LMFDB - Embedded newform 2790.2.d.c.559.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2790,2,Mod(559,2790)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2790, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2790.559");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2790.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:	$22.2782621639$
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 930)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			559.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	2790.559
Dual form			2790.2.d.c.559.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +2.00000i q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +2.00000i q^{7} +1.00000i q^{8} +(-1.00000 + 2.00000i) q^{10} +6.00000 q^{11} +2.00000i q^{13} +2.00000 q^{14} +1.00000 q^{16} -6.00000i q^{17} -8.00000 q^{19} +(2.00000 + 1.00000i) q^{20} -6.00000i q^{22} +4.00000i q^{23} +(3.00000 + 4.00000i) q^{25} +2.00000 q^{26} -2.00000i q^{28} -4.00000 q^{29} -1.00000 q^{31} -1.00000i q^{32} -6.00000 q^{34} +(2.00000 - 4.00000i) q^{35} +2.00000i q^{37} +8.00000i q^{38} +(1.00000 - 2.00000i) q^{40} -2.00000 q^{41} +4.00000i q^{43} -6.00000 q^{44} +4.00000 q^{46} -8.00000i q^{47} +3.00000 q^{49} +(4.00000 - 3.00000i) q^{50} -2.00000i q^{52} +10.0000i q^{53} +(-12.0000 - 6.00000i) q^{55} -2.00000 q^{56} +4.00000i q^{58} +6.00000 q^{59} -14.0000 q^{61} +1.00000i q^{62} -1.00000 q^{64} +(2.00000 - 4.00000i) q^{65} +4.00000i q^{67} +6.00000i q^{68} +(-4.00000 - 2.00000i) q^{70} -16.0000 q^{71} +8.00000i q^{73} +2.00000 q^{74} +8.00000 q^{76} +12.0000i q^{77} +(-2.00000 - 1.00000i) q^{80} +2.00000i q^{82} -4.00000i q^{83} +(-6.00000 + 12.0000i) q^{85} +4.00000 q^{86} +6.00000i q^{88} +10.0000 q^{89} -4.00000 q^{91} -4.00000i q^{92} -8.00000 q^{94} +(16.0000 + 8.00000i) q^{95} +16.0000i q^{97} -3.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} - 4 q^{5}+O(q^{10}) $ 2 * q - 2 * q^4 - 4 * q^5	$ 2 q - 2 q^{4} - 4 q^{5} - 2 q^{10} + 12 q^{11} + 4 q^{14} + 2 q^{16} - 16 q^{19} + 4 q^{20} + 6 q^{25} + 4 q^{26} - 8 q^{29} - 2 q^{31} - 12 q^{34} + 4 q^{35} + 2 q^{40} - 4 q^{41} - 12 q^{44} + 8 q^{46} + 6 q^{49} + 8 q^{50} - 24 q^{55} - 4 q^{56} + 12 q^{59} - 28 q^{61} - 2 q^{64} + 4 q^{65} - 8 q^{70} - 32 q^{71} + 4 q^{74} + 16 q^{76} - 4 q^{80} - 12 q^{85} + 8 q^{86} + 20 q^{89} - 8 q^{91} - 16 q^{94} + 32 q^{95}+O(q^{100}) $ 2 * q - 2 * q^4 - 4 * q^5 - 2 * q^10 + 12 * q^11 + 4 * q^14 + 2 * q^16 - 16 * q^19 + 4 * q^20 + 6 * q^25 + 4 * q^26 - 8 * q^29 - 2 * q^31 - 12 * q^34 + 4 * q^35 + 2 * q^40 - 4 * q^41 - 12 * q^44 + 8 * q^46 + 6 * q^49 + 8 * q^50 - 24 * q^55 - 4 * q^56 + 12 * q^59 - 28 * q^61 - 2 * q^64 + 4 * q^65 - 8 * q^70 - 32 * q^71 + 4 * q^74 + 16 * q^76 - 4 * q^80 - 12 * q^85 + 8 * q^86 + 20 * q^89 - 8 * q^91 - 16 * q^94 + 32 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2790\mathbb{Z}\right)^\times$.

$n$	$1117$	$1801$	$2171$
$\chi(n)$	$-1$	$1$	$1$

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
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$		0			0
$7$			2.00000i			0.755929i	0.925820	+	0.377964i	$0.123376\pi$
$7$			2.00000i			0.755929i	−0.925820	+	0.377964i	$0.876624\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−1.00000	+	2.00000i	−0.316228	+	0.632456i
$11$	6.00000			1.80907			0.904534	−	0.426401i	$-0.140219\pi$
$11$	6.00000			1.80907			0.904534	+	0.426401i	$0.140219\pi$
$12$		0			0
$13$			2.00000i			0.554700i	0.960769	+	0.277350i	$0.0894562\pi$
$13$			2.00000i			0.554700i	−0.960769	+	0.277350i	$0.910544\pi$
$14$	2.00000			0.534522
$15$		0			0
$16$	1.00000			0.250000
$17$		−	6.00000i		−	1.45521i	−0.685994	−	0.727607i	$-0.740633\pi$
$17$		−	6.00000i		−	1.45521i	0.685994	−	0.727607i	$-0.259367\pi$
$18$		0			0
$19$	−8.00000			−1.83533			−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−8.00000			−1.83533			−0.917663	+	0.397360i	$0.869927\pi$
$20$	2.00000	+	1.00000i	0.447214	+	0.223607i
$21$		0			0
$22$		−	6.00000i		−	1.27920i
$23$			4.00000i			0.834058i	0.908893	+	0.417029i	$0.136929\pi$
$23$			4.00000i			0.834058i	−0.908893	+	0.417029i	$0.863071\pi$
$24$		0			0
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	2.00000			0.392232
$27$		0			0
$28$		−	2.00000i		−	0.377964i
$29$	−4.00000			−0.742781			−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000			−0.742781			−0.371391	+	0.928477i	$0.621119\pi$
$30$		0			0
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−6.00000			−1.02899
$35$	2.00000	−	4.00000i	0.338062	−	0.676123i
$36$		0			0
$37$			2.00000i			0.328798i	0.986394	+	0.164399i	$0.0525685\pi$
$37$			2.00000i			0.328798i	−0.986394	+	0.164399i	$0.947432\pi$
$38$			8.00000i			1.29777i
$39$		0			0
$40$	1.00000	−	2.00000i	0.158114	−	0.316228i
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		0			0
$43$			4.00000i			0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$	−6.00000			−0.904534
$45$		0			0
$46$	4.00000			0.589768
$47$		−	8.00000i		−	1.16692i	−0.812142	−	0.583460i	$-0.801699\pi$
$47$		−	8.00000i		−	1.16692i	0.812142	−	0.583460i	$-0.198301\pi$
$48$		0			0
$49$	3.00000			0.428571
$50$	4.00000	−	3.00000i	0.565685	−	0.424264i
$51$		0			0
$52$		−	2.00000i		−	0.277350i
$53$			10.0000i			1.37361i	0.726844	+	0.686803i	$0.240986\pi$
$53$			10.0000i			1.37361i	−0.726844	+	0.686803i	$0.759014\pi$
$54$		0			0
$55$	−12.0000	−	6.00000i	−1.61808	−	0.809040i
$56$	−2.00000			−0.267261
$57$		0			0
$58$			4.00000i			0.525226i
$59$	6.00000			0.781133			0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000			0.781133			0.390567	+	0.920575i	$0.372279\pi$
$60$		0			0
$61$	−14.0000			−1.79252			−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000			−1.79252			−0.896258	+	0.443533i	$0.853725\pi$
$62$			1.00000i			0.127000i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	2.00000	−	4.00000i	0.248069	−	0.496139i
