LMFDB - Embedded newform 432.2.u.b.49.1

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:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			49.1
Root			$0.500000 - 1.80139i$ of defining polynomial
Character	$\chi$	$=$	432.49
Dual form			432.2.u.b.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.247510 - 1.71428i) q^{3} +(-1.96209 + 0.714144i) q^{5} +(0.696712 + 3.95125i) q^{7} +(-2.87748 + 0.848600i) q^{9} +O(q^{10})$	\(q+(-0.247510 - 1.71428i) q^{3} +(-1.96209 + 0.714144i) q^{5} +(0.696712 + 3.95125i) q^{7} +(-2.87748 + 0.848600i) q^{9} +(0.199635 + 0.0726611i) q^{11} +(3.98269 + 3.34187i) q^{13} +(1.70988 + 3.18681i) q^{15} +(-1.89276 + 3.27836i) q^{17} +(-0.636405 - 1.10229i) q^{19} +(6.60109 - 2.17233i) q^{21} +(-0.144031 + 0.816841i) q^{23} +(-0.490411 + 0.411503i) q^{25} +(2.16694 + 4.72275i) q^{27} +(7.05621 - 5.92087i) q^{29} +(-0.614003 + 3.48219i) q^{31} +(0.0751495 - 0.360213i) q^{33} +(-4.18878 - 7.25517i) q^{35} +(-1.77730 + 3.07838i) q^{37} +(4.74313 - 7.65457i) q^{39} +(2.09850 + 1.76085i) q^{41} +(6.48062 + 2.35875i) q^{43} +(5.03986 - 3.71997i) q^{45} +(0.221796 + 1.25787i) q^{47} +(-8.54912 + 3.11163i) q^{49} +(6.08849 + 2.43329i) q^{51} -11.2992 q^{53} -0.443592 q^{55} +(-1.73210 + 1.36380i) q^{57} +(-8.04363 + 2.92764i) q^{59} +(0.492064 + 2.79063i) q^{61} +(-5.35781 - 10.7784i) q^{63} +(-10.2010 - 3.71285i) q^{65} +(-7.47702 - 6.27396i) q^{67} +(1.43594 + 0.0447327i) q^{69} +(-5.86207 + 10.1534i) q^{71} +(-0.375162 - 0.649800i) q^{73} +(0.826812 + 0.738848i) q^{75} +(-0.148014 + 0.839430i) q^{77} +(1.81383 - 1.52198i) q^{79} +(7.55976 - 4.88366i) q^{81} +(8.73328 - 7.32809i) q^{83} +(1.37256 - 7.78415i) q^{85} +(-11.8965 - 10.6308i) q^{87} +(-2.69813 - 4.67329i) q^{89} +(-10.4298 + 18.0649i) q^{91} +(6.12140 + 0.190695i) q^{93} +(2.03588 + 1.70830i) q^{95} +(11.8055 + 4.29685i) q^{97} +(-0.636104 - 0.0396706i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{5} + 3 q^{7} - 12 q^{9}+O(q^{10}) $ 12 * q - 3 * q^5 + 3 * q^7 - 12 * q^9	$ 12 q - 3 q^{5} + 3 q^{7} - 12 q^{9} + 12 q^{11} + 12 q^{13} + 18 q^{15} - 6 q^{17} + 9 q^{19} + 24 q^{21} - 30 q^{23} - 9 q^{25} + 15 q^{29} + 36 q^{33} - 3 q^{35} - 15 q^{37} + 42 q^{39} - 12 q^{41} - 9 q^{43} + 18 q^{45} + 9 q^{47} - 39 q^{49} + 27 q^{51} - 12 q^{53} - 18 q^{55} + 18 q^{57} - 12 q^{59} - 36 q^{61} - 3 q^{63} - 15 q^{65} - 36 q^{67} + 18 q^{69} - 12 q^{71} - 21 q^{73} - 30 q^{75} + 3 q^{77} - 39 q^{79} - 18 q^{83} + 45 q^{85} - 27 q^{87} + 12 q^{89} + 6 q^{91} - 33 q^{93} + 15 q^{95} + 39 q^{97} - 9 q^{99}+O(q^{100}) $ 12 * q - 3 * q^5 + 3 * q^7 - 12 * q^9 + 12 * q^11 + 12 * q^13 + 18 * q^15 - 6 * q^17 + 9 * q^19 + 24 * q^21 - 30 * q^23 - 9 * q^25 + 15 * q^29 + 36 * q^33 - 3 * q^35 - 15 * q^37 + 42 * q^39 - 12 * q^41 - 9 * q^43 + 18 * q^45 + 9 * q^47 - 39 * q^49 + 27 * q^51 - 12 * q^53 - 18 * q^55 + 18 * q^57 - 12 * q^59 - 36 * q^61 - 3 * q^63 - 15 * q^65 - 36 * q^67 + 18 * q^69 - 12 * q^71 - 21 * q^73 - 30 * q^75 + 3 * q^77 - 39 * q^79 - 18 * q^83 + 45 * q^85 - 27 * q^87 + 12 * q^89 + 6 * q^91 - 33 * q^93 + 15 * q^95 + 39 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{9}\right)$

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
$3$	−0.247510	−	1.71428i	−0.142900	−	0.989737i
$3$	−0.247510	−	1.71428i	−0.142900	−	0.989737i
$4$		0			0
$5$	−1.96209	+	0.714144i	−0.877475	+	0.319375i	−0.741190	−	0.671295i	$-0.765738\pi$
$5$	−1.96209	+	0.714144i	−0.877475	+	0.319375i	−0.136285	+	0.990670i	$0.543516\pi$
$6$		0			0
$7$	0.696712	+	3.95125i	0.263332	+	1.49343i	0.773742	+	0.633501i	$0.218383\pi$
$7$	0.696712	+	3.95125i	0.263332	+	1.49343i	−0.510410	+	0.859931i	$0.670506\pi$
$8$		0			0
$9$	−2.87748	+	0.848600i	−0.959159	+	0.282867i
$10$		0			0
$11$	0.199635	+	0.0726611i	0.0601921	+	0.0219081i	0.371941	−	0.928256i	$-0.378692\pi$
$11$	0.199635	+	0.0726611i	0.0601921	+	0.0219081i	−0.311749	+	0.950165i	$0.600915\pi$
$12$		0			0
$13$	3.98269	+	3.34187i	1.10460	+	0.926868i	0.997726	−	0.0674046i	$-0.0214718\pi$
$13$	3.98269	+	3.34187i	1.10460	+	0.926868i	0.106873	+	0.994273i	$0.465916\pi$
$14$		0			0
$15$	1.70988	+	3.18681i	0.441488	+	0.822831i
$16$		0			0
$17$	−1.89276	+	3.27836i	−0.459062	+	0.795119i	−0.998912	−	0.0466426i	$-0.985148\pi$
$17$	−1.89276	+	3.27836i	−0.459062	+	0.795119i	0.539850	+	0.841762i	$0.318481\pi$
$18$		0			0
$19$	−0.636405	−	1.10229i	−0.146001	−	0.252882i	0.783745	−	0.621083i	$-0.213307\pi$
$19$	−0.636405	−	1.10229i	−0.146001	−	0.252882i	−0.929746	+	0.368201i	$0.879974\pi$
$20$		0			0
$21$	6.60109	−	2.17233i	1.44048	−	0.474041i
$22$		0			0
$23$	−0.144031	+	0.816841i	−0.0300326	+	0.170323i	−0.996135	−	0.0878361i	$-0.972005\pi$
$23$	−0.144031	+	0.816841i	−0.0300326	+	0.170323i	0.966102	+	0.258159i	$0.0831159\pi$
$24$		0			0
$25$	−0.490411	+	0.411503i	−0.0980821	+	0.0823007i
$26$		0			0
$27$	2.16694	+	4.72275i	0.417028	+	0.908894i
$28$		0			0
$29$	7.05621	−	5.92087i	1.31031	−	1.09948i	0.322041	−	0.946726i	$-0.395631\pi$
$29$	7.05621	−	5.92087i	1.31031	−	1.09948i	0.988265	−	0.152752i	$-0.0488134\pi$
$30$		0			0
$31$	−0.614003	+	3.48219i	−0.110278	+	0.625419i	0.878702	+	0.477371i	$0.158410\pi$
$31$	−0.614003	+	3.48219i	−0.110278	+	0.625419i	−0.988980	+	0.148048i	$0.952701\pi$
$32$		0			0
$33$	0.0751495	−	0.360213i	0.0130818	−	0.0627050i
$34$		0			0
$35$	−4.18878	−	7.25517i	−0.708032	−	1.22635i
$36$		0			0
$37$	−1.77730	+	3.07838i	−0.292187	+	0.506082i	−0.974326	−	0.225140i	$-0.927716\pi$
$37$	−1.77730	+	3.07838i	−0.292187	+	0.506082i	0.682140	+	0.731222i	$0.261049\pi$
$38$		0			0
$39$	4.74313	−	7.65457i	0.759509	−	1.22571i
$40$		0			0
$41$	2.09850	+	1.76085i	0.327730	+	0.274998i	0.791774	−	0.610814i	$-0.209158\pi$
$41$	2.09850	+	1.76085i	0.327730	+	0.274998i	−0.464044	+	0.885812i	$0.653602\pi$
$42$		0			0
$43$	6.48062	+	2.35875i	0.988286	+	0.359707i	0.785056	−	0.619425i	$-0.212634\pi$
$43$	6.48062	+	2.35875i	0.988286	+	0.359707i	0.203229	+	0.979131i	$0.434856\pi$
$44$		0			0
$45$	5.03986	−	3.71997i	0.751298	−	0.554540i
$46$		0			0
$47$	0.221796	+	1.25787i	0.0323523	+	0.183479i	0.996702	−	0.0811536i	$-0.0258604\pi$
$47$	0.221796	+	1.25787i	0.0323523	+	0.183479i	−0.964349	+	0.264633i	$0.914749\pi$
$48$		0			0
$49$	−8.54912	+	3.11163i	−1.22130	+	0.444518i
$50$		0			0
$51$	6.08849	+	2.43329i	0.852559	+	0.340728i
$52$		0			0
$53$	−11.2992			−1.55207			−0.776036	−	0.630689i	$-0.782772\pi$
$53$	−11.2992			−1.55207			−0.776036	+	0.630689i	$0.782772\pi$
$54$		0			0
$55$	−0.443592			−0.0598140
$56$		0			0
$57$	−1.73210	+	1.36380i	−0.229423	+	0.180640i
$58$		0			0
$59$	−8.04363	+	2.92764i	−1.04719	+	0.381147i	−0.807602	−	0.589728i	$-0.799235\pi$
$59$	−8.04363	+	2.92764i	−1.04719	+	0.381147i	−0.239589	+	0.970874i	$0.577013\pi$
$60$		0			0
$61$	0.492064	+	2.79063i	0.0630023	+	0.357304i	0.999969	+	0.00788485i	$0.00250985\pi$
$61$	0.492064	+	2.79063i	0.0630023	+	0.357304i	−0.936967	+	0.349419i	$0.886379\pi$
$62$		0			0
$63$	−5.35781	−	10.7784i	−0.675020	−	1.35795i
$64$		0			0
$65$	−10.2010	−	3.71285i	−1.26528	−	0.460523i
$66$		0			0
$67$	−7.47702	−	6.27396i	−0.913463	−	0.766487i	0.0593114	−	0.998240i	$-0.481110\pi$
