LMFDB - Embedded newform 392.3.g.d.99.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(99,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("392.99");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.g (of order $2$, degree $1$, 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:	$10.6812263629$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.2
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	392.99
Dual form			392.3.g.d.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} -1.00000 q^{3} +(-2.00000 + 3.46410i) q^{4} -5.19615i q^{5} +(-1.00000 - 1.73205i) q^{6} -8.00000 q^{8} -8.00000 q^{9} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} -1.00000 q^{3} +(-2.00000 + 3.46410i) q^{4} -5.19615i q^{5} +(-1.00000 - 1.73205i) q^{6} -8.00000 q^{8} -8.00000 q^{9} +(9.00000 - 5.19615i) q^{10} +17.0000 q^{11} +(2.00000 - 3.46410i) q^{12} -13.8564i q^{13} +5.19615i q^{15} +(-8.00000 - 13.8564i) q^{16} +25.0000 q^{17} +(-8.00000 - 13.8564i) q^{18} +7.00000 q^{19} +(18.0000 + 10.3923i) q^{20} +(17.0000 + 29.4449i) q^{22} -5.19615i q^{23} +8.00000 q^{24} -2.00000 q^{25} +(24.0000 - 13.8564i) q^{26} +17.0000 q^{27} -13.8564i q^{29} +(-9.00000 + 5.19615i) q^{30} -32.9090i q^{31} +(16.0000 - 27.7128i) q^{32} -17.0000 q^{33} +(25.0000 + 43.3013i) q^{34} +(16.0000 - 27.7128i) q^{36} -8.66025i q^{37} +(7.00000 + 12.1244i) q^{38} +13.8564i q^{39} +41.5692i q^{40} -26.0000 q^{41} +14.0000 q^{43} +(-34.0000 + 58.8897i) q^{44} +41.5692i q^{45} +(9.00000 - 5.19615i) q^{46} -50.2295i q^{47} +(8.00000 + 13.8564i) q^{48} +(-2.00000 - 3.46410i) q^{50} -25.0000 q^{51} +(48.0000 + 27.7128i) q^{52} +91.7987i q^{53} +(17.0000 + 29.4449i) q^{54} -88.3346i q^{55} -7.00000 q^{57} +(24.0000 - 13.8564i) q^{58} +55.0000 q^{59} +(-18.0000 - 10.3923i) q^{60} +22.5167i q^{61} +(57.0000 - 32.9090i) q^{62} +64.0000 q^{64} -72.0000 q^{65} +(-17.0000 - 29.4449i) q^{66} +17.0000 q^{67} +(-50.0000 + 86.6025i) q^{68} +5.19615i q^{69} +64.0000 q^{72} -119.000 q^{73} +(15.0000 - 8.66025i) q^{74} +2.00000 q^{75} +(-14.0000 + 24.2487i) q^{76} +(-24.0000 + 13.8564i) q^{78} -74.4782i q^{79} +(-72.0000 + 41.5692i) q^{80} +55.0000 q^{81} +(-26.0000 - 45.0333i) q^{82} -110.000 q^{83} -129.904i q^{85} +(14.0000 + 24.2487i) q^{86} +13.8564i q^{87} -136.000 q^{88} -71.0000 q^{89} +(-72.0000 + 41.5692i) q^{90} +(18.0000 + 10.3923i) q^{92} +32.9090i q^{93} +(87.0000 - 50.2295i) q^{94} -36.3731i q^{95} +(-16.0000 + 27.7128i) q^{96} +22.0000 q^{97} -136.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} - 4 q^{4} - 2 q^{6} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 - 2 * q^6 - 16 * q^8 - 16 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} - 4 q^{4} - 2 q^{6} - 16 q^{8} - 16 q^{9} + 18 q^{10} + 34 q^{11} + 4 q^{12} - 16 q^{16} + 50 q^{17} - 16 q^{18} + 14 q^{19} + 36 q^{20} + 34 q^{22} + 16 q^{24} - 4 q^{25} + 48 q^{26} + 34 q^{27} - 18 q^{30} + 32 q^{32} - 34 q^{33} + 50 q^{34} + 32 q^{36} + 14 q^{38} - 52 q^{41} + 28 q^{43} - 68 q^{44} + 18 q^{46} + 16 q^{48} - 4 q^{50} - 50 q^{51} + 96 q^{52} + 34 q^{54} - 14 q^{57} + 48 q^{58} + 110 q^{59} - 36 q^{60} + 114 q^{62} + 128 q^{64} - 144 q^{65} - 34 q^{66} + 34 q^{67} - 100 q^{68} + 128 q^{72} - 238 q^{73} + 30 q^{74} + 4 q^{75} - 28 q^{76} - 48 q^{78} - 144 q^{80} + 110 q^{81} - 52 q^{82} - 220 q^{83} + 28 q^{86} - 272 q^{88} - 142 q^{89} - 144 q^{90} + 36 q^{92} + 174 q^{94} - 32 q^{96} + 44 q^{97} - 272 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 - 2 * q^6 - 16 * q^8 - 16 * q^9 + 18 * q^10 + 34 * q^11 + 4 * q^12 - 16 * q^16 + 50 * q^17 - 16 * q^18 + 14 * q^19 + 36 * q^20 + 34 * q^22 + 16 * q^24 - 4 * q^25 + 48 * q^26 + 34 * q^27 - 18 * q^30 + 32 * q^32 - 34 * q^33 + 50 * q^34 + 32 * q^36 + 14 * q^38 - 52 * q^41 + 28 * q^43 - 68 * q^44 + 18 * q^46 + 16 * q^48 - 4 * q^50 - 50 * q^51 + 96 * q^52 + 34 * q^54 - 14 * q^57 + 48 * q^58 + 110 * q^59 - 36 * q^60 + 114 * q^62 + 128 * q^64 - 144 * q^65 - 34 * q^66 + 34 * q^67 - 100 * q^68 + 128 * q^72 - 238 * q^73 + 30 * q^74 + 4 * q^75 - 28 * q^76 - 48 * q^78 - 144 * q^80 + 110 * q^81 - 52 * q^82 - 220 * q^83 + 28 * q^86 - 272 * q^88 - 142 * q^89 - 144 * q^90 + 36 * q^92 + 174 * q^94 - 32 * q^96 + 44 * q^97 - 272 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.00000	+	1.73205i	0.500000	+	0.866025i
$2$	1.00000	+	1.73205i	0.500000	+	0.866025i
$3$	−1.00000			−0.333333			−0.166667	−	0.986013i	$-0.553300\pi$
$3$	−1.00000			−0.333333			−0.166667	+	0.986013i	$0.553300\pi$
$4$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$5$		−	5.19615i		−	1.03923i	−0.854400	−	0.519615i	$-0.826075\pi$
$5$		−	5.19615i		−	1.03923i	0.854400	−	0.519615i	$-0.173925\pi$
$6$	−1.00000	−	1.73205i	−0.166667	−	0.288675i
$7$		0			0
$7$		0			0
$8$	−8.00000			−1.00000
$9$	−8.00000			−0.888889
$10$	9.00000	−	5.19615i	0.900000	−	0.519615i
$11$	17.0000			1.54545			0.772727	−	0.634738i	$-0.218892\pi$
$11$	17.0000			1.54545			0.772727	+	0.634738i	$0.218892\pi$
$12$	2.00000	−	3.46410i	0.166667	−	0.288675i
$13$		−	13.8564i		−	1.06588i	−0.846154	−	0.532939i	$-0.821088\pi$
$13$		−	13.8564i		−	1.06588i	0.846154	−	0.532939i	$-0.178912\pi$
$14$		0			0
$15$			5.19615i			0.346410i
$16$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$17$	25.0000			1.47059			0.735294	−	0.677748i	$-0.237044\pi$
$17$	25.0000			1.47059			0.735294	+	0.677748i	$0.237044\pi$
$18$	−8.00000	−	13.8564i	−0.444444	−	0.769800i
$19$	7.00000			0.368421			0.184211	−	0.982887i	$-0.441027\pi$
$19$	7.00000			0.368421			0.184211	+	0.982887i	$0.441027\pi$
$20$	18.0000	+	10.3923i	0.900000	+	0.519615i
$21$		0			0
$22$	17.0000	+	29.4449i	0.772727	+	1.33840i
$23$		−	5.19615i		−	0.225920i	−0.993600	−	0.112960i	$-0.963967\pi$
$23$		−	5.19615i		−	0.225920i	0.993600	−	0.112960i	$-0.0360331\pi$
$24$	8.00000			0.333333
$25$	−2.00000			−0.0800000
$26$	24.0000	−	13.8564i	0.923077	−	0.532939i
$27$	17.0000			0.629630
$28$		0			0
$29$		−	13.8564i		−	0.477807i	−0.971043	−	0.238904i	$-0.923212\pi$
$29$		−	13.8564i		−	0.477807i	0.971043	−	0.238904i	$-0.0767880\pi$
$30$	−9.00000	+	5.19615i	−0.300000	+	0.173205i
$31$		−	32.9090i		−	1.06158i	−0.847504	−	0.530790i	$-0.821895\pi$
$31$		−	32.9090i		−	1.06158i	0.847504	−	0.530790i	$-0.178105\pi$
$32$	16.0000	−	27.7128i	0.500000	−	0.866025i
$33$	−17.0000			−0.515152
$34$	25.0000	+	43.3013i	0.735294	+	1.27357i
$35$		0			0
$36$	16.0000	−	27.7128i	0.444444	−	0.769800i
$37$		−	8.66025i		−	0.234061i	−0.993128	−	0.117030i	$-0.962662\pi$
$37$		−	8.66025i		−	0.234061i	0.993128	−	0.117030i	$-0.0373375\pi$
$38$	7.00000	+	12.1244i	0.184211	+	0.319062i
$39$			13.8564i			0.355292i
$40$			41.5692i			1.03923i
$41$	−26.0000			−0.634146			−0.317073	−	0.948401i	$-0.602700\pi$
$41$	−26.0000			−0.634146			−0.317073	+	0.948401i	$0.602700\pi$
$42$		0			0
$43$	14.0000			0.325581			0.162791	−	0.986661i	$-0.447950\pi$
$43$	14.0000			0.325581			0.162791	+	0.986661i	$0.447950\pi$
$44$	−34.0000	+	58.8897i	−0.772727	+	1.33840i
$45$			41.5692i			0.923760i
$46$	9.00000	−	5.19615i	0.195652	−	0.112960i
$47$		−	50.2295i		−	1.06871i	−0.845259	−	0.534356i	$-0.820554\pi$
$47$		−	50.2295i		−	1.06871i	0.845259	−	0.534356i	$-0.179446\pi$
$48$	8.00000	+	13.8564i	0.166667	+	0.288675i
$49$		0			0
$50$	−2.00000	−	3.46410i	−0.0400000	−	0.0692820i
$51$	−25.0000			−0.490196
$52$	48.0000	+	27.7128i	0.923077	+	0.532939i
