LMFDB - Embedded newform 297.2.t.a.17.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [297,2,Mod(8,297)] 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("297.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(297, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([5, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.t (of order $30$, degree $8$, 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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			17.6
Character	$\chi$	$=$	297.17
Dual form			297.2.t.a.35.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.536887 - 0.596273i) q^{2} +(0.141763 + 1.34878i) q^{4} +(2.14661 - 1.93281i) q^{5} +(0.542079 - 1.21753i) q^{7} +(2.17861 + 1.58285i) q^{8} -2.31767i q^{10} +(-2.22482 + 2.45971i) q^{11} +(-0.121914 + 0.573561i) q^{13} +(-0.434945 - 0.976903i) q^{14} +(-0.539671 + 0.114711i) q^{16} +(0.407327 - 1.25362i) q^{17} +(4.21041 - 5.79513i) q^{19} +(2.91125 + 2.62130i) q^{20} +(0.272182 + 2.64719i) q^{22} +(2.62500 + 1.51554i) q^{23} +(0.349510 - 3.32536i) q^{25} +(0.276545 + 0.380632i) q^{26} +(1.71903 + 0.558546i) q^{28} +(1.19216 + 0.530783i) q^{29} +(-7.38644 - 1.57004i) q^{31} +(-2.91425 + 5.04763i) q^{32} +(-0.528814 - 0.915932i) q^{34} +(-1.18963 - 3.66129i) q^{35} +(-3.23755 + 2.35222i) q^{37} +(-1.19497 - 5.62189i) q^{38} +(7.73596 - 0.813082i) q^{40} +(2.05694 - 0.915811i) q^{41} +(-11.2365 + 6.48742i) q^{43} +(-3.63301 - 2.65210i) q^{44} +(2.31301 - 0.751541i) q^{46} +(-11.5098 - 1.20973i) q^{47} +(3.49539 + 3.88202i) q^{49} +(-1.79518 - 1.99375i) q^{50} +(-0.790891 - 0.0831260i) q^{52} +(3.40948 - 1.10781i) q^{53} +(-0.0216557 + 9.58019i) q^{55} +(3.10815 - 1.79449i) q^{56} +(0.956546 - 0.425882i) q^{58} +(-5.95883 + 0.626298i) q^{59} +(-1.64415 - 7.73512i) q^{61} +(-4.90186 + 3.56141i) q^{62} +(1.10416 + 3.39825i) q^{64} +(0.846884 + 1.46685i) q^{65} +(-4.35166 + 7.53730i) q^{67} +(1.74861 + 0.371678i) q^{68} +(-2.82183 - 1.25636i) q^{70} +(-4.54327 - 1.47620i) q^{71} +(-5.16130 - 7.10392i) q^{73} +(-0.335634 + 3.19334i) q^{74} +(8.41325 + 4.85739i) q^{76} +(1.78874 + 4.04214i) q^{77} +(10.2545 + 9.23323i) q^{79} +(-0.936746 + 1.28932i) q^{80} +(0.558273 - 1.71819i) q^{82} +(10.5286 - 2.23793i) q^{83} +(-1.54865 - 3.47832i) q^{85} +(-2.16448 + 10.1831i) q^{86} +(-8.74036 + 1.83718i) q^{88} +8.87289i q^{89} +(0.632240 + 0.459350i) q^{91} +(-1.67201 + 3.75540i) q^{92} +(-6.90079 + 6.21350i) q^{94} +(-2.16281 - 20.5778i) q^{95} +(-0.548828 + 0.609535i) q^{97} +4.19137 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) $ 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	0.536887	−	0.596273i	0.379636	−	0.421629i	−0.522798	−	0.852457i	$-0.675112\pi$
$2$	0.536887	−	0.596273i	0.379636	−	0.421629i	0.902434	+	0.430828i	$0.141778\pi$
$3$		0			0
$3$		0			0
$4$	0.141763	+	1.34878i	0.0708813	+	0.674390i
$5$	2.14661	−	1.93281i	0.959991	−	0.864380i	−0.0308346	−	0.999525i	$-0.509817\pi$
$5$	2.14661	−	1.93281i	0.959991	−	0.864380i	0.990826	+	0.135144i	$0.0431498\pi$
$6$		0			0
$7$	0.542079	−	1.21753i	0.204887	−	0.460183i	−0.781651	−	0.623716i	$-0.785622\pi$
$7$	0.542079	−	1.21753i	0.204887	−	0.460183i	0.986538	+	0.163533i	$0.0522889\pi$
$8$	2.17861	+	1.58285i	0.770254	+	0.559622i
$9$		0			0
$10$		−	2.31767i		−	0.732910i
$11$	−2.22482	+	2.45971i	−0.670809	+	0.741630i
$11$	−2.22482	+	2.45971i	−0.670809	+	0.741630i
$12$		0			0
$13$	−0.121914	+	0.573561i	−0.0338129	+	0.159077i	−0.991815	−	0.127685i	$-0.959245\pi$
$13$	−0.121914	+	0.573561i	−0.0338129	+	0.159077i	0.958002	+	0.286762i	$0.0925788\pi$
$14$	−0.434945	−	0.976903i	−0.116244	−	0.261088i
$15$		0			0
$16$	−0.539671	+	0.114711i	−0.134918	+	0.0286776i
$17$	0.407327	−	1.25362i	0.0987913	−	0.304048i	−0.889432	−	0.457068i	$-0.848900\pi$
$17$	0.407327	−	1.25362i	0.0987913	−	0.304048i	0.988223	+	0.153019i	$0.0488997\pi$
$18$		0			0
$19$	4.21041	−	5.79513i	0.965935	−	1.32949i	0.0218608	−	0.999761i	$-0.493041\pi$
$19$	4.21041	−	5.79513i	0.965935	−	1.32949i	0.944074	−	0.329734i	$-0.106959\pi$
$20$	2.91125	+	2.62130i	0.650975	+	0.586141i
$21$		0			0
$22$	0.272182	+	2.64719i	0.0580294	+	0.564382i
$23$	2.62500	+	1.51554i	0.547350	+	0.316013i	0.748053	−	0.663639i	$-0.230989\pi$
$23$	2.62500	+	1.51554i	0.547350	+	0.316013i	−0.200702	+	0.979652i	$0.564322\pi$
$24$		0			0
$25$	0.349510	−	3.32536i	0.0699020	−	0.665073i
$26$	0.276545	+	0.380632i	0.0542349	+	0.0746480i
$27$		0			0
$28$	1.71903	+	0.558546i	0.324866	+	0.105555i
$29$	1.19216	+	0.530783i	0.221378	+	0.0985639i	0.514429	−	0.857533i	$-0.328004\pi$
$29$	1.19216	+	0.530783i	0.221378	+	0.0985639i	−0.293051	+	0.956097i	$0.594671\pi$
$30$		0			0
$31$	−7.38644	−	1.57004i	−1.32664	−	0.281987i	−0.510521	−	0.859865i	$-0.670548\pi$
$31$	−7.38644	−	1.57004i	−1.32664	−	0.281987i	−0.816123	+	0.577878i	$0.803881\pi$
$32$	−2.91425	+	5.04763i	−0.515171	+	0.892303i
$33$		0			0
$34$	−0.528814	−	0.915932i	−0.0906908	−	0.157081i
$35$	−1.18963	−	3.66129i	−0.201084	−	0.618872i
$36$		0			0
$37$	−3.23755	+	2.35222i	−0.532250	+	0.386702i	−0.821199	−	0.570642i	$-0.806694\pi$
$37$	−3.23755	+	2.35222i	−0.532250	+	0.386702i	0.288949	+	0.957345i	$0.406694\pi$
$38$	−1.19497	−	5.62189i	−0.193850	−	0.911991i
$39$		0			0
$40$	7.73596	−	0.813082i	1.22316	−	0.128560i
$41$	2.05694	−	0.915811i	0.321241	−	0.143026i	−0.239780	−	0.970827i	$-0.577075\pi$
$41$	2.05694	−	0.915811i	0.321241	−	0.143026i	0.561021	+	0.827802i	$0.310409\pi$
$42$		0			0
$43$	−11.2365	+	6.48742i	−1.71356	+	0.989322i	−0.783904	+	0.620882i	$0.786775\pi$
$43$	−11.2365	+	6.48742i	−1.71356	+	0.989322i	−0.929652	+	0.368440i	$0.879892\pi$
$44$	−3.63301	−	2.65210i	−0.547696	−	0.399819i
$45$		0			0
$46$	2.31301	−	0.751541i	0.341034	−	0.110809i
$47$	−11.5098	−	1.20973i	−1.67888	−	0.176457i	−0.783385	−	0.621537i	$-0.786509\pi$
$47$	−11.5098	−	1.20973i	−1.67888	−	0.176457i	−0.895491	+	0.445080i	$0.853175\pi$
$48$		0			0
$49$	3.49539	+	3.88202i	0.499341	+	0.554574i
$50$	−1.79518	−	1.99375i	−0.253877	−	0.281959i
$51$		0			0
$52$	−0.790891	−	0.0831260i	−0.109677	−	0.0115275i
$53$	3.40948	−	1.10781i	0.468328	−	0.152169i	−0.0653400	−	0.997863i	$-0.520813\pi$
$53$	3.40948	−	1.10781i	0.468328	−	0.152169i	0.533668	+	0.845694i	$0.320813\pi$
$54$		0			0
$55$	−0.0216557	+	9.58019i	−0.00292006	+	1.29179i
$56$	3.10815	−	1.79449i	0.415343	−	0.239799i
$57$		0			0
$58$	0.956546	−	0.425882i	0.125601	−	0.0559210i
$59$	−5.95883	+	0.626298i	−0.775773	+	0.0815370i	−0.484137	−	0.874992i	$-0.660866\pi$
$59$	−5.95883	+	0.626298i	−0.775773	+	0.0815370i	−0.291636	+	0.956529i	$0.594200\pi$
$60$		0			0
$61$	−1.64415	−	7.73512i	−0.210512	−	0.990381i	−0.948796	−	0.315890i	$-0.897697\pi$
$61$	−1.64415	−	7.73512i	−0.210512	−	0.990381i	0.738284	−	0.674490i	$-0.235637\pi$
$62$	−4.90186	+	3.56141i	−0.622536	+	0.452299i
$63$		0			0
$64$	1.10416	+	3.39825i	0.138020	+	0.424781i
$65$	0.846884	+	1.46685i	0.105043	+	0.181940i
$66$		0			0
$67$	−4.35166	+	7.53730i	−0.531640	+	0.920828i	0.467678	+	0.883899i	$0.345091\pi$
$67$	−4.35166	+	7.53730i	−0.531640	+	0.920828i	−0.999318	+	0.0369287i	$0.988243\pi$
$68$	1.74861	+	0.371678i	0.212050	+	0.0450726i
$69$		0			0
$70$	−2.82183	−	1.25636i	−0.337273	−	0.150164i
$71$	−4.54327	−	1.47620i	−0.539187	−	0.175192i	0.0267483	−	0.999642i	$-0.491485\pi$
$71$	−4.54327	−	1.47620i	−0.539187	−	0.175192i	−0.565935	+	0.824450i	$0.691485\pi$
$72$		0			0
$73$	−5.16130	−	7.10392i	−0.604084	−	0.831451i	0.391990	−	0.919969i	$-0.371787\pi$
$73$	−5.16130	−	7.10392i	−0.604084	−	0.831451i	−0.996075	+	0.0885185i	$0.971787\pi$
$74$	−0.335634	+	3.19334i	−0.0390166	+	0.371218i
$75$		0			0
$76$	8.41325	+	4.85739i	0.965065	+	0.557181i
$77$	1.78874	+	4.04214i	0.203846	+	0.460645i
