LMFDB - Embedded newform 405.2.r.a.368.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,2,Mod(8,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([2, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.r (of order $36$, degree $12$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			368.3
Character	$\chi$	$=$	405.368
Dual form			405.2.r.a.197.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.98905 - 0.174019i) q^{2} +(1.95641 + 0.344968i) q^{4} +(-0.840902 + 2.07193i) q^{5} +(1.15499 + 0.808730i) q^{7} +(0.0258608 + 0.00692938i) q^{8} +(2.03315 - 3.97483i) q^{10} +(1.21986 - 3.35154i) q^{11} +(0.265789 + 3.03799i) q^{13} +(-2.15659 - 1.80959i) q^{14} +(-3.78380 - 1.37719i) q^{16} +(-3.91899 + 1.05009i) q^{17} +(-1.42357 + 0.821896i) q^{19} +(-2.35990 + 3.76346i) q^{20} +(-3.00959 + 6.45408i) q^{22} +(3.67339 + 5.24614i) q^{23} +(-3.58577 - 3.48458i) q^{25} -6.08895i q^{26} +(1.98064 + 1.98064i) q^{28} +(2.12205 - 1.78061i) q^{29} +(-1.13538 + 6.43905i) q^{31} +(7.23797 + 3.37512i) q^{32} +(7.97779 - 1.40670i) q^{34} +(-2.64686 + 1.71298i) q^{35} +(0.751675 + 2.80529i) q^{37} +(2.97456 - 1.38706i) q^{38} +(-0.0361036 + 0.0477548i) q^{40} +(-5.92728 + 7.06386i) q^{41} +(2.41117 + 5.17078i) q^{43} +(3.54272 - 6.13617i) q^{44} +(-6.39361 - 11.0741i) q^{46} +(-4.56850 + 6.52449i) q^{47} +(-1.71419 - 4.70971i) q^{49} +(6.52587 + 7.55498i) q^{50} +(-0.528015 + 6.03524i) q^{52} +(-8.37726 + 8.37726i) q^{53} +(5.91836 + 5.34577i) q^{55} +(0.0242649 + 0.0289177i) q^{56} +(-4.53071 + 3.17244i) q^{58} +(13.4607 - 4.89929i) q^{59} +(1.11559 + 6.32681i) q^{61} +(3.37884 - 12.6100i) q^{62} +(-6.83499 - 3.94619i) q^{64} +(-6.51799 - 2.00395i) q^{65} +(-11.6234 + 1.01692i) q^{67} +(-8.02940 + 0.702481i) q^{68} +(5.56282 - 2.94660i) q^{70} +(-0.966172 - 0.557819i) q^{71} +(2.19579 - 8.19480i) q^{73} +(-1.00694 - 5.71065i) q^{74} +(-3.06861 + 1.11688i) q^{76} +(4.11941 - 2.88444i) q^{77} +(-3.51532 - 4.18939i) q^{79} +(6.03525 - 6.68168i) q^{80} +(13.0189 - 13.0189i) q^{82} +(-0.529499 + 6.05220i) q^{83} +(1.11978 - 9.00288i) q^{85} +(-3.89612 - 10.7045i) q^{86} +(0.0547706 - 0.0782205i) q^{88} +(0.0742532 + 0.128610i) q^{89} +(-2.14993 + 3.72378i) q^{91} +(5.37690 + 11.5308i) q^{92} +(10.2223 - 12.1825i) q^{94} +(-0.505829 - 3.64066i) q^{95} +(11.6922 - 5.45218i) q^{97} +(2.59003 + 9.66613i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Character values

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

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−1.98905	−	0.174019i	−1.40647	−	0.123050i	−0.641503	−	0.767121i	$-0.721689\pi$
$2$	−1.98905	−	0.174019i	−1.40647	−	0.123050i	−0.764966	+	0.644071i	$0.777244\pi$
$3$		0			0
$3$		0			0
$4$	1.95641	+	0.344968i	0.978205	+	0.172484i
$5$	−0.840902	+	2.07193i	−0.376063	+	0.926594i
$5$	−0.840902	+	2.07193i	−0.376063	+	0.926594i
$6$		0			0
$7$	1.15499	+	0.808730i	0.436543	+	0.305671i	0.771111	−	0.636701i	$-0.219701\pi$
$7$	1.15499	+	0.808730i	0.436543	+	0.305671i	−0.334567	+	0.942372i	$0.608590\pi$
$8$	0.0258608	+	0.00692938i	0.00914317	+	0.00244991i
$9$		0			0
$10$	2.03315	−	3.97483i	0.642938	−	1.25695i
$11$	1.21986	−	3.35154i	0.367801	−	1.01053i	−0.608394	−	0.793635i	$-0.708186\pi$
$11$	1.21986	−	3.35154i	0.367801	−	1.01053i	0.976196	−	0.216891i	$-0.0695917\pi$
$12$		0			0
$13$	0.265789	+	3.03799i	0.0737167	+	0.842586i	0.939585	+	0.342315i	$0.111211\pi$
$13$	0.265789	+	3.03799i	0.0737167	+	0.842586i	−0.865869	+	0.500271i	$0.833234\pi$
$14$	−2.15659	−	1.80959i	−0.576372	−	0.483633i
$15$		0			0
$16$	−3.78380	−	1.37719i	−0.945951	−	0.344298i
$17$	−3.91899	+	1.05009i	−0.950495	+	0.254684i	−0.700572	−	0.713582i	$-0.747072\pi$
$17$	−3.91899	+	1.05009i	−0.950495	+	0.254684i	−0.249922	+	0.968266i	$0.580405\pi$
$18$		0			0
$19$	−1.42357	+	0.821896i	−0.326588	+	0.188556i	−0.654325	−	0.756213i	$-0.727047\pi$
$19$	−1.42357	+	0.821896i	−0.326588	+	0.188556i	0.327737	+	0.944769i	$0.393714\pi$
$20$	−2.35990	+	3.76346i	−0.527689	+	0.841534i
$21$		0			0
$22$	−3.00959	+	6.45408i	−0.641646	+	1.37602i
$23$	3.67339	+	5.24614i	0.765954	+	1.09390i	0.992779	+	0.119960i	$0.0382767\pi$
$23$	3.67339	+	5.24614i	0.765954	+	1.09390i	−0.226824	+	0.973936i	$0.572834\pi$
$24$		0			0
$25$	−3.58577	−	3.48458i	−0.717153	−	0.696916i
$26$		−	6.08895i		−	1.19414i
$27$		0			0
$28$	1.98064	+	1.98064i	0.374306	+	0.374306i
$29$	2.12205	−	1.78061i	0.394054	−	0.330651i	−0.424136	−	0.905599i	$-0.639422\pi$
$29$	2.12205	−	1.78061i	0.394054	−	0.330651i	0.818190	+	0.574948i	$0.194978\pi$
$30$		0			0
$31$	−1.13538	+	6.43905i	−0.203920	+	1.15649i	0.695211	+	0.718806i	$0.255311\pi$
$31$	−1.13538	+	6.43905i	−0.203920	+	1.15649i	−0.899130	+	0.437681i	$0.855800\pi$
$32$	7.23797	+	3.37512i	1.27951	+	0.596643i
$33$		0			0
$34$	7.97779	−	1.40670i	1.36818	−	0.241247i
$35$	−2.64686	+	1.71298i	−0.447401	+	0.289547i
$36$		0			0
$37$	0.751675	+	2.80529i	0.123575	+	0.461186i	0.999785	−	0.0207425i	$-0.00660301\pi$
$37$	0.751675	+	2.80529i	0.123575	+	0.461186i	−0.876210	+	0.481929i	$0.839936\pi$
$38$	2.97456	−	1.38706i	0.482538	−	0.225011i
$39$		0			0
$40$	−0.0361036	+	0.0477548i	−0.00570848	+	0.00755069i
$41$	−5.92728	+	7.06386i	−0.925686	+	1.10319i	0.0687280	+	0.997635i	$0.478106\pi$
$41$	−5.92728	+	7.06386i	−0.925686	+	1.10319i	−0.994414	+	0.105554i	$0.966339\pi$
$42$		0			0
$43$	2.41117	+	5.17078i	0.367701	+	0.788536i	0.999906	+	0.0137353i	$0.00437223\pi$
$43$	2.41117	+	5.17078i	0.367701	+	0.788536i	−0.632205	+	0.774801i	$0.717850\pi$
$44$	3.54272	−	6.13617i	0.534085	−	0.925062i
$45$		0			0
$46$	−6.39361	−	11.0741i	−0.942687	−	1.63278i
$47$	−4.56850	+	6.52449i	−0.666384	+	0.951695i	0.333576	+	0.942723i	$0.391745\pi$
$47$	−4.56850	+	6.52449i	−0.666384	+	0.951695i	−0.999960	+	0.00897134i	$0.997144\pi$
$48$		0			0
$49$	−1.71419	−	4.70971i	−0.244885	−	0.672815i
$50$	6.52587	+	7.55498i	0.922898	+	1.06844i
$51$		0			0
$52$	−0.528015	+	6.03524i	−0.0732225	+	0.836937i
$53$	−8.37726	+	8.37726i	−1.15070	+	1.15070i	−0.164293	+	0.986412i	$0.552534\pi$
$53$	−8.37726	+	8.37726i	−1.15070	+	1.15070i	−0.986412	+	0.164293i	$0.947466\pi$
$54$		0			0
$55$	5.91836	+	5.34577i	0.798031	+	0.720824i
$56$	0.0242649	+	0.0289177i	0.00324253	+	0.00386429i
$57$		0			0
$58$	−4.53071	+	3.17244i	−0.594911	+	0.416561i
$59$	13.4607	−	4.89929i	1.75243	−	0.637833i	0.752643	−	0.658429i	$-0.228779\pi$
$59$	13.4607	−	4.89929i	1.75243	−	0.637833i	0.999788	+	0.0205964i	$0.00655651\pi$
$60$		0			0
$61$	1.11559	+	6.32681i	0.142836	+	0.810066i	0.969079	+	0.246751i	$0.0793630\pi$
$61$	1.11559	+	6.32681i	0.142836	+	0.810066i	−0.826242	+	0.563315i	$0.809526\pi$
$62$	3.37884	−	12.6100i	0.429113	−	1.60147i
$63$		0			0
$64$	−6.83499	−	3.94619i	−0.854374	−	0.493273i
$65$	−6.51799	−	2.00395i	−0.808457	−	0.248560i
$66$		0			0
$67$	−11.6234	+	1.01692i	−1.42002	+	0.124236i	−0.771147	−	0.636658i	$-0.780317\pi$
$67$	−11.6234	+	1.01692i	−1.42002	+	0.124236i	−0.648877	+	0.760893i	$0.724761\pi$
$68$	−8.02940	+	0.702481i	−0.973708	+	0.0851884i
$69$		0			0
$70$	5.56282	−	2.94660i	0.664884	−	0.352186i
$71$	−0.966172	−	0.557819i	−0.114663	−	0.0662010i	0.441571	−	0.897226i	$-0.354421\pi$
$71$	−0.966172	−	0.557819i	−0.114663	−	0.0662010i	−0.556235	+	0.831025i	$0.687755\pi$
$72$		0			0
$73$	2.19579	−	8.19480i	0.256998	−	0.959129i	−0.709970	−	0.704232i	$-0.751292\pi$
$73$	2.19579	−	8.19480i	0.256998	−	0.959129i	0.966968	−	0.254898i	$-0.0820417\pi$
$74$	−1.00694	−	5.71065i	−0.117055	−	0.663850i
$75$		0			0
$76$	−3.06861	+	1.11688i	−0.351993	+	0.128115i
$77$	4.11941	−	2.88444i	0.469450	−	0.328712i
$78$		0			0
$79$	−3.51532	−	4.18939i	−0.395504	−	0.471344i	0.531139	−	0.847284i	$-0.321764\pi$
