LMFDB - Embedded newform 847.2.f.i.372.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$847 = 7 \cdot 11^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	847.f (of order $5$ , degree $4$ , not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} - x^{3} + x^{2} - x + 1$ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			372.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	847.372
Dual form			847.2.f.i.148.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.42705 - 1.76336i) q^{3} +(1.61803 + 1.17557i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(0.809017 + 0.587785i) q^{7} +(1.85410 - 5.70634i) q^{9} +6.00000 q^{12} +(-1.23607 + 3.80423i) q^{13} +(-2.42705 - 1.76336i) q^{15} +(1.23607 + 3.80423i) q^{16} +(0.618034 + 1.90211i) q^{17} +(4.85410 - 3.52671i) q^{19} +(0.618034 - 1.90211i) q^{20} +3.00000 q^{21} -5.00000 q^{23} +(3.23607 - 2.35114i) q^{25} +(-2.78115 - 8.55951i) q^{27} +(0.618034 + 1.90211i) q^{28} +(-8.09017 - 5.87785i) q^{29} +(0.309017 - 0.951057i) q^{31} +(0.309017 - 0.951057i) q^{35} +(9.70820 - 7.05342i) q^{36} +(4.04508 + 2.93893i) q^{37} +(3.70820 + 11.4127i) q^{39} +(1.61803 - 1.17557i) q^{41} -8.00000 q^{43} -6.00000 q^{45} +(-6.47214 + 4.70228i) q^{47} +(9.70820 + 7.05342i) q^{48} +(0.309017 + 0.951057i) q^{49} +(4.85410 + 3.52671i) q^{51} +(-6.47214 + 4.70228i) q^{52} +(-1.85410 + 5.70634i) q^{53} +(5.56231 - 17.1190i) q^{57} +(-2.42705 - 1.76336i) q^{59} +(-1.85410 - 5.70634i) q^{60} +(-0.618034 - 1.90211i) q^{61} +(4.85410 - 3.52671i) q^{63} +(-2.47214 + 7.60845i) q^{64} +4.00000 q^{65} -3.00000 q^{67} +(-1.23607 + 3.80423i) q^{68} +(-12.1353 + 8.81678i) q^{69} +(0.309017 + 0.951057i) q^{71} +(-8.09017 - 5.87785i) q^{73} +(3.70820 - 11.4127i) q^{75} +12.0000 q^{76} +(1.85410 - 5.70634i) q^{79} +(3.23607 - 2.35114i) q^{80} +(-7.28115 - 5.29007i) q^{81} +(3.70820 + 11.4127i) q^{83} +(4.85410 + 3.52671i) q^{84} +(1.61803 - 1.17557i) q^{85} -30.0000 q^{87} -15.0000 q^{89} +(-3.23607 + 2.35114i) q^{91} +(-8.09017 - 5.87785i) q^{92} +(-0.927051 - 2.85317i) q^{93} +(-4.85410 - 3.52671i) q^{95} +(-1.54508 + 4.75528i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q + 3 q^{3} + 2 q^{4} + q^{5} + q^{7} - 6 q^{9} + 24 q^{12} + 4 q^{13} - 3 q^{15} - 4 q^{16} - 2 q^{17} + 6 q^{19} - 2 q^{20} + 12 q^{21} - 20 q^{23} + 4 q^{25} + 9 q^{27} - 2 q^{28} - 10 q^{29} - q^{31}+ \cdots + 5 q^{97}+O(q^{100})$ 4 * q + 3 * q^3 + 2 * q^4 + q^5 + q^7 - 6 * q^9 + 24 * q^12 + 4 * q^13 - 3 * q^15 - 4 * q^16 - 2 * q^17 + 6 * q^19 - 2 * q^20 + 12 * q^21 - 20 * q^23 + 4 * q^25 + 9 * q^27 - 2 * q^28 - 10 * q^29 - q^31 - q^35 + 12 * q^36 + 5 * q^37 - 12 * q^39 + 2 * q^41 - 32 * q^43 - 24 * q^45 - 8 * q^47 + 12 * q^48 - q^49 + 6 * q^51 - 8 * q^52 + 6 * q^53 - 18 * q^57 - 3 * q^59 + 6 * q^60 + 2 * q^61 + 6 * q^63 + 8 * q^64 + 16 * q^65 - 12 * q^67 + 4 * q^68 - 15 * q^69 - q^71 - 10 * q^73 - 12 * q^75 + 48 * q^76 - 6 * q^79 + 4 * q^80 - 9 * q^81 - 12 * q^83 + 6 * q^84 + 2 * q^85 - 120 * q^87 - 60 * q^89 - 4 * q^91 - 10 * q^92 + 3 * q^93 - 6 * q^95 + 5 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$ .

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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			0		−0.951057	−	0.309017i	$-0.900000\pi$
$2$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$3$	2.42705	−	1.76336i	1.40126	−	1.01807i	0.406737	−	0.913545i	$-0.366667\pi$
$3$	2.42705	−	1.76336i	1.40126	−	1.01807i	0.994522	−	0.104528i	$-0.0333333\pi$
$4$	1.61803	+	1.17557i	0.809017	+	0.587785i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i	0.857877	−	0.513855i	$-0.171783\pi$
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i	−0.996074	+	0.0885298i	$0.971783\pi$
$6$		0			0
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$8$		0			0
$9$	1.85410	−	5.70634i	0.618034	−	1.90211i
$10$		0			0
$11$		0			0
$11$		0			0
$12$	6.00000			1.73205
$13$	−1.23607	+	3.80423i	−0.342824	+	1.05510i	0.619915	+	0.784669i	$0.287167\pi$
$13$	−1.23607	+	3.80423i	−0.342824	+	1.05510i	−0.962739	+	0.270434i	$0.912833\pi$
$14$		0			0
$15$	−2.42705	−	1.76336i	−0.626662	−	0.455296i
$16$	1.23607	+	3.80423i	0.309017	+	0.951057i
$17$	0.618034	+	1.90211i	0.149895	+	0.461330i	0.997608	−	0.0691254i	$-0.0220209\pi$
$17$	0.618034	+	1.90211i	0.149895	+	0.461330i	−0.847713	+	0.530456i	$0.822021\pi$
$18$		0			0
$19$	4.85410	−	3.52671i	1.11361	−	0.809083i	0.130379	−	0.991464i	$-0.458380\pi$
$19$	4.85410	−	3.52671i	1.11361	−	0.809083i	0.983228	+	0.182381i	$0.0583804\pi$
$20$	0.618034	−	1.90211i	0.138197	−	0.425325i
$21$	3.00000			0.654654
$22$		0			0
$23$	−5.00000			−1.04257			−0.521286	−	0.853382i	$-0.674548\pi$
$23$	−5.00000			−1.04257			−0.521286	+	0.853382i	$0.674548\pi$
$24$		0			0
$25$	3.23607	−	2.35114i	0.647214	−	0.470228i
$26$		0			0
$27$	−2.78115	−	8.55951i	−0.535233	−	1.64728i
$28$	0.618034	+	1.90211i	0.116797	+	0.359466i
$29$	−8.09017	−	5.87785i	−1.50231	−	1.09149i	−0.969451	−	0.245284i	$-0.921119\pi$
$29$	−8.09017	−	5.87785i	−1.50231	−	1.09149i	−0.532855	−	0.846206i	$-0.678881\pi$
$30$		0			0
$31$	0.309017	−	0.951057i	0.0555011	−	0.170815i	−0.919463	−	0.393176i	$-0.871376\pi$
$31$	0.309017	−	0.951057i	0.0555011	−	0.170815i	0.974964	+	0.222361i	$0.0713764\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.309017	−	0.951057i	0.0522334	−	0.160758i
$36$	9.70820	−	7.05342i	1.61803	−	1.17557i
$37$	4.04508	+	2.93893i	0.665008	+	0.483157i	0.868350	−	0.495951i	$-0.165181\pi$
$37$	4.04508	+	2.93893i	0.665008	+	0.483157i	−0.203343	+	0.979108i	$0.565181\pi$
$38$		0			0
$39$	3.70820	+	11.4127i	0.593788	+	1.82749i
$40$		0			0
$41$	1.61803	−	1.17557i	0.252694	−	0.183593i	−0.454226	−	0.890887i	$-0.650084\pi$
$41$	1.61803	−	1.17557i	0.252694	−	0.183593i	0.706920	+	0.707293i	$0.250084\pi$
$42$		0			0
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$		0			0
$45$	−6.00000			−0.894427
$46$		0			0
$47$	−6.47214	+	4.70228i	−0.944058	+	0.685898i	−0.949394	−	0.314087i	$-0.898301\pi$
$47$	−6.47214	+	4.70228i	−0.944058	+	0.685898i	0.00533600	+	0.999986i	$0.498301\pi$
$48$	9.70820	+	7.05342i	1.40126	+	1.01807i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$		0			0
$51$	4.85410	+	3.52671i	0.679710	+	0.493838i
$52$	−6.47214	+	4.70228i	−0.897524	+	0.652089i
$53$	−1.85410	+	5.70634i	−0.254680	+	0.783826i	0.739212	+	0.673473i	$0.235198\pi$
$53$	−1.85410	+	5.70634i	−0.254680	+	0.783826i	−0.993892	+	0.110353i	$0.964802\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	5.56231	−	17.1190i	0.736745	−	2.26747i
$58$		0			0
$59$	−2.42705	−	1.76336i	−0.315975	−	0.229569i	0.418481	−	0.908226i	$-0.362563\pi$
$59$	−2.42705	−	1.76336i	−0.315975	−	0.229569i	−0.734456	+	0.678656i	$0.762563\pi$
$60$	−1.85410	−	5.70634i	−0.239364	−	0.736685i
$61$	−0.618034	−	1.90211i	−0.0791311	−	0.243541i	0.903663	−	0.428244i	$-0.140868\pi$
$61$	−0.618034	−	1.90211i	−0.0791311	−	0.243541i	−0.982794	+	0.184703i	$0.940868\pi$
$62$		0			0
