LMFDB - Embedded newform 108.2.i.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,2,Mod(13,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("108.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	108.i (of order $9$, degree $6$, 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:	$0.862384341830$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			13.2
Root			$1.20201 - 1.24706i$ of defining polynomial
Character	$\chi$	$=$	108.13
Dual form			108.2.i.a.25.2

$q$-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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

Coefficient data

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

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

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

$2$		0			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	0.909250	−	0.416251i	$-0.136656\pi$
$5$	1.46957	+	1.23312i	0.657212	+	0.551467i	−0.252038	+	0.967717i	$0.581101\pi$
$6$		0			0
$7$	−3.86125	−	1.40538i	−1.45941	−	0.531184i	−0.514211	−	0.857664i	$-0.671915\pi$
$7$	−3.86125	−	1.40538i	−1.45941	−	0.531184i	−0.945204	+	0.326480i	$0.894137\pi$
$8$		0			0
$9$	−0.921685	+	2.85491i	−0.307228	+	0.951636i
$10$		0			0
$11$	4.34920	−	3.64942i	1.31133	−	1.10034i	0.323269	−	0.946307i	$-0.395218\pi$
$11$	4.34920	−	3.64942i	1.31133	−	1.10034i	0.988066	−	0.154033i	$-0.0492262\pi$
$12$		0			0
$13$	−0.251022	+	1.42362i	−0.0696210	+	0.394840i	0.930006	+	0.367543i	$0.119801\pi$
$13$	−0.251022	+	1.42362i	−0.0696210	+	0.394840i	−0.999627	+	0.0272969i	$0.991310\pi$
$14$		0			0
$15$	−0.228667	+	3.31487i	−0.0590415	+	0.855896i
$16$		0			0
$17$	1.36924	−	2.37159i	0.332089	−	0.575195i	−0.650832	−	0.759222i	$-0.725580\pi$
$17$	1.36924	−	2.37159i	0.332089	−	0.575195i	0.982921	+	0.184026i	$0.0589132\pi$
$18$		0			0
$19$	−2.54610	−	4.40998i	−0.584116	−	1.01172i	−0.994985	−	0.100025i	$-0.968108\pi$
$19$	−2.54610	−	4.40998i	−0.584116	−	1.01172i	0.410869	−	0.911695i	$-0.365226\pi$
$20$		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	$-0.774518\pi$
$23$	−4.42643	+	1.61109i	−0.922974	+	0.335935i	−0.163553	+	0.986535i	$0.552295\pi$
$24$		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	0.969144	+	0.246494i	$0.0792784\pi$
$29$	0.768745	+	4.35977i	0.142752	+	0.809589i	−0.826392	+	0.563095i	$0.809610\pi$
$30$		0			0
$31$	−1.06475	+	0.387538i	−0.191235	+	0.0696039i	−0.435862	−	0.900013i	$-0.643557\pi$
$31$	−1.06475	+	0.387538i	−0.191235	+	0.0696039i	0.244627	+	0.969617i	$0.421334\pi$
$32$		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	−0.656839	−	0.754031i	$-0.728107\pi$
$37$	1.97441	−	3.41977i	0.324590	−	0.562207i	0.981429	+	0.191824i	$0.0614403\pi$
$38$		0			0
$39$	−2.24938	+	1.09972i	−0.360189	+	0.176095i
$40$		0			0
$41$	−0.0493888	+	0.280098i	−0.00771323	+	0.0437439i	−0.988421	−	0.151733i	$-0.951514\pi$
$41$	−0.0493888	+	0.280098i	−0.00771323	+	0.0437439i	0.980708	+	0.195477i	$0.0626256\pi$
$42$		0			0
$43$	−4.90028	+	4.11182i	−0.747286	+	0.627047i	−0.934784	−	0.355218i	$-0.884407\pi$
$43$	−4.90028	+	4.11182i	−0.747286	+	0.627047i	0.187498	+	0.982265i	$0.439962\pi$
$44$		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	$-0.240380\pi$
$47$	5.79555	+	2.10941i	0.845368	+	0.307689i	0.117218	+	0.993106i	$0.462602\pi$
$48$		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	0.952177	+	0.305546i	$0.0988390\pi$
$59$	10.8951	+	9.14210i	1.41843	+	1.19020i	0.466248	+	0.884654i	$0.345605\pi$
$60$		0			0
$61$	2.76413	+	1.00606i	0.353910	+	0.128813i	0.512856	−	0.858475i	$-0.328587\pi$
$61$	2.76413	+	1.00606i	0.353910	+	0.128813i	−0.158946	+	0.987287i	$0.550810\pi$
$62$		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	0.513350	+	0.858179i	$0.328404\pi$
$67$	−2.14911	+	12.1882i	−0.262556	+	1.48903i	−0.775906	+	0.630848i	$0.782707\pi$
$68$		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	$-0.955584\pi$
