LMFDB - Embedded newform 405.3.s.a.118.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,3,Mod(37,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([28, 9]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("405.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.s (of order $36$, degree $12$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$408$
Relative dimension:	$34$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			118.31
Character	$\chi$	$=$	405.118
Dual form			405.3.s.a.127.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.289276 - 3.30644i) q^{2} +(-6.90966 - 1.21836i) q^{4} +(-2.82783 + 4.12352i) q^{5} +(-7.54736 - 5.28472i) q^{7} +(-2.59108 + 9.67004i) q^{8} +O(q^{10})$	\(q+(0.289276 - 3.30644i) q^{2} +(-6.90966 - 1.21836i) q^{4} +(-2.82783 + 4.12352i) q^{5} +(-7.54736 - 5.28472i) q^{7} +(-2.59108 + 9.67004i) q^{8} +(12.8162 + 10.5429i) q^{10} +(13.3396 + 4.85522i) q^{11} +(1.78187 + 20.3669i) q^{13} +(-19.6569 + 23.4262i) q^{14} +(4.85144 + 1.76578i) q^{16} +(1.84989 + 6.90389i) q^{17} +(-5.44455 + 3.14341i) q^{19} +(24.5633 - 25.0468i) q^{20} +(19.9124 - 42.7022i) q^{22} +(11.4039 - 7.98508i) q^{23} +(-9.00679 - 23.3212i) q^{25} +67.8574 q^{26} +(45.7110 + 45.7110i) q^{28} +(15.3211 + 18.2589i) q^{29} +(-2.53387 + 14.3703i) q^{31} +(-9.68175 + 20.7626i) q^{32} +(23.3625 - 4.11943i) q^{34} +(43.1343 - 16.1774i) q^{35} +(10.8979 + 40.6717i) q^{37} +(8.81854 + 18.9114i) q^{38} +(-32.5475 - 38.0296i) q^{40} +(37.1665 + 31.1864i) q^{41} +(-21.6952 - 46.5255i) q^{43} +(-86.2568 - 49.8004i) q^{44} +(-23.1033 - 40.0161i) q^{46} +(16.4820 + 11.5409i) q^{47} +(12.2754 + 33.7265i) q^{49} +(-79.7156 + 23.0342i) q^{50} +(12.5020 - 142.899i) q^{52} +(-34.0482 - 34.0482i) q^{53} +(-57.7427 + 41.2764i) q^{55} +(70.6593 - 59.2902i) q^{56} +(64.8041 - 45.3763i) q^{58} +(-1.34848 - 3.70492i) q^{59} +(19.1645 + 108.687i) q^{61} +(46.7817 + 12.5351i) q^{62} +(83.7341 + 48.3439i) q^{64} +(-89.0219 - 50.2464i) q^{65} +(-101.309 + 8.86343i) q^{67} +(-4.37070 - 49.9574i) q^{68} +(-41.0120 - 147.301i) q^{70} +(-25.4902 + 44.1503i) q^{71} +(-7.97110 + 29.7485i) q^{73} +(137.631 - 24.2681i) q^{74} +(41.4498 - 15.0865i) q^{76} +(-75.0204 - 107.140i) q^{77} +(48.7203 + 58.0626i) q^{79} +(-21.0003 + 15.0117i) q^{80} +(113.868 - 113.868i) q^{82} +(-23.3920 - 2.04653i) q^{83} +(-33.6995 - 11.8949i) q^{85} +(-160.110 + 58.2752i) q^{86} +(-81.5142 + 116.414i) q^{88} +(-131.217 + 75.7582i) q^{89} +(94.1848 - 163.133i) q^{91} +(-88.5256 + 41.2801i) q^{92} +(42.9270 - 51.1585i) q^{94} +(2.43433 - 31.3397i) q^{95} +(-112.747 + 52.5748i) q^{97} +(115.066 - 30.8318i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 408 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 6 q^{8}+O(q^{10}) $ 408 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 6 * q^8	$ 408 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 6 q^{8} - 6 q^{10} + 60 q^{11} - 12 q^{13} - 24 q^{16} + 6 q^{17} + 300 q^{20} - 12 q^{22} + 156 q^{23} + 6 q^{25} + 48 q^{26} - 24 q^{28} - 24 q^{31} - 72 q^{32} - 156 q^{35} - 6 q^{37} + 252 q^{38} - 108 q^{40} + 384 q^{41} - 12 q^{43} - 12 q^{46} + 210 q^{47} - 276 q^{50} - 60 q^{52} - 516 q^{53} - 24 q^{55} - 912 q^{56} - 12 q^{58} - 312 q^{61} + 6 q^{62} - 420 q^{65} - 480 q^{67} + 540 q^{68} - 12 q^{70} + 12 q^{71} - 6 q^{73} - 216 q^{76} + 876 q^{77} + 1644 q^{80} - 24 q^{82} + 372 q^{83} - 12 q^{85} - 516 q^{86} + 348 q^{88} - 12 q^{91} - 2082 q^{92} - 198 q^{95} + 600 q^{97} + 1032 q^{98}+O(q^{100}) $ 408 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 6 * q^8 - 6 * q^10 + 60 * q^11 - 12 * q^13 - 24 * q^16 + 6 * q^17 + 300 * q^20 - 12 * q^22 + 156 * q^23 + 6 * q^25 + 48 * q^26 - 24 * q^28 - 24 * q^31 - 72 * q^32 - 156 * q^35 - 6 * q^37 + 252 * q^38 - 108 * q^40 + 384 * q^41 - 12 * q^43 - 12 * q^46 + 210 * q^47 - 276 * q^50 - 60 * q^52 - 516 * q^53 - 24 * q^55 - 912 * q^56 - 12 * q^58 - 312 * q^61 + 6 * q^62 - 420 * q^65 - 480 * q^67 + 540 * q^68 - 12 * q^70 + 12 * q^71 - 6 * q^73 - 216 * q^76 + 876 * q^77 + 1644 * q^80 - 24 * q^82 + 372 * q^83 - 12 * q^85 - 516 * q^86 + 348 * q^88 - 12 * q^91 - 2082 * q^92 - 198 * q^95 + 600 * q^97 + 1032 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	0.289276	−	3.30644i	0.144638	−	1.65322i	−0.483665	−	0.875253i	$-0.660695\pi$
$2$	0.289276	−	3.30644i	0.144638	−	1.65322i	0.628303	−	0.777969i	$-0.283750\pi$
$3$		0			0
$3$		0			0
$4$	−6.90966	−	1.21836i	−1.72742	−	0.304590i
$5$	−2.82783	+	4.12352i	−0.565565	+	0.824703i
$5$	−2.82783	+	4.12352i	−0.565565	+	0.824703i
$6$		0			0
$7$	−7.54736	−	5.28472i	−1.07819	−	0.754960i	−0.107242	−	0.994233i	$-0.534202\pi$
$7$	−7.54736	−	5.28472i	−1.07819	−	0.754960i	−0.970952	+	0.239273i	$0.923091\pi$
$8$	−2.59108	+	9.67004i	−0.323885	+	1.20876i
$9$		0			0
$10$	12.8162	+	10.5429i	1.28162	+	1.05429i
$11$	13.3396	+	4.85522i	1.21269	+	0.441384i	0.867637	−	0.497199i	$-0.165638\pi$
$11$	13.3396	+	4.85522i	1.21269	+	0.441384i	0.345055	+	0.938582i	$0.387860\pi$
$12$		0			0
$13$	1.78187	+	20.3669i	0.137067	+	1.56668i	0.683985	+	0.729496i	$0.260245\pi$
$13$	1.78187	+	20.3669i	0.137067	+	1.56668i	−0.546918	+	0.837186i	$0.684199\pi$
$14$	−19.6569	+	23.4262i	−1.40406	+	1.67330i
$15$		0			0
$16$	4.85144	+	1.76578i	0.303215	+	0.110361i
$17$	1.84989	+	6.90389i	0.108817	+	0.406111i	0.998750	−	0.0499800i	$-0.0159158\pi$
$17$	1.84989	+	6.90389i	0.108817	+	0.406111i	−0.889933	+	0.456091i	$0.849249\pi$
$18$		0			0
$19$	−5.44455	+	3.14341i	−0.286555	+	0.165443i	−0.636387	−	0.771370i	$-0.719572\pi$
$19$	−5.44455	+	3.14341i	−0.286555	+	0.165443i	0.349832	+	0.936812i	$0.386239\pi$
$20$	24.5633	−	25.0468i	1.22816	−	1.25234i
$21$		0			0
$22$	19.9124	−	42.7022i	0.905107	−	1.94101i
$23$	11.4039	−	7.98508i	0.495820	−	0.347177i	−0.298768	−	0.954326i	$-0.596576\pi$
$23$	11.4039	−	7.98508i	0.495820	−	0.347177i	0.794588	+	0.607149i	$0.207687\pi$
$24$		0			0
$25$	−9.00679	−	23.3212i	−0.360272	−	0.932847i
$26$	67.8574			2.60990
$27$		0			0
$28$	45.7110	+	45.7110i	1.63254	+	1.63254i
$29$	15.3211	+	18.2589i	0.528312	+	0.629618i	0.962525	−	0.271192i	$-0.0874179\pi$
$29$	15.3211	+	18.2589i	0.528312	+	0.629618i	−0.434213	+	0.900810i	$0.642974\pi$
$30$		0			0
$31$	−2.53387	+	14.3703i	−0.0817379	+	0.463559i	0.916275	+	0.400550i	$0.131181\pi$
$31$	−2.53387	+	14.3703i	−0.0817379	+	0.463559i	−0.998013	+	0.0630090i	$0.979930\pi$
$32$	−9.68175	+	20.7626i	−0.302555	+	0.648831i
$33$		0			0
$34$	23.3625	−	4.11943i	0.687131	−	0.121160i
$35$	43.1343	−	16.1774i	1.23241	−	0.462212i
$36$		0			0
$37$	10.8979	+	40.6717i	0.294539	+	1.09923i	0.941583	+	0.336781i	$0.109338\pi$
$37$	10.8979	+	40.6717i	0.294539	+	1.09923i	−0.647044	+	0.762453i	$0.723995\pi$
$38$	8.81854	+	18.9114i	0.232067	+	0.497669i
$39$		0			0
$40$	−32.5475	−	38.0296i	−0.813687	−	0.950739i
$41$	37.1665	+	31.1864i	0.906501	+	0.760644i	0.971450	−	0.237244i	$-0.0762441\pi$
$41$	37.1665	+	31.1864i	0.906501	+	0.760644i	−0.0649494	+	0.997889i	$0.520689\pi$
$42$		0			0
$43$	−21.6952	−	46.5255i	−0.504539	−	1.08199i	−0.979401	−	0.201927i	$-0.935280\pi$
$43$	−21.6952	−	46.5255i	−0.504539	−	1.08199i	0.474862	−	0.880060i	$-0.342498\pi$
$44$	−86.2568	−	49.8004i	−1.96038	−	1.13183i
$45$		0			0
$46$	−23.1033	−	40.0161i	−0.502246	−	0.869916i
$47$	16.4820	+	11.5409i	0.350682	+	0.245550i	0.735623	−	0.677391i	$-0.236889\pi$
$47$	16.4820	+	11.5409i	0.350682	+	0.245550i	−0.384941	+	0.922941i	$0.625778\pi$
$48$		0			0
$49$	12.2754	+	33.7265i	0.250519	+	0.688296i
$50$	−79.7156	+	23.0342i	−1.59431	+	0.460684i
$51$		0			0
$52$	12.5020	−	142.899i	0.240424	−	2.74806i
$53$	−34.0482	−	34.0482i	−0.642419	−	0.642419i	0.308730	−	0.951150i	$-0.400096\pi$
$53$	−34.0482	−	34.0482i	−0.642419	−	0.642419i	−0.951150	+	0.308730i	$0.900096\pi$
$54$		0			0
$55$	−57.7427	+	41.2764i	−1.04987	+	0.750480i
$56$	70.6593	−	59.2902i	1.26177	−	1.05875i
$57$		0			0
$58$	64.8041	−	45.3763i	1.11731	−	0.782350i
$59$	−1.34848	−	3.70492i	−0.0228556	−	0.0627953i	0.927740	−	0.373227i	$-0.121749\pi$
