LMFDB - Embedded newform 855.2.da.b.244.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(199,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("855.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.da (of order $18$, degree $6$, 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			244.4
Character	$\chi$	$=$	855.244
Dual form			855.2.da.b.424.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.288852 + 0.344240i) q^{2} +(0.312230 + 1.77075i) q^{4} +(0.869891 + 2.05992i) q^{5} +(-1.78470 + 1.03040i) q^{7} +(-1.47809 - 0.853374i) q^{8} +O(q^{10})$	\(q+(-0.288852 + 0.344240i) q^{2} +(0.312230 + 1.77075i) q^{4} +(0.869891 + 2.05992i) q^{5} +(-1.78470 + 1.03040i) q^{7} +(-1.47809 - 0.853374i) q^{8} +(-0.960378 - 0.295561i) q^{10} +(-1.15299 + 1.99705i) q^{11} +(1.50356 - 4.13099i) q^{13} +(0.160809 - 0.911996i) q^{14} +(-2.65854 + 0.967630i) q^{16} +(-3.51724 + 4.19168i) q^{17} +(-3.07246 + 3.09192i) q^{19} +(-3.37600 + 2.18353i) q^{20} +(-0.354418 - 0.973756i) q^{22} +(5.72917 - 1.01021i) q^{23} +(-3.48658 + 3.58382i) q^{25} +(0.987746 + 1.71083i) q^{26} +(-2.38181 - 2.83853i) q^{28} +(4.21681 - 3.53833i) q^{29} +(-0.378916 - 0.656302i) q^{31} +(1.60231 - 4.40231i) q^{32} +(-0.426984 - 2.42155i) q^{34} +(-3.67503 - 2.78001i) q^{35} -6.22555i q^{37} +(-0.176878 - 1.95077i) q^{38} +(0.472112 - 3.78709i) q^{40} +(-6.14398 + 2.23623i) q^{41} +(-3.11869 - 0.549909i) q^{43} +(-3.89626 - 1.41812i) q^{44} +(-1.30713 + 2.26401i) q^{46} +(-4.08888 - 4.87293i) q^{47} +(-1.37657 + 2.38429i) q^{49} +(-0.226589 - 2.23541i) q^{50} +(7.78439 + 1.37260i) q^{52} +(3.79178 - 0.668594i) q^{53} +(-5.11674 - 0.637871i) q^{55} +3.51725 q^{56} +2.47365i q^{58} +(1.95359 + 1.63926i) q^{59} +(1.72608 + 9.78909i) q^{61} +(0.335376 + 0.0591358i) q^{62} +(-1.77654 - 3.07705i) q^{64} +(9.81745 - 0.496295i) q^{65} +(1.09447 + 1.30434i) q^{67} +(-8.52060 - 4.91937i) q^{68} +(2.01853 - 0.462081i) q^{70} +(-1.71201 + 9.70931i) q^{71} +(3.49431 + 9.60054i) q^{73} +(2.14308 + 1.79826i) q^{74} +(-6.43433 - 4.47516i) q^{76} -4.75216i q^{77} +(2.26642 - 0.824910i) q^{79} +(-4.30589 - 4.63466i) q^{80} +(1.00490 - 2.76094i) q^{82} +(-6.11633 + 3.53126i) q^{83} +(-11.6942 - 3.59894i) q^{85} +(1.09014 - 0.914734i) q^{86} +(3.40845 - 1.96787i) q^{88} +(2.19373 + 0.798452i) q^{89} +(1.57316 + 8.92183i) q^{91} +(3.57764 + 9.82950i) q^{92} +2.85854 q^{94} +(-9.04183 - 3.63940i) q^{95} +(-4.38085 + 5.22089i) q^{97} +(-0.423142 - 1.16257i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 18 q^{4} + 6 q^{5}+O(q^{10}) $ 48 * q - 18 * q^4 + 6 * q^5	$ 48 q - 18 q^{4} + 6 q^{5} - 15 q^{10} + 12 q^{11} - 6 q^{14} - 42 q^{16} + 12 q^{19} - 42 q^{20} + 12 q^{25} - 12 q^{26} - 42 q^{31} - 36 q^{34} - 6 q^{35} + 66 q^{40} - 6 q^{41} + 6 q^{44} - 6 q^{46} + 12 q^{49} + 18 q^{50} - 36 q^{56} + 36 q^{59} + 48 q^{61} + 18 q^{65} - 123 q^{70} + 24 q^{71} - 84 q^{74} + 66 q^{76} + 48 q^{79} + 39 q^{80} - 84 q^{85} + 42 q^{86} + 12 q^{89} - 30 q^{91} - 72 q^{94} + 63 q^{95}+O(q^{100}) $ 48 * q - 18 * q^4 + 6 * q^5 - 15 * q^10 + 12 * q^11 - 6 * q^14 - 42 * q^16 + 12 * q^19 - 42 * q^20 + 12 * q^25 - 12 * q^26 - 42 * q^31 - 36 * q^34 - 6 * q^35 + 66 * q^40 - 6 * q^41 + 6 * q^44 - 6 * q^46 + 12 * q^49 + 18 * q^50 - 36 * q^56 + 36 * q^59 + 48 * q^61 + 18 * q^65 - 123 * q^70 + 24 * q^71 - 84 * q^74 + 66 * q^76 + 48 * q^79 + 39 * q^80 - 84 * q^85 + 42 * q^86 + 12 * q^89 - 30 * q^91 - 72 * q^94 + 63 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$172$	$191$	$496$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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

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

$2$	−0.288852	+	0.344240i	−0.204249	+	0.243414i	−0.858439	−	0.512916i	$-0.828565\pi$
$2$	−0.288852	+	0.344240i	−0.204249	+	0.243414i	0.654190	+	0.756330i	$0.273010\pi$
$3$		0			0
$3$		0			0
$4$	0.312230	+	1.77075i	0.156115	+	0.885374i
$5$	0.869891	+	2.05992i	0.389027	+	0.921226i
$5$	0.869891	+	2.05992i	0.389027	+	0.921226i
$6$		0			0
$7$	−1.78470	+	1.03040i	−0.674553	+	0.389453i	−0.797799	−	0.602923i	$-0.794003\pi$
$7$	−1.78470	+	1.03040i	−0.674553	+	0.389453i	0.123247	+	0.992376i	$0.460669\pi$
$8$	−1.47809	−	0.853374i	−0.522583	−	0.301713i
$9$		0			0
$10$	−0.960378	−	0.295561i	−0.303698	−	0.0934647i
$11$	−1.15299	+	1.99705i	−0.347641	+	0.602132i	−0.985830	−	0.167748i	$-0.946351\pi$
$11$	−1.15299	+	1.99705i	−0.347641	+	0.602132i	0.638189	+	0.769880i	$0.279684\pi$
$12$		0			0
$13$	1.50356	−	4.13099i	0.417012	−	1.14573i	−0.536375	−	0.843979i	$-0.680207\pi$
$13$	1.50356	−	4.13099i	0.417012	−	1.14573i	0.953387	−	0.301750i	$-0.0975709\pi$
$14$	0.160809	−	0.911996i	0.0429781	−	0.243741i
$15$		0			0
$16$	−2.65854	+	0.967630i	−0.664635	+	0.241907i
$17$	−3.51724	+	4.19168i	−0.853056	+	1.01663i	0.146568	+	0.989201i	$0.453177\pi$
$17$	−3.51724	+	4.19168i	−0.853056	+	1.01663i	−0.999624	+	0.0274318i	$0.991267\pi$
$18$		0			0
$19$	−3.07246	+	3.09192i	−0.704871	+	0.709336i
$19$	−3.07246	+	3.09192i	−0.704871	+	0.709336i
$20$	−3.37600	+	2.18353i	−0.754896	+	0.488252i
$21$		0			0
$22$	−0.354418	−	0.973756i	−0.0755622	−	0.207606i
$23$	5.72917	−	1.01021i	1.19461	−	0.210643i	0.459245	−	0.888309i	$-0.348120\pi$
$23$	5.72917	−	1.01021i	1.19461	−	0.210643i	0.735369	+	0.677667i	$0.237009\pi$
$24$		0			0
$25$	−3.48658	+	3.58382i	−0.697316	+	0.716764i
$26$	0.987746	+	1.71083i	0.193713	+	0.335521i
$27$		0			0
$28$	−2.38181	−	2.83853i	−0.450119	−	0.536431i
$29$	4.21681	−	3.53833i	0.783042	−	0.657051i	−0.160970	−	0.986959i	$-0.551462\pi$
$29$	4.21681	−	3.53833i	0.783042	−	0.657051i	0.944013	+	0.329909i	$0.107018\pi$
$30$		0			0
$31$	−0.378916	−	0.656302i	−0.0680553	−	0.117875i	0.829990	−	0.557778i	$-0.188346\pi$
$31$	−0.378916	−	0.656302i	−0.0680553	−	0.117875i	−0.898045	+	0.439903i	$0.855013\pi$
$32$	1.60231	−	4.40231i	0.283251	−	0.778227i
$33$		0			0
$34$	−0.426984	−	2.42155i	−0.0732272	−	0.415292i
$35$	−3.67503	−	2.78001i	−0.621194	−	0.469908i
$36$		0			0
$37$		−	6.22555i		−	1.02347i	−0.859142	−	0.511737i	$-0.829002\pi$
$37$		−	6.22555i		−	1.02347i	0.859142	−	0.511737i	$-0.170998\pi$
$38$	−0.176878	−	1.95077i	−0.0286935	−	0.316457i
$39$		0			0
$40$	0.472112	−	3.78709i	0.0746474	−	0.598792i
$41$	−6.14398	+	2.23623i	−0.959529	+	0.349240i	−0.773849	−	0.633370i	$-0.781671\pi$
$41$	−6.14398	+	2.23623i	−0.959529	+	0.349240i	−0.185680	+	0.982610i	$0.559449\pi$
$42$		0			0
$43$	−3.11869	−	0.549909i	−0.475595	−	0.0838603i	−0.0692878	−	0.997597i	$-0.522073\pi$
$43$	−3.11869	−	0.549909i	−0.475595	−	0.0838603i	−0.406307	+	0.913736i	$0.633184\pi$
$44$	−3.89626	−	1.41812i	−0.587384	−	0.213790i
$45$		0			0
$46$	−1.30713	+	2.26401i	−0.192725	+	0.333810i
$47$	−4.08888	−	4.87293i	−0.596424	−	0.710790i	0.380403	−	0.924821i	$-0.375785\pi$
$47$	−4.08888	−	4.87293i	−0.596424	−	0.710790i	−0.976827	+	0.214030i	$0.931341\pi$
$48$		0			0
$49$	−1.37657	+	2.38429i	−0.196653	+	0.340612i
$50$	−0.226589	−	2.23541i	−0.0320446	−	0.316135i
$51$		0			0
$52$	7.78439	+	1.37260i	1.07950	+	0.190345i
$53$	3.79178	−	0.668594i	0.520842	−	0.0918384i	0.0929540	−	0.995670i	$-0.470369\pi$
$53$	3.79178	−	0.668594i	0.520842	−	0.0918384i	0.427888	+	0.903832i	$0.359258\pi$
$54$		0			0
$55$	−5.11674	−	0.637871i	−0.689941	−	0.0860105i
$56$	3.51725			0.470013
$57$		0			0
$58$			2.47365i			0.324806i
$59$	1.95359	+	1.63926i	0.254336	+	0.213413i	0.761037	−	0.648709i	$-0.224691\pi$
$59$	1.95359	+	1.63926i	0.254336	+	0.213413i	−0.506701	+	0.862122i	$0.669135\pi$
$60$		0			0
$61$	1.72608	+	9.78909i	0.221002	+	1.25336i	0.870182	+	0.492730i	$0.164001\pi$
$61$	1.72608	+	9.78909i	0.221002	+	1.25336i	−0.649180	+	0.760634i	$0.724888\pi$
$62$	0.335376	+	0.0591358i	0.0425928	+	0.00751025i
$63$		0			0
$64$	−1.77654	−	3.07705i	−0.222067	−	0.384632i
$65$	9.81745	−	0.496295i	1.21771	−	0.0615578i
$66$		0			0
$67$	1.09447	+	1.30434i	0.133711	+	0.159350i	0.828745	−	0.559626i	$-0.189055\pi$