$79$	−3.51532	−	4.18939i	−0.395504	−	0.471344i	−0.926644	+	0.375941i	$0.877320\pi$
$80$	6.03525	−	6.68168i	0.674761	−	0.747035i
$81$		0			0
$82$	13.0189	−	13.0189i	1.43770	−	1.43770i
$83$	−0.529499	+	6.05220i	−0.0581201	+	0.664315i	0.910129	+	0.414326i	$0.135983\pi$
$83$	−0.529499	+	6.05220i	−0.0581201	+	0.664315i	−0.968249	+	0.249989i	$0.919573\pi$
$84$		0			0
$85$	1.11978	−	9.00288i	0.121457	−	0.976500i
$86$	−3.89612	−	10.7045i	−0.420130	−	1.15430i
$87$		0			0
$88$	0.0547706	−	0.0782205i	0.00583856	−	0.00833833i
$89$	0.0742532	+	0.128610i	0.00787082	+	0.0136327i	0.869934	−	0.493168i	$-0.164161\pi$
$89$	0.0742532	+	0.128610i	0.00787082	+	0.0136327i	−0.862063	+	0.506801i	$0.830828\pi$
$90$		0			0
$91$	−2.14993	+	3.72378i	−0.225374	+	0.390358i
$92$	5.37690	+	11.5308i	0.560581	+	1.20217i
$93$		0			0
$94$	10.2223	−	12.1825i	1.05435	−	1.25653i
$95$	−0.505829	−	3.64066i	−0.0518970	−	0.373524i
$96$		0			0
$97$	11.6922	−	5.45218i	1.18717	−	0.553585i	0.274222	−	0.961667i	$-0.411580\pi$
$97$	11.6922	−	5.45218i	1.18717	−	0.553585i	0.912946	+	0.408081i	$0.133802\pi$
$98$	2.59003	+	9.66613i	0.261633	+	0.976427i
$99$		0			0
$100$	−5.81316	−	8.05424i	−0.581316	−	0.805424i
$101$	5.20108	−	0.917090i	0.517526	−	0.0912539i	0.0912166	−	0.995831i	$-0.470924\pi$
$101$	5.20108	−	0.917090i	0.517526	−	0.0912539i	0.426310	+	0.904577i	$0.359813\pi$
$102$		0			0
$103$	−2.92471	−	1.36382i	−0.288181	−	0.134381i	0.273153	−	0.961971i	$-0.411934\pi$
$103$	−2.92471	−	1.36382i	−0.288181	−	0.134381i	−0.561333	+	0.827590i	$0.689711\pi$
$104$	−0.0141778	+	0.0804065i	−0.00139025	+	0.00788451i
$105$		0			0
$106$	18.1206	−	15.2050i	1.76002	−	1.47684i
$107$	−9.12902	−	9.12902i	−0.882536	−	0.882536i	0.111256	−	0.993792i	$-0.464513\pi$
$107$	−9.12902	−	9.12902i	−0.882536	−	0.882536i	−0.993792	+	0.111256i	$0.964513\pi$
$108$		0			0
$109$			7.32304i			0.701420i	0.936484	+	0.350710i	$0.114060\pi$
$109$			7.32304i			0.701420i	−0.936484	+	0.350710i	$0.885940\pi$
$110$	−10.8416	−	11.6629i	−1.03371	−	1.11201i
$111$		0			0
$112$	−3.25646	−	4.65071i	−0.307707	−	0.439451i
$113$	6.43209	−	13.7937i	0.605081	−	1.29760i	−0.330273	−	0.943885i	$-0.607141\pi$
$113$	6.43209	−	13.7937i	0.605081	−	1.29760i	0.935354	−	0.353714i	$-0.115081\pi$
$114$		0			0
$115$	−13.9586	+	3.19950i	−1.30164	+	0.298355i
$116$	4.76585	−	2.75156i	0.442498	−	0.255476i
$117$		0			0
$118$	−27.6265	+	7.40249i	−2.54322	+	0.681455i
$119$	−5.37561	−	1.95656i	−0.492782	−	0.179358i
$120$		0			0
$121$	−1.31824	−	1.10614i	−0.119840	−	0.100558i
$122$	−1.11797	−	12.7785i	−0.101216	−	1.15691i
$123$		0			0
$124$	−4.44253	+	12.2057i	−0.398951	+	1.09611i
$125$	10.2351	−	4.49926i	0.915453	−	0.402426i
$126$		0			0
$127$	6.42251	+	1.72091i	0.569905	+	0.152706i	0.532253	−	0.846585i	$-0.321345\pi$
$127$	6.42251	+	1.72091i	0.569905	+	0.152706i	0.0376522	+	0.999291i	$0.488012\pi$
$128$	−0.175446	−	0.122848i	−0.0155074	−	0.0108584i
$129$		0			0
$130$	12.6159	+	5.12021i	1.10648	+	0.449072i
$131$	−11.6386	−	2.05219i	−1.01687	−	0.179301i	−0.359717	−	0.933062i	$-0.617127\pi$
$131$	−11.6386	−	2.05219i	−1.01687	−	0.179301i	−0.657149	+	0.753761i	$0.728238\pi$
$132$		0			0
$133$	−2.30889	−	0.202002i	−0.200206	−	0.0175158i
$134$	23.2964			2.01251
$135$		0			0
$136$	−0.108625			−0.00931449
$137$	12.0706	+	1.05604i	1.03126	+	0.0902237i	0.590203	−	0.807255i	$-0.299048\pi$
$137$	12.0706	+	1.05604i	1.03126	+	0.0902237i	0.441059	+	0.897478i	$0.354603\pi$
$138$		0			0
$139$	12.8272	+	2.26177i	1.08799	+	0.191841i	0.688744	−	0.725005i	$-0.258162\pi$
$139$	12.8272	+	2.26177i	1.08799	+	0.191841i	0.399242	+	0.916846i	$0.369273\pi$
$140$	−5.76927	+	2.43822i	−0.487592	+	0.206067i
$141$		0			0
$142$	1.82469	+	1.27766i	0.153125	+	0.107219i
$143$	10.5061	+	2.81511i	0.878568	+	0.235412i
$144$		0			0
$145$	1.90486	+	5.89404i	0.158190	+	0.489474i
$146$	−5.79358	+	15.9177i	−0.479480	+	1.31736i
$147$		0			0
$148$	0.502850	+	5.74760i	0.0413340	+	0.472450i
$149$	−2.75179	−	2.30902i	−0.225435	−	0.189162i	0.523074	−	0.852288i	$-0.324785\pi$
$149$	−2.75179	−	2.30902i	−0.225435	−	0.189162i	−0.748509	+	0.663125i	$0.769230\pi$
$150$		0			0
$151$	0.415850	+	0.151357i	0.0338414	+	0.0123173i	0.358885	−	0.933382i	$-0.383157\pi$
$151$	0.415850	+	0.151357i	0.0338414	+	0.0123173i	−0.325044	+	0.945699i	$0.605379\pi$
$152$	−0.0425098	+	0.0113905i	−0.00344800	+	0.000923888i
$153$		0			0
$154$	−8.69564	+	5.02043i	−0.700715	+	0.404558i
$155$	−12.3865	−	7.76703i	−0.994907	−	0.623863i
$156$		0			0
$157$	−0.538818	+	1.15550i	−0.0430024	+	0.0922189i	−0.926635	−	0.375961i	$-0.877312\pi$
$157$	−0.538818	+	1.15550i	−0.0430024	+	0.0922189i	0.883633	+	0.468180i	$0.155090\pi$
$158$	6.26310	+	8.94463i	0.498265	+	0.711597i
$159$		0			0
$160$	−13.0794	+	12.1584i	−1.03402	+	0.961207i
$161$			9.02999i			0.711663i
$162$		0			0
$163$	−2.53097	−	2.53097i	−0.198241	−	0.198241i	0.601005	−	0.799245i	$-0.294767\pi$
$163$	−2.53097	−	2.53097i	−0.198241	−	0.198241i	−0.799245	+	0.601005i	$0.794767\pi$
$164$	−14.0330	+	11.7751i	−1.09579	+	0.919479i
$165$		0			0
$166$	2.10640	−	11.9460i	0.163488	−	0.927187i
$167$	10.9336	+	5.09841i	0.846066	+	0.394527i	0.796789	−	0.604258i	$-0.206530\pi$
$167$	10.9336	+	5.09841i	0.846066	+	0.394527i	0.0492772	+	0.998785i	$0.484308\pi$
$168$		0			0
$169$	3.64378	−	0.642497i	0.280291	−	0.0494228i
$170$	−3.79396	+	17.7123i	−0.290984	+	1.35847i
$171$		0			0
$172$	2.93349	+	10.9479i	0.223677	+	0.834773i
$173$	5.26639	−	2.45576i	0.400397	−	0.186708i	−0.211980	−	0.977274i	$-0.567991\pi$
$173$	5.26639	−	2.45576i	0.400397	−	0.186708i	0.612377	+	0.790566i	$0.290214\pi$
$174$		0			0
$175$	−1.32343	−	6.92455i	−0.100042	−	0.523447i
$176$	−9.23141	+	11.0016i	−0.695844	+	0.829274i
$177$		0			0
$178$	−0.125312	−	0.268733i	−0.00939256	−	0.0201424i
$179$	−9.76891	+	16.9203i	−0.730163	+	1.26468i	0.226651	+	0.973976i	$0.427222\pi$
$179$	−9.76891	+	16.9203i	−0.730163	+	1.26468i	−0.956813	+	0.290703i	$0.906111\pi$
$180$		0			0
$181$	5.30360	+	9.18610i	0.394213	+	0.682797i	0.993000	−	0.118111i	$-0.0376838\pi$
$181$	5.30360	+	9.18610i	0.394213	+	0.682797i	−0.598787	+	0.800908i	$0.704350\pi$
$182$	4.92432	−	7.03265i	0.365015	−	0.521295i
$183$		0			0
$184$	0.0586442	+	0.161124i	0.00432331	+	0.0118782i
$185$	−6.44444	−	0.801558i	−0.473804	−	0.0589317i
$186$		0			0
$187$	−1.26120	+	14.4156i	−0.0922282	+	1.05417i
$188$	−11.1886	+	11.1886i	−0.816012	+	0.816012i
$189$		0			0
$190$	0.372574	+	7.32947i	0.0270293	+	0.531735i
$191$	3.07377	+	3.66318i	0.222410	+	0.265058i	0.865698	−	0.500566i	$-0.166875\pi$
$191$	3.07377	+	3.66318i	0.222410	+	0.265058i	−0.643288	+	0.765624i	$0.722430\pi$
$192$		0			0
$193$	−4.45676	+	3.12066i	−0.320804	+	0.224630i	−0.722875	−	0.690979i	$-0.757180\pi$
$193$	−4.45676	+	3.12066i	−0.320804	+	0.224630i	0.402070	+	0.915609i	$0.368291\pi$
$194$	−24.2052	+	8.80997i	−1.73783	+	0.632519i
$195$		0			0
$196$	−1.72897	−	9.80546i	−0.123498	−	0.700390i
$197$	2.07911	−	7.75934i	0.148130	−	0.552830i	−0.851466	−	0.524410i	$-0.824286\pi$
$197$	2.07911	−	7.75934i	0.148130	−	0.552830i	0.999596	−	0.0284197i	$-0.00904750\pi$
$198$		0			0
$199$	10.5312	+	6.08020i	0.746539	+	0.431014i	0.824442	−	0.565947i	$-0.191489\pi$
$199$	10.5312	+	6.08020i	0.746539	+	0.431014i	−0.0779033	+	0.996961i	$0.524823\pi$
$200$	−0.0685848	−	0.114961i	−0.00484968	−	0.00812898i
$201$		0			0
$202$	−10.5048	+	0.919049i	−0.739114	+	0.0646641i
$203$	3.89096	−	0.340415i	0.273092	−	0.0238925i
$204$		0			0
$205$	−9.65154	−	18.2209i	−0.674092	−	1.27260i
$206$	5.58006	+	3.22165i	0.388781	+	0.224463i
$207$		0			0
$208$	3.17819	−	11.8612i	0.220368	−	0.822425i
$209$	1.01806	+	5.77373i	0.0704210	+	0.399377i
$210$		0			0
