611	+	0.0368728i	−0.326967	−	0.945036i	$-0.606027\pi$
$11$	−0.456405	+	0.122293i	−0.137611	+	0.0368728i	0.189356	+	0.981909i	$0.439360\pi$
$12$	−4.09779	−	0.737945i	−1.18293	−	0.213026i
$13$	3.17982	−	3.17982i	0.881923	−	0.881923i	−0.111807	−	0.993730i	$-0.535664\pi$
$13$	3.17982	−	3.17982i	0.881923	−	0.881923i	0.993730	+	0.111807i	$0.0356639\pi$
$14$		0			0
$15$	1.04184			0.269001
$16$	−2.54877	−	3.08282i	−0.637192	−	0.770705i
$17$	0.646137	−	1.11914i	0.156711	−	0.271432i	−0.776970	−	0.629538i	$-0.783244\pi$
$17$	0.646137	−	1.11914i	0.156711	−	0.271432i	0.933681	+	0.358106i	$0.116577\pi$
$18$	0.874235	−	1.67195i	0.206059	−	0.394083i
$19$	3.59560	+	0.963437i	0.824886	+	0.221028i	0.646482	−	0.762930i	$-0.276240\pi$
$19$	3.59560	+	0.963437i	0.824886	+	0.221028i	0.178405	+	0.983957i	$0.442906\pi$
$20$	0.764367	+	0.646137i	0.170918	+	0.144481i
$21$		0			0
$22$	0.452341	−	0.491843i	0.0964395	−	0.104861i
$23$	2.26039	−	1.30504i	0.471324	−	0.272119i	−0.245470	−	0.969404i	$-0.578942\pi$
$23$	2.26039	−	1.30504i	0.471324	−	0.272119i	0.716794	+	0.697285i	$0.245609\pi$
$24$	5.45237	−	2.22364i	1.11296	−	0.453898i
$25$	4.11324	+	2.37478i	0.822648	+	0.474956i
$26$	−1.38778	+	6.20637i	−0.272166	+	1.21717i
$27$	−2.45234	−	2.45234i	−0.471953	−	0.471953i
$28$		0			0
$29$	−6.98602	+	6.98602i	−1.29727	+	1.29727i	−0.367084	+	0.930188i	$0.619644\pi$
$29$	−6.98602	+	6.98602i	−1.29727	+	1.29727i	−0.930188	+	0.367084i	$0.880356\pi$
$30$	−1.24408	+	0.789383i	−0.227136	+	0.144121i
$31$	4.17982	−	7.23966i	0.750717	−	1.30028i	−0.196758	−	0.980452i	$-0.563041\pi$
$31$	4.17982	−	7.23966i	0.750717	−	1.30028i	0.947475	−	0.319829i	$-0.103625\pi$
$32$	5.37933	+	1.75009i	0.950940	+	0.309375i
$33$	0.491843	+	0.851898i	0.0856189	+	0.148296i
$34$	0.0763926	+	1.82596i	0.0131012	+	0.313149i
$35$		0			0
$36$	0.222871	+	2.65890i	0.0371452	+	0.443150i
$37$	−1.21525	+	4.53539i	−0.199786	+	0.745613i	0.791189	+	0.611571i	$0.209462\pi$
$37$	−1.21525	+	4.53539i	−0.199786	+	0.745613i	−0.990976	+	0.134042i	$0.957204\pi$
$38$	−5.02354	+	1.57387i	−0.814926	+	0.255315i
$39$	−8.10770	−	4.68099i	−1.29827	−	0.749558i
$40$	−1.40231	−	0.192415i	−0.221725	−	0.0304235i
$41$		−	9.93254i		−	1.55120i	−0.631223	−	0.775601i	$-0.717447\pi$
$41$		−	9.93254i		−	1.55120i	0.631223	−	0.775601i	$-0.282553\pi$
$42$		0			0
$43$	−7.61241	−	7.61241i	−1.16088	−	1.16088i	−0.984283	−	0.176598i	$-0.943491\pi$
$43$	−7.61241	−	7.61241i	−1.16088	−	1.16088i	−0.176598	−	0.984283i	$-0.556509\pi$
$44$	−0.167487	+	0.930050i	−0.0252496	+	0.140210i
$45$	−0.172798	−	0.644890i	−0.0257592	−	0.0961345i
$46$	−1.71036	+	3.27103i	−0.252180	+	0.482287i
$47$	−2.29805	−	3.98033i	−0.335205	−	0.580591i	0.648319	−	0.761368i	$-0.275472\pi$
$47$	−2.29805	−	3.98033i	−0.335205	−	0.580591i	−0.983524	+	0.180777i	$0.942139\pi$
$48$	−4.82596	+	6.78645i	−0.696567	+	0.979540i
$49$		0			0
$50$	−6.71102	+	0.280770i	−0.949082	+	0.0397068i
$51$	−2.59866	−	0.696308i	−0.363885	−	0.0975026i
$52$	−3.04530	−	8.46263i	−0.422307	−	1.17356i
$53$	5.38786	−	1.44367i	0.740079	−	0.198304i	0.130966	−	0.991387i	$-0.458192\pi$
$53$	5.38786	−	1.44367i	0.740079	−	0.198304i	0.609113	+	0.793083i	$0.291526\pi$
$54$	4.78648	+	1.07028i	0.651358	+	0.145647i
$55$		−	0.236459i		−	0.0318842i
$56$		0			0
$57$		−	7.74956i		−	1.02645i
$58$	3.04893	−	13.6353i	0.400344	−	1.79041i
$59$	−8.73669	+	2.34099i	−1.13742	+	0.304771i	−0.777913	−	0.628372i	$-0.783722\pi$
$59$	−8.73669	+	2.34099i	−1.13742	+	0.304771i	−0.359507	+	0.933142i	$0.617055\pi$
$60$	0.887469	−	1.88523i	0.114572	−	0.243382i
$61$	5.94749	+	1.59362i	0.761498	+	0.204043i	0.618612	−	0.785697i	$-0.287695\pi$
$61$	5.94749	+	1.59362i	0.761498	+	0.204043i	0.142886	+	0.989739i	$0.454362\pi$
$62$	0.494178	+	11.8120i	0.0627607	+	1.50012i
$63$		0			0
$64$	−7.74956	+	1.98602i	−0.968695	+	0.248253i
$65$	1.12522	+	1.94894i	0.139566	+	0.241736i
$66$	−1.23279	−	0.644604i	−0.151746	−	0.0793452i
$67$	−3.65002	−	13.6221i	−0.445921	−	1.66420i	−0.713493	−	0.700662i	$-0.752888\pi$
$67$	−3.65002	−	13.6221i	−0.445921	−	1.66420i	0.267572	−	0.963538i	$-0.413779\pi$
$68$	−1.47472	−	2.12252i	−0.178836	−	0.257394i
$69$	−3.84227	−	3.84227i	−0.462555	−	0.462555i
$70$		0			0
$71$		−	7.62395i		−	0.904797i	−0.891816	−	0.452398i	$-0.850569\pi$
$71$		−	7.62395i		−	0.904797i	0.891816	−	0.452398i	$-0.149431\pi$
$72$	−2.28074	−	3.00617i	−0.268788	−	0.354281i
$73$	−0.482023	−	0.278296i	−0.0564166	−	0.0325721i	0.471526	−	0.881852i	$-0.343703\pi$
$73$	−0.482023	−	0.278296i	−0.0564166	−	0.0325721i	−0.527943	+	0.849280i	$0.677037\pi$
$74$	−1.98523	−	6.33656i	−0.230779	−	0.736610i
$75$	2.55917	−	9.55097i	0.295508	−	1.10285i
$76$	4.80620	−	5.68564i	0.551309	−	0.652188i
$77$		0			0
$78$	13.2283	−	0.553431i	1.49780	−	0.0626638i
$79$	0.744616	+	1.28971i	0.0837758	+	0.145104i	0.904869	−	0.425690i	$-0.139969\pi$
$79$	0.744616	+	1.28971i	0.0837758	+	0.145104i	−0.821093	+	0.570794i	$0.806635\pi$
$80$	1.82031	−	0.832742i	0.203517	−	0.0931034i
$81$	−5.61124	+	9.71895i	−0.623471	+	1.07988i
$82$	7.52572	+	11.8606i	0.831077	+	1.30979i
$83$	−1.47209	+	1.47209i	−0.161583	+	0.161583i	−0.783268	−	0.621685i	$-0.786449\pi$
$83$	−1.47209	+	1.47209i	−0.161583	+	0.161583i	0.621685	+	0.783268i	$0.286449\pi$
$84$		0			0
$85$	0.457288	+	0.457288i	0.0495998	+	0.0495998i
$86$	14.8579	+	3.32231i	1.60217	+	0.358254i
$87$	17.8125	+	10.2841i	1.90970	+	1.10257i
$88$	−0.504685	−	1.23749i	−0.0537996	−	0.131917i
$89$	−10.6453	+	6.14609i	−1.12840	+	0.651484i	−0.943533	−	0.331279i	$-0.892520\pi$
$89$	−10.6453	+	6.14609i	−1.12840	+	0.651484i	−0.184871	+	0.982763i	$0.559187\pi$
$90$	0.694964	+	0.639148i	0.0732556	+	0.0673721i
$91$		0			0
$92$	−0.436028	−	5.20190i	−0.0454591	−	0.542336i
$93$	−16.8105	−	4.50437i	−1.74317	−	0.467081i
$94$	5.75997	+	3.01179i	0.594096	+	0.310643i
$95$	−0.931423	+	1.61327i	−0.0955620	+	0.165518i
$96$	0.620770	−	11.7604i	0.0633571	−	1.20029i
$97$	−5.50078			−0.558519			−0.279260	−	0.960216i	$-0.590089\pi$
$97$	−5.50078			−0.558519			−0.279260	+	0.960216i	$0.590089\pi$
$98$		0			0
$99$	0.445742	−	0.445742i	0.0447988	−	0.0447988i
$100$	7.80101	−	5.42011i	0.780101	−	0.542011i
$101$	9.60136	−	2.57268i	0.955371	−	0.255991i	0.252731	−	0.967537i	$-0.418671\pi$
$101$	9.60136	−	2.57268i	0.955371	−	0.255991i	0.702640	+	0.711546i	$0.252004\pi$
$102$	3.63068	−	1.13749i	0.359491	−	0.112628i
$103$	12.6446	−	7.30038i	1.24591	−	0.719328i	0.275621	−	0.961266i	$-0.411116\pi$
$103$	12.6446	−	7.30038i	1.24591	−	0.719328i	0.970292	+	0.241938i	$0.0777832\pi$
$104$	10.0484	+	7.79800i	0.985330	+	0.764657i
$105$		0			0
$106$	−5.33988	+	5.80620i	−0.518655	+	0.563948i
$107$	0.381339	−	1.42318i	0.0368654	−	0.137584i	−0.945040	−	0.326954i	$-0.893978\pi$
$107$	0.381339	−	1.42318i	0.0368654	−	0.137584i	0.981906	+	0.189370i	$0.0606446\pi$
$108$	−6.52656	+	2.34860i	−0.628018	+	0.225994i
$109$	−1.58554	−	5.91732i	−0.151867	−	0.566776i	−0.999353	−	0.0359585i	$-0.988552\pi$
$109$	−1.58554	−	5.91732i	−0.151867	−	0.566776i	0.847486	−	0.530818i	$-0.178115\pi$
$110$	0.179161	+	0.282360i	0.0170824	+	0.0269220i
$111$	9.77509			0.927810
$112$		0			0
$113$	17.6379			1.65924			0.829619	−	0.558331i	$-0.188558\pi$
$113$	17.6379			1.65924			0.829619	+	0.558331i	$0.188558\pi$
$114$	5.87172	+	9.25388i	0.549937	+	0.866706i
$115$	0.338064	+	1.26167i	0.0315246	+	0.117651i
$116$	6.69048	+	18.5923i	0.621195	+	1.72625i
$117$	−1.55276	+	5.79500i	−0.143553	+	0.535748i
$118$	8.65890	−	9.41506i	0.797116	−	0.866727i
$119$		0			0
$120$	0.368667	+	2.92361i	0.0336546	+	0.266888i
$121$	−9.33293	+	5.38837i	−0.848448	+	0.489852i
$122$	−8.30946	+	2.60334i	−0.752303	+	0.235695i
$123$	−19.9735	+	5.35188i	−1.80095	+	0.482563i
$124$	−9.53985	−	13.7305i	−0.856704	−	1.23303i
$125$	−3.45001	+	3.45001i	−0.308578	+	0.308578i
$126$		0			0
$127$	7.75122			0.687809			0.343905	−	0.939005i	$-0.388250\pi$
$127$	7.75122			0.687809			0.343905	+	0.939005i	$0.388250\pi$
$128$	7.74911	−	8.24326i	0.684931	−	0.728608i
$129$	−11.2062	+	19.4097i	−0.986648	+	1.70892i
$130$	−2.82032	−	1.47470i	−0.247358	−	0.129340i
$131$	2.07126	+	0.554991i	0.180966	+	0.0484898i	0.348164	−	0.937434i	$-0.386805\pi$
$131$	2.07126	+	0.554991i	0.180966	+	0.0484898i	−0.167198	+	0.985923i	$0.553472\pi$
$132$	1.96050	−	0.164331i	0.170639	−	0.0143031i
$133$		0			0
$134$	14.6798	+	13.5008i	1.26814	+	1.16629i
$135$	1.50306	−	0.867792i	0.129363	−	0.0746877i
