LMFDB - Embedded newform 855.2.da.b.424.8

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			424.8
Character	$\chi$	$=$	855.424
Dual form			855.2.da.b.244.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72697 + 2.05812i) q^{2} +(-0.906145 + 5.13900i) q^{4} +(-1.11892 + 1.93598i) q^{5} +(2.41018 + 1.39152i) q^{7} +(-7.48810 + 4.32326i) q^{8} +O(q^{10})$	\(q+(1.72697 + 2.05812i) q^{2} +(-0.906145 + 5.13900i) q^{4} +(-1.11892 + 1.93598i) q^{5} +(2.41018 + 1.39152i) q^{7} +(-7.48810 + 4.32326i) q^{8} +(-5.91682 + 1.04052i) q^{10} +(-1.19000 - 2.06113i) q^{11} +(-0.0138492 - 0.0380504i) q^{13} +(1.29839 + 7.36354i) q^{14} +(-12.0223 - 4.37577i) q^{16} +(-1.16714 - 1.39094i) q^{17} +(4.07652 + 1.54336i) q^{19} +(-8.93512 - 7.50439i) q^{20} +(2.18698 - 6.00867i) q^{22} +(2.50568 + 0.441819i) q^{23} +(-2.49605 - 4.33240i) q^{25} +(0.0543952 - 0.0942153i) q^{26} +(-9.33498 + 11.1250i) q^{28} +(2.25845 + 1.89507i) q^{29} +(1.44307 - 2.49947i) q^{31} +(-5.84176 - 16.0501i) q^{32} +(0.847116 - 4.80423i) q^{34} +(-5.39074 + 3.10907i) q^{35} +0.227089i q^{37} +(3.86361 + 11.0553i) q^{38} +(0.00880774 - 19.3342i) q^{40} +(7.55269 + 2.74896i) q^{41} +(-5.05471 + 0.891282i) q^{43} +(11.6705 - 4.24771i) q^{44} +(3.41791 + 5.92000i) q^{46} +(-7.11977 + 8.48501i) q^{47} +(0.372635 + 0.645423i) q^{49} +(4.60600 - 12.6191i) q^{50} +(0.208091 - 0.0366920i) q^{52} +(-5.62767 - 0.992310i) q^{53} +(5.32182 + 0.00242437i) q^{55} -24.0635 q^{56} +7.92088i q^{58} +(8.89878 - 7.46696i) q^{59} +(0.795974 - 4.51419i) q^{61} +(7.63635 - 1.34649i) q^{62} +(10.1506 - 17.5814i) q^{64} +(0.0891611 + 0.0157634i) q^{65} +(3.11931 - 3.71745i) q^{67} +(8.20566 - 4.73754i) q^{68} +(-15.7085 - 5.72552i) q^{70} +(1.34912 + 7.65124i) q^{71} +(-1.45279 + 3.99151i) q^{73} +(-0.467377 + 0.392176i) q^{74} +(-11.6252 + 19.5508i) q^{76} -6.62359i q^{77} +(10.9102 + 3.97100i) q^{79} +(21.9234 - 18.3789i) q^{80} +(7.38558 + 20.2917i) q^{82} +(3.87161 + 2.23528i) q^{83} +(3.99877 - 0.703214i) q^{85} +(-10.5637 - 8.86399i) q^{86} +(17.8216 + 10.2893i) q^{88} +(-14.4648 + 5.26476i) q^{89} +(0.0195687 - 0.110980i) q^{91} +(-4.54102 + 12.4764i) q^{92} -29.7588 q^{94} +(-7.54920 + 6.16519i) q^{95} +(-3.59666 - 4.28633i) q^{97} +(-0.684829 + 1.88155i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	1.72697	+	2.05812i	1.22115	+	1.45531i	0.850036	+	0.526724i	$0.176580\pi$
$2$	1.72697	+	2.05812i	1.22115	+	1.45531i	0.371115	+	0.928587i	$0.378976\pi$
$3$		0			0
$3$		0			0
$4$	−0.906145	+	5.13900i	−0.453073	+	2.56950i
$5$	−1.11892	+	1.93598i	−0.500394	+	0.865798i
$5$	−1.11892	+	1.93598i	−0.500394	+	0.865798i
$6$		0			0
$7$	2.41018	+	1.39152i	0.910961	+	0.525944i	0.880740	−	0.473600i	$-0.157046\pi$
$7$	2.41018	+	1.39152i	0.910961	+	0.525944i	0.0302209	+	0.999543i	$0.490379\pi$
$8$	−7.48810	+	4.32326i	−2.64744	+	1.52850i
$9$		0			0
$10$	−5.91682	+	1.04052i	−1.87106	+	0.329040i
$11$	−1.19000	−	2.06113i	−0.358797	−	0.621455i	0.628963	−	0.777435i	$-0.283480\pi$
$11$	−1.19000	−	2.06113i	−0.358797	−	0.621455i	−0.987760	+	0.155980i	$0.950146\pi$
$12$		0			0
$13$	−0.0138492	−	0.0380504i	−0.00384108	−	0.0105533i	0.937757	−	0.347291i	$-0.112899\pi$
$13$	−0.0138492	−	0.0380504i	−0.00384108	−	0.0105533i	−0.941598	+	0.336738i	$0.890676\pi$
$14$	1.29839	+	7.36354i	0.347010	+	1.96799i
$15$		0			0
$16$	−12.0223	−	4.37577i	−3.00558	−	1.09394i
$17$	−1.16714	−	1.39094i	−0.283073	−	0.337353i	0.605707	−	0.795688i	$-0.292891\pi$
$17$	−1.16714	−	1.39094i	−0.283073	−	0.337353i	−0.888780	+	0.458335i	$0.848446\pi$
$18$		0			0
$19$	4.07652	+	1.54336i	0.935219	+	0.354071i
$19$	4.07652	+	1.54336i	0.935219	+	0.354071i
$20$	−8.93512	−	7.50439i	−1.99795	−	1.67803i
$21$		0			0
$22$	2.18698	−	6.00867i	0.466265	−	1.28105i
$23$	2.50568	+	0.441819i	0.522471	+	0.0921257i	0.428663	−	0.903465i	$-0.358985\pi$
$23$	2.50568	+	0.441819i	0.522471	+	0.0921257i	0.0938080	+	0.995590i	$0.470096\pi$
$24$		0			0
$25$	−2.49605	−	4.33240i	−0.499211	−	0.866481i
$26$	0.0543952	−	0.0942153i	0.0106678	−	0.0184771i
$27$		0			0
$28$	−9.33498	+	11.1250i	−1.76414	+	2.10243i
$29$	2.25845	+	1.89507i	0.419384	+	0.351905i	0.827929	−	0.560833i	$-0.189519\pi$
$29$	2.25845	+	1.89507i	0.419384	+	0.351905i	−0.408545	+	0.912738i	$0.633964\pi$
$30$		0			0
$31$	1.44307	−	2.49947i	0.259183	−	0.448918i	−0.706840	−	0.707373i	$-0.749880\pi$
$31$	1.44307	−	2.49947i	0.259183	−	0.448918i	0.966023	+	0.258455i	$0.0832134\pi$
$32$	−5.84176	−	16.0501i	−1.03269	−	2.83728i
$33$		0			0
$34$	0.847116	−	4.80423i	0.145279	−	0.823919i
$35$	−5.39074	+	3.10907i	−0.911201	+	0.525529i
$36$		0			0
$37$			0.227089i			0.0373333i	0.999826	+	0.0186666i	$0.00594212\pi$
$37$			0.227089i			0.0373333i	−0.999826	+	0.0186666i	$0.994058\pi$
$38$	3.86361	+	11.0553i	0.626761	+	1.79341i
$39$		0			0
$40$	0.00880774	−	19.3342i	0.00139263	−	3.05700i
$41$	7.55269	+	2.74896i	1.17953	+	0.429315i	0.856037	−	0.516915i	$-0.172920\pi$
$41$	7.55269	+	2.74896i	1.17953	+	0.429315i	0.323496	+	0.946230i	$0.395142\pi$
$42$		0			0
$43$	−5.05471	+	0.891282i	−0.770836	+	0.135919i	−0.545215	−	0.838296i	$-0.683552\pi$
$43$	−5.05471	+	0.891282i	−0.770836	+	0.135919i	−0.225621	+	0.974215i	$0.572441\pi$
$44$	11.6705	−	4.24771i	1.75939	−	0.640366i
$45$		0			0
$46$	3.41791	+	5.92000i	0.503944	+	0.872857i
$47$	−7.11977	+	8.48501i	−1.03853	+	1.23767i	−0.0677434	+	0.997703i	$0.521580\pi$
$47$	−7.11977	+	8.48501i	−1.03853	+	1.23767i	−0.970782	+	0.239964i	$0.922865\pi$
$48$		0			0
$49$	0.372635	+	0.645423i	0.0532336	+	0.0922032i
$50$	4.60600	−	12.6191i	0.651387	−	1.78461i
$51$		0			0
$52$	0.208091	−	0.0366920i	0.0288570	−	0.00508827i
$53$	−5.62767	−	0.992310i	−0.773020	−	0.136304i	−0.226794	−	0.973943i	$-0.572825\pi$
$53$	−5.62767	−	0.992310i	−0.773020	−	0.136304i	−0.546225	+	0.837638i	$0.683936\pi$
$54$		0			0
$55$	5.32182	+	0.00242437i	0.717594	+	0.000326902i
$56$	−24.0635			−3.21562
$57$		0			0
$58$			7.92088i			1.04006i
$59$	8.89878	−	7.46696i	1.15852	−	0.972116i	0.158638	−	0.987337i	$-0.449290\pi$
$59$	8.89878	−	7.46696i	1.15852	−	0.972116i	0.999884	+	0.0152208i	$0.00484512\pi$
$60$		0			0
$61$	0.795974	−	4.51419i	0.101914	−	0.577983i	−0.890494	−	0.454995i	$-0.849641\pi$
$61$	0.795974	−	4.51419i	0.101914	−	0.577983i	0.992408	−	0.122988i	$-0.0392477\pi$
$62$	7.63635	−	1.34649i	0.969817	−	0.171005i
$63$		0			0
$64$	10.1506	−	17.5814i	1.26883	−	2.19767i
$65$	0.0891611	+	0.0157634i	0.0110591	+	0.00195521i
$66$		0			0
$67$	3.11931	−	3.71745i	0.381084	−	0.454159i	−0.541072	−	0.840976i	$-0.681981\pi$
$67$	3.11931	−	3.71745i	0.381084	−	0.454159i	0.922156	+	0.386818i	$0.126426\pi$
$68$	8.20566	−	4.73754i	0.995083	−	0.574511i
$69$		0			0
$70$	−15.7085	−	5.72552i	−1.87752	−	0.684331i
$71$	1.34912	+	7.65124i	0.160111	+	0.908035i	0.953963	+	0.299924i	$0.0969614\pi$
$71$	1.34912	+	7.65124i	0.160111	+	0.908035i	−0.793852	+	0.608111i	$0.791928\pi$
$72$		0			0
$73$	−1.45279	+	3.99151i	−0.170036	+	0.467171i	−0.995216	−	0.0976997i	$-0.968852\pi$
$73$	−1.45279	+	3.99151i	−0.170036	+	0.467171i	0.825180	+	0.564870i	$0.191074\pi$
$74$	−0.467377	+	0.392176i	−0.0543315	+	0.0455896i
$75$		0			0
$76$	−11.6252	+	19.5508i	−1.33351	+	2.24263i
$77$		−	6.62359i		−	0.754828i
$78$		0			0
$79$	10.9102	+	3.97100i	1.22750	+	0.446773i	0.872740	−	0.488185i	$-0.162341\pi$
$79$	10.9102	+	3.97100i	1.22750	+	0.446773i	0.354758	+	0.934958i	$0.384563\pi$
$80$	21.9234	−	18.3789i	2.45111	−	2.05482i
$81$		0			0
$82$	7.38558	+	20.2917i	0.815601	+	2.24085i
$83$	3.87161	+	2.23528i	0.424965	+	0.245354i	0.697199	−	0.716877i	$-0.254429\pi$
$83$	3.87161	+	2.23528i	0.424965	+	0.245354i	−0.272234	+	0.962231i	$0.587763\pi$