$59$	−1.34848	−	3.70492i	−0.0228556	−	0.0627953i	−0.950596	+	0.310432i	$0.899526\pi$
$60$		0			0
$61$	19.1645	+	108.687i	0.314172	+	1.78176i	0.576823	+	0.816869i	$0.304292\pi$
$61$	19.1645	+	108.687i	0.314172	+	1.78176i	−0.262651	+	0.964891i	$0.584597\pi$
$62$	46.7817	+	12.5351i	0.754543	+	0.202179i
$63$		0			0
$64$	83.7341	+	48.3439i	1.30834	+	0.755373i
$65$	−89.0219	−	50.2464i	−1.36957	−	0.773022i
$66$		0			0
$67$	−101.309	+	8.86343i	−1.51208	+	0.132290i	−0.812794	−	0.582551i	$-0.802055\pi$
$67$	−101.309	+	8.86343i	−1.51208	+	0.132290i	−0.699287	+	0.714841i	$0.746499\pi$
$68$	−4.37070	−	49.9574i	−0.0642750	−	0.734667i
$69$		0			0
$70$	−41.0120	−	147.301i	−0.585885	−	2.10430i
$71$	−25.4902	+	44.1503i	−0.359017	+	0.621835i	−0.987797	−	0.155748i	$-0.950221\pi$
$71$	−25.4902	+	44.1503i	−0.359017	+	0.621835i	0.628780	+	0.777583i	$0.283554\pi$
$72$		0			0
$73$	−7.97110	+	29.7485i	−0.109193	+	0.407514i	−0.998787	−	0.0492379i	$-0.984321\pi$
$73$	−7.97110	+	29.7485i	−0.109193	+	0.407514i	0.889594	+	0.456752i	$0.150987\pi$
$74$	137.631	−	24.2681i	1.85988	−	0.327947i
$75$		0			0
$76$	41.4498	−	15.0865i	0.545392	−	0.198506i
$77$	−75.0204	−	107.140i	−0.974291	−	1.39143i
$78$		0			0
$79$	48.7203	+	58.0626i	0.616713	+	0.734970i	0.980502	−	0.196512i	$-0.0629613\pi$
$79$	48.7203	+	58.0626i	0.616713	+	0.734970i	−0.363788	+	0.931482i	$0.618517\pi$
$80$	−21.0003	+	15.0117i	−0.262503	+	0.187646i
$81$		0			0
$82$	113.868	−	113.868i	1.38863	−	1.38863i
$83$	−23.3920	−	2.04653i	−0.281831	−	0.0246570i	−0.0546361	−	0.998506i	$-0.517400\pi$
$83$	−23.3920	−	2.04653i	−0.281831	−	0.0246570i	−0.227195	+	0.973849i	$0.572955\pi$
$84$		0			0
$85$	−33.6995	−	11.8949i	−0.396464	−	0.139941i
$86$	−160.110	+	58.2752i	−1.86174	+	0.677618i
$87$		0			0
$88$	−81.5142	+	116.414i	−0.926298	+	1.32289i
$89$	−131.217	+	75.7582i	−1.47435	+	0.851216i	−0.999582	−	0.0288962i	$-0.990801\pi$
$89$	−131.217	+	75.7582i	−1.47435	+	0.851216i	−0.474766	+	0.880112i	$0.657467\pi$
$90$		0			0
$91$	94.1848	−	163.133i	1.03500	−	1.79267i
$92$	−88.5256	+	41.2801i	−0.962234	+	0.448697i
$93$		0			0
$94$	42.9270	−	51.1585i	0.456671	−	0.544239i
$95$	2.43433	−	31.3397i	0.0256245	−	0.329892i
$96$		0			0
$97$	−112.747	+	52.5748i	−1.16234	+	0.542008i	−0.905459	−	0.424435i	$-0.860473\pi$
$97$	−112.747	+	52.5748i	−1.16234	+	0.542008i	−0.256882	+	0.966443i	$0.582695\pi$
$98$	115.066	−	30.8318i	1.17414	−	0.314610i
$99$		0			0
$100$	33.8203	+	172.115i	0.338203	+	1.72115i
$101$	28.8437	+	163.580i	0.285581	+	1.61961i	0.703204	+	0.710988i	$0.251752\pi$
$101$	28.8437	+	163.580i	0.285581	+	1.61961i	−0.417623	+	0.908620i	$0.637137\pi$
$102$		0			0
$103$	−84.6151	−	39.4567i	−0.821505	−	0.383074i	−0.0340304	−	0.999421i	$-0.510834\pi$
$103$	−84.6151	−	39.4567i	−0.821505	−	0.383074i	−0.787475	+	0.616347i	$0.788612\pi$
$104$	−201.565	−	35.5414i	−1.93813	−	0.341745i
$105$		0			0
$106$	−122.428	+	102.729i	−1.15498	+	0.969143i
$107$	62.9023	−	62.9023i	0.587872	−	0.587872i	−0.349183	−	0.937055i	$-0.613541\pi$
$107$	62.9023	−	62.9023i	0.587872	−	0.587872i	0.937055	+	0.349183i	$0.113541\pi$
$108$		0			0
$109$		−	3.14570i		−	0.0288597i	−0.999896	−	0.0144298i	$-0.995407\pi$
$109$		−	3.14570i		−	0.0288597i	0.999896	−	0.0144298i	$-0.00459332\pi$
$110$	119.774	+	202.863i	1.08886	+	1.84421i
$111$		0			0
$112$	−27.2839	−	38.9655i	−0.243606	−	0.347906i
$113$	55.1039	+	25.6954i	0.487645	+	0.227393i	0.650860	−	0.759198i	$-0.274409\pi$
$113$	55.1039	+	25.6954i	0.487645	+	0.227393i	−0.163215	+	0.986591i	$0.552186\pi$
$114$		0			0
$115$	0.678427	+	69.6045i	0.00589936	+	0.605256i
$116$	−83.6173	−	144.829i	−0.720839	−	1.24853i
$117$		0			0
$118$	−12.6402	+	3.38693i	−0.107120	+	0.0287028i
$119$	22.5233	−	61.8823i	0.189272	−	0.520019i
$120$		0			0
$121$	61.6807	+	51.7562i	0.509758	+	0.427737i
$122$	364.913	−	31.9257i	2.99109	−	0.261686i
$123$		0			0
$124$	35.0164	−	96.2068i	0.282390	−	0.775862i
$125$	121.635	+	28.8086i	0.973080	+	0.230469i
$126$		0			0
$127$	73.1040	+	19.5882i	0.575622	+	0.154237i	0.534874	−	0.844932i	$-0.320359\pi$
$127$	73.1040	+	19.5882i	0.575622	+	0.154237i	0.0407482	+	0.999169i	$0.487026\pi$
$128$	131.508	−	187.813i	1.02741	−	1.46729i
$129$		0			0
$130$	−191.889	+	279.811i	−1.47607	+	2.15239i
$131$	16.2279	−	92.0330i	0.123877	−	0.702542i	−0.858091	−	0.513497i	$-0.828350\pi$
$131$	16.2279	−	92.0330i	0.123877	−	0.702542i	0.981968	−	0.189045i	$-0.0605392\pi$
$132$		0			0
$133$	57.7041	+	5.04845i	0.433865	+	0.0379583i
$134$			337.538i			2.51894i
$135$		0			0
$136$	−71.5541			−0.526133
$137$	0.828382	−	9.46845i	0.00604658	−	0.0691128i	−0.992572	−	0.121660i	$-0.961178\pi$
$137$	0.828382	−	9.46845i	0.00604658	−	0.0691128i	0.998618	+	0.0525469i	$0.0167339\pi$
$138$		0			0
$139$	75.4696	+	13.3073i	0.542947	+	0.0957362i	0.438394	−	0.898783i	$-0.355548\pi$
$139$	75.4696	+	13.3073i	0.542947	+	0.0957362i	0.104553	+	0.994519i	$0.466659\pi$
$140$	−317.753	+	59.2273i	−2.26967	+	0.423052i
$141$		0			0
$142$	138.607	+	97.0535i	0.976104	+	0.683475i
$143$	−75.1162	+	280.337i	−0.525288	+	1.96040i
$144$		0			0
$145$	−118.616	+	11.5436i	−0.818043	+	0.0796108i
$146$	96.0561	+	34.9615i	0.657918	+	0.239463i
$147$		0			0
$148$	−25.7484	−	294.305i	−0.173975	−	1.98855i
$149$	42.4603	−	50.6022i	0.284969	−	0.339612i	−0.604503	−	0.796603i	$-0.706628\pi$
$149$	42.4603	−	50.6022i	0.284969	−	0.339612i	0.889472	+	0.456991i	$0.151073\pi$
$150$		0			0
$151$	−74.3944	−	27.0774i	−0.492678	−	0.179320i	0.0837196	−	0.996489i	$-0.473320\pi$
$151$	−74.3944	−	27.0774i	−0.492678	−	0.179320i	−0.576398	+	0.817169i	$0.695542\pi$
$152$	−16.2897	−	60.7939i	−0.107169	−	0.399960i
$153$		0			0
$154$	−375.955	+	217.058i	−2.44127	+	1.40947i
$155$	−52.0909	−	51.0852i	−0.336070	−	0.329582i
$156$		0			0
$157$	108.076	−	231.769i	0.688380	−	1.47624i	−0.181714	−	0.983351i	$-0.558165\pi$
$157$	108.076	−	231.769i	0.688380	−	1.47624i	0.870094	−	0.492885i	$-0.164058\pi$
$158$	206.074	−	144.295i	1.30427	−	0.913259i
$159$		0			0
$160$	−58.2365	−	98.6358i	−0.363978	−	0.616474i
$161$	−128.268			−0.796696
$162$		0			0
$163$	44.4356	+	44.4356i	0.272611	+	0.272611i	0.830150	−	0.557540i	$-0.188254\pi$
$163$	44.4356	+	44.4356i	0.272611	+	0.272611i	−0.557540	+	0.830150i	$0.688254\pi$
$164$	−218.812	−	260.770i	−1.33422	−	1.59006i
$165$		0			0
$166$	−13.5335	+	76.7522i	−0.0815270	+	0.462363i
$167$	0.375265	−	0.804759i	0.00224710	−	0.00481892i	−0.905181	−	0.425026i	$-0.860265\pi$
$167$	0.375265	−	0.804759i	0.00224710	−	0.00481892i	0.907428	+	0.420207i	$0.138043\pi$
$168$		0			0
$169$	−245.202	+	43.2357i	−1.45090	+	0.255832i
$170$	−49.0784	+	107.985i	−0.288697	+	0.635203i
$171$		0			0
$172$	93.2216	+	347.908i	0.541986	+	2.02272i
$173$	−35.9931	−	77.1875i	−0.208053	−	0.446170i	0.774397	−	0.632701i	$-0.218054\pi$
$173$	−35.9931	−	77.1875i	−0.208053	−	0.446170i	−0.982449	+	0.186530i	$0.940276\pi$
$174$		0			0
$175$	−55.2684	+	223.612i	−0.315820	+	1.27778i
$176$	56.1431	+	47.1096i	0.318995	+	0.267668i
$177$		0			0
$178$	212.532	+	455.777i	1.19400	+	2.56054i
$179$	−70.0000	−	40.4145i	−0.391061	−	0.225779i	0.291559	−	0.956553i	$-0.405826\pi$
$179$	−70.0000	−	40.4145i	−0.391061	−	0.225779i	−0.682620	+	0.730774i	$0.739160\pi$
$180$		0			0
$181$	−91.3450	−	158.214i	−0.504669	−	0.874112i	−0.999985	−	0.00539931i	$-0.998281\pi$
$181$	−91.3450	−	158.214i	−0.504669	−	0.874112i	0.495317	−	0.868712i	$-0.335052\pi$
$182$	−512.144	−	358.607i	−2.81398	−	1.97037i
$183$		0			0
$184$	47.6677	+	130.966i	0.259064	+	0.711771i
$185$	−198.528	−	70.0746i	−1.07312	−	0.378782i
$186$		0			0
$187$	−8.84308	+	101.077i	−0.0472892	+	0.540518i
$188$	−99.8244	−	99.8244i	−0.530981	−	0.530981i
$189$		0			0
$190$	−102.919	−	17.1148i	−0.541678	−	0.0900780i
$191$	3.06073	−	2.56825i	0.0160247	−	0.0134464i	−0.634740	−	0.772726i	$-0.718893\pi$
$191$	3.06073	−	2.56825i	0.0160247	−	0.0134464i	0.650765	+	0.759279i	$0.274448\pi$
$192$		0			0
$193$	17.6075	−	12.3289i	0.0912303	−	0.0638802i	−0.527071	−	0.849821i	$-0.676710\pi$
