LMFDB - Embedded newform 441.2.bb.c.163.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(37,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([0, 32])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.37"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			163.4
Character	$\chi$	$=$	441.163
Dual form			441.2.bb.c.46.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.712776 + 1.81612i) q^{2} +(-1.32415 + 1.22863i) q^{4} +(2.50104 - 1.70518i) q^{5} +(-1.59223 - 2.11301i) q^{7} +(0.340382 + 0.163920i) q^{8} +(4.87950 + 3.32679i) q^{10} +(3.38245 + 0.509823i) q^{11} +(2.71434 - 3.40367i) q^{13} +(2.70258 - 4.39779i) q^{14} +(-0.325060 + 4.33763i) q^{16} +(-7.31018 + 2.25489i) q^{17} +(0.230569 - 0.399358i) q^{19} +(-1.21672 + 5.33078i) q^{20} +(1.48503 + 6.50634i) q^{22} +(5.60675 + 1.72945i) q^{23} +(1.52086 - 3.87508i) q^{25} +(8.11620 + 2.50352i) q^{26} +(4.70447 + 0.841674i) q^{28} +(-1.51504 + 6.63784i) q^{29} +(-0.485737 - 0.841321i) q^{31} +(-7.38734 + 2.27869i) q^{32} +(-9.30568 - 11.6690i) q^{34} +(-7.58529 - 2.56967i) q^{35} +(-4.44084 - 4.12050i) q^{37} +(0.889627 + 0.134090i) q^{38} +(1.13082 - 0.170444i) q^{40} +(-5.80253 - 2.79435i) q^{41} +(-3.08316 + 1.48477i) q^{43} +(-5.10527 + 3.48071i) q^{44} +(0.855456 + 11.4153i) q^{46} +(-1.71875 - 4.37931i) q^{47} +(-1.92960 + 6.72879i) q^{49} +8.12166 q^{50} +(0.587670 + 7.84191i) q^{52} +(-5.16535 + 4.79274i) q^{53} +(9.32899 - 4.49260i) q^{55} +(-0.195605 - 0.980228i) q^{56} +(-13.1350 + 1.97979i) q^{58} +(9.14460 + 6.23468i) q^{59} +(-0.0508714 - 0.0472018i) q^{61} +(1.18172 - 1.48183i) q^{62} +(-3.97981 - 4.99052i) q^{64} +(0.984793 - 13.1411i) q^{65} +(1.88646 + 3.26744i) q^{67} +(6.90936 - 11.9674i) q^{68} +(-0.739771 - 15.6074i) q^{70} +(-1.17312 - 5.13977i) q^{71} +(-2.98140 + 7.59648i) q^{73} +(4.31801 - 11.0021i) q^{74} +(0.185356 + 0.812096i) q^{76} +(-4.30839 - 7.95890i) q^{77} +(5.82437 - 10.0881i) q^{79} +(6.58345 + 11.4029i) q^{80} +(0.938983 - 12.5299i) q^{82} +(-1.60339 - 2.01058i) q^{83} +(-14.4381 + 18.1047i) q^{85} +(-4.89414 - 4.54110i) q^{86} +(1.06776 + 0.727985i) q^{88} +(-2.46815 + 0.372014i) q^{89} +(-11.5138 - 0.315980i) q^{91} +(-9.54906 + 4.59859i) q^{92} +(6.72828 - 6.24293i) q^{94} +(-0.104314 - 1.39197i) q^{95} +2.26778 q^{97} +(-13.5957 + 1.29174i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} + 3 q^{4} - 6 q^{8} + 30 q^{10} + 9 q^{11} + 42 q^{14} + 29 q^{16} + 5 q^{17} - 26 q^{19} + 5 q^{20} + q^{22} + 4 q^{23} - 56 q^{25} + 62 q^{26} + 7 q^{28} - 12 q^{29} - 36 q^{31} + 14 q^{32}+ \cdots - 119 q^{98}+O(q^{100}) $ 48 * q + q^2 + 3 * q^4 - 6 * q^8 + 30 * q^10 + 9 * q^11 + 42 * q^14 + 29 * q^16 + 5 * q^17 - 26 * q^19 + 5 * q^20 + q^22 + 4 * q^23 - 56 * q^25 + 62 * q^26 + 7 * q^28 - 12 * q^29 - 36 * q^31 + 14 * q^32 - 76 * q^34 - 7 * q^35 - 20 * q^37 + 60 * q^38 + 28 * q^40 - 41 * q^41 + 12 * q^43 - 44 * q^44 + 16 * q^46 - 13 * q^47 - 84 * q^49 + 12 * q^50 + 92 * q^52 - 14 * q^53 - 38 * q^55 - 105 * q^56 + 3 * q^58 - 57 * q^59 + 11 * q^61 + 16 * q^62 - 110 * q^64 - 21 * q^65 + 34 * q^67 - 22 * q^68 - 6 * q^71 - 69 * q^73 + 90 * q^74 - 49 * q^76 + 34 * q^79 - 55 * q^80 + 91 * q^82 - 28 * q^83 - 44 * q^85 + 26 * q^86 + 45 * q^88 - 11 * q^89 - 84 * q^92 + 90 * q^94 - 150 * q^95 + 124 * q^97 - 119 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{10}{21}\right)$	$1$

Coefficient data

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

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

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

$2$	0.712776	+	1.81612i	0.504009	+	1.28419i	0.925976	+	0.377583i	$0.123245\pi$
$2$	0.712776	+	1.81612i	0.504009	+	1.28419i	−0.421967	+	0.906611i	$0.638660\pi$
$3$		0			0
$3$		0			0
$4$	−1.32415	+	1.22863i	−0.662077	+	0.614317i
$5$	2.50104	−	1.70518i	1.11850	−	0.762580i	0.144584	−	0.989493i	$-0.453816\pi$
$5$	2.50104	−	1.70518i	1.11850	−	0.762580i	0.973915	+	0.226913i	$0.0728632\pi$
$6$		0			0
$7$	−1.59223	−	2.11301i	−0.601807	−	0.798642i
$7$	−1.59223	−	2.11301i	−0.601807	−	0.798642i
$8$	0.340382	+	0.163920i	0.120343	+	0.0579543i
$9$		0			0
$10$	4.87950	+	3.32679i	1.54303	+	1.05202i
$11$	3.38245	+	0.509823i	1.01985	+	0.153717i	0.637620	−	0.770351i	$-0.279919\pi$
$11$	3.38245	+	0.509823i	1.01985	+	0.153717i	0.382227	+	0.924068i	$0.375157\pi$
$12$		0			0
$13$	2.71434	−	3.40367i	0.752821	−	0.944008i	−0.246865	−	0.969050i	$-0.579400\pi$
$13$	2.71434	−	3.40367i	0.752821	−	0.944008i	0.999686	+	0.0250418i	$0.00797190\pi$
$14$	2.70258	−	4.39779i	0.722294	−	1.17536i
$15$		0			0
$16$	−0.325060	+	4.33763i	−0.0812650	+	1.08441i
$17$	−7.31018	+	2.25489i	−1.77298	+	0.546891i	−0.996526	−	0.0832845i	$-0.973459\pi$
$17$	−7.31018	+	2.25489i	−1.77298	+	0.546891i	−0.776452	+	0.630176i	$0.782983\pi$
$18$		0			0
$19$	0.230569	−	0.399358i	0.0528962	−	0.0916189i	−0.838365	−	0.545109i	$-0.816488\pi$
$19$	0.230569	−	0.399358i	0.0528962	−	0.0916189i	0.891261	+	0.453491i	$0.149821\pi$
$20$	−1.21672	+	5.33078i	−0.272066	+	1.19200i
$21$		0			0
$22$	1.48503	+	6.50634i	0.316609	+	1.38716i
$23$	5.60675	+	1.72945i	1.16909	+	0.360616i	0.817717	−	0.575620i	$-0.195239\pi$
$23$	5.60675	+	1.72945i	1.16909	+	0.360616i	0.351371	+	0.936236i	$0.385716\pi$
$24$		0			0
$25$	1.52086	−	3.87508i	0.304171	−	0.775016i
$26$	8.11620	+	2.50352i	1.59172	+	0.490980i
$27$		0			0
$28$	4.70447	+	0.841674i	0.889062	+	0.159061i
$29$	−1.51504	+	6.63784i	−0.281337	+	1.23262i	0.614745	+	0.788726i	$0.289259\pi$
$29$	−1.51504	+	6.63784i	−0.281337	+	1.23262i	−0.896081	+	0.443890i	$0.853598\pi$
$30$		0			0
$31$	−0.485737	−	0.841321i	−0.0872409	−	0.151106i	0.819103	−	0.573646i	$-0.194472\pi$
$31$	−0.485737	−	0.841321i	−0.0872409	−	0.151106i	−0.906344	+	0.422541i	$0.861138\pi$
$32$	−7.38734	+	2.27869i	−1.30591	+	0.402820i
$33$		0			0
$34$	−9.30568	−	11.6690i	−1.59591	−	2.00121i
$35$	−7.58529	−	2.56967i	−1.28215	−	0.434354i
$36$		0			0
$37$	−4.44084	−	4.12050i	−0.730070	−	0.677406i	0.224808	−	0.974403i	$-0.427824\pi$
$37$	−4.44084	−	4.12050i	−0.730070	−	0.677406i	−0.954878	+	0.296997i	$0.904015\pi$
$38$	0.889627	+	0.134090i	0.144317	+	0.0217522i
$39$		0			0
$40$	1.13082	−	0.170444i	0.178799	−	0.0269496i
$41$	−5.80253	−	2.79435i	−0.906203	−	0.436404i	−0.0780774	−	0.996947i	$-0.524878\pi$
$41$	−5.80253	−	2.79435i	−0.906203	−	0.436404i	−0.828125	+	0.560543i	$0.810592\pi$
$42$		0			0
$43$	−3.08316	+	1.48477i	−0.470178	+	0.226426i	−0.653942	−	0.756544i	$-0.726886\pi$
$43$	−3.08316	+	1.48477i	−0.470178	+	0.226426i	0.183764	+	0.982970i	$0.441172\pi$
$44$	−5.10527	+	3.48071i	−0.769648	+	0.524737i
$45$		0			0
$46$	0.855456	+	11.4153i	0.126130	+	1.68309i
$47$	−1.71875	−	4.37931i	−0.250706	−	0.638788i	0.749012	−	0.662557i	$-0.230529\pi$
$47$	−1.71875	−	4.37931i	−0.250706	−	0.638788i	−0.999717	+	0.0237689i	$0.992433\pi$
$48$		0			0
$49$	−1.92960	+	6.72879i	−0.275657	+	0.961256i
$50$	8.12166			1.14858
$51$		0			0
$52$	0.587670	+	7.84191i	0.0814951	+	1.08748i
$53$	−5.16535	+	4.79274i	−0.709515	+	0.658334i	−0.949975	−	0.312325i	$-0.898892\pi$
$53$	−5.16535	+	4.79274i	−0.709515	+	0.658334i	0.240460	+	0.970659i	$0.422702\pi$
$54$		0			0
$55$	9.32899	−	4.49260i	1.25792	−	0.605783i
$56$	−0.195605	−	0.980228i	−0.0261388	−	0.130989i
$57$		0			0
$58$	−13.1350	+	1.97979i	−1.72471	+	0.259959i
$59$	9.14460	+	6.23468i	1.19052	+	0.811686i	0.985930	−	0.167161i	$-0.0534598\pi$
$59$	9.14460	+	6.23468i	1.19052	+	0.811686i	0.204595	+	0.978847i	$0.434412\pi$
$60$		0			0
$61$	−0.0508714	−	0.0472018i	−0.00651342	−	0.00604357i	0.676909	−	0.736066i	$-0.263319\pi$
$61$	−0.0508714	−	0.0472018i	−0.00651342	−	0.00604357i	−0.683423	+	0.730023i	$0.739509\pi$
$62$	1.18172	−	1.48183i	0.150079	−	0.188193i
$63$		0			0
$64$	−3.97981	−	4.99052i	−0.497476	−	0.623815i
$65$	0.984793	−	13.1411i	0.122149	−	1.62996i
$66$		0			0
$67$	1.88646	+	3.26744i	0.230467	+	0.399181i	0.957946	−	0.286949i	$-0.0926411\pi$
