LMFDB - Embedded newform 130.2.d.a.51.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [130,2,Mod(51,130)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(130, 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("130.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	130.d (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:	$1.03805522628$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	130.51
Dual form			130.2.d.a.51.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +2.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} -2.00000i q^{6} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +2.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} -2.00000i q^{6} +1.00000i q^{8} +1.00000 q^{9} -1.00000 q^{10} -2.00000 q^{12} +(2.00000 + 3.00000i) q^{13} -2.00000i q^{15} +1.00000 q^{16} -6.00000 q^{17} -1.00000i q^{18} +1.00000i q^{20} +2.00000i q^{24} -1.00000 q^{25} +(3.00000 - 2.00000i) q^{26} -4.00000 q^{27} +6.00000 q^{29} -2.00000 q^{30} +6.00000i q^{31} -1.00000i q^{32} +6.00000i q^{34} -1.00000 q^{36} +6.00000i q^{37} +(4.00000 + 6.00000i) q^{39} +1.00000 q^{40} -10.0000 q^{43} -1.00000i q^{45} -12.0000i q^{47} +2.00000 q^{48} +7.00000 q^{49} +1.00000i q^{50} -12.0000 q^{51} +(-2.00000 - 3.00000i) q^{52} +4.00000i q^{54} -6.00000i q^{58} -12.0000i q^{59} +2.00000i q^{60} +10.0000 q^{61} +6.00000 q^{62} -1.00000 q^{64} +(3.00000 - 2.00000i) q^{65} -12.0000i q^{67} +6.00000 q^{68} -6.00000i q^{71} +1.00000i q^{72} -6.00000i q^{73} +6.00000 q^{74} -2.00000 q^{75} +(6.00000 - 4.00000i) q^{78} -8.00000 q^{79} -1.00000i q^{80} -11.0000 q^{81} +12.0000i q^{83} +6.00000i q^{85} +10.0000i q^{86} +12.0000 q^{87} -12.0000i q^{89} -1.00000 q^{90} +12.0000i q^{93} -12.0000 q^{94} -2.00000i q^{96} +18.0000i q^{97} -7.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 2 q^{10} - 4 q^{12} + 4 q^{13} + 2 q^{16} - 12 q^{17} - 2 q^{25} + 6 q^{26} - 8 q^{27} + 12 q^{29} - 4 q^{30} - 2 q^{36} + 8 q^{39} + 2 q^{40} - 20 q^{43} + 4 q^{48} + 14 q^{49} - 24 q^{51} - 4 q^{52} + 20 q^{61} + 12 q^{62} - 2 q^{64} + 6 q^{65} + 12 q^{68} + 12 q^{74} - 4 q^{75} + 12 q^{78} - 16 q^{79} - 22 q^{81} + 24 q^{87} - 2 q^{90} - 24 q^{94}+O(q^{100}) $ 2 * q + 4 * q^3 - 2 * q^4 + 2 * q^9 - 2 * q^10 - 4 * q^12 + 4 * q^13 + 2 * q^16 - 12 * q^17 - 2 * q^25 + 6 * q^26 - 8 * q^27 + 12 * q^29 - 4 * q^30 - 2 * q^36 + 8 * q^39 + 2 * q^40 - 20 * q^43 + 4 * q^48 + 14 * q^49 - 24 * q^51 - 4 * q^52 + 20 * q^61 + 12 * q^62 - 2 * q^64 + 6 * q^65 + 12 * q^68 + 12 * q^74 - 4 * q^75 + 12 * q^78 - 16 * q^79 - 22 * q^81 + 24 * q^87 - 2 * q^90 - 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$-1$

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
$2$		−	1.00000i		−	0.707107i
$3$	2.00000			1.15470			0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000			1.15470			0.577350	+	0.816497i	$0.304087\pi$
$4$	−1.00000			−0.500000
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		−	2.00000i		−	0.816497i
$7$		0			0		1.00000			$0$
$7$		0			0		−1.00000			$\pi$
$8$			1.00000i			0.353553i
$9$	1.00000			0.333333
$10$	−1.00000			−0.316228
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$	−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
$15$		−	2.00000i		−	0.516398i
$16$	1.00000			0.250000
$17$	−6.00000			−1.45521			−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000			−1.45521			−0.727607	+	0.685994i	$0.759367\pi$
$18$		−	1.00000i		−	0.235702i
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$			1.00000i			0.223607i
$21$		0			0
$22$		0			0
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$			2.00000i			0.408248i
$25$	−1.00000			−0.200000
$26$	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	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$	−2.00000			−0.365148
$31$			6.00000i			1.07763i	0.842424	+	0.538816i	$0.181128\pi$
$31$			6.00000i			1.07763i	−0.842424	+	0.538816i	$0.818872\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$			6.00000i			1.02899i
$35$		0			0
$36$	−1.00000			−0.166667
$37$			6.00000i			0.986394i	0.869918	+	0.493197i	$0.164172\pi$
$37$			6.00000i			0.986394i	−0.869918	+	0.493197i	$0.835828\pi$
$38$		0			0
$39$	4.00000	+	6.00000i	0.640513	+	0.960769i
$40$	1.00000			0.158114
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$		0			0
$43$	−10.0000			−1.52499			−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000			−1.52499			−0.762493	+	0.646997i	$0.776025\pi$
$44$		0			0
$45$		−	1.00000i		−	0.149071i
$46$		0			0
$47$		−	12.0000i		−	1.75038i	−0.483779	−	0.875190i	$-0.660736\pi$
$47$		−	12.0000i		−	1.75038i	0.483779	−	0.875190i	$-0.339264\pi$
$48$	2.00000			0.288675
$49$	7.00000			1.00000
$50$			1.00000i			0.141421i
$51$	−12.0000			−1.68034
$52$	−2.00000	−	3.00000i	−0.277350	−	0.416025i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$			4.00000i			0.544331i
$55$		0			0
$56$		0			0
$57$		0			0
$58$		−	6.00000i		−	0.787839i
$59$		−	12.0000i		−	1.56227i	−0.624364	−	0.781133i	$-0.714642\pi$
$59$		−	12.0000i		−	1.56227i	0.624364	−	0.781133i	$-0.285358\pi$
$60$			2.00000i			0.258199i
$61$	10.0000			1.28037			0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000			1.28037			0.640184	+	0.768221i	$0.278858\pi$
$62$	6.00000			0.762001
$63$		0			0
$64$	−1.00000			−0.125000
$65$	3.00000	−	2.00000i	0.372104	−	0.248069i
$66$		0			0
$67$		−	12.0000i		−	1.46603i	−0.680211	−	0.733017i	$-0.738112\pi$
$67$		−	12.0000i		−	1.46603i	0.680211	−	0.733017i	$-0.261888\pi$
$68$	6.00000			0.727607
$69$		0			0
$70$		0			0
$71$		−	6.00000i		−	0.712069i	−0.934473	−	0.356034i	$-0.884129\pi$
$71$		−	6.00000i		−	0.712069i	0.934473	−	0.356034i	$-0.115871\pi$