$84$		0			0
$85$	3.99877	−	0.703214i	0.433728	−	0.0762742i
$86$	−10.5637	−	8.86399i	−1.13911	−	0.955828i
$87$		0			0
$88$	17.8216	+	10.2893i	1.89979	+	1.09684i
$89$	−14.4648	+	5.26476i	−1.53327	+	0.558064i	−0.964419	−	0.264378i	$-0.914833\pi$
$89$	−14.4648	+	5.26476i	−1.53327	+	0.558064i	−0.568849	+	0.822442i	$0.692611\pi$
$90$		0			0
$91$	0.0195687	−	0.110980i	0.00205136	−	0.0116338i
$92$	−4.54102	+	12.4764i	−0.473434	+	1.30075i
$93$		0			0
$94$	−29.7588			−3.06939
$95$	−7.54920	+	6.16519i	−0.774532	+	0.632535i
$96$		0			0
$97$	−3.59666	−	4.28633i	−0.365185	−	0.435211i	0.551895	−	0.833914i	$-0.313905\pi$
$97$	−3.59666	−	4.28633i	−0.365185	−	0.435211i	−0.917080	+	0.398703i	$0.869460\pi$
$98$	−0.684829	+	1.88155i	−0.0691782	+	0.190066i
$99$		0			0
$100$	24.5260	−	8.90144i	2.45260	−	0.890144i
$101$	11.2361	−	4.08961i	1.11804	−	0.406932i	0.284101	−	0.958794i	$-0.408305\pi$
$101$	11.2361	−	4.08961i	1.11804	−	0.406932i	0.833935	+	0.551863i	$0.186083\pi$
$102$		0			0
$103$	−12.2058	+	7.04702i	−1.20267	+	0.694363i	−0.961149	−	0.276031i	$-0.910981\pi$
$103$	−12.2058	+	7.04702i	−1.20267	+	0.694363i	−0.241524	+	0.970395i	$0.577647\pi$
$104$	0.268206	+	0.225052i	0.0262998	+	0.0220681i
$105$		0			0
$106$	−7.67651	−	13.2961i	−0.745609	−	1.29143i
$107$	10.1541	+	5.86249i	0.981637	+	0.566748i	0.902764	−	0.430137i	$-0.141535\pi$
$107$	10.1541	+	5.86249i	0.981637	+	0.566748i	0.0788727	+	0.996885i	$0.474868\pi$
$108$		0			0
$109$	1.16558	+	6.61032i	0.111642	+	0.633154i	0.988358	+	0.152145i	$0.0486182\pi$
$109$	1.16558	+	6.61032i	0.111642	+	0.633154i	−0.876716	+	0.481008i	$0.840271\pi$
$110$	9.18563	+	10.9571i	0.875815	+	1.04472i
$111$		0			0
$112$	−22.8870	−	27.2757i	−2.16262	−	2.57731i
$113$		−	2.46603i		−	0.231985i	−0.993250	−	0.115992i	$-0.962995\pi$
$113$		−	2.46603i		−	0.231985i	0.993250	−	0.115992i	$-0.0370048\pi$
$114$		0			0
$115$	−3.65900	+	4.35660i	−0.341204	+	0.406255i
$116$	−11.7852	+	9.88899i	−1.09423	+	0.918169i
$117$		0			0
$118$	30.7358	+	5.41956i	2.82946	+	0.498911i
$119$	−0.877494	−	4.97651i	−0.0804397	−	0.456196i
$120$		0			0
$121$	2.66782	−	4.62080i	0.242529	−	0.420073i
$122$	10.6654	−	6.15765i	0.965597	−	0.557488i
$123$		0			0
$124$	11.5372	+	9.68082i	1.03607	+	0.869364i
$125$	11.1803	+	0.0152797i	0.999999	+	0.00136666i
$126$		0			0
$127$	0.252761	+	0.694456i	0.0224289	+	0.0616230i	0.950402	−	0.311025i	$-0.100672\pi$
$127$	0.252761	+	0.694456i	0.0224289	+	0.0616230i	−0.927973	+	0.372648i	$0.878450\pi$
$128$	20.0731	−	3.53942i	1.77423	−	0.312844i
$129$		0			0
$130$	0.121535	+	0.210727i	0.0106594	+	0.0184820i
$131$	8.35925	−	7.01424i	0.730351	−	0.612837i	−0.199876	−	0.979821i	$-0.564054\pi$
$131$	8.35925	−	7.01424i	0.730351	−	0.612837i	0.930227	+	0.366984i	$0.119610\pi$
$132$		0			0
$133$	7.67754	+	9.39231i	0.665727	+	0.814417i
$134$	13.0379			1.12630
$135$		0			0
$136$	14.7531	+	5.36968i	1.26506	+	0.460446i
$137$	4.52066	+	0.797114i	0.386226	+	0.0681021i	0.363390	−	0.931637i	$-0.381619\pi$
$137$	4.52066	+	0.797114i	0.386226	+	0.0681021i	0.0228361	+	0.999739i	$0.492730\pi$
$138$		0			0
$139$	−7.37217	+	2.68325i	−0.625299	+	0.227590i	−0.635184	−	0.772361i	$-0.719076\pi$
$139$	−7.37217	+	2.68325i	−0.625299	+	0.227590i	0.00988487	+	0.999951i	$0.496853\pi$
$140$	−11.0927	−	30.5203i	−0.937507	−	2.57943i
$141$		0			0
$142$	−13.4173	+	15.9901i	−1.12595	+	1.34186i
$143$	−0.0619465	+	0.0738250i	−0.00518023	+	0.00617355i
$144$		0			0
$145$	−6.19583	+	2.25190i	−0.514536	+	0.187010i
$146$	−10.7239	+	3.90319i	−0.887518	+	0.323030i
$147$		0			0
$148$	−1.16701	−	0.205776i	−0.0959279	−	0.0169147i
$149$	20.4289	+	7.43550i	1.67360	+	0.609140i	0.992411	−	0.122968i	$-0.0392412\pi$
$149$	20.4289	+	7.43550i	1.67360	+	0.609140i	0.681188	+	0.732108i	$0.261463\pi$
$150$		0			0
$151$	9.68916			0.788493			0.394247	−	0.919005i	$-0.371006\pi$
$151$	9.68916			0.788493			0.394247	+	0.919005i	$0.371006\pi$
$152$	−37.1977	+	6.06704i	−3.01714	+	0.492102i
$153$		0			0
$154$	13.6322	−	11.4387i	1.09851	−	0.921760i
$155$	3.22426	+	5.59045i	0.258978	+	0.449036i
$156$		0			0
$157$	7.26744	−	1.28145i	0.580005	−	0.102271i	0.124054	−	0.992275i	$-0.460410\pi$
$157$	7.26744	−	1.28145i	0.580005	−	0.102271i	0.455951	+	0.890005i	$0.349299\pi$
$158$	10.6688	+	29.3124i	0.848767	+	2.33197i
$159$		0			0
$160$	37.6092	+	6.64918i	2.97326	+	0.525663i
$161$	5.42434	+	4.55156i	0.427498	+	0.358713i
$162$		0			0
$163$	4.24622	−	2.45155i	0.332589	−	0.192021i	−0.324401	−	0.945920i	$-0.605163\pi$
$163$	4.24622	−	2.45155i	0.332589	−	0.192021i	0.656990	+	0.753899i	$0.271829\pi$
$164$	−20.9707	+	36.3224i	−1.63754	+	2.83630i
$165$		0			0
$166$	2.08568	+	11.8285i	0.161880	+	0.918070i
$167$	−9.93844	−	1.75241i	−0.769059	−	0.135606i	−0.224666	−	0.974436i	$-0.572129\pi$
$167$	−9.93844	−	1.75241i	−0.769059	−	0.135606i	−0.544394	+	0.838830i	$0.683240\pi$
$168$		0			0
$169$	9.95732	−	8.35518i	0.765948	−	0.642707i
$170$	8.35305	+	7.01553i	0.640650	+	0.538067i
$171$		0			0
$172$		−	26.7838i		−	2.04225i
$173$	3.13636	+	3.73777i	0.238453	+	0.284177i	0.871978	−	0.489545i	$-0.162837\pi$
$173$	3.13636	+	3.73777i	0.238453	+	0.284177i	−0.633525	+	0.773722i	$0.718393\pi$
$174$		0			0
$175$	0.0126782	−	13.9152i	0.000958380	−	1.05189i
$176$	5.28748	+	29.9868i	0.398559	+	2.26034i
$177$		0			0
$178$	−35.8158	−	20.6783i	−2.68451	−	1.54990i
$179$	−11.9422	−	20.6845i	−0.892604	−	1.54604i	−0.836743	−	0.547597i	$-0.815543\pi$
$179$	−11.9422	−	20.6845i	−0.892604	−	1.54604i	−0.0558613	−	0.998439i	$-0.517790\pi$
$180$		0			0
$181$	1.96682	+	1.65036i	0.146193	+	0.122670i	0.712951	−	0.701214i	$-0.247358\pi$
$181$	1.96682	+	1.65036i	0.146193	+	0.122670i	−0.566758	+	0.823884i	$0.691803\pi$
$182$	0.262204	−	0.151384i	0.0194359	−	0.0112213i
$183$		0			0
$184$	−20.6729	+	7.52431i	−1.52403	+	0.554700i
$185$	−0.439641	−	0.254094i	−0.0323230	−	0.0186814i
$186$		0			0
$187$	−1.47803	+	4.06085i	−0.108084	+	0.296959i
$188$	−37.1530	−	44.2772i	−2.70966	−	3.22925i
$189$		0			0
$190$	−25.7259	−	4.89008i	−1.86636	−	0.354764i
$191$	−9.28746			−0.672017			−0.336008	−	0.941859i	$-0.609077\pi$
$191$	−9.28746			−0.672017			−0.336008	+	0.941859i	$0.609077\pi$
$192$		0			0
$193$	8.49293	−	23.3341i	0.611334	−	1.67963i	−0.115920	−	0.993259i	$-0.536982\pi$
$193$	8.49293	−	23.3341i	0.611334	−	1.67963i	0.727254	−	0.686368i	$-0.240796\pi$
$194$	2.61047	−	14.8047i	0.187421	−	1.06292i
$195$		0			0
$196$	−3.65449	+	1.33013i	−0.261035	+	0.0950090i
$197$	3.61406	+	2.08658i	0.257491	+	0.148663i	0.623190	−	0.782071i	$-0.285836\pi$
$197$	3.61406	+	2.08658i	0.257491	+	0.148663i	−0.365698	+	0.930733i	$0.619170\pi$
$198$		0			0
$199$	−17.1492	−	14.3899i	−1.21567	−	1.02007i	−0.999039	−	0.0438194i	$-0.986047\pi$
$199$	−17.1492	−	14.3899i	−1.21567	−	1.02007i	−0.216635	−	0.976253i	$-0.569508\pi$
$200$	37.4208	+	21.6504i	2.64605	+	1.53091i
$201$		0			0
$202$	27.8213	+	16.0627i	1.95750	+	1.13016i
$203$	2.80625	+	7.71012i	0.196960	+	0.541144i
$204$		0			0
$205$	−13.7728	+	11.5460i	−0.961931	+	0.806410i
$206$	−35.5826	−	12.9510i	−2.47916	−	0.902340i
$207$		0			0
$208$			0.518056i			0.0359207i
$209$	−1.66998	−	10.2388i	−0.115515	−	0.708236i
$210$		0			0
$211$	1.28817	−	1.08090i	0.0886814	−	0.0744125i	−0.597369	−	0.801966i	$-0.703787\pi$
$211$	1.28817	−	1.08090i	0.0886814	−	0.0744125i	0.686051	+	0.727554i	$0.259343\pi$
$212$	10.1990	−	28.0214i	0.700468	−	1.92452i
$213$		0			0
$214$	5.47015	+	31.0228i	0.373932	+	2.12067i
$215$	3.93029	−	10.7831i	0.268044	−	0.735401i
$216$		0			0
$217$	6.95611	−	4.01611i	0.472211	−	0.272631i
$218$	−11.5919	+	13.8147i	−0.785104	+	0.935650i
$219$		0			0
$220$	−4.83480	+	27.3467i	−0.325962	+	1.84371i
