LMFDB - Embedded newform 1078.2.e.d.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.d.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} -5.00000 q^{13} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(1.00000 + 1.73205i) q^{18} +(1.00000 - 1.73205i) q^{19} -1.00000 q^{22} +(-3.00000 + 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{25} +(2.50000 - 4.33013i) q^{26} +5.00000 q^{27} +3.00000 q^{29} +(4.00000 + 6.92820i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} -6.00000 q^{34} -2.00000 q^{36} +(-1.00000 + 1.73205i) q^{37} +(1.00000 + 1.73205i) q^{38} +(-2.50000 - 4.33013i) q^{39} +6.00000 q^{41} -4.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-3.00000 - 5.19615i) q^{46} +(3.00000 - 5.19615i) q^{47} -1.00000 q^{48} -5.00000 q^{50} +(-3.00000 + 5.19615i) q^{51} +(2.50000 + 4.33013i) q^{52} +(6.00000 + 10.3923i) q^{53} +(-2.50000 + 4.33013i) q^{54} +2.00000 q^{57} +(-1.50000 + 2.59808i) q^{58} +(-1.50000 - 2.59808i) q^{59} +(-3.50000 + 6.06218i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{66} +(6.50000 + 11.2583i) q^{67} +(3.00000 - 5.19615i) q^{68} -6.00000 q^{69} -12.0000 q^{71} +(1.00000 - 1.73205i) q^{72} +(-5.00000 - 8.66025i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-2.50000 + 4.33013i) q^{75} -2.00000 q^{76} +5.00000 q^{78} +(0.500000 - 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-3.00000 + 5.19615i) q^{82} -6.00000 q^{83} +(2.00000 - 3.46410i) q^{86} +(1.50000 + 2.59808i) q^{87} +(0.500000 + 0.866025i) q^{88} +(3.00000 - 5.19615i) q^{89} +6.00000 q^{92} +(-4.00000 + 6.92820i) q^{93} +(3.00000 + 5.19615i) q^{94} +(0.500000 - 0.866025i) q^{96} +13.0000 q^{97} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 + q^3 - q^4 - 2 * q^6 + 2 * q^8 + 2 * q^9	$ 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + 2 q^{8} + 2 q^{9} + q^{11} + q^{12} - 10 q^{13} - q^{16} + 6 q^{17} + 2 q^{18} + 2 q^{19} - 2 q^{22} - 6 q^{23} + q^{24} + 5 q^{25} + 5 q^{26} + 10 q^{27} + 6 q^{29} + 8 q^{31} - q^{32} - q^{33} - 12 q^{34} - 4 q^{36} - 2 q^{37} + 2 q^{38} - 5 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} + 5 q^{52} + 12 q^{53} - 5 q^{54} + 4 q^{57} - 3 q^{58} - 3 q^{59} - 7 q^{61} - 16 q^{62} + 2 q^{64} - q^{66} + 13 q^{67} + 6 q^{68} - 12 q^{69} - 24 q^{71} + 2 q^{72} - 10 q^{73} - 2 q^{74} - 5 q^{75} - 4 q^{76} + 10 q^{78} + q^{79} - q^{81} - 6 q^{82} - 12 q^{83} + 4 q^{86} + 3 q^{87} + q^{88} + 6 q^{89} + 12 q^{92} - 8 q^{93} + 6 q^{94} + q^{96} + 26 q^{97} + 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 - 10 * q^13 - q^16 + 6 * q^17 + 2 * q^18 + 2 * q^19 - 2 * q^22 - 6 * q^23 + q^24 + 5 * q^25 + 5 * q^26 + 10 * q^27 + 6 * q^29 + 8 * q^31 - q^32 - q^33 - 12 * q^34 - 4 * q^36 - 2 * q^37 + 2 * q^38 - 5 * 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 + 5 * q^52 + 12 * q^53 - 5 * q^54 + 4 * q^57 - 3 * q^58 - 3 * q^59 - 7 * q^61 - 16 * q^62 + 2 * q^64 - q^66 + 13 * q^67 + 6 * q^68 - 12 * q^69 - 24 * q^71 + 2 * q^72 - 10 * q^73 - 2 * q^74 - 5 * q^75 - 4 * q^76 + 10 * q^78 + q^79 - q^81 - 6 * q^82 - 12 * q^83 + 4 * q^86 + 3 * q^87 + q^88 + 6 * q^89 + 12 * q^92 - 8 * q^93 + 6 * q^94 + q^96 + 26 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

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
$13$	−5.00000			−1.38675			−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000			−1.38675			−0.693375	+	0.720577i	$0.743877\pi$
$14$		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	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$	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	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	2.50000	+	4.33013i	0.500000	+	0.866025i
$26$	2.50000	−	4.33013i	0.490290	−	0.849208i
$27$	5.00000			0.962250
$28$		0			0
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$		0			0
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	0.961625	+	0.274367i	$0.0884683\pi$
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	−0.243204	+	0.969975i	$0.578198\pi$
$32$	−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
$39$	−2.50000	−	4.33013i	−0.400320	−	0.693375i
$40$		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	−0.559908	−	0.828554i	$-0.689164\pi$
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	0.997503	+	0.0706177i	$0.0224970\pi$
$48$	−1.00000			−0.144338
$49$		0			0
$50$	−5.00000			−0.707107
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$	2.50000	+	4.33013i	0.346688	+	0.600481i
$53$	6.00000	+	10.3923i	0.824163	+	1.42749i	0.902557	+	0.430570i	$0.141688\pi$
$53$	6.00000	+	10.3923i	0.824163	+	1.42749i	−0.0783936	+	0.996922i	$0.524979\pi$
$54$	−2.50000	+	4.33013i	−0.340207	+	0.589256i
$55$		0			0
$56$		0			0
$57$	2.00000			0.264906
$58$	−1.50000	+	2.59808i	−0.196960	+	0.341144i
$59$	−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
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	−0.998264	−	0.0588933i	$-0.981243\pi$
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	0.550135	+	0.835076i	$0.314576\pi$
$62$	−8.00000			−1.01600
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$	−0.500000	−	0.866025i	−0.0615457	−	0.106600i
$67$	6.50000	+	11.2583i	0.794101	+	1.37542i	0.923408	+	0.383819i	$0.125391\pi$
$67$	6.50000	+	11.2583i	0.794101	+	1.37542i	−0.129307	+	0.991605i	$0.541275\pi$
$68$	3.00000	−	5.19615i	0.363803	−	0.630126i
$69$	−6.00000			−0.722315
$70$		0			0
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$	1.00000	−	1.73205i	0.117851	−	0.204124i
$73$	−5.00000	−	8.66025i	−0.585206	−	1.01361i	−0.994850	−	0.101361i	$-0.967680\pi$
$73$	−5.00000	−	8.66025i	−0.585206	−	1.01361i	0.409644	−	0.912245i	$-0.365653\pi$
$74$	−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
$78$	5.00000			0.566139
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	−0.836527	−	0.547926i	$-0.815418\pi$
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	0.892781	+	0.450490i	$0.148751\pi$
$80$		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	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$		0			0
$85$		0			0
$86$	2.00000	−	3.46410i	0.215666	−	0.373544i
$87$	1.50000	+	2.59808i	0.160817	+	0.278543i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	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	$0.0636557\pi$
$90$		0			0
$91$		0			0
$92$	6.00000			0.625543