$66$		0			0
$67$			4.00000i			0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$67$			4.00000i			0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$68$			6.00000i			0.727607i
$69$		0			0
$70$	−4.00000	−	2.00000i	−0.478091	−	0.239046i
$71$	−16.0000			−1.89885			−0.949425	−	0.313993i	$-0.898333\pi$
$71$	−16.0000			−1.89885			−0.949425	+	0.313993i	$0.898333\pi$
$72$		0			0
$73$			8.00000i			0.936329i	0.883641	+	0.468165i	$0.155085\pi$
$73$			8.00000i			0.936329i	−0.883641	+	0.468165i	$0.844915\pi$
$74$	2.00000			0.232495
$75$		0			0
$76$	8.00000			0.917663
$77$			12.0000i			1.36753i
$78$		0			0
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	−2.00000	−	1.00000i	−0.223607	−	0.111803i
$81$		0			0
$82$			2.00000i			0.220863i
$83$		−	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
$85$	−6.00000	+	12.0000i	−0.650791	+	1.30158i
$86$	4.00000			0.431331
$87$		0			0
$88$			6.00000i			0.639602i
$89$	10.0000			1.06000			0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000			1.06000			0.529999	+	0.847998i	$0.322192\pi$
$90$		0			0
$91$	−4.00000			−0.419314
$92$		−	4.00000i		−	0.417029i
$93$		0			0
$94$	−8.00000			−0.825137
$95$	16.0000	+	8.00000i	1.64157	+	0.820783i
$96$		0			0
$97$			16.0000i			1.62455i	0.583272	+	0.812277i	$0.301772\pi$
$97$			16.0000i			1.62455i	−0.583272	+	0.812277i	$0.698228\pi$
$98$		−	3.00000i		−	0.303046i
$99$		0			0
$100$	−3.00000	−	4.00000i	−0.300000	−	0.400000i
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$		0			0
$103$			6.00000i			0.591198i	0.955312	+	0.295599i	$0.0955191\pi$
$103$			6.00000i			0.591198i	−0.955312	+	0.295599i	$0.904481\pi$
$104$	−2.00000			−0.196116
$105$		0			0
$106$	10.0000			0.971286
$107$			4.00000i			0.386695i	0.981130	+	0.193347i	$0.0619344\pi$
$107$			4.00000i			0.386695i	−0.981130	+	0.193347i	$0.938066\pi$
$108$		0			0
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	−6.00000	+	12.0000i	−0.572078	+	1.14416i
$111$		0			0
$112$			2.00000i			0.188982i
$113$			18.0000i			1.69330i	0.532152	+	0.846649i	$0.321383\pi$
$113$			18.0000i			1.69330i	−0.532152	+	0.846649i	$0.678617\pi$
$114$		0			0
$115$	4.00000	−	8.00000i	0.373002	−	0.746004i
$116$	4.00000			0.371391
$117$		0			0
$118$		−	6.00000i		−	0.552345i
$119$	12.0000			1.10004
$120$		0			0
$121$	25.0000			2.27273
$122$			14.0000i			1.26750i
$123$		0			0
$124$	1.00000			0.0898027
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$		−	2.00000i		−	0.177471i	−0.996055	−	0.0887357i	$-0.971717\pi$
$127$		−	2.00000i		−	0.177471i	0.996055	−	0.0887357i	$-0.0282826\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	−4.00000	−	2.00000i	−0.350823	−	0.175412i
$131$	−10.0000			−0.873704			−0.436852	−	0.899533i	$-0.643907\pi$
$131$	−10.0000			−0.873704			−0.436852	+	0.899533i	$0.643907\pi$
$132$		0			0
$133$		−	16.0000i		−	1.38738i
$134$	4.00000			0.345547
$135$		0			0
$136$	6.00000			0.514496
$137$			14.0000i			1.19610i	0.801459	+	0.598050i	$0.204058\pi$
$137$			14.0000i			1.19610i	−0.801459	+	0.598050i	$0.795942\pi$
$138$		0			0
$139$	20.0000			1.69638			0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000			1.69638			0.848189	+	0.529694i	$0.177693\pi$
$140$	−2.00000	+	4.00000i	−0.169031	+	0.338062i
$141$		0			0
$142$			16.0000i			1.34269i
$143$			12.0000i			1.00349i
$144$		0			0
$145$	8.00000	+	4.00000i	0.664364	+	0.332182i
$146$	8.00000			0.662085
$147$		0			0
$148$		−	2.00000i		−	0.164399i
$149$	−12.0000			−0.983078			−0.491539	−	0.870855i	$-0.663566\pi$
$149$	−12.0000			−0.983078			−0.491539	+	0.870855i	$0.663566\pi$
$150$		0			0
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$		−	8.00000i		−	0.648886i
$153$		0			0
$154$	12.0000			0.966988
$155$	2.00000	+	1.00000i	0.160644	+	0.0803219i
$156$		0			0
$157$		−	6.00000i		−	0.478852i	−0.970915	−	0.239426i	$-0.923041\pi$
$157$		−	6.00000i		−	0.478852i	0.970915	−	0.239426i	$-0.0769593\pi$
$158$		0			0
$159$		0			0
$160$	−1.00000	+	2.00000i	−0.0790569	+	0.158114i
$161$	−8.00000			−0.630488
$162$		0			0
$163$			20.0000i			1.56652i	0.621694	+	0.783260i	$0.286445\pi$
$163$			20.0000i			1.56652i	−0.621694	+	0.783260i	$0.713555\pi$
$164$	2.00000			0.156174
$165$		0			0
$166$	−4.00000			−0.310460
$167$			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
$169$	9.00000			0.692308
$170$	12.0000	+	6.00000i	0.920358	+	0.460179i
$171$		0			0
$172$		−	4.00000i		−	0.304997i
$173$			14.0000i			1.06440i	0.846619	+	0.532200i	$0.178635\pi$
$173$			14.0000i			1.06440i	−0.846619	+	0.532200i	$0.821365\pi$
$174$		0			0
$175$	−8.00000	+	6.00000i	−0.604743	+	0.453557i
$176$	6.00000			0.452267
$177$		0			0
$178$		−	10.0000i		−	0.749532i
$179$	18.0000			1.34538			0.672692	−	0.739923i	$-0.265138\pi$
$179$	18.0000			1.34538			0.672692	+	0.739923i	$0.265138\pi$
$180$		0			0
$181$	10.0000			0.743294			0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$			4.00000i			0.296500i
$183$		0			0
$184$	−4.00000			−0.294884
$185$	2.00000	−	4.00000i	0.147043	−	0.294086i
$186$		0			0
$187$		−	36.0000i		−	2.63258i
$188$			8.00000i			0.583460i
$189$		0			0
$190$	8.00000	−	16.0000i	0.580381	−	1.16076i
$191$	−8.00000			−0.578860			−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000			−0.578860			−0.289430	+	0.957199i	$0.593466\pi$
$192$		0			0
$193$			20.0000i			1.43963i	0.694165	+	0.719816i	$0.255774\pi$
$193$			20.0000i			1.43963i	−0.694165	+	0.719816i	$0.744226\pi$
$194$	16.0000			1.14873
$195$		0			0
$196$	−3.00000			−0.214286
$197$		−	18.0000i		−	1.28245i	−0.767354	−	0.641223i	$-0.778427\pi$
$197$		−	18.0000i		−	1.28245i	0.767354	−	0.641223i	$-0.221573\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	−4.00000	+	3.00000i	−0.282843	+	0.212132i
$201$		0			0
$202$		0			0
$203$		−	8.00000i		−	0.561490i
$204$		0			0
$205$	4.00000	+	2.00000i	0.279372	+	0.139686i
$206$	6.00000			0.418040
$207$		0			0
$208$			2.00000i			0.138675i