$71$	−3.15719	+	5.46842i	−0.374690	+	0.648982i	0.615591	+	0.788066i	$0.288918\pi$
$72$		0			0
$73$	2.36669	+	4.09923i	0.277000	+	0.479779i	0.970638	−	0.240545i	$-0.0773263\pi$
$73$	2.36669	+	4.09923i	0.277000	+	0.479779i	−0.693637	+	0.720324i	$0.743993\pi$
$74$		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	−0.982607	−	0.185697i	$-0.940546\pi$
$79$	−1.09121	−	6.18856i	−0.122771	−	0.696267i	0.859836	−	0.510570i	$-0.170566\pi$
$80$		0			0
$81$	−7.30099	−	5.26265i	−0.811222	−	0.584739i
$82$		0			0
$83$	−2.82134	−	16.0006i	−0.309683	−	1.75630i	−0.600600	−	0.799550i	$-0.705071\pi$
$83$	−2.82134	−	16.0006i	−0.309683	−	1.75630i	0.290917	−	0.956748i	$-0.406040\pi$
$84$		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	0.915351	−	0.402658i	$-0.131914\pi$
$89$	1.02796	+	1.78048i	0.108963	+	0.188730i	−0.806387	+	0.591388i	$0.798580\pi$
$90$		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	−0.642347	−	0.766414i	$-0.722039\pi$
$97$	0.00867542	−	0.00727954i	0.000880855	−	0.000739125i	0.643228	+	0.765675i	$0.277595\pi$
$98$		0			0
$99$	6.41015	+	15.7802i	0.644244	+	1.58597i
$100$		0			0
$101$	2.55554	+	0.930139i	0.254285	+	0.0925523i	0.466018	−	0.884775i	$-0.345688\pi$
$101$	2.55554	+	0.930139i	0.254285	+	0.0925523i	−0.211732	+	0.977328i	$0.567911\pi$
$102$		0			0
$103$	−2.93683	−	2.46429i	−0.289374	−	0.242814i	0.486531	−	0.873663i	$-0.338262\pi$
$103$	−2.93683	−	2.46429i	−0.289374	−	0.242814i	−0.775905	+	0.630850i	$0.782706\pi$
$104$		0			0
$105$	5.54159	−	12.4782i	0.540804	−	1.21774i
$106$		0			0
$107$	2.63565			0.254798			0.127399	−	0.991852i	$-0.459337\pi$
$107$	2.63565			0.254798			0.127399	+	0.991852i	$0.459337\pi$
$108$		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	0.698860	−	0.715258i	$-0.253691\pi$
$113$	1.23122	+	1.03312i	0.115824	+	0.0971877i	−0.583036	+	0.812446i	$0.698135\pi$
$114$		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	$-0.00265818\pi$
$127$	5.55302	+	9.61811i	0.492751	+	0.853469i	−0.507215	+	0.861820i	$0.669325\pi$
$128$		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	$-0.544424\pi$
$131$	4.47367	−	1.62828i	0.390866	−	0.142264i	0.529975	+	0.848014i	$0.322201\pi$
$132$		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	0.868545	+	0.495610i	$0.165055\pi$
$137$	2.59714	+	14.7291i	0.221888	+	1.25839i	−0.646657	+	0.762781i	$0.723833\pi$
$138$		0			0
$139$	−3.09109	+	1.12507i	−0.262183	+	0.0954269i	−0.469767	−	0.882790i	$-0.655662\pi$
$139$	−3.09109	+	1.12507i	−0.262183	+	0.0954269i	0.207584	+	0.978217i	$0.433440\pi$
$140$		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	−0.0848922	−	0.996390i	$-0.527055\pi$
$149$	4.09732	−	23.2371i	0.335666	−	1.90366i	0.420558	−	0.907266i	$-0.361834\pi$
$150$		0			0
$151$	13.5314	−	11.3542i	1.10117	−	0.923992i	0.103667	−	0.994612i	$-0.466942\pi$
$151$	13.5314	−	11.3542i	1.10117	−	0.923992i	0.997503	+	0.0706202i	$0.0224978\pi$
$152$		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	0.0504927	−	0.998724i	$-0.483921\pi$
$157$	−11.5813	−	9.71789i	−0.924291	−	0.775572i	−0.974784	+	0.223152i	$0.928365\pi$
$158$		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	$-0.688350\pi$
$163$	−14.2428			−1.11558			−0.557789	+	0.829983i	$0.688350\pi$
$164$		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	$-0.0712821\pi$
$167$	11.9620	+	10.0373i	0.925644	+	0.776708i	−0.0493862	+	0.998780i	$0.515727\pi$
$168$		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	−0.171640	−	0.985160i	$-0.554906\pi$
$173$	10.1113	−	8.48440i	0.768749	−	0.645057i	0.940388	+	0.340103i	$0.110462\pi$
$174$		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	$-0.976600\pi$
$179$	−5.82046	+	10.0813i	−0.435042	+	0.753514i	0.562257	+	0.826962i	$0.309933\pi$
$180$		0			0
$181$	−8.69794	−	15.0653i	−0.646513	−	1.11979i	−0.983950	−	0.178445i	$-0.942893\pi$
$181$	−8.69794	−	15.0653i	−0.646513	−	1.11979i	0.337437	−	0.941348i	$-0.390440\pi$