$67$	1.09447	+	1.30434i	0.133711	+	0.159350i	−0.695034	+	0.718977i	$0.744611\pi$
$68$	−8.52060	−	4.91937i	−1.03327	−	0.596561i
$69$		0			0
$70$	2.01853	−	0.462081i	0.241260	−	0.0552293i
$71$	−1.71201	+	9.70931i	−0.203179	+	1.15228i	0.697102	+	0.716972i	$0.254473\pi$
$71$	−1.71201	+	9.70931i	−0.203179	+	1.15228i	−0.900280	+	0.435310i	$0.856639\pi$
$72$		0			0
$73$	3.49431	+	9.60054i	0.408978	+	1.12366i	0.957729	+	0.287672i	$0.0928815\pi$
$73$	3.49431	+	9.60054i	0.408978	+	1.12366i	−0.548751	+	0.835986i	$0.684896\pi$
$74$	2.14308	+	1.79826i	0.249128	+	0.209044i
$75$		0			0
$76$	−6.43433	−	4.47516i	−0.738068	−	0.513336i
$77$		−	4.75216i		−	0.541559i
$78$		0			0
$79$	2.26642	−	0.824910i	0.254992	−	0.0928096i	−0.211361	−	0.977408i	$-0.567790\pi$
$79$	2.26642	−	0.824910i	0.254992	−	0.0928096i	0.466354	+	0.884598i	$0.345567\pi$
$80$	−4.30589	−	4.63466i	−0.481413	−	0.518171i
$81$		0			0
$82$	1.00490	−	2.76094i	0.110973	−	0.304895i
$83$	−6.11633	+	3.53126i	−0.671354	+	0.387607i	−0.796590	−	0.604521i	$-0.793365\pi$
$83$	−6.11633	+	3.53126i	−0.671354	+	0.387607i	0.125235	+	0.992127i	$0.460031\pi$
$84$		0			0
$85$	−11.6942	−	3.59894i	−1.26841	−	0.390360i
$86$	1.09014	−	0.914734i	0.117553	−	0.0986383i
$87$		0			0
$88$	3.40845	−	1.96787i	0.363342	−	0.209776i
$89$	2.19373	+	0.798452i	0.232535	+	0.0846357i	0.455659	−	0.890154i	$-0.349404\pi$
$89$	2.19373	+	0.798452i	0.232535	+	0.0846357i	−0.223125	+	0.974790i	$0.571626\pi$
$90$		0			0
$91$	1.57316	+	8.92183i	0.164912	+	0.935261i
$92$	3.57764	+	9.82950i	0.372995	+	1.02480i
$93$		0			0
$94$	2.85854			0.294836
$95$	−9.04183	−	3.63940i	−0.927673	−	0.373395i
$96$		0			0
$97$	−4.38085	+	5.22089i	−0.444808	+	0.530101i	−0.941133	−	0.338035i	$-0.890238\pi$
$97$	−4.38085	+	5.22089i	−0.444808	+	0.530101i	0.496326	+	0.868136i	$0.334682\pi$
$98$	−0.423142	−	1.16257i	−0.0427438	−	0.117438i
$99$		0			0
$100$	−7.43465	−	5.05487i	−0.743465	−	0.505487i
$101$	11.4619	+	4.17181i	1.14051	+	0.415110i	0.842096	−	0.539327i	$-0.181321\pi$
$101$	11.4619	+	4.17181i	1.14051	+	0.415110i	0.298410	+	0.954438i	$0.403544\pi$
$102$		0			0
$103$	−11.1888	−	6.45986i	−1.10247	−	0.636509i	−0.165598	−	0.986193i	$-0.552955\pi$
$103$	−11.1888	−	6.45986i	−1.10247	−	0.636509i	−0.936868	+	0.349684i	$0.886289\pi$
$104$	−5.74767	+	4.82286i	−0.563605	+	0.472921i
$105$		0			0
$106$	−0.865106	+	1.49841i	−0.0840265	+	0.145538i
$107$	−13.1402	+	7.58647i	−1.27031	+	0.733412i	−0.975046	−	0.222005i	$-0.928740\pi$
$107$	−13.1402	+	7.58647i	−1.27031	+	0.733412i	−0.295261	+	0.955417i	$0.595407\pi$
$108$		0			0
$109$	3.33047	−	18.8880i	0.319001	−	1.80914i	−0.229852	−	0.973226i	$-0.573824\pi$
$109$	3.33047	−	18.8880i	0.319001	−	1.80914i	0.548853	−	0.835919i	$-0.315065\pi$
$110$	1.69756	−	1.57714i	0.161856	−	0.150374i
$111$		0			0
$112$	3.74765	−	4.46628i	0.354120	−	0.422024i
$113$			1.91146i			0.179815i	0.995950	+	0.0899075i	$0.0286571\pi$
$113$			1.91146i			0.179815i	−0.995950	+	0.0899075i	$0.971343\pi$
$114$		0			0
$115$	7.06470	+	10.9229i	0.658787	+	1.01856i
$116$	7.58210	+	6.36214i	0.703980	+	0.590709i
$117$		0			0
$118$	−1.12860	+	0.199002i	−0.103896	+	0.0183196i
$119$	1.95812	−	11.1050i	0.179500	−	1.01800i
$120$		0			0
$121$	2.84121	+	4.92111i	0.258292	+	0.447374i
$122$	−3.86838	−	2.23341i	−0.350226	−	0.202203i
$123$		0			0
$124$	1.04384	−	0.875882i	0.0937392	−	0.0786565i
$125$	−10.4153	−	4.06456i	−0.931576	−	0.363545i
$126$		0			0
$127$	−7.26311	+	19.9552i	−0.644496	+	1.77074i	−0.00737897	+	0.999973i	$0.502349\pi$
$127$	−7.26311	+	19.9552i	−0.644496	+	1.77074i	−0.637117	+	0.770767i	$0.719873\pi$
$128$	10.7997	+	1.90429i	0.954572	+	0.168317i
$129$		0			0
$130$	−2.66494	+	3.52291i	−0.233731	+	0.308980i
$131$	1.28137	+	1.07520i	0.111954	+	0.0939406i	0.697046	−	0.717026i	$-0.254497\pi$
$131$	1.28137	+	1.07520i	0.111954	+	0.0939406i	−0.585092	+	0.810967i	$0.698942\pi$
$132$		0			0
$133$	2.29751	−	8.68400i	0.199219	−	0.752998i
$134$	−0.765145			−0.0660984
$135$		0			0
$136$	8.77586	−	3.19415i	0.752524	−	0.273896i
$137$	17.0253	−	3.00203i	1.45457	−	0.256480i	0.610205	−	0.792244i	$-0.291087\pi$
$137$	17.0253	−	3.00203i	1.45457	−	0.256480i	0.844368	+	0.535763i	$0.179976\pi$
$138$		0			0
$139$	11.5832	+	4.21592i	0.982470	+	0.357590i	0.782800	−	0.622273i	$-0.213791\pi$
$139$	11.5832	+	4.21592i	0.982470	+	0.357590i	0.199670	+	0.979863i	$0.436013\pi$
$140$	3.77524	−	7.37556i	0.319066	−	0.623348i
$141$		0			0
$142$	−2.84781	−	3.39389i	−0.238983	−	0.284809i
$143$	6.51618	+	7.76568i	0.544910	+	0.649398i
$144$		0			0
$145$	10.9569	+	5.60836i	0.909917	+	0.465749i
$146$	−4.31423	−	1.57025i	−0.357048	−	0.129955i
$147$		0			0
$148$	11.0239	−	1.94381i	0.906157	−	0.159780i
$149$	−4.09613	+	1.49087i	−0.335568	+	0.122137i	−0.504308	−	0.863524i	$-0.668252\pi$
$149$	−4.09613	+	1.49087i	−0.335568	+	0.122137i	0.168740	+	0.985661i	$0.446030\pi$
$150$		0			0
$151$	4.44628			0.361833			0.180917	−	0.983498i	$-0.442094\pi$
$151$	4.44628			0.361833			0.180917	+	0.983498i	$0.442094\pi$
$152$	7.17993	−	1.94817i	0.582369	−	0.158018i
$153$		0			0
$154$	1.63588	+	1.37267i	0.131823	+	0.110613i
$155$	1.02232	−	1.35145i	0.0821145	−	0.108551i
$156$		0			0
$157$	19.5418	+	3.44574i	1.55960	+	0.275000i	0.885855	−	0.463962i	$-0.153573\pi$
$157$	19.5418	+	3.44574i	1.55960	+	0.275000i	0.673747	+	0.738962i	$0.264684\pi$
$158$	−0.370692	+	1.01847i	−0.0294907	+	0.0810250i
$159$		0			0
$160$	10.4623	−	0.528892i	0.827115	−	0.0418126i
$161$	−9.18393	+	7.70623i	−0.723795	+	0.607336i
$162$		0			0
$163$	−1.10928	−	0.640441i	−0.0868852	−	0.0501632i	0.455928	−	0.890017i	$-0.349307\pi$
$163$	−1.10928	−	0.640441i	−0.0868852	−	0.0501632i	−0.542813	+	0.839854i	$0.682641\pi$
$164$	−5.87813	−	10.1812i	−0.459005	−	0.795019i
$165$		0			0
$166$	0.551109	−	3.12549i	0.0427744	−	0.242585i
$167$	−7.91380	+	1.39542i	−0.612389	+	0.107981i	−0.471236	−	0.882007i	$-0.656192\pi$
$167$	−7.91380	+	1.39542i	−0.612389	+	0.107981i	−0.141153	+	0.989988i	$0.545081\pi$
$168$		0			0
$169$	−4.84580	−	4.06611i	−0.372754	−	0.312777i
$170$	4.61678	−	2.98604i	0.354091	−	0.229019i
$171$		0			0
$172$		−	5.69410i		−	0.434171i
$173$	−1.70923	+	2.03699i	−0.129951	+	0.154869i	−0.827096	−	0.562061i	$-0.810009\pi$
$173$	−1.70923	+	2.03699i	−0.129951	+	0.154869i	0.697145	+	0.716930i	$0.254453\pi$
$174$		0			0
$175$	2.52974	−	9.98860i	0.191230	−	0.755067i
$176$	1.13288	−	6.42490i	0.0853943	−	0.484295i
$177$		0			0
$178$	−0.908521	+	0.524535i	−0.0680965	+	0.0393155i
$179$	−4.05100	+	7.01654i	−0.302786	+	0.524441i	−0.976766	−	0.214309i	$-0.931250\pi$
$179$	−4.05100	+	7.01654i	−0.302786	+	0.524441i	0.673980	+	0.738750i	$0.264583\pi$
$180$		0			0
$181$	16.4717	−	13.8214i	1.22434	−	1.02734i	0.225749	−	0.974185i	$-0.427517\pi$
$181$	16.4717	−	13.8214i	1.22434	−	1.02734i	0.998586	−	0.0531539i	$-0.0169274\pi$
$182$	−3.52566	−	2.03554i	−0.261339	−	0.150884i
$183$		0			0
$184$	−9.33030	−	3.39595i	−0.687839	−	0.250353i
$185$	12.8242	−	5.41555i	0.942852	−	0.398159i
$186$		0			0
$187$	−4.31562	−	11.8571i	−0.315590	−	0.867075i
$188$	7.35206	−	8.76185i	0.536204	−	0.639023i
$189$		0			0
$190$	3.86457	−	2.06131i	0.280366	−	0.149543i
$191$	19.5939			1.41777			0.708884	−	0.705326i	$-0.249199\pi$
$191$	19.5939			1.41777			0.708884	+	0.705326i	$0.249199\pi$
$192$		0			0
$193$	0.165318	+	0.454207i	0.0118998	+	0.0326945i	0.945500	−	0.325621i	$-0.105573\pi$
$193$	0.165318	+	0.454207i	0.0118998	+	0.0326945i	−0.933600	+	0.358316i	$0.883351\pi$
$194$	−0.531824	−	3.01612i	−0.0381827	−	0.216545i
$195$		0			0
$196$	−4.65177	−	1.69311i	−0.332269	−	0.120936i
$197$	1.09283	−	0.630945i	0.0778609	−	0.0449530i	−0.460564	−	0.887626i	$-0.652353\pi$
$197$	1.09283	−	0.630945i	0.0778609	−	0.0449530i	0.538425	+	0.842673i	$0.319020\pi$
$198$		0			0
$199$	−15.8230	+	13.2771i	−1.12166	+	0.941186i	−0.998687	−	0.0512235i	$-0.983688\pi$
$199$	−15.8230	+	13.2771i	−1.12166	+	0.941186i	−0.122975	+	0.992410i	$0.539243\pi$
$200$	8.21181	−	2.32184i	0.580663	−	0.164179i
