LMFDB - Embedded newform 1800.2.k.d.901.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1800,2,Mod(901,1800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1800, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1800.901");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1800.k (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:	$14.3730723638$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-7}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 2 $ x^2 - x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			901.1
Root			$0.500000 - 1.32288i$ of defining polynomial
Character	$\chi$	$=$	1800.901
Dual form			1800.2.k.d.901.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 1.32288i) q^{2} +(-1.50000 + 1.32288i) q^{4} +4.00000 q^{7} +(2.50000 + 1.32288i) q^{8} +O(q^{10})$	\(q+(-0.500000 - 1.32288i) q^{2} +(-1.50000 + 1.32288i) q^{4} +4.00000 q^{7} +(2.50000 + 1.32288i) q^{8} +2.64575i q^{11} +(-2.00000 - 5.29150i) q^{14} +(0.500000 - 3.96863i) q^{16} +3.00000 q^{17} -2.64575i q^{19} +(3.50000 - 1.32288i) q^{22} -4.00000 q^{23} +(-6.00000 + 5.29150i) q^{28} +4.00000 q^{31} +(-5.50000 + 1.32288i) q^{32} +(-1.50000 - 3.96863i) q^{34} +10.5830i q^{37} +(-3.50000 + 1.32288i) q^{38} +5.00000 q^{41} +5.29150i q^{43} +(-3.50000 - 3.96863i) q^{44} +(2.00000 + 5.29150i) q^{46} +8.00000 q^{47} +9.00000 q^{49} +10.5830i q^{53} +(10.0000 + 5.29150i) q^{56} +5.29150i q^{59} -10.5830i q^{61} +(-2.00000 - 5.29150i) q^{62} +(4.50000 + 6.61438i) q^{64} -7.93725i q^{67} +(-4.50000 + 3.96863i) q^{68} -8.00000 q^{71} -7.00000 q^{73} +(14.0000 - 5.29150i) q^{74} +(3.50000 + 3.96863i) q^{76} +10.5830i q^{77} +4.00000 q^{79} +(-2.50000 - 6.61438i) q^{82} +7.93725i q^{83} +(7.00000 - 2.64575i) q^{86} +(-3.50000 + 6.61438i) q^{88} +1.00000 q^{89} +(6.00000 - 5.29150i) q^{92} +(-4.00000 - 10.5830i) q^{94} -2.00000 q^{97} +(-4.50000 - 11.9059i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 3 q^{4} + 8 q^{7} + 5 q^{8}+O(q^{10}) $ 2 * q - q^2 - 3 * q^4 + 8 * q^7 + 5 * q^8	$ 2 q - q^{2} - 3 q^{4} + 8 q^{7} + 5 q^{8} - 4 q^{14} + q^{16} + 6 q^{17} + 7 q^{22} - 8 q^{23} - 12 q^{28} + 8 q^{31} - 11 q^{32} - 3 q^{34} - 7 q^{38} + 10 q^{41} - 7 q^{44} + 4 q^{46} + 16 q^{47} + 18 q^{49} + 20 q^{56} - 4 q^{62} + 9 q^{64} - 9 q^{68} - 16 q^{71} - 14 q^{73} + 28 q^{74} + 7 q^{76} + 8 q^{79} - 5 q^{82} + 14 q^{86} - 7 q^{88} + 2 q^{89} + 12 q^{92} - 8 q^{94} - 4 q^{97} - 9 q^{98}+O(q^{100}) $ 2 * q - q^2 - 3 * q^4 + 8 * q^7 + 5 * q^8 - 4 * q^14 + q^16 + 6 * q^17 + 7 * q^22 - 8 * q^23 - 12 * q^28 + 8 * q^31 - 11 * q^32 - 3 * q^34 - 7 * q^38 + 10 * q^41 - 7 * q^44 + 4 * q^46 + 16 * q^47 + 18 * q^49 + 20 * q^56 - 4 * q^62 + 9 * q^64 - 9 * q^68 - 16 * q^71 - 14 * q^73 + 28 * q^74 + 7 * q^76 + 8 * q^79 - 5 * q^82 + 14 * q^86 - 7 * q^88 + 2 * q^89 + 12 * q^92 - 8 * q^94 - 4 * q^97 - 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1001$	$1351$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$	−0.500000	−	1.32288i	−0.353553	−	0.935414i
$2$	−0.500000	−	1.32288i	−0.353553	−	0.935414i
$3$		0			0
$3$		0			0
$4$	−1.50000	+	1.32288i	−0.750000	+	0.661438i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	4.00000			1.51186			0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000			1.51186			0.755929	+	0.654654i	$0.227186\pi$
$8$	2.50000	+	1.32288i	0.883883	+	0.467707i
$9$		0			0
$10$		0			0
$11$			2.64575i			0.797724i	0.917011	+	0.398862i	$0.130595\pi$
$11$			2.64575i			0.797724i	−0.917011	+	0.398862i	$0.869405\pi$
$12$		0			0
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$	−2.00000	−	5.29150i	−0.534522	−	1.41421i
$15$		0			0
$16$	0.500000	−	3.96863i	0.125000	−	0.992157i
$17$	3.00000			0.727607			0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000			0.727607			0.363803	+	0.931476i	$0.381478\pi$
$18$		0			0
$19$		−	2.64575i		−	0.606977i	−0.952835	−	0.303488i	$-0.901849\pi$
$19$		−	2.64575i		−	0.606977i	0.952835	−	0.303488i	$-0.0981514\pi$
$20$		0			0
$21$		0			0
$22$	3.50000	−	1.32288i	0.746203	−	0.282038i
$23$	−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
$25$		0			0
$26$		0			0
$27$		0			0
$28$	−6.00000	+	5.29150i	−1.13389	+	1.00000i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	−5.50000	+	1.32288i	−0.972272	+	0.233854i
$33$		0			0
$34$	−1.50000	−	3.96863i	−0.257248	−	0.680614i
$35$		0			0
$36$		0			0
$37$			10.5830i			1.73984i	0.493197	+	0.869918i	$0.335828\pi$
$37$			10.5830i			1.73984i	−0.493197	+	0.869918i	$0.664172\pi$
$38$	−3.50000	+	1.32288i	−0.567775	+	0.214599i
$39$		0			0
$40$		0			0
$41$	5.00000			0.780869			0.390434	−	0.920631i	$-0.372325\pi$
$41$	5.00000			0.780869			0.390434	+	0.920631i	$0.372325\pi$
$42$		0			0
$43$			5.29150i			0.806947i	0.914991	+	0.403473i	$0.132197\pi$
$43$			5.29150i			0.806947i	−0.914991	+	0.403473i	$0.867803\pi$
$44$	−3.50000	−	3.96863i	−0.527645	−	0.598293i
$45$		0			0
$46$	2.00000	+	5.29150i	0.294884	+	0.780189i
$47$	8.00000			1.16692			0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000			1.16692			0.583460	+	0.812142i	$0.301699\pi$
$48$		0			0
$49$	9.00000			1.28571
$50$		0			0
$51$		0			0
$52$		0			0
$53$			10.5830i			1.45369i	0.686803	+	0.726844i	$0.259014\pi$
$53$			10.5830i			1.45369i	−0.686803	+	0.726844i	$0.740986\pi$
$54$		0			0
$55$		0			0
$56$	10.0000	+	5.29150i	1.33631	+	0.707107i
$57$		0			0
$58$		0			0
$59$			5.29150i			0.688895i	0.938806	+	0.344447i	$0.111934\pi$
$59$			5.29150i			0.688895i	−0.938806	+	0.344447i	$0.888066\pi$
$60$		0			0
$61$		−	10.5830i		−	1.35501i	−0.735516	−	0.677507i	$-0.763060\pi$
$61$		−	10.5830i		−	1.35501i	0.735516	−	0.677507i	$-0.236940\pi$
$62$	−2.00000	−	5.29150i	−0.254000	−	0.672022i
$63$		0			0
$64$	4.50000	+	6.61438i	0.562500	+	0.826797i
$65$		0			0
$66$		0			0
$67$		−	7.93725i		−	0.969690i	−0.874600	−	0.484845i	$-0.838876\pi$
$67$		−	7.93725i		−	0.969690i	0.874600	−	0.484845i	$-0.161124\pi$
$68$	−4.50000	+	3.96863i	−0.545705	+	0.481267i
$69$		0			0
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$		0			0
