LMFDB - Embedded newform 1530.2.f.f.1189.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1530,2,Mod(1189,1530)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1530, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1530.1189");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1530.f (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:	$12.2171115093$
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			1189.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1530.1189
Dual form			1530.2.f.f.1189.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} +4.00000 q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} +4.00000 q^{7} -1.00000i q^{8} +(-1.00000 + 2.00000i) q^{10} -4.00000i q^{13} +4.00000i q^{14} +1.00000 q^{16} +(4.00000 + 1.00000i) q^{17} +4.00000 q^{19} +(-2.00000 - 1.00000i) q^{20} -4.00000 q^{23} +(3.00000 + 4.00000i) q^{25} +4.00000 q^{26} -4.00000 q^{28} -6.00000i q^{29} -4.00000i q^{31} +1.00000i q^{32} +(-1.00000 + 4.00000i) q^{34} +(8.00000 + 4.00000i) q^{35} -2.00000 q^{37} +4.00000i q^{38} +(1.00000 - 2.00000i) q^{40} -2.00000i q^{41} -12.0000i q^{43} -4.00000i q^{46} +8.00000i q^{47} +9.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} +4.00000i q^{52} +10.0000i q^{53} -4.00000i q^{56} +6.00000 q^{58} -4.00000 q^{59} -4.00000i q^{61} +4.00000 q^{62} -1.00000 q^{64} +(4.00000 - 8.00000i) q^{65} -4.00000i q^{67} +(-4.00000 - 1.00000i) q^{68} +(-4.00000 + 8.00000i) q^{70} +4.00000i q^{71} -14.0000 q^{73} -2.00000i q^{74} -4.00000 q^{76} +4.00000i q^{79} +(2.00000 + 1.00000i) q^{80} +2.00000 q^{82} +12.0000i q^{83} +(7.00000 + 6.00000i) q^{85} +12.0000 q^{86} +16.0000 q^{89} -16.0000i q^{91} +4.00000 q^{92} -8.00000 q^{94} +(8.00000 + 4.00000i) q^{95} -10.0000 q^{97} +9.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} + 4 q^{5} + 8 q^{7}+O(q^{10}) $ 2 * q - 2 * q^4 + 4 * q^5 + 8 * q^7	$ 2 q - 2 q^{4} + 4 q^{5} + 8 q^{7} - 2 q^{10} + 2 q^{16} + 8 q^{17} + 8 q^{19} - 4 q^{20} - 8 q^{23} + 6 q^{25} + 8 q^{26} - 8 q^{28} - 2 q^{34} + 16 q^{35} - 4 q^{37} + 2 q^{40} + 18 q^{49} - 8 q^{50} + 12 q^{58} - 8 q^{59} + 8 q^{62} - 2 q^{64} + 8 q^{65} - 8 q^{68} - 8 q^{70} - 28 q^{73} - 8 q^{76} + 4 q^{80} + 4 q^{82} + 14 q^{85} + 24 q^{86} + 32 q^{89} + 8 q^{92} - 16 q^{94} + 16 q^{95} - 20 q^{97}+O(q^{100}) $ 2 * q - 2 * q^4 + 4 * q^5 + 8 * q^7 - 2 * q^10 + 2 * q^16 + 8 * q^17 + 8 * q^19 - 4 * q^20 - 8 * q^23 + 6 * q^25 + 8 * q^26 - 8 * q^28 - 2 * q^34 + 16 * q^35 - 4 * q^37 + 2 * q^40 + 18 * q^49 - 8 * q^50 + 12 * q^58 - 8 * q^59 + 8 * q^62 - 2 * q^64 + 8 * q^65 - 8 * q^68 - 8 * q^70 - 28 * q^73 - 8 * q^76 + 4 * q^80 + 4 * q^82 + 14 * q^85 + 24 * q^86 + 32 * q^89 + 8 * q^92 - 16 * q^94 + 16 * q^95 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1530\mathbb{Z}\right)^\times$.

$n$	$307$	$1261$	$1361$
$\chi(n)$	$-1$	$-1$	$1$

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
$7$	4.00000			1.51186			0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000			1.51186			0.755929	+	0.654654i	$0.227186\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−1.00000	+	2.00000i	−0.316228	+	0.632456i
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$		0			0
$13$		−	4.00000i		−	1.10940i	−0.832050	−	0.554700i	$-0.812833\pi$
$13$		−	4.00000i		−	1.10940i	0.832050	−	0.554700i	$-0.187167\pi$
$14$			4.00000i			1.06904i
$15$		0			0
$16$	1.00000			0.250000
$17$	4.00000	+	1.00000i	0.970143	+	0.242536i
$17$	4.00000	+	1.00000i	0.970143	+	0.242536i
$18$		0			0
$19$	4.00000			0.917663			0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000			0.917663			0.458831	+	0.888523i	$0.348268\pi$
$20$	−2.00000	−	1.00000i	−0.447214	−	0.223607i
$21$		0			0
$22$		0			0
$23$	−4.00000			−0.834058			−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000			−0.834058			−0.417029	+	0.908893i	$0.636929\pi$
$24$		0			0
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	4.00000			0.784465
$27$		0			0
$28$	−4.00000			−0.755929
$29$		−	6.00000i		−	1.11417i	−0.830455	−	0.557086i	$-0.811919\pi$
$29$		−	6.00000i		−	1.11417i	0.830455	−	0.557086i	$-0.188081\pi$
$30$		0			0
$31$		−	4.00000i		−	0.718421i	−0.933257	−	0.359211i	$-0.883046\pi$
$31$		−	4.00000i		−	0.718421i	0.933257	−	0.359211i	$-0.116954\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−1.00000	+	4.00000i	−0.171499	+	0.685994i
$35$	8.00000	+	4.00000i	1.35225	+	0.676123i
$36$		0			0
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$			4.00000i			0.648886i
$39$		0			0
$40$	1.00000	−	2.00000i	0.158114	−	0.316228i
$41$		−	2.00000i		−	0.312348i	−0.987730	−	0.156174i	$-0.950084\pi$
$41$		−	2.00000i		−	0.312348i	0.987730	−	0.156174i	$-0.0499160\pi$
$42$		0			0
$43$		−	12.0000i		−	1.82998i	−0.403473	−	0.914991i	$-0.632197\pi$
$43$		−	12.0000i		−	1.82998i	0.403473	−	0.914991i	$-0.367803\pi$
$44$		0			0
$45$		0			0
$46$		−	4.00000i		−	0.589768i
$47$			8.00000i			1.16692i	0.812142	+	0.583460i	$0.198301\pi$
$47$			8.00000i			1.16692i	−0.812142	+	0.583460i	$0.801699\pi$
$48$		0			0
$49$	9.00000			1.28571
$50$	−4.00000	+	3.00000i	−0.565685	+	0.424264i
$51$		0			0
$52$			4.00000i			0.554700i
$53$			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
$55$		0			0
$56$		−	4.00000i		−	0.534522i
$57$		0			0
$58$	6.00000			0.787839
$59$	−4.00000			−0.520756			−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000			−0.520756			−0.260378	+	0.965507i	$0.583847\pi$
$60$		0			0
$61$		−	4.00000i		−	0.512148i	−0.966657	−	0.256074i	$-0.917571\pi$
$61$		−	4.00000i		−	0.512148i	0.966657	−	0.256074i	$-0.0824290\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	−1.00000			−0.125000
$65$	4.00000	−	8.00000i	0.496139	−	0.992278i
$66$		0			0
$67$		−	4.00000i		−	0.488678i	−0.969690	−	0.244339i	$-0.921429\pi$
$67$		−	4.00000i		−	0.488678i	0.969690	−	0.244339i	$-0.0785709\pi$
