LMFDB - Embedded newform 405.2.p.a.289.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,2,Mod(19,405)] 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("405.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([16, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.p (of order $18$, degree $6$, 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:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			289.8
Character	$\chi$	$=$	405.289
Dual form			405.2.p.a.199.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.133405 + 0.158986i) q^{2} +(0.339817 + 1.92720i) q^{4} +(-1.06091 + 1.96837i) q^{5} +(-2.83580 - 0.500029i) q^{7} +(-0.711201 - 0.410612i) q^{8} +(-0.171413 - 0.431259i) q^{10} +(-1.38169 + 0.502894i) q^{11} +(-1.55650 - 1.85496i) q^{13} +(0.457807 - 0.384146i) q^{14} +(-3.51766 + 1.28032i) q^{16} +(-1.21975 + 0.704220i) q^{17} +(2.34516 - 4.06194i) q^{19} +(-4.15395 - 1.37569i) q^{20} +(0.104371 - 0.286757i) q^{22} +(-2.36796 + 0.417535i) q^{23} +(-2.74896 - 4.17651i) q^{25} +0.502557 q^{26} -5.63507i q^{28} +(6.73596 + 5.65214i) q^{29} +(1.00865 + 5.72033i) q^{31} +(0.827470 - 2.27346i) q^{32} +(0.0507589 - 0.287868i) q^{34} +(3.99276 - 5.05143i) q^{35} +(-7.57034 + 4.37074i) q^{37} +(0.332934 + 0.914728i) q^{38} +(1.56275 - 0.964286i) q^{40} +(-8.32538 + 6.98582i) q^{41} +(2.63439 + 7.23793i) q^{43} +(-1.43870 - 2.49190i) q^{44} +(0.249515 - 0.432172i) q^{46} +(6.68918 + 1.17948i) q^{47} +(1.21391 + 0.441827i) q^{49} +(1.03073 + 0.120122i) q^{50} +(3.04596 - 3.63003i) q^{52} +5.43934i q^{53} +(0.475961 - 3.25320i) q^{55} +(1.81151 + 1.52004i) q^{56} +(-1.79722 + 0.316898i) q^{58} +(-6.83272 - 2.48691i) q^{59} +(-1.03952 + 5.89541i) q^{61} +(-1.04401 - 0.602759i) q^{62} +(-3.49236 - 6.04894i) q^{64} +(5.30255 - 1.09582i) q^{65} +(4.95280 + 5.90251i) q^{67} +(-1.77166 - 2.11138i) q^{68} +(0.270451 + 1.30868i) q^{70} +(-4.51802 - 7.82544i) q^{71} +(10.8910 + 6.28791i) q^{73} +(0.315035 - 1.78665i) q^{74} +(8.62507 + 3.13927i) q^{76} +(4.16966 - 0.735224i) q^{77} +(-1.14861 - 0.963795i) q^{79} +(1.21176 - 8.28236i) q^{80} -2.25556i q^{82} +(7.46590 - 8.89751i) q^{83} +(-0.0921308 - 3.14802i) q^{85} +(-1.50217 - 0.546744i) q^{86} +(1.18915 + 0.209680i) q^{88} +(5.96766 - 10.3363i) q^{89} +(3.48639 + 6.03861i) q^{91} +(-1.60934 - 4.42164i) q^{92} +(-1.07989 + 0.906134i) q^{94} +(5.50740 + 8.92547i) q^{95} +(-1.92260 - 5.28231i) q^{97} +(-0.232185 + 0.134052i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{4} + 9 q^{5} - 3 q^{10} + 6 q^{11} + 18 q^{14} - 24 q^{16} - 6 q^{19} + 57 q^{20} + 3 q^{25} - 48 q^{26} + 30 q^{29} - 30 q^{31} - 24 q^{34} + 12 q^{35} - 9 q^{40} + 12 q^{41} - 78 q^{44} - 6 q^{46}+ \cdots - 87 q^{95}+O(q^{100}) $ 96 * q - 12 * q^4 + 9 * q^5 - 3 * q^10 + 6 * q^11 + 18 * q^14 - 24 * q^16 - 6 * q^19 + 57 * q^20 + 3 * q^25 - 48 * q^26 + 30 * q^29 - 30 * q^31 - 24 * q^34 + 12 * q^35 - 9 * q^40 + 12 * q^41 - 78 * q^44 - 6 * q^46 - 30 * q^49 - 84 * q^50 - 12 * q^55 + 96 * q^56 - 66 * q^59 + 6 * q^61 - 45 * q^65 - 33 * q^70 + 90 * q^71 - 66 * q^74 + 12 * q^76 + 24 * q^79 - 30 * q^80 - 21 * q^85 - 18 * q^86 - 96 * q^89 - 6 * q^91 + 24 * q^94 - 87 * q^95

Character values

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

$n$	$82$	$326$
$\chi(n)$	$-1$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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

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

$2$	−0.133405	+	0.158986i	−0.0943314	+	0.112420i	−0.811145	−	0.584845i	$-0.801155\pi$
$2$	−0.133405	+	0.158986i	−0.0943314	+	0.112420i	0.716814	+	0.697265i	$0.245600\pi$
$3$		0			0
$3$		0			0
$4$	0.339817	+	1.92720i	0.169908	+	0.963598i
$5$	−1.06091	+	1.96837i	−0.474452	+	0.880282i
$5$	−1.06091	+	1.96837i	−0.474452	+	0.880282i
$6$		0			0
$7$	−2.83580	−	0.500029i	−1.07183	−	0.188993i	−0.390232	−	0.920717i	$-0.627605\pi$
$7$	−2.83580	−	0.500029i	−1.07183	−	0.188993i	−0.681602	+	0.731724i	$0.738716\pi$
$8$	−0.711201	−	0.410612i	−0.251448	−	0.145173i
$9$		0			0
$10$	−0.171413	−	0.431259i	−0.0542054	−	0.136376i
$11$	−1.38169	+	0.502894i	−0.416595	+	0.151628i	−0.541809	−	0.840502i	$-0.682260\pi$
$11$	−1.38169	+	0.502894i	−0.416595	+	0.151628i	0.125214	+	0.992130i	$0.460038\pi$
$12$		0			0
$13$	−1.55650	−	1.85496i	−0.431695	−	0.514474i	0.505715	−	0.862700i	$-0.331229\pi$
$13$	−1.55650	−	1.85496i	−0.431695	−	0.514474i	−0.937411	+	0.348226i	$0.886784\pi$
$14$	0.457807	−	0.384146i	0.122354	−	0.102667i
$15$		0			0
$16$	−3.51766	+	1.28032i	−0.879415	+	0.320081i
$17$	−1.21975	+	0.704220i	−0.295832	+	0.170799i	−0.640569	−	0.767901i	$-0.721301\pi$
$17$	−1.21975	+	0.704220i	−0.295832	+	0.170799i	0.344737	+	0.938699i	$0.387968\pi$
$18$		0			0
$19$	2.34516	−	4.06194i	0.538017	−	0.931872i	−0.460994	−	0.887403i	$-0.652507\pi$
$19$	2.34516	−	4.06194i	0.538017	−	0.931872i	0.999011	−	0.0444689i	$-0.0141595\pi$
$20$	−4.15395	−	1.37569i	−0.928851	−	0.307613i
$21$		0			0
$22$	0.104371	−	0.286757i	0.0222520	−	0.0611368i
$23$	−2.36796	+	0.417535i	−0.493753	+	0.0870620i	−0.414980	−	0.909831i	$-0.636211\pi$
$23$	−2.36796	+	0.417535i	−0.493753	+	0.0870620i	−0.0787733	+	0.996893i	$0.525100\pi$
$24$		0			0
$25$	−2.74896	−	4.17651i	−0.549791	−	0.835302i
$26$	0.502557			0.0985595
$27$		0			0
$28$		−	5.63507i		−	1.06493i
$29$	6.73596	+	5.65214i	1.25084	+	1.04958i	0.996596	+	0.0824353i	$0.0262698\pi$
$29$	6.73596	+	5.65214i	1.25084	+	1.04958i	0.254240	+	0.967141i	$0.418175\pi$
$30$		0			0
$31$	1.00865	+	5.72033i	0.181159	+	1.02740i	0.930792	+	0.365549i	$0.119119\pi$
$31$	1.00865	+	5.72033i	0.181159	+	1.02740i	−0.749634	+	0.661853i	$0.769770\pi$
$32$	0.827470	−	2.27346i	0.146277	−	0.401894i
$33$		0			0
$34$	0.0507589	−	0.287868i	0.00870509	−	0.0493690i
$35$	3.99276	−	5.05143i	0.674900	−	0.853847i
$36$		0			0
$37$	−7.57034	+	4.37074i	−1.24456	+	0.718545i	−0.970019	−	0.243031i	$-0.921858\pi$
$37$	−7.57034	+	4.37074i	−1.24456	+	0.718545i	−0.274538	+	0.961576i	$0.588525\pi$
$38$	0.332934	+	0.914728i	0.0540090	+	0.148388i
$39$		0			0
$40$	1.56275	−	0.964286i	0.247093	−	0.152467i
$41$	−8.32538	+	6.98582i	−1.30021	+	1.09100i	−0.310096	+	0.950705i	$0.600361\pi$
$41$	−8.32538	+	6.98582i	−1.30021	+	1.09100i	−0.990110	+	0.140297i	$0.955194\pi$
$42$		0			0
$43$	2.63439	+	7.23793i	0.401741	+	1.10377i	0.961425	+	0.275068i	$0.0887003\pi$
$43$	2.63439	+	7.23793i	0.401741	+	1.10377i	−0.559684	+	0.828706i	$0.689077\pi$
$44$	−1.43870	−	2.49190i	−0.216892	−	0.375667i
$45$		0			0
$46$	0.249515	−	0.432172i	0.0367889	−	0.0637203i
$47$	6.68918	+	1.17948i	0.975717	+	0.172045i	0.638702	−	0.769454i	$-0.279472\pi$
$47$	6.68918	+	1.17948i	0.975717	+	0.172045i	0.337015	+	0.941499i	$0.390583\pi$
$48$		0			0
$49$	1.21391	+	0.441827i	0.173416	+	0.0631181i
$50$	1.03073	+	0.120122i	0.145767	+	0.0169878i
$51$		0			0
$52$	3.04596	−	3.63003i	0.422398	−	0.503394i
$53$			5.43934i			0.747151i	0.927600	+	0.373575i	$0.121868\pi$
$53$			5.43934i			0.747151i	−0.927600	+	0.373575i	$0.878132\pi$
$54$		0			0
$55$	0.475961	−	3.25320i	0.0641786	−	0.438661i
$56$	1.81151	+	1.52004i	0.242073	+	0.203123i
$57$		0			0
$58$	−1.79722	+	0.316898i	−0.235986	+	0.0416108i
$59$	−6.83272	−	2.48691i	−0.889545	−	0.323768i	−0.143489	−	0.989652i	$-0.545832\pi$
$59$	−6.83272	−	2.48691i	−0.889545	−	0.323768i	−0.746055	+	0.665884i	$0.768055\pi$
$60$		0			0
$61$	−1.03952	+	5.89541i	−0.133097	+	0.754830i	0.843069	+	0.537805i	$0.180746\pi$
$61$	−1.03952	+	5.89541i	−0.133097	+	0.754830i	−0.976166	+	0.217025i	$0.930365\pi$
$62$	−1.04401	−	0.602759i	−0.132589	−	0.0765504i
$63$		0			0
$64$	−3.49236	−	6.04894i	−0.436545	−	0.756118i
$65$	5.30255	−	1.09582i	0.657701	−	0.135920i
$66$		0			0
$67$	4.95280	+	5.90251i	0.605081	+	0.721107i	0.978429	−	0.206584i	$-0.0662348\pi$
$67$	4.95280	+	5.90251i	0.605081	+	0.721107i	−0.373348	+	0.927691i	$0.621790\pi$