$78$		0			0
$79$	10.2545	+	9.23323i	1.15373	+	1.03882i	0.998703	+	0.0509087i	$0.0162118\pi$
$79$	10.2545	+	9.23323i	1.15373	+	1.03882i	0.155023	+	0.987911i	$0.450455\pi$
$80$	−0.936746	+	1.28932i	−0.104731	+	0.144150i
$81$		0			0
$82$	0.558273	−	1.71819i	0.0616510	−	0.189742i
$83$	10.5286	−	2.23793i	1.15567	−	0.245644i	0.410077	−	0.912051i	$-0.365502\pi$
$83$	10.5286	−	2.23793i	1.15567	−	0.245644i	0.745589	+	0.666407i	$0.232168\pi$
$84$		0			0
$85$	−1.54865	−	3.47832i	−0.167975	−	0.377277i
$86$	−2.16448	+	10.1831i	−0.233401	+	1.09807i
$87$		0			0
$88$	−8.74036	+	1.83718i	−0.931726	+	0.195844i
$89$			8.87289i			0.940524i	0.882527	+	0.470262i	$0.155841\pi$
$89$			8.87289i			0.940524i	−0.882527	+	0.470262i	$0.844159\pi$
$90$		0			0
$91$	0.632240	+	0.459350i	0.0662768	+	0.0481529i
$92$	−1.67201	+	3.75540i	−0.174319	+	0.391527i
$93$		0			0
$94$	−6.90079	+	6.21350i	−0.711762	+	0.640873i
$95$	−2.16281	−	20.5778i	−0.221900	−	2.11124i
$96$		0			0
$97$	−0.548828	+	0.609535i	−0.0557250	+	0.0618889i	−0.770363	−	0.637606i	$-0.779925\pi$
$97$	−0.548828	+	0.609535i	−0.0557250	+	0.0618889i	0.714638	+	0.699495i	$0.246592\pi$
$98$	4.19137			0.423392
$99$		0			0
$100$	4.53473			0.453473
$101$	11.4734	−	12.7425i	1.14165	−	1.26793i	0.183068	−	0.983100i	$-0.441397\pi$
$101$	11.4734	−	12.7425i	1.14165	−	1.26793i	0.958579	−	0.284827i	$-0.0919363\pi$
$102$		0			0
$103$	−1.01984	−	9.70315i	−0.100488	−	0.956080i	−0.922340	−	0.386379i	$-0.873726\pi$
$103$	−1.01984	−	9.70315i	−0.100488	−	0.956080i	0.821852	−	0.569701i	$-0.192941\pi$
$104$	−1.17346	+	1.05659i	−0.115068	+	0.103607i
$105$		0			0
$106$	1.16995	−	2.62775i	0.113636	−	0.255230i
$107$	−2.38113	−	1.72999i	−0.230193	−	0.167245i	0.466710	−	0.884410i	$-0.345439\pi$
$107$	−2.38113	−	1.72999i	−0.230193	−	0.167245i	−0.696903	+	0.717165i	$0.745439\pi$
$108$		0			0
$109$		−	1.43952i		−	0.137881i	−0.997621	−	0.0689404i	$-0.978038\pi$
$109$		−	1.43952i		−	0.137881i	0.997621	−	0.0689404i	$-0.0219618\pi$
$110$	5.70079	+	5.15639i	0.543549	+	0.491643i
$111$		0			0
$112$	−0.152881	+	0.719247i	−0.0144459	+	0.0679625i
$113$	−0.769359	−	1.72801i	−0.0723752	−	0.162557i	0.873735	−	0.486402i	$-0.161691\pi$
$113$	−0.769359	−	1.72801i	−0.0723752	−	0.162557i	−0.946110	+	0.323845i	$0.895024\pi$
$114$		0			0
$115$	8.56410	−	1.82036i	0.798607	−	0.169749i
$116$	−0.546906	+	1.68320i	−0.0507790	+	0.156282i
$117$		0			0
$118$	−2.82577	+	3.88934i	−0.260133	+	0.358043i
$119$	−1.30552	−	1.17550i	−0.119677	−	0.107758i
$120$		0			0
$121$	−1.10034	−	10.9448i	−0.100031	−	0.994984i
$122$	−5.49497	−	3.17252i	−0.497491	−	0.287227i
$123$		0			0
$124$	1.07051	−	10.1853i	0.0961351	−	0.914664i
$125$	2.81217	+	3.87062i	0.251528	+	0.346199i
$126$		0			0
$127$	−4.49091	−	1.45919i	−0.398504	−	0.129482i	0.102907	−	0.994691i	$-0.467186\pi$
$127$	−4.49091	−	1.45919i	−0.398504	−	0.129482i	−0.501411	+	0.865209i	$0.667186\pi$
$128$	−8.03010	−	3.57523i	−0.709768	−	0.316009i
$129$		0			0
$130$	1.32932	+	0.282556i	0.116589	+	0.0247818i
$131$	−3.94244	+	6.82851i	−0.344453	+	0.596609i	−0.985254	−	0.171097i	$-0.945269\pi$
$131$	−3.94244	+	6.82851i	−0.344453	+	0.596609i	0.640802	+	0.767707i	$0.278602\pi$
$132$		0			0
$133$	−4.77337	−	8.26772i	−0.413904	−	0.716903i
$134$	2.15794	+	6.64146i	0.186418	+	0.573735i
$135$		0			0
$136$	2.87170	−	2.08641i	0.246247	−	0.178909i
$137$	1.40050	+	6.58885i	0.119653	+	0.562923i	0.996604	+	0.0823435i	$0.0262404\pi$
$137$	1.40050	+	6.58885i	0.119653	+	0.562923i	−0.876951	+	0.480580i	$0.840426\pi$
$138$		0			0
$139$	−7.37491	+	0.775135i	−0.625532	+	0.0657461i	−0.411991	−	0.911188i	$-0.635166\pi$
$139$	−7.37491	+	0.775135i	−0.625532	+	0.0657461i	−0.213541	+	0.976934i	$0.568500\pi$
$140$	4.76964	−	2.12358i	0.403108	−	0.179475i
$141$		0			0
$142$	−3.31944	+	1.91648i	−0.278561	+	0.160827i
$143$	−1.13956	−	1.57594i	−0.0952945	−	0.131787i
$144$		0			0
$145$	3.58500	−	1.16484i	0.297718	−	0.0967344i
$146$	−7.00691	−	0.736456i	−0.579896	−	0.0609496i
$147$		0			0
$148$	−3.63159	−	4.03329i	−0.298515	−	0.331534i
$149$	−4.12377	−	4.57991i	−0.337832	−	0.375201i	0.550160	−	0.835059i	$-0.314567\pi$
$149$	−4.12377	−	4.57991i	−0.337832	−	0.375201i	−0.887992	+	0.459858i	$0.847900\pi$
$150$		0			0
$151$	19.6091	+	2.06100i	1.59577	+	0.167722i	0.860283	−	0.509817i	$-0.170287\pi$
$151$	19.6091	+	2.06100i	1.59577	+	0.167722i	0.735486	+	0.677539i	$0.236954\pi$
$152$	18.3457	−	5.96087i	1.48803	−	0.483490i
$153$		0			0
$154$	3.37057	+	1.10360i	0.271609	+	0.0889303i
$155$	−18.8904	+	10.9064i	−1.51731	+	0.876020i
$156$		0			0
$157$	4.45331	−	1.98274i	0.355413	−	0.158240i	−0.221261	−	0.975215i	$-0.571017\pi$
$157$	4.45331	−	1.98274i	0.355413	−	0.158240i	0.576674	+	0.816975i	$0.304350\pi$
$158$	11.0111	−	1.15731i	0.875993	−	0.0920706i
$159$		0			0
$160$	3.50037	+	16.4680i	0.276729	+	1.30191i
$161$	3.26818	−	2.37447i	0.257569	−	0.187134i
$162$		0			0
$163$	3.43006	+	10.5566i	0.268663	+	0.826859i	0.990827	+	0.135137i	$0.0431476\pi$
$163$	3.43006	+	10.5566i	0.268663	+	0.826859i	−0.722164	+	0.691722i	$0.756852\pi$
$164$	1.52683	+	2.64454i	0.119225	+	0.206504i
$165$		0			0
$166$	4.31826	−	7.47945i	0.335162	−	0.580518i
$167$	20.7753	+	4.41592i	1.60764	+	0.341714i	0.922289	−	0.386501i	$-0.126316\pi$
$167$	20.7753	+	4.41592i	1.60764	+	0.341714i	0.685349	+	0.728215i	$0.259650\pi$
$168$		0			0
$169$	11.5620	+	5.14773i	0.889383	+	0.395979i
$170$	−2.90548	−	0.944048i	−0.222840	−	0.0724052i
$171$		0			0
$172$	−10.3430	−	14.2360i	−0.788648	−	1.08548i
$173$	1.29542	−	12.3251i	0.0984892	−	0.937062i	−0.827997	−	0.560733i	$-0.810519\pi$
$173$	1.29542	−	12.3251i	0.0984892	−	0.937062i	0.926486	−	0.376329i	$-0.122814\pi$
$174$		0			0
$175$	−3.85927	−	2.22815i	−0.291733	−	0.168432i
$176$	0.918516	−	1.58264i	0.0692357	−	0.119296i
$177$		0			0
$178$	5.29067	+	4.76374i	0.396552	+	0.357057i
$179$	6.56098	−	9.03041i	0.490390	−	0.674964i	−0.490070	−	0.871683i	$-0.663029\pi$
$179$	6.56098	−	9.03041i	0.490390	−	0.674964i	0.980460	+	0.196719i	$0.0630286\pi$
$180$		0			0
$181$	−0.00588405	+	0.0181092i	−0.000437358	+	0.00134605i	−0.951275	−	0.308344i	$-0.900225\pi$
$181$	−0.00588405	+	0.0181092i	−0.000437358	+	0.00134605i	0.950838	+	0.309690i	$0.100225\pi$
$182$	0.613340	−	0.130369i	0.0454638	−	0.00966362i
$183$		0			0
$184$	3.31996	+	7.45676i	0.244751	+	0.549719i
$185$	−2.40335	+	11.3069i	−0.176698	+	0.831297i
$186$		0			0
$187$	2.17732	+	3.79099i	0.159221	+	0.277225i
$188$		−	15.6957i		−	1.14473i
$189$		0			0
$190$	−13.4312	−	9.75833i	−0.974401	−	0.707943i
$191$	−1.06374	+	2.38919i	−0.0769692	+	0.172876i	−0.947932	−	0.318474i	$-0.896830\pi$
$191$	−1.06374	+	2.38919i	−0.0769692	+	0.172876i	0.870962	+	0.491350i	$0.163496\pi$
$192$		0			0
$193$	9.54568	−	8.59497i	0.687113	−	0.618680i	−0.249777	−	0.968303i	$-0.580357\pi$
$193$	9.54568	−	8.59497i	0.687113	−	0.618680i	0.936890	+	0.349624i	$0.113691\pi$
$194$	0.0687910	+	0.654503i	0.00493891	+	0.0469906i
$195$		0			0
$196$	−4.74048	+	5.26483i	−0.338606	+	0.376060i
$197$	6.88153			0.490288			0.245144	−	0.969487i	$-0.421165\pi$
$197$	6.88153			0.490288			0.245144	+	0.969487i	$0.421165\pi$
$198$		0			0
$199$	0.0675681			0.00478977			0.00239489	−	0.999997i	$-0.499238\pi$
$199$	0.0675681			0.00478977			0.00239489	+	0.999997i	$0.499238\pi$
$200$	6.02500	−	6.69144i	0.426032	−	0.473156i
$201$		0			0
$202$	−1.43810	−	13.6826i	−0.101184	−	0.962703i
$203$	1.29249	−	1.16376i	0.0907149	−	0.0816800i
$204$		0			0
$205$	2.64536	−	5.94157i	0.184760	−	0.414978i
$206$	−6.33327	−	4.60139i	−0.441260	−	0.320594i
$207$		0			0
$208$		−	0.323519i		−	0.0224320i
$209$	4.88694	+	23.2495i	0.338036	+	1.60820i
$210$		0			0
