LMFDB - Embedded newform 432.2.u.c.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(49,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("432.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.u (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			49.1
Root			$0.500000 - 0.258654i$ of defining polynomial
Character	$\chi$	$=$	432.49
Dual form			432.2.u.c.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.159815 + 1.72466i) q^{3} +(-2.08159 + 0.757639i) q^{5} +(0.229151 + 1.29958i) q^{7} +(-2.94892 - 0.551252i) q^{9} +O(q^{10})$	\(q+(-0.159815 + 1.72466i) q^{3} +(-2.08159 + 0.757639i) q^{5} +(0.229151 + 1.29958i) q^{7} +(-2.94892 - 0.551252i) q^{9} +(-4.90067 - 1.78370i) q^{11} +(-0.0138336 - 0.0116078i) q^{13} +(-0.974001 - 3.71113i) q^{15} +(1.56640 - 2.71308i) q^{17} +(0.208676 + 0.361438i) q^{19} +(-2.27796 + 0.187516i) q^{21} +(0.179619 - 1.01867i) q^{23} +(-0.0712019 + 0.0597455i) q^{25} +(1.42200 - 4.99779i) q^{27} +(-5.98068 + 5.01839i) q^{29} +(-0.647649 + 3.67300i) q^{31} +(3.85948 - 8.16694i) q^{33} +(-1.46161 - 2.53159i) q^{35} +(-2.21238 + 3.83195i) q^{37} +(0.0222303 - 0.0220032i) q^{39} +(-2.81517 - 2.36221i) q^{41} +(-7.80685 - 2.84146i) q^{43} +(6.55610 - 1.08673i) q^{45} +(1.23254 + 6.99008i) q^{47} +(4.94145 - 1.79854i) q^{49} +(4.42881 + 3.13510i) q^{51} -1.30057 q^{53} +11.5526 q^{55} +(-0.656707 + 0.302133i) q^{57} +(-3.47856 + 1.26609i) q^{59} +(1.20064 + 6.80919i) q^{61} +(0.0406486 - 3.95868i) q^{63} +(0.0375905 + 0.0136818i) q^{65} +(8.44702 + 7.08789i) q^{67} +(1.72816 + 0.472581i) q^{69} +(-3.04214 + 5.26914i) q^{71} +(0.273486 + 0.473692i) q^{73} +(-0.0916617 - 0.132347i) q^{75} +(1.19507 - 6.77756i) q^{77} +(-0.374706 + 0.314416i) q^{79} +(8.39224 + 3.25120i) q^{81} +(-3.53428 + 2.96561i) q^{83} +(-1.20507 + 6.83430i) q^{85} +(-7.69922 - 11.1167i) q^{87} +(1.68653 + 2.92116i) q^{89} +(0.0119153 - 0.0206379i) q^{91} +(-6.23118 - 1.70398i) q^{93} +(-0.708218 - 0.594266i) q^{95} +(-9.34182 - 3.40014i) q^{97} +(13.4684 + 7.96149i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} - 3 q^{5} + 6 q^{7}+O(q^{10}) $ 12 * q + 6 * q^3 - 3 * q^5 + 6 * q^7	$ 12 q + 6 q^{3} - 3 q^{5} + 6 q^{7} - 3 q^{11} - 6 q^{13} - 9 q^{15} + 9 q^{17} + 3 q^{19} - 12 q^{21} + 12 q^{23} + 3 q^{25} + 9 q^{27} - 6 q^{29} - 3 q^{31} - 12 q^{35} - 3 q^{37} - 33 q^{39} + 15 q^{41} - 3 q^{43} - 9 q^{45} + 15 q^{47} + 12 q^{49} + 18 q^{51} - 18 q^{53} + 12 q^{55} - 3 q^{57} + 12 q^{59} + 12 q^{61} - 9 q^{63} + 3 q^{65} + 15 q^{67} + 9 q^{69} - 27 q^{71} + 6 q^{73} - 39 q^{75} + 15 q^{77} + 42 q^{79} + 36 q^{81} - 39 q^{83} - 27 q^{85} - 9 q^{87} + 9 q^{89} - 6 q^{91} - 39 q^{93} + 33 q^{95} + 3 q^{97} + 27 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 - 3 * q^5 + 6 * q^7 - 3 * q^11 - 6 * q^13 - 9 * q^15 + 9 * q^17 + 3 * q^19 - 12 * q^21 + 12 * q^23 + 3 * q^25 + 9 * q^27 - 6 * q^29 - 3 * q^31 - 12 * q^35 - 3 * q^37 - 33 * q^39 + 15 * q^41 - 3 * q^43 - 9 * q^45 + 15 * q^47 + 12 * q^49 + 18 * q^51 - 18 * q^53 + 12 * q^55 - 3 * q^57 + 12 * q^59 + 12 * q^61 - 9 * q^63 + 3 * q^65 + 15 * q^67 + 9 * q^69 - 27 * q^71 + 6 * q^73 - 39 * q^75 + 15 * q^77 + 42 * q^79 + 36 * q^81 - 39 * q^83 - 27 * q^85 - 9 * q^87 + 9 * q^89 - 6 * q^91 - 39 * q^93 + 33 * q^95 + 3 * q^97 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−0.159815	+	1.72466i	−0.0922690	+	0.995734i
$3$	−0.159815	+	1.72466i	−0.0922690	+	0.995734i
$4$		0			0
$5$	−2.08159	+	0.757639i	−0.930917	+	0.338826i	−0.762573	−	0.646902i	$-0.776064\pi$
$5$	−2.08159	+	0.757639i	−0.930917	+	0.338826i	−0.168344	+	0.985728i	$0.553842\pi$
$6$		0			0
$7$	0.229151	+	1.29958i	0.0866110	+	0.491195i	0.996997	+	0.0774361i	$0.0246734\pi$
$7$	0.229151	+	1.29958i	0.0866110	+	0.491195i	−0.910386	+	0.413759i	$0.864216\pi$
$8$		0			0
$9$	−2.94892	−	0.551252i	−0.982973	−	0.183751i
$10$		0			0
$11$	−4.90067	−	1.78370i	−1.47761	−	0.537805i	−0.527454	−	0.849584i	$-0.676853\pi$
$11$	−4.90067	−	1.78370i	−1.47761	−	0.537805i	−0.950155	+	0.311778i	$0.899075\pi$
$12$		0			0
$13$	−0.0138336	−	0.0116078i	−0.00383676	−	0.00321942i	0.640867	−	0.767652i	$-0.278575\pi$
$13$	−0.0138336	−	0.0116078i	−0.00383676	−	0.00321942i	−0.644704	+	0.764432i	$0.723019\pi$
$14$		0			0
$15$	−0.974001	−	3.71113i	−0.251486	−	0.958209i
$16$		0			0
$17$	1.56640	−	2.71308i	0.379907	−	0.658019i	−0.611141	−	0.791522i	$-0.709289\pi$
$17$	1.56640	−	2.71308i	0.379907	−	0.658019i	0.991048	+	0.133503i	$0.0426226\pi$
$18$		0			0
$19$	0.208676	+	0.361438i	0.0478736	+	0.0829195i	0.888969	−	0.457967i	$-0.151422\pi$
$19$	0.208676	+	0.361438i	0.0478736	+	0.0829195i	−0.841096	+	0.540886i	$0.818089\pi$
$20$		0			0
$21$	−2.27796	+	0.187516i	−0.497092	+	0.0409194i
$22$		0			0
$23$	0.179619	−	1.01867i	0.0374532	−	0.212408i	−0.960338	−	0.278839i	$-0.910050\pi$
$23$	0.179619	−	1.01867i	0.0374532	−	0.212408i	0.997791	+	0.0664316i	$0.0211614\pi$
$24$		0			0
$25$	−0.0712019	+	0.0597455i	−0.0142404	+	0.0119491i
$26$		0			0
$27$	1.42200	−	4.99779i	0.273665	−	0.961825i
$28$		0			0
$29$	−5.98068	+	5.01839i	−1.11058	+	0.931891i	−0.998091	−	0.0617615i	$-0.980328\pi$
$29$	−5.98068	+	5.01839i	−1.11058	+	0.931891i	−0.112493	+	0.993652i	$0.535884\pi$
$30$		0			0
$31$	−0.647649	+	3.67300i	−0.116321	+	0.659691i	0.869766	+	0.493464i	$0.164270\pi$
$31$	−0.647649	+	3.67300i	−0.116321	+	0.659691i	−0.986088	+	0.166227i	$0.946842\pi$
$32$		0			0
$33$	3.85948	−	8.16694i	0.671849	−	1.42168i
$34$		0			0
$35$	−1.46161	−	2.53159i	−0.247058	−	0.427916i
$36$		0			0
$37$	−2.21238	+	3.83195i	−0.363713	+	0.629969i	−0.988569	−	0.150771i	$-0.951824\pi$
$37$	−2.21238	+	3.83195i	−0.363713	+	0.629969i	0.624856	+	0.780740i	$0.285158\pi$
$38$		0			0
$39$	0.0222303	−	0.0220032i	0.00355970	−	0.00352334i
$40$		0			0