$209$	−48.0000			−3.32023
$210$		0			0
$211$	−20.0000			−1.37686			−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000			−1.37686			−0.688428	+	0.725304i	$0.741699\pi$
$212$		−	10.0000i		−	0.686803i
$213$		0			0
$214$	4.00000			0.273434
$215$	4.00000	−	8.00000i	0.272798	−	0.545595i
$216$		0			0
$217$		−	2.00000i		−	0.135769i
$218$			2.00000i			0.135457i
$219$		0			0
$220$	12.0000	+	6.00000i	0.809040	+	0.404520i
$221$	12.0000			0.807207
$222$		0			0
$223$		−	14.0000i		−	0.937509i	−0.883328	−	0.468755i	$-0.844703\pi$
$223$		−	14.0000i		−	0.937509i	0.883328	−	0.468755i	$-0.155297\pi$
$224$	2.00000			0.133631
$225$		0			0
$226$	18.0000			1.19734
$227$			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
$229$	−6.00000			−0.396491			−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000			−0.396491			−0.198246	+	0.980152i	$0.563524\pi$
$230$	−8.00000	−	4.00000i	−0.527504	−	0.263752i
$231$		0			0
$232$		−	4.00000i		−	0.262613i
$233$		−	18.0000i		−	1.17922i	−0.807688	−	0.589610i	$-0.799282\pi$
$233$		−	18.0000i		−	1.17922i	0.807688	−	0.589610i	$-0.200718\pi$
$234$		0			0
$235$	−8.00000	+	16.0000i	−0.521862	+	1.04372i
$236$	−6.00000			−0.390567
$237$		0			0
$238$		−	12.0000i		−	0.777844i
$239$	−20.0000			−1.29369			−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000			−1.29369			−0.646846	+	0.762620i	$0.723912\pi$
$240$		0			0
$241$	−18.0000			−1.15948			−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000			−1.15948			−0.579741	+	0.814801i	$0.696846\pi$
$242$		−	25.0000i		−	1.60706i
$243$		0			0
$244$	14.0000			0.896258
$245$	−6.00000	−	3.00000i	−0.383326	−	0.191663i
$246$		0			0
$247$		−	16.0000i		−	1.01806i
$248$		−	1.00000i		−	0.0635001i
$249$		0			0
$250$	−11.0000	+	2.00000i	−0.695701	+	0.126491i
$251$	−6.00000			−0.378717			−0.189358	−	0.981908i	$-0.560641\pi$
$251$	−6.00000			−0.378717			−0.189358	+	0.981908i	$0.560641\pi$
$252$		0			0
$253$			24.0000i			1.50887i
$254$	−2.00000			−0.125491
$255$		0			0
$256$	1.00000			0.0625000
$257$			14.0000i			0.873296i	0.899632	+	0.436648i	$0.143834\pi$
$257$			14.0000i			0.873296i	−0.899632	+	0.436648i	$0.856166\pi$
$258$		0			0
$259$	−4.00000			−0.248548
$260$	−2.00000	+	4.00000i	−0.124035	+	0.248069i
$261$		0			0
$262$			10.0000i			0.617802i
$263$		−	12.0000i		−	0.739952i	−0.929041	−	0.369976i	$-0.879366\pi$
$263$		−	12.0000i		−	0.739952i	0.929041	−	0.369976i	$-0.120634\pi$
$264$		0			0
$265$	10.0000	−	20.0000i	0.614295	−	1.22859i
$266$	−16.0000			−0.981023
$267$		0			0
$268$		−	4.00000i		−	0.244339i
$269$	−4.00000			−0.243884			−0.121942	−	0.992537i	$-0.538912\pi$
$269$	−4.00000			−0.243884			−0.121942	+	0.992537i	$0.538912\pi$
$270$		0			0
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$		−	6.00000i		−	0.363803i
$273$		0			0
$274$	14.0000			0.845771
$275$	18.0000	+	24.0000i	1.08544	+	1.44725i
$276$		0			0
$277$			10.0000i			0.600842i	0.953807	+	0.300421i	$0.0971271\pi$
$277$			10.0000i			0.600842i	−0.953807	+	0.300421i	$0.902873\pi$
$278$		−	20.0000i		−	1.19952i
$279$		0			0
$280$	4.00000	+	2.00000i	0.239046	+	0.119523i
$281$	−22.0000			−1.31241			−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000			−1.31241			−0.656205	+	0.754583i	$0.727839\pi$
$282$		0			0
$283$			20.0000i			1.18888i	0.804141	+	0.594438i	$0.202626\pi$
$283$			20.0000i			1.18888i	−0.804141	+	0.594438i	$0.797374\pi$
$284$	16.0000			0.949425
$285$		0			0
$286$	12.0000			0.709575
$287$		−	4.00000i		−	0.236113i
$288$		0			0
$289$	−19.0000			−1.11765
$290$	4.00000	−	8.00000i	0.234888	−	0.469776i
$291$		0			0
$292$		−	8.00000i		−	0.468165i
$293$		−	6.00000i		−	0.350524i	−0.984522	−	0.175262i	$-0.943923\pi$
$293$		−	6.00000i		−	0.350524i	0.984522	−	0.175262i	$-0.0560772\pi$
$294$		0			0
$295$	−12.0000	−	6.00000i	−0.698667	−	0.349334i
$296$	−2.00000			−0.116248
$297$		0			0
$298$			12.0000i			0.695141i
$299$	−8.00000			−0.462652
$300$		0			0
$301$	−8.00000			−0.461112
$302$		−	8.00000i		−	0.460348i
$303$		0			0
$304$	−8.00000			−0.458831
$305$	28.0000	+	14.0000i	1.60328	+	0.801638i
$306$		0			0
$307$		−	8.00000i		−	0.456584i	−0.973593	−	0.228292i	$-0.926686\pi$
$307$		−	8.00000i		−	0.456584i	0.973593	−	0.228292i	$-0.0733141\pi$
$308$		−	12.0000i		−	0.683763i
$309$		0			0
$310$	1.00000	−	2.00000i	0.0567962	−	0.113592i
$311$	8.00000			0.453638			0.226819	−	0.973937i	$-0.427167\pi$
$311$	8.00000			0.453638			0.226819	+	0.973937i	$0.427167\pi$
$312$		0			0
$313$		−	24.0000i		−	1.35656i	−0.734803	−	0.678280i	$-0.762726\pi$
$313$		−	24.0000i		−	1.35656i	0.734803	−	0.678280i	$-0.237274\pi$
$314$	−6.00000			−0.338600
$315$		0			0
$316$		0			0
$317$			18.0000i			1.01098i	0.862832	+	0.505490i	$0.168688\pi$
$317$			18.0000i			1.01098i	−0.862832	+	0.505490i	$0.831312\pi$
$318$		0			0
$319$	−24.0000			−1.34374
$320$	2.00000	+	1.00000i	0.111803	+	0.0559017i
$321$		0			0
$322$			8.00000i			0.445823i
$323$			48.0000i			2.67079i
$324$		0			0
$325$	−8.00000	+	6.00000i	−0.443760	+	0.332820i
$326$	20.0000			1.10770
$327$		0			0
$328$		−	2.00000i		−	0.110432i
$329$	16.0000			0.882109
$330$		0			0
$331$	8.00000			0.439720			0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000			0.439720			0.219860	+	0.975531i	$0.429440\pi$
$332$			4.00000i			0.219529i
$333$		0			0
$334$	12.0000			0.656611
$335$	4.00000	−	8.00000i	0.218543	−	0.437087i
$336$		0			0
$337$		−	8.00000i		−	0.435788i	−0.975972	−	0.217894i	$-0.930081\pi$
$337$		−	8.00000i		−	0.435788i	0.975972	−	0.217894i	$-0.0699187\pi$
$338$		−	9.00000i		−	0.489535i
$339$		0			0
$340$	6.00000	−	12.0000i	0.325396	−	0.650791i
$341$	−6.00000			−0.324918
$342$		0			0
$343$			20.0000i			1.07990i
$344$	−4.00000			−0.215666
$345$		0			0
$346$	14.0000			0.752645
$347$		−	4.00000i		−	0.214731i	−0.994220	−	0.107366i	$-0.965758\pi$
$347$		−	4.00000i		−	0.214731i	0.994220	−	0.107366i	$-0.0342415\pi$
$348$		0			0
