LMFDB - Embedded newform 26.3.d.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [26,3,Mod(5,26)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(26, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

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

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

chi := DirichletCharacter("26.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	26.d (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:	$0.708448687337$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	26.5
Dual form			26.3.d.a.21.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(-3.00000 + 3.00000i) q^{5} +(2.00000 + 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(-3.00000 + 3.00000i) q^{5} +(2.00000 + 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} -9.00000 q^{9} +6.00000i q^{10} +(6.00000 + 6.00000i) q^{11} -13.0000i q^{13} +4.00000 q^{14} -4.00000 q^{16} -6.00000i q^{17} +(-9.00000 + 9.00000i) q^{18} +(26.0000 - 26.0000i) q^{19} +(6.00000 + 6.00000i) q^{20} +12.0000 q^{22} +24.0000i q^{23} +7.00000i q^{25} +(-13.0000 - 13.0000i) q^{26} +(4.00000 - 4.00000i) q^{28} -48.0000 q^{29} +(-14.0000 + 14.0000i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-6.00000 - 6.00000i) q^{34} -12.0000 q^{35} +18.0000i q^{36} +(37.0000 + 37.0000i) q^{37} -52.0000i q^{38} +12.0000 q^{40} +(-9.00000 + 9.00000i) q^{41} -36.0000i q^{43} +(12.0000 - 12.0000i) q^{44} +(27.0000 - 27.0000i) q^{45} +(24.0000 + 24.0000i) q^{46} +(42.0000 + 42.0000i) q^{47} -41.0000i q^{49} +(7.00000 + 7.00000i) q^{50} -26.0000 q^{52} +30.0000 q^{53} -36.0000 q^{55} -8.00000i q^{56} +(-48.0000 + 48.0000i) q^{58} +(-54.0000 - 54.0000i) q^{59} -18.0000 q^{61} +28.0000i q^{62} +(-18.0000 - 18.0000i) q^{63} +8.00000i q^{64} +(39.0000 + 39.0000i) q^{65} +(-22.0000 + 22.0000i) q^{67} -12.0000 q^{68} +(-12.0000 + 12.0000i) q^{70} +(6.00000 - 6.00000i) q^{71} +(18.0000 + 18.0000i) q^{72} +(17.0000 + 17.0000i) q^{73} +74.0000 q^{74} +(-52.0000 - 52.0000i) q^{76} +24.0000i q^{77} -108.000 q^{79} +(12.0000 - 12.0000i) q^{80} +81.0000 q^{81} +18.0000i q^{82} +(78.0000 - 78.0000i) q^{83} +(18.0000 + 18.0000i) q^{85} +(-36.0000 - 36.0000i) q^{86} -24.0000i q^{88} +(-9.00000 - 9.00000i) q^{89} -54.0000i q^{90} +(26.0000 - 26.0000i) q^{91} +48.0000 q^{92} +84.0000 q^{94} +156.000i q^{95} +(-47.0000 + 47.0000i) q^{97} +(-41.0000 - 41.0000i) q^{98} +(-54.0000 - 54.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 6 q^{5} + 4 q^{7} - 4 q^{8} - 18 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 6 * q^5 + 4 * q^7 - 4 * q^8 - 18 * q^9	$ 2 q + 2 q^{2} - 6 q^{5} + 4 q^{7} - 4 q^{8} - 18 q^{9} + 12 q^{11} + 8 q^{14} - 8 q^{16} - 18 q^{18} + 52 q^{19} + 12 q^{20} + 24 q^{22} - 26 q^{26} + 8 q^{28} - 96 q^{29} - 28 q^{31} - 8 q^{32} - 12 q^{34} - 24 q^{35} + 74 q^{37} + 24 q^{40} - 18 q^{41} + 24 q^{44} + 54 q^{45} + 48 q^{46} + 84 q^{47} + 14 q^{50} - 52 q^{52} + 60 q^{53} - 72 q^{55} - 96 q^{58} - 108 q^{59} - 36 q^{61} - 36 q^{63} + 78 q^{65} - 44 q^{67} - 24 q^{68} - 24 q^{70} + 12 q^{71} + 36 q^{72} + 34 q^{73} + 148 q^{74} - 104 q^{76} - 216 q^{79} + 24 q^{80} + 162 q^{81} + 156 q^{83} + 36 q^{85} - 72 q^{86} - 18 q^{89} + 52 q^{91} + 96 q^{92} + 168 q^{94} - 94 q^{97} - 82 q^{98} - 108 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 6 * q^5 + 4 * q^7 - 4 * q^8 - 18 * q^9 + 12 * q^11 + 8 * q^14 - 8 * q^16 - 18 * q^18 + 52 * q^19 + 12 * q^20 + 24 * q^22 - 26 * q^26 + 8 * q^28 - 96 * q^29 - 28 * q^31 - 8 * q^32 - 12 * q^34 - 24 * q^35 + 74 * q^37 + 24 * q^40 - 18 * q^41 + 24 * q^44 + 54 * q^45 + 48 * q^46 + 84 * q^47 + 14 * q^50 - 52 * q^52 + 60 * q^53 - 72 * q^55 - 96 * q^58 - 108 * q^59 - 36 * q^61 - 36 * q^63 + 78 * q^65 - 44 * q^67 - 24 * q^68 - 24 * q^70 + 12 * q^71 + 36 * q^72 + 34 * q^73 + 148 * q^74 - 104 * q^76 - 216 * q^79 + 24 * q^80 + 162 * q^81 + 156 * q^83 + 36 * q^85 - 72 * q^86 - 18 * q^89 + 52 * q^91 + 96 * q^92 + 168 * q^94 - 94 * q^97 - 82 * q^98 - 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$3$		0			0			−	1.00000i	$-0.5\pi$
$3$		0			0				1.00000i	$0.5\pi$
$4$		−	2.00000i		−	0.500000i
$5$	−3.00000	+	3.00000i	−0.600000	+	0.600000i	−0.940312	−	0.340312i	$-0.889467\pi$
$5$	−3.00000	+	3.00000i	−0.600000	+	0.600000i	0.340312	+	0.940312i	$0.389467\pi$
$6$		0			0
$7$	2.00000	+	2.00000i	0.285714	+	0.285714i	0.835383	−	0.549669i	$-0.185246\pi$
$7$	2.00000	+	2.00000i	0.285714	+	0.285714i	−0.549669	+	0.835383i	$0.685246\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$	−9.00000			−1.00000
$10$			6.00000i			0.600000i
$11$	6.00000	+	6.00000i	0.545455	+	0.545455i	0.925123	−	0.379668i	$-0.123962\pi$
$11$	6.00000	+	6.00000i	0.545455	+	0.545455i	−0.379668	+	0.925123i	$0.623962\pi$
$12$		0			0
$13$		−	13.0000i		−	1.00000i
$13$		−	13.0000i		−	1.00000i
$14$	4.00000			0.285714
$15$		0			0
$16$	−4.00000			−0.250000
$17$		−	6.00000i		−	0.352941i	−0.984306	−	0.176471i	$-0.943532\pi$
$17$		−	6.00000i		−	0.352941i	0.984306	−	0.176471i	$-0.0564680\pi$
$18$	−9.00000	+	9.00000i	−0.500000	+	0.500000i
$19$	26.0000	−	26.0000i	1.36842	−	1.36842i	0.505728	−	0.862693i	$-0.331224\pi$
$19$	26.0000	−	26.0000i	1.36842	−	1.36842i	0.862693	−	0.505728i	$-0.168776\pi$
$20$	6.00000	+	6.00000i	0.300000	+	0.300000i
$21$		0			0
$22$	12.0000			0.545455
$23$			24.0000i			1.04348i	0.853105	+	0.521739i	$0.174717\pi$
$23$			24.0000i			1.04348i	−0.853105	+	0.521739i	$0.825283\pi$
$24$		0			0
$25$			7.00000i			0.280000i
$26$	−13.0000	−	13.0000i	−0.500000	−	0.500000i
$27$		0			0
$28$	4.00000	−	4.00000i	0.142857	−	0.142857i
$29$	−48.0000			−1.65517			−0.827586	−	0.561339i	$-0.810287\pi$
$29$	−48.0000			−1.65517			−0.827586	+	0.561339i	$0.810287\pi$
$30$		0			0
$31$	−14.0000	+	14.0000i	−0.451613	+	0.451613i	−0.895890	−	0.444277i	$-0.853461\pi$
$31$	−14.0000	+	14.0000i	−0.451613	+	0.451613i	0.444277	+	0.895890i	$0.353461\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$		0			0
$34$	−6.00000	−	6.00000i	−0.176471	−	0.176471i
$35$	−12.0000			−0.342857
$36$			18.0000i			0.500000i
$37$	37.0000	+	37.0000i	1.00000	+	1.00000i	1.00000			$0$
$37$	37.0000	+	37.0000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$38$		−	52.0000i		−	1.36842i
$39$		0			0
$40$	12.0000			0.300000
$41$	−9.00000	+	9.00000i	−0.219512	+	0.219512i	−0.808293	−	0.588781i	$-0.799608\pi$
$41$	−9.00000	+	9.00000i	−0.219512	+	0.219512i	0.588781	+	0.808293i	$0.299608\pi$
$42$		0			0
$43$		−	36.0000i		−	0.837209i	−0.908169	−	0.418605i	$-0.862519\pi$
$43$		−	36.0000i		−	0.837209i	0.908169	−	0.418605i	$-0.137481\pi$
$44$	12.0000	−	12.0000i	0.272727	−	0.272727i
$45$	27.0000	−	27.0000i	0.600000	−	0.600000i
$46$	24.0000	+	24.0000i	0.521739	+	0.521739i
$47$	42.0000	+	42.0000i	0.893617	+	0.893617i	0.994862	−	0.101245i	$-0.0322825\pi$
$47$	42.0000	+	42.0000i	0.893617	+	0.893617i	−0.101245	+	0.994862i	$0.532282\pi$
$48$		0			0
$49$		−	41.0000i		−	0.836735i
$50$	7.00000	+	7.00000i	0.140000	+	0.140000i
$51$		0			0
$52$	−26.0000			−0.500000
$53$	30.0000			0.566038			0.283019	−	0.959114i	$-0.408664\pi$
$53$	30.0000			0.566038			0.283019	+	0.959114i	$0.408664\pi$
$54$		0			0
$55$	−36.0000			−0.654545
$56$		−	8.00000i		−	0.142857i
$57$		0			0
$58$	−48.0000	+	48.0000i	−0.827586	+	0.827586i
$59$	−54.0000	−	54.0000i	−0.915254	−	0.915254i	0.0814252	−	0.996679i	$-0.474053\pi$
$59$	−54.0000	−	54.0000i	−0.915254	−	0.915254i	−0.996679	+	0.0814252i	$0.974053\pi$
