LMFDB - Embedded newform 220.2.l.b.23.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(23,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.23"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$220 = 2^{2} \cdot 5 \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	220.l (of order $4$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{2} + 1$ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	220.23
Dual form			220.2.l.b.67.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(2.00000 - 2.00000i) q^{3} +2.00000i q^{4} +(-1.00000 + 2.00000i) q^{5} +4.00000 q^{6} +(1.00000 + 1.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} -5.00000i q^{9} +(-3.00000 + 1.00000i) q^{10} -1.00000i q^{11} +(4.00000 + 4.00000i) q^{12} +(-4.00000 - 4.00000i) q^{13} +2.00000i q^{14} +(2.00000 + 6.00000i) q^{15} -4.00000 q^{16} +(2.00000 - 2.00000i) q^{17} +(5.00000 - 5.00000i) q^{18} -2.00000 q^{19} +(-4.00000 - 2.00000i) q^{20} +4.00000 q^{21} +(1.00000 - 1.00000i) q^{22} +(4.00000 - 4.00000i) q^{23} +8.00000i q^{24} +(-3.00000 - 4.00000i) q^{25} -8.00000i q^{26} +(-4.00000 - 4.00000i) q^{27} +(-2.00000 + 2.00000i) q^{28} +2.00000i q^{29} +(-4.00000 + 8.00000i) q^{30} +8.00000i q^{31} +(-4.00000 - 4.00000i) q^{32} +(-2.00000 - 2.00000i) q^{33} +4.00000 q^{34} +(-3.00000 + 1.00000i) q^{35} +10.0000 q^{36} +(-5.00000 + 5.00000i) q^{37} +(-2.00000 - 2.00000i) q^{38} -16.0000 q^{39} +(-2.00000 - 6.00000i) q^{40} -6.00000 q^{41} +(4.00000 + 4.00000i) q^{42} +(-1.00000 + 1.00000i) q^{43} +2.00000 q^{44} +(10.0000 + 5.00000i) q^{45} +8.00000 q^{46} +(4.00000 + 4.00000i) q^{47} +(-8.00000 + 8.00000i) q^{48} -5.00000i q^{49} +(1.00000 - 7.00000i) q^{50} -8.00000i q^{51} +(8.00000 - 8.00000i) q^{52} +(9.00000 + 9.00000i) q^{53} -8.00000i q^{54} +(2.00000 + 1.00000i) q^{55} -4.00000 q^{56} +(-4.00000 + 4.00000i) q^{57} +(-2.00000 + 2.00000i) q^{58} +8.00000 q^{59} +(-12.0000 + 4.00000i) q^{60} -10.0000 q^{61} +(-8.00000 + 8.00000i) q^{62} +(5.00000 - 5.00000i) q^{63} -8.00000i q^{64} +(12.0000 - 4.00000i) q^{65} -4.00000i q^{66} +(4.00000 + 4.00000i) q^{68} -16.0000i q^{69} +(-4.00000 - 2.00000i) q^{70} -12.0000i q^{71} +(10.0000 + 10.0000i) q^{72} +(2.00000 + 2.00000i) q^{73} -10.0000 q^{74} +(-14.0000 - 2.00000i) q^{75} -4.00000i q^{76} +(1.00000 - 1.00000i) q^{77} +(-16.0000 - 16.0000i) q^{78} +10.0000 q^{79} +(4.00000 - 8.00000i) q^{80} -1.00000 q^{81} +(-6.00000 - 6.00000i) q^{82} +(-1.00000 + 1.00000i) q^{83} +8.00000i q^{84} +(2.00000 + 6.00000i) q^{85} -2.00000 q^{86} +(4.00000 + 4.00000i) q^{87} +(2.00000 + 2.00000i) q^{88} +6.00000i q^{89} +(5.00000 + 15.0000i) q^{90} -8.00000i q^{91} +(8.00000 + 8.00000i) q^{92} +(16.0000 + 16.0000i) q^{93} +8.00000i q^{94} +(2.00000 - 4.00000i) q^{95} -16.0000 q^{96} +(-3.00000 + 3.00000i) q^{97} +(5.00000 - 5.00000i) q^{98} -5.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q + 2 q^{2} + 4 q^{3} - 2 q^{5} + 8 q^{6} + 2 q^{7} - 4 q^{8} - 6 q^{10} + 8 q^{12} - 8 q^{13} + 4 q^{15} - 8 q^{16} + 4 q^{17} + 10 q^{18} - 4 q^{19} - 8 q^{20} + 8 q^{21} + 2 q^{22} + 8 q^{23} - 6 q^{25}+ \cdots - 10 q^{99}+O(q^{100})$ 2 * q + 2 * q^2 + 4 * q^3 - 2 * q^5 + 8 * q^6 + 2 * q^7 - 4 * q^8 - 6 * q^10 + 8 * q^12 - 8 * q^13 + 4 * q^15 - 8 * q^16 + 4 * q^17 + 10 * q^18 - 4 * q^19 - 8 * q^20 + 8 * q^21 + 2 * q^22 + 8 * q^23 - 6 * q^25 - 8 * q^27 - 4 * q^28 - 8 * q^30 - 8 * q^32 - 4 * q^33 + 8 * q^34 - 6 * q^35 + 20 * q^36 - 10 * q^37 - 4 * q^38 - 32 * q^39 - 4 * q^40 - 12 * q^41 + 8 * q^42 - 2 * q^43 + 4 * q^44 + 20 * q^45 + 16 * q^46 + 8 * q^47 - 16 * q^48 + 2 * q^50 + 16 * q^52 + 18 * q^53 + 4 * q^55 - 8 * q^56 - 8 * q^57 - 4 * q^58 + 16 * q^59 - 24 * q^60 - 20 * q^61 - 16 * q^62 + 10 * q^63 + 24 * q^65 + 8 * q^68 - 8 * q^70 + 20 * q^72 + 4 * q^73 - 20 * q^74 - 28 * q^75 + 2 * q^77 - 32 * q^78 + 20 * q^79 + 8 * q^80 - 2 * q^81 - 12 * q^82 - 2 * q^83 + 4 * q^85 - 4 * q^86 + 8 * q^87 + 4 * q^88 + 10 * q^90 + 16 * q^92 + 32 * q^93 + 4 * q^95 - 32 * q^96 - 6 * q^97 + 10 * q^98 - 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$ .

$n$	$101$	$111$	$177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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

)

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

$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$3$	2.00000	−	2.00000i	1.15470	−	1.15470i	0.169102	−	0.985599i	$-0.445913\pi$
$3$	2.00000	−	2.00000i	1.15470	−	1.15470i	0.985599	−	0.169102i	$-0.0540867\pi$
$4$			2.00000i			1.00000i
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$6$	4.00000			1.63299
$7$	1.00000	+	1.00000i	0.377964	+	0.377964i	0.870367	−	0.492403i	$-0.163881\pi$
$7$	1.00000	+	1.00000i	0.377964	+	0.377964i	−0.492403	+	0.870367i	$0.663881\pi$
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$		−	5.00000i		−	1.66667i
$10$	−3.00000	+	1.00000i	−0.948683	+	0.316228i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	4.00000	+	4.00000i	1.15470	+	1.15470i
$13$	−4.00000	−	4.00000i	−1.10940	−	1.10940i	−0.993229	−	0.116171i	$-0.962938\pi$
$13$	−4.00000	−	4.00000i	−1.10940	−	1.10940i	−0.116171	−	0.993229i	$-0.537062\pi$
$14$			2.00000i			0.534522i
$15$	2.00000	+	6.00000i	0.516398	+	1.54919i
$16$	−4.00000			−1.00000
$17$	2.00000	−	2.00000i	0.485071	−	0.485071i	−0.421676	−	0.906747i	$-0.638558\pi$
$17$	2.00000	−	2.00000i	0.485071	−	0.485071i	0.906747	+	0.421676i	$0.138558\pi$
$18$	5.00000	−	5.00000i	1.17851	−	1.17851i
$19$	−2.00000			−0.458831			−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000			−0.458831			−0.229416	+	0.973329i	$0.573682\pi$
$20$	−4.00000	−	2.00000i	−0.894427	−	0.447214i
$21$	4.00000			0.872872
$22$	1.00000	−	1.00000i	0.213201	−	0.213201i
$23$	4.00000	−	4.00000i	0.834058	−	0.834058i	−0.154011	−	0.988069i	$-0.549219\pi$
$23$	4.00000	−	4.00000i	0.834058	−	0.834058i	0.988069	+	0.154011i	$0.0492193\pi$
$24$			8.00000i			1.63299i
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$		−	8.00000i		−	1.56893i
$27$	−4.00000	−	4.00000i	−0.769800	−	0.769800i
$28$	−2.00000	+	2.00000i	−0.377964	+	0.377964i
$29$			2.00000i			0.371391i	0.982607	+	0.185695i	$0.0594537\pi$
$29$			2.00000i			0.371391i	−0.982607	+	0.185695i	$0.940546\pi$
$30$	−4.00000	+	8.00000i	−0.730297	+	1.46059i
$31$			8.00000i			1.43684i	0.695608	+	0.718421i	$0.255135\pi$
$31$			8.00000i			1.43684i	−0.695608	+	0.718421i	$0.744865\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$	−2.00000	−	2.00000i	−0.348155	−	0.348155i
$34$	4.00000			0.685994
$35$	−3.00000	+	1.00000i	−0.507093	+	0.169031i
$36$	10.0000			1.66667
$37$	−5.00000	+	5.00000i	−0.821995	+	0.821995i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$	−5.00000	+	5.00000i	−0.821995	+	0.821995i	0.164399	+	0.986394i	$0.447432\pi$
$38$	−2.00000	−	2.00000i	−0.324443	−	0.324443i
$39$	−16.0000			−2.56205
$40$	−2.00000	−	6.00000i	−0.316228	−	0.948683i
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$	4.00000	+	4.00000i	0.617213	+	0.617213i
$43$	−1.00000	+	1.00000i	−0.152499	+	0.152499i	−0.779233	−	0.626734i	$-0.784391\pi$
$43$	−1.00000	+	1.00000i	−0.152499	+	0.152499i	0.626734	+	0.779233i	$0.284391\pi$
$44$	2.00000			0.301511
$45$	10.0000	+	5.00000i	1.49071	+	0.745356i
$46$	8.00000			1.17954
$47$	4.00000	+	4.00000i	0.583460	+	0.583460i	0.935852	−	0.352392i	$-0.114632\pi$
$47$	4.00000	+	4.00000i	0.583460	+	0.583460i	−0.352392	+	0.935852i	$0.614632\pi$
$48$	−8.00000	+	8.00000i	−1.15470	+	1.15470i
$49$		−	5.00000i		−	0.714286i
$50$	1.00000	−	7.00000i	0.141421	−	0.989949i
$51$		−	8.00000i		−	1.12022i
$52$	8.00000	−	8.00000i	1.10940	−	1.10940i
$53$	9.00000	+	9.00000i	1.23625	+	1.23625i	0.961524	+	0.274721i	$0.0885855\pi$
$53$	9.00000	+	9.00000i	1.23625	+	1.23625i	0.274721	+	0.961524i	$0.411414\pi$