$63$	4.85410	−	3.52671i	0.611559	−	0.444324i
$64$	−2.47214	+	7.60845i	−0.309017	+	0.951057i
$65$	4.00000			0.496139
$66$		0			0
$67$	−3.00000			−0.366508			−0.183254	−	0.983066i	$-0.558663\pi$
$67$	−3.00000			−0.366508			−0.183254	+	0.983066i	$0.558663\pi$
$68$	−1.23607	+	3.80423i	−0.149895	+	0.461330i
$69$	−12.1353	+	8.81678i	−1.46091	+	1.06142i
$70$		0			0
$71$	0.309017	+	0.951057i	0.0366736	+	0.112870i	0.967717	−	0.252038i	$-0.0811007\pi$
$71$	0.309017	+	0.951057i	0.0366736	+	0.112870i	−0.931044	+	0.364907i	$0.881101\pi$
$72$		0			0
$73$	−8.09017	−	5.87785i	−0.946883	−	0.687951i	0.00318477	−	0.999995i	$-0.498986\pi$
$73$	−8.09017	−	5.87785i	−0.946883	−	0.687951i	−0.950068	+	0.312044i	$0.898986\pi$
$74$		0			0
$75$	3.70820	−	11.4127i	0.428187	−	1.31782i
$76$	12.0000			1.37649
$77$		0			0
$78$		0			0
$79$	1.85410	−	5.70634i	0.208603	−	0.642013i	−0.790943	−	0.611889i	$-0.790410\pi$
$79$	1.85410	−	5.70634i	0.208603	−	0.642013i	0.999546	−	0.0301240i	$-0.00959021\pi$
$80$	3.23607	−	2.35114i	0.361803	−	0.262866i
$81$	−7.28115	−	5.29007i	−0.809017	−	0.587785i
$82$		0			0
$83$	3.70820	+	11.4127i	0.407028	+	1.25270i	0.919190	+	0.393815i	$0.128845\pi$
$83$	3.70820	+	11.4127i	0.407028	+	1.25270i	−0.512161	+	0.858889i	$0.671155\pi$
$84$	4.85410	+	3.52671i	0.529626	+	0.384796i
$85$	1.61803	−	1.17557i	0.175500	−	0.127509i
$86$		0			0
$87$	−30.0000			−3.21634
$88$		0			0
$89$	−15.0000			−1.59000			−0.794998	−	0.606612i	$-0.792528\pi$
$89$	−15.0000			−1.59000			−0.794998	+	0.606612i	$0.792528\pi$
$90$		0			0
$91$	−3.23607	+	2.35114i	−0.339232	+	0.246467i
$92$	−8.09017	−	5.87785i	−0.843459	−	0.612808i
$93$	−0.927051	−	2.85317i	−0.0961307	−	0.295860i
$94$		0			0
$95$	−4.85410	−	3.52671i	−0.498020	−	0.361833i
$96$		0			0
$97$	−1.54508	+	4.75528i	−0.156880	+	0.482826i	−0.998346	−	0.0574829i	$-0.981693\pi$
$97$	−1.54508	+	4.75528i	−0.156880	+	0.482826i	0.841467	+	0.540309i	$0.181693\pi$
$98$		0			0
$99$		0			0
$100$	8.00000			0.800000
$101$	−3.70820	+	11.4127i	−0.368980	+	1.13560i	0.578471	+	0.815703i	$0.303650\pi$
$101$	−3.70820	+	11.4127i	−0.368980	+	1.13560i	−0.947451	+	0.319901i	$0.896350\pi$
$102$		0			0
$103$	9.70820	+	7.05342i	0.956578	+	0.694994i	0.952353	−	0.304997i	$-0.0986553\pi$
$103$	9.70820	+	7.05342i	0.956578	+	0.694994i	0.00422434	+	0.999991i	$0.498655\pi$
$104$		0			0
$105$	−0.927051	−	2.85317i	−0.0904709	−	0.278441i
$106$		0			0
$107$	8.09017	−	5.87785i	0.782106	−	0.568233i	−0.123504	−	0.992344i	$-0.539413\pi$
$107$	8.09017	−	5.87785i	0.782106	−	0.568233i	0.905610	+	0.424111i	$0.139413\pi$
$108$	5.56231	−	17.1190i	0.535233	−	1.64728i
$109$	4.00000			0.383131			0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000			0.383131			0.191565	+	0.981480i	$0.438644\pi$
$110$		0			0
$111$	15.0000			1.42374
$112$	−1.23607	+	3.80423i	−0.116797	+	0.359466i
$113$	15.3713	−	11.1679i	1.44601	−	1.05059i	0.459270	−	0.888297i	$-0.348111\pi$
$113$	15.3713	−	11.1679i	1.44601	−	1.05059i	0.986743	−	0.162293i	$-0.0518889\pi$
$114$		0			0
$115$	1.54508	+	4.75528i	0.144080	+	0.443432i
$116$	−6.18034	−	19.0211i	−0.573830	−	1.76607i
$117$	19.4164	+	14.1068i	1.79505	+	1.30418i
$118$		0			0
$119$	−0.618034	+	1.90211i	−0.0566551	+	0.174366i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	1.85410	−	5.70634i	0.167179	−	0.514523i
$124$	1.61803	−	1.17557i	0.145304	−	0.105569i
$125$	−7.28115	−	5.29007i	−0.651246	−	0.473158i
$126$		0			0
$127$	0.618034	+	1.90211i	0.0548416	+	0.168785i	0.974726	−	0.223405i	$-0.0717174\pi$
$127$	0.618034	+	1.90211i	0.0548416	+	0.168785i	−0.919884	+	0.392191i	$0.871717\pi$
$128$		0			0
$129$	−19.4164	+	14.1068i	−1.70952	+	1.24204i
$130$		0			0
$131$	18.0000			1.57267			0.786334	−	0.617802i	$-0.211977\pi$
$131$	18.0000			1.57267			0.786334	+	0.617802i	$0.211977\pi$
$132$		0			0
$133$	6.00000			0.520266
$134$		0			0
$135$	−7.28115	+	5.29007i	−0.626662	+	0.455296i
$136$		0			0
$137$	−0.927051	−	2.85317i	−0.0792033	−	0.243763i	0.903613	−	0.428350i	$-0.140905\pi$
$137$	−0.927051	−	2.85317i	−0.0792033	−	0.243763i	−0.982816	+	0.184588i	$0.940905\pi$
$138$		0			0
$139$	8.09017	+	5.87785i	0.686199	+	0.498553i	0.875409	−	0.483384i	$-0.160592\pi$
$139$	8.09017	+	5.87785i	0.686199	+	0.498553i	−0.189209	+	0.981937i	$0.560592\pi$
$140$	1.61803	−	1.17557i	0.136749	−	0.0993538i
$141$	−7.41641	+	22.8254i	−0.624574	+	1.92224i
$142$		0			0
$143$		0			0
$144$	24.0000			2.00000
$145$	−3.09017	+	9.51057i	−0.256625	+	0.789809i
$146$		0			0
$147$	2.42705	+	1.76336i	0.200180	+	0.145439i
$148$	3.09017	+	9.51057i	0.254010	+	0.781764i
$149$	−6.79837	−	20.9232i	−0.556944	−	1.71410i	−0.690752	−	0.723092i	$-0.742720\pi$
$149$	−6.79837	−	20.9232i	−0.556944	−	1.71410i	0.133808	−	0.991007i	$-0.457280\pi$
$150$		0			0
$151$	−4.85410	+	3.52671i	−0.395021	+	0.287000i	−0.767510	−	0.641037i	$-0.778505\pi$
$151$	−4.85410	+	3.52671i	−0.395021	+	0.287000i	0.372489	+	0.928037i	$0.378505\pi$
$152$		0			0
$153$	12.0000			0.970143
$154$		0			0
$155$	−1.00000			−0.0803219
$156$	−7.41641	+	22.8254i	−0.593788	+	1.82749i
$157$	−5.66312	+	4.11450i	−0.451966	+	0.328373i	−0.790372	−	0.612628i	$-0.790112\pi$
$157$	−5.66312	+	4.11450i	−0.451966	+	0.328373i	0.338405	+	0.941000i	$0.390112\pi$
$158$		0			0
$159$	5.56231	+	17.1190i	0.441120	+	1.35763i
$160$		0			0
$161$	−4.04508	−	2.93893i	−0.318797	−	0.231620i
$162$		0			0
$163$	1.23607	−	3.80423i	0.0968163	−	0.297970i	−0.890906	−	0.454187i	$-0.849930\pi$
$163$	1.23607	−	3.80423i	0.0968163	−	0.297970i	0.987723	+	0.156217i	$0.0499299\pi$
$164$	4.00000			0.312348
$165$		0			0
$166$		0			0
$167$	−0.618034	+	1.90211i	−0.0478249	+	0.147190i	−0.972117	−	0.234495i	$-0.924656\pi$
$167$	−0.618034	+	1.90211i	−0.0478249	+	0.147190i	0.924292	+	0.381685i	$0.124656\pi$
$168$		0			0
$169$	−2.42705	−	1.76336i	−0.186696	−	0.135643i
$170$		0			0
$171$	−11.1246	−	34.2380i	−0.850720	−	2.61825i
$172$	−12.9443	−	9.40456i	−0.986991	−	0.717091i
$173$	−12.9443	+	9.40456i	−0.984135	+	0.715016i	−0.958629	−	0.284659i	$-0.908120\pi$
$173$	−12.9443	+	9.40456i	−0.984135	+	0.715016i	−0.0255059	+	0.999675i	$0.508120\pi$
$174$		0			0
$175$	4.00000			0.302372
$176$		0			0
$177$	−9.00000			−0.676481
$178$		0			0
$179$	−0.809017	+	0.587785i	−0.0604688	+	0.0439331i	−0.617609	−	0.786485i	$-0.711899\pi$
$179$	−0.809017	+	0.587785i	−0.0604688	+	0.0439331i	0.557140	+	0.830418i	$0.311899\pi$
$180$	−9.70820	−	7.05342i	−0.723607	−	0.525731i
$181$	1.54508	+	4.75528i	0.114845	+	0.353457i	0.991915	−	0.126906i	$-0.0405047\pi$
$181$	1.54508	+	4.75528i	0.114845	+	0.353457i	−0.877069	+	0.480364i	$0.840505\pi$
$182$		0			0
$183$	−4.85410	−	3.52671i	−0.358826	−	0.260702i
$184$		0			0
$185$	1.54508	−	4.75528i	0.113597	−	0.349615i
$186$		0			0
$187$		0			0
$188$	−16.0000			−1.16692
$189$	2.78115	−	8.55951i	0.202299	−	0.622613i
$190$		0			0
$191$	−4.04508	−	2.93893i	−0.292692	−	0.212653i	0.431742	−	0.901997i	$-0.357899\pi$
$191$	−4.04508	−	2.93893i	−0.292692	−	0.212653i	−0.724434	+	0.689344i	$0.757899\pi$