$67$	1.88646	+	3.26744i	0.230467	+	0.399181i	−0.727478	+	0.686131i	$0.759308\pi$
$68$	6.90936	−	11.9674i	0.837883	−	1.45126i
$69$		0			0
$70$	−0.739771	−	15.6074i	−0.0884195	−	1.86545i
$71$	−1.17312	−	5.13977i	−0.139224	−	0.609979i	−0.995606	−	0.0936372i	$-0.970151\pi$
$71$	−1.17312	−	5.13977i	−0.139224	−	0.609979i	0.856383	−	0.516342i	$-0.172707\pi$
$72$		0			0
$73$	−2.98140	+	7.59648i	−0.348946	+	0.889101i	0.643390	+	0.765538i	$0.277527\pi$
$73$	−2.98140	+	7.59648i	−0.348946	+	0.889101i	−0.992337	+	0.123563i	$0.960568\pi$
$74$	4.31801	−	11.0021i	0.501959	−	1.27897i
$75$		0			0
$76$	0.185356	+	0.812096i	0.0212618	+	0.0931538i
$77$	−4.30839	−	7.95890i	−0.490986	−	0.907001i
$78$		0			0
$79$	5.82437	−	10.0881i	0.655292	−	1.13500i	−0.326528	−	0.945188i	$-0.605879\pi$
$79$	5.82437	−	10.0881i	0.655292	−	1.13500i	0.981820	−	0.189812i	$-0.0607880\pi$
$80$	6.58345	+	11.4029i	0.736052	+	1.27488i
$81$		0			0
$82$	0.938983	−	12.5299i	0.103693	−	1.38369i
$83$	−1.60339	−	2.01058i	−0.175995	−	0.220690i	0.686008	−	0.727594i	$-0.259361\pi$
$83$	−1.60339	−	2.01058i	−0.175995	−	0.220690i	−0.862003	+	0.506904i	$0.830790\pi$
$84$		0			0
$85$	−14.4381	+	18.1047i	−1.56603	+	1.96374i
$86$	−4.89414	−	4.54110i	−0.527749	−	0.489679i
$87$		0			0
$88$	1.06776	+	0.727985i	0.113823	+	0.0776034i
$89$	−2.46815	+	0.372014i	−0.261623	+	0.0394334i	−0.278544	−	0.960423i	$-0.589852\pi$
$89$	−2.46815	+	0.372014i	−0.261623	+	0.0394334i	0.0169208	+	0.999857i	$0.494614\pi$
$90$		0			0
$91$	−11.5138	−	0.315980i	−1.20698	−	0.0331237i
$92$	−9.54906	+	4.59859i	−0.995559	+	0.479436i
$93$		0			0
$94$	6.72828	−	6.24293i	0.693969	−	0.643909i
$95$	−0.104314	−	1.39197i	−0.0107024	−	0.142813i
$96$		0			0
$97$	2.26778			0.230259			0.115129	−	0.993351i	$-0.463272\pi$
$97$	2.26778			0.230259			0.115129	+	0.993351i	$0.463272\pi$
$98$	−13.5957	+	1.29174i	−1.37337	+	0.130485i
$99$		0			0
$100$	2.74721	+	6.99978i	0.274721	+	0.699978i
$101$	−0.104409	−	1.39324i	−0.0103890	−	0.138632i	0.989597	−	0.143865i	$-0.0459532\pi$
$101$	−0.104409	−	1.39324i	−0.0103890	−	0.138632i	−0.999986	+	0.00523328i	$0.998334\pi$
$102$		0			0
$103$	16.4128	−	11.1901i	1.61720	−	1.10259i	0.692831	−	0.721100i	$-0.256363\pi$
$103$	16.4128	−	11.1901i	1.61720	−	1.10259i	0.924373	−	0.381490i	$-0.124589\pi$
$104$	1.48184	−	0.713617i	0.145306	−	0.0699759i
$105$		0			0
$106$	−12.3860	−	5.96476i	−1.20303	−	0.579349i
$107$	−6.35460	+	0.957802i	−0.614323	+	0.0925943i	−0.448831	−	0.893617i	$-0.648159\pi$
$107$	−6.35460	+	0.957802i	−0.614323	+	0.0925943i	−0.165492	+	0.986211i	$0.552921\pi$
$108$		0			0
$109$	−2.37836	−	0.358480i	−0.227805	−	0.0343362i	0.0341474	−	0.999417i	$-0.489128\pi$
$109$	−2.37836	−	0.358480i	−0.227805	−	0.0343362i	−0.261953	+	0.965081i	$0.584367\pi$
$110$	14.8086	+	13.7404i	1.41195	+	1.31009i
$111$		0			0
$112$	9.68301	−	6.21965i	0.914958	−	0.587702i
$113$	−0.680530	−	0.853357i	−0.0640189	−	0.0802771i	0.748791	−	0.662806i	$-0.230635\pi$
$113$	−0.680530	−	0.853357i	−0.0640189	−	0.0802771i	−0.812810	+	0.582529i	$0.802063\pi$
$114$		0			0
$115$	16.9717	−	5.23509i	1.58262	−	0.488175i
$116$	−6.14933	−	10.6510i	−0.570951	−	0.988916i
$117$		0			0
$118$	−4.80490	+	21.0517i	−0.442327	+	1.93796i
$119$	16.4041	+	11.8561i	1.50376	+	1.08685i
$120$		0			0
$121$	0.669760	+	0.206594i	0.0608873	+	0.0187812i
$122$	0.0494644	−	0.126033i	0.00447829	−	0.0114105i
$123$		0			0
$124$	1.67687	+	0.517244i	0.150587	+	0.0464499i
$125$	0.563888	+	2.47055i	0.0504357	+	0.220973i
$126$		0			0
$127$	1.69119	−	7.40960i	0.150069	−	0.657496i	−0.842794	−	0.538236i	$-0.819091\pi$
$127$	1.69119	−	7.40960i	0.150069	−	0.657496i	0.992863	−	0.119260i	$-0.0380521\pi$
$128$	−1.50410	+	2.60518i	−0.132945	+	0.230267i
$129$		0			0
$130$	24.5679	−	7.57819i	2.15475	−	0.664651i
$131$	0.0640034	−	0.854066i	0.00559200	−	0.0746201i	−0.993710	−	0.111988i	$-0.964278\pi$
$131$	0.0640034	−	0.854066i	0.00559200	−	0.0746201i	0.999302	+	0.0373677i	$0.0118973\pi$
$132$		0			0
$133$	−1.21097	+	0.148675i	−0.105004	+	0.0128918i
$134$	−4.58946	+	5.75500i	−0.396469	+	0.497156i
$135$		0			0
$136$	−2.85788	−	0.430756i	−0.245061	−	0.0369370i
$137$	−11.2091	−	7.64221i	−0.957654	−	0.652918i	−0.0197476	−	0.999805i	$-0.506286\pi$
$137$	−11.2091	−	7.64221i	−0.957654	−	0.652918i	−0.937907	+	0.346887i	$0.887239\pi$
$138$		0			0
$139$	−11.5141	−	5.54490i	−0.976613	−	0.470312i	−0.123674	−	0.992323i	$-0.539468\pi$
$139$	−11.5141	−	5.54490i	−0.976613	−	0.470312i	−0.852939	+	0.522011i	$0.825182\pi$
$140$	13.2013	−	5.91691i	1.11571	−	0.500070i
$141$		0			0
$142$	8.49829	−	5.79404i	0.713161	−	0.486225i
$143$	10.9164	−	10.1289i	0.912873	−	0.847023i
$144$		0			0
$145$	7.52953	+	19.1849i	0.625294	+	1.59322i
$146$	−15.9212			−1.31765
$147$		0			0
$148$	10.9429			0.899505
$149$	4.98264	+	12.6956i	0.408194	+	1.04006i	0.976168	+	0.217015i	$0.0696320\pi$
$149$	4.98264	+	12.6956i	0.408194	+	1.04006i	−0.567974	+	0.823046i	$0.692273\pi$
$150$		0			0
$151$	−13.7755	+	12.7818i	−1.12103	+	1.04017i	−0.122171	+	0.992509i	$0.538986\pi$
$151$	−13.7755	+	12.7818i	−1.12103	+	1.04017i	−0.998864	+	0.0476589i	$0.984824\pi$
$152$	0.143944	−	0.0981395i	0.0116754	−	0.00796017i
$153$		0			0
$154$	11.3834	−	13.4975i	0.917303	−	1.08766i
$155$	−2.64945	−	1.27591i	−0.212809	−	0.102483i
$156$		0			0
$157$	−10.0628	−	6.86068i	−0.803096	−	0.547542i	0.0907718	−	0.995872i	$-0.471067\pi$
$157$	−10.0628	−	6.86068i	−0.803096	−	0.547542i	−0.893868	+	0.448330i	$0.852019\pi$
$158$	22.4727	+	3.38722i	1.78783	+	0.269472i
$159$		0			0
$160$	−14.5905	+	18.2958i	−1.15348	+	1.44641i
$161$	−5.27290	−	14.6008i	−0.415563	−	1.15070i
$162$		0			0
$163$	−0.695173	+	9.27644i	−0.0544501	+	0.726587i	0.901448	+	0.432888i	$0.142505\pi$
$163$	−0.695173	+	9.27644i	−0.0544501	+	0.726587i	−0.955898	+	0.293699i	$0.905114\pi$
$164$	11.1167	−	3.42904i	0.868066	−	0.267763i
$165$		0			0
$166$	2.50861	−	4.34505i	0.194706	−	0.337241i
$167$	−3.07100	+	13.4549i	−0.237641	+	1.04117i	0.705481	+	0.708729i	$0.250731\pi$
$167$	−3.07100	+	13.4549i	−0.237641	+	1.04117i	−0.943122	+	0.332446i	$0.892126\pi$
$168$		0			0
$169$	−1.32457	−	5.80334i	−0.101890	−	0.446411i
$170$	−43.1716	−	13.3167i	−3.31111	−	1.02134i
$171$		0			0
$172$	2.25834	−	5.75415i	0.172197	−	0.438750i
$173$	−0.664509	−	0.204974i	−0.0505217	−	0.0155839i	0.269391	−	0.963031i	$-0.413178\pi$
$173$	−0.664509	−	0.204974i	−0.0505217	−	0.0155839i	−0.319913	+	0.947447i	$0.603654\pi$
$174$		0			0
$175$	−10.6096	+	2.95645i	−0.802013	+	0.223486i
$176$	−3.31092	+	14.5061i	−0.249570	+	1.09344i
$177$		0			0
$178$	−2.43486	−	4.21730i	−0.182500	−	0.316100i
$179$	−13.8009	+	4.25700i	−1.03152	+	0.318183i	−0.763896	−	0.645339i	$-0.776716\pi$
$179$	−13.8009	+	4.25700i	−1.03152	+	0.318183i	−0.267628	+	0.963522i	$0.586240\pi$
$180$		0			0
$181$	10.6896	+	13.4044i	0.794555	+	0.996340i	0.999844	+	0.0176387i	$0.00561488\pi$
$181$	10.6896	+	13.4044i	0.794555	+	0.996340i	−0.205290	+	0.978701i	$0.565814\pi$
$182$	−7.63292	−	21.1358i	−0.565790	−	1.56669i
$183$		0			0
$184$	1.62495	+	1.50773i	0.119793	+	0.111151i
$185$	−18.1329	−	2.73310i	−1.33316	−	0.200941i
$186$		0			0
$187$	−25.8759	+	3.90017i	−1.89223	+	0.285208i
$188$	7.65646	+	3.68716i	0.558405	+	0.268914i
$189$		0			0
$190$	2.45364	−	1.18161i	0.178006	−	0.0857231i
$191$	9.66226	−	6.58762i	0.699137	−	0.476663i	−0.160851	−	0.986979i	$-0.551424\pi$
$191$	9.66226	−	6.58762i	0.699137	−	0.476663i	0.859987	+	0.510315i	$0.170471\pi$
$192$		0			0
$193$	−2.01860	−	26.9363i	−0.145302	−	1.93892i	−0.306245	−	0.951953i	$-0.599073\pi$
$193$	−2.01860	−	26.9363i	−0.145302	−	1.93892i	0.160943	−	0.986964i	$-0.448547\pi$
$194$	1.61642	+	4.11858i	0.116052	+	0.295697i
$195$		0			0
$196$	−5.71215	−	11.2807i	−0.408010	−	0.805766i
$197$	23.3736			1.66530			0.832650	−	0.553800i	$-0.186823\pi$
$197$	23.3736			1.66530			0.832650	+	0.553800i	$0.186823\pi$
