LMFDB - Embedded newform 700.2.g.i.251.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(251,700)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("700.251"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-4,0,-4,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.5473632256.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 12x^{5} + 34x^{4} + 24x^{3} + 56x^{2} + 32x + 16 $ x^8 - 4x^7 + 14x^6 - 12x^5 + 34x^4 + 24x^3 + 56x^2 + 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.8
Root			$2.11137 + 2.44696i$ of defining polynomial
Character	$\chi$	$=$	700.251
Dual form			700.2.g.i.251.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.207107 + 1.39897i) q^{2} +1.47363 q^{3} +(-1.91421 + 0.579471i) q^{4} +(0.305198 + 2.06155i) q^{6} +(-2.51564 - 0.819496i) q^{7} +(-1.20711 - 2.55791i) q^{8} -0.828427 q^{9} +2.79793i q^{11} +(-2.82083 + 0.853923i) q^{12} +5.83095i q^{13} +(0.625441 - 3.68901i) q^{14} +(3.32843 - 2.21846i) q^{16} +4.12311i q^{17} +(-0.171573 - 1.15894i) q^{18} -5.64167 q^{19} +(-3.70711 - 1.20763i) q^{21} +(-3.91421 + 0.579471i) q^{22} +3.95687i q^{23} +(-1.77882 - 3.76940i) q^{24} +(-8.15731 + 1.20763i) q^{26} -5.64167 q^{27} +(5.29034 + 0.110951i) q^{28} -0.242641 q^{29} -2.08402 q^{31} +(3.79289 + 4.19690i) q^{32} +4.12311i q^{33} +(-5.76809 + 0.853923i) q^{34} +(1.58579 - 0.480049i) q^{36} +6.24264 q^{37} +(-1.16843 - 7.89250i) q^{38} +8.59264i q^{39} -4.12311i q^{41} +(0.921666 - 5.43623i) q^{42} -5.59587i q^{43} +(-1.62132 - 5.35584i) q^{44} +(-5.53553 + 0.819496i) q^{46} +6.25206 q^{47} +(4.90486 - 3.26918i) q^{48} +(5.65685 + 4.12311i) q^{49} +6.07591i q^{51} +(-3.37887 - 11.1617i) q^{52} +12.2426 q^{53} +(-1.16843 - 7.89250i) q^{54} +(0.940448 + 7.42399i) q^{56} -8.31371 q^{57} +(-0.0502525 - 0.339446i) q^{58} -2.94725 q^{59} -11.6619i q^{61} +(-0.431615 - 2.91548i) q^{62} +(2.08402 + 0.678892i) q^{63} +(-5.08579 + 6.17534i) q^{64} +(-5.76809 + 0.853923i) q^{66} +7.43370i q^{67} +(-2.38922 - 7.89250i) q^{68} +5.83095i q^{69} -7.23486i q^{71} +(1.00000 + 2.11904i) q^{72} +12.3693i q^{73} +(1.29289 + 8.73324i) q^{74} +(10.7994 - 3.26918i) q^{76} +(2.29289 - 7.03858i) q^{77} +(-12.0208 + 1.77959i) q^{78} -7.91375i q^{79} -5.82843 q^{81} +(5.76809 - 0.853923i) q^{82} +1.47363 q^{83} +(7.79598 + 0.163501i) q^{84} +(7.82843 - 1.15894i) q^{86} -0.357562 q^{87} +(7.15685 - 3.37740i) q^{88} +12.3693i q^{89} +(4.77844 - 14.6686i) q^{91} +(-2.29289 - 7.57430i) q^{92} -3.07107 q^{93} +(1.29484 + 8.74643i) q^{94} +(5.58931 + 6.18466i) q^{96} +8.24621i q^{97} +(-4.59651 + 8.76767i) q^{98} -2.31788i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} - 4 q^{8} + 16 q^{9} + 12 q^{14} + 4 q^{16} - 24 q^{18} - 24 q^{21} - 20 q^{22} - 16 q^{28} + 32 q^{29} + 36 q^{32} + 24 q^{36} + 16 q^{37} + 8 q^{42} + 4 q^{44} - 16 q^{46} + 64 q^{53}+ \cdots + 32 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 - 4 * q^8 + 16 * q^9 + 12 * q^14 + 4 * q^16 - 24 * q^18 - 24 * q^21 - 20 * q^22 - 16 * q^28 + 32 * q^29 + 36 * q^32 + 24 * q^36 + 16 * q^37 + 8 * q^42 + 4 * q^44 - 16 * q^46 + 64 * q^53 + 20 * q^56 + 24 * q^57 - 40 * q^58 - 52 * q^64 + 8 * q^72 + 16 * q^74 + 24 * q^77 - 24 * q^81 + 20 * q^84 + 40 * q^86 + 12 * q^88 - 24 * q^92 + 32 * q^93 + 32 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.207107	+	1.39897i	0.146447	+	0.989219i
$2$	0.207107	+	1.39897i	0.146447	+	0.989219i
$3$	1.47363			0.850798			0.425399	−	0.905006i	$-0.360134\pi$
$3$	1.47363			0.850798			0.425399	+	0.905006i	$0.360134\pi$
$4$	−1.91421	+	0.579471i	−0.957107	+	0.289735i
$5$		0			0
$5$		0			0
$6$	0.305198	+	2.06155i	0.124597	+	0.841625i
$7$	−2.51564	−	0.819496i	−0.950821	−	0.309740i
$7$	−2.51564	−	0.819496i	−0.950821	−	0.309740i
$8$	−1.20711	−	2.55791i	−0.426777	−	0.904357i
$9$	−0.828427			−0.276142
$10$		0			0
$11$			2.79793i			0.843608i	0.906687	+	0.421804i	$0.138603\pi$
$11$			2.79793i			0.843608i	−0.906687	+	0.421804i	$0.861397\pi$
$12$	−2.82083	+	0.853923i	−0.814305	+	0.246506i
$13$			5.83095i			1.61722i	0.588348	+	0.808608i	$0.299778\pi$
$13$			5.83095i			1.61722i	−0.588348	+	0.808608i	$0.700222\pi$
$14$	0.625441	−	3.68901i	0.167156	−	0.985930i
$15$		0			0
$16$	3.32843	−	2.21846i	0.832107	−	0.554615i
$17$			4.12311i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$17$			4.12311i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$18$	−0.171573	−	1.15894i	−0.0404401	−	0.273165i
$19$	−5.64167			−1.29429			−0.647144	−	0.762368i	$-0.724037\pi$
$19$	−5.64167			−1.29429			−0.647144	+	0.762368i	$0.724037\pi$
$20$		0			0
$21$	−3.70711	−	1.20763i	−0.808957	−	0.263526i
$22$	−3.91421	+	0.579471i	−0.834513	+	0.123544i
$23$			3.95687i			0.825065i	0.910943	+	0.412533i	$0.135356\pi$
$23$			3.95687i			0.825065i	−0.910943	+	0.412533i	$0.864644\pi$
$24$	−1.77882	−	3.76940i	−0.363101	−	0.769425i
$25$		0			0
$26$	−8.15731	+	1.20763i	−1.59978	+	0.236836i
$27$	−5.64167			−1.08574
$28$	5.29034	+	0.110951i	0.999780	+	0.0209678i
$29$	−0.242641			−0.0450572			−0.0225286	−	0.999746i	$-0.507172\pi$
$29$	−0.242641			−0.0450572			−0.0225286	+	0.999746i	$0.507172\pi$
$30$		0			0
$31$	−2.08402			−0.374301			−0.187151	−	0.982331i	$-0.559925\pi$
$31$	−2.08402			−0.374301			−0.187151	+	0.982331i	$0.559925\pi$
$32$	3.79289	+	4.19690i	0.670495	+	0.741914i
$33$			4.12311i			0.717741i
$34$	−5.76809	+	0.853923i	−0.989219	+	0.146447i
$35$		0			0
$36$	1.58579	−	0.480049i	0.264298	−	0.0800082i
$37$	6.24264			1.02628			0.513142	−	0.858304i	$-0.328481\pi$
$37$	6.24264			1.02628			0.513142	+	0.858304i	$0.328481\pi$
$38$	−1.16843	−	7.89250i	−0.189544	−	1.28033i
$39$			8.59264i			1.37592i
$40$		0			0
$41$		−	4.12311i		−	0.643921i	−0.946753	−	0.321960i	$-0.895658\pi$
$41$		−	4.12311i		−	0.643921i	0.946753	−	0.321960i	$-0.104342\pi$
$42$	0.921666	−	5.43623i	0.142216	−	0.838828i
$43$		−	5.59587i		−	0.853361i	−0.904402	−	0.426681i	$-0.859683\pi$
$43$		−	5.59587i		−	0.853361i	0.904402	−	0.426681i	$-0.140317\pi$
$44$	−1.62132	−	5.35584i	−0.244423	−	0.807423i
$45$		0			0
$46$	−5.53553	+	0.819496i	−0.816170	+	0.120828i
$47$	6.25206			0.911957			0.455979	−	0.889991i	$-0.349289\pi$
$47$	6.25206			0.911957			0.455979	+	0.889991i	$0.349289\pi$
$48$	4.90486	−	3.26918i	0.707955	−	0.471866i
$49$	5.65685	+	4.12311i	0.808122	+	0.589015i
$50$		0			0
$51$			6.07591i			0.850798i
$52$	−3.37887	−	11.1617i	−0.468564	−	1.54785i
$53$	12.2426			1.68166			0.840828	−	0.541302i	$-0.182069\pi$
$53$	12.2426			1.68166			0.840828	+	0.541302i	$0.182069\pi$
$54$	−1.16843	−	7.89250i	−0.159003	−	1.07403i
$55$		0			0
$56$	0.940448	+	7.42399i	0.125673	+	0.992072i
$57$	−8.31371			−1.10118
$58$	−0.0502525	−	0.339446i	−0.00659848	−	0.0445715i
$59$	−2.94725			−0.383699			−0.191850	−	0.981424i	$-0.561449\pi$
$59$	−2.94725			−0.383699			−0.191850	+	0.981424i	$0.561449\pi$
$60$		0			0
$61$		−	11.6619i		−	1.49315i	−0.665299	−	0.746577i	$-0.731696\pi$
$61$		−	11.6619i		−	1.49315i	0.665299	−	0.746577i	$-0.268304\pi$
$62$	−0.431615	−	2.91548i	−0.0548152	−	0.370266i
$63$	2.08402	+	0.678892i	0.262562	+	0.0855324i
$64$	−5.08579	+	6.17534i	−0.635723	+	0.771917i
$65$		0			0
$66$	−5.76809	+	0.853923i	−0.710002	+	0.105111i
$67$			7.43370i			0.908171i	0.890958	+	0.454085i	$0.150034\pi$
$67$			7.43370i			0.908171i	−0.890958	+	0.454085i	$0.849966\pi$
