LMFDB - Embedded newform 325.2.c.b.51.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(51,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("325.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.c (of order $2$, degree $1$, 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:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	325.51
Dual form			325.2.c.b.51.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -2.00000 q^{3} +1.00000 q^{4} -2.00000i q^{6} +3.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -2.00000 q^{3} +1.00000 q^{4} -2.00000i q^{6} +3.00000i q^{8} +1.00000 q^{9} +2.00000i q^{11} -2.00000 q^{12} +(2.00000 + 3.00000i) q^{13} -1.00000 q^{16} +1.00000i q^{18} +6.00000i q^{19} -2.00000 q^{22} -6.00000 q^{23} -6.00000i q^{24} +(-3.00000 + 2.00000i) q^{26} +4.00000 q^{27} -6.00000 q^{29} +6.00000i q^{31} +5.00000i q^{32} -4.00000i q^{33} +1.00000 q^{36} -6.00000i q^{37} -6.00000 q^{38} +(-4.00000 - 6.00000i) q^{39} -8.00000i q^{41} +6.00000 q^{43} +2.00000i q^{44} -6.00000i q^{46} +8.00000i q^{47} +2.00000 q^{48} +7.00000 q^{49} +(2.00000 + 3.00000i) q^{52} +12.0000 q^{53} +4.00000i q^{54} -12.0000i q^{57} -6.00000i q^{58} -2.00000i q^{59} +6.00000 q^{61} -6.00000 q^{62} -7.00000 q^{64} +4.00000 q^{66} -12.0000i q^{67} +12.0000 q^{69} -2.00000i q^{71} +3.00000i q^{72} -6.00000i q^{73} +6.00000 q^{74} +6.00000i q^{76} +(6.00000 - 4.00000i) q^{78} -11.0000 q^{81} +8.00000 q^{82} -4.00000i q^{83} +6.00000i q^{86} +12.0000 q^{87} -6.00000 q^{88} +8.00000i q^{89} -6.00000 q^{92} -12.0000i q^{93} -8.00000 q^{94} -10.0000i q^{96} +6.00000i q^{97} +7.00000i q^{98} +2.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{3} + 2 q^{4} + 2 q^{9}+O(q^{10}) $ 2 * q - 4 * q^3 + 2 * q^4 + 2 * q^9	$ 2 q - 4 q^{3} + 2 q^{4} + 2 q^{9} - 4 q^{12} + 4 q^{13} - 2 q^{16} - 4 q^{22} - 12 q^{23} - 6 q^{26} + 8 q^{27} - 12 q^{29} + 2 q^{36} - 12 q^{38} - 8 q^{39} + 12 q^{43} + 4 q^{48} + 14 q^{49} + 4 q^{52} + 24 q^{53} + 12 q^{61} - 12 q^{62} - 14 q^{64} + 8 q^{66} + 24 q^{69} + 12 q^{74} + 12 q^{78} - 22 q^{81} + 16 q^{82} + 24 q^{87} - 12 q^{88} - 12 q^{92} - 16 q^{94}+O(q^{100}) $ 2 * q - 4 * q^3 + 2 * q^4 + 2 * q^9 - 4 * q^12 + 4 * q^13 - 2 * q^16 - 4 * q^22 - 12 * q^23 - 6 * q^26 + 8 * q^27 - 12 * q^29 + 2 * q^36 - 12 * q^38 - 8 * q^39 + 12 * q^43 + 4 * q^48 + 14 * q^49 + 4 * q^52 + 24 * q^53 + 12 * q^61 - 12 * q^62 - 14 * q^64 + 8 * q^66 + 24 * q^69 + 12 * q^74 + 12 * q^78 - 22 * q^81 + 16 * q^82 + 24 * q^87 - 12 * q^88 - 12 * q^92 - 16 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$-1$

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 $

$2$			1.00000i			0.707107i	0.935414	+	0.353553i	$0.115027\pi$
$2$			1.00000i			0.707107i	−0.935414	+	0.353553i	$0.884973\pi$
$3$	−2.00000			−1.15470			−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−2.00000			−1.15470			−0.577350	+	0.816497i	$0.695913\pi$
$4$	1.00000			0.500000
$5$		0			0
$5$		0			0
$6$		−	2.00000i		−	0.816497i
$7$		0			0		1.00000			$0$
$7$		0			0		−1.00000			$\pi$
$8$			3.00000i			1.06066i
$9$	1.00000			0.333333
$10$		0			0
$11$			2.00000i			0.603023i	0.953463	+	0.301511i	$0.0974911\pi$
$11$			2.00000i			0.603023i	−0.953463	+	0.301511i	$0.902509\pi$
$12$	−2.00000			−0.577350
$13$	2.00000	+	3.00000i	0.554700	+	0.832050i
$13$	2.00000	+	3.00000i	0.554700	+	0.832050i
$14$		0			0
$15$		0			0
$16$	−1.00000			−0.250000
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$			1.00000i			0.235702i
$19$			6.00000i			1.37649i	0.725476	+	0.688247i	$0.241620\pi$
$19$			6.00000i			1.37649i	−0.725476	+	0.688247i	$0.758380\pi$
$20$		0			0
$21$		0			0
$22$	−2.00000			−0.426401
$23$	−6.00000			−1.25109			−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000			−1.25109			−0.625543	+	0.780189i	$0.715123\pi$
$24$		−	6.00000i		−	1.22474i
$25$		0			0
$26$	−3.00000	+	2.00000i	−0.588348	+	0.392232i
$27$	4.00000			0.769800
$28$		0			0
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$		0			0
$31$			6.00000i			1.07763i	0.842424	+	0.538816i	$0.181128\pi$
$31$			6.00000i			1.07763i	−0.842424	+	0.538816i	$0.818872\pi$
$32$			5.00000i			0.883883i
$33$		−	4.00000i		−	0.696311i
$34$		0			0
$35$		0			0
$36$	1.00000			0.166667
$37$		−	6.00000i		−	0.986394i	−0.869918	−	0.493197i	$-0.835828\pi$
$37$		−	6.00000i		−	0.986394i	0.869918	−	0.493197i	$-0.164172\pi$
$38$	−6.00000			−0.973329
$39$	−4.00000	−	6.00000i	−0.640513	−	0.960769i
$40$		0			0
$41$		−	8.00000i		−	1.24939i	−0.780869	−	0.624695i	$-0.785223\pi$
$41$		−	8.00000i		−	1.24939i	0.780869	−	0.624695i	$-0.214777\pi$
$42$		0			0
$43$	6.00000			0.914991			0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000			0.914991			0.457496	+	0.889212i	$0.348747\pi$
$44$			2.00000i			0.301511i
$45$		0			0
$46$		−	6.00000i		−	0.884652i
$47$			8.00000i			1.16692i	0.812142	+	0.583460i	$0.198301\pi$
$47$			8.00000i			1.16692i	−0.812142	+	0.583460i	$0.801699\pi$
$48$	2.00000			0.288675
$49$	7.00000			1.00000
$50$		0			0
$51$		0			0
$52$	2.00000	+	3.00000i	0.277350	+	0.416025i
$53$	12.0000			1.64833			0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000			1.64833			0.824163	+	0.566352i	$0.191646\pi$
$54$			4.00000i			0.544331i
$55$		0			0
$56$		0			0
$57$		−	12.0000i		−	1.58944i
$58$		−	6.00000i		−	0.787839i
$59$		−	2.00000i		−	0.260378i	−0.991489	−	0.130189i	$-0.958442\pi$
$59$		−	2.00000i		−	0.260378i	0.991489	−	0.130189i	$-0.0415584\pi$
$60$		0			0
$61$	6.00000			0.768221			0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000			0.768221			0.384111	+	0.923287i	$0.374508\pi$
$62$	−6.00000			−0.762001
$63$		0			0
$64$	−7.00000			−0.875000
$65$		0			0
$66$	4.00000			0.492366
$67$		−	12.0000i		−	1.46603i	−0.680211	−	0.733017i	$-0.738112\pi$
$67$		−	12.0000i		−	1.46603i	0.680211	−	0.733017i	$-0.261888\pi$
$68$		0			0
