LMFDB - Embedded newform 432.2.u.d.241.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(49,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("432.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.u (of order $9$, degree $6$, 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} + 24 x^{16} - 66 x^{15} + 153 x^{14} - 315 x^{13} + 651 x^{12} - 1350 x^{11} + \cdots + 19683 $ x^18 - 6x^17 + 24x^16 - 66x^15 + 153x^14 - 315x^13 + 651x^12 - 1350x^11 + 2700x^10 - 4941x^9 + 8100x^8 - 12150x^7 + 17577x^6 - 25515x^5 + 37179x^4 - 48114x^3 + 52488x^2 - 39366*x + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			241.2
Root			$1.20201 + 1.24706i$ of defining polynomial
Character	$\chi$	$=$	432.241
Dual form			432.2.u.d.337.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.01939 + 1.40030i) q^{3} +(1.46957 - 1.23312i) q^{5} +(3.86125 - 1.40538i) q^{7} +(-0.921685 - 2.85491i) q^{9} +O(q^{10})$	\(q+(-1.01939 + 1.40030i) q^{3} +(1.46957 - 1.23312i) q^{5} +(3.86125 - 1.40538i) q^{7} +(-0.921685 - 2.85491i) q^{9} +(-4.34920 - 3.64942i) q^{11} +(-0.251022 - 1.42362i) q^{13} +(0.228667 + 3.31487i) q^{15} +(1.36924 + 2.37159i) q^{17} +(2.54610 - 4.40998i) q^{19} +(-1.96817 + 6.83954i) q^{21} +(4.42643 + 1.61109i) q^{23} +(-0.229178 + 1.29973i) q^{25} +(4.93729 + 1.61963i) q^{27} +(0.768745 - 4.35977i) q^{29} +(1.06475 + 0.387538i) q^{31} +(9.54382 - 2.37001i) q^{33} +(3.94138 - 6.82668i) q^{35} +(1.97441 + 3.41977i) q^{37} +(2.24938 + 1.09972i) q^{39} +(-0.0493888 - 0.280098i) q^{41} +(4.90028 + 4.11182i) q^{43} +(-4.87492 - 3.05895i) q^{45} +(-5.79555 + 2.10941i) q^{47} +(7.57184 - 6.35352i) q^{49} +(-4.71673 - 0.500232i) q^{51} -8.16159 q^{53} -10.8916 q^{55} +(3.57983 + 8.06081i) q^{57} +(-10.8951 + 9.14210i) q^{59} +(2.76413 - 1.00606i) q^{61} +(-7.57108 - 9.72819i) q^{63} +(-2.12438 - 1.78257i) q^{65} +(2.14911 + 12.1882i) q^{67} +(-6.76826 + 4.55600i) q^{69} +(3.15719 + 5.46842i) q^{71} +(2.36669 - 4.09923i) q^{73} +(-1.58640 - 1.64585i) q^{75} +(-21.9222 - 7.97902i) q^{77} +(1.09121 - 6.18856i) q^{79} +(-7.30099 + 5.26265i) q^{81} +(2.82134 - 16.0006i) q^{83} +(4.93664 + 1.79679i) q^{85} +(5.32133 + 5.52078i) q^{87} +(1.02796 - 1.78048i) q^{89} +(-2.96998 - 5.14416i) q^{91} +(-1.62807 + 1.09592i) q^{93} +(-1.69634 - 9.62043i) q^{95} +(0.00867542 + 0.00727954i) q^{97} +(-6.41015 + 15.7802i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{5} + 6 q^{9}+O(q^{10}) $ 18 * q + 3 * q^5 + 6 * q^9	$ 18 q + 3 q^{5} + 6 q^{9} - 3 q^{11} + 9 q^{15} - 12 q^{17} - 30 q^{21} + 30 q^{23} + 9 q^{25} + 27 q^{27} - 24 q^{29} - 9 q^{31} - 18 q^{33} + 21 q^{35} - 3 q^{39} + 21 q^{41} + 9 q^{43} + 45 q^{45} - 45 q^{47} - 18 q^{49} - 63 q^{51} + 66 q^{53} + 54 q^{57} - 60 q^{59} - 18 q^{61} - 57 q^{63} + 33 q^{65} + 27 q^{67} - 9 q^{69} + 12 q^{71} + 9 q^{73} + 33 q^{75} - 75 q^{77} + 36 q^{79} - 54 q^{81} + 45 q^{83} - 36 q^{85} + 63 q^{87} - 48 q^{89} - 9 q^{91} - 33 q^{93} - 6 q^{95} - 27 q^{97} - 27 q^{99}+O(q^{100}) $ 18 * q + 3 * q^5 + 6 * q^9 - 3 * q^11 + 9 * q^15 - 12 * q^17 - 30 * q^21 + 30 * q^23 + 9 * q^25 + 27 * q^27 - 24 * q^29 - 9 * q^31 - 18 * q^33 + 21 * q^35 - 3 * q^39 + 21 * q^41 + 9 * q^43 + 45 * q^45 - 45 * q^47 - 18 * q^49 - 63 * q^51 + 66 * q^53 + 54 * q^57 - 60 * q^59 - 18 * q^61 - 57 * q^63 + 33 * q^65 + 27 * q^67 - 9 * q^69 + 12 * q^71 + 9 * q^73 + 33 * q^75 - 75 * q^77 + 36 * q^79 - 54 * q^81 + 45 * q^83 - 36 * q^85 + 63 * q^87 - 48 * q^89 - 9 * q^91 - 33 * q^93 - 6 * q^95 - 27 * q^97 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.01939	+	1.40030i	−0.588546	+	0.808464i
$3$	−1.01939	+	1.40030i	−0.588546	+	0.808464i
$4$		0			0
$5$	1.46957	−	1.23312i	0.657212	−	0.551467i	−0.252038	−	0.967717i	$-0.581101\pi$
$5$	1.46957	−	1.23312i	0.657212	−	0.551467i	0.909250	+	0.416251i	$0.136656\pi$
$6$		0			0
$7$	3.86125	−	1.40538i	1.45941	−	0.531184i	0.514211	−	0.857664i	$-0.328085\pi$
$7$	3.86125	−	1.40538i	1.45941	−	0.531184i	0.945204	+	0.326480i	$0.105863\pi$
$8$		0			0
$9$	−0.921685	−	2.85491i	−0.307228	−	0.951636i
$10$		0			0
$11$	−4.34920	−	3.64942i	−1.31133	−	1.10034i	−0.988066	−	0.154033i	$-0.950774\pi$
$11$	−4.34920	−	3.64942i	−1.31133	−	1.10034i	−0.323269	−	0.946307i	$-0.604782\pi$
$12$		0			0
$13$	−0.251022	−	1.42362i	−0.0696210	−	0.394840i	−0.999627	−	0.0272969i	$-0.991310\pi$
$13$	−0.251022	−	1.42362i	−0.0696210	−	0.394840i	0.930006	−	0.367543i	$-0.119801\pi$
$14$		0			0
$15$	0.228667	+	3.31487i	0.0590415	+	0.855896i
$16$		0			0
$17$	1.36924	+	2.37159i	0.332089	+	0.575195i	0.982921	−	0.184026i	$-0.0589132\pi$
$17$	1.36924	+	2.37159i	0.332089	+	0.575195i	−0.650832	+	0.759222i	$0.725580\pi$
$18$		0			0
$19$	2.54610	−	4.40998i	0.584116	−	1.01172i	−0.410869	−	0.911695i	$-0.634774\pi$
$19$	2.54610	−	4.40998i	0.584116	−	1.01172i	0.994985	−	0.100025i	$-0.0318922\pi$
$20$		0			0
$21$	−1.96817	+	6.83954i	−0.429489	+	1.49251i
$22$		0			0
$23$	4.42643	+	1.61109i	0.922974	+	0.335935i	0.759421	−	0.650600i	$-0.225482\pi$
$23$	4.42643	+	1.61109i	0.922974	+	0.335935i	0.163553	+	0.986535i	$0.447705\pi$
$24$		0			0
$25$	−0.229178	+	1.29973i	−0.0458356	+	0.259947i
$26$		0			0
$27$	4.93729	+	1.61963i	0.950181	+	0.311698i
$28$		0			0
$29$	0.768745	−	4.35977i	0.142752	−	0.809589i	−0.826392	−	0.563095i	$-0.809610\pi$
$29$	0.768745	−	4.35977i	0.142752	−	0.809589i	0.969144	−	0.246494i	$-0.0792784\pi$
$30$		0			0
$31$	1.06475	+	0.387538i	0.191235	+	0.0696039i	0.435862	−	0.900013i	$-0.356443\pi$
$31$	1.06475	+	0.387538i	0.191235	+	0.0696039i	−0.244627	+	0.969617i	$0.578666\pi$
$32$		0			0
$33$	9.54382	−	2.37001i	1.66137	−	0.412566i
$34$		0			0
$35$	3.94138	−	6.82668i	0.666215	−	1.15392i
$36$		0			0
$37$	1.97441	+	3.41977i	0.324590	+	0.562207i	0.981429	−	0.191824i	$-0.0614403\pi$
$37$	1.97441	+	3.41977i	0.324590	+	0.562207i	−0.656839	+	0.754031i	$0.728107\pi$
$38$		0			0
$39$	2.24938	+	1.09972i	0.360189	+	0.176095i
$40$		0			0
$41$	−0.0493888	−	0.280098i	−0.00771323	−	0.0437439i	0.980708	−	0.195477i	$-0.0626256\pi$
$41$	−0.0493888	−	0.280098i	−0.00771323	−	0.0437439i	−0.988421	+	0.151733i	$0.951514\pi$
$42$		0			0
$43$	4.90028	+	4.11182i	0.747286	+	0.627047i	0.934784	−	0.355218i	$-0.115593\pi$
$43$	4.90028	+	4.11182i	0.747286	+	0.627047i	−0.187498	+	0.982265i	$0.560038\pi$
$44$		0			0
$45$	−4.87492	−	3.05895i	−0.726710	−	0.456001i
$46$		0			0
$47$	−5.79555	+	2.10941i	−0.845368	+	0.307689i	−0.728150	−	0.685417i	$-0.759620\pi$
$47$	−5.79555	+	2.10941i	−0.845368	+	0.307689i	−0.117218	+	0.993106i	$0.537398\pi$
$48$		0			0
$49$	7.57184	−	6.35352i	1.08169	−	0.907646i
$50$		0			0
$51$	−4.71673	−	0.500232i	−0.660474	−	0.0700465i
$52$		0			0
$53$	−8.16159			−1.12108			−0.560540	−	0.828127i	$-0.689406\pi$
$53$	−8.16159			−1.12108			−0.560540	+	0.828127i	$0.689406\pi$
$54$		0			0
$55$	−10.8916			−1.46863
$56$		0			0
$57$	3.57983	+	8.06081i	0.474160	+	1.06768i
$58$		0			0
$59$	−10.8951	+	9.14210i	−1.41843	+	1.19020i	−0.466248	+	0.884654i	$0.654395\pi$
$59$	−10.8951	+	9.14210i	−1.41843	+	1.19020i	−0.952177	+	0.305546i	$0.901161\pi$
$60$		0			0
$61$	2.76413	−	1.00606i	0.353910	−	0.128813i	−0.158946	−	0.987287i	$-0.550810\pi$