$192$	7.41641	+	22.8254i	0.535233	+	1.64728i
$193$	4.32624	+	13.3148i	0.311409	+	0.958420i	0.977207	+	0.212287i	$0.0680913\pi$
$193$	4.32624	+	13.3148i	0.311409	+	0.958420i	−0.665798	+	0.746132i	$0.731909\pi$
$194$		0			0
$195$	9.70820	−	7.05342i	0.695219	−	0.505106i
$196$	−0.618034	+	1.90211i	−0.0441453	+	0.135865i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	−8.00000			−0.567105			−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000			−0.567105			−0.283552	+	0.958957i	$0.591513\pi$
$200$		0			0
$201$	−7.28115	+	5.29007i	−0.513573	+	0.373133i
$202$		0			0
$203$	−3.09017	−	9.51057i	−0.216887	−	0.667511i
$204$	3.70820	+	11.4127i	0.259626	+	0.799047i
$205$	−1.61803	−	1.17557i	−0.113008	−	0.0821054i
$206$		0			0
$207$	−9.27051	+	28.5317i	−0.644345	+	1.98309i
$208$	−16.0000			−1.10940
$209$		0			0
$210$		0			0
$211$	−0.618034	+	1.90211i	−0.0425472	+	0.130947i	−0.970074	−	0.242810i	$-0.921931\pi$
$211$	−0.618034	+	1.90211i	−0.0425472	+	0.130947i	0.927527	+	0.373757i	$0.121931\pi$
$212$	−9.70820	+	7.05342i	−0.666762	+	0.484431i
$213$	2.42705	+	1.76336i	0.166299	+	0.120823i
$214$		0			0
$215$	2.47214	+	7.60845i	0.168598	+	0.518892i
$216$		0			0
$217$	0.809017	−	0.587785i	0.0549197	−	0.0399015i
$218$		0			0
$219$	−30.0000			−2.02721
$220$		0			0
$221$	−8.00000			−0.538138
$222$		0			0
$223$	−0.809017	+	0.587785i	−0.0541758	+	0.0393610i	−0.614544	−	0.788883i	$-0.710660\pi$
$223$	−0.809017	+	0.587785i	−0.0541758	+	0.0393610i	0.560368	+	0.828244i	$0.310660\pi$
$224$		0			0
$225$	−7.41641	−	22.8254i	−0.494427	−	1.52169i
$226$		0			0
$227$	−3.23607	−	2.35114i	−0.214785	−	0.156051i	0.475191	−	0.879883i	$-0.342379\pi$
$227$	−3.23607	−	2.35114i	−0.214785	−	0.156051i	−0.689976	+	0.723832i	$0.742379\pi$
$228$	29.1246	−	21.1603i	1.92882	−	1.40137i
$229$	−2.16312	+	6.65740i	−0.142943	+	0.439933i	−0.996741	−	0.0806717i	$-0.974293\pi$
$229$	−2.16312	+	6.65740i	−0.142943	+	0.439933i	0.853798	+	0.520605i	$0.174293\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.85410	−	5.70634i	0.121466	−	0.373835i	−0.871774	−	0.489907i	$-0.837031\pi$
$233$	1.85410	−	5.70634i	0.121466	−	0.373835i	0.993241	+	0.116073i	$0.0370306\pi$
$234$		0			0
$235$	6.47214	+	4.70228i	0.422196	+	0.306743i
$236$	−1.85410	−	5.70634i	−0.120692	−	0.371451i
$237$	−5.56231	−	17.1190i	−0.361311	−	1.11200i
$238$		0			0
$239$	−3.23607	+	2.35114i	−0.209324	+	0.152083i	−0.687508	−	0.726177i	$-0.741295\pi$
$239$	−3.23607	+	2.35114i	−0.209324	+	0.152083i	0.478184	+	0.878260i	$0.341295\pi$
$240$	3.70820	−	11.4127i	0.239364	−	0.736685i
$241$	−12.0000			−0.772988			−0.386494	−	0.922292i	$-0.626314\pi$
$241$	−12.0000			−0.772988			−0.386494	+	0.922292i	$0.626314\pi$
$242$		0			0
$243$		0			0
$244$	1.23607	−	3.80423i	0.0791311	−	0.243541i
$245$	0.809017	−	0.587785i	0.0516862	−	0.0375522i
$246$		0			0
$247$	7.41641	+	22.8254i	0.471895	+	1.45234i
$248$		0			0
$249$	29.1246	+	21.1603i	1.84570	+	1.34098i
$250$		0			0
$251$	−6.48936	+	19.9722i	−0.409605	+	1.26063i	0.507384	+	0.861720i	$0.330613\pi$
$251$	−6.48936	+	19.9722i	−0.409605	+	1.26063i	−0.916989	+	0.398913i	$0.869387\pi$
$252$	12.0000			0.755929
$253$		0			0
$254$		0			0
$255$	1.85410	−	5.70634i	0.116108	−	0.357345i
$256$	−12.9443	+	9.40456i	−0.809017	+	0.587785i
$257$	4.85410	+	3.52671i	0.302791	+	0.219990i	0.728797	−	0.684730i	$-0.240080\pi$
$257$	4.85410	+	3.52671i	0.302791	+	0.219990i	−0.426006	+	0.904720i	$0.640080\pi$
$258$		0			0
$259$	1.54508	+	4.75528i	0.0960069	+	0.295479i
$260$	6.47214	+	4.70228i	0.401385	+	0.291623i
$261$	−48.5410	+	35.2671i	−3.00461	+	2.18298i
$262$		0			0
$263$	18.0000			1.10993			0.554964	−	0.831875i	$-0.312732\pi$
$263$	18.0000			1.10993			0.554964	+	0.831875i	$0.312732\pi$
$264$		0			0
$265$	6.00000			0.368577
$266$		0			0
$267$	−36.4058	+	26.4503i	−2.22800	+	1.61873i
$268$	−4.85410	−	3.52671i	−0.296511	−	0.215428i
$269$	−5.56231	−	17.1190i	−0.339140	−	1.04376i	−0.964647	−	0.263546i	$-0.915108\pi$
$269$	−5.56231	−	17.1190i	−0.339140	−	1.04376i	0.625507	−	0.780219i	$-0.284892\pi$
$270$		0			0
$271$	−12.9443	−	9.40456i	−0.786309	−	0.571287i	0.120557	−	0.992706i	$-0.461532\pi$
$271$	−12.9443	−	9.40456i	−0.786309	−	0.571287i	−0.906866	+	0.421420i	$0.861532\pi$
$272$	−6.47214	+	4.70228i	−0.392431	+	0.285118i
$273$	−3.70820	+	11.4127i	−0.224431	+	0.690727i
$274$		0			0
$275$		0			0
$276$	−30.0000			−1.80579
$277$	7.41641	−	22.8254i	0.445609	−	1.37144i	−0.436206	−	0.899847i	$-0.643678\pi$
$277$	7.41641	−	22.8254i	0.445609	−	1.37144i	0.881815	−	0.471596i	$-0.156322\pi$
$278$		0			0
$279$	−4.85410	−	3.52671i	−0.290607	−	0.211139i
$280$		0			0
$281$	−1.23607	−	3.80423i	−0.0737376	−	0.226941i	0.907394	−	0.420280i	$-0.138068\pi$
$281$	−1.23607	−	3.80423i	−0.0737376	−	0.226941i	−0.981132	+	0.193339i	$0.938068\pi$
$282$		0			0
$283$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$283$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$284$	−0.618034	+	1.90211i	−0.0366736	+	0.112870i
$285$	−18.0000			−1.06623
$286$		0			0
$287$	2.00000			0.118056
$288$		0			0
$289$	10.5172	−	7.64121i	0.618660	−	0.449483i
$290$		0			0
$291$	4.63525	+	14.2658i	0.271723	+	0.836279i
$292$	−6.18034	−	19.0211i	−0.361677	−	1.11313i
$293$	4.85410	+	3.52671i	0.283580	+	0.206033i	0.720477	−	0.693479i	$-0.243923\pi$
$293$	4.85410	+	3.52671i	0.283580	+	0.206033i	−0.436898	+	0.899511i	$0.643923\pi$
$294$		0			0
$295$	−0.927051	+	2.85317i	−0.0539750	+	0.166118i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.18034	−	19.0211i	0.357418	−	1.10002i
$300$	19.4164	−	14.1068i	1.12101	−	0.814459i
$301$	−6.47214	−	4.70228i	−0.373048	−	0.271035i
$302$		0			0
$303$	11.1246	+	34.2380i	0.639092	+	1.96692i
$304$	19.4164	+	14.1068i	1.11361	+	0.809083i
$305$	−1.61803	+	1.17557i	−0.0926484	+	0.0673130i
$306$		0			0
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$		0			0
$309$	36.0000			2.04797
$310$		0			0
$311$	−6.47214	+	4.70228i	−0.367001	+	0.266642i	−0.755966	−	0.654611i	$-0.772833\pi$
$311$	−6.47214	+	4.70228i	−0.367001	+	0.266642i	0.388965	+	0.921252i	$0.372833\pi$
$312$		0			0
$313$	−7.10739	−	21.8743i	−0.401733	−	1.23641i	−0.923592	−	0.383377i	$-0.874761\pi$
$313$	−7.10739	−	21.8743i	−0.401733	−	1.23641i	0.521859	−	0.853032i	$-0.325239\pi$
$314$		0			0
$315$	−4.85410	−	3.52671i	−0.273498	−	0.198708i
$316$	9.70820	−	7.05342i	0.546129	−	0.396786i
$317$	2.78115	−	8.55951i	0.156205	−	0.480750i	−0.842076	−	0.539359i	$-0.818667\pi$
$317$	2.78115	−	8.55951i	0.156205	−	0.480750i	0.998281	+	0.0586092i	$0.0186666\pi$
$318$		0			0
$319$		0			0
$320$	8.00000			0.447214
$321$	9.27051	−	28.5317i	0.517429	−	1.59248i
$322$		0			0
$323$	9.70820	+	7.05342i	0.540179	+	0.392463i
$324$	−5.56231	−	17.1190i	−0.309017	−	0.951057i
$325$	4.94427	+	15.2169i	0.274259	+	0.844082i
$326$		0			0
$327$	9.70820	−	7.05342i	0.536865	−	0.390055i
$328$		0			0
$329$	−8.00000			−0.441054
$330$		0			0
