LMFDB - Embedded newform 297.2.t.a.8.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(8,297)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			8.8
Character	$\chi$	$=$	297.8
Dual form			297.2.t.a.260.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.189668 + 1.80457i) q^{2} +(-1.26420 + 0.268714i) q^{4} +(1.19507 + 0.125607i) q^{5} +(3.59771 - 3.23939i) q^{7} +(0.396737 + 1.22103i) q^{8} +2.18041i q^{10} +(1.93170 - 2.69602i) q^{11} +(-1.24460 + 2.79542i) q^{13} +(6.52808 + 5.87791i) q^{14} +(-4.48960 + 1.99890i) q^{16} +(-1.80866 - 1.31407i) q^{17} +(-4.34428 + 1.41154i) q^{19} +(-1.54456 + 0.162340i) q^{20} +(5.23153 + 2.97455i) q^{22} +(-1.72112 + 0.993689i) q^{23} +(-3.47832 - 0.739340i) q^{25} +(-5.28060 - 1.71577i) q^{26} +(-3.67776 + 5.06200i) q^{28} +(1.13479 + 1.26031i) q^{29} +(4.85274 + 2.16058i) q^{31} +(-3.17481 - 5.49894i) q^{32} +(2.02828 - 3.51308i) q^{34} +(4.70641 - 3.41941i) q^{35} +(0.344857 - 1.06136i) q^{37} +(-3.37119 - 7.57182i) q^{38} +(0.320759 + 1.50905i) q^{40} +(-7.11427 + 7.90120i) q^{41} +(-3.28272 - 1.89528i) q^{43} +(-1.71760 + 3.92738i) q^{44} +(-2.11962 - 2.91741i) q^{46} +(0.678872 - 3.19384i) q^{47} +(1.71815 - 16.3471i) q^{49} +(0.674464 - 6.41710i) q^{50} +(0.822258 - 3.86842i) q^{52} +(0.749954 + 1.03222i) q^{53} +(2.64716 - 2.97930i) q^{55} +(5.38274 + 3.10773i) q^{56} +(-2.05908 + 2.28684i) q^{58} +(0.00657007 + 0.0309097i) q^{59} +(-0.482921 - 1.08466i) q^{61} +(-2.97851 + 9.16690i) q^{62} +(1.36926 - 0.994827i) q^{64} +(-1.83851 + 3.18440i) q^{65} +(1.05277 + 1.82345i) q^{67} +(2.63961 + 1.17523i) q^{68} +(7.06321 + 7.84449i) q^{70} +(2.26013 - 3.11080i) q^{71} +(6.69980 + 2.17690i) q^{73} +(1.98070 + 0.421012i) q^{74} +(5.11273 - 2.95184i) q^{76} +(-1.78375 - 15.9570i) q^{77} +(3.80026 - 0.399424i) q^{79} +(-5.61646 + 1.82490i) q^{80} +(-15.6076 - 11.3396i) q^{82} +(-6.64079 + 2.95667i) q^{83} +(-1.99642 - 1.79758i) q^{85} +(2.79753 - 6.28336i) q^{86} +(4.05830 + 1.28906i) q^{88} -10.2875i q^{89} +(4.57775 + 14.0889i) q^{91} +(1.90882 - 1.71871i) q^{92} +(5.89227 + 0.619302i) q^{94} +(-5.36902 + 1.14122i) q^{95} +(-1.51615 - 14.4252i) q^{97} +29.8254 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.189668	+	1.80457i	0.134115	+	1.27602i	0.829957	+	0.557828i	$0.188365\pi$
$2$	0.189668	+	1.80457i	0.134115	+	1.27602i	−0.695841	+	0.718195i	$0.744968\pi$
$3$		0			0
$3$		0			0
$4$	−1.26420	+	0.268714i	−0.632100	+	0.134357i
$5$	1.19507	+	0.125607i	0.534452	+	0.0561731i	0.367910	−	0.929861i	$-0.380073\pi$
$5$	1.19507	+	0.125607i	0.534452	+	0.0561731i	0.166542	+	0.986034i	$0.446740\pi$
$6$		0			0
$7$	3.59771	−	3.23939i	1.35981	−	1.22438i	0.409788	−	0.912181i	$-0.365603\pi$
$7$	3.59771	−	3.23939i	1.35981	−	1.22438i	0.950018	−	0.312195i	$-0.101064\pi$
$8$	0.396737	+	1.22103i	0.140268	+	0.431700i
$9$		0			0
$10$			2.18041i			0.689506i
$11$	1.93170	−	2.69602i	0.582431	−	0.812880i
$11$	1.93170	−	2.69602i	0.582431	−	0.812880i
$12$		0			0
$13$	−1.24460	+	2.79542i	−0.345191	+	0.775311i	0.654622	+	0.755956i	$0.272828\pi$
$13$	−1.24460	+	2.79542i	−0.345191	+	0.775311i	−0.999813	+	0.0193546i	$0.993839\pi$
$14$	6.52808	+	5.87791i	1.74470	+	1.57094i
$15$		0			0
$16$	−4.48960	+	1.99890i	−1.12240	+	0.499724i
$17$	−1.80866	−	1.31407i	−0.438664	−	0.318708i	0.346440	−	0.938072i	$-0.387390\pi$
$17$	−1.80866	−	1.31407i	−0.438664	−	0.318708i	−0.785104	+	0.619364i	$0.787390\pi$
$18$		0			0
$19$	−4.34428	+	1.41154i	−0.996645	+	0.323830i	−0.761524	−	0.648136i	$-0.775549\pi$
$19$	−4.34428	+	1.41154i	−0.996645	+	0.323830i	−0.235121	+	0.971966i	$0.575549\pi$
$20$	−1.54456	+	0.162340i	−0.345374	+	0.0363003i
$21$		0			0
$22$	5.23153	+	2.97455i	1.11537	+	0.634175i
$23$	−1.72112	+	0.993689i	−0.358878	+	0.207199i	−0.668589	−	0.743632i	$-0.733101\pi$
$23$	−1.72112	+	0.993689i	−0.358878	+	0.207199i	0.309710	+	0.950831i	$0.399768\pi$
$24$		0			0
$25$	−3.47832	−	0.739340i	−0.695664	−	0.147868i
$26$	−5.28060	−	1.71577i	−1.03561	−	0.336490i
$27$		0			0
$28$	−3.67776	+	5.06200i	−0.695030	+	0.956627i
$29$	1.13479	+	1.26031i	0.210725	+	0.234034i	0.839237	−	0.543766i	$-0.183002\pi$
$29$	1.13479	+	1.26031i	0.210725	+	0.234034i	−0.628512	+	0.777800i	$0.716336\pi$
$30$		0			0
$31$	4.85274	+	2.16058i	0.871579	+	0.388052i	0.793265	−	0.608877i	$-0.208380\pi$
$31$	4.85274	+	2.16058i	0.871579	+	0.388052i	0.0783139	+	0.996929i	$0.475046\pi$
$32$	−3.17481	−	5.49894i	−0.561233	−	0.972084i
$33$		0			0
$34$	2.02828	−	3.51308i	0.347847	−	0.602489i
$35$	4.70641	−	3.41941i	0.795528	−	0.577985i
$36$		0			0
$37$	0.344857	−	1.06136i	0.0566941	−	0.174486i	−0.918699	−	0.394957i	$-0.870759\pi$
$37$	0.344857	−	1.06136i	0.0566941	−	0.174486i	0.975394	+	0.220471i	$0.0707594\pi$
$38$	−3.37119	−	7.57182i	−0.546880	−	1.22831i
$39$		0			0
$40$	0.320759	+	1.50905i	0.0507164	+	0.238602i
$41$	−7.11427	+	7.90120i	−1.11106	+	1.23396i	−0.141285	+	0.989969i	$0.545123\pi$
$41$	−7.11427	+	7.90120i	−1.11106	+	1.23396i	−0.969778	+	0.243991i	$0.921543\pi$
$42$		0			0
$43$	−3.28272	−	1.89528i	−0.500609	−	0.289027i	0.228356	−	0.973578i	$-0.426665\pi$
$43$	−3.28272	−	1.89528i	−0.500609	−	0.289027i	−0.728965	+	0.684551i	$0.759998\pi$
$44$	−1.71760	+	3.92738i	−0.258938	+	0.592075i
$45$		0			0
$46$	−2.11962	−	2.91741i	−0.312521	−	0.430149i
$47$	0.678872	−	3.19384i	0.0990236	−	0.465870i	−0.900496	−	0.434865i	$-0.856796\pi$
$47$	0.678872	−	3.19384i	0.0990236	−	0.465870i	0.999519	−	0.0310045i	$-0.00987062\pi$
$48$		0			0
$49$	1.71815	−	16.3471i	0.245450	−	2.33530i
$50$	0.674464	−	6.41710i	0.0953837	−	0.907515i
$51$		0			0
$52$	0.822258	−	3.86842i	0.114027	−	0.536453i
$53$	0.749954	+	1.03222i	0.103014	+	0.141787i	0.857412	−	0.514631i	$-0.172071\pi$
$53$	0.749954	+	1.03222i	0.103014	+	0.141787i	−0.754398	+	0.656417i	$0.772071\pi$
$54$		0			0
$55$	2.64716	−	2.97930i	0.356943	−	0.401728i
$56$	5.38274	+	3.10773i	0.719299	+	0.415288i
$57$		0			0
$58$	−2.05908	+	2.28684i	−0.270371	+	0.300277i
$59$	0.00657007	+	0.0309097i	0.000855350	+	0.00402410i	0.978573	−	0.205899i	$-0.0660119\pi$
$59$	0.00657007	+	0.0309097i	0.000855350	+	0.00402410i	−0.977718	+	0.209923i	$0.932679\pi$
$60$		0			0
$61$	−0.482921	−	1.08466i	−0.0618317	−	0.138876i	0.879987	−	0.474998i	$-0.157551\pi$
$61$	−0.482921	−	1.08466i	−0.0618317	−	0.138876i	−0.941818	+	0.336122i	$0.890885\pi$
$62$	−2.97851	+	9.16690i	−0.378271	+	1.16420i
$63$		0			0
$64$	1.36926	−	0.994827i	0.171158	−	0.124353i
$65$	−1.83851	+	3.18440i	−0.228039	+	0.394976i
$66$		0			0
$67$	1.05277	+	1.82345i	0.128617	+	0.222770i	0.923141	−	0.384462i	$-0.125613\pi$
$67$	1.05277	+	1.82345i	0.128617	+	0.222770i	−0.794524	+	0.607232i	$0.792280\pi$
$68$	2.63961	+	1.17523i	0.320100	+	0.142518i
$69$		0			0
$70$	7.06321	+	7.84449i	0.844215	+	0.937595i
$71$	2.26013	−	3.11080i	0.268228	−	0.369184i	−0.653563	−	0.756873i	$-0.726726\pi$
$71$	2.26013	−	3.11080i	0.268228	−	0.369184i	0.921790	+	0.387688i	$0.126726\pi$
$72$		0			0
$73$	6.69980	+	2.17690i	0.784152	+	0.254786i	0.673612	−	0.739085i	$-0.264742\pi$
$73$	6.69980	+	2.17690i	0.784152	+	0.254786i	0.110540	+	0.993872i	$0.464742\pi$
$74$	1.98070	+	0.421012i	0.230252	+	0.0489416i
$75$		0			0
$76$	5.11273	−	2.95184i	0.586471	−	0.338599i
$77$	−1.78375	−	15.9570i	−0.203277	−	1.81847i
$78$		0			0
$79$	3.80026	−	0.399424i	0.427563	−	0.0449387i	0.111697	−	0.993742i	$-0.464372\pi$
$79$	3.80026	−	0.399424i	0.427563	−	0.0449387i	0.315866	+	0.948804i	$0.397705\pi$
$80$	−5.61646	+	1.82490i	−0.627940	+	0.204030i
$81$		0			0
$82$	−15.6076	−	11.3396i	−1.72357	−	1.25225i
$83$	−6.64079	+	2.95667i	−0.728922	+	0.324537i	−0.737427	−	0.675427i	$-0.763959\pi$
