LMFDB - Embedded newform 740.2.a.c.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(1,740)] 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("740.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	740.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

$q+3.00000 q^{3} -1.00000 q^{5} -3.00000 q^{7} +6.00000 q^{9} +5.00000 q^{11} +2.00000 q^{13} -3.00000 q^{15} +4.00000 q^{17} -4.00000 q^{19} -9.00000 q^{21} +6.00000 q^{23} +1.00000 q^{25} +9.00000 q^{27} +6.00000 q^{29} -4.00000 q^{31} +15.0000 q^{33} +3.00000 q^{35} -1.00000 q^{37} +6.00000 q^{39} -9.00000 q^{41} +10.0000 q^{43} -6.00000 q^{45} -11.0000 q^{47} +2.00000 q^{49} +12.0000 q^{51} -11.0000 q^{53} -5.00000 q^{55} -12.0000 q^{57} -8.00000 q^{59} -8.00000 q^{61} -18.0000 q^{63} -2.00000 q^{65} -8.00000 q^{67} +18.0000 q^{69} +3.00000 q^{71} +7.00000 q^{73} +3.00000 q^{75} -15.0000 q^{77} +8.00000 q^{79} +9.00000 q^{81} -9.00000 q^{83} -4.00000 q^{85} +18.0000 q^{87} -16.0000 q^{89} -6.00000 q^{91} -12.0000 q^{93} +4.00000 q^{95} +12.0000 q^{97} +30.0000 q^{99} +O(q^{100})$

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
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	−3.00000	−1.13389	−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000	−1.13389	−0.566947	+	0.823754i	$0.691875\pi$
$8$	0	0
$9$	6.00000	2.00000
$10$	0	0
$11$	5.00000	1.50756	0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000	1.50756	0.753778	+	0.657129i	$0.228229\pi$
$12$	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
$15$	−3.00000	−0.774597
$16$	0	0
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	0	0
$19$	−4.00000	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	0	0
$21$	−9.00000	−1.96396
$22$	0	0
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	9.00000	1.73205
$28$	0	0
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	0	0
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	0	0
$33$	15.0000	2.61116
$34$	0	0
$35$	3.00000	0.507093
$36$	0	0
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	0	0
$39$	6.00000	0.960769
$40$	0	0
$41$	−9.00000	−1.40556	−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000	−1.40556	−0.702782	+	0.711405i	$0.748059\pi$
$42$	0	0
$43$	10.0000	1.52499	0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000	1.52499	0.762493	+	0.646997i	$0.223975\pi$
$44$	0	0
$45$	−6.00000	−0.894427
$46$	0	0
$47$	−11.0000	−1.60451	−0.802257	−	0.596978i	$-0.796368\pi$
$47$	−11.0000	−1.60451	−0.802257	+	0.596978i	$0.796368\pi$
$48$	0	0
$49$	2.00000	0.285714
$50$	0	0
$51$	12.0000	1.68034
$52$	0	0
$53$	−11.0000	−1.51097	−0.755483	−	0.655168i	$-0.772598\pi$
$53$	−11.0000	−1.51097	−0.755483	+	0.655168i	$0.772598\pi$
$54$	0	0
$55$	−5.00000	−0.674200
$56$	0	0
$57$	−12.0000	−1.58944
$58$	0	0
$59$	−8.00000	−1.04151	−0.520756	−	0.853706i	$-0.674350\pi$
$59$	−8.00000	−1.04151	−0.520756	+	0.853706i	$0.674350\pi$
$60$	0	0
$61$	−8.00000	−1.02430	−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−8.00000	−1.02430	−0.512148	+	0.858898i	$0.671150\pi$
$62$	0	0
$63$	−18.0000	−2.26779
$64$	0	0
$65$	−2.00000	−0.248069
$66$	0	0
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	0	0
$69$	18.0000	2.16695
$70$	0	0
$71$	3.00000	0.356034	0.178017	−	0.984027i	$-0.443032\pi$
$71$	3.00000	0.356034	0.178017	+	0.984027i	$0.443032\pi$
$72$	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
$75$	3.00000	0.346410
$76$	0	0
$77$	−15.0000	−1.70941
$78$	0	0
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	0	0
$83$	−9.00000	−0.987878	−0.493939	−	0.869496i	$-0.664443\pi$
$83$	−9.00000	−0.987878	−0.493939	+	0.869496i	$0.664443\pi$
$84$	0	0
$85$	−4.00000	−0.433861
$86$	0	0
$87$	18.0000	1.92980
$88$	0	0
$89$	−16.0000	−1.69600	−0.847998	−	0.529999i	$-0.822192\pi$
$89$	−16.0000	−1.69600	−0.847998	+	0.529999i	$0.822192\pi$
$90$	0	0
$91$	−6.00000	−0.628971
$92$	0	0
$93$	−12.0000	−1.24434
$94$	0	0
$95$	4.00000	0.410391
$96$	0	0
$97$	12.0000	1.21842	0.609208	−	0.793011i	$-0.291488\pi$
$97$	12.0000	1.21842	0.609208	+	0.793011i	$0.291488\pi$
$98$	0	0
$99$	30.0000	3.01511
$100$	0	0
$101$	−9.00000	−0.895533	−0.447767	−	0.894150i	$-0.647781\pi$
