LMFDB - Embedded newform 3510.2.j.i.1171.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3510,2,Mod(1171,3510)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3510.1171"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3510, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 3510 = 2 \cdot 3^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3510.j (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [10,-5,0,-5,5,0,-5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$28.0274911095$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.8320271788800.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - 9x^{6} + 27x^{5} - 27x^{4} + 27x^{2} - 81x + 243 $ x^10 - x^9 + x^8 - 9x^6 + 27x^5 - 27x^4 + 27x^2 - 81*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 1170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1171.5
Root			$1.65783 - 0.501603i$ of defining polynomial
Character	$\chi$	$=$	3510.1171
Dual form			3510.2.j.i.2341.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.14433 + 1.98204i) q^{7} +1.00000 q^{8} -1.00000 q^{10} +(-1.04439 - 1.80893i) q^{11} +(0.500000 - 0.866025i) q^{13} +(1.14433 - 1.98204i) q^{14} +(-0.500000 - 0.866025i) q^{16} +1.34265 q^{17} -3.11577 q^{19} +(0.500000 + 0.866025i) q^{20} +(-1.04439 + 1.80893i) q^{22} +(-0.191931 + 0.332435i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{26} -2.28866 q^{28} +(-1.83626 - 3.18050i) q^{29} +(2.17417 - 3.76578i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.671326 - 1.16277i) q^{34} +2.28866 q^{35} -2.56472 q^{37} +(1.55789 + 2.69834i) q^{38} +(0.500000 - 0.866025i) q^{40} +(-0.565838 + 0.980061i) q^{41} +(-2.12657 - 3.68333i) q^{43} +2.08878 q^{44} +0.383863 q^{46} +(-1.67096 - 2.89419i) q^{47} +(0.881015 - 1.52596i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.500000 + 0.866025i) q^{52} -2.05399 q^{53} -2.08878 q^{55} +(1.14433 + 1.98204i) q^{56} +(-1.83626 + 3.18050i) q^{58} +(4.11577 - 7.12873i) q^{59} +(2.84691 + 4.93100i) q^{61} -4.34835 q^{62} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +(-0.770424 + 1.33441i) q^{67} +(-0.671326 + 1.16277i) q^{68} +(-1.14433 - 1.98204i) q^{70} +3.86359 q^{71} +2.98321 q^{73} +(1.28236 + 2.22111i) q^{74} +(1.55789 - 2.69834i) q^{76} +(2.39025 - 4.14004i) q^{77} +(-4.95999 - 8.59095i) q^{79} -1.00000 q^{80} +1.13168 q^{82} +(1.39736 + 2.42030i) q^{83} +(0.671326 - 1.16277i) q^{85} +(-2.12657 + 3.68333i) q^{86} +(-1.04439 - 1.80893i) q^{88} -3.50984 q^{89} +2.28866 q^{91} +(-0.191931 - 0.332435i) q^{92} +(-1.67096 + 2.89419i) q^{94} +(-1.55789 + 2.69834i) q^{95} +(2.28738 + 3.96185i) q^{97} -1.76203 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - 5 q^{4} + 5 q^{5} - 5 q^{7} + 10 q^{8} - 10 q^{10} + 2 q^{11} + 5 q^{13} - 5 q^{14} - 5 q^{16} - 16 q^{17} - 8 q^{19} + 5 q^{20} + 2 q^{22} + q^{23} - 5 q^{25} - 10 q^{26} + 10 q^{28}+ \cdots - 12 q^{98}+O(q^{100}) $ 10 * q - 5 * q^2 - 5 * q^4 + 5 * q^5 - 5 * q^7 + 10 * q^8 - 10 * q^10 + 2 * q^11 + 5 * q^13 - 5 * q^14 - 5 * q^16 - 16 * q^17 - 8 * q^19 + 5 * q^20 + 2 * q^22 + q^23 - 5 * q^25 - 10 * q^26 + 10 * q^28 + q^29 + 4 * q^31 - 5 * q^32 + 8 * q^34 - 10 * q^35 - 12 * q^37 + 4 * q^38 + 5 * q^40 + 11 * q^41 + 10 * q^43 - 4 * q^44 - 2 * q^46 + 27 * q^47 + 6 * q^49 - 5 * q^50 + 5 * q^52 - 24 * q^53 + 4 * q^55 - 5 * q^56 + q^58 + 18 * q^59 + 13 * q^61 - 8 * q^62 + 10 * q^64 - 5 * q^65 - 5 * q^67 + 8 * q^68 + 5 * q^70 - 12 * q^71 + 24 * q^73 + 6 * q^74 + 4 * q^76 + 8 * q^77 - 2 * q^79 - 10 * q^80 - 22 * q^82 + 9 * q^83 - 8 * q^85 + 10 * q^86 + 2 * q^88 - 2 * q^89 - 10 * q^91 + q^92 + 27 * q^94 - 4 * q^95 - 2 * q^97 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3510\mathbb{Z}\right)^\times$.

$n$	$1081$	$2081$	$2107$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	1.14433	+	1.98204i	0.432516	+	0.749140i	0.997089	−	0.0762430i	$-0.0242925\pi$
$7$	1.14433	+	1.98204i	0.432516	+	0.749140i	−0.564573	+	0.825383i	$0.690959\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.00000			−0.316228
$11$	−1.04439	−	1.80893i	−0.314895	−	0.545414i	0.664520	−	0.747270i	$-0.268636\pi$
$11$	−1.04439	−	1.80893i	−0.314895	−	0.545414i	−0.979415	+	0.201856i	$0.935303\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	1.14433	−	1.98204i	0.305835	−	0.529722i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.34265			0.325641			0.162820	−	0.986656i	$-0.447941\pi$
$17$	1.34265			0.325641			0.162820	+	0.986656i	$0.447941\pi$
$18$		0			0
$19$	−3.11577			−0.714807			−0.357404	−	0.933950i	$-0.616338\pi$
$19$	−3.11577			−0.714807			−0.357404	+	0.933950i	$0.616338\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$		0			0
$22$	−1.04439	+	1.80893i	−0.222664	+	0.385666i
$23$	−0.191931	+	0.332435i	−0.0400205	+	0.0693175i	−0.885342	−	0.464941i	$-0.846076\pi$
$23$	−0.191931	+	0.332435i	−0.0400205	+	0.0693175i	0.845321	+	0.534258i	$0.179409\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.00000			−0.196116
$27$		0			0
$28$	−2.28866			−0.432516
$29$	−1.83626	−	3.18050i	−0.340985	−	0.590604i	0.643631	−	0.765336i	$-0.277427\pi$
$29$	−1.83626	−	3.18050i	−0.340985	−	0.590604i	−0.984616	+	0.174732i	$0.944094\pi$
$30$		0			0
$31$	2.17417	−	3.76578i	0.390493	−	0.676354i	−0.602022	−	0.798480i	$-0.705638\pi$
$31$	2.17417	−	3.76578i	0.390493	−	0.676354i	0.992515	+	0.122126i	$0.0389712\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−0.671326	−	1.16277i	−0.115131	−	0.199413i
$35$	2.28866			0.386854
$36$		0			0
$37$	−2.56472			−0.421637			−0.210818	−	0.977525i	$-0.567613\pi$
$37$	−2.56472			−0.421637			−0.210818	+	0.977525i	$0.567613\pi$
$38$	1.55789	+	2.69834i	0.252723	+	0.437728i
$39$		0			0
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−0.565838	+	0.980061i	−0.0883691	+	0.153060i	−0.906822	−	0.421514i	$-0.861499\pi$
$41$	−0.565838	+	0.980061i	−0.0883691	+	0.153060i	0.818453	+	0.574574i	$0.194832\pi$
$42$		0			0
$43$	−2.12657	−	3.68333i	−0.324299	−	0.561703i	0.657071	−	0.753829i	$-0.271795\pi$
$43$	−2.12657	−	3.68333i	−0.324299	−	0.561703i	−0.981370	+	0.192126i	$0.938462\pi$
$44$	2.08878			0.314895
$45$		0			0
$46$	0.383863			0.0565975
$47$	−1.67096	−	2.89419i	−0.243735	−	0.422161i	0.718040	−	0.696001i	$-0.245039\pi$
$47$	−1.67096	−	2.89419i	−0.243735	−	0.422161i	−0.961775	+	0.273840i	$0.911706\pi$
$48$		0			0
$49$	0.881015	−	1.52596i	0.125859	−	0.217995i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$		0			0
$52$	0.500000	+	0.866025i	0.0693375	+	0.120096i
$53$	−2.05399			−0.282137			−0.141069	−	0.990000i	$-0.545054\pi$
$53$	−2.05399			−0.282137			−0.141069	+	0.990000i	$0.545054\pi$
$54$		0			0
$55$	−2.08878			−0.281651
$56$	1.14433	+	1.98204i	0.152918	+	0.264861i
$57$		0			0
$58$	−1.83626	+	3.18050i	−0.241113	+	0.417620i
$59$	4.11577	−	7.12873i	0.535828	−	0.928081i	−0.463295	−	0.886204i	$-0.653333\pi$
$59$	4.11577	−	7.12873i	0.535828	−	0.928081i	0.999123	−	0.0418771i	$-0.0133338\pi$
$60$		0			0
$61$	2.84691	+	4.93100i	0.364510	+	0.631349i	0.988697	−	0.149925i	$-0.0479033\pi$
$61$	2.84691	+	4.93100i	0.364510	+	0.631349i	−0.624188	+	0.781274i	$0.714570\pi$
$62$	−4.34835			−0.552241
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.500000	−	0.866025i	−0.0620174	−	0.107417i