$211$	2.80282	−	1.02014i	0.192954	−	0.0702295i	−0.243736	−	0.969842i	$-0.578373\pi$
$211$	2.80282	−	1.02014i	0.192954	−	0.0702295i	0.436690	+	0.899612i	$0.356151\pi$
$212$	−19.2792	+	13.4995i	−1.32410	+	0.927147i
$213$		0			0
$214$	16.5694	+	19.7467i	1.13266	+	1.34985i
$215$	−12.7410	+	0.647657i	−0.868932	+	0.0441698i
$216$		0			0
$217$	−6.51879	+	6.51879i	−0.442524	+	0.442524i
$218$	1.27435	−	14.5659i	0.0863097	−	0.986525i
$219$		0			0
$220$	9.73461	+	12.5002i	0.656307	+	0.842761i
$221$	−4.23179	−	11.6267i	−0.284661	−	0.782099i
$222$		0			0
$223$	4.64364	−	6.63181i	0.310961	−	0.444099i	−0.633002	−	0.774151i	$-0.718177\pi$
$223$	4.64364	−	6.63181i	0.310961	−	0.444099i	0.943963	+	0.330052i	$0.107066\pi$
$224$	5.63019	+	9.75178i	0.376183	+	0.651568i
$225$		0			0
$226$	−15.1941	+	26.3170i	−1.01070	+	1.75058i
$227$	3.25781	+	6.98639i	0.216228	+	0.463703i	0.984264	−	0.176704i	$-0.0565435\pi$
$227$	3.25781	+	6.98639i	0.216228	+	0.463703i	−0.768036	+	0.640407i	$0.778766\pi$
$228$		0			0
$229$	2.93595	−	3.49893i	0.194013	−	0.231216i	−0.660264	−	0.751033i	$-0.729556\pi$
$229$	2.93595	−	3.49893i	0.194013	−	0.231216i	0.854277	+	0.519818i	$0.174000\pi$
$230$	28.3211	−	3.93490i	1.86743	−	0.259459i
$231$		0			0
$232$	0.0672163	−	0.0313435i	0.00441297	−	0.00205780i
$233$	−5.18153	−	19.3377i	−0.339454	−	1.26686i	−0.898960	−	0.438032i	$-0.855676\pi$
$233$	−5.18153	−	19.3377i	−0.339454	−	1.26686i	0.559506	−	0.828826i	$-0.310991\pi$
$234$		0			0
$235$	−9.67661	−	14.9521i	−0.631232	−	0.975364i
$236$	28.0247	−	4.94151i	1.82425	−	0.321665i
$237$		0			0
$238$	10.3519	+	4.82716i	0.671012	+	0.312898i
$239$	2.31345	−	13.1202i	0.149645	−	0.848678i	−0.813875	−	0.581040i	$-0.802646\pi$
$239$	2.31345	−	13.1202i	0.149645	−	0.848678i	0.963520	−	0.267638i	$-0.0862431\pi$
$240$		0			0
$241$	19.5457	−	16.4008i	1.25905	−	1.05647i	0.263267	−	0.964723i	$-0.415200\pi$
$241$	19.5457	−	16.4008i	1.25905	−	1.05647i	0.995783	−	0.0917454i	$-0.0292446\pi$
$242$	2.42956	+	2.42956i	0.156178	+	0.156178i
$243$		0			0
$244$			12.7627i			0.817047i
$245$	11.1996	+	0.408720i	0.715519	+	0.0261122i
$246$		0			0
$247$	−2.87528	−	4.10632i	−0.182950	−	0.261279i
$248$	−0.0739804	+	0.158651i	−0.00469776	+	0.0100744i
$249$		0			0
$250$	−21.1410	+	7.16814i	−1.33707	+	0.453353i
$251$	−17.4693	+	10.0859i	−1.10265	+	0.636617i	−0.936917	−	0.349553i	$-0.886333\pi$
$251$	−17.4693	+	10.0859i	−1.10265	+	0.636617i	−0.165736	+	0.986170i	$0.553000\pi$
$252$		0			0
$253$	22.0636	−	5.91193i	1.38713	−	0.371680i
$254$	−12.4752	−	4.54060i	−0.782764	−	0.284903i
$255$		0			0
$256$	12.4194	+	10.4211i	0.776213	+	0.651320i
$257$	0.746929	+	8.53743i	0.0465921	+	0.532550i	0.983245	+	0.182291i	$0.0583512\pi$
$257$	0.746929	+	8.53743i	0.0465921	+	0.532550i	−0.936653	+	0.350260i	$0.886093\pi$
$258$		0			0
$259$	−1.40055	+	3.84797i	−0.0870257	+	0.239101i
$260$	−12.0606	−	6.16905i	−0.747964	−	0.382588i
$261$		0			0
$262$	22.7925	+	6.10724i	1.40813	+	0.377307i
$263$	16.5483	+	11.5873i	1.02041	+	0.714501i	0.958941	−	0.283607i	$-0.0915312\pi$
$263$	16.5483	+	11.5873i	1.02041	+	0.714501i	0.0614734	+	0.998109i	$0.480420\pi$
$264$		0			0
$265$	−10.3126	−	24.4015i	−0.633499	−	1.49897i
$266$	4.55734	+	0.803581i	0.279428	+	0.0492707i
$267$		0			0
$268$	−23.0909	−	2.02019i	−1.41050	−	0.123403i
$269$	11.8522			0.722639			0.361320	−	0.932442i	$-0.382326\pi$
$269$	11.8522			0.722639			0.361320	+	0.932442i	$0.382326\pi$
$270$		0			0
$271$	24.7671			1.50450			0.752249	−	0.658879i	$-0.228969\pi$
$271$	24.7671			1.50450			0.752249	+	0.658879i	$0.228969\pi$
$272$	16.2749	+	1.42387i	0.986808	+	0.0863345i
$273$		0			0
$274$	−23.8252	−	4.20103i	−1.43934	−	0.253794i
$275$	−16.0528	+	7.76713i	−0.968021	+	0.468375i
$276$		0			0
$277$	−23.8949	−	16.7314i	−1.43571	−	1.00529i	−0.994144	−	0.108064i	$-0.965535\pi$
$277$	−23.8949	−	16.7314i	−1.43571	−	1.00529i	−0.441564	−	0.897230i	$-0.645576\pi$
$278$	−25.1202	−	6.73095i	−1.50661	−	0.403695i
$279$		0			0
$280$	−0.0803198	+	0.0259580i	−0.00480003	+	0.00155129i
$281$	10.0345	−	27.5694i	0.598605	−	1.64465i	−0.155450	−	0.987844i	$-0.549683\pi$
$281$	10.0345	−	27.5694i	0.598605	−	1.64465i	0.754055	−	0.656811i	$-0.228095\pi$
$282$		0			0
$283$	1.18317	+	13.5237i	0.0703324	+	0.803902i	0.946670	+	0.322205i	$0.104424\pi$
$283$	1.18317	+	13.5237i	0.0703324	+	0.803902i	−0.876338	+	0.481697i	$0.840020\pi$
$284$	−1.69780	−	1.42462i	−0.100746	−	0.0845357i
$285$		0			0
$286$	−20.4073	−	7.42766i	−1.20671	−	0.439207i
$287$	−12.5587	+	3.36509i	−0.741315	+	0.198635i
$288$		0			0
$289$	−0.466643	+	0.269416i	−0.0274496	+	0.0158480i
$290$	−2.76317	−	12.0550i	−0.162259	−	0.707895i
$291$		0			0
$292$	7.12281	−	15.2749i	0.416831	−	0.893897i
$293$	−4.73624	−	6.76405i	−0.276694	−	0.395160i	0.656620	−	0.754222i	$-0.271986\pi$
$293$	−4.73624	−	6.76405i	−0.276694	−	0.395160i	−0.933314	+	0.359062i	$0.883097\pi$
$294$		0			0
$295$	−1.16815	+	32.0094i	−0.0680124	+	1.86366i
$296$			0.0777556i			0.00451945i
$297$		0			0
$298$	5.07162	+	5.07162i	0.293791	+	0.293791i
$299$	−14.9614	+	12.5541i	−0.865238	+	0.726021i
$300$		0			0
$301$	−1.39689	+	7.92216i	−0.0805155	+	0.456626i
$302$	−0.800806	−	0.373422i	−0.0460812	−	0.0214880i
$303$		0			0
$304$	6.51840	−	1.14937i	0.373856	−	0.0659209i
$305$	−14.0468	−	3.00882i	−0.804317	−	0.172284i
$306$		0			0
$307$	−2.68621	−	10.0251i	−0.153310	−	0.572161i	−0.999244	−	0.0388737i	$-0.987623\pi$
$307$	−2.68621	−	10.0251i	−0.153310	−	0.572161i	0.845934	−	0.533288i	$-0.179044\pi$
$308$	9.05429	−	4.22208i	0.515916	−	0.240575i
$309$		0			0
$310$	23.2857	+	17.6045i	1.32254	+	0.999867i
$311$	12.2675	−	14.6199i	0.695627	−	0.829016i	−0.296397	−	0.955065i	$-0.595785\pi$
$311$	12.2675	−	14.6199i	0.695627	−	0.829016i	0.992024	+	0.126049i	$0.0402297\pi$
$312$		0			0
$313$	6.95728	+	14.9199i	0.393249	+	0.843325i	0.998868	+	0.0475700i	$0.0151477\pi$
$313$	6.95728	+	14.9199i	0.393249	+	0.843325i	−0.605619	+	0.795755i	$0.707075\pi$
$314$	1.27281	−	2.20458i	0.0718291	−	0.124412i
$315$		0			0
$316$	−5.43220	−	9.40884i	−0.305585	−	0.529289i
$317$	−4.28594	+	6.12095i	−0.240722	+	0.343787i	−0.921275	−	0.388912i	$-0.872851\pi$
$317$	−4.28594	+	6.12095i	−0.240722	+	0.343787i	0.680553	+	0.732699i	$0.261740\pi$
$318$		0			0
$319$	−3.37917	−	9.28420i	−0.189197	−	0.519816i
$320$	13.9238	−	10.8433i	0.778363	−	0.606156i
$321$		0			0
$322$	1.57139	−	17.9611i	0.0875702	−	1.00093i
$323$	4.71587	−	4.71587i	0.262398	−	0.262398i
$324$		0			0
$325$	9.63304	−	11.8197i	0.534345	−	0.655638i
$326$	4.59378	+	5.47465i	0.254426	+	0.303213i
$327$		0			0
$328$	−0.202232	+	0.141605i	−0.0111664	+	0.00781881i
$329$	−10.5531	+	3.84101i	−0.581811	+	0.211762i
$330$		0			0
$331$	1.44127	+	8.17383i	0.0792192	+	0.449274i	0.998455	+	0.0555668i	$0.0176966\pi$
$331$	1.44127	+	8.17383i	0.0792192	+	0.449274i	−0.919236	+	0.393707i	$0.871192\pi$
$332$	−3.12373	+	11.6579i	−0.171437	+	0.639812i
$333$		0			0
$334$	−20.8602	−	12.0436i	−1.14142	−	0.658998i
$335$	7.66717	−	24.9380i	0.418902	−	1.36251i
$336$		0			0
$337$	15.6386	−	1.36820i	0.851888	−	0.0745305i	0.347157	−	0.937807i	$-0.387147\pi$
$337$	15.6386	−	1.36820i	0.851888	−	0.0745305i	0.504731	+	0.863277i	$0.331592\pi$
$338$	−7.35946	+	0.643869i	−0.400302	+	0.0350219i
$339$		0			0
$340$	5.29645	−	17.2270i	0.287240	−	0.934268i
$341$	20.1957	+	11.6600i	1.09366	+	0.631424i
$342$		0			0
$343$	4.38351	−	16.3595i	0.236687	−	0.883330i
$344$	0.0265246	+	0.150428i	0.00143011	+	0.00811056i
$345$		0			0
$346$	−10.9025	+	3.96817i	−0.586120	+	0.213330i
$347$	−0.751529	+	0.526226i	−0.0403442	+	0.0282493i	−0.593575	−	0.804779i	$-0.702284\pi$
$347$	−0.751529	+	0.526226i	−0.0403442	+	0.0282493i	0.553230	+	0.833028i	$0.313395\pi$
$348$		0			0