$101$	−9.00000	−0.895533	−0.447767	+	0.894150i	$0.647781\pi$
$102$	0	0
$103$	−6.00000	−0.591198	−0.295599	−	0.955312i	$-0.595519\pi$
$103$	−6.00000	−0.591198	−0.295599	+	0.955312i	$0.595519\pi$
$104$	0	0
$105$	9.00000	0.878310
$106$	0	0
$107$	4.00000	0.386695	0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000	0.386695	0.193347	+	0.981130i	$0.438066\pi$
$108$	0	0
$109$	12.0000	1.14939	0.574696	−	0.818367i	$-0.305120\pi$
$109$	12.0000	1.14939	0.574696	+	0.818367i	$0.305120\pi$
$110$	0	0
$111$	−3.00000	−0.284747
$112$	0	0
$113$	14.0000	1.31701	0.658505	−	0.752577i	$-0.271189\pi$
$113$	14.0000	1.31701	0.658505	+	0.752577i	$0.271189\pi$
$114$	0	0
$115$	−6.00000	−0.559503
$116$	0	0
$117$	12.0000	1.10940
$118$	0	0
$119$	−12.0000	−1.10004
$120$	0	0
$121$	14.0000	1.27273
$122$	0	0
$123$	−27.0000	−2.43451
$124$	0	0
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−13.0000	−1.15356	−0.576782	−	0.816898i	$-0.695692\pi$
$127$	−13.0000	−1.15356	−0.576782	+	0.816898i	$0.695692\pi$
$128$	0	0
$129$	30.0000	2.64135
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	12.0000	1.04053
$134$	0	0
$135$	−9.00000	−0.774597
$136$	0	0
$137$	18.0000	1.53784	0.768922	−	0.639343i	$-0.220793\pi$
$137$	18.0000	1.53784	0.768922	+	0.639343i	$0.220793\pi$
$138$	0	0
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	0	0
$141$	−33.0000	−2.77910
$142$	0	0
$143$	10.0000	0.836242
$144$	0	0
$145$	−6.00000	−0.498273
$146$	0	0
$147$	6.00000	0.494872
$148$	0	0
$149$	−1.00000	−0.0819232	−0.0409616	−	0.999161i	$-0.513042\pi$
$149$	−1.00000	−0.0819232	−0.0409616	+	0.999161i	$0.513042\pi$
$150$	0	0
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	0	0
$153$	24.0000	1.94029
$154$	0	0
$155$	4.00000	0.321288
$156$	0	0
$157$	3.00000	0.239426	0.119713	−	0.992809i	$-0.461803\pi$
$157$	3.00000	0.239426	0.119713	+	0.992809i	$0.461803\pi$
$158$	0	0
$159$	−33.0000	−2.61707
$160$	0	0
$161$	−18.0000	−1.41860
$162$	0	0
$163$	−10.0000	−0.783260	−0.391630	−	0.920123i	$-0.628089\pi$
$163$	−10.0000	−0.783260	−0.391630	+	0.920123i	$0.628089\pi$
$164$	0	0
$165$	−15.0000	−1.16775
$166$	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
$169$	−9.00000	−0.692308
$170$	0	0
$171$	−24.0000	−1.83533
$172$	0	0
$173$	−11.0000	−0.836315	−0.418157	−	0.908375i	$-0.637324\pi$
$173$	−11.0000	−0.836315	−0.418157	+	0.908375i	$0.637324\pi$
$174$	0	0
$175$	−3.00000	−0.226779
$176$	0	0
$177$	−24.0000	−1.80395
$178$	0	0
$179$	−2.00000	−0.149487	−0.0747435	−	0.997203i	$-0.523814\pi$
$179$	−2.00000	−0.149487	−0.0747435	+	0.997203i	$0.523814\pi$
$180$	0	0
$181$	25.0000	1.85824	0.929118	−	0.369784i	$-0.120568\pi$
$181$	25.0000	1.85824	0.929118	+	0.369784i	$0.120568\pi$
$182$	0	0
$183$	−24.0000	−1.77413
$184$	0	0
$185$	1.00000	0.0735215
$186$	0	0
$187$	20.0000	1.46254
$188$	0	0
$189$	−27.0000	−1.96396
$190$	0	0
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	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
$195$	−6.00000	−0.429669
$196$	0	0
$197$	23.0000	1.63868	0.819341	−	0.573306i	$-0.194340\pi$
$197$	23.0000	1.63868	0.819341	+	0.573306i	$0.194340\pi$
$198$	0	0
$199$	−2.00000	−0.141776	−0.0708881	−	0.997484i	$-0.522583\pi$
$199$	−2.00000	−0.141776	−0.0708881	+	0.997484i	$0.522583\pi$
$200$	0	0
$201$	−24.0000	−1.69283
$202$	0	0
$203$	−18.0000	−1.26335
$204$	0	0
$205$	9.00000	0.628587
$206$	0	0
$207$	36.0000	2.50217
$208$	0	0
$209$	−20.0000	−1.38343
$210$	0	0
$211$	−11.0000	−0.757271	−0.378636	−	0.925546i	$-0.623607\pi$
$211$	−11.0000	−0.757271	−0.378636	+	0.925546i	$0.623607\pi$
$212$	0	0
$213$	9.00000	0.616670
$214$	0	0
$215$	−10.0000	−0.681994
$216$	0	0
$217$	12.0000	0.814613
$218$	0	0
$219$	21.0000	1.41905
$220$	0	0
$221$	8.00000	0.538138
$222$	0	0
$223$	5.00000	0.334825	0.167412	−	0.985887i	$-0.446459\pi$
$223$	5.00000	0.334825	0.167412	+	0.985887i	$0.446459\pi$
$224$	0	0
$225$	6.00000	0.400000
$226$	0	0
$227$	−16.0000	−1.06196	−0.530979	−	0.847385i	$-0.678176\pi$
$227$	−16.0000	−1.06196	−0.530979	+	0.847385i	$0.678176\pi$
$228$	0	0
$229$	−21.0000	−1.38772	−0.693860	−	0.720110i	$-0.744091\pi$
$229$	−21.0000	−1.38772	−0.693860	+	0.720110i	$0.744091\pi$
$230$	0	0