$66$		0			0
$67$	−0.770424	+	1.33441i	−0.0941222	+	0.163024i	−0.909242	−	0.416268i	$-0.863338\pi$
$67$	−0.770424	+	1.33441i	−0.0941222	+	0.163024i	0.815120	+	0.579293i	$0.196671\pi$
$68$	−0.671326	+	1.16277i	−0.0814102	+	0.141007i
$69$		0			0
$70$	−1.14433	−	1.98204i	−0.136774	−	0.236899i
$71$	3.86359			0.458523			0.229262	−	0.973365i	$-0.426369\pi$
$71$	3.86359			0.458523			0.229262	+	0.973365i	$0.426369\pi$
$72$		0			0
$73$	2.98321			0.349159			0.174579	−	0.984643i	$-0.444143\pi$
$73$	2.98321			0.349159			0.174579	+	0.984643i	$0.444143\pi$
$74$	1.28236	+	2.22111i	0.149071	+	0.258199i
$75$		0			0
$76$	1.55789	−	2.69834i	0.178702	−	0.309521i
$77$	2.39025	−	4.14004i	0.272395	−	0.471801i
$78$		0			0
$79$	−4.95999	−	8.59095i	−0.558042	−	0.966557i	−0.997660	−	0.0683723i	$-0.978219\pi$
$79$	−4.95999	−	8.59095i	−0.558042	−	0.966557i	0.439618	−	0.898185i	$-0.355114\pi$
$80$	−1.00000			−0.111803
$81$		0			0
$82$	1.13168			0.124973
$83$	1.39736	+	2.42030i	0.153380	+	0.265662i	0.932468	−	0.361252i	$-0.117651\pi$
$83$	1.39736	+	2.42030i	0.153380	+	0.265662i	−0.779088	+	0.626915i	$0.784317\pi$
$84$		0			0
$85$	0.671326	−	1.16277i	0.0728155	−	0.126120i
$86$	−2.12657	+	3.68333i	−0.229314	+	0.397184i
$87$		0			0
$88$	−1.04439	−	1.80893i	−0.111332	−	0.192833i
$89$	−3.50984			−0.372043			−0.186021	−	0.982546i	$-0.559559\pi$
$89$	−3.50984			−0.372043			−0.186021	+	0.982546i	$0.559559\pi$
$90$		0			0
$91$	2.28866			0.239917
$92$	−0.191931	−	0.332435i	−0.0200102	−	0.0346587i
$93$		0			0
$94$	−1.67096	+	2.89419i	−0.172346	+	0.298513i
$95$	−1.55789	+	2.69834i	−0.159836	+	0.276844i
$96$		0			0
$97$	2.28738	+	3.96185i	0.232248	+	0.402265i	0.958469	−	0.285196i	$-0.0920586\pi$
$97$	2.28738	+	3.96185i	0.232248	+	0.402265i	−0.726221	+	0.687461i	$0.758725\pi$
$98$	−1.76203			−0.177992
$99$		0			0
$100$	1.00000			0.100000
$101$	1.48971	+	2.58026i	0.148232	+	0.256746i	0.930574	−	0.366104i	$-0.119308\pi$
$101$	1.48971	+	2.58026i	0.148232	+	0.256746i	−0.782342	+	0.622849i	$0.785975\pi$
$102$		0			0
$103$	9.57411	−	16.5828i	0.943365	−	1.63396i	0.184373	−	0.982856i	$-0.440975\pi$
$103$	9.57411	−	16.5828i	0.943365	−	1.63396i	0.758992	−	0.651100i	$-0.225692\pi$
$104$	0.500000	−	0.866025i	0.0490290	−	0.0849208i
$105$		0			0
$106$	1.02700	+	1.77881i	0.0997506	+	0.172773i
$107$	−12.4016			−1.19891			−0.599454	−	0.800409i	$-0.704616\pi$
$107$	−12.4016			−1.19891			−0.599454	+	0.800409i	$0.704616\pi$
$108$		0			0
$109$	−3.34548			−0.320439			−0.160219	−	0.987081i	$-0.551220\pi$
$109$	−3.34548			−0.320439			−0.160219	+	0.987081i	$0.551220\pi$
$110$	1.04439	+	1.80893i	0.0995786	+	0.172475i
$111$		0			0
$112$	1.14433	−	1.98204i	0.108129	−	0.187285i
$113$	1.93942	−	3.35917i	0.182445	−	0.316004i	−0.760268	−	0.649610i	$-0.774932\pi$
$113$	1.93942	−	3.35917i	0.182445	−	0.316004i	0.942713	+	0.333606i	$0.108266\pi$
$114$		0			0
$115$	0.191931	+	0.332435i	0.0178977	+	0.0309997i
$116$	3.67252			0.340985
$117$		0			0
$118$	−8.23155			−0.757775
$119$	1.53644	+	2.66119i	0.140845	+	0.243951i
$120$		0			0
$121$	3.31850	−	5.74782i	0.301682	−	0.522529i
$122$	2.84691	−	4.93100i	0.257747	−	0.446431i
$123$		0			0
$124$	2.17417	+	3.76578i	0.195247	+	0.338177i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	18.5652			1.64740			0.823698	−	0.567029i	$-0.191907\pi$
$127$	18.5652			1.64740			0.823698	+	0.567029i	$0.191907\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−0.500000	+	0.866025i	−0.0438529	+	0.0759555i
$131$	3.40750	−	5.90196i	0.297714	−	0.515656i	−0.677898	−	0.735156i	$-0.737109\pi$
$131$	3.40750	−	5.90196i	0.297714	−	0.515656i	0.975613	+	0.219499i	$0.0704424\pi$
$132$		0			0
$133$	−3.56547	−	6.17558i	−0.309166	−	0.535491i
$134$	1.54085			0.133109
$135$		0			0
$136$	1.34265			0.115131
$137$	−6.70290	−	11.6098i	−0.572667	−	0.991889i	−0.996291	−	0.0860507i	$-0.972575\pi$
$137$	−6.70290	−	11.6098i	−0.572667	−	0.991889i	0.423623	−	0.905838i	$-0.360758\pi$
$138$		0			0
$139$	7.24106	−	12.5419i	0.614179	−	1.06379i	−0.376349	−	0.926478i	$-0.622821\pi$
$139$	7.24106	−	12.5419i	0.614179	−	1.06379i	0.990528	−	0.137311i	$-0.0438459\pi$
$140$	−1.14433	+	1.98204i	−0.0967136	+	0.167513i
$141$		0			0
$142$	−1.93179	−	3.34596i	−0.162112	−	0.280787i
$143$	−2.08878			−0.174672
$144$		0			0
$145$	−3.67252			−0.304987
$146$	−1.49161	−	2.58354i	−0.123446	−	0.213815i
$147$		0			0
$148$	1.28236	−	2.22111i	0.105409	−	0.182574i
$149$	−2.60512	+	4.51221i	−0.213420	+	0.369654i	−0.952783	−	0.303653i	$-0.901794\pi$
$149$	−2.60512	+	4.51221i	−0.213420	+	0.369654i	0.739363	+	0.673307i	$0.235127\pi$
$150$		0			0
$151$	−5.61436	−	9.72436i	−0.456890	−	0.791357i	0.541905	−	0.840440i	$-0.317703\pi$
$151$	−5.61436	−	9.72436i	−0.456890	−	0.791357i	−0.998795	+	0.0490831i	$0.984370\pi$
$152$	−3.11577			−0.252723
$153$		0			0
$154$	−4.78050			−0.385224
$155$	−2.17417	−	3.76578i	−0.174634	−	0.302475i
$156$		0			0
$157$	2.67891	−	4.64001i	0.213801	−	0.370313i	−0.739100	−	0.673595i	$-0.764749\pi$
$157$	2.67891	−	4.64001i	0.213801	−	0.370313i	0.952901	+	0.303282i	$0.0980824\pi$
$158$	−4.95999	+	8.59095i	−0.394595	+	0.683459i
$159$		0			0
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−0.878532			−0.0692380
$162$		0			0
$163$	7.51764			0.588827			0.294413	−	0.955678i	$-0.404876\pi$
$163$	7.51764			0.588827			0.294413	+	0.955678i	$0.404876\pi$
$164$	−0.565838	−	0.980061i	−0.0441846	−	0.0765299i
$165$		0			0
$166$	1.39736	−	2.42030i	0.108456	−	0.187852i
$167$	7.73873	−	13.4039i	0.598841	−	1.03722i	−0.394152	−	0.919045i	$-0.628962\pi$
$167$	7.73873	−	13.4039i	0.598841	−	1.03722i	0.992993	−	0.118177i	$-0.0377051\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	−1.34265			−0.102977
$171$		0			0
$172$	4.25314			0.324299
$173$	12.3538	+	21.3974i	0.939240	+	1.62681i	0.766893	+	0.641775i	$0.221802\pi$
$173$	12.3538	+	21.3974i	0.939240	+	1.62681i	0.172347	+	0.985036i	$0.444865\pi$
$174$		0			0
$175$	1.14433	−	1.98204i	0.0865033	−	0.149828i
$176$	−1.04439	+	1.80893i	−0.0787238	+	0.136354i
$177$		0			0
$178$	1.75492	+	3.03961i	0.131537	+	0.227829i
$179$	−16.3016			−1.21844			−0.609219	−	0.793002i	$-0.708517\pi$
$179$	−16.3016			−1.21844			−0.609219	+	0.793002i	$0.708517\pi$
$180$		0			0
$181$	−0.219795			−0.0163372			−0.00816862	−	0.999967i	$-0.502600\pi$
$181$	−0.219795			−0.0163372			−0.00816862	+	0.999967i	$0.502600\pi$
$182$	−1.14433	−	1.98204i	−0.0848234	−	0.146918i
$183$		0			0
$184$	−0.191931	+	0.332435i	−0.0141494	+	0.0245074i
$185$	−1.28236	+	2.22111i	−0.0942809	+	0.163299i
$186$		0			0
$187$	−1.40225	−	2.42877i	−0.102543	−	0.177609i
$188$	3.34192			0.243735
$189$		0			0
$190$	3.11577			0.226042
$191$	0.0682066	+	0.118137i	0.00493526	+	0.00854812i	0.868482	−	0.495720i	$-0.165096\pi$
$191$	0.0682066	+	0.118137i	0.00493526	+	0.00854812i	−0.863547	+	0.504268i	$0.831762\pi$
$192$		0			0
$193$	9.94802	−	17.2305i	0.716074	−	1.24028i	−0.246470	−	0.969150i	$-0.579271\pi$
$193$	9.94802	−	17.2305i	0.716074	−	1.24028i	0.962544	−	0.271126i	$-0.0873960\pi$
$194$	2.28738	−	3.96185i	0.164224	−	0.284444i
$195$		0			0
$196$	0.881015	+	1.52596i	0.0629297	+	0.108997i