$201$		0			0
$202$	−4.74690	+	2.74063i	−0.333991	+	0.192830i
$203$	−3.87986	+	10.6598i	−0.272313	+	0.748174i
$204$		0			0
$205$	−9.95105	−	10.7109i	−0.695011	−	0.748079i
$206$	5.45564	−	1.98569i	0.380113	−	0.138350i
$207$		0			0
$208$			12.4373i			0.862371i
$209$	−2.63218	−	9.70081i	−0.182072	−	0.671019i
$210$		0			0
$211$	5.37147	+	4.50720i	0.369787	+	0.310288i	0.808677	−	0.588252i	$-0.200184\pi$
$211$	5.37147	+	4.50720i	0.369787	+	0.310288i	−0.438890	+	0.898541i	$0.644628\pi$
$212$	2.36782	+	6.50553i	0.162623	+	0.446802i
$213$		0			0
$214$	1.18399	−	6.71473i	0.0809358	−	0.459009i
$215$	−1.58015	−	6.90262i	−0.107765	−	0.470755i
$216$		0			0
$217$	1.35250	+	0.780867i	0.0918138	+	0.0530087i
$218$	5.54000	+	6.60232i	0.375216	+	0.447165i
$219$		0			0
$220$	−0.468095	−	9.25962i	−0.0315590	−	0.624283i
$221$	12.0274	+	20.8321i	0.809052	+	1.40132i
$222$		0			0
$223$	19.1421	+	3.37527i	1.28185	+	0.226025i	0.772765	−	0.634692i	$-0.218873\pi$
$223$	19.1421	+	3.37527i	1.28185	+	0.226025i	0.509084	+	0.860717i	$0.329984\pi$
$224$	1.67649	+	9.50782i	0.112015	+	0.635268i
$225$		0			0
$226$	−0.658001	−	0.552128i	−0.0437696	−	0.0367270i
$227$			6.53998i			0.434074i	0.976163	+	0.217037i	$0.0696392\pi$
$227$			6.53998i			0.434074i	−0.976163	+	0.217037i	$0.930361\pi$
$228$		0			0
$229$	20.4005			1.34810			0.674052	−	0.738684i	$-0.264552\pi$
$229$	20.4005			1.34810			0.674052	+	0.738684i	$0.264552\pi$
$230$	−5.80075	−	0.723141i	−0.382490	−	0.0476825i
$231$		0			0
$232$	−9.25233	+	1.63144i	−0.607445	+	0.107109i
$233$	−11.8660	−	2.09229i	−0.777365	−	0.137070i	−0.229131	−	0.973396i	$-0.573589\pi$
$233$	−11.8660	−	2.09229i	−0.777365	−	0.137070i	−0.548234	+	0.836325i	$0.684700\pi$
$234$		0			0
$235$	6.48100	−	12.6617i	0.422774	−	0.825958i
$236$	−2.29274	+	3.97114i	−0.149245	+	0.258499i
$237$		0			0
$238$	3.25719	+	3.88177i	0.211132	+	0.251618i
$239$	3.06250	−	5.30440i	0.198096	−	0.343113i	−0.749815	−	0.661648i	$-0.769857\pi$
$239$	3.06250	−	5.30440i	0.198096	−	0.343113i	0.947911	+	0.318535i	$0.103191\pi$
$240$		0			0
$241$	6.83446	+	2.48754i	0.440247	+	0.160237i	0.552627	−	0.833429i	$-0.313625\pi$
$241$	6.83446	+	2.48754i	0.440247	+	0.160237i	−0.112381	+	0.993665i	$0.535848\pi$
$242$	−2.51473	−	0.443415i	−0.161653	−	0.0285038i
$243$		0			0
$244$	−16.7951	+	6.11290i	−1.07519	+	0.391339i
$245$	−6.10891	−	0.761558i	−0.390284	−	0.0486542i
$246$		0			0
$247$	8.15308	+	17.3412i	0.518768	+	1.10339i
$248$			1.29343i			0.0821328i
$249$		0			0
$250$	4.40767	−	2.41132i	0.278766	−	0.152505i
$251$	4.19995	+	23.8191i	0.265099	+	1.50345i	0.768754	+	0.639545i	$0.220877\pi$
$251$	4.19995	+	23.8191i	0.265099	+	1.50345i	−0.503655	+	0.863905i	$0.668012\pi$
$252$		0			0
$253$	−4.58827	+	12.6062i	−0.288462	+	0.792544i
$254$	−4.77142	−	8.26435i	−0.299386	−	0.518551i
$255$		0			0
$256$	1.66857	−	1.40010i	0.104286	−	0.0875063i
$257$	7.86639	+	9.37480i	0.490692	+	0.584784i	0.953393	−	0.301730i	$-0.0975641\pi$
$257$	7.86639	+	9.37480i	0.490692	+	0.584784i	−0.462701	+	0.886514i	$0.653120\pi$
$258$		0			0
$259$	6.41478	+	11.1107i	0.398595	+	0.690387i
$260$	3.94412	+	17.2293i	0.244604	+	1.06851i
$261$		0			0
$262$	−0.740253	+	0.130527i	−0.0457330	+	0.00806396i
$263$	−4.23622	−	11.6389i	−0.261217	−	0.717687i	−0.999086	−	0.0427432i	$-0.986390\pi$
$263$	−4.23622	−	11.6389i	−0.261217	−	0.717687i	0.737870	−	0.674943i	$-0.235832\pi$
$264$		0			0
$265$	4.67569	+	7.22919i	0.287225	+	0.444085i
$266$	2.32574	+	3.29928i	0.142600	+	0.202292i
$267$		0			0
$268$	−1.96793	+	2.34528i	−0.120210	+	0.143261i
$269$	4.64095	−	1.68917i	0.282964	−	0.102990i	−0.196639	−	0.980476i	$-0.563003\pi$
$269$	4.64095	−	1.68917i	0.282964	−	0.102990i	0.479603	+	0.877485i	$0.340781\pi$
$270$		0			0
$271$	−1.19851	+	6.79708i	−0.0728042	+	0.412893i	0.926524	+	0.376236i	$0.122782\pi$
$271$	−1.19851	+	6.79708i	−0.0728042	+	0.412893i	−0.999328	+	0.0366568i	$0.988329\pi$
$272$	5.29473	−	14.5471i	0.321040	−	0.882050i
$273$		0			0
$274$	−3.88438	+	6.72794i	−0.234664	+	0.406450i
$275$	−3.13704	−	11.0950i	−0.189171	−	0.669053i
$276$		0			0
$277$	−3.43228	−	1.98163i	−0.206225	−	0.119064i	0.393331	−	0.919397i	$-0.371323\pi$
$277$	−3.43228	−	1.98163i	−0.206225	−	0.119064i	−0.599556	+	0.800333i	$0.704656\pi$
$278$	−4.79710	+	2.76961i	−0.287711	+	0.166110i
$279$		0			0
$280$	3.05963	+	7.24528i	0.182848	+	0.432988i
$281$	−5.41770	−	30.7253i	−0.323193	−	1.83292i	−0.522081	−	0.852896i	$-0.674844\pi$
$281$	−5.41770	−	30.7253i	−0.323193	−	1.83292i	0.198888	−	0.980022i	$-0.436267\pi$
$282$		0			0
$283$	−6.83092	+	8.14077i	−0.406056	+	0.483918i	−0.929856	−	0.367922i	$-0.880069\pi$
$283$	−6.83092	+	8.14077i	−0.406056	+	0.483918i	0.523801	+	0.851841i	$0.324514\pi$
$284$	−17.7273			−1.05192
$285$		0			0
$286$	−4.55546			−0.269370
$287$	8.66095	−	10.3217i	0.511240	−	0.609272i
$288$		0			0
$289$	−2.24721	−	12.7446i	−0.132189	−	0.749681i
$290$	−5.09552	+	2.15180i	−0.299220	+	0.126358i
$291$		0			0
$292$	−15.9091	+	9.18513i	−0.931010	+	0.537519i
$293$	−16.9968	−	9.81313i	−0.992966	−	0.573289i	−0.0868065	−	0.996225i	$-0.527666\pi$
$293$	−16.9968	−	9.81313i	−0.992966	−	0.573289i	−0.906160	+	0.422936i	$0.861000\pi$
$294$		0			0
$295$	−1.67734	+	5.45023i	−0.0976583	+	0.317325i
$296$	−5.31273	+	9.20191i	−0.308796	+	0.534850i
$297$		0			0
$298$	0.669957	−	1.84069i	0.0388096	−	0.106628i
$299$	4.44098	−	25.1860i	0.256828	−	1.45655i
$300$		0			0
$301$	6.13254	−	2.23206i	0.353474	−	0.128654i
$302$	−1.28432	+	1.53059i	−0.0739040	+	0.0880754i
$303$		0			0
$304$	5.17642	−	11.1930i	0.296888	−	0.641963i
$305$	−18.6633	+	12.0710i	−1.06866	+	0.691185i
$306$		0			0
$307$	−7.73849	−	21.2613i	−0.441659	−	1.21345i	−0.938401	−	0.345549i	$-0.887693\pi$
$307$	−7.73849	−	21.2613i	−0.441659	−	1.21345i	0.496742	−	0.867898i	$-0.334530\pi$
$308$	8.41488	−	1.48377i	0.479482	−	0.0845457i
$309$		0			0
$310$	0.169925	+	0.742291i	0.00965109	+	0.0421593i
$311$	12.4289	+	21.5274i	0.704776	+	1.22071i	0.966772	+	0.255639i	$0.0822859\pi$
$311$	12.4289	+	21.5274i	0.704776	+	1.22071i	−0.261996	+	0.965069i	$0.584381\pi$
$312$		0			0
$313$	−14.2716	−	17.0082i	−0.806678	−	0.961361i	0.193126	−	0.981174i	$-0.438137\pi$
$313$	−14.2716	−	17.0082i	−0.806678	−	0.961361i	−0.999804	+	0.0198129i	$0.993693\pi$
$314$	−6.83083	+	5.73175i	−0.385486	+	0.323461i
$315$		0			0
$316$	2.16835	+	3.75570i	0.121979	+	0.211274i
$317$	−0.697575	+	1.91657i	−0.0391797	+	0.107645i	−0.957740	−	0.287636i	$-0.907131\pi$
$317$	−0.697575	+	1.91657i	−0.0391797	+	0.107645i	0.918560	+	0.395281i	$0.129353\pi$
$318$		0			0
$319$	2.20423	+	12.5008i	0.123413	+	0.699912i
$320$	4.79311	−	6.33624i	0.267943	−	0.354206i
$321$		0			0
$322$		−	5.38743i		−	0.300230i
$323$	−2.15378	−	23.7538i	−0.119840	−	1.32170i
$324$		0			0
$325$	9.56244	+	19.7915i	0.530429	+	1.09783i
$326$	0.540882	−	0.196865i	0.0299567	−	0.0109033i
$327$		0			0
$328$	10.9897	+	1.93778i	0.606803	+	0.106996i
$329$	12.3185	+	4.48355i	0.679139	+	0.247186i
$330$		0			0
$331$	−16.8263	+	29.1439i	−0.924855	+	1.60190i	−0.133060	+	0.991108i	$0.542480\pi$
$331$	−16.8263	+	29.1439i	−0.924855	+	1.60190i	−0.791795	+	0.610787i	$0.790853\pi$
$332$	−8.16268	−	9.72790i	−0.447985	−	0.533888i
$333$		0			0
$334$	1.80556	−	3.12732i	0.0987956	−	0.171119i
$335$	−1.73477	+	3.38916i	−0.0947806	+	0.185169i
$336$		0			0
$337$	−2.54944	−	0.449535i	−0.138877	−	0.0244877i	0.103778	−	0.994601i	$-0.466907\pi$
$337$	−2.54944	−	0.449535i	−0.138877	−	0.0244877i	−0.242654	+	0.970113i	$0.578018\pi$
$338$	2.79943	−	0.493615i	0.152269	−	0.0268491i
$339$		0			0
$340$	2.72154	−	21.8311i	0.147596	−	1.18396i
$341$	1.74755			0.0946353
$342$		0			0
$343$		−	20.0992i		−	1.08525i
$344$	4.14041	+	3.47422i	0.223236	+	0.187317i
$345$		0			0
$346$	−0.207497	−	1.17677i	−0.0111551	−	0.0632637i
$347$	23.4416	+	4.13339i	1.25841	+	0.221892i	0.762791	−	0.646646i	$-0.223829\pi$
$347$	23.4416	+	4.13339i	1.25841	+	0.221892i	0.495623	+	0.868538i	$0.334940\pi$
