LMFDB - Embedded newform 855.2.da.b.244.1

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			244.1
Character	$\chi$	$=$	855.244
Dual form			855.2.da.b.424.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72697 + 2.05812i) q^{2} +(-0.906145 - 5.13900i) q^{4} +(1.71358 - 1.43654i) q^{5} +(-2.41018 + 1.39152i) q^{7} +(7.48810 + 4.32326i) q^{8} +O(q^{10})$	\(q+(-1.72697 + 2.05812i) q^{2} +(-0.906145 - 5.13900i) q^{4} +(1.71358 - 1.43654i) q^{5} +(-2.41018 + 1.39152i) q^{7} +(7.48810 + 4.32326i) q^{8} +(-0.00273678 + 6.00761i) q^{10} +(-1.19000 + 2.06113i) q^{11} +(0.0138492 - 0.0380504i) q^{13} +(1.29839 - 7.36354i) q^{14} +(-12.0223 + 4.37577i) q^{16} +(1.16714 - 1.39094i) q^{17} +(4.07652 - 1.54336i) q^{19} +(-8.93512 - 7.50439i) q^{20} +(-2.18698 - 6.00867i) q^{22} +(-2.50568 + 0.441819i) q^{23} +(0.872727 - 4.92325i) q^{25} +(0.0543952 + 0.0942153i) q^{26} +(9.33498 + 11.1250i) q^{28} +(2.25845 - 1.89507i) q^{29} +(1.44307 + 2.49947i) q^{31} +(5.84176 - 16.0501i) q^{32} +(0.847116 + 4.80423i) q^{34} +(-2.13107 + 5.84678i) q^{35} +0.227089i q^{37} +(-3.86361 + 11.0553i) q^{38} +(19.0420 - 3.34867i) q^{40} +(7.55269 - 2.74896i) q^{41} +(5.05471 + 0.891282i) q^{43} +(11.6705 + 4.24771i) q^{44} +(3.41791 - 5.92000i) q^{46} +(7.11977 + 8.48501i) q^{47} +(0.372635 - 0.645423i) q^{49} +(8.62546 + 10.2985i) q^{50} +(-0.208091 - 0.0366920i) q^{52} +(5.62767 - 0.992310i) q^{53} +(0.921737 + 5.24139i) q^{55} -24.0635 q^{56} +7.92088i q^{58} +(8.89878 + 7.46696i) q^{59} +(0.795974 + 4.51419i) q^{61} +(-7.63635 - 1.34649i) q^{62} +(10.1506 + 17.5814i) q^{64} +(-0.0309291 - 0.0850975i) q^{65} +(-3.11931 - 3.71745i) q^{67} +(-8.20566 - 4.73754i) q^{68} +(-8.35309 - 14.4832i) q^{70} +(1.34912 - 7.65124i) q^{71} +(1.45279 + 3.99151i) q^{73} +(-0.467377 - 0.392176i) q^{74} +(-11.6252 - 19.5508i) q^{76} -6.62359i q^{77} +(10.9102 - 3.97100i) q^{79} +(-14.3153 + 24.7688i) q^{80} +(-7.38558 + 20.2917i) q^{82} +(-3.87161 + 2.23528i) q^{83} +(0.00184961 - 4.06014i) q^{85} +(-10.5637 + 8.86399i) q^{86} +(-17.8216 + 10.2893i) q^{88} +(-14.4648 - 5.26476i) q^{89} +(0.0195687 + 0.110980i) q^{91} +(4.54102 + 12.4764i) q^{92} -29.7588 q^{94} +(4.76837 - 8.50074i) q^{95} +(3.59666 - 4.28633i) q^{97} +(0.684829 + 1.88155i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.72697	+	2.05812i	−1.22115	+	1.45531i	−0.371115	+	0.928587i	$0.621024\pi$
$2$	−1.72697	+	2.05812i	−1.22115	+	1.45531i	−0.850036	+	0.526724i	$0.823420\pi$
$3$		0			0
$3$		0			0
$4$	−0.906145	−	5.13900i	−0.453073	−	2.56950i
$5$	1.71358	−	1.43654i	0.766337	−	0.642439i
$5$	1.71358	−	1.43654i	0.766337	−	0.642439i
$6$		0			0
$7$	−2.41018	+	1.39152i	−0.910961	+	0.525944i	−0.880740	−	0.473600i	$-0.842954\pi$
$7$	−2.41018	+	1.39152i	−0.910961	+	0.525944i	−0.0302209	+	0.999543i	$0.509621\pi$
$8$	7.48810	+	4.32326i	2.64744	+	1.52850i
$9$		0			0
$10$	−0.00273678	+	6.00761i	−0.000865447	+	1.89977i
$11$	−1.19000	+	2.06113i	−0.358797	+	0.621455i	−0.987760	−	0.155980i	$-0.950146\pi$
$11$	−1.19000	+	2.06113i	−0.358797	+	0.621455i	0.628963	+	0.777435i	$0.283480\pi$
$12$		0			0
$13$	0.0138492	−	0.0380504i	0.00384108	−	0.0105533i	−0.937757	−	0.347291i	$-0.887101\pi$
$13$	0.0138492	−	0.0380504i	0.00384108	−	0.0105533i	0.941598	+	0.336738i	$0.109324\pi$
$14$	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	$-0.707109\pi$
$17$	1.16714	−	1.39094i	0.283073	−	0.337353i	0.888780	+	0.458335i	$0.151554\pi$
$18$		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	$-0.641015\pi$
$23$	−2.50568	+	0.441819i	−0.522471	+	0.0921257i	−0.0938080	+	0.995590i	$0.529904\pi$
$24$		0			0
$25$	0.872727	−	4.92325i	0.174545	−	0.984649i
$26$	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	−0.408545	−	0.912738i	$-0.633964\pi$
$29$	2.25845	−	1.89507i	0.419384	−	0.351905i	0.827929	+	0.560833i	$0.189519\pi$
$30$		0			0
$31$	1.44307	+	2.49947i	0.259183	+	0.448918i	0.966023	−	0.258455i	$-0.0832134\pi$
$31$	1.44307	+	2.49947i	0.259183	+	0.448918i	−0.706840	+	0.707373i	$0.749880\pi$
$32$	5.84176	−	16.0501i	1.03269	−	2.83728i
$33$		0			0
$34$	0.847116	+	4.80423i	0.145279	+	0.823919i
$35$	−2.13107	+	5.84678i	−0.360217	+	0.988287i
$36$		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
$40$	19.0420	−	3.34867i	3.01080	−	0.529472i
$41$	7.55269	−	2.74896i	1.17953	−	0.429315i	0.323496	−	0.946230i	$-0.395142\pi$
$41$	7.55269	−	2.74896i	1.17953	−	0.429315i	0.856037	+	0.516915i	$0.172920\pi$
$42$		0			0
$43$	5.05471	+	0.891282i	0.770836	+	0.135919i	0.545215	−	0.838296i	$-0.316448\pi$
$43$	5.05471	+	0.891282i	0.770836	+	0.135919i	0.225621	+	0.974215i	$0.427559\pi$
$44$	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	0.970782	+	0.239964i	$0.0771355\pi$
$47$	7.11977	+	8.48501i	1.03853	+	1.23767i	0.0677434	+	0.997703i	$0.478420\pi$
$48$		0			0
$49$	0.372635	−	0.645423i	0.0532336	−	0.0922032i
$50$	8.62546	+	10.2985i	1.21982	+	1.45642i
$51$		0			0
$52$	−0.208091	−	0.0366920i	−0.0288570	−	0.00508827i
$53$	5.62767	−	0.992310i	0.773020	−	0.136304i	0.226794	−	0.973943i	$-0.427175\pi$
$53$	5.62767	−	0.992310i	0.773020	−	0.136304i	0.546225	+	0.837638i	$0.316064\pi$
$54$		0			0
$55$	0.921737	+	5.24139i	0.124287	+	0.706749i
$56$	−24.0635			−3.21562
$57$		0			0
$58$			7.92088i			1.04006i
$59$	8.89878	+	7.46696i	1.15852	+	0.972116i	0.999884	−	0.0152208i	$-0.00484512\pi$
$59$	8.89878	+	7.46696i	1.15852	+	0.972116i	0.158638	+	0.987337i	$0.449290\pi$
$60$		0			0
$61$	0.795974	+	4.51419i	0.101914	+	0.577983i	0.992408	+	0.122988i	$0.0392477\pi$
$61$	0.795974	+	4.51419i	0.101914	+	0.577983i	−0.890494	+	0.454995i	$0.849641\pi$
$62$	−7.63635	−	1.34649i	−0.969817	−	0.171005i
$63$		0			0
$64$	10.1506	+	17.5814i	1.26883	+	2.19767i
$65$	−0.0309291	−	0.0850975i	−0.00383628	−	0.0105550i
$66$		0			0
$67$	−3.11931	−	3.71745i	−0.381084	−	0.454159i	0.541072	−	0.840976i	$-0.318019\pi$
