LMFDB - Embedded newform 2880.2.bc.a.593.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2880,2,Mod(593,2880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2880, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2, 3]))

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

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

chi := DirichletCharacter("2880.593");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2880 = 2^{6} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2880.bc (of order $4$, degree $2$, not 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:	$22.9969157821$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 720)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			593.19
Character	$\chi$	$=$	2880.593
Dual form			2880.2.bc.a.1457.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.885098 - 2.05344i) q^{5} +(2.95475 + 2.95475i) q^{7} +O(q^{10})$	$q+(-0.885098 - 2.05344i) q^{5} +(2.95475 + 2.95475i) q^{7} +(3.61713 + 3.61713i) q^{11} -1.28740i q^{13} +(2.43224 + 2.43224i) q^{17} +(-5.43015 + 5.43015i) q^{19} +(2.71144 + 2.71144i) q^{23} +(-3.43320 + 3.63498i) q^{25} +(-5.01100 - 5.01100i) q^{29} -2.34837 q^{31} +(3.45215 - 8.68264i) q^{35} +11.0475i q^{37} -3.26156 q^{41} -7.96224 q^{43} +(1.40195 + 1.40195i) q^{47} +10.4611i q^{49} -5.31895i q^{53} +(4.22603 - 10.6291i) q^{55} +(4.52081 - 4.52081i) q^{59} +(-3.56188 - 3.56188i) q^{61} +(-2.64359 + 1.13947i) q^{65} -10.3086 q^{67} +1.00768 q^{71} +(7.33627 - 7.33627i) q^{73} +21.3754i q^{77} +12.5700i q^{79} -8.27662 q^{83} +(2.84168 - 7.14723i) q^{85} +1.25100i q^{89} +(3.80394 - 3.80394i) q^{91} +(15.9567 + 6.34425i) q^{95} +(-5.33721 + 5.33721i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 16 q^{19} - 64 q^{43} + 32 q^{61}+O(q^{100}) $ 96 * q - 16 * q^19 - 64 * q^43 + 32 * q^61

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$2431$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.885098	−	2.05344i	−0.395828	−	0.918325i
$5$	−0.885098	−	2.05344i	−0.395828	−	0.918325i
$6$		0			0
$7$	2.95475	+	2.95475i	1.11679	+	1.11679i	0.992209	+	0.124582i	$0.0397591\pi$
$7$	2.95475	+	2.95475i	1.11679	+	1.11679i	0.124582	+	0.992209i	$0.460241\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.61713	+	3.61713i	1.09061	+	1.09061i	0.995464	+	0.0951414i	$0.0303303\pi$
$11$	3.61713	+	3.61713i	1.09061	+	1.09061i	0.0951414	+	0.995464i	$0.469670\pi$
$12$		0			0
$13$		−	1.28740i		−	0.357059i	−0.983935	−	0.178530i	$-0.942866\pi$
$13$		−	1.28740i		−	0.357059i	0.983935	−	0.178530i	$-0.0571341\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.43224	+	2.43224i	0.589905	+	0.589905i	0.937606	−	0.347700i	$-0.113037\pi$
$17$	2.43224	+	2.43224i	0.589905	+	0.589905i	−0.347700	+	0.937606i	$0.613037\pi$
$18$		0			0
$19$	−5.43015	+	5.43015i	−1.24576	+	1.24576i	−0.288186	+	0.957574i	$0.593052\pi$
$19$	−5.43015	+	5.43015i	−1.24576	+	1.24576i	−0.957574	+	0.288186i	$0.906948\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.71144	+	2.71144i	0.565375	+	0.565375i	0.930829	−	0.365454i	$-0.119086\pi$
$23$	2.71144	+	2.71144i	0.565375	+	0.565375i	−0.365454	+	0.930829i	$0.619086\pi$
$24$		0			0
$25$	−3.43320	+	3.63498i	−0.686641	+	0.726997i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−5.01100	−	5.01100i	−0.930519	−	0.930519i	0.0672192	−	0.997738i	$-0.478587\pi$
$29$	−5.01100	−	5.01100i	−0.930519	−	0.930519i	−0.997738	+	0.0672192i	$0.978587\pi$
$30$		0			0
$31$	−2.34837			−0.421780			−0.210890	−	0.977510i	$-0.567636\pi$
$31$	−2.34837			−0.421780			−0.210890	+	0.977510i	$0.567636\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.45215	−	8.68264i	0.583520	−	1.46763i
$36$		0			0
$37$			11.0475i			1.81620i	0.418757	+	0.908098i	$0.362466\pi$
$37$			11.0475i			1.81620i	−0.418757	+	0.908098i	$0.637534\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.26156			−0.509371			−0.254685	−	0.967024i	$-0.581972\pi$
$41$	−3.26156			−0.509371			−0.254685	+	0.967024i	$0.581972\pi$
$42$		0			0
$43$	−7.96224			−1.21423			−0.607115	−	0.794614i	$-0.707673\pi$
$43$	−7.96224			−1.21423			−0.607115	+	0.794614i	$0.707673\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.40195	+	1.40195i	0.204496	+	0.204496i	0.801923	−	0.597427i	$-0.203810\pi$
$47$	1.40195	+	1.40195i	0.204496	+	0.204496i	−0.597427	+	0.801923i	$0.703810\pi$
$48$		0			0
$49$			10.4611i			1.49445i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	5.31895i		−	0.730614i	−0.930887	−	0.365307i	$-0.880964\pi$
$53$		−	5.31895i		−	0.730614i	0.930887	−	0.365307i	$-0.119036\pi$
$54$		0			0
$55$	4.22603	−	10.6291i	0.569838	−	1.43322i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.52081	−	4.52081i	0.588559	−	0.588559i	−0.348682	−	0.937241i	$-0.613371\pi$
$59$	4.52081	−	4.52081i	0.588559	−	0.588559i	0.937241	+	0.348682i	$0.113371\pi$
$60$		0			0
$61$	−3.56188	−	3.56188i	−0.456052	−	0.456052i	0.441305	−	0.897357i	$-0.354516\pi$
$61$	−3.56188	−	3.56188i	−0.456052	−	0.456052i	−0.897357	+	0.441305i	$0.854516\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.64359	+	1.13947i	−0.327897	+	0.141334i
$66$		0			0
$67$	−10.3086			−1.25939			−0.629696	−	0.776841i	$-0.716821\pi$
$67$	−10.3086			−1.25939			−0.629696	+	0.776841i	$0.716821\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.00768			0.119589			0.0597945	−	0.998211i	$-0.480955\pi$
$71$	1.00768			0.119589			0.0597945	+	0.998211i	$0.480955\pi$
$72$		0			0
$73$	7.33627	−	7.33627i	0.858646	−	0.858646i	−0.132533	−	0.991179i	$-0.542311\pi$
$73$	7.33627	−	7.33627i	0.858646	−	0.858646i	0.991179	+	0.132533i	$0.0423109\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			21.3754i			2.43596i
$78$		0			0
$79$			12.5700i			1.41424i	0.707094	+	0.707119i	$0.250006\pi$
