LMFDB - Embedded newform 220.2.l.b.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,2,Mod(23,220)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			67.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	220.67
Dual form			220.2.l.b.23.1

$q$-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 $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

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

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	0.985599	+	0.169102i	$0.0540867\pi$
$3$	2.00000	+	2.00000i	1.15470	+	1.15470i	0.169102	+	0.985599i	$0.445913\pi$
$4$		−	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	−0.492403	−	0.870367i	$-0.663881\pi$
$7$	1.00000	−	1.00000i	0.377964	−	0.377964i	0.870367	+	0.492403i	$0.163881\pi$
$8$	−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	−0.116171	+	0.993229i	$0.537062\pi$
$13$	−4.00000	+	4.00000i	−1.10940	+	1.10940i	−0.993229	+	0.116171i	$0.962938\pi$
$14$		−	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	0.906747	−	0.421676i	$-0.138558\pi$
$17$	2.00000	+	2.00000i	0.485071	+	0.485071i	−0.421676	+	0.906747i	$0.638558\pi$
$18$	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	0.988069	−	0.154011i	$-0.0492193\pi$
$23$	4.00000	+	4.00000i	0.834058	+	0.834058i	−0.154011	+	0.988069i	$0.549219\pi$
$24$		−	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	$-0.940546\pi$
$29$		−	2.00000i		−	0.371391i	0.982607	−	0.185695i	$-0.0594537\pi$
$30$	−4.00000	−	8.00000i	−0.730297	−	1.46059i
$31$		−	8.00000i		−	1.43684i	−0.695608	−	0.718421i	$-0.744865\pi$
$31$		−	8.00000i		−	1.43684i	0.695608	−	0.718421i	$-0.255135\pi$
$32$	−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	0.164399	−	0.986394i	$-0.447432\pi$
$37$	−5.00000	−	5.00000i	−0.821995	−	0.821995i	−0.986394	+	0.164399i	$0.947432\pi$
$38$	−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	0.626734	−	0.779233i	$-0.284391\pi$
$43$	−1.00000	−	1.00000i	−0.152499	−	0.152499i	−0.779233	+	0.626734i	$0.784391\pi$
$44$	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	−0.352392	−	0.935852i	$-0.614632\pi$
$47$	4.00000	−	4.00000i	0.583460	−	0.583460i	0.935852	+	0.352392i	$0.114632\pi$
$48$	−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	0.274721	−	0.961524i	$-0.411414\pi$
$53$	9.00000	−	9.00000i	1.23625	−	1.23625i	0.961524	−	0.274721i	$-0.0885855\pi$
$54$			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	$-0.750000\pi$
$67$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$68$	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	$0.252242\pi$
$71$			12.0000i			1.42414i	−0.702109	+	0.712069i	$0.747758\pi$
$72$	10.0000	−	10.0000i	1.17851	−	1.17851i
$73$	2.00000	−	2.00000i	0.234082	−	0.234082i	−0.580312	−	0.814394i	$-0.697069\pi$
$73$	2.00000	−	2.00000i	0.234082	−	0.234082i	0.814394	+	0.580312i	$0.197069\pi$
$74$	−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	0.650092	−	0.759856i	$-0.274731\pi$
$83$	−1.00000	−	1.00000i	−0.109764	−	0.109764i	−0.759856	+	0.650092i	$0.774731\pi$
$84$		−	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	$-0.896989\pi$
$89$		−	6.00000i		−	0.635999i	0.948091	−	0.317999i	$-0.103011\pi$
$90$	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	0.538208	−	0.842812i	$-0.319101\pi$
$97$	−3.00000	−	3.00000i	−0.304604	−	0.304604i	−0.842812	+	0.538208i	$0.819101\pi$
$98$	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	0.937955	−	0.346757i	$-0.112717\pi$
$103$	6.00000	+	6.00000i	0.591198	+	0.591198i	−0.346757	+	0.937955i	$0.612717\pi$