$68$	−1.77166	−	2.11138i	−0.214845	−	0.256043i
$69$		0			0
$70$	0.270451	+	1.30868i	0.0323250	+	0.156417i
$71$	−4.51802	−	7.82544i	−0.536190	−	0.928708i	−0.999105	−	0.0423056i	$-0.986530\pi$
$71$	−4.51802	−	7.82544i	−0.536190	−	0.928708i	0.462915	−	0.886403i	$-0.346804\pi$
$72$		0			0
$73$	10.8910	+	6.28791i	1.27469	+	0.735944i	0.975867	−	0.218364i	$-0.0700721\pi$
$73$	10.8910	+	6.28791i	1.27469	+	0.735944i	0.298825	+	0.954308i	$0.403405\pi$
$74$	0.315035	−	1.78665i	0.0366221	−	0.207694i
$75$		0			0
$76$	8.62507	+	3.13927i	0.989364	+	0.360099i
$77$	4.16966	−	0.735224i	0.475177	−	0.0837865i
$78$		0			0
$79$	−1.14861	−	0.963795i	−0.129228	−	0.108435i	0.575883	−	0.817532i	$-0.304658\pi$
$79$	−1.14861	−	0.963795i	−0.129228	−	0.108435i	−0.705111	+	0.709097i	$0.749103\pi$
$80$	1.21176	−	8.28236i	0.135478	−	0.925996i
$81$		0			0
$82$		−	2.25556i		−	0.249085i
$83$	7.46590	−	8.89751i	0.819489	−	0.976629i	−0.180487	−	0.983577i	$-0.557767\pi$
$83$	7.46590	−	8.89751i	0.819489	−	0.976629i	0.999976	+	0.00694857i	$0.00221182\pi$
$84$		0			0
$85$	−0.0921308	−	3.14802i	−0.00999299	−	0.341451i
$86$	−1.50217	−	0.546744i	−0.161983	−	0.0589569i
$87$		0			0
$88$	1.18915	+	0.209680i	0.126764	+	0.0223519i
$89$	5.96766	−	10.3363i	0.632571	−	1.09564i	−0.354454	−	0.935074i	$-0.615333\pi$
$89$	5.96766	−	10.3363i	0.632571	−	1.09564i	0.987024	−	0.160571i	$-0.0513336\pi$
$90$		0			0
$91$	3.48639	+	6.03861i	0.365473	+	0.633018i
$92$	−1.60934	−	4.42164i	−0.167786	−	0.460987i
$93$		0			0
$94$	−1.07989	+	0.906134i	−0.111382	+	0.0934606i
$95$	5.50740	+	8.92547i	0.565047	+	0.915734i
$96$		0			0
$97$	−1.92260	−	5.28231i	−0.195211	−	0.536337i	0.803010	−	0.595966i	$-0.203231\pi$
$97$	−1.92260	−	5.28231i	−0.195211	−	0.536337i	−0.998221	+	0.0596285i	$0.981008\pi$
$98$	−0.232185	+	0.134052i	−0.0234543	+	0.0135413i
$99$		0			0
$100$	7.11481	−	6.71703i	0.711481	−	0.671703i
$101$	−1.86284	+	10.5647i	−0.185360	+	1.05123i	0.740133	+	0.672461i	$0.234763\pi$
$101$	−1.86284	+	10.5647i	−0.185360	+	1.05123i	−0.925492	+	0.378766i	$0.876348\pi$
$102$		0			0
$103$	−0.183395	+	0.503873i	−0.0180704	+	0.0496480i	−0.948400	−	0.317077i	$-0.897299\pi$
$103$	−0.183395	+	0.503873i	−0.0180704	+	0.0496480i	0.930329	+	0.366725i	$0.119521\pi$
$104$	0.345313	+	1.95837i	0.0338608	+	0.192034i
$105$		0			0
$106$	−0.864777	−	0.725634i	−0.0839945	−	0.0704798i
$107$		−	2.82482i		−	0.273086i	−0.990634	−	0.136543i	$-0.956401\pi$
$107$		−	2.82482i		−	0.273086i	0.990634	−	0.136543i	$-0.0435992\pi$
$108$		0			0
$109$	−0.479801			−0.0459566			−0.0229783	−	0.999736i	$-0.507315\pi$
$109$	−0.479801			−0.0459566			−0.0229783	+	0.999736i	$0.507315\pi$
$110$	0.453716	+	0.509663i	0.0432601	+	0.0485945i
$111$		0			0
$112$	10.6156	−	1.87182i	1.00308	−	0.176870i
$113$	1.45557	−	3.99915i	0.136928	−	0.376208i	−0.852209	−	0.523202i	$-0.824737\pi$
$113$	1.45557	−	3.99915i	0.136928	−	0.376208i	0.989137	+	0.146994i	$0.0469597\pi$
$114$		0			0
$115$	1.69032	−	5.10398i	0.157623	−	0.475949i
$116$	−8.60380	+	14.9022i	−0.798843	+	1.38364i
$117$		0			0
$118$	1.30690	−	0.754539i	0.120310	−	0.0694609i
$119$	3.81109	−	1.38712i	0.349362	−	0.127157i
$120$		0			0
$121$	−6.77033	+	5.68098i	−0.615484	+	0.516453i
$122$	−0.798608	−	0.951744i	−0.0723026	−	0.0861669i
$123$		0			0
$124$	−10.6814	+	3.88773i	−0.959222	+	0.349128i
$125$	11.1373	−	0.980081i	0.996150	−	0.0876611i
$126$		0			0
$127$	10.4667	+	6.04293i	0.928765	+	0.536223i	0.886421	−	0.462880i	$-0.153184\pi$
$127$	10.4667	+	6.04293i	0.928765	+	0.536223i	0.0423444	+	0.999103i	$0.486517\pi$
$128$	6.19280	+	1.09196i	0.547371	+	0.0965164i
$129$		0			0
$130$	−0.533166	+	0.989218i	−0.0467617	+	0.0867601i
$131$	−0.0451328	−	0.255961i	−0.00394327	−	0.0223634i	0.982773	−	0.184819i	$-0.0591698\pi$
$131$	−0.0451328	−	0.255961i	−0.00394327	−	0.0223634i	−0.986716	+	0.162455i	$0.948059\pi$
$132$		0			0
$133$	−8.68150	+	10.3462i	−0.752781	+	0.897130i
$134$	−1.59914			−0.138145
$135$		0			0
$136$	1.15665			0.0991816
$137$	−12.0038	+	14.3056i	−1.02555	+	1.22221i	−0.0508517	+	0.998706i	$0.516194\pi$
$137$	−12.0038	+	14.3056i	−1.02555	+	1.22221i	−0.974703	+	0.223503i	$0.928251\pi$
$138$		0			0
$139$	−1.20743	−	6.84769i	−0.102413	−	0.580813i	−0.992222	−	0.124480i	$-0.960274\pi$
$139$	−1.20743	−	6.84769i	−0.102413	−	0.580813i	0.889809	−	0.456333i	$-0.150837\pi$
$140$	11.0919	+	5.97828i	0.937437	+	0.505257i
$141$		0			0
$142$	1.84686	+	0.325651i	0.154985	+	0.0273280i
$143$	3.08345	+	1.78023i	0.257851	+	0.148870i
$144$		0			0
$145$	−18.2717	+	7.26247i	−1.51738	+	0.603115i
$146$	−2.45259	+	0.892671i	−0.202978	+	0.0738780i
$147$		0			0
$148$	−10.9958	−	13.1043i	−0.903850	−	1.07717i
$149$	6.29367	−	5.28102i	0.515598	−	0.432638i	−0.347496	−	0.937681i	$-0.612968\pi$
$149$	6.29367	−	5.28102i	0.515598	−	0.432638i	0.863094	+	0.505044i	$0.168524\pi$
$150$		0			0
$151$	8.32039	−	3.02837i	0.677103	−	0.246445i	0.0195001	−	0.999810i	$-0.493793\pi$
$151$	8.32039	−	3.02837i	0.677103	−	0.246445i	0.657603	+	0.753364i	$0.271570\pi$
$152$	−3.33576	+	1.92590i	−0.270566	+	0.156211i
$153$		0			0
$154$	−0.439363	+	0.760998i	−0.0354049	+	0.0613230i
$155$	−12.3298	−	4.08334i	−0.990354	−	0.327982i
$156$		0			0
$157$	2.12942	−	5.85053i	0.169946	−	0.466923i	−0.825256	−	0.564758i	$-0.808969\pi$
$157$	2.12942	−	5.85053i	0.169946	−	0.466923i	0.995203	+	0.0978347i	$0.0311917\pi$
$158$	0.306459	−	0.0540370i	0.0243806	−	0.00429895i
$159$		0			0
$160$	3.59713	+	4.04069i	0.284378	+	0.319445i
$161$	6.92384			0.545675
$162$		0			0
$163$		−	20.6617i		−	1.61835i	−0.587569	−	0.809174i	$-0.699915\pi$
$163$		−	20.6617i		−	1.61835i	0.587569	−	0.809174i	$-0.300085\pi$
$164$	−16.2922	−	13.6707i	−1.27220	−	1.06751i
$165$		0			0
$166$	0.418590	+	2.37394i	0.0324889	+	0.184254i
$167$	−2.14444	+	5.89179i	−0.165942	+	0.455921i	−0.994594	−	0.103843i	$-0.966886\pi$
$167$	−2.14444	+	5.89179i	−0.165942	+	0.455921i	0.828652	+	0.559764i	$0.189108\pi$
$168$		0			0
$169$	1.23923	−	7.02800i	0.0953251	−	0.540615i
$170$	0.512781	+	0.405314i	0.0393285	+	0.0310861i
$171$		0			0
$172$	−13.0537	+	7.53656i	−0.995336	+	0.574657i
$173$	1.35761	+	3.72999i	0.103217	+	0.283586i	0.980542	−	0.196311i	$-0.0628963\pi$
$173$	1.35761	+	3.72999i	0.103217	+	0.283586i	−0.877325	+	0.479897i	$0.840674\pi$
$174$		0			0
$175$	5.70713	+	13.2183i	0.431419	+	0.999211i
$176$	4.21645	−	3.53802i	0.317827	−	0.266688i
$177$		0			0
$178$	0.847207	+	2.32768i	0.0635008	+	0.174467i
$179$	7.02005	+	12.1591i	0.524703	+	0.908813i	0.999586	+	0.0287637i	$0.00915704\pi$
$179$	7.02005	+	12.1591i	0.524703	+	0.908813i	−0.474883	+	0.880049i	$0.657510\pi$
$180$		0			0
$181$	−3.31514	+	5.74198i	−0.246412	+	0.426798i	−0.962528	−	0.271183i	$-0.912585\pi$
$181$	−3.31514	+	5.74198i	−0.246412	+	0.426798i	0.716116	+	0.697982i	$0.245918\pi$
$182$	−1.42515	−	0.251293i	−0.105639	−	0.0186271i
$183$		0			0
$184$	1.85554	+	0.675361i	0.136792	+	0.0497883i
$185$	−0.571809	−	19.5382i	−0.0420403	−	1.43648i
$186$		0			0
$187$	1.33116	−	1.58642i	0.0973441	−	0.116010i
$188$			13.2922i			0.969431i
$189$		0			0
$190$	−2.15373	−	0.315104i	−0.156248	−	0.0228600i
$191$	−7.50310	−	6.29585i	−0.542905	−	0.455552i	0.329625	−	0.944112i	$-0.393078\pi$
$191$	−7.50310	−	6.29585i	−0.542905	−	0.455552i	−0.872530	+	0.488560i	$0.837522\pi$
$192$		0			0
$193$	−19.1316	+	3.37342i	−1.37712	+	0.242824i	−0.812710	−	0.582668i	$-0.802009\pi$
$193$	−19.1316	+	3.37342i	−1.37712	+	0.242824i	−0.564414	+	0.825492i	$0.690898\pi$
$194$	1.09630	+	0.399019i	0.0787094	+	0.0286479i
$195$		0			0
$196$	−0.438980	+	2.48958i	−0.0313557	+	0.177827i
$197$	−5.60720	−	3.23732i	−0.399497	−	0.230649i	0.286770	−	0.957999i	$-0.407418\pi$
$197$	−5.60720	−	3.23732i	−0.399497	−	0.230649i	−0.686267	+	0.727350i	$0.740752\pi$
$198$		0			0