$68$	−2.38922	−	7.89250i	−0.289735	−	0.957107i
$69$			5.83095i			0.701964i
$70$		0			0
$71$		−	7.23486i		−	0.858619i	−0.903157	−	0.429310i	$-0.858757\pi$
$71$		−	7.23486i		−	0.858619i	0.903157	−	0.429310i	$-0.141243\pi$
$72$	1.00000	+	2.11904i	0.117851	+	0.249731i
$73$			12.3693i			1.44772i	0.689947	+	0.723860i	$0.257634\pi$
$73$			12.3693i			1.44772i	−0.689947	+	0.723860i	$0.742366\pi$
$74$	1.29289	+	8.73324i	0.150296	+	1.01522i
$75$		0			0
$76$	10.7994	−	3.26918i	1.23877	−	0.375001i
$77$	2.29289	−	7.03858i	0.261299	−	0.802121i
$78$	−12.0208	+	1.77959i	−1.36109	+	0.201499i
$79$		−	7.91375i		−	0.890366i	−0.895440	−	0.445183i	$-0.853139\pi$
$79$		−	7.91375i		−	0.890366i	0.895440	−	0.445183i	$-0.146861\pi$
$80$		0			0
$81$	−5.82843			−0.647603
$82$	5.76809	−	0.853923i	0.636979	−	0.0943000i
$83$	1.47363			0.161751			0.0808757	−	0.996724i	$-0.474228\pi$
$83$	1.47363			0.161751			0.0808757	+	0.996724i	$0.474228\pi$
$84$	7.79598	+	0.163501i	0.850611	+	0.0178394i
$85$		0			0
$86$	7.82843	−	1.15894i	0.844161	−	0.124972i
$87$	−0.357562			−0.0383346
$88$	7.15685	−	3.37740i	0.762923	−	0.360032i
$89$			12.3693i			1.31114i	0.755132	+	0.655572i	$0.227573\pi$
$89$			12.3693i			1.31114i	−0.755132	+	0.655572i	$0.772427\pi$
$90$		0			0
$91$	4.77844	−	14.6686i	0.500916	−	1.53768i
$92$	−2.29289	−	7.57430i	−0.239051	−	0.789676i
$93$	−3.07107			−0.318455
$94$	1.29484	+	8.74643i	0.133553	+	0.902125i
$95$		0			0
$96$	5.58931	+	6.18466i	0.570456	+	0.631219i
$97$			8.24621i			0.837276i	0.908153	+	0.418638i	$0.137492\pi$
$97$			8.24621i			0.837276i	−0.908153	+	0.418638i	$0.862508\pi$
$98$	−4.59651	+	8.76767i	−0.464318	+	0.885669i
$99$		−	2.31788i		−	0.232956i
$100$		0			0
$101$			2.41526i			0.240327i	0.992754	+	0.120164i	$0.0383419\pi$
$101$			2.41526i			0.240327i	−0.992754	+	0.120164i	$0.961658\pi$
$102$	−8.50000	+	1.25836i	−0.841625	+	0.124597i
$103$	−7.11529			−0.701091			−0.350545	−	0.936546i	$-0.614004\pi$
$103$	−7.11529			−0.701091			−0.350545	+	0.936546i	$0.614004\pi$
$104$	14.9150	−	7.03858i	1.46254	−	0.690190i
$105$		0			0
$106$	2.53553	+	17.1270i	0.246273	+	1.66353i
$107$		−	13.0296i		−	1.25962i	−0.776751	−	0.629808i	$-0.783134\pi$
$107$		−	13.0296i		−	1.25962i	0.776751	−	0.629808i	$-0.216866\pi$
$108$	10.7994	−	3.26918i	1.03917	−	0.314577i
$109$	2.82843			0.270914			0.135457	−	0.990783i	$-0.456750\pi$
$109$	2.82843			0.270914			0.135457	+	0.990783i	$0.456750\pi$
$110$		0			0
$111$	9.19932			0.873160
$112$	−10.1911	+	2.85321i	−0.962971	+	0.269603i
$113$	−18.3137			−1.72281			−0.861404	−	0.507920i	$-0.830415\pi$
$113$	−18.3137			−1.72281			−0.861404	+	0.507920i	$0.830415\pi$
$114$	−1.72183	−	11.6306i	−0.161264	−	1.08931i
$115$		0			0
$116$	0.464466	−	0.140603i	0.0431246	−	0.0130547i
$117$		−	4.83052i		−	0.446582i
$118$	−0.610396	−	4.12311i	−0.0561915	−	0.379563i
$119$	3.37887	−	10.3722i	0.309740	−	0.950821i
$120$		0			0
$121$	3.17157			0.288325
$122$	16.3146	−	2.41526i	1.47706	−	0.218667i
$123$		−	6.07591i		−	0.547847i
$124$	3.98926	−	1.20763i	0.358246	−	0.108448i
$125$		0			0
$126$	−0.518132	+	3.05608i	−0.0461589	+	0.272257i
$127$			5.59587i			0.496553i	0.968689	+	0.248276i	$0.0798641\pi$
$127$			5.59587i			0.496553i	−0.968689	+	0.248276i	$0.920136\pi$
$128$	−9.69239	−	5.83589i	−0.856694	−	0.515825i
$129$		−	8.24621i		−	0.726038i
$130$		0			0
$131$	−13.0098			−1.13667			−0.568336	−	0.822797i	$-0.692412\pi$
$131$	−13.0098			−1.13667			−0.568336	+	0.822797i	$0.692412\pi$
$132$	−2.38922	−	7.89250i	−0.207955	−	0.686954i
$133$	14.1924	+	4.62332i	1.23064	+	0.400893i
$134$	−10.3995	+	1.53957i	−0.898380	+	0.132999i
$135$		0			0
$136$	10.5465	−	4.97703i	0.904357	−	0.426777i
$137$	3.48528			0.297768			0.148884	−	0.988855i	$-0.452432\pi$
$137$	3.48528			0.297768			0.148884	+	0.988855i	$0.452432\pi$
$138$	−8.15731	+	1.20763i	−0.694396	+	0.102800i
$139$	2.69442			0.228537			0.114269	−	0.993450i	$-0.463548\pi$
$139$	2.69442			0.228537			0.114269	+	0.993450i	$0.463548\pi$
$140$		0			0
$141$	9.21320			0.775892
$142$	10.1213	−	1.49839i	0.849362	−	0.125742i
$143$	−16.3146			−1.36430
$144$	−2.75736	+	1.83783i	−0.229780	+	0.153153i
$145$		0			0
$146$	−17.3043	+	2.56177i	−1.43211	+	0.212014i
$147$	8.33609	+	6.07591i	0.687549	+	0.501133i
$148$	−11.9497	+	3.61743i	−0.982263	+	0.297351i
$149$	2.00000			0.163846			0.0819232	−	0.996639i	$-0.473894\pi$
$149$	2.00000			0.163846			0.0819232	+	0.996639i	$0.473894\pi$
$150$		0			0
$151$			1.63899i			0.133379i	0.997774	+	0.0666896i	$0.0212437\pi$
$151$			1.63899i			0.133379i	−0.997774	+	0.0666896i	$0.978756\pi$
$152$	6.81010	+	14.4309i	0.552372	+	1.17050i
$153$		−	3.41569i		−	0.276142i
$154$	10.3216	+	1.74994i	0.831739	+	0.141014i
$155$		0			0
$156$	−4.97918	−	16.4481i	−0.398654	−	1.31691i
$157$			22.3234i			1.78160i	0.454396	+	0.890800i	$0.349855\pi$
$157$			22.3234i			1.78160i	−0.454396	+	0.890800i	$0.650145\pi$
$158$	11.0711	−	1.63899i	0.880767	−	0.130391i
$159$	18.0411			1.43075
$160$		0			0
$161$	3.24264	−	9.95406i	0.255556	−	0.784490i
$162$	−1.20711	−	8.15377i	−0.0948393	−	0.640621i
$163$			21.9034i			1.71561i	0.513977	+	0.857804i	$0.328172\pi$
$163$			21.9034i			1.71561i	−0.513977	+	0.857804i	$0.671828\pi$
$164$	2.38922	+	7.89250i	0.186567	+	0.616301i
$165$		0			0
$166$	0.305198	+	2.06155i	0.0236880	+	0.160008i
$167$	17.1778			1.32926			0.664631	−	0.747172i	$-0.268589\pi$
$167$	17.1778			1.32926			0.664631	+	0.747172i	$0.268589\pi$
$168$	1.38587	+	10.9402i	0.106922	+	0.844053i
$169$	−21.0000			−1.61538
$170$		0			0
$171$	4.67371			0.357408
$172$	3.24264	+	10.7117i	0.247249	+	0.816758i
$173$		−	14.0772i		−	1.07027i	−0.844768	−	0.535133i	$-0.820261\pi$
$173$		−	14.0772i		−	1.07027i	0.844768	−	0.535133i	$-0.179739\pi$
$174$	−0.0740534	−	0.500217i	−0.00561398	−	0.0379213i
$175$		0			0
$176$	6.20711	+	9.31271i	0.467878	+	0.701972i
$177$	−4.34315			−0.326451
$178$	−17.3043	+	2.56177i	−1.29701	+	0.192013i
$179$			10.7117i			0.800629i	0.916378	+	0.400314i	$0.131099\pi$
$179$			10.7117i			0.800629i	−0.916378	+	0.400314i	$0.868901\pi$
$180$		0			0
$181$			19.9081i			1.47976i	0.672740	+	0.739879i	$0.265117\pi$
$181$			19.9081i			1.47976i	−0.672740	+	0.739879i	$0.734883\pi$
$182$	21.5105	+	3.64692i	1.59446	+	0.270328i
$183$		−	17.1853i		−	1.27037i
$184$	10.1213	−	4.77637i	0.746154	−	0.352119i
$185$		0			0
$186$	−0.636039	−	4.29632i	−0.0466366	−	0.315021i
$187$	−11.5362			−0.843608
$188$	−11.9678	+	3.62289i	−0.872841	+	0.264226i
$189$	14.1924	+	4.62332i	1.03234	+	0.336297i
$190$		0			0
$191$			24.7013i			1.78733i	0.448738	+	0.893663i	$0.351874\pi$
$191$			24.7013i			1.78733i	−0.448738	+	0.893663i	$0.648126\pi$
$192$	−7.49455	+	9.10013i	−0.540872	+	0.656746i
$193$	8.31371			0.598434			0.299217	−	0.954185i	$-0.403275\pi$
$193$	8.31371			0.598434			0.299217	+	0.954185i	$0.403275\pi$
$194$	−11.5362	+	1.70785i	−0.828249	+	0.122616i
$195$		0			0
$196$	−13.2176	−	4.61452i	−0.944118	−	0.329609i
$197$	2.48528			0.177069			0.0885345	−	0.996073i	$-0.471782\pi$
$197$	2.48528			0.177069			0.0885345	+	0.996073i	$0.471782\pi$
$198$	3.24264	−	0.480049i	0.230444	−	0.0341156i
$199$	17.5354			1.24305			0.621526	−	0.783394i	$-0.286513\pi$
$199$	17.5354			1.24305			0.621526	+	0.783394i	$0.286513\pi$
$200$		0			0
$201$			10.9545i			0.772670i
$202$	−3.37887	+	0.500217i	−0.237736	+	0.0351951i