$73$	−7.00000			−0.819288			−0.409644	−	0.912245i	$-0.634347\pi$
$73$	−7.00000			−0.819288			−0.409644	+	0.912245i	$0.634347\pi$
$74$	14.0000	−	5.29150i	1.62747	−	0.615125i
$75$		0			0
$76$	3.50000	+	3.96863i	0.401478	+	0.455233i
$77$			10.5830i			1.20605i
$78$		0			0
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$		0			0
$81$		0			0
$82$	−2.50000	−	6.61438i	−0.276079	−	0.730436i
$83$			7.93725i			0.871227i	0.900134	+	0.435613i	$0.143469\pi$
$83$			7.93725i			0.871227i	−0.900134	+	0.435613i	$0.856531\pi$
$84$		0			0
$85$		0			0
$86$	7.00000	−	2.64575i	0.754829	−	0.285299i
$87$		0			0
$88$	−3.50000	+	6.61438i	−0.373101	+	0.705095i
$89$	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
$91$		0			0
$92$	6.00000	−	5.29150i	0.625543	−	0.551677i
$93$		0			0
$94$	−4.00000	−	10.5830i	−0.412568	−	1.09155i
$95$		0			0
$96$		0			0
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$	−4.50000	−	11.9059i	−0.454569	−	1.20268i
$99$		0			0
$100$		0			0
$101$		−	10.5830i		−	1.05305i	−0.850160	−	0.526524i	$-0.823495\pi$
$101$		−	10.5830i		−	1.05305i	0.850160	−	0.526524i	$-0.176505\pi$
$102$		0			0
$103$	8.00000			0.788263			0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000			0.788263			0.394132	+	0.919054i	$0.371045\pi$
$104$		0			0
$105$		0			0
$106$	14.0000	−	5.29150i	1.35980	−	0.513956i
$107$		−	2.64575i		−	0.255774i	−0.991789	−	0.127887i	$-0.959180\pi$
$107$		−	2.64575i		−	0.255774i	0.991789	−	0.127887i	$-0.0408196\pi$
$108$		0			0
$109$		−	10.5830i		−	1.01367i	−0.862044	−	0.506834i	$-0.830816\pi$
$109$		−	10.5830i		−	1.01367i	0.862044	−	0.506834i	$-0.169184\pi$
$110$		0			0
$111$		0			0
$112$	2.00000	−	15.8745i	0.188982	−	1.50000i
$113$	15.0000			1.41108			0.705541	−	0.708669i	$-0.250704\pi$
$113$	15.0000			1.41108			0.705541	+	0.708669i	$0.250704\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$	7.00000	−	2.64575i	0.644402	−	0.243561i
$119$	12.0000			1.10004
$120$		0			0
$121$	4.00000			0.363636
$122$	−14.0000	+	5.29150i	−1.26750	+	0.479070i
$123$		0			0
$124$	−6.00000	+	5.29150i	−0.538816	+	0.475191i
$125$		0			0
$126$		0			0
$127$	12.0000			1.06483			0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000			1.06483			0.532414	+	0.846484i	$0.321285\pi$
$128$	6.50000	−	9.26013i	0.574524	−	0.818488i
$129$		0			0
$130$		0			0
$131$		−	15.8745i		−	1.38696i	−0.720475	−	0.693481i	$-0.756076\pi$
$131$		−	15.8745i		−	1.38696i	0.720475	−	0.693481i	$-0.243924\pi$
$132$		0			0
$133$		−	10.5830i		−	0.917663i
$134$	−10.5000	+	3.96863i	−0.907062	+	0.342837i
$135$		0			0
$136$	7.50000	+	3.96863i	0.643120	+	0.340307i
$137$	19.0000			1.62328			0.811640	−	0.584158i	$-0.198575\pi$
$137$	19.0000			1.62328			0.811640	+	0.584158i	$0.198575\pi$
$138$		0			0
$139$			18.5203i			1.57087i	0.618945	+	0.785434i	$0.287560\pi$
$139$			18.5203i			1.57087i	−0.618945	+	0.785434i	$0.712440\pi$
$140$		0			0
$141$		0			0
$142$	4.00000	+	10.5830i	0.335673	+	0.888106i
$143$		0			0
$144$		0			0
$145$		0			0
$146$	3.50000	+	9.26013i	0.289662	+	0.766374i
$147$		0			0
$148$	−14.0000	−	15.8745i	−1.15079	−	1.30488i
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$		0			0
$151$	4.00000			0.325515			0.162758	−	0.986666i	$-0.447961\pi$
$151$	4.00000			0.325515			0.162758	+	0.986666i	$0.447961\pi$
$152$	3.50000	−	6.61438i	0.283887	−	0.536497i
$153$		0			0
$154$	14.0000	−	5.29150i	1.12815	−	0.426401i
$155$		0			0
$156$		0			0
$157$		−	10.5830i		−	0.844616i	−0.906452	−	0.422308i	$-0.861220\pi$
$157$		−	10.5830i		−	0.844616i	0.906452	−	0.422308i	$-0.138780\pi$
$158$	−2.00000	−	5.29150i	−0.159111	−	0.420969i
$159$		0			0
$160$		0			0
$161$	−16.0000			−1.26098
$162$		0			0
$163$			13.2288i			1.03616i	0.855333	+	0.518078i	$0.173352\pi$
$163$			13.2288i			1.03616i	−0.855333	+	0.518078i	$0.826648\pi$
$164$	−7.50000	+	6.61438i	−0.585652	+	0.516496i
$165$		0			0
$166$	10.5000	−	3.96863i	0.814958	−	0.308025i
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$		0			0
$169$	13.0000			1.00000
$170$		0			0
$171$		0			0
$172$	−7.00000	−	7.93725i	−0.533745	−	0.605210i
$173$		−	21.1660i		−	1.60922i	−0.593802	−	0.804611i	$-0.702374\pi$
$173$		−	21.1660i		−	1.60922i	0.593802	−	0.804611i	$-0.297626\pi$
$174$		0			0
$175$		0			0
$176$	10.5000	+	1.32288i	0.791467	+	0.0997155i
$177$		0			0
$178$	−0.500000	−	1.32288i	−0.0374766	−	0.0991537i
$179$			23.8118i			1.77977i	0.456180	+	0.889887i	$0.349217\pi$
$179$			23.8118i			1.77977i	−0.456180	+	0.889887i	$0.650783\pi$
$180$		0			0
$181$		−	10.5830i		−	0.786629i	−0.919404	−	0.393314i	$-0.871328\pi$
$181$		−	10.5830i		−	0.786629i	0.919404	−	0.393314i	$-0.128672\pi$
$182$		0			0
$183$		0			0
$184$	−10.0000	−	5.29150i	−0.737210	−	0.390095i
$185$		0			0
$186$		0			0
$187$			7.93725i			0.580429i
$188$	−12.0000	+	10.5830i	−0.875190	+	0.771845i
$189$		0			0
$190$		0			0
$191$	−4.00000			−0.289430			−0.144715	−	0.989473i	$-0.546227\pi$
$191$	−4.00000			−0.289430			−0.144715	+	0.989473i	$0.546227\pi$
$192$		0			0
$193$	5.00000			0.359908			0.179954	−	0.983675i	$-0.442405\pi$
$193$	5.00000			0.359908			0.179954	+	0.983675i	$0.442405\pi$
$194$	1.00000	+	2.64575i	0.0717958	+	0.189954i
$195$		0			0
$196$	−13.5000	+	11.9059i	−0.964286	+	0.850420i
$197$			10.5830i			0.754008i	0.926212	+	0.377004i	$0.123046\pi$
$197$			10.5830i			0.754008i	−0.926212	+	0.377004i	$0.876954\pi$
$198$		0			0
$199$	−24.0000			−1.70131			−0.850657	−	0.525720i	$-0.823796\pi$
$199$	−24.0000			−1.70131			−0.850657	+	0.525720i	$0.823796\pi$
$200$		0			0
$201$		0			0
$202$	−14.0000	+	5.29150i	−0.985037	+	0.372309i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−4.00000	−	10.5830i	−0.278693	−	0.737353i
$207$		0			0
$208$		0			0
$209$	7.00000			0.484200
$210$		0			0
$211$			7.93725i			0.546423i	0.961954	+	0.273212i	$0.0880859\pi$
$211$			7.93725i			0.546423i	−0.961954	+	0.273212i	$0.911914\pi$
$212$	−14.0000	−	15.8745i	−0.961524	−	1.09027i
$213$		0			0
$214$	−3.50000	+	1.32288i	−0.239255	+	0.0904299i
$215$		0			0
$216$		0			0