$69$	12.0000			1.44463
$70$		0			0
$71$		−	2.00000i		−	0.237356i	−0.992933	−	0.118678i	$-0.962134\pi$
$71$		−	2.00000i		−	0.237356i	0.992933	−	0.118678i	$-0.0378657\pi$
$72$			3.00000i			0.353553i
$73$		−	6.00000i		−	0.702247i	−0.936329	−	0.351123i	$-0.885800\pi$
$73$		−	6.00000i		−	0.702247i	0.936329	−	0.351123i	$-0.114200\pi$
$74$	6.00000			0.697486
$75$		0			0
$76$			6.00000i			0.688247i
$77$		0			0
$78$	6.00000	−	4.00000i	0.679366	−	0.452911i
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$		0			0
$81$	−11.0000			−1.22222
$82$	8.00000			0.883452
$83$		−	4.00000i		−	0.439057i	−0.975606	−	0.219529i	$-0.929548\pi$
$83$		−	4.00000i		−	0.439057i	0.975606	−	0.219529i	$-0.0704519\pi$
$84$		0			0
$85$		0			0
$86$			6.00000i			0.646997i
$87$	12.0000			1.28654
$88$	−6.00000			−0.639602
$89$			8.00000i			0.847998i	0.905663	+	0.423999i	$0.139374\pi$
$89$			8.00000i			0.847998i	−0.905663	+	0.423999i	$0.860626\pi$
$90$		0			0
$91$		0			0
$92$	−6.00000			−0.625543
$93$		−	12.0000i		−	1.24434i
$94$	−8.00000			−0.825137
$95$		0			0
$96$		−	10.0000i		−	1.02062i
$97$			6.00000i			0.609208i	0.952479	+	0.304604i	$0.0985241\pi$
$97$			6.00000i			0.609208i	−0.952479	+	0.304604i	$0.901476\pi$
$98$			7.00000i			0.707107i
$99$			2.00000i			0.201008i
$100$		0			0
$101$	6.00000			0.597022			0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000			0.597022			0.298511	+	0.954406i	$0.403510\pi$
$102$		0			0
$103$	−6.00000			−0.591198			−0.295599	−	0.955312i	$-0.595519\pi$
$103$	−6.00000			−0.591198			−0.295599	+	0.955312i	$0.595519\pi$
$104$	−9.00000	+	6.00000i	−0.882523	+	0.588348i
$105$		0			0
$106$			12.0000i			1.16554i
$107$	−6.00000			−0.580042			−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000			−0.580042			−0.290021	+	0.957020i	$0.593662\pi$
$108$	4.00000			0.384900
$109$		−	12.0000i		−	1.14939i	−0.818367	−	0.574696i	$-0.805120\pi$
$109$		−	12.0000i		−	1.14939i	0.818367	−	0.574696i	$-0.194880\pi$
$110$		0			0
$111$			12.0000i			1.13899i
$112$		0			0
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$	12.0000			1.12390
$115$		0			0
$116$	−6.00000			−0.557086
$117$	2.00000	+	3.00000i	0.184900	+	0.277350i
$118$	2.00000			0.184115
$119$		0			0
$120$		0			0
$121$	7.00000			0.636364
$122$			6.00000i			0.543214i
$123$			16.0000i			1.44267i
$124$			6.00000i			0.538816i
$125$		0			0
$126$		0			0
$127$	−2.00000			−0.177471			−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000			−0.177471			−0.0887357	+	0.996055i	$0.528283\pi$
$128$			3.00000i			0.265165i
$129$	−12.0000			−1.05654
$130$		0			0
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$		−	4.00000i		−	0.348155i
$133$		0			0
$134$	12.0000			1.03664
$135$		0			0
$136$		0			0
$137$		−	2.00000i		−	0.170872i	−0.996344	−	0.0854358i	$-0.972772\pi$
$137$		−	2.00000i		−	0.170872i	0.996344	−	0.0854358i	$-0.0272282\pi$
$138$			12.0000i			1.02151i
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$		−	16.0000i		−	1.34744i
$142$	2.00000			0.167836
$143$	−6.00000	+	4.00000i	−0.501745	+	0.334497i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	6.00000			0.496564
$147$	−14.0000			−1.15470
$148$		−	6.00000i		−	0.493197i
$149$		−	20.0000i		−	1.63846i	−0.573462	−	0.819232i	$-0.694400\pi$
$149$		−	20.0000i		−	1.63846i	0.573462	−	0.819232i	$-0.305600\pi$
$150$		0			0
$151$		−	18.0000i		−	1.46482i	−0.680864	−	0.732410i	$-0.738396\pi$
$151$		−	18.0000i		−	1.46482i	0.680864	−	0.732410i	$-0.261604\pi$
$152$	−18.0000			−1.45999
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−4.00000	−	6.00000i	−0.320256	−	0.480384i
$157$	12.0000			0.957704			0.478852	−	0.877896i	$-0.341053\pi$
$157$	12.0000			0.957704			0.478852	+	0.877896i	$0.341053\pi$
$158$		0			0
$159$	−24.0000			−1.90332
$160$		0			0
$161$		0			0
$162$		−	11.0000i		−	0.864242i
$163$			12.0000i			0.939913i	0.882690	+	0.469956i	$0.155730\pi$
$163$			12.0000i			0.939913i	−0.882690	+	0.469956i	$0.844270\pi$
$164$		−	8.00000i		−	0.624695i
$165$		0			0
$166$	4.00000			0.310460
$167$			16.0000i			1.23812i	0.785345	+	0.619059i	$0.212486\pi$
$167$			16.0000i			1.23812i	−0.785345	+	0.619059i	$0.787514\pi$
$168$		0			0
$169$	−5.00000	+	12.0000i	−0.384615	+	0.923077i
$170$		0			0
$171$			6.00000i			0.458831i
$172$	6.00000			0.457496
$173$	−12.0000			−0.912343			−0.456172	−	0.889892i	$-0.650780\pi$
$173$	−12.0000			−0.912343			−0.456172	+	0.889892i	$0.650780\pi$
$174$			12.0000i			0.909718i
$175$		0			0
$176$		−	2.00000i		−	0.150756i
$177$			4.00000i			0.300658i
$178$	−8.00000			−0.599625
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$	−12.0000			−0.887066
$184$		−	18.0000i		−	1.32698i
$185$		0			0
$186$	12.0000			0.879883
$187$		0			0
$188$			8.00000i			0.583460i
$189$		0			0
$190$		0			0
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$	14.0000			1.01036
$193$		−	6.00000i		−	0.431889i	−0.976406	−	0.215945i	$-0.930717\pi$
$193$		−	6.00000i		−	0.431889i	0.976406	−	0.215945i	$-0.0692831\pi$
$194$	−6.00000			−0.430775
$195$		0			0
$196$	7.00000			0.500000
$197$			2.00000i			0.142494i	0.997459	+	0.0712470i	$0.0226979\pi$
$197$			2.00000i			0.142494i	−0.997459	+	0.0712470i	$0.977302\pi$
$198$	−2.00000			−0.142134
$199$	24.0000			1.70131			0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000			1.70131			0.850657	+	0.525720i	$0.176204\pi$
$200$		0			0
$201$			24.0000i			1.69283i
$202$			6.00000i			0.422159i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		−	6.00000i		−	0.418040i
$207$	−6.00000			−0.417029
$208$	−2.00000	−	3.00000i	−0.138675	−	0.208013i
$209$	−12.0000			−0.830057
$210$		0			0
$211$	−12.0000			−0.826114			−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000			−0.826114			−0.413057	+	0.910705i	$0.635539\pi$
$212$	12.0000			0.824163
$213$			4.00000i			0.274075i
$214$		−	6.00000i		−	0.410152i
$215$		0			0