$203$	0.610396	+	0.198843i	0.0428414	+	0.0139560i
$204$	−3.52082	−	11.6306i	−0.246506	−	0.814305i
$205$		0			0
$206$	−1.47363	−	9.95406i	−0.102672	−	0.693532i
$207$		−	3.27798i		−	0.227835i
$208$	12.9357	+	19.4079i	0.896932	+	1.34570i
$209$		−	15.7850i		−	1.09187i
$210$		0			0
$211$		−	1.44015i		−	0.0991439i	−0.998771	−	0.0495719i	$-0.984214\pi$
$211$		−	1.44015i		−	0.0991439i	0.998771	−	0.0495719i	$-0.0157857\pi$
$212$	−23.4350	+	7.09425i	−1.60952	+	0.487235i
$213$		−	10.6615i		−	0.730512i
$214$	18.2279	−	2.69851i	1.24604	−	0.184466i
$215$		0			0
$216$	6.81010	+	14.4309i	0.463368	+	0.981896i
$217$	5.24264	+	1.70785i	0.355894	+	0.115936i
$218$	0.585786	+	3.95687i	0.0396745	+	0.267993i
$219$			18.2277i			1.23172i
$220$		0			0
$221$	−24.0416			−1.61722
$222$	1.90524	+	12.8695i	0.127871	+	0.863747i
$223$	−0.863230			−0.0578062			−0.0289031	−	0.999582i	$-0.509201\pi$
$223$	−0.863230			−0.0578062			−0.0289031	+	0.999582i	$0.509201\pi$
$224$	−6.10220	−	13.6661i	−0.407720	−	0.913107i
$225$		0			0
$226$	−3.79289	−	25.6203i	−0.252300	−	1.70423i
$227$	−7.11529			−0.472259			−0.236129	−	0.971722i	$-0.575879\pi$
$227$	−7.11529			−0.472259			−0.236129	+	0.971722i	$0.575879\pi$
$228$	15.9142	−	4.81755i	1.05394	−	0.319050i
$229$		−	14.0772i		−	0.930245i	−0.885246	−	0.465123i	$-0.846010\pi$
$229$		−	14.0772i		−	0.930245i	0.885246	−	0.465123i	$-0.153990\pi$
$230$		0			0
$231$	3.37887	−	10.3722i	0.222313	−	0.682443i
$232$	0.292893	+	0.620653i	0.0192294	+	0.0407478i
$233$	−15.7990			−1.03503			−0.517513	−	0.855675i	$-0.673142\pi$
$233$	−15.7990			−1.03503			−0.517513	+	0.855675i	$0.673142\pi$
$234$	6.75773	−	1.00043i	0.441767	−	0.0654004i
$235$		0			0
$236$	5.64167	−	1.70785i	0.367241	−	0.111171i
$237$		−	11.6619i		−	0.757522i
$238$	15.2102	+	2.57876i	0.985930	+	0.167156i
$239$		−	16.7876i		−	1.08590i	−0.839765	−	0.542950i	$-0.817307\pi$
$239$		−	16.7876i		−	1.08590i	0.839765	−	0.542950i	$-0.182693\pi$
$240$		0			0
$241$			15.7850i			1.01680i	0.861120	+	0.508401i	$0.169763\pi$
$241$			15.7850i			1.01680i	−0.861120	+	0.508401i	$0.830237\pi$
$242$	0.656854	+	4.43692i	0.0422242	+	0.285216i
$243$	8.33609			0.534760
$244$	6.75773	+	22.3234i	0.432620	+	1.42911i
$245$		0			0
$246$	8.50000	−	1.25836i	0.541940	−	0.0802303i
$247$		−	32.8963i		−	2.09314i
$248$	2.51564	+	5.33074i	0.159743	+	0.338502i
$249$	2.17157			0.137618
$250$		0			0
$251$	−13.9778			−0.882268			−0.441134	−	0.897441i	$-0.645424\pi$
$251$	−13.9778			−0.882268			−0.441134	+	0.897441i	$0.645424\pi$
$252$	−4.38266	−	0.0919152i	−0.276082	−	0.00579011i
$253$	−11.0711			−0.696032
$254$	−7.82843	+	1.15894i	−0.491199	+	0.0727185i
$255$		0			0
$256$	6.15685	−	14.7680i	0.384803	−	0.922999i
$257$		−	23.3238i		−	1.45490i	−0.686161	−	0.727450i	$-0.740706\pi$
$257$		−	23.3238i		−	1.45490i	0.686161	−	0.727450i	$-0.259294\pi$
$258$	11.5362	−	1.70785i	0.718211	−	0.106326i
$259$	−15.7042	−	5.11582i	−0.975812	−	0.317881i
$260$		0			0
$261$	0.201010			0.0124422
$262$	−2.69442	−	18.2003i	−0.166462	−	1.12442i
$263$			27.9793i			1.72528i	0.505819	+	0.862640i	$0.331190\pi$
$263$			27.9793i			1.72528i	−0.505819	+	0.862640i	$0.668810\pi$
$264$	10.5465	−	4.97703i	0.649094	−	0.306315i
$265$		0			0
$266$	−3.52853	+	20.8122i	−0.216348	+	1.27608i
$267$			18.2277i			1.11552i
$268$	−4.30761	−	14.2297i	−0.263129	−	0.869217i
$269$		−	2.41526i		−	0.147261i	−0.997286	−	0.0736305i	$-0.976541\pi$
$269$		−	2.41526i		−	0.147261i	0.997286	−	0.0736305i	$-0.0234585\pi$
$270$		0			0
$271$	27.2404			1.65474			0.827368	−	0.561660i	$-0.189837\pi$
$271$	27.2404			1.65474			0.827368	+	0.561660i	$0.189837\pi$
$272$	9.14695	+	13.7235i	0.554615	+	0.832107i
$273$	7.04163	−	21.6160i	0.426179	−	1.30826i
$274$	0.721825	+	4.87579i	0.0436071	+	0.294557i
$275$		0			0
$276$	−3.37887	−	11.1617i	−0.203384	−	0.671855i
$277$	6.10051			0.366544			0.183272	−	0.983062i	$-0.441331\pi$
$277$	6.10051			0.366544			0.183272	+	0.983062i	$0.441331\pi$
$278$	0.558032	+	3.76940i	0.0334685	+	0.226074i
$279$	1.72646			0.103360
$280$		0			0
$281$	32.9706			1.96686			0.983429	−	0.181291i	$-0.0580277\pi$
$281$	32.9706			1.96686			0.983429	+	0.181291i	$0.0580277\pi$
$282$	1.90812	+	12.8890i	0.113627	+	0.767526i
$283$	31.6613			1.88207			0.941033	−	0.338314i	$-0.109856\pi$
$283$	31.6613			1.88207			0.941033	+	0.338314i	$0.109856\pi$
$284$	4.19239	+	13.8491i	0.248772	+	0.821791i
$285$		0			0
$286$	−3.37887	−	22.8236i	−0.199797	−	1.34959i
$287$	−3.37887	+	10.3722i	−0.199448	+	0.612254i
$288$	−3.14214	−	3.47682i	−0.185152	−	0.204874i
$289$		0			0
$290$		0			0
$291$			12.1518i			0.712353i
$292$	−7.16766	−	23.6775i	−0.419455	−	1.38562i
$293$		−	16.4924i		−	0.963498i	−0.876309	−	0.481749i	$-0.840002\pi$
$293$		−	16.4924i		−	0.963498i	0.876309	−	0.481749i	$-0.159998\pi$
$294$	−6.77354	+	12.9203i	−0.395041	+	0.753525i
$295$		0			0
$296$	−7.53553	−	15.9681i	−0.437994	−	0.928127i
$297$		−	15.7850i		−	0.915939i
$298$	0.414214	+	2.79793i	0.0239947	+	0.162080i
$299$	−23.0723			−1.33431
$300$		0			0
$301$	−4.58579	+	14.0772i	−0.264320	+	0.811394i
$302$	−2.29289	+	0.339446i	−0.131941	+	0.0195329i
$303$			3.55919i			0.204470i
$304$	−18.7779	+	12.5158i	−1.07699	+	0.717832i
$305$		0			0
$306$	4.77844	−	0.707413i	0.273165	−	0.0404401i
$307$	−18.6515			−1.06450			−0.532248	−	0.846589i	$-0.678652\pi$
$307$	−18.6515			−1.06450			−0.532248	+	0.846589i	$0.678652\pi$
$308$	−0.310435	+	14.8020i	−0.0176887	+	0.843423i
$309$	−10.4853			−0.596487
$310$		0			0
$311$	−11.7890			−0.668493			−0.334247	−	0.942486i	$-0.608482\pi$
$311$	−11.7890			−0.668493			−0.334247	+	0.942486i	$0.608482\pi$
$312$	21.9792	−	10.3722i	1.24433	−	0.587212i
$313$		−	4.83052i		−	0.273037i	−0.990638	−	0.136519i	$-0.956409\pi$
$313$		−	4.83052i		−	0.273037i	0.990638	−	0.136519i	$-0.0435913\pi$
$314$	−31.2296	+	4.62332i	−1.76239	+	0.260909i
$315$		0			0
$316$	4.58579	+	15.1486i	0.257971	+	0.852176i
$317$	−25.6569			−1.44103			−0.720516	−	0.693438i	$-0.756095\pi$
$317$	−25.6569			−1.44103			−0.720516	+	0.693438i	$0.756095\pi$
$318$	3.73643	+	25.2389i	0.209528	+	1.41532i
$319$		−	0.678892i		−	0.0380107i
$320$		0			0
$321$		−	19.2007i		−	1.07168i
$322$	14.5970	+	2.47479i	0.813457	+	0.137915i
$323$		−	23.2612i		−	1.29429i
$324$	11.1569	−	3.37740i	0.619825	−	0.187634i
$325$		0			0
$326$	−30.6421	+	4.53635i	−1.69711	+	0.251245i
$327$	4.16804			0.230493
$328$	−10.5465	+	4.97703i	−0.582334	+	0.274810i
$329$	−15.7279	−	5.12354i	−0.867108	−	0.282470i
$330$		0			0
$331$			28.8571i			1.58613i	0.609139	+	0.793064i	$0.291515\pi$
$331$			28.8571i			1.58613i	−0.609139	+	0.793064i	$0.708485\pi$
$332$	−2.82083	+	0.853923i	−0.154813	+	0.0468651i
$333$	−5.17157			−0.283400
$334$	3.55765	+	24.0312i	0.194666	+	1.31493i
$335$		0			0
$336$	−15.0179	+	4.20457i	−0.819294	+	0.229378i
$337$	−14.7990			−0.806152			−0.403076	−	0.915166i	$-0.632059\pi$
$337$	−14.7990			−0.806152			−0.403076	+	0.915166i	$0.632059\pi$
$338$	−4.34924	−	29.3783i	−0.236568	−	1.59797i
$339$	−26.9876			−1.46576
$340$		0			0
$341$		−	5.83095i		−	0.315764i
$342$	0.967957	+	6.53836i	0.0523411	+	0.353554i
$343$	−10.8517	−	15.0080i	−0.585938	−	0.810356i
$344$	−14.3137	+	6.75481i	−0.771743	+	0.364195i
$345$		0			0
$346$	19.6935	−	2.91548i	1.05873	−	0.156737i
$347$		−	19.9832i		−	1.07276i	−0.843978	−	0.536378i	$-0.819792\pi$
