LMFDB - Embedded newform 1323.2.f.g.442.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(442,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1323.442");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 $ x^12 - 7x^10 + 37x^8 - 78x^6 + 123x^4 - 36*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			442.5
Root			$-1.82904 - 1.05600i$ of defining polynomial
Character	$\chi$	$=$	1323.442
Dual form			1323.2.f.g.883.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23025 + 2.13086i) q^{2} +(-2.02704 + 3.51094i) q^{4} +(-1.82904 + 3.16799i) q^{5} -5.05408 q^{8} +O(q^{10})$	\(q+(1.23025 + 2.13086i) q^{2} +(-2.02704 + 3.51094i) q^{4} +(-1.82904 + 3.16799i) q^{5} -5.05408 q^{8} -9.00071 q^{10} +(0.203210 + 0.351971i) q^{11} +(0.243398 - 0.421578i) q^{13} +(-2.16372 - 3.74766i) q^{16} -4.85584 q^{17} -1.97351 q^{19} +(-7.41507 - 12.8433i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(2.32383 - 4.02499i) q^{23} +(-4.19076 - 7.25860i) q^{25} +1.19777 q^{26} +(3.82383 + 6.62307i) q^{29} +(-3.51360 + 6.08573i) q^{31} +(0.269748 - 0.467216i) q^{32} +(-5.97391 - 10.3471i) q^{34} +2.32743 q^{37} +(-2.42792 - 4.20528i) q^{38} +(9.24411 - 16.0113i) q^{40} +(3.75700 - 6.50731i) q^{41} +(1.16372 + 2.01561i) q^{43} -1.64766 q^{44} +11.4356 q^{46} +(-3.15811 - 5.47002i) q^{47} +(10.3114 - 17.8598i) q^{50} +(0.986757 + 1.70911i) q^{52} +3.56867 q^{53} -1.48672 q^{55} +(-9.40856 + 16.2961i) q^{58} +(3.05919 - 5.29868i) q^{59} +(4.01356 + 6.95169i) q^{61} -17.2905 q^{62} -7.32743 q^{64} +(0.890369 + 1.54216i) q^{65} +(-1.80039 + 3.11836i) q^{67} +(9.84299 - 17.0486i) q^{68} -8.46050 q^{71} +1.97351 q^{73} +(2.86333 + 4.95943i) q^{74} +(4.00040 - 6.92889i) q^{76} +(-4.08113 - 7.06872i) q^{79} +15.8301 q^{80} +18.4882 q^{82} +(6.08600 + 10.5413i) q^{83} +(8.88151 - 15.3832i) q^{85} +(-2.86333 + 4.95943i) q^{86} +(-1.02704 - 1.77889i) q^{88} -14.8301 q^{89} +(9.42101 + 16.3177i) q^{92} +(7.77056 - 13.4590i) q^{94} +(3.60963 - 6.25206i) q^{95} +(4.74375 + 8.21642i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 6 q^{4} - 24 q^{8}+O(q^{10}) $ 12 * q + 2 * q^2 - 6 * q^4 - 24 * q^8	$ 12 q + 2 q^{2} - 6 q^{4} - 24 q^{8} + 8 q^{11} - 6 q^{16} - 6 q^{22} + 4 q^{23} - 12 q^{25} + 22 q^{29} + 16 q^{32} - 12 q^{37} - 6 q^{43} + 28 q^{44} + 24 q^{46} + 56 q^{50} - 56 q^{53} - 18 q^{58} - 48 q^{64} - 6 q^{65} - 76 q^{71} + 36 q^{74} + 6 q^{79} + 30 q^{85} - 36 q^{86} + 6 q^{88} + 62 q^{92} + 60 q^{95}+O(q^{100}) $ 12 * q + 2 * q^2 - 6 * q^4 - 24 * q^8 + 8 * q^11 - 6 * q^16 - 6 * q^22 + 4 * q^23 - 12 * q^25 + 22 * q^29 + 16 * q^32 - 12 * q^37 - 6 * q^43 + 28 * q^44 + 24 * q^46 + 56 * q^50 - 56 * q^53 - 18 * q^58 - 48 * q^64 - 6 * q^65 - 76 * q^71 + 36 * q^74 + 6 * q^79 + 30 * q^85 - 36 * q^86 + 6 * q^88 + 62 * q^92 + 60 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.23025	+	2.13086i	0.869920	+	1.50675i	0.862078	+	0.506776i	$0.169163\pi$
$2$	1.23025	+	2.13086i	0.869920	+	1.50675i	0.00784213	+	0.999969i	$0.497504\pi$
$3$		0			0
$3$		0			0
$4$	−2.02704	+	3.51094i	−1.01352	+	1.75547i
$5$	−1.82904	+	3.16799i	−0.817970	+	1.41677i	0.0892047	+	0.996013i	$0.471567\pi$
$5$	−1.82904	+	3.16799i	−0.817970	+	1.41677i	−0.907175	+	0.420753i	$0.861766\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−5.05408			−1.78689
$9$		0			0
$10$	−9.00071			−2.84628
$11$	0.203210	+	0.351971i	0.0612702	+	0.106123i	0.895033	−	0.445999i	$-0.147152\pi$
$11$	0.203210	+	0.351971i	0.0612702	+	0.106123i	−0.833763	+	0.552122i	$0.813818\pi$
$12$		0			0
$13$	0.243398	−	0.421578i	0.0675065	−	0.116925i	−0.830297	−	0.557322i	$-0.811829\pi$
$13$	0.243398	−	0.421578i	0.0675065	−	0.116925i	0.897803	+	0.440397i	$0.145162\pi$
$14$		0			0
$15$		0			0
$16$	−2.16372	−	3.74766i	−0.540929	−	0.936916i
$17$	−4.85584			−1.17771			−0.588857	−	0.808237i	$-0.700422\pi$
$17$	−4.85584			−1.17771			−0.588857	+	0.808237i	$0.700422\pi$
$18$		0			0
$19$	−1.97351			−0.452755			−0.226378	−	0.974040i	$-0.572688\pi$
$19$	−1.97351			−0.452755			−0.226378	+	0.974040i	$0.572688\pi$
$20$	−7.41507	−	12.8433i	−1.65806	−	2.87185i
$21$		0			0
$22$	−0.500000	+	0.866025i	−0.106600	+	0.184637i
$23$	2.32383	−	4.02499i	0.484552	−	0.839269i	−0.515290	−	0.857016i	$-0.672316\pi$
$23$	2.32383	−	4.02499i	0.484552	−	0.839269i	0.999843	+	0.0177464i	$0.00564915\pi$
$24$		0			0
$25$	−4.19076	−	7.25860i	−0.838151	−	1.45172i
$26$	1.19777			0.234901
$27$		0			0
$28$		0			0
$29$	3.82383	+	6.62307i	0.710068	+	1.22987i	0.964831	+	0.262870i	$0.0846690\pi$
$29$	3.82383	+	6.62307i	0.710068	+	1.22987i	−0.254764	+	0.967003i	$0.581998\pi$
$30$		0			0
$31$	−3.51360	+	6.08573i	−0.631061	+	1.09303i	0.356274	+	0.934381i	$0.384047\pi$
$31$	−3.51360	+	6.08573i	−0.631061	+	1.09303i	−0.987335	+	0.158648i	$0.949286\pi$
$32$	0.269748	−	0.467216i	0.0476851	−	0.0825930i
$33$		0			0
$34$	−5.97391	−	10.3471i	−1.02452	−	1.77452i
$35$		0			0
$36$		0			0
$37$	2.32743			0.382627			0.191314	−	0.981529i	$-0.438725\pi$
$37$	2.32743			0.382627			0.191314	+	0.981529i	$0.438725\pi$
$38$	−2.42792	−	4.20528i	−0.393861	−	0.682187i
$39$		0			0
$40$	9.24411	−	16.0113i	1.46162	−	2.53160i
$41$	3.75700	−	6.50731i	0.586744	−	1.01627i	−0.407911	−	0.913022i	$-0.633743\pi$
$41$	3.75700	−	6.50731i	0.586744	−	1.01627i	0.994655	−	0.103249i	$-0.0329240\pi$
$42$		0			0
$43$	1.16372	+	2.01561i	0.177465	+	0.307378i	0.941012	−	0.338374i	$-0.109877\pi$
$43$	1.16372	+	2.01561i	0.177465	+	0.307378i	−0.763547	+	0.645753i	$0.776544\pi$
$44$	−1.64766			−0.248395
$45$		0			0
$46$	11.4356			1.68609
$47$	−3.15811	−	5.47002i	−0.460658	−	0.797884i	0.538335	−	0.842731i	$-0.319053\pi$
$47$	−3.15811	−	5.47002i	−0.460658	−	0.797884i	−0.998994	+	0.0448469i	$0.985720\pi$
$48$		0			0
$49$		0			0
$50$	10.3114	−	17.8598i	1.45825	−	2.52576i
$51$		0			0
$52$	0.986757	+	1.70911i	0.136839	+	0.237011i
$53$	3.56867			0.490195			0.245097	−	0.969498i	$-0.421180\pi$
$53$	3.56867			0.490195			0.245097	+	0.969498i	$0.421180\pi$
$54$		0			0
$55$	−1.48672			−0.200469
$56$		0			0
$57$		0			0
$58$	−9.40856	+	16.2961i	−1.23540	+	2.13978i
$59$	3.05919	−	5.29868i	0.398273	−	0.689829i	−0.595240	−	0.803548i	$-0.702943\pi$
$59$	3.05919	−	5.29868i	0.398273	−	0.689829i	0.993513	+	0.113719i	$0.0362763\pi$
$60$		0			0
$61$	4.01356	+	6.95169i	0.513884	+	0.890073i	0.999870	+	0.0161063i	$0.00512703\pi$
$61$	4.01356	+	6.95169i	0.513884	+	0.890073i	−0.485987	+	0.873966i	$0.661540\pi$
$62$	−17.2905			−2.19589
$63$		0			0
$64$	−7.32743			−0.915929
$65$	0.890369	+	1.54216i	0.110437	+	0.191282i
$66$		0			0
$67$	−1.80039	+	3.11836i	−0.219952	+	0.380969i	−0.954793	−	0.297271i	$-0.903924\pi$
$67$	−1.80039	+	3.11836i	−0.219952	+	0.380969i	0.734841	+	0.678240i	$0.237257\pi$
$68$	9.84299	−	17.0486i	1.19364	−	2.06744i
$69$		0			0
$70$		0			0
$71$	−8.46050			−1.00408			−0.502039	−	0.864845i	$-0.667416\pi$
$71$	−8.46050			−1.00408			−0.502039	+	0.864845i	$0.667416\pi$