$198$		0			0
$199$	0.723875	+	9.65944i	0.0513141	+	0.684740i	0.962246	+	0.272182i	$0.0877453\pi$
$199$	0.723875	+	9.65944i	0.0513141	+	0.684740i	−0.910932	+	0.412557i	$0.864636\pi$
$200$	1.15287	−	1.06971i	0.0815205	−	0.0756400i
$201$		0			0
$202$	2.45587	−	1.18268i	0.172794	−	0.0832134i
$203$	16.4381	−	7.36768i	1.15373	−	0.517110i
$204$		0			0
$205$	−19.2772	+	2.90557i	−1.34638	+	0.202934i
$206$	32.0212	+	21.8317i	2.23102	+	1.52109i
$207$		0			0
$208$	13.8815	+	12.8802i	0.962510	+	0.893079i
$209$	0.983491	−	1.23326i	0.0680295	−	0.0853063i
$210$		0			0
$211$	7.65206	+	9.59538i	0.526790	+	0.660573i	0.972035	−	0.234835i	$-0.0754550\pi$
$211$	7.65206	+	9.59538i	0.526790	+	0.660573i	−0.445246	+	0.895409i	$0.646884\pi$
$212$	0.951183	−	12.6927i	0.0653275	−	0.871735i
$213$		0			0
$214$	−6.26890	−	10.8581i	−0.428533	−	0.742241i
$215$	−5.17931	+	8.97083i	−0.353226	+	0.611806i
$216$		0			0
$217$	−1.00431	+	2.36594i	−0.0681771	+	0.160611i
$218$	−1.04419	−	4.57491i	−0.0707217	−	0.309852i
$219$		0			0
$220$	−6.83324	+	17.4108i	−0.460697	+	1.17384i
$221$	−12.1674	+	31.0020i	−0.818466	+	2.08542i
$222$		0			0
$223$	−4.34871	−	19.0530i	−0.291211	−	1.27588i	−0.882842	−	0.469671i	$-0.844373\pi$
$223$	−4.34871	−	19.0530i	−0.291211	−	1.27588i	0.591630	−	0.806209i	$-0.298485\pi$
$224$	16.5772	+	11.9813i	1.10761	+	0.800534i
$225$		0			0
$226$	1.06474	−	1.84418i	0.0708253	−	0.122673i
$227$	−0.223240	−	0.386663i	−0.0148170	−	0.0256637i	0.858522	−	0.512777i	$-0.171383\pi$
$227$	−0.223240	−	0.386663i	−0.0148170	−	0.0256637i	−0.873339	+	0.487113i	$0.838050\pi$
$228$		0			0
$229$	0.233264	−	3.11269i	0.0154145	−	0.205692i	−0.984179	−	0.177178i	$-0.943303\pi$
$229$	0.233264	−	3.11269i	0.0154145	−	0.205692i	0.999593	−	0.0285146i	$-0.00907770\pi$
$230$	21.6046	+	27.0913i	1.42457	+	1.78635i
$231$		0			0
$232$	−1.60377	+	2.01106i	−0.105292	+	0.132033i
$233$	1.79855	+	1.66881i	0.117827	+	0.109327i	0.736886	−	0.676017i	$-0.236295\pi$
$233$	1.79855	+	1.66881i	0.117827	+	0.109327i	−0.619059	+	0.785344i	$0.712486\pi$
$234$		0			0
$235$	−11.7662	−	8.02204i	−0.767541	−	0.523301i
$236$	−19.7690	+	2.97970i	−1.28685	+	0.193962i
$237$		0			0
$238$	−9.83978	+	38.2426i	−0.637818	+	2.47890i
$239$	−15.2629	+	7.35021i	−0.987273	+	0.475446i	−0.856601	−	0.515980i	$-0.827428\pi$
$239$	−15.2629	+	7.35021i	−0.987273	+	0.475446i	−0.130672	+	0.991426i	$0.541714\pi$
$240$		0			0
$241$	−3.14831	+	2.92121i	−0.202801	+	0.188172i	−0.775034	−	0.631919i	$-0.782267\pi$
$241$	−3.14831	+	2.92121i	−0.202801	+	0.188172i	0.572234	+	0.820091i	$0.306077\pi$
$242$	0.102189	+	1.36362i	0.00656898	+	0.0876570i
$243$		0			0
$244$	0.125355			0.00802505
$245$	6.64781	+	20.1193i	0.424713	+	1.28537i
$246$		0			0
$247$	−0.733439	−	1.86877i	−0.0466676	−	0.118907i
$248$	−0.0274273	−	0.365992i	−0.00174164	−	0.0232405i
$249$		0			0
$250$	−4.08491	+	2.78504i	−0.258352	+	0.176142i
$251$	−10.6052	+	5.10721i	−0.669396	+	0.322364i	−0.737532	−	0.675312i	$-0.764009\pi$
$251$	−10.6052	+	5.10721i	−0.669396	+	0.322364i	0.0681364	+	0.997676i	$0.478295\pi$
$252$		0			0
$253$	18.0828	+	8.70824i	1.13686	+	0.547482i
$254$	14.6622	−	2.20997i	0.919988	−	0.138666i
$255$		0			0
$256$	−18.4271	−	2.77743i	−1.15169	−	0.173590i
$257$	−9.97662	−	9.25695i	−0.622324	−	0.577432i	0.304693	−	0.952451i	$-0.401446\pi$
$257$	−9.97662	−	9.25695i	−0.622324	−	0.577432i	−0.927018	+	0.375018i	$0.877637\pi$
$258$		0			0
$259$	−1.63580	+	15.9443i	−0.101643	+	0.990732i
$260$	14.8417	+	18.6108i	0.920440	+	1.15420i
$261$		0			0
$262$	1.59671	−	0.492520i	0.0986451	−	0.0304280i
$263$	0.494476	+	0.856457i	0.0304907	+	0.0528114i	0.880868	−	0.473362i	$-0.156960\pi$
$263$	0.494476	+	0.856457i	0.0304907	+	0.0528114i	−0.850377	+	0.526173i	$0.823626\pi$
$264$		0			0
$265$	−4.74626	+	20.7947i	−0.291560	+	1.27741i
$266$	−1.13316	−	2.09329i	−0.0694785	−	0.128348i
$267$		0			0
$268$	−6.51245	−	2.00882i	−0.397811	−	0.122708i
$269$	9.03288	−	23.0154i	0.550744	−	1.40327i	−0.336373	−	0.941729i	$-0.609200\pi$
$269$	9.03288	−	23.0154i	0.550744	−	1.40327i	0.887117	−	0.461544i	$-0.152704\pi$
$270$		0			0
$271$	24.3217	+	7.50226i	1.47744	+	0.455730i	0.925691	−	0.378281i	$-0.123485\pi$
$271$	24.3217	+	7.50226i	1.47744	+	0.455730i	0.551748	+	0.834011i	$0.313961\pi$
$272$	−7.40463	−	32.4418i	−0.448971	−	1.96707i
$273$		0			0
$274$	5.88965	−	25.8042i	0.355807	−	1.55889i
$275$	7.11983	−	12.3319i	0.429342	−	0.743642i
$276$		0			0
$277$	−9.53712	+	2.94181i	−0.573030	+	0.176756i	−0.567709	−	0.823230i	$-0.692170\pi$
$277$	−9.53712	+	2.94181i	−0.573030	+	0.176756i	−0.00532123	+	0.999986i	$0.501694\pi$
$278$	1.86325	−	24.8633i	0.111750	−	1.49120i
$279$		0			0
$280$	−2.16068	−	2.11805i	−0.129125	−	0.126578i
$281$	−4.97450	+	6.23783i	−0.296754	+	0.372118i	−0.907747	−	0.419518i	$-0.862199\pi$
$281$	−4.97450	+	6.23783i	−0.296754	+	0.372118i	0.610993	+	0.791636i	$0.290770\pi$
$282$		0			0
$283$	4.87245	+	0.734404i	0.289637	+	0.0436558i	0.292254	−	0.956341i	$-0.405595\pi$
$283$	4.87245	+	0.734404i	0.289637	+	0.0436558i	−0.00261652	+	0.999997i	$0.500833\pi$
$284$	7.86829	+	5.36451i	0.466897	+	0.318325i
$285$		0			0
$286$	26.1763	+	12.6058i	1.54784	+	0.745399i
$287$	3.33449	+	16.7100i	0.196829	+	0.986362i
$288$		0			0
$289$	34.3081	−	23.3909i	2.01812	−	1.37593i
$290$	−29.4753	+	27.3491i	−1.73085	+	1.60600i
$291$		0			0
$292$	−5.38547	−	13.7220i	−0.315161	−	0.803017i
$293$	−25.2335			−1.47416			−0.737079	−	0.675806i	$-0.763796\pi$
$293$	−25.2335			−1.47416			−0.737079	+	0.675806i	$0.763796\pi$
$294$		0			0
$295$	33.5023			1.95058
$296$	−0.836155	−	2.13049i	−0.0486005	−	0.123832i
$297$		0			0
$298$	−19.5052	+	18.0982i	−1.12991	+	1.04840i
$299$	21.1051	−	14.3892i	1.22054	−	0.832149i
$300$		0			0
$301$	8.04645	+	4.15064i	0.463790	+	0.239239i
$302$	−33.0322	−	15.9075i	−1.90079	−	0.915371i
$303$		0			0
$304$	1.65732	+	1.12994i	0.0950536	+	0.0648064i
$305$	−0.207719	−	0.0313086i	−0.0118940	−	0.00179273i
$306$		0			0
$307$	6.81355	−	8.54392i	0.388870	−	0.487627i	−0.548408	−	0.836211i	$-0.684766\pi$
$307$	6.81355	−	8.54392i	0.388870	−	0.487627i	0.937278	+	0.348584i	$0.113337\pi$
$308$	15.4835	+	5.24537i	0.882257	+	0.298883i
$309$		0			0
$310$	0.428742	−	5.72117i	0.0243509	−	0.324940i
$311$	9.28867	−	2.86518i	0.526712	−	0.162469i	−0.0199838	−	0.999800i	$-0.506361\pi$
$311$	9.28867	−	2.86518i	0.526712	−	0.162469i	0.546696	+	0.837331i	$0.315885\pi$
$312$		0			0
$313$	2.39374	−	4.14608i	0.135302	−	0.234350i	−0.790411	−	0.612577i	$-0.790133\pi$
$313$	2.39374	−	4.14608i	0.135302	−	0.234350i	0.925713	+	0.378227i	$0.123466\pi$
$314$	5.28734	−	23.1654i	0.298382	−	1.30730i
$315$		0			0
$316$	4.68223	+	20.5142i	0.263396	+	1.15401i
$317$	32.8042	+	10.1187i	1.84246	+	0.568325i	0.999541	+	0.0302917i	$0.00964363\pi$
$317$	32.8042	+	10.1187i	1.84246	+	0.568325i	0.842924	+	0.538033i	$0.180833\pi$
$318$		0			0
$319$	−8.50869	+	21.6798i	−0.476395	+	1.21383i
$320$	−18.4634	−	5.69521i	−1.03214	−	0.318372i
$321$		0			0
$322$	22.7585	−	19.9833i	1.26828	−	1.11363i
$323$	−0.784994	+	3.43928i	−0.0436782	+	0.191367i
$324$		0			0
$325$	−9.06138	−	15.6948i	−0.502635	−	0.870589i
$326$	−17.3427	+	5.34950i	−0.960521	+	0.296282i
$327$		0			0
$328$	−1.51703	−	1.90230i	−0.0837640	−	0.105037i
$329$	−6.51686	+	10.6046i	−0.359286	+	0.584651i
$330$		0			0
$331$	10.6694	+	9.89972i	0.586441	+	0.544138i	0.916609	−	0.399784i	$-0.130915\pi$
$331$	10.6694	+	9.89972i	0.586441	+	0.544138i	−0.330168	+	0.943922i	$0.607106\pi$
$332$	4.59340	+	0.692344i	0.252096	+	0.0379973i
$333$		0			0
$334$	−26.6248	+	4.01304i	−1.45684	+	0.219584i
$335$	10.2897	+	4.95525i	0.562185	+	0.270734i
$336$		0			0
$337$	17.6535	−	8.50148i	0.961647	−	0.463105i	0.113892	−	0.993493i	$-0.463668\pi$
$337$	17.6535	−	8.50148i	0.961647	−	0.463105i	0.847755	+	0.530388i	$0.177954\pi$
$338$	9.59546	−	6.54207i	0.521924	−	0.355842i
