LMFDB - Embedded newform 2790.2.d.f.559.2

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			559.2
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	2790.559
Dual form			2790.2.d.f.559.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} -1.00000i q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} -1.00000i q^{7} -1.00000i q^{8} +(-2.00000 + 1.00000i) q^{10} +3.00000 q^{11} -4.00000i q^{13} +1.00000 q^{14} +1.00000 q^{16} +1.00000 q^{19} +(-1.00000 - 2.00000i) q^{20} +3.00000i q^{22} -5.00000i q^{23} +(-3.00000 + 4.00000i) q^{25} +4.00000 q^{26} +1.00000i q^{28} +2.00000 q^{29} -1.00000 q^{31} +1.00000i q^{32} +(2.00000 - 1.00000i) q^{35} -4.00000i q^{37} +1.00000i q^{38} +(2.00000 - 1.00000i) q^{40} +10.0000 q^{41} -5.00000i q^{43} -3.00000 q^{44} +5.00000 q^{46} -8.00000i q^{47} +6.00000 q^{49} +(-4.00000 - 3.00000i) q^{50} +4.00000i q^{52} -5.00000i q^{53} +(3.00000 + 6.00000i) q^{55} -1.00000 q^{56} +2.00000i q^{58} -6.00000 q^{59} -2.00000 q^{61} -1.00000i q^{62} -1.00000 q^{64} +(8.00000 - 4.00000i) q^{65} -2.00000i q^{67} +(1.00000 + 2.00000i) q^{70} +5.00000 q^{71} -7.00000i q^{73} +4.00000 q^{74} -1.00000 q^{76} -3.00000i q^{77} -3.00000 q^{79} +(1.00000 + 2.00000i) q^{80} +10.0000i q^{82} +2.00000i q^{83} +5.00000 q^{86} -3.00000i q^{88} +1.00000 q^{89} -4.00000 q^{91} +5.00000i q^{92} +8.00000 q^{94} +(1.00000 + 2.00000i) q^{95} +10.0000i q^{97} +6.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} + 2 q^{5}+O(q^{10}) $ 2 * q - 2 * q^4 + 2 * q^5	$ 2 q - 2 q^{4} + 2 q^{5} - 4 q^{10} + 6 q^{11} + 2 q^{14} + 2 q^{16} + 2 q^{19} - 2 q^{20} - 6 q^{25} + 8 q^{26} + 4 q^{29} - 2 q^{31} + 4 q^{35} + 4 q^{40} + 20 q^{41} - 6 q^{44} + 10 q^{46} + 12 q^{49} - 8 q^{50} + 6 q^{55} - 2 q^{56} - 12 q^{59} - 4 q^{61} - 2 q^{64} + 16 q^{65} + 2 q^{70} + 10 q^{71} + 8 q^{74} - 2 q^{76} - 6 q^{79} + 2 q^{80} + 10 q^{86} + 2 q^{89} - 8 q^{91} + 16 q^{94} + 2 q^{95}+O(q^{100}) $ 2 * q - 2 * q^4 + 2 * q^5 - 4 * q^10 + 6 * q^11 + 2 * q^14 + 2 * q^16 + 2 * q^19 - 2 * q^20 - 6 * q^25 + 8 * q^26 + 4 * q^29 - 2 * q^31 + 4 * q^35 + 4 * q^40 + 20 * q^41 - 6 * q^44 + 10 * q^46 + 12 * q^49 - 8 * q^50 + 6 * q^55 - 2 * q^56 - 12 * q^59 - 4 * q^61 - 2 * q^64 + 16 * q^65 + 2 * q^70 + 10 * q^71 + 8 * q^74 - 2 * q^76 - 6 * q^79 + 2 * q^80 + 10 * q^86 + 2 * q^89 - 8 * q^91 + 16 * q^94 + 2 * 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
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$6$		0			0
$7$		−	1.00000i		−	0.377964i	−0.981981	−	0.188982i	$-0.939481\pi$
$7$		−	1.00000i		−	0.377964i	0.981981	−	0.188982i	$-0.0605189\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−2.00000	+	1.00000i	−0.632456	+	0.316228i
$11$	3.00000			0.904534			0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000			0.904534			0.452267	+	0.891883i	$0.350615\pi$
$12$		0			0
$13$		−	4.00000i		−	1.10940i	−0.832050	−	0.554700i	$-0.812833\pi$
$13$		−	4.00000i		−	1.10940i	0.832050	−	0.554700i	$-0.187167\pi$
$14$	1.00000			0.267261
$15$		0			0
$16$	1.00000			0.250000
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$		0			0
$19$	1.00000			0.229416			0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000			0.229416			0.114708	+	0.993399i	$0.463407\pi$
$20$	−1.00000	−	2.00000i	−0.223607	−	0.447214i
$21$		0			0
$22$			3.00000i			0.639602i
$23$		−	5.00000i		−	1.04257i	−0.853382	−	0.521286i	$-0.825452\pi$
$23$		−	5.00000i		−	1.04257i	0.853382	−	0.521286i	$-0.174548\pi$
$24$		0			0
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$	4.00000			0.784465
$27$		0			0
$28$			1.00000i			0.188982i
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$		0			0
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$			1.00000i			0.176777i
$33$		0			0
$34$		0			0
$35$	2.00000	−	1.00000i	0.338062	−	0.169031i
$36$		0			0
$37$		−	4.00000i		−	0.657596i	−0.944400	−	0.328798i	$-0.893356\pi$
$37$		−	4.00000i		−	0.657596i	0.944400	−	0.328798i	$-0.106644\pi$
$38$			1.00000i			0.162221i
$39$		0			0
$40$	2.00000	−	1.00000i	0.316228	−	0.158114i
$41$	10.0000			1.56174			0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000			1.56174			0.780869	+	0.624695i	$0.214777\pi$
$42$		0			0
$43$		−	5.00000i		−	0.762493i	−0.924473	−	0.381246i	$-0.875495\pi$
$43$		−	5.00000i		−	0.762493i	0.924473	−	0.381246i	$-0.124505\pi$
$44$	−3.00000			−0.452267
$45$		0			0
$46$	5.00000			0.737210
$47$		−	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
$49$	6.00000			0.857143
$50$	−4.00000	−	3.00000i	−0.565685	−	0.424264i
$51$		0			0
$52$			4.00000i			0.554700i
$53$		−	5.00000i		−	0.686803i	−0.939189	−	0.343401i	$-0.888421\pi$
$53$		−	5.00000i		−	0.686803i	0.939189	−	0.343401i	$-0.111579\pi$
$54$		0			0
$55$	3.00000	+	6.00000i	0.404520	+	0.809040i
$56$	−1.00000			−0.133631
$57$		0			0
$58$			2.00000i			0.262613i
$59$	−6.00000			−0.781133			−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000			−0.781133			−0.390567	+	0.920575i	$0.627721\pi$
$60$		0			0
$61$	−2.00000			−0.256074			−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000			−0.256074			−0.128037	+	0.991769i	$0.540868\pi$
$62$		−	1.00000i		−	0.127000i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	8.00000	−	4.00000i	0.992278	−	0.496139i
$66$		0			0
$67$		−	2.00000i		−	0.244339i	−0.992509	−	0.122169i	$-0.961015\pi$
$67$		−	2.00000i		−	0.244339i	0.992509	−	0.122169i	$-0.0389851\pi$
$68$		0			0
$69$		0			0
$70$	1.00000	+	2.00000i	0.119523	+	0.239046i
$71$	5.00000			0.593391			0.296695	−	0.954972i	$-0.404115\pi$
$71$	5.00000			0.593391			0.296695	+	0.954972i	$0.404115\pi$
$72$		0			0
$73$		−	7.00000i		−	0.819288i	−0.912245	−	0.409644i	$-0.865653\pi$
$73$		−	7.00000i		−	0.819288i	0.912245	−	0.409644i	$-0.134347\pi$