$349$	−23.1000	−	27.5295i	−1.23652	−	1.47362i	−0.827861	−	0.560934i	$-0.810442\pi$
$349$	−23.1000	−	27.5295i	−1.23652	−	1.47362i	−0.408655	−	0.912689i	$-0.634002\pi$
$350$	1.42736	+	14.0036i	0.0762953	+	0.748522i
$351$		0			0
$352$	20.1412	−	20.1412i	1.07353	−	1.07353i
$353$	0.420748	−	4.80917i	0.0223942	−	0.255966i	−0.976742	−	0.214417i	$-0.931215\pi$
$353$	0.420748	−	4.80917i	0.0223942	−	0.255966i	0.999136	−	0.0415497i	$-0.0132295\pi$
$354$		0			0
$355$	1.96822	−	1.53277i	0.104462	−	0.0813508i
$356$	0.100903	+	0.277229i	0.00534786	+	0.0146931i
$357$		0			0
$358$	22.3753	−	31.9552i	1.18257	−	1.68889i
$359$	−1.88801	−	3.27013i	−0.0996454	−	0.172591i	0.811892	−	0.583807i	$-0.198438\pi$
$359$	−1.88801	−	3.27013i	−0.0996454	−	0.172591i	−0.911538	+	0.411216i	$0.865104\pi$
$360$		0			0
$361$	−8.14897	+	14.1144i	−0.428893	+	0.742865i
$362$	−8.95055	−	19.1945i	−0.470430	−	1.00884i
$363$		0			0
$364$	−5.49072	+	6.54359i	−0.287792	+	0.342977i
$365$	15.1326	+	11.4406i	0.792076	+	0.598826i
$366$		0			0
$367$	−22.8495	+	10.6549i	−1.19273	+	0.556181i	−0.914600	−	0.404361i	$-0.867494\pi$
$367$	−22.8495	+	10.6549i	−1.19273	+	0.556181i	−0.278135	+	0.960542i	$0.589716\pi$
$368$	−6.67443	−	24.9093i	−0.347929	−	1.29849i
$369$		0			0
$370$	12.6788	+	2.71579i	0.659140	+	0.141187i
$371$	−16.4505	+	2.90067i	−0.854070	+	0.150596i
$372$		0			0
$373$	9.99084	+	4.65880i	0.517306	+	0.241224i	0.663695	−	0.748003i	$-0.268987\pi$
$373$	9.99084	+	4.65880i	0.517306	+	0.241224i	−0.146389	+	0.989227i	$0.546765\pi$
$374$	5.01718	−	28.4538i	0.259432	−	1.47131i
$375$		0			0
$376$	−0.163356	+	0.137072i	−0.00842442	+	0.00706893i
$377$	5.97348	+	5.97348i	0.307650	+	0.307650i
$378$		0			0
$379$			6.15292i			0.316054i	0.987435	+	0.158027i	$0.0505134\pi$
$379$			6.15292i			0.316054i	−0.987435	+	0.158027i	$0.949487\pi$
$380$	0.266301	−	7.29712i	0.0136610	−	0.374334i
$381$		0			0
$382$	−5.47641	−	7.82113i	−0.280198	−	0.400164i
$383$	−7.45128	+	15.9793i	−0.380743	+	0.816506i	0.618778	+	0.785566i	$0.287628\pi$
$383$	−7.45128	+	15.9793i	−0.380743	+	0.816506i	−0.999521	+	0.0309400i	$0.990150\pi$
$384$		0			0
$385$	2.51233	+	10.9606i	0.128040	+	0.558606i
$386$	9.40775	−	5.43157i	0.478842	−	0.276460i
$387$		0			0
$388$	24.7556	−	6.63326i	1.25678	−	0.336753i
$389$	13.1982	+	4.80373i	0.669173	+	0.243559i	0.654192	−	0.756329i	$-0.273009\pi$
$389$	13.1982	+	4.80373i	0.669173	+	0.243559i	0.0149811	+	0.999888i	$0.495231\pi$
$390$		0			0
$391$	−19.9049	−	16.7022i	−1.00663	−	0.844666i
$392$	−0.0116951	−	0.133675i	−0.000590689	−	0.00675161i
$393$		0			0
$394$	−5.48572	+	15.0719i	−0.276366	+	0.759311i
$395$	11.6362	−	3.76061i	0.585479	−	0.189217i
$396$		0			0
$397$	−29.2343	−	7.83331i	−1.46723	−	0.393143i	−0.565248	−	0.824921i	$-0.691220\pi$
$397$	−29.2343	−	7.83331i	−1.46723	−	0.393143i	−0.901980	+	0.431778i	$0.857886\pi$
$398$	−19.8890	−	13.9264i	−0.996947	−	0.698070i
$399$		0			0
$400$	8.76890	+	18.1232i	0.438445	+	0.906162i
$401$	16.0405	+	2.82837i	0.801024	+	0.141242i	0.559151	−	0.829066i	$-0.311127\pi$
$401$	16.0405	+	2.82837i	0.801024	+	0.141242i	0.241873	+	0.970308i	$0.422238\pi$
$402$		0			0
$403$	−19.8635	−	1.73783i	−0.989472	−	0.0865676i
$404$	10.4918			0.521987
$405$		0			0
$406$	−7.79855			−0.387035
$407$	10.3190	+	0.902792i	0.511492	+	0.0447497i
$408$		0			0
$409$	19.2731	+	3.39837i	0.952995	+	0.168039i	0.628466	−	0.777837i	$-0.283683\pi$
$409$	19.2731	+	3.39837i	0.952995	+	0.168039i	0.324529	+	0.945876i	$0.394794\pi$
$410$	16.0266	+	37.9218i	0.791496	+	1.87282i
$411$		0			0
$412$	−5.25147	−	3.67712i	−0.258721	−	0.181159i
$413$	19.5091	+	5.22744i	0.959979	+	0.257226i
$414$		0			0
$415$	−12.0945	−	6.18639i	−0.593694	−	0.303678i
$416$	−8.32980	+	22.8859i	−0.408402	+	1.12208i
$417$		0			0
$418$	−1.02024	−	11.6614i	−0.0499015	−	0.570377i
$419$	0.141106	+	0.118402i	0.00689349	+	0.00578432i	0.646228	−	0.763145i	$-0.276346\pi$
$419$	0.141106	+	0.118402i	0.00689349	+	0.00578432i	−0.639334	+	0.768929i	$0.720790\pi$
$420$		0			0
$421$	−17.1952	−	6.25854i	−0.838043	−	0.305023i	−0.112887	−	0.993608i	$-0.536010\pi$
$421$	−17.1952	−	6.25854i	−0.838043	−	0.305023i	−0.725155	+	0.688585i	$0.758232\pi$
$422$	−5.75246	+	1.54137i	−0.280025	+	0.0750325i
$423$		0			0
$424$	−0.274692	+	0.158593i	−0.0133402	+	0.00770197i
$425$	17.7117	+	9.89064i	0.859144	+	0.479767i
$426$		0			0
$427$	−3.82819	+	8.20959i	−0.185259	+	0.397290i
$428$	−14.7109	−	21.0093i	−0.711078	−	1.01552i
$429$		0			0
$430$	25.4552	+	0.928965i	1.22756	+	0.0447987i
$431$		−	20.4312i		−	0.984138i	−0.870556	−	0.492069i	$-0.836241\pi$
$431$		−	20.4312i		−	0.984138i	0.870556	−	0.492069i	$-0.163759\pi$
$432$		0			0
$433$	−1.40075	−	1.40075i	−0.0673156	−	0.0673156i	0.672647	−	0.739963i	$-0.265157\pi$
$433$	−1.40075	−	1.40075i	−0.0673156	−	0.0673156i	−0.739963	+	0.672647i	$0.765157\pi$
$434$	14.1006	−	11.8318i	0.676849	−	0.567944i
$435$		0			0
$436$	−2.52621	+	14.3269i	−0.120984	+	0.686132i
$437$	−9.54109	−	4.44908i	−0.456412	−	0.212829i
$438$		0			0
$439$	13.9335	−	2.45686i	0.665012	−	0.117259i	0.169055	−	0.985607i	$-0.445929\pi$
$439$	13.9335	−	2.45686i	0.665012	−	0.117259i	0.495957	+	0.868347i	$0.334817\pi$
$440$	0.116010	+	0.179257i	0.00553058	+	0.00854572i
$441$		0			0
$442$	6.39395	+	23.8625i	0.304129	+	1.13503i
$443$	−14.5440	+	6.78197i	−0.691005	+	0.322221i	−0.736207	−	0.676757i	$-0.763385\pi$
$443$	−14.5440	+	6.78197i	−0.691005	+	0.322221i	0.0452014	+	0.998978i	$0.485607\pi$
$444$		0			0
$445$	−0.328911	+	0.0456985i	−0.0155919	+	0.00216632i
$446$	−10.3905	+	12.3829i	−0.492004	+	0.586347i
$447$		0			0
$448$	−4.70292	−	10.0854i	−0.222192	−	0.476493i
$449$	2.86184	−	4.95685i	0.135059	−	0.233928i	−0.790561	−	0.612383i	$-0.790211\pi$
$449$	2.86184	−	4.95685i	0.135059	−	0.233928i	0.925620	+	0.378455i	$0.123544\pi$
$450$		0			0
$451$	16.4443	+	28.4824i	0.774333	+	1.34118i
$452$	17.3422	−	24.7672i	0.815708	−	1.16495i
$453$		0			0
$454$	−5.26417	−	14.4632i	−0.247060	−	0.678791i
$455$	−5.90753	−	7.58583i	−0.276949	−	0.355629i
$456$		0			0
$457$	1.72215	−	19.6843i	0.0805589	−	0.920793i	−0.843145	−	0.537686i	$-0.819299\pi$
$457$	1.72215	−	19.6843i	0.0805589	−	0.920793i	0.923704	−	0.383107i	$-0.125146\pi$
$458$	−6.44862	+	6.44862i	−0.301324	+	0.301324i
$459$		0			0
$460$	−28.4124	+	1.44427i	−1.32474	+	0.0673394i
$461$	11.6371	+	13.8685i	0.541993	+	0.645922i	0.965633	−	0.259909i	$-0.0836924\pi$
$461$	11.6371	+	13.8685i	0.541993	+	0.645922i	−0.423640	+	0.905830i	$0.639248\pi$
$462$		0			0
$463$	10.7175	−	7.50444i	0.498082	−	0.348761i	−0.297385	−	0.954758i	$-0.596114\pi$
$463$	10.7175	−	7.50444i	0.498082	−	0.348761i	0.795467	+	0.605997i	$0.207226\pi$
$464$	−10.4816	+	3.81501i	−0.486598	+	0.177107i
$465$		0			0
$466$	6.94118	+	39.3654i	0.321544	+	1.82357i
$467$	2.10904	−	7.87106i	0.0975949	−	0.364229i	−0.899805	−	0.436292i	$-0.856292\pi$
$467$	2.10904	−	7.87106i	0.0975949	−	0.364229i	0.997400	+	0.0720628i	$0.0229582\pi$
$468$		0			0
$469$	−14.2473	−	8.22566i	−0.657877	−	0.379826i
$470$	16.6453	+	31.4242i	0.767790	+	1.44949i
$471$		0			0
$472$	0.382053	−	0.0334253i	0.0175854	−	0.00153852i
$473$	20.2713	−	1.77351i	0.932077	−	0.0815462i
$474$		0			0
$475$	7.96853	+	2.01340i	0.365621	+	0.0923810i
$476$	−9.84196	−	5.68226i	−0.451105	−	0.260446i
$477$		0			0
$478$	−6.88474	+	25.6942i	−0.314901	+	1.17523i
$479$	4.41454	+	25.0361i	0.201706	+	1.14393i	0.902540	+	0.430606i	$0.141700\pi$
$479$	4.41454	+	25.0361i	0.201706	+	1.14393i	−0.700835	+	0.713324i	$0.747189\pi$
$480$		0			0
$481$	−8.32264	+	3.02919i	−0.379480	+	0.138119i
$482$	−41.7314	+	29.2206i	−1.90081	+	1.33096i
$483$		0			0
$484$	−2.19744	−	2.61881i	−0.0998838	−	0.119037i
