LMFDB - Embedded newform 1386.2.k.n.991.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(793,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1386.793");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.k (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.0672657201$
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			991.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1386.991
Dual form			1386.2.k.n.793.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{11} +5.00000 q^{13} +(0.500000 + 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(-1.00000 - 1.73205i) q^{19} -1.00000 q^{22} +(3.00000 + 5.19615i) q^{23} +(2.50000 - 4.33013i) q^{25} +(2.50000 + 4.33013i) q^{26} +(-2.00000 + 1.73205i) q^{28} -3.00000 q^{29} +(-4.00000 + 6.92820i) q^{31} +(0.500000 - 0.866025i) q^{32} +6.00000 q^{34} +(-1.00000 - 1.73205i) q^{37} +(1.00000 - 1.73205i) q^{38} +6.00000 q^{41} -4.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(3.00000 + 5.19615i) q^{47} +(5.50000 + 4.33013i) q^{49} +5.00000 q^{50} +(-2.50000 + 4.33013i) q^{52} +(-6.00000 + 10.3923i) q^{53} +(-2.50000 - 0.866025i) q^{56} +(-1.50000 - 2.59808i) q^{58} +(-1.50000 + 2.59808i) q^{59} +(3.50000 + 6.06218i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(6.50000 - 11.2583i) q^{67} +(3.00000 + 5.19615i) q^{68} +12.0000 q^{71} +(5.00000 - 8.66025i) q^{73} +(1.00000 - 1.73205i) q^{74} +2.00000 q^{76} +(-2.00000 + 1.73205i) q^{77} +(0.500000 + 0.866025i) q^{79} +(3.00000 + 5.19615i) q^{82} -6.00000 q^{83} +(-2.00000 - 3.46410i) q^{86} +(0.500000 - 0.866025i) q^{88} +(3.00000 + 5.19615i) q^{89} +(12.5000 + 4.33013i) q^{91} -6.00000 q^{92} +(-3.00000 + 5.19615i) q^{94} -13.0000 q^{97} +(-1.00000 + 6.92820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} + 5 q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 + 5 * q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} + 5 q^{7} - 2 q^{8} - q^{11} + 10 q^{13} + q^{14} - q^{16} + 6 q^{17} - 2 q^{19} - 2 q^{22} + 6 q^{23} + 5 q^{25} + 5 q^{26} - 4 q^{28} - 6 q^{29} - 8 q^{31} + q^{32} + 12 q^{34} - 2 q^{37} + 2 q^{38} + 12 q^{41} - 8 q^{43} - q^{44} - 6 q^{46} + 6 q^{47} + 11 q^{49} + 10 q^{50} - 5 q^{52} - 12 q^{53} - 5 q^{56} - 3 q^{58} - 3 q^{59} + 7 q^{61} - 16 q^{62} + 2 q^{64} + 13 q^{67} + 6 q^{68} + 24 q^{71} + 10 q^{73} + 2 q^{74} + 4 q^{76} - 4 q^{77} + q^{79} + 6 q^{82} - 12 q^{83} - 4 q^{86} + q^{88} + 6 q^{89} + 25 q^{91} - 12 q^{92} - 6 q^{94} - 26 q^{97} - 2 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 + 5 * q^7 - 2 * q^8 - q^11 + 10 * q^13 + q^14 - q^16 + 6 * q^17 - 2 * q^19 - 2 * q^22 + 6 * q^23 + 5 * q^25 + 5 * q^26 - 4 * q^28 - 6 * q^29 - 8 * q^31 + q^32 + 12 * q^34 - 2 * q^37 + 2 * q^38 + 12 * q^41 - 8 * q^43 - q^44 - 6 * q^46 + 6 * q^47 + 11 * q^49 + 10 * q^50 - 5 * q^52 - 12 * q^53 - 5 * q^56 - 3 * q^58 - 3 * q^59 + 7 * q^61 - 16 * q^62 + 2 * q^64 + 13 * q^67 + 6 * q^68 + 24 * q^71 + 10 * q^73 + 2 * q^74 + 4 * q^76 - 4 * q^77 + q^79 + 6 * q^82 - 12 * q^83 - 4 * q^86 + q^88 + 6 * q^89 + 25 * q^91 - 12 * q^92 - 6 * q^94 - 26 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$5$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$6$		0			0
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$	−1.00000			−0.353553
$9$		0			0
$10$		0			0
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$		0			0
$13$	5.00000			1.38675			0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000			1.38675			0.693375	+	0.720577i	$0.256123\pi$
$14$	0.500000	+	2.59808i	0.133631	+	0.694365i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$		0			0
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	0.728219	−	0.685344i	$-0.240348\pi$
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	−0.957635	+	0.287984i	$0.907015\pi$
$20$		0			0
$21$		0			0
$22$	−1.00000			−0.213201
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$	2.50000	+	4.33013i	0.490290	+	0.849208i
$27$		0			0
$28$	−2.00000	+	1.73205i	−0.377964	+	0.327327i
$29$	−3.00000			−0.557086			−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000			−0.557086			−0.278543	+	0.960424i	$0.589851\pi$
$30$		0			0
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	0.243204	+	0.969975i	$0.421802\pi$
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	−0.961625	+	0.274367i	$0.911532\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	6.00000			1.02899
$35$		0			0
$36$		0			0
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$	1.00000	−	1.73205i	0.162221	−	0.280976i
$39$		0			0
$40$		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	$-0.0224970\pi$
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	−0.559908	+	0.828554i	$0.689164\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	5.00000			0.707107
$51$		0			0
$52$	−2.50000	+	4.33013i	−0.346688	+	0.600481i
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	0.0783936	+	0.996922i	$0.475021\pi$
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	−0.902557	+	0.430570i	$0.858312\pi$
$54$		0			0
$55$		0			0
$56$	−2.50000	−	0.866025i	−0.334077	−	0.115728i
$57$		0			0
$58$	−1.50000	−	2.59808i	−0.196960	−	0.341144i
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	−0.946993	−	0.321253i	$-0.895896\pi$
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	0.751710	+	0.659494i	$0.229229\pi$
$60$		0			0
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	0.998264	−	0.0588933i	$-0.0187572\pi$
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	−0.550135	+	0.835076i	$0.685424\pi$
$62$	−8.00000			−1.01600
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	6.50000	−	11.2583i	0.794101	−	1.37542i	−0.129307	−	0.991605i	$-0.541275\pi$