$67$	−3.11931	−	3.71745i	−0.381084	−	0.454159i	−0.922156	+	0.386818i	$0.873574\pi$
$68$	−8.20566	−	4.73754i	−0.995083	−	0.574511i
$69$		0			0
$70$	−8.35309	−	14.4832i	−0.998386	−	1.73108i
$71$	1.34912	−	7.65124i	0.160111	−	0.908035i	−0.793852	−	0.608111i	$-0.791928\pi$
$71$	1.34912	−	7.65124i	0.160111	−	0.908035i	0.953963	−	0.299924i	$-0.0969614\pi$
$72$		0			0
$73$	1.45279	+	3.99151i	0.170036	+	0.467171i	0.995216	−	0.0976997i	$-0.0311485\pi$
$73$	1.45279	+	3.99151i	0.170036	+	0.467171i	−0.825180	+	0.564870i	$0.808926\pi$
$74$	−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	0.354758	−	0.934958i	$-0.384563\pi$
$79$	10.9102	−	3.97100i	1.22750	−	0.446773i	0.872740	+	0.488185i	$0.162341\pi$
$80$	−14.3153	+	24.7688i	−1.60050	+	2.76923i
$81$		0			0
$82$	−7.38558	+	20.2917i	−0.815601	+	2.24085i
$83$	−3.87161	+	2.23528i	−0.424965	+	0.245354i	−0.697199	−	0.716877i	$-0.745571\pi$
$83$	−3.87161	+	2.23528i	−0.424965	+	0.245354i	0.272234	+	0.962231i	$0.412237\pi$
$84$		0			0
$85$	0.00184961	−	4.06014i	0.000200618	−	0.440383i
$86$	−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	−0.568849	−	0.822442i	$-0.692611\pi$
$89$	−14.4648	−	5.26476i	−1.53327	−	0.558064i	−0.964419	+	0.264378i	$0.914833\pi$
$90$		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
$95$	4.76837	−	8.50074i	0.489224	−	0.872158i
$96$		0			0
$97$	3.59666	−	4.28633i	0.365185	−	0.435211i	−0.551895	−	0.833914i	$-0.686095\pi$
$97$	3.59666	−	4.28633i	0.365185	−	0.435211i	0.917080	+	0.398703i	$0.130540\pi$
$98$	0.684829	+	1.88155i	0.0691782	+	0.190066i
$99$		0			0
$100$	−26.0914	−	0.0237720i	−2.60914	−	0.00237720i
$101$	11.2361	+	4.08961i	1.11804	+	0.406932i	0.833935	−	0.551863i	$-0.186083\pi$
$101$	11.2361	+	4.08961i	1.11804	+	0.406932i	0.284101	+	0.958794i	$0.408305\pi$
$102$		0			0
$103$	12.2058	+	7.04702i	1.20267	+	0.694363i	0.961149	−	0.276031i	$-0.0890194\pi$
$103$	12.2058	+	7.04702i	1.20267	+	0.694363i	0.241524	+	0.970395i	$0.422353\pi$
$104$	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	$-0.858465\pi$
$107$	−10.1541	+	5.86249i	−0.981637	+	0.566748i	−0.0788727	+	0.996885i	$0.525132\pi$
$108$		0			0
$109$	1.16558	−	6.61032i	0.111642	−	0.633154i	−0.876716	−	0.481008i	$-0.840271\pi$
$109$	1.16558	−	6.61032i	0.111642	−	0.633154i	0.988358	−	0.152145i	$-0.0486182\pi$
$110$	−12.3792	−	7.15467i	−1.18031	−	0.682171i
$111$		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
$125$	−5.57693	−	9.69009i	−0.498816	−	0.866708i
$126$		0			0
$127$	−0.252761	+	0.694456i	−0.0224289	+	0.0616230i	−0.950402	−	0.311025i	$-0.899328\pi$
$127$	−0.252761	+	0.694456i	−0.0224289	+	0.0616230i	0.927973	+	0.372648i	$0.121550\pi$
$128$	−20.0731	−	3.53942i	−1.77423	−	0.312844i
$129$		0			0
$130$	0.228554	+	0.0833049i	0.0200455	+	0.00730632i
$131$	8.35925	+	7.01424i	0.730351	+	0.612837i	0.930227	−	0.366984i	$-0.119610\pi$
$131$	8.35925	+	7.01424i	0.730351	+	0.612837i	−0.199876	+	0.979821i	$0.564054\pi$
$132$		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	$-0.618381\pi$
$137$	−4.52066	+	0.797114i	−0.386226	+	0.0681021i	−0.0228361	+	0.999739i	$0.507270\pi$
$138$		0			0
$139$	−7.37217	−	2.68325i	−0.625299	−	0.227590i	0.00988487	−	0.999951i	$-0.496853\pi$
$139$	−7.37217	−	2.68325i	−0.625299	−	0.227590i	−0.635184	+	0.772361i	$0.719076\pi$
$140$	31.9777	+	5.65355i	2.70261	+	0.477813i
$141$		0			0
$142$	13.4173	+	15.9901i	1.12595	+	1.34186i
$143$	0.0619465	+	0.0738250i	0.00518023	+	0.00617355i
$144$		0			0
$145$	1.14771	−	6.49170i	0.0953122	−	0.539106i
$146$	−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	0.681188	−	0.732108i	$-0.261463\pi$
$149$	20.4289	−	7.43550i	1.67360	−	0.609140i	0.992411	+	0.122968i	$0.0392412\pi$
$150$		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
$155$	6.06340	+	2.21002i	0.487024	+	0.177513i
$156$		0			0
$157$	−7.26744	−	1.28145i	−0.580005	−	0.102271i	−0.124054	−	0.992275i	$-0.539590\pi$
$157$	−7.26744	−	1.28145i	−0.580005	−	0.102271i	−0.455951	+	0.890005i	$0.650701\pi$
$158$	−10.6688	+	29.3124i	−0.848767	+	2.33197i
$159$		0			0
$160$	−13.0462	−	35.8951i	−1.03139	−	2.83775i
$161$	5.42434	−	4.55156i	0.427498	−	0.358713i
$162$		0			0
$163$	−4.24622	−	2.45155i	−0.332589	−	0.192021i	0.324401	−	0.945920i	$-0.394837\pi$
$163$	−4.24622	−	2.45155i	−0.332589	−	0.192021i	−0.656990	+	0.753899i	$0.728171\pi$
$164$	−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	$-0.427871\pi$
$167$	9.93844	−	1.75241i	0.769059	−	0.135606i	0.544394	+	0.838830i	$0.316760\pi$
$168$		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	$-0.837163\pi$
$173$	−3.13636	+	3.73777i	−0.238453	+	0.284177i	0.633525	+	0.773722i	$0.281607\pi$
$174$		0			0
$175$	4.74735	+	13.0803i	0.358866	+	0.988778i
$176$	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	−0.0558613	+	0.998439i	$0.517790\pi$
$179$	−11.9422	+	20.6845i	−0.892604	+	1.54604i	−0.836743	+	0.547597i	$0.815543\pi$
$180$		0			0
$181$	1.96682	−	1.65036i	0.146193	−	0.122670i	−0.566758	−	0.823884i	$-0.691803\pi$
$181$	1.96682	−	1.65036i	0.146193	−	0.122670i	0.712951	+	0.701214i	$0.247358\pi$
$182$	−0.262204	−	0.151384i	−0.0194359	−	0.0112213i
$183$		0			0
$184$	−20.6729	−	7.52431i	−1.52403	−	0.554700i
$185$	0.326222	+	0.389136i	0.0239843	+	0.0286099i
$186$		0			0
$187$	1.47803	+	4.06085i	0.108084	+	0.296959i
$188$	37.1530	−	44.2772i	2.70966	−	3.22925i
$189$		0			0
$190$	9.26074	+	24.4944i	0.671845	+	1.77701i
$191$	−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	−0.727254	−	0.686368i	$-0.759204\pi$
$193$	−8.49293	−	23.3341i	−0.611334	−	1.67963i	0.115920	−	0.993259i	$-0.463018\pi$
$194$	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	$-0.714164\pi$
$197$	−3.61406	+	2.08658i	−0.257491	+	0.148663i	0.365698	+	0.930733i	$0.380830\pi$
$198$		0			0
$199$	−17.1492	+	14.3899i	−1.21567	+	1.02007i	−0.216635	+	0.976253i	$0.569508\pi$