$231$	−45.0000	−2.96078
$232$	0	0
$233$	14.0000	0.917170	0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000	0.917170	0.458585	+	0.888650i	$0.348356\pi$
$234$	0	0
$235$	11.0000	0.717561
$236$	0	0
$237$	24.0000	1.55897
$238$	0	0
$239$	6.00000	0.388108	0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000	0.388108	0.194054	+	0.980991i	$0.437836\pi$
$240$	0	0
$241$	14.0000	0.901819	0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000	0.901819	0.450910	+	0.892570i	$0.351100\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	−2.00000	−0.127775
$246$	0	0
$247$	−8.00000	−0.509028
$248$	0	0
$249$	−27.0000	−1.71106
$250$	0	0
$251$	−10.0000	−0.631194	−0.315597	−	0.948893i	$-0.602205\pi$
$251$	−10.0000	−0.631194	−0.315597	+	0.948893i	$0.602205\pi$
$252$	0	0
$253$	30.0000	1.88608
$254$	0	0
$255$	−12.0000	−0.751469
$256$	0	0
$257$	−16.0000	−0.998053	−0.499026	−	0.866587i	$-0.666309\pi$
$257$	−16.0000	−0.998053	−0.499026	+	0.866587i	$0.666309\pi$
$258$	0	0
$259$	3.00000	0.186411
$260$	0	0
$261$	36.0000	2.22834
$262$	0	0
$263$	−23.0000	−1.41824	−0.709120	−	0.705087i	$-0.750908\pi$
$263$	−23.0000	−1.41824	−0.709120	+	0.705087i	$0.750908\pi$
$264$	0	0
$265$	11.0000	0.675725
$266$	0	0
$267$	−48.0000	−2.93755
$268$	0	0
$269$	−22.0000	−1.34136	−0.670682	−	0.741745i	$-0.733998\pi$
$269$	−22.0000	−1.34136	−0.670682	+	0.741745i	$0.733998\pi$
$270$	0	0
$271$	−5.00000	−0.303728	−0.151864	−	0.988401i	$-0.548528\pi$
$271$	−5.00000	−0.303728	−0.151864	+	0.988401i	$0.548528\pi$
$272$	0	0
$273$	−18.0000	−1.08941
$274$	0	0
$275$	5.00000	0.301511
$276$	0	0
$277$	−4.00000	−0.240337	−0.120168	−	0.992754i	$-0.538343\pi$
$277$	−4.00000	−0.240337	−0.120168	+	0.992754i	$0.538343\pi$
$278$	0	0
$279$	−24.0000	−1.43684
$280$	0	0
$281$	−4.00000	−0.238620	−0.119310	−	0.992857i	$-0.538068\pi$
$281$	−4.00000	−0.238620	−0.119310	+	0.992857i	$0.538068\pi$
$282$	0	0
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	0	0
$285$	12.0000	0.710819
$286$	0	0
$287$	27.0000	1.59376
$288$	0	0
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	36.0000	2.11036
$292$	0	0
$293$	30.0000	1.75262	0.876309	−	0.481749i	$-0.159998\pi$
$293$	30.0000	1.75262	0.876309	+	0.481749i	$0.159998\pi$
$294$	0	0
$295$	8.00000	0.465778
$296$	0	0
$297$	45.0000	2.61116
$298$	0	0
$299$	12.0000	0.693978
$300$	0	0
$301$	−30.0000	−1.72917
$302$	0	0
$303$	−27.0000	−1.55111
$304$	0	0
$305$	8.00000	0.458079
$306$	0	0
$307$	−23.0000	−1.31268	−0.656340	−	0.754466i	$-0.727896\pi$
$307$	−23.0000	−1.31268	−0.656340	+	0.754466i	$0.727896\pi$
$308$	0	0
$309$	−18.0000	−1.02398
$310$	0	0
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	0	0
$313$	−22.0000	−1.24351	−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−22.0000	−1.24351	−0.621757	+	0.783210i	$0.713581\pi$
$314$	0	0
$315$	18.0000	1.01419
$316$	0	0
$317$	14.0000	0.786318	0.393159	−	0.919470i	$-0.371382\pi$
$317$	14.0000	0.786318	0.393159	+	0.919470i	$0.371382\pi$
$318$	0	0
$319$	30.0000	1.67968
$320$	0	0
$321$	12.0000	0.669775
$322$	0	0
$323$	−16.0000	−0.890264
$324$	0	0
$325$	2.00000	0.110940
$326$	0	0
$327$	36.0000	1.99080
$328$	0	0
$329$	33.0000	1.81935
$330$	0	0
$331$	−22.0000	−1.20923	−0.604615	−	0.796518i	$-0.706673\pi$
$331$	−22.0000	−1.20923	−0.604615	+	0.796518i	$0.706673\pi$
$332$	0	0
$333$	−6.00000	−0.328798
$334$	0	0
$335$	8.00000	0.437087
$336$	0	0
$337$	7.00000	0.381314	0.190657	−	0.981657i	$-0.438938\pi$
$337$	7.00000	0.381314	0.190657	+	0.981657i	$0.438938\pi$
$338$	0	0
$339$	42.0000	2.28113
$340$	0	0
$341$	−20.0000	−1.08306
$342$	0	0
$343$	15.0000	0.809924
$344$	0	0
$345$	−18.0000	−0.969087
$346$	0	0
$347$	10.0000	0.536828	0.268414	−	0.963304i	$-0.413500\pi$
$347$	10.0000	0.536828	0.268414	+	0.963304i	$0.413500\pi$
$348$	0	0
$349$	30.0000	1.60586	0.802932	−	0.596071i	$-0.203272\pi$
$349$	30.0000	1.60586	0.802932	+	0.596071i	$0.203272\pi$
$350$	0	0
$351$	18.0000	0.960769
$352$	0	0
$353$	−12.0000	−0.638696	−0.319348	−	0.947638i	$-0.603464\pi$
$353$	−12.0000	−0.638696	−0.319348	+	0.947638i	$0.603464\pi$
$354$	0	0
$355$	−3.00000	−0.159223
$356$	0	0
$357$	−36.0000	−1.90532
$358$	0	0
$359$	−21.0000	−1.10834	−0.554169	−	0.832404i	$-0.686964\pi$
