LMFDB - Embedded newform 1386.2.k.e.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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	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.e.793.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{11} -1.00000 q^{13} +(2.50000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(-1.00000 - 1.73205i) q^{19} +1.00000 q^{22} +(-3.00000 - 5.19615i) q^{23} +(2.50000 - 4.33013i) q^{25} +(0.500000 + 0.866025i) q^{26} +(-2.00000 - 1.73205i) q^{28} -9.00000 q^{29} +(2.00000 - 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +6.00000 q^{34} +(-1.00000 - 1.73205i) q^{37} +(-1.00000 + 1.73205i) q^{38} +6.00000 q^{41} -4.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(-3.00000 - 5.19615i) q^{47} +(-6.50000 - 2.59808i) q^{49} -5.00000 q^{50} +(0.500000 - 0.866025i) q^{52} +(-0.500000 + 2.59808i) q^{56} +(4.50000 + 7.79423i) q^{58} +(-1.50000 + 2.59808i) q^{59} +(-5.50000 - 9.52628i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(-5.50000 + 9.52628i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(-1.00000 + 1.73205i) q^{73} +(-1.00000 + 1.73205i) q^{74} +2.00000 q^{76} +(-2.00000 - 1.73205i) q^{77} +(-2.50000 - 4.33013i) q^{79} +(-3.00000 - 5.19615i) q^{82} +6.00000 q^{83} +(2.00000 + 3.46410i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(-9.00000 - 15.5885i) q^{89} +(0.500000 - 2.59808i) q^{91} +6.00000 q^{92} +(-3.00000 + 5.19615i) q^{94} -13.0000 q^{97} +(1.00000 + 6.92820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 - q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} - q^{7} + 2 q^{8} - q^{11} - 2 q^{13} + 5 q^{14} - q^{16} - 6 q^{17} - 2 q^{19} + 2 q^{22} - 6 q^{23} + 5 q^{25} + q^{26} - 4 q^{28} - 18 q^{29} + 4 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} - 13 q^{49} - 10 q^{50} + q^{52} - q^{56} + 9 q^{58} - 3 q^{59} - 11 q^{61} - 8 q^{62} + 2 q^{64} - 11 q^{67} - 6 q^{68} - 2 q^{73} - 2 q^{74} + 4 q^{76} - 4 q^{77} - 5 q^{79} - 6 q^{82} + 12 q^{83} + 4 q^{86} - q^{88} - 18 q^{89} + q^{91} + 12 q^{92} - 6 q^{94} - 26 q^{97} + 2 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 - q^7 + 2 * q^8 - q^11 - 2 * q^13 + 5 * q^14 - q^16 - 6 * q^17 - 2 * q^19 + 2 * q^22 - 6 * q^23 + 5 * q^25 + q^26 - 4 * q^28 - 18 * q^29 + 4 * 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 - 13 * q^49 - 10 * q^50 + q^52 - q^56 + 9 * q^58 - 3 * q^59 - 11 * q^61 - 8 * q^62 + 2 * q^64 - 11 * q^67 - 6 * q^68 - 2 * q^73 - 2 * q^74 + 4 * q^76 - 4 * q^77 - 5 * q^79 - 6 * q^82 + 12 * q^83 + 4 * q^86 - q^88 - 18 * q^89 + 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
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$8$	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
$13$	−1.00000			−0.277350			−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000			−0.277350			−0.138675	+	0.990338i	$0.544284\pi$
$14$	2.50000	−	0.866025i	0.668153	−	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	0.230285	+	0.973123i	$0.426034\pi$
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	−0.957892	+	0.287129i	$0.907299\pi$
$18$		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	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$	0.500000	+	0.866025i	0.0980581	+	0.169842i
$27$		0			0
$28$	−2.00000	−	1.73205i	−0.377964	−	0.327327i
$29$	−9.00000			−1.67126			−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000			−1.67126			−0.835629	+	0.549294i	$0.814897\pi$
$30$		0			0
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	−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	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$		0			0
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	−5.00000			−0.707107
$51$		0			0
$52$	0.500000	−	0.866025i	0.0693375	−	0.120096i
$53$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$53$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$54$		0			0
$55$		0			0
$56$	−0.500000	+	2.59808i	−0.0668153	+	0.347183i
$57$		0			0
$58$	4.50000	+	7.79423i	0.590879	+	1.02343i
$59$	−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
$61$	−5.50000	−	9.52628i	−0.704203	−	1.21972i	−0.966978	−	0.254858i	$-0.917971\pi$
$61$	−5.50000	−	9.52628i	−0.704203	−	1.21972i	0.262776	−	0.964857i	$-0.415362\pi$
$62$	−4.00000			−0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−5.50000	+	9.52628i	−0.671932	+	1.16382i	0.305424	+	0.952217i	$0.401202\pi$
$67$	−5.50000	+	9.52628i	−0.671932	+	1.16382i	−0.977356	+	0.211604i	$0.932131\pi$
$68$	−3.00000	−	5.19615i	−0.363803	−	0.630126i
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	−0.918594	−	0.395203i	$-0.870674\pi$
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	0.801553	+	0.597924i	$0.204008\pi$
$74$	−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
$79$	−2.50000	−	4.33013i	−0.281272	−	0.487177i	0.690426	−	0.723403i	$-0.257423\pi$
$79$	−2.50000	−	4.33013i	−0.281272	−	0.487177i	−0.971698	+	0.236225i	$0.924090\pi$
$80$		0			0
$81$		0			0
$82$	−3.00000	−	5.19615i	−0.331295	−	0.573819i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$		0			0
$85$		0			0
$86$	2.00000	+	3.46410i	0.215666	+	0.373544i
$87$		0			0
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	−9.00000	−	15.5885i	−0.953998	−	1.65237i	−0.736644	−	0.676280i	$-0.763591\pi$
$89$	−9.00000	−	15.5885i	−0.953998	−	1.65237i	−0.217354	−	0.976093i	$-0.569742\pi$
$90$		0			0
$91$	0.500000	−	2.59808i	0.0524142	−	0.272352i
$92$	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
$101$	−7.50000	+	12.9904i	−0.746278	+	1.29259i	0.203317	+	0.979113i	$0.434828\pi$
$101$	−7.50000	+	12.9904i	−0.746278	+	1.29259i	−0.949595	+	0.313478i	$0.898506\pi$
$102$		0			0
$103$	8.00000	+	13.8564i	0.788263	+	1.36531i	0.927030	+	0.374987i	$0.122353\pi$