$68$	−4.00000	−	1.00000i	−0.485071	−	0.121268i
$69$		0			0
$70$	−4.00000	+	8.00000i	−0.478091	+	0.956183i
$71$			4.00000i			0.474713i	0.971423	+	0.237356i	$0.0762809\pi$
$71$			4.00000i			0.474713i	−0.971423	+	0.237356i	$0.923719\pi$
$72$		0			0
$73$	−14.0000			−1.63858			−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000			−1.63858			−0.819288	+	0.573382i	$0.805631\pi$
$74$		−	2.00000i		−	0.232495i
$75$		0			0
$76$	−4.00000			−0.458831
$77$		0			0
$78$		0			0
$79$			4.00000i			0.450035i	0.974355	+	0.225018i	$0.0722440\pi$
$79$			4.00000i			0.450035i	−0.974355	+	0.225018i	$0.927756\pi$
$80$	2.00000	+	1.00000i	0.223607	+	0.111803i
$81$		0			0
$82$	2.00000			0.220863
$83$			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
$85$	7.00000	+	6.00000i	0.759257	+	0.650791i
$86$	12.0000			1.29399
$87$		0			0
$88$		0			0
$89$	16.0000			1.69600			0.847998	−	0.529999i	$-0.177808\pi$
$89$	16.0000			1.69600			0.847998	+	0.529999i	$0.177808\pi$
$90$		0			0
$91$		−	16.0000i		−	1.67726i
$92$	4.00000			0.417029
$93$		0			0
$94$	−8.00000			−0.825137
$95$	8.00000	+	4.00000i	0.820783	+	0.410391i
$96$		0			0
$97$	−10.0000			−1.01535			−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000			−1.01535			−0.507673	+	0.861550i	$0.669494\pi$
$98$			9.00000i			0.909137i
$99$		0			0
$100$	−3.00000	−	4.00000i	−0.300000	−	0.400000i
$101$	−4.00000			−0.398015			−0.199007	−	0.979998i	$-0.563772\pi$
$101$	−4.00000			−0.398015			−0.199007	+	0.979998i	$0.563772\pi$
$102$		0			0
$103$			8.00000i			0.788263i	0.919054	+	0.394132i	$0.128955\pi$
$103$			8.00000i			0.788263i	−0.919054	+	0.394132i	$0.871045\pi$
$104$	−4.00000			−0.392232
$105$		0			0
$106$	−10.0000			−0.971286
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$		0			0
$109$			12.0000i			1.14939i	0.818367	+	0.574696i	$0.194880\pi$
$109$			12.0000i			1.14939i	−0.818367	+	0.574696i	$0.805120\pi$
$110$		0			0
$111$		0			0
$112$	4.00000			0.377964
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$	−8.00000	−	4.00000i	−0.746004	−	0.373002i
$116$			6.00000i			0.557086i
$117$		0			0
$118$		−	4.00000i		−	0.368230i
$119$	16.0000	+	4.00000i	1.46672	+	0.366679i
$120$		0			0
$121$	11.0000			1.00000
$122$	4.00000			0.362143
$123$		0			0
$124$			4.00000i			0.359211i
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$		0			0
$127$			16.0000i			1.41977i	0.704317	+	0.709885i	$0.251253\pi$
$127$			16.0000i			1.41977i	−0.704317	+	0.709885i	$0.748747\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	8.00000	+	4.00000i	0.701646	+	0.350823i
$131$			8.00000i			0.698963i	0.936943	+	0.349482i	$0.113642\pi$
$131$			8.00000i			0.698963i	−0.936943	+	0.349482i	$0.886358\pi$
$132$		0			0
$133$	16.0000			1.38738
$134$	4.00000			0.345547
$135$		0			0
$136$	1.00000	−	4.00000i	0.0857493	−	0.342997i
$137$			10.0000i			0.854358i	0.904167	+	0.427179i	$0.140493\pi$
$137$			10.0000i			0.854358i	−0.904167	+	0.427179i	$0.859507\pi$
$138$		0			0
$139$			16.0000i			1.35710i	0.734553	+	0.678551i	$0.237392\pi$
$139$			16.0000i			1.35710i	−0.734553	+	0.678551i	$0.762608\pi$
$140$	−8.00000	−	4.00000i	−0.676123	−	0.338062i
$141$		0			0
$142$	−4.00000			−0.335673
$143$		0			0
$144$		0			0
$145$	6.00000	−	12.0000i	0.498273	−	0.996546i
$146$		−	14.0000i		−	1.15865i
$147$		0			0
$148$	2.00000			0.164399
$149$	4.00000			0.327693			0.163846	−	0.986486i	$-0.447610\pi$
$149$	4.00000			0.327693			0.163846	+	0.986486i	$0.447610\pi$
$150$		0			0
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$		−	4.00000i		−	0.324443i
$153$		0			0
$154$		0			0
$155$	4.00000	−	8.00000i	0.321288	−	0.642575i
$156$		0			0
$157$		−	12.0000i		−	0.957704i	−0.877896	−	0.478852i	$-0.841053\pi$
$157$		−	12.0000i		−	0.957704i	0.877896	−	0.478852i	$-0.158947\pi$
$158$	−4.00000			−0.318223
$159$		0			0
$160$	−1.00000	+	2.00000i	−0.0790569	+	0.158114i
$161$	−16.0000			−1.26098
$162$		0			0
$163$	16.0000			1.25322			0.626608	−	0.779334i	$-0.284443\pi$
$163$	16.0000			1.25322			0.626608	+	0.779334i	$0.284443\pi$
$164$			2.00000i			0.156174i
$165$		0			0
$166$	−12.0000			−0.931381
$167$	−12.0000			−0.928588			−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000			−0.928588			−0.464294	+	0.885681i	$0.653692\pi$
$168$		0			0
$169$	−3.00000			−0.230769
$170$	−6.00000	+	7.00000i	−0.460179	+	0.536875i
$171$		0			0
$172$			12.0000i			0.914991i
$173$	−20.0000			−1.52057			−0.760286	−	0.649589i	$-0.774941\pi$
$173$	−20.0000			−1.52057			−0.760286	+	0.649589i	$0.774941\pi$
$174$		0			0
$175$	12.0000	+	16.0000i	0.907115	+	1.20949i
$176$		0			0
$177$		0			0
$178$			16.0000i			1.19925i
$179$	−20.0000			−1.49487			−0.747435	−	0.664335i	$-0.768715\pi$
$179$	−20.0000			−1.49487			−0.747435	+	0.664335i	$0.768715\pi$
$180$		0			0
$181$		−	20.0000i		−	1.48659i	−0.668965	−	0.743294i	$-0.733262\pi$
$181$		−	20.0000i		−	1.48659i	0.668965	−	0.743294i	$-0.266738\pi$
$182$	16.0000			1.18600
$183$		0			0
$184$			4.00000i			0.294884i
$185$	−4.00000	−	2.00000i	−0.294086	−	0.147043i
$186$		0			0
$187$		0			0
$188$		−	8.00000i		−	0.583460i
$189$		0			0
$190$	−4.00000	+	8.00000i	−0.290191	+	0.580381i
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$		0			0
$193$	−10.0000			−0.719816			−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000			−0.719816			−0.359908	+	0.932988i	$0.617192\pi$
$194$		−	10.0000i		−	0.717958i
$195$		0			0
$196$	−9.00000			−0.642857
$197$	4.00000			0.284988			0.142494	−	0.989796i	$-0.454488\pi$
$197$	4.00000			0.284988			0.142494	+	0.989796i	$0.454488\pi$
$198$		0			0
$199$		−	20.0000i		−	1.41776i	−0.705328	−	0.708881i	$-0.749200\pi$
$199$		−	20.0000i		−	1.41776i	0.705328	−	0.708881i	$-0.250800\pi$
$200$	4.00000	−	3.00000i	0.282843	−	0.212132i
$201$		0			0
$202$		−	4.00000i		−	0.281439i
