LMFDB - Embedded newform 665.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [665,2,Mod(1,665)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(665, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("665.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 665 = 5 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	665.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:	$5.31005173442$
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	$\chi$	$=$	665.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +3.00000 q^{3} +2.00000 q^{4} +1.00000 q^{5} -6.00000 q^{6} +1.00000 q^{7} +6.00000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} +3.00000 q^{3} +2.00000 q^{4} +1.00000 q^{5} -6.00000 q^{6} +1.00000 q^{7} +6.00000 q^{9} -2.00000 q^{10} -3.00000 q^{11} +6.00000 q^{12} +3.00000 q^{13} -2.00000 q^{14} +3.00000 q^{15} -4.00000 q^{16} +3.00000 q^{17} -12.0000 q^{18} +1.00000 q^{19} +2.00000 q^{20} +3.00000 q^{21} +6.00000 q^{22} -4.00000 q^{23} +1.00000 q^{25} -6.00000 q^{26} +9.00000 q^{27} +2.00000 q^{28} +1.00000 q^{29} -6.00000 q^{30} +8.00000 q^{31} +8.00000 q^{32} -9.00000 q^{33} -6.00000 q^{34} +1.00000 q^{35} +12.0000 q^{36} -4.00000 q^{37} -2.00000 q^{38} +9.00000 q^{39} -8.00000 q^{41} -6.00000 q^{42} -4.00000 q^{43} -6.00000 q^{44} +6.00000 q^{45} +8.00000 q^{46} +1.00000 q^{47} -12.0000 q^{48} +1.00000 q^{49} -2.00000 q^{50} +9.00000 q^{51} +6.00000 q^{52} -12.0000 q^{53} -18.0000 q^{54} -3.00000 q^{55} +3.00000 q^{57} -2.00000 q^{58} +6.00000 q^{59} +6.00000 q^{60} -6.00000 q^{61} -16.0000 q^{62} +6.00000 q^{63} -8.00000 q^{64} +3.00000 q^{65} +18.0000 q^{66} +4.00000 q^{67} +6.00000 q^{68} -12.0000 q^{69} -2.00000 q^{70} +10.0000 q^{73} +8.00000 q^{74} +3.00000 q^{75} +2.00000 q^{76} -3.00000 q^{77} -18.0000 q^{78} +13.0000 q^{79} -4.00000 q^{80} +9.00000 q^{81} +16.0000 q^{82} +4.00000 q^{83} +6.00000 q^{84} +3.00000 q^{85} +8.00000 q^{86} +3.00000 q^{87} -6.00000 q^{89} -12.0000 q^{90} +3.00000 q^{91} -8.00000 q^{92} +24.0000 q^{93} -2.00000 q^{94} +1.00000 q^{95} +24.0000 q^{96} +5.00000 q^{97} -2.00000 q^{98} -18.0000 q^{99} +O(q^{100})\)

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 $

$2$	−2.00000	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$2$	−2.00000	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$3$	3.00000	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$3$	3.00000	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$4$	2.00000	1.00000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−6.00000	−2.44949
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0	0
$9$	6.00000	2.00000
$10$	−2.00000	−0.632456
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	6.00000	1.73205
$13$	3.00000	0.832050	0.416025	−	0.909353i	$-0.363423\pi$
$13$	3.00000	0.832050	0.416025	+	0.909353i	$0.363423\pi$
$14$	−2.00000	−0.534522
$15$	3.00000	0.774597
$16$	−4.00000	−1.00000
$17$	3.00000	0.727607	0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000	0.727607	0.363803	+	0.931476i	$0.381478\pi$
$18$	−12.0000	−2.82843
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.00000	0.447214
$21$	3.00000	0.654654
$22$	6.00000	1.27920
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	−6.00000	−1.17670
$27$	9.00000	1.73205
$28$	2.00000	0.377964
$29$	1.00000	0.185695	0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000	0.185695	0.0928477	+	0.995680i	$0.470403\pi$