$72$		0			0
$73$	1.97351			0.230982			0.115491	−	0.993309i	$-0.463156\pi$
$73$	1.97351			0.230982			0.115491	+	0.993309i	$0.463156\pi$
$74$	2.86333	+	4.95943i	0.332855	+	0.576522i
$75$		0			0
$76$	4.00040	−	6.92889i	0.458877	−	0.794798i
$77$		0			0
$78$		0			0
$79$	−4.08113	−	7.06872i	−0.459163	−	0.795293i	0.539754	−	0.841823i	$-0.318517\pi$
$79$	−4.08113	−	7.06872i	−0.459163	−	0.795293i	−0.998917	+	0.0465297i	$0.985184\pi$
$80$	15.8301			1.76986
$81$		0			0
$82$	18.4882			2.04168
$83$	6.08600	+	10.5413i	0.668025	+	1.15705i	0.978456	+	0.206457i	$0.0661933\pi$
$83$	6.08600	+	10.5413i	0.668025	+	1.15705i	−0.310431	+	0.950596i	$0.600473\pi$
$84$		0			0
$85$	8.88151	−	15.3832i	0.963336	−	1.66855i
$86$	−2.86333	+	4.95943i	−0.308760	+	0.534789i
$87$		0			0
$88$	−1.02704	−	1.77889i	−0.109483	−	0.189630i
$89$	−14.8301			−1.57199			−0.785996	−	0.618231i	$-0.787849\pi$
$89$	−14.8301			−1.57199			−0.785996	+	0.618231i	$0.787849\pi$
$90$		0			0
$91$		0			0
$92$	9.42101	+	16.3177i	0.982208	+	1.70123i
$93$		0			0
$94$	7.77056	−	13.4590i	0.801472	−	1.38819i
$95$	3.60963	−	6.25206i	0.370340	−	0.641448i
$96$		0			0
$97$	4.74375	+	8.21642i	0.481655	+	0.834251i	0.999778	−	0.0210547i	$-0.00670241\pi$
$97$	4.74375	+	8.21642i	0.481655	+	0.834251i	−0.518123	+	0.855306i	$0.673369\pi$
$98$		0			0
$99$		0			0
$100$	33.9794			3.39794
$101$	4.35588	+	7.54461i	0.433426	+	0.750716i	0.997166	−	0.0752364i	$-0.0239711\pi$
$101$	4.35588	+	7.54461i	0.433426	+	0.750716i	−0.563739	+	0.825953i	$0.690638\pi$
$102$		0			0
$103$	−4.01356	+	6.95169i	−0.395468	+	0.684970i	−0.993161	−	0.116755i	$-0.962751\pi$
$103$	−4.01356	+	6.95169i	−0.395468	+	0.684970i	0.597693	+	0.801725i	$0.296084\pi$
$104$	−1.23016	+	2.13069i	−0.120627	+	0.208931i
$105$		0			0
$106$	4.39037	+	7.60434i	0.426430	+	0.738599i
$107$	−12.8420			−1.24148			−0.620742	−	0.784015i	$-0.713169\pi$
$107$	−12.8420			−1.24148			−0.620742	+	0.784015i	$0.713169\pi$
$108$		0			0
$109$	2.60078			0.249109			0.124555	−	0.992213i	$-0.460250\pi$
$109$	2.60078			0.249109			0.124555	+	0.992213i	$0.460250\pi$
$110$	−1.82904	−	3.16799i	−0.174392	−	0.302056i
$111$		0			0
$112$		0			0
$113$	−6.97509	+	12.0812i	−0.656162	+	1.13651i	0.325440	+	0.945563i	$0.394488\pi$
$113$	−6.97509	+	12.0812i	−0.656162	+	1.13651i	−0.981601	+	0.190942i	$0.938846\pi$
$114$		0			0
$115$	8.50075	+	14.7237i	0.792699	+	1.37300i
$116$	−31.0043			−2.87867
$117$		0			0
$118$	15.0543			1.38586
$119$		0			0
$120$		0			0
$121$	5.41741	−	9.38323i	0.492492	−	0.853021i
$122$	−9.87538	+	17.1047i	−0.894075	+	1.54858i
$123$		0			0
$124$	−14.2444	−	24.6721i	−1.27919	−	2.21562i
$125$	12.3698			1.10639
$126$		0			0
$127$	−15.5438			−1.37929			−0.689643	−	0.724149i	$-0.742233\pi$
$127$	−15.5438			−1.37929			−0.689643	+	0.724149i	$0.742233\pi$
$128$	−9.55408	−	16.5482i	−0.844470	−	1.46266i
$129$		0			0
$130$	−2.19076	+	3.79450i	−0.192142	+	0.332800i
$131$	−4.25696	+	7.37327i	−0.371932	+	0.644205i	−0.989863	−	0.142027i	$-0.954638\pi$
$131$	−4.25696	+	7.37327i	−0.371932	+	0.644205i	0.617931	+	0.786233i	$0.287971\pi$
$132$		0			0
$133$		0			0
$134$	−8.85973			−0.765364
$135$		0			0
$136$	24.5418			2.10444
$137$	0.188621	+	0.326702i	0.0161150	+	0.0279120i	0.873970	−	0.485979i	$-0.161537\pi$
$137$	0.188621	+	0.326702i	0.0161150	+	0.0279120i	−0.857855	+	0.513891i	$0.828204\pi$
$138$		0			0
$139$	9.50067	−	16.4556i	0.805837	−	1.39575i	−0.109888	−	0.993944i	$-0.535049\pi$
$139$	9.50067	−	16.4556i	0.805837	−	1.39575i	0.915725	−	0.401806i	$-0.131617\pi$
$140$		0			0
$141$		0			0
$142$	−10.4086	−	18.0281i	−0.873467	−	1.51289i
$143$	0.197844			0.0165446
$144$		0			0
$145$	−27.9757			−2.32326
$146$	2.42792	+	4.20528i	0.200936	+	0.348032i
$147$		0			0
$148$	−4.71780	+	8.17147i	−0.387801	+	0.671691i
$149$	−4.85087	+	8.40196i	−0.397399	+	0.688315i	−0.993404	−	0.114665i	$-0.963420\pi$
$149$	−4.85087	+	8.40196i	−0.397399	+	0.688315i	0.596005	+	0.802981i	$0.296754\pi$
$150$		0			0
$151$	6.41741	+	11.1153i	0.522242	+	0.904549i	0.999665	+	0.0258756i	$0.00823738\pi$
$151$	6.41741	+	11.1153i	0.522242	+	0.904549i	−0.477424	+	0.878673i	$0.658429\pi$
$152$	9.97430			0.809023
$153$		0			0
$154$		0			0
$155$	−12.8530	−	22.2621i	−1.03238	−	1.78813i
$156$		0			0
$157$	−10.4743	+	18.1420i	−0.835937	+	1.44789i	0.0573276	+	0.998355i	$0.481742\pi$
$157$	−10.4743	+	18.1420i	−0.835937	+	1.44789i	−0.893265	+	0.449531i	$0.851591\pi$
$158$	10.0416	−	17.3926i	0.798869	−	1.38368i
$159$		0			0
$160$	0.986757	+	1.70911i	0.0780100	+	0.135117i
$161$		0			0
$162$		0			0
$163$	−11.1623			−0.874295			−0.437148	−	0.899390i	$-0.644011\pi$
$163$	−11.1623			−0.874295			−0.437148	+	0.899390i	$0.644011\pi$
$164$	15.2312	+	26.3812i	1.18936	+	2.06002i
$165$		0			0
$166$	−14.9746	+	25.9368i	−1.16226	+	2.01309i
$167$	1.73012	−	2.99665i	0.133880	−	0.231888i	−0.791289	−	0.611443i	$-0.790590\pi$
$167$	1.73012	−	2.99665i	0.133880	−	0.231888i	0.925169	+	0.379555i	$0.123923\pi$
$168$		0			0
$169$	6.38151	+	11.0531i	0.490886	+	0.850239i
$170$	43.7060			3.35210
$171$		0			0
$172$	−9.43560			−0.719458
$173$	−3.02680	−	5.24258i	−0.230124	−	0.398586i	0.727721	−	0.685874i	$-0.240580\pi$
$173$	−3.02680	−	5.24258i	−0.230124	−	0.398586i	−0.957844	+	0.287288i	$0.907246\pi$
$174$		0			0
$175$		0			0
$176$	0.879379	−	1.52313i	0.0662857	−	0.114810i
$177$		0			0
$178$	−18.2448	−	31.6010i	−1.36751	−	2.36859i
$179$	−9.13307			−0.682638			−0.341319	−	0.939948i	$-0.610874\pi$
$179$	−9.13307			−0.682638			−0.341319	+	0.939948i	$0.610874\pi$
$180$		0			0
$181$	11.9478			0.888074			0.444037	−	0.896008i	$-0.353546\pi$
$181$	11.9478			0.888074			0.444037	+	0.896008i	$0.353546\pi$
$182$		0			0
$183$		0			0
$184$	−11.7448	+	20.3427i	−0.865841	+	1.49968i
$185$	−4.25696	+	7.37327i	−0.312978	+	0.542093i
$186$		0			0
$187$	−0.986757	−	1.70911i	−0.0721588	−	0.124983i
$188$	25.6065			1.86755
$189$		0			0
$190$	17.7630			1.28867
$191$	4.57014	+	7.91571i	0.330683	+	0.572760i	0.982646	−	0.185491i	$-0.0593874\pi$
$191$	4.57014	+	7.91571i	0.330683	+	0.572760i	−0.651963	+	0.758251i	$0.726054\pi$
$192$		0			0
$193$	−8.47150	+	14.6731i	−0.609792	+	1.05619i	0.381483	+	0.924376i	$0.375414\pi$
$193$	−8.47150	+	14.6731i	−0.609792	+	1.05619i	−0.991274	+	0.131814i	$0.957920\pi$
$194$	−11.6720	+	20.2165i	−0.838003	+	1.45146i
$195$		0			0
$196$		0			0
$197$	21.3173			1.51880			0.759398	−	0.650627i	$-0.225494\pi$
$197$	21.3173			1.51880			0.759398	+	0.650627i	$0.225494\pi$
$198$		0			0
$199$	9.97430			0.707060			0.353530	−	0.935423i	$-0.384981\pi$
$199$	9.97430			0.707060			0.353530	+	0.935423i	$0.384981\pi$
$200$	21.1804	+	36.6856i	1.49768	+	2.59406i
$201$		0			0
$202$	−10.7177	+	18.5635i	−0.754092	+	1.30613i
$203$		0			0
$204$		0			0
$205$	13.7434	+	23.8042i	0.959879	+	1.66256i
$206$	−19.7508			−1.37610
$207$		0			0
$208$	−2.10658			−0.146065
