LMFDB - Embedded newform 855.2.dl.a.307.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [855,2,Mod(127,855)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(855, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([0, 9, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("855.127"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.dl (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,12,0,0,12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			307.8
Character	$\chi$	$=$	855.307
Dual form			855.2.dl.a.298.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.46340 - 0.215520i) q^{2} +(4.05227 - 0.714525i) q^{4} +(1.91831 - 1.14895i) q^{5} +(0.801323 - 2.99058i) q^{7} +(5.05128 - 1.35349i) q^{8} +(4.47794 - 3.24376i) q^{10} +(-2.71405 + 4.70087i) q^{11} +(-0.828132 - 1.77593i) q^{13} +(1.32945 - 7.53969i) q^{14} +(4.41834 - 1.60814i) q^{16} +(0.146177 + 1.67081i) q^{17} +(-2.83929 + 3.30733i) q^{19} +(6.95256 - 6.02655i) q^{20} +(-5.67266 + 12.1651i) q^{22} +(-1.93732 - 1.35652i) q^{23} +(2.35981 - 4.40809i) q^{25} +(-2.42277 - 4.19636i) q^{26} +(1.11034 - 12.6912i) q^{28} +(0.236581 - 0.198515i) q^{29} +(-3.68657 + 2.12844i) q^{31} +(1.05854 - 0.493605i) q^{32} +(0.720185 + 4.08437i) q^{34} +(-1.89885 - 6.65753i) q^{35} +(3.08090 - 3.08090i) q^{37} +(-6.28150 + 8.75921i) q^{38} +(8.13481 - 8.40008i) q^{40} +(3.63501 + 9.98710i) q^{41} +(3.28576 + 4.69255i) q^{43} +(-7.63918 + 20.9885i) q^{44} +(-5.06474 - 2.92413i) q^{46} +(2.92349 + 0.255773i) q^{47} +(-2.23925 - 1.29283i) q^{49} +(4.86313 - 11.3675i) q^{50} +(-4.62477 - 6.60485i) q^{52} +(3.97255 - 5.67339i) q^{53} +(0.194697 + 12.1360i) q^{55} -16.1908i q^{56} +(0.540010 - 0.540010i) q^{58} +(1.92632 + 1.61638i) q^{59} +(1.00075 + 5.67553i) q^{61} +(-8.62279 + 6.03774i) q^{62} +(-5.64270 + 3.25782i) q^{64} +(-3.62908 - 2.45530i) q^{65} +(0.197751 - 2.26031i) q^{67} +(1.78619 + 6.66614i) q^{68} +(-6.11245 - 15.9909i) q^{70} +(-8.76383 - 1.54530i) q^{71} +(5.20427 - 11.1606i) q^{73} +(6.92550 - 8.25349i) q^{74} +(-9.14239 + 15.4310i) q^{76} +(11.8835 + 11.8835i) q^{77} +(14.4810 - 5.27064i) q^{79} +(6.62806 - 8.16138i) q^{80} +(11.1069 + 23.8188i) q^{82} +(-3.66649 - 0.982433i) q^{83} +(2.20010 + 3.03718i) q^{85} +(9.10547 + 10.8515i) q^{86} +(-7.34685 + 27.4188i) q^{88} +(-3.79487 - 1.38122i) q^{89} +(-5.97467 + 1.05350i) q^{91} +(-8.81981 - 4.11274i) q^{92} +7.25686 q^{94} +(-1.64666 + 9.60669i) q^{95} +(-13.4973 + 1.18086i) q^{97} +(-5.79481 - 2.70216i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{2} + 12 q^{5} + 18 q^{8} - 12 q^{10} + 12 q^{11} - 12 q^{13} + 12 q^{16} + 30 q^{17} + 84 q^{20} - 24 q^{22} + 12 q^{25} + 48 q^{26} - 36 q^{31} - 18 q^{32} + 30 q^{35} - 54 q^{38} + 54 q^{40}+ \cdots + 90 q^{98}+O(q^{100}) $ 96 * q + 12 * q^2 + 12 * q^5 + 18 * q^8 - 12 * q^10 + 12 * q^11 - 12 * q^13 + 12 * q^16 + 30 * q^17 + 84 * q^20 - 24 * q^22 + 12 * q^25 + 48 * q^26 - 36 * q^31 - 18 * q^32 + 30 * q^35 - 54 * q^38 + 54 * q^40 - 12 * q^41 + 48 * q^43 - 36 * q^46 + 24 * q^47 - 126 * q^50 + 30 * q^53 + 18 * q^55 + 120 * q^58 - 48 * q^61 - 60 * q^62 - 72 * q^65 + 108 * q^67 - 18 * q^68 + 36 * q^70 + 24 * q^71 + 6 * q^73 + 60 * q^76 - 168 * q^77 + 60 * q^80 + 60 * q^82 - 36 * q^85 + 180 * q^86 - 198 * q^88 - 24 * q^91 + 72 * q^92 + 24 * q^95 - 72 * q^97 + 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	2.46340	−	0.215520i	1.74189	−	0.152395i	0.828634	−	0.559790i	$-0.189118\pi$
$2$	2.46340	−	0.215520i	1.74189	−	0.152395i	0.913252	+	0.407395i	$0.133563\pi$
$3$		0			0
$3$		0			0
$4$	4.05227	−	0.714525i	2.02614	−	0.357263i
$5$	1.91831	−	1.14895i	0.857894	−	0.513827i
$5$	1.91831	−	1.14895i	0.857894	−	0.513827i
$6$		0			0
$7$	0.801323	−	2.99058i	0.302871	−	1.13033i	−0.631891	−	0.775058i	$-0.717721\pi$
$7$	0.801323	−	2.99058i	0.302871	−	1.13033i	0.934762	−	0.355274i	$-0.115613\pi$
$8$	5.05128	−	1.35349i	1.78590	−	0.478529i
$9$		0			0
$10$	4.47794	−	3.24376i	1.41605	−	1.02577i
$11$	−2.71405	+	4.70087i	−0.818316	+	1.41737i	0.0886055	+	0.996067i	$0.471759\pi$
$11$	−2.71405	+	4.70087i	−0.818316	+	1.41737i	−0.906922	+	0.421299i	$0.861574\pi$
$12$		0			0
$13$	−0.828132	−	1.77593i	−0.229682	−	0.492556i	0.757364	−	0.652993i	$-0.226487\pi$
$13$	−0.828132	−	1.77593i	−0.229682	−	0.492556i	−0.987046	+	0.160438i	$0.948709\pi$
$14$	1.32945	−	7.53969i	0.355311	−	2.01507i
$15$		0			0
$16$	4.41834	−	1.60814i	1.10458	−	0.402036i
$17$	0.146177	+	1.67081i	0.0354531	+	0.405231i	0.993099	+	0.117282i	$0.0374180\pi$
$17$	0.146177	+	1.67081i	0.0354531	+	0.405231i	−0.957646	+	0.287950i	$0.907026\pi$
$18$		0			0
$19$	−2.83929	+	3.30733i	−0.651377	+	0.758754i
$19$	−2.83929	+	3.30733i	−0.651377	+	0.758754i
$20$	6.95256	−	6.02655i	1.55464	−	1.34758i
$21$		0			0
$22$	−5.67266	+	12.1651i	−1.20941	+	2.59360i
$23$	−1.93732	−	1.35652i	−0.403958	−	0.282855i	0.353888	−	0.935288i	$-0.384859\pi$
$23$	−1.93732	−	1.35652i	−0.403958	−	0.282855i	−0.757846	+	0.652433i	$0.773748\pi$
$24$		0			0
$25$	2.35981	−	4.40809i	0.471963	−	0.881618i
$26$	−2.42277	−	4.19636i	−0.475144	−	0.822973i
$27$		0			0
$28$	1.11034	−	12.6912i	0.209834	−	2.39841i
$29$	0.236581	−	0.198515i	0.0439320	−	0.0368633i	−0.620557	−	0.784161i	$-0.713094\pi$
$29$	0.236581	−	0.198515i	0.0439320	−	0.0368633i	0.664489	+	0.747298i	$0.268649\pi$
$30$		0			0
$31$	−3.68657	+	2.12844i	−0.662128	+	0.382280i	−0.793087	−	0.609108i	$-0.791528\pi$
$31$	−3.68657	+	2.12844i	−0.662128	+	0.382280i	0.130959	+	0.991388i	$0.458194\pi$
$32$	1.05854	−	0.493605i	0.187125	−	0.0872578i
$33$		0			0
$34$	0.720185	+	4.08437i	0.123511	+	0.700464i
$35$	−1.89885	−	6.65753i	−0.320964	−	1.12533i
$36$		0			0
$37$	3.08090	−	3.08090i	0.506497	−	0.506497i	−0.406952	−	0.913449i	$-0.633409\pi$
$37$	3.08090	−	3.08090i	0.506497	−	0.506497i	0.913449	+	0.406952i	$0.133409\pi$
$38$	−6.28150	+	8.75921i	−1.01899	+	1.42093i
$39$		0			0
$40$	8.13481	−	8.40008i	1.28623	−	1.32817i
$41$	3.63501	+	9.98710i	0.567693	+	1.55972i	0.808097	+	0.589050i	$0.200498\pi$
$41$	3.63501	+	9.98710i	0.567693	+	1.55972i	−0.240404	+	0.970673i	$0.577280\pi$
$42$		0			0
$43$	3.28576	+	4.69255i	0.501073	+	0.715607i	0.987413	−	0.158163i	$-0.0505572\pi$
$43$	3.28576	+	4.69255i	0.501073	+	0.715607i	−0.486340	+	0.873770i	$0.661668\pi$
$44$	−7.63918	+	20.9885i	−1.15165	+	3.16413i
$45$		0			0
$46$	−5.06474	−	2.92413i	−0.746756	−	0.431139i
$47$	2.92349	+	0.255773i	0.426435	+	0.0373083i	0.298354	−	0.954455i	$-0.403562\pi$
$47$	2.92349	+	0.255773i	0.426435	+	0.0373083i	0.128082	+	0.991764i	$0.459118\pi$
$48$		0			0
$49$	−2.23925	−	1.29283i	−0.319893	−	0.184691i
$50$	4.86313	−	11.3675i	0.687751	−	1.60760i
$51$		0			0
$52$	−4.62477	−	6.60485i	−0.641340	−	0.915928i
$53$	3.97255	−	5.67339i	0.545672	−	0.779300i	−0.447707	−	0.894180i	$-0.647759\pi$
$53$	3.97255	−	5.67339i	0.545672	−	0.779300i	0.993379	+	0.114880i	$0.0366482\pi$
$54$		0			0
$55$	0.194697	+	12.1360i	0.0262529	+	1.63642i
$56$		−	16.1908i		−	2.16359i
$57$		0			0
$58$	0.540010	−	0.540010i	0.0709068	−	0.0709068i
$59$	1.92632	+	1.61638i	0.250786	+	0.210435i	0.759511	−	0.650495i	$-0.225438\pi$
$59$	1.92632	+	1.61638i	0.250786	+	0.210435i	−0.508725	+	0.860929i	$0.669883\pi$
$60$		0			0
$61$	1.00075	+	5.67553i	0.128133	+	0.726677i	0.979398	+	0.201941i	$0.0647249\pi$
$61$	1.00075	+	5.67553i	0.128133	+	0.726677i	−0.851265	+	0.524736i	$0.824164\pi$
$62$	−8.62279	+	6.03774i	−1.09509	+	0.766794i
$63$		0			0
$64$	−5.64270	+	3.25782i	−0.705338	+	0.407227i
$65$	−3.62908	−	2.45530i	−0.450132	−	0.304543i
$66$		0			0
$67$	0.197751	−	2.26031i	0.0241592	−	0.276141i	−0.974501	−	0.224385i	$-0.927963\pi$
$67$	0.197751	−	2.26031i	0.0241592	−	0.276141i	0.998660	−	0.0517558i	$-0.0164817\pi$
$68$	1.78619	+	6.66614i	0.216607	+	0.808388i
$69$		0			0
$70$	−6.11245	−	15.9909i	−0.730578	−	1.91128i