$30$	−6.00000	−1.09545
$31$	8.00000	1.43684	0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$32$	8.00000	1.41421
$33$	−9.00000	−1.56670
$34$	−6.00000	−1.02899
$35$	1.00000	0.169031
$36$	12.0000	2.00000
$37$	−4.00000	−0.657596	−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000	−0.657596	−0.328798	+	0.944400i	$0.606644\pi$
$38$	−2.00000	−0.324443
$39$	9.00000	1.44115
$40$	0	0
$41$	−8.00000	−1.24939	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	−8.00000	−1.24939	−0.624695	+	0.780869i	$0.714777\pi$
$42$	−6.00000	−0.925820
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	−6.00000	−0.904534
$45$	6.00000	0.894427
$46$	8.00000	1.17954
$47$	1.00000	0.145865	0.0729325	−	0.997337i	$-0.476764\pi$
$47$	1.00000	0.145865	0.0729325	+	0.997337i	$0.476764\pi$
$48$	−12.0000	−1.73205
$49$	1.00000	0.142857
$50$	−2.00000	−0.282843
$51$	9.00000	1.26025
$52$	6.00000	0.832050
$53$	−12.0000	−1.64833	−0.824163	−	0.566352i	$-0.808354\pi$
$53$	−12.0000	−1.64833	−0.824163	+	0.566352i	$0.808354\pi$
$54$	−18.0000	−2.44949
$55$	−3.00000	−0.404520
$56$	0	0
$57$	3.00000	0.397360
$58$	−2.00000	−0.262613
$59$	6.00000	0.781133	0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000	0.781133	0.390567	+	0.920575i	$0.372279\pi$
$60$	6.00000	0.774597
$61$	−6.00000	−0.768221	−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000	−0.768221	−0.384111	+	0.923287i	$0.625492\pi$
$62$	−16.0000	−2.03200
$63$	6.00000	0.755929
$64$	−8.00000	−1.00000
$65$	3.00000	0.372104
$66$	18.0000	2.21565
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	6.00000	0.727607
$69$	−12.0000	−1.44463
$70$	−2.00000	−0.239046
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	10.0000	1.17041	0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000	1.17041	0.585206	+	0.810885i	$0.301014\pi$
$74$	8.00000	0.929981
$75$	3.00000	0.346410
$76$	2.00000	0.229416
$77$	−3.00000	−0.341882
$78$	−18.0000	−2.03810
$79$	13.0000	1.46261	0.731307	−	0.682048i	$-0.238911\pi$
$79$	13.0000	1.46261	0.731307	+	0.682048i	$0.238911\pi$
$80$	−4.00000	−0.447214
$81$	9.00000	1.00000
$82$	16.0000	1.76690
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	6.00000	0.654654
$85$	3.00000	0.325396
$86$	8.00000	0.862662
$87$	3.00000	0.321634
$88$	0	0
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	−12.0000	−1.26491
$91$	3.00000	0.314485
$92$	−8.00000	−0.834058
$93$	24.0000	2.48868
$94$	−2.00000	−0.206284
$95$	1.00000	0.102598
$96$	24.0000	2.44949
$97$	5.00000	0.507673	0.253837	−	0.967247i	$-0.418307\pi$
$97$	5.00000	0.507673	0.253837	+	0.967247i	$0.418307\pi$
$98$	−2.00000	−0.202031
$99$	−18.0000	−1.80907
$100$	2.00000	0.200000
$101$	18.0000	1.79107	0.895533	−	0.444994i	$-0.146794\pi$
$101$	18.0000	1.79107	0.895533	+	0.444994i	$0.146794\pi$
$102$	−18.0000	−1.78227
$103$	3.00000	0.295599	0.147799	−	0.989017i	$-0.452781\pi$
$103$	3.00000	0.295599	0.147799	+	0.989017i	$0.452781\pi$
$104$	0	0
$105$	3.00000	0.292770
$106$	24.0000	2.33109
$107$	−20.0000	−1.93347	−0.966736	−	0.255774i	$-0.917670\pi$
$107$	−20.0000	−1.93347	−0.966736	+	0.255774i	$0.917670\pi$
$108$	18.0000	1.73205
$109$	7.00000	0.670478	0.335239	−	0.942133i	$-0.391183\pi$
$109$	7.00000	0.670478	0.335239	+	0.942133i	$0.391183\pi$
$110$	6.00000	0.572078
$111$	−12.0000	−1.13899
$112$	−4.00000	−0.377964
$113$	−20.0000	−1.88144	−0.940721	−	0.339182i	$-0.889850\pi$