$54$		−	8.00000i		−	1.08866i
$55$	2.00000	+	1.00000i	0.269680	+	0.134840i
$56$	−4.00000			−0.534522
$57$	−4.00000	+	4.00000i	−0.529813	+	0.529813i
$58$	−2.00000	+	2.00000i	−0.262613	+	0.262613i
$59$	8.00000			1.04151			0.520756	−	0.853706i	$-0.325650\pi$
$59$	8.00000			1.04151			0.520756	+	0.853706i	$0.325650\pi$
$60$	−12.0000	+	4.00000i	−1.54919	+	0.516398i
$61$	−10.0000			−1.28037			−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000			−1.28037			−0.640184	+	0.768221i	$0.721142\pi$
$62$	−8.00000	+	8.00000i	−1.01600	+	1.01600i
$63$	5.00000	−	5.00000i	0.629941	−	0.629941i
$64$		−	8.00000i		−	1.00000i
$65$	12.0000	−	4.00000i	1.48842	−	0.496139i
$66$		−	4.00000i		−	0.492366i
$67$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$67$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$68$	4.00000	+	4.00000i	0.485071	+	0.485071i
$69$		−	16.0000i		−	1.92617i
$70$	−4.00000	−	2.00000i	−0.478091	−	0.239046i
$71$		−	12.0000i		−	1.42414i	−0.702109	−	0.712069i	$-0.747758\pi$
$71$		−	12.0000i		−	1.42414i	0.702109	−	0.712069i	$-0.252242\pi$
$72$	10.0000	+	10.0000i	1.17851	+	1.17851i
$73$	2.00000	+	2.00000i	0.234082	+	0.234082i	0.814394	−	0.580312i	$-0.197069\pi$
$73$	2.00000	+	2.00000i	0.234082	+	0.234082i	−0.580312	+	0.814394i	$0.697069\pi$
$74$	−10.0000			−1.16248
$75$	−14.0000	−	2.00000i	−1.61658	−	0.230940i
$76$		−	4.00000i		−	0.458831i
$77$	1.00000	−	1.00000i	0.113961	−	0.113961i
$78$	−16.0000	−	16.0000i	−1.81164	−	1.81164i
$79$	10.0000			1.12509			0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000			1.12509			0.562544	+	0.826767i	$0.309823\pi$
$80$	4.00000	−	8.00000i	0.447214	−	0.894427i
$81$	−1.00000			−0.111111
$82$	−6.00000	−	6.00000i	−0.662589	−	0.662589i
$83$	−1.00000	+	1.00000i	−0.109764	+	0.109764i	−0.759856	−	0.650092i	$-0.774731\pi$
$83$	−1.00000	+	1.00000i	−0.109764	+	0.109764i	0.650092	+	0.759856i	$0.274731\pi$
$84$			8.00000i			0.872872i
$85$	2.00000	+	6.00000i	0.216930	+	0.650791i
$86$	−2.00000			−0.215666
$87$	4.00000	+	4.00000i	0.428845	+	0.428845i
$88$	2.00000	+	2.00000i	0.213201	+	0.213201i
$89$			6.00000i			0.635999i	0.948091	+	0.317999i	$0.103011\pi$
$89$			6.00000i			0.635999i	−0.948091	+	0.317999i	$0.896989\pi$
$90$	5.00000	+	15.0000i	0.527046	+	1.58114i
$91$		−	8.00000i		−	0.838628i
$92$	8.00000	+	8.00000i	0.834058	+	0.834058i
$93$	16.0000	+	16.0000i	1.65912	+	1.65912i
$94$			8.00000i			0.825137i
$95$	2.00000	−	4.00000i	0.205196	−	0.410391i
$96$	−16.0000			−1.63299
$97$	−3.00000	+	3.00000i	−0.304604	+	0.304604i	−0.842812	−	0.538208i	$-0.819101\pi$
$97$	−3.00000	+	3.00000i	−0.304604	+	0.304604i	0.538208	+	0.842812i	$0.319101\pi$
$98$	5.00000	−	5.00000i	0.505076	−	0.505076i
$99$	−5.00000			−0.502519
$100$	8.00000	−	6.00000i	0.800000	−	0.600000i
$101$	−14.0000			−1.39305			−0.696526	−	0.717532i	$-0.745272\pi$
$101$	−14.0000			−1.39305			−0.696526	+	0.717532i	$0.745272\pi$
$102$	8.00000	−	8.00000i	0.792118	−	0.792118i
$103$	6.00000	−	6.00000i	0.591198	−	0.591198i	−0.346757	−	0.937955i	$-0.612717\pi$
$103$	6.00000	−	6.00000i	0.591198	−	0.591198i	0.937955	+	0.346757i	$0.112717\pi$
$104$	16.0000			1.56893
$105$	−4.00000	+	8.00000i	−0.390360	+	0.780720i
$106$			18.0000i			1.74831i
$107$	13.0000	+	13.0000i	1.25676	+	1.25676i	0.952632	+	0.304125i	$0.0983642\pi$
$107$	13.0000	+	13.0000i	1.25676	+	1.25676i	0.304125	+	0.952632i	$0.401636\pi$
$108$	8.00000	−	8.00000i	0.769800	−	0.769800i
$109$			2.00000i			0.191565i	0.995402	+	0.0957826i	$0.0305354\pi$
$109$			2.00000i			0.191565i	−0.995402	+	0.0957826i	$0.969465\pi$
$110$	1.00000	+	3.00000i	0.0953463	+	0.286039i
$111$			20.0000i			1.89832i
$112$	−4.00000	−	4.00000i	−0.377964	−	0.377964i
$113$	−1.00000	−	1.00000i	−0.0940721	−	0.0940721i	0.658505	−	0.752577i	$-0.271189\pi$
$113$	−1.00000	−	1.00000i	−0.0940721	−	0.0940721i	−0.752577	+	0.658505i	$0.771189\pi$
$114$	−8.00000			−0.749269
$115$	4.00000	+	12.0000i	0.373002	+	1.11901i
$116$	−4.00000			−0.371391
$117$	−20.0000	+	20.0000i	−1.84900	+	1.84900i
$118$	8.00000	+	8.00000i	0.736460	+	0.736460i
$119$	4.00000			0.366679
$120$	−16.0000	−	8.00000i	−1.46059	−	0.730297i
$121$	−1.00000			−0.0909091
$122$	−10.0000	−	10.0000i	−0.905357	−	0.905357i
$123$	−12.0000	+	12.0000i	−1.08200	+	1.08200i
$124$	−16.0000			−1.43684
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$	10.0000			0.890871
$127$	−1.00000	−	1.00000i	−0.0887357	−	0.0887357i	0.661346	−	0.750081i	$-0.269986\pi$
$127$	−1.00000	−	1.00000i	−0.0887357	−	0.0887357i	−0.750081	+	0.661346i	$0.769986\pi$
$128$	8.00000	−	8.00000i	0.707107	−	0.707107i
$129$			4.00000i			0.352180i
$130$	16.0000	+	8.00000i	1.40329	+	0.701646i
$131$		−	6.00000i		−	0.524222i	−0.965038	−	0.262111i	$-0.915581\pi$
$131$		−	6.00000i		−	0.524222i	0.965038	−	0.262111i	$-0.0844187\pi$
$132$	4.00000	−	4.00000i	0.348155	−	0.348155i
$133$	−2.00000	−	2.00000i	−0.173422	−	0.173422i
$134$		0			0
$135$	12.0000	−	4.00000i	1.03280	−	0.344265i
$136$			8.00000i			0.685994i
$137$	7.00000	−	7.00000i	0.598050	−	0.598050i	−0.341743	−	0.939793i	$-0.611017\pi$
$137$	7.00000	−	7.00000i	0.598050	−	0.598050i	0.939793	+	0.341743i	$0.111017\pi$
$138$	16.0000	−	16.0000i	1.36201	−	1.36201i
$139$	−20.0000			−1.69638			−0.848189	−	0.529694i	$-0.822307\pi$
$139$	−20.0000			−1.69638			−0.848189	+	0.529694i	$0.822307\pi$
$140$	−2.00000	−	6.00000i	−0.169031	−	0.507093i
$141$	16.0000			1.34744
$142$	12.0000	−	12.0000i	1.00702	−	1.00702i
$143$	−4.00000	+	4.00000i	−0.334497	+	0.334497i
$144$			20.0000i			1.66667i
$145$	−4.00000	−	2.00000i	−0.332182	−	0.166091i
$146$			4.00000i			0.331042i
$147$	−10.0000	−	10.0000i	−0.824786	−	0.824786i
$148$	−10.0000	−	10.0000i	−0.821995	−	0.821995i
$149$		−	18.0000i		−	1.47462i	−0.675556	−	0.737309i	$-0.736096\pi$
$149$		−	18.0000i		−	1.47462i	0.675556	−	0.737309i	$-0.263904\pi$
$150$	−12.0000	−	16.0000i	−0.979796	−	1.30639i
$151$			10.0000i			0.813788i	0.913475	+	0.406894i	$0.133388\pi$
$151$			10.0000i			0.813788i	−0.913475	+	0.406894i	$0.866612\pi$
$152$	4.00000	−	4.00000i	0.324443	−	0.324443i
$153$	−10.0000	−	10.0000i	−0.808452	−	0.808452i
$154$	2.00000			0.161165
$155$	−16.0000	−	8.00000i	−1.28515	−	0.642575i
$156$		−	32.0000i		−	2.56205i
$157$	3.00000	−	3.00000i	0.239426	−	0.239426i	−0.577186	−	0.816612i	$-0.695849\pi$
$157$	3.00000	−	3.00000i	0.239426	−	0.239426i	0.816612	+	0.577186i	$0.195849\pi$
$158$	10.0000	+	10.0000i	0.795557	+	0.795557i
$159$	36.0000			2.85499
$160$	12.0000	−	4.00000i	0.948683	−	0.316228i
$161$	8.00000			0.630488
$162$	−1.00000	−	1.00000i	−0.0785674	−	0.0785674i
$163$	−6.00000	+	6.00000i	−0.469956	+	0.469956i	−0.901900	−	0.431944i	$-0.857828\pi$
$163$	−6.00000	+	6.00000i	−0.469956	+	0.469956i	0.431944	+	0.901900i	$0.357828\pi$
$164$		−	12.0000i		−	0.937043i
$165$	6.00000	−	2.00000i	0.467099	−	0.155700i
$166$	−2.00000			−0.155230
$167$	−3.00000	−	3.00000i	−0.232147	−	0.232147i	0.581441	−	0.813588i	$-0.302489\pi$
$167$	−3.00000	−	3.00000i	−0.232147	−	0.232147i	−0.813588	+	0.581441i	$0.802489\pi$
$168$	−8.00000	+	8.00000i	−0.617213	+	0.617213i
$169$			19.0000i			1.46154i
$170$	−4.00000	+	8.00000i	−0.306786	+	0.613572i
$171$			10.0000i			0.764719i
$172$	−2.00000	−	2.00000i	−0.152499	−	0.152499i
$173$	−2.00000	−	2.00000i	−0.152057	−	0.152057i	0.626979	−	0.779036i	$-0.284291\pi$
$173$	−2.00000	−	2.00000i	−0.152057	−	0.152057i	−0.779036	+	0.626979i	$0.784291\pi$
$174$			8.00000i			0.606478i
$175$	1.00000	−	7.00000i	0.0755929	−	0.529150i
$176$			4.00000i			0.301511i
$177$	16.0000	−	16.0000i	1.20263	−	1.20263i
$178$	−6.00000	+	6.00000i	−0.449719	+	0.449719i
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$	−10.0000	+	20.0000i	−0.745356	+	1.49071i
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$	8.00000	−	8.00000i	0.592999	−	0.592999i