$359$	−21.0000	−1.10834	−0.554169	+	0.832404i	$0.686964\pi$
$360$	0	0
$361$	−3.00000	−0.157895
$362$	0	0
$363$	42.0000	2.20443
$364$	0	0
$365$	−7.00000	−0.366397
$366$	0	0
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	0	0
$369$	−54.0000	−2.81113
$370$	0	0
$371$	33.0000	1.71327
$372$	0	0
$373$	1.00000	0.0517780	0.0258890	−	0.999665i	$-0.491758\pi$
$373$	1.00000	0.0517780	0.0258890	+	0.999665i	$0.491758\pi$
$374$	0	0
$375$	−3.00000	−0.154919
$376$	0	0
$377$	12.0000	0.618031
$378$	0	0
$379$	17.0000	0.873231	0.436616	−	0.899648i	$-0.356177\pi$
$379$	17.0000	0.873231	0.436616	+	0.899648i	$0.356177\pi$
$380$	0	0
$381$	−39.0000	−1.99803
$382$	0	0
$383$	36.0000	1.83951	0.919757	−	0.392488i	$-0.128386\pi$
$383$	36.0000	1.83951	0.919757	+	0.392488i	$0.128386\pi$
$384$	0	0
$385$	15.0000	0.764471
$386$	0	0
$387$	60.0000	3.04997
$388$	0	0
$389$	4.00000	0.202808	0.101404	−	0.994845i	$-0.467667\pi$
$389$	4.00000	0.202808	0.101404	+	0.994845i	$0.467667\pi$
$390$	0	0
$391$	24.0000	1.21373
$392$	0	0
$393$	0	0
$394$	0	0
$395$	−8.00000	−0.402524
$396$	0	0
$397$	7.00000	0.351320	0.175660	−	0.984451i	$-0.443794\pi$
$397$	7.00000	0.351320	0.175660	+	0.984451i	$0.443794\pi$
$398$	0	0
$399$	36.0000	1.80225
$400$	0	0
$401$	−10.0000	−0.499376	−0.249688	−	0.968326i	$-0.580328\pi$
$401$	−10.0000	−0.499376	−0.249688	+	0.968326i	$0.580328\pi$
$402$	0	0
$403$	−8.00000	−0.398508
$404$	0	0
$405$	−9.00000	−0.447214
$406$	0	0
$407$	−5.00000	−0.247841
$408$	0	0
$409$	−4.00000	−0.197787	−0.0988936	−	0.995098i	$-0.531530\pi$
$409$	−4.00000	−0.197787	−0.0988936	+	0.995098i	$0.531530\pi$
$410$	0	0
$411$	54.0000	2.66362
$412$	0	0
$413$	24.0000	1.18096
$414$	0	0
$415$	9.00000	0.441793
$416$	0	0
$417$	−12.0000	−0.587643
$418$	0	0
$419$	1.00000	0.0488532	0.0244266	−	0.999702i	$-0.492224\pi$
$419$	1.00000	0.0488532	0.0244266	+	0.999702i	$0.492224\pi$
$420$	0	0
$421$	36.0000	1.75453	0.877266	−	0.480004i	$-0.159365\pi$
$421$	36.0000	1.75453	0.877266	+	0.480004i	$0.159365\pi$
$422$	0	0
$423$	−66.0000	−3.20903
$424$	0	0
$425$	4.00000	0.194029
$426$	0	0
$427$	24.0000	1.16144
$428$	0	0
$429$	30.0000	1.44841
$430$	0	0
$431$	−14.0000	−0.674356	−0.337178	−	0.941441i	$-0.609472\pi$
$431$	−14.0000	−0.674356	−0.337178	+	0.941441i	$0.609472\pi$
$432$	0	0
$433$	−23.0000	−1.10531	−0.552655	−	0.833410i	$-0.686385\pi$
$433$	−23.0000	−1.10531	−0.552655	+	0.833410i	$0.686385\pi$
$434$	0	0
$435$	−18.0000	−0.863034
$436$	0	0
$437$	−24.0000	−1.14808
$438$	0	0
$439$	28.0000	1.33637	0.668184	−	0.743996i	$-0.267072\pi$
$439$	28.0000	1.33637	0.668184	+	0.743996i	$0.267072\pi$
$440$	0	0
$441$	12.0000	0.571429
$442$	0	0
$443$	−9.00000	−0.427603	−0.213801	−	0.976877i	$-0.568585\pi$
$443$	−9.00000	−0.427603	−0.213801	+	0.976877i	$0.568585\pi$
$444$	0	0
$445$	16.0000	0.758473
$446$	0	0
$447$	−3.00000	−0.141895
$448$	0	0
$449$	−24.0000	−1.13263	−0.566315	−	0.824189i	$-0.691631\pi$
$449$	−24.0000	−1.13263	−0.566315	+	0.824189i	$0.691631\pi$
$450$	0	0
$451$	−45.0000	−2.11897
$452$	0	0
$453$	0	0
$454$	0	0
$455$	6.00000	0.281284
$456$	0	0
$457$	6.00000	0.280668	0.140334	−	0.990104i	$-0.455182\pi$
$457$	6.00000	0.280668	0.140334	+	0.990104i	$0.455182\pi$
$458$	0	0
$459$	36.0000	1.68034
$460$	0	0
$461$	10.0000	0.465746	0.232873	−	0.972507i	$-0.425187\pi$
$461$	10.0000	0.465746	0.232873	+	0.972507i	$0.425187\pi$
$462$	0	0
$463$	14.0000	0.650635	0.325318	−	0.945605i	$-0.394529\pi$
$463$	14.0000	0.650635	0.325318	+	0.945605i	$0.394529\pi$
$464$	0	0
$465$	12.0000	0.556487
$466$	0	0
$467$	10.0000	0.462745	0.231372	−	0.972865i	$-0.425678\pi$
$467$	10.0000	0.462745	0.231372	+	0.972865i	$0.425678\pi$
$468$	0	0
$469$	24.0000	1.10822
$470$	0	0
$471$	9.00000	0.414698
$472$	0	0
$473$	50.0000	2.29900
$474$	0	0
$475$	−4.00000	−0.183533
$476$	0	0
$477$	−66.0000	−3.02193
$478$	0	0
$479$	−14.0000	−0.639676	−0.319838	−	0.947472i	$-0.603629\pi$
$479$	−14.0000	−0.639676	−0.319838	+	0.947472i	$0.603629\pi$
$480$	0	0
$481$	−2.00000	−0.0911922
$482$	0	0
$483$	−54.0000	−2.45709
$484$	0	0
$485$	−12.0000	−0.544892
$486$	0	0
$487$	−4.00000	−0.181257	−0.0906287	−	0.995885i	$-0.528888\pi$