$136$	3.36919	+	1.41717i	0.288905	+	0.121521i
$137$	5.17194	+	2.98602i	0.441869	+	0.255113i	0.704390	−	0.709813i	$-0.251221\pi$
$137$	5.17194	+	2.98602i	0.441869	+	0.255113i	−0.262521	+	0.964926i	$0.584554\pi$
$138$	7.49934	+	1.67689i	0.638386	+	0.142747i
$139$	−9.10343	−	9.10343i	−0.772142	−	0.772142i	0.206338	−	0.978481i	$-0.433845\pi$
$139$	−9.10343	−	9.10343i	−0.772142	−	0.772142i	−0.978481	+	0.206338i	$0.933845\pi$
$140$		0			0
$141$	−6.76588	+	6.76588i	−0.569790	+	0.569790i
$142$	5.77655	+	9.10389i	0.484757	+	0.763982i
$143$	−1.06241	+	1.84016i	−0.0888436	+	0.153882i
$144$	5.00120	+	1.86164i	0.416766	+	0.155137i
$145$	−2.47209	−	4.28179i	−0.205296	−	0.355583i
$146$	0.786453	−	0.0329029i	0.0650873	−	0.00272306i
$147$		0			0
$148$	7.17171	+	6.06241i	0.589511	+	0.498327i
$149$	−1.14828	+	4.28543i	−0.0940706	+	0.351076i	−0.996877	−	0.0789711i	$-0.974837\pi$
$149$	−1.14828	+	4.28543i	−0.0940706	+	0.351076i	0.902806	+	0.430047i	$0.141503\pi$
$150$	4.18066	+	13.3440i	0.341349	+	1.08953i
$151$	10.4144	+	6.01276i	0.847513	+	0.489312i	0.859811	−	0.510613i	$-0.170581\pi$
$151$	10.4144	+	6.01276i	0.847513	+	0.489312i	−0.0122982	+	0.999924i	$0.503915\pi$
$152$	−1.43125	+	10.4309i	−0.116090	+	0.846058i
$153$			1.72404i			0.139380i
$154$		0			0
$155$	2.95816	+	2.95816i	0.237605	+	0.237605i
$156$	−15.3768	+	10.6837i	−1.23113	+	0.855380i
$157$	−3.05954	−	11.4183i	−0.244178	−	0.911283i	−0.973795	−	0.227428i	$-0.926968\pi$
$157$	−3.05954	−	11.4183i	−0.244178	−	0.911283i	0.729617	−	0.683856i	$-0.239698\pi$
$158$	−1.86635	−	0.975885i	−0.148479	−	0.0776372i
$159$	−5.80620	−	10.0566i	−0.460462	−	0.797543i
$160$	−1.54271	+	2.37361i	−0.121962	+	0.187651i
$161$		0			0
$162$	−0.663415	−	15.8571i	−0.0521228	−	1.24585i
$163$	1.25491	+	0.336253i	0.0982925	+	0.0263374i	0.307630	−	0.951506i	$-0.400464\pi$
$163$	1.25491	+	0.336253i	0.0982925	+	0.0263374i	−0.209338	+	0.977843i	$0.567131\pi$
$164$	−17.9732	−	8.46085i	−1.40347	−	0.660681i
$165$	−0.475500	+	0.127410i	−0.0370176	+	0.00991884i
$166$	0.642470	−	2.87323i	0.0498654	−	0.223006i
$167$			13.0690i			1.01131i	0.862736	+	0.505655i	$0.168749\pi$
$167$			13.0690i			1.01131i	−0.862736	+	0.505655i	$0.831251\pi$
$168$		0			0
$169$		−	7.22248i		−	0.555575i
$170$	−0.892535	−	0.199576i	−0.0684543	−	0.0153068i
$171$	−4.79693	+	1.28533i	−0.366830	+	0.0982918i
$172$	−20.2593	+	7.29037i	−1.54476	+	0.555885i
$173$	−5.20256	−	1.39402i	−0.395543	−	0.105986i	0.0555642	−	0.998455i	$-0.482304\pi$
$173$	−5.20256	−	1.39402i	−0.395543	−	0.105986i	−0.451108	+	0.892470i	$0.648971\pi$
$174$	−29.0623	+	1.21588i	−2.20321	+	0.0921758i
$175$		0			0
$176$	1.54028	+	1.09532i	0.116103	+	0.0825626i
$177$	9.41506	+	16.3074i	0.707679	+	1.22574i
$178$	8.05499	−	15.4049i	0.603747	−	1.15465i
$179$	3.23233	+	12.0632i	0.241596	+	0.901649i	0.975064	+	0.221924i	$0.0712338\pi$
$179$	3.23233	+	12.0632i	0.241596	+	0.901649i	−0.733468	+	0.679724i	$0.762100\pi$
$180$	−1.31414	−	0.236655i	−0.0979502	−	0.0176392i
$181$	1.37018	+	1.37018i	0.101844	+	0.101844i	0.756193	−	0.654349i	$-0.227057\pi$
$181$	1.37018	+	1.37018i	0.101844	+	0.101844i	−0.654349	+	0.756193i	$0.727057\pi$
$182$		0			0
$183$		−	12.8186i		−	0.947576i
$184$	4.46207	+	5.88131i	0.328948	+	0.433576i
$185$	−2.03494	−	1.17487i	−0.149612	−	0.0863783i
$186$	23.4866	−	7.35832i	1.72212	−	0.539538i
$187$	−0.158037	+	0.589801i	−0.0115568	+	0.0431305i
$188$	−9.16007	+	0.767805i	−0.668067	+	0.0559979i
$189$		0			0
$190$	−0.110122	−	2.63216i	−0.00798908	−	0.190957i
$191$	0.707725	+	1.22582i	0.0512092	+	0.0886970i	0.890494	−	0.454995i	$-0.150359\pi$
$191$	0.707725	+	1.22582i	0.0512092	+	0.0886970i	−0.839285	+	0.543692i	$0.817026\pi$
$192$	8.16937	+	14.5136i	0.589573	+	1.04743i
$193$	5.48485	−	9.50005i	0.394808	−	0.683828i	−0.598268	−	0.801296i	$-0.704144\pi$
$193$	5.48485	−	9.50005i	0.394808	−	0.683828i	0.993077	+	0.117468i	$0.0374776\pi$
$194$	6.56857	−	4.16785i	0.471596	−	0.299234i
$195$	3.31285	−	3.31285i	0.237238	−	0.237238i
$196$		0			0
$197$	8.92787	+	8.92787i	0.636084	+	0.636084i	0.949587	−	0.313503i	$-0.101503\pi$
$197$	8.92787	+	8.92787i	0.636084	+	0.636084i	−0.313503	+	0.949587i	$0.601503\pi$
$198$	−0.194537	+	0.870000i	−0.0138251	+	0.0618282i
$199$	7.58080	+	4.37678i	0.537388	+	0.310261i	0.744020	−	0.668157i	$-0.232917\pi$
$199$	7.58080	+	4.37678i	0.537388	+	0.310261i	−0.206631	+	0.978419i	$0.566250\pi$
$200$	−5.20860	+	12.3829i	−0.368303	+	0.875606i
$201$	−25.4261	+	14.6798i	−1.79342	+	1.03543i
$202$	−9.51587	+	10.3469i	−0.669535	+	0.728003i
$203$		0			0
$204$	−3.47360	+	4.10920i	−0.243201	+	0.287701i
$205$	4.80125	+	1.28649i	0.335334	+	0.0898524i
$206$	−9.56779	+	18.2981i	−0.666620	+	1.27489i
$207$	−1.74106	+	3.01561i	−0.121012	+	0.209600i
$208$	−17.9074	−	1.69819i	−1.24166	−	0.117748i
$209$	−1.75887			−0.121664
$210$		0			0
$211$	−9.88837	+	9.88837i	−0.680743	+	0.680743i	−0.960168	−	0.279424i	$-0.909856\pi$
$211$	−9.88837	+	9.88837i	−0.680743	+	0.680743i	0.279424	+	0.960168i	$0.409856\pi$
$212$	1.97718	−	10.9792i	0.135793	−	0.754057i
$213$	−15.3311	+	4.10796i	−1.05047	+	0.281473i
$214$	0.622954	+	1.98837i	0.0425843	+	0.135922i
$215$	4.66571	−	2.69375i	0.318199	−	0.183712i
$216$	6.01398	−	7.74956i	0.409199	−	0.527291i
$217$		0			0
$218$	6.37678	+	5.86463i	0.431890	+	0.397203i
$219$	−0.299905	+	1.11926i	−0.0202657	+	0.0756327i
$220$	−0.427879	−	0.201423i	−0.0288476	−	0.0135800i
$221$	−1.50407	−	5.61327i	−0.101175	−	0.377589i
$222$	−11.6726	+	7.40642i	−0.783413	+	0.497087i
$223$	−6.12483			−0.410149			−0.205074	−	0.978746i	$-0.565744\pi$
$223$	−6.12483			−0.410149			−0.205074	+	0.978746i	$0.565744\pi$
$224$		0			0
$225$	−6.33645			−0.422430
$226$	−21.0618	+	13.3640i	−1.40101	+	0.888958i
$227$	2.02602	+	7.56121i	0.134472	+	0.501855i	1.00000		0.000994262i	$0.000316483\pi$
$227$	2.02602	+	7.56121i	0.134472	+	0.501855i	−0.865528	+	0.500861i	$0.833017\pi$
$228$	−14.0230	−	6.60132i	−0.928698	−	0.437183i
$229$	−4.68228	+	17.4745i	−0.309414	+	1.15475i	0.619665	+	0.784866i	$0.287268\pi$
$229$	−4.68228	+	17.4745i	−0.309414	+	1.15475i	−0.929079	+	0.369882i	$0.879398\pi$
$230$	−1.35964	−	1.25044i	−0.0896517	−	0.0824514i
$231$		0			0
$232$	−22.0763	−	17.1321i	−1.44938	−	1.12478i
$233$	21.3351	−	12.3178i	1.39771	−	0.806966i	0.403554	−	0.914956i	$-0.367775\pi$
$233$	21.3351	−	12.3178i	1.39771	−	0.806966i	0.994152	+	0.107990i	$0.0344415\pi$
$234$	−2.53659	−	8.09641i	−0.165822	−	0.529279i
$235$	2.22169	−	0.595299i	0.144927	−	0.0388330i
$236$	−3.20610	+	17.8034i	−0.208699	+	1.15890i
$237$	2.19229	−	2.19229i	0.142404	−	0.142404i
$238$		0			0
$239$	−10.8844			−0.704052			−0.352026	−	0.935990i	$-0.614507\pi$
$239$	−10.8844			−0.704052			−0.352026	+	0.935990i	$0.614507\pi$
$240$	−2.65540	−	3.21180i	−0.171405	−	0.207321i
$241$	−7.57634	+	13.1226i	−0.488035	+	0.845302i	−0.999905	−	0.0137611i	$-0.995620\pi$
$241$	−7.57634	+	13.1226i	−0.488035	+	0.845302i	0.511870	+	0.859063i	$0.328953\pi$
$242$	7.06193	−	13.5058i	0.453958	−	0.868183i
$243$	12.5176	+	3.35408i	0.803003	+	0.215164i
$244$	7.94996	−	9.40463i	0.508944	−	0.602070i
$245$		0			0
$246$	19.7957	−	21.5244i	1.26213	−	1.37234i
$247$	14.4969	−	8.36979i	0.922415	−	0.532557i
$248$	21.7950	+	9.16758i	1.38399	+	0.582142i
$249$	3.75345	+	2.16706i	0.237865	+	0.137332i
$250$	1.50570	−	6.73372i	0.0952287	−	0.425878i
$251$	0.848041	+	0.848041i	0.0535279	+	0.0535279i	0.733364	−	0.679836i	$-0.237949\pi$
$251$	0.848041	+	0.848041i	0.0535279	+	0.0535279i	−0.679836	+	0.733364i	$0.737949\pi$
$252$		0			0
$253$	−0.872056	+	0.872056i	−0.0548257	+	0.0548257i
$254$	−9.25586	+	5.87297i	−0.580764	+	0.368503i
$255$	0.673170	−	1.16596i	0.0421555	−	0.0730155i
$256$	−3.00756	+	15.7148i	−0.187972	+	0.982174i
$257$	−5.82596	−	10.0909i	−0.363413	−	0.629450i	0.625107	−	0.780539i	$-0.285055\pi$
$257$	−5.82596	−	10.0909i	−0.363413	−	0.629450i	−0.988520	+	0.151089i	$0.951722\pi$
$258$	−1.32490	−	31.6681i	−0.0824848	−	1.97157i
$259$		0			0
$260$	4.48515	−	0.375949i	0.278157	−	0.0233154i
$261$	3.41141	−	12.7315i	0.211161	−	0.788062i
$262$	−2.89383	+	0.906632i	−0.178781	+	0.0560119i
$263$	15.7448	+	9.09027i	0.970867	+	0.560530i	0.899500	−	0.436920i	$-0.143931\pi$
$263$	15.7448	+	9.09027i	0.970867	+	0.560530i	0.0713665	+	0.997450i	$0.477264\pi$
$264$	−2.21655	+	1.68167i	−0.136419	+	0.103499i
$265$			2.79140i			0.171474i