$74$	4.00000			0.464991
$75$		0			0
$76$	−1.00000			−0.114708
$77$		−	3.00000i		−	0.341882i
$78$		0			0
$79$	−3.00000			−0.337526			−0.168763	−	0.985657i	$-0.553977\pi$
$79$	−3.00000			−0.337526			−0.168763	+	0.985657i	$0.553977\pi$
$80$	1.00000	+	2.00000i	0.111803	+	0.223607i
$81$		0			0
$82$			10.0000i			1.10432i
$83$			2.00000i			0.219529i	0.993958	+	0.109764i	$0.0350096\pi$
$83$			2.00000i			0.219529i	−0.993958	+	0.109764i	$0.964990\pi$
$84$		0			0
$85$		0			0
$86$	5.00000			0.539164
$87$		0			0
$88$		−	3.00000i		−	0.319801i
$89$	1.00000			0.106000			0.0529999	−	0.998595i	$-0.483122\pi$
$89$	1.00000			0.106000			0.0529999	+	0.998595i	$0.483122\pi$
$90$		0			0
$91$	−4.00000			−0.419314
$92$			5.00000i			0.521286i
$93$		0			0
$94$	8.00000			0.825137
$95$	1.00000	+	2.00000i	0.102598	+	0.205196i
$96$		0			0
$97$			10.0000i			1.01535i	0.861550	+	0.507673i	$0.169494\pi$
$97$			10.0000i			1.01535i	−0.861550	+	0.507673i	$0.830506\pi$
$98$			6.00000i			0.606092i
$99$		0			0
$100$	3.00000	−	4.00000i	0.300000	−	0.400000i
$101$	15.0000			1.49256			0.746278	−	0.665635i	$-0.231839\pi$
$101$	15.0000			1.49256			0.746278	+	0.665635i	$0.231839\pi$
$102$		0			0
$103$		0			0		1.00000			$0$
$103$		0			0		−1.00000			$\pi$
$104$	−4.00000			−0.392232
$105$		0			0
$106$	5.00000			0.485643
$107$			19.0000i			1.83680i	0.395654	+	0.918400i	$0.370518\pi$
$107$			19.0000i			1.83680i	−0.395654	+	0.918400i	$0.629482\pi$
$108$		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	+	3.00000i	−0.572078	+	0.286039i
$111$		0			0
$112$		−	1.00000i		−	0.0944911i
$113$			15.0000i			1.41108i	0.708669	+	0.705541i	$0.249296\pi$
$113$			15.0000i			1.41108i	−0.708669	+	0.705541i	$0.750704\pi$
$114$		0			0
$115$	10.0000	−	5.00000i	0.932505	−	0.466252i
$116$	−2.00000			−0.185695
$117$		0			0
$118$		−	6.00000i		−	0.552345i
$119$		0			0
$120$		0			0
$121$	−2.00000			−0.181818
$122$		−	2.00000i		−	0.181071i
$123$		0			0
$124$	1.00000			0.0898027
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$		0			0
$127$		−	8.00000i		−	0.709885i	−0.934888	−	0.354943i	$-0.884500\pi$
$127$		−	8.00000i		−	0.709885i	0.934888	−	0.354943i	$-0.115500\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	4.00000	+	8.00000i	0.350823	+	0.701646i
$131$	2.00000			0.174741			0.0873704	−	0.996176i	$-0.472154\pi$
$131$	2.00000			0.174741			0.0873704	+	0.996176i	$0.472154\pi$
$132$		0			0
$133$		−	1.00000i		−	0.0867110i
$134$	2.00000			0.172774
$135$		0			0
$136$		0			0
$137$			2.00000i			0.170872i	0.996344	+	0.0854358i	$0.0272282\pi$
$137$			2.00000i			0.170872i	−0.996344	+	0.0854358i	$0.972772\pi$
$138$		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	+	1.00000i	−0.169031	+	0.0845154i
$141$		0			0
$142$			5.00000i			0.419591i
$143$		−	12.0000i		−	1.00349i
$144$		0			0
$145$	2.00000	+	4.00000i	0.166091	+	0.332182i
$146$	7.00000			0.579324
$147$		0			0
$148$			4.00000i			0.328798i
$149$	15.0000			1.22885			0.614424	−	0.788976i	$-0.289388\pi$
$149$	15.0000			1.22885			0.614424	+	0.788976i	$0.289388\pi$
$150$		0			0
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$		−	1.00000i		−	0.0811107i
$153$		0			0
$154$	3.00000			0.241747
$155$	−1.00000	−	2.00000i	−0.0803219	−	0.160644i
$156$		0			0
$157$		−	9.00000i		−	0.718278i	−0.933284	−	0.359139i	$-0.883070\pi$
$157$		−	9.00000i		−	0.718278i	0.933284	−	0.359139i	$-0.116930\pi$
$158$		−	3.00000i		−	0.238667i
$159$		0			0
$160$	−2.00000	+	1.00000i	−0.158114	+	0.0790569i
$161$	−5.00000			−0.394055
$162$		0			0
$163$		−	4.00000i		−	0.313304i	−0.987654	−	0.156652i	$-0.949930\pi$
$163$		−	4.00000i		−	0.313304i	0.987654	−	0.156652i	$-0.0500701\pi$
$164$	−10.0000			−0.780869
$165$		0			0
$166$	−2.00000			−0.155230
$167$			21.0000i			1.62503i	0.582941	+	0.812514i	$0.301902\pi$
$167$			21.0000i			1.62503i	−0.582941	+	0.812514i	$0.698098\pi$
$168$		0			0
$169$	−3.00000			−0.230769
$170$		0			0
$171$		0			0
$172$			5.00000i			0.381246i
$173$			2.00000i			0.152057i	0.997106	+	0.0760286i	$0.0242240\pi$
$173$			2.00000i			0.152057i	−0.997106	+	0.0760286i	$0.975776\pi$
$174$		0			0
$175$	4.00000	+	3.00000i	0.302372	+	0.226779i
$176$	3.00000			0.226134
$177$		0			0
$178$			1.00000i			0.0749532i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		0			0
$181$	−5.00000			−0.371647			−0.185824	−	0.982583i	$-0.559495\pi$
$181$	−5.00000			−0.371647			−0.185824	+	0.982583i	$0.559495\pi$
$182$		−	4.00000i		−	0.296500i
$183$		0			0
$184$	−5.00000			−0.368605
$185$	8.00000	−	4.00000i	0.588172	−	0.294086i
$186$		0			0
$187$		0			0
$188$			8.00000i			0.583460i
$189$		0			0
$190$	−2.00000	+	1.00000i	−0.145095	+	0.0725476i
$191$	16.0000			1.15772			0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000			1.15772			0.578860	+	0.815427i	$0.303498\pi$
$192$		0			0
$193$		−	10.0000i		−	0.719816i	−0.932988	−	0.359908i	$-0.882808\pi$
$193$		−	10.0000i		−	0.719816i	0.932988	−	0.359908i	$-0.117192\pi$
$194$	−10.0000			−0.717958
$195$		0			0
$196$	−6.00000			−0.428571
$197$			18.0000i			1.28245i	0.767354	+	0.641223i	$0.221573\pi$
$197$			18.0000i			1.28245i	−0.767354	+	0.641223i	$0.778427\pi$
$198$		0			0
$199$	21.0000			1.48865			0.744325	−	0.667817i	$-0.232771\pi$
$199$	21.0000			1.48865			0.744325	+	0.667817i	$0.232771\pi$
$200$	4.00000	+	3.00000i	0.282843	+	0.212132i
$201$		0			0
$202$			15.0000i			1.05540i
$203$		−	2.00000i		−	0.140372i
$204$		0			0
$205$	10.0000	+	20.0000i	0.698430	+	1.39686i
$206$		0			0
$207$		0			0
$208$		−	4.00000i		−	0.277350i
$209$	3.00000			0.207514
$210$		0			0
$211$	7.00000			0.481900			0.240950	−	0.970538i	$-0.422541\pi$
$211$	7.00000			0.481900			0.240950	+	0.970538i	$0.422541\pi$
$212$			5.00000i			0.343401i
$213$		0			0