$113$	−20.0000	−1.88144	−0.940721	+	0.339182i	$0.889850\pi$
$114$	−6.00000	−0.561951
$115$	−4.00000	−0.373002
$116$	2.00000	0.185695
$117$	18.0000	1.66410
$118$	−12.0000	−1.10469
$119$	3.00000	0.275010
$120$	0	0
$121$	−2.00000	−0.181818
$122$	12.0000	1.08643
$123$	−24.0000	−2.16401
$124$	16.0000	1.43684
$125$	1.00000	0.0894427
$126$	−12.0000	−1.06904
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	0	0
$129$	−12.0000	−1.05654
$130$	−6.00000	−0.526235
$131$	14.0000	1.22319	0.611593	−	0.791173i	$-0.290529\pi$
$131$	14.0000	1.22319	0.611593	+	0.791173i	$0.290529\pi$
$132$	−18.0000	−1.56670
$133$	1.00000	0.0867110
$134$	−8.00000	−0.691095
$135$	9.00000	0.774597
$136$	0	0
$137$	−12.0000	−1.02523	−0.512615	−	0.858619i	$-0.671323\pi$
$137$	−12.0000	−1.02523	−0.512615	+	0.858619i	$0.671323\pi$
$138$	24.0000	2.04302
$139$	12.0000	1.01783	0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000	1.01783	0.508913	+	0.860818i	$0.330047\pi$
$140$	2.00000	0.169031
$141$	3.00000	0.252646
$142$	0	0
$143$	−9.00000	−0.752618
$144$	−24.0000	−2.00000
$145$	1.00000	0.0830455
$146$	−20.0000	−1.65521
$147$	3.00000	0.247436
$148$	−8.00000	−0.657596
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	−6.00000	−0.489898
$151$	13.0000	1.05792	0.528962	−	0.848645i	$-0.322581\pi$
$151$	13.0000	1.05792	0.528962	+	0.848645i	$0.322581\pi$
$152$	0	0
$153$	18.0000	1.45521
$154$	6.00000	0.483494
$155$	8.00000	0.642575
$156$	18.0000	1.44115
$157$	−18.0000	−1.43656	−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000	−1.43656	−0.718278	+	0.695756i	$0.755069\pi$
$158$	−26.0000	−2.06845
$159$	−36.0000	−2.85499
$160$	8.00000	0.632456
$161$	−4.00000	−0.315244
$162$	−18.0000	−1.41421
$163$	−22.0000	−1.72317	−0.861586	−	0.507611i	$-0.830529\pi$
$163$	−22.0000	−1.72317	−0.861586	+	0.507611i	$0.830529\pi$
$164$	−16.0000	−1.24939
$165$	−9.00000	−0.700649
$166$	−8.00000	−0.620920
$167$	3.00000	0.232147	0.116073	−	0.993241i	$-0.462969\pi$
$167$	3.00000	0.232147	0.116073	+	0.993241i	$0.462969\pi$
$168$	0	0
$169$	−4.00000	−0.307692
$170$	−6.00000	−0.460179
$171$	6.00000	0.458831
$172$	−8.00000	−0.609994
$173$	−11.0000	−0.836315	−0.418157	−	0.908375i	$-0.637324\pi$
$173$	−11.0000	−0.836315	−0.418157	+	0.908375i	$0.637324\pi$
$174$	−6.00000	−0.454859
$175$	1.00000	0.0755929
$176$	12.0000	0.904534
$177$	18.0000	1.35296
$178$	12.0000	0.899438
$179$	−20.0000	−1.49487	−0.747435	−	0.664335i	$-0.768715\pi$
$179$	−20.0000	−1.49487	−0.747435	+	0.664335i	$0.768715\pi$
$180$	12.0000	0.894427
$181$	−20.0000	−1.48659	−0.743294	−	0.668965i	$-0.766738\pi$
$181$	−20.0000	−1.48659	−0.743294	+	0.668965i	$0.766738\pi$
$182$	−6.00000	−0.444750
$183$	−18.0000	−1.33060
$184$	0	0
$185$	−4.00000	−0.294086
$186$	−48.0000	−3.51953
$187$	−9.00000	−0.658145
$188$	2.00000	0.145865
$189$	9.00000	0.654654
$190$	−2.00000	−0.145095
$191$	−27.0000	−1.95365	−0.976826	−	0.214036i	$-0.931339\pi$
$191$	−27.0000	−1.95365	−0.976826	+	0.214036i	$0.931339\pi$
$192$	−24.0000	−1.73205
$193$	20.0000	1.43963	0.719816	−	0.694165i	$-0.244226\pi$
$193$	20.0000	1.43963	0.719816	+	0.694165i	$0.244226\pi$
$194$	−10.0000	−0.717958
$195$	9.00000	0.644503
$196$	2.00000	0.142857
$197$	−6.00000	−0.427482	−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000	−0.427482	−0.213741	+	0.976890i	$0.568565\pi$
$198$	36.0000	2.55841
$199$	18.0000	1.27599	0.637993	−	0.770042i	$-0.279765\pi$