$348$		0			0
$349$	−1.24120	−	2.14983i	−0.0664402	−	0.115078i	0.830892	−	0.556434i	$-0.187831\pi$
$349$	−1.24120	−	2.14983i	−0.0664402	−	0.115078i	−0.897332	+	0.441356i	$0.854497\pi$
$350$	2.70775	+	3.75606i	0.144736	+	0.200770i
$351$		0			0
$352$	6.94416	+	8.27573i	0.370125	+	0.441098i
$353$	30.9547	+	17.8717i	1.64755	+	0.951216i	0.978040	+	0.208416i	$0.0668308\pi$
$353$	30.9547	+	17.8717i	1.64755	+	0.951216i	0.669514	+	0.742800i	$0.266503\pi$
$354$		0			0
$355$	−21.4897	+	4.91942i	−1.14055	+	0.261096i
$356$	−0.728907	+	4.13384i	−0.0386320	+	0.219093i
$357$		0			0
$358$	−1.24524	−	3.42126i	−0.0658127	−	0.180819i
$359$	−4.41575	−	3.70526i	−0.233055	−	0.195556i	0.518780	−	0.854908i	$-0.326386\pi$
$359$	−4.41575	−	3.70526i	−0.233055	−	0.195556i	−0.751835	+	0.659352i	$0.770831\pi$
$360$		0			0
$361$	−0.119978	−	18.9996i	−0.00631464	−	0.999980i
$362$			9.66258i			0.507854i
$363$		0			0
$364$	−15.3071	+	5.57133i	−0.802310	+	0.292017i
$365$	−16.7367	+	15.5494i	−0.876040	+	0.813895i
$366$		0			0
$367$	2.03751	−	5.59802i	0.106357	−	0.292214i	−0.875086	−	0.483968i	$-0.839195\pi$
$367$	2.03751	−	5.59802i	0.106357	−	0.292214i	0.981443	+	0.191753i	$0.0614174\pi$
$368$	−14.2537	+	8.22939i	−0.743027	+	0.428987i
$369$		0			0
$370$	−1.84003	+	5.97888i	−0.0956587	+	0.310827i
$371$	−6.07827	+	5.10028i	−0.315568	+	0.264793i
$372$		0			0
$373$	−3.86976	+	2.23420i	−0.200368	+	0.115683i	−0.596827	−	0.802370i	$-0.703572\pi$
$373$	−3.86976	+	2.23420i	−0.200368	+	0.115683i	0.396459	+	0.918052i	$0.370239\pi$
$374$	5.32825	+	1.93933i	0.275517	+	0.100280i
$375$		0			0
$376$	1.88528	+	10.6920i	0.0972260	+	0.551396i
$377$	−8.27656	−	22.7397i	−0.426265	−	1.17115i
$378$		0			0
$379$	−13.3179			−0.684095			−0.342047	−	0.939683i	$-0.611120\pi$
$379$	−13.3179			−0.684095			−0.342047	+	0.939683i	$0.611120\pi$
$380$	3.62132	−	17.1471i	0.185770	−	0.879629i
$381$		0			0
$382$	−5.65974	+	6.74501i	−0.289577	+	0.345105i
$383$	3.47959	+	9.56011i	0.177799	+	0.488499i	0.996294	−	0.0860152i	$-0.0274134\pi$
$383$	3.47959	+	9.56011i	0.177799	+	0.488499i	−0.818495	+	0.574514i	$0.805191\pi$
$384$		0			0
$385$	9.78910	−	4.13386i	0.498899	−	0.210681i
$386$	−0.204109	−	0.0742894i	−0.0103889	−	0.00378123i
$387$		0			0
$388$	−10.6127	−	6.12725i	−0.538779	−	0.311064i
$389$	−8.74087	+	7.33446i	−0.443180	+	0.371872i	−0.836898	−	0.547359i	$-0.815633\pi$
$389$	−8.74087	+	7.33446i	−0.443180	+	0.371872i	0.393718	+	0.919231i	$0.371189\pi$
$390$		0			0
$391$	−15.9164	+	27.5680i	−0.804927	+	1.39417i
$392$	4.06937	−	2.34945i	0.205534	−	0.118665i
$393$		0			0
$394$	−0.0984689	+	0.558445i	−0.00496079	+	0.0281340i
$395$	3.67079	+	3.95107i	0.184698	+	0.198800i
$396$		0			0
$397$	3.30555	−	3.93941i	0.165901	−	0.197713i	−0.676689	−	0.736269i	$-0.736586\pi$
$397$	3.30555	−	3.93941i	0.165901	−	0.197713i	0.842590	+	0.538556i	$0.181030\pi$
$398$		−	9.28201i		−	0.465265i
$399$		0			0
$400$	5.80141	−	12.9014i	0.290070	−	0.645072i
$401$	−13.0857	−	10.9802i	−0.653469	−	0.548326i	0.254652	−	0.967033i	$-0.418039\pi$
$401$	−13.0857	−	10.9802i	−0.653469	−	0.548326i	−0.908121	+	0.418707i	$0.862483\pi$
$402$		0			0
$403$	−3.28090	+	0.578511i	−0.163433	+	0.0288177i
$404$	−3.80845	+	21.5988i	−0.189477	+	1.07458i
$405$		0			0
$406$	−2.54884	−	4.41471i	−0.126497	−	0.219098i
$407$	12.4327	+	7.17803i	0.616267	+	0.355802i
$408$		0			0
$409$	19.9705	−	16.7572i	0.987476	−	0.828591i	0.00227581	−	0.999997i	$-0.499276\pi$
$409$	19.9705	−	16.7572i	0.987476	−	0.828591i	0.985200	+	0.171406i	$0.0548311\pi$
$410$	6.56148	−	0.331698i	0.324049	−	0.0163814i
$411$		0			0
$412$	7.94529	−	21.8295i	0.391436	−	1.07546i
$413$	−5.17566	−	0.912608i	−0.254677	−	0.0449065i
$414$		0			0
$415$	−12.5947	−	9.52736i	−0.618248	−	0.467680i
$416$	−15.7767	−	13.2383i	−0.773518	−	0.649059i
$417$		0			0
$418$	4.09972	+	1.89599i	0.200524	+	0.0927361i
$419$	5.77281			0.282020			0.141010	−	0.990008i	$-0.454965\pi$
$419$	5.77281			0.282020			0.141010	+	0.990008i	$0.454965\pi$
$420$		0			0
$421$	−23.7749	+	8.65335i	−1.15872	+	0.421738i	−0.848639	−	0.528973i	$-0.822577\pi$
$421$	−23.7749	+	8.65335i	−1.15872	+	0.421738i	−0.310078	+	0.950711i	$0.600355\pi$
$422$	−3.10311	+	0.547163i	−0.151057	+	0.0266355i
$423$		0			0
$424$	−6.17515	−	2.24757i	−0.299892	−	0.109152i
$425$	−2.75910	−	27.2198i	−0.133836	−	1.32035i
$426$		0			0
$427$	−13.1672	−	15.6920i	−0.637204	−	0.759390i
$428$	−17.5365	−	20.8992i	−0.847658	−	1.01020i
$429$		0			0
$430$	2.83258	+	1.44988i	0.136599	+	0.0699196i
$431$	−17.6314	−	6.41729i	−0.849272	−	0.309110i	−0.119529	−	0.992831i	$-0.538138\pi$
$431$	−17.6314	−	6.41729i	−0.849272	−	0.309110i	−0.729744	+	0.683721i	$0.760361\pi$
$432$		0			0
$433$	8.38365	−	1.47826i	0.402892	−	0.0710408i	0.0314698	−	0.999505i	$-0.489981\pi$
$433$	8.38365	−	1.47826i	0.402892	−	0.0710408i	0.371423	+	0.928464i	$0.378870\pi$
$434$	−0.659478	+	0.240030i	−0.0316560	+	0.0115218i
$435$		0			0
$436$	34.4858			1.65157
$437$	−14.4792	+	20.8180i	−0.692632	+	0.995859i
$438$		0			0
$439$	1.57445	+	1.32112i	0.0751444	+	0.0630537i	0.679586	−	0.733596i	$-0.262159\pi$
$439$	1.57445	+	1.32112i	0.0751444	+	0.0630537i	−0.604442	+	0.796649i	$0.706604\pi$
$440$	7.01865	+	5.30932i	0.334601	+	0.253112i
$441$		0			0
$442$	−10.6454	−	1.87707i	−0.506349	−	0.0892830i
$443$	−4.11804	+	11.3142i	−0.195654	+	0.537555i	−0.998261	−	0.0589538i	$-0.981224\pi$
$443$	−4.11804	+	11.3142i	−0.195654	+	0.537555i	0.802607	+	0.596508i	$0.203446\pi$
$444$		0			0
$445$	0.263553	+	5.21348i	0.0124936	+	0.247143i
$446$	−6.69112	+	5.61452i	−0.316834	+	0.265855i
$447$		0			0
$448$	6.34117	+	3.66108i	0.299592	+	0.172970i
$449$	−3.74700	−	6.48999i	−0.176832	−	0.306282i	0.763962	−	0.645261i	$-0.223252\pi$
$449$	−3.74700	−	6.48999i	−0.176832	−	0.306282i	−0.940794	+	0.338980i	$0.889918\pi$
$450$		0			0
$451$	2.61813	−	14.8482i	0.123283	−	0.699173i
$452$	−3.38471	+	0.596816i	−0.159203	+	0.0280719i
$453$		0			0
$454$	−2.25132	−	1.88908i	−0.105660	−	0.0886591i
$455$	−17.0098	+	11.0016i	−0.797432	+	0.515763i
$456$		0			0
$457$			14.0052i			0.655137i	0.944827	+	0.327568i	$0.106229\pi$
$457$			14.0052i			0.655137i	−0.944827	+	0.327568i	$0.893771\pi$
$458$	−5.89272	+	7.02267i	−0.275349	+	0.328148i
$459$		0			0
$460$	−17.1359	+	15.9203i	−0.798964	+	0.742286i
$461$	3.06924	−	17.4066i	0.142949	−	0.810704i	−0.826042	−	0.563608i	$-0.809413\pi$
$461$	3.06924	−	17.4066i	0.142949	−	0.810704i	0.968991	−	0.247096i	$-0.0794761\pi$
$462$		0			0
$463$	14.3696	−	8.29630i	0.667812	−	0.385562i	−0.127435	−	0.991847i	$-0.540674\pi$
$463$	14.3696	−	8.29630i	0.667812	−	0.385562i	0.795247	+	0.606285i	$0.207341\pi$
$464$	−7.78678	+	13.4871i	−0.361492	+	0.626123i
$465$		0			0
$466$	4.14775	−	3.48038i	0.192141	−	0.161225i
$467$	−13.8481	−	7.99522i	−0.640815	−	0.369975i	0.144113	−	0.989561i	$-0.453967\pi$
$467$	−13.8481	−	7.99522i	−0.640815	−	0.369975i	−0.784928	+	0.619586i	$0.787300\pi$
$468$		0			0
$469$	−3.29728	−	1.20011i	−0.152254	−	0.0554161i
$470$	2.48661	+	5.88837i	0.114699	+	0.271610i
$471$		0			0
$472$	−1.48868	−	4.09011i	−0.0685220	−	0.188263i
$473$	4.69402	−	5.59412i	0.215831	−	0.257218i
$474$		0			0
$475$	−0.368516	−	21.7914i	−0.0169087	−	0.999857i
$476$	20.2756			0.929331
$477$		0			0
$478$	0.941379	+	2.58642i	0.0430577	+	0.118300i
$479$	1.28429	+	7.28355i	0.0586805	+	0.332794i	0.999989	−	0.00475459i	$-0.00151344\pi$
$479$	1.28429	+	7.28355i	0.0586805	+	0.332794i	−0.941308	+	0.337548i	$0.890402\pi$
$480$		0			0
$481$	−25.7177	−	9.36047i	−1.17263	−	0.426801i
$482$	−2.83046	+	1.63417i	−0.128924	+	0.0744342i
$483$		0			0
$484$	−7.82694	+	6.56758i	−0.355770	+	0.298526i
$485$	−14.5655	−	4.48261i	−0.661385	−	0.203545i
$486$		0			0
$487$	−17.4834	+	10.0941i	−0.792250	+	0.457406i	−0.840754	−	0.541417i	$-0.817888\pi$
$487$	−17.4834	+	10.0941i	−0.792250	+	0.457406i	0.0485041	+	0.998823i	$0.484555\pi$
$488$	5.80246	−	15.9421i	0.262665	−	0.721666i
$489$		0			0
$490$	2.02673	−	1.88295i	0.0915582	−	0.0850632i