$83$	−6.64079	+	2.95667i	−0.728922	+	0.324537i	0.00850508	+	0.999964i	$0.497293\pi$
$84$		0			0
$85$	−1.99642	−	1.79758i	−0.216542	−	0.194975i
$86$	2.79753	−	6.28336i	0.301666	−	0.677552i
$87$		0			0
$88$	4.05830	+	1.28906i	0.432616	+	0.137414i
$89$		−	10.2875i		−	1.09048i	−0.838281	−	0.545238i	$-0.816439\pi$
$89$		−	10.2875i		−	1.09048i	0.838281	−	0.545238i	$-0.183561\pi$
$90$		0			0
$91$	4.57775	+	14.0889i	0.479879	+	1.47692i
$92$	1.90882	−	1.71871i	0.199009	−	0.179188i
$93$		0			0
$94$	5.89227	+	0.619302i	0.607741	+	0.0638761i
$95$	−5.36902	+	1.14122i	−0.550849	+	0.117087i
$96$		0			0
$97$	−1.51615	−	14.4252i	−0.153941	−	1.46465i	−0.749853	−	0.661605i	$-0.769876\pi$
$97$	−1.51615	−	14.4252i	−0.153941	−	1.46465i	0.595912	−	0.803050i	$-0.296791\pi$
$98$	29.8254			3.01282
$99$		0			0
$100$	4.59597			0.459597
$101$	1.68141	+	15.9976i	0.167307	+	1.59182i	0.679977	+	0.733234i	$0.261990\pi$
$101$	1.68141	+	15.9976i	0.167307	+	1.59182i	−0.512670	+	0.858586i	$0.671343\pi$
$102$		0			0
$103$	2.03569	−	0.432699i	0.200582	−	0.0426351i	−0.106525	−	0.994310i	$-0.533972\pi$
$103$	2.03569	−	0.432699i	0.200582	−	0.0426351i	0.307107	+	0.951675i	$0.400639\pi$
$104$	−3.90708	−	0.410651i	−0.383121	−	0.0402676i
$105$		0			0
$106$	−1.72047	+	1.54912i	−0.167107	+	0.150464i
$107$	−0.129361	−	0.398133i	−0.0125058	−	0.0384889i	0.944609	−	0.328198i	$-0.106441\pi$
$107$	−0.129361	−	0.398133i	−0.0125058	−	0.0384889i	−0.957115	+	0.289709i	$0.906441\pi$
$108$		0			0
$109$		−	14.6788i		−	1.40597i	−0.711205	−	0.702985i	$-0.751850\pi$
$109$		−	14.6788i		−	1.40597i	0.711205	−	0.702985i	$-0.248150\pi$
$110$	5.87843	+	4.21191i	0.560486	+	0.401590i
$111$		0			0
$112$	−9.67706	+	21.7350i	−0.914396	+	2.05377i
$113$	−2.37557	−	2.13897i	−0.223475	−	0.201218i	0.549786	−	0.835305i	$-0.314709\pi$
$113$	−2.37557	−	2.13897i	−0.223475	−	0.201218i	−0.773261	+	0.634088i	$0.781376\pi$
$114$		0			0
$115$	−2.18167	+	0.971344i	−0.203442	+	0.0905783i
$116$	−1.77326	−	1.28835i	−0.164643	−	0.119620i
$117$		0			0
$118$	−0.0545326	+	0.0177187i	−0.00502013	+	0.00163114i
$119$	−10.7638	+	1.13132i	−0.986716	+	0.103708i
$120$		0			0
$121$	−3.53703	−	10.4158i	−0.321548	−	0.946893i
$122$	1.86575	−	1.07719i	0.168917	−	0.0975241i
$123$		0			0
$124$	−6.71542	−	1.42741i	−0.603062	−	0.128185i
$125$	−9.77817	−	3.17712i	−0.874587	−	0.284170i
$126$		0			0
$127$	−13.1088	+	18.0428i	−1.16322	+	1.60104i	−0.464654	+	0.885492i	$0.653821\pi$
$127$	−13.1088	+	18.0428i	−1.16322	+	1.60104i	−0.698567	+	0.715545i	$0.746179\pi$
$128$	−6.44252	−	7.15514i	−0.569444	−	0.632431i
$129$		0			0
$130$	−6.09517	−	2.71375i	−0.534582	−	0.238011i
$131$	7.74960	+	13.4227i	0.677086	+	1.17275i	0.975855	+	0.218421i	$0.0700907\pi$
$131$	7.74960	+	13.4227i	0.677086	+	1.17275i	−0.298769	+	0.954326i	$0.596576\pi$
$132$		0			0
$133$	−11.0569	+	19.1511i	−0.958756	+	1.66061i
$134$	−3.09087	+	2.24565i	−0.267011	+	0.193995i
$135$		0			0
$136$	0.886955	−	2.72977i	0.0760557	−	0.234075i
$137$	−6.97178	−	15.6589i	−0.595639	−	1.33783i	−0.920009	−	0.391897i	$-0.871819\pi$
$137$	−6.97178	−	15.6589i	−0.595639	−	1.33783i	0.324370	−	0.945930i	$-0.394848\pi$
$138$		0			0
$139$	2.15559	+	10.1413i	0.182835	+	0.860172i	0.969938	+	0.243350i	$0.0782465\pi$
$139$	2.15559	+	10.1413i	0.182835	+	0.860172i	−0.787103	+	0.616821i	$0.788420\pi$
$140$	−5.03100	+	5.58749i	−0.425197	+	0.472229i
$141$		0			0
$142$	6.04233	+	3.48854i	0.507061	+	0.292752i
$143$	5.13231	+	8.75541i	0.429185	+	0.732164i
$144$		0			0
$145$	1.19785	+	1.64870i	0.0994759	+	0.136917i
$146$	−2.65762	+	12.5031i	−0.219946	+	1.03477i
$147$		0			0
$148$	−0.150766	+	1.43444i	−0.0123929	+	0.117910i
$149$	0.00422899	−	0.0402361i	0.000346452	−	0.00329627i	−0.994347	−	0.106176i	$-0.966139\pi$
$149$	0.00422899	−	0.0402361i	0.000346452	−	0.00329627i	0.994694	+	0.102880i	$0.0328058\pi$
$150$		0			0
$151$	−0.572095	+	2.69150i	−0.0465564	+	0.219031i	−0.995276	−	0.0970890i	$-0.969047\pi$
$151$	−0.572095	+	2.69150i	−0.0465564	+	0.219031i	0.948719	+	0.316120i	$0.102380\pi$
$152$	−3.44707	−	4.74449i	−0.279594	−	0.384829i
$153$		0			0
$154$	28.4573	−	6.24544i	2.29315	−	0.503272i
$155$	5.52799	+	3.19159i	0.444019	+	0.256354i
$156$		0			0
$157$	1.41178	−	1.56794i	0.112672	−	0.125135i	−0.684170	−	0.729322i	$-0.739835\pi$
$157$	1.41178	−	1.56794i	0.112672	−	0.125135i	0.796842	+	0.604187i	$0.206502\pi$
$158$	1.44158	+	6.78208i	0.114686	+	0.539553i
$159$		0			0
$160$	−3.10342	−	6.97040i	−0.245347	−	0.551058i
$161$	−2.97314	+	9.15039i	−0.234316	+	0.721152i
$162$		0			0
$163$	−11.8085	+	8.57941i	−0.924917	+	0.671991i	−0.944743	−	0.327812i	$-0.893689\pi$
$163$	−11.8085	+	8.57941i	−0.924917	+	0.671991i	0.0198264	+	0.999803i	$0.493689\pi$
$164$	6.87070	−	11.9004i	0.536512	−	0.929265i
$165$		0			0
$166$	−6.59506	−	11.4230i	−0.511876	−	0.886596i
$167$	−0.815131	−	0.362920i	−0.0630767	−	0.0280836i	0.374956	−	0.927043i	$-0.377658\pi$
$167$	−0.815131	−	0.362920i	−0.0630767	−	0.0280836i	−0.438033	+	0.898959i	$0.644325\pi$
$168$		0			0
$169$	2.43334	+	2.70250i	0.187180	+	0.207884i
$170$	2.86520	−	3.94362i	0.219751	−	0.302461i
$171$		0			0
$172$	4.65930	+	1.51390i	0.355268	+	0.115434i
$173$	12.9579	+	2.75430i	0.985175	+	0.209405i	0.672211	−	0.740360i	$-0.265345\pi$
$173$	12.9579	+	2.75430i	0.985175	+	0.209405i	0.312964	+	0.949765i	$0.398678\pi$
$174$		0			0
$175$	−14.9090	+	8.60772i	−1.12701	+	0.650682i
$176$	−3.28351	+	15.9653i	−0.247504	+	1.20343i
$177$		0			0
$178$	18.5646	−	1.95121i	1.39147	−	0.146250i
$179$	19.1587	−	6.22502i	1.43199	−	0.465280i	0.512596	−	0.858630i	$-0.328684\pi$
$179$	19.1587	−	6.22502i	1.43199	−	0.465280i	0.919389	+	0.393350i	$0.128684\pi$
$180$		0			0
$181$	3.63758	+	2.64286i	0.270379	+	0.196442i	0.714710	−	0.699421i	$-0.246559\pi$
$181$	3.63758	+	2.64286i	0.270379	+	0.196442i	−0.444331	+	0.895863i	$0.646559\pi$
$182$	−24.5561	+	10.9331i	−1.82022	+	0.810414i
$183$		0			0
$184$	−1.89616	−	1.70731i	−0.139787	−	0.125864i
$185$	0.545442	−	1.22508i	0.0401017	−	0.0900699i
$186$		0			0
$187$	−7.03654	+	2.33778i	−0.514563	+	0.170956i
$188$			4.22008i			0.307781i
$189$		0			0
$190$	−3.07774	−	9.47231i	−0.223283	−	0.687193i
$191$	13.2086	−	11.8931i	0.955742	−	0.860554i	−0.0345721	−	0.999402i	$-0.511007\pi$
$191$	13.2086	−	11.8931i	0.955742	−	0.860554i	0.990314	+	0.138849i	$0.0443402\pi$
$192$		0			0
$193$	−6.12522	−	0.643787i	−0.440903	−	0.0463408i	−0.118523	−	0.992951i	$-0.537816\pi$
$193$	−6.12522	−	0.643787i	−0.440903	−	0.0463408i	−0.322380	+	0.946610i	$0.604483\pi$
$194$	25.7437	−	5.47198i	1.84829	−	0.392866i
$195$		0			0
$196$	2.22062	+	21.1277i	0.158615	+	1.50912i
$197$	−22.5100			−1.60377			−0.801886	−	0.597477i	$-0.796170\pi$
$197$	−22.5100			−1.60377			−0.801886	+	0.597477i	$0.796170\pi$
$198$		0			0
$199$	9.30680			0.659742			0.329871	−	0.944026i	$-0.392995\pi$
$199$	9.30680			0.659742			0.329871	+	0.944026i	$0.392995\pi$
$200$	−0.477222	−	4.54046i	−0.0337447	−	0.321059i
$201$		0			0
$202$	−28.5498	+	6.06846i	−2.00876	+	0.426975i
$203$	8.16528	+	0.858206i	0.573090	+	0.0602342i
$204$		0			0
$205$	−9.49450	+	8.54889i	−0.663125	+	0.597080i
$206$	1.16694	+	3.59147i	0.0813046	+	0.250230i
$207$		0			0
$208$		−	15.0382i		−	1.04271i
$209$	−4.58632	+	14.4389i	−0.317242	+	0.998762i
$210$		0			0
$211$	5.69884	−	12.7998i	0.392325	−	0.881175i	−0.604118	−	0.796895i	$-0.706474\pi$
$211$	5.69884	−	12.7998i	0.392325	−	0.881175i	0.996442	−	0.0842801i	$-0.0268591\pi$
$212$	−1.22546	−	1.10341i	−0.0841652	−	0.0757827i
$213$		0			0
$214$	0.693922	−	0.308954i	0.0474355	−	0.0211197i
$215$	−3.68502	−	2.67732i	−0.251316	−	0.182592i
