LMFDB - Embedded newform 1078.2.e.k.177.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(67,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("1078.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.e (of order $3$, degree $2$, not 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:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1078.177
Dual form			1078.2.e.k.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{6} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} +1.00000 q^{13} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-1.00000 - 1.73205i) q^{18} +(1.00000 - 1.73205i) q^{19} +1.00000 q^{22} +(3.00000 - 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{25} +(0.500000 - 0.866025i) q^{26} +5.00000 q^{27} +9.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} -6.00000 q^{34} -2.00000 q^{36} +(-1.00000 + 1.73205i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(0.500000 + 0.866025i) q^{39} +6.00000 q^{41} -4.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-3.00000 - 5.19615i) q^{46} +(-3.00000 + 5.19615i) q^{47} -1.00000 q^{48} +5.00000 q^{50} +(3.00000 - 5.19615i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(2.50000 - 4.33013i) q^{54} +2.00000 q^{57} +(4.50000 - 7.79423i) q^{58} +(-1.50000 - 2.59808i) q^{59} +(5.50000 - 9.52628i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{66} +(-5.50000 - 9.52628i) q^{67} +(-3.00000 + 5.19615i) q^{68} +6.00000 q^{69} +(-1.00000 + 1.73205i) q^{72} +(1.00000 + 1.73205i) q^{73} +(1.00000 + 1.73205i) q^{74} +(-2.50000 + 4.33013i) q^{75} -2.00000 q^{76} +1.00000 q^{78} +(-2.50000 + 4.33013i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} +6.00000 q^{83} +(-2.00000 + 3.46410i) q^{86} +(4.50000 + 7.79423i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-9.00000 + 15.5885i) q^{89} -6.00000 q^{92} +(2.00000 - 3.46410i) q^{93} +(3.00000 + 5.19615i) q^{94} +(-0.500000 + 0.866025i) q^{96} +13.0000 q^{97} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} - q^{4} + 2 q^{6} - 2 q^{8} + 2 q^{9} + q^{11} + q^{12} + 2 q^{13} - q^{16} - 6 q^{17} - 2 q^{18} + 2 q^{19} + 2 q^{22} + 6 q^{23} - q^{24} + 5 q^{25} + q^{26} + 10 q^{27} + 18 q^{29}+ \cdots + 4 q^{99}+O(q^{100}) $ 2 * q + q^2 + q^3 - q^4 + 2 * q^6 - 2 * q^8 + 2 * q^9 + q^11 + q^12 + 2 * q^13 - q^16 - 6 * q^17 - 2 * q^18 + 2 * q^19 + 2 * q^22 + 6 * q^23 - q^24 + 5 * q^25 + q^26 + 10 * q^27 + 18 * q^29 - 4 * q^31 + q^32 - q^33 - 12 * q^34 - 4 * q^36 - 2 * q^37 - 2 * q^38 + q^39 + 12 * q^41 - 8 * q^43 + q^44 - 6 * q^46 - 6 * q^47 - 2 * q^48 + 10 * q^50 + 6 * q^51 - q^52 + 5 * q^54 + 4 * q^57 + 9 * q^58 - 3 * q^59 + 11 * q^61 - 8 * q^62 + 2 * q^64 + q^66 - 11 * q^67 - 6 * q^68 + 12 * q^69 - 2 * q^72 + 2 * q^73 + 2 * q^74 - 5 * q^75 - 4 * q^76 + 2 * q^78 - 5 * q^79 - q^81 + 6 * q^82 + 12 * q^83 - 4 * q^86 + 9 * q^87 - q^88 - 18 * q^89 - 12 * q^92 + 4 * q^93 + 6 * q^94 - q^96 + 26 * q^97 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	0.973494	−	0.228714i	$-0.0734519\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	−0.684819	+	0.728714i	$0.740119\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$5$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	1.00000			0.277350			0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000			0.277350			0.138675	+	0.990338i	$0.455716\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$	−1.00000	−	1.73205i	−0.235702	−	0.408248i
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929851\pi$
$20$		0			0
$21$		0			0
$22$	1.00000			0.213201
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	2.50000	+	4.33013i	0.500000	+	0.866025i
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$	5.00000			0.962250
$28$		0			0
$29$	9.00000			1.67126			0.835629	−	0.549294i	$-0.185103\pi$
$29$	9.00000			1.67126			0.835629	+	0.549294i	$0.185103\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$	−6.00000			−1.02899
$35$		0			0
$36$	−2.00000			−0.333333
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$	−1.00000	−	1.73205i	−0.162221	−	0.280976i
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$		0			0
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$		0			0
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	−0.997503	−	0.0706177i	$-0.977503\pi$
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	0.559908	+	0.828554i	$0.310836\pi$
$48$	−1.00000			−0.144338
$49$		0			0
$50$	5.00000			0.707107
$51$	3.00000	−	5.19615i	0.420084	−	0.727607i
$52$	−0.500000	−	0.866025i	−0.0693375	−	0.120096i
$53$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$53$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$54$	2.50000	−	4.33013i	0.340207	−	0.589256i
$55$		0			0
$56$		0			0
$57$	2.00000			0.264906
$58$	4.50000	−	7.79423i	0.590879	−	1.02343i
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	0.751710	−	0.659494i	$-0.229229\pi$
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	−0.946993	+	0.321253i	$0.895896\pi$
$60$		0			0
$61$	5.50000	−	9.52628i	0.704203	−	1.21972i	−0.262776	−	0.964857i	$-0.584638\pi$
$61$	5.50000	−	9.52628i	0.704203	−	1.21972i	0.966978	−	0.254858i	$-0.0820288\pi$
$62$	−4.00000			−0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$	0.500000	+	0.866025i	0.0615457	+	0.106600i
$67$	−5.50000	−	9.52628i	−0.671932	−	1.16382i	−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−5.50000	−	9.52628i	−0.671932	−	1.16382i	0.305424	−	0.952217i	$-0.401202\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$	6.00000			0.722315
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	−1.00000	+	1.73205i	−0.117851	+	0.204124i
$73$	1.00000	+	1.73205i	0.117041	+	0.202721i	0.918594	−	0.395203i	$-0.129326\pi$
$73$	1.00000	+	1.73205i	0.117041	+	0.202721i	−0.801553	+	0.597924i	$0.795992\pi$
$74$	1.00000	+	1.73205i	0.116248	+	0.201347i
$75$	−2.50000	+	4.33013i	−0.288675	+	0.500000i
$76$	−2.00000			−0.229416
$77$		0			0
$78$	1.00000			0.113228
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	−0.971698	−	0.236225i	$-0.924090\pi$
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	0.690426	+	0.723403i	$0.257423\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.00000	−	5.19615i	0.331295	−	0.573819i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$		0			0
$85$		0			0
$86$	−2.00000	+	3.46410i	−0.215666	+	0.373544i
$87$	4.50000	+	7.79423i	0.482451	+	0.835629i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	−9.00000	+	15.5885i	−0.953998	+	1.65237i	−0.217354	+	0.976093i	$0.569742\pi$
$89$	−9.00000	+	15.5885i	−0.953998	+	1.65237i	−0.736644	+	0.676280i	$0.763591\pi$
$90$		0			0
$91$		0			0
$92$	−6.00000			−0.625543
$93$	2.00000	−	3.46410i	0.207390	−	0.359211i
$94$	3.00000	+	5.19615i	0.309426	+	0.535942i
$95$		0			0
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	13.0000			1.31995			0.659975	−	0.751288i	$-0.270567\pi$