$72$			1.00000i			0.117851i
$73$		−	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
$75$	−2.00000			−0.230940
$76$		0			0
$77$		0			0
$78$	6.00000	−	4.00000i	0.679366	−	0.452911i
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−11.0000			−1.22222
$82$		0			0
$83$			12.0000i			1.31717i	0.752506	+	0.658586i	$0.228845\pi$
$83$			12.0000i			1.31717i	−0.752506	+	0.658586i	$0.771155\pi$
$84$		0			0
$85$			6.00000i			0.650791i
$86$			10.0000i			1.07833i
$87$	12.0000			1.28654
$88$		0			0
$89$		−	12.0000i		−	1.27200i	−0.771690	−	0.635999i	$-0.780588\pi$
$89$		−	12.0000i		−	1.27200i	0.771690	−	0.635999i	$-0.219412\pi$
$90$	−1.00000			−0.105409
$91$		0			0
$92$		0			0
$93$			12.0000i			1.24434i
$94$	−12.0000			−1.23771
$95$		0			0
$96$		−	2.00000i		−	0.204124i
$97$			18.0000i			1.82762i	0.406138	+	0.913812i	$0.366875\pi$
$97$			18.0000i			1.82762i	−0.406138	+	0.913812i	$0.633125\pi$
$98$		−	7.00000i		−	0.707107i
$99$		0			0
$100$	1.00000			0.100000
$101$	6.00000			0.597022			0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000			0.597022			0.298511	+	0.954406i	$0.403510\pi$
$102$			12.0000i			1.18818i
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$	−3.00000	+	2.00000i	−0.294174	+	0.196116i
$105$		0			0
$106$		0			0
$107$	−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
$109$		−	6.00000i		−	0.574696i	−0.957826	−	0.287348i	$-0.907226\pi$
$109$		−	6.00000i		−	0.574696i	0.957826	−	0.287348i	$-0.0927736\pi$
$110$		0			0
$111$			12.0000i			1.13899i
$112$		0			0
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$		0			0
$115$		0			0
$116$	−6.00000			−0.557086
$117$	2.00000	+	3.00000i	0.184900	+	0.277350i
$118$	−12.0000			−1.10469
$119$		0			0
$120$	2.00000			0.182574
$121$	11.0000			1.00000
$122$		−	10.0000i		−	0.905357i
$123$		0			0
$124$		−	6.00000i		−	0.538816i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	16.0000			1.41977			0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000			1.41977			0.709885	+	0.704317i	$0.248747\pi$
$128$			1.00000i			0.0883883i
$129$	−20.0000			−1.76090
$130$	−2.00000	−	3.00000i	−0.175412	−	0.263117i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$		0			0
$134$	−12.0000			−1.03664
$135$			4.00000i			0.344265i
$136$		−	6.00000i		−	0.514496i
$137$			18.0000i			1.53784i	0.639343	+	0.768922i	$0.279207\pi$
$137$			18.0000i			1.53784i	−0.639343	+	0.768922i	$0.720793\pi$
$138$		0			0
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$		0			0
$141$		−	24.0000i		−	2.02116i
$142$	−6.00000			−0.503509
$143$		0			0
$144$	1.00000			0.0833333
$145$		−	6.00000i		−	0.498273i
$146$	−6.00000			−0.496564
$147$	14.0000			1.15470
$148$		−	6.00000i		−	0.493197i
$149$			6.00000i			0.491539i	0.969328	+	0.245770i	$0.0790407\pi$
$149$			6.00000i			0.491539i	−0.969328	+	0.245770i	$0.920959\pi$
$150$			2.00000i			0.163299i
$151$			18.0000i			1.46482i	0.680864	+	0.732410i	$0.261604\pi$
$151$			18.0000i			1.46482i	−0.680864	+	0.732410i	$0.738396\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$		0			0
$155$	6.00000			0.481932
$156$	−4.00000	−	6.00000i	−0.320256	−	0.480384i
$157$	−4.00000			−0.319235			−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000			−0.319235			−0.159617	+	0.987179i	$0.551026\pi$
$158$			8.00000i			0.636446i
$159$		0			0
$160$	−1.00000			−0.0790569
$161$		0			0
$162$			11.0000i			0.864242i
$163$		−	12.0000i		−	0.939913i	−0.882690	−	0.469956i	$-0.844270\pi$
$163$		−	12.0000i		−	0.939913i	0.882690	−	0.469956i	$-0.155730\pi$
$164$		0			0
$165$		0			0
$166$	12.0000			0.931381
$167$			12.0000i			0.928588i	0.885681	+	0.464294i	$0.153692\pi$
$167$			12.0000i			0.928588i	−0.885681	+	0.464294i	$0.846308\pi$
$168$		0			0
$169$	−5.00000	+	12.0000i	−0.384615	+	0.923077i
$170$	6.00000			0.460179
$171$		0			0
$172$	10.0000			0.762493
$173$	−24.0000			−1.82469			−0.912343	−	0.409426i	$-0.865729\pi$
$173$	−24.0000			−1.82469			−0.912343	+	0.409426i	$0.865729\pi$
$174$		−	12.0000i		−	0.909718i
$175$		0			0
$176$		0			0
$177$		−	24.0000i		−	1.80395i
$178$	−12.0000			−0.899438
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$			1.00000i			0.0745356i
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$	20.0000			1.47844
$184$		0			0
$185$	6.00000			0.441129
$186$	12.0000			0.879883
$187$		0			0
$188$			12.0000i			0.875190i
$189$		0			0
$190$		0			0
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$	−2.00000			−0.144338
$193$		−	18.0000i		−	1.29567i	−0.761781	−	0.647834i	$-0.775675\pi$
$193$		−	18.0000i		−	1.29567i	0.761781	−	0.647834i	$-0.224325\pi$
$194$	18.0000			1.29232
$195$	6.00000	−	4.00000i	0.429669	−	0.286446i
$196$	−7.00000			−0.500000
$197$			6.00000i			0.427482i	0.976890	+	0.213741i	$0.0685649\pi$
$197$			6.00000i			0.427482i	−0.976890	+	0.213741i	$0.931435\pi$
$198$		0			0
$199$	16.0000			1.13421			0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000			1.13421			0.567105	+	0.823646i	$0.308063\pi$
$200$		−	1.00000i		−	0.0707107i
$201$		−	24.0000i		−	1.69283i
$202$		−	6.00000i		−	0.422159i
$203$		0			0
$204$	12.0000			0.840168
$205$		0			0
$206$			4.00000i			0.278693i
$207$		0			0
$208$	2.00000	+	3.00000i	0.138675	+	0.208013i
$209$		0			0
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$		0			0
$213$		−	12.0000i		−	0.822226i
$214$			6.00000i			0.410152i
$215$			10.0000i			0.681994i
$216$		−	4.00000i		−	0.272166i
$217$		0			0
$218$	−6.00000			−0.406371
$219$		−	12.0000i		−	0.810885i
$220$		0			0
$221$	−12.0000	−	18.0000i	−0.807207	−	1.21081i
$222$	12.0000			0.805387
$223$		−	12.0000i		−	0.803579i	−0.915732	−	0.401790i	$-0.868388\pi$
$223$		−	12.0000i		−	0.803579i	0.915732	−	0.401790i	$-0.131612\pi$