$67$	−7.47702	−	6.27396i	−0.913463	−	0.766487i	−0.972775	+	0.231753i	$0.925554\pi$
$68$		0			0
$69$	1.43594	+	0.0447327i	0.172867	+	0.00538518i
$70$		0			0
$71$	−5.86207	+	10.1534i	−0.695700	+	1.20499i	0.274244	+	0.961660i	$0.411572\pi$
$71$	−5.86207	+	10.1534i	−0.695700	+	1.20499i	−0.969944	+	0.243327i	$0.921761\pi$
$72$		0			0
$73$	−0.375162	−	0.649800i	−0.0439094	−	0.0760534i	0.843235	−	0.537544i	$-0.180648\pi$
$73$	−0.375162	−	0.649800i	−0.0439094	−	0.0760534i	−0.887145	+	0.461491i	$0.847315\pi$
$74$		0			0
$75$	0.826812	+	0.738848i	0.0954720	+	0.0853148i
$76$		0			0
$77$	−0.148014	+	0.839430i	−0.0168678	+	0.0956620i
$78$		0			0
$79$	1.81383	−	1.52198i	0.204071	−	0.171236i	−0.535024	−	0.844837i	$-0.679698\pi$
$79$	1.81383	−	1.52198i	0.204071	−	0.171236i	0.739096	+	0.673600i	$0.235253\pi$
$80$		0			0
$81$	7.55976	−	4.88366i	0.839973	−	0.542628i
$82$		0			0
$83$	8.73328	−	7.32809i	0.958602	−	0.804363i	−0.0221230	−	0.999755i	$-0.507043\pi$
$83$	8.73328	−	7.32809i	0.958602	−	0.804363i	0.980725	+	0.195393i	$0.0625981\pi$
$84$		0			0
$85$	1.37256	−	7.78415i	0.148875	−	0.844310i
$86$		0			0
$87$	−11.8965	−	10.6308i	−1.27544	−	1.13974i
$88$		0			0
$89$	−2.69813	−	4.67329i	−0.286001	−	0.495368i	0.686851	−	0.726799i	$-0.258993\pi$
$89$	−2.69813	−	4.67329i	−0.286001	−	0.495368i	−0.972851	+	0.231431i	$0.925659\pi$
$90$		0			0
$91$	−10.4298	+	18.0649i	−1.09334	+	1.89372i
$92$		0			0
$93$	6.12140	+	0.190695i	0.634759	+	0.0197741i
$94$		0			0
$95$	2.03588	+	1.70830i	0.208876	+	0.175268i
$96$		0			0
$97$	11.8055	+	4.29685i	1.19867	+	0.436279i	0.862759	−	0.505615i	$-0.168734\pi$
$97$	11.8055	+	4.29685i	1.19867	+	0.436279i	0.335909	+	0.941895i	$0.390957\pi$
$98$		0			0
$99$	−0.636104	−	0.0396706i	−0.0639309	−	0.00398705i
$100$		0			0
$101$	−0.502628	−	2.85055i	−0.0500134	−	0.283640i	0.949536	−	0.313658i	$-0.101555\pi$
$101$	−0.502628	−	2.85055i	−0.0500134	−	0.283640i	−0.999549	+	0.0300181i	$0.990443\pi$
$102$		0			0
$103$	15.6835	−	5.70832i	1.54534	−	0.562458i	0.578022	−	0.816021i	$-0.303825\pi$
$103$	15.6835	−	5.70832i	1.54534	−	0.562458i	0.967319	+	0.253564i	$0.0816027\pi$
$104$		0			0
$105$	−11.4006	+	8.97644i	−1.11258	+	0.876011i
$106$		0			0
$107$	−0.321371			−0.0310681			−0.0155341	−	0.999879i	$-0.504945\pi$
$107$	−0.321371			−0.0310681			−0.0155341	+	0.999879i	$0.504945\pi$
$108$		0			0
$109$	0.568378			0.0544407			0.0272204	−	0.999629i	$-0.491334\pi$
$109$	0.568378			0.0544407			0.0272204	+	0.999629i	$0.491334\pi$
$110$		0			0
$111$	5.71708	+	2.28485i	0.542642	+	0.216869i
$112$		0			0
$113$	1.27781	−	0.465084i	0.120206	−	0.0437514i	−0.281217	−	0.959644i	$-0.590738\pi$
$113$	1.27781	−	0.465084i	0.120206	−	0.0437514i	0.401423	+	0.915893i	$0.368516\pi$
$114$		0			0
$115$	−0.300739	−	1.70558i	−0.0280441	−	0.159046i
$116$		0			0
$117$	−14.2960	−	6.23645i	−1.32167	−	0.576560i
$118$		0			0
$119$	−14.2723	−	5.19470i	−1.30834	−	0.476198i
$120$		0			0
$121$	−8.39191	−	7.04165i	−0.762901	−	0.640150i
$122$		0			0
$123$	2.49918	−	4.03323i	0.225344	−	0.363664i
$124$		0			0
$125$	5.88840	−	10.1990i	0.526675	−	0.912227i
$126$		0			0
$127$	0.902007	+	1.56232i	0.0800402	+	0.138634i	0.903267	−	0.429079i	$-0.141162\pi$
$127$	0.902007	+	1.56232i	0.0800402	+	0.138634i	−0.823227	+	0.567713i	$0.807828\pi$
$128$		0			0
$129$	2.43953	−	11.6934i	0.214789	−	1.02954i
$130$		0			0
$131$	1.68689	−	9.56684i	0.147384	−	0.835859i	−0.818037	−	0.575165i	$-0.804938\pi$
$131$	1.68689	−	9.56684i	0.147384	−	0.835859i	0.965422	−	0.260694i	$-0.0839512\pi$
$132$		0			0
$133$	3.91201	−	3.28257i	0.339215	−	0.284635i
$134$		0			0
$135$	−7.62446	−	7.71898i	−0.656209	−	0.664344i
$136$		0			0
$137$	−6.94643	+	5.82875i	−0.593474	+	0.497984i	−0.889340	−	0.457246i	$-0.848836\pi$
$137$	−6.94643	+	5.82875i	−0.593474	+	0.497984i	0.295867	+	0.955229i	$0.404392\pi$
$138$		0			0
$139$	1.74358	−	9.88833i	0.147888	−	0.838717i	−0.817114	−	0.576476i	$-0.804427\pi$
$139$	1.74358	−	9.88833i	0.147888	−	0.838717i	0.965002	−	0.262241i	$-0.0844615\pi$
$140$		0			0
$141$	2.10144	−	0.691555i	0.176973	−	0.0582394i
$142$		0			0
$143$	0.552258	+	0.956539i	0.0461822	+	0.0799898i
$144$		0			0
$145$	−9.61660	+	16.6564i	−0.798615	+	1.38324i
$146$		0			0
$147$	7.45018	+	13.8854i	0.614480	+	1.14525i
$148$		0			0
$149$	12.1360	+	10.1833i	0.994221	+	0.834250i	0.986173	−	0.165718i	$-0.0529940\pi$
$149$	12.1360	+	10.1833i	0.994221	+	0.834250i	0.00804728	+	0.999968i	$0.497438\pi$
$150$		0			0
$151$	4.98746	+	1.81529i	0.405874	+	0.147726i	0.536886	−	0.843655i	$-0.319600\pi$
$151$	4.98746	+	1.81529i	0.405874	+	0.147726i	−0.131012	+	0.991381i	$0.541823\pi$
$152$		0			0
$153$	2.66436	−	11.0396i	0.215401	−	0.892499i
$154$		0			0
$155$	−1.28205	−	7.27086i	−0.102977	−	0.584010i
$156$		0			0
$157$	10.8225	−	3.93906i	0.863727	−	0.314371i	0.128103	−	0.991761i	$-0.459111\pi$
$157$	10.8225	−	3.93906i	0.863727	−	0.314371i	0.735624	+	0.677390i	$0.236889\pi$
$158$		0			0
$159$	2.79668	+	19.3700i	0.221791	+	1.53614i
$160$		0			0
$161$	−3.32789			−0.262275
$162$		0			0
$163$	−7.66336			−0.600241			−0.300120	−	0.953901i	$-0.597027\pi$
$163$	−7.66336			−0.600241			−0.300120	+	0.953901i	$0.597027\pi$
$164$		0			0
$165$	0.109794	+	0.760439i	0.00854741	+	0.0592001i
$166$		0			0
$167$	5.74151	−	2.08974i	0.444292	−	0.161709i	−0.110180	−	0.993912i	$-0.535143\pi$
$167$	5.74151	−	2.08974i	0.444292	−	0.161709i	0.554472	+	0.832203i	$0.312920\pi$
$168$		0			0
$169$	2.43626	+	13.8167i	0.187405	+	1.06283i
$170$		0			0
$171$	2.76664	+	2.63175i	0.211570	+	0.201255i
$172$		0			0
$173$	10.6218	+	3.86602i	0.807561	+	0.293928i	0.712616	−	0.701554i	$-0.247510\pi$
$173$	10.6218	+	3.86602i	0.807561	+	0.293928i	0.0949449	+	0.995483i	$0.469732\pi$
$174$		0			0
$175$	−1.96763	−	1.65104i	−0.148739	−	0.124807i
$176$		0			0
$177$	7.00966	+	13.0644i	0.526879	+	0.981979i
$178$		0			0
$179$	3.46495	−	6.00147i	0.258982	−	0.448571i	−0.706987	−	0.707226i	$-0.749946\pi$
$179$	3.46495	−	6.00147i	0.258982	−	0.448571i	0.965970	+	0.258656i	$0.0832795\pi$
$180$		0			0
$181$	−1.51882	−	2.63067i	−0.112893	−	0.195536i	0.804043	−	0.594572i	$-0.202678\pi$
$181$	−1.51882	−	2.63067i	−0.112893	−	0.195536i	−0.916935	+	0.399036i	$0.869345\pi$
$182$		0			0
$183$	4.66212	−	1.53424i	0.344634	−	0.113414i
$184$		0			0
$185$	1.28883	−	7.30931i	0.0947566	−	0.537391i
$186$		0			0
$187$	−0.616070	+	0.516944i	−0.0450515	+	0.0378027i
$188$		0			0
$189$	−17.1510	+	11.8525i	−1.24755	+	0.862144i
$190$		0			0
$191$	3.90467	−	3.27640i	0.282532	−	0.237072i	−0.490498	−	0.871443i	$-0.663185\pi$
$191$	3.90467	−	3.27640i	0.282532	−	0.237072i	0.773029	+	0.634370i	$0.218741\pi$
$192$		0			0
$193$	3.27644	−	18.5816i	0.235843	−	1.33753i	−0.604987	−	0.796235i	$-0.706822\pi$
$193$	3.27644	−	18.5816i	0.235843	−	1.33753i	0.840830	−	0.541299i	$-0.182067\pi$
$194$		0			0
$195$	−3.84001	+	18.4063i	−0.274989	+	1.31810i
$196$		0			0
$197$	10.0220	+	17.3586i	0.714036	+	1.23675i	0.963330	+	0.268319i	$0.0864682\pi$
$197$	10.0220	+	17.3586i	0.714036	+	1.23675i	−0.249294	+	0.968428i	$0.580199\pi$
$198$		0			0
$199$	2.75106	−	4.76498i	0.195018	−	0.337780i	−0.751889	−	0.659290i	$-0.770857\pi$