$71$	−8.76383	−	1.54530i	−1.04008	−	0.183393i	−0.372574	−	0.928002i	$-0.621525\pi$
$71$	−8.76383	−	1.54530i	−1.04008	−	0.183393i	−0.667501	+	0.744609i	$0.732636\pi$
$72$		0			0
$73$	5.20427	−	11.1606i	0.609114	−	1.30625i	−0.323791	−	0.946129i	$-0.604958\pi$
$73$	5.20427	−	11.1606i	0.609114	−	1.30625i	0.932906	−	0.360121i	$-0.117265\pi$
$74$	6.92550	−	8.25349i	0.805073	−	0.959448i
$75$		0			0
$76$	−9.14239	+	15.4310i	−1.04870	+	1.77005i
$77$	11.8835	+	11.8835i	1.35425	+	1.35425i
$78$		0			0
$79$	14.4810	−	5.27064i	1.62924	−	0.592993i	0.644125	−	0.764920i	$-0.277221\pi$
$79$	14.4810	−	5.27064i	1.62924	−	0.592993i	0.985110	+	0.171927i	$0.0549993\pi$
$80$	6.62806	−	8.16138i	0.741039	−	0.912470i
$81$		0			0
$82$	11.1069	+	23.8188i	1.22655	+	2.63035i
$83$	−3.66649	−	0.982433i	−0.402449	−	0.107836i	0.0519158	−	0.998651i	$-0.483467\pi$
$83$	−3.66649	−	0.982433i	−0.402449	−	0.107836i	−0.454365	+	0.890815i	$0.650134\pi$
$84$		0			0
$85$	2.20010	+	3.03718i	0.238634	+	0.329428i
$86$	9.10547	+	10.8515i	0.981868	+	1.17014i
$87$		0			0
$88$	−7.34685	+	27.4188i	−0.783177	+	2.92286i
$89$	−3.79487	−	1.38122i	−0.402256	−	0.146409i	0.132966	−	0.991121i	$-0.457550\pi$
$89$	−3.79487	−	1.38122i	−0.402256	−	0.146409i	−0.535222	+	0.844711i	$0.679772\pi$
$90$		0			0
$91$	−5.97467	+	1.05350i	−0.626315	+	0.110436i
$92$	−8.81981	−	4.11274i	−0.919529	−	0.428783i
$93$		0			0
$94$	7.25686			0.748488
$95$	−1.64666	+	9.60669i	−0.168943	+	0.985626i
$96$		0			0
$97$	−13.4973	+	1.18086i	−1.37044	+	0.119898i	−0.748484	−	0.663153i	$-0.769218\pi$
$97$	−13.4973	+	1.18086i	−1.37044	+	0.119898i	−0.621957	+	0.783051i	$0.713662\pi$
$98$	−5.79481	−	2.70216i	−0.585364	−	0.272960i
$99$		0			0
$100$	6.41292	−	19.5489i	0.641292	−	1.95489i
$101$	−13.6892	−	4.98245i	−1.36212	−	0.495772i	−0.445413	−	0.895325i	$-0.646943\pi$
$101$	−13.6892	−	4.98245i	−1.36212	−	0.495772i	−0.916710	+	0.399553i	$0.869165\pi$
$102$		0			0
$103$	−4.84062	+	1.29704i	−0.476961	+	0.127801i	−0.489287	−	0.872123i	$-0.662743\pi$
$103$	−4.84062	+	1.29704i	−0.476961	+	0.127801i	0.0123263	+	0.999924i	$0.496076\pi$
$104$	−6.58682	−	7.84987i	−0.645891	−	0.769743i
$105$		0			0
$106$	8.56326	−	14.8320i	0.831737	−	1.44061i
$107$	−17.1307	−	4.59016i	−1.65609	−	0.443748i	−0.694781	−	0.719221i	$-0.744499\pi$
$107$	−17.1307	−	4.59016i	−1.65609	−	0.443748i	−0.961309	+	0.275473i	$0.911165\pi$
$108$		0			0
$109$	0.821327	−	4.65798i	0.0786689	−	0.446154i	−0.919875	−	0.392211i	$-0.871710\pi$
$109$	0.821327	−	4.65798i	0.0786689	−	0.446154i	0.998544	−	0.0539422i	$-0.0171787\pi$
$110$	3.09517	+	29.8539i	0.295113	+	2.84646i
$111$		0			0
$112$	−1.26876	−	14.5020i	−0.119887	−	1.37031i
$113$	7.55406	+	7.55406i	0.710626	+	0.710626i	0.966666	−	0.256040i	$-0.0824180\pi$
$113$	7.55406	+	7.55406i	0.710626	+	0.710626i	−0.256040	+	0.966666i	$0.582418\pi$
$114$		0			0
$115$	−5.27495	−	0.376345i	−0.491892	−	0.0350943i
$116$	0.816847	−	0.973481i	0.0758424	−	0.0903854i
$117$		0			0
$118$	5.09367	+	3.56662i	0.468910	+	0.328334i
$119$	5.11382	+	0.901705i	0.468783	+	0.0826592i
$120$		0			0
$121$	−9.23212	−	15.9905i	−0.839283	−	1.45368i
$122$	3.68843	+	13.7654i	0.333935	+	1.24626i
$123$		0			0
$124$	−13.4182	+	11.2592i	−1.20499	+	1.01111i
$125$	−0.537841	−	11.1674i	−0.0481060	−	0.998842i
$126$		0			0
$127$	10.3632	−	4.83242i	0.919582	−	0.428808i	0.0955972	−	0.995420i	$-0.469524\pi$
$127$	10.3632	−	4.83242i	0.919582	−	0.428808i	0.823985	+	0.566612i	$0.191746\pi$
$128$	−15.1116	+	10.5813i	−1.33569	+	0.935260i
$129$		0			0
$130$	−9.46903	−	5.26626i	−0.830489	−	0.461882i
$131$	−6.27923	−	5.26890i	−0.548619	−	0.460346i	0.325854	−	0.945420i	$-0.394348\pi$
$131$	−6.27923	−	5.26890i	−0.548619	−	0.460346i	−0.874473	+	0.485074i	$0.838793\pi$
$132$		0			0
$133$	7.61565	+	11.1413i	0.660361	+	0.966077i
$134$		−	5.61067i		−	0.484688i
$135$		0			0
$136$	2.99980	+	8.24188i	0.257231	+	0.706735i
$137$	−0.234107	+	0.334339i	−0.0200011	+	0.0285645i	−0.829028	−	0.559207i	$-0.811106\pi$
$137$	−0.234107	+	0.334339i	−0.0200011	+	0.0285645i	0.809027	+	0.587772i	$0.199995\pi$
$138$		0			0
$139$	1.44655	−	3.97436i	0.122695	−	0.337101i	−0.863105	−	0.505024i	$-0.831484\pi$
$139$	1.44655	−	3.97436i	0.122695	−	0.337101i	0.985800	+	0.167923i	$0.0537060\pi$
$140$	−12.4516	−	25.6214i	−1.05235	−	2.16540i
$141$		0			0
$142$	−21.9219	−	1.91791i	−1.83964	−	0.160948i
$143$	10.5960	+	0.927032i	0.886084	+	0.0775223i
$144$		0			0
$145$	0.225751	−	0.652634i	0.0187476	−	0.0541983i
$146$	10.4149	−	28.6146i	0.861942	−	2.36817i
$147$		0			0
$148$	10.2833	−	14.6860i	0.845280	−	1.20718i
$149$	−1.86104	−	5.11315i	−0.152462	−	0.418886i	0.839824	−	0.542860i	$-0.182658\pi$
$149$	−1.86104	−	5.11315i	−0.152462	−	0.418886i	−0.992286	+	0.123974i	$0.960436\pi$
$150$		0			0
$151$			8.25723i			0.671964i	0.941868	+	0.335982i	$0.109068\pi$
$151$			8.25723i			0.671964i	−0.941868	+	0.335982i	$0.890932\pi$
$152$	−9.86559	+	20.5492i	−0.800205	+	1.66676i
$153$		0			0
$154$	31.8349	+	26.7126i	2.56533	+	2.15257i
$155$	−4.62650	+	8.31871i	−0.371610	+	0.668175i
$156$		0			0
$157$	−10.5943	+	7.41820i	−0.845516	+	0.592037i	−0.914045	−	0.405612i	$-0.867058\pi$
$157$	−10.5943	+	7.41820i	−0.845516	+	0.592037i	0.0685291	+	0.997649i	$0.478169\pi$
$158$	34.5365	−	16.1046i	2.74757	−	1.28121i
$159$		0			0
$160$	1.46347	−	2.16310i	0.115698	−	0.171008i
$161$	−5.60920	+	4.70668i	−0.442067	+	0.370938i
$162$		0			0
$163$	0.363027	+	1.35483i	0.0284344	+	0.106119i	0.978685	−	0.205369i	$-0.0658394\pi$
$163$	0.363027	+	1.35483i	0.0284344	+	0.106119i	−0.950250	+	0.311488i	$0.899173\pi$
$164$	21.8661	+	37.8732i	1.70745	+	2.95740i
$165$		0			0
$166$	−9.24376	−	1.62992i	−0.717455	−	0.126507i
$167$	−5.35159	−	3.74723i	−0.414119	−	0.289969i	0.347891	−	0.937535i	$-0.386898\pi$
$167$	−5.35159	−	3.74723i	−0.414119	−	0.289969i	−0.762009	+	0.647566i	$0.775787\pi$
$168$		0			0
$169$	5.88810	−	7.01716i	0.452931	−	0.539782i
$170$	6.07429	+	7.00763i	0.465877	+	0.537460i
$171$		0			0
$172$	16.6677	+	16.6677i	1.27090	+	1.27090i
$173$	0.0997187	+	1.13979i	0.00758147	+	0.0866566i	0.999043	−	0.0437450i	$-0.0139289\pi$
$173$	0.0997187	+	1.13979i	0.00758147	+	0.0866566i	−0.991461	+	0.130402i	$0.958373\pi$
$174$		0			0
$175$	−11.2918	−	10.5895i	−0.853577	−	0.800492i
$176$	−4.43191	+	25.1346i	−0.334068	+	1.89459i
$177$		0			0
$178$	−9.64597	−	2.58463i	−0.722996	−	0.193726i
$179$	−5.29184	+	9.16573i	−0.395531	+	0.685079i	−0.993169	−	0.116687i	$-0.962773\pi$
$179$	−5.29184	+	9.16573i	−0.395531	+	0.685079i	0.597638	+	0.801766i	$0.296106\pi$
$180$		0			0
$181$	−2.44168	−	2.90988i	−0.181489	−	0.216290i	0.667628	−	0.744495i	$-0.267310\pi$
$181$	−2.44168	−	2.90988i	−0.181489	−	0.216290i	−0.849117	+	0.528205i	$0.822865\pi$
$182$	−14.4909	+	3.88284i	−1.07414	+	0.287815i
$183$		0			0
$184$	−11.6220	−	4.23005i	−0.856782	−	0.311843i
$185$	2.37031	−	9.44993i	0.174268	−	0.694773i
$186$		0			0
$187$	−8.25100	−	3.84750i	−0.603373	−	0.281357i
$188$	12.0296	−	1.05245i	0.877345	−	0.0767578i
$189$		0			0
$190$	−1.98594	+	24.0200i	−0.144075	+	1.74259i
$191$	13.5399			0.979715			0.489857	−	0.871803i	$-0.337049\pi$
$191$	13.5399			0.979715			0.489857	+	0.871803i	$0.337049\pi$
$192$		0			0
$193$	−13.7567	−	6.41484i	−0.990227	−	0.461750i	−0.141132	−	0.989991i	$-0.545074\pi$
$193$	−13.7567	−	6.41484i	−0.990227	−	0.461750i	−0.849095	+	0.528241i	$0.822852\pi$
$194$	−32.9947	+	5.81785i	−2.36888	+	0.417698i
$195$		0			0
$196$	−9.99783	−	3.63891i	−0.714131	−	0.259922i
$197$	1.71651	−	6.40611i	0.122296	−	0.456416i	−0.877432	−	0.479700i	$-0.840745\pi$
$197$	1.71651	−	6.40611i	0.122296	−	0.456416i	0.999729	+	0.0232837i	$0.00741211\pi$
$198$		0			0
$199$	11.7318	+	13.9814i	0.831646	+	0.991118i	0.999985	+	0.00538842i	$0.00171520\pi$
$199$	11.7318	+	13.9814i	0.831646	+	0.991118i	−0.168339	+	0.985729i	$0.553840\pi$
$200$	5.95378	−	25.4605i	0.420996	−	1.80033i