$197$	−7.58032			−0.540076			−0.270038	−	0.962850i	$-0.587036\pi$
$197$	−7.58032			−0.540076			−0.270038	+	0.962850i	$0.587036\pi$
$198$		0			0
$199$	−23.0705			−1.63543			−0.817713	−	0.575626i	$-0.804759\pi$
$199$	−23.0705			−1.63543			−0.817713	+	0.575626i	$0.804759\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$		0			0
$202$	1.48971	−	2.58026i	0.104816	−	0.181547i
$203$	4.20258	−	7.27908i	0.294963	−	0.510892i
$204$		0			0
$205$	0.565838	+	0.980061i	0.0395199	+	0.0684504i
$206$	−19.1482			−1.33412
$207$		0			0
$208$	−1.00000			−0.0693375
$209$	3.25408	+	5.63623i	0.225089	+	0.389866i
$210$		0			0
$211$	−5.16571	+	8.94727i	−0.355622	+	0.615955i	−0.987224	−	0.159337i	$-0.949064\pi$
$211$	−5.16571	+	8.94727i	−0.355622	+	0.615955i	0.631602	+	0.775293i	$0.282398\pi$
$212$	1.02700	−	1.77881i	0.0705343	−	0.122169i
$213$		0			0
$214$	6.20080	+	10.7401i	0.423878	+	0.734179i
$215$	−4.25314			−0.290062
$216$		0			0
$217$	9.95189			0.675578
$218$	1.67274	+	2.89727i	0.113292	+	0.196228i
$219$		0			0
$220$	1.04439	−	1.80893i	0.0704127	−	0.121958i
$221$	0.671326	−	1.16277i	0.0451582	−	0.0782164i
$222$		0			0
$223$	−13.5749	−	23.5124i	−0.909041	−	1.57451i	−0.815399	−	0.578900i	$-0.803482\pi$
$223$	−13.5749	−	23.5124i	−0.909041	−	1.57451i	−0.0936426	−	0.995606i	$-0.529851\pi$
$224$	−2.28866			−0.152918
$225$		0			0
$226$	−3.87883			−0.258016
$227$	−1.96697	−	3.40689i	−0.130552	−	0.226123i	0.793337	−	0.608782i	$-0.208342\pi$
$227$	−1.96697	−	3.40689i	−0.130552	−	0.226123i	−0.923890	+	0.382659i	$0.875008\pi$
$228$		0			0
$229$	−3.73928	+	6.47663i	−0.247099	+	0.427988i	−0.962720	−	0.270501i	$-0.912811\pi$
$229$	−3.73928	+	6.47663i	−0.247099	+	0.427988i	0.715621	+	0.698489i	$0.246144\pi$
$230$	0.191931	−	0.332435i	0.0126556	−	0.0219201i
$231$		0			0
$232$	−1.83626	−	3.18050i	−0.120557	−	0.208810i
$233$	−11.1654			−0.731472			−0.365736	−	0.930719i	$-0.619183\pi$
$233$	−11.1654			−0.731472			−0.365736	+	0.930719i	$0.619183\pi$
$234$		0			0
$235$	−3.34192			−0.218003
$236$	4.11577	+	7.12873i	0.267914	+	0.464041i
$237$		0			0
$238$	1.53644	−	2.66119i	0.0995924	−	0.172499i
$239$	−1.79160	+	3.10313i	−0.115889	+	0.200725i	−0.918135	−	0.396269i	$-0.870305\pi$
$239$	−1.79160	+	3.10313i	−0.115889	+	0.200725i	0.802246	+	0.596994i	$0.203638\pi$
$240$		0			0
$241$	10.8567	+	18.8044i	0.699345	+	1.21130i	0.968694	+	0.248258i	$0.0798580\pi$
$241$	10.8567	+	18.8044i	0.699345	+	1.21130i	−0.269350	+	0.963042i	$0.586809\pi$
$242$	−6.63701			−0.426643
$243$		0			0
$244$	−5.69382			−0.364510
$245$	−0.881015	−	1.52596i	−0.0562860	−	0.0974902i
$246$		0			0
$247$	−1.55789	+	2.69834i	−0.0991259	+	0.171691i
$248$	2.17417	−	3.76578i	0.138060	−	0.239127i
$249$		0			0
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	1.57331			0.0993067			0.0496534	−	0.998767i	$-0.484188\pi$
$251$	1.57331			0.0993067			0.0496534	+	0.998767i	$0.484188\pi$
$252$		0			0
$253$	0.801804			0.0504090
$254$	−9.28260	−	16.0779i	−0.582442	−	1.00882i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.74680	−	4.75760i	0.171341	−	0.296771i	−0.767548	−	0.640991i	$-0.778523\pi$
$257$	2.74680	−	4.75760i	0.171341	−	0.296771i	0.938889	+	0.344221i	$0.111857\pi$
$258$		0			0
$259$	−2.93488	−	5.08337i	−0.182365	−	0.315865i
$260$	1.00000			0.0620174
$261$		0			0
$262$	−6.81499			−0.421032
$263$	5.12678	+	8.87984i	0.316131	+	0.547554i	0.979677	−	0.200581i	$-0.0642829\pi$
$263$	5.12678	+	8.87984i	0.316131	+	0.547554i	−0.663547	+	0.748135i	$0.730950\pi$
$264$		0			0
$265$	−1.02700	+	1.77881i	−0.0630878	+	0.109271i
$266$	−3.56547	+	6.17558i	−0.218613	+	0.378649i
$267$		0			0
$268$	−0.770424	−	1.33441i	−0.0470611	−	0.0815122i
$269$	−30.7132			−1.87262			−0.936310	−	0.351176i	$-0.885782\pi$
$269$	−30.7132			−1.87262			−0.936310	+	0.351176i	$0.885782\pi$
$270$		0			0
$271$	6.73125			0.408894			0.204447	−	0.978878i	$-0.434460\pi$
$271$	6.73125			0.408894			0.204447	+	0.978878i	$0.434460\pi$
$272$	−0.671326	−	1.16277i	−0.0407051	−	0.0705033i
$273$		0			0
$274$	−6.70290	+	11.6098i	−0.404937	+	0.701372i
$275$	−1.04439	+	1.80893i	−0.0629790	+	0.109083i
$276$		0			0
$277$	−11.6330	−	20.1489i	−0.698956	−	1.21063i	−0.968829	−	0.247732i	$-0.920315\pi$
$277$	−11.6330	−	20.1489i	−0.698956	−	1.21063i	0.269872	−	0.962896i	$-0.413019\pi$
$278$	−14.4821			−0.868580
$279$		0			0
$280$	2.28866			0.136774
$281$	−8.40089	−	14.5508i	−0.501155	−	0.868026i	−0.999999	−	0.00133444i	$-0.999575\pi$
$281$	−8.40089	−	14.5508i	−0.501155	−	0.868026i	0.498844	−	0.866692i	$-0.333758\pi$
$282$		0			0
$283$	−4.47654	+	7.75359i	−0.266102	+	0.460903i	−0.967852	−	0.251521i	$-0.919069\pi$
$283$	−4.47654	+	7.75359i	−0.266102	+	0.460903i	0.701749	+	0.712424i	$0.252403\pi$
$284$	−1.93179	+	3.34596i	−0.114631	+	0.198546i
$285$		0			0
$286$	1.04439	+	1.80893i	0.0617560	+	0.106965i
$287$	−2.59002			−0.152884
$288$		0			0
$289$	−15.1973			−0.893958
$290$	1.83626	+	3.18050i	0.107829	+	0.186765i
$291$		0			0
$292$	−1.49161	+	2.58354i	−0.0872897	+	0.151190i
$293$	−4.48711	+	7.77190i	−0.262140	+	0.454039i	−0.966810	−	0.255495i	$-0.917761\pi$
$293$	−4.48711	+	7.77190i	−0.262140	+	0.454039i	0.704671	+	0.709535i	$0.251095\pi$
$294$		0			0
$295$	−4.11577	−	7.12873i	−0.239630	−	0.415051i
$296$	−2.56472			−0.149071
$297$		0			0
$298$	5.21025			0.301821
$299$	0.191931	+	0.332435i	0.0110997	+	0.0192252i
$300$		0			0
$301$	4.86700	−	8.42990i	0.280529	−	0.485891i
$302$	−5.61436	+	9.72436i	−0.323070	+	0.559574i
$303$		0			0
$304$	1.55789	+	2.69834i	0.0893509	+	0.154760i
$305$	5.69382			0.326027
$306$		0			0
$307$	−5.51796			−0.314927			−0.157463	−	0.987525i	$-0.550332\pi$
$307$	−5.51796			−0.314927			−0.157463	+	0.987525i	$0.550332\pi$
$308$	2.39025	+	4.14004i	0.136197	+	0.235901i
$309$		0			0
$310$	−2.17417	+	3.76578i	−0.123485	+	0.213882i
$311$	13.0255	−	22.5609i	0.738610	−	1.27931i	−0.214511	−	0.976722i	$-0.568816\pi$
$311$	13.0255	−	22.5609i	0.738610	−	1.27931i	0.953121	−	0.302589i	$-0.0978510\pi$
$312$		0			0
$313$	−5.41949	−	9.38684i	−0.306328	−	0.530576i	0.671228	−	0.741251i	$-0.265767\pi$
$313$	−5.41949	−	9.38684i	−0.306328	−	0.530576i	−0.977556	+	0.210675i	$0.932434\pi$
$314$	−5.35783			−0.302360
$315$		0			0
$316$	9.91997			0.558042
$317$	−1.12747	−	1.95284i	−0.0633251	−	0.109682i	0.832625	−	0.553838i	$-0.186837\pi$
$317$	−1.12747	−	1.95284i	−0.0633251	−	0.109682i	−0.895950	+	0.444155i	$0.853504\pi$
$318$		0			0
$319$	−3.83554	+	6.64336i	−0.214749	+	0.371956i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$		0			0
$322$	0.439266	+	0.760831i	0.0244793	+	0.0423995i
$323$	−4.18340			−0.232770
$324$		0			0
$325$	−1.00000			−0.0554700
$326$	−3.75882	−	6.51046i	−0.208182	−	0.360581i
$327$		0			0
$328$	−0.565838	+	0.980061i	−0.0312432	+	0.0541148i
$329$	3.82426	−	6.62382i	0.210839	−	0.365183i
$330$		0			0
$331$	14.1948	+	24.5861i	0.780215	+	1.35137i	0.931816	+	0.362931i	$0.118224\pi$
$331$	14.1948	+	24.5861i	0.780215	+	1.35137i	−0.151601	+	0.988442i	$0.548443\pi$
$332$	−2.79472			−0.153380
$333$		0			0
$334$	−15.4775			−0.846889
$335$	0.770424	+	1.33441i	0.0420927	+	0.0729068i
$336$		0			0
$337$	14.1290	−	24.4722i	0.769657	−	1.33308i	−0.168092	−	0.985771i	$-0.553761\pi$