$199$	2.75106	−	4.76498i	0.195018	−	0.337780i	0.946906	+	0.321510i	$0.104190\pi$
$200$		0			0
$201$	−8.90466	+	14.3705i	−0.628087	+	1.01362i
$202$		0			0
$203$	28.3110	+	23.7557i	1.98704	+	1.66733i
$204$		0			0
$205$	−5.37495	−	1.95632i	−0.375403	−	0.136635i
$206$		0			0
$207$	−0.278725	−	2.47267i	−0.0193727	−	0.171862i
$208$		0			0
$209$	−0.0469552	−	0.266296i	−0.00324796	−	0.0184201i
$210$		0			0
$211$	−23.6287	+	8.60014i	−1.62667	+	0.592058i	−0.984636	−	0.174621i	$-0.944130\pi$
$211$	−23.6287	+	8.60014i	−1.62667	+	0.592058i	−0.642031	+	0.766679i	$0.721908\pi$
$212$		0			0
$213$	18.8566	+	7.53613i	1.29204	+	0.516367i
$214$		0			0
$215$	−14.4001			−0.982077
$216$		0			0
$217$	−14.1868			−0.963061
$218$		0			0
$219$	−1.02108	+	0.803963i	−0.0689982	+	0.0543268i
$220$		0			0
$221$	−18.4941	+	6.73131i	−1.24405	+	0.452797i
$222$		0			0
$223$	0.651596	+	3.69539i	0.0436341	+	0.247461i	0.998821	−	0.0485415i	$-0.0154573\pi$
$223$	0.651596	+	3.69539i	0.0436341	+	0.247461i	−0.955187	+	0.296003i	$0.904346\pi$
$224$		0			0
$225$	1.06194	−	1.60025i	0.0707963	−	0.106684i
$226$		0			0
$227$	17.5983	+	6.40524i	1.16804	+	0.425131i	0.851962	−	0.523603i	$-0.175412\pi$
$227$	17.5983	+	6.40524i	1.16804	+	0.425131i	0.316076	+	0.948734i	$0.397635\pi$
$228$		0			0
$229$	−3.17397	−	2.66328i	−0.209742	−	0.175994i	0.531865	−	0.846829i	$-0.321491\pi$
$229$	−3.17397	−	2.66328i	−0.209742	−	0.175994i	−0.741607	+	0.670835i	$0.765936\pi$
$230$		0			0
$231$	1.47565	+	0.0459697i	0.0970906	+	0.00302459i
$232$		0			0
$233$	0.958556	−	1.66027i	0.0627971	−	0.108768i	−0.832918	−	0.553397i	$-0.813331\pi$
$233$	0.958556	−	1.66027i	0.0627971	−	0.108768i	0.895715	+	0.444629i	$0.146665\pi$
$234$		0			0
$235$	−1.33348	−	2.30966i	−0.0869869	−	0.150666i
$236$		0			0
$237$	−3.05803	−	2.73269i	−0.198641	−	0.177507i
$238$		0			0
$239$	−4.20216	+	23.8316i	−0.271815	+	1.54154i	0.477085	+	0.878857i	$0.341693\pi$
$239$	−4.20216	+	23.8316i	−0.271815	+	1.54154i	−0.748900	+	0.662683i	$0.769418\pi$
$240$		0			0
$241$	10.1156	−	8.48797i	0.651601	−	0.546758i	−0.255955	−	0.966689i	$-0.582390\pi$
$241$	10.1156	−	8.48797i	0.651601	−	0.546758i	0.907556	+	0.419931i	$0.137946\pi$
$242$		0			0
$243$	−10.2430	−	11.7507i	−0.657092	−	0.753811i
$244$		0			0
$245$	14.5520	−	12.2106i	0.929695	−	0.780107i
$246$		0			0
$247$	1.14909	−	6.51684i	0.0731151	−	0.414656i
$248$		0			0
$249$	−14.7239	−	13.1575i	−0.933092	−	0.833821i
$250$		0			0
$251$	−4.32994	−	7.49967i	−0.273303	−	0.473375i	0.696402	−	0.717652i	$-0.254783\pi$
$251$	−4.32994	−	7.49967i	−0.273303	−	0.473375i	−0.969706	+	0.244276i	$0.921450\pi$
$252$		0			0
$253$	−0.0881062	+	0.152604i	−0.00553919	+	0.00959415i
$254$		0			0
$255$	−13.6839	−	0.426284i	−0.856919	−	0.0266949i
$256$		0			0
$257$	16.7233	+	14.0326i	1.04317	+	0.875326i	0.992359	−	0.123382i	$-0.0393739\pi$
$257$	16.7233	+	14.0326i	1.04317	+	0.875326i	0.0508142	+	0.998708i	$0.483818\pi$
$258$		0			0
$259$	−13.4017	−	4.87782i	−0.832741	−	0.303093i
$260$		0			0
$261$	−15.2796	+	23.0251i	−0.945786	+	1.42522i
$262$		0			0
$263$	0.987629	+	5.60112i	0.0608998	+	0.345380i	0.999998	+	0.00173240i	$0.000551441\pi$
$263$	0.987629	+	5.60112i	0.0608998	+	0.345380i	−0.939099	+	0.343648i	$0.888337\pi$
$264$		0			0
$265$	22.1702	−	8.06929i	1.36190	−	0.495692i
$266$		0			0
$267$	−7.34349	+	5.78201i	−0.449414	+	0.353854i
$268$		0			0
$269$	−22.7662			−1.38808			−0.694041	−	0.719936i	$-0.744171\pi$
$269$	−22.7662			−1.38808			−0.694041	+	0.719936i	$0.744171\pi$
$270$		0			0
$271$	19.8340			1.20483			0.602414	−	0.798184i	$-0.294206\pi$
$271$	19.8340			1.20483			0.602414	+	0.798184i	$0.294206\pi$
$272$		0			0
$273$	33.5497	+	13.4083i	2.03052	+	0.811505i
$274$		0			0
$275$	−0.127803	+	0.0465166i	−0.00770683	+	0.00280506i
$276$		0			0
$277$	−4.19132	−	23.7701i	−0.251832	−	1.42821i	−0.804076	−	0.594527i	$-0.797339\pi$
$277$	−4.19132	−	23.7701i	−0.251832	−	1.42821i	0.552244	−	0.833683i	$-0.313772\pi$
$278$		0			0
$279$	−1.18820	−	10.5410i	−0.0711358	−	0.631070i
$280$		0			0
$281$	22.2287	+	8.09058i	1.32605	+	0.482644i	0.905393	−	0.424575i	$-0.139576\pi$
$281$	22.2287	+	8.09058i	1.32605	+	0.482644i	0.420660	+	0.907219i	$0.361799\pi$
$282$		0			0
$283$	8.90462	+	7.47186i	0.529325	+	0.444156i	0.867868	−	0.496795i	$-0.165490\pi$
$283$	8.90462	+	7.47186i	0.529325	+	0.444156i	−0.338543	+	0.940951i	$0.609934\pi$
$284$		0			0
$285$	2.42460	−	3.91287i	0.143621	−	0.231779i
$286$		0			0
$287$	−5.49551	+	9.51850i	−0.324390	+	0.561859i
$288$		0			0
$289$	1.33491	+	2.31213i	0.0785239	+	0.136007i
$290$		0			0
$291$	4.44401	−	21.3014i	0.260512	−	1.24871i
$292$		0			0
$293$	−1.85993	+	10.5482i	−0.108658	+	0.616232i	0.881037	+	0.473046i	$0.156846\pi$
$293$	−1.85993	+	10.5482i	−0.108658	+	0.616232i	−0.989696	+	0.143186i	$0.954265\pi$
$294$		0			0
$295$	13.6916	−	11.4886i	0.797156	−	0.668893i
$296$		0			0
$297$	0.0894359	+	1.10028i	0.00518959	+	0.0638445i
$298$		0			0
$299$	−3.30341	+	2.77189i	−0.191041	+	0.160302i
$300$		0			0
$301$	−4.80490	+	27.2499i	−0.276950	+	1.57066i
$302$		0			0
$303$	−4.76222	+	1.56718i	−0.273582	+	0.0900323i
$304$		0			0
$305$	−2.95839	−	5.12408i	−0.169397	−	0.293404i
$306$		0			0
$307$	12.3938	−	21.4667i	0.707351	−	1.22517i	−0.258485	−	0.966015i	$-0.583223\pi$
$307$	12.3938	−	21.4667i	0.707351	−	1.22517i	0.965836	−	0.259153i	$-0.0834433\pi$
$308$		0			0
$309$	−13.6675	−	25.4730i	−0.777514	−	1.44911i
$310$		0			0
$311$	16.6871	+	14.0022i	0.946241	+	0.793990i	0.978660	−	0.205484i	$-0.0658768\pi$
$311$	16.6871	+	14.0022i	0.946241	+	0.793990i	−0.0324195	+	0.999474i	$0.510321\pi$
$312$		0			0
$313$	8.83542	+	3.21583i	0.499408	+	0.181770i	0.579428	−	0.815024i	$-0.303276\pi$
$313$	8.83542	+	3.21583i	0.499408	+	0.181770i	−0.0800199	+	0.996793i	$0.525498\pi$
$314$		0			0
$315$	18.2098	+	17.3220i	1.02601	+	0.975984i
$316$		0			0
$317$	−2.51892	−	14.2855i	−0.141477	−	0.802353i	−0.970129	−	0.242590i	$-0.922003\pi$
$317$	−2.51892	−	14.2855i	−0.141477	−	0.802353i	0.828652	−	0.559763i	$-0.189108\pi$
$318$		0			0
$319$	1.83888	−	0.669298i	0.102958	−	0.0374735i
$320$		0			0
$321$	0.0795426	+	0.550919i	0.00443963	+	0.0307493i
$322$		0			0
$323$	4.81825			0.268095
$324$		0			0
$325$	−3.32834			−0.184623
$326$		0			0
$327$	−0.140679	−	0.974356i	−0.00777957	−	0.0538820i
$328$		0			0
$329$	−4.81563	+	1.75274i	−0.265494	+	0.0966319i
$330$		0			0
$331$	−0.140089	−	0.794483i	−0.00769998	−	0.0436688i	0.980716	−	0.195440i	$-0.0626134\pi$
$331$	−0.140089	−	0.794483i	−0.00769998	−	0.0436688i	−0.988416	+	0.151771i	$0.951502\pi$
$332$		0			0
$333$	2.50183	−	10.3662i	0.137100	−	0.568063i
$334$		0			0
$335$	19.1511	+	6.97044i	1.04634	+	0.380836i
$336$		0			0
$337$	−20.4272	−	17.1404i	−1.11274	−	0.933700i	−0.114525	−	0.993420i	$-0.536535\pi$
$337$	−20.4272	−	17.1404i	−1.11274	−	0.933700i	−0.998215	+	0.0597207i	$0.980979\pi$
$338$		0			0
$339$	−1.11355	−	2.07540i	−0.0604798	−	0.112720i
$340$		0			0
$341$	−0.375596	+	0.650551i	−0.0203396	+	0.0352293i
$342$		0			0
$343$	−4.20838	−	7.28912i	−0.227231	−	0.393576i
$344$		0			0
$345$	−2.84939	+	0.937698i	−0.153406	+	0.0504839i
$346$		0			0
$347$	5.05391	−	28.6621i	0.271308	−	1.53866i	−0.479142	−	0.877737i	$-0.659052\pi$