$331$	−17.0000			−0.934405			−0.467202	−	0.884150i	$-0.654738\pi$
$331$	−17.0000			−0.934405			−0.467202	+	0.884150i	$0.654738\pi$
$332$	−7.41641	+	22.8254i	−0.407028	+	1.25270i
$333$	24.2705	−	17.6336i	1.33002	−	0.966313i
$334$		0			0
$335$	0.927051	+	2.85317i	0.0506502	+	0.155885i
$336$	3.70820	+	11.4127i	0.202299	+	0.622613i
$337$	14.5623	+	10.5801i	0.793259	+	0.576337i	0.908929	−	0.416951i	$-0.136901\pi$
$337$	14.5623	+	10.5801i	0.793259	+	0.576337i	−0.115670	+	0.993288i	$0.536901\pi$
$338$		0			0
$339$	17.6140	−	54.2102i	0.956659	−	2.94430i
$340$	4.00000			0.216930
$341$		0			0
$342$		0			0
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$		0			0
$345$	12.1353	+	8.81678i	0.653340	+	0.474679i
$346$		0			0
$347$	4.32624	+	13.3148i	0.232245	+	0.714775i	0.997475	+	0.0710189i	$0.0226251\pi$
$347$	4.32624	+	13.3148i	0.232245	+	0.714775i	−0.765230	+	0.643757i	$0.777375\pi$
$348$	−48.5410	−	35.2671i	−2.60207	−	1.89052i
$349$	27.5066	−	19.9847i	1.47239	−	1.06976i	0.492482	−	0.870323i	$-0.336090\pi$
$349$	27.5066	−	19.9847i	1.47239	−	1.06976i	0.979911	−	0.199434i	$-0.0639103\pi$
$350$		0			0
$351$	36.0000			1.92154
$352$		0			0
$353$	9.00000			0.479022			0.239511	−	0.970894i	$-0.423013\pi$
$353$	9.00000			0.479022			0.239511	+	0.970894i	$0.423013\pi$
$354$		0			0
$355$	0.809017	−	0.587785i	0.0429382	−	0.0311964i
$356$	−24.2705	−	17.6336i	−1.28633	−	0.934577i
$357$	1.85410	+	5.70634i	0.0981295	+	0.302011i
$358$		0			0
$359$	−6.47214	−	4.70228i	−0.341586	−	0.248177i	0.403745	−	0.914872i	$-0.367708\pi$
$359$	−6.47214	−	4.70228i	−0.341586	−	0.248177i	−0.745331	+	0.666695i	$0.767708\pi$
$360$		0			0
$361$	5.25329	−	16.1680i	0.276489	−	0.850945i
$362$		0			0
$363$		0			0
$364$	−8.00000			−0.419314
$365$	−3.09017	+	9.51057i	−0.161747	+	0.497806i
$366$		0			0
$367$	8.89919	+	6.46564i	0.464534	+	0.337504i	0.795307	−	0.606207i	$-0.207310\pi$
$367$	8.89919	+	6.46564i	0.464534	+	0.337504i	−0.330773	+	0.943710i	$0.607310\pi$
$368$	−6.18034	−	19.0211i	−0.322172	−	0.991545i
$369$	−3.70820	−	11.4127i	−0.193041	−	0.594120i
$370$		0			0
$371$	−4.85410	+	3.52671i	−0.252012	+	0.183098i
$372$	1.85410	−	5.70634i	0.0961307	−	0.295860i
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$		0			0
$375$	−27.0000			−1.39427
$376$		0			0
$377$	32.3607	−	23.5114i	1.66666	−	1.21090i
$378$		0			0
$379$	−8.96149	−	27.5806i	−0.460321	−	1.41672i	−0.864773	−	0.502163i	$-0.832538\pi$
$379$	−8.96149	−	27.5806i	−0.460321	−	1.41672i	0.404452	−	0.914559i	$-0.367462\pi$
$380$	−3.70820	−	11.4127i	−0.190227	−	0.585458i
$381$	4.85410	+	3.52671i	0.248683	+	0.180679i
$382$		0			0
$383$	5.25329	−	16.1680i	0.268431	−	0.826144i	−0.722453	−	0.691420i	$-0.756985\pi$
$383$	5.25329	−	16.1680i	0.268431	−	0.826144i	0.990883	−	0.134724i	$-0.0430147\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−14.8328	+	45.6507i	−0.753994	+	2.32056i
$388$	−8.09017	+	5.87785i	−0.410716	+	0.298403i
$389$	−7.28115	−	5.29007i	−0.369169	−	0.268217i	0.387697	−	0.921787i	$-0.373271\pi$
$389$	−7.28115	−	5.29007i	−0.369169	−	0.268217i	−0.756866	+	0.653570i	$0.773271\pi$
$390$		0			0
$391$	−3.09017	−	9.51057i	−0.156277	−	0.480970i
$392$		0			0
$393$	43.6869	−	31.7404i	2.20371	−	1.60109i
$394$		0			0
$395$	−6.00000			−0.301893
$396$		0			0
$397$	18.0000			0.903394			0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000			0.903394			0.451697	+	0.892171i	$0.350819\pi$
$398$		0			0
$399$	14.5623	−	10.5801i	0.729027	−	0.529669i
$400$	12.9443	+	9.40456i	0.647214	+	0.470228i
$401$	−1.85410	−	5.70634i	−0.0925894	−	0.284961i	0.894029	−	0.448010i	$-0.147867\pi$
$401$	−1.85410	−	5.70634i	−0.0925894	−	0.284961i	−0.986618	+	0.163049i	$0.947867\pi$
$402$		0			0
$403$	3.23607	+	2.35114i	0.161200	+	0.117119i
$404$	−19.4164	+	14.1068i	−0.966002	+	0.701842i
$405$	−2.78115	+	8.55951i	−0.138197	+	0.425325i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−8.03444	+	24.7275i	−0.397278	+	1.22269i	0.529896	+	0.848063i	$0.322231\pi$
$409$	−8.03444	+	24.7275i	−0.397278	+	1.22269i	−0.927174	+	0.374632i	$0.877769\pi$
$410$		0			0
$411$	−7.28115	−	5.29007i	−0.359153	−	0.260940i
$412$	7.41641	+	22.8254i	0.365380	+	1.12452i
$413$	−0.927051	−	2.85317i	−0.0456172	−	0.140395i
$414$		0			0
$415$	9.70820	−	7.05342i	0.476557	−	0.346239i
$416$		0			0
$417$	30.0000			1.46911
$418$		0			0
$419$	16.0000			0.781651			0.390826	−	0.920465i	$-0.372190\pi$
$419$	16.0000			0.781651			0.390826	+	0.920465i	$0.372190\pi$
$420$	1.85410	−	5.70634i	0.0904709	−	0.278441i
$421$	−17.7984	+	12.9313i	−0.867440	+	0.630232i	−0.929899	−	0.367816i	$-0.880106\pi$
$421$	−17.7984	+	12.9313i	−0.867440	+	0.630232i	0.0624590	+	0.998048i	$0.480106\pi$
$422$		0			0
$423$	14.8328	+	45.6507i	0.721196	+	2.21961i
$424$		0			0
$425$	6.47214	+	4.70228i	0.313945	+	0.228094i
$426$		0			0
$427$	0.618034	−	1.90211i	0.0299088	−	0.0920497i
$428$	20.0000			0.966736
$429$		0			0
$430$		0			0
$431$	−6.18034	+	19.0211i	−0.297696	+	0.916216i	0.684606	+	0.728913i	$0.259974\pi$
$431$	−6.18034	+	19.0211i	−0.297696	+	0.916216i	−0.982302	+	0.187302i	$0.940026\pi$
$432$	29.1246	−	21.1603i	1.40126	−	1.01807i
$433$	20.2254	+	14.6946i	0.971972	+	0.706179i	0.955900	−	0.293692i	$-0.0948840\pi$
$433$	20.2254	+	14.6946i	0.971972	+	0.706179i	0.0160718	+	0.999871i	$0.494884\pi$
$434$		0			0
$435$	9.27051	+	28.5317i	0.444487	+	1.36799i
$436$	6.47214	+	4.70228i	0.309959	+	0.225198i
$437$	−24.2705	+	17.6336i	−1.16102	+	0.843527i
$438$		0			0
$439$	−14.0000			−0.668184			−0.334092	−	0.942541i	$-0.608430\pi$
$439$	−14.0000			−0.668184			−0.334092	+	0.942541i	$0.608430\pi$
$440$		0			0
$441$	6.00000			0.285714
$442$		0			0
$443$	31.5517	−	22.9236i	1.49906	−	1.08913i	0.528313	−	0.849050i	$-0.322825\pi$
$443$	31.5517	−	22.9236i	1.49906	−	1.08913i	0.970752	−	0.240084i	$-0.0771751\pi$
$444$	24.2705	+	17.6336i	1.15183	+	0.836852i
$445$	4.63525	+	14.2658i	0.219732	+	0.676266i
$446$		0			0
$447$	−53.3951	−	38.7938i	−2.52550	−	1.83489i
$448$	−6.47214	+	4.70228i	−0.305780	+	0.222162i
$449$	4.63525	−	14.2658i	0.218751	−	0.673247i	−0.780115	−	0.625636i	$-0.784839\pi$
$449$	4.63525	−	14.2658i	0.218751	−	0.673247i	0.998866	−	0.0476105i	$-0.0151606\pi$
$450$		0			0
$451$		0			0
$452$	38.0000			1.78737
$453$	−5.56231	+	17.1190i	−0.261340	+	0.804322i
$454$		0			0
$455$	3.23607	+	2.35114i	0.151709	+	0.110223i
$456$		0			0
$457$	2.47214	+	7.60845i	0.115642	+	0.355908i	0.992080	−	0.125605i	$-0.0400872\pi$
$457$	2.47214	+	7.60845i	0.115642	+	0.355908i	−0.876439	+	0.481514i	$0.840087\pi$
$458$		0			0
$459$	14.5623	−	10.5801i	0.679710	−	0.493838i
$460$	−3.09017	+	9.51057i	−0.144080	+	0.443432i
$461$	18.0000			0.838344			0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000			0.838344			0.419172	+	0.907907i	$0.362320\pi$
$462$		0			0
$463$	13.0000			0.604161			0.302081	−	0.953282i	$-0.402319\pi$
$463$	13.0000			0.604161			0.302081	+	0.953282i	$0.402319\pi$
$464$	12.3607	−	38.0423i	0.573830	−	1.76607i
