LMFDB - Embedded newform 2576.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2576,2,Mod(1,2576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2576, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("2576.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2576 = 2^{4} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2576.a (trivial)

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:	yes
Analytic conductor:	$20.5694635607$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1288)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2576.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+3.00000 q^{3} -4.00000 q^{5} +1.00000 q^{7} +6.00000 q^{9} +O(q^{10})$

$q+3.00000 q^{3} -4.00000 q^{5} +1.00000 q^{7} +6.00000 q^{9} -2.00000 q^{11} +5.00000 q^{13} -12.0000 q^{15} +4.00000 q^{19} +3.00000 q^{21} -1.00000 q^{23} +11.0000 q^{25} +9.00000 q^{27} -3.00000 q^{29} -5.00000 q^{31} -6.00000 q^{33} -4.00000 q^{35} +4.00000 q^{37} +15.0000 q^{39} +5.00000 q^{41} +4.00000 q^{43} -24.0000 q^{45} +11.0000 q^{47} +1.00000 q^{49} +8.00000 q^{55} +12.0000 q^{57} +12.0000 q^{59} -6.00000 q^{61} +6.00000 q^{63} -20.0000 q^{65} +16.0000 q^{67} -3.00000 q^{69} -7.00000 q^{71} +7.00000 q^{73} +33.0000 q^{75} -2.00000 q^{77} -16.0000 q^{79} +9.00000 q^{81} -8.00000 q^{83} -9.00000 q^{87} -12.0000 q^{89} +5.00000 q^{91} -15.0000 q^{93} -16.0000 q^{95} +6.00000 q^{97} -12.0000 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

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
$3$	3.00000	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$3$	3.00000	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$4$	0	0
$5$	−4.00000	−1.78885	−0.894427	−	0.447214i	$-0.852416\pi$
$5$	−4.00000	−1.78885	−0.894427	+	0.447214i	$0.852416\pi$
$6$	0	0
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0	0
$9$	6.00000	2.00000
$10$	0	0
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	0	0
$13$	5.00000	1.38675	0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000	1.38675	0.693375	+	0.720577i	$0.256123\pi$
$14$	0	0
$15$	−12.0000	−3.09839
$16$	0	0
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0	0
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	0	0
$21$	3.00000	0.654654
$22$	0	0
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0	0
$25$	11.0000	2.20000
$26$	0	0
$27$	9.00000	1.73205
$28$	0	0
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	0	0
$31$	−5.00000	−0.898027	−0.449013	−	0.893525i	$-0.648224\pi$
$31$	−5.00000	−0.898027	−0.449013	+	0.893525i	$0.648224\pi$
$32$	0	0
$33$	−6.00000	−1.04447
$34$	0	0
$35$	−4.00000	−0.676123
$36$	0	0
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	0	0
$39$	15.0000	2.40192
$40$	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
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	0	0
$45$	−24.0000	−3.57771
$46$	0	0
$47$	11.0000	1.60451	0.802257	−	0.596978i	$-0.203632\pi$
$47$	11.0000	1.60451	0.802257	+	0.596978i	$0.203632\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	0	0
$52$	0	0
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	0	0
$55$	8.00000	1.07872
$56$	0	0
$57$	12.0000	1.58944
$58$	0	0
$59$	12.0000	1.56227	0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000	1.56227	0.781133	+	0.624364i	$0.214642\pi$
$60$	0	0
$61$	−6.00000	−0.768221	−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000	−0.768221	−0.384111	+	0.923287i	$0.625492\pi$
$62$	0	0
$63$	6.00000	0.755929
$64$	0	0
$65$	−20.0000	−2.48069
$66$	0	0
$67$	16.0000	1.95471	0.977356	−	0.211604i	$-0.0678686\pi$
$67$	16.0000	1.95471	0.977356	+	0.211604i	$0.0678686\pi$
$68$	0	0
$69$	−3.00000	−0.361158
$70$	0	0
$71$	−7.00000	−0.830747	−0.415374	−	0.909651i	$-0.636349\pi$
$71$	−7.00000	−0.830747	−0.415374	+	0.909651i	$0.636349\pi$
$72$	0	0
$73$	7.00000	0.819288	0.409644	−	0.912245i	$-0.365653\pi$
$73$	7.00000	0.819288	0.409644	+	0.912245i	$0.365653\pi$
$74$	0	0
$75$	33.0000	3.81051
$76$	0	0
$77$	−2.00000	−0.227921
$78$	0	0
$79$	−16.0000	−1.80014	−0.900070	−	0.435745i	$-0.856485\pi$
$79$	−16.0000	−1.80014	−0.900070	+	0.435745i	$0.856485\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	0	0