$337$	14.1290	−	24.4722i	0.769657	−	1.33308i	0.937749	−	0.347313i	$-0.112906\pi$
$338$	−0.500000	+	0.866025i	−0.0271964	+	0.0471056i
$339$		0			0
$340$	0.671326	+	1.16277i	0.0364077	+	0.0630601i
$341$	−9.08273			−0.491857
$342$		0			0
$343$	20.0533			1.08278
$344$	−2.12657	−	3.68333i	−0.114657	−	0.198592i
$345$		0			0
$346$	12.3538	−	21.3974i	0.664143	−	1.15033i
$347$	2.52604	−	4.37523i	0.135605	−	0.234875i	−0.790223	−	0.612819i	$-0.790036\pi$
$347$	2.52604	−	4.37523i	0.135605	−	0.234875i	0.925828	+	0.377944i	$0.123369\pi$
$348$		0			0
$349$	−0.545875	−	0.945483i	−0.0292200	−	0.0506105i	0.851046	−	0.525092i	$-0.175969\pi$
$349$	−0.545875	−	0.945483i	−0.0292200	−	0.0506105i	−0.880266	+	0.474481i	$0.842636\pi$
$350$	−2.28866			−0.122334
$351$		0			0
$352$	2.08878			0.111332
$353$	12.9246	+	22.3861i	0.687909	+	1.19149i	0.972513	+	0.232848i	$0.0748046\pi$
$353$	12.9246	+	22.3861i	0.687909	+	1.19149i	−0.284604	+	0.958645i	$0.591862\pi$
$354$		0			0
$355$	1.93179	−	3.34596i	0.102529	−	0.177585i
$356$	1.75492	−	3.03961i	0.0930107	−	0.161099i
$357$		0			0
$358$	8.15080	+	14.1176i	0.430783	+	0.746138i
$359$	−3.18085			−0.167879			−0.0839395	−	0.996471i	$-0.526750\pi$
$359$	−3.18085			−0.167879			−0.0839395	+	0.996471i	$0.526750\pi$
$360$		0			0
$361$	−9.29196			−0.489051
$362$	0.109898	+	0.190348i	0.00577609	+	0.0100045i
$363$		0			0
$364$	−1.14433	+	1.98204i	−0.0599792	+	0.103887i
$365$	1.49161	−	2.58354i	0.0780743	−	0.135229i
$366$		0			0
$367$	−15.0789	−	26.1173i	−0.787110	−	1.36331i	−0.927731	−	0.373250i	$-0.878243\pi$
$367$	−15.0789	−	26.1173i	−0.787110	−	1.36331i	0.140621	−	0.990063i	$-0.455090\pi$
$368$	0.383863			0.0200102
$369$		0			0
$370$	2.56472			0.133333
$371$	−2.35044	−	4.07109i	−0.122029	−	0.211360i
$372$		0			0
$373$	10.9732	−	19.0062i	0.568173	−	0.984104i	−0.428574	−	0.903507i	$-0.640984\pi$
$373$	10.9732	−	19.0062i	0.568173	−	0.984104i	0.996747	−	0.0805972i	$-0.0256827\pi$
$374$	−1.40225	+	2.42877i	−0.0725086	+	0.125589i
$375$		0			0
$376$	−1.67096	−	2.89419i	−0.0861732	−	0.149256i
$377$	−3.67252			−0.189145
$378$		0			0
$379$	−17.4708			−0.897413			−0.448707	−	0.893679i	$-0.648115\pi$
$379$	−17.4708			−0.897413			−0.448707	+	0.893679i	$0.648115\pi$
$380$	−1.55789	−	2.69834i	−0.0799179	−	0.138422i
$381$		0			0
$382$	0.0682066	−	0.118137i	0.00348975	−	0.00604443i
$383$	11.3764	−	19.7045i	0.581308	−	1.00685i	−0.414017	−	0.910269i	$-0.635875\pi$
$383$	11.3764	−	19.7045i	0.581308	−	1.00685i	0.995325	−	0.0965855i	$-0.0307921\pi$
$384$		0			0
$385$	−2.39025	−	4.14004i	−0.121819	−	0.210996i
$386$	−19.8960			−1.01268
$387$		0			0
$388$	−4.57475			−0.232248
$389$	10.9909	+	19.0368i	0.557261	+	0.965204i	0.997724	+	0.0674336i	$0.0214811\pi$
$389$	10.9909	+	19.0368i	0.557261	+	0.965204i	−0.440463	+	0.897771i	$0.645186\pi$
$390$		0			0
$391$	−0.257697	+	0.446344i	−0.0130323	+	0.0225726i
$392$	0.881015	−	1.52596i	0.0444980	−	0.0770728i
$393$		0			0
$394$	3.79016	+	6.56475i	0.190946	+	0.330727i
$395$	−9.91997			−0.499128
$396$		0			0
$397$	14.9767			0.751658			0.375829	−	0.926689i	$-0.377358\pi$
$397$	14.9767			0.751658			0.375829	+	0.926689i	$0.377358\pi$
$398$	11.5353	+	19.9797i	0.578211	+	1.00149i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−4.71659	+	8.16938i	−0.235535	+	0.407959i	−0.959428	−	0.281953i	$-0.909018\pi$
$401$	−4.71659	+	8.16938i	−0.235535	+	0.407959i	0.723893	+	0.689913i	$0.242351\pi$
$402$		0			0
$403$	−2.17417	−	3.76578i	−0.108303	−	0.187587i
$404$	−2.97943			−0.148232
$405$		0			0
$406$	−8.40516			−0.417141
$407$	2.67856	+	4.63941i	0.132771	+	0.229967i
$408$		0			0
$409$	−10.4365	+	18.0766i	−0.516053	+	0.893831i	0.483773	+	0.875194i	$0.339266\pi$
$409$	−10.4365	+	18.0766i	−0.516053	+	0.893831i	−0.999826	+	0.0186371i	$0.994067\pi$
$410$	0.565838	−	0.980061i	0.0279448	−	0.0484018i
$411$		0			0
$412$	9.57411	+	16.5828i	0.471683	+	0.816978i
$413$	18.8392			0.927017
$414$		0			0
$415$	2.79472			0.137187
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$		0			0
$418$	3.25408	−	5.63623i	0.159162	−	0.275677i
$419$	−2.78987	+	4.83220i	−0.136294	+	0.236069i	−0.926091	−	0.377300i	$-0.876853\pi$
$419$	−2.78987	+	4.83220i	−0.136294	+	0.236069i	0.789797	+	0.613368i	$0.210186\pi$
$420$		0			0
$421$	10.0500	+	17.4072i	0.489809	+	0.848375i	0.999931	−	0.0117273i	$-0.00373301\pi$
$421$	10.0500	+	17.4072i	0.489809	+	0.848375i	−0.510122	+	0.860102i	$0.670400\pi$
$422$	10.3314			0.502925
$423$		0			0
$424$	−2.05399			−0.0997506
$425$	−0.671326	−	1.16277i	−0.0325641	−	0.0564026i
$426$		0			0
$427$	−6.51562	+	11.2854i	−0.315313	+	0.546138i
$428$	6.20080	−	10.7401i	0.299727	−	0.519143i
$429$		0			0
$430$	2.12657	+	3.68333i	0.102552	+	0.177626i
$431$	28.0361			1.35045			0.675226	−	0.737611i	$-0.264046\pi$
$431$	28.0361			1.35045			0.675226	+	0.737611i	$0.264046\pi$
$432$		0			0
$433$	−4.99781			−0.240180			−0.120090	−	0.992763i	$-0.538318\pi$
$433$	−4.99781			−0.240180			−0.120090	+	0.992763i	$0.538318\pi$
$434$	−4.97595	−	8.61859i	−0.238853	−	0.413706i
$435$		0			0
$436$	1.67274	−	2.89727i	0.0801096	−	0.138754i
$437$	0.598015	−	1.03579i	0.0286069	−	0.0495486i
$438$		0			0
$439$	0.234001	+	0.405301i	0.0111682	+	0.0193440i	0.871556	−	0.490297i	$-0.163112\pi$
$439$	0.234001	+	0.405301i	0.0111682	+	0.0193440i	−0.860387	+	0.509641i	$0.829778\pi$
$440$	−2.08878			−0.0995786
$441$		0			0
$442$	−1.34265			−0.0638634
$443$	−0.620624	−	1.07495i	−0.0294868	−	0.0510726i	0.850905	−	0.525319i	$-0.176054\pi$
$443$	−0.620624	−	1.07495i	−0.0294868	−	0.0510726i	−0.880392	+	0.474246i	$0.842721\pi$
$444$		0			0
$445$	−1.75492	+	3.03961i	−0.0831913	+	0.144092i
$446$	−13.5749	+	23.5124i	−0.642789	+	1.11334i
$447$		0			0
$448$	1.14433	+	1.98204i	0.0540645	+	0.0936425i
$449$	−17.1091			−0.807429			−0.403714	−	0.914885i	$-0.632281\pi$
$449$	−17.1091			−0.807429			−0.403714	+	0.914885i	$0.632281\pi$
$450$		0			0
$451$	2.36382			0.111308
$452$	1.93942	+	3.35917i	0.0912224	+	0.158002i
$453$		0			0
$454$	−1.96697	+	3.40689i	−0.0923143	+	0.159893i
$455$	1.14433	−	1.98204i	0.0536470	−	0.0929194i
$456$		0			0
$457$	−6.22825	−	10.7876i	−0.291345	−	0.504625i	0.682783	−	0.730621i	$-0.260769\pi$
$457$	−6.22825	−	10.7876i	−0.291345	−	0.504625i	−0.974128	+	0.225997i	$0.927436\pi$
$458$	7.47857			0.349450
$459$		0			0
$460$	−0.383863			−0.0178977
$461$	−1.28757	−	2.23014i	−0.0599683	−	0.103868i	0.834483	−	0.551034i	$-0.185767\pi$
$461$	−1.28757	−	2.23014i	−0.0599683	−	0.103868i	−0.894451	+	0.447166i	$0.852433\pi$
$462$		0			0
$463$	−4.26765	+	7.39179i	−0.198335	+	0.343526i	−0.947989	−	0.318304i	$-0.896887\pi$
$463$	−4.26765	+	7.39179i	−0.198335	+	0.343526i	0.749654	+	0.661830i	$0.230220\pi$
$464$	−1.83626	+	3.18050i	−0.0852463	+	0.147651i
$465$		0			0
$466$	5.58272	+	9.66955i	0.258614	+	0.447933i
$467$	−0.426207			−0.0197225			−0.00986124	−	0.999951i	$-0.503139\pi$
$467$	−0.426207			−0.0197225			−0.00986124	+	0.999951i	$0.503139\pi$
$468$		0			0
$469$	−3.52648			−0.162838
$470$	1.67096	+	2.89419i	0.0770757	+	0.133499i
$471$		0			0
$472$	4.11577	−	7.12873i	0.189444	−	0.328126i
$473$	−4.44194	+	7.69366i	−0.204240	+	0.353755i
$474$		0			0
$475$	1.55789	+	2.69834i	0.0714807	+	0.123808i