$214$	−19.0000			−1.29881
$215$	10.0000	−	5.00000i	0.681994	−	0.340997i
$216$		0			0
$217$			1.00000i			0.0678844i
$218$		−	2.00000i		−	0.135457i
$219$		0			0
$220$	−3.00000	−	6.00000i	−0.202260	−	0.404520i
$221$		0			0
$222$		0			0
$223$		−	20.0000i		−	1.33930i	−0.742677	−	0.669650i	$-0.766444\pi$
$223$		−	20.0000i		−	1.33930i	0.742677	−	0.669650i	$-0.233556\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	−15.0000			−0.997785
$227$		−	9.00000i		−	0.597351i	−0.954355	−	0.298675i	$-0.903455\pi$
$227$		−	9.00000i		−	0.597351i	0.954355	−	0.298675i	$-0.0965448\pi$
$228$		0			0
$229$	−15.0000			−0.991228			−0.495614	−	0.868543i	$-0.665057\pi$
$229$	−15.0000			−0.991228			−0.495614	+	0.868543i	$0.665057\pi$
$230$	5.00000	+	10.0000i	0.329690	+	0.659380i
$231$		0			0
$232$		−	2.00000i		−	0.131306i
$233$			21.0000i			1.37576i	0.725826	+	0.687878i	$0.241458\pi$
$233$			21.0000i			1.37576i	−0.725826	+	0.687878i	$0.758542\pi$
$234$		0			0
$235$	16.0000	−	8.00000i	1.04372	−	0.521862i
$236$	6.00000			0.390567
$237$		0			0
$238$		0			0
$239$	−14.0000			−0.905585			−0.452792	−	0.891616i	$-0.649572\pi$
$239$	−14.0000			−0.905585			−0.452792	+	0.891616i	$0.649572\pi$
$240$		0			0
$241$	−12.0000			−0.772988			−0.386494	−	0.922292i	$-0.626314\pi$
$241$	−12.0000			−0.772988			−0.386494	+	0.922292i	$0.626314\pi$
$242$		−	2.00000i		−	0.128565i
$243$		0			0
$244$	2.00000			0.128037
$245$	6.00000	+	12.0000i	0.383326	+	0.766652i
$246$		0			0
$247$		−	4.00000i		−	0.254514i
$248$			1.00000i			0.0635001i
$249$		0			0
$250$	2.00000	−	11.0000i	0.126491	−	0.695701i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$		−	15.0000i		−	0.943042i
$254$	8.00000			0.501965
$255$		0			0
$256$	1.00000			0.0625000
$257$			5.00000i			0.311891i	0.987766	+	0.155946i	$0.0498425\pi$
$257$			5.00000i			0.311891i	−0.987766	+	0.155946i	$0.950158\pi$
$258$		0			0
$259$	−4.00000			−0.248548
$260$	−8.00000	+	4.00000i	−0.496139	+	0.248069i
$261$		0			0
$262$			2.00000i			0.123560i
$263$		−	24.0000i		−	1.47990i	−0.672660	−	0.739952i	$-0.734848\pi$
$263$		−	24.0000i		−	1.47990i	0.672660	−	0.739952i	$-0.265152\pi$
$264$		0			0
$265$	10.0000	−	5.00000i	0.614295	−	0.307148i
$266$	1.00000			0.0613139
$267$		0			0
$268$			2.00000i			0.122169i
$269$	2.00000			0.121942			0.0609711	−	0.998140i	$-0.480580\pi$
$269$	2.00000			0.121942			0.0609711	+	0.998140i	$0.480580\pi$
$270$		0			0
$271$	9.00000			0.546711			0.273356	−	0.961913i	$-0.411866\pi$
$271$	9.00000			0.546711			0.273356	+	0.961913i	$0.411866\pi$
$272$		0			0
$273$		0			0
$274$	−2.00000			−0.120824
$275$	−9.00000	+	12.0000i	−0.542720	+	0.723627i
$276$		0			0
$277$		−	2.00000i		−	0.120168i	−0.998193	−	0.0600842i	$-0.980863\pi$
$277$		−	2.00000i		−	0.120168i	0.998193	−	0.0600842i	$-0.0191369\pi$
$278$			20.0000i			1.19952i
$279$		0			0
$280$	−1.00000	−	2.00000i	−0.0597614	−	0.119523i
$281$	32.0000			1.90896			0.954480	−	0.298275i	$-0.0964112\pi$
$281$	32.0000			1.90896			0.954480	+	0.298275i	$0.0964112\pi$
$282$		0			0
$283$			14.0000i			0.832214i	0.909316	+	0.416107i	$0.136606\pi$
$283$			14.0000i			0.832214i	−0.909316	+	0.416107i	$0.863394\pi$
$284$	−5.00000			−0.296695
$285$		0			0
$286$	12.0000			0.709575
$287$		−	10.0000i		−	0.590281i
$288$		0			0
$289$	17.0000			1.00000
$290$	−4.00000	+	2.00000i	−0.234888	+	0.117444i
$291$		0			0
$292$			7.00000i			0.409644i
$293$			18.0000i			1.05157i	0.850617	+	0.525786i	$0.176229\pi$
$293$			18.0000i			1.05157i	−0.850617	+	0.525786i	$0.823771\pi$
$294$		0			0
$295$	−6.00000	−	12.0000i	−0.349334	−	0.698667i
$296$	−4.00000			−0.232495
$297$		0			0
$298$			15.0000i			0.868927i
$299$	−20.0000			−1.15663
$300$		0			0
$301$	−5.00000			−0.288195
$302$		−	16.0000i		−	0.920697i
$303$		0			0
$304$	1.00000			0.0573539
$305$	−2.00000	−	4.00000i	−0.114520	−	0.229039i
$306$		0			0
$307$			4.00000i			0.228292i	0.993464	+	0.114146i	$0.0364132\pi$
$307$			4.00000i			0.228292i	−0.993464	+	0.114146i	$0.963587\pi$
$308$			3.00000i			0.170941i
$309$		0			0
$310$	2.00000	−	1.00000i	0.113592	−	0.0567962i
$311$	−16.0000			−0.907277			−0.453638	−	0.891186i	$-0.649874\pi$
$311$	−16.0000			−0.907277			−0.453638	+	0.891186i	$0.649874\pi$
$312$		0			0
$313$		−	6.00000i		−	0.339140i	−0.985518	−	0.169570i	$-0.945762\pi$
$313$		−	6.00000i		−	0.339140i	0.985518	−	0.169570i	$-0.0542379\pi$
$314$	9.00000			0.507899
$315$		0			0
$316$	3.00000			0.168763
$317$			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
$319$	6.00000			0.335936
$320$	−1.00000	−	2.00000i	−0.0559017	−	0.111803i
$321$		0			0
$322$		−	5.00000i		−	0.278639i
$323$		0			0
$324$		0			0
$325$	16.0000	+	12.0000i	0.887520	+	0.665640i
$326$	4.00000			0.221540
$327$		0			0
$328$		−	10.0000i		−	0.552158i
$329$	−8.00000			−0.441054
$330$		0			0
$331$	8.00000			0.439720			0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000			0.439720			0.219860	+	0.975531i	$0.429440\pi$
$332$		−	2.00000i		−	0.109764i
$333$		0			0
$334$	−21.0000			−1.14907
$335$	4.00000	−	2.00000i	0.218543	−	0.109272i
$336$		0			0
$337$			34.0000i			1.85210i	0.377403	+	0.926049i	$0.376817\pi$
$337$			34.0000i			1.85210i	−0.377403	+	0.926049i	$0.623183\pi$
$338$		−	3.00000i		−	0.163178i
$339$		0			0
$340$		0			0
$341$	−3.00000			−0.162459
$342$		0			0
$343$		−	13.0000i		−	0.701934i
$344$	−5.00000			−0.269582
$345$		0			0
$346$	−2.00000			−0.107521
$347$		−	22.0000i		−	1.18102i	−0.807030	−	0.590511i	$-0.798926\pi$
$347$		−	22.0000i		−	1.18102i	0.807030	−	0.590511i	$-0.201074\pi$
$348$		0			0
$349$	−20.0000			−1.07058			−0.535288	−	0.844670i	$-0.679797\pi$
$349$	−20.0000			−1.07058			−0.535288	+	0.844670i	$0.679797\pi$
$350$	−3.00000	+	4.00000i	−0.160357	+	0.213809i
$351$		0			0