$79$			12.5700i			1.41424i	−0.707094	+	0.707119i	$0.749994\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−8.27662			−0.908478			−0.454239	−	0.890880i	$-0.650089\pi$
$83$	−8.27662			−0.908478			−0.454239	+	0.890880i	$0.650089\pi$
$84$		0			0
$85$	2.84168	−	7.14723i	0.308224	−	0.775225i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			1.25100i			0.132606i	0.997800	+	0.0663028i	$0.0211203\pi$
$89$			1.25100i			0.132606i	−0.997800	+	0.0663028i	$0.978880\pi$
$90$		0			0
$91$	3.80394	−	3.80394i	0.398761	−	0.398761i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	15.9567	+	6.34425i	1.63712	+	0.650906i
$96$		0			0
$97$	−5.33721	+	5.33721i	−0.541912	+	0.541912i	−0.924089	−	0.382177i	$-0.875174\pi$
$97$	−5.33721	+	5.33721i	−0.541912	+	0.541912i	0.382177	+	0.924089i	$0.375174\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.69709	+	2.69709i	0.268371	+	0.268371i	0.828444	−	0.560073i	$-0.189227\pi$
$101$	2.69709	+	2.69709i	0.268371	+	0.268371i	−0.560073	+	0.828444i	$0.689227\pi$
$102$		0			0
$103$	3.12997	−	3.12997i	0.308405	−	0.308405i	−0.535885	−	0.844291i	$-0.680022\pi$
$103$	3.12997	−	3.12997i	0.308405	−	0.308405i	0.844291	+	0.535885i	$0.180022\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7.25131			0.701011			0.350505	−	0.936561i	$-0.386010\pi$
$107$	7.25131			0.701011			0.350505	+	0.936561i	$0.386010\pi$
$108$		0			0
$109$	1.67047	−	1.67047i	0.160002	−	0.160002i	−0.622566	−	0.782568i	$-0.713910\pi$
$109$	1.67047	−	1.67047i	0.160002	−	0.160002i	0.782568	+	0.622566i	$0.213910\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.13172	−	3.13172i	0.294607	−	0.294607i	−0.544290	−	0.838897i	$-0.683201\pi$
$113$	3.13172	−	3.13172i	0.294607	−	0.294607i	0.838897	+	0.544290i	$0.183201\pi$
$114$		0			0
$115$	3.16788	−	7.96767i	0.295407	−	0.742989i
$116$		0			0
$117$		0			0
$118$		0			0
$119$			14.3733i			1.31760i
$120$		0			0
$121$			15.1672i			1.37884i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	10.5029	+	3.83255i	0.939411	+	0.342794i
$126$		0			0
$127$	1.43480	−	1.43480i	0.127318	−	0.127318i	−0.640577	−	0.767894i	$-0.721305\pi$
$127$	1.43480	−	1.43480i	0.127318	−	0.127318i	0.767894	+	0.640577i	$0.221305\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−11.3047	+	11.3047i	−0.987693	+	0.987693i	−0.999925	−	0.0122320i	$-0.996106\pi$
$131$	−11.3047	+	11.3047i	−0.987693	+	0.987693i	0.0122320	+	0.999925i	$0.496106\pi$
$132$		0			0
$133$	−32.0895			−2.78251
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−14.2813	+	14.2813i	−1.22013	+	1.22013i	−0.252546	+	0.967585i	$0.581268\pi$
$137$	−14.2813	+	14.2813i	−1.22013	+	1.22013i	−0.967585	+	0.252546i	$0.918732\pi$
$138$		0			0
$139$	5.63320	+	5.63320i	0.477802	+	0.477802i	0.904428	−	0.426626i	$-0.140298\pi$
$139$	5.63320	+	5.63320i	0.477802	+	0.477802i	−0.426626	+	0.904428i	$0.640298\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	4.65668	−	4.65668i	0.389411	−	0.389411i
$144$		0			0
$145$	−5.85454	+	14.7250i	−0.486193	+	1.22284i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	12.9642	−	12.9642i	1.06207	−	1.06207i	0.0641253	−	0.997942i	$-0.479574\pi$
$149$	12.9642	−	12.9642i	1.06207	−	1.06207i	0.997942	−	0.0641253i	$-0.0204257\pi$
$150$		0			0
$151$			5.31628i			0.432633i	0.976323	+	0.216317i	$0.0694043\pi$
$151$			5.31628i			0.432633i	−0.976323	+	0.216317i	$0.930596\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.07854	+	4.82223i	0.166952	+	0.387331i
$156$		0			0
$157$	2.14964			0.171560			0.0857799	−	0.996314i	$-0.472662\pi$
$157$	2.14964			0.171560			0.0857799	+	0.996314i	$0.472662\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			16.0233i			1.26281i
$162$		0			0
$163$			0.378998i			0.0296854i	0.999890	+	0.0148427i	$0.00472475\pi$
$163$			0.378998i			0.0296854i	−0.999890	+	0.0148427i	$0.995275\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.93888	−	4.93888i	0.382182	−	0.382182i	−0.489706	−	0.871888i	$-0.662896\pi$
$167$	4.93888	−	4.93888i	0.382182	−	0.382182i	0.871888	+	0.489706i	$0.162896\pi$
$168$		0			0
$169$	11.3426			0.872509
$170$		0			0
$171$		0			0
$172$		0			0
$173$	12.4612			0.947405			0.473703	−	0.880685i	$-0.342917\pi$
$173$	12.4612			0.947405			0.473703	+	0.880685i	$0.342917\pi$
$174$		0			0
$175$	−20.8848	+	0.596211i	−1.57874	+	0.0450693i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	8.19137	+	8.19137i	0.612252	+	0.612252i	0.943532	−	0.331281i	$-0.107481\pi$
$179$	8.19137	+	8.19137i	0.612252	+	0.612252i	−0.331281	+	0.943532i	$0.607481\pi$
$180$		0			0
$181$	8.88962	−	8.88962i	0.660761	−	0.660761i	−0.294799	−	0.955559i	$-0.595253\pi$
$181$	8.88962	−	8.88962i	0.660761	−	0.660761i	0.955559	+	0.294799i	$0.0952526\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	22.6853	−	9.77811i	1.66786	−	0.718901i
$186$		0			0
$187$			17.5955i			1.28671i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			3.22015i			0.233002i	0.993191	+	0.116501i	$0.0371679\pi$
$191$			3.22015i			0.233002i	−0.993191	+	0.116501i	$0.962832\pi$
$192$		0			0
$193$	11.6698	+	11.6698i	0.840012	+	0.840012i	0.988860	−	0.148848i	$-0.0475564\pi$
$193$	11.6698	+	11.6698i	0.840012	+	0.840012i	−0.148848	+	0.988860i	$0.547556\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	20.1837			1.43803			0.719015	−	0.694994i	$-0.244593\pi$
$197$	20.1837			1.43803			0.719015	+	0.694994i	$0.244593\pi$
$198$		0			0
$199$	14.7485			1.04549			0.522745	−	0.852489i	$-0.324908\pi$
$199$	14.7485			1.04549			0.522745	+	0.852489i	$0.324908\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		−	29.6125i		−	2.07839i
$204$		0			0
$205$	2.88680	+	6.69741i	0.201623	+	0.467768i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−39.2831			−2.71727
$210$		0			0