$104$	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	0.304125	−	0.952632i	$-0.401636\pi$
$107$	13.0000	−	13.0000i	1.25676	−	1.25676i	0.952632	−	0.304125i	$-0.0983642\pi$
$108$	8.00000	+	8.00000i	0.769800	+	0.769800i
$109$		−	2.00000i		−	0.191565i	−0.995402	−	0.0957826i	$-0.969465\pi$
$109$		−	2.00000i		−	0.191565i	0.995402	−	0.0957826i	$-0.0305354\pi$
$110$	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	−0.752577	−	0.658505i	$-0.771189\pi$
$113$	−1.00000	+	1.00000i	−0.0940721	+	0.0940721i	0.658505	+	0.752577i	$0.271189\pi$
$114$	−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	−0.750081	−	0.661346i	$-0.769986\pi$
$127$	−1.00000	+	1.00000i	−0.0887357	+	0.0887357i	0.661346	+	0.750081i	$0.269986\pi$
$128$	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	$0.0844187\pi$
$131$			6.00000i			0.524222i	−0.965038	+	0.262111i	$0.915581\pi$
$132$	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	0.939793	−	0.341743i	$-0.111017\pi$
$137$	7.00000	+	7.00000i	0.598050	+	0.598050i	−0.341743	+	0.939793i	$0.611017\pi$
$138$	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	$0.263904\pi$
$149$			18.0000i			1.47462i	−0.675556	+	0.737309i	$0.736096\pi$
$150$	−12.0000	+	16.0000i	−0.979796	+	1.30639i
$151$		−	10.0000i		−	0.813788i	−0.913475	−	0.406894i	$-0.866612\pi$
$151$		−	10.0000i		−	0.813788i	0.913475	−	0.406894i	$-0.133388\pi$
$152$	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	0.816612	−	0.577186i	$-0.195849\pi$
$157$	3.00000	+	3.00000i	0.239426	+	0.239426i	−0.577186	+	0.816612i	$0.695849\pi$
$158$	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	0.431944	−	0.901900i	$-0.357828\pi$
$163$	−6.00000	−	6.00000i	−0.469956	−	0.469956i	−0.901900	+	0.431944i	$0.857828\pi$
$164$			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	−0.813588	−	0.581441i	$-0.802489\pi$
$167$	−3.00000	+	3.00000i	−0.232147	+	0.232147i	0.581441	+	0.813588i	$0.302489\pi$
$168$	−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	−0.779036	−	0.626979i	$-0.784291\pi$
$173$	−2.00000	+	2.00000i	−0.152057	+	0.152057i	0.626979	+	0.779036i	$0.284291\pi$
$174$		−	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	$0.0462265\pi$
$191$			4.00000i			0.289430i	−0.989473	+	0.144715i	$0.953773\pi$
$192$	−16.0000	+	16.0000i	−1.15470	+	1.15470i
$193$	10.0000	−	10.0000i	0.719816	−	0.719816i	−0.248752	−	0.968567i	$-0.580020\pi$
$193$	10.0000	−	10.0000i	0.719816	−	0.719816i	0.968567	+	0.248752i	$0.0800203\pi$
$194$	−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	0.632261	−	0.774755i	$-0.282127\pi$
$197$	−2.00000	−	2.00000i	−0.142494	−	0.142494i	−0.774755	+	0.632261i	$0.782127\pi$
$198$	−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	$0.273468\pi$
$211$			22.0000i			1.51454i	−0.653101	+	0.757271i	$0.726532\pi$
$212$	−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	$-0.250000\pi$
$223$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$224$			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	−0.521431	−	0.853293i	$-0.674602\pi$
$227$	5.00000	−	5.00000i	0.331862	−	0.331862i	0.853293	+	0.521431i	$0.174602\pi$
$228$	−8.00000	+	8.00000i	−0.529813	+	0.529813i
$229$			4.00000i			0.264327i	0.991228	+	0.132164i	$0.0421925\pi$
$229$			4.00000i			0.264327i	−0.991228	+	0.132164i	$0.957808\pi$
$230$	−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	0.389010	−	0.921234i	$-0.372817\pi$
$233$	20.0000	−	20.0000i	1.31024	−	1.31024i	0.921234	−	0.389010i	$-0.127183\pi$