$201$		0			0
$202$	−34.7957	−	9.32348i	−2.44822	−	0.655998i
$203$	−0.404097	−	0.866589i	−0.0283620	−	0.0608226i
$204$		0			0
$205$	18.4478	+	14.9819i	1.28845	+	1.04638i
$206$	−11.6449	+	4.23838i	−0.811336	+	0.295302i
$207$		0			0
$208$	−6.51492	−	6.51492i	−0.451729	−	0.451729i
$209$	−7.84138	−	22.3234i	−0.542400	−	1.54414i
$210$		0			0
$211$	−9.92418	+	11.8272i	−0.683209	+	0.814217i	−0.990517	−	0.137394i	$-0.956127\pi$
$211$	−9.92418	+	11.8272i	−0.683209	+	0.814217i	0.307308	+	0.951610i	$0.400572\pi$
$212$	12.0441	−	25.8286i	0.827191	−	1.77392i
$213$		0			0
$214$	−43.1891	−	7.61540i	−2.95235	−	0.520578i
$215$	11.6946	+	5.22657i	0.797566	+	0.356449i
$216$		0			0
$217$	3.41114	+	12.7306i	0.231563	+	0.864206i
$218$	1.01937	−	11.6515i	0.0690406	−	0.789138i
$219$		0			0
$220$	9.46047	+	49.0394i	0.637825	+	3.30624i
$221$	2.84620	−	1.64325i	0.191456	−	0.110537i
$222$		0			0
$223$	9.78183	−	6.84931i	0.655040	−	0.458664i	−0.198215	−	0.980159i	$-0.563514\pi$
$223$	9.78183	−	6.84931i	0.655040	−	0.458664i	0.853254	+	0.521495i	$0.174625\pi$
$224$	−0.627932	−	3.56118i	−0.0419555	−	0.237941i
$225$		0			0
$226$	20.2367	+	16.9806i	1.34613	+	1.12953i
$227$	−5.86908	+	5.86908i	−0.389545	+	0.389545i	−0.874525	−	0.484980i	$-0.838827\pi$
$227$	−5.86908	+	5.86908i	−0.389545	+	0.389545i	0.484980	+	0.874525i	$0.338827\pi$
$228$		0			0
$229$		−	18.6144i		−	1.23007i	−0.788498	−	0.615037i	$-0.789141\pi$
$229$		−	18.6144i		−	1.23007i	0.788498	−	0.615037i	$-0.210859\pi$
$230$	−13.0754	+	0.209768i	−0.862168	+	0.0138317i
$231$		0			0
$232$	0.926349	−	1.32296i	0.0608178	−	0.0868568i
$233$	11.4458	+	16.3464i	0.749842	+	1.07089i	0.994849	+	0.101364i	$0.0323207\pi$
$233$	11.4458	+	16.3464i	0.749842	+	1.07089i	−0.245007	+	0.969521i	$0.578790\pi$
$234$		0			0
$235$	5.90203	−	2.86831i	0.385006	−	0.187108i
$236$	8.96094	+	5.17360i	0.583307	+	0.336773i
$237$		0			0
$238$	12.7917	+	1.11913i	0.829165	+	0.0725425i
$239$	12.7575	+	7.36555i	0.825214	+	0.476438i	0.852211	−	0.523198i	$-0.175261\pi$
$239$	12.7575	+	7.36555i	0.825214	+	0.476438i	−0.0269968	+	0.999636i	$0.508594\pi$
$240$		0			0
$241$	6.89416	−	18.9416i	0.444092	−	1.22013i	−0.492686	−	0.870207i	$-0.663985\pi$
$241$	6.89416	−	18.9416i	0.444092	−	1.22013i	0.936778	−	0.349925i	$-0.113793\pi$
$242$	−26.1887	−	37.4013i	−1.68347	−	2.40425i
$243$		0			0
$244$	8.11062	+	22.2837i	0.519229	+	1.42657i
$245$	−5.78099	+	0.0927437i	−0.369334	+	0.00592518i
$246$		0			0
$247$	8.22491	+	2.30348i	0.523338	+	0.146567i
$248$	−15.7411	+	15.7411i	−0.999560	+	0.999560i
$249$		0			0
$250$	−3.73171	−	27.3938i	−0.236014	−	1.73254i
$251$	1.07296	+	6.08505i	0.0677245	+	0.384085i	0.999764	+	0.0217279i	$0.00691676\pi$
$251$	1.07296	+	6.08505i	0.0677245	+	0.384085i	−0.932039	+	0.362357i	$0.881972\pi$
$252$		0			0
$253$	11.6348	−	5.42540i	0.731474	−	0.341092i
$254$	24.4871	−	14.1377i	1.53646	−	0.887075i
$255$		0			0
$256$	−24.9629	+	20.9464i	−1.56018	+	1.30915i
$257$	1.14349	−	13.0701i	0.0713288	−	0.815292i	−0.873307	−	0.487171i	$-0.838029\pi$
$257$	1.14349	−	13.0701i	0.0713288	−	0.815292i	0.944636	−	0.328121i	$-0.106416\pi$
$258$		0			0
$259$	−6.74488	−	11.6825i	−0.419106	−	0.725913i
$260$	−16.4604	−	7.35650i	−1.02083	−	0.456231i
$261$		0			0
$262$	−16.6038	−	11.6261i	−1.02579	−	0.718264i
$263$	5.91407	−	12.6828i	0.364677	−	0.782053i	−0.635275	−	0.772286i	$-0.719113\pi$
$263$	5.91407	−	12.6828i	0.364677	−	0.782053i	0.999952	−	0.00976677i	$-0.00310891\pi$
$264$		0			0
$265$	1.10212	−	15.4476i	0.0677026	−	0.948938i
$266$	21.1616	+	25.8043i	1.29750	+	1.58216i
$267$		0			0
$268$	−0.813705	−	9.30069i	−0.0497050	−	0.568130i
$269$	4.24483	−	1.54499i	0.258812	−	0.0941998i	−0.209356	−	0.977840i	$-0.567137\pi$
$269$	4.24483	−	1.54499i	0.258812	−	0.0941998i	0.468167	+	0.883640i	$0.344914\pi$
$270$		0			0
$271$	−1.61764	+	9.17407i	−0.0982644	+	0.557285i	0.895434	+	0.445195i	$0.146866\pi$
$271$	−1.61764	+	9.17407i	−0.0982644	+	0.557285i	−0.993698	+	0.112090i	$0.964245\pi$
$272$	3.33276	+	7.14714i	0.202079	+	0.433359i
$273$		0			0
$274$	−0.504642	+	0.874066i	−0.0304866	+	0.0528043i
$275$	14.3172	+	23.0570i	0.863361	+	1.39039i
$276$		0			0
$277$	18.0239	−	4.82949i	1.08295	−	0.290176i	0.327147	−	0.944973i	$-0.393913\pi$
$277$	18.0239	−	4.82949i	1.08295	−	0.290176i	0.755804	+	0.654798i	$0.227246\pi$
$278$	2.70688	−	10.1022i	0.162348	−	0.605889i
$279$		0			0
$280$	−18.6025	−	31.0590i	−1.11171	−	1.85613i
$281$	16.8479	−	2.97074i	1.00506	−	0.177219i	0.353191	−	0.935551i	$-0.385096\pi$
$281$	16.8479	−	2.97074i	1.00506	−	0.177219i	0.651869	+	0.758332i	$0.273985\pi$
$282$		0			0
$283$	0.300543	−	0.0262941i	0.0178655	−	0.00156302i	−0.0782195	−	0.996936i	$-0.524924\pi$
$283$	0.300543	−	0.0262941i	0.0178655	−	0.00156302i	0.0960850	+	0.995373i	$0.469368\pi$
$284$	−36.6176			−2.17286
$285$		0			0
$286$	26.3020			1.55527
$287$	32.7800	−	2.86788i	1.93494	−	0.169286i
$288$		0			0
$289$	13.9715	−	2.46355i	0.821852	−	0.144915i
$290$	0.415460	−	1.65635i	0.0243966	−	0.0972643i
$291$		0			0
$292$	13.1146	−	48.9444i	0.767475	−	2.86425i
$293$	−17.1633	+	4.59890i	−1.00269	+	0.268670i	−0.722573	−	0.691295i	$-0.757041\pi$
$293$	−17.1633	+	4.59890i	−1.00269	+	0.268670i	−0.280119	+	0.959965i	$0.590374\pi$
$294$		0			0
$295$	5.55243	+	0.887455i	0.323275	+	0.0516696i
$296$	11.3925	−	19.7324i	0.662177	−	1.14692i
$297$		0			0
$298$	−5.68646	−	12.1947i	−0.329408	−	0.706417i
$299$	−0.804743	+	4.56393i	−0.0465395	+	0.263939i
$300$		0			0
$301$	16.6664	−	6.06606i	0.960634	−	0.349642i
$302$	1.77959	+	20.3409i	0.102404	+	1.17048i
$303$		0			0
$304$	−7.22626	+	19.1789i	−0.414454	+	1.09999i
$305$	8.44066	+	9.73760i	0.483311	+	0.557573i
$306$		0			0
$307$	2.95182	−	6.33019i	0.168469	−	0.361283i	−0.803888	−	0.594780i	$-0.797239\pi$
$307$	2.95182	−	6.33019i	0.168469	−	0.361283i	0.972358	+	0.233497i	$0.0750169\pi$
$308$	56.6462	+	39.6641i	3.22772	+	2.26007i
$309$		0			0
$310$	−9.60408	+	21.4894i	−0.545475	+	1.22052i
$311$	−6.76709	−	11.7209i	−0.383726	−	0.664634i	0.607865	−	0.794040i	$-0.292026\pi$
$311$	−6.76709	−	11.7209i	−0.383726	−	0.664634i	−0.991592	+	0.129407i	$0.958693\pi$
$312$		0			0
$313$	−1.99501	+	22.8030i	−0.112764	+	1.28890i	0.703279	+	0.710914i	$0.251718\pi$
$313$	−1.99501	+	22.8030i	−0.112764	+	1.28890i	−0.816044	+	0.577990i	$0.803837\pi$
$314$	−24.4992	+	20.5573i	−1.38257	+	1.16011i
$315$		0			0
$316$	54.9148	−	31.7051i	3.08920	−	1.78355i
$317$	26.6863	−	12.4440i	1.49885	−	0.698927i	0.511769	−	0.859123i	$-0.328990\pi$
$317$	26.6863	−	12.4440i	1.49885	−	0.698927i	0.987085	+	0.160196i	$0.0512126\pi$
$318$		0			0
$319$	0.291101	+	1.65092i	0.0162985	+	0.0924336i
$320$	−7.08137	+	12.7327i	−0.395861	+	0.711780i
$321$		0			0
$322$	−12.8033	+	12.8033i	−0.713502	+	0.713502i
$323$	−5.94097	−	4.26045i	−0.330564	−	0.237058i
$324$		0			0
$325$	−9.78272	−	0.540393i	−0.542648	−	0.0299756i
$326$	1.18627	+	3.25926i	0.0657016	+	0.180514i
$327$		0			0
$328$	31.8788	+	45.5277i	1.76021	+	2.51384i
$329$	3.10757	−	8.53798i	0.171326	−	0.470714i
$330$		0			0
$331$	−8.86318	−	5.11716i	−0.487164	−	0.281264i	0.236233	−	0.971696i	$-0.424087\pi$
$331$	−8.86318	−	5.11716i	−0.487164	−	0.281264i	−0.723397	+	0.690432i	$0.757420\pi$
$332$	−15.5596	−	1.36129i	−0.853944	−	0.0747104i
$333$		0			0
$334$	−13.9907	−	8.07754i	−0.765538	−	0.441984i
$335$	−2.21764	−	4.56318i	−0.121163	−	0.249313i
$336$		0			0
$337$	0.174514	+	0.249231i	0.00950636	+	0.0135765i	0.823877	−	0.566768i	$-0.191807\pi$
$337$	0.174514	+	0.249231i	0.00950636	+	0.0135765i	−0.814371	+	0.580345i	$0.802918\pi$
$338$	12.9924	−	18.5551i	0.706694	−	1.00926i
$339$		0			0
$340$	11.0855	+	10.7355i	0.601198	+	0.582212i
$341$		−	23.1068i		−	1.25130i
$342$		0			0
$343$	9.66409	−	9.66409i	0.521812	−	0.521812i
$344$	22.9486	+	19.2561i	1.23730	+	1.03822i
$345$		0			0
$346$	0.491294	+	2.78627i	0.0264121	+	0.149791i
