LMFDB - Embedded newform 490.3.f.b.197.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,3,Mod(197,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("490.197");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	490.f (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:	$13.3515329537$
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:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	490.197
Dual form			490.3.f.b.393.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(2.00000 - 2.00000i) q^{3} +2.00000i q^{4} +5.00000i q^{5} -4.00000 q^{6} +(2.00000 - 2.00000i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(2.00000 - 2.00000i) q^{3} +2.00000i q^{4} +5.00000i q^{5} -4.00000 q^{6} +(2.00000 - 2.00000i) q^{8} +1.00000i q^{9} +(5.00000 - 5.00000i) q^{10} -8.00000 q^{11} +(4.00000 + 4.00000i) q^{12} +(-3.00000 + 3.00000i) q^{13} +(10.0000 + 10.0000i) q^{15} -4.00000 q^{16} +(-7.00000 - 7.00000i) q^{17} +(1.00000 - 1.00000i) q^{18} +20.0000i q^{19} -10.0000 q^{20} +(8.00000 + 8.00000i) q^{22} +(-2.00000 + 2.00000i) q^{23} -8.00000i q^{24} -25.0000 q^{25} +6.00000 q^{26} +(20.0000 + 20.0000i) q^{27} +40.0000i q^{29} -20.0000i q^{30} -52.0000 q^{31} +(4.00000 + 4.00000i) q^{32} +(-16.0000 + 16.0000i) q^{33} +14.0000i q^{34} -2.00000 q^{36} +(-3.00000 - 3.00000i) q^{37} +(20.0000 - 20.0000i) q^{38} +12.0000i q^{39} +(10.0000 + 10.0000i) q^{40} +8.00000 q^{41} +(-42.0000 + 42.0000i) q^{43} -16.0000i q^{44} -5.00000 q^{45} +4.00000 q^{46} +(18.0000 + 18.0000i) q^{47} +(-8.00000 + 8.00000i) q^{48} +(25.0000 + 25.0000i) q^{50} -28.0000 q^{51} +(-6.00000 - 6.00000i) q^{52} +(53.0000 - 53.0000i) q^{53} -40.0000i q^{54} -40.0000i q^{55} +(40.0000 + 40.0000i) q^{57} +(40.0000 - 40.0000i) q^{58} +20.0000i q^{59} +(-20.0000 + 20.0000i) q^{60} +48.0000 q^{61} +(52.0000 + 52.0000i) q^{62} -8.00000i q^{64} +(-15.0000 - 15.0000i) q^{65} +32.0000 q^{66} +(62.0000 + 62.0000i) q^{67} +(14.0000 - 14.0000i) q^{68} +8.00000i q^{69} -28.0000 q^{71} +(2.00000 + 2.00000i) q^{72} +(47.0000 - 47.0000i) q^{73} +6.00000i q^{74} +(-50.0000 + 50.0000i) q^{75} -40.0000 q^{76} +(12.0000 - 12.0000i) q^{78} -20.0000i q^{80} +71.0000 q^{81} +(-8.00000 - 8.00000i) q^{82} +(-18.0000 + 18.0000i) q^{83} +(35.0000 - 35.0000i) q^{85} +84.0000 q^{86} +(80.0000 + 80.0000i) q^{87} +(-16.0000 + 16.0000i) q^{88} -80.0000i q^{89} +(5.00000 + 5.00000i) q^{90} +(-4.00000 - 4.00000i) q^{92} +(-104.000 + 104.000i) q^{93} -36.0000i q^{94} -100.000 q^{95} +16.0000 q^{96} +(63.0000 + 63.0000i) q^{97} -8.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 4 q^{3} - 8 q^{6} + 4 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 + 4 * q^3 - 8 * q^6 + 4 * q^8	$ 2 q - 2 q^{2} + 4 q^{3} - 8 q^{6} + 4 q^{8} + 10 q^{10} - 16 q^{11} + 8 q^{12} - 6 q^{13} + 20 q^{15} - 8 q^{16} - 14 q^{17} + 2 q^{18} - 20 q^{20} + 16 q^{22} - 4 q^{23} - 50 q^{25} + 12 q^{26} + 40 q^{27} - 104 q^{31} + 8 q^{32} - 32 q^{33} - 4 q^{36} - 6 q^{37} + 40 q^{38} + 20 q^{40} + 16 q^{41} - 84 q^{43} - 10 q^{45} + 8 q^{46} + 36 q^{47} - 16 q^{48} + 50 q^{50} - 56 q^{51} - 12 q^{52} + 106 q^{53} + 80 q^{57} + 80 q^{58} - 40 q^{60} + 96 q^{61} + 104 q^{62} - 30 q^{65} + 64 q^{66} + 124 q^{67} + 28 q^{68} - 56 q^{71} + 4 q^{72} + 94 q^{73} - 100 q^{75} - 80 q^{76} + 24 q^{78} + 142 q^{81} - 16 q^{82} - 36 q^{83} + 70 q^{85} + 168 q^{86} + 160 q^{87} - 32 q^{88} + 10 q^{90} - 8 q^{92} - 208 q^{93} - 200 q^{95} + 32 q^{96} + 126 q^{97}+O(q^{100}) $ 2 * q - 2 * q^2 + 4 * q^3 - 8 * q^6 + 4 * q^8 + 10 * q^10 - 16 * q^11 + 8 * q^12 - 6 * q^13 + 20 * q^15 - 8 * q^16 - 14 * q^17 + 2 * q^18 - 20 * q^20 + 16 * q^22 - 4 * q^23 - 50 * q^25 + 12 * q^26 + 40 * q^27 - 104 * q^31 + 8 * q^32 - 32 * q^33 - 4 * q^36 - 6 * q^37 + 40 * q^38 + 20 * q^40 + 16 * q^41 - 84 * q^43 - 10 * q^45 + 8 * q^46 + 36 * q^47 - 16 * q^48 + 50 * q^50 - 56 * q^51 - 12 * q^52 + 106 * q^53 + 80 * q^57 + 80 * q^58 - 40 * q^60 + 96 * q^61 + 104 * q^62 - 30 * q^65 + 64 * q^66 + 124 * q^67 + 28 * q^68 - 56 * q^71 + 4 * q^72 + 94 * q^73 - 100 * q^75 - 80 * q^76 + 24 * q^78 + 142 * q^81 - 16 * q^82 - 36 * q^83 + 70 * q^85 + 168 * q^86 + 160 * q^87 - 32 * q^88 + 10 * q^90 - 8 * q^92 - 208 * q^93 - 200 * q^95 + 32 * q^96 + 126 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	2.00000	−	2.00000i	0.666667	−	0.666667i	−0.290276	−	0.956943i	$-0.593747\pi$
$3$	2.00000	−	2.00000i	0.666667	−	0.666667i	0.956943	+	0.290276i	$0.0937472\pi$
$4$			2.00000i			0.500000i
$5$			5.00000i			1.00000i
$5$			5.00000i			1.00000i
$6$	−4.00000			−0.666667
$7$		0			0
$7$		0			0
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$			1.00000i			0.111111i
$10$	5.00000	−	5.00000i	0.500000	−	0.500000i
$11$	−8.00000			−0.727273			−0.363636	−	0.931541i	$-0.618465\pi$
$11$	−8.00000			−0.727273			−0.363636	+	0.931541i	$0.618465\pi$
$12$	4.00000	+	4.00000i	0.333333	+	0.333333i
$13$	−3.00000	+	3.00000i	−0.230769	+	0.230769i	−0.813014	−	0.582245i	$-0.802175\pi$
$13$	−3.00000	+	3.00000i	−0.230769	+	0.230769i	0.582245	+	0.813014i	$0.302175\pi$
$14$		0			0
$15$	10.0000	+	10.0000i	0.666667	+	0.666667i
$16$	−4.00000			−0.250000
$17$	−7.00000	−	7.00000i	−0.411765	−	0.411765i	0.470588	−	0.882353i	$-0.344042\pi$
$17$	−7.00000	−	7.00000i	−0.411765	−	0.411765i	−0.882353	+	0.470588i	$0.844042\pi$
$18$	1.00000	−	1.00000i	0.0555556	−	0.0555556i
$19$			20.0000i			1.05263i	0.850289	+	0.526316i	$0.176427\pi$
$19$			20.0000i			1.05263i	−0.850289	+	0.526316i	$0.823573\pi$
$20$	−10.0000			−0.500000
$21$		0			0
$22$	8.00000	+	8.00000i	0.363636	+	0.363636i
$23$	−2.00000	+	2.00000i	−0.0869565	+	0.0869565i	−0.749247	−	0.662291i	$-0.769584\pi$
$23$	−2.00000	+	2.00000i	−0.0869565	+	0.0869565i	0.662291	+	0.749247i	$0.269584\pi$
$24$		−	8.00000i		−	0.333333i
$25$	−25.0000			−1.00000
$26$	6.00000			0.230769
$27$	20.0000	+	20.0000i	0.740741	+	0.740741i
$28$		0			0
$29$			40.0000i			1.37931i	0.724138	+	0.689655i	$0.242238\pi$
$29$			40.0000i			1.37931i	−0.724138	+	0.689655i	$0.757762\pi$
$30$		−	20.0000i		−	0.666667i
$31$	−52.0000			−1.67742			−0.838710	−	0.544579i	$-0.816690\pi$
$31$	−52.0000			−1.67742			−0.838710	+	0.544579i	$0.816690\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	−16.0000	+	16.0000i	−0.484848	+	0.484848i
$34$			14.0000i			0.411765i
$35$		0			0
$36$	−2.00000			−0.0555556
$37$	−3.00000	−	3.00000i	−0.0810811	−	0.0810811i	0.665403	−	0.746484i	$-0.268260\pi$
$37$	−3.00000	−	3.00000i	−0.0810811	−	0.0810811i	−0.746484	+	0.665403i	$0.768260\pi$
$38$	20.0000	−	20.0000i	0.526316	−	0.526316i
$39$			12.0000i			0.307692i
$40$	10.0000	+	10.0000i	0.250000	+	0.250000i
$41$	8.00000			0.195122			0.0975610	−	0.995230i	$-0.468896\pi$
$41$	8.00000			0.195122			0.0975610	+	0.995230i	$0.468896\pi$
$42$		0			0
$43$	−42.0000	+	42.0000i	−0.976744	+	0.976744i	−0.999736	−	0.0229915i	$-0.992681\pi$
$43$	−42.0000	+	42.0000i	−0.976744	+	0.976744i	0.0229915	+	0.999736i	$0.492681\pi$
$44$		−	16.0000i		−	0.363636i
$45$	−5.00000			−0.111111
$46$	4.00000			0.0869565
$47$	18.0000	+	18.0000i	0.382979	+	0.382979i	0.872174	−	0.489195i	$-0.162710\pi$
$47$	18.0000	+	18.0000i	0.382979	+	0.382979i	−0.489195	+	0.872174i	$0.662710\pi$
$48$	−8.00000	+	8.00000i	−0.166667	+	0.166667i
$49$		0			0
$50$	25.0000	+	25.0000i	0.500000	+	0.500000i
$51$	−28.0000			−0.549020
$52$	−6.00000	−	6.00000i	−0.115385	−	0.115385i
$53$	53.0000	−	53.0000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$53$	53.0000	−	53.0000i	1.00000	−	1.00000i	1.00000			$0$
$54$		−	40.0000i		−	0.740741i
$55$		−	40.0000i		−	0.727273i
$56$		0			0
$57$	40.0000	+	40.0000i	0.701754	+	0.701754i
$58$	40.0000	−	40.0000i	0.689655	−	0.689655i
$59$			20.0000i			0.338983i	0.985532	+	0.169492i	$0.0542125\pi$
$59$			20.0000i			0.338983i	−0.985532	+	0.169492i	$0.945787\pi$
