LMFDB - Embedded newform 403.2.f.a.373.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(94,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("403.94");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.f (of order $3$, 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:	$3.21797120146$
Analytic rank:	$1$
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:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	403.373
Dual form			403.2.f.a.94.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(-1.00000 - 1.73205i) q^{7} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(-1.00000 - 1.73205i) q^{7} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(1.50000 - 2.59808i) q^{10} +(-2.50000 - 2.59808i) q^{13} +2.00000 q^{14} +(0.500000 - 0.866025i) q^{16} +(-2.50000 - 4.33013i) q^{17} -3.00000 q^{18} +(-2.00000 - 3.46410i) q^{19} +(-1.50000 - 2.59808i) q^{20} +(-2.00000 + 3.46410i) q^{23} +4.00000 q^{25} +(3.50000 - 0.866025i) q^{26} +(1.00000 - 1.73205i) q^{28} +(-1.50000 + 2.59808i) q^{29} -1.00000 q^{31} +(-2.50000 - 4.33013i) q^{32} +5.00000 q^{34} +(3.00000 + 5.19615i) q^{35} +(-1.50000 + 2.59808i) q^{36} +(2.50000 - 4.33013i) q^{37} +4.00000 q^{38} +9.00000 q^{40} +(-3.50000 + 6.06218i) q^{41} +(1.00000 + 1.73205i) q^{43} +(-4.50000 - 7.79423i) q^{45} +(-2.00000 - 3.46410i) q^{46} -6.00000 q^{47} +(1.50000 - 2.59808i) q^{49} +(-2.00000 + 3.46410i) q^{50} +(1.00000 - 3.46410i) q^{52} -9.00000 q^{53} +(3.00000 + 5.19615i) q^{56} +(-1.50000 - 2.59808i) q^{58} +(3.00000 + 5.19615i) q^{59} +(0.500000 + 0.866025i) q^{61} +(0.500000 - 0.866025i) q^{62} +(3.00000 - 5.19615i) q^{63} +7.00000 q^{64} +(7.50000 + 7.79423i) q^{65} +(-5.00000 + 8.66025i) q^{67} +(2.50000 - 4.33013i) q^{68} -6.00000 q^{70} +(2.00000 + 3.46410i) q^{71} +(-4.50000 - 7.79423i) q^{72} -3.00000 q^{73} +(2.50000 + 4.33013i) q^{74} +(2.00000 - 3.46410i) q^{76} +2.00000 q^{79} +(-1.50000 + 2.59808i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-3.50000 - 6.06218i) q^{82} -2.00000 q^{83} +(7.50000 + 12.9904i) q^{85} -2.00000 q^{86} +(3.00000 - 5.19615i) q^{89} +9.00000 q^{90} +(-2.00000 + 6.92820i) q^{91} -4.00000 q^{92} +(3.00000 - 5.19615i) q^{94} +(6.00000 + 10.3923i) q^{95} +(9.00000 + 15.5885i) q^{97} +(1.50000 + 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{4} - 6 q^{5} - 2 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - q^2 + q^4 - 6 * q^5 - 2 * q^7 - 6 * q^8 + 3 * q^9	$ 2 q - q^{2} + q^{4} - 6 q^{5} - 2 q^{7} - 6 q^{8} + 3 q^{9} + 3 q^{10} - 5 q^{13} + 4 q^{14} + q^{16} - 5 q^{17} - 6 q^{18} - 4 q^{19} - 3 q^{20} - 4 q^{23} + 8 q^{25} + 7 q^{26} + 2 q^{28} - 3 q^{29} - 2 q^{31} - 5 q^{32} + 10 q^{34} + 6 q^{35} - 3 q^{36} + 5 q^{37} + 8 q^{38} + 18 q^{40} - 7 q^{41} + 2 q^{43} - 9 q^{45} - 4 q^{46} - 12 q^{47} + 3 q^{49} - 4 q^{50} + 2 q^{52} - 18 q^{53} + 6 q^{56} - 3 q^{58} + 6 q^{59} + q^{61} + q^{62} + 6 q^{63} + 14 q^{64} + 15 q^{65} - 10 q^{67} + 5 q^{68} - 12 q^{70} + 4 q^{71} - 9 q^{72} - 6 q^{73} + 5 q^{74} + 4 q^{76} + 4 q^{79} - 3 q^{80} - 9 q^{81} - 7 q^{82} - 4 q^{83} + 15 q^{85} - 4 q^{86} + 6 q^{89} + 18 q^{90} - 4 q^{91} - 8 q^{92} + 6 q^{94} + 12 q^{95} + 18 q^{97} + 3 q^{98}+O(q^{100}) $ 2 * q - q^2 + q^4 - 6 * q^5 - 2 * q^7 - 6 * q^8 + 3 * q^9 + 3 * q^10 - 5 * q^13 + 4 * q^14 + q^16 - 5 * q^17 - 6 * q^18 - 4 * q^19 - 3 * q^20 - 4 * q^23 + 8 * q^25 + 7 * q^26 + 2 * q^28 - 3 * q^29 - 2 * q^31 - 5 * q^32 + 10 * q^34 + 6 * q^35 - 3 * q^36 + 5 * q^37 + 8 * q^38 + 18 * q^40 - 7 * q^41 + 2 * q^43 - 9 * q^45 - 4 * q^46 - 12 * q^47 + 3 * q^49 - 4 * q^50 + 2 * q^52 - 18 * q^53 + 6 * q^56 - 3 * q^58 + 6 * q^59 + q^61 + q^62 + 6 * q^63 + 14 * q^64 + 15 * q^65 - 10 * q^67 + 5 * q^68 - 12 * q^70 + 4 * q^71 - 9 * q^72 - 6 * q^73 + 5 * q^74 + 4 * q^76 + 4 * q^79 - 3 * q^80 - 9 * q^81 - 7 * q^82 - 4 * q^83 + 15 * q^85 - 4 * q^86 + 6 * q^89 + 18 * q^90 - 4 * q^91 - 8 * q^92 + 6 * q^94 + 12 * q^95 + 18 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i	−0.986869	−	0.161521i	$-0.948360\pi$
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i	0.633316	+	0.773893i	$0.281693\pi$
$3$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$3$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−3.00000			−1.34164			−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000			−1.34164			−0.670820	+	0.741620i	$0.734058\pi$
$6$		0			0
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	0.612801	−	0.790237i	$-0.290043\pi$
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	−0.990766	+	0.135583i	$0.956709\pi$
$8$	−3.00000			−1.06066
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	1.50000	−	2.59808i	0.474342	−	0.821584i
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$		0			0
$13$	−2.50000	−	2.59808i	−0.693375	−	0.720577i
$13$	−2.50000	−	2.59808i	−0.693375	−	0.720577i
$14$	2.00000			0.534522
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−2.50000	−	4.33013i	−0.606339	−	1.05021i	−0.991838	−	0.127502i	$-0.959304\pi$
$17$	−2.50000	−	4.33013i	−0.606339	−	1.05021i	0.385499	−	0.922708i	$-0.374029\pi$
$18$	−3.00000			−0.707107
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	0.540068	−	0.841621i	$-0.318398\pi$
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	−0.998899	+	0.0469020i	$0.985065\pi$
$20$	−1.50000	−	2.59808i	−0.335410	−	0.580948i
$21$		0			0
$22$		0			0
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$	3.50000	−	0.866025i	0.686406	−	0.169842i
$27$		0			0
$28$	1.00000	−	1.73205i	0.188982	−	0.327327i
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$		0			0
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	−2.50000	−	4.33013i	−0.441942	−	0.765466i
$33$		0			0
$34$	5.00000			0.857493
$35$	3.00000	+	5.19615i	0.507093	+	0.878310i
$36$	−1.50000	+	2.59808i	−0.250000	+	0.433013i
$37$	2.50000	−	4.33013i	0.410997	−	0.711868i	−0.584002	−	0.811752i	$-0.698514\pi$
$37$	2.50000	−	4.33013i	0.410997	−	0.711868i	0.994999	+	0.0998840i	$0.0318472\pi$
$38$	4.00000			0.648886
$39$		0			0
$40$	9.00000			1.42302
$41$	−3.50000	+	6.06218i	−0.546608	+	0.946753i	0.451896	+	0.892071i	$0.350748\pi$
$41$	−3.50000	+	6.06218i	−0.546608	+	0.946753i	−0.998504	+	0.0546823i	$0.982585\pi$
$42$		0			0
$43$	1.00000	+	1.73205i	0.152499	+	0.264135i	0.932145	−	0.362084i	$-0.117935\pi$
$43$	1.00000	+	1.73205i	0.152499	+	0.264135i	−0.779647	+	0.626219i	$0.784601\pi$
$44$		0			0
$45$	−4.50000	−	7.79423i	−0.670820	−	1.16190i
$46$	−2.00000	−	3.46410i	−0.294884	−	0.510754i
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$		0			0
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$	−2.00000	+	3.46410i	−0.282843	+	0.489898i
$51$		0			0
$52$	1.00000	−	3.46410i	0.138675	−	0.480384i
$53$	−9.00000			−1.23625			−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000			−1.23625			−0.618123	+	0.786082i	$0.712106\pi$
$54$		0			0
$55$		0			0
$56$	3.00000	+	5.19615i	0.400892	+	0.694365i
$57$		0			0
$58$	−1.50000	−	2.59808i	−0.196960	−	0.341144i
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	0.992524	−	0.122047i	$-0.0389457\pi$
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	−0.601958	+	0.798528i	$0.705612\pi$
$60$		0			0
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$	0.500000	−	0.866025i	0.0635001	−	0.109985i