$61$	2.76413	−	1.00606i	0.353910	−	0.128813i	0.512856	+	0.858475i	$0.328587\pi$
$62$		0			0
$63$	−7.57108	−	9.72819i	−0.953867	−	1.22564i
$64$		0			0
$65$	−2.12438	−	1.78257i	−0.263497	−	0.221100i
$66$		0			0
$67$	2.14911	+	12.1882i	0.262556	+	1.48903i	0.775906	+	0.630848i	$0.217293\pi$
$67$	2.14911	+	12.1882i	0.262556	+	1.48903i	−0.513350	+	0.858179i	$0.671596\pi$
$68$		0			0
$69$	−6.76826	+	4.55600i	−0.814803	+	0.548478i
$70$		0			0
$71$	3.15719	+	5.46842i	0.374690	+	0.648982i	0.990281	−	0.139084i	$-0.0444158\pi$
$71$	3.15719	+	5.46842i	0.374690	+	0.648982i	−0.615591	+	0.788066i	$0.711082\pi$
$72$		0			0
$73$	2.36669	−	4.09923i	0.277000	−	0.479779i	−0.693637	−	0.720324i	$-0.743993\pi$
$73$	2.36669	−	4.09923i	0.277000	−	0.479779i	0.970638	+	0.240545i	$0.0773263\pi$
$74$		0			0
$75$	−1.58640	−	1.64585i	−0.183181	−	0.190047i
$76$		0			0
$77$	−21.9222	−	7.97902i	−2.49826	−	0.909293i
$78$		0			0
$79$	1.09121	−	6.18856i	0.122771	−	0.696267i	−0.859836	−	0.510570i	$-0.829434\pi$
$79$	1.09121	−	6.18856i	0.122771	−	0.696267i	0.982607	−	0.185697i	$-0.0594544\pi$
$80$		0			0
$81$	−7.30099	+	5.26265i	−0.811222	+	0.584739i
$82$		0			0
$83$	2.82134	−	16.0006i	0.309683	−	1.75630i	−0.290917	−	0.956748i	$-0.593960\pi$
$83$	2.82134	−	16.0006i	0.309683	−	1.75630i	0.600600	−	0.799550i	$-0.294929\pi$
$84$		0			0
$85$	4.93664	+	1.79679i	0.535454	+	0.194889i
$86$		0			0
$87$	5.32133	+	5.52078i	0.570507	+	0.591890i
$88$		0			0
$89$	1.02796	−	1.78048i	0.108963	−	0.188730i	−0.806387	−	0.591388i	$-0.798580\pi$
$89$	1.02796	−	1.78048i	0.108963	−	0.188730i	0.915351	+	0.402658i	$0.131914\pi$
$90$		0			0
$91$	−2.96998	−	5.14416i	−0.311338	−	0.539254i
$92$		0			0
$93$	−1.62807	+	1.09592i	−0.168823	+	0.113642i
$94$		0			0
$95$	−1.69634	−	9.62043i	−0.174041	−	0.987035i
$96$		0			0
$97$	0.00867542	+	0.00727954i	0.000880855	+	0.000739125i	0.643228	−	0.765675i	$-0.277595\pi$
$97$	0.00867542	+	0.00727954i	0.000880855	+	0.000739125i	−0.642347	+	0.766414i	$0.722039\pi$
$98$		0			0
$99$	−6.41015	+	15.7802i	−0.644244	+	1.58597i
$100$		0			0
$101$	2.55554	−	0.930139i	0.254285	−	0.0925523i	−0.211732	−	0.977328i	$-0.567911\pi$
$101$	2.55554	−	0.930139i	0.254285	−	0.0925523i	0.466018	+	0.884775i	$0.345688\pi$
$102$		0			0
$103$	2.93683	−	2.46429i	0.289374	−	0.242814i	−0.486531	−	0.873663i	$-0.661738\pi$
$103$	2.93683	−	2.46429i	0.289374	−	0.242814i	0.775905	+	0.630850i	$0.217294\pi$
$104$		0			0
$105$	5.54159	+	12.4782i	0.540804	+	1.21774i
$106$		0			0
$107$	−2.63565			−0.254798			−0.127399	−	0.991852i	$-0.540663\pi$
$107$	−2.63565			−0.254798			−0.127399	+	0.991852i	$0.540663\pi$
$108$		0			0
$109$	−14.3548			−1.37494			−0.687470	−	0.726212i	$-0.741279\pi$
$109$	−14.3548			−1.37494			−0.687470	+	0.726212i	$0.741279\pi$
$110$		0			0
$111$	−6.80140	−	0.721321i	−0.645560	−	0.0684648i
$112$		0			0
$113$	1.23122	−	1.03312i	0.115824	−	0.0971877i	−0.583036	−	0.812446i	$-0.698135\pi$
$113$	1.23122	−	1.03312i	0.115824	−	0.0971877i	0.698860	+	0.715258i	$0.253691\pi$
$114$		0			0
$115$	8.49161	−	3.09069i	0.791846	−	0.288209i
$116$		0			0
$117$	−3.83293	+	2.02877i	−0.354355	+	0.187560i
$118$		0			0
$119$	8.61996	+	7.23300i	0.790190	+	0.663048i
$120$		0			0
$121$	3.68721	+	20.9112i	0.335201	+	1.90102i
$122$		0			0
$123$	0.442567	+	0.216370i	0.0399050	+	0.0195094i
$124$		0			0
$125$	6.06190	+	10.4995i	0.542193	+	0.939106i
$126$		0			0
$127$	−5.55302	+	9.61811i	−0.492751	+	0.853469i	−0.999965	−	0.00835083i	$-0.997342\pi$
$127$	−5.55302	+	9.61811i	−0.492751	+	0.853469i	0.507215	+	0.861820i	$0.330675\pi$
$128$		0			0
$129$	−10.7531	+	2.67031i	−0.946757	+	0.235108i
$130$		0			0
$131$	−4.47367	−	1.62828i	−0.390866	−	0.142264i	0.139109	−	0.990277i	$-0.455576\pi$
$131$	−4.47367	−	1.62828i	−0.390866	−	0.142264i	−0.529975	+	0.848014i	$0.677799\pi$
$132$		0			0
$133$	3.63344	−	20.6063i	0.315059	−	1.78679i
$134$		0			0
$135$	9.25289	−	3.70809i	0.796362	−	0.319141i
$136$		0			0
$137$	2.59714	−	14.7291i	0.221888	−	1.25839i	−0.646657	−	0.762781i	$-0.723833\pi$
$137$	2.59714	−	14.7291i	0.221888	−	1.25839i	0.868545	−	0.495610i	$-0.165055\pi$
$138$		0			0
$139$	3.09109	+	1.12507i	0.262183	+	0.0954269i	0.469767	−	0.882790i	$-0.344338\pi$
$139$	3.09109	+	1.12507i	0.262183	+	0.0954269i	−0.207584	+	0.978217i	$0.566560\pi$
$140$		0			0
$141$	2.95413	−	10.2658i	0.248782	−	0.864539i
$142$		0			0
$143$	−4.10362	+	7.10768i	−0.343162	+	0.594374i
$144$		0			0
$145$	−4.24638	−	7.35494i	−0.352642	−	0.610795i
$146$		0			0
$147$	1.17819	+	17.0796i	0.0971751	+	1.40870i
$148$		0			0
$149$	4.09732	+	23.2371i	0.335666	+	1.90366i	0.420558	+	0.907266i	$0.361834\pi$
$149$	4.09732	+	23.2371i	0.335666	+	1.90366i	−0.0848922	+	0.996390i	$0.527055\pi$
$150$		0			0
$151$	−13.5314	−	11.3542i	−1.10117	−	0.923992i	−0.103667	−	0.994612i	$-0.533058\pi$
$151$	−13.5314	−	11.3542i	−1.10117	−	0.923992i	−0.997503	+	0.0706202i	$0.977502\pi$
$152$		0			0
$153$	5.50867	−	6.09491i	0.445349	−	0.492744i
$154$		0			0
$155$	2.04261	−	0.743449i	0.164066	−	0.0597152i
$156$		0			0
$157$	−11.5813	+	9.71789i	−0.924291	+	0.775572i	−0.974784	−	0.223152i	$-0.928365\pi$
$157$	−11.5813	+	9.71789i	−0.924291	+	0.775572i	0.0504927	+	0.998724i	$0.483921\pi$
$158$		0			0
$159$	8.31985	−	11.4287i	0.659807	−	0.906353i
$160$		0			0
$161$	19.3557			1.52544
$162$		0			0
$163$	14.2428			1.11558			0.557789	−	0.829983i	$-0.311650\pi$
$163$	14.2428			1.11558			0.557789	+	0.829983i	$0.311650\pi$
$164$		0			0
$165$	11.1028	−	15.2515i	0.864353	−	1.18733i
$166$		0			0
$167$	−11.9620	+	10.0373i	−0.925644	+	0.776708i	−0.975030	−	0.222072i	$-0.928718\pi$
$167$	−11.9620	+	10.0373i	−0.925644	+	0.776708i	0.0493862	+	0.998780i	$0.484273\pi$
$168$		0			0
$169$	10.2523	−	3.73154i	0.788641	−	0.287042i
$170$		0			0
$171$	−14.9368	−	3.20428i	−1.14225	−	0.245037i
$172$		0			0
$173$	10.1113	+	8.48440i	0.768749	+	0.645057i	0.940388	−	0.340103i	$-0.110462\pi$
$173$	10.1113	+	8.48440i	0.768749	+	0.645057i	−0.171640	+	0.985160i	$0.554906\pi$
$174$		0			0
$175$	0.941705	+	5.34067i	0.0711862	+	0.403717i
$176$		0			0
$177$	−1.69529	−	24.5758i	−0.127426	−	1.84723i
$178$		0			0
$179$	5.82046	+	10.0813i	0.435042	+	0.753514i	0.997299	−	0.0734481i	$-0.0234003\pi$
$179$	5.82046	+	10.0813i	0.435042	+	0.753514i	−0.562257	+	0.826962i	$0.690067\pi$
$180$		0			0
$181$	−8.69794	+	15.0653i	−0.646513	+	1.11979i	0.337437	+	0.941348i	$0.390440\pi$
$181$	−8.69794	+	15.0653i	−0.646513	+	1.11979i	−0.983950	+	0.178445i	$0.942893\pi$
$182$		0			0
$183$	−1.40894	+	4.89617i	−0.104152	+	0.361936i
$184$		0			0
$185$	7.11851	+	2.59092i	0.523363	+	0.190489i
$186$		0			0
$187$	2.69982	−	15.3115i	0.197431	−	1.11968i
$188$		0			0
$189$	21.3403	−	0.684963i	1.55228	−	0.0498237i
$190$		0			0
$191$	0.890593	−	5.05080i	0.0644410	−	0.365463i	−0.935486	−	0.353364i	$-0.885038\pi$
$191$	0.890593	−	5.05080i	0.0644410	−	0.365463i	0.999927	−	0.0120989i	$-0.00385130\pi$
$192$		0			0
$193$	−11.6739	−	4.24897i	−0.840309	−	0.305847i	−0.114226	−	0.993455i	$-0.536439\pi$
$193$	−11.6739	−	4.24897i	−0.840309	−	0.305847i	−0.726083	+	0.687607i	$0.758661\pi$
$194$		0			0
$195$	4.66170	−	1.15764i	0.333831	−	0.0829003i
$196$		0			0