$476$	−3.07287			−0.140845
$477$		0			0
$478$	3.58319			0.163891
$479$	3.51507	+	6.08829i	0.160608	+	0.278181i	0.935087	−	0.354419i	$-0.115321\pi$
$479$	3.51507	+	6.08829i	0.160608	+	0.278181i	−0.774479	+	0.632600i	$0.781988\pi$
$480$		0			0
$481$	−1.28236	+	2.22111i	−0.0584705	+	0.101274i
$482$	10.8567	−	18.8044i	0.494511	−	0.856519i
$483$		0			0
$484$	3.31850	+	5.74782i	0.150841	+	0.261264i
$485$	4.57475			0.207729
$486$		0			0
$487$	−0.382362			−0.0173265			−0.00866323	−	0.999962i	$-0.502758\pi$
$487$	−0.382362			−0.0173265			−0.00866323	+	0.999962i	$0.502758\pi$
$488$	2.84691	+	4.93100i	0.128874	+	0.223216i
$489$		0			0
$490$	−0.881015	+	1.52596i	−0.0398002	+	0.0689360i
$491$	15.3831	−	26.6443i	0.694230	−	1.20244i	−0.276210	−	0.961097i	$-0.589079\pi$
$491$	15.3831	−	26.6443i	0.694230	−	1.20244i	0.970440	−	0.241344i	$-0.0775881\pi$
$492$		0			0
$493$	−2.46546	−	4.27030i	−0.111039	−	0.192325i
$494$	3.11577			0.140185
$495$		0			0
$496$	−4.34835			−0.195247
$497$	4.42122	+	7.65778i	0.198319	+	0.343498i
$498$		0			0
$499$	−19.6155	+	33.9751i	−0.878111	+	1.52093i	−0.0246999	+	0.999695i	$0.507863\pi$
$499$	−19.6155	+	33.9751i	−0.878111	+	1.52093i	−0.853411	+	0.521238i	$0.825470\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$		0			0
$502$	−0.786657	−	1.36253i	−0.0351102	−	0.0608127i
$503$	14.9377			0.666040			0.333020	−	0.942920i	$-0.391932\pi$
$503$	14.9377			0.666040			0.333020	+	0.942920i	$0.391932\pi$
$504$		0			0
$505$	2.97943			0.132583
$506$	−0.400902	−	0.694383i	−0.0178223	−	0.0308691i
$507$		0			0
$508$	−9.28260	+	16.0779i	−0.411849	+	0.713343i
$509$	−10.0892	+	17.4750i	−0.447197	+	0.774568i	−0.998202	−	0.0599339i	$-0.980911\pi$
$509$	−10.0892	+	17.4750i	−0.447197	+	0.774568i	0.551005	+	0.834502i	$0.314244\pi$
$510$		0			0
$511$	3.41378	+	5.91284i	0.151017	+	0.261569i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−5.49360			−0.242312
$515$	−9.57411	−	16.5828i	−0.421886	−	0.730727i
$516$		0			0
$517$	−3.49027	+	6.04532i	−0.153502	+	0.265873i
$518$	−2.93488	+	5.08337i	−0.128951	+	0.223350i
$519$		0			0
$520$	−0.500000	−	0.866025i	−0.0219265	−	0.0379777i
$521$	23.8718			1.04584			0.522921	−	0.852381i	$-0.324842\pi$
$521$	23.8718			1.04584			0.522921	+	0.852381i	$0.324842\pi$
$522$		0			0
$523$	−31.3232			−1.36967			−0.684835	−	0.728698i	$-0.740126\pi$
$523$	−31.3232			−1.36967			−0.684835	+	0.728698i	$0.740126\pi$
$524$	3.40750	+	5.90196i	0.148857	+	0.257828i
$525$		0			0
$526$	5.12678	−	8.87984i	0.223538	−	0.387179i
$527$	2.91916	−	5.05613i	0.127160	−	0.220248i
$528$		0			0
$529$	11.4263	+	19.7910i	0.496797	+	0.860477i
$530$	2.05399			0.0892196
$531$		0			0
$532$	7.13095			0.309166
$533$	0.565838	+	0.980061i	0.0245092	+	0.0424511i
$534$		0			0
$535$	−6.20080	+	10.7401i	−0.268084	+	0.464335i
$536$	−0.770424	+	1.33441i	−0.0332772	+	0.0576379i
$537$		0			0
$538$	15.3566	+	26.5984i	0.662071	+	1.14674i
$539$	−3.68049			−0.158530
$540$		0			0
$541$	−28.2162			−1.21311			−0.606555	−	0.795042i	$-0.707449\pi$
$541$	−28.2162			−1.21311			−0.606555	+	0.795042i	$0.707449\pi$
$542$	−3.36563	−	5.82943i	−0.144566	−	0.250396i
$543$		0			0
$544$	−0.671326	+	1.16277i	−0.0287828	+	0.0498534i
$545$	−1.67274	+	2.89727i	−0.0716522	+	0.124105i
$546$		0			0
$547$	6.44808	+	11.1684i	0.275700	+	0.477526i	0.970311	−	0.241859i	$-0.0777570\pi$
$547$	6.44808	+	11.1684i	0.275700	+	0.477526i	−0.694611	+	0.719385i	$0.744424\pi$
$548$	13.4058			0.572667
$549$		0			0
$550$	2.08878			0.0890658
$551$	5.72138	+	9.90971i	0.243739	+	0.422168i
$552$		0			0
$553$	11.3517	−	19.6618i	0.482725	−	0.836104i
$554$	−11.6330	+	20.1489i	−0.494237	+	0.856043i
$555$		0			0
$556$	7.24106	+	12.5419i	0.307089	+	0.531894i
$557$	18.3270			0.776541			0.388271	−	0.921545i	$-0.373073\pi$
$557$	18.3270			0.776541			0.388271	+	0.921545i	$0.373073\pi$
$558$		0			0
$559$	−4.25314			−0.179889
$560$	−1.14433	−	1.98204i	−0.0483568	−	0.0837564i
$561$		0			0
$562$	−8.40089	+	14.5508i	−0.354370	+	0.613787i
$563$	17.3765	−	30.0969i	0.732331	−	1.26843i	−0.223554	−	0.974692i	$-0.571766\pi$
$563$	17.3765	−	30.0969i	0.732331	−	1.26843i	0.955885	−	0.293742i	$-0.0949007\pi$
$564$		0			0
$565$	−1.93942	−	3.35917i	−0.0815918	−	0.141321i
$566$	8.95307			0.376326
$567$		0			0
$568$	3.86359			0.162112
$569$	−3.06295	−	5.30518i	−0.128405	−	0.222405i	0.794654	−	0.607063i	$-0.207653\pi$
$569$	−3.06295	−	5.30518i	−0.128405	−	0.222405i	−0.923059	+	0.384659i	$0.874319\pi$
$570$		0			0
$571$	−10.1348	+	17.5539i	−0.424127	+	0.734609i	−0.996338	−	0.0854968i	$-0.972752\pi$
$571$	−10.1348	+	17.5539i	−0.424127	+	0.734609i	0.572212	+	0.820106i	$0.306086\pi$
$572$	1.04439	−	1.80893i	0.0436681	−	0.0756354i
$573$		0			0
$574$	1.29501	+	2.24303i	0.0540528	+	0.0936221i
$575$	0.383863			0.0160082
$576$		0			0
$577$	18.8064			0.782922			0.391461	−	0.920195i	$-0.371970\pi$
$577$	18.8064			0.782922			0.391461	+	0.920195i	$0.371970\pi$
$578$	7.59864	+	13.1612i	0.316062	+	0.547435i
$579$		0			0
$580$	1.83626	−	3.18050i	0.0762466	−	0.132063i
$581$	−3.19808	+	5.53924i	−0.132679	+	0.229807i
$582$		0			0
$583$	2.14516	+	3.71553i	0.0888436	+	0.153882i
$584$	2.98321			0.123446
$585$		0			0
$586$	8.97422			0.370722
$587$	3.15977	+	5.47288i	0.130418	+	0.225890i	0.923838	−	0.382785i	$-0.125035\pi$
$587$	3.15977	+	5.47288i	0.130418	+	0.225890i	−0.793420	+	0.608675i	$0.791702\pi$
$588$		0			0
$589$	−6.77423	+	11.7333i	−0.279127	+	0.483463i
$590$	−4.11577	+	7.12873i	−0.169444	+	0.293485i
$591$		0			0
$592$	1.28236	+	2.22111i	0.0527046	+	0.0912871i
$593$	7.58336			0.311411			0.155706	−	0.987804i	$-0.450235\pi$
$593$	7.58336			0.311411			0.155706	+	0.987804i	$0.450235\pi$
$594$		0			0
$595$	3.07287			0.125976
$596$	−2.60512	−	4.51221i	−0.106710	−	0.184827i
$597$		0			0
$598$	0.191931	−	0.332435i	0.00784866	−	0.0135943i
$599$	24.0482	−	41.6526i	0.982581	−	1.70188i	0.330352	−	0.943858i	$-0.392833\pi$
$599$	24.0482	−	41.6526i	0.982581	−	1.70188i	0.652229	−	0.758022i	$-0.273834\pi$
$600$		0			0
$601$	1.13416	+	1.96442i	0.0462634	+	0.0801305i	0.888230	−	0.459399i	$-0.151935\pi$
$601$	1.13416	+	1.96442i	0.0462634	+	0.0801305i	−0.841966	+	0.539530i	$0.818602\pi$
$602$	−9.73401			−0.396729
$603$		0			0
$604$	11.2287			0.456890
$605$	−3.31850	−	5.74782i	−0.134916	−	0.233682i
$606$		0			0
$607$	0.903270	−	1.56451i	0.0366626	−	0.0635015i	−0.847112	−	0.531415i	$-0.821661\pi$
$607$	0.903270	−	1.56451i	0.0366626	−	0.0635015i	0.883774	+	0.467913i	$0.154994\pi$
$608$	1.55789	−	2.69834i	0.0631806	−	0.109432i
$609$		0			0
$610$	−2.84691	−	4.93100i	−0.115268	−	0.199650i
$611$	−3.34192			−0.135200
$612$		0			0
$613$	8.41978			0.340072			0.170036	−	0.985438i	$-0.445612\pi$
$613$	8.41978			0.340072			0.170036	+	0.985438i	$0.445612\pi$
$614$	2.75898	+	4.77870i	0.111343	+	0.192853i
$615$		0			0
$616$	2.39025	−	4.14004i	0.0963060	−	0.166807i
$617$	15.6962	−	27.1867i	0.631906	−	1.09449i	−0.355256	−	0.934769i	$-0.615606\pi$
$617$	15.6962	−	27.1867i	0.631906	−	1.09449i	0.987162	−	0.159724i	$-0.0510605\pi$
$618$		0			0
$619$	8.18535	+	14.1774i	0.328997	+	0.569839i	0.982313	−	0.187246i	$-0.0599561\pi$
$619$	8.18535	+	14.1774i	0.328997	+	0.569839i	−0.653316	+	0.757085i	$0.726623\pi$