$211$	0.253153	−	1.19099i	0.0174278	−	0.0819911i	−0.968574	−	0.248725i	$-0.919989\pi$
$211$	0.253153	−	1.19099i	0.0174278	−	0.0819911i	0.986002	+	0.166733i	$0.0533219\pi$
$212$	1.97753	+	4.44160i	0.135817	+	0.305050i
$213$		0			0
$214$	−2.30995	+	0.490995i	−0.157905	+	0.0335637i
$215$	−11.5815	+	35.6440i	−0.789848	+	2.43090i
$216$		0			0
$217$	−5.91561	+	8.14213i	−0.401577	+	0.552724i
$218$	−0.858346	−	0.772858i	−0.0581345	−	0.0523446i
$219$		0			0
$220$	−12.9246	+	1.32890i	−0.871379	+	0.0895947i
$221$	0.669370	+	0.386461i	0.0450267	+	0.0259962i
$222$		0			0
$223$	1.36427	−	12.9801i	0.0913581	−	0.869214i	−0.848855	−	0.528626i	$-0.822707\pi$
$223$	1.36427	−	12.9801i	0.0913581	−	0.869214i	0.940213	−	0.340588i	$-0.110626\pi$
$224$	4.56588	+	6.28440i	0.305071	+	0.419894i
$225$		0			0
$226$	−1.44342	−	0.468997i	−0.0960151	−	0.0311972i
$227$	−0.722663	−	0.321750i	−0.0479649	−	0.0213553i	0.382614	−	0.923908i	$-0.375024\pi$
$227$	−0.722663	−	0.321750i	−0.0479649	−	0.0213553i	−0.430579	+	0.902553i	$0.641691\pi$
$228$		0			0
$229$	9.55393	+	2.03075i	0.631342	+	0.134196i	0.512458	−	0.858712i	$-0.328735\pi$
$229$	9.55393	+	2.03075i	0.631342	+	0.134196i	0.118884	+	0.992908i	$0.462068\pi$
$230$	3.51252	−	6.08387i	0.231609	−	0.401159i
$231$		0			0
$232$	1.75709	+	3.04337i	0.115359	+	0.199807i
$233$	−5.12103	−	15.7609i	−0.335490	−	1.03253i	−0.966480	−	0.256741i	$-0.917351\pi$
$233$	−5.12103	−	15.7609i	−0.335490	−	1.03253i	0.630991	−	0.775790i	$-0.282649\pi$
$234$		0			0
$235$	−27.0452	+	19.6495i	−1.76423	+	1.28179i
$236$	−1.68948	−	7.94836i	−0.109976	−	0.517394i
$237$		0			0
$238$	−1.40183	+	0.147339i	−0.0908674	+	0.00955055i
$239$	1.11131	−	0.494785i	0.0718844	−	0.0320050i	−0.370480	−	0.928841i	$-0.620807\pi$
$239$	1.11131	−	0.494785i	0.0718844	−	0.0320050i	0.442364	+	0.896836i	$0.354140\pi$
$240$		0			0
$241$	−0.657074	+	0.379362i	−0.0423258	+	0.0244368i	−0.521014	−	0.853548i	$-0.674446\pi$
$241$	−0.657074	+	0.379362i	−0.0423258	+	0.0244368i	0.478688	+	0.877985i	$0.341113\pi$
$242$	−7.11687	−	5.22003i	−0.457490	−	0.335556i
$243$		0			0
$244$	10.1999	−	3.31415i	0.652982	−	0.212167i
$245$	15.0064	+	1.57724i	0.958725	+	0.100766i
$246$		0			0
$247$	2.81055	+	3.12144i	0.178831	+	0.198612i
$248$	−13.6070	−	15.1121i	−0.864047	−	0.959621i
$249$		0			0
$250$	3.81777	+	0.401263i	0.241457	+	0.0253781i
$251$	−9.34419	+	3.03611i	−0.589800	+	0.191638i	−0.588686	−	0.808362i	$-0.700355\pi$
$251$	−9.34419	+	3.03611i	−0.589800	+	0.191638i	−0.00111390	+	0.999999i	$0.500355\pi$
$252$		0			0
$253$	−9.56795	+	3.08492i	−0.601532	+	0.193947i
$254$	−3.28119	+	1.89439i	−0.205880	+	0.118865i
$255$		0			0
$256$	−12.9715	+	5.77529i	−0.810719	+	0.360955i
$257$	−22.1626	+	2.32938i	−1.38246	+	0.145303i	−0.766385	−	0.642381i	$-0.777947\pi$
$257$	−22.1626	+	2.32938i	−1.38246	+	0.145303i	−0.616079	+	0.787684i	$0.711280\pi$
$258$		0			0
$259$	1.10889	+	5.21690i	0.0689029	+	0.324163i
$260$	−1.85840	+	1.35020i	−0.115253	+	0.0837361i
$261$		0			0
$262$	1.95501	+	6.01691i	0.120781	+	0.371726i
$263$	−7.68495	−	13.3107i	−0.473874	−	0.820774i	0.525678	−	0.850683i	$-0.323812\pi$
$263$	−7.68495	−	13.3107i	−0.473874	−	0.820774i	−0.999553	+	0.0299090i	$0.990478\pi$
$264$		0			0
$265$	5.17763	−	8.96791i	0.318059	−	0.550894i
$266$	−7.49259	−	1.59260i	−0.459400	−	0.0976485i
$267$		0			0
$268$	−10.7831	−	4.80093i	−0.658681	−	0.293264i
$269$	−0.906419	−	0.294513i	−0.0552653	−	0.0179568i	0.281254	−	0.959633i	$-0.409250\pi$
$269$	−0.906419	−	0.294513i	−0.0552653	−	0.0179568i	−0.336519	+	0.941677i	$0.609250\pi$
$270$		0			0
$271$	13.1444	+	18.0917i	0.798465	+	1.09899i	0.993002	+	0.118098i	$0.0376796\pi$
$271$	13.1444	+	18.0917i	0.798465	+	1.09899i	−0.194537	+	0.980895i	$0.562320\pi$
$272$	−0.0760186	+	0.723268i	−0.00460930	+	0.0438546i
$273$		0			0
$274$	4.68067	+	2.70238i	0.282769	+	0.163257i
$275$	7.40183	+	8.25803i	0.446347	+	0.497978i
$276$		0			0
$277$	7.70440	+	6.93707i	0.462912	+	0.416808i	0.867305	−	0.497777i	$-0.165850\pi$
$277$	7.70440	+	6.93707i	0.462912	+	0.416808i	−0.404392	+	0.914586i	$0.632517\pi$
$278$	−3.49730	+	4.81362i	−0.209754	+	0.288702i
$279$		0			0
$280$	3.20355	−	9.85952i	0.191449	−	0.589219i
$281$	9.29432	−	1.97557i	0.554453	−	0.117853i	0.0778399	−	0.996966i	$-0.475198\pi$
$281$	9.29432	−	1.97557i	0.554453	−	0.117853i	0.476613	+	0.879113i	$0.341864\pi$
$282$		0			0
$283$	−5.04823	−	11.3385i	−0.300086	−	0.674004i	0.699071	−	0.715052i	$-0.253597\pi$
$283$	−5.04823	−	11.3385i	−0.300086	−	0.674004i	−0.999157	+	0.0410477i	$0.986930\pi$
$284$	1.34700	−	6.33714i	0.0799298	−	0.376040i
$285$		0			0
$286$	−1.55151	−	0.166617i	−0.0917425	−	0.00985224i
$287$		−	3.00083i		−	0.177134i
$288$		0			0
$289$	12.3476	+	8.97108i	0.726331	+	0.527711i
$290$	1.23018	−	2.76302i	0.0722385	−	0.162250i
$291$		0			0
$292$	8.84995	−	7.96853i	0.517904	−	0.466323i
$293$	2.72141	+	25.8925i	0.158987	+	1.51266i	0.725281	+	0.688453i	$0.241710\pi$
$293$	2.72141	+	25.8925i	0.158987	+	1.51266i	−0.566294	+	0.824203i	$0.691623\pi$
$294$		0			0
$295$	−11.5807	+	12.8617i	−0.674256	+	0.748838i
$296$	−10.7766			−0.626375
$297$		0			0
$298$	−4.94488			−0.286449
$299$	−1.18928	+	1.32083i	−0.0687779	+	0.0763856i
$300$		0			0
$301$	1.80753	+	17.1975i	0.104184	+	0.991248i
$302$	11.7568	−	10.5859i	0.676529	−	0.609149i
$303$		0			0
$304$	−1.60747	+	3.61044i	−0.0921949	+	0.207073i
$305$	−18.4799	−	13.4264i	−1.05815	−	0.768795i
$306$		0			0
$307$			18.0274i			1.02888i	0.857527	+	0.514440i	$0.172000\pi$
$307$			18.0274i			1.02888i	−0.857527	+	0.514440i	$0.828000\pi$
$308$	−5.19839	+	2.98564i	−0.296206	+	0.170123i
$309$		0			0
$310$	−3.63882	+	17.1193i	−0.206671	+	0.972311i
$311$	−5.11443	−	11.4872i	−0.290013	−	0.651379i	0.708511	−	0.705700i	$-0.249367\pi$
$311$	−5.11443	−	11.4872i	−0.290013	−	0.651379i	−0.998524	+	0.0543209i	$0.982701\pi$
$312$		0			0
$313$	−11.4400	+	2.43166i	−0.646630	+	0.137445i	−0.519540	−	0.854446i	$-0.673897\pi$
$313$	−11.4400	+	2.43166i	−0.646630	+	0.137445i	−0.127089	+	0.991891i	$0.540563\pi$
$314$	1.20867	−	3.71990i	0.0682091	−	0.209926i
$315$		0			0
$316$	−10.9999	+	15.1401i	−0.618792	+	0.851695i
$317$	−12.2252	−	11.0076i	−0.686636	−	0.618250i	0.250128	−	0.968213i	$-0.419527\pi$
$317$	−12.2252	−	11.0076i	−0.686636	−	0.618250i	−0.936763	+	0.349963i	$0.886194\pi$
$318$		0			0
$319$	−3.95791	+	1.75147i	−0.221600	+	0.0980632i
$320$	8.93837	+	5.16057i	0.499670	+	0.288485i
$321$		0			0
$322$	0.338809	−	3.22355i	0.0188811	−	0.179641i
$323$	−5.54990	−	7.63878i	−0.308805	−	0.425033i
$324$		0			0
$325$	1.86469	+	0.605874i	0.103434	+	0.0336078i
$326$	8.13619	+	3.62247i	0.450622	+	0.200630i
$327$		0			0
$328$	5.93087	+	1.26064i	0.327477	+	0.0696074i
$329$	−7.71210	+	13.3578i	−0.425182	+	0.736437i
$330$		0			0
$331$	−9.81281	−	16.9963i	−0.539361	−	0.934201i	−0.998939	−	0.0460631i	$-0.985332\pi$
$331$	−9.81281	−	16.9963i	−0.539361	−	0.934201i	0.459577	−	0.888138i	$-0.348001\pi$
$332$	4.51104	+	13.8835i	0.247575	+	0.761958i
$333$		0			0
$334$	13.7871	−	10.0169i	0.754395	−	0.548100i
$335$	5.22688	+	24.5906i	0.285575	+	1.34353i
$336$		0			0
$337$	10.6020	−	1.11431i	0.577527	−	0.0607005i	0.188738	−	0.982027i	$-0.439560\pi$
$337$	10.6020	−	1.11431i	0.577527	−	0.0607005i	0.388789	+	0.921327i	$0.372894\pi$
$338$	9.27693	−	4.13036i	0.504598	−	0.224662i
$339$		0			0
$340$	4.47195	−	2.58188i	0.242526	−	0.140022i
$341$	20.2954	−	14.6755i	1.09905	−	0.794721i
$342$		0			0
$343$	15.4939	−	5.03428i	0.836592	−	0.271825i
$344$	−34.7486	−	3.65223i	−1.87352	−	0.196915i
$345$		0			0
$346$	−6.65365	−	7.38963i	−0.357703	−	0.397269i
$347$	−1.65292	−	1.83575i	−0.0887333	−	0.0985483i	0.697143	−	0.716932i	$-0.254454\pi$
$347$	−1.65292	−	1.83575i	−0.0887333	−	0.0985483i	−0.785876	+	0.618384i	$0.787788\pi$