$211$	9.01000	+	9.01000i	0.620274	+	0.620274i	0.945602	−	0.325327i	$-0.105474\pi$
$211$	9.01000	+	9.01000i	0.620274	+	0.620274i	−0.325327	+	0.945602i	$0.605474\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	7.04736	+	16.3500i	0.480626	+	1.11506i
$216$		0			0
$217$	−6.93885	−	6.93885i	−0.471040	−	0.471040i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	3.13126	−	3.13126i	0.210631	−	0.210631i
$222$		0			0
$223$	2.15425	+	2.15425i	0.144259	+	0.144259i	0.775548	−	0.631289i	$-0.217474\pi$
$223$	2.15425	+	2.15425i	0.144259	+	0.144259i	−0.631289	+	0.775548i	$0.717474\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		−	16.5732i		−	1.10000i	−0.835164	−	0.550001i	$-0.814627\pi$
$227$		−	16.5732i		−	1.10000i	0.835164	−	0.550001i	$-0.185373\pi$
$228$		0			0
$229$	8.49078	+	8.49078i	0.561086	+	0.561086i	0.929616	−	0.368530i	$-0.120139\pi$
$229$	8.49078	+	8.49078i	0.561086	+	0.561086i	−0.368530	+	0.929616i	$0.620139\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.11817	−	3.11817i	−0.204278	−	0.204278i	0.597552	−	0.801830i	$-0.296140\pi$
$233$	−3.11817	−	3.11817i	−0.204278	−	0.204278i	−0.801830	+	0.597552i	$0.796140\pi$
$234$		0			0
$235$	1.63796	−	4.11969i	0.106849	−	0.268739i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−12.1278			−0.784484			−0.392242	−	0.919862i	$-0.628300\pi$
$239$	−12.1278			−0.784484			−0.392242	+	0.919862i	$0.628300\pi$
$240$		0			0
$241$	−28.8486			−1.85830			−0.929150	−	0.369702i	$-0.879460\pi$
$241$	−28.8486			−1.85830			−0.929150	+	0.369702i	$0.879460\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	21.4813	−	9.25912i	1.37239	−	0.591544i
$246$		0			0
$247$	6.99075	+	6.99075i	0.444811	+	0.444811i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1.78976	−	1.78976i	−0.112969	−	0.112969i	0.648363	−	0.761331i	$-0.275454\pi$
$251$	−1.78976	−	1.78976i	−0.112969	−	0.112969i	−0.761331	+	0.648363i	$0.775454\pi$
$252$		0			0
$253$			19.6153i			1.23320i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−15.5378	−	15.5378i	−0.969219	−	0.969219i	0.0303213	−	0.999540i	$-0.490347\pi$
$257$	−15.5378	−	15.5378i	−0.969219	−	0.969219i	−0.999540	+	0.0303213i	$0.990347\pi$
$258$		0			0
$259$	−32.6426	+	32.6426i	−2.02831	+	2.02831i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3.41097	−	3.41097i	−0.210329	−	0.210329i	0.594078	−	0.804407i	$-0.297517\pi$
$263$	−3.41097	−	3.41097i	−0.210329	−	0.210329i	−0.804407	+	0.594078i	$0.797517\pi$
$264$		0			0
$265$	−10.9221	+	4.70779i	−0.670941	+	0.289197i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	11.6355	+	11.6355i	0.709432	+	0.709432i	0.966416	−	0.256984i	$-0.0827288\pi$
$269$	11.6355	+	11.6355i	0.709432	+	0.709432i	−0.256984	+	0.966416i	$0.582729\pi$
$270$		0			0
$271$	9.36936			0.569148			0.284574	−	0.958654i	$-0.408148\pi$
$271$	9.36936			0.569148			0.284574	+	0.958654i	$0.408148\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−25.5665	+	0.729865i	−1.54172	+	0.0440125i
$276$		0			0
$277$		−	5.69137i		−	0.341961i	−0.985274	−	0.170981i	$-0.945306\pi$
$277$		−	5.69137i		−	0.341961i	0.985274	−	0.170981i	$-0.0546936\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	23.1278			1.37969			0.689844	−	0.723958i	$-0.257679\pi$
$281$	23.1278			1.37969			0.689844	+	0.723958i	$0.257679\pi$
$282$		0			0
$283$	−0.740637			−0.0440263			−0.0220131	−	0.999758i	$-0.507008\pi$
$283$	−0.740637			−0.0440263			−0.0220131	+	0.999758i	$0.507008\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−9.63712	−	9.63712i	−0.568861	−	0.568861i
$288$		0			0
$289$		−	5.16840i		−	0.304024i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	11.1074i		−	0.648904i	−0.945902	−	0.324452i	$-0.894820\pi$
$293$		−	11.1074i		−	0.648904i	0.945902	−	0.324452i	$-0.105180\pi$
$294$		0			0
$295$	−13.2845	−	5.28184i	−0.773456	−	0.307520i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.49070	−	3.49070i	0.201872	−	0.201872i
$300$		0			0
$301$	−23.5265	−	23.5265i	−1.35604	−	1.35604i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−4.16148	+	10.4667i	−0.238286	+	0.599322i
$306$		0			0
$307$	11.4986			0.656259			0.328130	−	0.944633i	$-0.393582\pi$
$307$	11.4986			0.656259			0.328130	+	0.944633i	$0.393582\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.31180			0.0743854			0.0371927	−	0.999308i	$-0.488158\pi$
$311$	1.31180			0.0743854			0.0371927	+	0.999308i	$0.488158\pi$
$312$		0			0
$313$	8.64685	−	8.64685i	0.488749	−	0.488749i	−0.419162	−	0.907911i	$-0.637676\pi$
$313$	8.64685	−	8.64685i	0.488749	−	0.488749i	0.907911	+	0.419162i	$0.137676\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	13.3113i		−	0.747638i	−0.927502	−	0.373819i	$-0.878048\pi$
$317$		−	13.3113i		−	0.747638i	0.927502	−	0.373819i	$-0.121952\pi$
$318$		0			0
$319$		−	36.2508i		−	2.02966i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−26.4148			−1.46976
$324$		0			0
$325$	4.67966	+	4.41989i	0.259581	+	0.245172i
$326$		0			0
$327$		0			0
$328$		0			0
$329$			8.28485i			0.456759i
$330$		0			0
$331$	−10.2209	+	10.2209i	−0.561791	+	0.561791i	−0.929816	−	0.368025i	$-0.880034\pi$
$331$	−10.2209	+	10.2209i	−0.561791	+	0.561791i	0.368025	+	0.929816i	$0.380034\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	9.12410	+	21.1680i	0.498503	+	1.15653i
$336$		0			0
$337$	−5.56007	+	5.56007i	−0.302877	+	0.302877i	−0.842138	−	0.539262i	$-0.818703\pi$
$337$	−5.56007	+	5.56007i	−0.302877	+	0.302877i	0.539262	+	0.842138i	$0.318703\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−8.49435	−	8.49435i	−0.459995	−	0.459995i
$342$		0			0
$343$	−10.2268	+	10.2268i	−0.552194	+	0.552194i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−19.5961			−1.05198			−0.525988	−	0.850492i	$-0.676304\pi$
$347$	−19.5961			−1.05198			−0.525988	+	0.850492i	$0.676304\pi$