$83$	−8.00000	−0.878114	−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000	−0.878114	−0.439057	+	0.898459i	$0.644687\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−9.00000	−0.964901
$88$	0	0
$89$	−12.0000	−1.27200	−0.635999	−	0.771690i	$-0.719412\pi$
$89$	−12.0000	−1.27200	−0.635999	+	0.771690i	$0.719412\pi$
$90$	0	0
$91$	5.00000	0.524142
$92$	0	0
$93$	−15.0000	−1.55543
$94$	0	0
$95$	−16.0000	−1.64157
$96$	0	0
$97$	6.00000	0.609208	0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000	0.609208	0.304604	+	0.952479i	$0.401476\pi$
$98$	0	0
$99$	−12.0000	−1.20605
$100$	0	0
$101$	14.0000	1.39305	0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000	1.39305	0.696526	+	0.717532i	$0.254728\pi$
$102$	0	0
$103$	10.0000	0.985329	0.492665	−	0.870219i	$-0.336023\pi$
$103$	10.0000	0.985329	0.492665	+	0.870219i	$0.336023\pi$
$104$	0	0
$105$	−12.0000	−1.17108
$106$	0	0
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	0	0
$109$	20.0000	1.91565	0.957826	−	0.287348i	$-0.0927736\pi$
$109$	20.0000	1.91565	0.957826	+	0.287348i	$0.0927736\pi$
$110$	0	0
$111$	12.0000	1.13899
$112$	0	0
$113$	−4.00000	−0.376288	−0.188144	−	0.982141i	$-0.560247\pi$
$113$	−4.00000	−0.376288	−0.188144	+	0.982141i	$0.560247\pi$
$114$	0	0
$115$	4.00000	0.373002
$116$	0	0
$117$	30.0000	2.77350
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−7.00000	−0.636364
$122$	0	0
$123$	15.0000	1.35250
$124$	0	0
$125$	−24.0000	−2.14663
$126$	0	0
$127$	11.0000	0.976092	0.488046	−	0.872818i	$-0.337710\pi$
$127$	11.0000	0.976092	0.488046	+	0.872818i	$0.337710\pi$
$128$	0	0
$129$	12.0000	1.05654
$130$	0	0
$131$	7.00000	0.611593	0.305796	−	0.952097i	$-0.401077\pi$
$131$	7.00000	0.611593	0.305796	+	0.952097i	$0.401077\pi$
$132$	0	0
$133$	4.00000	0.346844
$134$	0	0
$135$	−36.0000	−3.09839
$136$	0	0
$137$	−18.0000	−1.53784	−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000	−1.53784	−0.768922	+	0.639343i	$0.779207\pi$
$138$	0	0
$139$	−19.0000	−1.61156	−0.805779	−	0.592216i	$-0.798253\pi$
$139$	−19.0000	−1.61156	−0.805779	+	0.592216i	$0.798253\pi$
$140$	0	0
$141$	33.0000	2.77910
$142$	0	0
$143$	−10.0000	−0.836242
$144$	0	0
$145$	12.0000	0.996546
$146$	0	0
$147$	3.00000	0.247436
$148$	0	0
$149$	12.0000	0.983078	0.491539	−	0.870855i	$-0.336434\pi$
$149$	12.0000	0.983078	0.491539	+	0.870855i	$0.336434\pi$
$150$	0	0
$151$	9.00000	0.732410	0.366205	−	0.930534i	$-0.380657\pi$
$151$	9.00000	0.732410	0.366205	+	0.930534i	$0.380657\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	20.0000	1.60644
$156$	0	0
$157$	−12.0000	−0.957704	−0.478852	−	0.877896i	$-0.658947\pi$
$157$	−12.0000	−0.957704	−0.478852	+	0.877896i	$0.658947\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	0	0
$163$	15.0000	1.17489	0.587445	−	0.809264i	$-0.300134\pi$
$163$	15.0000	1.17489	0.587445	+	0.809264i	$0.300134\pi$
$164$	0	0
$165$	24.0000	1.86840
$166$	0	0
$167$	8.00000	0.619059	0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000	0.619059	0.309529	+	0.950890i	$0.399829\pi$
$168$	0	0
$169$	12.0000	0.923077
$170$	0	0
$171$	24.0000	1.83533
$172$	0	0
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	0	0
$175$	11.0000	0.831522
$176$	0	0
$177$	36.0000	2.70593
$178$	0	0
$179$	−5.00000	−0.373718	−0.186859	−	0.982387i	$-0.559831\pi$
$179$	−5.00000	−0.373718	−0.186859	+	0.982387i	$0.559831\pi$
$180$	0	0
$181$	−26.0000	−1.93256	−0.966282	−	0.257485i	$-0.917106\pi$
$181$	−26.0000	−1.93256	−0.966282	+	0.257485i	$0.917106\pi$
$182$	0	0
$183$	−18.0000	−1.33060
$184$	0	0
$185$	−16.0000	−1.17634
$186$	0	0
$187$	0	0
$188$	0	0
$189$	9.00000	0.654654
$190$	0	0
$191$	4.00000	0.289430	0.144715	−	0.989473i	$-0.453773\pi$
$191$	4.00000	0.289430	0.144715	+	0.989473i	$0.453773\pi$
$192$	0	0
$193$	13.0000	0.935760	0.467880	−	0.883792i	$-0.345018\pi$
$193$	13.0000	0.935760	0.467880	+	0.883792i	$0.345018\pi$
$194$	0	0
$195$	−60.0000	−4.29669
$196$	0	0
$197$	−27.0000	−1.92367	−0.961835	−	0.273629i	$-0.911776\pi$
$197$	−27.0000	−1.92367	−0.961835	+	0.273629i	$0.911776\pi$
$198$	0	0
$199$	−18.0000	−1.27599	−0.637993	−	0.770042i	$-0.720235\pi$
$199$	−18.0000	−1.27599	−0.637993	+	0.770042i	$0.720235\pi$
$200$	0	0
$201$	48.0000	3.38566
$202$	0	0
$203$	−3.00000	−0.210559
$204$	0	0
$205$	−20.0000	−1.39686
$206$	0	0