$63$	3.00000	−	5.19615i	0.377964	−	0.654654i
$64$	7.00000			0.875000
$65$	7.50000	+	7.79423i	0.930261	+	0.966755i
$66$		0			0
$67$	−5.00000	+	8.66025i	−0.610847	+	1.05802i	0.380251	+	0.924883i	$0.375838\pi$
$67$	−5.00000	+	8.66025i	−0.610847	+	1.05802i	−0.991098	+	0.133135i	$0.957496\pi$
$68$	2.50000	−	4.33013i	0.303170	−	0.525105i
$69$		0			0
$70$	−6.00000			−0.717137
$71$	2.00000	+	3.46410i	0.237356	+	0.411113i	0.959955	−	0.280155i	$-0.0903858\pi$
$71$	2.00000	+	3.46410i	0.237356	+	0.411113i	−0.722599	+	0.691268i	$0.757052\pi$
$72$	−4.50000	−	7.79423i	−0.530330	−	0.918559i
$73$	−3.00000			−0.351123			−0.175562	−	0.984468i	$-0.556174\pi$
$73$	−3.00000			−0.351123			−0.175562	+	0.984468i	$0.556174\pi$
$74$	2.50000	+	4.33013i	0.290619	+	0.503367i
$75$		0			0
$76$	2.00000	−	3.46410i	0.229416	−	0.397360i
$77$		0			0
$78$		0			0
$79$	2.00000			0.225018			0.112509	−	0.993651i	$-0.464111\pi$
$79$	2.00000			0.225018			0.112509	+	0.993651i	$0.464111\pi$
$80$	−1.50000	+	2.59808i	−0.167705	+	0.290474i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−3.50000	−	6.06218i	−0.386510	−	0.669456i
$83$	−2.00000			−0.219529			−0.109764	−	0.993958i	$-0.535010\pi$
$83$	−2.00000			−0.219529			−0.109764	+	0.993958i	$0.535010\pi$
$84$		0			0
$85$	7.50000	+	12.9904i	0.813489	+	1.40900i
$86$	−2.00000			−0.215666
$87$		0			0
$88$		0			0
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$	9.00000			0.948683
$91$	−2.00000	+	6.92820i	−0.209657	+	0.726273i
$92$	−4.00000			−0.417029
$93$		0			0
$94$	3.00000	−	5.19615i	0.309426	−	0.535942i
$95$	6.00000	+	10.3923i	0.615587	+	1.06623i
$96$		0			0
$97$	9.00000	+	15.5885i	0.913812	+	1.58277i	0.808632	+	0.588315i	$0.200208\pi$
$97$	9.00000	+	15.5885i	0.913812	+	1.58277i	0.105180	+	0.994453i	$0.466458\pi$
$98$	1.50000	+	2.59808i	0.151523	+	0.262445i
$99$		0			0
$100$	2.00000	+	3.46410i	0.200000	+	0.346410i
$101$	3.50000	−	6.06218i	0.348263	−	0.603209i	−0.637678	−	0.770303i	$-0.720105\pi$
$101$	3.50000	−	6.06218i	0.348263	−	0.603209i	0.985941	+	0.167094i	$0.0534383\pi$
$102$		0			0
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$	7.50000	+	7.79423i	0.735436	+	0.764287i
$105$		0			0
$106$	4.50000	−	7.79423i	0.437079	−	0.757042i
$107$	−5.00000	+	8.66025i	−0.483368	+	0.837218i	−0.999818	−	0.0190994i	$-0.993920\pi$
$107$	−5.00000	+	8.66025i	−0.483368	+	0.837218i	0.516449	+	0.856318i	$0.327253\pi$
$108$		0			0
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$		0			0
$111$		0			0
$112$	−2.00000			−0.188982
$113$	0.500000	+	0.866025i	0.0470360	+	0.0814688i	0.888585	−	0.458712i	$-0.151689\pi$
$113$	0.500000	+	0.866025i	0.0470360	+	0.0814688i	−0.841549	+	0.540181i	$0.818356\pi$
$114$		0			0
$115$	6.00000	−	10.3923i	0.559503	−	0.969087i
$116$	−3.00000			−0.278543
$117$	3.00000	−	10.3923i	0.277350	−	0.960769i
$118$	−6.00000			−0.552345
$119$	−5.00000	+	8.66025i	−0.458349	+	0.793884i
$120$		0			0
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$	−1.00000			−0.0905357
$123$		0			0
$124$	−0.500000	−	0.866025i	−0.0449013	−	0.0777714i
$125$	3.00000			0.268328
$126$	3.00000	+	5.19615i	0.267261	+	0.462910i
$127$	−1.00000	+	1.73205i	−0.0887357	+	0.153695i	−0.906977	−	0.421180i	$-0.861616\pi$
$127$	−1.00000	+	1.73205i	−0.0887357	+	0.153695i	0.818241	+	0.574875i	$0.194949\pi$
$128$	1.50000	−	2.59808i	0.132583	−	0.229640i
$129$		0			0
$130$	−10.5000	+	2.59808i	−0.920911	+	0.227866i
$131$	−20.0000			−1.74741			−0.873704	−	0.486458i	$-0.838289\pi$
$131$	−20.0000			−1.74741			−0.873704	+	0.486458i	$0.838289\pi$
$132$		0			0
$133$	−4.00000	+	6.92820i	−0.346844	+	0.600751i
$134$	−5.00000	−	8.66025i	−0.431934	−	0.748132i
$135$		0			0
$136$	7.50000	+	12.9904i	0.643120	+	1.11392i
$137$	3.50000	+	6.06218i	0.299025	+	0.517927i	0.975913	−	0.218159i	$-0.0700052\pi$
$137$	3.50000	+	6.06218i	0.299025	+	0.517927i	−0.676888	+	0.736086i	$0.736672\pi$
$138$		0			0
$139$	−5.00000	−	8.66025i	−0.424094	−	0.734553i	0.572241	−	0.820086i	$-0.306074\pi$
$139$	−5.00000	−	8.66025i	−0.424094	−	0.734553i	−0.996335	+	0.0855324i	$0.972741\pi$
$140$	−3.00000	+	5.19615i	−0.253546	+	0.439155i
$141$		0			0
$142$	−4.00000			−0.335673
$143$		0			0
$144$	3.00000			0.250000
$145$	4.50000	−	7.79423i	0.373705	−	0.647275i
$146$	1.50000	−	2.59808i	0.124141	−	0.215018i
$147$		0			0
$148$	5.00000			0.410997
$149$	−6.50000	−	11.2583i	−0.532501	−	0.922318i	−0.999280	−	0.0379444i	$-0.987919\pi$
$149$	−6.50000	−	11.2583i	−0.532501	−	0.922318i	0.466779	−	0.884374i	$-0.345414\pi$
$150$		0			0
$151$	−14.0000			−1.13930			−0.569652	−	0.821886i	$-0.692922\pi$
$151$	−14.0000			−1.13930			−0.569652	+	0.821886i	$0.692922\pi$
$152$	6.00000	+	10.3923i	0.486664	+	0.842927i
$153$	7.50000	−	12.9904i	0.606339	−	1.05021i
$154$		0			0
$155$	3.00000			0.240966
$156$		0			0
$157$	9.00000			0.718278			0.359139	−	0.933284i	$-0.383070\pi$
$157$	9.00000			0.718278			0.359139	+	0.933284i	$0.383070\pi$
$158$	−1.00000	+	1.73205i	−0.0795557	+	0.137795i
$159$		0			0
$160$	7.50000	+	12.9904i	0.592927	+	1.02698i
$161$	8.00000			0.630488
$162$	−4.50000	−	7.79423i	−0.353553	−	0.612372i
$163$	−3.00000	−	5.19615i	−0.234978	−	0.406994i	0.724288	−	0.689497i	$-0.242169\pi$
$163$	−3.00000	−	5.19615i	−0.234978	−	0.406994i	−0.959266	+	0.282503i	$0.908835\pi$
$164$	−7.00000			−0.546608
$165$		0			0
$166$	1.00000	−	1.73205i	0.0776151	−	0.134433i
$167$	11.0000	−	19.0526i	0.851206	−	1.47433i	−0.0289155	−	0.999582i	$-0.509205\pi$
$167$	11.0000	−	19.0526i	0.851206	−	1.47433i	0.880121	−	0.474749i	$-0.157461\pi$
$168$		0			0
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$	−15.0000			−1.15045
$171$	6.00000	−	10.3923i	0.458831	−	0.794719i
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	−7.00000	−	12.1244i	−0.532200	−	0.921798i	−0.999293	−	0.0375896i	$-0.988032\pi$
$173$	−7.00000	−	12.1244i	−0.532200	−	0.921798i	0.467093	−	0.884208i	$-0.345301\pi$
$174$		0			0
$175$	−4.00000	−	6.92820i	−0.302372	−	0.523723i
$176$		0			0
$177$		0			0
$178$	3.00000	+	5.19615i	0.224860	+	0.389468i
$179$	10.0000	−	17.3205i	0.747435	−	1.29460i	−0.201613	−	0.979465i	$-0.564618\pi$
$179$	10.0000	−	17.3205i	0.747435	−	1.29460i	0.949048	−	0.315130i	$-0.102048\pi$
$180$	4.50000	−	7.79423i	0.335410	−	0.580948i
$181$	−1.00000			−0.0743294			−0.0371647	−	0.999309i	$-0.511833\pi$
$181$	−1.00000			−0.0743294			−0.0371647	+	0.999309i	$0.511833\pi$
$182$	−5.00000	−	5.19615i	−0.370625	−	0.385164i
$183$		0			0
$184$	6.00000	−	10.3923i	0.442326	−	0.766131i
$185$	−7.50000	+	12.9904i	−0.551411	+	0.955072i
$186$		0			0
$187$		0			0
$188$	−3.00000	−	5.19615i	−0.218797	−	0.378968i
$189$		0			0
$190$	−12.0000			−0.870572
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	0.973674	−	0.227946i	$-0.0732010\pi$
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	−0.684244	+	0.729253i	$0.739868\pi$
$192$		0			0
$193$	12.5000	−	21.6506i	0.899770	−	1.55845i	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	12.5000	−	21.6506i	0.899770	−	1.55845i	0.827788	−	0.561041i	$-0.189599\pi$
$194$	−18.0000			−1.29232
$195$		0			0
$196$	3.00000			0.214286
$197$	3.00000	−	5.19615i	0.213741	−	0.370211i	−0.739141	−	0.673550i	$-0.764768\pi$
$197$	3.00000	−	5.19615i	0.213741	−	0.370211i	0.952882	+	0.303340i	$0.0981018\pi$
$198$		0			0