$93$	−4.00000	+	6.92820i	−0.414781	+	0.718421i
$94$	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
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	0.930953	−	0.365140i	$-0.118979\pi$
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	−0.781697	+	0.623658i	$0.785646\pi$
$102$	−3.00000	−	5.19615i	−0.297044	−	0.514496i
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	−0.947576	−	0.319531i	$-0.896475\pi$
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	0.750510	+	0.660859i	$0.229808\pi$
$104$	−5.00000			−0.490290
$105$		0			0
$106$	−12.0000			−1.16554
$107$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$107$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$108$	−2.50000	−	4.33013i	−0.240563	−	0.416667i
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	−0.977769	−	0.209687i	$-0.932756\pi$
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	0.307290	−	0.951616i	$-0.400578\pi$
$110$		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
$116$	−1.50000	−	2.59808i	−0.139272	−	0.241225i
$117$	−5.00000	+	8.66025i	−0.462250	+	0.800641i
$118$	3.00000			0.276172
$119$		0			0
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−3.50000	−	6.06218i	−0.316875	−	0.548844i
$123$	3.00000	+	5.19615i	0.270501	+	0.468521i
$124$	4.00000	−	6.92820i	0.359211	−	0.622171i
$125$		0			0
$126$		0			0
$127$	−13.0000			−1.15356			−0.576782	−	0.816898i	$-0.695692\pi$
$127$	−13.0000			−1.15356			−0.576782	+	0.816898i	$0.695692\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−2.00000	−	3.46410i	−0.176090	−	0.304997i
$130$		0			0
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	−0.704692	−	0.709514i	$-0.748915\pi$
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	0.966803	+	0.255524i	$0.0822479\pi$
$132$	1.00000			0.0870388
$133$		0			0
$134$	−13.0000			−1.12303
$135$		0			0
$136$	3.00000	+	5.19615i	0.257248	+	0.445566i
$137$	−7.50000	−	12.9904i	−0.640768	−	1.10984i	−0.985262	−	0.171054i	$-0.945283\pi$
$137$	−7.50000	−	12.9904i	−0.640768	−	1.10984i	0.344493	−	0.938789i	$-0.388051\pi$
$138$	3.00000	−	5.19615i	0.255377	−	0.442326i
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$	−2.50000	−	4.33013i	−0.209061	−	0.362103i
$144$	1.00000	+	1.73205i	0.0833333	+	0.144338i
$145$		0			0
$146$	10.0000			0.827606
$147$		0			0
$148$	2.00000			0.164399
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$	−2.50000	−	4.33013i	−0.204124	−	0.353553i
$151$	0.500000	+	0.866025i	0.0406894	+	0.0704761i	0.885653	−	0.464348i	$-0.153711\pi$
$151$	0.500000	+	0.866025i	0.0406894	+	0.0704761i	−0.844963	+	0.534824i	$0.820378\pi$
$152$	1.00000	−	1.73205i	0.0811107	−	0.140488i
$153$	12.0000			0.970143
$154$		0			0
$155$		0			0
$156$	−2.50000	+	4.33013i	−0.200160	+	0.346688i
$157$	−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	$0.884359\pi$
$158$	0.500000	+	0.866025i	0.0397779	+	0.0688973i
$159$	−6.00000	+	10.3923i	−0.475831	+	0.824163i
$160$		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
$167$	−9.00000			−0.696441			−0.348220	−	0.937413i	$-0.613214\pi$
$167$	−9.00000			−0.696441			−0.348220	+	0.937413i	$0.613214\pi$
$168$		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
$173$	−7.50000	+	12.9904i	−0.570214	+	0.987640i	0.426329	+	0.904568i	$0.359807\pi$
$173$	−7.50000	+	12.9904i	−0.570214	+	0.987640i	−0.996544	+	0.0830722i	$0.973527\pi$
$174$	−3.00000			−0.227429
$175$		0			0
$176$	−1.00000			−0.0753778
$177$	1.50000	−	2.59808i	0.112747	−	0.195283i
$178$	3.00000	+	5.19615i	0.224860	+	0.389468i
$179$	−4.50000	−	7.79423i	−0.336346	−	0.582568i	0.647397	−	0.762153i	$-0.275858\pi$
$179$	−4.50000	−	7.79423i	−0.336346	−	0.582568i	−0.983742	+	0.179585i	$0.942524\pi$
$180$		0			0
$181$	10.0000			0.743294			0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$		0			0
$183$	−7.00000			−0.517455
$184$	−3.00000	+	5.19615i	−0.221163	+	0.383065i
$185$		0			0
$186$	−4.00000	−	6.92820i	−0.293294	−	0.508001i
$187$	−3.00000	+	5.19615i	−0.219382	+	0.379980i
$188$	−6.00000			−0.437595
$189$		0			0
$190$		0			0
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	−0.331611	−	0.943416i	$-0.607592\pi$
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	0.982828	−	0.184525i	$-0.0590746\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	11.0000	+	19.0526i	0.791797	+	1.37143i	0.924853	+	0.380325i	$0.124188\pi$
$193$	11.0000	+	19.0526i	0.791797	+	1.37143i	−0.133056	+	0.991109i	$0.542479\pi$
$194$	−6.50000	+	11.2583i	−0.466673	+	0.808301i
$195$		0			0
$196$		0			0
$197$	−9.00000			−0.641223			−0.320612	−	0.947211i	$-0.603888\pi$
$197$	−9.00000			−0.641223			−0.320612	+	0.947211i	$0.603888\pi$
$198$	−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
$201$	−6.50000	+	11.2583i	−0.458475	+	0.794101i
$202$	−3.00000			−0.211079
$203$		0			0
$204$	6.00000			0.420084
$205$		0			0
$206$	−2.00000	−	3.46410i	−0.139347	−	0.241355i
$207$	6.00000	+	10.3923i	0.417029	+	0.722315i
$208$	2.50000	−	4.33013i	0.173344	−	0.300240i
$209$	2.00000			0.138343
$210$		0			0
$211$	26.0000			1.78991			0.894957	−	0.446153i	$-0.147206\pi$
$211$	26.0000			1.78991			0.894957	+	0.446153i	$0.147206\pi$
$212$	6.00000	−	10.3923i	0.412082	−	0.713746i
$213$	−6.00000	−	10.3923i	−0.411113	−	0.712069i
$214$		0			0
$215$		0			0
$216$	5.00000			0.340207
$217$		0			0
$218$	14.0000			0.948200
$219$	5.00000	−	8.66025i	0.337869	−	0.585206i
$220$		0			0
$221$	−15.0000	−	25.9808i	−1.00901	−	1.74766i
$222$	1.00000	−	1.73205i	0.0671156	−	0.116248i
$223$	10.0000			0.669650			0.334825	−	0.942280i	$-0.391323\pi$
$223$	10.0000			0.669650			0.334825	+	0.942280i	$0.391323\pi$
$224$		0			0
$225$	10.0000			0.666667
$226$	−4.50000	+	7.79423i	−0.299336	+	0.518464i
$227$	−3.00000	−	5.19615i	−0.199117	−	0.344881i	0.749125	−	0.662428i	$-0.230474\pi$
$227$	−3.00000	−	5.19615i	−0.199117	−	0.344881i	−0.948242	+	0.317547i	$0.897141\pi$
$228$	−1.00000	−	1.73205i	−0.0662266	−	0.114708i
$229$	10.0000	−	17.3205i	0.660819	−	1.14457i	−0.319582	−	0.947559i	$-0.603543\pi$
$229$	10.0000	−	17.3205i	0.660819	−	1.14457i	0.980401	−	0.197013i	$-0.0631241\pi$
$230$		0			0
$231$		0			0
$232$	3.00000			0.196960
$233$	15.0000	−	25.9808i	0.982683	−	1.70206i	0.330870	−	0.943676i	$-0.392658\pi$
$233$	15.0000	−	25.9808i	0.982683	−	1.70206i	0.651813	−	0.758380i	$-0.274009\pi$
$234$	−5.00000	−	8.66025i	−0.326860	−	0.566139i