$349$	−2.00000			−0.107058			−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000			−0.107058			−0.0535288	+	0.998566i	$0.517047\pi$
$350$	6.00000	+	8.00000i	0.320713	+	0.427618i
$351$		0			0
$352$		−	6.00000i		−	0.319801i
$353$		−	18.0000i		−	0.958043i	−0.877803	−	0.479022i	$-0.840992\pi$
$353$		−	18.0000i		−	0.958043i	0.877803	−	0.479022i	$-0.159008\pi$
$354$		0			0
$355$	32.0000	+	16.0000i	1.69838	+	0.849192i
$356$	−10.0000			−0.529999
$357$		0			0
$358$		−	18.0000i		−	0.951330i
$359$	12.0000			0.633336			0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000			0.633336			0.316668	+	0.948536i	$0.397436\pi$
$360$		0			0
$361$	45.0000			2.36842
$362$		−	10.0000i		−	0.525588i
$363$		0			0
$364$	4.00000			0.209657
$365$	8.00000	−	16.0000i	0.418739	−	0.837478i
$366$		0			0
$367$		−	26.0000i		−	1.35719i	−0.734513	−	0.678594i	$-0.762589\pi$
$367$		−	26.0000i		−	1.35719i	0.734513	−	0.678594i	$-0.237411\pi$
$368$			4.00000i			0.208514i
$369$		0			0
$370$	−4.00000	−	2.00000i	−0.207950	−	0.103975i
$371$	−20.0000			−1.03835
$372$		0			0
$373$			22.0000i			1.13912i	0.821951	+	0.569558i	$0.192886\pi$
$373$			22.0000i			1.13912i	−0.821951	+	0.569558i	$0.807114\pi$
$374$	−36.0000			−1.86152
$375$		0			0
$376$	8.00000			0.412568
$377$		−	8.00000i		−	0.412021i
$378$		0			0
$379$	−36.0000			−1.84920			−0.924598	−	0.380945i	$-0.875599\pi$
$379$	−36.0000			−1.84920			−0.924598	+	0.380945i	$0.875599\pi$
$380$	−16.0000	−	8.00000i	−0.820783	−	0.410391i
$381$		0			0
$382$			8.00000i			0.409316i
$383$		−	16.0000i		−	0.817562i	−0.912633	−	0.408781i	$-0.865954\pi$
$383$		−	16.0000i		−	0.817562i	0.912633	−	0.408781i	$-0.134046\pi$
$384$		0			0
$385$	12.0000	−	24.0000i	0.611577	−	1.22315i
$386$	20.0000			1.01797
$387$		0			0
$388$		−	16.0000i		−	0.812277i
$389$	−16.0000			−0.811232			−0.405616	−	0.914044i	$-0.632943\pi$
$389$	−16.0000			−0.811232			−0.405616	+	0.914044i	$0.632943\pi$
$390$		0			0
$391$	24.0000			1.21373
$392$			3.00000i			0.151523i
$393$		0			0
$394$	−18.0000			−0.906827
$395$		0			0
$396$		0			0
$397$			22.0000i			1.10415i	0.833795	+	0.552074i	$0.186163\pi$
$397$			22.0000i			1.10415i	−0.833795	+	0.552074i	$0.813837\pi$
$398$		0			0
$399$		0			0
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$	−2.00000			−0.0998752			−0.0499376	−	0.998752i	$-0.515902\pi$
$401$	−2.00000			−0.0998752			−0.0499376	+	0.998752i	$0.515902\pi$
$402$		0			0
$403$		−	2.00000i		−	0.0996271i
$404$		0			0
$405$		0			0
$406$	−8.00000			−0.397033
$407$			12.0000i			0.594818i
$408$		0			0
$409$	−22.0000			−1.08783			−0.543915	−	0.839140i	$-0.683059\pi$
$409$	−22.0000			−1.08783			−0.543915	+	0.839140i	$0.683059\pi$
$410$	2.00000	−	4.00000i	0.0987730	−	0.197546i
$411$		0			0
$412$		−	6.00000i		−	0.295599i
$413$			12.0000i			0.590481i
$414$		0			0
$415$	−4.00000	+	8.00000i	−0.196352	+	0.392705i
$416$	2.00000			0.0980581
$417$		0			0
$418$			48.0000i			2.34776i
$419$	−6.00000			−0.293119			−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000			−0.293119			−0.146560	+	0.989202i	$0.546820\pi$
$420$		0			0
$421$	−2.00000			−0.0974740			−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000			−0.0974740			−0.0487370	+	0.998812i	$0.515520\pi$
$422$			20.0000i			0.973585i
$423$		0			0
$424$	−10.0000			−0.485643
$425$	24.0000	−	18.0000i	1.16417	−	0.873128i
$426$		0			0
$427$		−	28.0000i		−	1.35501i
$428$		−	4.00000i		−	0.193347i
$429$		0			0
$430$	−8.00000	−	4.00000i	−0.385794	−	0.192897i
$431$	−12.0000			−0.578020			−0.289010	−	0.957326i	$-0.593326\pi$
$431$	−12.0000			−0.578020			−0.289010	+	0.957326i	$0.593326\pi$
$432$		0			0
$433$		−	8.00000i		−	0.384455i	−0.981350	−	0.192228i	$-0.938429\pi$
$433$		−	8.00000i		−	0.384455i	0.981350	−	0.192228i	$-0.0615712\pi$
$434$	−2.00000			−0.0960031
$435$		0			0
$436$	2.00000			0.0957826
$437$		−	32.0000i		−	1.53077i
$438$		0			0
$439$	−32.0000			−1.52728			−0.763638	−	0.645644i	$-0.776589\pi$
$439$	−32.0000			−1.52728			−0.763638	+	0.645644i	$0.776589\pi$
$440$	6.00000	−	12.0000i	0.286039	−	0.572078i
$441$		0			0
$442$		−	12.0000i		−	0.570782i
$443$			4.00000i			0.190046i	0.995475	+	0.0950229i	$0.0302924\pi$
$443$			4.00000i			0.190046i	−0.995475	+	0.0950229i	$0.969708\pi$
$444$		0			0
$445$	−20.0000	−	10.0000i	−0.948091	−	0.474045i
$446$	−14.0000			−0.662919
$447$		0			0
$448$		−	2.00000i		−	0.0944911i
$449$	26.0000			1.22702			0.613508	−	0.789689i	$-0.289758\pi$
$449$	26.0000			1.22702			0.613508	+	0.789689i	$0.289758\pi$
$450$		0			0
$451$	−12.0000			−0.565058
$452$		−	18.0000i		−	0.846649i
$453$		0			0
$454$	12.0000			0.563188
$455$	8.00000	+	4.00000i	0.375046	+	0.187523i
$456$		0			0
$457$		−	12.0000i		−	0.561336i	−0.959805	−	0.280668i	$-0.909444\pi$
$457$		−	12.0000i		−	0.561336i	0.959805	−	0.280668i	$-0.0905560\pi$
$458$			6.00000i			0.280362i
$459$		0			0
$460$	−4.00000	+	8.00000i	−0.186501	+	0.373002i
$461$	32.0000			1.49039			0.745194	−	0.666847i	$-0.232357\pi$
$461$	32.0000			1.49039			0.745194	+	0.666847i	$0.232357\pi$
$462$		0			0
$463$		−	26.0000i		−	1.20832i	−0.796862	−	0.604161i	$-0.793508\pi$
$463$		−	26.0000i		−	1.20832i	0.796862	−	0.604161i	$-0.206492\pi$
$464$	−4.00000			−0.185695
$465$		0			0
$466$	−18.0000			−0.833834
$467$			4.00000i			0.185098i	0.995708	+	0.0925490i	$0.0295015\pi$
$467$			4.00000i			0.185098i	−0.995708	+	0.0925490i	$0.970499\pi$
$468$		0			0
$469$	−8.00000			−0.369406
$470$	16.0000	+	8.00000i	0.738025	+	0.369012i
$471$		0			0
$472$			6.00000i			0.276172i
$473$			24.0000i			1.10352i
$474$		0			0
$475$	−24.0000	−	32.0000i	−1.10120	−	1.46826i
$476$	−12.0000			−0.550019
$477$		0			0
$478$			20.0000i			0.914779i
$479$	−40.0000			−1.82765			−0.913823	−	0.406112i	$-0.866884\pi$
$479$	−40.0000			−1.82765			−0.913823	+	0.406112i	$0.866884\pi$
$480$		0			0
$481$	−4.00000			−0.182384
$482$			18.0000i			0.819878i
$483$		0			0
$484$	−25.0000			−1.13636