$67$	6.50000	−	11.2583i	0.794101	−	1.37542i	0.923408	−	0.383819i	$-0.125391\pi$
$68$	3.00000	+	5.19615i	0.363803	+	0.630126i
$69$		0			0
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$	5.00000	−	8.66025i	0.585206	−	1.01361i	−0.409644	−	0.912245i	$-0.634347\pi$
$73$	5.00000	−	8.66025i	0.585206	−	1.01361i	0.994850	−	0.101361i	$-0.0323196\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$		0			0
$76$	2.00000			0.229416
$77$	−2.00000	+	1.73205i	−0.227921	+	0.197386i
$78$		0			0
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	0.892781	−	0.450490i	$-0.148751\pi$
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	−0.836527	+	0.547926i	$0.815418\pi$
$80$		0			0
$81$		0			0
$82$	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
$87$		0			0
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$		0			0
$91$	12.5000	+	4.33013i	1.31036	+	0.453921i
$92$	−6.00000			−0.625543
$93$		0			0
$94$	−3.00000	+	5.19615i	−0.309426	+	0.535942i
$95$		0			0
$96$		0			0
$97$	−13.0000			−1.31995			−0.659975	−	0.751288i	$-0.729433\pi$
$97$	−13.0000			−1.31995			−0.659975	+	0.751288i	$0.729433\pi$
$98$	−1.00000	+	6.92820i	−0.101015	+	0.699854i
$99$		0			0
$100$	2.50000	+	4.33013i	0.250000	+	0.433013i
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	−0.781697	−	0.623658i	$-0.785646\pi$
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	0.930953	+	0.365140i	$0.118979\pi$
$102$		0			0
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	0.947576	−	0.319531i	$-0.103525\pi$
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	−0.750510	+	0.660859i	$0.770192\pi$
$104$	−5.00000			−0.490290
$105$		0			0
$106$	−12.0000			−1.16554
$107$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$107$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$108$		0			0
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	0.307290	+	0.951616i	$0.400578\pi$
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	−0.977769	+	0.209687i	$0.932756\pi$
$110$		0			0
$111$		0			0
$112$	−0.500000	−	2.59808i	−0.0472456	−	0.245495i
$113$	−9.00000			−0.846649			−0.423324	−	0.905978i	$-0.639137\pi$
$113$	−9.00000			−0.846649			−0.423324	+	0.905978i	$0.639137\pi$
$114$		0			0
$115$		0			0
$116$	1.50000	−	2.59808i	0.139272	−	0.241225i
$117$		0			0
$118$	−3.00000			−0.276172
$119$	12.0000	−	10.3923i	1.10004	−	0.952661i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−3.50000	+	6.06218i	−0.316875	+	0.548844i
$123$		0			0
$124$	−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
$129$		0			0
$130$		0			0
$131$	3.00000	+	5.19615i	0.262111	+	0.453990i	0.966803	−	0.255524i	$-0.0822479\pi$
$131$	3.00000	+	5.19615i	0.262111	+	0.453990i	−0.704692	+	0.709514i	$0.748915\pi$
$132$		0			0
$133$	−1.00000	−	5.19615i	−0.0867110	−	0.450564i
$134$	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	−0.344493	−	0.938789i	$-0.611949\pi$
$137$	7.50000	−	12.9904i	0.640768	−	1.10984i	0.985262	−	0.171054i	$-0.0547174\pi$
$138$		0			0
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$		0			0
$141$		0			0
$142$	6.00000	+	10.3923i	0.503509	+	0.872103i
$143$	−2.50000	+	4.33013i	−0.209061	+	0.362103i
$144$		0			0
$145$		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	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$		0			0
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	−0.844963	−	0.534824i	$-0.820378\pi$
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	0.885653	+	0.464348i	$0.153711\pi$
$152$	1.00000	+	1.73205i	0.0811107	+	0.140488i
$153$		0			0
$154$	−2.50000	−	0.866025i	−0.201456	−	0.0697863i
$155$		0			0
$156$		0			0
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	−0.775113	−	0.631822i	$-0.782307\pi$
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	0.934731	+	0.355357i	$0.115641\pi$
$158$	−0.500000	+	0.866025i	−0.0397779	+	0.0688973i
$159$		0			0
$160$		0			0
$161$	3.00000	+	15.5885i	0.236433	+	1.22854i
$162$		0			0
$163$	−8.50000	−	14.7224i	−0.665771	−	1.15315i	−0.979076	−	0.203497i	$-0.934769\pi$
$163$	−8.50000	−	14.7224i	−0.665771	−	1.15315i	0.313304	−	0.949653i	$-0.398564\pi$
$164$	−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
$171$		0			0
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	−7.50000	−	12.9904i	−0.570214	−	0.987640i	−0.996544	−	0.0830722i	$-0.973527\pi$
$173$	−7.50000	−	12.9904i	−0.570214	−	0.987640i	0.426329	−	0.904568i	$-0.359807\pi$
$174$		0			0
$175$	10.0000	−	8.66025i	0.755929	−	0.654654i
$176$	1.00000			0.0753778
$177$		0			0
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	4.50000	−	7.79423i	0.336346	−	0.582568i	−0.647397	−	0.762153i	$-0.724142\pi$
$179$	4.50000	−	7.79423i	0.336346	−	0.582568i	0.983742	+	0.179585i	$0.0574756\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	2.50000	+	12.9904i	0.185312	+	0.962911i
$183$		0			0
$184$	−3.00000	−	5.19615i	−0.221163	−	0.383065i
$185$		0			0
$186$		0			0
$187$	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	−0.982828	−	0.184525i	$-0.940925\pi$
$191$	−9.00000	−	15.5885i	−0.651217	−	1.12794i	0.331611	−	0.943416i	$-0.392408\pi$
$192$		0			0
$193$	11.0000	−	19.0526i	0.791797	−	1.37143i	−0.133056	−	0.991109i	$-0.542479\pi$
$193$	11.0000	−	19.0526i	0.791797	−	1.37143i	0.924853	−	0.380325i	$-0.124188\pi$
$194$	−6.50000	−	11.2583i	−0.466673	−	0.808301i
$195$		0			0
$196$	−6.50000	+	2.59808i	−0.464286	+	0.185577i
$197$	9.00000			0.641223			0.320612	−	0.947211i	$-0.396112\pi$
$197$	9.00000			0.641223			0.320612	+	0.947211i	$0.396112\pi$
$198$		0			0
$199$	−7.00000	+	12.1244i	−0.496217	+	0.859473i	−0.999990	−	0.00436292i	$-0.998611\pi$
$199$	−7.00000	+	12.1244i	−0.496217	+	0.859473i	0.503774	+	0.863836i	$0.331945\pi$