$53$			91.7987i			1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$53$			91.7987i			1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$54$	17.0000	+	29.4449i	0.314815	+	0.545275i
$55$		−	88.3346i		−	1.60608i
$56$		0			0
$57$	−7.00000			−0.122807
$58$	24.0000	−	13.8564i	0.413793	−	0.238904i
$59$	55.0000			0.932203			0.466102	−	0.884731i	$-0.345658\pi$
$59$	55.0000			0.932203			0.466102	+	0.884731i	$0.345658\pi$
$60$	−18.0000	−	10.3923i	−0.300000	−	0.173205i
$61$			22.5167i			0.369126i	0.982821	+	0.184563i	$0.0590869\pi$
$61$			22.5167i			0.369126i	−0.982821	+	0.184563i	$0.940913\pi$
$62$	57.0000	−	32.9090i	0.919355	−	0.530790i
$63$		0			0
$64$	64.0000			1.00000
$65$	−72.0000			−1.10769
$66$	−17.0000	−	29.4449i	−0.257576	−	0.446134i
$67$	17.0000			0.253731			0.126866	−	0.991920i	$-0.459508\pi$
$67$	17.0000			0.253731			0.126866	+	0.991920i	$0.459508\pi$
$68$	−50.0000	+	86.6025i	−0.735294	+	1.27357i
$69$			5.19615i			0.0753066i
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	64.0000			0.888889
$73$	−119.000			−1.63014			−0.815068	−	0.579365i	$-0.803301\pi$
$73$	−119.000			−1.63014			−0.815068	+	0.579365i	$0.803301\pi$
$74$	15.0000	−	8.66025i	0.202703	−	0.117030i
$75$	2.00000			0.0266667
$76$	−14.0000	+	24.2487i	−0.184211	+	0.319062i
$77$		0			0
$78$	−24.0000	+	13.8564i	−0.307692	+	0.177646i
$79$		−	74.4782i		−	0.942762i	−0.881930	−	0.471381i	$-0.843756\pi$
$79$		−	74.4782i		−	0.942762i	0.881930	−	0.471381i	$-0.156244\pi$
$80$	−72.0000	+	41.5692i	−0.900000	+	0.519615i
$81$	55.0000			0.679012
$82$	−26.0000	−	45.0333i	−0.317073	−	0.549187i
$83$	−110.000			−1.32530			−0.662651	−	0.748929i	$-0.730569\pi$
$83$	−110.000			−1.32530			−0.662651	+	0.748929i	$0.730569\pi$
$84$		0			0
$85$		−	129.904i		−	1.52828i
$86$	14.0000	+	24.2487i	0.162791	+	0.281962i
$87$			13.8564i			0.159269i
$88$	−136.000			−1.54545
$89$	−71.0000			−0.797753			−0.398876	−	0.917005i	$-0.630600\pi$
$89$	−71.0000			−0.797753			−0.398876	+	0.917005i	$0.630600\pi$
$90$	−72.0000	+	41.5692i	−0.800000	+	0.461880i
$91$		0			0
$92$	18.0000	+	10.3923i	0.195652	+	0.112960i
$93$			32.9090i			0.353860i
$94$	87.0000	−	50.2295i	0.925532	−	0.534356i
$95$		−	36.3731i		−	0.382874i
$96$	−16.0000	+	27.7128i	−0.166667	+	0.288675i
$97$	22.0000			0.226804			0.113402	−	0.993549i	$-0.463825\pi$
$97$	22.0000			0.226804			0.113402	+	0.993549i	$0.463825\pi$
$98$		0			0
$99$	−136.000			−1.37374
$100$	4.00000	−	6.92820i	0.0400000	−	0.0692820i
$101$		−	77.9423i		−	0.771706i	−0.922560	−	0.385853i	$-0.873907\pi$
$101$		−	77.9423i		−	0.771706i	0.922560	−	0.385853i	$-0.126093\pi$
$102$	−25.0000	−	43.3013i	−0.245098	−	0.424522i
$103$		−	161.081i		−	1.56389i	−0.623347	−	0.781945i	$-0.714228\pi$
$103$		−	161.081i		−	1.56389i	0.623347	−	0.781945i	$-0.285772\pi$
$104$			110.851i			1.06588i
$105$		0			0
$106$	−159.000	+	91.7987i	−1.50000	+	0.866025i
$107$	65.0000			0.607477			0.303738	−	0.952755i	$-0.401765\pi$
$107$	65.0000			0.607477			0.303738	+	0.952755i	$0.401765\pi$
$108$	−34.0000	+	58.8897i	−0.314815	+	0.545275i
$109$			8.66025i			0.0794519i	0.999211	+	0.0397259i	$0.0126485\pi$
$109$			8.66025i			0.0794519i	−0.999211	+	0.0397259i	$0.987352\pi$
$110$	153.000	−	88.3346i	1.39091	−	0.803042i
$111$			8.66025i			0.0780203i
$112$		0			0
$113$	122.000			1.07965			0.539823	−	0.841779i	$-0.318491\pi$
$113$	122.000			1.07965			0.539823	+	0.841779i	$0.318491\pi$
$114$	−7.00000	−	12.1244i	−0.0614035	−	0.106354i
$115$	−27.0000			−0.234783
$116$	48.0000	+	27.7128i	0.413793	+	0.238904i
$117$			110.851i			0.947447i
$118$	55.0000	+	95.2628i	0.466102	+	0.807312i
$119$		0			0
$120$		−	41.5692i		−	0.346410i
$121$	168.000			1.38843
$122$	−39.0000	+	22.5167i	−0.319672	+	0.184563i
$123$	26.0000			0.211382
$124$	114.000	+	65.8179i	0.919355	+	0.530790i
$125$		−	119.512i		−	0.956092i
$126$		0			0
$127$			166.277i			1.30927i	0.755947	+	0.654633i	$0.227177\pi$
$127$			166.277i			1.30927i	−0.755947	+	0.654633i	$0.772823\pi$
$128$	64.0000	+	110.851i	0.500000	+	0.866025i
$129$	−14.0000			−0.108527
$130$	−72.0000	−	124.708i	−0.553846	−	0.959290i
$131$	−17.0000			−0.129771			−0.0648855	−	0.997893i	$-0.520668\pi$
$131$	−17.0000			−0.129771			−0.0648855	+	0.997893i	$0.520668\pi$
$132$	34.0000	−	58.8897i	0.257576	−	0.446134i
$133$		0			0
$134$	17.0000	+	29.4449i	0.126866	+	0.219738i
$135$		−	88.3346i		−	0.654330i
$136$	−200.000			−1.47059
$137$	−145.000			−1.05839			−0.529197	−	0.848499i	$-0.677507\pi$
$137$	−145.000			−1.05839			−0.529197	+	0.848499i	$0.677507\pi$
$138$	−9.00000	+	5.19615i	−0.0652174	+	0.0376533i
$139$	82.0000			0.589928			0.294964	−	0.955508i	$-0.404692\pi$
$139$	82.0000			0.589928			0.294964	+	0.955508i	$0.404692\pi$
$140$		0			0
$141$			50.2295i			0.356237i
$142$		0			0
$143$		−	235.559i		−	1.64727i
$144$	64.0000	+	110.851i	0.444444	+	0.769800i
$145$	−72.0000			−0.496552
$146$	−119.000	−	206.114i	−0.815068	−	1.41174i
$147$		0			0
$148$	30.0000	+	17.3205i	0.202703	+	0.117030i
$149$			5.19615i			0.0348735i	0.999848	+	0.0174368i	$0.00555057\pi$
$149$			5.19615i			0.0348735i	−0.999848	+	0.0174368i	$0.994449\pi$
$150$	2.00000	+	3.46410i	0.0133333	+	0.0230940i
$151$		−	36.3731i		−	0.240881i	−0.992721	−	0.120441i	$-0.961569\pi$
$151$		−	36.3731i		−	0.240881i	0.992721	−	0.120441i	$-0.0384307\pi$
$152$	−56.0000			−0.368421
$153$	−200.000			−1.30719
$154$		0			0
$155$	−171.000			−1.10323
$156$	−48.0000	−	27.7128i	−0.307692	−	0.177646i
$157$			310.037i			1.97476i	0.158373	+	0.987379i	$0.449375\pi$
$157$			310.037i			1.97476i	−0.158373	+	0.987379i	$0.550625\pi$
$158$	129.000	−	74.4782i	0.816456	−	0.471381i
$159$		−	91.7987i		−	0.577350i
$160$	−144.000	−	83.1384i	−0.900000	−	0.519615i
$161$		0			0
$162$	55.0000	+	95.2628i	0.339506	+	0.588042i
$163$	17.0000			0.104294			0.0521472	−	0.998639i	$-0.483393\pi$
$163$	17.0000			0.104294			0.0521472	+	0.998639i	$0.483393\pi$
$164$	52.0000	−	90.0666i	0.317073	−	0.549187i
$165$			88.3346i			0.535361i
$166$	−110.000	−	190.526i	−0.662651	−	1.14774i
$167$		−	13.8564i		−	0.0829725i	−0.999139	−	0.0414862i	$-0.986791\pi$
$167$		−	13.8564i		−	0.0829725i	0.999139	−	0.0414862i	$-0.0132093\pi$
$168$		0			0
$169$	−23.0000			−0.136095
$170$	225.000	−	129.904i	1.32353	−	0.764140i
$171$	−56.0000			−0.327485
$172$	−28.0000	+	48.4974i	−0.162791	+	0.281962i
$173$			105.655i			0.610723i	0.952236	+	0.305362i	$0.0987773\pi$
$173$			105.655i			0.610723i	−0.952236	+	0.305362i	$0.901223\pi$
$174$	−24.0000	+	13.8564i	−0.137931	+	0.0796345i
$175$		0			0
$176$	−136.000	−	235.559i	−0.772727	−	1.33840i
$177$	−55.0000			−0.310734
$178$	−71.0000	−	122.976i	−0.398876	−	0.690874i
$179$	89.0000			0.497207			0.248603	−	0.968605i	$-0.420028\pi$
$179$	89.0000			0.497207			0.248603	+	0.968605i	$0.420028\pi$
$180$	−144.000	−	83.1384i	−0.800000	−	0.461880i
$181$			249.415i			1.37799i	0.724768	+	0.688993i	$0.241947\pi$
$181$			249.415i			1.37799i	−0.724768	+	0.688993i	$0.758053\pi$
$182$		0			0
$183$		−	22.5167i		−	0.123042i
$184$			41.5692i			0.225920i
$185$	−45.0000			−0.243243
$186$	−57.0000	+	32.9090i	−0.306452	+	0.176930i
$187$	425.000			2.27273
$188$	174.000	+	100.459i	0.925532	+	0.534356i
$189$		0			0
$190$	63.0000	−	36.3731i	0.331579	−	0.191437i
$191$			216.506i			1.13354i	0.823876	+	0.566771i	$0.191807\pi$
$191$			216.506i			1.13354i	−0.823876	+	0.566771i	$0.808193\pi$
$192$	−64.0000			−0.333333
$193$	−73.0000			−0.378238			−0.189119	−	0.981954i	$-0.560563\pi$
$193$	−73.0000			−0.378238			−0.189119	+	0.981954i	$0.560563\pi$
$194$	22.0000	+	38.1051i	0.113402	+	0.196418i