$207$	−6.00000	−0.417029
$208$	0	0
$209$	−8.00000	−0.553372
$210$	0	0
$211$	−12.0000	−0.826114	−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000	−0.826114	−0.413057	+	0.910705i	$0.635539\pi$
$212$	0	0
$213$	−21.0000	−1.43890
$214$	0	0
$215$	−16.0000	−1.09119
$216$	0	0
$217$	−5.00000	−0.339422
$218$	0	0
$219$	21.0000	1.41905
$220$	0	0
$221$	0	0
$222$	0	0
$223$	−12.0000	−0.803579	−0.401790	−	0.915732i	$-0.631612\pi$
$223$	−12.0000	−0.803579	−0.401790	+	0.915732i	$0.631612\pi$
$224$	0	0
$225$	66.0000	4.40000
$226$	0	0
$227$	−4.00000	−0.265489	−0.132745	−	0.991150i	$-0.542379\pi$
$227$	−4.00000	−0.265489	−0.132745	+	0.991150i	$0.542379\pi$
$228$	0	0
$229$	−2.00000	−0.132164	−0.0660819	−	0.997814i	$-0.521050\pi$
$229$	−2.00000	−0.132164	−0.0660819	+	0.997814i	$0.521050\pi$
$230$	0	0
$231$	−6.00000	−0.394771
$232$	0	0
$233$	−25.0000	−1.63780	−0.818902	−	0.573933i	$-0.805417\pi$
$233$	−25.0000	−1.63780	−0.818902	+	0.573933i	$0.805417\pi$
$234$	0	0
$235$	−44.0000	−2.87024
$236$	0	0
$237$	−48.0000	−3.11794
$238$	0	0
$239$	−11.0000	−0.711531	−0.355765	−	0.934575i	$-0.615780\pi$
$239$	−11.0000	−0.711531	−0.355765	+	0.934575i	$0.615780\pi$
$240$	0	0
$241$	−26.0000	−1.67481	−0.837404	−	0.546585i	$-0.815928\pi$
$241$	−26.0000	−1.67481	−0.837404	+	0.546585i	$0.815928\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	−4.00000	−0.255551
$246$	0	0
$247$	20.0000	1.27257
$248$	0	0
$249$	−24.0000	−1.52094
$250$	0	0
$251$	18.0000	1.13615	0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000	1.13615	0.568075	+	0.822977i	$0.307688\pi$
$252$	0	0
$253$	2.00000	0.125739
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−7.00000	−0.436648	−0.218324	−	0.975876i	$-0.570059\pi$
$257$	−7.00000	−0.436648	−0.218324	+	0.975876i	$0.570059\pi$
$258$	0	0
$259$	4.00000	0.248548
$260$	0	0
$261$	−18.0000	−1.11417
$262$	0	0
$263$	18.0000	1.10993	0.554964	−	0.831875i	$-0.312732\pi$
$263$	18.0000	1.10993	0.554964	+	0.831875i	$0.312732\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−36.0000	−2.20316
$268$	0	0
$269$	−5.00000	−0.304855	−0.152428	−	0.988315i	$-0.548709\pi$
$269$	−5.00000	−0.304855	−0.152428	+	0.988315i	$0.548709\pi$
$270$	0	0
$271$	−24.0000	−1.45790	−0.728948	−	0.684569i	$-0.759990\pi$
$271$	−24.0000	−1.45790	−0.728948	+	0.684569i	$0.759990\pi$
$272$	0	0
$273$	15.0000	0.907841
$274$	0	0
$275$	−22.0000	−1.32665
$276$	0	0
$277$	25.0000	1.50210	0.751052	−	0.660243i	$-0.229547\pi$
$277$	25.0000	1.50210	0.751052	+	0.660243i	$0.229547\pi$
$278$	0	0
$279$	−30.0000	−1.79605
$280$	0	0
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	0	0
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	0	0
$285$	−48.0000	−2.84327
$286$	0	0
$287$	5.00000	0.295141
$288$	0	0
$289$	−17.0000	−1.00000
$290$	0	0
$291$	18.0000	1.05518
$292$	0	0
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	0	0
$295$	−48.0000	−2.79467
$296$	0	0
$297$	−18.0000	−1.04447
$298$	0	0
$299$	−5.00000	−0.289157
$300$	0	0
$301$	4.00000	0.230556
$302$	0	0
$303$	42.0000	2.41284
$304$	0	0
$305$	24.0000	1.37424
$306$	0	0
$307$	−28.0000	−1.59804	−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000	−1.59804	−0.799022	+	0.601302i	$0.794649\pi$
$308$	0	0
$309$	30.0000	1.70664
$310$	0	0
$311$	−5.00000	−0.283524	−0.141762	−	0.989901i	$-0.545277\pi$
$311$	−5.00000	−0.283524	−0.141762	+	0.989901i	$0.545277\pi$
$312$	0	0
$313$	10.0000	0.565233	0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000	0.565233	0.282617	+	0.959233i	$0.408798\pi$
$314$	0	0
$315$	−24.0000	−1.35225
$316$	0	0
$317$	6.00000	0.336994	0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000	0.336994	0.168497	+	0.985702i	$0.446109\pi$
$318$	0	0
$319$	6.00000	0.335936
$320$	0	0
$321$	36.0000	2.00932
$322$	0	0
$323$	0	0
$324$	0	0
$325$	55.0000	3.05085
$326$	0	0
$327$	60.0000	3.31801
$328$	0	0
$329$	11.0000	0.606450
$330$	0	0
$331$	19.0000	1.04433	0.522167	−	0.852843i	$-0.325124\pi$
$331$	19.0000	1.04433	0.522167	+	0.852843i	$0.325124\pi$
$332$	0	0
$333$	24.0000	1.31519
$334$	0	0
$335$	−64.0000	−3.49669
$336$	0	0
$337$	−22.0000	−1.19842	−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000	−1.19842	−0.599208	+	0.800593i	$0.704518\pi$
$338$	0	0
$339$	−12.0000	−0.651751