$352$			3.00000i			0.159901i
$353$		−	24.0000i		−	1.27739i	−0.769460	−	0.638696i	$-0.779474\pi$
$353$		−	24.0000i		−	1.27739i	0.769460	−	0.638696i	$-0.220526\pi$
$354$		0			0
$355$	5.00000	+	10.0000i	0.265372	+	0.530745i
$356$	−1.00000			−0.0529999
$357$		0			0
$358$		0			0
$359$	3.00000			0.158334			0.0791670	−	0.996861i	$-0.474774\pi$
$359$	3.00000			0.158334			0.0791670	+	0.996861i	$0.474774\pi$
$360$		0			0
$361$	−18.0000			−0.947368
$362$		−	5.00000i		−	0.262794i
$363$		0			0
$364$	4.00000			0.209657
$365$	14.0000	−	7.00000i	0.732793	−	0.366397i
$366$		0			0
$367$		−	14.0000i		−	0.730794i	−0.930852	−	0.365397i	$-0.880933\pi$
$367$		−	14.0000i		−	0.730794i	0.930852	−	0.365397i	$-0.119067\pi$
$368$		−	5.00000i		−	0.260643i
$369$		0			0
$370$	4.00000	+	8.00000i	0.207950	+	0.415900i
$371$	−5.00000			−0.259587
$372$		0			0
$373$		−	11.0000i		−	0.569558i	−0.958593	−	0.284779i	$-0.908080\pi$
$373$		−	11.0000i		−	0.569558i	0.958593	−	0.284779i	$-0.0919203\pi$
$374$		0			0
$375$		0			0
$376$	−8.00000			−0.412568
$377$		−	8.00000i		−	0.412021i
$378$		0			0
$379$	15.0000			0.770498			0.385249	−	0.922813i	$-0.374116\pi$
$379$	15.0000			0.770498			0.385249	+	0.922813i	$0.374116\pi$
$380$	−1.00000	−	2.00000i	−0.0512989	−	0.102598i
$381$		0			0
$382$			16.0000i			0.818631i
$383$		−	28.0000i		−	1.43073i	−0.698749	−	0.715367i	$-0.746260\pi$
$383$		−	28.0000i		−	1.43073i	0.698749	−	0.715367i	$-0.253740\pi$
$384$		0			0
$385$	6.00000	−	3.00000i	0.305788	−	0.152894i
$386$	10.0000			0.508987
$387$		0			0
$388$		−	10.0000i		−	0.507673i
$389$	−28.0000			−1.41966			−0.709828	−	0.704375i	$-0.751227\pi$
$389$	−28.0000			−1.41966			−0.709828	+	0.704375i	$0.751227\pi$
$390$		0			0
$391$		0			0
$392$		−	6.00000i		−	0.303046i
$393$		0			0
$394$	−18.0000			−0.906827
$395$	−3.00000	−	6.00000i	−0.150946	−	0.301893i
$396$		0			0
$397$			31.0000i			1.55585i	0.628360	+	0.777923i	$0.283727\pi$
$397$			31.0000i			1.55585i	−0.628360	+	0.777923i	$0.716273\pi$
$398$			21.0000i			1.05263i
$399$		0			0
$400$	−3.00000	+	4.00000i	−0.150000	+	0.200000i
$401$	−5.00000			−0.249688			−0.124844	−	0.992176i	$-0.539843\pi$
$401$	−5.00000			−0.249688			−0.124844	+	0.992176i	$0.539843\pi$
$402$		0			0
$403$			4.00000i			0.199254i
$404$	−15.0000			−0.746278
$405$		0			0
$406$	2.00000			0.0992583
$407$		−	12.0000i		−	0.594818i
$408$		0			0
$409$	−4.00000			−0.197787			−0.0988936	−	0.995098i	$-0.531530\pi$
$409$	−4.00000			−0.197787			−0.0988936	+	0.995098i	$0.531530\pi$
$410$	−20.0000	+	10.0000i	−0.987730	+	0.493865i
$411$		0			0
$412$		0			0
$413$			6.00000i			0.295241i
$414$		0			0
$415$	−4.00000	+	2.00000i	−0.196352	+	0.0981761i
$416$	4.00000			0.196116
$417$		0			0
$418$			3.00000i			0.146735i
$419$	−18.0000			−0.879358			−0.439679	−	0.898155i	$-0.644908\pi$
$419$	−18.0000			−0.879358			−0.439679	+	0.898155i	$0.644908\pi$
$420$		0			0
$421$	−14.0000			−0.682318			−0.341159	−	0.940006i	$-0.610819\pi$
$421$	−14.0000			−0.682318			−0.341159	+	0.940006i	$0.610819\pi$
$422$			7.00000i			0.340755i
$423$		0			0
$424$	−5.00000			−0.242821
$425$		0			0
$426$		0			0
$427$			2.00000i			0.0967868i
$428$		−	19.0000i		−	0.918400i
$429$		0			0
$430$	5.00000	+	10.0000i	0.241121	+	0.482243i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$		0			0
$433$			19.0000i			0.913082i	0.889702	+	0.456541i	$0.150912\pi$
$433$			19.0000i			0.913082i	−0.889702	+	0.456541i	$0.849088\pi$
$434$	−1.00000			−0.0480015
$435$		0			0
$436$	2.00000			0.0957826
$437$		−	5.00000i		−	0.239182i
$438$		0			0
$439$	−20.0000			−0.954548			−0.477274	−	0.878755i	$-0.658375\pi$
$439$	−20.0000			−0.954548			−0.477274	+	0.878755i	$0.658375\pi$
$440$	6.00000	−	3.00000i	0.286039	−	0.143019i
$441$		0			0
$442$		0			0
$443$		−	29.0000i		−	1.37783i	−0.724841	−	0.688916i	$-0.758087\pi$
$443$		−	29.0000i		−	1.37783i	0.724841	−	0.688916i	$-0.241913\pi$
$444$		0			0
$445$	1.00000	+	2.00000i	0.0474045	+	0.0948091i
$446$	20.0000			0.947027
$447$		0			0
$448$			1.00000i			0.0472456i
$449$	2.00000			0.0943858			0.0471929	−	0.998886i	$-0.484972\pi$
$449$	2.00000			0.0943858			0.0471929	+	0.998886i	$0.484972\pi$
$450$		0			0
$451$	30.0000			1.41264
$452$		−	15.0000i		−	0.705541i
$453$		0			0
$454$	9.00000			0.422391
$455$	−4.00000	−	8.00000i	−0.187523	−	0.375046i
$456$		0			0
$457$		−	30.0000i		−	1.40334i	−0.712502	−	0.701670i	$-0.752438\pi$
$457$		−	30.0000i		−	1.40334i	0.712502	−	0.701670i	$-0.247562\pi$
$458$		−	15.0000i		−	0.700904i
$459$		0			0
$460$	−10.0000	+	5.00000i	−0.466252	+	0.233126i
$461$	−16.0000			−0.745194			−0.372597	−	0.927993i	$-0.621533\pi$
$461$	−16.0000			−0.745194			−0.372597	+	0.927993i	$0.621533\pi$
$462$		0			0
$463$		−	14.0000i		−	0.650635i	−0.945605	−	0.325318i	$-0.894529\pi$
$463$		−	14.0000i		−	0.650635i	0.945605	−	0.325318i	$-0.105471\pi$
$464$	2.00000			0.0928477
$465$		0			0
$466$	−21.0000			−0.972806
$467$			28.0000i			1.29569i	0.761774	+	0.647843i	$0.224329\pi$
$467$			28.0000i			1.29569i	−0.761774	+	0.647843i	$0.775671\pi$
$468$		0			0
$469$	−2.00000			−0.0923514
$470$	8.00000	+	16.0000i	0.369012	+	0.738025i
$471$		0			0
$472$			6.00000i			0.276172i
$473$		−	15.0000i		−	0.689701i
$474$		0			0
$475$	−3.00000	+	4.00000i	−0.137649	+	0.183533i
$476$		0			0
$477$		0			0
$478$		−	14.0000i		−	0.640345i
$479$	−25.0000			−1.14228			−0.571140	−	0.820853i	$-0.693499\pi$
$479$	−25.0000			−1.14228			−0.571140	+	0.820853i	$0.693499\pi$
$480$		0			0
$481$	−16.0000			−0.729537
$482$		−	12.0000i		−	0.546585i
$483$		0			0
$484$	2.00000			0.0909091
$485$	−20.0000	+	10.0000i	−0.908153	+	0.454077i
$486$		0			0
$487$			4.00000i			0.181257i	0.995885	+	0.0906287i	$0.0288876\pi$
$487$			4.00000i			0.181257i	−0.995885	+	0.0906287i	$0.971112\pi$