$199$	−17.1492	+	14.3899i	−1.21567	+	1.02007i	−0.999039	+	0.0438194i	$0.986047\pi$
$200$	27.8195	−	33.0927i	1.96714	−	2.34001i
$201$		0			0
$202$	−27.8213	+	16.0627i	−1.95750	+	1.13016i
$203$	−2.80625	+	7.71012i	−0.196960	+	0.541144i
$204$		0			0
$205$	8.99319	−	15.5603i	0.628111	−	1.08678i
$206$	−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	0.686051	−	0.727554i	$-0.259343\pi$
$211$	1.28817	+	1.08090i	0.0886814	+	0.0744125i	−0.597369	+	0.801966i	$0.703787\pi$
$212$	−10.1990	−	28.0214i	−0.700468	−	1.92452i
$213$		0			0
$214$	5.47015	−	31.0228i	0.373932	−	2.12067i
$215$	9.94202	−	5.73399i	0.678040	−	0.391055i
$216$		0			0
$217$	−6.95611	−	4.01611i	−0.472211	−	0.272631i
$218$	11.5919	+	13.8147i	0.785104	+	0.935650i
$219$		0			0
$220$	26.1003	−	9.48627i	1.75968	−	0.639564i
$221$	−0.0367620	−	0.0636737i	−0.00247288	−	0.00428316i
$222$		0			0
$223$	9.46555	+	1.66903i	0.633860	+	0.111767i	0.481340	−	0.876534i	$-0.340150\pi$
$223$	9.46555	+	1.66903i	0.633860	+	0.111767i	0.152520	+	0.988300i	$0.451261\pi$
$224$	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	$0.487472\pi$
$230$	−2.64742	−	15.0544i	−0.174566	−	0.992656i
$231$		0			0
$232$	25.1044	−	4.42658i	1.64818	−	0.290619i
$233$	22.7889	+	4.01831i	1.49295	+	0.263248i	0.859741	−	0.510730i	$-0.170625\pi$
$233$	22.7889	+	4.01831i	1.49295	+	0.263248i	0.633212	+	0.773978i	$0.281736\pi$
$234$		0			0
$235$	24.3893	+	4.31196i	1.59099	+	0.281281i
$236$	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	−0.979076	−	0.203496i	$-0.934770\pi$
$239$	−4.84358	+	8.38932i	−0.313305	+	0.542660i	0.665771	+	0.746156i	$0.268103\pi$
$240$		0			0
$241$	−14.8334	−	5.39891i	−0.955503	−	0.347775i	−0.183233	−	0.983070i	$-0.558656\pi$
$241$	−14.8334	−	5.39891i	−0.955503	−	0.347775i	−0.772270	+	0.635295i	$0.780879\pi$
$242$	−14.1174	−	2.48928i	−0.907502	−	0.160017i
$243$		0			0
$244$	22.4772	−	8.18102i	1.43895	−	0.523736i
$245$	−0.288633	−	1.64129i	−0.0184401	−	0.104858i
$246$		0			0
$247$	−0.00226874	−	0.176488i	−0.000144356	−	0.0112297i
$248$			24.9550i			1.58465i
$249$		0			0
$250$	29.5746	+	5.25648i	1.87046	+	0.332449i
$251$	−0.951469	−	5.39605i	−0.0600562	−	0.340596i	0.939944	−	0.341330i	$-0.110877\pi$
$251$	−0.951469	−	5.39605i	−0.0600562	−	0.340596i	−1.00000		0.000734411i	$0.999766\pi$
$252$		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	$-0.257518\pi$
$257$	−2.28060	−	2.71792i	−0.142260	−	0.169539i	−0.832470	+	0.554070i	$0.813074\pi$
$258$		0			0
$259$	−0.315999	−	0.547326i	−0.0196352	−	0.0340092i
$260$	−0.409290	+	0.236055i	−0.0253831	+	0.0146395i
$261$		0			0
$262$	−28.8723	+	5.09097i	−1.78374	+	0.314521i
$263$	−9.01141	−	24.7587i	−0.555668	−	1.52668i	−0.825858	−	0.563877i	$-0.809309\pi$
$263$	−9.01141	−	24.7587i	−0.555668	−	1.52668i	0.270191	−	0.962807i	$-0.412913\pi$
$264$		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	−0.904877	−	0.425673i	$-0.860037\pi$
$269$	−21.7224	+	7.90629i	−1.32444	+	0.482055i	−0.419559	+	0.907728i	$0.637815\pi$
$270$		0			0
$271$	3.20656	−	18.1853i	0.194785	−	1.10468i	−0.717941	−	0.696104i	$-0.754915\pi$
$271$	3.20656	−	18.1853i	0.194785	−	1.10468i	0.912725	−	0.408574i	$-0.133974\pi$
$272$	−7.94530	+	21.8295i	−0.481754	+	1.32361i
$273$		0			0
$274$	6.16648	−	10.6807i	0.372531	−	0.645242i
$275$	9.10892	+	7.65745i	0.549289	+	0.461761i
$276$		0			0
$277$	−25.9554	−	14.9854i	−1.55951	−	0.900384i	−0.997303	−	0.0733885i	$-0.976619\pi$
$277$	−25.9554	−	14.9854i	−1.55951	−	0.900384i	−0.562208	−	0.826996i	$-0.690048\pi$
$278$	18.2540	−	10.5389i	1.09480	−	0.632083i
$279$		0			0
$280$	−41.2348	+	34.5681i	−2.46425	+	2.06584i
$281$	0.690977	+	3.91872i	0.0412202	+	0.233771i	0.998457	−	0.0555351i	$-0.0176865\pi$
$281$	0.690977	+	3.91872i	0.0412202	+	0.233771i	−0.957237	+	0.289306i	$0.906575\pi$
$282$		0			0
$283$	5.81678	−	6.93217i	0.345772	−	0.412075i	−0.564930	−	0.825139i	$-0.691097\pi$
$283$	5.81678	−	6.93217i	0.345772	−	0.412075i	0.910702	+	0.413064i	$0.135541\pi$
$284$	−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
$290$	11.3786	+	13.5731i	0.668177	+	0.797039i
$291$		0			0
$292$	19.1959	−	11.0828i	1.12336	−	0.648570i
$293$	2.02341	+	1.16822i	0.118209	+	0.0682479i	0.557939	−	0.829882i	$-0.311592\pi$
$293$	2.02341	+	1.16822i	0.118209	+	0.0682479i	−0.439730	+	0.898130i	$0.644926\pi$
$294$		0			0
$295$	25.9754	+	0.0118331i	1.51234	+	0.000688952i
$296$	−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	$-0.0415133\pi$
$307$	2.59974	+	7.14274i	0.148375	+	0.407658i	−0.843132	+	0.537706i	$0.819291\pi$
$308$	−34.0387	+	6.00194i	−1.93953	+	0.341992i
$309$		0			0
$310$	−15.0198	+	8.66256i	−0.853067	+	0.492000i
$311$	−9.41207	−	16.3022i	−0.533709	−	0.924412i	−0.999225	−	0.0393720i	$-0.987464\pi$
$311$	−9.41207	−	16.3022i	−0.533709	−	0.924412i	0.465515	−	0.885040i	$-0.345869\pi$
$312$		0			0
$313$	14.2771	+	17.0147i	0.806987	+	0.961729i	0.999810	−	0.0195042i	$-0.00620878\pi$
$313$	14.2771	+	17.0147i	0.806987	+	0.961729i	−0.192823	+	0.981234i	$0.561764\pi$
$314$	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	$-0.852403\pi$
$317$	1.39295	−	3.82711i	0.0782360	−	0.214952i	0.972644	+	0.232300i	$0.0746251\pi$
$318$		0			0
$319$	1.21843	+	6.91009i	0.0682193	+	0.386891i
$320$	42.6502	+	15.5454i	2.38422	+	0.869015i
$321$		0			0
$322$			19.0243i			1.06018i
$323$	2.61115	−	7.47153i	0.145288	−	0.415727i
$324$		0			0
$325$	−0.175245	−	0.101391i	−0.00972085	−	0.00562415i
$326$	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	0.425132	+	0.905132i	$0.360228\pi$
$331$	−10.3939	+	18.0028i	−0.571301	+	0.989523i	−0.996433	+	0.0843910i	$0.973106\pi$
$332$	14.9953	+	17.8708i	0.822976	+	0.980785i
$333$		0			0
$334$	−13.5567	+	23.4809i	−0.741789	+	1.28482i
$335$	−10.6854	−	1.88915i	−0.583808	−	0.103215i
$336$		0			0
$337$	−25.7746	−	4.54476i	−1.40403	−	0.247569i	−0.580234	−	0.814450i	$-0.697039\pi$
$337$	−25.7746	−	4.54476i	−1.40403	−	0.247569i	−0.823800	+	0.566881i	$0.808150\pi$