$200$	−2.50000	+	4.33013i	−0.176777	+	0.306186i
$201$		0			0
$202$	3.00000			0.211079
$203$	−7.50000	−	2.59808i	−0.526397	−	0.182349i
$204$		0			0
$205$		0			0
$206$	−2.00000	+	3.46410i	−0.139347	+	0.241355i
$207$		0			0
$208$	−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
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−16.0000	+	13.8564i	−1.08615	+	0.940634i
$218$	−14.0000			−0.948200
$219$		0			0
$220$		0			0
$221$	15.0000	−	25.9808i	1.00901	−	1.74766i
$222$		0			0
$223$	−10.0000			−0.669650			−0.334825	−	0.942280i	$-0.608677\pi$
$223$	−10.0000			−0.669650			−0.334825	+	0.942280i	$0.608677\pi$
$224$	2.00000	−	1.73205i	0.133631	−	0.115728i
$225$		0			0
$226$	−4.50000	−	7.79423i	−0.299336	−	0.518464i
$227$	−3.00000	+	5.19615i	−0.199117	+	0.344881i	−0.948242	−	0.317547i	$-0.897141\pi$
$227$	−3.00000	+	5.19615i	−0.199117	+	0.344881i	0.749125	+	0.662428i	$0.230474\pi$
$228$		0			0
$229$	−10.0000	−	17.3205i	−0.660819	−	1.14457i	−0.980401	−	0.197013i	$-0.936876\pi$
$229$	−10.0000	−	17.3205i	−0.660819	−	1.14457i	0.319582	−	0.947559i	$-0.396457\pi$
$230$		0			0
$231$		0			0
$232$	3.00000			0.196960
$233$	−15.0000	−	25.9808i	−0.982683	−	1.70206i	−0.651813	−	0.758380i	$-0.725991\pi$
$233$	−15.0000	−	25.9808i	−0.982683	−	1.70206i	−0.330870	−	0.943676i	$-0.607342\pi$
$234$		0			0
$235$		0			0
$236$	−1.50000	−	2.59808i	−0.0976417	−	0.169120i
$237$		0			0
$238$	15.0000	+	5.19615i	0.972306	+	0.336817i
$239$	−21.0000			−1.35838			−0.679189	−	0.733964i	$-0.737668\pi$
$239$	−21.0000			−1.35838			−0.679189	+	0.733964i	$0.737668\pi$
$240$		0			0
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	−0.658838	−	0.752285i	$-0.728952\pi$
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	0.980917	+	0.194429i	$0.0622852\pi$
$242$	0.500000	−	0.866025i	0.0321412	−	0.0556702i
$243$		0			0
$244$	−7.00000			−0.448129
$245$		0			0
$246$		0			0
$247$	−5.00000	−	8.66025i	−0.318142	−	0.551039i
$248$	4.00000	−	6.92820i	0.254000	−	0.439941i
$249$		0			0
$250$		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	0.888110	+	0.459631i	$0.152018\pi$
$257$	13.5000	+	23.3827i	0.842107	+	1.45857i	−0.0460033	+	0.998941i	$0.514648\pi$
$258$		0			0
$259$	−1.00000	−	5.19615i	−0.0621370	−	0.322873i
$260$		0			0
$261$		0			0
$262$	−3.00000	+	5.19615i	−0.185341	+	0.321019i
$263$	−1.50000	+	2.59808i	−0.0924940	+	0.160204i	−0.908560	−	0.417755i	$-0.862817\pi$
$263$	−1.50000	+	2.59808i	−0.0924940	+	0.160204i	0.816066	+	0.577959i	$0.196151\pi$
$264$		0			0
$265$		0			0
$266$	4.00000	−	3.46410i	0.245256	−	0.212398i
$267$		0			0
$268$	6.50000	+	11.2583i	0.397051	+	0.687712i
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	0.224523	+	0.974469i	$0.427917\pi$
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	−0.956176	+	0.292791i	$0.905416\pi$
$270$		0			0
$271$	12.5000	+	21.6506i	0.759321	+	1.31518i	0.943197	+	0.332233i	$0.107802\pi$
$271$	12.5000	+	21.6506i	0.759321	+	1.31518i	−0.183876	+	0.982949i	$0.558865\pi$
$272$	−6.00000			−0.363803
$273$		0			0
$274$	15.0000			0.906183
$275$	2.50000	+	4.33013i	0.150756	+	0.261116i
$276$		0			0
$277$	0.500000	−	0.866025i	0.0300421	−	0.0520344i	−0.850613	−	0.525792i	$-0.823769\pi$
$277$	0.500000	−	0.866025i	0.0300421	−	0.0520344i	0.880656	+	0.473757i	$0.157103\pi$
$278$	−2.00000	−	3.46410i	−0.119952	−	0.207763i
$279$		0			0
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$	11.0000	−	19.0526i	0.653882	−	1.13256i	−0.328291	−	0.944577i	$-0.606473\pi$
$283$	11.0000	−	19.0526i	0.653882	−	1.13256i	0.982173	−	0.187980i	$-0.0601941\pi$
$284$	−6.00000	+	10.3923i	−0.356034	+	0.616670i
$285$		0			0
$286$	−5.00000			−0.295656
$287$	15.0000	+	5.19615i	0.885422	+	0.306719i
$288$		0			0
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$		0			0
$291$		0			0
$292$	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
$297$		0			0
$298$	3.00000	−	5.19615i	0.173785	−	0.301005i
$299$	15.0000	+	25.9808i	0.867472	+	1.50251i
$300$		0			0
$301$	−10.0000	−	3.46410i	−0.576390	−	0.199667i
$302$	1.00000			0.0575435
$303$		0			0
$304$	−1.00000	+	1.73205i	−0.0573539	+	0.0993399i
$305$		0			0
$306$		0			0
$307$	32.0000			1.82634			0.913168	−	0.407583i	$-0.133628\pi$
$307$	32.0000			1.82634			0.913168	+	0.407583i	$0.133628\pi$
$308$	−0.500000	−	2.59808i	−0.0284901	−	0.148039i
$309$		0			0
$310$		0			0
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	−0.294384	−	0.955687i	$-0.595114\pi$
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	0.974841	−	0.222900i	$-0.0715523\pi$
$312$		0			0
$313$	3.50000	+	6.06218i	0.197832	+	0.342655i	0.947825	−	0.318791i	$-0.103277\pi$
$313$	3.50000	+	6.06218i	0.197832	+	0.342655i	−0.749993	+	0.661445i	$0.769943\pi$
$314$	4.00000			0.225733
$315$		0			0
$316$	−1.00000			−0.0562544
$317$	−12.0000	−	20.7846i	−0.673987	−	1.16738i	−0.976764	−	0.214318i	$-0.931247\pi$
$317$	−12.0000	−	20.7846i	−0.673987	−	1.16738i	0.302777	−	0.953062i	$-0.402086\pi$
$318$		0			0
$319$	1.50000	−	2.59808i	0.0839839	−	0.145464i
$320$		0			0
$321$		0			0
$322$	−12.0000	+	10.3923i	−0.668734	+	0.579141i
$323$	−12.0000			−0.667698
$324$		0			0
$325$	12.5000	−	21.6506i	0.693375	−	1.20096i
$326$	8.50000	−	14.7224i	0.470771	−	0.815400i
$327$		0			0
$328$	−6.00000			−0.331295
$329$	3.00000	+	15.5885i	0.165395	+	0.859419i
$330$		0			0
$331$	6.50000	+	11.2583i	0.357272	+	0.618814i	0.987504	−	0.157593i	$-0.0503735\pi$
$331$	6.50000	+	11.2583i	0.357272	+	0.618814i	−0.630232	+	0.776407i	$0.717040\pi$
$332$	3.00000	−	5.19615i	0.164646	−	0.285176i
$333$		0			0
$334$	−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
$339$		0			0
$340$		0			0