$216$			12.0000i			0.816497i
$217$		0			0
$218$	12.0000			0.812743
$219$			12.0000i			0.810885i
$220$		0			0
$221$		0			0
$222$	−12.0000			−0.805387
$223$			24.0000i			1.60716i	0.595198	+	0.803579i	$0.297074\pi$
$223$			24.0000i			1.60716i	−0.595198	+	0.803579i	$0.702926\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			4.00000i			0.265489i	0.991150	+	0.132745i	$0.0423790\pi$
$227$			4.00000i			0.265489i	−0.991150	+	0.132745i	$0.957621\pi$
$228$		−	12.0000i		−	0.794719i
$229$			12.0000i			0.792982i	0.918039	+	0.396491i	$0.129772\pi$
$229$			12.0000i			0.792982i	−0.918039	+	0.396491i	$0.870228\pi$
$230$		0			0
$231$		0			0
$232$		−	18.0000i		−	1.18176i
$233$	24.0000			1.57229			0.786146	−	0.618041i	$-0.212073\pi$
$233$	24.0000			1.57229			0.786146	+	0.618041i	$0.212073\pi$
$234$	−3.00000	+	2.00000i	−0.196116	+	0.130744i
$235$		0			0
$236$		−	2.00000i		−	0.130189i
$237$		0			0
$238$		0			0
$239$			10.0000i			0.646846i	0.946254	+	0.323423i	$0.104834\pi$
$239$			10.0000i			0.646846i	−0.946254	+	0.323423i	$0.895166\pi$
$240$		0			0
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$			7.00000i			0.449977i
$243$	10.0000			0.641500
$244$	6.00000			0.384111
$245$		0			0
$246$	−16.0000			−1.02012
$247$	−18.0000	+	12.0000i	−1.14531	+	0.763542i
$248$	−18.0000			−1.14300
$249$			8.00000i			0.506979i
$250$		0			0
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$		−	12.0000i		−	0.754434i
$254$		−	2.00000i		−	0.125491i
$255$		0			0
$256$	−17.0000			−1.06250
$257$		0			0			−	1.00000i	$-0.5\pi$
$257$		0			0				1.00000i	$0.5\pi$
$258$		−	12.0000i		−	0.747087i
$259$		0			0
$260$		0			0
$261$	−6.00000			−0.371391
$262$		−	12.0000i		−	0.741362i
$263$	−6.00000			−0.369976			−0.184988	−	0.982741i	$-0.559225\pi$
$263$	−6.00000			−0.369976			−0.184988	+	0.982741i	$0.559225\pi$
$264$	12.0000			0.738549
$265$		0			0
$266$		0			0
$267$		−	16.0000i		−	0.979184i
$268$		−	12.0000i		−	0.733017i
$269$	18.0000			1.09748			0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000			1.09748			0.548740	+	0.835993i	$0.315108\pi$
$270$		0			0
$271$			6.00000i			0.364474i	0.983255	+	0.182237i	$0.0583338\pi$
$271$			6.00000i			0.364474i	−0.983255	+	0.182237i	$0.941666\pi$
$272$		0			0
$273$		0			0
$274$	2.00000			0.120824
$275$		0			0
$276$	12.0000			0.722315
$277$	−12.0000			−0.721010			−0.360505	−	0.932757i	$-0.617396\pi$
$277$	−12.0000			−0.721010			−0.360505	+	0.932757i	$0.617396\pi$
$278$			4.00000i			0.239904i
$279$			6.00000i			0.359211i
$280$		0			0
$281$			8.00000i			0.477240i	0.971113	+	0.238620i	$0.0766950\pi$
$281$			8.00000i			0.477240i	−0.971113	+	0.238620i	$0.923305\pi$
$282$	16.0000			0.952786
$283$	22.0000			1.30776			0.653882	−	0.756596i	$-0.273139\pi$
$283$	22.0000			1.30776			0.653882	+	0.756596i	$0.273139\pi$
$284$		−	2.00000i		−	0.118678i
$285$		0			0
$286$	−4.00000	−	6.00000i	−0.236525	−	0.354787i
$287$		0			0
$288$			5.00000i			0.294628i
$289$	−17.0000			−1.00000
$290$		0			0
$291$		−	12.0000i		−	0.703452i
$292$		−	6.00000i		−	0.351123i
$293$		−	26.0000i		−	1.51894i	−0.650545	−	0.759468i	$-0.725459\pi$
$293$		−	26.0000i		−	1.51894i	0.650545	−	0.759468i	$-0.274541\pi$
$294$		−	14.0000i		−	0.816497i
$295$		0			0
$296$	18.0000			1.04623
$297$			8.00000i			0.464207i
$298$	20.0000			1.15857
$299$	−12.0000	−	18.0000i	−0.693978	−	1.04097i
$300$		0			0
$301$		0			0
$302$	18.0000			1.03578
$303$	−12.0000			−0.689382
$304$		−	6.00000i		−	0.344124i
$305$		0			0
$306$		0			0
$307$		−	12.0000i		−	0.684876i	−0.939540	−	0.342438i	$-0.888747\pi$
$307$		−	12.0000i		−	0.684876i	0.939540	−	0.342438i	$-0.111253\pi$
$308$		0			0
$309$	12.0000			0.682656
$310$		0			0
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$	18.0000	−	12.0000i	1.01905	−	0.679366i
$313$	−8.00000			−0.452187			−0.226093	−	0.974106i	$-0.572595\pi$
$313$	−8.00000			−0.452187			−0.226093	+	0.974106i	$0.572595\pi$
$314$			12.0000i			0.677199i
$315$		0			0
$316$		0			0
$317$			2.00000i			0.112331i	0.998421	+	0.0561656i	$0.0178875\pi$
$317$			2.00000i			0.112331i	−0.998421	+	0.0561656i	$0.982113\pi$
$318$		−	24.0000i		−	1.34585i
$319$		−	12.0000i		−	0.671871i
$320$		0			0
$321$	12.0000			0.669775
$322$		0			0
$323$		0			0
$324$	−11.0000			−0.611111
$325$		0			0
$326$	−12.0000			−0.664619
$327$			24.0000i			1.32720i
$328$	24.0000			1.32518
$329$		0			0
$330$		0			0
$331$		−	30.0000i		−	1.64895i	−0.565899	−	0.824475i	$-0.691471\pi$
$331$		−	30.0000i		−	1.64895i	0.565899	−	0.824475i	$-0.308529\pi$
$332$		−	4.00000i		−	0.219529i
$333$		−	6.00000i		−	0.328798i
$334$	−16.0000			−0.875481
$335$		0			0
$336$		0			0
$337$	32.0000			1.74315			0.871576	−	0.490261i	$-0.163099\pi$
$337$	32.0000			1.74315			0.871576	+	0.490261i	$0.163099\pi$
$338$	−12.0000	−	5.00000i	−0.652714	−	0.271964i
$339$		0			0
$340$		0			0
$341$	−12.0000			−0.649836
$342$	−6.00000			−0.324443
$343$		0			0
$344$			18.0000i			0.970495i
$345$		0			0
$346$		−	12.0000i		−	0.645124i
$347$	−6.00000			−0.322097			−0.161048	−	0.986947i	$-0.551488\pi$
$347$	−6.00000			−0.322097			−0.161048	+	0.986947i	$0.551488\pi$
$348$	12.0000			0.643268
$349$		−	12.0000i		−	0.642345i	−0.947021	−	0.321173i	$-0.895923\pi$
$349$		−	12.0000i		−	0.642345i	0.947021	−	0.321173i	$-0.104077\pi$
$350$		0			0
$351$	8.00000	+	12.0000i	0.427008	+	0.640513i
$352$	−10.0000			−0.533002
$353$		−	14.0000i		−	0.745145i	−0.928003	−	0.372572i	$-0.878476\pi$
$353$		−	14.0000i		−	0.745145i	0.928003	−	0.372572i	$-0.121524\pi$
$354$	−4.00000			−0.212598
$355$		0			0
$356$			8.00000i			0.423999i
$357$		0			0
$358$			12.0000i			0.634220i
$359$			2.00000i			0.105556i	0.998606	+	0.0527780i	$0.0168076\pi$
$359$			2.00000i			0.105556i	−0.998606	+	0.0527780i	$0.983192\pi$
$360$		0			0
$361$	−17.0000			−0.894737
$362$		−	2.00000i		−	0.105118i
$363$	−14.0000			−0.734809