$235$		0			0
$236$	−1.50000	+	2.59808i	−0.0976417	+	0.169120i
$237$	1.00000			0.0649570
$238$		0			0
$239$	21.0000			1.35838			0.679189	−	0.733964i	$-0.262332\pi$
$239$	21.0000			1.35838			0.679189	+	0.733964i	$0.262332\pi$
$240$		0			0
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	0.658838	−	0.752285i	$-0.271048\pi$
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	−0.980917	+	0.194429i	$0.937715\pi$
$242$	−0.500000	−	0.866025i	−0.0321412	−	0.0556702i
$243$	8.00000	−	13.8564i	0.513200	−	0.888889i
$244$	7.00000			0.448129
$245$		0			0
$246$	−6.00000			−0.382546
$247$	−5.00000	+	8.66025i	−0.318142	+	0.551039i
$248$	4.00000	+	6.92820i	0.254000	+	0.439941i
$249$	−3.00000	−	5.19615i	−0.190117	−	0.329293i
$250$		0			0
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	−6.00000			−0.377217
$254$	6.50000	−	11.2583i	0.407846	−	0.706410i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	13.5000	−	23.3827i	0.842107	−	1.45857i	−0.0460033	−	0.998941i	$-0.514648\pi$
$257$	13.5000	−	23.3827i	0.842107	−	1.45857i	0.888110	−	0.459631i	$-0.152018\pi$
$258$	4.00000			0.249029
$259$		0			0
$260$		0			0
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$	3.00000	+	5.19615i	0.185341	+	0.321019i
$263$	1.50000	+	2.59808i	0.0924940	+	0.160204i	0.908560	−	0.417755i	$-0.137183\pi$
$263$	1.50000	+	2.59808i	0.0924940	+	0.160204i	−0.816066	+	0.577959i	$0.803849\pi$
$264$	−0.500000	+	0.866025i	−0.0307729	+	0.0533002i
$265$		0			0
$266$		0			0
$267$	6.00000			0.367194
$268$	6.50000	−	11.2583i	0.397051	−	0.687712i
$269$	−12.0000	−	20.7846i	−0.731653	−	1.26726i	−0.956176	−	0.292791i	$-0.905416\pi$
$269$	−12.0000	−	20.7846i	−0.731653	−	1.26726i	0.224523	−	0.974469i	$-0.427917\pi$
$270$		0			0
$271$	−12.5000	+	21.6506i	−0.759321	+	1.31518i	0.183876	+	0.982949i	$0.441135\pi$
$271$	−12.5000	+	21.6506i	−0.759321	+	1.31518i	−0.943197	+	0.332233i	$0.892198\pi$
$272$	−6.00000			−0.363803
$273$		0			0
$274$	15.0000			0.906183
$275$	−2.50000	+	4.33013i	−0.150756	+	0.261116i
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	0.880656	−	0.473757i	$-0.157103\pi$
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	−0.850613	+	0.525792i	$0.823769\pi$
$278$	−2.00000	+	3.46410i	−0.119952	+	0.207763i
$279$	16.0000			0.957895
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$	−3.00000	+	5.19615i	−0.178647	+	0.309426i
$283$	−11.0000	−	19.0526i	−0.653882	−	1.13256i	−0.982173	−	0.187980i	$-0.939806\pi$
$283$	−11.0000	−	19.0526i	−0.653882	−	1.13256i	0.328291	−	0.944577i	$-0.393527\pi$
$284$	6.00000	+	10.3923i	0.356034	+	0.616670i
$285$		0			0
$286$	5.00000			0.295656
$287$		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
$292$	−5.00000	+	8.66025i	−0.292603	+	0.506803i
$293$	18.0000			1.05157			0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000			1.05157			0.525786	+	0.850617i	$0.323771\pi$
$294$		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
$299$	15.0000	−	25.9808i	0.867472	−	1.50251i
$300$	5.00000			0.288675
$301$		0			0
$302$	−1.00000			−0.0575435
$303$	−1.50000	+	2.59808i	−0.0861727	+	0.149256i
$304$	1.00000	+	1.73205i	0.0573539	+	0.0993399i
$305$		0			0
$306$	−6.00000	+	10.3923i	−0.342997	+	0.594089i
$307$	−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
$309$	−4.00000			−0.227552
$310$		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	$0.595114\pi$
$312$	−2.50000	−	4.33013i	−0.141535	−	0.245145i
$313$	−3.50000	+	6.06218i	−0.197832	+	0.342655i	−0.947825	−	0.318791i	$-0.896723\pi$
$313$	−3.50000	+	6.06218i	−0.197832	+	0.342655i	0.749993	+	0.661445i	$0.230057\pi$
$314$	4.00000			0.225733
$315$		0			0
$316$	−1.00000			−0.0562544
$317$	12.0000	−	20.7846i	0.673987	−	1.16738i	−0.302777	−	0.953062i	$-0.597914\pi$
$317$	12.0000	−	20.7846i	0.673987	−	1.16738i	0.976764	−	0.214318i	$-0.0687530\pi$
$318$	−6.00000	−	10.3923i	−0.336463	−	0.582772i
$319$	1.50000	+	2.59808i	0.0839839	+	0.145464i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	12.0000			0.667698
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−12.5000	−	21.6506i	−0.693375	−	1.20096i
$326$	−8.50000	−	14.7224i	−0.470771	−	0.815400i
$327$	7.00000	−	12.1244i	0.387101	−	0.670478i
$328$	6.00000			0.331295
$329$		0			0
$330$		0			0
$331$	6.50000	−	11.2583i	0.357272	−	0.618814i	−0.630232	−	0.776407i	$-0.717040\pi$
$331$	6.50000	−	11.2583i	0.357272	−	0.618814i	0.987504	+	0.157593i	$0.0503735\pi$
$332$	3.00000	+	5.19615i	0.164646	+	0.285176i
$333$	2.00000	+	3.46410i	0.109599	+	0.189832i
$334$	4.50000	−	7.79423i	0.246229	−	0.426481i
$335$		0			0
$336$		0			0
$337$	−22.0000			−1.19842			−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000			−1.19842			−0.599208	+	0.800593i	$0.704518\pi$
$338$	−6.00000	+	10.3923i	−0.326357	+	0.565267i
$339$	4.50000	+	7.79423i	0.244406	+	0.423324i
$340$		0			0
$341$	−4.00000	+	6.92820i	−0.216612	+	0.375183i
$342$	4.00000			0.216295
$343$		0			0
$344$	−4.00000			−0.215666
$345$		0			0
$346$	−7.50000	−	12.9904i	−0.403202	−	0.698367i
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$	1.50000	−	2.59808i	0.0804084	−	0.139272i
$349$	34.0000			1.81998			0.909989	−	0.414632i	$-0.136090\pi$
$349$	34.0000			1.81998			0.909989	+	0.414632i	$0.136090\pi$
$350$		0			0
$351$	−25.0000			−1.33440
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	15.0000	+	25.9808i	0.798369	+	1.38282i	0.920677	+	0.390324i	$0.127637\pi$
$353$	15.0000	+	25.9808i	0.798369	+	1.38282i	−0.122308	+	0.992492i	$0.539030\pi$
$354$	1.50000	+	2.59808i	0.0797241	+	0.138086i
$355$		0			0
$356$	−6.00000			−0.317999
$357$		0			0
$358$	9.00000			0.475665
$359$	4.50000	−	7.79423i	0.237501	−	0.411364i	−0.722496	−	0.691375i	$-0.757005\pi$
$359$	4.50000	−	7.79423i	0.237501	−	0.411364i	0.959997	+	0.280012i	$0.0903384\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−5.00000	+	8.66025i	−0.262794	+	0.455173i
$363$	−1.00000			−0.0524864
$364$		0			0
$365$		0			0
$366$	3.50000	−	6.06218i	0.182948	−	0.316875i
$367$	19.0000	+	32.9090i	0.991792	+	1.71783i	0.606628	+	0.794986i	$0.292522\pi$
$367$	19.0000	+	32.9090i	0.991792	+	1.71783i	0.385164	+	0.922848i	$0.374145\pi$
$368$	−3.00000	−	5.19615i	−0.156386	−	0.270868i
$369$	6.00000	−	10.3923i	0.312348	−	0.541002i
$370$		0			0
$371$		0			0
$372$	8.00000			0.414781
$373$	−5.50000	+	9.52628i	−0.284779	+	0.493252i	−0.972556	−	0.232671i	$-0.925254\pi$