$216$		0			0
$217$	24.4577	−	7.94680i	1.66030	−	0.539464i
$218$	26.4888	−	2.78409i	1.79405	−	0.188562i
$219$		0			0
$220$	−2.54596	+	4.47776i	−0.171649	+	0.301890i
$221$	5.92443	−	3.42047i	0.398520	−	0.230086i
$222$		0			0
$223$	15.7802	+	3.35419i	1.05672	+	0.224613i	0.703331	−	0.710863i	$-0.251695\pi$
$223$	15.7802	+	3.35419i	1.05672	+	0.224613i	0.353391	+	0.935476i	$0.385029\pi$
$224$	−29.2353	−	9.49912i	−1.95336	−	0.634686i
$225$		0			0
$226$	3.40936	−	4.69258i	0.226787	−	0.312146i
$227$	9.84619	+	10.9353i	0.653515	+	0.725802i	0.975269	−	0.221022i	$-0.0709392\pi$
$227$	9.84619	+	10.9353i	0.653515	+	0.725802i	−0.321754	+	0.946823i	$0.604272\pi$
$228$		0			0
$229$	20.2798	+	9.02915i	1.34013	+	0.596663i	0.946529	−	0.322620i	$-0.104564\pi$
$229$	20.2798	+	9.02915i	1.34013	+	0.596663i	0.393598	+	0.919283i	$0.371230\pi$
$230$	−2.16665	−	3.75275i	−0.142865	−	0.247449i
$231$		0			0
$232$	−1.08867	+	1.88562i	−0.0714744	+	0.123797i
$233$	−4.18134	+	3.03792i	−0.273929	+	0.199021i	−0.716265	−	0.697828i	$-0.754150\pi$
$233$	−4.18134	+	3.03792i	−0.273929	+	0.199021i	0.442336	+	0.896849i	$0.354150\pi$
$234$		0			0
$235$	1.21247	−	3.73159i	0.0790927	−	0.243422i
$236$	−0.0166118	−	0.0373106i	−0.00108133	−	0.00242871i
$237$		0			0
$238$	−4.08309	−	19.2094i	−0.264668	−	1.24516i
$239$	9.14380	−	10.1552i	0.591463	−	0.656886i	−0.370894	−	0.928675i	$-0.620949\pi$
$239$	9.14380	−	10.1552i	0.591463	−	0.656886i	0.962357	+	0.271789i	$0.0876153\pi$
$240$		0			0
$241$	−6.10765	−	3.52625i	−0.393428	−	0.227146i	0.290216	−	0.956961i	$-0.406273\pi$
$241$	−6.10765	−	3.52625i	−0.393428	−	0.227146i	−0.683645	+	0.729815i	$0.739606\pi$
$242$	18.1252	−	8.35837i	1.16513	−	0.537296i
$243$		0			0
$244$	0.901971	+	1.24146i	0.0577428	+	0.0794761i
$245$	4.10663	−	19.3202i	0.262363	−	1.23432i
$246$		0			0
$247$	1.46104	−	13.9009i	0.0929640	−	0.884493i
$248$	−0.712873	+	6.78253i	−0.0452675	+	0.430691i
$249$		0			0
$250$	3.87873	−	18.2480i	0.245312	−	1.15410i
$251$	−3.95496	−	5.44354i	−0.249635	−	0.343593i	0.665748	−	0.746176i	$-0.268112\pi$
$251$	−3.95496	−	5.44354i	−0.249635	−	0.343593i	−0.915383	+	0.402583i	$0.868112\pi$
$252$		0			0
$253$	−0.645692	+	6.55969i	−0.0405943	+	0.412404i
$254$	−35.0457	−	20.2337i	−2.19897	−	1.26957i
$255$		0			0
$256$	13.9550	−	15.4986i	0.872189	−	0.968664i
$257$	2.94227	+	13.8423i	0.183534	+	0.863457i	0.969481	+	0.245165i	$0.0788420\pi$
$257$	2.94227	+	13.8423i	0.183534	+	0.863457i	−0.785948	+	0.618293i	$0.787825\pi$
$258$		0			0
$259$	−2.19747	−	4.93559i	−0.136544	−	0.306683i
$260$	1.46856	−	4.51975i	0.0910760	−	0.280303i
$261$		0			0
$262$	−22.7523	+	16.5305i	−1.40564	+	1.02126i
$263$	3.47292	−	6.01527i	0.214149	−	0.370917i	−0.738860	−	0.673859i	$-0.764635\pi$
$263$	3.47292	−	6.01527i	0.214149	−	0.370917i	0.953009	+	0.302942i	$0.0979688\pi$
$264$		0			0
$265$	0.766593	+	1.32778i	0.0470914	+	0.0815648i
$266$	−36.6567	−	16.3206i	−2.24757	−	1.00068i
$267$		0			0
$268$	−1.82090	−	2.02232i	−0.111229	−	0.123533i
$269$	4.05850	−	5.58605i	0.247451	−	0.340587i	−0.667165	−	0.744910i	$-0.732493\pi$
$269$	4.05850	−	5.58605i	0.247451	−	0.340587i	0.914617	+	0.404322i	$0.132493\pi$
$270$		0			0
$271$	−12.9581	−	4.21033i	−0.787146	−	0.255759i	−0.112258	−	0.993679i	$-0.535808\pi$
$271$	−12.9581	−	4.21033i	−0.787146	−	0.255759i	−0.674888	+	0.737920i	$0.735808\pi$
$272$	10.7468	+	2.28431i	0.651622	+	0.138507i
$273$		0			0
$274$	26.9352	−	15.5510i	1.62721	−	0.939473i
$275$	−8.71236	+	7.94943i	−0.525375	+	0.479369i
$276$		0			0
$277$	11.5914	−	1.21831i	0.696461	−	0.0732010i	0.250319	−	0.968163i	$-0.419464\pi$
$277$	11.5914	−	1.21831i	0.696461	−	0.0732010i	0.446142	+	0.894962i	$0.352798\pi$
$278$	−17.8918	+	5.81339i	−1.07308	+	0.348664i
$279$		0			0
$280$	6.04241	+	4.39007i	0.361103	+	0.262357i
$281$	19.9523	−	8.88333i	1.19025	−	0.529935i	0.286538	−	0.958069i	$-0.407495\pi$
$281$	19.9523	−	8.88333i	1.19025	−	0.529935i	0.903715	+	0.428134i	$0.140829\pi$
$282$		0			0
$283$	17.4451	+	15.7076i	1.03700	+	0.933722i	0.997852	−	0.0655115i	$-0.0208679\pi$
$283$	17.4451	+	15.7076i	1.03700	+	0.933722i	0.0391513	+	0.999233i	$0.487535\pi$
$284$	−2.02134	+	4.54000i	−0.119944	+	0.269400i
$285$		0			0
$286$	−14.8263	+	10.9222i	−0.876698	+	0.645845i
$287$			51.4721i			3.03830i
$288$		0			0
$289$	−3.70882	−	11.4146i	−0.218166	−	0.671445i
$290$	−2.74799	+	2.47431i	−0.161368	+	0.145296i
$291$		0			0
$292$	−9.05485	−	0.951703i	−0.529895	−	0.0556942i
$293$	−1.65959	+	0.352756i	−0.0969542	+	0.0206082i	−0.256133	−	0.966641i	$-0.582449\pi$
$293$	−1.65959	+	0.352756i	−0.0969542	+	0.0206082i	0.159179	+	0.987250i	$0.449115\pi$
$294$		0			0
$295$	0.00396922	+	0.0377646i	0.000231097	+	0.00219874i
$296$	1.43277			0.0832781
$297$		0			0
$298$	0.0734110			0.00425258
$299$	−0.635671	−	6.04801i	−0.0367618	−	0.349765i
$300$		0			0
$301$	−17.9498	+	3.81535i	−1.03461	+	0.219913i
$302$	−4.96550	−	0.521895i	−0.285732	−	0.0300317i
$303$		0			0
$304$	16.6825	−	15.0210i	0.956809	−	0.861514i
$305$	−0.440884	−	1.35690i	−0.0252449	−	0.0776959i
$306$		0			0
$307$			2.35281i			0.134282i	0.997743	+	0.0671410i	$0.0213877\pi$
$307$			2.35281i			0.134282i	−0.997743	+	0.0671410i	$0.978612\pi$
$308$	6.54290	+	19.6936i	0.372816	+	1.12215i
$309$		0			0
$310$	−4.71095	+	10.5810i	−0.267564	+	0.600959i
$311$	−7.88205	−	7.09703i	−0.446950	−	0.402436i	0.414684	−	0.909965i	$-0.363892\pi$
$311$	−7.88205	−	7.09703i	−0.446950	−	0.402436i	−0.861634	+	0.507530i	$0.830559\pi$
$312$		0			0
$313$	−23.1439	+	10.3043i	−1.30817	+	0.582435i	−0.938034	−	0.346543i	$-0.887355\pi$
$313$	−23.1439	+	10.3043i	−1.30817	+	0.582435i	−0.370136	+	0.928978i	$0.620689\pi$
$314$	3.09722	+	2.25026i	0.174786	+	0.126990i
$315$		0			0
$316$	−4.69696	+	1.52614i	−0.264225	+	0.0858518i
$317$	−26.6656	+	2.80266i	−1.49769	+	0.157413i	−0.817629	−	0.575745i	$-0.804712\pi$
$317$	−26.6656	+	2.80266i	−1.49769	+	0.157413i	−0.680058	+	0.733158i	$0.738045\pi$
$318$		0			0
$319$	5.58990	−	0.624864i	0.312974	−	0.0349856i
$320$	1.76132	−	1.01690i	0.0984609	−	0.0568464i
$321$		0			0
$322$	−17.0764	−	3.62971i	−0.951632	−	0.202276i
$323$	9.71216	+	3.15567i	0.540399	+	0.175586i
$324$		0			0
$325$	6.39590	−	8.80320i	0.354781	−	0.488314i
$326$	−17.7218	−	19.6821i	−0.981522	−	1.09009i
$327$		0			0
$328$	−12.4701	−	5.55205i	−0.688546	−	0.306561i
$329$	−7.90372	−	13.6896i	−0.435746	−	0.754735i
$330$		0			0
$331$	8.66186	−	15.0028i	0.476099	−	0.824627i	−0.523526	−	0.852010i	$-0.675384\pi$
$331$	8.66186	−	15.0028i	0.476099	−	0.824627i	0.999625	+	0.0273822i	$0.00871710\pi$
$332$	7.60079	−	5.52230i	0.417148	−	0.303076i
$333$		0			0
$334$	0.500309	−	1.53979i	0.0273757	−	0.0842538i
$335$	1.02910	+	2.31139i	0.0562256	+	0.126285i
$336$		0			0
$337$	2.70366	+	12.7197i	0.147278	+	0.692887i	0.988379	+	0.152009i	$0.0485743\pi$
$337$	2.70366	+	12.7197i	0.147278	+	0.692887i	−0.841101	+	0.540877i	$0.818092\pi$
$338$	−4.41532	+	4.90371i	−0.240162	+	0.266727i
$339$		0			0
$340$	3.00691	+	1.73604i	0.163072	+	0.0941499i
$341$	15.1990	−	8.90948i	0.823074	−	0.482476i
$342$		0			0
$343$	−26.8543	−	36.9618i	−1.45000	−	1.99575i
$344$	1.01182	−	4.76023i	0.0545535	−	0.256654i
$345$		0			0
$346$	−2.51261	+	23.9059i	−0.135079	+	1.28519i
$347$	2.22189	−	21.1399i	0.119277	−	1.13485i	−0.757126	−	0.653269i	$-0.773397\pi$
$347$	2.22189	−	21.1399i	0.119277	−	1.13485i	0.876403	−	0.481578i	$-0.159936\pi$
$348$		0			0
$349$	−1.94002	+	9.12708i	−0.103847	+	0.488562i	0.895230	+	0.445604i	$0.147011\pi$
$349$	−1.94002	+	9.12708i	−0.103847	+	0.488562i	−0.999077	+	0.0429571i	$0.986322\pi$