$183$	−20.0000	+	20.0000i	−1.47844	+	1.47844i
$184$			16.0000i			1.17954i
$185$	−5.00000	−	15.0000i	−0.367607	−	1.10282i
$186$			32.0000i			2.34635i
$187$	−2.00000	−	2.00000i	−0.146254	−	0.146254i
$188$	−8.00000	+	8.00000i	−0.583460	+	0.583460i
$189$		−	8.00000i		−	0.581914i
$190$	6.00000	−	2.00000i	0.435286	−	0.145095i
$191$		−	4.00000i		−	0.289430i	−0.989473	−	0.144715i	$-0.953773\pi$
$191$		−	4.00000i		−	0.289430i	0.989473	−	0.144715i	$-0.0462265\pi$
$192$	−16.0000	−	16.0000i	−1.15470	−	1.15470i
$193$	10.0000	+	10.0000i	0.719816	+	0.719816i	0.968567	−	0.248752i	$-0.0800203\pi$
$193$	10.0000	+	10.0000i	0.719816	+	0.719816i	−0.248752	+	0.968567i	$0.580020\pi$
$194$	−6.00000			−0.430775
$195$	16.0000	−	32.0000i	1.14578	−	2.29157i
$196$	10.0000			0.714286
$197$	−2.00000	+	2.00000i	−0.142494	+	0.142494i	−0.774755	−	0.632261i	$-0.782127\pi$
$197$	−2.00000	+	2.00000i	−0.142494	+	0.142494i	0.632261	+	0.774755i	$0.282127\pi$
$198$	−5.00000	−	5.00000i	−0.355335	−	0.355335i
$199$	−4.00000			−0.283552			−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000			−0.283552			−0.141776	+	0.989899i	$0.545281\pi$
$200$	14.0000	+	2.00000i	0.989949	+	0.141421i
$201$		0			0
$202$	−14.0000	−	14.0000i	−0.985037	−	0.985037i
$203$	−2.00000	+	2.00000i	−0.140372	+	0.140372i
$204$	16.0000			1.12022
$205$	6.00000	−	12.0000i	0.419058	−	0.838116i
$206$	12.0000			0.836080
$207$	−20.0000	−	20.0000i	−1.39010	−	1.39010i
$208$	16.0000	+	16.0000i	1.10940	+	1.10940i
$209$			2.00000i			0.138343i
$210$	−12.0000	+	4.00000i	−0.828079	+	0.276026i
$211$		−	22.0000i		−	1.51454i	−0.653101	−	0.757271i	$-0.726532\pi$
$211$		−	22.0000i		−	1.51454i	0.653101	−	0.757271i	$-0.273468\pi$
$212$	−18.0000	+	18.0000i	−1.23625	+	1.23625i
$213$	−24.0000	−	24.0000i	−1.64445	−	1.64445i
$214$			26.0000i			1.77732i
$215$	−1.00000	−	3.00000i	−0.0681994	−	0.204598i
$216$	16.0000			1.08866
$217$	−8.00000	+	8.00000i	−0.543075	+	0.543075i
$218$	−2.00000	+	2.00000i	−0.135457	+	0.135457i
$219$	8.00000			0.540590
$220$	−2.00000	+	4.00000i	−0.134840	+	0.269680i
$221$	−16.0000			−1.07628
$222$	−20.0000	+	20.0000i	−1.34231	+	1.34231i
$223$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$223$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$224$		−	8.00000i		−	0.534522i
$225$	−20.0000	+	15.0000i	−1.33333	+	1.00000i
$226$		−	2.00000i		−	0.133038i
$227$	5.00000	+	5.00000i	0.331862	+	0.331862i	0.853293	−	0.521431i	$-0.174602\pi$
$227$	5.00000	+	5.00000i	0.331862	+	0.331862i	−0.521431	+	0.853293i	$0.674602\pi$
$228$	−8.00000	−	8.00000i	−0.529813	−	0.529813i
$229$		−	4.00000i		−	0.264327i	−0.991228	−	0.132164i	$-0.957808\pi$
$229$		−	4.00000i		−	0.264327i	0.991228	−	0.132164i	$-0.0421925\pi$
$230$	−8.00000	+	16.0000i	−0.527504	+	1.05501i
$231$		−	4.00000i		−	0.263181i
$232$	−4.00000	−	4.00000i	−0.262613	−	0.262613i
$233$	20.0000	+	20.0000i	1.31024	+	1.31024i	0.921234	+	0.389010i	$0.127183\pi$
$233$	20.0000	+	20.0000i	1.31024	+	1.31024i	0.389010	+	0.921234i	$0.372817\pi$
$234$	−40.0000			−2.61488
$235$	−12.0000	+	4.00000i	−0.782794	+	0.260931i
$236$			16.0000i			1.04151i
$237$	20.0000	−	20.0000i	1.29914	−	1.29914i
$238$	4.00000	+	4.00000i	0.259281	+	0.259281i
$239$	−22.0000			−1.42306			−0.711531	−	0.702655i	$-0.751998\pi$
$239$	−22.0000			−1.42306			−0.711531	+	0.702655i	$0.751998\pi$
$240$	−8.00000	−	24.0000i	−0.516398	−	1.54919i
$241$	10.0000			0.644157			0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000			0.644157			0.322078	+	0.946713i	$0.395619\pi$
$242$	−1.00000	−	1.00000i	−0.0642824	−	0.0642824i
$243$	10.0000	−	10.0000i	0.641500	−	0.641500i
$244$		−	20.0000i		−	1.28037i
$245$	10.0000	+	5.00000i	0.638877	+	0.319438i
$246$	−24.0000			−1.53018
$247$	8.00000	+	8.00000i	0.509028	+	0.509028i
$248$	−16.0000	−	16.0000i	−1.01600	−	1.01600i
$249$			4.00000i			0.253490i
$250$	13.0000	+	9.00000i	0.822192	+	0.569210i
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$	10.0000	+	10.0000i	0.629941	+	0.629941i
$253$	−4.00000	−	4.00000i	−0.251478	−	0.251478i
$254$		−	2.00000i		−	0.125491i
$255$	16.0000	+	8.00000i	1.00196	+	0.500979i
$256$	16.0000			1.00000
$257$	1.00000	−	1.00000i	0.0623783	−	0.0623783i	−0.675229	−	0.737608i	$-0.735955\pi$
$257$	1.00000	−	1.00000i	0.0623783	−	0.0623783i	0.737608	+	0.675229i	$0.235955\pi$
$258$	−4.00000	+	4.00000i	−0.249029	+	0.249029i
$259$	−10.0000			−0.621370
$260$	8.00000	+	24.0000i	0.496139	+	1.48842i
$261$	10.0000			0.618984
$262$	6.00000	−	6.00000i	0.370681	−	0.370681i
$263$	5.00000	−	5.00000i	0.308313	−	0.308313i	−0.535942	−	0.844255i	$-0.680043\pi$
$263$	5.00000	−	5.00000i	0.308313	−	0.308313i	0.844255	+	0.535942i	$0.180043\pi$
$264$	8.00000			0.492366
$265$	−27.0000	+	9.00000i	−1.65860	+	0.552866i
$266$		−	4.00000i		−	0.245256i
$267$	12.0000	+	12.0000i	0.734388	+	0.734388i
$268$		0			0
$269$		−	26.0000i		−	1.58525i	−0.609711	−	0.792624i	$-0.708714\pi$
$269$		−	26.0000i		−	1.58525i	0.609711	−	0.792624i	$-0.291286\pi$
$270$	16.0000	+	8.00000i	0.973729	+	0.486864i
$271$			14.0000i			0.850439i	0.905090	+	0.425220i	$0.139803\pi$
$271$			14.0000i			0.850439i	−0.905090	+	0.425220i	$0.860197\pi$
$272$	−8.00000	+	8.00000i	−0.485071	+	0.485071i
$273$	−16.0000	−	16.0000i	−0.968364	−	0.968364i
$274$	14.0000			0.845771
$275$	−4.00000	+	3.00000i	−0.241209	+	0.180907i
$276$	32.0000			1.92617
$277$	−8.00000	+	8.00000i	−0.480673	+	0.480673i	−0.905347	−	0.424673i	$-0.860389\pi$
$277$	−8.00000	+	8.00000i	−0.480673	+	0.480673i	0.424673	+	0.905347i	$0.360389\pi$
$278$	−20.0000	−	20.0000i	−1.19952	−	1.19952i
$279$	40.0000			2.39474
$280$	4.00000	−	8.00000i	0.239046	−	0.478091i
$281$	−10.0000			−0.596550			−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000			−0.596550			−0.298275	+	0.954480i	$0.596411\pi$
$282$	16.0000	+	16.0000i	0.952786	+	0.952786i
$283$	21.0000	−	21.0000i	1.24832	−	1.24832i	0.291859	−	0.956461i	$-0.405726\pi$
$283$	21.0000	−	21.0000i	1.24832	−	1.24832i	0.956461	−	0.291859i	$-0.0942738\pi$
$284$	24.0000			1.42414
$285$	−4.00000	−	12.0000i	−0.236940	−	0.710819i
$286$	−8.00000			−0.473050
$287$	−6.00000	−	6.00000i	−0.354169	−	0.354169i
$288$	−20.0000	+	20.0000i	−1.17851	+	1.17851i
$289$			9.00000i			0.529412i
$290$	−2.00000	−	6.00000i	−0.117444	−	0.352332i
$291$			12.0000i			0.703452i
$292$	−4.00000	+	4.00000i	−0.234082	+	0.234082i
$293$	−8.00000	−	8.00000i	−0.467365	−	0.467365i	0.433695	−	0.901060i	$-0.357210\pi$
$293$	−8.00000	−	8.00000i	−0.467365	−	0.467365i	−0.901060	+	0.433695i	$0.857210\pi$
$294$		−	20.0000i		−	1.16642i
$295$	−8.00000	+	16.0000i	−0.465778	+	0.931556i
$296$		−	20.0000i		−	1.16248i
$297$	−4.00000	+	4.00000i	−0.232104	+	0.232104i
$298$	18.0000	−	18.0000i	1.04271	−	1.04271i
$299$	−32.0000			−1.85061
$300$	4.00000	−	28.0000i	0.230940	−	1.61658i
$301$	−2.00000			−0.115278
$302$	−10.0000	+	10.0000i	−0.575435	+	0.575435i
$303$	−28.0000	+	28.0000i	−1.60856	+	1.60856i
$304$	8.00000			0.458831
$305$	10.0000	−	20.0000i	0.572598	−	1.14520i
$306$		−	20.0000i		−	1.14332i
$307$	−15.0000	−	15.0000i	−0.856095	−	0.856095i	0.134780	−	0.990876i	$-0.456967\pi$
$307$	−15.0000	−	15.0000i	−0.856095	−	0.856095i	−0.990876	+	0.134780i	$0.956967\pi$
$308$	2.00000	+	2.00000i	0.113961	+	0.113961i
$309$		−	24.0000i		−	1.36531i
$310$	−8.00000	−	24.0000i	−0.454369	−	1.36311i
$311$		−	4.00000i		−	0.226819i	−0.993548	−	0.113410i	$-0.963823\pi$
$311$		−	4.00000i		−	0.226819i	0.993548	−	0.113410i	$-0.0361772\pi$
$312$	32.0000	−	32.0000i	1.81164	−	1.81164i
$313$	−9.00000	−	9.00000i	−0.508710	−	0.508710i	0.405420	−	0.914130i	$-0.367125\pi$
$313$	−9.00000	−	9.00000i	−0.508710	−	0.508710i	−0.914130	+	0.405420i	$0.867125\pi$
$314$	6.00000			0.338600
$315$	5.00000	+	15.0000i	0.281718	+	0.845154i