$97$	13.0000			1.31995			0.659975	+	0.751288i	$0.270567\pi$
$98$		0			0
$99$	2.00000			0.201008
$100$	2.50000	−	4.33013i	0.250000	−	0.433013i
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	−0.949595	−	0.313478i	$-0.898506\pi$
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	0.203317	−	0.979113i	$-0.434828\pi$
$102$	−3.00000	−	5.19615i	−0.297044	−	0.514496i
$103$	−8.00000	+	13.8564i	−0.788263	+	1.36531i	0.138767	+	0.990325i	$0.455686\pi$
$103$	−8.00000	+	13.8564i	−0.788263	+	1.36531i	−0.927030	+	0.374987i	$0.877647\pi$
$104$	−1.00000			−0.0980581
$105$		0			0
$106$		0			0
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$	−2.50000	−	4.33013i	−0.240563	−	0.416667i
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	0.814152	−	0.580651i	$-0.197202\pi$
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	−0.909935	+	0.414751i	$0.863869\pi$
$110$		0			0
$111$	−2.00000			−0.189832
$112$		0			0
$113$	9.00000			0.846649			0.423324	−	0.905978i	$-0.360863\pi$
$113$	9.00000			0.846649			0.423324	+	0.905978i	$0.360863\pi$
$114$	1.00000	−	1.73205i	0.0936586	−	0.162221i
$115$		0			0
$116$	−4.50000	−	7.79423i	−0.417815	−	0.723676i
$117$	1.00000	−	1.73205i	0.0924500	−	0.160128i
$118$	−3.00000			−0.276172
$119$		0			0
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−5.50000	−	9.52628i	−0.497947	−	0.862469i
$123$	3.00000	+	5.19615i	0.270501	+	0.468521i
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$		0			0
$126$		0			0
$127$	−7.00000			−0.621150			−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000			−0.621150			−0.310575	+	0.950549i	$0.600522\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−2.00000	−	3.46410i	−0.176090	−	0.304997i
$130$		0			0
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	−0.141865	−	0.989886i	$-0.545310\pi$
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	0.928199	−	0.372084i	$-0.121357\pi$
$132$	1.00000			0.0870388
$133$		0			0
$134$	−11.0000			−0.950255
$135$		0			0
$136$	3.00000	+	5.19615i	0.257248	+	0.445566i
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	0.991694	−	0.128618i	$-0.0410540\pi$
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	−0.607233	+	0.794524i	$0.707721\pi$
$138$	3.00000	−	5.19615i	0.255377	−	0.442326i
$139$	−8.00000			−0.678551			−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000			−0.678551			−0.339276	+	0.940687i	$0.610182\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$		0			0
$143$	0.500000	+	0.866025i	0.0418121	+	0.0724207i
$144$	1.00000	+	1.73205i	0.0833333	+	0.144338i
$145$		0			0
$146$	2.00000			0.165521
$147$		0			0
$148$	2.00000			0.164399
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$	2.50000	+	4.33013i	0.204124	+	0.353553i
$151$	9.50000	+	16.4545i	0.773099	+	1.33905i	0.935857	+	0.352381i	$0.114628\pi$
$151$	9.50000	+	16.4545i	0.773099	+	1.33905i	−0.162758	+	0.986666i	$0.552039\pi$
$152$	−1.00000	+	1.73205i	−0.0811107	+	0.140488i
$153$	−12.0000			−0.970143
$154$		0			0
$155$		0			0
$156$	0.500000	−	0.866025i	0.0400320	−	0.0693375i
$157$	−2.00000	−	3.46410i	−0.159617	−	0.276465i	0.775113	−	0.631822i	$-0.217693\pi$
$157$	−2.00000	−	3.46410i	−0.159617	−	0.276465i	−0.934731	+	0.355357i	$0.884359\pi$
$158$	2.50000	+	4.33013i	0.198889	+	0.344486i
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	−8.50000	+	14.7224i	−0.665771	+	1.15315i	0.313304	+	0.949653i	$0.398564\pi$
$163$	−8.50000	+	14.7224i	−0.665771	+	1.15315i	−0.979076	+	0.203497i	$0.934769\pi$
$164$	−3.00000	−	5.19615i	−0.234261	−	0.405751i
$165$		0			0
$166$	3.00000	−	5.19615i	0.232845	−	0.403300i
$167$	−3.00000			−0.232147			−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000			−0.232147			−0.116073	+	0.993241i	$0.537031\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$		0			0
$171$	−2.00000	−	3.46410i	−0.152944	−	0.264906i
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	−10.5000	+	18.1865i	−0.798300	+	1.38270i	0.122422	+	0.992478i	$0.460934\pi$
$173$	−10.5000	+	18.1865i	−0.798300	+	1.38270i	−0.920722	+	0.390218i	$0.872399\pi$
$174$	9.00000			0.682288
$175$		0			0
$176$	−1.00000			−0.0753778
$177$	1.50000	−	2.59808i	0.112747	−	0.195283i
$178$	9.00000	+	15.5885i	0.674579	+	1.16840i
$179$	7.50000	+	12.9904i	0.560576	+	0.970947i	0.997446	+	0.0714220i	$0.0227537\pi$
$179$	7.50000	+	12.9904i	0.560576	+	0.970947i	−0.436870	+	0.899525i	$0.643913\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$	11.0000			0.813143
$184$	−3.00000	+	5.19615i	−0.221163	+	0.383065i
$185$		0			0
$186$	−2.00000	−	3.46410i	−0.146647	−	0.254000i
$187$	3.00000	−	5.19615i	0.219382	−	0.379980i
$188$	6.00000			0.437595
$189$		0			0
$190$		0			0
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	−0.953912	−	0.300088i	$-0.902984\pi$
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	0.736839	+	0.676068i	$0.236317\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	−0.999990	−	0.00447566i	$-0.998575\pi$
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	0.496119	−	0.868255i	$-0.334758\pi$
$194$	6.50000	−	11.2583i	0.466673	−	0.808301i
$195$		0			0
$196$		0			0
$197$	−3.00000			−0.213741			−0.106871	−	0.994273i	$-0.534083\pi$
$197$	−3.00000			−0.213741			−0.106871	+	0.994273i	$0.534083\pi$
$198$	1.00000	−	1.73205i	0.0710669	−	0.123091i
$199$	7.00000	+	12.1244i	0.496217	+	0.859473i	0.999990	−	0.00436292i	$-0.00138876\pi$
$199$	7.00000	+	12.1244i	0.496217	+	0.859473i	−0.503774	+	0.863836i	$0.668055\pi$
$200$	−2.50000	−	4.33013i	−0.176777	−	0.306186i
$201$	5.50000	−	9.52628i	0.387940	−	0.671932i
$202$	−15.0000			−1.05540
$203$		0			0
$204$	−6.00000			−0.420084
$205$		0			0
$206$	8.00000	+	13.8564i	0.557386	+	0.965422i
$207$	−6.00000	−	10.3923i	−0.417029	−	0.722315i
$208$	−0.500000	+	0.866025i	−0.0346688	+	0.0600481i
$209$	2.00000			0.138343
$210$		0			0
$211$	−10.0000			−0.688428			−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000			−0.688428			−0.344214	+	0.938891i	$0.611855\pi$
$212$		0			0
$213$		0			0
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$		0			0
$216$	−5.00000			−0.340207
$217$		0			0
$218$	−2.00000			−0.135457
$219$	−1.00000	+	1.73205i	−0.0675737	+	0.117041i
$220$		0			0
$221$	−3.00000	−	5.19615i	−0.201802	−	0.349531i
$222$	−1.00000	+	1.73205i	−0.0671156	+	0.116248i
$223$	−26.0000			−1.74109			−0.870544	−	0.492090i	$-0.836233\pi$
$223$	−26.0000			−1.74109			−0.870544	+	0.492090i	$0.836233\pi$
$224$		0			0
$225$	10.0000			0.666667
$226$	4.50000	−	7.79423i	0.299336	−	0.518464i
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	0.993210	+	0.116331i	$0.0371134\pi$
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	−0.395860	+	0.918311i	$0.629553\pi$
$228$	−1.00000	−	1.73205i	−0.0662266	−	0.114708i
$229$	−8.00000	+	13.8564i	−0.528655	+	0.915657i	0.470787	+	0.882247i	$0.343970\pi$
$229$	−8.00000	+	13.8564i	−0.528655	+	0.915657i	−0.999442	+	0.0334101i	$0.989363\pi$
$230$		0			0