$217$	16.0000			1.08615
$218$	−14.0000	+	5.29150i	−0.948200	+	0.358386i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−16.0000			−1.07144			−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000			−1.07144			−0.535720	+	0.844396i	$0.679960\pi$
$224$	−22.0000	+	5.29150i	−1.46994	+	0.353553i
$225$		0			0
$226$	−7.50000	−	19.8431i	−0.498893	−	1.31995i
$227$			15.8745i			1.05363i	0.849981	+	0.526814i	$0.176614\pi$
$227$			15.8745i			1.05363i	−0.849981	+	0.526814i	$0.823386\pi$
$228$		0			0
$229$		−	21.1660i		−	1.39869i	−0.714785	−	0.699345i	$-0.753475\pi$
$229$		−	21.1660i		−	1.39869i	0.714785	−	0.699345i	$-0.246525\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$		0			0
$235$		0			0
$236$	−7.00000	−	7.93725i	−0.455661	−	0.516671i
$237$		0			0
$238$	−6.00000	−	15.8745i	−0.388922	−	1.02899i
$239$	8.00000			0.517477			0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000			0.517477			0.258738	+	0.965947i	$0.416693\pi$
$240$		0			0
$241$	−21.0000			−1.35273			−0.676364	−	0.736567i	$-0.736446\pi$
$241$	−21.0000			−1.35273			−0.676364	+	0.736567i	$0.736446\pi$
$242$	−2.00000	−	5.29150i	−0.128565	−	0.340151i
$243$		0			0
$244$	14.0000	+	15.8745i	0.896258	+	1.01626i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	10.0000	+	5.29150i	0.635001	+	0.336011i
$249$		0			0
$250$		0			0
$251$		−	7.93725i		−	0.500995i	−0.968117	−	0.250498i	$-0.919406\pi$
$251$		−	7.93725i		−	0.500995i	0.968117	−	0.250498i	$-0.0805942\pi$
$252$		0			0
$253$		−	10.5830i		−	0.665348i
$254$	−6.00000	−	15.8745i	−0.376473	−	0.996055i
$255$		0			0
$256$	−15.5000	−	3.96863i	−0.968750	−	0.248039i
$257$	−14.0000			−0.873296			−0.436648	−	0.899632i	$-0.643834\pi$
$257$	−14.0000			−0.873296			−0.436648	+	0.899632i	$0.643834\pi$
$258$		0			0
$259$			42.3320i			2.63038i
$260$		0			0
$261$		0			0
$262$	−21.0000	+	7.93725i	−1.29738	+	0.490365i
$263$	−12.0000			−0.739952			−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000			−0.739952			−0.369976	+	0.929041i	$0.620634\pi$
$264$		0			0
$265$		0			0
$266$	−14.0000	+	5.29150i	−0.858395	+	0.324443i
$267$		0			0
$268$	10.5000	+	11.9059i	0.641390	+	0.727267i
$269$		−	21.1660i		−	1.29051i	−0.763965	−	0.645257i	$-0.776750\pi$
$269$		−	21.1660i		−	1.29051i	0.763965	−	0.645257i	$-0.223250\pi$
$270$		0			0
$271$	−20.0000			−1.21491			−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000			−1.21491			−0.607457	+	0.794353i	$0.707810\pi$
$272$	1.50000	−	11.9059i	0.0909509	−	0.721900i
$273$		0			0
$274$	−9.50000	−	25.1346i	−0.573916	−	1.51844i
$275$		0			0
$276$		0			0
$277$			21.1660i			1.27174i	0.771795	+	0.635871i	$0.219359\pi$
$277$			21.1660i			1.27174i	−0.771795	+	0.635871i	$0.780641\pi$
$278$	24.5000	−	9.26013i	1.46941	−	0.555386i
$279$		0			0
$280$		0			0
$281$	22.0000			1.31241			0.656205	−	0.754583i	$-0.272161\pi$
$281$	22.0000			1.31241			0.656205	+	0.754583i	$0.272161\pi$
$282$		0			0
$283$			13.2288i			0.786368i	0.919460	+	0.393184i	$0.128626\pi$
$283$			13.2288i			0.786368i	−0.919460	+	0.393184i	$0.871374\pi$
$284$	12.0000	−	10.5830i	0.712069	−	0.627986i
$285$		0			0
$286$		0			0
$287$	20.0000			1.18056
$288$		0			0
$289$	−8.00000			−0.470588
$290$		0			0
$291$		0			0
$292$	10.5000	−	9.26013i	0.614466	−	0.541908i
$293$		−	10.5830i		−	0.618266i	−0.951019	−	0.309133i	$-0.899961\pi$
$293$		−	10.5830i		−	0.618266i	0.951019	−	0.309133i	$-0.100039\pi$
$294$		0			0
$295$		0			0
$296$	−14.0000	+	26.4575i	−0.813733	+	1.53781i
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$			21.1660i			1.21999i
$302$	−2.00000	−	5.29150i	−0.115087	−	0.304492i
$303$		0			0
$304$	−10.5000	−	1.32288i	−0.602216	−	0.0758721i
$305$		0			0
$306$		0			0
$307$			2.64575i			0.151001i	0.997146	+	0.0755005i	$0.0240554\pi$
$307$			2.64575i			0.151001i	−0.997146	+	0.0755005i	$0.975945\pi$
$308$	−14.0000	−	15.8745i	−0.797724	−	0.904534i
$309$		0			0
$310$		0			0
$311$	4.00000			0.226819			0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000			0.226819			0.113410	+	0.993548i	$0.463823\pi$
$312$		0			0
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$	−14.0000	+	5.29150i	−0.790066	+	0.298617i
$315$		0			0
$316$	−6.00000	+	5.29150i	−0.337526	+	0.297670i
$317$		0			0		1.00000			$0$
$317$		0			0		−1.00000			$\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$	8.00000	+	21.1660i	0.445823	+	1.17954i
$323$		−	7.93725i		−	0.441641i
$324$		0			0
$325$		0			0
$326$	17.5000	−	6.61438i	0.969235	−	0.366337i
$327$		0			0
$328$	12.5000	+	6.61438i	0.690197	+	0.365218i
$329$	32.0000			1.76422
$330$		0			0
$331$		−	2.64575i		−	0.145424i	−0.997353	−	0.0727118i	$-0.976835\pi$
$331$		−	2.64575i		−	0.145424i	0.997353	−	0.0727118i	$-0.0231653\pi$
$332$	−10.5000	−	11.9059i	−0.576262	−	0.653420i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−15.0000			−0.817102			−0.408551	−	0.912735i	$-0.633966\pi$
$337$	−15.0000			−0.817102			−0.408551	+	0.912735i	$0.633966\pi$
$338$	−6.50000	−	17.1974i	−0.353553	−	0.935414i
$339$		0			0
$340$		0			0
$341$			10.5830i			0.573102i
$342$		0			0
$343$	8.00000			0.431959
$344$	−7.00000	+	13.2288i	−0.377415	+	0.713247i
$345$		0			0
$346$	−28.0000	+	10.5830i	−1.50529	+	0.568946i
$347$		−	2.64575i		−	0.142031i	−0.997475	−	0.0710157i	$-0.977376\pi$
$347$		−	2.64575i		−	0.142031i	0.997475	−	0.0710157i	$-0.0226240\pi$
$348$		0			0
$349$			10.5830i			0.566495i	0.959047	+	0.283248i	$0.0914118\pi$
$349$			10.5830i			0.566495i	−0.959047	+	0.283248i	$0.908588\pi$
$350$		0			0
$351$		0			0
$352$	−3.50000	−	14.5516i	−0.186551	−	0.775605i
$353$	18.0000			0.958043			0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000			0.958043			0.479022	+	0.877803i	$0.340992\pi$
$354$		0			0
$355$		0			0
$356$	−1.50000	+	1.32288i	−0.0794998	+	0.0701123i
$357$		0			0
$358$	31.5000	−	11.9059i	1.66483	−	0.629245i
$359$	−36.0000			−1.90001			−0.950004	−	0.312239i	$-0.898921\pi$
$359$	−36.0000			−1.90001			−0.950004	+	0.312239i	$0.898921\pi$
$360$		0			0
$361$	12.0000			0.631579
$362$	−14.0000	+	5.29150i	−0.735824	+	0.278115i