$485$	1.46449	+	28.8102i	0.0664991	+	1.30821i
$486$		0			0
$487$	−20.8770	+	20.8770i	−0.946027	+	0.946027i	−0.998616	−	0.0525891i	$-0.983253\pi$
$487$	−20.8770	+	20.8770i	−0.946027	+	0.946027i	0.0525891	+	0.998616i	$0.483253\pi$
$488$	−0.0149909	+	0.171347i	−0.000678606	+	0.00775651i
$489$		0			0
$490$	−22.2055	−	2.76191i	−1.00314	−	0.124771i
$491$	4.08765	+	11.2307i	0.184473	+	0.506835i	0.997113	−	0.0759306i	$-0.0241927\pi$
$491$	4.08765	+	11.2307i	0.184473	+	0.506835i	−0.812640	+	0.582766i	$0.801971\pi$
$492$		0			0
$493$	−6.44648	+	9.20652i	−0.290335	+	0.414641i
$494$	5.00448	+	8.66802i	0.225162	+	0.389993i
$495$		0			0
$496$	13.1638	−	22.8004i	0.591074	−	1.02377i
$497$	−0.664789	−	1.42564i	−0.0298199	−	0.0639489i
$498$		0			0
$499$	3.31792	−	3.95415i	0.148531	−	0.177012i	−0.686649	−	0.726989i	$-0.740919\pi$
$499$	3.31792	−	3.95415i	0.148531	−	0.177012i	0.835180	+	0.549977i	$0.185364\pi$
$500$	21.5761	−	5.27162i	0.964912	−	0.235754i
$501$		0			0
$502$	36.5024	−	17.0214i	1.62918	−	0.759700i
$503$	2.60729	+	9.73055i	0.116253	+	0.433864i	0.999378	−	0.0352755i	$-0.0112309\pi$
$503$	2.60729	+	9.73055i	0.116253	+	0.433864i	−0.883124	+	0.469139i	$0.844564\pi$
$504$		0			0
$505$	−2.47345	+	11.5474i	−0.110067	+	0.513854i
$506$	−44.9144	+	7.91962i	−1.99669	+	0.352070i
$507$		0			0
$508$	11.9714	+	5.58236i	0.531145	+	0.247677i
$509$	5.57060	−	31.5924i	0.246912	−	1.40031i	−0.569097	−	0.822270i	$-0.692707\pi$
$509$	5.57060	−	31.5924i	0.246912	−	1.40031i	0.816009	−	0.578039i	$-0.196182\pi$
$510$		0			0
$511$	9.16349	−	7.68908i	0.405369	−	0.340145i
$512$	−22.5864	−	22.5864i	−0.998188	−	0.998188i
$513$		0			0
$514$		−	17.1113i		−	0.754749i
$515$	5.28513	−	4.91296i	0.232891	−	0.216491i
$516$		0			0
$517$	16.2941	+	23.2704i	0.716615	+	1.02343i
$518$	3.45537	−	7.41007i	0.151820	−	0.325580i
$519$		0			0
$520$	−0.154674	−	0.0969895i	−0.00678292	−	0.00425327i
$521$	5.58144	−	3.22245i	0.244528	−	0.141178i	−0.372728	−	0.927941i	$-0.621578\pi$
$521$	5.58144	−	3.22245i	0.244528	−	0.141178i	0.617256	+	0.786762i	$0.288244\pi$
$522$		0			0
$523$	−6.76374	+	1.81234i	−0.295758	+	0.0792481i	−0.403647	−	0.914915i	$-0.632258\pi$
$523$	−6.76374	+	1.81234i	−0.295758	+	0.0792481i	0.107889	+	0.994163i	$0.465591\pi$
$524$	−22.0619	−	8.02986i	−0.963777	−	0.350786i
$525$		0			0
$526$	−30.8990	−	25.9273i	−1.34726	−	1.13049i
$527$	−2.31205	−	26.4268i	−0.100714	−	1.15117i
$528$		0			0
$529$	−6.16176	+	16.9293i	−0.267902	+	0.736056i
$530$	16.2659	+	50.3304i	0.706547	+	2.18621i
$531$		0			0
$532$	−4.44745	−	1.19169i	−0.192821	−	0.0516663i
$533$	−23.0353	−	16.1295i	−0.997770	−	0.698646i
$534$		0			0
$535$	26.5913	−	11.2381i	1.14964	−	0.485863i
$536$	−0.307637	−	0.0542447i	−0.0132879	−	0.00234301i
$537$		0			0
$538$	−23.5745	−	2.06250i	−1.01637	−	0.0889208i
$539$	−17.8758			−0.769966
$540$		0			0
$541$	−34.0530			−1.46405			−0.732026	−	0.681276i	$-0.761425\pi$
$541$	−34.0530			−1.46405			−0.732026	+	0.681276i	$0.761425\pi$
$542$	−49.2630	−	4.30996i	−2.11603	−	0.185128i
$543$		0			0
$544$	−31.9097	−	5.62655i	−1.36812	−	0.241236i
$545$	−15.1728	−	6.15796i	−0.649931	−	0.263778i
$546$		0			0
$547$	20.2173	+	14.1563i	0.864431	+	0.605281i	0.919451	−	0.393204i	$-0.128633\pi$
$547$	20.2173	+	14.1563i	0.864431	+	0.605281i	−0.0550200	+	0.998485i	$0.517522\pi$
$548$	23.2508	+	6.23002i	0.993224	+	0.266133i
$549$		0			0
$550$	33.2814	−	12.6557i	1.41913	−	0.539640i
$551$	−1.55740	+	4.27891i	−0.0663474	+	0.182288i
$552$		0			0
$553$	−0.672056	−	7.68163i	−0.0285787	−	0.326656i
$554$	44.6166	+	37.4378i	1.89558	+	1.59058i
$555$		0			0
$556$	24.3149	+	8.84992i	1.03118	+	0.375320i
$557$	8.51625	−	2.28192i	0.360845	−	0.0966881i	−0.0738415	−	0.997270i	$-0.523526\pi$
$557$	8.51625	−	2.28192i	0.360845	−	0.0966881i	0.434686	+	0.900582i	$0.356859\pi$
$558$		0			0
$559$	−15.0679	+	8.69945i	−0.637304	+	0.367948i
$560$	12.3743	−	2.83636i	0.522910	−	0.119858i
$561$		0			0
$562$	−24.7566	+	53.0907i	−1.04429	+	2.23950i
$563$	13.3979	+	19.1342i	0.564655	+	0.806411i	0.995374	−	0.0960749i	$-0.0306288\pi$
$563$	13.3979	+	19.1342i	0.564655	+	0.806411i	−0.430719	+	0.902486i	$0.641740\pi$
$564$		0			0
$565$	23.1707	+	24.9260i	0.974800	+	1.04864i
$566$		−	27.1052i		−	1.13932i
$567$		0			0
$568$	−0.0211206	−	0.0211206i	−0.000886202	−	0.000886202i
$569$	−1.82798	+	1.53386i	−0.0766330	+	0.0643027i	−0.680300	−	0.732934i	$-0.738150\pi$
$569$	−1.82798	+	1.53386i	−0.0766330	+	0.0643027i	0.603667	+	0.797237i	$0.293706\pi$
$570$		0			0
$571$	6.32573	−	35.8750i	0.264724	−	1.50132i	−0.505097	−	0.863063i	$-0.668543\pi$
$571$	6.32573	−	35.8750i	0.264724	−	1.50132i	0.769821	−	0.638260i	$-0.220346\pi$
$572$	19.5832	+	9.13180i	0.818815	+	0.381820i
$573$		0			0
$574$	25.5654	−	4.50787i	1.06708	−	0.188155i
$575$	5.10868	−	31.6116i	0.213047	−	1.31830i
$576$		0			0
$577$	−6.50782	−	24.2875i	−0.270924	−	1.01110i	−0.958524	−	0.285012i	$-0.908002\pi$
$577$	−6.50782	−	24.2875i	−0.270924	−	1.01110i	0.687600	−	0.726090i	$-0.258664\pi$
$578$	0.975058	−	0.454677i	0.0405571	−	0.0189121i
$579$		0			0
$580$	1.69343	+	12.1883i	0.0703157	+	0.506091i
$581$	−5.50616	+	6.56198i	−0.228434	+	0.272237i
$582$		0			0
$583$	17.8576	+	38.2957i	0.739586	+	1.58605i
$584$	0.113570	−	0.196709i	0.00469955	−	0.00813986i
$585$		0			0
$586$	8.24353	+	14.2782i	0.340537	+	0.589828i
$587$	−17.4662	+	24.9444i	−0.720909	+	1.02956i	0.276734	+	0.960947i	$0.410748\pi$
$587$	−17.4662	+	24.9444i	−0.720909	+	1.02956i	−0.997643	+	0.0686181i	$0.978141\pi$
$588$		0			0
$589$	−3.67594	−	10.0996i	−0.151465	−	0.416145i
$590$	7.89375	−	63.4649i	0.324980	−	2.61281i
$591$		0			0
$592$	1.01923	−	11.6499i	0.0418901	−	0.478806i
$593$	26.7405	−	26.7405i	1.09810	−	1.09810i	0.103470	−	0.994633i	$-0.467005\pi$
$593$	26.7405	−	26.7405i	1.09810	−	1.09810i	0.994633	−	0.103470i	$-0.0329946\pi$
$594$		0			0
$595$	8.57423	−	9.49260i	0.351509	−	0.389159i
$596$	−4.58708	−	5.46667i	−0.187894	−	0.223924i
$597$		0			0
$598$	31.9435	−	22.3671i	1.30627	−	0.914658i
$599$	1.09294	−	0.397799i	0.0446564	−	0.0162536i	−0.319595	−	0.947554i	$-0.603547\pi$
$599$	1.09294	−	0.397799i	0.0446564	−	0.0162536i	0.364252	+	0.931301i	$0.381325\pi$
$600$		0			0
$601$	2.53128	+	14.3556i	0.103253	+	0.585578i	0.991904	+	0.126993i	$0.0405325\pi$
$601$	2.53128	+	14.3556i	0.103253	+	0.585578i	−0.888650	+	0.458585i	$0.848356\pi$
$602$	4.15709	−	15.5145i	0.169430	−	0.632323i
$603$		0			0
$604$	0.761360	+	0.439571i	0.0309793	+	0.0178859i
$605$	3.40035	−	1.80115i	0.138244	−	0.0732272i
$606$		0			0
$607$	−33.0709	+	2.89333i	−1.34231	+	0.117437i	−0.735560	−	0.677459i	$-0.763081\pi$
$607$	−33.0709	+	2.89333i	−1.34231	+	0.117437i	−0.606746	+	0.794896i	$0.707525\pi$
$608$	−13.0777	+	1.14415i	−0.530372	+	0.0464015i
$609$		0			0
$610$	27.4162	+	8.42909i	1.11005	+	0.341284i
$611$	−21.0356	−	12.1449i	−0.851008	−	0.491330i
$612$		0			0
$613$	3.05733	−	11.4101i	0.123484	−	0.460849i	−0.876297	−	0.481772i	$-0.839994\pi$
$613$	3.05733	−	11.4101i	0.123484	−	0.460849i	0.999781	+	0.0209221i	$0.00666018\pi$
$614$	3.59845	+	20.4078i	0.145221	+	0.823592i
$615$		0			0
$616$	0.126518	−	0.0460490i	0.00509757	−	0.00185537i
$617$	−37.7549	+	26.4363i	−1.51996	+	1.06428i	−0.545935	+	0.837827i	$0.683826\pi$
$617$	−37.7549	+	26.4363i	−1.51996	+	1.06428i	−0.974021	+	0.226458i	$0.927285\pi$
$618$		0			0
$619$	8.15117	+	9.71419i	0.327623	+	0.390446i	0.904563	−	0.426341i	$-0.140198\pi$
$619$	8.15117	+	9.71419i	0.327623	+	0.390446i	−0.576939	+	0.816787i	$0.695753\pi$
$620$	−21.5537	−	19.4684i	−0.865617	−	0.781871i
$621$		0			0
$622$	−26.9448	+	26.9448i	−1.08039	+	1.08039i
$623$	−0.0182496	+	0.208594i	−0.000731154	+	0.00835713i
$624$		0			0
$625$	0.715439	+	24.9898i	0.0286176	+	0.999590i
