LMFDB - Embedded newform 1340.2.i.c.1101.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1340,2,Mod(841,1340)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1340, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1340.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1340 = 2^{2} \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1340.i (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:	$10.6999538709$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 20 x^{14} - 11 x^{13} + 268 x^{12} - 118 x^{11} + 1854 x^{10} - 42 x^{9} + 8772 x^{8} + \cdots + 2304 $ x^16 - x^15 + 20x^14 - 11x^13 + 268x^12 - 118x^11 + 1854x^10 - 42x^9 + 8772x^8 + 23x^7 + 20578x^6 + 7075x^5 + 30422x^4 + 2273x^3 + 9145x^2 + 624x + 2304
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1101.5
Root			$-0.279640 + 0.484351i$ of defining polynomial
Character	$\chi$	$=$	1340.1101
Dual form			1340.2.i.c.841.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.559280 q^{3} -1.00000 q^{5} +(-0.701745 - 1.21546i) q^{7} -2.68721 q^{9} +O(q^{10})$	\(q+0.559280 q^{3} -1.00000 q^{5} +(-0.701745 - 1.21546i) q^{7} -2.68721 q^{9} +(1.50000 + 2.59808i) q^{11} +(2.41765 - 4.18750i) q^{13} -0.559280 q^{15} +(-3.91111 + 6.77424i) q^{17} +(2.71342 - 4.69978i) q^{19} +(-0.392472 - 0.679782i) q^{21} +(3.40758 - 5.90210i) q^{23} +1.00000 q^{25} -3.18074 q^{27} +(-4.69524 - 8.13239i) q^{29} +(-0.903279 - 1.56452i) q^{31} +(0.838921 + 1.45305i) q^{33} +(0.701745 + 1.21546i) q^{35} +(1.96341 - 3.40073i) q^{37} +(1.35215 - 2.34199i) q^{39} +(1.08009 + 1.87077i) q^{41} -10.3834 q^{43} +2.68721 q^{45} +(-5.22487 - 9.04974i) q^{47} +(2.51511 - 4.35630i) q^{49} +(-2.18741 + 3.78870i) q^{51} -10.6656 q^{53} +(-1.50000 - 2.59808i) q^{55} +(1.51756 - 2.62849i) q^{57} -5.47902 q^{59} +(5.43046 - 9.40583i) q^{61} +(1.88573 + 3.26618i) q^{63} +(-2.41765 + 4.18750i) q^{65} +(5.61753 - 5.95343i) q^{67} +(1.90579 - 3.30093i) q^{69} +(1.81315 + 3.14047i) q^{71} +(-1.65951 + 2.87436i) q^{73} +0.559280 q^{75} +(2.10523 - 3.64637i) q^{77} +(5.01450 + 8.68537i) q^{79} +6.28269 q^{81} +(-2.73577 + 4.73850i) q^{83} +(3.91111 - 6.77424i) q^{85} +(-2.62595 - 4.54828i) q^{87} -3.72067 q^{89} -6.78630 q^{91} +(-0.505186 - 0.875008i) q^{93} +(-2.71342 + 4.69978i) q^{95} +(6.34028 - 10.9817i) q^{97} +(-4.03081 - 6.98156i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} - 16 q^{5} + 30 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 - 16 * q^5 + 30 * q^9	$ 16 q - 2 q^{3} - 16 q^{5} + 30 q^{9} + 24 q^{11} + 2 q^{13} + 2 q^{15} - 3 q^{17} - 5 q^{21} + 3 q^{23} + 16 q^{25} - 14 q^{27} - 7 q^{29} + 7 q^{31} - 3 q^{33} - 11 q^{37} - 13 q^{39} - 15 q^{41} - 14 q^{43} - 30 q^{45} - 11 q^{47} - 10 q^{49} - 5 q^{51} + 12 q^{53} - 24 q^{55} + 26 q^{57} + 24 q^{59} + 9 q^{61} + 23 q^{63} - 2 q^{65} - q^{67} - q^{69} - 9 q^{71} - 13 q^{73} - 2 q^{75} + 5 q^{79} + 56 q^{81} - 8 q^{83} + 3 q^{85} + 14 q^{87} - 34 q^{89} + 30 q^{91} - 40 q^{93} + 25 q^{97} + 45 q^{99}+O(q^{100}) $ 16 * q - 2 * q^3 - 16 * q^5 + 30 * q^9 + 24 * q^11 + 2 * q^13 + 2 * q^15 - 3 * q^17 - 5 * q^21 + 3 * q^23 + 16 * q^25 - 14 * q^27 - 7 * q^29 + 7 * q^31 - 3 * q^33 - 11 * q^37 - 13 * q^39 - 15 * q^41 - 14 * q^43 - 30 * q^45 - 11 * q^47 - 10 * q^49 - 5 * q^51 + 12 * q^53 - 24 * q^55 + 26 * q^57 + 24 * q^59 + 9 * q^61 + 23 * q^63 - 2 * q^65 - q^67 - q^69 - 9 * q^71 - 13 * q^73 - 2 * q^75 + 5 * q^79 + 56 * q^81 - 8 * q^83 + 3 * q^85 + 14 * q^87 - 34 * q^89 + 30 * q^91 - 40 * q^93 + 25 * q^97 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1340\mathbb{Z}\right)^\times$.

$n$	$537$	$671$	$1141$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$2$		0			0
$3$	0.559280			0.322901			0.161450	−	0.986881i	$-0.448383\pi$
$3$	0.559280			0.322901			0.161450	+	0.986881i	$0.448383\pi$
$4$		0			0
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−0.701745	−	1.21546i	−0.265235	−	0.459400i	0.702390	−	0.711792i	$-0.252116\pi$
$7$	−0.701745	−	1.21546i	−0.265235	−	0.459400i	−0.967625	+	0.252392i	$0.918783\pi$
$8$		0			0
$9$	−2.68721			−0.895735
$10$		0			0
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$		0			0
$13$	2.41765	−	4.18750i	0.670536	−	1.16140i	−0.307216	−	0.951640i	$-0.599397\pi$
$13$	2.41765	−	4.18750i	0.670536	−	1.16140i	0.977752	−	0.209763i	$-0.0672693\pi$
$14$		0			0
$15$	−0.559280			−0.144406
$16$		0			0
$17$	−3.91111	+	6.77424i	−0.948583	+	1.64299i	−0.200170	+	0.979761i	$0.564149\pi$
$17$	−3.91111	+	6.77424i	−0.948583	+	1.64299i	−0.748413	+	0.663233i	$0.769184\pi$
$18$		0			0
$19$	2.71342	−	4.69978i	0.622501	−	1.07820i	−0.366517	−	0.930411i	$-0.619450\pi$
$19$	2.71342	−	4.69978i	0.622501	−	1.07820i	0.989018	−	0.147792i	$-0.0472167\pi$
$20$		0			0
$21$	−0.392472	−	0.679782i	−0.0856444	−	0.148340i
$22$		0			0
$23$	3.40758	−	5.90210i	0.710530	−	1.23067i	−0.254129	−	0.967170i	$-0.581789\pi$
$23$	3.40758	−	5.90210i	0.710530	−	1.23067i	0.964659	−	0.263503i	$-0.0848780\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−3.18074			−0.612134
$28$		0			0
$29$	−4.69524	−	8.13239i	−0.871883	−	1.51015i	−0.860046	−	0.510216i	$-0.829565\pi$
$29$	−4.69524	−	8.13239i	−0.871883	−	1.51015i	−0.0118371	−	0.999930i	$-0.503768\pi$
$30$		0			0
$31$	−0.903279	−	1.56452i	−0.162234	−	0.280997i	0.773436	−	0.633875i	$-0.218536\pi$
$31$	−0.903279	−	1.56452i	−0.162234	−	0.280997i	−0.935669	+	0.352878i	$0.885203\pi$
$32$		0			0
$33$	0.838921	+	1.45305i	0.146037	+	0.252944i
$34$		0			0
$35$	0.701745	+	1.21546i	0.118617	+	0.205450i
$36$		0			0
$37$	1.96341	−	3.40073i	0.322783	−	0.559076i	−0.658278	−	0.752775i	$-0.728715\pi$
$37$	1.96341	−	3.40073i	0.322783	−	0.559076i	0.981061	+	0.193698i	$0.0620483\pi$
$38$		0			0
$39$	1.35215	−	2.34199i	0.216517	−	0.375018i
$40$		0			0
$41$	1.08009	+	1.87077i	0.168682	+	0.292165i	0.937957	−	0.346753i	$-0.112716\pi$
$41$	1.08009	+	1.87077i	0.168682	+	0.292165i	−0.769275	+	0.638918i	$0.779382\pi$
$42$		0			0
$43$	−10.3834			−1.58345			−0.791726	−	0.610877i	$-0.790817\pi$
$43$	−10.3834			−1.58345			−0.791726	+	0.610877i	$0.790817\pi$
$44$		0			0
$45$	2.68721			0.400585
$46$		0			0
$47$	−5.22487	−	9.04974i	−0.762125	−	1.32004i	−0.941753	−	0.336305i	$-0.890823\pi$
$47$	−5.22487	−	9.04974i	−0.762125	−	1.32004i	0.179628	−	0.983735i	$-0.442511\pi$
$48$		0			0
$49$	2.51511	−	4.35630i	0.359301	−	0.622328i
$50$		0			0
$51$	−2.18741	+	3.78870i	−0.306298	+	0.530524i
$52$		0			0
$53$	−10.6656			−1.46504			−0.732519	−	0.680747i	$-0.761655\pi$
$53$	−10.6656			−1.46504			−0.732519	+	0.680747i	$0.761655\pi$
$54$		0			0