$620$	4.34835			0.174634
$621$		0			0
$622$	−26.0511			−1.04455
$623$	−4.01642	−	6.95665i	−0.160915	−	0.278712i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−5.41949	+	9.38684i	−0.216607	+	0.375174i
$627$		0			0
$628$	2.67891	+	4.64001i	0.106900	+	0.185157i
$629$	−3.44352			−0.137302
$630$		0			0
$631$	−26.7240			−1.06387			−0.531933	−	0.846787i	$-0.678534\pi$
$631$	−26.7240			−1.06387			−0.531933	+	0.846787i	$0.678534\pi$
$632$	−4.95999	−	8.59095i	−0.197298	−	0.341730i
$633$		0			0
$634$	−1.12747	+	1.95284i	−0.0447776	+	0.0775571i
$635$	9.28260	−	16.0779i	0.368369	−	0.638033i
$636$		0			0
$637$	−0.881015	−	1.52596i	−0.0349071	−	0.0604609i
$638$	7.67109			0.303701
$639$		0			0
$640$	−1.00000			−0.0395285
$641$	19.7860	+	34.2704i	0.781501	+	1.35360i	0.931067	+	0.364848i	$0.118879\pi$
$641$	19.7860	+	34.2704i	0.781501	+	1.35360i	−0.149566	+	0.988752i	$0.547788\pi$
$642$		0			0
$643$	−14.7925	+	25.6214i	−0.583360	+	1.01041i	0.411718	+	0.911311i	$0.364929\pi$
$643$	−14.7925	+	25.6214i	−0.583360	+	1.01041i	−0.995078	+	0.0990972i	$0.968405\pi$
$644$	0.439266	−	0.760831i	0.0173095	−	0.0299809i
$645$		0			0
$646$	2.09170	+	3.62293i	0.0822968	+	0.142542i
$647$	14.9579			0.588054			0.294027	−	0.955797i	$-0.405004\pi$
$647$	14.9579			0.588054			0.294027	+	0.955797i	$0.405004\pi$
$648$		0			0
$649$	−17.1939			−0.674918
$650$	0.500000	+	0.866025i	0.0196116	+	0.0339683i
$651$		0			0
$652$	−3.75882	+	6.51046i	−0.147207	+	0.254969i
$653$	−21.3270	+	36.9395i	−0.834590	+	1.44555i	0.0597734	+	0.998212i	$0.480962\pi$
$653$	−21.3270	+	36.9395i	−0.834590	+	1.44555i	−0.894364	+	0.447341i	$0.852371\pi$
$654$		0			0
$655$	−3.40750	−	5.90196i	−0.133142	−	0.230609i
$656$	1.13168			0.0441846
$657$		0			0
$658$	−7.64853			−0.298171
$659$	3.57781	+	6.19696i	0.139372	+	0.241399i	0.927259	−	0.374420i	$-0.122158\pi$
$659$	3.57781	+	6.19696i	0.139372	+	0.241399i	−0.787887	+	0.615820i	$0.788825\pi$
$660$		0			0
$661$	−8.03639	+	13.9194i	−0.312579	+	0.541403i	−0.978920	−	0.204244i	$-0.934526\pi$
$661$	−8.03639	+	13.9194i	−0.312579	+	0.541403i	0.666341	+	0.745647i	$0.267860\pi$
$662$	14.1948	−	24.5861i	0.551696	−	0.955565i
$663$		0			0
$664$	1.39736	+	2.42030i	0.0542281	+	0.0939258i
$665$	−7.13095			−0.276526
$666$		0			0
$667$	1.40975			0.0545856
$668$	7.73873	+	13.4039i	0.299420	+	0.518611i
$669$		0			0
$670$	0.770424	−	1.33441i	0.0297641	−	0.0515529i
$671$	5.94657	−	10.2998i	0.229565	−	0.397618i
$672$		0			0
$673$	−6.97003	−	12.0725i	−0.268675	−	0.465359i	0.699845	−	0.714295i	$-0.253252\pi$
$673$	−6.97003	−	12.0725i	−0.268675	−	0.465359i	−0.968520	+	0.248936i	$0.919919\pi$
$674$	−28.2580			−1.08846
$675$		0			0
$676$	1.00000			0.0384615
$677$	17.2974	+	29.9601i	0.664795	+	1.15146i	0.979341	+	0.202216i	$0.0648144\pi$
$677$	17.2974	+	29.9601i	0.664795	+	1.15146i	−0.314546	+	0.949242i	$0.601852\pi$
$678$		0			0
$679$	−5.23503	+	9.06734i	−0.200902	+	0.347972i
$680$	0.671326	−	1.16277i	0.0257442	−	0.0445902i
$681$		0			0
$682$	4.54136	+	7.86587i	0.173898	+	0.301200i
$683$	32.9086			1.25921			0.629605	−	0.776915i	$-0.283217\pi$
$683$	32.9086			1.25921			0.629605	+	0.776915i	$0.283217\pi$
$684$		0			0
$685$	−13.4058			−0.512209
$686$	−10.0267	−	17.3667i	−0.382820	−	0.663063i
$687$		0			0
$688$	−2.12657	+	3.68333i	−0.0810748	+	0.140426i
$689$	−1.02700	+	1.77881i	−0.0391254	+	0.0677672i
$690$		0			0
$691$	−8.92207	−	15.4535i	−0.339412	−	0.587878i	0.644911	−	0.764258i	$-0.276895\pi$
$691$	−8.92207	−	15.4535i	−0.339412	−	0.587878i	−0.984322	+	0.176380i	$0.943561\pi$
$692$	−24.7075			−0.939240
$693$		0			0
$694$	−5.05208			−0.191774
$695$	−7.24106	−	12.5419i	−0.274669	−	0.475741i
$696$		0			0
$697$	−0.759724	+	1.31588i	−0.0287766	+	0.0498425i
$698$	−0.545875	+	0.945483i	−0.0206617	+	0.0357870i
$699$		0			0
$700$	1.14433	+	1.98204i	0.0432516	+	0.0749140i
$701$	33.8350			1.27793			0.638964	−	0.769236i	$-0.279363\pi$
$701$	33.8350			1.27793			0.638964	+	0.769236i	$0.279363\pi$
$702$		0			0
$703$	7.99108			0.301389
$704$	−1.04439	−	1.80893i	−0.0393619	−	0.0681768i
$705$		0			0
$706$	12.9246	−	22.3861i	0.486425	−	0.842513i
$707$	−3.40945	+	5.90534i	−0.128226	+	0.222093i
$708$		0			0
$709$	14.1704	+	24.5439i	0.532181	+	0.921765i	0.999294	+	0.0375670i	$0.0119608\pi$
$709$	14.1704	+	24.5439i	0.532181	+	0.921765i	−0.467113	+	0.884198i	$0.654706\pi$
$710$	−3.86359			−0.144998
$711$		0			0
$712$	−3.50984			−0.131537
$713$	0.834584	+	1.44554i	0.0312554	+	0.0541360i
$714$		0			0
$715$	−1.04439	+	1.80893i	−0.0390579	+	0.0676503i
$716$	8.15080	−	14.1176i	0.304610	−	0.527599i
$717$		0			0
$718$	1.59043	+	2.75470i	0.0593542	+	0.102805i
$719$	−5.61477			−0.209396			−0.104698	−	0.994504i	$-0.533388\pi$
$719$	−5.61477			−0.209396			−0.104698	+	0.994504i	$0.533388\pi$
$720$		0			0
$721$	43.8238			1.63208
$722$	4.64598	+	8.04707i	0.172905	+	0.299481i
$723$		0			0
$724$	0.109898	−	0.190348i	0.00408431	−	0.00707423i
$725$	−1.83626	+	3.18050i	−0.0681971	+	0.118121i
$726$		0			0
$727$	−12.6476	−	21.9064i	−0.469075	−	0.812462i	0.530300	−	0.847810i	$-0.322079\pi$
$727$	−12.6476	−	21.9064i	−0.469075	−	0.812462i	−0.999375	+	0.0353480i	$0.988746\pi$
$728$	2.28866			0.0848234
$729$		0			0
$730$	−2.98321			−0.110414
$731$	−2.85525	−	4.94543i	−0.105605	−	0.182913i
$732$		0			0
$733$	−4.49916	+	7.79277i	−0.166180	+	0.287833i	−0.937074	−	0.349131i	$-0.886477\pi$
$733$	−4.49916	+	7.79277i	−0.166180	+	0.287833i	0.770894	+	0.636964i	$0.219810\pi$
$734$	−15.0789	+	26.1173i	−0.556571	+	0.964008i
$735$		0			0
$736$	−0.191931	−	0.332435i	−0.00707469	−	0.0122537i
$737$	3.21849			0.118555
$738$		0			0
$739$	−20.5564			−0.756178			−0.378089	−	0.925769i	$-0.623419\pi$
$739$	−20.5564			−0.756178			−0.378089	+	0.925769i	$0.623419\pi$
$740$	−1.28236	−	2.22111i	−0.0471404	−	0.0816496i
$741$		0			0
$742$	−2.35044	+	4.07109i	−0.0862875	+	0.149454i
$743$	−5.08377	+	8.80534i	−0.186505	+	0.323037i	−0.944083	−	0.329709i	$-0.893049\pi$
$743$	−5.08377	+	8.80534i	−0.186505	+	0.323037i	0.757577	+	0.652745i	$0.226383\pi$
$744$		0			0
$745$	2.60512	+	4.51221i	0.0954443	+	0.165314i
$746$	−21.9465			−0.803517
$747$		0			0
$748$	2.80450			0.102543
$749$	−14.1915	−	24.5805i	−0.518548	−	0.898151i
$750$		0			0
$751$	2.06969	−	3.58481i	0.0755242	−	0.130812i	−0.825790	−	0.563978i	$-0.809270\pi$
$751$	2.06969	−	3.58481i	0.0755242	−	0.130812i	0.901314	+	0.433166i	$0.142604\pi$
$752$	−1.67096	+	2.89419i	−0.0609337	+	0.105540i
$753$		0			0
$754$	1.83626	+	3.18050i	0.0668727	+	0.115827i
$755$	−11.2287			−0.408655
$756$		0			0
$757$	42.2348			1.53505			0.767524	−	0.641020i	$-0.221488\pi$
$757$	42.2348			1.53505			0.767524	+	0.641020i	$0.221488\pi$
$758$	8.73539	+	15.1301i	0.317284	+	0.549551i
$759$		0			0
$760$	−1.55789	+	2.69834i	−0.0565105	+	0.0978790i
$761$	−15.5543	+	26.9409i	−0.563843	+	0.976605i	0.433313	+	0.901244i	$0.357344\pi$
$761$	−15.5543	+	26.9409i	−0.563843	+	0.976605i	−0.997156	+	0.0753617i	$0.975989\pi$
$762$		0			0
$763$	−3.82833	−	6.63087i	−0.138595	−	0.240053i
$764$	−0.136413			−0.00493526
$765$		0			0
$766$	−22.7528			−0.822093
$767$	−4.11577	−	7.12873i	−0.148612	−	0.257403i
$768$		0			0