$60$	−20.0000	+	20.0000i	−0.333333	+	0.333333i
$61$	48.0000			0.786885			0.393443	−	0.919349i	$-0.371284\pi$
$61$	48.0000			0.786885			0.393443	+	0.919349i	$0.371284\pi$
$62$	52.0000	+	52.0000i	0.838710	+	0.838710i
$63$		0			0
$64$		−	8.00000i		−	0.125000i
$65$	−15.0000	−	15.0000i	−0.230769	−	0.230769i
$66$	32.0000			0.484848
$67$	62.0000	+	62.0000i	0.925373	+	0.925373i	0.997403	−	0.0720294i	$-0.0229475\pi$
$67$	62.0000	+	62.0000i	0.925373	+	0.925373i	−0.0720294	+	0.997403i	$0.522948\pi$
$68$	14.0000	−	14.0000i	0.205882	−	0.205882i
$69$			8.00000i			0.115942i
$70$		0			0
$71$	−28.0000			−0.394366			−0.197183	−	0.980367i	$-0.563179\pi$
$71$	−28.0000			−0.394366			−0.197183	+	0.980367i	$0.563179\pi$
$72$	2.00000	+	2.00000i	0.0277778	+	0.0277778i
$73$	47.0000	−	47.0000i	0.643836	−	0.643836i	−0.307661	−	0.951496i	$-0.599546\pi$
$73$	47.0000	−	47.0000i	0.643836	−	0.643836i	0.951496	+	0.307661i	$0.0995461\pi$
$74$			6.00000i			0.0810811i
$75$	−50.0000	+	50.0000i	−0.666667	+	0.666667i
$76$	−40.0000			−0.526316
$77$		0			0
$78$	12.0000	−	12.0000i	0.153846	−	0.153846i
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$		−	20.0000i		−	0.250000i
$81$	71.0000			0.876543
$82$	−8.00000	−	8.00000i	−0.0975610	−	0.0975610i
$83$	−18.0000	+	18.0000i	−0.216867	+	0.216867i	−0.807177	−	0.590310i	$-0.799006\pi$
$83$	−18.0000	+	18.0000i	−0.216867	+	0.216867i	0.590310	+	0.807177i	$0.299006\pi$
$84$		0			0
$85$	35.0000	−	35.0000i	0.411765	−	0.411765i
$86$	84.0000			0.976744
$87$	80.0000	+	80.0000i	0.919540	+	0.919540i
$88$	−16.0000	+	16.0000i	−0.181818	+	0.181818i
$89$		−	80.0000i		−	0.898876i	−0.893311	−	0.449438i	$-0.851624\pi$
$89$		−	80.0000i		−	0.898876i	0.893311	−	0.449438i	$-0.148376\pi$
$90$	5.00000	+	5.00000i	0.0555556	+	0.0555556i
$91$		0			0
$92$	−4.00000	−	4.00000i	−0.0434783	−	0.0434783i
$93$	−104.000	+	104.000i	−1.11828	+	1.11828i
$94$		−	36.0000i		−	0.382979i
$95$	−100.000			−1.05263
$96$	16.0000			0.166667
$97$	63.0000	+	63.0000i	0.649485	+	0.649485i	0.952868	−	0.303384i	$-0.0981164\pi$
$97$	63.0000	+	63.0000i	0.649485	+	0.649485i	−0.303384	+	0.952868i	$0.598116\pi$
$98$		0			0
$99$		−	8.00000i		−	0.0808081i
$100$		−	50.0000i		−	0.500000i
$101$	−62.0000			−0.613861			−0.306931	−	0.951732i	$-0.599302\pi$
$101$	−62.0000			−0.613861			−0.306931	+	0.951732i	$0.599302\pi$
$102$	28.0000	+	28.0000i	0.274510	+	0.274510i
$103$	−118.000	+	118.000i	−1.14563	+	1.14563i	−0.158229	+	0.987403i	$0.550578\pi$
$103$	−118.000	+	118.000i	−1.14563	+	1.14563i	−0.987403	+	0.158229i	$0.949422\pi$
$104$			12.0000i			0.115385i
$105$		0			0
$106$	−106.000			−1.00000
$107$	142.000	+	142.000i	1.32710	+	1.32710i	0.907886	+	0.419217i	$0.137695\pi$
$107$	142.000	+	142.000i	1.32710	+	1.32710i	0.419217	+	0.907886i	$0.362305\pi$
$108$	−40.0000	+	40.0000i	−0.370370	+	0.370370i
$109$		−	10.0000i		−	0.0917431i	−0.998947	−	0.0458716i	$-0.985394\pi$
$109$		−	10.0000i		−	0.0917431i	0.998947	−	0.0458716i	$-0.0146065\pi$
$110$	−40.0000	+	40.0000i	−0.363636	+	0.363636i
$111$	−12.0000			−0.108108
$112$		0			0
$113$	23.0000	−	23.0000i	0.203540	−	0.203540i	−0.597975	−	0.801515i	$-0.704028\pi$
$113$	23.0000	−	23.0000i	0.203540	−	0.203540i	0.801515	+	0.597975i	$0.204028\pi$
$114$		−	80.0000i		−	0.701754i
$115$	−10.0000	−	10.0000i	−0.0869565	−	0.0869565i
$116$	−80.0000			−0.689655
$117$	−3.00000	−	3.00000i	−0.0256410	−	0.0256410i
$118$	20.0000	−	20.0000i	0.169492	−	0.169492i
$119$		0			0
$120$	40.0000			0.333333
$121$	−57.0000			−0.471074
$122$	−48.0000	−	48.0000i	−0.393443	−	0.393443i
$123$	16.0000	−	16.0000i	0.130081	−	0.130081i
$124$		−	104.000i		−	0.838710i
$125$		−	125.000i		−	1.00000i
$126$		0			0
$127$	−118.000	−	118.000i	−0.929134	−	0.929134i	0.0685161	−	0.997650i	$-0.478174\pi$
$127$	−118.000	−	118.000i	−0.929134	−	0.929134i	−0.997650	+	0.0685161i	$0.978174\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$			168.000i			1.30233i
$130$			30.0000i			0.230769i
$131$	128.000			0.977099			0.488550	−	0.872536i	$-0.337526\pi$
$131$	128.000			0.977099			0.488550	+	0.872536i	$0.337526\pi$
$132$	−32.0000	−	32.0000i	−0.242424	−	0.242424i
$133$		0			0
$134$		−	124.000i		−	0.925373i
$135$	−100.000	+	100.000i	−0.740741	+	0.740741i
$136$	−28.0000			−0.205882
$137$	−63.0000	−	63.0000i	−0.459854	−	0.459854i	0.438753	−	0.898607i	$-0.355420\pi$
$137$	−63.0000	−	63.0000i	−0.459854	−	0.459854i	−0.898607	+	0.438753i	$0.855420\pi$
$138$	8.00000	−	8.00000i	0.0579710	−	0.0579710i
$139$		−	140.000i		−	1.00719i	−0.863939	−	0.503597i	$-0.832010\pi$
$139$		−	140.000i		−	1.00719i	0.863939	−	0.503597i	$-0.167990\pi$
$140$		0			0
$141$	72.0000			0.510638
$142$	28.0000	+	28.0000i	0.197183	+	0.197183i
$143$	24.0000	−	24.0000i	0.167832	−	0.167832i
$144$		−	4.00000i		−	0.0277778i
$145$	−200.000			−1.37931
$146$	−94.0000			−0.643836
$147$		0			0
$148$	6.00000	−	6.00000i	0.0405405	−	0.0405405i
$149$		−	150.000i		−	1.00671i	−0.864079	−	0.503356i	$-0.832099\pi$
$149$		−	150.000i		−	1.00671i	0.864079	−	0.503356i	$-0.167901\pi$
$150$	100.000			0.666667
$151$	52.0000			0.344371			0.172185	−	0.985065i	$-0.444917\pi$
$151$	52.0000			0.344371			0.172185	+	0.985065i	$0.444917\pi$
$152$	40.0000	+	40.0000i	0.263158	+	0.263158i
$153$	7.00000	−	7.00000i	0.0457516	−	0.0457516i
$154$		0			0
$155$		−	260.000i		−	1.67742i
$156$	−24.0000			−0.153846
$157$	−27.0000	−	27.0000i	−0.171975	−	0.171975i	0.615872	−	0.787846i	$-0.288804\pi$
$157$	−27.0000	−	27.0000i	−0.171975	−	0.171975i	−0.787846	+	0.615872i	$0.788804\pi$
$158$		0			0
$159$		−	212.000i		−	1.33333i
$160$	−20.0000	+	20.0000i	−0.125000	+	0.125000i
$161$		0			0
$162$	−71.0000	−	71.0000i	−0.438272	−	0.438272i
$163$	−82.0000	+	82.0000i	−0.503067	+	0.503067i	−0.912390	−	0.409322i	$-0.865765\pi$
$163$	−82.0000	+	82.0000i	−0.503067	+	0.503067i	0.409322	+	0.912390i	$0.365765\pi$
$164$			16.0000i			0.0975610i
$165$	−80.0000	−	80.0000i	−0.484848	−	0.484848i
$166$	36.0000			0.216867
$167$	−62.0000	−	62.0000i	−0.371257	−	0.371257i	0.496678	−	0.867935i	$-0.334553\pi$
$167$	−62.0000	−	62.0000i	−0.371257	−	0.371257i	−0.867935	+	0.496678i	$0.834553\pi$
$168$		0			0
$169$			151.000i			0.893491i
$170$	−70.0000			−0.411765
$171$	−20.0000			−0.116959
$172$	−84.0000	−	84.0000i	−0.488372	−	0.488372i
$173$	107.000	−	107.000i	0.618497	−	0.618497i	−0.326649	−	0.945146i	$-0.605919\pi$
$173$	107.000	−	107.000i	0.618497	−	0.618497i	0.945146	+	0.326649i	$0.105919\pi$
$174$		−	160.000i		−	0.919540i
$175$		0			0
$176$	32.0000			0.181818
$177$	40.0000	+	40.0000i	0.225989	+	0.225989i
$178$	−80.0000	+	80.0000i	−0.449438	+	0.449438i
$179$		−	220.000i		−	1.22905i	−0.788897	−	0.614525i	$-0.789348\pi$
$179$		−	220.000i		−	1.22905i	0.788897	−	0.614525i	$-0.210652\pi$
$180$		−	10.0000i		−	0.0555556i
$181$	−2.00000			−0.0110497			−0.00552486	−	0.999985i	$-0.501759\pi$
$181$	−2.00000			−0.0110497			−0.00552486	+	0.999985i	$0.501759\pi$
$182$		0			0
$183$	96.0000	−	96.0000i	0.524590	−	0.524590i
$184$			8.00000i			0.0434783i
$185$	15.0000	−	15.0000i	0.0810811	−	0.0810811i
$186$	208.000			1.11828
$187$	56.0000	+	56.0000i	0.299465	+	0.299465i
$188$	−36.0000	+	36.0000i	−0.191489	+	0.191489i
$189$		0			0
$190$	100.000	+	100.000i	0.526316	+	0.526316i
$191$	212.000			1.10995			0.554974	−	0.831868i	$-0.312728\pi$
$191$	212.000			1.10995			0.554974	+	0.831868i	$0.312728\pi$
$192$	−16.0000	−	16.0000i	−0.0833333	−	0.0833333i
$193$	−57.0000	+	57.0000i	−0.295337	+	0.295337i	−0.839184	−	0.543847i	$-0.816967\pi$
$193$	−57.0000	+	57.0000i	−0.295337	+	0.295337i	0.543847	+	0.839184i	$0.316967\pi$
$194$		−	126.000i		−	0.649485i
$195$	−60.0000			−0.307692
$196$		0			0
$197$	−3.00000	−	3.00000i	−0.0152284	−	0.0152284i	0.699452	−	0.714680i	$-0.253428\pi$
$197$	−3.00000	−	3.00000i	−0.0152284	−	0.0152284i	−0.714680	+	0.699452i	$0.753428\pi$