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0			−	1.00000i	$-0.5\pi$
$367$		0			0				1.00000i	$0.5\pi$
$368$	−2.00000	+	15.8745i	−0.104257	+	0.827516i
$369$		0			0
$370$		0			0
$371$			42.3320i			2.19777i
$372$		0			0
$373$		−	10.5830i		−	0.547967i	−0.961734	−	0.273984i	$-0.911659\pi$
$373$		−	10.5830i		−	0.547967i	0.961734	−	0.273984i	$-0.0883414\pi$
$374$	10.5000	−	3.96863i	0.542942	−	0.205213i
$375$		0			0
$376$	20.0000	+	10.5830i	1.03142	+	0.545777i
$377$		0			0
$378$		0			0
$379$			7.93725i			0.407709i	0.979001	+	0.203855i	$0.0653470\pi$
$379$			7.93725i			0.407709i	−0.979001	+	0.203855i	$0.934653\pi$
$380$		0			0
$381$		0			0
$382$	2.00000	+	5.29150i	0.102329	+	0.270737i
$383$	36.0000			1.83951			0.919757	−	0.392488i	$-0.128386\pi$
$383$	36.0000			1.83951			0.919757	+	0.392488i	$0.128386\pi$
$384$		0			0
$385$		0			0
$386$	−2.50000	−	6.61438i	−0.127247	−	0.336663i
$387$		0			0
$388$	3.00000	−	2.64575i	0.152302	−	0.134318i
$389$			10.5830i			0.536580i	0.963338	+	0.268290i	$0.0864585\pi$
$389$			10.5830i			0.536580i	−0.963338	+	0.268290i	$0.913542\pi$
$390$		0			0
$391$	−12.0000			−0.606866
$392$	22.5000	+	11.9059i	1.13642	+	0.601338i
$393$		0			0
$394$	14.0000	−	5.29150i	0.705310	−	0.266582i
$395$		0			0
$396$		0			0
$397$			21.1660i			1.06229i	0.847280	+	0.531146i	$0.178238\pi$
$397$			21.1660i			1.06229i	−0.847280	+	0.531146i	$0.821762\pi$
$398$	12.0000	+	31.7490i	0.601506	+	1.59143i
$399$		0			0
$400$		0			0
$401$	−27.0000			−1.34832			−0.674158	−	0.738587i	$-0.735493\pi$
$401$	−27.0000			−1.34832			−0.674158	+	0.738587i	$0.735493\pi$
$402$		0			0
$403$		0			0
$404$	14.0000	+	15.8745i	0.696526	+	0.789786i
$405$		0			0
$406$		0			0
$407$	−28.0000			−1.38791
$408$		0			0
$409$	3.00000			0.148340			0.0741702	−	0.997246i	$-0.476369\pi$
$409$	3.00000			0.148340			0.0741702	+	0.997246i	$0.476369\pi$
$410$		0			0
$411$		0			0
$412$	−12.0000	+	10.5830i	−0.591198	+	0.521387i
$413$			21.1660i			1.04151i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$	−3.50000	−	9.26013i	−0.171191	−	0.452928i
$419$		−	18.5203i		−	0.904774i	−0.891822	−	0.452387i	$-0.850573\pi$
$419$		−	18.5203i		−	0.904774i	0.891822	−	0.452387i	$-0.149427\pi$
$420$		0			0
$421$		−	21.1660i		−	1.03157i	−0.856719	−	0.515784i	$-0.827501\pi$
$421$		−	21.1660i		−	1.03157i	0.856719	−	0.515784i	$-0.172499\pi$
$422$	10.5000	−	3.96863i	0.511132	−	0.193190i
$423$		0			0
$424$	−14.0000	+	26.4575i	−0.679900	+	1.28489i
$425$		0			0
$426$		0			0
$427$		−	42.3320i		−	2.04859i
$428$	3.50000	+	3.96863i	0.169179	+	0.191831i
$429$		0			0
$430$		0			0
$431$	−12.0000			−0.578020			−0.289010	−	0.957326i	$-0.593326\pi$
$431$	−12.0000			−0.578020			−0.289010	+	0.957326i	$0.593326\pi$
$432$		0			0
$433$	37.0000			1.77811			0.889053	−	0.457804i	$-0.151364\pi$
$433$	37.0000			1.77811			0.889053	+	0.457804i	$0.151364\pi$
$434$	−8.00000	−	21.1660i	−0.384012	−	1.01600i
$435$		0			0
$436$	14.0000	+	15.8745i	0.670478	+	0.760251i
$437$			10.5830i			0.506254i
$438$		0			0
$439$	8.00000			0.381819			0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000			0.381819			0.190910	+	0.981608i	$0.438856\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			29.1033i			1.38274i	0.722502	+	0.691369i	$0.242992\pi$
$443$			29.1033i			1.38274i	−0.722502	+	0.691369i	$0.757008\pi$
$444$		0			0
$445$		0			0
$446$	8.00000	+	21.1660i	0.378811	+	1.00224i
$447$		0			0
$448$	18.0000	+	26.4575i	0.850420	+	1.25000i
$449$	−27.0000			−1.27421			−0.637104	−	0.770778i	$-0.719868\pi$
$449$	−27.0000			−1.27421			−0.637104	+	0.770778i	$0.719868\pi$
$450$		0			0
$451$			13.2288i			0.622918i
$452$	−22.5000	+	19.8431i	−1.05831	+	0.933343i
$453$		0			0
$454$	21.0000	−	7.93725i	0.985579	−	0.372514i
$455$		0			0
$456$		0			0
$457$	−27.0000			−1.26301			−0.631503	−	0.775373i	$-0.717562\pi$
$457$	−27.0000			−1.26301			−0.631503	+	0.775373i	$0.717562\pi$
$458$	−28.0000	+	10.5830i	−1.30835	+	0.494511i
$459$		0			0
$460$		0			0
$461$		−	42.3320i		−	1.97160i	−0.167927	−	0.985799i	$-0.553707\pi$
$461$		−	42.3320i		−	1.97160i	0.167927	−	0.985799i	$-0.446293\pi$
$462$		0			0
$463$	−8.00000			−0.371792			−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000			−0.371792			−0.185896	+	0.982569i	$0.559519\pi$
$464$		0			0
$465$		0			0
$466$	3.00000	+	7.93725i	0.138972	+	0.367686i
$467$		−	26.4575i		−	1.22431i	−0.790739	−	0.612154i	$-0.790303\pi$
$467$		−	26.4575i		−	1.22431i	0.790739	−	0.612154i	$-0.209697\pi$
$468$		0			0
$469$		−	31.7490i		−	1.46603i
$470$		0			0
$471$		0			0
$472$	−7.00000	+	13.2288i	−0.322201	+	0.608903i
$473$	−14.0000			−0.643721
$474$		0			0
$475$		0			0
$476$	−18.0000	+	15.8745i	−0.825029	+	0.727607i
$477$		0			0
$478$	−4.00000	−	10.5830i	−0.182956	−	0.484055i
$479$	−4.00000			−0.182765			−0.0913823	−	0.995816i	$-0.529129\pi$
$479$	−4.00000			−0.182765			−0.0913823	+	0.995816i	$0.529129\pi$
$480$		0			0
$481$		0			0
$482$	10.5000	+	27.7804i	0.478262	+	1.26536i
$483$		0			0
$484$	−6.00000	+	5.29150i	−0.272727	+	0.240523i
$485$		0			0
$486$		0			0
$487$	−12.0000			−0.543772			−0.271886	−	0.962329i	$-0.587647\pi$
$487$	−12.0000			−0.543772			−0.271886	+	0.962329i	$0.587647\pi$
$488$	14.0000	−	26.4575i	0.633750	−	1.19768i
$489$		0			0
$490$		0			0
$491$			5.29150i			0.238802i	0.992846	+	0.119401i	$0.0380974\pi$
$491$			5.29150i			0.238802i	−0.992846	+	0.119401i	$0.961903\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	2.00000	−	15.8745i	0.0898027	−	0.712786i
$497$	−32.0000			−1.43540
$498$		0			0
$499$		−	26.4575i		−	1.18440i	−0.805791	−	0.592200i	$-0.798259\pi$
$499$		−	26.4575i		−	1.18440i	0.805791	−	0.592200i	$-0.201741\pi$
$500$		0			0
$501$		0			0
$502$	−10.5000	+	3.96863i	−0.468638	+	0.177128i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$		0			0
$506$	−14.0000	+	5.29150i	−0.622376	+	0.235236i
$507$		0			0
$508$	−18.0000	+	15.8745i	−0.798621	+	0.704317i
$509$		−	31.7490i		−	1.40725i	−0.710571	−	0.703625i	$-0.751563\pi$
$509$		−	31.7490i		−	1.40725i	0.710571	−	0.703625i	$-0.248437\pi$