$231$		0			0
$232$	−9.00000			−0.590879
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	−0.750867	−	0.660454i	$-0.770364\pi$
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	0.947403	+	0.320043i	$0.103697\pi$
$234$	−1.00000	−	1.73205i	−0.0653720	−	0.113228i
$235$		0			0
$236$	−1.50000	+	2.59808i	−0.0976417	+	0.169120i
$237$	−5.00000			−0.324785
$238$		0			0
$239$	−9.00000			−0.582162			−0.291081	−	0.956698i	$-0.594015\pi$
$239$	−9.00000			−0.582162			−0.291081	+	0.956698i	$0.594015\pi$
$240$		0			0
$241$	13.0000	+	22.5167i	0.837404	+	1.45043i	0.892058	+	0.451920i	$0.149261\pi$
$241$	13.0000	+	22.5167i	0.837404	+	1.45043i	−0.0546547	+	0.998505i	$0.517406\pi$
$242$	0.500000	+	0.866025i	0.0321412	+	0.0556702i
$243$	8.00000	−	13.8564i	0.513200	−	0.888889i
$244$	−11.0000			−0.704203
$245$		0			0
$246$	6.00000			0.382546
$247$	1.00000	−	1.73205i	0.0636285	−	0.110208i
$248$	2.00000	+	3.46410i	0.127000	+	0.219971i
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$		0			0
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$	6.00000			0.377217
$254$	−3.50000	+	6.06218i	−0.219610	+	0.380375i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.50000	−	2.59808i	0.0935674	−	0.162064i	−0.815442	−	0.578838i	$-0.803506\pi$
$257$	1.50000	−	2.59808i	0.0935674	−	0.162064i	0.909010	+	0.416775i	$0.136840\pi$
$258$	−4.00000			−0.249029
$259$		0			0
$260$		0			0
$261$	9.00000	−	15.5885i	0.557086	−	0.964901i
$262$	−9.00000	−	15.5885i	−0.556022	−	0.963058i
$263$	4.50000	+	7.79423i	0.277482	+	0.480613i	0.970758	−	0.240059i	$-0.0771668\pi$
$263$	4.50000	+	7.79423i	0.277482	+	0.480613i	−0.693276	+	0.720672i	$0.743833\pi$
$264$	0.500000	−	0.866025i	0.0307729	−	0.0533002i
$265$		0			0
$266$		0			0
$267$	−18.0000			−1.10158
$268$	−5.50000	+	9.52628i	−0.335966	+	0.581910i
$269$	6.00000	+	10.3923i	0.365826	+	0.633630i	0.988908	−	0.148527i	$-0.0474530\pi$
$269$	6.00000	+	10.3923i	0.365826	+	0.633630i	−0.623082	+	0.782157i	$0.714120\pi$
$270$		0			0
$271$	14.5000	−	25.1147i	0.880812	−	1.52561i	0.0303728	−	0.999539i	$-0.490331\pi$
$271$	14.5000	−	25.1147i	0.880812	−	1.52561i	0.850439	−	0.526073i	$-0.176336\pi$
$272$	6.00000			0.363803
$273$		0			0
$274$	9.00000			0.543710
$275$	−2.50000	+	4.33013i	−0.150756	+	0.261116i
$276$	−3.00000	−	5.19615i	−0.180579	−	0.312772i
$277$	−14.5000	−	25.1147i	−0.871221	−	1.50900i	−0.860735	−	0.509053i	$-0.829996\pi$
$277$	−14.5000	−	25.1147i	−0.871221	−	1.50900i	−0.0104855	−	0.999945i	$-0.503338\pi$
$278$	−4.00000	+	6.92820i	−0.239904	+	0.415526i
$279$	−8.00000			−0.478947
$280$		0			0
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$	−3.00000	+	5.19615i	−0.178647	+	0.309426i
$283$	−5.00000	−	8.66025i	−0.297219	−	0.514799i	0.678280	−	0.734804i	$-0.262726\pi$
$283$	−5.00000	−	8.66025i	−0.297219	−	0.514799i	−0.975499	+	0.220005i	$0.929393\pi$
$284$		0			0
$285$		0			0
$286$	1.00000			0.0591312
$287$		0			0
$288$	2.00000			0.117851
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$	6.50000	+	11.2583i	0.381037	+	0.659975i
$292$	1.00000	−	1.73205i	0.0585206	−	0.101361i
$293$	30.0000			1.75262			0.876309	−	0.481749i	$-0.159998\pi$
$293$	30.0000			1.75262			0.876309	+	0.481749i	$0.159998\pi$
$294$		0			0
$295$		0			0
$296$	1.00000	−	1.73205i	0.0581238	−	0.100673i
$297$	2.50000	+	4.33013i	0.145065	+	0.251259i
$298$	3.00000	+	5.19615i	0.173785	+	0.301005i
$299$	3.00000	−	5.19615i	0.173494	−	0.300501i
$300$	5.00000			0.288675
$301$		0			0
$302$	19.0000			1.09333
$303$	7.50000	−	12.9904i	0.430864	−	0.746278i
$304$	1.00000	+	1.73205i	0.0573539	+	0.0993399i
$305$		0			0
$306$	−6.00000	+	10.3923i	−0.342997	+	0.594089i
$307$	−20.0000			−1.14146			−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000			−1.14146			−0.570730	+	0.821138i	$0.693340\pi$
$308$		0			0
$309$	−16.0000			−0.910208
$310$		0			0
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	0.974841	+	0.222900i	$0.0715523\pi$
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	−0.294384	+	0.955687i	$0.595114\pi$
$312$	−0.500000	−	0.866025i	−0.0283069	−	0.0490290i
$313$	8.50000	−	14.7224i	0.480448	−	0.832161i	−0.519300	−	0.854592i	$-0.673807\pi$
$313$	8.50000	−	14.7224i	0.480448	−	0.832161i	0.999748	+	0.0224310i	$0.00714060\pi$
$314$	−4.00000			−0.225733
$315$		0			0
$316$	5.00000			0.281272
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	−0.983866	−	0.178908i	$-0.942743\pi$
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	0.646872	+	0.762598i	$0.276077\pi$
$318$		0			0
$319$	4.50000	+	7.79423i	0.251952	+	0.436393i
$320$		0			0
$321$	−12.0000			−0.669775
$322$		0			0
$323$	−12.0000			−0.667698
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	2.50000	+	4.33013i	0.138675	+	0.240192i
$326$	8.50000	+	14.7224i	0.470771	+	0.815400i
$327$	1.00000	−	1.73205i	0.0553001	−	0.0957826i
$328$	−6.00000			−0.331295
$329$		0			0
$330$		0			0
$331$	−17.5000	+	30.3109i	−0.961887	+	1.66604i	−0.244131	+	0.969742i	$0.578503\pi$
$331$	−17.5000	+	30.3109i	−0.961887	+	1.66604i	−0.717756	+	0.696295i	$0.754831\pi$
$332$	−3.00000	−	5.19615i	−0.164646	−	0.285176i
$333$	2.00000	+	3.46410i	0.109599	+	0.189832i
$334$	−1.50000	+	2.59808i	−0.0820763	+	0.142160i
$335$		0			0
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$	−6.00000	+	10.3923i	−0.326357	+	0.565267i
$339$	4.50000	+	7.79423i	0.244406	+	0.423324i
$340$		0			0
$341$	2.00000	−	3.46410i	0.108306	−	0.187592i
$342$	−4.00000			−0.216295
$343$		0			0
$344$	4.00000			0.215666
$345$		0			0
$346$	10.5000	+	18.1865i	0.564483	+	0.977714i
$347$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$347$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$348$	4.50000	−	7.79423i	0.241225	−	0.417815i
$349$	−2.00000			−0.107058			−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000			−0.107058			−0.0535288	+	0.998566i	$0.517047\pi$
$350$		0			0
$351$	5.00000			0.266880
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	0.520689	−	0.853746i	$-0.325675\pi$
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	−0.999711	+	0.0240566i	$0.992342\pi$
$354$	−1.50000	−	2.59808i	−0.0797241	−	0.138086i
$355$		0			0
$356$	18.0000			0.953998
$357$		0			0
$358$	15.0000			0.792775
$359$	1.50000	−	2.59808i	0.0791670	−	0.137121i	−0.823724	−	0.566991i	$-0.808107\pi$
$359$	1.50000	−	2.59808i	0.0791670	−	0.137121i	0.902891	+	0.429870i	$0.141441\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−1.00000	+	1.73205i	−0.0525588	+	0.0910346i
$363$	−1.00000			−0.0524864
$364$		0			0
$365$		0			0
$366$	5.50000	−	9.52628i	0.287490	−	0.497947i
$367$	−5.00000	−	8.66025i	−0.260998	−	0.452062i	0.705509	−	0.708700i	$-0.250718\pi$
$367$	−5.00000	−	8.66025i	−0.260998	−	0.452062i	−0.966507	+	0.256639i	$0.917385\pi$
$368$	3.00000	+	5.19615i	0.156386	+	0.270868i
$369$	6.00000	−	10.3923i	0.312348	−	0.541002i
$370$		0			0
$371$		0			0
$372$	−4.00000			−0.207390