$347$		−	19.9832i		−	1.07276i	0.843978	−	0.536378i	$-0.180208\pi$
$348$	0.684449	−	0.207196i	0.0366903	−	0.0111069i
$349$		−	14.0772i		−	0.753533i	−0.926308	−	0.376767i	$-0.877036\pi$
$349$		−	14.0772i		−	0.753533i	0.926308	−	0.376767i	$-0.122964\pi$
$350$		0			0
$351$		−	32.8963i		−	1.75587i
$352$	−11.7426	+	10.6123i	−0.625885	+	0.565635i
$353$		−	11.6619i		−	0.620701i	−0.950622	−	0.310350i	$-0.899554\pi$
$353$		−	11.6619i		−	0.620701i	0.950622	−	0.310350i	$-0.100446\pi$
$354$	−0.899495	−	6.07591i	−0.0478076	−	0.322931i
$355$		0			0
$356$	−7.16766	−	23.6775i	−0.379885	−	1.25491i
$357$	4.97918	−	15.2848i	0.263526	−	0.808957i
$358$	−14.9853	+	2.21846i	−0.791997	+	0.117249i
$359$			20.4633i			1.08001i	0.841662	+	0.540005i	$0.181578\pi$
$359$			20.4633i			1.08001i	−0.841662	+	0.540005i	$0.818422\pi$
$360$		0			0
$361$	12.8284			0.675180
$362$	−27.8508	+	4.12311i	−1.46380	+	0.216706i
$363$	4.67371			0.245306
$364$	−0.646952	+	30.8477i	−0.0339095	+	1.61686i
$365$		0			0
$366$	24.0416	−	3.55919i	1.25668	−	0.186042i
$367$	15.9570			0.832951			0.416476	−	0.909147i	$-0.363265\pi$
$367$	15.9570			0.832951			0.416476	+	0.909147i	$0.363265\pi$
$368$	8.77817	+	13.1702i	0.457594	+	0.686542i
$369$			3.41569i			0.177814i
$370$		0			0
$371$	−30.7980	−	10.0328i	−1.59895	−	0.520876i
$372$	5.87868	−	1.77959i	0.304795	−	0.0922677i
$373$	−13.4142			−0.694562			−0.347281	−	0.937761i	$-0.612895\pi$
$373$	−13.4142			−0.694562			−0.347281	+	0.937761i	$0.612895\pi$
$374$	−2.38922	−	16.1387i	−0.123544	−	0.834513i
$375$		0			0
$376$	−7.54691	−	15.9922i	−0.389202	−	0.824735i
$377$		−	1.41483i		−	0.0728673i
$378$	−3.52853	+	20.8122i	−0.181488	+	1.07046i
$379$		−	4.15572i		−	0.213465i	−0.994288	−	0.106732i	$-0.965961\pi$
$379$		−	4.15572i		−	0.213465i	0.994288	−	0.106732i	$-0.0340388\pi$
$380$		0			0
$381$			8.24621i			0.422466i
$382$	−34.5563	+	5.11582i	−1.76806	+	0.261748i
$383$	18.3986			0.940126			0.470063	−	0.882633i	$-0.344231\pi$
$383$	18.3986			0.940126			0.470063	+	0.882633i	$0.344231\pi$
$384$	−14.2830	−	8.59992i	−0.728874	−	0.438863i
$385$		0			0
$386$	1.72183	+	11.6306i	0.0876386	+	0.591982i
$387$			4.63577i			0.235649i
$388$	−4.77844	−	15.7850i	−0.242588	−	0.801362i
$389$	15.5563			0.788738			0.394369	−	0.918952i	$-0.370963\pi$
$389$	15.5563			0.788738			0.394369	+	0.918952i	$0.370963\pi$
$390$		0			0
$391$	−16.3146			−0.825065
$392$	3.71810	−	19.4467i	0.187792	−	0.982209i
$393$	−19.1716			−0.967078
$394$	0.514719	+	3.47682i	0.0259311	+	0.175160i
$395$		0			0
$396$	1.34315	+	4.43692i	0.0674956	+	0.222964i
$397$			18.9077i			0.948949i	0.880269	+	0.474475i	$0.157362\pi$
$397$			18.9077i			0.948949i	−0.880269	+	0.474475i	$0.842638\pi$
$398$	3.63170	+	24.5314i	0.182041	+	1.22965i
$399$	20.9143	+	6.81305i	1.04702	+	0.341079i
$400$		0			0
$401$	−22.4558			−1.12139			−0.560696	−	0.828022i	$-0.689466\pi$
$401$	−22.4558			−1.12139			−0.560696	+	0.828022i	$0.689466\pi$
$402$	−15.3250	+	2.26875i	−0.764340	+	0.113155i
$403$		−	12.1518i		−	0.605326i
$404$	−1.39957	−	4.62332i	−0.0696313	−	0.230019i
$405$		0			0
$406$	−0.151757	+	0.895105i	−0.00753160	+	0.0444233i
$407$			17.4665i			0.865782i
$408$	15.5416	−	7.33428i	0.769425	−	0.363101i
$409$		−	15.7850i		−	0.780518i	−0.920705	−	0.390259i	$-0.872385\pi$
$409$		−	15.7850i		−	0.780518i	0.920705	−	0.390259i	$-0.127615\pi$
$410$		0			0
$411$	5.13600			0.253340
$412$	13.6202	−	4.12311i	0.671019	−	0.203131i
$413$	7.41421	+	2.41526i	0.364830	+	0.118847i
$414$	4.58579	−	0.678892i	0.225379	−	0.0333657i
$415$		0			0
$416$	−24.4719	+	22.1162i	−1.19983	+	1.08433i
$417$	3.97056			0.194439
$418$	22.0827	−	3.26918i	1.08010	−	0.159901i
$419$	−24.5460			−1.19915			−0.599575	−	0.800319i	$-0.704664\pi$
$419$	−24.5460			−1.19915			−0.599575	+	0.800319i	$0.704664\pi$
$420$		0			0
$421$	−0.686292			−0.0334478			−0.0167239	−	0.999860i	$-0.505324\pi$
$421$	−0.686292			−0.0334478			−0.0167239	+	0.999860i	$0.505324\pi$
$422$	2.01472	−	0.298264i	0.0980750	−	0.0145193i
$423$	−5.17938			−0.251830
$424$	−14.7782	−	31.3155i	−0.717692	−	1.52082i
$425$		0			0
$426$	14.9150	−	2.20806i	0.722636	−	0.106981i
$427$	−9.55688	+	29.3371i	−0.462490	+	1.41972i
$428$	7.55025	+	24.9414i	0.364955	+	1.20559i
$429$	−24.0416			−1.16074
$430$		0			0
$431$		−	8.19496i		−	0.394737i	−0.980329	−	0.197369i	$-0.936760\pi$
$431$		−	8.19496i		−	0.394737i	0.980329	−	0.197369i	$-0.0632396\pi$
$432$	−18.7779	+	12.5158i	−0.903451	+	0.602168i
$433$		−	4.12311i		−	0.198144i	−0.995080	−	0.0990719i	$-0.968413\pi$
$433$		−	4.12311i		−	0.198144i	0.995080	−	0.0990719i	$-0.0315874\pi$
$434$	−1.30343	+	7.68798i	−0.0625668	+	0.369035i
$435$		0			0
$436$	−5.41421	+	1.63899i	−0.259294	+	0.0784934i
$437$		−	22.3234i		−	1.06787i
$438$	−25.5000	+	3.77509i	−1.21844	+	0.180381i
$439$	2.94725			0.140665			0.0703323	−	0.997524i	$-0.477594\pi$
$439$	2.94725			0.140665			0.0703323	+	0.997524i	$0.477594\pi$
$440$		0			0
$441$	−4.68629	−	3.41569i	−0.223157	−	0.162652i
$442$	−4.97918	−	33.6334i	−0.236836	−	1.59978i
$443$		−	1.83783i		−	0.0873181i	−0.999046	−	0.0436591i	$-0.986098\pi$
$443$		−	1.83783i		−	0.0873181i	0.999046	−	0.0436591i	$-0.0139015\pi$
$444$	−17.6095	+	5.33074i	−0.835708	+	0.252986i
$445$		0			0
$446$	−0.178781	−	1.20763i	−0.00846552	−	0.0571829i
$447$	2.94725			0.139400
$448$	17.8547	−	11.3671i	0.843553	−	0.537046i
$449$	10.6569			0.502928			0.251464	−	0.967867i	$-0.419088\pi$
$449$	10.6569			0.502928			0.251464	+	0.967867i	$0.419088\pi$
$450$		0			0
$451$	11.5362			0.543217
$452$	35.0563	−	10.6123i	1.64891	−	0.499159i
$453$			2.41526i			0.113479i
$454$	−1.47363	−	9.95406i	−0.0691607	−	0.467167i
$455$		0			0
$456$	10.0355	+	21.2657i	0.469957	+	0.995858i
$457$	29.4853			1.37926			0.689632	−	0.724160i	$-0.257772\pi$
$457$	29.4853			1.37926			0.689632	+	0.724160i	$0.257772\pi$
$458$	19.6935	−	2.91548i	0.920216	−	0.136231i
$459$		−	23.2612i		−	1.08574i
$460$		0			0
$461$			2.41526i			0.112490i	0.998417	+	0.0562449i	$0.0179128\pi$
$461$			2.41526i			0.112490i	−0.998417	+	0.0562449i	$0.982087\pi$
$462$	15.2102	+	2.57876i	0.707642	+	0.119975i
$463$			1.35778i			0.0631016i	0.999502	+	0.0315508i	$0.0100446\pi$
$463$			1.35778i			0.0631016i	−0.999502	+	0.0315508i	$0.989955\pi$
$464$	−0.807612	+	0.538289i	−0.0374924	+	0.0249894i
$465$		0			0
$466$	−3.27208	−	22.1023i	−0.151576	−	1.02387i
$467$	7.62096			0.352656			0.176328	−	0.984331i	$-0.443578\pi$
$467$	7.62096			0.352656			0.176328	+	0.984331i	$0.443578\pi$
$468$	2.79914	+	9.24664i	0.129391	+	0.427426i
$469$	6.09188	−	18.7005i	0.281297	−	0.863508i
$470$		0			0
$471$			32.8963i			1.51578i
$472$	3.55765	+	7.53880i	0.163754	+	0.347001i
$473$	15.6569			0.719903
$474$	16.3146	−	2.41526i	0.749355	−	0.110937i
$475$		0			0
$476$	−0.457464	+	21.8126i	−0.0209678	+	0.999780i
$477$	−10.1421			−0.464376
$478$	23.4853	−	3.47682i	1.07419	−	0.159026i
$479$	8.84175			0.403990			0.201995	−	0.979387i	$-0.435258\pi$
$479$	8.84175			0.403990			0.201995	+	0.979387i	$0.435258\pi$
$480$		0			0
$481$			36.4005i			1.65972i
$482$	−22.0827	+	3.26918i	−1.00584	+	0.148907i
$483$	4.77844	−	14.6686i	0.217426	−	0.667442i
$484$	−6.07107	+	1.83783i	−0.275958	+	0.0835379i
$485$		0			0
$486$	1.72646	+	11.6619i	0.0783138	+	0.528995i
$487$			3.67567i			0.166560i	0.996526	+	0.0832802i	$0.0265397\pi$