$465$	−2.42705	+	1.76336i	−0.112552	+	0.0817737i
$466$		0			0
$467$	0.927051	+	2.85317i	0.0428988	+	0.132029i	0.970212	−	0.242257i	$-0.0778878\pi$
$467$	0.927051	+	2.85317i	0.0428988	+	0.132029i	−0.927313	+	0.374286i	$0.877888\pi$
$468$	14.8328	+	45.6507i	0.685647	+	2.11020i
$469$	−2.42705	−	1.76336i	−0.112071	−	0.0814242i
$470$		0			0
$471$	−6.48936	+	19.9722i	−0.299014	+	0.920270i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	7.41641	−	22.8254i	0.340288	−	1.04730i
$476$	−3.23607	+	2.35114i	−0.148325	+	0.107764i
$477$	29.1246	+	21.1603i	1.33352	+	0.968862i
$478$		0			0
$479$	−8.65248	−	26.6296i	−0.395342	−	1.21674i	−0.928695	−	0.370844i	$-0.879068\pi$
$479$	−8.65248	−	26.6296i	−0.395342	−	1.21674i	0.533353	−	0.845893i	$-0.320932\pi$
$480$		0			0
$481$	−16.1803	+	11.7557i	−0.737760	+	0.536014i
$482$		0			0
$483$	−15.0000			−0.682524
$484$		0			0
$485$	5.00000			0.227038
$486$		0			0
$487$	10.5172	−	7.64121i	0.476581	−	0.346256i	−0.323420	−	0.946256i	$-0.604833\pi$
$487$	10.5172	−	7.64121i	0.476581	−	0.346256i	0.800000	+	0.599999i	$0.204833\pi$
$488$		0			0
$489$	−3.70820	−	11.4127i	−0.167691	−	0.516099i
$490$		0			0
$491$	24.2705	+	17.6336i	1.09531	+	0.795791i	0.980289	−	0.197571i	$-0.0633054\pi$
$491$	24.2705	+	17.6336i	1.09531	+	0.795791i	0.115024	+	0.993363i	$0.463305\pi$
$492$	9.70820	−	7.05342i	0.437680	−	0.317993i
$493$	6.18034	−	19.0211i	0.278349	−	0.856669i
$494$		0			0
$495$		0			0
$496$	4.00000			0.179605
$497$	−0.309017	+	0.951057i	−0.0138613	+	0.0426607i
$498$		0			0
$499$	−35.5967	−	25.8626i	−1.59353	−	1.15777i	−0.898674	−	0.438617i	$-0.855468\pi$
$499$	−35.5967	−	25.8626i	−1.59353	−	1.15777i	−0.694855	−	0.719150i	$-0.744532\pi$
$500$	−5.56231	−	17.1190i	−0.248754	−	0.765586i
$501$	1.85410	+	5.70634i	0.0828352	+	0.254940i
$502$		0			0
$503$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$503$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$504$		0			0
$505$	12.0000			0.533993
$506$		0			0
$507$	−9.00000			−0.399704
$508$	−1.23607	+	3.80423i	−0.0548416	+	0.168785i
$509$	25.0795	−	18.2213i	1.11163	−	0.807647i	0.128711	−	0.991682i	$-0.458916\pi$
$509$	25.0795	−	18.2213i	1.11163	−	0.807647i	0.982920	+	0.184035i	$0.0589161\pi$
$510$		0			0
$511$	−3.09017	−	9.51057i	−0.136701	−	0.420723i
$512$		0			0
$513$	−43.6869	−	31.7404i	−1.92882	−	1.40137i
$514$		0			0
$515$	3.70820	−	11.4127i	0.163403	−	0.502903i
$516$	−48.0000			−2.11308
$517$		0			0
$518$		0			0
$519$	−14.8328	+	45.6507i	−0.651088	+	2.00384i
$520$		0			0
$521$	−5.66312	−	4.11450i	−0.248106	−	0.180259i	0.456781	−	0.889579i	$-0.349002\pi$
$521$	−5.66312	−	4.11450i	−0.248106	−	0.180259i	−0.704887	+	0.709320i	$0.749002\pi$
$522$		0			0
$523$	9.88854	+	30.4338i	0.432396	+	1.33078i	0.895732	+	0.444595i	$0.146652\pi$
$523$	9.88854	+	30.4338i	0.432396	+	1.33078i	−0.463336	+	0.886183i	$0.653348\pi$
$524$	29.1246	+	21.1603i	1.27231	+	0.924391i
$525$	9.70820	−	7.05342i	0.423701	−	0.307837i
$526$		0			0
$527$	2.00000			0.0871214
$528$		0			0
$529$	2.00000			0.0869565
$530$		0			0
$531$	−14.5623	+	10.5801i	−0.631950	+	0.459139i
$532$	9.70820	+	7.05342i	0.420904	+	0.305805i
$533$	2.47214	+	7.60845i	0.107080	+	0.329559i
$534$		0			0
$535$	−8.09017	−	5.87785i	−0.349769	−	0.254122i
$536$		0			0
$537$	−0.927051	+	2.85317i	−0.0400052	+	0.123123i
$538$		0			0
$539$		0			0
$540$	−18.0000			−0.774597
$541$	9.88854	−	30.4338i	0.425142	−	1.30845i	−0.477717	−	0.878514i	$-0.658536\pi$
$541$	9.88854	−	30.4338i	0.425142	−	1.30845i	0.902859	−	0.429938i	$-0.141464\pi$
$542$		0			0
$543$	12.1353	+	8.81678i	0.520774	+	0.378364i
$544$		0			0
$545$	−1.23607	−	3.80423i	−0.0529473	−	0.162955i
$546$		0			0
$547$	19.4164	−	14.1068i	0.830186	−	0.603165i	−0.0894262	−	0.995993i	$-0.528503\pi$
$547$	19.4164	−	14.1068i	0.830186	−	0.603165i	0.919612	+	0.392828i	$0.128503\pi$
$548$	1.85410	−	5.70634i	0.0792033	−	0.243763i
$549$	−12.0000			−0.512148
$550$		0			0
$551$	−60.0000			−2.55609
$552$		0			0
$553$	4.85410	−	3.52671i	0.206417	−	0.149971i
$554$		0			0
$555$	−4.63525	−	14.2658i	−0.196756	−	0.605552i
$556$	6.18034	+	19.0211i	0.262105	+	0.806676i
$557$	−11.3262	−	8.22899i	−0.479908	−	0.348674i	0.321382	−	0.946950i	$-0.395853\pi$
$557$	−11.3262	−	8.22899i	−0.479908	−	0.348674i	−0.801290	+	0.598276i	$0.795853\pi$
$558$		0			0
$559$	9.88854	−	30.4338i	0.418241	−	1.28721i
$560$	4.00000			0.169031
$561$		0			0
$562$		0			0
$563$	6.18034	−	19.0211i	0.260470	−	0.801645i	−0.732232	−	0.681055i	$-0.761521\pi$
$563$	6.18034	−	19.0211i	0.260470	−	0.801645i	0.992702	−	0.120590i	$-0.0384786\pi$
$564$	−38.8328	+	28.2137i	−1.63516	+	1.18801i
$565$	−15.3713	−	11.1679i	−0.646676	−	0.469838i
$566$		0			0
$567$	−2.78115	−	8.55951i	−0.116797	−	0.359466i
$568$		0			0
$569$	14.5623	−	10.5801i	0.610484	−	0.443542i	−0.239101	−	0.970995i	$-0.576853\pi$
$569$	14.5623	−	10.5801i	0.610484	−	0.443542i	0.849585	+	0.527452i	$0.176853\pi$
$570$		0			0
$571$	−20.0000			−0.836974			−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000			−0.836974			−0.418487	+	0.908223i	$0.637439\pi$
$572$		0			0
$573$	−15.0000			−0.626634
$574$		0			0
$575$	−16.1803	+	11.7557i	−0.674767	+	0.490247i
$576$	38.8328	+	28.2137i	1.61803	+	1.17557i
$577$	−7.72542	−	23.7764i	−0.321614	−	0.989825i	−0.972946	−	0.231032i	$-0.925790\pi$
$577$	−7.72542	−	23.7764i	−0.321614	−	0.989825i	0.651332	−	0.758793i	$-0.274210\pi$
$578$		0			0
$579$	33.9787	+	24.6870i	1.41211	+	1.02596i
$580$	−16.1803	+	11.7557i	−0.671852	+	0.488129i
$581$	−3.70820	+	11.4127i	−0.153842	+	0.473478i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	7.41641	−	22.8254i	0.306631	−	0.943712i
$586$		0			0
$587$	−29.1246	−	21.1603i	−1.20210	−	0.873378i	−0.207612	−	0.978211i	$-0.566569\pi$
$587$	−29.1246	−	21.1603i	−1.20210	−	0.873378i	−0.994490	+	0.104834i	$0.966569\pi$
$588$	1.85410	+	5.70634i	0.0764619	+	0.235325i
$589$	−1.85410	−	5.70634i	−0.0763969	−	0.235126i
$590$		0			0
$591$	43.6869	−	31.7404i	1.79704	−	1.30563i
$592$	−6.18034	+	19.0211i	−0.254010	+	0.781764i
$593$	30.0000			1.23195			0.615976	−	0.787765i	$-0.288762\pi$
$593$	30.0000			1.23195			0.615976	+	0.787765i	$0.288762\pi$
$594$		0			0
$595$	2.00000			0.0819920
$596$	13.5967	−	41.8465i	0.556944	−	1.71410i
$597$	−19.4164	+	14.1068i	−0.794661	+	0.577355i
$598$		0			0
$599$	−14.8328	−	45.6507i	−0.606052	−	1.86524i	−0.489388	−	0.872066i	$-0.662780\pi$
$599$	−14.8328	−	45.6507i	−0.606052	−	1.86524i	−0.116664	−	0.993171i	$-0.537220\pi$
$600$		0			0
$601$	−6.47214	−	4.70228i	−0.264004	−	0.191810i	0.447906	−	0.894080i	$-0.352170\pi$
$601$	−6.47214	−	4.70228i	−0.264004	−	0.191810i	−0.711910	+	0.702270i	$0.752170\pi$
$602$		0			0
$603$	−5.56231	+	17.1190i	−0.226515	+	0.697140i
$604$	−12.0000			−0.488273
$605$		0			0
$606$		0			0
$607$	−3.09017	+	9.51057i	−0.125426	+	0.386022i	−0.993978	−	0.109576i	$-0.965051\pi$
$607$	−3.09017	+	9.51057i	−0.125426	+	0.386022i	0.868552	+	0.495597i	$0.165051\pi$
$608$		0			0