$199$	−13.0000	−	22.5167i	−0.921546	−	1.59616i	−0.797025	−	0.603947i	$-0.793594\pi$
$199$	−13.0000	−	22.5167i	−0.921546	−	1.59616i	−0.124521	−	0.992217i	$-0.539739\pi$
$200$	−12.0000			−0.848528
$201$		0			0
$202$	3.50000	+	6.06218i	0.246259	+	0.426533i
$203$	6.00000			0.421117
$204$		0			0
$205$	10.5000	−	18.1865i	0.733352	−	1.27020i
$206$		0			0
$207$	−12.0000			−0.834058
$208$	−3.50000	+	0.866025i	−0.242681	+	0.0600481i
$209$		0			0
$210$		0			0
$211$	5.00000	−	8.66025i	0.344214	−	0.596196i	−0.640996	−	0.767544i	$-0.721479\pi$
$211$	5.00000	−	8.66025i	0.344214	−	0.596196i	0.985211	+	0.171347i	$0.0548120\pi$
$212$	−4.50000	−	7.79423i	−0.309061	−	0.535310i
$213$		0			0
$214$	−5.00000	−	8.66025i	−0.341793	−	0.592003i
$215$	−3.00000	−	5.19615i	−0.204598	−	0.354375i
$216$		0			0
$217$	1.00000	+	1.73205i	0.0678844	+	0.117579i
$218$	5.00000	−	8.66025i	0.338643	−	0.586546i
$219$		0			0
$220$		0			0
$221$	−5.00000	+	17.3205i	−0.336336	+	1.16510i
$222$		0			0
$223$	−7.00000	+	12.1244i	−0.468755	+	0.811907i	−0.999362	−	0.0357107i	$-0.988630\pi$
$223$	−7.00000	+	12.1244i	−0.468755	+	0.811907i	0.530607	+	0.847618i	$0.321964\pi$
$224$	−5.00000	+	8.66025i	−0.334077	+	0.578638i
$225$	6.00000	+	10.3923i	0.400000	+	0.692820i
$226$	−1.00000			−0.0665190
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	0.595274	−	0.803523i	$-0.297043\pi$
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	−0.993508	+	0.113761i	$0.963710\pi$
$228$		0			0
$229$	2.00000			0.132164			0.0660819	−	0.997814i	$-0.478950\pi$
$229$	2.00000			0.132164			0.0660819	+	0.997814i	$0.478950\pi$
$230$	6.00000	+	10.3923i	0.395628	+	0.685248i
$231$		0			0
$232$	4.50000	−	7.79423i	0.295439	−	0.511716i
$233$	14.0000			0.917170			0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000			0.917170			0.458585	+	0.888650i	$0.348356\pi$
$234$	7.50000	+	7.79423i	0.490290	+	0.509525i
$235$	18.0000			1.17419
$236$	−3.00000	+	5.19615i	−0.195283	+	0.338241i
$237$		0			0
$238$	−5.00000	−	8.66025i	−0.324102	−	0.561361i
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$		0			0
$241$	9.50000	+	16.4545i	0.611949	+	1.05993i	0.990912	+	0.134515i	$0.0429475\pi$
$241$	9.50000	+	16.4545i	0.611949	+	1.05993i	−0.378963	+	0.925412i	$0.623719\pi$
$242$	−11.0000			−0.707107
$243$		0			0
$244$	−0.500000	+	0.866025i	−0.0320092	+	0.0554416i
$245$	−4.50000	+	7.79423i	−0.287494	+	0.497955i
$246$		0			0
$247$	−4.00000	+	13.8564i	−0.254514	+	0.881662i
$248$	3.00000			0.190500
$249$		0			0
$250$	−1.50000	+	2.59808i	−0.0948683	+	0.164317i
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	0.990876	−	0.134778i	$-0.0430322\pi$
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	−0.612159	+	0.790735i	$0.709699\pi$
$252$	6.00000			0.377964
$253$		0			0
$254$	−1.00000	−	1.73205i	−0.0627456	−	0.108679i
$255$		0			0
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	−0.999325	−	0.0367485i	$-0.988300\pi$
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	0.531487	+	0.847066i	$0.321633\pi$
$258$		0			0
$259$	−10.0000			−0.621370
$260$	−3.00000	+	10.3923i	−0.186052	+	0.644503i
$261$	−9.00000			−0.557086
$262$	10.0000	−	17.3205i	0.617802	−	1.07006i
$263$	3.00000	−	5.19615i	0.184988	−	0.320408i	−0.758585	−	0.651575i	$-0.774109\pi$
$263$	3.00000	−	5.19615i	0.184988	−	0.320408i	0.943572	+	0.331166i	$0.107442\pi$
$264$		0			0
$265$	27.0000			1.65860
$266$	−4.00000	−	6.92820i	−0.245256	−	0.424795i
$267$		0			0
$268$	−10.0000			−0.610847
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	−0.998361	−	0.0572259i	$-0.981774\pi$
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	0.449622	−	0.893219i	$-0.351559\pi$
$270$		0			0
$271$	−12.0000	+	20.7846i	−0.728948	+	1.26258i	0.228380	+	0.973572i	$0.426657\pi$
$271$	−12.0000	+	20.7846i	−0.728948	+	1.26258i	−0.957328	+	0.289003i	$0.906676\pi$
$272$	−5.00000			−0.303170
$273$		0			0
$274$	−7.00000			−0.422885
$275$		0			0
$276$		0			0
$277$	−15.5000	−	26.8468i	−0.931305	−	1.61307i	−0.781094	−	0.624413i	$-0.785338\pi$
$277$	−15.5000	−	26.8468i	−0.931305	−	1.61307i	−0.150210	−	0.988654i	$-0.547995\pi$
$278$	10.0000			0.599760
$279$	−1.50000	−	2.59808i	−0.0898027	−	0.155543i
$280$	−9.00000	−	15.5885i	−0.537853	−	0.931589i
$281$	15.0000			0.894825			0.447412	−	0.894328i	$-0.352346\pi$
$281$	15.0000			0.894825			0.447412	+	0.894328i	$0.352346\pi$
$282$		0			0
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	−0.800439	−	0.599414i	$-0.795400\pi$
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	0.919327	+	0.393494i	$0.128734\pi$
$284$	−2.00000	+	3.46410i	−0.118678	+	0.205557i
$285$		0			0
$286$		0			0
$287$	14.0000			0.826394
$288$	7.50000	−	12.9904i	0.441942	−	0.765466i
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$	4.50000	+	7.79423i	0.264249	+	0.457693i
$291$		0			0
$292$	−1.50000	−	2.59808i	−0.0877809	−	0.152041i
$293$	9.50000	+	16.4545i	0.554996	+	0.961281i	0.997904	+	0.0647140i	$0.0206135\pi$
$293$	9.50000	+	16.4545i	0.554996	+	0.961281i	−0.442908	+	0.896567i	$0.646053\pi$
$294$		0			0
$295$	−9.00000	−	15.5885i	−0.524000	−	0.907595i
$296$	−7.50000	+	12.9904i	−0.435929	+	0.755051i
$297$		0			0
$298$	13.0000			0.753070
$299$	14.0000	−	3.46410i	0.809641	−	0.200334i
$300$		0			0
$301$	2.00000	−	3.46410i	0.115278	−	0.199667i
$302$	7.00000	−	12.1244i	0.402805	−	0.697678i
$303$		0			0
$304$	−4.00000			−0.229416
$305$	−1.50000	−	2.59808i	−0.0858898	−	0.148765i
$306$	7.50000	+	12.9904i	0.428746	+	0.742611i
$307$	−32.0000			−1.82634			−0.913168	−	0.407583i	$-0.866372\pi$
$307$	−32.0000			−1.82634			−0.913168	+	0.407583i	$0.866372\pi$
$308$		0			0
$309$		0			0
$310$	−1.50000	+	2.59808i	−0.0851943	+	0.147561i
$311$	−26.0000			−1.47432			−0.737162	−	0.675716i	$-0.763835\pi$
$311$	−26.0000			−1.47432			−0.737162	+	0.675716i	$0.763835\pi$
$312$		0			0
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$	−4.50000	+	7.79423i	−0.253950	+	0.439854i
$315$	−9.00000	+	15.5885i	−0.507093	+	0.878310i
$316$	1.00000	+	1.73205i	0.0562544	+	0.0974355i
$317$	−7.00000			−0.393159			−0.196580	−	0.980488i	$-0.562983\pi$
$317$	−7.00000			−0.393159			−0.196580	+	0.980488i	$0.562983\pi$
$318$		0			0
$319$		0			0
$320$	−21.0000			−1.17394
$321$		0			0
$322$	−4.00000	+	6.92820i	−0.222911	+	0.386094i
$323$	−10.0000	+	17.3205i	−0.556415	+	0.963739i
$324$	−9.00000			−0.500000
$325$	−10.0000	−	10.3923i	−0.554700	−	0.576461i
$326$	6.00000			0.332309
$327$		0			0
$328$	10.5000	−	18.1865i	0.579766	−	1.00418i
$329$	6.00000	+	10.3923i	0.330791	+	0.572946i
$330$		0			0
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	0.695266	−	0.718752i	$-0.255287\pi$
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	−0.970091	+	0.242742i	$0.921953\pi$
$332$	−1.00000	−	1.73205i	−0.0548821	−	0.0950586i
$333$	15.0000			0.821995
$334$	11.0000	+	19.0526i	0.601893	+	1.04251i
$335$	15.0000	−	25.9808i	0.819538	−	1.41948i
$336$		0			0
$337$	29.0000			1.57973			0.789865	−	0.613280i	$-0.210150\pi$
$337$	29.0000			1.57973			0.789865	+	0.613280i	$0.210150\pi$
$338$	−11.0000	−	6.92820i	−0.598321	−	0.376845i
$339$		0			0
$340$	−7.50000	+	12.9904i	−0.406745	+	0.704502i
$341$		0			0
$342$	6.00000	+	10.3923i	0.324443	+	0.561951i
$343$	−20.0000			−1.07990
$344$	−3.00000	−	5.19615i	−0.161749	−	0.280158i
$345$		0			0
$346$	14.0000			0.752645