$487$			3.67567i			0.166560i	−0.996526	+	0.0832802i	$0.973460\pi$
$488$	−29.8301	+	14.0772i	−1.35034	+	0.637243i
$489$			32.2774i			1.45964i
$490$		0			0
$491$		−	29.3371i		−	1.32397i	−0.749519	−	0.661983i	$-0.769715\pi$
$491$		−	29.3371i		−	1.32397i	0.749519	−	0.661983i	$-0.230285\pi$
$492$	3.52082	+	11.6306i	0.158731	+	0.524348i
$493$		−	1.00043i		−	0.0450572i
$494$	46.0208	−	6.81305i	2.07057	−	0.306533i
$495$		0			0
$496$	−6.93651	+	4.62332i	−0.311459	+	0.207593i
$497$	−5.92893	+	18.2003i	−0.265949	+	0.816394i
$498$	0.449747	+	3.03796i	0.0201537	+	0.136134i
$499$			16.7876i			0.751516i	0.926718	+	0.375758i	$0.122618\pi$
$499$			16.7876i			0.751516i	−0.926718	+	0.375758i	$0.877382\pi$
$500$		0			0
$501$	25.3137			1.13093
$502$	−2.89489	−	19.5544i	−0.129205	−	0.872756i
$503$	−31.0509			−1.38449			−0.692245	−	0.721663i	$-0.743378\pi$
$503$	−31.0509			−1.38449			−0.692245	+	0.721663i	$0.743378\pi$
$504$	−0.779092	−	6.15023i	−0.0347035	−	0.273953i
$505$		0			0
$506$	−2.29289	−	15.4881i	−0.101932	−	0.688528i
$507$	−30.9461			−1.37437
$508$	−3.24264	−	10.7117i	−0.143869	−	0.475254i
$509$		−	8.24621i		−	0.365507i	−0.983159	−	0.182753i	$-0.941499\pi$
$509$		−	8.24621i		−	0.365507i	0.983159	−	0.182753i	$-0.0585010\pi$
$510$		0			0
$511$	10.1366	−	31.1167i	0.448417	−	1.37652i
$512$	21.9350	+	5.55468i	0.969400	+	0.245485i
$513$	31.8284			1.40526
$514$	32.6292	−	4.83052i	1.43921	−	0.213065i
$515$		0			0
$516$	4.77844	+	15.7850i	0.210359	+	0.694896i
$517$			17.4929i			0.769335i
$518$	3.90440	−	23.0292i	0.171550	−	1.01184i
$519$		−	20.7445i		−	0.910581i
$520$		0			0
$521$		−	28.8617i		−	1.26446i	−0.774782	−	0.632228i	$-0.782141\pi$
$521$		−	28.8617i		−	1.26446i	0.774782	−	0.632228i	$-0.217859\pi$
$522$	0.0416306	+	0.281206i	0.00182212	+	0.0123081i
$523$	4.42088			0.193311			0.0966557	−	0.995318i	$-0.469185\pi$
$523$	4.42088			0.193311			0.0966557	+	0.995318i	$0.469185\pi$
$524$	24.9035	−	7.53880i	1.08792	−	0.329334i
$525$		0			0
$526$	−39.1421	+	5.79471i	−1.70668	+	0.252661i
$527$		−	8.59264i		−	0.374301i
$528$	9.14695	+	13.7235i	0.398070	+	0.597237i
$529$	7.34315			0.319267
$530$		0			0
$531$	2.44158			0.105956
$532$	−29.8463	−	0.625951i	−1.29400	−	0.0271384i
$533$	24.0416			1.04136
$534$	−25.5000	+	3.77509i	−1.10349	+	0.163364i
$535$		0			0
$536$	19.0147	−	8.97327i	0.821311	−	0.387586i
$537$			15.7850i			0.681173i
$538$	3.37887	−	0.500217i	0.145673	−	0.0215659i
$539$	−11.5362	+	15.8275i	−0.496898	+	0.681739i
$540$		0			0
$541$	10.2426			0.440366			0.220183	−	0.975459i	$-0.429335\pi$
$541$	10.2426			0.440366			0.220183	+	0.975459i	$0.429335\pi$
$542$	5.64167	+	38.1084i	0.242330	+	1.63690i
$543$			29.3371i			1.25898i
$544$	−17.3043	+	15.6385i	−0.741914	+	0.670495i
$545$		0			0
$546$	31.6984	+	5.37419i	1.35657	+	0.229994i
$547$		−	13.0296i		−	0.557104i	−0.960421	−	0.278552i	$-0.910146\pi$
$547$		−	13.0296i		−	0.557104i	0.960421	−	0.278552i	$-0.0898545\pi$
$548$	−6.67157	+	2.01962i	−0.284995	+	0.0862738i
$549$			9.66104i			0.412323i
$550$		0			0
$551$	1.36890			0.0583170
$552$	14.9150	−	7.03858i	0.634826	−	0.299582i
$553$	−6.48528	+	19.9081i	−0.275782	+	0.846579i
$554$	1.26346	+	8.53440i	0.0536791	+	0.362592i
$555$		0			0
$556$	−5.15769	+	1.56134i	−0.218735	+	0.0662154i
$557$	−10.6863			−0.452793			−0.226396	−	0.974035i	$-0.572694\pi$
$557$	−10.6863			−0.452793			−0.226396	+	0.974035i	$0.572694\pi$
$558$	0.357562	+	2.41526i	0.0151368	+	0.102246i
$559$	32.6292			1.38007
$560$		0			0
$561$	−17.0000			−0.717741
$562$	6.82843	+	46.1247i	0.288040	+	1.94565i
$563$	−13.7249			−0.578436			−0.289218	−	0.957263i	$-0.593395\pi$
$563$	−13.7249			−0.578436			−0.289218	+	0.957263i	$0.593395\pi$
$564$	−17.6360	+	5.33878i	−0.742611	+	0.224803i
$565$		0			0
$566$	6.55726	+	44.2930i	0.275622	+	1.86178i
$567$	14.6622	+	4.77637i	0.615755	+	0.200589i
$568$	−18.5061	+	8.73324i	−0.776499	+	0.366439i
$569$	3.68629			0.154537			0.0772687	−	0.997010i	$-0.475380\pi$
$569$	3.68629			0.154537			0.0772687	+	0.997010i	$0.475380\pi$
$570$		0			0
$571$		−	1.35778i		−	0.0568215i	−0.999596	−	0.0284108i	$-0.990955\pi$
$571$		−	1.35778i		−	0.0568215i	0.999596	−	0.0284108i	$-0.00904464\pi$
$572$	31.2296	−	9.45384i	1.30578	−	0.395285i
$573$			36.4005i			1.52065i
$574$	−15.2102	−	2.57876i	−0.634861	−	0.107635i
$575$		0			0
$576$	4.21320	−	5.11582i	0.175550	−	0.213159i
$577$			7.53880i			0.313844i	0.987611	+	0.156922i	$0.0501572\pi$
$577$			7.53880i			0.313844i	−0.987611	+	0.156922i	$0.949843\pi$
$578$		0			0
$579$	12.2513			0.509146
$580$		0			0
$581$	−3.70711	−	1.20763i	−0.153797	−	0.0501009i
$582$	−17.0000	+	2.51673i	−0.704673	+	0.104322i
$583$			34.2541i			1.41866i
$584$	31.6396	−	14.9311i	1.30925	−	0.617853i
$585$		0			0
$586$	23.0723	−	3.41569i	0.953110	−	0.141101i
$587$	0.967957			0.0399519			0.0199759	−	0.999800i	$-0.493641\pi$
$587$	0.967957			0.0399519			0.0199759	+	0.999800i	$0.493641\pi$
$588$	−19.4779	−	6.80008i	−0.803254	−	0.280431i
$589$	11.7574			0.484454
$590$		0			0
$591$	3.66237			0.150650
$592$	20.7782	−	13.8491i	0.853978	−	0.569193i
$593$			24.0312i			0.986844i	0.869790	+	0.493422i	$0.164254\pi$
$593$			24.0312i			0.986844i	−0.869790	+	0.493422i	$0.835746\pi$
$594$	22.0827	−	3.26918i	0.906064	−	0.134136i
$595$		0			0
$596$	−3.82843	+	1.15894i	−0.156818	+	0.0474721i
$597$	25.8406			1.05759
$598$	−4.77844	−	32.2774i	−0.195405	−	1.31992i
$599$		−	20.7445i		−	0.847596i	−0.905757	−	0.423798i	$-0.860697\pi$
$599$		−	20.7445i		−	0.847596i	0.905757	−	0.423798i	$-0.139303\pi$
$600$		0			0
$601$			15.7850i			0.643884i	0.946759	+	0.321942i	$0.104336\pi$
$601$			15.7850i			0.643884i	−0.946759	+	0.321942i	$0.895664\pi$
$602$	−20.6432	−	3.49988i	−0.841355	−	0.142645i
$603$		−	6.15828i		−	0.250784i
$604$	−0.949747	−	3.13738i	−0.0386447	−	0.127658i
$605$		0			0
$606$	−4.97918	+	0.737132i	−0.202266	+	0.0299439i
$607$	−16.6722			−0.676703			−0.338351	−	0.941020i	$-0.609869\pi$
$607$	−16.6722			−0.676703			−0.338351	+	0.941020i	$0.609869\pi$
$608$	−21.3982	−	23.6775i	−0.867814	−	0.960250i
$609$	0.899495	+	0.293020i	0.0364494	+	0.0118738i
$610$		0			0
$611$			36.4555i			1.47483i
$612$	1.97929	+	6.53836i	0.0800082	+	0.264298i
$613$	−17.1127			−0.691175			−0.345588	−	0.938386i	$-0.612320\pi$
$613$	−17.1127			−0.691175			−0.345588	+	0.938386i	$0.612320\pi$
$614$	−3.86285	−	26.0928i	−0.155892	−	1.05302i
$615$		0			0
$616$	−20.7718	+	2.63131i	−0.836920	+	0.106018i
$617$	22.0000			0.885687			0.442843	−	0.896599i	$-0.353970\pi$
$617$	22.0000			0.885687			0.442843	+	0.896599i	$0.353970\pi$
$618$	−2.17157	−	14.6686i	−0.0873535	−	0.590056i
$619$	18.9043			0.759828			0.379914	−	0.925022i	$-0.375954\pi$
$619$	18.9043			0.759828			0.379914	+	0.925022i	$0.375954\pi$
$620$		0			0
$621$		−	22.3234i		−	0.895806i
$622$	−2.44158	−	16.4924i	−0.0978986	−	0.661286i
$623$	10.1366	−	31.1167i	0.406114	−	1.24666i
$624$	19.0624	+	28.6000i	0.763109	+	1.14492i
$625$		0			0
$626$	6.75773	−	1.00043i	0.270093	−	0.0399854i
$627$		−	23.2612i		−	0.928963i
$628$	−12.9357	−	42.7317i	−0.516192	−	1.70518i
$629$			25.7391i			1.02628i
$630$		0			0
$631$			11.8706i			0.472562i	0.971685	+	0.236281i	$0.0759286\pi$
$631$			11.8706i			0.472562i	−0.971685	+	0.236281i	$0.924071\pi$
$632$	−20.2426	+	9.55274i	−0.805209	+	0.379988i
$633$		−	2.12224i		−	0.0843514i
$634$	−5.31371	−	35.8931i	−0.211034	−	1.42550i