$487$	−4.00000	−0.181257	−0.0906287	+	0.995885i	$0.528888\pi$
$488$	0	0
$489$	−30.0000	−1.35665
$490$	0	0
$491$	20.0000	0.902587	0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000	0.902587	0.451294	+	0.892375i	$0.350963\pi$
$492$	0	0
$493$	24.0000	1.08091
$494$	0	0
$495$	−30.0000	−1.34840
$496$	0	0
$497$	−9.00000	−0.403705
$498$	0	0
$499$	−44.0000	−1.96971	−0.984855	−	0.173379i	$-0.944532\pi$
$499$	−44.0000	−1.96971	−0.984855	+	0.173379i	$0.944532\pi$
$500$	0	0
$501$	24.0000	1.07224
$502$	0	0
$503$	12.0000	0.535054	0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000	0.535054	0.267527	+	0.963550i	$0.413794\pi$
$504$	0	0
$505$	9.00000	0.400495
$506$	0	0
$507$	−27.0000	−1.19911
$508$	0	0
$509$	21.0000	0.930809	0.465404	−	0.885098i	$-0.345909\pi$
$509$	21.0000	0.930809	0.465404	+	0.885098i	$0.345909\pi$
$510$	0	0
$511$	−21.0000	−0.928985
$512$	0	0
$513$	−36.0000	−1.58944
$514$	0	0
$515$	6.00000	0.264392
$516$	0	0
$517$	−55.0000	−2.41890
$518$	0	0
$519$	−33.0000	−1.44854
$520$	0	0
$521$	−41.0000	−1.79624	−0.898121	−	0.439748i	$-0.855068\pi$
$521$	−41.0000	−1.79624	−0.898121	+	0.439748i	$0.855068\pi$
$522$	0	0
$523$	−6.00000	−0.262362	−0.131181	−	0.991358i	$-0.541877\pi$
$523$	−6.00000	−0.262362	−0.131181	+	0.991358i	$0.541877\pi$
$524$	0	0
$525$	−9.00000	−0.392792
$526$	0	0
$527$	−16.0000	−0.696971
$528$	0	0
$529$	13.0000	0.565217
$530$	0	0
$531$	−48.0000	−2.08302
$532$	0	0
$533$	−18.0000	−0.779667
$534$	0	0
$535$	−4.00000	−0.172935
$536$	0	0
$537$	−6.00000	−0.258919
$538$	0	0
$539$	10.0000	0.430730
$540$	0	0
$541$	−36.0000	−1.54776	−0.773880	−	0.633332i	$-0.781687\pi$
$541$	−36.0000	−1.54776	−0.773880	+	0.633332i	$0.781687\pi$
$542$	0	0
$543$	75.0000	3.21856
$544$	0	0
$545$	−12.0000	−0.514024
$546$	0	0
$547$	16.0000	0.684111	0.342055	−	0.939680i	$-0.388877\pi$
$547$	16.0000	0.684111	0.342055	+	0.939680i	$0.388877\pi$
$548$	0	0
$549$	−48.0000	−2.04859
$550$	0	0
$551$	−24.0000	−1.02243
$552$	0	0
$553$	−24.0000	−1.02058
$554$	0	0
$555$	3.00000	0.127343
$556$	0	0
$557$	−10.0000	−0.423714	−0.211857	−	0.977301i	$-0.567951\pi$
$557$	−10.0000	−0.423714	−0.211857	+	0.977301i	$0.567951\pi$
$558$	0	0
$559$	20.0000	0.845910
$560$	0	0
$561$	60.0000	2.53320
$562$	0	0
$563$	42.0000	1.77009	0.885044	−	0.465506i	$-0.154128\pi$
$563$	42.0000	1.77009	0.885044	+	0.465506i	$0.154128\pi$
$564$	0	0
$565$	−14.0000	−0.588984
$566$	0	0
$567$	−27.0000	−1.13389
$568$	0	0
$569$	0	0		−	1.00000i	$-0.5\pi$
$569$	0	0			1.00000i	$0.5\pi$
$570$	0	0
$571$	33.0000	1.38101	0.690504	−	0.723329i	$-0.257389\pi$
$571$	33.0000	1.38101	0.690504	+	0.723329i	$0.257389\pi$
$572$	0	0
$573$	−36.0000	−1.50392
$574$	0	0
$575$	6.00000	0.250217
$576$	0	0
$577$	28.0000	1.16566	0.582828	−	0.812596i	$-0.301946\pi$
$577$	28.0000	1.16566	0.582828	+	0.812596i	$0.301946\pi$
$578$	0	0
$579$	78.0000	3.24157
$580$	0	0
$581$	27.0000	1.12015
$582$	0	0
$583$	−55.0000	−2.27787
$584$	0	0
$585$	−12.0000	−0.496139
$586$	0	0
$587$	−36.0000	−1.48588	−0.742940	−	0.669359i	$-0.766569\pi$
$587$	−36.0000	−1.48588	−0.742940	+	0.669359i	$0.766569\pi$
$588$	0	0
$589$	16.0000	0.659269
$590$	0	0
$591$	69.0000	2.83828
$592$	0	0
$593$	43.0000	1.76580	0.882899	−	0.469563i	$-0.155588\pi$
$593$	43.0000	1.76580	0.882899	+	0.469563i	$0.155588\pi$
$594$	0	0
$595$	12.0000	0.491952
$596$	0	0
$597$	−6.00000	−0.245564
$598$	0	0
$599$	−45.0000	−1.83865	−0.919325	−	0.393499i	$-0.871265\pi$
$599$	−45.0000	−1.83865	−0.919325	+	0.393499i	$0.871265\pi$
$600$	0	0
$601$	10.0000	0.407909	0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000	0.407909	0.203954	+	0.978980i	$0.434621\pi$
$602$	0	0
$603$	−48.0000	−1.95471
$604$	0	0
$605$	−14.0000	−0.569181
$606$	0	0
$607$	−12.0000	−0.487065	−0.243532	−	0.969893i	$-0.578306\pi$
$607$	−12.0000	−0.487065	−0.243532	+	0.969893i	$0.578306\pi$
$608$	0	0
$609$	−54.0000	−2.18819
$610$	0	0
$611$	−22.0000	−0.890025
$612$	0	0
$613$	27.0000	1.09052	0.545260	−	0.838267i	$-0.316431\pi$
$613$	27.0000	1.09052	0.545260	+	0.838267i	$0.316431\pi$
$614$	0	0
$615$	27.0000	1.08875
$616$	0	0
$617$	9.00000	0.362326	0.181163	−	0.983453i	$-0.442014\pi$
$617$	9.00000	0.362326	0.181163	+	0.983453i	$0.442014\pi$