$373$	−5.50000	+	9.52628i	−0.284779	+	0.493252i	0.687776	+	0.725923i	$0.258587\pi$
$374$	−3.00000	−	5.19615i	−0.155126	−	0.268687i
$375$		0			0
$376$	3.00000	−	5.19615i	0.154713	−	0.267971i
$377$	−15.0000			−0.772539
$378$		0			0
$379$	−25.0000			−1.28416			−0.642082	−	0.766636i	$-0.721929\pi$
$379$	−25.0000			−1.28416			−0.642082	+	0.766636i	$0.721929\pi$
$380$		0			0
$381$	−6.50000	−	11.2583i	−0.333005	−	0.576782i
$382$	9.00000	+	15.5885i	0.460480	+	0.797575i
$383$	6.00000	−	10.3923i	0.306586	−	0.531022i	−0.671027	−	0.741433i	$-0.734147\pi$
$383$	6.00000	−	10.3923i	0.306586	−	0.531022i	0.977613	+	0.210411i	$0.0674801\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−22.0000			−1.11977
$387$	−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
$393$	6.00000			0.302660
$394$	4.50000	−	7.79423i	0.226707	−	0.392668i
$395$		0			0
$396$	−1.00000	−	1.73205i	−0.0502519	−	0.0870388i
$397$	1.00000	−	1.73205i	0.0501886	−	0.0869291i	−0.839840	−	0.542834i	$-0.817351\pi$
$397$	1.00000	−	1.73205i	0.0501886	−	0.0869291i	0.890028	+	0.455905i	$0.150684\pi$
$398$	−14.0000			−0.701757
$399$		0			0
$400$	−5.00000			−0.250000
$401$	4.50000	−	7.79423i	0.224719	−	0.389225i	−0.731516	−	0.681824i	$-0.761187\pi$
$401$	4.50000	−	7.79423i	0.224719	−	0.389225i	0.956235	+	0.292599i	$0.0945202\pi$
$402$	−6.50000	−	11.2583i	−0.324191	−	0.561514i
$403$	−20.0000	−	34.6410i	−0.996271	−	1.72559i
$404$	1.50000	−	2.59808i	0.0746278	−	0.129259i
$405$		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
$411$	7.50000	−	12.9904i	0.369948	−	0.640768i
$412$	4.00000			0.197066
$413$		0			0
$414$	−12.0000			−0.589768
$415$		0			0
$416$	2.50000	+	4.33013i	0.122573	+	0.212302i
$417$	2.00000	+	3.46410i	0.0979404	+	0.169638i
$418$	−1.00000	+	1.73205i	−0.0489116	+	0.0847174i
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$		0			0
$421$	−16.0000			−0.779792			−0.389896	−	0.920859i	$-0.627489\pi$
$421$	−16.0000			−0.779792			−0.389896	+	0.920859i	$0.627489\pi$
$422$	−13.0000	+	22.5167i	−0.632830	+	1.09609i
$423$	−6.00000	−	10.3923i	−0.291730	−	0.505291i
$424$	6.00000	+	10.3923i	0.291386	+	0.504695i
$425$	−15.0000	+	25.9808i	−0.727607	+	1.26025i
$426$	12.0000			0.581402
$427$		0			0
$428$		0			0
$429$	2.50000	−	4.33013i	0.120701	−	0.209061i
$430$		0			0
$431$	−7.50000	−	12.9904i	−0.361262	−	0.625725i	0.626907	−	0.779094i	$-0.284321\pi$
$431$	−7.50000	−	12.9904i	−0.361262	−	0.625725i	−0.988169	+	0.153370i	$0.950987\pi$
$432$	−2.50000	+	4.33013i	−0.120281	+	0.208333i
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$		0			0
$436$	−7.00000	+	12.1244i	−0.335239	+	0.580651i
$437$	6.00000	+	10.3923i	0.287019	+	0.497131i
$438$	5.00000	+	8.66025i	0.238909	+	0.413803i
$439$	−9.50000	+	16.4545i	−0.453410	+	0.785330i	−0.998595	−	0.0529862i	$-0.983126\pi$
$439$	−9.50000	+	16.4545i	−0.453410	+	0.785330i	0.545185	+	0.838316i	$0.316459\pi$
$440$		0			0
$441$		0			0
$442$	30.0000			1.42695
$443$	−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
$446$	−5.00000	+	8.66025i	−0.236757	+	0.410075i
$447$	6.00000			0.283790
$448$		0			0
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$	−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
$453$	−0.500000	+	0.866025i	−0.0234920	+	0.0406894i
$454$	6.00000			0.281594
$455$		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	$-0.00537742\pi$
$458$	10.0000	+	17.3205i	0.467269	+	0.809334i
$459$	15.0000	+	25.9808i	0.700140	+	1.21268i
$460$		0			0
$461$	−39.0000			−1.81641			−0.908206	−	0.418524i	$-0.862547\pi$
$461$	−39.0000			−1.81641			−0.908206	+	0.418524i	$0.862547\pi$
$462$		0			0
$463$	26.0000			1.20832			0.604161	−	0.796862i	$-0.293508\pi$
$463$	26.0000			1.20832			0.604161	+	0.796862i	$0.293508\pi$
$464$	−1.50000	+	2.59808i	−0.0696358	+	0.120613i
$465$		0			0
$466$	15.0000	+	25.9808i	0.694862	+	1.20354i
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	−0.970799	−	0.239892i	$-0.922888\pi$
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	0.693153	+	0.720791i	$0.256221\pi$
$468$	10.0000			0.462250
$469$		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
$474$	−0.500000	+	0.866025i	−0.0229658	+	0.0397779i
$475$	10.0000			0.458831
$476$		0			0
$477$	24.0000			1.09888
$478$	−10.5000	+	18.1865i	−0.480259	+	0.831833i
$479$	−1.50000	−	2.59808i	−0.0685367	−	0.118709i	0.829721	−	0.558179i	$-0.188500\pi$
$479$	−1.50000	−	2.59808i	−0.0685367	−	0.118709i	−0.898257	+	0.439470i	$0.855166\pi$
$480$		0			0
$481$	5.00000	−	8.66025i	0.227980	−	0.394874i
$482$	10.0000			0.455488
$483$		0			0
$484$	1.00000			0.0454545
$485$		0			0
$486$	8.00000	+	13.8564i	0.362887	+	0.628539i
$487$	2.00000	+	3.46410i	0.0906287	+	0.156973i	0.907776	−	0.419456i	$-0.137779\pi$
$487$	2.00000	+	3.46410i	0.0906287	+	0.156973i	−0.817147	+	0.576429i	$0.804446\pi$
$488$	−3.50000	+	6.06218i	−0.158438	+	0.274422i
$489$	−17.0000			−0.768767
$490$		0			0
$491$	−30.0000			−1.35388			−0.676941	−	0.736038i	$-0.736695\pi$
$491$	−30.0000			−1.35388			−0.676941	+	0.736038i	$0.736695\pi$
$492$	3.00000	−	5.19615i	0.135250	−	0.234261i
$493$	9.00000	+	15.5885i	0.405340	+	0.702069i
$494$	−5.00000	−	8.66025i	−0.224961	−	0.389643i
$495$		0			0
$496$	−8.00000			−0.359211
$497$		0			0
$498$	6.00000			0.268866
$499$	−4.00000	+	6.92820i	−0.179065	+	0.310149i	−0.941560	−	0.336844i	$-0.890640\pi$
$499$	−4.00000	+	6.92820i	−0.179065	+	0.310149i	0.762496	+	0.646993i	$0.223974\pi$
$500$		0			0
$501$	−4.50000	−	7.79423i	−0.201045	−	0.348220i
$502$	6.00000	−	10.3923i	0.267793	−	0.463831i
$503$	−21.0000			−0.936344			−0.468172	−	0.883637i	$-0.655087\pi$
$503$	−21.0000			−0.936344			−0.468172	+	0.883637i	$0.655087\pi$
$504$		0			0
$505$		0			0
$506$	3.00000	−	5.19615i	0.133366	−	0.230997i
$507$	6.00000	+	10.3923i	0.266469	+	0.461538i
$508$	6.50000	+	11.2583i	0.288391	+	0.499508i
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	−0.791849	−	0.610718i	$-0.790881\pi$
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	0.924821	+	0.380402i	$0.124214\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$	5.00000	−	8.66025i	0.220755	−	0.382360i
$514$	13.5000	+	23.3827i	0.595459	+	1.03137i
$515$		0			0
$516$	−2.00000	+	3.46410i	−0.0880451	+	0.152499i
$517$	6.00000			0.263880
$518$		0			0
$519$	−15.0000			−0.658427
$520$		0			0