$266$		0			0
$267$	18.0952	+	18.0952i	1.10741	+	1.10741i
$268$	−27.7587	−	4.99889i	−1.69563	−	0.305356i
$269$	−8.21935	−	30.6750i	−0.501143	−	1.87029i	−0.492474	−	0.870327i	$-0.663907\pi$
$269$	−8.21935	−	30.6750i	−0.501143	−	1.87029i	−0.00866872	−	0.999962i	$-0.502759\pi$
$270$	−1.13732	+	2.17509i	−0.0692149	+	0.132372i
$271$	11.1066	+	19.2372i	0.674677	+	1.16857i	0.976563	+	0.215231i	$0.0690504\pi$
$271$	11.1066	+	19.2372i	0.674677	+	1.16857i	−0.301886	+	0.953344i	$0.597616\pi$
$272$	−5.09697	+	0.860511i	−0.309049	+	0.0521761i
$273$		0			0
$274$	−8.43836	+	0.353036i	−0.509780	+	0.0213277i
$275$	−2.16772	−	0.580840i	−0.130719	−	0.0350260i
$276$	−10.2256	+	3.67972i	−0.615512	+	0.221493i
$277$	11.1559	−	2.98921i	0.670291	−	0.179604i	0.0924053	−	0.995721i	$-0.470544\pi$
$277$	11.1559	−	2.98921i	0.670291	−	0.179604i	0.577886	+	0.816117i	$0.303878\pi$
$278$	17.7681	+	3.97304i	1.06566	+	0.238287i
$279$			11.1527i			0.667694i
$280$		0			0
$281$			26.7783i			1.59746i	0.601690	+	0.798730i	$0.294494\pi$
$281$			26.7783i			1.59746i	−0.601690	+	0.798730i	$0.705506\pi$
$282$	2.95285	−	13.2056i	0.175840	−	0.786384i
$283$	−16.0481	+	4.30009i	−0.953963	+	0.255614i	−0.702043	−	0.712135i	$-0.747729\pi$
$283$	−16.0481	+	4.30009i	−0.953963	+	0.255614i	−0.251920	+	0.967748i	$0.581062\pi$
$284$	−13.7957	−	6.49432i	−0.818627	−	0.385367i
$285$	3.74603	+	1.00374i	0.221895	+	0.0594567i
$286$	−0.125609	−	3.00234i	−0.00742741	−	0.177532i
$287$		0			0
$288$	−7.38255	+	1.56631i	−0.435021	+	0.0922955i
$289$	7.66501	+	13.2762i	0.450883	+	0.780952i
$290$	6.19621	+	3.23989i	0.363854	+	0.190253i
$291$	2.96395	+	11.0616i	0.173750	+	0.648442i
$292$	−0.914187	+	0.635173i	−0.0534987	+	0.0371707i
$293$	15.2256	+	15.2256i	0.889492	+	0.889492i	0.994474	−	0.104983i	$-0.0334787\pi$
$293$	15.2256	+	15.2256i	0.889492	+	0.889492i	−0.104983	+	0.994474i	$0.533479\pi$
$294$		0			0
$295$		−	4.52640i		−	0.263537i
$296$	−13.1573	−	1.80534i	−0.764750	−	0.104934i
$297$	1.41917	+	0.819356i	0.0823484	+	0.0475439i
$298$	−1.87582	−	5.98734i	−0.108664	−	0.346837i
$299$	3.03785	−	11.3374i	0.175683	−	0.655659i
$300$	−15.1027	−	12.7667i	−0.871957	−	0.737086i
$301$		0			0
$302$	−16.9918	+	0.710887i	−0.977768	+	0.0409069i
$303$	−10.3469	−	17.9213i	−0.594412	−	1.02955i
$304$	−6.19424	−	13.5402i	−0.355264	−	0.776581i
$305$	−1.54067	+	2.66852i	−0.0882185	+	0.152799i
$306$	−1.30628	−	2.05870i	−0.0746748	−	0.117688i
$307$	13.7596	−	13.7596i	0.785302	−	0.785302i	−0.195418	−	0.980720i	$-0.562606\pi$
$307$	13.7596	−	13.7596i	0.785302	−	0.785302i	0.980720	+	0.195418i	$0.0626064\pi$
$308$		0			0
$309$	−21.4937	−	21.4937i	−1.22273	−	1.22273i
$310$	−5.77374	−	1.29104i	−0.327927	−	0.0733262i
$311$	9.07434	+	5.23907i	0.514558	+	0.297080i	0.734705	−	0.678386i	$-0.237320\pi$
$311$	9.07434	+	5.23907i	0.514558	+	0.297080i	−0.220147	+	0.975467i	$0.570654\pi$
$312$	10.2668	−	24.4083i	0.581242	−	1.38185i
$313$	28.4453	−	16.4229i	1.60782	−	0.928276i	0.617964	−	0.786206i	$-0.287958\pi$
$313$	28.4453	−	16.4229i	1.60782	−	0.928276i	0.989857	−	0.142070i	$-0.0453757\pi$
$314$	12.3049	+	11.3167i	0.694408	+	0.638637i
$315$		0			0
$316$	2.96806	−	0.248785i	0.166966	−	0.0139952i
$317$	−8.11991	−	2.17572i	−0.456059	−	0.122201i	0.0234738	−	0.999724i	$-0.492527\pi$
$317$	−8.11991	−	2.17572i	−0.456059	−	0.122201i	−0.479533	+	0.877524i	$0.659194\pi$
$318$	14.5530	+	7.60954i	0.816094	+	0.426722i
$319$	2.33411	−	4.04280i	0.130685	−	0.226353i
$320$	0.0437305	−	4.00326i	0.00244461	−	0.223789i
$321$	−3.06736			−0.171203
$322$		0			0
$323$	3.40147	−	3.40147i	0.189263	−	0.189263i
$324$	12.8069	+	18.4326i	0.711493	+	1.02403i
$325$	20.6307	−	5.52799i	1.14439	−	0.306638i
$326$	−1.75329	+	0.549302i	−0.0971056	+	0.0304230i
$327$	−11.0449	+	6.37678i	−0.610784	+	0.352636i
$328$	27.8727	−	3.51476i	1.53901	−	0.194070i
$329$		0			0
$330$	0.471266	−	0.512421i	0.0259423	−	0.0282078i
$331$	−0.131636	+	0.491271i	−0.00723535	+	0.0270027i	−0.969449	−	0.245292i	$-0.921116\pi$
$331$	−0.131636	+	0.491271i	−0.00723535	+	0.0270027i	0.962214	+	0.272295i	$0.0877827\pi$
$332$	1.40982	+	3.91776i	0.0773737	+	0.215015i
$333$	−1.62128	−	6.05071i	−0.0888458	−	0.331577i
$334$	−9.90218	−	15.6059i	−0.541823	−	0.853919i
$335$	7.05747			0.385591
$336$		0			0
$337$	27.0287			1.47235			0.736174	−	0.676792i	$-0.236630\pi$
$337$	27.0287			1.47235			0.736174	+	0.676792i	$0.236630\pi$
$338$	5.47236	+	8.62449i	0.297657	+	0.469110i
$339$	−9.50373	−	35.4684i	−0.516172	−	1.92638i
$340$	1.21701	−	0.437942i	0.0660014	−	0.0237508i
$341$	−1.02233	+	3.81538i	−0.0553622	+	0.206614i
$342$	4.75422	−	5.16939i	0.257079	−	0.279529i
$343$		0			0
$344$	18.6682	−	24.0557i	1.00652	−	1.29700i
$345$	2.35496	−	1.35964i	0.126787	−	0.0732003i
$346$	7.26869	−	2.27727i	0.390767	−	0.122427i
$347$	−3.49011	+	0.935173i	−0.187359	+	0.0502027i	−0.351278	−	0.936271i	$-0.614253\pi$
$347$	−3.49011	+	0.935173i	−0.187359	+	0.0502027i	0.163919	+	0.986474i	$0.447586\pi$
$348$	33.7826	−	23.4719i	1.81093	−	1.25823i
$349$	−2.82678	+	2.82678i	−0.151314	+	0.151314i	−0.778705	−	0.627391i	$-0.784123\pi$
$349$	−2.82678	+	2.82678i	−0.151314	+	0.151314i	0.627391	+	0.778705i	$0.284123\pi$
$350$		0			0
$351$	−15.5960			−0.832453
$352$	−2.66918	−	0.140892i	−0.142268	−	0.00750959i
$353$	−0.424483	+	0.735225i	−0.0225929	+	0.0391321i	−0.877101	−	0.480306i	$-0.840525\pi$
$353$	−0.424483	+	0.735225i	−0.0225929	+	0.0391321i	0.854508	+	0.519438i	$0.173859\pi$
$354$	−23.5985	−	12.3393i	−1.25425	−	0.655824i
$355$	3.68531	+	0.987475i	0.195596	+	0.0524097i
$356$	2.05348	+	24.4984i	0.108834	+	1.29841i
$357$		0			0
$358$	−12.9999	−	11.9558i	−0.687066	−	0.631885i
$359$	24.8695	−	14.3584i	1.31256	−	0.757808i	0.330043	−	0.943966i	$-0.392937\pi$
$359$	24.8695	−	14.3584i	1.31256	−	0.757808i	0.982520	+	0.186158i	$0.0596035\pi$
$360$	1.74855	−	0.713108i	0.0921565	−	0.0375841i
$361$	−4.45438	−	2.57174i	−0.234441	−	0.135355i
$362$	−2.67431	−	0.597990i	−0.140559	−	0.0314297i
$363$	15.8644	+	15.8644i	0.832663	+	0.832663i
$364$		0			0
$365$	0.196957	−	0.196957i	0.0103092	−	0.0103092i
$366$	9.71243	+	15.3069i	0.507677	+	0.800103i
$367$	10.6496	−	18.4456i	0.555903	−	0.962853i	−0.441929	−	0.897050i	$-0.645706\pi$
$367$	10.6496	−	18.4456i	0.555903	−	0.962853i	0.997833	−	0.0658029i	$-0.0209609\pi$
$368$	−9.78440	−	3.64214i	−0.510047	−	0.189860i
$369$	6.62556	+	11.4758i	0.344913	+	0.597407i
$370$	3.32013	−	0.138905i	0.172606	−	0.00722131i
$371$		0			0
$372$	−22.4705	+	26.5821i	−1.16504	+	1.37822i
$373$	2.04320	−	7.62531i	0.105793	−	0.394824i	−0.892641	−	0.450768i	$-0.851150\pi$
$373$	2.04320	−	7.62531i	0.105793	−	0.394824i	0.998434	+	0.0559442i	$0.0178169\pi$
$374$	−0.258168	−	0.824033i	−0.0133496	−	0.0426097i
$375$	8.79661	+	5.07873i	0.454255	+	0.262264i
$376$	10.3564	−	7.85728i	0.534093	−	0.405208i
$377$			44.4286i			2.28819i
$378$		0			0
$379$	12.0442	+	12.0442i	0.618668	+	0.618668i	0.945190	−	0.326522i	$-0.105877\pi$
$379$	12.0442	+	12.0442i	0.618668	+	0.618668i	−0.326522	+	0.945190i	$0.605877\pi$
$380$	2.12584	+	3.05967i	0.109053	+	0.156958i
$381$	−4.17653	−	15.5870i	−0.213970	−	0.798548i
$382$	−1.77389	−	0.927536i	−0.0907600	−	0.0474569i
$383$	−0.0426634	−	0.0738952i	−0.00218000	−	0.00377587i	0.864933	−	0.501887i	$-0.167361\pi$
$383$	−0.0426634	−	0.0738952i	−0.00218000	−	0.00377587i	−0.867113	+	0.498111i	$0.834027\pi$
$384$	−20.7519	−	11.1411i	−1.05899	−	0.568544i
$385$		0			0
$386$	0.648472	+	15.5000i	0.0330064	+	0.788927i
$387$	13.8731	+	3.71728i	0.705209	+	0.188960i
$388$	−4.68573	+	9.95380i	−0.237882	+	0.505328i
$389$	−0.720006	+	0.192925i	−0.0365058	+	0.00978169i	−0.277026	−	0.960863i	$-0.589349\pi$
$389$	−0.720006	+	0.192925i	−0.0365058	+	0.00978169i	0.240520	+	0.970644i	$0.422682\pi$
$390$	−1.44584	+	6.46603i	−0.0732129	+	0.327420i
$391$		−	3.37293i		−	0.170576i
$392$		0			0
$393$		−	4.46416i		−	0.225187i
$394$	−17.4254	−	3.89642i	−0.877880	−	0.196299i
$395$	−0.719873	+	0.192889i	−0.0362207	+	0.00970532i
$396$	−0.426885	−	1.18628i	−0.0214518	−	0.0596128i
$397$	−20.6847	−	5.54245i	−1.03813	−	0.278167i	−0.300795	−	0.953689i	$-0.597252\pi$
$397$	−20.6847	−	5.54245i	−1.03813	−	0.278167i	−0.737340	+	0.675522i	$0.763919\pi$
$398$	−12.3686	+	0.517465i	−0.619980	+	0.0259382i
$399$		0			0
$400$	−3.16268	−	18.7332i	−0.158134	−	0.936658i
$401$	−17.1809	−	29.7583i	−0.857975	−	1.48606i	−0.873857	−	0.486182i	$-0.838389\pi$
