LMFDB - Embedded newform 9280.2.a.ba.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9280,2,Mod(1,9280)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("9280.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9280, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 9280 = 2^{6} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9280.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,0,0,0,-2,0,0,0,-6,0,0,0,4,0,0,0,-12,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(21)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$74.1011730757$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 4640)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	9280.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{5} +2.82843 q^{7} -3.00000 q^{9} -2.82843 q^{11} +2.00000 q^{13} -6.00000 q^{17} +2.82843 q^{19} +8.48528 q^{23} +1.00000 q^{25} -1.00000 q^{29} -8.48528 q^{31} -2.82843 q^{35} -6.00000 q^{37} +10.0000 q^{41} +3.00000 q^{45} +11.3137 q^{47} +1.00000 q^{49} -6.00000 q^{53} +2.82843 q^{55} -5.65685 q^{59} -14.0000 q^{61} -8.48528 q^{63} -2.00000 q^{65} +14.1421 q^{67} +5.65685 q^{71} +10.0000 q^{73} -8.00000 q^{77} -14.1421 q^{79} +9.00000 q^{81} -8.48528 q^{83} +6.00000 q^{85} +10.0000 q^{89} +5.65685 q^{91} -2.82843 q^{95} +2.00000 q^{97} +8.48528 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{5} - 6 q^{9} + 4 q^{13} - 12 q^{17} + 2 q^{25} - 2 q^{29} - 12 q^{37} + 20 q^{41} + 6 q^{45} + 2 q^{49} - 12 q^{53} - 28 q^{61} - 4 q^{65} + 20 q^{73} - 16 q^{77} + 18 q^{81} + 12 q^{85} + 20 q^{89}+ \cdots + 4 q^{97}+O(q^{100}) $ 2 * q - 2 * q^5 - 6 * q^9 + 4 * q^13 - 12 * q^17 + 2 * q^25 - 2 * q^29 - 12 * q^37 + 20 * q^41 + 6 * q^45 + 2 * q^49 - 12 * q^53 - 28 * q^61 - 4 * q^65 + 20 * q^73 - 16 * q^77 + 18 * q^81 + 12 * q^85 + 20 * q^89 + 4 * q^97

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		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	0	0
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	2.82843	1.06904	0.534522	−	0.845154i	$-0.320491\pi$
$7$	2.82843	1.06904	0.534522	+	0.845154i	$0.320491\pi$
$8$	0	0
$9$	−3.00000	−1.00000
$10$	0	0
$11$	−2.82843	−0.852803	−0.426401	−	0.904534i	$-0.640219\pi$
$11$	−2.82843	−0.852803	−0.426401	+	0.904534i	$0.640219\pi$
$12$	0	0
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	0	0
$19$	2.82843	0.648886	0.324443	−	0.945905i	$-0.394823\pi$
$19$	2.82843	0.648886	0.324443	+	0.945905i	$0.394823\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	8.48528	1.76930	0.884652	−	0.466252i	$-0.154396\pi$
$23$	8.48528	1.76930	0.884652	+	0.466252i	$0.154396\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	0	0
$28$	0	0
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0	0
$31$	−8.48528	−1.52400	−0.762001	−	0.647576i	$-0.775783\pi$
$31$	−8.48528	−1.52400	−0.762001	+	0.647576i	$0.775783\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	−2.82843	−0.478091
$36$	0	0
$37$	−6.00000	−0.986394	−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000	−0.986394	−0.493197	+	0.869918i	$0.664172\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	10.0000	1.56174	0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000	1.56174	0.780869	+	0.624695i	$0.214777\pi$
$42$	0	0
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	0	0
$45$	3.00000	0.447214
$46$	0	0
$47$	11.3137	1.65027	0.825137	−	0.564933i	$-0.191098\pi$
$47$	11.3137	1.65027	0.825137	+	0.564933i	$0.191098\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	0	0
$52$	0	0
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	0	0
$55$	2.82843	0.381385
$56$	0	0
$57$	0	0
$58$	0	0
$59$	−5.65685	−0.736460	−0.368230	−	0.929735i	$-0.620036\pi$
$59$	−5.65685	−0.736460	−0.368230	+	0.929735i	$0.620036\pi$
$60$	0	0
$61$	−14.0000	−1.79252	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000	−1.79252	−0.896258	+	0.443533i	$0.853725\pi$
$62$	0	0
$63$	−8.48528	−1.06904
$64$	0	0
$65$	−2.00000	−0.248069
$66$	0	0
$67$	14.1421	1.72774	0.863868	−	0.503718i	$-0.168035\pi$
$67$	14.1421	1.72774	0.863868	+	0.503718i	$0.168035\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	5.65685	0.671345	0.335673	−	0.941979i	$-0.391036\pi$
$71$	5.65685	0.671345	0.335673	+	0.941979i	$0.391036\pi$
$72$	0	0