$41$	−2.81517	−	2.36221i	−0.439655	−	0.368915i	0.395925	−	0.918283i	$-0.370424\pi$
$41$	−2.81517	−	2.36221i	−0.439655	−	0.368915i	−0.835580	+	0.549368i	$0.814868\pi$
$42$		0			0
$43$	−7.80685	−	2.84146i	−1.19053	−	0.433319i	−0.330622	−	0.943763i	$-0.607259\pi$
$43$	−7.80685	−	2.84146i	−1.19053	−	0.433319i	−0.859911	+	0.510445i	$0.829481\pi$
$44$		0			0
$45$	6.55610	−	1.08673i	0.977326	−	0.162000i
$46$		0			0
$47$	1.23254	+	6.99008i	0.179784	+	1.01961i	0.932475	+	0.361234i	$0.117644\pi$
$47$	1.23254	+	6.99008i	0.179784	+	1.01961i	−0.752691	+	0.658374i	$0.771245\pi$
$48$		0			0
$49$	4.94145	−	1.79854i	0.705921	−	0.256934i
$50$		0			0
$51$	4.42881	+	3.13510i	0.620158	+	0.439001i
$52$		0			0
$53$	−1.30057			−0.178648			−0.0893238	−	0.996003i	$-0.528471\pi$
$53$	−1.30057			−0.178648			−0.0893238	+	0.996003i	$0.528471\pi$
$54$		0			0
$55$	11.5526			1.55775
$56$		0			0
$57$	−0.656707	+	0.302133i	−0.0869830	+	0.0400185i
$58$		0			0
$59$	−3.47856	+	1.26609i	−0.452871	+	0.164831i	−0.558377	−	0.829587i	$-0.688576\pi$
$59$	−3.47856	+	1.26609i	−0.452871	+	0.164831i	0.105507	+	0.994419i	$0.466354\pi$
$60$		0			0
$61$	1.20064	+	6.80919i	0.153727	+	0.871828i	0.959941	+	0.280204i	$0.0904020\pi$
$61$	1.20064	+	6.80919i	0.153727	+	0.871828i	−0.806214	+	0.591624i	$0.798487\pi$
$62$		0			0
$63$	0.0406486	−	3.95868i	0.00512125	−	0.498747i
$64$		0			0
$65$	0.0375905	+	0.0136818i	0.00466253	+	0.00169702i
$66$		0			0
$67$	8.44702	+	7.08789i	1.03197	+	0.865923i	0.991084	−	0.133241i	$-0.0425383\pi$
$67$	8.44702	+	7.08789i	1.03197	+	0.865923i	0.0408835	+	0.999164i	$0.486983\pi$
$68$		0			0
$69$	1.72816	+	0.472581i	0.208046	+	0.0568921i
$70$		0			0
$71$	−3.04214	+	5.26914i	−0.361035	+	0.625332i	−0.988132	−	0.153610i	$-0.950910\pi$
$71$	−3.04214	+	5.26914i	−0.361035	+	0.625332i	0.627096	+	0.778942i	$0.284243\pi$
$72$		0			0
$73$	0.273486	+	0.473692i	0.0320092	+	0.0554415i	0.881586	−	0.472023i	$-0.156476\pi$
$73$	0.273486	+	0.473692i	0.0320092	+	0.0554415i	−0.849577	+	0.527465i	$0.823143\pi$
$74$		0			0
$75$	−0.0916617	−	0.132347i	−0.0105842	−	0.0152822i
$76$		0			0
$77$	1.19507	−	6.77756i	0.136190	−	0.772374i
$78$		0			0
$79$	−0.374706	+	0.314416i	−0.0421577	+	0.0353745i	−0.663623	−	0.748067i	$-0.730982\pi$
$79$	−0.374706	+	0.314416i	−0.0421577	+	0.0353745i	0.621465	+	0.783442i	$0.286538\pi$
$80$		0			0
$81$	8.39224	+	3.25120i	0.932471	+	0.361244i
$82$		0			0
$83$	−3.53428	+	2.96561i	−0.387937	+	0.325518i	−0.815809	−	0.578321i	$-0.803708\pi$
$83$	−3.53428	+	2.96561i	−0.387937	+	0.325518i	0.427872	+	0.903839i	$0.359263\pi$
$84$		0			0
$85$	−1.20507	+	6.83430i	−0.130708	+	0.741284i
$86$		0			0
$87$	−7.69922	−	11.1167i	−0.825443	−	1.19183i
$88$		0			0
$89$	1.68653	+	2.92116i	0.178772	+	0.309642i	0.941460	−	0.337124i	$-0.109454\pi$
$89$	1.68653	+	2.92116i	0.178772	+	0.309642i	−0.762688	+	0.646766i	$0.776121\pi$
$90$		0			0
$91$	0.0119153	−	0.0206379i	0.00124906	−	0.00216344i
$92$		0			0
$93$	−6.23118	−	1.70398i	−0.646144	−	0.176694i
$94$		0			0
$95$	−0.708218	−	0.594266i	−0.0726617	−	0.0609704i
$96$		0			0
$97$	−9.34182	−	3.40014i	−0.948518	−	0.345232i	−0.178994	−	0.983850i	$-0.557284\pi$
$97$	−9.34182	−	3.40014i	−0.948518	−	0.345232i	−0.769524	+	0.638618i	$0.779507\pi$
$98$		0			0
$99$	13.4684	+	7.96149i	1.35363	+	0.800160i
$100$		0			0
$101$	2.39626	+	13.5898i	0.238436	+	1.35224i	0.835255	+	0.549863i	$0.185320\pi$
$101$	2.39626	+	13.5898i	0.238436	+	1.35224i	−0.596818	+	0.802377i	$0.703569\pi$
$102$		0			0
$103$	4.28981	−	1.56136i	0.422687	−	0.153846i	−0.121914	−	0.992541i	$-0.538903\pi$
$103$	4.28981	−	1.56136i	0.422687	−	0.153846i	0.544601	+	0.838695i	$0.316681\pi$
$104$		0			0
$105$	4.59972	−	2.11620i	0.448887	−	0.206520i
$106$		0			0
$107$	11.2965			1.09207			0.546035	−	0.837762i	$-0.316136\pi$
$107$	11.2965			1.09207			0.546035	+	0.837762i	$0.316136\pi$
$108$		0			0
$109$	14.5032			1.38915			0.694577	−	0.719419i	$-0.255592\pi$
$109$	14.5032			1.38915			0.694577	+	0.719419i	$0.255592\pi$
$110$		0			0
$111$	−6.25525	−	4.42801i	−0.593722	−	0.420288i
$112$		0			0
$113$	−11.8011	+	4.29523i	−1.11015	+	0.404062i	−0.831049	−	0.556200i	$-0.812259\pi$
$113$	−11.8011	+	4.29523i	−1.11015	+	0.404062i	−0.279102	+	0.960262i	$0.590037\pi$
$114$		0			0
$115$	0.397890	+	2.25655i	0.0371035	+	0.210424i
$116$		0			0
$117$	0.0343954	+	0.0418563i	0.00317986	+	0.00386961i
$118$		0			0
$119$	3.88481	+	1.41395i	0.356120	+	0.129617i
$120$		0			0
$121$	12.4085	+	10.4120i	1.12805	+	0.946544i
$122$		0			0
$123$	4.52391	−	4.47770i	0.407907	−	0.403740i
$124$		0			0
$125$	5.64092	−	9.77035i	0.504539	−	0.873887i
$126$		0			0
$127$	−4.19749	−	7.27027i	−0.372467	−	0.645132i	0.617477	−	0.786589i	$-0.288155\pi$
$127$	−4.19749	−	7.27027i	−0.372467	−	0.645132i	−0.989944	+	0.141456i	$0.954821\pi$
$128$		0			0
$129$	6.14821	−	13.0101i	0.541319	−	1.14547i
$130$		0			0
$131$	2.69761	−	15.2989i	0.235691	−	1.33667i	−0.605463	−	0.795874i	$-0.707012\pi$
$131$	2.69761	−	15.2989i	0.235691	−	1.33667i	0.841154	−	0.540796i	$-0.181877\pi$
$132$		0			0
$133$	−0.421899	+	0.354015i	−0.0365833	+	0.0306970i
$134$		0			0
$135$	0.826482	+	11.4807i	0.0711323	+	0.988105i
$136$		0			0
$137$	9.19820	−	7.71820i	0.785855	−	0.659411i	−0.158861	−	0.987301i	$-0.550782\pi$
$137$	9.19820	−	7.71820i	0.785855	−	0.659411i	0.944716	+	0.327890i	$0.106338\pi$
$138$		0			0
$139$	−1.06709	+	6.05176i	−0.0905093	+	0.513304i	0.905522	+	0.424299i	$0.139480\pi$
$139$	−1.06709	+	6.05176i	−0.0905093	+	0.513304i	−0.996031	+	0.0890042i	$0.971632\pi$
$140$		0			0
$141$	−12.2525	+	1.00860i	−1.03185	+	0.0849392i
$142$		0			0
$143$	0.0470893	+	0.0815610i	0.00393780	+	0.00682047i
$144$		0			0
$145$	8.64723	−	14.9774i	0.718113	−	1.24381i
$146$		0			0
$147$	2.31216	+	8.80976i	0.190704	+	0.726617i