$199$	18.0000	1.27599	0.637993	+	0.770042i	$0.279765\pi$
$200$	0	0
$201$	12.0000	0.846415
$202$	−36.0000	−2.53295
$203$	1.00000	0.0701862
$204$	18.0000	1.26025
$205$	−8.00000	−0.558744
$206$	−6.00000	−0.418040
$207$	−24.0000	−1.66812
$208$	−12.0000	−0.832050
$209$	−3.00000	−0.207514
$210$	−6.00000	−0.414039
$211$	−27.0000	−1.85876	−0.929378	−	0.369129i	$-0.879656\pi$
$211$	−27.0000	−1.85876	−0.929378	+	0.369129i	$0.879656\pi$
$212$	−24.0000	−1.64833
$213$	0	0
$214$	40.0000	2.73434
$215$	−4.00000	−0.272798
$216$	0	0
$217$	8.00000	0.543075
$218$	−14.0000	−0.948200
$219$	30.0000	2.02721
$220$	−6.00000	−0.404520
$221$	9.00000	0.605406
$222$	24.0000	1.61077
$223$	−1.00000	−0.0669650	−0.0334825	−	0.999439i	$-0.510660\pi$
$223$	−1.00000	−0.0669650	−0.0334825	+	0.999439i	$0.510660\pi$
$224$	8.00000	0.534522
$225$	6.00000	0.400000
$226$	40.0000	2.66076
$227$	7.00000	0.464606	0.232303	−	0.972643i	$-0.425374\pi$
$227$	7.00000	0.464606	0.232303	+	0.972643i	$0.425374\pi$
$228$	6.00000	0.397360
$229$	16.0000	1.05731	0.528655	−	0.848837i	$-0.322697\pi$
$229$	16.0000	1.05731	0.528655	+	0.848837i	$0.322697\pi$
$230$	8.00000	0.527504
$231$	−9.00000	−0.592157
$232$	0	0
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	−36.0000	−2.35339
$235$	1.00000	0.0652328
$236$	12.0000	0.781133
$237$	39.0000	2.53332
$238$	−6.00000	−0.388922
$239$	23.0000	1.48775	0.743873	−	0.668321i	$-0.232987\pi$
$239$	23.0000	1.48775	0.743873	+	0.668321i	$0.232987\pi$
$240$	−12.0000	−0.774597
$241$	−18.0000	−1.15948	−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000	−1.15948	−0.579741	+	0.814801i	$0.696846\pi$
$242$	4.00000	0.257130
$243$	0	0
$244$	−12.0000	−0.768221
$245$	1.00000	0.0638877
$246$	48.0000	3.06037
$247$	3.00000	0.190885
$248$	0	0
$249$	12.0000	0.760469
$250$	−2.00000	−0.126491
$251$	18.0000	1.13615	0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000	1.13615	0.568075	+	0.822977i	$0.307688\pi$
$252$	12.0000	0.755929
$253$	12.0000	0.754434
$254$	16.0000	1.00393
$255$	9.00000	0.563602
$256$	16.0000	1.00000
$257$	26.0000	1.62184	0.810918	−	0.585160i	$-0.198968\pi$
$257$	26.0000	1.62184	0.810918	+	0.585160i	$0.198968\pi$
$258$	24.0000	1.49417
$259$	−4.00000	−0.248548
$260$	6.00000	0.372104
$261$	6.00000	0.371391
$262$	−28.0000	−1.72985
$263$	12.0000	0.739952	0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000	0.739952	0.369976	+	0.929041i	$0.379366\pi$
$264$	0	0
$265$	−12.0000	−0.737154
$266$	−2.00000	−0.122628
$267$	−18.0000	−1.10158
$268$	8.00000	0.488678
$269$	−10.0000	−0.609711	−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000	−0.609711	−0.304855	+	0.952399i	$0.598608\pi$
$270$	−18.0000	−1.09545
$271$	−20.0000	−1.21491	−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000	−1.21491	−0.607457	+	0.794353i	$0.707810\pi$
$272$	−12.0000	−0.727607
$273$	9.00000	0.544705
$274$	24.0000	1.44989
$275$	−3.00000	−0.180907
$276$	−24.0000	−1.44463
$277$	−16.0000	−0.961347	−0.480673	−	0.876900i	$-0.659608\pi$
$277$	−16.0000	−0.961347	−0.480673	+	0.876900i	$0.659608\pi$
$278$	−24.0000	−1.43942
$279$	48.0000	2.87368
$280$	0	0
$281$	−27.0000	−1.61068	−0.805342	−	0.592810i	$-0.798019\pi$
$281$	−27.0000	−1.61068	−0.805342	+	0.592810i	$0.798019\pi$
$282$	−6.00000	−0.357295
$283$	−17.0000	−1.01055	−0.505273	−	0.862960i	$-0.668608\pi$
$283$	−17.0000	−1.01055	−0.505273	+	0.862960i	$0.668608\pi$
$284$	0	0
$285$	3.00000	0.177705