$73$	10.0000	1.17041	0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000	1.17041	0.585206	+	0.810885i	$0.301014\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	−8.00000	−0.911685
$78$	0	0
$79$	−14.1421	−1.59111	−0.795557	−	0.605878i	$-0.792822\pi$
$79$	−14.1421	−1.59111	−0.795557	+	0.605878i	$0.792822\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	0	0
$83$	−8.48528	−0.931381	−0.465690	−	0.884948i	$-0.654194\pi$
$83$	−8.48528	−0.931381	−0.465690	+	0.884948i	$0.654194\pi$
$84$	0	0
$85$	6.00000	0.650791
$86$	0	0
$87$	0	0
$88$	0	0
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	0	0
$91$	5.65685	0.592999
$92$	0	0
$93$	0	0
$94$	0	0
$95$	−2.82843	−0.290191
$96$	0	0
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	0	0
$99$	8.48528	0.852803
$100$	0	0
$101$	10.0000	0.995037	0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000	0.995037	0.497519	+	0.867453i	$0.334245\pi$
$102$	0	0
$103$	8.48528	0.836080	0.418040	−	0.908429i	$-0.362717\pi$
$103$	8.48528	0.836080	0.418040	+	0.908429i	$0.362717\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	8.48528	0.820303	0.410152	−	0.912017i	$-0.365476\pi$
$107$	8.48528	0.820303	0.410152	+	0.912017i	$0.365476\pi$
$108$	0	0
$109$	−14.0000	−1.34096	−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000	−1.34096	−0.670478	+	0.741929i	$0.733911\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	2.00000	0.188144	0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000	0.188144	0.0940721	+	0.995565i	$0.470012\pi$
$114$	0	0
$115$	−8.48528	−0.791257
$116$	0	0
$117$	−6.00000	−0.554700
$118$	0	0
$119$	−16.9706	−1.55569
$120$	0	0
$121$	−3.00000	−0.272727
$122$	0	0
$123$	0	0
$124$	0	0
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	5.65685	0.501965	0.250982	−	0.967992i	$-0.419246\pi$
$127$	5.65685	0.501965	0.250982	+	0.967992i	$0.419246\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	2.82843	0.247121	0.123560	−	0.992337i	$-0.460569\pi$
$131$	2.82843	0.247121	0.123560	+	0.992337i	$0.460569\pi$
$132$	0	0
$133$	8.00000	0.693688
$134$	0	0
$135$	0	0
$136$	0	0
$137$	2.00000	0.170872	0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000	0.170872	0.0854358	+	0.996344i	$0.472772\pi$
$138$	0	0
$139$	−16.9706	−1.43942	−0.719712	−	0.694273i	$-0.755726\pi$
$139$	−16.9706	−1.43942	−0.719712	+	0.694273i	$0.755726\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	−5.65685	−0.473050
$144$	0	0
$145$	1.00000	0.0830455
$146$	0	0
$147$	0	0
$148$	0	0
$149$	18.0000	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$150$	0	0
$151$	16.9706	1.38104	0.690522	−	0.723311i	$-0.257381\pi$
$151$	16.9706	1.38104	0.690522	+	0.723311i	$0.257381\pi$
$152$	0	0
$153$	18.0000	1.45521
$154$	0	0
$155$	8.48528	0.681554
$156$	0	0
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	24.0000	1.89146
$162$	0	0
$163$	5.65685	0.443079	0.221540	−	0.975151i	$-0.428892\pi$
$163$	5.65685	0.443079	0.221540	+	0.975151i	$0.428892\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−14.1421	−1.09435	−0.547176	−	0.837018i	$-0.684297\pi$
$167$	−14.1421	−1.09435	−0.547176	+	0.837018i	$0.684297\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	0	0
$171$	−8.48528	−0.648886
$172$	0	0
$173$	18.0000	1.36851	0.684257	−	0.729241i	$-0.260127\pi$
$173$	18.0000	1.36851	0.684257	+	0.729241i	$0.260127\pi$
$174$	0	0
$175$	2.82843	0.213809
$176$	0	0
$177$	0	0
$178$	0	0
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	−14.0000	−1.04061	−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000	−1.04061	−0.520306	+	0.853980i	$0.674182\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	6.00000	0.441129
$186$	0	0
$187$	16.9706	1.24101
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−8.48528	−0.613973	−0.306987	−	0.951714i	$-0.599321\pi$
$191$	−8.48528	−0.613973	−0.306987	+	0.951714i	$0.599321\pi$
$192$	0	0
$193$	26.0000	1.87152	0.935760	−	0.352636i	$-0.114715\pi$
$193$	26.0000	1.87152	0.935760	+	0.352636i	$0.114715\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−6.00000	−0.427482	−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000	−0.427482	−0.213741	+	0.976890i	$0.568565\pi$
$198$	0	0
$199$	5.65685	0.401004	0.200502	−	0.979693i	$-0.435743\pi$
$199$	5.65685	0.401004	0.200502	+	0.979693i	$0.435743\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	−2.82843	−0.198517