$618$	0	0
$619$	25.0000	1.00483	0.502417	−	0.864625i	$-0.332444\pi$
$619$	25.0000	1.00483	0.502417	+	0.864625i	$0.332444\pi$
$620$	0	0
$621$	54.0000	2.16695
$622$	0	0
$623$	48.0000	1.92308
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	−60.0000	−2.39617
$628$	0	0
$629$	−4.00000	−0.159490
$630$	0	0
$631$	−48.0000	−1.91085	−0.955425	−	0.295234i	$-0.904602\pi$
$631$	−48.0000	−1.91085	−0.955425	+	0.295234i	$0.904602\pi$
$632$	0	0
$633$	−33.0000	−1.31163
$634$	0	0
$635$	13.0000	0.515889
$636$	0	0
$637$	4.00000	0.158486
$638$	0	0
$639$	18.0000	0.712069
$640$	0	0
$641$	47.0000	1.85639	0.928194	−	0.372096i	$-0.121361\pi$
$641$	47.0000	1.85639	0.928194	+	0.372096i	$0.121361\pi$
$642$	0	0
$643$	34.0000	1.34083	0.670415	−	0.741987i	$-0.266116\pi$
$643$	34.0000	1.34083	0.670415	+	0.741987i	$0.266116\pi$
$644$	0	0
$645$	−30.0000	−1.18125
$646$	0	0
$647$	−28.0000	−1.10079	−0.550397	−	0.834903i	$-0.685524\pi$
$647$	−28.0000	−1.10079	−0.550397	+	0.834903i	$0.685524\pi$
$648$	0	0
$649$	−40.0000	−1.57014
$650$	0	0
$651$	36.0000	1.41095
$652$	0	0
$653$	−8.00000	−0.313064	−0.156532	−	0.987673i	$-0.550031\pi$
$653$	−8.00000	−0.313064	−0.156532	+	0.987673i	$0.550031\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	42.0000	1.63858
$658$	0	0
$659$	−49.0000	−1.90877	−0.954384	−	0.298580i	$-0.903487\pi$
$659$	−49.0000	−1.90877	−0.954384	+	0.298580i	$0.903487\pi$
$660$	0	0
$661$	8.00000	0.311164	0.155582	−	0.987823i	$-0.450275\pi$
$661$	8.00000	0.311164	0.155582	+	0.987823i	$0.450275\pi$
$662$	0	0
$663$	24.0000	0.932083
$664$	0	0
$665$	−12.0000	−0.465340
$666$	0	0
$667$	36.0000	1.39393
$668$	0	0
$669$	15.0000	0.579934
$670$	0	0
$671$	−40.0000	−1.54418
$672$	0	0
$673$	19.0000	0.732396	0.366198	−	0.930537i	$-0.380659\pi$
$673$	19.0000	0.732396	0.366198	+	0.930537i	$0.380659\pi$
$674$	0	0
$675$	9.00000	0.346410
$676$	0	0
$677$	−7.00000	−0.269032	−0.134516	−	0.990911i	$-0.542948\pi$
$677$	−7.00000	−0.269032	−0.134516	+	0.990911i	$0.542948\pi$
$678$	0	0
$679$	−36.0000	−1.38155
$680$	0	0
$681$	−48.0000	−1.83936
$682$	0	0
$683$	18.0000	0.688751	0.344375	−	0.938832i	$-0.388091\pi$
$683$	18.0000	0.688751	0.344375	+	0.938832i	$0.388091\pi$
$684$	0	0
$685$	−18.0000	−0.687745
$686$	0	0
$687$	−63.0000	−2.40360
$688$	0	0
$689$	−22.0000	−0.838133
$690$	0	0
$691$	28.0000	1.06517	0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000	1.06517	0.532585	+	0.846376i	$0.321221\pi$
$692$	0	0
$693$	−90.0000	−3.41882
$694$	0	0
$695$	4.00000	0.151729
$696$	0	0
$697$	−36.0000	−1.36360
$698$	0	0
$699$	42.0000	1.58859
$700$	0	0
$701$	20.0000	0.755390	0.377695	−	0.925930i	$-0.376717\pi$
$701$	20.0000	0.755390	0.377695	+	0.925930i	$0.376717\pi$
$702$	0	0
$703$	4.00000	0.150863
$704$	0	0
$705$	33.0000	1.24285
$706$	0	0
$707$	27.0000	1.01544
$708$	0	0
$709$	36.0000	1.35201	0.676004	−	0.736898i	$-0.263710\pi$
$709$	36.0000	1.35201	0.676004	+	0.736898i	$0.263710\pi$
$710$	0	0
$711$	48.0000	1.80014
$712$	0	0
$713$	−24.0000	−0.898807
$714$	0	0
$715$	−10.0000	−0.373979
$716$	0	0
$717$	18.0000	0.672222
$718$	0	0
$719$	−19.0000	−0.708580	−0.354290	−	0.935136i	$-0.615277\pi$
$719$	−19.0000	−0.708580	−0.354290	+	0.935136i	$0.615277\pi$
$720$	0	0
$721$	18.0000	0.670355
$722$	0	0
$723$	42.0000	1.56200
$724$	0	0
$725$	6.00000	0.222834
$726$	0	0
$727$	4.00000	0.148352	0.0741759	−	0.997245i	$-0.476367\pi$
$727$	4.00000	0.148352	0.0741759	+	0.997245i	$0.476367\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	0	0
$731$	40.0000	1.47945
$732$	0	0
$733$	43.0000	1.58824	0.794121	−	0.607760i	$-0.207932\pi$
$733$	43.0000	1.58824	0.794121	+	0.607760i	$0.207932\pi$
$734$	0	0
$735$	−6.00000	−0.221313
$736$	0	0
$737$	−40.0000	−1.47342
$738$	0	0
$739$	−15.0000	−0.551784	−0.275892	−	0.961189i	$-0.588973\pi$
$739$	−15.0000	−0.551784	−0.275892	+	0.961189i	$0.588973\pi$
$740$	0	0
$741$	−24.0000	−0.881662
$742$	0	0
$743$	−9.00000	−0.330178	−0.165089	−	0.986279i	$-0.552791\pi$
$743$	−9.00000	−0.330178	−0.165089	+	0.986279i	$0.552791\pi$
$744$	0	0
$745$	1.00000	0.0366372
$746$	0	0
$747$	−54.0000	−1.97576
$748$	0	0
$749$	−12.0000	−0.438470
$750$	0	0