$197$	4.45190	−	7.71091i	0.317185	−	0.549380i	−0.662715	−	0.748872i	$-0.730596\pi$
$197$	4.45190	−	7.71091i	0.317185	−	0.549380i	0.979899	+	0.199492i	$0.0639292\pi$
$198$		0			0
$199$	0.393080	+	0.680834i	0.0278647	+	0.0482631i	0.879621	−	0.475674i	$-0.157796\pi$
$199$	0.393080	+	0.680834i	0.0278647	+	0.0482631i	−0.851757	+	0.523937i	$0.824463\pi$
$200$		0			0
$201$	−19.2580	−	9.41515i	−1.35835	−	0.664094i
$202$		0			0
$203$	−3.15881	−	17.9145i	−0.221705	−	1.25735i
$204$		0			0
$205$	−0.417973	−	0.350721i	−0.0291925	−	0.0244954i
$206$		0			0
$207$	0.519737	−	14.1220i	0.0361242	−	0.981543i
$208$		0			0
$209$	−27.1674	+	9.88812i	−1.87921	+	0.683976i
$210$		0			0
$211$	2.35690	−	1.97768i	0.162256	−	0.136149i	−0.558045	−	0.829811i	$-0.688448\pi$
$211$	2.35690	−	1.97768i	0.162256	−	0.136149i	0.720301	+	0.693662i	$0.244004\pi$
$212$		0			0
$213$	−10.8758	−	1.15344i	−0.745201	−	0.0790322i
$214$		0			0
$215$	12.2717			0.836921
$216$		0			0
$217$	4.65591			0.316064
$218$		0			0
$219$	3.32757	+	7.49280i	0.224857	+	0.506317i
$220$		0			0
$221$	3.03253	−	2.54459i	0.203990	−	0.171168i
$222$		0			0
$223$	−12.1923	+	4.43765i	−0.816459	+	0.297167i	−0.716289	−	0.697804i	$-0.754161\pi$
$223$	−12.1923	+	4.43765i	−0.816459	+	0.297167i	−0.100170	+	0.994970i	$0.531939\pi$
$224$		0			0
$225$	3.92185	−	0.543662i	0.261456	−	0.0362441i
$226$		0			0
$227$	3.67917	+	3.08719i	0.244195	+	0.204904i	0.756668	−	0.653799i	$-0.226826\pi$
$227$	3.67917	+	3.08719i	0.244195	+	0.204904i	−0.512473	+	0.858704i	$0.671270\pi$
$228$		0			0
$229$	1.52222	+	8.63293i	0.100591	+	0.570480i	0.992890	+	0.119035i	$0.0379801\pi$
$229$	1.52222	+	8.63293i	0.100591	+	0.570480i	−0.892299	+	0.451445i	$0.850909\pi$
$230$		0			0
$231$	33.5203	−	22.5639i	2.20547	−	1.48460i
$232$		0			0
$233$	−1.99833	−	3.46120i	−0.130915	−	0.226751i	0.793115	−	0.609072i	$-0.208458\pi$
$233$	−1.99833	−	3.46120i	−0.130915	−	0.226751i	−0.924029	+	0.382321i	$0.875125\pi$
$234$		0			0
$235$	−5.91583	+	10.2465i	−0.385906	+	0.668409i
$236$		0			0
$237$	7.55348	+	7.83658i	0.490651	+	0.509041i
$238$		0			0
$239$	7.08212	+	2.57768i	0.458105	+	0.166736i	0.560756	−	0.827981i	$-0.310510\pi$
$239$	7.08212	+	2.57768i	0.458105	+	0.166736i	−0.102652	+	0.994717i	$0.532733\pi$
$240$		0			0
$241$	−1.67523	+	9.50068i	−0.107911	+	0.611993i	0.882107	+	0.471049i	$0.156125\pi$
$241$	−1.67523	+	9.50068i	−0.107911	+	0.611993i	−0.990018	+	0.140943i	$0.954986\pi$
$242$		0			0
$243$	0.0732760	−	15.5883i	0.00470066	−	0.999989i
$244$		0			0
$245$	3.29272	−	18.6739i	0.210364	−	1.19303i
$246$		0			0
$247$	−6.91725	−	2.51767i	−0.440134	−	0.160196i
$248$		0			0
$249$	19.5297	+	20.2616i	1.23764	+	1.28403i
$250$		0			0
$251$	−1.24195	+	2.15112i	−0.0783912	+	0.135778i	−0.902556	−	0.430573i	$-0.858312\pi$
$251$	−1.24195	+	2.15112i	−0.0783912	+	0.135778i	0.824165	+	0.566350i	$0.191645\pi$
$252$		0			0
$253$	−13.3719	−	23.1608i	−0.840684	−	1.45611i
$254$		0			0
$255$	−7.54842	+	5.08115i	−0.472700	+	0.318194i
$256$		0			0
$257$	2.72311	+	15.4435i	0.169863	+	0.963340i	0.943908	+	0.330209i	$0.107119\pi$
$257$	2.72311	+	15.4435i	0.169863	+	0.963340i	−0.774045	+	0.633131i	$0.781770\pi$
$258$		0			0
$259$	12.4297	+	10.4298i	0.772347	+	0.648076i
$260$		0			0
$261$	−13.1553	+	1.82364i	−0.814291	+	0.112880i
$262$		0			0
$263$	11.2643	−	4.09987i	0.694586	−	0.252809i	0.0294886	−	0.999565i	$-0.490612\pi$
$263$	11.2643	−	4.09987i	0.694586	−	0.252809i	0.665098	+	0.746756i	$0.268390\pi$
$264$		0			0
$265$	−11.9940	+	10.0642i	−0.736788	+	0.618238i
$266$		0			0
$267$	1.44531	+	3.25445i	0.0884516	+	0.199169i
$268$		0			0
$269$	19.7528			1.20435			0.602174	−	0.798365i	$-0.294301\pi$
$269$	19.7528			1.20435			0.602174	+	0.798365i	$0.294301\pi$
$270$		0			0
$271$	−6.61217			−0.401661			−0.200830	−	0.979626i	$-0.564364\pi$
$271$	−6.61217			−0.401661			−0.200830	+	0.979626i	$0.564364\pi$
$272$		0			0
$273$	10.2309	+	1.08504i	0.619204	+	0.0656696i
$274$		0			0
$275$	5.74001	−	4.81644i	0.346135	−	0.290442i
$276$		0			0
$277$	15.0116	−	5.46379i	0.901962	−	0.328287i	0.150923	−	0.988545i	$-0.451775\pi$
$277$	15.0116	−	5.46379i	0.901962	−	0.328287i	0.751039	+	0.660258i	$0.229553\pi$
$278$		0			0
$279$	0.125020	−	3.39696i	0.00748473	−	0.203370i
$280$		0			0
$281$	−6.34624	−	5.32513i	−0.378585	−	0.317671i	0.433562	−	0.901124i	$-0.357257\pi$
$281$	−6.34624	−	5.32513i	−0.378585	−	0.317671i	−0.812147	+	0.583453i	$0.801701\pi$
$282$		0			0
$283$	−2.99620	−	16.9923i	−0.178106	−	1.01009i	−0.934498	−	0.355969i	$-0.884151\pi$
$283$	−2.99620	−	16.9923i	−0.178106	−	1.01009i	0.756392	−	0.654118i	$-0.226960\pi$
$284$		0			0
$285$	15.2007	+	7.43159i	0.900413	+	0.440209i
$286$		0			0
$287$	−0.584346	−	1.01212i	−0.0344928	−	0.0597434i
$288$		0			0
$289$	4.75037	−	8.22788i	0.279434	−	0.483993i
$290$		0			0
$291$	−0.0190372	+	0.00472750i	−0.00111598	+	0.000277131i
$292$		0			0
$293$	−10.0989	−	3.67569i	−0.589983	−	0.214736i	0.0297390	−	0.999558i	$-0.490532\pi$
$293$	−10.0989	−	3.67569i	−0.589983	−	0.214736i	−0.619722	+	0.784821i	$0.712755\pi$
$294$		0			0
$295$	−4.73789	+	26.8699i	−0.275851	+	1.56443i
$296$		0			0
$297$	−15.5626	−	25.0623i	−0.903031	−	1.45426i
$298$		0			0
$299$	1.18244	−	6.70595i	0.0683823	−	0.387815i
$300$		0			0
$301$	24.6999	+	8.99002i	1.42368	+	0.518176i
$302$		0			0
$303$	−1.30262	+	4.52669i	−0.0748333	+	0.260052i
$304$		0			0
$305$	2.82149	−	4.88696i	0.161558	−	0.279827i
$306$		0			0
$307$	1.32872	+	2.30142i	0.0758343	+	0.131349i	0.901449	−	0.432886i	$-0.142505\pi$
$307$	1.32872	+	2.30142i	0.0758343	+	0.131349i	−0.825614	+	0.564235i	$0.809171\pi$
$308$		0			0
$309$	0.456973	+	6.62452i	0.0259963	+	0.376856i
$310$		0			0
$311$	5.98755	+	33.9571i	0.339523	+	1.92553i	0.376957	+	0.926231i	$0.376970\pi$
$311$	5.98755	+	33.9571i	0.339523	+	1.92553i	−0.0374342	+	0.999299i	$0.511918\pi$
$312$		0			0
$313$	9.70435	+	8.14292i	0.548522	+	0.460265i	0.874440	−	0.485133i	$-0.161229\pi$
$313$	9.70435	+	8.14292i	0.548522	+	0.460265i	−0.325918	+	0.945398i	$0.605673\pi$
$314$		0			0
$315$	−23.1222	−	4.96024i	−1.30279	−	0.279478i
$316$		0			0
$317$	8.26564	−	3.00845i	0.464244	−	0.168971i	−0.0992989	−	0.995058i	$-0.531660\pi$
$317$	8.26564	−	3.00845i	0.464244	−	0.168971i	0.563543	+	0.826087i	$0.309438\pi$
$318$		0			0
$319$	−19.2540	+	16.1561i	−1.07802	+	0.904565i
$320$		0			0
$321$	2.68676	−	3.69071i	0.149960	−	0.205995i
$322$		0			0
$323$	13.9449			0.775915
$324$		0			0
$325$	1.90785			0.105828
$326$		0			0
$327$	14.6332	−	20.1010i	0.809215	−	1.11159i
$328$		0			0
$329$	−19.4135	+	16.2899i	−1.07030	+	0.898091i
$330$		0			0
$331$	−11.1353	+	4.05290i	−0.612049	+	0.222768i	−0.629400	−	0.777082i	$-0.716699\pi$
$331$	−11.1353	+	4.05290i	−0.612049	+	0.222768i	0.0173504	+	0.999849i	$0.494477\pi$
$332$		0			0
$333$	7.94335	−	8.78870i	0.435293	−	0.481618i
$334$		0			0
$335$	18.1878	+	15.2613i	0.993704	+	0.833816i
$336$		0			0
$337$	−3.26880	−	18.5383i	−0.178063	−	1.00984i	−0.934549	−	0.355834i	$-0.884197\pi$
$337$	−3.26880	−	18.5383i	−0.178063	−	1.00984i	0.756486	−	0.654009i	$-0.226914\pi$
$338$		0			0
$339$	0.191580	+	2.77724i	0.0104052	+	0.150839i
$340$		0			0
$341$	−3.21654	−	5.57120i	−0.174185	−	0.301698i