$182$		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	−0.999927	−	0.0120989i	$-0.996149\pi$
$191$	−0.890593	−	5.05080i	−0.0644410	−	0.365463i	0.935486	−	0.353364i	$-0.114962\pi$
$192$		0			0
$193$	−11.6739	+	4.24897i	−0.840309	+	0.305847i	−0.726083	−	0.687607i	$-0.758661\pi$
$193$	−11.6739	+	4.24897i	−0.840309	+	0.305847i	−0.114226	+	0.993455i	$0.536439\pi$
$194$		0			0
$195$	−4.66170	−	1.15764i	−0.333831	−	0.0829003i
$196$		0			0
$197$	4.45190	+	7.71091i	0.317185	+	0.549380i	0.979899	−	0.199492i	$-0.0639292\pi$
$197$	4.45190	+	7.71091i	0.317185	+	0.549380i	−0.662715	+	0.748872i	$0.730596\pi$
$198$		0			0
$199$	−0.393080	+	0.680834i	−0.0278647	+	0.0482631i	−0.879621	−	0.475674i	$-0.842204\pi$
$199$	−0.393080	+	0.680834i	−0.0278647	+	0.0482631i	0.851757	+	0.523937i	$0.175537\pi$
$200$		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	$-0.311552\pi$
$211$	−2.35690	−	1.97768i	−0.162256	−	0.136149i	−0.720301	+	0.693662i	$0.755996\pi$
$212$		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	$-0.245839\pi$
$223$	12.1923	+	4.43765i	0.816459	+	0.297167i	0.100170	+	0.994970i	$0.468061\pi$
$224$		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	$-0.773174\pi$
$227$	−3.67917	+	3.08719i	−0.244195	+	0.204904i	0.512473	+	0.858704i	$0.328730\pi$
$228$		0			0
$229$	1.52222	−	8.63293i	0.100591	−	0.570480i	−0.892299	−	0.451445i	$-0.850909\pi$
$229$	1.52222	−	8.63293i	0.100591	−	0.570480i	0.992890	−	0.119035i	$-0.0379801\pi$
$230$		0			0
$231$	−33.5203	−	22.5639i	−2.20547	−	1.48460i
$232$		0			0
$233$	−1.99833	+	3.46120i	−0.130915	+	0.226751i	−0.924029	−	0.382321i	$-0.875125\pi$
$233$	−1.99833	+	3.46120i	−0.130915	+	0.226751i	0.793115	+	0.609072i	$0.208458\pi$
$234$		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	$-0.689490\pi$
$239$	−7.08212	+	2.57768i	−0.458105	+	0.166736i	0.102652	+	0.994717i	$0.467267\pi$
$240$		0			0
$241$	−1.67523	−	9.50068i	−0.107911	−	0.611993i	−0.990018	−	0.140943i	$-0.954986\pi$
$241$	−1.67523	−	9.50068i	−0.107911	−	0.611993i	0.882107	−	0.471049i	$-0.156125\pi$
$242$		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	$-0.141688\pi$
$251$	1.24195	+	2.15112i	0.0783912	+	0.135778i	−0.824165	+	0.566350i	$0.808355\pi$
$252$		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	−0.774045	−	0.633131i	$-0.781770\pi$
$257$	2.72311	−	15.4435i	0.169863	−	0.963340i	0.943908	−	0.330209i	$-0.107119\pi$
$258$		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	$-0.509388\pi$
$263$	−11.2643	−	4.09987i	−0.694586	−	0.252809i	−0.665098	+	0.746756i	$0.731610\pi$
$264$		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	$-0.435636\pi$
$271$	6.61217			0.401661			0.200830	+	0.979626i	$0.435636\pi$
$272$		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	0.751039	−	0.660258i	$-0.229553\pi$
$277$	15.0116	+	5.46379i	0.901962	+	0.328287i	0.150923	+	0.988545i	$0.451775\pi$
$278$		0			0
$279$	−0.125020	−	3.39696i	−0.00748473	−	0.203370i
$280$		0			0
$281$	−6.34624	+	5.32513i	−0.378585	+	0.317671i	−0.812147	−	0.583453i	$-0.801701\pi$
$281$	−6.34624	+	5.32513i	−0.378585	+	0.317671i	0.433562	+	0.901124i	$0.357257\pi$
$282$		0			0
$283$	2.99620	−	16.9923i	0.178106	−	1.01009i	−0.756392	−	0.654118i	$-0.773040\pi$
$283$	2.99620	−	16.9923i	0.178106	−	1.01009i	0.934498	−	0.355969i	$-0.115849\pi$
$284$		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	−0.619722	−	0.784821i	$-0.712755\pi$
$293$	−10.0989	+	3.67569i	−0.589983	+	0.214736i	0.0297390	+	0.999558i	$0.490532\pi$
$294$		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	$-0.857495\pi$
$307$	−1.32872	+	2.30142i	−0.0758343	+	0.131349i	0.825614	+	0.564235i	$0.190829\pi$
$308$		0			0
$309$	0.456973	−	6.62452i	0.0259963	−	0.376856i
$310$		0			0
$311$	−5.98755	+	33.9571i	−0.339523	+	1.92553i	0.0374342	+	0.999299i	$0.488082\pi$
$311$	−5.98755	+	33.9571i	−0.339523	+	1.92553i	−0.376957	+	0.926231i	$0.623030\pi$