$103$	8.00000	+	13.8564i	0.788263	+	1.36531i	−0.138767	+	0.990325i	$0.544314\pi$
$104$	−1.00000			−0.0980581
$105$		0			0
$106$		0			0
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	0.995474	+	0.0950377i	$0.0302972\pi$
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	−0.415432	+	0.909624i	$0.636370\pi$
$108$		0			0
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	0.814152	+	0.580651i	$0.197202\pi$
$110$		0			0
$111$		0			0
$112$	2.50000	−	0.866025i	0.236228	−	0.0818317i
$113$	−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
$116$	4.50000	−	7.79423i	0.417815	−	0.723676i
$117$		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
$122$	−5.50000	+	9.52628i	−0.497947	+	0.862469i
$123$		0			0
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$		0			0
$126$		0			0
$127$	−7.00000			−0.621150			−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000			−0.621150			−0.310575	+	0.950549i	$0.600522\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$		0			0
$131$	9.00000	+	15.5885i	0.786334	+	1.36197i	0.928199	+	0.372084i	$0.121357\pi$
$131$	9.00000	+	15.5885i	0.786334	+	1.36197i	−0.141865	+	0.989886i	$0.545310\pi$
$132$		0			0
$133$	5.00000	−	1.73205i	0.433555	−	0.150188i
$134$	11.0000			0.950255
$135$		0			0
$136$	−3.00000	+	5.19615i	−0.257248	+	0.445566i
$137$	−4.50000	+	7.79423i	−0.384461	+	0.665906i	−0.991694	−	0.128618i	$-0.958946\pi$
$137$	−4.50000	+	7.79423i	−0.384461	+	0.665906i	0.607233	+	0.794524i	$0.292279\pi$
$138$		0			0
$139$	8.00000			0.678551			0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000			0.678551			0.339276	+	0.940687i	$0.389818\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.500000	−	0.866025i	0.0418121	−	0.0724207i
$144$		0			0
$145$		0			0
$146$	2.00000			0.165521
$147$		0			0
$148$	2.00000			0.164399
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	9.50000	−	16.4545i	0.773099	−	1.33905i	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	9.50000	−	16.4545i	0.773099	−	1.33905i	0.935857	−	0.352381i	$-0.114628\pi$
$152$	−1.00000	−	1.73205i	−0.0811107	−	0.140488i
$153$		0			0
$154$	−0.500000	+	2.59808i	−0.0402911	+	0.209359i
$155$		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	$0.115641\pi$
$158$	−2.50000	+	4.33013i	−0.198889	+	0.344486i
$159$		0			0
$160$		0			0
$161$	15.0000	−	5.19615i	1.18217	−	0.409514i
$162$		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
$167$	−3.00000			−0.232147			−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000			−0.232147			−0.116073	+	0.993241i	$0.537031\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$		0			0
$171$		0			0
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	−10.5000	−	18.1865i	−0.798300	−	1.38270i	−0.920722	−	0.390218i	$-0.872399\pi$
$173$	−10.5000	−	18.1865i	−0.798300	−	1.38270i	0.122422	−	0.992478i	$-0.460934\pi$
$174$		0			0
$175$	10.0000	+	8.66025i	0.755929	+	0.654654i
$176$	1.00000			0.0753778
$177$		0			0
$178$	−9.00000	+	15.5885i	−0.674579	+	1.16840i
$179$	−7.50000	+	12.9904i	−0.560576	+	0.970947i	0.436870	+	0.899525i	$0.356087\pi$
$179$	−7.50000	+	12.9904i	−0.560576	+	0.970947i	−0.997446	+	0.0714220i	$0.977246\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	−2.50000	+	0.866025i	−0.185312	+	0.0641941i
$183$		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
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	0.953912	−	0.300088i	$-0.0970159\pi$
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	−0.736839	+	0.676068i	$0.763683\pi$
$192$		0			0
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	0.496119	+	0.868255i	$0.334758\pi$
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	−0.999990	+	0.00447566i	$0.998575\pi$
$194$	6.50000	+	11.2583i	0.466673	+	0.808301i
$195$		0			0
$196$	5.50000	−	4.33013i	0.392857	−	0.309295i
$197$	3.00000			0.213741			0.106871	−	0.994273i	$-0.465917\pi$
$197$	3.00000			0.213741			0.106871	+	0.994273i	$0.465917\pi$
$198$		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
$202$	15.0000			1.05540
$203$	4.50000	−	23.3827i	0.315838	−	1.64114i
$204$		0			0
$205$		0			0
$206$	8.00000	−	13.8564i	0.557386	−	0.965422i
$207$		0			0
$208$	0.500000	+	0.866025i	0.0346688	+	0.0600481i
$209$	2.00000			0.138343
$210$		0			0
$211$	−10.0000			−0.688428			−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000			−0.688428			−0.344214	+	0.938891i	$0.611855\pi$
$212$		0			0
$213$		0			0
$214$	6.00000	−	10.3923i	0.410152	−	0.710403i
$215$		0			0
$216$		0			0
$217$	8.00000	+	6.92820i	0.543075	+	0.470317i
$218$	2.00000			0.135457
$219$		0			0
$220$		0			0
$221$	3.00000	−	5.19615i	0.201802	−	0.349531i
$222$		0			0
$223$	26.0000			1.74109			0.870544	−	0.492090i	$-0.163767\pi$
$223$	26.0000			1.74109			0.870544	+	0.492090i	$0.163767\pi$
$224$	−2.00000	−	1.73205i	−0.133631	−	0.115728i
$225$		0			0
$226$	4.50000	+	7.79423i	0.299336	+	0.518464i
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	−0.395860	−	0.918311i	$-0.629553\pi$
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	0.993210	−	0.116331i	$-0.0371134\pi$
$228$		0			0
$229$	8.00000	+	13.8564i	0.528655	+	0.915657i	0.999442	+	0.0334101i	$0.0106368\pi$
$229$	8.00000	+	13.8564i	0.528655	+	0.915657i	−0.470787	+	0.882247i	$0.656030\pi$
$230$		0			0
$231$		0			0
$232$	−9.00000			−0.590879
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	0.750867	−	0.660454i	$-0.229636\pi$
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	−0.947403	+	0.320043i	$0.896303\pi$
$234$		0			0
$235$		0			0
$236$	−1.50000	−	2.59808i	−0.0976417	−	0.169120i
$237$		0			0
$238$	−3.00000	+	15.5885i	−0.194461	+	1.01045i
$239$	9.00000			0.582162			0.291081	−	0.956698i	$-0.405985\pi$
$239$	9.00000			0.582162			0.291081	+	0.956698i	$0.405985\pi$