$203$		−	24.0000i		−	1.68447i
$204$		0			0
$205$	2.00000	−	4.00000i	0.139686	−	0.279372i
$206$	−8.00000			−0.557386
$207$		0			0
$208$		−	4.00000i		−	0.277350i
$209$		0			0
$210$		0			0
$211$		−	8.00000i		−	0.550743i	−0.961338	−	0.275371i	$-0.911199\pi$
$211$		−	8.00000i		−	0.550743i	0.961338	−	0.275371i	$-0.0888008\pi$
$212$		−	10.0000i		−	0.686803i
$213$		0			0
$214$		0			0
$215$	12.0000	−	24.0000i	0.818393	−	1.63679i
$216$		0			0
$217$		−	16.0000i		−	1.08615i
$218$	−12.0000			−0.812743
$219$		0			0
$220$		0			0
$221$	4.00000	−	16.0000i	0.269069	−	1.07628i
$222$		0			0
$223$			24.0000i			1.60716i	0.595198	+	0.803579i	$0.297074\pi$
$223$			24.0000i			1.60716i	−0.595198	+	0.803579i	$0.702926\pi$
$224$			4.00000i			0.267261i
$225$		0			0
$226$		0			0
$227$	−24.0000			−1.59294			−0.796468	−	0.604681i	$-0.793301\pi$
$227$	−24.0000			−1.59294			−0.796468	+	0.604681i	$0.793301\pi$
$228$		0			0
$229$	6.00000			0.396491			0.198246	−	0.980152i	$-0.436476\pi$
$229$	6.00000			0.396491			0.198246	+	0.980152i	$0.436476\pi$
$230$	4.00000	−	8.00000i	0.263752	−	0.527504i
$231$		0			0
$232$	−6.00000			−0.393919
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$		0			0
$235$	−8.00000	+	16.0000i	−0.521862	+	1.04372i
$236$	4.00000			0.260378
$237$		0			0
$238$	−4.00000	+	16.0000i	−0.259281	+	1.03713i
$239$	−24.0000			−1.55243			−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000			−1.55243			−0.776215	+	0.630468i	$0.782863\pi$
$240$		0			0
$241$		−	8.00000i		−	0.515325i	−0.966235	−	0.257663i	$-0.917048\pi$
$241$		−	8.00000i		−	0.515325i	0.966235	−	0.257663i	$-0.0829523\pi$
$242$			11.0000i			0.707107i
$243$		0			0
$244$			4.00000i			0.256074i
$245$	18.0000	+	9.00000i	1.14998	+	0.574989i
$246$		0			0
$247$		−	16.0000i		−	1.01806i
$248$	−4.00000			−0.254000
$249$		0			0
$250$	−11.0000	+	2.00000i	−0.695701	+	0.126491i
$251$	20.0000			1.26239			0.631194	−	0.775625i	$-0.282565\pi$
$251$	20.0000			1.26239			0.631194	+	0.775625i	$0.282565\pi$
$252$		0			0
$253$		0			0
$254$	−16.0000			−1.00393
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	30.0000i		−	1.87135i	−0.352865	−	0.935674i	$-0.614792\pi$
$257$		−	30.0000i		−	1.87135i	0.352865	−	0.935674i	$-0.385208\pi$
$258$		0			0
$259$	−8.00000			−0.497096
$260$	−4.00000	+	8.00000i	−0.248069	+	0.496139i
$261$		0			0
$262$	−8.00000			−0.494242
$263$		0			0		1.00000			$0$
$263$		0			0		−1.00000			$\pi$
$264$		0			0
$265$	−10.0000	+	20.0000i	−0.614295	+	1.22859i
$266$			16.0000i			0.981023i
$267$		0			0
$268$			4.00000i			0.244339i
$269$		−	10.0000i		−	0.609711i	−0.952399	−	0.304855i	$-0.901392\pi$
$269$		−	10.0000i		−	0.609711i	0.952399	−	0.304855i	$-0.0986081\pi$
$270$		0			0
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$	4.00000	+	1.00000i	0.242536	+	0.0606339i
$273$		0			0
$274$	−10.0000			−0.604122
$275$		0			0
$276$		0			0
$277$	30.0000			1.80253			0.901263	−	0.433273i	$-0.142641\pi$
$277$	30.0000			1.80253			0.901263	+	0.433273i	$0.142641\pi$
$278$	−16.0000			−0.959616
$279$		0			0
$280$	4.00000	−	8.00000i	0.239046	−	0.478091i
$281$	−16.0000			−0.954480			−0.477240	−	0.878773i	$-0.658363\pi$
$281$	−16.0000			−0.954480			−0.477240	+	0.878773i	$0.658363\pi$
$282$		0			0
$283$	−24.0000			−1.42665			−0.713326	−	0.700832i	$-0.752812\pi$
$283$	−24.0000			−1.42665			−0.713326	+	0.700832i	$0.752812\pi$
$284$		−	4.00000i		−	0.237356i
$285$		0			0
$286$		0			0
$287$		−	8.00000i		−	0.472225i
$288$		0			0
$289$	15.0000	+	8.00000i	0.882353	+	0.470588i
$290$	12.0000	+	6.00000i	0.704664	+	0.352332i
$291$		0			0
$292$	14.0000			0.819288
$293$		−	26.0000i		−	1.51894i	−0.650545	−	0.759468i	$-0.725459\pi$
$293$		−	26.0000i		−	1.51894i	0.650545	−	0.759468i	$-0.274541\pi$
$294$		0			0
$295$	−8.00000	−	4.00000i	−0.465778	−	0.232889i
$296$			2.00000i			0.116248i
$297$		0			0
$298$			4.00000i			0.231714i
$299$			16.0000i			0.925304i
$300$		0			0
$301$		−	48.0000i		−	2.76667i
$302$		−	8.00000i		−	0.460348i
$303$		0			0
$304$	4.00000			0.229416
$305$	4.00000	−	8.00000i	0.229039	−	0.458079i
$306$		0			0
$307$			20.0000i			1.14146i	0.821138	+	0.570730i	$0.193340\pi$
$307$			20.0000i			1.14146i	−0.821138	+	0.570730i	$0.806660\pi$
$308$		0			0
$309$		0			0
$310$	8.00000	+	4.00000i	0.454369	+	0.227185i
$311$			4.00000i			0.226819i	0.993548	+	0.113410i	$0.0361772\pi$
$311$			4.00000i			0.226819i	−0.993548	+	0.113410i	$0.963823\pi$
$312$		0			0
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$	12.0000			0.677199
$315$		0			0
$316$		−	4.00000i		−	0.225018i
$317$	12.0000			0.673987			0.336994	−	0.941507i	$-0.390590\pi$
$317$	12.0000			0.673987			0.336994	+	0.941507i	$0.390590\pi$
$318$		0			0
$319$		0			0
$320$	−2.00000	−	1.00000i	−0.111803	−	0.0559017i
$321$		0			0
$322$		−	16.0000i		−	0.891645i
$323$	16.0000	+	4.00000i	0.890264	+	0.222566i
$324$		0			0
$325$	16.0000	−	12.0000i	0.887520	−	0.665640i
$326$			16.0000i			0.886158i
$327$		0			0
$328$	−2.00000			−0.110432
$329$			32.0000i			1.76422i
$330$		0			0
$331$	4.00000			0.219860			0.109930	−	0.993939i	$-0.464937\pi$
$331$	4.00000			0.219860			0.109930	+	0.993939i	$0.464937\pi$
$332$		−	12.0000i		−	0.658586i
$333$		0			0
$334$		−	12.0000i		−	0.656611i
$335$	4.00000	−	8.00000i	0.218543	−	0.437087i
$336$		0			0
$337$	−10.0000			−0.544735			−0.272367	−	0.962193i	$-0.587807\pi$
$337$	−10.0000			−0.544735			−0.272367	+	0.962193i	$0.587807\pi$
$338$		−	3.00000i		−	0.163178i
$339$		0			0
$340$	−7.00000	−	6.00000i	−0.379628	−	0.325396i
$341$		0			0
$342$		0			0
$343$	8.00000			0.431959
$344$	−12.0000			−0.646997
$345$		0			0
$346$		−	20.0000i		−	1.07521i
$347$	−8.00000			−0.429463			−0.214731	−	0.976673i	$-0.568888\pi$
$347$	−8.00000			−0.429463			−0.214731	+	0.976673i	$0.568888\pi$
$348$		0			0