$347$	5.05391	−	28.6621i	0.271308	−	1.53866i	0.750450	−	0.660927i	$-0.229837\pi$
$348$		0			0
$349$	−22.6355	+	18.9934i	−1.21165	+	1.01669i	−0.212430	+	0.977176i	$0.568138\pi$
$349$	−22.6355	+	18.9934i	−1.21165	+	1.01669i	−0.999219	+	0.0395179i	$0.987418\pi$
$350$		0			0
$351$	−7.15259	+	26.0509i	−0.381777	+	1.39049i
$352$		0			0
$353$	4.78974	−	4.01907i	0.254932	−	0.213913i	−0.506361	−	0.862322i	$-0.669010\pi$
$353$	4.78974	−	4.01907i	0.254932	−	0.213913i	0.761293	+	0.648408i	$0.224565\pi$
$354$		0			0
$355$	4.25094	−	24.1083i	0.225617	−	1.27954i
$356$		0			0
$357$	−5.37261	+	25.7524i	−0.284348	+	1.36296i
$358$		0			0
$359$	−1.29314	−	2.23979i	−0.0682495	−	0.118212i	0.829881	−	0.557940i	$-0.188408\pi$
$359$	−1.29314	−	2.23979i	−0.0682495	−	0.118212i	−0.898131	+	0.439728i	$0.855075\pi$
$360$		0			0
$361$	8.68998	−	15.0515i	0.457367	−	0.792183i
$362$		0			0
$363$	−9.99425	+	16.1289i	−0.524562	+	0.846549i
$364$		0			0
$365$	1.20015	+	1.00705i	0.0628190	+	0.0527114i
$366$		0			0
$367$	17.5546	+	6.38935i	0.916342	+	0.333521i	0.756782	−	0.653667i	$-0.226770\pi$
$367$	17.5546	+	6.38935i	0.916342	+	0.333521i	0.159560	+	0.987188i	$0.448993\pi$
$368$		0			0
$369$	−7.53264	−	3.28602i	−0.392134	−	0.171063i
$370$		0			0
$371$	−7.87232	−	44.6462i	−0.408711	−	2.31791i
$372$		0			0
$373$	−12.7104	+	4.62621i	−0.658120	+	0.239536i	−0.649425	−	0.760426i	$-0.724990\pi$
$373$	−12.7104	+	4.62621i	−0.658120	+	0.239536i	−0.00869564	+	0.999962i	$0.502768\pi$
$374$		0			0
$375$	−18.9413	−	7.56998i	−0.978127	−	0.390912i
$376$		0			0
$377$	47.8894			2.46643
$378$		0			0
$379$	−30.2178			−1.55218			−0.776092	−	0.630620i	$-0.782801\pi$
$379$	−30.2178			−1.55218			−0.776092	+	0.630620i	$0.782801\pi$
$380$		0			0
$381$	2.45499	−	1.93298i	0.125773	−	0.0990295i
$382$		0			0
$383$	−36.2619	+	13.1982i	−1.85289	+	0.674398i	−0.869224	+	0.494419i	$0.835381\pi$
$383$	−36.2619	+	13.1982i	−1.85289	+	0.674398i	−0.983670	+	0.179980i	$0.942397\pi$
$384$		0			0
$385$	−0.309056	−	1.75274i	−0.0157510	−	0.0893281i
$386$		0			0
$387$	−20.6495	−	1.28780i	−1.04967	−	0.0654627i
$388$		0			0
$389$	5.28688	+	1.92427i	0.268056	+	0.0975642i	0.472551	−	0.881303i	$-0.343333\pi$
$389$	5.28688	+	1.92427i	0.268056	+	0.0975642i	−0.204496	+	0.978867i	$0.565555\pi$
$390$		0			0
$391$	−2.40528	−	2.01827i	−0.121640	−	0.102068i
$392$		0			0
$393$	−16.8177	−	0.523909i	−0.848342	−	0.0264277i
$394$		0			0
$395$	−2.47198	+	4.28160i	−0.124379	+	0.215431i
$396$		0			0
$397$	−3.85809	−	6.68240i	−0.193632	−	0.335380i	0.752819	−	0.658227i	$-0.228693\pi$
$397$	−3.85809	−	6.68240i	−0.193632	−	0.335380i	−0.946451	+	0.322847i	$0.895360\pi$
$398$		0			0
$399$	−6.59549	−	5.89380i	−0.330187	−	0.295059i
$400$		0			0
$401$	6.31721	−	35.8267i	0.315466	−	1.78910i	−0.254126	−	0.967171i	$-0.581788\pi$
$401$	6.31721	−	35.8267i	0.315466	−	1.78910i	0.569593	−	0.821927i	$-0.307101\pi$
$402$		0			0
$403$	−14.0824	+	11.8165i	−0.701494	+	0.588623i
$404$		0			0
$405$	−11.3453	+	14.9809i	−0.563753	+	0.744409i
$406$		0			0
$407$	−0.578489	+	0.485410i	−0.0286746	+	0.0240609i
$408$		0			0
$409$	1.01891	−	5.77853i	0.0503819	−	0.285730i	−0.949199	−	0.314676i	$-0.898104\pi$
$409$	1.01891	−	5.77853i	0.0503819	−	0.285730i	0.999581	+	0.0289462i	$0.00921516\pi$
$410$		0			0
$411$	11.7114	+	10.4654i	0.577680	+	0.516221i
$412$		0			0
$413$	−17.1719	−	29.7427i	−0.844976	−	1.46354i
$414$		0			0
$415$	−11.9022	+	20.6152i	−0.584256	+	1.01196i
$416$		0			0
$417$	−17.3829	−	0.541514i	−0.851243	−	0.0265181i
$418$		0			0
$419$	−16.1908	−	13.5857i	−0.790972	−	0.663704i	0.155014	−	0.987912i	$-0.450458\pi$
$419$	−16.1908	−	13.5857i	−0.790972	−	0.663704i	−0.945986	+	0.324208i	$0.894902\pi$
$420$		0			0
$421$	−6.99405	−	2.54563i	−0.340869	−	0.124066i	0.165913	−	0.986140i	$-0.446943\pi$
$421$	−6.99405	−	2.54563i	−0.340869	−	0.124066i	−0.506782	+	0.862074i	$0.669165\pi$
$422$		0			0
$423$	−1.70564	−	3.43127i	−0.0829311	−	0.166834i
$424$		0			0
$425$	−0.420826	−	2.38662i	−0.0204130	−	0.115768i
$426$		0			0
$427$	−10.6837	+	3.88853i	−0.517018	+	0.188179i
$428$		0			0
$429$	1.50308	−	1.18348i	0.0725695	−	0.0571387i
$430$		0			0
$431$	13.0502			0.628607			0.314303	−	0.949323i	$-0.398229\pi$
$431$	13.0502			0.628607			0.314303	+	0.949323i	$0.398229\pi$
$432$		0			0
$433$	0.143533			0.00689775			0.00344887	−	0.999994i	$-0.498902\pi$
$433$	0.143533			0.00689775			0.00344887	+	0.999994i	$0.498902\pi$
$434$		0			0
$435$	30.9339	+	12.3629i	1.48317	+	0.592754i
$436$		0			0
$437$	0.992054	−	0.361078i	0.0474564	−	0.0172727i
$438$		0			0
$439$	−2.35406	−	13.3506i	−0.112353	−	0.637187i	−0.988027	−	0.154283i	$-0.950693\pi$
$439$	−2.35406	−	13.3506i	−0.112353	−	0.637187i	0.875673	−	0.482904i	$-0.160418\pi$
$440$		0			0
$441$	21.9594	−	16.2084i	1.04569	−	0.771830i
$442$		0			0
$443$	11.5406	+	4.20044i	0.548311	+	0.199569i	0.601296	−	0.799026i	$-0.294651\pi$
$443$	11.5406	+	4.20044i	0.548311	+	0.199569i	−0.0529847	+	0.998595i	$0.516873\pi$
$444$		0			0
$445$	8.63138	+	7.24258i	0.409166	+	0.343331i
$446$		0			0
$447$	14.4532	−	23.3249i	0.683614	−	1.10323i
$448$		0			0
$449$	−20.3323	+	35.2165i	−0.959540	+	1.66197i	−0.235920	+	0.971772i	$0.575810\pi$
$449$	−20.3323	+	35.2165i	−0.959540	+	1.66197i	−0.723620	+	0.690199i	$0.757523\pi$
$450$		0			0
$451$	0.290988	+	0.504006i	0.0137021	+	0.0237327i
$452$		0			0
$453$	1.87746	−	8.99919i	0.0882106	−	0.422819i
$454$		0			0
$455$	7.56327	−	42.8934i	0.354571	−	2.01087i
$456$		0			0
$457$	24.9661	−	20.9491i	1.16787	−	0.979956i	0.167884	−	0.985807i	$-0.446307\pi$
$457$	24.9661	−	20.9491i	1.16787	−	0.979956i	0.999983	+	0.00585037i	$0.00186224\pi$
$458$		0			0
$459$	−19.5844	−	1.83504i	−0.914120	−	0.0856523i
$460$		0			0
$461$	−20.9287	+	17.5612i	−0.974745	+	0.817909i	−0.983288	−	0.182055i	$-0.941725\pi$
$461$	−20.9287	+	17.5612i	−0.974745	+	0.817909i	0.00854291	+	0.999964i	$0.497281\pi$
$462$		0			0
$463$	0.590262	−	3.34754i	0.0274318	−	0.155574i	−0.968015	−	0.250892i	$-0.919276\pi$
$463$	0.590262	−	3.34754i	0.0274318	−	0.155574i	0.995447	+	0.0953189i	$0.0303871\pi$
$464$		0			0
$465$	−12.1469	+	3.99740i	−0.563301	+	0.185375i
$466$		0			0
$467$	16.4988	+	28.5767i	0.763473	+	1.32237i	0.941050	+	0.338267i	$0.109841\pi$
$467$	16.4988	+	28.5767i	0.763473	+	1.32237i	−0.177577	+	0.984107i	$0.556826\pi$
$468$		0			0
$469$	19.5807	−	33.9147i	0.904152	−	1.56604i
$470$		0			0
$471$	−9.43130	−	17.5777i	−0.434571	−	0.809939i
$472$		0			0
$473$	1.12237	+	0.941778i	0.0516065	+	0.0433030i
$474$		0			0
$475$	0.765694	+	0.278690i	0.0351324	+	0.0127872i
$476$		0			0
$477$	32.5133	−	9.58855i	1.48868	−	0.439029i
$478$		0			0
$479$	4.00142	+	22.6932i	0.182830	+	1.03688i	0.928712	+	0.370801i	$0.120917\pi$
$479$	4.00142	+	22.6932i	0.182830	+	1.03688i	−0.745883	+	0.666077i	$0.767972\pi$
$480$		0			0
$481$	−17.3660	+	6.32070i	−0.791820	+	0.288199i
$482$		0			0
$483$	0.823686	+	5.70492i	0.0374790	+	0.259583i
$484$		0			0
$485$	−26.2321			−1.19114
$486$		0			0
$487$	−26.9315			−1.22038			−0.610192	−	0.792254i	$-0.708908\pi$
$487$	−26.9315			−1.22038			−0.610192	+	0.792254i	$0.708908\pi$
$488$		0			0
$489$	1.89676	+	13.1371i	0.0857743	+	0.594080i
