LMFDB - Embedded newform 441.2.bb.c.46.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.52140272914$
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			46.4
Character	$\chi$	$=$	441.46
Dual form			441.2.bb.c.163.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{11}{21}\right)$	$1$

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	−0.421967	−	0.906611i	$-0.638660\pi$
$2$	0.712776	−	1.81612i	0.504009	−	1.28419i	0.925976	−	0.377583i	$-0.123245\pi$
$3$		0			0
$3$		0			0
$4$	−1.32415	−	1.22863i	−0.662077	−	0.614317i
$5$	2.50104	+	1.70518i	1.11850	+	0.762580i	0.973915	−	0.226913i	$-0.0728632\pi$
$5$	2.50104	+	1.70518i	1.11850	+	0.762580i	0.144584	+	0.989493i	$0.453816\pi$
$6$		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	0.382227	−	0.924068i	$-0.375157\pi$
$11$	3.38245	−	0.509823i	1.01985	−	0.153717i	0.637620	+	0.770351i	$0.279919\pi$
$12$		0			0
$13$	2.71434	+	3.40367i	0.752821	+	0.944008i	0.999686	−	0.0250418i	$-0.00797190\pi$
$13$	2.71434	+	3.40367i	0.752821	+	0.944008i	−0.246865	+	0.969050i	$0.579400\pi$
$14$	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	−0.776452	−	0.630176i	$-0.782983\pi$
$17$	−7.31018	−	2.25489i	−1.77298	−	0.546891i	−0.996526	+	0.0832845i	$0.973459\pi$
$18$		0			0
$19$	0.230569	+	0.399358i	0.0528962	+	0.0916189i	0.891261	−	0.453491i	$-0.149821\pi$
$19$	0.230569	+	0.399358i	0.0528962	+	0.0916189i	−0.838365	+	0.545109i	$0.816488\pi$
$20$	−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	0.351371	−	0.936236i	$-0.385716\pi$
$23$	5.60675	−	1.72945i	1.16909	−	0.360616i	0.817717	+	0.575620i	$0.195239\pi$
$24$		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	−0.896081	−	0.443890i	$-0.853598\pi$
$29$	−1.51504	−	6.63784i	−0.281337	−	1.23262i	0.614745	−	0.788726i	$-0.289259\pi$
$30$		0			0
$31$	−0.485737	+	0.841321i	−0.0872409	+	0.151106i	−0.906344	−	0.422541i	$-0.861138\pi$
$31$	−0.485737	+	0.841321i	−0.0872409	+	0.151106i	0.819103	+	0.573646i	$0.194472\pi$
$32$	−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	−0.954878	−	0.296997i	$-0.904015\pi$
$37$	−4.44084	+	4.12050i	−0.730070	+	0.677406i	0.224808	+	0.974403i	$0.427824\pi$
$38$	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	−0.828125	−	0.560543i	$-0.810592\pi$
$41$	−5.80253	+	2.79435i	−0.906203	+	0.436404i	−0.0780774	+	0.996947i	$0.524878\pi$
$42$		0			0
$43$	−3.08316	−	1.48477i	−0.470178	−	0.226426i	0.183764	−	0.982970i	$-0.441172\pi$
$43$	−3.08316	−	1.48477i	−0.470178	−	0.226426i	−0.653942	+	0.756544i	$0.726886\pi$
$44$	−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	−0.999717	−	0.0237689i	$-0.992433\pi$
$47$	−1.71875	+	4.37931i	−0.250706	+	0.638788i	0.749012	+	0.662557i	$0.230529\pi$
$48$		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	0.240460	−	0.970659i	$-0.422702\pi$
$53$	−5.16535	−	4.79274i	−0.709515	−	0.658334i	−0.949975	+	0.312325i	$0.898892\pi$
$54$		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	0.204595	−	0.978847i	$-0.434412\pi$
$59$	9.14460	−	6.23468i	1.19052	−	0.811686i	0.985930	+	0.167161i	$0.0534598\pi$
$60$		0			0
$61$	−0.0508714	+	0.0472018i	−0.00651342	+	0.00604357i	−0.683423	−	0.730023i	$-0.739509\pi$
$61$	−0.0508714	+	0.0472018i	−0.00651342	+	0.00604357i	0.676909	+	0.736066i	$0.263319\pi$
$62$	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	−0.727478	−	0.686131i	$-0.759308\pi$
$67$	1.88646	−	3.26744i	0.230467	−	0.399181i	0.957946	+	0.286949i	$0.0926411\pi$
$68$	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	0.856383	+	0.516342i	$0.172707\pi$
$71$	−1.17312	+	5.13977i	−0.139224	+	0.609979i	−0.995606	+	0.0936372i	$0.970151\pi$
$72$		0			0
$73$	−2.98140	−	7.59648i	−0.348946	−	0.889101i	−0.992337	−	0.123563i	$-0.960568\pi$
$73$	−2.98140	−	7.59648i	−0.348946	−	0.889101i	0.643390	−	0.765538i	$-0.277527\pi$