$491$	8.77021	−	3.19210i	0.395794	−	0.144057i	−0.136453	−	0.990647i	$-0.543570\pi$
$491$	8.77021	−	3.19210i	0.395794	−	0.144057i	0.532247	+	0.846589i	$0.321348\pi$
$492$		0			0
$493$			30.1207i			1.35657i
$494$	−8.32455	−	2.20241i	−0.374539	−	0.0990911i
$495$		0			0
$496$	1.64242	+	1.37816i	0.0737469	+	0.0618810i
$497$	−6.94900	−	19.0922i	−0.311705	−	0.856404i
$498$		0			0
$499$	4.16083	−	23.5972i	0.186264	−	1.05636i	−0.738056	−	0.674739i	$-0.764256\pi$
$499$	4.16083	−	23.5972i	0.186264	−	1.05636i	0.924320	−	0.381618i	$-0.124633\pi$
$500$	3.94532	−	19.7120i	0.176440	−	0.881548i
$501$		0			0
$502$	−9.41265	−	5.43440i	−0.420107	−	0.242549i
$503$	−6.64247	−	7.91618i	−0.296173	−	0.352965i	0.597352	−	0.801979i	$-0.296220\pi$
$503$	−6.64247	−	7.91618i	−0.296173	−	0.352965i	−0.893525	+	0.449014i	$0.851775\pi$
$504$		0			0
$505$	1.37703	+	27.2398i	0.0612772	+	1.21215i
$506$	−3.01422	−	5.22078i	−0.133998	−	0.232092i
$507$		0			0
$508$	−37.6034	−	6.63050i	−1.66838	−	0.294181i
$509$	4.81206	+	27.2906i	0.213291	+	1.20963i	0.883848	+	0.467775i	$0.154944\pi$
$509$	4.81206	+	27.2906i	0.213291	+	1.20963i	−0.670557	+	0.741858i	$0.733945\pi$
$510$		0			0
$511$	−16.1287	−	13.5335i	−0.713490	−	0.598689i
$512$			22.9115i			1.01256i
$513$		0			0
$514$	−5.49940			−0.242568
$515$	3.57379	−	28.6675i	0.157480	−	1.26324i
$516$		0			0
$517$	14.4459	−	2.54721i	0.635331	−	0.112026i
$518$	−5.67768	−	1.00113i	−0.249463	−	0.0439870i
$519$		0			0
$520$	−14.9346	−	7.64439i	−0.654925	−	0.335229i
$521$	−5.28647	+	9.15643i	−0.231604	+	0.401151i	−0.958280	−	0.285830i	$-0.907731\pi$
$521$	−5.28647	+	9.15643i	−0.231604	+	0.401151i	0.726676	+	0.686980i	$0.241064\pi$
$522$		0			0
$523$	−11.6728	−	13.9111i	−0.510415	−	0.608289i	0.447872	−	0.894098i	$-0.352182\pi$
$523$	−11.6728	−	13.9111i	−0.510415	−	0.608289i	−0.958287	+	0.285809i	$0.907738\pi$
$524$	−1.50382	+	2.60470i	−0.0656948	+	0.113787i
$525$		0			0
$526$	5.23022	+	1.90364i	0.228048	+	0.0830028i
$527$	4.08375	+	0.720075i	0.177891	+	0.0313670i
$528$		0			0
$529$	10.1900	−	3.70884i	0.443041	−	0.161254i
$530$	−3.83915	−	0.478602i	−0.166762	−	0.0207892i
$531$		0			0
$532$	16.0945	+	1.35690i	0.697786	+	0.0588290i
$533$			28.7430i			1.24500i
$534$		0			0
$535$	−27.0581	−	20.4683i	−1.16982	−	0.884923i
$536$	−0.504633	−	2.86192i	−0.0217968	−	0.123616i
$537$		0			0
$538$	−0.759067	+	2.08552i	−0.0327257	+	0.0899131i
$539$	−3.17435	−	5.49814i	−0.136729	−	0.236821i
$540$		0			0
$541$	4.67676	−	3.92427i	0.201070	−	0.168717i	−0.536693	−	0.843777i	$-0.680327\pi$
$541$	4.67676	−	3.92427i	0.201070	−	0.168717i	0.737763	+	0.675060i	$0.235882\pi$
$542$	−1.99363	−	2.37592i	−0.0856340	−	0.102055i
$543$		0			0
$544$	12.8174	+	22.2004i	0.549541	+	0.951833i
$545$	41.8051	−	9.57001i	1.79073	−	0.409934i
$546$		0			0
$547$	10.7363	−	1.89310i	0.459051	−	0.0809430i	0.0606593	−	0.998159i	$-0.480680\pi$
$547$	10.7363	−	1.89310i	0.459051	−	0.0809430i	0.398391	+	0.917215i	$0.369569\pi$
$548$	10.6317	+	29.2102i	0.454162	+	1.24780i
$549$		0			0
$550$	4.72547	+	2.12491i	0.201495	+	0.0906064i
$551$	−2.01576	+	23.9094i	−0.0858741	+	1.01858i
$552$		0			0
$553$	−3.19489	+	3.80753i	−0.135861	+	0.161912i
$554$	1.67357	−	0.609131i	0.0711033	−	0.0258795i
$555$		0			0
$556$	−3.84872	+	21.8272i	−0.163222	+	0.925678i
$557$	−4.17801	+	11.4790i	−0.177028	+	0.486380i	−0.996193	−	0.0871778i	$-0.972215\pi$
$557$	−4.17801	+	11.4790i	−0.177028	+	0.486380i	0.819165	+	0.573558i	$0.194437\pi$
$558$		0			0
$559$	−6.96079	+	12.0564i	−0.294410	+	0.509933i
$560$	12.4602	+	3.83471i	0.526541	+	0.162046i
$561$		0			0
$562$	12.1418	+	7.01006i	0.512170	+	0.295702i
$563$	−15.8656	+	9.15999i	−0.668654	+	0.386048i	−0.795567	−	0.605866i	$-0.792827\pi$
$563$	−15.8656	+	9.15999i	−0.668654	+	0.386048i	0.126912	+	0.991914i	$0.459493\pi$
$564$		0			0
$565$	−3.93746	+	1.66276i	−0.165650	+	0.0699529i
$566$	−0.829256	−	4.70295i	−0.0348562	−	0.197680i
$567$		0			0
$568$	10.8162	−	12.8902i	0.453837	−	0.540861i
$569$	32.3240			1.35509			0.677546	−	0.735480i	$-0.263043\pi$
$569$	32.3240			1.35509			0.677546	+	0.735480i	$0.263043\pi$
$570$		0			0
$571$	−13.2641			−0.555083			−0.277542	−	0.960714i	$-0.589520\pi$
$571$	−13.2641			−0.555083			−0.277542	+	0.960714i	$0.589520\pi$
$572$	−11.7165	+	13.9632i	−0.489891	+	0.583830i
$573$		0			0
$574$	1.05142	+	5.96289i	0.0438854	+	0.248886i
$575$	−16.3548	+	24.0545i	−0.682043	+	1.00314i
$576$		0			0
$577$	18.8470	−	10.8813i	0.784613	−	0.452996i	−0.0534497	−	0.998571i	$-0.517022\pi$
$577$	18.8470	−	10.8813i	0.784613	−	0.452996i	0.838063	+	0.545574i	$0.183688\pi$
$578$	5.03630	+	2.90771i	0.209483	+	0.120945i
$579$		0			0
$580$	−6.50992	+	21.1529i	−0.270310	+	0.878327i
$581$	7.27720	−	12.6045i	0.301909	−	0.522922i
$582$		0			0
$583$	−3.03669	+	8.34325i	−0.125767	+	0.345542i
$584$	3.02796	−	17.1724i	0.125298	−	0.710599i
$585$		0			0
$586$	8.28764	−	3.01645i	0.342359	−	0.124609i
$587$	26.7247	−	31.8493i	1.10305	−	1.31456i	0.158067	−	0.987428i	$-0.449474\pi$
$587$	26.7247	−	31.8493i	1.10305	−	1.31456i	0.944979	−	0.327131i	$-0.106082\pi$
$588$		0			0
$589$	3.19344	+	0.844882i	0.131583	+	0.0348128i
$590$	−1.39168	−	2.15171i	−0.0572947	−	0.0885846i
$591$		0			0
$592$	6.02403	+	16.5509i	0.247586	+	0.680237i
$593$	8.45667	−	1.49114i	0.347274	−	0.0612337i	0.00270906	−	0.999996i	$-0.499138\pi$
$593$	8.45667	−	1.49114i	0.347274	−	0.0612337i	0.344565	+	0.938763i	$0.388027\pi$
$594$		0			0
$595$	24.5789	−	5.62660i	1.00764	−	0.230668i
$596$	−3.91889	−	6.78771i	−0.160524	−	0.278036i
$597$		0			0
$598$	7.38726	+	8.80379i	0.302087	+	0.360014i
$599$	31.6361	−	26.5459i	1.29262	−	1.08463i	0.301246	−	0.953546i	$-0.402597\pi$
$599$	31.6361	−	26.5459i	1.29262	−	1.08463i	0.991371	−	0.131088i	$-0.0418470\pi$
$600$		0			0
$601$	0.800603	+	1.38668i	0.0326573	+	0.0565640i	0.881892	−	0.471451i	$-0.156270\pi$
$601$	0.800603	+	1.38668i	0.0326573	+	0.0565640i	−0.849235	+	0.528015i	$0.822936\pi$
$602$	−1.00303	+	2.75580i	−0.0408804	+	0.112318i
$603$		0			0
$604$	1.38826	+	7.87324i	0.0564877	+	0.320358i
$605$	−7.66559	+	10.1335i	−0.311650	+	0.411986i
$606$		0			0
$607$			32.4708i			1.31795i	0.752165	+	0.658975i	$0.229010\pi$
$607$			32.4708i			1.31795i	−0.752165	+	0.658975i	$0.770990\pi$
$608$	8.68858	+	18.4802i	0.352368	+	0.749469i
$609$		0			0
$610$	1.23559	−	9.91138i	0.0500275	−	0.401300i
$611$	−26.2779	+	9.56437i	−1.06309	+	0.386933i
$612$		0			0
$613$	−13.7235	−	2.41983i	−0.554288	−	0.0977360i	−0.110514	−	0.993875i	$-0.535250\pi$
$613$	−13.7235	−	2.41983i	−0.554288	−	0.0977360i	−0.443774	+	0.896139i	$0.646361\pi$
$614$	9.55427	+	3.47747i	0.385579	+	0.140339i
$615$		0			0
$616$	−4.05537	+	7.02411i	−0.163396	+	0.283010i
$617$	9.27056	+	11.0482i	0.373219	+	0.444785i	0.919662	−	0.392712i	$-0.128463\pi$
$617$	9.27056	+	11.0482i	0.373219	+	0.444785i	−0.546443	+	0.837496i	$0.684019\pi$
$618$		0			0
$619$	−2.35653	+	4.08162i	−0.0947168	+	0.164054i	−0.909490	−	0.415725i	$-0.863528\pi$
$619$	−2.35653	+	4.08162i	−0.0947168	+	0.164054i	0.814774	+	0.579779i	$0.196861\pi$
$620$	2.71227	+	1.38830i	0.108928	+	0.0557555i
$621$		0			0
$622$	−11.0007	−	1.93972i	−0.441088	−	0.0777757i
$623$	−4.73786	+	0.835413i	−0.189819	+	0.0334701i
$624$		0			0
$625$	−0.687520	−	24.9905i	−0.0275008	−	0.999622i
$626$	9.97728			0.398772
$627$		0			0
$628$			35.6794i			1.42376i
$629$	26.0955	+	21.8968i	1.04050	+	0.873081i
$630$		0			0
$631$	0.575249	+	3.26240i	0.0229003	+	0.129874i	0.994115	−	0.108333i	$-0.0345514\pi$
$631$	0.575249	+	3.26240i	0.0229003	+	0.129874i	−0.971214	+	0.238207i	$0.923440\pi$
$632$	−4.05392	−	0.714816i	−0.161256	−	0.0284339i
$633$		0			0
$634$	−0.458265	−	0.793738i	−0.0182000	−	0.0315234i
$635$	−47.4244	+	2.39741i	−1.88198	+	0.0951383i
$636$		0			0
$637$	7.77970	+	9.27149i	0.308243	+	0.367350i
$638$	−4.93998	−	2.85210i	−0.195576	−	0.112916i
$639$		0			0
$640$	5.47191	+	23.9032i	0.216296	+	0.944856i