$55$	−1.50000	−	2.59808i	−0.202260	−	0.350325i
$56$		0			0
$57$	1.51756	−	2.62849i	0.201006	−	0.348153i
$58$		0			0
$59$	−5.47902			−0.713307			−0.356654	−	0.934237i	$-0.616082\pi$
$59$	−5.47902			−0.713307			−0.356654	+	0.934237i	$0.616082\pi$
$60$		0			0
$61$	5.43046	−	9.40583i	0.695299	−	1.20429i	−0.274781	−	0.961507i	$-0.588605\pi$
$61$	5.43046	−	9.40583i	0.695299	−	1.20429i	0.970080	−	0.242786i	$-0.0780613\pi$
$62$		0			0
$63$	1.88573	+	3.26618i	0.237580	+	0.411500i
$64$		0			0
$65$	−2.41765	+	4.18750i	−0.299873	+	0.519395i
$66$		0			0
$67$	5.61753	−	5.95343i	0.686291	−	0.727327i
$67$	5.61753	−	5.95343i	0.686291	−	0.727327i
$68$		0			0
$69$	1.90579	−	3.30093i	0.229431	−	0.397385i
$70$		0			0
$71$	1.81315	+	3.14047i	0.215182	+	0.372706i	0.953329	−	0.301934i	$-0.0976323\pi$
$71$	1.81315	+	3.14047i	0.215182	+	0.372706i	−0.738147	+	0.674640i	$0.764299\pi$
$72$		0			0
$73$	−1.65951	+	2.87436i	−0.194231	+	0.336418i	−0.946648	−	0.322269i	$-0.895555\pi$
$73$	−1.65951	+	2.87436i	−0.194231	+	0.336418i	0.752417	+	0.658687i	$0.228888\pi$
$74$		0			0
$75$	0.559280			0.0645801
$76$		0			0
$77$	2.10523	−	3.64637i	0.239914	−	0.415543i
$78$		0			0
$79$	5.01450	+	8.68537i	0.564176	+	0.977181i	0.997126	+	0.0757630i	$0.0241392\pi$
$79$	5.01450	+	8.68537i	0.564176	+	0.977181i	−0.432950	+	0.901418i	$0.642527\pi$
$80$		0			0
$81$	6.28269			0.698077
$82$		0			0
$83$	−2.73577	+	4.73850i	−0.300290	+	0.520118i	−0.976202	−	0.216865i	$-0.930417\pi$
$83$	−2.73577	+	4.73850i	−0.300290	+	0.520118i	0.675912	+	0.736983i	$0.263750\pi$
$84$		0			0
$85$	3.91111	−	6.77424i	0.424219	−	0.734769i
$86$		0			0
$87$	−2.62595	−	4.54828i	−0.281532	−	0.487627i
$88$		0			0
$89$	−3.72067			−0.394390			−0.197195	−	0.980364i	$-0.563183\pi$
$89$	−3.72067			−0.394390			−0.197195	+	0.980364i	$0.563183\pi$
$90$		0			0
$91$	−6.78630			−0.711398
$92$		0			0
$93$	−0.505186	−	0.875008i	−0.0523854	−	0.0907341i
$94$		0			0
$95$	−2.71342	+	4.69978i	−0.278391	+	0.482187i
$96$		0			0
$97$	6.34028	−	10.9817i	0.643758	−	1.11502i	−0.340829	−	0.940125i	$-0.610708\pi$
$97$	6.34028	−	10.9817i	0.643758	−	1.11502i	0.984587	−	0.174896i	$-0.0559590\pi$
$98$		0			0
$99$	−4.03081	−	6.98156i	−0.405111	−	0.701674i
$100$		0			0
$101$	6.58034	+	11.3975i	0.654768	+	1.13409i	0.981952	+	0.189131i	$0.0605671\pi$
$101$	6.58034	+	11.3975i	0.654768	+	1.13409i	−0.327184	+	0.944961i	$0.606100\pi$
$102$		0			0
$103$	−0.335075	−	0.580367i	−0.0330159	−	0.0571853i	0.849045	−	0.528320i	$-0.177178\pi$
$103$	−0.335075	−	0.580367i	−0.0330159	−	0.0571853i	−0.882061	+	0.471135i	$0.843845\pi$
$104$		0			0
$105$	0.392472	+	0.679782i	0.0383014	+	0.0663399i
$106$		0			0
$107$	6.76570			0.654065			0.327033	−	0.945013i	$-0.393951\pi$
$107$	6.76570			0.654065			0.327033	+	0.945013i	$0.393951\pi$
$108$		0			0
$109$	−12.0618			−1.15531			−0.577657	−	0.816280i	$-0.696033\pi$
$109$	−12.0618			−1.15531			−0.577657	+	0.816280i	$0.696033\pi$
$110$		0			0
$111$	1.09810	−	1.90196i	0.104227	−	0.180526i
$112$		0			0
$113$	−0.842658	−	1.45953i	−0.0792706	−	0.137301i	0.823665	−	0.567077i	$-0.191926\pi$
$113$	−0.842658	−	1.45953i	−0.0792706	−	0.137301i	−0.902935	+	0.429776i	$0.858592\pi$
$114$		0			0
$115$	−3.40758	+	5.90210i	−0.317759	+	0.550374i
$116$		0			0
$117$	−6.49673	+	11.2527i	−0.600623	+	1.04031i
$118$		0			0
$119$	10.9784			1.00639
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$	0.604072	+	1.04628i	0.0544674	+	0.0943403i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	4.61228	+	7.98871i	0.409274	+	0.708883i	0.994809	−	0.101764i	$-0.0324487\pi$
$127$	4.61228	+	7.98871i	0.409274	+	0.708883i	−0.585535	+	0.810647i	$0.699115\pi$
$128$		0			0
$129$	−5.80722			−0.511298
$130$		0			0
$131$	−2.87026			−0.250775			−0.125388	−	0.992108i	$-0.540017\pi$
$131$	−2.87026			−0.250775			−0.125388	+	0.992108i	$0.540017\pi$
$132$		0			0
$133$	−7.61651			−0.660435
$134$		0			0
$135$	3.18074			0.273755
$136$		0			0
$137$	1.06991			0.0914089			0.0457045	−	0.998955i	$-0.485447\pi$
$137$	1.06991			0.0914089			0.0457045	+	0.998955i	$0.485447\pi$
$138$		0			0
$139$	3.27617			0.277881			0.138941	−	0.990301i	$-0.455630\pi$
$139$	3.27617			0.277881			0.138941	+	0.990301i	$0.455630\pi$
$140$		0			0
$141$	−2.92217	−	5.06134i	−0.246091	−	0.426242i
$142$		0			0
$143$	14.5059			1.21305
$144$		0			0
$145$	4.69524	+	8.13239i	0.389918	+	0.675358i
$146$		0			0
$147$	1.40665	−	2.43639i	0.116019	−	0.200950i
$148$		0			0
$149$	5.68430			0.465676			0.232838	−	0.972516i	$-0.425199\pi$
$149$	5.68430			0.465676			0.232838	+	0.972516i	$0.425199\pi$
$150$		0			0
$151$	−11.9605	+	20.7162i	−0.973333	+	1.68586i	−0.288001	+	0.957630i	$0.592991\pi$
$151$	−11.9605	+	20.7162i	−0.973333	+	1.68586i	−0.685331	+	0.728232i	$0.740343\pi$
$152$		0			0
$153$	10.5100	−	18.2038i	0.849679	−	1.47169i
$154$		0			0
$155$	0.903279	+	1.56452i	0.0725531	+	0.125666i
$156$		0			0
$157$	7.92339	−	13.7237i	0.632355	−	1.09527i	−0.354714	−	0.934975i	$-0.615422\pi$
$157$	7.92339	−	13.7237i	0.632355	−	1.09527i	0.987069	−	0.160296i	$-0.0512450\pi$
$158$		0			0
$159$	−5.96508			−0.473062
$160$		0			0
$161$	−9.56501			−0.753828
$162$		0			0
$163$	−0.989517	−	1.71389i	−0.0775049	−	0.134242i	0.824668	−	0.565617i	$-0.191362\pi$
$163$	−0.989517	−	1.71389i	−0.0775049	−	0.134242i	−0.902173	+	0.431375i	$0.858029\pi$
$164$		0			0
$165$	−0.838921	−	1.45305i	−0.0653099	−	0.113120i
$166$		0			0
$167$	−3.64229	−	6.30863i	−0.281849	−	0.488176i	0.689991	−	0.723818i	$-0.257614\pi$
$167$	−3.64229	−	6.30863i	−0.281849	−	0.488176i	−0.971840	+	0.235641i	$0.924281\pi$
$168$		0			0
$169$	−5.19009	−	8.98950i	−0.399238	−	0.691500i
$170$		0			0
$171$	−7.29151	+	12.6293i	−0.557596	+	0.965785i
$172$		0			0
$173$	11.1055	−	19.2353i	0.844337	−	1.46243i	−0.0418586	−	0.999124i	$-0.513328\pi$
$173$	11.1055	−	19.2353i	0.844337	−	1.46243i	0.886196	−	0.463311i	$-0.153339\pi$
$174$		0			0
$175$	−0.701745	−	1.21546i	−0.0530469	−	0.0918799i
$176$		0			0
$177$	−3.06431			−0.230327
$178$		0			0
$179$	3.75877			0.280944			0.140472	−	0.990085i	$-0.455138\pi$
$179$	3.75877			0.280944			0.140472	+	0.990085i	$0.455138\pi$
$180$		0			0
$181$	5.91250	+	10.2408i	0.439473	+	0.761189i	0.997649	−	0.0685335i	$-0.0218320\pi$
$181$	5.91250	+	10.2408i	0.439473	+	0.761189i	−0.558176	+	0.829722i	$0.688499\pi$
$182$		0			0
$183$	3.03715	−	5.26050i	0.224512	−	0.388867i
$184$		0			0
$185$	−1.96341	+	3.40073i	−0.144353	+	0.250027i
$186$		0			0
$187$	−23.4666			−1.71605
$188$		0			0
$189$	2.23207	+	3.86606i	0.162359	+	0.281214i
$190$		0			0
$191$	6.61534	−	11.4581i	0.478669	−	0.829080i	−0.521032	−	0.853537i	$-0.674453\pi$