$339$		0			0
$340$	−3.12592	−	41.7125i	−0.169527	−	2.26218i
$341$	−1.21406	−	3.09337i	−0.0657448	−	0.167515i
$342$		0			0
$343$	17.2904	−	6.63655i	0.933591	−	0.358340i
$344$	−1.29284			−0.0697052
$345$		0			0
$346$	−0.101388	−	1.35293i	−0.00545067	−	0.0727341i
$347$	11.8971	−	11.0389i	0.638670	−	0.592599i	−0.292908	−	0.956141i	$-0.594623\pi$
$347$	11.8971	−	11.0389i	0.638670	−	0.592599i	0.931578	+	0.363542i	$0.118433\pi$
$348$		0			0
$349$	10.9710	−	5.28336i	0.587264	−	0.282812i	−0.116562	−	0.993183i	$-0.537187\pi$
$349$	10.9710	−	5.28336i	0.587264	−	0.282812i	0.703827	+	0.710372i	$0.251473\pi$
$350$	−12.9316	−	17.1611i	−0.691221	−	0.917301i
$351$		0			0
$352$	−26.1490	+	3.94133i	−1.39375	+	0.210074i
$353$	−8.59910	−	5.86277i	−0.457684	−	0.312044i	0.312440	−	0.949937i	$-0.398854\pi$
$353$	−8.59910	−	5.86277i	−0.457684	−	0.312044i	−0.770124	+	0.637894i	$0.779806\pi$
$354$		0			0
$355$	−11.6983	−	10.8544i	−0.620879	−	0.576092i
$356$	2.81114	−	3.52506i	0.148990	−	0.186828i
$357$		0			0
$358$	−17.5682	−	22.0298i	−0.928507	−	1.16431i
$359$	0.333449	−	4.44956i	0.0175987	−	0.234839i	−0.981467	−	0.191630i	$-0.938623\pi$
$359$	0.333449	−	4.44956i	0.0175987	−	0.234839i	0.999066	−	0.0432092i	$-0.0137582\pi$
$360$		0			0
$361$	9.39368	+	16.2703i	0.494404	+	0.856333i
$362$	−16.7247	+	28.9680i	−0.879031	+	1.52253i
$363$		0			0
$364$	15.6343	−	13.7279i	0.819460	−	0.719536i
$365$	5.49677	+	24.0829i	0.287714	+	1.26056i
$366$		0			0
$367$	6.21915	−	15.8461i	0.324637	−	0.827161i	−0.671634	−	0.740883i	$-0.734407\pi$
$367$	6.21915	−	15.8461i	0.324637	−	0.827161i	0.996271	−	0.0862781i	$-0.0274974\pi$
$368$	−9.32425	+	23.7578i	−0.486060	+	1.23846i
$369$		0			0
$370$	−7.96107	−	34.8797i	−0.413877	−	1.81331i
$371$	18.3515	+	3.28326i	0.952764	+	0.170458i
$372$		0			0
$373$	15.9489	−	27.6244i	0.825805	−	1.43034i	−0.0754976	−	0.997146i	$-0.524055\pi$
$373$	15.9489	−	27.6244i	0.825805	−	1.43034i	0.901303	−	0.433190i	$-0.142612\pi$
$374$	−25.5269	−	44.2139i	−1.31997	−	2.28625i
$375$		0			0
$376$	0.132821	−	1.77238i	0.00684973	−	0.0914033i
$377$	18.4807	+	23.1740i	0.951803	+	1.19352i
$378$		0			0
$379$	15.9882	−	20.0486i	0.821261	−	1.02983i	−0.177692	−	0.984086i	$-0.556863\pi$
$379$	15.9882	−	20.0486i	0.821261	−	1.02983i	0.998953	−	0.0457427i	$-0.0145654\pi$
$380$	1.84835	+	1.71502i	0.0948185	+	0.0879787i
$381$		0			0
$382$	18.8510	+	12.8524i	0.964499	+	0.657584i
$383$	0.466900	−	0.0703738i	0.0238575	−	0.00359594i	−0.137103	−	0.990557i	$-0.543779\pi$
$383$	0.466900	−	0.0703738i	0.0238575	−	0.00359594i	0.160960	+	0.986961i	$0.448541\pi$
$384$		0			0
$385$	−24.3468	−	12.5590i	−1.24083	−	0.640063i
$386$	47.4808	−	22.8656i	2.41671	−	1.16383i
$387$		0			0
$388$	−3.00289	+	2.78628i	−0.152449	+	0.141452i
$389$	−1.25556	−	16.7543i	−0.0636594	−	0.849475i	−0.934057	−	0.357125i	$-0.883757\pi$
$389$	−1.25556	−	16.7543i	−0.0636594	−	0.849475i	0.870397	−	0.492350i	$-0.163862\pi$
$390$		0			0
$391$	−44.8861			−2.26999
$392$	−1.75978	+	1.97406i	−0.0888824	+	0.0997053i
$393$		0			0
$394$	16.6601	+	42.4493i	0.839326	+	2.13857i
$395$	−2.63505	−	35.1623i	−0.132584	−	1.76921i
$396$		0			0
$397$	−22.1720	+	15.1166i	−1.11278	+	0.758680i	−0.972840	−	0.231480i	$-0.925643\pi$
$397$	−22.1720	+	15.1166i	−1.11278	+	0.758680i	−0.139939	+	0.990160i	$0.544691\pi$
$398$	−17.0268	+	8.19967i	−0.853475	+	0.411012i
$399$		0			0
$400$	16.3143	+	7.85655i	0.815714	+	0.392827i
$401$	−17.5058	+	2.63858i	−0.874199	+	0.131764i	−0.570790	−	0.821096i	$-0.693363\pi$
$401$	−17.5058	+	2.63858i	−0.874199	+	0.131764i	−0.303409	+	0.952860i	$0.598125\pi$
$402$		0			0
$403$	−4.18203	−	0.630339i	−0.208322	−	0.0313994i
$404$	1.85003	+	1.71658i	0.0920424	+	0.0854029i
$405$		0			0
$406$	25.0973	+	24.6021i	1.24556	+	1.22098i
$407$	−12.9202	−	16.2014i	−0.640431	−	0.803076i
$408$		0			0
$409$	−9.80566	+	3.02464i	−0.484859	+	0.149559i	−0.527541	−	0.849530i	$-0.676886\pi$
$409$	−9.80566	+	3.02464i	−0.484859	+	0.149559i	0.0426824	+	0.999089i	$0.486410\pi$
$410$	−19.0172	−	32.9388i	−0.939194	−	1.62673i
$411$		0			0
$412$	−7.98458	+	34.9827i	−0.393372	+	1.72348i
$413$	−1.38639	−	29.2496i	−0.0682199	−	1.43928i
$414$		0			0
$415$	−7.43854	−	2.29449i	−0.365144	−	0.112632i
$416$	−12.2958	+	31.3292i	−0.602851	+	1.53604i
$417$		0			0
$418$	2.94076	+	0.907104i	0.143837	+	0.0443679i
$419$	0.830080	+	3.63682i	0.0405521	+	0.177670i	0.991148	−	0.132760i	$-0.0423840\pi$
$419$	0.830080	+	3.63682i	0.0405521	+	0.177670i	−0.950596	+	0.310430i	$0.899527\pi$
$420$		0			0
$421$	−6.79690	+	29.7792i	−0.331260	+	1.45135i	0.485432	+	0.874274i	$0.338662\pi$
$421$	−6.79690	+	29.7792i	−0.331260	+	1.45135i	−0.816693	+	0.577073i	$0.804195\pi$
$422$	−11.9722	+	20.7365i	−0.582797	+	1.00943i
$423$		0			0
$424$	−2.54382	+	0.784664i	−0.123539	+	0.0381067i
$425$	−2.37985	+	31.7569i	−0.115440	+	1.54044i
$426$		0			0
$427$	−0.0187386	+	0.182648i	−0.000906825	+	0.00883895i
$428$	7.23768	−	9.07576i	0.349846	−	0.438694i
$429$		0			0
$430$	−19.9838	−	3.01208i	−0.963706	−	0.145255i
$431$	6.12611	+	4.17671i	0.295084	+	0.201185i	0.701808	−	0.712366i	$-0.252376\pi$
$431$	6.12611	+	4.17671i	0.295084	+	0.201185i	−0.406724	+	0.913551i	$0.633329\pi$
$432$		0			0
$433$	17.8059	+	8.57485i	0.855695	+	0.412081i	0.809688	−	0.586860i	$-0.199636\pi$
$433$	17.8059	+	8.57485i	0.855695	+	0.412081i	0.0460064	+	0.998941i	$0.485351\pi$
$434$	−5.01269	−	0.137566i	−0.240617	−	0.00660338i
$435$		0			0
$436$	3.58975	−	2.44745i	0.171918	−	0.117212i
$437$	1.98342	−	1.84034i	0.0948796	−	0.0880354i
$438$		0			0
$439$	7.43134	+	18.9348i	0.354679	+	0.903706i	0.991191	+	0.132440i	$0.0422812\pi$
$439$	7.43134	+	18.9348i	0.354679	+	0.903706i	−0.636512	+	0.771266i	$0.719624\pi$
$440$	3.91185			0.186490
$441$		0			0
$442$	−64.9760			−3.09059
$443$	−4.05982	−	10.3442i	−0.192888	−	0.491470i	0.801409	−	0.598116i	$-0.204084\pi$
$443$	−4.05982	−	10.3442i	−0.192888	−	0.491470i	−0.994297	+	0.106646i	$0.965989\pi$
$444$		0			0
$445$	−5.53859	+	5.13906i	−0.262554	+	0.243615i
$446$	31.5029	−	21.4783i	1.49170	−	1.01703i
$447$		0			0
$448$	−4.20823	+	16.3554i	−0.198820	+	0.772722i
$449$	36.2494	+	17.4568i	1.71071	+	0.823837i	0.991660	+	0.128884i	$0.0411394\pi$
$449$	36.2494	+	17.4568i	1.71071	+	0.823837i	0.719055	+	0.694953i	$0.244575\pi$
$450$		0			0
$451$	−18.2021	−	12.4100i	−0.857106	−	0.584365i
$452$	1.94959	+	0.293853i	0.0917010	+	0.0138217i
$453$		0			0
$454$	0.543108	−	0.681036i	0.0254893	−	0.0319626i
$455$	−29.3354	+	18.8429i	−1.37526	+	0.883368i
$456$		0			0
$457$	1.00228	−	13.3745i	0.0468847	−	0.625633i	−0.923427	−	0.383774i	$-0.874624\pi$
$457$	1.00228	−	13.3745i	0.0468847	−	0.625633i	0.970312	−	0.241858i	$-0.0777569\pi$
$458$	5.81930	−	1.79501i	0.271918	−	0.0838755i
$459$		0			0
$460$	−16.0412	+	27.7841i	−0.747923	+	1.29544i
$461$	5.42370	−	23.7628i	0.252607	−	1.10674i	−0.676357	−	0.736574i	$-0.736442\pi$
$461$	5.42370	−	23.7628i	0.252607	−	1.10674i	0.928964	−	0.370170i	$-0.120700\pi$
$462$		0			0
$463$	4.43592	+	19.4350i	0.206155	+	0.903223i	0.967098	+	0.254404i	$0.0818794\pi$
$463$	4.43592	+	19.4350i	0.206155	+	0.903223i	−0.760943	+	0.648818i	$0.775263\pi$
$464$	−28.3000	−	8.72939i	−1.31379	−	0.405252i
$465$		0			0
$466$	−1.74880	+	4.45587i	−0.0810117	+	0.206414i
$467$	31.4648	+	9.70561i	1.45602	+	0.449122i	0.918936	−	0.394408i	$-0.129050\pi$
$467$	31.4648	+	9.70561i	1.45602	+	0.449122i	0.537082	+	0.843530i	$0.319526\pi$
$468$		0			0
$469$	3.90045	−	9.18862i	0.180106	−	0.424291i
$470$	6.18238	−	27.0868i	0.285172	−	1.24942i
$471$		0			0
$472$	2.09067	+	3.62115i	0.0962311	+	0.166677i
$473$	−11.1856	+	3.45031i	−0.514316	+	0.158645i
$474$		0			0
$475$	−1.19688	−	1.50084i	−0.0549167	−	0.0688633i
$476$	−36.2884	+	4.45529i	−1.66328	+	0.204208i
$477$		0			0
$478$	−24.2279	−	22.4802i	−1.10816	−	1.02822i
$479$	−35.6287	−	5.37017i	−1.62792	−	0.245369i	−0.729331	−	0.684162i	$-0.760168\pi$