$193$	17.6075	−	12.3289i	0.0912303	−	0.0638802i	0.618302	+	0.785941i	$0.287821\pi$
$194$	141.221	+	388.000i	0.727941	+	2.00000i
$195$		0			0
$196$	−43.7281	−	247.994i	−0.223103	−	1.26528i
$197$	187.642	+	50.2785i	0.952498	+	0.255221i	0.701422	−	0.712746i	$-0.252549\pi$
$197$	187.642	+	50.2785i	0.952498	+	0.255221i	0.251076	+	0.967967i	$0.419216\pi$
$198$		0			0
$199$	−16.1708	−	9.33621i	−0.0812602	−	0.0469156i	0.458819	−	0.888530i	$-0.348273\pi$
$199$	−16.1708	−	9.33621i	−0.0812602	−	0.0469156i	−0.540080	+	0.841614i	$0.681606\pi$
$200$	248.854	−	26.6690i	1.24427	−	0.133345i
$201$		0			0
$202$	549.213	−	48.0500i	2.71888	−	0.237871i
$203$	−19.1403	−	218.774i	−0.0942870	−	1.07771i
$204$		0			0
$205$	−233.698	+	65.0670i	−1.13999	+	0.317400i
$206$	−154.938	+	268.361i	−0.752128	+	1.30272i
$207$		0			0
$208$	−27.3188	+	101.955i	−0.131340	+	0.490168i
$209$	−87.8901	+	15.4974i	−0.420527	+	0.0741502i
$210$		0			0
$211$	75.9377	−	27.6391i	0.359894	−	0.130991i	−0.155743	−	0.987798i	$-0.549777\pi$
$211$	75.9377	−	27.6391i	0.359894	−	0.130991i	0.515638	+	0.856807i	$0.327555\pi$
$212$	193.779	+	276.745i	0.914050	+	1.30540i
$213$		0			0
$214$	−189.787	−	226.179i	−0.886854	−	1.05691i
$215$	253.199	+	42.1055i	1.17767	+	0.195840i
$216$		0			0
$217$	95.0672	−	95.0672i	0.438098	−	0.438098i
$218$	−10.4011	−	0.909977i	−0.0477114	−	0.00417421i
$219$		0			0
$220$	449.272	−	214.854i	2.04215	−	0.976611i
$221$	−137.314	+	49.9783i	−0.621332	+	0.226146i
$222$		0			0
$223$	120.284	−	171.783i	0.539390	−	0.770328i	−0.453256	−	0.891380i	$-0.649738\pi$
$223$	120.284	−	171.783i	0.539390	−	0.770328i	0.992646	+	0.121052i	$0.0386267\pi$
$224$	182.796	−	105.537i	0.816054	−	0.471149i
$225$		0			0
$226$	100.901	−	174.765i	0.446463	−	0.773296i
$227$	−96.7270	+	45.1045i	−0.426110	+	0.198698i	−0.623830	−	0.781560i	$-0.714424\pi$
$227$	−96.7270	+	45.1045i	−0.426110	+	0.198698i	0.197720	+	0.980259i	$0.436646\pi$
$228$		0			0
$229$	287.026	−	342.064i	1.25339	−	1.49373i	0.456347	−	0.889802i	$-0.349158\pi$
$229$	287.026	−	342.064i	1.25339	−	1.49373i	0.797040	−	0.603927i	$-0.206398\pi$
$230$	230.340	+	17.8917i	1.00148	+	0.0777902i
$231$		0			0
$232$	−216.263	+	100.845i	−0.932167	+	0.434676i
$233$	210.914	−	56.5143i	0.905212	−	0.242551i	0.223959	−	0.974599i	$-0.428102\pi$
$233$	210.914	−	56.5143i	0.905212	−	0.242551i	0.681253	+	0.732048i	$0.261435\pi$
$234$		0			0
$235$	−94.1973	+	35.3285i	−0.400839	+	0.150334i
$236$	4.80362	+	27.2427i	0.0203543	+	0.115435i
$237$		0			0
$238$	−198.095	−	92.3732i	−0.832332	−	0.388123i
$239$	−90.5443	−	15.9654i	−0.378846	−	0.0668008i	−0.0190174	−	0.999819i	$-0.506054\pi$
$239$	−90.5443	−	15.9654i	−0.378846	−	0.0668008i	−0.359829	+	0.933018i	$0.617165\pi$
$240$		0			0
$241$	−337.995	+	283.612i	−1.40247	+	1.17681i	−0.442481	+	0.896778i	$0.645902\pi$
$241$	−337.995	+	283.612i	−1.40247	+	1.17681i	−0.959990	+	0.280035i	$0.909654\pi$
$242$	188.972	−	188.972i	0.780875	−	0.780875i
$243$		0			0
$244$		−	774.342i		−	3.17353i
$245$	−173.785	−	44.7547i	−0.709325	−	0.182672i
$246$		0			0
$247$	−73.7229	−	105.287i	−0.298473	−	0.426264i
$248$	−132.396	−	61.7373i	−0.533855	−	0.248941i
$249$		0			0
$250$	130.440	−	393.846i	0.521761	−	1.57538i
$251$	11.6308	+	20.1451i	0.0463378	+	0.0802594i	0.888264	−	0.459333i	$-0.151912\pi$
$251$	11.6308	+	20.1451i	0.0463378	+	0.0802594i	−0.841926	+	0.539593i	$0.818578\pi$
$252$		0			0
$253$	190.892	−	51.1495i	0.754516	−	0.202172i
$254$	85.9144	−	236.048i	0.338246	−	0.929322i
$255$		0			0
$256$	−286.684	−	240.556i	−1.11986	−	0.939674i
$257$	−187.037	+	16.3636i	−0.727769	+	0.0636715i	−0.445018	−	0.895522i	$-0.646803\pi$
$257$	−187.037	+	16.3636i	−0.727769	+	0.0636715i	−0.282751	+	0.959193i	$0.591247\pi$
$258$		0			0
$259$	132.688	−	364.556i	0.512308	−	1.40755i
$260$	553.893	+	455.646i	2.13036	+	1.75249i
$261$		0			0
$262$	−299.608	−	80.2797i	−1.14354	−	0.306411i
$263$	−202.921	+	289.801i	−0.771561	+	1.10190i	0.220406	+	0.975408i	$0.429262\pi$
$263$	−202.921	+	289.801i	−0.771561	+	1.10190i	−0.991967	+	0.126495i	$0.959627\pi$
$264$		0			0
$265$	236.681	−	44.1159i	0.893135	−	0.166475i
$266$	33.3848	−	189.335i	0.125507	−	0.711785i
$267$		0			0
$268$	710.813	+	62.1881i	2.65229	+	0.232045i
$269$			237.767i			0.883894i	0.897041	+	0.441947i	$0.145712\pi$
$269$			237.767i			0.883894i	−0.897041	+	0.441947i	$0.854288\pi$
$270$		0			0
$271$	254.610			0.939520			0.469760	−	0.882794i	$-0.344340\pi$
$271$	254.610			0.939520			0.469760	+	0.882794i	$0.344340\pi$
$272$	−3.21611	+	36.7603i	−0.0118239	+	0.135148i
$273$		0			0
$274$	−31.0673	−	5.47800i	−0.113384	−	0.0199927i
$275$	−6.91755	−	354.826i	−0.0251547	−	1.29027i
$276$		0			0
$277$	−352.275	−	246.666i	−1.27175	−	0.890490i	−0.274286	−	0.961648i	$-0.588442\pi$
$277$	−352.275	−	246.666i	−1.27175	−	0.890490i	−0.997465	+	0.0711581i	$0.977331\pi$
$278$	65.8315	−	245.687i	0.236804	−	0.883765i
$279$		0			0
$280$	44.6719	+	459.027i	0.159542	+	1.63938i
$281$	−196.476	−	71.5112i	−0.699201	−	0.254488i	−0.0321314	−	0.999484i	$-0.510230\pi$
$281$	−196.476	−	71.5112i	−0.699201	−	0.254488i	−0.667070	+	0.744995i	$0.732452\pi$
$282$		0			0
$283$	33.7336	+	385.577i	0.119200	+	1.36246i	0.786462	+	0.617639i	$0.211911\pi$
$283$	33.7336	+	385.577i	0.119200	+	1.36246i	−0.667262	+	0.744823i	$0.732534\pi$
$284$	229.919	−	274.007i	0.809575	−	0.964814i
$285$		0			0
$286$	905.191	+	329.462i	3.16500	+	1.15197i
$287$	−115.698	−	431.790i	−0.403128	−	1.50449i
$288$		0			0
$289$	206.040	−	118.957i	0.712940	−	0.411616i
$290$	3.85526	+	395.537i	0.0132940	+	1.36392i
$291$		0			0
$292$	91.3220	−	195.841i	0.312747	−	0.670687i
$293$	349.268	−	244.560i	1.19204	−	0.834676i	0.202550	−	0.979272i	$-0.435077\pi$
$293$	349.268	−	244.560i	1.19204	−	0.834676i	0.989491	+	0.144596i	$0.0461882\pi$
$294$		0			0
$295$	19.0906	+	4.91639i	0.0647139	+	0.0166657i
$296$	−421.534			−1.42410
$297$		0			0
$298$	−155.031	−	155.031i	−0.520237	−	0.520237i
$299$	182.951	+	218.033i	0.611877	+	0.729206i
$300$		0			0
$301$	−82.1327	+	465.797i	−0.272866	+	1.54750i
$302$	−111.050	+	238.148i	−0.367716	+	0.788570i
$303$		0			0
$304$	−31.9645	+	5.63620i	−0.105146	+	0.0185401i
$305$	−502.368	−	228.324i	−1.64711	−	0.748603i
$306$		0			0
$307$	−47.1158	−	175.839i	−0.153472	−	0.572764i	−0.999231	−	0.0392000i	$-0.987519\pi$
$307$	−47.1158	−	175.839i	−0.153472	−	0.572764i	0.845760	−	0.533564i	$-0.179148\pi$
$308$	387.830	+	831.705i	1.25919	+	2.70034i
$309$		0			0
$310$	−183.979	+	157.458i	−0.593481	+	0.507929i
$311$	328.812	+	275.906i	1.05727	+	0.887158i	0.993840	−	0.110828i	$-0.0353504\pi$
$311$	328.812	+	275.906i	1.05727	+	0.887158i	0.0634337	+	0.997986i	$0.479795\pi$
$312$		0			0
$313$	10.0981	+	21.6555i	0.0322624	+	0.0691870i	0.921779	−	0.387717i	$-0.126736\pi$
$313$	10.0981	+	21.6555i	0.0322624	+	0.0691870i	−0.889516	+	0.456904i	$0.848958\pi$
$314$	−735.068	−	424.392i	−2.34098	−	1.35157i
$315$		0			0
$316$	−265.900	−	460.552i	−0.841455	−	1.45744i
$317$	23.3464	+	16.3473i	0.0736479	+	0.0515688i	0.609821	−	0.792540i	$-0.291242\pi$
$317$	23.3464	+	16.3473i	0.0736479	+	0.0515688i	−0.536173	+	0.844108i	$0.680130\pi$
$318$		0			0
$319$	115.726	+	317.954i	0.362777	+	0.996721i
$320$	−436.132	+	208.571i	−1.36291	+	0.651783i
$321$		0			0
$322$	−37.1049	+	424.111i	−0.115233	+	1.31712i
$323$	−31.7736	−	31.7736i	−0.0983703	−	0.0983703i
$324$		0			0
$325$	458.931	−	224.995i	1.41209	−	0.692293i
$326$	159.778	−	134.070i	0.490116	−	0.411256i
$327$		0			0
$328$	−397.876	+	278.595i	−1.21304	+	0.849376i
$329$	−63.4058	−	174.206i	−0.192723	−	0.529502i
$330$		0			0
$331$	−0.811595	−	4.60278i	−0.00245195	−	0.0139057i	0.983557	−	0.180597i	$-0.0578029\pi$
$331$	−0.811595	−	4.60278i	−0.00245195	−	0.0139057i	−0.986009	+	0.166691i	$0.946692\pi$
$332$	159.137	+	42.6407i	0.479329	+	0.128436i
$333$		0			0
$334$	−2.55234	−	1.47359i	−0.00764172	−	0.00441195i
$335$	249.937	−	442.816i	0.746081	−	1.32184i
$336$		0			0
$337$	−413.812	+	36.2039i	−1.22793	+	0.107430i	−0.682600	−	0.730792i	$-0.739151\pi$
$337$	−413.812	+	36.2039i	−1.22793	+	0.107430i	−0.545329	+	0.838222i	$0.683595\pi$