$191$	6.61534	−	11.4581i	0.478669	−	0.829080i	0.999701	+	0.0244579i	$0.00778595\pi$
$192$		0			0
$193$	3.23362			0.232761			0.116380	−	0.993205i	$-0.462871\pi$
$193$	3.23362			0.232761			0.116380	+	0.993205i	$0.462871\pi$
$194$		0			0
$195$	−1.35215	+	2.34199i	−0.0968292	+	0.167713i
$196$		0			0
$197$	−2.55381	−	4.42333i	−0.181951	−	0.315149i	0.760594	−	0.649228i	$-0.224908\pi$
$197$	−2.55381	−	4.42333i	−0.181951	−	0.315149i	−0.942545	+	0.334079i	$0.891575\pi$
$198$		0			0
$199$	−6.61691	+	11.4608i	−0.469061	+	0.812437i	−0.999374	−	0.0353647i	$-0.988741\pi$
$199$	−6.61691	+	11.4608i	−0.469061	+	0.812437i	0.530314	+	0.847801i	$0.322074\pi$
$200$		0			0
$201$	3.14178	−	3.32964i	0.221604	−	0.234854i
$202$		0			0
$203$	−6.58971	+	11.4137i	−0.462507	+	0.801086i
$204$		0			0
$205$	−1.08009	−	1.87077i	−0.0754367	−	0.130660i
$206$		0			0
$207$	−9.15687	+	15.8602i	−0.636446	+	1.10236i
$208$		0			0
$209$	16.2805			1.12615
$210$		0			0
$211$	2.41192	−	4.17756i	0.166043	−	0.287595i	−0.770982	−	0.636857i	$-0.780234\pi$
$211$	2.41192	−	4.17756i	0.166043	−	0.287595i	0.937025	+	0.349262i	$0.113568\pi$
$212$		0			0
$213$	1.01406	+	1.75641i	0.0694823	+	0.120347i
$214$		0			0
$215$	10.3834			0.708141
$216$		0			0
$217$	−1.26774	+	2.19579i	−0.0860599	+	0.149060i
$218$		0			0
$219$	−0.928133	+	1.60757i	−0.0627174	+	0.108630i
$220$		0			0
$221$	18.9114	+	32.7555i	1.27212	+	2.20337i
$222$		0			0
$223$	−17.2990			−1.15843			−0.579213	−	0.815177i	$-0.696640\pi$
$223$	−17.2990			−1.15843			−0.579213	+	0.815177i	$0.696640\pi$
$224$		0			0
$225$	−2.68721			−0.179147
$226$		0			0
$227$	−0.848807	−	1.47018i	−0.0563373	−	0.0975790i	0.836481	−	0.547995i	$-0.184609\pi$
$227$	−0.848807	−	1.47018i	−0.0563373	−	0.0975790i	−0.892819	+	0.450416i	$0.851276\pi$
$228$		0			0
$229$	−8.74310	+	15.1435i	−0.577761	+	1.00071i	0.417975	+	0.908458i	$0.362740\pi$
$229$	−8.74310	+	15.1435i	−0.577761	+	1.00071i	−0.995736	+	0.0922522i	$0.970593\pi$
$230$		0			0
$231$	1.17742	−	2.03934i	0.0774683	−	0.134179i
$232$		0			0
$233$	2.09796	+	3.63378i	0.137442	+	0.238057i	0.926528	−	0.376227i	$-0.122779\pi$
$233$	2.09796	+	3.63378i	0.137442	+	0.238057i	−0.789086	+	0.614283i	$0.789445\pi$
$234$		0			0
$235$	5.22487	+	9.04974i	0.340833	+	0.590340i
$236$		0			0
$237$	2.80451	+	4.85756i	0.182173	+	0.315532i
$238$		0			0
$239$	6.64078	+	11.5022i	0.429556	+	0.744014i	0.996834	−	0.0795133i	$-0.0253366\pi$
$239$	6.64078	+	11.5022i	0.429556	+	0.744014i	−0.567277	+	0.823527i	$0.692003\pi$
$240$		0			0
$241$	−15.1368			−0.975044			−0.487522	−	0.873111i	$-0.662099\pi$
$241$	−15.1368			−0.975044			−0.487522	+	0.873111i	$0.662099\pi$
$242$		0			0
$243$	13.0560			0.837544
$244$		0			0
$245$	−2.51511	+	4.35630i	−0.160684	+	0.278314i
$246$		0			0
$247$	−13.1202	−	22.7249i	−0.834819	−	1.44595i
$248$		0			0
$249$	−1.53006	+	2.65015i	−0.0969638	+	0.167946i
$250$		0			0
$251$	−14.6331	+	25.3453i	−0.923633	+	1.59978i	−0.129888	+	0.991529i	$0.541462\pi$
$251$	−14.6331	+	25.3453i	−0.923633	+	1.59978i	−0.793745	+	0.608251i	$0.791871\pi$
$252$		0			0
$253$	20.4455			1.28540
$254$		0			0
$255$	2.18741	−	3.78870i	0.136981	−	0.237257i
$256$		0			0
$257$	0.226493	+	0.392298i	0.0141283	+	0.0244709i	0.873003	−	0.487715i	$-0.162169\pi$
$257$	0.226493	+	0.392298i	0.0141283	+	0.0244709i	−0.858875	+	0.512186i	$0.828836\pi$
$258$		0			0
$259$	−5.51125			−0.342453
$260$		0			0
$261$	12.6171	+	21.8534i	0.780976	+	1.35269i
$262$		0			0
$263$	−24.3357			−1.50060			−0.750302	−	0.661095i	$-0.770092\pi$
$263$	−24.3357			−1.50060			−0.750302	+	0.661095i	$0.770092\pi$
$264$		0			0
$265$	10.6656			0.655185
$266$		0			0
$267$	−2.08090			−0.127349
$268$		0			0
$269$	32.0398			1.95350			0.976752	−	0.214372i	$-0.0687706\pi$
$269$	32.0398			1.95350			0.976752	+	0.214372i	$0.0687706\pi$
$270$		0			0
$271$	0.00555326			0.000337337			0.000168668	−	1.00000i	$-0.499946\pi$
$271$	0.00555326			0.000337337			0.000168668		1.00000i	$0.499946\pi$
$272$		0			0
$273$	−3.79544			−0.229711
$274$		0			0
$275$	1.50000	+	2.59808i	0.0904534	+	0.156670i
$276$		0			0
$277$	10.3158			0.619813			0.309907	−	0.950767i	$-0.399702\pi$
$277$	10.3158			0.619813			0.309907	+	0.950767i	$0.399702\pi$
$278$		0			0
$279$	2.42730	+	4.20420i	0.145318	+	0.251699i
$280$		0			0
$281$	10.2661	−	17.7813i	0.612422	−	1.06075i	−0.378409	−	0.925639i	$-0.623529\pi$
$281$	10.2661	−	17.7813i	0.612422	−	1.06075i	0.990831	−	0.135108i	$-0.0431381\pi$
$282$		0			0
$283$	−7.53107			−0.447676			−0.223838	−	0.974626i	$-0.571859\pi$
$283$	−7.53107			−0.447676			−0.223838	+	0.974626i	$0.571859\pi$
$284$		0			0
$285$	−1.51756	+	2.62849i	−0.0898926	+	0.155699i
$286$		0			0
$287$	1.51589	−	2.62560i	0.0894803	−	0.154984i
$288$		0			0
$289$	−22.0935	−	38.2671i	−1.29962	−	2.25101i
$290$		0			0
$291$	3.54600	−	6.14184i	0.207870	−	0.360041i
$292$		0			0
$293$	23.1034			1.34972			0.674858	−	0.737948i	$-0.264205\pi$
$293$	23.1034			1.34972			0.674858	+	0.737948i	$0.264205\pi$
$294$		0			0
$295$	5.47902			0.319001
$296$		0			0
$297$	−4.77111	−	8.26381i	−0.276848	−	0.479515i
$298$		0			0
$299$	−16.4767	−	28.5385i	−0.952872	−	1.65042i
$300$		0			0
$301$	7.28649	+	12.6206i	0.419986	+	0.727437i
$302$		0			0
$303$	3.68026	+	6.37439i	0.211425	+	0.366199i
$304$		0			0
$305$	−5.43046	+	9.40583i	−0.310947	+	0.538576i
$306$		0			0
$307$	2.32042	−	4.01909i	0.132434	−	0.229382i	−0.792181	−	0.610287i	$-0.791054\pi$
$307$	2.32042	−	4.01909i	0.132434	−	0.229382i	0.924614	+	0.380905i	$0.124388\pi$
$308$		0			0
$309$	−0.187401	−	0.324588i	−0.0106609	−	0.0184652i
$310$		0			0
$311$	21.3353			1.20982			0.604908	−	0.796295i	$-0.293210\pi$
$311$	21.3353			1.20982			0.604908	+	0.796295i	$0.293210\pi$
$312$		0			0
$313$	6.77567			0.382984			0.191492	−	0.981494i	$-0.438667\pi$
$313$	6.77567			0.382984			0.191492	+	0.981494i	$0.438667\pi$
$314$		0			0
$315$	−1.88573	−	3.26618i	−0.106249	−	0.184029i
$316$		0			0
$317$	−2.16828	+	3.75557i	−0.121783	+	0.210934i	−0.920471	−	0.390812i	$-0.872194\pi$
$317$	−2.16828	+	3.75557i	−0.121783	+	0.210934i	0.798688	+	0.601745i	$0.205528\pi$
$318$		0			0
$319$	14.0857	−	24.3972i	0.788648	−	1.36598i
$320$		0			0
$321$	3.78393			0.211198
$322$		0			0
$323$	21.2250	+	36.7627i	1.18099	+	2.04553i
$324$		0			0
$325$	2.41765	−	4.18750i	0.134107	−	0.232281i
$326$		0			0
$327$	−6.74595			−0.373052
$328$		0			0
$329$	−7.33305	+	12.7012i	−0.404284	+	0.700240i
$330$		0			0
$331$	11.9836	+	20.7563i	0.658681	+	1.14087i	0.980957	+	0.194223i	$0.0622185\pi$