$209$	−0.401038	−	0.694619i	−0.0277404	−	0.0480478i
$210$		0			0
$211$	−2.44592	+	4.23645i	−0.168384	+	0.291649i	−0.937852	−	0.347036i	$-0.887188\pi$
$211$	−2.44592	+	4.23645i	−0.168384	+	0.291649i	0.769468	+	0.638685i	$0.220521\pi$
$212$	−7.23385	+	12.5294i	−0.496823	+	0.860523i
$213$		0			0
$214$	−15.7989	−	27.3645i	−1.07999	−	1.87060i
$215$	−8.51392			−0.580644
$216$		0			0
$217$		0			0
$218$	3.19961	+	5.54189i	0.216705	+	0.375344i
$219$		0			0
$220$	3.01364	−	5.21978i	0.203179	−	0.351917i
$221$	−1.18190	+	2.04712i	−0.0795034	+	0.137704i
$222$		0			0
$223$	11.7044	+	20.2727i	0.783786	+	1.35756i	0.929722	+	0.368263i	$0.120047\pi$
$223$	11.7044	+	20.2727i	0.783786	+	1.35756i	−0.145936	+	0.989294i	$0.546619\pi$
$224$		0			0
$225$		0			0
$226$	−34.3245			−2.28323
$227$	−3.05919	−	5.29868i	−0.203046	−	0.351686i	0.746463	−	0.665427i	$-0.231751\pi$
$227$	−3.05919	−	5.29868i	−0.203046	−	0.351686i	−0.949508	+	0.313742i	$0.898417\pi$
$228$		0			0
$229$	−0.730195	+	1.26473i	−0.0482526	+	0.0835760i	−0.889143	−	0.457630i	$-0.848699\pi$
$229$	−0.730195	+	1.26473i	−0.0482526	+	0.0835760i	0.840890	+	0.541206i	$0.182032\pi$
$230$	−20.9161	+	36.2278i	−1.37917	+	2.38879i
$231$		0			0
$232$	−19.3260	−	33.4736i	−1.26881	−	2.19765i
$233$	13.2484			0.867934			0.433967	−	0.900929i	$-0.357113\pi$
$233$	13.2484			0.867934			0.433967	+	0.900929i	$0.357113\pi$
$234$		0			0
$235$	23.1052			1.50722
$236$	12.4022	+	21.4813i	0.807316	+	1.39831i
$237$		0			0
$238$		0			0
$239$	9.69436	−	16.7911i	0.627076	−	1.08613i	−0.361060	−	0.932543i	$-0.617585\pi$
$239$	9.69436	−	16.7911i	0.627076	−	1.08613i	0.988136	−	0.153584i	$-0.0490817\pi$
$240$		0			0
$241$	2.52684	+	4.37662i	0.162768	+	0.281923i	0.935860	−	0.352371i	$-0.114624\pi$
$241$	2.52684	+	4.37662i	0.162768	+	0.281923i	−0.773092	+	0.634294i	$0.781291\pi$
$242$	26.6591			1.71371
$243$		0			0
$244$	−32.5426			−2.08333
$245$		0			0
$246$		0			0
$247$	−0.480350	+	0.831990i	−0.0305639	+	0.0529383i
$248$	17.7580	−	30.7578i	1.12764	−	1.95312i
$249$		0			0
$250$	15.2180	+	26.3584i	0.962472	+	1.66705i
$251$	15.0928			0.952647			0.476324	−	0.879270i	$-0.341969\pi$
$251$	15.0928			0.952647			0.476324	+	0.879270i	$0.341969\pi$
$252$		0			0
$253$	1.88891			0.118755
$254$	−19.1228	−	33.1216i	−1.19987	−	2.07823i
$255$		0			0
$256$	16.1804	−	28.0253i	1.01128	−	1.75158i
$257$	−3.85592	+	6.67865i	−0.240526	+	0.416603i	−0.960864	−	0.277020i	$-0.910653\pi$
$257$	−3.85592	+	6.67865i	−0.240526	+	0.416603i	0.720338	+	0.693623i	$0.243986\pi$
$258$		0			0
$259$		0			0
$260$	−7.21926			−0.447720
$261$		0			0
$262$	−20.9485			−1.29420
$263$	2.10603	+	3.64776i	0.129864	+	0.224930i	0.923624	−	0.383301i	$-0.125213\pi$
$263$	2.10603	+	3.64776i	0.129864	+	0.224930i	−0.793760	+	0.608231i	$0.791879\pi$
$264$		0			0
$265$	−6.52724	+	11.3055i	−0.400965	+	0.694492i
$266$		0			0
$267$		0			0
$268$	−7.29893	−	12.6421i	−0.445853	−	0.772240i
$269$	20.7507			1.26519			0.632596	−	0.774482i	$-0.281989\pi$
$269$	20.7507			1.26519			0.632596	+	0.774482i	$0.281989\pi$
$270$		0			0
$271$	28.4889			1.73057			0.865287	−	0.501276i	$-0.167136\pi$
$271$	28.4889			1.73057			0.865287	+	0.501276i	$0.167136\pi$
$272$	10.5067	+	18.1981i	0.637060	+	1.10342i
$273$		0			0
$274$	−0.464103	+	0.803851i	−0.0280375	+	0.0485624i
$275$	1.70321	−	2.95005i	0.102707	−	0.177895i
$276$		0			0
$277$	−8.58113	−	14.8629i	−0.515590	−	0.893028i	−0.999836	−	0.0180962i	$-0.994239\pi$
$277$	−8.58113	−	14.8629i	−0.515590	−	0.893028i	0.484246	−	0.874932i	$-0.339094\pi$
$278$	46.7529			2.80405
$279$		0			0
$280$		0			0
$281$	4.72140	+	8.17770i	0.281655	+	0.487841i	0.971793	−	0.235837i	$-0.0757833\pi$
$281$	4.72140	+	8.17770i	0.281655	+	0.487841i	−0.690138	+	0.723678i	$0.742450\pi$
$282$		0			0
$283$	8.43422	−	14.6085i	0.501362	−	0.868385i	−0.498636	−	0.866811i	$-0.666166\pi$
$283$	8.43422	−	14.6085i	0.501362	−	0.868385i	0.999999	−	0.00157378i	$-0.000500949\pi$
$284$	17.1498	−	29.7043i	1.01765	−	1.76263i
$285$		0			0
$286$	0.243398	+	0.421578i	0.0143924	+	0.0249284i
$287$		0			0
$288$		0			0
$289$	6.57918			0.387011
$290$	−34.4172	−	59.6124i	−2.02105	−	3.50056i
$291$		0			0
$292$	−4.00040	+	6.92889i	−0.234105	+	0.405483i
$293$	1.86143	−	3.22409i	0.108746	−	0.188353i	−0.806517	−	0.591211i	$-0.798650\pi$
$293$	1.86143	−	3.22409i	0.108746	−	0.188353i	0.915262	+	0.402858i	$0.131983\pi$
$294$		0			0
$295$	11.1908	+	19.3830i	0.651551	+	1.12852i
$296$	−11.7630			−0.683712
$297$		0			0
$298$	−23.8712			−1.38282
$299$	−1.13123	−	1.95935i	−0.0654209	−	0.113312i
$300$		0			0
$301$		0			0
$302$	−15.7901	+	27.3492i	−0.908617	+	1.57377i
$303$		0			0
$304$	4.27012	+	7.39607i	0.244908	+	0.424194i
$305$	−29.3638			−1.68137
$306$		0			0
$307$	−30.5691			−1.74467			−0.872335	−	0.488908i	$-0.837395\pi$
$307$	−30.5691			−1.74467			−0.872335	+	0.488908i	$0.837395\pi$
$308$		0			0
$309$		0			0
$310$	31.6249	−	54.7759i	1.79617	−	3.11106i
$311$	5.21739	−	9.03678i	0.295851	−	0.512429i	−0.679332	−	0.733831i	$-0.737730\pi$
$311$	5.21739	−	9.03678i	0.295851	−	0.512429i	0.975182	+	0.221403i	$0.0710635\pi$
$312$		0			0
$313$	−0.309930	−	0.536815i	−0.0175183	−	0.0303426i	0.857133	−	0.515095i	$-0.172243\pi$
$313$	−0.309930	−	0.536815i	−0.0175183	−	0.0303426i	−0.874652	+	0.484752i	$0.838910\pi$
$314$	−51.5440			−2.90879
$315$		0			0
$316$	33.0905			1.86148
$317$	5.12422	+	8.87541i	0.287805	+	0.498493i	0.973285	−	0.229598i	$-0.0737412\pi$
$317$	5.12422	+	8.87541i	0.287805	+	0.498493i	−0.685481	+	0.728091i	$0.740408\pi$
$318$		0			0
$319$	−1.55408	+	2.69175i	−0.0870120	+	0.150709i
$320$	13.4021	−	23.2132i	0.749203	−	1.29766i
$321$		0			0
$322$		0			0
$323$	9.58307			0.533216
$324$		0			0
$325$	−4.08009			−0.226323
$326$	−13.7324	−	23.7852i	−0.760567	−	1.31734i
$327$		0			0
$328$	−18.9882	+	32.8885i	−1.04845	+	1.81596i
$329$		0			0
$330$		0			0
$331$	10.1819	+	17.6356i	0.559648	+	0.969339i	0.997526	+	0.0703042i	$0.0223970\pi$
$331$	10.1819	+	17.6356i	0.559648	+	0.969339i	−0.437878	+	0.899035i	$0.644270\pi$
$332$	−49.3463			−2.70823
$333$		0			0
$334$	8.51392			0.465861
$335$	−6.58596	−	11.4072i	−0.359829	−	0.623242i
$336$		0			0
$337$	2.85594	−	4.94662i	0.155573	−	0.269460i	−0.777695	−	0.628642i	$-0.783611\pi$
$337$	2.85594	−	4.94662i	0.155573	−	0.269460i	0.933267	+	0.359182i	$0.116944\pi$
$338$	−15.7017	+	27.1962i	−0.854062	+	1.47928i
$339$		0			0
$340$	36.0064	+	62.3649i	1.95272	+	3.38221i
$341$	−2.85600			−0.154661
$342$		0			0
$343$		0			0
$344$	−5.88151	−	10.1871i	−0.317110	−	0.549251i
$345$		0			0
$346$	7.44746	−	12.8994i	0.400378	−	0.693475i
$347$	4.44066	−	7.69145i	0.238387	−	0.412899i	−0.721865	−	0.692034i	$-0.756715\pi$
$347$	4.44066	−	7.69145i	0.238387	−	0.412899i	0.960252	+	0.279136i	$0.0900480\pi$
$348$		0			0
$349$	−10.4874	−	18.1648i	−0.561379	−	0.972337i	−0.997376	−	0.0723893i	$-0.976938\pi$
$349$	−10.4874	−	18.1648i	−0.561379	−	0.972337i	0.435997	−	0.899948i	$-0.356396\pi$