$641$	0.00854330	−	0.0484515i	0.000337440	−	0.00191372i	−0.984639	−	0.174605i	$-0.944135\pi$
$641$	0.00854330	−	0.0484515i	0.000337440	−	0.00191372i	0.984976	+	0.172691i	$0.0552463\pi$
$642$		0			0
$643$	−4.10435	−	11.2766i	−0.161860	−	0.444706i	0.832077	−	0.554660i	$-0.187152\pi$
$643$	−4.10435	−	11.2766i	−0.161860	−	0.444706i	−0.993937	+	0.109954i	$0.964929\pi$
$644$	−16.5133	−	13.8563i	−0.650715	−	0.546014i
$645$		0			0
$646$	8.79913	+	6.11991i	0.346197	+	0.240785i
$647$		−	36.3971i		−	1.43092i	−0.698656	−	0.715458i	$-0.746218\pi$
$647$		−	36.3971i		−	1.43092i	0.698656	−	0.715458i	$-0.253782\pi$
$648$		0			0
$649$	−5.52615	+	2.01136i	−0.216920	+	0.0789526i
$650$	−9.57515	−	2.42503i	−0.375568	−	0.0951175i
$651$		0			0
$652$	0.787709	−	2.16421i	0.0308491	−	0.0847571i
$653$	27.5396	−	15.9000i	1.07771	−	0.622214i	0.147430	−	0.989073i	$-0.452900\pi$
$653$	27.5396	−	15.9000i	1.07771	−	0.622214i	0.930277	+	0.366858i	$0.119567\pi$
$654$		0			0
$655$	−1.10018	+	3.57484i	−0.0429874	+	0.139680i
$656$	14.1702	−	11.8902i	0.553253	−	0.464234i
$657$		0			0
$658$	−5.10163	+	2.94543i	−0.198882	+	0.114825i
$659$	−25.2226	−	9.18029i	−0.982534	−	0.357613i	−0.199709	−	0.979855i	$-0.564000\pi$
$659$	−25.2226	−	9.18029i	−0.982534	−	0.357613i	−0.782825	+	0.622242i	$0.786222\pi$
$660$		0			0
$661$	−5.95562	−	33.7760i	−0.231647	−	1.31373i	−0.849562	−	0.527489i	$-0.823134\pi$
$661$	−5.95562	−	33.7760i	−0.231647	−	1.31373i	0.617915	−	0.786245i	$-0.287978\pi$
$662$	−5.17221	−	14.2105i	−0.201024	−	0.552308i
$663$		0			0
$664$	12.0540			0.467784
$665$	19.8870	−	2.82144i	0.771184	−	0.109411i
$666$		0			0
$667$	20.5844	−	24.5315i	0.797031	−	0.949865i
$668$	−4.94186	−	13.5777i	−0.191206	−	0.525335i
$669$		0			0
$670$	−0.665592	−	1.57614i	−0.0257141	−	0.0608916i
$671$	−21.5394	−	7.83970i	−0.831520	−	0.302648i
$672$		0			0
$673$	−18.8097	−	10.8598i	−0.725062	−	0.418615i	0.0915508	−	0.995800i	$-0.470818\pi$
$673$	−18.8097	−	10.8598i	−0.725062	−	0.418615i	−0.816613	+	0.577186i	$0.804151\pi$
$674$	0.891158	−	0.747770i	0.0343261	−	0.0288030i
$675$		0			0
$676$	5.68704	−	9.85024i	0.218732	−	0.378856i
$677$	7.38775	−	4.26532i	0.283934	−	0.163930i	−0.351269	−	0.936275i	$-0.614250\pi$
$677$	7.38775	−	4.26532i	0.283934	−	0.163930i	0.635203	+	0.772345i	$0.280916\pi$
$678$		0			0
$679$	2.43891	−	13.8317i	0.0935966	−	0.530813i
$680$	14.2138	+	15.2990i	0.545073	+	0.586692i
$681$		0			0
$682$	−0.504783	+	0.601577i	−0.0193292	+	0.0230356i
$683$			17.3190i			0.662695i	0.943509	+	0.331347i	$0.107503\pi$
$683$			17.3190i			0.662695i	−0.943509	+	0.331347i	$0.892497\pi$
$684$		0			0
$685$	20.9941	+	32.4595i	0.802145	+	1.24021i
$686$	6.91894	+	5.80568i	0.264166	+	0.221662i
$687$		0			0
$688$	8.82326	−	1.55578i	0.336384	−	0.0593135i
$689$	2.93921	−	16.6691i	0.111975	−	0.635041i
$690$		0			0
$691$	−8.63543	−	14.9570i	−0.328507	−	0.568991i	0.653709	−	0.756746i	$-0.273212\pi$
$691$	−8.63543	−	14.9570i	−0.328507	−	0.568991i	−0.982216	+	0.187755i	$0.939879\pi$
$692$	−4.14066	−	2.39061i	−0.157404	−	0.0908774i
$693$		0			0
$694$	−8.19404	+	6.87561i	−0.311041	+	0.260995i
$695$	1.39159	+	27.5278i	0.0527862	+	1.04419i
$696$		0			0
$697$	12.2363	−	33.6190i	0.463483	−	1.27341i
$698$	1.09858	+	0.193710i	0.0415819	+	0.00733201i
$699$		0			0
$700$	18.4771	+	1.36079i	0.698370	+	0.0514329i
$701$	−16.7623	−	14.0652i	−0.633103	−	0.531236i	0.268789	−	0.963199i	$-0.413377\pi$
$701$	−16.7623	−	14.0652i	−0.633103	−	0.531236i	−0.901891	+	0.431963i	$0.857821\pi$
$702$		0			0
$703$	19.2489	+	19.1278i	0.725987	+	0.721417i
$704$	8.19336			0.308799
$705$		0			0
$706$	−15.0935	+	5.49358i	−0.568051	+	0.206754i
$707$	−24.7547	+	4.36493i	−0.930998	+	0.164160i
$708$		0			0
$709$	19.3220	+	7.03264i	0.725654	+	0.264116i	0.678324	−	0.734763i	$-0.262707\pi$
$709$	19.3220	+	7.03264i	0.725654	+	0.264116i	0.0473296	+	0.998879i	$0.484929\pi$
$710$	4.51387	−	8.81859i	0.169403	−	0.330956i
$711$		0			0
$712$	−2.56114	−	3.05225i	−0.0959829	−	0.114388i
$713$	−2.83388	−	3.37728i	−0.106129	−	0.126480i
$714$		0			0
$715$	−10.3283	+	20.1781i	−0.386258	+	0.754619i
$716$	−13.6894	−	4.98252i	−0.511596	−	0.186206i
$717$		0			0
$718$	2.55100	−	0.449809i	0.0952023	−	0.0167867i
$719$	−14.7270	+	5.36020i	−0.549225	+	0.199902i	−0.601702	−	0.798720i	$-0.705511\pi$
$719$	−14.7270	+	5.36020i	−0.549225	+	0.199902i	0.0524769	+	0.998622i	$0.483288\pi$
$720$		0			0
$721$	26.6249			0.991561
$722$	6.57508	+	5.44677i	0.244699	+	0.202708i
$723$		0			0
$724$	29.6173	+	24.8518i	1.10072	+	0.923611i
$725$	−2.02153	+	27.4489i	−0.0750779	+	1.01943i
$726$		0			0
$727$	−42.8621	−	7.55775i	−1.58967	−	0.280301i	−0.692308	−	0.721602i	$-0.743406\pi$
$727$	−42.8621	−	7.55775i	−1.58967	−	0.280301i	−0.897359	+	0.441300i	$0.854517\pi$
$728$	5.28839	−	14.5297i	0.196001	−	0.538508i
$729$		0			0
$730$	−0.518309	−	10.2529i	−0.0191835	−	0.379478i
$731$	13.2742	−	11.1384i	0.490964	−	0.411968i
$732$		0			0
$733$	−10.9902	−	6.34518i	−0.405931	−	0.234364i	0.283109	−	0.959088i	$-0.408634\pi$
$733$	−10.9902	−	6.34518i	−0.405931	−	0.234364i	−0.689040	+	0.724723i	$0.741968\pi$
$734$	1.33852	+	2.31839i	0.0494058	+	0.0855733i
$735$		0			0
$736$	4.73267	−	26.8403i	0.174448	−	0.989346i
$737$	−3.86674	+	0.681811i	−0.142433	+	0.0251148i
$738$		0			0
$739$	−21.5767	−	18.1050i	−0.793713	−	0.666004i	0.152949	−	0.988234i	$-0.451123\pi$
$739$	−21.5767	−	18.1050i	−0.793713	−	0.666004i	−0.946661	+	0.322230i	$0.895568\pi$
$740$	13.5937	+	21.0175i	0.499713	+	0.772617i
$741$		0			0
$742$		−	3.56561i		−	0.130898i
$743$	16.4322	−	19.5831i	0.602838	−	0.718434i	−0.375181	−	0.926952i	$-0.622419\pi$
$743$	16.4322	−	19.5831i	0.602838	−	0.718434i	0.978019	+	0.208518i	$0.0668639\pi$
$744$		0			0
$745$	−6.63426	−	7.14083i	−0.243061	−	0.261620i
$746$	0.348683	−	1.97748i	0.0127662	−	0.0724006i
$747$		0			0
$748$	19.6484	−	11.3440i	0.718417	−	0.414778i
$749$	15.6341	−	27.0791i	0.571259	−	0.989450i
$750$		0			0
$751$	26.5577	−	22.2846i	0.969106	−	0.813176i	−0.0133044	−	0.999911i	$-0.504235\pi$
$751$	26.5577	−	22.2846i	0.969106	−	0.813176i	0.982410	+	0.186735i	$0.0597906\pi$
$752$	15.5856	+	8.99838i	0.568350	+	0.328137i
$753$		0			0
$754$	10.2186	+	3.71927i	0.372139	+	0.135448i
$755$	3.86778	+	9.15900i	0.140763	+	0.333330i
$756$		0			0
$757$	15.6463	+	42.9878i	0.568674	+	1.56242i	0.806576	+	0.591131i	$0.201318\pi$
$757$	15.6463	+	42.9878i	0.568674	+	1.56242i	−0.237902	+	0.971289i	$0.576460\pi$
$758$	3.84690	−	4.58455i	0.139726	−	0.166518i
$759$		0			0
$760$	10.2588	+	13.0954i	0.372128	+	0.475021i
$761$	−2.85442			−0.103472			−0.0517362	−	0.998661i	$-0.516476\pi$
$761$	−2.85442			−0.103472			−0.0517362	+	0.998661i	$0.516476\pi$
$762$		0			0
$763$	13.5183	+	37.1411i	0.489394	+	1.34460i
$764$	6.11782	+	34.6959i	0.221335	+	1.25525i
$765$		0			0
$766$	−4.29606	−	1.56364i	−0.155223	−	0.0564965i
$767$	9.70909	−	5.60555i	0.350575	−	0.202405i
$768$		0			0
$769$	−14.9538	+	12.5477i	−0.539247	+	0.452482i	−0.871280	−	0.490786i	$-0.836710\pi$
$769$	−14.9538	+	12.5477i	−0.539247	+	0.452482i	0.332033	+	0.943268i	$0.392265\pi$
$770$	−1.40456	+	4.56387i	−0.0506167	+	0.164471i
$771$		0			0
$772$	−0.752669	+	0.434554i	−0.0270891	+	0.0156399i
$773$	−2.47924	+	6.81165i	−0.0891720	+	0.244998i	−0.976260	−	0.216603i	$-0.930502\pi$
$773$	−2.47924	+	6.81165i	−0.0891720	+	0.244998i	0.887088	+	0.461601i	$0.152725\pi$
$774$		0			0
$775$	3.67319	+	0.930282i	0.131945	+	0.0334167i
$776$	10.9306	−	3.97843i	0.392387	−	0.142817i
$777$		0			0
$778$		−	5.12753i		−	0.183831i
$779$	11.9629	−	25.8674i	0.428615	−	0.926797i
$780$		0			0
$781$	−17.4160	−	14.6137i	−0.623193	−	0.522921i
$782$	−4.89253	−	13.4421i	−0.174957	−	0.480689i
$783$		0			0
$784$	1.35256	−	7.67073i	0.0483056	−	0.273955i
$785$	9.90123	+	43.2520i	0.353390	+	1.54373i
$786$		0			0
$787$	3.64347	+	2.10356i	0.129876	+	0.0749837i	0.563530	−	0.826095i	$-0.309443\pi$
$787$	3.64347	+	2.10356i	0.129876	+	0.0749837i	−0.433655	+	0.901079i	$0.642776\pi$
