LMFDB - Embedded newform 297.2.t.a.62.8

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			62.8
Character	$\chi$	$=$	297.62
Dual form			297.2.t.a.206.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.65764 - 0.738027i) q^{2} +(0.864813 - 0.960472i) q^{4} +(0.488756 - 1.09776i) q^{5} +(1.00654 - 4.73540i) q^{7} +(-0.396737 + 1.22103i) q^{8} -2.18041i q^{10} +(-1.36897 + 3.02091i) q^{11} +(3.04321 + 0.319854i) q^{13} +(-1.82638 - 8.59243i) q^{14} +(0.513703 + 4.88755i) q^{16} +(1.80866 - 1.31407i) q^{17} +(-4.34428 - 1.41154i) q^{19} +(-0.631690 - 1.41880i) q^{20} +(-0.0397341 + 6.01791i) q^{22} +(-1.72112 + 0.993689i) q^{23} +(2.37945 + 2.64264i) q^{25} +(5.28060 - 1.71577i) q^{26} +(-3.67776 - 5.06200i) q^{28} +(1.65886 + 0.352601i) q^{29} +(-0.555254 + 5.28289i) q^{31} +(3.17481 + 5.49894i) q^{32} +(2.02828 - 3.51308i) q^{34} +(-4.70641 - 3.41941i) q^{35} +(0.344857 + 1.06136i) q^{37} +(-8.24299 + 0.866373i) q^{38} +(1.14650 + 1.03231i) q^{40} +(-10.3998 + 2.21054i) q^{41} +(3.28272 + 1.89528i) q^{43} +(1.71760 + 3.92738i) q^{44} +(-2.11962 + 2.91741i) q^{46} +(-2.42651 + 2.18484i) q^{47} +(-15.0161 - 6.68560i) q^{49} +(5.89460 + 2.62445i) q^{50} +(2.93902 - 2.64630i) q^{52} +(-0.749954 + 1.03222i) q^{53} +(2.64716 + 2.97930i) q^{55} +(5.38274 + 3.10773i) q^{56} +(3.01001 - 0.639797i) q^{58} +(-0.0234836 - 0.0211447i) q^{59} +(1.18080 - 0.124107i) q^{61} +(2.97851 + 9.16690i) q^{62} +(1.36926 + 0.994827i) q^{64} +(1.83851 - 3.18440i) q^{65} +(1.05277 + 1.82345i) q^{67} +(0.302026 - 2.87359i) q^{68} +(-10.3251 - 2.19467i) q^{70} +(-2.26013 - 3.11080i) q^{71} +(6.69980 - 2.17690i) q^{73} +(1.35496 + 1.50483i) q^{74} +(-5.11273 + 2.95184i) q^{76} +(12.9273 + 9.52329i) q^{77} +(-1.55422 - 3.49084i) q^{79} +(5.61646 + 1.82490i) q^{80} +(-15.6076 + 11.3396i) q^{82} +(-0.759844 - 7.22943i) q^{83} +(-0.558543 - 2.62774i) q^{85} +(6.84032 + 0.718946i) q^{86} +(-3.14551 - 2.87006i) q^{88} -10.2875i q^{89} +(4.57775 - 14.0889i) q^{91} +(-0.534037 + 2.51244i) q^{92} +(-2.40980 + 5.41250i) q^{94} +(-3.67283 + 4.07909i) q^{95} +(13.2506 - 5.89957i) q^{97} -29.8254 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	1.65764	−	0.738027i	1.17213	−	0.521864i	0.274055	−	0.961714i	$-0.411635\pi$
$2$	1.65764	−	0.738027i	1.17213	−	0.521864i	0.898071	+	0.439850i	$0.144968\pi$
$3$		0			0
$3$		0			0
$4$	0.864813	−	0.960472i	0.432407	−	0.480236i
$5$	0.488756	−	1.09776i	0.218579	−	0.490935i	−0.770660	−	0.637246i	$-0.780073\pi$
$5$	0.488756	−	1.09776i	0.218579	−	0.490935i	0.989239	+	0.146311i	$0.0467400\pi$
$6$		0			0
$7$	1.00654	−	4.73540i	0.380437	−	1.78981i	−0.204641	−	0.978837i	$-0.565603\pi$
$7$	1.00654	−	4.73540i	0.380437	−	1.78981i	0.585077	−	0.810977i	$-0.301064\pi$
$8$	−0.396737	+	1.22103i	−0.140268	+	0.431700i
$9$		0			0
$10$		−	2.18041i		−	0.689506i
$11$	−1.36897	+	3.02091i	−0.412759	+	0.910840i
$11$	−1.36897	+	3.02091i	−0.412759	+	0.910840i
$12$		0			0
$13$	3.04321	+	0.319854i	0.844034	+	0.0887116i	0.516668	−	0.856186i	$-0.327172\pi$
$13$	3.04321	+	0.319854i	0.844034	+	0.0887116i	0.327366	+	0.944897i	$0.393839\pi$
$14$	−1.82638	−	8.59243i	−0.488120	−	2.29642i
$15$		0			0
$16$	0.513703	+	4.88755i	0.128426	+	1.22189i
$17$	1.80866	−	1.31407i	0.438664	−	0.318708i	−0.346440	−	0.938072i	$-0.612610\pi$
$17$	1.80866	−	1.31407i	0.438664	−	0.318708i	0.785104	+	0.619364i	$0.212610\pi$
$18$		0			0
$19$	−4.34428	−	1.41154i	−0.996645	−	0.323830i	−0.235121	−	0.971966i	$-0.575549\pi$
$19$	−4.34428	−	1.41154i	−0.996645	−	0.323830i	−0.761524	+	0.648136i	$0.775549\pi$
$20$	−0.631690	−	1.41880i	−0.141250	−	0.317253i
$21$		0			0
$22$	−0.0397341	+	6.01791i	−0.00847133	+	1.28302i
$23$	−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
$25$	2.37945	+	2.64264i	0.475890	+	0.528529i
$26$	5.28060	−	1.71577i	1.03561	−	0.336490i
$27$		0			0
$28$	−3.67776	−	5.06200i	−0.695030	−	0.956627i
$29$	1.65886	+	0.352601i	0.308042	+	0.0654763i	0.359339	−	0.933207i	$-0.383002\pi$
$29$	1.65886	+	0.352601i	0.308042	+	0.0654763i	−0.0512972	+	0.998683i	$0.516336\pi$
$30$		0			0
$31$	−0.555254	+	5.28289i	−0.0997266	+	0.948835i	0.824209	+	0.566286i	$0.191620\pi$
$31$	−0.555254	+	5.28289i	−0.0997266	+	0.948835i	−0.923935	+	0.382549i	$0.875046\pi$
$32$	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	0.975394	−	0.220471i	$-0.0707594\pi$
$37$	0.344857	+	1.06136i	0.0566941	+	0.174486i	−0.918699	+	0.394957i	$0.870759\pi$
$38$	−8.24299	+	0.866373i	−1.33719	+	0.140544i
$39$		0			0
$40$	1.14650	+	1.03231i	0.181277	+	0.163223i
$41$	−10.3998	+	2.21054i	−1.62417	+	0.345228i	−0.927981	−	0.372628i	$-0.878457\pi$
$41$	−10.3998	+	2.21054i	−1.62417	+	0.345228i	−0.696191	+	0.717857i	$0.745123\pi$
$42$		0			0
$43$	3.28272	+	1.89528i	0.500609	+	0.289027i	0.728965	−	0.684551i	$-0.240002\pi$
$43$	3.28272	+	1.89528i	0.500609	+	0.289027i	−0.228356	+	0.973578i	$0.573335\pi$
$44$	1.71760	+	3.92738i	0.258938	+	0.592075i
$45$		0			0
$46$	−2.11962	+	2.91741i	−0.312521	+	0.430149i
$47$	−2.42651	+	2.18484i	−0.353943	+	0.318692i	−0.826852	−	0.562420i	$-0.809871\pi$
$47$	−2.42651	+	2.18484i	−0.353943	+	0.318692i	0.472909	+	0.881111i	$0.343204\pi$
$48$		0			0
$49$	−15.0161	−	6.68560i	−2.14516	−	0.955086i
$50$	5.89460	+	2.62445i	0.833623	+	0.371153i
$51$		0			0
$52$	2.93902	−	2.64630i	0.407569	−	0.366976i
$53$	−0.749954	+	1.03222i	−0.103014	+	0.141787i	−0.857412	−	0.514631i	$-0.827929\pi$
$53$	−0.749954	+	1.03222i	−0.103014	+	0.141787i	0.754398	+	0.656417i	$0.227929\pi$
$54$		0			0
$55$	2.64716	+	2.97930i	0.356943	+	0.401728i
$56$	5.38274	+	3.10773i	0.719299	+	0.415288i
$57$		0			0
$58$	3.01001	−	0.639797i	0.395233	−	0.0840095i
$59$	−0.0234836	−	0.0211447i	−0.00305730	−	0.00275281i	0.667601	−	0.744520i	$-0.267321\pi$
$59$	−0.0234836	−	0.0211447i	−0.00305730	−	0.00275281i	−0.670658	+	0.741767i	$0.733988\pi$
$60$		0			0
$61$	1.18080	−	0.124107i	0.151186	−	0.0158903i	−0.0286330	−	0.999590i	$-0.509115\pi$
$61$	1.18080	−	0.124107i	0.151186	−	0.0158903i	0.179819	+	0.983700i	$0.442449\pi$
$62$	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	$0.792280\pi$
$68$	0.302026	−	2.87359i	0.0366261	−	0.348474i
$69$		0			0
$70$	−10.3251	−	2.19467i	−1.23409	−	0.262314i
$71$	−2.26013	−	3.11080i	−0.268228	−	0.369184i	0.653563	−	0.756873i	$-0.273274\pi$
$71$	−2.26013	−	3.11080i	−0.268228	−	0.369184i	−0.921790	+	0.387688i	$0.873274\pi$
$72$		0			0
$73$	6.69980	−	2.17690i	0.784152	−	0.254786i	0.110540	−	0.993872i	$-0.464742\pi$
$73$	6.69980	−	2.17690i	0.784152	−	0.254786i	0.673612	+	0.739085i	$0.264742\pi$
$74$	1.35496	+	1.50483i	0.157511	+	0.174934i
$75$		0			0
$76$	−5.11273	+	2.95184i	−0.586471	+	0.338599i
$77$	12.9273	+	9.52329i	1.47321	+	1.08528i
$78$		0			0
$79$	−1.55422	−	3.49084i	−0.174863	−	0.392750i	0.804758	−	0.593603i	$-0.202295\pi$
$79$	−1.55422	−	3.49084i	−0.174863	−	0.392750i	−0.979621	+	0.200854i	$0.935628\pi$
$80$	5.61646	+	1.82490i	0.627940	+	0.204030i