$350$		0			0
$351$		0			0
$352$	0.219262			0.0116867
$353$	−7.38268	−	12.7872i	−0.392941	−	0.680593i	0.599895	−	0.800078i	$-0.295209\pi$
$353$	−7.38268	−	12.7872i	−0.392941	−	0.680593i	−0.992836	+	0.119485i	$0.961876\pi$
$354$		0			0
$355$	15.4746	−	26.8028i	0.821306	−	1.42254i
$356$	30.0613	−	52.0677i	1.59325	−	2.75959i
$357$		0			0
$358$	−11.2360	−	19.4613i	−0.593840	−	1.02856i
$359$	−7.21206			−0.380638			−0.190319	−	0.981722i	$-0.560952\pi$
$359$	−7.21206			−0.380638			−0.190319	+	0.981722i	$0.560952\pi$
$360$		0			0
$361$	−15.1052			−0.795013
$362$	14.6988	+	25.4591i	0.772554	+	1.33810i
$363$		0			0
$364$		0			0
$365$	−3.60963	+	6.25206i	−0.188937	+	0.327248i
$366$		0			0
$367$	5.48711	+	9.50396i	0.286425	+	0.496103i	0.972954	−	0.231000i	$-0.0741998\pi$
$367$	5.48711	+	9.50396i	0.286425	+	0.496103i	−0.686529	+	0.727103i	$0.740866\pi$
$368$	−20.1124			−1.04843
$369$		0			0
$370$	−20.9485			−1.08906
$371$		0			0
$372$		0			0
$373$	0.271884	−	0.470916i	0.0140776	−	0.0243831i	−0.858901	−	0.512142i	$-0.828852\pi$
$373$	0.271884	−	0.470916i	0.0140776	−	0.0243831i	0.872978	+	0.487759i	$0.162185\pi$
$374$	2.42792	−	4.20528i	0.125545	−	0.217450i
$375$		0			0
$376$	15.9614	+	27.6459i	0.823145	+	1.42573i
$377$	3.72286			0.191737
$378$		0			0
$379$	−22.6912			−1.16557			−0.582785	−	0.812626i	$-0.698037\pi$
$379$	−22.6912			−1.16557			−0.582785	+	0.812626i	$0.698037\pi$
$380$	14.6337	+	25.3464i	0.750695	+	1.30024i
$381$		0			0
$382$	−11.2448	+	19.4766i	−0.575336	+	0.996511i
$383$	17.8569	−	30.9291i	0.912447	−	1.58041i	0.101851	−	0.994800i	$-0.467523\pi$
$383$	17.8569	−	30.9291i	0.912447	−	1.58041i	0.810596	−	0.585606i	$-0.199143\pi$
$384$		0			0
$385$		0			0
$386$	−41.6883			−2.12188
$387$		0			0
$388$	−38.4632			−1.95267
$389$	19.3296	+	33.4798i	0.980048	+	1.69749i	0.662156	+	0.749366i	$0.269641\pi$
$389$	19.3296	+	33.4798i	0.980048	+	1.69749i	0.317892	+	0.948127i	$0.397025\pi$
$390$		0			0
$391$	−11.2842	+	19.5447i	−0.570664	+	0.988420i
$392$		0			0
$393$		0			0
$394$	26.2257	+	45.4242i	1.32123	+	2.28844i
$395$	29.8581			1.50233
$396$		0			0
$397$	−11.9478			−0.599644			−0.299822	−	0.953995i	$-0.596927\pi$
$397$	−11.9478			−0.599644			−0.299822	+	0.953995i	$0.596927\pi$
$398$	12.2709	+	21.2538i	0.615085	+	1.06536i
$399$		0			0
$400$	−18.1352	+	31.4111i	−0.906761	+	1.57056i
$401$	16.1783	−	28.0216i	0.807906	−	1.39933i	−0.106406	−	0.994323i	$-0.533934\pi$
$401$	16.1783	−	28.0216i	0.807906	−	1.39933i	0.914312	−	0.405011i	$-0.132732\pi$
$402$		0			0
$403$	1.71041	+	2.96251i	0.0852015	+	0.147573i
$404$	−35.3182			−1.75715
$405$		0			0
$406$		0			0
$407$	0.472958	+	0.819187i	0.0234437	+	0.0406056i
$408$		0			0
$409$	−9.48751	+	16.4328i	−0.469127	+	0.812552i	−0.999377	−	0.0352893i	$-0.988765\pi$
$409$	−9.48751	+	16.4328i	−0.469127	+	0.812552i	0.530250	+	0.847841i	$0.322098\pi$
$410$	−33.8157	+	58.5704i	−1.67004	+	2.89259i
$411$		0			0
$412$	−16.2713	−	28.1827i	−0.801630	−	1.38846i
$413$		0			0
$414$		0			0
$415$	−44.5261			−2.18570
$416$	−0.131312	−	0.227439i	−0.00643811	−	0.0111511i
$417$		0			0
$418$	0.986757	−	1.70911i	0.0482639	−	0.0835955i
$419$	−8.64523	+	14.9740i	−0.422347	+	0.731526i	−0.996169	−	0.0874539i	$-0.972127\pi$
$419$	−8.64523	+	14.9740i	−0.422347	+	0.731526i	0.573822	+	0.818980i	$0.305460\pi$
$420$		0			0
$421$	−9.30039	−	16.1087i	−0.453273	−	0.785092i	0.545314	−	0.838232i	$-0.316410\pi$
$421$	−9.30039	−	16.1087i	−0.453273	−	0.785092i	−0.998587	+	0.0531397i	$0.983077\pi$
$422$	−12.0364			−0.585922
$423$		0			0
$424$	−18.0364			−0.875924
$425$	20.3496	+	35.2466i	0.987103	+	1.70971i
$426$		0			0
$427$		0			0
$428$	26.0313	−	45.0876i	1.25827	−	2.17939i
$429$		0			0
$430$	−10.4743	−	18.1420i	−0.505114	−	0.874883i
$431$	15.8784			0.764835			0.382418	−	0.923990i	$-0.375092\pi$
$431$	15.8784			0.764835			0.382418	+	0.923990i	$0.375092\pi$
$432$		0			0
$433$	40.4367			1.94326			0.971631	−	0.236501i	$-0.0760007\pi$
$433$	40.4367			1.94326			0.971631	+	0.236501i	$0.0760007\pi$
$434$		0			0
$435$		0			0
$436$	−5.27188	+	9.13117i	−0.252477	+	0.437304i
$437$	−4.58611	+	7.94338i	−0.219384	+	0.379984i
$438$		0			0
$439$	−6.23047	−	10.7915i	−0.297364	−	0.515050i	0.678168	−	0.734907i	$-0.262774\pi$
$439$	−6.23047	−	10.7915i	−0.297364	−	0.515050i	−0.975532	+	0.219857i	$0.929441\pi$
$440$	7.51399			0.358216
$441$		0			0
$442$	−5.81616			−0.276646
$443$	−4.11537	−	7.12802i	−0.195527	−	0.338663i	0.751546	−	0.659680i	$-0.229308\pi$
$443$	−4.11537	−	7.12802i	−0.195527	−	0.338663i	−0.947073	+	0.321018i	$0.895975\pi$
$444$		0			0
$445$	27.1249	−	46.9817i	1.28584	−	2.22715i
$446$	−28.7988	+	49.8810i	−1.36366	+	2.36193i
$447$		0			0
$448$		0			0
$449$	−5.64474			−0.266392			−0.133196	−	0.991090i	$-0.542524\pi$
$449$	−5.64474			−0.266392			−0.133196	+	0.991090i	$0.542524\pi$
$450$		0			0
$451$	3.05384			0.143800
$452$	−28.2776	−	48.9783i	−1.33007	−	2.30374i
$453$		0			0
$454$	7.52716	−	13.0374i	0.353267	−	0.611876i
$455$		0			0
$456$		0			0
$457$	−2.53443	−	4.38977i	−0.118556	−	0.205345i	0.800640	−	0.599146i	$-0.204493\pi$
$457$	−2.53443	−	4.38977i	−0.118556	−	0.205345i	−0.919196	+	0.393801i	$0.871160\pi$
$458$	−3.59330			−0.167904
$459$		0			0
$460$	−68.9255			−3.21367
$461$	−3.88831	−	6.73475i	−0.181097	−	0.313669i	0.761158	−	0.648567i	$-0.224631\pi$
$461$	−3.88831	−	6.73475i	−0.181097	−	0.313669i	−0.942254	+	0.334898i	$0.891298\pi$
$462$		0			0
$463$	4.58998	−	7.95008i	0.213314	−	0.369472i	−0.739435	−	0.673228i	$-0.764907\pi$
$463$	4.58998	−	7.95008i	0.213314	−	0.369472i	0.952750	+	0.303756i	$0.0982408\pi$
$464$	16.5474	−	28.6609i	0.768192	−	1.33055i
$465$		0			0
$466$	16.2989	+	28.2306i	0.755033	+	1.30776i
$467$	13.7654			0.636989			0.318494	−	0.947925i	$-0.396823\pi$
$467$	13.7654			0.636989			0.318494	+	0.947925i	$0.396823\pi$
$468$		0			0
$469$		0			0
$470$	28.4253	+	49.2340i	1.31116	+	2.27100i
$471$		0			0
$472$	−15.4614	+	26.7800i	−0.711669	+	1.23265i
$473$	−0.472958	+	0.819187i	−0.0217466	+	0.0376663i
$474$		0			0
$475$	8.27052	+	14.3250i	0.379477	+	0.657274i
$476$		0			0
$477$		0			0
$478$	47.7060			2.18202
$479$	4.35588	+	7.54461i	0.199025	+	0.344722i	0.948213	−	0.317636i	$-0.102889\pi$
$479$	4.35588	+	7.54461i	0.199025	+	0.344722i	−0.749187	+	0.662358i	$0.769556\pi$
$480$		0			0
$481$	0.566492	−	0.981194i	0.0258298	−	0.0447386i
$482$	−6.21731	+	10.7687i	−0.283191	+	0.490501i
$483$		0			0
$484$	21.9626	+	38.0404i	0.998302	+	1.72911i
$485$	−34.7060			−1.57592
$486$		0			0
$487$	−18.0364			−0.817306			−0.408653	−	0.912690i	$-0.634001\pi$
$487$	−18.0364			−0.817306			−0.408653	+	0.912690i	$0.634001\pi$
$488$	−20.2849	−	35.1344i	−0.918253	−	1.59046i
$489$		0			0
$490$		0			0
$491$	1.02344	−	1.77266i	0.0461874	−	0.0799989i	−0.842007	−	0.539466i	$-0.818626\pi$
$491$	1.02344	−	1.77266i	0.0461874	−	0.0799989i	0.888195	+	0.459467i	$0.151960\pi$