$338$	−34.3920	+	6.06423i	−1.87068	+	0.329851i
$339$		0			0
$340$	−20.8667	+	3.66957i	−1.13166	+	0.199010i
$341$	−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	$-0.630924\pi$
$347$	−20.2859	−	3.57695i	−1.08901	−	0.192021i	−0.689194	+	0.724577i	$0.742035\pi$
$348$		0			0
$349$	−12.5153	−	21.6772i	−0.669929	−	1.16035i	−0.977924	−	0.208963i	$-0.932991\pi$
$349$	−12.5153	−	21.6772i	−0.669929	−	1.16035i	0.307994	−	0.951388i	$-0.400342\pi$
$350$	−35.1194	−	12.8187i	−1.87721	−	0.685186i
$351$		0			0
$352$	26.1297	+	31.1402i	1.39272	+	1.65978i
$353$	6.24627	+	3.60628i	0.332455	+	0.191943i	0.656931	−	0.753951i	$-0.271854\pi$
$353$	6.24627	+	3.60628i	0.332455	+	0.191943i	−0.324475	+	0.945894i	$0.605188\pi$
$354$		0			0
$355$	−8.67946	−	15.0491i	−0.460658	−	0.798723i
$356$	−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	0.903750	−	0.428060i	$-0.140803\pi$
$359$	12.1097	+	10.1613i	0.639128	+	0.536292i	−0.264622	+	0.964352i	$0.585247\pi$
$360$		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
$365$	8.22342	+	4.75279i	0.430433	+	0.248772i
$366$		0			0
$367$	−0.903831	+	2.48326i	−0.0471796	+	0.129625i	−0.961045	−	0.276393i	$-0.910861\pi$
$367$	−0.903831	+	2.48326i	−0.0471796	+	0.129625i	0.913865	+	0.406018i	$0.133083\pi$
$368$	28.1908	−	16.2760i	1.46955	−	0.848444i
$369$		0			0
$370$	−1.36426		0.000621494i	−0.0709248		3.23100e-5i
$371$	−12.1829	+	10.2226i	−0.632502	+	0.530733i
$372$		0			0
$373$	5.33853	−	3.08220i	0.276419	−	0.159590i	−0.355382	−	0.934721i	$-0.615649\pi$
$373$	5.33853	−	3.08220i	0.276419	−	0.159590i	0.631801	+	0.775131i	$0.282316\pi$
$374$	−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	$0.501277\pi$
$380$	−48.0062	−	16.8018i	−2.46267	−	0.861912i
$381$		0			0
$382$	16.0391	−	19.1147i	0.820634	−	0.977993i
$383$	−5.51405	−	15.1497i	−0.281755	−	0.774115i	−0.997153	−	0.0753983i	$-0.975977\pi$
$383$	−5.51405	−	15.1497i	−0.281755	−	0.774115i	0.715399	−	0.698716i	$-0.246245\pi$
$384$		0			0
$385$	−9.51503	−	11.3501i	−0.484931	−	0.578453i
$386$	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	−0.588537	−	0.808471i	$-0.700296\pi$
$389$	2.07987	−	1.74521i	0.105453	−	0.0884859i	0.693990	+	0.719985i	$0.255851\pi$
$390$		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
$395$	12.9911	−	22.4776i	0.653653	−	1.13097i
$396$		0			0
$397$	−10.1900	+	12.1440i	−0.511422	+	0.609488i	−0.958530	−	0.284991i	$-0.908009\pi$
$397$	−10.1900	+	12.1440i	−0.511422	+	0.609488i	0.447109	+	0.894480i	$0.352454\pi$
$398$		−	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	0.704175	−	0.710026i	$-0.251317\pi$
$401$	2.54746	+	2.13757i	0.127214	+	0.106745i	−0.576961	+	0.816772i	$0.695761\pi$
$402$		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	−0.773530	−	0.633760i	$-0.781511\pi$
$409$	−5.73789	+	4.81466i	−0.283720	+	0.238070i	0.489809	+	0.871830i	$0.337066\pi$
$410$	16.4940	+	45.3812i	0.814580	+	2.24122i
$411$		0			0
$412$	25.1544	−	69.1113i	1.23927	−	3.40487i
$413$	−31.8380	−	5.61391i	−1.56665	−	0.276242i
$414$		0			0
$415$	−3.42327	+	9.39204i	−0.168042	+	0.461037i
$416$	−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	0.651322	−	0.758802i	$-0.274215\pi$
$421$	33.6092	−	12.2327i	1.63801	−	0.596187i	0.986690	+	0.162614i	$0.0519927\pi$
$422$	−4.44926	+	0.784525i	−0.216587	+	0.0381901i
$423$		0			0
$424$	46.4305	+	16.8993i	2.25487	+	0.820704i
$425$	−5.82936	−	6.96003i	−0.282766	−	0.337611i
$426$		0			0
$427$	−8.20001	−	9.77239i	−0.396826	−	0.472919i
$428$	39.3285	+	46.8698i	1.90101	+	2.26554i
$429$		0			0
$430$	−5.36831	+	30.3643i	−0.258883	+	1.46430i
$431$	9.76286	+	3.55339i	0.470260	+	0.171161i	0.566270	−	0.824220i	$-0.308386\pi$
$431$	9.76286	+	3.55339i	0.470260	+	0.171161i	−0.0960100	+	0.995380i	$0.530608\pi$
$432$		0			0
$433$	34.5482	−	6.09178i	1.66028	−	0.292752i	0.736718	−	0.676200i	$-0.236374\pi$
$433$	34.5482	−	6.09178i	1.66028	−	0.292752i	0.923563	+	0.383448i	$0.125263\pi$
$434$	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	0.222272	−	0.974985i	$-0.428653\pi$
$439$	−14.6520	−	12.2945i	−0.699303	−	0.586785i	−0.921575	+	0.388199i	$0.873097\pi$
$440$	−15.7578	+	43.2330i	−0.751225	+	2.06105i
$441$		0			0
$442$	0.194535	+	0.0343018i	0.00925309	+	0.00163157i
$443$	7.86358	−	21.6050i	0.373610	−	1.02649i	−0.600344	−	0.799742i	$-0.704970\pi$
$443$	7.86358	−	21.6050i	0.373610	−	1.02649i	0.973954	−	0.226744i	$-0.0728080\pi$
$444$		0			0
$445$	−32.3497	+	11.7576i	−1.53352	+	0.557365i
$446$	−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	0.617698	−	0.786415i	$-0.288065\pi$
$449$	−7.88692	−	13.6605i	−0.372207	−	0.644681i	−0.989905	+	0.141734i	$0.954732\pi$
$450$		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
$460$	25.7041	+	14.8559i	1.19846	+	0.692661i
$461$	−4.26528	+	24.1896i	−0.198654	+	1.12662i	0.708465	+	0.705746i	$0.249388\pi$
$461$	−4.26528	+	24.1896i	−0.198654	+	1.12662i	−0.907119	+	0.420875i	$0.861723\pi$
$462$		0			0
$463$	−6.67368	+	3.85305i	−0.310152	+	0.179067i	−0.646995	−	0.762495i	$-0.723974\pi$
$463$	−6.67368	+	3.85305i	−0.310152	+	0.179067i	0.336842	+	0.941561i	$0.390641\pi$
$464$	−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	$-0.285139\pi$
$467$	5.64552	+	3.25944i	0.261243	+	0.150829i	−0.363658	+	0.931532i	$0.618472\pi$
$468$		0			0
$469$	12.6910	+	4.61914i	0.586015	+	0.213292i
$470$	−50.9941	+	42.7496i	−2.35218	+	1.97189i
$471$		0			0
$472$	34.3534	+	94.3851i	1.58124	+	4.34442i
$473$	−7.85213	+	9.35781i	−0.361041	+	0.430272i
$474$		0			0
$475$	−4.04064	−	21.4167i	−0.185397	−	0.982664i
$476$	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	0.993725	+	0.111851i	$0.0356779\pi$
$479$	2.14887	+	12.1868i	0.0981842	+	0.556830i	−0.895541	+	0.444979i	$0.853211\pi$
$480$		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
$485$	0.00569974	−	12.5117i	0.000258812	−	0.568127i