$224$		0			0
$225$	−1.00000			−0.0666667
$226$		−	6.00000i		−	0.399114i
$227$			12.0000i			0.796468i	0.917284	+	0.398234i	$0.130377\pi$
$227$			12.0000i			0.796468i	−0.917284	+	0.398234i	$0.869623\pi$
$228$		0			0
$229$		−	6.00000i		−	0.396491i	−0.980152	−	0.198246i	$-0.936476\pi$
$229$		−	6.00000i		−	0.396491i	0.980152	−	0.198246i	$-0.0635244\pi$
$230$		0			0
$231$		0			0
$232$			6.00000i			0.393919i
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$	3.00000	−	2.00000i	0.196116	−	0.130744i
$235$	−12.0000			−0.782794
$236$			12.0000i			0.781133i
$237$	−16.0000			−1.03931
$238$		0			0
$239$			18.0000i			1.16432i	0.813073	+	0.582162i	$0.197793\pi$
$239$			18.0000i			1.16432i	−0.813073	+	0.582162i	$0.802207\pi$
$240$		−	2.00000i		−	0.129099i
$241$			24.0000i			1.54598i	0.634421	+	0.772988i	$0.281239\pi$
$241$			24.0000i			1.54598i	−0.634421	+	0.772988i	$0.718761\pi$
$242$		−	11.0000i		−	0.707107i
$243$	−10.0000			−0.641500
$244$	−10.0000			−0.640184
$245$		−	7.00000i		−	0.447214i
$246$		0			0
$247$		0			0
$248$	−6.00000			−0.381000
$249$			24.0000i			1.52094i
$250$	1.00000			0.0632456
$251$	−24.0000			−1.51487			−0.757433	−	0.652913i	$-0.773547\pi$
$251$	−24.0000			−1.51487			−0.757433	+	0.652913i	$0.773547\pi$
$252$		0			0
$253$		0			0
$254$		−	16.0000i		−	1.00393i
$255$			12.0000i			0.751469i
$256$	1.00000			0.0625000
$257$	−30.0000			−1.87135			−0.935674	−	0.352865i	$-0.885208\pi$
$257$	−30.0000			−1.87135			−0.935674	+	0.352865i	$0.885208\pi$
$258$			20.0000i			1.24515i
$259$		0			0
$260$	−3.00000	+	2.00000i	−0.186052	+	0.124035i
$261$	6.00000			0.371391
$262$		0			0
$263$	24.0000			1.47990			0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000			1.47990			0.739952	+	0.672660i	$0.234848\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	24.0000i		−	1.46878i
$268$			12.0000i			0.733017i
$269$	−30.0000			−1.82913			−0.914566	−	0.404436i	$-0.867468\pi$
$269$	−30.0000			−1.82913			−0.914566	+	0.404436i	$0.867468\pi$
$270$	4.00000			0.243432
$271$		−	6.00000i		−	0.364474i	−0.983255	−	0.182237i	$-0.941666\pi$
$271$		−	6.00000i		−	0.364474i	0.983255	−	0.182237i	$-0.0583338\pi$
$272$	−6.00000			−0.363803
$273$		0			0
$274$	18.0000			1.08742
$275$		0			0
$276$		0			0
$277$	8.00000			0.480673			0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000			0.480673			0.240337	+	0.970690i	$0.422742\pi$
$278$			4.00000i			0.239904i
$279$			6.00000i			0.359211i
$280$		0			0
$281$			12.0000i			0.715860i	0.933748	+	0.357930i	$0.116517\pi$
$281$			12.0000i			0.715860i	−0.933748	+	0.357930i	$0.883483\pi$
$282$	−24.0000			−1.42918
$283$	−14.0000			−0.832214			−0.416107	−	0.909316i	$-0.636606\pi$
$283$	−14.0000			−0.832214			−0.416107	+	0.909316i	$0.636606\pi$
$284$			6.00000i			0.356034i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		−	1.00000i		−	0.0589256i
$289$	19.0000			1.11765
$290$	−6.00000			−0.352332
$291$			36.0000i			2.11036i
$292$			6.00000i			0.351123i
$293$			18.0000i			1.05157i	0.850617	+	0.525786i	$0.176229\pi$
$293$			18.0000i			1.05157i	−0.850617	+	0.525786i	$0.823771\pi$
$294$		−	14.0000i		−	0.816497i
$295$	−12.0000			−0.698667
$296$	−6.00000			−0.348743
$297$		0			0
$298$	6.00000			0.347571
$299$		0			0
$300$	2.00000			0.115470
$301$		0			0
$302$	18.0000			1.03578
$303$	12.0000			0.689382
$304$		0			0
$305$		−	10.0000i		−	0.572598i
$306$			6.00000i			0.342997i
$307$		−	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
$309$	−8.00000			−0.455104
$310$		−	6.00000i		−	0.340777i
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$	−6.00000	+	4.00000i	−0.339683	+	0.226455i
$313$	10.0000			0.565233			0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000			0.565233			0.282617	+	0.959233i	$0.408798\pi$
$314$			4.00000i			0.225733i
$315$		0			0
$316$	8.00000			0.450035
$317$		−	18.0000i		−	1.01098i	−0.862832	−	0.505490i	$-0.831312\pi$
$317$		−	18.0000i		−	1.01098i	0.862832	−	0.505490i	$-0.168688\pi$
$318$		0			0
$319$		0			0
$320$			1.00000i			0.0559017i
$321$	−12.0000			−0.669775
$322$		0			0
$323$		0			0
$324$	11.0000			0.611111
$325$	−2.00000	−	3.00000i	−0.110940	−	0.166410i
$326$	−12.0000			−0.664619
$327$		−	12.0000i		−	0.663602i
$328$		0			0
$329$		0			0
$330$		0			0
$331$		−	12.0000i		−	0.659580i	−0.944054	−	0.329790i	$-0.893022\pi$
$331$		−	12.0000i		−	0.659580i	0.944054	−	0.329790i	$-0.106978\pi$
$332$		−	12.0000i		−	0.658586i
$333$			6.00000i			0.328798i
$334$	12.0000			0.656611
$335$	−12.0000			−0.655630
$336$		0			0
$337$	22.0000			1.19842			0.599208	−	0.800593i	$-0.295482\pi$
$337$	22.0000			1.19842			0.599208	+	0.800593i	$0.295482\pi$
$338$	12.0000	+	5.00000i	0.652714	+	0.271964i
$339$	12.0000			0.651751
$340$		−	6.00000i		−	0.325396i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		−	10.0000i		−	0.539164i
$345$		0			0
$346$			24.0000i			1.29025i
$347$	−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
$349$			30.0000i			1.60586i	0.596071	+	0.802932i	$0.296728\pi$
$349$			30.0000i			1.60586i	−0.596071	+	0.802932i	$0.703272\pi$
$350$		0			0
$351$	−8.00000	−	12.0000i	−0.427008	−	0.640513i
$352$		0			0
$353$		−	6.00000i		−	0.319348i	−0.987170	−	0.159674i	$-0.948956\pi$
$353$		−	6.00000i		−	0.319348i	0.987170	−	0.159674i	$-0.0510443\pi$
$354$	−24.0000			−1.27559
$355$	−6.00000			−0.318447
$356$			12.0000i			0.635999i
$357$		0			0
$358$		0			0
$359$		−	6.00000i		−	0.316668i	−0.987386	−	0.158334i	$-0.949388\pi$
$359$		−	6.00000i		−	0.316668i	0.987386	−	0.158334i	$-0.0506123\pi$
$360$	1.00000			0.0527046
$361$	19.0000			1.00000
$362$		−	2.00000i		−	0.105118i
$363$	22.0000			1.15470
$364$		0			0
$365$	−6.00000			−0.314054