$350$	−18.3610	−	25.2717i	−0.981436	−	1.35083i
$351$		0			0
$352$	−20.9580	−	2.06297i	−1.11707	−	0.109957i
$353$	−7.89937	−	4.56070i	−0.420441	−	0.242742i	0.274825	−	0.961494i	$-0.411380\pi$
$353$	−7.89937	−	4.56070i	−0.420441	−	0.242742i	−0.695266	+	0.718753i	$0.744713\pi$
$354$		0			0
$355$	3.09175	−	3.43374i	0.164093	−	0.182244i
$356$	2.76440	+	13.0055i	0.146513	+	0.689290i
$357$		0			0
$358$	14.8673	+	33.3924i	0.785760	+	1.76484i
$359$	−2.41692	+	7.43851i	−0.127560	+	0.392589i	−0.994359	−	0.106069i	$-0.966174\pi$
$359$	−2.41692	+	7.43851i	−0.127560	+	0.392589i	0.866799	+	0.498658i	$0.166174\pi$
$360$		0			0
$361$	1.50897	−	1.09633i	0.0794193	−	0.0577015i
$362$	−4.07929	+	7.06553i	−0.214402	+	0.371356i
$363$		0			0
$364$	−9.57308	−	16.5811i	−0.501766	−	0.869084i
$365$	7.73330	+	3.44309i	0.404779	+	0.180219i
$366$		0			0
$367$	16.3966	+	18.2102i	0.855894	+	0.950567i	0.999235	−	0.0391068i	$-0.0124513\pi$
$367$	16.3966	+	18.2102i	0.855894	+	0.950567i	−0.143341	+	0.989673i	$0.545785\pi$
$368$	5.74086	−	7.90161i	0.299263	−	0.411900i
$369$		0			0
$370$	2.31420	+	0.751929i	0.120310	+	0.0390909i
$371$	6.04189	+	1.28424i	0.313679	+	0.0666746i
$372$		0			0
$373$	2.47795	−	1.43065i	0.128303	−	0.0740760i	−0.434475	−	0.900684i	$-0.643066\pi$
$373$	2.47795	−	1.43065i	0.128303	−	0.0740760i	0.562778	+	0.826608i	$0.309733\pi$
$374$	−5.55330	−	12.2545i	−0.287154	−	0.633666i
$375$		0			0
$376$	4.16911	−	0.438191i	0.215006	−	0.0225980i
$377$	−4.93546	+	1.60363i	−0.254189	+	0.0825911i
$378$		0			0
$379$	23.6747	+	17.2007i	1.21609	+	0.883540i	0.995769	−	0.0918872i	$-0.0292899\pi$
$379$	23.6747	+	17.2007i	1.21609	+	0.883540i	0.220320	+	0.975428i	$0.429290\pi$
$380$	6.48085	−	2.88546i	0.332461	−	0.148021i
$381$		0			0
$382$	23.9671	+	21.5801i	1.22627	+	1.10413i
$383$	−11.5755	+	25.9990i	−0.591480	+	1.32849i	0.331434	+	0.943478i	$0.392468\pi$
$383$	−11.5755	+	25.9990i	−0.591480	+	1.32849i	−0.922914	+	0.385007i	$0.874199\pi$
$384$		0			0
$385$	−0.127390	−	19.2938i	−0.00649240	−	0.983305i
$386$		−	11.1755i		−	0.568818i
$387$		0			0
$388$	5.79296	+	17.8289i	0.294093	+	0.905125i
$389$	−10.6132	+	9.55615i	−0.538110	+	0.484516i	−0.892791	−	0.450471i	$-0.851256\pi$
$389$	−10.6132	+	9.55615i	−0.538110	+	0.484516i	0.354681	+	0.934987i	$0.384589\pi$
$390$		0			0
$391$	4.41869	+	0.464423i	0.223463	+	0.0234869i
$392$	20.6420	−	4.38760i	1.04258	−	0.221607i
$393$		0			0
$394$	−4.26943	−	40.6209i	−0.215091	−	2.04645i
$395$	4.59175			0.231036
$396$		0			0
$397$	2.20687			0.110760			0.0553798	−	0.998465i	$-0.482363\pi$
$397$	2.20687			0.110760			0.0553798	+	0.998465i	$0.482363\pi$
$398$	1.76520	+	16.7948i	0.0884815	+	0.841845i
$399$		0			0
$400$	17.0941	−	3.63347i	0.854707	−	0.181673i
$401$	31.3702	+	3.29714i	1.56655	+	0.164651i	0.847687	−	0.530497i	$-0.177995\pi$
$401$	31.3702	+	3.29714i	1.56655	+	0.164651i	0.718866	+	0.695148i	$0.244661\pi$
$402$		0			0
$403$	−12.0795	+	10.8764i	−0.601722	+	0.541793i
$404$	−6.42442	−	19.7723i	−0.319627	−	0.983710i
$405$		0			0
$406$			14.8976i			0.739355i
$407$	−2.19528	−	2.97997i	−0.108816	−	0.147712i
$408$		0			0
$409$	−2.75694	+	6.19219i	−0.136322	+	0.306184i	−0.968788	−	0.247893i	$-0.920262\pi$
$409$	−2.75694	+	6.19219i	−0.136322	+	0.306184i	0.832466	+	0.554077i	$0.186929\pi$
$410$	−17.2279	−	15.5120i	−0.850823	−	0.766085i
$411$		0			0
$412$	−2.45725	+	1.09404i	−0.121060	+	0.0538993i
$413$	0.123766	+	0.0899212i	0.00609012	+	0.00442473i
$414$		0			0
$415$	−8.30760	+	2.69930i	−0.407804	+	0.132504i
$416$	19.3232	−	2.03095i	0.947400	−	0.0995757i
$417$		0			0
$418$	−26.9259	−	5.53773i	−1.31699	−	0.270859i
$419$	24.7759	−	14.3044i	1.21038	−	0.698815i	0.247541	−	0.968877i	$-0.420378\pi$
$419$	24.7759	−	14.3044i	1.21038	−	0.698815i	0.962843	+	0.270062i	$0.0870442\pi$
$420$		0			0
$421$	5.47106	+	1.16291i	0.266643	+	0.0566768i	0.339293	−	0.940681i	$-0.389812\pi$
$421$	5.47106	+	1.16291i	0.266643	+	0.0566768i	−0.0726497	+	0.997358i	$0.523146\pi$
$422$	24.1790	+	7.85624i	1.17702	+	0.382436i
$423$		0			0
$424$	−0.962842	+	1.32524i	−0.0467597	+	0.0643592i
$425$	5.31955	+	5.90796i	0.258036	+	0.286578i
$426$		0			0
$427$	−5.25104	−	2.33791i	−0.254116	−	0.113140i
$428$	0.270522	+	0.468558i	0.0130762	+	0.0226486i
$429$		0			0
$430$	4.13248	−	7.15767i	0.199286	−	0.345173i
$431$	15.7825	−	11.4667i	0.760216	−	0.552329i	−0.138760	−	0.990326i	$-0.544312\pi$
$431$	15.7825	−	11.4667i	0.760216	−	0.552329i	0.898977	+	0.437997i	$0.144312\pi$
$432$		0			0
$433$	−6.96921	+	21.4490i	−0.334919	+	1.03077i	0.631843	+	0.775096i	$0.282299\pi$
$433$	−6.96921	+	21.4490i	−0.334919	+	1.03077i	−0.966762	+	0.255678i	$0.917701\pi$
$434$	18.9794	+	42.6284i	0.911040	+	2.04623i
$435$		0			0
$436$	3.94439	+	18.5569i	0.188902	+	0.888714i
$437$	6.07439	−	6.74629i	0.290577	−	0.322719i
$438$		0			0
$439$	−25.9695	−	14.9935i	−1.23946	−	0.715601i	−0.270474	−	0.962727i	$-0.587181\pi$
$439$	−25.9695	−	14.9935i	−1.23946	−	0.715601i	−0.968983	+	0.247126i	$0.920514\pi$
$440$	4.68804	+	2.05027i	0.223494	+	0.0977428i
$441$		0			0
$442$	7.29615	+	10.0423i	0.347043	+	0.477663i
$443$	−6.55910	+	30.8582i	−0.311632	+	1.46612i	0.491794	+	0.870711i	$0.336341\pi$
$443$	−6.55910	+	30.8582i	−0.311632	+	1.46612i	−0.803427	+	0.595404i	$0.796992\pi$
$444$		0			0
$445$	1.29219	−	12.2943i	0.0612555	−	0.582807i
$446$	−3.05986	+	29.1127i	−0.144889	+	1.37852i
$447$		0			0
$448$	1.70357	−	8.01468i	0.0804862	−	0.378658i
$449$	22.3362	+	30.7432i	1.05411	+	1.45086i	0.885190	+	0.465229i	$0.154028\pi$
$449$	22.3362	+	30.7432i	1.05411	+	1.45086i	0.168921	+	0.985630i	$0.445972\pi$
$450$		0			0
$451$	7.55911	+	34.4430i	0.355944	+	1.62186i
$452$	3.57797	+	2.06574i	0.168294	+	0.0971644i
$453$		0			0
$454$	−17.8660	+	19.8422i	−0.838493	+	0.931241i
$455$	3.70108	+	17.4122i	0.173509	+	0.816297i
$456$		0			0
$457$	−15.9546	−	35.8347i	−0.746327	−	1.67628i	−0.736603	−	0.676325i	$-0.763571\pi$
$457$	−15.9546	−	35.8347i	−0.746327	−	1.67628i	−0.00972362	−	0.999953i	$-0.503095\pi$
$458$	−12.4473	+	38.3088i	−0.581624	+	1.79005i
$459$		0			0
$460$	2.49706	−	1.81422i	0.116426	−	0.0845885i
$461$	−8.77604	+	15.2006i	−0.408741	+	0.707960i	−0.994749	−	0.102345i	$-0.967365\pi$
$461$	−8.77604	+	15.2006i	−0.408741	+	0.707960i	0.586008	+	0.810305i	$0.300699\pi$
$462$		0			0
$463$	−2.53619	−	4.39282i	−0.117867	−	0.204151i	0.801055	−	0.598590i	$-0.204272\pi$
$463$	−2.53619	−	4.39282i	−0.117867	−	0.204151i	−0.918922	+	0.394439i	$0.870939\pi$
$464$	−7.61398	−	3.38996i	−0.353470	−	0.157375i
$465$		0			0
$466$	−6.27521	−	6.96932i	−0.290693	−	0.322848i
$467$	−9.96792	+	13.7197i	−0.461260	+	0.634870i	−0.974770	−	0.223214i	$-0.928345\pi$
$467$	−9.96792	+	13.7197i	−0.461260	+	0.634870i	0.513509	+	0.858084i	$0.328345\pi$
$468$		0			0
$469$	9.69445	+	3.14992i	0.447648	+	0.145450i
$470$	6.96389	+	1.48022i	0.321220	+	0.0682774i
$471$		0			0
$472$	−0.0351352	+	0.0202853i	−0.00161723	+	0.000933706i
$473$	−11.4509	+	5.18915i	−0.526515	+	0.238597i
$474$		0			0
$475$	16.1544	−	1.69790i	0.741215	−	0.0779048i
$476$	13.3036	−	4.32260i	0.609769	−	0.198126i
$477$		0			0
$478$	20.0601	+	14.5745i	0.917526	+	0.666622i
$479$	−16.5165	+	7.35362i	−0.754658	+	0.335996i	−0.747750	−	0.663981i	$-0.768866\pi$
$479$	−16.5165	+	7.35362i	−0.754658	+	0.335996i	−0.00690859	+	0.999976i	$0.502199\pi$
$480$		0			0
$481$	2.53774	+	2.28499i	0.115711	+	0.104187i
$482$	5.20495	−	11.6905i	0.237079	−	0.532488i
$483$		0			0
$484$	7.27040	+	12.2172i	0.330473	+	0.555329i
$485$		−	17.4295i		−	0.791435i
$486$		0			0
$487$	−8.03498	−	24.7291i	−0.364100	−	1.12058i	−0.950543	−	0.310594i	$-0.899472\pi$