$486$		0			0
$487$	33.5333	−	19.3605i	1.51954	−	0.877306i	0.519804	−	0.854285i	$-0.326005\pi$
$487$	33.5333	−	19.3605i	1.51954	−	0.877306i	0.999735	−	0.0230209i	$-0.00732844\pi$
$488$	−13.5557	+	37.2439i	−0.613636	+	1.68595i
$489$		0			0
$490$	3.87643	+	2.24041i	0.175119	+	0.101212i
$491$	−29.5147	+	10.7425i	−1.33198	+	0.484802i	−0.907278	−	0.420531i	$-0.861844\pi$
$491$	−29.5147	+	10.7425i	−1.33198	+	0.484802i	−0.424704	+	0.905332i	$0.639622\pi$
$492$		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	0.811333	+	0.584584i	$0.198742\pi$
$499$	−3.37331	+	19.1310i	−0.151010	+	0.856422i	−0.962343	+	0.271837i	$0.912369\pi$
$500$	−44.7439	+	37.4405i	−2.00101	+	1.67439i
$501$		0			0
$502$	12.7489	+	7.36057i	0.569010	+	0.328518i
$503$	−2.73706	−	3.26190i	−0.122039	−	0.145441i	0.701565	−	0.712605i	$-0.252485\pi$
$503$	−2.73706	−	3.26190i	−0.122039	−	0.145441i	−0.823605	+	0.567164i	$0.808040\pi$
$504$		0			0
$505$	25.1289	−	9.13321i	1.11822	−	0.406422i
$506$	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	0.943462	−	0.331480i	$-0.107548\pi$
$509$	−1.27413	−	7.22597i	−0.0564750	−	0.320286i	−0.999937	+	0.0111941i	$0.996437\pi$
$510$		0			0
$511$	−9.05573	−	7.59866i	−0.400602	−	0.336145i
$512$		−	2.72331i		−	0.120354i
$513$		0			0
$514$	9.53234			0.420453
$515$	31.0389	−	5.45842i	1.36774	−	0.240527i
$516$		0			0
$517$	−25.9612	+	4.57767i	−1.14177	+	0.201326i
$518$	1.67218	+	0.294851i	0.0734714	+	0.0129550i
$519$		0			0
$520$	0.136298	−	0.770932i	0.00597708	−	0.0338076i
$521$	−3.98404	+	6.90057i	−0.174544	+	0.302319i	−0.940003	−	0.341165i	$-0.889178\pi$
$521$	−3.98404	+	6.90057i	−0.174544	+	0.302319i	0.765459	+	0.643484i	$0.222512\pi$
$522$		0			0
$523$	10.0759	+	12.0080i	0.440590	+	0.525075i	0.939946	−	0.341322i	$-0.110875\pi$
$523$	10.0759	+	12.0080i	0.440590	+	0.525075i	−0.499357	+	0.866397i	$0.666430\pi$
$524$	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
$530$	5.94601	+	33.8116i	0.258278	+	1.46868i
$531$		0			0
$532$	55.2241	+	30.9441i	2.39427	+	1.34160i
$533$		−	0.325454i		−	0.0140970i
$534$		0			0
$535$	−8.97825	+	24.6326i	−0.388164	+	1.06496i
$536$	−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	−0.0215537	−	0.999768i	$-0.506861\pi$
$541$	22.3123	−	18.7223i	0.959283	−	0.804934i	0.980836	+	0.194834i	$0.0624168\pi$
$542$	31.8899	+	38.0049i	1.36979	+	1.63245i
$543$		0			0
$544$	−15.5066	−	26.8583i	−0.664841	−	1.15154i
$545$	−7.49865	−	13.0017i	−0.321207	−	0.556932i
$546$		0			0
$547$	−14.2470	+	2.51214i	−0.609160	+	0.107411i	−0.469714	−	0.882818i	$-0.655643\pi$
$547$	−14.2470	+	2.51214i	−0.609160	+	0.107411i	−0.139445	+	0.990230i	$0.544532\pi$
$548$	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	−0.414395	−	0.910097i	$-0.636007\pi$
$557$	11.5184	−	31.6465i	0.488049	−	1.34090i	0.902444	−	0.430807i	$-0.141771\pi$
$558$		0			0
$559$	0.103917	−	0.179990i	0.00439524	−	0.00761278i
$560$	0.0362698	−	79.6171i	0.00153268	−	3.36443i
$561$		0			0
$562$	−9.25850	−	5.34540i	−0.390546	−	0.225482i
$563$	21.5774	−	12.4577i	0.909378	−	0.525030i	0.0291473	−	0.999575i	$-0.490721\pi$
$563$	21.5774	−	12.4577i	0.909378	−	0.525030i	0.880231	+	0.474545i	$0.157387\pi$
$564$		0			0
$565$	−3.54254	−	4.22575i	−0.149036	−	0.177779i
$566$	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
$575$	−0.0115908	+	12.7217i	−0.000483369	+	0.530530i
$576$		0			0
$577$	−36.0832	+	20.8327i	−1.50216	+	0.867275i	−0.502167	+	0.864771i	$0.667464\pi$
$577$	−36.0832	+	20.8327i	−1.50216	+	0.867275i	−0.999997	+	0.00250405i	$0.999203\pi$
$578$	−31.8834	−	18.4079i	−1.32618	−	0.765668i
$579$		0			0
$580$	−34.4009	−	0.0156714i	−1.42842	−	0.000650719i
$581$	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	$-0.886081\pi$
$587$	−10.3943	+	12.3875i	−0.429020	+	0.511286i	0.507619	+	0.861581i	$0.330526\pi$
$588$		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	$-0.708168\pi$
$593$	−22.1249	+	3.90122i	−0.908562	+	0.160204i	−0.300212	+	0.953873i	$0.597057\pi$
$594$		0			0
$595$	5.64529	+	9.78822i	0.231434	+	0.401278i
$596$	−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	−0.608356	−	0.793664i	$-0.708171\pi$
$599$	1.65472	−	1.38847i	0.0676099	−	0.0567314i	0.675966	+	0.736932i	$0.263726\pi$
$600$		0			0
$601$	8.52974	+	14.7739i	0.347935	+	0.602641i	0.985883	−	0.167439i	$-0.0535496\pi$
$601$	8.52974	+	14.7739i	0.347935	+	0.602641i	−0.637947	+	0.770080i	$0.720216\pi$
$602$	13.1260	−	36.0633i	0.534975	−	1.46983i
$603$		0			0
$604$	−8.77979	−	49.7927i	−0.357245	−	2.02603i
$605$	11.2095	+	4.08570i	0.455730	+	0.166107i
$606$		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
$610$	−27.1217	+	4.76955i	−1.09812	+	0.193113i
$611$	0.421462	−	0.153400i	0.0170505	−	0.00620588i
$612$		0			0
$613$	−18.3007	−	3.22691i	−0.739159	−	0.130334i	−0.208623	−	0.977996i	$-0.566898\pi$
$613$	−18.3007	−	3.22691i	−0.739159	−	0.130334i	−0.530536	+	0.847663i	$0.678009\pi$
$614$	−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	$-0.353188\pi$
$617$	−12.7710	−	15.2199i	−0.514141	−	0.612729i	−0.959185	+	0.282779i	$0.908744\pi$
$618$		0			0
$619$	−4.21208	+	7.29553i	−0.169298	+	0.293232i	−0.938173	−	0.346166i	$-0.887483\pi$
$619$	−4.21208	+	7.29553i	−0.169298	+	0.293232i	0.768875	+	0.639399i	$0.220817\pi$
$620$	5.86301	−	33.1624i	0.235464	−	1.33184i
$621$		0			0
$622$	49.8062	+	8.78218i	1.99705	+	0.352133i
$623$	42.1888	−	7.43902i	1.69026	−	0.298038i
$624$		0			0
$625$	−23.4767	−	8.59330i	−0.939068	−	0.343732i
$626$	−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	0.989855	−	0.142083i	$-0.0453799\pi$
$631$	0.278838	+	1.58137i	0.0111004	+	0.0629534i	−0.978754	+	0.205036i	$0.934269\pi$
$632$	98.8646	+	17.4325i	3.93262	+	0.693428i
$633$		0			0
$634$	5.47106	+	9.47616i	0.217284	+	0.376346i
$635$	0.564484	+	1.55311i	0.0224009	+	0.0616332i
$636$		0			0
$637$	−0.0193979	−	0.0231175i	−0.000768573	−	0.000915950i