$204$	0	0
$205$	−10.0000	−0.698430
$206$	0	0
$207$	−25.4558	−1.76930
$208$	0	0
$209$	−8.00000	−0.553372
$210$	0	0
$211$	2.82843	0.194717	0.0973585	−	0.995249i	$-0.468961\pi$
$211$	2.82843	0.194717	0.0973585	+	0.995249i	$0.468961\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−24.0000	−1.62923
$218$	0	0
$219$	0	0
$220$	0	0
$221$	−12.0000	−0.807207
$222$	0	0
$223$	8.48528	0.568216	0.284108	−	0.958792i	$-0.408302\pi$
$223$	8.48528	0.568216	0.284108	+	0.958792i	$0.408302\pi$
$224$	0	0
$225$	−3.00000	−0.200000
$226$	0	0
$227$	19.7990	1.31411	0.657053	−	0.753845i	$-0.271803\pi$
$227$	19.7990	1.31411	0.657053	+	0.753845i	$0.271803\pi$
$228$	0	0
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	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
$235$	−11.3137	−0.738025
$236$	0	0
$237$	0	0
$238$	0	0
$239$	28.2843	1.82956	0.914779	−	0.403955i	$-0.132365\pi$
$239$	28.2843	1.82956	0.914779	+	0.403955i	$0.132365\pi$
$240$	0	0
$241$	10.0000	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	−1.00000	−0.0638877
$246$	0	0
$247$	5.65685	0.359937
$248$	0	0
$249$	0	0
$250$	0	0
$251$	8.48528	0.535586	0.267793	−	0.963476i	$-0.413706\pi$
$251$	8.48528	0.535586	0.267793	+	0.963476i	$0.413706\pi$
$252$	0	0
$253$	−24.0000	−1.50887
$254$	0	0
$255$	0	0
$256$	0	0
$257$	18.0000	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	0	0
$259$	−16.9706	−1.05450
$260$	0	0
$261$	3.00000	0.185695
$262$	0	0
$263$	22.6274	1.39527	0.697633	−	0.716455i	$-0.254237\pi$
$263$	22.6274	1.39527	0.697633	+	0.716455i	$0.254237\pi$
$264$	0	0
$265$	6.00000	0.368577
$266$	0	0
$267$	0	0
$268$	0	0
$269$	18.0000	1.09748	0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000	1.09748	0.548740	+	0.835993i	$0.315108\pi$
$270$	0	0
$271$	−25.4558	−1.54633	−0.773166	−	0.634203i	$-0.781328\pi$
$271$	−25.4558	−1.54633	−0.773166	+	0.634203i	$0.781328\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	−2.82843	−0.170561
$276$	0	0
$277$	26.0000	1.56219	0.781094	−	0.624413i	$-0.214662\pi$
$277$	26.0000	1.56219	0.781094	+	0.624413i	$0.214662\pi$
$278$	0	0
$279$	25.4558	1.52400
$280$	0	0
$281$	2.00000	0.119310	0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000	0.119310	0.0596550	+	0.998219i	$0.481000\pi$
$282$	0	0
$283$	−14.1421	−0.840663	−0.420331	−	0.907371i	$-0.638086\pi$
$283$	−14.1421	−0.840663	−0.420331	+	0.907371i	$0.638086\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	28.2843	1.66957
$288$	0	0
$289$	19.0000	1.11765
$290$	0	0
$291$	0	0
$292$	0	0
$293$	2.00000	0.116841	0.0584206	−	0.998292i	$-0.481394\pi$
$293$	2.00000	0.116841	0.0584206	+	0.998292i	$0.481394\pi$
$294$	0	0
$295$	5.65685	0.329355
$296$	0	0
$297$	0	0
$298$	0	0
$299$	16.9706	0.981433
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	14.0000	0.801638
$306$	0	0
$307$	−16.9706	−0.968561	−0.484281	−	0.874913i	$-0.660919\pi$
$307$	−16.9706	−0.968561	−0.484281	+	0.874913i	$0.660919\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	−8.48528	−0.481156	−0.240578	−	0.970630i	$-0.577337\pi$
$311$	−8.48528	−0.481156	−0.240578	+	0.970630i	$0.577337\pi$
$312$	0	0
$313$	26.0000	1.46961	0.734803	−	0.678280i	$-0.237274\pi$
$313$	26.0000	1.46961	0.734803	+	0.678280i	$0.237274\pi$
$314$	0	0
$315$	8.48528	0.478091
$316$	0	0
$317$	2.00000	0.112331	0.0561656	−	0.998421i	$-0.482113\pi$
$317$	2.00000	0.112331	0.0561656	+	0.998421i	$0.482113\pi$
$318$	0	0
$319$	2.82843	0.158362
$320$	0	0
$321$	0	0
$322$	0	0
$323$	−16.9706	−0.944267
$324$	0	0
$325$	2.00000	0.110940
$326$	0	0
$327$	0	0
$328$	0	0
$329$	32.0000	1.76422
$330$	0	0
$331$	−8.48528	−0.466393	−0.233197	−	0.972430i	$-0.574919\pi$
$331$	−8.48528	−0.466393	−0.233197	+	0.972430i	$0.574919\pi$
$332$	0	0
$333$	18.0000	0.986394
$334$	0	0
$335$	−14.1421	−0.772667
$336$	0	0
$337$	2.00000	0.108947	0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000	0.108947	0.0544735	+	0.998515i	$0.482652\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	24.0000	1.29967
$342$	0	0
$343$	−16.9706	−0.916324
$344$	0	0
$345$	0	0
$346$	0	0
$347$	−31.1127	−1.67022	−0.835109	−	0.550085i	$-0.814595\pi$
$347$	−31.1127	−1.67022	−0.835109	+	0.550085i	$0.814595\pi$
$348$	0	0
$349$	−30.0000	−1.60586	−0.802932	−	0.596071i	$-0.796728\pi$