$485$	16.0000	−	32.0000i	0.726523	−	1.45305i
$486$		0			0
$487$		−	14.0000i		−	0.634401i	−0.948359	−	0.317200i	$-0.897257\pi$
$487$		−	14.0000i		−	0.634401i	0.948359	−	0.317200i	$-0.102743\pi$
$488$		−	14.0000i		−	0.633750i
$489$		0			0
$490$	−3.00000	+	6.00000i	−0.135526	+	0.271052i
$491$	−30.0000			−1.35388			−0.676941	−	0.736038i	$-0.736695\pi$
$491$	−30.0000			−1.35388			−0.676941	+	0.736038i	$0.736695\pi$
$492$		0			0
$493$			24.0000i			1.08091i
$494$	−16.0000			−0.719874
$495$		0			0
$496$	−1.00000			−0.0449013
$497$		−	32.0000i		−	1.43540i
$498$		0			0
$499$	32.0000			1.43252			0.716258	−	0.697835i	$-0.245853\pi$
$499$	32.0000			1.43252			0.716258	+	0.697835i	$0.245853\pi$
$500$	2.00000	+	11.0000i	0.0894427	+	0.491935i
$501$		0			0
$502$			6.00000i			0.267793i
$503$		−	8.00000i		−	0.356702i	−0.983967	−	0.178351i	$-0.942924\pi$
$503$		−	8.00000i		−	0.356702i	0.983967	−	0.178351i	$-0.0570763\pi$
$504$		0			0
$505$		0			0
$506$	24.0000			1.06693
$507$		0			0
$508$			2.00000i			0.0887357i
$509$	20.0000			0.886484			0.443242	−	0.896402i	$-0.353828\pi$
$509$	20.0000			0.886484			0.443242	+	0.896402i	$0.353828\pi$
$510$		0			0
$511$	−16.0000			−0.707798
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	14.0000			0.617514
$515$	6.00000	−	12.0000i	0.264392	−	0.528783i
$516$		0			0
$517$		−	48.0000i		−	2.11104i
$518$			4.00000i			0.175750i
$519$		0			0
$520$	4.00000	+	2.00000i	0.175412	+	0.0877058i
$521$	42.0000			1.84005			0.920027	−	0.391856i	$-0.128167\pi$
$521$	42.0000			1.84005			0.920027	+	0.391856i	$0.128167\pi$
$522$		0			0
$523$			40.0000i			1.74908i	0.484955	+	0.874539i	$0.338836\pi$
$523$			40.0000i			1.74908i	−0.484955	+	0.874539i	$0.661164\pi$
$524$	10.0000			0.436852
$525$		0			0
$526$	−12.0000			−0.523225
$527$			6.00000i			0.261364i
$528$		0			0
$529$	7.00000			0.304348
$530$	−20.0000	−	10.0000i	−0.868744	−	0.434372i
$531$		0			0
$532$			16.0000i			0.693688i
$533$		−	4.00000i		−	0.173259i
$534$		0			0
$535$	4.00000	−	8.00000i	0.172935	−	0.345870i
$536$	−4.00000			−0.172774
$537$		0			0
$538$			4.00000i			0.172452i
$539$	18.0000			0.775315
$540$		0			0
$541$	18.0000			0.773880			0.386940	−	0.922105i	$-0.373532\pi$
$541$	18.0000			0.773880			0.386940	+	0.922105i	$0.373532\pi$
$542$		0			0
$543$		0			0
$544$	−6.00000			−0.257248
$545$	4.00000	+	2.00000i	0.171341	+	0.0856706i
$546$		0			0
$547$			8.00000i			0.342055i	0.985266	+	0.171028i	$0.0547087\pi$
$547$			8.00000i			0.342055i	−0.985266	+	0.171028i	$0.945291\pi$
$548$		−	14.0000i		−	0.598050i
$549$		0			0
$550$	24.0000	−	18.0000i	1.02336	−	0.767523i
$551$	32.0000			1.36325
$552$		0			0
$553$		0			0
$554$	10.0000			0.424859
$555$		0			0
$556$	−20.0000			−0.848189
$557$			30.0000i			1.27114i	0.772043	+	0.635570i	$0.219235\pi$
$557$			30.0000i			1.27114i	−0.772043	+	0.635570i	$0.780765\pi$
$558$		0			0
$559$	−8.00000			−0.338364
$560$	2.00000	−	4.00000i	0.0845154	−	0.169031i
$561$		0			0
$562$			22.0000i			0.928014i
$563$		−	36.0000i		−	1.51722i	−0.651546	−	0.758610i	$-0.725879\pi$
$563$		−	36.0000i		−	1.51722i	0.651546	−	0.758610i	$-0.274121\pi$
$564$		0			0
$565$	18.0000	−	36.0000i	0.757266	−	1.51453i
$566$	20.0000			0.840663
$567$		0			0
$568$		−	16.0000i		−	0.671345i
$569$	18.0000			0.754599			0.377300	−	0.926091i	$-0.376853\pi$
$569$	18.0000			0.754599			0.377300	+	0.926091i	$0.376853\pi$
$570$		0			0
$571$	−40.0000			−1.67395			−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000			−1.67395			−0.836974	+	0.547243i	$0.815677\pi$
$572$		−	12.0000i		−	0.501745i
$573$		0			0
$574$	−4.00000			−0.166957
$575$	−16.0000	+	12.0000i	−0.667246	+	0.500435i
$576$		0			0
$577$			16.0000i			0.666089i	0.942911	+	0.333044i	$0.108076\pi$
$577$			16.0000i			0.666089i	−0.942911	+	0.333044i	$0.891924\pi$
$578$			19.0000i			0.790296i
$579$		0			0
$580$	−8.00000	−	4.00000i	−0.332182	−	0.166091i
$581$	8.00000			0.331896
$582$		0			0
$583$			60.0000i			2.48495i
$584$	−8.00000			−0.331042
$585$		0			0
$586$	−6.00000			−0.247858
$587$			12.0000i			0.495293i	0.968850	+	0.247647i	$0.0796572\pi$
$587$			12.0000i			0.495293i	−0.968850	+	0.247647i	$0.920343\pi$
$588$		0			0
$589$	8.00000			0.329634
$590$	−6.00000	+	12.0000i	−0.247016	+	0.494032i
$591$		0			0
$592$			2.00000i			0.0821995i
$593$		−	30.0000i		−	1.23195i	−0.787765	−	0.615976i	$-0.788762\pi$
$593$		−	30.0000i		−	1.23195i	0.787765	−	0.615976i	$-0.211238\pi$
$594$		0			0
$595$	−24.0000	−	12.0000i	−0.983904	−	0.491952i
$596$	12.0000			0.491539
$597$		0			0
$598$			8.00000i			0.327144i
$599$	−20.0000			−0.817178			−0.408589	−	0.912719i	$-0.633979\pi$
$599$	−20.0000			−0.817178			−0.408589	+	0.912719i	$0.633979\pi$
$600$		0			0
$601$	10.0000			0.407909			0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000			0.407909			0.203954	+	0.978980i	$0.434621\pi$
$602$			8.00000i			0.326056i
$603$		0			0
$604$	−8.00000			−0.325515
$605$	−50.0000	−	25.0000i	−2.03279	−	1.01639i
$606$		0			0
$607$			6.00000i			0.243532i	0.992559	+	0.121766i	$0.0388558\pi$
$607$			6.00000i			0.243532i	−0.992559	+	0.121766i	$0.961144\pi$
$608$			8.00000i			0.324443i
$609$		0			0
$610$	14.0000	−	28.0000i	0.566843	−	1.13369i
$611$	16.0000			0.647291
$612$		0			0
$613$			30.0000i			1.21169i	0.795583	+	0.605844i	$0.207165\pi$
$613$			30.0000i			1.21169i	−0.795583	+	0.605844i	$0.792835\pi$
$614$	−8.00000			−0.322854
$615$		0			0
$616$	−12.0000			−0.483494
$617$		−	22.0000i		−	0.885687i	−0.896599	−	0.442843i	$-0.853970\pi$
$617$		−	22.0000i		−	0.885687i	0.896599	−	0.442843i	$-0.146030\pi$
$618$		0			0
$619$	12.0000			0.482321			0.241160	−	0.970485i	$-0.422472\pi$
$619$	12.0000			0.482321			0.241160	+	0.970485i	$0.422472\pi$
$620$	−2.00000	−	1.00000i	−0.0803219	−	0.0401610i
$621$		0			0
$622$		−	8.00000i		−	0.320771i
$623$			20.0000i			0.801283i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	−24.0000			−0.959233