$626$	−11.2420	−	30.8872i	−0.449321	−	1.23450i
$627$		0			0
$628$	−1.45276	+	2.07476i	−0.0579714	+	0.0827918i
$629$	−5.89161	−	10.2046i	−0.234914	−	0.406883i
$630$		0			0
$631$	16.7330	−	28.9824i	0.666131	−	1.15377i	−0.312847	−	0.949804i	$-0.601283\pi$
$631$	16.7330	−	28.9824i	0.666131	−	1.15377i	0.978977	−	0.203969i	$-0.0653841\pi$
$632$	−0.0618790	−	0.132700i	−0.00246142	−	0.00527852i
$633$		0			0
$634$	9.59010	−	11.4290i	0.380871	−	0.453905i
$635$	−8.96630	+	11.8599i	−0.355817	+	0.470644i
$636$		0			0
$637$	13.8524	−	6.45949i	0.548853	−	0.255934i
$638$	5.10571	+	19.0548i	0.202137	+	0.754385i
$639$		0			0
$640$	0.402066	−	0.260207i	0.0158930	−	0.0102856i
$641$	2.02936	−	0.357831i	0.0801548	−	0.0141335i	−0.133427	−	0.991059i	$-0.542598\pi$
$641$	2.02936	−	0.357831i	0.0801548	−	0.0141335i	0.213582	+	0.976925i	$0.431487\pi$
$642$		0			0
$643$	−29.5810	−	13.7938i	−1.16656	−	0.543976i	−0.259816	−	0.965658i	$-0.583662\pi$
$643$	−29.5810	−	13.7938i	−1.16656	−	0.543976i	−0.906744	+	0.421682i	$0.861440\pi$
$644$	−3.11506	+	17.6664i	−0.122750	+	0.696153i
$645$		0			0
$646$	−10.2007	+	8.55944i	−0.401343	+	0.336767i
$647$	10.7867	+	10.7867i	0.424069	+	0.424069i	0.886602	−	0.462533i	$-0.153059\pi$
$647$	10.7867	+	10.7867i	0.424069	+	0.424069i	−0.462533	+	0.886602i	$0.653059\pi$
$648$		0			0
$649$		−	51.0904i		−	2.00547i
$650$	−21.2174	+	21.8336i	−0.832216	+	0.856383i
$651$		0			0
$652$	−4.07851	−	5.82472i	−0.159727	−	0.228114i
$653$	7.69299	−	16.4977i	0.301050	−	0.645604i	−0.696347	−	0.717705i	$-0.745193\pi$
$653$	7.69299	−	16.4977i	0.301050	−	0.645604i	0.997397	+	0.0721010i	$0.0229704\pi$
$654$		0			0
$655$	14.0389	−	22.3886i	0.548545	−	0.874794i
$656$	32.1559	−	18.5652i	1.25548	−	0.724851i
$657$		0			0
$658$	21.6590	−	5.80351i	0.844356	−	0.226245i
$659$	1.94388	+	0.707516i	0.0757229	+	0.0275609i	0.379604	−	0.925149i	$-0.376060\pi$
$659$	1.94388	+	0.707516i	0.0757229	+	0.0275609i	−0.303881	+	0.952710i	$0.598283\pi$
$660$		0			0
$661$	10.2051	+	8.56308i	0.396932	+	0.333065i	0.819306	−	0.573356i	$-0.194359\pi$
$661$	10.2051	+	8.56308i	0.396932	+	0.333065i	−0.422374	+	0.906421i	$0.638803\pi$
$662$	−1.44434	−	16.5089i	−0.0561360	−	0.641638i
$663$		0			0
$664$	−0.0556313	+	0.152846i	−0.00215891	+	0.00593156i
$665$	2.36008	−	4.61399i	0.0915201	−	0.178923i
$666$		0			0
$667$	17.1364	+	4.59169i	0.663525	+	0.177791i
$668$	19.6318	+	13.7463i	0.759576	+	0.531861i
$669$		0			0
$670$	−19.5900	+	48.2685i	−0.756829	+	1.86478i
$671$	22.5654	+	3.97889i	0.871128	+	0.153603i
$672$		0			0
$673$	38.3246	+	3.35297i	1.47730	+	0.129247i	0.797132	−	0.603805i	$-0.206349\pi$
$673$	38.3246	+	3.35297i	1.47730	+	0.129247i	0.680172	+	0.733052i	$0.261905\pi$
$674$	−31.3440			−1.20732
$675$		0			0
$676$	7.35037			0.282707
$677$	−12.9913	−	1.13659i	−0.499297	−	0.0436829i	−0.165274	−	0.986248i	$-0.552851\pi$
$677$	−12.9913	−	1.13659i	−0.499297	−	0.0436829i	−0.334023	+	0.942565i	$0.608406\pi$
$678$		0			0
$679$	17.9137	+	3.15867i	0.687465	+	0.121219i
$680$	0.0913427	−	0.225062i	0.00350283	−	0.00863075i
$681$		0			0
$682$	−38.1411	−	26.7067i	−1.46050	−	1.02265i
$683$	−22.2351	−	5.95787i	−0.850801	−	0.227972i	−0.193033	−	0.981192i	$-0.561833\pi$
$683$	−22.2351	−	5.95787i	−0.850801	−	0.227972i	−0.657768	+	0.753221i	$0.728499\pi$
$684$		0			0
$685$	−12.3382	+	24.1214i	−0.471420	+	0.921631i
$686$	−11.5659	+	31.7770i	−0.441587	+	1.21325i
$687$		0			0
$688$	−2.00225	−	22.8859i	−0.0763352	−	0.872515i
$689$	−27.6766	−	23.2234i	−1.05439	−	0.884741i
$690$		0			0
$691$	−20.2420	−	7.36747i	−0.770040	−	0.280272i	−0.0730269	−	0.997330i	$-0.523266\pi$
$691$	−20.2420	−	7.36747i	−0.770040	−	0.280272i	−0.697013	+	0.717058i	$0.745488\pi$
$692$	11.1504	−	2.98774i	0.423874	−	0.113577i
$693$		0			0
$694$	1.58640	−	0.915908i	0.0602189	−	0.0347674i
$695$	−15.4726	+	24.6750i	−0.586910	+	0.935977i
$696$		0			0
$697$	15.8113	−	33.9074i	0.598894	−	1.28433i
$698$	41.1564	+	58.7774i	1.55779	+	2.22476i
$699$		0			0
$700$	−0.200418	−	14.0038i	−0.00757510	−	0.529294i
$701$			10.6311i			0.401531i	0.979639	+	0.200766i	$0.0643430\pi$
$701$			10.6311i			0.401531i	−0.979639	+	0.200766i	$0.935657\pi$
$702$		0			0
$703$	−3.37571	−	3.37571i	−0.127317	−	0.127317i
$704$	−21.5635	+	18.0939i	−0.812705	+	0.681941i
$705$		0			0
$706$	−1.67378	+	9.49245i	−0.0629934	+	0.357253i
$707$	6.74885	+	3.14704i	0.253816	+	0.118357i
$708$		0			0
$709$	−6.87515	+	1.21227i	−0.258202	+	0.0455279i	−0.301250	−	0.953545i	$-0.597404\pi$
$709$	−6.87515	+	1.21227i	−0.258202	+	0.0455279i	0.0430488	+	0.999073i	$0.486293\pi$
$710$	−4.18161	+	2.70624i	−0.156933	+	0.101563i
$711$		0			0
$712$	0.00102906	+	0.00384049i	3.85655e−5	+	0.000143929i
$713$	−37.9508	+	17.6968i	−1.42127	+	0.662749i
$714$		0			0
$715$	−14.6674	+	19.4007i	−0.548528	+	0.725546i
$716$	−24.9489	+	29.7330i	−0.932386	+	1.11117i
$717$		0			0
$718$	3.18628	+	6.83299i	0.118911	+	0.255005i
$719$	−2.82089	+	4.88592i	−0.105201	+	0.182214i	−0.913820	−	0.406118i	$-0.866882\pi$
$719$	−2.82089	+	4.88592i	−0.105201	+	0.182214i	0.808619	+	0.588333i	$0.200215\pi$
$720$		0			0
$721$	−2.27504	−	3.94049i	−0.0847271	−	0.146752i
$722$	18.6649	−	26.6562i	0.694635	−	0.992041i
$723$		0			0
$724$	7.20710	+	19.8013i	0.267850	+	0.735911i
$725$	−13.8138	−	1.00959i	−0.513033	−	0.0374952i
$726$		0			0
$727$	−1.05650	+	12.0758i	−0.0391832	+	0.447867i	0.951108	+	0.308858i	$0.0999469\pi$
$727$	−1.05650	+	12.0758i	−0.0391832	+	0.447867i	−0.990291	+	0.139008i	$0.955609\pi$
$728$	−0.0814023	+	0.0814023i	−0.00301697	+	0.00301697i
$729$		0			0
$730$	−28.1086	−	25.3892i	−1.04034	−	0.939695i
$731$	−14.8791	−	17.7323i	−0.550325	−	0.655852i
$732$		0			0
$733$	−1.15449	+	0.808383i	−0.0426421	+	0.0298583i	−0.594703	−	0.803945i	$-0.702730\pi$
$733$	−1.15449	+	0.808383i	−0.0426421	+	0.0298583i	0.552061	+	0.833804i	$0.313842\pi$
$734$	47.3029	−	17.2169i	1.74598	−	0.635486i
$735$		0			0
$736$	8.88151	+	50.3696i	0.327377	+	1.85665i
$737$	−10.7707	+	40.1967i	−0.396743	+	1.48066i
$738$		0			0
$739$	7.65920	+	4.42204i	0.281748	+	0.162667i	0.634215	−	0.773157i	$-0.281324\pi$
$739$	7.65920	+	4.42204i	0.281748	+	0.162667i	−0.352466	+	0.935824i	$0.614657\pi$
$740$	−12.3315	−	3.79130i	−0.453313	−	0.139371i
$741$		0			0
$742$	33.2257	−	2.90687i	1.21975	−	0.106715i
$743$	−20.2590	+	1.77243i	−0.743230	+	0.0650242i	−0.452480	−	0.891775i	$-0.649461\pi$
$743$	−20.2590	+	1.77243i	−0.743230	+	0.0650242i	−0.290751	+	0.956799i	$0.593905\pi$
$744$		0			0
$745$	7.09811	−	3.75984i	0.260055	−	0.137750i
$746$	−19.0615	−	11.0052i	−0.697892	−	0.402928i
$747$		0			0
$748$	−7.44034	+	27.7677i	−0.272046	+	1.01529i
$749$	−3.16098	−	17.9268i	−0.115500	−	0.655031i
$750$		0			0
$751$	−8.99657	+	3.27448i	−0.328290	+	0.119488i	−0.500906	−	0.865501i	$-0.667000\pi$
$751$	−8.99657	+	3.27448i	−0.328290	+	0.119488i	0.172617	+	0.984989i	$0.444778\pi$
$752$	26.2718	−	18.3957i	0.958032	−	0.670822i
$753$		0			0
$754$	−10.8420	−	12.9210i	−0.394844	−	0.470556i
$755$	−0.663290	+	0.734334i	−0.0241396	+	0.0267252i
$756$		0			0
$757$	−20.8479	+	20.8479i	−0.757730	+	0.757730i	−0.975909	−	0.218179i	$-0.929988\pi$
$757$	−20.8479	+	20.8479i	−0.757730	+	0.757730i	0.218179	+	0.975909i	$0.429988\pi$
$758$	1.07073	−	12.2385i	0.0388905	−	0.444521i
$759$		0			0
$760$	0.0121464	−	0.0976554i	0.000440595	−	0.00354233i
$761$	9.01441	+	24.7669i	0.326772	+	0.897799i	0.988923	+	0.148428i	$0.0474214\pi$
$761$	9.01441	+	24.7669i	0.326772	+	0.897799i	−0.662151	+	0.749370i	$0.730356\pi$
$762$		0			0
$763$	−5.92236	+	8.45800i	−0.214404	+	0.306200i
$764$	4.74988	+	8.22703i	0.171845	+	0.297644i
$765$		0			0
$766$	17.6017	−	30.4870i	0.635974	−	1.10154i
$767$	18.4617	+	39.5912i	0.666612	+	1.42955i