$769$	5.32217	−	9.21827i	0.191922	−	0.332419i	−0.753965	−	0.656915i	$-0.771861\pi$
$769$	5.32217	−	9.21827i	0.191922	−	0.332419i	0.945887	+	0.324495i	$0.105194\pi$
$770$	−2.39025	+	4.14004i	−0.0861387	+	0.149197i
$771$		0			0
$772$	9.94802	+	17.2305i	0.358037	+	0.620138i
$773$	42.7091			1.53614			0.768069	−	0.640367i	$-0.221218\pi$
$773$	42.7091			1.53614			0.768069	+	0.640367i	$0.221218\pi$
$774$		0			0
$775$	−4.34835			−0.156197
$776$	2.28738	+	3.96185i	0.0821120	+	0.142222i
$777$		0			0
$778$	10.9909	−	19.0368i	0.394043	−	0.682503i
$779$	1.76302	−	3.05365i	0.0631669	−	0.109408i
$780$		0			0
$781$	−4.03509	−	6.98898i	−0.144387	−	0.250085i
$782$	0.515394			0.0184304
$783$		0			0
$784$	−1.76203			−0.0629297
$785$	−2.67891	−	4.64001i	−0.0956145	−	0.165609i
$786$		0			0
$787$	−2.93651	+	5.08619i	−0.104675	+	0.181303i	−0.913606	−	0.406602i	$-0.866714\pi$
$787$	−2.93651	+	5.08619i	−0.104675	+	0.181303i	0.808930	+	0.587905i	$0.200047\pi$
$788$	3.79016	−	6.56475i	0.135019	−	0.233860i
$789$		0			0
$790$	4.95999	+	8.59095i	0.176468	+	0.305652i
$791$	8.87733			0.315642
$792$		0			0
$793$	5.69382			0.202194
$794$	−7.48834	−	12.9702i	−0.265751	−	0.460295i
$795$		0			0
$796$	11.5353	−	19.9797i	0.408857	−	0.708161i
$797$	15.7758	−	27.3244i	0.558806	−	0.967880i	−0.438791	−	0.898589i	$-0.644593\pi$
$797$	15.7758	−	27.3244i	0.558806	−	0.967880i	0.997597	−	0.0692909i	$-0.0220737\pi$
$798$		0			0
$799$	−2.24352	−	3.88589i	−0.0793700	−	0.137473i
$800$	1.00000			0.0353553
$801$		0			0
$802$	9.43319			0.333097
$803$	−3.11564	−	5.39644i	−0.109948	−	0.190436i
$804$		0			0
$805$	−0.439266	+	0.760831i	−0.0154821	+	0.0268158i
$806$	−2.17417	+	3.76578i	−0.0765820	+	0.132644i
$807$		0			0
$808$	1.48971	+	2.58026i	0.0524080	+	0.0907733i
$809$	−44.1579			−1.55251			−0.776254	−	0.630420i	$-0.782883\pi$
$809$	−44.1579			−1.55251			−0.776254	+	0.630420i	$0.782883\pi$
$810$		0			0
$811$	−10.6564			−0.374196			−0.187098	−	0.982341i	$-0.559908\pi$
$811$	−10.6564			−0.374196			−0.187098	+	0.982341i	$0.559908\pi$
$812$	4.20258	+	7.27908i	0.147482	+	0.255446i
$813$		0			0
$814$	2.67856	−	4.63941i	0.0938835	−	0.162611i
$815$	3.75882	−	6.51046i	0.131666	−	0.228052i
$816$		0			0
$817$	6.62592	+	11.4764i	0.231811	+	0.401509i
$818$	20.8731			0.729810
$819$		0			0
$820$	−1.13168			−0.0395199
$821$	26.3275	+	45.6005i	0.918834	+	1.59147i	0.801188	+	0.598412i	$0.204202\pi$
$821$	26.3275	+	45.6005i	0.918834	+	1.59147i	0.117646	+	0.993056i	$0.462465\pi$
$822$		0			0
$823$	−11.1693	+	19.3458i	−0.389338	+	0.674353i	−0.992361	−	0.123371i	$-0.960629\pi$
$823$	−11.1693	+	19.3458i	−0.389338	+	0.674353i	0.603023	+	0.797724i	$0.293963\pi$
$824$	9.57411	−	16.5828i	0.333530	−	0.577691i
$825$		0			0
$826$	−9.41961	−	16.3152i	−0.327750	−	0.567680i
$827$	30.1816			1.04952			0.524759	−	0.851251i	$-0.324155\pi$
$827$	30.1816			1.04952			0.524759	+	0.851251i	$0.324155\pi$
$828$		0			0
$829$	47.7093			1.65701			0.828506	−	0.559980i	$-0.189191\pi$
$829$	47.7093			1.65701			0.828506	+	0.559980i	$0.189191\pi$
$830$	−1.39736	−	2.42030i	−0.0485031	−	0.0840098i
$831$		0			0
$832$	0.500000	−	0.866025i	0.0173344	−	0.0300240i
$833$	1.18290	−	2.04884i	0.0409849	−	0.0709880i
$834$		0			0
$835$	−7.73873	−	13.4039i	−0.267810	−	0.463860i
$836$	−6.50816			−0.225089
$837$		0			0
$838$	5.57975			0.192749
$839$	−3.30450	−	5.72357i	−0.114084	−	0.197599i	0.803329	−	0.595535i	$-0.203060\pi$
$839$	−3.30450	−	5.72357i	−0.114084	−	0.197599i	−0.917413	+	0.397936i	$0.869727\pi$
$840$		0			0
$841$	7.75628	−	13.4343i	0.267458	−	0.463251i
$842$	10.0500	−	17.4072i	0.346348	−	0.599892i
$843$		0			0
$844$	−5.16571	−	8.94727i	−0.177811	−	0.307978i
$845$	−1.00000			−0.0344010
$846$		0			0
$847$	15.1899			0.521930
$848$	1.02700	+	1.77881i	0.0352672	+	0.0610845i
$849$		0			0
$850$	−0.671326	+	1.16277i	−0.0230263	+	0.0398827i
$851$	0.492250	−	0.852602i	0.0168741	−	0.0292268i
$852$		0			0
$853$	−12.2797	−	21.2690i	−0.420448	−	0.728237i	0.575536	−	0.817777i	$-0.304794\pi$
$853$	−12.2797	−	21.2690i	−0.420448	−	0.728237i	−0.995983	+	0.0895400i	$0.971460\pi$
$854$	13.0312			0.445920
$855$		0			0
$856$	−12.4016			−0.423878
$857$	24.4450	+	42.3401i	0.835027	+	1.44631i	0.894008	+	0.448050i	$0.147881\pi$
$857$	24.4450	+	42.3401i	0.835027	+	1.44631i	−0.0589816	+	0.998259i	$0.518785\pi$
$858$		0			0
$859$	−4.90171	+	8.49001i	−0.167244	+	0.289675i	−0.937450	−	0.348120i	$-0.886820\pi$
$859$	−4.90171	+	8.49001i	−0.167244	+	0.289675i	0.770206	+	0.637795i	$0.220153\pi$
$860$	2.12657	−	3.68333i	0.0725155	−	0.125601i
$861$		0			0
$862$	−14.0181	−	24.2800i	−0.477457	−	0.826980i
$863$	−46.2681			−1.57498			−0.787491	−	0.616326i	$-0.788621\pi$
$863$	−46.2681			−1.57498			−0.787491	+	0.616326i	$0.788621\pi$
$864$		0			0
$865$	24.7075			0.840082
$866$	2.49891	+	4.32823i	0.0849163	+	0.147079i
$867$		0			0
$868$	−4.97595	+	8.61859i	−0.168895	+	0.292534i
$869$	−10.3603	+	17.9446i	−0.351449	+	0.608728i
$870$		0			0
$871$	0.770424	+	1.33441i	0.0261048	+	0.0452149i
$872$	−3.34548			−0.113292
$873$		0			0
$874$	−1.19603			−0.0404563
$875$	−1.14433	−	1.98204i	−0.0386854	−	0.0670051i
$876$		0			0
$877$	−5.94165	+	10.2912i	−0.200635	+	0.347511i	−0.948733	−	0.316078i	$-0.897634\pi$
$877$	−5.94165	+	10.2912i	−0.200635	+	0.347511i	0.748098	+	0.663588i	$0.230967\pi$
$878$	0.234001	−	0.405301i	0.00789714	−	0.0136782i
$879$		0			0
$880$	1.04439	+	1.80893i	0.0352063	+	0.0609792i
$881$	35.8912			1.20920			0.604602	−	0.796528i	$-0.293332\pi$
$881$	35.8912			1.20920			0.604602	+	0.796528i	$0.293332\pi$
$882$		0			0
$883$	59.1872			1.99181			0.995904	−	0.0904131i	$-0.0288187\pi$
$883$	59.1872			1.99181			0.995904	+	0.0904131i	$0.0288187\pi$
$884$	0.671326	+	1.16277i	0.0225791	+	0.0391082i
$885$		0			0
$886$	−0.620624	+	1.07495i	−0.0208503	+	0.0361137i
$887$	−28.2254	+	48.8877i	−0.947715	+	1.64149i	−0.197492	+	0.980305i	$0.563280\pi$
$887$	−28.2254	+	48.8877i	−0.947715	+	1.64149i	−0.750223	+	0.661185i	$0.770054\pi$
$888$		0			0
$889$	21.2447	+	36.7969i	0.712525	+	1.23413i
$890$	3.50984			0.117650
$891$		0			0
$892$	27.1498			0.909041
$893$	5.20634	+	9.01764i	0.174223	+	0.301764i
$894$		0			0
$895$	−8.15080	+	14.1176i	−0.272451	+	0.471899i
$896$	1.14433	−	1.98204i	0.0382294	−	0.0662153i
$897$		0			0
$898$	8.55455	+	14.8169i	0.285469	+	0.494447i
$899$	−15.9694			−0.532610
$900$		0			0
$901$	−2.75779			−0.0918754
$902$	−1.18191	−	2.04713i	−0.0393533	−	0.0681619i
$903$		0			0
$904$	1.93942	−	3.35917i	0.0645040	−	0.111724i
$905$	−0.109898	+	0.190348i	−0.00365312	+	0.00632739i
$906$		0			0
$907$	3.55848	+	6.16347i	0.118157	+	0.204655i	0.919037	−	0.394170i	$-0.128968\pi$
$907$	3.55848	+	6.16347i	0.118157	+	0.204655i	−0.800880	+	0.598825i	$0.795635\pi$
$908$	3.93393			0.130552
$909$		0			0
$910$	−2.28866			−0.0758684
$911$	−8.19985	−	14.2026i	−0.271673	−	0.470552i	0.697617	−	0.716471i	$-0.254244\pi$
$911$	−8.19985	−	14.2026i	−0.271673	−	0.470552i	−0.969290	+	0.245919i	$0.920910\pi$
$912$		0			0
$913$	2.91878	−	5.05547i	0.0965974	−	0.167312i
$914$	−6.22825	+	10.7876i	−0.206012	+	0.356823i
$915$		0			0
$916$	−3.73928	−	6.47663i	−0.123549	−	0.213994i
$917$	15.5972			0.515065
$918$		0			0