$492$		0			0
$493$	−18.5679	−	32.1606i	−0.836257	−	1.44844i
$494$	−2.36381			−0.106353
$495$		0			0
$496$	30.4097			1.36544
$497$		0			0
$498$		0			0
$499$	19.5438	−	33.8508i	0.874899	−	1.51537i	0.0180291	−	0.999837i	$-0.494261\pi$
$499$	19.5438	−	33.8508i	0.874899	−	1.51537i	0.856870	−	0.515532i	$-0.172406\pi$
$500$	−25.0742	+	43.4297i	−1.12135	+	1.94224i
$501$		0			0
$502$	18.5679	+	32.1606i	0.828727	+	1.43540i
$503$	−5.11846			−0.228221			−0.114111	−	0.993468i	$-0.536402\pi$
$503$	−5.11846			−0.228221			−0.114111	+	0.993468i	$0.536402\pi$
$504$		0			0
$505$	−31.8683			−1.41812
$506$	2.32383	+	4.02499i	0.103307	+	0.178933i
$507$		0			0
$508$	31.5079	−	54.5732i	1.39794	−	2.42130i
$509$	−14.7636	+	25.5713i	−0.654386	+	1.13343i	0.327662	+	0.944795i	$0.393739\pi$
$509$	−14.7636	+	25.5713i	−0.654386	+	1.13343i	−0.982047	+	0.188634i	$0.939594\pi$
$510$		0			0
$511$		0			0
$512$	41.4078			1.82998
$513$		0			0
$514$	−18.9750			−0.836952
$515$	−14.6819	−	25.4298i	−0.646962	−	1.12057i
$516$		0			0
$517$	1.28352	−	2.22313i	0.0564493	−	0.0977730i
$518$		0			0
$519$		0			0
$520$	−4.50000	−	7.79423i	−0.197338	−	0.341800i
$521$	−1.06470			−0.0466454			−0.0233227	−	0.999728i	$-0.507425\pi$
$521$	−1.06470			−0.0466454			−0.0233227	+	0.999728i	$0.507425\pi$
$522$		0			0
$523$	13.3819			0.585149			0.292574	−	0.956243i	$-0.405488\pi$
$523$	13.3819			0.585149			0.292574	+	0.956243i	$0.405488\pi$
$524$	−17.2581	−	29.8918i	−0.753922	−	1.30583i
$525$		0			0
$526$	−5.18190	+	8.97532i	−0.225942	+	0.391343i
$527$	17.0615	−	29.5513i	0.743210	−	1.28728i
$528$		0			0
$529$	0.699612	+	1.21176i	0.0304179	+	0.0526853i
$530$	−32.1206			−1.39523
$531$		0			0
$532$		0			0
$533$	−1.82889	−	3.16774i	−0.0792181	−	0.137210i
$534$		0			0
$535$	23.4885	−	40.6833i	1.01550	−	1.75889i
$536$	9.09931	−	15.7605i	0.393031	−	0.680749i
$537$		0			0
$538$	25.5286	+	44.2168i	1.10062	+	1.90632i
$539$		0			0
$540$		0			0
$541$	−34.0875			−1.46554			−0.732769	−	0.680478i	$-0.761772\pi$
$541$	−34.0875			−1.46554			−0.732769	+	0.680478i	$0.761772\pi$
$542$	35.0485	+	60.7058i	1.50546	+	2.60754i
$543$		0			0
$544$	−1.30985	+	2.26873i	−0.0561594	+	0.0972709i
$545$	−4.75692	+	8.23922i	−0.203764	+	0.352930i
$546$		0			0
$547$	2.97150	+	5.14678i	0.127052	+	0.220060i	0.922533	−	0.385918i	$-0.126115\pi$
$547$	2.97150	+	5.14678i	0.127052	+	0.220060i	−0.795481	+	0.605978i	$0.792782\pi$
$548$	−1.52937			−0.0653316
$549$		0			0
$550$	8.38151			0.357389
$551$	−7.54638	−	13.0707i	−0.321487	−	0.556831i
$552$		0			0
$553$		0			0
$554$	21.1139	−	36.5704i	0.897044	−	1.55373i
$555$		0			0
$556$	38.5165	+	66.7126i	1.63346	+	2.82924i
$557$	30.0803			1.27454			0.637272	−	0.770639i	$-0.280063\pi$
$557$	30.0803			1.27454			0.637272	+	0.770639i	$0.280063\pi$
$558$		0			0
$559$	1.13298			0.0479202
$560$		0			0
$561$		0			0
$562$	−11.6170	+	20.1213i	−0.490035	+	0.848765i
$563$	9.81060	−	16.9925i	0.413468	−	0.716147i	−0.581799	−	0.813333i	$-0.697651\pi$
$563$	9.81060	−	16.9925i	0.413468	−	0.716147i	0.995266	+	0.0971860i	$0.0309842\pi$
$564$		0			0
$565$	−25.5154	−	44.1940i	−1.07344	−	1.85926i
$566$	41.5049			1.74458
$567$		0			0
$568$	42.7601			1.79417
$569$	−0.687159	−	1.19019i	−0.0288072	−	0.0498955i	0.851262	−	0.524740i	$-0.175838\pi$
$569$	−0.687159	−	1.19019i	−0.0288072	−	0.0498955i	−0.880070	+	0.474845i	$0.842504\pi$
$570$		0			0
$571$	−8.69076	+	15.0528i	−0.363697	+	0.629941i	−0.988566	−	0.150788i	$-0.951819\pi$
$571$	−8.69076	+	15.0528i	−0.363697	+	0.629941i	0.624869	+	0.780729i	$0.285152\pi$
$572$	−0.401038	+	0.694619i	−0.0167683	+	0.0290435i
$573$		0			0
$574$		0			0
$575$	−38.9545			−1.62451
$576$		0			0
$577$	27.0548			1.12631			0.563153	−	0.826353i	$-0.309588\pi$
$577$	27.0548			1.12631			0.563153	+	0.826353i	$0.309588\pi$
$578$	8.09406	+	14.0193i	0.336668	+	0.583127i
$579$		0			0
$580$	56.7080	−	98.2211i	2.35467	−	4.07841i
$581$		0			0
$582$		0			0
$583$	0.725191	+	1.25607i	0.0300344	+	0.0520210i
$584$	−9.97430			−0.412740
$585$		0			0
$586$	9.16010			0.378400
$587$	−3.75700	−	6.50731i	−0.155068	−	0.268585i	0.778016	−	0.628245i	$-0.216226\pi$
$587$	−3.75700	−	6.50731i	−0.155068	−	0.268585i	−0.933084	+	0.359659i	$0.882893\pi$
$588$		0			0
$589$	6.93414	−	12.0103i	0.285716	−	0.494875i
$590$	−27.5349	+	47.6919i	−1.13359	+	1.96344i
$591$		0			0
$592$	−5.03590	−	8.72243i	−0.206974	−	0.358490i
$593$	35.5808			1.46113			0.730565	−	0.682843i	$-0.239257\pi$
$593$	35.5808			1.46113			0.730565	+	0.682843i	$0.239257\pi$
$594$		0			0
$595$		0			0
$596$	−19.6659	−	34.0623i	−0.805545	−	1.39524i
$597$		0			0
$598$	2.78340	−	4.82100i	0.113822	−	0.197145i
$599$	−5.74105	+	9.94379i	−0.234573	+	0.406292i	−0.959148	−	0.282903i	$-0.908702\pi$
$599$	−5.74105	+	9.94379i	−0.234573	+	0.406292i	0.724576	+	0.689195i	$0.242036\pi$
$600$		0			0
$601$	−0.190030	−	0.329142i	−0.00775150	−	0.0134260i	0.862124	−	0.506698i	$-0.169134\pi$
$601$	−0.190030	−	0.329142i	−0.00775150	−	0.0134260i	−0.869875	+	0.493272i	$0.835801\pi$
$602$		0			0
$603$		0			0
$604$	−52.0335			−2.11721
$605$	19.8173	+	34.3246i	0.805688	+	1.39549i
$606$		0			0
$607$	−9.27044	+	16.0569i	−0.376275	+	0.651728i	−0.990517	−	0.137390i	$-0.956129\pi$
$607$	−9.27044	+	16.0569i	−0.376275	+	0.651728i	0.614242	+	0.789118i	$0.289462\pi$
$608$	−0.532351	+	0.922058i	−0.0215897	+	0.0373944i
$609$		0			0
$610$	−36.1249	−	62.5702i	−1.46265	−	2.53339i
$611$	−3.07472			−0.124390
$612$		0			0
$613$	7.32451			0.295834			0.147917	−	0.989000i	$-0.452743\pi$
$613$	7.32451			0.295834			0.147917	+	0.989000i	$0.452743\pi$
$614$	−37.6077	−	65.1385i	−1.51772	−	2.62877i
$615$		0			0
$616$		0			0
$617$	−12.7427	+	22.0710i	−0.513002	+	0.888546i	0.486884	+	0.873466i	$0.338133\pi$
$617$	−12.7427	+	22.0710i	−0.513002	+	0.888546i	−0.999886	+	0.0150791i	$0.995200\pi$
$618$		0			0
$619$	16.4482	+	28.4891i	0.661108	+	1.14507i	0.980325	+	0.197391i	$0.0632468\pi$
$619$	16.4482	+	28.4891i	0.661108	+	1.14507i	−0.319217	+	0.947682i	$0.603420\pi$
$620$	104.214			4.18535
$621$		0			0
$622$	25.6748			1.02947
$623$		0			0
$624$		0			0
$625$	−1.67111	+	2.89444i	−0.0668443	+	0.115778i
$626$	0.762585	−	1.32084i	0.0304790	−	0.0527912i
$627$		0			0
$628$	−42.4636	−	73.5490i	−1.69448	−	2.93493i
$629$	−11.3016			−0.450626
$630$		0			0
$631$	29.8683			1.18904			0.594519	−	0.804082i	$-0.297343\pi$
$631$	29.8683			1.18904			0.594519	+	0.804082i	$0.297343\pi$
$632$	20.6264	+	35.7259i	0.820472	+	1.42110i
$633$		0			0
$634$	−12.6082	+	21.8380i	−0.500734	+	0.867297i
$635$	28.4301	−	49.2424i	1.12822	−	1.95413i
$636$		0			0
$637$		0			0
$638$	−7.64766			−0.302774
$639$		0			0
$640$	69.8991			2.76301
$641$	5.73025	+	9.92509i	0.226331	+	0.392017i	0.956718	−	0.291016i	$-0.0939934\pi$
$641$	5.73025	+	9.92509i	0.226331	+	0.392017i	−0.730387	+	0.683034i	$0.760660\pi$
$642$		0			0