$401$	−17.1809	−	29.7583i	−0.857975	−	1.48606i	0.0158823	−	0.999874i	$-0.494944\pi$
$402$	19.2391	−	36.7943i	0.959560	−	1.83513i
$403$	−9.72973	−	36.3118i	−0.484672	−	1.80882i
$404$	3.52341	−	19.5654i	0.175296	−	0.973415i
$405$	−3.97122	−	3.97122i	−0.197331	−	0.197331i
$406$		0			0
$407$		−	2.21859i		−	0.109971i
$408$	1.03441	−	7.53875i	0.0512111	−	0.373224i
$409$	13.3958	+	7.73408i	0.662380	+	0.382425i	0.793183	−	0.608983i	$-0.208422\pi$
$409$	13.3958	+	7.73408i	0.662380	+	0.382425i	−0.130803	+	0.991408i	$0.541756\pi$
$410$	−6.70800	+	2.10161i	−0.331285	+	0.103791i
$411$	3.21788	−	12.0093i	0.158726	−	0.592374i
$412$	−2.43914	−	29.0995i	−0.120168	−	1.43363i
$413$		0			0
$414$	−0.205845	−	4.92017i	−0.0101168	−	0.241813i
$415$	−0.520919	−	0.902257i	−0.0255709	−	0.0442901i
$416$	22.6702	−	11.5403i	1.11150	−	0.565811i
$417$	−13.4011	+	23.2114i	−0.656254	+	1.13666i
$418$	2.10030	−	1.33267i	0.102729	−	0.0651829i
$419$	−26.1914	+	26.1914i	−1.27953	+	1.27953i	−0.338602	+	0.940930i	$0.609954\pi$
$419$	−26.1914	+	26.1914i	−1.27953	+	1.27953i	−0.940930	+	0.338602i	$0.890046\pi$
$420$		0			0
$421$	20.3620	+	20.3620i	0.992382	+	0.992382i	0.999971	−	0.00758948i	$-0.00241583\pi$
$421$	20.3620	+	20.3620i	0.992382	+	0.992382i	−0.00758948	+	0.999971i	$0.502416\pi$
$422$	4.31561	−	19.3001i	0.210081	−	0.939515i
$423$	5.31021	+	3.06585i	0.258191	+	0.149067i
$424$	5.95780	+	14.6086i	0.289336	+	0.709455i
$425$	5.31544	−	3.06887i	0.257837	−	0.148862i
$426$	15.1946	−	16.5215i	0.736182	−	0.800471i
$427$		0			0
$428$	−2.25044	−	1.90235i	−0.108779	−	0.0919534i
$429$	4.27285	+	1.14491i	0.206295	+	0.0552766i
$430$	−3.53039	+	6.75178i	−0.170251	+	0.325600i
$431$	12.6089	−	21.8392i	0.607347	−	1.05196i	−0.384329	−	0.923196i	$-0.625567\pi$
$431$	12.6089	−	21.8392i	0.607347	−	1.05196i	0.991676	−	0.128760i	$-0.0410997\pi$
$432$	−1.30968	+	13.8106i	−0.0630118	+	0.664462i
$433$	−11.8077			−0.567442			−0.283721	−	0.958907i	$-0.591569\pi$
$433$	−11.8077			−0.567442			−0.283721	+	0.958907i	$0.591569\pi$
$434$		0			0
$435$	−7.27830	+	7.27830i	−0.348968	+	0.348968i
$436$	−12.0582	−	2.17148i	−0.577481	−	0.103995i
$437$	9.38477	−	2.51464i	0.448934	−	0.120292i
$438$	−0.489924	−	1.56376i	−0.0234095	−	0.0747194i
$439$	−23.7665	+	13.7216i	−1.13431	+	0.654897i	−0.945016	−	0.327023i	$-0.893954\pi$
$439$	−23.7665	+	13.7216i	−1.13431	+	0.654897i	−0.189298	+	0.981920i	$0.560621\pi$
$440$	0.663553	−	0.0836741i	0.0316337	−	0.00398901i
$441$		0			0
$442$	6.04912	+	5.56329i	0.287727	+	0.264619i
$443$	−7.48700	+	27.9419i	−0.355718	+	1.32756i	0.523861	+	0.851804i	$0.324491\pi$
$443$	−7.48700	+	27.9419i	−0.355718	+	1.32756i	−0.879579	+	0.475753i	$0.842175\pi$
$444$	8.32672	−	17.6883i	0.395169	−	0.839448i
$445$	−1.59212	−	5.94186i	−0.0754736	−	0.281671i
$446$	7.31376	−	4.64068i	0.346317	−	0.219743i
$447$	9.23636			0.436865
$448$		0			0
$449$	−24.2497			−1.14441			−0.572206	−	0.820110i	$-0.693912\pi$
$449$	−24.2497			−1.14441			−0.572206	+	0.820110i	$0.693912\pi$
$450$	7.56646	−	4.80102i	0.356686	−	0.226322i
$451$	1.21468	+	4.53326i	0.0571972	+	0.213463i
$452$	15.0245	−	31.9163i	0.706695	−	1.50122i
$453$	6.47963	−	24.1823i	0.304440	−	1.13618i
$454$	−8.14831	−	7.49389i	−0.382419	−	0.351705i
$455$		0			0
$456$	21.7469	−	2.74228i	1.01839	−	0.128419i
$457$	−11.7825	+	6.80265i	−0.551164	+	0.318215i	−0.749591	−	0.661901i	$-0.769750\pi$
$457$	−11.7825	+	6.80265i	−0.551164	+	0.318215i	0.198427	+	0.980116i	$0.436417\pi$
$458$	−7.64896	−	24.4143i	−0.357412	−	1.14080i
$459$	−4.32907	+	1.15997i	−0.202064	+	0.0541428i
$460$	2.57100	+	0.462995i	0.119873	+	0.0215873i
$461$	28.1748	−	28.1748i	1.31223	−	1.31223i	0.392462	−	0.919768i	$-0.371624\pi$
$461$	28.1748	−	28.1748i	1.31223	−	1.31223i	0.919768	−	0.392462i	$-0.128376\pi$
$462$		0			0
$463$	−29.2805			−1.36078			−0.680391	−	0.732849i	$-0.738190\pi$
$463$	−29.2805			−1.36078			−0.680391	+	0.732849i	$0.738190\pi$
$464$	39.3424	+	3.73090i	1.82643	+	0.173202i
$465$	4.35469	−	7.54254i	0.201944	−	0.349777i
$466$	−16.1436	+	30.8741i	−0.747836	+	1.43022i
$467$	−30.3485	−	8.13184i	−1.40436	−	0.376297i	−0.524451	−	0.851441i	$-0.675729\pi$
$467$	−30.3485	−	8.13184i	−1.40436	−	0.376297i	−0.879908	+	0.475144i	$0.842396\pi$
$468$	9.16350	+	7.74612i	0.423583	+	0.358065i
$469$		0			0
$470$	−2.20190	+	2.39419i	−0.101566	+	0.110436i
$471$	−21.3128	+	12.3049i	−0.982041	+	0.566982i
$472$	−9.66088	−	23.6885i	−0.444678	−	1.09035i
$473$	4.40529	+	2.54339i	0.202555	+	0.116945i
$474$	−0.956787	+	4.27891i	−0.0439467	+	0.196537i
$475$	12.5016	+	12.5016i	0.573613	+	0.573613i
$476$		0			0
$477$	−5.26198	+	5.26198i	−0.240930	+	0.240930i
$478$	12.9972	−	8.24692i	0.594479	−	0.377205i
$479$	−16.8012	+	29.1005i	−0.767665	+	1.32963i	0.171162	+	0.985243i	$0.445248\pi$
$479$	−16.8012	+	29.1005i	−0.767665	+	1.32963i	−0.938826	+	0.344391i	$0.888085\pi$
$480$	5.60439	+	1.82331i	0.255804	+	0.0832221i
$481$	10.5574	+	18.2860i	0.481377	+	0.833769i
$482$	−0.895749	−	21.4104i	−0.0408002	−	0.975217i
$483$		0			0
$484$	1.80032	+	21.4782i	0.0818326	+	0.976280i
$485$	0.712476	−	2.65900i	0.0323519	−	0.120739i
$486$	−17.4888	+	5.47921i	−0.793307	+	0.248542i
$487$	−11.1651	−	6.44618i	−0.505939	−	0.292104i	0.225224	−	0.974307i	$-0.427689\pi$
$487$	−11.1651	−	6.44618i	−0.505939	−	0.292104i	−0.731163	+	0.682203i	$0.761022\pi$
$488$	−2.36744	+	17.2538i	−0.107169	+	0.781042i
$489$		−	2.70471i		−	0.122311i
$490$		0			0
$491$	5.46128	+	5.46128i	0.246464	+	0.246464i	0.819518	−	0.573054i	$-0.194241\pi$
$491$	5.46128	+	5.46128i	0.246464	+	0.246464i	−0.573054	+	0.819518i	$0.694241\pi$
$492$	−7.32967	+	40.7015i	−0.330447	+	1.83496i
$493$	3.30443	+	12.3323i	0.148824	+	0.555418i
$494$	−10.9693	+	20.9786i	−0.493534	+	0.943870i
$495$	0.157732	+	0.273199i	0.00708951	+	0.0122794i
$496$	−32.9719	+	5.56658i	−1.48048	+	0.249947i
$497$		0			0
$498$	−6.12400	+	0.256210i	−0.274423	+	0.0114811i
$499$	−21.6691	−	5.80620i	−0.970040	−	0.259921i	−0.261195	−	0.965286i	$-0.584117\pi$
$499$	−21.6691	−	5.80620i	−0.970040	−	0.259921i	−0.708845	+	0.705365i	$0.750783\pi$
$500$	3.30405	+	9.18170i	0.147762	+	0.410618i
$501$	26.2807	−	7.04189i	1.17413	−	0.314608i
$502$	−1.65521	−	0.370113i	−0.0738755	−	0.0165190i
$503$			2.46825i			0.110054i	0.998485	+	0.0550269i	$0.0175245\pi$
$503$			2.46825i			0.110054i	−0.998485	+	0.0550269i	$0.982476\pi$
$504$		0			0
$505$			4.97438i			0.221357i
$506$	0.380594	−	1.70208i	0.0169195	−	0.0756667i
$507$	−14.5238	+	3.89164i	−0.645025	+	0.172834i
$508$	6.60272	−	14.0260i	0.292949	−	0.622304i
$509$	18.2978	+	4.90288i	0.811036	+	0.217316i	0.640424	−	0.768022i	$-0.278759\pi$
$509$	18.2978	+	4.90288i	0.811036	+	0.217316i	0.170612	+	0.985338i	$0.445425\pi$
$510$	0.0795886	+	1.90235i	0.00352424	+	0.0842374i
$511$		0			0
$512$	−8.31546	−	21.0441i	−0.367495	−	0.930025i
$513$	−6.45495	−	11.1803i	−0.284993	−	0.493623i
$514$	14.6025	+	7.63542i	0.644091	+	0.336784i
$515$	1.89113	+	7.05780i	0.0833332	+	0.311004i
$516$	25.5765	+	36.8116i	1.12594	+	1.62054i
$517$	1.53561	+	1.53561i	0.0675360	+	0.0675360i
$518$		0			0
$519$			11.2130i			0.492198i
$520$	−5.07094	+	3.84725i	−0.222375	+	0.168713i
$521$	11.2226	+	6.47937i	0.491671	+	0.283867i	0.725268	−	0.688467i	$-0.241716\pi$
$521$	11.2226	+	6.47937i	0.491671	+	0.283867i	−0.233596	+	0.972334i	$0.575049\pi$
$522$	5.57286	+	17.7877i	0.243918	+	0.778547i
$523$	−6.94125	+	25.9051i	−0.303520	+	1.13275i	0.630693	+	0.776033i	$0.282771\pi$
$523$	−6.94125	+	25.9051i	−0.303520	+	1.13275i	−0.934212	+	0.356718i	$0.883896\pi$
$524$	2.76863	−	3.27523i	0.120948	−	0.143079i
$525$		0			0
$526$	−25.6887	+	1.07474i	−1.12008	+	0.0468609i
$527$	−5.40147	−	9.35562i	−0.235292	−	0.407537i
$528$	1.37265	−	3.68755i	0.0597370	−	0.160480i
$529$	−8.09376	+	14.0188i	−0.351903	+	0.609513i
$530$	−2.11500	−	3.33326i	−0.0918696	−	0.144787i
$531$	8.53258	−	8.53258i	0.370282	−	0.370282i
$532$		0			0
$533$	−31.5837	−	31.5837i	−1.36804	−	1.36804i
$534$	−35.3183	−	7.89736i	−1.52837	−	0.341752i
$535$	0.638550	+	0.368667i	0.0276069	+	0.0159389i
$536$	36.9347	−	15.0630i	1.59534	−	0.650624i
$537$	22.5165	−	12.9999i	0.971658	−	0.560987i
$538$	33.0568	+	30.4019i	1.42518	+	1.31072i
$539$		0			0
$540$	−0.289940	−	3.45904i	−0.0124770	−	0.148853i
$541$	15.3523	+	4.11365i	0.660049	+	0.176860i	0.573268	−	0.819368i	$-0.305675\pi$