$198$	−8.00000	+	8.00000i	−0.0404040	+	0.0404040i
$199$			120.000i			0.603015i	0.953464	+	0.301508i	$0.0974898\pi$
$199$			120.000i			0.603015i	−0.953464	+	0.301508i	$0.902510\pi$
$200$	−50.0000	+	50.0000i	−0.250000	+	0.250000i
$201$	248.000			1.23383
$202$	62.0000	+	62.0000i	0.306931	+	0.306931i
$203$		0			0
$204$		−	56.0000i		−	0.274510i
$205$			40.0000i			0.195122i
$206$	236.000			1.14563
$207$	−2.00000	−	2.00000i	−0.00966184	−	0.00966184i
$208$	12.0000	−	12.0000i	0.0576923	−	0.0576923i
$209$		−	160.000i		−	0.765550i
$210$		0			0
$211$	−328.000			−1.55450			−0.777251	−	0.629190i	$-0.783387\pi$
$211$	−328.000			−1.55450			−0.777251	+	0.629190i	$0.783387\pi$
$212$	106.000	+	106.000i	0.500000	+	0.500000i
$213$	−56.0000	+	56.0000i	−0.262911	+	0.262911i
$214$		−	284.000i		−	1.32710i
$215$	−210.000	−	210.000i	−0.976744	−	0.976744i
$216$	80.0000			0.370370
$217$		0			0
$218$	−10.0000	+	10.0000i	−0.0458716	+	0.0458716i
$219$		−	188.000i		−	0.858447i
$220$	80.0000			0.363636
$221$	42.0000			0.190045
$222$	12.0000	+	12.0000i	0.0540541	+	0.0540541i
$223$	−138.000	+	138.000i	−0.618834	+	0.618834i	−0.945232	−	0.326398i	$-0.894165\pi$
$223$	−138.000	+	138.000i	−0.618834	+	0.618834i	0.326398	+	0.945232i	$0.394165\pi$
$224$		0			0
$225$		−	25.0000i		−	0.111111i
$226$	−46.0000			−0.203540
$227$	−2.00000	−	2.00000i	−0.00881057	−	0.00881057i	0.702688	−	0.711498i	$-0.251983\pi$
$227$	−2.00000	−	2.00000i	−0.00881057	−	0.00881057i	−0.711498	+	0.702688i	$0.751983\pi$
$228$	−80.0000	+	80.0000i	−0.350877	+	0.350877i
$229$		−	120.000i		−	0.524017i	−0.965066	−	0.262009i	$-0.915615\pi$
$229$		−	120.000i		−	0.524017i	0.965066	−	0.262009i	$-0.0843849\pi$
$230$			20.0000i			0.0869565i
$231$		0			0
$232$	80.0000	+	80.0000i	0.344828	+	0.344828i
$233$	183.000	−	183.000i	0.785408	−	0.785408i	−0.195330	−	0.980738i	$-0.562578\pi$
$233$	183.000	−	183.000i	0.785408	−	0.785408i	0.980738	+	0.195330i	$0.0625777\pi$
$234$			6.00000i			0.0256410i
$235$	−90.0000	+	90.0000i	−0.382979	+	0.382979i
$236$	−40.0000			−0.169492
$237$		0			0
$238$		0			0
$239$			120.000i			0.502092i	0.967975	+	0.251046i	$0.0807746\pi$
$239$			120.000i			0.502092i	−0.967975	+	0.251046i	$0.919225\pi$
$240$	−40.0000	−	40.0000i	−0.166667	−	0.166667i
$241$	−232.000			−0.962656			−0.481328	−	0.876541i	$-0.659845\pi$
$241$	−232.000			−0.962656			−0.481328	+	0.876541i	$0.659845\pi$
$242$	57.0000	+	57.0000i	0.235537	+	0.235537i
$243$	−38.0000	+	38.0000i	−0.156379	+	0.156379i
$244$			96.0000i			0.393443i
$245$		0			0
$246$	−32.0000			−0.130081
$247$	−60.0000	−	60.0000i	−0.242915	−	0.242915i
$248$	−104.000	+	104.000i	−0.419355	+	0.419355i
$249$			72.0000i			0.289157i
$250$	−125.000	+	125.000i	−0.500000	+	0.500000i
$251$	48.0000			0.191235			0.0956175	−	0.995418i	$-0.469517\pi$
$251$	48.0000			0.191235			0.0956175	+	0.995418i	$0.469517\pi$
$252$		0			0
$253$	16.0000	−	16.0000i	0.0632411	−	0.0632411i
$254$			236.000i			0.929134i
$255$		−	140.000i		−	0.549020i
$256$	16.0000			0.0625000
$257$	313.000	+	313.000i	1.21790	+	1.21790i	0.968366	+	0.249532i	$0.0802769\pi$
$257$	313.000	+	313.000i	1.21790	+	1.21790i	0.249532	+	0.968366i	$0.419723\pi$
$258$	168.000	−	168.000i	0.651163	−	0.651163i
$259$		0			0
$260$	30.0000	−	30.0000i	0.115385	−	0.115385i
$261$	−40.0000			−0.153257
$262$	−128.000	−	128.000i	−0.488550	−	0.488550i
$263$	−262.000	+	262.000i	−0.996198	+	0.996198i	−0.999993	−	0.00379508i	$-0.998792\pi$
$263$	−262.000	+	262.000i	−0.996198	+	0.996198i	0.00379508	+	0.999993i	$0.498792\pi$
$264$			64.0000i			0.242424i
$265$	265.000	+	265.000i	1.00000	+	1.00000i
$266$		0			0
$267$	−160.000	−	160.000i	−0.599251	−	0.599251i
$268$	−124.000	+	124.000i	−0.462687	+	0.462687i
$269$		−	10.0000i		−	0.0371747i	−0.999827	−	0.0185874i	$-0.994083\pi$
$269$		−	10.0000i		−	0.0371747i	0.999827	−	0.0185874i	$-0.00591688\pi$
$270$	200.000			0.740741
$271$	−252.000			−0.929889			−0.464945	−	0.885340i	$-0.653926\pi$
$271$	−252.000			−0.929889			−0.464945	+	0.885340i	$0.653926\pi$
$272$	28.0000	+	28.0000i	0.102941	+	0.102941i
$273$		0			0
$274$			126.000i			0.459854i
$275$	200.000			0.727273
$276$	−16.0000			−0.0579710
$277$	267.000	+	267.000i	0.963899	+	0.963899i	0.999371	−	0.0354718i	$-0.0112934\pi$
$277$	267.000	+	267.000i	0.963899	+	0.963899i	−0.0354718	+	0.999371i	$0.511293\pi$
$278$	−140.000	+	140.000i	−0.503597	+	0.503597i
$279$		−	52.0000i		−	0.186380i
$280$		0			0
$281$	312.000			1.11032			0.555160	−	0.831743i	$-0.312657\pi$
$281$	312.000			1.11032			0.555160	+	0.831743i	$0.312657\pi$
$282$	−72.0000	−	72.0000i	−0.255319	−	0.255319i
$283$	262.000	−	262.000i	0.925795	−	0.925795i	−0.0716358	−	0.997431i	$-0.522822\pi$
$283$	262.000	−	262.000i	0.925795	−	0.925795i	0.997431	+	0.0716358i	$0.0228219\pi$
$284$		−	56.0000i		−	0.197183i
$285$	−200.000	+	200.000i	−0.701754	+	0.701754i
$286$	−48.0000			−0.167832
$287$		0			0
$288$	−4.00000	+	4.00000i	−0.0138889	+	0.0138889i
$289$		−	191.000i		−	0.660900i
$290$	200.000	+	200.000i	0.689655	+	0.689655i
$291$	252.000			0.865979
$292$	94.0000	+	94.0000i	0.321918	+	0.321918i
$293$	−243.000	+	243.000i	−0.829352	+	0.829352i	−0.987427	−	0.158075i	$-0.949471\pi$
$293$	−243.000	+	243.000i	−0.829352	+	0.829352i	0.158075	+	0.987427i	$0.449471\pi$
$294$		0			0
$295$	−100.000			−0.338983
$296$	−12.0000			−0.0405405
$297$	−160.000	−	160.000i	−0.538721	−	0.538721i
$298$	−150.000	+	150.000i	−0.503356	+	0.503356i
$299$		−	12.0000i		−	0.0401338i
$300$	−100.000	−	100.000i	−0.333333	−	0.333333i
$301$		0			0
$302$	−52.0000	−	52.0000i	−0.172185	−	0.172185i
$303$	−124.000	+	124.000i	−0.409241	+	0.409241i
$304$		−	80.0000i		−	0.263158i
$305$			240.000i			0.786885i
$306$	−14.0000			−0.0457516
$307$	18.0000	+	18.0000i	0.0586319	+	0.0586319i	0.735815	−	0.677183i	$-0.236799\pi$
$307$	18.0000	+	18.0000i	0.0586319	+	0.0586319i	−0.677183	+	0.735815i	$0.736799\pi$
$308$		0			0
$309$			472.000i			1.52751i
$310$	−260.000	+	260.000i	−0.838710	+	0.838710i
$311$	388.000			1.24759			0.623794	−	0.781589i	$-0.285590\pi$
$311$	388.000			1.24759			0.623794	+	0.781589i	$0.285590\pi$
$312$	24.0000	+	24.0000i	0.0769231	+	0.0769231i
$313$	−183.000	+	183.000i	−0.584665	+	0.584665i	−0.936182	−	0.351517i	$-0.885666\pi$
$313$	−183.000	+	183.000i	−0.584665	+	0.584665i	0.351517	+	0.936182i	$0.385666\pi$
$314$			54.0000i			0.171975i
$315$		0			0
$316$		0			0
$317$	−213.000	−	213.000i	−0.671924	−	0.671924i	0.286235	−	0.958159i	$-0.407596\pi$
$317$	−213.000	−	213.000i	−0.671924	−	0.671924i	−0.958159	+	0.286235i	$0.907596\pi$
$318$	−212.000	+	212.000i	−0.666667	+	0.666667i
$319$		−	320.000i		−	1.00313i
$320$	40.0000			0.125000
$321$	568.000			1.76947
$322$		0			0
$323$	140.000	−	140.000i	0.433437	−	0.433437i
$324$			142.000i			0.438272i
$325$	75.0000	−	75.0000i	0.230769	−	0.230769i
$326$	164.000			0.503067
$327$	−20.0000	−	20.0000i	−0.0611621	−	0.0611621i
$328$	16.0000	−	16.0000i	0.0487805	−	0.0487805i
$329$		0			0
$330$			160.000i			0.484848i
$331$	232.000			0.700906			0.350453	−	0.936580i	$-0.386028\pi$
$331$	232.000			0.700906			0.350453	+	0.936580i	$0.386028\pi$
$332$	−36.0000	−	36.0000i	−0.108434	−	0.108434i
$333$	3.00000	−	3.00000i	0.00900901	−	0.00900901i
$334$			124.000i			0.371257i
$335$	−310.000	+	310.000i	−0.925373	+	0.925373i
$336$		0			0
$337$	417.000	+	417.000i	1.23739	+	1.23739i	0.961064	+	0.276324i	$0.0891164\pi$
$337$	417.000	+	417.000i	1.23739	+	1.23739i	0.276324	+	0.961064i	$0.410884\pi$
$338$	151.000	−	151.000i	0.446746	−	0.446746i
$339$		−	92.0000i		−	0.271386i
$340$	70.0000	+	70.0000i	0.205882	+	0.205882i
$341$	416.000			1.21994
$342$	20.0000	+	20.0000i	0.0584795	+	0.0584795i
$343$		0			0
$344$			168.000i			0.488372i
$345$	−40.0000			−0.115942
$346$	−214.000			−0.618497
$347$	202.000	+	202.000i	0.582133	+	0.582133i	0.935489	−	0.353356i	$-0.114960\pi$