$510$		0			0
$511$	−28.0000			−1.23865
$512$	2.50000	+	22.4889i	0.110485	+	0.993878i
$513$		0			0
$514$	7.00000	+	18.5203i	0.308757	+	0.816894i
$515$		0			0
$516$		0			0
$517$			21.1660i			0.930880i
$518$	56.0000	−	21.1660i	2.46050	−	0.929981i
$519$		0			0
$520$		0			0
$521$	−3.00000			−0.131432			−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000			−0.131432			−0.0657162	+	0.997838i	$0.520933\pi$
$522$		0			0
$523$			2.64575i			0.115691i	0.998326	+	0.0578453i	$0.0184230\pi$
$523$			2.64575i			0.115691i	−0.998326	+	0.0578453i	$0.981577\pi$
$524$	21.0000	+	23.8118i	0.917389	+	1.04022i
$525$		0			0
$526$	6.00000	+	15.8745i	0.261612	+	0.692161i
$527$	12.0000			0.522728
$528$		0			0
$529$	−7.00000			−0.304348
$530$		0			0
$531$		0			0
$532$	14.0000	+	15.8745i	0.606977	+	0.688247i
$533$		0			0
$534$		0			0
$535$		0			0
$536$	10.5000	−	19.8431i	0.453531	−	0.857093i
$537$		0			0
$538$	−28.0000	+	10.5830i	−1.20717	+	0.456266i
$539$			23.8118i			1.02565i
$540$		0			0
$541$			21.1660i			0.909998i	0.890492	+	0.454999i	$0.150360\pi$
$541$			21.1660i			0.909998i	−0.890492	+	0.454999i	$0.849640\pi$
$542$	10.0000	+	26.4575i	0.429537	+	1.13645i
$543$		0			0
$544$	−16.5000	+	3.96863i	−0.707432	+	0.170153i
$545$		0			0
$546$		0			0
$547$		−	18.5203i		−	0.791869i	−0.918279	−	0.395935i	$-0.870421\pi$
$547$		−	18.5203i		−	0.791869i	0.918279	−	0.395935i	$-0.129579\pi$
$548$	−28.5000	+	25.1346i	−1.21746	+	1.07370i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$	16.0000			0.680389
$554$	28.0000	−	10.5830i	1.18961	−	0.449629i
$555$		0			0
$556$	−24.5000	−	27.7804i	−1.03903	−	1.17815i
$557$		0			0		1.00000			$0$
$557$		0			0		−1.00000			$\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−11.0000	−	29.1033i	−0.464007	−	1.22765i
$563$			15.8745i			0.669031i	0.942390	+	0.334515i	$0.108573\pi$
$563$			15.8745i			0.669031i	−0.942390	+	0.334515i	$0.891427\pi$
$564$		0			0
$565$		0			0
$566$	17.5000	−	6.61438i	0.735580	−	0.278023i
$567$		0			0
$568$	−20.0000	−	10.5830i	−0.839181	−	0.444053i
$569$	−11.0000			−0.461144			−0.230572	−	0.973055i	$-0.574060\pi$
$569$	−11.0000			−0.461144			−0.230572	+	0.973055i	$0.574060\pi$
$570$		0			0
$571$			37.0405i			1.55010i	0.631901	+	0.775049i	$0.282275\pi$
$571$			37.0405i			1.55010i	−0.631901	+	0.775049i	$0.717725\pi$
$572$		0			0
$573$		0			0
$574$	−10.0000	−	26.4575i	−0.417392	−	1.10432i
$575$		0			0
$576$		0			0
$577$	−7.00000			−0.291414			−0.145707	−	0.989328i	$-0.546546\pi$
$577$	−7.00000			−0.291414			−0.145707	+	0.989328i	$0.546546\pi$
$578$	4.00000	+	10.5830i	0.166378	+	0.440195i
$579$		0			0
$580$		0			0
$581$			31.7490i			1.31717i
$582$		0			0
$583$	−28.0000			−1.15964
$584$	−17.5000	−	9.26013i	−0.724155	−	0.383187i
$585$		0			0
$586$	−14.0000	+	5.29150i	−0.578335	+	0.218590i
$587$			7.93725i			0.327606i	0.986493	+	0.163803i	$0.0523761\pi$
$587$			7.93725i			0.327606i	−0.986493	+	0.163803i	$0.947624\pi$
$588$		0			0
$589$		−	10.5830i		−	0.436065i
$590$		0			0
$591$		0			0
$592$	42.0000	+	5.29150i	1.72619	+	0.217479i
$593$	−41.0000			−1.68367			−0.841834	−	0.539736i	$-0.818524\pi$
$593$	−41.0000			−1.68367			−0.841834	+	0.539736i	$0.818524\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	12.0000			0.490307			0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000			0.490307			0.245153	+	0.969484i	$0.421162\pi$
$600$		0			0
$601$	7.00000			0.285536			0.142768	−	0.989756i	$-0.454400\pi$
$601$	7.00000			0.285536			0.142768	+	0.989756i	$0.454400\pi$
$602$	28.0000	−	10.5830i	1.14119	−	0.431331i
$603$		0			0
$604$	−6.00000	+	5.29150i	−0.244137	+	0.215308i
$605$		0			0
$606$		0			0
$607$	−8.00000			−0.324710			−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000			−0.324710			−0.162355	+	0.986732i	$0.551909\pi$
$608$	3.50000	+	14.5516i	0.141944	+	0.590147i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$			10.5830i			0.427444i	0.976895	+	0.213722i	$0.0685586\pi$
$613$			10.5830i			0.427444i	−0.976895	+	0.213722i	$0.931441\pi$
$614$	3.50000	−	1.32288i	0.141249	−	0.0533869i
$615$		0			0
$616$	−14.0000	+	26.4575i	−0.564076	+	1.06600i
$617$	−6.00000			−0.241551			−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000			−0.241551			−0.120775	+	0.992680i	$0.538538\pi$
$618$		0			0
$619$		−	5.29150i		−	0.212683i	−0.994330	−	0.106342i	$-0.966086\pi$
$619$		−	5.29150i		−	0.212683i	0.994330	−	0.106342i	$-0.0339137\pi$
$620$		0			0
$621$		0			0
$622$	−2.00000	−	5.29150i	−0.0801927	−	0.212170i
$623$	4.00000			0.160257
$624$		0			0
$625$		0			0
$626$	−3.00000	−	7.93725i	−0.119904	−	0.317236i
$627$		0			0
$628$	14.0000	+	15.8745i	0.558661	+	0.633462i
$629$			31.7490i			1.26592i
$630$		0			0
$631$	36.0000			1.43314			0.716569	−	0.697517i	$-0.245712\pi$
$631$	36.0000			1.43314			0.716569	+	0.697517i	$0.245712\pi$
$632$	10.0000	+	5.29150i	0.397779	+	0.210485i
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−2.00000			−0.0789953			−0.0394976	−	0.999220i	$-0.512576\pi$
$641$	−2.00000			−0.0789953			−0.0394976	+	0.999220i	$0.512576\pi$
$642$		0			0
$643$		−	15.8745i		−	0.626029i	−0.949748	−	0.313015i	$-0.898661\pi$
$643$		−	15.8745i		−	0.626029i	0.949748	−	0.313015i	$-0.101339\pi$
$644$	24.0000	−	21.1660i	0.945732	−	0.834058i
$645$		0			0
$646$	−10.5000	+	3.96863i	−0.413117	+	0.156144i
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$		0			0
$649$	−14.0000			−0.549548
$650$		0			0
$651$		0			0
$652$	−17.5000	−	19.8431i	−0.685353	−	0.777117i
$653$		−	31.7490i		−	1.24243i	−0.783638	−	0.621217i	$-0.786638\pi$
$653$		−	31.7490i		−	1.24243i	0.783638	−	0.621217i	$-0.213362\pi$
$654$		0			0
$655$		0			0
$656$	2.50000	−	19.8431i	0.0976086	−	0.774744i
$657$		0			0
$658$	−16.0000	−	42.3320i	−0.623745	−	1.65027i
$659$		−	7.93725i		−	0.309192i	−0.987978	−	0.154596i	$-0.950592\pi$
$659$		−	7.93725i		−	0.309192i	0.987978	−	0.154596i	$-0.0494075\pi$
$660$		0			0
$661$		−	21.1660i		−	0.823262i	−0.911351	−	0.411631i	$-0.864959\pi$
$661$		−	21.1660i		−	0.823262i	0.911351	−	0.411631i	$-0.135041\pi$