$373$	15.5000	−	26.8468i	0.802560	−	1.39007i	−0.115367	−	0.993323i	$-0.536804\pi$
$373$	15.5000	−	26.8468i	0.802560	−	1.39007i	0.917926	−	0.396751i	$-0.129862\pi$
$374$	−3.00000	−	5.19615i	−0.155126	−	0.268687i
$375$		0			0
$376$	3.00000	−	5.19615i	0.154713	−	0.267971i
$377$	9.00000			0.463524
$378$		0			0
$379$	23.0000			1.18143			0.590715	−	0.806880i	$-0.298846\pi$
$379$	23.0000			1.18143			0.590715	+	0.806880i	$0.298846\pi$
$380$		0			0
$381$	−3.50000	−	6.06218i	−0.179310	−	0.310575i
$382$	3.00000	+	5.19615i	0.153493	+	0.265858i
$383$	−18.0000	+	31.1769i	−0.919757	+	1.59307i	−0.119974	+	0.992777i	$0.538281\pi$
$383$	−18.0000	+	31.1769i	−0.919757	+	1.59307i	−0.799783	+	0.600289i	$0.795052\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−14.0000			−0.712581
$387$	−4.00000	+	6.92820i	−0.203331	+	0.352180i
$388$	−6.50000	−	11.2583i	−0.329988	−	0.571555i
$389$	−6.00000	−	10.3923i	−0.304212	−	0.526911i	0.672874	−	0.739758i	$-0.265060\pi$
$389$	−6.00000	−	10.3923i	−0.304212	−	0.526911i	−0.977086	+	0.212847i	$0.931726\pi$
$390$		0			0
$391$	−36.0000			−1.82060
$392$		0			0
$393$	18.0000			0.907980
$394$	−1.50000	+	2.59808i	−0.0755689	+	0.130889i
$395$		0			0
$396$	−1.00000	−	1.73205i	−0.0502519	−	0.0870388i
$397$	−11.0000	+	19.0526i	−0.552074	+	0.956221i	0.446051	+	0.895008i	$0.352830\pi$
$397$	−11.0000	+	19.0526i	−0.552074	+	0.956221i	−0.998125	+	0.0612128i	$0.980503\pi$
$398$	14.0000			0.701757
$399$		0			0
$400$	−5.00000			−0.250000
$401$	16.5000	−	28.5788i	0.823971	−	1.42716i	−0.0787327	−	0.996896i	$-0.525087\pi$
$401$	16.5000	−	28.5788i	0.823971	−	1.42716i	0.902703	−	0.430263i	$-0.141579\pi$
$402$	−5.50000	−	9.52628i	−0.274315	−	0.475128i
$403$	−2.00000	−	3.46410i	−0.0996271	−	0.172559i
$404$	−7.50000	+	12.9904i	−0.373139	+	0.646296i
$405$		0			0
$406$		0			0
$407$	−2.00000			−0.0991363
$408$	−3.00000	+	5.19615i	−0.148522	+	0.257248i
$409$	−2.00000	−	3.46410i	−0.0988936	−	0.171289i	0.812333	−	0.583193i	$-0.198197\pi$
$409$	−2.00000	−	3.46410i	−0.0988936	−	0.171289i	−0.911227	+	0.411905i	$0.864864\pi$
$410$		0			0
$411$	−4.50000	+	7.79423i	−0.221969	+	0.384461i
$412$	16.0000			0.788263
$413$		0			0
$414$	−12.0000			−0.589768
$415$		0			0
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$	−4.00000	−	6.92820i	−0.195881	−	0.339276i
$418$	1.00000	−	1.73205i	0.0489116	−	0.0847174i
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		0			0
$421$	−28.0000			−1.36464			−0.682318	−	0.731055i	$-0.739028\pi$
$421$	−28.0000			−1.36464			−0.682318	+	0.731055i	$0.739028\pi$
$422$	−5.00000	+	8.66025i	−0.243396	+	0.421575i
$423$	6.00000	+	10.3923i	0.291730	+	0.505291i
$424$		0			0
$425$	15.0000	−	25.9808i	0.727607	−	1.26025i
$426$		0			0
$427$		0			0
$428$	12.0000			0.580042
$429$	−0.500000	+	0.866025i	−0.0241402	+	0.0418121i
$430$		0			0
$431$	1.50000	+	2.59808i	0.0722525	+	0.125145i	0.899888	−	0.436121i	$-0.143648\pi$
$431$	1.50000	+	2.59808i	0.0722525	+	0.125145i	−0.827636	+	0.561266i	$0.810315\pi$
$432$	−2.50000	+	4.33013i	−0.120281	+	0.208333i
$433$	34.0000			1.63394			0.816968	−	0.576683i	$-0.195653\pi$
$433$	34.0000			1.63394			0.816968	+	0.576683i	$0.195653\pi$
$434$		0			0
$435$		0			0
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$	−6.00000	−	10.3923i	−0.287019	−	0.497131i
$438$	1.00000	+	1.73205i	0.0477818	+	0.0827606i
$439$	−0.500000	+	0.866025i	−0.0238637	+	0.0413331i	−0.877711	−	0.479191i	$-0.840930\pi$
$439$	−0.500000	+	0.866025i	−0.0238637	+	0.0413331i	0.853847	+	0.520524i	$0.174263\pi$
$440$		0			0
$441$		0			0
$442$	−6.00000			−0.285391
$443$	−6.00000	+	10.3923i	−0.285069	+	0.493753i	−0.972626	−	0.232377i	$-0.925350\pi$
$443$	−6.00000	+	10.3923i	−0.285069	+	0.493753i	0.687557	+	0.726130i	$0.258683\pi$
$444$	1.00000	+	1.73205i	0.0474579	+	0.0821995i
$445$		0			0
$446$	−13.0000	+	22.5167i	−0.615568	+	1.06619i
$447$	−6.00000			−0.283790
$448$		0			0
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$	5.00000	−	8.66025i	0.235702	−	0.408248i
$451$	3.00000	+	5.19615i	0.141264	+	0.244677i
$452$	−4.50000	−	7.79423i	−0.211662	−	0.366610i
$453$	−9.50000	+	16.4545i	−0.446349	+	0.773099i
$454$	18.0000			0.844782
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	11.0000	−	19.0526i	0.514558	−	0.891241i	−0.485299	−	0.874348i	$-0.661289\pi$
$457$	11.0000	−	19.0526i	0.514558	−	0.891241i	0.999857	−	0.0168929i	$-0.00537742\pi$
$458$	8.00000	+	13.8564i	0.373815	+	0.647467i
$459$	−15.0000	−	25.9808i	−0.700140	−	1.21268i
$460$		0			0
$461$	−21.0000			−0.978068			−0.489034	−	0.872265i	$-0.662651\pi$
$461$	−21.0000			−0.978068			−0.489034	+	0.872265i	$0.662651\pi$
$462$		0			0
$463$	−22.0000			−1.02243			−0.511213	−	0.859454i	$-0.670804\pi$
$463$	−22.0000			−1.02243			−0.511213	+	0.859454i	$0.670804\pi$
$464$	−4.50000	+	7.79423i	−0.208907	+	0.361838i
$465$		0			0
$466$	−3.00000	−	5.19615i	−0.138972	−	0.240707i
$467$	6.00000	−	10.3923i	0.277647	−	0.480899i	−0.693153	−	0.720791i	$-0.743779\pi$
$467$	6.00000	−	10.3923i	0.277647	−	0.480899i	0.970799	+	0.239892i	$0.0771121\pi$
$468$	−2.00000			−0.0924500
$469$		0			0
$470$		0			0
$471$	2.00000	−	3.46410i	0.0921551	−	0.159617i
$472$	1.50000	+	2.59808i	0.0690431	+	0.119586i
$473$	−2.00000	−	3.46410i	−0.0919601	−	0.159280i
$474$	−2.50000	+	4.33013i	−0.114829	+	0.198889i
$475$	10.0000			0.458831
$476$		0			0
$477$		0			0
$478$	−4.50000	+	7.79423i	−0.205825	+	0.356500i
$479$	7.50000	+	12.9904i	0.342684	+	0.593546i	0.984930	−	0.172953i	$-0.0553307\pi$
$479$	7.50000	+	12.9904i	0.342684	+	0.593546i	−0.642246	+	0.766498i	$0.721997\pi$
$480$		0			0
$481$	−1.00000	+	1.73205i	−0.0455961	+	0.0789747i
$482$	26.0000			1.18427
$483$		0			0
$484$	1.00000			0.0454545
$485$		0			0
$486$	−8.00000	−	13.8564i	−0.362887	−	0.628539i
$487$	−10.0000	−	17.3205i	−0.453143	−	0.784867i	0.545436	−	0.838152i	$-0.316364\pi$
$487$	−10.0000	−	17.3205i	−0.453143	−	0.784867i	−0.998579	+	0.0532853i	$0.983031\pi$
$488$	−5.50000	+	9.52628i	−0.248973	+	0.431234i
$489$	−17.0000			−0.768767
$490$		0			0
$491$	42.0000			1.89543			0.947717	−	0.319113i	$-0.103385\pi$
$491$	42.0000			1.89543			0.947717	+	0.319113i	$0.103385\pi$
$492$	3.00000	−	5.19615i	0.135250	−	0.234261i
$493$	−27.0000	−	46.7654i	−1.21602	−	2.10621i
$494$	−1.00000	−	1.73205i	−0.0449921	−	0.0779287i
$495$		0			0
$496$	4.00000			0.179605
$497$		0			0
$498$	6.00000			0.268866
$499$	20.0000	−	34.6410i	0.895323	−	1.55074i	0.0619186	−	0.998081i	$-0.480278\pi$
$499$	20.0000	−	34.6410i	0.895323	−	1.55074i	0.833404	−	0.552664i	$-0.186389\pi$
$500$		0			0
$501$	−1.50000	−	2.59808i	−0.0670151	−	0.116073i
$502$	6.00000	−	10.3923i	0.267793	−	0.463831i
$503$	33.0000			1.47140			0.735699	−	0.677309i	$-0.236854\pi$
$503$	33.0000			1.47140			0.735699	+	0.677309i	$0.236854\pi$
$504$		0			0
$505$		0			0
$506$	3.00000	−	5.19615i	0.133366	−	0.230997i
$507$	−6.00000	−	10.3923i	−0.266469	−	0.461538i