$331$	11.9836	+	20.7563i	0.658681	+	1.14087i	−0.322277	+	0.946645i	$0.604448\pi$
$332$		0			0
$333$	−5.27609	+	9.13846i	−0.289128	+	0.500784i
$334$		0			0
$335$	−5.61753	+	5.95343i	−0.306919	+	0.325271i
$336$		0			0
$337$	12.6311	−	21.8778i	0.688062	−	1.19176i	−0.284402	−	0.958705i	$-0.591795\pi$
$337$	12.6311	−	21.8778i	0.688062	−	1.19176i	0.972464	−	0.233053i	$-0.0748715\pi$
$338$		0			0
$339$	−0.471282	−	0.816285i	−0.0255965	−	0.0443345i
$340$		0			0
$341$	2.70984	−	4.69357i	0.146746	−	0.254171i
$342$		0			0
$343$	−16.8843			−0.911666
$344$		0			0
$345$	−1.90579	+	3.30093i	−0.102604	+	0.177716i
$346$		0			0
$347$	7.56280	+	13.0992i	0.405992	+	0.703200i	0.994436	−	0.105338i	$-0.0335926\pi$
$347$	7.56280	+	13.0992i	0.405992	+	0.703200i	−0.588444	+	0.808538i	$0.700259\pi$
$348$		0			0
$349$	10.7671			0.576351			0.288176	−	0.957578i	$-0.406951\pi$
$349$	10.7671			0.576351			0.288176	+	0.957578i	$0.406951\pi$
$350$		0			0
$351$	−7.68993	+	13.3194i	−0.410458	+	0.710934i
$352$		0			0
$353$	−10.1499	+	17.5801i	−0.540224	+	0.935695i	0.458667	+	0.888608i	$0.348327\pi$
$353$	−10.1499	+	17.5801i	−0.540224	+	0.935695i	−0.998891	+	0.0470868i	$0.985006\pi$
$354$		0			0
$355$	−1.81315	−	3.14047i	−0.0962322	−	0.166679i
$356$		0			0
$357$	6.14000			0.324963
$358$		0			0
$359$	−21.2329			−1.12063			−0.560316	−	0.828279i	$-0.689320\pi$
$359$	−21.2329			−1.12063			−0.560316	+	0.828279i	$0.689320\pi$
$360$		0			0
$361$	−5.22529	−	9.05046i	−0.275015	−	0.476340i
$362$		0			0
$363$	0.559280	−	0.968702i	0.0293546	−	0.0508437i
$364$		0			0
$365$	1.65951	−	2.87436i	0.0868629	−	0.150451i
$366$		0			0
$367$	4.89829	+	8.48409i	0.255689	+	0.442866i	0.965082	−	0.261947i	$-0.0843645\pi$
$367$	4.89829	+	8.48409i	0.255689	+	0.442866i	−0.709394	+	0.704812i	$0.751031\pi$
$368$		0			0
$369$	−2.90242	−	5.02714i	−0.151094	−	0.261702i
$370$		0			0
$371$	7.48455	+	12.9636i	0.388579	+	0.673038i
$372$		0			0
$373$	−12.7980	−	22.1668i	−0.662656	−	1.14775i	−0.979915	−	0.199415i	$-0.936096\pi$
$373$	−12.7980	−	22.1668i	−0.662656	−	1.14775i	0.317259	−	0.948339i	$-0.397238\pi$
$374$		0			0
$375$	−0.559280			−0.0288811
$376$		0			0
$377$	−45.4058			−2.33852
$378$		0			0
$379$	4.72249	−	8.17959i	0.242578	−	0.420158i	−0.718870	−	0.695145i	$-0.755340\pi$
$379$	4.72249	−	8.17959i	0.242578	−	0.420158i	0.961448	+	0.274987i	$0.0886736\pi$
$380$		0			0
$381$	2.57956	+	4.46793i	0.132155	+	0.228899i
$382$		0			0
$383$	−13.7639	+	23.8398i	−0.703303	+	1.21816i	0.263997	+	0.964523i	$0.414959\pi$
$383$	−13.7639	+	23.8398i	−0.703303	+	1.21816i	−0.967300	+	0.253634i	$0.918374\pi$
$384$		0			0
$385$	−2.10523	+	3.64637i	−0.107293	+	0.185836i
$386$		0			0
$387$	27.9023			1.41835
$388$		0			0
$389$	−4.25337	+	7.36705i	−0.215654	+	0.373524i	−0.953475	−	0.301473i	$-0.902522\pi$
$389$	−4.25337	+	7.36705i	−0.215654	+	0.373524i	0.737820	+	0.674997i	$0.235855\pi$
$390$		0			0
$391$	26.6548	+	46.1675i	1.34799	+	2.33479i
$392$		0			0
$393$	−1.60528			−0.0809756
$394$		0			0
$395$	−5.01450	−	8.68537i	−0.252307	−	0.437009i
$396$		0			0
$397$	−31.3649			−1.57416			−0.787079	−	0.616852i	$-0.788408\pi$
$397$	−31.3649			−1.57416			−0.787079	+	0.616852i	$0.788408\pi$
$398$		0			0
$399$	−4.25977			−0.213255
$400$		0			0
$401$	−21.5816			−1.07773			−0.538866	−	0.842391i	$-0.681147\pi$
$401$	−21.5816			−1.07773			−0.538866	+	0.842391i	$0.681147\pi$
$402$		0			0
$403$	−8.73526			−0.435134
$404$		0			0
$405$	−6.28269			−0.312189
$406$		0			0
$407$	11.7805			0.583936
$408$		0			0
$409$	10.3327	+	17.8968i	0.510919	+	0.884938i	0.999920	+	0.0126545i	$0.00402816\pi$
$409$	10.3327	+	17.8968i	0.510919	+	0.884938i	−0.489001	+	0.872283i	$0.662639\pi$
$410$		0			0
$411$	0.598382			0.0295160
$412$		0			0
$413$	3.84487	+	6.65951i	0.189194	+	0.327693i
$414$		0			0
$415$	2.73577	−	4.73850i	0.134294	−	0.232604i
$416$		0			0
$417$	1.83230			0.0897280
$418$		0			0
$419$	−14.3052	+	24.7774i	−0.698856	+	1.21045i	0.270007	+	0.962858i	$0.412974\pi$
$419$	−14.3052	+	24.7774i	−0.698856	+	1.21045i	−0.968863	+	0.247596i	$0.920359\pi$
$420$		0			0
$421$	9.11798	−	15.7928i	0.444383	−	0.769694i	−0.553626	−	0.832765i	$-0.686756\pi$
$421$	9.11798	−	15.7928i	0.444383	−	0.769694i	0.998009	+	0.0630715i	$0.0200896\pi$
$422$		0			0
$423$	14.0403	+	24.3185i	0.682662	+	1.18241i
$424$		0			0
$425$	−3.91111	+	6.77424i	−0.189717	+	0.328599i
$426$		0			0
$427$	−15.2432			−0.737669
$428$		0			0
$429$	8.11288			0.391693
$430$		0			0
$431$	5.55465	+	9.62094i	0.267558	+	0.463424i	0.968231	−	0.250059i	$-0.0804499\pi$
$431$	5.55465	+	9.62094i	0.267558	+	0.463424i	−0.700673	+	0.713483i	$0.747117\pi$
$432$		0			0
$433$	−10.7272	−	18.5801i	−0.515518	−	0.892904i	−0.999838	−	0.0180126i	$-0.994266\pi$
$433$	−10.7272	−	18.5801i	−0.515518	−	0.892904i	0.484319	−	0.874891i	$-0.339067\pi$
$434$		0			0
$435$	2.62595	+	4.54828i	0.125905	+	0.218074i
$436$		0			0
$437$	−18.4924	−	32.0298i	−0.884611	−	1.53219i
$438$		0			0
$439$	2.13314	−	3.69471i	0.101809	−	0.176339i	−0.810621	−	0.585571i	$-0.800870\pi$
$439$	2.13314	−	3.69471i	0.101809	−	0.176339i	0.912430	+	0.409233i	$0.134204\pi$
$440$		0			0
$441$	−6.75861	+	11.7063i	−0.321839	+	0.557441i
$442$		0			0
$443$	−3.66691	−	6.35127i	−0.174220	−	0.301758i	0.765671	−	0.643232i	$-0.222407\pi$
$443$	−3.66691	−	6.35127i	−0.174220	−	0.301758i	−0.939891	+	0.341474i	$0.889074\pi$
$444$		0			0
$445$	3.72067			0.176377
$446$		0			0
$447$	3.17912			0.150367
$448$		0			0
$449$	18.7570	+	32.4881i	0.885198	+	1.53321i	0.845487	+	0.533996i	$0.179310\pi$
$449$	18.7570	+	32.4881i	0.885198	+	1.53321i	0.0397109	+	0.999211i	$0.487356\pi$
$450$		0			0
$451$	−3.24027	+	5.61231i	−0.152578	+	0.264273i
$452$		0			0
$453$	−6.68928	+	11.5862i	−0.314290	+	0.544366i
$454$		0			0
$455$	6.78630			0.318147
$456$		0			0
$457$	8.46325	+	14.6588i	0.395894	+	0.685709i	0.993215	−	0.116294i	$-0.0371014\pi$
$457$	8.46325	+	14.6588i	0.395894	+	0.685709i	−0.597321	+	0.802002i	$0.703768\pi$
$458$		0			0
$459$	12.4402	−	21.5471i	0.580660	−	1.00573i
$460$		0			0
$461$	36.2103			1.68648			0.843241	−	0.537536i	$-0.180645\pi$
$461$	36.2103			1.68648			0.843241	+	0.537536i	$0.180645\pi$
$462$		0			0
$463$	−6.85813	+	11.8786i	−0.318724	+	0.552047i	−0.980222	−	0.197900i	$-0.936588\pi$
$463$	−6.85813	+	11.8786i	−0.318724	+	0.552047i	0.661498	+	0.749947i	$0.269921\pi$
$464$		0			0
$465$	0.505186	+	0.875008i	0.0234274	+	0.0405775i
$466$		0			0
$467$	9.61971	−	16.6618i	0.445147	−	0.771017i	−0.552915	−	0.833237i	$-0.686485\pi$
$467$	9.61971	−	16.6618i	0.445147	−	0.771017i	0.998062	+	0.0622201i	$0.0198181\pi$
$468$		0			0