$490$		0			0
$491$	−0.233037	+	0.0848187i	−0.0105168	+	0.00382781i	−0.347273	−	0.937764i	$-0.612892\pi$
$491$	−0.233037	+	0.0848187i	−0.0105168	+	0.00382781i	0.336756	+	0.941592i	$0.390670\pi$
$492$		0			0
$493$	6.05500	+	34.3396i	0.272703	+	1.54658i
$494$		0			0
$495$	1.27643	−	0.376433i	0.0573711	−	0.0169194i
$496$		0			0
$497$	−44.2028	−	16.0885i	−1.98277	−	0.721668i
$498$		0			0
$499$	20.4674	+	17.1742i	0.916247	+	0.768822i	0.973297	−	0.229549i	$-0.0737252\pi$
$499$	20.4674	+	17.1742i	0.916247	+	0.768822i	−0.0570505	+	0.998371i	$0.518170\pi$
$500$		0			0
$501$	−5.00347	−	9.32530i	−0.223539	−	0.416624i
$502$		0			0
$503$	13.0871	−	22.6676i	0.583527	−	1.01070i	−0.411530	−	0.911396i	$-0.635006\pi$
$503$	13.0871	−	22.6676i	0.583527	−	1.01070i	0.995057	−	0.0993022i	$-0.0316611\pi$
$504$		0			0
$505$	3.02190	+	5.23409i	0.134473	+	0.232914i
$506$		0			0
$507$	23.0827	−	7.59621i	1.02514	−	0.337359i
$508$		0			0
$509$	0.947739	−	5.37490i	0.0420078	−	0.238238i	−0.956573	−	0.291492i	$-0.905848\pi$
$509$	0.947739	−	5.37490i	0.0420078	−	0.238238i	0.998581	+	0.0532542i	$0.0169594\pi$
$510$		0			0
$511$	2.30614	−	1.93508i	0.102018	−	0.0856031i
$512$		0			0
$513$	3.82677	−	5.39417i	0.168956	−	0.238158i
$514$		0			0
$515$	−26.6959	+	22.4005i	−1.17636	+	0.987086i
$516$		0			0
$517$	−0.0471199	+	0.267230i	−0.00207233	+	0.0117528i
$518$		0			0
$519$	3.99842	−	19.1656i	0.175511	−	0.841275i
$520$		0			0
$521$	13.0596	+	22.6199i	0.572151	+	0.990995i	0.996345	+	0.0854234i	$0.0272243\pi$
$521$	13.0596	+	22.6199i	0.572151	+	0.990995i	−0.424194	+	0.905572i	$0.639442\pi$
$522$		0			0
$523$	3.70382	−	6.41521i	0.161957	−	0.280518i	−0.773614	−	0.633658i	$-0.781553\pi$
$523$	3.70382	−	6.41521i	0.161957	−	0.280518i	0.935570	+	0.353140i	$0.114886\pi$
$524$		0			0
$525$	−2.34332	+	3.78170i	−0.102271	+	0.165047i
$526$		0			0
$527$	−10.2537	−	8.60387i	−0.446658	−	0.374791i
$528$		0			0
$529$	20.9664	+	7.63116i	0.911585	+	0.331790i
$530$		0			0
$531$	20.6610	−	15.2501i	0.896610	−	0.661796i
$532$		0			0
$533$	2.47313	+	14.0258i	0.107123	+	0.607526i
$534$		0			0
$535$	0.630560	−	0.229505i	0.0272615	−	0.00992238i
$536$		0			0
$537$	−11.1458	−	4.45445i	−0.480976	−	0.192224i
$538$		0			0
$539$	−1.93280			−0.0832514
$540$		0			0
$541$	11.3209			0.486725			0.243362	−	0.969935i	$-0.421750\pi$
$541$	11.3209			0.486725			0.243362	+	0.969935i	$0.421750\pi$
$542$		0			0
$543$	−4.13376	+	3.25479i	−0.177397	+	0.139676i
$544$		0			0
$545$	−1.11521	+	0.405903i	−0.0477704	+	0.0173870i
$546$		0			0
$547$	1.84721	+	10.4761i	0.0789811	+	0.447924i	0.998494	+	0.0548639i	$0.0174725\pi$
$547$	1.84721	+	10.4761i	0.0789811	+	0.447924i	−0.919513	+	0.393060i	$0.871416\pi$
$548$		0			0
$549$	−3.78403	−	7.61241i	−0.161499	−	0.324890i
$550$		0			0
$551$	−11.0171	−	4.00989i	−0.469344	−	0.170827i
$552$		0			0
$553$	7.27744	+	6.10650i	0.309468	+	0.259675i
$554$		0			0
$555$	−12.8492	−	0.400280i	−0.545417	−	0.0169909i
$556$		0			0
$557$	5.92385	−	10.2604i	0.251001	−	0.434747i	−0.712800	−	0.701367i	$-0.752573\pi$
$557$	5.92385	−	10.2604i	0.251001	−	0.434747i	0.963802	+	0.266620i	$0.0859068\pi$
$558$		0			0
$559$	17.9276	+	31.0516i	0.758258	+	1.31334i
$560$		0			0
$561$	1.03867	+	0.928164i	0.0438526	+	0.0391871i
$562$		0			0
$563$	−1.04327	+	5.91667i	−0.0439686	+	0.249358i	−0.998868	−	0.0475719i	$-0.984852\pi$
$563$	−1.04327	+	5.91667i	−0.0439686	+	0.249358i	0.954899	+	0.296930i	$0.0959628\pi$
$564$		0			0
$565$	−2.17504	+	1.82508i	−0.0915047	+	0.0767815i
$566$		0			0
$567$	24.5635	+	26.4680i	1.03157	+	1.11155i
$568$		0			0
$569$	−22.3596	+	18.7619i	−0.937363	+	0.786541i	−0.977124	−	0.212669i	$-0.931785\pi$
$569$	−22.3596	+	18.7619i	−0.937363	+	0.786541i	0.0397618	+	0.999209i	$0.487340\pi$
$570$		0			0
$571$	−3.78797	+	21.4826i	−0.158522	+	0.899021i	0.796974	+	0.604014i	$0.206433\pi$
$571$	−3.78797	+	21.4826i	−0.158522	+	0.899021i	−0.955495	+	0.295007i	$0.904678\pi$
$572$		0			0
$573$	−6.58310	−	5.88273i	−0.275013	−	0.245755i
$574$		0			0
$575$	−0.265499	−	0.459857i	−0.0110721	−	0.0191774i
$576$		0			0
$577$	−20.0399	+	34.7102i	−0.834273	+	1.44500i	0.0603476	+	0.998177i	$0.480779\pi$
$577$	−20.0399	+	34.7102i	−0.834273	+	1.44500i	−0.894621	+	0.446826i	$0.852554\pi$
$578$		0			0
$579$	−32.6649	−	1.01758i	−1.35751	−	0.0422894i
$580$		0			0
$581$	35.0397	+	29.4018i	1.45369	+	1.21979i
$582$		0			0
$583$	−2.25572	−	0.821016i	−0.0934224	−	0.0340030i
$584$		0			0
$585$	32.5038	+	2.02710i	1.34387	+	0.0838102i
$586$		0			0
$587$	4.66518	+	26.4576i	0.192553	+	1.09202i	0.915861	+	0.401495i	$0.131509\pi$
$587$	4.66518	+	26.4576i	0.192553	+	1.09202i	−0.723309	+	0.690525i	$0.757380\pi$
$588$		0			0
$589$	4.22912	−	1.53927i	0.174258	−	0.0634246i
$590$		0			0
$591$	27.2768	−	21.4768i	1.12202	−	0.883439i
$592$		0			0
$593$	30.4609			1.25088			0.625440	−	0.780272i	$-0.284919\pi$
$593$	30.4609			1.25088			0.625440	+	0.780272i	$0.284919\pi$
$594$		0			0
$595$	31.7134			1.30012
$596$		0			0
$597$	−8.84940	−	3.53670i	−0.362182	−	0.144747i
$598$		0			0
$599$	−27.4285	+	9.98317i	−1.12070	+	0.407901i	−0.834908	−	0.550390i	$-0.814479\pi$
$599$	−27.4285	+	9.98317i	−1.12070	+	0.407901i	−0.285792	+	0.958292i	$0.592257\pi$
$600$		0			0
$601$	−4.03243	−	22.8690i	−0.164486	−	0.932847i	−0.949593	−	0.313487i	$-0.898503\pi$
$601$	−4.03243	−	22.8690i	−0.164486	−	0.932847i	0.785106	−	0.619361i	$-0.212608\pi$
$602$		0			0
$603$	26.8390	+	11.7082i	1.09297	+	0.476794i
$604$		0			0
$605$	21.4945	+	7.82335i	0.873875	+	0.318064i
$606$		0			0
$607$	−32.6881	−	27.4286i	−1.32677	−	1.11329i	−0.984821	−	0.173574i	$-0.944468\pi$
$607$	−32.6881	−	27.4286i	−1.32677	−	1.11329i	−0.341950	−	0.939718i	$-0.611087\pi$
$608$		0			0
$609$	33.7166	−	54.4126i	1.36627	−	2.20491i
$610$		0			0
$611$	−3.32029	+	5.75091i	−0.134325	+	0.232657i
$612$		0			0
$613$	6.80411	+	11.7851i	0.274815	+	0.475994i	0.970089	−	0.242752i	$-0.0780500\pi$
$613$	6.80411	+	11.7851i	0.274815	+	0.475994i	−0.695273	+	0.718746i	$0.744717\pi$
$614$		0			0
$615$	−2.02332	+	9.69835i	−0.0815882	+	0.391075i
$616$		0			0
$617$	4.88447	−	27.7012i	0.196641	−	1.11521i	−0.713421	−	0.700736i	$-0.752855\pi$
$617$	4.88447	−	27.7012i	0.196641	−	1.11521i	0.910062	−	0.414472i	$-0.136034\pi$
$618$		0			0
$619$	14.9355	−	12.5323i	0.600307	−	0.503717i	−0.291237	−	0.956651i	$-0.594067\pi$
$619$	14.9355	−	12.5323i	0.600307	−	0.503717i	0.891544	+	0.452934i	$0.149623\pi$
$620$		0			0
$621$	−4.16984	+	1.08982i	−0.167330	+	0.0437330i
$622$		0			0
$623$	16.5855	−	13.9169i	0.664485	−	0.557569i
$624$		0			0
$625$	−3.71420	+	21.0643i	−0.148568	+	0.842571i
$626$		0			0
$627$	−0.444883	+	0.146405i	−0.0177669	+	0.00584686i
$628$		0			0
$629$	−6.72802	−	11.6533i	−0.268264	−	0.464646i
$630$		0			0
$631$	6.27471	−	10.8681i	0.249792	−	0.432653i	−0.713676	−	0.700476i	$-0.752971\pi$
$631$	6.27471	−	10.8681i	0.249792	−	0.432653i	0.963468	+	0.267823i	$0.0863044\pi$
$632$		0			0
$633$	20.5913	+	38.3775i	0.818433	+	1.52537i
$634$		0			0
$635$	−2.88555	−	2.42126i	−0.114509	−	0.0960848i
$636$		0			0
$637$	−44.4471	−	16.1774i	−1.76106	−	0.640973i
$638$		0			0
$639$	8.25180	−	34.1908i	0.326436	−	1.35257i