$487$	−8.03498	−	24.7291i	−0.364100	−	1.12058i	0.586443	−	0.809991i	$-0.300528\pi$
$488$	1.13281	−	1.01999i	0.0512798	−	0.0461726i
$489$		0			0
$490$	35.6435	+	3.74628i	1.61021	+	0.169240i
$491$	−7.17172	+	1.52440i	−0.323655	+	0.0687950i	−0.366874	−	0.930271i	$-0.619572\pi$
$491$	−7.17172	+	1.52440i	−0.323655	+	0.0687950i	0.0432191	+	0.999066i	$0.486239\pi$
$492$		0			0
$493$	−0.396312	−	3.77066i	−0.0178490	−	0.169822i
$494$	25.3622			1.14110
$495$		0			0
$496$	−26.1057			−1.17218
$497$	−1.94582	−	18.5132i	−0.0872818	−	0.830431i
$498$		0			0
$499$	9.21321	−	1.95833i	0.412440	−	0.0876668i	0.00298137	−	0.999996i	$-0.499051\pi$
$499$	9.21321	−	1.95833i	0.412440	−	0.0876668i	0.409458	+	0.912329i	$0.365718\pi$
$500$	13.2153	+	1.38898i	0.591007	+	0.0621173i
$501$		0			0
$502$	9.07311	−	8.16946i	0.404953	−	0.364621i
$503$	−10.3211	−	31.7652i	−0.460196	−	1.41634i	−0.864925	−	0.501902i	$-0.832634\pi$
$503$	−10.3211	−	31.7652i	−0.460196	−	1.41634i	0.404728	−	0.914437i	$-0.367366\pi$
$504$		0			0
$505$			19.3294i			0.860149i
$506$	−11.9599	+	0.0789666i	−0.531681	+	0.00351050i
$507$		0			0
$508$	11.7239	−	26.3322i	0.520162	−	1.16830i
$509$	−15.2373	−	13.7197i	−0.675379	−	0.608114i	0.258368	−	0.966047i	$-0.416815\pi$
$509$	−15.2373	−	13.7197i	−0.675379	−	0.608114i	−0.933748	+	0.357932i	$0.883482\pi$
$510$		0			0
$511$	31.1557	−	13.8714i	1.37825	−	0.613636i
$512$	15.0364	+	10.9246i	0.664521	+	0.482803i
$513$		0			0
$514$	−24.4213	+	7.93496i	−1.07718	+	0.349996i
$515$	2.48714	−	0.261409i	0.109597	−	0.0115191i
$516$		0			0
$517$	−7.29928	−	7.99981i	−0.321022	−	0.351831i
$518$	8.48982	−	4.90160i	0.373021	−	0.215364i
$519$		0			0
$520$	−4.61766	−	0.981513i	−0.202498	−	0.0430422i
$521$	−12.4115	−	4.03273i	−0.543757	−	0.176677i	0.0242430	−	0.999706i	$-0.492282\pi$
$521$	−12.4115	−	4.03273i	−0.543757	−	0.176677i	−0.568000	+	0.823029i	$0.692282\pi$
$522$		0			0
$523$	−4.85832	+	6.68690i	−0.212439	+	0.292398i	−0.901917	−	0.431909i	$-0.857840\pi$
$523$	−4.85832	+	6.68690i	−0.212439	+	0.292398i	0.689478	+	0.724307i	$0.257840\pi$
$524$	−13.4039	−	14.8866i	−0.585553	−	0.650322i
$525$		0			0
$526$	11.5137	+	5.12621i	0.502020	+	0.223514i
$527$	−5.93780	−	10.2846i	−0.258655	−	0.448003i
$528$		0			0
$529$	−9.52516	+	16.4981i	−0.414138	+	0.717307i
$530$	−2.25067	+	1.63521i	−0.0977628	+	0.0710289i
$531$		0			0
$532$	8.83197	−	27.1820i	0.382915	−	1.17849i
$533$	−13.2328	−	29.7213i	−0.573174	−	1.28737i
$534$		0			0
$535$	−0.104587	−	0.492045i	−0.00452171	−	0.0212730i
$536$	−1.80882	+	2.00890i	−0.0781292	+	0.0867712i
$537$		0			0
$538$	10.8502	+	6.26435i	0.467784	+	0.270075i
$539$	−40.7532	−	36.2100i	−1.75537	−	1.55968i
$540$		0			0
$541$	5.73469	+	7.89312i	0.246554	+	0.339352i	0.914301	−	0.405036i	$-0.132741\pi$
$541$	5.73469	+	7.89312i	0.246554	+	0.339352i	−0.667747	+	0.744388i	$0.732741\pi$
$542$	5.14010	−	24.1823i	0.220786	−	1.03872i
$543$		0			0
$544$	−1.48382	+	14.1176i	−0.0636183	+	0.605287i
$545$	1.84375	−	17.5421i	0.0789777	−	0.751423i
$546$		0			0
$547$	−1.61861	+	7.61497i	−0.0692068	+	0.325592i	−0.999109	−	0.0422157i	$-0.986558\pi$
$547$	−1.61861	+	7.61497i	−0.0692068	+	0.325592i	0.929902	+	0.367808i	$0.119892\pi$
$548$	13.0215	+	17.9225i	0.556250	+	0.765613i
$549$		0			0
$550$	−15.9978	−	14.2143i	−0.682147	−	0.606100i
$551$	−6.70882	−	3.87334i	−0.285805	−	0.165010i
$552$		0			0
$553$	12.3784	−	13.7476i	0.526381	−	0.584605i
$554$	4.39704	+	20.6864i	0.186812	+	0.878883i
$555$		0			0
$556$	−5.45021	−	12.2414i	−0.231140	−	0.519149i
$557$	1.09093	−	3.35755i	0.0462244	−	0.142264i	−0.925281	−	0.379283i	$-0.876171\pi$
$557$	1.09093	−	3.35755i	0.0462244	−	0.142264i	0.971505	+	0.237019i	$0.0761705\pi$
$558$		0			0
$559$	9.38378	−	6.81772i	0.396892	−	0.288359i
$560$	−14.2948	+	24.7594i	−0.604067	+	1.04627i
$561$		0			0
$562$	19.8149	+	34.3204i	0.835841	+	1.44772i
$563$	1.37274	+	0.611183i	0.0578540	+	0.0257583i	0.435460	−	0.900208i	$-0.356586\pi$
$563$	1.37274	+	0.611183i	0.0578540	+	0.0257583i	−0.377606	+	0.925966i	$0.623253\pi$
$564$		0			0
$565$	−2.57031	−	2.85461i	−0.108134	−	0.120095i
$566$	−25.0367	+	34.4601i	−1.05237	+	1.44847i
$567$		0			0
$568$	4.69506	+	1.52552i	0.197000	+	0.0640093i
$569$	14.5137	+	3.08499i	0.608447	+	0.129329i	0.501823	−	0.864970i	$-0.332663\pi$
$569$	14.5137	+	3.08499i	0.608447	+	0.129329i	0.106624	+	0.994299i	$0.465996\pi$
$570$		0			0
$571$	−25.8594	+	14.9299i	−1.08218	+	0.624798i	−0.931484	−	0.363782i	$-0.881485\pi$
$571$	−25.8594	+	14.9299i	−1.08218	+	0.624798i	−0.150697	+	0.988580i	$0.548152\pi$
$572$	−8.84097	−	9.68946i	−0.369659	−	0.405137i
$573$		0			0
$574$	−92.8850	+	9.76261i	−3.87695	+	0.407483i
$575$	6.72128	−	2.18388i	0.280297	−	0.0910740i
$576$		0			0
$577$	−20.6394	−	14.9954i	−0.859228	−	0.624266i	0.0684465	−	0.997655i	$-0.478196\pi$
$577$	−20.6394	−	14.9954i	−0.859228	−	0.624266i	−0.927675	+	0.373389i	$0.878196\pi$
$578$	19.8949	−	8.85780i	0.827520	−	0.368436i
$579$		0			0
$580$	−1.95735	−	1.76240i	−0.0812745	−	0.0731799i
$581$	−14.3138	+	32.1494i	−0.593838	+	1.33378i
$582$		0			0
$583$	4.23158	−	0.0279396i	0.175254	−	0.00115714i
$584$			9.04432i			0.374256i
$585$		0			0
$586$	−0.951344	−	2.92793i	−0.0392996	−	0.120952i
$587$	17.5588	−	15.8100i	0.724731	−	0.652550i	−0.221827	−	0.975086i	$-0.571202\pi$
$587$	17.5588	−	15.8100i	0.724731	−	0.652550i	0.946557	+	0.322536i	$0.104535\pi$
$588$		0			0
$589$	−24.1314	−	2.53631i	−0.994317	−	0.104507i
$590$	−0.0673959	+	0.0143254i	−0.00277465	+	0.000589769i
$591$		0			0
$592$	0.573282	+	5.45441i	0.0235617	+	0.224175i
$593$	−10.1681			−0.417553			−0.208777	−	0.977963i	$-0.566948\pi$
$593$	−10.1681			−0.417553			−0.208777	+	0.977963i	$0.566948\pi$
$594$		0			0
$595$	−13.0056			−0.533178
$596$	0.00546573	+	0.0520029i	0.000223885	+	0.00213012i
$597$		0			0
$598$	10.7935	−	2.29423i	0.441378	−	0.0938179i
$599$	−6.06202	−	0.637144i	−0.247687	−	0.0260330i	−0.0201288	−	0.999797i	$-0.506408\pi$
$599$	−6.06202	−	0.637144i	−0.247687	−	0.0260330i	−0.227559	+	0.973764i	$0.573074\pi$
$600$		0			0
$601$	−10.4219	+	9.38389i	−0.425117	+	0.382777i	−0.853734	−	0.520709i	$-0.825667\pi$
$601$	−10.4219	+	9.38389i	−0.425117	+	0.382777i	0.428617	+	0.903486i	$0.359001\pi$
$602$	−10.2896	−	31.6680i	−0.419371	−	1.29069i
$603$		0			0
$604$		−	3.55632i		−	0.144705i
$605$	−2.91870	−	12.8919i	−0.118662	−	0.524131i
$606$		0			0
$607$	−0.344302	+	0.773316i	−0.0139748	+	0.0313879i	−0.920398	−	0.390983i	$-0.872135\pi$
$607$	−0.344302	+	0.773316i	−0.0139748	+	0.0313879i	0.906423	+	0.422371i	$0.138802\pi$
$608$	21.5542	+	19.4075i	0.874140	+	0.787079i
$609$		0			0
$610$	2.36500	−	1.05297i	0.0957560	−	0.0426333i
$611$	8.08321	+	5.87280i	0.327012	+	0.237588i
$612$		0			0
$613$	−24.1513	+	7.84724i	−0.975462	+	0.316947i	−0.753019	−	0.657999i	$-0.771403\pi$
$613$	−24.1513	+	7.84724i	−0.975462	+	0.316947i	−0.222443	+	0.974946i	$0.571403\pi$
$614$	−4.24581	+	0.446253i	−0.171347	+	0.0180093i
$615$		0			0
$616$	18.7764	−	8.50876i	0.756521	−	0.342828i
$617$	−8.73291	+	5.04195i	−0.351574	+	0.202981i	−0.665378	−	0.746507i	$-0.731730\pi$
$617$	−8.73291	+	5.04195i	−0.351574	+	0.202981i	0.313805	+	0.949488i	$0.398396\pi$
$618$		0			0
$619$	25.4818	+	5.41633i	1.02420	+	0.217701i	0.689241	−	0.724532i	$-0.257944\pi$
$619$	25.4818	+	5.41633i	1.02420	+	0.217701i	0.334960	+	0.942232i	$0.391277\pi$
$620$	−7.84611	−	2.54935i	−0.315107	−	0.102385i
$621$		0			0
$622$	11.3121	−	15.5698i	0.453574	−	0.624291i
$623$	−33.3253	−	37.0115i	−1.33515	−	1.48284i
$624$		0			0
$625$	4.95643	+	2.20675i	0.198257	+	0.0882698i
$626$	−22.9845	−	39.8103i	−0.918646	−	1.59114i
$627$		0			0