$316$			20.0000i			1.12509i
$317$	−21.0000	+	21.0000i	−1.17948	+	1.17948i	−0.199600	+	0.979877i	$0.563964\pi$
$317$	−21.0000	+	21.0000i	−1.17948	+	1.17948i	−0.979877	+	0.199600i	$0.936036\pi$
$318$	36.0000	+	36.0000i	2.01878	+	2.01878i
$319$	2.00000			0.111979
$320$	16.0000	+	8.00000i	0.894427	+	0.447214i
$321$	52.0000			2.90236
$322$	8.00000	+	8.00000i	0.445823	+	0.445823i
$323$	−4.00000	+	4.00000i	−0.222566	+	0.222566i
$324$		−	2.00000i		−	0.111111i
$325$	−4.00000	+	28.0000i	−0.221880	+	1.55316i
$326$	−12.0000			−0.664619
$327$	4.00000	+	4.00000i	0.221201	+	0.221201i
$328$	12.0000	−	12.0000i	0.662589	−	0.662589i
$329$			8.00000i			0.441054i
$330$	8.00000	+	4.00000i	0.440386	+	0.220193i
$331$			8.00000i			0.439720i	0.975531	+	0.219860i	$0.0705600\pi$
$331$			8.00000i			0.439720i	−0.975531	+	0.219860i	$0.929440\pi$
$332$	−2.00000	−	2.00000i	−0.109764	−	0.109764i
$333$	25.0000	+	25.0000i	1.36999	+	1.36999i
$334$		−	6.00000i		−	0.328305i
$335$		0			0
$336$	−16.0000			−0.872872
$337$	18.0000	−	18.0000i	0.980522	−	0.980522i	−0.0192914	−	0.999814i	$-0.506141\pi$
$337$	18.0000	−	18.0000i	0.980522	−	0.980522i	0.999814	+	0.0192914i	$0.00614103\pi$
$338$	−19.0000	+	19.0000i	−1.03346	+	1.03346i
$339$	−4.00000			−0.217250
$340$	−12.0000	+	4.00000i	−0.650791	+	0.216930i
$341$	8.00000			0.433224
$342$	−10.0000	+	10.0000i	−0.540738	+	0.540738i
$343$	12.0000	−	12.0000i	0.647939	−	0.647939i
$344$		−	4.00000i		−	0.215666i
$345$	32.0000	+	16.0000i	1.72282	+	0.861411i
$346$		−	4.00000i		−	0.215041i
$347$	−5.00000	−	5.00000i	−0.268414	−	0.268414i	0.560047	−	0.828461i	$-0.310783\pi$
$347$	−5.00000	−	5.00000i	−0.268414	−	0.268414i	−0.828461	+	0.560047i	$0.810783\pi$
$348$	−8.00000	+	8.00000i	−0.428845	+	0.428845i
$349$			6.00000i			0.321173i	0.987022	+	0.160586i	$0.0513385\pi$
$349$			6.00000i			0.321173i	−0.987022	+	0.160586i	$0.948662\pi$
$350$	8.00000	−	6.00000i	0.427618	−	0.320713i
$351$			32.0000i			1.70803i
$352$	−4.00000	+	4.00000i	−0.213201	+	0.213201i
$353$	13.0000	+	13.0000i	0.691920	+	0.691920i	0.962654	−	0.270734i	$-0.0872664\pi$
$353$	13.0000	+	13.0000i	0.691920	+	0.691920i	−0.270734	+	0.962654i	$0.587266\pi$
$354$	32.0000			1.70078
$355$	24.0000	+	12.0000i	1.27379	+	0.636894i
$356$	−12.0000			−0.635999
$357$	8.00000	−	8.00000i	0.423405	−	0.423405i
$358$	12.0000	+	12.0000i	0.634220	+	0.634220i
$359$	22.0000			1.16112			0.580558	−	0.814219i	$-0.302835\pi$
$359$	22.0000			1.16112			0.580558	+	0.814219i	$0.302835\pi$
$360$	−30.0000	+	10.0000i	−1.58114	+	0.527046i
$361$	−15.0000			−0.789474
$362$	−16.0000	−	16.0000i	−0.840941	−	0.840941i
$363$	−2.00000	+	2.00000i	−0.104973	+	0.104973i
$364$	16.0000			0.838628
$365$	−6.00000	+	2.00000i	−0.314054	+	0.104685i
$366$	−40.0000			−2.09083
$367$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$367$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$368$	−16.0000	+	16.0000i	−0.834058	+	0.834058i
$369$			30.0000i			1.56174i
$370$	10.0000	−	20.0000i	0.519875	−	1.03975i
$371$			18.0000i			0.934513i
$372$	−32.0000	+	32.0000i	−1.65912	+	1.65912i
$373$	−14.0000	−	14.0000i	−0.724893	−	0.724893i	0.244705	−	0.969598i	$-0.421309\pi$
$373$	−14.0000	−	14.0000i	−0.724893	−	0.724893i	−0.969598	+	0.244705i	$0.921309\pi$
$374$		−	4.00000i		−	0.206835i
$375$	18.0000	−	26.0000i	0.929516	−	1.34263i
$376$	−16.0000			−0.825137
$377$	8.00000	−	8.00000i	0.412021	−	0.412021i
$378$	8.00000	−	8.00000i	0.411476	−	0.411476i
$379$	−24.0000			−1.23280			−0.616399	−	0.787434i	$-0.711409\pi$
$379$	−24.0000			−1.23280			−0.616399	+	0.787434i	$0.711409\pi$
$380$	8.00000	+	4.00000i	0.410391	+	0.205196i
$381$	−4.00000			−0.204926
$382$	4.00000	−	4.00000i	0.204658	−	0.204658i
$383$	−2.00000	+	2.00000i	−0.102195	+	0.102195i	−0.756356	−	0.654161i	$-0.773022\pi$
$383$	−2.00000	+	2.00000i	−0.102195	+	0.102195i	0.654161	+	0.756356i	$0.273022\pi$
$384$		−	32.0000i		−	1.63299i
$385$	1.00000	+	3.00000i	0.0509647	+	0.152894i
$386$			20.0000i			1.01797i
$387$	5.00000	+	5.00000i	0.254164	+	0.254164i
$388$	−6.00000	−	6.00000i	−0.304604	−	0.304604i
$389$			26.0000i			1.31825i	0.752032	+	0.659126i	$0.229074\pi$
$389$			26.0000i			1.31825i	−0.752032	+	0.659126i	$0.770926\pi$
$390$	48.0000	−	16.0000i	2.43057	−	0.810191i
$391$		−	16.0000i		−	0.809155i
$392$	10.0000	+	10.0000i	0.505076	+	0.505076i
$393$	−12.0000	−	12.0000i	−0.605320	−	0.605320i
$394$	−4.00000			−0.201517
$395$	−10.0000	+	20.0000i	−0.503155	+	1.00631i
$396$		−	10.0000i		−	0.502519i
$397$	−9.00000	+	9.00000i	−0.451697	+	0.451697i	−0.895918	−	0.444220i	$-0.853481\pi$
$397$	−9.00000	+	9.00000i	−0.451697	+	0.451697i	0.444220	+	0.895918i	$0.353481\pi$
$398$	−4.00000	−	4.00000i	−0.200502	−	0.200502i
$399$	−8.00000			−0.400501
$400$	12.0000	+	16.0000i	0.600000	+	0.800000i
$401$	8.00000			0.399501			0.199750	−	0.979847i	$-0.435987\pi$
$401$	8.00000			0.399501			0.199750	+	0.979847i	$0.435987\pi$
$402$		0			0
$403$	32.0000	−	32.0000i	1.59403	−	1.59403i
$404$		−	28.0000i		−	1.39305i
$405$	1.00000	−	2.00000i	0.0496904	−	0.0993808i
$406$	−4.00000			−0.198517
$407$	5.00000	+	5.00000i	0.247841	+	0.247841i
$408$	16.0000	+	16.0000i	0.792118	+	0.792118i
$409$		−	6.00000i		−	0.296681i	−0.988936	−	0.148340i	$-0.952607\pi$
$409$		−	6.00000i		−	0.296681i	0.988936	−	0.148340i	$-0.0473931\pi$
$410$	18.0000	−	6.00000i	0.888957	−	0.296319i
$411$		−	28.0000i		−	1.38114i
$412$	12.0000	+	12.0000i	0.591198	+	0.591198i
$413$	8.00000	+	8.00000i	0.393654	+	0.393654i
$414$		−	40.0000i		−	1.96589i
$415$	−1.00000	−	3.00000i	−0.0490881	−	0.147264i
$416$			32.0000i			1.56893i
$417$	−40.0000	+	40.0000i	−1.95881	+	1.95881i
$418$	−2.00000	+	2.00000i	−0.0978232	+	0.0978232i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$	−16.0000	−	8.00000i	−0.780720	−	0.390360i
$421$	6.00000			0.292422			0.146211	−	0.989253i	$-0.453292\pi$
$421$	6.00000			0.292422			0.146211	+	0.989253i	$0.453292\pi$
$422$	22.0000	−	22.0000i	1.07094	−	1.07094i
$423$	20.0000	−	20.0000i	0.972433	−	0.972433i
$424$	−36.0000			−1.74831
$425$	−14.0000	−	2.00000i	−0.679100	−	0.0970143i
$426$		−	48.0000i		−	2.32561i
$427$	−10.0000	−	10.0000i	−0.483934	−	0.483934i
$428$	−26.0000	+	26.0000i	−1.25676	+	1.25676i
$429$			16.0000i			0.772487i
$430$	2.00000	−	4.00000i	0.0964486	−	0.192897i
$431$		0			0		1.00000			$0$
$431$		0			0		−1.00000			$\pi$
$432$	16.0000	+	16.0000i	0.769800	+	0.769800i
$433$	−21.0000	−	21.0000i	−1.00920	−	1.00920i	−0.999957	−	0.00923827i	$-0.997059\pi$
$433$	−21.0000	−	21.0000i	−1.00920	−	1.00920i	−0.00923827	−	0.999957i	$-0.502941\pi$
$434$	−16.0000			−0.768025
$435$	−12.0000	+	4.00000i	−0.575356	+	0.191785i
$436$	−4.00000			−0.191565
$437$	−8.00000	+	8.00000i	−0.382692	+	0.382692i
$438$	8.00000	+	8.00000i	0.382255	+	0.382255i
$439$	−8.00000			−0.381819			−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000			−0.381819			−0.190910	+	0.981608i	$0.561144\pi$
$440$	−6.00000	+	2.00000i	−0.286039	+	0.0953463i
$441$	−25.0000			−1.19048
$442$	−16.0000	−	16.0000i	−0.761042	−	0.761042i
$443$	10.0000	−	10.0000i	0.475114	−	0.475114i	−0.428451	−	0.903565i	$-0.640940\pi$
$443$	10.0000	−	10.0000i	0.475114	−	0.475114i	0.903565	+	0.428451i	$0.140940\pi$
$444$	−40.0000			−1.89832
$445$	−12.0000	−	6.00000i	−0.568855	−	0.284427i
$446$		0			0
$447$	−36.0000	−	36.0000i	−1.70274	−	1.70274i
$448$	8.00000	−	8.00000i	0.377964	−	0.377964i
$449$			12.0000i			0.566315i	0.959073	+	0.283158i	$0.0913819\pi$
$449$			12.0000i			0.566315i	−0.959073	+	0.283158i	$0.908618\pi$
$450$	−35.0000	−	5.00000i	−1.64992	−	0.235702i
$451$			6.00000i			0.282529i
$452$	2.00000	−	2.00000i	0.0940721	−	0.0940721i
$453$	20.0000	+	20.0000i	0.939682	+	0.939682i
$454$			10.0000i			0.469323i
$455$	16.0000	+	8.00000i	0.750092	+	0.375046i