$199$	8.61414	+	14.9201i	0.610640	+	1.05766i	0.991133	+	0.132875i	$0.0424210\pi$
$199$	8.61414	+	14.9201i	0.610640	+	1.05766i	−0.380493	+	0.924784i	$0.624246\pi$
$200$	0.240136	+	4.09909i	0.0169802	+	0.289850i
$201$		0			0
$202$	−1.43112	−	1.70555i	−0.100693	−	0.120002i
$203$	−16.2756	−	19.3965i	−1.14233	−	1.36137i
$204$		0			0
$205$	−4.91824	−	23.7987i	−0.343504	−	1.66217i
$206$	−0.0556428	−	0.0963761i	−0.00387681	−	0.00671484i
$207$		0			0
$208$	7.85019	+	4.53231i	0.544313	+	0.314259i
$209$	−1.19756	+	6.79170i	−0.0828369	+	0.469792i
$210$		0			0
$211$	−18.9632	−	6.90203i	−1.30548	−	0.475156i	−0.406702	−	0.913561i	$-0.633321\pi$
$211$	−18.9632	−	6.90203i	−1.30548	−	0.475156i	−0.898777	+	0.438405i	$0.855543\pi$
$212$	−10.4827	+	1.84838i	−0.719953	+	0.126947i
$213$		0			0
$214$	0.449106	+	0.376845i	0.0307003	+	0.0257606i
$215$	−17.0418	−	2.49331i	−1.16224	−	0.170042i
$216$		0			0
$217$		−	16.7261i		−	1.13544i
$218$	0.0640078	−	0.0762815i	0.00433515	−	0.00516644i
$219$		0			0
$220$	6.43129	−	0.188220i	0.433598	−	0.0126898i
$221$	3.20484	+	1.16647i	0.215581	+	0.0784649i
$222$		0			0
$223$	9.20020	+	1.62224i	0.616091	+	0.108633i	0.472980	−	0.881073i	$-0.343178\pi$
$223$	9.20020	+	1.62224i	0.616091	+	0.108633i	0.143111	+	0.989707i	$0.454289\pi$
$224$	−3.48334	+	6.03332i	−0.232740	+	0.403118i
$225$		0			0
$226$	0.441627	+	0.764920i	0.0293766	+	0.0508817i
$227$	−2.68962	−	7.38967i	−0.178516	−	0.490470i	0.817870	−	0.575403i	$-0.195155\pi$
$227$	−2.68962	−	7.38967i	−0.178516	−	0.490470i	−0.996387	+	0.0849329i	$0.972932\pi$
$228$		0			0
$229$	12.7733	−	10.7181i	0.844086	−	0.708272i	−0.114393	−	0.993436i	$-0.536492\pi$
$229$	12.7733	−	10.7181i	0.844086	−	0.708272i	0.958479	+	0.285163i	$0.0920478\pi$
$230$	0.585963	+	0.949631i	0.0386373	+	0.0626168i
$231$		0			0
$232$	−2.46978	−	6.78568i	−0.162149	−	0.445502i
$233$	−25.8565	+	14.9283i	−1.69391	+	0.977982i	−0.742613	+	0.669720i	$0.766414\pi$
$233$	−25.8565	+	14.9283i	−1.69391	+	0.977982i	−0.951302	+	0.308262i	$0.900253\pi$
$234$		0			0
$235$	−9.41825	+	11.9155i	−0.614379	+	0.777279i
$236$	2.47089	−	14.0131i	0.160841	−	0.912174i
$237$		0			0
$238$	−0.287885	+	0.790957i	−0.0186608	+	0.0512701i
$239$	4.19886	+	23.8129i	0.271602	+	1.54033i	0.749554	+	0.661943i	$0.230268\pi$
$239$	4.19886	+	23.8129i	0.271602	+	1.54033i	−0.477952	+	0.878386i	$0.658621\pi$
$240$		0			0
$241$	11.3477	+	9.52183i	0.730968	+	0.613355i	0.930395	−	0.366558i	$-0.119464\pi$
$241$	11.3477	+	9.52183i	0.730968	+	0.613355i	−0.199427	+	0.979913i	$0.563908\pi$
$242$		−	1.83425i		−	0.117910i
$243$		0			0
$244$	−11.7149			−0.749967
$245$	−2.15752	+	1.92069i	−0.137839	+	0.122708i
$246$		0			0
$247$	−11.1850	+	1.97221i	−0.711683	+	0.125489i
$248$	1.63149	−	4.48247i	0.103599	−	0.284637i
$249$		0			0
$250$	−1.32995	+	1.90142i	−0.0841134	+	0.120256i
$251$	−3.98405	+	6.90057i	−0.251471	+	0.435560i	−0.963931	−	0.266152i	$-0.914248\pi$
$251$	−3.98405	+	6.90057i	−0.251471	+	0.435560i	0.712460	+	0.701712i	$0.247581\pi$
$252$		0			0
$253$	3.06181	−	1.76773i	0.192494	−	0.111137i
$254$	−2.35704	+	0.857892i	−0.147894	+	0.0538289i
$255$		0			0
$256$	9.70145	−	8.14048i	0.606341	−	0.508780i
$257$	13.0075	+	15.5017i	0.811386	+	0.966972i	0.999886	−	0.0151015i	$-0.00480713\pi$
$257$	13.0075	+	15.5017i	0.811386	+	0.966972i	−0.188500	+	0.982073i	$0.560363\pi$
$258$		0			0
$259$	23.6535	−	8.60917i	1.46976	−	0.534948i
$260$	3.91377	+	9.84668i	0.242721	+	0.610665i
$261$		0			0
$262$	0.0467150	+	0.0269709i	0.00288606	+	0.00166627i
$263$	21.4662	+	3.78508i	1.32367	+	0.233398i	0.790421	−	0.612563i	$-0.209862\pi$
$263$	21.4662	+	3.78508i	1.32367	+	0.233398i	0.533244	+	0.845961i	$0.320973\pi$
$264$		0			0
$265$	−10.7066	−	5.77063i	−0.657703	−	0.354487i
$266$	−0.486745	−	2.76047i	−0.0298442	−	0.169255i
$267$		0			0
$268$	−9.69226	+	11.5508i	−0.592049	+	0.705577i
$269$	4.34109			0.264681			0.132341	−	0.991204i	$-0.457751\pi$
$269$	4.34109			0.264681			0.132341	+	0.991204i	$0.457751\pi$
$270$		0			0
$271$	−13.1672			−0.799852			−0.399926	−	0.916547i	$-0.630964\pi$
$271$	−13.1672			−0.799852			−0.399926	+	0.916547i	$0.630964\pi$
$272$	3.38902	−	4.03888i	0.205490	−	0.244893i
$273$		0			0
$274$	−0.673017	−	3.81687i	−0.0406584	−	0.230585i
$275$	5.89855	+	4.38820i	0.355696	+	0.264619i
$276$		0			0
$277$	0.500044	+	0.0881712i	0.0300447	+	0.00529770i	0.188650	−	0.982044i	$-0.439589\pi$
$277$	0.500044	+	0.0881712i	0.0300447	+	0.00529770i	−0.158606	+	0.987342i	$0.550700\pi$
$278$	1.24976	+	0.721550i	0.0749557	+	0.0432757i
$279$		0			0
$280$	−4.91383	+	1.95310i	−0.293658	+	0.116720i
$281$	0.459552	−	0.167263i	0.0274146	−	0.00997809i	−0.328276	−	0.944582i	$-0.606468\pi$
$281$	0.459552	−	0.167263i	0.0274146	−	0.00997809i	0.355691	+	0.934604i	$0.384246\pi$
$282$		0			0
$283$	−2.70977	−	3.22938i	−0.161079	−	0.191967i	0.679468	−	0.733705i	$-0.262211\pi$
$283$	−2.70977	−	3.22938i	−0.161079	−	0.191967i	−0.840547	+	0.541739i	$0.817766\pi$
$284$	13.5459	−	11.3663i	0.803799	−	0.674467i
$285$		0			0
$286$	−0.694377	+	0.252733i	−0.0410594	+	0.0149444i
$287$	27.1023	−	15.6475i	1.59980	−	0.923642i
$288$		0			0
$289$	−7.50815	+	13.0045i	−0.441656	+	0.764970i
$290$	1.28291	−	3.87379i	0.0753349	−	0.227477i
$291$		0			0
$292$	−8.41710	+	23.1258i	−0.492573	+	1.35333i
$293$	−22.7756	+	4.01595i	−1.33056	+	0.234614i	−0.793315	−	0.608811i	$-0.791647\pi$
$293$	−22.7756	+	4.01595i	−1.33056	+	0.234614i	−0.537247	+	0.843425i	$0.680536\pi$
$294$		0			0
$295$	12.1440	−	10.8109i	0.707053	−	0.629438i
$296$	7.17872			0.417254
$297$		0			0
$298$			1.70512i			0.0987747i
$299$	4.46024	+	3.74258i	0.257942	+	0.216439i
$300$		0			0
$301$	−3.85144	−	21.8426i	−0.221994	−	1.25899i
$302$	−0.628511	+	1.72682i	−0.0361668	+	0.0993674i
$303$		0			0
$304$	−3.04888	+	17.2911i	−0.174865	+	0.991711i
$305$	−10.5015	−	8.30063i	−0.601315	−	0.475293i
$306$		0			0
$307$	2.88589	−	1.66617i	0.164706	−	0.0950932i	−0.415381	−	0.909648i	$-0.636352\pi$
$307$	2.88589	−	1.66617i	0.164706	−	0.0950932i	0.580087	+	0.814554i	$0.303018\pi$
$308$	2.83384	+	7.78592i	0.161473	+	0.443644i
$309$		0			0
$310$	2.29405	−	1.41552i	0.130293	−	0.0803964i
$311$	8.46844	−	7.10587i	0.480201	−	0.402937i	−0.370298	−	0.928913i	$-0.620744\pi$
$311$	8.46844	−	7.10587i	0.480201	−	0.402937i	0.850499	+	0.525976i	$0.176300\pi$
$312$		0			0
$313$	3.19684	+	8.78326i	0.180696	+	0.496459i	0.996662	−	0.0816417i	$-0.0260163\pi$
$313$	3.19684	+	8.78326i	0.180696	+	0.496459i	−0.815965	+	0.578101i	$0.803794\pi$
$314$	0.646076	+	1.11904i	0.0364602	+	0.0631509i
$315$		0			0
$316$	1.46711	−	2.54110i	0.0825312	−	0.142948i
$317$	−26.8303	−	4.73090i	−1.50694	−	0.265714i	−0.641654	−	0.766994i	$-0.721752\pi$
$317$	−26.8303	−	4.73090i	−1.50694	−	0.265714i	−0.865285	+	0.501280i	$0.832863\pi$
$318$		0			0
$319$	−12.1494	−	4.42203i	−0.680238	−	0.247586i
$320$	15.6116	−	0.456894i	0.872716	−	0.0255411i
$321$		0			0
$322$	−0.923674	+	1.10079i	−0.0514743	+	0.0613447i
$323$			6.60604i			0.367570i
$324$		0			0
$325$	−3.46852	+	11.6000i	−0.192399	+	0.643450i
$326$	3.28491	+	2.75637i	0.181934	+	0.152661i
$327$		0			0
$328$	8.78948	−	1.54982i	0.485318	−	0.0855746i
$329$	−18.3794	−	6.68956i	−1.01329	−	0.368808i
$330$		0			0
$331$	4.40921	−	25.0059i	0.242352	−	1.37445i	−0.584210	−	0.811602i	$-0.698596\pi$
$331$	4.40921	−	25.0059i	0.242352	−	1.37445i	0.826562	−	0.562845i	$-0.190293\pi$
$332$	19.6843	+	11.3647i	1.08032	+	0.623721i
$333$		0			0
$334$	−0.650632	−	1.12693i	−0.0356010	−	0.0616628i
$335$	−16.8728	+	3.48692i	−0.921859	+	0.190511i
$336$		0			0
$337$	−3.09214	−	3.68507i	−0.168440	−	0.200739i	0.675221	−	0.737616i	$-0.264048\pi$
$337$	−3.09214	−	3.68507i	−0.168440	−	0.200739i	−0.843661	+	0.536877i	$0.819604\pi$
$338$	0.952032	+	1.13459i	0.0517837	+	0.0617134i
$339$		0			0
$340$	6.03555	−	1.24730i	0.327324	−	0.0676446i