$312$		0			0
$313$	9.70435	−	8.14292i	0.548522	−	0.460265i	−0.325918	−	0.945398i	$-0.605673\pi$
$313$	9.70435	−	8.14292i	0.548522	−	0.460265i	0.874440	+	0.485133i	$0.161229\pi$
$314$		0			0
$315$	23.1222	−	4.96024i	1.30279	−	0.279478i
$316$		0			0
$317$	8.26564	+	3.00845i	0.464244	+	0.168971i	0.563543	−	0.826087i	$-0.309438\pi$
$317$	8.26564	+	3.00845i	0.464244	+	0.168971i	−0.0992989	+	0.995058i	$0.531660\pi$
$318$		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	$-0.283301\pi$
$331$	11.1353	+	4.05290i	0.612049	+	0.222768i	−0.0173504	+	0.999849i	$0.505523\pi$
$332$		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	0.756486	+	0.654009i	$0.226914\pi$
$337$	−3.26880	+	18.5383i	−0.178063	+	1.00984i	−0.934549	+	0.355834i	$0.884197\pi$
$338$		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	$-0.644004\pi$
$347$	−3.61122	+	1.31438i	−0.193861	+	0.0705595i	0.243265	+	0.969960i	$0.421781\pi$
$348$		0			0
$349$	−0.642364	−	3.64303i	−0.0343850	−	0.195007i	0.962777	−	0.270298i	$-0.0871224\pi$
$349$	−0.642364	−	3.64303i	−0.0343850	−	0.195007i	−0.997162	+	0.0752915i	$0.976011\pi$
$350$		0			0
$351$	−1.06637	−	7.43537i	−0.0569184	−	0.396870i
$352$		0			0
$353$	−2.34505	−	13.2995i	−0.124815	−	0.707859i	−0.981418	−	0.191883i	$-0.938541\pi$
$353$	−2.34505	−	13.2995i	−0.124815	−	0.707859i	0.856603	−	0.515976i	$-0.172571\pi$
$354$		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	$-0.0206878\pi$
$359$	8.38794	+	14.5283i	0.442699	+	0.766777i	−0.555190	+	0.831724i	$0.687354\pi$
$360$		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	$-0.565625\pi$
$367$	13.8640	−	11.6333i	0.723695	−	0.607252i	0.928405	+	0.371570i	$0.121181\pi$
$368$		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	0.866127	−	0.499825i	$-0.166602\pi$
$373$	10.1258	+	8.49660i	0.524297	+	0.439937i	−0.341830	+	0.939762i	$0.611047\pi$
$374$		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	$-0.195476\pi$
$379$	31.8219			1.63458			0.817289	+	0.576227i	$0.195476\pi$
$380$		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	$-0.233383\pi$
$383$	4.16826	+	3.49758i	0.212988	+	0.178718i	−0.530052	+	0.847965i	$0.677828\pi$
$384$		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	−0.288844	−	0.957376i	$-0.593271\pi$
$389$	11.9094	−	9.99317i	0.603831	−	0.506674i	0.892674	+	0.450702i	$0.148826\pi$
$390$		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	0.541264	−	0.840853i	$-0.317946\pi$
$397$	−9.11698	−	15.7911i	−0.457568	−	0.792531i	−0.998832	+	0.0483217i	$0.984613\pi$
$398$		0			0
$399$	−25.1511	+	26.0938i	−1.25913	+	1.30632i
$400$		0			0
$401$	33.0083	−	12.0140i	1.64836	−	0.599953i	0.659886	−	0.751366i	$-0.270605\pi$
$401$	33.0083	−	12.0140i	1.64836	−	0.599953i	0.988471	+	0.151413i	$0.0483823\pi$
$402$		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	−0.965707	−	0.259636i	$-0.916398\pi$
$409$	−31.1161	+	11.3253i	−1.53859	+	0.560001i	−0.572884	+	0.819637i	$0.694175\pi$
$410$		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	$-0.969863\pi$
$419$	−0.567077	+	3.21606i	−0.0277035	+	0.157115i	0.967818	+	0.251652i	$0.0809739\pi$
$420$		0			0
$421$	−17.0256	+	14.2861i	−0.829775	+	0.696264i	−0.955239	−	0.295835i	$-0.904402\pi$
$421$	−17.0256	+	14.2861i	−0.829775	+	0.696264i	0.125465	+	0.992098i	$0.459958\pi$
$422$		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	$-0.690631\pi$
$431$	−23.4064			−1.12744			−0.563722	+	0.825964i	$0.690631\pi$
$432$		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	$-0.693346\pi$
$439$	−32.1780	−	11.7118i	−1.53577	−	0.558975i	−0.965027	+	0.262152i	$0.915568\pi$
$440$		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	$-0.698834\pi$
$443$	2.36729	−	1.98639i	0.112473	−	0.0943762i	0.697290	+	0.716789i	$0.254389\pi$
$444$		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	−0.913771	−	0.406230i	$-0.866843\pi$