$74$	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	0.981820	+	0.189812i	$0.0607880\pi$
$79$	5.82437	+	10.0881i	0.655292	+	1.13500i	−0.326528	+	0.945188i	$0.605879\pi$
$80$	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	−0.862003	−	0.506904i	$-0.830790\pi$
$83$	−1.60339	+	2.01058i	−0.175995	+	0.220690i	0.686008	+	0.727594i	$0.259361\pi$
$84$		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	0.0169208	−	0.999857i	$-0.494614\pi$
$89$	−2.46815	−	0.372014i	−0.261623	−	0.0394334i	−0.278544	+	0.960423i	$0.589852\pi$
$90$		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	−0.999986	−	0.00523328i	$-0.998334\pi$
$101$	−0.104409	+	1.39324i	−0.0103890	+	0.138632i	0.989597	+	0.143865i	$0.0459532\pi$
$102$		0			0
$103$	16.4128	+	11.1901i	1.61720	+	1.10259i	0.924373	+	0.381490i	$0.124589\pi$
$103$	16.4128	+	11.1901i	1.61720	+	1.10259i	0.692831	+	0.721100i	$0.256363\pi$
$104$	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	−0.165492	−	0.986211i	$-0.552921\pi$
$107$	−6.35460	−	0.957802i	−0.614323	−	0.0925943i	−0.448831	+	0.893617i	$0.648159\pi$
$108$		0			0
$109$	−2.37836	+	0.358480i	−0.227805	+	0.0343362i	−0.261953	−	0.965081i	$-0.584367\pi$
$109$	−2.37836	+	0.358480i	−0.227805	+	0.0343362i	0.0341474	+	0.999417i	$0.489128\pi$
$110$	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	−0.812810	−	0.582529i	$-0.802063\pi$
$113$	−0.680530	+	0.853357i	−0.0640189	+	0.0802771i	0.748791	+	0.662806i	$0.230635\pi$
$114$		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	0.992863	+	0.119260i	$0.0380521\pi$
$127$	1.69119	+	7.40960i	0.150069	+	0.657496i	−0.842794	+	0.538236i	$0.819091\pi$
$128$	−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	0.999302	−	0.0373677i	$-0.0118973\pi$
$131$	0.0640034	+	0.854066i	0.00559200	+	0.0746201i	−0.993710	+	0.111988i	$0.964278\pi$
$132$		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	−0.937907	−	0.346887i	$-0.887239\pi$
$137$	−11.2091	+	7.64221i	−0.957654	+	0.652918i	−0.0197476	+	0.999805i	$0.506286\pi$
$138$		0			0
$139$	−11.5141	+	5.54490i	−0.976613	+	0.470312i	−0.852939	−	0.522011i	$-0.825182\pi$
$139$	−11.5141	+	5.54490i	−0.976613	+	0.470312i	−0.123674	+	0.992323i	$0.539468\pi$
$140$	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	−0.567974	−	0.823046i	$-0.692273\pi$
$149$	4.98264	−	12.6956i	0.408194	−	1.04006i	0.976168	−	0.217015i	$-0.0696320\pi$
$150$		0			0
$151$	−13.7755	−	12.7818i	−1.12103	−	1.04017i	−0.998864	−	0.0476589i	$-0.984824\pi$
$151$	−13.7755	−	12.7818i	−1.12103	−	1.04017i	−0.122171	−	0.992509i	$-0.538986\pi$
$152$	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	−0.893868	−	0.448330i	$-0.852019\pi$
$157$	−10.0628	+	6.86068i	−0.803096	+	0.547542i	0.0907718	+	0.995872i	$0.471067\pi$
$158$	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	−0.955898	−	0.293699i	$-0.905114\pi$
$163$	−0.695173	−	9.27644i	−0.0544501	−	0.726587i	0.901448	−	0.432888i	$-0.142505\pi$
$164$	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	−0.943122	−	0.332446i	$-0.892126\pi$
$167$	−3.07100	−	13.4549i	−0.237641	−	1.04117i	0.705481	−	0.708729i	$-0.250731\pi$
$168$		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	−0.319913	−	0.947447i	$-0.603654\pi$
$173$	−0.664509	+	0.204974i	−0.0505217	+	0.0155839i	0.269391	+	0.963031i	$0.413178\pi$
$174$		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	−0.267628	−	0.963522i	$-0.586240\pi$
$179$	−13.8009	−	4.25700i	−1.03152	−	0.318183i	−0.763896	+	0.645339i	$0.776716\pi$
$180$		0			0
$181$	10.6896	−	13.4044i	0.794555	−	0.996340i	−0.205290	−	0.978701i	$-0.565814\pi$
$181$	10.6896	−	13.4044i	0.794555	−	0.996340i	0.999844	−	0.0176387i	$-0.00561488\pi$
$182$	−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	0.859987	−	0.510315i	$-0.170471\pi$