$341$	−4.27036	−	7.39648i	−0.231253	−	0.400542i
$342$		0			0
$343$	14.2349	+	8.21851i	0.768611	+	0.443758i
$344$	1.09840	−	6.22934i	0.0592218	−	0.335863i
$345$		0			0
$346$	−0.774126	−	0.281759i	−0.0416173	−	0.0151474i
$347$	23.4852	−	4.14108i	1.26075	−	0.222305i	0.496964	−	0.867771i	$-0.334448\pi$
$347$	23.4852	−	4.14108i	1.26075	−	0.222305i	0.763789	+	0.645466i	$0.223337\pi$
$348$		0			0
$349$	10.1403	+	8.50874i	0.542799	+	0.455462i	0.872494	−	0.488625i	$-0.162501\pi$
$349$	10.1403	+	8.50874i	0.542799	+	0.455462i	−0.329695	+	0.944087i	$0.606946\pi$
$350$	−2.86288	−	0.856035i	−0.153027	−	0.0457570i
$351$		0			0
$352$			3.55734i			0.189607i
$353$	12.6452	−	15.0700i	0.673036	−	0.802093i	−0.316158	−	0.948707i	$-0.602393\pi$
$353$	12.6452	−	15.0700i	0.673036	−	0.802093i	0.989194	+	0.146614i	$0.0468375\pi$
$354$		0			0
$355$	20.1965	−	0.591077i	1.07192	−	0.0313711i
$356$	21.9480	+	7.98841i	1.16324	+	0.423385i
$357$		0			0
$358$	−2.86963	−	0.505993i	−0.151665	−	0.0267425i
$359$	−5.85683	+	10.1443i	−0.309112	+	0.535397i	−0.978168	−	0.207814i	$-0.933365\pi$
$359$	−5.85683	+	10.1443i	−0.309112	+	0.535397i	0.669057	+	0.743211i	$0.266698\pi$
$360$		0			0
$361$	−1.49955	−	2.59729i	−0.0789236	−	0.136700i
$362$	−0.470638	−	1.29307i	−0.0247362	−	0.0679621i
$363$		0			0
$364$	−10.4529	+	8.77098i	−0.547878	+	0.459724i
$365$	−23.9312	+	14.7666i	−1.25262	+	0.772918i
$366$		0			0
$367$	8.09527	+	22.2416i	0.422569	+	1.16100i	0.950231	+	0.311546i	$0.100847\pi$
$367$	8.09527	+	22.2416i	0.422569	+	1.16100i	−0.527662	+	0.849455i	$0.676931\pi$
$368$	7.79509	−	4.50050i	0.406347	−	0.234605i
$369$		0			0
$370$	3.18257	+	2.51558i	0.165454	+	0.130779i
$371$	2.71983	−	15.4249i	0.141206	−	0.800821i
$372$		0			0
$373$	7.08072	−	19.4541i	0.366626	−	1.00730i	−0.610010	−	0.792394i	$-0.708834\pi$
$373$	7.08072	−	19.4541i	0.366626	−	1.00730i	0.976636	−	0.214902i	$-0.0689434\pi$
$374$	0.0746341	+	0.423271i	0.00385924	+	0.0218868i
$375$		0			0
$376$	−4.27304	−	3.58551i	−0.220365	−	0.184908i
$377$		−	21.2925i		−	1.09662i
$378$		0			0
$379$	14.1618			0.727442			0.363721	−	0.931508i	$-0.381506\pi$
$379$	14.1618			0.727442			0.363721	+	0.931508i	$0.381506\pi$
$380$	−15.3296	+	13.6469i	−0.786394	+	0.700069i
$381$		0			0
$382$	2.00190	−	0.352989i	0.102426	−	0.0180605i
$383$	6.96733	−	19.1426i	0.356014	−	0.978140i	−0.624385	−	0.781117i	$-0.714650\pi$
$383$	6.96733	−	19.1426i	0.356014	−	0.978140i	0.980399	−	0.197023i	$-0.0631274\pi$
$384$		0			0
$385$	−2.97643	+	8.98744i	−0.151693	+	0.458042i
$386$	2.01592	−	3.49168i	0.102608	−	0.177722i
$387$		0			0
$388$	9.52672	−	5.50025i	0.483646	−	0.279233i
$389$	−10.7321	+	3.90618i	−0.544141	+	0.198051i	−0.599441	−	0.800419i	$-0.704611\pi$
$389$	−10.7321	+	3.90618i	−0.544141	+	0.198051i	0.0553005	+	0.998470i	$0.482388\pi$
$390$		0			0
$391$	2.59427	−	2.17685i	0.131198	−	0.110088i
$392$	−0.681914	−	0.812674i	−0.0344419	−	0.0410462i
$393$		0			0
$394$	1.26271	−	0.459590i	0.0636146	−	0.0231538i
$395$	3.11567	−	1.23839i	0.156766	−	0.0623099i
$396$		0			0
$397$	2.93301	+	1.69337i	0.147204	+	0.0849880i	0.571793	−	0.820398i	$-0.306248\pi$
$397$	2.93301	+	1.69337i	0.147204	+	0.0849880i	−0.424589	+	0.905386i	$0.639581\pi$
$398$	−3.52125	−	0.620891i	−0.176504	−	0.0311225i
$399$		0			0
$400$	15.0172	+	11.1720i	0.750859	+	0.558599i
$401$	−3.73348	−	21.1736i	−0.186441	−	1.05736i	−0.924090	−	0.382175i	$-0.875175\pi$
$401$	−3.73348	−	21.1736i	−0.186441	−	1.05736i	0.737649	−	0.675184i	$-0.235936\pi$
$402$		0			0
$403$	9.04105	−	10.7747i	0.450367	−	0.536726i
$404$	−20.9933			−1.04445
$405$		0			0
$406$	5.25502			0.260802
$407$	8.26184	−	9.84608i	0.409524	−	0.488052i
$408$		0			0
$409$	2.13010	+	12.0804i	0.105327	+	0.597338i	0.991089	+	0.133199i	$0.0425250\pi$
$409$	2.13010	+	12.0804i	0.105327	+	0.597338i	−0.885762	+	0.464139i	$0.846364\pi$
$410$	4.43977	+	2.39293i	0.219265	+	0.118179i
$411$		0			0
$412$	−1.03338	−	0.182213i	−0.0509111	−	0.00897700i
$413$	18.1327	+	10.4689i	0.892254	+	0.515143i
$414$		0			0
$415$	9.59298	+	24.1351i	0.470901	+	1.18474i
$416$	−5.50513	+	2.00370i	−0.269911	+	0.0982397i
$417$		0			0
$418$	−0.920022	−	1.09644i	−0.0449998	−	0.0536286i
$419$	23.2229	−	19.4864i	1.13451	−	0.951971i	0.135269	−	0.990809i	$-0.456810\pi$
$419$	23.2229	−	19.4864i	1.13451	−	0.951971i	0.999246	+	0.0388381i	$0.0123657\pi$
$420$		0			0
$421$	−8.53967	+	3.10819i	−0.416198	+	0.151484i	−0.541627	−	0.840619i	$-0.682191\pi$
$421$	−8.53967	+	3.10819i	−0.416198	+	0.151484i	0.125429	+	0.992103i	$0.459969\pi$
$422$	3.62710	−	2.09411i	0.176565	−	0.101940i
$423$		0			0
$424$	2.23346	−	3.86847i	0.108466	−	0.187869i
$425$	6.29421	+	3.15841i	0.305314	+	0.153205i
$426$		0			0
$427$	5.89575	−	16.1984i	0.285315	−	0.783897i
$428$	5.44399	−	0.959922i	0.263145	−	0.0463996i
$429$		0			0
$430$	2.66985	−	2.37678i	0.128752	−	0.114618i
$431$	17.7056			0.852847			0.426424	−	0.904524i	$-0.359773\pi$
$431$	17.7056			0.852847			0.426424	+	0.904524i	$0.359773\pi$
$432$		0			0
$433$		−	6.74677i		−	0.324229i	−0.986772	−	0.162114i	$-0.948169\pi$
$433$		−	6.74677i		−	0.324229i	0.986772	−	0.162114i	$-0.0518314\pi$
$434$	2.65921	+	2.23134i	0.127646	+	0.107108i
$435$		0			0
$436$	−0.163045	−	0.924672i	−0.00780842	−	0.0442837i
$437$	−3.85724	+	10.5977i	−0.184517	+	0.506956i
$438$		0			0
$439$	0.774036	−	4.38977i	0.0369427	−	0.209512i	−0.960749	−	0.277419i	$-0.910521\pi$
$439$	0.774036	−	4.38977i	0.0369427	−	0.209512i	0.997692	+	0.0679067i	$0.0216320\pi$
$440$	−1.67431	+	2.11824i	−0.0798195	+	0.100983i
$441$		0			0
$442$	−0.612991	+	0.353911i	−0.0291570	+	0.0168338i
$443$	−2.74386	−	7.53869i	−0.130365	−	0.358174i	0.857287	−	0.514838i	$-0.172148\pi$
$443$	−2.74386	−	7.53869i	−0.130365	−	0.358174i	−0.987652	+	0.156665i	$0.949926\pi$
$444$		0			0
$445$	14.0145	+	22.7124i	0.664352	+	1.07667i
$446$	−1.48526	+	1.24628i	−0.0703293	+	0.0590133i
$447$		0			0
$448$	6.87900	+	18.8999i	0.325002	+	0.892936i
$449$	−2.62606	−	4.54847i	−0.123931	−	0.214655i	0.797383	−	0.603473i	$-0.206217\pi$
$449$	−2.62606	−	4.54847i	−0.123931	−	0.214655i	−0.921315	+	0.388818i	$0.872884\pi$
$450$		0			0
$451$	7.98996	−	13.8390i	0.376232	−	0.651654i
$452$	8.20177	+	1.44619i	0.385779	+	0.0680232i
$453$		0			0
$454$	1.53366	+	0.558206i	0.0719782	+	0.0261979i
$455$	−15.5849	+	0.456113i	−0.730634	+	0.0213829i
$456$		0			0
$457$	1.94777	−	2.32127i	0.0911130	−	0.108584i	−0.718562	−	0.695463i	$-0.755199\pi$
$457$	1.94777	−	2.32127i	0.0911130	−	0.108584i	0.809675	+	0.586879i	$0.199644\pi$
$458$			3.46062i			0.161704i
$459$		0			0
$460$	10.4108	+	1.52316i	0.485405	+	0.0710175i
$461$	2.25112	+	1.88892i	0.104845	+	0.0879757i	0.693703	−	0.720261i	$-0.255978\pi$
$461$	2.25112	+	1.88892i	0.104845	+	0.0879757i	−0.588858	+	0.808236i	$0.700422\pi$
$462$		0			0
$463$	−18.1798	+	3.20559i	−0.844886	+	0.148976i	−0.579304	−	0.815112i	$-0.696675\pi$
$463$	−18.1798	+	3.20559i	−0.844886	+	0.148976i	−0.265583	+	0.964088i	$0.585564\pi$
$464$	−30.9314	−	11.2581i	−1.43595	−	0.522644i
$465$		0			0
$466$	1.07600	−	6.10231i	0.0498448	−	0.282684i
$467$	−18.7117	−	10.8032i	−0.865875	−	0.499913i	9.99457e−5	−	1.00000i	$-0.499968\pi$
$467$	−18.7117	−	10.8032i	−0.865875	−	0.499913i	−0.865975	+	0.500087i	$0.833302\pi$
$468$		0			0
$469$	−11.0937	−	19.2149i	−0.512261	−	0.887263i
$470$	−0.637947	−	3.08694i	−0.0294263	−	0.142390i
$471$		0			0
$472$	3.83828	+	4.57429i	0.176671	+	0.210549i
$473$	−7.27982	−	8.67575i	−0.334726	−	0.398911i
$474$		0			0
$475$	−23.4115	+	1.37151i	−1.07419	+	0.0629290i
$476$	3.96833	+	6.87335i	0.181888	+	0.315040i
$477$		0			0
$478$	−4.34606	−	2.50920i	−0.198784	−	0.114768i
$479$	−0.173381	+	0.983295i	−0.00792200	+	0.0449279i	−0.988513	−	0.151139i	$-0.951706\pi$
$479$	−0.173381	+	0.983295i	−0.00792200	+	0.0449279i	0.980591	+	0.196067i	$0.0628170\pi$
$480$		0			0