$240$		0			0
$241$	−13.0000	+	22.5167i	−0.837404	+	1.45043i	0.0546547	+	0.998505i	$0.482594\pi$
$241$	−13.0000	+	22.5167i	−0.837404	+	1.45043i	−0.892058	+	0.451920i	$0.850739\pi$
$242$	−0.500000	+	0.866025i	−0.0321412	+	0.0556702i
$243$		0			0
$244$	11.0000			0.704203
$245$		0			0
$246$		0			0
$247$	1.00000	+	1.73205i	0.0636285	+	0.110208i
$248$	2.00000	−	3.46410i	0.127000	−	0.219971i
$249$		0			0
$250$		0			0
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$	6.00000			0.377217
$254$	3.50000	+	6.06218i	0.219610	+	0.380375i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	0.909010	−	0.416775i	$-0.136840\pi$
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	−0.815442	+	0.578838i	$0.803506\pi$
$258$		0			0
$259$	5.00000	−	1.73205i	0.310685	−	0.107624i
$260$		0			0
$261$		0			0
$262$	9.00000	−	15.5885i	0.556022	−	0.963058i
$263$	−4.50000	+	7.79423i	−0.277482	+	0.480613i	−0.970758	−	0.240059i	$-0.922833\pi$
$263$	−4.50000	+	7.79423i	−0.277482	+	0.480613i	0.693276	+	0.720672i	$0.256167\pi$
$264$		0			0
$265$		0			0
$266$	−4.00000	−	3.46410i	−0.245256	−	0.212398i
$267$		0			0
$268$	−5.50000	−	9.52628i	−0.335966	−	0.581910i
$269$	6.00000	−	10.3923i	0.365826	−	0.633630i	−0.623082	−	0.782157i	$-0.714120\pi$
$269$	6.00000	−	10.3923i	0.365826	−	0.633630i	0.988908	+	0.148527i	$0.0474530\pi$
$270$		0			0
$271$	−14.5000	−	25.1147i	−0.880812	−	1.52561i	−0.850439	−	0.526073i	$-0.823664\pi$
$271$	−14.5000	−	25.1147i	−0.880812	−	1.52561i	−0.0303728	−	0.999539i	$-0.509669\pi$
$272$	6.00000			0.363803
$273$		0			0
$274$	9.00000			0.543710
$275$	2.50000	+	4.33013i	0.150756	+	0.261116i
$276$		0			0
$277$	−14.5000	+	25.1147i	−0.871221	+	1.50900i	−0.0104855	+	0.999945i	$0.503338\pi$
$277$	−14.5000	+	25.1147i	−0.871221	+	1.50900i	−0.860735	+	0.509053i	$0.829996\pi$
$278$	−4.00000	−	6.92820i	−0.239904	−	0.415526i
$279$		0			0
$280$		0			0
$281$	−18.0000			−1.07379			−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000			−1.07379			−0.536895	+	0.843649i	$0.680403\pi$
$282$		0			0
$283$	5.00000	−	8.66025i	0.297219	−	0.514799i	−0.678280	−	0.734804i	$-0.737274\pi$
$283$	5.00000	−	8.66025i	0.297219	−	0.514799i	0.975499	+	0.220005i	$0.0706075\pi$
$284$		0			0
$285$		0			0
$286$	−1.00000			−0.0591312
$287$	−3.00000	+	15.5885i	−0.177084	+	0.920158i
$288$		0			0
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$		0			0
$291$		0			0
$292$	−1.00000	−	1.73205i	−0.0585206	−	0.101361i
$293$	30.0000			1.75262			0.876309	−	0.481749i	$-0.159998\pi$
$293$	30.0000			1.75262			0.876309	+	0.481749i	$0.159998\pi$
$294$		0			0
$295$		0			0
$296$	−1.00000	−	1.73205i	−0.0581238	−	0.100673i
$297$		0			0
$298$	3.00000	−	5.19615i	0.173785	−	0.301005i
$299$	3.00000	+	5.19615i	0.173494	+	0.300501i
$300$		0			0
$301$	2.00000	−	10.3923i	0.115278	−	0.599002i
$302$	−19.0000			−1.09333
$303$		0			0
$304$	−1.00000	+	1.73205i	−0.0573539	+	0.0993399i
$305$		0			0
$306$		0			0
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$	2.50000	−	0.866025i	0.142451	−	0.0493464i
$309$		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
$313$	−8.50000	−	14.7224i	−0.480448	−	0.832161i	0.519300	−	0.854592i	$-0.326193\pi$
$313$	−8.50000	−	14.7224i	−0.480448	−	0.832161i	−0.999748	+	0.0224310i	$0.992859\pi$
$314$	−4.00000			−0.225733
$315$		0			0
$316$	5.00000			0.281272
$317$	6.00000	+	10.3923i	0.336994	+	0.583690i	0.983866	−	0.178908i	$-0.0572566\pi$
$317$	6.00000	+	10.3923i	0.336994	+	0.583690i	−0.646872	+	0.762598i	$0.723923\pi$
$318$		0			0
$319$	4.50000	−	7.79423i	0.251952	−	0.436393i
$320$		0			0
$321$		0			0
$322$	−12.0000	−	10.3923i	−0.668734	−	0.579141i
$323$	12.0000			0.667698
$324$		0			0
$325$	−2.50000	+	4.33013i	−0.138675	+	0.240192i
$326$	−8.50000	+	14.7224i	−0.470771	+	0.815400i
$327$		0			0
$328$	6.00000			0.331295
$329$	15.0000	−	5.19615i	0.826977	−	0.286473i
$330$		0			0
$331$	−17.5000	−	30.3109i	−0.961887	−	1.66604i	−0.717756	−	0.696295i	$-0.754831\pi$
$331$	−17.5000	−	30.3109i	−0.961887	−	1.66604i	−0.244131	−	0.969742i	$-0.578503\pi$
$332$	−3.00000	+	5.19615i	−0.164646	+	0.285176i
$333$		0			0
$334$	1.50000	+	2.59808i	0.0820763	+	0.142160i
$335$		0			0
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$	6.00000	+	10.3923i	0.326357	+	0.565267i
$339$		0			0
$340$		0			0
$341$	2.00000	+	3.46410i	0.108306	+	0.187592i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−4.00000			−0.215666
$345$		0			0
$346$	−10.5000	+	18.1865i	−0.564483	+	0.977714i
$347$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$347$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$348$		0			0
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$	2.50000	−	12.9904i	0.133631	−	0.694365i
$351$		0			0
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	−0.999711	−	0.0240566i	$-0.992342\pi$
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	0.520689	+	0.853746i	$0.325675\pi$
$354$		0			0
$355$		0			0
$356$	18.0000			0.953998
$357$		0			0
$358$	15.0000			0.792775
$359$	−1.50000	−	2.59808i	−0.0791670	−	0.137121i	0.823724	−	0.566991i	$-0.191893\pi$
$359$	−1.50000	−	2.59808i	−0.0791670	−	0.137121i	−0.902891	+	0.429870i	$0.858559\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	−1.00000	−	1.73205i	−0.0525588	−	0.0910346i
$363$		0			0
$364$	2.00000	+	1.73205i	0.104828	+	0.0907841i
$365$		0			0
$366$		0			0
$367$	5.00000	−	8.66025i	0.260998	−	0.452062i	−0.705509	−	0.708700i	$-0.749282\pi$
$367$	5.00000	−	8.66025i	0.260998	−	0.452062i	0.966507	+	0.256639i	$0.0826151\pi$
$368$	−3.00000	+	5.19615i	−0.156386	+	0.270868i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	15.5000	+	26.8468i	0.802560	+	1.39007i	0.917926	+	0.396751i	$0.129862\pi$
