LMFDB - Embedded newform 432.2.v.a.179.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [432,2,Mod(35,432)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(432, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("432.35"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.v (of order $12$, degree $4$, 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			179.4
Character	$\chi$	$=$	432.179
Dual form			432.2.v.a.251.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.25087 + 0.659799i) q^{2} +(1.12933 - 1.65064i) q^{4} +(-2.03779 + 0.546024i) q^{5} +(-0.0638076 - 0.110518i) q^{7} +(-0.323550 + 2.80986i) q^{8} +(2.18873 - 2.02753i) q^{10} +(0.678695 + 0.181856i) q^{11} +(-1.84311 + 0.493860i) q^{13} +(0.152734 + 0.0961430i) q^{14} +(-1.44923 - 3.72824i) q^{16} -4.32243i q^{17} +(-3.97707 + 3.97707i) q^{19} +(-1.40005 + 3.98030i) q^{20} +(-0.968944 + 0.220325i) q^{22} +(-6.81589 - 3.93516i) q^{23} +(-0.475689 + 0.274639i) q^{25} +(1.97963 - 1.83383i) q^{26} +(-0.254485 - 0.0194880i) q^{28} +(0.926957 + 0.248377i) q^{29} +(-4.91353 - 2.83683i) q^{31} +(4.27267 + 3.70733i) q^{32} +(2.85194 + 5.40679i) q^{34} +(0.190372 + 0.190372i) q^{35} +(-6.64358 + 6.64358i) q^{37} +(2.35071 - 7.59884i) q^{38} +(-0.874924 - 5.90257i) q^{40} +(-4.61325 + 7.99038i) q^{41} +(2.91294 - 10.8712i) q^{43} +(1.06665 - 0.914906i) q^{44} +(11.1222 + 0.425234i) q^{46} +(-5.92267 - 10.2584i) q^{47} +(3.49186 - 6.04807i) q^{49} +(0.413816 - 0.657395i) q^{50} +(-1.26629 + 3.60004i) q^{52} +(-0.00259022 - 0.00259022i) q^{53} -1.48233 q^{55} +(0.331185 - 0.143532i) q^{56} +(-1.32338 + 0.300919i) q^{58} +(1.09748 + 4.09587i) q^{59} +(-1.19213 + 4.44908i) q^{61} +(8.01790 + 0.306548i) q^{62} +(-7.79063 - 1.81826i) q^{64} +(3.48621 - 2.01276i) q^{65} +(-0.538862 - 2.01106i) q^{67} +(-7.13478 - 4.88146i) q^{68} +(-0.363737 - 0.112522i) q^{70} +3.80683i q^{71} +1.87674i q^{73} +(3.92680 - 12.6937i) q^{74} +(2.07328 + 11.0561i) q^{76} +(-0.0232076 - 0.0866118i) q^{77} +(3.00919 - 1.73736i) q^{79} +(4.98892 + 6.80604i) q^{80} +(0.498509 - 13.0387i) q^{82} +(0.394284 - 1.47149i) q^{83} +(2.36015 + 8.80821i) q^{85} +(3.52914 + 15.5204i) q^{86} +(-0.730581 + 1.84820i) q^{88} +10.5967 q^{89} +(0.172185 + 0.172185i) q^{91} +(-14.1929 + 6.80649i) q^{92} +(14.1769 + 8.92407i) q^{94} +(5.93284 - 10.2760i) q^{95} +(3.31795 + 5.74685i) q^{97} +(-0.377331 + 9.86925i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38}+ \cdots - 4 q^{97}+O(q^{100}) $ 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 + 48 * q^20 - 2 * q^22 + 12 * q^23 + 8 * q^28 + 6 * q^29 + 6 * q^32 + 2 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 40 * q^46 - 24 * q^49 - 72 * q^50 - 2 * q^52 - 16 * q^55 - 36 * q^56 + 16 * q^58 + 42 * q^59 - 2 * q^61 - 44 * q^64 + 12 * q^65 - 2 * q^67 - 96 * q^68 - 16 * q^70 - 78 * q^74 - 14 * q^76 + 6 * q^77 - 36 * q^82 - 54 * q^83 + 8 * q^85 - 54 * q^86 + 22 * q^88 + 20 * q^91 - 108 * q^92 + 6 * q^94 - 4 * q^97

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.25087	+	0.659799i	−0.884496	+	0.466548i
$2$	−1.25087	+	0.659799i	−0.884496	+	0.466548i
$3$		0			0
$3$		0			0
$4$	1.12933	−	1.65064i	0.564665	−	0.825320i
$5$	−2.03779	+	0.546024i	−0.911327	+	0.244189i	−0.683874	−	0.729600i	$-0.739706\pi$
$5$	−2.03779	+	0.546024i	−0.911327	+	0.244189i	−0.227452	+	0.973789i	$0.573040\pi$
$6$		0			0
$7$	−0.0638076	−	0.110518i	−0.0241170	−	0.0417719i	0.853715	−	0.520741i	$-0.174344\pi$
$7$	−0.0638076	−	0.110518i	−0.0241170	−	0.0417719i	−0.877832	+	0.478969i	$0.841011\pi$
$8$	−0.323550	+	2.80986i	−0.114392	+	0.993436i
$9$		0			0
$10$	2.18873	−	2.02753i	0.692138	−	0.641162i
$11$	0.678695	+	0.181856i	0.204634	+	0.0548316i	0.359680	−	0.933076i	$-0.382886\pi$
$11$	0.678695	+	0.181856i	0.204634	+	0.0548316i	−0.155046	+	0.987907i	$0.549553\pi$
$12$		0			0
$13$	−1.84311	+	0.493860i	−0.511187	+	0.136972i	−0.505187	−	0.863010i	$-0.668576\pi$
$13$	−1.84311	+	0.493860i	−0.511187	+	0.136972i	−0.00599967	+	0.999982i	$0.501910\pi$
$14$	0.152734	+	0.0961430i	0.0408200	+	0.0256953i
$15$		0			0
$16$	−1.44923	−	3.72824i	−0.362306	−	0.932059i
$17$		−	4.32243i		−	1.04834i	−0.851612	−	0.524172i	$-0.824375\pi$
$17$		−	4.32243i		−	1.04834i	0.851612	−	0.524172i	$-0.175625\pi$
$18$		0			0
$19$	−3.97707	+	3.97707i	−0.912401	+	0.912401i	−0.996461	−	0.0840594i	$-0.973211\pi$
$19$	−3.97707	+	3.97707i	−0.912401	+	0.912401i	0.0840594	+	0.996461i	$0.473211\pi$
$20$	−1.40005	+	3.98030i	−0.313060	+	0.890021i
$21$		0			0
$22$	−0.968944	+	0.220325i	−0.206580	+	0.0469735i
$23$	−6.81589	−	3.93516i	−1.42121	−	0.820537i	−0.424809	−	0.905283i	$-0.639659\pi$
$23$	−6.81589	−	3.93516i	−1.42121	−	0.820537i	−0.996403	+	0.0847463i	$0.972992\pi$
$24$		0			0
$25$	−0.475689	+	0.274639i	−0.0951377	+	0.0549278i
$26$	1.97963	−	1.83383i	0.388238	−	0.359644i
$27$		0			0
$28$	−0.254485	−	0.0194880i	−0.0480932	−	0.00368288i
$29$	0.926957	+	0.248377i	0.172132	+	0.0461225i	0.343855	−	0.939023i	$-0.388267\pi$
$29$	0.926957	+	0.248377i	0.172132	+	0.0461225i	−0.171724	+	0.985145i	$0.554934\pi$
$30$		0			0
$31$	−4.91353	−	2.83683i	−0.882496	−	0.509509i	−0.0110152	−	0.999939i	$-0.503506\pi$
$31$	−4.91353	−	2.83683i	−0.882496	−	0.509509i	−0.871480	+	0.490430i	$0.836840\pi$
$32$	4.27267	+	3.70733i	0.755309	+	0.655369i
$33$		0			0
$34$	2.85194	+	5.40679i	0.489103	+	0.927256i
$35$	0.190372	+	0.190372i	0.0321787	+	0.0321787i
$36$		0			0
$37$	−6.64358	+	6.64358i	−1.09220	+	1.09220i	−0.0969037	+	0.995294i	$0.530894\pi$
$37$	−6.64358	+	6.64358i	−1.09220	+	1.09220i	−0.995294	+	0.0969037i	$0.969106\pi$
$38$	2.35071	−	7.59884i	0.381336	−	1.23269i
$39$		0			0
$40$	−0.874924	−	5.90257i	−0.138338	−	0.933278i
$41$	−4.61325	+	7.99038i	−0.720469	+	1.24789i	0.240344	+	0.970688i	$0.422740\pi$
$41$	−4.61325	+	7.99038i	−0.720469	+	1.24789i	−0.960812	+	0.277200i	$0.910593\pi$
$42$		0			0
$43$	2.91294	−	10.8712i	0.444219	−	1.65785i	−0.273772	−	0.961795i	$-0.588271\pi$
$43$	2.91294	−	10.8712i	0.444219	−	1.65785i	0.717991	−	0.696053i	$-0.245062\pi$
$44$	1.06665	−	0.914906i	0.160803	−	0.137927i
$45$		0			0
$46$	11.1222	+	0.425234i	1.63988	+	0.0626973i
$47$	−5.92267	−	10.2584i	−0.863910	−	1.49634i	−0.868125	−	0.496345i	$-0.834675\pi$
$47$	−5.92267	−	10.2584i	−0.863910	−	1.49634i	0.00421475	−	0.999991i	$-0.498658\pi$
$48$		0			0
$49$	3.49186	−	6.04807i	0.498837	−	0.864011i
$50$	0.413816	−	0.657395i	0.0585224	−	0.0929698i
$51$		0			0
$52$	−1.26629	+	3.60004i	−0.175603	+	0.499236i
$53$	−0.00259022	−	0.00259022i	−0.000355794	−	0.000355794i	0.706929	−	0.707285i	$-0.250080\pi$
$53$	−0.00259022	−	0.00259022i	−0.000355794	−	0.000355794i	−0.707285	+	0.706929i	$0.750080\pi$
$54$		0			0
$55$	−1.48233			−0.199878
$56$	0.331185	−	0.143532i	0.0442565	−	0.0191803i
$57$		0			0
$58$	−1.32338	+	0.300919i	−0.173768	+	0.0395125i
$59$	1.09748	+	4.09587i	0.142880	+	0.533237i	0.999841	+	0.0178541i	$0.00568344\pi$
$59$	1.09748	+	4.09587i	0.142880	+	0.533237i	−0.856960	+	0.515382i	$0.827650\pi$
$60$		0			0
$61$	−1.19213	+	4.44908i	−0.152636	+	0.569646i	0.846660	+	0.532134i	$0.178610\pi$
$61$	−1.19213	+	4.44908i	−0.152636	+	0.569646i	−0.999296	+	0.0375117i	$0.988057\pi$
$62$	8.01790	+	0.306548i	1.01827	+	0.0389317i
$63$		0			0
$64$	−7.79063	−	1.81826i	−0.973829	−	0.227282i
$65$	3.48621	−	2.01276i	0.432411	−	0.249652i
$66$		0			0
$67$	−0.538862	−	2.01106i	−0.0658325	−	0.245690i	0.925166	−	0.379563i	$-0.123925\pi$
$67$	−0.538862	−	2.01106i	−0.0658325	−	0.245690i	−0.990999	+	0.133872i	$0.957259\pi$
$68$	−7.13478	−	4.88146i	−0.865220	−	0.591964i
$69$		0			0
$70$	−0.363737	−	0.112522i	−0.0434749	−	0.0134490i
$71$			3.80683i			0.451788i	0.974152	+	0.225894i	$0.0725303\pi$
$71$			3.80683i			0.451788i	−0.974152	+	0.225894i	$0.927470\pi$
$72$		0			0
$73$			1.87674i			0.219656i	0.993951	+	0.109828i	$0.0350300\pi$
