LMFDB - Embedded newform 432.2.u.b.97.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [432,2,Mod(49,432)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("432.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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			97.1
Root			$0.500000 + 1.80139i$ of defining polynomial
Character	$\chi$	$=$	432.97
Dual form			432.2.u.b.49.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{9}\right)$

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	−0.136285	−	0.990670i	$-0.543516\pi$
$5$	−1.96209	−	0.714144i	−0.877475	−	0.319375i	−0.741190	+	0.671295i	$0.765738\pi$
$6$		0			0
$7$	0.696712	−	3.95125i	0.263332	−	1.49343i	−0.510410	−	0.859931i	$-0.670506\pi$
$7$	0.696712	−	3.95125i	0.263332	−	1.49343i	0.773742	−	0.633501i	$-0.218383\pi$
$8$		0			0
$9$	−2.87748	−	0.848600i	−0.959159	−	0.282867i
$10$		0			0
$11$	0.199635	−	0.0726611i	0.0601921	−	0.0219081i	−0.311749	−	0.950165i	$-0.600915\pi$
$11$	0.199635	−	0.0726611i	0.0601921	−	0.0219081i	0.371941	+	0.928256i	$0.378692\pi$
$12$		0			0
$13$	3.98269	−	3.34187i	1.10460	−	0.926868i	0.106873	−	0.994273i	$-0.465916\pi$
$13$	3.98269	−	3.34187i	1.10460	−	0.926868i	0.997726	+	0.0674046i	$0.0214718\pi$
$14$		0			0
$15$	1.70988	−	3.18681i	0.441488	−	0.822831i
$16$		0			0
$17$	−1.89276	−	3.27836i	−0.459062	−	0.795119i	0.539850	−	0.841762i	$-0.318481\pi$
$17$	−1.89276	−	3.27836i	−0.459062	−	0.795119i	−0.998912	+	0.0466426i	$0.985148\pi$
$18$		0			0
$19$	−0.636405	+	1.10229i	−0.146001	+	0.252882i	−0.929746	−	0.368201i	$-0.879974\pi$
$19$	−0.636405	+	1.10229i	−0.146001	+	0.252882i	0.783745	+	0.621083i	$0.213307\pi$
$20$		0			0
$21$	6.60109	+	2.17233i	1.44048	+	0.474041i
$22$		0			0
$23$	−0.144031	−	0.816841i	−0.0300326	−	0.170323i	0.966102	−	0.258159i	$-0.0831159\pi$
$23$	−0.144031	−	0.816841i	−0.0300326	−	0.170323i	−0.996135	+	0.0878361i	$0.972005\pi$
$24$		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	0.988265	+	0.152752i	$0.0488134\pi$
$29$	7.05621	+	5.92087i	1.31031	+	1.09948i	0.322041	+	0.946726i	$0.395631\pi$
$30$		0			0
$31$	−0.614003	−	3.48219i	−0.110278	−	0.625419i	−0.988980	−	0.148048i	$-0.952701\pi$
$31$	−0.614003	−	3.48219i	−0.110278	−	0.625419i	0.878702	−	0.477371i	$-0.158410\pi$
$32$		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	0.682140	−	0.731222i	$-0.261049\pi$
$37$	−1.77730	−	3.07838i	−0.292187	−	0.506082i	−0.974326	+	0.225140i	$0.927716\pi$
$38$		0			0
$39$	4.74313	+	7.65457i	0.759509	+	1.22571i
$40$		0			0
$41$	2.09850	−	1.76085i	0.327730	−	0.274998i	−0.464044	−	0.885812i	$-0.653602\pi$
$41$	2.09850	−	1.76085i	0.327730	−	0.274998i	0.791774	+	0.610814i	$0.209158\pi$
$42$		0			0
$43$	6.48062	−	2.35875i	0.988286	−	0.359707i	0.203229	−	0.979131i	$-0.434856\pi$
$43$	6.48062	−	2.35875i	0.988286	−	0.359707i	0.785056	+	0.619425i	$0.212634\pi$
$44$		0			0
$45$	5.03986	+	3.71997i	0.751298	+	0.554540i
$46$		0			0
$47$	0.221796	−	1.25787i	0.0323523	−	0.183479i	−0.964349	−	0.264633i	$-0.914749\pi$
$47$	0.221796	−	1.25787i	0.0323523	−	0.183479i	0.996702	+	0.0811536i	$0.0258604\pi$
$48$		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	−0.239589	−	0.970874i	$-0.577013\pi$
$59$	−8.04363	−	2.92764i	−1.04719	−	0.381147i	−0.807602	+	0.589728i	$0.799235\pi$
$60$		0			0
$61$	0.492064	−	2.79063i	0.0630023	−	0.357304i	−0.936967	−	0.349419i	$-0.886379\pi$
$61$	0.492064	−	2.79063i	0.0630023	−	0.357304i	0.999969	−	0.00788485i	$-0.00250985\pi$
$62$		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	−0.972775	−	0.231753i	$-0.925554\pi$
$67$	−7.47702	+	6.27396i	−0.913463	+	0.766487i	0.0593114	+	0.998240i	$0.481110\pi$
$68$		0			0
$69$	1.43594	−	0.0447327i	0.172867	−	0.00538518i
$70$		0			0
$71$	−5.86207	−	10.1534i	−0.695700	−	1.20499i	−0.969944	−	0.243327i	$-0.921761\pi$