$449$	−2.22660	+	3.85659i	−0.105080	+	0.182004i	0.808691	+	0.588234i	$0.200176\pi$
$450$		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	0.940506	−	0.339778i	$-0.110352\pi$
$457$	−1.27178	−	7.21262i	−0.0594913	−	0.337392i	−0.999997	+	0.00238542i	$0.999241\pi$
$458$		0			0
$459$	−2.91922	+	13.9269i	−0.136258	+	0.650051i
$460$		0			0
$461$	2.58659	+	14.6693i	0.120470	+	0.683217i	0.983896	+	0.178742i	$0.0572027\pi$
$461$	2.58659	+	14.6693i	0.120470	+	0.683217i	−0.863426	+	0.504475i	$0.831686\pi$
$462$		0			0
$463$	7.59572	−	2.76462i	0.353003	−	0.128483i	−0.159431	−	0.987209i	$-0.550966\pi$
$463$	7.59572	−	2.76462i	0.353003	−	0.128483i	0.512434	+	0.858726i	$0.328744\pi$
$464$		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	$-0.226299\pi$
$467$	−4.02480	−	6.97116i	−0.186246	−	0.322587i	−0.943996	+	0.329958i	$0.892965\pi$
$468$		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	0.989545	+	0.144224i	$0.0460686\pi$
$479$	40.2766	+	14.6595i	1.84029	+	0.669809i	0.850741	+	0.525585i	$0.176154\pi$
$480$		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	$-0.534624\pi$
$487$	−4.79142			−0.217120			−0.108560	+	0.994090i	$0.534624\pi$
$488$		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	$-0.468385\pi$
$491$	−19.1356	−	16.0567i	−0.863576	−	0.724627i	−0.962735	+	0.270445i	$0.912829\pi$
$492$		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	$-0.987547\pi$
$499$	−1.04732	+	5.93966i	−0.0468845	+	0.265895i	0.952350	+	0.305006i	$0.0986586\pi$
$500$		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	$-0.705817\pi$
$503$	8.74621	−	15.1489i	0.389974	−	0.675455i	0.992446	+	0.122685i	$0.0391506\pi$
$504$		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	−0.577669	−	0.816271i	$-0.696037\pi$
$509$	−11.1790	+	4.06882i	−0.495500	+	0.180347i	0.0821690	+	0.996618i	$0.473815\pi$
$510$		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	0.961138	−	0.276070i	$-0.0890322\pi$
$521$	5.51200	+	9.54706i	0.241485	+	0.418264i	−0.719652	+	0.694334i	$0.755699\pi$
$522$		0			0
$523$	−17.7734	+	30.7844i	−0.777175	+	1.34611i	0.156388	+	0.987696i	$0.450015\pi$
$523$	−17.7734	+	30.7844i	−0.777175	+	1.34611i	−0.933564	+	0.358412i	$0.883318\pi$
$524$		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	$-0.455582\pi$
$547$	−9.14230	−	3.32752i	−0.390896	−	0.142275i	−0.529989	+	0.848005i	$0.677804\pi$
$548$		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	−0.532340	−	0.846531i	$-0.678687\pi$
$557$	11.0204	−	19.0878i	0.466948	−	0.808777i	0.999287	+	0.0377541i	$0.0120204\pi$
$558$		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	$-0.503633\pi$
$563$	14.7726	−	5.37678i	0.622590	−	0.226604i	0.634003	+	0.773331i	$0.281411\pi$
$564$		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	0.805505	+	0.592589i	$0.201894\pi$
$569$	5.99337	+	33.9901i	0.251255	+	1.42494i	−0.554250	+	0.832350i	$0.686995\pi$
$570$		0			0
$571$	−25.9253	+	9.43603i	−1.08494	+	0.394885i	−0.821744	−	0.569857i	$-0.806999\pi$
$571$	−25.9253	+	9.43603i	−1.08494	+	0.394885i	−0.263195	+	0.964743i	$0.584776\pi$
$572$		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	−0.0333036	−	0.999445i	$-0.510603\pi$
$577$	20.3911	−	35.3184i	0.848893	−	1.47033i	0.882197	−	0.470881i	$-0.156064\pi$
$578$		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	$-0.471042\pi$
$587$	−11.6219	−	4.23001i	−0.479685	−	0.174591i	−0.570535	+	0.821274i	$0.693264\pi$
$588$		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	$-0.483919\pi$
$599$	−22.6214	−	18.9816i	−0.924286	−	0.775568i	−0.974783	+	0.223157i	$0.928364\pi$
$600$		0			0
$601$	17.9678	+	6.53974i	0.732922	+	0.266762i	0.681401	−	0.731910i	$-0.261371\pi$
$601$	17.9678	+	6.53974i	0.732922	+	0.266762i	0.0515206	+	0.998672i	$0.483593\pi$
$602$		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	−0.669147	−	0.743130i	$-0.733340\pi$