$73$			1.87674i			0.219656i	−0.993951	+	0.109828i	$0.964970\pi$
$74$	3.92680	−	12.6937i	0.456481	−	1.47561i
$75$		0			0
$76$	2.07328	+	11.0561i	0.237822	+	1.26822i
$77$	−0.0232076	−	0.0866118i	−0.00264475	−	0.00987033i
$78$		0			0
$79$	3.00919	−	1.73736i	0.338560	−	0.195468i	−0.321075	−	0.947054i	$-0.604044\pi$
$79$	3.00919	−	1.73736i	0.338560	−	0.195468i	0.659635	+	0.751586i	$0.270711\pi$
$80$	4.98892	+	6.80604i	0.557778	+	0.760939i
$81$		0			0
$82$	0.498509	−	13.0387i	0.0550511	−	1.43989i
$83$	0.394284	−	1.47149i	0.0432783	−	0.161517i	−0.940905	−	0.338671i	$-0.890023\pi$
$83$	0.394284	−	1.47149i	0.0432783	−	0.161517i	0.984183	+	0.177155i	$0.0566892\pi$
$84$		0			0
$85$	2.36015	+	8.80821i	0.255994	+	0.955384i
$86$	3.52914	+	15.5204i	0.380556	+	1.67361i
$87$		0			0
$88$	−0.730581	+	1.84820i	−0.0778802	+	0.197019i
$89$	10.5967			1.12325			0.561624	−	0.827392i	$-0.310177\pi$
$89$	10.5967			1.12325			0.561624	+	0.827392i	$0.310177\pi$
$90$		0			0
$91$	0.172185	+	0.172185i	0.0180499	+	0.0180499i
$92$	−14.1929	+	6.80649i	−1.47971	+	0.709626i
$93$		0			0
$94$	14.1769	+	8.92407i	1.46224	+	0.920447i
$95$	5.93284	−	10.2760i	0.608697	−	1.05429i
$96$		0			0
$97$	3.31795	+	5.74685i	0.336886	+	0.583504i	0.983845	−	0.179021i	$-0.0572928\pi$
$97$	3.31795	+	5.74685i	0.336886	+	0.583504i	−0.646959	+	0.762525i	$0.723960\pi$
$98$	−0.377331	+	9.86925i	−0.0381162	+	0.996945i
$99$		0			0
$100$	−0.0838795	+	1.09535i	−0.00838795	+	0.109535i
$101$	−3.24008	+	12.0922i	−0.322400	+	1.20321i	0.594499	+	0.804096i	$0.297350\pi$
$101$	−3.24008	+	12.0922i	−0.322400	+	1.20321i	−0.916899	+	0.399118i	$0.869316\pi$
$102$		0			0
$103$	−4.21850	+	7.30665i	−0.415661	+	0.719946i	−0.995498	−	0.0947868i	$-0.969783\pi$
$103$	−4.21850	+	7.30665i	−0.415661	+	0.719946i	0.579837	+	0.814733i	$0.303116\pi$
$104$	−0.791339	−	5.33867i	−0.0775972	−	0.523499i
$105$		0			0
$106$	0.00494904	+	0.00153099i	0.000480693	+	0.000148703i
$107$	−7.25071	+	7.25071i	−0.700953	+	0.700953i	−0.964615	−	0.263662i	$-0.915070\pi$
$107$	−7.25071	+	7.25071i	−0.700953	+	0.700953i	0.263662	+	0.964615i	$0.415070\pi$
$108$		0			0
$109$	10.2850	+	10.2850i	0.985128	+	0.985128i	0.999891	−	0.0147630i	$-0.00469937\pi$
$109$	10.2850	+	10.2850i	0.985128	+	0.985128i	−0.0147630	+	0.999891i	$0.504699\pi$
$110$	1.85420	−	0.978042i	0.176791	−	0.0932527i
$111$		0			0
$112$	−0.319566	+	0.398055i	−0.0301961	+	0.0376127i
$113$	18.2964	+	10.5634i	1.72118	+	0.993722i	0.916526	+	0.399976i	$0.130981\pi$
$113$	18.2964	+	10.5634i	1.72118	+	0.993722i	0.804652	+	0.593747i	$0.202352\pi$
$114$		0			0
$115$	16.0380	+	4.29738i	1.49555	+	0.400732i
$116$	1.45682	−	1.24957i	0.135263	−	0.116020i
$117$		0			0
$118$	−4.07526	−	4.39926i	−0.375158	−	0.404985i
$119$	−0.477707	+	0.275804i	−0.0437913	+	0.0252829i
$120$		0			0
$121$	−9.09872	−	5.25315i	−0.827157	−	0.477559i
$122$	−1.44431	−	6.35176i	−0.130761	−	0.575061i
$123$		0			0
$124$	−10.2316	+	4.90675i	−0.918823	+	0.440639i
$125$	8.27822	−	8.27822i	0.740426	−	0.740426i
$126$		0			0
$127$		−	13.1109i		−	1.16340i	−0.813403	−	0.581700i	$-0.802388\pi$
$127$		−	13.1109i		−	1.16340i	0.813403	−	0.581700i	$-0.197612\pi$
$128$	10.9447	−	2.86585i	0.967386	−	0.253308i
$129$		0			0
$130$	−3.03276	+	4.81789i	−0.265990	+	0.422557i
$131$	−4.74891	+	1.27247i	−0.414914	+	0.111176i	−0.460236	−	0.887797i	$-0.652235\pi$
$131$	−4.74891	+	1.27247i	−0.414914	+	0.111176i	0.0453222	+	0.998972i	$0.485569\pi$
$132$		0			0
$133$	0.693305	+	0.185770i	0.0601171	+	0.0161083i
$134$	2.00094	+	2.16003i	0.172855	+	0.186598i
$135$		0			0
$136$	12.1454	+	1.39852i	1.04146	+	0.119922i
$137$	−3.41217	−	5.91005i	−0.291521	−	0.504930i	0.682648	−	0.730747i	$-0.260828\pi$
$137$	−3.41217	−	5.91005i	−0.291521	−	0.504930i	−0.974170	+	0.225817i	$0.927495\pi$
$138$		0			0
$139$	10.3427	−	2.77132i	0.877258	−	0.235061i	0.208035	−	0.978121i	$-0.433293\pi$
$139$	10.3427	−	2.77132i	0.877258	−	0.235061i	0.669224	+	0.743061i	$0.266627\pi$
$140$	0.529228	−	0.0992427i	0.0447279	−	0.00838754i
$141$		0			0
$142$	−2.51174	−	4.76184i	−0.210781	−	0.399604i
$143$	−1.34072			−0.112117
$144$		0			0
$145$	−2.02456			−0.168131
$146$	−1.23827	−	2.34755i	−0.102480	−	0.194285i
$147$		0			0
$148$	3.46336	+	18.4690i	0.284687	+	1.51814i
$149$	0.204036	−	0.0546714i	0.0167153	−	0.00447885i	−0.250452	−	0.968129i	$-0.580579\pi$
$149$	0.204036	−	0.0546714i	0.0167153	−	0.00447885i	0.267167	+	0.963650i	$0.413912\pi$
$150$		0			0
$151$	1.14798	+	1.98835i	0.0934210	+	0.161810i	0.908949	−	0.416908i	$-0.136886\pi$
$151$	1.14798	+	1.98835i	0.0934210	+	0.161810i	−0.815528	+	0.578718i	$0.803553\pi$
$152$	−9.88822	−	12.4618i	−0.802040	−	1.01078i
$153$		0			0
$154$	0.0861759	+	0.0930274i	0.00694425	+	0.00749636i
$155$	11.5617	+	3.09795i	0.928658	+	0.248833i
$156$		0			0
$157$	−16.2150	+	4.34480i	−1.29410	+	0.346753i	−0.839216	−	0.543799i	$-0.816985\pi$
$157$	−16.2150	+	4.34480i	−1.29410	+	0.346753i	−0.454883	+	0.890551i	$0.650319\pi$
$158$	−2.61779	+	4.15866i	−0.208260	+	0.330845i
$159$		0			0
$160$	−10.7311	−	5.22176i	−0.848367	−	0.412817i
$161$			1.00437i			0.0791556i
$162$		0			0
$163$	0.490399	−	0.490399i	0.0384110	−	0.0384110i	−0.687640	−	0.726051i	$-0.741353\pi$
$163$	0.490399	−	0.490399i	0.0384110	−	0.0384110i	0.726051	+	0.687640i	$0.241353\pi$
$164$	7.97936	+	16.6386i	0.623084	+	1.29926i
$165$		0			0
$166$	0.477690	+	2.10078i	0.0370759	+	0.163052i
$167$	−9.34175	−	5.39346i	−0.722887	−	0.417359i	0.0929276	−	0.995673i	$-0.470378\pi$
$167$	−9.34175	−	5.39346i	−0.722887	−	0.417359i	−0.815814	+	0.578314i	$0.803711\pi$
$168$		0			0
$169$	−8.10518	+	4.67953i	−0.623475	+	0.359963i
$170$	−8.76388	−	9.46066i	−0.672159	−	0.725599i
$171$		0			0
$172$	−14.6548	−	17.0854i	−1.11742	−	1.30275i
$173$	−4.61598	−	1.23685i	−0.350946	−	0.0940358i	0.0790394	−	0.996871i	$-0.474815\pi$
$173$	−4.61598	−	1.23685i	−0.350946	−	0.0940358i	−0.429986	+	0.902836i	$0.641481\pi$
$174$		0			0
$175$	0.0607051	+	0.0350481i	0.00458888	+	0.00264939i
$176$	−0.305581	−	2.79388i	−0.0230340	−	0.210597i
$177$		0			0
$178$	−13.2551	+	6.99170i	−0.993509	+	0.524050i
$179$	−3.52882	−	3.52882i	−0.263756	−	0.263756i	0.562822	−	0.826578i	$-0.309716\pi$
$179$	−3.52882	−	3.52882i	−0.263756	−	0.263756i	−0.826578	+	0.562822i	$0.809716\pi$
$180$		0			0
$181$	7.34860	−	7.34860i	0.546217	−	0.546217i	−0.379127	−	0.925344i	$-0.623776\pi$
$181$	7.34860	−	7.34860i	0.546217	−	0.546217i	0.925344	+	0.379127i	$0.123776\pi$
$182$	−0.328987	−	0.101773i	−0.0243862	−	0.00754390i
$183$		0			0
$184$	13.2625	−	17.8785i	0.977726	−	1.31802i
$185$	9.91065	−	17.1658i	0.728646	−	1.26205i
$186$		0			0
$187$	0.786059	−	2.93361i	0.0574824	−	0.214527i
$188$	−23.6215	−	1.80889i	−1.72278	−	0.131927i
$189$		0			0
$190$	−0.641105	+	16.7684i	−0.0465106	+	1.21651i
$191$	2.58888	+	4.48407i	0.187325	+	0.324456i	0.944357	−	0.328921i	$-0.106685\pi$
$191$	2.58888	+	4.48407i	0.187325	+	0.324456i	−0.757033	+	0.653377i	$0.773352\pi$
$192$		0			0
$193$	13.2173	−	22.8930i	0.951401	−	1.64787i	0.209003	−	0.977915i	$-0.432978\pi$
$193$	13.2173	−	22.8930i	0.951401	−	1.64787i	0.742398	−	0.669960i	$-0.233689\pi$
$194$	−7.94207	−	4.99936i	−0.570208	−	0.358933i
$195$		0			0
$196$	−6.03973	−	12.5941i	−0.431410	−	0.899577i
$197$	−5.14652	−	5.14652i	−0.366674	−	0.366674i	0.499588	−	0.866263i	$-0.333485\pi$
$197$	−5.14652	−	5.14652i	−0.366674	−	0.366674i	−0.866263	+	0.499588i	$0.833485\pi$
$198$		0			0
$199$	−1.37436			−0.0974261			−0.0487130	−	0.998813i	$-0.515512\pi$
$199$	−1.37436			−0.0974261			−0.0487130	+	0.998813i	$0.515512\pi$
$200$	−0.617788	−	1.42548i	−0.0436842	−	0.100797i
$201$		0			0
$202$	−3.92549	−	17.2635i	−0.276196	−	1.21465i
$203$	−0.0316967	−	0.118294i	−0.00222468	−	0.00830260i
$204$		0			0
$205$	5.03789	−	18.8017i	0.351861	−	1.31316i