$919$	5.18751			0.171120			0.0855601	−	0.996333i	$-0.472732\pi$
$919$	5.18751			0.171120			0.0855601	+	0.996333i	$0.472732\pi$
$920$	0.191931	+	0.332435i	0.00632779	+	0.0109601i
$921$		0			0
$922$	−1.28757	+	2.23014i	−0.0424040	+	0.0734459i
$923$	1.93179	−	3.34596i	0.0635858	−	0.110134i
$924$		0			0
$925$	1.28236	+	2.22111i	0.0421637	+	0.0730296i
$926$	8.53531			0.280488
$927$		0			0
$928$	3.67252			0.120557
$929$	2.35915	+	4.08616i	0.0774011	+	0.134063i	0.902128	−	0.431469i	$-0.142004\pi$
$929$	2.35915	+	4.08616i	0.0774011	+	0.134063i	−0.824727	+	0.565531i	$0.808671\pi$
$930$		0			0
$931$	−2.74504	+	4.75455i	−0.0899652	+	0.155824i
$932$	5.58272	−	9.66955i	0.182868	−	0.316737i
$933$		0			0
$934$	0.213103	+	0.369106i	0.00697295	+	0.0120775i
$935$	−2.80450			−0.0917170
$936$		0			0
$937$	41.4443			1.35393			0.676963	−	0.736017i	$-0.263296\pi$
$937$	41.4443			1.35393			0.676963	+	0.736017i	$0.263296\pi$
$938$	1.76324	+	3.05402i	0.0575718	+	0.0997172i
$939$		0			0
$940$	1.67096	−	2.89419i	0.0545007	−	0.0943981i
$941$	10.9111	−	18.8985i	0.355690	−	0.616074i	−0.631546	−	0.775339i	$-0.717579\pi$
$941$	10.9111	−	18.8985i	0.355690	−	0.616074i	0.987236	+	0.159265i	$0.0509125\pi$
$942$		0			0
$943$	−0.217204	−	0.376209i	−0.00707315	−	0.0122510i
$944$	−8.23155			−0.267914
$945$		0			0
$946$	8.88387			0.288840
$947$	7.23434	+	12.5302i	0.235084	+	0.407178i	0.959297	−	0.282398i	$-0.0911300\pi$
$947$	7.23434	+	12.5302i	0.235084	+	0.407178i	−0.724213	+	0.689577i	$0.757797\pi$
$948$		0			0
$949$	1.49161	−	2.58354i	0.0484196	−	0.0838652i
$950$	1.55789	−	2.69834i	0.0505445	−	0.0875457i
$951$		0			0
$952$	1.53644	+	2.66119i	0.0497962	+	0.0862496i
$953$	28.8687			0.935149			0.467575	−	0.883954i	$-0.345128\pi$
$953$	28.8687			0.935149			0.467575	+	0.883954i	$0.345128\pi$
$954$		0			0
$955$	0.136413			0.00441423
$956$	−1.79160	−	3.10313i	−0.0579443	−	0.100363i
$957$		0			0
$958$	3.51507	−	6.08829i	0.113567	−	0.196704i
$959$	15.3407	−	26.5708i	0.495376	−	0.858016i
$960$		0			0
$961$	6.04594	+	10.4719i	0.195030	+	0.337802i
$962$	2.56472			0.0826898
$963$		0			0
$964$	−21.7135			−0.699345
$965$	−9.94802	−	17.2305i	−0.320238	−	0.554668i
$966$		0			0
$967$	−10.9151	+	18.9054i	−0.351005	+	0.607958i	−0.986426	−	0.164208i	$-0.947493\pi$
$967$	−10.9151	+	18.9054i	−0.351005	+	0.607958i	0.635421	+	0.772166i	$0.280827\pi$
$968$	3.31850	−	5.74782i	0.106661	−	0.184742i
$969$		0			0
$970$	−2.28738	−	3.96185i	−0.0734432	−	0.127207i
$971$	31.1439			0.999454			0.499727	−	0.866183i	$-0.333434\pi$
$971$	31.1439			0.999454			0.499727	+	0.866183i	$0.333434\pi$
$972$		0			0
$973$	33.1447			1.06257
$974$	0.191181	+	0.331135i	0.00612583	+	0.0106103i
$975$		0			0
$976$	2.84691	−	4.93100i	0.0911274	−	0.157837i
$977$	−14.2814	+	24.7361i	−0.456903	+	0.791379i	−0.998795	−	0.0490686i	$-0.984375\pi$
$977$	−14.2814	+	24.7361i	−0.456903	+	0.791379i	0.541892	+	0.840448i	$0.317708\pi$
$978$		0			0
$979$	3.66564	+	6.34908i	0.117154	+	0.202917i
$980$	1.76203			0.0562860
$981$		0			0
$982$	−30.7662			−0.981789
$983$	−10.2967	−	17.8344i	−0.328414	−	0.568829i	0.653784	−	0.756682i	$-0.273181\pi$
$983$	−10.2967	−	17.8344i	−0.328414	−	0.568829i	−0.982197	+	0.187852i	$0.939847\pi$
$984$		0			0
$985$	−3.79016	+	6.56475i	−0.120765	+	0.209170i
$986$	−2.46546	+	4.27030i	−0.0785162	+	0.135994i
$987$		0			0
$988$	−1.55789	−	2.69834i	−0.0495630	−	0.0858456i
$989$	1.63262			0.0519144
$990$		0			0
$991$	0.397448			0.0126253			0.00631267	−	0.999980i	$-0.497991\pi$
$991$	0.397448			0.0126253			0.00631267	+	0.999980i	$0.497991\pi$
$992$	2.17417	+	3.76578i	0.0690301	+	0.119564i
$993$		0			0
$994$	4.42122	−	7.65778i	0.140233	−	0.242890i
$995$	−11.5353	+	19.9797i	−0.365693	+	0.633398i
$996$		0			0
$997$	18.5238	+	32.0842i	0.586656	+	1.01612i	0.994667	+	0.103140i	$0.0328891\pi$
$997$	18.5238	+	32.0842i	0.586656	+	1.01612i	−0.408011	+	0.912977i	$0.633778\pi$
$998$	39.2310			1.24184
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3510.2.j.i.1171.5		10
3.2	odd	2		1170.2.j.j.391.5	✓	10
9.2	odd	6		1170.2.j.j.781.5	yes	10
9.7	even	3	inner	3510.2.j.i.2341.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.j.j.391.5	✓	10	3.2	odd	2
1170.2.j.j.781.5	yes	10	9.2	odd	6
3510.2.j.i.1171.5		10	1.1	even	1	trivial
3510.2.j.i.2341.5		10	9.7	even	3	inner

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

Level:	\( N \)	\(=\)	\( 3510 = 2 \cdot 3^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3510.j (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.14433 + 1.98204i) q^{7} +1.00000 q^{8} -1.00000 q^{10} +(-1.04439 - 1.80893i) q^{11} +(0.500000 - 0.866025i) q^{13} +(1.14433 - 1.98204i) q^{14} +(-0.500000 - 0.866025i) q^{16} +1.34265 q^{17} -3.11577 q^{19} +(0.500000 + 0.866025i) q^{20} +(-1.04439 + 1.80893i) q^{22} +(-0.191931 + 0.332435i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{26} -2.28866 q^{28} +(-1.83626 - 3.18050i) q^{29} +(2.17417 - 3.76578i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.671326 - 1.16277i) q^{34} +2.28866 q^{35} -2.56472 q^{37} +(1.55789 + 2.69834i) q^{38} +(0.500000 - 0.866025i) q^{40} +(-0.565838 + 0.980061i) q^{41} +(-2.12657 - 3.68333i) q^{43} +2.08878 q^{44} +0.383863 q^{46} +(-1.67096 - 2.89419i) q^{47} +(0.881015 - 1.52596i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.500000 + 0.866025i) q^{52} -2.05399 q^{53} -2.08878 q^{55} +(1.14433 + 1.98204i) q^{56} +(-1.83626 + 3.18050i) q^{58} +(4.11577 - 7.12873i) q^{59} +(2.84691 + 4.93100i) q^{61} -4.34835 q^{62} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +(-0.770424 + 1.33441i) q^{67} +(-0.671326 + 1.16277i) q^{68} +(-1.14433 - 1.98204i) q^{70} +3.86359 q^{71} +2.98321 q^{73} +(1.28236 + 2.22111i) q^{74} +(1.55789 - 2.69834i) q^{76} +(2.39025 - 4.14004i) q^{77} +(-4.95999 - 8.59095i) q^{79} -1.00000 q^{80} +1.13168 q^{82} +(1.39736 + 2.42030i) q^{83} +(0.671326 - 1.16277i) q^{85} +(-2.12657 + 3.68333i) q^{86} +(-1.04439 - 1.80893i) q^{88} -3.50984 q^{89} +2.28866 q^{91} +(-0.191931 - 0.332435i) q^{92} +(-1.67096 + 2.89419i) q^{94} +(-1.55789 + 2.69834i) q^{95} +(2.28738 + 3.96185i) q^{97} -1.76203 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - 5 q^{4} + 5 q^{5} - 5 q^{7} + 10 q^{8} - 10 q^{10} + 2 q^{11} + 5 q^{13} - 5 q^{14} - 5 q^{16} - 16 q^{17} - 8 q^{19} + 5 q^{20} + 2 q^{22} + q^{23} - 5 q^{25} - 10 q^{26} + 10 q^{28}+ \cdots - 12 q^{98}+O(q^{100}) \) 10 * q - 5 * q^2 - 5 * q^4 + 5 * q^5 - 5 * q^7 + 10 * q^8 - 10 * q^10 + 2 * q^11 + 5 * q^13 - 5 * q^14 - 5 * q^16 - 16 * q^17 - 8 * q^19 + 5 * q^20 + 2 * q^22 + q^23 - 5 * q^25 - 10 * q^26 + 10 * q^28 + q^29 + 4 * q^31 - 5 * q^32 + 8 * q^34 - 10 * q^35 - 12 * q^37 + 4 * q^38 + 5 * q^40 + 11 * q^41 + 10 * q^43 - 4 * q^44 - 2 * q^46 + 27 * q^47 + 6 * q^49 - 5 * q^50 + 5 * q^52 - 24 * q^53 + 4 * q^55 - 5 * q^56 + q^58 + 18 * q^59 + 13 * q^61 - 8 * q^62 + 10 * q^64 - 5 * q^65 - 5 * q^67 + 8 * q^68 + 5 * q^70 - 12 * q^71 + 24 * q^73 + 6 * q^74 + 4 * q^76 + 8 * q^77 - 2 * q^79 - 10 * q^80 - 22 * q^82 + 9 * q^83 - 8 * q^85 + 10 * q^86 + 2 * q^88 - 2 * q^89 - 10 * q^91 + q^92 + 27 * q^94 - 4 * q^95 - 2 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more