$662$	−3.50000	+	1.32288i	−0.136031	+	0.0514150i
$663$		0			0
$664$	−10.5000	+	19.8431i	−0.407479	+	0.770063i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$	28.0000			1.08093
$672$		0			0
$673$	−34.0000			−1.31060			−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000			−1.31060			−0.655302	+	0.755367i	$0.727459\pi$
$674$	7.50000	+	19.8431i	0.288889	+	0.764329i
$675$		0			0
$676$	−19.5000	+	17.1974i	−0.750000	+	0.661438i
$677$		−	42.3320i		−	1.62695i	−0.581599	−	0.813476i	$-0.697573\pi$
$677$		−	42.3320i		−	1.62695i	0.581599	−	0.813476i	$-0.302427\pi$
$678$		0			0
$679$	−8.00000			−0.307012
$680$		0			0
$681$		0			0
$682$	14.0000	−	5.29150i	0.536088	−	0.202622i
$683$		−	23.8118i		−	0.911132i	−0.890202	−	0.455566i	$-0.849437\pi$
$683$		−	23.8118i		−	0.911132i	0.890202	−	0.455566i	$-0.150563\pi$
$684$		0			0
$685$		0			0
$686$	−4.00000	−	10.5830i	−0.152721	−	0.404061i
$687$		0			0
$688$	21.0000	+	2.64575i	0.800617	+	0.100868i
$689$		0			0
$690$		0			0
$691$		−	23.8118i		−	0.905842i	−0.891551	−	0.452921i	$-0.850382\pi$
$691$		−	23.8118i		−	0.905842i	0.891551	−	0.452921i	$-0.149618\pi$
$692$	28.0000	+	31.7490i	1.06440	+	1.20692i
$693$		0			0
$694$	−3.50000	+	1.32288i	−0.132858	+	0.0502157i
$695$		0			0
$696$		0			0
$697$	15.0000			0.568166
$698$	14.0000	−	5.29150i	0.529908	−	0.200286i
$699$		0			0
$700$		0			0
$701$			21.1660i			0.799429i	0.916640	+	0.399715i	$0.130891\pi$
$701$			21.1660i			0.799429i	−0.916640	+	0.399715i	$0.869109\pi$
$702$		0			0
$703$	28.0000			1.05604
$704$	−17.5000	+	11.9059i	−0.659556	+	0.448720i
$705$		0			0
$706$	−9.00000	−	23.8118i	−0.338719	−	0.896167i
$707$		−	42.3320i		−	1.59206i
$708$		0			0
$709$		−	21.1660i		−	0.794906i	−0.917622	−	0.397453i	$-0.869894\pi$
$709$		−	21.1660i		−	0.794906i	0.917622	−	0.397453i	$-0.130106\pi$
$710$		0			0
$711$		0			0
$712$	2.50000	+	1.32288i	0.0936915	+	0.0495769i
$713$	−16.0000			−0.599205
$714$		0			0
$715$		0			0
$716$	−31.5000	−	35.7176i	−1.17721	−	1.33483i
$717$		0			0
$718$	18.0000	+	47.6235i	0.671754	+	1.77729i
$719$	−36.0000			−1.34257			−0.671287	−	0.741198i	$-0.734258\pi$
$719$	−36.0000			−1.34257			−0.671287	+	0.741198i	$0.734258\pi$
$720$		0			0
$721$	32.0000			1.19174
$722$	−6.00000	−	15.8745i	−0.223297	−	0.590788i
$723$		0			0
$724$	14.0000	+	15.8745i	0.520306	+	0.589971i
$725$		0			0
$726$		0			0
$727$	−16.0000			−0.593407			−0.296704	−	0.954970i	$-0.595887\pi$
$727$	−16.0000			−0.593407			−0.296704	+	0.954970i	$0.595887\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$			15.8745i			0.587140i
$732$		0			0
$733$		0			0		1.00000			$0$
$733$		0			0		−1.00000			$\pi$
$734$		0			0
$735$		0			0
$736$	22.0000	−	5.29150i	0.810931	−	0.195047i
$737$	21.0000			0.773545
$738$		0			0
$739$			15.8745i			0.583953i	0.956425	+	0.291977i	$0.0943129\pi$
$739$			15.8745i			0.583953i	−0.956425	+	0.291977i	$0.905687\pi$
$740$		0			0
$741$		0			0
$742$	56.0000	−	21.1660i	2.05582	−	0.777029i
$743$	−36.0000			−1.32071			−0.660356	−	0.750953i	$-0.729595\pi$
$743$	−36.0000			−1.32071			−0.660356	+	0.750953i	$0.729595\pi$
$744$		0			0
$745$		0			0
$746$	−14.0000	+	5.29150i	−0.512576	+	0.193736i
$747$		0			0
$748$	−10.5000	−	11.9059i	−0.383918	−	0.435322i
$749$		−	10.5830i		−	0.386695i
$750$		0			0
$751$	8.00000			0.291924			0.145962	−	0.989290i	$-0.453372\pi$
$751$	8.00000			0.291924			0.145962	+	0.989290i	$0.453372\pi$
$752$	4.00000	−	31.7490i	0.145865	−	1.15777i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	21.1660i		−	0.769292i	−0.923064	−	0.384646i	$-0.874324\pi$
$757$		−	21.1660i		−	0.769292i	0.923064	−	0.384646i	$-0.125676\pi$
$758$	10.5000	−	3.96863i	0.381377	−	0.144147i
$759$		0			0
$760$		0			0
$761$	29.0000			1.05125			0.525625	−	0.850717i	$-0.323832\pi$
$761$	29.0000			1.05125			0.525625	+	0.850717i	$0.323832\pi$
$762$		0			0
$763$		−	42.3320i		−	1.53252i
$764$	6.00000	−	5.29150i	0.217072	−	0.191440i
$765$		0			0
$766$	−18.0000	−	47.6235i	−0.650366	−	1.72071i
$767$		0			0
$768$		0			0
$769$	−21.0000			−0.757279			−0.378640	−	0.925544i	$-0.623608\pi$
$769$	−21.0000			−0.757279			−0.378640	+	0.925544i	$0.623608\pi$
$770$		0			0
$771$		0			0
$772$	−7.50000	+	6.61438i	−0.269931	+	0.238057i
$773$		0			0		1.00000			$0$
$773$		0			0		−1.00000			$\pi$
$774$		0			0
$775$		0			0
$776$	−5.00000	−	2.64575i	−0.179490	−	0.0949769i
$777$		0			0
$778$	14.0000	−	5.29150i	0.501924	−	0.189710i
$779$		−	13.2288i		−	0.473969i
$780$		0			0
$781$		−	21.1660i		−	0.757379i
$782$	6.00000	+	15.8745i	0.214560	+	0.567671i
$783$		0			0
$784$	4.50000	−	35.7176i	0.160714	−	1.27563i
$785$		0			0
$786$		0			0
$787$			26.4575i			0.943108i	0.881837	+	0.471554i	$0.156307\pi$
$787$			26.4575i			0.943108i	−0.881837	+	0.471554i	$0.843693\pi$
$788$	−14.0000	−	15.8745i	−0.498729	−	0.565506i
$789$		0			0
$790$		0			0
$791$	60.0000			2.13335
$792$		0			0
$793$		0			0
$794$	28.0000	−	10.5830i	0.993683	−	0.375577i
$795$		0			0
$796$	36.0000	−	31.7490i	1.27599	−	1.12531i
$797$			31.7490i			1.12461i	0.826931	+	0.562304i	$0.190085\pi$
$797$			31.7490i			1.12461i	−0.826931	+	0.562304i	$0.809915\pi$
$798$		0			0
$799$	24.0000			0.849059
$800$		0			0
$801$		0			0
$802$	13.5000	+	35.7176i	0.476702	+	1.26123i
$803$		−	18.5203i		−	0.653566i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	14.0000	−	26.4575i	0.492518	−	0.930772i
$809$	−10.0000			−0.351581			−0.175791	−	0.984428i	$-0.556248\pi$
$809$	−10.0000			−0.351581			−0.175791	+	0.984428i	$0.556248\pi$
$810$		0			0
$811$		−	5.29150i		−	0.185810i	−0.995675	−	0.0929049i	$-0.970385\pi$
$811$		−	5.29150i		−	0.185810i	0.995675	−	0.0929049i	$-0.0296153\pi$
$812$		0			0
$813$		0			0
$814$	14.0000	+	37.0405i	0.490700	+	1.29827i
$815$		0			0
$816$		0			0
$817$	14.0000			0.489798
$818$	−1.50000	−	3.96863i	−0.0524463	−	0.138760i
$819$		0			0
$820$		0			0
$821$		−	10.5830i		−	0.369349i	−0.982800	−	0.184675i	$-0.940877\pi$
$821$		−	10.5830i		−	0.369349i	0.982800	−	0.184675i	$-0.0591232\pi$
$822$		0			0