$643$	−8.69078	+	15.0529i	−0.342731	+	0.593627i	−0.984939	−	0.172903i	$-0.944685\pi$
$643$	−8.69078	+	15.0529i	−0.342731	+	0.593627i	0.642208	+	0.766531i	$0.278019\pi$
$644$		0			0
$645$		0			0
$646$	11.7896	+	20.4202i	0.463855	+	0.803421i
$647$	25.3439			0.996372			0.498186	−	0.867070i	$-0.334000\pi$
$647$	25.3439			0.996372			0.498186	+	0.867070i	$0.334000\pi$
$648$		0			0
$649$	2.48664			0.0976091
$650$	−5.01954	−	8.69410i	−0.196883	−	0.341011i
$651$		0			0
$652$	22.6264	−	39.1900i	0.886116	−	1.53480i
$653$	7.04163	−	12.1965i	0.275560	−	0.477284i	−0.694716	−	0.719284i	$-0.744470\pi$
$653$	7.04163	−	12.1965i	0.275560	−	0.477284i	0.970276	+	0.242000i	$0.0778033\pi$
$654$		0			0
$655$	−15.5723	−	26.9720i	−0.608459	−	1.05388i
$656$	−32.5163			−1.26955
$657$		0			0
$658$		0			0
$659$	19.0854	+	33.0569i	0.743462	+	1.28771i	0.950910	+	0.309467i	$0.100151\pi$
$659$	19.0854	+	33.0569i	0.743462	+	1.28771i	−0.207449	+	0.978246i	$0.566516\pi$
$660$		0			0
$661$	−0.176866	+	0.306341i	−0.00687930	+	0.0119153i	−0.869445	−	0.494031i	$-0.835523\pi$
$661$	−0.176866	+	0.306341i	−0.00687930	+	0.0119153i	0.862565	+	0.505946i	$0.168856\pi$
$662$	−25.0526	+	43.3924i	−0.973698	+	1.68649i
$663$		0			0
$664$	−30.7591	−	53.2764i	−1.19369	−	2.06752i
$665$		0			0
$666$		0			0
$667$	35.5438			1.37626
$668$	7.01403	+	12.1487i	0.271381	+	0.470046i
$669$		0			0
$670$	16.2048	−	28.0675i	0.626045	−	1.08434i
$671$	−1.63119	+	2.82531i	−0.0629715	+	0.109070i
$672$		0			0
$673$	10.5555	+	18.2827i	0.406886	+	0.704748i	0.994539	−	0.104365i	$-0.0332811\pi$
$673$	10.5555	+	18.2827i	0.406886	+	0.704748i	−0.587653	+	0.809113i	$0.699948\pi$
$674$	14.0541			0.541343
$675$		0			0
$676$	−51.7424			−1.99009
$677$	−10.5732	−	18.3133i	−0.406361	−	0.703837i	0.588118	−	0.808775i	$-0.299869\pi$
$677$	−10.5732	−	18.3133i	−0.406361	−	0.703837i	−0.994479	+	0.104938i	$0.966536\pi$
$678$		0			0
$679$		0			0
$680$	−44.8879	+	77.7482i	−1.72137	+	2.98151i
$681$		0			0
$682$	−3.51360	−	6.08573i	−0.134543	−	0.233035i
$683$	−34.7716			−1.33050			−0.665249	−	0.746622i	$-0.731674\pi$
$683$	−34.7716			−1.33050			−0.665249	+	0.746622i	$0.731674\pi$
$684$		0			0
$685$	−1.37998			−0.0527264
$686$		0			0
$687$		0			0
$688$	5.03590	−	8.72243i	0.191992	−	0.332539i
$689$	0.868609	−	1.50447i	0.0330914	−	0.0573159i
$690$		0			0
$691$	17.3246	+	30.0071i	0.659059	+	1.14152i	0.980860	+	0.194716i	$0.0623785\pi$
$691$	17.3246	+	30.0071i	0.659059	+	1.14152i	−0.321801	+	0.946807i	$0.604288\pi$
$692$	24.5418			0.932940
$693$		0			0
$694$	21.8525			0.829511
$695$	34.7542	+	60.1960i	1.31830	+	2.28336i
$696$		0			0
$697$	−18.2434	+	31.5985i	−0.691017	+	1.19688i
$698$	25.8044	−	44.6945i	0.976710	−	1.69171i
$699$		0			0
$700$		0			0
$701$	48.6050			1.83579			0.917894	−	0.396826i	$-0.129889\pi$
$701$	48.6050			1.83579			0.917894	+	0.396826i	$0.129889\pi$
$702$		0			0
$703$	−4.59322			−0.173236
$704$	−1.48901	−	2.57904i	−0.0561192	−	0.0972012i
$705$		0			0
$706$	18.1651	−	31.4629i	0.683654	−	1.18412i
$707$		0			0
$708$		0			0
$709$	−2.05408	−	3.55778i	−0.0771428	−	0.133615i	0.824873	−	0.565318i	$-0.191246\pi$
$709$	−2.05408	−	3.55778i	−0.0771428	−	0.133615i	−0.902016	+	0.431702i	$0.857913\pi$
$710$	76.1506			2.85788
$711$		0			0
$712$	74.9528			2.80898
$713$	16.3300	+	28.2844i	0.611564	+	1.05926i
$714$		0			0
$715$	−0.361864	+	0.626767i	−0.0135330	+	0.0234398i
$716$	18.5131	−	32.0657i	0.691868	−	1.19835i
$717$		0			0
$718$	−8.87266	−	15.3679i	−0.331125	−	0.573525i
$719$	48.2816			1.80060			0.900299	−	0.435271i	$-0.143347\pi$
$719$	48.2816			1.80060			0.900299	+	0.435271i	$0.143347\pi$
$720$		0			0
$721$		0			0
$722$	−18.5833	−	32.1872i	−0.691597	−	1.19788i
$723$		0			0
$724$	−24.2187	+	41.9481i	−0.900082	+	1.55899i
$725$	32.0495	−	55.5114i	1.19029	−	2.06164i
$726$		0			0
$727$	−20.5151	−	35.5332i	−0.760863	−	1.31785i	−0.942406	−	0.334470i	$-0.891443\pi$
$727$	−20.5151	−	35.5332i	−0.760863	−	1.31785i	0.181543	−	0.983383i	$-0.441891\pi$
$728$		0			0
$729$		0			0
$730$	−17.7630			−0.657439
$731$	−5.65082	−	9.78750i	−0.209003	−	0.362004i
$732$		0			0
$733$	15.2714	−	26.4508i	0.564062	−	0.976983i	−0.433075	−	0.901358i	$-0.642571\pi$
$733$	15.2714	−	26.4508i	0.564062	−	0.976983i	0.997136	−	0.0756253i	$-0.0240953\pi$
$734$	−13.5011	+	23.3845i	−0.498334	+	0.863139i
$735$		0			0
$736$	−1.25370	−	2.17147i	−0.0462118	−	0.0800413i
$737$	−1.46343			−0.0539061
$738$		0			0
$739$	23.8200			0.876234			0.438117	−	0.898918i	$-0.355646\pi$
$739$	23.8200			0.876234			0.438117	+	0.898918i	$0.355646\pi$
$740$	−17.2581	−	29.8918i	−0.634419	−	1.09885i
$741$		0			0
$742$		0			0
$743$	5.26089	−	9.11213i	0.193003	−	0.334292i	−0.753241	−	0.657745i	$-0.771510\pi$
$743$	5.26089	−	9.11213i	0.193003	−	0.334292i	0.946244	+	0.323453i	$0.104844\pi$
$744$		0			0
$745$	−17.7449	−	30.7350i	−0.650121	−	1.12604i
$746$	1.33794			0.0489855
$747$		0			0
$748$	8.00079			0.292538
$749$		0			0
$750$		0			0
$751$	5.13521	−	8.89445i	0.187386	−	0.324563i	−0.756992	−	0.653425i	$-0.773332\pi$
$751$	5.13521	−	8.89445i	0.187386	−	0.324563i	0.944378	+	0.328862i	$0.106665\pi$
$752$	−13.6665	+	23.6711i	−0.498367	+	0.863197i
$753$		0			0
$754$	4.58005	+	7.93288i	0.166796	+	0.288899i
$755$	−46.9507			−1.70871
$756$		0			0
$757$	8.03930			0.292193			0.146097	−	0.989270i	$-0.453329\pi$
$757$	8.03930			0.292193			0.146097	+	0.989270i	$0.453329\pi$
$758$	−27.9159	−	48.3518i	−1.01395	−	1.75622i
$759$		0			0
$760$	−18.2434	+	31.5985i	−0.661757	+	1.14620i
$761$	−13.8302	+	23.9547i	−0.501345	+	0.868355i	0.498654	+	0.866801i	$0.333828\pi$
$761$	−13.8302	+	23.9547i	−0.501345	+	0.868355i	−0.999999	+	0.00155404i	$0.999505\pi$
$762$		0			0
$763$		0			0
$764$	−37.0554			−1.34062
$765$		0			0
$766$	87.8742			3.17502
$767$	−1.48920	−	2.57938i	−0.0537720	−	0.0931359i
$768$		0			0
$769$	−16.9613	+	29.3778i	−0.611640	+	1.05939i	0.379324	+	0.925264i	$0.376157\pi$
$769$	−16.9613	+	29.3778i	−0.611640	+	1.05939i	−0.990964	+	0.134128i	$0.957177\pi$
$770$		0			0
$771$		0			0
$772$	−34.3442	−	59.4858i	−1.23607	−	2.14094i
$773$	−28.5956			−1.02851			−0.514256	−	0.857637i	$-0.671932\pi$
$773$	−28.5956			−1.02851			−0.514256	+	0.857637i	$0.671932\pi$
$774$		0			0
$775$	58.8986			2.11570
$776$	−23.9753	−	41.5265i	−0.860664	−	1.49071i
$777$		0			0
$778$	−47.5605	+	82.3772i	−1.70513	+	2.95337i
$779$	−7.41449	+	12.8423i	−0.265652	+	0.460122i
$780$		0			0
$781$	−1.71926	−	2.97785i	−0.0615200	−	0.106556i
$782$	−55.5294			−1.98573
$783$		0			0
$784$		0			0
$785$	−38.3157	−	66.3647i	−1.36754	−	2.36866i
$786$		0			0
$787$	23.0017	−	39.8402i	0.819923	−	1.42015i	−0.0858145	−	0.996311i	$-0.527349\pi$
$787$	23.0017	−	39.8402i	0.819923	−	1.42015i	0.905738	−	0.423838i	$-0.139317\pi$
$788$	−43.2111	+	74.8438i	−1.53933	+	2.66620i
$789$		0			0
$790$	36.7330	+	63.6235i	1.30690	+	2.26362i
$791$		0			0
$792$		0			0
$793$	3.90757			0.138762