$341$	−4.00000	−	6.92820i	−0.216612	−	0.375183i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	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	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	−34.0000			−1.81998			−0.909989	−	0.414632i	$-0.863910\pi$
$349$	−34.0000			−1.81998			−0.909989	+	0.414632i	$0.863910\pi$
$350$	12.5000	+	4.33013i	0.668153	+	0.231455i
$351$		0			0
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	15.0000	−	25.9808i	0.798369	−	1.38282i	−0.122308	−	0.992492i	$-0.539030\pi$
$353$	15.0000	−	25.9808i	0.798369	−	1.38282i	0.920677	−	0.390324i	$-0.127637\pi$
$354$		0			0
$355$		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	$-0.242995\pi$
$359$	−4.50000	−	7.79423i	−0.237501	−	0.411364i	−0.959997	+	0.280012i	$0.909662\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	−5.00000	−	8.66025i	−0.262794	−	0.455173i
$363$		0			0
$364$	−10.0000	+	8.66025i	−0.524142	+	0.453921i
$365$		0			0
$366$		0			0
$367$	−19.0000	+	32.9090i	−0.991792	+	1.71783i	−0.385164	+	0.922848i	$0.625855\pi$
$367$	−19.0000	+	32.9090i	−0.991792	+	1.71783i	−0.606628	+	0.794986i	$0.707478\pi$
$368$	3.00000	−	5.19615i	0.156386	−	0.270868i
$369$		0			0
$370$		0			0
$371$	−24.0000	+	20.7846i	−1.24602	+	1.07908i
$372$		0			0
$373$	−5.50000	−	9.52628i	−0.284779	−	0.493252i	0.687776	−	0.725923i	$-0.258587\pi$
$373$	−5.50000	−	9.52628i	−0.284779	−	0.493252i	−0.972556	+	0.232671i	$0.925254\pi$
$374$	−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
$381$		0			0
$382$	9.00000	−	15.5885i	0.460480	−	0.797575i
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	0.977613	−	0.210411i	$-0.0674801\pi$
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	−0.671027	+	0.741433i	$0.734147\pi$
$384$		0			0
$385$		0			0
$386$	22.0000			1.11977
$387$		0			0
$388$	6.50000	−	11.2583i	0.329988	−	0.571555i
$389$	6.00000	−	10.3923i	0.304212	−	0.526911i	−0.672874	−	0.739758i	$-0.734940\pi$
$389$	6.00000	−	10.3923i	0.304212	−	0.526911i	0.977086	+	0.212847i	$0.0682735\pi$
$390$		0			0
$391$	36.0000			1.82060
$392$	−5.50000	−	4.33013i	−0.277792	−	0.218704i
$393$		0			0
$394$	4.50000	+	7.79423i	0.226707	+	0.392668i
$395$		0			0
$396$		0			0
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	0.839840	−	0.542834i	$-0.182649\pi$
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	−0.890028	+	0.455905i	$0.849316\pi$
$398$	−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	$-0.238813\pi$
$401$	−4.50000	−	7.79423i	−0.224719	−	0.389225i	−0.956235	+	0.292599i	$0.905480\pi$
$402$		0			0
$403$	−20.0000	+	34.6410i	−0.996271	+	1.72559i
$404$	1.50000	+	2.59808i	0.0746278	+	0.129259i
$405$		0			0
$406$	−1.50000	−	7.79423i	−0.0744438	−	0.386821i
$407$	2.00000			0.0991363
$408$		0			0
$409$	2.00000	−	3.46410i	0.0988936	−	0.171289i	−0.812333	−	0.583193i	$-0.801803\pi$
$409$	2.00000	−	3.46410i	0.0988936	−	0.171289i	0.911227	+	0.411905i	$0.135136\pi$
$410$		0			0
$411$		0			0
$412$	−4.00000			−0.197066
$413$	−6.00000	+	5.19615i	−0.295241	+	0.255686i
$414$		0			0
$415$		0			0
$416$	2.50000	−	4.33013i	0.122573	−	0.212302i
$417$		0			0
$418$	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
$423$		0			0
$424$	6.00000	−	10.3923i	0.291386	−	0.504695i
$425$	−15.0000	−	25.9808i	−0.727607	−	1.26025i
$426$		0			0
$427$	3.50000	+	18.1865i	0.169377	+	0.880108i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	7.50000	−	12.9904i	0.361262	−	0.625725i	−0.626907	−	0.779094i	$-0.715679\pi$
$431$	7.50000	−	12.9904i	0.361262	−	0.625725i	0.988169	+	0.153370i	$0.0490126\pi$
$432$		0			0
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$	−20.0000	−	6.92820i	−0.960031	−	0.332564i
$435$		0			0
$436$	−7.00000	−	12.1244i	−0.335239	−	0.580651i
$437$	6.00000	−	10.3923i	0.287019	−	0.497131i
$438$		0			0
$439$	9.50000	+	16.4545i	0.453410	+	0.785330i	0.998595	−	0.0529862i	$-0.0168739\pi$
$439$	9.50000	+	16.4545i	0.453410	+	0.785330i	−0.545185	+	0.838316i	$0.683541\pi$
$440$		0			0
$441$		0			0
$442$	30.0000			1.42695
$443$	6.00000	+	10.3923i	0.285069	+	0.493753i	0.972626	−	0.232377i	$-0.0746503\pi$
$443$	6.00000	+	10.3923i	0.285069	+	0.493753i	−0.687557	+	0.726130i	$0.741317\pi$
$444$		0			0
$445$		0			0
$446$	−5.00000	−	8.66025i	−0.236757	−	0.410075i
$447$		0			0
$448$	2.50000	+	0.866025i	0.118114	+	0.0409159i
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$		0			0
$451$	−3.00000	+	5.19615i	−0.141264	+	0.244677i
$452$	4.50000	−	7.79423i	0.211662	−	0.366610i
$453$		0			0
$454$	−6.00000			−0.281594
$455$		0			0
$456$		0			0
$457$	11.0000	+	19.0526i	0.514558	+	0.891241i	0.999857	+	0.0168929i	$0.00537742\pi$
$457$	11.0000	+	19.0526i	0.514558	+	0.891241i	−0.485299	+	0.874348i	$0.661289\pi$
$458$	10.0000	−	17.3205i	0.467269	−	0.809334i
$459$		0			0
$460$		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	0.693153	−	0.720791i	$-0.256221\pi$
$467$	−6.00000	−	10.3923i	−0.277647	−	0.480899i	−0.970799	+	0.239892i	$0.922888\pi$
$468$		0			0
$469$	26.0000	−	22.5167i	1.20057	−	1.03972i
$470$		0			0
$471$		0			0
$472$	1.50000	−	2.59808i	0.0690431	−	0.119586i
$473$	2.00000	−	3.46410i	0.0919601	−	0.159280i
$474$		0			0
$475$	−10.0000			−0.458831
$476$	3.00000	+	15.5885i	0.137505	+	0.714496i
$477$		0			0
$478$	−10.5000	−	18.1865i	−0.480259	−	0.831833i
$479$	−1.50000	+	2.59808i	−0.0685367	+	0.118709i	−0.898257	−	0.439470i	$-0.855166\pi$
$479$	−1.50000	+	2.59808i	−0.0685367	+	0.118709i	0.829721	+	0.558179i	$0.188500\pi$
$480$		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
$486$		0			0
$487$	2.00000	−	3.46410i	0.0906287	−	0.156973i	−0.817147	−	0.576429i	$-0.804446\pi$
$487$	2.00000	−	3.46410i	0.0906287	−	0.156973i	0.907776	+	0.419456i	$0.137779\pi$
$488$	−3.50000	−	6.06218i	−0.158438	−	0.274422i
$489$		0			0
$490$		0			0