$823$	−24.0000			−0.836587			−0.418294	−	0.908312i	$-0.637372\pi$
$823$	−24.0000			−0.836587			−0.418294	+	0.908312i	$0.637372\pi$
$824$	20.0000	+	10.5830i	0.696733	+	0.368676i
$825$		0			0
$826$	28.0000	−	10.5830i	0.974245	−	0.368230i
$827$		−	13.2288i		−	0.460009i	−0.973190	−	0.230004i	$-0.926126\pi$
$827$		−	13.2288i		−	0.460009i	0.973190	−	0.230004i	$-0.0738741\pi$
$828$		0			0
$829$			21.1660i			0.735126i	0.929999	+	0.367563i	$0.119808\pi$
$829$			21.1660i			0.735126i	−0.929999	+	0.367563i	$0.880192\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	27.0000			0.935495
$834$		0			0
$835$		0			0
$836$	−10.5000	+	9.26013i	−0.363150	+	0.320268i
$837$		0			0
$838$	−24.5000	+	9.26013i	−0.846338	+	0.319886i
$839$	−40.0000			−1.38095			−0.690477	−	0.723355i	$-0.742599\pi$
$839$	−40.0000			−1.38095			−0.690477	+	0.723355i	$0.742599\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$	−28.0000	+	10.5830i	−0.964944	+	0.364714i
$843$		0			0
$844$	−10.5000	−	11.9059i	−0.361425	−	0.409817i
$845$		0			0
$846$		0			0
$847$	16.0000			0.549767
$848$	42.0000	+	5.29150i	1.44229	+	0.181711i
$849$		0			0
$850$		0			0
$851$		−	42.3320i		−	1.45112i
$852$		0			0
$853$		−	52.9150i		−	1.81178i	−0.423517	−	0.905888i	$-0.639205\pi$
$853$		−	52.9150i		−	1.81178i	0.423517	−	0.905888i	$-0.360795\pi$
$854$	−56.0000	+	21.1660i	−1.91628	+	0.724286i
$855$		0			0
$856$	3.50000	−	6.61438i	0.119628	−	0.226075i
$857$	−21.0000			−0.717346			−0.358673	−	0.933463i	$-0.616771\pi$
$857$	−21.0000			−0.717346			−0.358673	+	0.933463i	$0.616771\pi$
$858$		0			0
$859$		−	2.64575i		−	0.0902719i	−0.998981	−	0.0451359i	$-0.985628\pi$
$859$		−	2.64575i		−	0.0902719i	0.998981	−	0.0451359i	$-0.0143721\pi$
$860$		0			0
$861$		0			0
$862$	6.00000	+	15.8745i	0.204361	+	0.540688i
$863$	−24.0000			−0.816970			−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000			−0.816970			−0.408485	+	0.912765i	$0.633943\pi$
$864$		0			0
$865$		0			0
$866$	−18.5000	−	48.9464i	−0.628656	−	1.66327i
$867$		0			0
$868$	−24.0000	+	21.1660i	−0.814613	+	0.718421i
$869$			10.5830i			0.359004i
$870$		0			0
$871$		0			0
$872$	14.0000	−	26.4575i	0.474100	−	0.895964i
$873$		0			0
$874$	14.0000	−	5.29150i	0.473557	−	0.178988i
$875$		0			0
$876$		0			0
$877$		−	42.3320i		−	1.42945i	−0.699405	−	0.714725i	$-0.746552\pi$
$877$		−	42.3320i		−	1.42945i	0.699405	−	0.714725i	$-0.253448\pi$
$878$	−4.00000	−	10.5830i	−0.134993	−	0.357159i
$879$		0			0
$880$		0			0
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$		0			0
$883$			44.9778i			1.51362i	0.653633	+	0.756811i	$0.273244\pi$
$883$			44.9778i			1.51362i	−0.653633	+	0.756811i	$0.726756\pi$
$884$		0			0
$885$		0			0
$886$	38.5000	−	14.5516i	1.29343	−	0.488872i
$887$	−56.0000			−1.88030			−0.940148	−	0.340766i	$-0.889313\pi$
$887$	−56.0000			−1.88030			−0.940148	+	0.340766i	$0.889313\pi$
$888$		0			0
$889$	48.0000			1.60987
$890$		0			0
$891$		0			0
$892$	24.0000	−	21.1660i	0.803579	−	0.708690i
$893$		−	21.1660i		−	0.708294i
$894$		0			0
$895$		0			0
$896$	26.0000	−	37.0405i	0.868599	−	1.23744i
$897$		0			0
$898$	13.5000	+	35.7176i	0.450501	+	1.19191i
$899$		0			0
$900$		0			0
$901$			31.7490i			1.05771i
$902$	17.5000	−	6.61438i	0.582686	−	0.220235i
$903$		0			0
$904$	37.5000	+	19.8431i	1.24723	+	0.659973i
$905$		0			0
$906$		0			0
$907$			5.29150i			0.175701i	0.996134	+	0.0878507i	$0.0279999\pi$
$907$			5.29150i			0.175701i	−0.996134	+	0.0878507i	$0.972000\pi$
$908$	−21.0000	−	23.8118i	−0.696909	−	0.790221i
$909$		0			0
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$		0			0
$913$	−21.0000			−0.694999
$914$	13.5000	+	35.7176i	0.446540	+	1.18143i
$915$		0			0
$916$	28.0000	+	31.7490i	0.925146	+	1.04902i
$917$		−	63.4980i		−	2.09689i
$918$		0			0
$919$	4.00000			0.131948			0.0659739	−	0.997821i	$-0.478985\pi$
$919$	4.00000			0.131948			0.0659739	+	0.997821i	$0.478985\pi$
$920$		0			0
$921$		0			0
$922$	−56.0000	+	21.1660i	−1.84426	+	0.697065i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	4.00000	+	10.5830i	0.131448	+	0.347779i
$927$		0			0
$928$		0			0
$929$	14.0000			0.459325			0.229663	−	0.973270i	$-0.426238\pi$
$929$	14.0000			0.459325			0.229663	+	0.973270i	$0.426238\pi$
$930$		0			0
$931$		−	23.8118i		−	0.780399i
$932$	9.00000	−	7.93725i	0.294805	−	0.259993i
$933$		0			0
$934$	−35.0000	+	13.2288i	−1.14523	+	0.432858i
$935$		0			0
$936$		0			0
$937$	−7.00000			−0.228680			−0.114340	−	0.993442i	$-0.536475\pi$
$937$	−7.00000			−0.228680			−0.114340	+	0.993442i	$0.536475\pi$
$938$	−42.0000	+	15.8745i	−1.37135	+	0.518321i
$939$		0			0
$940$		0			0
$941$			42.3320i			1.37998i	0.723817	+	0.689992i	$0.242386\pi$
$941$			42.3320i			1.37998i	−0.723817	+	0.689992i	$0.757614\pi$
$942$		0			0
$943$	−20.0000			−0.651290
$944$	21.0000	+	2.64575i	0.683492	+	0.0861119i
$945$		0			0
$946$	7.00000	+	18.5203i	0.227590	+	0.602146i
$947$			15.8745i			0.515852i	0.966165	+	0.257926i	$0.0830391\pi$
$947$			15.8745i			0.515852i	−0.966165	+	0.257926i	$0.916961\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$	30.0000	+	15.8745i	0.972306	+	0.514496i
$953$	−5.00000			−0.161966			−0.0809829	−	0.996715i	$-0.525806\pi$
$953$	−5.00000			−0.161966			−0.0809829	+	0.996715i	$0.525806\pi$
$954$		0			0
$955$		0			0
$956$	−12.0000	+	10.5830i	−0.388108	+	0.342279i
$957$		0			0
$958$	2.00000	+	5.29150i	0.0646171	+	0.170961i
$959$	76.0000			2.45417
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$		0			0
$964$	31.5000	−	27.7804i	1.01455	−	0.894746i
$965$		0			0
$966$		0			0
$967$	8.00000			0.257263			0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000			0.257263			0.128631	+	0.991692i	$0.458942\pi$
$968$	10.0000	+	5.29150i	0.321412	+	0.170075i
$969$		0			0
$970$		0			0
$971$			23.8118i			0.764156i	0.924130	+	0.382078i	$0.124791\pi$
$971$			23.8118i			0.764156i	−0.924130	+	0.382078i	$0.875209\pi$
$972$		0			0
$973$			74.0810i			2.37493i
$974$	6.00000	+	15.8745i	0.192252	+	0.508652i
$975$		0			0
$976$	−42.0000	−	5.29150i	−1.34439	−	0.169377i