$640$		0			0
$641$	−2.42288	−	13.7409i	−0.0956981	−	0.542731i	−0.994531	−	0.104440i	$-0.966695\pi$
$641$	−2.42288	−	13.7409i	−0.0956981	−	0.542731i	0.898833	−	0.438291i	$-0.144416\pi$
$642$		0			0
$643$	38.5754	−	14.0403i	1.52127	−	0.553695i	0.559802	−	0.828627i	$-0.310877\pi$
$643$	38.5754	−	14.0403i	1.52127	−	0.553695i	0.961464	+	0.274931i	$0.0886550\pi$
$644$		0			0
$645$	3.56416	+	24.6857i	0.140339	+	0.971998i
$646$		0			0
$647$	−0.303995			−0.0119513			−0.00597563	−	0.999982i	$-0.501902\pi$
$647$	−0.303995			−0.0119513			−0.00597563	+	0.999982i	$0.501902\pi$
$648$		0			0
$649$	−1.81851			−0.0713829
$650$		0			0
$651$	3.51137	+	24.3200i	0.137621	+	0.953177i
$652$		0			0
$653$	−44.2755	+	16.1150i	−1.73263	+	0.630627i	−0.998813	−	0.0487170i	$-0.984487\pi$
$653$	−44.2755	+	16.1150i	−1.73263	+	0.630627i	−0.733820	+	0.679344i	$0.762265\pi$
$654$		0			0
$655$	3.52226	+	19.9757i	0.137626	+	0.780516i
$656$		0			0
$657$	1.63094	+	1.55142i	0.0636291	+	0.0605268i
$658$		0			0
$659$	−40.3746	−	14.6952i	−1.57277	−	0.572442i	−0.599156	−	0.800633i	$-0.704497\pi$
$659$	−40.3746	−	14.6952i	−1.57277	−	0.572442i	−0.973617	+	0.228190i	$0.926719\pi$
$660$		0			0
$661$	21.0863	+	17.6935i	0.820161	+	0.688197i	0.953010	−	0.302939i	$-0.0979680\pi$
$661$	21.0863	+	17.6935i	0.820161	+	0.688197i	−0.132849	+	0.991136i	$0.542412\pi$
$662$		0			0
$663$	16.1168	+	30.0380i	0.625925	+	1.16658i
$664$		0			0
$665$	−5.33151	+	9.23445i	−0.206747	+	0.358097i
$666$		0			0
$667$	3.82009	+	6.61659i	0.147915	+	0.256196i
$668$		0			0
$669$	6.17363	−	2.03166i	0.238686	−	0.0785485i
$670$		0			0
$671$	−0.104537	+	0.592861i	−0.00403562	+	0.0228871i
$672$		0			0
$673$	−25.7719	+	21.6252i	−0.993433	+	0.833589i	−0.986061	−	0.166384i	$-0.946791\pi$
$673$	−25.7719	+	21.6252i	−0.993433	+	0.833589i	−0.00737169	+	0.999973i	$0.502347\pi$
$674$		0			0
$675$	−3.00612	−	1.42439i	−0.115706	−	0.0548246i
$676$		0			0
$677$	26.1138	−	21.9120i	1.00363	−	0.842148i	0.0161497	−	0.999870i	$-0.494859\pi$
$677$	26.1138	−	21.9120i	1.00363	−	0.842148i	0.987484	+	0.157721i	$0.0504147\pi$
$678$		0			0
$679$	−8.75290	+	49.6402i	−0.335906	+	1.90502i
$680$		0			0
$681$	6.62461	−	31.7536i	0.253855	−	1.21680i
$682$		0			0
$683$	−8.22650	−	14.2487i	−0.314778	−	0.545212i	0.664612	−	0.747189i	$-0.268597\pi$
$683$	−8.22650	−	14.2487i	−0.314778	−	0.545212i	−0.979390	+	0.201976i	$0.935264\pi$
$684$		0			0
$685$	9.46699	−	16.3973i	0.361715	−	0.626509i
$686$		0			0
$687$	−3.78000	+	6.10025i	−0.144216	+	0.232739i
$688$		0			0
$689$	−45.0014	−	37.7606i	−1.71442	−	1.43857i
$690$		0			0
$691$	−13.4086	−	4.88033i	−0.510087	−	0.185657i	0.0741383	−	0.997248i	$-0.476379\pi$
$691$	−13.4086	−	4.88033i	−0.510087	−	0.185657i	−0.584225	+	0.811591i	$0.698602\pi$
$692$		0			0
$693$	−0.286433	−	2.54105i	−0.0108807	−	0.0965264i
$694$		0			0
$695$	3.64062	+	20.6470i	0.138097	+	0.783185i
$696$		0			0
$697$	−9.74465	+	3.54676i	−0.369105	+	0.134343i
$698$		0			0
$699$	−3.08341	−	1.23230i	−0.116625	−	0.0466097i
$700$		0			0
$701$	15.8891			0.600123			0.300062	−	0.953920i	$-0.402993\pi$
$701$	15.8891			0.600123			0.300062	+	0.953920i	$0.402993\pi$
$702$		0			0
$703$	4.52433			0.170638
$704$		0			0
$705$	−3.62935	+	2.85762i	−0.136689	+	0.107624i
$706$		0			0
$707$	10.9130	−	3.97202i	0.410427	−	0.149383i
$708$		0			0
$709$	−1.43117	−	8.11659i	−0.0537488	−	0.304825i	0.946068	−	0.323968i	$-0.105017\pi$
$709$	−1.43117	−	8.11659i	−0.0537488	−	0.304825i	−0.999817	+	0.0191436i	$0.993906\pi$
$710$		0			0
$711$	−3.92769	+	5.91868i	−0.147300	+	0.221968i
$712$		0			0
$713$	−2.75596	−	1.00309i	−0.103211	−	0.0375659i
$714$		0			0
$715$	−1.76669	−	1.48243i	−0.0660704	−	0.0554397i
$716$		0			0
$717$	41.8940	+	1.30509i	1.56456	+	0.0487395i
$718$		0			0
$719$	10.9348	−	18.9397i	0.407801	−	0.706331i	−0.586842	−	0.809701i	$-0.699629\pi$
$719$	10.9348	−	18.9397i	0.407801	−	0.706331i	0.994643	+	0.103370i	$0.0329625\pi$
$720$		0			0
$721$	33.4819	+	57.9923i	1.24693	+	2.15975i
$722$		0			0
$723$	−17.0544	−	15.2400i	−0.634261	−	0.566782i
$724$		0			0
$725$	−1.02399	+	5.80731i	−0.0380299	+	0.215678i
$726$		0			0
$727$	−37.2742	+	31.2768i	−1.38242	+	1.15999i	−0.414119	+	0.910223i	$0.635910\pi$
$727$	−37.2742	+	31.2768i	−1.38242	+	1.15999i	−0.968305	+	0.249769i	$0.919645\pi$
$728$		0			0
$729$	−17.6088	+	20.4678i	−0.652176	+	0.758067i
$730$		0			0
$731$	−19.9991	+	16.7812i	−0.739694	+	0.620677i
$732$		0			0
$733$	−4.54580	+	25.7805i	−0.167903	+	0.952226i	0.778117	+	0.628119i	$0.216175\pi$
$733$	−4.54580	+	25.7805i	−0.167903	+	0.952226i	−0.946020	+	0.324107i	$0.894936\pi$
$734$		0			0
$735$	−24.5341	−	21.9239i	−0.904954	−	0.808677i
$736$		0			0
$737$	−1.03680	−	1.79579i	−0.0381910	−	0.0661487i
$738$		0			0
$739$	1.28655	−	2.22838i	0.0473267	−	0.0819722i	−0.841392	−	0.540426i	$-0.818263\pi$
$739$	1.28655	−	2.22838i	0.0473267	−	0.0819722i	0.888718	+	0.458454i	$0.151596\pi$
$740$		0			0
$741$	−11.4561	−	0.356882i	−0.420849	−	0.0131104i
$742$		0			0
$743$	37.5339	+	31.4947i	1.37699	+	1.15543i	0.970313	+	0.241854i	$0.0777555\pi$
$743$	37.5339	+	31.4947i	1.37699	+	1.15543i	0.406673	+	0.913574i	$0.366689\pi$
$744$		0			0
$745$	−31.0843	−	11.3138i	−1.13884	−	0.414505i
$746$		0			0
$747$	−18.9112	+	28.4975i	−0.691925	+	1.04267i
$748$		0			0
$749$	−0.223903	−	1.26982i	−0.00818124	−	0.0463981i
$750$		0			0
$751$	7.99761	−	2.91089i	0.291837	−	0.106220i	−0.191953	−	0.981404i	$-0.561482\pi$
$751$	7.99761	−	2.91089i	0.291837	−	0.106220i	0.483790	+	0.875184i	$0.339260\pi$
$752$		0			0
$753$	−11.7848	+	9.27895i	−0.429462	+	0.338144i
$754$		0			0
$755$	−11.0822			−0.403324
$756$		0			0
$757$	17.3242			0.629658			0.314829	−	0.949148i	$-0.398053\pi$
$757$	17.3242			0.629658			0.314829	+	0.949148i	$0.398053\pi$
$758$		0			0
$759$	0.283413	+	0.113267i	0.0102872	+	0.00411134i
$760$		0			0
$761$	−9.81674	+	3.57300i	−0.355856	+	0.129521i	−0.513761	−	0.857933i	$-0.671748\pi$
$761$	−9.81674	+	3.57300i	−0.355856	+	0.129521i	0.157905	+	0.987454i	$0.449526\pi$
$762$		0			0
$763$	0.395996	+	2.24580i	0.0143360	+	0.0813035i
$764$		0			0
$765$	2.65613	+	23.5635i	0.0960327	+	0.851939i
$766$		0			0
$767$	−41.8191	−	15.2209i	−1.51000	−	0.549595i
$768$		0			0
$769$	30.2202	+	25.3577i	1.08977	+	0.914423i	0.996695	−	0.0812363i	$-0.0258868\pi$
$769$	30.2202	+	25.3577i	1.08977	+	0.914423i	0.0930721	+	0.995659i	$0.470331\pi$
$770$		0			0
$771$	19.9165	−	32.1416i	0.717274	−	1.15755i
$772$		0			0
$773$	11.6713	−	20.2152i	0.419786	−	0.727091i	−0.576131	−	0.817357i	$-0.695438\pi$
$773$	11.6713	−	20.2152i	0.419786	−	0.727091i	0.995918	+	0.0902659i	$0.0287717\pi$
$774$		0			0
$775$	−1.13182	−	1.96037i	−0.0406561	−	0.0704184i
$776$		0			0
$777$	−5.04487	+	24.1815i	−0.180984	+	0.867507i
$778$		0			0
$779$	0.605464	−	3.43376i	0.0216930	−	0.123027i
$780$		0			0
$781$	−1.90803	+	1.60103i	−0.0682747	+	0.0572893i
$782$		0			0
$783$	43.2532	+	20.4946i	1.54574	+	0.732417i
$784$		0			0
$785$	−18.4216	+	15.4576i	−0.657497	+	0.551705i
$786$		0			0
$787$	−6.57945	+	37.3139i	−0.234532	+	1.33010i	0.609065	+	0.793120i	$0.291545\pi$
$787$	−6.57945	+	37.3139i	−0.234532	+	1.33010i	−0.843597	+	0.536977i	$0.819566\pi$