$347$	15.0000	+	25.9808i	0.805242	+	1.39472i	0.916127	+	0.400887i	$0.131298\pi$
$347$	15.0000	+	25.9808i	0.805242	+	1.39472i	−0.110885	+	0.993833i	$0.535369\pi$
$348$		0			0
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	−0.990282	−	0.139072i	$-0.955588\pi$
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	0.615581	+	0.788074i	$0.288921\pi$
$350$	8.00000			0.427618
$351$		0			0
$352$		0			0
$353$	9.50000	−	16.4545i	0.505634	−	0.875784i	−0.494345	−	0.869266i	$-0.664592\pi$
$353$	9.50000	−	16.4545i	0.505634	−	0.875784i	0.999979	−	0.00651782i	$-0.00207470\pi$
$354$		0			0
$355$	−6.00000	−	10.3923i	−0.318447	−	0.551566i
$356$	6.00000			0.317999
$357$		0			0
$358$	10.0000	+	17.3205i	0.528516	+	0.915417i
$359$	−30.0000			−1.58334			−0.791670	−	0.610949i	$-0.790788\pi$
$359$	−30.0000			−1.58334			−0.791670	+	0.610949i	$0.790788\pi$
$360$	13.5000	+	23.3827i	0.711512	+	1.23238i
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$	0.500000	−	0.866025i	0.0262794	−	0.0455173i
$363$		0			0
$364$	−7.00000	+	1.73205i	−0.366900	+	0.0907841i
$365$	9.00000			0.471082
$366$		0			0
$367$	−15.0000	+	25.9808i	−0.782994	+	1.35618i	0.147197	+	0.989107i	$0.452975\pi$
$367$	−15.0000	+	25.9808i	−0.782994	+	1.35618i	−0.930190	+	0.367078i	$0.880358\pi$
$368$	2.00000	+	3.46410i	0.104257	+	0.180579i
$369$	−21.0000			−1.09322
$370$	−7.50000	−	12.9904i	−0.389906	−	0.675338i
$371$	9.00000	+	15.5885i	0.467257	+	0.809312i
$372$		0			0
$373$	−6.50000	−	11.2583i	−0.336557	−	0.582934i	0.647225	−	0.762299i	$-0.275929\pi$
$373$	−6.50000	−	11.2583i	−0.336557	−	0.582934i	−0.983783	+	0.179364i	$0.942596\pi$
$374$		0			0
$375$		0			0
$376$	18.0000			0.928279
$377$	10.5000	−	2.59808i	0.540778	−	0.133808i
$378$		0			0
$379$	−3.00000	+	5.19615i	−0.154100	+	0.266908i	−0.932731	−	0.360573i	$-0.882581\pi$
$379$	−3.00000	+	5.19615i	−0.154100	+	0.266908i	0.778631	+	0.627482i	$0.215914\pi$
$380$	−6.00000	+	10.3923i	−0.307794	+	0.533114i
$381$		0			0
$382$	−8.00000			−0.409316
$383$	13.0000	+	22.5167i	0.664269	+	1.15055i	0.979483	+	0.201527i	$0.0645904\pi$
$383$	13.0000	+	22.5167i	0.664269	+	1.15055i	−0.315214	+	0.949021i	$0.602076\pi$
$384$		0			0
$385$		0			0
$386$	12.5000	+	21.6506i	0.636233	+	1.10199i
$387$	−3.00000	+	5.19615i	−0.152499	+	0.264135i
$388$	−9.00000	+	15.5885i	−0.456906	+	0.791384i
$389$	39.0000			1.97738			0.988689	−	0.149979i	$-0.0479205\pi$
$389$	39.0000			1.97738			0.988689	+	0.149979i	$0.0479205\pi$
$390$		0			0
$391$	20.0000			1.01144
$392$	−4.50000	+	7.79423i	−0.227284	+	0.393668i
$393$		0			0
$394$	3.00000	+	5.19615i	0.151138	+	0.261778i
$395$	−6.00000			−0.301893
$396$		0			0
$397$	−7.00000	−	12.1244i	−0.351320	−	0.608504i	0.635161	−	0.772380i	$-0.280934\pi$
$397$	−7.00000	−	12.1244i	−0.351320	−	0.608504i	−0.986481	+	0.163876i	$0.947600\pi$
$398$	26.0000			1.30326
$399$		0			0
$400$	2.00000	−	3.46410i	0.100000	−	0.173205i
$401$	15.5000	−	26.8468i	0.774033	−	1.34066i	−0.161303	−	0.986905i	$-0.551570\pi$
$401$	15.5000	−	26.8468i	0.774033	−	1.34066i	0.935336	−	0.353760i	$-0.115097\pi$
$402$		0			0
$403$	2.50000	+	2.59808i	0.124534	+	0.129419i
$404$	7.00000			0.348263
$405$	13.5000	−	23.3827i	0.670820	−	1.16190i
$406$	−3.00000	+	5.19615i	−0.148888	+	0.257881i
$407$		0			0
$408$		0			0
$409$	15.5000	+	26.8468i	0.766426	+	1.32749i	0.939490	+	0.342578i	$0.111300\pi$
$409$	15.5000	+	26.8468i	0.766426	+	1.32749i	−0.173064	+	0.984911i	$0.555367\pi$
$410$	10.5000	+	18.1865i	0.518558	+	0.898169i
$411$		0			0
$412$		0			0
$413$	6.00000	−	10.3923i	0.295241	−	0.511372i
$414$	6.00000	−	10.3923i	0.294884	−	0.510754i
$415$	6.00000			0.294528
$416$	−5.00000	+	17.3205i	−0.245145	+	0.849208i
$417$		0			0
$418$		0			0
$419$	18.0000	−	31.1769i	0.879358	−	1.52309i	0.0273103	−	0.999627i	$-0.491306\pi$
$419$	18.0000	−	31.1769i	0.879358	−	1.52309i	0.852047	−	0.523465i	$-0.175361\pi$
$420$		0			0
$421$	1.00000			0.0487370			0.0243685	−	0.999703i	$-0.492242\pi$
$421$	1.00000			0.0487370			0.0243685	+	0.999703i	$0.492242\pi$
$422$	5.00000	+	8.66025i	0.243396	+	0.421575i
$423$	−9.00000	−	15.5885i	−0.437595	−	0.757937i
$424$	27.0000			1.31124
$425$	−10.0000	−	17.3205i	−0.485071	−	0.840168i
$426$		0			0
$427$	1.00000	−	1.73205i	0.0483934	−	0.0838198i
$428$	−10.0000			−0.483368
$429$		0			0
$430$	6.00000			0.289346
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	−0.973574	−	0.228373i	$-0.926659\pi$
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	0.684564	+	0.728953i	$0.259993\pi$
$432$		0			0
$433$	5.50000	+	9.52628i	0.264313	+	0.457804i	0.967383	−	0.253317i	$-0.0815214\pi$
$433$	5.50000	+	9.52628i	0.264313	+	0.457804i	−0.703070	+	0.711120i	$0.748188\pi$
$434$	−2.00000			−0.0960031
$435$		0			0
$436$	−5.00000	−	8.66025i	−0.239457	−	0.414751i
$437$	16.0000			0.765384
$438$		0			0
$439$	5.00000	−	8.66025i	0.238637	−	0.413331i	−0.721686	−	0.692220i	$-0.756633\pi$
$439$	5.00000	−	8.66025i	0.238637	−	0.413331i	0.960323	+	0.278889i	$0.0899661\pi$
$440$		0			0
$441$	9.00000			0.428571
$442$	−12.5000	−	12.9904i	−0.594564	−	0.617889i
$443$	−22.0000			−1.04525			−0.522626	−	0.852562i	$-0.675047\pi$
$443$	−22.0000			−1.04525			−0.522626	+	0.852562i	$0.675047\pi$
$444$		0			0
$445$	−9.00000	+	15.5885i	−0.426641	+	0.738964i
$446$	−7.00000	−	12.1244i	−0.331460	−	0.574105i
$447$		0			0
$448$	−7.00000	−	12.1244i	−0.330719	−	0.572822i
$449$	−7.00000	−	12.1244i	−0.330350	−	0.572184i	0.652230	−	0.758021i	$-0.273834\pi$
$449$	−7.00000	−	12.1244i	−0.330350	−	0.572184i	−0.982581	+	0.185837i	$0.940500\pi$
$450$	−12.0000			−0.565685
$451$		0			0
$452$	−0.500000	+	0.866025i	−0.0235180	+	0.0407344i
$453$		0			0
$454$	12.0000			0.563188
$455$	6.00000	−	20.7846i	0.281284	−	0.974398i
$456$		0			0
$457$	−2.50000	+	4.33013i	−0.116945	+	0.202555i	−0.918556	−	0.395292i	$-0.870643\pi$
$457$	−2.50000	+	4.33013i	−0.116945	+	0.202555i	0.801611	+	0.597847i	$0.203977\pi$
$458$	−1.00000	+	1.73205i	−0.0467269	+	0.0809334i
$459$		0			0
$460$	12.0000			0.559503
$461$	16.5000	+	28.5788i	0.768482	+	1.33105i	0.938386	+	0.345589i	$0.112321\pi$
$461$	16.5000	+	28.5788i	0.768482	+	1.33105i	−0.169904	+	0.985461i	$0.554346\pi$
$462$		0			0
$463$	−42.0000			−1.95191			−0.975953	−	0.217982i	$-0.930053\pi$
$463$	−42.0000			−1.95191			−0.975953	+	0.217982i	$0.930053\pi$
$464$	1.50000	+	2.59808i	0.0696358	+	0.120613i
$465$		0			0
$466$	−7.00000	+	12.1244i	−0.324269	+	0.561650i
$467$	−12.0000			−0.555294			−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000			−0.555294			−0.277647	+	0.960683i	$0.589555\pi$
$468$	10.5000	−	2.59808i	0.485363	−	0.120096i
$469$	20.0000			0.923514
$470$	−9.00000	+	15.5885i	−0.415139	+	0.719042i
$471$		0			0
$472$	−9.00000	−	15.5885i	−0.414259	−	0.717517i
$473$		0			0
$474$		0			0
$475$	−8.00000	−	13.8564i	−0.367065	−	0.635776i
$476$	−10.0000			−0.458349
$477$	−13.5000	−	23.3827i	−0.618123	−	1.07062i
$478$	3.00000	−	5.19615i	0.137217	−	0.237666i
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	−0.450098	−	0.892979i	$-0.648611\pi$
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	0.998392	−	0.0566937i	$-0.0180558\pi$
$480$		0			0
$481$	−17.5000	+	4.33013i	−0.797931	+	0.197437i
$482$	−19.0000			−0.865426
$483$		0			0
$484$	−5.50000	+	9.52628i	−0.250000	+	0.433013i
$485$	−27.0000	−	46.7654i	−1.22601	−	2.12351i