$191$	9.66226	+	6.58762i	0.699137	+	0.476663i	−0.160851	+	0.986979i	$0.551424\pi$
$192$		0			0
$193$	−2.01860	+	26.9363i	−0.145302	+	1.93892i	0.160943	+	0.986964i	$0.448547\pi$
$193$	−2.01860	+	26.9363i	−0.145302	+	1.93892i	−0.306245	+	0.951953i	$0.599073\pi$
$194$	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	−0.910932	−	0.412557i	$-0.864636\pi$
$199$	0.723875	−	9.65944i	0.0513141	−	0.684740i	0.962246	−	0.272182i	$-0.0877453\pi$
$200$	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	−0.445246	−	0.895409i	$-0.646884\pi$
$211$	7.65206	−	9.59538i	0.526790	−	0.660573i	0.972035	+	0.234835i	$0.0754550\pi$
$212$	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	0.591630	+	0.806209i	$0.298485\pi$
$223$	−4.34871	+	19.0530i	−0.291211	+	1.27588i	−0.882842	+	0.469671i	$0.844373\pi$
$224$	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	−0.873339	−	0.487113i	$-0.838050\pi$
$227$	−0.223240	+	0.386663i	−0.0148170	+	0.0256637i	0.858522	+	0.512777i	$0.171383\pi$
$228$		0			0
$229$	0.233264	+	3.11269i	0.0154145	+	0.205692i	0.999593	+	0.0285146i	$0.00907770\pi$
$229$	0.233264	+	3.11269i	0.0154145	+	0.205692i	−0.984179	+	0.177178i	$0.943303\pi$
$230$	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	−0.619059	−	0.785344i	$-0.712486\pi$
$233$	1.79855	−	1.66881i	0.117827	−	0.109327i	0.736886	+	0.676017i	$0.236295\pi$
$234$		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	−0.130672	−	0.991426i	$-0.541714\pi$
$239$	−15.2629	−	7.35021i	−0.987273	−	0.475446i	−0.856601	+	0.515980i	$0.827428\pi$
$240$		0			0
$241$	−3.14831	−	2.92121i	−0.202801	−	0.188172i	0.572234	−	0.820091i	$-0.306077\pi$
$241$	−3.14831	−	2.92121i	−0.202801	−	0.188172i	−0.775034	+	0.631919i	$0.782267\pi$
$242$	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	0.0681364	−	0.997676i	$-0.478295\pi$
$251$	−10.6052	−	5.10721i	−0.669396	−	0.322364i	−0.737532	+	0.675312i	$0.764009\pi$
$252$		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	−0.927018	−	0.375018i	$-0.877637\pi$
$257$	−9.97662	+	9.25695i	−0.622324	+	0.577432i	0.304693	+	0.952451i	$0.401446\pi$
$258$		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	−0.850377	−	0.526173i	$-0.823626\pi$
$263$	0.494476	−	0.856457i	0.0304907	−	0.0528114i	0.880868	+	0.473362i	$0.156960\pi$
$264$		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	0.887117	+	0.461544i	$0.152704\pi$
$269$	9.03288	+	23.0154i	0.550744	+	1.40327i	−0.336373	+	0.941729i	$0.609200\pi$
$270$		0			0
$271$	24.3217	−	7.50226i	1.47744	−	0.455730i	0.551748	−	0.834011i	$-0.313961\pi$
$271$	24.3217	−	7.50226i	1.47744	−	0.455730i	0.925691	+	0.378281i	$0.123485\pi$
$272$	−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	−0.00532123	−	0.999986i	$-0.501694\pi$
$277$	−9.53712	−	2.94181i	−0.573030	−	0.176756i	−0.567709	+	0.823230i	$0.692170\pi$
$278$	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	0.610993	−	0.791636i	$-0.290770\pi$
$281$	−4.97450	−	6.23783i	−0.296754	−	0.372118i	−0.907747	+	0.419518i	$0.862199\pi$
$282$		0			0
$283$	4.87245	−	0.734404i	0.289637	−	0.0436558i	−0.00261652	−	0.999997i	$-0.500833\pi$
$283$	4.87245	−	0.734404i	0.289637	−	0.0436558i	0.292254	+	0.956341i	$0.405595\pi$
$284$	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	0.937278	−	0.348584i	$-0.113337\pi$
$307$	6.81355	+	8.54392i	0.388870	+	0.487627i	−0.548408	+	0.836211i	$0.684766\pi$
$308$	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	0.546696	−	0.837331i	$-0.315885\pi$
$311$	9.28867	+	2.86518i	0.526712	+	0.162469i	−0.0199838	+	0.999800i	$0.506361\pi$
$312$		0			0
$313$	2.39374	+	4.14608i	0.135302	+	0.234350i	0.925713	−	0.378227i	$-0.123466\pi$
$313$	2.39374	+	4.14608i	0.135302	+	0.234350i	−0.790411	+	0.612577i	$0.790133\pi$