$491$	30.0000			1.35388			0.676941	−	0.736038i	$-0.263305\pi$
$491$	30.0000			1.35388			0.676941	+	0.736038i	$0.263305\pi$
$492$		0			0
$493$	−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
$497$	30.0000	+	10.3923i	1.34568	+	0.466159i
$498$		0			0
$499$	−4.00000	−	6.92820i	−0.179065	−	0.310149i	0.762496	−	0.646993i	$-0.223974\pi$
$499$	−4.00000	−	6.92820i	−0.179065	−	0.310149i	−0.941560	+	0.336844i	$0.890640\pi$
$500$		0			0
$501$		0			0
$502$	−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
$507$		0			0
$508$	6.50000	−	11.2583i	0.288391	−	0.499508i
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	0.924821	−	0.380402i	$-0.124214\pi$
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	−0.791849	+	0.610718i	$0.790881\pi$
$510$		0			0
$511$	20.0000	−	17.3205i	0.884748	−	0.766214i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−13.5000	+	23.3827i	−0.595459	+	1.03137i
$515$		0			0
$516$		0			0
$517$	−6.00000			−0.263880
$518$	4.00000	−	3.46410i	0.175750	−	0.152204i
$519$		0			0
$520$		0			0
$521$	−9.00000	+	15.5885i	−0.394297	+	0.682943i	−0.993011	−	0.118020i	$-0.962345\pi$
$521$	−9.00000	+	15.5885i	−0.394297	+	0.682943i	0.598714	+	0.800963i	$0.295679\pi$
$522$		0			0
$523$	8.00000	+	13.8564i	0.349816	+	0.605898i	0.986216	−	0.165460i	$-0.0529109\pi$
$523$	8.00000	+	13.8564i	0.349816	+	0.605898i	−0.636401	+	0.771358i	$0.719578\pi$
$524$	−6.00000			−0.262111
$525$		0			0
$526$	−3.00000			−0.130806
$527$	24.0000	+	41.5692i	1.04546	+	1.81078i
$528$		0			0
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$		0			0
$532$	5.00000	+	1.73205i	0.216777	+	0.0750939i
$533$	30.0000			1.29944
$534$		0			0
$535$		0			0
$536$	−6.50000	+	11.2583i	−0.280757	+	0.486286i
$537$		0			0
$538$	−24.0000			−1.03471
$539$	−6.50000	+	2.59808i	−0.279975	+	0.111907i
$540$		0			0
$541$	−2.50000	−	4.33013i	−0.107483	−	0.186167i	0.807267	−	0.590187i	$-0.200946\pi$
$541$	−2.50000	−	4.33013i	−0.107483	−	0.186167i	−0.914750	+	0.404020i	$0.867613\pi$
$542$	−12.5000	+	21.6506i	−0.536921	+	0.929974i
$543$		0			0
$544$	−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
$549$		0			0
$550$	−2.50000	+	4.33013i	−0.106600	+	0.184637i
$551$	3.00000	+	5.19615i	0.127804	+	0.221364i
$552$		0			0
$553$	0.500000	+	2.59808i	0.0212622	+	0.110481i
$554$	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	$-0.873905\pi$
$557$	−3.00000	+	5.19615i	−0.127114	+	0.220168i	0.795443	+	0.606028i	$0.207238\pi$
$558$		0			0
$559$	−20.0000			−0.845910
$560$		0			0
$561$		0			0
$562$	3.00000	+	5.19615i	0.126547	+	0.219186i
$563$	9.00000	−	15.5885i	0.379305	−	0.656975i	−0.611656	−	0.791123i	$-0.709497\pi$
$563$	9.00000	−	15.5885i	0.379305	−	0.656975i	0.990961	+	0.134148i	$0.0428299\pi$
$564$		0			0
$565$		0			0
$566$	22.0000			0.924729
$567$		0			0
$568$	−12.0000			−0.503509
$569$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$569$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$570$		0			0
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	−0.995788	−	0.0916910i	$-0.970773\pi$
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	0.577301	+	0.816532i	$0.304106\pi$
$572$	−2.50000	−	4.33013i	−0.104530	−	0.181052i
$573$		0			0
$574$	3.00000	+	15.5885i	0.125218	+	0.650650i
$575$	30.0000			1.25109
$576$		0			0
$577$	3.50000	−	6.06218i	0.145707	−	0.252372i	−0.783930	−	0.620850i	$-0.786788\pi$
$577$	3.50000	−	6.06218i	0.145707	−	0.252372i	0.929636	+	0.368478i	$0.120121\pi$
$578$	9.50000	−	16.4545i	0.395148	−	0.684416i
$579$		0			0
$580$		0			0
$581$	−15.0000	−	5.19615i	−0.622305	−	0.215573i
$582$		0			0
$583$	−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
$591$		0			0
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$	12.0000	+	20.7846i	0.492781	+	0.853522i	0.999965	−	0.00831589i	$-0.00264706\pi$
$593$	12.0000	+	20.7846i	0.492781	+	0.853522i	−0.507184	+	0.861838i	$0.669314\pi$
$594$		0			0
$595$		0			0
$596$	6.00000			0.245770
$597$		0			0
$598$	−15.0000	+	25.9808i	−0.613396	+	1.06243i
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$		0			0
$601$	−10.0000			−0.407909			−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000			−0.407909			−0.203954	+	0.978980i	$0.565379\pi$
$602$	−2.00000	−	10.3923i	−0.0815139	−	0.423559i
$603$		0			0
$604$	0.500000	+	0.866025i	0.0203447	+	0.0352381i
$605$		0			0
$606$		0			0
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	0.773358	−	0.633970i	$-0.218576\pi$
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	−0.935713	+	0.352763i	$0.885242\pi$
$608$	−2.00000			−0.0811107
$609$		0			0
$610$		0			0
$611$	15.0000	+	25.9808i	0.606835	+	1.05107i
$612$		0			0
$613$	−13.0000	+	22.5167i	−0.525065	+	0.909439i	0.474509	+	0.880251i	$0.342626\pi$
$613$	−13.0000	+	22.5167i	−0.525065	+	0.909439i	−0.999574	+	0.0291886i	$0.990708\pi$
$614$	16.0000	+	27.7128i	0.645707	+	1.11840i
$615$		0			0
$616$	2.00000	−	1.73205i	0.0805823	−	0.0697863i
$617$	−21.0000			−0.845428			−0.422714	−	0.906263i	$-0.638923\pi$
$617$	−21.0000			−0.845428			−0.422714	+	0.906263i	$0.638923\pi$
$618$		0			0
$619$	−22.0000	+	38.1051i	−0.884255	+	1.53157i	−0.0376891	+	0.999290i	$0.512000\pi$
$619$	−22.0000	+	38.1051i	−0.884255	+	1.53157i	−0.846566	+	0.532284i	$0.821334\pi$
$620$		0			0
$621$		0			0
$622$	24.0000			0.962312
$623$	3.00000	+	15.5885i	0.120192	+	0.624538i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	−3.50000	+	6.06218i	−0.139888	+	0.242293i
$627$		0			0
$628$	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
$633$		0			0
$634$	12.0000	−	20.7846i	0.476581	−	0.825462i
$635$		0			0
$636$		0			0
$637$	27.5000	+	21.6506i	1.08959	+	0.857829i
$638$	3.00000			0.118771
$639$		0			0
$640$		0			0