$486$		0			0
$487$	13.0000	+	22.5167i	0.589086	+	1.02033i	0.994352	+	0.106129i	$0.0338455\pi$
$487$	13.0000	+	22.5167i	0.589086	+	1.02033i	−0.405266	+	0.914199i	$0.632821\pi$
$488$	−1.50000	−	2.59808i	−0.0679018	−	0.117609i
$489$		0			0
$490$	−4.50000	−	7.79423i	−0.203289	−	0.352107i
$491$	−12.0000	+	20.7846i	−0.541552	+	0.937996i	0.457263	+	0.889332i	$0.348830\pi$
$491$	−12.0000	+	20.7846i	−0.541552	+	0.937996i	−0.998815	+	0.0486647i	$0.984503\pi$
$492$		0			0
$493$	15.0000			0.675566
$494$	−10.0000	−	10.3923i	−0.449921	−	0.467572i
$495$		0			0
$496$	−0.500000	+	0.866025i	−0.0224507	+	0.0388857i
$497$	4.00000	−	6.92820i	0.179425	−	0.310772i
$498$		0			0
$499$	−6.00000			−0.268597			−0.134298	−	0.990941i	$-0.542878\pi$
$499$	−6.00000			−0.268597			−0.134298	+	0.990941i	$0.542878\pi$
$500$	1.50000	+	2.59808i	0.0670820	+	0.116190i
$501$		0			0
$502$	−12.0000			−0.535586
$503$	21.0000	+	36.3731i	0.936344	+	1.62179i	0.772220	+	0.635355i	$0.219146\pi$
$503$	21.0000	+	36.3731i	0.936344	+	1.62179i	0.164124	+	0.986440i	$0.447520\pi$
$504$	−9.00000	+	15.5885i	−0.400892	+	0.694365i
$505$	−10.5000	+	18.1865i	−0.467244	+	0.809290i
$506$		0			0
$507$		0			0
$508$	−2.00000			−0.0887357
$509$	2.50000	−	4.33013i	0.110811	−	0.191930i	−0.805287	−	0.592886i	$-0.797989\pi$
$509$	2.50000	−	4.33013i	0.110811	−	0.191930i	0.916097	+	0.400956i	$0.131322\pi$
$510$		0			0
$511$	3.00000	+	5.19615i	0.132712	+	0.229864i
$512$	−11.0000			−0.486136
$513$		0			0
$514$	−7.50000	−	12.9904i	−0.330811	−	0.572981i
$515$		0			0
$516$		0			0
$517$		0			0
$518$	5.00000	−	8.66025i	0.219687	−	0.380510i
$519$		0			0
$520$	−22.5000	−	23.3827i	−0.986690	−	1.02540i
$521$	−25.0000			−1.09527			−0.547635	−	0.836717i	$-0.684472\pi$
$521$	−25.0000			−1.09527			−0.547635	+	0.836717i	$0.684472\pi$
$522$	4.50000	−	7.79423i	0.196960	−	0.341144i
$523$	12.0000	−	20.7846i	0.524723	−	0.908848i	−0.474862	−	0.880060i	$-0.657502\pi$
$523$	12.0000	−	20.7846i	0.524723	−	0.908848i	0.999586	−	0.0287874i	$-0.00916457\pi$
$524$	−10.0000	−	17.3205i	−0.436852	−	0.756650i
$525$		0			0
$526$	3.00000	+	5.19615i	0.130806	+	0.226563i
$527$	2.50000	+	4.33013i	0.108902	+	0.188623i
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	−13.5000	+	23.3827i	−0.586403	+	1.01568i
$531$	−9.00000	+	15.5885i	−0.390567	+	0.676481i
$532$	−8.00000			−0.346844
$533$	24.5000	−	6.06218i	1.06121	−	0.262582i
$534$		0			0
$535$	15.0000	−	25.9808i	0.648507	−	1.12325i
$536$	15.0000	−	25.9808i	0.647901	−	1.12220i
$537$		0			0
$538$	18.0000			0.776035
$539$		0			0
$540$		0			0
$541$	−3.00000			−0.128980			−0.0644900	−	0.997918i	$-0.520542\pi$
$541$	−3.00000			−0.128980			−0.0644900	+	0.997918i	$0.520542\pi$
$542$	−12.0000	−	20.7846i	−0.515444	−	0.892775i
$543$		0			0
$544$	−12.5000	+	21.6506i	−0.535933	+	0.928263i
$545$	30.0000			1.28506
$546$		0			0
$547$	−22.0000			−0.940652			−0.470326	−	0.882493i	$-0.655864\pi$
$547$	−22.0000			−0.940652			−0.470326	+	0.882493i	$0.655864\pi$
$548$	−3.50000	+	6.06218i	−0.149513	+	0.258963i
$549$	−1.50000	+	2.59808i	−0.0640184	+	0.110883i
$550$		0			0
$551$	12.0000			0.511217
$552$		0			0
$553$	−2.00000	−	3.46410i	−0.0850487	−	0.147309i
$554$	31.0000			1.31706
$555$		0			0
$556$	5.00000	−	8.66025i	0.212047	−	0.367277i
$557$	18.5000	−	32.0429i	0.783870	−	1.35770i	−0.145802	−	0.989314i	$-0.546576\pi$
$557$	18.5000	−	32.0429i	0.783870	−	1.35770i	0.929672	−	0.368389i	$-0.120091\pi$
$558$	3.00000			0.127000
$559$	2.00000	−	6.92820i	0.0845910	−	0.293032i
$560$	6.00000			0.253546
$561$		0			0
$562$	−7.50000	+	12.9904i	−0.316368	+	0.547966i
$563$	3.00000	+	5.19615i	0.126435	+	0.218992i	0.922293	−	0.386492i	$-0.126313\pi$
$563$	3.00000	+	5.19615i	0.126435	+	0.218992i	−0.795858	+	0.605483i	$0.792980\pi$
$564$		0			0
$565$	−1.50000	−	2.59808i	−0.0631055	−	0.109302i
$566$	2.00000	+	3.46410i	0.0840663	+	0.145607i
$567$	18.0000			0.755929
$568$	−6.00000	−	10.3923i	−0.251754	−	0.436051i
$569$	−21.0000	+	36.3731i	−0.880366	+	1.52484i	−0.0294311	+	0.999567i	$0.509370\pi$
$569$	−21.0000	+	36.3731i	−0.880366	+	1.52484i	−0.850935	+	0.525271i	$0.823964\pi$
$570$		0			0
$571$	34.0000			1.42286			0.711428	−	0.702759i	$-0.248049\pi$
$571$	34.0000			1.42286			0.711428	+	0.702759i	$0.248049\pi$
$572$		0			0
$573$		0			0
$574$	−7.00000	+	12.1244i	−0.292174	+	0.506061i
$575$	−8.00000	+	13.8564i	−0.333623	+	0.577852i
$576$	10.5000	+	18.1865i	0.437500	+	0.757772i
$577$	−21.0000			−0.874241			−0.437121	−	0.899403i	$-0.644002\pi$
$577$	−21.0000			−0.874241			−0.437121	+	0.899403i	$0.644002\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$		0			0
$580$	9.00000			0.373705
$581$	2.00000	+	3.46410i	0.0829740	+	0.143715i
$582$		0			0
$583$		0			0
$584$	9.00000			0.372423
$585$	−9.00000	+	31.1769i	−0.372104	+	1.28901i
$586$	−19.0000			−0.784883
$587$	6.00000	−	10.3923i	0.247647	−	0.428936i	−0.715226	−	0.698893i	$-0.753676\pi$
$587$	6.00000	−	10.3923i	0.247647	−	0.428936i	0.962872	+	0.269957i	$0.0870095\pi$
$588$		0			0
$589$	2.00000	+	3.46410i	0.0824086	+	0.142736i
$590$	18.0000			0.741048
$591$		0			0
$592$	−2.50000	−	4.33013i	−0.102749	−	0.177967i
$593$	−45.0000			−1.84793			−0.923964	−	0.382479i	$-0.875070\pi$
$593$	−45.0000			−1.84793			−0.923964	+	0.382479i	$0.875070\pi$
$594$		0			0
$595$	15.0000	−	25.9808i	0.614940	−	1.06511i
$596$	6.50000	−	11.2583i	0.266250	−	0.461159i
$597$		0			0
$598$	−4.00000	+	13.8564i	−0.163572	+	0.566631i
$599$	6.00000			0.245153			0.122577	−	0.992459i	$-0.460884\pi$
$599$	6.00000			0.245153			0.122577	+	0.992459i	$0.460884\pi$
$600$		0			0
$601$	−4.50000	+	7.79423i	−0.183559	+	0.317933i	−0.943090	−	0.332538i	$-0.892095\pi$
$601$	−4.50000	+	7.79423i	−0.183559	+	0.317933i	0.759531	+	0.650471i	$0.225428\pi$
$602$	2.00000	+	3.46410i	0.0815139	+	0.141186i
$603$	−30.0000			−1.22169
$604$	−7.00000	−	12.1244i	−0.284826	−	0.493333i
$605$	−16.5000	−	28.5788i	−0.670820	−	1.16190i
$606$		0			0
$607$	−19.0000	−	32.9090i	−0.771186	−	1.33573i	−0.936913	−	0.349562i	$-0.886330\pi$
$607$	−19.0000	−	32.9090i	−0.771186	−	1.33573i	0.165727	−	0.986172i	$-0.447003\pi$
$608$	−10.0000	+	17.3205i	−0.405554	+	0.702439i
$609$		0			0
$610$	3.00000			0.121466
$611$	15.0000	+	15.5885i	0.606835	+	0.630641i
$612$	15.0000			0.606339
$613$	−15.5000	+	26.8468i	−0.626039	+	1.08433i	0.362300	+	0.932062i	$0.381992\pi$
$613$	−15.5000	+	26.8468i	−0.626039	+	1.08433i	−0.988339	+	0.152270i	$0.951342\pi$
$614$	16.0000	−	27.7128i	0.645707	−	1.11840i
$615$		0			0
$616$		0			0
$617$	−1.50000	−	2.59808i	−0.0603877	−	0.104595i	0.834251	−	0.551385i	$-0.185900\pi$
$617$	−1.50000	−	2.59808i	−0.0603877	−	0.104595i	−0.894639	+	0.446790i	$0.852567\pi$
$618$		0			0
$619$	−30.0000			−1.20580			−0.602901	−	0.797816i	$-0.705989\pi$
$619$	−30.0000			−1.20580			−0.602901	+	0.797816i	$0.705989\pi$
$620$	1.50000	+	2.59808i	0.0602414	+	0.104341i
$621$		0			0
$622$	13.0000	−	22.5167i	0.521253	−	0.902836i
$623$	−12.0000			−0.480770
$624$		0			0
$625$	−29.0000			−1.16000
$626$	−3.00000	+	5.19615i	−0.119904	+	0.207680i
$627$		0			0
$628$	4.50000	+	7.79423i	0.179570	+	0.311024i
$629$	−25.0000			−0.996815
$630$	−9.00000	−	15.5885i	−0.358569	−	0.621059i
$631$	7.00000	+	12.1244i	0.278666	+	0.482663i	0.971053	−	0.238863i	$-0.0767746\pi$