$348$		0			0
$349$	−12.7960	−	1.34492i	−0.684957	−	0.0719918i	−0.244343	−	0.969689i	$-0.578572\pi$
$349$	−12.7960	−	1.34492i	−0.684957	−	0.0719918i	−0.440613	+	0.897697i	$0.645239\pi$
$350$	−3.40058	+	1.10491i	−0.181768	+	0.0590602i
$351$		0			0
$352$	−5.93202	−	18.3983i	−0.316178	−	0.980631i
$353$	2.97223	−	1.71602i	0.158196	−	0.0913345i	−0.418812	−	0.908073i	$-0.637553\pi$
$353$	2.97223	−	1.71602i	0.158196	−	0.0913345i	0.577008	+	0.816738i	$0.304220\pi$
$354$		0			0
$355$	−12.6058	+	5.61247i	−0.669047	+	0.297879i
$356$	−11.9676	+	1.25784i	−0.634281	+	0.0666656i
$357$		0			0
$358$	−1.86209	−	8.76045i	−0.0984145	−	0.463004i
$359$	−4.07205	+	2.95852i	−0.214915	+	0.156145i	−0.690035	−	0.723776i	$-0.742405\pi$
$359$	−4.07205	+	2.95852i	−0.214915	+	0.156145i	0.475120	+	0.879921i	$0.342405\pi$
$360$		0			0
$361$	−9.98469	−	30.7297i	−0.525510	−	1.61735i
$362$	0.00763899	+	0.0132311i	0.000401496	+	0.000695412i
$363$		0			0
$364$	−0.529934	+	0.917872i	−0.0277761	+	0.0481096i
$365$	−24.8098	−	5.27349i	−1.29861	−	0.276027i
$366$		0			0
$367$	−2.83110	−	1.26049i	−0.147782	−	0.0657969i	0.331513	−	0.943451i	$-0.392441\pi$
$367$	−2.83110	−	1.26049i	−0.147782	−	0.0657969i	−0.479295	+	0.877654i	$0.659108\pi$
$368$	−1.59048	−	0.516779i	−0.0829097	−	0.0269390i
$369$		0			0
$370$	5.45166	+	7.50356i	0.283418	+	0.390092i
$371$	0.499420	−	4.75166i	0.0259286	−	0.246694i
$372$		0			0
$373$	−7.33934	−	4.23737i	−0.380016	−	0.219403i	0.297809	−	0.954625i	$-0.403744\pi$
$373$	−7.33934	−	4.23737i	−0.380016	−	0.219403i	−0.677825	+	0.735223i	$0.737077\pi$
$374$	3.42944	+	0.737057i	0.177332	+	0.0381123i
$375$		0			0
$376$	−23.1605	−	20.8538i	−1.19441	−	1.07545i
$377$	−0.449777	+	0.619065i	−0.0231647	+	0.0318835i
$378$		0			0
$379$	6.66353	−	20.5082i	0.342283	−	1.05344i	−0.620740	−	0.784016i	$-0.713168\pi$
$379$	6.66353	−	20.5082i	0.342283	−	1.05344i	0.963023	−	0.269421i	$-0.0868322\pi$
$380$	27.4483	−	5.83433i	1.40807	−	0.299295i
$381$		0			0
$382$	0.853505	+	1.91700i	0.0436691	+	0.0980824i
$383$	−6.68252	+	31.4388i	−0.341461	+	1.60645i	0.387486	+	0.921876i	$0.373344\pi$
$383$	−6.68252	+	31.4388i	−0.341461	+	1.60645i	−0.728947	+	0.684570i	$0.759990\pi$
$384$		0			0
$385$	11.6524	+	5.21959i	0.593863	+	0.266015i
$386$		−	10.3064i		−	0.524580i
$387$		0			0
$388$	−0.899932	−	0.653839i	−0.0456871	−	0.0331937i
$389$	−0.00565467	+	0.0127006i	−0.000286703	+	0.000643945i	−0.913689	−	0.406415i	$-0.866779\pi$
$389$	−0.00565467	+	0.0127006i	−0.000286703	+	0.000643945i	0.913402	+	0.407059i	$0.133446\pi$
$390$		0			0
$391$	2.96915	−	2.67344i	0.150157	−	0.135202i
$392$	1.47041	+	13.9901i	0.0742672	+	0.706605i
$393$		0			0
$394$	3.69460	−	4.10327i	0.186131	−	0.206720i
$395$	39.8586			2.00550
$396$		0			0
$397$	−13.9971			−0.702496			−0.351248	−	0.936283i	$-0.614243\pi$
$397$	−13.9971			−0.702496			−0.351248	+	0.936283i	$0.614243\pi$
$398$	0.0362764	−	0.0402890i	0.00181837	−	0.00201951i
$399$		0			0
$400$	0.192834	+	1.83469i	0.00964170	+	0.0917347i
$401$	26.4247	−	23.7930i	1.31959	−	1.18816i	0.351894	−	0.936040i	$-0.385538\pi$
$401$	26.4247	−	23.7930i	1.31959	−	1.18816i	0.967695	−	0.252123i	$-0.0811289\pi$
$402$		0			0
$403$	1.80102	−	4.04517i	0.0897154	−	0.201504i
$404$	18.8134	+	13.6687i	0.936000	+	0.680044i
$405$		0			0
$406$		−	1.39548i		−	0.0692567i
$407$	1.41720	−	13.1967i	0.0702478	−	0.654136i
$408$		0			0
$409$	−2.92170	+	13.7455i	−0.144469	+	0.679671i	0.844981	+	0.534796i	$0.179611\pi$
$409$	−2.92170	+	13.7455i	−0.144469	+	0.679671i	−0.989450	+	0.144875i	$0.953722\pi$
$410$	−2.12254	−	4.76731i	−0.104825	−	0.235441i
$411$		0			0
$412$	12.9429	−	2.75109i	0.637649	−	0.135536i
$413$	−2.46762	+	7.59455i	−0.121424	+	0.373703i
$414$		0			0
$415$	18.2753	−	25.1538i	0.897099	−	1.23475i
$416$	−2.53983	−	2.28688i	−0.124526	−	0.112123i
$417$		0			0
$418$	16.4868	+	9.56842i	0.806396	+	0.468007i
$419$	2.56407	+	1.48037i	0.125263	+	0.0723206i	0.561322	−	0.827597i	$-0.310293\pi$
$419$	2.56407	+	1.48037i	0.125263	+	0.0723206i	−0.436059	+	0.899918i	$0.643626\pi$
$420$		0			0
$421$	−2.20232	+	20.9537i	−0.107335	+	1.02122i	0.799767	+	0.600310i	$0.204956\pi$
$421$	−2.20232	+	20.9537i	−0.107335	+	1.02122i	−0.907102	+	0.420911i	$0.861710\pi$
$422$	−0.574241	−	0.790375i	−0.0279536	−	0.0384749i
$423$		0			0
$424$	9.18141	+	2.98322i	0.445889	+	0.144878i
$425$	−4.02639	−	1.79266i	−0.195309	−	0.0869570i
$426$		0			0
$427$	−10.3090	−	2.19125i	−0.498887	−	0.106042i
$428$	1.99583	−	3.45688i	0.0964720	−	0.167094i
$429$		0			0
$430$	15.0357	+	26.0425i	0.725084	+	1.25588i
$431$	11.7908	+	36.2884i	0.567944	+	1.74795i	0.659039	+	0.752109i	$0.270963\pi$
$431$	11.7908	+	36.2884i	0.567944	+	1.74795i	−0.0910950	+	0.995842i	$0.529037\pi$
$432$		0			0
$433$	17.1848	−	12.4855i	0.825848	−	0.600014i	−0.0925338	−	0.995710i	$-0.529497\pi$
$433$	17.1848	−	12.4855i	0.825848	−	0.600014i	0.918382	+	0.395696i	$0.129497\pi$
$434$	1.67893	+	7.89872i	0.0805910	+	0.379151i
$435$		0			0
$436$	1.94159	−	0.204070i	0.0929855	−	0.00977317i
$437$	19.8351	−	8.83116i	0.948842	−	0.422452i
$438$		0			0
$439$	23.8477	−	13.7685i	1.13819	−	0.657134i	0.192208	−	0.981354i	$-0.438435\pi$
$439$	23.8477	−	13.7685i	1.13819	−	0.657134i	0.945982	+	0.324220i	$0.105102\pi$
$440$	−15.2112	+	20.8372i	−0.725165	+	0.993374i
$441$		0			0
$442$	0.589813	−	0.191642i	0.0280545	−	0.00911547i
$443$	26.6084	+	2.79665i	1.26420	+	0.132873i	0.712801	−	0.701367i	$-0.247426\pi$
$443$	26.6084	+	2.79665i	1.26420	+	0.132873i	0.551402	+	0.834240i	$0.314093\pi$
$444$		0			0
$445$	17.1496	+	19.0466i	0.812971	+	0.902895i
$446$	−7.00725	−	7.78234i	−0.331803	−	0.368505i
$447$		0			0
$448$	4.73601	+	0.497775i	0.223755	+	0.0235176i
$449$	28.1364	−	9.14206i	1.32784	−	0.431441i	0.442658	−	0.896690i	$-0.354036\pi$
$449$	28.1364	−	9.14206i	1.32784	−	0.431441i	0.885179	+	0.465250i	$0.154036\pi$
$450$		0			0
$451$	−2.32371	+	7.09700i	−0.109419	+	0.334185i
$452$	2.22164	−	1.28266i	0.104497	−	0.0603314i
$453$		0			0
$454$	−0.579840	+	0.258161i	−0.0272132	+	0.0121161i
$455$	2.24501	−	0.235960i	0.105248	−	0.0110620i
$456$		0			0
$457$	0.0682681	+	0.321176i	0.00319345	+	0.0150240i	0.979715	−	0.200394i	$-0.0642221\pi$
$457$	0.0682681	+	0.321176i	0.00319345	+	0.0150240i	−0.976522	+	0.215418i	$0.930889\pi$
$458$	6.34026	−	4.60647i	0.296261	−	0.215246i
$459$		0			0
$460$	3.66933	+	11.2930i	0.171083	+	0.526541i
$461$	−1.59304	−	2.75923i	−0.0741955	−	0.128510i	0.826541	−	0.562877i	$-0.190306\pi$
$461$	−1.59304	−	2.75923i	−0.0741955	−	0.128510i	−0.900736	+	0.434367i	$0.856972\pi$
$462$		0			0
$463$	−13.6457	+	23.6350i	−0.634169	+	1.09841i	0.352521	+	0.935804i	$0.385324\pi$
$463$	−13.6457	+	23.6350i	−0.634169	+	1.09841i	−0.986691	+	0.162609i	$0.948009\pi$
$464$	−0.704259	−	0.149695i	−0.0326944	−	0.00694941i
$465$		0			0
$466$	−12.1472	−	5.40829i	−0.562709	−	0.250534i
$467$	−17.3622	−	5.64132i	−0.803427	−	0.261049i	−0.121615	−	0.992577i	$-0.538807\pi$
$467$	−17.3622	−	5.64132i	−0.803427	−	0.261049i	−0.681811	+	0.731528i	$0.738807\pi$
$468$		0			0
$469$	6.81794	+	9.38409i	0.314823	+	0.433317i
$470$	−2.80375	+	26.6759i	−0.129327	+	1.23047i
$471$		0			0
$472$	−13.9733	−	8.06747i	−0.643172	−	0.371336i
$473$	9.04212	−	42.0720i	0.415757	−	1.93447i
$474$		0			0
$475$	−17.7993	−	16.0266i	−0.816690	−	0.735351i
$476$	1.40041	−	1.92750i	0.0641878	−	0.0883469i
$477$		0			0
$478$	0.301618	−	0.928285i	0.0137957	−	0.0424588i
$479$	−12.3864	+	2.63282i	−0.565951	+	0.120297i	−0.481997	−	0.876173i	$-0.660088\pi$
$479$	−12.3864	+	2.63282i	−0.565951	+	0.120297i	−0.0839544	+	0.996470i	$0.526755\pi$
$480$		0			0
$481$	−0.954437	−	2.14370i	−0.0435186	−	0.0977444i