$221$	−0.0367620	+	0.0636737i	−0.00247288	+	0.00428316i
$222$		0			0
$223$	−9.46555	+	1.66903i	−0.633860	+	0.111767i	−0.481340	−	0.876534i	$-0.659850\pi$
$223$	−9.46555	+	1.66903i	−0.633860	+	0.111767i	−0.152520	+	0.988300i	$0.548739\pi$
$224$	8.25431	−	46.8125i	0.551514	−	3.12779i
$225$		0			0
$226$	5.07539	−	4.25876i	0.337610	−	0.283288i
$227$		−	23.4650i		−	1.55743i	−0.627379	−	0.778714i	$-0.715872\pi$
$227$		−	23.4650i		−	1.55743i	0.627379	−	0.778714i	$-0.284128\pi$
$228$		0			0
$229$	1.19088			0.0786952			0.0393476	−	0.999226i	$-0.487472\pi$
$229$	1.19088			0.0786952			0.0393476	+	0.999226i	$0.487472\pi$
$230$	−15.2854	−	0.00696329i	−1.00789	−	0.000459146i
$231$		0			0
$232$	−25.1044	−	4.42658i	−1.64818	−	0.290619i
$233$	−22.7889	+	4.01831i	−1.49295	+	0.263248i	−0.859741	−	0.510730i	$-0.829375\pi$
$233$	−22.7889	+	4.01831i	−1.49295	+	0.263248i	−0.633212	+	0.773978i	$0.718264\pi$
$234$		0			0
$235$	−8.46041	−	23.2778i	−0.551896	−	1.51847i
$236$	30.3092	+	52.4970i	1.97296	+	3.41727i
$237$		0			0
$238$	8.72686	−	10.4003i	0.565679	−	0.674149i
$239$	−4.84358	−	8.38932i	−0.313305	−	0.542660i	0.665771	−	0.746156i	$-0.268103\pi$
$239$	−4.84358	−	8.38932i	−0.313305	−	0.542660i	−0.979076	+	0.203496i	$0.934770\pi$
$240$		0			0
$241$	−14.8334	+	5.39891i	−0.955503	+	0.347775i	−0.772270	−	0.635295i	$-0.780879\pi$
$241$	−14.8334	+	5.39891i	−0.955503	+	0.347775i	−0.183233	+	0.983070i	$0.558656\pi$
$242$	14.1174	−	2.48928i	0.907502	−	0.160017i
$243$		0			0
$244$	22.4772	+	8.18102i	1.43895	+	0.523736i
$245$	−1.66647		0.000759167i	−0.106467		4.85014e-5i
$246$		0			0
$247$	0.00226874	−	0.176488i	0.000144356	−	0.0112297i
$248$			24.9550i			1.58465i
$249$		0			0
$250$	19.2766	+	23.0369i	1.21916	+	1.45698i
$251$	−0.951469	+	5.39605i	−0.0600562	+	0.340596i	−1.00000		0.000734411i	$-0.999766\pi$
$251$	−0.951469	+	5.39605i	−0.0600562	+	0.340596i	0.939944	+	0.341330i	$0.110877\pi$
$252$		0			0
$253$	−2.07110	−	5.69030i	−0.130209	−	0.357746i
$254$	−0.992764	+	1.71952i	−0.0622915	+	0.107892i
$255$		0			0
$256$	10.8468	+	9.10155i	0.677926	+	0.568847i
$257$	2.28060	−	2.71792i	0.142260	−	0.169539i	−0.690210	−	0.723609i	$-0.742482\pi$
$257$	2.28060	−	2.71792i	0.142260	−	0.169539i	0.832470	+	0.554070i	$0.186926\pi$
$258$		0			0
$259$	−0.315999	+	0.547326i	−0.0196352	+	0.0340092i
$260$	−0.161801	+	0.443915i	−0.0100345	+	0.0275305i
$261$		0			0
$262$	28.8723	+	5.09097i	1.78374	+	0.314521i
$263$	9.01141	−	24.7587i	0.555668	−	1.52668i	−0.270191	−	0.962807i	$-0.587087\pi$
$263$	9.01141	−	24.7587i	0.555668	−	1.52668i	0.825858	−	0.563877i	$-0.190691\pi$
$264$		0			0
$265$	8.21798	−	9.78475i	0.504827	−	0.601073i
$266$	−6.07166	+	32.0215i	−0.372277	+	1.96337i
$267$		0			0
$268$	16.2774	+	19.3987i	0.994303	+	1.18496i
$269$	−21.7224	−	7.90629i	−1.32444	−	0.482055i	−0.419559	−	0.907728i	$-0.637815\pi$
$269$	−21.7224	−	7.90629i	−1.32444	−	0.482055i	−0.904877	+	0.425673i	$0.860037\pi$
$270$		0			0
$271$	3.20656	+	18.1853i	0.194785	+	1.10468i	0.912725	+	0.408574i	$0.133974\pi$
$271$	3.20656	+	18.1853i	0.194785	+	1.10468i	−0.717941	+	0.696104i	$0.754915\pi$
$272$	7.94530	+	21.8295i	0.481754	+	1.32361i
$273$		0			0
$274$	6.16648	+	10.6807i	0.372531	+	0.645242i
$275$	−5.95937	+	10.3002i	−0.359363	+	0.621128i
$276$		0			0
$277$	25.9554	−	14.9854i	1.55951	−	0.900384i	0.562208	−	0.826996i	$-0.309952\pi$
$277$	25.9554	−	14.9854i	1.55951	−	0.900384i	0.997303	−	0.0733885i	$-0.0233813\pi$
$278$	−18.2540	−	10.5389i	−1.09480	−	0.632083i
$279$		0			0
$280$	26.9251	−	46.5865i	1.60908	−	2.78408i
$281$	0.690977	−	3.91872i	0.0412202	−	0.233771i	−0.957237	−	0.289306i	$-0.906575\pi$
$281$	0.690977	−	3.91872i	0.0412202	−	0.233771i	0.998457	+	0.0555351i	$0.0176865\pi$
$282$		0			0
$283$	−5.81678	−	6.93217i	−0.345772	−	0.412075i	0.564930	−	0.825139i	$-0.308903\pi$
$283$	−5.81678	−	6.93217i	−0.345772	−	0.412075i	−0.910702	+	0.413064i	$0.864459\pi$
$284$	−40.5423			−2.40574
$285$		0			0
$286$	−0.258920			−0.0153103
$287$	14.3781	+	17.1352i	0.848713	+	1.01146i
$288$		0			0
$289$	2.37951	−	13.4949i	0.139971	−	0.793816i
$290$	−15.3347	−	8.86280i	−0.900484	−	0.520442i
$291$		0			0
$292$	−19.1959	−	11.0828i	−1.12336	−	0.648570i
$293$	−2.02341	+	1.16822i	−0.118209	+	0.0682479i	−0.557939	−	0.829882i	$-0.688408\pi$
$293$	−2.02341	+	1.16822i	−0.118209	+	0.0682479i	0.439730	+	0.898130i	$0.355074\pi$
$294$		0			0
$295$	4.49892	+	25.5828i	0.261937	+	1.48949i
$296$	−0.981765	−	1.70047i	−0.0570640	−	0.0988377i
$297$		0			0
$298$	19.9769	+	54.8860i	1.15723	+	3.17946i
$299$	−0.0178903	−	0.101461i	−0.00103462	−	0.00586765i
$300$		0			0
$301$	−13.4230	−	4.88556i	−0.773687	−	0.281599i
$302$	16.7329	+	19.9415i	0.962869	+	1.14750i
$303$		0			0
$304$	−42.2559	−	36.3927i	−2.42354	−	2.08726i
$305$	7.84876	+	6.59199i	0.449419	+	0.377456i
$306$		0			0
$307$	−2.59974	+	7.14274i	−0.148375	+	0.407658i	−0.991508	−	0.130048i	$-0.958487\pi$
$307$	−2.59974	+	7.14274i	−0.148375	+	0.407658i	0.843132	+	0.537706i	$0.180709\pi$
$308$	34.0387	+	6.00194i	1.93953	+	0.341992i
$309$		0			0
$310$	−5.93764	+	16.2904i	−0.337235	+	0.925235i
$311$	−9.41207	+	16.3022i	−0.533709	+	0.924412i	0.465515	+	0.885040i	$0.345869\pi$
$311$	−9.41207	+	16.3022i	−0.533709	+	0.924412i	−0.999225	+	0.0393720i	$0.987464\pi$
$312$		0			0
$313$	−14.2771	+	17.0147i	−0.806987	+	0.961729i	−0.999810	−	0.0195042i	$-0.993791\pi$
$313$	−14.2771	+	17.0147i	−0.806987	+	0.961729i	0.192823	+	0.981234i	$0.438236\pi$
$314$	15.1880	+	12.7443i	0.857109	+	0.719200i
$315$		0			0
$316$	−30.2933	+	52.4695i	−1.70413	+	2.95164i
$317$	−1.39295	−	3.82711i	−0.0782360	−	0.214952i	0.894408	−	0.447252i	$-0.147597\pi$
$317$	−1.39295	−	3.82711i	−0.0782360	−	0.214952i	−0.972644	+	0.232300i	$0.925375\pi$
$318$		0			0
$319$	1.21843	−	6.91009i	0.0682193	−	0.386891i
$320$	22.6796	+	39.3235i	1.26783	+	2.19825i
$321$		0			0
$322$			19.0243i			1.06018i
$323$	−2.61115	−	7.47153i	−0.145288	−	0.415727i
$324$		0			0
$325$	−0.130281	+	0.154976i	−0.00722671	+	0.00859654i
$326$	12.3787	+	4.50547i	0.685591	+	0.249535i
$327$		0			0
$328$	−68.4398	+	12.0678i	−3.77895	+	0.666331i
$329$	−28.9669	+	10.5431i	−1.59700	+	0.581260i
$330$		0			0
$331$	−10.3939	−	18.0028i	−0.571301	−	0.989523i	−0.996433	−	0.0843910i	$-0.973106\pi$
$331$	−10.3939	−	18.0028i	−0.571301	−	0.989523i	0.425132	−	0.905132i	$-0.360228\pi$
$332$	−14.9953	+	17.8708i	−0.822976	+	0.980785i
$333$		0			0
$334$	−13.5567	−	23.4809i	−0.741789	−	1.28482i
$335$	3.70667	+	10.1984i	0.202517	+	0.557200i
$336$		0			0
$337$	25.7746	−	4.54476i	1.40403	−	0.247569i	0.580234	−	0.814450i	$-0.302961\pi$
$337$	25.7746	−	4.54476i	1.40403	−	0.247569i	0.823800	+	0.566881i	$0.191850\pi$
$338$	34.3920	+	6.06423i	1.87068	+	0.329851i
$339$		0			0
$340$	−0.00965176	+	21.1869i	−0.000523440	+	1.14902i
$341$	−6.86899			−0.371976
$342$		0			0
$343$		−	17.4071i		−	0.939896i
$344$	33.9969	−	28.5268i	1.83299	−	1.53806i
$345$		0			0
$346$	−2.27639	+	12.9100i	−0.122379	+	0.694047i
$347$	20.2859	−	3.57695i	1.08901	−	0.192021i	0.399811	−	0.916598i	$-0.369076\pi$
$347$	20.2859	−	3.57695i	1.08901	−	0.192021i	0.689194	+	0.724577i	$0.257965\pi$
$348$		0			0
$349$	−12.5153	+	21.6772i	−0.669929	+	1.16035i	0.307994	+	0.951388i	$0.400342\pi$
$349$	−12.5153	+	21.6772i	−0.669929	+	1.16035i	−0.977924	+	0.208963i	$0.932991\pi$
$350$	28.6610	−	24.0049i	1.53199	−	1.28312i
$351$		0			0
$352$	−26.1297	+	31.1402i	−1.39272	+	1.65978i
$353$	−6.24627	+	3.60628i	−0.332455	+	0.191943i	−0.656931	−	0.753951i	$-0.728146\pi$
$353$	−6.24627	+	3.60628i	−0.332455	+	0.191943i	0.324475	+	0.945894i	$0.394812\pi$
$354$		0			0