$71$	−5.86207	−	10.1534i	−0.695700	−	1.20499i	0.274244	−	0.961660i	$-0.411572\pi$
$72$		0			0
$73$	−0.375162	+	0.649800i	−0.0439094	+	0.0760534i	−0.887145	−	0.461491i	$-0.847315\pi$
$73$	−0.375162	+	0.649800i	−0.0439094	+	0.0760534i	0.843235	+	0.537544i	$0.180648\pi$
$74$		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	0.739096	−	0.673600i	$-0.235253\pi$
$79$	1.81383	+	1.52198i	0.204071	+	0.171236i	−0.535024	+	0.844837i	$0.679698\pi$
$80$		0			0
$81$	7.55976	+	4.88366i	0.839973	+	0.542628i
$82$		0			0
$83$	8.73328	+	7.32809i	0.958602	+	0.804363i	0.980725	−	0.195393i	$-0.0625981\pi$
$83$	8.73328	+	7.32809i	0.958602	+	0.804363i	−0.0221230	+	0.999755i	$0.507043\pi$
$84$		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	−0.972851	−	0.231431i	$-0.925659\pi$
$89$	−2.69813	+	4.67329i	−0.286001	+	0.495368i	0.686851	+	0.726799i	$0.258993\pi$
$90$		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	0.335909	−	0.941895i	$-0.390957\pi$
$97$	11.8055	−	4.29685i	1.19867	−	0.436279i	0.862759	+	0.505615i	$0.168734\pi$
$98$		0			0
$99$	−0.636104	+	0.0396706i	−0.0639309	+	0.00398705i
$100$		0			0
$101$	−0.502628	+	2.85055i	−0.0500134	+	0.283640i	−0.999549	−	0.0300181i	$-0.990443\pi$
$101$	−0.502628	+	2.85055i	−0.0500134	+	0.283640i	0.949536	+	0.313658i	$0.101555\pi$
$102$		0			0
$103$	15.6835	+	5.70832i	1.54534	+	0.562458i	0.967319	−	0.253564i	$-0.0816027\pi$
$103$	15.6835	+	5.70832i	1.54534	+	0.562458i	0.578022	+	0.816021i	$0.303825\pi$
$104$		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	0.401423	−	0.915893i	$-0.368516\pi$
$113$	1.27781	+	0.465084i	0.120206	+	0.0437514i	−0.281217	+	0.959644i	$0.590738\pi$
$114$		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	−0.823227	−	0.567713i	$-0.807828\pi$
$127$	0.902007	−	1.56232i	0.0800402	−	0.138634i	0.903267	+	0.429079i	$0.141162\pi$
$128$		0			0
$129$	2.43953	+	11.6934i	0.214789	+	1.02954i
$130$		0			0
$131$	1.68689	+	9.56684i	0.147384	+	0.835859i	0.965422	+	0.260694i	$0.0839512\pi$
$131$	1.68689	+	9.56684i	0.147384	+	0.835859i	−0.818037	+	0.575165i	$0.804938\pi$
$132$		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	0.295867	−	0.955229i	$-0.404392\pi$
$137$	−6.94643	−	5.82875i	−0.593474	−	0.497984i	−0.889340	+	0.457246i	$0.848836\pi$
$138$		0			0
$139$	1.74358	+	9.88833i	0.147888	+	0.838717i	0.965002	+	0.262241i	$0.0844615\pi$
$139$	1.74358	+	9.88833i	0.147888	+	0.838717i	−0.817114	+	0.576476i	$0.804427\pi$
$140$		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	0.00804728	−	0.999968i	$-0.497438\pi$
$149$	12.1360	−	10.1833i	0.994221	−	0.834250i	0.986173	+	0.165718i	$0.0529940\pi$
$150$		0			0
$151$	4.98746	−	1.81529i	0.405874	−	0.147726i	−0.131012	−	0.991381i	$-0.541823\pi$
$151$	4.98746	−	1.81529i	0.405874	−	0.147726i	0.536886	+	0.843655i	$0.319600\pi$
$152$		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	0.735624	−	0.677390i	$-0.236889\pi$
$157$	10.8225	+	3.93906i	0.863727	+	0.314371i	0.128103	+	0.991761i	$0.459111\pi$
$158$		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	0.554472	−	0.832203i	$-0.312920\pi$
$167$	5.74151	+	2.08974i	0.444292	+	0.161709i	−0.110180	+	0.993912i	$0.535143\pi$
$168$		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	0.0949449	−	0.995483i	$-0.469732\pi$
$173$	10.6218	−	3.86602i	0.807561	−	0.293928i	0.712616	+	0.701554i	$0.247510\pi$
$174$		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	0.965970	−	0.258656i	$-0.0832795\pi$
$179$	3.46495	+	6.00147i	0.258982	+	0.448571i	−0.706987	+	0.707226i	$0.749946\pi$
$180$		0			0
$181$	−1.51882	+	2.63067i	−0.112893	+	0.195536i	−0.916935	−	0.399036i	$-0.869345\pi$
$181$	−1.51882	+	2.63067i	−0.112893	+	0.195536i	0.804043	+	0.594572i	$0.202678\pi$
$182$		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	0.773029	−	0.634370i	$-0.218741\pi$