$469$	−11.1782	−	2.65009i	−0.516162	−	0.122370i
$470$		0			0
$471$	4.43140	−	7.67540i	0.204188	−	0.353664i
$472$		0			0
$473$	−15.5751	−	26.9768i	−0.716143	−	1.24040i
$474$		0			0
$475$	2.71342	−	4.69978i	0.124500	−	0.215641i
$476$		0			0
$477$	28.6607			1.31229
$478$		0			0
$479$	−4.47176	+	7.74532i	−0.204320	+	0.353893i	−0.949916	−	0.312506i	$-0.898832\pi$
$479$	−4.47176	+	7.74532i	−0.204320	+	0.353893i	0.745596	+	0.666398i	$0.232165\pi$
$480$		0			0
$481$	−9.49369	−	16.4436i	−0.432875	−	0.749762i
$482$		0			0
$483$	−5.34952			−0.243412
$484$		0			0
$485$	−6.34028	+	10.9817i	−0.287897	+	0.498653i
$486$		0			0
$487$	2.51298	−	4.35261i	0.113874	−	0.197235i	−0.803455	−	0.595365i	$-0.797007\pi$
$487$	2.51298	−	4.35261i	0.113874	−	0.197235i	0.917329	+	0.398130i	$0.130341\pi$
$488$		0			0
$489$	−0.553417	−	0.958547i	−0.0250264	−	0.0433470i
$490$		0			0
$491$	24.7814			1.11837			0.559184	−	0.829043i	$-0.311114\pi$
$491$	24.7814			1.11837			0.559184	+	0.829043i	$0.311114\pi$
$492$		0			0
$493$	73.4543			3.30821
$494$		0			0
$495$	4.03081	+	6.98156i	0.181171	+	0.313798i
$496$		0			0
$497$	2.54474	−	4.40762i	0.114147	−	0.197709i
$498$		0			0
$499$	12.8756	−	22.3011i	0.576390	−	0.998336i	−0.419500	−	0.907756i	$-0.637794\pi$
$499$	12.8756	−	22.3011i	0.576390	−	0.998336i	0.995889	−	0.0905805i	$-0.0288723\pi$
$500$		0			0
$501$	−2.03706	−	3.52829i	−0.0910092	−	0.157633i
$502$		0			0
$503$	−18.3258	−	31.7412i	−0.817107	−	1.41527i	−0.907805	−	0.419393i	$-0.862243\pi$
$503$	−18.3258	−	31.7412i	−0.817107	−	1.41527i	0.0906979	−	0.995878i	$-0.471090\pi$
$504$		0			0
$505$	−6.58034	−	11.3975i	−0.292821	−	0.507181i
$506$		0			0
$507$	−2.90272	−	5.02765i	−0.128914	−	0.223286i
$508$		0			0
$509$	−3.61979			−0.160444			−0.0802222	−	0.996777i	$-0.525563\pi$
$509$	−3.61979			−0.160444			−0.0802222	+	0.996777i	$0.525563\pi$
$510$		0			0
$511$	4.65822			0.206067
$512$		0			0
$513$	−8.63069	+	14.9488i	−0.381054	+	0.660005i
$514$		0			0
$515$	0.335075	+	0.580367i	0.0147652	+	0.0255740i
$516$		0			0
$517$	15.6746	−	27.1492i	0.689368	−	1.19402i
$518$		0			0
$519$	6.21110	−	10.7579i	0.272637	−	0.472221i
$520$		0			0
$521$	−31.9578			−1.40009			−0.700047	−	0.714096i	$-0.746838\pi$
$521$	−31.9578			−1.40009			−0.700047	+	0.714096i	$0.746838\pi$
$522$		0			0
$523$	1.90603	−	3.30134i	0.0833449	−	0.144358i	−0.821340	−	0.570439i	$-0.806773\pi$
$523$	1.90603	−	3.30134i	0.0833449	−	0.144358i	0.904685	+	0.426082i	$0.140106\pi$
$524$		0			0
$525$	−0.392472	−	0.679782i	−0.0171289	−	0.0296681i
$526$		0			0
$527$	14.1313			0.615568
$528$		0			0
$529$	−11.7232	−	20.3052i	−0.509705	−	0.882835i
$530$		0			0
$531$	14.7232			0.638934
$532$		0			0
$533$	10.4451			0.452428
$534$		0			0
$535$	−6.76570			−0.292507
$536$		0			0
$537$	2.10221			0.0907169
$538$		0			0
$539$	15.0907			0.650000
$540$		0			0
$541$	−20.3102			−0.873203			−0.436602	−	0.899655i	$-0.643818\pi$
$541$	−20.3102			−0.873203			−0.436602	+	0.899655i	$0.643818\pi$
$542$		0			0
$543$	3.30675	+	5.72745i	0.141906	+	0.245788i
$544$		0			0
$545$	12.0618			0.516672
$546$		0			0
$547$	−14.9731	−	25.9342i	−0.640205	−	1.10887i	−0.985387	−	0.170332i	$-0.945516\pi$
$547$	−14.9731	−	25.9342i	−0.640205	−	1.10887i	0.345182	−	0.938536i	$-0.387817\pi$
$548$		0			0
$549$	−14.5928	+	25.2754i	−0.622804	+	1.07873i
$550$		0			0
$551$	−50.9606			−2.17099
$552$		0			0
$553$	7.03780	−	12.1898i	0.299278	−	0.518364i
$554$		0			0
$555$	−1.09810	+	1.90196i	−0.0466116	+	0.0807337i
$556$		0			0
$557$	−10.7497	−	18.6190i	−0.455478	−	0.788911i	0.543238	−	0.839579i	$-0.317198\pi$
$557$	−10.7497	−	18.6190i	−0.455478	−	0.788911i	−0.998716	+	0.0506683i	$0.983865\pi$
$558$		0			0
$559$	−25.1034	+	43.4804i	−1.06176	+	1.83902i
$560$		0			0
$561$	−13.1244			−0.554114
$562$		0			0
$563$	−30.2986			−1.27693			−0.638467	−	0.769649i	$-0.720431\pi$
$563$	−30.2986			−1.27693			−0.638467	+	0.769649i	$0.720431\pi$
$564$		0			0
$565$	0.842658	+	1.45953i	0.0354509	+	0.0614028i
$566$		0			0
$567$	−4.40884	−	7.63634i	−0.185154	−	0.320696i
$568$		0			0
$569$	−3.11569	−	5.39653i	−0.130616	−	0.226234i	0.793298	−	0.608834i	$-0.208362\pi$
$569$	−3.11569	−	5.39653i	−0.130616	−	0.226234i	−0.923914	+	0.382599i	$0.875029\pi$
$570$		0			0
$571$	−2.91014	−	5.04052i	−0.121786	−	0.210939i	0.798686	−	0.601748i	$-0.205529\pi$
$571$	−2.91014	−	5.04052i	−0.121786	−	0.210939i	−0.920472	+	0.390809i	$0.872195\pi$
$572$		0			0
$573$	3.69983	−	6.40830i	0.154563	−	0.267710i
$574$		0			0
$575$	3.40758	−	5.90210i	0.142106	−	0.246135i
$576$		0			0
$577$	1.26330	+	2.18810i	0.0525918	+	0.0910917i	0.891123	−	0.453762i	$-0.149918\pi$
$577$	1.26330	+	2.18810i	0.0525918	+	0.0910917i	−0.838531	+	0.544854i	$0.816585\pi$
$578$		0			0
$579$	1.80850			0.0751586
$580$		0			0
$581$	7.67925			0.318589
$582$		0			0
$583$	−15.9985	−	27.7101i	−0.662588	−	1.14764i
$584$		0			0
$585$	6.49673	−	11.2527i	0.268607	−	0.465240i
$586$		0			0
$587$	−7.00376	+	12.1309i	−0.289076	+	0.500694i	−0.973589	−	0.228306i	$-0.926681\pi$
$587$	−7.00376	+	12.1309i	−0.289076	+	0.500694i	0.684514	+	0.729000i	$0.260015\pi$
$588$		0			0
$589$	−9.80390			−0.403962
$590$		0			0
$591$	−1.42829	−	2.47388i	−0.0587522	−	0.101762i
$592$		0			0
$593$	17.2103	−	29.8092i	0.706744	−	1.22412i	−0.259314	−	0.965793i	$-0.583497\pi$
$593$	17.2103	−	29.8092i	0.706744	−	1.22412i	0.966058	−	0.258324i	$-0.0831701\pi$
$594$		0			0
$595$	−10.9784			−0.450070
$596$		0			0
$597$	−3.70071	+	6.40982i	−0.151460	+	0.262336i
$598$		0			0
$599$	−15.9280	−	27.5882i	−0.650802	−	1.12722i	−0.982929	−	0.183988i	$-0.941099\pi$
$599$	−15.9280	−	27.5882i	−0.650802	−	1.12722i	0.332126	−	0.943235i	$-0.392234\pi$
$600$		0			0
$601$	−5.99841	+	10.3896i	−0.244680	+	0.423799i	−0.962042	−	0.272903i	$-0.912016\pi$
$601$	−5.99841	+	10.3896i	−0.244680	+	0.423799i	0.717361	+	0.696701i	$0.245350\pi$
$602$		0			0
$603$	−15.0955	+	15.9981i	−0.614735	+	0.651492i
$604$		0			0
$605$	−1.00000	+	1.73205i	−0.0406558	+	0.0704179i
$606$		0			0
$607$	7.83139	+	13.5644i	0.317866	+	0.550561i	0.980043	−	0.198787i	$-0.0637003\pi$
$607$	7.83139	+	13.5644i	0.317866	+	0.550561i	−0.662176	+	0.749348i	$0.730367\pi$
$608$		0			0
$609$	−3.68550	+	6.38347i	−0.149344	+	0.258671i
$610$		0			0
$611$	−50.5277			−2.04413
$612$		0			0
$613$	15.2632	−	26.4367i	0.616476	−	1.06777i	−0.373648	−	0.927571i	$-0.621893\pi$
$613$	15.2632	−	26.4367i	0.616476	−	1.06777i	0.990124	−	0.140197i	$-0.0447736\pi$
$614$		0			0
$615$	−0.604072	−	1.04628i	−0.0243586	−	0.0421903i
$616$		0			0
$617$	31.1638			1.25461			0.627304	−	0.778774i	$-0.284158\pi$