$81$		0			0
$82$	−15.6076	+	11.3396i	−1.72357	+	1.25225i
$83$	−0.759844	−	7.22943i	−0.0834037	−	0.793533i	−0.953650	−	0.300917i	$-0.902707\pi$
$83$	−0.759844	−	7.22943i	−0.0834037	−	0.793533i	0.870247	−	0.492616i	$-0.163959\pi$
$84$		0			0
$85$	−0.558543	−	2.62774i	−0.0605825	−	0.285018i
$86$	6.84032	+	0.718946i	0.737610	+	0.0775260i
$87$		0			0
$88$	−3.14551	−	2.87006i	−0.335313	−	0.305950i
$89$		−	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
$92$	−0.534037	+	2.51244i	−0.0556772	+	0.261940i
$93$		0			0
$94$	−2.40980	+	5.41250i	−0.248552	+	0.558257i
$95$	−3.67283	+	4.07909i	−0.376825	+	0.418506i
$96$		0			0
$97$	13.2506	−	5.89957i	1.34540	−	0.599010i	0.397506	−	0.917600i	$-0.369876\pi$
$97$	13.2506	−	5.89957i	1.34540	−	0.599010i	0.947893	+	0.318589i	$0.103209\pi$
$98$	−29.8254			−3.01282
$99$		0			0
$100$	4.59597			0.459597
$101$	14.6950	−	6.54265i	1.46221	−	0.651018i	0.487222	−	0.873278i	$-0.338010\pi$
$101$	14.6950	−	6.54265i	1.46221	−	0.651018i	0.974987	+	0.222260i	$0.0713435\pi$
$102$		0			0
$103$	−1.39257	+	1.54661i	−0.137214	+	0.152392i	−0.807835	−	0.589408i	$-0.799361\pi$
$103$	−1.39257	+	1.54661i	−0.137214	+	0.152392i	0.670621	+	0.741800i	$0.266028\pi$
$104$	−1.59791	+	3.58896i	−0.156688	+	0.351926i
$105$		0			0
$106$	−0.481342	+	2.26454i	−0.0467521	+	0.219951i
$107$	0.129361	−	0.398133i	0.0125058	−	0.0384889i	−0.944609	−	0.328198i	$-0.893559\pi$
$107$	0.129361	−	0.398133i	0.0125058	−	0.0384889i	0.957115	+	0.289709i	$0.0935586\pi$
$108$		0			0
$109$			14.6788i			1.40597i	0.711205	+	0.702985i	$0.248150\pi$
$109$			14.6788i			1.40597i	−0.711205	+	0.702985i	$0.751850\pi$
$110$	6.58684	+	2.98491i	0.628030	+	0.284600i
$111$		0			0
$112$	23.6616	+	2.48694i	2.23581	+	0.234993i
$113$	0.664620	+	3.12679i	0.0625222	+	0.294144i	0.998289	−	0.0584761i	$-0.0186242\pi$
$113$	0.664620	+	3.12679i	0.0625222	+	0.294144i	−0.935767	+	0.352620i	$0.885291\pi$
$114$		0			0
$115$	0.249629	+	2.37506i	0.0232780	+	0.221475i
$116$	1.77326	−	1.28835i	0.164643	−	0.119620i
$117$		0			0
$118$	−0.0545326	−	0.0177187i	−0.00502013	−	0.00163114i
$119$	−4.40215	−	9.88738i	−0.403544	−	0.906375i
$120$		0			0
$121$	−7.25185	−	8.27107i	−0.659259	−	0.751916i
$122$	1.86575	−	1.07719i	0.168917	−	0.0975241i
$123$		0			0
$124$	4.59388	+	5.10202i	0.412543	+	0.458175i
$125$	9.77817	−	3.17712i	0.874587	−	0.284170i
$126$		0			0
$127$	−13.1088	−	18.0428i	−1.16322	−	1.60104i	−0.698567	−	0.715545i	$-0.746179\pi$
$127$	−13.1088	−	18.0428i	−1.16322	−	1.60104i	−0.464654	−	0.885492i	$-0.653821\pi$
$128$	−9.41780	−	2.00181i	−0.832423	−	0.176937i
$129$		0			0
$130$	0.697414	−	6.63545i	0.0611672	−	0.581967i
$131$	−7.74960	−	13.4227i	−0.677086	−	1.17275i	−0.975855	−	0.218421i	$-0.929909\pi$
$131$	−7.74960	−	13.4227i	−0.677086	−	1.17275i	0.298769	−	0.954326i	$-0.403424\pi$
$132$		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
$137$	−17.0469	+	1.79170i	−1.45641	+	0.153075i	−0.799397	−	0.600803i	$-0.794848\pi$
$137$	−17.0469	+	1.79170i	−1.45641	+	0.153075i	−0.657015	+	0.753878i	$0.728181\pi$
$138$		0			0
$139$	7.70480	+	6.93744i	0.653513	+	0.588426i	0.927734	−	0.373241i	$-0.121753\pi$
$139$	7.70480	+	6.93744i	0.653513	+	0.588426i	−0.274222	+	0.961667i	$0.588420\pi$
$140$	−7.35441	+	1.56323i	−0.621561	+	0.132117i
$141$		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
$146$	9.49922	−	8.55313i	0.786161	−	0.707862i
$147$		0			0
$148$	1.31764	+	0.586653i	0.108310	+	0.0482225i
$149$	0.0369600	+	0.0164557i	0.00302788	+	0.00134810i	0.408250	−	0.912870i	$-0.366139\pi$
$149$	0.0369600	+	0.0164557i	0.00302788	+	0.00134810i	−0.405222	+	0.914218i	$0.632806\pi$
$150$		0			0
$151$	−2.04486	+	1.84120i	−0.166408	+	0.149834i	−0.748127	−	0.663555i	$-0.769047\pi$
$151$	−2.04486	+	1.84120i	−0.166408	+	0.149834i	0.581719	+	0.813390i	$0.302380\pi$
$152$	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
$157$	−2.06376	+	0.438666i	−0.164706	+	0.0350094i	−0.289527	−	0.957170i	$-0.593498\pi$
$157$	−2.06376	+	0.438666i	−0.164706	+	0.0350094i	0.124820	+	0.992179i	$0.460165\pi$
$158$	−5.15266	−	4.63948i	−0.409924	−	0.369097i
$159$		0			0
$160$	7.58825	−	0.797557i	0.599904	−	0.0630525i
$161$	2.97314	+	9.15039i	0.234316	+	0.721152i
$162$		0			0
$163$	−11.8085	−	8.57941i	−0.924917	−	0.671991i	0.0198264	−	0.999803i	$-0.493689\pi$
$163$	−11.8085	−	8.57941i	−0.924917	−	0.671991i	−0.944743	+	0.327812i	$0.893689\pi$
$164$	−6.87070	+	11.9004i	−0.536512	+	0.929265i
$165$		0			0
$166$	−6.59506	−	11.4230i	−0.511876	−	0.886596i
$167$	−0.0932678	+	0.887384i	−0.00721728	+	0.0686678i	−0.997538	−	0.0701322i	$-0.977658\pi$
$167$	−0.0932678	+	0.887384i	−0.00721728	+	0.0686678i	0.990320	+	0.138800i	$0.0443245\pi$
$168$		0			0
$169$	−3.55710	−	0.756085i	−0.273623	−	0.0581604i
$170$	−2.86520	−	3.94362i	−0.219751	−	0.302461i
$171$		0			0
$172$	4.65930	−	1.51390i	0.355268	−	0.115434i
$173$	8.86427	+	9.84476i	0.673938	+	0.748484i	0.979003	−	0.203848i	$-0.0653448\pi$
$173$	8.86427	+	9.84476i	0.673938	+	0.748484i	−0.305065	+	0.952332i	$0.598678\pi$
$174$		0			0
$175$	14.9090	−	8.60772i	1.12701	−	0.650682i
$176$	−15.4681	−	5.13906i	−1.16595	−	0.387371i
$177$		0			0
$178$	−7.59248	−	17.0530i	−0.569080	−	1.27817i
$179$	−19.1587	−	6.22502i	−1.43199	−	0.465280i	−0.512596	−	0.858630i	$-0.671316\pi$
$179$	−19.1587	−	6.22502i	−1.43199	−	0.465280i	−0.919389	+	0.393350i	$0.871316\pi$
$180$		0			0
$181$	3.63758	−	2.64286i	0.270379	−	0.196442i	−0.444331	−	0.895863i	$-0.646559\pi$
$181$	3.63758	−	2.64286i	0.270379	−	0.196442i	0.714710	+	0.699421i	$0.246559\pi$
$182$	−2.80973	−	26.7328i	−0.208271	−	1.98156i
$183$		0			0
$184$	−0.530493	−	2.49578i	−0.0391085	−	0.183991i
$185$	1.33367	+	0.140175i	0.0980537	+	0.0103059i
$186$		0			0
$187$	1.49369	+	7.26271i	0.109229	+	0.531102i
$188$			4.22008i			0.307781i
$189$		0			0
$190$	−3.07774	+	9.47231i	−0.223283	+	0.687193i
$191$	−3.69541	+	17.3855i	−0.267390	+	1.25797i	0.615403	+	0.788212i	$0.288993\pi$
$191$	−3.69541	+	17.3855i	−0.267390	+	1.25797i	−0.882794	+	0.469761i	$0.844340\pi$
$192$		0			0
$193$	2.50508	−	5.62649i	0.180319	−	0.405004i	−0.800659	−	0.599120i	$-0.795517\pi$
$193$	2.50508	−	5.62649i	0.180319	−	0.405004i	0.980979	+	0.194116i	$0.0621839\pi$
$194$	17.6107	−	19.5587i	1.26438	−	1.40423i
$195$		0			0
$196$	−19.4075	+	8.64076i	−1.38625	+	0.617197i
$197$	22.5100			1.60377			0.801886	−	0.597477i	$-0.203830\pi$
$197$	22.5100			1.60377			0.801886	+	0.597477i	$0.203830\pi$
$198$		0			0
$199$	9.30680			0.659742			0.329871	−	0.944026i	$-0.392995\pi$
$199$	9.30680			0.659742			0.329871	+	0.944026i	$0.392995\pi$
$200$	−4.17077	+	1.85695i	−0.294918	+	0.131306i
$201$		0			0
$202$	19.5304	−	21.6907i	1.37415	−	1.52615i
$203$	3.33941	−	7.50044i	0.234381	−	0.526428i
$204$		0			0
$205$	−2.65630	+	12.4969i	−0.185524	+	0.872823i
$206$	−1.16694	+	3.59147i	−0.0813046	+	0.250230i
$207$		0			0