$338$	72.0253	+	823.253i	0.213092	+	2.43566i
$339$		0			0
$340$	218.360	+	123.248i	0.642234	+	0.362494i
$341$	−103.572	+	179.392i	−0.303730	+	0.526076i
$342$		0			0
$343$	−31.2606	+	116.666i	−0.0911388	+	0.340135i
$344$	506.117	−	89.2421i	1.47127	−	0.259425i
$345$		0			0
$346$	−265.628	+	96.6807i	−0.767711	+	0.279424i
$347$	−296.039	−	422.788i	−0.853139	−	1.21841i	−0.974183	−	0.225761i	$-0.927513\pi$
$347$	−296.039	−	422.788i	−0.853139	−	1.21841i	0.121044	−	0.992647i	$-0.461376\pi$
$348$		0			0
$349$	68.0083	+	81.0492i	0.194866	+	0.232233i	0.854626	−	0.519244i	$-0.173786\pi$
$349$	68.0083	+	81.0492i	0.194866	+	0.232233i	−0.659760	+	0.751477i	$0.729342\pi$
$350$	723.372	+	247.428i	2.06678	+	0.706936i
$351$		0			0
$352$	−229.958	+	229.958i	−0.653289	+	0.653289i
$353$	238.688	+	20.8825i	0.676171	+	0.0591573i	0.420069	−	0.907492i	$-0.362006\pi$
$353$	238.688	+	20.8825i	0.676171	+	0.0591573i	0.256102	+	0.966650i	$0.417562\pi$
$354$		0			0
$355$	−109.973	−	229.958i	−0.309782	−	0.647770i
$356$	998.966	−	363.594i	2.80608	−	1.02133i
$357$		0			0
$358$	−153.878	+	219.760i	−0.429826	+	0.613855i
$359$	412.289	−	238.035i	1.14844	−	0.663051i	0.199932	−	0.979810i	$-0.435928\pi$
$359$	412.289	−	238.035i	1.14844	−	0.663051i	0.948506	+	0.316759i	$0.102595\pi$
$360$		0			0
$361$	−160.738	+	278.406i	−0.445257	+	0.771208i
$362$	−549.550	+	256.260i	−1.51810	+	0.707899i
$363$		0			0
$364$	−849.539	+	1012.44i	−2.33390	+	2.78143i
$365$	−100.128	−	116.993i	−0.274323	−	0.320528i
$366$		0			0
$367$	−405.407	+	189.044i	−1.10465	+	0.515107i	−0.887396	−	0.461008i	$-0.847488\pi$
$367$	−405.407	+	189.044i	−1.10465	+	0.515107i	−0.217255	+	0.976115i	$0.569710\pi$
$368$	69.4251	−	18.6024i	0.188655	−	0.0505500i
$369$		0			0
$370$	−289.127	+	636.150i	−0.781425	+	1.71932i
$371$	77.0389	+	436.910i	0.207652	+	1.17765i
$372$		0			0
$373$	75.5955	+	35.2508i	0.202669	+	0.0945061i	0.521303	−	0.853372i	$-0.325446\pi$
$373$	75.5955	+	35.2508i	0.202669	+	0.0945061i	−0.318634	+	0.947878i	$0.603224\pi$
$374$	331.647	+	58.4783i	0.886756	+	0.156359i
$375$		0			0
$376$	−154.307	+	129.479i	−0.410391	+	0.344359i
$377$	−344.577	+	344.577i	−0.913997	+	0.913997i
$378$		0			0
$379$		−	200.528i		−	0.529099i	−0.964372	−	0.264549i	$-0.914777\pi$
$379$		−	200.528i		−	0.529099i	0.964372	−	0.264549i	$-0.0852232\pi$
$380$	−55.0034	+	213.581i	−0.144746	+	0.562055i
$381$		0			0
$382$	−7.60639	−	10.8631i	−0.0199120	−	0.0284373i
$383$	642.442	+	299.575i	1.67739	+	0.782181i	0.998866	+	0.0476063i	$0.0151593\pi$
$383$	642.442	+	299.575i	1.67739	+	0.782181i	0.678527	+	0.734575i	$0.262619\pi$
$384$		0			0
$385$	653.939	−	6.37387i	1.69854	−	0.0165555i
$386$	−35.6713	−	61.7845i	−0.0924127	−	0.160063i
$387$		0			0
$388$	843.099	−	225.908i	2.17293	−	0.582236i
$389$	108.210	−	297.303i	0.278174	−	0.764276i	−0.719396	−	0.694600i	$-0.755581\pi$
$389$	108.210	−	297.303i	0.278174	−	0.764276i	0.997570	−	0.0696760i	$-0.0221965\pi$
$390$		0			0
$391$	76.2240	+	63.9595i	0.194946	+	0.163579i
$392$	−357.943	+	31.3160i	−0.913121	+	0.0798877i
$393$		0			0
$394$	220.524	−	605.883i	0.559704	−	1.53778i
$395$	−377.195	+	36.7081i	−0.954924	+	0.0929318i
$396$		0			0
$397$	66.5324	+	17.8273i	0.167588	+	0.0449051i	0.341637	−	0.939832i	$-0.389019\pi$
$397$	66.5324	+	17.8273i	0.167588	+	0.0449051i	−0.174049	+	0.984737i	$0.555685\pi$
$398$	−35.5475	+	50.7671i	−0.0893153	+	0.127555i
$399$		0			0
$400$	−2.51582	−	129.045i	−0.00628955	−	0.322613i
$401$	102.421	−	580.856i	0.255413	−	1.44852i	−0.539598	−	0.841923i	$-0.681424\pi$
$401$	102.421	−	580.856i	0.255413	−	1.44852i	0.795010	−	0.606596i	$-0.207465\pi$
$402$		0			0
$403$	−297.193	−	26.0010i	−0.737452	−	0.0645187i
$404$		−	1165.43i		−	2.88472i
$405$		0			0
$406$	−728.901			−1.79532
$407$	−52.0957	+	595.456i	−0.127999	+	1.46304i
$408$		0			0
$409$	−550.479	−	97.0642i	−1.34591	−	0.237321i	−0.546176	−	0.837671i	$-0.683917\pi$
$409$	−550.479	−	97.0642i	−1.34591	−	0.237321i	−0.799738	+	0.600350i	$0.795028\pi$
$410$	147.537	+	791.533i	0.359847	+	1.93057i
$411$		0			0
$412$	536.589	+	375.724i	1.30240	+	0.911951i
$413$	−9.40200	+	35.0888i	−0.0227651	+	0.0849607i
$414$		0			0
$415$	74.5873	−	90.6699i	0.179729	−	0.218482i
$416$	−440.120	−	160.191i	−1.05798	−	0.385074i
$417$		0			0
$418$	25.8168	+	295.087i	0.0617626	+	0.705949i
$419$	−458.479	+	546.394i	−1.09422	+	1.30404i	−0.145002	+	0.989431i	$0.546319\pi$
$419$	−458.479	+	546.394i	−1.09422	+	1.30404i	−0.949220	+	0.314612i	$0.898126\pi$
$420$		0			0
$421$	336.248	+	122.384i	0.798689	+	0.290699i	0.708943	−	0.705266i	$-0.249172\pi$
$421$	336.248	+	122.384i	0.798689	+	0.290699i	0.0897456	+	0.995965i	$0.471395\pi$
$422$	−69.4201	−	259.079i	−0.164503	−	0.613932i
$423$		0			0
$424$	417.469	−	241.026i	0.984598	−	0.568458i
$425$	144.345	−	105.324i	0.339636	−	0.247820i
$426$		0			0
$427$	429.741	−	921.582i	1.00642	−	2.15827i
$428$	−511.271	+	357.996i	−1.19456	+	0.836439i
$429$		0			0
$430$	212.464	−	825.007i	0.494102	−	1.91862i
$431$	−223.781			−0.519214			−0.259607	−	0.965714i	$-0.583593\pi$
$431$	−223.781			−0.519214			−0.259607	+	0.965714i	$0.583593\pi$
$432$		0			0
$433$	−377.815	−	377.815i	−0.872552	−	0.872552i	0.120198	−	0.992750i	$-0.461647\pi$
$433$	−377.815	−	377.815i	−0.872552	−	0.872552i	−0.992750	+	0.120198i	$0.961647\pi$
$434$	−286.834	−	341.835i	−0.660907	−	0.787638i
$435$		0			0
$436$	−3.83260	+	21.7357i	−0.00879036	+	0.0498526i
$437$	−36.9885	+	79.3222i	−0.0846420	+	0.181515i
$438$		0			0
$439$	140.560	−	24.7844i	0.320181	−	0.0564566i	−0.0112478	−	0.999937i	$-0.503580\pi$
$439$	140.560	−	24.7844i	0.320181	−	0.0564566i	0.331429	+	0.943480i	$0.392469\pi$
$440$	−249.529	−	665.325i	−0.567110	−	1.51210i
$441$		0			0
$442$	125.529	+	468.480i	0.284002	+	1.05991i
$443$	111.757	+	239.664i	0.252274	+	0.541003i	0.991136	−	0.132854i	$-0.0424141\pi$
$443$	111.757	+	239.664i	0.252274	+	0.541003i	−0.738862	+	0.673857i	$0.764636\pi$
$444$		0			0
$445$	58.6689	−	755.307i	0.131840	−	1.69732i
$446$	−533.196	−	447.405i	−1.19551	−	1.00315i
$447$		0			0
$448$	−376.487	−	807.380i	−0.840374	−	1.80219i
$449$	428.776	+	247.554i	0.954958	+	0.551345i	0.894618	−	0.446832i	$-0.147448\pi$
$449$	428.776	+	247.554i	0.954958	+	0.551345i	0.0603406	+	0.998178i	$0.480781\pi$
$450$		0			0
$451$	344.370	+	596.466i	0.763570	+	1.32254i
$452$	−349.443	−	244.683i	−0.773104	−	0.541333i
$453$		0			0
$454$	121.155	+	332.870i	0.266861	+	0.733194i
$455$	406.343	+	849.684i	0.893061	+	1.86744i
$456$		0			0
$457$	−13.9912	+	159.920i	−0.0306152	+	0.349934i	0.965402	+	0.260768i	$0.0839757\pi$
$457$	−13.9912	+	159.920i	−0.0306152	+	0.349934i	−0.996017	+	0.0891658i	$0.971580\pi$
$458$	−1047.99	−	1047.99i	−2.28818	−	2.28818i
$459$		0			0
$460$	80.1156	−	481.770i	0.174164	−	1.04733i
$461$	−174.971	+	146.818i	−0.379547	+	0.318478i	−0.812525	−	0.582927i	$-0.801907\pi$
$461$	−174.971	+	146.818i	−0.379547	+	0.318478i	0.432977	+	0.901405i	$0.357463\pi$
$462$		0			0
$463$	−230.345	+	161.289i	−0.497506	+	0.348357i	−0.795243	−	0.606290i	$-0.792657\pi$
$463$	−230.345	+	161.289i	−0.497506	+	0.348357i	0.297737	+	0.954648i	$0.403768\pi$
$464$	42.0879	+	115.636i	0.0907067	+	0.249215i
$465$		0			0
$466$	−125.849	−	713.725i	−0.270062	−	1.53160i
$467$	320.222	+	85.8032i	0.685700	+	0.183733i	0.584817	−	0.811165i	$-0.301166\pi$
$467$	320.222	+	85.8032i	0.685700	+	0.183733i	0.100883	+	0.994898i	$0.467833\pi$
$468$		0			0
$469$	811.460	+	468.497i	1.73019	+	0.998927i
$470$	89.5625	+	321.678i	0.190559	+	0.684421i
$471$		0			0
$472$	39.3208	−	3.44012i	0.0833068	−	0.00728840i
$473$	−63.5138	−	725.966i	−0.134279	−	1.53481i
$474$		0			0
$475$	122.346	+	98.6613i	0.257571	+	0.207708i
$476$	−231.023	+	400.144i	−0.485343	+	0.840639i
$477$		0			0
$478$	−78.9810	+	294.761i	−0.165232	+	0.616655i
$479$	818.976	−	144.408i	1.70976	−	0.301477i	0.768675	−	0.639640i	$-0.220916\pi$
$479$	818.976	−	144.408i	1.70976	−	0.301477i	0.941088	+	0.338163i	$0.109805\pi$
$480$		0			0
$481$	−808.936	+	294.428i	−1.68178	+	0.612117i