$617$	31.1638			1.25461			0.627304	+	0.778774i	$0.284158\pi$
$618$		0			0
$619$	20.5986	−	35.6779i	0.827929	−	1.43401i	−0.0717318	−	0.997424i	$-0.522853\pi$
$619$	20.5986	−	35.6779i	0.827929	−	1.43401i	0.899660	−	0.436590i	$-0.143814\pi$
$620$		0			0
$621$	−10.8386	+	18.7731i	−0.434940	+	0.753337i
$622$		0			0
$623$	2.61096	+	4.52232i	0.104606	+	0.181183i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	9.10537			0.363634
$628$		0			0
$629$	15.3582	+	26.6012i	0.612373	+	1.06066i
$630$		0			0
$631$	22.5614	−	39.0776i	0.898157	−	1.55565i	0.0683085	−	0.997664i	$-0.478240\pi$
$631$	22.5614	−	39.0776i	0.898157	−	1.55565i	0.829848	−	0.557989i	$-0.188427\pi$
$632$		0			0
$633$	1.34894	−	2.33643i	0.0536155	−	0.0928647i
$634$		0			0
$635$	−4.61228	−	7.98871i	−0.183033	−	0.317022i
$636$		0			0
$637$	−12.1613	−	21.0640i	−0.481849	−	0.834587i
$638$		0			0
$639$	−4.87232	−	8.43910i	−0.192746	−	0.333846i
$640$		0			0
$641$	−2.95234	−	5.11360i	−0.116610	−	0.201975i	0.801812	−	0.597576i	$-0.203870\pi$
$641$	−2.95234	−	5.11360i	−0.116610	−	0.201975i	−0.918422	+	0.395601i	$0.870536\pi$
$642$		0			0
$643$	−27.8955			−1.10009			−0.550045	−	0.835135i	$-0.685389\pi$
$643$	−27.8955			−1.10009			−0.550045	+	0.835135i	$0.685389\pi$
$644$		0			0
$645$	5.80722			0.228659
$646$		0			0
$647$	8.42926	−	14.5999i	0.331388	−	0.573982i	−0.651396	−	0.758738i	$-0.725816\pi$
$647$	8.42926	−	14.5999i	0.331388	−	0.573982i	0.982784	+	0.184756i	$0.0591496\pi$
$648$		0			0
$649$	−8.21853	−	14.2349i	−0.322605	−	0.558769i
$650$		0			0
$651$	−0.709023	+	1.22806i	−0.0277888	+	0.0481316i
$652$		0			0
$653$	12.6108	−	21.8425i	0.493497	−	0.854762i	−0.506475	−	0.862255i	$-0.669052\pi$
$653$	12.6108	−	21.8425i	0.493497	−	0.854762i	0.999972	+	0.00749286i	$0.00238507\pi$
$654$		0			0
$655$	2.87026			0.112150
$656$		0			0
$657$	4.45945	−	7.72400i	0.173980	−	0.301342i
$658$		0			0
$659$	15.0415	+	26.0526i	0.585933	+	1.01487i	0.994758	+	0.102253i	$0.0326052\pi$
$659$	15.0415	+	26.0526i	0.585933	+	1.01487i	−0.408825	+	0.912613i	$0.634061\pi$
$660$		0			0
$661$	7.27105			0.282811			0.141406	−	0.989952i	$-0.454838\pi$
$661$	7.27105			0.282811			0.141406	+	0.989952i	$0.454838\pi$
$662$		0			0
$663$	10.5768	+	18.3195i	0.410768	+	0.711471i
$664$		0			0
$665$	7.61651			0.295356
$666$		0			0
$667$	−63.9976			−2.47800
$668$		0			0
$669$	−9.67498			−0.374056
$670$		0			0
$671$	32.5827			1.25784
$672$		0			0
$673$	0.971125			0.0374341			0.0187171	−	0.999825i	$-0.494042\pi$
$673$	0.971125			0.0374341			0.0187171	+	0.999825i	$0.494042\pi$
$674$		0			0
$675$	−3.18074			−0.122427
$676$		0			0
$677$	4.99286	+	8.64788i	0.191891	+	0.332365i	0.945877	−	0.324526i	$-0.105205\pi$
$677$	4.99286	+	8.64788i	0.191891	+	0.332365i	−0.753986	+	0.656891i	$0.771871\pi$
$678$		0			0
$679$	−17.7970			−0.682988
$680$		0			0
$681$	−0.474721	−	0.822241i	−0.0181913	−	0.0315083i
$682$		0			0
$683$	15.8767	−	27.4993i	0.607505	−	1.05223i	−0.384145	−	0.923273i	$-0.625504\pi$
$683$	15.8767	−	27.4993i	0.607505	−	1.05223i	0.991650	−	0.128957i	$-0.0411629\pi$
$684$		0			0
$685$	−1.06991			−0.0408793
$686$		0			0
$687$	−4.88985	+	8.46946i	−0.186559	+	0.323130i
$688$		0			0
$689$	−25.7858	+	44.6623i	−0.982361	+	1.70150i
$690$		0			0
$691$	14.5514	+	25.2038i	0.553563	+	0.958799i	0.998014	+	0.0629956i	$0.0200654\pi$
$691$	14.5514	+	25.2038i	0.553563	+	0.958799i	−0.444451	+	0.895803i	$0.646601\pi$
$692$		0			0
$693$	−5.65720	+	9.79855i	−0.214899	+	0.372216i
$694$		0			0
$695$	−3.27617			−0.124272
$696$		0			0
$697$	−16.8974			−0.640034
$698$		0			0
$699$	1.17335	+	2.03230i	0.0443801	+	0.0768687i
$700$		0			0
$701$	5.44464	+	9.43039i	0.205641	+	0.356181i	0.950337	−	0.311223i	$-0.100739\pi$
$701$	5.44464	+	9.43039i	0.205641	+	0.356181i	−0.744696	+	0.667404i	$0.767405\pi$
$702$		0			0
$703$	−10.6551	−	18.4552i	−0.401865	−	0.696051i
$704$		0			0
$705$	2.92217	+	5.06134i	0.110055	+	0.190621i
$706$		0			0
$707$	9.23544	−	15.9962i	0.347334	−	0.601601i
$708$		0			0
$709$	7.42892	−	12.8673i	0.278999	−	0.483240i	−0.692137	−	0.721766i	$-0.743331\pi$
$709$	7.42892	−	12.8673i	0.278999	−	0.483240i	0.971136	+	0.238526i	$0.0766641\pi$
$710$		0			0
$711$	−13.4750	−	23.3394i	−0.505352	−	0.875295i
$712$		0			0
$713$	−12.3120			−0.461087
$714$		0			0
$715$	−14.5059			−0.542491
$716$		0			0
$717$	3.71406	+	6.43294i	0.138704	+	0.240242i
$718$		0			0
$719$	15.8265	−	27.4123i	0.590229	−	1.02231i	−0.403973	−	0.914771i	$-0.632371\pi$
$719$	15.8265	−	27.4123i	0.590229	−	1.02231i	0.994201	−	0.107535i	$-0.0342958\pi$
$720$		0			0
$721$	−0.470274	+	0.814539i	−0.0175139	+	0.0303350i
$722$		0			0
$723$	−8.46569			−0.314842
$724$		0			0
$725$	−4.69524	−	8.13239i	−0.174377	−	0.302029i
$726$		0			0
$727$	−11.0529	+	19.1442i	−0.409929	+	0.710018i	−0.994881	−	0.101050i	$-0.967780\pi$
$727$	−11.0529	+	19.1442i	−0.409929	+	0.710018i	0.584952	+	0.811068i	$0.301113\pi$
$728$		0			0
$729$	−11.5461			−0.427633
$730$		0			0
$731$	40.6105	−	70.3395i	1.50204	−	2.60160i
$732$		0			0
$733$	19.6212	+	33.9849i	0.724725	+	1.25526i	0.959087	+	0.283111i	$0.0913665\pi$
$733$	19.6212	+	33.9849i	0.724725	+	1.25526i	−0.234362	+	0.972149i	$0.575300\pi$
$734$		0			0
$735$	−1.40665	+	2.43639i	−0.0518851	+	0.0898676i
$736$		0			0
$737$	23.8938	+	5.66464i	0.880138	+	0.208660i
$738$		0			0
$739$	17.0784	−	29.5807i	0.628240	−	1.08814i	−0.359665	−	0.933081i	$-0.617109\pi$
$739$	17.0784	−	29.5807i	0.628240	−	1.08814i	0.987905	−	0.155061i	$-0.0495576\pi$
$740$		0			0
$741$	−7.33788	−	12.7096i	−0.269564	−	0.466898i
$742$		0			0
$743$	19.4123	−	33.6231i	0.712169	−	1.23351i	−0.251872	−	0.967760i	$-0.581046\pi$
$743$	19.4123	−	33.6231i	0.712169	−	1.23351i	0.964041	−	0.265752i	$-0.0856204\pi$
$744$		0			0
$745$	−5.68430			−0.208257
$746$		0			0
$747$	7.35158	−	12.7333i	0.268980	−	0.465888i
$748$		0			0
$749$	−4.74780	−	8.22342i	−0.173481	−	0.300477i
$750$		0			0
$751$	−49.5011			−1.80632			−0.903161	−	0.429301i	$-0.858760\pi$
$751$	−49.5011			−1.80632			−0.903161	+	0.429301i	$0.858760\pi$
$752$		0			0
$753$	−8.18401	+	14.1751i	−0.298242	+	0.516570i
$754$		0			0
$755$	11.9605	−	20.7162i	0.435288	−	0.753940i
$756$		0			0
$757$	4.49946	+	7.79329i	0.163536	+	0.283252i	0.936134	−	0.351643i	$-0.114377\pi$
$757$	4.49946	+	7.79329i	0.163536	+	0.283252i	−0.772599	+	0.634895i	$0.781043\pi$
$758$		0			0
$759$	11.4348			0.415055
$760$		0			0
$761$	25.6709			0.930570			0.465285	−	0.885161i	$-0.345952\pi$
$761$	25.6709			0.930570			0.465285	+	0.885161i	$0.345952\pi$
$762$		0			0
$763$	8.46433	+	14.6606i	0.306429	+	0.530751i
$764$		0			0