$364$		0			0
$365$		0			0
$366$		−	12.0000i		−	0.627250i
$367$	−18.0000			−0.939592			−0.469796	−	0.882775i	$-0.655673\pi$
$367$	−18.0000			−0.939592			−0.469796	+	0.882775i	$0.655673\pi$
$368$	6.00000			0.312772
$369$		−	8.00000i		−	0.416463i
$370$		0			0
$371$		0			0
$372$		−	12.0000i		−	0.622171i
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$		0			0
$375$		0			0
$376$	−24.0000			−1.23771
$377$	−12.0000	−	18.0000i	−0.618031	−	0.927047i
$378$		0			0
$379$		−	18.0000i		−	0.924598i	−0.886724	−	0.462299i	$-0.847025\pi$
$379$		−	18.0000i		−	0.924598i	0.886724	−	0.462299i	$-0.152975\pi$
$380$		0			0
$381$	4.00000			0.204926
$382$		0			0
$383$			8.00000i			0.408781i	0.978889	+	0.204390i	$0.0655212\pi$
$383$			8.00000i			0.408781i	−0.978889	+	0.204390i	$0.934479\pi$
$384$		−	6.00000i		−	0.306186i
$385$		0			0
$386$	6.00000			0.305392
$387$	6.00000			0.304997
$388$			6.00000i			0.304604i
$389$	−6.00000			−0.304212			−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000			−0.304212			−0.152106	+	0.988364i	$0.548606\pi$
$390$		0			0
$391$		0			0
$392$			21.0000i			1.06066i
$393$	24.0000			1.21064
$394$	−2.00000			−0.100759
$395$		0			0
$396$			2.00000i			0.100504i
$397$			18.0000i			0.903394i	0.892171	+	0.451697i	$0.149181\pi$
$397$			18.0000i			0.903394i	−0.892171	+	0.451697i	$0.850819\pi$
$398$			24.0000i			1.20301i
$399$		0			0
$400$		0			0
$401$			16.0000i			0.799002i	0.916733	+	0.399501i	$0.130817\pi$
$401$			16.0000i			0.799002i	−0.916733	+	0.399501i	$0.869183\pi$
$402$	−24.0000			−1.19701
$403$	−18.0000	+	12.0000i	−0.896644	+	0.597763i
$404$	6.00000			0.298511
$405$		0			0
$406$		0			0
$407$	12.0000			0.594818
$408$		0			0
$409$			24.0000i			1.18672i	0.804936	+	0.593362i	$0.202200\pi$
$409$			24.0000i			1.18672i	−0.804936	+	0.593362i	$0.797800\pi$
$410$		0			0
$411$			4.00000i			0.197305i
$412$	−6.00000			−0.295599
$413$		0			0
$414$		−	6.00000i		−	0.294884i
$415$		0			0
$416$	−15.0000	+	10.0000i	−0.735436	+	0.490290i
$417$	−8.00000			−0.391762
$418$		−	12.0000i		−	0.586939i
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		0			0
$421$			36.0000i			1.75453i	0.480004	+	0.877266i	$0.340635\pi$
$421$			36.0000i			1.75453i	−0.480004	+	0.877266i	$0.659365\pi$
$422$		−	12.0000i		−	0.584151i
$423$			8.00000i			0.388973i
$424$			36.0000i			1.74831i
$425$		0			0
$426$	−4.00000			−0.193801
$427$		0			0
$428$	−6.00000			−0.290021
$429$	12.0000	−	8.00000i	0.579365	−	0.386244i
$430$		0			0
$431$		−	10.0000i		−	0.481683i	−0.970564	−	0.240842i	$-0.922577\pi$
$431$		−	10.0000i		−	0.481683i	0.970564	−	0.240842i	$-0.0774234\pi$
$432$	−4.00000			−0.192450
$433$	−16.0000			−0.768911			−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000			−0.768911			−0.384455	+	0.923144i	$0.625611\pi$
$434$		0			0
$435$		0			0
$436$		−	12.0000i		−	0.574696i
$437$		−	36.0000i		−	1.72211i
$438$	−12.0000			−0.573382
$439$	−8.00000			−0.381819			−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000			−0.381819			−0.190910	+	0.981608i	$0.561144\pi$
$440$		0			0
$441$	7.00000			0.333333
$442$		0			0
$443$	6.00000			0.285069			0.142534	−	0.989790i	$-0.454475\pi$
$443$	6.00000			0.285069			0.142534	+	0.989790i	$0.454475\pi$
$444$			12.0000i			0.569495i
$445$		0			0
$446$	−24.0000			−1.13643
$447$			40.0000i			1.89194i
$448$		0			0
$449$			16.0000i			0.755087i	0.925992	+	0.377543i	$0.123231\pi$
$449$			16.0000i			0.755087i	−0.925992	+	0.377543i	$0.876769\pi$
$450$		0			0
$451$	16.0000			0.753411
$452$		0			0
$453$			36.0000i			1.69143i
$454$	−4.00000			−0.187729
$455$		0			0
$456$	36.0000			1.68585
$457$			30.0000i			1.40334i	0.712502	+	0.701670i	$0.247562\pi$
$457$			30.0000i			1.40334i	−0.712502	+	0.701670i	$0.752438\pi$
$458$	−12.0000			−0.560723
$459$		0			0
$460$		0			0
$461$		−	4.00000i		−	0.186299i	−0.995652	−	0.0931493i	$-0.970307\pi$
$461$		−	4.00000i		−	0.186299i	0.995652	−	0.0931493i	$-0.0296934\pi$
$462$		0			0
$463$		−	24.0000i		−	1.11537i	−0.830051	−	0.557687i	$-0.811689\pi$
$463$		−	24.0000i		−	1.11537i	0.830051	−	0.557687i	$-0.188311\pi$
$464$	6.00000			0.278543
$465$		0			0
$466$			24.0000i			1.11178i
$467$	18.0000			0.832941			0.416470	−	0.909149i	$-0.363267\pi$
$467$	18.0000			0.832941			0.416470	+	0.909149i	$0.363267\pi$
$468$	2.00000	+	3.00000i	0.0924500	+	0.138675i
$469$		0			0
$470$		0			0
$471$	−24.0000			−1.10586
$472$	6.00000			0.276172
$473$			12.0000i			0.551761i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	12.0000			0.549442
$478$	−10.0000			−0.457389
$479$		−	22.0000i		−	1.00521i	−0.864517	−	0.502603i	$-0.832376\pi$
$479$		−	22.0000i		−	1.00521i	0.864517	−	0.502603i	$-0.167624\pi$
$480$		0			0
$481$	18.0000	−	12.0000i	0.820729	−	0.547153i
$482$		0			0
$483$		0			0
$484$	7.00000			0.318182
$485$		0			0
$486$			10.0000i			0.453609i
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$			18.0000i			0.814822i
$489$		−	24.0000i		−	1.08532i
$490$		0			0
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$			16.0000i			0.721336i
$493$		0			0
$494$	−12.0000	−	18.0000i	−0.539906	−	0.809858i
$495$		0			0
$496$		−	6.00000i		−	0.269408i
$497$		0			0
$498$	−8.00000			−0.358489
$499$			6.00000i			0.268597i	0.990941	+	0.134298i	$0.0428781\pi$
$499$			6.00000i			0.268597i	−0.990941	+	0.134298i	$0.957122\pi$
$500$		0			0
$501$		−	32.0000i		−	1.42965i
$502$			12.0000i			0.535586i
$503$	−6.00000			−0.267527			−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$		0			0
$505$		0			0
$506$	12.0000			0.533465
$507$	10.0000	−	24.0000i	0.444116	−	1.06588i
$508$	−2.00000			−0.0887357
$509$			20.0000i			0.886484i	0.896402	+	0.443242i	$0.146172\pi$
$509$			20.0000i			0.886484i	−0.896402	+	0.443242i	$0.853828\pi$
$510$		0			0
$511$		0			0
$512$		−	11.0000i		−	0.486136i
$513$			24.0000i			1.05963i
$514$		0			0
$515$		0			0