$347$	202.000	+	202.000i	0.582133	+	0.582133i	−0.353356	+	0.935489i	$0.614960\pi$
$348$	−160.000	+	160.000i	−0.459770	+	0.459770i
$349$			440.000i			1.26074i	0.776293	+	0.630372i	$0.217098\pi$
$349$			440.000i			1.26074i	−0.776293	+	0.630372i	$0.782902\pi$
$350$		0			0
$351$	−120.000			−0.341880
$352$	−32.0000	−	32.0000i	−0.0909091	−	0.0909091i
$353$	447.000	−	447.000i	1.26629	−	1.26629i	0.318298	−	0.947991i	$-0.396889\pi$
$353$	447.000	−	447.000i	1.26629	−	1.26629i	0.947991	−	0.318298i	$-0.103111\pi$
$354$		−	80.0000i		−	0.225989i
$355$		−	140.000i		−	0.394366i
$356$	160.000			0.449438
$357$		0			0
$358$	−220.000	+	220.000i	−0.614525	+	0.614525i
$359$		−	400.000i		−	1.11421i	−0.830443	−	0.557103i	$-0.811913\pi$
$359$		−	400.000i		−	1.11421i	0.830443	−	0.557103i	$-0.188087\pi$
$360$	−10.0000	+	10.0000i	−0.0277778	+	0.0277778i
$361$	−39.0000			−0.108033
$362$	2.00000	+	2.00000i	0.00552486	+	0.00552486i
$363$	−114.000	+	114.000i	−0.314050	+	0.314050i
$364$		0			0
$365$	235.000	+	235.000i	0.643836	+	0.643836i
$366$	−192.000			−0.524590
$367$	118.000	+	118.000i	0.321526	+	0.321526i	0.849352	−	0.527826i	$-0.176993\pi$
$367$	118.000	+	118.000i	0.321526	+	0.321526i	−0.527826	+	0.849352i	$0.676993\pi$
$368$	8.00000	−	8.00000i	0.0217391	−	0.0217391i
$369$			8.00000i			0.0216802i
$370$	−30.0000			−0.0810811
$371$		0			0
$372$	−208.000	−	208.000i	−0.559140	−	0.559140i
$373$	−107.000	+	107.000i	−0.286863	+	0.286863i	−0.835839	−	0.548975i	$-0.815018\pi$
$373$	−107.000	+	107.000i	−0.286863	+	0.286863i	0.548975	+	0.835839i	$0.315018\pi$
$374$		−	112.000i		−	0.299465i
$375$	−250.000	−	250.000i	−0.666667	−	0.666667i
$376$	72.0000			0.191489
$377$	−120.000	−	120.000i	−0.318302	−	0.318302i
$378$		0			0
$379$			340.000i			0.897098i	0.893758	+	0.448549i	$0.148059\pi$
$379$			340.000i			0.897098i	−0.893758	+	0.448549i	$0.851941\pi$
$380$		−	200.000i		−	0.526316i
$381$	−472.000			−1.23885
$382$	−212.000	−	212.000i	−0.554974	−	0.554974i
$383$	342.000	−	342.000i	0.892950	−	0.892950i	−0.101849	−	0.994800i	$-0.532476\pi$
$383$	342.000	−	342.000i	0.892950	−	0.892950i	0.994800	+	0.101849i	$0.0324760\pi$
$384$			32.0000i			0.0833333i
$385$		0			0
$386$	114.000			0.295337
$387$	−42.0000	−	42.0000i	−0.108527	−	0.108527i
$388$	−126.000	+	126.000i	−0.324742	+	0.324742i
$389$			390.000i			1.00257i	0.865282	+	0.501285i	$0.167139\pi$
$389$			390.000i			1.00257i	−0.865282	+	0.501285i	$0.832861\pi$
$390$	60.0000	+	60.0000i	0.153846	+	0.153846i
$391$	28.0000			0.0716113
$392$		0			0
$393$	256.000	−	256.000i	0.651399	−	0.651399i
$394$			6.00000i			0.0152284i
$395$		0			0
$396$	16.0000			0.0404040
$397$	323.000	+	323.000i	0.813602	+	0.813602i	0.985172	−	0.171570i	$-0.0548839\pi$
$397$	323.000	+	323.000i	0.813602	+	0.813602i	−0.171570	+	0.985172i	$0.554884\pi$
$398$	120.000	−	120.000i	0.301508	−	0.301508i
$399$		0			0
$400$	100.000			0.250000
$401$	642.000			1.60100			0.800499	−	0.599334i	$-0.204568\pi$
$401$	642.000			1.60100			0.800499	+	0.599334i	$0.204568\pi$
$402$	−248.000	−	248.000i	−0.616915	−	0.616915i
$403$	156.000	−	156.000i	0.387097	−	0.387097i
$404$		−	124.000i		−	0.306931i
$405$			355.000i			0.876543i
$406$		0			0
$407$	24.0000	+	24.0000i	0.0589681	+	0.0589681i
$408$	−56.0000	+	56.0000i	−0.137255	+	0.137255i
$409$			150.000i			0.366748i	0.983043	+	0.183374i	$0.0587020\pi$
$409$			150.000i			0.366748i	−0.983043	+	0.183374i	$0.941298\pi$
$410$	40.0000	−	40.0000i	0.0975610	−	0.0975610i
$411$	−252.000			−0.613139
$412$	−236.000	−	236.000i	−0.572816	−	0.572816i
$413$		0			0
$414$			4.00000i			0.00966184i
$415$	−90.0000	−	90.0000i	−0.216867	−	0.216867i
$416$	−24.0000			−0.0576923
$417$	−280.000	−	280.000i	−0.671463	−	0.671463i
$418$	−160.000	+	160.000i	−0.382775	+	0.382775i
$419$		−	300.000i		−	0.715990i	−0.933723	−	0.357995i	$-0.883460\pi$
$419$		−	300.000i		−	0.715990i	0.933723	−	0.357995i	$-0.116540\pi$
$420$		0			0
$421$	−208.000			−0.494062			−0.247031	−	0.969008i	$-0.579455\pi$
$421$	−208.000			−0.494062			−0.247031	+	0.969008i	$0.579455\pi$
$422$	328.000	+	328.000i	0.777251	+	0.777251i
$423$	−18.0000	+	18.0000i	−0.0425532	+	0.0425532i
$424$		−	212.000i		−	0.500000i
$425$	175.000	+	175.000i	0.411765	+	0.411765i
$426$	112.000			0.262911
$427$		0			0
$428$	−284.000	+	284.000i	−0.663551	+	0.663551i
$429$		−	96.0000i		−	0.223776i
$430$			420.000i			0.976744i
$431$	−788.000			−1.82831			−0.914153	−	0.405369i	$-0.867143\pi$
$431$	−788.000			−1.82831			−0.914153	+	0.405369i	$0.867143\pi$
$432$	−80.0000	−	80.0000i	−0.185185	−	0.185185i
$433$	367.000	−	367.000i	0.847575	−	0.847575i	−0.142255	−	0.989830i	$-0.545435\pi$
$433$	367.000	−	367.000i	0.847575	−	0.847575i	0.989830	+	0.142255i	$0.0454353\pi$
$434$		0			0
$435$	−400.000	+	400.000i	−0.919540	+	0.919540i
$436$	20.0000			0.0458716
$437$	−40.0000	−	40.0000i	−0.0915332	−	0.0915332i
$438$	−188.000	+	188.000i	−0.429224	+	0.429224i
$439$		−	560.000i		−	1.27563i	−0.770191	−	0.637813i	$-0.779839\pi$
$439$		−	560.000i		−	1.27563i	0.770191	−	0.637813i	$-0.220161\pi$
$440$	−80.0000	−	80.0000i	−0.181818	−	0.181818i
$441$		0			0
$442$	−42.0000	−	42.0000i	−0.0950226	−	0.0950226i
$443$	378.000	−	378.000i	0.853273	−	0.853273i	−0.137262	−	0.990535i	$-0.543830\pi$
$443$	378.000	−	378.000i	0.853273	−	0.853273i	0.990535	+	0.137262i	$0.0438301\pi$
$444$		−	24.0000i		−	0.0540541i
$445$	400.000			0.898876
$446$	276.000			0.618834
$447$	−300.000	−	300.000i	−0.671141	−	0.671141i
$448$		0			0
$449$		−	410.000i		−	0.913140i	−0.889687	−	0.456570i	$-0.849078\pi$
$449$		−	410.000i		−	0.913140i	0.889687	−	0.456570i	$-0.150922\pi$
$450$	−25.0000	+	25.0000i	−0.0555556	+	0.0555556i
$451$	−64.0000			−0.141907
$452$	46.0000	+	46.0000i	0.101770	+	0.101770i
$453$	104.000	−	104.000i	0.229581	−	0.229581i
$454$			4.00000i			0.00881057i
$455$		0			0
$456$	160.000			0.350877
$457$	−393.000	−	393.000i	−0.859956	−	0.859956i	0.131376	−	0.991333i	$-0.458060\pi$
$457$	−393.000	−	393.000i	−0.859956	−	0.859956i	−0.991333	+	0.131376i	$0.958060\pi$
$458$	−120.000	+	120.000i	−0.262009	+	0.262009i
$459$		−	280.000i		−	0.610022i
$460$	20.0000	−	20.0000i	0.0434783	−	0.0434783i
$461$	−622.000			−1.34924			−0.674620	−	0.738165i	$-0.735693\pi$
$461$	−622.000			−1.34924			−0.674620	+	0.738165i	$0.735693\pi$
$462$		0			0
$463$	278.000	−	278.000i	0.600432	−	0.600432i	−0.339995	−	0.940427i	$-0.610425\pi$
$463$	278.000	−	278.000i	0.600432	−	0.600432i	0.940427	+	0.339995i	$0.110425\pi$
$464$		−	160.000i		−	0.344828i
$465$	−520.000	−	520.000i	−1.11828	−	1.11828i
$466$	−366.000			−0.785408
$467$	38.0000	+	38.0000i	0.0813704	+	0.0813704i	0.746621	−	0.665250i	$-0.231675\pi$
$467$	38.0000	+	38.0000i	0.0813704	+	0.0813704i	−0.665250	+	0.746621i	$0.731675\pi$
$468$	6.00000	−	6.00000i	0.0128205	−	0.0128205i
$469$		0			0
$470$	180.000			0.382979
$471$	−108.000			−0.229299
$472$	40.0000	+	40.0000i	0.0847458	+	0.0847458i
$473$	336.000	−	336.000i	0.710359	−	0.710359i
$474$		0			0
$475$		−	500.000i		−	1.05263i
$476$		0			0
$477$	53.0000	+	53.0000i	0.111111	+	0.111111i
$478$	120.000	−	120.000i	0.251046	−	0.251046i
$479$			440.000i			0.918580i	0.888286	+	0.459290i	$0.151896\pi$
$479$			440.000i			0.918580i	−0.888286	+	0.459290i	$0.848104\pi$
$480$			80.0000i			0.166667i
$481$	18.0000			0.0374220
$482$	232.000	+	232.000i	0.481328	+	0.481328i
$483$		0			0
$484$		−	114.000i		−	0.235537i
$485$	−315.000	+	315.000i	−0.649485	+	0.649485i
$486$	76.0000			0.156379
$487$	522.000	+	522.000i	1.07187	+	1.07187i	0.997209	+	0.0746595i	$0.0237870\pi$
$487$	522.000	+	522.000i	1.07187	+	1.07187i	0.0746595	+	0.997209i	$0.476213\pi$
$488$	96.0000	−	96.0000i	0.196721	−	0.196721i
$489$			328.000i			0.670757i
$490$		0			0
$491$	−328.000			−0.668024			−0.334012	−	0.942569i	$-0.608403\pi$