$373$	15.5000	+	26.8468i	0.802560	+	1.39007i	−0.115367	+	0.993323i	$0.536804\pi$
$374$	−3.00000	+	5.19615i	−0.155126	+	0.268687i
$375$		0			0
$376$	−3.00000	−	5.19615i	−0.154713	−	0.267971i
$377$	9.00000			0.463524
$378$		0			0
$379$	23.0000			1.18143			0.590715	−	0.806880i	$-0.298846\pi$
$379$	23.0000			1.18143			0.590715	+	0.806880i	$0.298846\pi$
$380$		0			0
$381$		0			0
$382$	3.00000	−	5.19615i	0.153493	−	0.265858i
$383$	−18.0000	−	31.1769i	−0.919757	−	1.59307i	−0.799783	−	0.600289i	$-0.795052\pi$
$383$	−18.0000	−	31.1769i	−0.919757	−	1.59307i	−0.119974	−	0.992777i	$-0.538281\pi$
$384$		0			0
$385$		0			0
$386$	14.0000			0.712581
$387$		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
$392$	−6.50000	−	2.59808i	−0.328300	−	0.131223i
$393$		0			0
$394$	−1.50000	−	2.59808i	−0.0755689	−	0.130889i
$395$		0			0
$396$		0			0
$397$	11.0000	+	19.0526i	0.552074	+	0.956221i	0.998125	+	0.0612128i	$0.0194968\pi$
$397$	11.0000	+	19.0526i	0.552074	+	0.956221i	−0.446051	+	0.895008i	$0.647170\pi$
$398$	14.0000			0.701757
$399$		0			0
$400$	−5.00000			−0.250000
$401$	−16.5000	−	28.5788i	−0.823971	−	1.42716i	−0.902703	−	0.430263i	$-0.858421\pi$
$401$	−16.5000	−	28.5788i	−0.823971	−	1.42716i	0.0787327	−	0.996896i	$-0.474913\pi$
$402$		0			0
$403$	−2.00000	+	3.46410i	−0.0996271	+	0.172559i
$404$	−7.50000	−	12.9904i	−0.373139	−	0.646296i
$405$		0			0
$406$	−22.5000	+	7.79423i	−1.11666	+	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
$412$	−16.0000			−0.788263
$413$	−6.00000	−	5.19615i	−0.295241	−	0.255686i
$414$		0			0
$415$		0			0
$416$	0.500000	−	0.866025i	0.0245145	−	0.0424604i
$417$		0			0
$418$	−1.00000	−	1.73205i	−0.0489116	−	0.0847174i
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		0			0
$421$	−28.0000			−1.36464			−0.682318	−	0.731055i	$-0.739028\pi$
$421$	−28.0000			−1.36464			−0.682318	+	0.731055i	$0.739028\pi$
$422$	5.00000	+	8.66025i	0.243396	+	0.421575i
$423$		0			0
$424$		0			0
$425$	15.0000	+	25.9808i	0.727607	+	1.26025i
$426$		0			0
$427$	27.5000	−	9.52628i	1.33082	−	0.461009i
$428$	−12.0000			−0.580042
$429$		0			0
$430$		0			0
$431$	−1.50000	+	2.59808i	−0.0722525	+	0.125145i	−0.899888	−	0.436121i	$-0.856352\pi$
$431$	−1.50000	+	2.59808i	−0.0722525	+	0.125145i	0.827636	+	0.561266i	$0.189685\pi$
$432$		0			0
$433$	−34.0000			−1.63394			−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000			−1.63394			−0.816968	+	0.576683i	$0.804347\pi$
$434$	2.00000	−	10.3923i	0.0960031	−	0.498847i
$435$		0			0
$436$	−1.00000	−	1.73205i	−0.0478913	−	0.0829502i
$437$	−6.00000	+	10.3923i	−0.287019	+	0.497131i
$438$		0			0
$439$	0.500000	+	0.866025i	0.0238637	+	0.0413331i	0.877711	−	0.479191i	$-0.159070\pi$
$439$	0.500000	+	0.866025i	0.0238637	+	0.0413331i	−0.853847	+	0.520524i	$0.825737\pi$
$440$		0			0
$441$		0			0
$442$	−6.00000			−0.285391
$443$	6.00000	+	10.3923i	0.285069	+	0.493753i	0.972626	−	0.232377i	$-0.0746503\pi$
$443$	6.00000	+	10.3923i	0.285069	+	0.493753i	−0.687557	+	0.726130i	$0.741317\pi$
$444$		0			0
$445$		0			0
$446$	−13.0000	−	22.5167i	−0.615568	−	1.06619i
$447$		0			0
$448$	−0.500000	+	2.59808i	−0.0236228	+	0.122748i
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$		0			0
$451$	−3.00000	+	5.19615i	−0.141264	+	0.244677i
$452$	4.50000	−	7.79423i	0.211662	−	0.366610i
$453$		0			0
$454$	−18.0000			−0.844782
$455$		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	$0.661289\pi$
$458$	8.00000	−	13.8564i	0.373815	−	0.647467i
$459$		0			0
$460$		0			0
$461$	−21.0000			−0.978068			−0.489034	−	0.872265i	$-0.662651\pi$
$461$	−21.0000			−0.978068			−0.489034	+	0.872265i	$0.662651\pi$
$462$		0			0
$463$	−22.0000			−1.02243			−0.511213	−	0.859454i	$-0.670804\pi$
$463$	−22.0000			−1.02243			−0.511213	+	0.859454i	$0.670804\pi$
$464$	4.50000	+	7.79423i	0.208907	+	0.361838i
$465$		0			0
$466$	−3.00000	+	5.19615i	−0.138972	+	0.240707i
$467$	6.00000	+	10.3923i	0.277647	+	0.480899i	0.970799	−	0.239892i	$-0.0771121\pi$
$467$	6.00000	+	10.3923i	0.277647	+	0.480899i	−0.693153	+	0.720791i	$0.743779\pi$
$468$		0			0
$469$	−22.0000	−	19.0526i	−1.01587	−	0.879765i
$470$		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
$476$	15.0000	−	5.19615i	0.687524	−	0.238165i
$477$		0			0
$478$	−4.50000	−	7.79423i	−0.205825	−	0.356500i
$479$	7.50000	−	12.9904i	0.342684	−	0.593546i	−0.642246	−	0.766498i	$-0.721997\pi$
$479$	7.50000	−	12.9904i	0.342684	−	0.593546i	0.984930	+	0.172953i	$0.0553307\pi$
$480$		0			0
$481$	1.00000	+	1.73205i	0.0455961	+	0.0789747i
$482$	26.0000			1.18427
$483$		0			0
$484$	1.00000			0.0454545
$485$		0			0
$486$		0			0
$487$	−10.0000	+	17.3205i	−0.453143	+	0.784867i	−0.998579	−	0.0532853i	$-0.983031\pi$
$487$	−10.0000	+	17.3205i	−0.453143	+	0.784867i	0.545436	+	0.838152i	$0.316364\pi$
$488$	−5.50000	−	9.52628i	−0.248973	−	0.431234i
$489$		0			0
$490$		0			0
$491$	−42.0000			−1.89543			−0.947717	−	0.319113i	$-0.896615\pi$
$491$	−42.0000			−1.89543			−0.947717	+	0.319113i	$0.896615\pi$
$492$		0			0
$493$	27.0000	−	46.7654i	1.21602	−	2.10621i
$494$	1.00000	−	1.73205i	0.0449921	−	0.0779287i
$495$		0			0
$496$	−4.00000			−0.179605
$497$		0			0
$498$		0			0
$499$	20.0000	+	34.6410i	0.895323	+	1.55074i	0.833404	+	0.552664i	$0.186389\pi$
$499$	20.0000	+	34.6410i	0.895323	+	1.55074i	0.0619186	+	0.998081i	$0.480278\pi$
$500$		0			0
$501$		0			0
$502$	−6.00000	−	10.3923i	−0.267793	−	0.463831i
$503$	33.0000			1.47140			0.735699	−	0.677309i	$-0.236854\pi$
$503$	33.0000			1.47140			0.735699	+	0.677309i	$0.236854\pi$
$504$		0			0
$505$		0			0
$506$	−3.00000	−	5.19615i	−0.133366	−	0.230997i
$507$		0			0
$508$	3.50000	−	6.06218i	0.155287	−	0.268966i
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	0.791849	−	0.610718i	$-0.209119\pi$