$349$	−30.0000	−1.60586	−0.802932	+	0.596071i	$0.796728\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	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
$355$	−5.65685	−0.300235
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−25.4558	−1.34351	−0.671754	−	0.740774i	$-0.734459\pi$
$359$	−25.4558	−1.34351	−0.671754	+	0.740774i	$0.734459\pi$
$360$	0	0
$361$	−11.0000	−0.578947
$362$	0	0
$363$	0	0
$364$	0	0
$365$	−10.0000	−0.523424
$366$	0	0
$367$	−5.65685	−0.295285	−0.147643	−	0.989041i	$-0.547169\pi$
$367$	−5.65685	−0.295285	−0.147643	+	0.989041i	$0.547169\pi$
$368$	0	0
$369$	−30.0000	−1.56174
$370$	0	0
$371$	−16.9706	−0.881068
$372$	0	0
$373$	26.0000	1.34623	0.673114	−	0.739538i	$-0.264956\pi$
$373$	26.0000	1.34623	0.673114	+	0.739538i	$0.264956\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−2.00000	−0.103005
$378$	0	0
$379$	14.1421	0.726433	0.363216	−	0.931705i	$-0.381679\pi$
$379$	14.1421	0.726433	0.363216	+	0.931705i	$0.381679\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	−8.48528	−0.433578	−0.216789	−	0.976219i	$-0.569558\pi$
$383$	−8.48528	−0.433578	−0.216789	+	0.976219i	$0.569558\pi$
$384$	0	0
$385$	8.00000	0.407718
$386$	0	0
$387$	0	0
$388$	0	0
$389$	10.0000	0.507020	0.253510	−	0.967333i	$-0.418415\pi$
$389$	10.0000	0.507020	0.253510	+	0.967333i	$0.418415\pi$
$390$	0	0
$391$	−50.9117	−2.57471
$392$	0	0
$393$	0	0
$394$	0	0
$395$	14.1421	0.711568
$396$	0	0
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	34.0000	1.69788	0.848939	−	0.528490i	$-0.177242\pi$
$401$	34.0000	1.69788	0.848939	+	0.528490i	$0.177242\pi$
$402$	0	0
$403$	−16.9706	−0.845364
$404$	0	0
$405$	−9.00000	−0.447214
$406$	0	0
$407$	16.9706	0.841200
$408$	0	0
$409$	10.0000	0.494468	0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000	0.494468	0.247234	+	0.968956i	$0.420478\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	−16.0000	−0.787309
$414$	0	0
$415$	8.48528	0.416526
$416$	0	0
$417$	0	0
$418$	0	0
$419$	22.6274	1.10542	0.552711	−	0.833373i	$-0.313593\pi$
$419$	22.6274	1.10542	0.552711	+	0.833373i	$0.313593\pi$
$420$	0	0
$421$	−38.0000	−1.85201	−0.926003	−	0.377515i	$-0.876779\pi$
$421$	−38.0000	−1.85201	−0.926003	+	0.377515i	$0.876779\pi$
$422$	0	0
$423$	−33.9411	−1.65027
$424$	0	0
$425$	−6.00000	−0.291043
$426$	0	0
$427$	−39.5980	−1.91628
$428$	0	0
$429$	0	0
$430$	0	0
$431$	−22.6274	−1.08992	−0.544962	−	0.838461i	$-0.683456\pi$
$431$	−22.6274	−1.08992	−0.544962	+	0.838461i	$0.683456\pi$
$432$	0	0
$433$	−6.00000	−0.288342	−0.144171	−	0.989553i	$-0.546051\pi$
$433$	−6.00000	−0.288342	−0.144171	+	0.989553i	$0.546051\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	24.0000	1.14808
$438$	0	0
$439$	33.9411	1.61992	0.809961	−	0.586484i	$-0.199488\pi$
$439$	33.9411	1.61992	0.809961	+	0.586484i	$0.199488\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	0	0
$443$	39.5980	1.88136	0.940678	−	0.339300i	$-0.110190\pi$
$443$	39.5980	1.88136	0.940678	+	0.339300i	$0.110190\pi$
$444$	0	0
$445$	−10.0000	−0.474045
$446$	0	0
$447$	0	0
$448$	0	0
$449$	2.00000	0.0943858	0.0471929	−	0.998886i	$-0.484972\pi$
$449$	2.00000	0.0943858	0.0471929	+	0.998886i	$0.484972\pi$
$450$	0	0
$451$	−28.2843	−1.33185
$452$	0	0
$453$	0	0
$454$	0	0
$455$	−5.65685	−0.265197
$456$	0	0
$457$	−6.00000	−0.280668	−0.140334	−	0.990104i	$-0.544818\pi$
$457$	−6.00000	−0.280668	−0.140334	+	0.990104i	$0.544818\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	2.00000	0.0931493	0.0465746	−	0.998915i	$-0.485169\pi$
$461$	2.00000	0.0931493	0.0465746	+	0.998915i	$0.485169\pi$
$462$	0	0
$463$	25.4558	1.18303	0.591517	−	0.806293i	$-0.298529\pi$
$463$	25.4558	1.18303	0.591517	+	0.806293i	$0.298529\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	16.9706	0.785304	0.392652	−	0.919687i	$-0.371558\pi$
$467$	16.9706	0.785304	0.392652	+	0.919687i	$0.371558\pi$
$468$	0	0
$469$	40.0000	1.84703
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	2.82843	0.129777
$476$	0	0
$477$	18.0000	0.824163
$478$	0	0
$479$	−19.7990	−0.904639	−0.452319	−	0.891856i	$-0.649403\pi$
$479$	−19.7990	−0.904639	−0.452319	+	0.891856i	$0.649403\pi$
$480$	0	0
$481$	−12.0000	−0.547153
$482$	0	0
$483$	0	0
$484$	0	0
$485$	−2.00000	−0.0908153
$486$	0	0
$487$	−31.1127	−1.40985	−0.704925	−	0.709281i	$-0.749020\pi$