$607$	5.26774	−	29.8748i	0.213811	−	1.21258i	0.882958	−	0.469452i	$-0.155549\pi$
$608$		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	0.916240	+	0.400629i	$0.131208\pi$
$613$	19.9327	+	34.5245i	0.805075	+	1.39443i	−0.111165	+	0.993802i	$0.535458\pi$
$614$		0			0
$615$	−0.917194	−	0.227766i	−0.0369848	−	0.00918443i
$616$		0			0
$617$	16.4318	−	5.98068i	0.661519	−	0.240773i	0.0106270	−	0.999944i	$-0.496617\pi$
$617$	16.4318	−	5.98068i	0.661519	−	0.240773i	0.650892	+	0.759170i	$0.274395\pi$
$618$		0			0
$619$	−3.81674	−	21.6458i	−0.153408	−	0.870019i	−0.960227	−	0.279220i	$-0.909924\pi$
$619$	−3.81674	−	21.6458i	−0.153408	−	0.870019i	0.806819	−	0.590798i	$-0.201187\pi$
$620$		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	$-0.830491\pi$
$631$	0.224323	−	0.388538i	0.00893014	−	0.0154675i	0.870456	+	0.492246i	$0.163824\pi$
$632$		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	−0.685313	−	0.728248i	$-0.740335\pi$
$641$	−42.4938	−	15.4665i	−1.67840	−	0.610889i	−0.993089	+	0.117360i	$0.962557\pi$
$642$		0			0
$643$	20.4317	+	17.1442i	0.805747	+	0.676102i	0.949589	−	0.313499i	$-0.101501\pi$
$643$	20.4317	+	17.1442i	0.805747	+	0.676102i	−0.143842	+	0.989601i	$0.545946\pi$
$644$		0			0
$645$	−12.5096	−	17.1840i	−0.492566	−	0.676621i
$646$		0			0
$647$	−34.1104			−1.34102			−0.670508	−	0.741902i	$-0.733924\pi$
$647$	−34.1104			−1.34102			−0.670508	+	0.741902i	$0.733924\pi$
$648$		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	0.599794	−	0.800155i	$-0.295249\pi$
$653$	−2.14784	−	1.80225i	−0.0840514	−	0.0705275i	−0.683845	+	0.729627i	$0.739694\pi$
$654$		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	−0.323840	+	0.946112i	$0.604974\pi$
$659$	−33.6755	+	28.2571i	−1.31181	+	1.10074i	−0.987972	+	0.154630i	$0.950581\pi$
$660$		0			0
$661$	0.685986	−	3.89042i	0.0266818	−	0.151320i	−0.968556	−	0.248795i	$-0.919965\pi$
$661$	0.685986	−	3.89042i	0.0266818	−	0.151320i	0.995238	+	0.0974750i	$0.0310766\pi$
$662$		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	−0.999948	−	0.0102164i	$-0.996748\pi$
$673$	−1.65507	−	9.38639i	−0.0637984	−	0.361819i	0.936149	−	0.351603i	$-0.114363\pi$
$674$		0			0
$675$	3.23661	+	6.04597i	0.124577	+	0.232709i
$676$		0			0
$677$	1.22825	+	6.96575i	0.0472055	+	0.267716i	0.999271	−	0.0381788i	$-0.0121556\pi$
$677$	1.22825	+	6.96575i	0.0472055	+	0.267716i	−0.952065	+	0.305894i	$0.901045\pi$
$678$		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	−0.890828	−	0.454341i	$-0.849875\pi$
$683$	−21.9236	−	37.9729i	−0.838885	−	1.45299i	0.0519432	−	0.998650i	$-0.483459\pi$
$684$		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	$-0.471653\pi$
$691$	28.5288	−	23.9385i	1.08529	−	0.910663i	0.996349	+	0.0853743i	$0.0272086\pi$
$692$		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	−0.752507	−	0.658585i	$-0.771155\pi$
$709$	−46.6583	−	16.9822i	−1.75229	−	0.637781i	−0.999784	+	0.0208033i	$0.993378\pi$
$710$		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	$-0.725375\pi$
$719$	8.92100	−	15.4516i	0.332697	−	0.576248i	0.983040	+	0.183393i	$0.0587080\pi$
$720$		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	0.677768	+	0.735276i	$0.262947\pi$
$727$	7.88271	+	44.7051i	0.292354	+	1.65802i	−0.385414	+	0.922744i	$0.625941\pi$
$728$		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	−0.906555	−	0.422088i	$-0.861297\pi$
$733$	−36.0003	+	13.1031i	−1.32970	+	0.483972i	−0.423148	+	0.906061i	$0.639075\pi$
$734$		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	$-0.712525\pi$
$739$	10.0715	−	17.4443i	0.370485	−	0.641698i	0.989640	+	0.143570i	$0.0458583\pi$
$740$		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	$-0.941248\pi$
$743$	0.0950690	−	0.539163i	0.00348774	−	0.0197800i	0.986502	+	0.163749i	$0.0523589\pi$
$744$		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	$-0.504872\pi$
$751$	−27.4772	−	23.0561i	−1.00266	−	0.841328i	−0.987350	+	0.158555i	$0.949317\pi$