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	−0.924821	+	0.380402i	$0.875786\pi$
$510$		0			0
$511$	−4.00000	−	3.46410i	−0.176950	−	0.153243i
$512$	1.00000			0.0441942
$513$		0			0
$514$	1.50000	−	2.59808i	0.0661622	−	0.114596i
$515$		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
$521$	−21.0000	+	36.3731i	−0.920027	+	1.59353i	−0.120656	+	0.992694i	$0.538500\pi$
$521$	−21.0000	+	36.3731i	−0.920027	+	1.59353i	−0.799370	+	0.600839i	$0.794833\pi$
$522$		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	$0.719578\pi$
$524$	−18.0000			−0.786334
$525$		0			0
$526$	9.00000			0.392419
$527$	12.0000	+	20.7846i	0.522728	+	0.905392i
$528$		0			0
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$		0			0
$532$	−1.00000	+	5.19615i	−0.0433555	+	0.225282i
$533$	−6.00000			−0.259889
$534$		0			0
$535$		0			0
$536$	−5.50000	+	9.52628i	−0.237564	+	0.411473i
$537$		0			0
$538$	−12.0000			−0.517357
$539$	5.50000	−	4.33013i	0.236902	−	0.186512i
$540$		0			0
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	0.999042	+	0.0437584i	$0.0139332\pi$
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	−0.461625	+	0.887075i	$0.652733\pi$
$542$	−14.5000	+	25.1147i	−0.622828	+	1.07877i
$543$		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	$0.704275\pi$
$548$	−4.50000	−	7.79423i	−0.192230	−	0.332953i
$549$		0			0
$550$	2.50000	−	4.33013i	0.106600	−	0.184637i
$551$	9.00000	+	15.5885i	0.383413	+	0.664091i
$552$		0			0
$553$	12.5000	−	4.33013i	0.531554	−	0.184136i
$554$	29.0000			1.23209
$555$		0			0
$556$	−4.00000	+	6.92820i	−0.169638	+	0.293821i
$557$	−9.00000	+	15.5885i	−0.381342	+	0.660504i	−0.991254	−	0.131965i	$-0.957871\pi$
$557$	−9.00000	+	15.5885i	−0.381342	+	0.660504i	0.609912	+	0.792469i	$0.291205\pi$
$558$		0			0
$559$	4.00000			0.169182
$560$		0			0
$561$		0			0
$562$	9.00000	+	15.5885i	0.379642	+	0.657559i
$563$	−9.00000	+	15.5885i	−0.379305	+	0.656975i	−0.990961	−	0.134148i	$-0.957170\pi$
$563$	−9.00000	+	15.5885i	−0.379305	+	0.656975i	0.611656	+	0.791123i	$0.290503\pi$
$564$		0			0
$565$		0			0
$566$	−10.0000			−0.420331
$567$		0			0
$568$		0			0
$569$	−18.0000	−	31.1769i	−0.754599	−	1.30700i	−0.945573	−	0.325409i	$-0.894498\pi$
$569$	−18.0000	−	31.1769i	−0.754599	−	1.30700i	0.190974	−	0.981595i	$-0.438835\pi$
$570$		0			0
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	0.308443	+	0.951243i	$0.400192\pi$
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	−0.978022	+	0.208502i	$0.933141\pi$
$572$	0.500000	+	0.866025i	0.0209061	+	0.0362103i
$573$		0			0
$574$	15.0000	−	5.19615i	0.626088	−	0.216883i
$575$	−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
$581$	−3.00000	+	15.5885i	−0.124461	+	0.646718i
$582$		0			0
$583$		0			0
$584$	−1.00000	+	1.73205i	−0.0413803	+	0.0716728i
$585$		0			0
$586$	−15.0000	−	25.9808i	−0.619644	−	1.07326i
$587$	−9.00000			−0.371470			−0.185735	−	0.982600i	$-0.559467\pi$
$587$	−9.00000			−0.371470			−0.185735	+	0.982600i	$0.559467\pi$
$588$		0			0
$589$	−8.00000			−0.329634
$590$		0			0
$591$		0			0
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$	18.0000	+	31.1769i	0.739171	+	1.28028i	0.952869	+	0.303383i	$0.0981160\pi$
$593$	18.0000	+	31.1769i	0.739171	+	1.28028i	−0.213697	+	0.976900i	$0.568551\pi$
$594$		0			0
$595$		0			0
$596$	−6.00000			−0.245770
$597$		0			0
$598$	3.00000	−	5.19615i	0.122679	−	0.212486i
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$		0			0
$601$	2.00000			0.0815817			0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000			0.0815817			0.0407909	+	0.999168i	$0.487012\pi$
$602$	−10.0000	+	3.46410i	−0.407570	+	0.141186i
$603$		0			0
$604$	9.50000	+	16.4545i	0.386550	+	0.669523i
$605$		0			0
$606$		0			0
$607$	20.0000	+	34.6410i	0.811775	+	1.40604i	0.911621	+	0.411033i	$0.134832\pi$
$607$	20.0000	+	34.6410i	0.811775	+	1.40604i	−0.0998457	+	0.995003i	$0.531835\pi$
$608$	2.00000			0.0811107
$609$		0			0
$610$		0			0
$611$	3.00000	+	5.19615i	0.121367	+	0.210214i
$612$		0			0
$613$	5.00000	−	8.66025i	0.201948	−	0.349784i	−0.747208	−	0.664590i	$-0.768606\pi$
$613$	5.00000	−	8.66025i	0.201948	−	0.349784i	0.949156	+	0.314806i	$0.101939\pi$
$614$	−10.0000	−	17.3205i	−0.403567	−	0.698999i
$615$		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
$619$	−10.0000	+	17.3205i	−0.401934	+	0.696170i	−0.993959	−	0.109749i	$-0.964995\pi$
$619$	−10.0000	+	17.3205i	−0.401934	+	0.696170i	0.592025	+	0.805919i	$0.298329\pi$
$620$		0			0
$621$		0			0
$622$	−24.0000			−0.962312
$623$	45.0000	−	15.5885i	1.80289	−	0.624538i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	−8.50000	+	14.7224i	−0.339728	+	0.588427i
$627$		0			0
$628$	2.00000	+	3.46410i	0.0798087	+	0.138233i
$629$	12.0000			0.478471
$630$		0			0
$631$	20.0000			0.796187			0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000			0.796187			0.398094	+	0.917345i	$0.369672\pi$
$632$	−2.50000	−	4.33013i	−0.0994447	−	0.172243i
$633$		0			0
$634$	6.00000	−	10.3923i	0.238290	−	0.412731i
$635$		0			0
$636$		0			0
$637$	6.50000	+	2.59808i	0.257539	+	0.102940i
$638$	−9.00000			−0.356313
$639$		0			0
$640$		0			0
$641$	4.50000	−	7.79423i	0.177739	−	0.307854i	−0.763367	−	0.645966i	$-0.776455\pi$
$641$	4.50000	−	7.79423i	0.177739	−	0.307854i	0.941106	+	0.338112i	$0.109788\pi$
$642$		0			0
$643$	5.00000			0.197181			0.0985904	−	0.995128i	$-0.468567\pi$
$643$	5.00000			0.197181			0.0985904	+	0.995128i	$0.468567\pi$
$644$	−3.00000	+	15.5885i	−0.118217	+	0.614271i
$645$		0			0
$646$	−6.00000	−	10.3923i	−0.236067	−	0.408880i
$647$	−6.00000	+	10.3923i	−0.235884	+	0.408564i	−0.959529	−	0.281609i	$-0.909132\pi$
$647$	−6.00000	+	10.3923i	−0.235884	+	0.408564i	0.723645	+	0.690172i	$0.242465\pi$
$648$		0			0
$649$	−1.50000	−	2.59808i	−0.0588802	−	0.101983i