$508$	3.50000	+	6.06218i	0.155287	+	0.268966i
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	−0.924821	−	0.380402i	$-0.875786\pi$
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	0.791849	+	0.610718i	$0.209119\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	5.00000	−	8.66025i	0.220755	−	0.382360i
$514$	−1.50000	−	2.59808i	−0.0661622	−	0.114596i
$515$		0			0
$516$	−2.00000	+	3.46410i	−0.0880451	+	0.152499i
$517$	−6.00000			−0.263880
$518$		0			0
$519$	−21.0000			−0.921798
$520$		0			0
$521$	−21.0000	−	36.3731i	−0.920027	−	1.59353i	−0.799370	−	0.600839i	$-0.794833\pi$
$521$	−21.0000	−	36.3731i	−0.920027	−	1.59353i	−0.120656	−	0.992694i	$-0.538500\pi$
$522$	−9.00000	−	15.5885i	−0.393919	−	0.682288i
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	−0.986216	−	0.165460i	$-0.947089\pi$
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	0.636401	+	0.771358i	$0.280422\pi$
$524$	−18.0000			−0.786334
$525$		0			0
$526$	9.00000			0.392419
$527$	−12.0000	+	20.7846i	−0.522728	+	0.905392i
$528$	−0.500000	−	0.866025i	−0.0217597	−	0.0376889i
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$		0			0
$531$	−6.00000			−0.260378
$532$		0			0
$533$	6.00000			0.259889
$534$	−9.00000	+	15.5885i	−0.389468	+	0.674579i
$535$		0			0
$536$	5.50000	+	9.52628i	0.237564	+	0.411473i
$537$	−7.50000	+	12.9904i	−0.323649	+	0.560576i
$538$	12.0000			0.517357
$539$		0			0
$540$		0			0
$541$	12.5000	−	21.6506i	0.537417	−	0.930834i	−0.461625	−	0.887075i	$-0.652733\pi$
$541$	12.5000	−	21.6506i	0.537417	−	0.930834i	0.999042	−	0.0437584i	$-0.0139332\pi$
$542$	−14.5000	−	25.1147i	−0.622828	−	1.07877i
$543$	−1.00000	−	1.73205i	−0.0429141	−	0.0743294i
$544$	3.00000	−	5.19615i	0.128624	−	0.222783i
$545$		0			0
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$	4.50000	−	7.79423i	0.192230	−	0.332953i
$549$	−11.0000	−	19.0526i	−0.469469	−	0.813143i
$550$	2.50000	+	4.33013i	0.106600	+	0.184637i
$551$	9.00000	−	15.5885i	0.383413	−	0.664091i
$552$	−6.00000			−0.255377
$553$		0			0
$554$	−29.0000			−1.23209
$555$		0			0
$556$	4.00000	+	6.92820i	0.169638	+	0.293821i
$557$	9.00000	+	15.5885i	0.381342	+	0.660504i	0.991254	−	0.131965i	$-0.0421286\pi$
$557$	9.00000	+	15.5885i	0.381342	+	0.660504i	−0.609912	+	0.792469i	$0.708795\pi$
$558$	−4.00000	+	6.92820i	−0.169334	+	0.293294i
$559$	−4.00000			−0.169182
$560$		0			0
$561$	6.00000			0.253320
$562$	9.00000	−	15.5885i	0.379642	−	0.657559i
$563$	−9.00000	−	15.5885i	−0.379305	−	0.656975i	0.611656	−	0.791123i	$-0.290503\pi$
$563$	−9.00000	−	15.5885i	−0.379305	−	0.656975i	−0.990961	+	0.134148i	$0.957170\pi$
$564$	3.00000	+	5.19615i	0.126323	+	0.218797i
$565$		0			0
$566$	−10.0000			−0.420331
$567$		0			0
$568$		0			0
$569$	18.0000	−	31.1769i	0.754599	−	1.30700i	−0.190974	−	0.981595i	$-0.561165\pi$
$569$	18.0000	−	31.1769i	0.754599	−	1.30700i	0.945573	−	0.325409i	$-0.105502\pi$
$570$		0			0
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	−0.978022	−	0.208502i	$-0.933141\pi$
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	0.308443	−	0.951243i	$-0.400192\pi$
$572$	0.500000	−	0.866025i	0.0209061	−	0.0362103i
$573$	−6.00000			−0.250654
$574$		0			0
$575$	30.0000			1.25109
$576$	1.00000	−	1.73205i	0.0416667	−	0.0721688i
$577$	−3.50000	−	6.06218i	−0.145707	−	0.252372i	0.783930	−	0.620850i	$-0.213212\pi$
$577$	−3.50000	−	6.06218i	−0.145707	−	0.252372i	−0.929636	+	0.368478i	$0.879879\pi$
$578$	9.50000	+	16.4545i	0.395148	+	0.684416i
$579$	7.00000	−	12.1244i	0.290910	−	0.503871i
$580$		0			0
$581$		0			0
$582$	13.0000			0.538867
$583$		0			0
$584$	−1.00000	−	1.73205i	−0.0413803	−	0.0716728i
$585$		0			0
$586$	15.0000	−	25.9808i	0.619644	−	1.07326i
$587$	−9.00000			−0.371470			−0.185735	−	0.982600i	$-0.559467\pi$
$587$	−9.00000			−0.371470			−0.185735	+	0.982600i	$0.559467\pi$
$588$		0			0
$589$	−8.00000			−0.329634
$590$		0			0
$591$	−1.50000	−	2.59808i	−0.0617018	−	0.106871i
$592$	−1.00000	−	1.73205i	−0.0410997	−	0.0711868i
$593$	18.0000	−	31.1769i	0.739171	−	1.28028i	−0.213697	−	0.976900i	$-0.568551\pi$
$593$	18.0000	−	31.1769i	0.739171	−	1.28028i	0.952869	−	0.303383i	$-0.0981160\pi$
$594$	5.00000			0.205152
$595$		0			0
$596$	6.00000			0.245770
$597$	−7.00000	+	12.1244i	−0.286491	+	0.496217i
$598$	−3.00000	−	5.19615i	−0.122679	−	0.212486i
$599$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$	2.50000	−	4.33013i	0.102062	−	0.176777i
$601$	−2.00000			−0.0815817			−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000			−0.0815817			−0.0407909	+	0.999168i	$0.512988\pi$
$602$		0			0
$603$	−22.0000			−0.895909
$604$	9.50000	−	16.4545i	0.386550	−	0.669523i
$605$		0			0
$606$	−7.50000	−	12.9904i	−0.304667	−	0.527698i
$607$	−20.0000	+	34.6410i	−0.811775	+	1.40604i	0.0998457	+	0.995003i	$0.468165\pi$
$607$	−20.0000	+	34.6410i	−0.811775	+	1.40604i	−0.911621	+	0.411033i	$0.865168\pi$
$608$	2.00000			0.0811107
$609$		0			0
$610$		0			0
$611$	−3.00000	+	5.19615i	−0.121367	+	0.210214i
$612$	6.00000	+	10.3923i	0.242536	+	0.420084i
$613$	5.00000	+	8.66025i	0.201948	+	0.349784i	0.949156	−	0.314806i	$-0.101939\pi$
$613$	5.00000	+	8.66025i	0.201948	+	0.349784i	−0.747208	+	0.664590i	$0.768606\pi$
$614$	−10.0000	+	17.3205i	−0.403567	+	0.698999i
$615$		0			0
$616$		0			0
$617$	21.0000			0.845428			0.422714	−	0.906263i	$-0.361077\pi$
$617$	21.0000			0.845428			0.422714	+	0.906263i	$0.361077\pi$
$618$	−8.00000	+	13.8564i	−0.321807	+	0.557386i
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	0.993959	−	0.109749i	$-0.0350048\pi$
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	−0.592025	+	0.805919i	$0.701671\pi$
$620$		0			0
$621$	15.0000	−	25.9808i	0.601929	−	1.04257i
$622$	24.0000			0.962312
$623$		0			0
$624$	−1.00000			−0.0400320
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$	−8.50000	−	14.7224i	−0.339728	−	0.588427i
$627$	1.00000	+	1.73205i	0.0399362	+	0.0691714i
$628$	−2.00000	+	3.46410i	−0.0798087	+	0.138233i
$629$	12.0000			0.478471
$630$		0			0
$631$	20.0000			0.796187			0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000			0.796187			0.398094	+	0.917345i	$0.369672\pi$
$632$	2.50000	−	4.33013i	0.0994447	−	0.172243i
$633$	−5.00000	−	8.66025i	−0.198732	−	0.344214i
$634$	6.00000	+	10.3923i	0.238290	+	0.412731i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	9.00000			0.356313
$639$		0			0
$640$		0			0
$641$	−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	$0.890212\pi$
$642$	−6.00000	+	10.3923i	−0.236801	+	0.410152i
$643$	−5.00000			−0.197181			−0.0985904	−	0.995128i	$-0.531433\pi$
$643$	−5.00000			−0.197181			−0.0985904	+	0.995128i	$0.531433\pi$
$644$		0			0
$645$		0			0
$646$	−6.00000	+	10.3923i	−0.236067	+	0.408880i
$647$	−6.00000	−	10.3923i	−0.235884	−	0.408564i	0.723645	−	0.690172i	$-0.242465\pi$
$647$	−6.00000	−	10.3923i	−0.235884	−	0.408564i	−0.959529	+	0.281609i	$0.909132\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	1.50000	−	2.59808i	0.0588802	−	0.101983i