$342$		0			0
$343$	5.92593	−	10.2640i	0.319970	−	0.554205i
$344$		0			0
$345$	−4.32837	+	15.0414i	−0.233031	+	0.809803i
$346$		0			0
$347$	3.61122	+	1.31438i	0.193861	+	0.0705595i	0.437126	−	0.899400i	$-0.355996\pi$
$347$	3.61122	+	1.31438i	0.193861	+	0.0705595i	−0.243265	+	0.969960i	$0.578219\pi$
$348$		0			0
$349$	−0.642364	+	3.64303i	−0.0343850	+	0.195007i	−0.997162	−	0.0752915i	$-0.976011\pi$
$349$	−0.642364	+	3.64303i	−0.0343850	+	0.195007i	0.962777	+	0.270298i	$0.0871224\pi$
$350$		0			0
$351$	1.06637	−	7.43537i	0.0569184	−	0.396870i
$352$		0			0
$353$	−2.34505	+	13.2995i	−0.124815	+	0.707859i	0.856603	+	0.515976i	$0.172571\pi$
$353$	−2.34505	+	13.2995i	−0.124815	+	0.707859i	−0.981418	+	0.191883i	$0.938541\pi$
$354$		0			0
$355$	11.3829	+	4.14304i	0.604143	+	0.219890i
$356$		0			0
$357$	−18.9155	+	4.69727i	−1.00111	+	0.248606i
$358$		0			0
$359$	−8.38794	+	14.5283i	−0.442699	+	0.766777i	−0.997889	−	0.0649470i	$-0.979312\pi$
$359$	−8.38794	+	14.5283i	−0.442699	+	0.766777i	0.555190	+	0.831724i	$0.312646\pi$
$360$		0			0
$361$	−3.46530	−	6.00207i	−0.182384	−	0.315898i
$362$		0			0
$363$	−33.0407	−	16.1535i	−1.73419	−	0.847839i
$364$		0			0
$365$	−1.57681	−	8.94252i	−0.0825339	−	0.468073i
$366$		0			0
$367$	−13.8640	−	11.6333i	−0.723695	−	0.607252i	0.204710	−	0.978823i	$-0.434375\pi$
$367$	−13.8640	−	11.6333i	−0.723695	−	0.607252i	−0.928405	+	0.371570i	$0.878819\pi$
$368$		0			0
$369$	−0.754132	+	0.399162i	−0.0392585	+	0.0207795i
$370$		0			0
$371$	−31.5139	+	11.4701i	−1.63612	+	0.595499i
$372$		0			0
$373$	10.1258	−	8.49660i	0.524297	−	0.439937i	−0.341830	−	0.939762i	$-0.611047\pi$
$373$	10.1258	−	8.49660i	0.524297	−	0.439937i	0.866127	+	0.499825i	$0.166602\pi$
$374$		0			0
$375$	−20.8819	−	2.21463i	−1.07834	−	0.114363i
$376$		0			0
$377$	−6.39961			−0.329597
$378$		0			0
$379$	−31.8219			−1.63458			−0.817289	−	0.576227i	$-0.804524\pi$
$379$	−31.8219			−1.63458			−0.817289	+	0.576227i	$0.804524\pi$
$380$		0			0
$381$	−7.80755	−	17.5805i	−0.399993	−	0.900676i
$382$		0			0
$383$	−4.16826	+	3.49758i	−0.212988	+	0.178718i	−0.743040	−	0.669247i	$-0.766617\pi$
$383$	−4.16826	+	3.49758i	−0.212988	+	0.178718i	0.530052	+	0.847965i	$0.322172\pi$
$384$		0			0
$385$	−42.0553	+	15.3069i	−2.14333	+	0.780110i
$386$		0			0
$387$	7.22236	−	17.7797i	0.367133	−	0.903791i
$388$		0			0
$389$	11.9094	+	9.99317i	0.603831	+	0.506674i	0.892674	−	0.450702i	$-0.148826\pi$
$389$	11.9094	+	9.99317i	0.603831	+	0.506674i	−0.288844	+	0.957376i	$0.593271\pi$
$390$		0			0
$391$	2.23999	+	12.7036i	0.113281	+	0.642450i
$392$		0			0
$393$	6.84050	−	4.60462i	0.345057	−	0.232273i
$394$		0			0
$395$	−6.02761	−	10.4401i	−0.303282	−	0.525299i
$396$		0			0
$397$	−9.11698	+	15.7911i	−0.457568	+	0.792531i	−0.998832	−	0.0483217i	$-0.984613\pi$
$397$	−9.11698	+	15.7911i	−0.457568	+	0.792531i	0.541264	+	0.840853i	$0.317946\pi$
$398$		0			0
$399$	25.1511	+	26.0938i	1.25913	+	1.30632i
$400$		0			0
$401$	33.0083	+	12.0140i	1.64836	+	0.599953i	0.988471	−	0.151413i	$-0.0483823\pi$
$401$	33.0083	+	12.0140i	1.64836	+	0.599953i	0.659886	+	0.751366i	$0.270605\pi$
$402$		0			0
$403$	0.284429	−	1.61308i	0.0141684	−	0.0803532i
$404$		0			0
$405$	−4.23987	+	16.7368i	−0.210681	+	0.831659i
$406$		0			0
$407$	3.89307	−	22.0787i	0.192972	−	1.09440i
$408$		0			0
$409$	−31.1161	−	11.3253i	−1.53859	−	0.560001i	−0.572884	−	0.819637i	$-0.694175\pi$
$409$	−31.1161	−	11.3253i	−1.53859	−	0.560001i	−0.965707	+	0.259636i	$0.916398\pi$
$410$		0			0
$411$	17.9777	+	18.6515i	0.886772	+	0.920009i
$412$		0			0
$413$	−29.2207	+	50.6117i	−1.43786	+	2.49044i
$414$		0			0
$415$	−15.5845	−	26.9931i	−0.765012	−	1.32504i
$416$		0			0
$417$	−4.72647	+	3.18158i	−0.231456	+	0.155803i
$418$		0			0
$419$	0.567077	+	3.21606i	0.0277035	+	0.157115i	0.995521	−	0.0945375i	$-0.0301372\pi$
$419$	0.567077	+	3.21606i	0.0277035	+	0.157115i	−0.967818	+	0.251652i	$0.919026\pi$
$420$		0			0
$421$	−17.0256	−	14.2861i	−0.829775	−	0.696264i	0.125465	−	0.992098i	$-0.459958\pi$
$421$	−17.0256	−	14.2861i	−0.829775	−	0.696264i	−0.955239	+	0.295835i	$0.904402\pi$
$422$		0			0
$423$	11.3638	+	14.6016i	0.552529	+	0.709952i
$424$		0			0
$425$	−3.39623	+	1.23613i	−0.164742	+	0.0599610i
$426$		0			0
$427$	9.25908	−	7.76929i	0.448078	−	0.375982i
$428$		0			0
$429$	−5.76970	−	12.9918i	−0.278564	−	0.627251i
$430$		0			0
$431$	23.4064			1.12744			0.563722	−	0.825964i	$-0.309369\pi$
$431$	23.4064			1.12744			0.563722	+	0.825964i	$0.309369\pi$
$432$		0			0
$433$	−20.5736			−0.988706			−0.494353	−	0.869261i	$-0.664595\pi$
$433$	−20.5736			−0.988706			−0.494353	+	0.869261i	$0.664595\pi$
$434$		0			0
$435$	14.6278	+	1.55135i	0.701352	+	0.0743817i
$436$		0			0
$437$	18.3750	−	15.4185i	0.878996	−	0.737565i
$438$		0			0
$439$	32.1780	−	11.7118i	1.53577	−	0.558975i	0.570745	−	0.821127i	$-0.306654\pi$
$439$	32.1780	−	11.7118i	1.53577	−	0.558975i	0.965027	+	0.262152i	$0.0844321\pi$
$440$		0			0
$441$	−25.1176	−	15.7609i	−1.19607	−	0.750521i
$442$		0			0
$443$	−2.36729	−	1.98639i	−0.112473	−	0.0943762i	0.584817	−	0.811166i	$-0.301166\pi$
$443$	−2.36729	−	1.98639i	−0.112473	−	0.0943762i	−0.697290	+	0.716789i	$0.745611\pi$
$444$		0			0
$445$	−0.684877	−	3.88413i	−0.0324663	−	0.184125i
$446$		0			0
$447$	−36.7157	−	17.9502i	−1.73659	−	0.849014i
$448$		0			0
$449$	−2.22660	−	3.85659i	−0.105080	−	0.182004i	0.808691	−	0.588234i	$-0.200176\pi$
$449$	−2.22660	−	3.85659i	−0.105080	−	0.182004i	−0.913771	+	0.406230i	$0.866843\pi$
$450$		0			0
$451$	−0.807391	+	1.39844i	−0.0380186	+	0.0658501i
$452$		0			0
$453$	29.6931	−	7.37368i	1.39510	−	0.346446i
$454$		0			0
$455$	−10.7079	−	3.89737i	−0.501996	−	0.182712i
$456$		0			0
$457$	−1.27178	+	7.21262i	−0.0594913	+	0.337392i	−0.999997	−	0.00238542i	$-0.999241\pi$
$457$	−1.27178	+	7.21262i	−0.0594913	+	0.337392i	0.940506	+	0.339778i	$0.110352\pi$
$458$		0			0
$459$	2.91922	+	13.9269i	0.136258	+	0.650051i
$460$		0			0
$461$	2.58659	−	14.6693i	0.120470	−	0.683217i	−0.863426	−	0.504475i	$-0.831686\pi$
$461$	2.58659	−	14.6693i	0.120470	−	0.683217i	0.983896	−	0.178742i	$-0.0572027\pi$
$462$		0			0
$463$	−7.59572	−	2.76462i	−0.353003	−	0.128483i	0.159431	−	0.987209i	$-0.449034\pi$
$463$	−7.59572	−	2.76462i	−0.353003	−	0.128483i	−0.512434	+	0.858726i	$0.671256\pi$
$464$		0			0
$465$	−1.04116	+	3.61813i	−0.0482828	+	0.167787i
$466$		0			0
$467$	4.02480	−	6.97116i	0.186246	−	0.322587i	−0.757750	−	0.652545i	$-0.773701\pi$
$467$	4.02480	−	6.97116i	0.186246	−	0.322587i	0.943996	+	0.329958i	$0.107035\pi$
$468$		0			0
$469$	25.4273	+	44.0414i	1.17412	+	2.03364i
$470$		0			0
$471$	−1.80207	−	26.1237i	−0.0830349	−	1.20372i
$472$		0			0
$473$	−6.30657	−	35.7663i	−0.289976	−	1.64454i
$474$		0			0
$475$	5.14829	+	4.31993i	0.236220	+	0.198212i
$476$		0			0
$477$	7.52241	+	23.3006i	0.344428	+	1.06686i
$478$		0			0
$479$	−40.2766	+	14.6595i	−1.84029	+	0.669809i	−0.850741	+	0.525585i	$0.823846\pi$
$479$	−40.2766	+	14.6595i	−1.84029	+	0.669809i	−0.989545	+	0.144224i	$0.953931\pi$
$480$		0			0
$481$	4.37282	−	3.66923i	0.199384	−	0.167303i
$482$		0			0
$483$	−19.7310	+	27.1038i	−0.897794	+	1.23327i
$484$		0			0
$485$	0.0217257			0.000986511