$60$		0			0
$61$	−18.0000			−0.295082			−0.147541	−	0.989056i	$-0.547136\pi$
$61$	−18.0000			−0.295082			−0.147541	+	0.989056i	$0.547136\pi$
$62$			28.0000i			0.451613i
$63$	−18.0000	−	18.0000i	−0.285714	−	0.285714i
$64$			8.00000i			0.125000i
$65$	39.0000	+	39.0000i	0.600000	+	0.600000i
$66$		0			0
$67$	−22.0000	+	22.0000i	−0.328358	+	0.328358i	−0.851962	−	0.523604i	$-0.824587\pi$
$67$	−22.0000	+	22.0000i	−0.328358	+	0.328358i	0.523604	+	0.851962i	$0.324587\pi$
$68$	−12.0000			−0.176471
$69$		0			0
$70$	−12.0000	+	12.0000i	−0.171429	+	0.171429i
$71$	6.00000	−	6.00000i	0.0845070	−	0.0845070i	−0.663590	−	0.748097i	$-0.730968\pi$
$71$	6.00000	−	6.00000i	0.0845070	−	0.0845070i	0.748097	+	0.663590i	$0.230968\pi$
$72$	18.0000	+	18.0000i	0.250000	+	0.250000i
$73$	17.0000	+	17.0000i	0.232877	+	0.232877i	0.813892	−	0.581016i	$-0.197345\pi$
$73$	17.0000	+	17.0000i	0.232877	+	0.232877i	−0.581016	+	0.813892i	$0.697345\pi$
$74$	74.0000			1.00000
$75$		0			0
$76$	−52.0000	−	52.0000i	−0.684211	−	0.684211i
$77$			24.0000i			0.311688i
$78$		0			0
$79$	−108.000			−1.36709			−0.683544	−	0.729909i	$-0.739562\pi$
$79$	−108.000			−1.36709			−0.683544	+	0.729909i	$0.739562\pi$
$80$	12.0000	−	12.0000i	0.150000	−	0.150000i
$81$	81.0000			1.00000
$82$			18.0000i			0.219512i
$83$	78.0000	−	78.0000i	0.939759	−	0.939759i	−0.0585268	−	0.998286i	$-0.518640\pi$
$83$	78.0000	−	78.0000i	0.939759	−	0.939759i	0.998286	+	0.0585268i	$0.0186403\pi$
$84$		0			0
$85$	18.0000	+	18.0000i	0.211765	+	0.211765i
$86$	−36.0000	−	36.0000i	−0.418605	−	0.418605i
$87$		0			0
$88$		−	24.0000i		−	0.272727i
$89$	−9.00000	−	9.00000i	−0.101124	−	0.101124i	0.654735	−	0.755859i	$-0.272780\pi$
$89$	−9.00000	−	9.00000i	−0.101124	−	0.101124i	−0.755859	+	0.654735i	$0.772780\pi$
$90$		−	54.0000i		−	0.600000i
$91$	26.0000	−	26.0000i	0.285714	−	0.285714i
$92$	48.0000			0.521739
$93$		0			0
$94$	84.0000			0.893617
$95$			156.000i			1.64211i
$96$		0			0
$97$	−47.0000	+	47.0000i	−0.484536	+	0.484536i	−0.906577	−	0.422041i	$-0.861314\pi$
$97$	−47.0000	+	47.0000i	−0.484536	+	0.484536i	0.422041	+	0.906577i	$0.361314\pi$
$98$	−41.0000	−	41.0000i	−0.418367	−	0.418367i
$99$	−54.0000	−	54.0000i	−0.545455	−	0.545455i
$100$	14.0000			0.140000
$101$		−	120.000i		−	1.18812i	−0.804421	−	0.594059i	$-0.797524\pi$
$101$		−	120.000i		−	1.18812i	0.804421	−	0.594059i	$-0.202476\pi$
$102$		0			0
$103$			144.000i			1.39806i	0.715093	+	0.699029i	$0.246384\pi$
$103$			144.000i			1.39806i	−0.715093	+	0.699029i	$0.753616\pi$
$104$	−26.0000	+	26.0000i	−0.250000	+	0.250000i
$105$		0			0
$106$	30.0000	−	30.0000i	0.283019	−	0.283019i
$107$	120.000			1.12150			0.560748	−	0.827987i	$-0.310514\pi$
$107$	120.000			1.12150			0.560748	+	0.827987i	$0.310514\pi$
$108$		0			0
$109$	−19.0000	+	19.0000i	−0.174312	+	0.174312i	−0.788871	−	0.614559i	$-0.789334\pi$
$109$	−19.0000	+	19.0000i	−0.174312	+	0.174312i	0.614559	+	0.788871i	$0.289334\pi$
$110$	−36.0000	+	36.0000i	−0.327273	+	0.327273i
$111$		0			0
$112$	−8.00000	−	8.00000i	−0.0714286	−	0.0714286i
$113$	−120.000			−1.06195			−0.530973	−	0.847388i	$-0.678174\pi$
$113$	−120.000			−1.06195			−0.530973	+	0.847388i	$0.678174\pi$
$114$		0			0
$115$	−72.0000	−	72.0000i	−0.626087	−	0.626087i
$116$			96.0000i			0.827586i
$117$			117.000i			1.00000i
$118$	−108.000			−0.915254
$119$	12.0000	−	12.0000i	0.100840	−	0.100840i
$120$		0			0
$121$		−	49.0000i		−	0.404959i
$122$	−18.0000	+	18.0000i	−0.147541	+	0.147541i
$123$		0			0
$124$	28.0000	+	28.0000i	0.225806	+	0.225806i
$125$	−96.0000	−	96.0000i	−0.768000	−	0.768000i
$126$	−36.0000			−0.285714
$127$		−	56.0000i		−	0.440945i	−0.975393	−	0.220472i	$-0.929240\pi$
$127$		−	56.0000i		−	0.440945i	0.975393	−	0.220472i	$-0.0707599\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$		0			0
$130$	78.0000			0.600000
$131$	72.0000			0.549618			0.274809	−	0.961499i	$-0.411385\pi$
$131$	72.0000			0.549618			0.274809	+	0.961499i	$0.411385\pi$
$132$		0			0
$133$	104.000			0.781955
$134$			44.0000i			0.328358i
$135$		0			0
$136$	−12.0000	+	12.0000i	−0.0882353	+	0.0882353i
$137$	−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	$0.855420\pi$
$138$		0			0
$139$	152.000			1.09353			0.546763	−	0.837288i	$-0.315860\pi$
$139$	152.000			1.09353			0.546763	+	0.837288i	$0.315860\pi$
$140$			24.0000i			0.171429i
$141$		0			0
$142$		−	12.0000i		−	0.0845070i
$143$	78.0000	−	78.0000i	0.545455	−	0.545455i
$144$	36.0000			0.250000
$145$	144.000	−	144.000i	0.993103	−	0.993103i
$146$	34.0000			0.232877
$147$		0			0
$148$	74.0000	−	74.0000i	0.500000	−	0.500000i
$149$	−99.0000	+	99.0000i	−0.664430	+	0.664430i	−0.956421	−	0.291991i	$-0.905682\pi$
$149$	−99.0000	+	99.0000i	−0.664430	+	0.664430i	0.291991	+	0.956421i	$0.405682\pi$
$150$		0			0
$151$	106.000	+	106.000i	0.701987	+	0.701987i	0.964837	−	0.262850i	$-0.0846624\pi$
$151$	106.000	+	106.000i	0.701987	+	0.701987i	−0.262850	+	0.964837i	$0.584662\pi$
$152$	−104.000			−0.684211
$153$			54.0000i			0.352941i
$154$	24.0000	+	24.0000i	0.155844	+	0.155844i
$155$		−	84.0000i		−	0.541935i
$156$		0			0
$157$	−80.0000			−0.509554			−0.254777	−	0.967000i	$-0.582002\pi$
$157$	−80.0000			−0.509554			−0.254777	+	0.967000i	$0.582002\pi$
$158$	−108.000	+	108.000i	−0.683544	+	0.683544i
$159$		0			0
$160$		−	24.0000i		−	0.150000i
$161$	−48.0000	+	48.0000i	−0.298137	+	0.298137i
$162$	81.0000	−	81.0000i	0.500000	−	0.500000i
$163$	82.0000	+	82.0000i	0.503067	+	0.503067i	0.912390	−	0.409322i	$-0.134235\pi$
$163$	82.0000	+	82.0000i	0.503067	+	0.503067i	−0.409322	+	0.912390i	$0.634235\pi$
$164$	18.0000	+	18.0000i	0.109756	+	0.109756i
$165$		0			0
$166$		−	156.000i		−	0.939759i
$167$	−138.000	−	138.000i	−0.826347	−	0.826347i	0.160662	−	0.987009i	$-0.448637\pi$
$167$	−138.000	−	138.000i	−0.826347	−	0.826347i	−0.987009	+	0.160662i	$0.948637\pi$
$168$		0			0
$169$	−169.000			−1.00000
$170$	36.0000			0.211765
$171$	−234.000	+	234.000i	−1.36842	+	1.36842i
$172$	−72.0000			−0.418605
$173$			24.0000i			0.138728i	0.997591	+	0.0693642i	$0.0220970\pi$
$173$			24.0000i			0.138728i	−0.997591	+	0.0693642i	$0.977903\pi$
$174$		0			0
$175$	−14.0000	+	14.0000i	−0.0800000	+	0.0800000i
$176$	−24.0000	−	24.0000i	−0.136364	−	0.136364i
$177$		0			0
$178$	−18.0000			−0.101124
$179$			300.000i			1.67598i	0.545687	+	0.837989i	$0.316269\pi$
$179$			300.000i			1.67598i	−0.545687	+	0.837989i	$0.683731\pi$
$180$	−54.0000	−	54.0000i	−0.300000	−	0.300000i
$181$		−	90.0000i		−	0.497238i	−0.968601	−	0.248619i	$-0.920023\pi$
$181$		−	90.0000i		−	0.497238i	0.968601	−	0.248619i	$-0.0799766\pi$
$182$		−	52.0000i		−	0.285714i
$183$		0			0
$184$	48.0000	−	48.0000i	0.260870	−	0.260870i
$185$	−222.000			−1.20000
$186$		0			0
$187$	36.0000	−	36.0000i	0.192513	−	0.192513i
$188$	84.0000	−	84.0000i	0.446809	−	0.446809i
$189$		0			0
$190$	156.000	+	156.000i	0.821053	+	0.821053i
$191$	252.000			1.31937			0.659686	−	0.751541i	$-0.270689\pi$
$191$	252.000			1.31937			0.659686	+	0.751541i	$0.270689\pi$
$192$		0			0
$193$	257.000	+	257.000i	1.33161	+	1.33161i	0.903934	+	0.427672i	$0.140666\pi$
$193$	257.000	+	257.000i	1.33161	+	1.33161i	0.427672	+	0.903934i	$0.359334\pi$
$194$			94.0000i			0.484536i
$195$		0			0
$196$	−82.0000			−0.418367
$197$	123.000	−	123.000i	0.624365	−	0.624365i	−0.322279	−	0.946645i	$-0.604449\pi$
$197$	123.000	−	123.000i	0.624365	−	0.624365i	0.946645	+	0.322279i	$0.104449\pi$