$148$		0			0
$149$	0.676280	+	0.567466i	0.0554030	+	0.0464886i	0.670069	−	0.742299i	$-0.266265\pi$
$149$	0.676280	+	0.567466i	0.0554030	+	0.0464886i	−0.614666	+	0.788788i	$0.710709\pi$
$150$		0			0
$151$	7.72942	+	2.81328i	0.629011	+	0.228941i	0.636801	−	0.771028i	$-0.280257\pi$
$151$	7.72942	+	2.81328i	0.629011	+	0.228941i	−0.00778980	+	0.999970i	$0.502480\pi$
$152$		0			0
$153$	−6.11477	+	7.13717i	−0.494350	+	0.577006i
$154$		0			0
$155$	−1.43466	−	8.13639i	−0.115235	−	0.653530i
$156$		0			0
$157$	−11.8024	+	4.29571i	−0.941932	+	0.342835i	−0.766928	−	0.641733i	$-0.778216\pi$
$157$	−11.8024	+	4.29571i	−0.941932	+	0.342835i	−0.175003	+	0.984568i	$0.555994\pi$
$158$		0			0
$159$	0.207851	−	2.24305i	0.0164836	−	0.177886i
$160$		0			0
$161$	1.36501			0.107578
$162$		0			0
$163$	−3.31466			−0.259624			−0.129812	−	0.991539i	$-0.541437\pi$
$163$	−3.31466			−0.259624			−0.129812	+	0.991539i	$0.541437\pi$
$164$		0			0
$165$	−1.84628	+	19.9244i	−0.143732	+	1.55111i
$166$		0			0
$167$	−19.3229	+	7.03295i	−1.49525	+	0.544226i	−0.954826	−	0.297167i	$-0.903958\pi$
$167$	−19.3229	+	7.03295i	−1.49525	+	0.544226i	−0.540424	+	0.841393i	$0.681736\pi$
$168$		0			0
$169$	−2.25737	−	12.8022i	−0.173644	−	0.984783i
$170$		0			0
$171$	−0.416126	−	1.18088i	−0.0318219	−	0.0903044i
$172$		0			0
$173$	−13.1870	−	4.79966i	−1.00259	−	0.364911i	−0.212005	−	0.977269i	$-0.567999\pi$
$173$	−13.1870	−	4.79966i	−1.00259	−	0.364911i	−0.790581	+	0.612357i	$0.790221\pi$
$174$		0			0
$175$	−0.0939601	−	0.0788419i	−0.00710272	−	0.00595989i
$176$		0			0
$177$	−1.62766	−	6.20169i	−0.122342	−	0.466148i
$178$		0			0
$179$	5.09500	−	8.82479i	0.380818	−	0.659596i	−0.610361	−	0.792123i	$-0.708976\pi$
$179$	5.09500	−	8.82479i	0.380818	−	0.659596i	0.991179	+	0.132527i	$0.0423091\pi$
$180$		0			0
$181$	−12.0274	−	20.8320i	−0.893987	−	1.54843i	−0.835054	−	0.550169i	$-0.814563\pi$
$181$	−12.0274	−	20.8320i	−0.893987	−	1.54843i	−0.0589331	−	0.998262i	$-0.518770\pi$
$182$		0			0
$183$	−11.9354	+	0.982498i	−0.882293	+	0.0726283i
$184$		0			0
$185$	1.70204	−	9.65275i	0.125137	−	0.709685i
$186$		0			0
$187$	−12.5157	+	10.5019i	−0.915240	+	0.767978i
$188$		0			0
$189$	6.82089	+	0.702760i	0.496146	+	0.0511182i
$190$		0			0
$191$	−8.38541	+	7.03619i	−0.606747	+	0.509121i	−0.893606	−	0.448852i	$-0.851833\pi$
$191$	−8.38541	+	7.03619i	−0.606747	+	0.509121i	0.286860	+	0.957973i	$0.407389\pi$
$192$		0			0
$193$	−1.87644	+	10.6418i	−0.135069	+	0.766013i	0.839743	+	0.542984i	$0.182706\pi$
$193$	−1.87644	+	10.6418i	−0.135069	+	0.766013i	−0.974812	+	0.223029i	$0.928405\pi$
$194$		0			0
$195$	−0.0296040	+	0.0626444i	−0.00211999	+	0.00448606i
$196$		0			0
$197$	11.0367	+	19.1161i	0.786331	+	1.36196i	0.928201	+	0.372080i	$0.121355\pi$
$197$	11.0367	+	19.1161i	0.786331	+	1.36196i	−0.141870	+	0.989885i	$0.545311\pi$
$198$		0			0
$199$	6.44338	−	11.1603i	0.456759	−	0.791130i	−0.542028	−	0.840360i	$-0.682343\pi$
$199$	6.44338	−	11.1603i	0.456759	−	0.791130i	0.998787	+	0.0492301i	$0.0156768\pi$
$200$		0			0
$201$	−13.5742	+	13.4355i	−0.957448	+	0.947667i
$202$		0			0
$203$	−7.89228	−	6.62241i	−0.553929	−	0.464802i
$204$		0			0
$205$	7.64974	+	2.78428i	0.534281	+	0.194462i
$206$		0			0
$207$	−1.09123	+	2.90496i	−0.0758456	+	0.201909i
$208$		0			0
$209$	−0.377957	−	2.14350i	−0.0261439	−	0.148269i
$210$		0			0
$211$	−22.5485	+	8.20699i	−1.55230	+	0.564992i	−0.968957	−	0.247230i	$-0.920480\pi$
$211$	−22.5485	+	8.20699i	−1.55230	+	0.564992i	−0.583347	+	0.812223i	$0.698257\pi$
$212$		0			0
$213$	−8.60131	−	6.08875i	−0.589352	−	0.417194i
$214$		0			0
$215$	18.4035			1.25511
$216$		0			0
$217$	−4.92177			−0.334112
$218$		0			0
$219$	−0.860667	+	0.395969i	−0.0581585	+	0.0267571i
$220$		0			0
$221$	−0.0531618	+	0.0193493i	−0.00357605	+	0.00130158i
$222$		0			0
$223$	−3.76160	−	21.3331i	−0.251895	−	1.42857i	−0.803918	−	0.594740i	$-0.797255\pi$
$223$	−3.76160	−	21.3331i	−0.251895	−	1.42857i	0.552023	−	0.833829i	$-0.313856\pi$
$224$		0			0
$225$	0.242903	−	0.136934i	0.0161936	−	0.00912896i
$226$		0			0
$227$	20.3367	+	7.40196i	1.34979	+	0.491285i	0.912884	−	0.408220i	$-0.133850\pi$
$227$	20.3367	+	7.40196i	1.34979	+	0.491285i	0.436911	+	0.899505i	$0.356072\pi$
$228$		0			0
$229$	−8.27739	−	6.94555i	−0.546985	−	0.458975i	0.326934	−	0.945047i	$-0.393985\pi$
$229$	−8.27739	−	6.94555i	−0.546985	−	0.458975i	−0.873919	+	0.486072i	$0.838429\pi$
$230$		0			0
$231$	11.4980	+	3.14424i	0.756513	+	0.206876i
$232$		0			0
$233$	−3.81950	+	6.61557i	−0.250224	+	0.433400i	−0.963587	−	0.267394i	$-0.913838\pi$
$233$	−3.81950	+	6.61557i	−0.250224	+	0.433400i	0.713364	+	0.700794i	$0.247171\pi$
$234$		0			0
$235$	−7.86160	−	13.6167i	−0.512834	−	0.888255i
$236$		0			0
$237$	−0.482377	−	0.696490i	−0.0313338	−	0.0452419i
$238$		0			0
$239$	0.561143	−	3.18240i	0.0362973	−	0.205852i	−0.961266	−	0.275623i	$-0.911116\pi$
$239$	0.561143	−	3.18240i	0.0362973	−	0.205852i	0.997563	+	0.0697711i	$0.0222269\pi$
$240$		0			0
$241$	−20.3346	+	17.0628i	−1.30987	+	1.09911i	−0.321518	+	0.946903i	$0.604193\pi$
$241$	−20.3346	+	17.0628i	−1.30987	+	1.09911i	−0.988349	+	0.152206i	$0.951362\pi$
$242$		0			0
$243$	−6.94842	+	13.9542i	−0.445741	+	0.895162i
$244$		0			0
$245$	−8.92345	+	7.48766i	−0.570098	+	0.478369i
$246$		0			0
$247$	0.00130875	−	0.00742226i	8.32735e−5	−	0.000472267i
$248$		0			0
$249$	−4.54985	−	6.56938i	−0.288335	−	0.416318i
$250$		0			0
$251$	−2.24965	−	3.89651i	−0.141997	−	0.245945i	0.786252	−	0.617906i	$-0.212019\pi$
$251$	−2.24965	−	3.89651i	−0.141997	−	0.245945i	−0.928248	+	0.371961i	$0.878686\pi$
$252$		0			0
$253$	−2.69726	+	4.67179i	−0.169575	+	0.293713i
$254$		0			0
$255$	−11.5943	−	3.17056i	−0.726061	−	0.198548i
$256$		0			0
$257$	10.5219	+	8.82895i	0.656340	+	0.550735i	0.908987	−	0.416824i	$-0.136857\pi$