$349$	−2.00000			−0.107058			−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000			−0.107058			−0.0535288	+	0.998566i	$0.517047\pi$
$350$	−16.0000	+	12.0000i	−0.855236	+	0.641427i
$351$		0			0
$352$		0			0
$353$			14.0000i			0.745145i	0.928003	+	0.372572i	$0.121524\pi$
$353$			14.0000i			0.745145i	−0.928003	+	0.372572i	$0.878476\pi$
$354$		0			0
$355$	−4.00000	+	8.00000i	−0.212298	+	0.424596i
$356$	−16.0000			−0.847998
$357$		0			0
$358$		−	20.0000i		−	1.05703i
$359$	−24.0000			−1.26667			−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000			−1.26667			−0.633336	+	0.773877i	$0.718315\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$	20.0000			1.05118
$363$		0			0
$364$			16.0000i			0.838628i
$365$	−28.0000	−	14.0000i	−1.46559	−	0.732793i
$366$		0			0
$367$	−20.0000			−1.04399			−0.521996	−	0.852948i	$-0.674812\pi$
$367$	−20.0000			−1.04399			−0.521996	+	0.852948i	$0.674812\pi$
$368$	−4.00000			−0.208514
$369$		0			0
$370$	2.00000	−	4.00000i	0.103975	−	0.207950i
$371$			40.0000i			2.07670i
$372$		0			0
$373$			4.00000i			0.207112i	0.994624	+	0.103556i	$0.0330221\pi$
$373$			4.00000i			0.207112i	−0.994624	+	0.103556i	$0.966978\pi$
$374$		0			0
$375$		0			0
$376$	8.00000			0.412568
$377$	−24.0000			−1.23606
$378$		0			0
$379$			8.00000i			0.410932i	0.978664	+	0.205466i	$0.0658711\pi$
$379$			8.00000i			0.410932i	−0.978664	+	0.205466i	$0.934129\pi$
$380$	−8.00000	−	4.00000i	−0.410391	−	0.205196i
$381$		0			0
$382$		0			0
$383$		−	8.00000i		−	0.408781i	−0.978889	−	0.204390i	$-0.934479\pi$
$383$		−	8.00000i		−	0.408781i	0.978889	−	0.204390i	$-0.0655212\pi$
$384$		0			0
$385$		0			0
$386$		−	10.0000i		−	0.508987i
$387$		0			0
$388$	10.0000			0.507673
$389$	28.0000			1.41966			0.709828	−	0.704375i	$-0.248773\pi$
$389$	28.0000			1.41966			0.709828	+	0.704375i	$0.248773\pi$
$390$		0			0
$391$	−16.0000	−	4.00000i	−0.809155	−	0.202289i
$392$		−	9.00000i		−	0.454569i
$393$		0			0
$394$			4.00000i			0.201517i
$395$	−4.00000	+	8.00000i	−0.201262	+	0.402524i
$396$		0			0
$397$	−6.00000			−0.301131			−0.150566	−	0.988600i	$-0.548110\pi$
$397$	−6.00000			−0.301131			−0.150566	+	0.988600i	$0.548110\pi$
$398$	20.0000			1.00251
$399$		0			0
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$		−	38.0000i		−	1.89763i	−0.315833	−	0.948815i	$-0.602284\pi$
$401$		−	38.0000i		−	1.89763i	0.315833	−	0.948815i	$-0.397716\pi$
$402$		0			0
$403$	−16.0000			−0.797017
$404$	4.00000			0.199007
$405$		0			0
$406$	24.0000			1.19110
$407$		0			0
$408$		0			0
$409$	26.0000			1.28562			0.642809	−	0.766027i	$-0.277769\pi$
$409$	26.0000			1.28562			0.642809	+	0.766027i	$0.277769\pi$
$410$	4.00000	+	2.00000i	0.197546	+	0.0987730i
$411$		0			0
$412$		−	8.00000i		−	0.394132i
$413$	−16.0000			−0.787309
$414$		0			0
$415$	−12.0000	+	24.0000i	−0.589057	+	1.17811i
$416$	4.00000			0.196116
$417$		0			0
$418$		0			0
$419$		−	24.0000i		−	1.17248i	−0.810139	−	0.586238i	$-0.800608\pi$
$419$		−	24.0000i		−	1.17248i	0.810139	−	0.586238i	$-0.199392\pi$
$420$		0			0
$421$	26.0000			1.26716			0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000			1.26716			0.633581	+	0.773676i	$0.281584\pi$
$422$	8.00000			0.389434
$423$		0			0
$424$	10.0000			0.485643
$425$	8.00000	+	19.0000i	0.388057	+	0.921635i
$426$		0			0
$427$		−	16.0000i		−	0.774294i
$428$		0			0
$429$		0			0
$430$	24.0000	+	12.0000i	1.15738	+	0.578691i
$431$		−	36.0000i		−	1.73406i	−0.498257	−	0.867029i	$-0.666026\pi$
$431$		−	36.0000i		−	1.73406i	0.498257	−	0.867029i	$-0.333974\pi$
$432$		0			0
$433$		−	24.0000i		−	1.15337i	−0.816968	−	0.576683i	$-0.804347\pi$
$433$		−	24.0000i		−	1.15337i	0.816968	−	0.576683i	$-0.195653\pi$
$434$	16.0000			0.768025
$435$		0			0
$436$		−	12.0000i		−	0.574696i
$437$	−16.0000			−0.765384
$438$		0			0
$439$			36.0000i			1.71819i	0.511819	+	0.859093i	$0.328972\pi$
$439$			36.0000i			1.71819i	−0.511819	+	0.859093i	$0.671028\pi$
$440$		0			0
$441$		0			0
$442$	16.0000	+	4.00000i	0.761042	+	0.190261i
$443$		−	4.00000i		−	0.190046i	−0.995475	−	0.0950229i	$-0.969708\pi$
$443$		−	4.00000i		−	0.190046i	0.995475	−	0.0950229i	$-0.0302924\pi$
$444$		0			0
$445$	32.0000	+	16.0000i	1.51695	+	0.758473i
$446$	−24.0000			−1.13643
$447$		0			0
$448$	−4.00000			−0.188982
$449$		−	10.0000i		−	0.471929i	−0.971762	−	0.235965i	$-0.924175\pi$
$449$		−	10.0000i		−	0.471929i	0.971762	−	0.235965i	$-0.0758249\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$		−	24.0000i		−	1.12638i
$455$	16.0000	−	32.0000i	0.750092	−	1.50018i
$456$		0			0
$457$			24.0000i			1.12267i	0.827588	+	0.561336i	$0.189713\pi$
$457$			24.0000i			1.12267i	−0.827588	+	0.561336i	$0.810287\pi$
$458$			6.00000i			0.280362i
$459$		0			0
$460$	8.00000	+	4.00000i	0.373002	+	0.186501i
$461$	28.0000			1.30409			0.652045	−	0.758180i	$-0.273911\pi$
$461$	28.0000			1.30409			0.652045	+	0.758180i	$0.273911\pi$
$462$		0			0
$463$			8.00000i			0.371792i	0.982569	+	0.185896i	$0.0595187\pi$
$463$			8.00000i			0.371792i	−0.982569	+	0.185896i	$0.940481\pi$
$464$		−	6.00000i		−	0.278543i
$465$		0			0
$466$		0			0
$467$		−	12.0000i		−	0.555294i	−0.960683	−	0.277647i	$-0.910445\pi$
$467$		−	12.0000i		−	0.555294i	0.960683	−	0.277647i	$-0.0895545\pi$
$468$		0			0
$469$		−	16.0000i		−	0.738811i
$470$	−16.0000	−	8.00000i	−0.738025	−	0.369012i
$471$		0			0
$472$			4.00000i			0.184115i
$473$		0			0
$474$		0			0
$475$	12.0000	+	16.0000i	0.550598	+	0.734130i
$476$	−16.0000	−	4.00000i	−0.733359	−	0.183340i
$477$		0			0
$478$		−	24.0000i		−	1.09773i
$479$		−	12.0000i		−	0.548294i	−0.961688	−	0.274147i	$-0.911605\pi$
$479$		−	12.0000i		−	0.548294i	0.961688	−	0.274147i	$-0.0883955\pi$
$480$		0			0
$481$			8.00000i			0.364769i
$482$	8.00000			0.364390
$483$		0			0
$484$	−11.0000			−0.500000
$485$	−20.0000	−	10.0000i	−0.908153	−	0.454077i
$486$		0			0