$366$		−	20.0000i		−	1.04542i
$367$	−28.0000			−1.46159			−0.730794	−	0.682598i	$-0.760850\pi$
$367$	−28.0000			−1.46159			−0.730794	+	0.682598i	$0.760850\pi$
$368$		0			0
$369$		0			0
$370$		−	6.00000i		−	0.311925i
$371$		0			0
$372$		−	12.0000i		−	0.622171i
$373$	4.00000			0.207112			0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000			0.207112			0.103556	+	0.994624i	$0.466978\pi$
$374$		0			0
$375$			2.00000i			0.103280i
$376$	12.0000			0.618853
$377$	12.0000	+	18.0000i	0.618031	+	0.927047i
$378$		0			0
$379$		−	24.0000i		−	1.23280i	−0.787434	−	0.616399i	$-0.788591\pi$
$379$		−	24.0000i		−	1.23280i	0.787434	−	0.616399i	$-0.211409\pi$
$380$		0			0
$381$	32.0000			1.63941
$382$		0			0
$383$		0			0		1.00000			$0$
$383$		0			0		−1.00000			$\pi$
$384$			2.00000i			0.102062i
$385$		0			0
$386$	−18.0000			−0.916176
$387$	−10.0000			−0.508329
$388$		−	18.0000i		−	0.913812i
$389$	18.0000			0.912636			0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000			0.912636			0.456318	+	0.889817i	$0.349168\pi$
$390$	−4.00000	−	6.00000i	−0.202548	−	0.303822i
$391$		0			0
$392$			7.00000i			0.353553i
$393$		0			0
$394$	6.00000			0.302276
$395$			8.00000i			0.402524i
$396$		0			0
$397$		−	30.0000i		−	1.50566i	−0.658217	−	0.752828i	$-0.728689\pi$
$397$		−	30.0000i		−	1.50566i	0.658217	−	0.752828i	$-0.271311\pi$
$398$		−	16.0000i		−	0.802008i
$399$		0			0
$400$	−1.00000			−0.0500000
$401$		−	12.0000i		−	0.599251i	−0.954057	−	0.299626i	$-0.903138\pi$
$401$		−	12.0000i		−	0.599251i	0.954057	−	0.299626i	$-0.0968618\pi$
$402$	−24.0000			−1.19701
$403$	−18.0000	+	12.0000i	−0.896644	+	0.597763i
$404$	−6.00000			−0.298511
$405$			11.0000i			0.546594i
$406$		0			0
$407$		0			0
$408$		−	12.0000i		−	0.594089i
$409$			12.0000i			0.593362i	0.954977	+	0.296681i	$0.0958798\pi$
$409$			12.0000i			0.593362i	−0.954977	+	0.296681i	$0.904120\pi$
$410$		0			0
$411$			36.0000i			1.77575i
$412$	4.00000			0.197066
$413$		0			0
$414$		0			0
$415$	12.0000			0.589057
$416$	3.00000	−	2.00000i	0.147087	−	0.0980581i
$417$	−8.00000			−0.391762
$418$		0			0
$419$	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
$421$		−	30.0000i		−	1.46211i	−0.682318	−	0.731055i	$-0.739028\pi$
$421$		−	30.0000i		−	1.46211i	0.682318	−	0.731055i	$-0.260972\pi$
$422$		−	4.00000i		−	0.194717i
$423$		−	12.0000i		−	0.583460i
$424$		0			0
$425$	6.00000			0.291043
$426$	−12.0000			−0.581402
$427$		0			0
$428$	6.00000			0.290021
$429$		0			0
$430$	10.0000			0.482243
$431$		−	30.0000i		−	1.44505i	−0.691345	−	0.722525i	$-0.742982\pi$
$431$		−	30.0000i		−	1.44505i	0.691345	−	0.722525i	$-0.257018\pi$
$432$	−4.00000			−0.192450
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$		0			0
$435$		−	12.0000i		−	0.575356i
$436$			6.00000i			0.287348i
$437$		0			0
$438$	−12.0000			−0.573382
$439$	8.00000			0.381819			0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000			0.381819			0.190910	+	0.981608i	$0.438856\pi$
$440$		0			0
$441$	7.00000			0.333333
$442$	−18.0000	+	12.0000i	−0.856173	+	0.570782i
$443$	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
$445$	−12.0000			−0.568855
$446$	−12.0000			−0.568216
$447$			12.0000i			0.567581i
$448$		0			0
$449$			12.0000i			0.566315i	0.959073	+	0.283158i	$0.0913819\pi$
$449$			12.0000i			0.566315i	−0.959073	+	0.283158i	$0.908618\pi$
$450$			1.00000i			0.0471405i
$451$		0			0
$452$	−6.00000			−0.282216
$453$			36.0000i			1.69143i
$454$	12.0000			0.563188
$455$		0			0
$456$		0			0
$457$			18.0000i			0.842004i	0.907060	+	0.421002i	$0.138322\pi$
$457$			18.0000i			0.842004i	−0.907060	+	0.421002i	$0.861678\pi$
$458$	−6.00000			−0.280362
$459$	24.0000			1.12022
$460$		0			0
$461$		−	30.0000i		−	1.39724i	−0.715493	−	0.698620i	$-0.753798\pi$
$461$		−	30.0000i		−	1.39724i	0.715493	−	0.698620i	$-0.246202\pi$
$462$		0			0
$463$		−	12.0000i		−	0.557687i	−0.960337	−	0.278844i	$-0.910049\pi$
$463$		−	12.0000i		−	0.557687i	0.960337	−	0.278844i	$-0.0899511\pi$
$464$	6.00000			0.278543
$465$	12.0000			0.556487
$466$		−	18.0000i		−	0.833834i
$467$	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
$470$			12.0000i			0.553519i
$471$	−8.00000			−0.368621
$472$	12.0000			0.552345
$473$		0			0
$474$			16.0000i			0.734904i
$475$		0			0
$476$		0			0
$477$		0			0
$478$	18.0000			0.823301
$479$			42.0000i			1.91903i	0.281659	+	0.959514i	$0.409115\pi$
$479$			42.0000i			1.91903i	−0.281659	+	0.959514i	$0.590885\pi$
$480$	−2.00000			−0.0912871
$481$	−18.0000	+	12.0000i	−0.820729	+	0.547153i
$482$	24.0000			1.09317
$483$		0			0
$484$	−11.0000			−0.500000
$485$	18.0000			0.817338
$486$			10.0000i			0.453609i
$487$			24.0000i			1.08754i	0.839233	+	0.543772i	$0.183004\pi$
$487$			24.0000i			1.08754i	−0.839233	+	0.543772i	$0.816996\pi$
$488$			10.0000i			0.452679i
$489$		−	24.0000i		−	1.08532i
$490$	−7.00000			−0.316228
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$		0			0
$493$	−36.0000			−1.62136
$494$		0			0
$495$		0			0
$496$			6.00000i			0.269408i
$497$		0			0
$498$	24.0000			1.07547
$499$		−	12.0000i		−	0.537194i	−0.963253	−	0.268597i	$-0.913440\pi$
$499$		−	12.0000i		−	0.537194i	0.963253	−	0.268597i	$-0.0865599\pi$
$500$		−	1.00000i		−	0.0447214i
$501$			24.0000i			1.07224i
$502$			24.0000i			1.07117i
$503$	−12.0000			−0.535054			−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000			−0.535054			−0.267527	+	0.963550i	$0.586206\pi$
$504$		0			0
$505$		−	6.00000i		−	0.266996i
$506$		0			0
$507$	−10.0000	+	24.0000i	−0.444116	+	1.06588i
$508$	−16.0000			−0.709885
$509$			6.00000i			0.265945i	0.991120	+	0.132973i	$0.0424523\pi$
$509$			6.00000i			0.265945i	−0.991120	+	0.132973i	$0.957548\pi$
$510$	12.0000			0.531369