$198$	−108.000			−0.545455
$199$		−	200.000i		−	1.00503i	−0.864570	−	0.502513i	$-0.832409\pi$
$199$		−	200.000i		−	1.00503i	0.864570	−	0.502513i	$-0.167591\pi$
$200$	14.0000	−	14.0000i	0.0700000	−	0.0700000i
$201$		0			0
$202$	−120.000	−	120.000i	−0.594059	−	0.594059i
$203$	−96.0000	−	96.0000i	−0.472906	−	0.472906i
$204$		0			0
$205$		−	54.0000i		−	0.263415i
$206$	144.000	+	144.000i	0.699029	+	0.699029i
$207$		−	216.000i		−	1.04348i
$208$			52.0000i			0.250000i
$209$	312.000			1.49282
$210$		0			0
$211$	−288.000			−1.36493			−0.682464	−	0.730919i	$-0.739092\pi$
$211$	−288.000			−1.36493			−0.682464	+	0.730919i	$0.739092\pi$
$212$		−	60.0000i		−	0.283019i
$213$		0			0
$214$	120.000	−	120.000i	0.560748	−	0.560748i
$215$	108.000	+	108.000i	0.502326	+	0.502326i
$216$		0			0
$217$	−56.0000			−0.258065
$218$			38.0000i			0.174312i
$219$		0			0
$220$			72.0000i			0.327273i
$221$	−78.0000			−0.352941
$222$		0			0
$223$	38.0000	−	38.0000i	0.170404	−	0.170404i	−0.616753	−	0.787157i	$-0.711552\pi$
$223$	38.0000	−	38.0000i	0.170404	−	0.170404i	0.787157	+	0.616753i	$0.211552\pi$
$224$	−16.0000			−0.0714286
$225$		−	63.0000i		−	0.280000i
$226$	−120.000	+	120.000i	−0.530973	+	0.530973i
$227$	138.000	−	138.000i	0.607930	−	0.607930i	−0.334475	−	0.942405i	$-0.608559\pi$
$227$	138.000	−	138.000i	0.607930	−	0.607930i	0.942405	+	0.334475i	$0.108559\pi$
$228$		0			0
$229$	131.000	+	131.000i	0.572052	+	0.572052i	0.932702	−	0.360649i	$-0.117445\pi$
$229$	131.000	+	131.000i	0.572052	+	0.572052i	−0.360649	+	0.932702i	$0.617445\pi$
$230$	−144.000			−0.626087
$231$		0			0
$232$	96.0000	+	96.0000i	0.413793	+	0.413793i
$233$		−	336.000i		−	1.44206i	−0.692904	−	0.721030i	$-0.743669\pi$
$233$		−	336.000i		−	1.44206i	0.692904	−	0.721030i	$-0.256331\pi$
$234$	117.000	+	117.000i	0.500000	+	0.500000i
$235$	−252.000			−1.07234
$236$	−108.000	+	108.000i	−0.457627	+	0.457627i
$237$		0			0
$238$		−	24.0000i		−	0.100840i
$239$	−114.000	+	114.000i	−0.476987	+	0.476987i	−0.904167	−	0.427179i	$-0.859507\pi$
$239$	−114.000	+	114.000i	−0.476987	+	0.476987i	0.427179	+	0.904167i	$0.359507\pi$
$240$		0			0
$241$	151.000	+	151.000i	0.626556	+	0.626556i	0.947200	−	0.320644i	$-0.103899\pi$
$241$	151.000	+	151.000i	0.626556	+	0.626556i	−0.320644	+	0.947200i	$0.603899\pi$
$242$	−49.0000	−	49.0000i	−0.202479	−	0.202479i
$243$		0			0
$244$			36.0000i			0.147541i
$245$	123.000	+	123.000i	0.502041	+	0.502041i
$246$		0			0
$247$	−338.000	−	338.000i	−1.36842	−	1.36842i
$248$	56.0000			0.225806
$249$		0			0
$250$	−192.000			−0.768000
$251$			180.000i			0.717131i	0.933504	+	0.358566i	$0.116734\pi$
$251$			180.000i			0.717131i	−0.933504	+	0.358566i	$0.883266\pi$
$252$	−36.0000	+	36.0000i	−0.142857	+	0.142857i
$253$	−144.000	+	144.000i	−0.569170	+	0.569170i
$254$	−56.0000	−	56.0000i	−0.220472	−	0.220472i
$255$		0			0
$256$	16.0000			0.0625000
$257$			144.000i			0.560311i	0.959955	+	0.280156i	$0.0903861\pi$
$257$			144.000i			0.560311i	−0.959955	+	0.280156i	$0.909614\pi$
$258$		0			0
$259$			148.000i			0.571429i
$260$	78.0000	−	78.0000i	0.300000	−	0.300000i
$261$	432.000			1.65517
$262$	72.0000	−	72.0000i	0.274809	−	0.274809i
$263$	−60.0000			−0.228137			−0.114068	−	0.993473i	$-0.536388\pi$
$263$	−60.0000			−0.228137			−0.114068	+	0.993473i	$0.536388\pi$
$264$		0			0
$265$	−90.0000	+	90.0000i	−0.339623	+	0.339623i
$266$	104.000	−	104.000i	0.390977	−	0.390977i
$267$		0			0
$268$	44.0000	+	44.0000i	0.164179	+	0.164179i
$269$	−288.000			−1.07063			−0.535316	−	0.844652i	$-0.679807\pi$
$269$	−288.000			−1.07063			−0.535316	+	0.844652i	$0.679807\pi$
$270$		0			0
$271$	−134.000	−	134.000i	−0.494465	−	0.494465i	0.415245	−	0.909710i	$-0.363696\pi$
$271$	−134.000	−	134.000i	−0.494465	−	0.494465i	−0.909710	+	0.415245i	$0.863696\pi$
$272$			24.0000i			0.0882353i
$273$		0			0
$274$	−126.000			−0.459854
$275$	−42.0000	+	42.0000i	−0.152727	+	0.152727i
$276$		0			0
$277$		−	216.000i		−	0.779783i	−0.920861	−	0.389892i	$-0.872512\pi$
$277$		−	216.000i		−	0.779783i	0.920861	−	0.389892i	$-0.127488\pi$
$278$	152.000	−	152.000i	0.546763	−	0.546763i
$279$	126.000	−	126.000i	0.451613	−	0.451613i
$280$	24.0000	+	24.0000i	0.0857143	+	0.0857143i
$281$	−159.000	−	159.000i	−0.565836	−	0.565836i	0.365123	−	0.930959i	$-0.381027\pi$
$281$	−159.000	−	159.000i	−0.565836	−	0.565836i	−0.930959	+	0.365123i	$0.881027\pi$
$282$		0			0
$283$			404.000i			1.42756i	0.700369	+	0.713781i	$0.253019\pi$
$283$			404.000i			1.42756i	−0.700369	+	0.713781i	$0.746981\pi$
$284$	−12.0000	−	12.0000i	−0.0422535	−	0.0422535i
$285$		0			0
$286$		−	156.000i		−	0.545455i
$287$	−36.0000			−0.125436
$288$	36.0000	−	36.0000i	0.125000	−	0.125000i
$289$	253.000			0.875433
$290$		−	288.000i		−	0.993103i
$291$		0			0
$292$	34.0000	−	34.0000i	0.116438	−	0.116438i
$293$	147.000	+	147.000i	0.501706	+	0.501706i	0.911968	−	0.410261i	$-0.134563\pi$
$293$	147.000	+	147.000i	0.501706	+	0.501706i	−0.410261	+	0.911968i	$0.634563\pi$
$294$		0			0
$295$	324.000			1.09831
$296$		−	148.000i		−	0.500000i
$297$		0			0
$298$			198.000i			0.664430i
$299$	312.000			1.04348
$300$		0			0
$301$	72.0000	−	72.0000i	0.239203	−	0.239203i
$302$	212.000			0.701987
$303$		0			0
$304$	−104.000	+	104.000i	−0.342105	+	0.342105i
$305$	54.0000	−	54.0000i	0.177049	−	0.177049i
$306$	54.0000	+	54.0000i	0.176471	+	0.176471i
$307$	82.0000	+	82.0000i	0.267101	+	0.267101i	0.827931	−	0.560830i	$-0.189518\pi$
$307$	82.0000	+	82.0000i	0.267101	+	0.267101i	−0.560830	+	0.827931i	$0.689518\pi$
$308$	48.0000			0.155844
$309$		0			0
$310$	−84.0000	−	84.0000i	−0.270968	−	0.270968i
$311$			120.000i			0.385852i	0.981213	+	0.192926i	$0.0617977\pi$
$311$			120.000i			0.385852i	−0.981213	+	0.192926i	$0.938202\pi$
$312$		0			0
$313$	−360.000			−1.15016			−0.575080	−	0.818097i	$-0.695029\pi$
$313$	−360.000			−1.15016			−0.575080	+	0.818097i	$0.695029\pi$
$314$	−80.0000	+	80.0000i	−0.254777	+	0.254777i
$315$	108.000			0.342857
$316$			216.000i			0.683544i
$317$	−147.000	+	147.000i	−0.463722	+	0.463722i	−0.899873	−	0.436151i	$-0.856341\pi$
$317$	−147.000	+	147.000i	−0.463722	+	0.463722i	0.436151	+	0.899873i	$0.356341\pi$
$318$		0			0
$319$	−288.000	−	288.000i	−0.902821	−	0.902821i
$320$	−24.0000	−	24.0000i	−0.0750000	−	0.0750000i
$321$		0			0
$322$			96.0000i			0.298137i
$323$	−156.000	−	156.000i	−0.482972	−	0.482972i
$324$		−	162.000i		−	0.500000i
$325$	91.0000			0.280000
$326$	164.000			0.503067
$327$		0			0
$328$	36.0000			0.109756
$329$			168.000i			0.510638i
$330$		0			0
$331$	−214.000	+	214.000i	−0.646526	+	0.646526i	−0.952152	−	0.305626i	$-0.901134\pi$
$331$	−214.000	+	214.000i	−0.646526	+	0.646526i	0.305626	+	0.952152i	$0.401134\pi$
$332$	−156.000	−	156.000i	−0.469880	−	0.469880i
$333$	−333.000	−	333.000i	−1.00000	−	1.00000i
$334$	−276.000			−0.826347
$335$		−	132.000i		−	0.394030i
$336$		0			0
$337$			314.000i			0.931751i	0.884850	+	0.465875i	$0.154260\pi$
$337$			314.000i			0.931751i	−0.884850	+	0.465875i	$0.845740\pi$
$338$	−169.000	+	169.000i	−0.500000	+	0.500000i
$339$		0			0
$340$	36.0000	−	36.0000i	0.105882	−	0.105882i
$341$	−168.000			−0.492669
$342$			468.000i			1.36842i
$343$	180.000	−	180.000i	0.524781	−	0.524781i
$344$	−72.0000	+	72.0000i	−0.209302	+	0.209302i
$345$		0			0
$346$	24.0000	+	24.0000i	0.0693642	+	0.0693642i
$347$	−120.000			−0.345821			−0.172911	−	0.984938i	$-0.555317\pi$
$347$	−120.000			−0.345821			−0.172911	+	0.984938i	$0.555317\pi$