$609$	−24.2705	−	17.6336i	−0.983491	−	0.714548i
$610$		0			0
$611$	−9.88854	−	30.4338i	−0.400048	−	1.23122i
$612$	19.4164	+	14.1068i	0.784862	+	0.570235i
$613$	−12.9443	+	9.40456i	−0.522814	+	0.379847i	−0.817663	−	0.575697i	$-0.804731\pi$
$613$	−12.9443	+	9.40456i	−0.522814	+	0.379847i	0.294849	+	0.955544i	$0.404731\pi$
$614$		0			0
$615$	−6.00000			−0.241943
$616$		0			0
$617$	−30.0000			−1.20775			−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000			−1.20775			−0.603877	+	0.797077i	$0.706378\pi$
$618$		0			0
$619$	−13.7533	+	9.99235i	−0.552791	+	0.401626i	−0.828814	−	0.559525i	$-0.810984\pi$
$619$	−13.7533	+	9.99235i	−0.552791	+	0.401626i	0.276022	+	0.961151i	$0.410984\pi$
$620$	−1.61803	−	1.17557i	−0.0649818	−	0.0472120i
$621$	13.9058	+	42.7975i	0.558019	+	1.71741i
$622$		0			0
$623$	−12.1353	−	8.81678i	−0.486189	−	0.353237i
$624$	−38.8328	+	28.2137i	−1.55456	+	1.12945i
$625$	3.39919	−	10.4616i	0.135967	−	0.418465i
$626$		0			0
$627$		0			0
$628$	−14.0000			−0.558661
$629$	−3.09017	+	9.51057i	−0.123213	+	0.379211i
$630$		0			0
$631$	−21.8435	−	15.8702i	−0.869574	−	0.631783i	0.0608983	−	0.998144i	$-0.480603\pi$
$631$	−21.8435	−	15.8702i	−0.869574	−	0.631783i	−0.930473	+	0.366361i	$0.880603\pi$
$632$		0			0
$633$	1.85410	+	5.70634i	0.0736939	+	0.226807i
$634$		0			0
$635$	1.61803	−	1.17557i	0.0642097	−	0.0466511i
$636$	−11.1246	+	34.2380i	−0.441120	+	1.35763i
$637$	−4.00000			−0.158486
$638$		0			0
$639$	6.00000			0.237356
$640$		0			0
$641$	−12.1353	+	8.81678i	−0.479314	+	0.348242i	−0.801060	−	0.598584i	$-0.795730\pi$
$641$	−12.1353	+	8.81678i	−0.479314	+	0.348242i	0.321746	+	0.946826i	$0.395730\pi$
$642$		0			0
$643$	−8.96149	−	27.5806i	−0.353407	−	1.08767i	−0.956928	−	0.290327i	$-0.906236\pi$
$643$	−8.96149	−	27.5806i	−0.353407	−	1.08767i	0.603521	−	0.797347i	$-0.293764\pi$
$644$	−3.09017	−	9.51057i	−0.121770	−	0.374769i
$645$	19.4164	+	14.1068i	0.764520	+	0.555457i
$646$		0			0
$647$	−6.48936	+	19.9722i	−0.255123	+	0.785188i	0.738682	+	0.674054i	$0.235448\pi$
$647$	−6.48936	+	19.9722i	−0.255123	+	0.785188i	−0.993805	+	0.111134i	$0.964552\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	0.927051	−	2.85317i	0.0363340	−	0.111825i
$652$	6.47214	−	4.70228i	0.253468	−	0.184156i
$653$	13.7533	+	9.99235i	0.538208	+	0.391031i	0.823419	−	0.567434i	$-0.192064\pi$
$653$	13.7533	+	9.99235i	0.538208	+	0.391031i	−0.285211	+	0.958465i	$0.592064\pi$
$654$		0			0
$655$	−5.56231	−	17.1190i	−0.217337	−	0.668895i
$656$	6.47214	+	4.70228i	0.252694	+	0.183593i
$657$	−48.5410	+	35.2671i	−1.89377	+	1.37590i
$658$		0			0
$659$	−2.00000			−0.0779089			−0.0389545	−	0.999241i	$-0.512403\pi$
$659$	−2.00000			−0.0779089			−0.0389545	+	0.999241i	$0.512403\pi$
$660$		0			0
$661$	35.0000			1.36134			0.680671	−	0.732589i	$-0.261688\pi$
$661$	35.0000			1.36134			0.680671	+	0.732589i	$0.261688\pi$
$662$		0			0
$663$	−19.4164	+	14.1068i	−0.754071	+	0.547865i
$664$		0			0
$665$	−1.85410	−	5.70634i	−0.0718990	−	0.221282i
$666$		0			0
$667$	40.4508	+	29.3893i	1.56626	+	1.13796i
$668$	−3.23607	+	2.35114i	−0.125207	+	0.0909684i
$669$	−0.927051	+	2.85317i	−0.0358419	+	0.110310i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.23607	−	3.80423i	0.0476469	−	0.146642i	−0.924403	−	0.381418i	$-0.875436\pi$
$673$	1.23607	−	3.80423i	0.0476469	−	0.146642i	0.972049	+	0.234776i	$0.0754357\pi$
$674$		0			0
$675$	−29.1246	−	21.1603i	−1.12101	−	0.814459i
$676$	−1.85410	−	5.70634i	−0.0713116	−	0.219475i
$677$	11.7426	+	36.1401i	0.451307	+	1.38898i	0.875417	+	0.483368i	$0.160587\pi$
$677$	11.7426	+	36.1401i	0.451307	+	1.38898i	−0.424111	+	0.905610i	$0.639413\pi$
$678$		0			0
$679$	−4.04508	+	2.93893i	−0.155236	+	0.112786i
$680$		0			0
$681$	−12.0000			−0.459841
$682$		0			0
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$	22.2492	−	68.4761i	0.850720	−	2.61825i
$685$	−2.42705	+	1.76336i	−0.0927329	+	0.0673744i
$686$		0			0
$687$	6.48936	+	19.9722i	0.247584	+	0.761986i
$688$	−9.88854	−	30.4338i	−0.376997	−	1.16028i
$689$	−19.4164	−	14.1068i	−0.739706	−	0.537428i
$690$		0			0
$691$	4.63525	−	14.2658i	0.176333	−	0.542698i	−0.823358	−	0.567522i	$-0.807902\pi$
$691$	4.63525	−	14.2658i	0.176333	−	0.542698i	0.999692	+	0.0248233i	$0.00790230\pi$
$692$	−32.0000			−1.21646
$693$		0			0
$694$		0			0
$695$	3.09017	−	9.51057i	0.117217	−	0.360756i
$696$		0			0
$697$	3.23607	+	2.35114i	0.122575	+	0.0890558i
$698$		0			0
$699$	−5.56231	−	17.1190i	−0.210386	−	0.647501i
$700$	6.47214	+	4.70228i	0.244624	+	0.177730i
$701$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$701$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$702$		0			0
$703$	30.0000			1.13147
$704$		0			0
$705$	24.0000			0.903892
$706$		0			0
$707$	−9.70820	+	7.05342i	−0.365115	+	0.265271i
$708$	−14.5623	−	10.5801i	−0.547285	−	0.397626i
$709$	12.0517	+	37.0912i	0.452610	+	1.39299i	0.873919	+	0.486072i	$0.161571\pi$
$709$	12.0517	+	37.0912i	0.452610	+	1.39299i	−0.421309	+	0.906917i	$0.638429\pi$
$710$		0			0
$711$	−29.1246	−	21.1603i	−1.09226	−	0.793572i
$712$		0			0
$713$	−1.54508	+	4.75528i	−0.0578639	+	0.178087i
$714$		0			0
$715$		0			0
$716$	−2.00000			−0.0747435
$717$	−3.70820	+	11.4127i	−0.138485	+	0.426214i
$718$		0			0
$719$	8.89919	+	6.46564i	0.331884	+	0.241128i	0.741229	−	0.671252i	$-0.234243\pi$
$719$	8.89919	+	6.46564i	0.331884	+	0.241128i	−0.409346	+	0.912379i	$0.634243\pi$
$720$	−7.41641	−	22.8254i	−0.276393	−	0.850651i
$721$	3.70820	+	11.4127i	0.138101	+	0.425030i
$722$		0			0
$723$	−29.1246	+	21.1603i	−1.08316	+	0.786959i
$724$	−3.09017	+	9.51057i	−0.114845	+	0.353457i
$725$	−40.0000			−1.48556
$726$		0			0
$727$	−19.0000			−0.704671			−0.352335	−	0.935874i	$-0.614612\pi$
$727$	−19.0000			−0.704671			−0.352335	+	0.935874i	$0.614612\pi$
$728$		0			0
$729$	21.8435	−	15.8702i	0.809017	−	0.587785i
$730$		0			0
$731$	−4.94427	−	15.2169i	−0.182871	−	0.562818i
$732$	−3.70820	−	11.4127i	−0.137059	−	0.421825i
$733$	3.23607	+	2.35114i	0.119527	+	0.0868414i	0.645943	−	0.763386i	$-0.276464\pi$
$733$	3.23607	+	2.35114i	0.119527	+	0.0868414i	−0.526416	+	0.850227i	$0.676464\pi$
$734$		0			0
$735$	0.927051	−	2.85317i	0.0341948	−	0.105241i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−5.56231	+	17.1190i	−0.204613	+	0.629733i	0.795116	+	0.606457i	$0.207410\pi$
$739$	−5.56231	+	17.1190i	−0.204613	+	0.629733i	−0.999729	+	0.0232763i	$0.992590\pi$
$740$	8.09017	−	5.87785i	0.297401	−	0.216074i
$741$	58.2492	+	42.3205i	2.13984	+	1.55468i
$742$		0			0
$743$	−7.41641	−	22.8254i	−0.272082	−	0.837381i	−0.989977	−	0.141230i	$-0.954894\pi$
$743$	−7.41641	−	22.8254i	−0.272082	−	0.837381i	0.717895	−	0.696151i	$-0.245106\pi$
$744$		0			0
$745$	−17.7984	+	12.9313i	−0.652082	+	0.473765i
$746$		0			0
$747$	72.0000			2.63434
$748$		0			0
$749$	10.0000			0.365392
$750$		0			0
$751$	18.6074	−	13.5191i	0.678993	−	0.493318i	−0.194030	−	0.980996i	$-0.562156\pi$
$751$	18.6074	−	13.5191i	0.678993	−	0.493318i	0.873024	+	0.487678i	$0.162156\pi$