$482$	−0.126571	+	0.595470i	−0.00576515	+	0.0271229i
$483$		0			0
$484$	14.6062	−	3.03569i	0.663918	−	0.137986i
$485$			2.36921i			0.107580i
$486$		0			0
$487$	12.3473	+	8.97085i	0.559510	+	0.406508i	0.831280	−	0.555854i	$-0.187609\pi$
$487$	12.3473	+	8.97085i	0.559510	+	0.406508i	−0.271769	+	0.962362i	$0.587609\pi$
$488$	8.66158	−	19.4542i	0.392091	−	0.880652i
$489$		0			0
$490$	8.99722	−	8.10113i	0.406453	−	0.365972i
$491$	−2.96920	−	28.2501i	−0.133998	−	1.27491i	−0.830364	−	0.557222i	$-0.811867\pi$
$491$	−2.96920	−	28.2501i	−0.133998	−	1.27491i	0.696365	−	0.717687i	$-0.254799\pi$
$492$		0			0
$493$	1.15100	−	1.27831i	0.0518384	−	0.0575724i
$494$	3.37018			0.151632
$495$		0			0
$496$	4.16635			0.187074
$497$	−4.26013	+	4.73135i	−0.191093	+	0.212230i
$498$		0			0
$499$	2.28531	+	21.7433i	0.102305	+	0.973363i	0.918456	+	0.395524i	$0.129437\pi$
$499$	2.28531	+	21.7433i	0.102305	+	0.973363i	−0.816151	+	0.577839i	$0.803896\pi$
$500$	−4.82196	+	4.34171i	−0.215644	+	0.194167i
$501$		0			0
$502$	−3.20642	+	7.20174i	−0.143110	+	0.321429i
$503$	−16.0796	−	11.6825i	−0.716954	−	0.520898i	0.168455	−	0.985709i	$-0.446122\pi$
$503$	−16.0796	−	11.6825i	−0.716954	−	0.520898i	−0.885410	+	0.464812i	$0.846122\pi$
$504$		0			0
$505$		−	49.5291i		−	2.20402i
$506$	−3.29745	+	7.36137i	−0.146590	+	0.327253i
$507$		0			0
$508$	1.33148	−	6.26412i	0.0590748	−	0.277925i
$509$	12.5317	+	28.1466i	0.555457	+	1.24758i	0.945151	+	0.326633i	$0.105914\pi$
$509$	12.5317	+	28.1466i	0.555457	+	1.24758i	−0.389694	+	0.920945i	$0.627419\pi$
$510$		0			0
$511$	−11.4471	+	2.43315i	−0.506388	+	0.107636i
$512$	1.91196	−	5.88441i	0.0844976	−	0.260057i
$513$		0			0
$514$	−10.5099	+	14.4656i	−0.463570	+	0.638049i
$515$	−20.9436	−	18.8577i	−0.922884	−	0.830969i
$516$		0			0
$517$	28.5828	−	25.6193i	1.25707	−	1.12674i
$518$	3.70605	+	2.13969i	0.162834	+	0.0940125i
$519$		0			0
$520$	−0.476771	+	4.53617i	−0.0209078	+	0.198924i
$521$	16.6718	+	22.9468i	0.730405	+	1.00532i	0.999114	+	0.0420947i	$0.0134031\pi$
$521$	16.6718	+	22.9468i	0.730405	+	1.00532i	−0.268709	+	0.963221i	$0.586597\pi$
$522$		0			0
$523$	−12.9420	−	4.20510i	−0.565913	−	0.183876i	0.0120671	−	0.999927i	$-0.496159\pi$
$523$	−12.9420	−	4.20510i	−0.565913	−	0.183876i	−0.577980	+	0.816051i	$0.696159\pi$
$524$	−9.76905	−	4.34946i	−0.426763	−	0.190007i
$525$		0			0
$526$	−12.0628	−	2.56402i	−0.525962	−	0.111797i
$527$	−4.97693	+	8.62030i	−0.216799	+	0.375506i
$528$		0			0
$529$	−6.90625	−	11.9620i	−0.300272	−	0.520086i
$530$	−2.56753	−	7.90204i	−0.111526	−	0.343242i
$531$		0			0
$532$	10.4747	−	7.61029i	0.454134	−	0.329948i
$533$	0.274503	+	1.29143i	0.0118900	+	0.0559382i
$534$		0			0
$535$	−8.45511	+	0.888668i	−0.365546	+	0.0384205i
$536$	−21.4110	+	9.53278i	−0.924813	+	0.411753i
$537$		0			0
$538$	−0.662255	+	0.382353i	−0.0285518	+	0.0164844i
$539$	−17.3252	−	0.0391632i	−0.746251	−	0.00168688i
$540$		0			0
$541$	−17.0525	+	5.54068i	−0.733142	+	0.238212i	−0.651712	−	0.758467i	$-0.725949\pi$
$541$	−17.0525	+	5.54068i	−0.733142	+	0.238212i	−0.0814304	+	0.996679i	$0.525949\pi$
$542$	17.8447	+	1.87555i	0.766494	+	0.0805617i
$543$		0			0
$544$	5.14077	+	5.70941i	0.220409	+	0.244789i
$545$	−2.78232	−	3.09008i	−0.119181	−	0.132364i
$546$		0			0
$547$	−20.8643	−	2.19293i	−0.892095	−	0.0937630i	−0.352622	−	0.935766i	$-0.614710\pi$
$547$	−20.8643	−	2.19293i	−0.892095	−	0.0937630i	−0.539473	+	0.842003i	$0.681376\pi$
$548$	−8.68837	+	2.82302i	−0.371149	+	0.120594i
$549$		0			0
$550$	8.89799	+	0.0201137i	0.379412	+	0.000857649i
$551$	8.09543	−	4.67390i	0.344877	−	0.199115i
$552$		0			0
$553$	16.8005	−	7.48007i	0.714430	−	0.318085i
$554$	8.27278	−	0.869505i	0.351477	−	0.0369417i
$555$		0			0
$556$	−2.09097	−	9.83726i	−0.0886770	−	0.417193i
$557$	−6.91677	+	5.02533i	−0.293073	+	0.212930i	−0.724599	−	0.689170i	$-0.757975\pi$
$557$	−6.91677	+	5.02533i	−0.293073	+	0.212930i	0.431526	+	0.902100i	$0.357975\pi$
$558$		0			0
$559$	−2.35104	−	7.23574i	−0.0994382	−	0.306039i
$560$	1.06200	+	1.83943i	0.0448775	+	0.0777301i
$561$		0			0
$562$	3.81202	−	6.60262i	0.160800	−	0.278515i
$563$	−32.7814	−	6.96790i	−1.38157	−	0.293662i	−0.543585	−	0.839354i	$-0.682933\pi$
$563$	−32.7814	−	6.96790i	−1.38157	−	0.293662i	−0.837986	+	0.545692i	$0.816267\pi$
$564$		0			0
$565$	−4.99143	−	2.22233i	−0.209991	−	0.0934939i
$566$	−9.47118	−	3.07737i	−0.398103	−	0.129352i
$567$		0			0
$568$	−7.56140	−	10.4074i	−0.317269	−	0.436683i
$569$	−4.15034	+	39.4878i	−0.173991	+	1.65542i	0.464343	+	0.885656i	$0.346291\pi$
$569$	−4.15034	+	39.4878i	−0.173991	+	1.65542i	−0.638334	+	0.769760i	$0.720376\pi$
$570$		0			0
$571$	−11.7014	−	6.75580i	−0.489688	−	0.282721i	0.234757	−	0.972054i	$-0.424570\pi$
$571$	−11.7014	−	6.75580i	−0.489688	−	0.282721i	−0.724445	+	0.689333i	$0.757904\pi$
$572$	1.96406	−	1.76042i	0.0821213	−	0.0736069i
$573$		0			0
$574$	−1.78932	−	1.61111i	−0.0746847	−	0.0672464i
$575$	5.95720	−	8.19938i	0.248432	−	0.341938i
$576$		0			0
$577$	−10.9864	+	33.8127i	−0.457370	+	1.40764i	0.410960	+	0.911654i	$0.365194\pi$
$577$	−10.9864	+	33.8127i	−0.457370	+	1.40764i	−0.868330	+	0.495987i	$0.834806\pi$
$578$	11.9785	−	2.54611i	0.498240	−	0.105904i
$579$		0			0
$580$	2.07933	+	4.67024i	0.0863393	+	0.193921i
$581$	2.98260	−	14.0320i	0.123739	−	0.582147i
$582$		0			0
$583$	−4.86060	+	10.8510i	−0.201305	+	0.449403i
$584$		−	23.6462i		−	0.978487i
$585$		0			0
$586$	16.9001	+	12.2786i	0.698137	+	0.507226i
$587$	10.3483	−	23.2428i	0.427122	−	0.959331i	−0.563926	−	0.825825i	$-0.690710\pi$
$587$	10.3483	−	23.2428i	0.427122	−	0.959331i	0.991048	−	0.133506i	$-0.0426235\pi$
$588$		0			0
$589$	−40.1985	+	36.1949i	−1.65635	+	1.49139i
$590$	1.45155	+	13.8106i	0.0597593	+	0.568572i
$591$		0			0
$592$	1.47739	−	1.64080i	0.0607202	−	0.0674366i
$593$	−26.4048			−1.08431			−0.542157	−	0.840277i	$-0.682392\pi$
$593$	−26.4048			−1.08431			−0.542157	+	0.840277i	$0.682392\pi$
$594$		0			0
$595$	−5.07445			−0.208032
$596$	5.59270	−	6.21132i	0.229086	−	0.254426i
$597$		0			0
$598$	0.149067	+	1.41827i	0.00609578	+	0.0579975i
$599$	−8.53053	+	7.68093i	−0.348548	+	0.313834i	−0.824745	−	0.565504i	$-0.808682\pi$
$599$	−8.53053	+	7.68093i	−0.348548	+	0.313834i	0.476197	+	0.879339i	$0.342015\pi$
$600$		0			0
$601$	−12.2205	+	27.4476i	−0.498483	+	1.11961i	0.472689	+	0.881229i	$0.343283\pi$
$601$	−12.2205	+	27.4476i	−0.498483	+	1.11961i	−0.971172	+	0.238381i	$0.923383\pi$
$602$	11.2249	+	8.15534i	0.457491	+	0.332387i
$603$		0			0
$604$			26.7406i			1.08806i
$605$	−23.5163	−	21.3675i	−0.956074	−	0.868711i
$606$		0			0
$607$	8.03806	−	37.8161i	0.326255	−	1.53491i	−0.443327	−	0.896360i	$-0.646202\pi$
$607$	8.03806	−	37.8161i	0.326255	−	1.53491i	0.769582	−	0.638549i	$-0.220465\pi$
$608$	16.9815	+	38.1411i	0.688690	+	1.54682i
$609$		0			0
$610$	−17.9274	+	3.81059i	−0.725860	+	0.154286i
$611$	2.09706	−	6.45408i	0.0848379	−	0.261104i
$612$		0			0
$613$	17.6204	−	24.2524i	0.711681	−	0.979545i	−0.288078	−	0.957607i	$-0.593016\pi$
$613$	17.6204	−	24.2524i	0.711681	−	0.979545i	0.999759	−	0.0219380i	$-0.00698363\pi$
$614$	10.7493	+	9.67869i	0.433805	+	0.390600i
$615$		0			0
$616$	−2.50115	+	11.6375i	−0.100774	+	0.468890i
$617$	3.50285	+	2.02237i	0.141019	+	0.0814176i	0.568850	−	0.822441i	$-0.307389\pi$
$617$	3.50285	+	2.02237i	0.141019	+	0.0814176i	−0.427830	+	0.903859i	$0.640722\pi$
$618$		0			0
$619$	2.74139	−	26.0826i	0.110186	−	1.04835i	−0.790079	−	0.613005i	$-0.789961\pi$
$619$	2.74139	−	26.0826i	0.110186	−	1.04835i	0.900265	−	0.435343i	$-0.143373\pi$
$620$	−17.3882	−	23.9329i	−0.698328	−	0.961167i
$621$		0			0
$622$	−9.59538	−	3.11773i	−0.384740	−	0.125009i
$623$	10.8030	+	4.80981i	0.432813	+	0.192701i
$624$		0			0