$486$		0			0
$487$	4.79142			0.217120			0.108560	−	0.994090i	$-0.465376\pi$
$487$	4.79142			0.217120			0.108560	+	0.994090i	$0.465376\pi$
$488$		0			0
$489$	−14.5189	+	19.9441i	−0.656569	+	0.901905i
$490$		0			0
$491$	19.1356	−	16.0567i	0.863576	−	0.724627i	−0.0991590	−	0.995072i	$-0.531615\pi$
$491$	19.1356	−	16.0567i	0.863576	−	0.724627i	0.962735	+	0.270445i	$0.0871708\pi$
$492$		0			0
$493$	11.3922	−	4.14641i	0.513078	−	0.186745i
$494$		0			0
$495$	10.0386	+	31.0946i	0.451203	+	1.39760i
$496$		0			0
$497$	19.8759	+	16.6779i	0.891557	+	0.748105i
$498$		0			0
$499$	1.04732	+	5.93966i	0.0468845	+	0.265895i	0.999235	−	0.0391108i	$-0.0124525\pi$
$499$	1.04732	+	5.93966i	0.0468845	+	0.265895i	−0.952350	+	0.305006i	$0.901341\pi$
$500$		0			0
$501$	−1.86129	−	26.9822i	−0.0831564	−	1.20548i
$502$		0			0
$503$	−8.74621	−	15.1489i	−0.389974	−	0.675455i	0.602472	−	0.798140i	$-0.294183\pi$
$503$	−8.74621	−	15.1489i	−0.389974	−	0.675455i	−0.992446	+	0.122685i	$0.960849\pi$
$504$		0			0
$505$	2.60857	−	4.51818i	0.116080	−	0.201056i
$506$		0			0
$507$	−5.22585	+	18.1602i	−0.232088	+	0.806525i
$508$		0			0
$509$	−11.1790	−	4.06882i	−0.495500	−	0.180347i	0.0821690	−	0.996618i	$-0.473815\pi$
$509$	−11.1790	−	4.06882i	−0.495500	−	0.180347i	−0.577669	+	0.816271i	$0.696037\pi$
$510$		0			0
$511$	3.37741	−	19.1543i	0.149408	−	0.847334i
$512$		0			0
$513$	19.7134	−	17.6496i	0.870367	−	0.779249i
$514$		0			0
$515$	1.27712	−	7.24290i	0.0562766	−	0.319160i
$516$		0			0
$517$	32.9041	+	11.9761i	1.44712	+	0.526710i
$518$		0			0
$519$	−22.1881	+	5.50996i	−0.973949	+	0.241860i
$520$		0			0
$521$	5.51200	−	9.54706i	0.241485	−	0.418264i	−0.719652	−	0.694334i	$-0.755699\pi$
$521$	5.51200	−	9.54706i	0.241485	−	0.418264i	0.961138	+	0.276070i	$0.0890322\pi$
$522$		0			0
$523$	17.7734	+	30.7844i	0.777175	+	1.34611i	0.933564	+	0.358412i	$0.116682\pi$
$523$	17.7734	+	30.7844i	0.777175	+	1.34611i	−0.156388	+	0.987696i	$0.549985\pi$
$524$		0			0
$525$	−8.43852	−	4.12556i	−0.368287	−	0.180054i
$526$		0			0
$527$	0.538818	+	3.05579i	0.0234713	+	0.133112i
$528$		0			0
$529$	−0.621378	−	0.521398i	−0.0270164	−	0.0226695i
$530$		0			0
$531$	36.1417	+	22.6785i	1.56842	+	0.984161i
$532$		0			0
$533$	−0.386354	+	0.140621i	−0.0167349	+	0.00609099i
$534$		0			0
$535$	−3.87328	+	3.25007i	−0.167456	+	0.140513i
$536$		0			0
$537$	−20.0502	−	2.12642i	−0.865231	−	0.0917619i
$538$		0			0
$539$	−56.1181			−2.41718
$540$		0			0
$541$	−14.1225			−0.607173			−0.303586	−	0.952804i	$-0.598184\pi$
$541$	−14.1225			−0.607173			−0.303586	+	0.952804i	$0.598184\pi$
$542$		0			0
$543$	−12.2293	−	27.5371i	−0.524810	−	1.18173i
$544$		0			0
$545$	−21.0954	+	17.7011i	−0.903628	+	0.758234i
$546$		0			0
$547$	9.14230	−	3.32752i	0.390896	−	0.142275i	−0.139092	−	0.990279i	$-0.544418\pi$
$547$	9.14230	−	3.32752i	0.390896	−	0.142275i	0.529989	+	0.848005i	$0.322196\pi$
$548$		0			0
$549$	−5.41986	−	6.96405i	−0.231314	−	0.297219i
$550$		0			0
$551$	−17.2692	−	14.4906i	−0.735692	−	0.617319i
$552$		0			0
$553$	−4.48384	−	25.4291i	−0.190672	−	1.08136i
$554$		0			0
$555$	−10.8846	+	7.32689i	−0.462026	+	0.311009i
$556$		0			0
$557$	11.0204	+	19.0878i	0.466948	+	0.808777i	0.999287	−	0.0377541i	$-0.0120204\pi$
$557$	11.0204	+	19.0878i	0.466948	+	0.808777i	−0.532340	+	0.846531i	$0.678687\pi$
$558$		0			0
$559$	4.62358	−	8.00828i	0.195557	−	0.338714i
$560$		0			0
$561$	18.6885	+	19.3889i	0.789028	+	0.818601i
$562$		0			0
$563$	−14.7726	−	5.37678i	−0.622590	−	0.226604i	0.0114132	−	0.999935i	$-0.496367\pi$
$563$	−14.7726	−	5.37678i	−0.622590	−	0.226604i	−0.634003	+	0.773331i	$0.718589\pi$
$564$		0			0
$565$	0.535414	−	3.03649i	0.0225251	−	0.127746i
$566$		0			0
$567$	−20.7949	+	30.5811i	−0.873305	+	1.28428i
$568$		0			0
$569$	5.99337	−	33.9901i	0.251255	−	1.42494i	−0.554250	−	0.832350i	$-0.686995\pi$
$569$	5.99337	−	33.9901i	0.251255	−	1.42494i	0.805505	−	0.592589i	$-0.201894\pi$
$570$		0			0
$571$	25.9253	+	9.43603i	1.08494	+	0.394885i	0.821744	−	0.569857i	$-0.193001\pi$
$571$	25.9253	+	9.43603i	1.08494	+	0.394885i	0.263195	+	0.964743i	$0.415224\pi$
$572$		0			0
$573$	6.16478	+	6.39584i	0.257537	+	0.267190i
$574$		0			0
$575$	−3.10842	+	5.38395i	−0.129630	+	0.224526i
$576$		0			0
$577$	20.3911	+	35.3184i	0.848893	+	1.47033i	0.882197	+	0.470881i	$0.156064\pi$
$577$	20.3911	+	35.3184i	0.848893	+	1.47033i	−0.0333036	+	0.999445i	$0.510603\pi$
$578$		0			0
$579$	17.8501	−	12.0157i	0.741827	−	0.499354i
$580$		0			0
$581$	−11.5931	−	65.7475i	−0.480961	−	2.72767i
$582$		0			0
$583$	35.4964	+	29.7850i	1.47011	+	1.23357i
$584$		0			0
$585$	−3.13105	+	7.70787i	−0.129453	+	0.318681i
$586$		0			0
$587$	11.6219	−	4.23001i	0.479685	−	0.174591i	−0.0908495	−	0.995865i	$-0.528958\pi$
$587$	11.6219	−	4.23001i	0.479685	−	0.174591i	0.570535	+	0.821274i	$0.306736\pi$
$588$		0			0
$589$	4.42000	−	3.70882i	0.182123	−	0.152819i
$590$		0			0
$591$	6.25937	+	14.0944i	0.257476	+	0.579767i
$592$		0			0
$593$	−30.9594			−1.27135			−0.635674	−	0.771957i	$-0.719278\pi$
$593$	−30.9594			−1.27135			−0.635674	+	0.771957i	$0.719278\pi$
$594$		0			0
$595$	21.5868			0.884971
$596$		0			0
$597$	−1.35407	−	0.143606i	−0.0554186	−	0.00587741i
$598$		0			0
$599$	22.6214	−	18.9816i	0.924286	−	0.775568i	−0.0504971	−	0.998724i	$-0.516081\pi$
$599$	22.6214	−	18.9816i	0.924286	−	0.775568i	0.974783	+	0.223157i	$0.0716361\pi$
$600$		0			0
$601$	17.9678	−	6.53974i	0.732922	−	0.266762i	0.0515206	−	0.998672i	$-0.483593\pi$
$601$	17.9678	−	6.53974i	0.732922	−	0.266762i	0.681401	+	0.731910i	$0.261371\pi$
$602$		0			0
$603$	32.8154	−	17.3692i	1.33635	−	0.707329i
$604$		0			0
$605$	31.2046	+	26.1838i	1.26865	+	1.06452i
$606$		0			0
$607$	−5.26774	−	29.8748i	−0.213811	−	1.21258i	−0.882958	−	0.469452i	$-0.844451\pi$
$607$	−5.26774	−	29.8748i	−0.213811	−	1.21258i	0.669147	−	0.743130i	$-0.266660\pi$
$608$		0			0
$609$	28.3058	+	13.8386i	1.14701	+	0.560769i
$610$		0			0
$611$	4.45780	+	7.72113i	0.180343	+	0.312364i
$612$		0			0
$613$	19.9327	−	34.5245i	0.805075	−	1.39443i	−0.111165	−	0.993802i	$-0.535458\pi$
$613$	19.9327	−	34.5245i	0.805075	−	1.39443i	0.916240	−	0.400629i	$-0.131208\pi$
$614$		0			0
$615$	0.917194	−	0.227766i	0.0369848	−	0.00918443i
$616$		0			0
$617$	16.4318	+	5.98068i	0.661519	+	0.240773i	0.650892	−	0.759170i	$-0.274395\pi$
$617$	16.4318	+	5.98068i	0.661519	+	0.240773i	0.0106270	+	0.999944i	$0.496617\pi$
$618$		0			0
$619$	3.81674	−	21.6458i	0.153408	−	0.870019i	−0.806819	−	0.590798i	$-0.798813\pi$
$619$	3.81674	−	21.6458i	0.153408	−	0.870019i	0.960227	−	0.279220i	$-0.0900760\pi$
$620$		0			0
$621$	19.2452	+	15.1236i	0.772282	+	0.606888i
$622$		0			0
$623$	1.46696	−	8.31953i	0.0587724	−	0.333315i
$624$		0			0
$625$	15.6546	+	5.69780i	0.626183	+	0.227912i
$626$		0			0
$627$	13.8478	−	48.1224i	0.553030	−	1.92182i
$628$		0			0
$629$	−5.40686	+	9.36496i	−0.215586	+	0.373406i
$630$		0			0
$631$	−0.224323	−	0.388538i	−0.00893014	−	0.0154675i	0.861526	−	0.507714i	$-0.169509\pi$
$631$	−0.224323	−	0.388538i	−0.00893014	−	0.0154675i	−0.870456	+	0.492246i	$0.836176\pi$
$632$		0			0
$633$	0.366737	+	5.31640i	0.0145765	+	0.211308i
$634$		0			0