$751$	11.0000	0.401396	0.200698	−	0.979653i	$-0.435679\pi$
$751$	11.0000	0.401396	0.200698	+	0.979653i	$0.435679\pi$
$752$	0	0
$753$	−30.0000	−1.09326
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−2.00000	−0.0726912	−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000	−0.0726912	−0.0363456	+	0.999339i	$0.511572\pi$
$758$	0	0
$759$	90.0000	3.26679
$760$	0	0
$761$	−3.00000	−0.108750	−0.0543750	−	0.998521i	$-0.517317\pi$
$761$	−3.00000	−0.108750	−0.0543750	+	0.998521i	$0.517317\pi$
$762$	0	0
$763$	−36.0000	−1.30329
$764$	0	0
$765$	−24.0000	−0.867722
$766$	0	0
$767$	−16.0000	−0.577727
$768$	0	0
$769$	42.0000	1.51456	0.757279	−	0.653091i	$-0.226528\pi$
$769$	42.0000	1.51456	0.757279	+	0.653091i	$0.226528\pi$
$770$	0	0
$771$	−48.0000	−1.72868
$772$	0	0
$773$	35.0000	1.25886	0.629431	−	0.777056i	$-0.283288\pi$
$773$	35.0000	1.25886	0.629431	+	0.777056i	$0.283288\pi$
$774$	0	0
$775$	−4.00000	−0.143684
$776$	0	0
$777$	9.00000	0.322873
$778$	0	0
$779$	36.0000	1.28983
$780$	0	0
$781$	15.0000	0.536742
$782$	0	0
$783$	54.0000	1.92980
$784$	0	0
$785$	−3.00000	−0.107075
$786$	0	0
$787$	21.0000	0.748569	0.374285	−	0.927314i	$-0.377888\pi$
$787$	21.0000	0.748569	0.374285	+	0.927314i	$0.377888\pi$
$788$	0	0
$789$	−69.0000	−2.45647
$790$	0	0
$791$	−42.0000	−1.49335
$792$	0	0
$793$	−16.0000	−0.568177
$794$	0	0
$795$	33.0000	1.17039
$796$	0	0
$797$	12.0000	0.425062	0.212531	−	0.977154i	$-0.431829\pi$
$797$	12.0000	0.425062	0.212531	+	0.977154i	$0.431829\pi$
$798$	0	0
$799$	−44.0000	−1.55661
$800$	0	0
$801$	−96.0000	−3.39199
$802$	0	0
$803$	35.0000	1.23512
$804$	0	0
$805$	18.0000	0.634417
$806$	0	0
$807$	−66.0000	−2.32331
$808$	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
$811$	49.0000	1.72062	0.860311	−	0.509769i	$-0.170269\pi$
$811$	49.0000	1.72062	0.860311	+	0.509769i	$0.170269\pi$
$812$	0	0
$813$	−15.0000	−0.526073
$814$	0	0
$815$	10.0000	0.350285
$816$	0	0
$817$	−40.0000	−1.39942
$818$	0	0
$819$	−36.0000	−1.25794
$820$	0	0
$821$	21.0000	0.732905	0.366453	−	0.930437i	$-0.380572\pi$
$821$	21.0000	0.732905	0.366453	+	0.930437i	$0.380572\pi$
$822$	0	0
$823$	8.00000	0.278862	0.139431	−	0.990232i	$-0.455473\pi$
$823$	8.00000	0.278862	0.139431	+	0.990232i	$0.455473\pi$
$824$	0	0
$825$	15.0000	0.522233
$826$	0	0
$827$	−30.0000	−1.04320	−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000	−1.04320	−0.521601	+	0.853189i	$0.674665\pi$
$828$	0	0
$829$	52.0000	1.80603	0.903017	−	0.429604i	$-0.141347\pi$
$829$	52.0000	1.80603	0.903017	+	0.429604i	$0.141347\pi$
$830$	0	0
$831$	−12.0000	−0.416275
$832$	0	0
$833$	8.00000	0.277184
$834$	0	0
$835$	−8.00000	−0.276851
$836$	0	0
$837$	−36.0000	−1.24434
$838$	0	0
$839$	12.0000	0.414286	0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000	0.414286	0.207143	+	0.978311i	$0.433583\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	0	0
$843$	−12.0000	−0.413302
$844$	0	0
$845$	9.00000	0.309609
$846$	0	0
$847$	−42.0000	−1.44314
$848$	0	0
$849$	12.0000	0.411839
$850$	0	0
$851$	−6.00000	−0.205677
$852$	0	0
$853$	10.0000	0.342393	0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000	0.342393	0.171197	+	0.985237i	$0.445237\pi$
$854$	0	0
$855$	24.0000	0.820783
$856$	0	0
$857$	−12.0000	−0.409912	−0.204956	−	0.978771i	$-0.565705\pi$
$857$	−12.0000	−0.409912	−0.204956	+	0.978771i	$0.565705\pi$
$858$	0	0
$859$	56.0000	1.91070	0.955348	−	0.295484i	$-0.0954809\pi$
$859$	56.0000	1.91070	0.955348	+	0.295484i	$0.0954809\pi$
$860$	0	0
$861$	81.0000	2.76047
$862$	0	0
$863$	−24.0000	−0.816970	−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000	−0.816970	−0.408485	+	0.912765i	$0.633943\pi$
$864$	0	0
$865$	11.0000	0.374011
$866$	0	0
$867$	−3.00000	−0.101885
$868$	0	0
$869$	40.0000	1.35691
$870$	0	0
$871$	−16.0000	−0.542139
$872$	0	0
$873$	72.0000	2.43683
$874$	0	0
$875$	3.00000	0.101419
$876$	0	0
$877$	−54.0000	−1.82345	−0.911725	−	0.410801i	$-0.865249\pi$
$877$	−54.0000	−1.82345	−0.911725	+	0.410801i	$0.865249\pi$
$878$	0	0
$879$	90.0000	3.03562
$880$	0	0
$881$	42.0000	1.41502	0.707508	−	0.706705i	$-0.249819\pi$
$881$	42.0000	1.41502	0.707508	+	0.706705i	$0.249819\pi$
$882$	0	0