$625$	29.8709	+	6.34925i	1.19483	+	0.253970i
$626$	−4.69208	+	8.12692i	−0.187533	+	0.324817i
$627$		0			0
$628$	3.30560	+	5.72546i	0.131908	+	0.228471i
$629$	1.63005	+	5.01679i	0.0649945	+	0.200033i
$630$		0			0
$631$	12.4984	−	9.08065i	0.497555	−	0.361495i	−0.310527	−	0.950564i	$-0.600506\pi$
$631$	12.4984	−	9.08065i	0.497555	−	0.361495i	0.808082	+	0.589070i	$0.200506\pi$
$632$	7.72579	+	36.3470i	0.307315	+	1.44581i
$633$		0			0
$634$	−13.1271	+	1.37971i	−0.521344	+	0.0547955i
$635$	−12.4606	+	5.54780i	−0.494482	+	0.220158i
$636$		0			0
$637$	−2.65271	+	1.53154i	−0.105104	+	0.0606819i
$638$	−1.08060	+	3.30034i	−0.0427813	+	0.130662i
$639$		0			0
$640$	−24.1477	+	7.84607i	−0.954522	+	0.310143i
$641$	−12.4339	−	1.30685i	−0.491108	−	0.0516176i	−0.144262	−	0.989540i	$-0.546081\pi$
$641$	−12.4339	−	1.30685i	−0.491108	−	0.0516176i	−0.346846	+	0.937922i	$0.612747\pi$
$642$		0			0
$643$	−3.46334	−	3.84642i	−0.136581	−	0.151688i	0.670974	−	0.741481i	$-0.265876\pi$
$643$	−3.46334	−	3.84642i	−0.136581	−	0.151688i	−0.807555	+	0.589793i	$0.799209\pi$
$644$	3.66595	+	4.07144i	0.144458	+	0.160437i
$645$		0			0
$646$	−7.53447	−	0.791905i	−0.296440	−	0.0311571i
$647$	−5.07677	+	1.64954i	−0.199588	+	0.0648502i	−0.407105	−	0.913381i	$-0.633462\pi$
$647$	−5.07677	+	1.64954i	−0.199588	+	0.0648502i	0.207517	+	0.978231i	$0.433462\pi$
$648$		0			0
$649$	11.7168	−	16.0504i	0.459925	−	0.630033i
$650$	1.36239	−	0.786578i	0.0534375	−	0.0308521i
$651$		0			0
$652$	−13.7523	+	6.12293i	−0.538583	+	0.239793i
$653$	4.72225	−	0.496328i	0.184796	−	0.0194228i	−0.0116784	−	0.999932i	$-0.503717\pi$
$653$	4.72225	−	0.496328i	0.184796	−	0.0194228i	0.196474	+	0.980509i	$0.437051\pi$
$654$		0			0
$655$	4.73536	+	22.2781i	0.185026	+	0.870478i
$656$	−1.00502	+	0.730189i	−0.0392394	+	0.0285091i
$657$		0			0
$658$	3.82435	+	11.7701i	0.149089	+	0.458847i
$659$	−19.9356	−	34.5295i	−0.776581	−	1.34508i	−0.933902	−	0.357529i	$-0.883619\pi$
$659$	−19.9356	−	34.5295i	−0.776581	−	1.34508i	0.157321	−	0.987547i	$-0.449714\pi$
$660$		0			0
$661$	−10.4257	+	18.0579i	−0.405515	+	0.702372i	−0.994381	−	0.105858i	$-0.966241\pi$
$661$	−10.4257	+	18.0579i	−0.405515	+	0.702372i	0.588867	+	0.808230i	$0.299574\pi$
$662$	−15.4028	−	3.27397i	−0.598647	−	0.127246i
$663$		0			0
$664$	26.4800	+	11.7897i	1.02762	+	0.457528i
$665$	−26.2265	−	8.52151i	−1.01702	−	0.330450i
$666$		0			0
$667$	2.32499	+	3.20007i	0.0900239	+	0.123907i
$668$	−3.01095	+	28.6473i	−0.116497	+	1.10840i
$669$		0			0
$670$	17.4689	+	10.0857i	0.674884	+	0.389645i
$671$	22.6841	+	13.1651i	0.875710	+	0.508234i
$672$		0			0
$673$	−15.2185	−	13.7028i	−0.586629	−	0.528203i	0.321491	−	0.946913i	$-0.395816\pi$
$673$	−15.2185	−	13.7028i	−0.586629	−	0.528203i	−0.908120	+	0.418709i	$0.862483\pi$
$674$	5.02763	−	6.91994i	0.193657	−	0.266546i
$675$		0			0
$676$	−5.30410	+	16.3243i	−0.204004	+	0.627859i
$677$	6.69542	−	1.42315i	0.257326	−	0.0546963i	−0.0774423	−	0.996997i	$-0.524675\pi$
$677$	6.69542	−	1.42315i	0.257326	−	0.0546963i	0.334768	+	0.942301i	$0.391342\pi$
$678$		0			0
$679$	0.444619	+	0.998630i	0.0170629	+	0.0383239i
$680$	2.13177	−	10.0292i	0.0817495	−	0.384601i
$681$		0			0
$682$	2.14573	−	19.9806i	0.0821641	−	0.765098i
$683$		−	4.76117i		−	0.182181i	−0.995843	−	0.0910905i	$-0.970965\pi$
$683$		−	4.76117i		−	0.182181i	0.995843	−	0.0910905i	$-0.0290353\pi$
$684$		0			0
$685$	15.7413	+	11.4368i	0.601446	+	0.436976i
$686$	5.31667	−	11.9414i	0.202992	−	0.455926i
$687$		0			0
$688$	5.31985	−	4.79002i	0.202817	−	0.182618i
$689$	0.219731	+	2.09060i	0.00837109	+	0.0796456i
$690$		0			0
$691$	33.1686	−	36.8375i	1.26179	−	1.40136i	0.383290	−	0.923628i	$-0.374791\pi$
$691$	33.1686	−	36.8375i	1.26179	−	1.40136i	0.878504	−	0.477735i	$-0.158542\pi$
$692$	16.8075			0.638927
$693$		0			0
$694$	−1.98204			−0.0752372
$695$	−14.3328	+	15.9182i	−0.543676	+	0.603813i
$696$		0			0
$697$	−0.310233	−	2.95167i	−0.0117509	−	0.111802i
$698$	−7.67197	+	6.90787i	−0.290388	+	0.261467i
$699$		0			0
$700$	2.45819	−	5.52117i	0.0929107	−	0.208681i
$701$	−18.5663	−	13.4892i	−0.701240	−	0.509480i	0.179096	−	0.983832i	$-0.442683\pi$
$701$	−18.5663	−	13.4892i	−0.701240	−	0.509480i	−0.880336	+	0.474351i	$0.842683\pi$
$702$		0			0
$703$			28.6659i			1.08115i
$704$	−10.8153	−	4.84459i	−0.407615	−	0.182587i
$705$		0			0
$706$	0.572536	−	2.69357i	0.0215477	−	0.101374i
$707$	−9.29489	−	20.8767i	−0.349570	−	0.785148i
$708$		0			0
$709$	−26.9762	+	5.73396i	−1.01311	+	0.215343i	−0.684415	−	0.729092i	$-0.739942\pi$
$709$	−26.9762	+	5.73396i	−1.01311	+	0.215343i	−0.328696	+	0.944436i	$0.606609\pi$
$710$	−3.42133	+	10.5298i	−0.128400	+	0.395176i
$711$		0			0
$712$	−14.0445	+	19.3305i	−0.526338	+	0.724443i
$713$	−17.0100	−	15.3158i	−0.637028	−	0.573582i
$714$		0			0
$715$	−5.49218	−	1.18038i	−0.205396	−	0.0441438i
$716$	13.1101	+	7.56915i	0.489949	+	0.282872i
$717$		0			0
$718$	−0.422145	+	4.01644i	−0.0157543	+	0.149892i
$719$	21.5090	+	29.6046i	0.802151	+	1.10407i	0.992487	+	0.122347i	$0.0390421\pi$
$719$	21.5090	+	29.6046i	0.802151	+	1.10407i	−0.190337	+	0.981719i	$0.560958\pi$
$720$		0			0
$721$	−12.3667	−	4.01819i	−0.460561	−	0.149645i
$722$	−23.6840	−	10.5448i	−0.881426	−	0.392436i
$723$		0			0
$724$	−0.0252595	−	0.00536908i	−0.000938763	−	0.000199540i
$725$	2.18172	−	3.77884i	0.0810269	−	0.140343i
$726$		0			0
$727$	20.4497	+	35.4200i	0.758438	+	1.31365i	0.943647	+	0.330955i	$0.107371\pi$
$727$	20.4497	+	35.4200i	0.758438	+	1.31365i	−0.185208	+	0.982699i	$0.559296\pi$
$728$	0.650321	+	2.00148i	0.0241025	+	0.0741799i
$729$		0			0
$730$	−16.4645	+	11.9622i	−0.609379	+	0.442740i
$731$	3.55583	+	16.7289i	0.131517	+	0.618740i
$732$		0			0
$733$	−9.27530	+	0.974873i	−0.342591	+	0.0360078i	−0.274262	−	0.961655i	$-0.588433\pi$
$733$	−9.27530	+	0.974873i	−0.342591	+	0.0360078i	−0.0683291	+	0.997663i	$0.521767\pi$
$734$	−2.27158	+	1.01137i	−0.0838454	+	0.0373304i
$735$		0			0
$736$	−15.2998	+	8.83335i	−0.563958	+	0.325601i
$737$	−8.85790	−	27.4730i	−0.326285	−	1.01198i
$738$		0			0
$739$	−25.6359	+	8.32960i	−0.943031	+	0.306409i	−0.739881	−	0.672738i	$-0.765118\pi$
$739$	−25.6359	+	8.32960i	−0.943031	+	0.306409i	−0.203150	+	0.979148i	$0.565118\pi$
$740$	−15.5912	−	1.63870i	−0.573144	−	0.0602398i
$741$		0			0
$742$	−2.56516	−	2.84890i	−0.0941699	−	0.104586i
$743$	−14.2469	−	15.8228i	−0.522667	−	0.580481i	0.422790	−	0.906228i	$-0.361051\pi$
$743$	−14.2469	−	15.8228i	−0.522667	−	0.580481i	−0.945457	+	0.325747i	$0.894384\pi$
$744$		0			0
$745$	−17.7042	−	1.86079i	−0.648632	−	0.0681740i
$746$	−6.46702	+	2.10126i	−0.236775	+	0.0769327i
$747$		0			0
$748$	−4.80456	+	3.47415i	−0.175672	+	0.127027i
$749$	−3.39708	+	1.96131i	−0.124127	+	0.0716646i
$750$		0			0
$751$	21.5176	−	9.58027i	0.785190	−	0.349589i	0.0253327	−	0.999679i	$-0.491935\pi$
$751$	21.5176	−	9.58027i	0.785190	−	0.349589i	0.759857	+	0.650090i	$0.225269\pi$
$752$	6.35027	−	0.667440i	0.231570	−	0.0243390i
$753$		0			0
$754$	0.127653	+	0.600558i	0.00464883	+	0.0218710i
$755$	46.0766	−	33.4766i	1.67690	−	1.21834i
$756$		0			0
$757$	−10.5548	−	32.4845i	−0.383622	−	1.18067i	−0.937475	−	0.348053i	$-0.886843\pi$
$757$	−10.5548	−	32.4845i	−0.383622	−	1.18067i	0.553853	−	0.832615i	$-0.313157\pi$
$758$	−8.65095	−	14.9839i	−0.314217	−	0.544239i
$759$		0			0
$760$	27.8597	−	48.2544i	1.01058	−	1.75037i
$761$	35.6019	+	7.56741i	1.29057	+	0.274318i	0.801535	−	0.597948i	$-0.204017\pi$
$761$	35.6019	+	7.56741i	1.29057	+	0.274318i	0.489031	+	0.872266i	$0.337350\pi$
$762$		0			0
$763$	−1.75266	−	0.780333i	−0.0634504	−	0.0282499i
$764$	−3.37329	−	1.09605i	−0.122041	−	0.0396537i
$765$		0			0
$766$	15.1583	+	20.8637i	0.547693	+	0.753835i