$348$		0			0
$349$	14.5563	−	14.5563i	0.779180	−	0.779180i	−0.200511	−	0.979691i	$-0.564260\pi$
$349$	14.5563	−	14.5563i	0.779180	−	0.779180i	0.979691	+	0.200511i	$0.0642602\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	4.78573	−	4.78573i	0.254719	−	0.254719i	−0.568183	−	0.822902i	$-0.692354\pi$
$353$	4.78573	−	4.78573i	0.254719	−	0.254719i	0.822902	+	0.568183i	$0.192354\pi$
$354$		0			0
$355$	−0.891891	−	2.06920i	−0.0473367	−	0.109822i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			29.0637i			1.53392i	0.641694	+	0.766961i	$0.278232\pi$
$359$			29.0637i			1.53392i	−0.641694	+	0.766961i	$0.721768\pi$
$360$		0			0
$361$		−	39.9730i		−	2.10384i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−21.5579	−	8.57125i	−1.12839	−	0.448640i
$366$		0			0
$367$	−7.48950	+	7.48950i	−0.390949	+	0.390949i	−0.875026	−	0.484077i	$-0.839156\pi$
$367$	−7.48950	+	7.48950i	−0.390949	+	0.390949i	0.484077	+	0.875026i	$0.339156\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	15.7162	−	15.7162i	0.815944	−	0.815944i
$372$		0			0
$373$	−2.29737			−0.118953			−0.0594767	−	0.998230i	$-0.518943\pi$
$373$	−2.29737			−0.118953			−0.0594767	+	0.998230i	$0.518943\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−6.45114	+	6.45114i	−0.332251	+	0.332251i
$378$		0			0
$379$	−9.49672	−	9.49672i	−0.487814	−	0.487814i	0.419802	−	0.907616i	$-0.362100\pi$
$379$	−9.49672	−	9.49672i	−0.487814	−	0.487814i	−0.907616	+	0.419802i	$0.862100\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.76742	−	2.76742i	0.141409	−	0.141409i	−0.632859	−	0.774267i	$-0.718119\pi$
$383$	2.76742	−	2.76742i	0.141409	−	0.141409i	0.774267	+	0.632859i	$0.218119\pi$
$384$		0			0
$385$	43.8931	−	18.9194i	2.23700	−	0.964220i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−12.1823	+	12.1823i	−0.617668	+	0.617668i	−0.944933	−	0.327264i	$-0.893873\pi$
$389$	−12.1823	+	12.1823i	−0.617668	+	0.617668i	0.327264	+	0.944933i	$0.393873\pi$
$390$		0			0
$391$			13.1898i			0.667035i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	25.8118	−	11.1257i	1.29873	−	0.559795i
$396$		0			0
$397$	−6.87502			−0.345047			−0.172524	−	0.985005i	$-0.555192\pi$
$397$	−6.87502			−0.345047			−0.172524	+	0.985005i	$0.555192\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			17.9268i			0.895220i	0.894229	+	0.447610i	$0.147725\pi$
$401$			17.9268i			0.895220i	−0.894229	+	0.447610i	$0.852275\pi$
$402$		0			0
$403$			3.02328i			0.150600i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−39.9602	+	39.9602i	−1.98075	+	1.98075i
$408$		0			0
$409$	17.4547			0.863077			0.431539	−	0.902094i	$-0.357971\pi$
$409$	17.4547			0.863077			0.431539	+	0.902094i	$0.357971\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	26.7157			1.31460
$414$		0			0
$415$	7.32562	+	16.9955i	0.359601	+	0.834277i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.120315	+	0.120315i	0.00587776	+	0.00587776i	0.710040	−	0.704162i	$-0.248677\pi$
$419$	0.120315	+	0.120315i	0.00587776	+	0.00587776i	−0.704162	+	0.710040i	$0.748677\pi$
$420$		0			0
$421$	20.7067	−	20.7067i	1.00918	−	1.00918i	0.00922753	−	0.999957i	$-0.497063\pi$
$421$	20.7067	−	20.7067i	1.00918	−	1.00918i	0.999957	−	0.00922753i	$-0.00293726\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−17.1915	+	0.490779i	−0.833912	+	0.0238063i
$426$		0			0
$427$		−	21.0489i		−	1.01863i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	17.8033i		−	0.857553i	−0.903411	−	0.428777i	$-0.858945\pi$
$431$		−	17.8033i		−	0.857553i	0.903411	−	0.428777i	$-0.141055\pi$
$432$		0			0
$433$	10.5630	+	10.5630i	0.507626	+	0.507626i	0.913797	−	0.406171i	$-0.133136\pi$
$433$	10.5630	+	10.5630i	0.507626	+	0.507626i	−0.406171	+	0.913797i	$0.633136\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−29.4471			−1.40864
$438$		0			0
$439$	36.3479			1.73479			0.867396	−	0.497619i	$-0.165792\pi$
$439$	36.3479			1.73479			0.867396	+	0.497619i	$0.165792\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	10.7946i		−	0.512867i	−0.966562	−	0.256433i	$-0.917453\pi$
$443$		−	10.7946i		−	0.512867i	0.966562	−	0.256433i	$-0.0825474\pi$
$444$		0			0
$445$	2.56885	−	1.10726i	0.121775	−	0.0524890i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	9.02050			0.425704			0.212852	−	0.977084i	$-0.431725\pi$
$449$	9.02050			0.425704			0.212852	+	0.977084i	$0.431725\pi$
$450$		0			0
$451$	−11.7975	−	11.7975i	−0.555522	−	0.555522i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−11.1780	−	4.44429i	−0.524033	−	0.208351i
$456$		0			0
$457$	2.43844	+	2.43844i	0.114065	+	0.114065i	0.761836	−	0.647770i	$-0.224298\pi$
$457$	2.43844	+	2.43844i	0.114065	+	0.114065i	−0.647770	+	0.761836i	$0.724298\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−6.84645	+	6.84645i	−0.318871	+	0.318871i	−0.848333	−	0.529463i	$-0.822394\pi$
$461$	−6.84645	+	6.84645i	−0.318871	+	0.318871i	0.529463	+	0.848333i	$0.322394\pi$
$462$		0			0
$463$	−16.8447	−	16.8447i	−0.782840	−	0.782840i	0.197469	−	0.980309i	$-0.436728\pi$
$463$	−16.8447	−	16.8447i	−0.782840	−	0.782840i	−0.980309	+	0.197469i	$0.936728\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	25.2999i		−	1.17074i	−0.810766	−	0.585371i	$-0.800949\pi$
$467$		−	25.2999i		−	1.17074i	0.810766	−	0.585371i	$-0.199051\pi$
$468$		0			0
$469$	−30.4593	−	30.4593i	−1.40648	−	1.40648i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−28.8005	−	28.8005i	−1.32425	−	1.32425i
$474$		0			0
$475$	−1.09570	−	38.3813i	−0.0502740	−	1.76105i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	24.2039			1.10591			0.552953	−	0.833213i	$-0.313501\pi$
$479$	24.2039			1.10591			0.552953	+	0.833213i	$0.313501\pi$
$480$		0			0
$481$	14.2225			0.648490
$482$		0			0
$483$		0			0
$484$		0			0