$628$	−1.36344	+	2.36155i	−0.0544073	+	0.0942362i
$629$	−2.01842	+	1.46647i	−0.0804798	+	0.0584720i
$630$		0			0
$631$	3.44605	−	10.6058i	0.137185	−	0.422212i	−0.858739	−	0.512414i	$-0.828751\pi$
$631$	3.44605	−	10.6058i	0.137185	−	0.422212i	0.995923	+	0.0902022i	$0.0287513\pi$
$632$	1.99541	+	4.48177i	0.0793733	+	0.178275i
$633$		0			0
$634$	−10.1152	−	47.5883i	−0.401726	−	1.88997i
$635$	−17.9323	+	19.9158i	−0.711621	+	0.790335i
$636$		0			0
$637$	43.5588	+	25.1487i	1.72586	+	0.996426i
$638$	2.18783	+	9.96884i	0.0866172	+	0.394670i
$639$		0			0
$640$	−6.80053	−	9.36013i	−0.268815	−	0.369991i
$641$	−2.29516	+	10.7979i	−0.0906534	+	0.426491i	0.909293	+	0.416156i	$0.136623\pi$
$641$	−2.29516	+	10.7979i	−0.0906534	+	0.426491i	−0.999947	+	0.0103346i	$0.996710\pi$
$642$		0			0
$643$	−3.84039	+	36.5389i	−0.151450	+	1.44095i	0.609831	+	0.792532i	$0.291237\pi$
$643$	−3.84039	+	36.5389i	−0.151450	+	1.44095i	−0.761281	+	0.648422i	$0.775429\pi$
$644$	1.29981	−	12.3669i	0.0512196	−	0.487322i
$645$		0			0
$646$	−3.85255	+	18.1248i	−0.151576	+	0.713111i
$647$	1.59821	+	2.19975i	0.0628321	+	0.0864810i	0.839277	−	0.543705i	$-0.182979\pi$
$647$	1.59821	+	2.19975i	0.0628321	+	0.0864810i	−0.776445	+	0.630186i	$0.782979\pi$
$648$		0			0
$649$	0.0960246	+	0.0419955i	0.00376930	+	0.00164847i
$650$	17.0991	+	9.87215i	0.670681	+	0.387218i
$651$		0			0
$652$	12.6230	−	14.0192i	0.494353	−	0.549035i
$653$	−9.19912	−	43.2784i	−0.359989	−	1.69362i	−0.669575	−	0.742745i	$-0.733524\pi$
$653$	−9.19912	−	43.2784i	−0.359989	−	1.69362i	0.309586	−	0.950872i	$-0.399810\pi$
$654$		0			0
$655$	7.57534	+	17.0145i	0.295993	+	0.664811i
$656$	16.1465	−	49.6939i	0.630416	−	1.94022i
$657$		0			0
$658$	23.2048	−	16.8593i	0.904618	−	0.657244i
$659$	4.58714	−	7.94516i	0.178690	−	0.309499i	−0.762742	−	0.646702i	$-0.776148\pi$
$659$	4.58714	−	7.94516i	0.178690	−	0.309499i	0.941432	+	0.337203i	$0.109481\pi$
$660$		0			0
$661$	4.94816	+	8.57046i	0.192461	+	0.333352i	0.946065	−	0.323976i	$-0.105020\pi$
$661$	4.94816	+	8.57046i	0.192461	+	0.333352i	−0.753604	+	0.657328i	$0.771686\pi$
$662$	28.7164	+	12.7854i	1.11610	+	0.496918i
$663$		0			0
$664$	−6.24484	−	6.93560i	−0.242347	−	0.269153i
$665$	−15.6193	+	21.4981i	−0.605691	+	0.833662i
$666$		0			0
$667$	−3.20547	−	1.04152i	−0.124116	−	0.0403278i
$668$	1.12801	+	0.239766i	0.0436440	+	0.00927682i
$669$		0			0
$670$	−3.97588	+	2.29547i	−0.153602	+	0.0886819i
$671$	−3.85712	−	0.793275i	−0.148902	−	0.0306241i
$672$		0			0
$673$	17.5860	−	1.84836i	0.677891	−	0.0712492i	0.240675	−	0.970606i	$-0.422631\pi$
$673$	17.5860	−	1.84836i	0.677891	−	0.0712492i	0.437216	+	0.899357i	$0.355965\pi$
$674$	−22.4408	+	7.29146i	−0.864387	+	0.280856i
$675$		0			0
$676$	−3.80243	−	2.76263i	−0.146247	−	0.106255i
$677$	10.8673	−	4.83844i	0.417665	−	0.185956i	−0.187134	−	0.982334i	$-0.559920\pi$
$677$	10.8673	−	4.83844i	0.417665	−	0.185956i	0.604799	+	0.796378i	$0.293253\pi$
$678$		0			0
$679$	−52.1835	−	46.9862i	−2.00262	−	1.80316i
$680$	1.40285	−	3.15085i	0.0537969	−	0.120830i
$681$		0			0
$682$	18.9605	+	25.7379i	0.726037	+	0.985554i
$683$			18.2564i			0.698561i	0.937018	+	0.349280i	$0.113574\pi$
$683$			18.2564i			0.698561i	−0.937018	+	0.349280i	$0.886426\pi$
$684$		0			0
$685$	−6.36490	−	19.5892i	−0.243190	−	0.748463i
$686$	61.6066	−	55.4709i	2.35215	−	2.11789i
$687$		0			0
$688$	18.5265	+	1.94722i	0.706318	+	0.0742370i
$689$	−3.81889	+	0.811731i	−0.145488	+	0.0309245i
$690$		0			0
$691$	−1.88403	−	17.9254i	−0.0716720	−	0.681914i	−0.970086	−	0.242763i	$-0.921946\pi$
$691$	−1.88403	−	17.9254i	−0.0716720	−	0.681914i	0.898414	−	0.439150i	$-0.144721\pi$
$692$	−17.1216			−0.650864
$693$		0			0
$694$	38.5698			1.46409
$695$	1.30227	+	12.3903i	0.0493980	+	0.469991i
$696$		0			0
$697$	23.2500	−	4.94193i	0.880655	−	0.187189i
$698$	−16.8384	−	1.76979i	−0.637343	−	0.0669875i
$699$		0			0
$700$	16.5350	−	14.8881i	0.624962	−	0.562719i
$701$	−2.60431	−	8.01524i	−0.0983635	−	0.302732i	0.889752	−	0.456444i	$-0.150877\pi$
$701$	−2.60431	−	8.01524i	−0.0983635	−	0.302732i	−0.988116	+	0.153712i	$0.950877\pi$
$702$		0			0
$703$			5.09762i			0.192260i
$704$	−0.0370623	−	5.61327i	−0.00139684	−	0.211558i
$705$		0			0
$706$	6.73185	−	15.1200i	0.253356	−	0.569048i
$707$	57.8717	+	52.1079i	2.17649	+	1.95972i
$708$		0			0
$709$	18.9224	−	8.42480i	0.710646	−	0.316400i	−0.0193869	−	0.999812i	$-0.506171\pi$
$709$	18.9224	−	8.42480i	0.710646	−	0.316400i	0.730033	+	0.683412i	$0.239505\pi$
$710$	6.78282	+	4.92801i	0.254555	+	0.184945i
$711$		0			0
$712$	12.5614	−	4.08144i	0.470758	−	0.152959i
$713$	−10.4991	+	1.10350i	−0.393194	+	0.0413264i
$714$		0			0
$715$	5.03373	+	11.1080i	0.188251	+	0.415415i
$716$	−22.5476	+	13.0179i	−0.842644	+	0.486501i
$717$		0			0
$718$	−13.8817	−	2.95065i	−0.518061	−	0.110117i
$719$	−34.3009	−	11.1450i	−1.27921	−	0.415640i	−0.410906	−	0.911678i	$-0.634788\pi$
$719$	−34.3009	−	11.1450i	−1.27921	−	0.415640i	−0.868301	+	0.496038i	$0.834788\pi$
$720$		0			0
$721$	5.92214	−	8.15112i	0.220552	−	0.303564i
$722$	2.26460	+	2.51510i	0.0842798	+	0.0936022i
$723$		0			0
$724$	−5.30880	−	2.36363i	−0.197300	−	0.0878437i
$725$	−3.01536	−	5.22276i	−0.111988	−	0.193968i
$726$		0			0
$727$	10.4928	−	18.1741i	0.389158	−	0.674042i	−0.603178	−	0.797606i	$-0.706099\pi$
$727$	10.4928	−	18.1741i	0.389158	−	0.674042i	0.992337	+	0.123565i	$0.0394327\pi$
$728$	−15.3868	+	11.1792i	−0.570273	+	0.414327i
$729$		0			0
$730$	−4.74653	+	14.6083i	−0.175677	+	0.540678i
$731$	3.44679	+	7.74161i	0.127484	+	0.286334i
$732$		0			0
$733$	−8.44604	−	39.7355i	−0.311962	−	1.46766i	−0.802714	−	0.596364i	$-0.796611\pi$
$733$	−8.44604	−	39.7355i	−0.311962	−	1.46766i	0.490752	−	0.871299i	$-0.336722\pi$
$734$	−29.7517	+	33.0426i	−1.09816	+	1.21963i
$735$		0			0
$736$	10.9285	+	6.30956i	0.402829	+	0.232573i
$737$	6.94971	+	0.684083i	0.255996	+	0.0251985i
$738$		0			0
$739$	−0.159730	−	0.219850i	−0.00587578	−	0.00808731i	0.806069	−	0.591822i	$-0.201591\pi$
$739$	−0.159730	−	0.219850i	−0.00587578	−	0.00808731i	−0.811945	+	0.583734i	$0.801591\pi$
$740$	−0.360351	+	1.69532i	−0.0132468	+	0.0623212i
$741$		0			0
$742$	−1.17155	+	11.1466i	−0.0430091	+	0.409204i
$743$	2.14939	−	20.4500i	0.0788533	−	0.750239i	−0.881637	−	0.471927i	$-0.843558\pi$
$743$	2.14939	−	20.4500i	0.0788533	−	0.750239i	0.960491	−	0.278312i	$-0.0897749\pi$
$744$		0			0
$745$	0.0101079	−	0.0475538i	0.000370324	−	0.00174224i
$746$	3.05169	+	4.20029i	0.111730	+	0.153783i
$747$		0			0
$748$	8.26740	−	4.84624i	0.302286	−	0.177196i
$749$	−1.75511	−	1.01331i	−0.0641304	−	0.0370257i
$750$		0			0
$751$	−34.8745	+	38.7320i	−1.27259	+	1.41335i	−0.406351	+	0.913717i	$0.633199\pi$
$751$	−34.8745	+	38.7320i	−1.27259	+	1.41335i	−0.866237	+	0.499634i	$0.833468\pi$
$752$	3.33630	+	15.6961i	0.121662	+	0.572376i
$753$		0			0
$754$	−3.82996	−	8.60223i	−0.139479	−	0.313275i
$755$	−1.02176	+	3.14467i	−0.0371858	+	0.114446i
$756$		0			0
$757$	30.2153	−	21.9527i	1.09819	−	0.797884i	0.117429	−	0.993081i	$-0.462535\pi$
$757$	30.2153	−	21.9527i	1.09819	−	0.797884i	0.980764	+	0.195197i	$0.0625347\pi$
$758$	−26.5495	+	45.9851i	−0.964322	+	1.67025i
$759$		0			0
$760$	−3.52355	−	6.10297i	−0.127813	−	0.221378i
$761$	40.7814	+	18.1571i	1.47833	+	0.658193i	0.978182	−	0.207749i	$-0.0666138\pi$
$761$	40.7814	+	18.1571i	1.47833	+	0.658193i	0.500144	+	0.865942i	$0.333280\pi$
$762$		0			0
$763$	−47.5502	−	52.8099i	−1.72143	−	1.91185i
$764$	−13.5025	+	18.5846i	−0.488503	+	0.672367i
$765$		0			0
$766$	−49.1124	−	15.9576i	−1.77450	−	0.576571i
$767$	−0.0945829	−	0.0201042i	−0.00341519	−	0.000725921i