$752$		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	0.723491	−	0.690334i	$-0.242536\pi$
$761$	4.66973	+	3.91837i	0.169278	+	0.142041i	−0.554213	+	0.832375i	$0.686981\pi$
$762$		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	0.348776	+	0.937206i	$0.386597\pi$
$769$	−8.30566	+	47.1037i	−0.299510	+	1.69860i	−0.648285	+	0.761397i	$0.724514\pi$
$770$		0			0
$771$	24.4015	−	11.9298i	0.878798	−	0.429642i
$772$		0			0
$773$	−9.33612	+	16.1706i	−0.335797	+	0.581617i	−0.983638	−	0.180159i	$-0.942339\pi$
$773$	−9.33612	+	16.1706i	−0.335797	+	0.581617i	0.647841	+	0.761776i	$0.275672\pi$
$774$		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	$-0.346351\pi$
$787$	38.9691	−	14.1836i	1.38910	−	0.505591i	0.924924	+	0.380152i	$0.124128\pi$
$788$		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	−0.879263	−	0.476337i	$-0.841964\pi$
$797$	3.10235	−	17.5943i	0.109891	−	0.623222i	0.989154	−	0.146885i	$-0.0469247\pi$
$798$		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	$-0.608617\pi$
$811$	−19.0602			−0.669294			−0.334647	+	0.942344i	$0.608617\pi$
$812$		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	−0.905604	−	0.424125i	$-0.860582\pi$
$821$	−18.4864	+	15.5119i	−0.645178	+	0.541369i	0.260425	+	0.965494i	$0.416137\pi$
$822$		0			0
$823$	8.74245	−	49.5809i	0.304743	−	1.72828i	−0.319972	−	0.947427i	$-0.603673\pi$
$823$	8.74245	−	49.5809i	0.304743	−	1.72828i	0.624714	−	0.780854i	$-0.285216\pi$
$824$		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	$-0.808821\pi$
$827$	2.21235	−	3.83190i	0.0769310	−	0.133248i	0.901924	+	0.431894i	$0.142155\pi$
$828$		0			0
$829$	−9.40772	−	16.2947i	−0.326744	−	0.565937i	0.655120	−	0.755525i	$-0.272618\pi$
$829$	−9.40772	−	16.2947i	−0.326744	−	0.565937i	−0.981864	+	0.189588i	$0.939285\pi$
$830$		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	0.948738	+	0.316063i	$0.102361\pi$
$839$	4.78845	+	27.1567i	0.165316	+	0.937553i	−0.783422	+	0.621490i	$0.786528\pi$
$840$		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	−0.324608	−	0.945849i	$-0.605232\pi$
$853$	16.0781	−	13.4911i	0.550504	−	0.461928i	0.875112	+	0.483921i	$0.160788\pi$
$854$		0			0
$855$	25.9019	+	13.7099i	0.885828	+	0.468869i
$856$		0			0
$857$	−5.88556	−	2.14217i	−0.201047	−	0.0731751i	0.239534	−	0.970888i	$-0.423005\pi$
$857$	−5.88556	−	2.14217i	−0.201047	−	0.0731751i	−0.440581	+	0.897713i	$0.645228\pi$
$858$		0			0
$859$	−21.9084	−	18.3833i	−0.747505	−	0.627232i	0.187336	−	0.982296i	$-0.440015\pi$
$859$	−21.9084	−	18.3833i	−0.747505	−	0.627232i	−0.934842	+	0.355064i	$0.884459\pi$
$860$		0			0
$861$	2.01294	−	0.213483i	0.0686010	−	0.00727547i
$862$		0			0
$863$	48.0721			1.63639			0.818196	−	0.574940i	$-0.194974\pi$
$863$	48.0721			1.63639			0.818196	+	0.574940i	$0.194974\pi$
$864$		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	−0.337800	−	0.941218i	$-0.609683\pi$
$877$	8.92997	−	50.6444i	0.301544	−	1.71014i	0.639344	−	0.768921i	$-0.279206\pi$
$878$		0			0
$879$	−15.4418	−	10.3945i	−0.520838	−	0.350598i
$880$		0			0
$881$	−4.25145	+	7.36372i	−0.143235	+	0.248090i	−0.928713	−	0.370799i	$-0.879084\pi$
$881$	−4.25145	+	7.36372i	−0.143235	+	0.248090i	0.785478	+	0.618889i	$0.212417\pi$
$882$		0			0
$883$	−12.2957	−	21.2968i	−0.413784	−	0.716695i	0.581516	−	0.813535i	$-0.302460\pi$
$883$	−12.2957	−	21.2968i	−0.413784	−	0.716695i	−0.995300	+	0.0968398i	$0.969127\pi$
$884$		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	$-0.485667\pi$
$887$	21.4921	−	7.82247i	0.721633	−	0.262653i	0.676619	+	0.736333i	$0.263445\pi$
$888$		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	$-0.919685\pi$
$907$	−26.8226	+	22.5069i	−0.890631	+	0.747328i	0.0777056	+	0.996976i	$0.475241\pi$
$908$		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	$-0.229550\pi$
$911$	27.2243	+	9.90882i	0.901980	+	0.328294i	0.150934	+	0.988544i	$0.451772\pi$