$348$		0			0
$349$	101.000	+	101.000i	0.289398	+	0.289398i	0.836842	−	0.547444i	$-0.184399\pi$
$349$	101.000	+	101.000i	0.289398	+	0.289398i	−0.547444	+	0.836842i	$0.684399\pi$
$350$			28.0000i			0.0800000i
$351$		0			0
$352$	−48.0000			−0.136364
$353$	33.0000	−	33.0000i	0.0934844	−	0.0934844i	−0.658818	−	0.752302i	$-0.728943\pi$
$353$	33.0000	−	33.0000i	0.0934844	−	0.0934844i	0.752302	+	0.658818i	$0.228943\pi$
$354$		0			0
$355$			36.0000i			0.101408i
$356$	−18.0000	+	18.0000i	−0.0505618	+	0.0505618i
$357$		0			0
$358$	300.000	+	300.000i	0.837989	+	0.837989i
$359$	186.000	+	186.000i	0.518106	+	0.518106i	0.916998	−	0.398892i	$-0.130605\pi$
$359$	186.000	+	186.000i	0.518106	+	0.518106i	−0.398892	+	0.916998i	$0.630605\pi$
$360$	−108.000			−0.300000
$361$		−	991.000i		−	2.74515i
$362$	−90.0000	−	90.0000i	−0.248619	−	0.248619i
$363$		0			0
$364$	−52.0000	−	52.0000i	−0.142857	−	0.142857i
$365$	−102.000			−0.279452
$366$		0			0
$367$	580.000			1.58038			0.790191	−	0.612861i	$-0.209981\pi$
$367$	580.000			1.58038			0.790191	+	0.612861i	$0.209981\pi$
$368$		−	96.0000i		−	0.260870i
$369$	81.0000	−	81.0000i	0.219512	−	0.219512i
$370$	−222.000	+	222.000i	−0.600000	+	0.600000i
$371$	60.0000	+	60.0000i	0.161725	+	0.161725i
$372$		0			0
$373$		0			0			−	1.00000i	$-0.5\pi$
$373$		0			0				1.00000i	$0.5\pi$
$374$		−	72.0000i		−	0.192513i
$375$		0			0
$376$		−	168.000i		−	0.446809i
$377$			624.000i			1.65517i
$378$		0			0
$379$	226.000	−	226.000i	0.596306	−	0.596306i	−0.343021	−	0.939328i	$-0.611450\pi$
$379$	226.000	−	226.000i	0.596306	−	0.596306i	0.939328	+	0.343021i	$0.111450\pi$
$380$	312.000			0.821053
$381$		0			0
$382$	252.000	−	252.000i	0.659686	−	0.659686i
$383$	78.0000	−	78.0000i	0.203655	−	0.203655i	−0.597909	−	0.801564i	$-0.704002\pi$
$383$	78.0000	−	78.0000i	0.203655	−	0.203655i	0.801564	+	0.597909i	$0.204002\pi$
$384$		0			0
$385$	−72.0000	−	72.0000i	−0.187013	−	0.187013i
$386$	514.000			1.33161
$387$			324.000i			0.837209i
$388$	94.0000	+	94.0000i	0.242268	+	0.242268i
$389$		−	150.000i		−	0.385604i	−0.981238	−	0.192802i	$-0.938242\pi$
$389$		−	150.000i		−	0.385604i	0.981238	−	0.192802i	$-0.0617575\pi$
$390$		0			0
$391$	144.000			0.368286
$392$	−82.0000	+	82.0000i	−0.209184	+	0.209184i
$393$		0			0
$394$		−	246.000i		−	0.624365i
$395$	324.000	−	324.000i	0.820253	−	0.820253i
$396$	−108.000	+	108.000i	−0.272727	+	0.272727i
$397$	−253.000	−	253.000i	−0.637280	−	0.637280i	0.312604	−	0.949884i	$-0.398799\pi$
$397$	−253.000	−	253.000i	−0.637280	−	0.637280i	−0.949884	+	0.312604i	$0.898799\pi$
$398$	−200.000	−	200.000i	−0.502513	−	0.502513i
$399$		0			0
$400$		−	28.0000i		−	0.0700000i
$401$	−249.000	−	249.000i	−0.620948	−	0.620948i	0.324826	−	0.945774i	$-0.394694\pi$
$401$	−249.000	−	249.000i	−0.620948	−	0.620948i	−0.945774	+	0.324826i	$0.894694\pi$
$402$		0			0
$403$	182.000	+	182.000i	0.451613	+	0.451613i
$404$	−240.000			−0.594059
$405$	−243.000	+	243.000i	−0.600000	+	0.600000i
$406$	−192.000			−0.472906
$407$			444.000i			1.09091i
$408$		0			0
$409$	−319.000	+	319.000i	−0.779951	+	0.779951i	−0.979822	−	0.199871i	$-0.935948\pi$
$409$	−319.000	+	319.000i	−0.779951	+	0.779951i	0.199871	+	0.979822i	$0.435948\pi$
$410$	−54.0000	−	54.0000i	−0.131707	−	0.131707i
$411$		0			0
$412$	288.000			0.699029
$413$		−	216.000i		−	0.523002i
$414$	−216.000	−	216.000i	−0.521739	−	0.521739i
$415$			468.000i			1.12771i
$416$	52.0000	+	52.0000i	0.125000	+	0.125000i
$417$		0			0
$418$	312.000	−	312.000i	0.746411	−	0.746411i
$419$	−48.0000			−0.114558			−0.0572792	−	0.998358i	$-0.518243\pi$
$419$	−48.0000			−0.114558			−0.0572792	+	0.998358i	$0.518243\pi$
$420$		0			0
$421$	11.0000	−	11.0000i	0.0261283	−	0.0261283i	−0.693922	−	0.720050i	$-0.744119\pi$
$421$	11.0000	−	11.0000i	0.0261283	−	0.0261283i	0.720050	+	0.693922i	$0.244119\pi$
$422$	−288.000	+	288.000i	−0.682464	+	0.682464i
$423$	−378.000	−	378.000i	−0.893617	−	0.893617i
$424$	−60.0000	−	60.0000i	−0.141509	−	0.141509i
$425$	42.0000			0.0988235
$426$		0			0
$427$	−36.0000	−	36.0000i	−0.0843091	−	0.0843091i
$428$		−	240.000i		−	0.560748i
$429$		0			0
$430$	216.000			0.502326
$431$	−414.000	+	414.000i	−0.960557	+	0.960557i	−0.999251	−	0.0386943i	$-0.987680\pi$
$431$	−414.000	+	414.000i	−0.960557	+	0.960557i	0.0386943	+	0.999251i	$0.487680\pi$
$432$		0			0
$433$		−	16.0000i		−	0.0369515i	−0.999829	−	0.0184758i	$-0.994119\pi$
$433$		−	16.0000i		−	0.0369515i	0.999829	−	0.0184758i	$-0.00588135\pi$
$434$	−56.0000	+	56.0000i	−0.129032	+	0.129032i
$435$		0			0
$436$	38.0000	+	38.0000i	0.0871560	+	0.0871560i
$437$	624.000	+	624.000i	1.42792	+	1.42792i
$438$		0			0
$439$		−	360.000i		−	0.820046i	−0.912075	−	0.410023i	$-0.865521\pi$
$439$		−	360.000i		−	0.820046i	0.912075	−	0.410023i	$-0.134479\pi$
$440$	72.0000	+	72.0000i	0.163636	+	0.163636i
$441$			369.000i			0.836735i
$442$	−78.0000	+	78.0000i	−0.176471	+	0.176471i
$443$	−600.000			−1.35440			−0.677201	−	0.735798i	$-0.736807\pi$
$443$	−600.000			−1.35440			−0.677201	+	0.735798i	$0.736807\pi$
$444$		0			0
$445$	54.0000			0.121348
$446$		−	76.0000i		−	0.170404i
$447$		0			0
$448$	−16.0000	+	16.0000i	−0.0357143	+	0.0357143i
$449$	−9.00000	−	9.00000i	−0.0200445	−	0.0200445i	0.697013	−	0.717058i	$-0.254512\pi$
$449$	−9.00000	−	9.00000i	−0.0200445	−	0.0200445i	−0.717058	+	0.697013i	$0.754512\pi$
$450$	−63.0000	−	63.0000i	−0.140000	−	0.140000i
$451$	−108.000			−0.239468
$452$			240.000i			0.530973i
$453$		0			0
$454$		−	276.000i		−	0.607930i
$455$			156.000i			0.342857i
$456$		0			0
$457$	−47.0000	+	47.0000i	−0.102845	+	0.102845i	−0.756657	−	0.653812i	$-0.773169\pi$
$457$	−47.0000	+	47.0000i	−0.102845	+	0.102845i	0.653812	+	0.756657i	$0.273169\pi$
$458$	262.000			0.572052
$459$		0			0
$460$	−144.000	+	144.000i	−0.313043	+	0.313043i
$461$	171.000	−	171.000i	0.370933	−	0.370933i	−0.496884	−	0.867817i	$-0.665523\pi$
$461$	171.000	−	171.000i	0.370933	−	0.370933i	0.867817	+	0.496884i	$0.165523\pi$
$462$		0			0
$463$	202.000	+	202.000i	0.436285	+	0.436285i	0.890760	−	0.454475i	$-0.150173\pi$
$463$	202.000	+	202.000i	0.436285	+	0.436285i	−0.454475	+	0.890760i	$0.650173\pi$
$464$	192.000			0.413793
$465$		0			0
$466$	−336.000	−	336.000i	−0.721030	−	0.721030i
$467$		−	516.000i		−	1.10493i	−0.833538	−	0.552463i	$-0.813688\pi$
$467$		−	516.000i		−	1.10493i	0.833538	−	0.552463i	$-0.186312\pi$
$468$	234.000			0.500000
$469$	−88.0000			−0.187633
$470$	−252.000	+	252.000i	−0.536170	+	0.536170i
$471$		0			0
$472$			216.000i			0.457627i
$473$	216.000	−	216.000i	0.456660	−	0.456660i
$474$		0			0
$475$	182.000	+	182.000i	0.383158	+	0.383158i
$476$	−24.0000	−	24.0000i	−0.0504202	−	0.0504202i
$477$	−270.000			−0.566038
$478$			228.000i			0.476987i
$479$	−234.000	−	234.000i	−0.488518	−	0.488518i	0.419321	−	0.907838i	$-0.362268\pi$
$479$	−234.000	−	234.000i	−0.488518	−	0.488518i	−0.907838	+	0.419321i	$0.862268\pi$
$480$		0			0
$481$	481.000	−	481.000i	1.00000	−	1.00000i
$482$	302.000			0.626556
$483$		0			0
$484$	−98.0000			−0.202479
$485$		−	282.000i		−	0.581443i
$486$		0			0
$487$	298.000	−	298.000i	0.611910	−	0.611910i	−0.331534	−	0.943443i	$-0.607566\pi$
$487$	298.000	−	298.000i	0.611910	−	0.611910i	0.943443	+	0.331534i	$0.107566\pi$
$488$	36.0000	+	36.0000i	0.0737705	+	0.0737705i
$489$		0			0
$490$	246.000			0.502041
$491$		−	420.000i		−	0.855397i	−0.903921	−	0.427699i	$-0.859324\pi$