$650$	5.00000			0.196116
$651$		0			0
$652$	17.0000			0.665771
$653$	−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	$0.281232\pi$
$654$	−1.00000	−	1.73205i	−0.0391031	−	0.0677285i
$655$		0			0
$656$	−3.00000	+	5.19615i	−0.117130	+	0.202876i
$657$	4.00000			0.156055
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	0.969442	−	0.245319i	$-0.0788928\pi$
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	−0.697174	+	0.716902i	$0.745559\pi$
$662$	17.5000	+	30.3109i	0.680157	+	1.17807i
$663$	3.00000	−	5.19615i	0.116510	−	0.201802i
$664$	−6.00000			−0.232845
$665$		0			0
$666$	4.00000			0.154997
$667$	27.0000	−	46.7654i	1.04544	−	1.81076i
$668$	1.50000	+	2.59808i	0.0580367	+	0.100523i
$669$	−13.0000	−	22.5167i	−0.502609	−	0.870544i
$670$		0			0
$671$	11.0000			0.424650
$672$		0			0
$673$	−28.0000			−1.07932			−0.539660	−	0.841883i	$-0.681447\pi$
$673$	−28.0000			−1.07932			−0.539660	+	0.841883i	$0.681447\pi$
$674$	7.00000	−	12.1244i	0.269630	−	0.467013i
$675$	12.5000	+	21.6506i	0.481125	+	0.833333i
$676$	6.00000	+	10.3923i	0.230769	+	0.399704i
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	−0.802600	−	0.596518i	$-0.796551\pi$
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	0.917899	+	0.396813i	$0.129884\pi$
$678$	9.00000			0.345643
$679$		0			0
$680$		0			0
$681$	−9.00000	+	15.5885i	−0.344881	+	0.597351i
$682$	−2.00000	−	3.46410i	−0.0765840	−	0.132647i
$683$	10.5000	+	18.1865i	0.401771	+	0.695888i	0.993940	−	0.109926i	$-0.0350613\pi$
$683$	10.5000	+	18.1865i	0.401771	+	0.695888i	−0.592168	+	0.805814i	$0.701728\pi$
$684$	−2.00000	+	3.46410i	−0.0764719	+	0.132453i
$685$		0			0
$686$		0			0
$687$	−16.0000			−0.610438
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$		0			0
$690$		0			0
$691$	5.50000	−	9.52628i	0.209230	−	0.362397i	−0.742242	−	0.670132i	$-0.766238\pi$
$691$	5.50000	−	9.52628i	0.209230	−	0.362397i	0.951472	+	0.307735i	$0.0995710\pi$
$692$	21.0000			0.798300
$693$		0			0
$694$		0			0
$695$		0			0
$696$	−4.50000	−	7.79423i	−0.170572	−	0.295439i
$697$	−18.0000	−	31.1769i	−0.681799	−	1.18091i
$698$	−1.00000	+	1.73205i	−0.0378506	+	0.0655591i
$699$	6.00000			0.226941
$700$		0			0
$701$	39.0000			1.47301			0.736505	−	0.676432i	$-0.236475\pi$
$701$	39.0000			1.47301			0.736505	+	0.676432i	$0.236475\pi$
$702$	2.50000	−	4.33013i	0.0943564	−	0.163430i
$703$	2.00000	+	3.46410i	0.0754314	+	0.130651i
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$		0			0
$706$	−18.0000			−0.677439
$707$		0			0
$708$	−3.00000			−0.112747
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	−0.999908	−	0.0135434i	$-0.995689\pi$
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	0.511683	+	0.859174i	$0.329022\pi$
$710$		0			0
$711$	5.00000	+	8.66025i	0.187515	+	0.324785i
$712$	9.00000	−	15.5885i	0.337289	−	0.584202i
$713$	−24.0000			−0.898807
$714$		0			0
$715$		0			0
$716$	7.50000	−	12.9904i	0.280288	−	0.485473i
$717$	−4.50000	−	7.79423i	−0.168056	−	0.291081i
$718$	−1.50000	−	2.59808i	−0.0559795	−	0.0969593i
$719$	−21.0000	+	36.3731i	−0.783168	+	1.35649i	0.146920	+	0.989148i	$0.453064\pi$
$719$	−21.0000	+	36.3731i	−0.783168	+	1.35649i	−0.930087	+	0.367338i	$0.880269\pi$
$720$		0			0
$721$		0			0
$722$	15.0000			0.558242
$723$	−13.0000	+	22.5167i	−0.483475	+	0.837404i
$724$	1.00000	+	1.73205i	0.0371647	+	0.0643712i
$725$	22.5000	+	38.9711i	0.835629	+	1.44735i
$726$	−0.500000	+	0.866025i	−0.0185567	+	0.0321412i
$727$	−14.0000			−0.519231			−0.259616	−	0.965712i	$-0.583596\pi$
$727$	−14.0000			−0.519231			−0.259616	+	0.965712i	$0.583596\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	12.0000	+	20.7846i	0.443836	+	0.768747i
$732$	−5.50000	−	9.52628i	−0.203286	−	0.352101i
$733$	−12.5000	+	21.6506i	−0.461698	+	0.799684i	−0.999046	−	0.0436764i	$-0.986093\pi$
$733$	−12.5000	+	21.6506i	−0.461698	+	0.799684i	0.537348	+	0.843361i	$0.319426\pi$
$734$	−10.0000			−0.369107
$735$		0			0
$736$	6.00000			0.221163
$737$	5.50000	−	9.52628i	0.202595	−	0.350905i
$738$	−6.00000	−	10.3923i	−0.220863	−	0.382546i
$739$	−25.0000	−	43.3013i	−0.919640	−	1.59286i	−0.799962	−	0.600050i	$-0.795147\pi$
$739$	−25.0000	−	43.3013i	−0.919640	−	1.59286i	−0.119677	−	0.992813i	$-0.538186\pi$
$740$		0			0
$741$	2.00000			0.0734718
$742$		0			0
$743$	−36.0000			−1.32071			−0.660356	−	0.750953i	$-0.729595\pi$
$743$	−36.0000			−1.32071			−0.660356	+	0.750953i	$0.729595\pi$
$744$	−2.00000	+	3.46410i	−0.0733236	+	0.127000i
$745$		0			0
$746$	−15.5000	−	26.8468i	−0.567495	−	0.982931i
$747$	6.00000	−	10.3923i	0.219529	−	0.380235i
$748$	−6.00000			−0.219382
$749$		0			0
$750$		0			0
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	−0.827225	−	0.561870i	$-0.810082\pi$
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	0.900207	+	0.435463i	$0.143415\pi$
$752$	−3.00000	−	5.19615i	−0.109399	−	0.189484i
$753$	6.00000	+	10.3923i	0.218652	+	0.378717i
$754$	4.50000	−	7.79423i	0.163880	−	0.283849i
$755$		0			0
$756$		0			0
$757$	−46.0000			−1.67190			−0.835949	−	0.548807i	$-0.815082\pi$
$757$	−46.0000			−1.67190			−0.835949	+	0.548807i	$0.815082\pi$
$758$	11.5000	−	19.9186i	0.417699	−	0.723476i
$759$	3.00000	+	5.19615i	0.108893	+	0.188608i
$760$		0			0
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	−0.981764	−	0.190101i	$-0.939118\pi$
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	0.655515	+	0.755182i	$0.272452\pi$
$762$	−7.00000			−0.253583
$763$		0			0
$764$	6.00000			0.217072
$765$		0			0
$766$	18.0000	+	31.1769i	0.650366	+	1.12647i
$767$	−1.50000	−	2.59808i	−0.0541619	−	0.0938111i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	22.0000			0.793340			0.396670	−	0.917961i	$-0.370166\pi$
$769$	22.0000			0.793340			0.396670	+	0.917961i	$0.370166\pi$
$770$		0			0
$771$	3.00000			0.108042
$772$	−7.00000	+	12.1244i	−0.251936	+	0.436365i
$773$	12.0000	+	20.7846i	0.431610	+	0.747570i	0.997012	−	0.0772449i	$-0.0246123\pi$
$773$	12.0000	+	20.7846i	0.431610	+	0.747570i	−0.565402	+	0.824815i	$0.691279\pi$
$774$	4.00000	+	6.92820i	0.143777	+	0.249029i
$775$	10.0000	−	17.3205i	0.359211	−	0.622171i
$776$	−13.0000			−0.466673
$777$		0			0
$778$	−12.0000			−0.430221
$779$	6.00000	−	10.3923i	0.214972	−	0.372343i
$780$		0			0
$781$		0			0
$782$	−18.0000	+	31.1769i	−0.643679	+	1.11488i
$783$	45.0000			1.60817
$784$		0			0
$785$		0			0
$786$	9.00000	−	15.5885i	0.321019	−	0.556022i
$787$	7.00000	+	12.1244i	0.249523	+	0.432187i	0.963394	−	0.268091i	$-0.0863928\pi$
$787$	7.00000	+	12.1244i	0.249523	+	0.432187i	−0.713871	+	0.700278i	$0.753059\pi$
$788$	1.50000	+	2.59808i	0.0534353	+	0.0925526i
$789$	−4.50000	+	7.79423i	−0.160204	+	0.277482i
$790$		0			0
$791$		0			0
$792$	−2.00000			−0.0710669
$793$	5.50000	−	9.52628i	0.195311	−	0.338288i
$794$	11.0000	+	19.0526i	0.390375	+	0.676150i
$795$		0			0
$796$	7.00000	−	12.1244i	0.248108	−	0.429736i