$195$	72.0000			0.369231
$196$		0			0
$197$		−	207.846i		−	1.05506i	−0.849538	−	0.527528i	$-0.823119\pi$
$197$		−	207.846i		−	1.05506i	0.849538	−	0.527528i	$-0.176881\pi$
$198$	−136.000	−	235.559i	−0.686869	−	1.18969i
$199$			64.0859i			0.322040i	0.986951	+	0.161020i	$0.0514783\pi$
$199$			64.0859i			0.322040i	−0.986951	+	0.161020i	$0.948522\pi$
$200$	16.0000			0.0800000
$201$	−17.0000			−0.0845771
$202$	135.000	−	77.9423i	0.668317	−	0.385853i
$203$		0			0
$204$	50.0000	−	86.6025i	0.245098	−	0.424522i
$205$			135.100i			0.659024i
$206$	279.000	−	161.081i	1.35437	−	0.781945i
$207$			41.5692i			0.200817i
$208$	−192.000	+	110.851i	−0.923077	+	0.532939i
$209$	119.000			0.569378
$210$		0			0
$211$	302.000			1.43128			0.715640	−	0.698470i	$-0.246135\pi$
$211$	302.000			1.43128			0.715640	+	0.698470i	$0.246135\pi$
$212$	−318.000	−	183.597i	−1.50000	−	0.866025i
$213$		0			0
$214$	65.0000	+	112.583i	0.303738	+	0.526090i
$215$		−	72.7461i		−	0.338354i
$216$	−136.000			−0.629630
$217$		0			0
$218$	−15.0000	+	8.66025i	−0.0688073	+	0.0397259i
$219$	119.000			0.543379
$220$	306.000	+	176.669i	1.39091	+	0.803042i
$221$		−	346.410i		−	1.56747i
$222$	−15.0000	+	8.66025i	−0.0675676	+	0.0390102i
$223$			138.564i			0.621364i	0.950514	+	0.310682i	$0.100557\pi$
$223$			138.564i			0.621364i	−0.950514	+	0.310682i	$0.899443\pi$
$224$		0			0
$225$	16.0000			0.0711111
$226$	122.000	+	211.310i	0.539823	+	0.935001i
$227$	55.0000			0.242291			0.121145	−	0.992635i	$-0.461343\pi$
$227$	55.0000			0.242291			0.121145	+	0.992635i	$0.461343\pi$
$228$	14.0000	−	24.2487i	0.0614035	−	0.106354i
$229$			327.358i			1.42951i	0.699375	+	0.714755i	$0.253462\pi$
$229$			327.358i			1.42951i	−0.699375	+	0.714755i	$0.746538\pi$
$230$	−27.0000	−	46.7654i	−0.117391	−	0.203328i
$231$		0			0
$232$			110.851i			0.477807i
$233$	−385.000			−1.65236			−0.826180	−	0.563406i	$-0.809491\pi$
$233$	−385.000			−1.65236			−0.826180	+	0.563406i	$0.809491\pi$
$234$	−192.000	+	110.851i	−0.820513	+	0.473723i
$235$	−261.000			−1.11064
$236$	−110.000	+	190.526i	−0.466102	+	0.807312i
$237$			74.4782i			0.314254i
$238$		0			0
$239$			429.549i			1.79727i	0.438693	+	0.898637i	$0.355442\pi$
$239$			429.549i			1.79727i	−0.438693	+	0.898637i	$0.644558\pi$
$240$	72.0000	−	41.5692i	0.300000	−	0.173205i
$241$	145.000			0.601660			0.300830	−	0.953678i	$-0.402736\pi$
$241$	145.000			0.601660			0.300830	+	0.953678i	$0.402736\pi$
$242$	168.000	+	290.985i	0.694215	+	1.20242i
$243$	−208.000			−0.855967
$244$	−78.0000	−	45.0333i	−0.319672	−	0.184563i
$245$		0			0
$246$	26.0000	+	45.0333i	0.105691	+	0.183062i
$247$		−	96.9948i		−	0.392692i
$248$			263.272i			1.06158i
$249$	110.000			0.441767
$250$	207.000	−	119.512i	0.828000	−	0.478046i
$251$	58.0000			0.231076			0.115538	−	0.993303i	$-0.463141\pi$
$251$	58.0000			0.231076			0.115538	+	0.993303i	$0.463141\pi$
$252$		0			0
$253$		−	88.3346i		−	0.349149i
$254$	−288.000	+	166.277i	−1.13386	+	0.654633i
$255$			129.904i			0.509427i
$256$	−128.000	+	221.703i	−0.500000	+	0.866025i
$257$	−119.000			−0.463035			−0.231518	−	0.972831i	$-0.574369\pi$
$257$	−119.000			−0.463035			−0.231518	+	0.972831i	$0.574369\pi$
$258$	−14.0000	−	24.2487i	−0.0542636	−	0.0939873i
$259$		0			0
$260$	144.000	−	249.415i	0.553846	−	0.959290i
$261$			110.851i			0.424717i
$262$	−17.0000	−	29.4449i	−0.0648855	−	0.112385i
$263$		−	327.358i		−	1.24471i	−0.782737	−	0.622353i	$-0.786177\pi$
$263$		−	327.358i		−	1.24471i	0.782737	−	0.622353i	$-0.213823\pi$
$264$	136.000			0.515152
$265$	477.000			1.80000
$266$		0			0
$267$	71.0000			0.265918
$268$	−34.0000	+	58.8897i	−0.126866	+	0.219738i
$269$		−	133.368i		−	0.495791i	−0.968787	−	0.247896i	$-0.920261\pi$
$269$		−	133.368i		−	0.495791i	0.968787	−	0.247896i	$-0.0797390\pi$
$270$	153.000	−	88.3346i	0.566667	−	0.327165i
$271$			434.745i			1.60422i	0.597174	+	0.802112i	$0.296290\pi$
$271$			434.745i			1.60422i	−0.597174	+	0.802112i	$0.703710\pi$
$272$	−200.000	−	346.410i	−0.735294	−	1.27357i
$273$		0			0
$274$	−145.000	−	251.147i	−0.529197	−	0.916596i
$275$	−34.0000			−0.123636
$276$	−18.0000	−	10.3923i	−0.0652174	−	0.0376533i
$277$			202.650i			0.731588i	0.930696	+	0.365794i	$0.119203\pi$
$277$			202.650i			0.731588i	−0.930696	+	0.365794i	$0.880797\pi$
$278$	82.0000	+	142.028i	0.294964	+	0.510893i
$279$			263.272i			0.943626i
$280$		0			0
$281$	74.0000			0.263345			0.131673	−	0.991293i	$-0.457965\pi$
$281$	74.0000			0.263345			0.131673	+	0.991293i	$0.457965\pi$
$282$	−87.0000	+	50.2295i	−0.308511	+	0.178119i
$283$	463.000			1.63604			0.818021	−	0.575188i	$-0.195071\pi$
$283$	463.000			1.63604			0.818021	+	0.575188i	$0.195071\pi$
$284$		0			0
$285$			36.3731i			0.127625i
$286$	408.000	−	235.559i	1.42657	−	0.823633i
$287$		0			0
$288$	−128.000	+	221.703i	−0.444444	+	0.769800i
$289$	336.000			1.16263
$290$	−72.0000	−	124.708i	−0.248276	−	0.430026i
$291$	−22.0000			−0.0756014
$292$	238.000	−	412.228i	0.815068	−	1.41174i
$293$			110.851i			0.378332i	0.981945	+	0.189166i	$0.0605784\pi$
$293$			110.851i			0.378332i	−0.981945	+	0.189166i	$0.939422\pi$
$294$		0			0
$295$		−	285.788i		−	0.968774i
$296$			69.2820i			0.234061i
$297$	289.000			0.973064
$298$	−9.00000	+	5.19615i	−0.0302013	+	0.0174368i
$299$	−72.0000			−0.240803
$300$	−4.00000	+	6.92820i	−0.0133333	+	0.0230940i
$301$		0			0
$302$	63.0000	−	36.3731i	0.208609	−	0.120441i
$303$			77.9423i			0.257235i
$304$	−56.0000	−	96.9948i	−0.184211	−	0.319062i
$305$	117.000			0.383607
$306$	−200.000	−	346.410i	−0.653595	−	1.13206i
$307$	274.000			0.892508			0.446254	−	0.894906i	$-0.352758\pi$
$307$	274.000			0.892508			0.446254	+	0.894906i	$0.352758\pi$
$308$		0			0
$309$			161.081i			0.521297i
$310$	−171.000	−	296.181i	−0.551613	−	0.955422i
$311$			50.2295i			0.161510i	0.996734	+	0.0807548i	$0.0257331\pi$
$311$			50.2295i			0.161510i	−0.996734	+	0.0807548i	$0.974267\pi$
$312$		−	110.851i		−	0.355292i
$313$	409.000			1.30671			0.653355	−	0.757052i	$-0.273361\pi$
$313$	409.000			1.30671			0.653355	+	0.757052i	$0.273361\pi$
$314$	−537.000	+	310.037i	−1.71019	+	0.987379i
$315$		0			0
$316$	258.000	+	148.956i	0.816456	+	0.471381i
$317$		−	188.794i		−	0.595563i	−0.954634	−	0.297782i	$-0.903753\pi$
$317$		−	188.794i		−	0.595563i	0.954634	−	0.297782i	$-0.0962467\pi$
$318$	159.000	−	91.7987i	0.500000	−	0.288675i
$319$		−	235.559i		−	0.738429i
$320$		−	332.554i		−	1.03923i
$321$	−65.0000			−0.202492
$322$		0			0
$323$	175.000			0.541796
$324$	−110.000	+	190.526i	−0.339506	+	0.588042i
$325$			27.7128i			0.0852702i
$326$	17.0000	+	29.4449i	0.0521472	+	0.0903217i
$327$		−	8.66025i		−	0.0264840i
$328$	208.000			0.634146
$329$		0			0
$330$	−153.000	+	88.3346i	−0.463636	+	0.267681i
$331$	−295.000			−0.891239			−0.445619	−	0.895223i	$-0.647017\pi$
$331$	−295.000			−0.891239			−0.445619	+	0.895223i	$0.647017\pi$
$332$	220.000	−	381.051i	0.662651	−	1.14774i
$333$			69.2820i			0.208054i
$334$	24.0000	−	13.8564i	0.0718563	−	0.0414862i
$335$		−	88.3346i		−	0.263685i
$336$		0			0
$337$	26.0000			0.0771513			0.0385757	−	0.999256i	$-0.487718\pi$
$337$	26.0000			0.0771513			0.0385757	+	0.999256i	$0.487718\pi$
$338$	−23.0000	−	39.8372i	−0.0680473	−	0.117861i
$339$	−122.000			−0.359882
$340$	450.000	+	259.808i	1.32353	+	0.764140i
$341$		−	559.452i		−	1.64062i
$342$	−56.0000	−	96.9948i	−0.163743	−	0.283611i
$343$		0			0
$344$	−112.000			−0.325581
$345$	27.0000			0.0782609
$346$	−183.000	+	105.655i	−0.528902	+	0.305362i