$638$	−16.3260	−	9.42582i	−0.646352	−	0.373172i
$639$		0			0
$640$	−39.4814	+	22.7706i	−1.56064	+	0.900087i
$641$	7.96102	−	45.1492i	0.314442	−	1.78329i	−0.260892	−	0.965368i	$-0.584017\pi$
$641$	7.96102	−	45.1492i	0.314442	−	1.78329i	0.575334	−	0.817919i	$-0.304872\pi$
$642$		0			0
$643$	−6.26834	−	17.2221i	−0.247199	−	0.679175i	−0.999786	−	0.0206816i	$-0.993416\pi$
$643$	−6.26834	−	17.2221i	−0.247199	−	0.679175i	0.752587	−	0.658493i	$-0.228806\pi$
$644$	−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
$650$	0.511317	−	0.185577i	0.0200555	−	0.00727892i
$651$		0			0
$652$	−8.75086	+	24.0428i	−0.342710	+	0.941588i
$653$	−0.604989	+	0.349290i	−0.0236750	+	0.0136688i	−0.511791	−	0.859110i	$-0.671018\pi$
$653$	−0.604989	+	0.349290i	−0.0236750	+	0.0136688i	0.488116	+	0.872779i	$0.337684\pi$
$654$		0			0
$655$	24.4005	+	0.0111157i	0.953406	+	0.000434326i
$656$	−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	−0.0587281	−	0.998274i	$-0.518705\pi$
$659$	−19.1350	−	6.96458i	−0.745395	−	0.271301i	−0.686667	+	0.726973i	$0.740927\pi$
$660$		0			0
$661$	−6.03199	−	34.2091i	−0.234617	−	1.33058i	−0.843418	−	0.537258i	$-0.819460\pi$
$661$	−6.03199	−	34.2091i	−0.234617	−	1.33058i	0.608801	−	0.793323i	$-0.291651\pi$
$662$	−19.1019	−	52.4822i	−0.742418	−	2.03978i
$663$		0			0
$664$	−38.6547			−1.50009
$665$	0.336313	+	27.1236i	0.0130416	+	1.05181i
$666$		0			0
$667$	−4.82168	+	5.74626i	−0.186696	+	0.222496i
$668$	−18.0113	−	49.4857i	−0.696879	−	1.91466i
$669$		0			0
$670$	22.3415	−	18.7294i	0.863128	−	0.723581i
$671$	−10.2516	−	3.73126i	−0.395757	−	0.144044i
$672$		0			0
$673$	22.1298	+	12.7767i	0.853043	+	0.492505i	0.861676	−	0.507458i	$-0.169415\pi$
$673$	22.1298	+	12.7767i	0.853043	+	0.492505i	−0.00863342	+	0.999963i	$0.502748\pi$
$674$	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	$-0.927640\pi$
$677$	−32.9463	+	19.0216i	−1.26623	+	0.731058i	−0.291957	+	0.956431i	$0.594307\pi$
$678$		0			0
$679$	−2.70408	+	15.3356i	−0.103773	+	0.588527i
$680$	17.5669	−	30.3947i	0.673658	−	1.16558i
$681$		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	0.824281	−	0.566181i	$-0.191580\pi$
$691$	−2.05528	−	3.55984i	−0.0781864	−	0.135423i	−0.902467	+	0.430758i	$0.858246\pi$
$692$	22.0504	+	12.7308i	0.838231	+	0.483953i
$693$		0			0
$694$	42.3949	−	35.5736i	1.60929	−	1.35035i
$695$	−16.4874	+	5.99242i	−0.625403	+	0.227305i
$696$		0			0
$697$	4.99141	−	13.7138i	0.189063	−	0.519447i
$698$	66.2277	+	11.6777i	2.50676	+	0.442009i
$699$		0			0
$700$	62.9180	−	36.2493i	2.37808	−	1.37010i
$701$	3.40592	+	2.85791i	0.128640	+	0.107942i	0.704838	−	0.709369i	$-0.251020\pi$
$701$	3.40592	+	2.85791i	0.128640	+	0.107942i	−0.576198	+	0.817310i	$0.695464\pi$
$702$		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	0.400554	−	0.916273i	$-0.368818\pi$
$709$	3.15334	+	1.14772i	0.118426	+	0.0431036i	−0.282127	+	0.959377i	$0.591040\pi$
$710$	45.9620	+	8.12593i	1.72492	+	0.304961i
$711$		0			0
$712$	−85.5531	−	101.958i	−3.20624	−	3.82104i
$713$	−4.72019	−	5.62530i	−0.176772	−	0.210669i
$714$		0			0
$715$	0.212203	+	0.0375167i	0.00793593	+	0.00140305i
$716$	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	−0.939801	−	0.341721i	$-0.888990\pi$
$719$	−38.6145	+	14.0545i	−1.44008	+	0.524145i	−0.500275	+	0.865866i	$0.666768\pi$
$720$		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
$725$	−7.35886	−	12.7728i	−0.273301	−	0.474369i
$726$		0			0
$727$	−11.8832	−	2.09533i	−0.440723	−	0.0777114i	−0.0511164	−	0.998693i	$-0.516278\pi$
$727$	−11.8832	−	2.09533i	−0.440723	−	0.0777114i	−0.389607	+	0.920981i	$0.627389\pi$
$728$	−0.333261	+	0.915628i	−0.0123515	+	0.0339354i
$729$		0			0
$730$	−23.9834	+	8.71687i	−0.887665	+	0.322626i
$731$	7.13928	−	5.99056i	0.264056	−	0.221569i
$732$		0			0
$733$	−11.8082	−	6.81748i	−0.436147	−	0.251809i	0.265815	−	0.964024i	$-0.414359\pi$
$733$	−11.8082	−	6.81748i	−0.436147	−	0.251809i	−0.701962	+	0.712215i	$0.747692\pi$
$734$	−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	−0.0812609	−	0.996693i	$-0.525895\pi$
$739$	−29.2757	−	24.5652i	−1.07692	−	0.903645i	−0.995662	+	0.0930476i	$0.970339\pi$
$740$	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	$-0.813312\pi$
$743$	−3.90379	+	4.65236i	−0.143216	+	0.170679i	0.689668	+	0.724126i	$0.257757\pi$
$744$		0			0
$745$	24.3252	−	42.0882i	0.891206	−	1.54199i
$746$	−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	−0.639925	−	0.768437i	$-0.721035\pi$
$751$	0.156655	−	0.131449i	0.00571641	−	0.00479664i	0.645641	+	0.763641i	$0.276590\pi$
$752$	−122.725	−	70.8551i	−4.47531	−	2.58382i
$753$		0			0
$754$	0.301393	+	0.109698i	0.0109761	+	0.00399497i
$755$	16.6032	−	13.9188i	0.604252	−	0.506558i
$756$		0			0
$757$	−6.28814	−	17.2765i	−0.228546	−	0.627926i	0.771418	−	0.636328i	$-0.219548\pi$
$757$	−6.28814	−	17.2765i	−0.228546	−	0.627926i	−0.999965	+	0.00840229i	$0.997325\pi$
$758$	0.269652	−	0.321359i	0.00979421	−	0.0116723i
$759$		0			0
$760$	72.4569	−	43.0395i	2.62829	−	1.56121i
$761$	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	−0.293807	−	0.955865i	$-0.594922\pi$
$769$	16.5419	−	13.8803i	0.596516	−	0.500537i	0.890324	+	0.455328i	$0.150478\pi$
$770$	39.7920	+	0.0181273i	1.43400	+	0.000653264i
$771$		0			0
$772$	−112.218	+	64.7893i	−4.03883	+	2.33182i
$773$	−12.6854	+	34.8529i	−0.456263	+	1.25357i	0.471983	+	0.881607i	$0.343538\pi$
$773$	−12.6854	+	34.8529i	−0.456263	+	1.25357i	−0.928247	+	0.371965i	$0.878684\pi$
$774$		0			0
$775$	13.5649	−	4.92323i	0.487266	−	0.176848i
$776$	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
$785$	−14.2942	+	8.24408i	−0.510182	+	0.294244i
$786$		0			0
$787$	−1.73479	−	1.00158i	−0.0618385	−	0.0357025i	0.468762	−	0.883325i	$-0.344700\pi$
$787$	−1.73479	−	1.00158i	−0.0618385	−	0.0357025i	−0.530600	+	0.847622i	$0.678034\pi$
$788$	13.9978	+	16.6819i	0.498652	+	0.594270i