$767$	0.367245	−	3.49410i	0.0132605	−	0.126165i
$768$		0			0
$769$	13.6195	+	7.86320i	0.491130	+	0.283554i	0.725043	−	0.688703i	$-0.241820\pi$
$769$	13.6195	+	7.86320i	0.491130	+	0.283554i	−0.233913	+	0.972258i	$0.575153\pi$
$770$	9.36834	−	4.14570i	0.337611	−	0.149401i
$771$		0			0
$772$	12.9460	+	11.6566i	0.465935	+	0.419530i
$773$	−5.16073	+	7.10313i	−0.185619	+	0.255482i	−0.891678	−	0.452671i	$-0.850471\pi$
$773$	−5.16073	+	7.10313i	−0.185619	+	0.255482i	0.706059	+	0.708153i	$0.250471\pi$
$774$		0			0
$775$	−7.80258	+	24.0139i	−0.280277	+	0.862604i
$776$	−2.16048	+	0.459225i	−0.0775568	+	0.0164852i
$777$		0			0
$778$	0.00453711	+	0.0101905i	0.000162663	+	0.000365347i
$779$	3.35334	−	15.7762i	0.120146	−	0.565241i
$780$		0			0
$781$	13.7390	−	7.89085i	0.491619	−	0.282357i
$782$		−	3.20576i		−	0.114638i
$783$		0			0
$784$	−2.33166	−	1.69405i	−0.0832737	−	0.0605019i
$785$	5.72724	−	12.8636i	0.204414	−	0.459121i
$786$		0			0
$787$	−6.03768	+	5.43635i	−0.215220	+	0.193785i	−0.769688	−	0.638420i	$-0.779588\pi$
$787$	−6.03768	+	5.43635i	−0.215220	+	0.193785i	0.554468	+	0.832205i	$0.312922\pi$
$788$	0.975543	+	9.28167i	0.0347523	+	0.330646i
$789$		0			0
$790$	21.3995	−	23.7666i	0.761362	−	0.845578i
$791$	−2.52095			−0.0896348
$792$		0			0
$793$	4.63701			0.164665
$794$	−7.51487	+	8.34611i	−0.266693	+	0.296192i
$795$		0			0
$796$	0.00957862	+	0.0911345i	0.000339505	+	0.00323018i
$797$	0.960021	−	0.864407i	0.0340057	−	0.0306189i	−0.651953	−	0.758260i	$-0.726050\pi$
$797$	0.960021	−	0.864407i	0.0340057	−	0.0306189i	0.685958	+	0.727641i	$0.259383\pi$
$798$		0			0
$799$	−6.20479	+	13.9362i	−0.219510	+	0.493027i
$800$	15.7666	+	11.4551i	0.557435	+	0.405000i
$801$		0			0
$802$		−	28.5305i		−	1.00745i
$803$	28.9565	+	3.10965i	1.02185	+	0.109737i
$804$		0			0
$805$	2.42608	−	11.4138i	0.0855082	−	0.402285i
$806$	−1.44508	−	3.24570i	−0.0509007	−	0.114325i
$807$		0			0
$808$	45.1655	−	9.60023i	1.58892	−	0.337735i
$809$	−12.8311	+	39.4900i	−0.451117	+	1.38840i	0.424517	+	0.905420i	$0.360444\pi$
$809$	−12.8311	+	39.4900i	−0.451117	+	1.38840i	−0.875634	+	0.482975i	$0.839556\pi$
$810$		0			0
$811$	8.32868	−	11.4634i	0.292459	−	0.402536i	−0.637352	−	0.770573i	$-0.719970\pi$
$811$	8.32868	−	11.4634i	0.292459	−	0.402536i	0.929811	+	0.368037i	$0.119970\pi$
$812$	1.75289	+	1.57831i	0.0615142	+	0.0553877i
$813$		0			0
$814$	−7.10797	−	7.93017i	−0.249134	−	0.277952i
$815$	27.7670	+	16.0313i	0.972635	+	0.561551i
$816$		0			0
$817$	−9.71499	+	92.4319i	−0.339884	+	3.23378i
$818$	6.62746	+	9.12191i	0.231724	+	0.318940i
$819$		0			0
$820$	8.38889	+	2.72572i	0.292953	+	0.0951862i
$821$	49.5964	+	22.0817i	1.73093	+	0.770658i	0.995679	+	0.0928594i	$0.0296007\pi$
$821$	49.5964	+	22.0817i	1.73093	+	0.770658i	0.735247	+	0.677799i	$0.237066\pi$
$822$		0			0
$823$	−25.4218	−	5.40357i	−0.886148	−	0.188357i	−0.257716	−	0.966221i	$-0.582970\pi$
$823$	−25.4218	−	5.40357i	−0.886148	−	0.188357i	−0.628432	+	0.777864i	$0.716303\pi$
$824$	13.1368	−	22.7536i	0.457642	−	0.792660i
$825$		0			0
$826$	3.20360	+	5.54879i	0.111467	+	0.193067i
$827$	−6.86114	−	21.1164i	−0.238585	−	0.734290i	−0.996626	−	0.0820821i	$-0.973843\pi$
$827$	−6.86114	−	21.1164i	−0.238585	−	0.734290i	0.758040	−	0.652208i	$-0.226157\pi$
$828$		0			0
$829$	6.23980	−	4.53348i	0.216717	−	0.157454i	−0.474131	−	0.880455i	$-0.657238\pi$
$829$	6.23980	−	4.53348i	0.216717	−	0.157454i	0.690848	+	0.723000i	$0.257238\pi$
$830$	−5.18677	−	24.4018i	−0.180035	−	0.846999i
$831$		0			0
$832$	−2.08371	+	0.219007i	−0.0722398	+	0.00759271i
$833$	6.29035	−	2.80065i	0.217948	−	0.0970366i
$834$		0			0
$835$	53.1314	−	30.6755i	1.83869	−	1.06157i
$836$	−30.6657	+	9.88732i	−1.06060	+	0.341960i
$837$		0			0
$838$	2.25932	−	0.734097i	0.0780468	−	0.0253589i
$839$	46.6084	+	4.89874i	1.60910	+	0.169123i	0.865996	−	0.500052i	$-0.166686\pi$
$839$	46.6084	+	4.89874i	1.60910	+	0.169123i	0.743105	+	0.669175i	$0.233352\pi$
$840$		0			0
$841$	−18.2653	−	20.2856i	−0.629837	−	0.699505i
$842$	11.3117	+	12.5630i	0.389829	+	0.432948i
$843$		0			0
$844$	1.64227	+	0.172610i	0.0565293	+	0.00594147i
$845$	34.7686	−	11.2970i	1.19608	−	0.388629i
$846$		0			0
$847$	−13.9221	−	4.59326i	−0.478370	−	0.157826i
$848$	−1.71292	+	0.988954i	−0.0588219	+	0.0339608i
$849$		0			0
$850$	−3.23063	+	1.43837i	−0.110810	+	0.0493357i
$851$	−12.0635	+	1.26792i	−0.413530	+	0.0434638i
$852$		0			0
$853$	−6.89791	−	32.4521i	−0.236180	−	1.11114i	−0.923146	−	0.384450i	$-0.874391\pi$
$853$	−6.89791	−	32.4521i	−0.236180	−	1.11114i	0.686966	−	0.726690i	$-0.258942\pi$
$854$	−6.84135	+	4.97053i	−0.234106	+	0.170088i
$855$		0			0
$856$	−2.44923	−	7.53796i	−0.0837130	−	0.257642i
$857$	1.62627	+	2.81679i	0.0555524	+	0.0962196i	0.892464	−	0.451118i	$-0.148975\pi$
$857$	1.62627	+	2.81679i	0.0555524	+	0.0962196i	−0.836912	+	0.547338i	$0.815641\pi$
$858$		0			0
$859$	−3.97946	+	6.89262i	−0.135777	+	0.235173i	−0.925894	−	0.377783i	$-0.876686\pi$
$859$	−3.97946	+	6.89262i	−0.135777	+	0.235173i	0.790117	+	0.612956i	$0.210020\pi$
$860$	−49.7178	−	10.5678i	−1.69536	−	0.360361i
$861$		0			0
$862$	27.9682	+	12.4522i	0.952599	+	0.424124i
$863$	38.4621	+	12.4971i	1.30926	+	0.425405i	0.878795	−	0.477200i	$-0.158348\pi$
$863$	38.4621	+	12.4971i	1.30926	+	0.425405i	0.430469	+	0.902605i	$0.358348\pi$
$864$		0			0
$865$	−21.0414	−	28.9610i	−0.715429	−	0.984704i
$866$	1.78153	−	16.9501i	0.0605388	−	0.575988i
$867$		0			0
$868$	−11.8206	−	6.82461i	−0.401216	−	0.231642i
$869$	−45.5256	+	4.68091i	−1.54435	+	0.158789i
$870$		0			0
$871$	−3.79257	−	3.41485i	−0.128506	−	0.115708i
$872$	2.27854	−	3.13614i	0.0771611	−	0.106203i
$873$		0			0
$874$	5.38343	−	16.5685i	0.182097	−	0.560437i
$875$	6.23701	−	1.32572i	0.210850	−	0.0448175i
$876$		0			0
$877$	−11.4141	−	25.6365i	−0.385427	−	0.865684i	−0.997209	−	0.0746577i	$-0.976214\pi$
$877$	−11.4141	−	25.6365i	−0.385427	−	0.865684i	0.611782	−	0.791027i	$-0.290453\pi$
$878$	4.59375	−	21.6119i	0.155032	−	0.729366i
$879$		0			0
$880$	−1.08726	−	5.17263i	−0.0366516	−	0.174369i
$881$			23.2639i			0.783780i	0.920012	+	0.391890i	$0.128179\pi$
$881$			23.2639i			0.783780i	−0.920012	+	0.391890i	$0.871821\pi$
$882$		0			0
$883$	−23.6812	−	17.2054i	−0.796937	−	0.579008i	0.113077	−	0.993586i	$-0.463929\pi$
$883$	−23.6812	−	17.2054i	−0.796937	−	0.579008i	−0.910014	+	0.414578i	$0.863929\pi$
$884$	−0.426360	+	0.957620i	−0.0143400	+	0.0322082i
$885$		0			0
$886$	15.9533	−	14.3644i	0.535960	−	0.482581i
$887$	0.509963	+	4.85197i	0.0171229	+	0.162913i	0.999742	−	0.0227207i	$-0.00723284\pi$
$887$	0.509963	+	4.85197i	0.0171229	+	0.162913i	−0.982619	+	0.185634i	$0.940566\pi$
$888$		0			0
$889$	−4.21104	+	4.67683i	−0.141234	+	0.156856i
$890$	20.5644			0.689320
$891$		0			0
$892$	17.7008			0.592665
$893$	−55.4715	+	61.6074i	−1.85628	+	2.06161i
$894$		0			0
$895$	−3.37026	−	32.0659i	−0.112655	−	1.07184i
$896$	−8.70590	+	7.83883i	−0.290844	+	0.261877i
$897$		0			0
$898$	9.65488	−	21.6852i	0.322188	−	0.723645i
$899$	−7.97246	−	5.79233i	−0.265896	−	0.193185i
$900$		0			0
$901$		−	4.72544i		−	0.157427i
$902$	2.98419	+	5.19585i	0.0993626	+	0.173003i
$903$		0			0
$904$	1.05905	−	4.98243i	0.0352234	−	0.165713i
$905$	0.0223710	+	0.0502462i	0.000743638	+	0.00167024i
$906$		0			0
$907$	10.0126	−	2.12823i	0.332461	−	0.0706669i	−0.0386566	−	0.999253i	$-0.512308\pi$
$907$	10.0126	−	2.12823i	0.332461	−	0.0706669i	0.371118	+	0.928586i	$0.378975\pi$
$908$	0.331524	−	1.02033i	0.0110020	−	0.0338607i
$909$		0			0
$910$	1.06462	−	1.46532i	0.0352918	−	0.0485749i
$911$	4.84142	+	4.35923i	0.160403	+	0.144428i	0.745424	−	0.666590i	$-0.232247\pi$
$911$	4.84142	+	4.35923i	0.160403	+	0.144428i	−0.585021	+	0.811018i	$0.698914\pi$
$912$		0			0