$347$	377.000			1.08646			0.543228	−	0.839585i	$-0.317202\pi$
$347$	377.000			1.08646			0.543228	+	0.839585i	$0.317202\pi$
$348$	−48.0000	−	27.7128i	−0.137931	−	0.0796345i
$349$			96.9948i			0.277922i	0.990298	+	0.138961i	$0.0443763\pi$
$349$			96.9948i			0.277922i	−0.990298	+	0.138961i	$0.955624\pi$
$350$		0			0
$351$		−	235.559i		−	0.671108i
$352$	272.000	−	471.118i	0.772727	−	1.33840i
$353$	−503.000			−1.42493			−0.712465	−	0.701708i	$-0.752421\pi$
$353$	−503.000			−1.42493			−0.712465	+	0.701708i	$0.752421\pi$
$354$	−55.0000	−	95.2628i	−0.155367	−	0.269104i
$355$		0			0
$356$	142.000	−	245.951i	0.398876	−	0.690874i
$357$		0			0
$358$	89.0000	+	154.153i	0.248603	+	0.430594i
$359$		−	185.329i		−	0.516238i	−0.966113	−	0.258119i	$-0.916897\pi$
$359$		−	185.329i		−	0.516238i	0.966113	−	0.258119i	$-0.0831027\pi$
$360$		−	332.554i		−	0.923760i
$361$	−312.000			−0.864266
$362$	−432.000	+	249.415i	−1.19337	+	0.688993i
$363$	−168.000			−0.462810
$364$		0			0
$365$			618.342i			1.69409i
$366$	39.0000	−	22.5167i	0.106557	−	0.0615209i
$367$		−	296.181i		−	0.807032i	−0.914973	−	0.403516i	$-0.867788\pi$
$367$		−	296.181i		−	0.807032i	0.914973	−	0.403516i	$-0.132212\pi$
$368$	−72.0000	+	41.5692i	−0.195652	+	0.112960i
$369$	208.000			0.563686
$370$	−45.0000	−	77.9423i	−0.121622	−	0.210655i
$371$		0			0
$372$	−114.000	−	65.8179i	−0.306452	−	0.176930i
$373$		−	119.512i		−	0.320406i	−0.987084	−	0.160203i	$-0.948785\pi$
$373$		−	119.512i		−	0.320406i	0.987084	−	0.160203i	$-0.0512149\pi$
$374$	425.000	+	736.122i	1.13636	+	1.96824i
$375$			119.512i			0.318697i
$376$			401.836i			1.06871i
$377$	−192.000			−0.509284
$378$		0			0
$379$	−634.000			−1.67282			−0.836412	−	0.548102i	$-0.815351\pi$
$379$	−634.000			−1.67282			−0.836412	+	0.548102i	$0.815351\pi$
$380$	126.000	+	72.7461i	0.331579	+	0.191437i
$381$		−	166.277i		−	0.436422i
$382$	−375.000	+	216.506i	−0.981675	+	0.566771i
$383$		−	244.219i		−	0.637648i	−0.947814	−	0.318824i	$-0.896712\pi$
$383$		−	244.219i		−	0.637648i	0.947814	−	0.318824i	$-0.103288\pi$
$384$	−64.0000	−	110.851i	−0.166667	−	0.288675i
$385$		0			0
$386$	−73.0000	−	126.440i	−0.189119	−	0.327564i
$387$	−112.000			−0.289406
$388$	−44.0000	+	76.2102i	−0.113402	+	0.196418i
$389$		−	587.165i		−	1.50942i	−0.656057	−	0.754711i	$-0.727777\pi$
$389$		−	587.165i		−	1.50942i	0.656057	−	0.754711i	$-0.272223\pi$
$390$	72.0000	+	124.708i	0.184615	+	0.319763i
$391$		−	129.904i		−	0.332235i
$392$		0			0
$393$	17.0000			0.0432570
$394$	360.000	−	207.846i	0.913706	−	0.527528i
$395$	−387.000			−0.979747
$396$	272.000	−	471.118i	0.686869	−	1.18969i
$397$		−	240.755i		−	0.606436i	−0.952921	−	0.303218i	$-0.901939\pi$
$397$		−	240.755i		−	0.606436i	0.952921	−	0.303218i	$-0.0980610\pi$
$398$	−111.000	+	64.0859i	−0.278894	+	0.161020i
$399$		0			0
$400$	16.0000	+	27.7128i	0.0400000	+	0.0692820i
$401$	119.000			0.296758			0.148379	−	0.988931i	$-0.452594\pi$
$401$	119.000			0.296758			0.148379	+	0.988931i	$0.452594\pi$
$402$	−17.0000	−	29.4449i	−0.0422886	−	0.0732459i
$403$	−456.000			−1.13151
$404$	270.000	+	155.885i	0.668317	+	0.385853i
$405$		−	285.788i		−	0.705650i
$406$		0			0
$407$		−	147.224i		−	0.361731i
$408$	200.000			0.490196
$409$	145.000			0.354523			0.177262	−	0.984164i	$-0.443276\pi$
$409$	145.000			0.354523			0.177262	+	0.984164i	$0.443276\pi$
$410$	−234.000	+	135.100i	−0.570732	+	0.329512i
$411$	145.000			0.352798
$412$	558.000	+	322.161i	1.35437	+	0.781945i
$413$		0			0
$414$	−72.0000	+	41.5692i	−0.173913	+	0.100409i
$415$			571.577i			1.37729i
$416$	−384.000	−	221.703i	−0.923077	−	0.532939i
$417$	−82.0000			−0.196643
$418$	119.000	+	206.114i	0.284689	+	0.493096i
$419$	−302.000			−0.720764			−0.360382	−	0.932805i	$-0.617354\pi$
$419$	−302.000			−0.720764			−0.360382	+	0.932805i	$0.617354\pi$
$420$		0			0
$421$			401.836i			0.954479i	0.878773	+	0.477240i	$0.158363\pi$
$421$			401.836i			0.954479i	−0.878773	+	0.477240i	$0.841637\pi$
$422$	302.000	+	523.079i	0.715640	+	1.23952i
$423$			401.836i			0.949966i
$424$		−	734.390i		−	1.73205i
$425$	−50.0000			−0.117647
$426$		0			0
$427$		0			0
$428$	−130.000	+	225.167i	−0.303738	+	0.526090i
$429$			235.559i			0.549088i
$430$	126.000	−	72.7461i	0.293023	−	0.169177i
$431$			808.868i			1.87672i	0.345655	+	0.938362i	$0.387657\pi$
$431$			808.868i			1.87672i	−0.345655	+	0.938362i	$0.612343\pi$
$432$	−136.000	−	235.559i	−0.314815	−	0.545275i
$433$	−410.000			−0.946882			−0.473441	−	0.880825i	$-0.656988\pi$
$433$	−410.000			−0.946882			−0.473441	+	0.880825i	$0.656988\pi$
$434$		0			0
$435$	72.0000			0.165517
$436$	−30.0000	−	17.3205i	−0.0688073	−	0.0397259i
$437$		−	36.3731i		−	0.0832336i
$438$	119.000	+	206.114i	0.271689	+	0.470580i
$439$			490.170i			1.11656i	0.829652	+	0.558281i	$0.188539\pi$
$439$			490.170i			1.11656i	−0.829652	+	0.558281i	$0.811461\pi$
$440$			706.677i			1.60608i
$441$		0			0
$442$	600.000	−	346.410i	1.35747	−	0.783733i
$443$	401.000			0.905192			0.452596	−	0.891716i	$-0.350498\pi$
$443$	401.000			0.905192			0.452596	+	0.891716i	$0.350498\pi$
$444$	−30.0000	−	17.3205i	−0.0675676	−	0.0390102i
$445$			368.927i			0.829049i
$446$	−240.000	+	138.564i	−0.538117	+	0.310682i
$447$		−	5.19615i		−	0.0116245i
$448$		0			0
$449$	−310.000			−0.690423			−0.345212	−	0.938525i	$-0.612193\pi$
$449$	−310.000			−0.690423			−0.345212	+	0.938525i	$0.612193\pi$
$450$	16.0000	+	27.7128i	0.0355556	+	0.0615840i
$451$	−442.000			−0.980044
$452$	−244.000	+	422.620i	−0.539823	+	0.935001i
$453$			36.3731i			0.0802937i
$454$	55.0000	+	95.2628i	0.121145	+	0.209830i
$455$		0			0
$456$	56.0000			0.122807
$457$	167.000			0.365427			0.182713	−	0.983166i	$-0.441512\pi$
$457$	167.000			0.365427			0.182713	+	0.983166i	$0.441512\pi$
$458$	−567.000	+	327.358i	−1.23799	+	0.714755i
$459$	425.000			0.925926
$460$	54.0000	−	93.5307i	0.117391	−	0.203328i
$461$			13.8564i			0.0300573i	0.999887	+	0.0150286i	$0.00478394\pi$
$461$			13.8564i			0.0300573i	−0.999887	+	0.0150286i	$0.995216\pi$
$462$		0			0
$463$		−	609.682i		−	1.31681i	−0.752665	−	0.658404i	$-0.771232\pi$
$463$		−	609.682i		−	1.31681i	0.752665	−	0.658404i	$-0.228768\pi$
$464$	−192.000	+	110.851i	−0.413793	+	0.238904i
$465$	171.000			0.367742
$466$	−385.000	−	666.840i	−0.826180	−	1.43099i
$467$	−785.000			−1.68094			−0.840471	−	0.541856i	$-0.817722\pi$
$467$	−785.000			−1.68094			−0.840471	+	0.541856i	$0.817722\pi$
$468$	−384.000	−	221.703i	−0.820513	−	0.473723i
$469$		0			0
$470$	−261.000	−	452.065i	−0.555319	−	0.961841i
$471$		−	310.037i		−	0.658253i
$472$	−440.000			−0.932203
$473$	238.000			0.503171
$474$	−129.000	+	74.4782i	−0.272152	+	0.157127i
$475$	−14.0000			−0.0294737
$476$		0			0
$477$		−	734.390i		−	1.53960i
$478$	−744.000	+	429.549i	−1.55649	+	0.898637i
$479$			618.342i			1.29090i	0.763802	+	0.645451i	$0.223331\pi$
$479$			618.342i			1.29090i	−0.763802	+	0.645451i	$0.776669\pi$
$480$	144.000	+	83.1384i	0.300000	+	0.173205i
$481$	−120.000			−0.249480
$482$	145.000	+	251.147i	0.300830	+	0.521053i
$483$		0			0
$484$	−336.000	+	581.969i	−0.694215	+	1.20242i
$485$		−	114.315i		−	0.235702i
$486$	−208.000	−	360.267i	−0.427984	−	0.741289i
$487$			393.176i			0.807342i	0.914904	+	0.403671i	$0.132266\pi$
$487$			393.176i			0.807342i	−0.914904	+	0.403671i	$0.867734\pi$
$488$		−	180.133i		−	0.369126i
$489$	−17.0000			−0.0347648
$490$		0			0
$491$	422.000			0.859470			0.429735	−	0.902955i	$-0.358607\pi$