$541$	15.3523	+	4.11365i	0.660049	+	0.176860i	0.0867808	+	0.996227i	$0.472342\pi$
$542$	−27.8383	−	14.5562i	−1.19576	−	0.625240i
$543$	2.01703	−	3.49359i	0.0865589	−	0.149924i
$544$	5.43438	−	4.88944i	0.232997	−	0.209633i
$545$	3.06571			0.131321
$546$		0			0
$547$	19.2062	−	19.2062i	0.821196	−	0.821196i	−0.165083	−	0.986280i	$-0.552789\pi$
$547$	19.2062	−	19.2062i	0.821196	−	0.821196i	0.986280	+	0.165083i	$0.0527893\pi$
$548$	9.80890	−	6.81518i	0.419016	−	0.291130i
$549$	−7.93461	+	2.12607i	−0.338641	+	0.0907386i
$550$	3.02861	−	0.948859i	0.129140	−	0.0404595i
$551$	−31.8495	+	18.3883i	−1.35683	+	0.783369i
$552$	9.42255	−	12.1418i	0.401051	−	0.516790i
$553$		0			0
$554$	−11.0565	+	12.0221i	−0.469748	+	0.510769i
$555$	−1.26610	+	4.72513i	−0.0537428	+	0.200571i
$556$	−24.2275	+	8.71831i	−1.02747	+	0.369739i
$557$	1.54045	+	5.74906i	0.0652712	+	0.243595i	0.990852	−	0.134956i	$-0.0430892\pi$
$557$	1.54045	+	5.74906i	0.0652712	+	0.243595i	−0.925580	+	0.378551i	$0.876423\pi$
$558$	−8.45021	−	13.3176i	−0.357726	−	0.563780i
$559$	−48.4121			−2.04762
$560$		0			0
$561$	1.27119			0.0536698
$562$	−20.2895	−	31.9764i	−0.855860	−	1.34884i
$563$	−4.19155	−	15.6431i	−0.176653	−	0.659276i	−0.996264	−	0.0863570i	$-0.972477\pi$
$563$	−4.19155	−	15.6431i	−0.176653	−	0.659276i	0.819612	−	0.572919i	$-0.194189\pi$
$564$	6.47965	+	18.0064i	0.272842	+	0.758207i
$565$	−2.28451	+	8.52592i	−0.0961102	+	0.358688i
$566$	15.9053	−	17.2942i	0.668548	−	0.726930i
$567$		0			0
$568$	21.3944	−	2.69783i	0.897688	−	0.113199i
$569$	−13.0326	+	7.52436i	−0.546354	+	0.315437i	−0.747650	−	0.664093i	$-0.768818\pi$
$569$	−13.0326	+	7.52436i	−0.546354	+	0.315437i	0.201296	+	0.979530i	$0.435485\pi$
$570$	−5.23371	+	1.63971i	−0.219216	+	0.0686801i
$571$	17.1302	−	4.59003i	0.716877	−	0.192087i	0.118099	−	0.993002i	$-0.462320\pi$
$571$	17.1302	−	4.59003i	0.716877	−	0.192087i	0.598778	+	0.800915i	$0.295653\pi$
$572$	2.42481	+	3.48997i	0.101386	+	0.145923i
$573$	2.08367	−	2.08367i	0.0870467	−	0.0870467i
$574$		0			0
$575$	12.3967			0.516978
$576$	7.62886	−	7.46399i	0.317869	−	0.311000i
$577$	−23.1600	+	40.1142i	−0.964162	+	1.66998i	−0.252313	+	0.967646i	$0.581191\pi$
$577$	−23.1600	+	40.1142i	−0.964162	+	1.66998i	−0.711850	+	0.702332i	$0.752142\pi$
$578$	−19.2121	−	10.0457i	−0.799117	−	0.417845i
$579$	−22.0592	−	5.91073i	−0.916747	−	0.245642i
$580$	−9.85381	+	0.825955i	−0.409157	+	0.0342959i
$581$		0			0
$582$	−11.9205	−	10.9631i	−0.494120	−	0.454436i
$583$	−2.28249	+	1.31780i	−0.0945312	+	0.0545776i
$584$	0.610386	−	1.45114i	0.0252580	−	0.0600484i
$585$	−2.60010	−	1.50117i	−0.107501	−	0.0620656i
$586$	−29.7174	−	6.64498i	−1.22762	−	0.274501i
$587$	−4.90812	−	4.90812i	−0.202580	−	0.202580i	0.598525	−	0.801104i	$-0.295754\pi$
$587$	−4.90812	−	4.90812i	−0.202580	−	0.202580i	−0.801104	+	0.598525i	$0.795754\pi$
$588$		0			0
$589$	22.0039	−	22.0039i	0.906654	−	0.906654i
$590$	3.42958	+	5.40505i	0.141194	+	0.222522i
$591$	13.1427	−	22.7637i	0.540616	−	0.936375i
$592$	17.0792	−	7.81324i	0.701950	−	0.321122i
$593$	−12.0345	−	20.8443i	−0.494196	−	0.855972i	0.505782	−	0.862662i	$-0.331204\pi$
$593$	−12.0345	−	20.8443i	−0.494196	−	0.855972i	−0.999978	+	0.00668902i	$0.997871\pi$
$594$	−2.31546	+	0.0968722i	−0.0950046	+	0.00397471i
$595$		0			0
$596$	6.77646	+	5.72830i	0.277575	+	0.234640i
$597$	4.71662	−	17.6027i	0.193038	−	0.720429i
$598$	4.96262	+	15.8399i	0.202937	+	0.647742i
$599$	5.33990	+	3.08299i	0.218182	+	0.125968i	0.605108	−	0.796143i	$-0.293130\pi$
$599$	5.33990	+	3.08299i	0.218182	+	0.125968i	−0.386926	+	0.922111i	$0.626463\pi$
$600$	27.7076	+	3.80183i	1.13116	+	0.155209i
$601$		−	16.2922i		−	0.664572i	−0.943179	−	0.332286i	$-0.892180\pi$
$601$		−	16.2922i		−	0.664572i	0.943179	−	0.332286i	$-0.107820\pi$
$602$		0			0
$603$	13.3038	+	13.3038i	0.541773	+	0.541773i
$604$	19.7516	−	13.7233i	0.803680	−	0.558393i
$605$	−1.39583	−	5.20932i	−0.0567487	−	0.211789i
$606$	25.9341	+	13.5605i	1.05350	+	0.550857i
$607$	17.4917	+	30.2966i	0.709968	+	1.22970i	0.964868	+	0.262733i	$0.0846240\pi$
$607$	17.4917	+	30.2966i	0.709968	+	1.22970i	−0.254900	+	0.966967i	$0.582043\pi$
$608$	17.6558	+	11.4753i	0.716037	+	0.465383i
$609$		0			0
$610$	−0.182153	−	4.35386i	−0.00737515	−	0.176283i
$611$	−19.9641	−	5.34937i	−0.807661	−	0.216412i
$612$	3.11969	+	1.46859i	0.126106	+	0.0593642i
$613$	−20.6418	+	5.53096i	−0.833715	+	0.223393i	−0.650334	−	0.759649i	$-0.725371\pi$
$613$	−20.6418	+	5.53096i	−0.833715	+	0.223393i	−0.183381	+	0.983042i	$0.558704\pi$
$614$	−6.00515	+	26.8560i	−0.242348	+	1.08382i
$615$		−	10.3481i		−	0.417275i
$616$		0			0
$617$			2.21451i			0.0891526i	0.999006	+	0.0445763i	$0.0141938\pi$
$617$			2.21451i			0.0891526i	−0.999006	+	0.0445763i	$0.985806\pi$
$618$	41.9514	+	9.38056i	1.68753	+	0.377341i
$619$	−2.70864	+	0.725777i	−0.108869	+	0.0291714i	−0.312842	−	0.949805i	$-0.601281\pi$
$619$	−2.70864	+	0.725777i	−0.108869	+	0.0291714i	0.203973	+	0.978977i	$0.434615\pi$
$620$	7.87273	−	2.83302i	0.316176	−	0.113777i
$621$	−8.74364	−	2.34285i	−0.350870	−	0.0940154i
$622$	−14.8054	+	0.619414i	−0.593642	+	0.0248362i
$623$		0			0
$624$	6.23403	+	36.9253i	0.249561	+	1.47820i
$625$	10.6531	+	18.4517i	0.426123	+	0.738067i
$626$	−21.5236	+	41.1633i	−0.860257	+	1.64522i
$627$	0.947720	+	3.53694i	0.0378483	+	0.141252i
$628$	−23.2680	−	4.19019i	−0.928494	−	0.167207i
$629$	4.29052	+	4.29052i	0.171074	+	0.171074i
$630$		0			0
$631$		−	24.6123i		−	0.979801i	−0.871778	−	0.489900i	$-0.837033\pi$
$631$		−	24.6123i		−	0.979801i	0.871778	−	0.489900i	$-0.162967\pi$
$632$	−3.35571	+	2.54593i	−0.133483	+	0.101271i
$633$	25.2128	+	14.5566i	1.00212	+	0.578573i
$634$	11.3446	−	3.55425i	0.450553	−	0.141157i
$635$	−1.00396	+	3.74682i	−0.0398409	+	0.148688i
$636$	−23.1437	+	1.93992i	−0.917706	+	0.0769229i
$637$		0			0
$638$	0.275961	+	6.59609i	0.0109254	+	0.261142i
$639$	5.08560	+	8.80852i	0.201183	+	0.348460i
$640$	2.98099	+	4.81350i	0.117834	+	0.190270i
$641$	11.7655	−	20.3784i	0.464709	−	0.804899i	−0.534480	−	0.845181i	$-0.679492\pi$
$641$	11.7655	−	20.3784i	0.464709	−	0.804899i	0.999188	+	0.0402822i	$0.0128257\pi$
$642$	3.66279	−	2.32409i	0.144559	−	0.0917245i
$643$	8.79484	−	8.79484i	0.346835	−	0.346835i	−0.512095	−	0.858929i	$-0.671130\pi$
$643$	8.79484	−	8.79484i	0.346835	−	0.346835i	0.858929	+	0.512095i	$0.171130\pi$
$644$		0			0
$645$	−7.93089	−	7.93089i	−0.312278	−	0.312278i
$646$	−1.48452	+	6.63900i	−0.0584075	+	0.261208i
$647$	−18.3033	−	10.5674i	−0.719577	−	0.415448i	0.0950202	−	0.995475i	$-0.469708\pi$
$647$	−18.3033	−	10.5674i	−0.719577	−	0.415448i	−0.814597	+	0.580028i	$0.803042\pi$
$648$	−29.2590	−	12.3071i	−1.14940	−	0.483469i
$649$	3.70118	−	2.13688i	0.145284	−	0.0838798i
$650$	−20.4470	+	22.2326i	−0.801999	+	0.872036i
$651$		0			0
$652$	1.67743	−	1.98437i	0.0656934	−	0.0777139i
$653$	−9.11215	−	2.44159i	−0.356586	−	0.0955470i	0.0760787	−	0.997102i	$-0.475760\pi$
$653$	−9.11215	−	2.44159i	−0.356586	−	0.0955470i	−0.432665	+	0.901555i	$0.642427\pi$
$654$	8.35732	−	15.9832i	0.326797	−	0.624991i
$655$	−0.536549	+	0.929331i	−0.0209647	+	0.0363120i
$656$	−30.6202	+	25.3157i	−1.19552	+	0.988414i
$657$	0.742557			0.0289699
$658$		0			0
$659$	−2.68220	+	2.68220i	−0.104484	+	0.104484i	−0.757416	−	0.652932i	$-0.773539\pi$
$659$	−2.68220	+	2.68220i	−0.104484	+	0.104484i	0.652932	+	0.757416i	$0.273539\pi$
$660$	−0.174494	+	0.968961i	−0.00679217	+	0.0377167i
$661$	−0.793258	+	0.212553i	−0.0308542	+	0.00826735i	−0.274213	−	0.961669i	$-0.588417\pi$
$661$	−0.793258	+	0.212553i	−0.0308542	+	0.00826735i	0.243359	+	0.969936i	$0.421751\pi$
$662$	−0.215040	−	0.686373i	−0.00835775	−	0.0266767i
$663$	−10.4774	+	6.04912i	−0.406908	+	0.234928i
$664$	−4.65191	−	3.61007i	−0.180529	−	0.140098i
$665$		0			0
$666$	6.52053	+	5.99684i	0.252665	+	0.232373i
$667$	−6.67412	+	24.9081i	−0.258423	+	0.964447i
$668$	23.6487	+	11.1326i	0.914996	+	0.430733i
$669$	3.30020	+	12.3165i	0.127593	+	0.476184i
$670$	−8.42744	+	5.34733i	−0.325581	+	0.206585i
$671$	−2.90935			−0.112314
$672$		0			0
$673$	−7.60472			−0.293140			−0.146570	−	0.989200i	$-0.546823\pi$
$673$	−7.60472			−0.293140			−0.146570	+	0.989200i	$0.546823\pi$
$674$	−32.2755	+	20.4792i	−1.24320	+	0.788830i
$675$	−4.26330	−	15.9108i	−0.164094	−	0.612409i
$676$	−13.0693	−	6.15233i	−0.502664	−	0.236628i
$677$	7.74876	−	28.9188i	0.297809	−	1.11144i	−0.641152	−	0.767414i	$-0.721543\pi$