$456$		−	16.0000i		−	0.749269i
$457$	16.0000	−	16.0000i	0.748448	−	0.748448i	−0.225739	−	0.974188i	$-0.572480\pi$
$457$	16.0000	−	16.0000i	0.748448	−	0.748448i	0.974188	+	0.225739i	$0.0724798\pi$
$458$	4.00000	−	4.00000i	0.186908	−	0.186908i
$459$	−16.0000			−0.746816
$460$	−24.0000	+	8.00000i	−1.11901	+	0.373002i
$461$	10.0000			0.465746			0.232873	−	0.972507i	$-0.425187\pi$
$461$	10.0000			0.465746			0.232873	+	0.972507i	$0.425187\pi$
$462$	4.00000	−	4.00000i	0.186097	−	0.186097i
$463$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$463$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$464$		−	8.00000i		−	0.371391i
$465$	−48.0000	+	16.0000i	−2.22595	+	0.741982i
$466$			40.0000i			1.85296i
$467$	−12.0000	−	12.0000i	−0.555294	−	0.555294i	0.372670	−	0.927964i	$-0.378442\pi$
$467$	−12.0000	−	12.0000i	−0.555294	−	0.555294i	−0.927964	+	0.372670i	$0.878442\pi$
$468$	−40.0000	−	40.0000i	−1.84900	−	1.84900i
$469$		0			0
$470$	−16.0000	−	8.00000i	−0.738025	−	0.369012i
$471$		−	12.0000i		−	0.552931i
$472$	−16.0000	+	16.0000i	−0.736460	+	0.736460i
$473$	1.00000	+	1.00000i	0.0459800	+	0.0459800i
$474$	40.0000			1.83726
$475$	6.00000	+	8.00000i	0.275299	+	0.367065i
$476$			8.00000i			0.366679i
$477$	45.0000	−	45.0000i	2.06041	−	2.06041i
$478$	−22.0000	−	22.0000i	−1.00626	−	1.00626i
$479$	−18.0000			−0.822441			−0.411220	−	0.911536i	$-0.634897\pi$
$479$	−18.0000			−0.822441			−0.411220	+	0.911536i	$0.634897\pi$
$480$	16.0000	−	32.0000i	0.730297	−	1.46059i
$481$	40.0000			1.82384
$482$	10.0000	+	10.0000i	0.455488	+	0.455488i
$483$	16.0000	−	16.0000i	0.728025	−	0.728025i
$484$		−	2.00000i		−	0.0909091i
$485$	−3.00000	−	9.00000i	−0.136223	−	0.408669i
$486$	20.0000			0.907218
$487$	−16.0000	−	16.0000i	−0.725029	−	0.725029i	0.244596	−	0.969625i	$-0.421345\pi$
$487$	−16.0000	−	16.0000i	−0.725029	−	0.725029i	−0.969625	+	0.244596i	$0.921345\pi$
$488$	20.0000	−	20.0000i	0.905357	−	0.905357i
$489$			24.0000i			1.08532i
$490$	5.00000	+	15.0000i	0.225877	+	0.677631i
$491$			12.0000i			0.541552i	0.962642	+	0.270776i	$0.0872803\pi$
$491$			12.0000i			0.541552i	−0.962642	+	0.270776i	$0.912720\pi$
$492$	−24.0000	−	24.0000i	−1.08200	−	1.08200i
$493$	4.00000	+	4.00000i	0.180151	+	0.180151i
$494$			16.0000i			0.719874i
$495$	5.00000	−	10.0000i	0.224733	−	0.449467i
$496$		−	32.0000i		−	1.43684i
$497$	12.0000	−	12.0000i	0.538274	−	0.538274i
$498$	−4.00000	+	4.00000i	−0.179244	+	0.179244i
$499$	−8.00000			−0.358129			−0.179065	−	0.983837i	$-0.557307\pi$
$499$	−8.00000			−0.358129			−0.179065	+	0.983837i	$0.557307\pi$
$500$	4.00000	+	22.0000i	0.178885	+	0.983870i
$501$	−12.0000			−0.536120
$502$		0			0
$503$	−19.0000	+	19.0000i	−0.847168	+	0.847168i	−0.989779	−	0.142611i	$-0.954450\pi$
$503$	−19.0000	+	19.0000i	−0.847168	+	0.847168i	0.142611	+	0.989779i	$0.454450\pi$
$504$			20.0000i			0.890871i
$505$	14.0000	−	28.0000i	0.622992	−	1.24598i
$506$		−	8.00000i		−	0.355643i
$507$	38.0000	+	38.0000i	1.68764	+	1.68764i
$508$	2.00000	−	2.00000i	0.0887357	−	0.0887357i
$509$			28.0000i			1.24108i	0.784176	+	0.620539i	$0.213086\pi$
$509$			28.0000i			1.24108i	−0.784176	+	0.620539i	$0.786914\pi$
$510$	8.00000	+	24.0000i	0.354246	+	1.06274i
$511$			4.00000i			0.176950i
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$	8.00000	+	8.00000i	0.353209	+	0.353209i
$514$	2.00000			0.0882162
$515$	6.00000	+	18.0000i	0.264392	+	0.793175i
$516$	−8.00000			−0.352180
$517$	4.00000	−	4.00000i	0.175920	−	0.175920i
$518$	−10.0000	−	10.0000i	−0.439375	−	0.439375i
$519$	−8.00000			−0.351161
$520$	−16.0000	+	32.0000i	−0.701646	+	1.40329i
$521$	−24.0000			−1.05146			−0.525730	−	0.850652i	$-0.676208\pi$
$521$	−24.0000			−1.05146			−0.525730	+	0.850652i	$0.676208\pi$
$522$	10.0000	+	10.0000i	0.437688	+	0.437688i
$523$	3.00000	−	3.00000i	0.131181	−	0.131181i	−0.638468	−	0.769649i	$-0.720431\pi$
$523$	3.00000	−	3.00000i	0.131181	−	0.131181i	0.769649	+	0.638468i	$0.220431\pi$
$524$	12.0000			0.524222
$525$	−12.0000	−	16.0000i	−0.523723	−	0.698297i
$526$	10.0000			0.436021
$527$	16.0000	+	16.0000i	0.696971	+	0.696971i
$528$	8.00000	+	8.00000i	0.348155	+	0.348155i
$529$		−	9.00000i		−	0.391304i
$530$	−36.0000	−	18.0000i	−1.56374	−	0.781870i
$531$		−	40.0000i		−	1.73585i
$532$	4.00000	−	4.00000i	0.173422	−	0.173422i
$533$	24.0000	+	24.0000i	1.03956	+	1.03956i
$534$			24.0000i			1.03858i
$535$	−39.0000	+	13.0000i	−1.68612	+	0.562039i
$536$		0			0
$537$	24.0000	−	24.0000i	1.03568	−	1.03568i
$538$	26.0000	−	26.0000i	1.12094	−	1.12094i
$539$	−5.00000			−0.215365
$540$	8.00000	+	24.0000i	0.344265	+	1.03280i
$541$	6.00000			0.257960			0.128980	−	0.991647i	$-0.458830\pi$
$541$	6.00000			0.257960			0.128980	+	0.991647i	$0.458830\pi$
$542$	−14.0000	+	14.0000i	−0.601351	+	0.601351i
$543$	−32.0000	+	32.0000i	−1.37325	+	1.37325i
$544$	−16.0000			−0.685994
$545$	−4.00000	−	2.00000i	−0.171341	−	0.0856706i
$546$		−	32.0000i		−	1.36947i
$547$	31.0000	+	31.0000i	1.32546	+	1.32546i	0.909281	+	0.416184i	$0.136633\pi$
$547$	31.0000	+	31.0000i	1.32546	+	1.32546i	0.416184	+	0.909281i	$0.363367\pi$
$548$	14.0000	+	14.0000i	0.598050	+	0.598050i
$549$			50.0000i			2.13395i
$550$	−7.00000	−	1.00000i	−0.298481	−	0.0426401i
$551$		−	4.00000i		−	0.170406i
$552$	32.0000	+	32.0000i	1.36201	+	1.36201i
$553$	10.0000	+	10.0000i	0.425243	+	0.425243i
$554$	−16.0000			−0.679775
$555$	−40.0000	−	20.0000i	−1.69791	−	0.848953i
$556$		−	40.0000i		−	1.69638i
$557$	10.0000	−	10.0000i	0.423714	−	0.423714i	−0.462767	−	0.886480i	$-0.653143\pi$
$557$	10.0000	−	10.0000i	0.423714	−	0.423714i	0.886480	+	0.462767i	$0.153143\pi$
$558$	40.0000	+	40.0000i	1.69334	+	1.69334i
$559$	8.00000			0.338364
$560$	12.0000	−	4.00000i	0.507093	−	0.169031i
$561$	−8.00000			−0.337760
$562$	−10.0000	−	10.0000i	−0.421825	−	0.421825i
$563$	−9.00000	+	9.00000i	−0.379305	+	0.379305i	−0.870851	−	0.491547i	$-0.836432\pi$
$563$	−9.00000	+	9.00000i	−0.379305	+	0.379305i	0.491547	+	0.870851i	$0.336432\pi$
$564$			32.0000i			1.34744i
$565$	3.00000	−	1.00000i	0.126211	−	0.0420703i
$566$	42.0000			1.76539
$567$	−1.00000	−	1.00000i	−0.0419961	−	0.0419961i
$568$	24.0000	+	24.0000i	1.00702	+	1.00702i
$569$			10.0000i			0.419222i	0.977785	+	0.209611i	$0.0672197\pi$
$569$			10.0000i			0.419222i	−0.977785	+	0.209611i	$0.932780\pi$
$570$	8.00000	−	16.0000i	0.335083	−	0.670166i
$571$			4.00000i			0.167395i	0.996491	+	0.0836974i	$0.0266729\pi$
$571$			4.00000i			0.167395i	−0.996491	+	0.0836974i	$0.973327\pi$
$572$	−8.00000	−	8.00000i	−0.334497	−	0.334497i
$573$	−8.00000	−	8.00000i	−0.334205	−	0.334205i
$574$		−	12.0000i		−	0.500870i
$575$	−28.0000	−	4.00000i	−1.16768	−	0.166812i
$576$	−40.0000			−1.66667
$577$	13.0000	−	13.0000i	0.541197	−	0.541197i	−0.382683	−	0.923880i	$-0.625000\pi$
$577$	13.0000	−	13.0000i	0.541197	−	0.541197i	0.923880	+	0.382683i	$0.125000\pi$
$578$	−9.00000	+	9.00000i	−0.374351	+	0.374351i
$579$	40.0000			1.66234
$580$	4.00000	−	8.00000i	0.166091	−	0.332182i
$581$	−2.00000			−0.0829740
$582$	−12.0000	+	12.0000i	−0.497416	+	0.497416i
$583$	9.00000	−	9.00000i	0.372742	−	0.372742i
$584$	−8.00000			−0.331042
$585$	−20.0000	−	60.0000i	−0.826898	−	2.48069i
$586$		−	16.0000i		−	0.660954i
$587$	24.0000	+	24.0000i	0.990586	+	0.990586i	0.999956	−	0.00937009i	$-0.00298264\pi$
$587$	24.0000	+	24.0000i	0.990586	+	0.990586i	−0.00937009	+	0.999956i	$0.502983\pi$
$588$	20.0000	−	20.0000i	0.824786	−	0.824786i
$589$		−	16.0000i		−	0.659269i
$590$	−24.0000	+	8.00000i	−0.988064	+	0.329355i
$591$			8.00000i			0.329076i
$592$	20.0000	−	20.0000i	0.821995	−	0.821995i
$593$	−22.0000	−	22.0000i	−0.903432	−	0.903432i	0.0922996	−	0.995731i	$-0.470578\pi$
$593$	−22.0000	−	22.0000i	−0.903432	−	0.903432i	−0.995731	+	0.0922996i	$0.970578\pi$