$491$	−328.000			−0.668024			−0.334012	+	0.942569i	$0.608403\pi$
$492$	32.0000	+	32.0000i	0.0650407	+	0.0650407i
$493$	280.000	−	280.000i	0.567951	−	0.567951i
$494$			120.000i			0.242915i
$495$	40.0000			0.0808081
$496$	208.000			0.419355
$497$		0			0
$498$	72.0000	−	72.0000i	0.144578	−	0.144578i
$499$			380.000i			0.761523i	0.924673	+	0.380762i	$0.124338\pi$
$499$			380.000i			0.761523i	−0.924673	+	0.380762i	$0.875662\pi$
$500$	250.000			0.500000
$501$	−248.000			−0.495010
$502$	−48.0000	−	48.0000i	−0.0956175	−	0.0956175i
$503$	42.0000	−	42.0000i	0.0834990	−	0.0834990i	−0.664124	−	0.747623i	$-0.731195\pi$
$503$	42.0000	−	42.0000i	0.0834990	−	0.0834990i	0.747623	+	0.664124i	$0.231195\pi$
$504$		0			0
$505$		−	310.000i		−	0.613861i
$506$	−32.0000			−0.0632411
$507$	302.000	+	302.000i	0.595661	+	0.595661i
$508$	236.000	−	236.000i	0.464567	−	0.464567i
$509$			440.000i			0.864440i	0.901768	+	0.432220i	$0.142270\pi$
$509$			440.000i			0.864440i	−0.901768	+	0.432220i	$0.857730\pi$
$510$	−140.000	+	140.000i	−0.274510	+	0.274510i
$511$		0			0
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	−400.000	+	400.000i	−0.779727	+	0.779727i
$514$		−	626.000i		−	1.21790i
$515$	−590.000	−	590.000i	−1.14563	−	1.14563i
$516$	−336.000			−0.651163
$517$	−144.000	−	144.000i	−0.278530	−	0.278530i
$518$		0			0
$519$		−	428.000i		−	0.824663i
$520$	−60.0000			−0.115385
$521$	258.000			0.495202			0.247601	−	0.968862i	$-0.420358\pi$
$521$	258.000			0.495202			0.247601	+	0.968862i	$0.420358\pi$
$522$	40.0000	+	40.0000i	0.0766284	+	0.0766284i
$523$	−258.000	+	258.000i	−0.493308	+	0.493308i	−0.909347	−	0.416039i	$-0.863418\pi$
$523$	−258.000	+	258.000i	−0.493308	+	0.493308i	0.416039	+	0.909347i	$0.363418\pi$
$524$			256.000i			0.488550i
$525$		0			0
$526$	524.000			0.996198
$527$	364.000	+	364.000i	0.690702	+	0.690702i
$528$	64.0000	−	64.0000i	0.121212	−	0.121212i
$529$			521.000i			0.984877i
$530$		−	530.000i		−	1.00000i
$531$	−20.0000			−0.0376648
$532$		0			0
$533$	−24.0000	+	24.0000i	−0.0450281	+	0.0450281i
$534$			320.000i			0.599251i
$535$	−710.000	+	710.000i	−1.32710	+	1.32710i
$536$	248.000			0.462687
$537$	−440.000	−	440.000i	−0.819367	−	0.819367i
$538$	−10.0000	+	10.0000i	−0.0185874	+	0.0185874i
$539$		0			0
$540$	−200.000	−	200.000i	−0.370370	−	0.370370i
$541$	−338.000			−0.624769			−0.312384	−	0.949956i	$-0.601128\pi$
$541$	−338.000			−0.624769			−0.312384	+	0.949956i	$0.601128\pi$
$542$	252.000	+	252.000i	0.464945	+	0.464945i
$543$	−4.00000	+	4.00000i	−0.00736648	+	0.00736648i
$544$		−	56.0000i		−	0.102941i
$545$	50.0000			0.0917431
$546$		0			0
$547$	−558.000	−	558.000i	−1.02011	−	1.02011i	−0.999794	−	0.0203161i	$-0.993533\pi$
$547$	−558.000	−	558.000i	−1.02011	−	1.02011i	−0.0203161	−	0.999794i	$-0.506467\pi$
$548$	126.000	−	126.000i	0.229927	−	0.229927i
$549$			48.0000i			0.0874317i
$550$	−200.000	−	200.000i	−0.363636	−	0.363636i
$551$	−800.000			−1.45191
$552$	16.0000	+	16.0000i	0.0289855	+	0.0289855i
$553$		0			0
$554$		−	534.000i		−	0.963899i
$555$		−	60.0000i		−	0.108108i
$556$	280.000			0.503597
$557$	−3.00000	−	3.00000i	−0.00538600	−	0.00538600i	0.704409	−	0.709795i	$-0.251212\pi$
$557$	−3.00000	−	3.00000i	−0.00538600	−	0.00538600i	−0.709795	+	0.704409i	$0.751212\pi$
$558$	−52.0000	+	52.0000i	−0.0931900	+	0.0931900i
$559$		−	252.000i		−	0.450805i
$560$		0			0
$561$	224.000			0.399287
$562$	−312.000	−	312.000i	−0.555160	−	0.555160i
$563$	42.0000	−	42.0000i	0.0746004	−	0.0746004i	−0.668822	−	0.743422i	$-0.733201\pi$
$563$	42.0000	−	42.0000i	0.0746004	−	0.0746004i	0.743422	+	0.668822i	$0.233201\pi$
$564$			144.000i			0.255319i
$565$	115.000	+	115.000i	0.203540	+	0.203540i
$566$	−524.000			−0.925795
$567$		0			0
$568$	−56.0000	+	56.0000i	−0.0985915	+	0.0985915i
$569$			950.000i			1.66960i	0.550557	+	0.834798i	$0.314416\pi$
$569$			950.000i			1.66960i	−0.550557	+	0.834798i	$0.685584\pi$
$570$	400.000			0.701754
$571$	392.000			0.686515			0.343257	−	0.939241i	$-0.388470\pi$
$571$	392.000			0.686515			0.343257	+	0.939241i	$0.388470\pi$
$572$	48.0000	+	48.0000i	0.0839161	+	0.0839161i
$573$	424.000	−	424.000i	0.739965	−	0.739965i
$574$		0			0
$575$	50.0000	−	50.0000i	0.0869565	−	0.0869565i
$576$	8.00000			0.0138889
$577$	473.000	+	473.000i	0.819757	+	0.819757i	0.986073	−	0.166315i	$-0.0531869\pi$
$577$	473.000	+	473.000i	0.819757	+	0.819757i	−0.166315	+	0.986073i	$0.553187\pi$
$578$	−191.000	+	191.000i	−0.330450	+	0.330450i
$579$			228.000i			0.393782i
$580$		−	400.000i		−	0.689655i
$581$		0			0
$582$	−252.000	−	252.000i	−0.432990	−	0.432990i
$583$	−424.000	+	424.000i	−0.727273	+	0.727273i
$584$		−	188.000i		−	0.321918i
$585$	15.0000	−	15.0000i	0.0256410	−	0.0256410i
$586$	486.000			0.829352
$587$	198.000	+	198.000i	0.337308	+	0.337308i	0.855353	−	0.518045i	$-0.173340\pi$
$587$	198.000	+	198.000i	0.337308	+	0.337308i	−0.518045	+	0.855353i	$0.673340\pi$
$588$		0			0
$589$		−	1040.00i		−	1.76570i
$590$	100.000	+	100.000i	0.169492	+	0.169492i
$591$	−12.0000			−0.0203046
$592$	12.0000	+	12.0000i	0.0202703	+	0.0202703i
$593$	47.0000	−	47.0000i	0.0792580	−	0.0792580i	−0.666366	−	0.745624i	$-0.732151\pi$
$593$	47.0000	−	47.0000i	0.0792580	−	0.0792580i	0.745624	+	0.666366i	$0.232151\pi$
$594$			320.000i			0.538721i
$595$		0			0
$596$	300.000			0.503356
$597$	240.000	+	240.000i	0.402010	+	0.402010i
$598$	−12.0000	+	12.0000i	−0.0200669	+	0.0200669i
$599$			520.000i			0.868114i	0.900886	+	0.434057i	$0.142918\pi$
$599$			520.000i			0.868114i	−0.900886	+	0.434057i	$0.857082\pi$
$600$			200.000i			0.333333i
$601$	328.000			0.545757			0.272879	−	0.962048i	$-0.412024\pi$
$601$	328.000			0.545757			0.272879	+	0.962048i	$0.412024\pi$
$602$		0			0
$603$	−62.0000	+	62.0000i	−0.102819	+	0.102819i
$604$			104.000i			0.172185i
$605$		−	285.000i		−	0.471074i
$606$	248.000			0.409241
$607$	−462.000	−	462.000i	−0.761120	−	0.761120i	0.215405	−	0.976525i	$-0.430893\pi$
$607$	−462.000	−	462.000i	−0.761120	−	0.761120i	−0.976525	+	0.215405i	$0.930893\pi$
$608$	−80.0000	+	80.0000i	−0.131579	+	0.131579i
$609$		0			0
$610$	240.000	−	240.000i	0.393443	−	0.393443i
$611$	−108.000			−0.176759
$612$	14.0000	+	14.0000i	0.0228758	+	0.0228758i
$613$	723.000	−	723.000i	1.17945	−	1.17945i	0.199560	−	0.979886i	$-0.436049\pi$
$613$	723.000	−	723.000i	1.17945	−	1.17945i	0.979886	−	0.199560i	$-0.0639512\pi$
$614$		−	36.0000i		−	0.0586319i
$615$	80.0000	+	80.0000i	0.130081	+	0.130081i
$616$		0			0
$617$	327.000	+	327.000i	0.529984	+	0.529984i	0.920567	−	0.390584i	$-0.127727\pi$
$617$	327.000	+	327.000i	0.529984	+	0.529984i	−0.390584	+	0.920567i	$0.627727\pi$
$618$	472.000	−	472.000i	0.763754	−	0.763754i
$619$			660.000i			1.06624i	0.846041	+	0.533118i	$0.178980\pi$
$619$			660.000i			1.06624i	−0.846041	+	0.533118i	$0.821020\pi$
$620$	520.000			0.838710
$621$	−80.0000			−0.128824
$622$	−388.000	−	388.000i	−0.623794	−	0.623794i
$623$		0			0
$624$		−	48.0000i		−	0.0769231i
$625$	625.000			1.00000
$626$	366.000			0.584665
$627$	−320.000	−	320.000i	−0.510367	−	0.510367i
$628$	54.0000	−	54.0000i	0.0859873	−	0.0859873i
$629$			42.0000i			0.0667727i
$630$		0			0
$631$	−548.000			−0.868463			−0.434231	−	0.900801i	$-0.642980\pi$
$631$	−548.000			−0.868463			−0.434231	+	0.900801i	$0.642980\pi$
$632$		0			0
$633$	−656.000	+	656.000i	−1.03633	+	1.03633i
$634$			426.000i			0.671924i
$635$	590.000	−	590.000i	0.929134	−	0.929134i
$636$	424.000			0.666667
$637$		0			0
$638$	−320.000	+	320.000i	−0.501567	+	0.501567i
$639$		−	28.0000i		−	0.0438185i
$640$	−40.0000	−	40.0000i	−0.0625000	−	0.0625000i
$641$	−568.000			−0.886115			−0.443058	−	0.896493i	$-0.646106\pi$
$641$	−568.000			−0.886115			−0.443058	+	0.896493i	$0.646106\pi$
$642$	−568.000	−	568.000i	−0.884735	−	0.884735i
$643$	342.000	−	342.000i	0.531882	−	0.531882i	−0.389250	−	0.921132i	$-0.627266\pi$