$677$	7.74876	−	28.9188i	0.297809	−	1.11144i	0.938961	−	0.344024i	$-0.111790\pi$
$678$	38.2224	+	35.1526i	1.46792	+	1.35003i
$679$		0			0
$680$	−1.12143	+	1.44506i	−0.0430047	+	0.0554155i
$681$	14.1133	−	8.14831i	0.540822	−	0.312244i
$682$	−1.67007	−	5.33061i	−0.0639504	−	0.204120i
$683$	−8.04672	+	2.15611i	−0.307899	+	0.0825013i	−0.409460	−	0.912328i	$-0.634283\pi$
$683$	−8.04672	+	2.15611i	−0.307899	+	0.0825013i	0.101561	+	0.994829i	$0.467616\pi$
$684$	−1.76033	+	9.77505i	−0.0673078	+	0.373758i
$685$	−2.11328	+	2.11328i	−0.0807444	+	0.0807444i
$686$		0			0
$687$	37.6627			1.43692
$688$	−4.06542	+	42.8699i	−0.154993	+	1.63440i
$689$	12.5418	−	21.7230i	0.477804	−	0.827581i
$690$	−1.78192	+	3.40788i	−0.0678366	+	0.129736i
$691$	16.3753	+	4.38774i	0.622945	+	0.166918i	0.556466	−	0.830870i	$-0.312157\pi$
$691$	16.3753	+	4.38774i	0.622945	+	0.166918i	0.0664786	+	0.997788i	$0.478824\pi$
$692$	−6.95422	+	8.22670i	−0.264360	+	0.312732i
$693$		0			0
$694$	3.45904	−	3.76111i	0.131303	−	0.142770i
$695$	5.57956	−	3.22136i	0.211645	−	0.122193i
$696$	−22.5560	+	53.6247i	−0.854983	+	2.03264i
$697$	−11.1159	−	6.41779i	−0.421046	−	0.243091i
$698$	1.23370	−	5.51731i	0.0466963	−	0.208833i
$699$	−36.2659	−	36.2659i	−1.37170	−	1.37170i
$700$		0			0
$701$	−12.6791	+	12.6791i	−0.478882	+	0.478882i	−0.904774	−	0.425892i	$-0.859960\pi$
$701$	−12.6791	+	12.6791i	−0.478882	+	0.478882i	0.425892	+	0.904774i	$0.359960\pi$
$702$	18.6234	−	11.8168i	0.702897	−	0.445998i
$703$	−8.73912	+	15.1366i	−0.329602	+	0.570888i
$704$	3.29406	−	1.85415i	0.124150	−	0.0698809i
$705$	−2.39419	−	4.14686i	−0.0901704	−	0.156180i
$706$	−0.0501864	−	1.19957i	−0.00188879	−	0.0451464i
$707$		0			0
$708$	37.5286	−	3.14568i	1.41041	−	0.118222i
$709$	−4.14517	+	15.4700i	−0.155675	+	0.580987i	0.843372	+	0.537331i	$0.180567\pi$
$709$	−4.14517	+	15.4700i	−0.155675	+	0.580987i	−0.999047	+	0.0436562i	$0.986099\pi$
$710$	−5.14888	+	1.61314i	−0.193234	+	0.0605399i
$711$	−1.72062	−	0.993401i	−0.0645283	−	0.0372554i
$712$	−21.0142	−	27.6981i	−0.787539	−	1.03803i
$713$		−	21.8193i		−	0.817138i
$714$		0			0
$715$	−0.751898	−	0.751898i	−0.0281194	−	0.0281194i
$716$	24.5821	+	4.42684i	0.918678	+	0.165439i
$717$	5.86476	+	21.8876i	0.219023	+	0.817406i
$718$	−18.8180	+	35.9889i	−0.702280	+	1.34309i
$719$	−0.669732	−	1.16001i	−0.0249768	−	0.0432611i	0.853267	−	0.521475i	$-0.174618\pi$
$719$	−0.669732	−	1.16001i	−0.0249768	−	0.0432611i	−0.878244	+	0.478213i	$0.841285\pi$
$720$	−1.54766	+	2.17638i	−0.0576778	+	0.0811089i
$721$		0			0
$722$	7.26762	−	0.304056i	0.270473	−	0.0113158i
$723$	30.4708	+	8.16462i	1.13322	+	0.303645i
$724$	3.64653	−	1.31221i	0.135522	−	0.0487679i
$725$	−45.3255	+	12.1449i	−1.68335	+	0.451051i
$726$	−30.9641	−	6.92373i	−1.14918	−	0.256964i
$727$			3.87352i			0.143661i	0.997417	+	0.0718304i	$0.0228840\pi$
$727$			3.87352i			0.143661i	−0.997417	+	0.0718304i	$0.977116\pi$
$728$		0			0
$729$			6.68839i			0.247718i
$730$	−0.0859588	+	0.384422i	−0.00318148	+	0.0142281i
$731$	−13.4380	+	3.60071i	−0.497024	+	0.133177i
$732$	−23.1955	−	10.9193i	−0.857332	−	0.403587i
$733$	41.2353	+	11.0490i	1.52306	+	0.408103i	0.920748	−	0.390158i	$-0.127580\pi$
$733$	41.2353	+	11.0490i	1.52306	+	0.408103i	0.602312	+	0.798261i	$0.294246\pi$
$734$	1.25910	+	30.0952i	0.0464741	+	1.11083i
$735$		0			0
$736$	14.4433	−	3.06434i	0.532387	−	0.112953i
$737$	3.33178	+	5.77081i	0.122728	+	0.212570i
$738$	−16.6067	−	8.68338i	−0.611302	−	0.319640i
$739$	6.97402	+	26.0274i	0.256544	+	0.957434i	0.967225	+	0.253920i	$0.0817200\pi$
$739$	6.97402	+	26.0274i	0.256544	+	0.957434i	−0.710682	+	0.703514i	$0.751613\pi$
$740$	−3.85938	+	2.68148i	−0.141874	+	0.0985731i
$741$	−24.6422	−	24.6422i	−0.905254	−	0.905254i
$742$		0			0
$743$			13.4783i			0.494470i	0.968956	+	0.247235i	$0.0795219\pi$
$743$			13.4783i			0.494470i	−0.968956	+	0.247235i	$0.920478\pi$
$744$	6.69155	−	48.7677i	0.245324	−	1.78791i
$745$	−1.92279	−	1.11012i	−0.0704455	−	0.0406717i
$746$	3.33776	+	10.6536i	0.122204	+	0.390056i
$747$	0.718850	−	2.68279i	0.0263014	−	0.0981580i
$748$	0.932639	+	0.788382i	0.0341007	+	0.0288261i
$749$		0			0
$750$	−14.3523	+	0.600456i	−0.524070	+	0.0219256i
$751$	17.8616	+	30.9372i	0.651780	+	1.12892i	0.982691	+	0.185254i	$0.0593108\pi$
$751$	17.8616	+	30.9372i	0.651780	+	1.12892i	−0.330911	+	0.943662i	$0.607356\pi$
$752$	−6.41346	+	17.2294i	−0.233875	+	0.628292i
$753$	1.24839	−	2.16228i	0.0454940	−	0.0787980i
$754$	−33.6628	−	53.0529i	−1.22593	−	1.93207i
$755$	−4.25538	+	4.25538i	−0.154869	+	0.154869i
$756$		0			0
$757$	10.1603	+	10.1603i	0.369284	+	0.369284i	0.867216	−	0.497932i	$-0.165907\pi$
$757$	10.1603	+	10.1603i	0.369284	+	0.369284i	−0.497932	+	0.867216i	$0.665907\pi$
$758$	−23.5078	−	5.25648i	−0.853843	−	0.190924i
$759$	2.22351	+	1.28375i	0.0807085	+	0.0465971i
$760$	−4.85677	−	2.04289i	−0.176173	−	0.0741033i
$761$	19.1505	−	11.0565i	0.694205	−	0.400799i	−0.110980	−	0.993823i	$-0.535399\pi$
$761$	19.1505	−	11.0565i	0.694205	−	0.400799i	0.805185	+	0.593023i	$0.202066\pi$
$762$	16.7973	+	15.4483i	0.608503	+	0.559631i
$763$		0			0
$764$	2.82101	−	0.236459i	0.102061	−	0.00855480i
$765$	−0.833375	−	0.223302i	−0.0301307	−	0.00807351i
$766$	0.106934	+	0.0559141i	0.00386369	+	0.00202026i
$767$	−20.3372	+	35.2250i	−0.734332	+	1.27190i
$768$	33.2217	−	2.41955i	1.19878	−	0.0873079i
$769$	−18.2859			−0.659405			−0.329702	−	0.944085i	$-0.606948\pi$
$769$	−18.2859			−0.659405			−0.329702	+	0.944085i	$0.606948\pi$
$770$		0			0
$771$	−17.1527	+	17.1527i	−0.617739	+	0.617739i
$772$	−12.5184	−	18.0174i	−0.450548	−	0.648461i
$773$	12.5013	−	3.34971i	0.449640	−	0.120481i	−0.0268907	−	0.999638i	$-0.508561\pi$
$773$	12.5013	−	3.34971i	0.449640	−	0.120481i	0.476531	+	0.879158i	$0.341894\pi$
$774$	−19.3826	+	6.07254i	−0.696694	+	0.218273i
$775$	34.3852	−	19.8523i	1.23515	−	0.713116i
$776$	−1.94652	−	15.4363i	−0.0698760	−	0.554131i
$777$		0			0
$778$	0.713596	−	0.775912i	0.0255836	−	0.0278178i
$779$	9.56938	−	35.7134i	0.342859	−	1.27957i
$780$	−3.17270	−	8.81668i	−0.113601	−	0.315688i
$781$	0.932359	+	3.47961i	0.0333624	+	0.124510i
$782$	2.55561	+	4.02767i	0.0913886	+	0.144029i
$783$	34.2642			1.22450
$784$		0			0
$785$	5.91574			0.211142
$786$	3.38242	+	5.33073i	0.120647	+	0.190141i
$787$	8.86450	+	33.0828i	0.315985	+	1.17927i	0.923069	+	0.384635i	$0.125673\pi$
$787$	8.86450	+	33.0828i	0.315985	+	1.17927i	−0.607083	+	0.794638i	$0.707661\pi$
$788$	23.7603	−	8.55018i	0.846424	−	0.304588i
$789$	9.79610	−	36.5595i	0.348750	−	1.30155i
$790$	0.713463	−	0.775769i	0.0253839	−	0.0276006i
$791$		0			0
$792$	1.40858	+	1.09311i	0.0500516	+	0.0388421i
$793$	23.9794	−	13.8445i	0.851532	−	0.491632i
$794$	28.8994	−	9.05412i	1.02560	−	0.321319i
$795$	5.61327	−	1.50407i	0.199082	−	0.0533439i
$796$	14.3774	−	9.98938i	0.509595	−	0.354064i
$797$	−12.6836	+	12.6836i	−0.449277	+	0.449277i	−0.895114	−	0.445837i	$-0.852906\pi$
$797$	−12.6836	+	12.6836i	−0.449277	+	0.449277i	0.445837	+	0.895114i	$0.352906\pi$
$798$		0			0
$799$	−5.93942			−0.210121
$800$	17.9704	+	19.9733i	0.635350	+	0.706162i
$801$	8.19957	−	14.2021i	0.289718	−	0.501805i
$802$	43.0634	+	22.5171i	1.52062	+	0.795107i
$803$	0.254032	+	0.0680676i	0.00896459	+	0.00240205i
$804$	4.90468	+	58.5139i	0.172975	+	2.06363i
$805$		0			0
$806$	39.1313	+	35.9885i	1.37834	+	1.26764i
$807$	−57.2561	+	33.0568i	−2.01551	+	1.16366i
$808$	10.6170	+	26.0330i	0.373506	+	0.915838i
$809$	−7.52353	−	4.34371i	−0.264513	−	0.152717i	0.361878	−	0.932225i	$-0.382136\pi$
$809$	−7.52353	−	4.34371i	−0.264513	−	0.152717i	−0.626392	+	0.779509i	$0.715469\pi$
$810$	7.75102	+	1.73317i	0.272343	+	0.0608974i
$811$	2.41161	+	2.41161i	0.0846830	+	0.0846830i	0.748179	−	0.663496i	$-0.230928\pi$
$811$	2.41161	+	2.41161i	0.0846830	+	0.0846830i	−0.663496	+	0.748179i	$0.730928\pi$
$812$		0			0
$813$	32.6998	−	32.6998i	1.14683	−	1.14683i
$814$	1.68099	+	2.64926i	0.0589187	+	0.0928564i
$815$	−0.325080	+	0.563055i	−0.0113871	+	0.0197229i
$816$	4.47678	+	9.78591i	0.156719	+	0.342575i
$817$	−20.0371	−	34.7052i	−0.701008	−	1.21418i
$818$	−21.8561	+	0.914397i	−0.764182	+	0.0319711i
$819$		0			0
$820$	6.41779	−	7.59211i	0.224119	−	0.265128i
$821$	−2.42543	+	9.05181i	−0.0846479	+	0.315910i	−0.995247	−	0.0973798i	$-0.968954\pi$
$821$	−2.42543	+	9.05181i	−0.0846479	+	0.315910i	0.910599	+	0.413290i	$0.135621\pi$