$635$		0			0
$636$	−34.5345	+	10.4543i	−1.36938	+	0.414539i
$637$	−24.0416	+	32.9848i	−0.952564	+	1.30691i
$638$	0.949747	−	0.140603i	0.0376009	−	0.00556653i
$639$			5.99355i			0.237101i
$640$		0			0
$641$	−21.1716			−0.836227			−0.418113	−	0.908395i	$-0.637309\pi$
$641$	−21.1716			−0.836227			−0.418113	+	0.908395i	$0.637309\pi$
$642$	26.8611	−	3.97660i	1.06012	−	0.156944i
$643$	25.5139			1.00617			0.503086	−	0.864237i	$-0.332198\pi$
$643$	25.5139			1.00617			0.503086	+	0.864237i	$0.332198\pi$
$644$	−0.439021	+	20.9332i	−0.0172998	+	0.824884i
$645$		0			0
$646$	32.5416	−	4.81755i	1.28033	−	0.189544i
$647$	46.8598			1.84225			0.921125	−	0.389268i	$-0.127272\pi$
$647$	46.8598			1.84225			0.921125	+	0.389268i	$0.127272\pi$
$648$	7.03553	+	14.9086i	0.276382	+	0.585664i
$649$		−	8.24621i		−	0.323692i
$650$		0			0
$651$	7.72569	+	2.51673i	0.302794	+	0.0986383i
$652$	−12.6924	−	41.9278i	−0.497072	−	1.64202i
$653$	−29.5563			−1.15663			−0.578315	−	0.815814i	$-0.696289\pi$
$653$	−29.5563			−1.15663			−0.578315	+	0.815814i	$0.696289\pi$
$654$	0.863230	+	5.83095i	0.0337550	+	0.228008i
$655$		0			0
$656$	−9.14695	−	13.7235i	−0.357128	−	0.535811i
$657$		−	10.2471i		−	0.399777i
$658$	3.91030	−	23.0640i	0.152439	−	0.899126i
$659$		−	6.47360i		−	0.252176i	−0.992019	−	0.126088i	$-0.959758\pi$
$659$		−	6.47360i		−	0.252176i	0.992019	−	0.126088i	$-0.0402421\pi$
$660$		0			0
$661$		−	27.1539i		−	1.05616i	−0.849193	−	0.528082i	$-0.822911\pi$
$661$		−	27.1539i		−	1.05616i	0.849193	−	0.528082i	$-0.177089\pi$
$662$	−40.3701	+	5.97649i	−1.56903	+	0.232283i
$663$	−35.4284			−1.37592
$664$	−1.77882	−	3.76940i	−0.0690317	−	0.146281i
$665$		0			0
$666$	−1.07107	−	7.23486i	−0.0415030	−	0.280345i
$667$		−	0.960099i		−	0.0371752i
$668$	−32.8821	+	9.95406i	−1.27224	+	0.385134i
$669$	−1.27208			−0.0491814
$670$		0			0
$671$	32.6292			1.25964
$672$	−8.99236	−	20.1388i	−0.346888	−	0.776870i
$673$	4.00000			0.154189			0.0770943	−	0.997024i	$-0.475436\pi$
$673$	4.00000			0.154189			0.0770943	+	0.997024i	$0.475436\pi$
$674$	−3.06497	−	20.7033i	−0.118058	−	0.797461i
$675$		0			0
$676$	40.1985	−	12.1689i	1.54610	−	0.468034i
$677$			11.6619i			0.448203i	0.974566	+	0.224102i	$0.0719448\pi$
$677$			11.6619i			0.448203i	−0.974566	+	0.224102i	$0.928055\pi$
$678$	−5.58931	−	37.7547i	−0.214656	−	1.44996i
$679$	6.75773	−	20.7445i	0.259338	−	0.796100i
$680$		0			0
$681$	−10.4853			−0.401797
$682$	8.15731	−	1.20763i	0.312359	−	0.0462425i
$683$			26.5392i			1.01549i	0.861506	+	0.507747i	$0.169521\pi$
$683$			26.5392i			1.01549i	−0.861506	+	0.507747i	$0.830479\pi$
$684$	−8.94648	+	2.70828i	−0.342077	+	0.103554i
$685$		0			0
$686$	18.7482	−	18.2895i	0.715811	−	0.698295i
$687$		−	20.7445i		−	0.791451i
$688$	−12.4142	−	18.6254i	−0.473287	−	0.710088i
$689$			71.3862i			2.71960i
$690$		0			0
$691$	−48.3334			−1.83869			−0.919345	−	0.393452i	$-0.871281\pi$
$691$	−48.3334			−1.83869			−0.919345	+	0.393452i	$0.871281\pi$
$692$	8.15731	+	26.9467i	0.310094	+	1.02436i
$693$	−1.89949	+	5.83095i	−0.0721558	+	0.221500i
$694$	27.9558	−	4.13866i	1.06119	−	0.157101i
$695$		0			0
$696$	0.431615	+	0.914610i	0.0163603	+	0.0346682i
$697$	17.0000			0.643921
$698$	19.6935	−	2.91548i	0.745409	−	0.110352i
$699$	−23.2818			−0.880598
$700$		0			0
$701$	−16.8284			−0.635601			−0.317800	−	0.948158i	$-0.602944\pi$
$701$	−16.8284			−0.635601			−0.317800	+	0.948158i	$0.602944\pi$
$702$	46.0208	−	6.81305i	1.73694	−	0.257142i
$703$	−35.2189			−1.32831
$704$	−17.2782	−	14.2297i	−0.651196	−	0.536302i
$705$		0			0
$706$	16.3146	−	2.41526i	0.614008	−	0.0908995i
$707$	1.97929	−	6.07591i	0.0744390	−	0.228508i
$708$	8.31371	−	2.51673i	0.312448	−	0.0945844i
$709$	−28.0000			−1.05156			−0.525781	−	0.850620i	$-0.676227\pi$
$709$	−28.0000			−1.05156			−0.525781	+	0.850620i	$0.676227\pi$
$710$		0			0
$711$			6.55596i			0.245868i
$712$	31.6396	−	14.9311i	1.18574	−	0.559566i
$713$		−	8.24621i		−	0.308823i
$714$	22.4141	+	3.80013i	0.838828	+	0.142216i
$715$		0			0
$716$	−6.20711	−	20.5044i	−0.231970	−	0.766287i
$717$		−	24.7386i		−	0.923881i
$718$	−28.6274	+	4.23808i	−1.06837	+	0.158164i
$719$	36.9454			1.37783			0.688915	−	0.724842i	$-0.258087\pi$
$719$	36.9454			1.37783			0.688915	+	0.724842i	$0.258087\pi$
$720$		0			0
$721$	17.8995	+	5.83095i	0.666612	+	0.217156i
$722$	2.65685	+	17.9465i	0.0988779	+	0.667901i
$723$			23.2612i			0.865093i
$724$	−11.5362	−	38.1084i	−0.428738	−	1.41629i
$725$		0			0
$726$	0.967957	+	6.53836i	0.0359243	+	0.242661i
$727$	32.2717			1.19689			0.598445	−	0.801164i	$-0.295786\pi$
$727$	32.2717			1.19689			0.598445	+	0.801164i	$0.295786\pi$
$728$	−43.2889	+	5.48371i	−1.60439	+	0.203240i
$729$	29.7696			1.10258
$730$		0			0
$731$	23.0723			0.853361
$732$	9.95837	+	32.8963i	0.368072	+	1.21588i
$733$			24.7386i			0.913742i	0.889533	+	0.456871i	$0.151030\pi$
$733$			24.7386i			0.913742i	−0.889533	+	0.456871i	$0.848970\pi$
$734$	3.30481	+	22.3234i	0.121983	+	0.823971i
$735$		0			0
$736$	−16.6066	+	15.0080i	−0.612127	+	0.553202i
$737$	−20.7990			−0.766141
$738$	−4.77844	+	0.707413i	−0.175897	+	0.0260402i
$739$			18.7078i			0.688177i	0.938937	+	0.344089i	$0.111812\pi$
$739$			18.7078i			0.688177i	−0.938937	+	0.344089i	$0.888188\pi$
$740$		0			0
$741$		−	48.4768i		−	1.78084i
$742$	7.65705	−	45.1633i	0.281099	−	1.65800i
$743$			16.5064i			0.605561i	0.953060	+	0.302780i	$0.0979149\pi$
$743$			16.5064i			0.605561i	−0.953060	+	0.302780i	$0.902085\pi$
$744$	3.70711	+	7.85551i	0.135909	+	0.287997i
$745$		0			0
$746$	−2.77817	−	18.7660i	−0.101716	−	0.687073i
$747$	−1.22079			−0.0446664
$748$	22.0827	−	6.68488i	0.807423	−	0.244423i
$749$	−10.6777	+	32.7776i	−0.390154	+	1.19767i
$750$		0			0
$751$			21.1422i			0.771488i	0.922606	+	0.385744i	$0.126055\pi$
$751$			21.1422i			0.771488i	−0.922606	+	0.385744i	$0.873945\pi$
$752$	20.8095	−	13.8700i	0.758846	−	0.505786i
$753$	−20.5980			−0.750632
$754$	1.97929	−	0.293020i	0.0720816	−	0.0106712i
$755$		0			0
$756$	−29.8463	−	0.625951i	−1.08550	−	0.0227656i
$757$	12.5858			0.457438			0.228719	−	0.973492i	$-0.426546\pi$
$757$	12.5858			0.457438			0.228719	+	0.973492i	$0.426546\pi$
$758$	5.81371	−	0.860677i	0.211163	−	0.0312612i
$759$	−16.3146			−0.592183
$760$		0			0
$761$		−	39.1088i		−	1.41769i	−0.705363	−	0.708847i	$-0.749216\pi$
$761$		−	39.1088i		−	1.41769i	0.705363	−	0.708847i	$-0.250784\pi$
$762$	−11.5362	+	1.70785i	−0.417911	+	0.0618687i
$763$	−7.11529	−	2.31788i	−0.257591	−	0.0839130i
$764$	−14.3137	−	47.2836i	−0.517852	−	1.71066i
$765$		0			0
$766$	3.81048	+	25.7391i	0.137678	+	0.929990i
$767$		−	17.1853i		−	0.620525i
$768$	9.07290	−	21.7625i	0.327390	−	0.785286i
$769$		−	40.5236i		−	1.46132i	−0.682742	−	0.730660i	$-0.739212\pi$
$769$		−	40.5236i		−	1.46132i	0.682742	−	0.730660i	$-0.260788\pi$
$770$		0			0
$771$		−	34.3706i		−	1.23783i
$772$	−15.9142	+	4.81755i	−0.572765	+	0.173387i
$773$			36.4005i			1.30924i	0.755960	+	0.654618i	$0.227171\pi$
$773$			36.4005i			1.30924i	−0.755960	+	0.654618i	$0.772829\pi$
$774$	−6.48528	+	0.960099i	−0.233109	+	0.0345100i
$775$		0			0
$776$	21.0930	−	9.95406i	0.757196	−	0.357330i
$777$	−23.1421	−	7.53880i	−0.830219	−	0.270453i
$778$	3.22183	+	21.7628i	0.115508	+	0.780234i
$779$			23.2612i			0.833419i
$780$		0			0
$781$	20.2426			0.724339
$782$	−3.37887	−	22.8236i	−0.120828	−	0.816170i