$752$	−25.8885	−	18.8091i	−0.944058	−	0.685898i
$753$	19.4681	+	59.9166i	0.709456	+	2.18348i
$754$		0			0
$755$	4.85410	+	3.52671i	0.176659	+	0.128350i
$756$	14.5623	−	10.5801i	0.529626	−	0.384796i
$757$	11.7426	−	36.1401i	0.426794	−	1.31354i	−0.474473	−	0.880270i	$-0.657361\pi$
$757$	11.7426	−	36.1401i	0.426794	−	1.31354i	0.901266	−	0.433266i	$-0.142639\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−14.8328	+	45.6507i	−0.537689	+	1.65484i	0.200077	+	0.979780i	$0.435881\pi$
$761$	−14.8328	+	45.6507i	−0.537689	+	1.65484i	−0.737766	+	0.675057i	$0.764119\pi$
$762$		0			0
$763$	3.23607	+	2.35114i	0.117154	+	0.0851170i
$764$	−3.09017	−	9.51057i	−0.111798	−	0.344080i
$765$	−3.70820	−	11.4127i	−0.134070	−	0.412626i
$766$		0			0
$767$	9.70820	−	7.05342i	0.350543	−	0.254684i
$768$	−14.8328	+	45.6507i	−0.535233	+	1.64728i
$769$	40.0000			1.44244			0.721218	−	0.692708i	$-0.243582\pi$
$769$	40.0000			1.44244			0.721218	+	0.692708i	$0.243582\pi$
$770$		0			0
$771$	18.0000			0.648254
$772$	−8.65248	+	26.6296i	−0.311409	+	0.958420i
$773$	4.85410	−	3.52671i	0.174590	−	0.126847i	−0.497059	−	0.867717i	$-0.665587\pi$
$773$	4.85410	−	3.52671i	0.174590	−	0.126847i	0.671648	+	0.740870i	$0.265587\pi$
$774$		0			0
$775$	−1.23607	−	3.80423i	−0.0444009	−	0.136652i
$776$		0			0
$777$	12.1353	+	8.81678i	0.435350	+	0.316300i
$778$		0			0
$779$	3.70820	−	11.4127i	0.132860	−	0.408902i
$780$	24.0000			0.859338
$781$		0			0
$782$		0			0
$783$	−27.8115	+	85.5951i	−0.993903	+	3.05892i
$784$	−3.23607	+	2.35114i	−0.115574	+	0.0839693i
$785$	5.66312	+	4.11450i	0.202125	+	0.146853i
$786$		0			0
$787$	−6.79837	−	20.9232i	−0.242336	−	0.745833i	−0.996063	−	0.0886458i	$-0.971746\pi$
$787$	−6.79837	−	20.9232i	−0.242336	−	0.745833i	0.753727	−	0.657187i	$-0.228254\pi$
$788$	29.1246	+	21.1603i	1.03752	+	0.753803i
$789$	43.6869	−	31.7404i	1.55530	−	1.12999i
$790$		0			0
$791$	19.0000			0.675562
$792$		0			0
$793$	8.00000			0.284088
$794$		0			0
$795$	14.5623	−	10.5801i	0.516472	−	0.375239i
$796$	−12.9443	−	9.40456i	−0.458798	−	0.333336i
$797$	7.10739	+	21.8743i	0.251757	+	0.774827i	0.994451	+	0.105197i	$0.0335474\pi$
$797$	7.10739	+	21.8743i	0.251757	+	0.774827i	−0.742695	+	0.669630i	$0.766453\pi$
$798$		0			0
$799$	−12.9443	−	9.40456i	−0.457935	−	0.332710i
$800$		0			0
$801$	−27.8115	+	85.5951i	−0.982672	+	3.02435i
$802$		0			0
$803$		0			0
$804$	−18.0000			−0.634811
$805$	−1.54508	+	4.75528i	−0.0544571	+	0.167602i
$806$		0			0
$807$	−43.6869	−	31.7404i	−1.53785	−	1.11732i
$808$		0			0
$809$	9.27051	+	28.5317i	0.325934	+	1.00312i	0.971017	+	0.239009i	$0.0768225\pi$
$809$	9.27051	+	28.5317i	0.325934	+	1.00312i	−0.645084	+	0.764112i	$0.723177\pi$
$810$		0			0
$811$	17.7984	−	12.9313i	0.624985	−	0.454078i	−0.229674	−	0.973268i	$-0.573766\pi$
$811$	17.7984	−	12.9313i	0.624985	−	0.454078i	0.854659	+	0.519189i	$0.173766\pi$
$812$	6.18034	−	19.0211i	0.216887	−	0.667511i
$813$	−48.0000			−1.68343
$814$		0			0
$815$	−4.00000			−0.140114
$816$	−7.41641	+	22.8254i	−0.259626	+	0.799047i
$817$	−38.8328	+	28.2137i	−1.35859	+	0.987072i
$818$		0			0
$819$	7.41641	+	22.8254i	0.259150	+	0.797582i
$820$	−1.23607	−	3.80423i	−0.0431654	−	0.132849i
$821$	−14.5623	−	10.5801i	−0.508228	−	0.369249i	0.303923	−	0.952697i	$-0.401703\pi$
$821$	−14.5623	−	10.5801i	−0.508228	−	0.369249i	−0.812151	+	0.583447i	$0.801703\pi$
$822$		0			0
$823$	−7.72542	+	23.7764i	−0.269291	+	0.828794i	0.721382	+	0.692537i	$0.243507\pi$
$823$	−7.72542	+	23.7764i	−0.269291	+	0.828794i	−0.990674	+	0.136257i	$0.956493\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	6.18034	−	19.0211i	0.214911	−	0.661430i	−0.784248	−	0.620447i	$-0.786951\pi$
$827$	6.18034	−	19.0211i	0.214911	−	0.661430i	0.999160	−	0.0409825i	$-0.0130488\pi$
$828$	−48.5410	+	35.2671i	−1.68692	+	1.22562i
$829$	23.4615	+	17.0458i	0.814851	+	0.592024i	0.915233	−	0.402925i	$-0.132006\pi$
$829$	23.4615	+	17.0458i	0.814851	+	0.592024i	−0.100382	+	0.994949i	$0.532006\pi$
$830$		0			0
$831$	−22.2492	−	68.4761i	−0.771817	−	2.37541i
$832$	−25.8885	−	18.8091i	−0.897524	−	0.652089i
$833$	−1.61803	+	1.17557i	−0.0560616	+	0.0407311i
$834$		0			0
$835$	2.00000			0.0692129
$836$		0			0
$837$	−9.00000			−0.311086
$838$		0			0
$839$	−36.4058	+	26.4503i	−1.25687	+	0.913167i	−0.998599	−	0.0529065i	$-0.983151\pi$
$839$	−36.4058	+	26.4503i	−1.25687	+	0.913167i	−0.258267	+	0.966074i	$0.583151\pi$
$840$		0			0
$841$	21.9402	+	67.5250i	0.756559	+	2.32845i
$842$		0			0
$843$	−9.70820	−	7.05342i	−0.334368	−	0.242933i
$844$	−3.23607	+	2.35114i	−0.111390	+	0.0809296i
$845$	−0.927051	+	2.85317i	−0.0318915	+	0.0981520i
$846$		0			0
$847$		0			0
$848$	−24.0000			−0.824163
$849$		0			0
$850$		0			0
$851$	−20.2254	−	14.6946i	−0.693319	−	0.503725i
$852$	1.85410	+	5.70634i	0.0635205	+	0.195496i
$853$	−10.5066	−	32.3359i	−0.359738	−	1.10716i	−0.953211	−	0.302307i	$-0.902243\pi$
$853$	−10.5066	−	32.3359i	−0.359738	−	1.10716i	0.593472	−	0.804854i	$-0.297757\pi$
$854$		0			0
$855$	−29.1246	+	21.1603i	−0.996041	+	0.723666i
$856$		0			0
$857$	−28.0000			−0.956462			−0.478231	−	0.878234i	$-0.658722\pi$
$857$	−28.0000			−0.956462			−0.478231	+	0.878234i	$0.658722\pi$
$858$		0			0
$859$	55.0000			1.87658			0.938288	−	0.345855i	$-0.112411\pi$
$859$	55.0000			1.87658			0.938288	+	0.345855i	$0.112411\pi$
$860$	−4.94427	+	15.2169i	−0.168598	+	0.518892i
$861$	4.85410	−	3.52671i	0.165427	−	0.120190i
$862$		0			0
$863$	16.0689	+	49.4549i	0.546991	+	1.68347i	0.716208	+	0.697887i	$0.245876\pi$
$863$	16.0689	+	49.4549i	0.546991	+	1.68347i	−0.169217	+	0.985579i	$0.554124\pi$
$864$		0			0
$865$	12.9443	+	9.40456i	0.440118	+	0.319765i
$866$		0			0
$867$	12.0517	−	37.0912i	0.409296	−	1.25968i
$868$	2.00000			0.0678844
$869$		0			0
$870$		0			0
$871$	3.70820	−	11.4127i	0.125648	−	0.386704i
$872$		0			0
$873$	24.2705	+	17.6336i	0.821432	+	0.596806i
$874$		0			0
$875$	−2.78115	−	8.55951i	−0.0940201	−	0.289364i
$876$	−48.5410	−	35.2671i	−1.64005	−	1.19157i
$877$	30.7426	−	22.3358i	1.03811	−	0.754228i	0.0681906	−	0.997672i	$-0.478277\pi$
$877$	30.7426	−	22.3358i	1.03811	−	0.754228i	0.969915	+	0.243445i	$0.0782774\pi$
$878$		0			0
$879$	18.0000			0.607125
$880$		0			0
$881$	27.0000			0.909653			0.454827	−	0.890580i	$-0.349701\pi$
$881$	27.0000			0.909653			0.454827	+	0.890580i	$0.349701\pi$
$882$		0			0
$883$	35.5967	−	25.8626i	1.19793	−	0.870344i	0.203847	−	0.979003i	$-0.434656\pi$
$883$	35.5967	−	25.8626i	1.19793	−	0.870344i	0.994079	+	0.108659i	$0.0346555\pi$
$884$	−12.9443	−	9.40456i	−0.435363	−	0.316310i
$885$	2.78115	+	8.55951i	0.0934874	+	0.287725i
$886$		0			0
$887$	1.61803	+	1.17557i	0.0543283	+	0.0394718i	0.614618	−	0.788825i	$-0.289310\pi$
$887$	1.61803	+	1.17557i	0.0543283	+	0.0394718i	−0.560290	+	0.828297i	$0.689310\pi$
$888$		0			0
$889$	−0.618034	+	1.90211i	−0.0207282	+	0.0637948i
$890$		0			0
$891$		0			0
$892$	−2.00000			−0.0669650