$788$		0			0
$789$	9.35742	−	3.07940i	0.333133	−	0.109630i
$790$		0			0
$791$	2.72793	+	4.72491i	0.0969939	+	0.167998i
$792$		0			0
$793$	−7.36619	+	12.7586i	−0.261581	+	0.453072i
$794$		0			0
$795$	−19.3203	−	36.0086i	−0.685221	−	1.27709i
$796$		0			0
$797$	−2.07175	−	1.73841i	−0.0733853	−	0.0615776i	0.605357	−	0.795954i	$-0.293030\pi$
$797$	−2.07175	−	1.73841i	−0.0733853	−	0.0615776i	−0.678742	+	0.734376i	$0.737475\pi$
$798$		0			0
$799$	−4.54355	−	1.65372i	−0.160739	−	0.0585043i
$800$		0			0
$801$	11.7295	+	11.1577i	0.414443	+	0.394236i
$802$		0			0
$803$	−0.0276802	−	0.156982i	−0.000976814	−	0.00553979i
$804$		0			0
$805$	6.52964	−	2.37659i	0.230139	−	0.0837639i
$806$		0			0
$807$	5.63487	+	39.0276i	0.198357	+	1.37384i
$808$		0			0
$809$	−22.3977			−0.787460			−0.393730	−	0.919226i	$-0.628815\pi$
$809$	−22.3977			−0.787460			−0.393730	+	0.919226i	$0.628815\pi$
$810$		0			0
$811$	35.0916			1.23223			0.616117	−	0.787655i	$-0.288705\pi$
$811$	35.0916			1.23223			0.616117	+	0.787655i	$0.288705\pi$
$812$		0			0
$813$	−4.90910	−	34.0009i	−0.172170	−	1.19246i
$814$		0			0
$815$	15.0362	−	5.47274i	0.526696	−	0.191702i
$816$		0			0
$817$	−1.52428	−	8.64462i	−0.0533278	−	0.302437i
$818$		0			0
$819$	14.6816	−	60.8321i	0.513016	−	2.12565i
$820$		0			0
$821$	−13.3135	−	4.84571i	−0.464644	−	0.169117i	0.0990807	−	0.995079i	$-0.468410\pi$
$821$	−13.3135	−	4.84571i	−0.464644	−	0.169117i	−0.563724	+	0.825963i	$0.690632\pi$
$822$		0			0
$823$	26.5050	+	22.2404i	0.923907	+	0.775250i	0.974713	−	0.223458i	$-0.0717347\pi$
$823$	26.5050	+	22.2404i	0.923907	+	0.775250i	−0.0508063	+	0.998709i	$0.516179\pi$
$824$		0			0
$825$	0.111375	+	0.207577i	0.00387757	+	0.00722689i
$826$		0			0
$827$	25.3847	−	43.9676i	0.882713	−	1.52890i	0.0344011	−	0.999408i	$-0.489048\pi$
$827$	25.3847	−	43.9676i	0.882713	−	1.52890i	0.848312	−	0.529496i	$-0.177619\pi$
$828$		0			0
$829$	−27.2911	−	47.2695i	−0.947859	−	1.64174i	−0.749924	−	0.661524i	$-0.769910\pi$
$829$	−27.2911	−	47.2695i	−0.947859	−	1.64174i	−0.197935	−	0.980215i	$-0.563423\pi$
$830$		0			0
$831$	−39.7112	+	13.0684i	−1.37757	+	0.453338i
$832$		0			0
$833$	5.98042	−	33.9167i	0.207209	−	1.17514i
$834$		0			0
$835$	−9.77302	+	8.20053i	−0.338209	+	0.283791i
$836$		0			0
$837$	−17.7760	+	4.64590i	−0.614429	+	0.160586i
$838$		0			0
$839$	8.48661	−	7.12111i	0.292990	−	0.245848i	−0.484429	−	0.874830i	$-0.660973\pi$
$839$	8.48661	−	7.12111i	0.292990	−	0.245848i	0.777420	+	0.628982i	$0.216528\pi$
$840$		0			0
$841$	9.69769	−	54.9984i	0.334403	−	1.89650i
$842$		0			0
$843$	8.36766	−	40.1086i	0.288198	−	1.38141i
$844$		0			0
$845$	−14.6473	−	25.3699i	−0.503883	−	0.872751i
$846$		0			0
$847$	21.9766	−	38.0646i	0.755124	−	1.30791i
$848$		0			0
$849$	10.6048	−	17.1143i	0.363957	−	0.587362i
$850$		0			0
$851$	−2.25856	−	1.89516i	−0.0774224	−	0.0649651i
$852$		0			0
$853$	23.9039	+	8.70031i	0.818454	+	0.297893i	0.717111	−	0.696959i	$-0.245464\pi$
$853$	23.9039	+	8.70031i	0.818454	+	0.297893i	0.101343	+	0.994852i	$0.467686\pi$
$854$		0			0
$855$	−7.30785	−	3.18796i	−0.249923	−	0.109026i
$856$		0			0
$857$	8.19583	+	46.4809i	0.279964	+	1.58776i	0.722738	+	0.691123i	$0.242884\pi$
$857$	8.19583	+	46.4809i	0.279964	+	1.58776i	−0.442773	+	0.896634i	$0.646005\pi$
$858$		0			0
$859$	−23.0571	+	8.39211i	−0.786699	+	0.286335i	−0.703963	−	0.710236i	$-0.748588\pi$
$859$	−23.0571	+	8.39211i	−0.786699	+	0.286335i	−0.0827360	+	0.996571i	$0.526366\pi$
$860$		0			0
$861$	17.6775	+	7.06489i	0.602448	+	0.240771i
$862$		0			0
$863$	−28.4215			−0.967479			−0.483740	−	0.875212i	$-0.660722\pi$
$863$	−28.4215			−0.967479			−0.483740	+	0.875212i	$0.660722\pi$
$864$		0			0
$865$	−23.6019			−0.802488
$866$		0			0
$867$	3.63322	−	2.86067i	0.123391	−	0.0971535i
$868$		0			0
$869$	0.472691	−	0.172045i	0.0160349	−	0.00583624i
$870$		0			0
$871$	−8.81185	−	49.9745i	−0.298578	−	1.69332i
$872$		0			0
$873$	−37.6164	−	2.34594i	−1.27312	−	0.0793982i
$874$		0			0
$875$	44.4014	+	16.1608i	1.50104	+	0.546334i
$876$		0			0
$877$	33.1323	+	27.8013i	1.11880	+	0.938784i	0.998543	−	0.0539587i	$-0.0171839\pi$
$877$	33.1323	+	27.8013i	1.11880	+	0.938784i	0.120256	+	0.992743i	$0.461628\pi$
$878$		0			0
$879$	18.5429	+	0.577651i	0.625435	+	0.0194837i
$880$		0			0
$881$	10.2218	−	17.7047i	0.344381	−	0.596485i	−0.640860	−	0.767658i	$-0.721422\pi$
$881$	10.2218	−	17.7047i	0.344381	−	0.596485i	0.985241	+	0.171173i	$0.0547555\pi$
$882$		0			0
$883$	−14.1469	−	24.5031i	−0.476080	−	0.824595i	0.523544	−	0.851999i	$-0.324609\pi$
$883$	−14.1469	−	24.5031i	−0.476080	−	0.824595i	−0.999624	+	0.0274033i	$0.991276\pi$
$884$		0			0
$885$	−23.0835	−	20.6276i	−0.775942	−	0.693390i
$886$		0			0
$887$	9.97456	−	56.5686i	0.334913	−	1.89939i	−0.0931752	−	0.995650i	$-0.529702\pi$
$887$	9.97456	−	56.5686i	0.334913	−	1.89939i	0.428088	−	0.903737i	$-0.359187\pi$
$888$		0			0
$889$	−5.54469	+	4.65255i	−0.185963	+	0.156041i
$890$		0			0
$891$	1.86404	−	0.425647i	0.0624477	−	0.0142597i
$892$		0			0
$893$	1.24538	−	1.04500i	0.0416750	−	0.0349695i
$894$		0			0
$895$	−2.51264	+	14.2499i	−0.0839885	+	0.476322i
$896$		0			0
$897$	5.56941	+	4.97688i	0.185957	+	0.166173i
$898$		0			0
$899$	16.2850	+	28.2065i	0.543136	+	0.940739i
$900$		0			0
$901$	21.3868	−	37.0430i	0.712497	−	1.23408i
$902$		0			0
$903$	47.9031	+	1.49229i	1.59412	+	0.0496602i
$904$		0			0
$905$	4.85873	+	4.07696i	0.161510	+	0.135523i
$906$		0			0
$907$	−26.7707	−	9.74375i	−0.888908	−	0.323536i	−0.143109	−	0.989707i	$-0.545710\pi$
$907$	−26.7707	−	9.74375i	−0.888908	−	0.323536i	−0.745799	+	0.666171i	$0.767932\pi$
$908$		0			0
$909$	3.86528	+	7.77586i	0.128203	+	0.257909i
$910$		0			0
$911$	3.29560	+	18.6903i	0.109188	+	0.619236i	0.989465	+	0.144775i	$0.0462459\pi$
$911$	3.29560	+	18.6903i	0.109188	+	0.619236i	−0.880277	+	0.474461i	$0.842643\pi$
$912$		0			0
$913$	2.27593	−	0.828372i	0.0753224	−	0.0274151i
$914$		0			0
$915$	−8.05185	+	6.33975i	−0.266186	+	0.209586i
$916$		0			0
$917$	38.9763			1.28711
$918$		0			0
$919$	13.1481			0.433715			0.216857	−	0.976203i	$-0.430419\pi$
$919$	13.1481			0.433715			0.216857	+	0.976203i	$0.430419\pi$
$920$		0			0
$921$	−39.8674	−	15.9332i	−1.31367	−	0.525015i
$922$		0			0
$923$	−57.2782	+	20.8475i	−1.88533	+	0.686205i
$924$		0			0
$925$	−0.395155	−	2.24103i	−0.0129926	−	0.0736848i
$926$		0			0
$927$	−40.2848	+	29.7346i	−1.32313	+	0.976612i
$928$		0			0
$929$	−25.7306	−	9.36519i	−0.844195	−	0.307262i	−0.116524	−	0.993188i	$-0.537175\pi$
$929$	−25.7306	−	9.36519i	−0.844195	−	0.307262i	−0.727671	+	0.685926i	$0.759397\pi$
$930$		0			0
$931$	8.87060	+	7.44332i	0.290722	+	0.243945i
$932$		0			0
$933$	19.8733	−	32.0720i	0.650624	−	1.04999i
$934$		0			0
$935$	0.839615	−	1.45426i	0.0274583	−	0.0475592i
$936$		0			0
$937$	−20.0466	−	34.7218i	−0.654895	−	1.13431i	−0.981920	−	0.189296i	$-0.939380\pi$
$937$	−20.0466	−	34.7218i	−0.654895	−	1.13431i	0.327025	−	0.945016i	$-0.393954\pi$
$938$		0			0
$939$	3.32596	−	15.9423i	0.108539	−	0.520257i
$940$		0			0
$941$	−0.591978	+	3.35727i	−0.0192979	+	0.109444i	−0.992935	−	0.118658i	$-0.962141\pi$
$941$	−0.591978	+	3.35727i	−0.0192979	+	0.109444i	0.973637	+	0.228102i	$0.0732519\pi$