$912$		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	$-0.708093\pi$
$919$	−36.8729			−1.21632			−0.608162	+	0.793813i	$0.708093\pi$
$920$		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	−0.911915	−	0.410380i	$-0.865396\pi$
$929$	−20.3030	+	17.0363i	−0.666121	+	0.558942i	0.245793	+	0.969322i	$0.420952\pi$
$930$		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	0.917707	−	0.397259i	$-0.130038\pi$
$937$	3.51461	+	6.08749i	0.114817	+	0.198870i	−0.802889	+	0.596128i	$0.796705\pi$
$938$		0			0
$939$	21.2951	+	5.28819i	0.694938	+	0.172574i
$940$		0			0
$941$	24.9101	−	9.06653i	0.812045	−	0.295560i	0.0975769	−	0.995228i	$-0.468891\pi$
$941$	24.9101	−	9.06653i	0.812045	−	0.295560i	0.714468	+	0.699668i	$0.246669\pi$
$942$		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	−0.915103	−	0.403220i	$-0.867891\pi$
$947$	−5.94224	−	33.7001i	−0.193097	−	1.09511i	0.722006	−	0.691887i	$-0.243220\pi$
$948$		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	0.922105	−	0.386941i	$-0.126468\pi$
$953$	3.88821	+	6.73458i	0.125952	+	0.218155i	−0.796153	+	0.605095i	$0.793135\pi$
$954$		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	$-0.265320\pi$
$967$	1.86408	+	1.56415i	0.0599447	+	0.0502996i	−0.612323	+	0.790608i	$0.709765\pi$
$968$		0			0
$969$	−14.2153	−	19.5271i	−0.456661	−	0.627299i
$970$		0			0
$971$	28.2097			0.905293			0.452647	−	0.891690i	$-0.350480\pi$
$971$	28.2097			0.905293			0.452647	+	0.891690i	$0.350480\pi$
$972$		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	0.999762	−	0.0218295i	$-0.00694909\pi$
$977$	36.0040	+	30.2110i	1.15187	+	0.966534i	0.152109	+	0.988364i	$0.451394\pi$
$978$		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	$-0.509906\pi$
$983$	29.7166	−	24.9352i	0.947812	−	0.795309i	0.978928	+	0.204207i	$0.0654616\pi$
$984$		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	$-0.0597484\pi$
$991$	10.3763	+	17.9722i	0.329613	+	0.570906i	−0.652822	+	0.757511i	$0.726415\pi$
$992$		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	−0.734298	−	0.678827i	$-0.762488\pi$
$997$	−8.72919	−	49.5057i	−0.276456	−	1.56786i	0.457842	−	0.889034i	$-0.348623\pi$
$998$		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	108.2.i.a.13.2	✓	18
3.2	odd	2		324.2.i.a.253.2		18
4.3	odd	2		432.2.u.d.337.2		18
9.2	odd	6		972.2.i.d.109.2		18
9.4	even	3		972.2.i.c.433.2		18
9.5	odd	6		972.2.i.b.433.2		18
9.7	even	3		972.2.i.a.109.2		18
27.2	odd	18		324.2.i.a.73.2		18
27.4	even	9		2916.2.e.c.1945.4		18
27.5	odd	18		2916.2.a.c.1.4		9
27.7	even	9		972.2.i.a.865.2		18
27.11	odd	18		972.2.i.b.541.2		18
27.13	even	9		2916.2.e.c.973.4		18
27.14	odd	18		2916.2.e.d.973.6		18
27.16	even	9		972.2.i.c.541.2		18
27.20	odd	18		972.2.i.d.865.2		18
27.22	even	9		2916.2.a.d.1.6		9
27.23	odd	18		2916.2.e.d.1945.6		18
27.25	even	9	inner	108.2.i.a.25.2	yes	18
108.79	odd	18		432.2.u.d.241.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.i.a.13.2	✓	18	1.1	even	1	trivial
108.2.i.a.25.2	yes	18	27.25	even	9	inner
324.2.i.a.73.2		18	27.2	odd	18
324.2.i.a.253.2		18	3.2	odd	2
432.2.u.d.241.2		18	108.79	odd	18
432.2.u.d.337.2		18	4.3	odd	2
972.2.i.a.109.2		18	9.7	even	3
972.2.i.a.865.2		18	27.7	even	9
972.2.i.b.433.2		18	9.5	odd	6
972.2.i.b.541.2		18	27.11	odd	18
972.2.i.c.433.2		18	9.4	even	3
972.2.i.c.541.2		18	27.16	even	9
972.2.i.d.109.2		18	9.2	odd	6
972.2.i.d.865.2		18	27.20	odd	18
2916.2.a.c.1.4		9	27.5	odd	18
2916.2.a.d.1.6		9	27.22	even	9
2916.2.e.c.973.4		18	27.13	even	9
2916.2.e.c.1945.4		18	27.4	even	9
2916.2.e.d.973.6		18	27.14	odd	18
2916.2.e.d.1945.6		18	27.23	odd	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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	108.i (of order \(9\), degree \(6\), 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

Modular forms

Varieties

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