$340$	0	0
$341$	10.0000	0.541530
$342$	0	0
$343$	1.00000	0.0539949
$344$	0	0
$345$	12.0000	0.646058
$346$	0	0
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	0	0
$349$	−9.00000	−0.481759	−0.240879	−	0.970555i	$-0.577436\pi$
$349$	−9.00000	−0.481759	−0.240879	+	0.970555i	$0.577436\pi$
$350$	0	0
$351$	45.0000	2.40192
$352$	0	0
$353$	19.0000	1.01127	0.505634	−	0.862748i	$-0.331259\pi$
$353$	19.0000	1.01127	0.505634	+	0.862748i	$0.331259\pi$
$354$	0	0
$355$	28.0000	1.48609
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−12.0000	−0.633336	−0.316668	−	0.948536i	$-0.602564\pi$
$359$	−12.0000	−0.633336	−0.316668	+	0.948536i	$0.602564\pi$
$360$	0	0
$361$	−3.00000	−0.157895
$362$	0	0
$363$	−21.0000	−1.10221
$364$	0	0
$365$	−28.0000	−1.46559
$366$	0	0
$367$	32.0000	1.67039	0.835193	−	0.549957i	$-0.185356\pi$
$367$	32.0000	1.67039	0.835193	+	0.549957i	$0.185356\pi$
$368$	0	0
$369$	30.0000	1.56174
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−14.0000	−0.724893	−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000	−0.724893	−0.362446	+	0.932005i	$0.618058\pi$
$374$	0	0
$375$	−72.0000	−3.71806
$376$	0	0
$377$	−15.0000	−0.772539
$378$	0	0
$379$	−2.00000	−0.102733	−0.0513665	−	0.998680i	$-0.516358\pi$
$379$	−2.00000	−0.102733	−0.0513665	+	0.998680i	$0.516358\pi$
$380$	0	0
$381$	33.0000	1.69064
$382$	0	0
$383$	−6.00000	−0.306586	−0.153293	−	0.988181i	$-0.548988\pi$
$383$	−6.00000	−0.306586	−0.153293	+	0.988181i	$0.548988\pi$
$384$	0	0
$385$	8.00000	0.407718
$386$	0	0
$387$	24.0000	1.21999
$388$	0	0
$389$	−20.0000	−1.01404	−0.507020	−	0.861934i	$-0.669253\pi$
$389$	−20.0000	−1.01404	−0.507020	+	0.861934i	$0.669253\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	21.0000	1.05931
$394$	0	0
$395$	64.0000	3.22019
$396$	0	0
$397$	−11.0000	−0.552074	−0.276037	−	0.961147i	$-0.589021\pi$
$397$	−11.0000	−0.552074	−0.276037	+	0.961147i	$0.589021\pi$
$398$	0	0
$399$	12.0000	0.600751
$400$	0	0
$401$	−18.0000	−0.898877	−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000	−0.898877	−0.449439	+	0.893311i	$0.648376\pi$
$402$	0	0
$403$	−25.0000	−1.24534
$404$	0	0
$405$	−36.0000	−1.78885
$406$	0	0
$407$	−8.00000	−0.396545
$408$	0	0
$409$	−17.0000	−0.840596	−0.420298	−	0.907386i	$-0.638074\pi$
$409$	−17.0000	−0.840596	−0.420298	+	0.907386i	$0.638074\pi$
$410$	0	0
$411$	−54.0000	−2.66362
$412$	0	0
$413$	12.0000	0.590481
$414$	0	0
$415$	32.0000	1.57082
$416$	0	0
$417$	−57.0000	−2.79130
$418$	0	0
$419$	−20.0000	−0.977064	−0.488532	−	0.872546i	$-0.662467\pi$
$419$	−20.0000	−0.977064	−0.488532	+	0.872546i	$0.662467\pi$
$420$	0	0
$421$	−20.0000	−0.974740	−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000	−0.974740	−0.487370	+	0.873195i	$0.662044\pi$
$422$	0	0
$423$	66.0000	3.20903
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−6.00000	−0.290360
$428$	0	0
$429$	−30.0000	−1.44841
$430$	0	0
$431$	38.0000	1.83040	0.915198	−	0.403005i	$-0.132034\pi$
$431$	38.0000	1.83040	0.915198	+	0.403005i	$0.132034\pi$
$432$	0	0
$433$	−26.0000	−1.24948	−0.624740	−	0.780833i	$-0.714795\pi$
$433$	−26.0000	−1.24948	−0.624740	+	0.780833i	$0.714795\pi$
$434$	0	0
$435$	36.0000	1.72607
$436$	0	0
$437$	−4.00000	−0.191346
$438$	0	0
$439$	9.00000	0.429547	0.214773	−	0.976664i	$-0.431099\pi$
$439$	9.00000	0.429547	0.214773	+	0.976664i	$0.431099\pi$
$440$	0	0
$441$	6.00000	0.285714
$442$	0	0
$443$	9.00000	0.427603	0.213801	−	0.976877i	$-0.431415\pi$
$443$	9.00000	0.427603	0.213801	+	0.976877i	$0.431415\pi$
$444$	0	0
$445$	48.0000	2.27542
$446$	0	0
$447$	36.0000	1.70274
$448$	0	0
$449$	−26.0000	−1.22702	−0.613508	−	0.789689i	$-0.710242\pi$
$449$	−26.0000	−1.22702	−0.613508	+	0.789689i	$0.710242\pi$
$450$	0	0
$451$	−10.0000	−0.470882
$452$	0	0
$453$	27.0000	1.26857
$454$	0	0
$455$	−20.0000	−0.937614
$456$	0	0
$457$	16.0000	0.748448	0.374224	−	0.927338i	$-0.377909\pi$
$457$	16.0000	0.748448	0.374224	+	0.927338i	$0.377909\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	15.0000	0.698620	0.349310	−	0.937007i	$-0.386416\pi$
$461$	15.0000	0.698620	0.349310	+	0.937007i	$0.386416\pi$
$462$	0	0
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	0	0
$465$	60.0000	2.78243
$466$	0	0