$208$			15.0382i			1.04271i
$209$	10.2113	−	11.1913i	0.706332	−	0.774121i
$210$		0			0
$211$	−13.9344	−	1.46456i	−0.959282	−	0.100825i	−0.388073	−	0.921629i	$-0.626859\pi$
$211$	−13.9344	−	1.46456i	−0.959282	−	0.100825i	−0.571210	+	0.820804i	$0.693526\pi$
$212$	0.342852	+	1.61299i	0.0235471	+	0.110781i
$213$		0			0
$214$	−0.0793990	−	0.755431i	−0.00542761	−	0.0516402i
$215$	3.68502	−	2.67732i	0.251316	−	0.182592i
$216$		0			0
$217$	24.4577	+	7.94680i	1.66030	+	0.539464i
$218$	10.8333	+	24.3320i	0.733725	+	1.64797i
$219$		0			0
$220$	5.15083	+	0.0340091i	0.347269	+	0.00229289i
$221$	5.92443	−	3.42047i	0.398520	−	0.230086i
$222$		0			0
$223$	−10.7949	−	11.9890i	−0.722881	−	0.802841i	0.263960	−	0.964534i	$-0.414971\pi$
$223$	−10.7949	−	11.9890i	−0.722881	−	0.802841i	−0.986841	+	0.161693i	$0.948305\pi$
$224$	29.2353	−	9.49912i	1.95336	−	0.634686i
$225$		0			0
$226$	3.40936	+	4.69258i	0.226787	+	0.312146i
$227$	14.3933	+	3.05940i	0.955320	+	0.203060i	0.659096	−	0.752059i	$-0.270939\pi$
$227$	14.3933	+	3.05940i	0.955320	+	0.203060i	0.296224	+	0.955118i	$0.404272\pi$
$228$		0			0
$229$	−2.32043	+	22.0774i	−0.153338	+	1.45892i	0.599323	+	0.800507i	$0.295436\pi$
$229$	−2.32043	+	22.0774i	−0.153338	+	1.45892i	−0.752661	+	0.658408i	$0.771230\pi$
$230$	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	$-0.245850\pi$
$233$	4.18134	+	3.03792i	0.273929	+	0.199021i	−0.442336	+	0.896849i	$0.645850\pi$
$234$		0			0
$235$	1.21247	+	3.73159i	0.0790927	+	0.243422i
$236$	−0.0406178	+	0.00426911i	−0.00264400	+	0.000277895i
$237$		0			0
$238$	−14.5943	−	13.1408i	−0.946009	−	0.851790i
$239$	13.3666	−	2.84115i	0.864612	−	0.183779i	0.245802	−	0.969320i	$-0.420949\pi$
$239$	13.3666	−	2.84115i	0.864612	−	0.183779i	0.618809	+	0.785541i	$0.287615\pi$
$240$		0			0
$241$	6.10765	+	3.52625i	0.393428	+	0.227146i	0.683645	−	0.729815i	$-0.260394\pi$
$241$	6.10765	+	3.52625i	0.393428	+	0.227146i	−0.290216	+	0.956961i	$0.593727\pi$
$242$	−18.1252	−	8.35837i	−1.16513	−	0.537296i
$243$		0			0
$244$	0.901971	−	1.24146i	0.0577428	−	0.0794761i
$245$	−14.6784	+	13.2165i	−0.937771	+	0.844373i
$246$		0			0
$247$	−12.7691	−	5.68515i	−0.812476	−	0.361737i
$248$	−6.23028	−	2.77390i	−0.395623	−	0.176143i
$249$		0			0
$250$	13.8639	−	12.4831i	0.876827	−	0.789499i
$251$	3.95496	−	5.44354i	0.249635	−	0.343593i	−0.665748	−	0.746176i	$-0.731888\pi$
$251$	3.95496	−	5.44354i	0.249635	−	0.343593i	0.915383	+	0.402583i	$0.131888\pi$
$252$		0			0
$253$	−0.645692	−	6.55969i	−0.0405943	−	0.412404i
$254$	−35.0457	−	20.2337i	−2.19897	−	1.26957i
$255$		0			0
$256$	−20.3997	+	4.33609i	−1.27498	+	0.271006i
$257$	−10.5166	−	9.46922i	−0.656009	−	0.590673i	0.272422	−	0.962178i	$-0.412175\pi$
$257$	−10.5166	−	9.46922i	−0.656009	−	0.590673i	−0.928431	+	0.371504i	$0.878842\pi$
$258$		0			0
$259$	5.37308	−	0.564733i	0.333867	−	0.0350908i
$260$	−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	−0.953009	−	0.302942i	$-0.902031\pi$
$263$	−3.47292	+	6.01527i	−0.214149	+	0.370917i	0.738860	+	0.673859i	$0.235365\pi$
$264$		0			0
$265$	0.766593	+	1.32778i	0.0470914	+	0.0815648i
$266$	−4.19428	+	39.9059i	−0.257168	+	2.44679i
$267$		0			0
$268$	2.66183	+	0.565789i	0.162597	+	0.0345611i
$269$	−4.05850	−	5.58605i	−0.247451	−	0.340587i	0.667165	−	0.744910i	$-0.267507\pi$
$269$	−4.05850	−	5.58605i	−0.247451	−	0.340587i	−0.914617	+	0.404322i	$0.867507\pi$
$270$		0			0
$271$	−12.9581	+	4.21033i	−0.787146	+	0.255759i	−0.674888	−	0.737920i	$-0.735808\pi$
$271$	−12.9581	+	4.21033i	−0.787146	+	0.255759i	−0.112258	+	0.993679i	$0.535808\pi$
$272$	7.35168	+	8.16487i	0.445761	+	0.495068i
$273$		0			0
$274$	−26.9352	+	15.5510i	−1.62721	+	0.939473i
$275$	−11.2406	+	3.57041i	−0.677833	+	0.215304i
$276$		0			0
$277$	−4.74062	−	10.6476i	−0.284836	−	0.639753i	0.713294	−	0.700864i	$-0.247202\pi$
$277$	−4.74062	−	10.6476i	−0.284836	−	0.639753i	−0.998131	+	0.0611112i	$0.980536\pi$
$278$	17.8918	+	5.81339i	1.07308	+	0.348664i
$279$		0			0
$280$	6.04241	−	4.39007i	0.361103	−	0.262357i
$281$	2.28295	+	21.7209i	0.136190	+	1.29576i	0.822632	+	0.568574i	$0.192505\pi$
$281$	2.28295	+	21.7209i	0.136190	+	1.29576i	−0.686443	+	0.727184i	$0.740829\pi$
$282$		0			0
$283$	4.88066	+	22.9617i	0.290125	+	1.36493i	0.845786	+	0.533523i	$0.179132\pi$
$283$	4.88066	+	22.9617i	0.290125	+	1.36493i	−0.555661	+	0.831409i	$0.687535\pi$
$284$	−4.94243	−	0.519470i	−0.293279	−	0.0308249i
$285$		0			0
$286$	−2.04577	+	18.3011i	−0.120969	+	1.08216i
$287$			51.4721i			3.03830i
$288$		0			0
$289$	−3.70882	+	11.4146i	−0.218166	+	0.671445i
$290$	0.768814	−	3.61699i	0.0451463	−	0.212397i
$291$		0			0
$292$	3.70322	−	8.31758i	0.216715	−	0.486749i
$293$	−1.13529	+	1.26087i	−0.0663243	+	0.0736606i	−0.775394	−	0.631478i	$-0.782449\pi$
$293$	−1.13529	+	1.26087i	−0.0663243	+	0.0736606i	0.709069	+	0.705139i	$0.249115\pi$
$294$		0			0
$295$	−0.0346897	+	0.0154448i	−0.00201971	+	0.000899233i
$296$	−1.43277			−0.0832781
$297$		0			0
$298$	0.0734110			0.00425258
$299$	−5.55557	+	2.47350i	−0.321287	+	0.143046i
$300$		0			0
$301$	12.2791	−	13.6373i	0.707755	−	0.786042i
$302$	−2.03077	+	4.56119i	−0.116858	+	0.262467i
$303$		0			0
$304$	4.66732	−	21.9580i	0.267689	−	1.25938i
$305$	0.440884	−	1.35690i	0.0252449	−	0.0776959i
$306$		0			0
$307$		−	2.35281i		−	0.134282i	−0.997743	−	0.0671410i	$-0.978612\pi$
$307$		−	2.35281i		−	0.134282i	0.997743	−	0.0671410i	$-0.0213877\pi$
$308$	20.3266	−	4.18047i	1.15821	−	0.238205i
$309$		0			0
$310$	11.5189	+	1.21068i	0.654228	+	0.0687621i
$311$	2.20518	+	10.3746i	0.125044	+	0.588288i	0.995395	+	0.0958557i	$0.0305587\pi$
$311$	2.20518	+	10.3746i	0.125044	+	0.588288i	−0.870351	+	0.492432i	$0.836108\pi$
$312$		0			0
$313$	2.64814	+	25.1954i	0.149682	+	1.42413i	0.769132	+	0.639090i	$0.220689\pi$
$313$	2.64814	+	25.1954i	0.149682	+	1.42413i	−0.619450	+	0.785036i	$0.712645\pi$
$314$	−3.09722	+	2.25026i	−0.174786	+	0.126990i
$315$		0			0
$316$	−4.69696	−	1.52614i	−0.264225	−	0.0858518i
$317$	−10.9056	−	24.4944i	−0.612520	−	1.37574i	−0.907424	−	0.420215i	$-0.861955\pi$
$317$	−10.9056	−	24.4944i	−0.612520	−	1.37574i	0.294905	−	0.955527i	$-0.404712\pi$
$318$		0			0
$319$	−3.33610	+	4.52856i	−0.186786	+	0.253551i
$320$	1.76132	−	1.01690i	0.0984609	−	0.0568464i
$321$		0			0
$322$	11.6816	+	12.9738i	0.650992	+	0.722999i
$323$	−9.71216	+	3.15567i	−0.540399	+	0.175586i
$324$		0			0
$325$	6.39590	+	8.80320i	0.354781	+	0.488314i
$326$	−25.9061	−	5.50651i	−1.43481	−	0.304978i
$327$		0			0
$328$	1.42684	−	13.5755i	0.0787839	−	0.749579i
$329$	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
$335$	2.51627	−	0.264471i	0.137479	−	0.0144496i
$336$		0			0
$337$	9.66376	+	8.70129i	0.526419	+	0.473989i	0.888964	−	0.457977i	$-0.151426\pi$
$337$	9.66376	+	8.70129i	0.526419	+	0.473989i	−0.362546	+	0.931966i	$0.618092\pi$
$338$	−6.45439	+	1.37192i	−0.351073	+	0.0746228i
$339$		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