$797$	18.0000			0.637593			0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000			0.637593			0.318796	+	0.947823i	$0.396721\pi$
$798$		0			0
$799$	36.0000			1.27359
$800$	−2.50000	+	4.33013i	−0.0883883	+	0.153093i
$801$	18.0000	+	31.1769i	0.635999	+	1.10158i
$802$	−16.5000	−	28.5788i	−0.582635	−	1.00915i
$803$	−1.00000	+	1.73205i	−0.0352892	+	0.0611227i
$804$	−11.0000			−0.387940
$805$		0			0
$806$	−4.00000			−0.140894
$807$	−6.00000	+	10.3923i	−0.211210	+	0.365826i
$808$	7.50000	+	12.9904i	0.263849	+	0.457000i
$809$	24.0000	+	41.5692i	0.843795	+	1.46150i	0.886664	+	0.462415i	$0.153017\pi$
$809$	24.0000	+	41.5692i	0.843795	+	1.46150i	−0.0428684	+	0.999081i	$0.513650\pi$
$810$		0			0
$811$	−20.0000			−0.702295			−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000			−0.702295			−0.351147	+	0.936320i	$0.614208\pi$
$812$		0			0
$813$	29.0000			1.01707
$814$	−1.00000	+	1.73205i	−0.0350500	+	0.0607083i
$815$		0			0
$816$	3.00000	+	5.19615i	0.105021	+	0.181902i
$817$	−4.00000	+	6.92820i	−0.139942	+	0.242387i
$818$	−4.00000			−0.139857
$819$		0			0
$820$		0			0
$821$	7.50000	−	12.9904i	0.261752	−	0.453367i	−0.704956	−	0.709251i	$-0.749033\pi$
$821$	7.50000	−	12.9904i	0.261752	−	0.453367i	0.966708	+	0.255884i	$0.0823665\pi$
$822$	4.50000	+	7.79423i	0.156956	+	0.271855i
$823$	5.00000	+	8.66025i	0.174289	+	0.301877i	0.939915	−	0.341409i	$-0.110904\pi$
$823$	5.00000	+	8.66025i	0.174289	+	0.301877i	−0.765626	+	0.643286i	$0.777571\pi$
$824$	8.00000	−	13.8564i	0.278693	−	0.482711i
$825$	−5.00000			−0.174078
$826$		0			0
$827$	30.0000			1.04320			0.521601	−	0.853189i	$-0.325335\pi$
$827$	30.0000			1.04320			0.521601	+	0.853189i	$0.325335\pi$
$828$	−6.00000	+	10.3923i	−0.208514	+	0.361158i
$829$	−26.0000	−	45.0333i	−0.903017	−	1.56407i	−0.823557	−	0.567234i	$-0.808014\pi$
$829$	−26.0000	−	45.0333i	−0.903017	−	1.56407i	−0.0794606	−	0.996838i	$-0.525320\pi$
$830$		0			0
$831$	14.5000	−	25.1147i	0.502999	−	0.871221i
$832$	1.00000			0.0346688
$833$		0			0
$834$	−8.00000			−0.277017
$835$		0			0
$836$	−1.00000	−	1.73205i	−0.0345857	−	0.0599042i
$837$	−10.0000	−	17.3205i	−0.345651	−	0.598684i
$838$	6.00000	−	10.3923i	0.207267	−	0.358996i
$839$	−6.00000			−0.207143			−0.103572	−	0.994622i	$-0.533027\pi$
$839$	−6.00000			−0.207143			−0.103572	+	0.994622i	$0.533027\pi$
$840$		0			0
$841$	52.0000			1.79310
$842$	−14.0000	+	24.2487i	−0.482472	+	0.835666i
$843$	9.00000	+	15.5885i	0.309976	+	0.536895i
$844$	5.00000	+	8.66025i	0.172107	+	0.298098i
$845$		0			0
$846$	12.0000			0.412568
$847$		0			0
$848$		0			0
$849$	5.00000	−	8.66025i	0.171600	−	0.297219i
$850$	−15.0000	−	25.9808i	−0.514496	−	0.891133i
$851$	6.00000	+	10.3923i	0.205677	+	0.356244i
$852$		0			0
$853$	46.0000			1.57501			0.787505	−	0.616308i	$-0.211372\pi$
$853$	46.0000			1.57501			0.787505	+	0.616308i	$0.211372\pi$
$854$		0			0
$855$		0			0
$856$	6.00000	−	10.3923i	0.205076	−	0.355202i
$857$	18.0000	+	31.1769i	0.614868	+	1.06498i	0.990408	+	0.138177i	$0.0441242\pi$
$857$	18.0000	+	31.1769i	0.614868	+	1.06498i	−0.375539	+	0.926806i	$0.622542\pi$
$858$	0.500000	+	0.866025i	0.0170697	+	0.0295656i
$859$	−18.5000	+	32.0429i	−0.631212	+	1.09329i	0.356092	+	0.934451i	$0.384109\pi$
$859$	−18.5000	+	32.0429i	−0.631212	+	1.09329i	−0.987304	+	0.158840i	$0.949225\pi$
$860$		0			0
$861$		0			0
$862$	3.00000			0.102180
$863$	−15.0000	+	25.9808i	−0.510606	+	0.884395i	0.489319	+	0.872105i	$0.337246\pi$
$863$	−15.0000	+	25.9808i	−0.510606	+	0.884395i	−0.999924	+	0.0122903i	$0.996088\pi$
$864$	2.50000	+	4.33013i	0.0850517	+	0.147314i
$865$		0			0
$866$	17.0000	−	29.4449i	0.577684	−	1.00058i
$867$	−19.0000			−0.645274
$868$		0			0
$869$	−5.00000			−0.169613
$870$		0			0
$871$	−5.50000	−	9.52628i	−0.186360	−	0.322786i
$872$	1.00000	+	1.73205i	0.0338643	+	0.0586546i
$873$	13.0000	−	22.5167i	0.439983	−	0.762073i
$874$	−12.0000			−0.405906
$875$		0			0
$876$	2.00000			0.0675737
$877$	−8.50000	+	14.7224i	−0.287025	+	0.497141i	−0.973098	−	0.230391i	$-0.925999\pi$
$877$	−8.50000	+	14.7224i	−0.287025	+	0.497141i	0.686074	+	0.727532i	$0.259333\pi$
$878$	0.500000	+	0.866025i	0.0168742	+	0.0292269i
$879$	15.0000	+	25.9808i	0.505937	+	0.876309i
$880$		0			0
$881$	−33.0000			−1.11180			−0.555899	−	0.831250i	$-0.687626\pi$
$881$	−33.0000			−1.11180			−0.555899	+	0.831250i	$0.687626\pi$
$882$		0			0
$883$	29.0000			0.975928			0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000			0.975928			0.487964	+	0.872864i	$0.337740\pi$
$884$	−3.00000	+	5.19615i	−0.100901	+	0.174766i
$885$		0			0
$886$	6.00000	+	10.3923i	0.201574	+	0.349136i
$887$	1.50000	−	2.59808i	0.0503651	−	0.0872349i	−0.839744	−	0.542983i	$-0.817295\pi$
$887$	1.50000	−	2.59808i	0.0503651	−	0.0872349i	0.890109	+	0.455748i	$0.150628\pi$
$888$	2.00000			0.0671156
$889$		0			0
$890$		0			0
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	13.0000	+	22.5167i	0.435272	+	0.753914i
$893$	6.00000	+	10.3923i	0.200782	+	0.347765i
$894$	−3.00000	+	5.19615i	−0.100335	+	0.173785i
$895$		0			0
$896$		0			0
$897$	6.00000			0.200334
$898$	−9.00000	+	15.5885i	−0.300334	+	0.520194i
$899$	−18.0000	−	31.1769i	−0.600334	−	1.03981i
$900$	−5.00000	−	8.66025i	−0.166667	−	0.288675i
$901$		0			0
$902$	6.00000			0.199778
$903$		0			0
$904$	−9.00000			−0.299336
$905$		0			0
$906$	9.50000	+	16.4545i	0.315616	+	0.546664i
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	0.999195	−	0.0401089i	$-0.0127705\pi$
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	−0.534333	+	0.845274i	$0.679437\pi$
$908$	9.00000	−	15.5885i	0.298675	−	0.517321i
$909$	−30.0000			−0.995037
$910$		0			0
$911$	−6.00000			−0.198789			−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000			−0.198789			−0.0993944	+	0.995048i	$0.531691\pi$
$912$	−1.00000	+	1.73205i	−0.0331133	+	0.0573539i
$913$	3.00000	+	5.19615i	0.0992855	+	0.171968i
$914$	−11.0000	−	19.0526i	−0.363848	−	0.630203i
$915$		0			0
$916$	16.0000			0.528655
$917$		0			0
$918$	−30.0000			−0.990148
$919$	−16.0000	+	27.7128i	−0.527791	+	0.914161i	0.471684	+	0.881768i	$0.343646\pi$
$919$	−16.0000	+	27.7128i	−0.527791	+	0.914161i	−0.999475	+	0.0323936i	$0.989687\pi$
$920$		0			0
$921$	−10.0000	−	17.3205i	−0.329511	−	0.570730i
$922$	−10.5000	+	18.1865i	−0.345799	+	0.598942i
$923$		0			0
$924$		0			0
$925$	−10.0000			−0.328798
$926$	−11.0000	+	19.0526i	−0.361482	+	0.626106i
$927$	16.0000	+	27.7128i	0.525509	+	0.910208i
$928$	4.50000	+	7.79423i	0.147720	+	0.255858i
$929$	19.5000	−	33.7750i	0.639774	−	1.10812i	−0.345708	−	0.938342i	$-0.612361\pi$
$929$	19.5000	−	33.7750i	0.639774	−	1.10812i	0.985482	−	0.169779i	$-0.0543055\pi$
$930$		0			0
$931$		0			0
$932$	−6.00000			−0.196537
$933$	−12.0000	+	20.7846i	−0.392862	+	0.680458i
$934$	−6.00000	−	10.3923i	−0.196326	−	0.340047i
$935$		0			0
$936$	−1.00000	+	1.73205i	−0.0326860	+	0.0566139i