$482$	839.973	+	1199.61i	1.74268	+	2.48881i
$483$		0			0
$484$	−363.135	−	432.767i	−0.750279	−	0.894147i
$485$	102.036	−	613.587i	0.210383	−	1.26513i
$486$		0			0
$487$	−265.967	+	265.967i	−0.546133	+	0.546133i	−0.925320	−	0.379187i	$-0.876204\pi$
$487$	−265.967	+	265.967i	−0.546133	+	0.546133i	0.379187	+	0.925320i	$0.376204\pi$
$488$	−1100.67	−	96.2960i	−2.25547	−	0.197328i
$489$		0			0
$490$	−198.251	+	561.662i	−0.404593	+	1.14625i
$491$	−12.4040	+	4.51470i	−0.0252628	+	0.00919492i	−0.354621	−	0.935010i	$-0.615390\pi$
$491$	−12.4040	+	4.51470i	−0.0252628	+	0.00919492i	0.329358	+	0.944205i	$0.393168\pi$
$492$		0			0
$493$	−97.7153	+	139.552i	−0.198205	+	0.283067i
$494$	−369.453	+	213.304i	−0.747880	+	0.431789i
$495$		0			0
$496$	−37.6677	+	65.2424i	−0.0759430	+	0.131537i
$497$	425.705	−	198.510i	0.856550	−	0.399416i
$498$		0			0
$499$	−190.371	+	226.875i	−0.381505	+	0.454660i	−0.922289	−	0.386502i	$-0.873683\pi$
$499$	−190.371	+	226.875i	−0.381505	+	0.454660i	0.540784	+	0.841162i	$0.318128\pi$
$500$	−805.357	−	347.253i	−1.61071	−	0.694506i
$501$		0			0
$502$	69.9732	−	32.6290i	0.139389	−	0.0649980i
$503$	483.819	−	129.639i	0.961867	−	0.257731i	0.256476	−	0.966550i	$-0.417438\pi$
$503$	483.819	−	129.639i	0.961867	−	0.257731i	0.705390	+	0.708819i	$0.250772\pi$
$504$		0			0
$505$	−756.092	−	343.640i	−1.49721	−	0.680475i
$506$	−113.902	−	645.972i	−0.225103	−	1.27662i
$507$		0			0
$508$	−481.258	−	224.414i	−0.947359	−	0.441761i
$509$	−340.367	−	60.0158i	−0.668697	−	0.117909i	−0.171014	−	0.985269i	$-0.554704\pi$
$509$	−340.367	−	60.0158i	−0.668697	−	0.117909i	−0.497683	+	0.867359i	$0.665816\pi$
$510$		0			0
$511$	217.374	−	182.398i	0.425389	−	0.356943i
$512$	−229.822	+	229.822i	−0.448870	+	0.448870i
$513$		0			0
$514$			623.160i			1.21237i
$515$	401.977	−	237.335i	0.780538	−	0.460845i
$516$		0			0
$517$	163.831	+	233.974i	0.316887	+	0.452562i
$518$	−1167.00	−	544.182i	−2.25290	−	1.05054i
$519$		0			0
$520$	716.548	−	730.654i	1.37798	−	1.40510i
$521$	166.005	+	287.529i	0.318628	+	0.551879i	0.980202	−	0.198000i	$-0.0634447\pi$
$521$	166.005	+	287.529i	0.318628	+	0.551879i	−0.661574	+	0.749880i	$0.730111\pi$
$522$		0			0
$523$	170.989	−	45.8164i	0.326939	−	0.0876030i	−0.0916162	−	0.995794i	$-0.529203\pi$
$523$	170.989	−	45.8164i	0.326939	−	0.0876030i	0.418555	+	0.908191i	$0.362537\pi$
$524$	−224.259	+	616.146i	−0.427975	+	1.17585i
$525$		0			0
$526$	899.509	+	754.778i	1.71009	+	1.43494i
$527$	−103.898	+	9.08994i	−0.197151	+	0.0172485i
$528$		0			0
$529$	−114.642	+	314.976i	−0.216714	+	0.595418i
$530$	−77.4007	−	795.334i	−0.146039	−	1.50063i
$531$		0			0
$532$	−392.565	−	105.187i	−0.737903	−	0.197721i
$533$	−568.944	+	812.536i	−1.06744	+	1.52446i
$534$		0			0
$535$	81.5019	+	437.255i	0.152340	+	0.817300i
$536$	176.791	−	1002.63i	0.329834	−	1.87058i
$537$		0			0
$538$	786.165	+	68.7805i	1.46127	+	0.127845i
$539$			509.498i			0.945266i
$540$		0			0
$541$	−249.309			−0.460830			−0.230415	−	0.973092i	$-0.574008\pi$
$541$	−249.309			−0.460830			−0.230415	+	0.973092i	$0.574008\pi$
$542$	73.6527	−	841.854i	0.135891	−	1.55324i
$543$		0			0
$544$	−161.253	−	28.4332i	−0.296420	−	0.0522669i
$545$	12.9714	+	8.89550i	0.0238007	+	0.0163220i
$546$		0			0
$547$	−23.7833	−	16.6533i	−0.0434796	−	0.0304447i	0.551635	−	0.834086i	$-0.314004\pi$
$547$	−23.7833	−	16.6533i	−0.0434796	−	0.0304447i	−0.595114	+	0.803641i	$0.702893\pi$
$548$	−17.2598	+	64.4145i	−0.0314960	+	0.117545i
$549$		0			0
$550$	−1175.21	−	79.7702i	−2.13675	−	0.145037i
$551$	−140.812	−	51.2512i	−0.255556	−	0.0930149i
$552$		0			0
$553$	−60.8653	−	695.693i	−0.110064	−	1.25803i
$554$	−917.491	+	1093.42i	−1.65612	+	1.97369i
$555$		0			0
$556$	−505.256	−	183.898i	−0.908734	−	0.330752i
$557$	89.7265	+	334.864i	0.161089	+	0.601192i	0.998507	+	0.0546285i	$0.0173975\pi$
$557$	89.7265	+	334.864i	0.161089	+	0.601192i	−0.837418	+	0.546563i	$0.815936\pi$
$558$		0			0
$559$	908.920	−	524.765i	1.62597	−	0.938757i
$560$	237.829	−	2.31809i	0.424695	−	0.00413945i
$561$		0			0
$562$	−293.284	+	628.949i	−0.521857	+	1.11913i
$563$	−71.7390	+	50.2322i	−0.127423	+	0.0892224i	−0.635550	−	0.772059i	$-0.719227\pi$
$563$	−71.7390	+	50.2322i	−0.127423	+	0.0892224i	0.508128	+	0.861282i	$0.330338\pi$
$564$		0			0
$565$	−261.780	+	154.560i	−0.463327	+	0.273557i
$566$	1284.65			2.26969
$567$		0			0
$568$	−360.888	−	360.888i	−0.635366	−	0.635366i
$569$	243.481	+	290.169i	0.427910	+	0.509963i	0.936318	−	0.351153i	$-0.114210\pi$
$569$	243.481	+	290.169i	0.427910	+	0.509963i	−0.508408	+	0.861116i	$0.669766\pi$
$570$		0			0
$571$	132.080	−	749.064i	0.231314	−	1.31185i	−0.618926	−	0.785449i	$-0.712432\pi$
$571$	132.080	−	749.064i	0.231314	−	1.31185i	0.850240	−	0.526396i	$-0.176457\pi$
$572$	860.579	−	1845.52i	1.50451	−	3.22643i
$573$		0			0
$574$	−1461.16	+	257.642i	−2.54557	+	0.448853i
$575$	−288.934	−	194.032i	−0.502493	−	0.337447i
$576$		0			0
$577$	19.4711	+	72.6672i	0.0337454	+	0.125940i	0.980744	−	0.195299i	$-0.0625676\pi$
$577$	19.4711	+	72.6672i	0.0337454	+	0.125940i	−0.946998	+	0.321238i	$0.895901\pi$
$578$	−333.723	−	715.670i	−0.577375	−	1.23818i
$579$		0			0
$580$	833.662	+	64.7552i	1.43735	+	0.111647i
$581$	165.732	+	139.066i	0.285254	+	0.239356i
$582$		0			0
$583$	−288.878	−	619.502i	−0.495503	−	1.06261i
$584$	−267.016	−	154.162i	−0.457219	−	0.263976i
$585$		0			0
$586$	−707.589	−	1225.58i	−1.20749	−	2.09143i
$587$	148.339	+	103.868i	0.252707	+	0.176947i	0.693065	−	0.720875i	$-0.256260\pi$
$587$	148.339	+	103.868i	0.252707	+	0.176947i	−0.440358	+	0.897822i	$0.645149\pi$
$588$		0			0
$589$	−31.3760	−	86.2049i	−0.0532700	−	0.146358i
$590$	21.7782	−	61.6998i	0.0369123	−	0.104576i
$591$		0			0
$592$	−18.9465	+	216.559i	−0.0320042	+	0.365810i
$593$	−550.097	−	550.097i	−0.927651	−	0.927651i	0.0699032	−	0.997554i	$-0.477731\pi$
$593$	−550.097	−	550.097i	−0.927651	−	0.927651i	−0.997554	+	0.0699032i	$0.977731\pi$
$594$		0			0
$595$	191.481	+	267.868i	0.321816	+	0.450198i
$596$	−355.038	+	297.912i	−0.595701	+	0.499853i
$597$		0			0
$598$	773.836	−	541.846i	1.29404	−	0.906097i
$599$	−97.4219	−	267.665i	−0.162641	−	0.446852i	0.831424	−	0.555638i	$-0.187526\pi$
$599$	−97.4219	−	267.665i	−0.162641	−	0.446852i	−0.994065	+	0.108786i	$0.965304\pi$
$600$		0			0
$601$	85.0903	+	482.571i	0.141581	+	0.802947i	0.970049	+	0.242910i	$0.0781020\pi$
$601$	85.0903	+	482.571i	0.141581	+	0.802947i	−0.828468	+	0.560037i	$0.810787\pi$
$602$	1516.37	+	406.311i	2.51889	+	0.674936i
$603$		0			0
$604$	481.050	+	277.735i	0.796441	+	0.459825i
$605$	−387.840	+	107.984i	−0.641058	+	0.178485i
$606$		0			0
$607$	546.471	−	47.8100i	0.900281	−	0.0787644i	0.372390	−	0.928076i	$-0.378538\pi$
$607$	546.471	−	47.8100i	0.900281	−	0.0787644i	0.527891	+	0.849312i	$0.322983\pi$
$608$	−12.5526	−	143.477i	−0.0206457	−	0.235981i
$609$		0			0
$610$	−900.263	+	1595.00i	−1.47584	+	2.61476i
$611$	−205.682	+	356.252i	−0.336632	+	0.583064i
$612$		0			0
$613$	1.56209	−	5.82981i	0.00254828	−	0.00951030i	−0.964640	−	0.263571i	$-0.915100\pi$
$613$	1.56209	−	5.82981i	0.00254828	−	0.00951030i	0.967188	+	0.254061i	$0.0817663\pi$
$614$	−595.030	+	104.920i	−0.969104	+	0.170879i
$615$		0			0
$616$	1230.43	−	447.842i	1.99746	−	0.727016i
$617$	663.165	+	947.098i	1.07482	+	1.53500i	0.823681	+	0.567053i	$0.191917\pi$
$617$	663.165	+	947.098i	1.07482	+	1.53500i	0.251141	+	0.967951i	$0.419194\pi$
$618$		0			0
$619$	318.344	+	379.388i	0.514288	+	0.612905i	0.959220	−	0.282660i	$-0.0912167\pi$
$619$	318.344	+	379.388i	0.514288	+	0.612905i	−0.444932	+	0.895564i	$0.646772\pi$
$620$	297.690	+	416.447i	0.480145	+	0.671689i
$621$		0			0
$622$	1007.39	−	1007.39i	1.61959	−	1.61959i
$623$	1390.70	+	121.671i	2.23227	+	0.195298i
$624$		0			0
$625$	−462.755	+	420.098i	−0.740409	+	0.672157i
$626$	74.5240	−	27.1245i	0.119048	−	0.0433299i
$627$		0			0
$628$	−1029.14	+	1469.77i	−1.63877	+	2.34040i
$629$	−260.633	+	150.476i	−0.414360	+	0.239231i
$630$		0			0
$631$	−358.229	+	620.471i	−0.567717	+	0.983314i	0.429075	+	0.903269i	$0.358840\pi$