$344$	−3.61657	+	3.25637i	−0.194992	+	0.175572i
$345$		0			0
$346$	21.9594	+	9.77697i	1.18055	+	0.525613i
$347$	19.4186	+	8.64572i	1.04244	+	0.464126i	0.855260	−	0.518198i	$-0.173397\pi$
$347$	19.4186	+	8.64572i	1.04244	+	0.464126i	0.187185	+	0.982325i	$0.440064\pi$
$348$		0			0
$349$	−6.93428	+	6.24365i	−0.371183	+	0.334215i	−0.833520	−	0.552490i	$-0.813678\pi$
$349$	−6.93428	+	6.24365i	−0.371183	+	0.334215i	0.462337	+	0.886705i	$0.347011\pi$
$350$	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
$355$	−4.51958	+	0.960666i	−0.239874	+	0.0509869i
$356$	−9.88089	−	8.89679i	−0.523686	−	0.471529i
$357$		0			0
$358$	−36.3523	+	3.82078i	−1.92128	+	0.201935i
$359$	2.41692	+	7.43851i	0.127560	+	0.392589i	0.994359	−	0.106069i	$-0.0338263\pi$
$359$	2.41692	+	7.43851i	0.127560	+	0.392589i	−0.866799	+	0.498658i	$0.833826\pi$
$360$		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
$365$	0.884849	−	8.41877i	0.0463151	−	0.440659i
$366$		0			0
$367$	−23.9688	−	5.09473i	−1.25116	−	0.265943i	−0.465750	−	0.884916i	$-0.654215\pi$
$367$	−23.9688	−	5.09473i	−1.25116	−	0.265943i	−0.785412	+	0.618974i	$0.787549\pi$
$368$	−5.74086	−	7.90161i	−0.299263	−	0.411900i
$369$		0			0
$370$	2.31420	−	0.751929i	0.120310	−	0.0390909i
$371$	4.13313	+	4.59031i	0.214582	+	0.238317i
$372$		0			0
$373$	−2.47795	+	1.43065i	−0.128303	+	0.0740760i	−0.562778	−	0.826608i	$-0.690267\pi$
$373$	−2.47795	+	1.43065i	−0.128303	+	0.0740760i	0.434475	+	0.900684i	$0.356934\pi$
$374$	7.83607	+	10.9366i	0.405194	+	0.565516i
$375$		0			0
$376$	−1.70507	−	3.82965i	−0.0879324	−	0.197499i
$377$	4.93546	+	1.60363i	0.254189	+	0.0825911i
$378$		0			0
$379$	23.6747	−	17.2007i	1.21609	−	0.883540i	0.220320	−	0.975428i	$-0.429290\pi$
$379$	23.6747	−	17.2007i	1.21609	−	0.883540i	0.995769	+	0.0918872i	$0.0292899\pi$
$380$	0.741543	+	7.05531i	0.0380404	+	0.361930i
$381$		0			0
$382$	6.70535	+	31.5462i	0.343076	+	1.61404i
$383$	−28.3035	−	2.97482i	−1.44624	−	0.152006i	−0.651359	−	0.758769i	$-0.725801\pi$
$383$	−28.3035	−	2.97482i	−1.44624	−	0.152006i	−0.794883	+	0.606763i	$0.792468\pi$
$384$		0			0
$385$	16.7727	−	9.53660i	0.854814	−	0.486030i
$386$		−	11.1755i		−	0.568818i
$387$		0			0
$388$	5.79296	−	17.8289i	0.294093	−	0.905125i
$389$	2.96928	−	13.9694i	0.150548	−	0.708275i	−0.836515	−	0.547944i	$-0.815411\pi$
$389$	2.96928	−	13.9694i	0.150548	−	0.708275i	0.987063	−	0.160331i	$-0.0512560\pi$
$390$		0			0
$391$	−1.80714	+	4.05891i	−0.0913911	+	0.205268i
$392$	14.1208	−	15.6827i	0.713207	−	0.792097i
$393$		0			0
$394$	37.3134	−	16.6130i	1.87982	−	0.836951i
$395$	−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	$0.482363\pi$
$398$	15.4273	−	6.86867i	0.773300	−	0.344295i
$399$		0			0
$400$	−11.6937	+	12.9872i	−0.584687	+	0.649361i
$401$	12.8297	−	28.8160i	0.640684	−	1.43900i	−0.242583	−	0.970131i	$-0.577995\pi$
$401$	12.8297	−	28.8160i	0.640684	−	1.43900i	0.883267	−	0.468870i	$-0.155339\pi$
$402$		0			0
$403$	−3.37951	+	15.8993i	−0.168345	+	0.792003i
$404$	6.42442	−	19.7723i	0.319627	−	0.983710i
$405$		0			0
$406$		−	14.8976i		−	0.739355i
$407$	−3.67837	−	0.411185i	−0.182330	−	0.0203817i
$408$		0			0
$409$	6.74107	+	0.708515i	0.333324	+	0.0350338i	0.269712	−	0.962941i	$-0.413071\pi$
$409$	6.74107	+	0.708515i	0.333324	+	0.0350338i	0.0636119	+	0.997975i	$0.479738\pi$
$410$	4.81989	+	22.6758i	0.238037	+	1.11988i
$411$		0			0
$412$	0.281160	+	2.67506i	0.0138517	+	0.131791i
$413$	−0.123766	+	0.0899212i	−0.00609012	+	0.00442473i
$414$		0			0
$415$	−8.30760	−	2.69930i	−0.407804	−	0.132504i
$416$	7.90276	+	17.7499i	0.387465	+	0.870260i
$417$		0			0
$418$	8.66715	−	26.0874i	0.423924	−	1.27598i
$419$	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
$421$	−3.74264	−	4.15662i	−0.182405	−	0.202582i	0.645007	−	0.764177i	$-0.276854\pi$
$421$	−3.74264	−	4.15662i	−0.182405	−	0.202582i	−0.827412	+	0.561595i	$0.810188\pi$
$422$	−24.1790	+	7.85624i	−1.17702	+	0.382436i
$423$		0			0
$424$	−0.962842	−	1.32524i	−0.0467597	−	0.0643592i
$425$	7.77622	+	1.65289i	0.377202	+	0.0801767i
$426$		0			0
$427$	0.600828	−	5.71649i	0.0290761	−	0.276640i
$428$	−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	$-0.455688\pi$
$431$	−15.7825	−	11.4667i	−0.760216	−	0.552329i	−0.898977	+	0.437997i	$0.855688\pi$
$432$		0			0
$433$	−6.96921	−	21.4490i	−0.334919	−	1.03077i	−0.966762	−	0.255678i	$-0.917701\pi$
$433$	−6.96921	−	21.4490i	−0.334919	−	1.03077i	0.631843	−	0.775096i	$-0.282299\pi$
$434$	46.4070	−	4.87757i	2.22761	−	0.234131i
$435$		0			0
$436$	14.0985	+	12.6944i	0.675198	+	0.607951i
$437$	8.87966	−	1.88743i	0.424772	−	0.0902880i
$438$		0			0
$439$	25.9695	+	14.9935i	1.23946	+	0.715601i	0.968983	−	0.247126i	$-0.0794861\pi$
$439$	25.9695	+	14.9935i	1.23946	+	0.715601i	0.270474	+	0.962727i	$0.412819\pi$
$440$	−4.68804	+	2.05027i	−0.223494	+	0.0977428i
$441$		0			0
$442$	7.29615	−	10.0423i	0.347043	−	0.477663i
$443$	23.4444	−	21.1094i	1.11388	−	1.00294i	0.113922	−	0.993490i	$-0.463659\pi$
$443$	23.4444	−	21.1094i	1.11388	−	1.00294i	0.999955	−	0.00944948i	$-0.00300791\pi$
$444$		0			0
$445$	−11.2933	−	5.02810i	−0.535353	−	0.238355i
$446$	−26.7422	−	11.9064i	−1.26628	−	0.563785i
$447$		0			0
$448$	6.08913	−	5.48268i	0.287684	−	0.259032i
$449$	−22.3362	+	30.7432i	−1.05411	+	1.45086i	−0.168921	+	0.985630i	$0.554028\pi$
$449$	−22.3362	+	30.7432i	−1.05411	+	1.45086i	−0.885190	+	0.465229i	$0.845972\pi$
$450$		0			0
$451$	7.55911	−	34.4430i	0.355944	−	1.62186i
$452$	3.57797	+	2.06574i	0.168294	+	0.0971644i
$453$		0			0
$454$	26.1169	−	5.55131i	1.22572	−	0.260536i
$455$	−13.2289	−	11.9113i	−0.620179	−	0.558412i
$456$		0			0
$457$	39.0111	−	4.10023i	1.82486	−	0.191801i	0.870846	−	0.491555i	$-0.163571\pi$
$457$	39.0111	−	4.10023i	1.82486	−	0.191801i	0.954016	+	0.299755i	$0.0969048\pi$
$458$	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	−0.586008	−	0.810305i	$-0.699301\pi$
$461$	8.77604	−	15.2006i	0.408741	−	0.707960i	0.994749	+	0.102345i	$0.0326346\pi$
$462$		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	$0.870939\pi$
$464$	−0.871196	+	8.28888i	−0.0404443	+	0.384802i
$465$		0			0
$466$	9.17322	+	1.94983i	0.424941	+	0.0903240i
$467$	9.96792	+	13.7197i	0.461260	+	0.634870i	0.974770	−	0.223214i	$-0.0716548\pi$
$467$	9.96792	+	13.7197i	0.461260	+	0.634870i	−0.513509	+	0.858084i	$0.671655\pi$
$468$		0			0
$469$	9.69445	−	3.14992i	0.447648	−	0.145450i
$470$	4.76385	+	5.29079i	0.219740	+	0.244046i
$471$		0			0
$472$	0.0351352	−	0.0202853i	0.00161723	−	0.000933706i
$473$	−10.2194	+	7.32223i	−0.469889	+	0.336677i
$474$		0			0
$475$	−6.60678	−	14.8391i	−0.303140	−	0.680863i
$476$	−13.3036	−	4.32260i	−0.609769	−	0.198126i
$477$		0			0
$478$	20.0601	−	14.5745i	0.917526	−	0.666622i
$479$	−1.88983	−	17.9805i	−0.0863485	−	0.821551i	−0.948899	−	0.315580i	$-0.897801\pi$
$479$	−1.88983	−	17.9805i	−0.0863485	−	0.821551i	0.862550	−	0.505971i	$-0.168866\pi$