$768$		0			0
$769$	−19.3337	+	11.1623i	−0.697192	+	0.402524i	−0.806301	−	0.591506i	$-0.798534\pi$
$769$	−19.3337	+	11.1623i	−0.697192	+	0.402524i	0.109109	+	0.994030i	$0.465200\pi$
$770$	34.7929	−	3.88931i	1.25385	−	0.140161i
$771$		0			0
$772$	7.91650	−	0.832058i	0.284921	−	0.0299464i
$773$	19.1268	−	6.21468i	0.687944	−	0.223526i	0.0558738	−	0.998438i	$-0.482206\pi$
$773$	19.1268	−	6.21468i	0.687944	−	0.223526i	0.632070	+	0.774911i	$0.282206\pi$
$774$		0			0
$775$	−15.2820	−	11.1030i	−0.548946	−	0.398832i
$776$	17.0121	−	7.57426i	0.610698	−	0.271900i
$777$		0			0
$778$	−19.2577	−	17.3397i	−0.690423	−	0.621659i
$779$	19.7535	−	44.3671i	0.707742	−	1.58962i
$780$		0			0
$781$	−4.02087	−	12.1025i	−0.143878	−	0.433061i
$782$			8.06192i			0.288294i
$783$		0			0
$784$	24.9624	+	76.8265i	0.891516	+	2.74380i
$785$	1.88412	−	1.69647i	0.0672471	−	0.0605495i
$786$		0			0
$787$	34.6278	+	3.63953i	1.23435	+	0.129735i	0.699139	−	0.714985i	$-0.253567\pi$
$787$	34.6278	+	3.63953i	1.23435	+	0.129735i	0.535208	+	0.844721i	$0.320233\pi$
$788$	28.4572	−	6.04876i	1.01374	−	0.215478i
$789$		0			0
$790$	0.870908	+	8.28613i	0.0309855	+	0.294807i
$791$	−15.4756			−0.550249
$792$		0			0
$793$	3.63312			0.129016
$794$	0.418572	+	3.98245i	0.0148546	+	0.141332i
$795$		0			0
$796$	−11.7657	+	2.50087i	−0.417023	+	0.0886409i
$797$	−0.782420	−	0.0822356i	−0.0277147	−	0.00291294i	0.0906609	−	0.995882i	$-0.471102\pi$
$797$	−0.782420	−	0.0822356i	−0.0277147	−	0.00291294i	−0.118376	+	0.992969i	$0.537769\pi$
$798$		0			0
$799$	−5.42477	+	4.88448i	−0.191914	+	0.172800i
$800$	6.97744	+	21.4743i	0.246690	+	0.759233i
$801$		0			0
$802$			57.2351i			2.02104i
$803$	18.8110	−	13.8577i	0.663825	−	0.489026i
$804$		0			0
$805$	−4.70247	+	10.5619i	−0.165740	+	0.372259i
$806$	−21.9183	−	19.7353i	−0.772040	−	0.695148i
$807$		0			0
$808$	−18.8665	+	8.39990i	−0.663720	+	0.295507i
$809$	24.9035	+	18.0934i	0.875560	+	0.636131i	0.932073	−	0.362270i	$-0.117998\pi$
$809$	24.9035	+	18.0934i	0.875560	+	0.636131i	−0.0565132	+	0.998402i	$0.517998\pi$
$810$		0			0
$811$	41.4535	−	13.4691i	1.45563	−	0.472963i	0.528898	−	0.848686i	$-0.322606\pi$
$811$	41.4535	−	13.4691i	1.45563	−	0.472963i	0.926732	+	0.375723i	$0.122606\pi$
$812$	−10.5532	+	1.10918i	−0.370343	+	0.0389247i
$813$		0			0
$814$	4.96119	−	4.52675i	0.173890	−	0.158662i
$815$	−15.1897	+	8.76976i	−0.532071	+	0.307191i
$816$		0			0
$817$	16.9363	+	3.59992i	0.592526	+	0.125945i
$818$	−11.6971	−	3.80063i	−0.408981	−	0.132886i
$819$		0			0
$820$	9.70574	−	13.3588i	0.338939	−	0.466510i
$821$	26.0695	+	28.9531i	0.909833	+	1.01047i	0.999894	+	0.0145354i	$0.00462691\pi$
$821$	26.0695	+	28.9531i	0.909833	+	1.01047i	−0.0900617	+	0.995936i	$0.528706\pi$
$822$		0			0
$823$	34.3311	+	15.2852i	1.19671	+	0.532809i	0.905703	−	0.423913i	$-0.139344\pi$
$823$	34.3311	+	15.2852i	1.19671	+	0.532809i	0.291005	+	0.956721i	$0.406010\pi$
$824$	1.33597	+	2.31397i	0.0465408	+	0.0806111i
$825$		0			0
$826$	−0.138795	+	0.240399i	−0.00482928	+	0.00836456i
$827$	36.8905	−	26.8025i	1.28281	−	0.932015i	0.283175	−	0.959068i	$-0.408612\pi$
$827$	36.8905	−	26.8025i	1.28281	−	0.932015i	0.999634	+	0.0270532i	$0.00861234\pi$
$828$		0			0
$829$	8.83146	−	27.1804i	0.306729	−	0.944016i	−0.672297	−	0.740282i	$-0.734692\pi$
$829$	8.83146	−	27.1804i	0.306729	−	0.944016i	0.979026	−	0.203734i	$-0.0653078\pi$
$830$	−6.44676	−	14.4797i	−0.223770	−	0.502596i
$831$		0			0
$832$	1.07678	+	5.06583i	0.0373305	+	0.175626i
$833$	−24.5888	+	27.3086i	−0.851950	+	0.946187i
$834$		0			0
$835$	−0.928554	−	0.536101i	−0.0321339	−	0.0185525i
$836$	1.91808	−	19.4861i	0.0663382	−	0.673941i
$837$		0			0
$838$	30.5125	+	41.9968i	1.05404	+	1.45076i
$839$	1.18333	−	5.56715i	0.0408532	−	0.192199i	−0.952989	−	0.303005i	$-0.902010\pi$
$839$	1.18333	−	5.56715i	0.0408532	−	0.192199i	0.993842	+	0.110806i	$0.0353433\pi$
$840$		0			0
$841$	2.73069	−	25.9808i	0.0941617	−	0.895888i
$842$	−1.06087	+	10.0935i	−0.0365599	+	0.347844i
$843$		0			0
$844$	−3.76499	+	17.7129i	−0.129596	+	0.609703i
$845$	2.56856	+	3.53532i	0.0883612	+	0.121619i
$846$		0			0
$847$	−46.4662	−	26.0153i	−1.59660	−	0.893895i
$848$	−5.43030	−	3.13518i	−0.186477	−	0.107663i
$849$		0			0
$850$	−9.65237	+	10.7200i	−0.331074	+	0.367694i
$851$	0.461122	+	2.16941i	0.0158071	+	0.0743664i
$852$		0			0
$853$	10.1942	+	22.8965i	0.349042	+	0.783962i	0.999698	+	0.0245888i	$0.00782763\pi$
$853$	10.1942	+	22.8965i	0.349042	+	0.783962i	−0.650655	+	0.759373i	$0.725506\pi$
$854$	3.22297	−	9.91929i	0.110288	−	0.339431i
$855$		0			0
$856$	0.434810	−	0.315908i	0.0148615	−	0.0107975i
$857$	−17.9582	+	31.1045i	−0.613440	+	1.06251i	0.377216	+	0.926126i	$0.376882\pi$
$857$	−17.9582	+	31.1045i	−0.613440	+	1.06251i	−0.990656	+	0.136385i	$0.956452\pi$
$858$		0			0
$859$	7.86620	+	13.6247i	0.268391	+	0.464868i	0.968447	−	0.249221i	$-0.0801746\pi$
$859$	7.86620	+	13.6247i	0.268391	+	0.464868i	−0.700055	+	0.714089i	$0.746841\pi$
$860$	5.37803	+	2.39445i	0.183389	+	0.0816502i
$861$		0			0
$862$	23.6858	+	26.3058i	0.806742	+	0.895978i
$863$	16.0883	−	22.1436i	0.547652	−	0.753778i	−0.442039	−	0.896996i	$-0.645745\pi$
$863$	16.0883	−	22.1436i	0.547652	−	0.753778i	0.989691	+	0.143217i	$0.0457448\pi$
$864$		0			0
$865$	15.1397	+	4.91919i	0.514765	+	0.167257i
$866$	−40.0281	−	8.50823i	−1.36021	−	0.289121i
$867$		0			0
$868$	−28.7841	+	16.6185i	−0.976995	+	0.564068i
$869$	6.26413	−	11.0171i	0.212496	−	0.373731i
$870$		0			0
$871$	−6.40761	+	0.673467i	−0.217114	+	0.0228196i
$872$	17.9232	−	5.82361i	0.606957	−	0.197212i
$873$		0			0
$874$	13.3263	+	9.68210i	0.450768	+	0.327502i
$875$	−45.4710	+	20.2450i	−1.53720	+	0.684405i
$876$		0			0
$877$	−38.6754	−	34.8235i	−1.30597	−	1.17590i	−0.972437	−	0.233168i	$-0.925091\pi$
$877$	−38.6754	−	34.8235i	−1.30597	−	1.17590i	−0.333538	−	0.942737i	$-0.608242\pi$
$878$	22.1312	−	49.7076i	0.746893	−	1.67755i
$879$		0			0
$880$	−5.92938	+	18.6673i	−0.199880	+	0.629273i
$881$		−	39.9758i		−	1.34682i	−0.739270	−	0.673409i	$-0.764829\pi$
$881$		−	39.9758i		−	1.34682i	0.739270	−	0.673409i	$-0.235171\pi$
$882$		0			0
$883$	−5.74452	−	17.6798i	−0.193318	−	0.594973i	−0.999992	−	0.00397571i	$-0.998734\pi$
$883$	−5.74452	−	17.6798i	−0.193318	−	0.594973i	0.806674	−	0.590997i	$-0.201266\pi$
$884$	−6.57054	+	5.91614i	−0.220991	+	0.198981i
$885$		0			0
$886$	−56.9297	−	5.98356i	−1.91259	−	0.201021i
$887$	−53.3355	+	11.3368i	−1.79083	+	0.380653i	−0.979100	−	0.203379i	$-0.934808\pi$
$887$	−53.3355	+	11.3368i	−1.79083	+	0.380653i	−0.811731	+	0.584032i	$0.801474\pi$
$888$		0			0
$889$	11.2858	+	107.377i	0.378514	+	3.60132i
$890$	22.4310			0.751890
$891$		0			0
$892$	−20.8507			−0.698132
$893$	1.55903	+	14.8332i	0.0521710	+	0.496374i
$894$		0			0
$895$	23.6779	−	5.03288i	0.791463	−	0.168231i
$896$	−46.3566	−	4.87228i	−1.54867	−	0.162771i
$897$		0			0
$898$	−51.2417	+	46.1382i	−1.70996	+	1.53965i
$899$	2.78384	+	8.56777i	0.0928461	+	0.285751i
$900$		0			0
$901$		−	2.85243i		−	0.0950281i
$902$	−60.7210	+	20.1737i	−2.02179	+	0.671709i
$903$		0			0
$904$	1.66928	−	3.74926i	0.0555193	−	0.124698i
$905$	4.01520	+	3.61531i	0.133470	+	0.120177i
$906$		0			0
$907$	−11.3582	+	5.05700i	−0.377143	+	0.167915i	−0.586549	−	0.809914i	$-0.699514\pi$
$907$	−11.3582	+	5.05700i	−0.377143	+	0.167915i	0.209406	+	0.977829i	$0.432847\pi$
$908$	−15.3860	−	11.1786i	−0.510603	−	0.370975i
$909$		0			0
$910$	−30.7195	+	9.98139i	−1.01834	+	0.330880i
$911$	44.7416	−	4.70253i	1.48235	−	0.155802i	0.671481	−	0.741022i	$-0.265659\pi$
$911$	44.7416	−	4.70253i	1.48235	−	0.155802i	0.810874	+	0.585220i	$0.198992\pi$