$631$	7.00000	+	12.1244i	0.278666	+	0.482663i	−0.692388	+	0.721526i	$0.743441\pi$
$632$	−6.00000			−0.238667
$633$		0			0
$634$	3.50000	−	6.06218i	0.139003	−	0.240760i
$635$	3.00000	−	5.19615i	0.119051	−	0.206203i
$636$		0			0
$637$	−10.5000	+	2.59808i	−0.416025	+	0.102940i
$638$		0			0
$639$	−6.00000	+	10.3923i	−0.237356	+	0.411113i
$640$	−4.50000	+	7.79423i	−0.177878	+	0.308094i
$641$	−4.50000	−	7.79423i	−0.177739	−	0.307854i	0.763367	−	0.645966i	$-0.223545\pi$
$641$	−4.50000	−	7.79423i	−0.177739	−	0.307854i	−0.941106	+	0.338112i	$0.890212\pi$
$642$		0			0
$643$	23.0000	+	39.8372i	0.907031	+	1.57102i	0.818167	+	0.574981i	$0.194991\pi$
$643$	23.0000	+	39.8372i	0.907031	+	1.57102i	0.0888646	+	0.996044i	$0.471676\pi$
$644$	4.00000	+	6.92820i	0.157622	+	0.273009i
$645$		0			0
$646$	−10.0000	−	17.3205i	−0.393445	−	0.681466i
$647$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$647$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$648$	13.5000	−	23.3827i	0.530330	−	0.918559i
$649$		0			0
$650$	14.0000	−	3.46410i	0.549125	−	0.135873i
$651$		0			0
$652$	3.00000	−	5.19615i	0.117489	−	0.203497i
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	−0.986634	−	0.162951i	$-0.947899\pi$
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	0.634437	+	0.772975i	$0.281232\pi$
$654$		0			0
$655$	60.0000			2.34439
$656$	3.50000	+	6.06218i	0.136652	+	0.236688i
$657$	−4.50000	−	7.79423i	−0.175562	−	0.304082i
$658$	−12.0000			−0.467809
$659$	−14.0000	−	24.2487i	−0.545363	−	0.944596i	−0.998584	−	0.0531977i	$-0.983059\pi$
$659$	−14.0000	−	24.2487i	−0.545363	−	0.944596i	0.453221	−	0.891398i	$-0.350275\pi$
$660$		0			0
$661$	−6.50000	+	11.2583i	−0.252821	+	0.437898i	−0.964301	−	0.264807i	$-0.914692\pi$
$661$	−6.50000	+	11.2583i	−0.252821	+	0.437898i	0.711481	+	0.702706i	$0.248025\pi$
$662$	10.0000			0.388661
$663$		0			0
$664$	6.00000			0.232845
$665$	12.0000	−	20.7846i	0.465340	−	0.805993i
$666$	−7.50000	+	12.9904i	−0.290619	+	0.503367i
$667$	−6.00000	−	10.3923i	−0.232321	−	0.402392i
$668$	22.0000			0.851206
$669$		0			0
$670$	15.0000	+	25.9808i	0.579501	+	1.00372i
$671$		0			0
$672$		0			0
$673$	−20.5000	+	35.5070i	−0.790217	+	1.36870i	0.135615	+	0.990762i	$0.456699\pi$
$673$	−20.5000	+	35.5070i	−0.790217	+	1.36870i	−0.925832	+	0.377934i	$0.876635\pi$
$674$	−14.5000	+	25.1147i	−0.558519	+	0.967384i
$675$		0			0
$676$	−11.5000	+	6.06218i	−0.442308	+	0.233161i
$677$	2.00000			0.0768662			0.0384331	−	0.999261i	$-0.487763\pi$
$677$	2.00000			0.0768662			0.0384331	+	0.999261i	$0.487763\pi$
$678$		0			0
$679$	18.0000	−	31.1769i	0.690777	−	1.19646i
$680$	−22.5000	−	38.9711i	−0.862836	−	1.49448i
$681$		0			0
$682$		0			0
$683$	−19.0000	−	32.9090i	−0.727015	−	1.25923i	−0.958139	−	0.286302i	$-0.907574\pi$
$683$	−19.0000	−	32.9090i	−0.727015	−	1.25923i	0.231125	−	0.972924i	$-0.425760\pi$
$684$	12.0000			0.458831
$685$	−10.5000	−	18.1865i	−0.401184	−	0.694872i
$686$	10.0000	−	17.3205i	0.381802	−	0.661300i
$687$		0			0
$688$	2.00000			0.0762493
$689$	22.5000	+	23.3827i	0.857182	+	0.890809i
$690$		0			0
$691$	−10.0000	+	17.3205i	−0.380418	+	0.658903i	−0.991122	−	0.132956i	$-0.957553\pi$
$691$	−10.0000	+	17.3205i	−0.380418	+	0.658903i	0.610704	+	0.791859i	$0.290887\pi$
$692$	7.00000	−	12.1244i	0.266100	−	0.460899i
$693$		0			0
$694$	−30.0000			−1.13878
$695$	15.0000	+	25.9808i	0.568982	+	0.985506i
$696$		0			0
$697$	35.0000			1.32572
$698$	−7.00000	−	12.1244i	−0.264954	−	0.458914i
$699$		0			0
$700$	4.00000	−	6.92820i	0.151186	−	0.261861i
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$		0			0
$703$	−20.0000			−0.754314
$704$		0			0
$705$		0			0
$706$	9.50000	+	16.4545i	0.357537	+	0.619273i
$707$	−14.0000			−0.526524
$708$		0			0
$709$	−17.5000	−	30.3109i	−0.657226	−	1.13835i	−0.981331	−	0.192328i	$-0.938396\pi$
$709$	−17.5000	−	30.3109i	−0.657226	−	1.13835i	0.324104	−	0.946021i	$-0.394937\pi$
$710$	12.0000			0.450352
$711$	3.00000	+	5.19615i	0.112509	+	0.194871i
$712$	−9.00000	+	15.5885i	−0.337289	+	0.584202i
$713$	2.00000	−	3.46410i	0.0749006	−	0.129732i
$714$		0			0
$715$		0			0
$716$	20.0000			0.747435
$717$		0			0
$718$	15.0000	−	25.9808i	0.559795	−	0.969593i
$719$	−20.0000	−	34.6410i	−0.745874	−	1.29189i	−0.949785	−	0.312903i	$-0.898699\pi$
$719$	−20.0000	−	34.6410i	−0.745874	−	1.29189i	0.203911	−	0.978989i	$-0.434635\pi$
$720$	−9.00000			−0.335410
$721$		0			0
$722$	1.50000	+	2.59808i	0.0558242	+	0.0966904i
$723$		0			0
$724$	−0.500000	−	0.866025i	−0.0185824	−	0.0321856i
$725$	−6.00000	+	10.3923i	−0.222834	+	0.385961i
$726$		0			0
$727$	16.0000			0.593407			0.296704	−	0.954970i	$-0.404113\pi$
$727$	16.0000			0.593407			0.296704	+	0.954970i	$0.404113\pi$
$728$	6.00000	−	20.7846i	0.222375	−	0.770329i
$729$	−27.0000			−1.00000
$730$	−4.50000	+	7.79423i	−0.166552	+	0.288477i
$731$	5.00000	−	8.66025i	0.184932	−	0.320311i
$732$		0			0
$733$	41.0000			1.51437			0.757185	−	0.653201i	$-0.226574\pi$
$733$	41.0000			1.51437			0.757185	+	0.653201i	$0.226574\pi$
$734$	−15.0000	−	25.9808i	−0.553660	−	0.958967i
$735$		0			0
$736$	20.0000			0.737210
$737$		0			0
$738$	10.5000	−	18.1865i	0.386510	−	0.669456i
$739$	−25.0000	+	43.3013i	−0.919640	+	1.59286i	−0.119677	+	0.992813i	$0.538186\pi$
$739$	−25.0000	+	43.3013i	−0.919640	+	1.59286i	−0.799962	+	0.600050i	$0.795147\pi$
$740$	−15.0000			−0.551411
$741$		0			0
$742$	−18.0000			−0.660801
$743$	4.00000	−	6.92820i	0.146746	−	0.254171i	−0.783277	−	0.621673i	$-0.786453\pi$
$743$	4.00000	−	6.92820i	0.146746	−	0.254171i	0.930023	+	0.367502i	$0.119787\pi$
$744$		0			0
$745$	19.5000	+	33.7750i	0.714425	+	1.23742i
$746$	13.0000			0.475964
$747$	−3.00000	−	5.19615i	−0.109764	−	0.190117i
$748$		0			0
$749$	20.0000			0.730784
$750$		0			0
$751$	10.0000	−	17.3205i	0.364905	−	0.632034i	−0.623856	−	0.781540i	$-0.714435\pi$
$751$	10.0000	−	17.3205i	0.364905	−	0.632034i	0.988761	+	0.149505i	$0.0477681\pi$
$752$	−3.00000	+	5.19615i	−0.109399	+	0.189484i
$753$		0			0
$754$	−3.00000	+	10.3923i	−0.109254	+	0.378465i
$755$	42.0000			1.52854
$756$		0			0
$757$	3.00000	−	5.19615i	0.109037	−	0.188857i	−0.806343	−	0.591448i	$-0.798557\pi$
$757$	3.00000	−	5.19615i	0.109037	−	0.188857i	0.915380	+	0.402590i	$0.131890\pi$
$758$	−3.00000	−	5.19615i	−0.108965	−	0.188733i
$759$		0			0
$760$	−18.0000	−	31.1769i	−0.652929	−	1.13091i
$761$	5.00000	+	8.66025i	0.181250	+	0.313934i	0.942306	−	0.334752i	$-0.108652\pi$
$761$	5.00000	+	8.66025i	0.181250	+	0.313934i	−0.761057	+	0.648686i	$0.775319\pi$
$762$		0			0
$763$	10.0000	+	17.3205i	0.362024	+	0.627044i
$764$	−4.00000	+	6.92820i	−0.144715	+	0.250654i
$765$	−22.5000	+	38.9711i	−0.813489	+	1.40900i
$766$	−26.0000			−0.939418
$767$	6.00000	−	20.7846i	0.216647	−	0.750489i
$768$		0			0
$769$	−15.0000	+	25.9808i	−0.540914	+	0.936890i	0.457938	+	0.888984i	$0.348588\pi$
$769$	−15.0000	+	25.9808i	−0.540914	+	0.936890i	−0.998852	+	0.0479061i	$0.984745\pi$
$770$		0			0
$771$		0			0
$772$	25.0000			0.899770
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	0.657542	−	0.753418i	$-0.271596\pi$
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	−0.981250	+	0.192740i	$0.938263\pi$
$774$	−3.00000	−	5.19615i	−0.107833	−	0.186772i
$775$	−4.00000			−0.143684
$776$	−27.0000	−	46.7654i	−0.969244	−	1.67878i
$777$		0			0