$206$	0.455852	−	11.9230i	0.0317607	−	0.830715i
$207$		0			0
$208$	4.51231	+	6.15583i	0.312872	+	0.426830i
$209$	−3.42246	+	1.97596i	−0.236737	+	0.136680i
$210$		0			0
$211$	−2.98444	−	11.1381i	−0.205457	−	0.766776i	−0.989310	−	0.145829i	$-0.953415\pi$
$211$	−2.98444	−	11.1381i	−0.205457	−	0.766776i	0.783853	−	0.620947i	$-0.213252\pi$
$212$	−0.00720073	+	0.00135031i	−0.000494548	+	9.27394e-5i
$213$		0			0
$214$	4.28566	−	13.8537i	0.292961	−	0.947018i
$215$			23.7438i			1.61931i
$216$		0			0
$217$			0.724045i			0.0491514i
$218$	−19.6513	−	6.07914i	−1.33095	−	0.411732i
$219$		0			0
$220$	−1.67404	+	2.44680i	−0.112864	+	0.164963i
$221$	2.13468	+	7.96672i	0.143594	+	0.535900i
$222$		0			0
$223$	−17.9819	+	10.3819i	−1.20416	+	0.695220i	−0.961477	−	0.274886i	$-0.911360\pi$
$223$	−17.9819	+	10.3819i	−1.20416	+	0.695220i	−0.242680	+	0.970106i	$0.578026\pi$
$224$	0.137097	−	0.708763i	0.00916019	−	0.0473562i
$225$		0			0
$226$	−29.8560	−	1.14149i	−1.98599	−	0.0759305i
$227$	−2.05090	+	7.65406i	−0.136123	+	0.508018i	0.863868	+	0.503718i	$0.168035\pi$
$227$	−2.05090	+	7.65406i	−0.136123	+	0.508018i	−0.999991	+	0.00429906i	$0.998632\pi$
$228$		0			0
$229$	−0.120227	−	0.448692i	−0.00794481	−	0.0296504i	0.961840	−	0.273614i	$-0.0882190\pi$
$229$	−0.120227	−	0.448692i	−0.00794481	−	0.0296504i	−0.969784	+	0.243963i	$0.921552\pi$
$230$	−22.8968	+	5.20643i	−1.50977	+	0.343302i
$231$		0			0
$232$	−0.997823	+	2.52426i	−0.0655103	+	0.165726i
$233$	−9.13737			−0.598609			−0.299305	−	0.954158i	$-0.596755\pi$
$233$	−9.13737			−0.598609			−0.299305	+	0.954158i	$0.596755\pi$
$234$		0			0
$235$	17.6705	+	17.6705i	1.15269	+	1.15269i
$236$	8.00023	+	2.81404i	0.520770	+	0.183178i
$237$		0			0
$238$	0.415572	−	0.660185i	0.0269375	−	0.0427934i
$239$	3.65824	−	6.33626i	0.236632	−	0.409859i	−0.723114	−	0.690729i	$-0.757290\pi$
$239$	3.65824	−	6.33626i	0.236632	−	0.409859i	0.959746	+	0.280870i	$0.0906231\pi$
$240$		0			0
$241$	−1.24858	−	2.16261i	−0.0804282	−	0.139306i	0.823006	−	0.568033i	$-0.192295\pi$
$241$	−1.24858	−	2.16261i	−0.0804282	−	0.139306i	−0.903434	+	0.428727i	$0.858962\pi$
$242$	14.8473	+	0.567657i	0.954421	+	0.0364904i
$243$		0			0
$244$	5.99752	+	6.99225i	0.383952	+	0.447633i
$245$	−3.81327	+	14.2313i	−0.243621	+	0.909206i
$246$		0			0
$247$	5.36605	−	9.29428i	0.341434	−	0.591381i
$248$	9.56086	−	12.8885i	0.607115	−	0.818419i
$249$		0			0
$250$	−4.89298	+	15.8169i	−0.309459	+	1.00035i
$251$	2.77626	−	2.77626i	0.175236	−	0.175236i	−0.614039	−	0.789275i	$-0.710456\pi$
$251$	2.77626	−	2.77626i	0.175236	−	0.175236i	0.789275	+	0.614039i	$0.210456\pi$
$252$		0			0
$253$	−3.91028	−	3.91028i	−0.245837	−	0.245837i
$254$	8.65053	+	16.3999i	0.542783	+	1.02902i
$255$		0			0
$256$	−11.7995	+	10.8061i	−0.737468	+	0.675382i
$257$	9.61957	+	5.55386i	0.600052	+	0.346440i	0.769062	−	0.639174i	$-0.220724\pi$
$257$	9.61957	+	5.55386i	0.600052	+	0.346440i	−0.169010	+	0.985614i	$0.554057\pi$
$258$		0			0
$259$	1.15815	+	0.310324i	0.0719637	+	0.0192826i
$260$	0.614733	−	8.02755i	0.0381241	−	0.497847i
$261$		0			0
$262$	5.10067	−	4.72501i	0.315121	−	0.291912i
$263$	16.6320	−	9.60247i	1.02557	−	0.592114i	0.109858	−	0.993947i	$-0.464960\pi$
$263$	16.6320	−	9.60247i	1.02557	−	0.592114i	0.915713	+	0.401834i	$0.131627\pi$
$264$		0			0
$265$	0.00669264	+	0.00386400i	0.000411125	+	0.000237363i
$266$	−0.989802	+	0.225068i	−0.0606887	+	0.0137998i
$267$		0			0
$268$	−3.92809	−	1.38169i	−0.239947	−	0.0843999i
$269$	−7.66476	+	7.66476i	−0.467329	+	0.467329i	−0.901048	−	0.433719i	$-0.857201\pi$
$269$	−7.66476	+	7.66476i	−0.467329	+	0.467329i	0.433719	+	0.901048i	$0.357201\pi$
$270$		0			0
$271$		−	12.9801i		−	0.788486i	−0.919006	−	0.394243i	$-0.871007\pi$
$271$		−	12.9801i		−	0.788486i	0.919006	−	0.394243i	$-0.128993\pi$
$272$	−16.1151	+	6.26418i	−0.977119	+	0.379822i
$273$		0			0
$274$	8.16761	+	5.14133i	0.493423	+	0.310599i
$275$	−0.372792	+	0.0998893i	−0.0224802	+	0.00602355i
$276$		0			0
$277$	23.9833	+	6.42631i	1.44102	+	0.386119i	0.892890	−	0.450276i	$-0.148674\pi$
$277$	23.9833	+	6.42631i	1.44102	+	0.386119i	0.548127	+	0.836395i	$0.315341\pi$
$278$	−11.1088	+	10.2907i	−0.666264	+	0.617194i
$279$		0			0
$280$	−0.596513	+	0.473324i	−0.0356485	+	0.0282865i
$281$	−3.69120	−	6.39334i	−0.220198	−	0.381395i	0.734670	−	0.678425i	$-0.237337\pi$
$281$	−3.69120	−	6.39334i	−0.220198	−	0.381395i	−0.954868	+	0.297030i	$0.904004\pi$
$282$		0			0
$283$	−5.99708	+	1.60691i	−0.356490	+	0.0955211i	−0.432619	−	0.901577i	$-0.642410\pi$
$283$	−5.99708	+	1.60691i	−0.356490	+	0.0955211i	0.0761294	+	0.997098i	$0.475744\pi$
$284$	6.28371	+	4.29917i	0.372870	+	0.255109i
$285$		0			0
$286$	1.67706	−	0.884606i	0.0991667	−	0.0523078i
$287$	1.17744			0.0695022
$288$		0			0
$289$	−1.68344			−0.0990261
$290$	2.53246	−	1.33580i	0.148711	−	0.0784411i
$291$		0			0
$292$	3.09783	+	2.11946i	0.181287	+	0.124032i
$293$	−24.0140	+	6.43453i	−1.40291	+	0.375909i	−0.879390	−	0.476103i	$-0.842049\pi$
$293$	−24.0140	+	6.43453i	−1.40291	+	0.375909i	−0.523522	+	0.852012i	$0.675382\pi$
$294$		0			0
$295$	−4.47288	−	7.74726i	−0.260421	−	0.451063i
$296$	−16.5180	−	20.8171i	−0.960089	−	1.20997i
$297$		0			0
$298$	−0.219150	+	0.203009i	−0.0126950	+	0.0117600i
$299$	14.5058	+	3.88683i	0.838895	+	0.224781i
$300$		0			0
$301$	−1.38734	+	0.371735i	−0.0799647	+	0.0214265i
$302$	−2.74788	−	1.72973i	−0.158123	−	0.0995347i
$303$		0			0
$304$	20.5911	+	9.06377i	1.18098	+	0.519843i
$305$		−	9.71720i		−	0.556406i
$306$		0			0
$307$	−17.3773	+	17.3773i	−0.991773	+	0.991773i	−0.999966	−	0.00819381i	$-0.997392\pi$
$307$	−17.3773	+	17.3773i	−0.991773	+	0.991773i	0.00819381	+	0.999966i	$0.497392\pi$
$308$	−0.169174	−	0.0595060i	−0.00963958	−	0.00339067i
$309$		0			0
$310$	−16.5062	+	3.75328i	−0.937487	+	0.213172i
$311$	11.9437	+	6.89568i	0.677264	+	0.391018i	0.798823	−	0.601566i	$-0.205456\pi$
$311$	11.9437	+	6.89568i	0.677264	+	0.391018i	−0.121560	+	0.992584i	$0.538790\pi$
$312$		0			0
$313$	17.6368	−	10.1826i	0.996890	−	0.575555i	0.0895635	−	0.995981i	$-0.471453\pi$
$313$	17.6368	−	10.1826i	0.996890	−	0.575555i	0.907327	+	0.420426i	$0.138119\pi$
$314$	17.4161	−	16.1334i	0.982848	−	0.910461i
$315$		0			0
$316$	0.530619	−	6.92914i	0.0298497	−	0.389795i
$317$	−20.3136	−	5.44301i	−1.14092	−	0.305710i	−0.361601	−	0.932333i	$-0.617770\pi$
$317$	−20.3136	−	5.44301i	−1.14092	−	0.305710i	−0.779322	+	0.626623i	$0.784437\pi$
$318$		0			0
$319$	0.583952	+	0.337145i	0.0326950	+	0.0188765i
$320$	16.8685	−	0.548641i	0.942976	−	0.0306700i
$321$		0			0
$322$	−0.662684	−	1.25633i	−0.0369299	−	0.0700128i
$323$	17.1906	+	17.1906i	0.956511	+	0.956511i
$324$		0			0
$325$	0.741113	−	0.741113i	0.0411096	−	0.0411096i
$326$	−0.289859	+	0.936989i	−0.0160538	+	0.0518950i
$327$		0			0
$328$	−20.9592	−	15.5479i	−1.15728	−	0.858488i
$329$	−0.755823	+	1.30912i	−0.0416699	+	0.0721743i
$330$		0			0
$331$	−4.57199	+	17.0629i	−0.251299	+	0.937862i	0.718813	+	0.695204i	$0.244686\pi$
$331$	−4.57199	+	17.0629i	−0.251299	+	0.937862i	−0.970112	+	0.242658i	$0.921981\pi$
$332$	−1.98362	−	2.31262i	−0.108865	−	0.126921i
$333$		0			0
$334$	15.2439	+	0.582819i	0.834108	+	0.0318904i
$335$	2.19618	+	3.80389i	0.119990	+	0.207829i
$336$		0			0
$337$	−4.82538	+	8.35780i	−0.262855	+	0.455279i	−0.966999	−	0.254778i	$-0.917997\pi$
$337$	−4.82538	+	8.35780i	−0.262855	+	0.455279i	0.704144	+	0.710057i	$0.251331\pi$
$338$	7.05094	−	11.2012i	0.383521	−	0.609267i
$339$		0			0
$340$	17.2046	+	6.05161i	0.933049	+	0.328195i
$341$	−2.81889	−	2.81889i	−0.152652	−	0.152652i
$342$		0			0
$343$	−1.78454			−0.0963558
$344$	29.6042	+	11.7023i	1.59615	+	0.630948i
$345$		0			0
$346$	6.59004	−	1.49849i	0.354283	−	0.0805592i
$347$	−4.93125	−	18.4037i	−0.264723	−	0.987960i	−0.962420	−	0.271567i	$-0.912458\pi$