$355$	−16.3222	−	5.94922i	−0.866293	−	0.315752i
$356$	−13.9484	−	79.1054i	−0.739265	−	4.19258i
$357$		0			0
$358$	21.9474	−	60.3001i	1.15996	−	3.18696i
$359$	12.1097	−	10.1613i	0.639128	−	0.536292i	−0.264622	−	0.964352i	$-0.585247\pi$
$359$	12.1097	−	10.1613i	0.639128	−	0.536292i	0.903750	+	0.428060i	$0.140803\pi$
$360$		0			0
$361$	14.2361	+	12.5831i	0.749268	+	0.662267i
$362$			6.89807i			0.362554i
$363$		0			0
$364$	0.552593	+	0.201127i	0.0289637	+	0.0105419i
$365$	−6.10194	−	7.27874i	−0.319390	−	0.380986i
$366$		0			0
$367$	0.903831	+	2.48326i	0.0471796	+	0.129625i	0.961045	−	0.276393i	$-0.0891392\pi$
$367$	0.903831	+	2.48326i	0.0471796	+	0.129625i	−0.913865	+	0.406018i	$0.866917\pi$
$368$	−28.1908	−	16.2760i	−1.46955	−	0.848444i
$369$		0			0
$370$	−0.236290	−	1.34365i	−0.0122841	−	0.0698529i
$371$	−12.1829	−	10.2226i	−0.632502	−	0.530733i
$372$		0			0
$373$	−5.33853	−	3.08220i	−0.276419	−	0.159590i	0.355382	−	0.934721i	$-0.384351\pi$
$373$	−5.33853	−	3.08220i	−0.276419	−	0.159590i	−0.631801	+	0.775131i	$0.717684\pi$
$374$	−10.9102	+	3.97100i	−0.564154	+	0.205335i
$375$		0			0
$376$	16.6307	−	94.3172i	0.857661	−	4.86404i
$377$	0.0408303	−	0.112180i	0.00210287	−	0.00577758i
$378$		0			0
$379$	−0.156142			−0.00802047			−0.00401024	−	0.999992i	$-0.501277\pi$
$379$	−0.156142			−0.00802047			−0.00401024	+	0.999992i	$0.501277\pi$
$380$	−24.8423	−	44.3819i	−1.27438	−	2.27674i
$381$		0			0
$382$	−16.0391	−	19.1147i	−0.820634	−	0.977993i
$383$	5.51405	−	15.1497i	0.281755	−	0.774115i	−0.715399	−	0.698716i	$-0.753755\pi$
$383$	5.51405	−	15.1497i	0.281755	−	0.774115i	0.997153	−	0.0753983i	$-0.0240228\pi$
$384$		0			0
$385$	12.8232	+	7.41124i	0.653529	+	0.377712i
$386$	62.6915	−	22.8178i	3.19091	−	1.16140i
$387$		0			0
$388$	25.2866	−	14.5992i	1.28373	−	0.741162i
$389$	2.07987	+	1.74521i	0.105453	+	0.0884859i	0.693990	−	0.719985i	$-0.255851\pi$
$389$	2.07987	+	1.74521i	0.105453	+	0.0884859i	−0.588537	+	0.808471i	$0.700296\pi$
$390$		0			0
$391$	−2.30994	−	4.00093i	−0.116818	−	0.202336i
$392$	−5.58065	−	3.22199i	−0.281866	−	0.162735i
$393$		0			0
$394$	1.94694	+	11.0416i	0.0980854	+	0.556270i
$395$	−19.8954	+	16.6788i	−1.00105	+	0.839202i
$396$		0			0
$397$	10.1900	+	12.1440i	0.511422	+	0.609488i	0.958530	−	0.284991i	$-0.0919907\pi$
$397$	10.1900	+	12.1440i	0.511422	+	0.609488i	−0.447109	+	0.894480i	$0.647546\pi$
$398$		−	60.1460i		−	3.01485i
$399$		0			0
$400$	11.0508	+	63.0077i	0.552539	+	3.15039i
$401$	2.54746	−	2.13757i	0.127214	−	0.106745i	−0.576961	−	0.816772i	$-0.695761\pi$
$401$	2.54746	−	2.13757i	0.127214	−	0.106745i	0.704175	+	0.710026i	$0.251317\pi$
$402$		0			0
$403$	−0.115091	−	0.0202937i	−0.00573311	−	0.00101090i
$404$	10.8350	+	61.4483i	0.539061	+	3.05717i
$405$		0			0
$406$	−11.0220	+	19.0907i	−0.547015	+	0.947457i
$407$	0.468061	−	0.270235i	0.0232009	−	0.0133951i
$408$		0			0
$409$	−5.73789	−	4.81466i	−0.283720	−	0.238070i	0.489809	−	0.871830i	$-0.337066\pi$
$409$	−5.73789	−	4.81466i	−0.283720	−	0.238070i	−0.773530	+	0.633760i	$0.781511\pi$
$410$	−47.5482	−	8.40637i	−2.34824	−	0.415161i
$411$		0			0
$412$	−25.1544	−	69.1113i	−1.23927	−	3.40487i
$413$	31.8380	−	5.61391i	1.56665	−	0.276242i
$414$		0			0
$415$	−8.65947	+	4.99429i	−0.425076	+	0.245160i
$416$	−0.529810	+	0.444563i	−0.0259761	+	0.0217965i
$417$		0			0
$418$	18.1888	−	21.1192i	0.889642	−	1.03297i
$419$	14.4108			0.704012			0.352006	−	0.935998i	$-0.385500\pi$
$419$	14.4108			0.704012			0.352006	+	0.935998i	$0.385500\pi$
$420$		0			0
$421$	33.6092	+	12.2327i	1.63801	+	0.596187i	0.986690	−	0.162614i	$-0.0519927\pi$
$421$	33.6092	+	12.2327i	1.63801	+	0.596187i	0.651322	+	0.758802i	$0.274215\pi$
$422$	4.44926	+	0.784525i	0.216587	+	0.0381901i
$423$		0			0
$424$	46.4305	−	16.8993i	2.25487	−	0.820704i
$425$	−3.11288	+	8.52839i	−0.150997	+	0.413688i
$426$		0			0
$427$	8.20001	−	9.77239i	0.396826	−	0.472919i
$428$	−39.3285	+	46.8698i	−1.90101	+	2.26554i
$429$		0			0
$430$	28.9804	−	10.5331i	1.39756	−	0.507949i
$431$	9.76286	−	3.55339i	0.470260	−	0.171161i	−0.0960100	−	0.995380i	$-0.530608\pi$
$431$	9.76286	−	3.55339i	0.470260	−	0.171161i	0.566270	+	0.824220i	$0.308386\pi$
$432$		0			0
$433$	−34.5482	−	6.09178i	−1.66028	−	0.292752i	−0.736718	−	0.676200i	$-0.763626\pi$
$433$	−34.5482	−	6.09178i	−1.66028	−	0.292752i	−0.923563	+	0.383448i	$0.874737\pi$
$434$	20.2786	+	7.38081i	0.973405	+	0.354290i
$435$		0			0
$436$	−35.0266			−1.67747
$437$	9.53258	+	5.66825i	0.456005	+	0.271149i
$438$		0			0
$439$	−14.6520	+	12.2945i	−0.699303	+	0.586785i	−0.921575	−	0.388199i	$-0.873097\pi$
$439$	−14.6520	+	12.2945i	−0.699303	+	0.586785i	0.222272	+	0.974985i	$0.428653\pi$
$440$	−39.8608	+	22.9894i	−1.90029	+	1.09598i
$441$		0			0
$442$	−0.194535	+	0.0343018i	−0.00925309	+	0.00163157i
$443$	−7.86358	−	21.6050i	−0.373610	−	1.02649i	−0.973954	−	0.226744i	$-0.927192\pi$
$443$	−7.86358	−	21.6050i	−0.373610	−	1.02649i	0.600344	−	0.799742i	$-0.295030\pi$
$444$		0			0
$445$	5.99243	−	33.8945i	0.284068	−	1.60675i
$446$	−19.7818	−	16.5989i	−0.936694	−	0.785980i
$447$		0			0
$448$	48.9296	−	28.2495i	2.31171	−	1.33466i
$449$	−7.88692	+	13.6605i	−0.372207	+	0.644681i	−0.989905	−	0.141734i	$-0.954732\pi$
$449$	−7.88692	+	13.6605i	−0.372207	+	0.644681i	0.617698	+	0.786415i	$0.288065\pi$
$450$		0			0
$451$	−3.32171	−	18.8384i	−0.156413	−	0.887063i
$452$	12.6729	+	2.23458i	0.596085	+	0.105106i
$453$		0			0
$454$	48.2939	−	40.5234i	2.26654	−	1.90186i
$455$	0.192959	+	0.162062i	0.00904606	+	0.00759757i
$456$		0			0
$457$			34.6414i			1.62046i	0.586114	+	0.810229i	$0.300657\pi$
$457$			34.6414i			1.62046i	−0.586114	+	0.810229i	$0.699343\pi$
$458$	2.05660	+	2.45096i	0.0960988	+	0.114526i
$459$		0			0
$460$	−19.0730	−	22.7513i	−0.889282	−	1.06079i
$461$	−4.26528	−	24.1896i	−0.198654	−	1.12662i	−0.907119	−	0.420875i	$-0.861723\pi$
$461$	−4.26528	−	24.1896i	−0.198654	−	1.12662i	0.708465	−	0.705746i	$-0.249388\pi$
$462$		0			0
$463$	6.67368	+	3.85305i	0.310152	+	0.179067i	0.646995	−	0.762495i	$-0.276026\pi$
$463$	6.67368	+	3.85305i	0.310152	+	0.179067i	−0.336842	+	0.941561i	$0.609359\pi$
$464$	−18.8595	−	32.6656i	−0.875529	−	1.51646i
$465$		0			0
$466$	−47.6260	−	39.9629i	−2.20623	−	1.85125i
$467$	−5.64552	+	3.25944i	−0.261243	+	0.150829i	−0.624902	−	0.780704i	$-0.714861\pi$
$467$	−5.64552	+	3.25944i	−0.261243	+	0.150829i	0.363658	+	0.931532i	$0.381528\pi$
$468$		0			0
$469$	12.6910	−	4.61914i	0.586015	−	0.213292i
$470$	33.2976	−	57.6125i	1.53590	−	2.65747i
$471$		0			0
$472$	−34.3534	+	94.3851i	−1.58124	+	4.34442i
$473$	7.85213	+	9.35781i	0.361041	+	0.430272i
$474$		0			0
$475$	−3.48877	−	21.5134i	−0.160076	−	0.987105i
$476$	26.3695			1.20864
$477$		0			0
$478$	8.90153	−	24.4568i	0.407147	−	1.11863i
$479$	2.14887	−	12.1868i	0.0981842	−	0.556830i	−0.895541	−	0.444979i	$-0.853211\pi$
$479$	2.14887	−	12.1868i	0.0981842	−	0.556830i	0.993725	−	0.111851i	$-0.0356779\pi$
$480$		0			0
$481$	0.00864085	−	0.00314501i	0.000393989	−	0.000143400i
$482$	−36.7284	−	21.2052i	−1.67293	−	0.965868i
$483$		0			0
$484$	21.3289	+	17.8971i	0.969495	+	0.813503i
$485$	12.3226	−	2.16702i	0.559541	−	0.0983994i
$486$		0			0
$487$	−33.5333	−	19.3605i	−1.51954	−	0.877306i	−0.999735	−	0.0230209i	$-0.992672\pi$
$487$	−33.5333	−	19.3605i	−1.51954	−	0.877306i	−0.519804	−	0.854285i	$-0.673995\pi$
$488$	13.5557	+	37.2439i	0.613636	+	1.68595i
$489$		0			0
$490$	−2.87639	−	3.43112i	−0.129942	−	0.155002i
$491$	−29.5147	−	10.7425i	−1.33198	−	0.484802i	−0.424704	−	0.905332i	$-0.639622\pi$
$491$	−29.5147	−	10.7425i	−1.33198	−	0.484802i	−0.907278	+	0.420531i	$0.861844\pi$
$492$		0			0
$493$		−	5.35319i		−	0.241095i