$491$		−	420.000i		−	0.855397i	0.903921	−	0.427699i	$-0.140676\pi$
$492$		0			0
$493$			288.000i			0.584178i
$494$	−676.000			−1.36842
$495$	324.000			0.654545
$496$	56.0000	−	56.0000i	0.112903	−	0.112903i
$497$	24.0000			0.0482897
$498$		0			0
$499$	346.000	−	346.000i	0.693387	−	0.693387i	−0.269589	−	0.962976i	$-0.586888\pi$
$499$	346.000	−	346.000i	0.693387	−	0.693387i	0.962976	+	0.269589i	$0.0868878\pi$
$500$	−192.000	+	192.000i	−0.384000	+	0.384000i
$501$		0			0
$502$	180.000	+	180.000i	0.358566	+	0.358566i
$503$	−420.000			−0.834990			−0.417495	−	0.908679i	$-0.637092\pi$
$503$	−420.000			−0.834990			−0.417495	+	0.908679i	$0.637092\pi$
$504$			72.0000i			0.142857i
$505$	360.000	+	360.000i	0.712871	+	0.712871i
$506$			288.000i			0.569170i
$507$		0			0
$508$	−112.000			−0.220472
$509$	381.000	−	381.000i	0.748527	−	0.748527i	−0.225676	−	0.974202i	$-0.572459\pi$
$509$	381.000	−	381.000i	0.748527	−	0.748527i	0.974202	+	0.225676i	$0.0724590\pi$
$510$		0			0
$511$			68.0000i			0.133072i
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$		0			0
$514$	144.000	+	144.000i	0.280156	+	0.280156i
$515$	−432.000	−	432.000i	−0.838835	−	0.838835i
$516$		0			0
$517$			504.000i			0.974855i
$518$	148.000	+	148.000i	0.285714	+	0.285714i
$519$		0			0
$520$		−	156.000i		−	0.300000i
$521$	312.000			0.598848			0.299424	−	0.954120i	$-0.403205\pi$
$521$	312.000			0.598848			0.299424	+	0.954120i	$0.403205\pi$
$522$	432.000	−	432.000i	0.827586	−	0.827586i
$523$	−560.000			−1.07075			−0.535373	−	0.844616i	$-0.679829\pi$
$523$	−560.000			−1.07075			−0.535373	+	0.844616i	$0.679829\pi$
$524$		−	144.000i		−	0.274809i
$525$		0			0
$526$	−60.0000	+	60.0000i	−0.114068	+	0.114068i
$527$	84.0000	+	84.0000i	0.159393	+	0.159393i
$528$		0			0
$529$	−47.0000			−0.0888469
$530$			180.000i			0.339623i
$531$	486.000	+	486.000i	0.915254	+	0.915254i
$532$		−	208.000i		−	0.390977i
$533$	117.000	+	117.000i	0.219512	+	0.219512i
$534$		0			0
$535$	−360.000	+	360.000i	−0.672897	+	0.672897i
$536$	88.0000			0.164179
$537$		0			0
$538$	−288.000	+	288.000i	−0.535316	+	0.535316i
$539$	246.000	−	246.000i	0.456401	−	0.456401i
$540$		0			0
$541$	−379.000	−	379.000i	−0.700555	−	0.700555i	0.263975	−	0.964530i	$-0.414966\pi$
$541$	−379.000	−	379.000i	−0.700555	−	0.700555i	−0.964530	+	0.263975i	$0.914966\pi$
$542$	−268.000			−0.494465
$543$		0			0
$544$	24.0000	+	24.0000i	0.0441176	+	0.0441176i
$545$		−	114.000i		−	0.209174i
$546$		0			0
$547$	−400.000			−0.731261			−0.365631	−	0.930760i	$-0.619147\pi$
$547$	−400.000			−0.731261			−0.365631	+	0.930760i	$0.619147\pi$
$548$	−126.000	+	126.000i	−0.229927	+	0.229927i
$549$	162.000			0.295082
$550$			84.0000i			0.152727i
$551$	−1248.00	+	1248.00i	−2.26497	+	2.26497i
$552$		0			0
$553$	−216.000	−	216.000i	−0.390597	−	0.390597i
$554$	−216.000	−	216.000i	−0.389892	−	0.389892i
$555$		0			0
$556$		−	304.000i		−	0.546763i
$557$	117.000	+	117.000i	0.210054	+	0.210054i	0.804290	−	0.594236i	$-0.202546\pi$
$557$	117.000	+	117.000i	0.210054	+	0.210054i	−0.594236	+	0.804290i	$0.702546\pi$
$558$		−	252.000i		−	0.451613i
$559$	−468.000			−0.837209
$560$	48.0000			0.0857143
$561$		0			0
$562$	−318.000			−0.565836
$563$		−	876.000i		−	1.55595i	−0.628295	−	0.777975i	$-0.716247\pi$
$563$		−	876.000i		−	1.55595i	0.628295	−	0.777975i	$-0.283753\pi$
$564$		0			0
$565$	360.000	−	360.000i	0.637168	−	0.637168i
$566$	404.000	+	404.000i	0.713781	+	0.713781i
$567$	162.000	+	162.000i	0.285714	+	0.285714i
$568$	−24.0000			−0.0422535
$569$			720.000i			1.26538i	0.774406	+	0.632689i	$0.218049\pi$
$569$			720.000i			1.26538i	−0.774406	+	0.632689i	$0.781951\pi$
$570$		0			0
$571$			460.000i			0.805604i	0.915287	+	0.402802i	$0.131964\pi$
$571$			460.000i			0.805604i	−0.915287	+	0.402802i	$0.868036\pi$
$572$	−156.000	−	156.000i	−0.272727	−	0.272727i
$573$		0			0
$574$	−36.0000	+	36.0000i	−0.0627178	+	0.0627178i
$575$	−168.000			−0.292174
$576$		−	72.0000i		−	0.125000i
$577$	−377.000	+	377.000i	−0.653380	+	0.653380i	−0.953805	−	0.300426i	$-0.902871\pi$
$577$	−377.000	+	377.000i	−0.653380	+	0.653380i	0.300426	+	0.953805i	$0.402871\pi$
$578$	253.000	−	253.000i	0.437716	−	0.437716i
$579$		0			0
$580$	−288.000	−	288.000i	−0.496552	−	0.496552i
$581$	312.000			0.537005
$582$		0			0
$583$	180.000	+	180.000i	0.308748	+	0.308748i
$584$		−	68.0000i		−	0.116438i
$585$	−351.000	−	351.000i	−0.600000	−	0.600000i
$586$	294.000			0.501706
$587$	738.000	−	738.000i	1.25724	−	1.25724i	0.304835	−	0.952405i	$-0.401399\pi$
$587$	738.000	−	738.000i	1.25724	−	1.25724i	0.952405	−	0.304835i	$-0.0986013\pi$
$588$		0			0
$589$			728.000i			1.23599i
$590$	324.000	−	324.000i	0.549153	−	0.549153i
$591$		0			0
$592$	−148.000	−	148.000i	−0.250000	−	0.250000i
$593$	327.000	+	327.000i	0.551433	+	0.551433i	0.926854	−	0.375421i	$-0.122502\pi$
$593$	327.000	+	327.000i	0.551433	+	0.551433i	−0.375421	+	0.926854i	$0.622502\pi$
$594$		0			0
$595$			72.0000i			0.121008i
$596$	198.000	+	198.000i	0.332215	+	0.332215i
$597$		0			0
$598$	312.000	−	312.000i	0.521739	−	0.521739i
$599$	372.000			0.621035			0.310518	−	0.950568i	$-0.399498\pi$
$599$	372.000			0.621035			0.310518	+	0.950568i	$0.399498\pi$
$600$		0			0
$601$	−648.000			−1.07820			−0.539101	−	0.842241i	$-0.681236\pi$
$601$	−648.000			−1.07820			−0.539101	+	0.842241i	$0.681236\pi$
$602$		−	144.000i		−	0.239203i
$603$	198.000	−	198.000i	0.328358	−	0.328358i
$604$	212.000	−	212.000i	0.350993	−	0.350993i
$605$	147.000	+	147.000i	0.242975	+	0.242975i
$606$		0			0
$607$	−260.000			−0.428336			−0.214168	−	0.976797i	$-0.568704\pi$
$607$	−260.000			−0.428336			−0.214168	+	0.976797i	$0.568704\pi$
$608$			208.000i			0.342105i
$609$		0			0
$610$		−	108.000i		−	0.177049i
$611$	546.000	−	546.000i	0.893617	−	0.893617i
$612$	108.000			0.176471
$613$	−197.000	+	197.000i	−0.321370	+	0.321370i	−0.849293	−	0.527922i	$-0.822971\pi$
$613$	−197.000	+	197.000i	−0.321370	+	0.321370i	0.527922	+	0.849293i	$0.322971\pi$
$614$	164.000			0.267101
$615$		0			0
$616$	48.0000	−	48.0000i	0.0779221	−	0.0779221i
$617$	753.000	−	753.000i	1.22042	−	1.22042i	0.252939	−	0.967482i	$-0.418603\pi$
$617$	753.000	−	753.000i	1.22042	−	1.22042i	0.967482	−	0.252939i	$-0.0813973\pi$
$618$		0			0
$619$	−34.0000	−	34.0000i	−0.0549273	−	0.0549273i	0.679110	−	0.734037i	$-0.262366\pi$
$619$	−34.0000	−	34.0000i	−0.0549273	−	0.0549273i	−0.734037	+	0.679110i	$0.762366\pi$
$620$	−168.000			−0.270968
$621$		0			0
$622$	120.000	+	120.000i	0.192926	+	0.192926i
$623$		−	36.0000i		−	0.0577849i
$624$		0			0
$625$	401.000			0.641600
$626$	−360.000	+	360.000i	−0.575080	+	0.575080i
$627$		0			0
$628$			160.000i			0.254777i
$629$	222.000	−	222.000i	0.352941	−	0.352941i
$630$	108.000	−	108.000i	0.171429	−	0.171429i
$631$	386.000	+	386.000i	0.611727	+	0.611727i	0.943396	−	0.331669i	$-0.107612\pi$
$631$	386.000	+	386.000i	0.611727	+	0.611727i	−0.331669	+	0.943396i	$0.607612\pi$
$632$	216.000	+	216.000i	0.341772	+	0.341772i
$633$		0			0
$634$			294.000i			0.463722i
$635$	168.000	+	168.000i	0.264567	+	0.264567i
$636$		0			0
$637$	−533.000			−0.836735
$638$	−576.000			−0.902821
$639$	−54.0000	+	54.0000i	−0.0845070	+	0.0845070i
$640$	−48.0000			−0.0750000
$641$		−	90.0000i		−	0.140406i	−0.997533	−	0.0702028i	$-0.977635\pi$
$641$		−	90.0000i		−	0.140406i	0.997533	−	0.0702028i	$-0.0223646\pi$
$642$		0			0
$643$	−202.000	+	202.000i	−0.314152	+	0.314152i	−0.846516	−	0.532363i	$-0.821304\pi$