$794$	−14.6988	−	25.4591i	−0.521642	−	0.903511i
$795$		0			0
$796$	−20.2183	+	35.0192i	−0.716620	+	1.24122i
$797$	18.4558	−	31.9664i	0.653739	−	1.13231i	−0.328469	−	0.944515i	$-0.606533\pi$
$797$	18.4558	−	31.9664i	0.653739	−	1.13231i	0.982208	−	0.187795i	$-0.0601339\pi$
$798$		0			0
$799$	15.3353	+	26.5615i	0.542524	+	0.939679i
$800$	−4.52179			−0.159869
$801$		0			0
$802$	79.6136			2.81125
$803$	0.401038	+	0.694619i	0.0141523	+	0.0245126i
$804$		0			0
$805$		0			0
$806$	−4.20847	+	7.28928i	−0.148237	+	0.256754i
$807$		0			0
$808$	−22.0150	−	38.1311i	−0.774484	−	1.34145i
$809$	−47.6887			−1.67665			−0.838323	−	0.545174i	$-0.816463\pi$
$809$	−47.6887			−1.67665			−0.838323	+	0.545174i	$0.816463\pi$
$810$		0			0
$811$	6.02728			0.211646			0.105823	−	0.994385i	$-0.466252\pi$
$811$	6.02728			0.211646			0.105823	+	0.994385i	$0.466252\pi$
$812$		0			0
$813$		0			0
$814$	−1.16372	+	2.01561i	−0.0407882	+	0.0706472i
$815$	20.4162	−	35.3619i	0.715148	−	1.23867i
$816$		0			0
$817$	−2.29661	−	3.97784i	−0.0803481	−	0.139167i
$818$	−46.6881			−1.63241
$819$		0			0
$820$	−111.434			−3.89143
$821$	−19.6321	−	34.0038i	−0.685165	−	1.18674i	−0.973385	−	0.229176i	$-0.926397\pi$
$821$	−19.6321	−	34.0038i	−0.685165	−	1.18674i	0.288220	−	0.957564i	$-0.406936\pi$
$822$		0			0
$823$	−11.3815	+	19.7134i	−0.396735	+	0.687165i	−0.993321	−	0.115384i	$-0.963190\pi$
$823$	−11.3815	+	19.7134i	−0.396735	+	0.687165i	0.596586	+	0.802549i	$0.296523\pi$
$824$	20.2849	−	35.1344i	0.706657	−	1.22397i
$825$		0			0
$826$		0			0
$827$	28.9286			1.00595			0.502973	−	0.864302i	$-0.332240\pi$
$827$	28.9286			1.00595			0.502973	+	0.864302i	$0.332240\pi$
$828$		0			0
$829$	−33.9767			−1.18006			−0.590029	−	0.807382i	$-0.700884\pi$
$829$	−33.9767			−1.18006			−0.590029	+	0.807382i	$0.700884\pi$
$830$	−54.7783	−	94.8788i	−1.90138	−	3.29329i
$831$		0			0
$832$	−1.78348	+	3.08908i	−0.0618312	+	0.107095i
$833$		0			0
$834$		0			0
$835$	6.32889	+	10.9620i	0.219020	+	0.379354i
$836$	3.25169			0.112462
$837$		0			0
$838$	−42.5432			−1.46963
$839$	19.0206	+	32.9446i	0.656663	+	1.13737i	0.981474	+	0.191595i	$0.0613659\pi$
$839$	19.0206	+	32.9446i	0.656663	+	1.13737i	−0.324811	+	0.945779i	$0.605301\pi$
$840$		0			0
$841$	−14.7434	+	25.5363i	−0.508392	+	0.880561i
$842$	22.8837	−	39.6356i	0.788623	−	1.36593i
$843$		0			0
$844$	−9.91595	−	17.1749i	−0.341321	−	0.591185i
$845$	−46.6881			−1.60612
$846$		0			0
$847$		0			0
$848$	−7.72159	−	13.3742i	−0.265161	−	0.459272i
$849$		0			0
$850$	−50.0704	+	86.7245i	−1.71740	+	2.97463i
$851$	5.40856	−	9.36790i	0.185403	−	0.321127i
$852$		0			0
$853$	−4.90746	−	8.49996i	−0.168028	−	0.291033i	0.769698	−	0.638408i	$-0.220407\pi$
$853$	−4.90746	−	8.49996i	−0.168028	−	0.291033i	−0.937726	+	0.347374i	$0.887073\pi$
$854$		0			0
$855$		0			0
$856$	64.9046			2.21840
$857$	13.3680	+	23.1541i	0.456642	+	0.790928i	0.998781	−	0.0493613i	$-0.0157186\pi$
$857$	13.3680	+	23.1541i	0.456642	+	0.790928i	−0.542139	+	0.840289i	$0.682385\pi$
$858$		0			0
$859$	9.24411	−	16.0113i	0.315405	−	0.546297i	−0.664119	−	0.747627i	$-0.731193\pi$
$859$	9.24411	−	16.0113i	0.315405	−	0.546297i	0.979523	+	0.201330i	$0.0645263\pi$
$860$	17.2581	−	29.8918i	0.588495	−	1.01930i
$861$		0			0
$862$	19.5344	+	33.8346i	0.665345	+	1.15241i
$863$	9.14786			0.311397			0.155698	−	0.987805i	$-0.450237\pi$
$863$	9.14786			0.311397			0.155698	+	0.987805i	$0.450237\pi$
$864$		0			0
$865$	22.1445			0.752937
$866$	49.7473	+	86.1649i	1.69048	+	2.92800i
$867$		0			0
$868$		0			0
$869$	1.65865	−	2.87287i	0.0562660	−	0.0974555i
$870$		0			0
$871$	0.876423	+	1.51801i	0.0296964	+	0.0514358i
$872$	−13.1445			−0.445130
$873$		0			0
$874$	−22.5683			−0.763385
$875$		0			0
$876$		0			0
$877$	−11.3442	+	19.6487i	−0.383065	+	0.663488i	−0.991499	−	0.130117i	$-0.958465\pi$
$877$	−11.3442	+	19.6487i	−0.383065	+	0.663488i	0.608434	+	0.793605i	$0.291798\pi$
$878$	15.3301	−	26.5525i	0.517366	−	0.896104i
$879$		0			0
$880$	3.21683	+	5.57172i	0.108439	+	0.187823i
$881$	−15.3696			−0.517815			−0.258907	−	0.965902i	$-0.583362\pi$
$881$	−15.3696			−0.517815			−0.258907	+	0.965902i	$0.583362\pi$
$882$		0			0
$883$	29.6372			0.997370			0.498685	−	0.866783i	$-0.333817\pi$
$883$	29.6372			0.997370			0.498685	+	0.866783i	$0.333817\pi$
$884$	−4.79153	−	8.29918i	−0.161157	−	0.279132i
$885$		0			0
$886$	10.1259	−	17.5385i	0.340185	−	0.589219i
$887$	−9.38252	+	16.2510i	−0.315034	+	0.545655i	−0.979445	−	0.201712i	$-0.935349\pi$
$887$	−9.38252	+	16.2510i	−0.315034	+	0.545655i	0.664410	+	0.747368i	$0.268683\pi$
$888$		0			0
$889$		0			0
$890$	133.482			4.47432
$891$		0			0
$892$	−94.9014			−3.17753
$893$	6.23258	+	10.7952i	0.208565	+	0.361246i
$894$		0			0
$895$	16.7047	−	28.9335i	0.558378	−	0.967139i
$896$		0			0
$897$		0			0
$898$	−6.94445	−	12.0281i	−0.231739	−	0.401384i
$899$	−53.7416			−1.79238
$900$		0			0
$901$	−17.3289			−0.577310
$902$	3.75700	+	6.50731i	0.125094	+	0.216670i
$903$		0			0
$904$	35.2527	−	61.0595i	1.17249	−	2.03081i
$905$	−21.8530	+	37.8505i	−0.726419	+	1.25819i
$906$		0			0
$907$	15.5541	+	26.9405i	0.516465	+	0.894543i	0.999817	+	0.0191175i	$0.00608567\pi$
$907$	15.5541	+	26.9405i	0.516465	+	0.894543i	−0.483352	+	0.875426i	$0.660581\pi$
$908$	24.8045			0.823165
$909$		0			0
$910$		0			0
$911$	8.73764	+	15.1340i	0.289491	+	0.501413i	0.973688	−	0.227884i	$-0.0731806\pi$
$911$	8.73764	+	15.1340i	0.289491	+	0.501413i	−0.684197	+	0.729297i	$0.739847\pi$
$912$		0			0
$913$	−2.47347	+	4.28418i	−0.0818600	+	0.141786i
$914$	6.23599	−	10.8010i	0.206268	−	0.357267i
$915$		0			0
$916$	−2.96027	−	5.12734i	−0.0978101	−	0.169412i
$917$		0			0
$918$		0			0
$919$	42.1986			1.39200			0.696002	−	0.718040i	$-0.254960\pi$
$919$	42.1986			1.39200			0.696002	+	0.718040i	$0.254960\pi$
$920$	−42.9635	−	74.4150i	−1.41647	−	2.45339i
$921$		0			0
$922$	9.56720	−	16.5709i	0.315079	−	0.545733i
$923$	−2.05927	+	3.56676i	−0.0677818	+	0.117401i
$924$		0			0
$925$	−9.75370	−	16.8939i	−0.320700	−	0.555468i
$926$	22.5873			0.742266
$927$		0			0
$928$	4.12588			0.135439
$929$	24.2056	+	41.9253i	0.794159	+	1.37552i	0.923372	+	0.383907i	$0.125422\pi$
$929$	24.2056	+	41.9253i	0.794159	+	1.37552i	−0.129213	+	0.991617i	$0.541245\pi$
$930$		0			0
$931$		0			0
$932$	−26.8551	+	46.5145i	−0.879670	+	1.52363i
$933$		0			0
$934$	16.9350	+	29.3322i	0.554129	+	0.959780i
$935$	7.21926			0.236095
$936$		0			0
$937$	−22.6750			−0.740762			−0.370381	−	0.928880i	$-0.620773\pi$
$937$	−22.6750			−0.740762			−0.370381	+	0.928880i	$0.620773\pi$
$938$		0			0
$939$		0			0
$940$	−46.8353	+	81.1211i	−1.52760	+	2.64588i
$941$	−24.9753	+	43.2584i	−0.814170	+	1.41018i	0.0957523	+	0.995405i	$0.469474\pi$
$941$	−24.9753	+	43.2584i	−0.814170	+	1.41018i	−0.909922	+	0.414779i	$0.863859\pi$
$942$		0			0
$943$	−17.4613	−	30.2438i	−0.568617	−	0.984873i
$944$	−26.4769			−0.861749
$945$		0			0
$946$	−2.32743			−0.0756713