$822$	5.25671	+	16.7786i	0.183349	+	0.585221i
$823$	8.76954	+	5.06310i	0.305687	+	0.176488i	0.644995	−	0.764187i	$-0.276860\pi$
$823$	8.76954	+	5.06310i	0.305687	+	0.176488i	−0.339308	+	0.940675i	$0.610193\pi$
$824$	24.9608	+	32.9001i	0.869552	+	1.14613i
$825$			4.67208i			0.162661i
$826$		0			0
$827$	2.96806	+	2.96806i	0.103209	+	0.103209i	0.756826	−	0.653617i	$-0.226749\pi$
$827$	2.96806	+	2.96806i	0.103209	+	0.103209i	−0.653617	+	0.756826i	$0.726749\pi$
$828$	3.97374	+	5.71929i	0.138097	+	0.198759i
$829$	11.2070	+	41.8251i	0.389235	+	1.45265i	0.831381	+	0.555702i	$0.187551\pi$
$829$	11.2070	+	41.8251i	0.389235	+	1.45265i	−0.442146	+	0.896943i	$0.645783\pi$
$830$	1.30566	+	0.682709i	0.0453202	+	0.0236972i
$831$	−12.0221	−	20.8229i	−0.417042	−	0.722337i
$832$	−18.3270	+	30.9574i	−0.635375	+	1.07325i
$833$		0			0
$834$	−1.58441	−	37.8709i	−0.0548635	−	1.31136i
$835$	−6.31737	−	1.69273i	−0.218622	−	0.0585795i
$836$	−1.49826	+	3.18272i	−0.0518184	+	0.110077i
$837$	−28.0044	+	7.50377i	−0.967975	+	0.259368i
$838$	11.4308	−	51.1203i	0.394870	−	1.76592i
$839$		−	51.7749i		−	1.78747i	−0.448598	−	0.893734i	$-0.648076\pi$
$839$		−	51.7749i		−	1.78747i	0.448598	−	0.893734i	$-0.351924\pi$
$840$		0			0
$841$		−	68.6090i		−	2.36583i
$842$	−39.7425	−	8.88664i	−1.36962	−	0.306254i
$843$	53.8489	−	14.4288i	1.85465	−	0.496953i
$844$	9.47004	+	26.3165i	0.325972	+	0.905851i
$845$	3.49124	+	0.935475i	0.120102	+	0.0321813i
$846$	−8.66396	+	0.362475i	−0.297873	+	0.0124621i
$847$		0			0
$848$	−18.1830	−	12.9302i	−0.624406	−	0.444025i
$849$	17.2942	+	29.9545i	0.593536	+	1.02803i
$850$	−4.02202	+	7.69201i	−0.137954	+	0.263834i
$851$	3.17190	+	11.8377i	0.108731	+	0.405791i
$852$	−5.62606	+	31.2414i	−0.192746	+	1.07031i
$853$	5.56576	+	5.56576i	0.190568	+	0.190568i	0.795941	−	0.605374i	$-0.206976\pi$
$853$	5.56576	+	5.56576i	0.190568	+	0.190568i	−0.605374	+	0.795941i	$0.706976\pi$
$854$		0			0
$855$		−	2.48524i		−	0.0849936i
$856$	4.12866	+	0.566506i	0.141115	+	0.0193628i
$857$	−28.0770	−	16.2103i	−0.959093	−	0.553733i	−0.0631996	−	0.998001i	$-0.520130\pi$
$857$	−28.0770	−	16.2103i	−0.959093	−	0.553733i	−0.895894	+	0.444268i	$0.853464\pi$
$858$	−5.96976	+	1.87032i	−0.203804	+	0.0638516i
$859$	−2.80958	+	10.4855i	−0.0958618	+	0.357761i	−0.997149	−	0.0754617i	$-0.975957\pi$
$859$	−2.80958	+	10.4855i	−0.0958618	+	0.357761i	0.901287	+	0.433223i	$0.142624\pi$
$860$	−0.900012	−	10.7373i	−0.0306902	−	0.366140i
$861$		0			0
$862$	1.49074	+	35.6321i	0.0507748	+	1.21363i
$863$	16.5015	+	28.5814i	0.561716	+	0.972921i	0.997347	+	0.0727955i	$0.0231921\pi$
$863$	16.5015	+	28.5814i	0.561716	+	0.972921i	−0.435631	+	0.900126i	$0.643475\pi$
$864$	−8.90014	−	17.4838i	−0.302789	−	0.594810i
$865$	1.34770	−	2.33428i	0.0458232	−	0.0793681i
$866$	14.0998	−	8.94651i	0.479130	−	0.304015i
$867$	22.5672	−	22.5672i	0.766423	−	0.766423i
$868$		0			0
$869$	−0.497570	−	0.497570i	−0.0168789	−	0.0168789i
$870$	3.17649	−	14.2058i	0.107693	−	0.481621i
$871$	−54.9221	−	31.7093i	−1.86096	−	1.07443i
$872$	16.0441	−	6.54327i	0.543323	−	0.221583i
$873$	6.35546	−	3.66933i	0.215100	−	0.124188i
$874$	−9.30121	+	10.1135i	−0.314618	+	0.342093i
$875$		0			0
$876$	1.76986	+	1.49611i	0.0597981	+	0.0505488i
$877$	46.1420	+	12.3637i	1.55810	+	0.417493i	0.932063	−	0.362296i	$-0.118007\pi$
$877$	46.1420	+	12.3637i	1.55810	+	0.417493i	0.626042	+	0.779789i	$0.284674\pi$
$878$	17.9834	−	34.3927i	0.606909	−	1.16070i
$879$	22.4136	−	38.8214i	0.755990	−	1.30941i
$880$	−0.728962	+	0.602680i	−0.0245733	+	0.0203163i
$881$	46.9509			1.58181			0.790907	−	0.611936i	$-0.209609\pi$
$881$	46.9509			1.58181			0.790907	+	0.611936i	$0.209609\pi$
$882$		0			0
$883$	13.8628	−	13.8628i	0.466522	−	0.466522i	−0.434264	−	0.900786i	$-0.642991\pi$
$883$	13.8628	−	13.8628i	0.466522	−	0.466522i	0.900786	+	0.434264i	$0.142991\pi$
$884$	−11.4386	−	2.05990i	−0.384721	−	0.0692819i
$885$	−9.10221	+	2.43893i	−0.305967	+	0.0819837i
$886$	−12.2307	−	39.0386i	−0.410900	−	1.31153i
$887$	6.75025	−	3.89726i	0.226651	−	0.130857i	−0.382375	−	0.924007i	$-0.624894\pi$
$887$	6.75025	−	3.89726i	0.226651	−	0.130857i	0.609026	+	0.793150i	$0.291560\pi$
$888$	3.45904	+	27.4309i	0.116078	+	0.920520i
$889$		0			0
$890$	6.40322	+	5.88895i	0.214637	+	0.197398i
$891$	1.37244	−	5.12200i	0.0459783	−	0.171593i
$892$	−5.21732	+	11.0830i	−0.174689	+	0.371088i
$893$	−4.42805	−	16.5257i	−0.148179	−	0.553011i
$894$	−11.0293	+	6.99824i	−0.368875	+	0.234056i
$895$	−6.24985			−0.208910
$896$		0			0
$897$	−24.4354			−0.815875
$898$	28.9569	−	18.3736i	0.966305	−	0.613134i
$899$	21.3761	+	79.7767i	0.712933	+	2.66070i
$900$	−5.39758	+	11.4660i	−0.179919	+	0.382199i
$901$	1.86562	−	6.96259i	0.0621528	−	0.231958i
$902$	−4.88525	−	4.49290i	−0.162661	−	0.149597i
$903$		0			0
$904$	6.24141	+	49.4956i	0.207586	+	1.64620i
$905$	−0.839792	+	0.484854i	−0.0279156	+	0.0161171i
$906$	10.5851	+	33.7860i	0.351667	+	1.12247i
$907$	9.28586	−	2.48814i	0.308332	−	0.0826173i	−0.101335	−	0.994852i	$-0.532311\pi$
$907$	9.28586	−	2.48814i	0.308332	−	0.0826173i	0.409667	+	0.912235i	$0.365645\pi$
$908$	15.4080	+	2.77474i	0.511333	+	0.0920828i
$909$	−9.37705	+	9.37705i	−0.311017	+	0.311017i
$910$		0			0
$911$	−6.36372			−0.210839			−0.105420	−	0.994428i	$-0.533619\pi$
$911$	−6.36372			−0.210839			−0.105420	+	0.994428i	$0.533619\pi$
$912$	−23.8905	+	19.7518i	−0.791094	+	0.654049i
$913$	0.491843	−	0.851898i	0.0162776	−	0.0281937i
$914$	8.91547	−	17.0506i	0.294898	−	0.563984i
$915$	6.19631	+	1.66030i	0.204844	+	0.0548877i
$916$	27.6321	+	23.3580i	0.912989	+	0.771771i
$917$		0			0
$918$	4.29052	−	4.66521i	0.141608	−	0.153975i
$919$	14.5846	−	8.42040i	0.481100	−	0.277763i	−0.239775	−	0.970829i	$-0.577074\pi$
$919$	14.5846	−	8.42040i	0.481100	−	0.277763i	0.720875	+	0.693065i	$0.243740\pi$
$920$	−3.42088	+	1.39513i	−0.112783	+	0.0459962i
$921$	−35.0834	−	20.2554i	−1.15604	−	0.667438i
$922$	−12.2964	+	54.9915i	−0.404961	+	1.81105i
$923$	−24.2428	−	24.2428i	−0.797961	−	0.797961i
$924$		0			0
$925$	−15.7692	+	15.7692i	−0.518487	+	0.518487i
$926$	34.9644	−	22.1854i	1.14900	−	0.729057i
$927$	−9.73953	+	16.8694i	−0.319888	+	0.554062i
$928$	−49.8063	+	25.3540i	−1.63497	+	0.832285i
$929$	10.8991	+	18.8778i	0.357587	+	0.619360i	0.987557	−	0.157260i	$-0.0502661\pi$
$929$	10.8991	+	18.8778i	0.357587	+	0.619360i	−0.629970	+	0.776620i	$0.716933\pi$
$930$	0.514853	+	12.3062i	0.0168827	+	0.403535i
$931$		0			0
$932$	−4.11552	−	49.0990i	−0.134808	−	1.60829i
$933$	5.64587	−	21.0707i	0.184837	−	0.689822i
$934$	42.4010	−	13.2842i	1.38740	−	0.434671i
$935$	−0.264632	−	0.152785i	−0.00865438	−	0.00499661i
$936$	−16.8114	−	2.30674i	−0.549498	−	0.0753982i
$937$		−	21.3450i		−	0.697310i	−0.937251	−	0.348655i	$-0.886639\pi$
$937$		−	21.3450i		−	0.697310i	0.937251	−	0.348655i	$-0.113361\pi$
$938$		0			0
$939$	−48.3520	−	48.3520i	−1.57791	−	1.57791i
$940$	0.815291	−	4.52729i	0.0265919	−	0.147664i
$941$	−13.4819	−	50.3151i	−0.439497	−	1.64022i	−0.730071	−	0.683372i	$-0.760513\pi$
$941$	−13.4819	−	50.3151i	−0.439497	−	1.64022i	0.290574	−	0.956853i	$-0.406154\pi$
$942$	16.1267	−	30.8419i	0.525436	−	1.00488i
$943$	−12.9623	−	22.4514i	−0.422112	−	0.731119i
$944$	29.4846	+	20.9670i	0.959643	+	0.682418i
$945$		0			0
$946$	−7.18752	+	0.300705i	−0.233686	+	0.00977675i
$947$	−2.10513	−	0.564067i	−0.0684074	−	0.0183297i	0.224453	−	0.974485i	$-0.427940\pi$
$947$	−2.10513	−	0.564067i	−0.0684074	−	0.0183297i	−0.292860	+	0.956155i	$0.594607\pi$
$948$	−2.09954	−	5.83446i	−0.0681900	−	0.189494i
$949$	−2.41768	+	0.647815i	−0.0784812	+	0.0210290i
$950$	−24.4006	−	5.45612i	−0.791661	−	0.177020i
$951$			17.5008i			0.567502i
$952$		0			0
$953$		−	7.31316i		−	0.236897i	−0.992960	−	0.118448i	$-0.962208\pi$
$953$		−	7.31316i		−	0.236897i	0.992960	−	0.118448i	$-0.0377920\pi$
$954$	2.29650	−	10.2703i	0.0743521	−	0.332515i
$955$	−0.684208	+	0.183333i	−0.0221405	+	0.00593252i
$956$	−9.27165	+	19.6956i	−0.299867	+	0.637000i
$957$	−9.38740	−	2.51535i	−0.303452	−	0.0813096i
$958$	−1.98640	−	47.4793i	−0.0641775	−	1.53399i
$959$		0			0
$960$	−8.07378	+	2.06911i	−0.260580	+	0.0667803i
$961$	−19.4418	−	33.6741i	−0.627153	−	1.08626i
$962$	−26.4618	−	13.8364i	−0.853162	−	0.446104i
$963$	0.508749	+	1.89868i	0.0163942	+	0.0611840i
$964$	17.2919	+	24.8878i	0.556936	+	0.801583i