$257$	10.5219	+	8.82895i	0.656340	+	0.550735i	−0.252647	+	0.967559i	$0.581301\pi$
$258$		0			0
$259$	−5.48690	−	1.99707i	−0.340939	−	0.124092i
$260$		0			0
$261$	20.4029	−	11.5020i	1.26291	−	0.711953i
$262$		0			0
$263$	4.20273	+	23.8349i	0.259151	+	1.46972i	0.785187	+	0.619258i	$0.212567\pi$
$263$	4.20273	+	23.8349i	0.259151	+	1.46972i	−0.526036	+	0.850462i	$0.676322\pi$
$264$		0			0
$265$	2.70727	−	0.985365i	0.166306	−	0.0605305i
$266$		0			0
$267$	−5.30755	+	2.44185i	−0.324817	+	0.149439i
$268$		0			0
$269$	12.0062			0.732032			0.366016	−	0.930609i	$-0.380722\pi$
$269$	12.0062			0.732032			0.366016	+	0.930609i	$0.380722\pi$
$270$		0			0
$271$	−3.71777			−0.225839			−0.112919	−	0.993604i	$-0.536020\pi$
$271$	−3.71777			−0.225839			−0.112919	+	0.993604i	$0.536020\pi$
$272$		0			0
$273$	0.0336891	+	0.0238481i	0.00203896	+	0.00144335i
$274$		0			0
$275$	0.455505	−	0.165790i	0.0274680	−	0.00999753i
$276$		0			0
$277$	−4.07780	−	23.1264i	−0.245011	−	1.38953i	−0.820466	−	0.571695i	$-0.806286\pi$
$277$	−4.07780	−	23.1264i	−0.245011	−	1.38953i	0.575455	−	0.817833i	$-0.304825\pi$
$278$		0			0
$279$	3.93462	−	10.4744i	0.235559	−	0.627084i
$280$		0			0
$281$	19.1432	+	6.96754i	1.14199	+	0.415649i	0.842630	−	0.538493i	$-0.181006\pi$
$281$	19.1432	+	6.96754i	1.14199	+	0.415649i	0.299356	+	0.954142i	$0.403228\pi$
$282$		0			0
$283$	−8.88607	−	7.45630i	−0.528222	−	0.443231i	0.339265	−	0.940691i	$-0.389822\pi$
$283$	−8.88607	−	7.45630i	−0.528222	−	0.443231i	−0.867487	+	0.497460i	$0.834266\pi$
$284$		0			0
$285$	1.13809	−	1.12646i	0.0674147	−	0.0667260i
$286$		0			0
$287$	2.42478	−	4.19984i	0.143130	−	0.247909i
$288$		0			0
$289$	3.59280	+	6.22291i	0.211341	+	0.366053i
$290$		0			0
$291$	7.35706	−	15.5681i	0.431279	−	0.912618i
$292$		0			0
$293$	5.48280	−	31.0945i	0.320308	−	1.81656i	−0.220470	−	0.975394i	$-0.570759\pi$
$293$	5.48280	−	31.0945i	0.320308	−	1.81656i	0.540779	−	0.841165i	$-0.318130\pi$
$294$		0			0
$295$	6.28172	−	5.27099i	0.365736	−	0.306889i
$296$		0			0
$297$	−15.8833	+	21.9561i	−0.921644	+	1.27402i
$298$		0			0
$299$	−0.0143093	+	0.0120069i	−0.000827529	+	0.000694379i
$300$		0			0
$301$	1.90376	−	10.7968i	0.109731	−	0.622315i
$302$		0			0
$303$	−23.8208	+	1.96088i	−1.36847	+	0.112649i
$304$		0			0
$305$	−7.65816	−	13.2643i	−0.438505	−	0.759513i
$306$		0			0
$307$	−4.06027	+	7.03259i	−0.231732	+	0.401371i	−0.958318	−	0.285704i	$-0.907773\pi$
$307$	−4.06027	+	7.03259i	−0.231732	+	0.401371i	0.726586	+	0.687075i	$0.241106\pi$
$308$		0			0
$309$	2.00725	+	7.64800i	0.114188	+	0.435079i
$310$		0			0
$311$	18.2691	+	15.3296i	1.03594	+	0.869259i	0.991546	−	0.129754i	$-0.0414189\pi$
$311$	18.2691	+	15.3296i	1.03594	+	0.869259i	0.0443970	+	0.999014i	$0.485863\pi$
$312$		0			0
$313$	−25.2876	−	9.20392i	−1.42934	−	0.520236i	−0.492596	−	0.870258i	$-0.663952\pi$
$313$	−25.2876	−	9.20392i	−1.42934	−	0.520236i	−0.936742	+	0.350022i	$0.886174\pi$
$314$		0			0
$315$	2.91463	+	8.27116i	0.164221	+	0.466027i
$316$		0			0
$317$	−1.44689	−	8.20574i	−0.0812657	−	0.460881i	−0.998100	−	0.0616130i	$-0.980376\pi$
$317$	−1.44689	−	8.20574i	−0.0812657	−	0.460881i	0.916834	−	0.399268i	$-0.130736\pi$
$318$		0			0
$319$	38.2606	−	13.9257i	2.14218	−	0.779692i
$320$		0			0
$321$	−1.80534	+	19.4826i	−0.100764	+	1.08741i
$322$		0			0
$323$	1.30748			0.0727501
$324$		0			0
$325$	0.00167849			9.31061e−5
$326$		0			0
$327$	−2.31782	+	25.0131i	−0.128176	+	1.38323i
$328$		0			0
$329$	−8.80173	+	3.20357i	−0.485255	+	0.176618i
$330$		0			0
$331$	1.11487	+	6.32272i	0.0612786	+	0.347528i	0.999996	+	0.00284030i	$0.000904096\pi$
$331$	1.11487	+	6.32272i	0.0612786	+	0.347528i	−0.938717	+	0.344688i	$0.887985\pi$
$332$		0			0
$333$	8.63650	−	10.0805i	0.473277	−	0.552410i
$334$		0			0
$335$	−22.9533	−	8.35432i	−1.25407	−	0.456446i
$336$		0			0
$337$	5.72610	+	4.80477i	0.311921	+	0.261732i	0.785285	−	0.619134i	$-0.212516\pi$
$337$	5.72610	+	4.80477i	0.311921	+	0.261732i	−0.473365	+	0.880867i	$0.656961\pi$
$338$		0			0
$339$	−5.52185	−	21.0393i	−0.299906	−	1.14270i
$340$		0			0
$341$	9.72545	−	16.8450i	0.526663	−	0.912206i
$342$		0			0
$343$	8.08839	+	14.0095i	0.436732	+	0.756442i
$344$		0			0
$345$	−3.95537	+	0.325597i	−0.212950	+	0.0175296i
$346$		0			0
$347$	5.46202	−	30.9766i	0.293216	−	1.66291i	−0.381148	−	0.924514i	$-0.624471\pi$
$347$	5.46202	−	30.9766i	0.293216	−	1.66291i	0.674364	−	0.738399i	$-0.264418\pi$
$348$		0			0
$349$	9.07988	−	7.61893i	0.486035	−	0.407832i	−0.366568	−	0.930391i	$-0.619467\pi$
$349$	9.07988	−	7.61893i	0.486035	−	0.407832i	0.852603	+	0.522560i	$0.175023\pi$
$350$		0			0
$351$	−0.0776848	+	0.0526312i	−0.00414651	+	0.00280925i
$352$		0			0
$353$	−6.28699	+	5.27541i	−0.334623	+	0.280782i	−0.794580	−	0.607159i	$-0.792309\pi$
$353$	−6.28699	+	5.27541i	−0.334623	+	0.280782i	0.459958	+	0.887941i	$0.347865\pi$
$354$		0			0
$355$	2.34040	−	13.2731i	0.124215	−	0.704461i
$356$		0			0
$357$	−3.05944	+	6.47401i	−0.161923	+	0.342641i
$358$		0			0
$359$	8.86365	+	15.3523i	0.467806	+	0.810263i	0.999323	−	0.0367840i	$-0.0117114\pi$
$359$	8.86365	+	15.3523i	0.467806	+	0.810263i	−0.531517	+	0.847047i	$0.678378\pi$
$360$		0			0
$361$	9.41291	−	16.3036i	0.495416	−	0.858086i
$362$		0			0
$363$	−19.9402	+	19.7365i	−1.04659	+	1.03590i
$364$		0			0
$365$	−0.928176	−	0.778832i	−0.0485829	−	0.0407659i
$366$		0			0
$367$	−19.0941	−	6.94969i	−0.996704	−	0.362771i	−0.208392	−	0.978045i	$-0.566823\pi$
$367$	−19.0941	−	6.94969i	−0.996704	−	0.362771i	−0.788313	+	0.615275i	$0.789045\pi$
$368$		0			0
$369$	6.99953	+	8.51782i	0.364381	+	0.443420i
$370$		0			0
$371$	−0.298028	−	1.69020i	−0.0154728	−	0.0877509i
$372$		0			0
$373$	9.09758	−	3.31125i	0.471055	−	0.171450i	−0.0955754	−	0.995422i	$-0.530469\pi$