$947$	8.85613	+	15.3393i	0.287786	+	0.498459i	0.973281	−	0.229618i	$-0.0737476\pi$
$947$	8.85613	+	15.3393i	0.287786	+	0.498459i	−0.685495	+	0.728077i	$0.740414\pi$
$948$		0			0
$949$	0.480350	−	0.831990i	0.0155928	−	0.0270075i
$950$	−20.3496	+	35.2466i	−0.660230	+	1.14355i
$951$		0			0
$952$		0			0
$953$	−38.0229			−1.23168			−0.615842	−	0.787870i	$-0.711184\pi$
$953$	−38.0229			−1.23168			−0.615842	+	0.787870i	$0.711184\pi$
$954$		0			0
$955$	−33.4358			−1.08196
$956$	39.3017	+	68.0726i	1.27111	+	2.20163i
$957$		0			0
$958$	−10.7177	+	18.5635i	−0.346272	+	0.599761i
$959$		0			0
$960$		0			0
$961$	−9.19076	−	15.9189i	−0.296476	−	0.513512i
$962$	2.78771			0.0898795
$963$		0			0
$964$	−20.4881			−0.659876
$965$	−30.9894	−	53.6752i	−0.997583	−	1.72786i
$966$		0			0
$967$	15.5064	−	26.8579i	0.498652	−	0.863691i	−0.501346	−	0.865247i	$-0.667162\pi$
$967$	15.5064	−	26.8579i	0.498652	−	0.863691i	0.999999	+	0.00155529i	$0.000495066\pi$
$968$	−27.3801	+	47.4236i	−0.880028	+	1.52425i
$969$		0			0
$970$	−42.6972	−	73.9537i	−1.37092	−	2.37451i
$971$	14.5675			0.467494			0.233747	−	0.972297i	$-0.424901\pi$
$971$	14.5675			0.467494			0.233747	+	0.972297i	$0.424901\pi$
$972$		0			0
$973$		0			0
$974$	−22.1893	−	38.4330i	−0.710991	−	1.23147i
$975$		0			0
$976$	17.3684	−	30.0830i	0.555949	−	0.962932i
$977$	−23.9399	+	41.4651i	−0.765904	+	1.32659i	0.173863	+	0.984770i	$0.444375\pi$
$977$	−23.9399	+	41.4651i	−0.765904	+	1.32659i	−0.939767	+	0.341815i	$0.888958\pi$
$978$		0			0
$979$	−3.01364	−	5.21978i	−0.0963163	−	0.166825i
$980$		0			0
$981$		0			0
$982$	5.03638			0.160717
$983$	−22.2128	−	38.4737i	−0.708479	−	1.22712i	−0.965421	−	0.260695i	$-0.916048\pi$
$983$	−22.2128	−	38.4737i	−0.708479	−	1.22712i	0.256942	−	0.966427i	$-0.417285\pi$
$984$		0			0
$985$	−38.9902	+	67.5329i	−1.24233	+	2.15178i
$986$	45.6864	−	79.1313i	1.45495	−	2.52005i
$987$		0			0
$988$	−1.94738	−	3.37296i	−0.0619544	−	0.107308i
$989$	10.8171			0.343964
$990$		0			0
$991$	−41.6156			−1.32196			−0.660981	−	0.750403i	$-0.729860\pi$
$991$	−41.6156			−1.32196			−0.660981	+	0.750403i	$0.729860\pi$
$992$	1.89557	+	3.28322i	0.0601844	+	0.104242i
$993$		0			0
$994$		0			0
$995$	−18.2434	+	31.5985i	−0.578354	+	1.00174i
$996$		0			0
$997$	−6.51407	−	11.2827i	−0.206303	−	0.357327i	0.744244	−	0.667908i	$-0.232810\pi$
$997$	−6.51407	−	11.2827i	−0.206303	−	0.357327i	−0.950547	+	0.310581i	$0.899477\pi$
$998$	96.1751			3.04437
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.f.g.442.5		12
3.2	odd	2		441.2.f.g.148.2	yes	12
7.2	even	3		1323.2.g.g.361.6		12
7.3	odd	6		1323.2.h.g.226.2		12
7.4	even	3		1323.2.h.g.226.1		12
7.5	odd	6		1323.2.g.g.361.5		12
7.6	odd	2	inner	1323.2.f.g.442.6		12
9.2	odd	6		441.2.f.g.295.2	yes	12
9.4	even	3		3969.2.a.bd.1.2		6
9.5	odd	6		3969.2.a.be.1.5		6
9.7	even	3	inner	1323.2.f.g.883.5		12
21.2	odd	6		441.2.g.g.67.1		12
21.5	even	6		441.2.g.g.67.2		12
21.11	odd	6		441.2.h.g.373.5		12
21.17	even	6		441.2.h.g.373.6		12
21.20	even	2		441.2.f.g.148.1	✓	12
63.2	odd	6		441.2.h.g.214.5		12
63.11	odd	6		441.2.g.g.79.1		12
63.13	odd	6		3969.2.a.bd.1.1		6
63.16	even	3		1323.2.h.g.802.1		12
63.20	even	6		441.2.f.g.295.1	yes	12
63.25	even	3		1323.2.g.g.667.6		12
63.34	odd	6	inner	1323.2.f.g.883.6		12
63.38	even	6		441.2.g.g.79.2		12
63.41	even	6		3969.2.a.be.1.6		6
63.47	even	6		441.2.h.g.214.6		12
63.52	odd	6		1323.2.g.g.667.5		12
63.61	odd	6		1323.2.h.g.802.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.g.148.1	✓	12	21.20	even	2
441.2.f.g.148.2	yes	12	3.2	odd	2
441.2.f.g.295.1	yes	12	63.20	even	6
441.2.f.g.295.2	yes	12	9.2	odd	6
441.2.g.g.67.1		12	21.2	odd	6
441.2.g.g.67.2		12	21.5	even	6
441.2.g.g.79.1		12	63.11	odd	6
441.2.g.g.79.2		12	63.38	even	6
441.2.h.g.214.5		12	63.2	odd	6
441.2.h.g.214.6		12	63.47	even	6
441.2.h.g.373.5		12	21.11	odd	6
441.2.h.g.373.6		12	21.17	even	6
1323.2.f.g.442.5		12	1.1	even	1	trivial
1323.2.f.g.442.6		12	7.6	odd	2	inner
1323.2.f.g.883.5		12	9.7	even	3	inner
1323.2.f.g.883.6		12	63.34	odd	6	inner
1323.2.g.g.361.5		12	7.5	odd	6
1323.2.g.g.361.6		12	7.2	even	3
1323.2.g.g.667.5		12	63.52	odd	6
1323.2.g.g.667.6		12	63.25	even	3
1323.2.h.g.226.1		12	7.4	even	3
1323.2.h.g.226.2		12	7.3	odd	6
1323.2.h.g.802.1		12	63.16	even	3
1323.2.h.g.802.2		12	63.61	odd	6
3969.2.a.bd.1.1		6	63.13	odd	6
3969.2.a.bd.1.2		6	9.4	even	3
3969.2.a.be.1.5		6	9.5	odd	6
3969.2.a.be.1.6		6	63.41	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.23025 + 2.13086i) q^{2} +(-2.02704 + 3.51094i) q^{4} +(-1.82904 + 3.16799i) q^{5} -5.05408 q^{8} +O(q^{10})\)	\(q+(1.23025 + 2.13086i) q^{2} +(-2.02704 + 3.51094i) q^{4} +(-1.82904 + 3.16799i) q^{5} -5.05408 q^{8} -9.00071 q^{10} +(0.203210 + 0.351971i) q^{11} +(0.243398 - 0.421578i) q^{13} +(-2.16372 - 3.74766i) q^{16} -4.85584 q^{17} -1.97351 q^{19} +(-7.41507 - 12.8433i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(2.32383 - 4.02499i) q^{23} +(-4.19076 - 7.25860i) q^{25} +1.19777 q^{26} +(3.82383 + 6.62307i) q^{29} +(-3.51360 + 6.08573i) q^{31} +(0.269748 - 0.467216i) q^{32} +(-5.97391 - 10.3471i) q^{34} +2.32743 q^{37} +(-2.42792 - 4.20528i) q^{38} +(9.24411 - 16.0113i) q^{40} +(3.75700 - 6.50731i) q^{41} +(1.16372 + 2.01561i) q^{43} -1.64766 q^{44} +11.4356 q^{46} +(-3.15811 - 5.47002i) q^{47} +(10.3114 - 17.8598i) q^{50} +(0.986757 + 1.70911i) q^{52} +3.56867 q^{53} -1.48672 q^{55} +(-9.40856 + 16.2961i) q^{58} +(3.05919 - 5.29868i) q^{59} +(4.01356 + 6.95169i) q^{61} -17.2905 q^{62} -7.32743 q^{64} +(0.890369 + 1.54216i) q^{65} +(-1.80039 + 3.11836i) q^{67} +(9.84299 - 17.0486i) q^{68} -8.46050 q^{71} +1.97351 q^{73} +(2.86333 + 4.95943i) q^{74} +(4.00040 - 6.92889i) q^{76} +(-4.08113 - 7.06872i) q^{79} +15.8301 q^{80} +18.4882 q^{82} +(6.08600 + 10.5413i) q^{83} +(8.88151 - 15.3832i) q^{85} +(-2.86333 + 4.95943i) q^{86} +(-1.02704 - 1.77889i) q^{88} -14.8301 q^{89} +(9.42101 + 16.3177i) q^{92} +(7.77056 - 13.4590i) q^{94} +(3.60963 - 6.25206i) q^{95} +(4.74375 + 8.21642i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 6 q^{4} - 24 q^{8}+O(q^{10}) \) 12 * q + 2 * q^2 - 6 * q^4 - 24 * q^8	\( 12 q + 2 q^{2} - 6 q^{4} - 24 q^{8} + 8 q^{11} - 6 q^{16} - 6 q^{22} + 4 q^{23} - 12 q^{25} + 22 q^{29} + 16 q^{32} - 12 q^{37} - 6 q^{43} + 28 q^{44} + 24 q^{46} + 56 q^{50} - 56 q^{53} - 18 q^{58} - 48 q^{64} - 6 q^{65} - 76 q^{71} + 36 q^{74} + 6 q^{79} + 30 q^{85} - 36 q^{86} + 6 q^{88} + 62 q^{92} + 60 q^{95}+O(q^{100}) \) 12 * q + 2 * q^2 - 6 * q^4 - 24 * q^8 + 8 * q^11 - 6 * q^16 - 6 * q^22 + 4 * q^23 - 12 * q^25 + 22 * q^29 + 16 * q^32 - 12 * q^37 - 6 * q^43 + 28 * q^44 + 24 * q^46 + 56 * q^50 - 56 * q^53 - 18 * q^58 - 48 * q^64 - 6 * q^65 - 76 * q^71 + 36 * q^74 + 6 * q^79 + 30 * q^85 - 36 * q^86 + 6 * q^88 + 62 * q^92 + 60 * q^95

Introduction

L-functions

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