$788$	1.45846	+	1.73812i	0.0519554	+	0.0619181i
$789$		0			0
$790$	−2.42043	+	0.122358i	−0.0861151	+	0.00435331i
$791$	−1.96956	−	3.41138i	−0.0700295	−	0.121295i
$792$		0			0
$793$	43.0339	+	7.58803i	1.52818	+	0.269459i
$794$	0.401286	+	2.27581i	0.0142411	+	0.0807654i
$795$		0			0
$796$	−28.4507	−	23.8730i	−1.00841	−	0.846156i
$797$			25.6411i			0.908253i	0.890937	+	0.454127i	$0.150049\pi$
$797$			25.6411i			0.908253i	−0.890937	+	0.454127i	$0.849951\pi$
$798$		0			0
$799$	34.8074			1.23140
$800$	10.1905	+	21.0914i	0.360289	+	0.745694i
$801$		0			0
$802$	7.55965	−	1.33297i	0.266941	−	0.0470688i
$803$	−23.2016	−	4.09108i	−0.818768	−	0.144371i
$804$		0			0
$805$	−23.8633	−	12.2146i	−0.841070	−	0.430509i
$806$	0.748546	−	1.29652i	0.0263664	−	0.0456679i
$807$		0			0
$808$	−13.3816	−	15.9476i	−0.470765	−	0.561036i
$809$	0.258028	−	0.446918i	0.00907179	−	0.0157128i	−0.861454	−	0.507836i	$-0.830446\pi$
$809$	0.258028	−	0.446918i	0.00907179	−	0.0157128i	0.870526	+	0.492123i	$0.163779\pi$
$810$		0			0
$811$	22.5880	+	8.22138i	0.793174	+	0.288692i	0.706655	−	0.707559i	$-0.250203\pi$
$811$	22.5880	+	8.22138i	0.793174	+	0.288692i	0.0865190	+	0.996250i	$0.472426\pi$
$812$	−20.0873	−	3.54193i	−0.704925	−	0.124297i
$813$		0			0
$814$	−6.06217	+	2.20645i	−0.212479	+	0.0773360i
$815$	0.354311	−	2.84214i	0.0124110	−	0.0995558i
$816$		0			0
$817$	11.2823	−	7.95317i	0.394718	−	0.278246i
$818$			11.7150i			0.409605i
$819$		0			0
$820$	15.8592	−	20.9650i	0.553828	−	0.732131i
$821$	−6.73014	−	38.1685i	−0.234884	−	1.33209i	−0.842859	−	0.538135i	$-0.819129\pi$
$821$	−6.73014	−	38.1685i	−0.234884	−	1.33209i	0.607975	−	0.793956i	$-0.291982\pi$
$822$		0			0
$823$	−1.19306	+	3.27790i	−0.0415874	+	0.114260i	−0.958748	−	0.284257i	$-0.908253\pi$
$823$	−1.19306	+	3.27790i	−0.0415874	+	0.114260i	0.917161	+	0.398518i	$0.130475\pi$
$824$	11.0254	+	19.0965i	0.384086	+	0.665257i
$825$		0			0
$826$	1.80915	−	1.51806i	0.0629485	−	0.0528200i
$827$	17.6651	+	21.0525i	0.614277	+	0.732067i	0.980075	−	0.198628i	$-0.0636484\pi$
$827$	17.6651	+	21.0525i	0.614277	+	0.732067i	−0.365798	+	0.930694i	$0.619204\pi$
$828$		0			0
$829$	−4.30473	−	7.45600i	−0.149509	−	0.258958i	0.781537	−	0.623859i	$-0.214436\pi$
$829$	−4.30473	−	7.45600i	−0.149509	−	0.258958i	−0.931046	+	0.364901i	$0.881103\pi$
$830$	6.91769	−	1.58360i	0.240116	−	0.0549674i
$831$		0			0
$832$	−15.3824	+	2.71233i	−0.533289	+	0.0940332i
$833$	−5.15245	−	14.1562i	−0.178522	−	0.490485i
$834$		0			0
$835$	−9.75860	−	15.0880i	−0.337710	−	0.522141i
$836$	16.3558	−	7.68982i	0.565678	−	0.265958i
$837$		0			0
$838$	−1.66749	+	1.98723i	−0.0576023	+	0.0686478i
$839$	−11.2197	+	4.08363i	−0.387347	+	0.140983i	−0.528350	−	0.849026i	$-0.677189\pi$
$839$	−11.2197	+	4.08363i	−0.387347	+	0.140983i	0.141004	+	0.990009i	$0.454967\pi$
$840$		0			0
$841$	0.225961	−	1.28149i	0.00779176	−	0.0441893i
$842$	3.88858	−	10.6838i	0.134009	−	0.368188i
$843$		0			0
$844$	−6.30397	+	10.9188i	−0.216992	+	0.375841i
$845$	4.16056	−	13.5190i	0.143128	−	0.465069i
$846$		0			0
$847$	−10.1414	−	5.85514i	−0.348462	−	0.201185i
$848$	−9.43366	+	5.44653i	−0.323953	+	0.187035i
$849$		0			0
$850$	10.1671	+	6.91269i	0.348729	+	0.237103i
$851$	−6.28910	−	35.6673i	−0.215588	−	1.22266i
$852$		0			0
$853$	18.5878	−	22.1521i	0.636435	−	0.758474i	−0.347367	−	0.937729i	$-0.612924\pi$
$853$	18.5878	−	22.1521i	0.636435	−	0.758474i	0.983803	+	0.179255i	$0.0573688\pi$
$854$	9.20518			0.314995
$855$		0			0
$856$	25.8964			0.885121
$857$	−35.4914	+	42.2970i	−1.21236	+	1.44484i	−0.351355	+	0.936242i	$0.614279\pi$
$857$	−35.4914	+	42.2970i	−1.21236	+	1.44484i	−0.861006	+	0.508594i	$0.830165\pi$
$858$		0			0
$859$	4.62898	+	26.2522i	0.157939	+	0.895714i	0.956050	+	0.293204i	$0.0947216\pi$
$859$	4.62898	+	26.2522i	0.157939	+	0.895714i	−0.798111	+	0.602510i	$0.794167\pi$
$860$	11.7294	−	4.95325i	0.399970	−	0.168904i
$861$		0			0
$862$	7.30193	−	4.21577i	0.248705	−	0.143590i
$863$	1.04896	+	0.605615i	0.0357068	+	0.0206154i	0.517747	−	0.855534i	$-0.326771\pi$
$863$	1.04896	+	0.605615i	0.0357068	+	0.0206154i	−0.482040	+	0.876149i	$0.660104\pi$
$864$		0			0
$865$	−5.68289	−	1.74894i	−0.193224	−	0.0594657i
$866$	−1.91275	+	3.31298i	−0.0649980	+	0.112580i
$867$		0			0
$868$	−0.960426	+	2.63875i	−0.0325990	+	0.0895650i
$869$	−0.965789	+	5.47726i	−0.0327621	+	0.185803i
$870$		0			0
$871$	7.03380	−	2.56010i	0.238331	−	0.0867455i
$872$	−21.0413	+	25.0760i	−0.712547	+	0.849181i
$873$		0			0
$874$	−2.98405	−	10.9976i	−0.100937	−	0.372000i
$875$	22.7764	−	3.47791i	0.769981	−	0.117575i
$876$		0			0
$877$	−16.9444	−	46.5543i	−0.572171	−	1.57203i	−0.801067	−	0.598575i	$-0.795734\pi$
$877$	−16.9444	−	46.5543i	−0.572171	−	1.57203i	0.228896	−	0.973451i	$-0.426488\pi$
$878$	−0.909565	+	0.160381i	−0.0306963	+	0.00541259i
$879$		0			0
$880$	14.2203	−	3.25531i	0.479366	−	0.109736i
$881$	−15.2819	−	26.4691i	−0.514861	−	0.891766i	−0.999851	−	0.0172462i	$-0.994510\pi$
$881$	−15.2819	−	26.4691i	−0.514861	−	0.891766i	0.484990	−	0.874520i	$-0.338823\pi$
$882$		0			0
$883$	−3.58574	−	4.27331i	−0.120670	−	0.143808i	0.702328	−	0.711854i	$-0.252144\pi$
$883$	−3.58574	−	4.27331i	−0.120670	−	0.143808i	−0.822997	+	0.568045i	$0.807700\pi$
$884$	−33.1331	+	27.8019i	−1.11439	+	0.935080i
$885$		0			0
$886$	−2.70530	−	4.68572i	−0.0908864	−	0.157420i
$887$	0.227909	−	0.626174i	0.00765242	−	0.0210248i	−0.935808	−	0.352511i	$-0.885328\pi$
$887$	0.227909	−	0.626174i	0.00765242	−	0.0210248i	0.943460	+	0.331486i	$0.107550\pi$
$888$		0			0
$889$	−7.59933	−	43.0979i	−0.254873	−	1.44546i
$890$	−1.87082	−	1.41520i	−0.0627099	−	0.0474375i
$891$		0			0
$892$			34.9497i			1.17020i
$893$	27.6297	+	2.32940i	0.924591	+	0.0779504i
$894$		0			0
$895$	−17.9775	−	2.24113i	−0.600921	−	0.0749129i
$896$	−21.2365	+	7.72944i	−0.709460	+	0.258222i
$897$		0			0
$898$	3.31644	+	0.584778i	0.110671	+	0.0195143i
$899$	−3.92003	−	1.42677i	−0.130740	−	0.0475856i
$900$		0			0
$901$	−10.5341	+	18.2456i	−0.350941	+	0.607848i
$902$	4.35508	+	5.19018i	0.145008	+	0.172814i
$903$		0			0
$904$	1.63119	−	2.82530i	0.0542526	−	0.0939682i
$905$	42.7997	+	21.9074i	1.42271	+	0.728227i
$906$		0			0
$907$	51.9794	+	9.16536i	1.72595	+	0.304331i	0.946635	−	0.322307i	$-0.104458\pi$
$907$	51.9794	+	9.16536i	1.72595	+	0.304331i	0.779311	+	0.626638i	$0.215569\pi$
$908$	−11.5807	+	2.04198i	−0.384317	+	0.0677655i
$909$		0			0
$910$	1.12612	−	9.03329i	0.0373305	−	0.299451i
$911$	13.0586			0.432650			0.216325	−	0.976321i	$-0.430593\pi$
$911$	13.0586			0.432650			0.216325	+	0.976321i	$0.430593\pi$
$912$		0			0
$913$		−	16.2861i		−	0.538992i
$914$	−4.82116	−	4.04543i	−0.159470	−	0.133811i
$915$		0			0
$916$	6.36966	+	36.1242i	0.210460	+	1.19358i
$917$	−3.39475	−	0.598585i	−0.112104	−	0.0197670i
$918$		0			0
$919$	−23.0270	−	39.8839i	−0.759589	−	1.31565i	−0.943060	−	0.332622i	$-0.892067\pi$
$919$	−23.0270	−	39.8839i	−0.759589	−	1.31565i	0.183471	−	0.983025i	$-0.441267\pi$
$920$	−1.12094	−	22.1738i	−0.0369562	−	0.731049i
$921$		0			0
$922$	5.10547	+	6.08447i	0.168140	+	0.200381i
$923$	37.5349	+	21.6708i	1.23548	+	0.713303i
$924$		0			0
$925$	22.3113	+	21.7059i	0.733590	+	0.713685i
$926$	−1.29477	+	7.34299i	−0.0425487	+	0.241306i
$927$		0			0
$928$	−8.82018	−	24.2332i	−0.289536	−	0.795495i
$929$	23.7272	+	19.9094i	0.778463	+	0.653208i	0.942861	−	0.333186i	$-0.108124\pi$
$929$	23.7272	+	19.9094i	0.778463	+	0.653208i	−0.164398	+	0.986394i	$0.552568\pi$
$930$		0			0
$931$	−3.14258	−	11.5819i	−0.102994	−	0.379580i
$932$		−	21.6649i		−	0.709657i
$933$		0			0
$934$	6.75233	−	2.45765i	0.220943	−	0.0804166i
$935$	20.6706	−	19.2042i	0.676000	−	0.628045i
$936$		0			0
$937$	−11.9068	+	32.7138i	−0.388979	+	1.06871i	0.578483	+	0.815695i	$0.303645\pi$
$937$	−11.9068	+	32.7138i	−0.388979	+	1.06871i	−0.967462	+	0.253017i	$0.918577\pi$
$938$	1.36555	−	0.788402i	0.0445869	−	0.0257422i
$939$		0			0
$940$	24.4442	+	7.52284i	0.797283	+	0.245368i