$768$		0			0
$769$	−28.0565	+	33.4364i	−1.01174	+	1.20575i	−0.0332544	+	0.999447i	$0.510587\pi$
$769$	−28.0565	+	33.4364i	−1.01174	+	1.20575i	−0.978489	+	0.206301i	$0.933857\pi$
$770$	−3.08978	−	22.2384i	−0.111348	−	0.801417i
$771$		0			0
$772$	−9.79577	+	4.56784i	−0.352558	+	0.164400i
$773$	3.07418	+	11.4730i	0.110571	+	0.412655i	0.998917	−	0.0465178i	$-0.0148124\pi$
$773$	3.07418	+	11.4730i	0.110571	+	0.412655i	−0.888347	+	0.459173i	$0.848146\pi$
$774$		0			0
$775$	26.5086	−	19.1326i	0.952216	−	0.687263i
$776$	0.340151	−	0.0599778i	0.0122107	−	0.00215308i
$777$		0			0
$778$	−25.4158	−	11.8516i	−0.911201	−	0.424900i
$779$	2.63212	−	14.9275i	0.0943053	−	0.534832i
$780$		0			0
$781$	−3.04814	+	2.55770i	−0.109071	+	0.0915216i
$782$	36.6853	+	36.6853i	1.31186	+	1.31186i
$783$		0			0
$784$			20.1814i			0.720763i
$785$	−1.94102	−	2.08806i	−0.0692779	−	0.0745259i
$786$		0			0
$787$	31.0074	+	44.2832i	1.10529	+	1.57852i	0.771909	+	0.635733i	$0.219302\pi$
$787$	31.0074	+	44.2832i	1.10529	+	1.57852i	0.333385	+	0.942791i	$0.391809\pi$
$788$	6.74431	−	14.4632i	0.240256	−	0.515231i
$789$		0			0
$790$	−23.7993	+	5.45512i	−0.846741	+	0.194085i
$791$	18.5843	−	10.7297i	0.660783	−	0.381503i
$792$		0			0
$793$	−18.9243	+	5.07074i	−0.672020	+	0.180067i
$794$	56.7853	+	20.6681i	2.01523	+	0.733485i
$795$		0			0
$796$	18.5059	+	15.5283i	0.655925	+	0.550386i
$797$	0.986343	+	11.2740i	0.0349381	+	0.399344i	0.993448	+	0.114285i	$0.0364577\pi$
$797$	0.986343	+	11.2740i	0.0349381	+	0.399344i	−0.958510	+	0.285059i	$0.907987\pi$
$798$		0			0
$799$	11.0526	−	30.3667i	0.391012	−	1.07430i
$800$	−14.1928	−	37.3237i	−0.501791	−	1.31959i
$801$		0			0
$802$	−31.4131	−	8.41712i	−1.10924	−	0.297219i
$803$	−24.7866	−	17.3558i	−0.874701	−	0.612472i
$804$		0			0
$805$	−18.7095	−	7.59334i	−0.659423	−	0.267630i
$806$	39.2070	+	6.91326i	1.38101	+	0.243509i
$807$		0			0
$808$	0.140859	+	0.0123236i	0.00495540	+	0.000433541i
$809$	−3.55739			−0.125071			−0.0625355	−	0.998043i	$-0.519919\pi$
$809$	−3.55739			−0.125071			−0.0625355	+	0.998043i	$0.519919\pi$
$810$		0			0
$811$	46.5652			1.63512			0.817562	−	0.575840i	$-0.195325\pi$
$811$	46.5652			1.63512			0.817562	+	0.575840i	$0.195325\pi$
$812$	7.72975	+	0.676266i	0.271261	+	0.0237323i
$813$		0			0
$814$	−20.3678	−	3.59139i	−0.713891	−	0.125878i
$815$	7.37228	−	3.11569i	0.258240	−	0.109138i
$816$		0			0
$817$	−7.68231	−	5.37921i	−0.268770	−	0.188195i
$818$	−37.7438	−	10.1134i	−1.31968	−	0.353607i
$819$		0			0
$820$	−12.5967	−	38.9770i	−0.439897	−	1.36114i
$821$	14.8508	−	40.8021i	0.518295	−	1.42400i	−0.354102	−	0.935207i	$-0.615213\pi$
$821$	14.8508	−	40.8021i	0.518295	−	1.42400i	0.872397	−	0.488798i	$-0.162564\pi$
$822$		0			0
$823$	1.59358	+	18.2148i	0.0555489	+	0.634926i	0.972031	+	0.234851i	$0.0754604\pi$
$823$	1.59358	+	18.2148i	0.0555489	+	0.634926i	−0.916482	+	0.400075i	$0.868984\pi$
$824$	−0.0661850	−	0.0555358i	−0.00230567	−	0.00193468i
$825$		0			0
$826$	−37.8948	−	13.7926i	−1.31853	−	0.479905i
$827$	38.7367	−	10.3795i	1.34701	−	0.360929i	0.487978	−	0.872856i	$-0.337735\pi$
$827$	38.7367	−	10.3795i	1.34701	−	0.360929i	0.859029	+	0.511927i	$0.171068\pi$
$828$		0			0
$829$	−23.7438	+	13.7085i	−0.824656	+	0.476115i	−0.852019	−	0.523510i	$-0.824622\pi$
$829$	−23.7438	+	13.7085i	−0.824656	+	0.476115i	0.0273634	+	0.999626i	$0.491289\pi$
$830$	22.9799	+	14.4097i	0.797644	+	0.500168i
$831$		0			0
$832$	10.1718	−	21.8135i	0.352643	−	0.756246i
$833$	11.6635	+	16.6572i	0.404117	+	0.577139i
$834$		0			0
$835$	−19.7576	+	18.3663i	−0.683740	+	0.635593i
$836$			11.6470i			0.402819i
$837$		0			0
$838$	−0.260063	−	0.260063i	−0.00898371	−	0.00898371i
$839$	29.8408	−	25.0394i	1.03022	−	0.864456i	0.0393413	−	0.999226i	$-0.487474\pi$
$839$	29.8408	−	25.0394i	1.03022	−	0.864456i	0.990877	+	0.134770i	$0.0430296\pi$
$840$		0			0
$841$	−3.70328	+	21.0024i	−0.127699	+	0.724219i
$842$	33.1130	+	15.4408i	1.14115	+	0.532126i
$843$		0			0
$844$	5.83537	−	1.02893i	0.200862	−	0.0354174i
$845$	−1.73286	+	8.08993i	−0.0596121	+	0.278302i
$846$		0			0
$847$	−0.627986	−	2.34368i	−0.0215779	−	0.0805297i
$848$	43.2350	−	20.1608i	1.48469	−	0.692324i
$849$		0			0
$850$	−33.5082	−	22.7551i	−1.14932	−	0.780495i
$851$	−11.9557	+	14.2483i	−0.409838	+	0.488425i
$852$		0			0
$853$	−17.4323	−	37.3837i	−0.596871	−	1.27999i	−0.940150	−	0.340761i	$-0.889315\pi$
$853$	−17.4323	−	37.3837i	−0.596871	−	1.27999i	0.343279	−	0.939234i	$-0.388462\pi$
$854$	9.04308	−	15.6631i	0.309448	−	0.535980i
$855$		0			0
$856$	−0.172825	−	0.299342i	−0.00590705	−	0.0102313i
$857$	19.3368	−	27.6158i	0.660532	−	0.943338i	−0.339464	−	0.940619i	$-0.610246\pi$
$857$	19.3368	−	27.6158i	0.660532	−	0.943338i	0.999996	−	0.00271892i	$-0.000865461\pi$
$858$		0			0
$859$	10.4264	+	28.6463i	0.355745	+	0.977401i	0.980489	+	0.196572i	$0.0629808\pi$
$859$	10.4264	+	28.6463i	0.355745	+	0.977401i	−0.624745	+	0.780829i	$0.714797\pi$
$860$	−25.1501	−	3.12817i	−0.857612	−	0.106670i
$861$		0			0
$862$	−3.55542	+	40.6387i	−0.121098	+	1.38416i
$863$	32.8323	−	32.8323i	1.11763	−	1.11763i	0.125536	−	0.992089i	$-0.459935\pi$
$863$	32.8323	−	32.8323i	1.11763	−	1.11763i	0.992089	−	0.125536i	$-0.0400652\pi$
$864$		0			0
$865$	0.659633	+	12.9766i	0.0224282	+	0.441219i
$866$	2.54240	+	3.02991i	0.0863941	+	0.102960i
$867$		0			0
$868$	−15.0022	+	10.5047i	−0.509208	+	0.356551i
$869$	−18.3291	+	6.67124i	−0.621772	+	0.226306i
$870$		0			0
$871$	−6.17875	−	35.0414i	−0.209359	−	1.18733i
$872$	−0.0507441	+	0.189380i	−0.00171841	+	0.00641320i
$873$		0			0
$874$	18.2035	+	10.5098i	0.615741	+	0.355498i
$875$	15.4600	+	3.08083i	0.522645	+	0.104151i
$876$		0			0
$877$	29.3879	−	2.57111i	0.992358	−	0.0868201i	0.420603	−	0.907245i	$-0.361818\pi$
$877$	29.3879	−	2.57111i	0.992358	−	0.0868201i	0.571755	+	0.820425i	$0.306263\pi$
$878$	−28.1420	+	2.46211i	−0.949747	+	0.0830921i
$879$		0			0
$880$	−15.0317	−	28.3781i	−0.506720	−	0.956624i
$881$	−12.5327	−	7.23578i	−0.422239	−	0.243780i	0.273796	−	0.961788i	$-0.411721\pi$
$881$	−12.5327	−	7.23578i	−0.422239	−	0.243780i	−0.696035	+	0.718008i	$0.745054\pi$
$882$		0			0
$883$	−8.19438	+	30.5819i	−0.275763	+	1.02916i	0.679565	+	0.733615i	$0.262168\pi$
$883$	−8.19438	+	30.5819i	−0.275763	+	1.02916i	−0.955328	+	0.295547i	$0.904498\pi$
$884$	−4.26826	−	24.2065i	−0.143557	−	0.814153i
$885$		0			0
$886$	30.1088	−	10.9587i	1.01153	−	0.368166i
$887$	−10.4193	+	7.29567i	−0.349846	+	0.244965i	−0.735269	−	0.677775i	$-0.762944\pi$
$887$	−10.4193	+	7.29567i	−0.349846	+	0.244965i	0.385423	+	0.922740i	$0.374055\pi$
$888$		0			0
$889$	6.02616	+	7.18169i	0.202111	+	0.240866i
$890$	0.662171	−	0.0336597i	0.0221960	−	0.00112828i
$891$		0			0
$892$	11.3726	−	11.3726i	0.380784	−	0.380784i
$893$	1.14110	−	13.0429i	0.0381856	−	0.436463i
$894$		0			0
$895$	−26.8428	−	34.4688i	−0.897257	−	1.15216i
$896$	−0.103286	−	0.283776i	−0.00345055	−	0.00948030i
$897$		0			0
$898$	−6.55492	+	9.36140i	−0.218741	+	0.312394i
$899$	9.05610	+	15.6856i	0.302038	+	0.523145i
$900$		0			0
$901$	24.0335	−	41.6272i	0.800672	−	1.38680i
$902$	−27.7520	−	59.5145i	−0.924042	−	1.98161i
$903$		0			0
$904$	0.261921	−	0.312145i	0.00871135	−	0.0103818i
$905$	−23.4927	+	3.26405i	−0.780925	+	0.108501i
$906$		0			0
$907$	49.0966	−	22.8941i	1.63023	−	0.760188i	0.630357	−	0.776305i	$-0.282908\pi$
$907$	49.0966	−	22.8941i	1.63023	−	0.760188i	0.999870	+	0.0161177i	$0.00513063\pi$
$908$	3.96353	+	14.7921i	0.131534	+	0.490892i
$909$		0			0
$910$	10.4303	+	16.1166i	0.345760	+	0.534260i
$911$	11.6520	−	2.05456i	0.386047	−	0.0680705i	0.0227434	−	0.999741i	$-0.492760\pi$
$911$	11.6520	−	2.05456i	0.386047	−	0.0680705i	0.363303	+	0.931671i	$0.381649\pi$