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	0.598714	−	0.800963i	$-0.295679\pi$
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	−0.993011	+	0.118020i	$0.962345\pi$
$522$	3.00000	+	5.19615i	0.131306	+	0.227429i
$523$	−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	$0.280422\pi$
$524$	−6.00000			−0.262111
$525$		0			0
$526$	−3.00000			−0.130806
$527$	−24.0000	+	41.5692i	−1.04546	+	1.81078i
$528$	−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
$533$	−30.0000			−1.29944
$534$	−3.00000	+	5.19615i	−0.129823	+	0.224860i
$535$		0			0
$536$	6.50000	+	11.2583i	0.280757	+	0.486286i
$537$	4.50000	−	7.79423i	0.194189	−	0.336346i
$538$	24.0000			1.03471
$539$		0			0
$540$		0			0
$541$	−2.50000	+	4.33013i	−0.107483	+	0.186167i	−0.914750	−	0.404020i	$-0.867613\pi$
$541$	−2.50000	+	4.33013i	−0.107483	+	0.186167i	0.807267	+	0.590187i	$0.200946\pi$
$542$	−12.5000	−	21.6506i	−0.536921	−	0.929974i
$543$	5.00000	+	8.66025i	0.214571	+	0.371647i
$544$	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	$0.704275\pi$
$548$	−7.50000	+	12.9904i	−0.320384	+	0.554922i
$549$	7.00000	+	12.1244i	0.298753	+	0.517455i
$550$	−2.50000	−	4.33013i	−0.106600	−	0.184637i
$551$	3.00000	−	5.19615i	0.127804	−	0.221364i
$552$	−6.00000			−0.255377
$553$		0			0
$554$	−1.00000			−0.0424859
$555$		0			0
$556$	−2.00000	−	3.46410i	−0.0848189	−	0.146911i
$557$	3.00000	+	5.19615i	0.127114	+	0.220168i	0.922557	−	0.385860i	$-0.126095\pi$
$557$	3.00000	+	5.19615i	0.127114	+	0.220168i	−0.795443	+	0.606028i	$0.792762\pi$
$558$	−8.00000	+	13.8564i	−0.338667	+	0.586588i
$559$	20.0000			0.845910
$560$		0			0
$561$	−6.00000			−0.253320
$562$	3.00000	−	5.19615i	0.126547	−	0.219186i
$563$	9.00000	+	15.5885i	0.379305	+	0.656975i	0.990961	−	0.134148i	$-0.0428299\pi$
$563$	9.00000	+	15.5885i	0.379305	+	0.656975i	−0.611656	+	0.791123i	$0.709497\pi$
$564$	−3.00000	−	5.19615i	−0.126323	−	0.218797i
$565$		0			0
$566$	22.0000			0.924729
$567$		0			0
$568$	−12.0000			−0.503509
$569$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$569$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$570$		0			0
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	−2.50000	+	4.33013i	−0.104530	+	0.181052i
$573$	18.0000			0.751961
$574$		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
$579$	−11.0000	+	19.0526i	−0.457144	+	0.791797i
$580$		0			0
$581$		0			0
$582$	−13.0000			−0.538867
$583$	−6.00000	+	10.3923i	−0.248495	+	0.430405i
$584$	−5.00000	−	8.66025i	−0.206901	−	0.358364i
$585$		0			0
$586$	−9.00000	+	15.5885i	−0.371787	+	0.643953i
$587$	−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
$589$	16.0000			0.659269
$590$		0			0
$591$	−4.50000	−	7.79423i	−0.185105	−	0.320612i
$592$	−1.00000	−	1.73205i	−0.0410997	−	0.0711868i
$593$	12.0000	−	20.7846i	0.492781	−	0.853522i	−0.507184	−	0.861838i	$-0.669314\pi$
$593$	12.0000	−	20.7846i	0.492781	−	0.853522i	0.999965	+	0.00831589i	$0.00264706\pi$
$594$	−5.00000			−0.205152
$595$		0			0
$596$	−6.00000			−0.245770
$597$	−7.00000	+	12.1244i	−0.286491	+	0.496217i
$598$	15.0000	+	25.9808i	0.613396	+	1.06243i
$599$		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
$601$	10.0000			0.407909			0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000			0.407909			0.203954	+	0.978980i	$0.434621\pi$
$602$		0			0
$603$	26.0000			1.05880
$604$	0.500000	−	0.866025i	0.0203447	−	0.0352381i
$605$		0			0
$606$	−1.50000	−	2.59808i	−0.0609333	−	0.105540i
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	−0.773358	−	0.633970i	$-0.781424\pi$
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	0.935713	+	0.352763i	$0.114758\pi$
$608$	−2.00000			−0.0811107
$609$		0			0
$610$		0			0
$611$	−15.0000	+	25.9808i	−0.606835	+	1.05107i
$612$	−6.00000	−	10.3923i	−0.242536	−	0.420084i
$613$	−13.0000	−	22.5167i	−0.525065	−	0.909439i	−0.999574	−	0.0291886i	$-0.990708\pi$
$613$	−13.0000	−	22.5167i	−0.525065	−	0.909439i	0.474509	−	0.880251i	$-0.342626\pi$
$614$	16.0000	−	27.7128i	0.645707	−	1.11840i
$615$		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	$0.361077\pi$
$618$	2.00000	−	3.46410i	0.0804518	−	0.139347i
$619$	22.0000	+	38.1051i	0.884255	+	1.53157i	0.846566	+	0.532284i	$0.178666\pi$
$619$	22.0000	+	38.1051i	0.884255	+	1.53157i	0.0376891	+	0.999290i	$0.488000\pi$
$620$		0			0
$621$	−15.0000	+	25.9808i	−0.601929	+	1.04257i
$622$	−24.0000			−0.962312
$623$		0			0
$624$	5.00000			0.200160
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$	−3.50000	−	6.06218i	−0.139888	−	0.242293i
$627$	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
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$	0.500000	−	0.866025i	0.0198889	−	0.0344486i
$633$	13.0000	+	22.5167i	0.516704	+	0.894957i
$634$	12.0000	+	20.7846i	0.476581	+	0.825462i
$635$		0			0
$636$	12.0000			0.475831
$637$		0			0
$638$	−3.00000			−0.118771
$639$	−12.0000	+	20.7846i	−0.474713	+	0.822226i
$640$		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	$0.890212\pi$
$642$		0			0
$643$	19.0000			0.749287			0.374643	−	0.927169i	$-0.377765\pi$
$643$	19.0000			0.749287			0.374643	+	0.927169i	$0.377765\pi$
$644$		0			0
$645$		0			0
$646$	−6.00000	+	10.3923i	−0.236067	+	0.408880i
$647$	18.0000	+	31.1769i	0.707653	+	1.22569i	0.965726	+	0.259565i	$0.0835793\pi$
$647$	18.0000	+	31.1769i	0.707653	+	1.22569i	−0.258073	+	0.966126i	$0.583087\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	1.50000	−	2.59808i	0.0588802	−	0.101983i
$650$	25.0000			0.980581
$651$		0			0
$652$	17.0000			0.665771
$653$	15.0000	−	25.9808i	0.586995	−	1.01671i	−0.407628	−	0.913148i	$-0.633644\pi$
$653$	15.0000	−	25.9808i	0.586995	−	1.01671i	0.994623	−	0.103558i	$-0.0330227\pi$
$654$	7.00000	+	12.1244i	0.273722	+	0.474100i
$655$		0			0
$656$	−3.00000	+	5.19615i	−0.117130	+	0.202876i
$657$	−20.0000			−0.780274
$658$		0			0
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$		0			0
$661$	−17.0000	−	29.4449i	−0.661223	−	1.14527i	−0.980294	−	0.197542i	$-0.936704\pi$
$661$	−17.0000	−	29.4449i	−0.661223	−	1.14527i	0.319071	−	0.947731i	$-0.396629\pi$
$662$	6.50000	+	11.2583i	0.252630	+	0.437567i
$663$	15.0000	−	25.9808i	0.582552	−	1.00901i
$664$	−6.00000			−0.232845
$665$		0			0
$666$	−4.00000			−0.154997
$667$	−9.00000	+	15.5885i	−0.348481	+	0.603587i
$668$	4.50000	+	7.79423i	0.174110	+	0.301568i
$669$	5.00000	+	8.66025i	0.193311	+	0.334825i
$670$		0			0