$893$	−14.8328	+	45.6507i	−0.496361	+	1.52764i
$894$		0			0
$895$	0.809017	+	0.587785i	0.0270425	+	0.0196475i
$896$		0			0
$897$	−18.5410	−	57.0634i	−0.619067	−	1.90529i
$898$		0			0
$899$	−8.09017	+	5.87785i	−0.269822	+	0.196037i
$900$	14.8328	−	45.6507i	0.494427	−	1.52169i
$901$	−12.0000			−0.399778
$902$		0			0
$903$	−24.0000			−0.798670
$904$		0			0
$905$	4.04508	−	2.93893i	0.134463	−	0.0976932i
$906$		0			0
$907$	−12.3607	−	38.0423i	−0.410430	−	1.26317i	−0.916275	−	0.400549i	$-0.868820\pi$
$907$	−12.3607	−	38.0423i	−0.410430	−	1.26317i	0.505846	−	0.862624i	$-0.331180\pi$
$908$	−2.47214	−	7.60845i	−0.0820407	−	0.252495i
$909$	58.2492	+	42.3205i	1.93200	+	1.40368i
$910$		0			0
$911$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$911$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$912$	72.0000			2.38416
$913$		0			0
$914$		0			0
$915$	−1.85410	+	5.70634i	−0.0612947	+	0.188646i
$916$	−11.3262	+	8.22899i	−0.374229	+	0.271894i
$917$	14.5623	+	10.5801i	0.480890	+	0.349387i
$918$		0			0
$919$	14.8328	+	45.6507i	0.489289	+	1.50588i	0.825671	+	0.564152i	$0.190797\pi$
$919$	14.8328	+	45.6507i	0.489289	+	1.50588i	−0.336381	+	0.941726i	$0.609203\pi$
$920$		0			0
$921$	−67.9574	+	49.3740i	−2.23927	+	1.62693i
$922$		0			0
$923$	−4.00000			−0.131662
$924$		0			0
$925$	20.0000			0.657596
$926$		0			0
$927$	58.2492	−	42.3205i	1.91316	−	1.38999i
$928$		0			0
$929$	−9.27051	−	28.5317i	−0.304156	−	0.936095i	−0.979991	−	0.199042i	$-0.936217\pi$
$929$	−9.27051	−	28.5317i	−0.304156	−	0.936095i	0.675835	−	0.737053i	$-0.263783\pi$
$930$		0			0
$931$	4.85410	+	3.52671i	0.159087	+	0.115583i
$932$	9.70820	−	7.05342i	0.318003	−	0.231043i
$933$	−7.41641	+	22.8254i	−0.242802	+	0.747269i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	11.1246	−	34.2380i	0.363425	−	1.11851i	−0.587536	−	0.809198i	$-0.699902\pi$
$937$	11.1246	−	34.2380i	0.363425	−	1.11851i	0.950961	−	0.309310i	$-0.100098\pi$
$938$		0			0
$939$	−55.8222	−	40.5572i	−1.82169	−	1.32353i
$940$	4.94427	+	15.2169i	0.161264	+	0.496321i
$941$	17.9230	+	55.1613i	0.584273	+	1.79821i	0.602172	+	0.798366i	$0.294302\pi$
$941$	17.9230	+	55.1613i	0.584273	+	1.79821i	−0.0178992	+	0.999840i	$0.505698\pi$
$942$		0			0
$943$	−8.09017	+	5.87785i	−0.263452	+	0.191409i
$944$	3.70820	−	11.4127i	0.120692	−	0.371451i
$945$	−9.00000			−0.292770
$946$		0			0
$947$	5.00000			0.162478			0.0812391	−	0.996695i	$-0.474112\pi$
$947$	5.00000			0.162478			0.0812391	+	0.996695i	$0.474112\pi$
$948$	11.1246	−	34.2380i	0.361311	−	1.11200i
$949$	32.3607	−	23.5114i	1.05047	−	0.763213i
$950$		0			0
$951$	−8.34346	−	25.6785i	−0.270555	−	0.832683i
$952$		0			0
$953$	−35.5967	−	25.8626i	−1.15309	−	0.837770i	−0.164203	−	0.986427i	$-0.552505\pi$
$953$	−35.5967	−	25.8626i	−1.15309	−	0.837770i	−0.988889	+	0.148656i	$0.952505\pi$
$954$		0			0
$955$	−1.54508	+	4.75528i	−0.0499978	+	0.153877i
$956$	−8.00000			−0.258738
$957$		0			0
$958$		0			0
$959$	0.927051	−	2.85317i	0.0299360	−	0.0921337i
$960$	19.4164	−	14.1068i	0.626662	−	0.455296i
$961$	24.2705	+	17.6336i	0.782920	+	0.568824i
$962$		0			0
$963$	−18.5410	−	57.0634i	−0.597476	−	1.83884i
$964$	−19.4164	−	14.1068i	−0.625360	−	0.454351i
$965$	11.3262	−	8.22899i	0.364604	−	0.264901i
$966$		0			0
$967$	−34.0000			−1.09337			−0.546683	−	0.837340i	$-0.684110\pi$
$967$	−34.0000			−1.09337			−0.546683	+	0.837340i	$0.684110\pi$
$968$		0			0
$969$	36.0000			1.15649
$970$		0			0
$971$	−23.4615	+	17.0458i	−0.752915	+	0.547025i	−0.896729	−	0.442580i	$-0.854063\pi$
$971$	−23.4615	+	17.0458i	−0.752915	+	0.547025i	0.143814	+	0.989605i	$0.454063\pi$
$972$		0			0
$973$	3.09017	+	9.51057i	0.0990663	+	0.304895i
$974$		0			0
$975$	38.8328	+	28.2137i	1.24365	+	0.903561i
$976$	6.47214	−	4.70228i	0.207168	−	0.150516i
$977$	−9.57953	+	29.4828i	−0.306476	+	0.943237i	0.672646	+	0.739964i	$0.265158\pi$
$977$	−9.57953	+	29.4828i	−0.306476	+	0.943237i	−0.979122	+	0.203272i	$0.934842\pi$
$978$		0			0
$979$		0			0
$980$	2.00000			0.0638877
$981$	7.41641	−	22.8254i	0.236788	−	0.728758i
$982$		0			0
$983$	21.8435	+	15.8702i	0.696698	+	0.506181i	0.878855	−	0.477089i	$-0.158308\pi$
$983$	21.8435	+	15.8702i	0.696698	+	0.506181i	−0.182157	+	0.983269i	$0.558308\pi$
$984$		0			0
$985$	−5.56231	−	17.1190i	−0.177230	−	0.545457i
$986$		0			0
$987$	−19.4164	+	14.1068i	−0.618031	+	0.449026i
$988$	−14.8328	+	45.6507i	−0.471895	+	1.45234i
$989$	40.0000			1.27193
$990$		0			0
$991$	−32.0000			−1.01651			−0.508257	−	0.861206i	$-0.669710\pi$
$991$	−32.0000			−1.01651			−0.508257	+	0.861206i	$0.669710\pi$
$992$		0			0
$993$	−41.2599	+	29.9770i	−1.30934	+	0.951293i
$994$		0			0
$995$	2.47214	+	7.60845i	0.0783720	+	0.241204i
$996$	22.2492	+	68.4761i	0.704994	+	2.16975i
$997$	9.70820	+	7.05342i	0.307462	+	0.223384i	0.730807	−	0.682585i	$-0.239144\pi$
$997$	9.70820	+	7.05342i	0.307462	+	0.223384i	−0.423345	+	0.905969i	$0.639144\pi$
$998$		0			0
$999$	13.9058	−	42.7975i	0.439959	−	1.35405i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.i.372.1		4
11.2	odd	10		847.2.f.h.729.1		4
11.3	even	5	inner	847.2.f.i.323.1		4
11.4	even	5		77.2.a.a.1.1	✓	1
11.5	even	5	inner	847.2.f.i.148.1		4
11.6	odd	10		847.2.f.h.148.1		4
11.7	odd	10		847.2.a.b.1.1		1
11.8	odd	10		847.2.f.h.323.1		4
11.9	even	5	inner	847.2.f.i.729.1		4
11.10	odd	2		847.2.f.h.372.1		4
33.26	odd	10		693.2.a.c.1.1		1
33.29	even	10		7623.2.a.j.1.1		1
44.15	odd	10		1232.2.a.l.1.1		1
55.4	even	10		1925.2.a.h.1.1		1
55.37	odd	20		1925.2.b.e.1849.2		2
55.48	odd	20		1925.2.b.e.1849.1		2
77.4	even	15		539.2.e.f.177.1		2
77.26	odd	30		539.2.e.c.67.1		2
77.37	even	15		539.2.e.f.67.1		2
77.48	odd	10		539.2.a.c.1.1		1
77.59	odd	30		539.2.e.c.177.1		2
77.62	even	10		5929.2.a.f.1.1		1
88.37	even	10		4928.2.a.bj.1.1		1
88.59	odd	10		4928.2.a.a.1.1		1
231.125	even	10		4851.2.a.j.1.1		1
308.279	even	10		8624.2.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.a.a.1.1	✓	1	11.4	even	5
539.2.a.c.1.1		1	77.48	odd	10
539.2.e.c.67.1		2	77.26	odd	30
539.2.e.c.177.1		2	77.59	odd	30
539.2.e.f.67.1		2	77.37	even	15
539.2.e.f.177.1		2	77.4	even	15
693.2.a.c.1.1		1	33.26	odd	10
847.2.a.b.1.1		1	11.7	odd	10
847.2.f.h.148.1		4	11.6	odd	10
847.2.f.h.323.1		4	11.8	odd	10
847.2.f.h.372.1		4	11.10	odd	2
847.2.f.h.729.1		4	11.2	odd	10
847.2.f.i.148.1		4	11.5	even	5	inner
847.2.f.i.323.1		4	11.3	even	5	inner
847.2.f.i.372.1		4	1.1	even	1	trivial
847.2.f.i.729.1		4	11.9	even	5	inner
1232.2.a.l.1.1		1	44.15	odd	10
1925.2.a.h.1.1		1	55.4	even	10
1925.2.b.e.1849.1		2	55.48	odd	20
1925.2.b.e.1849.2		2	55.37	odd	20
4851.2.a.j.1.1		1	231.125	even	10
4928.2.a.a.1.1		1	88.59	odd	10
4928.2.a.bj.1.1		1	88.37	even	10
5929.2.a.f.1.1		1	77.62	even	10
7623.2.a.j.1.1		1	33.29	even	10
8624.2.a.a.1.1		1	308.279	even	10

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	847.2.f.i.372.1

Level	$847$
Weight	$2$
Character	847.372
Analytic conductor	$6.763$
Analytic rank	$0$
Dimension	$4$
Inner twists	$4$