$937$	−8.00000			−0.261349			−0.130674	−	0.991425i	$-0.541714\pi$
$937$	−8.00000			−0.261349			−0.130674	+	0.991425i	$0.541714\pi$
$938$		0			0
$939$	17.0000			0.554774
$940$		0			0
$941$	7.50000	+	12.9904i	0.244493	+	0.423474i	0.961989	−	0.273088i	$-0.0880451\pi$
$941$	7.50000	+	12.9904i	0.244493	+	0.423474i	−0.717496	+	0.696563i	$0.754712\pi$
$942$	−2.00000	−	3.46410i	−0.0651635	−	0.112867i
$943$	18.0000	−	31.1769i	0.586161	−	1.01526i
$944$	3.00000			0.0976417
$945$		0			0
$946$	−4.00000			−0.130051
$947$	−12.0000	+	20.7846i	−0.389948	+	0.675409i	−0.992442	−	0.122714i	$-0.960840\pi$
$947$	−12.0000	+	20.7846i	−0.389948	+	0.675409i	0.602494	+	0.798123i	$0.294174\pi$
$948$	2.50000	+	4.33013i	0.0811962	+	0.140636i
$949$	1.00000	+	1.73205i	0.0324614	+	0.0562247i
$950$	5.00000	−	8.66025i	0.162221	−	0.280976i
$951$	−12.0000			−0.389127
$952$		0			0
$953$	−36.0000			−1.16615			−0.583077	−	0.812417i	$-0.698151\pi$
$953$	−36.0000			−1.16615			−0.583077	+	0.812417i	$0.698151\pi$
$954$		0			0
$955$		0			0
$956$	4.50000	+	7.79423i	0.145540	+	0.252083i
$957$	−4.50000	+	7.79423i	−0.145464	+	0.251952i
$958$	15.0000			0.484628
$959$		0			0
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	1.00000	+	1.73205i	0.0322413	+	0.0558436i
$963$	12.0000	+	20.7846i	0.386695	+	0.669775i
$964$	13.0000	−	22.5167i	0.418702	−	0.725213i
$965$		0			0
$966$		0			0
$967$	−40.0000			−1.28631			−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000			−1.28631			−0.643157	+	0.765735i	$0.722376\pi$
$968$	0.500000	−	0.866025i	0.0160706	−	0.0278351i
$969$	−6.00000	−	10.3923i	−0.192748	−	0.333849i
$970$		0			0
$971$	7.50000	−	12.9904i	0.240686	−	0.416881i	−0.720224	−	0.693742i	$-0.755961\pi$
$971$	7.50000	−	12.9904i	0.240686	−	0.416881i	0.960910	+	0.276861i	$0.0892941\pi$
$972$	−16.0000			−0.513200
$973$		0			0
$974$	−20.0000			−0.640841
$975$	−2.50000	+	4.33013i	−0.0800641	+	0.138675i
$976$	5.50000	+	9.52628i	0.176051	+	0.304929i
$977$	9.00000	+	15.5885i	0.287936	+	0.498719i	0.973317	−	0.229465i	$-0.0736978\pi$
$977$	9.00000	+	15.5885i	0.287936	+	0.498719i	−0.685381	+	0.728184i	$0.740364\pi$
$978$	−8.50000	+	14.7224i	−0.271800	+	0.470771i
$979$	−18.0000			−0.575282
$980$		0			0
$981$	−4.00000			−0.127710
$982$	21.0000	−	36.3731i	0.670137	−	1.16071i
$983$	−3.00000	−	5.19615i	−0.0956851	−	0.165732i	0.814209	−	0.580572i	$-0.197171\pi$
$983$	−3.00000	−	5.19615i	−0.0956851	−	0.165732i	−0.909894	+	0.414840i	$0.863838\pi$
$984$	−3.00000	−	5.19615i	−0.0956365	−	0.165647i
$985$		0			0
$986$	−54.0000			−1.71971
$987$		0			0
$988$	−2.00000			−0.0636285
$989$	−12.0000	+	20.7846i	−0.381578	+	0.660912i
$990$		0			0
$991$	20.0000	+	34.6410i	0.635321	+	1.10041i	0.986447	+	0.164080i	$0.0524655\pi$
$991$	20.0000	+	34.6410i	0.635321	+	1.10041i	−0.351126	+	0.936328i	$0.614201\pi$
$992$	2.00000	−	3.46410i	0.0635001	−	0.109985i
$993$	−35.0000			−1.11069
$994$		0			0
$995$		0			0
$996$	3.00000	−	5.19615i	0.0950586	−	0.164646i
$997$	−17.0000	−	29.4449i	−0.538395	−	0.932528i	−0.998991	−	0.0449179i	$-0.985697\pi$
$997$	−17.0000	−	29.4449i	−0.538395	−	0.932528i	0.460595	−	0.887610i	$-0.347636\pi$
$998$	−20.0000	−	34.6410i	−0.633089	−	1.09654i
$999$	−5.00000	+	8.66025i	−0.158193	+	0.273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.e.k.177.1		2
7.2	even	3		1078.2.a.c.1.1		1
7.3	odd	6		154.2.e.c.67.1	yes	2
7.4	even	3	inner	1078.2.e.k.67.1		2
7.5	odd	6		1078.2.a.e.1.1		1
7.6	odd	2		154.2.e.c.23.1	✓	2
21.2	odd	6		9702.2.a.bs.1.1		1
21.5	even	6		9702.2.a.br.1.1		1
21.17	even	6		1386.2.k.e.991.1		2
21.20	even	2		1386.2.k.e.793.1		2
28.3	even	6		1232.2.q.d.529.1		2
28.19	even	6		8624.2.a.k.1.1		1
28.23	odd	6		8624.2.a.u.1.1		1
28.27	even	2		1232.2.q.d.177.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.e.c.23.1	✓	2	7.6	odd	2
154.2.e.c.67.1	yes	2	7.3	odd	6
1078.2.a.c.1.1		1	7.2	even	3
1078.2.a.e.1.1		1	7.5	odd	6
1078.2.e.k.67.1		2	7.4	even	3	inner
1078.2.e.k.177.1		2	1.1	even	1	trivial
1232.2.q.d.177.1		2	28.27	even	2
1232.2.q.d.529.1		2	28.3	even	6
1386.2.k.e.793.1		2	21.20	even	2
1386.2.k.e.991.1		2	21.17	even	6
8624.2.a.k.1.1		1	28.19	even	6
8624.2.a.u.1.1		1	28.23	odd	6
9702.2.a.br.1.1		1	21.5	even	6
9702.2.a.bs.1.1		1	21.2	odd	6

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:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{6} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} +1.00000 q^{13} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-1.00000 - 1.73205i) q^{18} +(1.00000 - 1.73205i) q^{19} +1.00000 q^{22} +(3.00000 - 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{25} +(0.500000 - 0.866025i) q^{26} +5.00000 q^{27} +9.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} -6.00000 q^{34} -2.00000 q^{36} +(-1.00000 + 1.73205i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(0.500000 + 0.866025i) q^{39} +6.00000 q^{41} -4.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-3.00000 - 5.19615i) q^{46} +(-3.00000 + 5.19615i) q^{47} -1.00000 q^{48} +5.00000 q^{50} +(3.00000 - 5.19615i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(2.50000 - 4.33013i) q^{54} +2.00000 q^{57} +(4.50000 - 7.79423i) q^{58} +(-1.50000 - 2.59808i) q^{59} +(5.50000 - 9.52628i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{66} +(-5.50000 - 9.52628i) q^{67} +(-3.00000 + 5.19615i) q^{68} +6.00000 q^{69} +(-1.00000 + 1.73205i) q^{72} +(1.00000 + 1.73205i) q^{73} +(1.00000 + 1.73205i) q^{74} +(-2.50000 + 4.33013i) q^{75} -2.00000 q^{76} +1.00000 q^{78} +(-2.50000 + 4.33013i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} +6.00000 q^{83} +(-2.00000 + 3.46410i) q^{86} +(4.50000 + 7.79423i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-9.00000 + 15.5885i) q^{89} -6.00000 q^{92} +(2.00000 - 3.46410i) q^{93} +(3.00000 + 5.19615i) q^{94} +(-0.500000 + 0.866025i) q^{96} +13.0000 q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} + 2 q^{6} - 2 q^{8} + 2 q^{9} + q^{11} + q^{12} + 2 q^{13} - q^{16} - 6 q^{17} - 2 q^{18} + 2 q^{19} + 2 q^{22} + 6 q^{23} - q^{24} + 5 q^{25} + q^{26} + 10 q^{27} + 18 q^{29}+ \cdots + 4 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 + 2 * q^6 - 2 * q^8 + 2 * q^9 + q^11 + q^12 + 2 * q^13 - q^16 - 6 * q^17 - 2 * q^18 + 2 * q^19 + 2 * q^22 + 6 * q^23 - q^24 + 5 * q^25 + q^26 + 10 * q^27 + 18 * q^29 - 4 * q^31 + q^32 - q^33 - 12 * q^34 - 4 * q^36 - 2 * q^37 - 2 * q^38 + q^39 + 12 * q^41 - 8 * q^43 + q^44 - 6 * q^46 - 6 * q^47 - 2 * q^48 + 10 * q^50 + 6 * q^51 - q^52 + 5 * q^54 + 4 * q^57 + 9 * q^58 - 3 * q^59 + 11 * q^61 - 8 * q^62 + 2 * q^64 + q^66 - 11 * q^67 - 6 * q^68 + 12 * q^69 - 2 * q^72 + 2 * q^73 + 2 * q^74 - 5 * q^75 - 4 * q^76 + 2 * q^78 - 5 * q^79 - q^81 + 6 * q^82 + 12 * q^83 - 4 * q^86 + 9 * q^87 - q^88 - 18 * q^89 - 12 * q^92 + 4 * q^93 + 6 * q^94 - q^96 + 26 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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