$467$	−10.0000	−0.462745	−0.231372	−	0.972865i	$-0.574322\pi$
$467$	−10.0000	−0.462745	−0.231372	+	0.972865i	$0.574322\pi$
$468$	0	0
$469$	16.0000	0.738811
$470$	0	0
$471$	−36.0000	−1.65879
$472$	0	0
$473$	−8.00000	−0.367840
$474$	0	0
$475$	44.0000	2.01886
$476$	0	0
$477$	0	0
$478$	0	0
$479$	6.00000	0.274147	0.137073	−	0.990561i	$-0.456230\pi$
$479$	6.00000	0.274147	0.137073	+	0.990561i	$0.456230\pi$
$480$	0	0
$481$	20.0000	0.911922
$482$	0	0
$483$	−3.00000	−0.136505
$484$	0	0
$485$	−24.0000	−1.08978
$486$	0	0
$487$	43.0000	1.94852	0.974258	−	0.225436i	$-0.0723806\pi$
$487$	43.0000	1.94852	0.974258	+	0.225436i	$0.0723806\pi$
$488$	0	0
$489$	45.0000	2.03497
$490$	0	0
$491$	15.0000	0.676941	0.338470	−	0.940977i	$-0.390091\pi$
$491$	15.0000	0.676941	0.338470	+	0.940977i	$0.390091\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	48.0000	2.15744
$496$	0	0
$497$	−7.00000	−0.313993
$498$	0	0
$499$	−35.0000	−1.56682	−0.783408	−	0.621508i	$-0.786520\pi$
$499$	−35.0000	−1.56682	−0.783408	+	0.621508i	$0.786520\pi$
$500$	0	0
$501$	24.0000	1.07224
$502$	0	0
$503$	−4.00000	−0.178351	−0.0891756	−	0.996016i	$-0.528423\pi$
$503$	−4.00000	−0.178351	−0.0891756	+	0.996016i	$0.528423\pi$
$504$	0	0
$505$	−56.0000	−2.49197
$506$	0	0
$507$	36.0000	1.59882
$508$	0	0
$509$	7.00000	0.310270	0.155135	−	0.987893i	$-0.450419\pi$
$509$	7.00000	0.310270	0.155135	+	0.987893i	$0.450419\pi$
$510$	0	0
$511$	7.00000	0.309662
$512$	0	0
$513$	36.0000	1.58944
$514$	0	0
$515$	−40.0000	−1.76261
$516$	0	0
$517$	−22.0000	−0.967559
$518$	0	0
$519$	−18.0000	−0.790112
$520$	0	0
$521$	−24.0000	−1.05146	−0.525730	−	0.850652i	$-0.676208\pi$
$521$	−24.0000	−1.05146	−0.525730	+	0.850652i	$0.676208\pi$
$522$	0	0
$523$	−22.0000	−0.961993	−0.480996	−	0.876723i	$-0.659725\pi$
$523$	−22.0000	−0.961993	−0.480996	+	0.876723i	$0.659725\pi$
$524$	0	0
$525$	33.0000	1.44024
$526$	0	0
$527$	0	0
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	72.0000	3.12453
$532$	0	0
$533$	25.0000	1.08287
$534$	0	0
$535$	−48.0000	−2.07522
$536$	0	0
$537$	−15.0000	−0.647298
$538$	0	0
$539$	−2.00000	−0.0861461
$540$	0	0
$541$	41.0000	1.76273	0.881364	−	0.472438i	$-0.156626\pi$
$541$	41.0000	1.76273	0.881364	+	0.472438i	$0.156626\pi$
$542$	0	0
$543$	−78.0000	−3.34730
$544$	0	0
$545$	−80.0000	−3.42682
$546$	0	0
$547$	15.0000	0.641354	0.320677	−	0.947189i	$-0.396090\pi$
$547$	15.0000	0.641354	0.320677	+	0.947189i	$0.396090\pi$
$548$	0	0
$549$	−36.0000	−1.53644
$550$	0	0
$551$	−12.0000	−0.511217
$552$	0	0
$553$	−16.0000	−0.680389
$554$	0	0
$555$	−48.0000	−2.03749
$556$	0	0
$557$	2.00000	0.0847427	0.0423714	−	0.999102i	$-0.486509\pi$
$557$	2.00000	0.0847427	0.0423714	+	0.999102i	$0.486509\pi$
$558$	0	0
$559$	20.0000	0.845910
$560$	0	0
$561$	0	0
$562$	0	0
$563$	−14.0000	−0.590030	−0.295015	−	0.955493i	$-0.595325\pi$
$563$	−14.0000	−0.590030	−0.295015	+	0.955493i	$0.595325\pi$
$564$	0	0
$565$	16.0000	0.673125
$566$	0	0
$567$	9.00000	0.377964
$568$	0	0
$569$	32.0000	1.34151	0.670755	−	0.741679i	$-0.265970\pi$
$569$	32.0000	1.34151	0.670755	+	0.741679i	$0.265970\pi$
$570$	0	0
$571$	−10.0000	−0.418487	−0.209243	−	0.977864i	$-0.567100\pi$
$571$	−10.0000	−0.418487	−0.209243	+	0.977864i	$0.567100\pi$
$572$	0	0
$573$	12.0000	0.501307
$574$	0	0
$575$	−11.0000	−0.458732
$576$	0	0
$577$	−17.0000	−0.707719	−0.353860	−	0.935299i	$-0.615131\pi$
$577$	−17.0000	−0.707719	−0.353860	+	0.935299i	$0.615131\pi$
$578$	0	0
$579$	39.0000	1.62078
$580$	0	0
$581$	−8.00000	−0.331896
$582$	0	0
$583$	0	0
$584$	0	0
$585$	−120.000	−4.96139
$586$	0	0
$587$	3.00000	0.123823	0.0619116	−	0.998082i	$-0.480280\pi$
$587$	3.00000	0.123823	0.0619116	+	0.998082i	$0.480280\pi$
$588$	0	0
$589$	−20.0000	−0.824086
$590$	0	0
$591$	−81.0000	−3.33189
$592$	0	0
$593$	−14.0000	−0.574911	−0.287456	−	0.957794i	$-0.592809\pi$
$593$	−14.0000	−0.574911	−0.287456	+	0.957794i	$0.592809\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−54.0000	−2.21007
$598$	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
$601$	23.0000	0.938190	0.469095	−	0.883148i	$-0.344580\pi$
$601$	23.0000	0.938190	0.469095	+	0.883148i	$0.344580\pi$
$602$	0	0
$603$	96.0000	3.90942
$604$	0	0
$605$	28.0000	1.13836
$606$	0	0