$643$	−202.000	+	202.000i	−0.314152	+	0.314152i	0.532363	+	0.846516i	$0.321304\pi$
$644$	96.0000	+	96.0000i	0.149068	+	0.149068i
$645$		0			0
$646$	−312.000			−0.482972
$647$			144.000i			0.222566i	0.993789	+	0.111283i	$0.0354960\pi$
$647$			144.000i			0.222566i	−0.993789	+	0.111283i	$0.964504\pi$
$648$	−162.000	−	162.000i	−0.250000	−	0.250000i
$649$		−	648.000i		−	0.998459i
$650$	91.0000	−	91.0000i	0.140000	−	0.140000i
$651$		0			0
$652$	164.000	−	164.000i	0.251534	−	0.251534i
$653$	−240.000			−0.367534			−0.183767	−	0.982970i	$-0.558829\pi$
$653$	−240.000			−0.367534			−0.183767	+	0.982970i	$0.558829\pi$
$654$		0			0
$655$	−216.000	+	216.000i	−0.329771	+	0.329771i
$656$	36.0000	−	36.0000i	0.0548780	−	0.0548780i
$657$	−153.000	−	153.000i	−0.232877	−	0.232877i
$658$	168.000	+	168.000i	0.255319	+	0.255319i
$659$	−168.000			−0.254932			−0.127466	−	0.991843i	$-0.540684\pi$
$659$	−168.000			−0.254932			−0.127466	+	0.991843i	$0.540684\pi$
$660$		0			0
$661$	−509.000	−	509.000i	−0.770045	−	0.770045i	0.208069	−	0.978114i	$-0.433282\pi$
$661$	−509.000	−	509.000i	−0.770045	−	0.770045i	−0.978114	+	0.208069i	$0.933282\pi$
$662$			428.000i			0.646526i
$663$		0			0
$664$	−312.000			−0.469880
$665$	−312.000	+	312.000i	−0.469173	+	0.469173i
$666$	−666.000			−1.00000
$667$		−	1152.00i		−	1.72714i
$668$	−276.000	+	276.000i	−0.413174	+	0.413174i
$669$		0			0
$670$	−132.000	−	132.000i	−0.197015	−	0.197015i
$671$	−108.000	−	108.000i	−0.160954	−	0.160954i
$672$		0			0
$673$			954.000i			1.41753i	0.705443	+	0.708767i	$0.250748\pi$
$673$			954.000i			1.41753i	−0.705443	+	0.708767i	$0.749252\pi$
$674$	314.000	+	314.000i	0.465875	+	0.465875i
$675$		0			0
$676$			338.000i			0.500000i
$677$	−930.000			−1.37371			−0.686854	−	0.726796i	$-0.741009\pi$
$677$	−930.000			−1.37371			−0.686854	+	0.726796i	$0.741009\pi$
$678$		0			0
$679$	−188.000			−0.276878
$680$		−	72.0000i		−	0.105882i
$681$		0			0
$682$	−168.000	+	168.000i	−0.246334	+	0.246334i
$683$	342.000	+	342.000i	0.500732	+	0.500732i	0.911665	−	0.410933i	$-0.134797\pi$
$683$	342.000	+	342.000i	0.500732	+	0.500732i	−0.410933	+	0.911665i	$0.634797\pi$
$684$	468.000	+	468.000i	0.684211	+	0.684211i
$685$	378.000			0.551825
$686$		−	360.000i		−	0.524781i
$687$		0			0
$688$			144.000i			0.209302i
$689$		−	390.000i		−	0.566038i
$690$		0			0
$691$	−254.000	+	254.000i	−0.367583	+	0.367583i	−0.866595	−	0.499012i	$-0.833696\pi$
$691$	−254.000	+	254.000i	−0.367583	+	0.367583i	0.499012	+	0.866595i	$0.333696\pi$
$692$	48.0000			0.0693642
$693$		−	216.000i		−	0.311688i
$694$	−120.000	+	120.000i	−0.172911	+	0.172911i
$695$	−456.000	+	456.000i	−0.656115	+	0.656115i
$696$		0			0
$697$	54.0000	+	54.0000i	0.0774749	+	0.0774749i
$698$	202.000			0.289398
$699$		0			0
$700$	28.0000	+	28.0000i	0.0400000	+	0.0400000i
$701$		−	150.000i		−	0.213980i	−0.994260	−	0.106990i	$-0.965879\pi$
$701$		−	150.000i		−	0.213980i	0.994260	−	0.106990i	$-0.0341213\pi$
$702$		0			0
$703$	1924.00			2.73684
$704$	−48.0000	+	48.0000i	−0.0681818	+	0.0681818i
$705$		0			0
$706$		−	66.0000i		−	0.0934844i
$707$	240.000	−	240.000i	0.339463	−	0.339463i
$708$		0			0
$709$	−299.000	−	299.000i	−0.421721	−	0.421721i	0.464075	−	0.885796i	$-0.346387\pi$
$709$	−299.000	−	299.000i	−0.421721	−	0.421721i	−0.885796	+	0.464075i	$0.846387\pi$
$710$	36.0000	+	36.0000i	0.0507042	+	0.0507042i
$711$	972.000			1.36709
$712$			36.0000i			0.0505618i
$713$	−336.000	−	336.000i	−0.471248	−	0.471248i
$714$		0			0
$715$			468.000i			0.654545i
$716$	600.000			0.837989
$717$		0			0
$718$	372.000			0.518106
$719$			1200.00i			1.66898i	0.551020	+	0.834492i	$0.314239\pi$
$719$			1200.00i			1.66898i	−0.551020	+	0.834492i	$0.685761\pi$
$720$	−108.000	+	108.000i	−0.150000	+	0.150000i
$721$	−288.000	+	288.000i	−0.399445	+	0.399445i
$722$	−991.000	−	991.000i	−1.37258	−	1.37258i
$723$		0			0
$724$	−180.000			−0.248619
$725$		−	336.000i		−	0.463448i
$726$		0			0
$727$		−	1336.00i		−	1.83769i	−0.394620	−	0.918845i	$-0.629124\pi$
$727$		−	1336.00i		−	1.83769i	0.394620	−	0.918845i	$-0.370876\pi$
$728$	−104.000			−0.142857
$729$	−729.000			−1.00000
$730$	−102.000	+	102.000i	−0.139726	+	0.139726i
$731$	−216.000			−0.295486
$732$		0			0
$733$	283.000	−	283.000i	0.386085	−	0.386085i	−0.487204	−	0.873288i	$-0.661983\pi$
$733$	283.000	−	283.000i	0.386085	−	0.386085i	0.873288	+	0.487204i	$0.161983\pi$
$734$	580.000	−	580.000i	0.790191	−	0.790191i
$735$		0			0
$736$	−96.0000	−	96.0000i	−0.130435	−	0.130435i
$737$	−264.000			−0.358209
$738$		−	162.000i		−	0.219512i
$739$	926.000	+	926.000i	1.25304	+	1.25304i	0.954348	+	0.298696i	$0.0965518\pi$
$739$	926.000	+	926.000i	1.25304	+	1.25304i	0.298696	+	0.954348i	$0.403448\pi$
$740$			444.000i			0.600000i
$741$		0			0
$742$	120.000			0.161725
$743$	798.000	−	798.000i	1.07402	−	1.07402i	0.0769926	−	0.997032i	$-0.475468\pi$
$743$	798.000	−	798.000i	1.07402	−	1.07402i	0.997032	−	0.0769926i	$-0.0245318\pi$
$744$		0			0
$745$		−	594.000i		−	0.797315i
$746$		0			0
$747$	−702.000	+	702.000i	−0.939759	+	0.939759i
$748$	−72.0000	−	72.0000i	−0.0962567	−	0.0962567i
$749$	240.000	+	240.000i	0.320427	+	0.320427i
$750$		0			0
$751$		−	1080.00i		−	1.43808i	−0.694967	−	0.719041i	$-0.744581\pi$
$751$		−	1080.00i		−	1.43808i	0.694967	−	0.719041i	$-0.255419\pi$
$752$	−168.000	−	168.000i	−0.223404	−	0.223404i
$753$		0			0
$754$	624.000	+	624.000i	0.827586	+	0.827586i
$755$	−636.000			−0.842384
$756$		0			0
$757$	990.000			1.30779			0.653897	−	0.756584i	$-0.273133\pi$
$757$	990.000			1.30779			0.653897	+	0.756584i	$0.273133\pi$
$758$		−	452.000i		−	0.596306i
$759$		0			0
$760$	312.000	−	312.000i	0.410526	−	0.410526i
$761$	801.000	+	801.000i	1.05256	+	1.05256i	0.998540	+	0.0540227i	$0.0172043\pi$
$761$	801.000	+	801.000i	1.05256	+	1.05256i	0.0540227	+	0.998540i	$0.482796\pi$
$762$		0			0
$763$	−76.0000			−0.0996068
$764$		−	504.000i		−	0.659686i
$765$	−162.000	−	162.000i	−0.211765	−	0.211765i
$766$		−	156.000i		−	0.203655i
$767$	−702.000	+	702.000i	−0.915254	+	0.915254i
$768$		0			0
$769$	−329.000	+	329.000i	−0.427828	+	0.427828i	−0.887888	−	0.460060i	$-0.847828\pi$
$769$	−329.000	+	329.000i	−0.427828	+	0.427828i	0.460060	+	0.887888i	$0.347828\pi$
$770$	−144.000			−0.187013
$771$		0			0
$772$	514.000	−	514.000i	0.665803	−	0.665803i
$773$	−867.000	+	867.000i	−1.12160	+	1.12160i	−0.130104	+	0.991500i	$0.541531\pi$
$773$	−867.000	+	867.000i	−1.12160	+	1.12160i	−0.991500	+	0.130104i	$0.958469\pi$
$774$	324.000	+	324.000i	0.418605	+	0.418605i
$775$	−98.0000	−	98.0000i	−0.126452	−	0.126452i
$776$	188.000			0.242268
$777$		0			0
$778$	−150.000	−	150.000i	−0.192802	−	0.192802i
$779$			468.000i			0.600770i
$780$		0			0
$781$	72.0000			0.0921895
$782$	144.000	−	144.000i	0.184143	−	0.184143i
$783$		0			0
$784$			164.000i			0.209184i
$785$	240.000	−	240.000i	0.305732	−	0.305732i
$786$		0			0
$787$	−158.000	−	158.000i	−0.200762	−	0.200762i	0.599564	−	0.800327i	$-0.295341\pi$
$787$	−158.000	−	158.000i	−0.200762	−	0.200762i	−0.800327	+	0.599564i	$0.795341\pi$
$788$	−246.000	−	246.000i	−0.312183	−	0.312183i
$789$		0			0
$790$		−	648.000i		−	0.820253i
$791$	−240.000	−	240.000i	−0.303413	−	0.303413i
$792$			216.000i			0.272727i
$793$			234.000i			0.295082i
$794$	−506.000			−0.637280
$795$		0			0
$796$	−400.000			−0.502513
$797$			954.000i			1.19699i	0.801127	+	0.598494i	$0.204234\pi$
$797$			954.000i			1.19699i	−0.801127	+	0.598494i	$0.795766\pi$