$479$	−35.6287	−	5.37017i	−1.62792	−	0.245369i	−0.898589	+	0.438792i	$0.855406\pi$
$480$		0			0
$481$	−26.0788	+	3.93074i	−1.18909	+	0.179226i
$482$	−7.54932	−	3.63556i	−0.343862	−	0.165595i
$483$		0			0
$484$	−1.14069	+	0.549329i	−0.0518497	+	0.0249695i
$485$	5.67182	−	3.86698i	0.257544	−	0.175591i
$486$		0			0
$487$	−0.952918	−	12.7158i	−0.0431808	−	0.576208i	−0.976269	−	0.216561i	$-0.930516\pi$
$487$	−0.952918	−	12.7158i	−0.0431808	−	0.576208i	0.933088	−	0.359647i	$-0.117103\pi$
$488$	−0.00957844	−	0.0244055i	−0.000433596	−	0.00110478i
$489$		0			0
$490$	−31.8007	+	26.4138i	−1.43661	+	1.19325i
$491$	30.1941			1.36264			0.681321	−	0.731985i	$-0.261406\pi$
$491$	30.1941			1.36264			0.681321	+	0.731985i	$0.261406\pi$
$492$		0			0
$493$	−3.89237	−	51.9401i	−0.175303	−	2.33926i
$494$	2.87114	−	2.66403i	0.129179	−	0.119861i
$495$		0			0
$496$	3.80723	−	1.83346i	0.170950	−	0.0823250i
$497$	−8.99250	+	10.6625i	−0.403369	+	0.478279i
$498$		0			0
$499$	34.6900	−	5.22868i	1.55294	−	0.234068i	0.684183	−	0.729310i	$-0.260159\pi$
$499$	34.6900	−	5.22868i	1.55294	−	0.234068i	0.868755	+	0.495242i	$0.164921\pi$
$500$	−3.78208	−	2.57858i	−0.169140	−	0.115318i
$501$		0			0
$502$	−16.8345	−	15.6201i	−0.751359	−	0.697160i
$503$	15.1573	−	19.0067i	0.675831	−	0.847466i	−0.319131	−	0.947710i	$-0.603391\pi$
$503$	15.1573	−	19.0067i	0.675831	−	0.847466i	0.994963	+	0.100245i	$0.0319626\pi$
$504$		0			0
$505$	−2.63685	−	3.30650i	−0.117338	−	0.147137i
$506$	−2.92622	+	39.0477i	−0.130086	+	1.73588i
$507$		0			0
$508$	6.86429	+	11.8893i	0.304554	+	0.527503i
$509$	−8.11625	+	14.0578i	−0.359747	+	0.623099i	−0.987918	−	0.154975i	$-0.950470\pi$
$509$	−8.11625	+	14.0578i	−0.359747	+	0.623099i	0.628172	+	0.778075i	$0.283804\pi$
$510$		0			0
$511$	20.7985	−	5.79564i	0.920071	−	0.256384i
$512$	−6.75143	−	29.5800i	−0.298374	−	1.30726i
$513$		0			0
$514$	9.70067	−	24.7169i	0.427878	−	1.09022i
$515$	21.9680	−	55.9736i	0.968027	−	2.46649i
$516$		0			0
$517$	−3.58093	−	15.6891i	−0.157489	−	0.690004i
$518$	−30.1228	+	8.39393i	−1.32352	+	0.368808i
$519$		0			0
$520$	2.48930	−	4.31159i	0.109163	−	0.189076i
$521$	6.66345	+	11.5414i	0.291931	+	0.505639i	0.974266	−	0.225400i	$-0.0723689\pi$
$521$	6.66345	+	11.5414i	0.291931	+	0.505639i	−0.682335	+	0.731039i	$0.739036\pi$
$522$		0			0
$523$	0.807242	−	10.7719i	0.0352982	−	0.471022i	−0.951345	−	0.308127i	$-0.900298\pi$
$523$	0.807242	−	10.7719i	0.0352982	−	0.471022i	0.986643	−	0.162895i	$-0.0520832\pi$
$524$	0.964585	+	1.20955i	0.0421381	+	0.0528395i
$525$		0			0
$526$	−1.20298	+	1.50849i	−0.0524525	+	0.0657734i
$527$	5.44791	+	5.05492i	0.237315	+	0.220196i
$528$		0			0
$529$	9.44115	+	6.43687i	0.410485	+	0.279864i
$530$	−41.1488	+	6.20218i	−1.78739	+	0.269406i
$531$		0			0
$532$	1.42084	−	1.68470i	0.0616010	−	0.0730411i
$533$	−25.2611	+	12.1651i	−1.09418	+	0.526928i
$534$		0			0
$535$	−14.2599	+	13.2312i	−0.616509	+	0.572037i
$536$	0.106520	+	1.42141i	0.00460095	+	0.0613954i
$537$		0			0
$538$	48.2372			2.07965
$539$	−9.95726	+	21.7761i	−0.428889	+	0.937962i
$540$		0			0
$541$	4.49073	+	11.4422i	0.193071	+	0.491938i	0.994325	−	0.106387i	$-0.0339283\pi$
$541$	4.49073	+	11.4422i	0.193071	+	0.491938i	−0.801253	+	0.598325i	$0.795833\pi$
$542$	3.71091	+	49.5187i	0.159397	+	2.12701i
$543$		0			0
$544$	48.8646	−	33.3153i	2.09505	−	1.42838i
$545$	−6.55965	+	3.15896i	−0.280984	+	0.135315i
$546$		0			0
$547$	−24.0469	−	11.5804i	−1.02817	−	0.495141i	−0.157765	−	0.987477i	$-0.550429\pi$
$547$	−24.0469	−	11.5804i	−1.02817	−	0.495141i	−0.870405	+	0.492336i	$0.836143\pi$
$548$	24.2320	−	3.65238i	1.03514	−	0.156022i
$549$		0			0
$550$	27.4711	+	4.14061i	1.17137	+	0.176556i
$551$	2.30155	+	2.13553i	0.0980494	+	0.0909765i
$552$		0			0
$553$	−30.5900	+	3.75566i	−1.30082	+	0.159707i
$554$	−12.1405	−	15.2237i	−0.515802	−	0.646795i
$555$		0			0
$556$	22.0591	−	6.80432i	0.935513	−	0.288568i
$557$	−9.85957	−	17.0773i	−0.417763	−	0.723587i	0.577951	−	0.816072i	$-0.303853\pi$
$557$	−9.85957	−	17.0773i	−0.417763	−	0.723587i	−0.995714	+	0.0924844i	$0.970519\pi$
$558$		0			0
$559$	−3.31506	+	14.5242i	−0.140212	+	0.614310i
$560$	13.6120	−	32.0669i	0.575210	−	1.35507i
$561$		0			0
$562$	−14.8744	−	4.58814i	−0.627438	−	0.193539i
$563$	0.653897	−	1.66610i	0.0275585	−	0.0702178i	−0.916432	−	0.400190i	$-0.868944\pi$
$563$	0.653897	−	1.66610i	0.0275585	−	0.0702178i	0.943991	+	0.329972i	$0.107039\pi$
$564$		0			0
$565$	−3.15716	−	0.973855i	−0.132823	−	0.0409704i
$566$	2.13920	+	9.37245i	0.0899173	+	0.393953i
$567$		0			0
$568$	0.443200	−	1.94179i	0.0185963	−	0.0814755i
$569$	21.9029	−	37.9370i	0.918219	−	1.59040i	0.116101	−	0.993237i	$-0.462960\pi$
$569$	21.9029	−	37.9370i	0.918219	−	1.59040i	0.802119	−	0.597165i	$-0.203706\pi$
$570$		0			0
$571$	11.6165	−	3.58321i	0.486134	−	0.149953i	−0.0419927	−	0.999118i	$-0.513371\pi$
$571$	11.6165	−	3.58321i	0.486134	−	0.149953i	0.528127	+	0.849165i	$0.322894\pi$
$572$	−2.01022	+	26.8245i	−0.0840514	+	1.12159i
$573$		0			0
$574$	−27.9708	+	17.9664i	−1.16748	+	0.749901i
$575$	15.2288	−	19.0964i	0.635087	−	0.796373i
$576$		0			0
$577$	5.10571	+	0.769562i	0.212553	+	0.0320373i	0.254456	−	0.967084i	$-0.418104\pi$
$577$	5.10571	+	0.769562i	0.212553	+	0.0320373i	−0.0419022	+	0.999122i	$0.513342\pi$
$578$	66.9347	+	45.6353i	2.78412	+	1.89818i
$579$		0			0
$580$	−33.5415	−	16.1527i	−1.39274	−	0.670706i
$581$	−1.69541	+	6.58928i	−0.0703376	+	0.273370i
$582$		0			0
$583$	−19.9150	+	13.5778i	−0.824795	+	0.562336i
$584$	−2.26003	+	2.09700i	−0.0935206	+	0.0867744i
$585$		0			0
$586$	−17.9859	−	45.8272i	−0.742989	−	1.89311i
$587$	−19.1939			−0.792218			−0.396109	−	0.918203i	$-0.629640\pi$
$587$	−19.1939			−0.792218			−0.396109	+	0.918203i	$0.629640\pi$
$588$		0			0
$589$	−0.447984			−0.0184589
$590$	23.8796	+	60.8443i	0.983108	+	2.50492i
$591$		0			0
$592$	19.3167	−	17.9233i	0.793913	−	0.736644i
$593$	−7.88708	+	5.37732i	−0.323884	+	0.220820i	−0.714336	−	0.699803i	$-0.753271\pi$
$593$	−7.88708	+	5.37732i	−0.323884	+	0.220820i	0.390452	+	0.920623i	$0.372319\pi$
$594$		0			0
$595$	61.2442	+	1.68076i	2.51077	+	0.0689043i
$596$	−22.1960	−	10.6890i	−0.909183	−	0.437840i
$597$		0			0
$598$	41.1758	+	28.0732i	1.68380	+	1.14800i
$599$	12.9057	+	1.94522i	0.527313	+	0.0794796i	0.407303	−	0.913293i	$-0.366469\pi$
$599$	12.9057	+	1.94522i	0.527313	+	0.0794796i	0.120010	+	0.992773i	$0.461707\pi$
$600$		0			0
$601$	1.03502	−	1.29787i	0.0422193	−	0.0529414i	−0.760274	−	0.649603i	$-0.774935\pi$
$601$	1.03502	−	1.29787i	0.0422193	−	0.0529414i	0.802493	+	0.596662i	$0.203507\pi$
$602$	−1.80277	+	17.5718i	−0.0734753	+	0.716174i
$603$		0			0
$604$	2.53672	−	33.8501i	0.103217	−	1.37734i
$605$	2.02738	−	0.625363i	0.0824246	−	0.0254246i
$606$		0			0
$607$	−10.2847	+	17.8136i	−0.417442	+	0.723031i	−0.995681	−	0.0928362i	$-0.970407\pi$
$607$	−10.2847	+	17.8136i	−0.417442	+	0.723031i	0.578239	+	0.815867i	$0.303740\pi$
$608$	−0.793280	+	3.47559i	−0.0321718	+	0.140954i
$609$		0			0
$610$	−0.0911969	−	0.399560i	−0.00369245	−	0.0161777i
$611$	−19.5710	−	6.03685i	−0.791757	−	0.244225i
$612$		0			0
$613$	0.833246	−	2.12308i	0.0336545	−	0.0857502i	−0.913059	−	0.407828i	$-0.866286\pi$
$613$	0.833246	−	2.12308i	0.0336545	−	0.0857502i	0.946713	+	0.322078i	$0.104381\pi$
$614$	20.3733	+	6.28435i	0.822201	+	0.253616i
$615$		0			0
$616$	−0.161880	−	3.41530i	−0.00652235	−	0.137606i
$617$	5.23564	−	22.9389i	0.210779	−	0.923484i	−0.753260	−	0.657723i	$-0.771520\pi$
$617$	5.23564	−	22.9389i	0.210779	−	0.923484i	0.964039	−	0.265761i	$-0.0856231\pi$
$618$		0			0
$619$	13.5222	+	23.4211i	0.543503	+	0.941375i	0.998699	+	0.0509838i	$0.0162357\pi$
$619$	13.5222	+	23.4211i	0.543503	+	0.941375i	−0.455196	+	0.890391i	$0.650431\pi$
$620$	5.07590	−	1.56571i	0.203853	−	0.0628804i
$621$		0			0
$622$	11.8243	+	14.8272i	0.474110	+	0.594515i