$631$	−358.229	+	620.471i	−0.567717	+	0.983314i	−0.996791	+	0.0800451i	$0.974494\pi$
$632$	−687.707	+	320.683i	−1.08814	+	0.507410i
$633$		0			0
$634$	60.8050	−	72.4646i	0.0959069	−	0.114297i
$635$	−287.497	+	246.054i	−0.452752	+	0.387486i
$636$		0			0
$637$	−665.030	+	310.108i	−1.04400	+	0.486826i
$638$	1084.77	−	290.664i	1.70027	−	0.455587i
$639$		0			0
$640$	402.569	+	1073.38i	0.629014	+	1.67716i
$641$	−41.0049	−	232.550i	−0.0639702	−	0.362793i	−0.999943	−	0.0107194i	$-0.996588\pi$
$641$	−41.0049	−	232.550i	−0.0639702	−	0.362793i	0.935972	−	0.352073i	$-0.114523\pi$
$642$		0			0
$643$	887.509	+	413.852i	1.38026	+	0.643627i	0.964070	−	0.265650i	$-0.0855864\pi$
$643$	887.509	+	413.852i	1.38026	+	0.643627i	0.416193	+	0.909276i	$0.363364\pi$
$644$	886.289	+	156.277i	1.37622	+	0.242666i
$645$		0			0
$646$	−114.249	+	95.8663i	−0.176856	+	0.148400i
$647$	−803.224	+	803.224i	−1.24146	+	1.24146i	−0.282063	+	0.959396i	$0.591019\pi$
$647$	−803.224	+	803.224i	−1.24146	+	1.24146i	−0.959396	+	0.282063i	$0.908981\pi$
$648$		0			0
$649$		−	55.9694i		−	0.0862395i
$650$	−611.177	−	1582.51i	−0.940272	−	2.43464i
$651$		0			0
$652$	−252.896	−	361.173i	−0.387878	−	0.553947i
$653$	−358.820	−	167.320i	−0.549494	−	0.256233i	0.127984	−	0.991776i	$-0.459149\pi$
$653$	−358.820	−	167.320i	−0.549494	−	0.256233i	−0.677478	+	0.735543i	$0.736927\pi$
$654$		0			0
$655$	333.610	+	327.170i	0.509328	+	0.499496i
$656$	125.243	+	216.927i	0.190919	+	0.330681i
$657$		0			0
$658$	−594.344	+	159.254i	−0.903259	+	0.242027i
$659$	239.670	−	658.487i	0.363687	−	0.999222i	−0.614028	−	0.789284i	$-0.710452\pi$
$659$	239.670	−	658.487i	0.363687	−	0.999222i	0.977715	−	0.209938i	$-0.0673261\pi$
$660$		0			0
$661$	−581.205	−	487.689i	−0.879281	−	0.737804i	0.0867503	−	0.996230i	$-0.472352\pi$
$661$	−581.205	−	487.689i	−0.879281	−	0.737804i	−0.966031	+	0.258426i	$0.916796\pi$
$662$	−15.4536	+	1.35202i	−0.0233438	+	0.00204232i
$663$		0			0
$664$	80.4005	−	220.899i	0.121085	−	0.332679i
$665$	−183.994	+	223.668i	−0.276683	+	0.336342i
$666$		0			0
$667$	320.518	+	85.8826i	0.480537	+	0.128759i
$668$	−3.57344	+	5.10340i	−0.00534946	+	0.00763983i
$669$		0			0
$670$	−1391.84	−	954.499i	−2.07738	−	1.42463i
$671$	−272.054	+	1542.90i	−0.405446	+	2.29940i
$672$		0			0
$673$	988.110	+	86.4484i	1.46822	+	0.128452i	0.793025	−	0.609190i	$-0.208505\pi$
$673$	988.110	+	86.4484i	1.46822	+	0.128452i	0.675192	+	0.737642i	$0.264061\pi$
$674$			1378.72i			2.04558i
$675$		0			0
$676$	1746.94			2.58423
$677$	76.7531	−	877.292i	0.113372	−	1.29585i	−0.700014	−	0.714129i	$-0.746823\pi$
$677$	76.7531	−	877.292i	0.113372	−	1.29585i	0.813387	−	0.581723i	$-0.197621\pi$
$678$		0			0
$679$	1128.79	+	199.035i	1.66242	+	0.293130i
$680$	202.343	−	295.055i	0.297563	−	0.433904i
$681$		0			0
$682$	563.188	+	394.349i	0.825789	+	0.578224i
$683$	−63.8434	+	238.267i	−0.0934750	+	0.348854i	−0.996784	−	0.0801374i	$-0.974464\pi$
$683$	−63.8434	+	238.267i	−0.0934750	+	0.348854i	0.903309	+	0.428991i	$0.141131\pi$
$684$		0			0
$685$	36.7008	+	30.1910i	0.0535778	+	0.0440744i
$686$	376.707	+	137.110i	0.549136	+	0.199869i
$687$		0			0
$688$	−23.0991	−	264.024i	−0.0335743	−	0.383756i
$689$	632.786	−	754.125i	0.918412	−	1.09452i
$690$		0			0
$691$	885.130	+	322.161i	1.28094	+	0.466224i	0.890743	−	0.454507i	$-0.150184\pi$
$691$	885.130	+	322.161i	1.28094	+	0.466224i	0.390198	+	0.920731i	$0.372407\pi$
$692$	154.658	+	577.192i	0.223494	+	0.834092i
$693$		0			0
$694$	−1483.56	+	856.535i	−2.13770	+	1.23420i
$695$	−268.288	+	273.569i	−0.386026	+	0.393625i
$696$		0			0
$697$	−146.554	+	314.285i	−0.210263	+	0.450911i
$698$	287.658	−	201.420i	0.412117	−	0.288568i
$699$		0			0
$700$	654.326	−	1477.75i	0.934751	−	2.11106i
$701$	200.155			0.285528			0.142764	−	0.989757i	$-0.454401\pi$
$701$	200.155			0.285528			0.142764	+	0.989757i	$0.454401\pi$
$702$		0			0
$703$	−187.182	−	187.182i	−0.266262	−	0.266262i
$704$	882.259	+	1051.44i	1.25321	+	1.49352i
$705$		0			0
$706$	138.094	−	783.169i	0.195600	−	1.10930i
$707$	646.784	−	1387.03i	0.914828	−	1.96186i
$708$		0			0
$709$	−45.1150	+	7.95500i	−0.0636319	+	0.0112200i	−0.205373	−	0.978684i	$-0.565841\pi$
$709$	−45.1150	+	7.95500i	−0.0636319	+	0.0112200i	0.141742	+	0.989904i	$0.454730\pi$
$710$	−792.157	+	297.097i	−1.11571	+	0.418446i
$711$		0			0
$712$	−392.591	−	1465.17i	−0.551392	−	2.05782i
$713$	85.8521	+	184.110i	0.120410	+	0.258219i
$714$		0			0
$715$	−943.561	−	1102.49i	−1.31967	−	1.54194i
$716$	434.437	+	364.536i	0.606755	+	0.509128i
$717$		0			0
$718$	−667.785	−	1432.07i	−0.930063	−	1.99453i
$719$	974.694	+	562.740i	1.35563	+	0.782671i	0.989031	−	0.147710i	$-0.0471903\pi$
$719$	974.694	+	562.740i	1.35563	+	0.782671i	0.366594	+	0.930381i	$0.380524\pi$
$720$		0			0
$721$	430.103	+	744.961i	0.596537	+	1.03323i
$722$	874.037	+	612.007i	1.21058	+	0.847656i
$723$		0			0
$724$	438.401	+	1204.50i	0.605527	+	1.66367i
$725$	287.826	−	521.759i	0.397002	−	0.719668i
$726$		0			0
$727$	109.566	−	1252.35i	0.150710	−	1.72262i	−0.425192	−	0.905103i	$-0.639794\pi$
$727$	109.566	−	1252.35i	0.150710	−	1.72262i	0.575902	−	0.817519i	$-0.304651\pi$
$728$	1333.46	+	1333.46i	1.83168	+	1.83168i
$729$		0			0
$730$	−415.794	+	297.224i	−0.569581	+	0.407156i
$731$	281.073	−	235.848i	0.384505	−	0.322638i
$732$		0			0
$733$	13.2331	−	9.26591i	0.0180533	−	0.0126411i	−0.564515	−	0.825423i	$-0.690937\pi$
$733$	13.2331	−	9.26591i	0.0180533	−	0.0126411i	0.582568	+	0.812782i	$0.302048\pi$
$734$	507.790	+	1395.14i	0.691812	+	1.90074i
$735$		0			0
$736$	55.3814	+	314.083i	0.0752464	+	0.426744i
$737$	−1394.46	−	373.645i	−1.89208	−	0.506981i
$738$		0			0
$739$	−549.176	−	317.067i	−0.743134	−	0.429049i	0.0800738	−	0.996789i	$-0.474484\pi$
$739$	−549.176	−	317.067i	−0.743134	−	0.429049i	−0.823208	+	0.567740i	$0.807818\pi$
$740$	1286.38	+	726.070i	1.73836	+	0.981175i
$741$		0			0
$742$	1466.90	−	128.337i	1.97696	−	0.172961i
$743$	48.3188	+	552.286i	0.0650320	+	0.743319i	0.956785	+	0.290796i	$0.0939202\pi$
$743$	48.3188	+	552.286i	0.0650320	+	0.743319i	−0.891753	+	0.452523i	$0.850524\pi$
$744$		0			0
$745$	88.5888	+	318.180i	0.118911	+	0.427087i
$746$	138.423	−	239.755i	0.185553	−	0.321388i
$747$		0			0
$748$	184.251	−	687.632i	0.246324	−	0.919295i
$749$	−807.167	+	142.325i	−1.07766	+	0.190021i
$750$		0			0
$751$	781.444	−	284.422i	1.04054	−	0.378725i	0.235454	−	0.971885i	$-0.424342\pi$
$751$	781.444	−	284.422i	1.04054	−	0.378725i	0.805084	+	0.593161i	$0.202120\pi$
$752$	59.5830	+	85.0934i	0.0792328	+	0.113156i
$753$		0			0
$754$	1039.65	+	1239.00i	1.37884	+	1.64324i
$755$	322.029	−	230.197i	0.426528	−	0.304896i
$756$		0			0
$757$	−202.491	+	202.491i	−0.267491	+	0.267491i	−0.828088	−	0.560598i	$-0.810572\pi$
$757$	−202.491	+	202.491i	−0.267491	+	0.267491i	0.560598	+	0.828088i	$0.310572\pi$
$758$	−663.036	−	58.0082i	−0.874718	−	0.0765279i
$759$		0			0
$760$	296.749	+	104.744i	0.390459	+	0.137821i
$761$	1002.16	−	364.758i	1.31690	−	0.479314i	0.414440	−	0.910077i	$-0.363978\pi$
$761$	1002.16	−	364.758i	1.31690	−	0.479314i	0.902465	+	0.430763i	$0.141755\pi$
$762$		0			0
$763$	−16.6242	+	23.7418i	−0.0217879	+	0.0311163i
$764$	−24.2776	+	14.0167i	−0.0317770	+	0.0183465i
$765$		0			0
$766$	1176.37	−	2037.54i	1.53573	−	2.65997i
$767$	73.0549	−	34.0660i	0.0952475	−	0.0444147i
$768$		0			0
$769$	−385.998	+	460.015i	−0.501948	+	0.598199i	−0.956214	−	0.292667i	$-0.905457\pi$
$769$	−385.998	+	460.015i	−0.501948	+	0.598199i	0.454266	+	0.890866i	$0.349902\pi$
$770$	168.094	−	2164.06i	0.218304	−	2.81046i
$771$		0			0
$772$	−136.682	+	63.7361i	−0.177050	+	0.0825597i
$773$	−1121.62	+	300.538i	−1.45100	+	0.388794i	−0.896371	−	0.443305i	$-0.853806\pi$
$773$	−1121.62	+	300.538i	−1.45100	+	0.388794i	−0.554627	+	0.832099i	$0.687139\pi$
$774$		0			0
$775$	357.955	−	70.3374i	0.461877	−	0.0907580i
$776$	−216.264	−	1226.49i	−0.278691	−	1.58053i
$777$		0			0
$778$	−951.715	−	443.792i	−1.22328	−	0.570427i
$779$	−300.387	−	52.9663i	−0.385606	−	0.0679927i