$912$		0			0
$913$	19.6383	+	9.15747i	0.649931	+	0.303068i
$914$	−6.85089	+	38.8533i	−0.226607	+	1.28515i
$915$		0			0
$916$	6.95094	−	5.83253i	0.229666	−	0.192712i
$917$	−11.7827	−	11.7827i	−0.389099	−	0.389099i
$918$		0			0
$919$		−	33.2177i		−	1.09575i	−0.836560	−	0.547875i	$-0.815437\pi$
$919$		−	33.2177i		−	1.09575i	0.836560	−	0.547875i	$-0.184563\pi$
$920$	−0.383151	−	0.0139827i	−0.0126321	−	0.000460997i
$921$		0			0
$922$	−20.7333	−	29.6102i	−0.682815	−	0.975161i
$923$	1.43785	−	3.08348i	0.0473274	−	0.101494i
$924$		0			0
$925$	7.07991	−	12.6784i	0.232786	−	0.416862i
$926$	−22.6234	+	13.0616i	−0.743452	+	0.429232i
$927$		0			0
$928$	21.3691	−	5.72583i	0.701475	−	0.187960i
$929$	−29.9496	−	10.9008i	−0.982616	−	0.357643i	−0.199759	−	0.979845i	$-0.564016\pi$
$929$	−29.9496	−	10.9008i	−0.982616	−	0.357643i	−0.782857	+	0.622202i	$0.786238\pi$
$930$		0			0
$931$	6.31115	+	5.29569i	0.206840	+	0.173559i
$932$	−3.46630	−	39.6200i	−0.113543	−	1.29780i
$933$		0			0
$934$	−5.56470	+	15.2889i	−0.182083	+	0.500268i
$935$	−28.8075	−	14.7352i	−0.942107	−	0.481893i
$936$		0			0
$937$	9.56398	+	2.56266i	0.312441	+	0.0837184i	0.411632	−	0.911350i	$-0.364959\pi$
$937$	9.56398	+	2.56266i	0.312441	+	0.0837184i	−0.0991909	+	0.995068i	$0.531625\pi$
$938$	26.9070	+	18.8405i	0.878546	+	0.615165i
$939$		0			0
$940$	−13.7734	−	32.5905i	−0.449240	−	1.06298i
$941$	31.4053	+	5.53759i	1.02378	+	0.180520i	0.660238	−	0.751057i	$-0.270455\pi$
$941$	31.4053	+	5.53759i	1.02378	+	0.180520i	0.363544	+	0.931577i	$0.381567\pi$
$942$		0			0
$943$	−58.8312	−	5.14706i	−1.91581	−	0.167611i
$944$	−57.6798			−1.87732
$945$		0			0
$946$	−40.6293			−1.32097
$947$	14.1237	+	1.23567i	0.458959	+	0.0401537i	0.314291	−	0.949327i	$-0.398233\pi$
$947$	14.1237	+	1.23567i	0.458959	+	0.0401537i	0.144668	+	0.989480i	$0.453789\pi$
$948$		0			0
$949$	25.4793	+	4.49269i	0.827094	+	0.145839i
$950$	−15.4994	−	5.39142i	−0.502868	−	0.174921i
$951$		0			0
$952$	−0.125460	−	0.0878480i	−0.00406618	−	0.00284717i
$953$	−19.5249	−	5.23169i	−0.632475	−	0.169471i	−0.0716822	−	0.997428i	$-0.522837\pi$
$953$	−19.5249	−	5.23169i	−0.632475	−	0.169471i	−0.560792	+	0.827956i	$0.689503\pi$
$954$		0			0
$955$	−10.1746	+	3.28826i	−0.329242	+	0.106405i
$956$	9.05213	−	24.8705i	0.292767	−	0.804370i
$957$		0			0
$958$	−4.42397	−	50.5662i	−0.142932	−	1.63372i
$959$	13.0873	+	10.9816i	0.422612	+	0.354613i
$960$		0			0
$961$	−11.0418	−	4.01888i	−0.356186	−	0.129641i
$962$	17.0813	−	4.57691i	0.550722	−	0.147565i
$963$		0			0
$964$	43.8972	−	25.3440i	1.41383	−	0.816277i
$965$	−2.71807	−	11.8582i	−0.0874979	−	0.381730i
$966$		0			0
$967$	7.28255	−	15.6175i	0.234191	−	0.502224i	−0.753730	−	0.657185i	$-0.771747\pi$
$967$	7.28255	−	15.6175i	0.234191	−	0.502224i	0.987921	+	0.154960i	$0.0495250\pi$
$968$	−0.0264260	−	0.0377402i	−0.000849363	−	0.00121302i
$969$		0			0
$970$	2.10059	−	57.5597i	0.0674458	−	1.84813i
$971$			4.56855i			0.146612i	0.997310	+	0.0733058i	$0.0233549\pi$
$971$			4.56855i			0.146612i	−0.997310	+	0.0733058i	$0.976645\pi$
$972$		0			0
$973$	12.9860	+	12.9860i	0.416313	+	0.416313i
$974$	45.1583	−	37.8923i	1.44697	−	1.21415i
$975$		0			0
$976$	4.49207	−	25.4758i	0.143788	−	0.815460i
$977$	16.0559	+	7.48700i	0.513675	+	0.239530i	0.662130	−	0.749389i	$-0.269652\pi$
$977$	16.0559	+	7.48700i	0.513675	+	0.239530i	−0.148456	+	0.988919i	$0.547430\pi$
$978$		0			0
$979$	0.521620	−	0.0919757i	0.0166711	−	0.00293956i
$980$	21.7701	+	4.66314i	0.695420	+	0.148959i
$981$		0			0
$982$	−6.17616	−	23.0498i	−0.197089	−	0.735547i
$983$	−39.7929	+	18.5557i	−1.26920	+	0.591836i	−0.936324	−	0.351136i	$-0.885795\pi$
$983$	−39.7929	+	18.5557i	−1.26920	+	0.591836i	−0.332872	+	0.942972i	$0.608018\pi$
$984$		0			0
$985$	14.3285	+	10.8326i	0.456543	+	0.345156i
$986$	14.4245	−	17.1904i	0.459368	−	0.547454i
$987$		0			0
$988$	−4.20867	−	9.02553i	−0.133896	−	0.287140i
$989$	−18.2695	+	31.6436i	−0.580935	+	1.00621i
$990$		0			0
$991$	13.5103	+	23.4004i	0.429167	+	0.743340i	0.996799	−	0.0799428i	$-0.0254738\pi$
$991$	13.5103	+	23.4004i	0.429167	+	0.743340i	−0.567632	+	0.823282i	$0.692140\pi$
$992$	−29.9504	+	42.7736i	−0.950926	+	1.35806i
$993$		0			0
$994$	1.07421	+	2.95136i	0.0340718	+	0.0936115i
$995$	−21.4535	+	16.7071i	−0.680121	+	0.529650i
$996$		0			0
$997$	1.63906	−	18.7346i	0.0519096	−	0.593329i	−0.925041	−	0.379866i	$-0.875970\pi$
$997$	1.63906	−	18.7346i	0.0519096	−	0.593329i	0.976951	−	0.213463i	$-0.0684744\pi$
$998$	−7.28760	+	7.28760i	−0.230685	+	0.230685i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.368.3		192
3.2	odd	2		135.2.q.a.113.14	yes	192
5.2	odd	4	inner	405.2.r.a.287.14		192
15.2	even	4		135.2.q.a.32.3	✓	192
15.8	even	4		675.2.ba.b.32.14		192
15.14	odd	2		675.2.ba.b.518.3		192
27.11	odd	18	inner	405.2.r.a.278.14		192
27.16	even	9		135.2.q.a.38.3	yes	192
135.43	odd	36		675.2.ba.b.632.3		192
135.92	even	36	inner	405.2.r.a.197.3		192
135.97	odd	36		135.2.q.a.92.14	yes	192
135.124	even	18		675.2.ba.b.443.14		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.3	✓	192	15.2	even	4
135.2.q.a.38.3	yes	192	27.16	even	9
135.2.q.a.92.14	yes	192	135.97	odd	36
135.2.q.a.113.14	yes	192	3.2	odd	2
405.2.r.a.197.3		192	135.92	even	36	inner
405.2.r.a.278.14		192	27.11	odd	18	inner
405.2.r.a.287.14		192	5.2	odd	4	inner
405.2.r.a.368.3		192	1.1	even	1	trivial
675.2.ba.b.32.14		192	15.8	even	4
675.2.ba.b.443.14		192	135.124	even	18
675.2.ba.b.518.3		192	15.14	odd	2
675.2.ba.b.632.3		192	135.43	odd	36

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.r (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.98905 - 0.174019i) q^{2} +(1.95641 + 0.344968i) q^{4} +(-0.840902 + 2.07193i) q^{5} +(1.15499 + 0.808730i) q^{7} +(0.0258608 + 0.00692938i) q^{8} +(2.03315 - 3.97483i) q^{10} +(1.21986 - 3.35154i) q^{11} +(0.265789 + 3.03799i) q^{13} +(-2.15659 - 1.80959i) q^{14} +(-3.78380 - 1.37719i) q^{16} +(-3.91899 + 1.05009i) q^{17} +(-1.42357 + 0.821896i) q^{19} +(-2.35990 + 3.76346i) q^{20} +(-3.00959 + 6.45408i) q^{22} +(3.67339 + 5.24614i) q^{23} +(-3.58577 - 3.48458i) q^{25} -6.08895i q^{26} +(1.98064 + 1.98064i) q^{28} +(2.12205 - 1.78061i) q^{29} +(-1.13538 + 6.43905i) q^{31} +(7.23797 + 3.37512i) q^{32} +(7.97779 - 1.40670i) q^{34} +(-2.64686 + 1.71298i) q^{35} +(0.751675 + 2.80529i) q^{37} +(2.97456 - 1.38706i) q^{38} +(-0.0361036 + 0.0477548i) q^{40} +(-5.92728 + 7.06386i) q^{41} +(2.41117 + 5.17078i) q^{43} +(3.54272 - 6.13617i) q^{44} +(-6.39361 - 11.0741i) q^{46} +(-4.56850 + 6.52449i) q^{47} +(-1.71419 - 4.70971i) q^{49} +(6.52587 + 7.55498i) q^{50} +(-0.528015 + 6.03524i) q^{52} +(-8.37726 + 8.37726i) q^{53} +(5.91836 + 5.34577i) q^{55} +(0.0242649 + 0.0289177i) q^{56} +(-4.53071 + 3.17244i) q^{58} +(13.4607 - 4.89929i) q^{59} +(1.11559 + 6.32681i) q^{61} +(3.37884 - 12.6100i) q^{62} +(-6.83499 - 3.94619i) q^{64} +(-6.51799 - 2.00395i) q^{65} +(-11.6234 + 1.01692i) q^{67} +(-8.02940 + 0.702481i) q^{68} +(5.56282 - 2.94660i) q^{70} +(-0.966172 - 0.557819i) q^{71} +(2.19579 - 8.19480i) q^{73} +(-1.00694 - 5.71065i) q^{74} +(-3.06861 + 1.11688i) q^{76} +(4.11941 - 2.88444i) q^{77} +(-3.51532 - 4.18939i) q^{79} +(6.03525 - 6.68168i) q^{80} +(13.0189 - 13.0189i) q^{82} +(-0.529499 + 6.05220i) q^{83} +(1.11978 - 9.00288i) q^{85} +(-3.89612 - 10.7045i) q^{86} +(0.0547706 - 0.0782205i) q^{88} +(0.0742532 + 0.128610i) q^{89} +(-2.14993 + 3.72378i) q^{91} +(5.37690 + 11.5308i) q^{92} +(10.2223 - 12.1825i) q^{94} +(-0.505829 - 3.64066i) q^{95} +(11.6922 - 5.45218i) q^{97} +(2.59003 + 9.66613i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

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