$347$	−15.3106	+	10.7206i	−0.821917	+	0.575512i	−0.907130	−	0.420850i	$-0.861732\pi$
$347$	−15.3106	+	10.7206i	−0.821917	+	0.575512i	0.0852133	+	0.996363i	$0.472843\pi$
$348$		0			0
$349$	3.58331	−	2.06882i	0.191810	−	0.110742i	−0.401020	−	0.916069i	$-0.631344\pi$
$349$	3.58331	−	2.06882i	0.191810	−	0.110742i	0.592830	+	0.805328i	$0.298011\pi$
$350$	−30.0984	−	23.6526i	−1.60883	−	1.26428i
$351$		0			0
$352$	−0.552554	+	6.31572i	−0.0294512	+	0.336629i
$353$	1.09756	+	4.09617i	0.0584175	+	0.218017i	0.988964	−	0.148157i	$-0.0473341\pi$
$353$	1.09756	+	4.09617i	0.0584175	+	0.218017i	−0.930546	+	0.366174i	$0.880667\pi$
$354$		0			0
$355$	−18.5872	+	7.10487i	−0.986507	+	0.377087i
$356$	−16.3648	−	2.88555i	−0.867332	−	0.152934i
$357$		0			0
$358$	−11.0605	+	23.7194i	−0.584567	+	1.25361i
$359$	6.02747	−	7.18326i	0.318118	−	0.379118i	−0.583162	−	0.812356i	$-0.698185\pi$
$359$	6.02747	−	7.18326i	0.318118	−	0.379118i	0.901280	+	0.433238i	$0.142629\pi$
$360$		0			0
$361$	−2.87691	−	18.7809i	−0.151416	−	0.988470i
$362$	−6.64197	−	6.64197i	−0.349094	−	0.349094i
$363$		0			0
$364$	−23.4582	+	8.53810i	−1.22955	+	0.447518i
$365$	−2.83961	−	27.3889i	−0.148632	−	1.43360i
$366$		0			0
$367$	−3.73449	−	8.00863i	−0.194939	−	0.418047i	0.784405	−	0.620248i	$-0.212968\pi$
$367$	−3.73449	−	8.00863i	−0.194939	−	0.418047i	−0.979344	+	0.202201i	$0.935190\pi$
$368$	−10.7412	−	2.87810i	−0.559924	−	0.150031i
$369$		0			0
$370$	3.80237	−	23.7898i	0.197676	−	1.23677i
$371$	−13.7834	−	16.4264i	−0.715600	−	0.852818i
$372$		0			0
$373$	−5.66992	+	21.1604i	−0.293577	+	1.09565i	0.648764	+	0.760990i	$0.275286\pi$
$373$	−5.66992	+	21.1604i	−0.293577	+	1.09565i	−0.942341	+	0.334655i	$0.891380\pi$
$374$	−21.1547	−	7.69969i	−1.09388	−	0.398141i
$375$		0			0
$376$	15.1136	−	2.66493i	0.779422	−	0.137433i
$377$	−0.548470	−	0.255756i	−0.0282476	−	0.0131721i
$378$		0			0
$379$	−18.4965			−0.950102			−0.475051	−	0.879958i	$-0.657570\pi$
$379$	−18.4965			−0.950102			−0.475051	+	0.879958i	$0.657570\pi$
$380$	0.191525	+	40.1055i	0.00982504	+	2.05737i
$381$		0			0
$382$	33.3543	−	2.91812i	1.70655	−	0.149304i
$383$	−32.0674	−	14.9533i	−1.63857	−	0.764076i	−0.638580	−	0.769555i	$-0.720478\pi$
$383$	−32.0674	−	14.9533i	−1.63857	−	0.764076i	−0.999985	+	0.00547951i	$0.998256\pi$
$384$		0			0
$385$	36.4498	+	9.14262i	1.85765	+	0.465951i
$386$	−35.2707	−	12.8375i	−1.79523	−	0.653411i
$387$		0			0
$388$	−53.8509	+	14.4293i	−2.73387	+	0.732537i
$389$	−9.07995	−	10.8211i	−0.460372	−	0.548650i	0.485055	−	0.874484i	$-0.338799\pi$
$389$	−9.07995	−	10.8211i	−0.460372	−	0.548650i	−0.945427	+	0.325834i	$0.894355\pi$
$390$		0			0
$391$	1.98330	−	3.43518i	0.100300	−	0.173725i
$392$	−13.0609	−	3.49966i	−0.659676	−	0.176760i
$393$		0			0
$394$	2.84781	−	16.1508i	0.143471	−	0.813663i
$395$	21.7232	−	26.7487i	1.09301	−	1.34587i
$396$		0			0
$397$	2.68339	+	30.6713i	0.134676	+	1.53935i	0.699796	+	0.714342i	$0.253274\pi$
$397$	2.68339	+	30.6713i	0.134676	+	1.53935i	−0.565121	+	0.825008i	$0.691170\pi$
$398$	31.9134	+	31.9134i	1.59968	+	1.59968i
$399$		0			0
$400$	3.33761	−	23.2714i	0.166881	−	1.16357i
$401$	−8.65698	+	10.3170i	−0.432309	+	0.515206i	−0.937587	−	0.347751i	$-0.886946\pi$
$401$	−8.65698	+	10.3170i	−0.432309	+	0.515206i	0.505278	+	0.862957i	$0.331390\pi$
$402$		0			0
$403$	6.83295	+	4.78448i	0.340373	+	0.238332i
$404$	−59.0323	−	10.4090i	−2.93697	−	0.517867i
$405$		0			0
$406$	−1.18222	−	2.04766i	−0.0586725	−	0.101624i
$407$	6.12120	+	22.8446i	0.303417	+	1.13237i
$408$		0			0
$409$	−18.4492	+	15.4807i	−0.912253	+	0.765471i	−0.972546	−	0.232709i	$-0.925241\pi$
$409$	−18.4492	+	15.4807i	−0.912253	+	0.765471i	0.0602932	+	0.998181i	$0.480796\pi$
$410$	48.6731	+	32.9305i	2.40379	+	1.62632i
$411$		0			0
$412$	−18.6888	+	8.71472i	−0.920730	+	0.429343i
$413$	6.37751	−	4.46558i	0.313817	−	0.219737i
$414$		0			0
$415$	−8.16223	+	2.32802i	−0.400668	+	0.114278i
$416$	−1.75322	−	1.47113i	−0.0859586	−	0.0721279i
$417$		0			0
$418$	−24.1276	−	53.3014i	−1.18012	−	2.60706i
$419$			2.43513i			0.118964i	0.998229	+	0.0594819i	$0.0189449\pi$
$419$			2.43513i			0.118964i	−0.998229	+	0.0594819i	$0.981055\pi$
$420$		0			0
$421$	−1.44925	−	3.98178i	−0.0706322	−	0.194060i	0.899354	−	0.437222i	$-0.144038\pi$
$421$	−1.44925	−	3.98178i	−0.0706322	−	0.194060i	−0.969986	+	0.243162i	$0.921815\pi$
$422$	−21.8982	+	31.2739i	−1.06599	+	1.52239i
$423$		0			0
$424$	12.3876	−	34.0347i	0.601595	−	1.65287i
$425$	7.71004	+	3.29844i	0.373992	+	0.159998i
$426$		0			0
$427$	17.7750	+	1.55511i	0.860194	+	0.0752572i
$428$	−72.6982	−	6.36027i	−3.51400	−	0.307435i
$429$		0			0
$430$	29.9349	+	10.3547i	1.44359	+	0.499349i
$431$	−7.01388	+	19.2705i	−0.337847	+	0.928227i	0.648157	+	0.761506i	$0.275540\pi$
$431$	−7.01388	+	19.2705i	−0.337847	+	0.928227i	−0.986004	+	0.166720i	$0.946682\pi$
$432$		0			0
$433$	13.0904	−	18.6950i	0.629083	−	0.898424i	−0.370454	−	0.928851i	$-0.620798\pi$
$433$	13.0904	−	18.6950i	0.629083	−	0.898424i	0.999537	+	0.0304269i	$0.00968669\pi$
$434$	11.1467	+	30.6253i	0.535058	+	1.47006i
$435$		0			0
$436$		−	19.4623i		−	0.932074i
$437$	9.98707	−	2.55579i	0.477746	−	0.122260i
$438$		0			0
$439$	−2.59554	−	2.17792i	−0.123878	−	0.103946i	0.578744	−	0.815509i	$-0.303543\pi$
$439$	−2.59554	−	2.17792i	−0.123878	−	0.103946i	−0.702622	+	0.711563i	$0.747988\pi$
$440$	17.4094	+	61.0389i	0.829961	+	2.90992i
$441$		0			0
$442$	6.65717	−	4.66140i	0.316649	−	0.221720i
$443$	2.63672	−	1.22952i	0.125275	−	0.0584165i	−0.358970	−	0.933349i	$-0.616872\pi$
$443$	2.63672	−	1.22952i	0.125275	−	0.0584165i	0.484245	+	0.874932i	$0.339094\pi$
$444$		0			0
$445$	−8.86669	+	1.71052i	−0.420322	+	0.0810866i
$446$	22.6204	−	18.9808i	1.07111	−	0.898766i
$447$		0			0
$448$	5.22113	+	19.4855i	0.246675	+	0.920604i
$449$	−1.95617	−	3.38818i	−0.0923173	−	0.159898i	0.816169	−	0.577814i	$-0.196094\pi$
$449$	−1.95617	−	3.38818i	−0.0923173	−	0.159898i	−0.908486	+	0.417916i	$0.862761\pi$
$450$		0			0
$451$	−56.8136	−	10.0178i	−2.67525	−	0.471719i
$452$	36.0087	+	25.2135i	1.69371	+	1.18595i
$453$		0			0
$454$	−13.1930	+	15.7228i	−0.619178	+	0.737908i
$455$	−10.2508	+	8.88554i	−0.480567	+	0.416561i
$456$		0			0
$457$	24.4163	+	24.4163i	1.14214	+	1.14214i	0.988057	+	0.154088i	$0.0492439\pi$
$457$	24.4163	+	24.4163i	1.14214	+	1.14214i	0.154088	+	0.988057i	$0.450756\pi$
$458$	−4.01176	−	45.8547i	−0.187457	−	2.14265i
$459$		0			0
$460$	−21.6445	+	2.24403i	−1.00918	+	0.104629i
$461$	1.39327	−	7.90163i	0.0648911	−	0.368015i	−0.935019	−	0.354598i	$-0.884618\pi$
$461$	1.39327	−	7.90163i	0.0648911	−	0.368015i	0.999910	−	0.0134177i	$-0.00427110\pi$
$462$		0			0
$463$	18.7746	+	5.03065i	0.872532	+	0.233794i	0.667182	−	0.744895i	$-0.267500\pi$
$463$	18.7746	+	5.03065i	0.872532	+	0.233794i	0.205350	+	0.978689i	$0.434167\pi$
$464$	0.726055	−	1.25756i	0.0337062	−	0.0583809i
$465$		0			0
$466$	31.7186	+	37.8008i	1.46934	+	1.75109i
$467$	17.5390	−	4.69956i	0.811608	−	0.217470i	0.170934	−	0.985282i	$-0.445322\pi$
$467$	17.5390	−	4.69956i	0.811608	−	0.217470i	0.640674	+	0.767813i	$0.278655\pi$
$468$		0			0
$469$	−6.60117	−	2.40263i	−0.304814	−	0.110943i
$470$	13.9209	−	8.33779i	0.642123	−	0.384594i
$471$		0			0
$472$	11.9181	+	5.55752i	0.548577	+	0.255806i
$473$	−30.9767	+	2.71011i	−1.42431	+	0.124611i
$474$		0			0
$475$	7.87885	+	20.3205i	0.361506	+	0.932370i
$476$	21.3669			0.979351
$477$		0			0
$478$	33.0143	+	15.3948i	1.51004	+	0.704142i
$479$	28.0837	−	4.95191i	1.28318	−	0.226259i	0.509848	−	0.860264i	$-0.329701\pi$
$479$	28.0837	−	4.95191i	1.28318	−	0.226259i	0.773328	+	0.634006i	$0.218590\pi$
$480$		0			0
$481$	−8.02287	−	2.92009i	−0.365811	−	0.133144i
$482$	12.9008	−	48.1465i	0.587615	−	2.19301i
$483$		0			0
$484$	−48.8367	−	58.2013i	−2.21985	−	2.64551i
$485$	−24.5352	+	17.7730i	−1.11409	+	0.807030i