$594$	−8.00000			−0.328244
$595$	−4.00000	+	8.00000i	−0.163984	+	0.327968i
$596$	36.0000			1.47462
$597$	−8.00000	+	8.00000i	−0.327418	+	0.327418i
$598$	−32.0000	−	32.0000i	−1.30858	−	1.30858i
$599$	20.0000			0.817178			0.408589	−	0.912719i	$-0.366021\pi$
$599$	20.0000			0.817178			0.408589	+	0.912719i	$0.366021\pi$
$600$	32.0000	−	24.0000i	1.30639	−	0.979796i
$601$	34.0000			1.38689			0.693444	−	0.720510i	$-0.256092\pi$
$601$	34.0000			1.38689			0.693444	+	0.720510i	$0.256092\pi$
$602$	−2.00000	−	2.00000i	−0.0815139	−	0.0815139i
$603$		0			0
$604$	−20.0000			−0.813788
$605$	1.00000	−	2.00000i	0.0406558	−	0.0813116i
$606$	−56.0000			−2.27484
$607$	15.0000	+	15.0000i	0.608831	+	0.608831i	0.942641	−	0.333809i	$-0.108334\pi$
$607$	15.0000	+	15.0000i	0.608831	+	0.608831i	−0.333809	+	0.942641i	$0.608334\pi$
$608$	8.00000	+	8.00000i	0.324443	+	0.324443i
$609$			8.00000i			0.324176i
$610$	30.0000	−	10.0000i	1.21466	−	0.404888i
$611$		−	32.0000i		−	1.29458i
$612$	20.0000	−	20.0000i	0.808452	−	0.808452i
$613$	−2.00000	−	2.00000i	−0.0807792	−	0.0807792i	0.665563	−	0.746342i	$-0.268192\pi$
$613$	−2.00000	−	2.00000i	−0.0807792	−	0.0807792i	−0.746342	+	0.665563i	$0.768192\pi$
$614$		−	30.0000i		−	1.21070i
$615$	−12.0000	−	36.0000i	−0.483887	−	1.45166i
$616$			4.00000i			0.161165i
$617$	11.0000	−	11.0000i	0.442843	−	0.442843i	−0.450123	−	0.892966i	$-0.648620\pi$
$617$	11.0000	−	11.0000i	0.442843	−	0.442843i	0.892966	+	0.450123i	$0.148620\pi$
$618$	24.0000	−	24.0000i	0.965422	−	0.965422i
$619$	36.0000			1.44696			0.723481	−	0.690344i	$-0.242541\pi$
$619$	36.0000			1.44696			0.723481	+	0.690344i	$0.242541\pi$
$620$	16.0000	−	32.0000i	0.642575	−	1.28515i
$621$	−32.0000			−1.28412
$622$	4.00000	−	4.00000i	0.160385	−	0.160385i
$623$	−6.00000	+	6.00000i	−0.240385	+	0.240385i
$624$	64.0000			2.56205
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$		−	18.0000i		−	0.719425i
$627$	4.00000	+	4.00000i	0.159745	+	0.159745i
$628$	6.00000	+	6.00000i	0.239426	+	0.239426i
$629$			20.0000i			0.797452i
$630$	−10.0000	+	20.0000i	−0.398410	+	0.796819i
$631$		−	28.0000i		−	1.11466i	−0.830290	−	0.557331i	$-0.811825\pi$
$631$		−	28.0000i		−	1.11466i	0.830290	−	0.557331i	$-0.188175\pi$
$632$	−20.0000	+	20.0000i	−0.795557	+	0.795557i
$633$	−44.0000	−	44.0000i	−1.74884	−	1.74884i
$634$	−42.0000			−1.66803
$635$	3.00000	−	1.00000i	0.119051	−	0.0396838i
$636$			72.0000i			2.85499i
$637$	−20.0000	+	20.0000i	−0.792429	+	0.792429i
$638$	2.00000	+	2.00000i	0.0791808	+	0.0791808i
$639$	−60.0000			−2.37356
$640$	8.00000	+	24.0000i	0.316228	+	0.948683i
$641$	−30.0000			−1.18493			−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000			−1.18493			−0.592464	+	0.805597i	$0.701845\pi$
$642$	52.0000	+	52.0000i	2.05228	+	2.05228i
$643$	−10.0000	+	10.0000i	−0.394362	+	0.394362i	−0.876239	−	0.481877i	$-0.839955\pi$
$643$	−10.0000	+	10.0000i	−0.394362	+	0.394362i	0.481877	+	0.876239i	$0.339955\pi$
$644$			16.0000i			0.630488i
$645$	−8.00000	−	4.00000i	−0.315000	−	0.157500i
$646$	−8.00000			−0.314756
$647$	30.0000	+	30.0000i	1.17942	+	1.17942i	0.979892	+	0.199530i	$0.0639415\pi$
$647$	30.0000	+	30.0000i	1.17942	+	1.17942i	0.199530	+	0.979892i	$0.436058\pi$
$648$	2.00000	−	2.00000i	0.0785674	−	0.0785674i
$649$		−	8.00000i		−	0.314027i
$650$	−32.0000	+	24.0000i	−1.25514	+	0.941357i
$651$			32.0000i			1.25418i
$652$	−12.0000	−	12.0000i	−0.469956	−	0.469956i
$653$	−19.0000	−	19.0000i	−0.743527	−	0.743527i	0.229728	−	0.973255i	$-0.426216\pi$
$653$	−19.0000	−	19.0000i	−0.743527	−	0.743527i	−0.973255	+	0.229728i	$0.926216\pi$
$654$			8.00000i			0.312825i
$655$	12.0000	+	6.00000i	0.468879	+	0.234439i
$656$	24.0000			0.937043
$657$	10.0000	−	10.0000i	0.390137	−	0.390137i
$658$	−8.00000	+	8.00000i	−0.311872	+	0.311872i
$659$	12.0000			0.467454			0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000			0.467454			0.233727	+	0.972302i	$0.424908\pi$
$660$	4.00000	+	12.0000i	0.155700	+	0.467099i
$661$	40.0000			1.55582			0.777910	−	0.628376i	$-0.216280\pi$
$661$	40.0000			1.55582			0.777910	+	0.628376i	$0.216280\pi$
$662$	−8.00000	+	8.00000i	−0.310929	+	0.310929i
$663$	−32.0000	+	32.0000i	−1.24278	+	1.24278i
$664$		−	4.00000i		−	0.155230i
$665$	6.00000	−	2.00000i	0.232670	−	0.0775567i
$666$			50.0000i			1.93746i
$667$	8.00000	+	8.00000i	0.309761	+	0.309761i
$668$	6.00000	−	6.00000i	0.232147	−	0.232147i
$669$		0			0
$670$		0			0
$671$			10.0000i			0.386046i
$672$	−16.0000	−	16.0000i	−0.617213	−	0.617213i
$673$	−30.0000	−	30.0000i	−1.15642	−	1.15642i	−0.985241	−	0.171174i	$-0.945244\pi$
$673$	−30.0000	−	30.0000i	−1.15642	−	1.15642i	−0.171174	−	0.985241i	$-0.554756\pi$
$674$	36.0000			1.38667
$675$	−4.00000	+	28.0000i	−0.153960	+	1.07772i
$676$	−38.0000			−1.46154
$677$	16.0000	−	16.0000i	0.614930	−	0.614930i	−0.329297	−	0.944227i	$-0.606812\pi$
$677$	16.0000	−	16.0000i	0.614930	−	0.614930i	0.944227	+	0.329297i	$0.106812\pi$
$678$	−4.00000	−	4.00000i	−0.153619	−	0.153619i
$679$	−6.00000			−0.230259
$680$	−16.0000	−	8.00000i	−0.613572	−	0.306786i
$681$	20.0000			0.766402
$682$	8.00000	+	8.00000i	0.306336	+	0.306336i
$683$	−4.00000	+	4.00000i	−0.153056	+	0.153056i	−0.779481	−	0.626426i	$-0.784517\pi$
$683$	−4.00000	+	4.00000i	−0.153056	+	0.153056i	0.626426	+	0.779481i	$0.284517\pi$
$684$	−20.0000			−0.764719
$685$	7.00000	+	21.0000i	0.267456	+	0.802369i
$686$	24.0000			0.916324
$687$	−8.00000	−	8.00000i	−0.305219	−	0.305219i
$688$	4.00000	−	4.00000i	0.152499	−	0.152499i
$689$		−	72.0000i		−	2.74298i
$690$	16.0000	+	48.0000i	0.609110	+	1.82733i
$691$		−	8.00000i		−	0.304334i	−0.988355	−	0.152167i	$-0.951375\pi$
$691$		−	8.00000i		−	0.304334i	0.988355	−	0.152167i	$-0.0486252\pi$
$692$	4.00000	−	4.00000i	0.152057	−	0.152057i
$693$	−5.00000	−	5.00000i	−0.189934	−	0.189934i
$694$		−	10.0000i		−	0.379595i
$695$	20.0000	−	40.0000i	0.758643	−	1.51729i
$696$	−16.0000			−0.606478
$697$	−12.0000	+	12.0000i	−0.454532	+	0.454532i
$698$	−6.00000	+	6.00000i	−0.227103	+	0.227103i
$699$	80.0000			3.02588
$700$	14.0000	+	2.00000i	0.529150	+	0.0755929i
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$	−32.0000	+	32.0000i	−1.20776	+	1.20776i
$703$	10.0000	−	10.0000i	0.377157	−	0.377157i
$704$	−8.00000			−0.301511
$705$	−16.0000	+	32.0000i	−0.602595	+	1.20519i
$706$			26.0000i			0.978523i
$707$	−14.0000	−	14.0000i	−0.526524	−	0.526524i
$708$	32.0000	+	32.0000i	1.20263	+	1.20263i
$709$		−	38.0000i		−	1.42712i	−0.700594	−	0.713560i	$-0.747082\pi$
$709$		−	38.0000i		−	1.42712i	0.700594	−	0.713560i	$-0.252918\pi$
$710$	12.0000	+	36.0000i	0.450352	+	1.35106i
$711$		−	50.0000i		−	1.87515i
$712$	−12.0000	−	12.0000i	−0.449719	−	0.449719i
$713$	32.0000	+	32.0000i	1.19841	+	1.19841i
$714$	16.0000			0.598785
$715$	−4.00000	−	12.0000i	−0.149592	−	0.448775i
$716$			24.0000i			0.896922i
$717$	−44.0000	+	44.0000i	−1.64321	+	1.64321i
$718$	22.0000	+	22.0000i	0.821033	+	0.821033i
$719$	20.0000			0.745874			0.372937	−	0.927857i	$-0.378351\pi$
$719$	20.0000			0.745874			0.372937	+	0.927857i	$0.378351\pi$
$720$	−40.0000	−	20.0000i	−1.49071	−	0.745356i
$721$	12.0000			0.446903
$722$	−15.0000	−	15.0000i	−0.558242	−	0.558242i
$723$	20.0000	−	20.0000i	0.743808	−	0.743808i
$724$		−	32.0000i		−	1.18927i
$725$	8.00000	−	6.00000i	0.297113	−	0.222834i
$726$	−4.00000			−0.148454
$727$	−2.00000	−	2.00000i	−0.0741759	−	0.0741759i	0.669046	−	0.743221i	$-0.266703\pi$
$727$	−2.00000	−	2.00000i	−0.0741759	−	0.0741759i	−0.743221	+	0.669046i	$0.766703\pi$
$728$	16.0000	+	16.0000i	0.592999	+	0.592999i
$729$		−	43.0000i		−	1.59259i
$730$	−8.00000	−	4.00000i	−0.296093	−	0.148047i
$731$			4.00000i			0.147945i
$732$	−40.0000	−	40.0000i	−1.47844	−	1.47844i
$733$	6.00000	+	6.00000i	0.221615	+	0.221615i	0.809178	−	0.587563i	$-0.199913\pi$