$286$	18.0000	1.06436
$287$	−8.00000	−0.472225
$288$	48.0000	2.82843
$289$	−8.00000	−0.470588
$290$	−2.00000	−0.117444
$291$	15.0000	0.879316
$292$	20.0000	1.17041
$293$	−23.0000	−1.34367	−0.671837	−	0.740699i	$-0.734495\pi$
$293$	−23.0000	−1.34367	−0.671837	+	0.740699i	$0.734495\pi$
$294$	−6.00000	−0.349927
$295$	6.00000	0.349334
$296$	0	0
$297$	−27.0000	−1.56670
$298$	12.0000	0.695141
$299$	−12.0000	−0.693978
$300$	6.00000	0.346410
$301$	−4.00000	−0.230556
$302$	−26.0000	−1.49613
$303$	54.0000	3.10222
$304$	−4.00000	−0.229416
$305$	−6.00000	−0.343559
$306$	−36.0000	−2.05798
$307$	−3.00000	−0.171219	−0.0856095	−	0.996329i	$-0.527284\pi$
$307$	−3.00000	−0.171219	−0.0856095	+	0.996329i	$0.527284\pi$
$308$	−6.00000	−0.341882
$309$	9.00000	0.511992
$310$	−16.0000	−0.908739
$311$	14.0000	0.793867	0.396934	−	0.917847i	$-0.370074\pi$
$311$	14.0000	0.793867	0.396934	+	0.917847i	$0.370074\pi$
$312$	0	0
$313$	9.00000	0.508710	0.254355	−	0.967111i	$-0.418137\pi$
$313$	9.00000	0.508710	0.254355	+	0.967111i	$0.418137\pi$
$314$	36.0000	2.03160
$315$	6.00000	0.338062
$316$	26.0000	1.46261
$317$	10.0000	0.561656	0.280828	−	0.959758i	$-0.409391\pi$
$317$	10.0000	0.561656	0.280828	+	0.959758i	$0.409391\pi$
$318$	72.0000	4.03756
$319$	−3.00000	−0.167968
$320$	−8.00000	−0.447214
$321$	−60.0000	−3.34887
$322$	8.00000	0.445823
$323$	3.00000	0.166924
$324$	18.0000	1.00000
$325$	3.00000	0.166410
$326$	44.0000	2.43693
$327$	21.0000	1.16130
$328$	0	0
$329$	1.00000	0.0551318
$330$	18.0000	0.990867
$331$	−24.0000	−1.31916	−0.659580	−	0.751635i	$-0.729266\pi$
$331$	−24.0000	−1.31916	−0.659580	+	0.751635i	$0.729266\pi$
$332$	8.00000	0.439057
$333$	−24.0000	−1.31519
$334$	−6.00000	−0.328305
$335$	4.00000	0.218543
$336$	−12.0000	−0.654654
$337$	32.0000	1.74315	0.871576	−	0.490261i	$-0.163099\pi$
$337$	32.0000	1.74315	0.871576	+	0.490261i	$0.163099\pi$
$338$	8.00000	0.435143
$339$	−60.0000	−3.25875
$340$	6.00000	0.325396
$341$	−24.0000	−1.29967
$342$	−12.0000	−0.648886
$343$	1.00000	0.0539949
$344$	0	0
$345$	−12.0000	−0.646058
$346$	22.0000	1.18273
$347$	−20.0000	−1.07366	−0.536828	−	0.843692i	$-0.680378\pi$
$347$	−20.0000	−1.07366	−0.536828	+	0.843692i	$0.680378\pi$
$348$	6.00000	0.321634
$349$	20.0000	1.07058	0.535288	−	0.844670i	$-0.320203\pi$
$349$	20.0000	1.07058	0.535288	+	0.844670i	$0.320203\pi$
$350$	−2.00000	−0.106904
$351$	27.0000	1.44115
$352$	−24.0000	−1.27920
$353$	−21.0000	−1.11772	−0.558859	−	0.829263i	$-0.688761\pi$
$353$	−21.0000	−1.11772	−0.558859	+	0.829263i	$0.688761\pi$
$354$	−36.0000	−1.91338
$355$	0	0
$356$	−12.0000	−0.635999
$357$	9.00000	0.476331
$358$	40.0000	2.11407
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	40.0000	2.10235
$363$	−6.00000	−0.314918
$364$	6.00000	0.314485
$365$	10.0000	0.523424
$366$	36.0000	1.88175
$367$	13.0000	0.678594	0.339297	−	0.940679i	$-0.389811\pi$
$367$	13.0000	0.678594	0.339297	+	0.940679i	$0.389811\pi$
$368$	16.0000	0.834058
$369$	−48.0000	−2.49878
$370$	8.00000	0.415900
$371$	−12.0000	−0.623009
$372$	48.0000	2.48868
$373$	4.00000	0.207112	0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000	0.207112	0.103556	+	0.994624i	$0.466978\pi$
$374$	18.0000	0.930758
$375$	3.00000	0.154919
$376$	0	0
$377$	3.00000	0.154508
$378$	−18.0000	−0.925820
$379$	−4.00000	−0.205466	−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000	−0.205466	−0.102733	+	0.994709i	$0.532759\pi$