$491$	422.000			0.859470			0.429735	+	0.902955i	$0.358607\pi$
$492$	−52.0000	+	90.0666i	−0.105691	+	0.183062i
$493$		−	346.410i		−	0.702658i
$494$	168.000	−	96.9948i	0.340081	−	0.196346i
$495$			706.677i			1.42763i
$496$	−456.000	+	263.272i	−0.919355	+	0.530790i
$497$		0			0
$498$	110.000	+	190.526i	0.220884	+	0.382582i
$499$	65.0000			0.130261			0.0651303	−	0.997877i	$-0.479254\pi$
$499$	65.0000			0.130261			0.0651303	+	0.997877i	$0.479254\pi$
$500$	414.000	+	239.023i	0.828000	+	0.478046i
$501$			13.8564i			0.0276575i
$502$	58.0000	+	100.459i	0.115538	+	0.200117i
$503$		−	249.415i		−	0.495855i	−0.968779	−	0.247928i	$-0.920250\pi$
$503$		−	249.415i		−	0.495855i	0.968779	−	0.247928i	$-0.0797496\pi$
$504$		0			0
$505$	−405.000			−0.801980
$506$	153.000	−	88.3346i	0.302372	−	0.174574i
$507$	23.0000			0.0453649
$508$	−576.000	−	332.554i	−1.13386	−	0.654633i
$509$		−	545.596i		−	1.07190i	−0.844250	−	0.535949i	$-0.819954\pi$
$509$		−	545.596i		−	1.07190i	0.844250	−	0.535949i	$-0.180046\pi$
$510$	−225.000	+	129.904i	−0.441176	+	0.254713i
$511$		0			0
$512$	−512.000			−1.00000
$513$	119.000			0.231969
$514$	−119.000	−	206.114i	−0.231518	−	0.401000i
$515$	−837.000			−1.62524
$516$	28.0000	−	48.4974i	0.0542636	−	0.0939873i
$517$		−	853.901i		−	1.65165i
$518$		0			0
$519$		−	105.655i		−	0.203574i
$520$	576.000			1.10769
$521$	25.0000			0.0479846			0.0239923	−	0.999712i	$-0.492362\pi$
$521$	25.0000			0.0479846			0.0239923	+	0.999712i	$0.492362\pi$
$522$	−192.000	+	110.851i	−0.367816	+	0.212359i
$523$	−593.000			−1.13384			−0.566922	−	0.823772i	$-0.691866\pi$
$523$	−593.000			−1.13384			−0.566922	+	0.823772i	$0.691866\pi$
$524$	34.0000	−	58.8897i	0.0648855	−	0.112385i
$525$		0			0
$526$	567.000	−	327.358i	1.07795	−	0.622353i
$527$		−	822.724i		−	1.56115i
$528$	136.000	+	235.559i	0.257576	+	0.446134i
$529$	502.000			0.948960
$530$	477.000	+	826.188i	0.900000	+	1.55885i
$531$	−440.000			−0.828625
$532$		0			0
$533$			360.267i			0.675922i
$534$	71.0000	+	122.976i	0.132959	+	0.230291i
$535$		−	337.750i		−	0.631308i
$536$	−136.000			−0.253731
$537$	−89.0000			−0.165736
$538$	231.000	−	133.368i	0.429368	−	0.247896i
$539$		0			0
$540$	306.000	+	176.669i	0.566667	+	0.327165i
$541$		−	756.906i		−	1.39909i	−0.714590	−	0.699544i	$-0.753387\pi$
$541$		−	756.906i		−	1.39909i	0.714590	−	0.699544i	$-0.246613\pi$
$542$	−753.000	+	434.745i	−1.38930	+	0.802112i
$543$		−	249.415i		−	0.459328i
$544$	400.000	−	692.820i	0.735294	−	1.27357i
$545$	45.0000			0.0825688
$546$		0			0
$547$	662.000			1.21024			0.605119	−	0.796135i	$-0.293126\pi$
$547$	662.000			1.21024			0.605119	+	0.796135i	$0.293126\pi$
$548$	290.000	−	502.295i	0.529197	−	0.916596i
$549$		−	180.133i		−	0.328112i
$550$	−34.0000	−	58.8897i	−0.0618182	−	0.107072i
$551$		−	96.9948i		−	0.176034i
$552$		−	41.5692i		−	0.0753066i
$553$		0			0
$554$	−351.000	+	202.650i	−0.633574	+	0.365794i
$555$	45.0000			0.0810811
$556$	−164.000	+	284.056i	−0.294964	+	0.510893i
$557$			590.629i			1.06038i	0.847880	+	0.530188i	$0.177879\pi$
$557$			590.629i			1.06038i	−0.847880	+	0.530188i	$0.822121\pi$
$558$	−456.000	+	263.272i	−0.817204	+	0.471813i
$559$		−	193.990i		−	0.347030i
$560$		0			0
$561$	−425.000			−0.757576
$562$	74.0000	+	128.172i	0.131673	+	0.228064i
$563$	−737.000			−1.30906			−0.654529	−	0.756037i	$-0.727133\pi$
$563$	−737.000			−1.30906			−0.654529	+	0.756037i	$0.727133\pi$
$564$	−174.000	−	100.459i	−0.308511	−	0.178119i
$565$		−	633.931i		−	1.12200i
$566$	463.000	+	801.940i	0.818021	+	1.41685i
$567$		0			0
$568$		0			0
$569$	−121.000			−0.212654			−0.106327	−	0.994331i	$-0.533909\pi$
$569$	−121.000			−0.212654			−0.106327	+	0.994331i	$0.533909\pi$
$570$	−63.0000	+	36.3731i	−0.110526	+	0.0638124i
$571$	737.000			1.29072			0.645359	−	0.763879i	$-0.276708\pi$
$571$	737.000			1.29072			0.645359	+	0.763879i	$0.276708\pi$
$572$	816.000	+	471.118i	1.42657	+	0.823633i
$573$		−	216.506i		−	0.377847i
$574$		0			0
$575$			10.3923i			0.0180736i
$576$	−512.000			−0.888889
$577$	−47.0000			−0.0814558			−0.0407279	−	0.999170i	$-0.512968\pi$
$577$	−47.0000			−0.0814558			−0.0407279	+	0.999170i	$0.512968\pi$
$578$	336.000	+	581.969i	0.581315	+	1.00687i
$579$	73.0000			0.126079
$580$	144.000	−	249.415i	0.248276	−	0.430026i
$581$		0			0
$582$	−22.0000	−	38.1051i	−0.0378007	−	0.0654727i
$583$			1560.58i			2.67681i
$584$	952.000			1.63014
$585$	576.000			0.984615
$586$	−192.000	+	110.851i	−0.327645	+	0.189166i
$587$	−446.000			−0.759796			−0.379898	−	0.925028i	$-0.624041\pi$
$587$	−446.000			−0.759796			−0.379898	+	0.925028i	$0.624041\pi$
$588$		0			0
$589$		−	230.363i		−	0.391108i
$590$	495.000	−	285.788i	0.838983	−	0.484387i
$591$			207.846i			0.351685i
$592$	−120.000	+	69.2820i	−0.202703	+	0.117030i
$593$	−215.000			−0.362563			−0.181282	−	0.983431i	$-0.558025\pi$
$593$	−215.000			−0.362563			−0.181282	+	0.983431i	$0.558025\pi$
$594$	289.000	+	500.563i	0.486532	+	0.842698i
$595$		0			0
$596$	−18.0000	−	10.3923i	−0.0302013	−	0.0174368i
$597$		−	64.0859i		−	0.107347i
$598$	−72.0000	−	124.708i	−0.120401	−	0.208541i
$599$			282.324i			0.471326i	0.971835	+	0.235663i	$0.0757262\pi$
$599$			282.324i			0.471326i	−0.971835	+	0.235663i	$0.924274\pi$
$600$	−16.0000			−0.0266667
$601$	−266.000			−0.442596			−0.221298	−	0.975206i	$-0.571029\pi$
$601$	−266.000			−0.442596			−0.221298	+	0.975206i	$0.571029\pi$
$602$		0			0
$603$	−136.000			−0.225539
$604$	126.000	+	72.7461i	0.208609	+	0.120441i
$605$		−	872.954i		−	1.44290i
$606$	−135.000	+	77.9423i	−0.222772	+	0.128618i
$607$		−	659.911i		−	1.08717i	−0.839355	−	0.543584i	$-0.817067\pi$
$607$		−	659.911i		−	1.08717i	0.839355	−	0.543584i	$-0.182933\pi$
$608$	112.000	−	193.990i	0.184211	−	0.319062i
$609$		0			0
$610$	117.000	+	202.650i	0.191803	+	0.332213i
$611$	−696.000			−1.13912
$612$	400.000	−	692.820i	0.653595	−	1.13206i
$613$		−	698.016i		−	1.13869i	−0.822099	−	0.569345i	$-0.807197\pi$
$613$		−	698.016i		−	1.13869i	0.822099	−	0.569345i	$-0.192803\pi$
$614$	274.000	+	474.582i	0.446254	+	0.772935i
$615$		−	135.100i		−	0.219675i
$616$		0			0
$617$	−118.000			−0.191248			−0.0956240	−	0.995418i	$-0.530485\pi$
$617$	−118.000			−0.191248			−0.0956240	+	0.995418i	$0.530485\pi$
$618$	−279.000	+	161.081i	−0.451456	+	0.260648i
$619$	919.000			1.48465			0.742326	−	0.670039i	$-0.233722\pi$
$619$	919.000			1.48465			0.742326	+	0.670039i	$0.233722\pi$
$620$	342.000	−	592.361i	0.551613	−	0.955422i
$621$		−	88.3346i		−	0.142246i
$622$	−87.0000	+	50.2295i	−0.139871	+	0.0807548i
$623$		0			0
$624$	192.000	−	110.851i	0.307692	−	0.177646i
$625$	−671.000			−1.07360
$626$	409.000	+	708.409i	0.653355	+	1.13164i
$627$	−119.000			−0.189793
$628$	−1074.00	−	620.074i	−1.71019	−	0.987379i
$629$		−	216.506i		−	0.344207i
$630$		0			0
$631$			166.277i			0.263513i	0.991282	+	0.131757i	$0.0420617\pi$
$631$			166.277i			0.263513i	−0.991282	+	0.131757i	$0.957938\pi$
$632$			595.825i			0.942762i
$633$	−302.000			−0.477093
$634$	327.000	−	188.794i	0.515773	−	0.297782i
$635$	864.000			1.36063
$636$	318.000	+	183.597i	0.500000	+	0.288675i
$637$		0			0
$638$	408.000	−	235.559i	0.639498	−	0.369215i
$639$		0			0
$640$	576.000	−	332.554i	0.900000	−	0.519615i
$641$	−1.00000			−0.00156006			−0.000780031	−	1.00000i	$-0.500248\pi$
$641$	−1.00000			−0.00156006			−0.000780031		1.00000i	$0.500248\pi$
$642$	−65.0000	−	112.583i	−0.101246	−	0.175363i
$643$	514.000			0.799378			0.399689	−	0.916651i	$-0.369118\pi$