$488$			2.00000i			0.0905357i
$489$		0			0
$490$	−12.0000	+	6.00000i	−0.542105	+	0.271052i
$491$	−33.0000			−1.48927			−0.744635	−	0.667472i	$-0.767376\pi$
$491$	−33.0000			−1.48927			−0.744635	+	0.667472i	$0.767376\pi$
$492$		0			0
$493$		0			0
$494$	4.00000			0.179969
$495$		0			0
$496$	−1.00000			−0.0449013
$497$		−	5.00000i		−	0.224281i
$498$		0			0
$499$	−22.0000			−0.984855			−0.492428	−	0.870353i	$-0.663890\pi$
$499$	−22.0000			−0.984855			−0.492428	+	0.870353i	$0.663890\pi$
$500$	11.0000	+	2.00000i	0.491935	+	0.0894427i
$501$		0			0
$502$		−	12.0000i		−	0.535586i
$503$		−	14.0000i		−	0.624229i	−0.950044	−	0.312115i	$-0.898963\pi$
$503$		−	14.0000i		−	0.624229i	0.950044	−	0.312115i	$-0.101037\pi$
$504$		0			0
$505$	15.0000	+	30.0000i	0.667491	+	1.33498i
$506$	15.0000			0.666831
$507$		0			0
$508$			8.00000i			0.354943i
$509$	32.0000			1.41838			0.709188	−	0.705020i	$-0.249062\pi$
$509$	32.0000			1.41838			0.709188	+	0.705020i	$0.249062\pi$
$510$		0			0
$511$	−7.00000			−0.309662
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−5.00000			−0.220541
$515$		0			0
$516$		0			0
$517$		−	24.0000i		−	1.05552i
$518$		−	4.00000i		−	0.175750i
$519$		0			0
$520$	−4.00000	−	8.00000i	−0.175412	−	0.350823i
$521$		0			0			−	1.00000i	$-0.5\pi$
$521$		0			0				1.00000i	$0.5\pi$
$522$		0			0
$523$			19.0000i			0.830812i	0.909636	+	0.415406i	$0.136360\pi$
$523$			19.0000i			0.830812i	−0.909636	+	0.415406i	$0.863640\pi$
$524$	−2.00000			−0.0873704
$525$		0			0
$526$	24.0000			1.04645
$527$		0			0
$528$		0			0
$529$	−2.00000			−0.0869565
$530$	5.00000	+	10.0000i	0.217186	+	0.434372i
$531$		0			0
$532$			1.00000i			0.0433555i
$533$		−	40.0000i		−	1.73259i
$534$		0			0
$535$	−38.0000	+	19.0000i	−1.64288	+	0.821442i
$536$	−2.00000			−0.0863868
$537$		0			0
$538$			2.00000i			0.0862261i
$539$	18.0000			0.775315
$540$		0			0
$541$	24.0000			1.03184			0.515920	−	0.856637i	$-0.327450\pi$
$541$	24.0000			1.03184			0.515920	+	0.856637i	$0.327450\pi$
$542$			9.00000i			0.386583i
$543$		0			0
$544$		0			0
$545$	−2.00000	−	4.00000i	−0.0856706	−	0.171341i
$546$		0			0
$547$		−	28.0000i		−	1.19719i	−0.801050	−	0.598597i	$-0.795725\pi$
$547$		−	28.0000i		−	1.19719i	0.801050	−	0.598597i	$-0.204275\pi$
$548$		−	2.00000i		−	0.0854358i
$549$		0			0
$550$	−12.0000	−	9.00000i	−0.511682	−	0.383761i
$551$	2.00000			0.0852029
$552$		0			0
$553$			3.00000i			0.127573i
$554$	2.00000			0.0849719
$555$		0			0
$556$	−20.0000			−0.848189
$557$			9.00000i			0.381342i	0.981654	+	0.190671i	$0.0610664\pi$
$557$			9.00000i			0.381342i	−0.981654	+	0.190671i	$0.938934\pi$
$558$		0			0
$559$	−20.0000			−0.845910
$560$	2.00000	−	1.00000i	0.0845154	−	0.0422577i
$561$		0			0
$562$			32.0000i			1.34984i
$563$		−	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
$565$	−30.0000	+	15.0000i	−1.26211	+	0.631055i
$566$	−14.0000			−0.588464
$567$		0			0
$568$		−	5.00000i		−	0.209795i
$569$	−39.0000			−1.63497			−0.817483	−	0.575953i	$-0.804631\pi$
$569$	−39.0000			−1.63497			−0.817483	+	0.575953i	$0.804631\pi$
$570$		0			0
$571$	26.0000			1.08807			0.544033	−	0.839064i	$-0.316897\pi$
$571$	26.0000			1.08807			0.544033	+	0.839064i	$0.316897\pi$
$572$			12.0000i			0.501745i
$573$		0			0
$574$	10.0000			0.417392
$575$	20.0000	+	15.0000i	0.834058	+	0.625543i
$576$		0			0
$577$			34.0000i			1.41544i	0.706494	+	0.707719i	$0.250276\pi$
$577$			34.0000i			1.41544i	−0.706494	+	0.707719i	$0.749724\pi$
$578$			17.0000i			0.707107i
$579$		0			0
$580$	−2.00000	−	4.00000i	−0.0830455	−	0.166091i
$581$	2.00000			0.0829740
$582$		0			0
$583$		−	15.0000i		−	0.621237i
$584$	−7.00000			−0.289662
$585$		0			0
$586$	−18.0000			−0.743573
$587$			6.00000i			0.247647i	0.992304	+	0.123823i	$0.0395156\pi$
$587$			6.00000i			0.247647i	−0.992304	+	0.123823i	$0.960484\pi$
$588$		0			0
$589$	−1.00000			−0.0412043
$590$	12.0000	−	6.00000i	0.494032	−	0.247016i
$591$		0			0
$592$		−	4.00000i		−	0.164399i
$593$		−	6.00000i		−	0.246390i	−0.992382	−	0.123195i	$-0.960686\pi$
$593$		−	6.00000i		−	0.246390i	0.992382	−	0.123195i	$-0.0393141\pi$
$594$		0			0
$595$		0			0
$596$	−15.0000			−0.614424
$597$		0			0
$598$		−	20.0000i		−	0.817861i
$599$	13.0000			0.531166			0.265583	−	0.964088i	$-0.414436\pi$
$599$	13.0000			0.531166			0.265583	+	0.964088i	$0.414436\pi$
$600$		0			0
$601$	−44.0000			−1.79480			−0.897399	−	0.441221i	$-0.854546\pi$
$601$	−44.0000			−1.79480			−0.897399	+	0.441221i	$0.854546\pi$
$602$		−	5.00000i		−	0.203785i
$603$		0			0
$604$	16.0000			0.651031
$605$	−2.00000	−	4.00000i	−0.0813116	−	0.162623i
$606$		0			0
$607$			27.0000i			1.09590i	0.836512	+	0.547948i	$0.184591\pi$
$607$			27.0000i			1.09590i	−0.836512	+	0.547948i	$0.815409\pi$
$608$			1.00000i			0.0405554i
$609$		0			0
$610$	4.00000	−	2.00000i	0.161955	−	0.0809776i
$611$	−32.0000			−1.29458
$612$		0			0
$613$			24.0000i			0.969351i	0.874694	+	0.484675i	$0.161062\pi$
$613$			24.0000i			0.969351i	−0.874694	+	0.484675i	$0.838938\pi$
$614$	−4.00000			−0.161427
$615$		0			0
$616$	−3.00000			−0.120873
$617$			5.00000i			0.201292i	0.994922	+	0.100646i	$0.0320910\pi$
$617$			5.00000i			0.201292i	−0.994922	+	0.100646i	$0.967909\pi$
$618$		0			0
$619$	12.0000			0.482321			0.241160	−	0.970485i	$-0.422472\pi$
$619$	12.0000			0.482321			0.241160	+	0.970485i	$0.422472\pi$
$620$	1.00000	+	2.00000i	0.0401610	+	0.0803219i
$621$		0			0
$622$		−	16.0000i		−	0.641542i
$623$		−	1.00000i		−	0.0400642i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	6.00000			0.239808
$627$		0			0
$628$			9.00000i			0.359139i
$629$		0			0
$630$		0			0
$631$	25.0000			0.995234			0.497617	−	0.867397i	$-0.334208\pi$