$380$	2.00000	0.102598
$381$	−24.0000	−1.22956
$382$	54.0000	2.76288
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	−3.00000	−0.152894
$386$	−40.0000	−2.03595
$387$	−24.0000	−1.21999
$388$	10.0000	0.507673
$389$	9.00000	0.456318	0.228159	−	0.973624i	$-0.426729\pi$
$389$	9.00000	0.456318	0.228159	+	0.973624i	$0.426729\pi$
$390$	−18.0000	−0.911465
$391$	−12.0000	−0.606866
$392$	0	0
$393$	42.0000	2.11862
$394$	12.0000	0.604551
$395$	13.0000	0.654101
$396$	−36.0000	−1.80907
$397$	31.0000	1.55585	0.777923	−	0.628360i	$-0.216273\pi$
$397$	31.0000	1.55585	0.777923	+	0.628360i	$0.216273\pi$
$398$	−36.0000	−1.80452
$399$	3.00000	0.150188
$400$	−4.00000	−0.200000
$401$	−5.00000	−0.249688	−0.124844	−	0.992176i	$-0.539843\pi$
$401$	−5.00000	−0.249688	−0.124844	+	0.992176i	$0.539843\pi$
$402$	−24.0000	−1.19701
$403$	24.0000	1.19553
$404$	36.0000	1.79107
$405$	9.00000	0.447214
$406$	−2.00000	−0.0992583
$407$	12.0000	0.594818
$408$	0	0
$409$	−28.0000	−1.38451	−0.692255	−	0.721653i	$-0.743383\pi$
$409$	−28.0000	−1.38451	−0.692255	+	0.721653i	$0.743383\pi$
$410$	16.0000	0.790184
$411$	−36.0000	−1.77575
$412$	6.00000	0.295599
$413$	6.00000	0.295241
$414$	48.0000	2.35907
$415$	4.00000	0.196352
$416$	24.0000	1.17670
$417$	36.0000	1.76293
$418$	6.00000	0.293470
$419$	−6.00000	−0.293119	−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000	−0.293119	−0.146560	+	0.989202i	$0.546820\pi$
$420$	6.00000	0.292770
$421$	−13.0000	−0.633581	−0.316791	−	0.948495i	$-0.602605\pi$
$421$	−13.0000	−0.633581	−0.316791	+	0.948495i	$0.602605\pi$
$422$	54.0000	2.62868
$423$	6.00000	0.291730
$424$	0	0
$425$	3.00000	0.145521
$426$	0	0
$427$	−6.00000	−0.290360
$428$	−40.0000	−1.93347
$429$	−27.0000	−1.30357
$430$	8.00000	0.385794
$431$	19.0000	0.915198	0.457599	−	0.889159i	$-0.348710\pi$
$431$	19.0000	0.915198	0.457599	+	0.889159i	$0.348710\pi$
$432$	−36.0000	−1.73205
$433$	−34.0000	−1.63394	−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000	−1.63394	−0.816968	+	0.576683i	$0.804347\pi$
$434$	−16.0000	−0.768025
$435$	3.00000	0.143839
$436$	14.0000	0.670478
$437$	−4.00000	−0.191346
$438$	−60.0000	−2.86691
$439$	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
$441$	6.00000	0.285714
$442$	−18.0000	−0.856173
$443$	24.0000	1.14027	0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000	1.14027	0.570137	+	0.821549i	$0.306890\pi$
$444$	−24.0000	−1.13899
$445$	−6.00000	−0.284427
$446$	2.00000	0.0947027
$447$	−18.0000	−0.851371
$448$	−8.00000	−0.377964
$449$	13.0000	0.613508	0.306754	−	0.951789i	$-0.400757\pi$
$449$	13.0000	0.613508	0.306754	+	0.951789i	$0.400757\pi$
$450$	−12.0000	−0.565685
$451$	24.0000	1.13012
$452$	−40.0000	−1.88144
$453$	39.0000	1.83238
$454$	−14.0000	−0.657053
$455$	3.00000	0.140642
$456$	0	0
$457$	−24.0000	−1.12267	−0.561336	−	0.827588i	$-0.689713\pi$
$457$	−24.0000	−1.12267	−0.561336	+	0.827588i	$0.689713\pi$
$458$	−32.0000	−1.49526
$459$	27.0000	1.26025
$460$	−8.00000	−0.373002
$461$	34.0000	1.58354	0.791769	−	0.610821i	$-0.209160\pi$
$461$	34.0000	1.58354	0.791769	+	0.610821i	$0.209160\pi$
$462$	18.0000	0.837436
$463$	6.00000	0.278844	0.139422	−	0.990233i	$-0.455476\pi$
$463$	6.00000	0.278844	0.139422	+	0.990233i	$0.455476\pi$
$464$	−4.00000	−0.185695
$465$	24.0000	1.11297
$466$	−12.0000	−0.555889
$467$	3.00000	0.138823	0.0694117	−	0.997588i	$-0.477888\pi$
$467$	3.00000	0.138823	0.0694117	+	0.997588i	$0.477888\pi$