$607$	−8.00000	−0.324710	−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000	−0.324710	−0.162355	+	0.986732i	$0.551909\pi$
$608$	0	0
$609$	−9.00000	−0.364698
$610$	0	0
$611$	55.0000	2.22506
$612$	0	0
$613$	18.0000	0.727013	0.363507	−	0.931592i	$-0.381579\pi$
$613$	18.0000	0.727013	0.363507	+	0.931592i	$0.381579\pi$
$614$	0	0
$615$	−60.0000	−2.41943
$616$	0	0
$617$	40.0000	1.61034	0.805170	−	0.593045i	$-0.202074\pi$
$617$	40.0000	1.61034	0.805170	+	0.593045i	$0.202074\pi$
$618$	0	0
$619$	14.0000	0.562708	0.281354	−	0.959604i	$-0.409217\pi$
$619$	14.0000	0.562708	0.281354	+	0.959604i	$0.409217\pi$
$620$	0	0
$621$	−9.00000	−0.361158
$622$	0	0
$623$	−12.0000	−0.480770
$624$	0	0
$625$	41.0000	1.64000
$626$	0	0
$627$	−24.0000	−0.958468
$628$	0	0
$629$	0	0
$630$	0	0
$631$	−24.0000	−0.955425	−0.477712	−	0.878516i	$-0.658534\pi$
$631$	−24.0000	−0.955425	−0.477712	+	0.878516i	$0.658534\pi$
$632$	0	0
$633$	−36.0000	−1.43087
$634$	0	0
$635$	−44.0000	−1.74609
$636$	0	0
$637$	5.00000	0.198107
$638$	0	0
$639$	−42.0000	−1.66149
$640$	0	0
$641$	−12.0000	−0.473972	−0.236986	−	0.971513i	$-0.576159\pi$
$641$	−12.0000	−0.473972	−0.236986	+	0.971513i	$0.576159\pi$
$642$	0	0
$643$	8.00000	0.315489	0.157745	−	0.987480i	$-0.449578\pi$
$643$	8.00000	0.315489	0.157745	+	0.987480i	$0.449578\pi$
$644$	0	0
$645$	−48.0000	−1.89000
$646$	0	0
$647$	11.0000	0.432455	0.216227	−	0.976343i	$-0.430625\pi$
$647$	11.0000	0.432455	0.216227	+	0.976343i	$0.430625\pi$
$648$	0	0
$649$	−24.0000	−0.942082
$650$	0	0
$651$	−15.0000	−0.587896
$652$	0	0
$653$	7.00000	0.273931	0.136966	−	0.990576i	$-0.456265\pi$
$653$	7.00000	0.273931	0.136966	+	0.990576i	$0.456265\pi$
$654$	0	0
$655$	−28.0000	−1.09405
$656$	0	0
$657$	42.0000	1.63858
$658$	0	0
$659$	6.00000	0.233727	0.116863	−	0.993148i	$-0.462716\pi$
$659$	6.00000	0.233727	0.116863	+	0.993148i	$0.462716\pi$
$660$	0	0
$661$	44.0000	1.71140	0.855701	−	0.517471i	$-0.173126\pi$
$661$	44.0000	1.71140	0.855701	+	0.517471i	$0.173126\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	−16.0000	−0.620453
$666$	0	0
$667$	3.00000	0.116160
$668$	0	0
$669$	−36.0000	−1.39184
$670$	0	0
$671$	12.0000	0.463255
$672$	0	0
$673$	−5.00000	−0.192736	−0.0963679	−	0.995346i	$-0.530723\pi$
$673$	−5.00000	−0.192736	−0.0963679	+	0.995346i	$0.530723\pi$
$674$	0	0
$675$	99.0000	3.81051
$676$	0	0
$677$	24.0000	0.922395	0.461197	−	0.887298i	$-0.347420\pi$
$677$	24.0000	0.922395	0.461197	+	0.887298i	$0.347420\pi$
$678$	0	0
$679$	6.00000	0.230259
$680$	0	0
$681$	−12.0000	−0.459841
$682$	0	0
$683$	39.0000	1.49229	0.746147	−	0.665782i	$-0.231902\pi$
$683$	39.0000	1.49229	0.746147	+	0.665782i	$0.231902\pi$
$684$	0	0
$685$	72.0000	2.75098
$686$	0	0
$687$	−6.00000	−0.228914
$688$	0	0
$689$	0	0
$690$	0	0
$691$	20.0000	0.760836	0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000	0.760836	0.380418	+	0.924815i	$0.375780\pi$
$692$	0	0
$693$	−12.0000	−0.455842
$694$	0	0
$695$	76.0000	2.88284
$696$	0	0
$697$	0	0
$698$	0	0
$699$	−75.0000	−2.83676
$700$	0	0
$701$	30.0000	1.13308	0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000	1.13308	0.566542	+	0.824033i	$0.308281\pi$
$702$	0	0
$703$	16.0000	0.603451
$704$	0	0
$705$	−132.000	−4.97141
$706$	0	0
$707$	14.0000	0.526524
$708$	0	0
$709$	−24.0000	−0.901339	−0.450669	−	0.892691i	$-0.648815\pi$
$709$	−24.0000	−0.901339	−0.450669	+	0.892691i	$0.648815\pi$
$710$	0	0
$711$	−96.0000	−3.60028
$712$	0	0
$713$	5.00000	0.187251
$714$	0	0
$715$	40.0000	1.49592
$716$	0	0
$717$	−33.0000	−1.23241
$718$	0	0
$719$	−32.0000	−1.19340	−0.596699	−	0.802465i	$-0.703521\pi$
$719$	−32.0000	−1.19340	−0.596699	+	0.802465i	$0.703521\pi$
$720$	0	0
$721$	10.0000	0.372419
$722$	0	0
$723$	−78.0000	−2.90085
$724$	0	0
$725$	−33.0000	−1.22559
$726$	0	0
$727$	32.0000	1.18681	0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000	1.18681	0.593407	+	0.804902i	$0.297782\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	8.00000	0.295487	0.147743	−	0.989026i	$-0.452799\pi$
$733$	8.00000	0.295487	0.147743	+	0.989026i	$0.452799\pi$
$734$	0	0
$735$	−12.0000	−0.442627
$736$	0	0
$737$	−32.0000	−1.17874
$738$	0	0
$739$	−1.00000	−0.0367856	−0.0183928	−	0.999831i	$-0.505855\pi$
$739$	−1.00000	−0.0367856	−0.0183928	+	0.999831i	$0.505855\pi$