$191$	3.90467	+	3.27640i	0.282532	+	0.237072i	−0.490498	+	0.871443i	$0.663185\pi$
$192$		0			0
$193$	3.27644	+	18.5816i	0.235843	+	1.33753i	0.840830	+	0.541299i	$0.182067\pi$
$193$	3.27644	+	18.5816i	0.235843	+	1.33753i	−0.604987	+	0.796235i	$0.706822\pi$
$194$		0			0
$195$	−3.84001	−	18.4063i	−0.274989	−	1.31810i
$196$		0			0
$197$	10.0220	−	17.3586i	0.714036	−	1.23675i	−0.249294	−	0.968428i	$-0.580199\pi$
$197$	10.0220	−	17.3586i	0.714036	−	1.23675i	0.963330	−	0.268319i	$-0.0864682\pi$
$198$		0			0
$199$	2.75106	+	4.76498i	0.195018	+	0.337780i	0.946906	−	0.321510i	$-0.104190\pi$
$199$	2.75106	+	4.76498i	0.195018	+	0.337780i	−0.751889	+	0.659290i	$0.770857\pi$
$200$		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	−0.642031	−	0.766679i	$-0.721908\pi$
$211$	−23.6287	−	8.60014i	−1.62667	−	0.592058i	−0.984636	+	0.174621i	$0.944130\pi$
$212$		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	−0.955187	−	0.296003i	$-0.904346\pi$
$223$	0.651596	−	3.69539i	0.0436341	−	0.247461i	0.998821	+	0.0485415i	$0.0154573\pi$
$224$		0			0
$225$	1.06194	+	1.60025i	0.0707963	+	0.106684i
$226$		0			0
$227$	17.5983	−	6.40524i	1.16804	−	0.425131i	0.316076	−	0.948734i	$-0.397635\pi$
$227$	17.5983	−	6.40524i	1.16804	−	0.425131i	0.851962	+	0.523603i	$0.175412\pi$
$228$		0			0
$229$	−3.17397	+	2.66328i	−0.209742	+	0.175994i	−0.741607	−	0.670835i	$-0.765936\pi$
$229$	−3.17397	+	2.66328i	−0.209742	+	0.175994i	0.531865	+	0.846829i	$0.321491\pi$
$230$		0			0
$231$	1.47565	−	0.0459697i	0.0970906	−	0.00302459i
$232$		0			0
$233$	0.958556	+	1.66027i	0.0627971	+	0.108768i	0.895715	−	0.444629i	$-0.146665\pi$
$233$	0.958556	+	1.66027i	0.0627971	+	0.108768i	−0.832918	+	0.553397i	$0.813331\pi$
$234$		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	−0.748900	−	0.662683i	$-0.769418\pi$
$239$	−4.20216	−	23.8316i	−0.271815	−	1.54154i	0.477085	−	0.878857i	$-0.341693\pi$
$240$		0			0
$241$	10.1156	+	8.48797i	0.651601	+	0.546758i	0.907556	−	0.419931i	$-0.137946\pi$
$241$	10.1156	+	8.48797i	0.651601	+	0.546758i	−0.255955	+	0.966689i	$0.582390\pi$
$242$		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	−0.969706	−	0.244276i	$-0.921450\pi$
$251$	−4.32994	+	7.49967i	−0.273303	+	0.473375i	0.696402	+	0.717652i	$0.254783\pi$
$252$		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	0.0508142	−	0.998708i	$-0.483818\pi$
$257$	16.7233	−	14.0326i	1.04317	−	0.875326i	0.992359	+	0.123382i	$0.0393739\pi$
$258$		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	−0.939099	−	0.343648i	$-0.888337\pi$
$263$	0.987629	−	5.60112i	0.0608998	−	0.345380i	0.999998	−	0.00173240i	$-0.000551441\pi$
$264$		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	0.552244	+	0.833683i	$0.313772\pi$
$277$	−4.19132	+	23.7701i	−0.251832	+	1.42821i	−0.804076	+	0.594527i	$0.797339\pi$
$278$		0			0
$279$	−1.18820	+	10.5410i	−0.0711358	+	0.631070i
$280$		0			0
$281$	22.2287	−	8.09058i	1.32605	−	0.482644i	0.420660	−	0.907219i	$-0.361799\pi$
$281$	22.2287	−	8.09058i	1.32605	−	0.482644i	0.905393	+	0.424575i	$0.139576\pi$
$282$		0			0
$283$	8.90462	−	7.47186i	0.529325	−	0.444156i	−0.338543	−	0.940951i	$-0.609934\pi$
$283$	8.90462	−	7.47186i	0.529325	−	0.444156i	0.867868	+	0.496795i	$0.165490\pi$
$284$		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	−0.989696	−	0.143186i	$-0.954265\pi$
$293$	−1.85993	−	10.5482i	−0.108658	−	0.616232i	0.881037	−	0.473046i	$-0.156846\pi$
$294$		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	0.965836	+	0.259153i	$0.0834433\pi$
$307$	12.3938	+	21.4667i	0.707351	+	1.22517i	−0.258485	+	0.966015i	$0.583223\pi$
$308$		0			0
$309$	−13.6675	+	25.4730i	−0.777514	+	1.44911i
$310$		0			0
$311$	16.6871	−	14.0022i	0.946241	−	0.793990i	−0.0324195	−	0.999474i	$-0.510321\pi$
$311$	16.6871	−	14.0022i	0.946241	−	0.793990i	0.978660	+	0.205484i	$0.0658768\pi$
$312$		0			0