$347$	−4.93125	−	18.4037i	−0.264723	−	0.987960i	0.697696	−	0.716393i	$-0.254208\pi$
$348$		0			0
$349$	4.68226	−	17.4744i	0.250636	−	0.935385i	−0.719831	−	0.694150i	$-0.755781\pi$
$349$	4.68226	−	17.4744i	0.250636	−	0.935385i	0.970467	−	0.241236i	$-0.0775527\pi$
$350$	−0.0990587	−	0.00378731i	−0.00529491	−	0.000202440i
$351$		0			0
$352$	2.22564	+	3.29315i	0.118627	+	0.175526i
$353$	−5.65589	+	3.26543i	−0.301033	+	0.173801i	−0.642907	−	0.765944i	$-0.722272\pi$
$353$	−5.65589	+	3.26543i	−0.301033	+	0.173801i	0.341874	+	0.939746i	$0.388938\pi$
$354$		0			0
$355$	−2.07862	−	7.75752i	−0.110322	−	0.411726i
$356$	11.9672	−	17.4914i	0.634259	−	0.927040i
$357$		0			0
$358$	6.74239	+	2.08577i	0.356346	+	0.110236i
$359$		−	22.8075i		−	1.20373i	−0.798597	−	0.601866i	$-0.794424\pi$
$359$		−	22.8075i		−	1.20373i	0.798597	−	0.601866i	$-0.205576\pi$
$360$		0			0
$361$		−	12.6341i		−	0.664952i
$362$	−4.34351	+	14.0407i	−0.228290	+	0.737963i
$363$		0			0
$364$	0.478669	−	0.0897616i	0.0250891	−	0.00470479i
$365$	−1.02475	−	3.82440i	−0.0536377	−	0.200178i
$366$		0			0
$367$	−20.7702	+	11.9917i	−1.08419	+	0.625959i	−0.932025	−	0.362395i	$-0.881959\pi$
$367$	−20.7702	+	11.9917i	−1.08419	+	0.625959i	−0.152169	+	0.988355i	$0.548626\pi$
$368$	−4.79343	+	31.1142i	−0.249875	+	1.62194i
$369$		0			0
$370$	−1.07095	+	28.0111i	−0.0556759	+	1.45623i
$371$	−0.000120990	0	0.000451542i	−6.28150e−6	0	2.34429e-5i
$372$		0			0
$373$	6.20866	+	23.1710i	0.321472	+	1.19975i	0.917811	+	0.397018i	$0.129955\pi$
$373$	6.20866	+	23.1710i	0.321472	+	1.19975i	−0.596338	+	0.802733i	$0.703378\pi$
$374$	0.952341	+	4.18820i	0.0492444	+	0.216567i
$375$		0			0
$376$	30.7409	−	13.3228i	1.58534	−	0.687070i
$377$	−1.83115			−0.0943089
$378$		0			0
$379$	9.96634	+	9.96634i	0.511936	+	0.511936i	0.915119	−	0.403183i	$-0.132096\pi$
$379$	9.96634	+	9.96634i	0.511936	+	0.511936i	−0.403183	+	0.915119i	$0.632096\pi$
$380$	−10.2618	−	21.3980i	−0.526420	−	1.09769i
$381$		0			0
$382$	−6.19692	−	3.90083i	−0.317062	−	0.199584i
$383$	−2.30770	+	3.99705i	−0.117918	+	0.204240i	−0.918942	−	0.394392i	$-0.870955\pi$
$383$	−2.30770	+	3.99705i	−0.117918	+	0.204240i	0.801024	+	0.598632i	$0.204289\pi$
$384$		0			0
$385$	0.0945842	+	0.163825i	0.00482046	+	0.00834927i
$386$	−1.42826	+	37.3568i	−0.0726967	+	1.90141i
$387$		0			0
$388$	13.2330	+	1.01336i	0.671806	+	0.0514455i
$389$	3.31091	−	12.3565i	0.167870	−	0.626498i	−0.829787	−	0.558080i	$-0.811538\pi$
$389$	3.31091	−	12.3565i	0.167870	−	0.626498i	0.997657	−	0.0684178i	$-0.0217951\pi$
$390$		0			0
$391$	−17.0095	+	29.4612i	−0.860205	+	1.48992i
$392$	15.8645	+	11.7685i	0.801276	+	0.594398i
$393$		0			0
$394$	9.83328	+	3.04194i	0.495393	+	0.153251i
$395$	−5.18345	+	5.18345i	−0.260808	+	0.260808i
$396$		0			0
$397$	−3.70313	−	3.70313i	−0.185855	−	0.185855i	0.608047	−	0.793901i	$-0.291953\pi$
$397$	−3.70313	−	3.70313i	−0.185855	−	0.185855i	−0.793901	+	0.608047i	$0.791953\pi$
$398$	1.71915	−	0.906804i	0.0861730	−	0.0454540i
$399$		0			0
$400$	1.71330	+	1.37547i	0.0856650	+	0.0687733i
$401$	−11.5871	−	6.68983i	−0.578633	−	0.334074i	0.181957	−	0.983307i	$-0.441757\pi$
$401$	−11.5871	−	6.68983i	−0.578633	−	0.334074i	−0.760590	+	0.649232i	$0.775090\pi$
$402$		0			0
$403$	10.4572	+	2.80199i	0.520908	+	0.139577i
$404$	16.3007	+	19.0043i	0.810989	+	0.945497i
$405$		0			0
$406$	0.117699	+	0.127056i	0.00584128	+	0.00630570i
$407$	−5.71713	+	3.30079i	−0.283388	+	0.163614i
$408$		0			0
$409$	24.1053	+	13.9172i	1.19193	+	0.688161i	0.958744	−	0.284272i	$-0.0917518\pi$
$409$	24.1053	+	13.9172i	1.19193	+	0.688161i	0.233185	+	0.972432i	$0.425085\pi$
$410$	6.10359	+	26.8423i	0.301435	+	1.32565i
$411$		0			0
$412$	7.29658	+	15.2148i	0.359477	+	0.749582i
$413$	0.382639	−	0.382639i	0.0188285	−	0.0188285i
$414$		0			0
$415$			3.21387i			0.157763i
$416$	−9.70590	−	4.72290i	−0.475871	−	0.231559i
$417$		0			0
$418$	2.97731	−	4.72980i	0.145625	−	0.231342i
$419$	−9.97902	+	2.67387i	−0.487507	+	0.130627i	−0.494196	−	0.869350i	$-0.664538\pi$
$419$	−9.97902	+	2.67387i	−0.487507	+	0.130627i	0.00668892	+	0.999978i	$0.497871\pi$
$420$		0			0
$421$	−29.8528	−	7.99904i	−1.45494	−	0.389849i	−0.557199	−	0.830379i	$-0.688124\pi$
$421$	−29.8528	−	7.99904i	−1.45494	−	0.389849i	−0.897738	+	0.440529i	$0.854791\pi$
$422$	11.0820	+	11.9631i	0.539464	+	0.582354i
$423$		0			0
$424$	0.00811622	−	0.00644009i	0.000394158	−	0.000312758i
$425$	1.18711	+	2.05613i	0.0575833	+	0.0997371i
$426$		0			0
$427$	0.567770	−	0.152134i	0.0274763	−	0.00736226i
$428$	3.77987	+	20.1568i	0.182707	+	0.974314i
$429$		0			0
$430$	−15.6661	−	29.7003i	−0.755488	−	1.43228i
$431$	−14.8449			−0.715053			−0.357526	−	0.933903i	$-0.616380\pi$
$431$	−14.8449			−0.715053			−0.357526	+	0.933903i	$0.616380\pi$
$432$		0			0
$433$	−32.1617			−1.54559			−0.772796	−	0.634654i	$-0.781143\pi$
$433$	−32.1617			−1.54559			−0.772796	+	0.634654i	$0.781143\pi$
$434$	−0.477724	−	0.905683i	−0.0229315	−	0.0434742i
$435$		0			0
$436$	28.5921	−	5.36169i	1.36931	−	0.256778i
$437$	42.7576	−	11.4569i	2.04537	−	0.548056i
$438$		0			0
$439$	−0.140035	−	0.242548i	−0.00668352	−	0.0115762i	0.862664	−	0.505777i	$-0.168794\pi$
$439$	−0.140035	−	0.242548i	−0.00668352	−	0.0115762i	−0.869348	+	0.494201i	$0.835461\pi$
$440$	0.479609	−	4.16515i	0.0228644	−	0.198566i
$441$		0			0
$442$	−7.92663	−	8.55684i	−0.377031	−	0.407007i
$443$	24.2588	+	6.50011i	1.15257	+	0.308830i	0.783994	−	0.620768i	$-0.213179\pi$
$443$	24.2588	+	6.50011i	1.15257	+	0.308830i	0.368574	+	0.929598i	$0.379846\pi$
$444$		0			0
$445$	−21.5938	+	5.78605i	−1.02365	+	0.274285i
$446$	15.6430	−	24.8507i	0.740717	−	1.17672i
$447$		0			0
$448$	0.296151	+	0.977024i	0.0139918	+	0.0461601i
$449$		−	14.2885i		−	0.674318i	−0.941448	−	0.337159i	$-0.890534\pi$
$449$		−	14.2885i		−	0.674318i	0.941448	−	0.337159i	$-0.109466\pi$
$450$		0			0
$451$	−4.58408	+	4.58408i	−0.215856	+	0.215856i
$452$	38.0990	−	18.2711i	1.79203	−	0.859402i
$453$		0			0
$454$	−2.48474	−	10.9274i	−0.116615	−	0.512847i
$455$	−0.444893	−	0.256859i	−0.0208569	−	0.0120417i
$456$		0			0
$457$	−24.1097	+	13.9198i	−1.12781	+	0.651139i	−0.943382	−	0.331708i	$-0.892375\pi$
$457$	−24.1097	+	13.9198i	−1.12781	+	0.651139i	−0.184424	+	0.982847i	$0.559042\pi$
$458$	0.446434	+	0.481928i	0.0208605	+	0.0225190i
$459$		0			0
$460$	25.2057	−	21.6199i	1.17522	−	1.00803i
$461$	−16.1887	−	4.33776i	−0.753985	−	0.202030i	−0.138700	−	0.990334i	$-0.544292\pi$
$461$	−16.1887	−	4.33776i	−0.753985	−	0.202030i	−0.615285	+	0.788305i	$0.710959\pi$
$462$		0			0
$463$	26.1951	+	15.1238i	1.21739	+	0.702861i	0.964359	−	0.264597i	$-0.0852389\pi$
$463$	26.1951	+	15.1238i	1.21739	+	0.702861i	0.253032	+	0.967458i	$0.418572\pi$
$464$	−0.417361	−	3.81587i	−0.0193755	−	0.177147i
$465$		0			0
$466$	11.4296	−	6.02883i	0.529467	−	0.279280i
$467$	−15.9369	−	15.9369i	−0.737469	−	0.737469i	0.234618	−	0.972088i	$-0.424616\pi$
$467$	−15.9369	−	15.9369i	−0.737469	−	0.737469i	−0.972088	+	0.234618i	$0.924616\pi$
$468$		0			0
$469$	−0.187875	+	0.187875i	−0.00867527	+	0.00867527i
$470$	−33.7623	−	10.4444i	−1.55734	−	0.481765i
$471$		0			0
$472$	−11.8639	+	1.75856i	−0.546081	+	0.0809443i
$473$	3.95399	−	6.84851i	0.181805	−	0.314895i
$474$		0			0
$475$	0.799588	−	2.98410i	0.0366876	−	0.136920i
$476$	−0.0842354	+	1.10000i	−0.00386092	+	0.0504183i
$477$		0			0
$478$	−0.395311	+	10.3395i	−0.0180811	+	0.472919i
$479$	14.8100	+	25.6516i	0.676684	+	1.17205i	0.975973	+	0.217889i	$0.0699172\pi$
$479$	14.8100	+	25.6516i	0.676684	+	1.17205i	−0.299289	+	0.954163i	$0.596749\pi$
$480$		0			0
$481$	8.96385	−	15.5258i	0.408716	−	0.707917i
$482$	2.98869	+	1.88132i	0.136131	+	0.0856916i
$483$		0			0
$484$	−18.9465	+	9.08618i	−0.861206	+	0.413008i
$485$	−9.89919	−	9.89919i	−0.449499	−	0.449499i