$516$	−12.0000			−0.528271
$517$	−16.0000			−0.703679
$518$		0			0
$519$	24.0000			1.05348
$520$		0			0
$521$	−30.0000			−1.31432			−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000			−1.31432			−0.657162	+	0.753749i	$0.728243\pi$
$522$		−	6.00000i		−	0.262613i
$523$	−42.0000			−1.83653			−0.918266	−	0.395964i	$-0.870410\pi$
$523$	−42.0000			−1.83653			−0.918266	+	0.395964i	$0.870410\pi$
$524$	−12.0000			−0.524222
$525$		0			0
$526$		−	6.00000i		−	0.261612i
$527$		0			0
$528$			4.00000i			0.174078i
$529$	13.0000			0.565217
$530$		0			0
$531$		−	2.00000i		−	0.0867926i
$532$		0			0
$533$	24.0000	−	16.0000i	1.03956	−	0.693037i
$534$	16.0000			0.692388
$535$		0			0
$536$	36.0000			1.55496
$537$	−24.0000			−1.03568
$538$			18.0000i			0.776035i
$539$			14.0000i			0.603023i
$540$		0			0
$541$			12.0000i			0.515920i	0.966156	+	0.257960i	$0.0830503\pi$
$541$			12.0000i			0.515920i	−0.966156	+	0.257960i	$0.916950\pi$
$542$	−6.00000			−0.257722
$543$	4.00000			0.171656
$544$		0			0
$545$		0			0
$546$		0			0
$547$	18.0000			0.769624			0.384812	−	0.922995i	$-0.374266\pi$
$547$	18.0000			0.769624			0.384812	+	0.922995i	$0.374266\pi$
$548$		−	2.00000i		−	0.0854358i
$549$	6.00000			0.256074
$550$		0			0
$551$		−	36.0000i		−	1.53365i
$552$			36.0000i			1.53226i
$553$		0			0
$554$		−	12.0000i		−	0.509831i
$555$		0			0
$556$	4.00000			0.169638
$557$		−	14.0000i		−	0.593199i	−0.955002	−	0.296600i	$-0.904147\pi$
$557$		−	14.0000i		−	0.593199i	0.955002	−	0.296600i	$-0.0958526\pi$
$558$	−6.00000			−0.254000
$559$	12.0000	+	18.0000i	0.507546	+	0.761319i
$560$		0			0
$561$		0			0
$562$	−8.00000			−0.337460
$563$	30.0000			1.26435			0.632175	−	0.774826i	$-0.282163\pi$
$563$	30.0000			1.26435			0.632175	+	0.774826i	$0.282163\pi$
$564$		−	16.0000i		−	0.673722i
$565$		0			0
$566$			22.0000i			0.924729i
$567$		0			0
$568$	6.00000			0.251754
$569$	−18.0000			−0.754599			−0.377300	−	0.926091i	$-0.623147\pi$
$569$	−18.0000			−0.754599			−0.377300	+	0.926091i	$0.623147\pi$
$570$		0			0
$571$	12.0000			0.502184			0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000			0.502184			0.251092	+	0.967963i	$0.419210\pi$
$572$	−6.00000	+	4.00000i	−0.250873	+	0.167248i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−7.00000			−0.291667
$577$		−	18.0000i		−	0.749350i	−0.927156	−	0.374675i	$-0.877754\pi$
$577$		−	18.0000i		−	0.749350i	0.927156	−	0.374675i	$-0.122246\pi$
$578$		−	17.0000i		−	0.707107i
$579$			12.0000i			0.498703i
$580$		0			0
$581$		0			0
$582$	12.0000			0.497416
$583$			24.0000i			0.993978i
$584$	18.0000			0.744845
$585$		0			0
$586$	26.0000			1.07405
$587$		−	20.0000i		−	0.825488i	−0.910847	−	0.412744i	$-0.864570\pi$
$587$		−	20.0000i		−	0.825488i	0.910847	−	0.412744i	$-0.135430\pi$
$588$	−14.0000			−0.577350
$589$	−36.0000			−1.48335
$590$		0			0
$591$		−	4.00000i		−	0.164538i
$592$			6.00000i			0.246598i
$593$		−	22.0000i		−	0.903432i	−0.892162	−	0.451716i	$-0.850812\pi$
$593$		−	22.0000i		−	0.903432i	0.892162	−	0.451716i	$-0.149188\pi$
$594$	−8.00000			−0.328244
$595$		0			0
$596$		−	20.0000i		−	0.819232i
$597$	−48.0000			−1.96451
$598$	18.0000	−	12.0000i	0.736075	−	0.490716i
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$		0			0
$601$	−6.00000			−0.244745			−0.122373	−	0.992484i	$-0.539050\pi$
$601$	−6.00000			−0.244745			−0.122373	+	0.992484i	$0.539050\pi$
$602$		0			0
$603$		−	12.0000i		−	0.488678i
$604$		−	18.0000i		−	0.732410i
$605$		0			0
$606$		−	12.0000i		−	0.487467i
$607$	−18.0000			−0.730597			−0.365299	−	0.930890i	$-0.619033\pi$
$607$	−18.0000			−0.730597			−0.365299	+	0.930890i	$0.619033\pi$
$608$	−30.0000			−1.21666
$609$		0			0
$610$		0			0
$611$	−24.0000	+	16.0000i	−0.970936	+	0.647291i
$612$		0			0
$613$			30.0000i			1.21169i	0.795583	+	0.605844i	$0.207165\pi$
$613$			30.0000i			1.21169i	−0.795583	+	0.605844i	$0.792835\pi$
$614$	12.0000			0.484281
$615$		0			0
$616$		0			0
$617$		−	34.0000i		−	1.36879i	−0.729112	−	0.684394i	$-0.760067\pi$
$617$		−	34.0000i		−	1.36879i	0.729112	−	0.684394i	$-0.239933\pi$
$618$			12.0000i			0.482711i
$619$		−	18.0000i		−	0.723481i	−0.932279	−	0.361741i	$-0.882183\pi$
$619$		−	18.0000i		−	0.723481i	0.932279	−	0.361741i	$-0.117817\pi$
$620$		0			0
$621$	−24.0000			−0.963087
$622$			24.0000i			0.962312i
$623$		0			0
$624$	4.00000	+	6.00000i	0.160128	+	0.240192i
$625$		0			0
$626$		−	8.00000i		−	0.319744i
$627$	24.0000			0.958468
$628$	12.0000			0.478852
$629$		0			0
$630$		0			0
$631$			30.0000i			1.19428i	0.802137	+	0.597141i	$0.203697\pi$
$631$			30.0000i			1.19428i	−0.802137	+	0.597141i	$0.796303\pi$
$632$		0			0
$633$	24.0000			0.953914
$634$	−2.00000			−0.0794301
$635$		0			0
$636$	−24.0000			−0.951662
$637$	14.0000	+	21.0000i	0.554700	+	0.832050i
$638$	12.0000			0.475085
$639$		−	2.00000i		−	0.0791188i
$640$		0			0
$641$	−30.0000			−1.18493			−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000			−1.18493			−0.592464	+	0.805597i	$0.701845\pi$
$642$			12.0000i			0.473602i
$643$		−	36.0000i		−	1.41970i	−0.704352	−	0.709851i	$-0.748762\pi$
$643$		−	36.0000i		−	1.41970i	0.704352	−	0.709851i	$-0.251238\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	6.00000			0.235884			0.117942	−	0.993020i	$-0.462370\pi$
$647$	6.00000			0.235884			0.117942	+	0.993020i	$0.462370\pi$
$648$		−	33.0000i		−	1.29636i
$649$	4.00000			0.157014
$650$		0			0
$651$		0			0
$652$			12.0000i			0.469956i
$653$	36.0000			1.40879			0.704394	−	0.709809i	$-0.251219\pi$
$653$	36.0000			1.40879			0.704394	+	0.709809i	$0.251219\pi$
$654$	−24.0000			−0.938474
$655$		0			0
$656$			8.00000i			0.312348i
$657$		−	6.00000i		−	0.234082i
$658$		0			0
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$		0			0
$661$		−	12.0000i		−	0.466746i	−0.972387	−	0.233373i	$-0.925024\pi$
$661$		−	12.0000i		−	0.466746i	0.972387	−	0.233373i	$-0.0749763\pi$