$942$		0			0
$943$	−1.74058	+	1.46052i	−0.0566812	+	0.0475612i
$944$		0			0
$945$	25.1876	−	35.5041i	0.819351	−	1.15495i
$946$		0			0
$947$	−2.93783	+	2.46513i	−0.0954666	+	0.0801060i	−0.689272	−	0.724503i	$-0.742069\pi$
$947$	−2.93783	+	2.46513i	−0.0954666	+	0.0801060i	0.593805	+	0.804609i	$0.297625\pi$
$948$		0			0
$949$	0.677394	−	3.84169i	0.0219892	−	0.124707i
$950$		0			0
$951$	−23.8658	+	7.85392i	−0.773902	+	0.254681i
$952$		0			0
$953$	26.3964	+	45.7200i	0.855065	+	1.48102i	0.876585	+	0.481247i	$0.159816\pi$
$953$	26.3964	+	45.7200i	0.855065	+	1.48102i	−0.0215205	+	0.999768i	$0.506851\pi$
$954$		0			0
$955$	−5.32150	+	9.21711i	−0.172200	+	0.298259i
$956$		0			0
$957$	−1.60250	−	2.98669i	−0.0518015	−	0.0965460i
$958$		0			0
$959$	−27.8705	−	23.3861i	−0.899986	−	0.755178i
$960$		0			0
$961$	17.3819	+	6.32648i	0.560705	+	0.204080i
$962$		0			0
$963$	0.924738	−	0.272716i	0.0297993	−	0.00878814i
$964$		0			0
$965$	6.84126	+	38.7987i	0.220228	+	1.24898i
$966$		0			0
$967$	9.43802	−	3.43516i	0.303506	−	0.110467i	−0.185778	−	0.982592i	$-0.559480\pi$
$967$	9.43802	−	3.43516i	0.303506	−	0.110467i	0.489284	+	0.872125i	$0.337258\pi$
$968$		0			0
$969$	−1.19256	−	8.25980i	−0.0383107	−	0.265343i
$970$		0			0
$971$	−4.06174			−0.130348			−0.0651738	−	0.997874i	$-0.520760\pi$
$971$	−4.06174			−0.130348			−0.0651738	+	0.997874i	$0.520760\pi$
$972$		0			0
$973$	40.2860			1.29151
$974$		0			0
$975$	0.823798	+	5.70570i	0.0263827	+	0.182728i
$976$		0			0
$977$	−17.1297	+	6.23470i	−0.548027	+	0.199466i	−0.601170	−	0.799121i	$-0.705298\pi$
$977$	−17.1297	+	6.23470i	−0.548027	+	0.199466i	0.0531425	+	0.998587i	$0.483076\pi$
$978$		0			0
$979$	−0.199073	−	1.12900i	−0.00636240	−	0.0360830i
$980$		0			0
$981$	−1.63549	+	0.482325i	−0.0522173	+	0.0153995i
$982$		0			0
$983$	−39.5076	−	14.3796i	−1.26010	−	0.458638i	−0.376296	−	0.926500i	$-0.622802\pi$
$983$	−39.5076	−	14.3796i	−1.26010	−	0.458638i	−0.883802	+	0.467862i	$0.845025\pi$
$984$		0			0
$985$	−32.0606	−	26.9020i	−1.02153	−	0.857170i
$986$		0			0
$987$	4.19660	+	7.82149i	0.133579	+	0.248961i
$988$		0			0
$989$	−2.86014	+	4.95391i	−0.0909471	+	0.157525i
$990$		0			0
$991$	−15.9365	−	27.6029i	−0.506241	−	0.876834i	−0.999974	−	0.00722097i	$-0.997701\pi$
$991$	−15.9365	−	27.6029i	−0.506241	−	0.876834i	0.493733	−	0.869613i	$-0.335632\pi$
$992$		0			0
$993$	−1.32729	+	0.436793i	−0.0421203	+	0.0138612i
$994$		0			0
$995$	−1.99496	+	11.3140i	−0.0632445	+	0.358677i
$996$		0			0
$997$	−24.5132	+	20.5690i	−0.776342	+	0.651428i	−0.942324	−	0.334701i	$-0.891365\pi$
$997$	−24.5132	+	20.5690i	−0.776342	+	0.651428i	0.165983	+	0.986129i	$0.446920\pi$
$998$		0			0
$999$	−18.3897	−	1.72310i	−0.581825	−	0.0545165i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.u.b.49.1		12
4.3	odd	2		54.2.e.b.49.2	yes	12
12.11	even	2		162.2.e.b.37.2		12
27.16	even	9	inner	432.2.u.b.97.1		12
36.7	odd	6		486.2.e.h.433.2		12
36.11	even	6		486.2.e.e.433.1		12
36.23	even	6		486.2.e.g.271.1		12
36.31	odd	6		486.2.e.f.271.2		12
108.7	odd	18		486.2.e.f.217.2		12
108.11	even	18		162.2.e.b.127.2		12
108.23	even	18		1458.2.a.f.1.3		6
108.31	odd	18		1458.2.a.g.1.4		6
108.43	odd	18		54.2.e.b.43.2	✓	12
108.47	even	18		486.2.e.g.217.1		12
108.59	even	18		1458.2.c.g.973.4		12
108.67	odd	18		1458.2.c.f.487.3		12
108.79	odd	18		486.2.e.h.55.2		12
108.83	even	18		486.2.e.e.55.1		12
108.95	even	18		1458.2.c.g.487.4		12
108.103	odd	18		1458.2.c.f.973.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.b.43.2	✓	12	108.43	odd	18
54.2.e.b.49.2	yes	12	4.3	odd	2
162.2.e.b.37.2		12	12.11	even	2
162.2.e.b.127.2		12	108.11	even	18
432.2.u.b.49.1		12	1.1	even	1	trivial
432.2.u.b.97.1		12	27.16	even	9	inner
486.2.e.e.55.1		12	108.83	even	18
486.2.e.e.433.1		12	36.11	even	6
486.2.e.f.217.2		12	108.7	odd	18
486.2.e.f.271.2		12	36.31	odd	6
486.2.e.g.217.1		12	108.47	even	18
486.2.e.g.271.1		12	36.23	even	6
486.2.e.h.55.2		12	108.79	odd	18
486.2.e.h.433.2		12	36.7	odd	6
1458.2.a.f.1.3		6	108.23	even	18
1458.2.a.g.1.4		6	108.31	odd	18
1458.2.c.f.487.3		12	108.67	odd	18
1458.2.c.f.973.3		12	108.103	odd	18
1458.2.c.g.487.4		12	108.95	even	18
1458.2.c.g.973.4		12	108.59	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)

\(f(q)\)	\(=\)	\(q+(-0.247510 - 1.71428i) q^{3} +(-1.96209 + 0.714144i) q^{5} +(0.696712 + 3.95125i) q^{7} +(-2.87748 + 0.848600i) q^{9} +O(q^{10})\)	\(q+(-0.247510 - 1.71428i) q^{3} +(-1.96209 + 0.714144i) q^{5} +(0.696712 + 3.95125i) q^{7} +(-2.87748 + 0.848600i) q^{9} +(0.199635 + 0.0726611i) q^{11} +(3.98269 + 3.34187i) q^{13} +(1.70988 + 3.18681i) q^{15} +(-1.89276 + 3.27836i) q^{17} +(-0.636405 - 1.10229i) q^{19} +(6.60109 - 2.17233i) q^{21} +(-0.144031 + 0.816841i) q^{23} +(-0.490411 + 0.411503i) q^{25} +(2.16694 + 4.72275i) q^{27} +(7.05621 - 5.92087i) q^{29} +(-0.614003 + 3.48219i) q^{31} +(0.0751495 - 0.360213i) q^{33} +(-4.18878 - 7.25517i) q^{35} +(-1.77730 + 3.07838i) q^{37} +(4.74313 - 7.65457i) q^{39} +(2.09850 + 1.76085i) q^{41} +(6.48062 + 2.35875i) q^{43} +(5.03986 - 3.71997i) q^{45} +(0.221796 + 1.25787i) q^{47} +(-8.54912 + 3.11163i) q^{49} +(6.08849 + 2.43329i) q^{51} -11.2992 q^{53} -0.443592 q^{55} +(-1.73210 + 1.36380i) q^{57} +(-8.04363 + 2.92764i) q^{59} +(0.492064 + 2.79063i) q^{61} +(-5.35781 - 10.7784i) q^{63} +(-10.2010 - 3.71285i) q^{65} +(-7.47702 - 6.27396i) q^{67} +(1.43594 + 0.0447327i) q^{69} +(-5.86207 + 10.1534i) q^{71} +(-0.375162 - 0.649800i) q^{73} +(0.826812 + 0.738848i) q^{75} +(-0.148014 + 0.839430i) q^{77} +(1.81383 - 1.52198i) q^{79} +(7.55976 - 4.88366i) q^{81} +(8.73328 - 7.32809i) q^{83} +(1.37256 - 7.78415i) q^{85} +(-11.8965 - 10.6308i) q^{87} +(-2.69813 - 4.67329i) q^{89} +(-10.4298 + 18.0649i) q^{91} +(6.12140 + 0.190695i) q^{93} +(2.03588 + 1.70830i) q^{95} +(11.8055 + 4.29685i) q^{97} +(-0.636104 - 0.0396706i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{5} + 3 q^{7} - 12 q^{9}+O(q^{10}) \) 12 * q - 3 * q^5 + 3 * q^7 - 12 * q^9	\( 12 q - 3 q^{5} + 3 q^{7} - 12 q^{9} + 12 q^{11} + 12 q^{13} + 18 q^{15} - 6 q^{17} + 9 q^{19} + 24 q^{21} - 30 q^{23} - 9 q^{25} + 15 q^{29} + 36 q^{33} - 3 q^{35} - 15 q^{37} + 42 q^{39} - 12 q^{41} - 9 q^{43} + 18 q^{45} + 9 q^{47} - 39 q^{49} + 27 q^{51} - 12 q^{53} - 18 q^{55} + 18 q^{57} - 12 q^{59} - 36 q^{61} - 3 q^{63} - 15 q^{65} - 36 q^{67} + 18 q^{69} - 12 q^{71} - 21 q^{73} - 30 q^{75} + 3 q^{77} - 39 q^{79} - 18 q^{83} + 45 q^{85} - 27 q^{87} + 12 q^{89} + 6 q^{91} - 33 q^{93} + 15 q^{95} + 39 q^{97} - 9 q^{99}+O(q^{100}) \) 12 * q - 3 * q^5 + 3 * q^7 - 12 * q^9 + 12 * q^11 + 12 * q^13 + 18 * q^15 - 6 * q^17 + 9 * q^19 + 24 * q^21 - 30 * q^23 - 9 * q^25 + 15 * q^29 + 36 * q^33 - 3 * q^35 - 15 * q^37 + 42 * q^39 - 12 * q^41 - 9 * q^43 + 18 * q^45 + 9 * q^47 - 39 * q^49 + 27 * q^51 - 12 * q^53 - 18 * q^55 + 18 * q^57 - 12 * q^59 - 36 * q^61 - 3 * q^63 - 15 * q^65 - 36 * q^67 + 18 * q^69 - 12 * q^71 - 21 * q^73 - 30 * q^75 + 3 * q^77 - 39 * q^79 - 18 * q^83 + 45 * q^85 - 27 * q^87 + 12 * q^89 + 6 * q^91 - 33 * q^93 + 15 * q^95 + 39 * q^97 - 9 * q^99

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