$234$	−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	0.737608	−	0.675229i	$-0.235955\pi$
$257$	1.00000	+	1.00000i	0.0623783	+	0.0623783i	−0.675229	+	0.737608i	$0.735955\pi$
$258$	−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	0.844255	−	0.535942i	$-0.180043\pi$
$263$	5.00000	+	5.00000i	0.308313	+	0.308313i	−0.535942	+	0.844255i	$0.680043\pi$
$264$	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	$0.291286\pi$
$269$			26.0000i			1.58525i	−0.609711	+	0.792624i	$0.708714\pi$
$270$	16.0000	−	8.00000i	0.973729	−	0.486864i
$271$		−	14.0000i		−	0.850439i	−0.905090	−	0.425220i	$-0.860197\pi$
$271$		−	14.0000i		−	0.850439i	0.905090	−	0.425220i	$-0.139803\pi$
$272$	−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	0.424673	−	0.905347i	$-0.360389\pi$
$277$	−8.00000	−	8.00000i	−0.480673	−	0.480673i	−0.905347	+	0.424673i	$0.860389\pi$
$278$	−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	0.956461	+	0.291859i	$0.0942738\pi$
$283$	21.0000	+	21.0000i	1.24832	+	1.24832i	0.291859	+	0.956461i	$0.405726\pi$
$284$	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	−0.901060	−	0.433695i	$-0.857210\pi$
$293$	−8.00000	+	8.00000i	−0.467365	+	0.467365i	0.433695	+	0.901060i	$0.357210\pi$
$294$			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	−0.990876	−	0.134780i	$-0.956967\pi$
$307$	−15.0000	+	15.0000i	−0.856095	+	0.856095i	0.134780	+	0.990876i	$0.456967\pi$
$308$	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	$0.0361772\pi$
$311$			4.00000i			0.226819i	−0.993548	+	0.113410i	$0.963823\pi$
$312$	32.0000	+	32.0000i	1.81164	+	1.81164i
$313$	−9.00000	+	9.00000i	−0.508710	+	0.508710i	−0.914130	−	0.405420i	$-0.867125\pi$
$313$	−9.00000	+	9.00000i	−0.508710	+	0.508710i	0.405420	+	0.914130i	$0.367125\pi$
$314$	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	−0.979877	−	0.199600i	$-0.936036\pi$
$317$	−21.0000	−	21.0000i	−1.17948	−	1.17948i	−0.199600	−	0.979877i	$-0.563964\pi$
$318$	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	$-0.929440\pi$
$331$		−	8.00000i		−	0.439720i	0.975531	−	0.219860i	$-0.0705600\pi$
$332$	−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	0.999814	−	0.0192914i	$-0.00614103\pi$
$337$	18.0000	+	18.0000i	0.980522	+	0.980522i	−0.0192914	+	0.999814i	$0.506141\pi$
$338$	−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	−0.828461	−	0.560047i	$-0.810783\pi$
$347$	−5.00000	+	5.00000i	−0.268414	+	0.268414i	0.560047	+	0.828461i	$0.310783\pi$
$348$	−8.00000	−	8.00000i	−0.428845	−	0.428845i
$349$		−	6.00000i		−	0.321173i	−0.987022	−	0.160586i	$-0.948662\pi$
$349$		−	6.00000i		−	0.321173i	0.987022	−	0.160586i	$-0.0513385\pi$
$350$	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	−0.270734	−	0.962654i	$-0.587266\pi$
$353$	13.0000	−	13.0000i	0.691920	−	0.691920i	0.962654	+	0.270734i	$0.0872664\pi$
$354$	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	$-0.750000\pi$
$367$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$368$	−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	−0.969598	−	0.244705i	$-0.921309\pi$
$373$	−14.0000	+	14.0000i	−0.724893	+	0.724893i	0.244705	+	0.969598i	$0.421309\pi$
$374$			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	0.654161	−	0.756356i	$-0.273022\pi$
$383$	−2.00000	−	2.00000i	−0.102195	−	0.102195i	−0.756356	+	0.654161i	$0.773022\pi$
$384$			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	$-0.770926\pi$
$389$		−	26.0000i		−	1.31825i	0.752032	−	0.659126i	$-0.229074\pi$