$627$		0			0
$628$			6.00000i			0.239426i
$629$	12.0000			0.478471
$630$		0			0
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$		0			0
$633$		0			0
$634$	18.0000			0.714871
$635$	−2.00000	+	4.00000i	−0.0793676	+	0.158735i
$636$		0			0
$637$			6.00000i			0.237729i
$638$			24.0000i			0.950169i
$639$		0			0
$640$	1.00000	−	2.00000i	0.0395285	−	0.0790569i
$641$	−14.0000			−0.552967			−0.276483	−	0.961019i	$-0.589169\pi$
$641$	−14.0000			−0.552967			−0.276483	+	0.961019i	$0.589169\pi$
$642$		0			0
$643$			32.0000i			1.26196i	0.775800	+	0.630978i	$0.217346\pi$
$643$			32.0000i			1.26196i	−0.775800	+	0.630978i	$0.782654\pi$
$644$	8.00000			0.315244
$645$		0			0
$646$	48.0000			1.88853
$647$		−	32.0000i		−	1.25805i	−0.777385	−	0.629025i	$-0.783454\pi$
$647$		−	32.0000i		−	1.25805i	0.777385	−	0.629025i	$-0.216546\pi$
$648$		0			0
$649$	36.0000			1.41312
$650$	6.00000	+	8.00000i	0.235339	+	0.313786i
$651$		0			0
$652$		−	20.0000i		−	0.783260i
$653$		−	42.0000i		−	1.64359i	−0.569785	−	0.821794i	$-0.692974\pi$
$653$		−	42.0000i		−	1.64359i	0.569785	−	0.821794i	$-0.307026\pi$
$654$		0			0
$655$	20.0000	+	10.0000i	0.781465	+	0.390732i
$656$	−2.00000			−0.0780869
$657$		0			0
$658$		−	16.0000i		−	0.623745i
$659$	18.0000			0.701180			0.350590	−	0.936529i	$-0.385981\pi$
$659$	18.0000			0.701180			0.350590	+	0.936529i	$0.385981\pi$
$660$		0			0
$661$	18.0000			0.700119			0.350059	−	0.936727i	$-0.386161\pi$
$661$	18.0000			0.700119			0.350059	+	0.936727i	$0.386161\pi$
$662$		−	8.00000i		−	0.310929i
$663$		0			0
$664$	4.00000			0.155230
$665$	−16.0000	+	32.0000i	−0.620453	+	1.24091i
$666$		0			0
$667$		−	16.0000i		−	0.619522i
$668$		−	12.0000i		−	0.464294i
$669$		0			0
$670$	−8.00000	−	4.00000i	−0.309067	−	0.154533i
$671$	−84.0000			−3.24278
$672$		0			0
$673$		−	24.0000i		−	0.925132i	−0.886585	−	0.462566i	$-0.846929\pi$
$673$		−	24.0000i		−	0.925132i	0.886585	−	0.462566i	$-0.153071\pi$
$674$	−8.00000			−0.308148
$675$		0			0
$676$	−9.00000			−0.346154
$677$			10.0000i			0.384331i	0.981363	+	0.192166i	$0.0615511\pi$
$677$			10.0000i			0.384331i	−0.981363	+	0.192166i	$0.938449\pi$
$678$		0			0
$679$	−32.0000			−1.22805
$680$	−12.0000	−	6.00000i	−0.460179	−	0.230089i
$681$		0			0
$682$			6.00000i			0.229752i
$683$			4.00000i			0.153056i	0.997067	+	0.0765279i	$0.0243834\pi$
$683$			4.00000i			0.153056i	−0.997067	+	0.0765279i	$0.975617\pi$
$684$		0			0
$685$	14.0000	−	28.0000i	0.534913	−	1.06983i
$686$	20.0000			0.763604
$687$		0			0
$688$			4.00000i			0.152499i
$689$	−20.0000			−0.761939
$690$		0			0
$691$	−32.0000			−1.21734			−0.608669	−	0.793424i	$-0.708296\pi$
$691$	−32.0000			−1.21734			−0.608669	+	0.793424i	$0.708296\pi$
$692$		−	14.0000i		−	0.532200i
$693$		0			0
$694$	−4.00000			−0.151838
$695$	−40.0000	−	20.0000i	−1.51729	−	0.758643i
$696$		0			0
$697$			12.0000i			0.454532i
$698$			2.00000i			0.0757011i
$699$		0			0
$700$	8.00000	−	6.00000i	0.302372	−	0.226779i
$701$	−16.0000			−0.604312			−0.302156	−	0.953259i	$-0.597706\pi$
$701$	−16.0000			−0.604312			−0.302156	+	0.953259i	$0.597706\pi$
$702$		0			0
$703$		−	16.0000i		−	0.603451i
$704$	−6.00000			−0.226134
$705$		0			0
$706$	−18.0000			−0.677439
$707$		0			0
$708$		0			0
$709$	10.0000			0.375558			0.187779	−	0.982211i	$-0.439871\pi$
$709$	10.0000			0.375558			0.187779	+	0.982211i	$0.439871\pi$
$710$	16.0000	−	32.0000i	0.600469	−	1.20094i
$711$		0			0
$712$			10.0000i			0.374766i
$713$		−	4.00000i		−	0.149801i
$714$		0			0
$715$	12.0000	−	24.0000i	0.448775	−	0.897549i
$716$	−18.0000			−0.672692
$717$		0			0
$718$		−	12.0000i		−	0.447836i
$719$	−8.00000			−0.298350			−0.149175	−	0.988811i	$-0.547662\pi$
$719$	−8.00000			−0.298350			−0.149175	+	0.988811i	$0.547662\pi$
$720$		0			0
$721$	−12.0000			−0.446903
$722$		−	45.0000i		−	1.67473i
$723$		0			0
$724$	−10.0000			−0.371647
$725$	−12.0000	−	16.0000i	−0.445669	−	0.594225i
$726$		0			0
$727$			38.0000i			1.40934i	0.709534	+	0.704671i	$0.248905\pi$
$727$			38.0000i			1.40934i	−0.709534	+	0.704671i	$0.751095\pi$
$728$		−	4.00000i		−	0.148250i
$729$		0			0
$730$	−16.0000	−	8.00000i	−0.592187	−	0.296093i
$731$	24.0000			0.887672
$732$		0			0
$733$		−	22.0000i		−	0.812589i	−0.913742	−	0.406294i	$-0.866821\pi$
$733$		−	22.0000i		−	0.812589i	0.913742	−	0.406294i	$-0.133179\pi$
$734$	−26.0000			−0.959678
$735$		0			0
$736$	4.00000			0.147442
$737$			24.0000i			0.884051i
$738$		0			0
$739$	24.0000			0.882854			0.441427	−	0.897297i	$-0.354472\pi$
$739$	24.0000			0.882854			0.441427	+	0.897297i	$0.354472\pi$
$740$	−2.00000	+	4.00000i	−0.0735215	+	0.147043i
$741$		0			0
$742$			20.0000i			0.734223i
$743$			24.0000i			0.880475i	0.897881	+	0.440237i	$0.145106\pi$
$743$			24.0000i			0.880475i	−0.897881	+	0.440237i	$0.854894\pi$
$744$		0			0
$745$	24.0000	+	12.0000i	0.879292	+	0.439646i
$746$	22.0000			0.805477
$747$		0			0
$748$			36.0000i			1.31629i
$749$	−8.00000			−0.292314
$750$		0			0
$751$	40.0000			1.45962			0.729810	−	0.683650i	$-0.239608\pi$
$751$	40.0000			1.45962			0.729810	+	0.683650i	$0.239608\pi$
$752$		−	8.00000i		−	0.291730i
$753$		0			0
$754$	−8.00000			−0.291343
$755$	−16.0000	−	8.00000i	−0.582300	−	0.291150i
$756$		0			0
$757$			34.0000i			1.23575i	0.786276	+	0.617876i	$0.212006\pi$
$757$			34.0000i			1.23575i	−0.786276	+	0.617876i	$0.787994\pi$
$758$			36.0000i			1.30758i
$759$		0			0
$760$	−8.00000	+	16.0000i	−0.290191	+	0.580381i
$761$	54.0000			1.95750			0.978749	−	0.205061i	$-0.0657392\pi$
$761$	54.0000			1.95750			0.978749	+	0.205061i	$0.0657392\pi$
$762$		0			0
$763$		−	4.00000i		−	0.144810i
$764$	8.00000			0.289430
$765$		0			0
$766$	−16.0000			−0.578103
$767$			12.0000i			0.433295i
$768$		0			0
$769$	30.0000			1.08183			0.540914	−	0.841078i	$-0.318079\pi$
$769$	30.0000			1.08183			0.540914	+	0.841078i	$0.318079\pi$
$770$	−24.0000	−	12.0000i	−0.864900	−	0.432450i
$771$		0			0