$635$	3.69969	+	20.9820i	0.146818	+	0.832646i
$636$		0			0
$637$	−10.9457	−	9.18452i	−0.433684	−	0.363904i
$638$		0			0
$639$	12.7019	−	14.0537i	0.502479	−	0.555954i
$640$		0			0
$641$	−42.4938	+	15.4665i	−1.67840	+	0.610889i	−0.993089	−	0.117360i	$-0.962557\pi$
$641$	−42.4938	+	15.4665i	−1.67840	+	0.610889i	−0.685313	+	0.728248i	$0.740335\pi$
$642$		0			0
$643$	−20.4317	+	17.1442i	−0.805747	+	0.676102i	−0.949589	−	0.313499i	$-0.898499\pi$
$643$	−20.4317	+	17.1442i	−0.805747	+	0.676102i	0.143842	+	0.989601i	$0.454054\pi$
$644$		0			0
$645$	−12.5096	+	17.1840i	−0.492566	+	0.676621i
$646$		0			0
$647$	34.1104			1.34102			0.670508	−	0.741902i	$-0.266076\pi$
$647$	34.1104			1.34102			0.670508	+	0.741902i	$0.266076\pi$
$648$		0			0
$649$	80.7485			3.16965
$650$		0			0
$651$	−4.74619	+	6.51967i	−0.186018	+	0.255526i
$652$		0			0
$653$	−2.14784	+	1.80225i	−0.0840514	+	0.0705275i	−0.683845	−	0.729627i	$-0.739694\pi$
$653$	−2.14784	+	1.80225i	−0.0840514	+	0.0705275i	0.599794	+	0.800155i	$0.295249\pi$
$654$		0			0
$655$	−8.58223	+	3.12368i	−0.335336	+	0.122052i
$656$		0			0
$657$	−13.8843	−	2.97849i	−0.541677	−	0.116202i
$658$		0			0
$659$	33.6755	+	28.2571i	1.31181	+	1.10074i	0.987972	+	0.154630i	$0.0494185\pi$
$659$	33.6755	+	28.2571i	1.31181	+	1.10074i	0.323840	+	0.946112i	$0.395026\pi$
$660$		0			0
$661$	0.685986	+	3.89042i	0.0266818	+	0.151320i	0.995238	−	0.0974750i	$-0.0310766\pi$
$661$	0.685986	+	3.89042i	0.0266818	+	0.151320i	−0.968556	+	0.248795i	$0.919965\pi$
$662$		0			0
$663$	0.471864	+	6.84038i	0.0183257	+	0.265659i
$664$		0			0
$665$	−20.0703	−	34.7629i	−0.778295	−	1.34805i
$666$		0			0
$667$	10.4268	−	18.0597i	0.403726	−	0.699273i
$668$		0			0
$669$	6.21471	−	21.5966i	0.240275	−	0.834974i
$670$		0			0
$671$	−15.6933	−	5.71188i	−0.605832	−	0.220505i
$672$		0			0
$673$	−1.65507	+	9.38639i	−0.0637984	+	0.361819i	0.936149	+	0.351603i	$0.114363\pi$
$673$	−1.65507	+	9.38639i	−0.0637984	+	0.361819i	−0.999948	+	0.0102164i	$0.996748\pi$
$674$		0			0
$675$	−3.23661	+	6.04597i	−0.124577	+	0.232709i
$676$		0			0
$677$	1.22825	−	6.96575i	0.0472055	−	0.267716i	−0.952065	−	0.305894i	$-0.901045\pi$
$677$	1.22825	−	6.96575i	0.0472055	−	0.267716i	0.999271	+	0.0381788i	$0.0121556\pi$
$678$		0			0
$679$	0.0437284	+	0.0159159i	0.00167814	+	0.000610794i
$680$		0			0
$681$	−8.07351	+	2.00489i	−0.309378	+	0.0768276i
$682$		0			0
$683$	21.9236	−	37.9729i	0.838885	−	1.45299i	−0.0519432	−	0.998650i	$-0.516541\pi$
$683$	21.9236	−	37.9729i	0.838885	−	1.45299i	0.890828	−	0.454341i	$-0.150125\pi$
$684$		0			0
$685$	−14.3460	−	24.8480i	−0.548133	−	0.949394i
$686$		0			0
$687$	−13.6404	−	6.66876i	−0.520415	−	0.254429i
$688$		0			0
$689$	2.04874	+	11.6190i	0.0780507	+	0.442648i
$690$		0			0
$691$	−28.5288	−	23.9385i	−1.08529	−	0.910663i	−0.0889369	−	0.996037i	$-0.528347\pi$
$691$	−28.5288	−	23.9385i	−1.08529	−	0.910663i	−0.996349	+	0.0853743i	$0.972791\pi$
$692$		0			0
$693$	−2.57403	+	69.9399i	−0.0977793	+	2.65680i
$694$		0			0
$695$	5.92992	−	2.15832i	0.224935	−	0.0818696i
$696$		0			0
$697$	0.596652	−	0.500651i	0.0225998	−	0.0189635i
$698$		0			0
$699$	6.88380	+	0.730061i	0.260369	+	0.0276134i
$700$		0			0
$701$	−35.6893			−1.34797			−0.673984	−	0.738746i	$-0.735418\pi$
$701$	−35.6893			−1.34797			−0.673984	+	0.738746i	$0.735418\pi$
$702$		0			0
$703$	20.1082			0.758394
$704$		0			0
$705$	−8.31766	−	18.7291i	−0.313261	−	0.705380i
$706$		0			0
$707$	8.56036	−	7.18299i	0.321945	−	0.270144i
$708$		0			0
$709$	−46.6583	+	16.9822i	−1.75229	+	0.637781i	−0.999784	−	0.0208033i	$-0.993378\pi$
$709$	−46.6583	+	16.9822i	−1.75229	+	0.637781i	−0.752507	+	0.658585i	$0.771155\pi$
$710$		0			0
$711$	−18.6735	+	2.58860i	−0.700312	+	0.0970800i
$712$		0			0
$713$	4.08869	+	3.43082i	0.153123	+	0.128485i
$714$		0			0
$715$	2.73404	+	15.5055i	0.102247	+	0.579873i
$716$		0			0
$717$	−10.8290	+	7.28944i	−0.404416	+	0.272229i
$718$		0			0
$719$	−8.92100	−	15.4516i	−0.332697	−	0.576248i	0.650343	−	0.759641i	$-0.274625\pi$
$719$	−8.92100	−	15.4516i	−0.332697	−	0.576248i	−0.983040	+	0.183393i	$0.941292\pi$
$720$		0			0
$721$	7.87655	−	13.6426i	0.293338	−	0.508077i
$722$		0			0
$723$	−11.5961	−	12.0307i	−0.431264	−	0.447428i
$724$		0			0
$725$	5.49035	+	1.99833i	0.203907	+	0.0742160i
$726$		0			0
$727$	−7.88271	+	44.7051i	−0.292354	+	1.65802i	0.385414	+	0.922744i	$0.374059\pi$
$727$	−7.88271	+	44.7051i	−0.292354	+	1.65802i	−0.677768	+	0.735276i	$0.737053\pi$
$728$		0			0
$729$	21.7536	+	15.9932i	0.805689	+	0.592339i
$730$		0			0
$731$	−3.04191	+	17.2515i	−0.112509	+	0.638071i
$732$		0			0
$733$	−36.0003	−	13.1031i	−1.32970	−	0.483972i	−0.423148	−	0.906061i	$-0.639075\pi$
$733$	−36.0003	−	13.1031i	−1.32970	−	0.483972i	−0.906555	+	0.422088i	$0.861297\pi$
$734$		0			0
$735$	22.7925	+	23.6468i	0.840715	+	0.872226i
$736$		0			0
$737$	35.1329	−	60.8520i	1.29414	−	2.24151i
$738$		0			0
$739$	−10.0715	−	17.4443i	−0.370485	−	0.641698i	0.619156	−	0.785268i	$-0.287475\pi$
$739$	−10.0715	−	17.4443i	−0.370485	−	0.641698i	−0.989640	+	0.143570i	$0.954142\pi$
$740$		0			0
$741$	10.5769	−	7.11974i	0.388552	−	0.261550i
$742$		0			0
$743$	−0.0950690	−	0.539163i	−0.00348774	−	0.0197800i	0.983014	−	0.183529i	$-0.0587523\pi$
$743$	−0.0950690	−	0.539163i	−0.00348774	−	0.0197800i	−0.986502	+	0.163749i	$0.947641\pi$
$744$		0			0
$745$	34.6753	+	29.0961i	1.27041	+	1.06600i
$746$		0			0
$747$	−48.2807	+	6.69287i	−1.76650	+	0.244879i
$748$		0			0
$749$	−10.1769	+	3.70409i	−0.371856	+	0.135345i
$750$		0			0
$751$	27.4772	−	23.0561i	1.00266	−	0.841328i	0.0153056	−	0.999883i	$-0.495128\pi$
$751$	27.4772	−	23.0561i	1.00266	−	0.841328i	0.987350	+	0.158555i	$0.0506834\pi$
$752$		0			0
$753$	−1.74618	−	3.93194i	−0.0636345	−	0.143288i
$754$		0			0
$755$	−33.8864			−1.23325
$756$		0			0
$757$	−18.7777			−0.682486			−0.341243	−	0.939975i	$-0.610848\pi$
$757$	−18.7777			−0.682486			−0.341243	+	0.939975i	$0.610848\pi$
$758$		0			0
$759$	46.0633	+	4.88524i	1.67199	+	0.177323i
$760$		0			0
$761$	4.66973	−	3.91837i	0.169278	−	0.142041i	−0.554213	−	0.832375i	$-0.686981\pi$
$761$	4.66973	−	3.91837i	0.169278	−	0.142041i	0.723491	+	0.690334i	$0.242536\pi$
$762$		0			0
$763$	−55.4275	+	20.1739i	−2.00661	+	0.730346i
$764$		0			0
$765$	0.579645	−	15.7497i	0.0209571	−	0.569433i
$766$		0			0
$767$	15.7498	+	13.2156i	0.568691	+	0.477188i
$768$		0			0
$769$	−8.30566	−	47.1037i	−0.299510	−	1.69860i	−0.648285	−	0.761397i	$-0.724514\pi$
$769$	−8.30566	−	47.1037i	−0.299510	−	1.69860i	0.348776	−	0.937206i	$-0.386597\pi$
$770$		0			0
$771$	−24.4015	−	11.9298i	−0.878798	−	0.429642i
$772$		0			0
$773$	−9.33612	−	16.1706i	−0.335797	−	0.581617i	0.647841	−	0.761776i	$-0.275672\pi$
$773$	−9.33612	−	16.1706i	−0.335797	−	0.581617i	−0.983638	+	0.180159i	$0.942339\pi$
$774$		0			0
$775$	−0.747714	+	1.29508i	−0.0268587	+	0.0465206i
$776$		0			0
$777$	−27.2756	+	6.77335i	−0.978507	+	0.242992i
$778$		0			0
$779$	−1.36097	−	0.495354i	−0.0487620	−	0.0177479i
$780$		0			0
$781$	6.22526	−	35.3052i	0.222757	−	1.26332i
$782$		0			0
$783$	10.8567	−	20.2803i	0.387988	−	0.724760i
$784$		0			0
$785$	−5.03630	+	28.5623i	−0.179753	+	1.01943i
$786$		0			0