$780$		0			0
$781$	−554.388	+	465.187i	−0.709844	+	0.595630i
$782$	233.528	−	233.528i	0.298630	−	0.298630i
$783$		0			0
$784$			185.298i			0.236349i
$785$	650.085	+	1101.06i	0.828133	+	1.40262i
$786$		0			0
$787$	−239.615	−	342.206i	−0.304467	−	0.434824i	0.637540	−	0.770417i	$-0.279952\pi$
$787$	−239.615	−	342.206i	−0.304467	−	0.434824i	−0.942007	+	0.335594i	$0.891063\pi$
$788$	−1235.29	−	576.023i	−1.56762	−	0.730994i
$789$		0			0
$790$	12.2596	+	1257.79i	0.0155184	+	1.59214i
$791$	−280.096	−	485.141i	−0.354104	−	0.613326i
$792$		0			0
$793$	−2179.47	+	583.988i	−2.74839	+	0.736429i
$794$	78.1912	−	214.829i	0.0984776	−	0.270565i
$795$		0			0
$796$	100.360	+	84.2119i	0.126080	+	0.105794i
$797$	−458.311	+	40.0970i	−0.575046	+	0.0503100i	−0.370969	−	0.928645i	$-0.620975\pi$
$797$	−458.311	+	40.0970i	−0.575046	+	0.0503100i	−0.204076	+	0.978955i	$0.565419\pi$
$798$		0			0
$799$	−49.1868	+	135.140i	−0.0615604	+	0.169136i
$800$	571.410	+	38.7857i	0.714262	+	0.0484821i
$801$		0			0
$802$	−1890.94	−	506.676i	−2.35778	−	0.631765i
$803$	−250.767	+	358.133i	−0.312288	+	0.445993i
$804$		0			0
$805$	362.720	−	528.915i	0.450584	−	0.657038i
$806$	−171.942	+	975.132i	−0.213328	+	1.20984i
$807$		0			0
$808$	−1656.57	−	144.931i	−2.05021	−	0.179370i
$809$		−	462.495i		−	0.571687i	−0.958276	−	0.285843i	$-0.907726\pi$
$809$		−	462.495i		−	0.571687i	0.958276	−	0.285843i	$-0.0922737\pi$
$810$		0			0
$811$	508.177			0.626605			0.313303	−	0.949653i	$-0.398565\pi$
$811$	508.177			0.626605			0.313303	+	0.949653i	$0.398565\pi$
$812$	−134.293	+	1534.97i	−0.165385	+	1.89036i
$813$		0			0
$814$	1953.77	+	344.503i	2.40021	+	0.423222i
$815$	−308.887	+	57.5747i	−0.379002	+	0.0706439i
$816$		0			0
$817$	264.369	+	185.113i	0.323585	+	0.226577i
$818$	−480.178	+	1792.05i	−0.587014	+	2.19077i
$819$		0			0
$820$	1694.05	−	164.863i	2.06592	−	0.201052i
$821$	−329.136	−	119.796i	−0.400896	−	0.145914i	0.133700	−	0.991022i	$-0.457314\pi$
$821$	−329.136	−	119.796i	−0.400896	−	0.145914i	−0.534596	+	0.845108i	$0.679536\pi$
$822$		0			0
$823$	−1.56822	−	17.9249i	−0.00190550	−	0.0217799i	0.995182	−	0.0980405i	$-0.0312575\pi$
$823$	−1.56822	−	17.9249i	−0.00190550	−	0.0217799i	−0.997088	+	0.0762606i	$0.975702\pi$
$824$	600.792	−	715.996i	0.729117	−	0.868927i
$825$		0			0
$826$	113.299	+	41.2375i	0.137166	+	0.0499244i
$827$	−2.28847	−	8.54068i	−0.00276719	−	0.0103273i	0.964528	−	0.263979i	$-0.0850350\pi$
$827$	−2.28847	−	8.54068i	−0.00276719	−	0.0103273i	−0.967296	+	0.253652i	$0.918368\pi$
$828$		0			0
$829$	−102.570	+	59.2189i	−0.123728	+	0.0714342i	−0.560586	−	0.828096i	$-0.689424\pi$
$829$	−102.570	+	59.2189i	−0.123728	+	0.0714342i	0.436859	+	0.899530i	$0.356091\pi$
$830$	−278.219	−	272.848i	−0.335203	−	0.328732i
$831$		0			0
$832$	−835.410	+	1791.54i	−1.00410	+	2.15330i
$833$	−210.136	+	147.139i	−0.252264	+	0.176637i
$834$		0			0
$835$	2.25725	+	3.82313i	0.00270330	+	0.00457860i
$836$	626.172			0.749010
$837$		0			0
$838$	1673.99	+	1673.99i	1.99761	+	1.99761i
$839$	−715.586	−	852.802i	−0.852903	−	1.01645i	−0.999628	−	0.0272732i	$-0.991318\pi$
$839$	−715.586	−	852.802i	−0.852903	−	1.01645i	0.146725	−	0.989177i	$-0.453127\pi$
$840$		0			0
$841$	47.3846	−	268.732i	0.0563432	−	0.319538i
$842$	501.925	−	1076.38i	0.596111	−	1.27836i
$843$		0			0
$844$	−558.378	+	98.4572i	−0.661586	+	0.116655i
$845$	515.105	−	1133.36i	0.609591	−	1.34125i
$846$		0			0
$847$	−192.009	−	716.588i	−0.226693	−	0.846031i
$848$	−105.061	−	225.304i	−0.123893	−	0.265689i
$849$		0			0
$850$	−306.491	−	507.737i	−0.360577	−	0.597338i
$851$	449.045	+	376.793i	0.527667	+	0.442766i
$852$		0			0
$853$	−128.951	−	276.537i	−0.151174	−	0.324193i	0.816107	−	0.577900i	$-0.196128\pi$
$853$	−128.951	−	276.537i	−0.151174	−	0.324193i	−0.967281	+	0.253707i	$0.918350\pi$
$854$	−2922.85	−	1687.51i	−3.42254	−	1.97600i
$855$		0			0
$856$	445.283	+	771.253i	0.520190	+	0.900996i
$857$	−6.84211	−	4.79090i	−0.00798379	−	0.00559031i	0.569578	−	0.821937i	$-0.307107\pi$
$857$	−6.84211	−	4.79090i	−0.00798379	−	0.00559031i	−0.577562	+	0.816347i	$0.695996\pi$
$858$		0			0
$859$	−401.677	−	1103.60i	−0.467610	−	1.28475i	−0.919646	−	0.392748i	$-0.871525\pi$
$859$	−401.677	−	1103.60i	−0.467610	−	1.28475i	0.452037	−	0.891999i	$-0.350698\pi$
$860$	−1698.22	−	599.422i	−1.97467	−	0.697002i
$861$		0			0
$862$	−64.7347	+	739.920i	−0.0750982	+	0.858376i
$863$	1098.88	+	1098.88i	1.27332	+	1.27332i	0.944333	+	0.328991i	$0.106709\pi$
$863$	1098.88	+	1098.88i	1.27332	+	1.27332i	0.328991	+	0.944333i	$0.393291\pi$
$864$		0			0
$865$	420.066	+	69.8546i	0.485626	+	0.0807568i
$866$	−1358.52	+	1139.93i	−1.56873	+	1.31632i
$867$		0			0
$868$	−772.708	+	541.056i	−0.890216	+	0.623336i
$869$	368.003	+	1011.08i	0.423479	+	1.16350i
$870$		0			0
$871$	−361.041	−	2047.56i	−0.414513	−	2.35082i
$872$	30.4191	+	8.15077i	0.0348843	+	0.00934721i
$873$		0			0
$874$	251.574	+	145.247i	0.287843	+	0.166186i
$875$	−765.778	−	860.236i	−0.875175	−	0.983127i
$876$		0			0
$877$	−588.741	+	51.5082i	−0.671313	+	0.0587322i	−0.417716	−	0.908578i	$-0.637169\pi$
$877$	−588.741	+	51.5082i	−0.671313	+	0.0587322i	−0.253597	+	0.967310i	$0.581614\pi$
$878$	−41.2878	−	471.922i	−0.0470248	−	0.537496i
$879$		0			0
$880$	−353.020	+	98.2890i	−0.401159	+	0.111692i
$881$	474.462	−	821.792i	0.538549	−	0.932795i	−0.460433	−	0.887694i	$-0.652306\pi$
$881$	474.462	−	821.792i	0.538549	−	0.932795i	0.998982	−	0.0451006i	$-0.0143608\pi$
$882$		0			0
$883$	−174.740	+	652.140i	−0.197894	+	0.738550i	0.793605	+	0.608434i	$0.208202\pi$
$883$	−174.740	+	652.140i	−0.197894	+	0.738550i	−0.991499	+	0.130117i	$0.958465\pi$
$884$	1009.69	−	178.035i	1.14218	−	0.201397i
$885$		0			0
$886$	824.766	−	300.190i	0.930887	−	0.338815i
$887$	−384.892	−	549.682i	−0.433925	−	0.619709i	0.541325	−	0.840813i	$-0.317923\pi$
$887$	−384.892	−	549.682i	−0.433925	−	0.619709i	−0.975250	+	0.221104i	$0.929034\pi$
$888$		0			0
$889$	−448.224	−	534.173i	−0.504189	−	0.600870i
$890$	−2480.41	−	412.478i	−2.78698	−	0.463458i
$891$		0			0
$892$	−1040.41	+	1040.41i	−1.16638	+	1.16638i
$893$	−126.015	−	11.0249i	−0.141114	−	0.0123459i
$894$		0			0
$895$	364.598	−	174.361i	0.407372	−	0.194817i
$896$	−1985.08	+	722.511i	−2.21550	+	0.806374i
$897$		0			0
$898$	942.559	−	1346.11i	1.04962	−	1.49901i
$899$	−301.208	+	173.903i	−0.335048	+	0.193440i
$900$		0			0
$901$	172.080	−	298.051i	0.190987	−	0.330800i
$902$	2071.80	−	966.097i	2.29690	−	1.07106i
$903$		0			0
$904$	−391.254	+	466.278i	−0.432803	+	0.515795i
$905$	910.707	+	70.7397i	1.00631	+	0.0781654i
$906$		0			0
$907$	555.082	−	258.839i	0.611997	−	0.285379i	−0.0918026	−	0.995777i	$-0.529263\pi$
$907$	555.082	−	258.839i	0.611997	−	0.285379i	0.703800	+	0.710398i	$0.251485\pi$
$908$	723.304	−	193.809i	0.796591	−	0.213446i
$909$		0			0
$910$	2926.98	−	1097.76i	3.21646	−	1.20633i
$911$	−189.868	−	1076.79i	−0.208417	−	1.18199i	−0.891972	−	0.452091i	$-0.850678\pi$
$911$	−189.868	−	1076.79i	−0.208417	−	1.18199i	0.683555	−	0.729899i	$-0.260433\pi$
$912$		0			0
$913$	−302.103	−	140.873i	−0.330891	−	0.154297i
$914$	524.718	+	92.5219i	0.574090	+	0.101228i
$915$		0			0
$916$	−2400.01	+	2013.84i	−2.62009	+	2.19852i
$917$	−608.847	+	608.847i	−0.663955	+	0.663955i
$918$		0			0
$919$			10.4429i			0.0113633i	0.999984	+	0.00568167i	$0.00180854\pi$
$919$			10.4429i			0.0113633i	−0.999984	+	0.00568167i	$0.998191\pi$
$920$	−674.836	−	173.790i	−0.733518	−	0.188903i
$921$		0			0
$922$	434.832	+	621.004i	0.471618	+	0.673540i
$923$	−944.623	−	440.485i	−1.02343	−	0.477232i
$924$		0			0
$925$	850.356	−	620.474i	0.919304	−	0.670783i
$926$	466.661	+	808.281i	0.503954	+	0.872873i
$927$		0			0
$928$	−527.437	+	141.326i	−0.568359	+	0.152291i
$929$	330.191	−	907.192i	0.355426	−	0.976525i	−0.625170	−	0.780488i	$-0.714970\pi$
$929$	330.191	−	907.192i	0.355426	−	0.976525i	0.980596	−	0.196037i	$-0.0628073\pi$
$930$		0			0
$931$	−172.850	−	145.039i	−0.185661	−	0.155788i
$932$	−1526.20	+	133.525i	−1.63755	+	0.143267i
$933$		0			0
$934$	376.336	−	1033.98i	0.402930	−	1.10704i