$390$	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	0.444220	−	0.895918i	$-0.353481\pi$
$397$	−9.00000	−	9.00000i	−0.451697	−	0.451697i	−0.895918	+	0.444220i	$0.853481\pi$
$398$	−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	$0.0473931\pi$
$409$			6.00000i			0.296681i	−0.988936	+	0.148340i	$0.952607\pi$
$410$	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	−0.00923827	+	0.999957i	$0.502941\pi$
$433$	−21.0000	+	21.0000i	−1.00920	+	1.00920i	−0.999957	+	0.00923827i	$0.997059\pi$
$434$	−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	0.903565	−	0.428451i	$-0.140940\pi$
$443$	10.0000	+	10.0000i	0.475114	+	0.475114i	−0.428451	+	0.903565i	$0.640940\pi$
$444$	−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	$-0.908618\pi$
$449$		−	12.0000i		−	0.566315i	0.959073	−	0.283158i	$-0.0913819\pi$
$450$	−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	0.974188	−	0.225739i	$-0.0724798\pi$
$457$	16.0000	+	16.0000i	0.748448	+	0.748448i	−0.225739	+	0.974188i	$0.572480\pi$
$458$	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	$-0.250000\pi$
$463$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$464$			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	−0.927964	−	0.372670i	$-0.878442\pi$
$467$	−12.0000	+	12.0000i	−0.555294	+	0.555294i	0.372670	+	0.927964i	$0.378442\pi$
$468$	−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	−0.969625	−	0.244596i	$-0.921345\pi$
$487$	−16.0000	+	16.0000i	−0.725029	+	0.725029i	0.244596	+	0.969625i	$0.421345\pi$
$488$	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	$-0.912720\pi$
$491$		−	12.0000i		−	0.541552i	0.962642	−	0.270776i	$-0.0872803\pi$
$492$	−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	0.142611	−	0.989779i	$-0.454450\pi$
$503$	−19.0000	−	19.0000i	−0.847168	−	0.847168i	−0.989779	+	0.142611i	$0.954450\pi$
$504$		−	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	$-0.786914\pi$
$509$		−	28.0000i		−	1.24108i	0.784176	−	0.620539i	$-0.213086\pi$
$510$	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	0.769649	−	0.638468i	$-0.220431\pi$
$523$	3.00000	+	3.00000i	0.131181	+	0.131181i	−0.638468	+	0.769649i	$0.720431\pi$
$524$	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	0.416184	−	0.909281i	$-0.363367\pi$
$547$	31.0000	−	31.0000i	1.32546	−	1.32546i	0.909281	−	0.416184i	$-0.136633\pi$
$548$	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	0.886480	−	0.462767i	$-0.153143\pi$
$557$	10.0000	+	10.0000i	0.423714	+	0.423714i	−0.462767	+	0.886480i	$0.653143\pi$
$558$	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	0.491547	−	0.870851i	$-0.336432\pi$
$563$	−9.00000	−	9.00000i	−0.379305	−	0.379305i	−0.870851	+	0.491547i	$0.836432\pi$
$564$		−	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	$-0.932780\pi$
$569$		−	10.0000i		−	0.419222i	0.977785	−	0.209611i	$-0.0672197\pi$
$570$	8.00000	+	16.0000i	0.335083	+	0.670166i
$571$		−	4.00000i		−	0.167395i	−0.996491	−	0.0836974i	$-0.973327\pi$
$571$		−	4.00000i		−	0.167395i	0.996491	−	0.0836974i	$-0.0266729\pi$
$572$	−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	0.923880	−	0.382683i	$-0.125000\pi$
$577$	13.0000	+	13.0000i	0.541197	+	0.541197i	−0.382683	+	0.923880i	$0.625000\pi$
$578$	−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	−0.00937009	−	0.999956i	$-0.502983\pi$
$587$	24.0000	−	24.0000i	0.990586	−	0.990586i	0.999956	+	0.00937009i	$0.00298264\pi$