$487$	−31.1127	−1.40985	−0.704925	+	0.709281i	$0.749020\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	−19.7990	−0.893516	−0.446758	−	0.894655i	$-0.647421\pi$
$491$	−19.7990	−0.893516	−0.446758	+	0.894655i	$0.647421\pi$
$492$	0	0
$493$	6.00000	0.270226
$494$	0	0
$495$	−8.48528	−0.381385
$496$	0	0
$497$	16.0000	0.717698
$498$	0	0
$499$	0	0		−	1.00000i	$-0.5\pi$
$499$	0	0			1.00000i	$0.5\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	−39.5980	−1.76559	−0.882793	−	0.469762i	$-0.844340\pi$
$503$	−39.5980	−1.76559	−0.882793	+	0.469762i	$0.844340\pi$
$504$	0	0
$505$	−10.0000	−0.444994
$506$	0	0
$507$	0	0
$508$	0	0
$509$	2.00000	0.0886484	0.0443242	−	0.999017i	$-0.485887\pi$
$509$	2.00000	0.0886484	0.0443242	+	0.999017i	$0.485887\pi$
$510$	0	0
$511$	28.2843	1.25122
$512$	0	0
$513$	0	0
$514$	0	0
$515$	−8.48528	−0.373906
$516$	0	0
$517$	−32.0000	−1.40736
$518$	0	0
$519$	0	0
$520$	0	0
$521$	18.0000	0.788594	0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000	0.788594	0.394297	+	0.918983i	$0.370988\pi$
$522$	0	0
$523$	14.1421	0.618392	0.309196	−	0.950998i	$-0.399940\pi$
$523$	14.1421	0.618392	0.309196	+	0.950998i	$0.399940\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	50.9117	2.21775
$528$	0	0
$529$	49.0000	2.13043
$530$	0	0
$531$	16.9706	0.736460
$532$	0	0
$533$	20.0000	0.866296
$534$	0	0
$535$	−8.48528	−0.366851
$536$	0	0
$537$	0	0
$538$	0	0
$539$	−2.82843	−0.121829
$540$	0	0
$541$	−30.0000	−1.28980	−0.644900	−	0.764267i	$-0.723101\pi$
$541$	−30.0000	−1.28980	−0.644900	+	0.764267i	$0.723101\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	14.0000	0.599694
$546$	0	0
$547$	−2.82843	−0.120935	−0.0604674	−	0.998170i	$-0.519259\pi$
$547$	−2.82843	−0.120935	−0.0604674	+	0.998170i	$0.519259\pi$
$548$	0	0
$549$	42.0000	1.79252
$550$	0	0
$551$	−2.82843	−0.120495
$552$	0	0
$553$	−40.0000	−1.70097
$554$	0	0
$555$	0	0
$556$	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
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	28.2843	1.19204	0.596020	−	0.802970i	$-0.296748\pi$
$563$	28.2843	1.19204	0.596020	+	0.802970i	$0.296748\pi$
$564$	0	0
$565$	−2.00000	−0.0841406
$566$	0	0
$567$	25.4558	1.06904
$568$	0	0
$569$	42.0000	1.76073	0.880366	−	0.474295i	$-0.157297\pi$
$569$	42.0000	1.76073	0.880366	+	0.474295i	$0.157297\pi$
$570$	0	0
$571$	−33.9411	−1.42039	−0.710196	−	0.704004i	$-0.751394\pi$
$571$	−33.9411	−1.42039	−0.710196	+	0.704004i	$0.751394\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	8.48528	0.353861
$576$	0	0
$577$	−22.0000	−0.915872	−0.457936	−	0.888985i	$-0.651411\pi$
$577$	−22.0000	−0.915872	−0.457936	+	0.888985i	$0.651411\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	−24.0000	−0.995688
$582$	0	0
$583$	16.9706	0.702849
$584$	0	0
$585$	6.00000	0.248069
$586$	0	0
$587$	19.7990	0.817192	0.408596	−	0.912715i	$-0.366019\pi$
$587$	19.7990	0.817192	0.408596	+	0.912715i	$0.366019\pi$
$588$	0	0
$589$	−24.0000	−0.988903
$590$	0	0
$591$	0	0
$592$	0	0
$593$	2.00000	0.0821302	0.0410651	−	0.999156i	$-0.486925\pi$
$593$	2.00000	0.0821302	0.0410651	+	0.999156i	$0.486925\pi$
$594$	0	0
$595$	16.9706	0.695725
$596$	0	0
$597$	0	0
$598$	0	0
$599$	31.1127	1.27123	0.635615	−	0.772006i	$-0.280747\pi$
$599$	31.1127	1.27123	0.635615	+	0.772006i	$0.280747\pi$
$600$	0	0
$601$	26.0000	1.06056	0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000	1.06056	0.530281	+	0.847822i	$0.322086\pi$
$602$	0	0
$603$	−42.4264	−1.72774
$604$	0	0
$605$	3.00000	0.121967
$606$	0	0
$607$	0	0		−	1.00000i	$-0.5\pi$
$607$	0	0			1.00000i	$0.5\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	22.6274	0.915407
$612$	0	0
$613$	10.0000	0.403896	0.201948	−	0.979396i	$-0.435273\pi$
$613$	10.0000	0.403896	0.201948	+	0.979396i	$0.435273\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	10.0000	0.402585	0.201292	−	0.979531i	$-0.435486\pi$
$617$	10.0000	0.402585	0.201292	+	0.979531i	$0.435486\pi$
$618$	0	0
$619$	−2.82843	−0.113684	−0.0568420	−	0.998383i	$-0.518103\pi$
$619$	−2.82843	−0.113684	−0.0568420	+	0.998383i	$0.518103\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	28.2843	1.13319
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	36.0000	1.43541
$630$	0	0
$631$	16.9706	0.675587	0.337794	−	0.941220i	$-0.390319\pi$