$935$	−391.785	−	322.292i	−0.419022	−	0.344698i
$936$		0			0
$937$	130.525	+	34.9742i	0.139301	+	0.0373257i	0.327796	−	0.944749i	$-0.393694\pi$
$937$	130.525	+	34.9742i	0.139301	+	0.0373257i	−0.188495	+	0.982074i	$0.560361\pi$
$938$	1783.79	−	2547.52i	1.90170	−	2.71591i
$939$		0			0
$940$	693.914	−	129.342i	0.738206	−	0.137597i
$941$	55.0313	−	312.098i	0.0584818	−	0.331667i	−0.941504	−	0.337002i	$-0.890587\pi$
$941$	55.0313	−	312.098i	0.0584818	−	0.331667i	0.999986	+	0.00533525i	$0.00169827\pi$
$942$		0			0
$943$	672.868	+	58.8683i	0.713540	+	0.0624267i
$944$		−	20.3553i		−	0.0215629i
$945$		0			0
$946$	−2418.74			−2.55681
$947$	47.1522	−	538.952i	0.0497911	−	0.569115i	−0.929793	−	0.368082i	$-0.880015\pi$
$947$	47.1522	−	538.952i	0.0497911	−	0.569115i	0.979584	−	0.201033i	$-0.0644298\pi$
$948$		0			0
$949$	−620.088	−	109.338i	−0.653412	−	0.115214i
$950$	361.610	−	375.990i	0.380642	−	0.395779i
$951$		0			0
$952$	540.045	+	378.144i	0.567274	+	0.397210i
$953$	434.654	−	1622.15i	0.456091	−	1.70215i	−0.228771	−	0.973480i	$-0.573471\pi$
$953$	434.654	−	1622.15i	0.456091	−	1.70215i	0.684861	−	0.728673i	$-0.259863\pi$
$954$		0			0
$955$	1.93504	+	19.8835i	0.00202622	+	0.0208205i
$956$	606.178	+	220.631i	0.634078	+	0.230785i
$957$		0			0
$958$	−240.565	−	2749.67i	−0.251112	−	2.87022i
$959$	−56.2902	+	67.0841i	−0.0586968	+	0.0699521i
$960$		0			0
$961$	702.959	+	255.856i	0.731487	+	0.266240i
$962$	739.505	+	2759.87i	0.768717	+	2.86889i
$963$		0			0
$964$	2680.98	−	1547.86i	2.78109	−	1.60567i
$965$	1.04748	+	107.469i	0.00108548	+	0.111366i
$966$		0			0
$967$	357.588	−	766.851i	0.369791	−	0.793020i	−0.630073	−	0.776536i	$-0.716975\pi$
$967$	357.588	−	766.851i	0.369791	−	0.793020i	0.999864	−	0.0164842i	$-0.00524731\pi$
$968$	−660.305	+	462.350i	−0.682133	+	0.477635i
$969$		0			0
$970$	−1999.27	−	514.872i	−2.06111	−	0.530796i
$971$	80.1220			0.0825149			0.0412575	−	0.999149i	$-0.486864\pi$
$971$	80.1220			0.0825149			0.0412575	+	0.999149i	$0.486864\pi$
$972$		0			0
$973$	−499.271	−	499.271i	−0.513125	−	0.513125i
$974$	802.466	+	956.342i	0.823887	+	0.981870i
$975$		0			0
$976$	−98.9424	+	561.130i	−0.101375	+	0.574929i
$977$	−706.907	+	1515.97i	−0.723549	+	1.55166i	0.106718	+	0.994289i	$0.465966\pi$
$977$	−706.907	+	1515.97i	−0.723549	+	1.55166i	−0.830267	+	0.557366i	$0.811812\pi$
$978$		0			0
$979$	−2118.21	+	373.497i	−2.16364	+	0.381509i
$980$	1146.26	+	520.972i	1.16966	+	0.531604i
$981$		0			0
$982$	11.3394	+	42.3193i	0.0115473	+	0.0430950i
$983$	−400.761	−	859.434i	−0.407691	−	0.874297i	−0.997757	−	0.0669416i	$-0.978676\pi$
$983$	−400.761	−	859.434i	−0.407691	−	0.874297i	0.590066	−	0.807355i	$-0.299102\pi$
$984$		0			0
$985$	−737.943	+	631.566i	−0.749181	+	0.641184i
$986$	433.154	+	363.459i	0.439304	+	0.368620i
$987$		0			0
$988$	381.123	+	817.320i	0.385752	+	0.827247i
$989$	−618.918	−	357.333i	−0.625802	−	0.361307i
$990$		0			0
$991$	472.183	+	817.844i	0.476471	+	0.825272i	0.999637	−	0.0269592i	$-0.00858243\pi$
$991$	472.183	+	817.844i	0.476471	+	0.825272i	−0.523166	+	0.852231i	$0.675249\pi$
$992$	−273.832	−	191.740i	−0.276041	−	0.193286i
$993$		0			0
$994$	−533.215	−	1465.00i	−0.536433	−	1.47384i
$995$	84.2262	−	40.2793i	0.0846495	−	0.0404818i
$996$		0			0
$997$	67.3920	−	770.294i	0.0675948	−	0.772612i	−0.884446	−	0.466642i	$-0.845464\pi$
$997$	67.3920	−	770.294i	0.0675948	−	0.772612i	0.952041	−	0.305970i	$-0.0989808\pi$
$998$	695.080	+	695.080i	0.696473	+	0.696473i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.s.a.118.31		408
3.2	odd	2		135.3.r.a.103.4	yes	408
5.2	odd	4	inner	405.3.s.a.37.31		408
15.2	even	4		135.3.r.a.22.4	✓	408
27.11	odd	18		135.3.r.a.43.4	yes	408
27.16	even	9	inner	405.3.s.a.208.31		408
135.92	even	36		135.3.r.a.97.4	yes	408
135.97	odd	36	inner	405.3.s.a.127.31		408

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.r.a.22.4	✓	408	15.2	even	4
135.3.r.a.43.4	yes	408	27.11	odd	18
135.3.r.a.97.4	yes	408	135.92	even	36
135.3.r.a.103.4	yes	408	3.2	odd	2
405.3.s.a.37.31		408	5.2	odd	4	inner
405.3.s.a.118.31		408	1.1	even	1	trivial
405.3.s.a.127.31		408	135.97	odd	36	inner
405.3.s.a.208.31		408	27.16	even	9	inner

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.s (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.289276 - 3.30644i) q^{2} +(-6.90966 - 1.21836i) q^{4} +(-2.82783 + 4.12352i) q^{5} +(-7.54736 - 5.28472i) q^{7} +(-2.59108 + 9.67004i) q^{8} +O(q^{10})\)	\(q+(0.289276 - 3.30644i) q^{2} +(-6.90966 - 1.21836i) q^{4} +(-2.82783 + 4.12352i) q^{5} +(-7.54736 - 5.28472i) q^{7} +(-2.59108 + 9.67004i) q^{8} +(12.8162 + 10.5429i) q^{10} +(13.3396 + 4.85522i) q^{11} +(1.78187 + 20.3669i) q^{13} +(-19.6569 + 23.4262i) q^{14} +(4.85144 + 1.76578i) q^{16} +(1.84989 + 6.90389i) q^{17} +(-5.44455 + 3.14341i) q^{19} +(24.5633 - 25.0468i) q^{20} +(19.9124 - 42.7022i) q^{22} +(11.4039 - 7.98508i) q^{23} +(-9.00679 - 23.3212i) q^{25} +67.8574 q^{26} +(45.7110 + 45.7110i) q^{28} +(15.3211 + 18.2589i) q^{29} +(-2.53387 + 14.3703i) q^{31} +(-9.68175 + 20.7626i) q^{32} +(23.3625 - 4.11943i) q^{34} +(43.1343 - 16.1774i) q^{35} +(10.8979 + 40.6717i) q^{37} +(8.81854 + 18.9114i) q^{38} +(-32.5475 - 38.0296i) q^{40} +(37.1665 + 31.1864i) q^{41} +(-21.6952 - 46.5255i) q^{43} +(-86.2568 - 49.8004i) q^{44} +(-23.1033 - 40.0161i) q^{46} +(16.4820 + 11.5409i) q^{47} +(12.2754 + 33.7265i) q^{49} +(-79.7156 + 23.0342i) q^{50} +(12.5020 - 142.899i) q^{52} +(-34.0482 - 34.0482i) q^{53} +(-57.7427 + 41.2764i) q^{55} +(70.6593 - 59.2902i) q^{56} +(64.8041 - 45.3763i) q^{58} +(-1.34848 - 3.70492i) q^{59} +(19.1645 + 108.687i) q^{61} +(46.7817 + 12.5351i) q^{62} +(83.7341 + 48.3439i) q^{64} +(-89.0219 - 50.2464i) q^{65} +(-101.309 + 8.86343i) q^{67} +(-4.37070 - 49.9574i) q^{68} +(-41.0120 - 147.301i) q^{70} +(-25.4902 + 44.1503i) q^{71} +(-7.97110 + 29.7485i) q^{73} +(137.631 - 24.2681i) q^{74} +(41.4498 - 15.0865i) q^{76} +(-75.0204 - 107.140i) q^{77} +(48.7203 + 58.0626i) q^{79} +(-21.0003 + 15.0117i) q^{80} +(113.868 - 113.868i) q^{82} +(-23.3920 - 2.04653i) q^{83} +(-33.6995 - 11.8949i) q^{85} +(-160.110 + 58.2752i) q^{86} +(-81.5142 + 116.414i) q^{88} +(-131.217 + 75.7582i) q^{89} +(94.1848 - 163.133i) q^{91} +(-88.5256 + 41.2801i) q^{92} +(42.9270 - 51.1585i) q^{94} +(2.43433 - 31.3397i) q^{95} +(-112.747 + 52.5748i) q^{97} +(115.066 - 30.8318i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 408 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 6 q^{8}+O(q^{10}) \) 408 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 6 * q^8	\( 408 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 6 q^{8} - 6 q^{10} + 60 q^{11} - 12 q^{13} - 24 q^{16} + 6 q^{17} + 300 q^{20} - 12 q^{22} + 156 q^{23} + 6 q^{25} + 48 q^{26} - 24 q^{28} - 24 q^{31} - 72 q^{32} - 156 q^{35} - 6 q^{37} + 252 q^{38} - 108 q^{40} + 384 q^{41} - 12 q^{43} - 12 q^{46} + 210 q^{47} - 276 q^{50} - 60 q^{52} - 516 q^{53} - 24 q^{55} - 912 q^{56} - 12 q^{58} - 312 q^{61} + 6 q^{62} - 420 q^{65} - 480 q^{67} + 540 q^{68} - 12 q^{70} + 12 q^{71} - 6 q^{73} - 216 q^{76} + 876 q^{77} + 1644 q^{80} - 24 q^{82} + 372 q^{83} - 12 q^{85} - 516 q^{86} + 348 q^{88} - 12 q^{91} - 2082 q^{92} - 198 q^{95} + 600 q^{97} + 1032 q^{98}+O(q^{100}) \) 408 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 6 * q^8 - 6 * q^10 + 60 * q^11 - 12 * q^13 - 24 * q^16 + 6 * q^17 + 300 * q^20 - 12 * q^22 + 156 * q^23 + 6 * q^25 + 48 * q^26 - 24 * q^28 - 24 * q^31 - 72 * q^32 - 156 * q^35 - 6 * q^37 + 252 * q^38 - 108 * q^40 + 384 * q^41 - 12 * q^43 - 12 * q^46 + 210 * q^47 - 276 * q^50 - 60 * q^52 - 516 * q^53 - 24 * q^55 - 912 * q^56 - 12 * q^58 - 312 * q^61 + 6 * q^62 - 420 * q^65 - 480 * q^67 + 540 * q^68 - 12 * q^70 + 12 * q^71 - 6 * q^73 - 216 * q^76 + 876 * q^77 + 1644 * q^80 - 24 * q^82 + 372 * q^83 - 12 * q^85 - 516 * q^86 + 348 * q^88 - 12 * q^91 - 2082 * q^92 - 198 * q^95 + 600 * q^97 + 1032 * q^98

Introduction

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