$481$	19.8908	+	7.23966i	0.906942	+	0.330100i
$482$	−3.02767	+	0.533859i	−0.137906	+	0.0243166i
$483$		0			0
$484$	−13.2490	−	11.1173i	−0.602229	−	0.505330i
$485$	12.4372	+	1.81964i	0.564746	+	0.0826255i
$486$		0			0
$487$			18.3516i			0.831589i	0.909459	+	0.415794i	$0.136496\pi$
$487$			18.3516i			0.831589i	−0.909459	+	0.415794i	$0.863504\pi$
$488$	3.16003	−	3.76598i	0.143048	−	0.170478i
$489$		0			0
$490$	−0.0175376	−	0.599243i	−0.000792269	−	0.0270711i
$491$	10.2329	+	3.72447i	0.461805	+	0.168083i	0.562436	−	0.826841i	$-0.309864\pi$
$491$	10.2329	+	3.72447i	0.461805	+	0.168083i	−0.100632	+	0.994924i	$0.532086\pi$
$492$		0			0
$493$	−12.1965	−	2.15057i	−0.549303	−	0.0968570i
$494$	1.17858	−	2.04135i	0.0530266	−	0.0918449i
$495$		0			0
$496$	−10.8720	−	18.8308i	−0.488165	−	0.845527i
$497$	8.89927	+	24.4505i	0.399187	+	1.09676i
$498$		0			0
$499$	−22.2753	+	18.6912i	−0.997180	+	0.836733i	−0.986591	−	0.163211i	$-0.947815\pi$
$499$	−22.2753	+	18.6912i	−0.997180	+	0.836733i	−0.0105884	+	0.999944i	$0.503370\pi$
$500$	5.67345	+	21.1307i	0.253724	+	0.944994i
$501$		0			0
$502$	−0.565600	−	1.55397i	−0.0252440	−	0.0693573i
$503$	−16.5027	+	9.52781i	−0.735817	+	0.424824i	−0.820546	−	0.571580i	$-0.806331\pi$
$503$	−16.5027	+	9.52781i	−0.735817	+	0.424824i	0.0847294	+	0.996404i	$0.472997\pi$
$504$		0			0
$505$	−18.8189	−	14.8749i	−0.837432	−	0.661925i
$506$	−0.127415	+	0.722607i	−0.00566429	+	0.0321238i
$507$		0			0
$508$	−8.08916	+	22.2248i	−0.358898	+	0.986065i
$509$	6.00851	+	34.0759i	0.266322	+	1.51039i	0.765243	+	0.643741i	$0.222619\pi$
$509$	6.00851	+	34.0759i	0.266322	+	1.51039i	−0.498921	+	0.866648i	$0.666270\pi$
$510$		0			0
$511$	−27.7405	−	23.2771i	−1.22717	−	1.02972i
$512$			15.2050i			0.671974i
$513$		0			0
$514$	−4.19981			−0.185246
$515$	−0.797243	−	0.895550i	−0.0351307	−	0.0394626i
$516$		0			0
$517$	−9.83552	+	1.73427i	−0.432566	+	0.0762730i
$518$	−1.78676	+	4.90907i	−0.0785055	+	0.215692i
$519$		0			0
$520$	−4.22114	−	1.39794i	−0.185109	−	0.0613038i
$521$	10.0641	−	17.4315i	0.440915	−	0.763686i	−0.556843	−	0.830618i	$-0.687988\pi$
$521$	10.0641	−	17.4315i	0.440915	−	0.763686i	0.997758	+	0.0669313i	$0.0213208\pi$
$522$		0			0
$523$	15.9232	−	9.19327i	0.696274	−	0.401994i	−0.109684	−	0.993966i	$-0.534984\pi$
$523$	15.9232	−	9.19327i	0.696274	−	0.401994i	0.805958	+	0.591973i	$0.201651\pi$
$524$	0.477950	−	0.173960i	0.0208793	−	0.00759946i
$525$		0			0
$526$	−3.46547	+	2.90788i	−0.151102	+	0.126789i
$527$	−5.25867	−	6.26704i	−0.229071	−	0.272996i
$528$		0			0
$529$	−16.1800	+	5.88905i	−0.703480	+	0.256046i
$530$	2.34576	−	0.932371i	0.101893	−	0.0404996i
$531$		0			0
$532$	−22.8893	−	13.2151i	−0.992377	−	0.572949i
$533$	25.9169	+	4.56985i	1.12259	+	0.197942i
$534$		0			0
$535$	5.56030	+	2.99687i	0.240393	+	0.129566i
$536$	−1.09879	−	6.23155i	−0.0474605	−	0.269162i
$537$		0			0
$538$	−0.579122	+	0.690171i	−0.0249677	+	0.0297554i
$539$	−1.89944			−0.0818146
$540$		0			0
$541$	4.17044			0.179301			0.0896506	−	0.995973i	$-0.471425\pi$
$541$	4.17044			0.179301			0.0896506	+	0.995973i	$0.471425\pi$
$542$	1.75657	−	2.09340i	0.0754512	−	0.0899192i
$543$		0			0
$544$	0.591711	+	3.35576i	0.0253694	+	0.143877i
$545$	0.509024	−	0.944427i	0.0218042	−	0.0404548i
$546$		0			0
$547$	−23.2507	−	4.09973i	−0.994128	−	0.175292i	−0.347158	−	0.937807i	$-0.612853\pi$
$547$	−23.2507	−	4.09973i	−0.994128	−	0.175292i	−0.646970	+	0.762515i	$0.723964\pi$
$548$	−31.6488	−	18.2724i	−1.35197	−	0.780560i
$549$		0			0
$550$	−1.48456	+	0.352376i	−0.0633016	+	0.0150254i
$551$	38.7555	−	14.1059i	1.65104	−	0.600930i
$552$		0			0
$553$	2.77530	+	3.30747i	0.118018	+	0.140648i
$554$	−0.0807262	+	0.0677373i	−0.00342973	+	0.00287788i
$555$		0			0
$556$	12.7865	−	4.65392i	0.542270	−	0.197370i
$557$	−23.3763	+	13.4963i	−0.990484	+	0.571856i	−0.905419	−	0.424519i	$-0.860443\pi$
$557$	−23.3763	+	13.4963i	−0.990484	+	0.571856i	−0.0850648	+	0.996375i	$0.527110\pi$
$558$		0			0
$559$	9.32567	−	16.1525i	0.394434	−	0.683179i
$560$	−7.57772	+	22.8812i	−0.320217	+	0.966909i
$561$		0			0
$562$	−0.0347140	+	0.0953759i	−0.00146432	+	0.00402319i
$563$	13.8182	−	2.43652i	0.582366	−	0.102687i	0.125299	−	0.992119i	$-0.460011\pi$
$563$	13.8182	−	2.43652i	0.582366	−	0.102687i	0.457067	+	0.889432i	$0.348900\pi$
$564$		0			0
$565$	6.32757	+	7.10782i	0.266203	+	0.299028i
$566$	0.874921			0.0367757
$567$		0			0
$568$			7.42061i			0.311362i
$569$	17.5672	+	14.7406i	0.736454	+	0.617958i	0.931883	−	0.362760i	$-0.118165\pi$
$569$	17.5672	+	14.7406i	0.736454	+	0.617958i	−0.195429	+	0.980718i	$0.562610\pi$
$570$		0			0
$571$	0.200726	+	1.13838i	0.00840013	+	0.0476395i	0.988720	−	0.149778i	$-0.0478558\pi$
$571$	0.200726	+	1.13838i	0.00840013	+	0.0476395i	−0.980320	+	0.197417i	$0.936745\pi$
$572$	−2.38305	+	6.54736i	−0.0996401	+	0.273759i
$573$		0			0
$574$	−1.12784	+	6.39632i	−0.0470753	+	0.266977i
$575$	8.25325	+	8.74201i	0.344184	+	0.364567i
$576$		0			0
$577$	22.9770	−	13.2658i	0.956544	−	0.552261i	0.0614366	−	0.998111i	$-0.480432\pi$
$577$	22.9770	−	13.2658i	0.956544	−	0.552261i	0.895108	+	0.445850i	$0.147098\pi$
$578$	−1.06590	−	2.92855i	−0.0443358	−	0.121812i
$579$		0			0
$580$	−20.2052	−	32.7453i	−0.838977	−	1.35967i
$581$	−25.6208	+	21.4984i	−1.06293	+	0.891906i
$582$		0			0
$583$	−2.73541	−	7.51548i	−0.113289	−	0.311259i
$584$	−5.16378	−	8.94393i	−0.213679	−	0.370102i
$585$		0			0
$586$	2.39989	−	4.15673i	0.0991385	−	0.171713i
$587$	−31.2941	−	5.51799i	−1.29165	−	0.227752i	−0.514728	−	0.857354i	$-0.672107\pi$
$587$	−31.2941	−	5.51799i	−1.29165	−	0.227752i	−0.776918	+	0.629602i	$0.783218\pi$
$588$		0			0
$589$	25.6011	+	9.31802i	1.05487	+	0.383942i
$590$	0.0987138	+	3.37296i	0.00406398	+	0.138862i
$591$		0			0
$592$	21.0339	−	25.0673i	0.864489	−	1.03026i
$593$			10.3324i			0.424303i	0.977237	+	0.212151i	$0.0680470\pi$
$593$			10.3324i			0.424303i	−0.977237	+	0.212151i	$0.931953\pi$
$594$		0			0
$595$	−1.31284	+	8.97324i	−0.0538210	+	0.367867i
$596$	12.3163	+	10.3346i	0.504494	+	0.423320i
$597$		0			0
$598$	−1.19003	+	0.209835i	−0.0486641	+	0.00858079i
$599$	−30.6411	−	11.1524i	−1.25196	−	0.455677i	−0.370897	−	0.928674i	$-0.620950\pi$
$599$	−30.6411	−	11.1524i	−1.25196	−	0.455677i	−0.881064	+	0.472997i	$0.843172\pi$
$600$		0			0
$601$	−4.69496	+	26.6264i	−0.191511	+	1.08611i	0.725789	+	0.687918i	$0.241475\pi$
$601$	−4.69496	+	26.6264i	−0.191511	+	1.08611i	−0.917300	+	0.398197i	$0.869636\pi$
$602$	3.98646	+	2.30159i	0.162476	+	0.0938056i
$603$		0			0
$604$	8.66368	+	15.0059i	0.352520	+	0.610583i
$605$	−3.99959	−	19.3535i	−0.162606	−	0.786831i
$606$		0			0
$607$	4.08135	+	4.86396i	0.165657	+	0.197422i	0.842486	−	0.538718i	$-0.181091\pi$
$607$	4.08135	+	4.86396i	0.165657	+	0.197422i	−0.676830	+	0.736140i	$0.736647\pi$
$608$	−7.29408	−	8.69275i	−0.295814	−	0.352537i
$609$		0			0
$610$	2.72063	−	0.562245i	0.110155	−	0.0227646i
$611$	−8.22381	−	14.2440i	−0.332700	−	0.576253i
$612$		0			0
$613$	−33.0811	−	19.0994i	−1.33613	−	0.771416i	−0.349900	−	0.936787i	$-0.613784\pi$
$613$	−33.0811	−	19.0994i	−1.33613	−	0.771416i	−0.986231	+	0.165371i	$0.947118\pi$
$614$	−0.120094	+	0.681089i	−0.00484661	+	0.0274865i
$615$		0			0
$616$	−3.26736	−	1.18922i	−0.131646	−	0.0479151i
$617$	−16.9692	+	2.99213i	−0.683155	+	0.120459i	−0.504446	−	0.863443i	$-0.668303\pi$
$617$	−16.9692	+	2.99213i	−0.683155	+	0.120459i	−0.178709	+	0.983902i	$0.557192\pi$
$618$		0			0
$619$	3.05553	+	2.56390i	0.122812	+	0.103052i	0.702125	−	0.712053i	$-0.252235\pi$
$619$	3.05553	+	2.56390i	0.122812	+	0.103052i	−0.579313	+	0.815105i	$0.696679\pi$
$620$	3.67952	−	25.1495i	0.147773	−	1.01003i
$621$		0			0
$622$			2.29432i			0.0919937i
$623$	−22.0916	+	26.3277i	−0.885080	+	1.05480i
$624$		0			0
$625$	−9.88647	+	22.9621i	−0.395459	+	0.918484i
$626$	−1.82289	−	0.663476i	−0.0728571	−	0.0265178i