$588$	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	−0.995731	−	0.0922996i	$-0.970578\pi$
$593$	−22.0000	+	22.0000i	−0.903432	+	0.903432i	0.0922996	+	0.995731i	$0.470578\pi$
$594$	−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	−0.333809	−	0.942641i	$-0.608334\pi$
$607$	15.0000	−	15.0000i	0.608831	−	0.608831i	0.942641	+	0.333809i	$0.108334\pi$
$608$	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	−0.746342	−	0.665563i	$-0.768192\pi$
$613$	−2.00000	+	2.00000i	−0.0807792	+	0.0807792i	0.665563	+	0.746342i	$0.268192\pi$
$614$			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	0.892966	−	0.450123i	$-0.148620\pi$
$617$	11.0000	+	11.0000i	0.442843	+	0.442843i	−0.450123	+	0.892966i	$0.648620\pi$
$618$	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	$0.188175\pi$
$631$			28.0000i			1.11466i	−0.830290	+	0.557331i	$0.811825\pi$
$632$	−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	0.481877	−	0.876239i	$-0.339955\pi$
$643$	−10.0000	−	10.0000i	−0.394362	−	0.394362i	−0.876239	+	0.481877i	$0.839955\pi$
$644$		−	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	0.199530	−	0.979892i	$-0.436058\pi$
$647$	30.0000	−	30.0000i	1.17942	−	1.17942i	0.979892	−	0.199530i	$-0.0639415\pi$
$648$	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	−0.973255	−	0.229728i	$-0.926216\pi$
$653$	−19.0000	+	19.0000i	−0.743527	+	0.743527i	0.229728	+	0.973255i	$0.426216\pi$
$654$		−	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	−0.171174	+	0.985241i	$0.554756\pi$
$673$	−30.0000	+	30.0000i	−1.15642	+	1.15642i	−0.985241	+	0.171174i	$0.945244\pi$
$674$	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	0.944227	−	0.329297i	$-0.106812\pi$
$677$	16.0000	+	16.0000i	0.614930	+	0.614930i	−0.329297	+	0.944227i	$0.606812\pi$
$678$	−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	0.626426	−	0.779481i	$-0.284517\pi$
$683$	−4.00000	−	4.00000i	−0.153056	−	0.153056i	−0.779481	+	0.626426i	$0.784517\pi$
$684$	−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	$0.0486252\pi$
$691$			8.00000i			0.304334i	−0.988355	+	0.152167i	$0.951375\pi$
$692$	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	$0.252918\pi$
$709$			38.0000i			1.42712i	−0.700594	+	0.713560i	$0.747082\pi$
$710$	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	−0.743221	−	0.669046i	$-0.766703\pi$
$727$	−2.00000	+	2.00000i	−0.0741759	+	0.0741759i	0.669046	+	0.743221i	$0.266703\pi$
$728$	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	−0.587563	−	0.809178i	$-0.699913\pi$
$733$	6.00000	−	6.00000i	0.221615	−	0.221615i	0.809178	+	0.587563i	$0.199913\pi$
$734$		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	0.963772	−	0.266729i	$-0.0859429\pi$
$743$	19.0000	+	19.0000i	0.697042	+	0.697042i	−0.266729	+	0.963772i	$0.585943\pi$
$744$	−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	$-0.801546\pi$
$751$		−	32.0000i		−	1.16770i	0.811863	−	0.583848i	$-0.198454\pi$
$752$	−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	0.379860	−	0.925044i	$-0.375972\pi$
$757$	−15.0000	−	15.0000i	−0.545184	−	0.545184i	−0.925044	+	0.379860i	$0.875972\pi$
$758$	−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	$0.0577084\pi$
$769$			10.0000i			0.360609i	−0.983611	+	0.180305i	$0.942292\pi$
$770$	−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	−0.307226	+	0.951637i	$0.599401\pi$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(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

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