$641$	4.50000	−	7.79423i	0.177739	−	0.307854i	−0.763367	−	0.645966i	$-0.776455\pi$
$641$	4.50000	−	7.79423i	0.177739	−	0.307854i	0.941106	+	0.338112i	$0.109788\pi$
$642$		0			0
$643$	−19.0000			−0.749287			−0.374643	−	0.927169i	$-0.622235\pi$
$643$	−19.0000			−0.749287			−0.374643	+	0.927169i	$0.622235\pi$
$644$	−15.0000	−	5.19615i	−0.591083	−	0.204757i
$645$		0			0
$646$	−6.00000	−	10.3923i	−0.236067	−	0.408880i
$647$	18.0000	−	31.1769i	0.707653	−	1.22569i	−0.258073	−	0.966126i	$-0.583087\pi$
$647$	18.0000	−	31.1769i	0.707653	−	1.22569i	0.965726	−	0.259565i	$-0.0835793\pi$
$648$		0			0
$649$	−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	−0.994623	−	0.103558i	$-0.966977\pi$
$653$	−15.0000	−	25.9808i	−0.586995	−	1.01671i	0.407628	−	0.913148i	$-0.366356\pi$
$654$		0			0
$655$		0			0
$656$	−3.00000	−	5.19615i	−0.117130	−	0.202876i
$657$		0			0
$658$	−12.0000	+	10.3923i	−0.467809	+	0.405134i
$659$	12.0000			0.467454			0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000			0.467454			0.233727	+	0.972302i	$0.424908\pi$
$660$		0			0
$661$	17.0000	−	29.4449i	0.661223	−	1.14527i	−0.319071	−	0.947731i	$-0.603371\pi$
$661$	17.0000	−	29.4449i	0.661223	−	1.14527i	0.980294	−	0.197542i	$-0.0632958\pi$
$662$	−6.50000	+	11.2583i	−0.252630	+	0.437567i
$663$		0			0
$664$	6.00000			0.232845
$665$		0			0
$666$		0			0
$667$	−9.00000	−	15.5885i	−0.348481	−	0.603587i
$668$	4.50000	−	7.79423i	0.174110	−	0.301568i
$669$		0			0
$670$		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
$675$		0			0
$676$	−6.00000	+	10.3923i	−0.230769	+	0.399704i
$677$	21.0000	+	36.3731i	0.807096	+	1.39793i	0.914867	+	0.403755i	$0.132295\pi$
$677$	21.0000	+	36.3731i	0.807096	+	1.39793i	−0.107772	+	0.994176i	$0.534372\pi$
$678$		0			0
$679$	−32.5000	−	11.2583i	−1.24724	−	0.432055i
$680$		0			0
$681$		0			0
$682$	4.00000	−	6.92820i	0.153168	−	0.265295i
$683$	−22.5000	+	38.9711i	−0.860939	+	1.49119i	0.0100856	+	0.999949i	$0.496790\pi$
$683$	−22.5000	+	38.9711i	−0.860939	+	1.49119i	−0.871024	+	0.491240i	$0.836544\pi$
$684$		0			0
$685$		0			0
$686$	−8.50000	+	16.4545i	−0.324532	+	0.628235i
$687$		0			0
$688$	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	−0.979086	−	0.203445i	$-0.934786\pi$
$691$	−17.5000	−	30.3109i	−0.665731	−	1.15308i	0.313355	−	0.949636i	$-0.398547\pi$
$692$	15.0000			0.570214
$693$		0			0
$694$	12.0000			0.455514
$695$		0			0
$696$		0			0
$697$	18.0000	−	31.1769i	0.681799	−	1.18091i
$698$	−17.0000	−	29.4449i	−0.643459	−	1.11450i
$699$		0			0
$700$	2.50000	+	12.9904i	0.0944911	+	0.490990i
$701$	3.00000			0.113308			0.0566542	−	0.998394i	$-0.481957\pi$
$701$	3.00000			0.113308			0.0566542	+	0.998394i	$0.481957\pi$
$702$		0			0
$703$	−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
$707$	6.00000	−	5.19615i	0.225653	−	0.195421i
$708$		0			0
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$		0			0
$711$		0			0
$712$	−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
$717$		0			0
$718$	4.50000	−	7.79423i	0.167939	−	0.290878i
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	0.804648	−	0.593753i	$-0.202354\pi$
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	−0.916529	+	0.399969i	$0.869021\pi$
$720$		0			0
$721$	2.00000	+	10.3923i	0.0744839	+	0.387030i
$722$	15.0000			0.558242
$723$		0			0
$724$	5.00000	−	8.66025i	0.185824	−	0.321856i
$725$	−7.50000	+	12.9904i	−0.278543	+	0.482451i
$726$		0			0
$727$	50.0000			1.85440			0.927199	−	0.374570i	$-0.122210\pi$
$727$	50.0000			1.85440			0.927199	+	0.374570i	$0.122210\pi$
$728$	−12.5000	−	4.33013i	−0.463281	−	0.160485i
$729$		0			0
$730$		0			0
$731$	−12.0000	+	20.7846i	−0.443836	+	0.768747i
$732$		0			0
$733$	21.5000	+	37.2391i	0.794121	+	1.37546i	0.923396	+	0.383849i	$0.125402\pi$
$733$	21.5000	+	37.2391i	0.794121	+	1.37546i	−0.129275	+	0.991609i	$0.541265\pi$
$734$	−38.0000			−1.40261
$735$		0			0
$736$	6.00000			0.221163
$737$	6.50000	+	11.2583i	0.239431	+	0.414706i
$738$		0			0
$739$	−1.00000	+	1.73205i	−0.0367856	+	0.0637145i	−0.883832	−	0.467804i	$-0.845045\pi$
$739$	−1.00000	+	1.73205i	−0.0367856	+	0.0637145i	0.847046	+	0.531519i	$0.178379\pi$
$740$		0			0
$741$		0			0
$742$	−30.0000	−	10.3923i	−1.10133	−	0.381514i
$743$	36.0000			1.32071			0.660356	−	0.750953i	$-0.270405\pi$
$743$	36.0000			1.32071			0.660356	+	0.750953i	$0.270405\pi$
$744$		0			0
$745$		0			0
$746$	5.50000	−	9.52628i	0.201369	−	0.348782i
$747$		0			0
$748$	−6.00000			−0.219382
$749$		0			0
$750$		0			0
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	0.974265	−	0.225407i	$-0.0723712\pi$
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	−0.682341	+	0.731034i	$0.739038\pi$
$752$	3.00000	−	5.19615i	0.109399	−	0.189484i
$753$		0			0
$754$	−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
$759$		0			0
$760$		0			0
$761$	15.0000	+	25.9808i	0.543750	+	0.941802i	0.998684	+	0.0512772i	$0.0163292\pi$
$761$	15.0000	+	25.9808i	0.543750	+	0.941802i	−0.454935	+	0.890525i	$0.650337\pi$
$762$		0			0
$763$	−28.0000	+	24.2487i	−1.01367	+	0.877862i
$764$	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			0
$769$	2.00000			0.0721218			0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000			0.0721218			0.0360609	+	0.999350i	$0.488519\pi$
$770$		0			0
$771$		0			0
$772$	11.0000	+	19.0526i	0.395899	+	0.685717i
$773$	−12.0000	+	20.7846i	−0.431610	+	0.747570i	−0.997012	−	0.0772449i	$-0.975388\pi$
$773$	−12.0000	+	20.7846i	−0.431610	+	0.747570i	0.565402	+	0.824815i	$0.308721\pi$
$774$		0			0
$775$	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
$783$		0			0
$784$	1.00000	−	6.92820i	0.0357143	−	0.247436i
$785$		0			0
$786$		0			0
$787$	−7.00000	+	12.1244i	−0.249523	+	0.432187i	−0.963394	−	0.268091i	$-0.913607\pi$