$798$		0			0
$799$	252.000	−	252.000i	0.315394	−	0.315394i
$800$	−28.0000	−	28.0000i	−0.0350000	−	0.0350000i
$801$	81.0000	+	81.0000i	0.101124	+	0.101124i
$802$	−498.000			−0.620948
$803$			204.000i			0.254047i
$804$		0			0
$805$		−	288.000i		−	0.357764i
$806$	364.000			0.451613
$807$		0			0
$808$	−240.000	+	240.000i	−0.297030	+	0.297030i
$809$	312.000			0.385661			0.192831	−	0.981232i	$-0.438233\pi$
$809$	312.000			0.385661			0.192831	+	0.981232i	$0.438233\pi$
$810$			486.000i			0.600000i
$811$	566.000	−	566.000i	0.697904	−	0.697904i	−0.266054	−	0.963958i	$-0.585720\pi$
$811$	566.000	−	566.000i	0.697904	−	0.697904i	0.963958	+	0.266054i	$0.0857200\pi$
$812$	−192.000	+	192.000i	−0.236453	+	0.236453i
$813$		0			0
$814$	444.000	+	444.000i	0.545455	+	0.545455i
$815$	−492.000			−0.603681
$816$		0			0
$817$	−936.000	−	936.000i	−1.14565	−	1.14565i
$818$			638.000i			0.779951i
$819$	−234.000	+	234.000i	−0.285714	+	0.285714i
$820$	−108.000			−0.131707
$821$	−339.000	+	339.000i	−0.412911	+	0.412911i	−0.882751	−	0.469840i	$-0.844311\pi$
$821$	−339.000	+	339.000i	−0.412911	+	0.412911i	0.469840	+	0.882751i	$0.344311\pi$
$822$		0			0
$823$			1224.00i			1.48724i	0.668601	+	0.743621i	$0.266893\pi$
$823$			1224.00i			1.48724i	−0.668601	+	0.743621i	$0.733107\pi$
$824$	288.000	−	288.000i	0.349515	−	0.349515i
$825$		0			0
$826$	−216.000	−	216.000i	−0.261501	−	0.261501i
$827$	−678.000	−	678.000i	−0.819831	−	0.819831i	0.166253	−	0.986083i	$-0.446833\pi$
$827$	−678.000	−	678.000i	−0.819831	−	0.819831i	−0.986083	+	0.166253i	$0.946833\pi$
$828$	−432.000			−0.521739
$829$			920.000i			1.10977i	0.831927	+	0.554885i	$0.187238\pi$
$829$			920.000i			1.10977i	−0.831927	+	0.554885i	$0.812762\pi$
$830$	468.000	+	468.000i	0.563855	+	0.563855i
$831$		0			0
$832$	104.000			0.125000
$833$	−246.000			−0.295318
$834$		0			0
$835$	828.000			0.991617
$836$		−	624.000i		−	0.746411i
$837$		0			0
$838$	−48.0000	+	48.0000i	−0.0572792	+	0.0572792i
$839$	−774.000	−	774.000i	−0.922527	−	0.922527i	0.0746807	−	0.997207i	$-0.476206\pi$
$839$	−774.000	−	774.000i	−0.922527	−	0.922527i	−0.997207	+	0.0746807i	$0.976206\pi$
$840$		0			0
$841$	1463.00			1.73960
$842$		−	22.0000i		−	0.0261283i
$843$		0			0
$844$			576.000i			0.682464i
$845$	507.000	−	507.000i	0.600000	−	0.600000i
$846$	−756.000			−0.893617
$847$	98.0000	−	98.0000i	0.115702	−	0.115702i
$848$	−120.000			−0.141509
$849$		0			0
$850$	42.0000	−	42.0000i	0.0494118	−	0.0494118i
$851$	−888.000	+	888.000i	−1.04348	+	1.04348i
$852$		0			0
$853$	−443.000	−	443.000i	−0.519343	−	0.519343i	0.398029	−	0.917373i	$-0.369694\pi$
$853$	−443.000	−	443.000i	−0.519343	−	0.519343i	−0.917373	+	0.398029i	$0.869694\pi$
$854$	−72.0000			−0.0843091
$855$		−	1404.00i		−	1.64211i
$856$	−240.000	−	240.000i	−0.280374	−	0.280374i
$857$			384.000i			0.448075i	0.974581	+	0.224037i	$0.0719238\pi$
$857$			384.000i			0.448075i	−0.974581	+	0.224037i	$0.928076\pi$
$858$		0			0
$859$	72.0000			0.0838184			0.0419092	−	0.999121i	$-0.486656\pi$
$859$	72.0000			0.0838184			0.0419092	+	0.999121i	$0.486656\pi$
$860$	216.000	−	216.000i	0.251163	−	0.251163i
$861$		0			0
$862$			828.000i			0.960557i
$863$	−702.000	+	702.000i	−0.813441	+	0.813441i	−0.985148	−	0.171707i	$-0.945072\pi$
$863$	−702.000	+	702.000i	−0.813441	+	0.813441i	0.171707	+	0.985148i	$0.445072\pi$
$864$		0			0
$865$	−72.0000	−	72.0000i	−0.0832370	−	0.0832370i
$866$	−16.0000	−	16.0000i	−0.0184758	−	0.0184758i
$867$		0			0
$868$			112.000i			0.129032i
$869$	−648.000	−	648.000i	−0.745685	−	0.745685i
$870$		0			0
$871$	286.000	+	286.000i	0.328358	+	0.328358i
$872$	76.0000			0.0871560
$873$	423.000	−	423.000i	0.484536	−	0.484536i
$874$	1248.00			1.42792
$875$		−	384.000i		−	0.438857i
$876$		0			0
$877$	733.000	−	733.000i	0.835804	−	0.835804i	−0.152500	−	0.988304i	$-0.548732\pi$
$877$	733.000	−	733.000i	0.835804	−	0.835804i	0.988304	+	0.152500i	$0.0487323\pi$
$878$	−360.000	−	360.000i	−0.410023	−	0.410023i
$879$		0			0
$880$	144.000			0.163636
$881$		−	960.000i		−	1.08967i	−0.838543	−	0.544835i	$-0.816592\pi$
$881$		−	960.000i		−	1.08967i	0.838543	−	0.544835i	$-0.183408\pi$
$882$	369.000	+	369.000i	0.418367	+	0.418367i
$883$		−	236.000i		−	0.267271i	−0.991031	−	0.133635i	$-0.957335\pi$
$883$		−	236.000i		−	0.267271i	0.991031	−	0.133635i	$-0.0426651\pi$
$884$			156.000i			0.176471i
$885$		0			0
$886$	−600.000	+	600.000i	−0.677201	+	0.677201i
$887$	1380.00			1.55581			0.777903	−	0.628384i	$-0.216283\pi$
$887$	1380.00			1.55581			0.777903	+	0.628384i	$0.216283\pi$
$888$		0			0
$889$	112.000	−	112.000i	0.125984	−	0.125984i
$890$	54.0000	−	54.0000i	0.0606742	−	0.0606742i
$891$	486.000	+	486.000i	0.545455	+	0.545455i
$892$	−76.0000	−	76.0000i	−0.0852018	−	0.0852018i
$893$	2184.00			2.44569
$894$		0			0
$895$	−900.000	−	900.000i	−1.00559	−	1.00559i
$896$			32.0000i			0.0357143i
$897$		0			0
$898$	−18.0000			−0.0200445
$899$	672.000	−	672.000i	0.747497	−	0.747497i
$900$	−126.000			−0.140000
$901$		−	180.000i		−	0.199778i
$902$	−108.000	+	108.000i	−0.119734	+	0.119734i
$903$		0			0
$904$	240.000	+	240.000i	0.265487	+	0.265487i
$905$	270.000	+	270.000i	0.298343	+	0.298343i
$906$		0			0
$907$			1444.00i			1.59206i	0.605256	+	0.796031i	$0.293071\pi$
$907$			1444.00i			1.59206i	−0.605256	+	0.796031i	$0.706929\pi$
$908$	−276.000	−	276.000i	−0.303965	−	0.303965i
$909$			1080.00i			1.18812i
$910$	156.000	+	156.000i	0.171429	+	0.171429i
$911$	612.000			0.671789			0.335895	−	0.941900i	$-0.390961\pi$
$911$	612.000			0.671789			0.335895	+	0.941900i	$0.390961\pi$
$912$		0			0
$913$	936.000			1.02519
$914$			94.0000i			0.102845i
$915$		0			0
$916$	262.000	−	262.000i	0.286026	−	0.286026i
$917$	144.000	+	144.000i	0.157034	+	0.157034i
$918$		0			0
$919$	−1548.00			−1.68444			−0.842220	−	0.539134i	$-0.818752\pi$
$919$	−1548.00			−1.68444			−0.842220	+	0.539134i	$0.818752\pi$
$920$			288.000i			0.313043i
$921$		0			0
$922$		−	342.000i		−	0.370933i
$923$	−78.0000	−	78.0000i	−0.0845070	−	0.0845070i
$924$		0			0
$925$	−259.000	+	259.000i	−0.280000	+	0.280000i
$926$	404.000			0.436285
$927$		−	1296.00i		−	1.39806i
$928$	192.000	−	192.000i	0.206897	−	0.206897i
$929$	−969.000	+	969.000i	−1.04306	+	1.04306i	−0.0440267	+	0.999030i	$0.514019\pi$
$929$	−969.000	+	969.000i	−1.04306	+	1.04306i	−0.999030	+	0.0440267i	$0.985981\pi$
$930$		0			0
$931$	−1066.00	−	1066.00i	−1.14501	−	1.14501i
$932$	−672.000			−0.721030
$933$		0			0
$934$	−516.000	−	516.000i	−0.552463	−	0.552463i
$935$			216.000i			0.231016i
$936$	234.000	−	234.000i	0.250000	−	0.250000i
$937$	−450.000			−0.480256			−0.240128	−	0.970741i	$-0.577189\pi$
$937$	−450.000			−0.480256			−0.240128	+	0.970741i	$0.577189\pi$
$938$	−88.0000	+	88.0000i	−0.0938166	+	0.0938166i
$939$		0			0
$940$			504.000i			0.536170i
$941$	411.000	−	411.000i	0.436769	−	0.436769i	−0.454154	−	0.890923i	$-0.650058\pi$
$941$	411.000	−	411.000i	0.436769	−	0.436769i	0.890923	+	0.454154i	$0.150058\pi$
$942$		0			0
$943$	−216.000	−	216.000i	−0.229056	−	0.229056i
$944$	216.000	+	216.000i	0.228814	+	0.228814i
$945$		0			0
$946$		−	432.000i		−	0.456660i
$947$	582.000	+	582.000i	0.614572	+	0.614572i	0.944134	−	0.329562i	$-0.106901\pi$
$947$	582.000	+	582.000i	0.614572	+	0.614572i	−0.329562	+	0.944134i	$0.606901\pi$
$948$		0			0
$949$	221.000	−	221.000i	0.232877	−	0.232877i
$950$	364.000			0.383158
$951$		0			0
$952$	−48.0000			−0.0504202