$486$		0			0
$487$	25.6320			1.16150			0.580749	−	0.814083i	$-0.302760\pi$
$487$	25.6320			1.16150			0.580749	+	0.814083i	$0.302760\pi$
$488$	−12.1156	−	4.78921i	−0.548446	−	0.216797i
$489$		0			0
$490$	−4.61993	−	20.3175i	−0.208707	−	0.917850i
$491$	1.40692	+	5.25069i	0.0634933	+	0.236960i	0.990379	−	0.138385i	$-0.0441910\pi$
$491$	1.40692	+	5.25069i	0.0634933	+	0.236960i	−0.926885	+	0.375345i	$0.877524\pi$
$492$		0			0
$493$	1.07360	−	4.00671i	0.0483523	−	0.180453i
$494$	−0.579857	+	15.1664i	−0.0260890	+	0.682369i
$495$		0			0
$496$	−3.45555	+	22.4300i	−0.155159	+	1.00714i
$497$	0.420724	−	0.242905i	0.0188720	−	0.0108958i
$498$		0			0
$499$	5.78179	+	21.5779i	0.258829	+	0.965961i	0.965920	+	0.258840i	$0.0833401\pi$
$499$	5.78179	+	21.5779i	0.258829	+	0.965961i	−0.707092	+	0.707122i	$0.749993\pi$
$500$	−4.31551	−	23.0132i	−0.192996	−	1.02918i
$501$		0			0
$502$	−1.64096	+	5.30451i	−0.0732395	+	0.236752i
$503$		−	24.7337i		−	1.10282i	−0.834235	−	0.551410i	$-0.814090\pi$
$503$		−	24.7337i		−	1.10282i	0.834235	−	0.551410i	$-0.185910\pi$
$504$		0			0
$505$		−	26.4104i		−	1.17525i
$506$	7.47123	+	2.31124i	0.332137	+	0.102747i
$507$		0			0
$508$	−21.6413	−	14.8065i	−0.960178	−	0.656932i
$509$	2.31048	+	8.62284i	0.102410	+	0.382201i	0.998039	−	0.0626029i	$-0.0199402\pi$
$509$	2.31048	+	8.62284i	0.102410	+	0.382201i	−0.895628	+	0.444804i	$0.853274\pi$
$510$		0			0
$511$	0.207414	−	0.119751i	0.00917545	−	0.00529745i
$512$	7.62971	−	21.3023i	0.337189	−	0.941437i
$513$		0			0
$514$	−15.6972	−	0.600152i	−0.692375	−	0.0264716i
$515$	4.60680	−	17.1928i	0.203000	−	0.757606i
$516$		0			0
$517$	−2.15414	−	8.03937i	−0.0947391	−	0.353571i
$518$	−1.65344	+	0.375970i	−0.0726479	+	0.0165192i
$519$		0			0
$520$	4.52762	+	10.4470i	0.198549	+	0.458131i
$521$	−14.1129			−0.618299			−0.309149	−	0.951013i	$-0.600044\pi$
$521$	−14.1129			−0.618299			−0.309149	+	0.951013i	$0.600044\pi$
$522$		0			0
$523$	−27.5776	−	27.5776i	−1.20588	−	1.20588i	−0.972349	−	0.233534i	$-0.924971\pi$
$523$	−27.5776	−	27.5776i	−1.20588	−	1.20588i	−0.233534	−	0.972349i	$-0.575029\pi$
$524$	−3.26270	+	9.27577i	−0.142532	+	0.405214i
$525$		0			0
$526$	−14.4687	+	22.9852i	−0.630863	+	1.00220i
$527$	−12.2620	+	21.2384i	−0.534141	+	0.925159i
$528$		0			0
$529$	19.4709	+	33.7246i	0.846561	+	1.46629i
$530$	−0.0109211		0.000417544i	−0.000474380		1.81370e-5i
$531$		0			0
$532$	1.08961	−	0.934600i	0.0472406	−	0.0405201i
$533$	4.55660	−	17.0054i	0.197368	−	0.736588i
$534$		0			0
$535$	10.8164	−	18.7345i	0.467632	−	0.809962i
$536$	5.82515	−	0.863450i	0.251608	−	0.0372953i
$537$		0			0
$538$	4.53038	−	14.6448i	0.195319	−	0.631381i
$539$	3.46978	−	3.46978i	0.149454	−	0.149454i
$540$		0			0
$541$	7.82995	+	7.82995i	0.336636	+	0.336636i	0.855100	−	0.518464i	$-0.173496\pi$
$541$	7.82995	+	7.82995i	0.336636	+	0.336636i	−0.518464	+	0.855100i	$0.673496\pi$
$542$	8.56427	+	16.2364i	0.367867	+	0.697412i
$543$		0			0
$544$	16.0247	−	18.4684i	0.687052	−	0.791824i
$545$	−26.5746	−	15.3429i	−1.13833	−	0.657216i
$546$		0			0
$547$	−21.7416	−	5.82566i	−0.929606	−	0.249087i	−0.237919	−	0.971285i	$-0.576465\pi$
$547$	−21.7416	−	5.82566i	−0.929606	−	0.249087i	−0.691686	+	0.722198i	$0.743132\pi$
$548$	−13.6088	−	1.04214i	−0.581340	−	0.0445178i
$549$		0			0
$550$	0.400406	−	0.370916i	0.0170734	−	0.0158159i
$551$	−4.67438	+	2.69876i	−0.199135	+	0.114971i
$552$		0			0
$553$	−0.384019	−	0.221713i	−0.0163301	−	0.00942821i
$554$	−34.2400	+	7.78571i	−1.45472	+	0.330783i
$555$		0			0
$556$	7.10589	−	20.2019i	0.301357	−	0.856750i
$557$	25.5918	−	25.5918i	1.08436	−	1.08436i	0.0882628	−	0.996097i	$-0.471868\pi$
$557$	25.5918	−	25.5918i	1.08436	−	1.08436i	0.996097	−	0.0882628i	$-0.0281315\pi$
$558$		0			0
$559$			21.4755i			0.908315i
$560$	0.433859	−	0.985643i	0.0183339	−	0.0416510i
$561$		0			0
$562$	8.83552	+	5.56176i	0.372704	+	0.234609i
$563$	−11.3728	+	3.04735i	−0.479308	+	0.128430i	−0.490381	−	0.871508i	$-0.663142\pi$
$563$	−11.3728	+	3.04735i	−0.479308	+	0.128430i	0.0110721	+	0.999939i	$0.496476\pi$
$564$		0			0
$565$	−43.0520	−	11.5357i	−1.81121	−	0.485313i
$566$	6.44131	−	5.96690i	0.270748	−	0.250808i
$567$		0			0
$568$	−10.6967	−	1.23170i	−0.448822	−	0.0516810i
$569$	−0.819418	−	1.41927i	−0.0343518	−	0.0594990i	0.848338	−	0.529454i	$-0.177603\pi$
$569$	−0.819418	−	1.41927i	−0.0343518	−	0.0594990i	−0.882690	+	0.469955i	$0.844270\pi$
$570$		0			0
$571$	−32.7015	+	8.76233i	−1.36851	+	0.366692i	−0.866936	−	0.498420i	$-0.833914\pi$
$571$	−32.7015	+	8.76233i	−1.36851	+	0.366692i	−0.501578	+	0.865112i	$0.667247\pi$
$572$	−1.51412	+	2.21305i	−0.0633083	+	0.0925321i
$573$		0			0
$574$	−1.47282	+	0.776875i	−0.0614744	+	0.0324261i
$575$	4.32299			0.180281
$576$		0			0
$577$	−16.0429			−0.667873			−0.333936	−	0.942596i	$-0.608377\pi$
$577$	−16.0429			−0.667873			−0.333936	+	0.942596i	$0.608377\pi$
$578$	2.10576	−	1.11073i	0.0875882	−	0.0462005i
$579$		0			0
$580$	−2.28640	+	3.34182i	−0.0949376	+	0.138762i
$581$	−0.187784	+	0.0503166i	−0.00779060	+	0.00208749i
$582$		0			0
$583$	−0.00128692	−	0.00222901i	−5.32988e−5	−	9.23163e-5i
$584$	−5.27339	−	0.607220i	−0.218214	−	0.0251269i
$585$		0			0
$586$	25.7928	−	23.8931i	1.06549	−	0.987016i
$587$	−36.9837	−	9.90974i	−1.52648	−	0.409019i	−0.604611	−	0.796521i	$-0.706671\pi$
$587$	−36.9837	−	9.90974i	−1.52648	−	0.409019i	−0.921869	+	0.387502i	$0.873338\pi$
$588$		0			0
$589$	30.8237	−	8.25918i	1.27007	−	0.340313i
$590$	10.7066	+	6.73958i	0.440784	+	0.277464i
$591$		0			0
$592$	34.3969	+	15.1408i	1.41370	+	0.622282i
$593$			32.2597i			1.32475i	0.749173	+	0.662374i	$0.230451\pi$
$593$			32.2597i			1.32475i	−0.749173	+	0.662374i	$0.769549\pi$
$594$		0			0
$595$	0.822870	−	0.822870i	0.0337344	−	0.0337344i
$596$	0.140182	−	0.398533i	0.00574206	−	0.0163245i
$597$		0			0
$598$	−20.7094	+	4.70904i	−0.846870	+	0.192567i
$599$	−11.7417	−	6.77905i	−0.479751	−	0.276984i	0.240562	−	0.970634i	$-0.422668\pi$
$599$	−11.7417	−	6.77905i	−0.479751	−	0.276984i	−0.720313	+	0.693649i	$0.756002\pi$
$600$		0			0
$601$	−0.496416	+	0.286606i	−0.0202492	+	0.0116909i	−0.510090	−	0.860121i	$-0.670388\pi$
$601$	−0.496416	+	0.286606i	−0.0202492	+	0.0116909i	0.489841	+	0.871812i	$0.337055\pi$
$602$	1.49010	−	1.38035i	0.0607319	−	0.0562590i
$603$		0			0
$604$	4.57850	+	0.350612i	0.186297	+	0.0142662i
$605$	21.4096	+	5.73669i	0.870425	+	0.233230i
$606$		0			0
$607$	29.1103	+	16.8068i	1.18155	+	0.682168i	0.956373	−	0.292149i	$-0.0943705\pi$
$607$	29.1103	+	16.8068i	1.18155	+	0.682168i	0.225178	+	0.974318i	$0.427704\pi$
$608$	−31.7370	+	2.24843i	−1.28710	+	0.0911858i
$609$		0			0
$610$	6.41140	+	12.1549i	0.259590	+	0.492138i
$611$	15.9823	+	15.9823i	0.646576	+	0.646576i
$612$		0			0
$613$	26.5621	−	26.5621i	1.07283	−	1.07283i	0.0757042	−	0.997130i	$-0.475880\pi$
$613$	26.5621	−	26.5621i	1.07283	−	1.07283i	0.997130	−	0.0757042i	$-0.0241205\pi$
$614$	10.2711	−	33.2021i	0.414509	−	1.33993i
$615$		0			0
$616$	0.250876	−	0.0371868i	0.0101081	−	0.00149830i
$617$	−11.8730	+	20.5647i	−0.477991	+	0.827904i	−0.999682	−	0.0252305i	$-0.991968\pi$
$617$	−11.8730	+	20.5647i	−0.477991	+	0.827904i	0.521691	+	0.853134i	$0.325301\pi$
$618$		0			0
$619$	4.60330	−	17.1798i	0.185022	−	0.690513i	−0.809603	−	0.586977i	$-0.800318\pi$
$619$	4.60330	−	17.1798i	0.185022	−	0.690513i	0.994626	−	0.103535i	$-0.0330155\pi$
$620$	18.1706	−	15.5856i	0.729748	−	0.625933i
$621$		0			0
$622$	−19.4897	−	0.745149i	−0.781466	−	0.0298778i
$623$	−0.676151	−	1.17113i	−0.0270894	−	0.0469202i
$624$		0			0
$625$	−10.9760	+	19.0109i	−0.439038	+	0.760436i
$626$	−15.3428	+	24.3738i	−0.613221	+	0.974173i
$627$		0			0
$628$	−11.1404	+	31.6719i	−0.444550	+	1.26384i
$629$	28.7164	+	28.7164i	1.14500	+	1.14500i
$630$		0			0
$631$	16.0572			0.639228			0.319614	−	0.947548i	$-0.396447\pi$