$468$	36.0000	1.66410
$469$	4.00000	0.184703
$470$	−2.00000	−0.0922531
$471$	−54.0000	−2.48819
$472$	0	0
$473$	12.0000	0.551761
$474$	−78.0000	−3.58266
$475$	1.00000	0.0458831
$476$	6.00000	0.275010
$477$	−72.0000	−3.29665
$478$	−46.0000	−2.10399
$479$	40.0000	1.82765	0.913823	−	0.406112i	$-0.133116\pi$
$479$	40.0000	1.82765	0.913823	+	0.406112i	$0.133116\pi$
$480$	24.0000	1.09545
$481$	−12.0000	−0.547153
$482$	36.0000	1.63976
$483$	−12.0000	−0.546019
$484$	−4.00000	−0.181818
$485$	5.00000	0.227038
$486$	0	0
$487$	−20.0000	−0.906287	−0.453143	−	0.891438i	$-0.649697\pi$
$487$	−20.0000	−0.906287	−0.453143	+	0.891438i	$0.649697\pi$
$488$	0	0
$489$	−66.0000	−2.98462
$490$	−2.00000	−0.0903508
$491$	27.0000	1.21849	0.609246	−	0.792981i	$-0.291472\pi$
$491$	27.0000	1.21849	0.609246	+	0.792981i	$0.291472\pi$
$492$	−48.0000	−2.16401
$493$	3.00000	0.135113
$494$	−6.00000	−0.269953
$495$	−18.0000	−0.809040
$496$	−32.0000	−1.43684
$497$	0	0
$498$	−24.0000	−1.07547
$499$	25.0000	1.11915	0.559577	−	0.828778i	$-0.310964\pi$
$499$	25.0000	1.11915	0.559577	+	0.828778i	$0.310964\pi$
$500$	2.00000	0.0894427
$501$	9.00000	0.402090
$502$	−36.0000	−1.60676
$503$	11.0000	0.490466	0.245233	−	0.969464i	$-0.421136\pi$
$503$	11.0000	0.490466	0.245233	+	0.969464i	$0.421136\pi$
$504$	0	0
$505$	18.0000	0.800989
$506$	−24.0000	−1.06693
$507$	−12.0000	−0.532939
$508$	−16.0000	−0.709885
$509$	24.0000	1.06378	0.531891	−	0.846813i	$-0.321482\pi$
$509$	24.0000	1.06378	0.531891	+	0.846813i	$0.321482\pi$
$510$	−18.0000	−0.797053
$511$	10.0000	0.442374
$512$	−32.0000	−1.41421
$513$	9.00000	0.397360
$514$	−52.0000	−2.29362
$515$	3.00000	0.132196
$516$	−24.0000	−1.05654
$517$	−3.00000	−0.131940
$518$	8.00000	0.351500
$519$	−33.0000	−1.44854
$520$	0	0
$521$	−2.00000	−0.0876216	−0.0438108	−	0.999040i	$-0.513950\pi$
$521$	−2.00000	−0.0876216	−0.0438108	+	0.999040i	$0.513950\pi$
$522$	−12.0000	−0.525226
$523$	−20.0000	−0.874539	−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000	−0.874539	−0.437269	+	0.899331i	$0.644054\pi$
$524$	28.0000	1.22319
$525$	3.00000	0.130931
$526$	−24.0000	−1.04645
$527$	24.0000	1.04546
$528$	36.0000	1.56670
$529$	−7.00000	−0.304348
$530$	24.0000	1.04249
$531$	36.0000	1.56227
$532$	2.00000	0.0867110
$533$	−24.0000	−1.03956
$534$	36.0000	1.55787
$535$	−20.0000	−0.864675
$536$	0	0
$537$	−60.0000	−2.58919
$538$	20.0000	0.862261
$539$	−3.00000	−0.129219
$540$	18.0000	0.774597
$541$	19.0000	0.816874	0.408437	−	0.912787i	$-0.366074\pi$
$541$	19.0000	0.816874	0.408437	+	0.912787i	$0.366074\pi$
$542$	40.0000	1.71815
$543$	−60.0000	−2.57485
$544$	24.0000	1.02899
$545$	7.00000	0.299847
$546$	−18.0000	−0.770329
$547$	26.0000	1.11168	0.555840	−	0.831289i	$-0.312397\pi$
$547$	26.0000	1.11168	0.555840	+	0.831289i	$0.312397\pi$
$548$	−24.0000	−1.02523
$549$	−36.0000	−1.53644
$550$	6.00000	0.255841
$551$	1.00000	0.0426014
$552$	0	0
$553$	13.0000	0.552816
$554$	32.0000	1.35955
$555$	−12.0000	−0.509372
$556$	24.0000	1.01783
$557$	40.0000	1.69485	0.847427	−	0.530912i	$-0.178150\pi$
$557$	40.0000	1.69485	0.847427	+	0.530912i	$0.178150\pi$
$558$	−96.0000	−4.06400
$559$	−12.0000	−0.507546
$560$	−4.00000	−0.169031
$561$	−27.0000	−1.13994
$562$	54.0000	2.27785
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	6.00000	0.252646
$565$	−20.0000	−0.841406
$566$	34.0000	1.42913
$567$	9.00000	0.377964
$568$	0	0