$643$	342.000	−	342.000i	0.531882	−	0.531882i	0.921132	+	0.389250i	$0.127266\pi$
$644$		0			0
$645$	−840.000			−1.30233
$646$	−280.000			−0.433437
$647$	118.000	+	118.000i	0.182380	+	0.182380i	0.792392	−	0.610012i	$-0.208835\pi$
$647$	118.000	+	118.000i	0.182380	+	0.182380i	−0.610012	+	0.792392i	$0.708835\pi$
$648$	142.000	−	142.000i	0.219136	−	0.219136i
$649$		−	160.000i		−	0.246533i
$650$	−150.000			−0.230769
$651$		0			0
$652$	−164.000	−	164.000i	−0.251534	−	0.251534i
$653$	453.000	−	453.000i	0.693721	−	0.693721i	−0.269327	−	0.963049i	$-0.586801\pi$
$653$	453.000	−	453.000i	0.693721	−	0.693721i	0.963049	+	0.269327i	$0.0868014\pi$
$654$			40.0000i			0.0611621i
$655$			640.000i			0.977099i
$656$	−32.0000			−0.0487805
$657$	47.0000	+	47.0000i	0.0715373	+	0.0715373i
$658$		0			0
$659$			140.000i			0.212443i	0.994342	+	0.106222i	$0.0338753\pi$
$659$			140.000i			0.212443i	−0.994342	+	0.106222i	$0.966125\pi$
$660$	160.000	−	160.000i	0.242424	−	0.242424i
$661$	−512.000			−0.774584			−0.387292	−	0.921957i	$-0.626589\pi$
$661$	−512.000			−0.774584			−0.387292	+	0.921957i	$0.626589\pi$
$662$	−232.000	−	232.000i	−0.350453	−	0.350453i
$663$	84.0000	−	84.0000i	0.126697	−	0.126697i
$664$			72.0000i			0.108434i
$665$		0			0
$666$	−6.00000			−0.00900901
$667$	−80.0000	−	80.0000i	−0.119940	−	0.119940i
$668$	124.000	−	124.000i	0.185629	−	0.185629i
$669$			552.000i			0.825112i
$670$	620.000			0.925373
$671$	−384.000			−0.572280
$672$		0			0
$673$	193.000	−	193.000i	0.286776	−	0.286776i	−0.549028	−	0.835804i	$-0.685002\pi$
$673$	193.000	−	193.000i	0.286776	−	0.286776i	0.835804	+	0.549028i	$0.185002\pi$
$674$		−	834.000i		−	1.23739i
$675$	−500.000	−	500.000i	−0.740741	−	0.740741i
$676$	−302.000			−0.446746
$677$	−157.000	−	157.000i	−0.231905	−	0.231905i	0.581582	−	0.813488i	$-0.302434\pi$
$677$	−157.000	−	157.000i	−0.231905	−	0.231905i	−0.813488	+	0.581582i	$0.802434\pi$
$678$	−92.0000	+	92.0000i	−0.135693	+	0.135693i
$679$		0			0
$680$		−	140.000i		−	0.205882i
$681$	−8.00000			−0.0117474
$682$	−416.000	−	416.000i	−0.609971	−	0.609971i
$683$	438.000	−	438.000i	0.641288	−	0.641288i	−0.309584	−	0.950872i	$-0.600190\pi$
$683$	438.000	−	438.000i	0.641288	−	0.641288i	0.950872	+	0.309584i	$0.100190\pi$
$684$		−	40.0000i		−	0.0584795i
$685$	315.000	−	315.000i	0.459854	−	0.459854i
$686$		0			0
$687$	−240.000	−	240.000i	−0.349345	−	0.349345i
$688$	168.000	−	168.000i	0.244186	−	0.244186i
$689$			318.000i			0.461538i
$690$	40.0000	+	40.0000i	0.0579710	+	0.0579710i
$691$	−1032.00			−1.49349			−0.746744	−	0.665112i	$-0.768384\pi$
$691$	−1032.00			−1.49349			−0.746744	+	0.665112i	$0.768384\pi$
$692$	214.000	+	214.000i	0.309249	+	0.309249i
$693$		0			0
$694$		−	404.000i		−	0.582133i
$695$	700.000			1.00719
$696$	320.000			0.459770
$697$	−56.0000	−	56.0000i	−0.0803443	−	0.0803443i
$698$	440.000	−	440.000i	0.630372	−	0.630372i
$699$		−	732.000i		−	1.04721i
$700$		0			0
$701$	−128.000			−0.182596			−0.0912981	−	0.995824i	$-0.529102\pi$
$701$	−128.000			−0.182596			−0.0912981	+	0.995824i	$0.529102\pi$
$702$	120.000	+	120.000i	0.170940	+	0.170940i
$703$	60.0000	−	60.0000i	0.0853485	−	0.0853485i
$704$			64.0000i			0.0909091i
$705$			360.000i			0.510638i
$706$	−894.000			−1.26629
$707$		0			0
$708$	−80.0000	+	80.0000i	−0.112994	+	0.112994i
$709$			760.000i			1.07193i	0.844239	+	0.535966i	$0.180053\pi$
$709$			760.000i			1.07193i	−0.844239	+	0.535966i	$0.819947\pi$
$710$	−140.000	+	140.000i	−0.197183	+	0.197183i
$711$		0			0
$712$	−160.000	−	160.000i	−0.224719	−	0.224719i
$713$	104.000	−	104.000i	0.145863	−	0.145863i
$714$		0			0
$715$	120.000	+	120.000i	0.167832	+	0.167832i
$716$	440.000			0.614525
$717$	240.000	+	240.000i	0.334728	+	0.334728i
$718$	−400.000	+	400.000i	−0.557103	+	0.557103i
$719$			1160.00i			1.61335i	0.590994	+	0.806676i	$0.298736\pi$
$719$			1160.00i			1.61335i	−0.590994	+	0.806676i	$0.701264\pi$
$720$	20.0000			0.0277778
$721$		0			0
$722$	39.0000	+	39.0000i	0.0540166	+	0.0540166i
$723$	−464.000	+	464.000i	−0.641770	+	0.641770i
$724$		−	4.00000i		−	0.00552486i
$725$		−	1000.00i		−	1.37931i
$726$	228.000			0.314050
$727$	558.000	+	558.000i	0.767538	+	0.767538i	0.977672	−	0.210135i	$-0.0673902\pi$
$727$	558.000	+	558.000i	0.767538	+	0.767538i	−0.210135	+	0.977672i	$0.567390\pi$
$728$		0			0
$729$			791.000i			1.08505i
$730$		−	470.000i		−	0.643836i
$731$	588.000			0.804378
$732$	192.000	+	192.000i	0.262295	+	0.262295i
$733$	827.000	−	827.000i	1.12824	−	1.12824i	0.137777	−	0.990463i	$-0.456004\pi$
$733$	827.000	−	827.000i	1.12824	−	1.12824i	0.990463	−	0.137777i	$-0.0439957\pi$
$734$		−	236.000i		−	0.321526i
$735$		0			0
$736$	−16.0000			−0.0217391
$737$	−496.000	−	496.000i	−0.672999	−	0.672999i
$738$	8.00000	−	8.00000i	0.0108401	−	0.0108401i
$739$		−	700.000i		−	0.947226i	−0.880733	−	0.473613i	$-0.842950\pi$
$739$		−	700.000i		−	0.947226i	0.880733	−	0.473613i	$-0.157050\pi$
$740$	30.0000	+	30.0000i	0.0405405	+	0.0405405i
$741$	−240.000			−0.323887
$742$		0			0
$743$	−382.000	+	382.000i	−0.514132	+	0.514132i	−0.915790	−	0.401658i	$-0.868434\pi$
$743$	−382.000	+	382.000i	−0.514132	+	0.514132i	0.401658	+	0.915790i	$0.368434\pi$
$744$			416.000i			0.559140i
$745$	750.000			1.00671
$746$	214.000			0.286863
$747$	−18.0000	−	18.0000i	−0.0240964	−	0.0240964i
$748$	−112.000	+	112.000i	−0.149733	+	0.149733i
$749$		0			0
$750$			500.000i			0.666667i
$751$	−588.000			−0.782956			−0.391478	−	0.920187i	$-0.628036\pi$
$751$	−588.000			−0.782956			−0.391478	+	0.920187i	$0.628036\pi$
$752$	−72.0000	−	72.0000i	−0.0957447	−	0.0957447i
$753$	96.0000	−	96.0000i	0.127490	−	0.127490i
$754$			240.000i			0.318302i
$755$			260.000i			0.344371i
$756$		0			0
$757$	987.000	+	987.000i	1.30383	+	1.30383i	0.925788	+	0.378043i	$0.123403\pi$
$757$	987.000	+	987.000i	1.30383	+	1.30383i	0.378043	+	0.925788i	$0.376597\pi$
$758$	340.000	−	340.000i	0.448549	−	0.448549i
$759$		−	64.0000i		−	0.0843215i
$760$	−200.000	+	200.000i	−0.263158	+	0.263158i
$761$	158.000			0.207622			0.103811	−	0.994597i	$-0.466896\pi$
$761$	158.000			0.207622			0.103811	+	0.994597i	$0.466896\pi$
$762$	472.000	+	472.000i	0.619423	+	0.619423i
$763$		0			0
$764$			424.000i			0.554974i
$765$	35.0000	+	35.0000i	0.0457516	+	0.0457516i
$766$	−684.000			−0.892950
$767$	−60.0000	−	60.0000i	−0.0782269	−	0.0782269i
$768$	32.0000	−	32.0000i	0.0416667	−	0.0416667i
$769$		−	80.0000i		−	0.104031i	−0.998646	−	0.0520156i	$-0.983435\pi$
$769$		−	80.0000i		−	0.104031i	0.998646	−	0.0520156i	$-0.0165646\pi$
$770$		0			0
$771$	1252.00			1.62387
$772$	−114.000	−	114.000i	−0.147668	−	0.147668i
$773$	−243.000	+	243.000i	−0.314360	+	0.314360i	−0.846596	−	0.532236i	$-0.821352\pi$
$773$	−243.000	+	243.000i	−0.314360	+	0.314360i	0.532236	+	0.846596i	$0.321352\pi$
$774$			84.0000i			0.108527i
$775$	1300.00			1.67742
$776$	252.000			0.324742
$777$		0			0
$778$	390.000	−	390.000i	0.501285	−	0.501285i
$779$			160.000i			0.205392i
$780$		−	120.000i		−	0.153846i
$781$	224.000			0.286812
$782$	−28.0000	−	28.0000i	−0.0358056	−	0.0358056i
$783$	−800.000	+	800.000i	−1.02171	+	1.02171i
$784$		0			0
$785$	135.000	−	135.000i	0.171975	−	0.171975i
$786$	−512.000			−0.651399
$787$	−262.000	−	262.000i	−0.332910	−	0.332910i	0.520781	−	0.853690i	$-0.325641\pi$
$787$	−262.000	−	262.000i	−0.332910	−	0.332910i	−0.853690	+	0.520781i	$0.825641\pi$
$788$	6.00000	−	6.00000i	0.00761421	−	0.00761421i
$789$			1048.00i			1.32826i
$790$		0			0
$791$		0			0
$792$	−16.0000	−	16.0000i	−0.0202020	−	0.0202020i
$793$	−144.000	+	144.000i	−0.181589	+	0.181589i
$794$		−	646.000i		−	0.813602i
$795$	1060.00			1.33333
$796$	−240.000			−0.301508
$797$	−267.000	−	267.000i	−0.335006	−	0.335006i	0.519478	−	0.854484i	$-0.326127\pi$
$797$	−267.000	−	267.000i	−0.335006	−	0.335006i	−0.854484	+	0.519478i	$0.826127\pi$