$485$	15.6836	+	6.23567i	0.712155	+	0.283147i
$486$		0			0
$487$	16.5530	+	16.5530i	0.750087	+	0.750087i	0.974495	−	0.224408i	$-0.0720449\pi$
$487$	16.5530	+	16.5530i	0.750087	+	0.750087i	−0.224408	+	0.974495i	$0.572045\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	16.5518	+	16.5518i	0.746973	+	0.746973i	0.973910	−	0.226936i	$-0.0728710\pi$
$491$	16.5518	+	16.5518i	0.746973	+	0.746973i	−0.226936	+	0.973910i	$0.572871\pi$
$492$		0			0
$493$		−	24.3759i		−	1.09784i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.97743	+	2.97743i	0.133556	+	0.133556i
$498$		0			0
$499$	6.54897	−	6.54897i	0.293172	−	0.293172i	−0.545160	−	0.838332i	$-0.683531\pi$
$499$	6.54897	−	6.54897i	0.293172	−	0.293172i	0.838332	+	0.545160i	$0.183531\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−13.0246	−	13.0246i	−0.580737	−	0.580737i	0.354369	−	0.935106i	$-0.384696\pi$
$503$	−13.0246	−	13.0246i	−0.580737	−	0.580737i	−0.935106	+	0.354369i	$0.884696\pi$
$504$		0			0
$505$	3.15112	−	7.92551i	0.140223	−	0.352680i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−6.24626	−	6.24626i	−0.276861	−	0.276861i	0.554994	−	0.831854i	$-0.312721\pi$
$509$	−6.24626	−	6.24626i	−0.276861	−	0.276861i	−0.831854	+	0.554994i	$0.812721\pi$
$510$		0			0
$511$	43.3538			1.91786
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−9.19753	−	3.65687i	−0.405292	−	0.161141i
$516$		0			0
$517$			10.1421i			0.446049i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	38.4835			1.68599			0.842997	−	0.537919i	$-0.180789\pi$
$521$	38.4835			1.68599			0.842997	+	0.537919i	$0.180789\pi$
$522$		0			0
$523$	−27.4115			−1.19862			−0.599310	−	0.800517i	$-0.704558\pi$
$523$	−27.4115			−1.19862			−0.599310	+	0.800517i	$0.704558\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−5.71180	−	5.71180i	−0.248810	−	0.248810i
$528$		0			0
$529$		−	8.29615i		−	0.360702i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			4.19892i			0.181876i
$534$		0			0
$535$	−6.41812	−	14.8901i	−0.277479	−	0.643756i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−37.8392	+	37.8392i	−1.62985	+	1.62985i
$540$		0			0
$541$	20.3334	+	20.3334i	0.874203	+	0.874203i	0.992927	−	0.118724i	$-0.0378805\pi$
$541$	20.3334	+	20.3334i	0.874203	+	0.874203i	−0.118724	+	0.992927i	$0.537881\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−4.90873	−	1.95167i	−0.210267	−	0.0836005i
$546$		0			0
$547$	18.4013			0.786782			0.393391	−	0.919371i	$-0.371302\pi$
$547$	18.4013			0.786782			0.393391	+	0.919371i	$0.371302\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	54.4209			2.31841
$552$		0			0
$553$	−37.1413	+	37.1413i	−1.57941	+	1.57941i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	18.2292i		−	0.772396i	−0.922416	−	0.386198i	$-0.873788\pi$
$557$		−	18.2292i		−	0.772396i	0.922416	−	0.386198i	$-0.126212\pi$
$558$		0			0
$559$			10.2506i			0.433553i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	11.3820			0.479693			0.239846	−	0.970811i	$-0.422903\pi$
$563$	11.3820			0.479693			0.239846	+	0.970811i	$0.422903\pi$
$564$		0			0
$565$	−9.20267	−	3.65891i	−0.387159	−	0.153931i
$566$		0			0
$567$		0			0
$568$		0			0
$569$			2.07077i			0.0868110i	0.999058	+	0.0434055i	$0.0138207\pi$
$569$			2.07077i			0.0868110i	−0.999058	+	0.0434055i	$0.986179\pi$
$570$		0			0
$571$	−5.83887	+	5.83887i	−0.244349	+	0.244349i	−0.818647	−	0.574297i	$-0.805275\pi$
$571$	−5.83887	+	5.83887i	−0.244349	+	0.244349i	0.574297	+	0.818647i	$0.305275\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−19.1650	+	0.547116i	−0.799235	+	0.0228163i
$576$		0			0
$577$	−12.6573	+	12.6573i	−0.526930	+	0.526930i	−0.919656	−	0.392726i	$-0.871532\pi$
$577$	−12.6573	+	12.6573i	−0.526930	+	0.526930i	0.392726	+	0.919656i	$0.371532\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−24.4554	−	24.4554i	−1.01458	−	1.01458i
$582$		0			0
$583$	19.2393	−	19.2393i	0.796812	−	0.796812i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−7.73169			−0.319121			−0.159561	−	0.987188i	$-0.551008\pi$
$587$	−7.73169			−0.319121			−0.159561	+	0.987188i	$0.551008\pi$
$588$		0			0
$589$	12.7520	−	12.7520i	0.525437	−	0.525437i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	12.3552	−	12.3552i	0.507368	−	0.507368i	−0.406350	−	0.913718i	$-0.633199\pi$
$593$	12.3552	−	12.3552i	0.507368	−	0.507368i	0.913718	+	0.406350i	$0.133199\pi$
$594$		0			0
$595$	29.5148	−	12.7218i	1.20999	−	0.521544i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			7.97017i			0.325652i	0.986655	+	0.162826i	$0.0520610\pi$
$599$			7.97017i			0.325652i	−0.986655	+	0.162826i	$0.947939\pi$
$600$		0			0
$601$			43.9508i			1.79279i	0.443254	+	0.896396i	$0.353824\pi$
$601$			43.9508i			1.79279i	−0.443254	+	0.896396i	$0.646176\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	31.1450	−	13.4245i	1.26622	−	0.545783i
$606$		0			0
$607$	14.2979	−	14.2979i	0.580333	−	0.580333i	−0.354661	−	0.934995i	$-0.615404\pi$
$607$	14.2979	−	14.2979i	0.580333	−	0.580333i	0.934995	+	0.354661i	$0.115404\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.80487	−	1.80487i	0.0730172	−	0.0730172i
$612$		0			0
$613$	−45.4796			−1.83690			−0.918452	−	0.395533i	$-0.870560\pi$
$613$	−45.4796			−1.83690			−0.918452	+	0.395533i	$0.870560\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.52703	−	1.52703i	0.0614757	−	0.0614757i	−0.675701	−	0.737176i	$-0.736159\pi$
$617$	1.52703	−	1.52703i	0.0614757	−	0.0614757i	0.737176	+	0.675701i	$0.236159\pi$
$618$		0			0
$619$	24.8382	+	24.8382i	0.998333	+	0.998333i	0.999999	−	0.00166609i	$-0.000530334\pi$
$619$	24.8382	+	24.8382i	0.998333	+	0.998333i	−0.00166609	+	0.999999i	$0.500530\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.69639	+	3.69639i	−0.148093	+	0.148093i