$313$	8.83542	−	3.21583i	0.499408	−	0.181770i	−0.0800199	−	0.996793i	$-0.525498\pi$
$313$	8.83542	−	3.21583i	0.499408	−	0.181770i	0.579428	+	0.815024i	$0.303276\pi$
$314$		0			0
$315$	18.2098	−	17.3220i	1.02601	−	0.975984i
$316$		0			0
$317$	−2.51892	+	14.2855i	−0.141477	+	0.802353i	0.828652	+	0.559763i	$0.189108\pi$
$317$	−2.51892	+	14.2855i	−0.141477	+	0.802353i	−0.970129	+	0.242590i	$0.922003\pi$
$318$		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	−0.988416	−	0.151771i	$-0.951502\pi$
$331$	−0.140089	+	0.794483i	−0.00769998	+	0.0436688i	0.980716	+	0.195440i	$0.0626134\pi$
$332$		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	−0.998215	−	0.0597207i	$-0.980979\pi$
$337$	−20.4272	+	17.1404i	−1.11274	+	0.933700i	−0.114525	+	0.993420i	$0.536535\pi$
$338$		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	0.750450	+	0.660927i	$0.229837\pi$
$347$	5.05391	+	28.6621i	0.271308	+	1.53866i	−0.479142	+	0.877737i	$0.659052\pi$
$348$		0			0
$349$	−22.6355	−	18.9934i	−1.21165	−	1.01669i	−0.999219	−	0.0395179i	$-0.987418\pi$
$349$	−22.6355	−	18.9934i	−1.21165	−	1.01669i	−0.212430	−	0.977176i	$-0.568138\pi$
$350$		0			0
$351$	−7.15259	−	26.0509i	−0.381777	−	1.39049i
$352$		0			0
$353$	4.78974	+	4.01907i	0.254932	+	0.213913i	0.761293	−	0.648408i	$-0.224565\pi$
$353$	4.78974	+	4.01907i	0.254932	+	0.213913i	−0.506361	+	0.862322i	$0.669010\pi$
$354$		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	−0.898131	−	0.439728i	$-0.855075\pi$
$359$	−1.29314	+	2.23979i	−0.0682495	+	0.118212i	0.829881	+	0.557940i	$0.188408\pi$
$360$		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	0.159560	−	0.987188i	$-0.448993\pi$
$367$	17.5546	−	6.38935i	0.916342	−	0.333521i	0.756782	+	0.653667i	$0.226770\pi$
$368$		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	−0.00869564	−	0.999962i	$-0.502768\pi$
$373$	−12.7104	−	4.62621i	−0.658120	−	0.239536i	−0.649425	+	0.760426i	$0.724990\pi$
$374$		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	−0.983670	−	0.179980i	$-0.942397\pi$
$383$	−36.2619	−	13.1982i	−1.85289	−	0.674398i	−0.869224	−	0.494419i	$-0.835381\pi$
$384$		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	−0.204496	−	0.978867i	$-0.565555\pi$
$389$	5.28688	−	1.92427i	0.268056	−	0.0975642i	0.472551	+	0.881303i	$0.343333\pi$
$390$		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	−0.946451	−	0.322847i	$-0.895360\pi$
$397$	−3.85809	+	6.68240i	−0.193632	+	0.335380i	0.752819	+	0.658227i	$0.228693\pi$
$398$		0			0
$399$	−6.59549	+	5.89380i	−0.330187	+	0.295059i
$400$		0			0
$401$	6.31721	+	35.8267i	0.315466	+	1.78910i	0.569593	+	0.821927i	$0.307101\pi$
$401$	6.31721	+	35.8267i	0.315466	+	1.78910i	−0.254126	+	0.967171i	$0.581788\pi$
$402$		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	0.999581	−	0.0289462i	$-0.00921516\pi$
$409$	1.01891	+	5.77853i	0.0503819	+	0.285730i	−0.949199	+	0.314676i	$0.898104\pi$
$410$		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	−0.945986	−	0.324208i	$-0.894902\pi$
$419$	−16.1908	+	13.5857i	−0.790972	+	0.663704i	0.155014	+	0.987912i	$0.450458\pi$
$420$		0			0
$421$	−6.99405	+	2.54563i	−0.340869	+	0.124066i	−0.506782	−	0.862074i	$-0.669165\pi$
$421$	−6.99405	+	2.54563i	−0.340869	+	0.124066i	0.165913	+	0.986140i	$0.446943\pi$
$422$		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	0.875673	+	0.482904i	$0.160418\pi$
$439$	−2.35406	+	13.3506i	−0.112353	+	0.637187i	−0.988027	+	0.154283i	$0.950693\pi$
$440$		0			0
$441$	21.9594	+	16.2084i	1.04569	+	0.771830i
$442$		0			0
$443$	11.5406	−	4.20044i	0.548311	−	0.199569i	−0.0529847	−	0.998595i	$-0.516873\pi$
$443$	11.5406	−	4.20044i	0.548311	−	0.199569i	0.601296	+	0.799026i	$0.294651\pi$
$444$		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	−0.723620	−	0.690199i	$-0.757523\pi$