$662$	30.0000			1.16598
$663$		0			0
$664$	12.0000			0.465690
$665$		0			0
$666$	6.00000			0.232495
$667$	36.0000			1.39393
$668$			16.0000i			0.619059i
$669$		−	48.0000i		−	1.85579i
$670$		0			0
$671$			12.0000i			0.463255i
$672$		0			0
$673$	−48.0000			−1.85026			−0.925132	−	0.379646i	$-0.876046\pi$
$673$	−48.0000			−1.85026			−0.925132	+	0.379646i	$0.876046\pi$
$674$			32.0000i			1.23259i
$675$		0			0
$676$	−5.00000	+	12.0000i	−0.192308	+	0.461538i
$677$	36.0000			1.38359			0.691796	−	0.722093i	$-0.256820\pi$
$677$	36.0000			1.38359			0.691796	+	0.722093i	$0.256820\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		−	8.00000i		−	0.306561i
$682$		−	12.0000i		−	0.459504i
$683$		−	44.0000i		−	1.68361i	−0.539779	−	0.841807i	$-0.681492\pi$
$683$		−	44.0000i		−	1.68361i	0.539779	−	0.841807i	$-0.318508\pi$
$684$			6.00000i			0.229416i
$685$		0			0
$686$		0			0
$687$		−	24.0000i		−	0.915657i
$688$	−6.00000			−0.228748
$689$	24.0000	+	36.0000i	0.914327	+	1.37149i
$690$		0			0
$691$			42.0000i			1.59776i	0.601494	+	0.798878i	$0.294573\pi$
$691$			42.0000i			1.59776i	−0.601494	+	0.798878i	$0.705427\pi$
$692$	−12.0000			−0.456172
$693$		0			0
$694$		−	6.00000i		−	0.227757i
$695$		0			0
$696$			36.0000i			1.36458i
$697$		0			0
$698$	12.0000			0.454207
$699$	−48.0000			−1.81553
$700$		0			0
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$	−12.0000	+	8.00000i	−0.452911	+	0.301941i
$703$	36.0000			1.35777
$704$		−	14.0000i		−	0.527645i
$705$		0			0
$706$	14.0000			0.526897
$707$		0			0
$708$			4.00000i			0.150329i
$709$			12.0000i			0.450669i	0.974281	+	0.225335i	$0.0723476\pi$
$709$			12.0000i			0.450669i	−0.974281	+	0.225335i	$0.927652\pi$
$710$		0			0
$711$		0			0
$712$	−24.0000			−0.899438
$713$		−	36.0000i		−	1.34821i
$714$		0			0
$715$		0			0
$716$	12.0000			0.448461
$717$		−	20.0000i		−	0.746914i
$718$	−2.00000			−0.0746393
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$		0			0
$722$		−	17.0000i		−	0.632674i
$723$		0			0
$724$	−2.00000			−0.0743294
$725$		0			0
$726$		−	14.0000i		−	0.519589i
$727$	−26.0000			−0.964287			−0.482143	−	0.876092i	$-0.660142\pi$
$727$	−26.0000			−0.964287			−0.482143	+	0.876092i	$0.660142\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$		0			0
$732$	−12.0000			−0.443533
$733$		−	42.0000i		−	1.55131i	−0.631160	−	0.775653i	$-0.717421\pi$
$733$		−	42.0000i		−	1.55131i	0.631160	−	0.775653i	$-0.282579\pi$
$734$		−	18.0000i		−	0.664392i
$735$		0			0
$736$		−	30.0000i		−	1.10581i
$737$	24.0000			0.884051
$738$	8.00000			0.294484
$739$			6.00000i			0.220714i	0.993892	+	0.110357i	$0.0351994\pi$
$739$			6.00000i			0.220714i	−0.993892	+	0.110357i	$0.964801\pi$
$740$		0			0
$741$	36.0000	−	24.0000i	1.32249	−	0.881662i
$742$		0			0
$743$		−	16.0000i		−	0.586983i	−0.955962	−	0.293492i	$-0.905183\pi$
$743$		−	16.0000i		−	0.586983i	0.955962	−	0.293492i	$-0.0948173\pi$
$744$	36.0000			1.31982
$745$		0			0
$746$		−	4.00000i		−	0.146450i
$747$		−	4.00000i		−	0.146352i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−32.0000			−1.16770			−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000			−1.16770			−0.583848	+	0.811863i	$0.698454\pi$
$752$		−	8.00000i		−	0.291730i
$753$	−24.0000			−0.874609
$754$	18.0000	−	12.0000i	0.655521	−	0.437014i
$755$		0			0
$756$		0			0
$757$	20.0000			0.726912			0.363456	−	0.931611i	$-0.381597\pi$
$757$	20.0000			0.726912			0.363456	+	0.931611i	$0.381597\pi$
$758$	18.0000			0.653789
$759$			24.0000i			0.871145i
$760$		0			0
$761$		−	40.0000i		−	1.45000i	−0.688749	−	0.724999i	$-0.741840\pi$
$761$		−	40.0000i		−	1.45000i	0.688749	−	0.724999i	$-0.258160\pi$
$762$			4.00000i			0.144905i
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−8.00000			−0.289052
$767$	6.00000	−	4.00000i	0.216647	−	0.144432i
$768$	34.0000			1.22687
$769$		0			0		1.00000			$0$
$769$		0			0		−1.00000			$\pi$
$770$		0			0
$771$		0			0
$772$		−	6.00000i		−	0.215945i
$773$			38.0000i			1.36677i	0.730061	+	0.683383i	$0.239492\pi$
$773$			38.0000i			1.36677i	−0.730061	+	0.683383i	$0.760508\pi$
$774$			6.00000i			0.215666i
$775$		0			0
$776$	−18.0000			−0.646162
$777$		0			0
$778$		−	6.00000i		−	0.215110i
$779$	48.0000			1.71978
$780$		0			0
$781$	4.00000			0.143131
$782$		0			0
$783$	−24.0000			−0.857690
$784$	−7.00000			−0.250000
$785$		0			0
$786$			24.0000i			0.856052i
$787$		−	12.0000i		−	0.427754i	−0.976861	−	0.213877i	$-0.931391\pi$
$787$		−	12.0000i		−	0.427754i	0.976861	−	0.213877i	$-0.0686091\pi$
$788$			2.00000i			0.0712470i
$789$	12.0000			0.427211
$790$		0			0
$791$		0			0
$792$	−6.00000			−0.213201
$793$	12.0000	+	18.0000i	0.426132	+	0.639199i
$794$	−18.0000			−0.638796
$795$		0			0
$796$	24.0000			0.850657
$797$	12.0000			0.425062			0.212531	−	0.977154i	$-0.431829\pi$
$797$	12.0000			0.425062			0.212531	+	0.977154i	$0.431829\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$			8.00000i			0.282666i
$802$	−16.0000			−0.564980
$803$	12.0000			0.423471
$804$			24.0000i			0.846415i
$805$		0			0
$806$	−12.0000	−	18.0000i	−0.422682	−	0.634023i
$807$	−36.0000			−1.26726
$808$			18.0000i			0.633238i
$809$	30.0000			1.05474			0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000			1.05474			0.527372	+	0.849635i	$0.323177\pi$
$810$		0			0
$811$		−	30.0000i		−	1.05344i	−0.850038	−	0.526721i	$-0.823421\pi$
$811$		−	30.0000i		−	1.05344i	0.850038	−	0.526721i	$-0.176579\pi$
$812$		0			0
$813$		−	12.0000i		−	0.420858i
$814$			12.0000i			0.420600i
$815$		0			0
$816$		0			0
$817$			36.0000i			1.25948i
$818$	−24.0000			−0.839140
$819$		0			0
$820$		0			0
$821$			20.0000i			0.698005i	0.937122	+	0.349002i	$0.113479\pi$
$821$			20.0000i			0.698005i	−0.937122	+	0.349002i	$0.886521\pi$
$822$	−4.00000			−0.139516
$823$	42.0000			1.46403			0.732014	−	0.681290i	$-0.238581\pi$