$787$	−7.00000	+	12.1244i	−0.249523	+	0.432187i	0.713871	+	0.700278i	$0.246941\pi$
$788$	−4.50000	+	7.79423i	−0.160306	+	0.277658i
$789$		0			0
$790$		0			0
$791$	−22.5000	−	7.79423i	−0.800008	−	0.277131i
$792$		0			0
$793$	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
$801$		0			0
$802$	4.50000	−	7.79423i	0.158901	−	0.275224i
$803$	5.00000	+	8.66025i	0.176446	+	0.305614i
$804$		0			0
$805$		0			0
$806$	−40.0000			−1.40894
$807$		0			0
$808$	−1.50000	+	2.59808i	−0.0527698	+	0.0914000i
$809$	18.0000	−	31.1769i	0.632846	−	1.09612i	−0.354121	−	0.935200i	$-0.615220\pi$
$809$	18.0000	−	31.1769i	0.632846	−	1.09612i	0.986967	−	0.160922i	$-0.0514468\pi$
$810$		0			0
$811$	−16.0000			−0.561836			−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000			−0.561836			−0.280918	+	0.959732i	$0.590639\pi$
$812$	6.00000	−	5.19615i	0.210559	−	0.182349i
$813$		0			0
$814$	1.00000	+	1.73205i	0.0350500	+	0.0607083i
$815$		0			0
$816$		0			0
$817$	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	$-0.0105045\pi$
$821$	13.5000	+	23.3827i	0.471153	+	0.816061i	−0.528302	+	0.849056i	$0.677171\pi$
$822$		0			0
$823$	−13.0000	+	22.5167i	−0.453152	+	0.784881i	−0.998580	−	0.0532760i	$-0.983034\pi$
$823$	−13.0000	+	22.5167i	−0.453152	+	0.784881i	0.545428	+	0.838157i	$0.316367\pi$
$824$	−2.00000	−	3.46410i	−0.0696733	−	0.120678i
$825$		0			0
$826$	−7.50000	−	2.59808i	−0.260958	−	0.0903986i
$827$	−42.0000			−1.46048			−0.730242	−	0.683189i	$-0.760592\pi$
$827$	−42.0000			−1.46048			−0.730242	+	0.683189i	$0.760592\pi$
$828$		0			0
$829$	8.00000	−	13.8564i	0.277851	−	0.481253i	−0.692999	−	0.720938i	$-0.743711\pi$
$829$	8.00000	−	13.8564i	0.277851	−	0.481253i	0.970851	+	0.239686i	$0.0770444\pi$
$830$		0			0
$831$		0			0
$832$	5.00000			0.173344
$833$	39.0000	−	15.5885i	1.35127	−	0.540108i
$834$		0			0
$835$		0			0
$836$	−1.00000	+	1.73205i	−0.0345857	+	0.0599042i
$837$		0			0
$838$	−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
$843$		0			0
$844$	−13.0000	+	22.5167i	−0.447478	+	0.775055i
$845$		0			0
$846$		0			0
$847$	−0.500000	−	2.59808i	−0.0171802	−	0.0892710i
$848$	12.0000			0.412082
$849$		0			0
$850$	15.0000	−	25.9808i	0.514496	−	0.891133i
$851$	6.00000	−	10.3923i	0.205677	−	0.356244i
$852$		0			0
$853$	−58.0000			−1.98588			−0.992941	−	0.118609i	$-0.962157\pi$
$853$	−58.0000			−1.98588			−0.992941	+	0.118609i	$0.962157\pi$
$854$	−14.0000	+	12.1244i	−0.479070	+	0.414887i
$855$		0			0
$856$		0			0
$857$	24.0000	−	41.5692i	0.819824	−	1.41998i	−0.0859870	−	0.996296i	$-0.527404\pi$
$857$	24.0000	−	41.5692i	0.819824	−	1.41998i	0.905811	−	0.423681i	$-0.139262\pi$
$858$		0			0
$859$	−17.5000	−	30.3109i	−0.597092	−	1.03419i	−0.993248	−	0.116011i	$-0.962989\pi$
$859$	−17.5000	−	30.3109i	−0.597092	−	1.03419i	0.396156	−	0.918183i	$-0.370344\pi$
$860$		0			0
$861$		0			0
$862$	15.0000			0.510902
$863$	3.00000	+	5.19615i	0.102121	+	0.176879i	0.912558	−	0.408946i	$-0.134104\pi$
$863$	3.00000	+	5.19615i	0.102121	+	0.176879i	−0.810437	+	0.585826i	$0.800770\pi$
$864$		0			0
$865$		0			0
$866$	7.00000	+	12.1244i	0.237870	+	0.412002i
$867$		0			0
$868$	−4.00000	−	20.7846i	−0.135769	−	0.705476i
$869$	−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
$873$		0			0
$874$	12.0000			0.405906
$875$		0			0
$876$		0			0
$877$	18.5000	+	32.0429i	0.624701	+	1.08201i	0.988599	+	0.150574i	$0.0481123\pi$
$877$	18.5000	+	32.0429i	0.624701	+	1.08201i	−0.363898	+	0.931439i	$0.618554\pi$
$878$	−9.50000	+	16.4545i	−0.320609	+	0.555312i
$879$		0			0
$880$		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	0.729873	+	0.683582i	$0.239579\pi$
$887$	28.5000	+	49.3634i	0.956936	+	1.65746i	0.227063	+	0.973880i	$0.427088\pi$
$888$		0			0
$889$	−32.5000	−	11.2583i	−1.09002	−	0.377592i
$890$		0			0
$891$		0			0
$892$	5.00000	−	8.66025i	0.167412	−	0.289967i
$893$	6.00000	−	10.3923i	0.200782	−	0.347765i
$894$		0			0
$895$		0			0
$896$	0.500000	+	2.59808i	0.0167038	+	0.0867956i
$897$		0			0
$898$	−15.0000	−	25.9808i	−0.500556	−	0.866989i
$899$	12.0000	−	20.7846i	0.400222	−	0.693206i
$900$		0			0
$901$	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			0
$907$	−22.0000	+	38.1051i	−0.730498	+	1.26526i	0.226173	+	0.974087i	$0.427379\pi$
$907$	−22.0000	+	38.1051i	−0.730498	+	1.26526i	−0.956671	+	0.291172i	$0.905955\pi$
$908$	−3.00000	−	5.19615i	−0.0995585	−	0.172440i
$909$		0			0
$910$		0			0
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$		0			0
$913$	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
$917$	3.00000	+	15.5885i	0.0990687	+	0.514776i
$918$		0			0
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	0.967274	−	0.253735i	$-0.0816592\pi$
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	−0.703378	+	0.710816i	$0.748326\pi$
$920$		0			0
$921$		0			0
$922$	−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
$927$		0			0
$928$	−1.50000	+	2.59808i	−0.0492399	+	0.0852860i
$929$	7.50000	+	12.9904i	0.246067	+	0.426201i	0.962431	−	0.271526i	$-0.0875283\pi$
$929$	7.50000	+	12.9904i	0.246067	+	0.426201i	−0.716364	+	0.697727i	$0.754195\pi$
$930$		0			0
$931$	2.00000	−	13.8564i	0.0655474	−	0.454125i
$932$	30.0000			0.982683
$933$		0			0
$934$	6.00000	−	10.3923i	0.196326	−	0.340047i
$935$		0			0
$936$		0			0
$937$	−52.0000			−1.69877			−0.849383	−	0.527777i	$-0.823026\pi$
$937$	−52.0000			−1.69877			−0.849383	+	0.527777i	$0.823026\pi$
$938$	32.5000	+	11.2583i	1.06116	+	0.367598i
$939$		0			0
$940$		0			0
$941$	−13.5000	+	23.3827i	−0.440087	+	0.762254i	−0.997695	−	0.0678506i	$-0.978386\pi$
$941$	−13.5000	+	23.3827i	−0.440087	+	0.762254i	0.557608	+	0.830104i	$0.311719\pi$
$942$		0			0