$778$	−19.5000	+	33.7750i	−0.699109	+	1.21089i
$779$	28.0000			1.00320
$780$		0			0
$781$		0			0
$782$	−10.0000	+	17.3205i	−0.357599	+	0.619380i
$783$		0			0
$784$	−1.50000	−	2.59808i	−0.0535714	−	0.0927884i
$785$	−27.0000			−0.963671
$786$		0			0
$787$	−23.0000	−	39.8372i	−0.819861	−	1.42004i	−0.905784	−	0.423740i	$-0.860717\pi$
$787$	−23.0000	−	39.8372i	−0.819861	−	1.42004i	0.0859225	−	0.996302i	$-0.472616\pi$
$788$	6.00000			0.213741
$789$		0			0
$790$	3.00000	−	5.19615i	0.106735	−	0.184871i
$791$	1.00000	−	1.73205i	0.0355559	−	0.0615846i
$792$		0			0
$793$	1.00000	−	3.46410i	0.0355110	−	0.123014i
$794$	14.0000			0.496841
$795$		0			0
$796$	13.0000	−	22.5167i	0.460773	−	0.798082i
$797$	19.0000	+	32.9090i	0.673015	+	1.16570i	0.977045	+	0.213033i	$0.0683342\pi$
$797$	19.0000	+	32.9090i	0.673015	+	1.16570i	−0.304030	+	0.952662i	$0.598332\pi$
$798$		0			0
$799$	15.0000	+	25.9808i	0.530662	+	0.919133i
$800$	−10.0000	−	17.3205i	−0.353553	−	0.612372i
$801$	18.0000			0.635999
$802$	15.5000	+	26.8468i	0.547324	+	0.947993i
$803$		0			0
$804$		0			0
$805$	−24.0000			−0.845889
$806$	−3.50000	+	0.866025i	−0.123282	+	0.0305044i
$807$		0			0
$808$	−10.5000	+	18.1865i	−0.369389	+	0.639800i
$809$	17.5000	−	30.3109i	0.615267	−	1.06567i	−0.375070	−	0.926996i	$-0.622381\pi$
$809$	17.5000	−	30.3109i	0.615267	−	1.06567i	0.990338	−	0.138678i	$-0.0442852\pi$
$810$	13.5000	+	23.3827i	0.474342	+	0.821584i
$811$	54.0000			1.89620			0.948098	−	0.317978i	$-0.103004\pi$
$811$	54.0000			1.89620			0.948098	+	0.317978i	$0.103004\pi$
$812$	3.00000	+	5.19615i	0.105279	+	0.182349i
$813$		0			0
$814$		0			0
$815$	9.00000	+	15.5885i	0.315256	+	0.546040i
$816$		0			0
$817$	4.00000	−	6.92820i	0.139942	−	0.242387i
$818$	−31.0000			−1.08389
$819$	−21.0000	+	5.19615i	−0.733799	+	0.181568i
$820$	21.0000			0.733352
$821$	15.0000	−	25.9808i	0.523504	−	0.906735i	−0.476122	−	0.879379i	$-0.657958\pi$
$821$	15.0000	−	25.9808i	0.523504	−	0.906735i	0.999626	−	0.0273557i	$-0.00870868\pi$
$822$		0			0
$823$	7.00000	+	12.1244i	0.244005	+	0.422628i	0.961851	−	0.273573i	$-0.0882054\pi$
$823$	7.00000	+	12.1244i	0.244005	+	0.422628i	−0.717847	+	0.696201i	$0.754872\pi$
$824$		0			0
$825$		0			0
$826$	6.00000	+	10.3923i	0.208767	+	0.361595i
$827$	24.0000			0.834562			0.417281	−	0.908778i	$-0.362983\pi$
$827$	24.0000			0.834562			0.417281	+	0.908778i	$0.362983\pi$
$828$	−6.00000	−	10.3923i	−0.208514	−	0.361158i
$829$	−9.50000	+	16.4545i	−0.329949	+	0.571488i	−0.982501	−	0.186256i	$-0.940365\pi$
$829$	−9.50000	+	16.4545i	−0.329949	+	0.571488i	0.652553	+	0.757743i	$0.273698\pi$
$830$	−3.00000	+	5.19615i	−0.104132	+	0.180361i
$831$		0			0
$832$	−17.5000	−	18.1865i	−0.606703	−	0.630505i
$833$	−15.0000			−0.519719
$834$		0			0
$835$	−33.0000	+	57.1577i	−1.14201	+	1.97802i
$836$		0			0
$837$		0			0
$838$	18.0000	+	31.1769i	0.621800	+	1.07699i
$839$	15.0000	+	25.9808i	0.517858	+	0.896956i	0.999785	+	0.0207443i	$0.00660359\pi$
$839$	15.0000	+	25.9808i	0.517858	+	0.896956i	−0.481927	+	0.876211i	$0.660063\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	−0.500000	+	0.866025i	−0.0172311	+	0.0298452i
$843$		0			0
$844$	10.0000			0.344214
$845$	1.50000	−	38.9711i	0.0516016	−	1.34065i
$846$	18.0000			0.618853
$847$	11.0000	−	19.0526i	0.377964	−	0.654654i
$848$	−4.50000	+	7.79423i	−0.154531	+	0.267655i
$849$		0			0
$850$	20.0000			0.685994
$851$	10.0000	+	17.3205i	0.342796	+	0.593739i
$852$		0			0
$853$	−7.00000			−0.239675			−0.119838	−	0.992793i	$-0.538237\pi$
$853$	−7.00000			−0.239675			−0.119838	+	0.992793i	$0.538237\pi$
$854$	1.00000	+	1.73205i	0.0342193	+	0.0592696i
$855$	−18.0000	+	31.1769i	−0.615587	+	1.06623i
$856$	15.0000	−	25.9808i	0.512689	−	0.888004i
$857$	−21.0000			−0.717346			−0.358673	−	0.933463i	$-0.616771\pi$
$857$	−21.0000			−0.717346			−0.358673	+	0.933463i	$0.616771\pi$
$858$		0			0
$859$	50.0000			1.70598			0.852989	−	0.521929i	$-0.174787\pi$
$859$	50.0000			1.70598			0.852989	+	0.521929i	$0.174787\pi$
$860$	3.00000	−	5.19615i	0.102299	−	0.177187i
$861$		0			0
$862$	−6.00000	−	10.3923i	−0.204361	−	0.353963i
$863$	48.0000			1.63394			0.816970	−	0.576681i	$-0.195652\pi$
$863$	48.0000			1.63394			0.816970	+	0.576681i	$0.195652\pi$
$864$		0			0
$865$	21.0000	+	36.3731i	0.714021	+	1.23672i
$866$	−11.0000			−0.373795
$867$		0			0
$868$	−1.00000	+	1.73205i	−0.0339422	+	0.0587896i
$869$		0			0
$870$		0			0
$871$	35.0000	−	8.66025i	1.18593	−	0.293442i
$872$	30.0000			1.01593
$873$	−27.0000	+	46.7654i	−0.913812	+	1.58277i
$874$	−8.00000	+	13.8564i	−0.270604	+	0.468700i
$875$	−3.00000	−	5.19615i	−0.101419	−	0.175662i
$876$		0			0
$877$	15.5000	+	26.8468i	0.523398	+	0.906552i	0.999629	+	0.0272316i	$0.00866915\pi$
$877$	15.5000	+	26.8468i	0.523398	+	0.906552i	−0.476231	+	0.879320i	$0.657998\pi$
$878$	5.00000	+	8.66025i	0.168742	+	0.292269i
$879$		0			0
$880$		0			0
$881$	13.5000	−	23.3827i	0.454827	−	0.787783i	−0.543852	−	0.839181i	$-0.683035\pi$
$881$	13.5000	−	23.3827i	0.454827	−	0.787783i	0.998678	+	0.0513987i	$0.0163679\pi$
$882$	−4.50000	+	7.79423i	−0.151523	+	0.262445i
$883$	−50.0000			−1.68263			−0.841317	−	0.540542i	$-0.818219\pi$
$883$	−50.0000			−1.68263			−0.841317	+	0.540542i	$0.818219\pi$
$884$	−17.5000	+	4.33013i	−0.588589	+	0.145638i
$885$		0			0
$886$	11.0000	−	19.0526i	0.369552	−	0.640083i
$887$	10.0000	−	17.3205i	0.335767	−	0.581566i	−0.647865	−	0.761755i	$-0.724338\pi$
$887$	10.0000	−	17.3205i	0.335767	−	0.581566i	0.983632	+	0.180190i	$0.0576711\pi$
$888$		0			0
$889$	4.00000			0.134156
$890$	−9.00000	−	15.5885i	−0.301681	−	0.522526i
$891$		0			0
$892$	−14.0000			−0.468755
$893$	12.0000	+	20.7846i	0.401565	+	0.695530i
$894$		0			0
$895$	−30.0000	+	51.9615i	−1.00279	+	1.73688i
$896$	−6.00000			−0.200446
$897$		0			0
$898$	14.0000			0.467186
$899$	1.50000	−	2.59808i	0.0500278	−	0.0866507i
$900$	−6.00000	+	10.3923i	−0.200000	+	0.346410i
$901$	22.5000	+	38.9711i	0.749584	+	1.29832i
$902$		0			0
$903$		0			0
$904$	−1.50000	−	2.59808i	−0.0498893	−	0.0864107i
$905$	3.00000			0.0997234
$906$		0			0
$907$	14.0000	−	24.2487i	0.464862	−	0.805165i	−0.534333	−	0.845274i	$-0.679437\pi$
$907$	14.0000	−	24.2487i	0.464862	−	0.805165i	0.999195	+	0.0401089i	$0.0127705\pi$
$908$	6.00000	−	10.3923i	0.199117	−	0.344881i
$909$	21.0000			0.696526
$910$	15.0000	+	15.5885i	0.497245	+	0.516752i
$911$	20.0000			0.662630			0.331315	−	0.943520i	$-0.392508\pi$
$911$	20.0000			0.662630			0.331315	+	0.943520i	$0.392508\pi$
$912$		0			0
$913$		0			0
$914$	−2.50000	−	4.33013i	−0.0826927	−	0.143228i
$915$		0			0
$916$	1.00000	+	1.73205i	0.0330409	+	0.0572286i
$917$	20.0000	+	34.6410i	0.660458	+	1.14395i
$918$		0			0
$919$	−19.0000	−	32.9090i	−0.626752	−	1.08557i	−0.988199	−	0.153174i	$-0.951051\pi$
$919$	−19.0000	−	32.9090i	−0.626752	−	1.08557i	0.361447	−	0.932393i	$-0.382283\pi$
$920$	−18.0000	+	31.1769i	−0.593442	+	1.02787i
$921$		0			0
$922$	−33.0000			−1.08680
$923$	4.00000	−	13.8564i	0.131662	−	0.456089i
$924$		0			0
$925$	10.0000	−	17.3205i	0.328798	−	0.569495i
$926$	21.0000	−	36.3731i	0.690103	−	1.19529i
$927$		0			0
$928$	15.0000			0.492399
$929$	−22.5000	−	38.9711i	−0.738201	−	1.27860i	−0.953305	−	0.302010i	$-0.902342\pi$
$929$	−22.5000	−	38.9711i	−0.738201	−	1.27860i	0.215104	−	0.976591i	$-0.430991\pi$