$449$	−20.3323	−	35.2165i	−0.959540	−	1.66197i	−0.235920	−	0.971772i	$-0.575810\pi$
$450$		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	0.999983	−	0.00585037i	$-0.00186224\pi$
$457$	24.9661	+	20.9491i	1.16787	+	0.979956i	0.167884	+	0.985807i	$0.446307\pi$
$458$		0			0
$459$	−19.5844	+	1.83504i	−0.914120	+	0.0856523i
$460$		0			0
$461$	−20.9287	−	17.5612i	−0.974745	−	0.817909i	0.00854291	−	0.999964i	$-0.497281\pi$
$461$	−20.9287	−	17.5612i	−0.974745	−	0.817909i	−0.983288	+	0.182055i	$0.941725\pi$
$462$		0			0
$463$	0.590262	+	3.34754i	0.0274318	+	0.155574i	0.995447	−	0.0953189i	$-0.0303871\pi$
$463$	0.590262	+	3.34754i	0.0274318	+	0.155574i	−0.968015	+	0.250892i	$0.919276\pi$
$464$		0			0
$465$	−12.1469	−	3.99740i	−0.563301	−	0.185375i
$466$		0			0
$467$	16.4988	−	28.5767i	0.763473	−	1.32237i	−0.177577	−	0.984107i	$-0.556826\pi$
$467$	16.4988	−	28.5767i	0.763473	−	1.32237i	0.941050	−	0.338267i	$-0.109841\pi$
$468$		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	−0.745883	−	0.666077i	$-0.767972\pi$
$479$	4.00142	−	22.6932i	0.182830	−	1.03688i	0.928712	−	0.370801i	$-0.120917\pi$
$480$		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	0.336756	−	0.941592i	$-0.390670\pi$
$491$	−0.233037	−	0.0848187i	−0.0105168	−	0.00382781i	−0.347273	+	0.937764i	$0.612892\pi$
$492$		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	−0.0570505	−	0.998371i	$-0.518170\pi$
$499$	20.4674	−	17.1742i	0.916247	−	0.768822i	0.973297	+	0.229549i	$0.0737252\pi$
$500$		0			0
$501$	−5.00347	+	9.32530i	−0.223539	+	0.416624i
$502$		0			0
$503$	13.0871	+	22.6676i	0.583527	+	1.01070i	0.995057	+	0.0993022i	$0.0316611\pi$
$503$	13.0871	+	22.6676i	0.583527	+	1.01070i	−0.411530	+	0.911396i	$0.635006\pi$
$504$		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	0.998581	−	0.0532542i	$-0.0169594\pi$
$509$	0.947739	+	5.37490i	0.0420078	+	0.238238i	−0.956573	+	0.291492i	$0.905848\pi$
$510$		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	−0.424194	−	0.905572i	$-0.639442\pi$
$521$	13.0596	−	22.6199i	0.572151	−	0.990995i	0.996345	−	0.0854234i	$-0.0272243\pi$
$522$		0			0
$523$	3.70382	+	6.41521i	0.161957	+	0.280518i	0.935570	−	0.353140i	$-0.114886\pi$
$523$	3.70382	+	6.41521i	0.161957	+	0.280518i	−0.773614	+	0.633658i	$0.781553\pi$
$524$		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	−0.919513	−	0.393060i	$-0.871416\pi$
$547$	1.84721	−	10.4761i	0.0789811	−	0.447924i	0.998494	−	0.0548639i	$-0.0174725\pi$
$548$		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	0.963802	−	0.266620i	$-0.0859068\pi$
$557$	5.92385	+	10.2604i	0.251001	+	0.434747i	−0.712800	+	0.701367i	$0.752573\pi$
$558$		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	0.954899	−	0.296930i	$-0.0959628\pi$
$563$	−1.04327	−	5.91667i	−0.0439686	−	0.249358i	−0.998868	+	0.0475719i	$0.984852\pi$
$564$		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	0.0397618	−	0.999209i	$-0.487340\pi$
$569$	−22.3596	−	18.7619i	−0.937363	−	0.786541i	−0.977124	+	0.212669i	$0.931785\pi$
$570$		0			0
$571$	−3.78797	−	21.4826i	−0.158522	−	0.899021i	−0.955495	−	0.295007i	$-0.904678\pi$
$571$	−3.78797	−	21.4826i	−0.158522	−	0.899021i	0.796974	−	0.604014i	$-0.206433\pi$
$572$		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	−0.894621	−	0.446826i	$-0.852554\pi$
$577$	−20.0399	−	34.7102i	−0.834273	−	1.44500i	0.0603476	−	0.998177i	$-0.480779\pi$
$578$		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	−0.723309	−	0.690525i	$-0.757380\pi$
$587$	4.66518	−	26.4576i	0.192553	−	1.09202i	0.915861	−	0.401495i	$-0.131509\pi$
$588$		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	−0.285792	−	0.958292i	$-0.592257\pi$
$599$	−27.4285	−	9.98317i	−1.12070	−	0.407901i	−0.834908	+	0.550390i	$0.814479\pi$
$600$		0			0
$601$	−4.03243	+	22.8690i	−0.164486	+	0.932847i	0.785106	+	0.619361i	$0.212608\pi$