$943$	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	$-0.294174\pi$
$947$	−12.0000	−	20.7846i	−0.389948	−	0.675409i	−0.992442	+	0.122714i	$0.960840\pi$
$948$		0			0
$949$	25.0000	−	43.3013i	0.811534	−	1.40562i
$950$	−5.00000	−	8.66025i	−0.162221	−	0.280976i
$951$		0			0
$952$	−12.0000	+	10.3923i	−0.388922	+	0.336817i
$953$	−24.0000			−0.777436			−0.388718	−	0.921357i	$-0.627082\pi$
$953$	−24.0000			−0.777436			−0.388718	+	0.921357i	$0.627082\pi$
$954$		0			0
$955$		0			0
$956$	10.5000	−	18.1865i	0.339594	−	0.588195i
$957$		0			0
$958$	−3.00000			−0.0969256
$959$	30.0000	−	25.9808i	0.968751	−	0.838963i
$960$		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
$969$		0			0
$970$		0			0
$971$	−16.5000	−	28.5788i	−0.529510	−	0.917139i	−0.999408	−	0.0344175i	$-0.989042\pi$
$971$	−16.5000	−	28.5788i	−0.529510	−	0.917139i	0.469897	−	0.882721i	$-0.344291\pi$
$972$		0			0
$973$	−10.0000	−	3.46410i	−0.320585	−	0.111054i
$974$	4.00000			0.128168
$975$		0			0
$976$	3.50000	−	6.06218i	0.112032	−	0.194046i
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	−0.973317	−	0.229465i	$-0.926302\pi$
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	0.685381	+	0.728184i	$0.259636\pi$
$978$		0			0
$979$	−6.00000			−0.191761
$980$		0			0
$981$		0			0
$982$	15.0000	+	25.9808i	0.478669	+	0.829079i
$983$	−3.00000	+	5.19615i	−0.0956851	+	0.165732i	−0.909894	−	0.414840i	$-0.863838\pi$
$983$	−3.00000	+	5.19615i	−0.0956851	+	0.165732i	0.814209	+	0.580572i	$0.197171\pi$
$984$		0			0
$985$		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	−0.710530	−	0.703667i	$-0.751545\pi$
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	0.964658	+	0.263504i	$0.0848781\pi$
$992$	4.00000	+	6.92820i	0.127000	+	0.219971i
$993$		0			0
$994$	6.00000	+	31.1769i	0.190308	+	0.988872i
$995$		0			0
$996$		0			0
$997$	23.0000	−	39.8372i	0.728417	−	1.26166i	−0.229135	−	0.973395i	$-0.573590\pi$
$997$	23.0000	−	39.8372i	0.728417	−	1.26166i	0.957552	−	0.288261i	$-0.0930771\pi$
$998$	4.00000	−	6.92820i	0.126618	−	0.219308i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.k.n.991.1		2
3.2	odd	2		154.2.e.b.67.1	yes	2
7.2	even	3	inner	1386.2.k.n.793.1		2
7.3	odd	6		9702.2.a.l.1.1		1
7.4	even	3		9702.2.a.o.1.1		1
12.11	even	2		1232.2.q.c.529.1		2
21.2	odd	6		154.2.e.b.23.1	✓	2
21.5	even	6		1078.2.e.d.177.1		2
21.11	odd	6		1078.2.a.k.1.1		1
21.17	even	6		1078.2.a.i.1.1		1
21.20	even	2		1078.2.e.d.67.1		2
84.11	even	6		8624.2.a.l.1.1		1
84.23	even	6		1232.2.q.c.177.1		2
84.59	odd	6		8624.2.a.t.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.e.b.23.1	✓	2	21.2	odd	6
154.2.e.b.67.1	yes	2	3.2	odd	2
1078.2.a.i.1.1		1	21.17	even	6
1078.2.a.k.1.1		1	21.11	odd	6
1078.2.e.d.67.1		2	21.20	even	2
1078.2.e.d.177.1		2	21.5	even	6
1232.2.q.c.177.1		2	84.23	even	6
1232.2.q.c.529.1		2	12.11	even	2
1386.2.k.n.793.1		2	7.2	even	3	inner
1386.2.k.n.991.1		2	1.1	even	1	trivial
8624.2.a.l.1.1		1	84.11	even	6
8624.2.a.t.1.1		1	84.59	odd	6
9702.2.a.l.1.1		1	7.3	odd	6
9702.2.a.o.1.1		1	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{11} +5.00000 q^{13} +(0.500000 + 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(-1.00000 - 1.73205i) q^{19} -1.00000 q^{22} +(3.00000 + 5.19615i) q^{23} +(2.50000 - 4.33013i) q^{25} +(2.50000 + 4.33013i) q^{26} +(-2.00000 + 1.73205i) q^{28} -3.00000 q^{29} +(-4.00000 + 6.92820i) q^{31} +(0.500000 - 0.866025i) q^{32} +6.00000 q^{34} +(-1.00000 - 1.73205i) q^{37} +(1.00000 - 1.73205i) q^{38} +6.00000 q^{41} -4.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(3.00000 + 5.19615i) q^{47} +(5.50000 + 4.33013i) q^{49} +5.00000 q^{50} +(-2.50000 + 4.33013i) q^{52} +(-6.00000 + 10.3923i) q^{53} +(-2.50000 - 0.866025i) q^{56} +(-1.50000 - 2.59808i) q^{58} +(-1.50000 + 2.59808i) q^{59} +(3.50000 + 6.06218i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(6.50000 - 11.2583i) q^{67} +(3.00000 + 5.19615i) q^{68} +12.0000 q^{71} +(5.00000 - 8.66025i) q^{73} +(1.00000 - 1.73205i) q^{74} +2.00000 q^{76} +(-2.00000 + 1.73205i) q^{77} +(0.500000 + 0.866025i) q^{79} +(3.00000 + 5.19615i) q^{82} -6.00000 q^{83} +(-2.00000 - 3.46410i) q^{86} +(0.500000 - 0.866025i) q^{88} +(3.00000 + 5.19615i) q^{89} +(12.5000 + 4.33013i) q^{91} -6.00000 q^{92} +(-3.00000 + 5.19615i) q^{94} -13.0000 q^{97} +(-1.00000 + 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} + 5 q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 + 5 * q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} + 5 q^{7} - 2 q^{8} - q^{11} + 10 q^{13} + q^{14} - q^{16} + 6 q^{17} - 2 q^{19} - 2 q^{22} + 6 q^{23} + 5 q^{25} + 5 q^{26} - 4 q^{28} - 6 q^{29} - 8 q^{31} + q^{32} + 12 q^{34} - 2 q^{37} + 2 q^{38} + 12 q^{41} - 8 q^{43} - q^{44} - 6 q^{46} + 6 q^{47} + 11 q^{49} + 10 q^{50} - 5 q^{52} - 12 q^{53} - 5 q^{56} - 3 q^{58} - 3 q^{59} + 7 q^{61} - 16 q^{62} + 2 q^{64} + 13 q^{67} + 6 q^{68} + 24 q^{71} + 10 q^{73} + 2 q^{74} + 4 q^{76} - 4 q^{77} + q^{79} + 6 q^{82} - 12 q^{83} - 4 q^{86} + q^{88} + 6 q^{89} + 25 q^{91} - 12 q^{92} - 6 q^{94} - 26 q^{97} - 2 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 + 5 * q^7 - 2 * q^8 - q^11 + 10 * q^13 + q^14 - q^16 + 6 * q^17 - 2 * q^19 - 2 * q^22 + 6 * q^23 + 5 * q^25 + 5 * q^26 - 4 * q^28 - 6 * q^29 - 8 * q^31 + q^32 + 12 * q^34 - 2 * q^37 + 2 * q^38 + 12 * q^41 - 8 * q^43 - q^44 - 6 * q^46 + 6 * q^47 + 11 * q^49 + 10 * q^50 - 5 * q^52 - 12 * q^53 - 5 * q^56 - 3 * q^58 - 3 * q^59 + 7 * q^61 - 16 * q^62 + 2 * q^64 + 13 * q^67 + 6 * q^68 + 24 * q^71 + 10 * q^73 + 2 * q^74 + 4 * q^76 - 4 * q^77 + q^79 + 6 * q^82 - 12 * q^83 - 4 * q^86 + q^88 + 6 * q^89 + 25 * q^91 - 12 * q^92 - 6 * q^94 - 26 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more