$823$	42.0000			1.46403			0.732014	+	0.681290i	$0.238581\pi$
$824$		−	18.0000i		−	0.627060i
$825$		0			0
$826$		0			0
$827$		−	4.00000i		−	0.139094i	−0.997579	−	0.0695468i	$-0.977845\pi$
$827$		−	4.00000i		−	0.139094i	0.997579	−	0.0695468i	$-0.0221553\pi$
$828$	−6.00000			−0.208514
$829$	−6.00000			−0.208389			−0.104194	−	0.994557i	$-0.533226\pi$
$829$	−6.00000			−0.208389			−0.104194	+	0.994557i	$0.533226\pi$
$830$		0			0
$831$	24.0000			0.832551
$832$	−14.0000	−	21.0000i	−0.485363	−	0.728044i
$833$		0			0
$834$		−	8.00000i		−	0.277017i
$835$		0			0
$836$	−12.0000			−0.415029
$837$			24.0000i			0.829561i
$838$			12.0000i			0.414533i
$839$		−	46.0000i		−	1.58810i	−0.607855	−	0.794048i	$-0.707970\pi$
$839$		−	46.0000i		−	1.58810i	0.607855	−	0.794048i	$-0.292030\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	−36.0000			−1.24064
$843$		−	16.0000i		−	0.551069i
$844$	−12.0000			−0.413057
$845$		0			0
$846$	−8.00000			−0.275046
$847$		0			0
$848$	−12.0000			−0.412082
$849$	−44.0000			−1.51008
$850$		0			0
$851$			36.0000i			1.23406i
$852$			4.00000i			0.137038i
$853$			54.0000i			1.84892i	0.381273	+	0.924462i	$0.375486\pi$
$853$			54.0000i			1.84892i	−0.381273	+	0.924462i	$0.624514\pi$
$854$		0			0
$855$		0			0
$856$		−	18.0000i		−	0.615227i
$857$	24.0000			0.819824			0.409912	−	0.912125i	$-0.365559\pi$
$857$	24.0000			0.819824			0.409912	+	0.912125i	$0.365559\pi$
$858$	8.00000	+	12.0000i	0.273115	+	0.409673i
$859$	36.0000			1.22830			0.614152	−	0.789188i	$-0.289498\pi$
$859$	36.0000			1.22830			0.614152	+	0.789188i	$0.289498\pi$
$860$		0			0
$861$		0			0
$862$	10.0000			0.340601
$863$		−	8.00000i		−	0.272323i	−0.990687	−	0.136162i	$-0.956523\pi$
$863$		−	8.00000i		−	0.272323i	0.990687	−	0.136162i	$-0.0434766\pi$
$864$			20.0000i			0.680414i
$865$		0			0
$866$		−	16.0000i		−	0.543702i
$867$	34.0000			1.15470
$868$		0			0
$869$		0			0
$870$		0			0
$871$	36.0000	−	24.0000i	1.21981	−	0.813209i
$872$	36.0000			1.21911
$873$			6.00000i			0.203069i
$874$	36.0000			1.21772
$875$		0			0
$876$			12.0000i			0.405442i
$877$		−	6.00000i		−	0.202606i	−0.994856	−	0.101303i	$-0.967699\pi$
$877$		−	6.00000i		−	0.202606i	0.994856	−	0.101303i	$-0.0323011\pi$
$878$		−	8.00000i		−	0.269987i
$879$			52.0000i			1.75392i
$880$		0			0
$881$	42.0000			1.41502			0.707508	−	0.706705i	$-0.249819\pi$
$881$	42.0000			1.41502			0.707508	+	0.706705i	$0.249819\pi$
$882$			7.00000i			0.235702i
$883$	−2.00000			−0.0673054			−0.0336527	−	0.999434i	$-0.510714\pi$
$883$	−2.00000			−0.0673054			−0.0336527	+	0.999434i	$0.510714\pi$
$884$		0			0
$885$		0			0
$886$			6.00000i			0.201574i
$887$	−42.0000			−1.41022			−0.705111	−	0.709097i	$-0.749103\pi$
$887$	−42.0000			−1.41022			−0.705111	+	0.709097i	$0.749103\pi$
$888$	−36.0000			−1.20808
$889$		0			0
$890$		0			0
$891$		−	22.0000i		−	0.737028i
$892$			24.0000i			0.803579i
$893$	−48.0000			−1.60626
$894$	−40.0000			−1.33780
$895$		0			0
$896$		0			0
$897$	24.0000	+	36.0000i	0.801337	+	1.20201i
$898$	−16.0000			−0.533927
$899$		−	36.0000i		−	1.20067i
$900$		0			0
$901$		0			0
$902$			16.0000i			0.532742i
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−36.0000			−1.19602
$907$	10.0000			0.332045			0.166022	−	0.986122i	$-0.446908\pi$
$907$	10.0000			0.332045			0.166022	+	0.986122i	$0.446908\pi$
$908$			4.00000i			0.132745i
$909$	6.00000			0.199007
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$			12.0000i			0.397360i
$913$	8.00000			0.264761
$914$	−30.0000			−0.992312
$915$		0			0
$916$			12.0000i			0.396491i
$917$		0			0
$918$		0			0
$919$	−24.0000			−0.791687			−0.395843	−	0.918318i	$-0.629548\pi$
$919$	−24.0000			−0.791687			−0.395843	+	0.918318i	$0.629548\pi$
$920$		0			0
$921$			24.0000i			0.790827i
$922$	4.00000			0.131733
$923$	6.00000	−	4.00000i	0.197492	−	0.131662i
$924$		0			0
$925$		0			0
$926$	24.0000			0.788689
$927$	−6.00000			−0.197066
$928$		−	30.0000i		−	0.984798i
$929$		−	16.0000i		−	0.524943i	−0.964940	−	0.262471i	$-0.915462\pi$
$929$		−	16.0000i		−	0.524943i	0.964940	−	0.262471i	$-0.0845376\pi$
$930$		0			0
$931$			42.0000i			1.37649i
$932$	24.0000			0.786146
$933$	−48.0000			−1.57145
$934$			18.0000i			0.588978i
$935$		0			0
$936$	−9.00000	+	6.00000i	−0.294174	+	0.196116i
$937$	−56.0000			−1.82944			−0.914720	−	0.404088i	$-0.867589\pi$
$937$	−56.0000			−1.82944			−0.914720	+	0.404088i	$0.867589\pi$
$938$		0			0
$939$	16.0000			0.522140
$940$		0			0
$941$			28.0000i			0.912774i	0.889781	+	0.456387i	$0.150857\pi$
$941$			28.0000i			0.912774i	−0.889781	+	0.456387i	$0.849143\pi$
$942$		−	24.0000i		−	0.781962i
$943$			48.0000i			1.56310i
$944$			2.00000i			0.0650945i
$945$		0			0
$946$	−12.0000			−0.390154
$947$		−	28.0000i		−	0.909878i	−0.890523	−	0.454939i	$-0.849661\pi$
$947$		−	28.0000i		−	0.909878i	0.890523	−	0.454939i	$-0.150339\pi$
$948$		0			0
$949$	18.0000	−	12.0000i	0.584305	−	0.389536i
$950$		0			0
$951$		−	4.00000i		−	0.129709i
$952$		0			0
$953$	−24.0000			−0.777436			−0.388718	−	0.921357i	$-0.627082\pi$
$953$	−24.0000			−0.777436			−0.388718	+	0.921357i	$0.627082\pi$
$954$			12.0000i			0.388514i
$955$		0			0
$956$			10.0000i			0.323423i
$957$			24.0000i			0.775810i
$958$	22.0000			0.710788
$959$		0			0
$960$		0			0
$961$	−5.00000			−0.161290
$962$	12.0000	+	18.0000i	0.386896	+	0.580343i
$963$	−6.00000			−0.193347
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	48.0000i		−	1.54358i	−0.635880	−	0.771788i	$-0.719363\pi$
$967$		−	48.0000i		−	1.54358i	0.635880	−	0.771788i	$-0.280637\pi$
$968$			21.0000i			0.674966i
$969$		0			0
$970$		0			0
$971$	12.0000			0.385098			0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000			0.385098			0.192549	+	0.981287i	$0.438325\pi$
$972$	10.0000			0.320750
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−6.00000			−0.192055