$787$	−38.9691	−	14.1836i	−1.38910	−	0.505591i	−0.464176	−	0.885743i	$-0.653649\pi$
$787$	−38.9691	−	14.1836i	−1.38910	−	0.505591i	−0.924924	+	0.380152i	$0.875872\pi$
$788$		0			0
$789$	−5.74167	+	19.9528i	−0.204409	+	0.710337i
$790$		0			0
$791$	3.30214	−	5.71947i	0.117410	−	0.203361i
$792$		0			0
$793$	−2.12610	−	3.68251i	−0.0755000	−	0.130770i
$794$		0			0
$795$	−1.86628	−	27.0546i	−0.0661903	−	0.959528i
$796$		0			0
$797$	3.10235	+	17.5943i	0.109891	+	0.623222i	0.989154	+	0.146885i	$0.0469247\pi$
$797$	3.10235	+	17.5943i	0.109891	+	0.623222i	−0.879263	+	0.476337i	$0.841964\pi$
$798$		0			0
$799$	−12.9381	−	10.8564i	−0.457719	−	0.384072i
$800$		0			0
$801$	−6.03055	−	1.29369i	−0.213079	−	0.0457103i
$802$		0			0
$803$	−25.2530	+	9.19135i	−0.891160	+	0.324356i
$804$		0			0
$805$	28.4446	−	23.8679i	1.00254	−	0.841232i
$806$		0			0
$807$	−20.1358	+	27.6598i	−0.708813	+	0.973672i
$808$		0			0
$809$	23.9533			0.842153			0.421076	−	0.907025i	$-0.361652\pi$
$809$	23.9533			0.842153			0.421076	+	0.907025i	$0.361652\pi$
$810$		0			0
$811$	19.0602			0.669294			0.334647	−	0.942344i	$-0.391383\pi$
$811$	19.0602			0.669294			0.334647	+	0.942344i	$0.391383\pi$
$812$		0			0
$813$	6.74038	−	9.25902i	0.236396	−	0.324728i
$814$		0			0
$815$	20.9307	−	17.5630i	0.733172	−	0.615204i
$816$		0			0
$817$	30.6097	−	11.1410i	1.07090	−	0.389775i
$818$		0			0
$819$	−11.9487	+	13.2203i	−0.417522	+	0.461955i
$820$		0			0
$821$	−18.4864	−	15.5119i	−0.645178	−	0.541369i	0.260425	−	0.965494i	$-0.416137\pi$
$821$	−18.4864	−	15.5119i	−0.645178	−	0.541369i	−0.905604	+	0.424125i	$0.860582\pi$
$822$		0			0
$823$	−8.74245	−	49.5809i	−0.304743	−	1.72828i	−0.624714	−	0.780854i	$-0.714784\pi$
$823$	−8.74245	−	49.5809i	−0.304743	−	1.72828i	0.319972	−	0.947427i	$-0.396327\pi$
$824$		0			0
$825$	0.893151	+	12.9476i	0.0310955	+	0.450777i
$826$		0			0
$827$	−2.21235	−	3.83190i	−0.0769310	−	0.133248i	0.824993	−	0.565142i	$-0.191179\pi$
$827$	−2.21235	−	3.83190i	−0.0769310	−	0.133248i	−0.901924	+	0.431894i	$0.857845\pi$
$828$		0			0
$829$	−9.40772	+	16.2947i	−0.326744	+	0.565937i	−0.981864	−	0.189588i	$-0.939285\pi$
$829$	−9.40772	+	16.2947i	−0.326744	+	0.565937i	0.655120	+	0.755525i	$0.272618\pi$
$830$		0			0
$831$	−7.65178	+	26.5906i	−0.265437	+	0.922416i
$832$		0			0
$833$	25.4356	+	9.25781i	0.881292	+	0.320764i
$834$		0			0
$835$	−5.20182	+	29.5010i	−0.180016	+	1.02092i
$836$		0			0
$837$	4.62932	+	3.63789i	0.160013	+	0.125744i
$838$		0			0
$839$	−4.78845	+	27.1567i	−0.165316	+	0.937553i	0.783422	+	0.621490i	$0.213472\pi$
$839$	−4.78845	+	27.1567i	−0.165316	+	0.937553i	−0.948738	+	0.316063i	$0.897639\pi$
$840$		0			0
$841$	8.83448	+	3.21549i	0.304637	+	0.110879i
$842$		0			0
$843$	13.9261	−	3.45826i	0.479640	−	0.119109i
$844$		0			0
$845$	10.4651	−	18.1261i	0.360011	−	0.623556i
$846$		0			0
$847$	43.6254	+	75.5615i	1.49899	+	2.59632i
$848$		0			0
$849$	26.8486	+	13.1262i	0.921443	+	0.450490i
$850$		0			0
$851$	3.23001	+	18.3183i	0.110723	+	0.627943i
$852$		0			0
$853$	16.0781	+	13.4911i	0.550504	+	0.461928i	0.875112	−	0.483921i	$-0.160788\pi$
$853$	16.0781	+	13.4911i	0.550504	+	0.461928i	−0.324608	+	0.945849i	$0.605232\pi$
$854$		0			0
$855$	−25.9019	+	13.7099i	−0.885828	+	0.468869i
$856$		0			0
$857$	−5.88556	+	2.14217i	−0.201047	+	0.0731751i	−0.440581	−	0.897713i	$-0.645228\pi$
$857$	−5.88556	+	2.14217i	−0.201047	+	0.0731751i	0.239534	+	0.970888i	$0.423005\pi$
$858$		0			0
$859$	21.9084	−	18.3833i	0.747505	−	0.627232i	−0.187336	−	0.982296i	$-0.559985\pi$
$859$	21.9084	−	18.3833i	0.747505	−	0.627232i	0.934842	+	0.355064i	$0.115541\pi$
$860$		0			0
$861$	2.01294	+	0.213483i	0.0686010	+	0.00727547i
$862$		0			0
$863$	−48.0721			−1.63639			−0.818196	−	0.574940i	$-0.805026\pi$
$863$	−48.0721			−1.63639			−0.818196	+	0.574940i	$0.805026\pi$
$864$		0			0
$865$	25.3215			0.860958
$866$		0			0
$867$	6.67903	+	15.0394i	0.226832	+	0.510764i
$868$		0			0
$869$	−27.3305	+	22.9330i	−0.927125	+	0.777950i
$870$		0			0
$871$	16.8119	−	6.11902i	0.569649	−	0.207335i
$872$		0			0
$873$	0.0127864	−	0.0314769i	0.000432754	−	0.00106533i
$874$		0			0
$875$	38.1623	+	32.0220i	1.29012	+	1.08254i
$876$		0			0
$877$	8.92997	+	50.6444i	0.301544	+	1.71014i	0.639344	+	0.768921i	$0.279206\pi$
$877$	8.92997	+	50.6444i	0.301544	+	1.71014i	−0.337800	+	0.941218i	$0.609683\pi$
$878$		0			0
$879$	15.4418	−	10.3945i	0.520838	−	0.350598i
$880$		0			0
$881$	−4.25145	−	7.36372i	−0.143235	−	0.248090i	0.785478	−	0.618889i	$-0.212417\pi$
$881$	−4.25145	−	7.36372i	−0.143235	−	0.248090i	−0.928713	+	0.370799i	$0.879084\pi$
$882$		0			0
$883$	12.2957	−	21.2968i	0.413784	−	0.716695i	−0.581516	−	0.813535i	$-0.697540\pi$
$883$	12.2957	−	21.2968i	0.413784	−	0.716695i	0.995300	+	0.0968398i	$0.0308735\pi$
$884$		0			0
$885$	−32.7962	−	34.0254i	−1.10243	−	1.14375i
$886$		0			0
$887$	−21.4921	−	7.82247i	−0.721633	−	0.262653i	−0.0450141	−	0.998986i	$-0.514333\pi$
$887$	−21.4921	−	7.82247i	−0.721633	−	0.262653i	−0.676619	+	0.736333i	$0.736555\pi$
$888$		0			0
$889$	−7.92449	+	44.9420i	−0.265779	+	1.50731i
$890$		0			0
$891$	50.9591	+	3.75603i	1.70719	+	0.125832i
$892$		0			0
$893$	−5.45363	+	30.9291i	−0.182499	+	1.03500i
$894$		0			0
$895$	20.9850	+	7.63793i	0.701453	+	0.255308i
$896$		0			0
$897$	8.18498	+	8.49176i	0.273289	+	0.283532i
$898$		0			0
$899$	2.50810	−	4.34415i	0.0836497	−	0.144886i
$900$		0			0
$901$	−11.1752	−	19.3560i	−0.372299	−	0.644840i
$902$		0			0
$903$	−37.7676	+	25.4229i	−1.25683	+	0.846022i
$904$		0			0
$905$	5.79500	+	32.8651i	0.192632	+	1.09247i
$906$		0			0
$907$	26.8226	+	22.5069i	0.890631	+	0.747328i	0.968337	−	0.249648i	$-0.0803150\pi$
$907$	26.8226	+	22.5069i	0.890631	+	0.747328i	−0.0777056	+	0.996976i	$0.524759\pi$
$908$		0			0
$909$	−5.01086	−	6.43852i	−0.166200	−	0.213552i
$910$		0			0
$911$	−27.2243	+	9.90882i	−0.901980	+	0.328294i	−0.751046	−	0.660250i	$-0.770450\pi$
$911$	−27.2243	+	9.90882i	−0.901980	+	0.328294i	−0.150934	+	0.988544i	$0.548228\pi$
$912$		0			0
$913$	−70.6636	+	59.2938i	−2.33862	+	1.96234i
$914$		0			0
$915$	3.96702	+	8.93266i	0.131146	+	0.295305i
$916$		0			0
$917$	−19.5623			−0.646004
$918$		0			0
$919$	36.8729			1.21632			0.608162	−	0.793813i	$-0.291907\pi$
$919$	36.8729			1.21632			0.608162	+	0.793813i	$0.291907\pi$
$920$		0			0
$921$	−4.57716	−	0.485431i	−0.150823	−	0.0159955i
$922$		0			0
$923$	6.99241	−	5.86733i	0.230158	−	0.193125i
$924$		0			0
$925$	−4.89728	+	1.78246i	−0.161022	+	0.0586070i
$926$		0			0
$927$	−9.74215	−	6.11307i	−0.319974	−	0.200780i
$928$		0			0
$929$	−20.3030	−	17.0363i	−0.666121	−	0.558942i	0.245793	−	0.969322i	$-0.420952\pi$
$929$	−20.3030	−	17.0363i	−0.666121	−	0.558942i	−0.911915	+	0.410380i	$0.865396\pi$
$930$		0			0
$931$	−8.74025	−	49.5684i	−0.286450	−	1.62454i
$932$		0			0
$933$	−53.6538	−	26.2312i	−1.75655	−	0.858770i
$934$		0			0
$935$	−14.9132	−	25.8305i	−0.487715	−	0.844747i
$936$		0			0
$937$	3.51461	−	6.08749i	0.114817	−	0.198870i	−0.802889	−	0.596128i	$-0.796705\pi$
$937$	3.51461	−	6.08749i	0.114817	−	0.198870i	0.917707	+	0.397259i	$0.130038\pi$
$938$		0			0
$939$	−21.2951	+	5.28819i	−0.694938	+	0.172574i
$940$		0			0