$789$		0			0
$790$	23.8264	+	65.5554i	0.847705	+	2.33236i
$791$	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
$800$	−73.9203	−	42.7678i	−2.61348	−	1.51207i
$801$		0			0
$802$	−8.79877	+	1.55146i	−0.310695	+	0.0547840i
$803$	−9.95584	−	1.75548i	−0.351334	−	0.0619496i
$804$		0			0
$805$	2.75657	−	15.5917i	0.0971562	−	0.549536i
$806$	−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	−0.989969	−	0.141286i	$-0.954876\pi$
$809$	−10.5986	+	18.3573i	−0.372627	+	0.645410i	0.617341	+	0.786695i	$0.288210\pi$
$810$		0			0
$811$	8.40909	+	3.06066i	0.295283	+	0.107474i	0.485414	−	0.874284i	$-0.338669\pi$
$811$	8.40909	+	3.06066i	0.295283	+	0.107474i	−0.190131	+	0.981759i	$0.560891\pi$
$812$	42.1652	+	7.43486i	1.47971	+	0.260912i
$813$		0			0
$814$	1.36450	−	0.496639i	0.0478258	−	0.0174072i
$815$	−10.7980	+	1.89890i	−0.378237	+	0.0665157i
$816$		0			0
$817$	21.9812	−	4.16789i	0.769025	−	0.145816i
$818$		−	20.1240i		−	0.703621i
$819$		0			0
$820$	−88.1135	−	32.1161i	−3.07706	−	1.12154i
$821$	0.600509	+	3.40566i	0.0209579	+	0.118858i	0.993492	−	0.113903i	$-0.0363352\pi$
$821$	0.600509	+	3.40566i	0.0209579	+	0.118858i	−0.972534	+	0.232761i	$0.925224\pi$
$822$		0			0
$823$	−6.20022	+	17.0350i	−0.216126	+	0.593801i	−0.999619	−	0.0275992i	$-0.991214\pi$
$823$	−6.20022	+	17.0350i	−0.216126	+	0.593801i	0.783493	+	0.621401i	$0.213436\pi$
$824$	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	$-0.0515059\pi$
$827$	18.8909	+	22.5132i	0.656899	+	0.782862i	−0.330038	+	0.943968i	$0.607061\pi$
$828$		0			0
$829$	−1.73389	−	3.00318i	−0.0602204	−	0.104305i	0.834343	−	0.551245i	$-0.185847\pi$
$829$	−1.73389	−	3.00318i	−0.0602204	−	0.104305i	−0.894564	+	0.446940i	$0.852514\pi$
$830$	−13.4181	−	23.2653i	−0.465748	−	0.807549i
$831$		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	−0.894438	−	0.447192i	$-0.852424\pi$
$839$	−37.4283	+	13.6228i	−1.29217	+	0.470311i	−0.397730	+	0.917503i	$0.630202\pi$
$840$		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
$845$	29.0652	+	0.0132407i	0.999874	+	0.000455495i
$846$		0			0
$847$	−12.8598	−	7.42463i	−0.441869	−	0.255113i
$848$	−63.3156	+	36.5553i	−2.17427	+	1.25531i
$849$		0			0
$850$	24.3917	+	0.0222234i	0.836629	+	0.000762257i
$851$	−0.100332	−	0.569014i	−0.00343935	−	0.0195055i
$852$		0			0
$853$	10.2917	−	12.2652i	0.352383	−	0.419953i	−0.560513	−	0.828145i	$-0.689396\pi$
$853$	10.2917	−	12.2652i	0.352383	−	0.419953i	0.912896	+	0.408192i	$0.133841\pi$
$854$	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	$-0.867266\pi$
$857$	−10.4417	+	12.4439i	−0.356680	+	0.425075i	0.557630	+	0.830090i	$0.311711\pi$
$858$		0			0
$859$	9.76555	+	55.3832i	0.333196	+	1.88965i	0.444360	+	0.895849i	$0.353431\pi$
$859$	9.76555	+	55.3832i	0.333196	+	1.88965i	−0.111163	+	0.993802i	$0.535458\pi$
$860$	−38.4759	−	45.8962i	−1.31202	−	1.56505i
$861$		0			0
$862$	−24.1734	+	13.9565i	−0.823351	+	0.475362i
$863$	12.2619	+	7.07944i	0.417402	+	0.240987i	0.693965	−	0.720009i	$-0.255862\pi$
$863$	12.2619	+	7.07944i	0.417402	+	0.240987i	−0.276563	+	0.960996i	$0.589196\pi$
$864$		0			0
$865$	−0.00497030	+	10.9105i	−0.000168995	+	0.370967i
$866$	−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	$-0.0766059\pi$
$877$	2.19162	+	6.02143i	0.0740058	+	0.203329i	−0.897174	+	0.441677i	$0.854384\pi$
$878$	50.6072	−	8.92342i	1.70791	−	0.301151i
$879$		0			0
$880$	−34.0166	−	58.9804i	−1.14670	−	1.98823i
$881$	−5.80585	−	10.0560i	−0.195604	−	0.338796i	0.751494	−	0.659740i	$-0.229333\pi$
$881$	−5.80585	−	10.0560i	−0.195604	−	0.338796i	−0.947098	+	0.320943i	$0.896000\pi$
$882$		0			0
$883$	−16.9859	−	20.2430i	−0.571620	−	0.681231i	0.400342	−	0.916366i	$-0.368891\pi$
$883$	−16.9859	−	20.2430i	−0.571620	−	0.681231i	−0.971963	+	0.235135i	$0.924447\pi$
$884$	−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	−0.485149	−	0.874431i	$-0.661235\pi$
$887$	13.3596	−	36.7051i	0.448570	−	1.23244i	0.933720	−	0.358005i	$-0.116543\pi$
$888$		0			0
$889$	−0.357147	−	2.02548i	−0.0119783	−	0.0679325i
$890$	31.6682	−	86.8846i	1.06152	−	2.91238i
$891$		0			0
$892$		−	50.1559i		−	1.67934i
$893$	42.1193	+	23.6010i	1.40947	+	0.789777i
$894$		0			0
$895$	9.25011	+	52.6001i	0.309197	+	1.75823i
$896$	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
$905$	0.999508	−	5.65343i	0.0332248	−	0.187926i
$906$		0			0
$907$	56.4681	+	9.95684i	1.87499	+	0.330612i	0.990672	−	0.136270i	$-0.0435115\pi$
$907$	56.4681	+	9.95684i	1.87499	+	0.330612i	0.884320	+	0.466882i	$0.154623\pi$
$908$	−120.587	+	21.2627i	−4.00182	+	0.705628i
$909$		0			0
$910$	−0.666777	+	0.117258i	−0.0221034	+	0.00388705i
$911$	−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	0.924377	+	0.381480i	$0.124585\pi$
$919$	24.0265	+	41.6150i	0.792560	+	1.37275i	−0.131817	+	0.991274i	$0.542081\pi$
$920$	−46.2336	+	16.8038i	−1.52428	+	0.554006i
$921$		0			0
$922$	−42.4191	−	50.5531i	−1.39700	−	1.66488i
$923$	−0.272449	−	0.157298i	−0.00896776	−	0.00517754i
$924$		0			0
$925$	1.11802	+	0.198187i	0.0367602	+	0.00651635i
$926$	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	0.739455	−	0.673205i	$-0.235083\pi$
$929$	6.24472	+	5.23994i	0.204883	+	0.171917i	−0.534573	+	0.845122i	$0.679528\pi$
$930$		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
$935$	8.36628	+	4.83536i	0.273607	+	0.158133i
$936$		0			0
$937$	−12.0229	+	33.0325i	−0.392770	+	1.07913i	0.572962	+	0.819582i	$0.305794\pi$
$937$	−12.0229	+	33.0325i	−0.392770	+	1.07913i	−0.965731	+	0.259544i	$0.916428\pi$
$938$	−31.4237	+	18.1425i	−1.02602	+	0.592372i
$939$		0			0
$940$	0.0588775	−	129.244i	0.00192037	−	4.21548i
$941$	11.4837	−	9.63598i	0.374358	−	0.314124i	−0.436124	−	0.899886i	$-0.643649\pi$
$941$	11.4837	−	9.63598i	0.374358	−	0.314124i	0.810483	+	0.585762i	$0.199205\pi$
$942$		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	0.976636	+	0.214901i	$0.0689430\pi$