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$			30.0000i			1.32324i
$515$			4.00000i			0.176261i
$516$	20.0000			0.880451
$517$		0			0
$518$		0			0
$519$	−48.0000			−2.10697
$520$	2.00000	+	3.00000i	0.0877058	+	0.131559i
$521$	6.00000			0.262865			0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000			0.262865			0.131432	+	0.991325i	$0.458042\pi$
$522$		−	6.00000i		−	0.262613i
$523$	−34.0000			−1.48672			−0.743358	−	0.668894i	$-0.766768\pi$
$523$	−34.0000			−1.48672			−0.743358	+	0.668894i	$0.766768\pi$
$524$		0			0
$525$		0			0
$526$		−	24.0000i		−	1.04645i
$527$		−	36.0000i		−	1.56818i
$528$		0			0
$529$	−23.0000			−1.00000
$530$		0			0
$531$		−	12.0000i		−	0.520756i
$532$		0			0
$533$		0			0
$534$	−24.0000			−1.03858
$535$			6.00000i			0.259403i
$536$	12.0000			0.518321
$537$		0			0
$538$			30.0000i			1.29339i
$539$		0			0
$540$		−	4.00000i		−	0.172133i
$541$			18.0000i			0.773880i	0.922105	+	0.386940i	$0.126468\pi$
$541$			18.0000i			0.773880i	−0.922105	+	0.386940i	$0.873532\pi$
$542$	−6.00000			−0.257722
$543$	4.00000			0.171656
$544$			6.00000i			0.257248i
$545$	−6.00000			−0.257012
$546$		0			0
$547$	−10.0000			−0.427569			−0.213785	−	0.976881i	$-0.568579\pi$
$547$	−10.0000			−0.427569			−0.213785	+	0.976881i	$0.568579\pi$
$548$		−	18.0000i		−	0.768922i
$549$	10.0000			0.426790
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		−	8.00000i		−	0.339887i
$555$	12.0000			0.509372
$556$	4.00000			0.169638
$557$			18.0000i			0.762684i	0.924434	+	0.381342i	$0.124538\pi$
$557$			18.0000i			0.762684i	−0.924434	+	0.381342i	$0.875462\pi$
$558$	6.00000			0.254000
$559$	−20.0000	−	30.0000i	−0.845910	−	1.26886i
$560$		0			0
$561$		0			0
$562$	12.0000			0.506189
$563$	6.00000			0.252870			0.126435	−	0.991975i	$-0.459647\pi$
$563$	6.00000			0.252870			0.126435	+	0.991975i	$0.459647\pi$
$564$			24.0000i			1.01058i
$565$		−	6.00000i		−	0.252422i
$566$			14.0000i			0.588464i
$567$		0			0
$568$	6.00000			0.251754
$569$	−6.00000			−0.251533			−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000			−0.251533			−0.125767	+	0.992060i	$0.540139\pi$
$570$		0			0
$571$	−32.0000			−1.33916			−0.669579	−	0.742741i	$-0.733526\pi$
$571$	−32.0000			−1.33916			−0.669579	+	0.742741i	$0.733526\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−1.00000			−0.0416667
$577$		−	18.0000i		−	0.749350i	−0.927156	−	0.374675i	$-0.877754\pi$
$577$		−	18.0000i		−	0.749350i	0.927156	−	0.374675i	$-0.122246\pi$
$578$		−	19.0000i		−	0.790296i
$579$		−	36.0000i		−	1.49611i
$580$			6.00000i			0.249136i
$581$		0			0
$582$	36.0000			1.49225
$583$		0			0
$584$	6.00000			0.248282
$585$	3.00000	−	2.00000i	0.124035	−	0.0826898i
$586$	18.0000			0.743573
$587$			36.0000i			1.48588i	0.669359	+	0.742940i	$0.266569\pi$
$587$			36.0000i			1.48588i	−0.669359	+	0.742940i	$0.733431\pi$
$588$	−14.0000			−0.577350
$589$		0			0
$590$			12.0000i			0.494032i
$591$			12.0000i			0.493614i
$592$			6.00000i			0.246598i
$593$		−	18.0000i		−	0.739171i	−0.929197	−	0.369586i	$-0.879500\pi$
$593$		−	18.0000i		−	0.739171i	0.929197	−	0.369586i	$-0.120500\pi$
$594$		0			0
$595$		0			0
$596$		−	6.00000i		−	0.245770i
$597$	32.0000			1.30967
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		−	2.00000i		−	0.0816497i
$601$	−26.0000			−1.06056			−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000			−1.06056			−0.530281	+	0.847822i	$0.677914\pi$
$602$		0			0
$603$		−	12.0000i		−	0.488678i
$604$		−	18.0000i		−	0.732410i
$605$		−	11.0000i		−	0.447214i
$606$		−	12.0000i		−	0.487467i
$607$	32.0000			1.29884			0.649420	−	0.760430i	$-0.275012\pi$
$607$	32.0000			1.29884			0.649420	+	0.760430i	$0.275012\pi$
$608$		0			0
$609$		0			0
$610$	−10.0000			−0.404888
$611$	36.0000	−	24.0000i	1.45640	−	0.970936i
$612$	6.00000			0.242536
$613$		−	6.00000i		−	0.242338i	−0.992632	−	0.121169i	$-0.961336\pi$
$613$		−	6.00000i		−	0.242338i	0.992632	−	0.121169i	$-0.0386643\pi$
$614$	−12.0000			−0.484281
$615$		0			0
$616$		0			0
$617$		−	6.00000i		−	0.241551i	−0.992680	−	0.120775i	$-0.961462\pi$
$617$		−	6.00000i		−	0.241551i	0.992680	−	0.120775i	$-0.0385381\pi$
$618$			8.00000i			0.321807i
$619$		−	36.0000i		−	1.44696i	−0.690344	−	0.723481i	$-0.742541\pi$
$619$		−	36.0000i		−	1.44696i	0.690344	−	0.723481i	$-0.257459\pi$
$620$	−6.00000			−0.240966
$621$		0			0
$622$		−	24.0000i		−	0.962312i
$623$		0			0
$624$	4.00000	+	6.00000i	0.160128	+	0.240192i
$625$	1.00000			0.0400000
$626$		−	10.0000i		−	0.399680i
$627$		0			0
$628$	4.00000			0.159617
$629$		−	36.0000i		−	1.43541i
$630$		0			0
$631$		−	6.00000i		−	0.238856i	−0.992843	−	0.119428i	$-0.961894\pi$
$631$		−	6.00000i		−	0.238856i	0.992843	−	0.119428i	$-0.0381061\pi$
$632$		−	8.00000i		−	0.318223i
$633$	8.00000			0.317971
$634$	−18.0000			−0.714871
$635$		−	16.0000i		−	0.634941i
$636$		0			0
$637$	14.0000	+	21.0000i	0.554700	+	0.832050i
$638$		0			0
$639$		−	6.00000i		−	0.237356i
$640$	1.00000			0.0395285
$641$	6.00000			0.236986			0.118493	−	0.992955i	$-0.462194\pi$
$641$	6.00000			0.236986			0.118493	+	0.992955i	$0.462194\pi$
$642$			12.0000i			0.473602i
$643$			36.0000i			1.41970i	0.704352	+	0.709851i	$0.251238\pi$
$643$			36.0000i			1.41970i	−0.704352	+	0.709851i	$0.748762\pi$
$644$		0			0
$645$			20.0000i			0.787499i
$646$		0			0
$647$	12.0000			0.471769			0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000			0.471769			0.235884	+	0.971781i	$0.424201\pi$
$648$		−	11.0000i		−	0.432121i
$649$		0			0
$650$	−3.00000	+	2.00000i	−0.117670	+	0.0784465i
$651$		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	$0.251219\pi$
$654$	−12.0000			−0.469237
$655$		0			0
$656$		0			0