$941$	24.9101	+	9.06653i	0.812045	+	0.295560i	0.714468	−	0.699668i	$-0.246669\pi$
$941$	24.9101	+	9.06653i	0.812045	+	0.295560i	0.0975769	+	0.995228i	$0.468891\pi$
$942$		0			0
$943$	0.232646	−	1.31940i	0.00757600	−	0.0429656i
$944$		0			0
$945$	30.5164	−	27.3217i	0.992700	−	0.888774i
$946$		0			0
$947$	5.94224	−	33.7001i	0.193097	−	1.09511i	−0.722006	−	0.691887i	$-0.756780\pi$
$947$	5.94224	−	33.7001i	0.193097	−	1.09511i	0.915103	−	0.403220i	$-0.132109\pi$
$948$		0			0
$949$	−6.42983	−	2.34027i	−0.208721	−	0.0759682i
$950$		0			0
$951$	−4.21319	+	14.6412i	−0.136622	+	0.474772i
$952$		0			0
$953$	3.88821	−	6.73458i	0.125952	−	0.218155i	−0.796153	−	0.605095i	$-0.793135\pi$
$953$	3.88821	−	6.73458i	0.125952	−	0.218155i	0.922105	+	0.386941i	$0.126468\pi$
$954$		0			0
$955$	−4.91944	−	8.52072i	−0.159189	−	0.275724i
$956$		0			0
$957$	−2.99595	−	43.4308i	−0.0968452	−	1.40392i
$958$		0			0
$959$	−10.6718	−	60.5226i	−0.344609	−	1.95438i
$960$		0			0
$961$	−22.7639	−	19.1012i	−0.734318	−	0.616166i
$962$		0			0
$963$	2.42924	+	7.52455i	0.0782812	+	0.242475i
$964$		0			0
$965$	−22.3952	+	8.15117i	−0.720926	+	0.262396i
$966$		0			0
$967$	−1.86408	+	1.56415i	−0.0599447	+	0.0502996i	−0.672268	−	0.740308i	$-0.734680\pi$
$967$	−1.86408	+	1.56415i	−0.0599447	+	0.0502996i	0.612323	+	0.790608i	$0.290235\pi$
$968$		0			0
$969$	−14.2153	+	19.5271i	−0.456661	+	0.627299i
$970$		0			0
$971$	−28.2097			−0.905293			−0.452647	−	0.891690i	$-0.649520\pi$
$971$	−28.2097			−0.905293			−0.452647	+	0.891690i	$0.649520\pi$
$972$		0			0
$973$	13.5166			0.433323
$974$		0			0
$975$	−1.94484	+	2.67156i	−0.0622849	+	0.0855585i
$976$		0			0
$977$	36.0040	−	30.2110i	1.15187	−	0.966534i	0.152109	−	0.988364i	$-0.451394\pi$
$977$	36.0040	−	30.2110i	1.15187	−	0.966534i	0.999762	+	0.0218295i	$0.00694909\pi$
$978$		0			0
$979$	−10.9685	+	3.99221i	−0.350555	+	0.127592i
$980$		0			0
$981$	13.2306	+	40.9816i	0.422421	+	1.30844i
$982$		0			0
$983$	−29.7166	−	24.9352i	−0.947812	−	0.795309i	0.0311156	−	0.999516i	$-0.490094\pi$
$983$	−29.7166	−	24.9352i	−0.947812	−	0.795309i	−0.978928	+	0.204207i	$0.934538\pi$
$984$		0			0
$985$	−2.96607	−	16.8214i	−0.0945070	−	0.535976i
$986$		0			0
$987$	−3.02077	−	43.7906i	−0.0961521	−	1.39387i
$988$		0			0
$989$	15.0662	+	26.0955i	0.479078	+	0.829788i
$990$		0			0
$991$	−10.3763	+	17.9722i	−0.329613	+	0.570906i	−0.982435	−	0.186605i	$-0.940252\pi$
$991$	−10.3763	+	17.9722i	−0.329613	+	0.570906i	0.652822	+	0.757511i	$0.273585\pi$
$992$		0			0
$993$	5.67590	−	19.7242i	0.180119	−	0.625929i
$994$		0			0
$995$	1.41721	+	0.515821i	0.0449285	+	0.0163526i
$996$		0			0
$997$	−8.72919	+	49.5057i	−0.276456	+	1.56786i	0.457842	+	0.889034i	$0.348623\pi$
$997$	−8.72919	+	49.5057i	−0.276456	+	1.56786i	−0.734298	+	0.678827i	$0.762488\pi$
$998$		0			0
$999$	4.20944	+	20.0822i	0.133181	+	0.635373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.u.d.241.2		18
4.3	odd	2		108.2.i.a.25.2	yes	18
12.11	even	2		324.2.i.a.73.2		18
27.13	even	9	inner	432.2.u.d.337.2		18
36.7	odd	6		972.2.i.c.541.2		18
36.11	even	6		972.2.i.b.541.2		18
36.23	even	6		972.2.i.d.865.2		18
36.31	odd	6		972.2.i.a.865.2		18
108.7	odd	18		2916.2.e.c.973.4		18
108.11	even	18		2916.2.a.c.1.4		9
108.23	even	18		972.2.i.d.109.2		18
108.31	odd	18		972.2.i.a.109.2		18
108.43	odd	18		2916.2.a.d.1.6		9
108.47	even	18		2916.2.e.d.973.6		18
108.59	even	18		972.2.i.b.433.2		18
108.67	odd	18		108.2.i.a.13.2	✓	18
108.79	odd	18		2916.2.e.c.1945.4		18
108.83	even	18		2916.2.e.d.1945.6		18
108.95	even	18		324.2.i.a.253.2		18
108.103	odd	18		972.2.i.c.433.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.i.a.13.2	✓	18	108.67	odd	18
108.2.i.a.25.2	yes	18	4.3	odd	2
324.2.i.a.73.2		18	12.11	even	2
324.2.i.a.253.2		18	108.95	even	18
432.2.u.d.241.2		18	1.1	even	1	trivial
432.2.u.d.337.2		18	27.13	even	9	inner
972.2.i.a.109.2		18	108.31	odd	18
972.2.i.a.865.2		18	36.31	odd	6
972.2.i.b.433.2		18	108.59	even	18
972.2.i.b.541.2		18	36.11	even	6
972.2.i.c.433.2		18	108.103	odd	18
972.2.i.c.541.2		18	36.7	odd	6
972.2.i.d.109.2		18	108.23	even	18
972.2.i.d.865.2		18	36.23	even	6
2916.2.a.c.1.4		9	108.11	even	18
2916.2.a.d.1.6		9	108.43	odd	18
2916.2.e.c.973.4		18	108.7	odd	18
2916.2.e.c.1945.4		18	108.79	odd	18
2916.2.e.d.973.6		18	108.47	even	18
2916.2.e.d.1945.6		18	108.83	even	18

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.01939 + 1.40030i) q^{3} +(1.46957 - 1.23312i) q^{5} +(3.86125 - 1.40538i) q^{7} +(-0.921685 - 2.85491i) q^{9} +O(q^{10})\)	\(q+(-1.01939 + 1.40030i) q^{3} +(1.46957 - 1.23312i) q^{5} +(3.86125 - 1.40538i) q^{7} +(-0.921685 - 2.85491i) q^{9} +(-4.34920 - 3.64942i) q^{11} +(-0.251022 - 1.42362i) q^{13} +(0.228667 + 3.31487i) q^{15} +(1.36924 + 2.37159i) q^{17} +(2.54610 - 4.40998i) q^{19} +(-1.96817 + 6.83954i) q^{21} +(4.42643 + 1.61109i) q^{23} +(-0.229178 + 1.29973i) q^{25} +(4.93729 + 1.61963i) q^{27} +(0.768745 - 4.35977i) q^{29} +(1.06475 + 0.387538i) q^{31} +(9.54382 - 2.37001i) q^{33} +(3.94138 - 6.82668i) q^{35} +(1.97441 + 3.41977i) q^{37} +(2.24938 + 1.09972i) q^{39} +(-0.0493888 - 0.280098i) q^{41} +(4.90028 + 4.11182i) q^{43} +(-4.87492 - 3.05895i) q^{45} +(-5.79555 + 2.10941i) q^{47} +(7.57184 - 6.35352i) q^{49} +(-4.71673 - 0.500232i) q^{51} -8.16159 q^{53} -10.8916 q^{55} +(3.57983 + 8.06081i) q^{57} +(-10.8951 + 9.14210i) q^{59} +(2.76413 - 1.00606i) q^{61} +(-7.57108 - 9.72819i) q^{63} +(-2.12438 - 1.78257i) q^{65} +(2.14911 + 12.1882i) q^{67} +(-6.76826 + 4.55600i) q^{69} +(3.15719 + 5.46842i) q^{71} +(2.36669 - 4.09923i) q^{73} +(-1.58640 - 1.64585i) q^{75} +(-21.9222 - 7.97902i) q^{77} +(1.09121 - 6.18856i) q^{79} +(-7.30099 + 5.26265i) q^{81} +(2.82134 - 16.0006i) q^{83} +(4.93664 + 1.79679i) q^{85} +(5.32133 + 5.52078i) q^{87} +(1.02796 - 1.78048i) q^{89} +(-2.96998 - 5.14416i) q^{91} +(-1.62807 + 1.09592i) q^{93} +(-1.69634 - 9.62043i) q^{95} +(0.00867542 + 0.00727954i) q^{97} +(-6.41015 + 15.7802i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 18 * q + 3 * q^5 + 6 * q^9	\( 18 q + 3 q^{5} + 6 q^{9} - 3 q^{11} + 9 q^{15} - 12 q^{17} - 30 q^{21} + 30 q^{23} + 9 q^{25} + 27 q^{27} - 24 q^{29} - 9 q^{31} - 18 q^{33} + 21 q^{35} - 3 q^{39} + 21 q^{41} + 9 q^{43} + 45 q^{45} - 45 q^{47} - 18 q^{49} - 63 q^{51} + 66 q^{53} + 54 q^{57} - 60 q^{59} - 18 q^{61} - 57 q^{63} + 33 q^{65} + 27 q^{67} - 9 q^{69} + 12 q^{71} + 9 q^{73} + 33 q^{75} - 75 q^{77} + 36 q^{79} - 54 q^{81} + 45 q^{83} - 36 q^{85} + 63 q^{87} - 48 q^{89} - 9 q^{91} - 33 q^{93} - 6 q^{95} - 27 q^{97} - 27 q^{99}+O(q^{100}) \) 18 * q + 3 * q^5 + 6 * q^9 - 3 * q^11 + 9 * q^15 - 12 * q^17 - 30 * q^21 + 30 * q^23 + 9 * q^25 + 27 * q^27 - 24 * q^29 - 9 * q^31 - 18 * q^33 + 21 * q^35 - 3 * q^39 + 21 * q^41 + 9 * q^43 + 45 * q^45 - 45 * q^47 - 18 * q^49 - 63 * q^51 + 66 * q^53 + 54 * q^57 - 60 * q^59 - 18 * q^61 - 57 * q^63 + 33 * q^65 + 27 * q^67 - 9 * q^69 + 12 * q^71 + 9 * q^73 + 33 * q^75 - 75 * q^77 + 36 * q^79 - 54 * q^81 + 45 * q^83 - 36 * q^85 + 63 * q^87 - 48 * q^89 - 9 * q^91 - 33 * q^93 - 6 * q^95 - 27 * q^97 - 27 * q^99

Introduction

L-functions

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