$373$	9.09758	−	3.31125i	0.471055	−	0.171450i	0.566630	+	0.823972i	$0.308247\pi$
$374$		0			0
$375$	15.9491	+	11.2901i	0.823606	+	0.583019i
$376$		0			0
$377$	0.140987			0.00726119
$378$		0			0
$379$	4.12905			0.212095			0.106048	−	0.994361i	$-0.466180\pi$
$379$	4.12905			0.212095			0.106048	+	0.994361i	$0.466180\pi$
$380$		0			0
$381$	13.2096	−	6.07736i	0.676748	−	0.311353i
$382$		0			0
$383$	4.46371	−	1.62466i	0.228085	−	0.0830162i	−0.225450	−	0.974255i	$-0.572385\pi$
$383$	4.46371	−	1.62466i	0.228085	−	0.0830162i	0.453535	+	0.891239i	$0.350163\pi$
$384$		0			0
$385$	2.64729	+	15.0136i	0.134919	+	0.765162i
$386$		0			0
$387$	21.4554	+	12.6828i	1.09064	+	0.644702i
$388$		0			0
$389$	20.4978	+	7.46059i	1.03928	+	0.378267i	0.804607	−	0.593807i	$-0.202376\pi$
$389$	20.4978	+	7.46059i	1.03928	+	0.378267i	0.234673	+	0.972074i	$0.424598\pi$
$390$		0			0
$391$	−2.48238	−	2.08297i	−0.125539	−	0.105340i
$392$		0			0
$393$	25.9543	+	7.09745i	1.30922	+	0.358019i
$394$		0			0
$395$	0.541773	−	0.938378i	0.0272595	−	0.0472149i
$396$		0			0
$397$	17.4245	+	30.1802i	0.874512	+	1.51470i	0.857282	+	0.514847i	$0.172151\pi$
$397$	17.4245	+	30.1802i	0.874512	+	1.51470i	0.0172294	+	0.999852i	$0.494515\pi$
$398$		0			0
$399$	−0.543131	−	0.784210i	−0.0271906	−	0.0392596i
$400$		0			0
$401$	−3.26911	+	18.5401i	−0.163252	+	0.925847i	0.787597	+	0.616191i	$0.211325\pi$
$401$	−3.26911	+	18.5401i	−0.163252	+	0.925847i	−0.950849	+	0.309656i	$0.899786\pi$
$402$		0			0
$403$	0.0515948	−	0.0432932i	0.00257012	−	0.00215659i
$404$		0			0
$405$	−19.9325	−	0.409386i	−0.990453	−	0.0203426i
$406$		0			0
$407$	17.6772	−	14.8329i	0.876226	−	0.735241i
$408$		0			0
$409$	−1.10439	+	6.26334i	−0.0546088	+	0.309702i	−0.999862	−	0.0166371i	$-0.994704\pi$
$409$	−1.10439	+	6.26334i	−0.0546088	+	0.309702i	0.945253	+	0.326339i	$0.105815\pi$
$410$		0			0
$411$	11.8413	+	17.0973i	0.584088	+	0.843346i
$412$		0			0
$413$	−2.44251	−	4.23055i	−0.120188	−	0.208172i
$414$		0			0
$415$	5.11007	−	8.85090i	0.250843	−	0.434474i
$416$		0			0
$417$	−10.2667	−	2.80753i	−0.502763	−	0.137485i
$418$		0			0
$419$	18.6286	+	15.6313i	0.910069	+	0.763638i	0.972132	−	0.234434i	$-0.0753236\pi$
$419$	18.6286	+	15.6313i	0.910069	+	0.763638i	−0.0620632	+	0.998072i	$0.519768\pi$
$420$		0			0
$421$	7.50818	+	2.73275i	0.365926	+	0.133186i	0.518438	−	0.855115i	$-0.326514\pi$
$421$	7.50818	+	2.73275i	0.365926	+	0.133186i	−0.152511	+	0.988302i	$0.548736\pi$
$422$		0			0
$423$	0.218637	−	21.2926i	0.0106305	−	1.03528i
$424$		0			0
$425$	0.0505638	+	0.286762i	0.00245271	+	0.0139100i
$426$		0			0
$427$	−8.57397	+	3.12067i	−0.414924	+	0.151020i
$428$		0			0
$429$	−0.148191	+	0.0681784i	−0.00715472	+	0.00329169i
$430$		0			0
$431$	−9.87124			−0.475481			−0.237740	−	0.971329i	$-0.576407\pi$
$431$	−9.87124			−0.475481			−0.237740	+	0.971329i	$0.576407\pi$
$432$		0			0
$433$	−6.10369			−0.293325			−0.146662	−	0.989187i	$-0.546853\pi$
$433$	−6.10369			−0.293325			−0.146662	+	0.989187i	$0.546853\pi$
$434$		0			0
$435$	24.4491	+	17.3072i	1.17224	+	0.829815i
$436$		0			0
$437$	0.405669	−	0.147651i	0.0194058	−	0.00706312i
$438$		0			0
$439$	2.62800	+	14.9041i	0.125427	+	0.711334i	0.981053	+	0.193739i	$0.0620615\pi$
$439$	2.62800	+	14.9041i	0.125427	+	0.711334i	−0.855626	+	0.517595i	$0.826827\pi$
$440$		0			0
$441$	−15.5634	+	2.57976i	−0.741113	+	0.122846i
$442$		0			0
$443$	−0.679204	−	0.247210i	−0.0322699	−	0.0117453i	0.325835	−	0.945427i	$-0.394355\pi$
$443$	−0.679204	−	0.247210i	−0.0322699	−	0.0117453i	−0.358105	+	0.933681i	$0.616577\pi$
$444$		0			0
$445$	−5.72386	−	4.80289i	−0.271337	−	0.227679i
$446$		0			0
$447$	−1.08677	+	1.07566i	−0.0514023	+	0.0508772i
$448$		0			0
$449$	−0.834224	+	1.44492i	−0.0393695	+	0.0681899i	−0.885039	−	0.465517i	$-0.845868\pi$
$449$	−0.834224	+	1.44492i	−0.0393695	+	0.0681899i	0.845669	+	0.533707i	$0.179202\pi$
$450$		0			0
$451$	9.58275	+	16.5978i	0.451234	+	0.781560i
$452$		0			0
$453$	−6.08723	+	12.8810i	−0.286003	+	0.605204i
$454$		0			0
$455$	−0.00916673	+	0.0519871i	−0.000429743	+	0.00243719i
$456$		0			0
$457$	8.49041	−	7.12430i	0.397165	−	0.333261i	−0.422232	−	0.906488i	$-0.638753\pi$
$457$	8.49041	−	7.12430i	0.397165	−	0.333261i	0.819397	+	0.573227i	$0.194309\pi$
$458$		0			0
$459$	−11.3320	−	11.6865i	−0.528932	−	0.545481i
$460$		0			0
$461$	−16.7644	+	14.0670i	−0.780797	+	0.655166i	−0.943449	−	0.331517i	$-0.892439\pi$
$461$	−16.7644	+	14.0670i	−0.780797	+	0.655166i	0.162653	+	0.986683i	$0.447995\pi$
$462$		0			0
$463$	−4.31546	+	24.4742i	−0.200556	+	1.13741i	0.703724	+	0.710473i	$0.251519\pi$
$463$	−4.31546	+	24.4742i	−0.200556	+	1.13741i	−0.904281	+	0.426938i	$0.859592\pi$
$464$		0			0
$465$	14.2618	−	1.17400i	0.661375	−	0.0544429i
$466$		0			0
$467$	−5.91777	−	10.2499i	−0.273842	−	0.474308i	0.696001	−	0.718041i	$-0.254961\pi$
$467$	−5.91777	−	10.2499i	−0.273842	−	0.474308i	−0.969842	+	0.243734i	$0.921628\pi$
$468$		0			0
$469$	−7.27564	+	12.6018i	−0.335958	+	0.581896i
$470$		0			0
$471$	−5.52246	−	21.0416i	−0.254462	−	0.969547i
$472$		0			0
$473$	33.1905	+	27.8501i	1.52610	+	1.28055i
$474$		0			0
$475$	−0.0364524	−	0.0132676i	−0.00167255	−	0.000608759i
$476$		0			0
$477$	3.83529	+	0.716944i	0.175606	+	0.0328266i
$478$		0			0
$479$	−0.501383	−	2.84349i	−0.0229088	−	0.129922i	0.971209	−	0.238231i	$-0.0765676\pi$
$479$	−0.501383	−	2.84349i	−0.0229088	−	0.129922i	−0.994117	+	0.108309i	$0.965456\pi$
$480$		0			0
$481$	0.0750857	−	0.0273290i	0.00342361	−	0.00124609i
$482$		0			0
$483$	−0.218148	+	2.35417i	−0.00992607	+	0.107119i
$484$		0			0
$485$	22.0220			0.999966
$486$		0			0
$487$	−8.75903			−0.396910			−0.198455	−	0.980110i	$-0.563592\pi$
$487$	−8.75903			−0.396910			−0.198455	+	0.980110i	$0.563592\pi$
$488$		0			0