$631$	16.9706	0.675587	0.337794	+	0.941220i	$0.390319\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	−5.65685	−0.224485
$636$	0	0
$637$	2.00000	0.0792429
$638$	0	0
$639$	−16.9706	−0.671345
$640$	0	0
$641$	2.00000	0.0789953	0.0394976	−	0.999220i	$-0.487424\pi$
$641$	2.00000	0.0789953	0.0394976	+	0.999220i	$0.487424\pi$
$642$	0	0
$643$	42.4264	1.67313	0.836567	−	0.547865i	$-0.184559\pi$
$643$	42.4264	1.67313	0.836567	+	0.547865i	$0.184559\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	31.1127	1.22317	0.611583	−	0.791180i	$-0.290533\pi$
$647$	31.1127	1.22317	0.611583	+	0.791180i	$0.290533\pi$
$648$	0	0
$649$	16.0000	0.628055
$650$	0	0
$651$	0	0
$652$	0	0
$653$	42.0000	1.64359	0.821794	−	0.569785i	$-0.192974\pi$
$653$	42.0000	1.64359	0.821794	+	0.569785i	$0.192974\pi$
$654$	0	0
$655$	−2.82843	−0.110516
$656$	0	0
$657$	−30.0000	−1.17041
$658$	0	0
$659$	48.0833	1.87306	0.936529	−	0.350590i	$-0.114019\pi$
$659$	48.0833	1.87306	0.936529	+	0.350590i	$0.114019\pi$
$660$	0	0
$661$	18.0000	0.700119	0.350059	−	0.936727i	$-0.386161\pi$
$661$	18.0000	0.700119	0.350059	+	0.936727i	$0.386161\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	−8.00000	−0.310227
$666$	0	0
$667$	−8.48528	−0.328551
$668$	0	0
$669$	0	0
$670$	0	0
$671$	39.5980	1.52866
$672$	0	0
$673$	34.0000	1.31060	0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000	1.31060	0.655302	+	0.755367i	$0.272541\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	−30.0000	−1.15299	−0.576497	−	0.817099i	$-0.695581\pi$
$677$	−30.0000	−1.15299	−0.576497	+	0.817099i	$0.695581\pi$
$678$	0	0
$679$	5.65685	0.217090
$680$	0	0
$681$	0	0
$682$	0	0
$683$	36.7696	1.40695	0.703474	−	0.710721i	$-0.251631\pi$
$683$	36.7696	1.40695	0.703474	+	0.710721i	$0.251631\pi$
$684$	0	0
$685$	−2.00000	−0.0764161
$686$	0	0
$687$	0	0
$688$	0	0
$689$	−12.0000	−0.457164
$690$	0	0
$691$	45.2548	1.72158	0.860788	−	0.508965i	$-0.169972\pi$
$691$	45.2548	1.72158	0.860788	+	0.508965i	$0.169972\pi$
$692$	0	0
$693$	24.0000	0.911685
$694$	0	0
$695$	16.9706	0.643730
$696$	0	0
$697$	−60.0000	−2.27266
$698$	0	0
$699$	0	0
$700$	0	0
$701$	−6.00000	−0.226617	−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000	−0.226617	−0.113308	+	0.993560i	$0.536145\pi$
$702$	0	0
$703$	−16.9706	−0.640057
$704$	0	0
$705$	0	0
$706$	0	0
$707$	28.2843	1.06374
$708$	0	0
$709$	−6.00000	−0.225335	−0.112667	−	0.993633i	$-0.535939\pi$
$709$	−6.00000	−0.225335	−0.112667	+	0.993633i	$0.535939\pi$
$710$	0	0
$711$	42.4264	1.59111
$712$	0	0
$713$	−72.0000	−2.69642
$714$	0	0
$715$	5.65685	0.211554
$716$	0	0
$717$	0	0
$718$	0	0
$719$	−16.9706	−0.632895	−0.316448	−	0.948610i	$-0.602490\pi$
$719$	−16.9706	−0.632895	−0.316448	+	0.948610i	$0.602490\pi$
$720$	0	0
$721$	24.0000	0.893807
$722$	0	0
$723$	0	0
$724$	0	0
$725$	−1.00000	−0.0371391
$726$	0	0
$727$	−50.9117	−1.88821	−0.944105	−	0.329645i	$-0.893071\pi$
$727$	−50.9117	−1.88821	−0.944105	+	0.329645i	$0.893071\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	34.0000	1.25582	0.627909	−	0.778287i	$-0.283911\pi$
$733$	34.0000	1.25582	0.627909	+	0.778287i	$0.283911\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−40.0000	−1.47342
$738$	0	0
$739$	−42.4264	−1.56068	−0.780340	−	0.625355i	$-0.784954\pi$
$739$	−42.4264	−1.56068	−0.780340	+	0.625355i	$0.784954\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	5.65685	0.207530	0.103765	−	0.994602i	$-0.466911\pi$
$743$	5.65685	0.207530	0.103765	+	0.994602i	$0.466911\pi$
$744$	0	0
$745$	−18.0000	−0.659469
$746$	0	0
$747$	25.4558	0.931381
$748$	0	0
$749$	24.0000	0.876941
$750$	0	0
$751$	−36.7696	−1.34174	−0.670870	−	0.741575i	$-0.734079\pi$
$751$	−36.7696	−1.34174	−0.670870	+	0.741575i	$0.734079\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	−16.9706	−0.617622
$756$	0	0
$757$	34.0000	1.23575	0.617876	−	0.786276i	$-0.287994\pi$
$757$	34.0000	1.23575	0.617876	+	0.786276i	$0.287994\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	18.0000	0.652499	0.326250	−	0.945284i	$-0.394215\pi$
$761$	18.0000	0.652499	0.326250	+	0.945284i	$0.394215\pi$
$762$	0	0
$763$	−39.5980	−1.43354
$764$	0	0
$765$	−18.0000	−0.650791
$766$	0	0
$767$	−11.3137	−0.408514
$768$	0	0