$913$	−17.9196	+	30.8763i	−0.593053	+	1.02186i
$914$	0.228161	+	0.131729i	0.00754689	+	0.00435720i
$915$		0			0
$916$	−1.38465	+	13.1740i	−0.0457501	+	0.435283i
$917$	6.17680	+	8.50163i	0.203976	+	0.280749i
$918$		0			0
$919$	22.0654	+	7.16949i	0.727871	+	0.236500i	0.649432	−	0.760419i	$-0.275007\pi$
$919$	22.0654	+	7.16949i	0.727871	+	0.236500i	0.0784385	+	0.996919i	$0.475007\pi$
$920$	21.5392	+	9.58985i	0.710125	+	0.316168i
$921$		0			0
$922$	−2.50054	−	0.531507i	−0.0823510	−	0.0175042i
$923$	1.40058	−	2.42587i	0.0461006	−	0.0798485i
$924$		0			0
$925$	6.69043	+	11.5882i	0.219980	+	0.381016i
$926$	6.76675	+	20.8259i	0.222369	+	0.684382i
$927$		0			0
$928$	−6.15344	+	4.47074i	−0.201997	+	0.146759i
$929$	1.54441	+	7.26589i	0.0506705	+	0.238386i	0.996194	−	0.0871692i	$-0.0277821\pi$
$929$	1.54441	+	7.26589i	0.0506705	+	0.238386i	−0.945523	+	0.325555i	$0.894449\pi$
$930$		0			0
$931$	37.2138	−	3.91133i	1.21963	−	0.128189i
$932$	20.5320	−	9.14145i	0.672549	−	0.299438i
$933$		0			0
$934$	−12.6853	+	7.32387i	−0.415076	+	0.239644i
$935$	12.0011	+	3.92942i	0.392479	+	0.128506i
$936$		0			0
$937$	−44.2612	+	14.3813i	−1.44595	+	0.469817i	−0.923747	−	0.383004i	$-0.874890\pi$
$937$	−44.2612	+	14.3813i	−1.44595	+	0.469817i	−0.522203	+	0.852821i	$0.674890\pi$
$938$	9.25595	+	0.972839i	0.302217	+	0.0317643i
$939$		0			0
$940$	−30.3368	−	33.6924i	−0.989478	−	1.09893i
$941$	−11.8484	−	13.1590i	−0.386247	−	0.428971i	0.518396	−	0.855141i	$-0.326529\pi$
$941$	−11.8484	−	13.1590i	−0.386247	−	0.428971i	−0.904643	+	0.426170i	$0.859863\pi$
$942$		0			0
$943$	6.78743	+	0.713388i	0.221029	+	0.0232311i
$944$	3.14396	−	1.02153i	0.102327	−	0.0332481i
$945$		0			0
$946$	−20.2318	−	27.9795i	−0.657792	−	0.909691i
$947$	−24.8531	+	14.3490i	−0.807618	+	0.466278i	−0.846128	−	0.532980i	$-0.821072\pi$
$947$	−24.8531	+	14.3490i	−0.807618	+	0.466278i	0.0385102	+	0.999258i	$0.487739\pi$
$948$		0			0
$949$	4.70377	−	2.09425i	0.152691	−	0.0679823i
$950$	−19.1125	+	2.00880i	−0.620091	+	0.0651742i
$951$		0			0
$952$	−0.983581	−	4.62739i	−0.0318781	−	0.149974i
$953$	−30.0074	+	21.8016i	−0.972033	+	0.706224i	−0.955914	−	0.293646i	$-0.905131\pi$
$953$	−30.0074	+	21.8016i	−0.972033	+	0.706224i	−0.0161193	+	0.999870i	$0.505131\pi$
$954$		0			0
$955$	2.33443	+	7.18465i	0.0755405	+	0.232490i
$956$	0.824898	+	1.42877i	0.0266791	+	0.0462096i
$957$		0			0
$958$	−5.08024	+	8.79924i	−0.164135	+	0.284290i
$959$	8.78130	+	1.86652i	0.283563	+	0.0602732i
$960$		0			0
$961$	23.7746	+	10.5851i	0.766923	+	0.341456i
$962$	−1.79066	−	0.581820i	−0.0577331	−	0.0187586i
$963$		0			0
$964$	−0.604824	−	0.832469i	−0.0194801	−	0.0268120i
$965$	3.87835	−	36.9000i	0.124848	−	1.18785i
$966$		0			0
$967$	47.1454	+	27.2194i	1.51609	+	0.875317i	0.999822	+	0.0188923i	$0.00601398\pi$
$967$	47.1454	+	27.2194i	1.51609	+	0.875317i	0.516272	+	0.856425i	$0.327319\pi$
$968$	14.9268	−	25.5862i	0.479766	−	0.822370i
$969$		0			0
$970$	1.41270	+	1.27200i	0.0453590	+	0.0408414i
$971$	4.73162	−	6.51252i	0.151845	−	0.208997i	−0.726317	−	0.687360i	$-0.758770\pi$
$971$	4.73162	−	6.51252i	0.151845	−	0.208997i	0.878162	+	0.478363i	$0.158770\pi$
$972$		0			0
$973$	−3.05404	+	9.39936i	−0.0979080	+	0.301330i
$974$	11.9782	−	2.54604i	0.383806	−	0.0815805i
$975$		0			0
$976$	1.77460	+	3.98582i	0.0568035	+	0.127583i
$977$	−2.64186	+	12.4290i	−0.0845205	+	0.397638i	−0.999989	−	0.00475272i	$-0.998487\pi$
$977$	−2.64186	+	12.4290i	−0.0845205	+	0.397638i	0.915468	+	0.402390i	$0.131820\pi$
$978$		0			0
$979$	−21.8247	−	19.7406i	−0.697522	−	0.630912i
$980$			20.4640i			0.653698i
$981$		0			0
$982$	−18.4389	−	13.3967i	−0.588409	−	0.427504i
$983$	−2.14903	+	4.82680i	−0.0685434	+	0.153951i	−0.944568	−	0.328315i	$-0.893519\pi$
$983$	−2.14903	+	4.82680i	−0.0685434	+	0.153951i	0.876025	+	0.482266i	$0.160186\pi$
$984$		0			0
$985$	14.7719	−	13.3007i	0.470673	−	0.423796i
$986$	−0.144268	−	1.37262i	−0.00459444	−	0.0437132i
$987$		0			0
$988$	−3.81170	+	4.23332i	−0.121266	+	0.134680i
$989$	−39.3279			−1.25055
$990$		0			0
$991$	54.4977			1.73118			0.865589	−	0.500756i	$-0.166945\pi$
$991$	54.4977			1.73118			0.865589	+	0.500756i	$0.166945\pi$
$992$	29.4509	−	32.7085i	0.935067	−	1.03850i
$993$		0			0
$994$	0.533972	+	5.08040i	0.0169365	+	0.161141i
$995$	0.145042	−	0.130596i	0.00459814	−	0.00414018i
$996$		0			0
$997$	3.11130	−	6.98810i	0.0985360	−	0.221315i	−0.857551	−	0.514399i	$-0.828015\pi$
$997$	3.11130	−	6.98810i	0.0985360	−	0.221315i	0.956087	+	0.293084i	$0.0946816\pi$
$998$	14.1919	+	10.3110i	0.449236	+	0.326389i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.t.a.17.6		80
3.2	odd	2		99.2.p.a.50.5	yes	80
9.2	odd	6	inner	297.2.t.a.116.6		80
9.4	even	3		891.2.k.a.809.13		80
9.5	odd	6		891.2.k.a.809.8		80
9.7	even	3		99.2.p.a.83.5	yes	80
11.2	odd	10	inner	297.2.t.a.233.6		80
33.2	even	10		99.2.p.a.68.5	yes	80
99.2	even	30	inner	297.2.t.a.35.6		80
99.13	odd	30		891.2.k.a.728.8		80
99.68	even	30		891.2.k.a.728.13		80
99.79	odd	30		99.2.p.a.2.5	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.2.5	✓	80	99.79	odd	30
99.2.p.a.50.5	yes	80	3.2	odd	2
99.2.p.a.68.5	yes	80	33.2	even	10
99.2.p.a.83.5	yes	80	9.7	even	3
297.2.t.a.17.6		80	1.1	even	1	trivial
297.2.t.a.35.6		80	99.2	even	30	inner
297.2.t.a.116.6		80	9.2	odd	6	inner
297.2.t.a.233.6		80	11.2	odd	10	inner
891.2.k.a.728.8		80	99.13	odd	30
891.2.k.a.728.13		80	99.68	even	30
891.2.k.a.809.8		80	9.5	odd	6
891.2.k.a.809.13		80	9.4	even	3

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.t (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.536887 - 0.596273i) q^{2} +(0.141763 + 1.34878i) q^{4} +(2.14661 - 1.93281i) q^{5} +(0.542079 - 1.21753i) q^{7} +(2.17861 + 1.58285i) q^{8} -2.31767i q^{10} +(-2.22482 + 2.45971i) q^{11} +(-0.121914 + 0.573561i) q^{13} +(-0.434945 - 0.976903i) q^{14} +(-0.539671 + 0.114711i) q^{16} +(0.407327 - 1.25362i) q^{17} +(4.21041 - 5.79513i) q^{19} +(2.91125 + 2.62130i) q^{20} +(0.272182 + 2.64719i) q^{22} +(2.62500 + 1.51554i) q^{23} +(0.349510 - 3.32536i) q^{25} +(0.276545 + 0.380632i) q^{26} +(1.71903 + 0.558546i) q^{28} +(1.19216 + 0.530783i) q^{29} +(-7.38644 - 1.57004i) q^{31} +(-2.91425 + 5.04763i) q^{32} +(-0.528814 - 0.915932i) q^{34} +(-1.18963 - 3.66129i) q^{35} +(-3.23755 + 2.35222i) q^{37} +(-1.19497 - 5.62189i) q^{38} +(7.73596 - 0.813082i) q^{40} +(2.05694 - 0.915811i) q^{41} +(-11.2365 + 6.48742i) q^{43} +(-3.63301 - 2.65210i) q^{44} +(2.31301 - 0.751541i) q^{46} +(-11.5098 - 1.20973i) q^{47} +(3.49539 + 3.88202i) q^{49} +(-1.79518 - 1.99375i) q^{50} +(-0.790891 - 0.0831260i) q^{52} +(3.40948 - 1.10781i) q^{53} +(-0.0216557 + 9.58019i) q^{55} +(3.10815 - 1.79449i) q^{56} +(0.956546 - 0.425882i) q^{58} +(-5.95883 + 0.626298i) q^{59} +(-1.64415 - 7.73512i) q^{61} +(-4.90186 + 3.56141i) q^{62} +(1.10416 + 3.39825i) q^{64} +(0.846884 + 1.46685i) q^{65} +(-4.35166 + 7.53730i) q^{67} +(1.74861 + 0.371678i) q^{68} +(-2.82183 - 1.25636i) q^{70} +(-4.54327 - 1.47620i) q^{71} +(-5.16130 - 7.10392i) q^{73} +(-0.335634 + 3.19334i) q^{74} +(8.41325 + 4.85739i) q^{76} +(1.78874 + 4.04214i) q^{77} +(10.2545 + 9.23323i) q^{79} +(-0.936746 + 1.28932i) q^{80} +(0.558273 - 1.71819i) q^{82} +(10.5286 - 2.23793i) q^{83} +(-1.54865 - 3.47832i) q^{85} +(-2.16448 + 10.1831i) q^{86} +(-8.74036 + 1.83718i) q^{88} +8.87289i q^{89} +(0.632240 + 0.459350i) q^{91} +(-1.67201 + 3.75540i) q^{92} +(-6.90079 + 6.21350i) q^{94} +(-2.16281 - 20.5778i) q^{95} +(-0.548828 + 0.609535i) q^{97} +4.19137 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) \) 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

Introduction

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