$650$	5.00000			0.196116
$651$		0			0
$652$	17.0000			0.665771
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	0.986634	−	0.162951i	$-0.0521013\pi$
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	−0.634437	+	0.772975i	$0.718768\pi$
$654$		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
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	−0.969442	−	0.245319i	$-0.921107\pi$
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	0.697174	+	0.716902i	$0.254441\pi$
$662$	−17.5000	+	30.3109i	−0.680157	+	1.17807i
$663$		0			0
$664$	6.00000			0.232845
$665$		0			0
$666$		0			0
$667$	27.0000	+	46.7654i	1.04544	+	1.81076i
$668$	1.50000	−	2.59808i	0.0580367	−	0.100523i
$669$		0			0
$670$		0			0
$671$	11.0000			0.424650
$672$		0			0
$673$	−28.0000			−1.07932			−0.539660	−	0.841883i	$-0.681447\pi$
$673$	−28.0000			−1.07932			−0.539660	+	0.841883i	$0.681447\pi$
$674$	−7.00000	−	12.1244i	−0.269630	−	0.467013i
$675$		0			0
$676$	6.00000	−	10.3923i	0.230769	−	0.399704i
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	0.917899	−	0.396813i	$-0.129884\pi$
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	−0.802600	+	0.596518i	$0.796551\pi$
$678$		0			0
$679$	6.50000	−	33.7750i	0.249447	−	1.29617i
$680$		0			0
$681$		0			0
$682$	2.00000	−	3.46410i	0.0765840	−	0.132647i
$683$	−10.5000	+	18.1865i	−0.401771	+	0.695888i	−0.993940	−	0.109926i	$-0.964939\pi$
$683$	−10.5000	+	18.1865i	−0.401771	+	0.695888i	0.592168	+	0.805814i	$0.298272\pi$
$684$		0			0
$685$		0			0
$686$	−18.5000	−	0.866025i	−0.706333	−	0.0330650i
$687$		0			0
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$		0			0
$690$		0			0
$691$	−5.50000	−	9.52628i	−0.209230	−	0.362397i	0.742242	−	0.670132i	$-0.233762\pi$
$691$	−5.50000	−	9.52628i	−0.209230	−	0.362397i	−0.951472	+	0.307735i	$0.900429\pi$
$692$	21.0000			0.798300
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−18.0000	+	31.1769i	−0.681799	+	1.18091i
$698$	−1.00000	−	1.73205i	−0.0378506	−	0.0655591i
$699$		0			0
$700$	−12.5000	+	4.33013i	−0.472456	+	0.163663i
$701$	−39.0000			−1.47301			−0.736505	−	0.676432i	$-0.763525\pi$
$701$	−39.0000			−1.47301			−0.736505	+	0.676432i	$0.763525\pi$
$702$		0			0
$703$	−2.00000	+	3.46410i	−0.0754314	+	0.130651i
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$		0			0
$706$	18.0000			0.677439
$707$	−30.0000	−	25.9808i	−1.12827	−	0.977107i
$708$		0			0
$709$	−13.0000	−	22.5167i	−0.488225	−	0.845631i	0.511683	−	0.859174i	$-0.329022\pi$
$709$	−13.0000	−	22.5167i	−0.488225	−	0.845631i	−0.999908	+	0.0135434i	$0.995689\pi$
$710$		0			0
$711$		0			0
$712$	−9.00000	−	15.5885i	−0.337289	−	0.584202i
$713$	−24.0000			−0.898807
$714$		0			0
$715$		0			0
$716$	−7.50000	−	12.9904i	−0.280288	−	0.485473i
$717$		0			0
$718$	−1.50000	+	2.59808i	−0.0559795	+	0.0969593i
$719$	−21.0000	−	36.3731i	−0.783168	−	1.35649i	−0.930087	−	0.367338i	$-0.880269\pi$
$719$	−21.0000	−	36.3731i	−0.783168	−	1.35649i	0.146920	−	0.989148i	$-0.453064\pi$
$720$		0			0
$721$	−40.0000	+	13.8564i	−1.48968	+	0.516040i
$722$	−15.0000			−0.558242
$723$		0			0
$724$	−1.00000	+	1.73205i	−0.0371647	+	0.0643712i
$725$	−22.5000	+	38.9711i	−0.835629	+	1.44735i
$726$		0			0
$727$	14.0000			0.519231			0.259616	−	0.965712i	$-0.416404\pi$
$727$	14.0000			0.519231			0.259616	+	0.965712i	$0.416404\pi$
$728$	0.500000	−	2.59808i	0.0185312	−	0.0962911i
$729$		0			0
$730$		0			0
$731$	12.0000	−	20.7846i	0.443836	−	0.768747i
$732$		0			0
$733$	12.5000	+	21.6506i	0.461698	+	0.799684i	0.999046	−	0.0436764i	$-0.0139070\pi$
$733$	12.5000	+	21.6506i	0.461698	+	0.799684i	−0.537348	+	0.843361i	$0.680574\pi$
$734$	−10.0000			−0.369107
$735$		0			0
$736$	6.00000			0.221163
$737$	−5.50000	−	9.52628i	−0.202595	−	0.350905i
$738$		0			0
$739$	−25.0000	+	43.3013i	−0.919640	+	1.59286i	−0.119677	+	0.992813i	$0.538186\pi$
$739$	−25.0000	+	43.3013i	−0.919640	+	1.59286i	−0.799962	+	0.600050i	$0.795147\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	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
$746$	15.5000	−	26.8468i	0.567495	−	0.982931i
$747$		0			0
$748$	6.00000			0.219382
$749$	−30.0000	+	10.3923i	−1.09618	+	0.379727i
$750$		0			0
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	0.900207	−	0.435463i	$-0.143415\pi$
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	−0.827225	+	0.561870i	$0.810082\pi$
$752$	−3.00000	+	5.19615i	−0.109399	+	0.189484i
$753$		0			0
$754$	−4.50000	−	7.79423i	−0.163880	−	0.283849i
$755$		0			0
$756$		0			0
$757$	−46.0000			−1.67190			−0.835949	−	0.548807i	$-0.815082\pi$
$757$	−46.0000			−1.67190			−0.835949	+	0.548807i	$0.815082\pi$
$758$	−11.5000	−	19.9186i	−0.417699	−	0.723476i
$759$		0			0
$760$		0			0
$761$	−9.00000	−	15.5885i	−0.326250	−	0.565081i	0.655515	−	0.755182i	$-0.272452\pi$
$761$	−9.00000	−	15.5885i	−0.326250	−	0.565081i	−0.981764	+	0.190101i	$0.939118\pi$
$762$		0			0
$763$	−4.00000	−	3.46410i	−0.144810	−	0.125409i
$764$	−6.00000			−0.217072
$765$		0			0
$766$	−18.0000	+	31.1769i	−0.650366	+	1.12647i
$767$	1.50000	−	2.59808i	0.0541619	−	0.0938111i
$768$		0			0
$769$	−22.0000			−0.793340			−0.396670	−	0.917961i	$-0.629834\pi$
$769$	−22.0000			−0.793340			−0.396670	+	0.917961i	$0.629834\pi$
$770$		0			0
$771$		0			0
$772$	−7.00000	−	12.1244i	−0.251936	−	0.436365i
$773$	12.0000	−	20.7846i	0.431610	−	0.747570i	−0.565402	−	0.824815i	$-0.691279\pi$
$773$	12.0000	−	20.7846i	0.431610	−	0.747570i	0.997012	+	0.0772449i	$0.0246123\pi$
$774$		0			0
$775$	−10.0000	−	17.3205i	−0.359211	−	0.622171i
$776$	−13.0000			−0.466673
$777$		0			0
$778$	−12.0000			−0.430221
$779$	−6.00000	−	10.3923i	−0.214972	−	0.372343i
$780$		0			0
$781$		0			0
$782$	−18.0000	−	31.1769i	−0.643679	−	1.11488i