$631$	16.0572			0.639228			0.319614	+	0.947548i	$0.396447\pi$
$632$	3.90811	+	9.01753i	0.155456	+	0.358698i
$633$		0			0
$634$	29.0008	−	6.59441i	1.15177	−	0.261897i
$635$	7.15884	+	26.7172i	0.284090	+	1.06024i
$636$		0			0
$637$	−3.44897	+	12.8717i	−0.136653	+	0.509997i
$638$	−0.952893	−	0.0364320i	−0.0377254	−	0.00144235i
$639$		0			0
$640$	−20.7382	+	11.8161i	−0.819749	+	0.467071i
$641$	−35.3930	+	20.4342i	−1.39794	+	0.807102i	−0.994177	−	0.107761i	$-0.965632\pi$
$641$	−35.3930	+	20.4342i	−1.39794	+	0.807102i	−0.403764	+	0.914863i	$0.632298\pi$
$642$		0			0
$643$	−8.91467	−	33.2700i	−0.351560	−	1.31204i	−0.884758	−	0.466050i	$-0.845677\pi$
$643$	−8.91467	−	33.2700i	−0.351560	−	1.31204i	0.533198	−	0.845991i	$-0.320990\pi$
$644$	1.65786	+	1.13427i	0.0653287	+	0.0446964i
$645$		0			0
$646$	−32.8455	−	10.1608i	−1.29229	−	0.399771i
$647$			28.1696i			1.10746i	0.832696	+	0.553730i	$0.186796\pi$
$647$			28.1696i			1.10746i	−0.832696	+	0.553730i	$0.813204\pi$
$648$		0			0
$649$			2.97943i			0.116953i
$650$	−0.438047	+	1.41602i	−0.0171816	+	0.0555408i
$651$		0			0
$652$	−0.255650	−	1.36330i	−0.0100120	−	0.0533908i
$653$	−2.17456	−	8.11558i	−0.0850972	−	0.317587i	0.910235	−	0.414091i	$-0.135901\pi$
$653$	−2.17456	−	8.11558i	−0.0850972	−	0.317587i	−0.995333	+	0.0965042i	$0.969234\pi$
$654$		0			0
$655$	8.98247	−	5.18603i	0.350974	−	0.202635i
$656$	36.4757	+	5.61941i	1.42414	+	0.219401i
$657$		0			0
$658$	0.0816744	−	2.13623i	0.00318400	−	0.0832789i
$659$	6.62788	−	24.7356i	0.258186	−	0.963562i	−0.708105	−	0.706107i	$-0.750450\pi$
$659$	6.62788	−	24.7356i	0.258186	−	0.963562i	0.966290	−	0.257455i	$-0.0828838\pi$
$660$		0			0
$661$	−5.44473	−	20.3200i	−0.211775	−	0.790357i	−0.987277	−	0.159011i	$-0.949170\pi$
$661$	−5.44473	−	20.3200i	−0.211775	−	0.790357i	0.775501	−	0.631346i	$-0.217497\pi$
$662$	−5.53914	−	24.3600i	−0.215285	−	0.946778i
$663$		0			0
$664$	4.00710	+	1.58398i	0.155506	+	0.0614704i
$665$	−1.51424			−0.0587198
$666$		0			0
$667$	−5.34063	−	5.34063i	−0.206790	−	0.206790i
$668$	−19.4526	+	9.32887i	−0.752644	+	0.360945i
$669$		0			0
$670$	−5.25692	−	3.30912i	−0.203093	−	0.127842i
$671$	−1.61818	+	2.80277i	−0.0624691	+	0.108200i
$672$		0			0
$673$	−12.5221	−	21.6890i	−0.482693	−	0.836048i	0.517110	−	0.855919i	$-0.327008\pi$
$673$	−12.5221	−	21.6890i	−0.482693	−	0.836048i	−0.999803	+	0.0198709i	$0.993674\pi$
$674$	0.521432	−	13.6383i	0.0200848	−	0.525327i
$675$		0			0
$676$	−1.42921	+	18.6635i	−0.0549696	+	0.717825i
$677$	4.91241	−	18.3334i	0.188799	−	0.704608i	−0.804986	−	0.593294i	$-0.797827\pi$
$677$	4.91241	−	18.3334i	0.188799	−	0.704608i	0.993785	−	0.111314i	$-0.0355060\pi$
$678$		0			0
$679$	0.423420	−	0.733386i	0.0162494	−	0.0281448i
$680$	−25.5135	+	3.78180i	−0.978396	+	0.145026i
$681$		0			0
$682$	5.38596	+	1.66615i	0.206239	+	0.0638003i
$683$	−3.70253	+	3.70253i	−0.141673	+	0.141673i	−0.774386	−	0.632713i	$-0.781941\pi$
$683$	−3.70253	+	3.70253i	−0.141673	+	0.141673i	0.632713	+	0.774386i	$0.281941\pi$
$684$		0			0
$685$	10.1803	+	10.1803i	0.388969	+	0.388969i
$686$	2.23221	−	1.17743i	0.0852263	−	0.0449547i
$687$		0			0
$688$	−44.7520	+	4.89475i	−1.70616	+	0.186611i
$689$	0.00605326	+	0.00349485i	0.000230611	+	0.000133143i
$690$		0			0
$691$	8.18783	+	2.19392i	0.311480	+	0.0834607i	0.411173	−	0.911558i	$-0.365119\pi$
$691$	8.18783	+	2.19392i	0.311480	+	0.0834607i	−0.0996929	+	0.995018i	$0.531786\pi$
$692$	−7.25455	+	6.22251i	−0.275777	+	0.236544i
$693$		0			0
$694$	18.3110	+	19.7669i	0.695078	+	0.750340i
$695$	−19.5631	+	11.2947i	−0.742070	+	0.428434i
$696$		0			0
$697$	34.5379	+	19.9405i	1.30822	+	0.755299i
$698$	5.67274	+	24.9475i	0.214716	+	0.944278i
$699$		0			0
$700$	0.126408	−	0.0606214i	0.00477777	−	0.00229127i
$701$	−16.2977	+	16.2977i	−0.615557	+	0.615557i	−0.944389	−	0.328831i	$-0.893345\pi$
$701$	−16.2977	+	16.2977i	−0.615557	+	0.615557i	0.328831	+	0.944389i	$0.393345\pi$
$702$		0			0
$703$		−	52.8439i		−	1.99304i
$704$	−4.95680	−	2.65081i	−0.186816	−	0.0999063i
$705$		0			0
$706$	4.92023	−	7.81637i	0.185175	−	0.294173i
$707$	1.54314	−	0.413484i	0.0580359	−	0.0155507i
$708$		0			0
$709$	−18.6437	−	4.99557i	−0.700180	−	0.187613i	−0.108869	−	0.994056i	$-0.534723\pi$
$709$	−18.6437	−	4.99557i	−0.700180	−	0.187613i	−0.591311	+	0.806443i	$0.701390\pi$
$710$	7.71848	+	8.33214i	0.289669	+	0.312700i
$711$		0			0
$712$	−3.42856	+	29.7753i	−0.128491	+	1.11588i
$713$	22.3267	+	38.6710i	0.836142	+	1.44824i
$714$		0			0
$715$	2.73210	−	0.732065i	0.102175	−	0.0273777i
$716$	−9.81001	+	1.83961i	−0.366617	+	0.0687493i
$717$		0			0
$718$	15.0483	+	28.5291i	0.561599	+	1.06470i
$719$	24.2401			0.904003			0.452002	−	0.892017i	$-0.350710\pi$
$719$	24.2401			0.904003			0.452002	+	0.892017i	$0.350710\pi$
$720$		0			0
$721$	1.07669			0.0400980
$722$	8.33596	+	15.8036i	0.310232	+	0.588148i
$723$		0			0
$724$	−3.83090	−	20.4289i	−0.142374	−	0.759234i
$725$	−0.509157	+	0.136428i	−0.0189096	+	0.00506682i
$726$		0			0
$727$	−8.10074	−	14.0309i	−0.300440	−	0.520377i	0.675796	−	0.737089i	$-0.263800\pi$
$727$	−8.10074	−	14.0309i	−0.300440	−	0.520377i	−0.976236	+	0.216712i	$0.930467\pi$
$728$	−0.539526	+	0.428105i	−0.0199962	+	0.0158666i
$729$		0			0
$730$	3.80516	+	4.10769i	0.140835	+	0.152032i
$731$	−46.9902	−	12.5910i	−1.73800	−	0.465694i
$732$		0			0
$733$	8.04180	−	2.15479i	0.297031	−	0.0795891i	−0.107226	−	0.994235i	$-0.534197\pi$
$733$	8.04180	−	2.15479i	0.297031	−	0.0795891i	0.404257	+	0.914646i	$0.367530\pi$
$734$	18.0686	−	28.7041i	0.666924	−	1.05949i
$735$		0			0
$736$	−14.5332	−	42.0824i	−0.535700	−	1.55118i
$737$		−	1.46289i		−	0.0538863i
$738$		0			0
$739$	22.8405	−	22.8405i	0.840203	−	0.840203i	−0.148682	−	0.988885i	$-0.547503\pi$
$739$	22.8405	−	22.8405i	0.840203	−	0.840203i	0.988885	+	0.148682i	$0.0475030\pi$
$740$	−17.1421	−	35.7447i	−0.630155	−	1.31400i
$741$		0			0
$742$	−0.000146584	0	0.000644647i	−5.38128e−6	0	2.36657e-5i
$743$	7.19608	+	4.15466i	0.263999	+	0.152420i	0.626157	−	0.779697i	$-0.284627\pi$
$743$	7.19608	+	4.15466i	0.263999	+	0.152420i	−0.362159	+	0.932116i	$0.617960\pi$
$744$		0			0
$745$	−0.385931	+	0.222817i	−0.0141394	+	0.00816339i
$746$	−23.0544	−	24.8874i	−0.844083	−	0.911192i
$747$		0			0
$748$	−3.95462	−	4.61052i	−0.144595	−	0.168577i
$749$	1.26399	+	0.338684i	0.0461850	+	0.0123752i
$750$		0			0
$751$	28.0215	+	16.1782i	1.02252	+	0.590352i	0.914833	−	0.403833i	$-0.132322\pi$
$751$	28.0215	+	16.1782i	1.02252	+	0.590352i	0.107687	+	0.994185i	$0.465656\pi$
$752$	−29.6623	+	36.9478i	−1.08167	+	1.34735i
$753$		0			0
$754$	2.29052	−	1.20819i	0.0834158	−	0.0439996i
$755$	−3.42502	−	3.42502i	−0.124649	−	0.124649i
$756$		0			0
$757$	3.76265	−	3.76265i	0.136756	−	0.136756i	−0.635415	−	0.772171i	$-0.719171\pi$
$757$	3.76265	−	3.76265i	0.136756	−	0.136756i	0.772171	+	0.635415i	$0.219171\pi$
$758$	−19.0423	−	5.89077i	−0.691649	−	0.213962i
$759$		0			0
$760$	26.9545	+	19.9953i	0.977743	+	0.725304i
$761$	−13.1168	+	22.7190i	−0.475485	+	0.823564i	−0.999606	−	0.0280801i	$-0.991061\pi$
$761$	−13.1168	+	22.7190i	−0.475485	+	0.823564i	0.524121	+	0.851644i	$0.324394\pi$
$762$		0			0
$763$	0.480419	−	1.79295i	0.0173923	−	0.0649090i
$764$	10.3253	+	0.790689i	0.373556	+	0.0286061i
$765$		0			0
$766$	0.249371	−	6.52239i	0.00901012	−	0.235664i
$767$	−4.04557	−	7.00713i	−0.146077	−	0.253013i
$768$		0			0
$769$	−9.31591	+	16.1356i	−0.335940	+	0.581865i	−0.983665	−	0.180009i	$-0.942387\pi$
$769$	−9.31591	+	16.1356i	−0.335940	+	0.581865i	0.647725	+	0.761874i	$0.275721\pi$
$770$	−0.226403	−	0.142516i	−0.00815901	−	0.00513592i
$771$		0			0
$772$	−22.8614	−	47.6707i	−0.822801	−	1.71571i
$773$	4.69430	+	4.69430i	0.168842	+	0.168842i	0.786470	−	0.617628i	$-0.211906\pi$
$773$	4.69430	+	4.69430i	0.168842	+	0.168842i	−0.617628	+	0.786470i	$0.711906\pi$