$486$		0			0
$487$	15.2837	+	4.09527i	0.692573	+	0.185574i	0.587901	−	0.808933i	$-0.299954\pi$
$487$	15.2837	+	4.09527i	0.692573	+	0.185574i	0.104671	+	0.994507i	$0.466621\pi$
$488$	12.7368	+	27.3142i	0.576568	+	1.23645i
$489$		0			0
$490$	−14.2209	+	1.47438i	−0.642434	+	0.0666057i
$491$	−0.0823077	+	0.0299576i	−0.00371449	+	0.00135197i	−0.343877	−	0.939015i	$-0.611740\pi$
$491$	−0.0823077	+	0.0299576i	−0.00371449	+	0.00135197i	0.340162	+	0.940367i	$0.389518\pi$
$492$		0			0
$493$	0.366264	+	0.366264i	0.0164957	+	0.0164957i
$494$	20.7577	+	3.90176i	0.933932	+	0.175548i
$495$		0			0
$496$	−12.8657	+	15.3327i	−0.577687	+	0.688460i
$497$	−11.6440	+	24.9706i	−0.522305	+	1.12009i
$498$		0			0
$499$	−7.86525	−	1.38686i	−0.352097	−	0.0620842i	−0.00519746	−	0.999986i	$-0.501654\pi$
$499$	−7.86525	−	1.38686i	−0.352097	−	0.0620842i	−0.346900	+	0.937902i	$0.612766\pi$
$500$	−10.1589	−	44.8690i	−0.454318	−	2.00660i
$501$		0			0
$502$	3.95457	+	14.7587i	0.176501	+	0.658712i
$503$	−3.66919	+	41.9391i	−0.163601	+	1.86997i	0.262010	+	0.965065i	$0.415615\pi$
$503$	−3.66919	+	41.9391i	−0.163601	+	1.86997i	−0.425611	+	0.904906i	$0.639941\pi$
$504$		0			0
$505$	−31.9846	+	6.17034i	−1.42330	+	0.274576i
$506$	27.4919	−	15.8725i	1.22216	−	0.705617i
$507$		0			0
$508$	38.5415	−	26.9870i	1.71000	−	1.19736i
$509$	−4.08730	−	23.1803i	−0.181167	−	1.02745i	−0.930782	−	0.365574i	$-0.880873\pi$
$509$	−4.08730	−	23.1803i	−0.181167	−	1.02745i	0.749616	−	0.661873i	$-0.230238\pi$
$510$		0			0
$511$	−29.2063	−	24.5070i	−1.29201	−	1.08413i
$512$	−30.8901	+	30.8901i	−1.36516	+	1.36516i
$513$		0			0
$514$		−	32.4434i		−	1.43102i
$515$	−7.79557	+	8.04978i	−0.343514	+	0.354715i
$516$		0			0
$517$	−9.13686	+	13.0488i	−0.401839	+	0.573885i
$518$	−19.1331	−	27.3249i	−0.840661	−	1.20059i
$519$		0			0
$520$	−21.6547	−	7.49052i	−0.949621	−	0.328481i
$521$	1.35610	+	0.782946i	0.0594119	+	0.0343015i	0.529412	−	0.848365i	$-0.322413\pi$
$521$	1.35610	+	0.782946i	0.0594119	+	0.0343015i	−0.470000	+	0.882667i	$0.655746\pi$
$522$		0			0
$523$	−21.8473	−	1.91139i	−0.955314	−	0.0835791i	−0.401173	−	0.916002i	$-0.631397\pi$
$523$	−21.8473	−	1.91139i	−0.955314	−	0.0835791i	−0.554140	+	0.832423i	$0.686953\pi$
$524$	−29.2099	−	16.8644i	−1.27604	−	0.736723i
$525$		0			0
$526$	11.8353	−	32.5173i	0.516045	−	1.41782i
$527$	−4.09512	−	5.84844i	−0.178386	−	0.254762i
$528$		0			0
$529$	−5.95342	−	16.3569i	−0.258845	−	0.711170i
$530$	−0.614300	−	38.2911i	−0.0266835	−	1.66326i
$531$		0			0
$532$	38.8215	+	39.7062i	1.68312	+	1.72148i
$533$	14.7262	−	14.7262i	0.637861	−	0.637861i
$534$		0			0
$535$	−38.1359	+	10.8771i	−1.64876	+	0.470256i
$536$	−2.06040	−	11.6851i	−0.0889957	−	0.504719i
$537$		0			0
$538$	10.1237	−	4.72077i	0.436465	−	0.203527i
$539$	12.1549	−	7.01763i	0.523548	−	0.302271i
$540$		0			0
$541$	18.0266	−	15.1261i	0.775024	−	0.650323i	−0.166966	−	0.985963i	$-0.553397\pi$
$541$	18.0266	−	15.1261i	0.775024	−	0.650323i	0.941990	+	0.335640i	$0.108953\pi$
$542$	−2.00769	+	22.9480i	−0.0862378	+	0.985703i
$543$		0			0
$544$	0.979454	+	1.69646i	0.0419938	+	0.0727353i
$545$	−3.77624	−	9.87911i	−0.161756	−	0.423174i
$546$		0			0
$547$	5.84197	+	4.09059i	0.249785	+	0.174901i	0.691763	−	0.722125i	$-0.256834\pi$
$547$	5.84197	+	4.09059i	0.249785	+	0.174901i	−0.441978	+	0.897026i	$0.645723\pi$
$548$	−0.709772	+	1.52211i	−0.0303199	+	0.0650213i
$549$		0			0
$550$	40.2383	+	53.7129i	1.71577	+	2.29032i
$551$	−0.0151658	+	1.34609i	−0.000646083	+	0.0573455i
$552$		0			0
$553$	−4.15833	−	47.5299i	−0.176830	−	2.02118i
$554$	43.3592	−	15.7815i	1.84216	−	0.670490i
$555$		0			0
$556$	3.02203	−	17.1388i	0.128163	−	0.726847i
$557$	19.3619	+	41.5217i	0.820389	+	1.75933i	0.628331	+	0.777946i	$0.283738\pi$
$557$	19.3619	+	41.5217i	0.820389	+	1.75933i	0.192058	+	0.981384i	$0.438484\pi$
$558$		0			0
$559$	5.61261	−	9.72133i	0.237388	−	0.411169i
$560$	−19.0960	−	26.3616i	−0.806954	−	1.11398i
$561$		0			0
$562$	40.8628	−	10.9492i	1.72369	−	0.461862i
$563$	−5.36843	+	20.0353i	−0.226252	+	0.844386i	0.755646	+	0.654980i	$0.227323\pi$
$563$	−5.36843	+	20.0353i	−0.226252	+	0.844386i	−0.981899	+	0.189406i	$0.939344\pi$
$564$		0			0
$565$	23.1703	+	5.81175i	0.974780	+	0.244502i
$566$	0.734692	−	0.129546i	0.0308814	−	0.00544522i
$567$		0			0
$568$	−46.3601	+	4.05598i	−1.94523	+	0.170185i
$569$	9.83327			0.412232			0.206116	−	0.978528i	$-0.433918\pi$
$569$	9.83327			0.412232			0.206116	+	0.978528i	$0.433918\pi$
$570$		0			0
$571$	−3.68436			−0.154186			−0.0770929	−	0.997024i	$-0.524564\pi$
$571$	−3.68436			−0.154186			−0.0770929	+	0.997024i	$0.524564\pi$
$572$	43.6004	−	3.81454i	1.82302	−	0.159494i
$573$		0			0
$574$	80.1322	−	14.1295i	3.34465	−	0.589752i
$575$	−10.5514	+	5.33873i	−0.440023	+	0.222640i
$576$		0			0
$577$	8.84916	−	33.0255i	0.368395	−	1.37487i	−0.494363	−	0.869255i	$-0.664599\pi$
$577$	8.84916	−	33.0255i	0.368395	−	1.37487i	0.862759	−	0.505615i	$-0.168735\pi$
$578$	33.8864	−	9.07984i	1.40949	−	0.377672i
$579$		0			0
$580$	0.448481	−	2.80596i	0.0186222	−	0.116511i
$581$	−5.87608	+	10.1777i	−0.243781	+	0.422241i
$582$		0			0
$583$	15.8882	+	34.0723i	0.658021	+	1.41113i
$584$	11.1825	−	63.4192i	0.462736	−	2.62430i
$585$		0			0
$586$	−41.2889	+	15.0279i	−1.70563	+	0.620799i
$587$	0.100658	+	1.15053i	0.00415460	+	0.0474873i	0.997989	−	0.0633873i	$-0.0201903\pi$
$587$	0.100658	+	1.15053i	0.00415460	+	0.0474873i	−0.993834	+	0.110875i	$0.964635\pi$
$588$		0			0
$589$	3.42776	−	18.2360i	0.141239	−	0.751401i
$590$	13.8691	+	0.989500i	0.570982	+	0.0407371i
$591$		0			0
$592$	8.65793	−	18.5670i	0.355839	−	0.763099i
$593$	15.7132	+	11.0025i	0.645264	+	0.451819i	0.849846	−	0.527031i	$-0.176695\pi$
$593$	15.7132	+	11.0025i	0.645264	+	0.451819i	−0.204582	+	0.978849i	$0.565584\pi$
$594$		0			0
$595$	10.8459	−	4.14580i	0.444639	−	0.169961i
$596$	−11.1949	−	19.3901i	−0.458561	−	0.794251i
$597$		0			0
$598$	−0.998789	+	11.4162i	−0.0408435	+	0.466844i
$599$	4.65988	−	3.91010i	0.190397	−	0.159762i	−0.542606	−	0.839987i	$-0.682562\pi$
$599$	4.65988	−	3.91010i	0.190397	−	0.159762i	0.733003	+	0.680225i	$0.238118\pi$
$600$		0			0
$601$	−17.2461	+	9.95705i	−0.703483	+	0.406156i	−0.808644	−	0.588299i	$-0.799798\pi$
$601$	−17.2461	+	9.95705i	−0.703483	+	0.406156i	0.105160	+	0.994455i	$0.466465\pi$
$602$	39.7486	−	18.5351i	1.62003	−	0.755433i
$603$		0			0
$604$	5.90000	+	33.4606i	0.240068	+	1.36149i
$605$	−36.0824	−	20.0674i	−1.46696	−	0.815857i
$606$		0			0
$607$	−1.67102	+	1.67102i	−0.0678245	+	0.0678245i	−0.740205	−	0.672381i	$-0.765272\pi$
$607$	−1.67102	+	1.67102i	−0.0678245	+	0.0678245i	0.672381	+	0.740205i	$0.265272\pi$
$608$	−1.37298	+	4.90243i	−0.0556816	+	0.198820i
$609$		0			0
$610$	22.8914	+	22.1685i	0.926844	+	0.897575i
$611$	−1.96680	−	5.40375i	−0.0795683	−	0.218612i
$612$		0			0
$613$	−5.24933	−	7.49682i	−0.212018	−	0.302794i	0.699031	−	0.715092i	$-0.253615\pi$
$613$	−5.24933	−	7.49682i	−0.212018	−	0.302794i	−0.911049	+	0.412298i	$0.864726\pi$
$614$	5.90722	−	16.2300i	0.238396	−	0.654988i
$615$		0			0
$616$	76.1109	+	43.9426i	3.06659	+	1.77050i
$617$	13.2416	+	1.15849i	0.533086	+	0.0466390i	0.350521	−	0.936555i	$-0.386005\pi$
$617$	13.2416	+	1.15849i	0.533086	+	0.0466390i	0.182565	+	0.983194i	$0.441560\pi$
$618$		0			0
$619$	13.3404	+	7.70210i	0.536197	+	0.309573i	0.743536	−	0.668696i	$-0.233147\pi$
$619$	13.3404	+	7.70210i	0.536197	+	0.309573i	−0.207339	+	0.978269i	$0.566480\pi$
$620$	−12.8039	+	37.0155i	−0.514218	+	1.48658i
$621$		0			0
$622$	−19.1961	−	27.4149i	−0.769695	−	1.09924i
$623$	−7.17156	+	10.2421i	−0.287323	+	0.410339i
$624$		0			0
$625$	−13.8626	−	20.8046i	−0.554502	−	0.832182i
$626$			56.6029i			2.26231i
$627$		0			0
$628$	−37.6305	+	37.6305i	−1.50162	+	1.50162i
$629$	5.59796	+	4.69725i	0.223205	+	0.187292i
$630$		0			0