$627$		0			0
$628$	11.9987	+	2.11570i	0.478802	+	0.0844257i
$629$	6.15593	−	10.6624i	0.245453	−	0.425137i
$630$		0			0
$631$	−3.17235	−	5.49468i	−0.126289	−	0.218740i	0.795947	−	0.605367i	$-0.206973\pi$
$631$	−3.17235	−	5.49468i	−0.126289	−	0.218740i	−0.922236	+	0.386627i	$0.873640\pi$
$632$	0.421144	+	1.15708i	0.0167522	+	0.0460263i
$633$		0			0
$634$	4.33143	−	3.63450i	0.172023	−	0.144345i
$635$	−22.9988	+	14.1913i	−0.912681	+	0.563163i
$636$		0			0
$637$	−1.06988	−	2.93946i	−0.0423900	−	0.116466i
$638$	2.32383	−	1.34166i	0.0920014	−	0.0531170i
$639$		0			0
$640$	−8.71936	+	11.0313i	−0.344663	+	0.436049i
$641$	−5.63430	+	31.9537i	−0.222542	+	1.26210i	0.644788	+	0.764362i	$0.276946\pi$
$641$	−5.63430	+	31.9537i	−0.222542	+	1.26210i	−0.867329	+	0.497734i	$0.834165\pi$
$642$		0			0
$643$	5.98189	−	16.4351i	0.235903	−	0.648137i	−0.764093	−	0.645106i	$-0.776813\pi$
$643$	5.98189	−	16.4351i	0.235903	−	0.648137i	0.999995	−	0.00303079i	$-0.000964731\pi$
$644$	2.35284	+	13.3436i	0.0927148	+	0.525812i
$645$		0			0
$646$	−1.05026	−	0.881277i	−0.0413221	−	0.0346734i
$647$			3.69757i			0.145367i	0.997355	+	0.0726833i	$0.0231562\pi$
$647$			3.69757i			0.145367i	−0.997355	+	0.0726833i	$0.976844\pi$
$648$		0			0
$649$	10.6913			0.419672
$650$	−1.38151	−	2.09893i	−0.0541872	−	0.0823270i
$651$		0			0
$652$	39.8191	−	7.02118i	1.55944	−	0.274971i
$653$	−9.02248	+	24.7891i	−0.353077	+	0.970071i	0.628299	+	0.777972i	$0.283752\pi$
$653$	−9.02248	+	24.7891i	−0.353077	+	0.970071i	−0.981376	+	0.192099i	$0.938471\pi$
$654$		0			0
$655$	0.551707	+	0.182712i	0.0215570	+	0.00713916i
$656$	20.3417	−	35.2329i	0.794211	−	1.37561i
$657$		0			0
$658$	3.51545	−	2.02964i	0.137046	−	0.0791238i
$659$	14.2209	−	5.17599i	0.553968	−	0.201628i	−0.0498407	−	0.998757i	$-0.515871\pi$
$659$	14.2209	−	5.17599i	0.553968	−	0.201628i	0.603809	+	0.797129i	$0.293649\pi$
$660$		0			0
$661$	14.8757	−	12.4822i	0.578598	−	0.485501i	−0.305889	−	0.952067i	$-0.598953\pi$
$661$	14.8757	−	12.4822i	0.578598	−	0.485501i	0.884486	+	0.466566i	$0.154509\pi$
$662$	3.38736	+	4.03690i	0.131654	+	0.156899i
$663$		0			0
$664$	−8.96318	+	3.26233i	−0.347839	+	0.126603i
$665$	−11.1549	−	28.0648i	−0.432569	−	1.08830i
$666$		0			0
$667$	−18.3104	−	10.5715i	−0.708983	−	0.409332i
$668$	−12.0834	−	2.13062i	−0.467519	−	0.0824363i
$669$		0			0
$670$	1.69654	−	3.14770i	0.0655430	−	0.121606i
$671$	−1.52847	−	8.66839i	−0.0590060	−	0.334640i
$672$		0			0
$673$	−15.8772	+	18.9217i	−0.612021	+	0.729378i	−0.979677	−	0.200584i	$-0.935716\pi$
$673$	−15.8772	+	18.9217i	−0.612021	+	0.729378i	0.367656	+	0.929962i	$0.380161\pi$
$674$	0.998381			0.0384562
$675$		0			0
$676$	13.9654			0.537133
$677$	−6.58819	+	7.85150i	−0.253205	+	0.301758i	−0.877641	−	0.479318i	$-0.840884\pi$
$677$	−6.58819	+	7.85150i	−0.253205	+	0.301758i	0.624437	+	0.781075i	$0.285329\pi$
$678$		0			0
$679$	2.81082	+	15.9410i	0.107869	+	0.611758i
$680$	−1.22709	+	2.27671i	−0.0470568	+	0.0873077i
$681$		0			0
$682$	1.74562	+	0.307800i	0.0668432	+	0.0117863i
$683$	12.1386	+	7.00820i	0.464469	+	0.268161i	0.713921	−	0.700226i	$-0.246917\pi$
$683$	12.1386	+	7.00820i	0.464469	+	0.268161i	−0.249453	+	0.968387i	$0.580251\pi$
$684$		0			0
$685$	−15.4238	−	38.8048i	−0.589312	−	1.48266i
$686$	−3.20562	+	1.16675i	−0.122391	+	0.0445468i
$687$		0			0
$688$	−18.5338	−	22.0877i	−0.706594	−	0.842086i
$689$	10.0898	−	8.46633i	0.384390	−	0.322542i
$690$		0			0
$691$	−15.6160	+	5.68375i	−0.594060	+	0.216220i	−0.621514	−	0.783403i	$-0.713482\pi$
$691$	−15.6160	+	5.68375i	−0.594060	+	0.216220i	0.0274543	+	0.999623i	$0.491260\pi$
$692$	−6.72709	+	3.88389i	−0.255725	+	0.147643i
$693$		0			0
$694$	−2.47467	+	4.28625i	−0.0939372	+	0.162704i
$695$	14.7597	+	4.88808i	0.559869	+	0.185415i
$696$		0			0
$697$	5.23528	−	14.3838i	0.198301	−	0.544826i
$698$	−2.70553	+	0.477058i	−0.102406	+	0.0180569i
$699$		0			0
$700$	−23.5349	+	15.4906i	−0.889537	+	0.585489i
$701$	−23.2471			−0.878029			−0.439015	−	0.898480i	$-0.644672\pi$
$701$	−23.2471			−0.878029			−0.439015	+	0.898480i	$0.644672\pi$
$702$		0			0
$703$			41.0003i			1.54636i
$704$	7.86733	+	6.60147i	0.296511	+	0.248802i
$705$		0			0
$706$	0.708977	+	4.02081i	0.0266827	+	0.151325i
$707$	10.5653	−	29.0280i	0.397349	−	1.09171i
$708$		0			0
$709$	0.376750	−	2.13666i	0.0141492	−	0.0802438i	−0.976916	−	0.213626i	$-0.931473\pi$
$709$	0.376750	−	2.13666i	0.0141492	−	0.0802438i	0.991065	+	0.133382i	$0.0425837\pi$
$710$	−2.60034	+	3.28981i	−0.0975891	+	0.123464i
$711$		0			0
$712$	−8.48841	+	4.90079i	−0.318117	+	0.183665i
$713$	−4.77688	−	13.1244i	−0.178895	−	0.491511i
$714$		0			0
$715$	−6.77540	+	4.18071i	−0.253386	+	0.156350i
$716$	−21.0474	+	17.6609i	−0.786579	+	0.660018i
$717$		0			0
$718$	−0.831472	−	2.28445i	−0.0310303	−	0.0852550i
$719$	−2.14999	−	3.72389i	−0.0801810	−	0.138878i	0.823147	−	0.567829i	$-0.192217\pi$
$719$	−2.14999	−	3.72389i	−0.0801810	−	0.138878i	−0.903328	+	0.428951i	$0.858883\pi$
$720$		0			0
$721$	0.772022	−	1.33718i	0.0287516	−	0.0497992i
$722$	0.612979	+	0.108085i	0.0228127	+	0.00402250i
$723$		0			0
$724$	−12.1925	−	4.43770i	−0.453130	−	0.164926i
$725$	5.08936	−	43.6703i	0.189014	−	1.62187i
$726$		0			0
$727$	−14.7760	+	17.6094i	−0.548011	+	0.653095i	−0.966964	−	0.254914i	$-0.917953\pi$
$727$	−14.7760	+	17.6094i	−0.548011	+	0.653095i	0.418952	+	0.908008i	$0.362397\pi$
$728$		−	5.72622i		−	0.212228i
$729$		0			0
$730$	0.844864	−	5.77465i	0.0312698	−	0.213729i
$731$	−8.31038	−	6.97324i	−0.307371	−	0.257915i
$732$		0			0
$733$	−1.93062	+	0.340421i	−0.0713092	+	0.0125737i	−0.209189	−	0.977875i	$-0.567082\pi$
$733$	−1.93062	+	0.340421i	−0.0713092	+	0.0125737i	0.137880	+	0.990449i	$0.455971\pi$
$734$	−4.61603	−	1.68010i	−0.170381	−	0.0620136i
$735$		0			0
$736$	−1.01017	+	5.72894i	−0.0372353	+	0.211172i
$737$	−9.81157	−	5.66471i	−0.361414	−	0.208662i
$738$		0			0
$739$	2.11839	+	3.66916i	0.0779263	+	0.134972i	0.902355	−	0.430993i	$-0.141837\pi$
$739$	2.11839	+	3.66916i	0.0779263	+	0.134972i	−0.824429	+	0.565966i	$0.808503\pi$
$740$	37.4596	−	7.74139i	1.37704	−	0.284579i
$741$		0			0
$742$	2.08950	+	2.49017i	0.0767080	+	0.0914170i
$743$	26.6003	+	31.7011i	0.975872	+	1.16300i	0.986617	+	0.163057i	$0.0521353\pi$
$743$	26.6003	+	31.7011i	0.975872	+	1.16300i	−0.0107448	+	0.999942i	$0.503420\pi$
$744$		0			0
$745$	3.71800	+	17.9909i	0.136217	+	0.659137i
$746$	2.14832	+	3.72101i	0.0786557	+	0.136236i
$747$		0			0
$748$	3.50969	+	2.02632i	0.128327	+	0.0740895i
$749$	−1.41249	+	8.01065i	−0.0516114	+	0.292703i
$750$		0			0
$751$	−16.4803	−	5.99834i	−0.601375	−	0.218883i	0.0233500	−	0.999727i	$-0.492567\pi$
$751$	−16.4803	−	5.99834i	−0.601375	−	0.218883i	−0.624725	+	0.780845i	$0.714789\pi$
$752$	−25.0404	+	4.41529i	−0.913129	+	0.161009i
$753$		0			0
$754$	3.38520	+	2.84052i	0.123282	+	0.103446i
$755$	−2.86619	+	19.5904i	−0.104311	+	0.712968i
$756$		0			0
$757$			31.2786i			1.13684i	0.822739	+	0.568420i	$0.192445\pi$
$757$			31.2786i			1.13684i	−0.822739	+	0.568420i	$0.807555\pi$
$758$	−1.88925	+	2.25152i	−0.0686206	+	0.0817789i
$759$		0			0
$760$	−0.251959	−	8.60921i	−0.00913953	−	0.312289i
$761$	−12.3465	−	4.49377i	−0.447561	−	0.162899i	0.108400	−	0.994107i	$-0.465427\pi$
$761$	−12.3465	−	4.49377i	−0.447561	−	0.162899i	−0.555961	+	0.831208i	$0.687650\pi$
$762$		0			0
$763$	1.36062	+	0.239915i	0.0492579	+	0.00868549i
$764$	9.58366	−	16.5994i	0.346725	−	0.600545i
$765$		0			0
$766$	2.11392	+	3.66141i	0.0763790	+	0.132292i
$767$	6.02200	+	16.5453i	0.217442	+	0.597417i
$768$		0			0
$769$	36.6235	−	30.7307i	1.32068	−	1.10818i	0.334514	−	0.942391i	$-0.391428\pi$
$769$	36.6235	−	30.7307i	1.32068	−	1.10818i	0.986161	−	0.165788i	$-0.0530166\pi$
$770$	−1.03180	−	1.67218i	−0.0371836	−	0.0602610i
$771$		0			0
$772$	−13.0025	−	35.7240i	−0.467970	−	1.28574i