$601$	−4.03243	+	22.8690i	−0.164486	+	0.932847i	−0.949593	+	0.313487i	$0.898503\pi$
$602$		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	−0.341950	+	0.939718i	$0.611087\pi$
$607$	−32.6881	+	27.4286i	−1.32677	+	1.11329i	−0.984821	+	0.173574i	$0.944468\pi$
$608$		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	−0.695273	−	0.718746i	$-0.744717\pi$
$613$	6.80411	−	11.7851i	0.274815	−	0.475994i	0.970089	+	0.242752i	$0.0780500\pi$
$614$		0			0
$615$	−2.02332	−	9.69835i	−0.0815882	−	0.391075i
$616$		0			0
$617$	4.88447	+	27.7012i	0.196641	+	1.11521i	0.910062	+	0.414472i	$0.136034\pi$
$617$	4.88447	+	27.7012i	0.196641	+	1.11521i	−0.713421	+	0.700736i	$0.752855\pi$
$618$		0			0
$619$	14.9355	+	12.5323i	0.600307	+	0.503717i	0.891544	−	0.452934i	$-0.149623\pi$
$619$	14.9355	+	12.5323i	0.600307	+	0.503717i	−0.291237	+	0.956651i	$0.594067\pi$
$620$		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	0.963468	−	0.267823i	$-0.0863044\pi$
$631$	6.27471	+	10.8681i	0.249792	+	0.432653i	−0.713676	+	0.700476i	$0.752971\pi$
$632$		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	0.898833	+	0.438291i	$0.144416\pi$
$641$	−2.42288	+	13.7409i	−0.0956981	+	0.542731i	−0.994531	+	0.104440i	$0.966695\pi$
$642$		0			0
$643$	38.5754	+	14.0403i	1.52127	+	0.553695i	0.961464	−	0.274931i	$-0.0886550\pi$
$643$	38.5754	+	14.0403i	1.52127	+	0.553695i	0.559802	+	0.828627i	$0.310877\pi$
$644$		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	−0.733820	−	0.679344i	$-0.762265\pi$
$653$	−44.2755	−	16.1150i	−1.73263	−	0.630627i	−0.998813	+	0.0487170i	$0.984487\pi$
$654$		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	−0.973617	−	0.228190i	$-0.926719\pi$
$659$	−40.3746	+	14.6952i	−1.57277	+	0.572442i	−0.599156	+	0.800633i	$0.704497\pi$
$660$		0			0
$661$	21.0863	−	17.6935i	0.820161	−	0.688197i	−0.132849	−	0.991136i	$-0.542412\pi$
$661$	21.0863	−	17.6935i	0.820161	−	0.688197i	0.953010	+	0.302939i	$0.0979680\pi$
$662$		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	−0.00737169	−	0.999973i	$-0.502347\pi$
$673$	−25.7719	−	21.6252i	−0.993433	−	0.833589i	−0.986061	+	0.166384i	$0.946791\pi$
$674$		0			0
$675$	−3.00612	+	1.42439i	−0.115706	+	0.0548246i
$676$		0			0
$677$	26.1138	+	21.9120i	1.00363	+	0.842148i	0.987484	−	0.157721i	$-0.0504147\pi$
$677$	26.1138	+	21.9120i	1.00363	+	0.842148i	0.0161497	+	0.999870i	$0.494859\pi$
$678$		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	−0.979390	−	0.201976i	$-0.935264\pi$
$683$	−8.22650	+	14.2487i	−0.314778	+	0.545212i	0.664612	+	0.747189i	$0.268597\pi$
$684$		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	−0.584225	−	0.811591i	$-0.698602\pi$
$691$	−13.4086	+	4.88033i	−0.510087	+	0.185657i	0.0741383	+	0.997248i	$0.476379\pi$
$692$		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	−0.999817	−	0.0191436i	$-0.993906\pi$
$709$	−1.43117	+	8.11659i	−0.0537488	+	0.304825i	0.946068	+	0.323968i	$0.105017\pi$
$710$		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	0.994643	−	0.103370i	$-0.0329625\pi$
$719$	10.9348	+	18.9397i	0.407801	+	0.706331i	−0.586842	+	0.809701i	$0.699629\pi$
$720$		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	−0.968305	−	0.249769i	$-0.919645\pi$
$727$	−37.2742	−	31.2768i	−1.38242	−	1.15999i	−0.414119	−	0.910223i	$-0.635910\pi$
$728$		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	−0.946020	−	0.324107i	$-0.894936\pi$
$733$	−4.54580	−	25.7805i	−0.167903	−	0.952226i	0.778117	−	0.628119i	$-0.216175\pi$
$734$		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	0.888718	−	0.458454i	$-0.151596\pi$
$739$	1.28655	+	2.22838i	0.0473267	+	0.0819722i	−0.841392	+	0.540426i	$0.818263\pi$
$740$		0			0
$741$	−11.4561	+	0.356882i	−0.420849	+	0.0131104i
$742$		0			0
$743$	37.5339	−	31.4947i	1.37699	−	1.15543i	0.406673	−	0.913574i	$-0.366689\pi$