$623$	4.71593	+	4.62288i	0.188940	+	0.185212i
$624$		0			0
$625$	20.8809	+	19.3747i	0.835238	+	0.774988i
$626$	9.23599	+	1.39210i	0.369145	+	0.0556396i
$627$		0			0
$628$	21.7539	−	3.27888i	0.868076	−	0.130841i
$629$	41.7546	+	20.1080i	1.66487	+	0.801758i
$630$		0			0
$631$	−2.69955	+	1.30003i	−0.107467	+	0.0517536i	−0.486845	−	0.873488i	$-0.661852\pi$
$631$	−2.69955	+	1.30003i	−0.107467	+	0.0517536i	0.379378	+	0.925242i	$0.376138\pi$
$632$	3.63615	−	2.47908i	0.144638	−	0.0986127i
$633$		0			0
$634$	5.00513	+	66.7888i	0.198779	+	2.65252i
$635$	−8.40497	−	21.4155i	−0.333541	−	0.849848i
$636$		0			0
$637$	17.6650	+	24.8319i	0.699913	+	0.983876i
$638$	−45.4380			−1.79891
$639$		0			0
$640$	0.680483	+	9.08042i	0.0268985	+	0.358935i
$641$	−12.7310	+	11.8126i	−0.502844	+	0.466571i	−0.890337	−	0.455302i	$-0.849531\pi$
$641$	−12.7310	+	11.8126i	−0.502844	+	0.466571i	0.387493	+	0.921872i	$0.373341\pi$
$642$		0			0
$643$	32.6018	−	15.7002i	1.28569	−	0.619155i	0.338843	−	0.940843i	$-0.389964\pi$
$643$	32.6018	−	15.7002i	1.28569	−	0.619155i	0.946846	+	0.321688i	$0.104250\pi$
$644$	24.9212	+	12.8552i	0.982031	+	0.506567i
$645$		0			0
$646$	−6.80569	+	1.02579i	−0.267766	+	0.0403593i
$647$	−18.3861	−	12.5355i	−0.722834	−	0.492820i	0.145151	−	0.989409i	$-0.453633\pi$
$647$	−18.3861	−	12.5355i	−0.722834	−	0.492820i	−0.867985	+	0.496590i	$0.834585\pi$
$648$		0			0
$649$	27.7526	+	25.7506i	1.08938	+	1.01080i
$650$	22.0449	−	27.6434i	0.864673	−	1.08427i
$651$		0			0
$652$	−10.4768	−	13.1375i	−0.410305	−	0.514506i
$653$	−1.91414	+	25.5424i	−0.0749059	+	0.999550i	0.825472	+	0.564442i	$0.190909\pi$
$653$	−1.91414	+	25.5424i	−0.0749059	+	0.999550i	−0.900378	+	0.435108i	$0.856710\pi$
$654$		0			0
$655$	−1.29626	−	2.24519i	−0.0506491	−	0.0877268i
$656$	14.0070	−	24.2609i	0.546882	−	0.947228i
$657$		0			0
$658$	−23.9043	−	4.27671i	−0.931888	−	0.166724i
$659$	−3.91920	−	17.1712i	−0.152671	−	0.668893i	−0.992103	−	0.125429i	$-0.959969\pi$
$659$	−3.91920	−	17.1712i	−0.152671	−	0.668893i	0.839432	−	0.543465i	$-0.182888\pi$
$660$		0			0
$661$	4.12689	−	10.5151i	0.160517	−	0.408992i	−0.827875	−	0.560912i	$-0.810451\pi$
$661$	4.12689	−	10.5151i	0.160517	−	0.408992i	0.988393	+	0.151920i	$0.0485458\pi$
$662$	−10.3742	+	26.4332i	−0.403207	+	1.02735i
$663$		0			0
$664$	−0.216191	−	0.947194i	−0.00838983	−	0.0367582i
$665$	−2.77515	+	2.43676i	−0.107616	+	0.0944934i
$666$		0			0
$667$	−19.9743	+	34.5965i	−0.773408	+	1.33958i
$668$	−12.4647	−	21.5895i	−0.482275	−	0.835325i
$669$		0			0
$670$	−1.66511	+	22.2193i	−0.0643287	+	0.858407i
$671$	−0.148006	−	0.185593i	−0.00571369	−	0.00716474i
$672$		0			0
$673$	−30.1357	+	37.7890i	−1.16165	+	1.45666i	−0.296574	+	0.955010i	$0.595844\pi$
$673$	−30.1357	+	37.7890i	−1.16165	+	1.45666i	−0.865072	+	0.501648i	$0.832727\pi$
$674$	28.0227	+	26.0013i	1.07940	+	1.00153i
$675$		0			0
$676$	8.88412	+	6.05709i	0.341697	+	0.232965i
$677$	−35.1547	+	5.29871i	−1.35110	+	0.203646i	−0.784390	−	0.620268i	$-0.787024\pi$
$677$	−35.1547	+	5.29871i	−1.35110	+	0.203646i	−0.566714	+	0.823915i	$0.691786\pi$
$678$		0			0
$679$	−3.61084	−	4.79184i	−0.138571	−	0.183894i
$680$	−7.88218	+	3.79586i	−0.302268	+	0.145564i
$681$		0			0
$682$	4.75259	−	4.40975i	0.181986	−	0.168858i
$683$	0.123938	+	1.65384i	0.00474236	+	0.0632825i	0.999073	−	0.0430512i	$-0.0137079\pi$
$683$	0.123938	+	1.65384i	0.00474236	+	0.0632825i	−0.994331	+	0.106334i	$0.966089\pi$
$684$		0			0
$685$	−41.0656			−1.56904
$686$	24.3769	+	26.6711i	0.930716	+	1.01831i
$687$		0			0
$688$	−5.43818	−	13.8563i	−0.207329	−	0.528265i
$689$	2.29242	+	30.5903i	0.0873344	+	1.16540i
$690$		0			0
$691$	18.1959	−	12.4058i	0.692206	−	0.471938i	−0.165412	−	0.986225i	$-0.552895\pi$
$691$	18.1959	−	12.4058i	0.692206	−	0.471938i	0.857619	+	0.514286i	$0.171943\pi$
$692$	1.13175	−	0.545022i	0.0430227	−	0.0207186i
$693$		0			0
$694$	28.5280	+	13.7384i	1.08291	+	0.521501i
$695$	−38.2523	+	5.76560i	−1.45099	+	0.218702i
$696$		0			0
$697$	48.7185	+	7.34313i	1.84534	+	0.278141i
$698$	17.4151	+	16.1589i	0.659171	+	0.611622i
$699$		0			0
$700$	10.4164	−	16.9501i	0.393702	−	0.640655i
$701$	7.66942	+	9.61715i	0.289670	+	0.363235i	0.905279	−	0.424817i	$-0.139661\pi$
$701$	7.66942	+	9.61715i	0.289670	+	0.363235i	−0.615609	+	0.788052i	$0.711090\pi$
$702$		0			0
$703$	−2.66948	+	0.823424i	−0.100681	+	0.0310560i
$704$	−10.9172	−	18.9092i	−0.411459	−	0.712667i
$705$		0			0
$706$	4.51828	−	19.7959i	0.170048	−	0.745028i
$707$	−2.77767	+	2.43897i	−0.104465	+	0.0917269i
$708$		0			0
$709$	−38.8180	−	11.9738i	−1.45784	−	0.449684i	−0.538324	−	0.842738i	$-0.680942\pi$
$709$	−38.8180	−	11.9738i	−1.45784	−	0.449684i	−0.919516	+	0.393054i	$0.871419\pi$
$710$	11.3747	−	28.9823i	0.426885	−	1.08768i
$711$		0			0
$712$	−0.901095	−	0.277951i	−0.0337699	−	0.0104166i
$713$	−1.26838	−	5.55713i	−0.0475012	−	0.208116i
$714$		0			0
$715$	10.0307	−	43.9472i	0.375126	−	1.64353i
$716$	13.0442	−	22.5931i	0.487483	−	0.844345i
$717$		0			0
$718$	8.31863	−	2.56596i	0.310449	−	0.0957607i
$719$	0.737799	−	9.84525i	0.0275153	−	0.367166i	−0.966402	−	0.257036i	$-0.917254\pi$
$719$	0.737799	−	9.84525i	0.0275153	−	0.367166i	0.993917	−	0.110130i	$-0.0351268\pi$
$720$		0			0
$721$	−49.7777	−	16.8632i	−1.85382	−	0.628019i
$722$	−22.8533	+	28.6572i	−0.850513	+	1.06651i
$723$		0			0
$724$	−30.6238	−	4.61580i	−1.13812	−	0.171545i
$725$	23.4180	+	15.9661i	0.869723	+	0.592967i
$726$		0			0
$727$	13.9445	+	6.71531i	0.517172	+	0.249057i	0.674215	−	0.738535i	$-0.264482\pi$
$727$	13.9445	+	6.71531i	0.517172	+	0.249057i	−0.157043	+	0.987592i	$0.550196\pi$
$728$	−3.86731	−	1.99490i	−0.143332	−	0.0739357i
$729$		0			0
$730$	−39.8196	+	27.1486i	−1.47379	+	1.00481i
$731$	19.1905	−	17.8062i	0.709785	−	0.658585i
$732$		0			0
$733$	1.03965	+	2.64899i	0.0384004	+	0.0978426i	0.948788	−	0.315915i	$-0.102311\pi$
$733$	1.03965	+	2.64899i	0.0384004	+	0.0978426i	−0.910387	+	0.413757i	$0.864216\pi$
$734$	33.2114			1.22585
$735$		0			0
$736$	−45.3599			−1.67199
$737$	4.71504	+	12.0137i	0.173681	+	0.442531i
$738$		0			0
$739$	6.92190	−	6.42259i	0.254626	−	0.236259i	−0.542523	−	0.840041i	$-0.682531\pi$
$739$	6.92190	−	6.42259i	0.254626	−	0.236259i	0.797149	+	0.603782i	$0.206340\pi$
$740$	27.3688	−	18.6597i	1.00610	−	0.685944i
$741$		0			0
$742$	7.11773	+	35.6689i	0.261300	+	1.30945i
$743$	22.8595	+	11.0086i	0.838635	+	0.403865i	0.803347	−	0.595512i	$-0.203051\pi$
$743$	22.8595	+	11.0086i	0.838635	+	0.403865i	0.0352884	+	0.999377i	$0.488765\pi$
$744$		0			0
$745$	34.1100	+	23.2558i	1.24969	+	0.852027i
$746$	61.5373	+	9.27526i	2.25304	+	0.339591i
$747$		0			0
$748$	29.4718	−	36.9565i	1.07760	−	1.35126i
$749$	12.1418	+	11.9023i	0.443653	+	0.434900i
$750$		0			0
$751$	−0.876307	+	11.6935i	−0.0319769	+	0.426702i	0.958125	+	0.286351i	$0.0924422\pi$
$751$	−0.876307	+	11.6935i	−0.0319769	+	0.426702i	−0.990102	+	0.140351i	$0.955177\pi$
$752$	19.5545	−	6.03176i	0.713079	−	0.219956i
$753$		0			0
$754$	−28.9143	+	50.0811i	−1.05300	+	1.82385i
$755$	−12.6578	+	55.4575i	−0.460665	+	2.01831i
$756$		0			0
$757$	−11.0281	−	48.3174i	−0.400824	−	1.75613i	−0.624074	−	0.781365i	$-0.714524\pi$
$757$	−11.0281	−	48.3174i	−0.400824	−	1.75613i	0.223250	−	0.974761i	$-0.428333\pi$
$758$	47.8068	+	14.7465i	1.73642	+	0.535615i
$759$		0			0
$760$	0.192665	−	0.490902i	0.00698869	−	0.0178069i
$761$	−38.3876	−	11.8410i	−1.39155	−	0.429236i	−0.493735	−	0.869613i	$-0.664369\pi$
$761$	−38.3876	−	11.8410i	−1.39155	−	0.429236i	−0.897813	+	0.440377i	$0.854845\pi$
$762$		0			0
$763$	3.02943	+	5.59627i	0.109673	+	0.202599i
$764$	−4.70054	+	20.5944i	−0.170060	+	0.745079i
$765$		0			0
$766$	0.460603	+	0.797787i	0.0166423	+	0.0288252i
$767$	46.0423	−	14.2022i	1.66249	−	0.512810i
$768$		0			0
$769$	−22.3501	−	28.0261i	−0.805965	−	1.01065i	−0.999563	−	0.0295668i	$-0.990587\pi$
$769$	−22.3501	−	28.0261i	−0.805965	−	1.01065i	0.193598	−	0.981081i	$-0.437984\pi$