$773$	45.6728	−	26.3692i	1.64274	−	0.948434i	0.662881	−	0.748725i	$-0.269333\pi$
$773$	45.6728	−	26.3692i	1.64274	−	0.948434i	0.979855	−	0.199710i	$-0.0639999\pi$
$774$		0			0
$775$	21.1183	−	19.9376i	0.758591	−	0.716179i
$776$	−0.801623	+	4.54623i	−0.0287766	+	0.163200i
$777$		0			0
$778$	0.810692	−	2.22736i	0.0290647	−	0.0798546i
$779$	8.85162	+	50.2000i	0.317142	+	1.79860i
$780$		0			0
$781$	10.1779	+	8.54024i	0.364192	+	0.305594i
$782$			0.702854i			0.0251340i
$783$		0			0
$784$	−4.83580			−0.172707
$785$	9.25690	+	10.3984i	0.330393	+	0.371133i
$786$		0			0
$787$	−8.67001	+	1.52876i	−0.309053	+	0.0544943i	−0.326023	−	0.945362i	$-0.605709\pi$
$787$	−8.67001	+	1.52876i	−0.309053	+	0.0544943i	0.0169709	+	0.999856i	$0.494598\pi$
$788$	4.33353	−	11.9063i	0.154376	−	0.424144i
$789$		0			0
$790$	−0.218759	+	0.660553i	−0.00778311	+	0.0235014i
$791$	−6.12740	+	10.6130i	−0.217865	+	0.377354i
$792$		0			0
$793$	12.5538	−	7.24793i	0.445798	−	0.257382i
$794$	−0.660500	+	0.240402i	−0.0234403	+	0.00853156i
$795$		0			0
$796$	−25.8268	+	21.6712i	−0.915406	+	0.768117i
$797$	5.59255	+	6.66494i	0.198098	+	0.236084i	0.855944	−	0.517068i	$-0.172977\pi$
$797$	5.59255	+	6.66494i	0.198098	+	0.236084i	−0.657846	+	0.753153i	$0.728532\pi$
$798$		0			0
$799$	−8.98971	+	3.27199i	−0.318033	+	0.115755i
$800$	−11.7698	+	2.79370i	−0.416125	+	0.0987720i
$801$		0			0
$802$	3.86436	+	2.23109i	0.136455	+	0.0787825i
$803$	−18.2101	−	3.21093i	−0.642620	−	0.113311i
$804$		0			0
$805$	−7.34555	+	13.6287i	−0.258897	+	0.480348i
$806$	0.506903	+	2.87479i	0.0178549	+	0.101260i
$807$		0			0
$808$	5.66285	−	6.74872i	0.199218	−	0.237419i
$809$	37.8226			1.32977			0.664886	−	0.746945i	$-0.268480\pi$
$809$	37.8226			1.32977			0.664886	+	0.746945i	$0.268480\pi$
$810$		0			0
$811$	−0.322691			−0.0113312			−0.00566561	−	0.999984i	$-0.501803\pi$
$811$	−0.322691			−0.0113312			−0.00566561	+	0.999984i	$0.501803\pi$
$812$	31.8502	−	37.9576i	1.11772	−	1.33205i
$813$		0			0
$814$	0.463216	+	2.62703i	0.0162357	+	0.0920773i
$815$	40.6698	+	21.9201i	1.42460	+	0.767827i
$816$		0			0
$817$	35.5781	+	6.27337i	1.24472	+	0.219478i
$818$	−2.20478	−	1.27293i	−0.0770883	−	0.0445069i
$819$		0			0
$820$	44.1935	−	17.5656i	1.54330	−	0.613418i
$821$	0.715925	−	0.260575i	0.0249859	−	0.00909414i	−0.329497	−	0.944157i	$-0.606879\pi$
$821$	0.715925	−	0.260575i	0.0249859	−	0.00909414i	0.354483	+	0.935063i	$0.384657\pi$
$822$		0			0
$823$	34.5795	+	41.2102i	1.20537	+	1.43650i	0.869033	+	0.494755i	$0.164742\pi$
$823$	34.5795	+	41.2102i	1.20537	+	1.43650i	0.336332	+	0.941743i	$0.390813\pi$
$824$	0.337327	−	0.283051i	0.0117513	−	0.00986054i
$825$		0			0
$826$	−4.08340	+	1.48624i	−0.142080	+	0.0517128i
$827$	−15.4598	+	8.92572i	−0.537590	+	0.310378i	−0.744102	−	0.668066i	$-0.767122\pi$
$827$	−15.4598	+	8.92572i	−0.537590	+	0.310378i	0.206512	+	0.978444i	$0.433789\pi$
$828$		0			0
$829$	3.49405	−	6.05188i	0.121354	−	0.210190i	−0.798948	−	0.601400i	$-0.794610\pi$
$829$	3.49405	−	6.05188i	0.121354	−	0.210190i	0.920302	+	0.391209i	$0.127943\pi$
$830$	−5.11688	−	1.69459i	−0.177609	−	0.0588200i
$831$		0			0
$832$	−5.78471	+	15.8934i	−0.200549	+	0.551003i
$833$	−1.79180	+	0.315943i	−0.0620823	+	0.0109468i
$834$		0			0
$835$	−9.32218	−	10.4717i	−0.322607	−	0.362388i
$836$	−13.4959			−0.466765
$837$		0			0
$838$			6.29168i			0.217343i
$839$	−34.2020	−	28.6989i	−1.18078	−	0.990795i	−0.999974	−	0.00727705i	$-0.997684\pi$
$839$	−34.2020	−	28.6989i	−1.18078	−	0.990795i	−0.180810	−	0.983518i	$-0.557872\pi$
$840$		0			0
$841$	8.39066	+	47.5858i	0.289333	+	1.64089i
$842$	0.645076	−	1.77233i	0.0222308	−	0.0610786i
$843$		0			0
$844$	6.85757	−	38.8912i	0.236047	−	1.33869i
$845$	12.5190	+	9.89530i	0.430667	+	0.340409i
$846$		0			0
$847$	22.0400	−	12.7248i	0.757302	−	0.437229i
$848$	−6.96412	−	19.1338i	−0.239149	−	0.657056i
$849$		0			0
$850$	−1.34182	+	0.579342i	−0.0460240	+	0.0198713i
$851$	16.1013	−	13.5106i	0.551946	−	0.463138i
$852$		0			0
$853$	−6.47405	−	17.7873i	−0.221667	−	0.609026i	0.778151	−	0.628077i	$-0.216158\pi$
$853$	−6.47405	−	17.7873i	−0.221667	−	0.609026i	−0.999819	+	0.0190511i	$0.993935\pi$
$854$	1.78880	+	3.09829i	0.0612114	+	0.106021i
$855$		0			0
$856$	−1.15991	+	2.00902i	−0.0396448	+	0.0686668i
$857$	55.0204	+	9.70158i	1.87946	+	0.331400i	0.991665	−	0.128840i	$-0.0411252\pi$
$857$	55.0204	+	9.70158i	1.87946	+	0.331400i	0.887795	+	0.460239i	$0.152236\pi$
$858$		0			0
$859$	5.69311	+	2.07212i	0.194246	+	0.0706999i	0.437312	−	0.899310i	$-0.355931\pi$
$859$	5.69311	+	2.07212i	0.194246	+	0.0706999i	−0.243065	+	0.970010i	$0.578153\pi$
$860$	−0.985983	−	33.6901i	−0.0336217	−	1.14882i
$861$		0			0
$862$	−2.36201	+	2.81493i	−0.0804503	+	0.0958769i
$863$		−	31.2067i		−	1.06229i	−0.847281	−	0.531145i	$-0.821762\pi$
$863$		−	31.2067i		−	1.06229i	0.847281	−	0.531145i	$-0.178238\pi$
$864$		0			0
$865$	−8.78229	−	1.28490i	−0.298607	−	0.0436879i
$866$	1.07264	+	0.900051i	0.0364497	+	0.0305850i
$867$		0			0
$868$	32.2345	−	5.68381i	1.09411	−	0.192921i
$869$	2.07170	+	0.754038i	0.0702777	+	0.0255790i
$870$		0			0
$871$	3.23992	−	18.3745i	0.109781	−	0.622597i
$872$	0.341235	+	0.197012i	0.0115557	+	0.00667168i
$873$		0			0
$874$	−1.17030	−	2.02703i	−0.0395861	−	0.0685652i
$875$	−32.0733	−	2.78965i	−1.08427	−	0.0943075i
$876$		0			0
$877$	0.574169	+	0.684268i	0.0193883	+	0.0231061i	0.775651	−	0.631161i	$-0.217421\pi$
$877$	0.574169	+	0.684268i	0.0193883	+	0.0231061i	−0.756263	+	0.654268i	$0.772977\pi$
$878$	0.594651	+	0.708677i	0.0200685	+	0.0239167i
$879$		0			0
$880$	2.49088	+	12.0530i	0.0839674	+	0.406308i
$881$	28.2154	+	48.8706i	0.950602	+	1.64649i	0.744126	+	0.668039i	$0.232866\pi$
$881$	28.2154	+	48.8706i	0.950602	+	1.64649i	0.206476	+	0.978452i	$0.433801\pi$
$882$		0			0
$883$	−45.6611	−	26.3625i	−1.53662	−	0.887168i	−0.999033	−	0.0439585i	$-0.986003\pi$
$883$	−45.6611	−	26.3625i	−1.53662	−	0.887168i	−0.537586	−	0.843209i	$-0.680664\pi$
$884$	−1.15895	+	6.57273i	−0.0389797	+	0.221065i
$885$		0			0
$886$	1.56459	+	0.569463i	0.0525633	+	0.0191315i
$887$	51.5601	−	9.09144i	1.73122	−	0.305261i	0.782799	−	0.622275i	$-0.213792\pi$
$887$	51.5601	−	9.09144i	1.73122	−	0.305261i	0.948421	+	0.317015i	$0.102680\pi$
$888$		0			0
$889$	−26.6597	−	22.3702i	−0.894139	−	0.750272i
$890$	−5.48055	−	0.801835i	−0.183708	−	0.0268776i
$891$		0			0
$892$			18.2819i			0.612122i
$893$	20.4782	−	24.4049i	0.685276	−	0.816680i
$894$		0			0
$895$	−31.3812	+	0.918410i	−1.04896	+	0.0306991i
$896$	−17.0156	−	6.19316i	−0.568450	−	0.206899i
$897$		0			0
$898$	1.07347	+	0.189282i	0.0358221	+	0.00631641i
$899$	−25.5379	+	44.2330i	−0.851737	+	1.47525i
$900$		0			0
$901$	−3.83049	−	6.63461i	−0.127612	−	0.221031i
$902$	1.13431	+	3.11648i	0.0377682	+	0.103767i
$903$		0			0
$904$	−2.67730	+	2.24652i	−0.0890457	+	0.0747182i
$905$	−7.78530	−	12.6171i	−0.258792	−	0.419407i
$906$		0			0
$907$	6.80568	+	18.6984i	0.225979	+	0.620872i	0.999923	−	0.0123817i	$-0.00394131\pi$
$907$	6.80568	+	18.6984i	0.225979	+	0.620872i	−0.773945	+	0.633253i	$0.781719\pi$
$908$	13.3274	−	7.69456i	0.442284	−	0.255353i
$909$		0			0
$910$	2.00659	−	2.53863i	0.0665178	−	0.0841548i
$911$	2.63013	−	14.9162i	0.0871400	−	0.494195i	−0.909734	−	0.415191i	$-0.863715\pi$
$911$	2.63013	−	14.9162i	0.0871400	−	0.494195i	0.996874	−	0.0790044i	$-0.0251741\pi$
$912$		0			0
$913$	−5.84105	+	16.0482i	−0.193311	+	0.531116i
$914$	0.109206	+	0.619336i	0.00361220	+	0.0204858i
$915$		0			0
$916$	24.9965	+	20.9746i	0.825907	+	0.693019i
$917$			0.748423i			0.0247151i
$918$		0			0
$919$	31.1704			1.02822			0.514109	−	0.857725i	$-0.328123\pi$
$919$	31.1704			1.02822			0.514109	+	0.857725i	$0.328123\pi$
$920$	−3.29791	+	2.93589i	−0.108729	+	0.0967935i
$921$		0			0
$922$	−0.600621	+	0.105906i	−0.0197804	+	0.00348782i