$733$	6.00000	+	6.00000i	0.221615	+	0.221615i	−0.587563	+	0.809178i	$0.699913\pi$
$734$		0			0
$735$	30.0000	−	10.0000i	1.10657	−	0.368856i
$736$	−32.0000			−1.17954
$737$		0			0
$738$	−30.0000	+	30.0000i	−1.10432	+	1.10432i
$739$	−36.0000			−1.32428			−0.662141	−	0.749380i	$-0.730352\pi$
$739$	−36.0000			−1.32428			−0.662141	+	0.749380i	$0.730352\pi$
$740$	30.0000	−	10.0000i	1.10282	−	0.367607i
$741$	32.0000			1.17555
$742$	−18.0000	+	18.0000i	−0.660801	+	0.660801i
$743$	19.0000	−	19.0000i	0.697042	−	0.697042i	−0.266729	−	0.963772i	$-0.585943\pi$
$743$	19.0000	−	19.0000i	0.697042	−	0.697042i	0.963772	+	0.266729i	$0.0859429\pi$
$744$	−64.0000			−2.34635
$745$	36.0000	+	18.0000i	1.31894	+	0.659469i
$746$		−	28.0000i		−	1.02515i
$747$	5.00000	+	5.00000i	0.182940	+	0.182940i
$748$	4.00000	−	4.00000i	0.146254	−	0.146254i
$749$			26.0000i			0.950019i
$750$	44.0000	−	8.00000i	1.60665	−	0.292119i
$751$			32.0000i			1.16770i	0.811863	+	0.583848i	$0.198454\pi$
$751$			32.0000i			1.16770i	−0.811863	+	0.583848i	$0.801546\pi$
$752$	−16.0000	−	16.0000i	−0.583460	−	0.583460i
$753$		0			0
$754$	16.0000			0.582686
$755$	−20.0000	−	10.0000i	−0.727875	−	0.363937i
$756$	16.0000			0.581914
$757$	−15.0000	+	15.0000i	−0.545184	+	0.545184i	−0.925044	−	0.379860i	$-0.875972\pi$
$757$	−15.0000	+	15.0000i	−0.545184	+	0.545184i	0.379860	+	0.925044i	$0.375972\pi$
$758$	−24.0000	−	24.0000i	−0.871719	−	0.871719i
$759$	−16.0000			−0.580763
$760$	4.00000	+	12.0000i	0.145095	+	0.435286i
$761$	−22.0000			−0.797499			−0.398750	−	0.917060i	$-0.630556\pi$
$761$	−22.0000			−0.797499			−0.398750	+	0.917060i	$0.630556\pi$
$762$	−4.00000	−	4.00000i	−0.144905	−	0.144905i
$763$	−2.00000	+	2.00000i	−0.0724049	+	0.0724049i
$764$	8.00000			0.289430
$765$	30.0000	−	10.0000i	1.08465	−	0.361551i
$766$	−4.00000			−0.144526
$767$	−32.0000	−	32.0000i	−1.15545	−	1.15545i
$768$	32.0000	−	32.0000i	1.15470	−	1.15470i
$769$		−	10.0000i		−	0.360609i	−0.983611	−	0.180305i	$-0.942292\pi$
$769$		−	10.0000i		−	0.360609i	0.983611	−	0.180305i	$-0.0577084\pi$
$770$	−2.00000	+	4.00000i	−0.0720750	+	0.144150i
$771$		−	4.00000i		−	0.144056i
$772$	−20.0000	+	20.0000i	−0.719816	+	0.719816i
$773$	−35.0000	−	35.0000i	−1.25886	−	1.25886i	−0.951637	−	0.307226i	$-0.900599\pi$
$773$	−35.0000	−	35.0000i	−1.25886	−	1.25886i	−0.307226	−	0.951637i	$-0.599401\pi$
$774$			10.0000i			0.359443i
$775$	32.0000	−	24.0000i	1.14947	−	0.862105i
$776$		−	12.0000i		−	0.430775i
$777$	−20.0000	+	20.0000i	−0.717496	+	0.717496i
$778$	−26.0000	+	26.0000i	−0.932145	+	0.932145i
$779$	12.0000			0.429945
$780$	64.0000	+	32.0000i	2.29157	+	1.14578i
$781$	−12.0000			−0.429394
$782$	16.0000	−	16.0000i	0.572159	−	0.572159i
$783$	8.00000	−	8.00000i	0.285897	−	0.285897i
$784$			20.0000i			0.714286i
$785$	3.00000	+	9.00000i	0.107075	+	0.321224i
$786$		−	24.0000i		−	0.856052i
$787$	17.0000	+	17.0000i	0.605985	+	0.605985i	0.941894	−	0.335910i	$-0.109044\pi$
$787$	17.0000	+	17.0000i	0.605985	+	0.605985i	−0.335910	+	0.941894i	$0.609044\pi$
$788$	−4.00000	−	4.00000i	−0.142494	−	0.142494i
$789$		−	20.0000i		−	0.712019i
$790$	−30.0000	+	10.0000i	−1.06735	+	0.355784i
$791$		−	2.00000i		−	0.0711118i
$792$	10.0000	−	10.0000i	0.355335	−	0.355335i
$793$	40.0000	+	40.0000i	1.42044	+	1.42044i
$794$	−18.0000			−0.638796
$795$	−36.0000	+	72.0000i	−1.27679	+	2.55358i
$796$		−	8.00000i		−	0.283552i
$797$	5.00000	−	5.00000i	0.177109	−	0.177109i	−0.612985	−	0.790094i	$-0.710032\pi$
$797$	5.00000	−	5.00000i	0.177109	−	0.177109i	0.790094	+	0.612985i	$0.210032\pi$
$798$	−8.00000	−	8.00000i	−0.283197	−	0.283197i
$799$	16.0000			0.566039
$800$	−4.00000	+	28.0000i	−0.141421	+	0.989949i
$801$	30.0000			1.06000
$802$	8.00000	+	8.00000i	0.282490	+	0.282490i
$803$	2.00000	−	2.00000i	0.0705785	−	0.0705785i
$804$		0			0
$805$	−8.00000	+	16.0000i	−0.281963	+	0.563926i
$806$	64.0000			2.25430
$807$	−52.0000	−	52.0000i	−1.83049	−	1.83049i
$808$	28.0000	−	28.0000i	0.985037	−	0.985037i
$809$			38.0000i			1.33601i	0.744157	+	0.668004i	$0.232851\pi$
$809$			38.0000i			1.33601i	−0.744157	+	0.668004i	$0.767149\pi$
$810$	3.00000	−	1.00000i	0.105409	−	0.0351364i
$811$		−	44.0000i		−	1.54505i	−0.634985	−	0.772524i	$-0.718994\pi$
$811$		−	44.0000i		−	1.54505i	0.634985	−	0.772524i	$-0.281006\pi$
$812$	−4.00000	−	4.00000i	−0.140372	−	0.140372i
$813$	28.0000	+	28.0000i	0.982003	+	0.982003i
$814$			10.0000i			0.350500i
$815$	−6.00000	−	18.0000i	−0.210171	−	0.630512i
$816$			32.0000i			1.12022i
$817$	2.00000	−	2.00000i	0.0699711	−	0.0699711i
$818$	6.00000	−	6.00000i	0.209785	−	0.209785i
$819$	−40.0000			−1.39771
$820$	24.0000	+	12.0000i	0.838116	+	0.419058i
$821$	−6.00000			−0.209401			−0.104701	−	0.994504i	$-0.533388\pi$
$821$	−6.00000			−0.209401			−0.104701	+	0.994504i	$0.533388\pi$
$822$	28.0000	−	28.0000i	0.976612	−	0.976612i
$823$	−18.0000	+	18.0000i	−0.627441	+	0.627441i	−0.947423	−	0.319983i	$-0.896323\pi$
$823$	−18.0000	+	18.0000i	−0.627441	+	0.627441i	0.319983	+	0.947423i	$0.396323\pi$
$824$			24.0000i			0.836080i
$825$	−2.00000	+	14.0000i	−0.0696311	+	0.487417i
$826$			16.0000i			0.556711i
$827$	25.0000	+	25.0000i	0.869335	+	0.869335i	0.992399	−	0.123064i	$-0.0392719\pi$
$827$	25.0000	+	25.0000i	0.869335	+	0.869335i	−0.123064	+	0.992399i	$0.539272\pi$
$828$	40.0000	−	40.0000i	1.39010	−	1.39010i
$829$		−	20.0000i		−	0.694629i	−0.937749	−	0.347314i	$-0.887094\pi$
$829$		−	20.0000i		−	0.694629i	0.937749	−	0.347314i	$-0.112906\pi$
$830$	2.00000	−	4.00000i	0.0694210	−	0.138842i
$831$			32.0000i			1.11007i
$832$	−32.0000	+	32.0000i	−1.10940	+	1.10940i
$833$	−10.0000	−	10.0000i	−0.346479	−	0.346479i
$834$	−80.0000			−2.77017
$835$	9.00000	−	3.00000i	0.311458	−	0.103819i
$836$	−4.00000			−0.138343
$837$	32.0000	−	32.0000i	1.10608	−	1.10608i
$838$		0			0
$839$	−4.00000			−0.138095			−0.0690477	−	0.997613i	$-0.521996\pi$
$839$	−4.00000			−0.138095			−0.0690477	+	0.997613i	$0.521996\pi$
$840$	−8.00000	−	24.0000i	−0.276026	−	0.828079i
$841$	25.0000			0.862069
$842$	6.00000	+	6.00000i	0.206774	+	0.206774i
$843$	−20.0000	+	20.0000i	−0.688837	+	0.688837i
$844$	44.0000			1.51454
$845$	−38.0000	−	19.0000i	−1.30724	−	0.653620i
$846$	40.0000			1.37523
$847$	−1.00000	−	1.00000i	−0.0343604	−	0.0343604i
$848$	−36.0000	−	36.0000i	−1.23625	−	1.23625i
$849$		−	84.0000i		−	2.88287i
$850$	−12.0000	−	16.0000i	−0.411597	−	0.548795i
$851$			40.0000i			1.37118i
$852$	48.0000	−	48.0000i	1.64445	−	1.64445i
$853$	18.0000	+	18.0000i	0.616308	+	0.616308i	0.944582	−	0.328274i	$-0.106467\pi$
$853$	18.0000	+	18.0000i	0.616308	+	0.616308i	−0.328274	+	0.944582i	$0.606467\pi$
$854$		−	20.0000i		−	0.684386i
$855$	−20.0000	−	10.0000i	−0.683986	−	0.341993i
$856$	−52.0000			−1.77732
$857$	−2.00000	+	2.00000i	−0.0683187	+	0.0683187i	−0.740441	−	0.672122i	$-0.765383\pi$
$857$	−2.00000	+	2.00000i	−0.0683187	+	0.0683187i	0.672122	+	0.740441i	$0.265383\pi$
$858$	−16.0000	+	16.0000i	−0.546231	+	0.546231i
$859$	−4.00000			−0.136478			−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000			−0.136478			−0.0682391	+	0.997669i	$0.521738\pi$
$860$	6.00000	−	2.00000i	0.204598	−	0.0681994i
$861$	−24.0000			−0.817918
$862$		0			0
$863$	22.0000	−	22.0000i	0.748889	−	0.748889i	−0.225382	−	0.974271i	$-0.572363\pi$
$863$	22.0000	−	22.0000i	0.748889	−	0.748889i	0.974271	+	0.225382i	$0.0723629\pi$
$864$			32.0000i			1.08866i
$865$	6.00000	−	2.00000i	0.204006	−	0.0680020i
$866$		−	42.0000i		−	1.42722i
$867$	18.0000	+	18.0000i	0.611312	+	0.611312i
$868$	−16.0000	−	16.0000i	−0.543075	−	0.543075i
$869$		−	10.0000i		−	0.339227i
$870$	−16.0000	−	8.00000i	−0.542451	−	0.271225i
$871$		0			0
$872$	−4.00000	−	4.00000i	−0.135457	−	0.135457i