$487$	28.0000			1.26880			0.634401	−	0.773004i	$-0.281247\pi$
$487$	28.0000			1.26880			0.634401	+	0.773004i	$0.281247\pi$
$488$	−4.00000			−0.181071
$489$		0			0
$490$	−9.00000	+	18.0000i	−0.406579	+	0.813157i
$491$	−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
$493$	6.00000	−	24.0000i	0.270226	−	1.08091i
$494$	16.0000			0.719874
$495$		0			0
$496$		−	4.00000i		−	0.179605i
$497$			16.0000i			0.717698i
$498$		0			0
$499$		−	24.0000i		−	1.07439i	−0.843459	−	0.537194i	$-0.819484\pi$
$499$		−	24.0000i		−	1.07439i	0.843459	−	0.537194i	$-0.180516\pi$
$500$	−2.00000	−	11.0000i	−0.0894427	−	0.491935i
$501$		0			0
$502$			20.0000i			0.892644i
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		0			0
$505$	−8.00000	−	4.00000i	−0.355995	−	0.177998i
$506$		0			0
$507$		0			0
$508$		−	16.0000i		−	0.709885i
$509$	−28.0000			−1.24108			−0.620539	−	0.784176i	$-0.713086\pi$
$509$	−28.0000			−1.24108			−0.620539	+	0.784176i	$0.713086\pi$
$510$		0			0
$511$	−56.0000			−2.47729
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	30.0000			1.32324
$515$	−8.00000	+	16.0000i	−0.352522	+	0.705044i
$516$		0			0
$517$		0			0
$518$		−	8.00000i		−	0.351500i
$519$		0			0
$520$	−8.00000	−	4.00000i	−0.350823	−	0.175412i
$521$			34.0000i			1.48957i	0.667306	+	0.744784i	$0.267447\pi$
$521$			34.0000i			1.48957i	−0.667306	+	0.744784i	$0.732553\pi$
$522$		0			0
$523$		−	20.0000i		−	0.874539i	−0.899331	−	0.437269i	$-0.855946\pi$
$523$		−	20.0000i		−	0.874539i	0.899331	−	0.437269i	$-0.144054\pi$
$524$		−	8.00000i		−	0.349482i
$525$		0			0
$526$		0			0
$527$	4.00000	−	16.0000i	0.174243	−	0.696971i
$528$		0			0
$529$	−7.00000			−0.304348
$530$	−20.0000	−	10.0000i	−0.868744	−	0.434372i
$531$		0			0
$532$	−16.0000			−0.693688
$533$	−8.00000			−0.346518
$534$		0			0
$535$		0			0
$536$	−4.00000			−0.172774
$537$		0			0
$538$	10.0000			0.431131
$539$		0			0
$540$		0			0
$541$			20.0000i			0.859867i	0.902861	+	0.429934i	$0.141463\pi$
$541$			20.0000i			0.859867i	−0.902861	+	0.429934i	$0.858537\pi$
$542$		−	8.00000i		−	0.343629i
$543$		0			0
$544$	−1.00000	+	4.00000i	−0.0428746	+	0.171499i
$545$	−12.0000	+	24.0000i	−0.514024	+	1.02805i
$546$		0			0
$547$	−8.00000			−0.342055			−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000			−0.342055			−0.171028	+	0.985266i	$0.554709\pi$
$548$		−	10.0000i		−	0.427179i
$549$		0			0
$550$		0			0
$551$		−	24.0000i		−	1.02243i
$552$		0			0
$553$			16.0000i			0.680389i
$554$			30.0000i			1.27458i
$555$		0			0
$556$		−	16.0000i		−	0.678551i
$557$			18.0000i			0.762684i	0.924434	+	0.381342i	$0.124538\pi$
$557$			18.0000i			0.762684i	−0.924434	+	0.381342i	$0.875462\pi$
$558$		0			0
$559$	−48.0000			−2.03018
$560$	8.00000	+	4.00000i	0.338062	+	0.169031i
$561$		0			0
$562$		−	16.0000i		−	0.674919i
$563$			12.0000i			0.505740i	0.967500	+	0.252870i	$0.0813744\pi$
$563$			12.0000i			0.505740i	−0.967500	+	0.252870i	$0.918626\pi$
$564$		0			0
$565$		0			0
$566$		−	24.0000i		−	1.00880i
$567$		0			0
$568$	4.00000			0.167836
$569$	24.0000			1.00613			0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000			1.00613			0.503066	+	0.864248i	$0.332205\pi$
$570$		0			0
$571$		−	8.00000i		−	0.334790i	−0.985890	−	0.167395i	$-0.946465\pi$
$571$		−	8.00000i		−	0.334790i	0.985890	−	0.167395i	$-0.0535355\pi$
$572$		0			0
$573$		0			0
$574$	8.00000			0.333914
$575$	−12.0000	−	16.0000i	−0.500435	−	0.667246i
$576$		0			0
$577$			32.0000i			1.33218i	0.745873	+	0.666089i	$0.232033\pi$
$577$			32.0000i			1.33218i	−0.745873	+	0.666089i	$0.767967\pi$
$578$	−8.00000	+	15.0000i	−0.332756	+	0.623918i
$579$		0			0
$580$	−6.00000	+	12.0000i	−0.249136	+	0.498273i
$581$			48.0000i			1.99138i
$582$		0			0
$583$		0			0
$584$			14.0000i			0.579324i
$585$		0			0
$586$	26.0000			1.07405
$587$			36.0000i			1.48588i	0.669359	+	0.742940i	$0.266569\pi$
$587$			36.0000i			1.48588i	−0.669359	+	0.742940i	$0.733431\pi$
$588$		0			0
$589$		−	16.0000i		−	0.659269i
$590$	4.00000	−	8.00000i	0.164677	−	0.329355i
$591$		0			0
$592$	−2.00000			−0.0821995
$593$		−	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
$595$	28.0000	+	24.0000i	1.14789	+	0.983904i
$596$	−4.00000			−0.163846
$597$		0			0
$598$	−16.0000			−0.654289
$599$	−8.00000			−0.326871			−0.163436	−	0.986554i	$-0.552258\pi$
$599$	−8.00000			−0.326871			−0.163436	+	0.986554i	$0.552258\pi$
$600$		0			0
$601$		−	48.0000i		−	1.95796i	−0.203954	−	0.978980i	$-0.565379\pi$
$601$		−	48.0000i		−	1.95796i	0.203954	−	0.978980i	$-0.434621\pi$
$602$	48.0000			1.95633
$603$		0			0
$604$	8.00000			0.325515
$605$	22.0000	+	11.0000i	0.894427	+	0.447214i
$606$		0			0
$607$	−28.0000			−1.13648			−0.568242	−	0.822861i	$-0.692376\pi$
$607$	−28.0000			−1.13648			−0.568242	+	0.822861i	$0.692376\pi$
$608$			4.00000i			0.162221i
$609$		0			0
$610$	8.00000	+	4.00000i	0.323911	+	0.161955i
$611$	32.0000			1.29458
$612$		0			0
$613$			4.00000i			0.161558i	0.996732	+	0.0807792i	$0.0257409\pi$
$613$			4.00000i			0.161558i	−0.996732	+	0.0807792i	$0.974259\pi$
$614$	−20.0000			−0.807134
$615$		0			0
$616$		0			0
$617$	−48.0000			−1.93241			−0.966204	−	0.257780i	$-0.917009\pi$
$617$	−48.0000			−1.93241			−0.966204	+	0.257780i	$0.917009\pi$
$618$		0			0
$619$			32.0000i			1.28619i	0.765787	+	0.643094i	$0.222350\pi$
$619$			32.0000i			1.28619i	−0.765787	+	0.643094i	$0.777650\pi$
$620$	−4.00000	+	8.00000i	−0.160644	+	0.321288i
$621$		0			0
$622$	−4.00000			−0.160385
$623$	64.0000			2.56411
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$			14.0000i			0.559553i
$627$		0			0
$628$			12.0000i			0.478852i
$629$	−8.00000	−	2.00000i	−0.318981	−	0.0797452i
$630$		0			0
$631$	−40.0000			−1.59237			−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000			−1.59237			−0.796187	+	0.605050i	$0.793153\pi$
$632$	4.00000			0.159111
$633$		0			0