$480$		0			0
$481$	0.709991	+	3.34024i	0.0323728	+	0.152302i
$482$	12.7267	+	1.33763i	0.579687	+	0.0609276i
$483$		0			0
$484$	−14.2156	−	0.187729i	−0.646165	−	0.00853315i
$485$		−	17.4295i		−	0.791435i
$486$		0			0
$487$	−8.03498	+	24.7291i	−0.364100	+	1.12058i	0.586443	+	0.809991i	$0.300528\pi$
$487$	−8.03498	+	24.7291i	−0.364100	+	1.12058i	−0.950543	+	0.310594i	$0.899472\pi$
$488$	−0.316929	+	1.49103i	−0.0143467	+	0.0674959i
$489$		0			0
$490$	−14.5774	+	32.7413i	−0.658538	+	1.47910i
$491$	−4.90602	+	5.44869i	−0.221406	+	0.245896i	−0.843607	−	0.536962i	$-0.819572\pi$
$491$	−4.90602	+	5.44869i	−0.221406	+	0.245896i	0.622201	+	0.782858i	$0.286239\pi$
$492$		0			0
$493$	3.46364	−	1.54211i	0.155995	−	0.0694532i
$494$	−25.3622			−1.14110
$495$		0			0
$496$	−26.1057			−1.17218
$497$	−17.0058	+	7.57147i	−0.762815	+	0.339627i
$498$		0			0
$499$	−6.30257	+	6.99971i	−0.282142	+	0.313350i	−0.867512	−	0.497416i	$-0.834282\pi$
$499$	−6.30257	+	6.99971i	−0.282142	+	0.313350i	0.585371	+	0.810766i	$0.300949\pi$
$500$	5.40476	−	12.1393i	0.241708	−	0.542885i
$501$		0			0
$502$	2.53841	−	11.9423i	0.113295	−	0.533010i
$503$	10.3211	−	31.7652i	0.460196	−	1.41634i	−0.404728	−	0.914437i	$-0.632634\pi$
$503$	10.3211	−	31.7652i	0.460196	−	1.41634i	0.864925	−	0.501902i	$-0.167366\pi$
$504$		0			0
$505$		−	19.3294i		−	0.860149i
$506$	−5.91155	−	10.3970i	−0.262800	−	0.462205i
$507$		0			0
$508$	−28.6663	−	3.01295i	−1.27186	−	0.133678i
$509$	4.26297	+	20.0557i	0.188953	+	0.888953i	0.965805	+	0.259270i	$0.0834819\pi$
$509$	4.26297	+	20.0557i	0.188953	+	0.888953i	−0.776852	+	0.629683i	$0.783185\pi$
$510$		0			0
$511$	−3.56486	−	33.9174i	−0.157700	−	1.50042i
$512$	−15.0364	+	10.9246i	−0.664521	+	0.482803i
$513$		0			0
$514$	−24.4213	−	7.93496i	−1.07718	−	0.349996i
$515$	1.01718	+	2.28463i	0.0448225	+	0.100673i
$516$		0			0
$517$	−3.27840	−	10.3213i	−0.144184	−	0.453929i
$518$	8.48982	−	4.90160i	0.373021	−	0.215364i
$519$		0			0
$520$	3.15884	+	3.50825i	0.138524	+	0.153847i
$521$	12.4115	−	4.03273i	0.543757	−	0.176677i	−0.0242430	−	0.999706i	$-0.507718\pi$
$521$	12.4115	−	4.03273i	0.543757	−	0.176677i	0.568000	+	0.823029i	$0.307718\pi$
$522$		0			0
$523$	−4.85832	−	6.68690i	−0.212439	−	0.292398i	0.689478	−	0.724307i	$-0.257840\pi$
$523$	−4.85832	−	6.68690i	−0.212439	−	0.292398i	−0.901917	+	0.431909i	$0.857840\pi$
$524$	−19.5941	−	4.16485i	−0.855972	−	0.181942i
$525$		0			0
$526$	−1.31740	+	12.5342i	−0.0574414	+	0.546519i
$527$	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
$533$	−32.3557	+	3.40073i	−1.40148	+	0.147302i
$534$		0			0
$535$	−0.373830	−	0.336598i	−0.0161621	−	0.0145524i
$536$	−2.64417	+	0.562035i	−0.114211	+	0.0242762i
$537$		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	−0.667747	−	0.744388i	$-0.732741\pi$
$541$	5.73469	−	7.89312i	0.246554	−	0.339352i	0.914301	+	0.405036i	$0.132741\pi$
$542$	−18.3724	+	16.5426i	−0.789163	+	0.710565i
$543$		0			0
$544$	12.9681	+	5.77378i	0.556003	+	0.247549i
$545$	16.1138	+	7.17434i	0.690240	+	0.307315i
$546$		0			0
$547$	−5.78545	+	5.20924i	−0.247368	+	0.222731i	−0.783482	−	0.621414i	$-0.786558\pi$
$547$	−5.78545	+	5.20924i	−0.247368	+	0.222731i	0.536114	+	0.844146i	$0.319892\pi$
$548$	−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
$553$	−18.0949	+	3.84619i	−0.769474	+	0.163557i
$554$	−15.7165	−	14.1512i	−0.667729	−	0.601225i
$555$		0			0
$556$	13.3264	−	1.40066i	0.565167	−	0.0594014i
$557$	−1.09093	−	3.35755i	−0.0462244	−	0.142264i	0.925281	−	0.379283i	$-0.123829\pi$
$557$	−1.09093	−	3.35755i	−0.0462244	−	0.142264i	−0.971505	+	0.237019i	$0.923829\pi$
$558$		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
$563$	0.157070	−	1.49442i	0.00661970	−	0.0629822i	−0.990713	−	0.135967i	$-0.956586\pi$
$563$	0.157070	−	1.49442i	0.00661970	−	0.0629822i	0.997333	+	0.0729849i	$0.0232525\pi$
$564$		0			0
$565$	3.75732	+	0.798643i	0.158072	+	0.0335992i
$566$	25.0367	+	34.4601i	1.05237	+	1.44847i
$567$		0			0
$568$	4.69506	−	1.52552i	0.197000	−	0.0640093i
$569$	9.92854	+	11.0268i	0.416226	+	0.462266i	0.914400	−	0.404811i	$-0.132663\pi$
$569$	9.92854	+	11.0268i	0.416226	+	0.462266i	−0.498174	+	0.867077i	$0.665996\pi$
$570$		0			0
$571$	25.8594	−	14.9299i	1.08218	−	0.624798i	0.150697	−	0.988580i	$-0.451848\pi$
$571$	25.8594	−	14.9299i	1.08218	−	0.624798i	0.931484	+	0.363782i	$0.118515\pi$
$572$	3.97084	+	12.5012i	0.166029	+	0.522703i
$573$		0			0
$574$	37.9878	+	85.3221i	1.58558	+	3.56128i
$575$	−6.72128	−	2.18388i	−0.280297	−	0.0910740i
$576$		0			0
$577$	−20.6394	+	14.9954i	−0.859228	+	0.624266i	−0.927675	−	0.373389i	$-0.878196\pi$
$577$	−20.6394	+	14.9954i	−0.859228	+	0.624266i	0.0684465	+	0.997655i	$0.478196\pi$
$578$	2.27639	+	21.6584i	0.0946854	+	0.900871i
$579$		0			0
$580$	−0.547613	−	2.57632i	−0.0227384	−	0.106976i
$581$	−34.9991	−	3.67855i	−1.45201	−	0.152612i
$582$		0			0
$583$	−2.09159	−	3.67863i	−0.0866250	−	0.152353i
$584$			9.04432i			0.374256i
$585$		0			0
$586$	−0.951344	+	2.92793i	−0.0392996	+	0.120952i
$587$	−4.91248	+	23.1114i	−0.202760	+	0.953910i	0.752603	+	0.658475i	$0.228798\pi$
$587$	−4.91248	+	23.1114i	−0.202760	+	0.953910i	−0.955363	+	0.295436i	$0.904535\pi$
$588$		0			0
$589$	9.86919	−	22.1666i	0.406653	−	0.913358i
$590$	−0.0461042	+	0.0512039i	−0.00189808	+	0.00210803i
$591$		0			0
$592$	−5.01030	+	2.23073i	−0.205922	+	0.0916824i
$593$	10.1681			0.417553			0.208777	−	0.977963i	$-0.433052\pi$
$593$	10.1681			0.417553			0.208777	+	0.977963i	$0.433052\pi$
$594$		0			0
$595$	−13.0056			−0.533178
$596$	0.0477687	−	0.0212680i	0.00195668	−	0.000871171i
$597$		0			0
$598$	−7.38360	+	8.20032i	−0.301938	+	0.335336i
$599$	−2.47923	+	5.56843i	−0.101298	+	0.227520i	−0.957084	−	0.289811i	$-0.906408\pi$
$599$	−2.47923	+	5.56843i	−0.101298	+	0.227520i	0.855786	+	0.517331i	$0.173074\pi$
$600$		0			0
$601$	−2.91575	+	13.7175i	−0.118936	+	0.559550i	0.877815	+	0.479001i	$0.159001\pi$
$601$	−2.91575	+	13.7175i	−0.118936	+	0.559550i	−0.996751	+	0.0805495i	$0.974333\pi$
$602$	10.2896	−	31.6680i	0.419371	−	1.29069i
$603$		0			0
$604$			3.55632i			0.144705i
$605$	−12.6241	+	3.91829i	−0.513242	+	0.159301i
$606$		0			0
$607$	0.841863	+	0.0884833i	0.0341701	+	0.00359143i	0.121598	−	0.992579i	$-0.461198\pi$
$607$	0.841863	+	0.0884833i	0.0341701	+	0.00359143i	−0.0874280	+	0.996171i	$0.527865\pi$
$608$	−6.03029	−	28.3703i	−0.244561	−	1.15057i
$609$		0			0
$610$	−0.270605	−	2.57463i	−0.0109565	−	0.104244i
$611$	−8.08321	+	5.87280i	−0.327012	+	0.237588i
$612$		0			0
$613$	−24.1513	−	7.84724i	−0.975462	−	0.316947i	−0.222443	−	0.974946i	$-0.571403\pi$
$613$	−24.1513	−	7.84724i	−0.975462	−	0.316947i	−0.753019	+	0.657999i	$0.771403\pi$
$614$	−1.73644	−	3.90011i	−0.0700770	−	0.157395i
$615$		0			0
$616$	−16.7570	+	12.0064i	−0.675158	+	0.483753i
$617$	−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