$930$		0			0
$931$	−12.0000			−0.393284
$932$	7.00000	+	12.1244i	0.229293	+	0.397146i
$933$		0			0
$934$	6.00000	−	10.3923i	0.196326	−	0.340047i
$935$		0			0
$936$	−9.00000	+	31.1769i	−0.294174	+	1.01905i
$937$	−29.0000			−0.947389			−0.473694	−	0.880689i	$-0.657080\pi$
$937$	−29.0000			−0.947389			−0.473694	+	0.880689i	$0.657080\pi$
$938$	−10.0000	+	17.3205i	−0.326512	+	0.565535i
$939$		0			0
$940$	9.00000	+	15.5885i	0.293548	+	0.508439i
$941$	−18.0000			−0.586783			−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000			−0.586783			−0.293392	+	0.955992i	$0.594784\pi$
$942$		0			0
$943$	−14.0000	−	24.2487i	−0.455903	−	0.789647i
$944$	6.00000			0.195283
$945$		0			0
$946$		0			0
$947$	−16.0000	+	27.7128i	−0.519930	+	0.900545i	0.479801	+	0.877377i	$0.340709\pi$
$947$	−16.0000	+	27.7128i	−0.519930	+	0.900545i	−0.999732	+	0.0231683i	$0.992625\pi$
$948$		0			0
$949$	7.50000	+	7.79423i	0.243460	+	0.253011i
$950$	16.0000			0.519109
$951$		0			0
$952$	15.0000	−	25.9808i	0.486153	−	0.842041i
$953$	−9.00000	−	15.5885i	−0.291539	−	0.504960i	0.682635	−	0.730759i	$-0.260834\pi$
$953$	−9.00000	−	15.5885i	−0.291539	−	0.504960i	−0.974174	+	0.225800i	$0.927501\pi$
$954$	27.0000			0.874157
$955$	−12.0000	−	20.7846i	−0.388311	−	0.672574i
$956$	−3.00000	−	5.19615i	−0.0970269	−	0.168056i
$957$		0			0
$958$	12.0000	+	20.7846i	0.387702	+	0.671520i
$959$	7.00000	−	12.1244i	0.226042	−	0.391516i
$960$		0			0
$961$	1.00000			0.0322581
$962$	5.00000	−	17.3205i	0.161206	−	0.558436i
$963$	−30.0000			−0.966736
$964$	−9.50000	+	16.4545i	−0.305974	+	0.529963i
$965$	−37.5000	+	64.9519i	−1.20717	+	2.09088i
$966$		0			0
$967$	−18.0000			−0.578841			−0.289420	−	0.957202i	$-0.593463\pi$
$967$	−18.0000			−0.578841			−0.289420	+	0.957202i	$0.593463\pi$
$968$	−16.5000	−	28.5788i	−0.530330	−	0.918559i
$969$		0			0
$970$	54.0000			1.73384
$971$	−11.0000	−	19.0526i	−0.353007	−	0.611426i	0.633768	−	0.773523i	$-0.281507\pi$
$971$	−11.0000	−	19.0526i	−0.353007	−	0.611426i	−0.986775	+	0.162098i	$0.948174\pi$
$972$		0			0
$973$	−10.0000	+	17.3205i	−0.320585	+	0.555270i
$974$	−26.0000			−0.833094
$975$		0			0
$976$	1.00000			0.0320092
$977$	28.5000	−	49.3634i	0.911796	−	1.57928i	0.100270	−	0.994960i	$-0.468029\pi$
$977$	28.5000	−	49.3634i	0.911796	−	1.57928i	0.811526	−	0.584316i	$-0.198637\pi$
$978$		0			0
$979$		0			0
$980$	−9.00000			−0.287494
$981$	−15.0000	−	25.9808i	−0.478913	−	0.829502i
$982$	−12.0000	−	20.7846i	−0.382935	−	0.663264i
$983$	−36.0000			−1.14822			−0.574111	−	0.818778i	$-0.694652\pi$
$983$	−36.0000			−1.14822			−0.574111	+	0.818778i	$0.694652\pi$
$984$		0			0
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$	−7.50000	+	12.9904i	−0.238849	+	0.413698i
$987$		0			0
$988$	−14.0000	+	3.46410i	−0.445399	+	0.110208i
$989$	−8.00000			−0.254385
$990$		0			0
$991$	−10.0000	+	17.3205i	−0.317660	+	0.550204i	−0.979999	−	0.199000i	$-0.936231\pi$
$991$	−10.0000	+	17.3205i	−0.317660	+	0.550204i	0.662339	+	0.749204i	$0.269564\pi$
$992$	2.50000	+	4.33013i	0.0793751	+	0.137482i
$993$		0			0
$994$	4.00000	+	6.92820i	0.126872	+	0.219749i
$995$	39.0000	+	67.5500i	1.23638	+	2.14148i
$996$		0			0
$997$	−20.5000	−	35.5070i	−0.649242	−	1.12452i	−0.983304	−	0.181968i	$-0.941753\pi$
$997$	−20.5000	−	35.5070i	−0.649242	−	1.12452i	0.334063	−	0.942551i	$-0.391580\pi$
$998$	3.00000	−	5.19615i	0.0949633	−	0.164481i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.f.a.373.1	yes	2
13.3	even	3	inner	403.2.f.a.94.1	✓	2
13.4	even	6		5239.2.a.a.1.1		1
13.9	even	3		5239.2.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.f.a.94.1	✓	2	13.3	even	3	inner
403.2.f.a.373.1	yes	2	1.1	even	1	trivial
5239.2.a.a.1.1		1	13.4	even	6
5239.2.a.d.1.1		1	13.9	even	3

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(-1.00000 - 1.73205i) q^{7} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(-1.00000 - 1.73205i) q^{7} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(1.50000 - 2.59808i) q^{10} +(-2.50000 - 2.59808i) q^{13} +2.00000 q^{14} +(0.500000 - 0.866025i) q^{16} +(-2.50000 - 4.33013i) q^{17} -3.00000 q^{18} +(-2.00000 - 3.46410i) q^{19} +(-1.50000 - 2.59808i) q^{20} +(-2.00000 + 3.46410i) q^{23} +4.00000 q^{25} +(3.50000 - 0.866025i) q^{26} +(1.00000 - 1.73205i) q^{28} +(-1.50000 + 2.59808i) q^{29} -1.00000 q^{31} +(-2.50000 - 4.33013i) q^{32} +5.00000 q^{34} +(3.00000 + 5.19615i) q^{35} +(-1.50000 + 2.59808i) q^{36} +(2.50000 - 4.33013i) q^{37} +4.00000 q^{38} +9.00000 q^{40} +(-3.50000 + 6.06218i) q^{41} +(1.00000 + 1.73205i) q^{43} +(-4.50000 - 7.79423i) q^{45} +(-2.00000 - 3.46410i) q^{46} -6.00000 q^{47} +(1.50000 - 2.59808i) q^{49} +(-2.00000 + 3.46410i) q^{50} +(1.00000 - 3.46410i) q^{52} -9.00000 q^{53} +(3.00000 + 5.19615i) q^{56} +(-1.50000 - 2.59808i) q^{58} +(3.00000 + 5.19615i) q^{59} +(0.500000 + 0.866025i) q^{61} +(0.500000 - 0.866025i) q^{62} +(3.00000 - 5.19615i) q^{63} +7.00000 q^{64} +(7.50000 + 7.79423i) q^{65} +(-5.00000 + 8.66025i) q^{67} +(2.50000 - 4.33013i) q^{68} -6.00000 q^{70} +(2.00000 + 3.46410i) q^{71} +(-4.50000 - 7.79423i) q^{72} -3.00000 q^{73} +(2.50000 + 4.33013i) q^{74} +(2.00000 - 3.46410i) q^{76} +2.00000 q^{79} +(-1.50000 + 2.59808i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-3.50000 - 6.06218i) q^{82} -2.00000 q^{83} +(7.50000 + 12.9904i) q^{85} -2.00000 q^{86} +(3.00000 - 5.19615i) q^{89} +9.00000 q^{90} +(-2.00000 + 6.92820i) q^{91} -4.00000 q^{92} +(3.00000 - 5.19615i) q^{94} +(6.00000 + 10.3923i) q^{95} +(9.00000 + 15.5885i) q^{97} +(1.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{4} - 6 q^{5} - 2 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - q^2 + q^4 - 6 * q^5 - 2 * q^7 - 6 * q^8 + 3 * q^9	\( 2 q - q^{2} + q^{4} - 6 q^{5} - 2 q^{7} - 6 q^{8} + 3 q^{9} + 3 q^{10} - 5 q^{13} + 4 q^{14} + q^{16} - 5 q^{17} - 6 q^{18} - 4 q^{19} - 3 q^{20} - 4 q^{23} + 8 q^{25} + 7 q^{26} + 2 q^{28} - 3 q^{29} - 2 q^{31} - 5 q^{32} + 10 q^{34} + 6 q^{35} - 3 q^{36} + 5 q^{37} + 8 q^{38} + 18 q^{40} - 7 q^{41} + 2 q^{43} - 9 q^{45} - 4 q^{46} - 12 q^{47} + 3 q^{49} - 4 q^{50} + 2 q^{52} - 18 q^{53} + 6 q^{56} - 3 q^{58} + 6 q^{59} + q^{61} + q^{62} + 6 q^{63} + 14 q^{64} + 15 q^{65} - 10 q^{67} + 5 q^{68} - 12 q^{70} + 4 q^{71} - 9 q^{72} - 6 q^{73} + 5 q^{74} + 4 q^{76} + 4 q^{79} - 3 q^{80} - 9 q^{81} - 7 q^{82} - 4 q^{83} + 15 q^{85} - 4 q^{86} + 6 q^{89} + 18 q^{90} - 4 q^{91} - 8 q^{92} + 6 q^{94} + 12 q^{95} + 18 q^{97} + 3 q^{98}+O(q^{100}) \) 2 * q - q^2 + q^4 - 6 * q^5 - 2 * q^7 - 6 * q^8 + 3 * q^9 + 3 * q^10 - 5 * q^13 + 4 * q^14 + q^16 - 5 * q^17 - 6 * q^18 - 4 * q^19 - 3 * q^20 - 4 * q^23 + 8 * q^25 + 7 * q^26 + 2 * q^28 - 3 * q^29 - 2 * q^31 - 5 * q^32 + 10 * q^34 + 6 * q^35 - 3 * q^36 + 5 * q^37 + 8 * q^38 + 18 * q^40 - 7 * q^41 + 2 * q^43 - 9 * q^45 - 4 * q^46 - 12 * q^47 + 3 * q^49 - 4 * q^50 + 2 * q^52 - 18 * q^53 + 6 * q^56 - 3 * q^58 + 6 * q^59 + q^61 + q^62 + 6 * q^63 + 14 * q^64 + 15 * q^65 - 10 * q^67 + 5 * q^68 - 12 * q^70 + 4 * q^71 - 9 * q^72 - 6 * q^73 + 5 * q^74 + 4 * q^76 + 4 * q^79 - 3 * q^80 - 9 * q^81 - 7 * q^82 - 4 * q^83 + 15 * q^85 - 4 * q^86 + 6 * q^89 + 18 * q^90 - 4 * q^91 - 8 * q^92 + 6 * q^94 + 12 * q^95 + 18 * q^97 + 3 * q^98

Introduction

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