$634$			12.0000i			0.476581i
$635$	−16.0000	+	32.0000i	−0.634941	+	1.26988i
$636$		0			0
$637$		−	36.0000i		−	1.42637i
$638$		0			0
$639$		0			0
$640$	1.00000	−	2.00000i	0.0395285	−	0.0790569i
$641$			22.0000i			0.868948i	0.900684	+	0.434474i	$0.143066\pi$
$641$			22.0000i			0.868948i	−0.900684	+	0.434474i	$0.856934\pi$
$642$		0			0
$643$	24.0000			0.946468			0.473234	−	0.880937i	$-0.343087\pi$
$643$	24.0000			0.946468			0.473234	+	0.880937i	$0.343087\pi$
$644$	16.0000			0.630488
$645$		0			0
$646$	−4.00000	+	16.0000i	−0.157378	+	0.629512i
$647$			8.00000i			0.314512i	0.987558	+	0.157256i	$0.0502649\pi$
$647$			8.00000i			0.314512i	−0.987558	+	0.157256i	$0.949735\pi$
$648$		0			0
$649$		0			0
$650$	12.0000	+	16.0000i	0.470679	+	0.627572i
$651$		0			0
$652$	−16.0000			−0.626608
$653$	12.0000			0.469596			0.234798	−	0.972044i	$-0.424557\pi$
$653$	12.0000			0.469596			0.234798	+	0.972044i	$0.424557\pi$
$654$		0			0
$655$	−8.00000	+	16.0000i	−0.312586	+	0.625172i
$656$		−	2.00000i		−	0.0780869i
$657$		0			0
$658$	−32.0000			−1.24749
$659$	−4.00000			−0.155818			−0.0779089	−	0.996960i	$-0.524824\pi$
$659$	−4.00000			−0.155818			−0.0779089	+	0.996960i	$0.524824\pi$
$660$		0			0
$661$	10.0000			0.388955			0.194477	−	0.980907i	$-0.437699\pi$
$661$	10.0000			0.388955			0.194477	+	0.980907i	$0.437699\pi$
$662$			4.00000i			0.155464i
$663$		0			0
$664$	12.0000			0.465690
$665$	32.0000	+	16.0000i	1.24091	+	0.620453i
$666$		0			0
$667$			24.0000i			0.929284i
$668$	12.0000			0.464294
$669$		0			0
$670$	8.00000	+	4.00000i	0.309067	+	0.154533i
$671$		0			0
$672$		0			0
$673$	−10.0000			−0.385472			−0.192736	−	0.981251i	$-0.561736\pi$
$673$	−10.0000			−0.385472			−0.192736	+	0.981251i	$0.561736\pi$
$674$		−	10.0000i		−	0.385186i
$675$		0			0
$676$	3.00000			0.115385
$677$	−28.0000			−1.07613			−0.538064	−	0.842904i	$-0.680844\pi$
$677$	−28.0000			−1.07613			−0.538064	+	0.842904i	$0.680844\pi$
$678$		0			0
$679$	−40.0000			−1.53506
$680$	6.00000	−	7.00000i	0.230089	−	0.268438i
$681$		0			0
$682$		0			0
$683$		0			0			−	1.00000i	$-0.5\pi$
$683$		0			0				1.00000i	$0.5\pi$
$684$		0			0
$685$	−10.0000	+	20.0000i	−0.382080	+	0.764161i
$686$			8.00000i			0.305441i
$687$		0			0
$688$		−	12.0000i		−	0.457496i
$689$	40.0000			1.52388
$690$		0			0
$691$		−	24.0000i		−	0.913003i	−0.889723	−	0.456502i	$-0.849102\pi$
$691$		−	24.0000i		−	0.913003i	0.889723	−	0.456502i	$-0.150898\pi$
$692$	20.0000			0.760286
$693$		0			0
$694$		−	8.00000i		−	0.303676i
$695$	−16.0000	+	32.0000i	−0.606915	+	1.21383i
$696$		0			0
$697$	2.00000	−	8.00000i	0.0757554	−	0.303022i
$698$		−	2.00000i		−	0.0757011i
$699$		0			0
$700$	−12.0000	−	16.0000i	−0.453557	−	0.604743i
$701$	36.0000			1.35970			0.679851	−	0.733351i	$-0.262045\pi$
$701$	36.0000			1.35970			0.679851	+	0.733351i	$0.262045\pi$
$702$		0			0
$703$	−8.00000			−0.301726
$704$		0			0
$705$		0			0
$706$	−14.0000			−0.526897
$707$	−16.0000			−0.601742
$708$		0			0
$709$		−	20.0000i		−	0.751116i	−0.926799	−	0.375558i	$-0.877451\pi$
$709$		−	20.0000i		−	0.751116i	0.926799	−	0.375558i	$-0.122549\pi$
$710$	−8.00000	−	4.00000i	−0.300235	−	0.150117i
$711$		0			0
$712$		−	16.0000i		−	0.599625i
$713$			16.0000i			0.599205i
$714$		0			0
$715$		0			0
$716$	20.0000			0.747435
$717$		0			0
$718$		−	24.0000i		−	0.895672i
$719$			36.0000i			1.34257i	0.741198	+	0.671287i	$0.234258\pi$
$719$			36.0000i			1.34257i	−0.741198	+	0.671287i	$0.765742\pi$
$720$		0			0
$721$			32.0000i			1.19174i
$722$		−	3.00000i		−	0.111648i
$723$		0			0
$724$			20.0000i			0.743294i
$725$	24.0000	−	18.0000i	0.891338	−	0.668503i
$726$		0			0
$727$			48.0000i			1.78022i	0.455744	+	0.890111i	$0.349373\pi$
$727$			48.0000i			1.78022i	−0.455744	+	0.890111i	$0.650627\pi$
$728$	−16.0000			−0.592999
$729$		0			0
$730$	14.0000	−	28.0000i	0.518163	−	1.03633i
$731$	12.0000	−	48.0000i	0.443836	−	1.77534i
$732$		0			0
$733$		−	36.0000i		−	1.32969i	−0.746981	−	0.664845i	$-0.768498\pi$
$733$		−	36.0000i		−	1.32969i	0.746981	−	0.664845i	$-0.231502\pi$
$734$		−	20.0000i		−	0.738213i
$735$		0			0
$736$		−	4.00000i		−	0.147442i
$737$		0			0
$738$		0			0
$739$	−36.0000			−1.32428			−0.662141	−	0.749380i	$-0.730352\pi$
$739$	−36.0000			−1.32428			−0.662141	+	0.749380i	$0.730352\pi$
$740$	4.00000	+	2.00000i	0.147043	+	0.0735215i
$741$		0			0
$742$	−40.0000			−1.46845
$743$	44.0000			1.61420			0.807102	−	0.590412i	$-0.201035\pi$
$743$	44.0000			1.61420			0.807102	+	0.590412i	$0.201035\pi$
$744$		0			0
$745$	8.00000	+	4.00000i	0.293097	+	0.146549i
$746$	−4.00000			−0.146450
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		−	4.00000i		−	0.145962i	−0.997333	−	0.0729810i	$-0.976749\pi$
$751$		−	4.00000i		−	0.145962i	0.997333	−	0.0729810i	$-0.0232513\pi$
$752$			8.00000i			0.291730i
$753$		0			0
$754$		−	24.0000i		−	0.874028i
$755$	−16.0000	−	8.00000i	−0.582300	−	0.291150i
$756$		0			0
$757$			44.0000i			1.59921i	0.600528	+	0.799604i	$0.294957\pi$
$757$			44.0000i			1.59921i	−0.600528	+	0.799604i	$0.705043\pi$
$758$	−8.00000			−0.290573
$759$		0			0
$760$	4.00000	−	8.00000i	0.145095	−	0.290191i
$761$	−40.0000			−1.45000			−0.724999	−	0.688749i	$-0.758160\pi$
$761$	−40.0000			−1.45000			−0.724999	+	0.688749i	$0.758160\pi$
$762$		0			0
$763$			48.0000i			1.73772i
$764$		0			0
$765$		0			0
$766$	8.00000			0.289052
$767$			16.0000i			0.577727i
$768$		0			0
$769$	14.0000			0.504853			0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000			0.504853			0.252426	+	0.967616i	$0.418771\pi$
$770$		0			0
$771$		0			0
$772$	10.0000			0.359908
$773$			38.0000i			1.36677i	0.730061	+	0.683383i	$0.239492\pi$
$773$			38.0000i			1.36677i	−0.730061	+	0.683383i	$0.760508\pi$
$774$		0			0
$775$	16.0000	−	12.0000i	0.574737	−	0.431053i
$776$			10.0000i			0.358979i