$671$	−7.00000			−0.270232
$672$		0			0
$673$	−4.00000			−0.154189			−0.0770943	−	0.997024i	$-0.524564\pi$
$673$	−4.00000			−0.154189			−0.0770943	+	0.997024i	$0.524564\pi$
$674$	11.0000	−	19.0526i	0.423704	−	0.733877i
$675$	12.5000	+	21.6506i	0.481125	+	0.833333i
$676$	−6.00000	−	10.3923i	−0.230769	−	0.399704i
$677$	21.0000	−	36.3731i	0.807096	−	1.39793i	−0.107772	−	0.994176i	$-0.534372\pi$
$677$	21.0000	−	36.3731i	0.807096	−	1.39793i	0.914867	−	0.403755i	$-0.132295\pi$
$678$	−9.00000			−0.345643
$679$		0			0
$680$		0			0
$681$	3.00000	−	5.19615i	0.114960	−	0.199117i
$682$	−4.00000	−	6.92820i	−0.153168	−	0.265295i
$683$	22.5000	+	38.9711i	0.860939	+	1.49119i	0.871024	+	0.491240i	$0.163456\pi$
$683$	22.5000	+	38.9711i	0.860939	+	1.49119i	−0.0100856	+	0.999949i	$0.503210\pi$
$684$	−2.00000	+	3.46410i	−0.0764719	+	0.132453i
$685$		0			0
$686$		0			0
$687$	20.0000			0.763048
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	−30.0000	−	51.9615i	−1.14291	−	1.97958i
$690$		0			0
$691$	17.5000	−	30.3109i	0.665731	−	1.15308i	−0.313355	−	0.949636i	$-0.601453\pi$
$691$	17.5000	−	30.3109i	0.665731	−	1.15308i	0.979086	−	0.203445i	$-0.0652137\pi$
$692$	15.0000			0.570214
$693$		0			0
$694$	12.0000			0.455514
$695$		0			0
$696$	1.50000	+	2.59808i	0.0568574	+	0.0984798i
$697$	18.0000	+	31.1769i	0.681799	+	1.18091i
$698$	−17.0000	+	29.4449i	−0.643459	+	1.11450i
$699$	30.0000			1.13470
$700$		0			0
$701$	−3.00000			−0.113308			−0.0566542	−	0.998394i	$-0.518043\pi$
$701$	−3.00000			−0.113308			−0.0566542	+	0.998394i	$0.518043\pi$
$702$	12.5000	−	21.6506i	0.471782	−	0.817151i
$703$	2.00000	+	3.46410i	0.0754314	+	0.130651i
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$		0			0
$706$	−30.0000			−1.12906
$707$		0			0
$708$	−3.00000			−0.112747
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	−0.756730	−	0.653727i	$-0.773204\pi$
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	0.944509	+	0.328484i	$0.106538\pi$
$710$		0			0
$711$	−1.00000	−	1.73205i	−0.0375029	−	0.0649570i
$712$	3.00000	−	5.19615i	0.112430	−	0.194734i
$713$	−48.0000			−1.79761
$714$		0			0
$715$		0			0
$716$	−4.50000	+	7.79423i	−0.168173	+	0.291284i
$717$	10.5000	+	18.1865i	0.392130	+	0.679189i
$718$	4.50000	+	7.79423i	0.167939	+	0.290878i
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	−0.916529	−	0.399969i	$-0.869021\pi$
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	0.804648	+	0.593753i	$0.202354\pi$
$720$		0			0
$721$		0			0
$722$	−15.0000			−0.558242
$723$	5.00000	−	8.66025i	0.185952	−	0.322078i
$724$	−5.00000	−	8.66025i	−0.185824	−	0.321856i
$725$	7.50000	+	12.9904i	0.278543	+	0.482451i
$726$	0.500000	−	0.866025i	0.0185567	−	0.0321412i
$727$	−50.0000			−1.85440			−0.927199	−	0.374570i	$-0.877790\pi$
$727$	−50.0000			−1.85440			−0.927199	+	0.374570i	$0.877790\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−12.0000	−	20.7846i	−0.443836	−	0.768747i
$732$	3.50000	+	6.06218i	0.129364	+	0.224065i
$733$	−21.5000	+	37.2391i	−0.794121	+	1.37546i	0.129275	+	0.991609i	$0.458735\pi$
$733$	−21.5000	+	37.2391i	−0.794121	+	1.37546i	−0.923396	+	0.383849i	$0.874598\pi$
$734$	−38.0000			−1.40261
$735$		0			0
$736$	6.00000			0.221163
$737$	−6.50000	+	11.2583i	−0.239431	+	0.414706i
$738$	6.00000	+	10.3923i	0.220863	+	0.382546i
$739$	−1.00000	−	1.73205i	−0.0367856	−	0.0637145i	0.847046	−	0.531519i	$-0.178379\pi$
$739$	−1.00000	−	1.73205i	−0.0367856	−	0.0637145i	−0.883832	+	0.467804i	$0.845045\pi$
$740$		0			0
$741$	−10.0000			−0.367359
$742$		0			0
$743$	−36.0000			−1.32071			−0.660356	−	0.750953i	$-0.729595\pi$
$743$	−36.0000			−1.32071			−0.660356	+	0.750953i	$0.729595\pi$
$744$	−4.00000	+	6.92820i	−0.146647	+	0.254000i
$745$		0			0
$746$	−5.50000	−	9.52628i	−0.201369	−	0.348782i
$747$	−6.00000	+	10.3923i	−0.219529	+	0.380235i
$748$	6.00000			0.219382
$749$		0			0
$750$		0			0
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	−0.682341	−	0.731034i	$-0.739038\pi$
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	0.974265	+	0.225407i	$0.0723712\pi$
$752$	3.00000	+	5.19615i	0.109399	+	0.189484i
$753$	−6.00000	−	10.3923i	−0.218652	−	0.378717i
$754$	7.50000	−	12.9904i	0.273134	−	0.473082i
$755$		0			0
$756$		0			0
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$	12.5000	−	21.6506i	0.454020	−	0.786386i
$759$	−3.00000	−	5.19615i	−0.108893	−	0.188608i
$760$		0			0
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	−0.454935	−	0.890525i	$-0.650337\pi$
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	0.998684	−	0.0512772i	$-0.0163292\pi$
$762$	13.0000			0.470940
$763$		0			0
$764$	−18.0000			−0.651217
$765$		0			0
$766$	6.00000	+	10.3923i	0.216789	+	0.375489i
$767$	7.50000	+	12.9904i	0.270809	+	0.469055i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−2.00000			−0.0721218			−0.0360609	−	0.999350i	$-0.511481\pi$
$769$	−2.00000			−0.0721218			−0.0360609	+	0.999350i	$0.511481\pi$
$770$		0			0
$771$	27.0000			0.972381
$772$	11.0000	−	19.0526i	0.395899	−	0.685717i
$773$	−12.0000	−	20.7846i	−0.431610	−	0.747570i	0.565402	−	0.824815i	$-0.308721\pi$
$773$	−12.0000	−	20.7846i	−0.431610	−	0.747570i	−0.997012	+	0.0772449i	$0.975388\pi$
$774$	−4.00000	−	6.92820i	−0.143777	−	0.249029i
$775$	−20.0000	+	34.6410i	−0.718421	+	1.24434i
$776$	13.0000			0.466673
$777$		0			0
$778$	12.0000			0.430221
$779$	6.00000	−	10.3923i	0.214972	−	0.372343i
$780$		0			0
$781$	−6.00000	−	10.3923i	−0.214697	−	0.371866i
$782$	18.0000	−	31.1769i	0.643679	−	1.11488i
$783$	15.0000			0.536056
$784$		0			0
$785$		0			0
$786$	−3.00000	+	5.19615i	−0.107006	+	0.185341i
$787$	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	$0.753059\pi$
$788$	4.50000	+	7.79423i	0.160306	+	0.277658i
$789$	−1.50000	+	2.59808i	−0.0534014	+	0.0924940i
$790$		0			0
$791$		0			0
$792$	2.00000			0.0710669
$793$	17.5000	−	30.3109i	0.621443	−	1.07637i
$794$	1.00000	+	1.73205i	0.0354887	+	0.0614682i
$795$		0			0
$796$	7.00000	−	12.1244i	0.248108	−	0.429736i
$797$	−6.00000			−0.212531			−0.106265	−	0.994338i	$-0.533889\pi$
$797$	−6.00000			−0.212531			−0.106265	+	0.994338i	$0.533889\pi$
$798$		0			0
$799$	36.0000			1.27359
$800$	2.50000	−	4.33013i	0.0883883	−	0.153093i
$801$	−6.00000	−	10.3923i	−0.212000	−	0.367194i
$802$	4.50000	+	7.79423i	0.158901	+	0.275224i
$803$	5.00000	−	8.66025i	0.176446	−	0.305614i