$770$	5.45478	−	53.1686i	0.196577	−	1.91606i
$771$		0			0
$772$	35.7678	+	33.1877i	1.28731	+	1.19445i
$773$	−7.87836	−	1.18747i	−0.283365	−	0.0427104i	0.00582201	−	0.999983i	$-0.498147\pi$
$773$	−7.87836	−	1.18747i	−0.283365	−	0.0427104i	−0.289187	+	0.957273i	$0.593385\pi$
$774$		0			0
$775$	−3.99892	+	0.602740i	−0.143646	+	0.0216511i
$776$	0.771914	+	0.371734i	0.0277101	+	0.0133445i
$777$		0			0
$778$	29.5329	−	14.2223i	1.05881	−	0.509894i
$779$	−2.45383	+	1.67299i	−0.0879176	+	0.0599412i
$780$		0			0
$781$	−1.34765	−	17.9831i	−0.0482227	−	0.643487i
$782$	−31.9937	−	81.5187i	−1.14409	−	2.91510i
$783$		0			0
$784$	−28.5598	−	10.5571i	−1.01999	−	0.377040i
$785$	−36.8661			−1.31581
$786$		0			0
$787$	1.87042	+	24.9590i	0.0666732	+	0.889693i	0.925820	+	0.377964i	$0.123376\pi$
$787$	1.87042	+	24.9590i	0.0666732	+	0.889693i	−0.859147	+	0.511729i	$0.829005\pi$
$788$	−30.9502	+	28.7176i	−1.10256	+	1.02302i
$789$		0			0
$790$	61.9810	−	29.8485i	2.20518	−	1.06196i
$791$	−0.719589	+	2.79671i	−0.0255856	+	0.0994394i
$792$		0			0
$793$	−0.298741	+	0.0450280i	−0.0106086	+	0.00159899i
$794$	−43.2572	−	29.4923i	−1.53514	−	1.04664i
$795$		0			0
$796$	−12.8264	−	11.9012i	−0.454621	−	0.421827i
$797$	4.58996	−	5.75562i	0.162585	−	0.203875i	−0.693865	−	0.720105i	$-0.744094\pi$
$797$	4.58996	−	5.75562i	0.162585	−	0.203875i	0.856450	+	0.516230i	$0.172665\pi$
$798$		0			0
$799$	22.4392	+	28.1379i	0.793843	+	0.995448i
$800$	−2.40497	+	32.0921i	−0.0850286	+	1.13463i
$801$		0			0
$802$	−17.2697	−	29.9120i	−0.609815	−	1.05623i
$803$	−13.9573	+	24.1747i	−0.492542	+	0.853108i
$804$		0			0
$805$	−38.0847	−	27.5259i	−1.34231	−	0.970162i
$806$	−1.83608	−	8.04437i	−0.0646730	−	0.283351i
$807$		0			0
$808$	0.192840	−	0.491347i	0.00678408	−	0.0172855i
$809$	−0.767250	+	1.95492i	−0.0269751	+	0.0687314i	−0.943727	−	0.330726i	$-0.892706\pi$
$809$	−0.767250	+	1.95492i	−0.0269751	+	0.0687314i	0.916752	+	0.399458i	$0.130802\pi$
$810$		0			0
$811$	1.31295	+	5.75241i	0.0461039	+	0.201994i	0.992734	−	0.120326i	$-0.0383941\pi$
$811$	1.31295	+	5.75241i	0.0461039	+	0.201994i	−0.946630	+	0.322321i	$0.895537\pi$
$812$	−12.7144	+	29.9524i	−0.446187	+	1.05112i
$813$		0			0
$814$	20.2146	−	35.0127i	0.708522	−	1.22720i
$815$	14.0793	+	24.3861i	0.493178	+	0.854209i
$816$		0			0
$817$	−0.117927	+	1.57363i	−0.00412575	+	0.0550543i
$818$	−12.4824	−	15.6524i	−0.436436	−	0.547273i
$819$		0			0
$820$	21.9561	−	27.5321i	0.766741	−	0.961462i
$821$	−5.93814	−	5.50979i	−0.207243	−	0.192293i	0.569722	−	0.821838i	$-0.307051\pi$
$821$	−5.93814	−	5.50979i	−0.207243	−	0.192293i	−0.776964	+	0.629545i	$0.783241\pi$
$822$		0			0
$823$	−35.9258	−	24.4938i	−1.25229	−	0.853800i	−0.258607	−	0.965983i	$-0.583263\pi$
$823$	−35.9258	−	24.4938i	−1.25229	−	0.853800i	−0.993688	+	0.112183i	$0.964216\pi$
$824$	7.42091	−	1.11852i	0.258520	−	0.0389656i
$825$		0			0
$826$	52.1328	−	23.3663i	1.81393	−	0.813018i
$827$	−4.92118	+	2.36992i	−0.171126	+	0.0824101i	−0.517486	−	0.855692i	$-0.673132\pi$
$827$	−4.92118	+	2.36992i	−0.171126	+	0.0824101i	0.346360	+	0.938102i	$0.387418\pi$
$828$		0			0
$829$	−27.5164	+	25.5315i	−0.955686	+	0.886747i	−0.993648	−	0.112532i	$-0.964104\pi$
$829$	−27.5164	+	25.5315i	−0.955686	+	0.886747i	0.0379623	+	0.999279i	$0.487913\pi$
$830$	−1.13494	−	15.1448i	−0.0393945	−	0.525683i
$831$		0			0
$832$	−27.7886			−0.963397
$833$	−1.06700	−	53.5397i	−0.0369694	−	1.85504i
$834$		0			0
$835$	15.2624	+	38.8880i	0.528177	+	1.34577i
$836$	0.212932	+	2.84137i	0.00736439	+	0.0982710i
$837$		0			0
$838$	−6.01325	+	4.09977i	−0.207724	+	0.141624i
$839$	16.0015	−	7.70590i	0.552432	−	0.266037i	−0.136774	−	0.990602i	$-0.543674\pi$
$839$	16.0015	−	7.70590i	0.552432	−	0.266037i	0.689207	+	0.724565i	$0.257959\pi$
$840$		0			0
$841$	−15.6375	−	7.53062i	−0.539224	−	0.259676i
$842$	−58.9273	+	8.88186i	−2.03077	+	0.306089i
$843$		0			0
$844$	−21.9217	−	3.30417i	−0.754577	−	0.113734i
$845$	−13.2086	−	12.2557i	−0.454388	−	0.421611i
$846$		0			0
$847$	−0.629879	−	1.74415i	−0.0216429	−	0.0599298i
$848$	−19.1101	−	23.9633i	−0.656243	−	0.822903i
$849$		0			0
$850$	−59.3708	+	18.3135i	−2.03640	+	0.628146i
$851$	−17.7725	−	30.7829i	−0.609233	−	1.05522i
$852$		0			0
$853$	4.02744	−	17.6454i	0.137897	−	0.604166i	−0.857998	−	0.513653i	$-0.828292\pi$
$853$	4.02744	−	17.6454i	0.137897	−	0.604166i	0.995895	−	0.0905136i	$-0.0288509\pi$
$854$	−0.345068	+	0.0961554i	−0.0118080	+	0.00329037i
$855$		0			0
$856$	−2.32000	−	0.715625i	−0.0792959	−	0.0244595i
$857$	−1.44920	+	3.69250i	−0.0495036	+	0.126133i	−0.953487	−	0.301435i	$-0.902534\pi$
$857$	−1.44920	+	3.69250i	−0.0495036	+	0.126133i	0.903983	+	0.427568i	$0.140630\pi$
$858$		0			0
$859$	−39.3390	−	12.1345i	−1.34223	−	0.414022i	−0.461288	−	0.887251i	$-0.652612\pi$
$859$	−39.3390	−	12.1345i	−1.34223	−	0.414022i	−0.880940	+	0.473228i	$0.843089\pi$
$860$	−4.16367	−	18.2422i	−0.141980	−	0.622055i
$861$		0			0
$862$	−3.21888	+	14.1028i	−0.109636	+	0.480345i
$863$	−0.761312	+	1.31863i	−0.0259154	+	0.0448867i	−0.878692	−	0.477389i	$-0.841583\pi$
$863$	−0.761312	+	1.31863i	−0.0259154	+	0.0448867i	0.852777	+	0.522275i	$0.174917\pi$
$864$		0			0
$865$	−2.01148	+	0.620460i	−0.0683925	+	0.0210963i
$866$	−2.88140	+	38.4496i	−0.0979139	+	1.30657i
$867$		0			0
$868$	−1.57702	−	4.36680i	−0.0535274	−	0.148219i
$869$	24.8438	−	31.1531i	0.842768	−	1.05680i
$870$		0			0
$871$	16.2418	+	2.44805i	0.550331	+	0.0829491i
$872$	−0.750790	−	0.511880i	−0.0254249	−	0.0173344i
$873$		0			0
$874$	4.75602	+	2.29038i	0.160875	+	0.0774732i
$875$	4.32246	−	5.12519i	0.146126	−	0.173263i
$876$		0			0
$877$	−20.1100	+	13.7108i	−0.679068	+	0.462981i	−0.853092	−	0.521761i	$-0.825275\pi$
$877$	−20.1100	+	13.7108i	−0.679068	+	0.462981i	0.174024	+	0.984741i	$0.444323\pi$
$878$	−29.0910	+	26.9925i	−0.981773	+	0.910952i
$879$		0			0
$880$	16.4548	+	41.9260i	0.554690	+	1.41333i
$881$	−25.5874			−0.862060			−0.431030	−	0.902338i	$-0.641850\pi$
$881$	−25.5874			−0.862060			−0.431030	+	0.902338i	$0.641850\pi$
$882$		0			0
$883$	−21.2143			−0.713917			−0.356958	−	0.934120i	$-0.616186\pi$
$883$	−21.2143			−0.713917			−0.356958	+	0.934120i	$0.616186\pi$
$884$	−21.9786	−	56.0006i	−0.739221	−	1.88350i
$885$		0			0
$886$	15.8927	−	14.7463i	0.533926	−	0.495411i
$887$	−37.1508	+	25.3290i	−1.24740	+	0.850463i	−0.993170	−	0.116680i	$-0.962775\pi$
$887$	−37.1508	+	25.3290i	−1.24740	+	0.850463i	−0.254231	+	0.967144i	$0.581822\pi$
$888$		0			0
$889$	−18.3493	+	8.22430i	−0.615416	+	0.275834i
$890$	−13.2809	−	6.39577i	−0.445178	−	0.214387i
$891$		0			0
$892$	29.1675	+	19.8860i	0.976599	+	0.665834i
$893$	−2.14520	−	0.323337i	−0.0717864	−	0.0108201i
$894$		0			0
$895$	−27.2576	+	34.1799i	−0.911120	+	1.14251i
$896$	7.89964	−	0.969873i	0.263908	−	0.0324012i
$897$		0			0
$898$	−5.86599	+	78.2762i	−0.195751	+	2.61211i
$899$	6.32047	−	1.94961i	0.210799	−	0.0650230i
$900$		0			0
$901$	26.9525	−	46.6831i	0.897918	−	1.55524i
$902$	9.56407	−	41.9029i	0.318449	−	1.39521i
$903$		0			0
$904$	−0.0917584	−	0.402020i	−0.00305184	−	0.0133710i
$905$	49.5921	+	15.2971i	1.64850	+	0.508494i
$906$		0			0
$907$	−1.88228	+	4.79598i	−0.0625002	+	0.159248i	−0.958712	−	0.284378i	$-0.908213\pi$
$907$	−1.88228	+	4.79598i	−0.0625002	+	0.159248i	0.896212	+	0.443626i	$0.146308\pi$
$908$	0.770672	+	0.237721i	0.0255756	+	0.00788904i
$909$		0			0
$910$	−55.1305	−	39.8459i	−1.82756	−	1.32088i
$911$	−4.34392	+	19.0320i	−0.143920	+	0.630557i	0.850582	+	0.525843i	$0.176250\pi$
$911$	−4.34392	+	19.0320i	−0.143920	+	0.630557i	−0.994502	+	0.104714i	$0.966607\pi$
$912$		0			0
$913$	−4.39834	−	7.61815i	−0.145564	−	0.252124i
$914$	25.0042	−	7.71276i	0.827064	−	0.255115i
$915$		0			0
$916$	3.51548	+	4.40827i	0.116155	+	0.145653i
$917$	−1.90656	+	1.22463i	−0.0629600	+	0.0404409i
$918$		0			0