$631$	25.0000			0.995234			0.497617	+	0.867397i	$0.334208\pi$
$632$			3.00000i			0.119334i
$633$		0			0
$634$	−18.0000			−0.714871
$635$	16.0000	−	8.00000i	0.634941	−	0.317470i
$636$		0			0
$637$		−	24.0000i		−	0.950915i
$638$			6.00000i			0.237542i
$639$		0			0
$640$	2.00000	−	1.00000i	0.0790569	−	0.0395285i
$641$	−50.0000			−1.97488			−0.987441	−	0.157991i	$-0.949498\pi$
$641$	−50.0000			−1.97488			−0.987441	+	0.157991i	$0.949498\pi$
$642$		0			0
$643$		−	7.00000i		−	0.276053i	−0.990429	−	0.138027i	$-0.955924\pi$
$643$		−	7.00000i		−	0.276053i	0.990429	−	0.138027i	$-0.0440759\pi$
$644$	5.00000			0.197028
$645$		0			0
$646$		0			0
$647$			7.00000i			0.275198i	0.990488	+	0.137599i	$0.0439386\pi$
$647$			7.00000i			0.275198i	−0.990488	+	0.137599i	$0.956061\pi$
$648$		0			0
$649$	−18.0000			−0.706562
$650$	−12.0000	+	16.0000i	−0.470679	+	0.627572i
$651$		0			0
$652$			4.00000i			0.156652i
$653$			42.0000i			1.64359i	0.569785	+	0.821794i	$0.307026\pi$
$653$			42.0000i			1.64359i	−0.569785	+	0.821794i	$0.692974\pi$
$654$		0			0
$655$	2.00000	+	4.00000i	0.0781465	+	0.156293i
$656$	10.0000			0.390434
$657$		0			0
$658$		−	8.00000i		−	0.311872i
$659$	6.00000			0.233727			0.116863	−	0.993148i	$-0.462716\pi$
$659$	6.00000			0.233727			0.116863	+	0.993148i	$0.462716\pi$
$660$		0			0
$661$	36.0000			1.40024			0.700119	−	0.714026i	$-0.253130\pi$
$661$	36.0000			1.40024			0.700119	+	0.714026i	$0.253130\pi$
$662$			8.00000i			0.310929i
$663$		0			0
$664$	2.00000			0.0776151
$665$	2.00000	−	1.00000i	0.0775567	−	0.0387783i
$666$		0			0
$667$		−	10.0000i		−	0.387202i
$668$		−	21.0000i		−	0.812514i
$669$		0			0
$670$	2.00000	+	4.00000i	0.0772667	+	0.154533i
$671$	−6.00000			−0.231627
$672$		0			0
$673$		−	30.0000i		−	1.15642i	−0.815890	−	0.578208i	$-0.803752\pi$
$673$		−	30.0000i		−	1.15642i	0.815890	−	0.578208i	$-0.196248\pi$
$674$	−34.0000			−1.30963
$675$		0			0
$676$	3.00000			0.115385
$677$			13.0000i			0.499631i	0.968294	+	0.249815i	$0.0803699\pi$
$677$			13.0000i			0.499631i	−0.968294	+	0.249815i	$0.919630\pi$
$678$		0			0
$679$	10.0000			0.383765
$680$		0			0
$681$		0			0
$682$		−	3.00000i		−	0.114876i
$683$		−	35.0000i		−	1.33924i	−0.742705	−	0.669619i	$-0.766457\pi$
$683$		−	35.0000i		−	1.33924i	0.742705	−	0.669619i	$-0.233543\pi$
$684$		0			0
$685$	−4.00000	+	2.00000i	−0.152832	+	0.0764161i
$686$	13.0000			0.496342
$687$		0			0
$688$		−	5.00000i		−	0.190623i
$689$	−20.0000			−0.761939
$690$		0			0
$691$	−41.0000			−1.55971			−0.779857	−	0.625958i	$-0.784708\pi$
$691$	−41.0000			−1.55971			−0.779857	+	0.625958i	$0.784708\pi$
$692$		−	2.00000i		−	0.0760286i
$693$		0			0
$694$	22.0000			0.835109
$695$	20.0000	+	40.0000i	0.758643	+	1.51729i
$696$		0			0
$697$		0			0
$698$		−	20.0000i		−	0.757011i
$699$		0			0
$700$	−4.00000	−	3.00000i	−0.151186	−	0.113389i
$701$	35.0000			1.32193			0.660966	−	0.750416i	$-0.270147\pi$
$701$	35.0000			1.32193			0.660966	+	0.750416i	$0.270147\pi$
$702$		0			0
$703$		−	4.00000i		−	0.150863i
$704$	−3.00000			−0.113067
$705$		0			0
$706$	24.0000			0.903252
$707$		−	15.0000i		−	0.564133i
$708$		0			0
$709$	−5.00000			−0.187779			−0.0938895	−	0.995583i	$-0.529930\pi$
$709$	−5.00000			−0.187779			−0.0938895	+	0.995583i	$0.529930\pi$
$710$	−10.0000	+	5.00000i	−0.375293	+	0.187647i
$711$		0			0
$712$		−	1.00000i		−	0.0374766i
$713$			5.00000i			0.187251i
$714$		0			0
$715$	24.0000	−	12.0000i	0.897549	−	0.448775i
$716$		0			0
$717$		0			0
$718$			3.00000i			0.111959i
$719$	10.0000			0.372937			0.186469	−	0.982461i	$-0.440296\pi$
$719$	10.0000			0.372937			0.186469	+	0.982461i	$0.440296\pi$
$720$		0			0
$721$		0			0
$722$		−	18.0000i		−	0.669891i
$723$		0			0
$724$	5.00000			0.185824
$725$	−6.00000	+	8.00000i	−0.222834	+	0.297113i
$726$		0			0
$727$		−	49.0000i		−	1.81731i	−0.417548	−	0.908655i	$-0.637111\pi$
$727$		−	49.0000i		−	1.81731i	0.417548	−	0.908655i	$-0.362889\pi$
$728$			4.00000i			0.148250i
$729$		0			0
$730$	7.00000	+	14.0000i	0.259082	+	0.518163i
$731$		0			0
$732$		0			0
$733$		−	22.0000i		−	0.812589i	−0.913742	−	0.406294i	$-0.866821\pi$
$733$		−	22.0000i		−	0.812589i	0.913742	−	0.406294i	$-0.133179\pi$
$734$	14.0000			0.516749
$735$		0			0
$736$	5.00000			0.184302
$737$		−	6.00000i		−	0.221013i
$738$		0			0
$739$	18.0000			0.662141			0.331070	−	0.943606i	$-0.392590\pi$
$739$	18.0000			0.662141			0.331070	+	0.943606i	$0.392590\pi$
$740$	−8.00000	+	4.00000i	−0.294086	+	0.147043i
$741$		0			0
$742$		−	5.00000i		−	0.183556i
$743$		−	15.0000i		−	0.550297i	−0.961402	−	0.275148i	$-0.911273\pi$
$743$		−	15.0000i		−	0.550297i	0.961402	−	0.275148i	$-0.0887270\pi$
$744$		0			0
$745$	15.0000	+	30.0000i	0.549557	+	1.09911i
$746$	11.0000			0.402739
$747$		0			0
$748$		0			0
$749$	19.0000			0.694245
$750$		0			0
$751$	22.0000			0.802791			0.401396	−	0.915905i	$-0.368525\pi$
$751$	22.0000			0.802791			0.401396	+	0.915905i	$0.368525\pi$
$752$		−	8.00000i		−	0.291730i
$753$		0			0
$754$	8.00000			0.291343
$755$	−16.0000	−	32.0000i	−0.582300	−	1.16460i
$756$		0			0
$757$		−	20.0000i		−	0.726912i	−0.931611	−	0.363456i	$-0.881597\pi$
$757$		−	20.0000i		−	0.726912i	0.931611	−	0.363456i	$-0.118403\pi$
$758$			15.0000i			0.544825i
$759$		0			0
$760$	2.00000	−	1.00000i	0.0725476	−	0.0362738i
$761$	−21.0000			−0.761249			−0.380625	−	0.924730i	$-0.624291\pi$
$761$	−21.0000			−0.761249			−0.380625	+	0.924730i	$0.624291\pi$
$762$		0			0
$763$			2.00000i			0.0724049i
$764$	−16.0000			−0.578860
$765$		0			0
$766$	28.0000			1.01168
$767$			24.0000i			0.866590i
$768$		0			0
$769$	−45.0000			−1.62274			−0.811371	−	0.584532i	$-0.801278\pi$
$769$	−45.0000			−1.62274			−0.811371	+	0.584532i	$0.801278\pi$
$770$	3.00000	+	6.00000i	0.108112	+	0.216225i