$783$	1.36890			0.0489204
$784$	27.9754	+	1.17394i	0.999121	+	0.0419265i
$785$		0			0
$786$	−3.97056	−	26.8204i	−0.141625	−	0.956651i
$787$	−20.6308			−0.735407			−0.367704	−	0.929943i	$-0.619856\pi$
$787$	−20.6308			−0.735407			−0.367704	+	0.929943i	$0.619856\pi$
$788$	−4.75736	+	1.44015i	−0.169474	+	0.0513032i
$789$			41.2311i			1.46786i
$790$		0			0
$791$	46.0706	+	15.0080i	1.63808	+	0.533623i
$792$	−5.92893	+	2.79793i	−0.210675	+	0.0994202i
$793$	68.0000			2.41475
$794$	−26.4512	+	3.91591i	−0.938718	+	0.138970i
$795$		0			0
$796$	−33.5665	+	10.1613i	−1.18973	+	0.360156i
$797$		−	26.7395i		−	0.947162i	−0.880750	−	0.473581i	$-0.842961\pi$
$797$		−	26.7395i		−	0.947162i	0.880750	−	0.473581i	$-0.157039\pi$
$798$	−5.19974	+	30.6694i	−0.184069	+	1.08568i
$799$			25.7779i			0.911957i
$800$		0			0
$801$		−	10.2471i		−	0.362063i
$802$	−4.65076	−	31.4150i	−0.164224	−	1.10930i
$803$	−34.6085			−1.22131
$804$	−6.34781	−	20.9692i	−0.223870	−	0.739528i
$805$		0			0
$806$	17.0000	−	2.51673i	0.598799	−	0.0886479i
$807$		−	3.55919i		−	0.125289i
$808$	6.17801	−	2.91548i	0.217342	−	0.102566i
$809$	−1.17157			−0.0411903			−0.0205952	−	0.999788i	$-0.506556\pi$
$809$	−1.17157			−0.0411903			−0.0205952	+	0.999788i	$0.506556\pi$
$810$		0			0
$811$	36.0821			1.26702			0.633508	−	0.773736i	$-0.281615\pi$
$811$	36.0821			1.26702			0.633508	+	0.773736i	$0.281615\pi$
$812$	−1.28365	−	0.0269213i	−0.0450473	−	0.000944753i
$813$	40.1421			1.40785
$814$	−24.4350	+	3.61743i	−0.856447	+	0.126791i
$815$		0			0
$816$	13.4792	+	20.2232i	0.471866	+	0.707955i
$817$			31.5700i			1.10450i
$818$	22.0827	−	3.26918i	0.772103	−	0.114304i
$819$	−3.95859	+	12.1518i	−0.138324	+	0.424619i
$820$		0			0
$821$	14.5858			0.509047			0.254524	−	0.967067i	$-0.418081\pi$
$821$	14.5858			0.509047			0.254524	+	0.967067i	$0.418081\pi$
$822$	1.06370	+	7.18509i	0.0371008	+	0.250609i
$823$		−	49.1215i		−	1.71227i	−0.516755	−	0.856134i	$-0.672860\pi$
$823$		−	49.1215i		−	1.71227i	0.516755	−	0.856134i	$-0.327140\pi$
$824$	8.58892	+	18.2003i	0.299209	+	0.634036i
$825$		0			0
$826$	−1.84333	+	10.8725i	−0.0641377	+	0.378301i
$827$			47.0024i			1.63444i	0.576329	+	0.817218i	$0.304485\pi$
$827$			47.0024i			1.63444i	−0.576329	+	0.817218i	$0.695515\pi$
$828$	1.89949	+	6.27476i	0.0660120	+	0.218063i
$829$			26.7395i			0.928701i	0.885651	+	0.464351i	$0.153712\pi$
$829$			26.7395i			0.928701i	−0.885651	+	0.464351i	$0.846288\pi$
$830$		0			0
$831$	8.98986			0.311855
$832$	−36.0081	−	29.6550i	−1.24836	−	1.02810i
$833$	−17.0000	+	23.3238i	−0.589015	+	0.808122i
$834$	0.822330	+	5.55468i	0.0284750	+	0.192343i
$835$		0			0
$836$	9.14695	+	30.2159i	0.316354	+	1.04504i
$837$	11.7574			0.406394
$838$	−5.08364	−	34.3390i	−0.175611	−	1.18622i
$839$	37.6605			1.30018			0.650092	−	0.759855i	$-0.274730\pi$
$839$	37.6605			1.30018			0.650092	+	0.759855i	$0.274730\pi$
$840$		0			0
$841$	−28.9411			−0.997970
$842$	−0.142136	−	0.960099i	−0.00489832	−	0.0330872i
$843$	48.5863			1.67340
$844$	0.834524	+	2.75675i	0.0287255	+	0.0948913i
$845$		0			0
$846$	−1.07268	−	7.24578i	−0.0368797	−	0.249115i
$847$	−7.97852	−	2.59909i	−0.274145	−	0.0893058i
$848$	40.7487	−	27.1598i	1.39932	−	0.932672i
$849$	46.6569			1.60126
$850$		0			0
$851$			24.7013i			0.846751i
$852$	6.17801	+	20.4083i	0.211655	+	0.699178i
$853$		−	15.0776i		−	0.516247i	−0.966112	−	0.258124i	$-0.916896\pi$
$853$		−	15.0776i		−	0.516247i	0.966112	−	0.258124i	$-0.0831042\pi$
$854$	−43.0209	−	7.29384i	−1.47215	−	0.249590i
$855$		0			0
$856$	−33.3284	+	15.7281i	−1.13914	+	0.537575i
$857$		−	5.53793i		−	0.189172i	−0.995517	−	0.0945861i	$-0.969847\pi$
$857$		−	5.53793i		−	0.189172i	0.995517	−	0.0945861i	$-0.0301528\pi$
$858$	−4.97918	−	33.6334i	−0.169987	−	1.14823i
$859$	−36.3350			−1.23973			−0.619867	−	0.784707i	$-0.712813\pi$
$859$	−36.3350			−1.23973			−0.619867	+	0.784707i	$0.712813\pi$
$860$		0			0
$861$	−4.97918	+	15.2848i	−0.169690	+	0.520904i
$862$	11.4645	−	1.69723i	0.390481	−	0.0578079i
$863$		−	12.1518i		−	0.413653i	−0.978378	−	0.206827i	$-0.933686\pi$
$863$		−	12.1518i		−	0.413653i	0.978378	−	0.206827i	$-0.0663136\pi$
$864$	−21.3982	−	23.6775i	−0.727983	−	0.805525i
$865$		0			0
$866$	5.76809	−	0.853923i	0.196008	−	0.0290175i
$867$		0			0
$868$	−11.0252	−	0.231225i	−0.374219	−	0.00784829i
$869$	22.1421			0.751121
$870$		0			0
$871$	−43.3455			−1.46871
$872$	−3.41421	−	7.23486i	−0.115620	−	0.245003i
$873$		−	6.83139i		−	0.231207i
$874$	31.2296	−	4.62332i	1.05636	−	0.156386i
$875$		0			0
$876$	−10.5624	−	34.8918i	−0.356872	−	1.17888i
$877$	4.97056			0.167844			0.0839220	−	0.996472i	$-0.473255\pi$
$877$	4.97056			0.167844			0.0839220	+	0.996472i	$0.473255\pi$
$878$	0.610396	+	4.12311i	0.0205999	+	0.139148i
$879$		−	24.3037i		−	0.819742i
$880$		0			0
$881$			11.6619i			0.392900i	0.980514	+	0.196450i	$0.0629413\pi$
$881$			11.6619i			0.392900i	−0.980514	+	0.196450i	$0.937059\pi$
$882$	3.80788	−	7.26338i	0.128218	−	0.244571i
$883$		−	7.99611i		−	0.269091i	−0.990907	−	0.134545i	$-0.957043\pi$
$883$		−	7.99611i		−	0.269091i	0.990907	−	0.134545i	$-0.0429574\pi$
$884$	46.0208	−	13.9314i	1.54785	−	0.468564i
$885$		0			0
$886$	2.57107	−	0.380628i	0.0863767	−	0.0127874i
$887$	−10.9258			−0.366852			−0.183426	−	0.983034i	$-0.558719\pi$
$887$	−10.9258			−0.366852			−0.183426	+	0.983034i	$0.558719\pi$
$888$	−11.1046	−	23.5310i	−0.372645	−	0.789649i
$889$	4.58579	−	14.0772i	0.153802	−	0.472133i
$890$		0			0
$891$		−	16.3075i		−	0.546323i
$892$	1.65241	−	0.500217i	0.0553267	−	0.0167485i
$893$	−35.2721			−1.18034
$894$	0.610396	+	4.12311i	0.0204147	+	0.137897i
$895$		0			0
$896$	19.6000	+	22.6238i	0.654791	+	0.755810i
$897$	−34.0000			−1.13523
$898$	2.20711	+	14.9086i	0.0736521	+	0.497506i
$899$	0.505668			0.0168650
$900$		0			0
$901$			50.4777i			1.68166i
$902$	2.38922	+	16.1387i	0.0795523	+	0.537360i
$903$	−6.75773	+	20.7445i	−0.224883	+	0.690333i
$904$	22.1066	+	46.8448i	0.735255	+	1.55803i
$905$		0			0
$906$	−3.37887	+	0.500217i	−0.112255	+	0.0166186i
$907$			39.5687i			1.31386i	0.753952	+	0.656929i	$0.228145\pi$
$907$			39.5687i			1.31386i	−0.753952	+	0.656929i	$0.771855\pi$
$908$	13.6202	−	4.12311i	0.452002	−	0.136830i
$909$		−	2.00087i		−	0.0663645i
$910$		0			0
$911$		−	30.2972i		−	1.00379i	−0.864928	−	0.501896i	$-0.832636\pi$
$911$		−	30.2972i		−	1.00379i	0.864928	−	0.501896i	$-0.167364\pi$
$912$	−27.6716	+	18.4436i	−0.916297	+	0.610730i
$913$			4.12311i			0.136455i
$914$	6.10660	+	41.2489i	0.201988	+	1.36439i
$915$		0			0
$916$	8.15731	+	26.9467i	0.269525	+	0.890344i
$917$	32.7279	+	10.6615i	1.08077	+	0.352073i
$918$	32.5416	−	4.81755i	1.07403	−	0.159003i
$919$		−	22.7811i		−	0.751481i	−0.926725	−	0.375740i	$-0.877388\pi$
$919$		−	22.7811i		−	0.751481i	0.926725	−	0.375740i	$-0.122612\pi$
$920$		0			0
$921$	−27.4853			−0.905671
$922$	−3.37887	+	0.500217i	−0.111277	+	0.0164738i
$923$	42.1861			1.38857
$924$	−0.457464	+	21.8126i	−0.0150495	+	0.717583i
$925$		0			0
$926$	−1.89949	+	0.281206i	−0.0624213	+	0.00924102i
$927$	5.89450			0.193601
$928$	−0.920310	−	1.01834i	−0.0302107	−	0.0334286i
$929$		−	39.8162i		−	1.30633i	−0.757216	−	0.653164i	$-0.773441\pi$
$929$		−	39.8162i		−	1.30633i	0.757216	−	0.653164i	$-0.226559\pi$
$930$		0			0
$931$	−31.9141	−	23.2612i	−1.04594	−	0.762355i