$740$	0	0
$741$	60.0000	2.20416
$742$	0	0
$743$	−8.00000	−0.293492	−0.146746	−	0.989174i	$-0.546880\pi$
$743$	−8.00000	−0.293492	−0.146746	+	0.989174i	$0.546880\pi$
$744$	0	0
$745$	−48.0000	−1.75858
$746$	0	0
$747$	−48.0000	−1.75623
$748$	0	0
$749$	12.0000	0.438470
$750$	0	0
$751$	−28.0000	−1.02173	−0.510867	−	0.859660i	$-0.670676\pi$
$751$	−28.0000	−1.02173	−0.510867	+	0.859660i	$0.670676\pi$
$752$	0	0
$753$	54.0000	1.96787
$754$	0	0
$755$	−36.0000	−1.31017
$756$	0	0
$757$	−38.0000	−1.38113	−0.690567	−	0.723269i	$-0.742639\pi$
$757$	−38.0000	−1.38113	−0.690567	+	0.723269i	$0.742639\pi$
$758$	0	0
$759$	6.00000	0.217786
$760$	0	0
$761$	15.0000	0.543750	0.271875	−	0.962333i	$-0.412356\pi$
$761$	15.0000	0.543750	0.271875	+	0.962333i	$0.412356\pi$
$762$	0	0
$763$	20.0000	0.724049
$764$	0	0
$765$	0	0
$766$	0	0
$767$	60.0000	2.16647
$768$	0	0
$769$	−28.0000	−1.00971	−0.504853	−	0.863205i	$-0.668453\pi$
$769$	−28.0000	−1.00971	−0.504853	+	0.863205i	$0.668453\pi$
$770$	0	0
$771$	−21.0000	−0.756297
$772$	0	0
$773$	14.0000	0.503545	0.251773	−	0.967786i	$-0.418987\pi$
$773$	14.0000	0.503545	0.251773	+	0.967786i	$0.418987\pi$
$774$	0	0
$775$	−55.0000	−1.97566
$776$	0	0
$777$	12.0000	0.430498
$778$	0	0
$779$	20.0000	0.716574
$780$	0	0
$781$	14.0000	0.500959
$782$	0	0
$783$	−27.0000	−0.964901
$784$	0	0
$785$	48.0000	1.71319
$786$	0	0
$787$	−32.0000	−1.14068	−0.570338	−	0.821410i	$-0.693188\pi$
$787$	−32.0000	−1.14068	−0.570338	+	0.821410i	$0.693188\pi$
$788$	0	0
$789$	54.0000	1.92245
$790$	0	0
$791$	−4.00000	−0.142224
$792$	0	0
$793$	−30.0000	−1.06533
$794$	0	0
$795$	0	0
$796$	0	0
$797$	36.0000	1.27519	0.637593	−	0.770374i	$-0.279930\pi$
$797$	36.0000	1.27519	0.637593	+	0.770374i	$0.279930\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	−72.0000	−2.54399
$802$	0	0
$803$	−14.0000	−0.494049
$804$	0	0
$805$	4.00000	0.140981
$806$	0	0
$807$	−15.0000	−0.528025
$808$	0	0
$809$	−46.0000	−1.61727	−0.808637	−	0.588308i	$-0.799794\pi$
$809$	−46.0000	−1.61727	−0.808637	+	0.588308i	$0.799794\pi$
$810$	0	0
$811$	−25.0000	−0.877869	−0.438934	−	0.898519i	$-0.644644\pi$
$811$	−25.0000	−0.877869	−0.438934	+	0.898519i	$0.644644\pi$
$812$	0	0
$813$	−72.0000	−2.52515
$814$	0	0
$815$	−60.0000	−2.10171
$816$	0	0
$817$	16.0000	0.559769
$818$	0	0
$819$	30.0000	1.04828
$820$	0	0
$821$	−10.0000	−0.349002	−0.174501	−	0.984657i	$-0.555831\pi$
$821$	−10.0000	−0.349002	−0.174501	+	0.984657i	$0.555831\pi$
$822$	0	0
$823$	−39.0000	−1.35945	−0.679727	−	0.733465i	$-0.737902\pi$
$823$	−39.0000	−1.35945	−0.679727	+	0.733465i	$0.737902\pi$
$824$	0	0
$825$	−66.0000	−2.29783
$826$	0	0
$827$	28.0000	0.973655	0.486828	−	0.873498i	$-0.338154\pi$
$827$	28.0000	0.973655	0.486828	+	0.873498i	$0.338154\pi$
$828$	0	0
$829$	−46.0000	−1.59765	−0.798823	−	0.601566i	$-0.794544\pi$
$829$	−46.0000	−1.59765	−0.798823	+	0.601566i	$0.794544\pi$
$830$	0	0
$831$	75.0000	2.60172
$832$	0	0
$833$	0	0
$834$	0	0
$835$	−32.0000	−1.10741
$836$	0	0
$837$	−45.0000	−1.55543
$838$	0	0
$839$	−6.00000	−0.207143	−0.103572	−	0.994622i	$-0.533027\pi$
$839$	−6.00000	−0.207143	−0.103572	+	0.994622i	$0.533027\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	0	0
$843$	−18.0000	−0.619953
$844$	0	0
$845$	−48.0000	−1.65125
$846$	0	0
$847$	−7.00000	−0.240523
$848$	0	0
$849$	42.0000	1.44144
$850$	0	0
$851$	−4.00000	−0.137118
$852$	0	0
$853$	14.0000	0.479351	0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000	0.479351	0.239675	+	0.970853i	$0.422959\pi$
$854$	0	0
$855$	−96.0000	−3.28313
$856$	0	0
$857$	−39.0000	−1.33221	−0.666107	−	0.745856i	$-0.732041\pi$
$857$	−39.0000	−1.33221	−0.666107	+	0.745856i	$0.732041\pi$
$858$	0	0
$859$	31.0000	1.05771	0.528853	−	0.848713i	$-0.322622\pi$
$859$	31.0000	1.05771	0.528853	+	0.848713i	$0.322622\pi$
$860$	0	0
$861$	15.0000	0.511199
$862$	0	0
$863$	−13.0000	−0.442525	−0.221263	−	0.975214i	$-0.571018\pi$
$863$	−13.0000	−0.442525	−0.221263	+	0.975214i	$0.571018\pi$
$864$	0	0
$865$	24.0000	0.816024
$866$	0	0
$867$	−51.0000	−1.73205
$868$	0	0
$869$	32.0000	1.08553
$870$	0	0
$871$	80.0000	2.71070
$872$	0	0
$873$	36.0000	1.21842
$874$	0	0
$875$	−24.0000	−0.811348
$876$	0	0
$877$	6.00000	0.202606	0.101303	−	0.994856i	$-0.467699\pi$