$977$	−37.0000			−1.18373			−0.591867	−	0.806035i	$-0.701609\pi$
$977$	−37.0000			−1.18373			−0.591867	+	0.806035i	$0.701609\pi$
$978$		0			0
$979$			2.64575i			0.0845586i
$980$		0			0
$981$		0			0
$982$	7.00000	−	2.64575i	0.223379	−	0.0844293i
$983$	28.0000			0.893061			0.446531	−	0.894768i	$-0.352659\pi$
$983$	28.0000			0.893061			0.446531	+	0.894768i	$0.352659\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	21.1660i		−	0.673040i
$990$		0			0
$991$	44.0000			1.39771			0.698853	−	0.715265i	$-0.253694\pi$
$991$	44.0000			1.39771			0.698853	+	0.715265i	$0.253694\pi$
$992$	−22.0000	+	5.29150i	−0.698501	+	0.168005i
$993$		0			0
$994$	16.0000	+	42.3320i	0.507489	+	1.34269i
$995$		0			0
$996$		0			0
$997$		−	42.3320i		−	1.34067i	−0.742059	−	0.670334i	$-0.766151\pi$
$997$		−	42.3320i		−	1.34067i	0.742059	−	0.670334i	$-0.233849\pi$
$998$	−35.0000	+	13.2288i	−1.10791	+	0.418749i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1800.2.k.d.901.1		2
3.2	odd	2		200.2.d.c.101.2	yes	2
4.3	odd	2		7200.2.k.b.3601.1		2
5.2	odd	4		1800.2.d.m.1549.3		4
5.3	odd	4		1800.2.d.m.1549.2		4
5.4	even	2		1800.2.k.f.901.2		2
8.3	odd	2		7200.2.k.b.3601.2		2
8.5	even	2	inner	1800.2.k.d.901.2		2
12.11	even	2		800.2.d.a.401.1		2
15.2	even	4		200.2.f.d.149.2		4
15.8	even	4		200.2.f.d.149.3		4
15.14	odd	2		200.2.d.b.101.1	✓	2
20.3	even	4		7200.2.d.m.2449.3		4
20.7	even	4		7200.2.d.m.2449.1		4
20.19	odd	2		7200.2.k.i.3601.1		2
24.5	odd	2		200.2.d.c.101.1	yes	2
24.11	even	2		800.2.d.a.401.2		2
40.3	even	4		7200.2.d.m.2449.4		4
40.13	odd	4		1800.2.d.m.1549.4		4
40.19	odd	2		7200.2.k.i.3601.2		2
40.27	even	4		7200.2.d.m.2449.2		4
40.29	even	2		1800.2.k.f.901.1		2
40.37	odd	4		1800.2.d.m.1549.1		4
48.5	odd	4		6400.2.a.bg.1.2		2
48.11	even	4		6400.2.a.cb.1.1		2
48.29	odd	4		6400.2.a.bg.1.1		2
48.35	even	4		6400.2.a.cb.1.2		2
60.23	odd	4		800.2.f.d.49.4		4
60.47	odd	4		800.2.f.d.49.1		4
60.59	even	2		800.2.d.d.401.2		2
120.29	odd	2		200.2.d.b.101.2	yes	2
120.53	even	4		200.2.f.d.149.1		4
120.59	even	2		800.2.d.d.401.1		2
120.77	even	4		200.2.f.d.149.4		4
120.83	odd	4		800.2.f.d.49.2		4
120.107	odd	4		800.2.f.d.49.3		4
240.29	odd	4		6400.2.a.cc.1.2		2
240.59	even	4		6400.2.a.bh.1.2		2
240.149	odd	4		6400.2.a.cc.1.1		2
240.179	even	4		6400.2.a.bh.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.d.b.101.1	✓	2	15.14	odd	2
200.2.d.b.101.2	yes	2	120.29	odd	2
200.2.d.c.101.1	yes	2	24.5	odd	2
200.2.d.c.101.2	yes	2	3.2	odd	2
200.2.f.d.149.1		4	120.53	even	4
200.2.f.d.149.2		4	15.2	even	4
200.2.f.d.149.3		4	15.8	even	4
200.2.f.d.149.4		4	120.77	even	4
800.2.d.a.401.1		2	12.11	even	2
800.2.d.a.401.2		2	24.11	even	2
800.2.d.d.401.1		2	120.59	even	2
800.2.d.d.401.2		2	60.59	even	2
800.2.f.d.49.1		4	60.47	odd	4
800.2.f.d.49.2		4	120.83	odd	4
800.2.f.d.49.3		4	120.107	odd	4
800.2.f.d.49.4		4	60.23	odd	4
1800.2.d.m.1549.1		4	40.37	odd	4
1800.2.d.m.1549.2		4	5.3	odd	4
1800.2.d.m.1549.3		4	5.2	odd	4
1800.2.d.m.1549.4		4	40.13	odd	4
1800.2.k.d.901.1		2	1.1	even	1	trivial
1800.2.k.d.901.2		2	8.5	even	2	inner
1800.2.k.f.901.1		2	40.29	even	2
1800.2.k.f.901.2		2	5.4	even	2
6400.2.a.bg.1.1		2	48.29	odd	4
6400.2.a.bg.1.2		2	48.5	odd	4
6400.2.a.bh.1.1		2	240.179	even	4
6400.2.a.bh.1.2		2	240.59	even	4
6400.2.a.cb.1.1		2	48.11	even	4
6400.2.a.cb.1.2		2	48.35	even	4
6400.2.a.cc.1.1		2	240.149	odd	4
6400.2.a.cc.1.2		2	240.29	odd	4
7200.2.d.m.2449.1		4	20.7	even	4
7200.2.d.m.2449.2		4	40.27	even	4
7200.2.d.m.2449.3		4	20.3	even	4
7200.2.d.m.2449.4		4	40.3	even	4
7200.2.k.b.3601.1		2	4.3	odd	2
7200.2.k.b.3601.2		2	8.3	odd	2
7200.2.k.i.3601.1		2	20.19	odd	2
7200.2.k.i.3601.2		2	40.19	odd	2

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:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1800.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 1.32288i) q^{2} +(-1.50000 + 1.32288i) q^{4} +4.00000 q^{7} +(2.50000 + 1.32288i) q^{8} +O(q^{10})\)	\(q+(-0.500000 - 1.32288i) q^{2} +(-1.50000 + 1.32288i) q^{4} +4.00000 q^{7} +(2.50000 + 1.32288i) q^{8} +2.64575i q^{11} +(-2.00000 - 5.29150i) q^{14} +(0.500000 - 3.96863i) q^{16} +3.00000 q^{17} -2.64575i q^{19} +(3.50000 - 1.32288i) q^{22} -4.00000 q^{23} +(-6.00000 + 5.29150i) q^{28} +4.00000 q^{31} +(-5.50000 + 1.32288i) q^{32} +(-1.50000 - 3.96863i) q^{34} +10.5830i q^{37} +(-3.50000 + 1.32288i) q^{38} +5.00000 q^{41} +5.29150i q^{43} +(-3.50000 - 3.96863i) q^{44} +(2.00000 + 5.29150i) q^{46} +8.00000 q^{47} +9.00000 q^{49} +10.5830i q^{53} +(10.0000 + 5.29150i) q^{56} +5.29150i q^{59} -10.5830i q^{61} +(-2.00000 - 5.29150i) q^{62} +(4.50000 + 6.61438i) q^{64} -7.93725i q^{67} +(-4.50000 + 3.96863i) q^{68} -8.00000 q^{71} -7.00000 q^{73} +(14.0000 - 5.29150i) q^{74} +(3.50000 + 3.96863i) q^{76} +10.5830i q^{77} +4.00000 q^{79} +(-2.50000 - 6.61438i) q^{82} +7.93725i q^{83} +(7.00000 - 2.64575i) q^{86} +(-3.50000 + 6.61438i) q^{88} +1.00000 q^{89} +(6.00000 - 5.29150i) q^{92} +(-4.00000 - 10.5830i) q^{94} -2.00000 q^{97} +(-4.50000 - 11.9059i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 3 q^{4} + 8 q^{7} + 5 q^{8}+O(q^{10}) \) 2 * q - q^2 - 3 * q^4 + 8 * q^7 + 5 * q^8	\( 2 q - q^{2} - 3 q^{4} + 8 q^{7} + 5 q^{8} - 4 q^{14} + q^{16} + 6 q^{17} + 7 q^{22} - 8 q^{23} - 12 q^{28} + 8 q^{31} - 11 q^{32} - 3 q^{34} - 7 q^{38} + 10 q^{41} - 7 q^{44} + 4 q^{46} + 16 q^{47} + 18 q^{49} + 20 q^{56} - 4 q^{62} + 9 q^{64} - 9 q^{68} - 16 q^{71} - 14 q^{73} + 28 q^{74} + 7 q^{76} + 8 q^{79} - 5 q^{82} + 14 q^{86} - 7 q^{88} + 2 q^{89} + 12 q^{92} - 8 q^{94} - 4 q^{97} - 9 q^{98}+O(q^{100}) \) 2 * q - q^2 - 3 * q^4 + 8 * q^7 + 5 * q^8 - 4 * q^14 + q^16 + 6 * q^17 + 7 * q^22 - 8 * q^23 - 12 * q^28 + 8 * q^31 - 11 * q^32 - 3 * q^34 - 7 * q^38 + 10 * q^41 - 7 * q^44 + 4 * q^46 + 16 * q^47 + 18 * q^49 + 20 * q^56 - 4 * q^62 + 9 * q^64 - 9 * q^68 - 16 * q^71 - 14 * q^73 + 28 * q^74 + 7 * q^76 + 8 * q^79 - 5 * q^82 + 14 * q^86 - 7 * q^88 + 2 * q^89 + 12 * q^92 - 8 * q^94 - 4 * q^97 - 9 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more