$314$	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	0.842924	−	0.538033i	$-0.180833\pi$
$317$	32.8042	−	10.1187i	1.84246	−	0.568325i	0.999541	−	0.0302917i	$-0.00964363\pi$
$318$		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	−0.330168	−	0.943922i	$-0.607106\pi$
$331$	10.6694	−	9.89972i	0.586441	−	0.544138i	0.916609	+	0.399784i	$0.130915\pi$
$332$	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	0.847755	−	0.530388i	$-0.177954\pi$
$337$	17.6535	+	8.50148i	0.961647	+	0.463105i	0.113892	+	0.993493i	$0.463668\pi$
$338$	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	0.931578	−	0.363542i	$-0.118433\pi$
$347$	11.8971	+	11.0389i	0.638670	+	0.592599i	−0.292908	+	0.956141i	$0.594623\pi$
$348$		0			0
$349$	10.9710	+	5.28336i	0.587264	+	0.282812i	0.703827	−	0.710372i	$-0.251473\pi$
$349$	10.9710	+	5.28336i	0.587264	+	0.282812i	−0.116562	+	0.993183i	$0.537187\pi$
$350$	−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	−0.770124	−	0.637894i	$-0.779806\pi$
$353$	−8.59910	+	5.86277i	−0.457684	+	0.312044i	0.312440	+	0.949937i	$0.398854\pi$
$354$		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	0.999066	+	0.0432092i	$0.0137582\pi$
$359$	0.333449	+	4.44956i	0.0175987	+	0.234839i	−0.981467	+	0.191630i	$0.938623\pi$
$360$		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	0.996271	+	0.0862781i	$0.0274974\pi$
$367$	6.21915	+	15.8461i	0.324637	+	0.827161i	−0.671634	+	0.740883i	$0.734407\pi$
$368$	−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	0.901303	+	0.433190i	$0.142612\pi$
$373$	15.9489	+	27.6244i	0.825805	+	1.43034i	−0.0754976	+	0.997146i	$0.524055\pi$
$374$	−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	0.998953	+	0.0457427i	$0.0145654\pi$
$379$	15.9882	+	20.0486i	0.821261	+	1.02983i	−0.177692	+	0.984086i	$0.556863\pi$
$380$	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	0.160960	−	0.986961i	$-0.448541\pi$
$383$	0.466900	+	0.0703738i	0.0238575	+	0.00359594i	−0.137103	+	0.990557i	$0.543779\pi$
$384$		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	0.870397	+	0.492350i	$0.163862\pi$
$389$	−1.25556	+	16.7543i	−0.0636594	+	0.849475i	−0.934057	+	0.357125i	$0.883757\pi$
$390$		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	−0.139939	−	0.990160i	$-0.544691\pi$
$397$	−22.1720	−	15.1166i	−1.11278	−	0.758680i	−0.972840	+	0.231480i	$0.925643\pi$
$398$	−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	−0.303409	−	0.952860i	$-0.598125\pi$
$401$	−17.5058	−	2.63858i	−0.874199	−	0.131764i	−0.570790	+	0.821096i	$0.693363\pi$
$402$		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	0.0426824	−	0.999089i	$-0.486410\pi$
$409$	−9.80566	−	3.02464i	−0.484859	−	0.149559i	−0.527541	+	0.849530i	$0.676886\pi$
$410$	−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	−0.950596	−	0.310430i	$-0.899527\pi$
$419$	0.830080	−	3.63682i	0.0405521	−	0.177670i	0.991148	+	0.132760i	$0.0423840\pi$
$420$		0			0
$421$	−6.79690	−	29.7792i	−0.331260	−	1.45135i	−0.816693	−	0.577073i	$-0.804195\pi$
$421$	−6.79690	−	29.7792i	−0.331260	−	1.45135i	0.485432	−	0.874274i	$-0.338662\pi$
$422$	−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	−0.406724	−	0.913551i	$-0.633329\pi$
$431$	6.12611	−	4.17671i	0.295084	−	0.201185i	0.701808	+	0.712366i	$0.252376\pi$
$432$		0			0
$433$	17.8059	−	8.57485i	0.855695	−	0.412081i	0.0460064	−	0.998941i	$-0.485351\pi$
$433$	17.8059	−	8.57485i	0.855695	−	0.412081i	0.809688	+	0.586860i	$0.199636\pi$
$434$	−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	−0.636512	−	0.771266i	$-0.719624\pi$
$439$	7.43134	−	18.9348i	0.354679	−	0.903706i	0.991191	−	0.132440i	$-0.0422812\pi$
$440$	3.91185			0.186490
$441$		0			0
$442$	−64.9760			−3.09059
$443$	−4.05982	+	10.3442i	−0.192888	+	0.491470i	−0.994297	−	0.106646i	$-0.965989\pi$