$494$	0.367151	−	0.300120i	0.0165189	−	0.0135030i
$495$		0			0
$496$	−28.2862	+	23.7349i	−1.27009	+	1.06573i
$497$	−7.39521	+	20.3182i	−0.331720	+	0.911394i
$498$		0			0
$499$	−3.37331	−	19.1310i	−0.151010	−	0.856422i	−0.962343	−	0.271837i	$-0.912369\pi$
$499$	−3.37331	−	19.1310i	−0.151010	−	0.856422i	0.811333	−	0.584584i	$-0.198742\pi$
$500$	−10.2095	+	57.4419i	−0.456584	+	2.56888i
$501$		0			0
$502$	−12.7489	+	7.36057i	−0.569010	+	0.328518i
$503$	2.73706	−	3.26190i	0.122039	−	0.145441i	−0.701565	−	0.712605i	$-0.747515\pi$
$503$	2.73706	−	3.26190i	0.122039	−	0.145441i	0.823605	+	0.567164i	$0.191960\pi$
$504$		0			0
$505$	−4.65486	+	26.3289i	−0.207138	+	1.17162i
$506$	8.13461	−	14.0896i	0.361627	−	0.626357i
$507$		0			0
$508$	−3.79785	+	0.669664i	−0.168502	+	0.0297115i
$509$	−1.27413	+	7.22597i	−0.0564750	+	0.320286i	−0.999937	−	0.0111941i	$-0.996437\pi$
$509$	−1.27413	+	7.22597i	−0.0564750	+	0.320286i	0.943462	+	0.331480i	$0.107548\pi$
$510$		0			0
$511$	−9.05573	+	7.59866i	−0.400602	+	0.336145i
$512$		−	2.72331i		−	0.120354i
$513$		0			0
$514$	9.53234			0.420453
$515$	0.0143568	−	31.5152i	0.000632638	−	1.38873i
$516$		0			0
$517$	25.9612	+	4.57767i	1.14177	+	0.201326i
$518$	−1.67218	+	0.294851i	−0.0734714	+	0.0129550i
$519$		0			0
$520$	−0.735796	+	0.267428i	−0.0322668	+	0.0117275i
$521$	−3.98404	−	6.90057i	−0.174544	−	0.302319i	0.765459	−	0.643484i	$-0.222512\pi$
$521$	−3.98404	−	6.90057i	−0.174544	−	0.302319i	−0.940003	+	0.341165i	$0.889178\pi$
$522$		0			0
$523$	−10.0759	+	12.0080i	−0.440590	+	0.525075i	−0.939946	−	0.341322i	$-0.889125\pi$
$523$	−10.0759	+	12.0080i	−0.440590	+	0.525075i	0.499357	+	0.866397i	$0.333570\pi$
$524$	28.4715	+	49.3141i	1.24378	+	2.15430i
$525$		0			0
$526$	66.5187	−	24.2108i	2.90035	−	1.05564i
$527$	−5.16089	+	0.910003i	−0.224812	+	0.0396404i
$528$		0			0
$529$	−15.5297	−	5.65235i	−0.675204	−	0.245754i
$530$	34.3304	+	0.0156393i	1.49122	+	0.000679328i
$531$		0			0
$532$	−55.2241	+	30.9441i	−2.39427	+	1.34160i
$533$		−	0.325454i		−	0.0140970i
$534$		0			0
$535$	−22.7113	+	13.0986i	−0.981895	+	0.566301i
$536$	−7.28622	+	41.3222i	−0.314717	+	1.78485i
$537$		0			0
$538$	−21.2417	−	58.3612i	−0.915796	−	2.51613i
$539$	0.886868	−	1.53610i	0.0382001	−	0.0661645i
$540$		0			0
$541$	22.3123	+	18.7223i	0.959283	+	0.804934i	0.980836	−	0.194834i	$-0.0624168\pi$
$541$	22.3123	+	18.7223i	0.959283	+	0.804934i	−0.0215537	+	0.999768i	$0.506861\pi$
$542$	−31.8899	+	38.0049i	−1.36979	+	1.63245i
$543$		0			0
$544$	−15.5066	+	26.8583i	−0.664841	+	1.15154i
$545$	−14.1016	−	5.13986i	−0.604048	−	0.220167i
$546$		0			0
$547$	14.2470	+	2.51214i	0.609160	+	0.107411i	0.469714	−	0.882818i	$-0.344357\pi$
$547$	14.2470	+	2.51214i	0.609160	+	0.107411i	0.139445	+	0.990230i	$0.455468\pi$
$548$	−8.19275	+	22.5094i	−0.349977	+	0.961553i
$549$		0			0
$550$	−31.4908	+	5.52309i	−1.34277	+	0.235506i
$551$	6.28187	+	11.2109i	0.267617	+	0.477599i
$552$		0			0
$553$	20.7699	+	24.7526i	0.883226	+	1.05259i
$554$	75.6660	+	27.5402i	3.21474	+	1.17007i
$555$		0			0
$556$	−7.10898	−	40.3170i	−0.301488	−	1.70982i
$557$	−11.5184	−	31.6465i	−0.488049	−	1.34090i	−0.902444	−	0.430807i	$-0.858229\pi$
$557$	−11.5184	−	31.6465i	−0.488049	−	1.34090i	0.414395	−	0.910097i	$-0.363993\pi$
$558$		0			0
$559$	0.103917	+	0.179990i	0.00439524	+	0.00761278i
$560$	78.4138	−	13.7896i	3.31359	−	0.582719i
$561$		0			0
$562$	9.25850	−	5.34540i	0.390546	−	0.225482i
$563$	−21.5774	−	12.4577i	−0.909378	−	0.525030i	−0.0291473	−	0.999575i	$-0.509279\pi$
$563$	−21.5774	−	12.4577i	−0.909378	−	0.525030i	−0.880231	+	0.474545i	$0.842613\pi$
$564$		0			0
$565$	4.77419	+	2.75928i	0.200852	+	0.116084i
$566$	4.22185	−	23.9433i	0.177457	−	1.00641i
$567$		0			0
$568$	−43.1806	−	51.4607i	−1.81182	−	2.15924i
$569$	19.7304			0.827141			0.413571	−	0.910472i	$-0.364281\pi$
$569$	19.7304			0.827141			0.413571	+	0.910472i	$0.364281\pi$
$570$		0			0
$571$	−13.8463			−0.579452			−0.289726	−	0.957110i	$-0.593564\pi$
$571$	−13.8463			−0.579452			−0.289726	+	0.957110i	$0.593564\pi$
$572$	−0.323254	−	0.385239i	−0.0135159	−	0.0161077i
$573$		0			0
$574$	−10.4357	+	59.1838i	−0.435578	+	2.47028i
$575$	−4.34018	−	11.9584i	−0.180998	−	0.498701i
$576$		0			0
$577$	36.0832	+	20.8327i	1.50216	+	0.867275i	0.999997	+	0.00250405i	$0.000797064\pi$
$577$	36.0832	+	20.8327i	1.50216	+	0.867275i	0.502167	+	0.864771i	$0.332536\pi$
$578$	31.8834	−	18.4079i	1.32618	−	0.765668i
$579$		0			0
$580$	−5.95821	−	33.8809i	−0.247401	−	1.40683i
$581$	6.22085	+	10.7748i	0.258084	+	0.447015i
$582$		0			0
$583$	4.65162	+	12.7802i	0.192650	+	0.529302i
$584$	−6.37767	−	36.1696i	−0.263910	−	1.49671i
$585$		0			0
$586$	−5.89869	−	2.14695i	−0.243673	−	0.0886896i
$587$	10.3943	+	12.3875i	0.429020	+	0.511286i	0.936639	−	0.350296i	$-0.113919\pi$
$587$	10.3943	+	12.3875i	0.429020	+	0.511286i	−0.507619	+	0.861581i	$0.669474\pi$
$588$		0			0
$589$	9.74028	−	7.96198i	0.401341	−	0.328068i
$590$	−44.8830	+	53.4400i	−1.84780	+	2.20009i
$591$		0			0
$592$	0.993691	−	2.73014i	0.0408405	−	0.112208i
$593$	22.1249	+	3.90122i	0.908562	+	0.160204i	0.608350	−	0.793669i	$-0.291832\pi$
$593$	22.1249	+	3.90122i	0.908562	+	0.160204i	0.300212	+	0.953873i	$0.402943\pi$
$594$		0			0
$595$	10.6163	+	3.86949i	0.435225	+	0.158634i
$596$	−56.7226	+	98.2464i	−2.32345	+	4.02433i
$597$		0			0
$598$	0.177923	−	0.212041i	0.00727582	−	0.00867099i
$599$	1.65472	+	1.38847i	0.0676099	+	0.0567314i	0.675966	−	0.736932i	$-0.263726\pi$
$599$	1.65472	+	1.38847i	0.0676099	+	0.0567314i	−0.608356	+	0.793664i	$0.708171\pi$
$600$		0			0
$601$	8.52974	−	14.7739i	0.347935	−	0.602641i	−0.637947	−	0.770080i	$-0.720216\pi$
$601$	8.52974	−	14.7739i	0.347935	−	0.602641i	0.985883	+	0.167439i	$0.0535496\pi$
$602$	−13.1260	−	36.0633i	−0.534975	−	1.46983i
$603$		0			0
$604$	−8.77979	+	49.7927i	−0.357245	+	2.02603i
$605$	5.96072	+	10.3351i	0.242338	+	0.420183i
$606$		0			0
$607$			3.47625i			0.141097i	0.997508	+	0.0705483i	$0.0224749\pi$
$607$			3.47625i			0.141097i	−0.997508	+	0.0705483i	$0.977525\pi$
$608$	0.956978	−	74.4446i	0.0388106	−	3.01913i
$609$		0			0
$610$	−0.0125449	+	27.5379i	−0.000507930	+	1.11498i
$611$	0.421462	+	0.153400i	0.0170505	+	0.00620588i
$612$		0			0
$613$	18.3007	−	3.22691i	0.739159	−	0.130334i	0.208623	−	0.977996i	$-0.433102\pi$
$613$	18.3007	−	3.22691i	0.739159	−	0.130334i	0.530536	+	0.847663i	$0.321991\pi$
$614$	−19.1903	+	6.98470i	−0.774457	+	0.281879i
$615$		0			0
$616$	28.6355	+	49.5981i	1.15376	+	1.99837i
$617$	12.7710	−	15.2199i	0.514141	−	0.612729i	−0.445044	−	0.895509i	$-0.646812\pi$
$617$	12.7710	−	15.2199i	0.514141	−	0.612729i	0.959185	+	0.282779i	$0.0912565\pi$
$618$		0			0
$619$	−4.21208	−	7.29553i	−0.169298	−	0.293232i	0.768875	−	0.639399i	$-0.220817\pi$
$619$	−4.21208	−	7.29553i	−0.169298	−	0.293232i	−0.938173	+	0.346166i	$0.887483\pi$
$620$	−31.6510	+	11.5037i	−1.27114	+	0.462000i
$621$		0			0
$622$	−49.8062	+	8.78218i	−1.99705	+	0.352133i
$623$	−42.1888	−	7.43902i	−1.69026	−	0.298038i
$624$		0			0
$625$	−12.5394	+	21.6278i	−0.501577	+	0.865113i
$626$	−59.6744			−2.38507
$627$		0			0
$628$			38.5086i			1.53666i
$629$	0.315868	−	0.265045i	0.0125945	−	0.0105680i
$630$		0			0
$631$	0.278838	−	1.58137i	0.0111004	−	0.0629534i	−0.978754	−	0.205036i	$-0.934269\pi$
$631$	0.278838	−	1.58137i	0.0111004	−	0.0629534i	0.989855	+	0.142083i	$0.0453799\pi$
$632$	−98.8646	+	17.4325i	−3.93262	+	0.693428i
$633$		0			0
$634$	5.47106	−	9.47616i	0.217284	−	0.376346i
$635$	−1.62727	−	0.287697i	−0.0645764	−	0.0114169i
$636$		0			0
$637$	0.0193979	−	0.0231175i	0.000768573	−	0.000915950i
$638$	16.3260	−	9.42582i	0.646352	−	0.373172i