$777$		0			0
$778$			28.0000i			1.00385i
$779$		−	8.00000i		−	0.286630i
$780$		0			0
$781$		0			0
$782$	4.00000	−	16.0000i	0.143040	−	0.572159i
$783$		0			0
$784$	9.00000			0.321429
$785$	12.0000	−	24.0000i	0.428298	−	0.856597i
$786$		0			0
$787$	32.0000			1.14068			0.570338	−	0.821410i	$-0.306812\pi$
$787$	32.0000			1.14068			0.570338	+	0.821410i	$0.306812\pi$
$788$	−4.00000			−0.142494
$789$		0			0
$790$	−8.00000	−	4.00000i	−0.284627	−	0.142314i
$791$		0			0
$792$		0			0
$793$	−16.0000			−0.568177
$794$		−	6.00000i		−	0.212932i
$795$		0			0
$796$			20.0000i			0.708881i
$797$			34.0000i			1.20434i	0.798367	+	0.602171i	$0.205697\pi$
$797$			34.0000i			1.20434i	−0.798367	+	0.602171i	$0.794303\pi$
$798$		0			0
$799$	−8.00000	+	32.0000i	−0.283020	+	1.13208i
$800$	−4.00000	+	3.00000i	−0.141421	+	0.106066i
$801$		0			0
$802$	38.0000			1.34183
$803$		0			0
$804$		0			0
$805$	−32.0000	−	16.0000i	−1.12785	−	0.563926i
$806$		−	16.0000i		−	0.563576i
$807$		0			0
$808$			4.00000i			0.140720i
$809$		−	30.0000i		−	1.05474i	−0.849635	−	0.527372i	$-0.823177\pi$
$809$		−	30.0000i		−	1.05474i	0.849635	−	0.527372i	$-0.176823\pi$
$810$		0			0
$811$		−	24.0000i		−	0.842754i	−0.906886	−	0.421377i	$-0.861547\pi$
$811$		−	24.0000i		−	0.842754i	0.906886	−	0.421377i	$-0.138453\pi$
$812$			24.0000i			0.842235i
$813$		0			0
$814$		0			0
$815$	32.0000	+	16.0000i	1.12091	+	0.560456i
$816$		0			0
$817$		−	48.0000i		−	1.67931i
$818$			26.0000i			0.909069i
$819$		0			0
$820$	−2.00000	+	4.00000i	−0.0698430	+	0.139686i
$821$		−	30.0000i		−	1.04701i	−0.852023	−	0.523504i	$-0.824625\pi$
$821$		−	30.0000i		−	1.04701i	0.852023	−	0.523504i	$-0.175375\pi$
$822$		0			0
$823$	44.0000			1.53374			0.766872	−	0.641800i	$-0.221812\pi$
$823$	44.0000			1.53374			0.766872	+	0.641800i	$0.221812\pi$
$824$	8.00000			0.278693
$825$		0			0
$826$		−	16.0000i		−	0.556711i
$827$	24.0000			0.834562			0.417281	−	0.908778i	$-0.362983\pi$
$827$	24.0000			0.834562			0.417281	+	0.908778i	$0.362983\pi$
$828$		0			0
$829$	−2.00000			−0.0694629			−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000			−0.0694629			−0.0347314	+	0.999397i	$0.511058\pi$
$830$	−24.0000	−	12.0000i	−0.833052	−	0.416526i
$831$		0			0
$832$			4.00000i			0.138675i
$833$	36.0000	+	9.00000i	1.24733	+	0.311832i
$834$		0			0
$835$	−24.0000	−	12.0000i	−0.830554	−	0.415277i
$836$		0			0
$837$		0			0
$838$	24.0000			0.829066
$839$		−	12.0000i		−	0.414286i	−0.978311	−	0.207143i	$-0.933583\pi$
$839$		−	12.0000i		−	0.414286i	0.978311	−	0.207143i	$-0.0664165\pi$
$840$		0			0
$841$	−7.00000			−0.241379
$842$			26.0000i			0.896019i
$843$		0			0
$844$			8.00000i			0.275371i
$845$	−6.00000	−	3.00000i	−0.206406	−	0.103203i
$846$		0			0
$847$	44.0000			1.51186
$848$			10.0000i			0.343401i
$849$		0			0
$850$	−19.0000	+	8.00000i	−0.651695	+	0.274398i
$851$	8.00000			0.274236
$852$		0			0
$853$	−34.0000			−1.16414			−0.582069	−	0.813139i	$-0.697757\pi$
$853$	−34.0000			−1.16414			−0.582069	+	0.813139i	$0.697757\pi$
$854$	16.0000			0.547509
$855$		0			0
$856$		0			0
$857$	8.00000			0.273275			0.136637	−	0.990621i	$-0.456370\pi$
$857$	8.00000			0.273275			0.136637	+	0.990621i	$0.456370\pi$
$858$		0			0
$859$	44.0000			1.50126			0.750630	−	0.660722i	$-0.229750\pi$
$859$	44.0000			1.50126			0.750630	+	0.660722i	$0.229750\pi$
$860$	−12.0000	+	24.0000i	−0.409197	+	0.818393i
$861$		0			0
$862$	36.0000			1.22616
$863$		0			0		1.00000			$0$
$863$		0			0		−1.00000			$\pi$
$864$		0			0
$865$	−40.0000	−	20.0000i	−1.36004	−	0.680020i
$866$	24.0000			0.815553
$867$		0			0
$868$			16.0000i			0.543075i
$869$		0			0
$870$		0			0
$871$	−16.0000			−0.542139
$872$	12.0000			0.406371
$873$		0			0
$874$		−	16.0000i		−	0.541208i
$875$	8.00000	+	44.0000i	0.270449	+	1.48747i
$876$		0			0
$877$	10.0000			0.337676			0.168838	−	0.985644i	$-0.445999\pi$
$877$	10.0000			0.337676			0.168838	+	0.985644i	$0.445999\pi$
$878$	−36.0000			−1.21494
$879$		0			0
$880$		0			0
$881$			42.0000i			1.41502i	0.706705	+	0.707508i	$0.250181\pi$
$881$			42.0000i			1.41502i	−0.706705	+	0.707508i	$0.749819\pi$
$882$		0			0
$883$		−	4.00000i		−	0.134611i	−0.997732	−	0.0673054i	$-0.978560\pi$
$883$		−	4.00000i		−	0.134611i	0.997732	−	0.0673054i	$-0.0214402\pi$
$884$	−4.00000	+	16.0000i	−0.134535	+	0.538138i
$885$		0			0
$886$	4.00000			0.134383
$887$	−44.0000			−1.47738			−0.738688	−	0.674048i	$-0.764554\pi$
$887$	−44.0000			−1.47738			−0.738688	+	0.674048i	$0.764554\pi$
$888$		0			0
$889$			64.0000i			2.14649i
$890$	−16.0000	+	32.0000i	−0.536321	+	1.07264i
$891$		0			0
$892$		−	24.0000i		−	0.803579i
$893$			32.0000i			1.07084i
$894$		0			0
$895$	−40.0000	−	20.0000i	−1.33705	−	0.668526i
$896$		−	4.00000i		−	0.133631i
$897$		0			0
$898$	10.0000			0.333704
$899$	−24.0000			−0.800445
$900$		0			0
$901$	−10.0000	+	40.0000i	−0.333148	+	1.33259i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	20.0000	−	40.0000i	0.664822	−	1.32964i
$906$		0			0
$907$	−16.0000			−0.531271			−0.265636	−	0.964073i	$-0.585582\pi$
$907$	−16.0000			−0.531271			−0.265636	+	0.964073i	$0.585582\pi$
$908$	24.0000			0.796468
$909$		0			0
$910$	32.0000	+	16.0000i	1.06079	+	0.530395i
$911$		−	36.0000i		−	1.19273i	−0.802712	−	0.596367i	$-0.796610\pi$
$911$		−	36.0000i		−	1.19273i	0.802712	−	0.596367i	$-0.203390\pi$
$912$		0			0
$913$		0			0
$914$	−24.0000			−0.793849
$915$		0			0
$916$	−6.00000			−0.198246
$917$			32.0000i			1.05673i
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$	−4.00000	+	8.00000i	−0.131876	+	0.263752i
$921$		0			0
$922$			28.0000i			0.922131i
$923$	16.0000			0.526646
$924$		0			0
$925$	−6.00000	−	8.00000i	−0.197279	−	0.263038i
$926$	−8.00000			−0.262896
$927$		0			0
$928$	6.00000			0.196960
$929$		−	54.0000i		−	1.77168i	−0.463988	−	0.885841i	$-0.653582\pi$