$624$		0			0
$625$	−1.42622	−	24.9593i	−0.0570489	−	0.998371i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−26.8702	+	26.8702i	−1.07138	+	1.07138i
$630$		0			0
$631$		−	18.7937i		−	0.748167i	−0.927395	−	0.374083i	$-0.877957\pi$
$631$		−	18.7937i		−	0.748167i	0.927395	−	0.374083i	$-0.122043\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−4.21620	−	1.67633i	−0.167315	−	0.0665232i
$636$		0			0
$637$	13.4676			0.533606
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	32.0706i		−	1.26671i	−0.773860	−	0.633357i	$-0.781677\pi$
$641$		−	32.0706i		−	1.26671i	0.773860	−	0.633357i	$-0.218323\pi$
$642$		0			0
$643$			38.0443i			1.50032i	0.661257	+	0.750160i	$0.270023\pi$
$643$			38.0443i			1.50032i	−0.661257	+	0.750160i	$0.729977\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	26.0073	−	26.0073i	1.02245	−	1.02245i	0.0227090	−	0.999742i	$-0.492771\pi$
$647$	26.0073	−	26.0073i	1.02245	−	1.02245i	0.999742	−	0.0227090i	$-0.00722912\pi$
$648$		0			0
$649$	32.7047			1.28377
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−48.4527			−1.89610			−0.948050	−	0.318122i	$-0.896948\pi$
$653$	−48.4527			−1.89610			−0.948050	+	0.318122i	$0.896948\pi$
$654$		0			0
$655$	33.2191	+	13.2077i	1.29798	+	0.516067i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.300307	−	0.300307i	−0.0116983	−	0.0116983i	0.701233	−	0.712932i	$-0.252633\pi$
$659$	−0.300307	−	0.300307i	−0.0116983	−	0.0116983i	−0.712932	+	0.701233i	$0.752633\pi$
$660$		0			0
$661$	7.37111	−	7.37111i	0.286703	−	0.286703i	−0.549072	−	0.835775i	$-0.685019\pi$
$661$	7.37111	−	7.37111i	0.286703	−	0.286703i	0.835775	+	0.549072i	$0.185019\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	28.4023	+	65.8937i	1.10139	+	2.55525i
$666$		0			0
$667$		−	27.1741i		−	1.05218i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		−	25.7676i		−	0.994745i
$672$		0			0
$673$	−11.9645	−	11.9645i	−0.461198	−	0.461198i	0.437850	−	0.899048i	$-0.355740\pi$
$673$	−11.9645	−	11.9645i	−0.461198	−	0.461198i	−0.899048	+	0.437850i	$0.855740\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	22.5056			0.864959			0.432480	−	0.901644i	$-0.357639\pi$
$677$	22.5056			0.864959			0.432480	+	0.901644i	$0.357639\pi$
$678$		0			0
$679$	−31.5403			−1.21041
$680$		0			0
$681$		0			0
$682$		0			0
$683$			13.0831i			0.500612i	0.968167	+	0.250306i	$0.0805312\pi$
$683$			13.0831i			0.500612i	−0.968167	+	0.250306i	$0.919469\pi$
$684$		0			0
$685$	41.9660	+	16.6854i	1.60344	+	0.637515i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−6.84760			−0.260873
$690$		0			0
$691$	−25.4481	−	25.4481i	−0.968090	−	0.968090i	0.0314163	−	0.999506i	$-0.489998\pi$
$691$	−25.4481	−	25.4481i	−0.968090	−	0.968090i	−0.999506	+	0.0314163i	$0.989998\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	6.58149	−	16.5534i	0.249650	−	0.627905i
$696$		0			0
$697$	−7.93291	−	7.93291i	−0.300480	−	0.300480i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−35.4058	+	35.4058i	−1.33726	+	1.33726i	−0.438552	+	0.898706i	$0.644509\pi$
$701$	−35.4058	+	35.4058i	−1.33726	+	1.33726i	−0.898706	+	0.438552i	$0.855491\pi$
$702$		0			0
$703$	−59.9895	−	59.9895i	−2.26255	−	2.26255i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			15.9385i			0.599429i
$708$		0			0
$709$	3.37702	+	3.37702i	0.126827	+	0.126827i	0.767671	−	0.640844i	$-0.221416\pi$
$709$	3.37702	+	3.37702i	0.126827	+	0.126827i	−0.640844	+	0.767671i	$0.721416\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−6.36747	−	6.36747i	−0.238464	−	0.238464i
$714$		0			0
$715$	−13.6838	−	5.44058i	−0.511745	−	0.203466i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−18.3683			−0.685022			−0.342511	−	0.939514i	$-0.611277\pi$
$719$	−18.3683			−0.685022			−0.342511	+	0.939514i	$0.611277\pi$
$720$		0			0
$721$	18.4966			0.688849
$722$		0			0
$723$		0			0
$724$		0			0
$725$	35.4187	−	1.01112i	1.31542	−	0.0375521i
$726$		0			0
$727$	−30.6246	−	30.6246i	−1.13580	−	1.13580i	−0.989195	−	0.146609i	$-0.953164\pi$
$727$	−30.6246	−	30.6246i	−1.13580	−	1.13580i	−0.146609	−	0.989195i	$-0.546836\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−19.3661	−	19.3661i	−0.716281	−	0.716281i
$732$		0			0
$733$			10.5919i			0.391220i	0.980682	+	0.195610i	$0.0626687\pi$
$733$			10.5919i			0.391220i	−0.980682	+	0.195610i	$0.937331\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−37.2874	−	37.2874i	−1.37350	−	1.37350i
$738$		0			0
$739$	15.1294	−	15.1294i	0.556543	−	0.556543i	−0.371778	−	0.928321i	$-0.621252\pi$
$739$	15.1294	−	15.1294i	0.556543	−	0.556543i	0.928321	+	0.371778i	$0.121252\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−36.7699	−	36.7699i	−1.34896	−	1.34896i	−0.886794	−	0.462164i	$-0.847073\pi$
$743$	−36.7699	−	36.7699i	−1.34896	−	1.34896i	−0.462164	−	0.886794i	$-0.652927\pi$
$744$		0			0
$745$	−38.0957	−	15.1466i	−1.39572	−	0.554927i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	21.4258	+	21.4258i	0.782883	+	0.782883i
$750$		0			0
$751$	46.7636			1.70643			0.853214	−	0.521562i	$-0.174650\pi$
$751$	46.7636			1.70643			0.853214	+	0.521562i	$0.174650\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	10.9167	−	4.70543i	0.397298	−	0.171248i
$756$		0			0
$757$			32.3314i			1.17510i	0.809186	+	0.587552i	$0.199908\pi$
$757$			32.3314i			1.17510i	−0.809186	+	0.587552i	$0.800092\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−46.1502			−1.67294			−0.836471	−	0.548011i	$-0.815385\pi$
$761$	−46.1502			−1.67294			−0.836471	+	0.548011i	$0.815385\pi$
$762$		0			0
$763$	9.87164			0.357377
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5.82007	−	5.82007i	−0.210151	−	0.210151i
$768$		0			0
$769$			46.0181i			1.65945i	0.558169	+	0.829727i	$0.311504\pi$