$489$	0.529731	−	5.71667i	0.0239553	−	0.258517i
$490$		0			0
$491$	−21.2117	+	7.72044i	−0.957272	+	0.348418i	−0.772964	−	0.634450i	$-0.781227\pi$
$491$	−21.2117	+	7.72044i	−0.957272	+	0.348418i	−0.184308	+	0.982869i	$0.559004\pi$
$492$		0			0
$493$	4.24716	+	24.0869i	0.191283	+	1.08482i
$494$		0			0
$495$	−34.0677	−	6.36840i	−1.53123	−	0.286238i
$496$		0			0
$497$	−7.54478	−	2.74608i	−0.338430	−	0.123178i
$498$		0			0
$499$	19.4061	+	16.2836i	0.868734	+	0.728955i	0.963831	−	0.266513i	$-0.0858716\pi$
$499$	19.4061	+	16.2836i	0.868734	+	0.728955i	−0.0950968	+	0.995468i	$0.530316\pi$
$500$		0			0
$501$	−9.04139	−	34.4494i	−0.403940	−	1.53909i
$502$		0			0
$503$	1.87207	−	3.24252i	0.0834714	−	0.144577i	−0.821267	−	0.570543i	$-0.806733\pi$
$503$	1.87207	−	3.24252i	0.0834714	−	0.144577i	0.904739	+	0.425967i	$0.140066\pi$
$504$		0			0
$505$	−15.2842	−	26.4731i	−0.680139	−	1.17804i
$506$		0			0
$507$	22.4402	−	1.84723i	0.996604	−	0.0820382i
$508$		0			0
$509$	4.22831	−	23.9800i	0.187417	−	1.06289i	−0.735394	−	0.677640i	$-0.763003\pi$
$509$	4.22831	−	23.9800i	0.187417	−	1.06289i	0.922811	−	0.385253i	$-0.125886\pi$
$510$		0			0
$511$	−0.552932	+	0.463965i	−0.0244603	+	0.0205246i
$512$		0			0
$513$	2.10313	−	0.528954i	0.0928554	−	0.0233539i
$514$		0			0
$515$	−7.74669	+	6.50025i	−0.341360	+	0.286435i
$516$		0			0
$517$	6.42792	−	36.4546i	0.282700	−	1.60327i
$518$		0			0
$519$	10.3853	−	21.9760i	0.455862	−	0.964639i
$520$		0			0
$521$	−9.81046	−	16.9922i	−0.429804	−	0.744443i	0.567051	−	0.823682i	$-0.308084\pi$
$521$	−9.81046	−	16.9922i	−0.429804	−	0.744443i	−0.996856	+	0.0792397i	$0.974751\pi$
$522$		0			0
$523$	10.4077	−	18.0267i	0.455097	−	0.788251i	−0.543597	−	0.839346i	$-0.682938\pi$
$523$	10.4077	−	18.0267i	0.455097	−	0.788251i	0.998694	+	0.0510956i	$0.0162713\pi$
$524$		0			0
$525$	0.150992	−	0.149449i	0.00658982	−	0.00652251i
$526$		0			0
$527$	8.95067	+	7.51051i	0.389897	+	0.327163i
$528$		0			0
$529$	20.6075	+	7.50052i	0.895978	+	0.326109i
$530$		0			0
$531$	10.9559	−	1.81604i	0.475447	−	0.0788095i
$532$		0			0
$533$	0.0115240	+	0.0653558i	0.000499159	+	0.00283087i
$534$		0			0
$535$	−23.5147	+	8.55864i	−1.01663	+	0.370022i
$536$		0			0
$537$	14.4055	+	10.1975i	0.621645	+	0.440054i
$538$		0			0
$539$	−27.4245			−1.18126
$540$		0			0
$541$	−30.6272			−1.31676			−0.658382	−	0.752684i	$-0.728759\pi$
$541$	−30.6272			−1.31676			−0.658382	+	0.752684i	$0.728759\pi$
$542$		0			0
$543$	37.8503	−	17.4139i	1.62431	−	0.747301i
$544$		0			0
$545$	−30.1898	+	10.9882i	−1.29319	+	0.470682i
$546$		0			0
$547$	−3.93273	−	22.3036i	−0.168151	−	0.953633i	−0.945756	−	0.324879i	$-0.894676\pi$
$547$	−3.93273	−	22.3036i	−0.168151	−	0.953633i	0.777604	−	0.628754i	$-0.216435\pi$
$548$		0			0
$549$	0.212980	−	20.7416i	0.00908976	−	0.885231i
$550$		0			0
$551$	−3.06186	−	1.11443i	−0.130440	−	0.0474761i
$552$		0			0
$553$	−0.494473	−	0.414912i	−0.0210271	−	0.0176439i
$554$		0			0
$555$	16.3757	+	4.47810i	0.695111	+	0.190085i
$556$		0			0
$557$	−18.2259	+	31.5682i	−0.772256	+	1.33759i	0.164067	+	0.986449i	$0.447539\pi$
$557$	−18.2259	+	31.5682i	−0.772256	+	1.33759i	−0.936324	+	0.351138i	$0.885795\pi$
$558$		0			0
$559$	0.0750139	+	0.129928i	0.00317275	+	0.00549537i
$560$		0			0
$561$	−16.1121	−	23.2637i	−0.680253	−	0.982196i
$562$		0			0
$563$	−4.60450	+	26.1134i	−0.194056	+	1.10055i	0.719700	+	0.694285i	$0.244279\pi$
$563$	−4.60450	+	26.1134i	−0.194056	+	1.10055i	−0.913756	+	0.406263i	$0.866832\pi$
$564$		0			0
$565$	21.3108	−	17.8819i	0.896552	−	0.752296i
$566$		0			0
$567$	−2.30210	+	11.6514i	−0.0966791	+	0.489313i
$568$		0			0
$569$	17.5941	−	14.7632i	0.737581	−	0.618904i	−0.194606	−	0.980882i	$-0.562343\pi$
$569$	17.5941	−	14.7632i	0.737581	−	0.618904i	0.932187	+	0.361978i	$0.117898\pi$
$570$		0			0
$571$	0.833165	−	4.72511i	0.0348669	−	0.197740i	−0.962399	−	0.271641i	$-0.912434\pi$
$571$	0.833165	−	4.72511i	0.0348669	−	0.197740i	0.997266	+	0.0739009i	$0.0235449\pi$
$572$		0			0
$573$	−10.7949	−	15.5865i	−0.450965	−	0.651134i
$574$		0			0
$575$	0.0480718	+	0.0832628i	0.00200473	+	0.00347230i
$576$		0			0
$577$	2.15666	−	3.73545i	0.0897831	−	0.155509i	−0.817636	−	0.575735i	$-0.804716\pi$
$577$	2.15666	−	3.73545i	0.0897831	−	0.155509i	0.907419	+	0.420226i	$0.138049\pi$
$578$		0			0
$579$	−18.0536	−	4.93693i	−0.750283	−	0.205172i
$580$		0			0
$581$	−4.66393	−	3.91351i	−0.193493	−	0.162360i
$582$		0			0
$583$	6.37369	+	2.31983i	0.263971	+	0.0960777i
$584$		0			0
$585$	−0.103309	−	0.0610685i	−0.00427131	−	0.00252487i
$586$		0			0
$587$	−7.26235	−	41.1868i	−0.299749	−	1.69996i	−0.647246	−	0.762281i	$-0.724079\pi$
$587$	−7.26235	−	41.1868i	−0.299749	−	1.69996i	0.347497	−	0.937681i	$-0.387032\pi$
$588$		0			0
$589$	−1.46271	+	0.532383i	−0.0602699	+	0.0219365i
$590$		0			0
$591$	−34.7326	+	15.9795i	−1.42871	+	0.657309i
$592$		0			0
$593$	−31.5370			−1.29507			−0.647536	−	0.762035i	$-0.724200\pi$
$593$	−31.5370			−1.29507			−0.647536	+	0.762035i	$0.724200\pi$
$594$		0			0
$595$	−9.15786			−0.375436
$596$		0			0
$597$	18.2179	+	12.8962i	0.745611	+	0.527807i
$598$		0			0
$599$	−11.8686	+	4.31982i	−0.484938	+	0.176503i	−0.572907	−	0.819620i	$-0.694184\pi$
$599$	−11.8686	+	4.31982i	−0.484938	+	0.176503i	0.0879695	+	0.996123i	$0.471962\pi$
$600$		0			0
$601$	3.56725	+	20.2309i	0.145511	+	0.825235i	0.966955	+	0.254946i	$0.0820577\pi$
$601$	3.56725	+	20.2309i	0.145511	+	0.825235i	−0.821444	+	0.570289i	$0.806831\pi$
$602$		0			0
$603$	−21.0023	−	25.5580i	−0.855282	−	1.04080i
$604$		0			0
$605$	−33.7180	−	12.2724i	−1.37083	−	0.498942i
$606$		0			0
$607$	−9.89160	−	8.30003i	−0.401487	−	0.336888i	0.419581	−	0.907718i	$-0.362177\pi$
$607$	−9.89160	−	8.30003i	−0.401487	−	0.336888i	−0.821068	+	0.570830i	$0.806622\pi$
$608$		0			0