$743$	37.5339	−	31.4947i	1.37699	−	1.15543i	0.970313	−	0.241854i	$-0.0777555\pi$
$744$		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	0.483790	−	0.875184i	$-0.339260\pi$
$751$	7.99761	+	2.91089i	0.291837	+	0.106220i	−0.191953	+	0.981404i	$0.561482\pi$
$752$		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	0.157905	−	0.987454i	$-0.449526\pi$
$761$	−9.81674	−	3.57300i	−0.355856	−	0.129521i	−0.513761	+	0.857933i	$0.671748\pi$
$762$		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	0.0930721	−	0.995659i	$-0.470331\pi$
$769$	30.2202	−	25.3577i	1.08977	−	0.914423i	0.996695	+	0.0812363i	$0.0258868\pi$
$770$		0			0
$771$	19.9165	+	32.1416i	0.717274	+	1.15755i
$772$		0			0
$773$	11.6713	+	20.2152i	0.419786	+	0.727091i	0.995918	−	0.0902659i	$-0.0287717\pi$
$773$	11.6713	+	20.2152i	0.419786	+	0.727091i	−0.576131	+	0.817357i	$0.695438\pi$
$774$		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	−0.843597	−	0.536977i	$-0.819566\pi$
$787$	−6.57945	−	37.3139i	−0.234532	−	1.33010i	0.609065	−	0.793120i	$-0.291545\pi$
$788$		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	−0.678742	−	0.734376i	$-0.737475\pi$
$797$	−2.07175	+	1.73841i	−0.0733853	+	0.0615776i	0.605357	+	0.795954i	$0.293030\pi$
$798$		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	−0.563724	−	0.825963i	$-0.690632\pi$
$821$	−13.3135	+	4.84571i	−0.464644	+	0.169117i	0.0990807	+	0.995079i	$0.468410\pi$
$822$		0			0
$823$	26.5050	−	22.2404i	0.923907	−	0.775250i	−0.0508063	−	0.998709i	$-0.516179\pi$
$823$	26.5050	−	22.2404i	0.923907	−	0.775250i	0.974713	+	0.223458i	$0.0717347\pi$
$824$		0			0
$825$	0.111375	−	0.207577i	0.00387757	−	0.00722689i
$826$		0			0
$827$	25.3847	+	43.9676i	0.882713	+	1.52890i	0.848312	+	0.529496i	$0.177619\pi$
$827$	25.3847	+	43.9676i	0.882713	+	1.52890i	0.0344011	+	0.999408i	$0.489048\pi$
$828$		0			0
$829$	−27.2911	+	47.2695i	−0.947859	+	1.64174i	−0.197935	+	0.980215i	$0.563423\pi$
$829$	−27.2911	+	47.2695i	−0.947859	+	1.64174i	−0.749924	+	0.661524i	$0.769910\pi$
$830$		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	0.777420	−	0.628982i	$-0.216528\pi$
$839$	8.48661	+	7.12111i	0.292990	+	0.245848i	−0.484429	+	0.874830i	$0.660973\pi$
$840$		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	0.101343	−	0.994852i	$-0.467686\pi$
$853$	23.9039	−	8.70031i	0.818454	−	0.297893i	0.717111	+	0.696959i	$0.245464\pi$
$854$		0			0
$855$	−7.30785	+	3.18796i	−0.249923	+	0.109026i
$856$		0			0
$857$	8.19583	−	46.4809i	0.279964	−	1.58776i	−0.442773	−	0.896634i	$-0.646005\pi$
$857$	8.19583	−	46.4809i	0.279964	−	1.58776i	0.722738	−	0.691123i	$-0.242884\pi$
$858$		0			0
$859$	−23.0571	−	8.39211i	−0.786699	−	0.286335i	−0.0827360	−	0.996571i	$-0.526366\pi$
$859$	−23.0571	−	8.39211i	−0.786699	−	0.286335i	−0.703963	+	0.710236i	$0.748588\pi$
$860$		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	0.120256	−	0.992743i	$-0.461628\pi$
$877$	33.1323	−	27.8013i	1.11880	−	0.938784i	0.998543	+	0.0539587i	$0.0171839\pi$
$878$		0			0
$879$	18.5429	−	0.577651i	0.625435	−	0.0194837i
$880$		0			0
$881$	10.2218	+	17.7047i	0.344381	+	0.596485i	0.985241	−	0.171173i	$-0.0547555\pi$
$881$	10.2218	+	17.7047i	0.344381	+	0.596485i	−0.640860	+	0.767658i	$0.721422\pi$
$882$		0			0
$883$	−14.1469	+	24.5031i	−0.476080	+	0.824595i	−0.999624	−	0.0274033i	$-0.991276\pi$
$883$	−14.1469	+	24.5031i	−0.476080	+	0.824595i	0.523544	+	0.851999i	$0.324609\pi$
$884$		0			0
$885$	−23.0835	+	20.6276i	−0.775942	+	0.693390i
$886$		0			0
$887$	9.97456	+	56.5686i	0.334913	+	1.89939i	0.428088	+	0.903737i	$0.359187\pi$
$887$	9.97456	+	56.5686i	0.334913	+	1.89939i	−0.0931752	+	0.995650i	$0.529702\pi$
$888$		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	−0.745799	−	0.666171i	$-0.767932\pi$
$907$	−26.7707	+	9.74375i	−0.888908	+	0.323536i	−0.143109	+	0.989707i	$0.545710\pi$