$798$		0			0
$799$		−	252.000i		−	0.315394i
$800$	−100.000	−	100.000i	−0.125000	−	0.125000i
$801$	80.0000			0.0998752
$802$	−642.000	−	642.000i	−0.800499	−	0.800499i
$803$	−376.000	+	376.000i	−0.468244	+	0.468244i
$804$			496.000i			0.616915i
$805$		0			0
$806$	−312.000			−0.387097
$807$	−20.0000	−	20.0000i	−0.0247831	−	0.0247831i
$808$	−124.000	+	124.000i	−0.153465	+	0.153465i
$809$			560.000i			0.692213i	0.938195	+	0.346106i	$0.112496\pi$
$809$			560.000i			0.692213i	−0.938195	+	0.346106i	$0.887504\pi$
$810$	355.000	−	355.000i	0.438272	−	0.438272i
$811$	208.000			0.256473			0.128237	−	0.991744i	$-0.459068\pi$
$811$	208.000			0.256473			0.128237	+	0.991744i	$0.459068\pi$
$812$		0			0
$813$	−504.000	+	504.000i	−0.619926	+	0.619926i
$814$		−	48.0000i		−	0.0589681i
$815$	−410.000	−	410.000i	−0.503067	−	0.503067i
$816$	112.000			0.137255
$817$	−840.000	−	840.000i	−1.02815	−	1.02815i
$818$	150.000	−	150.000i	0.183374	−	0.183374i
$819$		0			0
$820$	−80.0000			−0.0975610
$821$	−1568.00			−1.90987			−0.954933	−	0.296821i	$-0.904073\pi$
$821$	−1568.00			−1.90987			−0.954933	+	0.296821i	$0.904073\pi$
$822$	252.000	+	252.000i	0.306569	+	0.306569i
$823$	−562.000	+	562.000i	−0.682868	+	0.682868i	−0.960645	−	0.277778i	$-0.910402\pi$
$823$	−562.000	+	562.000i	−0.682868	+	0.682868i	0.277778	+	0.960645i	$0.410402\pi$
$824$			472.000i			0.572816i
$825$	400.000	−	400.000i	0.484848	−	0.484848i
$826$		0			0
$827$	762.000	+	762.000i	0.921403	+	0.921403i	0.997129	−	0.0757260i	$-0.0241274\pi$
$827$	762.000	+	762.000i	0.921403	+	0.921403i	−0.0757260	+	0.997129i	$0.524127\pi$
$828$	4.00000	−	4.00000i	0.00483092	−	0.00483092i
$829$		−	170.000i		−	0.205066i	−0.994730	−	0.102533i	$-0.967305\pi$
$829$		−	170.000i		−	0.205066i	0.994730	−	0.102533i	$-0.0326948\pi$
$830$			180.000i			0.216867i
$831$	1068.00			1.28520
$832$	24.0000	+	24.0000i	0.0288462	+	0.0288462i
$833$		0			0
$834$			560.000i			0.671463i
$835$	310.000	−	310.000i	0.371257	−	0.371257i
$836$	320.000			0.382775
$837$	−1040.00	−	1040.00i	−1.24253	−	1.24253i
$838$	−300.000	+	300.000i	−0.357995	+	0.357995i
$839$			280.000i			0.333731i	0.985980	+	0.166865i	$0.0533645\pi$
$839$			280.000i			0.333731i	−0.985980	+	0.166865i	$0.946635\pi$
$840$		0			0
$841$	−759.000			−0.902497
$842$	208.000	+	208.000i	0.247031	+	0.247031i
$843$	624.000	−	624.000i	0.740214	−	0.740214i
$844$		−	656.000i		−	0.777251i
$845$	−755.000			−0.893491
$846$	36.0000			0.0425532
$847$		0			0
$848$	−212.000	+	212.000i	−0.250000	+	0.250000i
$849$		−	1048.00i		−	1.23439i
$850$		−	350.000i		−	0.411765i
$851$	12.0000			0.0141011
$852$	−112.000	−	112.000i	−0.131455	−	0.131455i
$853$	−1123.00	+	1123.00i	−1.31653	+	1.31653i	−0.400026	+	0.916504i	$0.630999\pi$
$853$	−1123.00	+	1123.00i	−1.31653	+	1.31653i	−0.916504	+	0.400026i	$0.869001\pi$
$854$		0			0
$855$		−	100.000i		−	0.116959i
$856$	568.000			0.663551
$857$	−417.000	−	417.000i	−0.486581	−	0.486581i	0.420644	−	0.907226i	$-0.361804\pi$
$857$	−417.000	−	417.000i	−0.486581	−	0.486581i	−0.907226	+	0.420644i	$0.861804\pi$
$858$	−96.0000	+	96.0000i	−0.111888	+	0.111888i
$859$			1300.00i			1.51339i	0.653769	+	0.756694i	$0.273187\pi$
$859$			1300.00i			1.51339i	−0.653769	+	0.756694i	$0.726813\pi$
$860$	420.000	−	420.000i	0.488372	−	0.488372i
$861$		0			0
$862$	788.000	+	788.000i	0.914153	+	0.914153i
$863$	−242.000	+	242.000i	−0.280417	+	0.280417i	−0.833275	−	0.552858i	$-0.813537\pi$
$863$	−242.000	+	242.000i	−0.280417	+	0.280417i	0.552858	+	0.833275i	$0.313537\pi$
$864$			160.000i			0.185185i
$865$	535.000	+	535.000i	0.618497	+	0.618497i
$866$	−734.000			−0.847575
$867$	−382.000	−	382.000i	−0.440600	−	0.440600i
$868$		0			0
$869$		0			0
$870$	800.000			0.919540
$871$	−372.000			−0.427095
$872$	−20.0000	−	20.0000i	−0.0229358	−	0.0229358i
$873$	−63.0000	+	63.0000i	−0.0721649	+	0.0721649i
$874$			80.0000i			0.0915332i
$875$		0			0
$876$	376.000			0.429224
$877$	−453.000	−	453.000i	−0.516534	−	0.516534i	0.399987	−	0.916521i	$-0.369015\pi$
$877$	−453.000	−	453.000i	−0.516534	−	0.516534i	−0.916521	+	0.399987i	$0.869015\pi$
$878$	−560.000	+	560.000i	−0.637813	+	0.637813i
$879$			972.000i			1.10580i
$880$			160.000i			0.181818i
$881$	−712.000			−0.808173			−0.404086	−	0.914721i	$-0.632410\pi$
$881$	−712.000			−0.808173			−0.404086	+	0.914721i	$0.632410\pi$
$882$		0			0
$883$	118.000	−	118.000i	0.133635	−	0.133635i	−0.637125	−	0.770760i	$-0.719877\pi$
$883$	118.000	−	118.000i	0.133635	−	0.133635i	0.770760	+	0.637125i	$0.219877\pi$
$884$			84.0000i			0.0950226i
$885$	−200.000	+	200.000i	−0.225989	+	0.225989i
$886$	−756.000			−0.853273
$887$	1158.00	+	1158.00i	1.30552	+	1.30552i	0.924611	+	0.380914i	$0.124390\pi$
$887$	1158.00	+	1158.00i	1.30552	+	1.30552i	0.380914	+	0.924611i	$0.375610\pi$
$888$	−24.0000	+	24.0000i	−0.0270270	+	0.0270270i
$889$		0			0
$890$	−400.000	−	400.000i	−0.449438	−	0.449438i
$891$	−568.000			−0.637486
$892$	−276.000	−	276.000i	−0.309417	−	0.309417i
$893$	−360.000	+	360.000i	−0.403135	+	0.403135i
$894$			600.000i			0.671141i
$895$	1100.00			1.22905
$896$		0			0
$897$	−24.0000	−	24.0000i	−0.0267559	−	0.0267559i
$898$	−410.000	+	410.000i	−0.456570	+	0.456570i
$899$		−	2080.00i		−	2.31368i
$900$	50.0000			0.0555556
$901$	−742.000			−0.823529
$902$	64.0000	+	64.0000i	0.0709534	+	0.0709534i
$903$		0			0
$904$		−	92.0000i		−	0.101770i
$905$		−	10.0000i		−	0.0110497i
$906$	−208.000			−0.229581
$907$	142.000	+	142.000i	0.156560	+	0.156560i	0.781040	−	0.624480i	$-0.214689\pi$
$907$	142.000	+	142.000i	0.156560	+	0.156560i	−0.624480	+	0.781040i	$0.714689\pi$
$908$	4.00000	−	4.00000i	0.00440529	−	0.00440529i
$909$		−	62.0000i		−	0.0682068i
$910$		0			0
$911$	1172.00			1.28650			0.643249	−	0.765657i	$-0.277586\pi$
$911$	1172.00			1.28650			0.643249	+	0.765657i	$0.277586\pi$
$912$	−160.000	−	160.000i	−0.175439	−	0.175439i
$913$	144.000	−	144.000i	0.157722	−	0.157722i
$914$			786.000i			0.859956i
$915$	480.000	+	480.000i	0.524590	+	0.524590i
$916$	240.000			0.262009
$917$		0			0
$918$	−280.000	+	280.000i	−0.305011	+	0.305011i
$919$			920.000i			1.00109i	0.865711	+	0.500544i	$0.166867\pi$
$919$			920.000i			1.00109i	−0.865711	+	0.500544i	$0.833133\pi$
$920$	−40.0000			−0.0434783
$921$	72.0000			0.0781759
$922$	622.000	+	622.000i	0.674620	+	0.674620i
$923$	84.0000	−	84.0000i	0.0910076	−	0.0910076i
$924$		0			0
$925$	75.0000	+	75.0000i	0.0810811	+	0.0810811i
$926$	−556.000			−0.600432
$927$	−118.000	−	118.000i	−0.127292	−	0.127292i
$928$	−160.000	+	160.000i	−0.172414	+	0.172414i
$929$			1190.00i			1.28095i	0.767980	+	0.640474i	$0.221262\pi$
$929$			1190.00i			1.28095i	−0.767980	+	0.640474i	$0.778738\pi$
$930$			1040.00i			1.11828i
$931$		0			0
$932$	366.000	+	366.000i	0.392704	+	0.392704i
$933$	776.000	−	776.000i	0.831726	−	0.831726i
$934$		−	76.0000i		−	0.0813704i
$935$	−280.000	+	280.000i	−0.299465	+	0.299465i
$936$	−12.0000			−0.0128205
$937$	233.000	+	233.000i	0.248666	+	0.248666i	0.820423	−	0.571757i	$-0.193738\pi$
$937$	233.000	+	233.000i	0.248666	+	0.248666i	−0.571757	+	0.820423i	$0.693738\pi$
$938$		0			0
$939$			732.000i			0.779553i
$940$	−180.000	−	180.000i	−0.191489	−	0.191489i
$941$	78.0000			0.0828905			0.0414453	−	0.999141i	$-0.486804\pi$
$941$	78.0000			0.0828905			0.0414453	+	0.999141i	$0.486804\pi$
$942$	108.000	+	108.000i	0.114650	+	0.114650i
$943$	−16.0000	+	16.0000i	−0.0169671	+	0.0169671i
$944$		−	80.0000i		−	0.0847458i
$945$		0			0
$946$	−672.000			−0.710359
$947$	62.0000	+	62.0000i	0.0654699	+	0.0654699i	0.739084	−	0.673614i	$-0.235259\pi$
$947$	62.0000	+	62.0000i	0.0654699	+	0.0654699i	−0.673614	+	0.739084i	$0.735259\pi$
$948$		0			0
$949$			282.000i			0.297155i
$950$	−500.000	+	500.000i	−0.526316	+	0.526316i
$951$	−852.000			−0.895899
$952$		0			0