$643$	514.000			0.799378			0.399689	+	0.916651i	$0.369118\pi$
$644$		0			0
$645$			72.7461i			0.112785i
$646$	175.000	+	303.109i	0.270898	+	0.469209i
$647$		−	60.6218i		−	0.0936967i	−0.998902	−	0.0468484i	$-0.985082\pi$
$647$		−	60.6218i		−	0.0936967i	0.998902	−	0.0468484i	$-0.0149178\pi$
$648$	−440.000			−0.679012
$649$	935.000			1.44068
$650$	−48.0000	+	27.7128i	−0.0738462	+	0.0426351i
$651$		0			0
$652$	−34.0000	+	58.8897i	−0.0521472	+	0.0903217i
$653$		−	327.358i		−	0.501313i	−0.968076	−	0.250657i	$-0.919353\pi$
$653$		−	327.358i		−	0.501313i	0.968076	−	0.250657i	$-0.0806465\pi$
$654$	15.0000	−	8.66025i	0.0229358	−	0.0132420i
$655$			88.3346i			0.134862i
$656$	208.000	+	360.267i	0.317073	+	0.549187i
$657$	952.000			1.44901
$658$		0			0
$659$	542.000			0.822458			0.411229	−	0.911532i	$-0.365100\pi$
$659$	542.000			0.822458			0.411229	+	0.911532i	$0.365100\pi$
$660$	−306.000	−	176.669i	−0.463636	−	0.267681i
$661$			1182.99i			1.78970i	0.446368	+	0.894849i	$0.352717\pi$
$661$			1182.99i			1.78970i	−0.446368	+	0.894849i	$0.647283\pi$
$662$	−295.000	−	510.955i	−0.445619	−	0.771835i
$663$			346.410i			0.522489i
$664$	880.000			1.32530
$665$		0			0
$666$	−120.000	+	69.2820i	−0.180180	+	0.104027i
$667$	−72.0000			−0.107946
$668$	48.0000	+	27.7128i	0.0718563	+	0.0414862i
$669$		−	138.564i		−	0.207121i
$670$	153.000	−	88.3346i	0.228358	−	0.131843i
$671$			382.783i			0.570467i
$672$		0			0
$673$	218.000			0.323923			0.161961	−	0.986797i	$-0.448218\pi$
$673$	218.000			0.323923			0.161961	+	0.986797i	$0.448218\pi$
$674$	26.0000	+	45.0333i	0.0385757	+	0.0668150i
$675$	−34.0000			−0.0503704
$676$	46.0000	−	79.6743i	0.0680473	−	0.117861i
$677$		−	642.591i		−	0.949174i	−0.880209	−	0.474587i	$-0.842597\pi$
$677$		−	642.591i		−	0.949174i	0.880209	−	0.474587i	$-0.157403\pi$
$678$	−122.000	−	211.310i	−0.179941	−	0.311667i
$679$		0			0
$680$			1039.23i			1.52828i
$681$	−55.0000			−0.0807636
$682$	969.000	−	559.452i	1.42082	−	0.820311i
$683$	−367.000			−0.537335			−0.268668	−	0.963233i	$-0.586583\pi$
$683$	−367.000			−0.537335			−0.268668	+	0.963233i	$0.586583\pi$
$684$	112.000	−	193.990i	0.163743	−	0.283611i
$685$			753.442i			1.09992i
$686$		0			0
$687$		−	327.358i		−	0.476503i
$688$	−112.000	−	193.990i	−0.162791	−	0.281962i
$689$	1272.00			1.84615
$690$	27.0000	+	46.7654i	0.0391304	+	0.0677759i
$691$	−497.000			−0.719247			−0.359624	−	0.933097i	$-0.617095\pi$
$691$	−497.000			−0.719247			−0.359624	+	0.933097i	$0.617095\pi$
$692$	−366.000	−	211.310i	−0.528902	−	0.305362i
$693$		0			0
$694$	377.000	+	652.983i	0.543228	+	0.940898i
$695$		−	426.084i		−	0.613071i
$696$		−	110.851i		−	0.159269i
$697$	−650.000			−0.932568
$698$	−168.000	+	96.9948i	−0.240688	+	0.138961i
$699$	385.000			0.550787
$700$		0			0
$701$			332.554i			0.474399i	0.971461	+	0.237200i	$0.0762295\pi$
$701$			332.554i			0.474399i	−0.971461	+	0.237200i	$0.923770\pi$
$702$	408.000	−	235.559i	0.581197	−	0.335554i
$703$		−	60.6218i		−	0.0862330i
$704$	1088.00			1.54545
$705$	261.000			0.370213
$706$	−503.000	−	871.222i	−0.712465	−	1.23402i
$707$		0			0
$708$	110.000	−	190.526i	0.155367	−	0.269104i
$709$		−	396.640i		−	0.559435i	−0.960082	−	0.279718i	$-0.909759\pi$
$709$		−	396.640i		−	0.559435i	0.960082	−	0.279718i	$-0.0902409\pi$
$710$		0			0
$711$			595.825i			0.838011i
$712$	568.000			0.797753
$713$	−171.000			−0.239832
$714$		0			0
$715$	−1224.00			−1.71189
$716$	−178.000	+	308.305i	−0.248603	+	0.430594i
$717$		−	429.549i		−	0.599091i
$718$	321.000	−	185.329i	0.447075	−	0.258119i
$719$		−	64.0859i		−	0.0891320i	−0.999006	−	0.0445660i	$-0.985810\pi$
$719$		−	64.0859i		−	0.0891320i	0.999006	−	0.0445660i	$-0.0141905\pi$
$720$	576.000	−	332.554i	0.800000	−	0.461880i
$721$		0			0
$722$	−312.000	−	540.400i	−0.432133	−	0.748476i
$723$	−145.000			−0.200553
$724$	−864.000	−	498.831i	−1.19337	−	0.688993i
$725$			27.7128i			0.0382246i
$726$	−168.000	−	290.985i	−0.231405	−	0.400805i
$727$			55.4256i			0.0762388i	0.999273	+	0.0381194i	$0.0121367\pi$
$727$			55.4256i			0.0762388i	−0.999273	+	0.0381194i	$0.987863\pi$
$728$		0			0
$729$	−287.000			−0.393690
$730$	−1071.00	+	618.342i	−1.46712	+	0.847044i
$731$	350.000			0.478796
$732$	78.0000	+	45.0333i	0.106557	+	0.0615209i
$733$			826.188i			1.12713i	0.826071	+	0.563566i	$0.190571\pi$
$733$			826.188i			1.12713i	−0.826071	+	0.563566i	$0.809429\pi$
$734$	513.000	−	296.181i	0.698910	−	0.403516i
$735$		0			0
$736$	−144.000	−	83.1384i	−0.195652	−	0.112960i
$737$	289.000			0.392130
$738$	208.000	+	360.267i	0.281843	+	0.488166i
$739$	713.000			0.964817			0.482409	−	0.875946i	$-0.339762\pi$
$739$	713.000			0.964817			0.482409	+	0.875946i	$0.339762\pi$
$740$	90.0000	−	155.885i	0.121622	−	0.210655i
$741$			96.9948i			0.130897i
$742$		0			0
$743$			637.395i			0.857866i	0.903336	+	0.428933i	$0.141110\pi$
$743$			637.395i			0.857866i	−0.903336	+	0.428933i	$0.858890\pi$
$744$		−	263.272i		−	0.353860i
$745$	27.0000			0.0362416
$746$	207.000	−	119.512i	0.277480	−	0.160203i
$747$	880.000			1.17805
$748$	−850.000	+	1472.24i	−1.13636	+	1.96824i
$749$		0			0
$750$	−207.000	+	119.512i	−0.276000	+	0.159349i
$751$		−	1169.13i		−	1.55677i	−0.627787	−	0.778385i	$-0.716039\pi$
$751$		−	1169.13i		−	1.55677i	0.627787	−	0.778385i	$-0.283961\pi$
$752$	−696.000	+	401.836i	−0.925532	+	0.534356i
$753$	−58.0000			−0.0770252
$754$	−192.000	−	332.554i	−0.254642	−	0.441053i
$755$	−189.000			−0.250331
$756$		0			0
$757$			1039.23i			1.37283i	0.727211	+	0.686414i	$0.240816\pi$
$757$			1039.23i			1.37283i	−0.727211	+	0.686414i	$0.759184\pi$
$758$	−634.000	−	1098.12i	−0.836412	−	1.44871i
$759$			88.3346i			0.116383i
$760$			290.985i			0.382874i
$761$	−863.000			−1.13403			−0.567017	−	0.823706i	$-0.691903\pi$
$761$	−863.000			−1.13403			−0.567017	+	0.823706i	$0.691903\pi$
$762$	288.000	−	166.277i	0.377953	−	0.218211i
$763$		0			0
$764$	−750.000	−	433.013i	−0.981675	−	0.566771i
$765$			1039.23i			1.35847i
$766$	423.000	−	244.219i	0.552219	−	0.318824i
$767$		−	762.102i		−	0.993615i
$768$	128.000	−	221.703i	0.166667	−	0.288675i
$769$	−410.000			−0.533160			−0.266580	−	0.963813i	$-0.585894\pi$
$769$	−410.000			−0.533160			−0.266580	+	0.963813i	$0.585894\pi$
$770$		0			0
$771$	119.000			0.154345
$772$	146.000	−	252.879i	0.189119	−	0.327564i
$773$		−	798.475i		−	1.03296i	−0.856300	−	0.516478i	$-0.827243\pi$
$773$		−	798.475i		−	1.03296i	0.856300	−	0.516478i	$-0.172757\pi$
$774$	−112.000	−	193.990i	−0.144703	−	0.250633i
$775$			65.8179i			0.0849264i
$776$	−176.000			−0.226804
$777$		0			0
$778$	1017.00	−	587.165i	1.30720	−	0.754711i
$779$	−182.000			−0.233633
$780$	−144.000	+	249.415i	−0.184615	+	0.319763i
$781$		0			0
$782$	225.000	−	129.904i	0.287724	−	0.166117i
$783$		−	235.559i		−	0.300842i
$784$		0			0
$785$	1611.00			2.05223
$786$	17.0000	+	29.4449i	0.0216285	+	0.0374617i
$787$	31.0000			0.0393901			0.0196950	−	0.999806i	$-0.493730\pi$
$787$	31.0000			0.0393901			0.0196950	+	0.999806i	$0.493730\pi$
$788$	720.000	+	415.692i	0.913706	+	0.527528i
$789$			327.358i			0.414902i
$790$	−387.000	−	670.304i	−0.489873	−	0.848486i
$791$		0			0
$792$	1088.00			1.37374
$793$	312.000			0.393443
$794$	417.000	−	240.755i	0.525189	−	0.303218i
$795$	−477.000			−0.600000
$796$	−222.000	−	128.172i	−0.278894	−	0.161020i
$797$		−	595.825i		−	0.747585i	−0.927512	−	0.373793i	$-0.878057\pi$
$797$		−	595.825i		−	0.747585i	0.927512	−	0.373793i	$-0.121943\pi$
$798$		0			0
$799$		−	1255.74i		−	1.57164i