$769$			46.0181i			1.65945i	−0.558169	+	0.829727i	$0.688496\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	21.0373i		−	0.756657i	−0.925671	−	0.378329i	$-0.876499\pi$
$773$		−	21.0373i		−	0.756657i	0.925671	−	0.378329i	$-0.123501\pi$
$774$		0			0
$775$	8.06243	−	8.53629i	0.289611	−	0.306632i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	17.7108	−	17.7108i	0.634554	−	0.634554i
$780$		0			0
$781$	3.64489	+	3.64489i	0.130424	+	0.130424i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.90264	−	4.41415i	−0.0679082	−	0.157548i
$786$		0			0
$787$	46.0531			1.64162			0.820808	−	0.571205i	$-0.193524\pi$
$787$	46.0531			1.64162			0.820808	+	0.571205i	$0.193524\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	18.5069			0.658030
$792$		0			0
$793$	−4.58555	+	4.58555i	−0.162838	+	0.162838i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			10.7798i			0.381839i	0.981606	+	0.190920i	$0.0611470\pi$
$797$			10.7798i			0.381839i	−0.981606	+	0.190920i	$0.938853\pi$
$798$		0			0
$799$			6.81978i			0.241266i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	53.0725			1.87289
$804$		0			0
$805$	32.9028	−	14.1822i	1.15967	−	0.499856i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	19.3383i		−	0.679897i	−0.940444	−	0.339949i	$-0.889590\pi$
$809$		−	19.3383i		−	0.679897i	0.940444	−	0.339949i	$-0.110410\pi$
$810$		0			0
$811$	36.9491	−	36.9491i	1.29746	−	1.29746i	0.367392	−	0.930066i	$-0.380251\pi$
$811$	36.9491	−	36.9491i	1.29746	−	1.29746i	0.930066	−	0.367392i	$-0.119749\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.778248	−	0.335450i	0.0272608	−	0.0117503i
$816$		0			0
$817$	43.2361	−	43.2361i	1.51264	−	1.51264i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	11.1156	+	11.1156i	0.387937	+	0.387937i	0.873951	−	0.486014i	$-0.161550\pi$
$821$	11.1156	+	11.1156i	0.387937	+	0.387937i	−0.486014	+	0.873951i	$0.661550\pi$
$822$		0			0
$823$	18.9259	−	18.9259i	0.659716	−	0.659716i	−0.295597	−	0.955313i	$-0.595518\pi$
$823$	18.9259	−	18.9259i	0.659716	−	0.659716i	0.955313	+	0.295597i	$0.0955184\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−16.8372			−0.585486			−0.292743	−	0.956191i	$-0.594568\pi$
$827$	−16.8372			−0.585486			−0.292743	+	0.956191i	$0.594568\pi$
$828$		0			0
$829$	4.66660	−	4.66660i	0.162078	−	0.162078i	−0.621409	−	0.783486i	$-0.713439\pi$
$829$	4.66660	−	4.66660i	0.162078	−	0.162078i	0.783486	+	0.621409i	$0.213439\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−25.4440	+	25.4440i	−0.881582	+	0.881582i
$834$		0			0
$835$	−14.5131	−	5.77029i	−0.502246	−	0.199689i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	54.2954i		−	1.87449i	−0.348678	−	0.937243i	$-0.613369\pi$
$839$		−	54.2954i		−	1.87449i	0.348678	−	0.937243i	$-0.386631\pi$
$840$		0			0
$841$			21.2202i			0.731731i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−10.0393	−	23.2913i	−0.345363	−	0.801246i
$846$		0			0
$847$	−44.8154	+	44.8154i	−1.53988	+	1.53988i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−29.9547	+	29.9547i	−1.02683	+	1.02683i
$852$		0			0
$853$	26.3640			0.902687			0.451343	−	0.892350i	$-0.350945\pi$
$853$	26.3640			0.902687			0.451343	+	0.892350i	$0.350945\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−26.0031	+	26.0031i	−0.888247	+	0.888247i	−0.994355	−	0.106107i	$-0.966161\pi$
$857$	−26.0031	+	26.0031i	−0.888247	+	0.888247i	0.106107	+	0.994355i	$0.466161\pi$
$858$		0			0
$859$	−2.02623	−	2.02623i	−0.0691342	−	0.0691342i	0.671694	−	0.740828i	$-0.265567\pi$
$859$	−2.02623	−	2.02623i	−0.0691342	−	0.0691342i	−0.740828	+	0.671694i	$0.765567\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.26790	+	1.26790i	−0.0431597	+	0.0431597i	−0.728357	−	0.685198i	$-0.759716\pi$
$863$	−1.26790	+	1.26790i	−0.0431597	+	0.0431597i	0.685198	+	0.728357i	$0.259716\pi$
$864$		0			0
$865$	−11.0294	−	25.5882i	−0.375009	−	0.870025i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−45.4674	+	45.4674i	−1.54238	+	1.54238i
$870$		0			0
$871$			13.2712i			0.449678i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	19.7093	+	42.3578i	0.666297	+	1.43196i
$876$		0			0
$877$	−32.0131			−1.08101			−0.540503	−	0.841342i	$-0.681766\pi$
$877$	−32.0131			−1.08101			−0.540503	+	0.841342i	$0.681766\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			12.7366i			0.429105i	0.976712	+	0.214553i	$0.0688294\pi$
$881$			12.7366i			0.429105i	−0.976712	+	0.214553i	$0.931171\pi$
$882$		0			0
$883$			31.1851i			1.04946i	0.851268	+	0.524730i	$0.175834\pi$
$883$			31.1851i			1.04946i	−0.851268	+	0.524730i	$0.824166\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−4.63991	+	4.63991i	−0.155793	+	0.155793i	−0.780699	−	0.624907i	$-0.785137\pi$
$887$	−4.63991	+	4.63991i	−0.155793	+	0.155793i	0.624907	+	0.780699i	$0.285137\pi$
$888$		0			0
$889$	8.47895			0.284375
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−15.2256			−0.509506
$894$		0			0
$895$	9.57029	−	24.0706i	0.319900	−	0.804592i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	11.7677	+	11.7677i	0.392474	+	0.392474i
$900$		0			0
$901$	12.9370	−	12.9370i	0.430993	−	0.430993i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−26.1225	−	10.3861i	−0.868340	−	0.345245i
$906$		0			0
$907$			54.4221i			1.80706i	0.428527	+	0.903529i	$0.359033\pi$
$907$			54.4221i			1.80706i	−0.428527	+	0.903529i	$0.640967\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			15.2223i			0.504337i	0.967683	+	0.252168i	$0.0811437\pi$
$911$			15.2223i			0.504337i	−0.967683	+	0.252168i	$0.918856\pi$
$912$		0			0
$913$	−29.9376	−	29.9376i	−0.990790	−	0.990790i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−66.8050			−2.20609
$918$		0			0
$919$	−55.1891			−1.82052			−0.910261	−	0.414035i	$-0.864119\pi$