$443$	−4.05982	+	10.3442i	−0.192888	+	0.491470i	0.801409	+	0.598116i	$0.204084\pi$
$444$		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	0.719055	−	0.694953i	$-0.244575\pi$
$449$	36.2494	−	17.4568i	1.71071	−	0.823837i	0.991660	−	0.128884i	$-0.0411394\pi$
$450$		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	0.970312	+	0.241858i	$0.0777569\pi$
$457$	1.00228	+	13.3745i	0.0468847	+	0.625633i	−0.923427	+	0.383774i	$0.874624\pi$
$458$	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	0.928964	+	0.370170i	$0.120700\pi$
$461$	5.42370	+	23.7628i	0.252607	+	1.10674i	−0.676357	+	0.736574i	$0.736442\pi$
$462$		0			0
$463$	4.43592	−	19.4350i	0.206155	−	0.903223i	−0.760943	−	0.648818i	$-0.775263\pi$
$463$	4.43592	−	19.4350i	0.206155	−	0.903223i	0.967098	−	0.254404i	$-0.0818794\pi$
$464$	−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	0.537082	−	0.843530i	$-0.319526\pi$
$467$	31.4648	−	9.70561i	1.45602	−	0.449122i	0.918936	+	0.394408i	$0.129050\pi$
$468$		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	−0.898589	−	0.438792i	$-0.855406\pi$
$479$	−35.6287	+	5.37017i	−1.62792	+	0.245369i	−0.729331	+	0.684162i	$0.760168\pi$
$480$		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	0.933088	+	0.359647i	$0.117103\pi$
$487$	−0.952918	+	12.7158i	−0.0431808	+	0.576208i	−0.976269	+	0.216561i	$0.930516\pi$
$488$	−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	0.868755	−	0.495242i	$-0.164921\pi$
$499$	34.6900	+	5.22868i	1.55294	+	0.234068i	0.684183	+	0.729310i	$0.260159\pi$
$500$	−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	0.994963	−	0.100245i	$-0.0319626\pi$
$503$	15.1573	+	19.0067i	0.675831	+	0.847466i	−0.319131	+	0.947710i	$0.603391\pi$
$504$		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	0.628172	−	0.778075i	$-0.283804\pi$
$509$	−8.11625	−	14.0578i	−0.359747	−	0.623099i	−0.987918	+	0.154975i	$0.950470\pi$
$510$		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	−0.682335	−	0.731039i	$-0.739036\pi$
$521$	6.66345	−	11.5414i	0.291931	−	0.505639i	0.974266	+	0.225400i	$0.0723689\pi$
$522$		0			0
$523$	0.807242	+	10.7719i	0.0352982	+	0.471022i	0.986643	+	0.162895i	$0.0520832\pi$
$523$	0.807242	+	10.7719i	0.0352982	+	0.471022i	−0.951345	+	0.308127i	$0.900298\pi$
$524$	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	−0.801253	−	0.598325i	$-0.795833\pi$
$541$	4.49073	−	11.4422i	0.193071	−	0.491938i	0.994325	+	0.106387i	$0.0339283\pi$
$542$	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	−0.870405	−	0.492336i	$-0.836143\pi$
$547$	−24.0469	+	11.5804i	−1.02817	+	0.495141i	−0.157765	+	0.987477i	$0.550429\pi$
$548$	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	−0.995714	−	0.0924844i	$-0.970519\pi$
$557$	−9.85957	+	17.0773i	−0.417763	+	0.723587i	0.577951	+	0.816072i	$0.303853\pi$
$558$		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	0.943991	−	0.329972i	$-0.107039\pi$
$563$	0.653897	+	1.66610i	0.0275585	+	0.0702178i	−0.916432	+	0.400190i	$0.868944\pi$
$564$		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	0.802119	+	0.597165i	$0.203706\pi$
$569$	21.9029	+	37.9370i	0.918219	+	1.59040i	0.116101	+	0.993237i	$0.462960\pi$
$570$		0			0
$571$	11.6165	+	3.58321i	0.486134	+	0.149953i	0.528127	−	0.849165i	$-0.322894\pi$
$571$	11.6165	+	3.58321i	0.486134	+	0.149953i	−0.0419927	+	0.999118i	$0.513371\pi$
$572$	−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	−0.0419022	−	0.999122i	$-0.513342\pi$
$577$	5.10571	−	0.769562i	0.212553	−	0.0320373i	0.254456	+	0.967084i	$0.418104\pi$
$578$	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	0.390452	−	0.920623i	$-0.372319\pi$
$593$	−7.88708	−	5.37732i	−0.323884	−	0.220820i	−0.714336	+	0.699803i	$0.753271\pi$