$769$	2.00000	0.0721218	0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000	0.0721218	0.0360609	+	0.999350i	$0.488519\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	−6.00000	−0.215805	−0.107903	−	0.994161i	$-0.534413\pi$
$773$	−6.00000	−0.215805	−0.107903	+	0.994161i	$0.534413\pi$
$774$	0	0
$775$	−8.48528	−0.304800
$776$	0	0
$777$	0	0
$778$	0	0
$779$	28.2843	1.01339
$780$	0	0
$781$	−16.0000	−0.572525
$782$	0	0
$783$	0	0
$784$	0	0
$785$	−10.0000	−0.356915
$786$	0	0
$787$	14.1421	0.504113	0.252056	−	0.967713i	$-0.418893\pi$
$787$	14.1421	0.504113	0.252056	+	0.967713i	$0.418893\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	5.65685	0.201135
$792$	0	0
$793$	−28.0000	−0.994309
$794$	0	0
$795$	0	0
$796$	0	0
$797$	26.0000	0.920967	0.460484	−	0.887668i	$-0.347676\pi$
$797$	26.0000	0.920967	0.460484	+	0.887668i	$0.347676\pi$
$798$	0	0
$799$	−67.8823	−2.40150
$800$	0	0
$801$	−30.0000	−1.06000
$802$	0	0
$803$	−28.2843	−0.998130
$804$	0	0
$805$	−24.0000	−0.845889
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−6.00000	−0.210949	−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000	−0.210949	−0.105474	+	0.994422i	$0.533636\pi$
$810$	0	0
$811$	50.9117	1.78775	0.893876	−	0.448315i	$-0.147976\pi$
$811$	50.9117	1.78775	0.893876	+	0.448315i	$0.147976\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	−5.65685	−0.198151
$816$	0	0
$817$	0	0
$818$	0	0
$819$	−16.9706	−0.592999
$820$	0	0
$821$	−30.0000	−1.04701	−0.523504	−	0.852023i	$-0.675375\pi$
$821$	−30.0000	−1.04701	−0.523504	+	0.852023i	$0.675375\pi$
$822$	0	0
$823$	−33.9411	−1.18311	−0.591557	−	0.806263i	$-0.701486\pi$
$823$	−33.9411	−1.18311	−0.591557	+	0.806263i	$0.701486\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−45.2548	−1.57366	−0.786832	−	0.617167i	$-0.788280\pi$
$827$	−45.2548	−1.57366	−0.786832	+	0.617167i	$0.788280\pi$
$828$	0	0
$829$	50.0000	1.73657	0.868286	−	0.496064i	$-0.165222\pi$
$829$	50.0000	1.73657	0.868286	+	0.496064i	$0.165222\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	−6.00000	−0.207888
$834$	0	0
$835$	14.1421	0.489409
$836$	0	0
$837$	0	0
$838$	0	0
$839$	2.82843	0.0976481	0.0488241	−	0.998807i	$-0.484453\pi$
$839$	2.82843	0.0976481	0.0488241	+	0.998807i	$0.484453\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	0	0
$843$	0	0
$844$	0	0
$845$	9.00000	0.309609
$846$	0	0
$847$	−8.48528	−0.291558
$848$	0	0
$849$	0	0
$850$	0	0
$851$	−50.9117	−1.74523
$852$	0	0
$853$	−54.0000	−1.84892	−0.924462	−	0.381273i	$-0.875486\pi$
$853$	−54.0000	−1.84892	−0.924462	+	0.381273i	$0.875486\pi$
$854$	0	0
$855$	8.48528	0.290191
$856$	0	0
$857$	−54.0000	−1.84460	−0.922302	−	0.386469i	$-0.873695\pi$
$857$	−54.0000	−1.84460	−0.922302	+	0.386469i	$0.873695\pi$
$858$	0	0
$859$	−25.4558	−0.868542	−0.434271	−	0.900782i	$-0.642994\pi$
$859$	−25.4558	−0.868542	−0.434271	+	0.900782i	$0.642994\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	2.82843	0.0962808	0.0481404	−	0.998841i	$-0.484671\pi$
$863$	2.82843	0.0962808	0.0481404	+	0.998841i	$0.484671\pi$
$864$	0	0
$865$	−18.0000	−0.612018
$866$	0	0
$867$	0	0
$868$	0	0
$869$	40.0000	1.35691
$870$	0	0
$871$	28.2843	0.958376
$872$	0	0
$873$	−6.00000	−0.203069
$874$	0	0
$875$	−2.82843	−0.0956183
$876$	0	0
$877$	2.00000	0.0675352	0.0337676	−	0.999430i	$-0.489249\pi$
$877$	2.00000	0.0675352	0.0337676	+	0.999430i	$0.489249\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	18.0000	0.606435	0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000	0.606435	0.303218	+	0.952921i	$0.401939\pi$
$882$	0	0
$883$	31.1127	1.04703	0.523513	−	0.852018i	$-0.324621\pi$
$883$	31.1127	1.04703	0.523513	+	0.852018i	$0.324621\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	5.65685	0.189939	0.0949693	−	0.995480i	$-0.469725\pi$
$887$	5.65685	0.189939	0.0949693	+	0.995480i	$0.469725\pi$
$888$	0	0
$889$	16.0000	0.536623
$890$	0	0
$891$	−25.4558	−0.852803
$892$	0	0
$893$	32.0000	1.07084
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	0	0
$899$	8.48528	0.283000
$900$	0	0
$901$	36.0000	1.19933
$902$	0	0
$903$	0	0
$904$	0	0
$905$	14.0000	0.465376
$906$	0	0
$907$	11.3137	0.375666	0.187833	−	0.982201i	$-0.439854\pi$
$907$	11.3137	0.375666	0.187833	+	0.982201i	$0.439854\pi$
$908$	0	0
$909$	−30.0000	−0.995037
$910$	0	0
$911$	−2.82843	−0.0937100	−0.0468550	−	0.998902i	$-0.514920\pi$