$619$	−17.4316	−	19.3597i	−0.700635	−	0.778134i	0.282842	−	0.959166i	$-0.408723\pi$
$619$	−17.4316	−	19.3597i	−0.700635	−	0.778134i	−0.983477	+	0.181033i	$0.942056\pi$
$620$	7.84611	−	2.54935i	0.315107	−	0.102385i
$621$		0			0
$622$	11.3121	+	15.5698i	0.453574	+	0.624291i
$623$	−48.7156	−	10.3548i	−1.95175	−	0.414857i
$624$		0			0
$625$	−0.567118	+	5.39577i	−0.0226847	+	0.215831i
$626$	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	0.995923	−	0.0902022i	$-0.0287513\pi$
$631$	3.44605	+	10.6058i	0.137185	+	0.422212i	−0.858739	+	0.512414i	$0.828751\pi$
$632$	4.87904	−	0.512807i	0.194078	−	0.0203984i
$633$		0			0
$634$	−36.1551	−	32.5542i	−1.43590	−	1.29289i
$635$	−26.2137	+	5.57190i	−1.04026	+	0.221114i
$636$		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
$641$	8.20366	−	7.38661i	0.324025	−	0.291754i	−0.491023	−	0.871146i	$-0.663377\pi$
$641$	8.20366	−	7.38661i	0.324025	−	0.291754i	0.815048	+	0.579393i	$0.196710\pi$
$642$		0			0
$643$	33.5638	+	14.9436i	1.32363	+	0.589317i	0.942190	−	0.335078i	$-0.108763\pi$
$643$	33.5638	+	14.9436i	1.32363	+	0.589317i	0.381437	+	0.924395i	$0.375429\pi$
$644$	11.3599	+	5.05776i	0.447643	+	0.199304i
$645$		0			0
$646$	−13.7703	+	12.3988i	−0.541784	+	0.487824i
$647$	−1.59821	+	2.19975i	−0.0628321	+	0.0864810i	−0.839277	−	0.543705i	$-0.817021\pi$
$647$	−1.59821	+	2.19975i	−0.0628321	+	0.0864810i	0.776445	+	0.630186i	$0.217021\pi$
$648$		0			0
$649$	0.0960246	−	0.0419955i	0.00376930	−	0.00164847i
$650$	17.0991	+	9.87215i	0.670681	+	0.387218i
$651$		0			0
$652$	−18.4525	+	3.92219i	−0.722655	+	0.153605i
$653$	32.8807	+	29.6059i	1.28672	+	1.15857i	0.978272	+	0.207327i	$0.0664764\pi$
$653$	32.8807	+	29.6059i	1.28672	+	1.15857i	0.308448	+	0.951241i	$0.400190\pi$
$654$		0			0
$655$	−18.5226	+	1.94681i	−0.723739	+	0.0760681i
$656$	−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	−0.941432	−	0.337203i	$-0.890519\pi$
$659$	−4.58714	+	7.94516i	−0.178690	+	0.309499i	0.762742	+	0.646702i	$0.223852\pi$
$660$		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	$0.771686\pi$
$662$	3.28575	−	31.2618i	0.127704	−	1.21503i
$663$		0			0
$664$	9.12882	+	1.94039i	0.354267	+	0.0753018i
$665$	15.6193	+	21.4981i	0.605691	+	0.833662i
$666$		0			0
$667$	−3.20547	+	1.04152i	−0.124116	+	0.0403278i
$668$	0.771649	+	0.857003i	0.0298560	+	0.0331584i
$669$		0			0
$670$	3.97588	−	2.29547i	0.153602	−	0.0886819i
$671$	−1.24156	+	3.73700i	−0.0479300	+	0.144265i
$672$		0			0
$673$	−7.19227	−	16.1541i	−0.277242	−	0.622695i	0.720232	−	0.693733i	$-0.244035\pi$
$673$	−7.19227	−	16.1541i	−0.277242	−	0.622695i	−0.997474	+	0.0710383i	$0.977369\pi$
$674$	22.4408	+	7.29146i	0.864387	+	0.280856i
$675$		0			0
$676$	−3.80243	+	2.76263i	−0.146247	+	0.106255i
$677$	1.24345	+	11.8306i	0.0477895	+	0.454687i	0.992083	+	0.125583i	$0.0400800\pi$
$677$	1.24345	+	11.8306i	0.0477895	+	0.454687i	−0.944294	+	0.329104i	$0.893253\pi$
$678$		0			0
$679$	−14.5995	−	68.6853i	−0.560278	−	2.63590i
$680$	3.43015	+	0.360523i	0.131540	+	0.0138254i
$681$		0			0
$682$	−31.7699	−	3.55138i	−1.21653	−	0.135989i
$683$			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
$686$	−17.2359	+	81.0883i	−0.658068	+	3.09597i
$687$		0			0
$688$	−7.57693	+	17.0181i	−0.288868	+	0.648808i
$689$	−2.61243	+	2.90139i	−0.0995255	+	0.110534i
$690$		0			0
$691$	16.4659	−	7.33107i	0.626391	−	0.278887i	−0.0688913	−	0.997624i	$-0.521946\pi$
$691$	16.4659	−	7.33107i	0.626391	−	0.278887i	0.695282	+	0.718737i	$0.255279\pi$
$692$	17.1216			0.650864
$693$		0			0
$694$	38.5698			1.46409
$695$	11.3814	−	5.06735i	0.431723	−	0.192215i
$696$		0			0
$697$	−15.9048	+	17.6641i	−0.602438	+	0.669075i
$698$	−6.88652	+	15.4674i	−0.260659	+	0.585449i
$699$		0			0
$700$	4.62603	−	21.7638i	0.174847	−	0.822593i
$701$	2.60431	−	8.01524i	0.0983635	−	0.302732i	−0.889752	−	0.456444i	$-0.849123\pi$
$701$	2.60431	−	8.01524i	0.0983635	−	0.302732i	0.988116	+	0.153712i	$0.0491229\pi$
$702$		0			0
$703$		−	5.09762i		−	0.192260i
$704$	−4.87977	+	2.77454i	−0.183913	+	0.104569i
$705$		0			0
$706$	−16.4602	−	1.73004i	−0.619488	−	0.0651108i
$707$	−16.1909	−	76.1723i	−0.608923	−	2.86476i
$708$		0			0
$709$	−2.16511	−	20.5997i	−0.0813126	−	0.773637i	−0.956869	−	0.290521i	$-0.906171\pi$
$709$	−2.16511	−	20.5997i	−0.0813126	−	0.773637i	0.875556	−	0.483116i	$-0.160495\pi$
$710$	−6.78282	+	4.92801i	−0.254555	+	0.184945i
$711$		0			0
$712$	12.5614	+	4.08144i	0.470758	+	0.152959i
$713$	−4.29389	−	9.64424i	−0.160808	−	0.361180i
$714$		0			0
$715$	7.10293	+	9.91333i	0.265634	+	0.370738i
$716$	−22.5476	+	13.0179i	−0.842644	+	0.486501i
$717$		0			0
$718$	9.49619	+	10.5466i	0.354395	+	0.393595i
$719$	34.3009	−	11.1450i	1.27921	−	0.415640i	0.410906	−	0.911678i	$-0.365212\pi$
$719$	34.3009	−	11.1450i	1.27921	−	0.415640i	0.868301	+	0.496038i	$0.165212\pi$
$720$		0			0
$721$	5.92214	+	8.15112i	0.220552	+	0.303564i
$722$	3.31044	+	0.703656i	0.123202	+	0.0261874i
$723$		0			0
$724$	0.607437	−	5.77937i	0.0225752	−	0.214789i
$725$	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
$731$	8.42783	−	0.885800i	0.311714	−	0.0327625i
$732$		0			0
$733$	−30.1889	−	27.1822i	−1.11505	−	1.00400i	−0.999943	−	0.0106457i	$-0.996611\pi$
$733$	−30.1889	−	27.1822i	−1.11505	−	1.00400i	−0.115110	−	0.993353i	$-0.536722\pi$
$734$	−43.4916	+	9.24443i	−1.60531	+	0.341218i
$735$		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	−0.811945	−	0.583734i	$-0.801591\pi$
$739$	−0.159730	+	0.219850i	−0.00587578	+	0.00808731i	0.806069	+	0.591822i	$0.201591\pi$
$740$	1.28801	−	1.15973i	0.0473483	−	0.0426326i
$741$		0			0
$742$	10.2390	+	4.55870i	0.375886	+	0.167355i
$743$	18.7849	+	8.36360i	0.689153	+	0.306831i	0.721271	−	0.692653i	$-0.243558\pi$
$743$	18.7849	+	8.36360i	0.689153	+	0.306831i	−0.0321177	+	0.999484i	$0.510225\pi$
$744$		0			0
$745$	0.0361289	−	0.0325306i	0.00132366	−	0.00119183i
$746$	−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
$751$	50.9801	−	10.8362i	1.86029	−	0.395417i	0.865814	−	0.500366i	$-0.166801\pi$
$751$	50.9801	−	10.8362i	1.86029	−	0.395417i	0.994478	+	0.104949i	$0.0334678\pi$
$752$	−11.9250	−	10.7374i	−0.434861	−	0.391551i
$753$		0			0
$754$	9.36473	−	0.984272i	0.341043	−	0.0358451i
$755$	1.02176	+	3.14467i	0.0371858	+	0.114446i
$756$		0			0
$757$	30.2153	+	21.9527i	1.09819	+	0.797884i	0.980764	−	0.195197i	$-0.0625347\pi$
$757$	30.2153	+	21.9527i	1.09819	+	0.797884i	0.117429	+	0.993081i	$0.462535\pi$
$758$	26.5495	−	45.9851i	0.964322	−	1.67025i
$759$		0			0
$760$	−3.52355	−	6.10297i	−0.127813	−	0.221378i
$761$	4.66624	−	44.3963i	0.169151	−	1.60936i	−0.499856	−	0.866109i	$-0.666614\pi$
$761$	4.66624	−	44.3963i	0.169151	−	1.60936i	0.669007	−	0.743256i	$-0.266720\pi$
$762$		0			0
$763$	69.5098	+	14.7748i	2.51642	+	0.534883i
$764$	13.5025	+	18.5846i	0.488503	+	0.672367i
$765$		0			0
$766$	−49.1124	+	15.9576i	−1.77450	+	0.576571i
$767$	−0.0647022	−	0.0718591i	−0.00233626	−	0.00259468i