$783$		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	$0.246941\pi$
$788$	−1.50000	+	2.59808i	−0.0534353	+	0.0925526i
$789$		0			0
$790$		0			0
$791$	4.50000	−	23.3827i	0.160002	−	0.831393i
$792$		0			0
$793$	5.50000	+	9.52628i	0.195311	+	0.338288i
$794$	11.0000	−	19.0526i	0.390375	−	0.676150i
$795$		0			0
$796$	−7.00000	−	12.1244i	−0.248108	−	0.429736i
$797$	18.0000			0.637593			0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000			0.637593			0.318796	+	0.947823i	$0.396721\pi$
$798$		0			0
$799$	36.0000			1.27359
$800$	2.50000	+	4.33013i	0.0883883	+	0.153093i
$801$		0			0
$802$	−16.5000	+	28.5788i	−0.582635	+	1.00915i
$803$	−1.00000	−	1.73205i	−0.0352892	−	0.0611227i
$804$		0			0
$805$		0			0
$806$	4.00000			0.140894
$807$		0			0
$808$	−7.50000	+	12.9904i	−0.263849	+	0.457000i
$809$	−24.0000	+	41.5692i	−0.843795	+	1.46150i	0.0428684	+	0.999081i	$0.486350\pi$
$809$	−24.0000	+	41.5692i	−0.843795	+	1.46150i	−0.886664	+	0.462415i	$0.846983\pi$
$810$		0			0
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	18.0000	+	15.5885i	0.631676	+	0.547048i
$813$		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
$821$	−7.50000	−	12.9904i	−0.261752	−	0.453367i	0.704956	−	0.709251i	$-0.250967\pi$
$821$	−7.50000	−	12.9904i	−0.261752	−	0.453367i	−0.966708	+	0.255884i	$0.917634\pi$
$822$		0			0
$823$	5.00000	−	8.66025i	0.174289	−	0.301877i	−0.765626	−	0.643286i	$-0.777571\pi$
$823$	5.00000	−	8.66025i	0.174289	−	0.301877i	0.939915	+	0.341409i	$0.110904\pi$
$824$	8.00000	+	13.8564i	0.278693	+	0.482711i
$825$		0			0
$826$	−1.50000	+	7.79423i	−0.0521917	+	0.271196i
$827$	−30.0000			−1.04320			−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000			−1.04320			−0.521601	+	0.853189i	$0.674665\pi$
$828$		0			0
$829$	26.0000	−	45.0333i	0.903017	−	1.56407i	0.0794606	−	0.996838i	$-0.474680\pi$
$829$	26.0000	−	45.0333i	0.903017	−	1.56407i	0.823557	−	0.567234i	$-0.191986\pi$
$830$		0			0
$831$		0			0
$832$	−1.00000			−0.0346688
$833$	33.0000	−	25.9808i	1.14338	−	0.900180i
$834$		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
$839$	−6.00000			−0.207143			−0.103572	−	0.994622i	$-0.533027\pi$
$839$	−6.00000			−0.207143			−0.103572	+	0.994622i	$0.533027\pi$
$840$		0			0
$841$	52.0000			1.79310
$842$	14.0000	+	24.2487i	0.482472	+	0.835666i
$843$		0			0
$844$	5.00000	−	8.66025i	0.172107	−	0.298098i
$845$		0			0
$846$		0			0
$847$	2.50000	−	0.866025i	0.0859010	−	0.0297570i
$848$		0			0
$849$		0			0
$850$	15.0000	−	25.9808i	0.514496	−	0.891133i
$851$	−6.00000	+	10.3923i	−0.205677	+	0.356244i
$852$		0			0
$853$	−46.0000			−1.57501			−0.787505	−	0.616308i	$-0.788628\pi$
$853$	−46.0000			−1.57501			−0.787505	+	0.616308i	$0.788628\pi$
$854$	−22.0000	−	19.0526i	−0.752825	−	0.651965i
$855$		0			0
$856$	6.00000	+	10.3923i	0.205076	+	0.355202i
$857$	18.0000	−	31.1769i	0.614868	−	1.06498i	−0.375539	−	0.926806i	$-0.622542\pi$
$857$	18.0000	−	31.1769i	0.614868	−	1.06498i	0.990408	−	0.138177i	$-0.0441242\pi$
$858$		0			0
$859$	18.5000	+	32.0429i	0.631212	+	1.09329i	0.987304	+	0.158840i	$0.0507755\pi$
$859$	18.5000	+	32.0429i	0.631212	+	1.09329i	−0.356092	+	0.934451i	$0.615891\pi$
$860$		0			0
$861$		0			0
$862$	3.00000			0.102180
$863$	15.0000	+	25.9808i	0.510606	+	0.884395i	0.999924	+	0.0122903i	$0.00391222\pi$
$863$	15.0000	+	25.9808i	0.510606	+	0.884395i	−0.489319	+	0.872105i	$0.662754\pi$
$864$		0			0
$865$		0			0
$866$	17.0000	+	29.4449i	0.577684	+	1.00058i
$867$		0			0
$868$	−10.0000	+	3.46410i	−0.339422	+	0.117579i
$869$	5.00000			0.169613
$870$		0			0
$871$	5.50000	−	9.52628i	0.186360	−	0.322786i
$872$	−1.00000	+	1.73205i	−0.0338643	+	0.0586546i
$873$		0			0
$874$	12.0000			0.405906
$875$		0			0
$876$		0			0
$877$	−8.50000	−	14.7224i	−0.287025	−	0.497141i	0.686074	−	0.727532i	$-0.259333\pi$
$877$	−8.50000	−	14.7224i	−0.287025	−	0.497141i	−0.973098	+	0.230391i	$0.925999\pi$
$878$	0.500000	−	0.866025i	0.0168742	−	0.0292269i
$879$		0			0
$880$		0			0
$881$	−33.0000			−1.11180			−0.555899	−	0.831250i	$-0.687626\pi$
$881$	−33.0000			−1.11180			−0.555899	+	0.831250i	$0.687626\pi$
$882$		0			0
$883$	29.0000			0.975928			0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000			0.975928			0.487964	+	0.872864i	$0.337740\pi$
$884$	3.00000	+	5.19615i	0.100901	+	0.174766i
$885$		0			0
$886$	6.00000	−	10.3923i	0.201574	−	0.349136i
$887$	1.50000	+	2.59808i	0.0503651	+	0.0872349i	0.890109	−	0.455748i	$-0.150628\pi$
$887$	1.50000	+	2.59808i	0.0503651	+	0.0872349i	−0.839744	+	0.542983i	$0.817295\pi$
$888$		0			0
$889$	3.50000	−	18.1865i	0.117386	−	0.609957i
$890$		0			0
$891$		0			0
$892$	−13.0000	+	22.5167i	−0.435272	+	0.753914i
$893$	−6.00000	+	10.3923i	−0.200782	+	0.347765i
$894$		0			0
$895$		0			0
$896$	2.50000	−	0.866025i	0.0835191	−	0.0289319i
$897$		0			0
$898$	−9.00000	−	15.5885i	−0.300334	−	0.520194i
$899$	−18.0000	+	31.1769i	−0.600334	+	1.03981i
$900$		0			0
$901$		0			0
$902$	6.00000			0.199778
$903$		0			0
$904$	−9.00000			−0.299336
$905$		0			0
$906$		0			0
$907$	14.0000	−	24.2487i	0.464862	−	0.805165i	−0.534333	−	0.845274i	$-0.679437\pi$
$907$	14.0000	−	24.2487i	0.464862	−	0.805165i	0.999195	+	0.0401089i	$0.0127705\pi$
$908$	9.00000	+	15.5885i	0.298675	+	0.517321i
$909$		0			0
$910$		0			0
$911$	6.00000			0.198789			0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000			0.198789			0.0993944	+	0.995048i	$0.468309\pi$
$912$		0			0
$913$	−3.00000	+	5.19615i	−0.0992855	+	0.171968i
$914$	11.0000	−	19.0526i	0.363848	−	0.630203i
$915$		0			0
$916$	−16.0000			−0.528655
$917$	−45.0000	+	15.5885i	−1.48603	+	0.514776i
$918$		0			0
$919$	−16.0000	−	27.7128i	−0.527791	−	0.914161i	−0.999475	−	0.0323936i	$-0.989687\pi$
$919$	−16.0000	−	27.7128i	−0.527791	−	0.914161i	0.471684	−	0.881768i	$-0.343646\pi$