$873$	15.0000	+	15.0000i	0.507673	+	0.507673i
$874$	−16.0000			−0.541208
$875$	13.0000	+	9.00000i	0.439480	+	0.304256i
$876$			16.0000i			0.540590i
$877$	22.0000	−	22.0000i	0.742887	−	0.742887i	−0.230245	−	0.973133i	$-0.573953\pi$
$877$	22.0000	−	22.0000i	0.742887	−	0.742887i	0.973133	+	0.230245i	$0.0739529\pi$
$878$	−8.00000	−	8.00000i	−0.269987	−	0.269987i
$879$	−32.0000			−1.07933
$880$	−8.00000	−	4.00000i	−0.269680	−	0.134840i
$881$	−12.0000			−0.404290			−0.202145	−	0.979356i	$-0.564791\pi$
$881$	−12.0000			−0.404290			−0.202145	+	0.979356i	$0.564791\pi$
$882$	−25.0000	−	25.0000i	−0.841794	−	0.841794i
$883$	−30.0000	+	30.0000i	−1.00958	+	1.00958i	−0.00962672	+	0.999954i	$0.503064\pi$
$883$	−30.0000	+	30.0000i	−1.00958	+	1.00958i	−0.999954	+	0.00962672i	$0.996936\pi$
$884$		−	32.0000i		−	1.07628i
$885$	16.0000	+	48.0000i	0.537834	+	1.61350i
$886$	20.0000			0.671913
$887$	−23.0000	−	23.0000i	−0.772264	−	0.772264i	0.206238	−	0.978502i	$-0.433878\pi$
$887$	−23.0000	−	23.0000i	−0.772264	−	0.772264i	−0.978502	+	0.206238i	$0.933878\pi$
$888$	−40.0000	−	40.0000i	−1.34231	−	1.34231i
$889$		−	2.00000i		−	0.0670778i
$890$	−6.00000	−	18.0000i	−0.201120	−	0.603361i
$891$			1.00000i			0.0335013i
$892$		0			0
$893$	−8.00000	−	8.00000i	−0.267710	−	0.267710i
$894$		−	72.0000i		−	2.40804i
$895$	−12.0000	+	24.0000i	−0.401116	+	0.802232i
$896$	16.0000			0.534522
$897$	−64.0000	+	64.0000i	−2.13690	+	2.13690i
$898$	−12.0000	+	12.0000i	−0.400445	+	0.400445i
$899$	−16.0000			−0.533630
$900$	−30.0000	−	40.0000i	−1.00000	−	1.33333i
$901$	36.0000			1.19933
$902$	−6.00000	+	6.00000i	−0.199778	+	0.199778i
$903$	−4.00000	+	4.00000i	−0.133112	+	0.133112i
$904$	4.00000			0.133038
$905$	16.0000	−	32.0000i	0.531858	−	1.06372i
$906$			40.0000i			1.32891i
$907$	40.0000	+	40.0000i	1.32818	+	1.32818i	0.906959	+	0.421219i	$0.138398\pi$
$907$	40.0000	+	40.0000i	1.32818	+	1.32818i	0.421219	+	0.906959i	$0.361602\pi$
$908$	−10.0000	+	10.0000i	−0.331862	+	0.331862i
$909$			70.0000i			2.32175i
$910$	8.00000	+	24.0000i	0.265197	+	0.795592i
$911$		−	36.0000i		−	1.19273i	−0.802712	−	0.596367i	$-0.796610\pi$
$911$		−	36.0000i		−	1.19273i	0.802712	−	0.596367i	$-0.203390\pi$
$912$	16.0000	−	16.0000i	0.529813	−	0.529813i
$913$	1.00000	+	1.00000i	0.0330952	+	0.0330952i
$914$	32.0000			1.05847
$915$	−20.0000	−	60.0000i	−0.661180	−	1.98354i
$916$	8.00000			0.264327
$917$	6.00000	−	6.00000i	0.198137	−	0.198137i
$918$	−16.0000	−	16.0000i	−0.528079	−	0.528079i
$919$	24.0000			0.791687			0.395843	−	0.918318i	$-0.370452\pi$
$919$	24.0000			0.791687			0.395843	+	0.918318i	$0.370452\pi$
$920$	−32.0000	−	16.0000i	−1.05501	−	0.527504i
$921$	−60.0000			−1.97707
$922$	10.0000	+	10.0000i	0.329332	+	0.329332i
$923$	−48.0000	+	48.0000i	−1.57994	+	1.57994i
$924$	8.00000			0.263181
$925$	35.0000	+	5.00000i	1.15079	+	0.164399i
$926$		0			0
$927$	−30.0000	−	30.0000i	−0.985329	−	0.985329i
$928$	8.00000	−	8.00000i	0.262613	−	0.262613i
$929$			50.0000i			1.64045i	0.572043	+	0.820223i	$0.306151\pi$
$929$			50.0000i			1.64045i	−0.572043	+	0.820223i	$0.693849\pi$
$930$	−64.0000	−	32.0000i	−2.09864	−	1.04932i
$931$			10.0000i			0.327737i
$932$	−40.0000	+	40.0000i	−1.31024	+	1.31024i
$933$	−8.00000	−	8.00000i	−0.261908	−	0.261908i
$934$		−	24.0000i		−	0.785304i
$935$	6.00000	−	2.00000i	0.196221	−	0.0654070i
$936$		−	80.0000i		−	2.61488i
$937$	−8.00000	+	8.00000i	−0.261349	+	0.261349i	−0.825602	−	0.564253i	$-0.809164\pi$
$937$	−8.00000	+	8.00000i	−0.261349	+	0.261349i	0.564253	+	0.825602i	$0.309164\pi$
$938$		0			0
$939$	−36.0000			−1.17482
$940$	−8.00000	−	24.0000i	−0.260931	−	0.782794i
$941$	−38.0000			−1.23876			−0.619382	−	0.785090i	$-0.712617\pi$
$941$	−38.0000			−1.23876			−0.619382	+	0.785090i	$0.712617\pi$
$942$	12.0000	−	12.0000i	0.390981	−	0.390981i
$943$	−24.0000	+	24.0000i	−0.781548	+	0.781548i
$944$	−32.0000			−1.04151
$945$	16.0000	+	8.00000i	0.520480	+	0.260240i
$946$			2.00000i			0.0650256i
$947$	−20.0000	−	20.0000i	−0.649913	−	0.649913i	0.303059	−	0.952972i	$-0.401992\pi$
$947$	−20.0000	−	20.0000i	−0.649913	−	0.649913i	−0.952972	+	0.303059i	$0.901992\pi$
$948$	40.0000	+	40.0000i	1.29914	+	1.29914i
$949$		−	16.0000i		−	0.519382i
$950$	−2.00000	+	14.0000i	−0.0648886	+	0.454220i
$951$			84.0000i			2.72389i
$952$	−8.00000	+	8.00000i	−0.259281	+	0.259281i
$953$	36.0000	+	36.0000i	1.16615	+	1.16615i	0.983103	+	0.183051i	$0.0585973\pi$
$953$	36.0000	+	36.0000i	1.16615	+	1.16615i	0.183051	+	0.983103i	$0.441403\pi$
$954$	90.0000			2.91386
$955$	8.00000	+	4.00000i	0.258874	+	0.129437i
$956$		−	44.0000i		−	1.42306i
$957$	4.00000	−	4.00000i	0.129302	−	0.129302i
$958$	−18.0000	−	18.0000i	−0.581554	−	0.581554i
$959$	14.0000			0.452084
$960$	48.0000	−	16.0000i	1.54919	−	0.516398i
$961$	−33.0000			−1.06452
$962$	40.0000	+	40.0000i	1.28965	+	1.28965i
$963$	65.0000	−	65.0000i	2.09460	−	2.09460i
$964$			20.0000i			0.644157i
$965$	−30.0000	+	10.0000i	−0.965734	+	0.321911i
$966$	32.0000			1.02958
$967$	−27.0000	−	27.0000i	−0.868261	−	0.868261i	0.124018	−	0.992280i	$-0.460422\pi$
$967$	−27.0000	−	27.0000i	−0.868261	−	0.868261i	−0.992280	+	0.124018i	$0.960422\pi$
$968$	2.00000	−	2.00000i	0.0642824	−	0.0642824i
$969$			16.0000i			0.513994i
$970$	6.00000	−	12.0000i	0.192648	−	0.385297i
$971$		−	36.0000i		−	1.15529i	−0.816286	−	0.577647i	$-0.803971\pi$
$971$		−	36.0000i		−	1.15529i	0.816286	−	0.577647i	$-0.196029\pi$
$972$	20.0000	+	20.0000i	0.641500	+	0.641500i
$973$	−20.0000	−	20.0000i	−0.641171	−	0.641171i
$974$		−	32.0000i		−	1.02535i
$975$	48.0000	+	64.0000i	1.53723	+	2.04964i
$976$	40.0000			1.28037
$977$	−7.00000	+	7.00000i	−0.223950	+	0.223950i	−0.810159	−	0.586210i	$-0.800620\pi$
$977$	−7.00000	+	7.00000i	−0.223950	+	0.223950i	0.586210	+	0.810159i	$0.300620\pi$
$978$	−24.0000	+	24.0000i	−0.767435	+	0.767435i
$979$	6.00000			0.191761
$980$	−10.0000	+	20.0000i	−0.319438	+	0.638877i
$981$	10.0000			0.319275
$982$	−12.0000	+	12.0000i	−0.382935	+	0.382935i
$983$	10.0000	−	10.0000i	0.318950	−	0.318950i	−0.529413	−	0.848364i	$-0.677588\pi$
$983$	10.0000	−	10.0000i	0.318950	−	0.318950i	0.848364	+	0.529413i	$0.177588\pi$
$984$		−	48.0000i		−	1.53018i
$985$	−2.00000	−	6.00000i	−0.0637253	−	0.191176i
$986$			8.00000i			0.254772i
$987$	16.0000	+	16.0000i	0.509286	+	0.509286i
$988$	−16.0000	+	16.0000i	−0.509028	+	0.509028i
$989$			8.00000i			0.254385i
$990$	15.0000	−	5.00000i	0.476731	−	0.158910i
$991$			52.0000i			1.65183i	0.563791	+	0.825917i	$0.309342\pi$
$991$			52.0000i			1.65183i	−0.563791	+	0.825917i	$0.690658\pi$
$992$	32.0000	−	32.0000i	1.01600	−	1.01600i
$993$	16.0000	+	16.0000i	0.507745	+	0.507745i
$994$	24.0000			0.761234
$995$	4.00000	−	8.00000i	0.126809	−	0.253617i
$996$	−8.00000			−0.253490
$997$	−30.0000	+	30.0000i	−0.950110	+	0.950110i	−0.998813	−	0.0487037i	$-0.984491\pi$
$997$	−30.0000	+	30.0000i	−0.950110	+	0.950110i	0.0487037	+	0.998813i	$0.484491\pi$
$998$	−8.00000	−	8.00000i	−0.253236	−	0.253236i
$999$	40.0000			1.26554

Display

a_p

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p

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.l.b.23.1	yes	2
4.3	odd	2		220.2.l.a.23.1	✓	2
5.2	odd	4		220.2.l.a.67.1	yes	2
20.7	even	4	inner	220.2.l.b.67.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.l.a.23.1	✓	2	4.3	odd	2
220.2.l.a.67.1	yes	2	5.2	odd	4
220.2.l.b.23.1	yes	2	1.1	even	1	trivial
220.2.l.b.67.1	yes	2	20.7	even	4	inner

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Elliptic curves over $\Q$
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Newspace parameters

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	220.2.l.b.23.1

Level	$220$
Weight	$2$
Character	220.23
Analytic conductor	$1.757$
Analytic rank	$0$
Dimension	$2$
Inner twists	$2$