$768$		0			0
$769$	19.3337	−	11.1623i	0.697192	−	0.402524i	−0.109109	−	0.994030i	$-0.534800\pi$
$769$	19.3337	−	11.1623i	0.697192	−	0.402524i	0.806301	+	0.591506i	$0.201466\pi$
$770$	20.7647	−	28.1869i	0.748308	−	1.01579i
$771$		0			0
$772$	−3.23767	−	7.27192i	−0.116526	−	0.261722i
$773$	−19.1268	−	6.21468i	−0.687944	−	0.223526i	−0.0558738	−	0.998438i	$-0.517794\pi$
$773$	−19.1268	−	6.21468i	−0.687944	−	0.223526i	−0.632070	+	0.774911i	$0.717794\pi$
$774$		0			0
$775$	−15.2820	+	11.1030i	−0.548946	+	0.398832i
$776$	1.94653	+	18.5200i	0.0698765	+	0.664830i
$777$		0			0
$778$	−5.38778	−	25.3475i	−0.193161	−	0.908753i
$779$	48.2998	+	5.07651i	1.73052	+	0.181885i
$780$		0			0
$781$	12.4915	−	2.56907i	0.446981	−	0.0919285i
$782$			8.06192i			0.288294i
$783$		0			0
$784$	24.9624	−	76.8265i	0.891516	−	2.74380i
$785$	−0.527125	+	2.47993i	−0.0188139	+	0.0885124i
$786$		0			0
$787$	−14.1620	+	31.8083i	−0.504820	+	1.13384i	0.463946	+	0.885864i	$0.346433\pi$
$787$	−14.1620	+	31.8083i	−0.504820	+	1.13384i	−0.968765	+	0.247980i	$0.920233\pi$
$788$	19.4670	−	21.6203i	0.693482	−	0.770190i
$789$		0			0
$790$	−7.61146	+	3.38884i	−0.270803	+	0.120569i
$791$	15.4756			0.550249
$792$		0			0
$793$	3.63312			0.129016
$794$	3.65819	−	1.62873i	0.129824	−	0.0578014i
$795$		0			0
$796$	8.04865	−	8.93893i	0.285277	−	0.316832i
$797$	−0.319992	+	0.718713i	−0.0113347	+	0.0254581i	−0.919124	−	0.393968i	$-0.871102\pi$
$797$	−0.319992	+	0.718713i	−0.0113347	+	0.0254581i	0.907789	+	0.419426i	$0.137769\pi$
$798$		0			0
$799$	−1.51770	+	7.14022i	−0.0536924	+	0.252603i
$800$	−6.97744	+	21.4743i	−0.246690	+	0.759233i
$801$		0			0
$802$		−	57.2351i		−	2.02104i
$803$	−2.59559	+	23.2196i	−0.0915964	+	0.819402i
$804$		0			0
$805$	11.4981	+	1.20850i	0.405255	+	0.0425941i
$806$	6.13215	+	28.8495i	0.215996	+	1.01618i
$807$		0			0
$808$	2.15871	+	20.5388i	0.0759433	+	0.722552i
$809$	−24.9035	+	18.0934i	−0.875560	+	0.636131i	−0.932073	−	0.362270i	$-0.882002\pi$
$809$	−24.9035	+	18.0934i	−0.875560	+	0.636131i	0.0565132	+	0.998402i	$0.482002\pi$
$810$		0			0
$811$	41.4535	+	13.4691i	1.45563	+	0.472963i	0.926732	−	0.375723i	$-0.122606\pi$
$811$	41.4535	+	13.4691i	1.45563	+	0.472963i	0.528898	+	0.848686i	$0.322606\pi$
$812$	−4.31600	−	9.69390i	−0.151462	−	0.340189i
$813$		0			0
$814$	−6.40087	+	2.03315i	−0.224351	+	0.0712617i
$815$	−15.1897	+	8.76976i	−0.532071	+	0.307191i
$816$		0			0
$817$	−11.5858	−	12.8673i	−0.405335	−	0.450170i
$818$	11.6971	−	3.80063i	0.408981	−	0.132886i
$819$		0			0
$820$	9.70574	+	13.3588i	0.338939	+	0.466510i
$821$	38.1089	+	8.10030i	1.33001	+	0.282702i	0.817475	−	0.575964i	$-0.195373\pi$
$821$	38.1089	+	8.10030i	1.33001	+	0.282702i	0.512535	+	0.858666i	$0.328706\pi$
$822$		0			0
$823$	−3.92819	+	37.3742i	−0.136928	+	1.30278i	0.683042	+	0.730379i	$0.260656\pi$
$823$	−3.92819	+	37.3742i	−0.136928	+	1.30278i	−0.819971	+	0.572406i	$0.806010\pi$
$824$	−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	$-0.591388\pi$
$827$	−36.8905	−	26.8025i	−1.28281	−	0.932015i	−0.999634	+	0.0270532i	$0.991388\pi$
$828$		0			0
$829$	8.83146	+	27.1804i	0.306729	+	0.944016i	0.979026	+	0.203734i	$0.0653078\pi$
$829$	8.83146	+	27.1804i	0.306729	+	0.944016i	−0.672297	+	0.740282i	$0.734692\pi$
$830$	−15.7631	+	1.65677i	−0.547146	+	0.0575074i
$831$		0			0
$832$	3.84875	+	3.46543i	0.133431	+	0.120142i
$833$	−35.9443	+	7.64020i	−1.24540	+	0.264717i
$834$		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
$839$	−4.22962	+	3.80837i	−0.146023	+	0.131480i	−0.738905	−	0.673810i	$-0.764657\pi$
$839$	−4.22962	+	3.80837i	−0.146023	+	0.131480i	0.592882	+	0.805289i	$0.297990\pi$
$840$		0			0
$841$	−23.8653	−	10.6255i	−0.822943	−	0.366398i
$842$	−9.27164	−	4.12800i	−0.319522	−	0.142260i
$843$		0			0
$844$	−13.4573	+	12.1170i	−0.463220	+	0.417085i
$845$	−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
$850$	14.1100	−	2.99918i	0.483969	−	0.102871i
$851$	−1.64820	−	1.48405i	−0.0564996	−	0.0508725i
$852$		0			0
$853$	−24.9261	+	2.61983i	−0.853452	+	0.0897014i	−0.521143	−	0.853469i	$-0.674494\pi$
$853$	−24.9261	+	2.61983i	−0.853452	+	0.0897014i	−0.332309	+	0.943171i	$0.607828\pi$
$854$	−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	$-0.623118\pi$
$857$	17.9582	−	31.1045i	0.613440	−	1.06251i	0.990656	−	0.136385i	$-0.0435483\pi$
$858$		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	$0.746841\pi$
$860$	0.615358	−	5.85474i	0.0209835	−	0.199645i
$861$		0			0
$862$	−34.6244	−	7.35963i	−1.17931	−	0.250670i
$863$	−16.0883	−	22.1436i	−0.547652	−	0.753778i	0.442039	−	0.896996i	$-0.354255\pi$
$863$	−16.0883	−	22.1436i	−0.547652	−	0.753778i	−0.989691	+	0.143217i	$0.954255\pi$
$864$		0			0
$865$	15.1397	−	4.91919i	0.514765	−	0.167257i
$866$	−27.3824	−	30.4112i	−0.930491	−	1.03342i
$867$		0			0
$868$	28.7841	−	16.6185i	0.976995	−	0.564068i
$869$	12.6732	+	0.0836764i	0.429909	+	0.00283853i
$870$		0			0
$871$	2.62057	+	5.88589i	0.0887945	+	0.199436i
$872$	−17.9232	−	5.82361i	−0.606957	−	0.197212i
$873$		0			0
$874$	13.3263	−	9.68210i	0.450768	−	0.327502i
$875$	−5.20282	−	49.5015i	−0.175887	−	1.67346i
$876$		0			0
$877$	−10.8203	−	50.9056i	−0.365376	−	1.71896i	−0.649665	−	0.760221i	$-0.725091\pi$
$877$	−10.8203	−	50.9056i	−0.365376	−	1.71896i	0.284289	−	0.958739i	$-0.408242\pi$
$878$	54.1137	+	5.68757i	1.82625	+	0.191946i
$879$		0			0
$880$	−13.2016	+	14.4686i	−0.445027	+	0.487737i
$881$		−	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	0.806674	+	0.590997i	$0.201266\pi$
$883$	−5.74452	+	17.6798i	−0.193318	+	0.594973i	−0.999992	+	0.00397571i	$0.998734\pi$
$884$	1.83826	−	8.64832i	0.0618273	−	0.290875i
$885$		0			0
$886$	23.2830	−	52.2944i	0.782206	−	1.75686i
$887$	−36.4857	+	40.5215i	−1.22507	+	1.36058i	−0.313419	+	0.949615i	$0.601474\pi$
$887$	−36.4857	+	40.5215i	−1.22507	+	1.36058i	−0.911652	+	0.410964i	$0.865192\pi$
$888$		0			0
$889$	−98.6344	+	43.9149i	−3.30809	+	1.47286i
$890$	−22.4310			−0.751890
$891$		0			0
$892$	−20.8507			−0.698132
$893$	13.6254	−	6.06643i	0.455958	−	0.203005i
$894$		0			0
$895$	−16.1975	+	17.9892i	−0.541424	+	0.601312i
$896$	−18.9588	+	42.5822i	−0.633369	+	1.42257i
$897$		0			0
$898$	−14.3360	+	67.4457i	−0.478399	+	2.25069i
$899$	−2.78384	+	8.56777i	−0.0928461	+	0.285751i
$900$		0			0
$901$			2.85243i			0.0950281i
$902$	−12.8896	−	62.6728i	−0.429177	−	2.08678i
$903$		0			0
$904$	−4.08159	−	0.428993i	−0.135752	−	0.0142681i
$905$	−1.12334	−	5.28492i	−0.0373412	−	0.175677i
$906$		0			0
$907$	1.29961	+	12.3650i	0.0431530	+	0.410573i	0.994680	+	0.103009i	$0.0328471\pi$
$907$	1.29961	+	12.3650i	0.0431530	+	0.410573i	−0.951527	+	0.307564i	$0.900486\pi$
$908$	15.3860	−	11.1786i	0.510603	−	0.370975i
$909$		0			0
$910$	−30.7195	−	9.98139i	−1.01834	−	0.330880i
$911$	18.2983	+	41.0986i	0.606249	+	1.36166i	0.912253	+	0.409628i	$0.134341\pi$