$631$	−0.849162	−	4.81584i	−0.0338046	−	0.191715i	0.963229	−	0.268681i	$-0.0865878\pi$
$631$	−0.849162	−	4.81584i	−0.0338046	−	0.191715i	−0.997034	+	0.0769659i	$0.975477\pi$
$632$	66.0136	−	46.2232i	2.62588	−	1.83866i
$633$		0			0
$634$	63.0572	−	36.4061i	2.50432	−	1.44587i
$635$	14.3275	−	21.1769i	0.568570	−	0.840378i
$636$		0			0
$637$	−0.441591	+	5.04740i	−0.0174965	+	0.199985i
$638$	1.07290	+	4.00413i	0.0424767	+	0.158525i
$639$		0			0
$640$	−16.8313	+	37.6606i	−0.665317	+	1.48867i
$641$	−42.5461	−	7.50202i	−1.68047	−	0.296312i	−0.749661	−	0.661821i	$-0.769784\pi$
$641$	−42.5461	−	7.50202i	−1.68047	−	0.296312i	−0.930808	+	0.365509i	$0.880895\pi$
$642$		0			0
$643$	−0.745234	+	1.59816i	−0.0293892	+	0.0630253i	−0.920454	−	0.390850i	$-0.872181\pi$
$643$	−0.745234	+	1.59816i	−0.0293892	+	0.0630253i	0.891065	+	0.453875i	$0.149959\pi$
$644$	−19.3670	+	23.0807i	−0.763166	+	0.909506i
$645$		0			0
$646$	−15.5532	−	9.21481i	−0.611932	−	0.362552i
$647$	−34.4348	−	34.4348i	−1.35377	−	1.35377i	−0.881400	−	0.472370i	$-0.843398\pi$
$647$	−34.4348	−	34.4348i	−1.35377	−	1.35377i	−0.472370	−	0.881400i	$-0.656602\pi$
$648$		0			0
$649$	−12.8265	+	4.66847i	−0.503485	+	0.183254i
$650$	−24.2152	+	0.777164i	−0.949799	+	0.0304829i
$651$		0			0
$652$	2.43915	+	5.23077i	0.0955243	+	0.204853i
$653$	38.2422	+	10.2470i	1.49653	+	0.400994i	0.911937	−	0.410331i	$-0.134587\pi$
$653$	38.2422	+	10.2470i	1.49653	+	0.400994i	0.584595	+	0.811325i	$0.301253\pi$
$654$		0			0
$655$	−18.0992	−	2.89284i	−0.707195	−	0.113032i
$656$	32.1214	+	38.2808i	1.25413	+	1.49461i
$657$		0			0
$658$	5.81508	−	21.7022i	0.226696	−	0.846039i
$659$	20.0906	+	7.31236i	0.782617	+	0.284849i	0.702263	−	0.711917i	$-0.252173\pi$
$659$	20.0906	+	7.31236i	0.782617	+	0.284849i	0.0803534	+	0.996766i	$0.474395\pi$
$660$		0			0
$661$	8.57682	−	1.51232i	0.333600	−	0.0588226i	−0.00433950	−	0.999991i	$-0.501381\pi$
$661$	8.57682	−	1.51232i	0.333600	−	0.0588226i	0.337939	+	0.941168i	$0.390270\pi$
$662$	−22.9364	−	10.6954i	−0.891448	−	0.415689i
$663$		0			0
$664$	−19.8502			−0.770336
$665$	27.4100	+	12.6225i	1.06292	+	0.489480i
$666$		0			0
$667$	−0.727623	+	0.0636588i	−0.0281737	+	0.00246488i
$668$	−24.3636	−	11.3609i	−0.942657	−	0.439568i
$669$		0			0
$670$	−6.44639	−	10.7630i	−0.249046	−	0.415810i
$671$	−29.3960	−	10.6993i	−1.13482	−	0.413041i
$672$		0			0
$673$	41.2828	−	11.0617i	1.59133	−	0.426397i	0.648923	−	0.760854i	$-0.275220\pi$
$673$	41.2828	−	11.0617i	1.59133	−	0.426397i	0.942411	+	0.334457i	$0.108553\pi$
$674$	0.483611	+	0.576345i	0.0186280	+	0.0222000i
$675$		0			0
$676$	18.8463	−	32.6427i	0.724856	−	1.25549i
$677$	31.5745	+	8.46037i	1.21351	+	0.325158i	0.808137	−	0.588994i	$-0.200476\pi$
$677$	31.5745	+	8.46037i	1.21351	+	0.325158i	0.405370	+	0.914153i	$0.367143\pi$
$678$		0			0
$679$	−7.28422	+	41.3109i	−0.279543	+	1.58537i
$680$	15.2241	+	12.3638i	0.583817	+	0.474132i
$681$		0			0
$682$	−4.97997	−	56.9213i	−0.190693	−	2.17963i
$683$	−18.2414	−	18.2414i	−0.697987	−	0.697987i	0.265989	−	0.963976i	$-0.414302\pi$
$683$	−18.2414	−	18.2414i	−0.697987	−	0.697987i	−0.963976	+	0.265989i	$0.914302\pi$
$684$		0			0
$685$	−0.0649491	+	0.910344i	−0.00248158	+	0.0347825i
$686$	21.7237	−	25.8893i	0.829416	−	0.988459i
$687$		0			0
$688$	22.0639	+	15.4493i	0.841177	+	0.588999i
$689$	−13.3654	−	2.35668i	−0.509180	−	0.0897822i
$690$		0			0
$691$	23.6260	+	40.9214i	0.898775	+	1.55672i	0.829062	+	0.559157i	$0.188875\pi$
$691$	23.6260	+	40.9214i	0.898775	+	1.55672i	0.0697129	+	0.997567i	$0.477792\pi$
$692$	1.21850	+	4.54749i	0.0463203	+	0.172870i
$693$		0			0
$694$	−35.4057	+	29.7089i	−1.34398	+	1.12773i
$695$	−1.79143	−	9.28606i	−0.0679527	−	0.352240i
$696$		0			0
$697$	−16.1552	+	7.53329i	−0.611922	+	0.285344i
$698$	8.38125	−	5.86862i	0.317235	−	0.222130i
$699$		0			0
$700$	−53.3238	−	34.8433i	−2.01545	−	1.31695i
$701$	38.3021	+	32.1393i	1.44665	+	1.21388i	0.934978	+	0.354705i	$0.115419\pi$
$701$	38.3021	+	32.1393i	1.44665	+	1.21388i	0.511673	+	0.859180i	$0.329026\pi$
$702$		0			0
$703$	1.44201	+	18.9371i	0.0543863	+	0.714227i
$704$		−	35.3675i		−	1.33296i
$705$		0			0
$706$	3.58654	+	9.85395i	0.134981	+	0.370858i
$707$	−25.8698	+	36.9460i	−0.972935	+	1.38950i
$708$		0			0
$709$	−12.3224	+	33.8554i	−0.462776	+	1.27147i	0.460612	+	0.887601i	$0.347630\pi$
$709$	−12.3224	+	33.8554i	−0.462776	+	1.27147i	−0.923389	+	0.383866i	$0.874592\pi$
$710$	−44.2565	+	21.5080i	−1.66092	+	0.807182i
$711$		0			0
$712$	−21.0384	−	1.84062i	−0.788448	−	0.0689802i
$713$	10.0293	+	0.877454i	0.375602	+	0.0328609i
$714$		0			0
$715$	21.3916	−	10.3960i	0.799999	−	0.388788i
$716$	−14.8948	+	40.9232i	−0.556646	+	1.52937i
$717$		0			0
$718$	13.2999	−	18.9943i	0.496350	−	0.708861i
$719$	−5.27833	−	14.5021i	−0.196849	−	0.540837i	0.801518	−	0.597971i	$-0.204026\pi$
$719$	−5.27833	−	14.5021i	−0.196849	−	0.540837i	−0.998367	+	0.0571336i	$0.981804\pi$
$720$		0			0
$721$			15.5156i			0.577831i
$722$	−11.1346	−	45.6449i	−0.414388	−	1.69873i
$723$		0			0
$724$	−11.9735	−	10.0470i	−0.444993	−	0.373393i
$725$	−0.316786	−	1.51133i	−0.0117651	−	0.0561294i
$726$		0			0
$727$	8.70839	−	6.09768i	0.322976	−	0.226150i	−0.400832	−	0.916152i	$-0.631279\pi$
$727$	8.70839	−	6.09768i	0.322976	−	0.226150i	0.723808	+	0.690001i	$0.242390\pi$
$728$	−28.7538	+	13.4081i	−1.06569	+	0.496938i
$729$		0			0
$730$	−12.8979	−	66.8579i	−0.477374	−	2.47452i
$731$	−7.36006	+	6.17582i	−0.272222	+	0.228421i
$732$		0			0
$733$	4.28018	+	15.9739i	0.158092	+	0.590008i	0.998821	+	0.0485512i	$0.0154604\pi$
$733$	4.28018	+	15.9739i	0.158092	+	0.590008i	−0.840728	+	0.541457i	$0.817873\pi$
$734$	−10.9255	−	18.9236i	−0.403269	−	0.698483i
$735$		0			0
$736$	−2.72031	−	0.479664i	−0.100272	−	0.0176807i
$737$	10.0887	+	7.06419i	0.371623	+	0.260213i
$738$		0			0
$739$	25.6826	−	30.6074i	0.944751	−	1.12591i	−0.0471489	−	0.998888i	$-0.515014\pi$
$739$	25.6826	−	30.6074i	0.944751	−	1.12591i	0.991900	−	0.127022i	$-0.0405420\pi$
$740$	2.85292	−	39.9873i	0.104876	−	1.46996i
$741$		0			0
$742$	−37.4943	−	37.4943i	−1.37646	−	1.37646i
$743$	−4.09692	−	46.8280i	−0.150301	−	1.71795i	−0.579693	−	0.814835i	$-0.696827\pi$
$743$	−4.09692	−	46.8280i	−0.150301	−	1.71795i	0.429391	−	0.903119i	$-0.358728\pi$
$744$		0			0
$745$	−9.44481	−	7.67036i	−0.346031	−	0.281020i
$746$	−9.40679	+	53.3486i	−0.344407	+	1.95323i
$747$		0			0
$748$	−36.1844	−	9.69559i	−1.32303	−	0.354506i
$749$	−27.4545	+	47.5526i	−1.00316	+	1.73753i
$750$		0			0
$751$	13.6766	+	16.2991i	0.499066	+	0.594764i	0.955499	−	0.294994i	$-0.0953177\pi$
$751$	13.6766	+	16.2991i	0.499066	+	0.594764i	−0.456433	+	0.889758i	$0.650873\pi$
$752$	13.3283	−	3.57131i	0.486033	−	0.130232i
$753$		0			0
$754$	−1.40622	−	0.511823i	−0.0512116	−	0.0186395i
$755$	9.48717	+	15.8399i	0.345273	+	0.576473i
$756$		0			0
$757$	17.5651	+	8.19074i	0.638415	+	0.297698i	0.714745	−	0.699385i	$-0.246543\pi$
$757$	17.5651	+	8.19074i	0.638415	+	0.297698i	−0.0763306	+	0.997083i	$0.524320\pi$
$758$	−45.5643	+	3.98636i	−1.65497	+	0.144791i
$759$		0			0
$760$	4.68481	+	50.7548i	0.169936	+	1.84107i
$761$	0.0276948			0.00100394			0.000501968	−	1.00000i	$-0.499840\pi$
$761$	0.0276948			0.00100394			0.000501968		1.00000i	$0.499840\pi$
$762$		0			0
$763$	−13.2719	−	6.18879i	−0.480475	−	0.224049i
$764$	54.8675	−	9.67462i	1.98504	−	0.350016i
$765$		0			0
$766$	−82.2174	−	29.9247i	−2.97064	−	1.08122i
$767$	1.27533	−	4.75960i	0.0460495	−	0.171859i
$768$		0			0
$769$	2.74069	+	3.26623i	0.0988319	+	0.117783i	0.813193	−	0.581994i	$-0.197727\pi$
$769$	2.74069	+	3.26623i	0.0988319	+	0.117783i	−0.714361	+	0.699777i	$0.753283\pi$
$770$	91.7607	+	14.6663i	3.30683	+	0.528537i
$771$		0			0
$772$	−60.3294	−	16.1652i	−2.17130	−	0.581798i
$773$	−2.51427	−	5.39187i	−0.0904320	−	0.193932i	0.855890	−	0.517159i	$-0.173010\pi$
$773$	−2.51427	−	5.39187i	−0.0904320	−	0.193932i	−0.946322	+	0.323226i	$0.895232\pi$