$639$		0			0
$640$	−15.6078	+	42.8214i	−0.616953	+	1.69267i
$641$	7.96102	+	45.1492i	0.314442	+	1.78329i	0.575334	+	0.817919i	$0.304872\pi$
$641$	7.96102	+	45.1492i	0.314442	+	1.78329i	−0.260892	+	0.965368i	$0.584017\pi$
$642$		0			0
$643$	6.26834	−	17.2221i	0.247199	−	0.679175i	−0.752587	−	0.658493i	$-0.771194\pi$
$643$	6.26834	−	17.2221i	0.247199	−	0.679175i	0.999786	−	0.0206816i	$-0.00658362\pi$
$644$	−28.3057	+	23.7513i	−1.11540	+	0.935933i
$645$		0			0
$646$	10.8679	−	18.2772i	0.427593	−	0.719105i
$647$			25.1770i			0.989808i	0.868948	+	0.494904i	$0.164797\pi$
$647$			25.1770i			0.989808i	−0.868948	+	0.494904i	$0.835203\pi$
$648$		0			0
$649$	−25.9799	−	9.45592i	−1.01980	−	0.371177i
$650$	−0.543952		0.000495598i	−0.0213356		1.94389e-5i
$651$		0			0
$652$	8.75086	+	24.0428i	0.342710	+	0.941588i
$653$	0.604989	+	0.349290i	0.0236750	+	0.0136688i	0.511791	−	0.859110i	$-0.328982\pi$
$653$	0.604989	+	0.349290i	0.0236750	+	0.0136688i	−0.488116	+	0.872779i	$0.662316\pi$
$654$		0			0
$655$	4.22615	+	24.0317i	0.165129	+	0.938997i
$656$	−78.7722	−	66.0977i	−3.07554	−	2.58068i
$657$		0			0
$658$	−71.7240	−	41.4099i	−2.79609	−	1.61432i
$659$	−19.1350	+	6.96458i	−0.745395	+	0.271301i	−0.686667	−	0.726973i	$-0.740927\pi$
$659$	−19.1350	+	6.96458i	−0.745395	+	0.271301i	−0.0587281	+	0.998274i	$0.518705\pi$
$660$		0			0
$661$	−6.03199	+	34.2091i	−0.234617	+	1.33058i	0.608801	+	0.793323i	$0.291651\pi$
$661$	−6.03199	+	34.2091i	−0.234617	+	1.33058i	−0.843418	+	0.537258i	$0.819460\pi$
$662$	19.1019	−	52.4822i	0.742418	−	2.03978i
$663$		0			0
$664$	−38.6547			−1.50009
$665$	−26.7739	+	4.35436i	−1.03825	+	0.168855i
$666$		0			0
$667$	4.82168	+	5.74626i	0.186696	+	0.222496i
$668$	18.0113	−	49.4857i	0.696879	−	1.91466i
$669$		0			0
$670$	−14.5883	+	25.2412i	−0.563596	+	0.975151i
$671$	−10.2516	+	3.73126i	−0.395757	+	0.144044i
$672$		0			0
$673$	−22.1298	+	12.7767i	−0.853043	+	0.492505i	−0.861676	−	0.507458i	$-0.830585\pi$
$673$	−22.1298	+	12.7767i	−0.853043	+	0.492505i	0.00863342	+	0.999963i	$0.497252\pi$
$674$	53.8656	+	45.1986i	2.07483	+	1.74099i
$675$		0			0
$676$	33.9146	+	58.7417i	1.30441	+	2.25930i
$677$	32.9463	+	19.0216i	1.26623	+	0.731058i	0.974273	−	0.225373i	$-0.0723601\pi$
$677$	32.9463	+	19.0216i	1.26623	+	0.731058i	0.291957	+	0.956431i	$0.405693\pi$
$678$		0			0
$679$	−2.70408	−	15.3356i	−0.103773	−	0.588527i
$680$	−26.9030	+	22.5535i	−1.03168	+	0.864885i
$681$		0			0
$682$	−11.8625	−	14.1372i	−0.454239	−	0.541342i
$683$			31.7070i			1.21324i	0.794994	+	0.606618i	$0.207474\pi$
$683$			31.7070i			1.21324i	−0.794994	+	0.606618i	$0.792526\pi$
$684$		0			0
$685$	−6.60144	+	7.86001i	−0.252228	+	0.300316i
$686$	35.8260	−	30.0615i	1.36784	−	1.14775i
$687$		0			0
$688$	64.6694	+	11.4030i	2.46550	+	0.434734i
$689$	0.0401810	+	0.227878i	0.00153078	+	0.00868146i
$690$		0			0
$691$	−2.05528	+	3.55984i	−0.0781864	+	0.135423i	−0.902467	−	0.430758i	$-0.858246\pi$
$691$	−2.05528	+	3.55984i	−0.0781864	+	0.135423i	0.824281	+	0.566181i	$0.191580\pi$
$692$	−22.0504	+	12.7308i	−0.838231	+	0.483953i
$693$		0			0
$694$	42.3949	+	35.5736i	1.60929	+	1.35035i
$695$	3.05411	−	17.2747i	0.115849	−	0.655267i
$696$		0			0
$697$	−4.99141	−	13.7138i	−0.189063	−	0.519447i
$698$	−66.2277	+	11.6777i	−2.50676	+	0.442009i
$699$		0			0
$700$	71.4986	+	12.6743i	2.70239	+	0.479044i
$701$	3.40592	−	2.85791i	0.128640	−	0.107942i	−0.576198	−	0.817310i	$-0.695464\pi$
$701$	3.40592	−	2.85791i	0.128640	−	0.107942i	0.704838	+	0.709369i	$0.251020\pi$
$702$		0			0
$703$	−0.350480	+	0.925735i	−0.0132186	+	0.0349148i
$704$	−48.3168			−1.82101
$705$		0			0
$706$	−18.2093	−	6.62763i	−0.685315	−	0.249434i
$707$	32.7718	+	5.77855i	1.23251	+	0.217325i
$708$		0			0
$709$	3.15334	−	1.14772i	0.118426	−	0.0431036i	−0.282127	−	0.959377i	$-0.591040\pi$
$709$	3.15334	−	1.14772i	0.118426	−	0.0431036i	0.400554	+	0.916273i	$0.368818\pi$
$710$	−15.9437	−	43.8672i	−0.598358	−	1.64631i
$711$		0			0
$712$	85.5531	−	101.958i	3.20624	−	3.82104i
$713$	4.72019	−	5.62530i	0.176772	−	0.210669i
$714$		0			0
$715$	−0.0736109	−	0.202531i	−0.00275289	−	0.00757424i
$716$	117.119	−	42.6279i	4.37695	−	1.59308i
$717$		0			0
$718$	41.8263	+	7.37510i	1.56094	+	0.275236i
$719$	−38.6145	−	14.0545i	−1.44008	−	0.524145i	−0.500275	−	0.865866i	$-0.666768\pi$
$719$	−38.6145	−	14.0545i	−1.44008	−	0.524145i	−0.939801	+	0.341721i	$0.888990\pi$
$720$		0			0
$721$	−39.2242			−1.46078
$722$	−1.31219	+	51.0302i	−0.0488348	+	1.89915i
$723$		0			0
$724$	−10.2634	+	8.61203i	−0.381437	+	0.320064i
$725$	2.57297	−	14.5147i	0.0955578	−	0.539063i
$726$		0			0
$727$	11.8832	−	2.09533i	0.440723	−	0.0777114i	0.0511164	−	0.998693i	$-0.483722\pi$
$727$	11.8832	−	2.09533i	0.440723	−	0.0777114i	0.389607	+	0.920981i	$0.372611\pi$
$728$	0.333261	+	0.915628i	0.0123515	+	0.0339354i
$729$		0			0
$730$	4.44267	−	25.1287i	0.164430	−	0.930054i
$731$	7.13928	+	5.99056i	0.264056	+	0.221569i
$732$		0			0
$733$	11.8082	−	6.81748i	0.436147	−	0.251809i	−0.265815	−	0.964024i	$-0.585641\pi$
$733$	11.8082	−	6.81748i	0.436147	−	0.251809i	0.701962	+	0.712215i	$0.252308\pi$
$734$	−3.54995	+	6.14870i	−0.131031	+	0.226953i
$735$		0			0
$736$	−7.54634	−	42.7974i	−0.278162	−	1.57753i
$737$	−11.3741	−	2.00556i	−0.418971	−	0.0738759i
$738$		0			0
$739$	−29.2757	+	24.5652i	−1.07692	+	0.903645i	−0.995662	−	0.0930476i	$-0.970339\pi$
$739$	−29.2757	+	24.5652i	−1.07692	+	0.903645i	−0.0812609	+	0.996693i	$0.525895\pi$
$740$	1.70417	−	2.02907i	0.0626465	−	0.0745901i
$741$		0			0
$742$		−	42.7280i		−	1.56859i
$743$	3.90379	+	4.65236i	0.143216	+	0.170679i	0.832884	−	0.553447i	$-0.186688\pi$
$743$	3.90379	+	4.65236i	0.143216	+	0.170679i	−0.689668	+	0.724126i	$0.742243\pi$
$744$		0			0
$745$	−37.2532	+	31.2302i	−1.36485	+	1.14419i
$746$	−2.87593	−	16.3102i	−0.105295	−	0.597159i
$747$		0			0
$748$	−19.5294	−	11.2753i	−0.714066	−	0.412266i
$749$	16.3155	+	28.2593i	0.596155	+	1.03257i
$750$		0			0
$751$	0.156655	+	0.131449i	0.00571641	+	0.00479664i	0.645641	−	0.763641i	$-0.276590\pi$
$751$	0.156655	+	0.131449i	0.00571641	+	0.00479664i	−0.639925	+	0.768437i	$0.721035\pi$
$752$	122.725	−	70.8551i	4.47531	−	2.58382i
$753$		0			0
$754$	0.301393	−	0.109698i	0.0109761	−	0.00399497i
$755$	−10.8414	+	18.7581i	−0.394558	+	0.682675i
$756$		0			0
$757$	6.28814	−	17.2765i	0.228546	−	0.627926i	−0.771418	−	0.636328i	$-0.780452\pi$
$757$	6.28814	−	17.2765i	0.228546	−	0.627926i	0.999965	+	0.00840229i	$0.00267456\pi$
$758$	−0.269652	−	0.321359i	−0.00979421	−	0.0116723i
$759$		0			0
$760$	29.8755	−	78.8027i	1.08370	−	2.85847i
$761$	31.4304			1.13935			0.569675	−	0.821870i	$-0.307069\pi$
$761$	31.4304			1.13935			0.569675	+	0.821870i	$0.307069\pi$
$762$		0			0
$763$	−6.38912	+	17.5540i	−0.231302	+	0.635496i
$764$	8.41578	−	47.7283i	0.304472	−	1.72675i
$765$		0			0
$766$	40.7026	−	14.8145i	1.47064	−	0.535270i
$767$	−0.407363	−	0.235191i	−0.0147090	−	0.00849225i
$768$		0			0
$769$	16.5419	+	13.8803i	0.596516	+	0.500537i	0.890324	−	0.455328i	$-0.150478\pi$
$769$	16.5419	+	13.8803i	0.596516	+	0.500537i	−0.293807	+	0.955865i	$0.594922\pi$
$770$	6.89195	+	39.1906i	0.248369	+	1.41233i
$771$		0			0
$772$	112.218	+	64.7893i	4.03883	+	2.33182i
$773$	12.6854	+	34.8529i	0.456263	+	1.25357i	0.928247	+	0.371965i	$0.121316\pi$
$773$	12.6854	+	34.8529i	0.456263	+	1.25357i	−0.471983	+	0.881607i	$0.656462\pi$
$774$		0			0
$775$	−14.4307	−	0.0131479i	−0.518366	−	0.000472286i
$776$	45.4630	+	16.5472i	1.63203	+	0.594009i
$777$		0			0
$778$			7.29454i			0.261522i
$779$	26.5461	+	22.8627i	0.951113	+	0.819141i
$780$		0			0
$781$	14.1648	−	11.8857i	0.506856	−	0.425302i