$923$	−7.48361	+	20.5610i	−0.246326	+	0.676775i
$924$		0			0
$925$	39.0650	+	19.6026i	1.28445	+	0.644531i
$926$	1.91563	−	3.31796i	0.0629514	−	0.109035i
$927$		0			0
$928$	18.4237	−	10.6369i	0.604788	−	0.349174i
$929$	−9.60870	+	3.49728i	−0.315251	+	0.114742i	−0.494800	−	0.869007i	$-0.664759\pi$
$929$	−9.60870	+	3.49728i	−0.315251	+	0.114742i	0.179548	+	0.983749i	$0.442536\pi$
$930$		0			0
$931$	4.64148	−	3.89467i	0.152118	−	0.127643i
$932$	−37.5561	−	44.7577i	−1.23019	−	1.46609i
$933$		0			0
$934$	4.21379	−	1.53369i	0.137879	−	0.0501840i
$935$	1.71042	+	4.30326i	0.0559366	+	0.140731i
$936$		0			0
$937$	0.758718	+	0.438046i	0.0247862	+	0.0143103i	0.512342	−	0.858782i	$-0.328778\pi$
$937$	0.758718	+	0.438046i	0.0247862	+	0.0143103i	−0.487556	+	0.873092i	$0.662111\pi$
$938$	4.53485	+	0.799617i	0.148068	+	0.0261084i
$939$		0			0
$940$	−26.1639	−	14.1017i	−0.853373	−	0.459948i
$941$	−0.921099	−	5.22381i	−0.0300270	−	0.170291i	0.966107	−	0.258144i	$-0.0831108\pi$
$941$	−0.921099	−	5.22381i	−0.0300270	−	0.170291i	−0.996134	+	0.0878522i	$0.972000\pi$
$942$		0			0
$943$	16.7973	−	20.0183i	0.546996	−	0.651884i
$944$	27.2192			0.885911
$945$		0			0
$946$	2.35048			0.0764208
$947$	−14.4581	+	17.2305i	−0.469825	+	0.559916i	−0.947968	−	0.318366i	$-0.896866\pi$
$947$	−14.4581	+	17.2305i	−0.469825	+	0.559916i	0.478143	+	0.878282i	$0.341310\pi$
$948$		0			0
$949$	−5.28795	−	29.9895i	−0.171654	−	0.973500i
$950$	2.90515	−	3.90505i	0.0942555	−	0.126697i
$951$		0			0
$952$	−3.28002	−	0.578356i	−0.106306	−	0.0187446i
$953$	−3.69060	−	2.13077i	−0.119550	−	0.0690223i	0.439032	−	0.898471i	$-0.355321\pi$
$953$	−3.69060	−	2.13077i	−0.119550	−	0.0690223i	−0.558583	+	0.829449i	$0.688655\pi$
$954$		0			0
$955$	20.3526	−	8.08957i	0.658596	−	0.261772i
$956$	−44.4653	+	16.1840i	−1.43811	+	0.523430i
$957$		0			0
$958$	−0.133200	−	0.158741i	−0.00430349	−	0.00512870i
$959$	41.1937	−	34.5656i	1.33021	−	1.11618i
$960$		0			0
$961$	−2.57434	+	0.936985i	−0.0830434	+	0.0302253i
$962$	−3.80453	+	2.19655i	−0.122663	+	0.0708195i
$963$		0			0
$964$	−14.4943	+	25.1049i	−0.466830	+	0.808573i
$965$	13.6567	−	41.2370i	0.439625	−	1.32747i
$966$		0			0
$967$	−1.30770	+	3.59289i	−0.0420529	+	0.115539i	−0.958942	−	0.283604i	$-0.908470\pi$
$967$	−1.30770	+	3.59289i	−0.0420529	+	0.115539i	0.916889	+	0.399143i	$0.130692\pi$
$968$	7.14774	−	1.26034i	0.229737	−	0.0405089i
$969$		0			0
$970$	−1.94848	+	1.73459i	−0.0625620	+	0.0556944i
$971$	−57.0974			−1.83234			−0.916171	−	0.400787i	$-0.868737\pi$
$971$	−57.0974			−1.83234			−0.916171	+	0.400787i	$0.868737\pi$
$972$		0			0
$973$			20.0225i			0.641890i
$974$	−2.91763	−	2.44819i	−0.0934870	−	0.0784449i
$975$		0			0
$976$	−3.89136	−	22.0690i	−0.124559	−	0.706411i
$977$	9.83942	−	27.0336i	0.314791	−	0.864881i	−0.676881	−	0.736092i	$-0.736669\pi$
$977$	9.83942	−	27.0336i	0.314791	−	0.864881i	0.991672	−	0.128789i	$-0.0411089\pi$
$978$		0			0
$979$	−3.04740	+	17.2826i	−0.0973952	+	0.552356i
$980$	−4.43470	−	3.50529i	−0.141661	−	0.111972i
$981$		0			0
$982$	−1.95726	+	1.13002i	−0.0624586	+	0.0360605i
$983$	14.8222	+	40.7237i	0.472756	+	1.29889i	0.915529	+	0.402252i	$0.131772\pi$
$983$	14.8222	+	40.7237i	0.472756	+	1.29889i	−0.442773	+	0.896634i	$0.646005\pi$
$984$		0			0
$985$	12.3210	−	7.60255i	0.392578	−	0.242238i
$986$	1.96898	−	1.65217i	0.0627052	−	0.0526159i
$987$		0			0
$988$	−7.60169	−	20.8855i	−0.241842	−	0.664455i
$989$	−9.26022	−	16.0392i	−0.294458	−	0.510016i
$990$		0			0
$991$	−23.9951	+	41.5607i	−0.762230	+	1.32022i	0.179469	+	0.983764i	$0.442562\pi$
$991$	−23.9951	+	41.5607i	−0.762230	+	1.32022i	−0.941699	+	0.336457i	$0.890771\pi$
$992$	13.8395	+	2.44028i	0.439406	+	0.0774791i
$993$		0			0
$994$	−5.07449	−	1.84696i	−0.160953	−	0.0585821i
$995$	−38.5071	+	1.12696i	−1.22076	+	0.0357270i
$996$		0			0
$997$	−21.4919	+	25.6130i	−0.680655	+	0.811173i	−0.990192	−	0.139715i	$-0.955382\pi$
$997$	−21.4919	+	25.6130i	−0.680655	+	0.811173i	0.309537	+	0.950887i	$0.399826\pi$
$998$		−	6.03495i		−	0.191033i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.p.a.289.8		96
3.2	odd	2		135.2.p.a.124.9	yes	96
5.4	even	2	inner	405.2.p.a.289.9		96
15.2	even	4		675.2.l.h.151.9		96
15.8	even	4		675.2.l.h.151.8		96
15.14	odd	2		135.2.p.a.124.8	yes	96
27.5	odd	18		135.2.p.a.49.8	✓	96
27.22	even	9	inner	405.2.p.a.199.9		96
135.32	even	36		675.2.l.h.76.9		96
135.49	even	18	inner	405.2.p.a.199.8		96
135.59	odd	18		135.2.p.a.49.9	yes	96
135.113	even	36		675.2.l.h.76.8		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.p.a.49.8	✓	96	27.5	odd	18
135.2.p.a.49.9	yes	96	135.59	odd	18
135.2.p.a.124.8	yes	96	15.14	odd	2
135.2.p.a.124.9	yes	96	3.2	odd	2
405.2.p.a.199.8		96	135.49	even	18	inner
405.2.p.a.199.9		96	27.22	even	9	inner
405.2.p.a.289.8		96	1.1	even	1	trivial
405.2.p.a.289.9		96	5.4	even	2	inner
675.2.l.h.76.8		96	135.113	even	36
675.2.l.h.76.9		96	135.32	even	36
675.2.l.h.151.8		96	15.8	even	4
675.2.l.h.151.9		96	15.2	even	4

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.p (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.133405 + 0.158986i) q^{2} +(0.339817 + 1.92720i) q^{4} +(-1.06091 + 1.96837i) q^{5} +(-2.83580 - 0.500029i) q^{7} +(-0.711201 - 0.410612i) q^{8} +(-0.171413 - 0.431259i) q^{10} +(-1.38169 + 0.502894i) q^{11} +(-1.55650 - 1.85496i) q^{13} +(0.457807 - 0.384146i) q^{14} +(-3.51766 + 1.28032i) q^{16} +(-1.21975 + 0.704220i) q^{17} +(2.34516 - 4.06194i) q^{19} +(-4.15395 - 1.37569i) q^{20} +(0.104371 - 0.286757i) q^{22} +(-2.36796 + 0.417535i) q^{23} +(-2.74896 - 4.17651i) q^{25} +0.502557 q^{26} -5.63507i q^{28} +(6.73596 + 5.65214i) q^{29} +(1.00865 + 5.72033i) q^{31} +(0.827470 - 2.27346i) q^{32} +(0.0507589 - 0.287868i) q^{34} +(3.99276 - 5.05143i) q^{35} +(-7.57034 + 4.37074i) q^{37} +(0.332934 + 0.914728i) q^{38} +(1.56275 - 0.964286i) q^{40} +(-8.32538 + 6.98582i) q^{41} +(2.63439 + 7.23793i) q^{43} +(-1.43870 - 2.49190i) q^{44} +(0.249515 - 0.432172i) q^{46} +(6.68918 + 1.17948i) q^{47} +(1.21391 + 0.441827i) q^{49} +(1.03073 + 0.120122i) q^{50} +(3.04596 - 3.63003i) q^{52} +5.43934i q^{53} +(0.475961 - 3.25320i) q^{55} +(1.81151 + 1.52004i) q^{56} +(-1.79722 + 0.316898i) q^{58} +(-6.83272 - 2.48691i) q^{59} +(-1.03952 + 5.89541i) q^{61} +(-1.04401 - 0.602759i) q^{62} +(-3.49236 - 6.04894i) q^{64} +(5.30255 - 1.09582i) q^{65} +(4.95280 + 5.90251i) q^{67} +(-1.77166 - 2.11138i) q^{68} +(0.270451 + 1.30868i) q^{70} +(-4.51802 - 7.82544i) q^{71} +(10.8910 + 6.28791i) q^{73} +(0.315035 - 1.78665i) q^{74} +(8.62507 + 3.13927i) q^{76} +(4.16966 - 0.735224i) q^{77} +(-1.14861 - 0.963795i) q^{79} +(1.21176 - 8.28236i) q^{80} -2.25556i q^{82} +(7.46590 - 8.89751i) q^{83} +(-0.0921308 - 3.14802i) q^{85} +(-1.50217 - 0.546744i) q^{86} +(1.18915 + 0.209680i) q^{88} +(5.96766 - 10.3363i) q^{89} +(3.48639 + 6.03861i) q^{91} +(-1.60934 - 4.42164i) q^{92} +(-1.07989 + 0.906134i) q^{94} +(5.50740 + 8.92547i) q^{95} +(-1.92260 - 5.28231i) q^{97} +(-0.232185 + 0.134052i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{4} + 9 q^{5} - 3 q^{10} + 6 q^{11} + 18 q^{14} - 24 q^{16} - 6 q^{19} + 57 q^{20} + 3 q^{25} - 48 q^{26} + 30 q^{29} - 30 q^{31} - 24 q^{34} + 12 q^{35} - 9 q^{40} + 12 q^{41} - 78 q^{44} - 6 q^{46}+ \cdots - 87 q^{95}+O(q^{100}) \) 96 * q - 12 * q^4 + 9 * q^5 - 3 * q^10 + 6 * q^11 + 18 * q^14 - 24 * q^16 - 6 * q^19 + 57 * q^20 + 3 * q^25 - 48 * q^26 + 30 * q^29 - 30 * q^31 - 24 * q^34 + 12 * q^35 - 9 * q^40 + 12 * q^41 - 78 * q^44 - 6 * q^46 - 30 * q^49 - 84 * q^50 - 12 * q^55 + 96 * q^56 - 66 * q^59 + 6 * q^61 - 45 * q^65 - 33 * q^70 + 90 * q^71 - 66 * q^74 + 12 * q^76 + 24 * q^79 - 30 * q^80 - 21 * q^85 - 18 * q^86 - 96 * q^89 - 6 * q^91 + 24 * q^94 - 87 * q^95

Introduction

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