$908$		0			0
$909$	3.86528	−	7.77586i	0.128203	−	0.257909i
$910$		0			0
$911$	3.29560	−	18.6903i	0.109188	−	0.619236i	−0.880277	−	0.474461i	$-0.842643\pi$
$911$	3.29560	−	18.6903i	0.109188	−	0.619236i	0.989465	−	0.144775i	$-0.0462459\pi$
$912$		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	−0.727671	−	0.685926i	$-0.759397\pi$
$929$	−25.7306	+	9.36519i	−0.844195	+	0.307262i	−0.116524	+	0.993188i	$0.537175\pi$
$930$		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	0.327025	+	0.945016i	$0.393954\pi$
$937$	−20.0466	+	34.7218i	−0.654895	+	1.13431i	−0.981920	+	0.189296i	$0.939380\pi$
$938$		0			0
$939$	3.32596	+	15.9423i	0.108539	+	0.520257i
$940$		0			0
$941$	−0.591978	−	3.35727i	−0.0192979	−	0.109444i	0.973637	−	0.228102i	$-0.0732519\pi$
$941$	−0.591978	−	3.35727i	−0.0192979	−	0.109444i	−0.992935	+	0.118658i	$0.962141\pi$
$942$		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	0.593805	−	0.804609i	$-0.297625\pi$
$947$	−2.93783	−	2.46513i	−0.0954666	−	0.0801060i	−0.689272	+	0.724503i	$0.742069\pi$
$948$		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	−0.0215205	−	0.999768i	$-0.506851\pi$
$953$	26.3964	−	45.7200i	0.855065	−	1.48102i	0.876585	−	0.481247i	$-0.159816\pi$
$954$		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	0.489284	−	0.872125i	$-0.337258\pi$
$967$	9.43802	+	3.43516i	0.303506	+	0.110467i	−0.185778	+	0.982592i	$0.559480\pi$
$968$		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	0.0531425	−	0.998587i	$-0.483076\pi$
$977$	−17.1297	−	6.23470i	−0.548027	−	0.199466i	−0.601170	+	0.799121i	$0.705298\pi$
$978$		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	−0.883802	−	0.467862i	$-0.845025\pi$
$983$	−39.5076	+	14.3796i	−1.26010	+	0.458638i	−0.376296	+	0.926500i	$0.622802\pi$
$984$		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	0.493733	+	0.869613i	$0.335632\pi$
$991$	−15.9365	+	27.6029i	−0.506241	+	0.876834i	−0.999974	+	0.00722097i	$0.997701\pi$
$992$		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	0.165983	−	0.986129i	$-0.446920\pi$
$997$	−24.5132	−	20.5690i	−0.776342	−	0.651428i	−0.942324	+	0.334701i	$0.891365\pi$
$998$		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.97.1		12
4.3	odd	2		54.2.e.b.43.2	✓	12
12.11	even	2		162.2.e.b.127.2		12
27.22	even	9	inner	432.2.u.b.49.1		12
36.7	odd	6		486.2.e.f.217.2		12
36.11	even	6		486.2.e.g.217.1		12
36.23	even	6		486.2.e.e.55.1		12
36.31	odd	6		486.2.e.h.55.2		12
108.7	odd	18		1458.2.a.g.1.4		6
108.11	even	18		1458.2.c.g.487.4		12
108.23	even	18		486.2.e.g.271.1		12
108.31	odd	18		486.2.e.f.271.2		12
108.43	odd	18		1458.2.c.f.487.3		12
108.47	even	18		1458.2.a.f.1.3		6
108.59	even	18		162.2.e.b.37.2		12
108.67	odd	18		486.2.e.h.433.2		12
108.79	odd	18		1458.2.c.f.973.3		12
108.83	even	18		1458.2.c.g.973.4		12
108.95	even	18		486.2.e.e.433.1		12
108.103	odd	18		54.2.e.b.49.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.b.43.2	✓	12	4.3	odd	2
54.2.e.b.49.2	yes	12	108.103	odd	18
162.2.e.b.37.2		12	108.59	even	18
162.2.e.b.127.2		12	12.11	even	2
432.2.u.b.49.1		12	27.22	even	9	inner
432.2.u.b.97.1		12	1.1	even	1	trivial
486.2.e.e.55.1		12	36.23	even	6
486.2.e.e.433.1		12	108.95	even	18
486.2.e.f.217.2		12	36.7	odd	6
486.2.e.f.271.2		12	108.31	odd	18
486.2.e.g.217.1		12	36.11	even	6
486.2.e.g.271.1		12	108.23	even	18
486.2.e.h.55.2		12	36.31	odd	6
486.2.e.h.433.2		12	108.67	odd	18
1458.2.a.f.1.3		6	108.47	even	18
1458.2.a.g.1.4		6	108.7	odd	18
1458.2.c.f.487.3		12	108.43	odd	18
1458.2.c.f.973.3		12	108.79	odd	18
1458.2.c.g.487.4		12	108.11	even	18
1458.2.c.g.973.4		12	108.83	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

Introduction

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Database

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