$919$	−55.1891			−1.82052			−0.910261	+	0.414035i	$0.864119\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	1.29728i		−	0.0427004i
$924$		0			0
$925$	−40.1575	−	37.9283i	−1.32037	−	1.24707i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	35.9272			1.17873			0.589366	−	0.807866i	$-0.299377\pi$
$929$	35.9272			1.17873			0.589366	+	0.807866i	$0.299377\pi$
$930$		0			0
$931$	−56.8055	−	56.8055i	−1.86172	−	1.86172i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	36.1312	−	15.5737i	1.18162	−	0.509314i
$936$		0			0
$937$	−1.87222	−	1.87222i	−0.0611628	−	0.0611628i	0.675864	−	0.737027i	$-0.263771\pi$
$937$	−1.87222	−	1.87222i	−0.0611628	−	0.0611628i	−0.737027	+	0.675864i	$0.763771\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	34.0315	−	34.0315i	1.10940	−	1.10940i	0.116165	−	0.993230i	$-0.462940\pi$
$941$	34.0315	−	34.0315i	1.10940	−	1.10940i	0.993230	−	0.116165i	$-0.0370602\pi$
$942$		0			0
$943$	−8.84355	−	8.84355i	−0.287985	−	0.287985i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			0.345881i			0.0112396i	0.999984	+	0.00561981i	$0.00178885\pi$
$947$			0.345881i			0.0112396i	−0.999984	+	0.00561981i	$0.998211\pi$
$948$		0			0
$949$	−9.44469	−	9.44469i	−0.306588	−	0.306588i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−20.5423	−	20.5423i	−0.665431	−	0.665431i	0.291224	−	0.956655i	$-0.405938\pi$
$953$	−20.5423	−	20.5423i	−0.665431	−	0.665431i	−0.956655	+	0.291224i	$0.905938\pi$
$954$		0			0
$955$	6.61238	−	2.85015i	0.213972	−	0.0922287i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−84.3952			−2.72526
$960$		0			0
$961$	−25.4852			−0.822102
$962$		0			0
$963$		0			0
$964$		0			0
$965$	13.6343	−	34.2922i	0.438904	−	1.10390i
$966$		0			0
$967$	10.4316	+	10.4316i	0.335457	+	0.335457i	0.854654	−	0.519197i	$-0.173769\pi$
$967$	10.4316	+	10.4316i	0.335457	+	0.335457i	−0.519197	+	0.854654i	$0.673769\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	11.3512	+	11.3512i	0.364279	+	0.364279i	0.865385	−	0.501107i	$-0.167074\pi$
$971$	11.3512	+	11.3512i	0.364279	+	0.364279i	−0.501107	+	0.865385i	$0.667074\pi$
$972$		0			0
$973$			33.2895i			1.06721i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	16.7335	+	16.7335i	0.535353	+	0.535353i	0.922160	−	0.386808i	$-0.126422\pi$
$977$	16.7335	+	16.7335i	0.535353	+	0.535353i	−0.386808	+	0.922160i	$0.626422\pi$
$978$		0			0
$979$	−4.52502	+	4.52502i	−0.144620	+	0.144620i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	10.2253	+	10.2253i	0.326135	+	0.326135i	0.851115	−	0.524980i	$-0.175927\pi$
$983$	10.2253	+	10.2253i	0.326135	+	0.326135i	−0.524980	+	0.851115i	$0.675927\pi$
$984$		0			0
$985$	−17.8646	−	41.4460i	−0.569212	−	1.32058i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−21.5892	−	21.5892i	−0.686496	−	0.686496i
$990$		0			0
$991$	14.7871			0.469727			0.234864	−	0.972028i	$-0.424536\pi$
$991$	14.7871			0.469727			0.234864	+	0.972028i	$0.424536\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−13.0538	−	30.2850i	−0.413834	−	0.960099i
$996$		0			0
$997$		−	50.8279i		−	1.60973i	−0.593455	−	0.804867i	$-0.702236\pi$
$997$		−	50.8279i		−	1.60973i	0.593455	−	0.804867i	$-0.297764\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2880.2.bc.a.593.19		96
3.2	odd	2	inner	2880.2.bc.a.593.30		96
4.3	odd	2		720.2.bc.a.413.38	yes	96
5.2	odd	4		2880.2.bg.a.17.6		96
12.11	even	2		720.2.bc.a.413.11	yes	96
15.2	even	4		2880.2.bg.a.17.43		96
16.5	even	4		2880.2.bg.a.2033.43		96
16.11	odd	4		720.2.bg.a.53.35	yes	96
20.7	even	4		720.2.bg.a.557.14	yes	96
48.5	odd	4		2880.2.bg.a.2033.6		96
48.11	even	4		720.2.bg.a.53.14	yes	96
60.47	odd	4		720.2.bg.a.557.35	yes	96
80.27	even	4		720.2.bc.a.197.11	✓	96
80.37	odd	4	inner	2880.2.bc.a.1457.30		96
240.107	odd	4		720.2.bc.a.197.38	yes	96
240.197	even	4	inner	2880.2.bc.a.1457.19		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.bc.a.197.11	✓	96	80.27	even	4
720.2.bc.a.197.38	yes	96	240.107	odd	4
720.2.bc.a.413.11	yes	96	12.11	even	2
720.2.bc.a.413.38	yes	96	4.3	odd	2
720.2.bg.a.53.14	yes	96	48.11	even	4
720.2.bg.a.53.35	yes	96	16.11	odd	4
720.2.bg.a.557.14	yes	96	20.7	even	4
720.2.bg.a.557.35	yes	96	60.47	odd	4
2880.2.bc.a.593.19		96	1.1	even	1	trivial
2880.2.bc.a.593.30		96	3.2	odd	2	inner
2880.2.bc.a.1457.19		96	240.197	even	4	inner
2880.2.bc.a.1457.30		96	80.37	odd	4	inner
2880.2.bg.a.17.6		96	5.2	odd	4
2880.2.bg.a.17.43		96	15.2	even	4
2880.2.bg.a.2033.6		96	48.5	odd	4
2880.2.bg.a.2033.43		96	16.5	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:	\( N \)	\(=\)	\( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2880.bc (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.885098 - 2.05344i) q^{5} +(2.95475 + 2.95475i) q^{7} +O(q^{10})\)	\(q+(-0.885098 - 2.05344i) q^{5} +(2.95475 + 2.95475i) q^{7} +(3.61713 + 3.61713i) q^{11} -1.28740i q^{13} +(2.43224 + 2.43224i) q^{17} +(-5.43015 + 5.43015i) q^{19} +(2.71144 + 2.71144i) q^{23} +(-3.43320 + 3.63498i) q^{25} +(-5.01100 - 5.01100i) q^{29} -2.34837 q^{31} +(3.45215 - 8.68264i) q^{35} +11.0475i q^{37} -3.26156 q^{41} -7.96224 q^{43} +(1.40195 + 1.40195i) q^{47} +10.4611i q^{49} -5.31895i q^{53} +(4.22603 - 10.6291i) q^{55} +(4.52081 - 4.52081i) q^{59} +(-3.56188 - 3.56188i) q^{61} +(-2.64359 + 1.13947i) q^{65} -10.3086 q^{67} +1.00768 q^{71} +(7.33627 - 7.33627i) q^{73} +21.3754i q^{77} +12.5700i q^{79} -8.27662 q^{83} +(2.84168 - 7.14723i) q^{85} +1.25100i q^{89} +(3.80394 - 3.80394i) q^{91} +(15.9567 + 6.34425i) q^{95} +(-5.33721 + 5.33721i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 16 q^{19} - 64 q^{43} + 32 q^{61}+O(q^{100}) \) 96 * q - 16 * q^19 - 64 * q^43 + 32 * q^61

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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