$919$	39.1234	+	36.3012i	1.29056	+	1.19747i	0.968009	+	0.250916i	$0.0807317\pi$
$919$	39.1234	+	36.3012i	1.29056	+	1.19747i	0.322554	+	0.946551i	$0.395459\pi$
$920$	6.63501	+	1.00007i	0.218750	+	0.0329713i
$921$		0			0
$922$	47.0221	−	7.08744i	1.54859	−	0.233412i
$923$	−20.6783	−	9.95816i	−0.680635	−	0.327777i
$924$		0			0
$925$	−22.7212	+	10.9419i	−0.747068	+	0.359769i
$926$	−32.1346	+	21.9090i	−1.05601	+	0.719975i
$927$		0			0
$928$	−3.93345	−	52.4883i	−0.129122	−	1.72301i
$929$	6.87983	+	17.5295i	0.225720	+	0.575125i	0.998204	−	0.0599093i	$-0.0190812\pi$
$929$	6.87983	+	17.5295i	0.225720	+	0.575125i	−0.772484	+	0.635034i	$0.780986\pi$
$930$		0			0
$931$	2.24229	+	2.32205i	0.0734881	+	0.0761022i
$932$	−4.43191			−0.145172
$933$		0			0
$934$	4.80078	+	64.0619i	0.157086	+	2.09617i
$935$	−58.0662	+	53.8776i	−1.89897	+	1.76199i
$936$		0			0
$937$	−13.3793	+	6.44315i	−0.437084	+	0.210488i	−0.639468	−	0.768818i	$-0.720845\pi$
$937$	−13.3793	+	6.44315i	−0.437084	+	0.210488i	0.202384	+	0.979306i	$0.435131\pi$
$938$	19.4678	+	0.534266i	0.635647	+	0.0174444i
$939$		0			0
$940$	25.4364	−	3.83392i	0.829643	−	0.125049i
$941$	12.2965	+	8.38362i	0.400855	+	0.273298i	0.746922	−	0.664911i	$-0.231531\pi$
$941$	12.2965	+	8.38362i	0.400855	+	0.273298i	−0.346067	+	0.938210i	$0.612483\pi$
$942$		0			0
$943$	−27.7006	−	25.7024i	−0.902057	−	0.836986i
$944$	−30.0163	+	37.6392i	−0.976946	+	1.22505i
$945$		0			0
$946$	−14.2390	−	17.8552i	−0.462951	−	0.580522i
$947$	−3.19198	+	42.5940i	−0.103725	+	1.38412i	0.666100	+	0.745863i	$0.267962\pi$
$947$	−3.19198	+	42.5940i	−0.103725	+	1.38412i	−0.769825	+	0.638255i	$0.779657\pi$
$948$		0			0
$949$	17.7634	+	30.7671i	0.576624	+	0.998742i
$950$	1.87261	−	3.24345i	0.0607553	−	0.105231i
$951$		0			0
$952$	3.64021	+	6.72457i	0.117980	+	0.217945i
$953$	−2.15522	−	9.44264i	−0.0698144	−	0.305877i	0.927950	−	0.372704i	$-0.121569\pi$
$953$	−2.15522	−	9.44264i	−0.0698144	−	0.305877i	−0.997765	+	0.0668274i	$0.978712\pi$
$954$		0			0
$955$	12.9326	−	32.9518i	0.418490	−	1.06630i
$956$	11.1797	−	28.4853i	0.361576	−	0.921280i
$957$		0			0
$958$	−15.6424	−	68.5340i	−0.505384	−	2.21423i
$959$	1.69938	+	35.8530i	0.0548759	+	1.15775i
$960$		0			0
$961$	15.0281	−	26.0295i	0.484778	−	0.839660i
$962$	−25.7270	−	44.5605i	−0.829473	−	1.43669i
$963$		0			0
$964$	0.579752	−	7.73625i	0.0186726	−	0.249168i
$965$	−50.9798	−	63.9267i	−1.64110	−	2.05787i
$966$		0			0
$967$	5.99430	−	7.51661i	0.192764	−	0.241718i	−0.676052	−	0.736854i	$-0.736310\pi$
$967$	5.99430	−	7.51661i	0.192764	−	0.241718i	0.868815	+	0.495136i	$0.164882\pi$
$968$	0.194110	+	0.180108i	0.00623892	+	0.00578888i
$969$		0			0
$970$	11.0657	+	7.54444i	0.355297	+	0.242237i
$971$	−13.5790	+	2.04670i	−0.435769	+	0.0656817i	−0.363264	−	0.931686i	$-0.618338\pi$
$971$	−13.5790	+	2.04670i	−0.435769	+	0.0656817i	−0.0725056	+	0.997368i	$0.523100\pi$
$972$		0			0
$973$	6.61670	+	33.1581i	0.212122	+	1.06300i
$974$	22.4143	−	10.7941i	0.718199	−	0.345866i
$975$		0			0
$976$	0.221280	−	0.205318i	0.00708300	−	0.00657206i
$977$	−1.67126	−	22.3014i	−0.0534683	−	0.713485i	−0.957943	−	0.286958i	$-0.907356\pi$
$977$	−1.67126	−	22.3014i	−0.0534683	−	0.713485i	0.904475	−	0.426527i	$-0.140263\pi$
$978$		0			0
$979$	−8.53805			−0.272877
$980$	−33.5220	−	18.4733i	−1.07082	−	0.590108i
$981$		0			0
$982$	21.5216	+	54.8363i	0.686783	+	1.74990i
$983$	3.43993	+	45.9026i	0.109717	+	1.46407i	0.732016	+	0.681287i	$0.238580\pi$
$983$	3.43993	+	45.9026i	0.109717	+	1.46407i	−0.622300	+	0.782779i	$0.713801\pi$
$984$		0			0
$985$	58.4583	−	39.8562i	1.86264	−	1.26992i
$986$	91.5552	−	44.0907i	2.91571	−	1.40413i
$987$		0			0
$988$	3.26722	+	1.57341i	0.103944	+	0.0500569i
$989$	−19.8544	+	2.99257i	−0.631333	+	0.0951581i
$990$		0			0
$991$	21.8811	+	3.29805i	0.695076	+	0.104766i	0.487072	−	0.873362i	$-0.338065\pi$
$991$	21.8811	+	3.29805i	0.695076	+	0.104766i	0.208004	+	0.978128i	$0.433303\pi$
$992$	5.50541	+	5.10828i	0.174797	+	0.162188i
$993$		0			0
$994$	−25.7741	−	8.73150i	−0.817505	−	0.276946i
$995$	18.2815	+	22.9243i	0.579563	+	0.726750i
$996$		0			0
$997$	−6.11128	+	1.88508i	−0.193546	+	0.0597011i	−0.390013	−	0.920809i	$-0.627529\pi$
$997$	−6.11128	+	1.88508i	−0.193546	+	0.0597011i	0.196467	+	0.980511i	$0.437053\pi$
$998$	34.2221	+	59.2745i	1.08328	+	1.87630i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.c.163.4		48
3.2	odd	2		147.2.m.a.16.1	✓	48
49.46	even	21	inner	441.2.bb.c.46.4		48
147.86	odd	42		7203.2.a.i.1.6		24
147.95	odd	42		147.2.m.a.46.1	yes	48
147.110	even	42		7203.2.a.k.1.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.a.16.1	✓	48	3.2	odd	2
147.2.m.a.46.1	yes	48	147.95	odd	42
441.2.bb.c.46.4		48	49.46	even	21	inner
441.2.bb.c.163.4		48	1.1	even	1	trivial
7203.2.a.i.1.6		24	147.86	odd	42
7203.2.a.k.1.6		24	147.110	even	42

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.712776 + 1.81612i) q^{2} +(-1.32415 + 1.22863i) q^{4} +(2.50104 - 1.70518i) q^{5} +(-1.59223 - 2.11301i) q^{7} +(0.340382 + 0.163920i) q^{8} +(4.87950 + 3.32679i) q^{10} +(3.38245 + 0.509823i) q^{11} +(2.71434 - 3.40367i) q^{13} +(2.70258 - 4.39779i) q^{14} +(-0.325060 + 4.33763i) q^{16} +(-7.31018 + 2.25489i) q^{17} +(0.230569 - 0.399358i) q^{19} +(-1.21672 + 5.33078i) q^{20} +(1.48503 + 6.50634i) q^{22} +(5.60675 + 1.72945i) q^{23} +(1.52086 - 3.87508i) q^{25} +(8.11620 + 2.50352i) q^{26} +(4.70447 + 0.841674i) q^{28} +(-1.51504 + 6.63784i) q^{29} +(-0.485737 - 0.841321i) q^{31} +(-7.38734 + 2.27869i) q^{32} +(-9.30568 - 11.6690i) q^{34} +(-7.58529 - 2.56967i) q^{35} +(-4.44084 - 4.12050i) q^{37} +(0.889627 + 0.134090i) q^{38} +(1.13082 - 0.170444i) q^{40} +(-5.80253 - 2.79435i) q^{41} +(-3.08316 + 1.48477i) q^{43} +(-5.10527 + 3.48071i) q^{44} +(0.855456 + 11.4153i) q^{46} +(-1.71875 - 4.37931i) q^{47} +(-1.92960 + 6.72879i) q^{49} +8.12166 q^{50} +(0.587670 + 7.84191i) q^{52} +(-5.16535 + 4.79274i) q^{53} +(9.32899 - 4.49260i) q^{55} +(-0.195605 - 0.980228i) q^{56} +(-13.1350 + 1.97979i) q^{58} +(9.14460 + 6.23468i) q^{59} +(-0.0508714 - 0.0472018i) q^{61} +(1.18172 - 1.48183i) q^{62} +(-3.97981 - 4.99052i) q^{64} +(0.984793 - 13.1411i) q^{65} +(1.88646 + 3.26744i) q^{67} +(6.90936 - 11.9674i) q^{68} +(-0.739771 - 15.6074i) q^{70} +(-1.17312 - 5.13977i) q^{71} +(-2.98140 + 7.59648i) q^{73} +(4.31801 - 11.0021i) q^{74} +(0.185356 + 0.812096i) q^{76} +(-4.30839 - 7.95890i) q^{77} +(5.82437 - 10.0881i) q^{79} +(6.58345 + 11.4029i) q^{80} +(0.938983 - 12.5299i) q^{82} +(-1.60339 - 2.01058i) q^{83} +(-14.4381 + 18.1047i) q^{85} +(-4.89414 - 4.54110i) q^{86} +(1.06776 + 0.727985i) q^{88} +(-2.46815 + 0.372014i) q^{89} +(-11.5138 - 0.315980i) q^{91} +(-9.54906 + 4.59859i) q^{92} +(6.72828 - 6.24293i) q^{94} +(-0.104314 - 1.39197i) q^{95} +2.26778 q^{97} +(-13.5957 + 1.29174i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} + 3 q^{4} - 6 q^{8} + 30 q^{10} + 9 q^{11} + 42 q^{14} + 29 q^{16} + 5 q^{17} - 26 q^{19} + 5 q^{20} + q^{22} + 4 q^{23} - 56 q^{25} + 62 q^{26} + 7 q^{28} - 12 q^{29} - 36 q^{31} + 14 q^{32}+ \cdots - 119 q^{98}+O(q^{100}) \) 48 * q + q^2 + 3 * q^4 - 6 * q^8 + 30 * q^10 + 9 * q^11 + 42 * q^14 + 29 * q^16 + 5 * q^17 - 26 * q^19 + 5 * q^20 + q^22 + 4 * q^23 - 56 * q^25 + 62 * q^26 + 7 * q^28 - 12 * q^29 - 36 * q^31 + 14 * q^32 - 76 * q^34 - 7 * q^35 - 20 * q^37 + 60 * q^38 + 28 * q^40 - 41 * q^41 + 12 * q^43 - 44 * q^44 + 16 * q^46 - 13 * q^47 - 84 * q^49 + 12 * q^50 + 92 * q^52 - 14 * q^53 - 38 * q^55 - 105 * q^56 + 3 * q^58 - 57 * q^59 + 11 * q^61 + 16 * q^62 - 110 * q^64 - 21 * q^65 + 34 * q^67 - 22 * q^68 - 6 * q^71 - 69 * q^73 + 90 * q^74 - 49 * q^76 + 34 * q^79 - 55 * q^80 + 91 * q^82 - 28 * q^83 - 44 * q^85 + 26 * q^86 + 45 * q^88 - 11 * q^89 - 84 * q^92 + 90 * q^94 - 150 * q^95 + 124 * q^97 - 119 * q^98

Introduction

L-functions

Modular forms

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