$804$	13.0000			0.458475
$805$		0			0
$806$	40.0000			1.40894
$807$	12.0000	−	20.7846i	0.422420	−	0.731653i
$808$	1.50000	+	2.59808i	0.0527698	+	0.0914000i
$809$	−18.0000	−	31.1769i	−0.632846	−	1.09612i	−0.986967	−	0.160922i	$-0.948553\pi$
$809$	−18.0000	−	31.1769i	−0.632846	−	1.09612i	0.354121	−	0.935200i	$-0.384780\pi$
$810$		0			0
$811$	16.0000			0.561836			0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000			0.561836			0.280918	+	0.959732i	$0.409361\pi$
$812$		0			0
$813$	−25.0000			−0.876788
$814$	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
$821$	−13.5000	+	23.3827i	−0.471153	+	0.816061i	−0.999456	−	0.0329950i	$-0.989495\pi$
$821$	−13.5000	+	23.3827i	−0.471153	+	0.816061i	0.528302	+	0.849056i	$0.322829\pi$
$822$	7.50000	+	12.9904i	0.261593	+	0.453092i
$823$	−13.0000	−	22.5167i	−0.453152	−	0.784881i	0.545428	−	0.838157i	$-0.316367\pi$
$823$	−13.0000	−	22.5167i	−0.453152	−	0.784881i	−0.998580	+	0.0532760i	$0.983034\pi$
$824$	−2.00000	+	3.46410i	−0.0696733	+	0.120678i
$825$	−5.00000			−0.174078
$826$		0			0
$827$	42.0000			1.46048			0.730242	−	0.683189i	$-0.239408\pi$
$827$	42.0000			1.46048			0.730242	+	0.683189i	$0.239408\pi$
$828$	6.00000	−	10.3923i	0.208514	−	0.361158i
$829$	−8.00000	−	13.8564i	−0.277851	−	0.481253i	0.692999	−	0.720938i	$-0.256289\pi$
$829$	−8.00000	−	13.8564i	−0.277851	−	0.481253i	−0.970851	+	0.239686i	$0.922956\pi$
$830$		0			0
$831$	−0.500000	+	0.866025i	−0.0173448	+	0.0300421i
$832$	−5.00000			−0.173344
$833$		0			0
$834$	−4.00000			−0.138509
$835$		0			0
$836$	−1.00000	−	1.73205i	−0.0345857	−	0.0599042i
$837$	20.0000	+	34.6410i	0.691301	+	1.19737i
$838$	6.00000	−	10.3923i	0.207267	−	0.358996i
$839$	−30.0000			−1.03572			−0.517858	−	0.855467i	$-0.673270\pi$
$839$	−30.0000			−1.03572			−0.517858	+	0.855467i	$0.673270\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$	8.00000	−	13.8564i	0.275698	−	0.477523i
$843$	−3.00000	−	5.19615i	−0.103325	−	0.178965i
$844$	−13.0000	−	22.5167i	−0.447478	−	0.775055i
$845$		0			0
$846$	12.0000			0.412568
$847$		0			0
$848$	−12.0000			−0.412082
$849$	11.0000	−	19.0526i	0.377519	−	0.653882i
$850$	−15.0000	−	25.9808i	−0.514496	−	0.891133i
$851$	−6.00000	−	10.3923i	−0.205677	−	0.356244i
$852$	−6.00000	+	10.3923i	−0.205557	+	0.356034i
$853$	58.0000			1.98588			0.992941	−	0.118609i	$-0.0378434\pi$
$853$	58.0000			1.98588			0.992941	+	0.118609i	$0.0378434\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	24.0000	+	41.5692i	0.819824	+	1.41998i	0.905811	+	0.423681i	$0.139262\pi$
$857$	24.0000	+	41.5692i	0.819824	+	1.41998i	−0.0859870	+	0.996296i	$0.527404\pi$
$858$	2.50000	+	4.33013i	0.0853486	+	0.147828i
$859$	17.5000	−	30.3109i	0.597092	−	1.03419i	−0.396156	−	0.918183i	$-0.629656\pi$
$859$	17.5000	−	30.3109i	0.597092	−	1.03419i	0.993248	−	0.116011i	$-0.0370107\pi$
$860$		0			0
$861$		0			0
$862$	15.0000			0.510902
$863$	−3.00000	+	5.19615i	−0.102121	+	0.176879i	−0.912558	−	0.408946i	$-0.865896\pi$
$863$	−3.00000	+	5.19615i	−0.102121	+	0.176879i	0.810437	+	0.585826i	$0.199230\pi$
$864$	−2.50000	−	4.33013i	−0.0850517	−	0.147314i
$865$		0			0
$866$	7.00000	−	12.1244i	0.237870	−	0.412002i
$867$	−19.0000			−0.645274
$868$		0			0
$869$	1.00000			0.0339227
$870$		0			0
$871$	−32.5000	−	56.2917i	−1.10122	−	1.90737i
$872$	−7.00000	−	12.1244i	−0.237050	−	0.410582i
$873$	13.0000	−	22.5167i	0.439983	−	0.762073i
$874$	−12.0000			−0.405906
$875$		0			0
$876$	−10.0000			−0.337869
$877$	18.5000	−	32.0429i	0.624701	−	1.08201i	−0.363898	−	0.931439i	$-0.618554\pi$
$877$	18.5000	−	32.0429i	0.624701	−	1.08201i	0.988599	−	0.150574i	$-0.0481123\pi$
$878$	−9.50000	−	16.4545i	−0.320609	−	0.555312i
$879$	9.00000	+	15.5885i	0.303562	+	0.525786i
$880$		0			0
$881$	15.0000			0.505363			0.252681	−	0.967550i	$-0.418688\pi$
$881$	15.0000			0.505363			0.252681	+	0.967550i	$0.418688\pi$
$882$		0			0
$883$	−19.0000			−0.639401			−0.319700	−	0.947519i	$-0.603582\pi$
$883$	−19.0000			−0.639401			−0.319700	+	0.947519i	$0.603582\pi$
$884$	−15.0000	+	25.9808i	−0.504505	+	0.873828i
$885$		0			0
$886$	−6.00000	−	10.3923i	−0.201574	−	0.349136i
$887$	28.5000	−	49.3634i	0.956936	−	1.65746i	0.227063	−	0.973880i	$-0.427088\pi$
$887$	28.5000	−	49.3634i	0.956936	−	1.65746i	0.729873	−	0.683582i	$-0.239579\pi$
$888$	−2.00000			−0.0671156
$889$		0			0
$890$		0			0
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	−5.00000	−	8.66025i	−0.167412	−	0.289967i
$893$	−6.00000	−	10.3923i	−0.200782	−	0.347765i
$894$	−3.00000	+	5.19615i	−0.100335	+	0.173785i
$895$		0			0
$896$		0			0
$897$	30.0000			1.00167
$898$	−15.0000	+	25.9808i	−0.500556	+	0.866989i
$899$	12.0000	+	20.7846i	0.400222	+	0.693206i
$900$	−5.00000	−	8.66025i	−0.166667	−	0.288675i
$901$	−36.0000	+	62.3538i	−1.19933	+	2.07731i
$902$	−6.00000			−0.199778
$903$		0			0
$904$	9.00000			0.299336
$905$		0			0
$906$	−0.500000	−	0.866025i	−0.0166114	−	0.0287718i
$907$	−22.0000	−	38.1051i	−0.730498	−	1.26526i	−0.956671	−	0.291172i	$-0.905955\pi$
$907$	−22.0000	−	38.1051i	−0.730498	−	1.26526i	0.226173	−	0.974087i	$-0.427379\pi$
$908$	−3.00000	+	5.19615i	−0.0995585	+	0.172440i
$909$	6.00000			0.199007
$910$		0			0
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$	−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
$916$	−20.0000			−0.660819
$917$		0			0
$918$	−30.0000			−0.990148
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	−0.703378	−	0.710816i	$-0.748326\pi$
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	0.967274	+	0.253735i	$0.0816592\pi$
$920$		0			0
$921$	−16.0000	−	27.7128i	−0.527218	−	0.913168i
$922$	19.5000	−	33.7750i	0.642198	−	1.11232i
$923$	60.0000			1.97492
$924$		0			0
$925$	−10.0000			−0.328798
$926$	−13.0000	+	22.5167i	−0.427207	+	0.739943i
$927$	4.00000	+	6.92820i	0.131377	+	0.227552i
$928$	−1.50000	−	2.59808i	−0.0492399	−	0.0852860i
$929$	7.50000	−	12.9904i	0.246067	−	0.426201i	−0.716364	−	0.697727i	$-0.754195\pi$
$929$	7.50000	−	12.9904i	0.246067	−	0.426201i	0.962431	+	0.271526i	$0.0875283\pi$
$930$		0			0
$931$		0			0
$932$	−30.0000			−0.982683
$933$	−12.0000	+	20.7846i	−0.392862	+	0.680458i
$934$	−6.00000	−	10.3923i	−0.196326	−	0.340047i
$935$		0			0
$936$	−5.00000	+	8.66025i	−0.163430	+	0.283069i
$937$	52.0000			1.69877			0.849383	−	0.527777i	$-0.176974\pi$
$937$	52.0000			1.69877			0.849383	+	0.527777i	$0.176974\pi$