$883$	−16.0000	−0.538443	−0.269221	−	0.963078i	$-0.586766\pi$
$883$	−16.0000	−0.538443	−0.269221	+	0.963078i	$0.586766\pi$
$884$	0	0
$885$	24.0000	0.806751
$886$	0	0
$887$	−37.0000	−1.24234	−0.621169	−	0.783676i	$-0.713342\pi$
$887$	−37.0000	−1.24234	−0.621169	+	0.783676i	$0.713342\pi$
$888$	0	0
$889$	39.0000	1.30802
$890$	0	0
$891$	45.0000	1.50756
$892$	0	0
$893$	44.0000	1.47240
$894$	0	0
$895$	2.00000	0.0668526
$896$	0	0
$897$	36.0000	1.20201
$898$	0	0
$899$	−24.0000	−0.800445
$900$	0	0
$901$	−44.0000	−1.46585
$902$	0	0
$903$	−90.0000	−2.99501
$904$	0	0
$905$	−25.0000	−0.831028
$906$	0	0
$907$	4.00000	0.132818	0.0664089	−	0.997792i	$-0.478846\pi$
$907$	4.00000	0.132818	0.0664089	+	0.997792i	$0.478846\pi$
$908$	0	0
$909$	−54.0000	−1.79107
$910$	0	0
$911$	42.0000	1.39152	0.695761	−	0.718273i	$-0.255067\pi$
$911$	42.0000	1.39152	0.695761	+	0.718273i	$0.255067\pi$
$912$	0	0
$913$	−45.0000	−1.48928
$914$	0	0
$915$	24.0000	0.793416
$916$	0	0
$917$	0	0
$918$	0	0
$919$	14.0000	0.461817	0.230909	−	0.972975i	$-0.425830\pi$
$919$	14.0000	0.461817	0.230909	+	0.972975i	$0.425830\pi$
$920$	0	0
$921$	−69.0000	−2.27363
$922$	0	0
$923$	6.00000	0.197492
$924$	0	0
$925$	−1.00000	−0.0328798
$926$	0	0
$927$	−36.0000	−1.18240
$928$	0	0
$929$	18.0000	0.590561	0.295280	−	0.955411i	$-0.404587\pi$
$929$	18.0000	0.590561	0.295280	+	0.955411i	$0.404587\pi$
$930$	0	0
$931$	−8.00000	−0.262189
$932$	0	0
$933$	36.0000	1.17859
$934$	0	0
$935$	−20.0000	−0.654070
$936$	0	0
$937$	13.0000	0.424691	0.212346	−	0.977195i	$-0.431890\pi$
$937$	13.0000	0.424691	0.212346	+	0.977195i	$0.431890\pi$
$938$	0	0
$939$	−66.0000	−2.15383
$940$	0	0
$941$	−18.0000	−0.586783	−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000	−0.586783	−0.293392	+	0.955992i	$0.594784\pi$
$942$	0	0
$943$	−54.0000	−1.75848
$944$	0	0
$945$	27.0000	0.878310
$946$	0	0
$947$	8.00000	0.259965	0.129983	−	0.991516i	$-0.458508\pi$
$947$	8.00000	0.259965	0.129983	+	0.991516i	$0.458508\pi$
$948$	0	0
$949$	14.0000	0.454459
$950$	0	0
$951$	42.0000	1.36194
$952$	0	0
$953$	−51.0000	−1.65205	−0.826026	−	0.563632i	$-0.809404\pi$
$953$	−51.0000	−1.65205	−0.826026	+	0.563632i	$0.809404\pi$
$954$	0	0
$955$	12.0000	0.388311
$956$	0	0
$957$	90.0000	2.90929
$958$	0	0
$959$	−54.0000	−1.74375
$960$	0	0
$961$	−15.0000	−0.483871
$962$	0	0
$963$	24.0000	0.773389
$964$	0	0
$965$	−26.0000	−0.836970
$966$	0	0
$967$	−2.00000	−0.0643157	−0.0321578	−	0.999483i	$-0.510238\pi$
$967$	−2.00000	−0.0643157	−0.0321578	+	0.999483i	$0.510238\pi$
$968$	0	0
$969$	−48.0000	−1.54198
$970$	0	0
$971$	−24.0000	−0.770197	−0.385098	−	0.922876i	$-0.625832\pi$
$971$	−24.0000	−0.770197	−0.385098	+	0.922876i	$0.625832\pi$
$972$	0	0
$973$	12.0000	0.384702
$974$	0	0
$975$	6.00000	0.192154
$976$	0	0
$977$	28.0000	0.895799	0.447900	−	0.894084i	$-0.352172\pi$
$977$	28.0000	0.895799	0.447900	+	0.894084i	$0.352172\pi$
$978$	0	0
$979$	−80.0000	−2.55681
$980$	0	0
$981$	72.0000	2.29878
$982$	0	0
$983$	27.0000	0.861166	0.430583	−	0.902551i	$-0.358308\pi$
$983$	27.0000	0.861166	0.430583	+	0.902551i	$0.358308\pi$
$984$	0	0
$985$	−23.0000	−0.732841
$986$	0	0
$987$	99.0000	3.15120
$988$	0	0
$989$	60.0000	1.90789
$990$	0	0
$991$	−34.0000	−1.08005	−0.540023	−	0.841650i	$-0.681584\pi$
$991$	−34.0000	−1.08005	−0.540023	+	0.841650i	$0.681584\pi$
$992$	0	0
$993$	−66.0000	−2.09445
$994$	0	0
$995$	2.00000	0.0634043
$996$	0	0
$997$	46.0000	1.45683	0.728417	−	0.685134i	$-0.240256\pi$
$997$	46.0000	1.45683	0.728417	+	0.685134i	$0.240256\pi$
$998$	0	0
$999$	−9.00000	−0.284747

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.a.c.1.1	✓	1
3.2	odd	2		6660.2.a.b.1.1		1
4.3	odd	2		2960.2.a.a.1.1		1
5.2	odd	4		3700.2.d.a.149.1		2
5.3	odd	4		3700.2.d.a.149.2		2
5.4	even	2		3700.2.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.a.c.1.1	✓	1	1.1	even	1	trivial
2960.2.a.a.1.1		1	4.3	odd	2
3700.2.a.a.1.1		1	5.4	even	2
3700.2.d.a.149.1		2	5.2	odd	4
3700.2.d.a.149.2		2	5.3	odd	4
6660.2.a.b.1.1		1	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.a (trivial)

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L-functions

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