$609$	12.6827	−	12.5532i	0.513930	−	0.508680i
$610$		0			0
$611$	0.0640889	−	0.111005i	0.00259276	−	0.00449079i
$612$		0			0
$613$	15.5799	+	26.9851i	0.629265	+	1.08992i	0.987699	+	0.156364i	$0.0499774\pi$
$613$	15.5799	+	26.9851i	0.629265	+	1.08992i	−0.358434	+	0.933555i	$0.616689\pi$
$614$		0			0
$615$	−6.02447	+	12.7482i	−0.242930	+	0.514059i
$616$		0			0
$617$	−1.23998	+	7.03230i	−0.0499199	+	0.283110i	−0.999541	−	0.0302901i	$-0.990357\pi$
$617$	−1.23998	+	7.03230i	−0.0499199	+	0.283110i	0.949621	+	0.313400i	$0.101468\pi$
$618$		0			0
$619$	7.68412	−	6.44774i	0.308851	−	0.259157i	−0.475166	−	0.879896i	$-0.657612\pi$
$619$	7.68412	−	6.44774i	0.308851	−	0.259157i	0.784017	+	0.620740i	$0.213168\pi$
$620$		0			0
$621$	−4.83569	−	2.34625i	−0.194049	−	0.0941520i
$622$		0			0
$623$	−3.40981	+	2.86117i	−0.136611	+	0.114630i
$624$		0			0
$625$	−4.25900	+	24.1540i	−0.170360	+	0.966160i
$626$		0			0
$627$	3.75722	−	0.309286i	0.150049	−	0.0123517i
$628$		0			0
$629$	6.93093	+	12.0047i	0.276354	+	0.478660i
$630$		0			0
$631$	−3.53780	+	6.12765i	−0.140838	+	0.243938i	−0.927812	−	0.373047i	$-0.878313\pi$
$631$	−3.53780	+	6.12765i	−0.140838	+	0.243938i	0.786975	+	0.616985i	$0.211646\pi$
$632$		0			0
$633$	−10.5507	−	40.2002i	−0.419353	−	1.59781i
$634$		0			0
$635$	14.2457	+	11.9536i	0.565324	+	0.474363i
$636$		0			0
$637$	−0.0892352	−	0.0324790i	−0.00353563	−	0.00128686i
$638$		0			0
$639$	11.8756	−	13.8613i	0.469793	−	0.548344i
$640$		0			0
$641$	−0.870188	−	4.93508i	−0.0343704	−	0.194924i	0.962788	−	0.270258i	$-0.0871089\pi$
$641$	−0.870188	−	4.93508i	−0.0343704	−	0.194924i	−0.997158	+	0.0753337i	$0.975998\pi$
$642$		0			0
$643$	1.53960	−	0.560367i	0.0607157	−	0.0220987i	−0.311484	−	0.950251i	$-0.600826\pi$
$643$	1.53960	−	0.560367i	0.0607157	−	0.0220987i	0.372199	+	0.928153i	$0.378604\pi$
$644$		0			0
$645$	−2.94115	+	31.7398i	−0.115807	+	1.24975i
$646$		0			0
$647$	−34.4927			−1.35605			−0.678024	−	0.735040i	$-0.737164\pi$
$647$	−34.4927			−1.35605			−0.678024	+	0.735040i	$0.737164\pi$
$648$		0			0
$649$	19.3056			0.757813
$650$		0			0
$651$	0.786571	−	8.48840i	0.0308282	−	0.332687i
$652$		0			0
$653$	−36.4230	+	13.2569i	−1.42534	+	0.518783i	−0.935593	−	0.353080i	$-0.885134\pi$
$653$	−36.4230	+	13.2569i	−1.42534	+	0.518783i	−0.489751	+	0.871862i	$0.662912\pi$
$654$		0			0
$655$	5.97570	+	33.8899i	0.233490	+	1.32419i
$656$		0			0
$657$	−0.545365	−	1.54764i	−0.0212767	−	0.0603792i
$658$		0			0
$659$	8.82552	+	3.21223i	0.343794	+	0.125131i	0.508146	−	0.861271i	$-0.330331\pi$
$659$	8.82552	+	3.21223i	0.343794	+	0.125131i	−0.164352	+	0.986402i	$0.552553\pi$
$660$		0			0
$661$	−18.4980	−	15.5217i	−0.719489	−	0.603723i	0.207755	−	0.978181i	$-0.433384\pi$
$661$	−18.4980	−	15.5217i	−0.719489	−	0.603723i	−0.927244	+	0.374458i	$0.877829\pi$
$662$		0			0
$663$	−0.0248750	−	0.0947785i	−0.000966065	−	0.00368089i
$664$		0			0
$665$	0.610007	−	1.05656i	0.0236551	−	0.0409718i
$666$		0			0
$667$	4.03784	+	6.99375i	0.156346	+	0.270799i
$668$		0			0
$669$	37.3935	−	3.07815i	1.44572	−	0.119008i
$670$		0			0
$671$	6.26159	−	35.5112i	0.241726	−	1.37090i
$672$		0			0
$673$	−20.2742	+	17.0121i	−0.781514	+	0.655768i	−0.943630	−	0.331003i	$-0.892613\pi$
$673$	−20.2742	+	17.0121i	−0.781514	+	0.655768i	0.162115	+	0.986772i	$0.448168\pi$
$674$		0			0
$675$	0.197346	+	0.440811i	0.00759585	+	0.0169668i
$676$		0			0
$677$	23.7986	−	19.9694i	0.914654	−	0.767486i	−0.0583448	−	0.998296i	$-0.518582\pi$
$677$	23.7986	−	19.9694i	0.914654	−	0.767486i	0.972999	+	0.230811i	$0.0741378\pi$
$678$		0			0
$679$	2.27807	−	12.9196i	0.0874245	−	0.495809i
$680$		0			0
$681$	−16.0160	+	33.8910i	−0.613734	+	1.29871i
$682$		0			0
$683$	19.0681	+	33.0268i	0.729619	+	1.26374i	0.957044	+	0.289942i	$0.0936359\pi$
$683$	19.0681	+	33.0268i	0.729619	+	1.26374i	−0.227425	+	0.973796i	$0.573031\pi$
$684$		0			0
$685$	−13.2993	+	23.0351i	−0.508140	+	0.880125i
$686$		0			0
$687$	13.3016	−	13.1657i	0.507487	−	0.502303i
$688$		0			0
$689$	0.0179917	+	0.0150968i	0.000685428	+	0.000575142i
$690$		0			0
$691$	30.9436	+	11.2626i	1.17715	+	0.428448i	0.855195	−	0.518306i	$-0.173437\pi$
$691$	30.9436	+	11.2626i	1.17715	+	0.428448i	0.321957	+	0.946754i	$0.395659\pi$
$692$		0			0
$693$	−7.26030	+	19.3277i	−0.275796	+	0.734198i
$694$		0			0
$695$	−2.36380	−	13.4058i	−0.0896641	−	0.508510i
$696$		0			0
$697$	−10.8185	+	3.93762i	−0.409781	+	0.149148i
$698$		0			0
$699$	−10.7992	−	7.64461i	−0.408463	−	0.289146i
$700$		0			0
$701$	−2.30710			−0.0871381			−0.0435690	−	0.999050i	$-0.513873\pi$
$701$	−2.30710			−0.0871381			−0.0435690	+	0.999050i	$0.513873\pi$
$702$		0			0
$703$	−1.84668			−0.0696490
$704$		0			0
$705$	24.7406	−	11.3825i	0.931784	−	0.428688i
$706$		0			0
$707$	−17.1120	+	6.22826i	−0.643563	+	0.234238i
$708$		0			0
$709$	−1.93654	−	10.9826i	−0.0727281	−	0.412462i	−0.999336	−	0.0364329i	$-0.988400\pi$
$709$	−1.93654	−	10.9826i	−0.0727281	−	0.412462i	0.926608	−	0.376029i	$-0.122711\pi$
$710$		0			0
$711$	1.27830	−	0.720629i	0.0479400	−	0.0270257i
$712$		0			0
$713$	3.62525	+	1.31948i	0.135767	+	0.0494151i
$714$		0			0
$715$	−0.159815	−	0.134100i	−0.00597673	−	0.00501507i
$716$		0			0
$717$	5.39888	+	1.47637i	0.201625	+	0.0551362i
$718$		0			0
$719$	−16.0850	+	27.8600i	−0.599869	+	1.03900i	0.392971	+	0.919551i	$0.371447\pi$
$719$	−16.0850	+	27.8600i	−0.599869	+	1.03900i	−0.992840	+	0.119453i	$0.961886\pi$
$720$		0			0
$721$	3.01213	+	5.21717i	0.112178	+	0.194297i
$722$		0			0
$723$	−26.1777	−	37.7972i	−0.973560	−	1.40569i
$724$		0			0
$725$	0.126010	−	0.714637i	0.00467989	−	0.0265410i
$726$		0			0
$727$	4.11022	−	3.44888i	0.152440	−	0.127912i	−0.563378	−	0.826199i	$-0.690499\pi$
$727$	4.11022	−	3.44888i	0.152440	−	0.127912i	0.715818	+	0.698287i	$0.246054\pi$