$765$	−10.5100	+	18.2038i	−0.379988	+	0.658159i
$766$		0			0
$767$	−13.2464	+	22.9434i	−0.478298	+	0.828437i
$768$		0			0
$769$	−11.5996	−	20.0910i	−0.418291	−	0.724502i	0.577476	−	0.816407i	$-0.304038\pi$
$769$	−11.5996	−	20.0910i	−0.418291	−	0.724502i	−0.995768	+	0.0919056i	$0.970704\pi$
$770$		0			0
$771$	0.126673	+	0.219405i	0.00456203	+	0.00790167i
$772$		0			0
$773$	−22.3141	−	38.6492i	−0.802583	−	1.39011i	−0.917911	−	0.396787i	$-0.870125\pi$
$773$	−22.3141	−	38.6492i	−0.802583	−	1.39011i	0.115327	−	0.993328i	$-0.463208\pi$
$774$		0			0
$775$	−0.903279	−	1.56452i	−0.0324467	−	0.0561994i
$776$		0			0
$777$	−3.08234			−0.110578
$778$		0			0
$779$	11.7229			0.420018
$780$		0			0
$781$	−5.43946	+	9.42142i	−0.194639	+	0.337125i
$782$		0			0
$783$	14.9343	+	25.8670i	0.533710	+	0.924412i
$784$		0			0
$785$	−7.92339	+	13.7237i	−0.282798	+	0.489820i
$786$		0			0
$787$	18.0934	−	31.3388i	0.644961	−	1.11711i	−0.339349	−	0.940661i	$-0.610207\pi$
$787$	18.0934	−	31.3388i	0.644961	−	1.11711i	0.984310	−	0.176445i	$-0.0564599\pi$
$788$		0			0
$789$	−13.6105			−0.484546
$790$		0			0
$791$	−1.18266	+	2.04843i	−0.0420506	+	0.0728338i
$792$		0			0
$793$	−26.2579	−	45.4801i	−0.932446	−	1.61504i
$794$		0			0
$795$	5.96508			0.211560
$796$		0			0
$797$	−17.8715	−	30.9544i	−0.633041	−	1.09646i	−0.986926	−	0.161171i	$-0.948473\pi$
$797$	−17.8715	−	30.9544i	−0.633041	−	1.09646i	0.353885	−	0.935289i	$-0.384860\pi$
$798$		0			0
$799$	81.7401			2.89176
$800$		0			0
$801$	9.99821			0.353269
$802$		0			0
$803$	−9.95708			−0.351378
$804$		0			0
$805$	9.56501			0.337122
$806$		0			0
$807$	17.9193			0.630788
$808$		0			0
$809$	46.0139			1.61776			0.808882	−	0.587972i	$-0.200073\pi$
$809$	46.0139			1.61776			0.808882	+	0.587972i	$0.200073\pi$
$810$		0			0
$811$	2.15029	+	3.72442i	0.0755070	+	0.130782i	0.901307	−	0.433182i	$-0.142609\pi$
$811$	2.15029	+	3.72442i	0.0755070	+	0.130782i	−0.825800	+	0.563964i	$0.809276\pi$
$812$		0			0
$813$	0.00310583			0.000108926
$814$		0			0
$815$	0.989517	+	1.71389i	0.0346613	+	0.0600351i
$816$		0			0
$817$	−28.1745	+	48.7996i	−0.985700	+	1.70728i
$818$		0			0
$819$	18.2362			0.637224
$820$		0			0
$821$	4.42972	−	7.67250i	0.154598	−	0.267772i	−0.778314	−	0.627875i	$-0.783925\pi$
$821$	4.42972	−	7.67250i	0.154598	−	0.267772i	0.932913	+	0.360103i	$0.117258\pi$
$822$		0			0
$823$	−11.6241	+	20.1335i	−0.405189	+	0.701808i	−0.994343	−	0.106212i	$-0.966128\pi$
$823$	−11.6241	+	20.1335i	−0.405189	+	0.701808i	0.589154	+	0.808020i	$0.299461\pi$
$824$		0			0
$825$	0.838921	+	1.45305i	0.0292075	+	0.0505888i
$826$		0			0
$827$	−23.6667	+	40.9918i	−0.822970	+	1.42543i	0.0804905	+	0.996755i	$0.474351\pi$
$827$	−23.6667	+	40.9918i	−0.822970	+	1.42543i	−0.903461	+	0.428671i	$0.858982\pi$
$828$		0			0
$829$	−42.1784			−1.46492			−0.732459	−	0.680812i	$-0.761627\pi$
$829$	−42.1784			−1.46492			−0.732459	+	0.680812i	$0.761627\pi$
$830$		0			0
$831$	5.76940			0.200138
$832$		0			0
$833$	19.6737	+	34.0759i	0.681654	+	1.18066i
$834$		0			0
$835$	3.64229	+	6.30863i	0.126047	+	0.218319i
$836$		0			0
$837$	2.87310	+	4.97635i	0.0993088	+	0.172008i
$838$		0			0
$839$	−24.0500	−	41.6558i	−0.830298	−	1.43812i	−0.897802	−	0.440400i	$-0.854837\pi$
$839$	−24.0500	−	41.6558i	−0.830298	−	1.43812i	0.0675035	−	0.997719i	$-0.478497\pi$
$840$		0			0
$841$	−29.5905	+	51.2522i	−1.02036	+	1.76732i
$842$		0			0
$843$	5.74161	−	9.94476i	0.197752	−	0.342516i
$844$		0			0
$845$	5.19009	+	8.98950i	0.178545	+	0.309248i
$846$		0			0
$847$	−2.80698			−0.0964489
$848$		0			0
$849$	−4.21198			−0.144555
$850$		0			0
$851$	−13.3810	−	23.1765i	−0.458694	−	0.794481i
$852$		0			0
$853$	0.886153	−	1.53486i	0.0303413	−	0.0525527i	−0.850456	−	0.526046i	$-0.823674\pi$
$853$	0.886153	−	1.53486i	0.0303413	−	0.0525527i	0.880797	+	0.473493i	$0.157007\pi$
$854$		0			0
$855$	7.29151	−	12.6293i	0.249365	−	0.431912i
$856$		0			0
$857$	−35.6374			−1.21735			−0.608674	−	0.793420i	$-0.708298\pi$
$857$	−35.6374			−1.21735			−0.608674	+	0.793420i	$0.708298\pi$
$858$		0			0
$859$	4.08932	+	7.08292i	0.139526	+	0.241666i	0.927317	−	0.374276i	$-0.122109\pi$
$859$	4.08932	+	7.08292i	0.139526	+	0.241666i	−0.787791	+	0.615942i	$0.788775\pi$
$860$		0			0
$861$	0.847809	−	1.46845i	0.0288933	−	0.0500446i
$862$		0			0
$863$	−6.32324			−0.215246			−0.107623	−	0.994192i	$-0.534324\pi$
$863$	−6.32324			−0.215246			−0.107623	+	0.994192i	$0.534324\pi$
$864$		0			0
$865$	−11.1055	+	19.2353i	−0.377599	+	0.654021i
$866$		0			0
$867$	−12.3565	−	21.4020i	−0.419648	−	0.726852i
$868$		0			0
$869$	−15.0435	+	26.0561i	−0.510316	+	0.883893i
$870$		0			0
$871$	−11.3487	−	37.9167i	−0.384537	−	1.28476i
$872$		0			0
$873$	−17.0376	+	29.5101i	−0.576637	+	0.998764i
$874$		0			0
$875$	0.701745	+	1.21546i	0.0237233	+	0.0410900i
$876$		0			0
$877$	−5.33551	+	9.24137i	−0.180167	+	0.312059i	−0.941937	−	0.335789i	$-0.890997\pi$
$877$	−5.33551	+	9.24137i	−0.180167	+	0.312059i	0.761770	+	0.647847i	$0.224331\pi$
$878$		0			0
$879$	12.9213			0.435824
$880$		0			0
$881$	−10.1637	+	17.6041i	−0.342424	+	0.593096i	−0.984882	−	0.173225i	$-0.944581\pi$
$881$	−10.1637	+	17.6041i	−0.342424	+	0.593096i	0.642458	+	0.766321i	$0.277915\pi$
$882$		0			0
$883$	22.4064	+	38.8091i	0.754037	+	1.30603i	0.945852	+	0.324599i	$0.105229\pi$
$883$	22.4064	+	38.8091i	0.754037	+	1.30603i	−0.191815	+	0.981431i	$0.561437\pi$
$884$		0			0
$885$	3.06431			0.103006
$886$		0			0
$887$	−5.20092	+	9.00825i	−0.174630	+	0.302467i	−0.940033	−	0.341083i	$-0.889206\pi$
$887$	−5.20092	+	9.00825i	−0.174630	+	0.302467i	0.765403	+	0.643551i	$0.222539\pi$
$888$		0			0
$889$	6.47329	−	11.2121i	0.217107	−	0.376041i
$890$		0			0
$891$	9.42403	+	16.3229i	0.315717	+	0.546838i
$892$		0			0
$893$	−56.7090			−1.89770
$894$		0			0
$895$	−3.75877			−0.125642
$896$		0			0
$897$	−9.21509	−	15.9610i	−0.307683	−	0.532923i
$898$		0			0
$899$	−8.48221	+	14.6916i	−0.282898	+	0.489993i
$900$		0			0
$901$	41.7144	−	72.2515i	1.38971	−	2.40705i
$902$		0			0
$903$	4.07519	+	7.05843i	0.135614	+	0.234890i
$904$		0			0
$905$	−5.91250	−	10.2408i	−0.196538	−	0.340414i
$906$		0			0
$907$	15.7103	+	27.2110i	0.521652	+	0.903528i	0.999683	+	0.0251847i	$0.00801738\pi$
$907$	15.7103	+	27.2110i	0.521652	+	0.903528i	−0.478031	+	0.878343i	$0.658649\pi$
$908$		0			0
$909$	−17.6827	−	30.6274i	−0.586499	−	1.01585i
$910$		0			0
$911$	−19.3919			−0.642483			−0.321241	−	0.946997i	$-0.604100\pi$
$911$	−19.3919			−0.642483			−0.321241	+	0.946997i	$0.604100\pi$
$912$		0			0
$913$	−16.4146			−0.543245
$914$		0			0
$915$	−3.03715	+	5.26050i	−0.100405	+	0.173907i