$911$	−2.82843	−0.0937100	−0.0468550	+	0.998902i	$0.514920\pi$
$912$	0	0
$913$	24.0000	0.794284
$914$	0	0
$915$	0	0
$916$	0	0
$917$	8.00000	0.264183
$918$	0	0
$919$	50.9117	1.67942	0.839711	−	0.543034i	$-0.182724\pi$
$919$	50.9117	1.67942	0.839711	+	0.543034i	$0.182724\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	11.3137	0.372395
$924$	0	0
$925$	−6.00000	−0.197279
$926$	0	0
$927$	−25.4558	−0.836080
$928$	0	0
$929$	−14.0000	−0.459325	−0.229663	−	0.973270i	$-0.573762\pi$
$929$	−14.0000	−0.459325	−0.229663	+	0.973270i	$0.573762\pi$
$930$	0	0
$931$	2.82843	0.0926980
$932$	0	0
$933$	0	0
$934$	0	0
$935$	−16.9706	−0.554997
$936$	0	0
$937$	−22.0000	−0.718709	−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000	−0.718709	−0.359354	+	0.933201i	$0.617003\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	10.0000	0.325991	0.162995	−	0.986627i	$-0.447884\pi$
$941$	10.0000	0.325991	0.162995	+	0.986627i	$0.447884\pi$
$942$	0	0
$943$	84.8528	2.76319
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−39.5980	−1.28676	−0.643381	−	0.765546i	$-0.722469\pi$
$947$	−39.5980	−1.28676	−0.643381	+	0.765546i	$0.722469\pi$
$948$	0	0
$949$	20.0000	0.649227
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−6.00000	−0.194359	−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000	−0.194359	−0.0971795	+	0.995267i	$0.530982\pi$
$954$	0	0
$955$	8.48528	0.274577
$956$	0	0
$957$	0	0
$958$	0	0
$959$	5.65685	0.182669
$960$	0	0
$961$	41.0000	1.32258
$962$	0	0
$963$	−25.4558	−0.820303
$964$	0	0
$965$	−26.0000	−0.836970
$966$	0	0
$967$	−33.9411	−1.09147	−0.545737	−	0.837957i	$-0.683750\pi$
$967$	−33.9411	−1.09147	−0.545737	+	0.837957i	$0.683750\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	−14.1421	−0.453843	−0.226921	−	0.973913i	$-0.572866\pi$
$971$	−14.1421	−0.453843	−0.226921	+	0.973913i	$0.572866\pi$
$972$	0	0
$973$	−48.0000	−1.53881
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−46.0000	−1.47167	−0.735835	−	0.677161i	$-0.763210\pi$
$977$	−46.0000	−1.47167	−0.735835	+	0.677161i	$0.763210\pi$
$978$	0	0
$979$	−28.2843	−0.903969
$980$	0	0
$981$	42.0000	1.34096
$982$	0	0
$983$	−5.65685	−0.180426	−0.0902128	−	0.995923i	$-0.528755\pi$
$983$	−5.65685	−0.180426	−0.0902128	+	0.995923i	$0.528755\pi$
$984$	0	0
$985$	6.00000	0.191176
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	50.9117	1.61726	0.808632	−	0.588315i	$-0.200209\pi$
$991$	50.9117	1.61726	0.808632	+	0.588315i	$0.200209\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	−5.65685	−0.179334
$996$	0	0
$997$	50.0000	1.58352	0.791758	−	0.610835i	$-0.209166\pi$
$997$	50.0000	1.58352	0.791758	+	0.610835i	$0.209166\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9280.2.a.ba.1.2		2
4.3	odd	2	inner	9280.2.a.ba.1.1		2
8.3	odd	2		4640.2.a.h.1.1	✓	2
8.5	even	2		4640.2.a.h.1.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4640.2.a.h.1.1	✓	2	8.3	odd	2
4640.2.a.h.1.2	yes	2	8.5	even	2
9280.2.a.ba.1.1		2	4.3	odd	2	inner
9280.2.a.ba.1.2		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 9280 = 2^{6} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9280.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{5} +2.82843 q^{7} -3.00000 q^{9} -2.82843 q^{11} +2.00000 q^{13} -6.00000 q^{17} +2.82843 q^{19} +8.48528 q^{23} +1.00000 q^{25} -1.00000 q^{29} -8.48528 q^{31} -2.82843 q^{35} -6.00000 q^{37} +10.0000 q^{41} +3.00000 q^{45} +11.3137 q^{47} +1.00000 q^{49} -6.00000 q^{53} +2.82843 q^{55} -5.65685 q^{59} -14.0000 q^{61} -8.48528 q^{63} -2.00000 q^{65} +14.1421 q^{67} +5.65685 q^{71} +10.0000 q^{73} -8.00000 q^{77} -14.1421 q^{79} +9.00000 q^{81} -8.48528 q^{83} +6.00000 q^{85} +10.0000 q^{89} +5.65685 q^{91} -2.82843 q^{95} +2.00000 q^{97} +8.48528 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{5} - 6 q^{9} + 4 q^{13} - 12 q^{17} + 2 q^{25} - 2 q^{29} - 12 q^{37} + 20 q^{41} + 6 q^{45} + 2 q^{49} - 12 q^{53} - 28 q^{61} - 4 q^{65} + 20 q^{73} - 16 q^{77} + 18 q^{81} + 12 q^{85} + 20 q^{89}+ \cdots + 4 q^{97}+O(q^{100}) \) 2 * q - 2 * q^5 - 6 * q^9 + 4 * q^13 - 12 * q^17 + 2 * q^25 - 2 * q^29 - 12 * q^37 + 20 * q^41 + 6 * q^45 + 2 * q^49 - 12 * q^53 - 28 * q^61 - 4 * q^65 + 20 * q^73 - 16 * q^77 + 18 * q^81 + 12 * q^85 + 20 * q^89 + 4 * q^97

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