$594$		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	0.120010	−	0.992773i	$-0.461707\pi$
$599$	12.9057	−	1.94522i	0.527313	−	0.0794796i	0.407303	+	0.913293i	$0.366469\pi$
$600$		0			0
$601$	1.03502	+	1.29787i	0.0422193	+	0.0529414i	0.802493	−	0.596662i	$-0.203507\pi$
$601$	1.03502	+	1.29787i	0.0422193	+	0.0529414i	−0.760274	+	0.649603i	$0.774935\pi$
$602$	−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	0.578239	−	0.815867i	$-0.303740\pi$
$607$	−10.2847	−	17.8136i	−0.417442	−	0.723031i	−0.995681	+	0.0928362i	$0.970407\pi$
$608$	−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	0.946713	−	0.322078i	$-0.104381\pi$
$613$	0.833246	+	2.12308i	0.0336545	+	0.0857502i	−0.913059	+	0.407828i	$0.866286\pi$
$614$	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	0.964039	+	0.265761i	$0.0856231\pi$
$617$	5.23564	+	22.9389i	0.210779	+	0.923484i	−0.753260	+	0.657723i	$0.771520\pi$
$618$		0			0
$619$	13.5222	−	23.4211i	0.543503	−	0.941375i	−0.455196	−	0.890391i	$-0.650431\pi$
$619$	13.5222	−	23.4211i	0.543503	−	0.941375i	0.998699	−	0.0509838i	$-0.0162357\pi$
$620$	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	0.379378	−	0.925242i	$-0.376138\pi$
$631$	−2.69955	−	1.30003i	−0.107467	−	0.0517536i	−0.486845	+	0.873488i	$0.661852\pi$
$632$	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	0.387493	−	0.921872i	$-0.373341\pi$
$641$	−12.7310	−	11.8126i	−0.502844	−	0.466571i	−0.890337	+	0.455302i	$0.849531\pi$
$642$		0			0
$643$	32.6018	+	15.7002i	1.28569	+	0.619155i	0.946846	−	0.321688i	$-0.104250\pi$
$643$	32.6018	+	15.7002i	1.28569	+	0.619155i	0.338843	+	0.940843i	$0.389964\pi$
$644$	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	−0.867985	−	0.496590i	$-0.834585\pi$
$647$	−18.3861	+	12.5355i	−0.722834	+	0.492820i	0.145151	+	0.989409i	$0.453633\pi$
$648$		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	−0.900378	−	0.435108i	$-0.856710\pi$
$653$	−1.91414	−	25.5424i	−0.0749059	−	0.999550i	0.825472	−	0.564442i	$-0.190909\pi$
$654$		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	0.839432	+	0.543465i	$0.182888\pi$
$659$	−3.91920	+	17.1712i	−0.152671	+	0.668893i	−0.992103	+	0.125429i	$0.959969\pi$
$660$		0			0
$661$	4.12689	+	10.5151i	0.160517	+	0.408992i	0.988393	−	0.151920i	$-0.0485458\pi$
$661$	4.12689	+	10.5151i	0.160517	+	0.408992i	−0.827875	+	0.560912i	$0.810451\pi$
$662$	−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	−0.865072	−	0.501648i	$-0.832727\pi$
$673$	−30.1357	−	37.7890i	−1.16165	−	1.45666i	−0.296574	−	0.955010i	$-0.595844\pi$
$674$	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	−0.566714	−	0.823915i	$-0.691786\pi$
$677$	−35.1547	−	5.29871i	−1.35110	−	0.203646i	−0.784390	+	0.620268i	$0.787024\pi$
$678$		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	−0.994331	−	0.106334i	$-0.966089\pi$
$683$	0.123938	−	1.65384i	0.00474236	−	0.0632825i	0.999073	+	0.0430512i	$0.0137079\pi$
$684$		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	0.857619	−	0.514286i	$-0.171943\pi$
$691$	18.1959	+	12.4058i	0.692206	+	0.471938i	−0.165412	+	0.986225i	$0.552895\pi$
$692$	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	−0.615609	−	0.788052i	$-0.711090\pi$
$701$	7.66942	−	9.61715i	0.289670	−	0.363235i	0.905279	+	0.424817i	$0.139661\pi$
$702$		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	−0.919516	−	0.393054i	$-0.871419\pi$
$709$	−38.8180	+	11.9738i	−1.45784	+	0.449684i	−0.538324	+	0.842738i	$0.680942\pi$
$710$	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	0.993917	+	0.110130i	$0.0351268\pi$
$719$	0.737799	+	9.84525i	0.0275153	+	0.367166i	−0.966402	+	0.257036i	$0.917254\pi$
$720$		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	−0.157043	−	0.987592i	$-0.550196\pi$