$800$	−32.0000	+	55.4256i	−0.0400000	+	0.0692820i
$801$	568.000			0.709114
$802$	119.000	+	206.114i	0.148379	+	0.257000i
$803$	−2023.00			−2.51930
$804$	34.0000	−	58.8897i	0.0422886	−	0.0732459i
$805$		0			0
$806$	−456.000	−	789.815i	−0.565757	−	0.979920i
$807$			133.368i			0.165264i
$808$			623.538i			0.771706i
$809$	−313.000			−0.386897			−0.193449	−	0.981110i	$-0.561967\pi$
$809$	−313.000			−0.386897			−0.193449	+	0.981110i	$0.561967\pi$
$810$	495.000	−	285.788i	0.611111	−	0.352825i
$811$	1138.00			1.40321			0.701603	−	0.712568i	$-0.252468\pi$
$811$	1138.00			1.40321			0.701603	+	0.712568i	$0.252468\pi$
$812$		0			0
$813$		−	434.745i		−	0.534741i
$814$	255.000	−	147.224i	0.313268	−	0.180865i
$815$		−	88.3346i		−	0.108386i
$816$	200.000	+	346.410i	0.245098	+	0.424522i
$817$	98.0000			0.119951
$818$	145.000	+	251.147i	0.177262	+	0.307026i
$819$		0			0
$820$	−468.000	−	270.200i	−0.570732	−	0.329512i
$821$			1224.56i			1.49155i	0.666200	+	0.745773i	$0.267920\pi$
$821$			1224.56i			1.49155i	−0.666200	+	0.745773i	$0.732080\pi$
$822$	145.000	+	251.147i	0.176399	+	0.305532i
$823$			116.047i			0.141005i	0.997512	+	0.0705027i	$0.0224603\pi$
$823$			116.047i			0.141005i	−0.997512	+	0.0705027i	$0.977540\pi$
$824$			1288.65i			1.56389i
$825$	34.0000			0.0412121
$826$		0			0
$827$	−754.000			−0.911729			−0.455865	−	0.890049i	$-0.650670\pi$
$827$	−754.000			−0.911729			−0.455865	+	0.890049i	$0.650670\pi$
$828$	−144.000	−	83.1384i	−0.173913	−	0.100409i
$829$			905.863i			1.09272i	0.837551	+	0.546359i	$0.183986\pi$
$829$			905.863i			1.09272i	−0.837551	+	0.546359i	$0.816014\pi$
$830$	−990.000	+	571.577i	−1.19277	+	0.688647i
$831$		−	202.650i		−	0.243863i
$832$		−	886.810i		−	1.06588i
$833$		0			0
$834$	−82.0000	−	142.028i	−0.0983213	−	0.170298i
$835$	−72.0000			−0.0862275
$836$	−238.000	+	412.228i	−0.284689	+	0.493096i
$837$		−	559.452i		−	0.668402i
$838$	−302.000	−	523.079i	−0.360382	−	0.624200i
$839$			1053.09i			1.25517i	0.778548	+	0.627585i	$0.215956\pi$
$839$			1053.09i			1.25517i	−0.778548	+	0.627585i	$0.784044\pi$
$840$		0			0
$841$	649.000			0.771700
$842$	−696.000	+	401.836i	−0.826603	+	0.477240i
$843$	−74.0000			−0.0877817
$844$	−604.000	+	1046.16i	−0.715640	+	1.23952i
$845$			119.512i			0.141434i
$846$	−696.000	+	401.836i	−0.822695	+	0.474983i
$847$		0			0
$848$	1272.00	−	734.390i	1.50000	−	0.866025i
$849$	−463.000			−0.545347
$850$	−50.0000	−	86.6025i	−0.0588235	−	0.101885i
$851$	−45.0000			−0.0528790
$852$		0			0
$853$			845.241i			0.990904i	0.868635	+	0.495452i	$0.164997\pi$
$853$			845.241i			0.990904i	−0.868635	+	0.495452i	$0.835003\pi$
$854$		0			0
$855$			290.985i			0.340333i
$856$	−520.000			−0.607477
$857$	−887.000			−1.03501			−0.517503	−	0.855681i	$-0.673138\pi$
$857$	−887.000			−1.03501			−0.517503	+	0.855681i	$0.673138\pi$
$858$	−408.000	+	235.559i	−0.475524	+	0.274544i
$859$	1663.00			1.93597			0.967986	−	0.251004i	$-0.0807608\pi$
$859$	1663.00			1.93597			0.967986	+	0.251004i	$0.0807608\pi$
$860$	252.000	+	145.492i	0.293023	+	0.169177i
$861$		0			0
$862$	−1401.00	+	808.868i	−1.62529	+	0.938362i
$863$			562.917i			0.652279i	0.945322	+	0.326139i	$0.105748\pi$
$863$			562.917i			0.652279i	−0.945322	+	0.326139i	$0.894252\pi$
$864$	272.000	−	471.118i	0.314815	−	0.545275i
$865$	549.000			0.634682
$866$	−410.000	−	710.141i	−0.473441	−	0.820024i
$867$	−336.000			−0.387543
$868$		0			0
$869$		−	1266.13i		−	1.45700i
$870$	72.0000	+	124.708i	0.0827586	+	0.143342i
$871$		−	235.559i		−	0.270447i
$872$		−	69.2820i		−	0.0794519i
$873$	−176.000			−0.201604
$874$	63.0000	−	36.3731i	0.0720824	−	0.0416168i
$875$		0			0
$876$	−238.000	+	412.228i	−0.271689	+	0.470580i
$877$		−	119.512i		−	0.136273i	−0.997676	−	0.0681365i	$-0.978295\pi$
$877$		−	119.512i		−	0.136273i	0.997676	−	0.0681365i	$-0.0217054\pi$
$878$	−849.000	+	490.170i	−0.966970	+	0.558281i
$879$		−	110.851i		−	0.126111i
$880$	−1224.00	+	706.677i	−1.39091	+	0.803042i
$881$	574.000			0.651532			0.325766	−	0.945450i	$-0.394378\pi$
$881$	574.000			0.651532			0.325766	+	0.945450i	$0.394378\pi$
$882$		0			0
$883$	1166.00			1.32050			0.660249	−	0.751047i	$-0.270451\pi$
$883$	1166.00			1.32050			0.660249	+	0.751047i	$0.270451\pi$
$884$	1200.00	+	692.820i	1.35747	+	0.783733i
$885$			285.788i			0.322925i
$886$	401.000	+	694.552i	0.452596	+	0.783919i
$887$			545.596i			0.615103i	0.951532	+	0.307551i	$0.0995096\pi$
$887$			545.596i			0.615103i	−0.951532	+	0.307551i	$0.900490\pi$
$888$		−	69.2820i		−	0.0780203i
$889$		0			0
$890$	−639.000	+	368.927i	−0.717978	+	0.414525i
$891$	935.000			1.04938
$892$	−480.000	−	277.128i	−0.538117	−	0.310682i
$893$		−	351.606i		−	0.393736i
$894$	9.00000	−	5.19615i	0.0100671	−	0.00581225i
$895$		−	462.458i		−	0.516712i
$896$		0			0
$897$	72.0000			0.0802676
$898$	−310.000	−	536.936i	−0.345212	−	0.597924i
$899$	−456.000			−0.507230
$900$	−32.0000	+	55.4256i	−0.0355556	+	0.0615840i
$901$			2294.97i			2.54713i
$902$	−442.000	−	765.566i	−0.490022	−	0.848743i
$903$		0			0
$904$	−976.000			−1.07965
$905$	1296.00			1.43204
$906$	−63.0000	+	36.3731i	−0.0695364	+	0.0401469i
$907$	521.000			0.574421			0.287211	−	0.957867i	$-0.407272\pi$
$907$	521.000			0.574421			0.287211	+	0.957867i	$0.407272\pi$
$908$	−110.000	+	190.526i	−0.121145	+	0.209830i
$909$			623.538i			0.685961i
$910$		0			0
$911$			1191.65i			1.30807i	0.756465	+	0.654035i	$0.226925\pi$
$911$			1191.65i			1.30807i	−0.756465	+	0.654035i	$0.773075\pi$
$912$	56.0000	+	96.9948i	0.0614035	+	0.106354i
$913$	−1870.00			−2.04819
$914$	167.000	+	289.252i	0.182713	+	0.316469i
$915$	−117.000			−0.127869
$916$	−1134.00	−	654.715i	−1.23799	−	0.714755i
$917$		0			0
$918$	425.000	+	736.122i	0.462963	+	0.801875i
$919$			1394.30i			1.51719i	0.651560	+	0.758597i	$0.274115\pi$
$919$			1394.30i			1.51719i	−0.651560	+	0.758597i	$0.725885\pi$
$920$	216.000			0.234783
$921$	−274.000			−0.297503
$922$	−24.0000	+	13.8564i	−0.0260304	+	0.0150286i
$923$		0			0
$924$		0			0
$925$			17.3205i			0.0187249i
$926$	1056.00	−	609.682i	1.14039	−	0.658404i
$927$			1288.65i			1.39012i
$928$	−384.000	−	221.703i	−0.413793	−	0.238904i
$929$	961.000			1.03445			0.517223	−	0.855851i	$-0.326966\pi$
$929$	961.000			1.03445			0.517223	+	0.855851i	$0.326966\pi$
$930$	171.000	+	296.181i	0.183871	+	0.318474i
$931$		0			0
$932$	770.000	−	1333.68i	0.826180	−	1.43099i
$933$		−	50.2295i		−	0.0538365i
$934$	−785.000	−	1359.66i	−0.840471	−	1.45574i
$935$		−	2208.36i		−	2.36189i
$936$		−	886.810i		−	0.947447i
$937$	142.000			0.151547			0.0757737	−	0.997125i	$-0.475857\pi$
$937$	142.000			0.151547			0.0757737	+	0.997125i	$0.475857\pi$
$938$		0			0
$939$	−409.000			−0.435570
$940$	522.000	−	904.131i	0.555319	−	0.961841i
$941$			1224.56i			1.30134i	0.759361	+	0.650669i	$0.225512\pi$
$941$			1224.56i			1.30134i	−0.759361	+	0.650669i	$0.774488\pi$
$942$	537.000	−	310.037i	0.570064	−	0.329126i
$943$			135.100i			0.143266i
$944$	−440.000	−	762.102i	−0.466102	−	0.807312i
$945$		0			0
$946$	238.000	+	412.228i	0.251586	+	0.435759i
$947$	−175.000			−0.184794			−0.0923970	−	0.995722i	$-0.529453\pi$
$947$	−175.000			−0.184794			−0.0923970	+	0.995722i	$0.529453\pi$
$948$	−258.000	−	148.956i	−0.272152	−	0.157127i
$949$			1648.91i			1.73753i
$950$	−14.0000	−	24.2487i	−0.0147368	−	0.0255250i
$951$			188.794i			0.198521i
$952$		0			0
$953$	−454.000			−0.476390			−0.238195	−	0.971217i	$-0.576556\pi$
$953$	−454.000			−0.476390			−0.238195	+	0.971217i	$0.576556\pi$