$771$		0			0
$772$			10.0000i			0.359908i
$773$			29.0000i			1.04306i	0.853234	+	0.521529i	$0.174638\pi$
$773$			29.0000i			1.04306i	−0.853234	+	0.521529i	$0.825362\pi$
$774$		0			0
$775$	3.00000	−	4.00000i	0.107763	−	0.143684i
$776$	10.0000			0.358979
$777$		0			0
$778$		−	28.0000i		−	1.00385i
$779$	10.0000			0.358287
$780$		0			0
$781$	15.0000			0.536742
$782$		0			0
$783$		0			0
$784$	6.00000			0.214286
$785$	18.0000	−	9.00000i	0.642448	−	0.321224i
$786$		0			0
$787$		−	27.0000i		−	0.962446i	−0.876598	−	0.481223i	$-0.840193\pi$
$787$		−	27.0000i		−	0.962446i	0.876598	−	0.481223i	$-0.159807\pi$
$788$		−	18.0000i		−	0.641223i
$789$		0			0
$790$	6.00000	−	3.00000i	0.213470	−	0.106735i
$791$	15.0000			0.533339
$792$		0			0
$793$			8.00000i			0.284088i
$794$	−31.0000			−1.10015
$795$		0			0
$796$	−21.0000			−0.744325
$797$		−	22.0000i		−	0.779280i	−0.920967	−	0.389640i	$-0.872599\pi$
$797$		−	22.0000i		−	0.779280i	0.920967	−	0.389640i	$-0.127401\pi$
$798$		0			0
$799$		0			0
$800$	−4.00000	−	3.00000i	−0.141421	−	0.106066i
$801$		0			0
$802$		−	5.00000i		−	0.176556i
$803$		−	21.0000i		−	0.741074i
$804$		0			0
$805$	−5.00000	−	10.0000i	−0.176227	−	0.352454i
$806$	−4.00000			−0.140894
$807$		0			0
$808$		−	15.0000i		−	0.527698i
$809$	9.00000			0.316423			0.158212	−	0.987405i	$-0.449427\pi$
$809$	9.00000			0.316423			0.158212	+	0.987405i	$0.449427\pi$
$810$		0			0
$811$	35.0000			1.22902			0.614508	−	0.788911i	$-0.289355\pi$
$811$	35.0000			1.22902			0.614508	+	0.788911i	$0.289355\pi$
$812$			2.00000i			0.0701862i
$813$		0			0
$814$	12.0000			0.420600
$815$	8.00000	−	4.00000i	0.280228	−	0.140114i
$816$		0			0
$817$		−	5.00000i		−	0.174928i
$818$		−	4.00000i		−	0.139857i
$819$		0			0
$820$	−10.0000	−	20.0000i	−0.349215	−	0.698430i
$821$	−18.0000			−0.628204			−0.314102	−	0.949389i	$-0.601703\pi$
$821$	−18.0000			−0.628204			−0.314102	+	0.949389i	$0.601703\pi$
$822$		0			0
$823$		−	6.00000i		−	0.209147i	−0.994517	−	0.104573i	$-0.966652\pi$
$823$		−	6.00000i		−	0.209147i	0.994517	−	0.104573i	$-0.0333477\pi$
$824$		0			0
$825$		0			0
$826$	−6.00000			−0.208767
$827$			14.0000i			0.486828i	0.969923	+	0.243414i	$0.0782673\pi$
$827$			14.0000i			0.486828i	−0.969923	+	0.243414i	$0.921733\pi$
$828$		0			0
$829$	25.0000			0.868286			0.434143	−	0.900844i	$-0.357051\pi$
$829$	25.0000			0.868286			0.434143	+	0.900844i	$0.357051\pi$
$830$	−2.00000	−	4.00000i	−0.0694210	−	0.138842i
$831$		0			0
$832$			4.00000i			0.138675i
$833$		0			0
$834$		0			0
$835$	−42.0000	+	21.0000i	−1.45347	+	0.726735i
$836$	−3.00000			−0.103757
$837$		0			0
$838$		−	18.0000i		−	0.621800i
$839$	39.0000			1.34643			0.673215	−	0.739447i	$-0.264913\pi$
$839$	39.0000			1.34643			0.673215	+	0.739447i	$0.264913\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$		−	14.0000i		−	0.482472i
$843$		0			0
$844$	−7.00000			−0.240950
$845$	−3.00000	−	6.00000i	−0.103203	−	0.206406i
$846$		0			0
$847$			2.00000i			0.0687208i
$848$		−	5.00000i		−	0.171701i
$849$		0			0
$850$		0			0
$851$	−20.0000			−0.685591
$852$		0			0
$853$		−	55.0000i		−	1.88316i	−0.336784	−	0.941582i	$-0.609339\pi$
$853$		−	55.0000i		−	1.88316i	0.336784	−	0.941582i	$-0.390661\pi$
$854$	−2.00000			−0.0684386
$855$		0			0
$856$	19.0000			0.649407
$857$		−	22.0000i		−	0.751506i	−0.926720	−	0.375753i	$-0.877384\pi$
$857$		−	22.0000i		−	0.751506i	0.926720	−	0.375753i	$-0.122616\pi$
$858$		0			0
$859$	32.0000			1.09183			0.545913	−	0.837842i	$-0.316183\pi$
$859$	32.0000			1.09183			0.545913	+	0.837842i	$0.316183\pi$
$860$	−10.0000	+	5.00000i	−0.340997	+	0.170499i
$861$		0			0
$862$		0			0
$863$			29.0000i			0.987171i	0.869697	+	0.493586i	$0.164314\pi$
$863$			29.0000i			0.987171i	−0.869697	+	0.493586i	$0.835686\pi$
$864$		0			0
$865$	−4.00000	+	2.00000i	−0.136004	+	0.0680020i
$866$	−19.0000			−0.645646
$867$		0			0
$868$		−	1.00000i		−	0.0339422i
$869$	−9.00000			−0.305304
$870$		0			0
$871$	−8.00000			−0.271070
$872$			2.00000i			0.0677285i
$873$		0			0
$874$	5.00000			0.169128
$875$	−2.00000	+	11.0000i	−0.0676123	+	0.371868i
$876$		0			0
$877$		−	42.0000i		−	1.41824i	−0.705088	−	0.709120i	$-0.749093\pi$
$877$		−	42.0000i		−	1.41824i	0.705088	−	0.709120i	$-0.250907\pi$
$878$		−	20.0000i		−	0.674967i
$879$		0			0
$880$	3.00000	+	6.00000i	0.101130	+	0.202260i
$881$	−42.0000			−1.41502			−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000			−1.41502			−0.707508	+	0.706705i	$0.750181\pi$
$882$		0			0
$883$		−	35.0000i		−	1.17784i	−0.808190	−	0.588922i	$-0.799553\pi$
$883$		−	35.0000i		−	1.17784i	0.808190	−	0.588922i	$-0.200447\pi$
$884$		0			0
$885$		0			0
$886$	29.0000			0.974274
$887$		0			0		1.00000			$0$
$887$		0			0		−1.00000			$\pi$
$888$		0			0
$889$	−8.00000			−0.268311
$890$	−2.00000	+	1.00000i	−0.0670402	+	0.0335201i
$891$		0			0
$892$			20.0000i			0.669650i
$893$		−	8.00000i		−	0.267710i
$894$		0			0
$895$		0			0
$896$	−1.00000			−0.0334077
$897$		0			0
$898$			2.00000i			0.0667409i
$899$	−2.00000			−0.0667037
$900$		0			0
$901$		0			0
$902$			30.0000i			0.998891i
$903$		0			0
$904$	15.0000			0.498893
$905$	−5.00000	−	10.0000i	−0.166206	−	0.332411i
$906$		0			0
$907$			36.0000i			1.19536i	0.801735	+	0.597680i	$0.203911\pi$
$907$			36.0000i			1.19536i	−0.801735	+	0.597680i	$0.796089\pi$
$908$			9.00000i			0.298675i
$909$		0			0
$910$	8.00000	−	4.00000i	0.265197	−	0.132599i
$911$	46.0000			1.52405			0.762024	−	0.647549i	$-0.224206\pi$
$911$	46.0000			1.52405			0.762024	+	0.647549i	$0.224206\pi$
$912$		0			0
$913$			6.00000i			0.198571i
$914$	30.0000			0.992312
$915$		0			0
$916$	15.0000			0.495614
$917$		−	2.00000i		−	0.0660458i
$918$		0			0
$919$	−20.0000			−0.659739			−0.329870	−	0.944027i	$-0.607005\pi$