$727$	13.9445	−	6.71531i	0.517172	−	0.249057i	0.674215	+	0.738535i	$0.264482\pi$
$728$	−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	−0.910387	−	0.413757i	$-0.864216\pi$
$733$	1.03965	−	2.64899i	0.0384004	−	0.0978426i	0.948788	+	0.315915i	$0.102311\pi$
$734$	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	0.797149	−	0.603782i	$-0.206340\pi$
$739$	6.92190	+	6.42259i	0.254626	+	0.236259i	−0.542523	+	0.840041i	$0.682531\pi$
$740$	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	0.0352884	−	0.999377i	$-0.488765\pi$
$743$	22.8595	−	11.0086i	0.838635	−	0.403865i	0.803347	+	0.595512i	$0.203051\pi$
$744$		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	−0.990102	−	0.140351i	$-0.955177\pi$
$751$	−0.876307	−	11.6935i	−0.0319769	−	0.426702i	0.958125	−	0.286351i	$-0.0924422\pi$
$752$	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	0.223250	+	0.974761i	$0.428333\pi$
$757$	−11.0281	+	48.3174i	−0.400824	+	1.75613i	−0.624074	+	0.781365i	$0.714524\pi$
$758$	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	−0.897813	−	0.440377i	$-0.854845\pi$
$761$	−38.3876	+	11.8410i	−1.39155	+	0.429236i	−0.493735	+	0.869613i	$0.664369\pi$
$762$		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	0.193598	+	0.981081i	$0.437984\pi$
$769$	−22.3501	+	28.0261i	−0.805965	+	1.01065i	−0.999563	+	0.0295668i	$0.990587\pi$
$770$	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	−0.289187	−	0.957273i	$-0.593385\pi$
$773$	−7.87836	+	1.18747i	−0.283365	+	0.0427104i	0.00582201	+	0.999983i	$0.498147\pi$
$774$		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	−0.859147	−	0.511729i	$-0.829005\pi$
$787$	1.87042	−	24.9590i	0.0666732	−	0.889693i	0.925820	−	0.377964i	$-0.123376\pi$
$788$	−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	0.856450	−	0.516230i	$-0.172665\pi$
$797$	4.58996	+	5.75562i	0.162585	+	0.203875i	−0.693865	+	0.720105i	$0.744094\pi$
$798$		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	0.916752	−	0.399458i	$-0.130802\pi$
$809$	−0.767250	−	1.95492i	−0.0269751	−	0.0687314i	−0.943727	+	0.330726i	$0.892706\pi$
$810$		0			0
$811$	1.31295	−	5.75241i	0.0461039	−	0.201994i	−0.946630	−	0.322321i	$-0.895537\pi$
$811$	1.31295	−	5.75241i	0.0461039	−	0.201994i	0.992734	+	0.120326i	$0.0383941\pi$
$812$	−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	−0.776964	−	0.629545i	$-0.783241\pi$
$821$	−5.93814	+	5.50979i	−0.207243	+	0.192293i	0.569722	+	0.821838i	$0.307051\pi$
$822$		0			0
$823$	−35.9258	+	24.4938i	−1.25229	+	0.853800i	−0.993688	−	0.112183i	$-0.964216\pi$
$823$	−35.9258	+	24.4938i	−1.25229	+	0.853800i	−0.258607	+	0.965983i	$0.583263\pi$
$824$	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	0.346360	−	0.938102i	$-0.387418\pi$
$827$	−4.92118	−	2.36992i	−0.171126	−	0.0824101i	−0.517486	+	0.855692i	$0.673132\pi$
$828$		0			0
$829$	−27.5164	−	25.5315i	−0.955686	−	0.886747i	0.0379623	−	0.999279i	$-0.487913\pi$
$829$	−27.5164	−	25.5315i	−0.955686	−	0.886747i	−0.993648	+	0.112532i	$0.964104\pi$
$830$	−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	0.689207	−	0.724565i	$-0.257959\pi$
$839$	16.0015	+	7.70590i	0.552432	+	0.266037i	−0.136774	+	0.990602i	$0.543674\pi$
$840$		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	0.995895	+	0.0905136i	$0.0288509\pi$
$853$	4.02744	+	17.6454i	0.137897	+	0.604166i	−0.857998	+	0.513653i	$0.828292\pi$
$854$	−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	0.903983	−	0.427568i	$-0.140630\pi$
$857$	−1.44920	−	3.69250i	−0.0495036	−	0.126133i	−0.953487	+	0.301435i	$0.902534\pi$
$858$		0			0
$859$	−39.3390	+	12.1345i	−1.34223	+	0.414022i	−0.880940	−	0.473228i	$-0.843089\pi$
$859$	−39.3390	+	12.1345i	−1.34223	+	0.414022i	−0.461288	+	0.887251i	$0.652612\pi$