$916$		0			0
$917$	2.01419	+	3.48867i	0.0665143	+	0.115206i
$918$		0			0
$919$	8.04267	−	13.9303i	0.265303	−	0.459519i	−0.702340	−	0.711842i	$-0.747861\pi$
$919$	8.04267	−	13.9303i	0.265303	−	0.459519i	0.967643	+	0.252323i	$0.0811946\pi$
$920$		0			0
$921$	1.29777	−	2.24780i	0.0427629	−	0.0740675i
$922$		0			0
$923$	17.5343			0.577149
$924$		0			0
$925$	1.96341	−	3.40073i	0.0645566	−	0.111815i
$926$		0			0
$927$	0.900416	+	1.55957i	0.0295735	+	0.0512229i
$928$		0			0
$929$	14.4153			0.472950			0.236475	−	0.971638i	$-0.424008\pi$
$929$	14.4153			0.472950			0.236475	+	0.971638i	$0.424008\pi$
$930$		0			0
$931$	−13.6491	−	23.6409i	−0.447331	−	0.774800i
$932$		0			0
$933$	11.9324			0.390651
$934$		0			0
$935$	23.4666			0.767441
$936$		0			0
$937$	28.0182			0.915314			0.457657	−	0.889129i	$-0.348689\pi$
$937$	28.0182			0.915314			0.457657	+	0.889129i	$0.348689\pi$
$938$		0			0
$939$	3.78950			0.123666
$940$		0			0
$941$	−14.5139			−0.473141			−0.236570	−	0.971614i	$-0.576023\pi$
$941$	−14.5139			−0.473141			−0.236570	+	0.971614i	$0.576023\pi$
$942$		0			0
$943$	14.7220			0.479413
$944$		0			0
$945$	−2.23207	−	3.86606i	−0.0726092	−	0.125763i
$946$		0			0
$947$	−15.9155			−0.517185			−0.258592	−	0.965987i	$-0.583259\pi$
$947$	−15.9155			−0.517185			−0.258592	+	0.965987i	$0.583259\pi$
$948$		0			0
$949$	8.02425	+	13.8984i	0.260478	+	0.451162i
$950$		0			0
$951$	−1.21268	+	2.10041i	−0.0393237	+	0.0681106i
$952$		0			0
$953$	−8.22107			−0.266307			−0.133153	−	0.991095i	$-0.542510\pi$
$953$	−8.22107			−0.266307			−0.133153	+	0.991095i	$0.542510\pi$
$954$		0			0
$955$	−6.61534	+	11.4581i	−0.214067	+	0.370776i
$956$		0			0
$957$	7.87786	−	13.6449i	0.254655	−	0.441075i
$958$		0			0
$959$	−0.750807	−	1.30044i	−0.0242448	−	0.0419932i
$960$		0			0
$961$	13.8682	−	24.0204i	0.447360	−	0.774851i
$962$		0			0
$963$	−18.1808			−0.585869
$964$		0			0
$965$	−3.23362			−0.104094
$966$		0			0
$967$	−4.07330	−	7.05516i	−0.130988	−	0.226879i	0.793069	−	0.609131i	$-0.208482\pi$
$967$	−4.07330	−	7.05516i	−0.130988	−	0.226879i	−0.924058	+	0.382253i	$0.875148\pi$
$968$		0			0
$969$	11.8707	+	20.5607i	0.381342	+	0.660503i
$970$		0			0
$971$	−13.4774	−	23.3436i	−0.432512	−	0.749133i	0.564577	−	0.825380i	$-0.309039\pi$
$971$	−13.4774	−	23.3436i	−0.432512	−	0.749133i	−0.997089	+	0.0762478i	$0.975706\pi$
$972$		0			0
$973$	−2.29903	−	3.98205i	−0.0737037	−	0.127659i
$974$		0			0
$975$	1.35215	−	2.34199i	0.0433033	−	0.0750036i
$976$		0			0
$977$	6.52009	−	11.2931i	0.208596	−	0.361299i	−0.742676	−	0.669651i	$-0.766444\pi$
$977$	6.52009	−	11.2931i	0.208596	−	0.361299i	0.951273	+	0.308351i	$0.0997772\pi$
$978$		0			0
$979$	−5.58101	−	9.66659i	−0.178370	−	0.308945i
$980$		0			0
$981$	32.4126			1.03486
$982$		0			0
$983$	31.7995			1.01425			0.507124	−	0.861873i	$-0.330709\pi$
$983$	31.7995			1.01425			0.507124	+	0.861873i	$0.330709\pi$
$984$		0			0
$985$	2.55381	+	4.42333i	0.0813711	+	0.140939i
$986$		0			0
$987$	−4.10123	+	7.10354i	−0.130544	+	0.226108i
$988$		0			0
$989$	−35.3822	+	61.2838i	−1.12509	+	1.94871i
$990$		0			0
$991$	41.5352			1.31941			0.659704	−	0.751525i	$-0.270682\pi$
$991$	41.5352			1.31941			0.659704	+	0.751525i	$0.270682\pi$
$992$		0			0
$993$	6.70222	+	11.6086i	0.212688	+	0.368387i
$994$		0			0
$995$	6.61691	−	11.4608i	0.209770	−	0.363333i
$996$		0			0
$997$	−11.5060			−0.364399			−0.182200	−	0.983262i	$-0.558322\pi$
$997$	−11.5060			−0.364399			−0.182200	+	0.983262i	$0.558322\pi$
$998$		0			0
$999$	−6.24511	+	10.8168i	−0.197586	+	0.342230i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1340.2.i.c.1101.5	yes	16
67.37	even	3	inner	1340.2.i.c.841.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1340.2.i.c.841.5	✓	16	67.37	even	3	inner
1340.2.i.c.1101.5	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1340 = 2^{2} \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1340.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.559280 q^{3} -1.00000 q^{5} +(-0.701745 - 1.21546i) q^{7} -2.68721 q^{9} +O(q^{10})\)	\(q+0.559280 q^{3} -1.00000 q^{5} +(-0.701745 - 1.21546i) q^{7} -2.68721 q^{9} +(1.50000 + 2.59808i) q^{11} +(2.41765 - 4.18750i) q^{13} -0.559280 q^{15} +(-3.91111 + 6.77424i) q^{17} +(2.71342 - 4.69978i) q^{19} +(-0.392472 - 0.679782i) q^{21} +(3.40758 - 5.90210i) q^{23} +1.00000 q^{25} -3.18074 q^{27} +(-4.69524 - 8.13239i) q^{29} +(-0.903279 - 1.56452i) q^{31} +(0.838921 + 1.45305i) q^{33} +(0.701745 + 1.21546i) q^{35} +(1.96341 - 3.40073i) q^{37} +(1.35215 - 2.34199i) q^{39} +(1.08009 + 1.87077i) q^{41} -10.3834 q^{43} +2.68721 q^{45} +(-5.22487 - 9.04974i) q^{47} +(2.51511 - 4.35630i) q^{49} +(-2.18741 + 3.78870i) q^{51} -10.6656 q^{53} +(-1.50000 - 2.59808i) q^{55} +(1.51756 - 2.62849i) q^{57} -5.47902 q^{59} +(5.43046 - 9.40583i) q^{61} +(1.88573 + 3.26618i) q^{63} +(-2.41765 + 4.18750i) q^{65} +(5.61753 - 5.95343i) q^{67} +(1.90579 - 3.30093i) q^{69} +(1.81315 + 3.14047i) q^{71} +(-1.65951 + 2.87436i) q^{73} +0.559280 q^{75} +(2.10523 - 3.64637i) q^{77} +(5.01450 + 8.68537i) q^{79} +6.28269 q^{81} +(-2.73577 + 4.73850i) q^{83} +(3.91111 - 6.77424i) q^{85} +(-2.62595 - 4.54828i) q^{87} -3.72067 q^{89} -6.78630 q^{91} +(-0.505186 - 0.875008i) q^{93} +(-2.71342 + 4.69978i) q^{95} +(6.34028 - 10.9817i) q^{97} +(-4.03081 - 6.98156i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} - 16 q^{5} + 30 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 - 16 * q^5 + 30 * q^9	\( 16 q - 2 q^{3} - 16 q^{5} + 30 q^{9} + 24 q^{11} + 2 q^{13} + 2 q^{15} - 3 q^{17} - 5 q^{21} + 3 q^{23} + 16 q^{25} - 14 q^{27} - 7 q^{29} + 7 q^{31} - 3 q^{33} - 11 q^{37} - 13 q^{39} - 15 q^{41} - 14 q^{43} - 30 q^{45} - 11 q^{47} - 10 q^{49} - 5 q^{51} + 12 q^{53} - 24 q^{55} + 26 q^{57} + 24 q^{59} + 9 q^{61} + 23 q^{63} - 2 q^{65} - q^{67} - q^{69} - 9 q^{71} - 13 q^{73} - 2 q^{75} + 5 q^{79} + 56 q^{81} - 8 q^{83} + 3 q^{85} + 14 q^{87} - 34 q^{89} + 30 q^{91} - 40 q^{93} + 25 q^{97} + 45 q^{99}+O(q^{100}) \) 16 * q - 2 * q^3 - 16 * q^5 + 30 * q^9 + 24 * q^11 + 2 * q^13 + 2 * q^15 - 3 * q^17 - 5 * q^21 + 3 * q^23 + 16 * q^25 - 14 * q^27 - 7 * q^29 + 7 * q^31 - 3 * q^33 - 11 * q^37 - 13 * q^39 - 15 * q^41 - 14 * q^43 - 30 * q^45 - 11 * q^47 - 10 * q^49 - 5 * q^51 + 12 * q^53 - 24 * q^55 + 26 * q^57 + 24 * q^59 + 9 * q^61 + 23 * q^63 - 2 * q^65 - q^67 - q^69 - 9 * q^71 - 13 * q^73 - 2 * q^75 + 5 * q^79 + 56 * q^81 - 8 * q^83 + 3 * q^85 + 14 * q^87 - 34 * q^89 + 30 * q^91 - 40 * q^93 + 25 * q^97 + 45 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more