$977$		−	34.0000i		−	1.08776i	−0.839164	−	0.543878i	$-0.816955\pi$
$977$		−	34.0000i		−	1.08776i	0.839164	−	0.543878i	$-0.183045\pi$
$978$	24.0000			0.767435
$979$	−16.0000			−0.511362
$980$		0			0
$981$		−	12.0000i		−	0.383131i
$982$			12.0000i			0.382935i
$983$			16.0000i			0.510321i	0.966899	+	0.255160i	$0.0821283\pi$
$983$			16.0000i			0.510321i	−0.966899	+	0.255160i	$0.917872\pi$
$984$	−48.0000			−1.53018
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−18.0000	+	12.0000i	−0.572656	+	0.381771i
$989$	−36.0000			−1.14473
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$	−30.0000			−0.952501
$993$			60.0000i			1.90404i
$994$		0			0
$995$		0			0
$996$			8.00000i			0.253490i
$997$	−60.0000			−1.90022			−0.950110	−	0.311916i	$-0.899029\pi$
$997$	−60.0000			−1.90022			−0.950110	+	0.311916i	$0.899029\pi$
$998$	−6.00000			−0.189927
$999$		−	24.0000i		−	0.759326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.c.b.51.2		2
5.2	odd	4		65.2.d.a.64.2	yes	2
5.3	odd	4		65.2.d.b.64.1	yes	2
5.4	even	2		325.2.c.e.51.1		2
13.5	odd	4		4225.2.a.k.1.1		1
13.8	odd	4		4225.2.a.e.1.1		1
13.12	even	2	inner	325.2.c.b.51.1		2
15.2	even	4		585.2.h.c.64.1		2
15.8	even	4		585.2.h.b.64.1		2
20.3	even	4		1040.2.f.b.129.2		2
20.7	even	4		1040.2.f.a.129.1		2
65.2	even	12		845.2.n.b.529.1		4
65.3	odd	12		845.2.l.a.654.2		4
65.7	even	12		845.2.n.a.484.1		4
65.8	even	4		845.2.b.a.339.2		2
65.12	odd	4		65.2.d.b.64.2	yes	2
65.17	odd	12		845.2.l.a.699.2		4
65.18	even	4		845.2.b.b.339.1		2
65.22	odd	12		845.2.l.b.699.2		4
65.23	odd	12		845.2.l.b.654.2		4
65.28	even	12		845.2.n.b.529.2		4
65.32	even	12		845.2.n.b.484.2		4
65.33	even	12		845.2.n.a.484.2		4
65.34	odd	4		4225.2.a.m.1.1		1
65.37	even	12		845.2.n.a.529.2		4
65.38	odd	4		65.2.d.a.64.1	✓	2
65.42	odd	12		845.2.l.b.654.1		4
65.43	odd	12		845.2.l.b.699.1		4
65.44	odd	4		4225.2.a.h.1.1		1
65.47	even	4		845.2.b.a.339.1		2
65.48	odd	12		845.2.l.a.699.1		4
65.57	even	4		845.2.b.b.339.2		2
65.58	even	12		845.2.n.b.484.1		4
65.62	odd	12		845.2.l.a.654.1		4
65.63	even	12		845.2.n.a.529.1		4
65.64	even	2		325.2.c.e.51.2		2
195.38	even	4		585.2.h.c.64.2		2
195.77	even	4		585.2.h.b.64.2		2
260.103	even	4		1040.2.f.a.129.2		2
260.207	even	4		1040.2.f.b.129.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.d.a.64.1	✓	2	65.38	odd	4
65.2.d.a.64.2	yes	2	5.2	odd	4
65.2.d.b.64.1	yes	2	5.3	odd	4
65.2.d.b.64.2	yes	2	65.12	odd	4
325.2.c.b.51.1		2	13.12	even	2	inner
325.2.c.b.51.2		2	1.1	even	1	trivial
325.2.c.e.51.1		2	5.4	even	2
325.2.c.e.51.2		2	65.64	even	2
585.2.h.b.64.1		2	15.8	even	4
585.2.h.b.64.2		2	195.77	even	4
585.2.h.c.64.1		2	15.2	even	4
585.2.h.c.64.2		2	195.38	even	4
845.2.b.a.339.1		2	65.47	even	4
845.2.b.a.339.2		2	65.8	even	4
845.2.b.b.339.1		2	65.18	even	4
845.2.b.b.339.2		2	65.57	even	4
845.2.l.a.654.1		4	65.62	odd	12
845.2.l.a.654.2		4	65.3	odd	12
845.2.l.a.699.1		4	65.48	odd	12
845.2.l.a.699.2		4	65.17	odd	12
845.2.l.b.654.1		4	65.42	odd	12
845.2.l.b.654.2		4	65.23	odd	12
845.2.l.b.699.1		4	65.43	odd	12
845.2.l.b.699.2		4	65.22	odd	12
845.2.n.a.484.1		4	65.7	even	12
845.2.n.a.484.2		4	65.33	even	12
845.2.n.a.529.1		4	65.63	even	12
845.2.n.a.529.2		4	65.37	even	12
845.2.n.b.484.1		4	65.58	even	12
845.2.n.b.484.2		4	65.32	even	12
845.2.n.b.529.1		4	65.2	even	12
845.2.n.b.529.2		4	65.28	even	12
1040.2.f.a.129.1		2	20.7	even	4
1040.2.f.a.129.2		2	260.103	even	4
1040.2.f.b.129.1		2	260.207	even	4
1040.2.f.b.129.2		2	20.3	even	4
4225.2.a.e.1.1		1	13.8	odd	4
4225.2.a.h.1.1		1	65.44	odd	4
4225.2.a.k.1.1		1	13.5	odd	4
4225.2.a.m.1.1		1	65.34	odd	4

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -2.00000 q^{3} +1.00000 q^{4} -2.00000i q^{6} +3.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -2.00000 q^{3} +1.00000 q^{4} -2.00000i q^{6} +3.00000i q^{8} +1.00000 q^{9} +2.00000i q^{11} -2.00000 q^{12} +(2.00000 + 3.00000i) q^{13} -1.00000 q^{16} +1.00000i q^{18} +6.00000i q^{19} -2.00000 q^{22} -6.00000 q^{23} -6.00000i q^{24} +(-3.00000 + 2.00000i) q^{26} +4.00000 q^{27} -6.00000 q^{29} +6.00000i q^{31} +5.00000i q^{32} -4.00000i q^{33} +1.00000 q^{36} -6.00000i q^{37} -6.00000 q^{38} +(-4.00000 - 6.00000i) q^{39} -8.00000i q^{41} +6.00000 q^{43} +2.00000i q^{44} -6.00000i q^{46} +8.00000i q^{47} +2.00000 q^{48} +7.00000 q^{49} +(2.00000 + 3.00000i) q^{52} +12.0000 q^{53} +4.00000i q^{54} -12.0000i q^{57} -6.00000i q^{58} -2.00000i q^{59} +6.00000 q^{61} -6.00000 q^{62} -7.00000 q^{64} +4.00000 q^{66} -12.0000i q^{67} +12.0000 q^{69} -2.00000i q^{71} +3.00000i q^{72} -6.00000i q^{73} +6.00000 q^{74} +6.00000i q^{76} +(6.00000 - 4.00000i) q^{78} -11.0000 q^{81} +8.00000 q^{82} -4.00000i q^{83} +6.00000i q^{86} +12.0000 q^{87} -6.00000 q^{88} +8.00000i q^{89} -6.00000 q^{92} -12.0000i q^{93} -8.00000 q^{94} -10.0000i q^{96} +6.00000i q^{97} +7.00000i q^{98} +2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{3} + 2 q^{4} + 2 q^{9}+O(q^{10}) \) 2 * q - 4 * q^3 + 2 * q^4 + 2 * q^9	\( 2 q - 4 q^{3} + 2 q^{4} + 2 q^{9} - 4 q^{12} + 4 q^{13} - 2 q^{16} - 4 q^{22} - 12 q^{23} - 6 q^{26} + 8 q^{27} - 12 q^{29} + 2 q^{36} - 12 q^{38} - 8 q^{39} + 12 q^{43} + 4 q^{48} + 14 q^{49} + 4 q^{52} + 24 q^{53} + 12 q^{61} - 12 q^{62} - 14 q^{64} + 8 q^{66} + 24 q^{69} + 12 q^{74} + 12 q^{78} - 22 q^{81} + 16 q^{82} + 24 q^{87} - 12 q^{88} - 12 q^{92} - 16 q^{94}+O(q^{100}) \) 2 * q - 4 * q^3 + 2 * q^4 + 2 * q^9 - 4 * q^12 + 4 * q^13 - 2 * q^16 - 4 * q^22 - 12 * q^23 - 6 * q^26 + 8 * q^27 - 12 * q^29 + 2 * q^36 - 12 * q^38 - 8 * q^39 + 12 * q^43 + 4 * q^48 + 14 * q^49 + 4 * q^52 + 24 * q^53 + 12 * q^61 - 12 * q^62 - 14 * q^64 + 8 * q^66 + 24 * q^69 + 12 * q^74 + 12 * q^78 - 22 * q^81 + 16 * q^82 + 24 * q^87 - 12 * q^88 - 12 * q^92 - 16 * q^94

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