$782$	4.24520	−	11.6636i	0.151808	−	0.417089i
$783$		0			0
$784$	−1.65572	−	9.39005i	−0.0591328	−	0.335359i
$785$	−5.65080	+	15.5035i	−0.201686	+	0.553343i
$786$		0			0
$787$	1.73479	−	1.00158i	0.0618385	−	0.0357025i	−0.468762	−	0.883325i	$-0.655300\pi$
$787$	1.73479	−	1.00158i	0.0618385	−	0.0357025i	0.530600	+	0.847622i	$0.321966\pi$
$788$	−13.9978	+	16.6819i	−0.498652	+	0.594270i
$789$		0			0
$790$	−68.6858	−	12.1434i	−2.44373	−	0.432044i
$791$	3.43152	−	5.94357i	0.122011	−	0.211329i
$792$		0			0
$793$	−0.182791	+	0.0322309i	−0.00649108	+	0.00114455i
$794$	−7.39595	+	41.9445i	−0.262472	+	1.48856i
$795$		0			0
$796$	89.4894	−	75.0905i	3.17187	−	2.66151i
$797$		−	12.8587i		−	0.455480i	−0.973722	−	0.227740i	$-0.926866\pi$
$797$		−	12.8587i		−	0.455480i	0.973722	−	0.227740i	$-0.0731336\pi$
$798$		0			0
$799$	20.1119			0.711509
$800$	−54.9542	+	65.3708i	−1.94292	+	2.31121i
$801$		0			0
$802$	8.79877	+	1.55146i	0.310695	+	0.0547840i
$803$	9.95584	−	1.75548i	0.351334	−	0.0619496i
$804$		0			0
$805$	−14.8811	+	5.40861i	−0.524490	+	0.190628i
$806$	−0.156992	−	0.271918i	−0.00552981	−	0.00957792i
$807$		0			0
$808$	−66.4567	+	79.2001i	−2.33794	+	2.78625i
$809$	−10.5986	−	18.3573i	−0.372627	−	0.645410i	0.617341	−	0.786695i	$-0.288210\pi$
$809$	−10.5986	−	18.3573i	−0.372627	−	0.645410i	−0.989969	+	0.141286i	$0.954876\pi$
$810$		0			0
$811$	8.40909	−	3.06066i	0.295283	−	0.107474i	−0.190131	−	0.981759i	$-0.560891\pi$
$811$	8.40909	−	3.06066i	0.295283	−	0.107474i	0.485414	+	0.874284i	$0.338669\pi$
$812$	−42.1652	+	7.43486i	−1.47971	+	0.260912i
$813$		0			0
$814$	1.36450	+	0.496639i	0.0478258	+	0.0174072i
$815$	−0.00499453	+	10.9637i	−0.000174951	+	0.384041i
$816$		0			0
$817$	−21.9812	−	4.16789i	−0.769025	−	0.145816i
$818$		−	20.1240i		−	0.703621i
$819$		0			0
$820$	−46.8550	−	81.2406i	−1.63625	−	2.83705i
$821$	0.600509	−	3.40566i	0.0209579	−	0.118858i	−0.972534	−	0.232761i	$-0.925224\pi$
$821$	0.600509	−	3.40566i	0.0209579	−	0.118858i	0.993492	+	0.113903i	$0.0363352\pi$
$822$		0			0
$823$	6.20022	+	17.0350i	0.216126	+	0.593801i	0.999619	−	0.0275992i	$-0.00878621\pi$
$823$	6.20022	+	17.0350i	0.216126	+	0.593801i	−0.783493	+	0.621401i	$0.786564\pi$
$824$	60.9321	−	105.538i	2.12267	−	3.67657i
$825$		0			0
$826$	66.5374	+	55.8315i	2.31513	+	1.94263i
$827$	−18.8909	+	22.5132i	−0.656899	+	0.782862i	−0.986937	−	0.161105i	$-0.948494\pi$
$827$	−18.8909	+	22.5132i	−0.656899	+	0.782862i	0.330038	+	0.943968i	$0.392939\pi$
$828$		0			0
$829$	−1.73389	+	3.00318i	−0.0602204	+	0.104305i	−0.894564	−	0.446940i	$-0.852514\pi$
$829$	−1.73389	+	3.00318i	−0.0602204	+	0.104305i	0.834343	+	0.551245i	$0.185847\pi$
$830$	−25.2335	−	9.19725i	−0.875867	−	0.319241i
$831$		0			0
$832$	−0.809558	−	0.142747i	−0.0280664	−	0.00494886i
$833$	0.462829	−	1.27161i	0.0160361	−	0.0440588i
$834$		0			0
$835$	14.5129	−	17.2798i	0.502240	−	0.597993i
$836$	54.1307	+	0.695845i	1.87215	+	0.0240663i
$837$		0			0
$838$	24.8869	+	29.6591i	0.859705	+	1.02456i
$839$	−37.4283	−	13.6228i	−1.29217	−	0.470311i	−0.397730	−	0.917503i	$-0.630202\pi$
$839$	−37.4283	−	13.6228i	−1.29217	−	0.470311i	−0.894438	+	0.447192i	$0.852424\pi$
$840$		0			0
$841$	−3.52647	−	19.9996i	−0.121602	−	0.689641i
$842$	32.8655	+	90.2973i	1.13262	+	3.11185i
$843$		0			0
$844$	4.38750	+	7.59938i	0.151024	+	0.261581i
$845$	5.03408	+	28.6259i	0.173178	+	0.984763i
$846$		0			0
$847$	12.8598	−	7.42463i	0.441869	−	0.255113i
$848$	63.3156	+	36.5553i	2.17427	+	1.25531i
$849$		0			0
$850$	−22.9283	+	8.32157i	−0.786435	+	0.285428i
$851$	−0.100332	+	0.569014i	−0.00343935	+	0.0195055i
$852$		0			0
$853$	−10.2917	−	12.2652i	−0.352383	−	0.419953i	0.560513	−	0.828145i	$-0.310604\pi$
$853$	−10.2917	−	12.2652i	−0.352383	−	0.419953i	−0.912896	+	0.408192i	$0.866159\pi$
$854$	34.2739			1.17283
$855$		0			0
$856$	−101.380			−3.46510
$857$	10.4417	+	12.4439i	0.356680	+	0.425075i	0.914310	−	0.405015i	$-0.132734\pi$
$857$	10.4417	+	12.4439i	0.356680	+	0.425075i	−0.557630	+	0.830090i	$0.688289\pi$
$858$		0			0
$859$	9.76555	−	55.3832i	0.333196	−	1.88965i	−0.111163	−	0.993802i	$-0.535458\pi$
$859$	9.76555	−	55.3832i	0.333196	−	1.88965i	0.444360	−	0.895849i	$-0.353431\pi$
$860$	51.8530	+	29.9688i	1.76817	+	1.02193i
$861$		0			0
$862$	24.1734	+	13.9565i	0.823351	+	0.475362i
$863$	−12.2619	+	7.07944i	−0.417402	+	0.240987i	−0.693965	−	0.720009i	$-0.744138\pi$
$863$	−12.2619	+	7.07944i	−0.417402	+	0.240987i	0.276563	+	0.960996i	$0.410804\pi$
$864$		0			0
$865$	−10.7456	+	1.88969i	−0.365361	+	0.0642514i
$866$	−47.1260	−	81.6247i	−1.60141	−	2.77372i
$867$		0			0
$868$	14.3356	+	39.3866i	0.486581	+	1.33687i
$869$	−4.79838	−	27.2129i	−0.162774	−	0.923136i
$870$		0			0
$871$	−0.184651	−	0.0672073i	−0.00625665	−	0.00227723i
$872$	−37.3061	−	44.4596i	−1.26334	−	1.50559i
$873$		0			0
$874$	4.79653	+	29.4081i	0.162245	+	0.994744i
$875$	26.9253	+	15.5944i	0.910242	+	0.527188i
$876$		0			0
$877$	−2.19162	+	6.02143i	−0.0740058	+	0.203329i	−0.971180	−	0.238348i	$-0.923394\pi$
$877$	−2.19162	+	6.02143i	−0.0740058	+	0.203329i	0.897174	+	0.441677i	$0.145616\pi$
$878$	−50.6072	−	8.92342i	−1.70791	−	0.301151i
$879$		0			0
$880$	−63.9701	−	23.3162i	−2.15643	−	0.785990i
$881$	−5.80585	+	10.0560i	−0.195604	+	0.338796i	−0.947098	−	0.320943i	$-0.896000\pi$
$881$	−5.80585	+	10.0560i	−0.195604	+	0.338796i	0.751494	+	0.659740i	$0.229333\pi$
$882$		0			0
$883$	16.9859	−	20.2430i	0.571620	−	0.681231i	−0.400342	−	0.916366i	$-0.631109\pi$
$883$	16.9859	−	20.2430i	0.571620	−	0.681231i	0.971963	+	0.235135i	$0.0755533\pi$
$884$	−0.293908	−	0.246618i	−0.00988518	−	0.00829465i
$885$		0			0
$886$	30.8856	−	53.4954i	1.03762	−	1.79721i
$887$	−13.3596	−	36.7051i	−0.448570	−	1.23244i	−0.933720	−	0.358005i	$-0.883457\pi$
$887$	−13.3596	−	36.7051i	−0.448570	−	1.23244i	0.485149	−	0.874431i	$-0.338765\pi$
$888$		0			0
$889$	−0.357147	+	2.02548i	−0.0119783	+	0.0679325i
$890$	80.1076	−	46.2015i	2.68521	−	1.54868i
$891$		0			0
$892$		−	50.1559i		−	1.67934i
$893$	−42.1193	+	23.6010i	−1.40947	+	0.789777i
$894$		0			0
$895$	53.4072	+	0.0243298i	1.78521	+	0.000813256i
$896$	53.3048	+	19.4014i	1.78079	+	0.648154i
$897$		0			0
$898$	−41.7355	+	7.35910i	−1.39273	+	0.245576i
$899$	7.99576	−	2.91022i	0.266674	−	0.0970613i
$900$		0			0
$901$	5.18803	+	8.98593i	0.172838	+	0.299365i
$902$	33.0351	−	39.3697i	1.09995	−	1.31087i
$903$		0			0
$904$	10.6613	+	18.4659i	0.354589	+	0.614166i
$905$	−5.39577	+	1.96112i	−0.179361	+	0.0651897i
$906$		0			0
$907$	−56.4681	+	9.95684i	−1.87499	+	0.330612i	−0.990672	−	0.136270i	$-0.956489\pi$
$907$	−56.4681	+	9.95684i	−1.87499	+	0.330612i	−0.884320	+	0.466882i	$0.845377\pi$
$908$	120.587	+	21.2627i	4.00182	+	0.705628i
$909$		0			0
$910$	−0.000308413		0.677008i	−1.02238e−5		0.0224426i
$911$	−22.2118			−0.735909			−0.367954	−	0.929844i	$-0.619942\pi$
$911$	−22.2118			−0.735909			−0.367954	+	0.929844i	$0.619942\pi$
$912$		0			0
$913$		−	10.6399i		−	0.352129i
$914$	−71.2962	+	59.8247i	−2.35827	+	1.97882i
$915$		0			0
$916$	−1.07911	+	6.11991i	−0.0356546	+	0.202208i
$917$	29.9077	−	5.27354i	0.987640	−	0.174148i
$918$		0			0
$919$	24.0265	−	41.6150i	0.792560	−	1.37275i	−0.131817	−	0.991274i	$-0.542081\pi$
$919$	24.0265	−	41.6150i	0.792560	−	1.37275i	0.924377	−	0.381480i	$-0.124585\pi$
$920$	8.56428	−	48.4414i	0.282356	−	1.59707i
$921$		0			0
$922$	42.4191	−	50.5531i	1.39700	−	1.66488i
$923$	0.272449	−	0.157298i	0.00896776	−	0.00517754i
$924$		0			0
$925$	0.983843	−	0.566827i	0.0323485	−	0.0186372i
$926$	3.59519	+	20.3893i	0.118145	+	0.670035i
$927$		0			0
$928$	17.2227	−	47.3189i	0.565362	−	1.55332i