$953$			1344.00i			1.41028i	0.709066	+	0.705142i	$0.249117\pi$
$953$			1344.00i			1.41028i	−0.709066	+	0.705142i	$0.750883\pi$
$954$	−270.000	+	270.000i	−0.283019	+	0.283019i
$955$	−756.000	+	756.000i	−0.791623	+	0.791623i
$956$	228.000	+	228.000i	0.238494	+	0.238494i
$957$		0			0
$958$	−468.000			−0.488518
$959$		−	252.000i		−	0.262774i
$960$		0			0
$961$			569.000i			0.592092i
$962$		−	962.000i		−	1.00000i
$963$	−1080.00			−1.12150
$964$	302.000	−	302.000i	0.313278	−	0.313278i
$965$	−1542.00			−1.59793
$966$		0			0
$967$	−562.000	+	562.000i	−0.581179	+	0.581179i	−0.935227	−	0.354048i	$-0.884805\pi$
$967$	−562.000	+	562.000i	−0.581179	+	0.581179i	0.354048	+	0.935227i	$0.384805\pi$
$968$	−98.0000	+	98.0000i	−0.101240	+	0.101240i
$969$		0			0
$970$	−282.000	−	282.000i	−0.290722	−	0.290722i
$971$	−1248.00			−1.28527			−0.642636	−	0.766171i	$-0.722159\pi$
$971$	−1248.00			−1.28527			−0.642636	+	0.766171i	$0.722159\pi$
$972$		0			0
$973$	304.000	+	304.000i	0.312436	+	0.312436i
$974$		−	596.000i		−	0.611910i
$975$		0			0
$976$	72.0000			0.0737705
$977$	33.0000	−	33.0000i	0.0337769	−	0.0337769i	−0.690017	−	0.723794i	$-0.742397\pi$
$977$	33.0000	−	33.0000i	0.0337769	−	0.0337769i	0.723794	+	0.690017i	$0.242397\pi$
$978$		0			0
$979$		−	108.000i		−	0.110317i
$980$	246.000	−	246.000i	0.251020	−	0.251020i
$981$	171.000	−	171.000i	0.174312	−	0.174312i
$982$	−420.000	−	420.000i	−0.427699	−	0.427699i
$983$	702.000	+	702.000i	0.714140	+	0.714140i	0.967399	−	0.253258i	$-0.0815023\pi$
$983$	702.000	+	702.000i	0.714140	+	0.714140i	−0.253258	+	0.967399i	$0.581502\pi$
$984$		0			0
$985$			738.000i			0.749239i
$986$	288.000	+	288.000i	0.292089	+	0.292089i
$987$		0			0
$988$	−676.000	+	676.000i	−0.684211	+	0.684211i
$989$	864.000			0.873610
$990$	324.000	−	324.000i	0.327273	−	0.327273i
$991$	−268.000			−0.270434			−0.135217	−	0.990816i	$-0.543173\pi$
$991$	−268.000			−0.270434			−0.135217	+	0.990816i	$0.543173\pi$
$992$		−	112.000i		−	0.112903i
$993$		0			0
$994$	24.0000	−	24.0000i	0.0241449	−	0.0241449i
$995$	600.000	+	600.000i	0.603015	+	0.603015i
$996$		0			0
$997$	−1310.00			−1.31394			−0.656971	−	0.753916i	$-0.728163\pi$
$997$	−1310.00			−1.31394			−0.656971	+	0.753916i	$0.728163\pi$
$998$		−	692.000i		−	0.693387i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.3.d.a.5.1	✓	2
3.2	odd	2		234.3.i.a.109.1		2
4.3	odd	2		208.3.t.b.161.1		2
5.2	odd	4		650.3.f.e.499.1		2
5.3	odd	4		650.3.f.b.499.1		2
5.4	even	2		650.3.k.b.551.1		2
13.2	odd	12		338.3.f.g.319.1		4
13.3	even	3		338.3.f.b.19.1		4
13.4	even	6		338.3.f.g.249.1		4
13.5	odd	4		338.3.d.a.99.1		2
13.6	odd	12		338.3.f.g.89.1		4
13.7	odd	12		338.3.f.b.89.1		4
13.8	odd	4	inner	26.3.d.a.21.1	yes	2
13.9	even	3		338.3.f.b.249.1		4
13.10	even	6		338.3.f.g.19.1		4
13.11	odd	12		338.3.f.b.319.1		4
13.12	even	2		338.3.d.a.239.1		2
39.8	even	4		234.3.i.a.73.1		2
52.47	even	4		208.3.t.b.177.1		2
65.8	even	4		650.3.f.e.99.1		2
65.34	odd	4		650.3.k.b.151.1		2
65.47	even	4		650.3.f.b.99.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.3.d.a.5.1	✓	2	1.1	even	1	trivial
26.3.d.a.21.1	yes	2	13.8	odd	4	inner
208.3.t.b.161.1		2	4.3	odd	2
208.3.t.b.177.1		2	52.47	even	4
234.3.i.a.73.1		2	39.8	even	4
234.3.i.a.109.1		2	3.2	odd	2
338.3.d.a.99.1		2	13.5	odd	4
338.3.d.a.239.1		2	13.12	even	2
338.3.f.b.19.1		4	13.3	even	3
338.3.f.b.89.1		4	13.7	odd	12
338.3.f.b.249.1		4	13.9	even	3
338.3.f.b.319.1		4	13.11	odd	12
338.3.f.g.19.1		4	13.10	even	6
338.3.f.g.89.1		4	13.6	odd	12
338.3.f.g.249.1		4	13.4	even	6
338.3.f.g.319.1		4	13.2	odd	12
650.3.f.b.99.1		2	65.47	even	4
650.3.f.b.499.1		2	5.3	odd	4
650.3.f.e.99.1		2	65.8	even	4
650.3.f.e.499.1		2	5.2	odd	4
650.3.k.b.151.1		2	65.34	odd	4
650.3.k.b.551.1		2	5.4	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:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	26.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(-3.00000 + 3.00000i) q^{5} +(2.00000 + 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(-3.00000 + 3.00000i) q^{5} +(2.00000 + 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} -9.00000 q^{9} +6.00000i q^{10} +(6.00000 + 6.00000i) q^{11} -13.0000i q^{13} +4.00000 q^{14} -4.00000 q^{16} -6.00000i q^{17} +(-9.00000 + 9.00000i) q^{18} +(26.0000 - 26.0000i) q^{19} +(6.00000 + 6.00000i) q^{20} +12.0000 q^{22} +24.0000i q^{23} +7.00000i q^{25} +(-13.0000 - 13.0000i) q^{26} +(4.00000 - 4.00000i) q^{28} -48.0000 q^{29} +(-14.0000 + 14.0000i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-6.00000 - 6.00000i) q^{34} -12.0000 q^{35} +18.0000i q^{36} +(37.0000 + 37.0000i) q^{37} -52.0000i q^{38} +12.0000 q^{40} +(-9.00000 + 9.00000i) q^{41} -36.0000i q^{43} +(12.0000 - 12.0000i) q^{44} +(27.0000 - 27.0000i) q^{45} +(24.0000 + 24.0000i) q^{46} +(42.0000 + 42.0000i) q^{47} -41.0000i q^{49} +(7.00000 + 7.00000i) q^{50} -26.0000 q^{52} +30.0000 q^{53} -36.0000 q^{55} -8.00000i q^{56} +(-48.0000 + 48.0000i) q^{58} +(-54.0000 - 54.0000i) q^{59} -18.0000 q^{61} +28.0000i q^{62} +(-18.0000 - 18.0000i) q^{63} +8.00000i q^{64} +(39.0000 + 39.0000i) q^{65} +(-22.0000 + 22.0000i) q^{67} -12.0000 q^{68} +(-12.0000 + 12.0000i) q^{70} +(6.00000 - 6.00000i) q^{71} +(18.0000 + 18.0000i) q^{72} +(17.0000 + 17.0000i) q^{73} +74.0000 q^{74} +(-52.0000 - 52.0000i) q^{76} +24.0000i q^{77} -108.000 q^{79} +(12.0000 - 12.0000i) q^{80} +81.0000 q^{81} +18.0000i q^{82} +(78.0000 - 78.0000i) q^{83} +(18.0000 + 18.0000i) q^{85} +(-36.0000 - 36.0000i) q^{86} -24.0000i q^{88} +(-9.00000 - 9.00000i) q^{89} -54.0000i q^{90} +(26.0000 - 26.0000i) q^{91} +48.0000 q^{92} +84.0000 q^{94} +156.000i q^{95} +(-47.0000 + 47.0000i) q^{97} +(-41.0000 - 41.0000i) q^{98} +(-54.0000 - 54.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 6 q^{5} + 4 q^{7} - 4 q^{8} - 18 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 6 * q^5 + 4 * q^7 - 4 * q^8 - 18 * q^9	\( 2 q + 2 q^{2} - 6 q^{5} + 4 q^{7} - 4 q^{8} - 18 q^{9} + 12 q^{11} + 8 q^{14} - 8 q^{16} - 18 q^{18} + 52 q^{19} + 12 q^{20} + 24 q^{22} - 26 q^{26} + 8 q^{28} - 96 q^{29} - 28 q^{31} - 8 q^{32} - 12 q^{34} - 24 q^{35} + 74 q^{37} + 24 q^{40} - 18 q^{41} + 24 q^{44} + 54 q^{45} + 48 q^{46} + 84 q^{47} + 14 q^{50} - 52 q^{52} + 60 q^{53} - 72 q^{55} - 96 q^{58} - 108 q^{59} - 36 q^{61} - 36 q^{63} + 78 q^{65} - 44 q^{67} - 24 q^{68} - 24 q^{70} + 12 q^{71} + 36 q^{72} + 34 q^{73} + 148 q^{74} - 104 q^{76} - 216 q^{79} + 24 q^{80} + 162 q^{81} + 156 q^{83} + 36 q^{85} - 72 q^{86} - 18 q^{89} + 52 q^{91} + 96 q^{92} + 168 q^{94} - 94 q^{97} - 82 q^{98} - 108 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 6 * q^5 + 4 * q^7 - 4 * q^8 - 18 * q^9 + 12 * q^11 + 8 * q^14 - 8 * q^16 - 18 * q^18 + 52 * q^19 + 12 * q^20 + 24 * q^22 - 26 * q^26 + 8 * q^28 - 96 * q^29 - 28 * q^31 - 8 * q^32 - 12 * q^34 - 24 * q^35 + 74 * q^37 + 24 * q^40 - 18 * q^41 + 24 * q^44 + 54 * q^45 + 48 * q^46 + 84 * q^47 + 14 * q^50 - 52 * q^52 + 60 * q^53 - 72 * q^55 - 96 * q^58 - 108 * q^59 - 36 * q^61 - 36 * q^63 + 78 * q^65 - 44 * q^67 - 24 * q^68 - 24 * q^70 + 12 * q^71 + 36 * q^72 + 34 * q^73 + 148 * q^74 - 104 * q^76 - 216 * q^79 + 24 * q^80 + 162 * q^81 + 156 * q^83 + 36 * q^85 - 72 * q^86 - 18 * q^89 + 52 * q^91 + 96 * q^92 + 168 * q^94 - 94 * q^97 - 82 * q^98 - 108 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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