$932$	30.2426	−	9.15505i	0.990631	−	0.299884i
$933$	−17.3726			−0.568753
$934$	1.57835	+	10.6615i	0.0516453	+	0.348854i
$935$		0			0
$936$	−12.3560	+	5.83095i	−0.403869	+	0.190591i
$937$			10.9545i			0.357868i	0.983861	+	0.178934i	$0.0572648\pi$
$937$			10.9545i			0.357868i	−0.983861	+	0.178934i	$0.942735\pi$
$938$	27.4230	+	4.64934i	0.895393	+	0.151806i
$939$		−	7.11838i		−	0.232299i
$940$		0			0
$941$		−	24.7386i		−	0.806456i	−0.915099	−	0.403228i	$-0.867888\pi$
$941$		−	24.7386i		−	0.806456i	0.915099	−	0.403228i	$-0.132112\pi$
$942$	−46.0208	+	6.81305i	−1.49944	+	0.221981i
$943$	16.3146			0.531277
$944$	−9.80971	+	6.53836i	−0.319279	+	0.212806i
$945$		0			0
$946$	3.24264	+	21.9034i	0.105427	+	0.712141i
$947$		−	19.5032i		−	0.633768i	−0.948464	−	0.316884i	$-0.897363\pi$
$947$		−	19.5032i		−	0.633768i	0.948464	−	0.316884i	$-0.102637\pi$
$948$	6.75773	+	22.3234i	0.219481	+	0.725029i
$949$	−72.1249			−2.34127
$950$		0			0
$951$	−37.8086			−1.22603
$952$	−30.6099	+	3.87757i	−0.992072	+	0.125673i
$953$	53.7696			1.74177			0.870883	−	0.491490i	$-0.163547\pi$
$953$	53.7696			1.74177			0.870883	+	0.491490i	$0.163547\pi$
$954$	−2.10051	−	14.1885i	−0.0680064	−	0.459370i
$955$		0			0
$956$	9.72792	+	32.1350i	0.314623	+	1.03932i
$957$		−	1.00043i		−	0.0323394i
$958$	1.83119	+	12.3693i	0.0591630	+	0.399634i
$959$	−8.76770	−	2.85617i	−0.283124	−	0.0922306i
$960$		0			0
$961$	−26.6569			−0.859899
$962$	−50.9231	+	7.53880i	−1.64183	+	0.243061i
$963$			10.7940i			0.347833i
$964$	−9.14695	−	30.2159i	−0.294604	−	0.973188i
$965$		0			0
$966$	21.5105	+	3.64692i	0.692088	+	0.117338i
$967$			9.55274i			0.307195i	0.988133	+	0.153598i	$0.0490860\pi$
$967$			9.55274i			0.307195i	−0.988133	+	0.153598i	$0.950914\pi$
$968$	−3.82843	−	8.11259i	−0.123050	−	0.260749i
$969$		−	34.2783i		−	1.10118i
$970$		0			0
$971$	−4.92655			−0.158100			−0.0790502	−	0.996871i	$-0.525189\pi$
$971$	−4.92655			−0.158100			−0.0790502	+	0.996871i	$0.525189\pi$
$972$	−15.9570	+	4.83052i	−0.511823	+	0.154939i
$973$	−6.77817	−	2.20806i	−0.217298	−	0.0707872i
$974$	−5.14214	+	0.761256i	−0.164765	+	0.0243922i
$975$		0			0
$976$	−25.8715	−	38.8158i	−0.828126	−	1.24246i
$977$	−7.28427			−0.233044			−0.116522	−	0.993188i	$-0.537175\pi$
$977$	−7.28427			−0.233044			−0.116522	+	0.993188i	$0.537175\pi$
$978$	−45.1550	+	6.68488i	−1.44390	+	0.213759i
$979$	−34.6085			−1.10609
$980$		0			0
$981$	−2.34315			−0.0748109
$982$	41.0416	−	6.07591i	1.30969	−	0.193890i
$983$	11.6409			0.371287			0.185644	−	0.982617i	$-0.440563\pi$
$983$	11.6409			0.371287			0.185644	+	0.982617i	$0.440563\pi$
$984$	−15.5416	+	7.33428i	−0.495449	+	0.233808i
$985$		0			0
$986$	1.39957	−	0.207196i	0.0445715	−	0.00659848i
$987$	−23.1771	−	7.55018i	−0.737734	−	0.240325i
$988$	19.0624	+	62.9705i	0.606457	+	2.00336i
$989$	22.1421			0.704079
$990$		0			0
$991$		−	6.27476i		−	0.199324i	−0.995021	−	0.0996621i	$-0.968224\pi$
$991$		−	6.27476i		−	0.199324i	0.995021	−	0.0996621i	$-0.0317762\pi$
$992$	−7.90447	−	8.74643i	−0.250967	−	0.277699i
$993$			42.5245i			1.34947i
$994$	−26.6895	−	4.52498i	−0.846539	−	0.143524i
$995$		0			0
$996$	−4.15685	+	1.25836i	−0.131715	+	0.0398728i
$997$		−	2.41526i		−	0.0764920i	−0.999268	−	0.0382460i	$-0.987823\pi$
$997$		−	2.41526i		−	0.0764920i	0.999268	−	0.0382460i	$-0.0121771\pi$
$998$	−23.4853	+	3.47682i	−0.743414	+	0.110057i
$999$	−35.2189			−1.11428

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.g.i.251.8	yes	8
4.3	odd	2	inner	700.2.g.i.251.5	✓	8
5.2	odd	4		700.2.c.k.699.3		16
5.3	odd	4		700.2.c.k.699.14		16
5.4	even	2		700.2.g.k.251.1	yes	8
7.6	odd	2	inner	700.2.g.i.251.7	yes	8
20.3	even	4		700.2.c.k.699.1		16
20.7	even	4		700.2.c.k.699.16		16
20.19	odd	2		700.2.g.k.251.4	yes	8
28.27	even	2	inner	700.2.g.i.251.6	yes	8
35.13	even	4		700.2.c.k.699.13		16
35.27	even	4		700.2.c.k.699.4		16
35.34	odd	2		700.2.g.k.251.2	yes	8
140.27	odd	4		700.2.c.k.699.15		16
140.83	odd	4		700.2.c.k.699.2		16
140.139	even	2		700.2.g.k.251.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.c.k.699.1		16	20.3	even	4
700.2.c.k.699.2		16	140.83	odd	4
700.2.c.k.699.3		16	5.2	odd	4
700.2.c.k.699.4		16	35.27	even	4
700.2.c.k.699.13		16	35.13	even	4
700.2.c.k.699.14		16	5.3	odd	4
700.2.c.k.699.15		16	140.27	odd	4
700.2.c.k.699.16		16	20.7	even	4
700.2.g.i.251.5	✓	8	4.3	odd	2	inner
700.2.g.i.251.6	yes	8	28.27	even	2	inner
700.2.g.i.251.7	yes	8	7.6	odd	2	inner
700.2.g.i.251.8	yes	8	1.1	even	1	trivial
700.2.g.k.251.1	yes	8	5.4	even	2
700.2.g.k.251.2	yes	8	35.34	odd	2
700.2.g.k.251.3	yes	8	140.139	even	2
700.2.g.k.251.4	yes	8	20.19	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.207107 + 1.39897i) q^{2} +1.47363 q^{3} +(-1.91421 + 0.579471i) q^{4} +(0.305198 + 2.06155i) q^{6} +(-2.51564 - 0.819496i) q^{7} +(-1.20711 - 2.55791i) q^{8} -0.828427 q^{9} +2.79793i q^{11} +(-2.82083 + 0.853923i) q^{12} +5.83095i q^{13} +(0.625441 - 3.68901i) q^{14} +(3.32843 - 2.21846i) q^{16} +4.12311i q^{17} +(-0.171573 - 1.15894i) q^{18} -5.64167 q^{19} +(-3.70711 - 1.20763i) q^{21} +(-3.91421 + 0.579471i) q^{22} +3.95687i q^{23} +(-1.77882 - 3.76940i) q^{24} +(-8.15731 + 1.20763i) q^{26} -5.64167 q^{27} +(5.29034 + 0.110951i) q^{28} -0.242641 q^{29} -2.08402 q^{31} +(3.79289 + 4.19690i) q^{32} +4.12311i q^{33} +(-5.76809 + 0.853923i) q^{34} +(1.58579 - 0.480049i) q^{36} +6.24264 q^{37} +(-1.16843 - 7.89250i) q^{38} +8.59264i q^{39} -4.12311i q^{41} +(0.921666 - 5.43623i) q^{42} -5.59587i q^{43} +(-1.62132 - 5.35584i) q^{44} +(-5.53553 + 0.819496i) q^{46} +6.25206 q^{47} +(4.90486 - 3.26918i) q^{48} +(5.65685 + 4.12311i) q^{49} +6.07591i q^{51} +(-3.37887 - 11.1617i) q^{52} +12.2426 q^{53} +(-1.16843 - 7.89250i) q^{54} +(0.940448 + 7.42399i) q^{56} -8.31371 q^{57} +(-0.0502525 - 0.339446i) q^{58} -2.94725 q^{59} -11.6619i q^{61} +(-0.431615 - 2.91548i) q^{62} +(2.08402 + 0.678892i) q^{63} +(-5.08579 + 6.17534i) q^{64} +(-5.76809 + 0.853923i) q^{66} +7.43370i q^{67} +(-2.38922 - 7.89250i) q^{68} +5.83095i q^{69} -7.23486i q^{71} +(1.00000 + 2.11904i) q^{72} +12.3693i q^{73} +(1.29289 + 8.73324i) q^{74} +(10.7994 - 3.26918i) q^{76} +(2.29289 - 7.03858i) q^{77} +(-12.0208 + 1.77959i) q^{78} -7.91375i q^{79} -5.82843 q^{81} +(5.76809 - 0.853923i) q^{82} +1.47363 q^{83} +(7.79598 + 0.163501i) q^{84} +(7.82843 - 1.15894i) q^{86} -0.357562 q^{87} +(7.15685 - 3.37740i) q^{88} +12.3693i q^{89} +(4.77844 - 14.6686i) q^{91} +(-2.29289 - 7.57430i) q^{92} -3.07107 q^{93} +(1.29484 + 8.74643i) q^{94} +(5.58931 + 6.18466i) q^{96} +8.24621i q^{97} +(-4.59651 + 8.76767i) q^{98} -2.31788i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} - 4 q^{8} + 16 q^{9} + 12 q^{14} + 4 q^{16} - 24 q^{18} - 24 q^{21} - 20 q^{22} - 16 q^{28} + 32 q^{29} + 36 q^{32} + 24 q^{36} + 16 q^{37} + 8 q^{42} + 4 q^{44} - 16 q^{46} + 64 q^{53}+ \cdots + 32 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 - 4 * q^8 + 16 * q^9 + 12 * q^14 + 4 * q^16 - 24 * q^18 - 24 * q^21 - 20 * q^22 - 16 * q^28 + 32 * q^29 + 36 * q^32 + 24 * q^36 + 16 * q^37 + 8 * q^42 + 4 * q^44 - 16 * q^46 + 64 * q^53 + 20 * q^56 + 24 * q^57 - 40 * q^58 - 52 * q^64 + 8 * q^72 + 16 * q^74 + 24 * q^77 - 24 * q^81 + 20 * q^84 + 40 * q^86 + 12 * q^88 - 24 * q^92 + 32 * q^93 + 32 * q^98

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