$965$	3.88177	+	3.88177i	0.124959	+	0.124959i
$966$		0			0
$967$			42.1882i			1.35668i	0.734748	+	0.678341i	$0.237301\pi$
$967$			42.1882i			1.35668i	−0.734748	+	0.678341i	$0.762699\pi$
$968$	−18.4234	−	24.2834i	−0.592152	−	0.780497i
$969$	−8.67287	−	5.00728i	−0.278613	−	0.160857i
$970$	1.16390	+	3.71498i	0.0373705	+	0.119281i
$971$	−15.4813	+	57.7769i	−0.496818	+	1.85415i	0.0227850	+	0.999740i	$0.492747\pi$
$971$	−15.4813	+	57.7769i	−0.496818	+	1.85415i	−0.519603	+	0.854408i	$0.673920\pi$
$972$	16.7321	−	19.7938i	0.536684	−	0.634886i
$973$		0			0
$974$	18.2166	−	0.762130i	0.583698	−	0.0244202i
$975$	−22.2326	−	38.5080i	−0.712014	−	1.23324i
$976$	−10.2459	−	22.3968i	−0.327964	−	0.716904i
$977$	3.53396	−	6.12099i	0.113061	−	0.195828i	−0.803942	−	0.594708i	$-0.797268\pi$
$977$	3.53396	−	6.12099i	0.113061	−	0.195828i	0.917003	+	0.398880i	$0.130601\pi$
$978$	2.04931	+	3.22974i	0.0655298	+	0.103276i
$979$	4.10696	−	4.10696i	0.131259	−	0.131259i
$980$		0			0
$981$	5.77907	+	5.77907i	0.184512	+	0.184512i
$982$	−10.6593	−	2.38348i	−0.340153	−	0.0760600i
$983$	36.6563	+	21.1635i	1.16915	+	0.675011i	0.953480	−	0.301455i	$-0.0974722\pi$
$983$	36.6563	+	21.1635i	1.16915	+	0.675011i	0.215673	+	0.976466i	$0.430806\pi$
$984$	−22.0864	−	54.1559i	−0.704087	−	1.72643i
$985$	−5.47196	+	3.15924i	−0.174351	+	0.100662i
$986$	−13.2898	−	12.2225i	−0.423235	−	0.389243i
$987$		0			0
$988$	−2.79644	−	33.3621i	−0.0889667	−	1.06139i
$989$	−27.1415	−	7.27254i	−0.863049	−	0.231253i
$990$	−0.395348	−	0.206721i	−0.0125650	−	0.00657003i
$991$	−8.73586	+	15.1310i	−0.277504	+	0.480651i	−0.970764	−	0.240037i	$-0.922840\pi$
$991$	−8.73586	+	15.1310i	−0.277504	+	0.480651i	0.693260	+	0.720688i	$0.256174\pi$
$992$	35.1547	−	31.6295i	1.11616	−	1.00424i
$993$	1.05883			0.0336010
$994$		0			0
$995$	−3.09755	+	3.09755i	−0.0981991	+	0.0981991i
$996$	7.11865	−	4.94600i	0.225563	−	0.156720i
$997$	−4.77839	+	1.28037i	−0.151333	+	0.0405496i	−0.333690	−	0.942683i	$-0.608294\pi$
$997$	−4.77839	+	1.28037i	−0.151333	+	0.0405496i	0.182357	+	0.983232i	$0.441627\pi$
$998$	30.2746	−	9.48500i	0.958327	−	0.300242i
$999$	14.1025	−	8.14210i	0.446184	−	0.257605i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.j.165.1		16
7.2	even	3	inner	784.2.x.j.373.4		16
7.3	odd	6		112.2.m.c.85.2	yes	8
7.4	even	3		784.2.m.g.197.2		8
7.5	odd	6		784.2.x.k.373.4		16
7.6	odd	2		784.2.x.k.165.1		16
16.13	even	4	inner	784.2.x.j.557.4		16
28.3	even	6		448.2.m.c.113.1		8
56.3	even	6		896.2.m.f.225.4		8
56.45	odd	6		896.2.m.e.225.1		8
112.3	even	12		448.2.m.c.337.1		8
112.13	odd	4		784.2.x.k.557.4		16
112.45	odd	12		112.2.m.c.29.2	✓	8
112.59	even	12		896.2.m.f.673.4		8
112.61	odd	12		784.2.x.k.765.1		16
112.93	even	12	inner	784.2.x.j.765.1		16
112.101	odd	12		896.2.m.e.673.1		8
112.109	even	12		784.2.m.g.589.2		8
224.3	even	24		7168.2.a.bd.1.2		8
224.45	odd	24		7168.2.a.bc.1.2		8
224.115	even	24		7168.2.a.bd.1.7		8
224.157	odd	24		7168.2.a.bc.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.c.29.2	✓	8	112.45	odd	12
112.2.m.c.85.2	yes	8	7.3	odd	6
448.2.m.c.113.1		8	28.3	even	6
448.2.m.c.337.1		8	112.3	even	12
784.2.m.g.197.2		8	7.4	even	3
784.2.m.g.589.2		8	112.109	even	12
784.2.x.j.165.1		16	1.1	even	1	trivial
784.2.x.j.373.4		16	7.2	even	3	inner
784.2.x.j.557.4		16	16.13	even	4	inner
784.2.x.j.765.1		16	112.93	even	12	inner
784.2.x.k.165.1		16	7.6	odd	2
784.2.x.k.373.4		16	7.5	odd	6
784.2.x.k.557.4		16	112.13	odd	4
784.2.x.k.765.1		16	112.61	odd	12
896.2.m.e.225.1		8	56.45	odd	6
896.2.m.e.673.1		8	112.101	odd	12
896.2.m.f.225.4		8	56.3	even	6
896.2.m.f.673.4		8	112.59	even	12
7168.2.a.bc.1.2		8	224.45	odd	24
7168.2.a.bc.1.7		8	224.157	odd	24
7168.2.a.bd.1.2		8	224.3	even	24
7168.2.a.bd.1.7		8	224.115	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)

\(f(q)\)	\(=\)	\(q+(-1.19412 + 0.757684i) q^{2} +(-0.538823 - 2.01092i) q^{3} +(0.851831 - 1.80953i) q^{4} +(-0.129523 + 0.483385i) q^{5} +(2.16706 + 1.99301i) q^{6} +(0.353863 + 2.80620i) q^{8} +(-1.15537 + 0.667056i) q^{9} +O(q^{10})\)	\(q+(-1.19412 + 0.757684i) q^{2} +(-0.538823 - 2.01092i) q^{3} +(0.851831 - 1.80953i) q^{4} +(-0.129523 + 0.483385i) q^{5} +(2.16706 + 1.99301i) q^{6} +(0.353863 + 2.80620i) q^{8} +(-1.15537 + 0.667056i) q^{9} +(-0.211588 - 0.675356i) q^{10} +(-0.456405 + 0.122293i) q^{11} +(-4.09779 - 0.737945i) q^{12} +(3.17982 - 3.17982i) q^{13} +1.04184 q^{15} +(-2.54877 - 3.08282i) q^{16} +(0.646137 - 1.11914i) q^{17} +(0.874235 - 1.67195i) q^{18} +(3.59560 + 0.963437i) q^{19} +(0.764367 + 0.646137i) q^{20} +(0.452341 - 0.491843i) q^{22} +(2.26039 - 1.30504i) q^{23} +(5.45237 - 2.22364i) q^{24} +(4.11324 + 2.37478i) q^{25} +(-1.38778 + 6.20637i) q^{26} +(-2.45234 - 2.45234i) q^{27} +(-6.98602 + 6.98602i) q^{29} +(-1.24408 + 0.789383i) q^{30} +(4.17982 - 7.23966i) q^{31} +(5.37933 + 1.75009i) q^{32} +(0.491843 + 0.851898i) q^{33} +(0.0763926 + 1.82596i) q^{34} +(0.222871 + 2.65890i) q^{36} +(-1.21525 + 4.53539i) q^{37} +(-5.02354 + 1.57387i) q^{38} +(-8.10770 - 4.68099i) q^{39} +(-1.40231 - 0.192415i) q^{40} -9.93254i q^{41} +(-7.61241 - 7.61241i) q^{43} +(-0.167487 + 0.930050i) q^{44} +(-0.172798 - 0.644890i) q^{45} +(-1.71036 + 3.27103i) q^{46} +(-2.29805 - 3.98033i) q^{47} +(-4.82596 + 6.78645i) q^{48} +(-6.71102 + 0.280770i) q^{50} +(-2.59866 - 0.696308i) q^{51} +(-3.04530 - 8.46263i) q^{52} +(5.38786 - 1.44367i) q^{53} +(4.78648 + 1.07028i) q^{54} -0.236459i q^{55} -7.74956i q^{57} +(3.04893 - 13.6353i) q^{58} +(-8.73669 + 2.34099i) q^{59} +(0.887469 - 1.88523i) q^{60} +(5.94749 + 1.59362i) q^{61} +(0.494178 + 11.8120i) q^{62} +(-7.74956 + 1.98602i) q^{64} +(1.12522 + 1.94894i) q^{65} +(-1.23279 - 0.644604i) q^{66} +(-3.65002 - 13.6221i) q^{67} +(-1.47472 - 2.12252i) q^{68} +(-3.84227 - 3.84227i) q^{69} -7.62395i q^{71} +(-2.28074 - 3.00617i) q^{72} +(-0.482023 - 0.278296i) q^{73} +(-1.98523 - 6.33656i) q^{74} +(2.55917 - 9.55097i) q^{75} +(4.80620 - 5.68564i) q^{76} +(13.2283 - 0.553431i) q^{78} +(0.744616 + 1.28971i) q^{79} +(1.82031 - 0.832742i) q^{80} +(-5.61124 + 9.71895i) q^{81} +(7.52572 + 11.8606i) q^{82} +(-1.47209 + 1.47209i) q^{83} +(0.457288 + 0.457288i) q^{85} +(14.8579 + 3.32231i) q^{86} +(17.8125 + 10.2841i) q^{87} +(-0.504685 - 1.23749i) q^{88} +(-10.6453 + 6.14609i) q^{89} +(0.694964 + 0.639148i) q^{90} +(-0.436028 - 5.20190i) q^{92} +(-16.8105 - 4.50437i) q^{93} +(5.75997 + 3.01179i) q^{94} +(-0.931423 + 1.61327i) q^{95} +(0.620770 - 11.7604i) q^{96} -5.50078 q^{97} +(0.445742 - 0.445742i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 32 q^{6} - 8 q^{8}+O(q^{10}) \) 16 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 32 * q^6 - 8 * q^8	\( 16 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 32 q^{6} - 8 q^{8} + 12 q^{10} - 12 q^{12} - 16 q^{15} - 8 q^{16} + 24 q^{17} - 6 q^{18} - 12 q^{19} + 16 q^{20} - 8 q^{22} + 8 q^{26} - 24 q^{27} - 32 q^{29} - 20 q^{30} + 16 q^{31} + 28 q^{32} - 24 q^{33} + 24 q^{34} + 48 q^{36} - 16 q^{37} - 16 q^{38} + 28 q^{40} - 64 q^{43} + 32 q^{44} - 8 q^{45} - 20 q^{46} + 24 q^{47} - 40 q^{48} - 28 q^{50} - 8 q^{51} + 32 q^{52} + 8 q^{53} - 16 q^{54} - 12 q^{58} - 28 q^{59} + 28 q^{60} + 28 q^{61} - 40 q^{62} - 64 q^{64} + 48 q^{65} - 16 q^{66} + 28 q^{68} - 88 q^{69} - 44 q^{72} + 4 q^{74} + 28 q^{75} + 48 q^{76} + 24 q^{78} + 24 q^{79} - 12 q^{80} - 40 q^{81} + 4 q^{82} - 80 q^{85} + 40 q^{88} + 32 q^{90} + 72 q^{92} - 16 q^{93} + 28 q^{94} - 16 q^{95} + 8 q^{96} + 64 q^{97} + 96 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 32 * q^6 - 8 * q^8 + 12 * q^10 - 12 * q^12 - 16 * q^15 - 8 * q^16 + 24 * q^17 - 6 * q^18 - 12 * q^19 + 16 * q^20 - 8 * q^22 + 8 * q^26 - 24 * q^27 - 32 * q^29 - 20 * q^30 + 16 * q^31 + 28 * q^32 - 24 * q^33 + 24 * q^34 + 48 * q^36 - 16 * q^37 - 16 * q^38 + 28 * q^40 - 64 * q^43 + 32 * q^44 - 8 * q^45 - 20 * q^46 + 24 * q^47 - 40 * q^48 - 28 * q^50 - 8 * q^51 + 32 * q^52 + 8 * q^53 - 16 * q^54 - 12 * q^58 - 28 * q^59 + 28 * q^60 + 28 * q^61 - 40 * q^62 - 64 * q^64 + 48 * q^65 - 16 * q^66 + 28 * q^68 - 88 * q^69 - 44 * q^72 + 4 * q^74 + 28 * q^75 + 48 * q^76 + 24 * q^78 + 24 * q^79 - 12 * q^80 - 40 * q^81 + 4 * q^82 - 80 * q^85 + 40 * q^88 + 32 * q^90 + 72 * q^92 - 16 * q^93 + 28 * q^94 - 16 * q^95 + 8 * q^96 + 64 * q^97 + 96 * q^99

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