$774$		0			0
$775$	0.682752	+	21.2735i	0.0245252	+	0.764166i
$776$	−66.5802	+	24.2332i	−2.39009	+	0.869921i
$777$		0			0
$778$	−24.6997	−	24.6997i	−0.885527	−	0.885527i
$779$	−43.3515	−	16.3341i	−1.55323	−	0.585228i
$780$		0			0
$781$	31.0497	−	37.0036i	1.11105	−	1.32409i
$782$	4.14532	−	8.88967i	0.148236	−	0.317894i
$783$		0			0
$784$	−11.9728	−	2.11114i	−0.427602	−	0.0753977i
$785$	−11.7999	+	26.4027i	−0.421158	+	0.942354i
$786$		0			0
$787$	10.4752	+	39.0940i	0.373401	+	1.39355i	0.855668	+	0.517526i	$0.173147\pi$
$787$	10.4752	+	39.0940i	0.373401	+	1.39355i	−0.482267	+	0.876024i	$0.660187\pi$
$788$	2.37845	−	27.1858i	0.0847288	−	0.968454i
$789$		0			0
$790$	47.7481	−	70.5744i	1.69880	−	2.51092i
$791$	28.6442	−	16.5377i	1.01847	−	0.588015i
$792$		0			0
$793$	9.25061	−	6.47735i	0.328499	−	0.230017i
$794$	13.2205	+	74.9775i	0.469180	+	2.66085i
$795$		0			0
$796$	57.5306	+	48.2739i	2.03912	+	1.71102i
$797$	6.47982	−	6.47982i	0.229527	−	0.229527i	−0.582968	−	0.812495i	$-0.698109\pi$
$797$	6.47982	−	6.47982i	0.229527	−	0.229527i	0.812495	+	0.582968i	$0.198109\pi$
$798$		0			0
$799$			4.92199i			0.174128i
$800$	0.322099	−	5.83095i	0.0113879	−	0.206155i
$801$		0			0
$802$	−19.1021	+	27.2806i	−0.674518	+	0.963312i
$803$	38.3399	+	54.7550i	1.35299	+	1.93226i
$804$		0			0
$805$	−5.35243	+	15.4736i	−0.188648	+	0.545372i
$806$	17.8634	+	10.3135i	0.629212	+	0.363276i
$807$		0			0
$808$	−75.8914	−	6.63964i	−2.66985	−	0.233582i
$809$	−24.5586	−	14.1789i	−0.863435	−	0.498504i	0.00172606	−	0.999999i	$-0.499451\pi$
$809$	−24.5586	−	14.1789i	−0.863435	−	0.498504i	−0.865161	+	0.501494i	$0.832784\pi$
$810$		0			0
$811$	−13.5351	+	37.1874i	−0.475282	+	1.30583i	0.438175	+	0.898890i	$0.355625\pi$
$811$	−13.5351	+	37.1874i	−0.475282	+	1.30583i	−0.913457	+	0.406936i	$0.866597\pi$
$812$	−2.25671	−	3.22292i	−0.0791950	−	0.113102i
$813$		0			0
$814$	20.0024	+	54.9562i	0.701085	+	1.92621i
$815$	2.25304	+	2.18189i	0.0789204	+	0.0764282i
$816$		0			0
$817$	−24.8490	−	2.45639i	−0.869357	−	0.0859382i
$818$	−42.1113	+	42.1113i	−1.47239	+	1.47239i
$819$		0			0
$820$	85.4604	+	47.5293i	2.98441	+	1.65980i
$821$	−8.76478	−	49.7076i	−0.305893	−	1.73481i	−0.619271	−	0.785177i	$-0.712572\pi$
$821$	−8.76478	−	49.7076i	−0.305893	−	1.73481i	0.313378	−	0.949629i	$-0.398539\pi$
$822$		0			0
$823$	−47.1143	+	21.9698i	−1.64230	+	0.765818i	−1.00000		0.000632369i	$-0.999799\pi$
$823$	−47.1143	+	21.9698i	−1.64230	+	0.765818i	−0.642303	+	0.766451i	$0.722021\pi$
$824$	−22.6958	+	13.1034i	−0.790646	+	0.456480i
$825$		0			0
$826$	14.7479	−	12.3750i	0.513146	−	0.430581i
$827$	3.98677	−	45.5690i	0.138633	−	1.58459i	−0.534566	−	0.845127i	$-0.679525\pi$
$827$	3.98677	−	45.5690i	0.138633	−	1.58459i	0.673199	−	0.739461i	$-0.264920\pi$
$828$		0			0
$829$	−8.78600	−	15.2178i	−0.305150	−	0.528536i	0.672144	−	0.740420i	$-0.265373\pi$
$829$	−8.78600	−	15.2178i	−0.305150	−	0.528536i	−0.977295	+	0.211884i	$0.932040\pi$
$830$	−19.6051	+	7.49395i	−0.680503	+	0.260119i
$831$		0			0
$832$	10.4586	+	7.32317i	0.362586	+	0.253885i
$833$	1.83275	−	3.93035i	0.0635012	−	0.136179i
$834$		0			0
$835$	−14.5714	−	1.03961i	−0.504264	−	0.0359770i
$836$	−47.7261	−	84.8576i	−1.65064	−	2.93486i
$837$		0			0
$838$	0.524818	+	5.99870i	0.0181295	+	0.207222i
$839$	−19.4605	+	7.08305i	−0.671852	+	0.244534i	−0.655345	−	0.755330i	$-0.727477\pi$
$839$	−19.4605	+	7.08305i	−0.671852	+	0.244534i	−0.0165070	+	0.999864i	$0.505255\pi$
$840$		0			0
$841$	−5.01923	+	28.4655i	−0.173077	+	0.981569i
$842$	−4.42824	−	9.49638i	−0.152607	−	0.327267i
$843$		0			0
$844$	−31.7647	+	55.0181i	−1.09339	+	1.89380i
$845$	3.23280	−	20.2262i	0.111212	−	0.695804i
$846$		0			0
$847$	−55.2187	+	14.7958i	−1.89734	+	0.508390i
$848$	8.42845	−	31.4554i	0.289434	−	1.08018i
$849$		0			0
$850$	19.7038	+	6.46371i	0.675834	+	0.221704i
$851$	−10.1480	+	1.78937i	−0.347869	+	0.0613387i
$852$		0			0
$853$	−52.3721	+	4.58196i	−1.79319	+	0.156883i	−0.934580	−	0.355753i	$-0.884224\pi$
$853$	−52.3721	+	4.58196i	−1.79319	+	0.156883i	−0.858606	+	0.512636i	$0.828669\pi$
$854$	44.1222			1.50983
$855$		0			0
$856$	−92.7448			−3.16995
$857$	−35.1511	+	3.07532i	−1.20074	+	0.105051i	−0.669919	−	0.742434i	$-0.733671\pi$
$857$	−35.1511	+	3.07532i	−1.20074	+	0.105051i	−0.530819	+	0.847485i	$0.678116\pi$
$858$		0			0
$859$	−5.19081	+	0.915280i	−0.177108	+	0.0312290i	−0.261499	−	0.965204i	$-0.584217\pi$
$859$	−5.19081	+	0.915280i	−0.177108	+	0.0312290i	0.0843906	+	0.996433i	$0.473106\pi$
$860$	51.1243	+	12.8234i	1.74332	+	0.437274i
$861$		0			0
$862$	−13.1248	+	48.9825i	−0.447033	+	1.66835i
$863$	21.2517	−	5.69437i	0.723415	−	0.193839i	0.121720	−	0.992564i	$-0.461159\pi$
$863$	21.2517	−	5.69437i	0.723415	−	0.193839i	0.601695	+	0.798726i	$0.294492\pi$
$864$		0			0
$865$	1.50086	+	2.07190i	0.0510306	+	0.0704466i
$866$	28.2177	−	48.8745i	0.958876	−	1.66082i
$867$		0			0
$868$	22.9192	+	49.1504i	0.777928	+	1.66827i
$869$	−14.5254	+	82.3779i	−0.492742	+	2.79448i
$870$		0			0
$871$	−4.17792	+	1.52064i	−0.141564	+	0.0515249i
$872$	−2.15576	−	24.6404i	−0.0730031	−	0.834429i
$873$		0			0
$874$	24.0513	−	8.44835i	0.813548	−	0.285770i
$875$	−33.8279	−	7.34023i	−1.14359	−	0.248145i
$876$		0			0
$877$	3.55398	−	7.62154i	0.120009	−	0.257361i	−0.837121	−	0.547017i	$-0.815763\pi$
$877$	3.55398	−	7.62154i	0.120009	−	0.257361i	0.957131	+	0.289656i	$0.0935410\pi$
$878$	−6.86324	−	4.80569i	−0.231623	−	0.162184i
$879$		0			0
$880$	20.3767	+	53.3080i	0.686899	+	1.79701i
$881$	4.46298	+	7.73011i	0.150362	+	0.260434i	0.931360	−	0.364099i	$-0.118623\pi$
$881$	4.46298	+	7.73011i	0.150362	+	0.260434i	−0.780999	+	0.624532i	$0.785290\pi$
$882$		0			0
$883$	−0.291138	+	3.32772i	−0.00979757	+	0.111987i	−0.999519	−	0.0310246i	$-0.990123\pi$
$883$	−0.291138	+	3.32772i	−0.00979757	+	0.111987i	0.989721	+	0.143011i	$0.0456785\pi$
$884$	10.3594	−	8.69259i	0.348425	−	0.292363i
$885$		0			0
$886$	6.23032	−	3.59708i	0.209312	−	0.120846i
$887$	−45.7577	+	21.3372i	−1.53639	+	0.716432i	−0.992445	−	0.122687i	$-0.960849\pi$
$887$	−45.7577	+	21.3372i	−1.53639	+	0.716432i	−0.543948	+	0.839119i	$0.683071\pi$
$888$		0			0
$889$	−6.14749	−	34.8642i	−0.206180	−	1.16931i
$890$	−21.4736	+	6.12465i	−0.719795	+	0.205299i
$891$		0			0
$892$	34.7447	−	34.7447i	1.16334	−	1.16334i
$893$	−9.14656	+	8.94276i	−0.306078	+	0.299258i
$894$		0			0
$895$	0.379619	+	23.6628i	0.0126893	+	0.790959i
$896$	19.5348	+	53.6714i	0.652612	+	1.79304i
$897$		0			0
$898$	−5.54904	−	7.92486i	−0.185174	−	0.264456i
$899$	−0.449645	+	1.23539i	−0.0149965	+	0.0412026i
$900$		0			0
$901$	10.0599	+	5.80807i	0.335143	+	0.193495i
$902$	−142.114	−	12.4333i	−4.73187	−	0.413985i
$903$		0			0
$904$	48.3819	+	27.9333i	1.60916	+	0.929048i
$905$	−8.02721	−	2.77667i	−0.266833	−	0.0922997i
$906$		0			0
$907$	−5.23635	−	7.47829i	−0.173870	−	0.248312i	0.722753	−	0.691106i	$-0.242876\pi$
$907$	−5.23635	−	7.47829i	−0.173870	−	0.248312i	−0.896624	+	0.442794i	$0.853987\pi$
$908$	−19.5895	+	27.9767i	−0.650101	+	0.928441i
$909$		0			0
$910$	−23.3369	+	24.0979i	−0.773611	+	0.798838i
$911$			33.9640i			1.12528i	0.826703	+	0.562639i	$0.190214\pi$
$911$			33.9640i			1.12528i	−0.826703	+	0.562639i	$0.809786\pi$
$912$		0			0
$913$	14.5693	−	14.5693i	0.482174	−	0.482174i
$914$	65.4092	+	54.8849i	2.16354	+	1.81543i
$915$		0			0
$916$	−13.3005	−	75.4306i	−0.439459	−	2.49230i
$917$	−20.7887	+	14.5564i	−0.686505	+	0.480696i
$918$		0			0
$919$	4.54228	−	2.62249i	0.149836	−	0.0865079i	−0.423208	−	0.906033i	$-0.639096\pi$
$919$	4.54228	−	2.62249i	0.149836	−	0.0865079i	0.573044	+	0.819525i	$0.305763\pi$
$920$	−27.1546	+	5.23855i	−0.895261	+	0.172710i
$921$		0			0
$922$	1.72923	−	19.7651i	0.0569490	−	0.650930i
$923$	4.51326	+	16.8437i	0.148556	+	0.554417i
$924$		0			0
$925$	−6.31054	−	20.8512i	−0.207489	−	0.685585i