$657$		−	6.00000i		−	0.234082i
$658$		0			0
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$		0			0
$661$			42.0000i			1.63361i	0.576913	+	0.816805i	$0.304257\pi$
$661$			42.0000i			1.63361i	−0.576913	+	0.816805i	$0.695743\pi$
$662$	−12.0000			−0.466393
$663$	−24.0000	−	36.0000i	−0.932083	−	1.39812i
$664$	−12.0000			−0.465690
$665$		0			0
$666$	6.00000			0.232495
$667$		0			0
$668$		−	12.0000i		−	0.464294i
$669$		−	24.0000i		−	0.927894i
$670$			12.0000i			0.463600i
$671$		0			0
$672$		0			0
$673$	26.0000			1.00223			0.501113	−	0.865382i	$-0.332924\pi$
$673$	26.0000			1.00223			0.501113	+	0.865382i	$0.332924\pi$
$674$		−	22.0000i		−	0.847408i
$675$	4.00000			0.153960
$676$	5.00000	−	12.0000i	0.192308	−	0.461538i
$677$	12.0000			0.461197			0.230599	−	0.973049i	$-0.425932\pi$
$677$	12.0000			0.461197			0.230599	+	0.973049i	$0.425932\pi$
$678$		−	12.0000i		−	0.460857i
$679$		0			0
$680$	−6.00000			−0.230089
$681$			24.0000i			0.919682i
$682$		0			0
$683$			12.0000i			0.459167i	0.973289	+	0.229584i	$0.0737364\pi$
$683$			12.0000i			0.459167i	−0.973289	+	0.229584i	$0.926264\pi$
$684$		0			0
$685$	18.0000			0.687745
$686$		0			0
$687$		−	12.0000i		−	0.457829i
$688$	−10.0000			−0.381246
$689$		0			0
$690$		0			0
$691$			36.0000i			1.36950i	0.728776	+	0.684752i	$0.240090\pi$
$691$			36.0000i			1.36950i	−0.728776	+	0.684752i	$0.759910\pi$
$692$	24.0000			0.912343
$693$		0			0
$694$			6.00000i			0.227757i
$695$			4.00000i			0.151729i
$696$			12.0000i			0.454859i
$697$		0			0
$698$	30.0000			1.13552
$699$	36.0000			1.36165
$700$		0			0
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$	−12.0000	+	8.00000i	−0.452911	+	0.301941i
$703$		0			0
$704$		0			0
$705$	−24.0000			−0.903892
$706$	−6.00000			−0.225813
$707$		0			0
$708$			24.0000i			0.901975i
$709$			18.0000i			0.676004i	0.941145	+	0.338002i	$0.109751\pi$
$709$			18.0000i			0.676004i	−0.941145	+	0.338002i	$0.890249\pi$
$710$			6.00000i			0.225176i
$711$	−8.00000			−0.300023
$712$	12.0000			0.449719
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$			36.0000i			1.34444i
$718$	−6.00000			−0.223918
$719$	−48.0000			−1.79010			−0.895049	−	0.445968i	$-0.852860\pi$
$719$	−48.0000			−1.79010			−0.895049	+	0.445968i	$0.852860\pi$
$720$		−	1.00000i		−	0.0372678i
$721$		0			0
$722$		−	19.0000i		−	0.707107i
$723$			48.0000i			1.78514i
$724$	−2.00000			−0.0743294
$725$	−6.00000			−0.222834
$726$		−	22.0000i		−	0.816497i
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$			6.00000i			0.222070i
$731$	60.0000			2.21918
$732$	−20.0000			−0.739221
$733$		−	18.0000i		−	0.664845i	−0.943131	−	0.332423i	$-0.892134\pi$
$733$		−	18.0000i		−	0.664845i	0.943131	−	0.332423i	$-0.107866\pi$
$734$			28.0000i			1.03350i
$735$		−	14.0000i		−	0.516398i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		1.00000			$0$
$739$		0			0		−1.00000			$\pi$
$740$	−6.00000			−0.220564
$741$		0			0
$742$		0			0
$743$		−	24.0000i		−	0.880475i	−0.897881	−	0.440237i	$-0.854894\pi$
$743$		−	24.0000i		−	0.880475i	0.897881	−	0.440237i	$-0.145106\pi$
$744$	−12.0000			−0.439941
$745$	6.00000			0.219823
$746$		−	4.00000i		−	0.146450i
$747$			12.0000i			0.439057i
$748$		0			0
$749$		0			0
$750$	2.00000			0.0730297
$751$	−40.0000			−1.45962			−0.729810	−	0.683650i	$-0.760392\pi$
$751$	−40.0000			−1.45962			−0.729810	+	0.683650i	$0.760392\pi$
$752$		−	12.0000i		−	0.437595i
$753$	−48.0000			−1.74922
$754$	18.0000	−	12.0000i	0.655521	−	0.437014i
$755$	18.0000			0.655087
$756$		0			0
$757$	16.0000			0.581530			0.290765	−	0.956795i	$-0.406090\pi$
$757$	16.0000			0.581530			0.290765	+	0.956795i	$0.406090\pi$
$758$	−24.0000			−0.871719
$759$		0			0
$760$		0			0
$761$			12.0000i			0.435000i	0.976060	+	0.217500i	$0.0697902\pi$
$761$			12.0000i			0.435000i	−0.976060	+	0.217500i	$0.930210\pi$
$762$		−	32.0000i		−	1.15924i
$763$		0			0
$764$		0			0
$765$			6.00000i			0.216930i
$766$		0			0
$767$	36.0000	−	24.0000i	1.29988	−	0.866590i
$768$	2.00000			0.0721688
$769$		−	48.0000i		−	1.73092i	−0.500974	−	0.865462i	$-0.667025\pi$
$769$		−	48.0000i		−	1.73092i	0.500974	−	0.865462i	$-0.332975\pi$
$770$		0			0
$771$	−60.0000			−2.16085
$772$			18.0000i			0.647834i
$773$			6.00000i			0.215805i	0.994161	+	0.107903i	$0.0344134\pi$
$773$			6.00000i			0.215805i	−0.994161	+	0.107903i	$0.965587\pi$
$774$			10.0000i			0.359443i
$775$		−	6.00000i		−	0.215526i
$776$	−18.0000			−0.646162
$777$		0			0
$778$		−	18.0000i		−	0.645331i
$779$		0			0
$780$	−6.00000	+	4.00000i	−0.214834	+	0.143223i
$781$		0			0
$782$		0			0
$783$	−24.0000			−0.857690
$784$	7.00000			0.250000
$785$			4.00000i			0.142766i
$786$		0			0
$787$		−	36.0000i		−	1.28326i	−0.767014	−	0.641631i	$-0.778258\pi$
$787$		−	36.0000i		−	1.28326i	0.767014	−	0.641631i	$-0.221742\pi$
$788$		−	6.00000i		−	0.213741i
$789$	48.0000			1.70885
$790$	8.00000			0.284627
$791$		0			0
$792$		0			0
$793$	20.0000	+	30.0000i	0.710221	+	1.06533i
$794$	−30.0000			−1.06466
$795$		0			0
$796$	−16.0000			−0.567105
$797$	−48.0000			−1.70025			−0.850124	−	0.526583i	$-0.823473\pi$
$797$	−48.0000			−1.70025			−0.850124	+	0.526583i	$0.823473\pi$
$798$		0			0
$799$			72.0000i			2.54718i
$800$			1.00000i			0.0353553i
$801$		−	12.0000i		−	0.423999i
$802$	−12.0000			−0.423735
$803$		0			0
$804$			24.0000i			0.846415i
$805$		0			0
$806$	12.0000	+	18.0000i	0.422682	+	0.634023i
$807$	−60.0000			−2.11210
$808$			6.00000i			0.211079i
$809$	42.0000			1.47664			0.738321	−	0.674450i	$-0.235619\pi$
$809$	42.0000			1.47664			0.738321	+	0.674450i	$0.235619\pi$
$810$	11.0000			0.386501
$811$		−	24.0000i		−	0.842754i	−0.906886	−	0.421377i	$-0.861547\pi$