$941$	12.4217	−	10.4230i	0.404934	−	0.339780i	−0.417463	−	0.908694i	$-0.637081\pi$
$941$	12.4217	−	10.4230i	0.404934	−	0.339780i	0.822397	+	0.568914i	$0.192636\pi$
$942$		0			0
$943$	−32.9409	+	19.0184i	−1.07270	+	0.619325i
$944$	−6.77990	−	2.46768i	−0.220667	−	0.0803162i
$945$		0			0
$946$	0.569843	+	3.23174i	0.0185272	+	0.105073i
$947$	5.00728	+	13.7574i	0.162715	+	0.447055i	0.994077	−	0.108675i	$-0.0346609\pi$
$947$	5.00728	+	13.7574i	0.162715	+	0.447055i	−0.831363	+	0.555730i	$0.812439\pi$
$948$		0			0
$949$	44.9136			1.45796
$950$	7.60791	+	6.16762i	0.246833	+	0.200104i
$951$		0			0
$952$	−12.3710	+	14.7432i	−0.400947	+	0.477830i
$953$	−13.9637	−	38.3650i	−0.452329	−	1.24276i	−0.931081	−	0.364813i	$-0.881133\pi$
$953$	−13.9637	−	38.3650i	−0.452329	−	1.24276i	0.478752	−	0.877950i	$-0.341089\pi$
$954$		0			0
$955$	17.0446	+	40.3620i	0.551550	+	1.30608i
$956$	10.3490	+	3.76671i	0.334709	+	0.121824i
$957$		0			0
$958$	−2.87826	−	1.66176i	−0.0929922	−	0.0536891i
$959$	−27.2918	+	22.9006i	−0.881299	+	0.739498i
$960$		0			0
$961$	15.2128	−	26.3494i	0.490737	−	0.849981i
$962$	10.6508	−	6.14926i	0.343397	−	0.198260i
$963$		0			0
$964$	−2.27088	+	12.8788i	−0.0731401	+	0.414798i
$965$	−0.791824	+	0.735653i	−0.0254897	+	0.0236815i
$966$		0			0
$967$	15.5302	−	18.5082i	0.499419	−	0.595184i	−0.456168	−	0.889894i	$-0.650778\pi$
$967$	15.5302	−	18.5082i	0.499419	−	0.595184i	0.955587	+	0.294710i	$0.0952229\pi$
$968$		−	9.69845i		−	0.311720i
$969$		0			0
$970$	5.75036	−	3.71922i	0.184633	−	0.119417i
$971$	−21.2648	−	17.8433i	−0.682420	−	0.572618i	0.234292	−	0.972166i	$-0.424723\pi$
$971$	−21.2648	−	17.8433i	−0.682420	−	0.572618i	−0.916712	+	0.399548i	$0.869167\pi$
$972$		0			0
$973$	−25.0165	+	4.41109i	−0.801992	+	0.141413i
$974$	1.57534	−	8.93418i	0.0504771	−	0.286270i
$975$		0			0
$976$	−14.0611	−	24.3545i	−0.450084	−	0.779568i
$977$	−3.08737	−	1.78249i	−0.0987737	−	0.0570270i	0.449799	−	0.893130i	$-0.351495\pi$
$977$	−3.08737	−	1.78249i	−0.0987737	−	0.0570270i	−0.548573	+	0.836103i	$0.684829\pi$
$978$		0			0
$979$	−4.12390	+	3.46036i	−0.131800	+	0.110594i
$980$	−0.558862	−	11.0551i	−0.0178522	−	0.353143i
$981$		0			0
$982$	−1.43444	+	3.94110i	−0.0457749	+	0.125766i
$983$	1.61065	+	0.284002i	0.0513718	+	0.00905824i	0.199275	−	0.979944i	$-0.436141\pi$
$983$	1.61065	+	0.284002i	0.0513718	+	0.00905824i	−0.147903	+	0.989002i	$0.547252\pi$
$984$		0			0
$985$	2.25034	+	1.70229i	0.0717018	+	0.0542395i
$986$	−10.3687	−	8.70041i	−0.330208	−	0.277077i
$987$		0			0
$988$	−28.1612	+	19.8515i	−0.895927	+	0.631560i
$989$	−18.4230			−0.585818
$990$		0			0
$991$	−1.41335	+	0.514417i	−0.0448965	+	0.0163410i	−0.364371	−	0.931254i	$-0.618716\pi$
$991$	−1.41335	+	0.514417i	−0.0448965	+	0.0163410i	0.319474	+	0.947595i	$0.396494\pi$
$992$	−3.49639	+	0.616508i	−0.111010	+	0.0195741i
$993$		0			0
$994$	8.57954	+	3.12270i	0.272126	+	0.0990459i
$995$	−41.1140	−	21.0446i	−1.30340	−	0.667158i
$996$		0			0
$997$	33.0482	+	39.3853i	1.04665	+	1.24734i	0.968134	+	0.250431i	$0.0805724\pi$
$997$	33.0482	+	39.3853i	1.04665	+	1.24734i	0.0785117	+	0.996913i	$0.474983\pi$
$998$	6.92124	+	8.24842i	0.219088	+	0.261099i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.da.b.244.4		48
3.2	odd	2		95.2.p.a.54.5	yes	48
5.4	even	2	inner	855.2.da.b.244.5		48
15.2	even	4		475.2.l.f.301.5		48
15.8	even	4		475.2.l.f.301.4		48
15.14	odd	2		95.2.p.a.54.4	yes	48
19.6	even	9	inner	855.2.da.b.424.5		48
57.5	odd	18		1805.2.b.k.1084.10		24
57.14	even	18		1805.2.b.l.1084.15		24
57.44	odd	18		95.2.p.a.44.4	✓	48
95.44	even	18	inner	855.2.da.b.424.4		48
285.14	even	18		1805.2.b.l.1084.10		24
285.44	odd	18		95.2.p.a.44.5	yes	48
285.62	even	36		9025.2.a.cu.1.15		24
285.119	odd	18		1805.2.b.k.1084.15		24
285.128	odd	36		9025.2.a.ct.1.15		24
285.158	even	36		475.2.l.f.101.4		48
285.233	even	36		9025.2.a.cu.1.10		24
285.242	odd	36		9025.2.a.ct.1.10		24
285.272	even	36		475.2.l.f.101.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.44.4	✓	48	57.44	odd	18
95.2.p.a.44.5	yes	48	285.44	odd	18
95.2.p.a.54.4	yes	48	15.14	odd	2
95.2.p.a.54.5	yes	48	3.2	odd	2
475.2.l.f.101.4		48	285.158	even	36
475.2.l.f.101.5		48	285.272	even	36
475.2.l.f.301.4		48	15.8	even	4
475.2.l.f.301.5		48	15.2	even	4
855.2.da.b.244.4		48	1.1	even	1	trivial
855.2.da.b.244.5		48	5.4	even	2	inner
855.2.da.b.424.4		48	95.44	even	18	inner
855.2.da.b.424.5		48	19.6	even	9	inner
1805.2.b.k.1084.10		24	57.5	odd	18
1805.2.b.k.1084.15		24	285.119	odd	18
1805.2.b.l.1084.10		24	285.14	even	18
1805.2.b.l.1084.15		24	57.14	even	18
9025.2.a.ct.1.10		24	285.242	odd	36
9025.2.a.ct.1.15		24	285.128	odd	36
9025.2.a.cu.1.10		24	285.233	even	36
9025.2.a.cu.1.15		24	285.62	even	36

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.da (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.288852 + 0.344240i) q^{2} +(0.312230 + 1.77075i) q^{4} +(0.869891 + 2.05992i) q^{5} +(-1.78470 + 1.03040i) q^{7} +(-1.47809 - 0.853374i) q^{8} +O(q^{10})\)	\(q+(-0.288852 + 0.344240i) q^{2} +(0.312230 + 1.77075i) q^{4} +(0.869891 + 2.05992i) q^{5} +(-1.78470 + 1.03040i) q^{7} +(-1.47809 - 0.853374i) q^{8} +(-0.960378 - 0.295561i) q^{10} +(-1.15299 + 1.99705i) q^{11} +(1.50356 - 4.13099i) q^{13} +(0.160809 - 0.911996i) q^{14} +(-2.65854 + 0.967630i) q^{16} +(-3.51724 + 4.19168i) q^{17} +(-3.07246 + 3.09192i) q^{19} +(-3.37600 + 2.18353i) q^{20} +(-0.354418 - 0.973756i) q^{22} +(5.72917 - 1.01021i) q^{23} +(-3.48658 + 3.58382i) q^{25} +(0.987746 + 1.71083i) q^{26} +(-2.38181 - 2.83853i) q^{28} +(4.21681 - 3.53833i) q^{29} +(-0.378916 - 0.656302i) q^{31} +(1.60231 - 4.40231i) q^{32} +(-0.426984 - 2.42155i) q^{34} +(-3.67503 - 2.78001i) q^{35} -6.22555i q^{37} +(-0.176878 - 1.95077i) q^{38} +(0.472112 - 3.78709i) q^{40} +(-6.14398 + 2.23623i) q^{41} +(-3.11869 - 0.549909i) q^{43} +(-3.89626 - 1.41812i) q^{44} +(-1.30713 + 2.26401i) q^{46} +(-4.08888 - 4.87293i) q^{47} +(-1.37657 + 2.38429i) q^{49} +(-0.226589 - 2.23541i) q^{50} +(7.78439 + 1.37260i) q^{52} +(3.79178 - 0.668594i) q^{53} +(-5.11674 - 0.637871i) q^{55} +3.51725 q^{56} +2.47365i q^{58} +(1.95359 + 1.63926i) q^{59} +(1.72608 + 9.78909i) q^{61} +(0.335376 + 0.0591358i) q^{62} +(-1.77654 - 3.07705i) q^{64} +(9.81745 - 0.496295i) q^{65} +(1.09447 + 1.30434i) q^{67} +(-8.52060 - 4.91937i) q^{68} +(2.01853 - 0.462081i) q^{70} +(-1.71201 + 9.70931i) q^{71} +(3.49431 + 9.60054i) q^{73} +(2.14308 + 1.79826i) q^{74} +(-6.43433 - 4.47516i) q^{76} -4.75216i q^{77} +(2.26642 - 0.824910i) q^{79} +(-4.30589 - 4.63466i) q^{80} +(1.00490 - 2.76094i) q^{82} +(-6.11633 + 3.53126i) q^{83} +(-11.6942 - 3.59894i) q^{85} +(1.09014 - 0.914734i) q^{86} +(3.40845 - 1.96787i) q^{88} +(2.19373 + 0.798452i) q^{89} +(1.57316 + 8.92183i) q^{91} +(3.57764 + 9.82950i) q^{92} +2.85854 q^{94} +(-9.04183 - 3.63940i) q^{95} +(-4.38085 + 5.22089i) q^{97} +(-0.423142 - 1.16257i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 18 q^{4} + 6 q^{5}+O(q^{10}) \) 48 * q - 18 * q^4 + 6 * q^5	\( 48 q - 18 q^{4} + 6 q^{5} - 15 q^{10} + 12 q^{11} - 6 q^{14} - 42 q^{16} + 12 q^{19} - 42 q^{20} + 12 q^{25} - 12 q^{26} - 42 q^{31} - 36 q^{34} - 6 q^{35} + 66 q^{40} - 6 q^{41} + 6 q^{44} - 6 q^{46} + 12 q^{49} + 18 q^{50} - 36 q^{56} + 36 q^{59} + 48 q^{61} + 18 q^{65} - 123 q^{70} + 24 q^{71} - 84 q^{74} + 66 q^{76} + 48 q^{79} + 39 q^{80} - 84 q^{85} + 42 q^{86} + 12 q^{89} - 30 q^{91} - 72 q^{94} + 63 q^{95}+O(q^{100}) \) 48 * q - 18 * q^4 + 6 * q^5 - 15 * q^10 + 12 * q^11 - 6 * q^14 - 42 * q^16 + 12 * q^19 - 42 * q^20 + 12 * q^25 - 12 * q^26 - 42 * q^31 - 36 * q^34 - 6 * q^35 + 66 * q^40 - 6 * q^41 + 6 * q^44 - 6 * q^46 + 12 * q^49 + 18 * q^50 - 36 * q^56 + 36 * q^59 + 48 * q^61 + 18 * q^65 - 123 * q^70 + 24 * q^71 - 84 * q^74 + 66 * q^76 + 48 * q^79 + 39 * q^80 - 84 * q^85 + 42 * q^86 + 12 * q^89 - 30 * q^91 - 72 * q^94 + 63 * q^95

Introduction

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