$728$		0			0
$729$	−22.9558	−	14.2138i	−0.850215	−	0.526435i
$730$		0			0
$731$	−19.9377	+	16.7297i	−0.737424	+	0.618772i
$732$		0			0
$733$	−2.53463	+	14.3746i	−0.0936187	+	0.530938i	0.901543	+	0.432689i	$0.142435\pi$
$733$	−2.53463	+	14.3746i	−0.0936187	+	0.530938i	−0.995162	+	0.0982489i	$0.968676\pi$
$734$		0			0
$735$	−11.4876	−	16.5866i	−0.423726	−	0.611805i
$736$		0			0
$737$	−28.7534	−	49.8023i	−1.05915	−	1.83449i
$738$		0			0
$739$	−21.6083	+	37.4266i	−0.794873	+	1.37676i	0.128047	+	0.991768i	$0.459129\pi$
$739$	−21.6083	+	37.4266i	−0.794873	+	1.37676i	−0.922920	+	0.384992i	$0.874204\pi$
$740$		0			0
$741$	0.0125917	+	0.00344333i	0.000462569	+	0.000126494i
$742$		0			0
$743$	−6.21431	−	5.21443i	−0.227981	−	0.191299i	0.521641	−	0.853165i	$-0.325320\pi$
$743$	−6.21431	−	5.21443i	−0.227981	−	0.191299i	−0.749622	+	0.661866i	$0.769765\pi$
$744$		0			0
$745$	−1.83767	−	0.668859i	−0.0673272	−	0.0245051i
$746$		0			0
$747$	12.0571	−	6.79706i	0.441146	−	0.248692i
$748$		0			0
$749$	2.58860	+	14.6807i	0.0945854	+	0.536420i
$750$		0			0
$751$	8.22744	−	2.99454i	0.300223	−	0.109272i	−0.187516	−	0.982261i	$-0.560044\pi$
$751$	8.22744	−	2.99454i	0.300223	−	0.109272i	0.487740	+	0.872989i	$0.337822\pi$
$752$		0			0
$753$	7.07968	−	3.25717i	0.257998	−	0.118698i
$754$		0			0
$755$	−18.2210			−0.663129
$756$		0			0
$757$	−32.1511			−1.16855			−0.584276	−	0.811555i	$-0.698622\pi$
$757$	−32.1511			−1.16855			−0.584276	+	0.811555i	$0.698622\pi$
$758$		0			0
$759$	−7.62620	−	5.39848i	−0.276813	−	0.195952i
$760$		0			0
$761$	23.0656	−	8.39520i	0.836128	−	0.304326i	0.111756	−	0.993736i	$-0.464352\pi$
$761$	23.0656	−	8.39520i	0.836128	−	0.304326i	0.724371	+	0.689410i	$0.242130\pi$
$762$		0			0
$763$	3.32342	+	18.8481i	0.120316	+	0.682346i
$764$		0			0
$765$	7.32108	−	19.4895i	0.264694	−	0.704644i
$766$		0			0
$767$	0.0628177	+	0.0228638i	0.00226822	+	0.000825563i
$768$		0			0
$769$	24.0648	+	20.1928i	0.867800	+	0.728170i	0.963634	−	0.267227i	$-0.0861073\pi$
$769$	24.0648	+	20.1928i	0.867800	+	0.728170i	−0.0958338	+	0.995397i	$0.530552\pi$
$770$		0			0
$771$	−16.9085	+	16.7358i	−0.608945	+	0.602725i
$772$		0			0
$773$	−14.3573	+	24.8675i	−0.516395	+	0.894422i	0.483424	+	0.875386i	$0.339393\pi$
$773$	−14.3573	+	24.8675i	−0.516395	+	0.894422i	−0.999819	+	0.0190355i	$0.993940\pi$
$774$		0			0
$775$	−0.173332	−	0.300219i	−0.00622625	−	0.0107842i
$776$		0			0
$777$	4.32116	−	9.14389i	0.155021	−	0.328035i
$778$		0			0
$779$	0.266332	−	1.51044i	0.00954233	−	0.0541173i
$780$		0			0
$781$	24.3071	−	20.3961i	0.869776	−	0.729829i
$782$		0			0
$783$	16.5763	+	37.0263i	0.592388	+	1.32321i
$784$		0			0
$785$	21.3132	−	17.8839i	0.760699	−	0.638303i
$786$		0			0
$787$	6.74033	−	38.2263i	0.240267	−	1.36262i	−0.590966	−	0.806697i

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.159815 + 1.72466i) q^{3} +(-2.08159 + 0.757639i) q^{5} +(0.229151 + 1.29958i) q^{7} +(-2.94892 - 0.551252i) q^{9} +O(q^{10})\)	\(q+(-0.159815 + 1.72466i) q^{3} +(-2.08159 + 0.757639i) q^{5} +(0.229151 + 1.29958i) q^{7} +(-2.94892 - 0.551252i) q^{9} +(-4.90067 - 1.78370i) q^{11} +(-0.0138336 - 0.0116078i) q^{13} +(-0.974001 - 3.71113i) q^{15} +(1.56640 - 2.71308i) q^{17} +(0.208676 + 0.361438i) q^{19} +(-2.27796 + 0.187516i) q^{21} +(0.179619 - 1.01867i) q^{23} +(-0.0712019 + 0.0597455i) q^{25} +(1.42200 - 4.99779i) q^{27} +(-5.98068 + 5.01839i) q^{29} +(-0.647649 + 3.67300i) q^{31} +(3.85948 - 8.16694i) q^{33} +(-1.46161 - 2.53159i) q^{35} +(-2.21238 + 3.83195i) q^{37} +(0.0222303 - 0.0220032i) q^{39} +(-2.81517 - 2.36221i) q^{41} +(-7.80685 - 2.84146i) q^{43} +(6.55610 - 1.08673i) q^{45} +(1.23254 + 6.99008i) q^{47} +(4.94145 - 1.79854i) q^{49} +(4.42881 + 3.13510i) q^{51} -1.30057 q^{53} +11.5526 q^{55} +(-0.656707 + 0.302133i) q^{57} +(-3.47856 + 1.26609i) q^{59} +(1.20064 + 6.80919i) q^{61} +(0.0406486 - 3.95868i) q^{63} +(0.0375905 + 0.0136818i) q^{65} +(8.44702 + 7.08789i) q^{67} +(1.72816 + 0.472581i) q^{69} +(-3.04214 + 5.26914i) q^{71} +(0.273486 + 0.473692i) q^{73} +(-0.0916617 - 0.132347i) q^{75} +(1.19507 - 6.77756i) q^{77} +(-0.374706 + 0.314416i) q^{79} +(8.39224 + 3.25120i) q^{81} +(-3.53428 + 2.96561i) q^{83} +(-1.20507 + 6.83430i) q^{85} +(-7.69922 - 11.1167i) q^{87} +(1.68653 + 2.92116i) q^{89} +(0.0119153 - 0.0206379i) q^{91} +(-6.23118 - 1.70398i) q^{93} +(-0.708218 - 0.594266i) q^{95} +(-9.34182 - 3.40014i) q^{97} +(13.4684 + 7.96149i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} - 3 q^{5} + 6 q^{7}+O(q^{10}) \) 12 * q + 6 * q^3 - 3 * q^5 + 6 * q^7	\( 12 q + 6 q^{3} - 3 q^{5} + 6 q^{7} - 3 q^{11} - 6 q^{13} - 9 q^{15} + 9 q^{17} + 3 q^{19} - 12 q^{21} + 12 q^{23} + 3 q^{25} + 9 q^{27} - 6 q^{29} - 3 q^{31} - 12 q^{35} - 3 q^{37} - 33 q^{39} + 15 q^{41} - 3 q^{43} - 9 q^{45} + 15 q^{47} + 12 q^{49} + 18 q^{51} - 18 q^{53} + 12 q^{55} - 3 q^{57} + 12 q^{59} + 12 q^{61} - 9 q^{63} + 3 q^{65} + 15 q^{67} + 9 q^{69} - 27 q^{71} + 6 q^{73} - 39 q^{75} + 15 q^{77} + 42 q^{79} + 36 q^{81} - 39 q^{83} - 27 q^{85} - 9 q^{87} + 9 q^{89} - 6 q^{91} - 39 q^{93} + 33 q^{95} + 3 q^{97} + 27 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 - 3 * q^5 + 6 * q^7 - 3 * q^11 - 6 * q^13 - 9 * q^15 + 9 * q^17 + 3 * q^19 - 12 * q^21 + 12 * q^23 + 3 * q^25 + 9 * q^27 - 6 * q^29 - 3 * q^31 - 12 * q^35 - 3 * q^37 - 33 * q^39 + 15 * q^41 - 3 * q^43 - 9 * q^45 + 15 * q^47 + 12 * q^49 + 18 * q^51 - 18 * q^53 + 12 * q^55 - 3 * q^57 + 12 * q^59 + 12 * q^61 - 9 * q^63 + 3 * q^65 + 15 * q^67 + 9 * q^69 - 27 * q^71 + 6 * q^73 - 39 * q^75 + 15 * q^77 + 42 * q^79 + 36 * q^81 - 39 * q^83 - 27 * q^85 - 9 * q^87 + 9 * q^89 - 6 * q^91 - 39 * q^93 + 33 * q^95 + 3 * q^97 + 27 * q^99

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