$811$		−	24.0000i		−	0.842754i	0.906886	−	0.421377i	$-0.138453\pi$
$812$		0			0
$813$		−	12.0000i		−	0.420858i
$814$		0			0
$815$	−12.0000			−0.420342
$816$	−12.0000			−0.420084
$817$		0			0
$818$	12.0000			0.419570
$819$		0			0
$820$		0			0
$821$			18.0000i			0.628204i	0.949389	+	0.314102i	$0.101703\pi$
$821$			18.0000i			0.628204i	−0.949389	+	0.314102i	$0.898297\pi$
$822$	36.0000			1.25564
$823$	32.0000			1.11545			0.557725	−	0.830026i	$-0.311674\pi$
$823$	32.0000			1.11545			0.557725	+	0.830026i	$0.311674\pi$
$824$		−	4.00000i		−	0.139347i
$825$		0			0
$826$		0			0
$827$			36.0000i			1.25184i	0.779886	+	0.625921i	$0.215277\pi$
$827$			36.0000i			1.25184i	−0.779886	+	0.625921i	$0.784723\pi$
$828$		0			0
$829$	−2.00000			−0.0694629			−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000			−0.0694629			−0.0347314	+	0.999397i	$0.511058\pi$
$830$		−	12.0000i		−	0.416526i
$831$	16.0000			0.555034
$832$	−2.00000	−	3.00000i	−0.0693375	−	0.104006i
$833$	−42.0000			−1.45521
$834$			8.00000i			0.277017i
$835$	12.0000			0.415277
$836$		0			0
$837$		−	24.0000i		−	0.829561i
$838$		−	12.0000i		−	0.414533i
$839$			30.0000i			1.03572i	0.855467	+	0.517858i	$0.173270\pi$
$839$			30.0000i			1.03572i	−0.855467	+	0.517858i	$0.826730\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	−30.0000			−1.03387
$843$			24.0000i			0.826604i
$844$	−4.00000			−0.137686
$845$	12.0000	+	5.00000i	0.412813	+	0.172005i
$846$	−12.0000			−0.412568
$847$		0			0
$848$		0			0
$849$	−28.0000			−0.960958
$850$		−	6.00000i		−	0.205798i
$851$		0			0
$852$			12.0000i			0.411113i
$853$			6.00000i			0.205436i	0.994711	+	0.102718i	$0.0327539\pi$
$853$			6.00000i			0.205436i	−0.994711	+	0.102718i	$0.967246\pi$
$854$		0			0
$855$		0			0
$856$		−	6.00000i		−	0.205076i
$857$	6.00000			0.204956			0.102478	−	0.994735i	$-0.467323\pi$
$857$	6.00000			0.204956			0.102478	+	0.994735i	$0.467323\pi$
$858$		0			0
$859$	40.0000			1.36478			0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000			1.36478			0.682391	+	0.730987i	$0.260940\pi$
$860$		−	10.0000i		−	0.340997i
$861$		0			0
$862$	−30.0000			−1.02180
$863$			12.0000i			0.408485i	0.978920	+	0.204242i	$0.0654731\pi$
$863$			12.0000i			0.408485i	−0.978920	+	0.204242i	$0.934527\pi$
$864$			4.00000i			0.136083i
$865$			24.0000i			0.816024i
$866$			2.00000i			0.0679628i
$867$	38.0000			1.29055
$868$		0			0
$869$		0			0
$870$	−12.0000			−0.406838
$871$	36.0000	−	24.0000i	1.21981	−	0.813209i
$872$	6.00000			0.203186
$873$			18.0000i			0.609208i
$874$		0			0
$875$		0			0
$876$			12.0000i			0.405442i
$877$		−	18.0000i		−	0.607817i	−0.952701	−	0.303908i	$-0.901708\pi$
$877$		−	18.0000i		−	0.607817i	0.952701	−	0.303908i	$-0.0982917\pi$
$878$		−	8.00000i		−	0.269987i
$879$			36.0000i			1.21425i
$880$		0			0
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$		−	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	$0.510714\pi$
$884$	12.0000	+	18.0000i	0.403604	+	0.605406i
$885$	−24.0000			−0.806751
$886$		−	6.00000i		−	0.201574i
$887$	−48.0000			−1.61168			−0.805841	−	0.592132i	$-0.798286\pi$
$887$	−48.0000			−1.61168			−0.805841	+	0.592132i	$0.798286\pi$
$888$	−12.0000			−0.402694
$889$		0			0
$890$			12.0000i			0.402241i
$891$		0			0
$892$			12.0000i			0.401790i
$893$		0			0
$894$	12.0000			0.401340
$895$		0			0
$896$		0			0
$897$		0			0
$898$	12.0000			0.400445
$899$			36.0000i			1.20067i
$900$	1.00000			0.0333333
$901$		0			0
$902$		0			0
$903$		0			0
$904$			6.00000i			0.199557i
$905$		−	2.00000i		−	0.0664822i
$906$	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	$0.446908\pi$
$908$		−	12.0000i		−	0.398234i
$909$	6.00000			0.199007
$910$		0			0
$911$	24.0000			0.795155			0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000			0.795155			0.397578	+	0.917568i	$0.369851\pi$
$912$		0			0
$913$		0			0
$914$	18.0000			0.595387
$915$		−	20.0000i		−	0.661180i
$916$			6.00000i			0.198246i
$917$		0			0
$918$		−	24.0000i		−	0.792118i
$919$	16.0000			0.527791			0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000			0.527791			0.263896	+	0.964551i	$0.414993\pi$
$920$		0			0
$921$		−	24.0000i		−	0.790827i
$922$	−30.0000			−0.987997
$923$	18.0000	−	12.0000i	0.592477	−	0.394985i
$924$		0			0
$925$		−	6.00000i		−	0.197279i
$926$	−12.0000			−0.394344
$927$	−4.00000			−0.131377
$928$		−	6.00000i		−	0.196960i
$929$		−	36.0000i		−	1.18112i	−0.806993	−	0.590561i	$-0.798907\pi$
$929$		−	36.0000i		−	1.18112i	0.806993	−	0.590561i	$-0.201093\pi$
$930$		−	12.0000i		−	0.393496i
$931$		0			0
$932$	−18.0000			−0.589610
$933$	48.0000			1.57145
$934$		−	18.0000i		−	0.588978i
$935$		0			0
$936$	−3.00000	+	2.00000i	−0.0980581	+	0.0653720i
$937$	−38.0000			−1.24141			−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000			−1.24141			−0.620703	+	0.784046i	$0.713153\pi$
$938$		0			0
$939$	20.0000			0.652675
$940$	12.0000			0.391397
$941$		−	18.0000i		−	0.586783i	−0.955992	−	0.293392i	$-0.905216\pi$
$941$		−	18.0000i		−	0.586783i	0.955992	−	0.293392i	$-0.0947840\pi$
$942$			8.00000i			0.260654i
$943$		0			0
$944$		−	12.0000i		−	0.390567i
$945$		0			0
$946$		0			0
$947$		−	12.0000i		−	0.389948i	−0.980808	−	0.194974i	$-0.937538\pi$
$947$		−	12.0000i		−	0.389948i	0.980808	−	0.194974i	$-0.0624622\pi$
$948$	16.0000			0.519656
$949$	18.0000	−	12.0000i	0.584305	−	0.389536i
$950$		0			0
$951$		−	36.0000i		−	1.16738i
$952$		0			0
$953$	−18.0000			−0.583077			−0.291539	−	0.956559i	$-0.594167\pi$
$953$	−18.0000			−0.583077			−0.291539	+	0.956559i	$0.594167\pi$
$954$		0			0
$955$		0			0
$956$		−	18.0000i		−	0.582162i
$957$		0			0
$958$	42.0000			1.35696
$959$		0			0
$960$			2.00000i			0.0645497i
$961$	−5.00000			−0.161290