$772$		−	20.0000i		−	0.719816i
$773$		−	34.0000i		−	1.22290i	−0.791285	−	0.611448i	$-0.790588\pi$
$773$		−	34.0000i		−	1.22290i	0.791285	−	0.611448i	$-0.209412\pi$
$774$		0			0
$775$	−3.00000	−	4.00000i	−0.107763	−	0.143684i
$776$	−16.0000			−0.574367
$777$		0			0
$778$			16.0000i			0.573628i
$779$	16.0000			0.573259
$780$		0			0
$781$	−96.0000			−3.43515
$782$		−	24.0000i		−	0.858238i
$783$		0			0
$784$	3.00000			0.107143
$785$	−6.00000	+	12.0000i	−0.214149	+	0.428298i
$786$		0			0
$787$		0			0		1.00000			$0$
$787$		0			0		−1.00000			$\pi$
$788$			18.0000i			0.641223i
$789$		0			0
$790$		0			0
$791$	−36.0000			−1.28001
$792$		0			0
$793$		−	28.0000i		−	0.994309i
$794$	22.0000			0.780751
$795$		0			0
$796$		0			0
$797$			50.0000i			1.77109i	0.464553	+	0.885545i	$0.346215\pi$
$797$			50.0000i			1.77109i	−0.464553	+	0.885545i	$0.653785\pi$
$798$		0			0
$799$	−48.0000			−1.69812
$800$	4.00000	−	3.00000i	0.141421	−	0.106066i
$801$		0			0
$802$			2.00000i			0.0706225i
$803$			48.0000i			1.69388i
$804$		0			0
$805$	16.0000	+	8.00000i	0.563926	+	0.281963i
$806$	−2.00000			−0.0704470
$807$		0			0
$808$		0			0
$809$	−18.0000			−0.632846			−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000			−0.632846			−0.316423	+	0.948618i	$0.602482\pi$
$810$		0			0
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$			8.00000i			0.280745i
$813$		0			0
$814$	12.0000			0.420600
$815$	20.0000	−	40.0000i	0.700569	−	1.40114i
$816$		0			0
$817$		−	32.0000i		−	1.11954i
$818$			22.0000i			0.769212i
$819$		0			0
$820$	−4.00000	−	2.00000i	−0.139686	−	0.0698430i
$821$	−36.0000			−1.25641			−0.628204	−	0.778048i	$-0.716210\pi$
$821$	−36.0000			−1.25641			−0.628204	+	0.778048i	$0.716210\pi$
$822$		0			0
$823$			54.0000i			1.88232i	0.337959	+	0.941161i	$0.390263\pi$
$823$			54.0000i			1.88232i	−0.337959	+	0.941161i	$0.609737\pi$
$824$	−6.00000			−0.209020
$825$		0			0
$826$	12.0000			0.417533
$827$		−	4.00000i		−	0.139094i	−0.997579	−	0.0695468i	$-0.977845\pi$
$827$		−	4.00000i		−	0.139094i	0.997579	−	0.0695468i	$-0.0221553\pi$
$828$		0			0
$829$	−2.00000			−0.0694629			−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000			−0.0694629			−0.0347314	+	0.999397i	$0.511058\pi$
$830$	8.00000	+	4.00000i	0.277684	+	0.138842i
$831$		0			0
$832$		−	2.00000i		−	0.0693375i
$833$		−	18.0000i		−	0.623663i
$834$		0			0
$835$	12.0000	−	24.0000i	0.415277	−	0.830554i
$836$	48.0000			1.66011
$837$		0			0
$838$			6.00000i			0.207267i
$839$	−12.0000			−0.414286			−0.207143	−	0.978311i	$-0.566417\pi$
$839$	−12.0000			−0.414286			−0.207143	+	0.978311i	$0.566417\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$			2.00000i			0.0689246i
$843$		0			0
$844$	20.0000			0.688428
$845$	−18.0000	−	9.00000i	−0.619219	−	0.309609i
$846$		0			0
$847$			50.0000i			1.71802i
$848$			10.0000i			0.343401i
$849$		0			0
$850$	−18.0000	−	24.0000i	−0.617395	−	0.823193i
$851$	−8.00000			−0.274236
$852$		0			0
$853$		−	22.0000i		−	0.753266i	−0.926363	−	0.376633i	$-0.877082\pi$
$853$		−	22.0000i		−	0.753266i	0.926363	−	0.376633i	$-0.122918\pi$
$854$	−28.0000			−0.958140
$855$		0			0
$856$	−4.00000			−0.136717
$857$		−	46.0000i		−	1.57133i	−0.618652	−	0.785665i	$-0.712321\pi$
$857$		−	46.0000i		−	1.57133i	0.618652	−	0.785665i	$-0.287679\pi$
$858$		0			0
$859$	−4.00000			−0.136478			−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000			−0.136478			−0.0682391	+	0.997669i	$0.521738\pi$
$860$	−4.00000	+	8.00000i	−0.136399	+	0.272798i
$861$		0			0
$862$			12.0000i			0.408722i
$863$			44.0000i			1.49778i	0.662696	+	0.748889i	$0.269412\pi$
$863$			44.0000i			1.49778i	−0.662696	+	0.748889i	$0.730588\pi$
$864$		0			0
$865$	14.0000	−	28.0000i	0.476014	−	0.952029i
$866$	−8.00000			−0.271851
$867$		0			0
$868$			2.00000i			0.0678844i
$869$		0			0
$870$		0			0
$871$	−8.00000			−0.271070
$872$		−	2.00000i		−	0.0677285i
$873$		0			0
$874$	−32.0000			−1.08242
$875$	22.0000	−	4.00000i	0.743736	−	0.135225i
$876$		0			0
$877$		−	30.0000i		−	1.01303i	−0.862232	−	0.506514i	$-0.830934\pi$
$877$		−	30.0000i		−	1.01303i	0.862232	−	0.506514i	$-0.169066\pi$
$878$			32.0000i			1.07995i
$879$		0			0
$880$	−12.0000	−	6.00000i	−0.404520	−	0.202260i
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$		−	56.0000i		−	1.88455i	−0.334840	−	0.942275i	$-0.608682\pi$
$883$		−	56.0000i		−	1.88455i	0.334840	−	0.942275i	$-0.391318\pi$
$884$	−12.0000			−0.403604
$885$		0			0
$886$	4.00000			0.134383
$887$		−	12.0000i		−	0.402921i	−0.979497	−	0.201460i	$-0.935431\pi$
$887$		−	12.0000i		−	0.402921i	0.979497	−	0.201460i	$-0.0645687\pi$
$888$		0			0
$889$	4.00000			0.134156
$890$	−10.0000	+	20.0000i	−0.335201	+	0.670402i
$891$		0			0
$892$			14.0000i			0.468755i
$893$			64.0000i			2.14168i
$894$		0			0
$895$	−36.0000	−	18.0000i	−1.20335	−	0.601674i
$896$	−2.00000			−0.0668153
$897$		0			0
$898$		−	26.0000i		−	0.867631i
$899$	4.00000			0.133407
$900$		0			0
$901$	60.0000			1.99889
$902$			12.0000i			0.399556i
$903$		0			0
$904$	−18.0000			−0.598671
$905$	−20.0000	−	10.0000i	−0.664822	−	0.332411i
$906$		0			0
$907$		−	24.0000i		−	0.796907i	−0.917189	−	0.398453i	$-0.869547\pi$
$907$		−	24.0000i		−	0.796907i	0.917189	−	0.398453i	$-0.130453\pi$
$908$		−	12.0000i		−	0.398234i
$909$		0			0
$910$	4.00000	−	8.00000i	0.132599	−	0.265197i
$911$	16.0000			0.530104			0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000			0.530104			0.265052	+	0.964234i	$0.414611\pi$
$912$		0			0
$913$		−	24.0000i		−	0.794284i
$914$	−12.0000			−0.396925
$915$		0			0
$916$	6.00000			0.198246
$917$		−	20.0000i		−	0.660458i
$918$		0			0
$919$	16.0000			0.527791			0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000			0.527791			0.263896	+	0.964551i	$0.414993\pi$
$920$	8.00000	+	4.00000i	0.263752	+	0.131876i
$921$		0			0
$922$		−	32.0000i		−	1.05386i
$923$		−	32.0000i		−	1.05329i
$924$		0			0