$774$		0			0
$775$	3.11641			0.111945
$776$	−17.2214	+	7.46357i	−0.618211	+	0.267927i
$777$		0			0
$778$	4.01129	+	17.6408i	0.143812	+	0.632454i
$779$	−13.4311	−	50.1255i	−0.481218	−	1.79593i
$780$		0			0
$781$	−0.692294	+	2.58368i	−0.0247722	+	0.0924512i
$782$	1.83805	−	48.0749i	0.0657284	−	1.71915i
$783$		0			0
$784$	−27.6091	−	4.25344i	−0.986041	−	0.151909i
$785$	30.6704	−	17.7076i	1.09467	−	0.632010i
$786$		0			0
$787$	−11.7352	−	43.7964i	−0.418315	−	1.56117i	−0.778101	−	0.628139i	$-0.783817\pi$
$787$	−11.7352	−	43.7964i	−0.418315	−	1.56117i	0.359786	−	0.933035i	$-0.382850\pi$
$788$	−14.3072	+	2.68293i	−0.509672	+	0.0955755i
$789$		0			0
$790$	3.06377	−	9.90384i	0.109004	−	0.352363i
$791$		−	2.69611i		−	0.0958625i
$792$		0			0
$793$		−	8.78888i		−	0.312102i
$794$	7.07544	+	2.18880i	0.251098	+	0.0776775i
$795$		0			0
$796$	−1.55211	+	2.26858i	−0.0550131	+	0.0804077i
$797$	9.77347	+	36.4751i	0.346194	+	1.29201i	0.891211	+	0.453589i	$0.149857\pi$
$797$	9.77347	+	36.4751i	0.346194	+	1.29201i	−0.545017	+	0.838425i	$0.683477\pi$
$798$		0			0
$799$	−44.3411	+	25.6004i	−1.56868	+	0.905676i
$800$	−3.05064	−	0.590090i	−0.107856	−	0.0208628i
$801$		0			0
$802$	18.9079	+	0.722905i	0.667660	+	0.0255266i
$803$	−0.341296	+	1.27374i	−0.0120441	+	0.0449492i
$804$		0			0
$805$	−0.548411	−	2.04670i	−0.0193289	−	0.0721366i
$806$	−14.9293	+	3.39472i	−0.525861	+	0.119574i
$807$		0			0
$808$	−32.9290	−	13.0166i	−1.15844	−	0.457922i
$809$	24.0071			0.844045			0.422023	−	0.906585i	$-0.361320\pi$
$809$	24.0071			0.844045			0.422023	+	0.906585i	$0.361320\pi$
$810$		0			0
$811$	−0.243845	−	0.243845i	−0.00856256	−	0.00856256i	0.702813	−	0.711375i	$-0.251927\pi$
$811$	−0.243845	−	0.243845i	−0.00856256	−	0.00856256i	−0.711375	+	0.702813i	$0.751927\pi$
$812$	−0.231057	−	0.0812729i	−0.00810850	−	0.00285212i
$813$		0			0
$814$	4.97351	−	7.90100i	0.174321	−	0.276930i
$815$	−0.731560	+	1.26710i	−0.0256254	+	0.0443846i
$816$		0			0
$817$	31.6507	+	54.8205i	1.10732	+	1.91793i
$818$	−39.3350	−	1.50389i	−1.37532	−	0.0525824i
$819$		0			0
$820$	−25.3453	−	29.5490i	−0.885097	−	1.03190i
$821$	12.4067	−	46.3025i	0.432998	−	1.61597i	−0.312815	−	0.949814i	$-0.601272\pi$
$821$	12.4067	−	46.3025i	0.432998	−	1.61597i	0.745813	−	0.666156i	$-0.232061\pi$
$822$		0			0
$823$	−0.737958	+	1.27818i	−0.0257236	+	0.0445546i	−0.878601	−	0.477557i	$-0.841522\pi$
$823$	−0.737958	+	1.27818i	−0.0257236	+	0.0445546i	0.852877	+	0.522112i	$0.174856\pi$
$824$	−19.1658	−	14.2175i	−0.667672	−	0.495289i
$825$		0			0
$826$	−0.226165	+	0.731096i	−0.00786930	+	0.0254381i
$827$	11.5464	−	11.5464i	0.401509	−	0.401509i	−0.477256	−	0.878764i	$-0.658368\pi$
$827$	11.5464	−	11.5464i	0.401509	−	0.401509i	0.878764	+	0.477256i	$0.158368\pi$
$828$		0			0
$829$	34.7961	+	34.7961i	1.20852	+	1.20852i	0.971507	+	0.237010i	$0.0761675\pi$
$829$	34.7961	+	34.7961i	1.20852	+	1.20852i	0.237010	+	0.971507i	$0.423833\pi$
$830$	−2.12051	−	4.02012i	−0.0736039	−	0.139540i
$831$		0			0
$832$	15.2569	−	0.496227i	0.528940	−	0.0172036i
$833$	−26.1424	−	15.0933i	−0.905781	−	0.522953i
$834$		0			0
$835$	21.9815	+	5.88992i	0.760700	+	0.203829i
$836$	−0.603493	+	7.88077i	−0.0208722	+	0.272562i
$837$		0			0
$838$	10.7182	−	9.92880i	0.370254	−	0.342985i
$839$	41.3065	−	23.8483i	1.42606	−	0.823335i	0.429252	−	0.903185i	$-0.358777\pi$
$839$	41.3065	−	23.8483i	1.42606	−	0.823335i	0.996807	+	0.0798497i	$0.0254440\pi$
$840$		0			0
$841$	−24.3172	−	14.0395i	−0.838523	−	0.484122i
$842$	42.6196	−	9.69114i	1.46877	−	0.333979i
$843$		0			0
$844$	−21.7553	−	7.65233i	−0.748850	−	0.263404i
$845$	13.9615	−	13.9615i	0.480290	−	0.480290i
$846$		0			0
$847$			1.34076i			0.0460692i
$848$	−0.00590313	+	0.0134108i	−0.000202714	+	0.000460527i
$849$		0			0
$850$	−2.84155	−	1.78869i	−0.0974643	−	0.0613517i
$851$	71.4254	−	19.1384i	2.44843	−	0.656055i
$852$		0			0
$853$	42.5120	+	11.3911i	1.45558	+	0.390023i	0.897962	−	0.440072i	$-0.145047\pi$
$853$	42.5120	+	11.3911i	1.45558	+	0.390023i	0.557622	+	0.830095i	$0.311714\pi$
$854$	−0.609827	+	0.564913i	−0.0208678	+	0.0193309i
$855$		0			0
$856$	−18.0275	−	22.7195i	−0.616168	−	0.776535i
$857$	−4.36756	−	7.56483i	−0.149193	−	0.258410i	0.781736	−	0.623609i	$-0.214334\pi$
$857$	−4.36756	−	7.56483i	−0.149193	−	0.258410i	−0.930929	+	0.365199i	$0.881001\pi$
$858$		0			0
$859$	−48.4800	+	12.9902i	−1.65411	+	0.443219i	−0.960761	−	0.277378i	$-0.910534\pi$
$859$	−48.4800	+	12.9902i	−1.65411	+	0.443219i	−0.693354	+	0.720597i	$0.743868\pi$
$860$	39.1925	+	26.8146i	1.33645	+	0.914370i
$861$		0			0
$862$	18.5690	−	9.79464i	0.632461	−	0.333607i
$863$	3.87853			0.132027			0.0660134	−	0.997819i	$-0.478972\pi$
$863$	3.87853			0.132027			0.0660134	+	0.997819i	$0.478972\pi$
$864$		0			0
$865$	10.0817			0.342789
$866$	40.2300	−	21.2203i	1.36707	−	0.721094i
$867$		0			0
$868$	1.19514	+	0.817686i	0.0405656	+	0.0277541i
$869$	2.35827	−	0.631896i	0.0799988	−	0.0214356i
$870$		0			0
$871$	1.98636	+	3.44049i	0.0673054	+	0.116576i
$872$	−32.2272	+	25.5718i	−1.09135	+	0.865970i
$873$		0			0
$874$	−45.9248	+	42.5424i	−1.55343	+	1.43902i
$875$	−1.44311	−	0.386679i	−0.0487859	−	0.0130721i
$876$		0			0
$877$	−20.2871	+	5.43592i	−0.685047	+	0.183558i	−0.584524	−	0.811377i	$-0.698719\pi$
$877$	−20.2871	+	5.43592i	−0.685047	+	0.183558i	−0.100524	+	0.994935i	$0.532052\pi$
$878$	0.335198	+	0.211000i	0.0113124	+	0.00712091i
$879$		0			0
$880$	2.14824	+	5.52649i	0.0724170	+	0.186298i
$881$			7.45496i			0.251164i	0.992083	+	0.125582i	$0.0400798\pi$
$881$			7.45496i			0.251164i	−0.992083	+	0.125582i	$0.959920\pi$
$882$		0			0
$883$	−9.55597	+	9.55597i	−0.321584	+	0.321584i	−0.849375	−	0.527791i	$-0.823021\pi$
$883$	−9.55597	+	9.55597i	−0.321584	+	0.321584i	0.527791	+	0.849375i	$0.323021\pi$
$884$	15.5609	+	5.47348i	0.523371	+	0.184093i
$885$		0			0
$886$	−34.6332	+	7.87514i	−1.16353	+	0.264570i
$887$	41.0581	+	23.7049i	1.37860	+	0.795934i	0.991991	−	0.126311i	$-0.0403138\pi$
$887$	41.0581	+	23.7049i	1.37860	+	0.795934i	0.386607	+	0.922245i	$0.373647\pi$
$888$		0			0
$889$	−1.44899	+	0.836573i	−0.0485975	+	0.0280578i
$890$	23.1934	−	21.4852i	0.777444	−	0.720185i
$891$		0			0
$892$	−3.17080	+	41.4062i	−0.106166	+	1.38638i
$893$	64.3530	+	17.2433i	2.15349	+	0.577027i
$894$		0			0
$895$	9.11780	+	5.26416i	0.304774	+	0.175962i
$896$	−1.01508	−	1.02673i	−0.0339116	−	0.0343005i
$897$		0			0
$898$	9.42757	+	17.8731i	0.314602	+	0.596431i
$899$	−3.85003	−	3.85003i	−0.128406	−	0.128406i
$900$		0			0
$901$	−0.0111960	+	0.0111960i	−0.000372994	+	0.000372994i
$902$	2.70950	−	8.75865i	0.0902165	−	0.291631i
$903$		0			0
$904$	−35.6015	+	47.9925i	−1.18409	+	1.59621i
$905$	−10.9624	+	18.9874i	−0.364402	+	0.631162i
$906$		0			0
$907$	−3.66301	+	13.6705i	−0.121628	+	0.453923i	−0.999697	−	0.0246114i	$-0.992165\pi$
$907$	−3.66301	+	13.6705i	−0.121628	+	0.453923i	0.878069	+	0.478534i	$0.158832\pi$
$908$	10.3180	+	12.0293i	0.342413	+	0.399205i
$909$		0			0
$910$	0.725977	+	0.0277563i	0.0240659	+	0.000920111i
$911$	−20.0062	−	34.6517i	−0.662834	−	1.14806i	−0.979868	−	0.199648i	$-0.936020\pi$
$911$	−20.0062	−	34.6517i	−0.662834	−	1.14806i	0.317034	−	0.948414i	$-0.397313\pi$
$912$		0			0
$913$	0.535197	−	0.926988i	0.0177124	−	0.0306788i
$914$	20.9738	−	33.3193i	0.693751	−	1.10211i
$915$		0			0
$916$	−0.876405	−	0.308271i	−0.0289572	−	0.0101856i
$917$	0.443647	+	0.443647i	0.0146505	+	0.0146505i
$918$		0			0
$919$	−18.6876			−0.616446			−0.308223	−	0.951314i	$-0.599734\pi$
$919$	−18.6876			−0.616446			−0.308223	+	0.951314i	$0.599734\pi$
$920$	−17.2641	+	43.6742i	−0.569182	+	1.43990i
$921$		0			0
$922$	23.1120	−	5.25536i	0.761153	−	0.173076i
$923$	−1.88004	−	7.01641i	−0.0618823	−	0.230948i
$924$		0			0
$925$	1.33569	−	4.98486i	0.0439172	−	0.163901i