$912$		0			0
$913$	−4.85681	+	23.6151i	−0.160737	+	0.781546i
$914$	61.6402	−	35.5880i	2.03887	−	1.17715i
$915$		0			0
$916$	−28.0640	−	5.96518i	−0.927260	−	0.197095i
$917$	71.3622	+	23.1870i	2.35659	+	0.765702i
$918$		0			0
$919$	13.6185	−	18.7442i	0.449232	−	0.618315i	−0.523000	−	0.852333i	$-0.675187\pi$
$919$	13.6185	−	18.7442i	0.449232	−	0.618315i	0.972232	+	0.234017i	$0.0751872\pi$
$920$	−2.05159	−	2.27852i	−0.0676390	−	0.0751207i
$921$		0			0
$922$	−29.0950	−	12.9539i	−0.958192	−	0.426615i
$923$	5.88304	+	10.1897i	0.193643	+	0.335399i
$924$		0			0
$925$	−1.98423	+	3.43678i	−0.0652410	+	0.113001i
$926$	7.44610	−	5.40991i	0.244694	−	0.177781i
$927$		0			0
$928$	3.32763	−	10.2414i	0.109235	−	0.336190i
$929$	4.70492	+	10.5674i	0.154364	+	0.346706i	0.974129	−	0.225993i	$-0.0725628\pi$
$929$	4.70492	+	10.5674i	0.154364	+	0.346706i	−0.819765	+	0.572700i	$0.805896\pi$
$930$		0			0
$931$	15.6105	+	73.4417i	0.511614	+	2.40696i
$932$	4.46972	−	4.96413i	0.146411	−	0.162605i
$933$		0			0
$934$	−26.6487	−	15.3856i	−0.871971	−	0.503433i
$935$	−8.70280	+	1.90998i	−0.284612	+	0.0624630i
$936$		0			0
$937$	15.1544	+	20.8582i	0.495071	+	0.681407i	0.981313	−	0.192417i	$-0.0616326\pi$
$937$	15.1544	+	20.8582i	0.495071	+	0.681407i	−0.486242	+	0.873824i	$0.661633\pi$
$938$	−3.84552	+	18.0917i	−0.125561	+	0.590716i
$939$		0			0
$940$	−0.530071	+	5.04329i	−0.0172890	+	0.164494i
$941$	−6.18370	+	58.8340i	−0.201583	+	1.91793i	0.162756	+	0.986666i	$0.447962\pi$
$941$	−6.18370	+	58.8340i	−0.201583	+	1.91793i	−0.364339	+	0.931267i	$0.618705\pi$
$942$		0			0
$943$	4.39318	−	20.6683i	0.143062	−	0.673052i
$944$	−0.0912824	−	0.125639i	−0.00297099	−	0.00408921i
$945$		0			0
$946$	−11.5361	−	19.6798i	−0.375069	−	0.639845i
$947$	−0.104615	−	0.0603997i	−0.00339954	−	0.00196272i	0.498299	−	0.867005i	$-0.333958\pi$
$947$	−0.104615	−	0.0603997i	−0.00339954	−	0.00196272i	−0.501699	+	0.865042i	$0.667291\pi$
$948$		0			0
$949$	−14.4239	+	16.0194i	−0.468221	+	0.520012i
$950$	6.12794	+	28.8297i	0.198817	+	0.935359i
$951$		0			0
$952$	−5.65178	−	12.6941i	−0.183175	−	0.411418i
$953$	−2.50261	+	7.70223i	−0.0810674	+	0.249500i	−0.983373	−	0.181597i	$-0.941873\pi$
$953$	−2.50261	+	7.70223i	−0.0810674	+	0.249500i	0.902306	+	0.431097i	$0.141873\pi$
$954$		0			0
$955$	17.2791	−	12.5540i	0.559138	−	0.406237i
$956$	−8.83074	+	15.2953i	−0.285607	+	0.494685i
$957$		0			0
$958$	−16.4028	−	28.4104i	−0.529949	−	0.917899i
$959$	−75.8077	−	33.7517i	−2.44796	−	1.08990i
$960$		0			0
$961$	−1.86203	−	2.06800i	−0.0600656	−	0.0667096i
$962$	−3.64210	+	5.01292i	−0.117426	+	0.161623i
$963$		0			0
$964$	8.66885	+	2.81668i	0.279205	+	0.0907192i
$965$	−7.23921	−	1.53874i	−0.233038	−	0.0495338i
$966$		0			0
$967$	8.61320	−	4.97284i	0.276982	−	0.159916i	−0.355074	−	0.934838i	$-0.615544\pi$
$967$	8.61320	−	4.97284i	0.276982	−	0.159916i	0.632056	+	0.774922i	$0.282211\pi$
$968$	11.3148	−	8.45117i	0.363671	−	0.271631i
$969$		0			0
$970$	31.4528	−	3.30582i	1.00989	−	0.106144i
$971$	−36.6171	+	11.8976i	−1.17510	+	0.381813i	−0.830544	−	0.556953i	$-0.811970\pi$
$971$	−36.6171	+	11.8976i	−1.17510	+	0.381813i	−0.344555	+	0.938766i	$0.611970\pi$
$972$		0			0
$973$	40.6068	+	29.5025i	1.30179	+	0.945808i
$974$	43.1015	−	19.1900i	1.38106	−	0.614887i
$975$		0			0
$976$	4.33624	+	3.90437i	0.138800	+	0.124976i
$977$	8.26143	−	18.5555i	0.264307	−	0.593642i	−0.731827	−	0.681490i	$-0.761332\pi$
$977$	8.26143	−	18.5555i	0.264307	−	0.593642i	0.996134	+	0.0878477i	$0.0279989\pi$
$978$		0			0
$979$	−27.7354	−	19.8725i	−0.886426	−	0.635127i
$980$			25.5281i			0.815464i
$981$		0			0
$982$	−4.11112	−	12.6527i	−0.131191	−	0.403765i
$983$	7.22568	−	6.50603i	0.230464	−	0.207510i	−0.545806	−	0.837912i	$-0.683776\pi$
$983$	7.22568	−	6.50603i	0.230464	−	0.207510i	0.776269	+	0.630401i	$0.217110\pi$
$984$		0			0
$985$	−26.9011	−	2.82742i	−0.857139	−	0.0900889i
$986$	6.72924	−	1.43034i	0.214303	−	0.0455515i
$987$		0			0
$988$	1.88832	+	17.9661i	0.0600753	+	0.571579i
$989$	7.53327			0.239544
$990$		0			0
$991$	−22.9196			−0.728065			−0.364032	−	0.931386i	$-0.618600\pi$
$991$	−22.9196			−0.728065			−0.364032	+	0.931386i	$0.618600\pi$
$992$	−3.52566	−	33.5444i	−0.111940	−	1.06504i
$993$		0			0
$994$	33.0393	−	7.02272i	1.04794	−	0.222747i
$995$	11.1223	+	1.16900i	0.352600	+	0.0370598i
$996$		0			0
$997$	15.9789	−	14.3875i	0.506057	−	0.455656i	−0.376122	−	0.926570i	$-0.622743\pi$
$997$	15.9789	−	14.3875i	0.506057	−	0.455656i	0.882179	+	0.470914i	$0.156076\pi$
$998$	5.28139	+	16.2544i	0.167179	+	0.514525i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.t.a.8.8		80
3.2	odd	2		99.2.p.a.74.3	yes	80
9.2	odd	6		891.2.k.a.404.5		80
9.4	even	3		99.2.p.a.41.3	yes	80
9.5	odd	6	inner	297.2.t.a.206.8		80
9.7	even	3		891.2.k.a.404.16		80
11.7	odd	10	inner	297.2.t.a.62.8		80
33.29	even	10		99.2.p.a.29.3	✓	80
99.7	odd	30		891.2.k.a.161.5		80
99.29	even	30		891.2.k.a.161.16		80
99.40	odd	30		99.2.p.a.95.3	yes	80
99.95	even	30	inner	297.2.t.a.260.8		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.3	✓	80	33.29	even	10
99.2.p.a.41.3	yes	80	9.4	even	3
99.2.p.a.74.3	yes	80	3.2	odd	2
99.2.p.a.95.3	yes	80	99.40	odd	30
297.2.t.a.8.8		80	1.1	even	1	trivial
297.2.t.a.62.8		80	11.7	odd	10	inner
297.2.t.a.206.8		80	9.5	odd	6	inner
297.2.t.a.260.8		80	99.95	even	30	inner
891.2.k.a.161.5		80	99.7	odd	30
891.2.k.a.161.16		80	99.29	even	30
891.2.k.a.404.5		80	9.2	odd	6
891.2.k.a.404.16		80	9.7	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.189668 + 1.80457i) q^{2} +(-1.26420 + 0.268714i) q^{4} +(1.19507 + 0.125607i) q^{5} +(3.59771 - 3.23939i) q^{7} +(0.396737 + 1.22103i) q^{8} +2.18041i q^{10} +(1.93170 - 2.69602i) q^{11} +(-1.24460 + 2.79542i) q^{13} +(6.52808 + 5.87791i) q^{14} +(-4.48960 + 1.99890i) q^{16} +(-1.80866 - 1.31407i) q^{17} +(-4.34428 + 1.41154i) q^{19} +(-1.54456 + 0.162340i) q^{20} +(5.23153 + 2.97455i) q^{22} +(-1.72112 + 0.993689i) q^{23} +(-3.47832 - 0.739340i) q^{25} +(-5.28060 - 1.71577i) q^{26} +(-3.67776 + 5.06200i) q^{28} +(1.13479 + 1.26031i) q^{29} +(4.85274 + 2.16058i) q^{31} +(-3.17481 - 5.49894i) q^{32} +(2.02828 - 3.51308i) q^{34} +(4.70641 - 3.41941i) q^{35} +(0.344857 - 1.06136i) q^{37} +(-3.37119 - 7.57182i) q^{38} +(0.320759 + 1.50905i) q^{40} +(-7.11427 + 7.90120i) q^{41} +(-3.28272 - 1.89528i) q^{43} +(-1.71760 + 3.92738i) q^{44} +(-2.11962 - 2.91741i) q^{46} +(0.678872 - 3.19384i) q^{47} +(1.71815 - 16.3471i) q^{49} +(0.674464 - 6.41710i) q^{50} +(0.822258 - 3.86842i) q^{52} +(0.749954 + 1.03222i) q^{53} +(2.64716 - 2.97930i) q^{55} +(5.38274 + 3.10773i) q^{56} +(-2.05908 + 2.28684i) q^{58} +(0.00657007 + 0.0309097i) q^{59} +(-0.482921 - 1.08466i) q^{61} +(-2.97851 + 9.16690i) q^{62} +(1.36926 - 0.994827i) q^{64} +(-1.83851 + 3.18440i) q^{65} +(1.05277 + 1.82345i) q^{67} +(2.63961 + 1.17523i) q^{68} +(7.06321 + 7.84449i) q^{70} +(2.26013 - 3.11080i) q^{71} +(6.69980 + 2.17690i) q^{73} +(1.98070 + 0.421012i) q^{74} +(5.11273 - 2.95184i) q^{76} +(-1.78375 - 15.9570i) q^{77} +(3.80026 - 0.399424i) q^{79} +(-5.61646 + 1.82490i) q^{80} +(-15.6076 - 11.3396i) q^{82} +(-6.64079 + 2.95667i) q^{83} +(-1.99642 - 1.79758i) q^{85} +(2.79753 - 6.28336i) q^{86} +(4.05830 + 1.28906i) q^{88} -10.2875i q^{89} +(4.57775 + 14.0889i) q^{91} +(1.90882 - 1.71871i) q^{92} +(5.89227 + 0.619302i) q^{94} +(-5.36902 + 1.14122i) q^{95} +(-1.51615 - 14.4252i) q^{97} +29.8254 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) \) 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

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