$920$		0			0
$921$		0			0
$922$	10.5000	+	18.1865i	0.345799	+	0.598942i
$923$		0			0
$924$		0			0
$925$	−10.0000			−0.328798
$926$	11.0000	+	19.0526i	0.361482	+	0.626106i
$927$		0			0
$928$	4.50000	−	7.79423i	0.147720	−	0.255858i
$929$	19.5000	+	33.7750i	0.639774	+	1.10812i	0.985482	+	0.169779i	$0.0543055\pi$
$929$	19.5000	+	33.7750i	0.639774	+	1.10812i	−0.345708	+	0.938342i	$0.612361\pi$
$930$		0			0
$931$	2.00000	+	13.8564i	0.0655474	+	0.454125i
$932$	6.00000			0.196537
$933$		0			0
$934$	6.00000	−	10.3923i	0.196326	−	0.340047i
$935$		0			0
$936$		0			0
$937$	8.00000			0.261349			0.130674	−	0.991425i	$-0.458286\pi$
$937$	8.00000			0.261349			0.130674	+	0.991425i	$0.458286\pi$
$938$	−5.50000	+	28.5788i	−0.179581	+	0.933132i
$939$		0			0
$940$		0			0
$941$	7.50000	−	12.9904i	0.244493	−	0.423474i	−0.717496	−	0.696563i	$-0.754712\pi$
$941$	7.50000	−	12.9904i	0.244493	−	0.423474i	0.961989	+	0.273088i	$0.0880451\pi$
$942$		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	0.992442	−	0.122714i	$-0.0391598\pi$
$947$	12.0000	+	20.7846i	0.389948	+	0.675409i	−0.602494	+	0.798123i	$0.705826\pi$
$948$		0			0
$949$	1.00000	−	1.73205i	0.0324614	−	0.0562247i
$950$	5.00000	+	8.66025i	0.162221	+	0.280976i
$951$		0			0
$952$	−12.0000	−	10.3923i	−0.388922	−	0.336817i
$953$	36.0000			1.16615			0.583077	−	0.812417i	$-0.301849\pi$
$953$	36.0000			1.16615			0.583077	+	0.812417i	$0.301849\pi$
$954$		0			0
$955$		0			0
$956$	−4.50000	+	7.79423i	−0.145540	+	0.252083i
$957$		0			0
$958$	−15.0000			−0.484628
$959$	−18.0000	−	15.5885i	−0.581250	−	0.503378i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	1.00000	−	1.73205i	0.0322413	−	0.0558436i
$963$		0			0
$964$	−13.0000	−	22.5167i	−0.418702	−	0.725213i
$965$		0			0
$966$		0			0
$967$	−40.0000			−1.28631			−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000			−1.28631			−0.643157	+	0.765735i	$0.722376\pi$
$968$	−0.500000	−	0.866025i	−0.0160706	−	0.0278351i
$969$		0			0
$970$		0			0
$971$	7.50000	+	12.9904i	0.240686	+	0.416881i	0.960910	−	0.276861i	$-0.0892941\pi$
$971$	7.50000	+	12.9904i	0.240686	+	0.416881i	−0.720224	+	0.693742i	$0.755961\pi$
$972$		0			0
$973$	−4.00000	+	20.7846i	−0.128234	+	0.666324i
$974$	20.0000			0.640841
$975$		0			0
$976$	−5.50000	+	9.52628i	−0.176051	+	0.304929i
$977$	−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
$979$	18.0000			0.575282
$980$		0			0
$981$		0			0
$982$	21.0000	+	36.3731i	0.670137	+	1.16071i
$983$	−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
$986$	−54.0000			−1.71971
$987$		0			0
$988$	−2.00000			−0.0636285
$989$	12.0000	+	20.7846i	0.381578	+	0.660912i
$990$		0			0
$991$	20.0000	−	34.6410i	0.635321	−	1.10041i	−0.351126	−	0.936328i	$-0.614201\pi$
$991$	20.0000	−	34.6410i	0.635321	−	1.10041i	0.986447	−	0.164080i	$-0.0524655\pi$
$992$	2.00000	+	3.46410i	0.0635001	+	0.109985i
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	17.0000	−	29.4449i	0.538395	−	0.932528i	−0.460595	−	0.887610i	$-0.652364\pi$
$997$	17.0000	−	29.4449i	0.538395	−	0.932528i	0.998991	−	0.0449179i	$-0.0143026\pi$
$998$	20.0000	−	34.6410i	0.633089	−	1.09654i
$999$		0			0

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{11} -1.00000 q^{13} +(2.50000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(-1.00000 - 1.73205i) q^{19} +1.00000 q^{22} +(-3.00000 - 5.19615i) q^{23} +(2.50000 - 4.33013i) q^{25} +(0.500000 + 0.866025i) q^{26} +(-2.00000 - 1.73205i) q^{28} -9.00000 q^{29} +(2.00000 - 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +6.00000 q^{34} +(-1.00000 - 1.73205i) q^{37} +(-1.00000 + 1.73205i) q^{38} +6.00000 q^{41} -4.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(-3.00000 - 5.19615i) q^{47} +(-6.50000 - 2.59808i) q^{49} -5.00000 q^{50} +(0.500000 - 0.866025i) q^{52} +(-0.500000 + 2.59808i) q^{56} +(4.50000 + 7.79423i) q^{58} +(-1.50000 + 2.59808i) q^{59} +(-5.50000 - 9.52628i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(-5.50000 + 9.52628i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(-1.00000 + 1.73205i) q^{73} +(-1.00000 + 1.73205i) q^{74} +2.00000 q^{76} +(-2.00000 - 1.73205i) q^{77} +(-2.50000 - 4.33013i) q^{79} +(-3.00000 - 5.19615i) q^{82} +6.00000 q^{83} +(2.00000 + 3.46410i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(-9.00000 - 15.5885i) q^{89} +(0.500000 - 2.59808i) q^{91} +6.00000 q^{92} +(-3.00000 + 5.19615i) q^{94} -13.0000 q^{97} +(1.00000 + 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 - q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} - q^{7} + 2 q^{8} - q^{11} - 2 q^{13} + 5 q^{14} - q^{16} - 6 q^{17} - 2 q^{19} + 2 q^{22} - 6 q^{23} + 5 q^{25} + q^{26} - 4 q^{28} - 18 q^{29} + 4 q^{31} - q^{32} + 12 q^{34} - 2 q^{37} - 2 q^{38} + 12 q^{41} - 8 q^{43} - q^{44} - 6 q^{46} - 6 q^{47} - 13 q^{49} - 10 q^{50} + q^{52} - q^{56} + 9 q^{58} - 3 q^{59} - 11 q^{61} - 8 q^{62} + 2 q^{64} - 11 q^{67} - 6 q^{68} - 2 q^{73} - 2 q^{74} + 4 q^{76} - 4 q^{77} - 5 q^{79} - 6 q^{82} + 12 q^{83} + 4 q^{86} - q^{88} - 18 q^{89} + q^{91} + 12 q^{92} - 6 q^{94} - 26 q^{97} + 2 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 - q^7 + 2 * q^8 - q^11 - 2 * q^13 + 5 * q^14 - q^16 - 6 * q^17 - 2 * q^19 + 2 * q^22 - 6 * q^23 + 5 * q^25 + q^26 - 4 * q^28 - 18 * q^29 + 4 * 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 - 13 * q^49 - 10 * q^50 + q^52 - q^56 + 9 * q^58 - 3 * q^59 - 11 * q^61 - 8 * q^62 + 2 * q^64 - 11 * q^67 - 6 * q^68 - 2 * q^73 - 2 * q^74 + 4 * q^76 - 4 * q^77 - 5 * q^79 - 6 * q^82 + 12 * q^83 + 4 * q^86 - q^88 - 18 * q^89 + q^91 + 12 * q^92 - 6 * q^94 - 26 * q^97 + 2 * q^98

Introduction

L-functions

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