$925$	−8.00000	+	6.00000i	−0.263038	+	0.197279i
$926$	−26.0000			−0.854413
$927$		0			0
$928$			4.00000i			0.131306i
$929$	50.0000			1.64045			0.820223	−	0.572043i	$-0.193849\pi$
$929$	50.0000			1.64045			0.820223	+	0.572043i	$0.193849\pi$
$930$		0			0
$931$	−24.0000			−0.786568
$932$			18.0000i			0.589610i
$933$		0			0
$934$	4.00000			0.130884
$935$	−36.0000	+	72.0000i	−1.17733	+	2.35465i
$936$		0			0
$937$		−	16.0000i		−	0.522697i	−0.965244	−	0.261349i	$-0.915833\pi$
$937$		−	16.0000i		−	0.522697i	0.965244	−	0.261349i	$-0.0841672\pi$
$938$			8.00000i			0.261209i
$939$		0			0
$940$	8.00000	−	16.0000i	0.260931	−	0.521862i
$941$	−16.0000			−0.521585			−0.260793	−	0.965395i	$-0.583984\pi$
$941$	−16.0000			−0.521585			−0.260793	+	0.965395i	$0.583984\pi$
$942$		0			0
$943$		−	8.00000i		−	0.260516i
$944$	6.00000			0.195283
$945$		0			0
$946$	24.0000			0.780307
$947$		−	44.0000i		−	1.42981i	−0.699223	−	0.714904i	$-0.746470\pi$
$947$		−	44.0000i		−	1.42981i	0.699223	−	0.714904i	$-0.253530\pi$
$948$		0			0
$949$	−16.0000			−0.519382
$950$	−32.0000	+	24.0000i	−1.03822	+	0.778663i
$951$		0			0
$952$			12.0000i			0.388922i
$953$		−	38.0000i		−	1.23094i	−0.788160	−	0.615470i	$-0.788966\pi$
$953$		−	38.0000i		−	1.23094i	0.788160	−	0.615470i	$-0.211034\pi$
$954$		0			0
$955$	16.0000	+	8.00000i	0.517748	+	0.258874i
$956$	20.0000			0.646846
$957$		0			0
$958$			40.0000i			1.29234i
$959$	−28.0000			−0.904167
$960$		0			0
$961$	1.00000			0.0322581
$962$			4.00000i			0.128965i
$963$		0			0
$964$	18.0000			0.579741
$965$	20.0000	−	40.0000i	0.643823	−	1.28765i
$966$		0			0
$967$			14.0000i			0.450210i	0.974335	+	0.225105i	$0.0722725\pi$
$967$			14.0000i			0.450210i	−0.974335	+	0.225105i	$0.927728\pi$
$968$			25.0000i			0.803530i
$969$		0			0
$970$	−32.0000	−	16.0000i	−1.02746	−	0.513729i
$971$	30.0000			0.962746			0.481373	−	0.876516i	$-0.340138\pi$
$971$	30.0000			0.962746			0.481373	+	0.876516i	$0.340138\pi$
$972$		0			0
$973$			40.0000i			1.28234i
$974$	−14.0000			−0.448589
$975$		0			0
$976$	−14.0000			−0.448129
$977$		−	30.0000i		−	0.959785i	−0.877327	−	0.479893i	$-0.840676\pi$
$977$		−	30.0000i		−	0.959785i	0.877327	−	0.479893i	$-0.159324\pi$
$978$		0			0
$979$	60.0000			1.91761
$980$	6.00000	+	3.00000i	0.191663	+	0.0958315i
$981$		0			0
$982$			30.0000i			0.957338i
$983$		0			0		1.00000			$0$
$983$		0			0		−1.00000			$\pi$
$984$		0			0
$985$	−18.0000	+	36.0000i	−0.573528	+	1.14706i
$986$	24.0000			0.764316
$987$		0			0
$988$			16.0000i			0.509028i
$989$	−16.0000			−0.508770
$990$		0			0
$991$	16.0000			0.508257			0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000			0.508257			0.254128	+	0.967170i	$0.418211\pi$
$992$			1.00000i			0.0317500i
$993$		0			0
$994$	−32.0000			−1.01498
$995$		0			0
$996$		0			0
$997$		−	30.0000i		−	0.950110i	−0.879956	−	0.475055i	$-0.842428\pi$
$997$		−	30.0000i		−	0.950110i	0.879956	−	0.475055i	$-0.157572\pi$
$998$		−	32.0000i		−	1.01294i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2790.2.d.c.559.1		2
3.2	odd	2		930.2.d.e.559.2	yes	2
5.4	even	2	inner	2790.2.d.c.559.2		2
15.2	even	4		4650.2.a.c.1.1		1
15.8	even	4		4650.2.a.bs.1.1		1
15.14	odd	2		930.2.d.e.559.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.d.e.559.1	✓	2	15.14	odd	2
930.2.d.e.559.2	yes	2	3.2	odd	2
2790.2.d.c.559.1		2	1.1	even	1	trivial
2790.2.d.c.559.2		2	5.4	even	2	inner
4650.2.a.c.1.1		1	15.2	even	4
4650.2.a.bs.1.1		1	15.8	even	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:	\( N \)	\(=\)	\( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2790.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +2.00000i q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +2.00000i q^{7} +1.00000i q^{8} +(-1.00000 + 2.00000i) q^{10} +6.00000 q^{11} +2.00000i q^{13} +2.00000 q^{14} +1.00000 q^{16} -6.00000i q^{17} -8.00000 q^{19} +(2.00000 + 1.00000i) q^{20} -6.00000i q^{22} +4.00000i q^{23} +(3.00000 + 4.00000i) q^{25} +2.00000 q^{26} -2.00000i q^{28} -4.00000 q^{29} -1.00000 q^{31} -1.00000i q^{32} -6.00000 q^{34} +(2.00000 - 4.00000i) q^{35} +2.00000i q^{37} +8.00000i q^{38} +(1.00000 - 2.00000i) q^{40} -2.00000 q^{41} +4.00000i q^{43} -6.00000 q^{44} +4.00000 q^{46} -8.00000i q^{47} +3.00000 q^{49} +(4.00000 - 3.00000i) q^{50} -2.00000i q^{52} +10.0000i q^{53} +(-12.0000 - 6.00000i) q^{55} -2.00000 q^{56} +4.00000i q^{58} +6.00000 q^{59} -14.0000 q^{61} +1.00000i q^{62} -1.00000 q^{64} +(2.00000 - 4.00000i) q^{65} +4.00000i q^{67} +6.00000i q^{68} +(-4.00000 - 2.00000i) q^{70} -16.0000 q^{71} +8.00000i q^{73} +2.00000 q^{74} +8.00000 q^{76} +12.0000i q^{77} +(-2.00000 - 1.00000i) q^{80} +2.00000i q^{82} -4.00000i q^{83} +(-6.00000 + 12.0000i) q^{85} +4.00000 q^{86} +6.00000i q^{88} +10.0000 q^{89} -4.00000 q^{91} -4.00000i q^{92} -8.00000 q^{94} +(16.0000 + 8.00000i) q^{95} +16.0000i q^{97} -3.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} - 4 q^{5}+O(q^{10}) \) 2 * q - 2 * q^4 - 4 * q^5	\( 2 q - 2 q^{4} - 4 q^{5} - 2 q^{10} + 12 q^{11} + 4 q^{14} + 2 q^{16} - 16 q^{19} + 4 q^{20} + 6 q^{25} + 4 q^{26} - 8 q^{29} - 2 q^{31} - 12 q^{34} + 4 q^{35} + 2 q^{40} - 4 q^{41} - 12 q^{44} + 8 q^{46} + 6 q^{49} + 8 q^{50} - 24 q^{55} - 4 q^{56} + 12 q^{59} - 28 q^{61} - 2 q^{64} + 4 q^{65} - 8 q^{70} - 32 q^{71} + 4 q^{74} + 16 q^{76} - 4 q^{80} - 12 q^{85} + 8 q^{86} + 20 q^{89} - 8 q^{91} - 16 q^{94} + 32 q^{95}+O(q^{100}) \) 2 * q - 2 * q^4 - 4 * q^5 - 2 * q^10 + 12 * q^11 + 4 * q^14 + 2 * q^16 - 16 * q^19 + 4 * q^20 + 6 * q^25 + 4 * q^26 - 8 * q^29 - 2 * q^31 - 12 * q^34 + 4 * q^35 + 2 * q^40 - 4 * q^41 - 12 * q^44 + 8 * q^46 + 6 * q^49 + 8 * q^50 - 24 * q^55 - 4 * q^56 + 12 * q^59 - 28 * q^61 - 2 * q^64 + 4 * q^65 - 8 * q^70 - 32 * q^71 + 4 * q^74 + 16 * q^76 - 4 * q^80 - 12 * q^85 + 8 * q^86 + 20 * q^89 - 8 * q^91 - 16 * q^94 + 32 * q^95

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