$962$	12.0000	+	18.0000i	0.386896	+	0.580343i
$963$	−6.00000			−0.193347
$964$		−	24.0000i		−	0.772988i
$965$	−18.0000			−0.579441
$966$		0			0
$967$		−	12.0000i		−	0.385894i	−0.981209	−	0.192947i	$-0.938195\pi$
$967$		−	12.0000i		−	0.385894i	0.981209	−	0.192947i	$-0.0618045\pi$
$968$			11.0000i			0.353553i
$969$		0			0
$970$		−	18.0000i		−	0.577945i
$971$	36.0000			1.15529			0.577647	−	0.816286i	$-0.303971\pi$
$971$	36.0000			1.15529			0.577647	+	0.816286i	$0.303971\pi$
$972$	10.0000			0.320750
$973$		0			0
$974$	24.0000			0.769010
$975$	−4.00000	−	6.00000i	−0.128103	−	0.192154i
$976$	10.0000			0.320092
$977$		−	42.0000i		−	1.34370i	−0.740688	−	0.671850i	$-0.765500\pi$
$977$		−	42.0000i		−	1.34370i	0.740688	−	0.671850i	$-0.234500\pi$
$978$	−24.0000			−0.767435
$979$		0			0
$980$			7.00000i			0.223607i
$981$		−	6.00000i		−	0.191565i
$982$			12.0000i			0.382935i
$983$		−	36.0000i		−	1.14822i	−0.818778	−	0.574111i	$-0.805348\pi$
$983$		−	36.0000i		−	1.14822i	0.818778	−	0.574111i	$-0.194652\pi$
$984$		0			0
$985$	6.00000			0.191176
$986$			36.0000i			1.14647i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	56.0000			1.77890			0.889449	−	0.457034i	$-0.151088\pi$
$991$	56.0000			1.77890			0.889449	+	0.457034i	$0.151088\pi$
$992$	6.00000			0.190500
$993$		−	24.0000i		−	0.761617i
$994$		0			0
$995$		−	16.0000i		−	0.507234i
$996$		−	24.0000i		−	0.760469i
$997$	−28.0000			−0.886769			−0.443384	−	0.896332i	$-0.646222\pi$
$997$	−28.0000			−0.886769			−0.443384	+	0.896332i	$0.646222\pi$
$998$	−12.0000			−0.379853
$999$		−	24.0000i		−	0.759326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.2.d.a.51.1	✓	2
3.2	odd	2		1170.2.b.a.181.2		2
4.3	odd	2		1040.2.k.a.961.1		2
5.2	odd	4		650.2.c.c.649.1		2
5.3	odd	4		650.2.c.b.649.2		2
5.4	even	2		650.2.d.a.51.2		2
13.2	odd	12		1690.2.e.f.191.1		2
13.3	even	3		1690.2.l.b.1161.2		4
13.4	even	6		1690.2.l.b.361.2		4
13.5	odd	4		1690.2.a.d.1.1		1
13.6	odd	12		1690.2.e.f.991.1		2
13.7	odd	12		1690.2.e.b.991.1		2
13.8	odd	4		1690.2.a.i.1.1		1
13.9	even	3		1690.2.l.b.361.1		4
13.10	even	6		1690.2.l.b.1161.1		4
13.11	odd	12		1690.2.e.b.191.1		2
13.12	even	2	inner	130.2.d.a.51.2	yes	2
39.38	odd	2		1170.2.b.a.181.1		2
52.51	odd	2		1040.2.k.a.961.2		2
65.12	odd	4		650.2.c.b.649.1		2
65.34	odd	4		8450.2.a.b.1.1		1
65.38	odd	4		650.2.c.c.649.2		2
65.44	odd	4		8450.2.a.o.1.1		1
65.64	even	2		650.2.d.a.51.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.d.a.51.1	✓	2	1.1	even	1	trivial
130.2.d.a.51.2	yes	2	13.12	even	2	inner
650.2.c.b.649.1		2	65.12	odd	4
650.2.c.b.649.2		2	5.3	odd	4
650.2.c.c.649.1		2	5.2	odd	4
650.2.c.c.649.2		2	65.38	odd	4
650.2.d.a.51.1		2	65.64	even	2
650.2.d.a.51.2		2	5.4	even	2
1040.2.k.a.961.1		2	4.3	odd	2
1040.2.k.a.961.2		2	52.51	odd	2
1170.2.b.a.181.1		2	39.38	odd	2
1170.2.b.a.181.2		2	3.2	odd	2
1690.2.a.d.1.1		1	13.5	odd	4
1690.2.a.i.1.1		1	13.8	odd	4
1690.2.e.b.191.1		2	13.11	odd	12
1690.2.e.b.991.1		2	13.7	odd	12
1690.2.e.f.191.1		2	13.2	odd	12
1690.2.e.f.991.1		2	13.6	odd	12
1690.2.l.b.361.1		4	13.9	even	3
1690.2.l.b.361.2		4	13.4	even	6
1690.2.l.b.1161.1		4	13.10	even	6
1690.2.l.b.1161.2		4	13.3	even	3
8450.2.a.b.1.1		1	65.34	odd	4
8450.2.a.o.1.1		1	65.44	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:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	130.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +2.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} -2.00000i q^{6} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +2.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} -2.00000i q^{6} +1.00000i q^{8} +1.00000 q^{9} -1.00000 q^{10} -2.00000 q^{12} +(2.00000 + 3.00000i) q^{13} -2.00000i q^{15} +1.00000 q^{16} -6.00000 q^{17} -1.00000i q^{18} +1.00000i q^{20} +2.00000i q^{24} -1.00000 q^{25} +(3.00000 - 2.00000i) q^{26} -4.00000 q^{27} +6.00000 q^{29} -2.00000 q^{30} +6.00000i q^{31} -1.00000i q^{32} +6.00000i q^{34} -1.00000 q^{36} +6.00000i q^{37} +(4.00000 + 6.00000i) q^{39} +1.00000 q^{40} -10.0000 q^{43} -1.00000i q^{45} -12.0000i q^{47} +2.00000 q^{48} +7.00000 q^{49} +1.00000i q^{50} -12.0000 q^{51} +(-2.00000 - 3.00000i) q^{52} +4.00000i q^{54} -6.00000i q^{58} -12.0000i q^{59} +2.00000i q^{60} +10.0000 q^{61} +6.00000 q^{62} -1.00000 q^{64} +(3.00000 - 2.00000i) q^{65} -12.0000i q^{67} +6.00000 q^{68} -6.00000i q^{71} +1.00000i q^{72} -6.00000i q^{73} +6.00000 q^{74} -2.00000 q^{75} +(6.00000 - 4.00000i) q^{78} -8.00000 q^{79} -1.00000i q^{80} -11.0000 q^{81} +12.0000i q^{83} +6.00000i q^{85} +10.0000i q^{86} +12.0000 q^{87} -12.0000i q^{89} -1.00000 q^{90} +12.0000i q^{93} -12.0000 q^{94} -2.00000i q^{96} +18.0000i q^{97} -7.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{3} - 2 q^{4} + 2 q^{9}+O(q^{10}) \) 2 * q + 4 * q^3 - 2 * q^4 + 2 * q^9	\( 2 q + 4 q^{3} - 2 q^{4} + 2 q^{9} - 2 q^{10} - 4 q^{12} + 4 q^{13} + 2 q^{16} - 12 q^{17} - 2 q^{25} + 6 q^{26} - 8 q^{27} + 12 q^{29} - 4 q^{30} - 2 q^{36} + 8 q^{39} + 2 q^{40} - 20 q^{43} + 4 q^{48} + 14 q^{49} - 24 q^{51} - 4 q^{52} + 20 q^{61} + 12 q^{62} - 2 q^{64} + 6 q^{65} + 12 q^{68} + 12 q^{74} - 4 q^{75} + 12 q^{78} - 16 q^{79} - 22 q^{81} + 24 q^{87} - 2 q^{90} - 24 q^{94}+O(q^{100}) \) 2 * q + 4 * q^3 - 2 * q^4 + 2 * q^9 - 2 * q^10 - 4 * q^12 + 4 * q^13 + 2 * q^16 - 12 * q^17 - 2 * q^25 + 6 * q^26 - 8 * q^27 + 12 * q^29 - 4 * q^30 - 2 * q^36 + 8 * q^39 + 2 * q^40 - 20 * q^43 + 4 * q^48 + 14 * q^49 - 24 * q^51 - 4 * q^52 + 20 * q^61 + 12 * q^62 - 2 * q^64 + 6 * q^65 + 12 * q^68 + 12 * q^74 - 4 * q^75 + 12 * q^78 - 16 * q^79 - 22 * q^81 + 24 * q^87 - 2 * q^90 - 24 * q^94

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