$919$	−20.0000			−0.659739			−0.329870	+	0.944027i	$0.607005\pi$
$920$	−5.00000	−	10.0000i	−0.164845	−	0.329690i
$921$		0			0
$922$		−	16.0000i		−	0.526932i
$923$		−	20.0000i		−	0.658308i
$924$		0			0
$925$	16.0000	+	12.0000i	0.526077	+	0.394558i
$926$	14.0000			0.460069
$927$		0			0
$928$			2.00000i			0.0656532i
$929$	−1.00000			−0.0328089			−0.0164045	−	0.999865i	$-0.505222\pi$
$929$	−1.00000			−0.0328089			−0.0164045	+	0.999865i	$0.505222\pi$
$930$		0			0
$931$	6.00000			0.196642
$932$		−	21.0000i		−	0.687878i
$933$		0			0
$934$	−28.0000			−0.916188
$935$		0			0
$936$		0			0
$937$			2.00000i			0.0653372i	0.999466	+	0.0326686i	$0.0104006\pi$
$937$			2.00000i			0.0653372i	−0.999466	+	0.0326686i	$0.989599\pi$
$938$		−	2.00000i		−	0.0653023i
$939$		0			0
$940$	−16.0000	+	8.00000i	−0.521862	+	0.260931i
$941$	−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
$943$		−	50.0000i		−	1.62822i
$944$	−6.00000			−0.195283
$945$		0			0
$946$	15.0000			0.487692
$947$			46.0000i			1.49480i	0.664375	+	0.747400i	$0.268698\pi$
$947$			46.0000i			1.49480i	−0.664375	+	0.747400i	$0.731302\pi$
$948$		0			0
$949$	−28.0000			−0.908918
$950$	−4.00000	−	3.00000i	−0.129777	−	0.0973329i
$951$		0			0
$952$		0			0
$953$			28.0000i			0.907009i	0.891254	+	0.453504i	$0.149826\pi$
$953$			28.0000i			0.907009i	−0.891254	+	0.453504i	$0.850174\pi$
$954$		0			0
$955$	16.0000	+	32.0000i	0.517748	+	1.03550i
$956$	14.0000			0.452792
$957$		0			0
$958$		−	25.0000i		−	0.807713i
$959$	2.00000			0.0645834
$960$		0			0
$961$	1.00000			0.0322581
$962$		−	16.0000i		−	0.515861i
$963$		0			0
$964$	12.0000			0.386494
$965$	20.0000	−	10.0000i	0.643823	−	0.321911i
$966$		0			0
$967$			8.00000i			0.257263i	0.991692	+	0.128631i	$0.0410584\pi$
$967$			8.00000i			0.257263i	−0.991692	+	0.128631i	$0.958942\pi$
$968$			2.00000i			0.0642824i
$969$		0			0
$970$	−10.0000	−	20.0000i	−0.321081	−	0.642161i
$971$	18.0000			0.577647			0.288824	−	0.957382i	$-0.406736\pi$
$971$	18.0000			0.577647			0.288824	+	0.957382i	$0.406736\pi$
$972$		0			0
$973$		−	20.0000i		−	0.641171i
$974$	−4.00000			−0.128168
$975$		0			0
$976$	−2.00000			−0.0640184
$977$			6.00000i			0.191957i	0.995383	+	0.0959785i	$0.0305980\pi$
$977$			6.00000i			0.191957i	−0.995383	+	0.0959785i	$0.969402\pi$
$978$		0			0
$979$	3.00000			0.0958804
$980$	−6.00000	−	12.0000i	−0.191663	−	0.383326i
$981$		0			0
$982$		−	33.0000i		−	1.05307i
$983$			36.0000i			1.14822i	0.818778	+	0.574111i	$0.194652\pi$
$983$			36.0000i			1.14822i	−0.818778	+	0.574111i	$0.805348\pi$
$984$		0			0
$985$	−36.0000	+	18.0000i	−1.14706	+	0.573528i
$986$		0			0
$987$		0			0
$988$			4.00000i			0.127257i
$989$	−25.0000			−0.794954
$990$		0			0
$991$	−53.0000			−1.68360			−0.841800	−	0.539789i	$-0.818504\pi$
$991$	−53.0000			−1.68360			−0.841800	+	0.539789i	$0.818504\pi$
$992$		−	1.00000i		−	0.0317500i
$993$		0			0
$994$	5.00000			0.158590
$995$	21.0000	+	42.0000i	0.665745	+	1.33149i
$996$		0			0
$997$		−	6.00000i		−	0.190022i	−0.995476	−	0.0950110i	$-0.969711\pi$
$997$		−	6.00000i		−	0.190022i	0.995476	−	0.0950110i	$-0.0302886\pi$
$998$		−	22.0000i		−	0.696398i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.d.a.559.1	✓	2	3.2	odd	2
930.2.d.a.559.2	yes	2	15.14	odd	2
2790.2.d.f.559.1		2	5.4	even	2	inner
2790.2.d.f.559.2		2	1.1	even	1	trivial
4650.2.a.p.1.1		1	15.8	even	4
4650.2.a.bc.1.1		1	15.2	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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} -1.00000i q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} -1.00000i q^{7} -1.00000i q^{8} +(-2.00000 + 1.00000i) q^{10} +3.00000 q^{11} -4.00000i q^{13} +1.00000 q^{14} +1.00000 q^{16} +1.00000 q^{19} +(-1.00000 - 2.00000i) q^{20} +3.00000i q^{22} -5.00000i q^{23} +(-3.00000 + 4.00000i) q^{25} +4.00000 q^{26} +1.00000i q^{28} +2.00000 q^{29} -1.00000 q^{31} +1.00000i q^{32} +(2.00000 - 1.00000i) q^{35} -4.00000i q^{37} +1.00000i q^{38} +(2.00000 - 1.00000i) q^{40} +10.0000 q^{41} -5.00000i q^{43} -3.00000 q^{44} +5.00000 q^{46} -8.00000i q^{47} +6.00000 q^{49} +(-4.00000 - 3.00000i) q^{50} +4.00000i q^{52} -5.00000i q^{53} +(3.00000 + 6.00000i) q^{55} -1.00000 q^{56} +2.00000i q^{58} -6.00000 q^{59} -2.00000 q^{61} -1.00000i q^{62} -1.00000 q^{64} +(8.00000 - 4.00000i) q^{65} -2.00000i q^{67} +(1.00000 + 2.00000i) q^{70} +5.00000 q^{71} -7.00000i q^{73} +4.00000 q^{74} -1.00000 q^{76} -3.00000i q^{77} -3.00000 q^{79} +(1.00000 + 2.00000i) q^{80} +10.0000i q^{82} +2.00000i q^{83} +5.00000 q^{86} -3.00000i q^{88} +1.00000 q^{89} -4.00000 q^{91} +5.00000i q^{92} +8.00000 q^{94} +(1.00000 + 2.00000i) q^{95} +10.0000i q^{97} +6.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} + 2 q^{5}+O(q^{10}) \) 2 * q - 2 * q^4 + 2 * q^5	\( 2 q - 2 q^{4} + 2 q^{5} - 4 q^{10} + 6 q^{11} + 2 q^{14} + 2 q^{16} + 2 q^{19} - 2 q^{20} - 6 q^{25} + 8 q^{26} + 4 q^{29} - 2 q^{31} + 4 q^{35} + 4 q^{40} + 20 q^{41} - 6 q^{44} + 10 q^{46} + 12 q^{49} - 8 q^{50} + 6 q^{55} - 2 q^{56} - 12 q^{59} - 4 q^{61} - 2 q^{64} + 16 q^{65} + 2 q^{70} + 10 q^{71} + 8 q^{74} - 2 q^{76} - 6 q^{79} + 2 q^{80} + 10 q^{86} + 2 q^{89} - 8 q^{91} + 16 q^{94} + 2 q^{95}+O(q^{100}) \) 2 * q - 2 * q^4 + 2 * q^5 - 4 * q^10 + 6 * q^11 + 2 * q^14 + 2 * q^16 + 2 * q^19 - 2 * q^20 - 6 * q^25 + 8 * q^26 + 4 * q^29 - 2 * q^31 + 4 * q^35 + 4 * q^40 + 20 * q^41 - 6 * q^44 + 10 * q^46 + 12 * q^49 - 8 * q^50 + 6 * q^55 - 2 * q^56 - 12 * q^59 - 4 * q^61 - 2 * q^64 + 16 * q^65 + 2 * q^70 + 10 * q^71 + 8 * q^74 - 2 * q^76 - 6 * q^79 + 2 * q^80 + 10 * q^86 + 2 * q^89 - 8 * q^91 + 16 * q^94 + 2 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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