$926$	−42.7452	−	1.63428i	−1.40470	−	0.0537057i
$927$		0			0
$928$	3.03977	+	4.49777i	0.0997853	+	0.147646i
$929$	8.76538	−	5.06070i	0.287583	−	0.166036i	−0.349268	−	0.937023i	$-0.613570\pi$
$929$	8.76538	−	5.06070i	0.287583	−	0.166036i	0.636851	+	0.770987i	$0.280237\pi$
$930$		0			0
$931$	10.1662	+	37.9409i	0.333185	+	1.24346i
$932$	−10.3191	+	15.0825i	−0.338014	+	0.494044i
$933$		0			0
$934$	30.4500	+	9.41974i	0.996354	+	0.308223i
$935$			6.40729i			0.209541i
$936$		0			0
$937$			19.1375i			0.625194i	0.949886	+	0.312597i	$0.101199\pi$
$937$			19.1375i			0.625194i	−0.949886	+	0.312597i	$0.898801\pi$
$938$	0.111047	−	0.358966i	0.00362580	−	0.0117207i
$939$		0			0
$940$	49.1234	−	9.21178i	1.60223	−	0.300455i
$941$	−11.1081	−	41.4559i	−0.362113	−	1.35142i	−0.871292	−	0.490764i	$-0.836718\pi$
$941$	−11.1081	−	41.4559i	−0.362113	−	1.35142i	0.509179	−	0.860660i	$-0.329949\pi$
$942$		0			0
$943$	62.8868	−	36.3077i	2.04788	−	1.18234i
$944$	13.6799	−	10.0275i	0.445241	−	0.326368i
$945$		0			0
$946$	−0.427269	+	11.1754i	−0.0138917	+	0.363344i
$947$	−12.0721	+	45.0535i	−0.392289	+	1.46404i	0.434060	+	0.900884i	$0.357081\pi$
$947$	−12.0721	+	45.0535i	−0.392289	+	1.46404i	−0.826349	+	0.563159i	$0.809586\pi$
$948$		0			0
$949$	−0.926848	−	3.45904i	−0.0300867	−	0.112285i
$950$	0.968731	+	4.26028i	0.0314298	+	0.138222i
$951$		0			0
$952$	−0.620410	−	1.43153i	−0.0201076	−	0.0463960i
$953$	20.2249			0.655149			0.327575	−	0.944825i	$-0.393769\pi$
$953$	20.2249			0.655149			0.327575	+	0.944825i	$0.393769\pi$
$954$		0			0
$955$	−7.72399	−	7.72399i	−0.249943	−	0.249943i
$956$	−6.32752	−	13.1942i	−0.204647	−	0.426730i
$957$		0			0
$958$	−35.4502	−	22.3151i	−1.14534	−	0.720969i
$959$	−0.435445	+	0.754212i	−0.0140612	+	0.0243548i
$960$		0			0
$961$	0.595170	+	1.03087i	0.0191990	+	0.0332537i
$962$	−0.968635	+	25.3351i	−0.0312301	+	0.816836i
$963$		0			0
$964$	−4.97974	−	0.381338i	−0.160387	−	0.0122821i
$965$	−14.4339	+	53.8680i	−0.464644	+	1.73407i
$966$		0			0
$967$	15.9815	−	27.6807i	0.513930	−	0.890152i	−0.485940	−	0.873992i	$-0.661523\pi$
$967$	15.9815	−	27.6807i	0.513930	−	0.890152i	0.999869	−	0.0161601i	$-0.00514413\pi$
$968$	17.7045	−	23.8665i	0.569045	−	0.767098i
$969$		0			0
$970$	18.9140	+	5.85108i	0.607293	+	0.187867i
$971$	−4.69660	+	4.69660i	−0.150721	+	0.150721i	−0.778440	−	0.627719i	$-0.783989\pi$
$971$	−4.69660	+	4.69660i	−0.150721	+	0.150721i	0.627719	+	0.778440i	$0.283989\pi$
$972$		0			0
$973$	−0.966226	−	0.966226i	−0.0309758	−	0.0309758i
$974$	−32.0622	+	16.9120i	−1.02734	+	0.541895i
$975$		0			0
$976$	18.3149	−	2.00319i	0.586245	−	0.0641205i
$977$	22.7888	+	13.1571i	0.729079	+	0.420934i	0.818085	−	0.575097i	$-0.195036\pi$
$977$	22.7888	+	13.1571i	0.729079	+	0.420934i	−0.0890064	+	0.996031i	$0.528369\pi$
$978$		0			0
$979$	7.19193	+	1.92707i	0.229855	+	0.0615895i
$980$	19.1844	+	22.3662i	0.612822	+	0.714463i
$981$		0			0
$982$	−5.22426	−	5.63962i	−0.166713	−	0.179968i
$983$	−19.6448	+	11.3420i	−0.626573	+	0.361752i	−0.779424	−	0.626497i	$-0.784488\pi$
$983$	−19.6448	+	11.3420i	−0.626573	+	0.361752i	0.152851	+	0.988249i	$0.451155\pi$
$984$		0			0
$985$	13.2976	+	7.67740i	0.423698	+	0.244622i
$986$	1.30070	+	5.72022i	0.0414228	+	0.182169i
$987$		0			0
$988$	−9.28146	−	19.3537i	−0.295283	−	0.615724i
$989$	−62.6343	+	62.6343i	−1.99165	+	1.99165i
$990$		0			0
$991$			13.0577i			0.414793i	0.978257	+	0.207396i	$0.0664990\pi$
$991$			13.0577i			0.414793i	−0.978257	+	0.207396i	$0.933501\pi$
$992$	−10.4769	−	30.3369i	−0.332641	−	0.963197i
$993$		0			0
$994$	−0.366000	+	0.581435i	−0.0116088	+	0.0184420i
$995$	2.80066	−	0.750435i	0.0887870	−	0.0237904i
$996$		0			0
$997$	7.68222	+	2.05844i	0.243298	+	0.0651916i	0.378407	−	0.925639i	$-0.376472\pi$
$997$	7.68222	+	2.05844i	0.243298	+	0.0651916i	−0.135109	+	0.990831i	$0.543139\pi$
$998$	−21.4694	−	23.1763i	−0.679601	−	0.733633i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.v.a.179.4		88
3.2	odd	2		144.2.u.a.131.19	yes	88
4.3	odd	2		1728.2.z.a.1583.5		88
9.2	odd	6	inner	432.2.v.a.35.4		88
9.7	even	3		144.2.u.a.83.19	yes	88
12.11	even	2		576.2.y.a.239.22		88
16.5	even	4		1728.2.z.a.719.5		88
16.11	odd	4	inner	432.2.v.a.395.4		88
36.7	odd	6		576.2.y.a.47.11		88
36.11	even	6		1728.2.z.a.1007.5		88
48.5	odd	4		576.2.y.a.527.11		88
48.11	even	4		144.2.u.a.59.19	yes	88
144.11	even	12	inner	432.2.v.a.251.4		88
144.43	odd	12		144.2.u.a.11.19	✓	88
144.101	odd	12		1728.2.z.a.143.5		88
144.133	even	12		576.2.y.a.335.22		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.19	✓	88	144.43	odd	12
144.2.u.a.59.19	yes	88	48.11	even	4
144.2.u.a.83.19	yes	88	9.7	even	3
144.2.u.a.131.19	yes	88	3.2	odd	2
432.2.v.a.35.4		88	9.2	odd	6	inner
432.2.v.a.179.4		88	1.1	even	1	trivial
432.2.v.a.251.4		88	144.11	even	12	inner
432.2.v.a.395.4		88	16.11	odd	4	inner
576.2.y.a.47.11		88	36.7	odd	6
576.2.y.a.239.22		88	12.11	even	2
576.2.y.a.335.22		88	144.133	even	12
576.2.y.a.527.11		88	48.5	odd	4
1728.2.z.a.143.5		88	144.101	odd	12
1728.2.z.a.719.5		88	16.5	even	4
1728.2.z.a.1007.5		88	36.11	even	6
1728.2.z.a.1583.5		88	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.v (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.25087 + 0.659799i) q^{2} +(1.12933 - 1.65064i) q^{4} +(-2.03779 + 0.546024i) q^{5} +(-0.0638076 - 0.110518i) q^{7} +(-0.323550 + 2.80986i) q^{8} +(2.18873 - 2.02753i) q^{10} +(0.678695 + 0.181856i) q^{11} +(-1.84311 + 0.493860i) q^{13} +(0.152734 + 0.0961430i) q^{14} +(-1.44923 - 3.72824i) q^{16} -4.32243i q^{17} +(-3.97707 + 3.97707i) q^{19} +(-1.40005 + 3.98030i) q^{20} +(-0.968944 + 0.220325i) q^{22} +(-6.81589 - 3.93516i) q^{23} +(-0.475689 + 0.274639i) q^{25} +(1.97963 - 1.83383i) q^{26} +(-0.254485 - 0.0194880i) q^{28} +(0.926957 + 0.248377i) q^{29} +(-4.91353 - 2.83683i) q^{31} +(4.27267 + 3.70733i) q^{32} +(2.85194 + 5.40679i) q^{34} +(0.190372 + 0.190372i) q^{35} +(-6.64358 + 6.64358i) q^{37} +(2.35071 - 7.59884i) q^{38} +(-0.874924 - 5.90257i) q^{40} +(-4.61325 + 7.99038i) q^{41} +(2.91294 - 10.8712i) q^{43} +(1.06665 - 0.914906i) q^{44} +(11.1222 + 0.425234i) q^{46} +(-5.92267 - 10.2584i) q^{47} +(3.49186 - 6.04807i) q^{49} +(0.413816 - 0.657395i) q^{50} +(-1.26629 + 3.60004i) q^{52} +(-0.00259022 - 0.00259022i) q^{53} -1.48233 q^{55} +(0.331185 - 0.143532i) q^{56} +(-1.32338 + 0.300919i) q^{58} +(1.09748 + 4.09587i) q^{59} +(-1.19213 + 4.44908i) q^{61} +(8.01790 + 0.306548i) q^{62} +(-7.79063 - 1.81826i) q^{64} +(3.48621 - 2.01276i) q^{65} +(-0.538862 - 2.01106i) q^{67} +(-7.13478 - 4.88146i) q^{68} +(-0.363737 - 0.112522i) q^{70} +3.80683i q^{71} +1.87674i q^{73} +(3.92680 - 12.6937i) q^{74} +(2.07328 + 11.0561i) q^{76} +(-0.0232076 - 0.0866118i) q^{77} +(3.00919 - 1.73736i) q^{79} +(4.98892 + 6.80604i) q^{80} +(0.498509 - 13.0387i) q^{82} +(0.394284 - 1.47149i) q^{83} +(2.36015 + 8.80821i) q^{85} +(3.52914 + 15.5204i) q^{86} +(-0.730581 + 1.84820i) q^{88} +10.5967 q^{89} +(0.172185 + 0.172185i) q^{91} +(-14.1929 + 6.80649i) q^{92} +(14.1769 + 8.92407i) q^{94} +(5.93284 - 10.2760i) q^{95} +(3.31795 + 5.74685i) q^{97} +(-0.377331 + 9.86925i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38}+ \cdots - 4 q^{97}+O(q^{100}) \) 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 + 48 * q^20 - 2 * q^22 + 12 * q^23 + 8 * q^28 + 6 * q^29 + 6 * q^32 + 2 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 40 * q^46 - 24 * q^49 - 72 * q^50 - 2 * q^52 - 16 * q^55 - 36 * q^56 + 16 * q^58 + 42 * q^59 - 2 * q^61 - 44 * q^64 + 12 * q^65 - 2 * q^67 - 96 * q^68 - 16 * q^70 - 78 * q^74 - 14 * q^76 + 6 * q^77 - 36 * q^82 - 54 * q^83 + 8 * q^85 - 54 * q^86 + 22 * q^88 + 20 * q^91 - 108 * q^92 + 6 * q^94 - 4 * q^97

Introduction

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