$953$	−1017.00	+	1017.00i	−1.06716	+	1.06716i	−0.0695800	+	0.997576i	$0.522166\pi$
$953$	−1017.00	+	1017.00i	−1.06716	+	1.06716i	−0.997576	+	0.0695800i	$0.977834\pi$
$954$		−	106.000i		−	0.111111i
$955$			1060.00i			1.10995i
$956$	−240.000			−0.251046
$957$	−640.000	−	640.000i	−0.668757	−	0.668757i
$958$	440.000	−	440.000i	0.459290	−	0.459290i
$959$		0			0
$960$	80.0000	−	80.0000i	0.0833333	−	0.0833333i
$961$	1743.00			1.81374
$962$	−18.0000	−	18.0000i	−0.0187110	−	0.0187110i
$963$	−142.000	+	142.000i	−0.147456	+	0.147456i
$964$		−	464.000i		−	0.481328i
$965$	−285.000	−	285.000i	−0.295337	−	0.295337i
$966$		0			0
$967$	502.000	+	502.000i	0.519131	+	0.519131i	0.917309	−	0.398177i	$-0.130357\pi$
$967$	502.000	+	502.000i	0.519131	+	0.519131i	−0.398177	+	0.917309i	$0.630357\pi$
$968$	−114.000	+	114.000i	−0.117769	+	0.117769i
$969$		−	560.000i		−	0.577915i
$970$	630.000			0.649485
$971$	−992.000			−1.02163			−0.510814	−	0.859691i	$-0.670656\pi$
$971$	−992.000			−1.02163			−0.510814	+	0.859691i	$0.670656\pi$
$972$	−76.0000	−	76.0000i	−0.0781893	−	0.0781893i
$973$		0			0
$974$		−	1044.00i		−	1.07187i
$975$		−	300.000i		−	0.307692i
$976$	−192.000			−0.196721
$977$	−783.000	−	783.000i	−0.801433	−	0.801433i	0.181887	−	0.983320i	$-0.441780\pi$
$977$	−783.000	−	783.000i	−0.801433	−	0.801433i	−0.983320	+	0.181887i	$0.941780\pi$
$978$	328.000	−	328.000i	0.335378	−	0.335378i
$979$			640.000i			0.653728i
$980$		0			0
$981$	10.0000			0.0101937
$982$	328.000	+	328.000i	0.334012	+	0.334012i
$983$	−1058.00	+	1058.00i	−1.07630	+	1.07630i	−0.0794589	+	0.996838i	$0.525319\pi$
$983$	−1058.00	+	1058.00i	−1.07630	+	1.07630i	−0.996838	+	0.0794589i	$0.974681\pi$
$984$		−	64.0000i		−	0.0650407i
$985$	15.0000	−	15.0000i	0.0152284	−	0.0152284i
$986$	−560.000			−0.567951
$987$		0			0
$988$	120.000	−	120.000i	0.121457	−	0.121457i
$989$		−	168.000i		−	0.169869i
$990$	−40.0000	−	40.0000i	−0.0404040	−	0.0404040i
$991$	−68.0000			−0.0686176			−0.0343088	−	0.999411i	$-0.510923\pi$
$991$	−68.0000			−0.0686176			−0.0343088	+	0.999411i	$0.510923\pi$
$992$	−208.000	−	208.000i	−0.209677	−	0.209677i
$993$	464.000	−	464.000i	0.467271	−	0.467271i
$994$		0			0
$995$	−600.000			−0.603015
$996$	−144.000			−0.144578
$997$	773.000	+	773.000i	0.775326	+	0.775326i	0.979032	−	0.203706i	$-0.0652987\pi$
$997$	773.000	+	773.000i	0.775326	+	0.775326i	−0.203706	+	0.979032i	$0.565299\pi$
$998$	380.000	−	380.000i	0.380762	−	0.380762i
$999$		−	120.000i		−	0.120120i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.3.f.b.197.1		2
5.3	odd	4	inner	490.3.f.b.393.1		2
7.6	odd	2		10.3.c.a.7.1	yes	2
21.20	even	2		90.3.g.b.37.1		2
28.27	even	2		80.3.p.c.17.1		2
35.13	even	4		10.3.c.a.3.1	✓	2
35.27	even	4		50.3.c.c.43.1		2
35.34	odd	2		50.3.c.c.7.1		2
56.13	odd	2		320.3.p.h.257.1		2
56.27	even	2		320.3.p.a.257.1		2
84.83	odd	2		720.3.bh.c.577.1		2
105.62	odd	4		450.3.g.b.343.1		2
105.83	odd	4		90.3.g.b.73.1		2
105.104	even	2		450.3.g.b.307.1		2
140.27	odd	4		400.3.p.b.193.1		2
140.83	odd	4		80.3.p.c.33.1		2
140.139	even	2		400.3.p.b.257.1		2
280.13	even	4		320.3.p.h.193.1		2
280.83	odd	4		320.3.p.a.193.1		2
420.83	even	4		720.3.bh.c.433.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.3.c.a.3.1	✓	2	35.13	even	4
10.3.c.a.7.1	yes	2	7.6	odd	2
50.3.c.c.7.1		2	35.34	odd	2
50.3.c.c.43.1		2	35.27	even	4
80.3.p.c.17.1		2	28.27	even	2
80.3.p.c.33.1		2	140.83	odd	4
90.3.g.b.37.1		2	21.20	even	2
90.3.g.b.73.1		2	105.83	odd	4
320.3.p.a.193.1		2	280.83	odd	4
320.3.p.a.257.1		2	56.27	even	2
320.3.p.h.193.1		2	280.13	even	4
320.3.p.h.257.1		2	56.13	odd	2
400.3.p.b.193.1		2	140.27	odd	4
400.3.p.b.257.1		2	140.139	even	2
450.3.g.b.307.1		2	105.104	even	2
450.3.g.b.343.1		2	105.62	odd	4
490.3.f.b.197.1		2	1.1	even	1	trivial
490.3.f.b.393.1		2	5.3	odd	4	inner
720.3.bh.c.433.1		2	420.83	even	4
720.3.bh.c.577.1		2	84.83	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	490.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(2.00000 - 2.00000i) q^{3} +2.00000i q^{4} +5.00000i q^{5} -4.00000 q^{6} +(2.00000 - 2.00000i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(2.00000 - 2.00000i) q^{3} +2.00000i q^{4} +5.00000i q^{5} -4.00000 q^{6} +(2.00000 - 2.00000i) q^{8} +1.00000i q^{9} +(5.00000 - 5.00000i) q^{10} -8.00000 q^{11} +(4.00000 + 4.00000i) q^{12} +(-3.00000 + 3.00000i) q^{13} +(10.0000 + 10.0000i) q^{15} -4.00000 q^{16} +(-7.00000 - 7.00000i) q^{17} +(1.00000 - 1.00000i) q^{18} +20.0000i q^{19} -10.0000 q^{20} +(8.00000 + 8.00000i) q^{22} +(-2.00000 + 2.00000i) q^{23} -8.00000i q^{24} -25.0000 q^{25} +6.00000 q^{26} +(20.0000 + 20.0000i) q^{27} +40.0000i q^{29} -20.0000i q^{30} -52.0000 q^{31} +(4.00000 + 4.00000i) q^{32} +(-16.0000 + 16.0000i) q^{33} +14.0000i q^{34} -2.00000 q^{36} +(-3.00000 - 3.00000i) q^{37} +(20.0000 - 20.0000i) q^{38} +12.0000i q^{39} +(10.0000 + 10.0000i) q^{40} +8.00000 q^{41} +(-42.0000 + 42.0000i) q^{43} -16.0000i q^{44} -5.00000 q^{45} +4.00000 q^{46} +(18.0000 + 18.0000i) q^{47} +(-8.00000 + 8.00000i) q^{48} +(25.0000 + 25.0000i) q^{50} -28.0000 q^{51} +(-6.00000 - 6.00000i) q^{52} +(53.0000 - 53.0000i) q^{53} -40.0000i q^{54} -40.0000i q^{55} +(40.0000 + 40.0000i) q^{57} +(40.0000 - 40.0000i) q^{58} +20.0000i q^{59} +(-20.0000 + 20.0000i) q^{60} +48.0000 q^{61} +(52.0000 + 52.0000i) q^{62} -8.00000i q^{64} +(-15.0000 - 15.0000i) q^{65} +32.0000 q^{66} +(62.0000 + 62.0000i) q^{67} +(14.0000 - 14.0000i) q^{68} +8.00000i q^{69} -28.0000 q^{71} +(2.00000 + 2.00000i) q^{72} +(47.0000 - 47.0000i) q^{73} +6.00000i q^{74} +(-50.0000 + 50.0000i) q^{75} -40.0000 q^{76} +(12.0000 - 12.0000i) q^{78} -20.0000i q^{80} +71.0000 q^{81} +(-8.00000 - 8.00000i) q^{82} +(-18.0000 + 18.0000i) q^{83} +(35.0000 - 35.0000i) q^{85} +84.0000 q^{86} +(80.0000 + 80.0000i) q^{87} +(-16.0000 + 16.0000i) q^{88} -80.0000i q^{89} +(5.00000 + 5.00000i) q^{90} +(-4.00000 - 4.00000i) q^{92} +(-104.000 + 104.000i) q^{93} -36.0000i q^{94} -100.000 q^{95} +16.0000 q^{96} +(63.0000 + 63.0000i) q^{97} -8.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 4 q^{3} - 8 q^{6} + 4 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 + 4 * q^3 - 8 * q^6 + 4 * q^8	\( 2 q - 2 q^{2} + 4 q^{3} - 8 q^{6} + 4 q^{8} + 10 q^{10} - 16 q^{11} + 8 q^{12} - 6 q^{13} + 20 q^{15} - 8 q^{16} - 14 q^{17} + 2 q^{18} - 20 q^{20} + 16 q^{22} - 4 q^{23} - 50 q^{25} + 12 q^{26} + 40 q^{27} - 104 q^{31} + 8 q^{32} - 32 q^{33} - 4 q^{36} - 6 q^{37} + 40 q^{38} + 20 q^{40} + 16 q^{41} - 84 q^{43} - 10 q^{45} + 8 q^{46} + 36 q^{47} - 16 q^{48} + 50 q^{50} - 56 q^{51} - 12 q^{52} + 106 q^{53} + 80 q^{57} + 80 q^{58} - 40 q^{60} + 96 q^{61} + 104 q^{62} - 30 q^{65} + 64 q^{66} + 124 q^{67} + 28 q^{68} - 56 q^{71} + 4 q^{72} + 94 q^{73} - 100 q^{75} - 80 q^{76} + 24 q^{78} + 142 q^{81} - 16 q^{82} - 36 q^{83} + 70 q^{85} + 168 q^{86} + 160 q^{87} - 32 q^{88} + 10 q^{90} - 8 q^{92} - 208 q^{93} - 200 q^{95} + 32 q^{96} + 126 q^{97}+O(q^{100}) \) 2 * q - 2 * q^2 + 4 * q^3 - 8 * q^6 + 4 * q^8 + 10 * q^10 - 16 * q^11 + 8 * q^12 - 6 * q^13 + 20 * q^15 - 8 * q^16 - 14 * q^17 + 2 * q^18 - 20 * q^20 + 16 * q^22 - 4 * q^23 - 50 * q^25 + 12 * q^26 + 40 * q^27 - 104 * q^31 + 8 * q^32 - 32 * q^33 - 4 * q^36 - 6 * q^37 + 40 * q^38 + 20 * q^40 + 16 * q^41 - 84 * q^43 - 10 * q^45 + 8 * q^46 + 36 * q^47 - 16 * q^48 + 50 * q^50 - 56 * q^51 - 12 * q^52 + 106 * q^53 + 80 * q^57 + 80 * q^58 - 40 * q^60 + 96 * q^61 + 104 * q^62 - 30 * q^65 + 64 * q^66 + 124 * q^67 + 28 * q^68 - 56 * q^71 + 4 * q^72 + 94 * q^73 - 100 * q^75 - 80 * q^76 + 24 * q^78 + 142 * q^81 - 16 * q^82 - 36 * q^83 + 70 * q^85 + 168 * q^86 + 160 * q^87 - 32 * q^88 + 10 * q^90 - 8 * q^92 - 208 * q^93 - 200 * q^95 + 32 * q^96 + 126 * q^97

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