$938$		0			0
$939$	−7.00000			−0.228436
$940$		0			0
$941$	−13.5000	−	23.3827i	−0.440087	−	0.762254i	0.557608	−	0.830104i	$-0.311719\pi$
$941$	−13.5000	−	23.3827i	−0.440087	−	0.762254i	−0.997695	+	0.0678506i	$0.978386\pi$
$942$	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	−0.602494	−	0.798123i	$-0.705826\pi$
$947$	12.0000	−	20.7846i	0.389948	−	0.675409i	0.992442	+	0.122714i	$0.0391598\pi$
$948$	−0.500000	−	0.866025i	−0.0162392	−	0.0281272i
$949$	25.0000	+	43.3013i	0.811534	+	1.40562i
$950$	−5.00000	+	8.66025i	−0.162221	+	0.280976i
$951$	24.0000			0.778253
$952$		0			0
$953$	24.0000			0.777436			0.388718	−	0.921357i	$-0.372918\pi$
$953$	24.0000			0.777436			0.388718	+	0.921357i	$0.372918\pi$
$954$	−12.0000	+	20.7846i	−0.388514	+	0.672927i
$955$		0			0
$956$	−10.5000	−	18.1865i	−0.339594	−	0.588195i
$957$	−1.50000	+	2.59808i	−0.0484881	+	0.0839839i
$958$	3.00000			0.0969256
$959$		0			0
$960$		0			0
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$	5.00000	+	8.66025i	0.161206	+	0.279218i
$963$		0			0
$964$	−5.00000	+	8.66025i	−0.161039	+	0.278928i
$965$		0			0
$966$		0			0
$967$	32.0000			1.02905			0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000			1.02905			0.514525	+	0.857475i	$0.327968\pi$
$968$	−0.500000	+	0.866025i	−0.0160706	+	0.0278351i
$969$	6.00000	+	10.3923i	0.192748	+	0.333849i
$970$		0			0
$971$	−16.5000	+	28.5788i	−0.529510	+	0.917139i	0.469897	+	0.882721i	$0.344291\pi$
$971$	−16.5000	+	28.5788i	−0.529510	+	0.917139i	−0.999408	+	0.0344175i	$0.989042\pi$
$972$	−16.0000			−0.513200
$973$		0			0
$974$	−4.00000			−0.128168
$975$	12.5000	−	21.6506i	0.400320	−	0.693375i
$976$	−3.50000	−	6.06218i	−0.112032	−	0.194046i
$977$	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
$979$	6.00000			0.191761
$980$		0			0
$981$	−28.0000			−0.893971
$982$	15.0000	−	25.9808i	0.478669	−	0.829079i
$983$	−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
$986$	−18.0000			−0.573237
$987$		0			0
$988$	10.0000			0.318142
$989$	12.0000	−	20.7846i	0.381578	−	0.660912i
$990$		0			0
$991$	8.00000	+	13.8564i	0.254128	+	0.440163i	0.964658	−	0.263504i	$-0.0848781\pi$
$991$	8.00000	+	13.8564i	0.254128	+	0.440163i	−0.710530	+	0.703667i	$0.751545\pi$
$992$	4.00000	−	6.92820i	0.127000	−	0.219971i
$993$	13.0000			0.412543
$994$		0			0
$995$		0			0
$996$	−3.00000	+	5.19615i	−0.0950586	+	0.164646i
$997$	−23.0000	−	39.8372i	−0.728417	−	1.26166i	−0.957552	−	0.288261i	$-0.906923\pi$
$997$	−23.0000	−	39.8372i	−0.728417	−	1.26166i	0.229135	−	0.973395i	$-0.426410\pi$
$998$	−4.00000	−	6.92820i	−0.126618	−	0.219308i
$999$	−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.d.177.1		2
7.2	even	3		1078.2.a.i.1.1		1
7.3	odd	6		154.2.e.b.67.1	yes	2
7.4	even	3	inner	1078.2.e.d.67.1		2
7.5	odd	6		1078.2.a.k.1.1		1
7.6	odd	2		154.2.e.b.23.1	✓	2
21.2	odd	6		9702.2.a.l.1.1		1
21.5	even	6		9702.2.a.o.1.1		1
21.17	even	6		1386.2.k.n.991.1		2
21.20	even	2		1386.2.k.n.793.1		2
28.3	even	6		1232.2.q.c.529.1		2
28.19	even	6		8624.2.a.l.1.1		1
28.23	odd	6		8624.2.a.t.1.1		1
28.27	even	2		1232.2.q.c.177.1		2

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} -5.00000 q^{13} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(1.00000 + 1.73205i) q^{18} +(1.00000 - 1.73205i) q^{19} -1.00000 q^{22} +(-3.00000 + 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{25} +(2.50000 - 4.33013i) q^{26} +5.00000 q^{27} +3.00000 q^{29} +(4.00000 + 6.92820i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} -6.00000 q^{34} -2.00000 q^{36} +(-1.00000 + 1.73205i) q^{37} +(1.00000 + 1.73205i) q^{38} +(-2.50000 - 4.33013i) q^{39} +6.00000 q^{41} -4.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-3.00000 - 5.19615i) q^{46} +(3.00000 - 5.19615i) q^{47} -1.00000 q^{48} -5.00000 q^{50} +(-3.00000 + 5.19615i) q^{51} +(2.50000 + 4.33013i) q^{52} +(6.00000 + 10.3923i) q^{53} +(-2.50000 + 4.33013i) q^{54} +2.00000 q^{57} +(-1.50000 + 2.59808i) q^{58} +(-1.50000 - 2.59808i) q^{59} +(-3.50000 + 6.06218i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{66} +(6.50000 + 11.2583i) q^{67} +(3.00000 - 5.19615i) q^{68} -6.00000 q^{69} -12.0000 q^{71} +(1.00000 - 1.73205i) q^{72} +(-5.00000 - 8.66025i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-2.50000 + 4.33013i) q^{75} -2.00000 q^{76} +5.00000 q^{78} +(0.500000 - 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-3.00000 + 5.19615i) q^{82} -6.00000 q^{83} +(2.00000 - 3.46410i) q^{86} +(1.50000 + 2.59808i) q^{87} +(0.500000 + 0.866025i) q^{88} +(3.00000 - 5.19615i) q^{89} +6.00000 q^{92} +(-4.00000 + 6.92820i) q^{93} +(3.00000 + 5.19615i) q^{94} +(0.500000 - 0.866025i) q^{96} +13.0000 q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 - q^4 - 2 * q^6 + 2 * q^8 + 2 * q^9	\( 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + 2 q^{8} + 2 q^{9} + q^{11} + q^{12} - 10 q^{13} - q^{16} + 6 q^{17} + 2 q^{18} + 2 q^{19} - 2 q^{22} - 6 q^{23} + q^{24} + 5 q^{25} + 5 q^{26} + 10 q^{27} + 6 q^{29} + 8 q^{31} - q^{32} - q^{33} - 12 q^{34} - 4 q^{36} - 2 q^{37} + 2 q^{38} - 5 q^{39} + 12 q^{41} - 8 q^{43} + q^{44} - 6 q^{46} + 6 q^{47} - 2 q^{48} - 10 q^{50} - 6 q^{51} + 5 q^{52} + 12 q^{53} - 5 q^{54} + 4 q^{57} - 3 q^{58} - 3 q^{59} - 7 q^{61} - 16 q^{62} + 2 q^{64} - q^{66} + 13 q^{67} + 6 q^{68} - 12 q^{69} - 24 q^{71} + 2 q^{72} - 10 q^{73} - 2 q^{74} - 5 q^{75} - 4 q^{76} + 10 q^{78} + q^{79} - q^{81} - 6 q^{82} - 12 q^{83} + 4 q^{86} + 3 q^{87} + q^{88} + 6 q^{89} + 12 q^{92} - 8 q^{93} + 6 q^{94} + q^{96} + 26 q^{97} + 4 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 - 2 * q^6 + 2 * q^8 + 2 * q^9 + q^11 + q^12 - 10 * q^13 - q^16 + 6 * q^17 + 2 * q^18 + 2 * q^19 - 2 * q^22 - 6 * q^23 + q^24 + 5 * q^25 + 5 * q^26 + 10 * q^27 + 6 * q^29 + 8 * q^31 - q^32 - q^33 - 12 * q^34 - 4 * q^36 - 2 * q^37 + 2 * q^38 - 5 * 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 + 5 * q^52 + 12 * q^53 - 5 * q^54 + 4 * q^57 - 3 * q^58 - 3 * q^59 - 7 * q^61 - 16 * q^62 + 2 * q^64 - q^66 + 13 * q^67 + 6 * q^68 - 12 * q^69 - 24 * q^71 + 2 * q^72 - 10 * q^73 - 2 * q^74 - 5 * q^75 - 4 * q^76 + 10 * q^78 + q^79 - q^81 - 6 * q^82 - 12 * q^83 + 4 * q^86 + 3 * q^87 + q^88 + 6 * q^89 + 12 * q^92 - 8 * q^93 + 6 * q^94 + q^96 + 26 * q^97 + 4 * q^99

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