$926$	47.3337	+	8.34620i	1.55548	+	0.274273i
$927$		0			0
$928$	0.152442	−	0.326913i	0.00500416	−	0.0107315i
$929$	8.88045	−	10.5833i	0.291358	−	0.347227i	−0.600433	−	0.799675i	$-0.705005\pi$
$929$	8.88045	−	10.5833i	0.291358	−	0.347227i	0.891791	+	0.452448i	$0.149449\pi$
$930$		0			0
$931$	10.6337	−	3.73523i	0.348506	−	0.122417i
$932$	58.0616	+	58.0616i	1.90187	+	1.90187i
$933$		0			0
$934$	42.1927	−	15.3569i	1.38059	−	0.502493i
$935$	−20.2486	+	2.09931i	−0.662199	+	0.0686548i
$936$		0			0
$937$	2.26833	+	4.86445i	0.0741031	+	0.158915i	0.939870	−	0.341534i	$-0.110946\pi$
$937$	2.26833	+	4.86445i	0.0741031	+	0.158915i	−0.865766	+	0.500448i	$0.833169\pi$
$938$	−16.7791	−	4.49595i	−0.547858	−	0.146798i
$939$		0			0
$940$	21.8672	−	15.8403i	0.713229	−	0.516654i
$941$	8.71929	+	10.3912i	0.284241	+	0.338745i	0.889206	−	0.457507i	$-0.151257\pi$
$941$	8.71929	+	10.3912i	0.284241	+	0.338745i	−0.604965	+	0.796252i	$0.706813\pi$
$942$		0			0
$943$	6.50558	−	24.2791i	0.211851	−	0.790638i
$944$	11.1105	+	4.04390i	0.361617	+	0.131618i
$945$		0			0
$946$	−75.7240	+	13.3522i	−2.46200	+	0.434117i
$947$	52.4149	+	24.4415i	1.70326	+	0.794241i	0.996201	+	0.0870813i	$0.0277540\pi$
$947$	52.4149	+	24.4415i	1.70326	+	0.794241i	0.707054	+	0.707160i	$0.250024\pi$
$948$		0			0
$949$	−24.1303			−0.783303
$950$	23.7882	+	48.3595i	0.771792	+	1.56899i
$951$		0			0
$952$	27.0518	−	2.36672i	0.876753	−	0.0767060i
$953$	−29.4153	−	13.7166i	−0.952855	−	0.444324i	−0.116914	−	0.993142i	$-0.537300\pi$
$953$	−29.4153	−	13.7166i	−0.952855	−	0.444324i	−0.835942	+	0.548818i	$0.815078\pi$
$954$		0			0
$955$	25.9738	−	15.5567i	0.840491	−	0.503404i
$956$	56.9598	+	20.7317i	1.84221	+	0.670510i
$957$		0			0
$958$	68.1141	−	18.2511i	2.20067	−	0.589667i
$959$	0.812272	+	0.968029i	0.0262296	+	0.0312593i
$960$		0			0
$961$	−6.43945	+	11.1534i	−0.207724	+	0.359789i
$962$	−20.3929	−	5.46425i	−0.657492	−	0.176175i
$963$		0			0
$964$	14.4028	−	81.6824i	0.463883	−	2.63081i
$965$	−33.7599	+	3.50013i	−1.08677	+	0.112673i
$966$		0			0
$967$	−1.08658	−	12.4197i	−0.0349422	−	0.399391i	−0.993445	−	0.114309i	$-0.963535\pi$
$967$	−1.08658	−	12.4197i	−0.0349422	−	0.399391i	0.958503	−	0.285082i	$-0.0920209\pi$
$968$	−68.2769	−	68.2769i	−2.19450	−	2.19450i
$969$		0			0
$970$	−56.6095	+	49.0698i	−1.81762	+	1.57554i
$971$	−32.5288	+	38.7663i	−1.04390	+	1.24407i	−0.0748516	+	0.997195i	$0.523848\pi$
$971$	−32.5288	+	38.7663i	−1.04390	+	1.24407i	−0.969047	+	0.246875i	$0.920596\pi$
$972$		0			0
$973$	−10.7265	−	7.51076i	−0.343875	−	0.240784i
$974$	38.5326	+	6.79433i	1.23466	+	0.217704i
$975$		0			0
$976$	13.5487	+	23.4671i	0.433684	+	0.751162i
$977$	−8.10975	−	30.2660i	−0.259454	−	0.968296i	−0.965558	−	0.260188i	$-0.916216\pi$
$977$	−8.10975	−	30.2660i	−0.259454	−	0.968296i	0.706104	−	0.708108i	$-0.250451\pi$
$978$		0			0
$979$	16.7924	−	14.0905i	0.536688	−	0.450334i
$980$	−23.3599	+	4.50648i	−0.746204	+	0.143954i
$981$		0			0
$982$	−0.196300	+	0.0915364i	−0.00626420	+	0.00292104i
$983$	−17.9317	+	12.5559i	−0.571934	+	0.400472i	−0.823457	−	0.567379i	$-0.807957\pi$
$983$	−17.9317	+	12.5559i	−0.571934	+	0.400472i	0.251523	+	0.967851i	$0.419069\pi$
$984$		0			0
$985$	−4.06752	−	14.2611i	−0.129602	−	0.454396i
$986$	0.981192	+	0.823318i	0.0312475	+	0.0262198i
$987$		0			0
$988$	34.9755	+	3.45742i	1.11272	+	0.109995i
$989$		−	13.5482i		−	0.430806i
$990$		0			0
$991$	18.6813	+	51.3264i	0.593431	+	1.63044i	0.764092	+	0.645107i	$0.223187\pi$
$991$	18.6813	+	51.3264i	0.593431	+	1.63044i	−0.170661	+	0.985330i	$0.554590\pi$
$992$	−2.85177	+	4.07275i	−0.0905438	+	0.129310i
$993$		0			0
$994$	−23.3022	+	64.0221i	−0.739100	+	2.03066i
$995$	38.5693	+	13.3414i	1.22273	+	0.422951i
$996$		0			0
$997$	−40.6095	−	3.55287i	−1.28612	−	0.112521i	−0.576494	−	0.817102i	$-0.695579\pi$
$997$	−40.6095	−	3.55287i	−1.28612	−	0.112521i	−0.709624	+	0.704581i	$0.751135\pi$
$998$	−19.6742	−	1.72127i	−0.622774	−	0.0544857i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.dl.a.307.8		96
3.2	odd	2		95.2.r.a.22.1	yes	96
5.3	odd	4	inner	855.2.dl.a.478.1		96
15.2	even	4		475.2.bb.b.193.1		96
15.8	even	4		95.2.r.a.3.8	✓	96
15.14	odd	2		475.2.bb.b.307.8		96
19.13	odd	18	inner	855.2.dl.a.127.1		96
57.32	even	18		95.2.r.a.32.8	yes	96
95.13	even	36	inner	855.2.dl.a.298.8		96
285.32	odd	36		475.2.bb.b.393.8		96
285.89	even	18		475.2.bb.b.32.1		96
285.203	odd	36		95.2.r.a.13.1	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.r.a.3.8	✓	96	15.8	even	4
95.2.r.a.13.1	yes	96	285.203	odd	36
95.2.r.a.22.1	yes	96	3.2	odd	2
95.2.r.a.32.8	yes	96	57.32	even	18
475.2.bb.b.32.1		96	285.89	even	18
475.2.bb.b.193.1		96	15.2	even	4
475.2.bb.b.307.8		96	15.14	odd	2
475.2.bb.b.393.8		96	285.32	odd	36
855.2.dl.a.127.1		96	19.13	odd	18	inner
855.2.dl.a.298.8		96	95.13	even	36	inner
855.2.dl.a.307.8		96	1.1	even	1	trivial
855.2.dl.a.478.1		96	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.dl (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.46340 - 0.215520i) q^{2} +(4.05227 - 0.714525i) q^{4} +(1.91831 - 1.14895i) q^{5} +(0.801323 - 2.99058i) q^{7} +(5.05128 - 1.35349i) q^{8} +(4.47794 - 3.24376i) q^{10} +(-2.71405 + 4.70087i) q^{11} +(-0.828132 - 1.77593i) q^{13} +(1.32945 - 7.53969i) q^{14} +(4.41834 - 1.60814i) q^{16} +(0.146177 + 1.67081i) q^{17} +(-2.83929 + 3.30733i) q^{19} +(6.95256 - 6.02655i) q^{20} +(-5.67266 + 12.1651i) q^{22} +(-1.93732 - 1.35652i) q^{23} +(2.35981 - 4.40809i) q^{25} +(-2.42277 - 4.19636i) q^{26} +(1.11034 - 12.6912i) q^{28} +(0.236581 - 0.198515i) q^{29} +(-3.68657 + 2.12844i) q^{31} +(1.05854 - 0.493605i) q^{32} +(0.720185 + 4.08437i) q^{34} +(-1.89885 - 6.65753i) q^{35} +(3.08090 - 3.08090i) q^{37} +(-6.28150 + 8.75921i) q^{38} +(8.13481 - 8.40008i) q^{40} +(3.63501 + 9.98710i) q^{41} +(3.28576 + 4.69255i) q^{43} +(-7.63918 + 20.9885i) q^{44} +(-5.06474 - 2.92413i) q^{46} +(2.92349 + 0.255773i) q^{47} +(-2.23925 - 1.29283i) q^{49} +(4.86313 - 11.3675i) q^{50} +(-4.62477 - 6.60485i) q^{52} +(3.97255 - 5.67339i) q^{53} +(0.194697 + 12.1360i) q^{55} -16.1908i q^{56} +(0.540010 - 0.540010i) q^{58} +(1.92632 + 1.61638i) q^{59} +(1.00075 + 5.67553i) q^{61} +(-8.62279 + 6.03774i) q^{62} +(-5.64270 + 3.25782i) q^{64} +(-3.62908 - 2.45530i) q^{65} +(0.197751 - 2.26031i) q^{67} +(1.78619 + 6.66614i) q^{68} +(-6.11245 - 15.9909i) q^{70} +(-8.76383 - 1.54530i) q^{71} +(5.20427 - 11.1606i) q^{73} +(6.92550 - 8.25349i) q^{74} +(-9.14239 + 15.4310i) q^{76} +(11.8835 + 11.8835i) q^{77} +(14.4810 - 5.27064i) q^{79} +(6.62806 - 8.16138i) q^{80} +(11.1069 + 23.8188i) q^{82} +(-3.66649 - 0.982433i) q^{83} +(2.20010 + 3.03718i) q^{85} +(9.10547 + 10.8515i) q^{86} +(-7.34685 + 27.4188i) q^{88} +(-3.79487 - 1.38122i) q^{89} +(-5.97467 + 1.05350i) q^{91} +(-8.81981 - 4.11274i) q^{92} +7.25686 q^{94} +(-1.64666 + 9.60669i) q^{95} +(-13.4973 + 1.18086i) q^{97} +(-5.79481 - 2.70216i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{2} + 12 q^{5} + 18 q^{8} - 12 q^{10} + 12 q^{11} - 12 q^{13} + 12 q^{16} + 30 q^{17} + 84 q^{20} - 24 q^{22} + 12 q^{25} + 48 q^{26} - 36 q^{31} - 18 q^{32} + 30 q^{35} - 54 q^{38} + 54 q^{40}+ \cdots + 90 q^{98}+O(q^{100}) \) 96 * q + 12 * q^2 + 12 * q^5 + 18 * q^8 - 12 * q^10 + 12 * q^11 - 12 * q^13 + 12 * q^16 + 30 * q^17 + 84 * q^20 - 24 * q^22 + 12 * q^25 + 48 * q^26 - 36 * q^31 - 18 * q^32 + 30 * q^35 - 54 * q^38 + 54 * q^40 - 12 * q^41 + 48 * q^43 - 36 * q^46 + 24 * q^47 - 126 * q^50 + 30 * q^53 + 18 * q^55 + 120 * q^58 - 48 * q^61 - 60 * q^62 - 72 * q^65 + 108 * q^67 - 18 * q^68 + 36 * q^70 + 24 * q^71 + 6 * q^73 + 60 * q^76 - 168 * q^77 + 60 * q^80 + 60 * q^82 - 36 * q^85 + 180 * q^86 - 198 * q^88 - 24 * q^91 + 72 * q^92 + 24 * q^95 - 72 * q^97 + 90 * q^98

Introduction

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