$947$	11.2823	+	30.9978i	0.366625	+	1.00729i	−0.610011	+	0.792393i	$0.708835\pi$
$948$		0			0
$949$	0.171999			0.00558331
$950$	51.0561	+	28.6698i	1.65648	+	0.930170i
$951$		0			0
$952$	−28.0855	+	33.4710i	−0.910256	+	1.08480i
$953$	9.90142	+	27.2039i	0.320739	+	0.881222i	0.990360	+	0.138519i	$0.0442342\pi$
$953$	9.90142	+	27.2039i	0.320739	+	0.881222i	−0.669621	+	0.742703i	$0.733544\pi$
$954$		0			0
$955$	−15.9148	+	13.3418i	−0.514991	+	0.431729i
$956$	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
$965$	−48.0736	−	27.7845i	−1.54755	−	0.894416i
$966$		0			0
$967$	−21.4472	+	25.5597i	−0.689694	+	0.821945i	−0.991319	−	0.131481i	$-0.958027\pi$
$967$	−21.4472	+	25.5597i	−0.689694	+	0.821945i	0.301625	+	0.953427i	$0.402471\pi$
$968$			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	0.722629	−	0.691236i	$-0.242934\pi$
$971$	5.21562	+	4.37643i	0.167377	+	0.140446i	−0.555252	+	0.831682i	$0.687378\pi$
$972$		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	$-0.333674\pi$
$977$	−0.0579657	−	0.0334665i	−0.00185449	−	0.00107069i	−0.500927	+	0.865490i	$0.667007\pi$
$978$		0			0
$979$	28.0644	−	23.5489i	0.896944	−	0.752625i
$980$	−8.17304	+	2.97053i	−0.261078	+	0.0948901i
$981$		0			0
$982$	28.8617	−	79.2969i	0.921014	−	2.53046i
$983$	49.5418	+	8.73556i	1.58014	+	0.278621i	0.893733	−	0.448599i	$-0.148077\pi$
$983$	49.5418	+	8.73556i	1.58014	+	0.278621i	0.686405	+	0.727220i	$0.259188\pi$
$984$		0			0
$985$	−3.19555	+	8.76726i	−0.101819	+	0.279348i
$986$	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	−0.404644	−	0.914475i	$-0.632604\pi$
$991$	−3.99186	+	1.45292i	−0.126806	+	0.0461534i	0.277838	+	0.960628i	$0.410382\pi$
$992$	48.5468	−	8.56011i	1.54136	−	0.271784i
$993$		0			0
$994$	−54.5885	−	19.8686i	−1.73144	−	0.630194i
$995$	−8.71497	+	49.2937i	−0.276283	+	1.56272i
$996$		0			0
$997$	29.5816	+	35.2540i	0.936858	+	1.11650i	0.993004	+	0.118082i	$0.0376744\pi$
$997$	29.5816	+	35.2540i	0.936858	+	1.11650i	−0.0561457	+	0.998423i	$0.517881\pi$
$998$	−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.244.1		48
3.2	odd	2		95.2.p.a.54.8	yes	48
5.4	even	2	inner	855.2.da.b.244.8		48
15.2	even	4		475.2.l.f.301.8		48
15.8	even	4		475.2.l.f.301.1		48
15.14	odd	2		95.2.p.a.54.1	yes	48
19.6	even	9	inner	855.2.da.b.424.8		48
57.5	odd	18		1805.2.b.k.1084.1		24
57.14	even	18		1805.2.b.l.1084.24		24
57.44	odd	18		95.2.p.a.44.1	✓	48
95.44	even	18	inner	855.2.da.b.424.1		48
285.14	even	18		1805.2.b.l.1084.1		24
285.44	odd	18		95.2.p.a.44.8	yes	48
285.62	even	36		9025.2.a.cu.1.24		24
285.119	odd	18		1805.2.b.k.1084.24		24
285.128	odd	36		9025.2.a.ct.1.24		24
285.158	even	36		475.2.l.f.101.1		48
285.233	even	36		9025.2.a.cu.1.1		24
285.242	odd	36		9025.2.a.ct.1.1		24
285.272	even	36		475.2.l.f.101.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.44.1	✓	48	57.44	odd	18
95.2.p.a.44.8	yes	48	285.44	odd	18
95.2.p.a.54.1	yes	48	15.14	odd	2
95.2.p.a.54.8	yes	48	3.2	odd	2
475.2.l.f.101.1		48	285.158	even	36
475.2.l.f.101.8		48	285.272	even	36
475.2.l.f.301.1		48	15.8	even	4
475.2.l.f.301.8		48	15.2	even	4
855.2.da.b.244.1		48	1.1	even	1	trivial
855.2.da.b.244.8		48	5.4	even	2	inner
855.2.da.b.424.1		48	95.44	even	18	inner
855.2.da.b.424.8		48	19.6	even	9	inner
1805.2.b.k.1084.1		24	57.5	odd	18
1805.2.b.k.1084.24		24	285.119	odd	18
1805.2.b.l.1084.1		24	285.14	even	18
1805.2.b.l.1084.24		24	57.14	even	18
9025.2.a.ct.1.1		24	285.242	odd	36
9025.2.a.ct.1.24		24	285.128	odd	36
9025.2.a.cu.1.1		24	285.233	even	36
9025.2.a.cu.1.24		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)

\(f(q)\)	\(=\)	\(q+(-1.72697 + 2.05812i) q^{2} +(-0.906145 - 5.13900i) q^{4} +(1.71358 - 1.43654i) q^{5} +(-2.41018 + 1.39152i) q^{7} +(7.48810 + 4.32326i) q^{8} +O(q^{10})\)	\(q+(-1.72697 + 2.05812i) q^{2} +(-0.906145 - 5.13900i) q^{4} +(1.71358 - 1.43654i) q^{5} +(-2.41018 + 1.39152i) q^{7} +(7.48810 + 4.32326i) q^{8} +(-0.00273678 + 6.00761i) q^{10} +(-1.19000 + 2.06113i) q^{11} +(0.0138492 - 0.0380504i) q^{13} +(1.29839 - 7.36354i) q^{14} +(-12.0223 + 4.37577i) q^{16} +(1.16714 - 1.39094i) q^{17} +(4.07652 - 1.54336i) q^{19} +(-8.93512 - 7.50439i) q^{20} +(-2.18698 - 6.00867i) q^{22} +(-2.50568 + 0.441819i) q^{23} +(0.872727 - 4.92325i) q^{25} +(0.0543952 + 0.0942153i) q^{26} +(9.33498 + 11.1250i) q^{28} +(2.25845 - 1.89507i) q^{29} +(1.44307 + 2.49947i) q^{31} +(5.84176 - 16.0501i) q^{32} +(0.847116 + 4.80423i) q^{34} +(-2.13107 + 5.84678i) q^{35} +0.227089i q^{37} +(-3.86361 + 11.0553i) q^{38} +(19.0420 - 3.34867i) q^{40} +(7.55269 - 2.74896i) q^{41} +(5.05471 + 0.891282i) q^{43} +(11.6705 + 4.24771i) q^{44} +(3.41791 - 5.92000i) q^{46} +(7.11977 + 8.48501i) q^{47} +(0.372635 - 0.645423i) q^{49} +(8.62546 + 10.2985i) q^{50} +(-0.208091 - 0.0366920i) q^{52} +(5.62767 - 0.992310i) q^{53} +(0.921737 + 5.24139i) q^{55} -24.0635 q^{56} +7.92088i q^{58} +(8.89878 + 7.46696i) q^{59} +(0.795974 + 4.51419i) q^{61} +(-7.63635 - 1.34649i) q^{62} +(10.1506 + 17.5814i) q^{64} +(-0.0309291 - 0.0850975i) q^{65} +(-3.11931 - 3.71745i) q^{67} +(-8.20566 - 4.73754i) q^{68} +(-8.35309 - 14.4832i) q^{70} +(1.34912 - 7.65124i) q^{71} +(1.45279 + 3.99151i) q^{73} +(-0.467377 - 0.392176i) q^{74} +(-11.6252 - 19.5508i) q^{76} -6.62359i q^{77} +(10.9102 - 3.97100i) q^{79} +(-14.3153 + 24.7688i) q^{80} +(-7.38558 + 20.2917i) q^{82} +(-3.87161 + 2.23528i) q^{83} +(0.00184961 - 4.06014i) q^{85} +(-10.5637 + 8.86399i) q^{86} +(-17.8216 + 10.2893i) q^{88} +(-14.4648 - 5.26476i) q^{89} +(0.0195687 + 0.110980i) q^{91} +(4.54102 + 12.4764i) q^{92} -29.7588 q^{94} +(4.76837 - 8.50074i) q^{95} +(3.59666 - 4.28633i) q^{97} +(0.684829 + 1.88155i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 18 q^{4} + 6 q^{5}+O(q^{10}) \) 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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