$929$		−	54.0000i		−	1.77168i	0.463988	−	0.885841i	$-0.346418\pi$
$930$		0			0
$931$	36.0000			1.17985
$932$		0			0
$933$		0			0
$934$	12.0000			0.392652
$935$		0			0
$936$		0			0
$937$		−	32.0000i		−	1.04539i	−0.852518	−	0.522697i	$-0.824926\pi$
$937$		−	32.0000i		−	1.04539i	0.852518	−	0.522697i	$-0.175074\pi$
$938$	16.0000			0.522419
$939$		0			0
$940$	8.00000	−	16.0000i	0.260931	−	0.521862i
$941$		−	42.0000i		−	1.36916i	−0.728937	−	0.684580i	$-0.759985\pi$
$941$		−	42.0000i		−	1.36916i	0.728937	−	0.684580i	$-0.240015\pi$
$942$		0			0
$943$			8.00000i			0.260516i
$944$	−4.00000			−0.130189
$945$		0			0
$946$		0			0
$947$	−48.0000			−1.55979			−0.779895	−	0.625910i	$-0.784728\pi$
$947$	−48.0000			−1.55979			−0.779895	+	0.625910i	$0.784728\pi$
$948$		0			0
$949$			56.0000i			1.81784i
$950$	−16.0000	+	12.0000i	−0.519109	+	0.389331i
$951$		0			0
$952$	4.00000	−	16.0000i	0.129641	−	0.518563i
$953$		−	26.0000i		−	0.842223i	−0.907009	−	0.421111i	$-0.861640\pi$
$953$		−	26.0000i		−	0.842223i	0.907009	−	0.421111i	$-0.138360\pi$
$954$		0			0
$955$		0			0
$956$	24.0000			0.776215
$957$		0			0
$958$	12.0000			0.387702
$959$			40.0000i			1.29167i
$960$		0			0
$961$	15.0000			0.483871
$962$	−8.00000			−0.257930
$963$		0			0
$964$			8.00000i			0.257663i
$965$	−20.0000	−	10.0000i	−0.643823	−	0.321911i
$966$		0			0
$967$		−	32.0000i		−	1.02905i	−0.857475	−	0.514525i	$-0.827968\pi$
$967$		−	32.0000i		−	1.02905i	0.857475	−	0.514525i	$-0.172032\pi$
$968$		−	11.0000i		−	0.353553i
$969$		0			0
$970$	10.0000	−	20.0000i	0.321081	−	0.642161i
$971$	−36.0000			−1.15529			−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000			−1.15529			−0.577647	+	0.816286i	$0.696029\pi$
$972$		0			0
$973$			64.0000i			2.05175i
$974$			28.0000i			0.897178i
$975$		0			0
$976$		−	4.00000i		−	0.128037i
$977$			2.00000i			0.0639857i	0.999488	+	0.0319928i	$0.0101854\pi$
$977$			2.00000i			0.0639857i	−0.999488	+	0.0319928i	$0.989815\pi$
$978$		0			0
$979$		0			0
$980$	−18.0000	−	9.00000i	−0.574989	−	0.287494i
$981$		0			0
$982$		−	12.0000i		−	0.382935i
$983$	36.0000			1.14822			0.574111	−	0.818778i	$-0.305348\pi$
$983$	36.0000			1.14822			0.574111	+	0.818778i	$0.305348\pi$
$984$		0			0
$985$	8.00000	+	4.00000i	0.254901	+	0.127451i
$986$	24.0000	+	6.00000i	0.764316	+	0.191079i
$987$		0			0
$988$			16.0000i			0.509028i
$989$			48.0000i			1.52631i
$990$		0			0
$991$			52.0000i			1.65183i	0.563791	+	0.825917i	$0.309342\pi$
$991$			52.0000i			1.65183i	−0.563791	+	0.825917i	$0.690658\pi$
$992$	4.00000			0.127000
$993$		0			0
$994$	−16.0000			−0.507489
$995$	20.0000	−	40.0000i	0.634043	−	1.26809i
$996$		0			0
$997$	−18.0000			−0.570066			−0.285033	−	0.958518i	$-0.592005\pi$
$997$	−18.0000			−0.570066			−0.285033	+	0.958518i	$0.592005\pi$
$998$	24.0000			0.759707
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1530.2.f.f.1189.2	yes	2
3.2	odd	2		1530.2.f.c.1189.1	yes	2
5.4	even	2		1530.2.f.a.1189.1	✓	2
15.14	odd	2		1530.2.f.d.1189.2	yes	2
17.16	even	2		1530.2.f.a.1189.2	yes	2
51.50	odd	2		1530.2.f.d.1189.1	yes	2
85.84	even	2	inner	1530.2.f.f.1189.1	yes	2
255.254	odd	2		1530.2.f.c.1189.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1530.2.f.a.1189.1	✓	2	5.4	even	2
1530.2.f.a.1189.2	yes	2	17.16	even	2
1530.2.f.c.1189.1	yes	2	3.2	odd	2
1530.2.f.c.1189.2	yes	2	255.254	odd	2
1530.2.f.d.1189.1	yes	2	51.50	odd	2
1530.2.f.d.1189.2	yes	2	15.14	odd	2
1530.2.f.f.1189.1	yes	2	85.84	even	2	inner
1530.2.f.f.1189.2	yes	2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1530.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} +4.00000 q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} +4.00000 q^{7} -1.00000i q^{8} +(-1.00000 + 2.00000i) q^{10} -4.00000i q^{13} +4.00000i q^{14} +1.00000 q^{16} +(4.00000 + 1.00000i) q^{17} +4.00000 q^{19} +(-2.00000 - 1.00000i) q^{20} -4.00000 q^{23} +(3.00000 + 4.00000i) q^{25} +4.00000 q^{26} -4.00000 q^{28} -6.00000i q^{29} -4.00000i q^{31} +1.00000i q^{32} +(-1.00000 + 4.00000i) q^{34} +(8.00000 + 4.00000i) q^{35} -2.00000 q^{37} +4.00000i q^{38} +(1.00000 - 2.00000i) q^{40} -2.00000i q^{41} -12.0000i q^{43} -4.00000i q^{46} +8.00000i q^{47} +9.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} +4.00000i q^{52} +10.0000i q^{53} -4.00000i q^{56} +6.00000 q^{58} -4.00000 q^{59} -4.00000i q^{61} +4.00000 q^{62} -1.00000 q^{64} +(4.00000 - 8.00000i) q^{65} -4.00000i q^{67} +(-4.00000 - 1.00000i) q^{68} +(-4.00000 + 8.00000i) q^{70} +4.00000i q^{71} -14.0000 q^{73} -2.00000i q^{74} -4.00000 q^{76} +4.00000i q^{79} +(2.00000 + 1.00000i) q^{80} +2.00000 q^{82} +12.0000i q^{83} +(7.00000 + 6.00000i) q^{85} +12.0000 q^{86} +16.0000 q^{89} -16.0000i q^{91} +4.00000 q^{92} -8.00000 q^{94} +(8.00000 + 4.00000i) q^{95} -10.0000 q^{97} +9.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} + 4 q^{5} + 8 q^{7}+O(q^{10}) \) 2 * q - 2 * q^4 + 4 * q^5 + 8 * q^7	\( 2 q - 2 q^{4} + 4 q^{5} + 8 q^{7} - 2 q^{10} + 2 q^{16} + 8 q^{17} + 8 q^{19} - 4 q^{20} - 8 q^{23} + 6 q^{25} + 8 q^{26} - 8 q^{28} - 2 q^{34} + 16 q^{35} - 4 q^{37} + 2 q^{40} + 18 q^{49} - 8 q^{50} + 12 q^{58} - 8 q^{59} + 8 q^{62} - 2 q^{64} + 8 q^{65} - 8 q^{68} - 8 q^{70} - 28 q^{73} - 8 q^{76} + 4 q^{80} + 4 q^{82} + 14 q^{85} + 24 q^{86} + 32 q^{89} + 8 q^{92} - 16 q^{94} + 16 q^{95} - 20 q^{97}+O(q^{100}) \) 2 * q - 2 * q^4 + 4 * q^5 + 8 * q^7 - 2 * q^10 + 2 * q^16 + 8 * q^17 + 8 * q^19 - 4 * q^20 - 8 * q^23 + 6 * q^25 + 8 * q^26 - 8 * q^28 - 2 * q^34 + 16 * q^35 - 4 * q^37 + 2 * q^40 + 18 * q^49 - 8 * q^50 + 12 * q^58 - 8 * q^59 + 8 * q^62 - 2 * q^64 + 8 * q^65 - 8 * q^68 - 8 * q^70 - 28 * q^73 - 8 * q^76 + 4 * q^80 + 4 * q^82 + 14 * q^85 + 24 * q^86 + 32 * q^89 + 8 * q^92 - 16 * q^94 + 16 * q^95 - 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more