$877$	6.00000	0.202606	0.101303	+	0.994856i	$0.467699\pi$
$878$	0	0
$879$	18.0000	0.607125
$880$	0	0
$881$	−30.0000	−1.01073	−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000	−1.01073	−0.505363	+	0.862907i	$0.668641\pi$
$882$	0	0
$883$	−4.00000	−0.134611	−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000	−0.134611	−0.0673054	+	0.997732i	$0.521440\pi$
$884$	0	0
$885$	−144.000	−4.84051
$886$	0	0
$887$	−17.0000	−0.570804	−0.285402	−	0.958408i	$-0.592127\pi$
$887$	−17.0000	−0.570804	−0.285402	+	0.958408i	$0.592127\pi$
$888$	0	0
$889$	11.0000	0.368928
$890$	0	0
$891$	−18.0000	−0.603023
$892$	0	0
$893$	44.0000	1.47240
$894$	0	0
$895$	20.0000	0.668526
$896$	0	0
$897$	−15.0000	−0.500835
$898$	0	0
$899$	15.0000	0.500278
$900$	0	0
$901$	0	0
$902$	0	0
$903$	12.0000	0.399335
$904$	0	0
$905$	104.000	3.45708
$906$	0	0
$907$	16.0000	0.531271	0.265636	−	0.964073i	$-0.414418\pi$
$907$	16.0000	0.531271	0.265636	+	0.964073i	$0.414418\pi$
$908$	0	0
$909$	84.0000	2.78610
$910$	0	0
$911$	6.00000	0.198789	0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000	0.198789	0.0993944	+	0.995048i	$0.468309\pi$
$912$	0	0
$913$	16.0000	0.529523
$914$	0	0
$915$	72.0000	2.38025
$916$	0	0
$917$	7.00000	0.231160
$918$	0	0
$919$	46.0000	1.51740	0.758700	−	0.651440i	$-0.225835\pi$
$919$	46.0000	1.51740	0.758700	+	0.651440i	$0.225835\pi$
$920$	0	0
$921$	−84.0000	−2.76789
$922$	0	0
$923$	−35.0000	−1.15204
$924$	0	0
$925$	44.0000	1.44671
$926$	0	0
$927$	60.0000	1.97066
$928$	0	0
$929$	−35.0000	−1.14831	−0.574156	−	0.818746i	$-0.694670\pi$
$929$	−35.0000	−1.14831	−0.574156	+	0.818746i	$0.694670\pi$
$930$	0	0
$931$	4.00000	0.131095
$932$	0	0
$933$	−15.0000	−0.491078
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−32.0000	−1.04539	−0.522697	−	0.852518i	$-0.675074\pi$
$937$	−32.0000	−1.04539	−0.522697	+	0.852518i	$0.675074\pi$
$938$	0	0
$939$	30.0000	0.979013
$940$	0	0
$941$	−6.00000	−0.195594	−0.0977972	−	0.995206i	$-0.531180\pi$
$941$	−6.00000	−0.195594	−0.0977972	+	0.995206i	$0.531180\pi$
$942$	0	0
$943$	−5.00000	−0.162822
$944$	0	0
$945$	−36.0000	−1.17108
$946$	0	0
$947$	−43.0000	−1.39731	−0.698656	−	0.715458i	$-0.746218\pi$
$947$	−43.0000	−1.39731	−0.698656	+	0.715458i	$0.746218\pi$
$948$	0	0
$949$	35.0000	1.13615
$950$	0	0
$951$	18.0000	0.583690
$952$	0	0
$953$	6.00000	0.194359	0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000	0.194359	0.0971795	+	0.995267i	$0.469018\pi$
$954$	0	0
$955$	−16.0000	−0.517748
$956$	0	0
$957$	18.0000	0.581857
$958$	0	0
$959$	−18.0000	−0.581250
$960$	0	0
$961$	−6.00000	−0.193548
$962$	0	0
$963$	72.0000	2.32017
$964$	0	0
$965$	−52.0000	−1.67394
$966$	0	0
$967$	−5.00000	−0.160789	−0.0803946	−	0.996763i	$-0.525618\pi$
$967$	−5.00000	−0.160789	−0.0803946	+	0.996763i	$0.525618\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	0	0
$973$	−19.0000	−0.609112
$974$	0	0
$975$	165.000	5.28423
$976$	0	0
$977$	44.0000	1.40768	0.703842	−	0.710356i	$-0.251466\pi$
$977$	44.0000	1.40768	0.703842	+	0.710356i	$0.251466\pi$
$978$	0	0
$979$	24.0000	0.767043
$980$	0	0
$981$	120.000	3.83131
$982$	0	0
$983$	12.0000	0.382741	0.191370	−	0.981518i	$-0.438707\pi$
$983$	12.0000	0.382741	0.191370	+	0.981518i	$0.438707\pi$
$984$	0	0
$985$	108.000	3.44117
$986$	0	0
$987$	33.0000	1.05040
$988$	0	0
$989$	−4.00000	−0.127193
$990$	0	0
$991$	−32.0000	−1.01651	−0.508257	−	0.861206i	$-0.669710\pi$
$991$	−32.0000	−1.01651	−0.508257	+	0.861206i	$0.669710\pi$
$992$	0	0
$993$	57.0000	1.80884
$994$	0	0
$995$	72.0000	2.28255
$996$	0	0
$997$	−38.0000	−1.20347	−0.601736	−	0.798695i	$-0.705524\pi$
$997$	−38.0000	−1.20347	−0.601736	+	0.798695i	$0.705524\pi$
$998$	0	0
$999$	36.0000	1.13899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2576.2.a.o.1.1		1
4.3	odd	2		1288.2.a.a.1.1	✓	1
28.27	even	2		9016.2.a.o.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1288.2.a.a.1.1	✓	1	4.3	odd	2
2576.2.a.o.1.1		1	1.1	even	1	trivial
9016.2.a.o.1.1		1	28.27	even	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:	\( N \)	\(=\)	\( 2576 = 2^{4} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2576.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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