$929$	6.24472	−	5.23994i	0.204883	−	0.171917i	−0.534573	−	0.845122i	$-0.679528\pi$
$929$	6.24472	−	5.23994i	0.204883	−	0.171917i	0.739455	+	0.673205i	$0.235083\pi$
$930$		0			0
$931$	0.522937	+	3.20619i	0.0171386	+	0.105079i
$932$		−	120.754i		−	3.95542i
$933$		0			0
$934$	−16.4579	−	5.99020i	−0.538521	−	0.196005i
$935$	−6.20794	−	7.40518i	−0.203021	−	0.242175i
$936$		0			0
$937$	12.0229	+	33.0325i	0.392770	+	1.07913i	0.965731	+	0.259544i	$0.0835721\pi$
$937$	12.0229	+	33.0325i	0.392770	+	1.07913i	−0.572962	+	0.819582i	$0.694206\pi$
$938$	31.4237	+	18.1425i	1.02602	+	0.592372i
$939$		0			0
$940$	127.291	−	22.3850i	4.15177	−	0.730119i
$941$	11.4837	+	9.63598i	0.374358	+	0.314124i	0.810483	−	0.585762i	$-0.199205\pi$
$941$	11.4837	+	9.63598i	0.374358	+	0.314124i	−0.436124	+	0.899886i	$0.643649\pi$
$942$		0			0
$943$	17.7101	+	10.2249i	0.576720	+	0.332970i
$944$	−139.658	+	50.8313i	−4.54547	+	1.65442i
$945$		0			0
$946$	−5.69911	+	32.3213i	−0.185294	+	1.05086i
$947$	−11.2823	+	30.9978i	−0.366625	+	1.00729i	0.610011	+	0.792393i	$0.291165\pi$
$947$	−11.2823	+	30.9978i	−0.366625	+	1.00729i	−0.976636	+	0.214901i	$0.931057\pi$
$948$		0			0
$949$	0.171999			0.00558331
$950$	38.2523	−	44.3334i	1.24107	−	1.43836i
$951$		0			0
$952$	28.0855	+	33.4710i	0.910256	+	1.08480i
$953$	−9.90142	+	27.2039i	−0.320739	+	0.881222i	0.669621	+	0.742703i	$0.266456\pi$
$953$	−9.90142	+	27.2039i	−0.320739	+	0.881222i	−0.990360	+	0.138519i	$0.955766\pi$
$954$		0			0
$955$	10.3919	−	17.9803i	0.336273	−	0.581830i
$956$	47.5017	−	17.2892i	1.53632	−	0.559173i
$957$		0			0
$958$	28.7930	−	16.6236i	0.930259	−	0.537085i
$959$	9.78639	+	8.21176i	0.316019	+	0.265171i
$960$		0			0
$961$	11.3351	+	19.6330i	0.365648	+	0.633322i
$962$	0.0213953	+	0.0123526i	0.000689812	+	0.000398263i
$963$		0			0
$964$	−14.3038	−	81.1210i	−0.460695	−	2.61273i
$965$	35.6716	+	42.5511i	1.14831	+	1.36977i
$966$		0			0
$967$	21.4472	+	25.5597i	0.689694	+	0.821945i	0.991319	−	0.131481i	$-0.0419734\pi$
$967$	21.4472	+	25.5597i	0.689694	+	0.821945i	−0.301625	+	0.953427i	$0.597529\pi$
$968$			46.1347i			1.48283i
$969$		0			0
$970$	25.7408	+	21.6190i	0.826486	+	0.694146i
$971$	5.21562	−	4.37643i	0.167377	−	0.140446i	−0.555252	−	0.831682i	$-0.687378\pi$
$971$	5.21562	−	4.37643i	0.167377	−	0.140446i	0.722629	+	0.691236i	$0.242934\pi$
$972$		0			0
$973$	−21.5020	−	3.79138i	−0.689323	−	0.121546i
$974$	−18.0648	−	102.451i	−0.578833	−	3.28273i
$975$		0			0
$976$	−29.3225	+	50.7881i	−0.938591	+	1.62569i
$977$	0.0579657	−	0.0334665i	0.00185449	−	0.00107069i	−0.499072	−	0.866560i	$-0.666326\pi$
$977$	0.0579657	−	0.0334665i	0.00185449	−	0.00107069i	0.500927	+	0.865490i	$0.332993\pi$
$978$		0			0
$979$	28.0644	+	23.5489i	0.896944	+	0.752625i
$980$	1.51397	−	8.56333i	0.0483620	−	0.273546i
$981$		0			0
$982$	−28.8617	−	79.2969i	−0.921014	−	2.53046i
$983$	−49.5418	+	8.73556i	−1.58014	+	0.278621i	−0.893733	−	0.448599i	$-0.851923\pi$
$983$	−49.5418	+	8.73556i	−1.58014	+	0.278621i	−0.686405	+	0.727220i	$0.740812\pi$
$984$		0			0
$985$	−8.08342	+	4.66206i	−0.257559	+	0.148545i
$986$	11.0175	−	9.24478i	0.350869	−	0.294414i
$987$		0			0
$988$	0.904916	+	0.171583i	0.0287892	+	0.00545877i
$989$	−13.0593			−0.415261
$990$		0			0
$991$	−3.99186	−	1.45292i	−0.126806	−	0.0461534i	0.277838	−	0.960628i	$-0.410382\pi$
$991$	−3.99186	−	1.45292i	−0.126806	−	0.0461534i	−0.404644	+	0.914475i	$0.632604\pi$
$992$	−48.5468	−	8.56011i	−1.54136	−	0.271784i
$993$		0			0
$994$	−54.5885	+	19.8686i	−1.73144	+	0.630194i
$995$	47.0471	−	17.0995i	1.49149	−	0.542090i
$996$		0			0
$997$	−29.5816	+	35.2540i	−0.936858	+	1.11650i	0.0561457	+	0.998423i	$0.482119\pi$
$997$	−29.5816	+	35.2540i	−0.936858	+	1.11650i	−0.993004	+	0.118082i	$0.962326\pi$
$998$	33.5483	−	39.9813i	1.06195	−	1.26559i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.da.b.424.8		48
3.2	odd	2		95.2.p.a.44.1	✓	48
5.4	even	2	inner	855.2.da.b.424.1		48
15.2	even	4		475.2.l.f.101.8		48
15.8	even	4		475.2.l.f.101.1		48
15.14	odd	2		95.2.p.a.44.8	yes	48
19.16	even	9	inner	855.2.da.b.244.1		48
57.23	odd	18		1805.2.b.k.1084.1		24
57.35	odd	18		95.2.p.a.54.8	yes	48
57.53	even	18		1805.2.b.l.1084.24		24
95.54	even	18	inner	855.2.da.b.244.8		48
285.23	even	36		9025.2.a.cu.1.1		24
285.53	odd	36		9025.2.a.ct.1.24		24
285.92	even	36		475.2.l.f.301.8		48
285.137	even	36		9025.2.a.cu.1.24		24
285.149	odd	18		95.2.p.a.54.1	yes	48
285.167	odd	36		9025.2.a.ct.1.1		24
285.194	odd	18		1805.2.b.k.1084.24		24
285.224	even	18		1805.2.b.l.1084.1		24
285.263	even	36		475.2.l.f.301.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.44.1	✓	48	3.2	odd	2
95.2.p.a.44.8	yes	48	15.14	odd	2
95.2.p.a.54.1	yes	48	285.149	odd	18
95.2.p.a.54.8	yes	48	57.35	odd	18
475.2.l.f.101.1		48	15.8	even	4
475.2.l.f.101.8		48	15.2	even	4
475.2.l.f.301.1		48	285.263	even	36
475.2.l.f.301.8		48	285.92	even	36
855.2.da.b.244.1		48	19.16	even	9	inner
855.2.da.b.244.8		48	95.54	even	18	inner
855.2.da.b.424.1		48	5.4	even	2	inner
855.2.da.b.424.8		48	1.1	even	1	trivial
1805.2.b.k.1084.1		24	57.23	odd	18
1805.2.b.k.1084.24		24	285.194	odd	18
1805.2.b.l.1084.1		24	285.224	even	18
1805.2.b.l.1084.24		24	57.53	even	18
9025.2.a.ct.1.1		24	285.167	odd	36
9025.2.a.ct.1.24		24	285.53	odd	36
9025.2.a.cu.1.1		24	285.23	even	36
9025.2.a.cu.1.24		24	285.137	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)

\(f(q)\)	\(=\)	\(q+(1.72697 + 2.05812i) q^{2} +(-0.906145 + 5.13900i) q^{4} +(-1.11892 + 1.93598i) q^{5} +(2.41018 + 1.39152i) q^{7} +(-7.48810 + 4.32326i) q^{8} +O(q^{10})\)	\(q+(1.72697 + 2.05812i) q^{2} +(-0.906145 + 5.13900i) q^{4} +(-1.11892 + 1.93598i) q^{5} +(2.41018 + 1.39152i) q^{7} +(-7.48810 + 4.32326i) q^{8} +(-5.91682 + 1.04052i) q^{10} +(-1.19000 - 2.06113i) q^{11} +(-0.0138492 - 0.0380504i) q^{13} +(1.29839 + 7.36354i) q^{14} +(-12.0223 - 4.37577i) q^{16} +(-1.16714 - 1.39094i) q^{17} +(4.07652 + 1.54336i) q^{19} +(-8.93512 - 7.50439i) q^{20} +(2.18698 - 6.00867i) q^{22} +(2.50568 + 0.441819i) q^{23} +(-2.49605 - 4.33240i) q^{25} +(0.0543952 - 0.0942153i) q^{26} +(-9.33498 + 11.1250i) q^{28} +(2.25845 + 1.89507i) q^{29} +(1.44307 - 2.49947i) q^{31} +(-5.84176 - 16.0501i) q^{32} +(0.847116 - 4.80423i) q^{34} +(-5.39074 + 3.10907i) q^{35} +0.227089i q^{37} +(3.86361 + 11.0553i) q^{38} +(0.00880774 - 19.3342i) q^{40} +(7.55269 + 2.74896i) q^{41} +(-5.05471 + 0.891282i) q^{43} +(11.6705 - 4.24771i) q^{44} +(3.41791 + 5.92000i) q^{46} +(-7.11977 + 8.48501i) q^{47} +(0.372635 + 0.645423i) q^{49} +(4.60600 - 12.6191i) q^{50} +(0.208091 - 0.0366920i) q^{52} +(-5.62767 - 0.992310i) q^{53} +(5.32182 + 0.00242437i) q^{55} -24.0635 q^{56} +7.92088i q^{58} +(8.89878 - 7.46696i) q^{59} +(0.795974 - 4.51419i) q^{61} +(7.63635 - 1.34649i) q^{62} +(10.1506 - 17.5814i) q^{64} +(0.0891611 + 0.0157634i) q^{65} +(3.11931 - 3.71745i) q^{67} +(8.20566 - 4.73754i) q^{68} +(-15.7085 - 5.72552i) q^{70} +(1.34912 + 7.65124i) q^{71} +(-1.45279 + 3.99151i) q^{73} +(-0.467377 + 0.392176i) q^{74} +(-11.6252 + 19.5508i) q^{76} -6.62359i q^{77} +(10.9102 + 3.97100i) q^{79} +(21.9234 - 18.3789i) q^{80} +(7.38558 + 20.2917i) q^{82} +(3.87161 + 2.23528i) q^{83} +(3.99877 - 0.703214i) q^{85} +(-10.5637 - 8.86399i) q^{86} +(17.8216 + 10.2893i) q^{88} +(-14.4648 + 5.26476i) q^{89} +(0.0195687 - 0.110980i) q^{91} +(-4.54102 + 12.4764i) q^{92} -29.7588 q^{94} +(-7.54920 + 6.16519i) q^{95} +(-3.59666 - 4.28633i) q^{97} +(-0.684829 + 1.88155i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 18 q^{4} + 6 q^{5}+O(q^{10}) \) 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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