$954$	1272.00	−	734.390i	1.33333	−	0.769800i
$955$	1125.00			1.17801
$956$	−1488.00	−	859.097i	−1.55649	−	0.898637i
$957$			235.559i			0.246143i
$958$	−1071.00	+	618.342i	−1.11795	+	0.645451i
$959$		0			0
$960$			332.554i			0.346410i
$961$	−122.000			−0.126951
$962$	−120.000	−	207.846i	−0.124740	−	0.216056i
$963$	−520.000			−0.539979
$964$	−290.000	+	502.295i	−0.300830	+	0.521053i
$965$			379.319i			0.393077i
$966$		0			0
$967$			720.533i			0.745122i	0.928008	+	0.372561i	$0.121520\pi$
$967$			720.533i			0.745122i	−0.928008	+	0.372561i	$0.878480\pi$
$968$	−1344.00			−1.38843
$969$	−175.000			−0.180599
$970$	198.000	−	114.315i	0.204124	−	0.117851i
$971$	1639.00			1.68795			0.843975	−	0.536382i	$-0.180209\pi$
$971$	1639.00			1.68795			0.843975	+	0.536382i	$0.180209\pi$
$972$	416.000	−	720.533i	0.427984	−	0.741289i
$973$		0			0
$974$	−681.000	+	393.176i	−0.699179	+	0.403671i
$975$		−	27.7128i		−	0.0284234i
$976$	312.000	−	180.133i	0.319672	−	0.184563i
$977$	−793.000			−0.811668			−0.405834	−	0.913947i	$-0.633019\pi$
$977$	−793.000			−0.811668			−0.405834	+	0.913947i	$0.633019\pi$
$978$	−17.0000	−	29.4449i	−0.0173824	−	0.0301072i
$979$	−1207.00			−1.23289
$980$		0			0
$981$		−	69.2820i		−	0.0706239i
$982$	422.000	+	730.925i	0.429735	+	0.744323i
$983$		−	1543.26i		−	1.56995i	−0.619530	−	0.784973i	$-0.712677\pi$
$983$		−	1543.26i		−	1.56995i	0.619530	−	0.784973i	$-0.287323\pi$
$984$	−208.000			−0.211382
$985$	−1080.00			−1.09645
$986$	600.000	−	346.410i	0.608519	−	0.351329i
$987$		0			0
$988$	336.000	+	193.990i	0.340081	+	0.196346i
$989$		−	72.7461i		−	0.0735552i
$990$	−1224.00	+	706.677i	−1.23636	+	0.713815i
$991$		−	895.470i		−	0.903603i	−0.892119	−	0.451801i	$-0.850782\pi$
$991$		−	895.470i		−	0.903603i	0.892119	−	0.451801i	$-0.149218\pi$
$992$	−912.000	−	526.543i	−0.919355	−	0.530790i
$993$	295.000			0.297080
$994$		0			0
$995$	333.000			0.334673
$996$	−220.000	+	381.051i	−0.220884	+	0.382582i
$997$			795.011i			0.797404i	0.917081	+	0.398702i	$0.130539\pi$
$997$			795.011i			0.797404i	−0.917081	+	0.398702i	$0.869461\pi$
$998$	65.0000	+	112.583i	0.0651303	+	0.112809i
$999$		−	147.224i		−	0.147372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.g.d.99.2		2
4.3	odd	2		1568.3.g.f.687.1		2
7.2	even	3		392.3.k.c.67.1		2
7.3	odd	6		56.3.k.a.51.1	yes	2
7.4	even	3		392.3.k.a.275.1		2
7.5	odd	6		56.3.k.b.11.1	yes	2
7.6	odd	2		392.3.g.e.99.2		2
8.3	odd	2	inner	392.3.g.d.99.1		2
8.5	even	2		1568.3.g.f.687.2		2
28.3	even	6		224.3.o.a.79.1		2
28.19	even	6		224.3.o.b.207.1		2
28.27	even	2		1568.3.g.c.687.2		2
56.3	even	6		56.3.k.b.51.1	yes	2
56.5	odd	6		224.3.o.a.207.1		2
56.11	odd	6		392.3.k.c.275.1		2
56.13	odd	2		1568.3.g.c.687.1		2
56.19	even	6		56.3.k.a.11.1	✓	2
56.27	even	2		392.3.g.e.99.1		2
56.45	odd	6		224.3.o.b.79.1		2
56.51	odd	6		392.3.k.a.67.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.k.a.11.1	✓	2	56.19	even	6
56.3.k.a.51.1	yes	2	7.3	odd	6
56.3.k.b.11.1	yes	2	7.5	odd	6
56.3.k.b.51.1	yes	2	56.3	even	6
224.3.o.a.79.1		2	28.3	even	6
224.3.o.a.207.1		2	56.5	odd	6
224.3.o.b.79.1		2	56.45	odd	6
224.3.o.b.207.1		2	28.19	even	6
392.3.g.d.99.1		2	8.3	odd	2	inner
392.3.g.d.99.2		2	1.1	even	1	trivial
392.3.g.e.99.1		2	56.27	even	2
392.3.g.e.99.2		2	7.6	odd	2
392.3.k.a.67.1		2	56.51	odd	6
392.3.k.a.275.1		2	7.4	even	3
392.3.k.c.67.1		2	7.2	even	3
392.3.k.c.275.1		2	56.11	odd	6
1568.3.g.c.687.1		2	56.13	odd	2
1568.3.g.c.687.2		2	28.27	even	2
1568.3.g.f.687.1		2	4.3	odd	2
1568.3.g.f.687.2		2	8.5	even	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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} -1.00000 q^{3} +(-2.00000 + 3.46410i) q^{4} -5.19615i q^{5} +(-1.00000 - 1.73205i) q^{6} -8.00000 q^{8} -8.00000 q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} -1.00000 q^{3} +(-2.00000 + 3.46410i) q^{4} -5.19615i q^{5} +(-1.00000 - 1.73205i) q^{6} -8.00000 q^{8} -8.00000 q^{9} +(9.00000 - 5.19615i) q^{10} +17.0000 q^{11} +(2.00000 - 3.46410i) q^{12} -13.8564i q^{13} +5.19615i q^{15} +(-8.00000 - 13.8564i) q^{16} +25.0000 q^{17} +(-8.00000 - 13.8564i) q^{18} +7.00000 q^{19} +(18.0000 + 10.3923i) q^{20} +(17.0000 + 29.4449i) q^{22} -5.19615i q^{23} +8.00000 q^{24} -2.00000 q^{25} +(24.0000 - 13.8564i) q^{26} +17.0000 q^{27} -13.8564i q^{29} +(-9.00000 + 5.19615i) q^{30} -32.9090i q^{31} +(16.0000 - 27.7128i) q^{32} -17.0000 q^{33} +(25.0000 + 43.3013i) q^{34} +(16.0000 - 27.7128i) q^{36} -8.66025i q^{37} +(7.00000 + 12.1244i) q^{38} +13.8564i q^{39} +41.5692i q^{40} -26.0000 q^{41} +14.0000 q^{43} +(-34.0000 + 58.8897i) q^{44} +41.5692i q^{45} +(9.00000 - 5.19615i) q^{46} -50.2295i q^{47} +(8.00000 + 13.8564i) q^{48} +(-2.00000 - 3.46410i) q^{50} -25.0000 q^{51} +(48.0000 + 27.7128i) q^{52} +91.7987i q^{53} +(17.0000 + 29.4449i) q^{54} -88.3346i q^{55} -7.00000 q^{57} +(24.0000 - 13.8564i) q^{58} +55.0000 q^{59} +(-18.0000 - 10.3923i) q^{60} +22.5167i q^{61} +(57.0000 - 32.9090i) q^{62} +64.0000 q^{64} -72.0000 q^{65} +(-17.0000 - 29.4449i) q^{66} +17.0000 q^{67} +(-50.0000 + 86.6025i) q^{68} +5.19615i q^{69} +64.0000 q^{72} -119.000 q^{73} +(15.0000 - 8.66025i) q^{74} +2.00000 q^{75} +(-14.0000 + 24.2487i) q^{76} +(-24.0000 + 13.8564i) q^{78} -74.4782i q^{79} +(-72.0000 + 41.5692i) q^{80} +55.0000 q^{81} +(-26.0000 - 45.0333i) q^{82} -110.000 q^{83} -129.904i q^{85} +(14.0000 + 24.2487i) q^{86} +13.8564i q^{87} -136.000 q^{88} -71.0000 q^{89} +(-72.0000 + 41.5692i) q^{90} +(18.0000 + 10.3923i) q^{92} +32.9090i q^{93} +(87.0000 - 50.2295i) q^{94} -36.3731i q^{95} +(-16.0000 + 27.7128i) q^{96} +22.0000 q^{97} -136.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} - 4 q^{4} - 2 q^{6} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 - 2 * q^6 - 16 * q^8 - 16 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} - 4 q^{4} - 2 q^{6} - 16 q^{8} - 16 q^{9} + 18 q^{10} + 34 q^{11} + 4 q^{12} - 16 q^{16} + 50 q^{17} - 16 q^{18} + 14 q^{19} + 36 q^{20} + 34 q^{22} + 16 q^{24} - 4 q^{25} + 48 q^{26} + 34 q^{27} - 18 q^{30} + 32 q^{32} - 34 q^{33} + 50 q^{34} + 32 q^{36} + 14 q^{38} - 52 q^{41} + 28 q^{43} - 68 q^{44} + 18 q^{46} + 16 q^{48} - 4 q^{50} - 50 q^{51} + 96 q^{52} + 34 q^{54} - 14 q^{57} + 48 q^{58} + 110 q^{59} - 36 q^{60} + 114 q^{62} + 128 q^{64} - 144 q^{65} - 34 q^{66} + 34 q^{67} - 100 q^{68} + 128 q^{72} - 238 q^{73} + 30 q^{74} + 4 q^{75} - 28 q^{76} - 48 q^{78} - 144 q^{80} + 110 q^{81} - 52 q^{82} - 220 q^{83} + 28 q^{86} - 272 q^{88} - 142 q^{89} - 144 q^{90} + 36 q^{92} + 174 q^{94} - 32 q^{96} + 44 q^{97} - 272 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 - 2 * q^6 - 16 * q^8 - 16 * q^9 + 18 * q^10 + 34 * q^11 + 4 * q^12 - 16 * q^16 + 50 * q^17 - 16 * q^18 + 14 * q^19 + 36 * q^20 + 34 * q^22 + 16 * q^24 - 4 * q^25 + 48 * q^26 + 34 * q^27 - 18 * q^30 + 32 * q^32 - 34 * q^33 + 50 * q^34 + 32 * q^36 + 14 * q^38 - 52 * q^41 + 28 * q^43 - 68 * q^44 + 18 * q^46 + 16 * q^48 - 4 * q^50 - 50 * q^51 + 96 * q^52 + 34 * q^54 - 14 * q^57 + 48 * q^58 + 110 * q^59 - 36 * q^60 + 114 * q^62 + 128 * q^64 - 144 * q^65 - 34 * q^66 + 34 * q^67 - 100 * q^68 + 128 * q^72 - 238 * q^73 + 30 * q^74 + 4 * q^75 - 28 * q^76 - 48 * q^78 - 144 * q^80 + 110 * q^81 - 52 * q^82 - 220 * q^83 + 28 * q^86 - 272 * q^88 - 142 * q^89 - 144 * q^90 + 36 * q^92 + 174 * q^94 - 32 * q^96 + 44 * q^97 - 272 * q^99

Introduction

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