$860$	−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	0.852777	−	0.522275i	$-0.174917\pi$
$863$	−0.761312	−	1.31863i	−0.0259154	−	0.0448867i	−0.878692	+	0.477389i	$0.841583\pi$
$864$		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	0.174024	−	0.984741i	$-0.444323\pi$
$877$	−20.1100	−	13.7108i	−0.679068	−	0.462981i	−0.853092	+	0.521761i	$0.825275\pi$
$878$	−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	−0.254231	−	0.967144i	$-0.581822\pi$
$887$	−37.1508	−	25.3290i	−1.24740	−	0.850463i	−0.993170	+	0.116680i	$0.962775\pi$
$888$		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	0.896212	−	0.443626i	$-0.146308\pi$
$907$	−1.88228	−	4.79598i	−0.0625002	−	0.159248i	−0.958712	+	0.284378i	$0.908213\pi$
$908$	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	−0.994502	−	0.104714i	$-0.966607\pi$
$911$	−4.34392	−	19.0320i	−0.143920	−	0.630557i	0.850582	−	0.525843i	$-0.176250\pi$
$912$		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	0.322554	−	0.946551i	$-0.395459\pi$
$919$	39.1234	−	36.3012i	1.29056	−	1.19747i	0.968009	−	0.250916i	$-0.0807317\pi$
$920$	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	−0.772484	−	0.635034i	$-0.780986\pi$
$929$	6.87983	−	17.5295i	0.225720	−	0.575125i	0.998204	+	0.0599093i	$0.0190812\pi$
$930$		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	0.202384	−	0.979306i	$-0.435131\pi$
$937$	−13.3793	−	6.44315i	−0.437084	−	0.210488i	−0.639468	+	0.768818i	$0.720845\pi$
$938$	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	−0.346067	−	0.938210i	$-0.612483\pi$
$941$	12.2965	−	8.38362i	0.400855	−	0.273298i	0.746922	+	0.664911i	$0.231531\pi$
$942$		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	−0.769825	−	0.638255i	$-0.779657\pi$
$947$	−3.19198	−	42.5940i	−0.103725	−	1.38412i	0.666100	−	0.745863i	$-0.267962\pi$
$948$		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	−0.997765	−	0.0668274i	$-0.978712\pi$
$953$	−2.15522	+	9.44264i	−0.0698144	+	0.305877i	0.927950	+	0.372704i	$0.121569\pi$
$954$		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	0.868815	−	0.495136i	$-0.164882\pi$
$967$	5.99430	+	7.51661i	0.192764	+	0.241718i	−0.676052	+	0.736854i	$0.736310\pi$
$968$	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	−0.0725056	−	0.997368i	$-0.523100\pi$
$971$	−13.5790	−	2.04670i	−0.435769	−	0.0656817i	−0.363264	+	0.931686i	$0.618338\pi$
$972$		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	0.904475	+	0.426527i	$0.140263\pi$
$977$	−1.67126	+	22.3014i	−0.0534683	+	0.713485i	−0.957943	+	0.286958i	$0.907356\pi$
$978$		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	−0.622300	−	0.782779i	$-0.713801\pi$
$983$	3.43993	−	45.9026i	0.109717	−	1.46407i	0.732016	−	0.681287i	$-0.238580\pi$
$984$		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	0.208004	−	0.978128i	$-0.433303\pi$
$991$	21.8811	−	3.29805i	0.695076	−	0.104766i	0.487072	+	0.873362i	$0.338065\pi$
$992$	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	0.196467	−	0.980511i	$-0.437053\pi$
$997$	−6.11128	−	1.88508i	−0.193546	−	0.0597011i	−0.390013	+	0.920809i	$0.627529\pi$
$998$	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.46.4		48
3.2	odd	2		147.2.m.a.46.1	yes	48
49.16	even	21	inner	441.2.bb.c.163.4		48
147.53	odd	42		7203.2.a.i.1.6		24
147.65	odd	42		147.2.m.a.16.1	✓	48
147.143	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	147.65	odd	42
147.2.m.a.46.1	yes	48	3.2	odd	2
441.2.bb.c.46.4		48	1.1	even	1	trivial
441.2.bb.c.163.4		48	49.16	even	21	inner
7203.2.a.i.1.6		24	147.53	odd	42
7203.2.a.k.1.6		24	147.143	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 $\F_{q}$

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

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

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