$911$	18.2983	+	41.0986i	0.606249	+	1.36166i	−0.306004	+	0.952030i	$0.598992\pi$
$912$		0			0
$913$	22.8797	+	7.60144i	0.757208	+	0.251571i
$914$	61.6402	−	35.5880i	2.03887	−	1.17715i
$915$		0			0
$916$	19.1980	+	21.3215i	0.634319	+	0.704483i
$917$	−71.3622	+	23.1870i	−2.35659	+	0.765702i
$918$		0			0
$919$	13.6185	+	18.7442i	0.449232	+	0.618315i	0.972232	−	0.234017i	$-0.0751872\pi$
$919$	13.6185	+	18.7442i	0.449232	+	0.618315i	−0.523000	+	0.852333i	$0.675187\pi$
$920$	−2.99906	−	0.637469i	−0.0988760	−	0.0210167i
$921$		0			0
$922$	3.32907	−	31.6740i	0.109637	−	1.04313i
$923$	−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
$929$	11.5041	−	1.20913i	0.377438	−	0.0396703i	0.0860898	−	0.996287i	$-0.472563\pi$
$929$	11.5041	−	1.20913i	0.377438	−	0.0396703i	0.291348	+	0.956617i	$0.405896\pi$
$930$		0			0
$931$	55.7971	+	50.2400i	1.82868	+	1.64655i
$932$	6.53392	−	1.38883i	0.214026	−	0.0454926i
$933$		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	−0.486242	−	0.873824i	$-0.661633\pi$
$937$	15.1544	−	20.8582i	0.495071	−	0.681407i	0.981313	+	0.192417i	$0.0616326\pi$
$938$	13.7451	−	12.3762i	0.448795	−	0.404097i
$939$		0			0
$940$	4.63265	+	2.06259i	0.151100	+	0.0672743i
$941$	−54.0436	−	24.0617i	−1.76177	−	0.784391i	−0.988670	−	0.150107i	$-0.952038\pi$
$941$	−54.0436	−	24.0617i	−1.76177	−	0.784391i	−0.773100	−	0.634284i	$-0.781295\pi$
$942$		0			0
$943$	15.7027	−	14.1387i	0.511349	−	0.460421i
$944$	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
$949$	21.0852	−	4.48179i	0.684454	−	0.145485i
$950$	−21.9033	−	19.7218i	−0.710636	−	0.639860i
$951$		0			0
$952$	13.8193	−	1.45247i	0.447886	−	0.0470747i
$953$	2.50261	+	7.70223i	0.0810674	+	0.249500i	0.983373	−	0.181597i	$-0.0581267\pi$
$953$	2.50261	+	7.70223i	0.0810674	+	0.249500i	−0.902306	+	0.431097i	$0.858127\pi$
$954$		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
$959$	−8.67396	+	82.5272i	−0.280097	+	2.66494i
$960$		0			0
$961$	2.72196	+	0.578570i	0.0878050	+	0.0186635i
$962$	3.64210	+	5.01292i	0.117426	+	0.161623i
$963$		0			0
$964$	8.66885	−	2.81668i	0.279205	−	0.0907192i
$965$	−4.95219	−	5.49997i	−0.159417	−	0.177050i
$966$		0			0
$967$	−8.61320	+	4.97284i	−0.276982	+	0.159916i	−0.632056	−	0.774922i	$-0.717789\pi$
$967$	−8.61320	+	4.97284i	−0.276982	+	0.159916i	0.355074	+	0.934838i	$0.384456\pi$
$968$	12.9763	−	5.57330i	0.417075	−	0.179133i
$969$		0			0
$970$	−12.8635	−	28.8918i	−0.413021	−	0.927661i
$971$	36.6171	+	11.8976i	1.17510	+	0.381813i	0.830544	−	0.556953i	$-0.188030\pi$
$971$	36.6171	+	11.8976i	1.17510	+	0.381813i	0.344555	+	0.938766i	$0.388030\pi$
$972$		0			0
$973$	40.6068	−	29.5025i	1.30179	−	0.945808i
$974$	4.93170	+	46.9220i	0.158022	+	1.50348i
$975$		0			0
$976$	1.21316	+	5.70748i	0.0388324	+	0.182692i
$977$	20.2002	+	2.12313i	0.646263	+	0.0679250i	0.421989	−	0.906601i	$-0.361332\pi$
$977$	20.2002	+	2.12313i	0.646263	+	0.0679250i	0.224274	+	0.974526i	$0.427999\pi$
$978$		0			0
$979$	31.0777	+	14.0833i	0.993249	+	0.450104i
$980$			25.5281i			0.815464i
$981$		0			0
$982$	−4.11112	+	12.6527i	−0.131191	+	0.403765i
$983$	−2.02155	+	9.51064i	−0.0644774	+	0.303342i	−0.998556	−	0.0537258i	$-0.982890\pi$
$983$	−2.02155	+	9.51064i	−0.0644774	+	0.303342i	0.934078	+	0.357068i	$0.116224\pi$
$984$		0			0
$985$	11.0019	−	24.7107i	0.350550	−	0.787349i
$986$	4.60334	−	5.11252i	0.146600	−	0.162816i
$987$		0			0
$988$	−16.5033	+	7.34773i	−0.525039	+	0.233763i
$989$	−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	$0.618600\pi$
$992$	−30.8131	+	13.7189i	−0.978317	+	0.435575i
$993$		0			0
$994$	−22.6015	+	25.1015i	−0.716876	+	0.796171i
$995$	4.54876	−	10.2167i	0.144205	−	0.323891i
$996$		0			0
$997$	4.47047	−	21.0319i	0.141581	−	0.666087i	−0.848913	−	0.528532i	$-0.822743\pi$
$997$	4.47047	−	21.0319i	0.141581	−	0.666087i	0.990494	−	0.137554i	$-0.0439242\pi$
$998$	−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.62.8		80
3.2	odd	2		99.2.p.a.29.3	✓	80
9.2	odd	6		891.2.k.a.161.16		80
9.4	even	3		99.2.p.a.95.3	yes	80
9.5	odd	6	inner	297.2.t.a.260.8		80
9.7	even	3		891.2.k.a.161.5		80
11.8	odd	10	inner	297.2.t.a.8.8		80
33.8	even	10		99.2.p.a.74.3	yes	80
99.41	even	30	inner	297.2.t.a.206.8		80
99.52	odd	30		891.2.k.a.404.16		80
99.74	even	30		891.2.k.a.404.5		80
99.85	odd	30		99.2.p.a.41.3	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.3	✓	80	3.2	odd	2
99.2.p.a.41.3	yes	80	99.85	odd	30
99.2.p.a.74.3	yes	80	33.8	even	10
99.2.p.a.95.3	yes	80	9.4	even	3
297.2.t.a.8.8		80	11.8	odd	10	inner
297.2.t.a.62.8		80	1.1	even	1	trivial
297.2.t.a.206.8		80	99.41	even	30	inner
297.2.t.a.260.8		80	9.5	odd	6	inner
891.2.k.a.161.5		80	9.7	even	3
891.2.k.a.161.16		80	9.2	odd	6
891.2.k.a.404.5		80	99.74	even	30
891.2.k.a.404.16		80	99.52	odd	30

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)

\(f(q)\)	\(=\)	\(q+(1.65764 - 0.738027i) q^{2} +(0.864813 - 0.960472i) q^{4} +(0.488756 - 1.09776i) q^{5} +(1.00654 - 4.73540i) q^{7} +(-0.396737 + 1.22103i) q^{8} -2.18041i q^{10} +(-1.36897 + 3.02091i) q^{11} +(3.04321 + 0.319854i) q^{13} +(-1.82638 - 8.59243i) q^{14} +(0.513703 + 4.88755i) q^{16} +(1.80866 - 1.31407i) q^{17} +(-4.34428 - 1.41154i) q^{19} +(-0.631690 - 1.41880i) q^{20} +(-0.0397341 + 6.01791i) q^{22} +(-1.72112 + 0.993689i) q^{23} +(2.37945 + 2.64264i) q^{25} +(5.28060 - 1.71577i) q^{26} +(-3.67776 - 5.06200i) q^{28} +(1.65886 + 0.352601i) q^{29} +(-0.555254 + 5.28289i) q^{31} +(3.17481 + 5.49894i) q^{32} +(2.02828 - 3.51308i) q^{34} +(-4.70641 - 3.41941i) q^{35} +(0.344857 + 1.06136i) q^{37} +(-8.24299 + 0.866373i) q^{38} +(1.14650 + 1.03231i) q^{40} +(-10.3998 + 2.21054i) q^{41} +(3.28272 + 1.89528i) q^{43} +(1.71760 + 3.92738i) q^{44} +(-2.11962 + 2.91741i) q^{46} +(-2.42651 + 2.18484i) q^{47} +(-15.0161 - 6.68560i) q^{49} +(5.89460 + 2.62445i) q^{50} +(2.93902 - 2.64630i) q^{52} +(-0.749954 + 1.03222i) q^{53} +(2.64716 + 2.97930i) q^{55} +(5.38274 + 3.10773i) q^{56} +(3.01001 - 0.639797i) q^{58} +(-0.0234836 - 0.0211447i) q^{59} +(1.18080 - 0.124107i) q^{61} +(2.97851 + 9.16690i) q^{62} +(1.36926 + 0.994827i) q^{64} +(1.83851 - 3.18440i) q^{65} +(1.05277 + 1.82345i) q^{67} +(0.302026 - 2.87359i) q^{68} +(-10.3251 - 2.19467i) q^{70} +(-2.26013 - 3.11080i) q^{71} +(6.69980 - 2.17690i) q^{73} +(1.35496 + 1.50483i) q^{74} +(-5.11273 + 2.95184i) q^{76} +(12.9273 + 9.52329i) q^{77} +(-1.55422 - 3.49084i) q^{79} +(5.61646 + 1.82490i) q^{80} +(-15.6076 + 11.3396i) q^{82} +(-0.759844 - 7.22943i) q^{83} +(-0.558543 - 2.62774i) q^{85} +(6.84032 + 0.718946i) q^{86} +(-3.14551 - 2.87006i) q^{88} -10.2875i q^{89} +(4.57775 - 14.0889i) q^{91} +(-0.534037 + 2.51244i) q^{92} +(-2.40980 + 5.41250i) q^{94} +(-3.67283 + 4.07909i) q^{95} +(13.2506 - 5.89957i) q^{97} -29.8254 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) \) 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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