$569$	−38.0000	−1.59304	−0.796521	−	0.604610i	$-0.793329\pi$
$569$	−38.0000	−1.59304	−0.796521	+	0.604610i	$0.793329\pi$
$570$	−6.00000	−0.251312
$571$	28.0000	1.17176	0.585882	−	0.810397i	$-0.300748\pi$
$571$	28.0000	1.17176	0.585882	+	0.810397i	$0.300748\pi$
$572$	−18.0000	−0.752618
$573$	−81.0000	−3.38382
$574$	16.0000	0.667827
$575$	−4.00000	−0.166812
$576$	−48.0000	−2.00000
$577$	−7.00000	−0.291414	−0.145707	−	0.989328i	$-0.546546\pi$
$577$	−7.00000	−0.291414	−0.145707	+	0.989328i	$0.546546\pi$
$578$	16.0000	0.665512
$579$	60.0000	2.49351
$580$	2.00000	0.0830455
$581$	4.00000	0.165948
$582$	−30.0000	−1.24354
$583$	36.0000	1.49097
$584$	0	0
$585$	18.0000	0.744208
$586$	46.0000	1.90024
$587$	32.0000	1.32078	0.660391	−	0.750922i	$-0.270391\pi$
$587$	32.0000	1.32078	0.660391	+	0.750922i	$0.270391\pi$
$588$	6.00000	0.247436
$589$	8.00000	0.329634
$590$	−12.0000	−0.494032
$591$	−18.0000	−0.740421
$592$	16.0000	0.657596
$593$	13.0000	0.533846	0.266923	−	0.963718i	$-0.413993\pi$
$593$	13.0000	0.533846	0.266923	+	0.963718i	$0.413993\pi$
$594$	54.0000	2.21565
$595$	3.00000	0.122988
$596$	−12.0000	−0.491539
$597$	54.0000	2.21007
$598$	24.0000	0.981433
$599$	3.00000	0.122577	0.0612883	−	0.998120i	$-0.480479\pi$
$599$	3.00000	0.122577	0.0612883	+	0.998120i	$0.480479\pi$
$600$	0	0
$601$	20.0000	0.815817	0.407909	−	0.913023i	$-0.366258\pi$
$601$	20.0000	0.815817	0.407909	+	0.913023i	$0.366258\pi$
$602$	8.00000	0.326056
$603$	24.0000	0.977356
$604$	26.0000	1.05792
$605$	−2.00000	−0.0813116
$606$	−108.000	−4.38720
$607$	−43.0000	−1.74532	−0.872658	−	0.488332i	$-0.837606\pi$
$607$	−43.0000	−1.74532	−0.872658	+	0.488332i	$0.837606\pi$
$608$	8.00000	0.324443
$609$	3.00000	0.121566
$610$	12.0000	0.485866
$611$	3.00000	0.121367
$612$	36.0000	1.45521
$613$	−12.0000	−0.484675	−0.242338	−	0.970192i	$-0.577914\pi$
$613$	−12.0000	−0.484675	−0.242338	+	0.970192i	$0.577914\pi$
$614$	6.00000	0.242140
$615$	−24.0000	−0.967773
$616$	0	0
$617$	2.00000	0.0805170	0.0402585	−	0.999189i	$-0.487182\pi$
$617$	2.00000	0.0805170	0.0402585	+	0.999189i	$0.487182\pi$
$618$	−18.0000	−0.724066
$619$	−26.0000	−1.04503	−0.522514	−	0.852631i	$-0.675006\pi$
$619$	−26.0000	−1.04503	−0.522514	+	0.852631i	$0.675006\pi$
$620$	16.0000	0.642575
$621$	−36.0000	−1.44463
$622$	−28.0000	−1.12270
$623$	−6.00000	−0.240385
$624$	−36.0000	−1.44115
$625$	1.00000	0.0400000
$626$	−18.0000	−0.719425
$627$	−9.00000	−0.359425
$628$	−36.0000	−1.43656
$629$	−12.0000	−0.478471
$630$	−12.0000	−0.478091
$631$	−11.0000	−0.437903	−0.218952	−	0.975736i	$-0.570264\pi$
$631$	−11.0000	−0.437903	−0.218952	+	0.975736i	$0.570264\pi$
$632$	0	0
$633$	−81.0000	−3.21946
$634$	−20.0000	−0.794301
$635$	−8.00000	−0.317470
$636$	−72.0000	−2.85499
$637$	3.00000	0.118864
$638$	6.00000	0.237542
$639$	0	0
$640$	0	0
$641$	30.0000	1.18493	0.592464	−	0.805597i	$-0.298155\pi$
$641$	30.0000	1.18493	0.592464	+	0.805597i	$0.298155\pi$
$642$	120.000	4.73602
$643$	41.0000	1.61688	0.808441	−	0.588577i	$-0.200312\pi$
$643$	41.0000	1.61688	0.808441	+	0.588577i	$0.200312\pi$
$644$	−8.00000	−0.315244
$645$	−12.0000	−0.472500
$646$	−6.00000	−0.236067
$647$	−24.0000	−0.943537	−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000	−0.943537	−0.471769	+	0.881722i	$0.656384\pi$
$648$	0	0
$649$	−18.0000	−0.706562
$650$	−6.00000	−0.235339
$651$	24.0000	0.940634
$652$	−44.0000	−1.72317
$653$	−26.0000	−1.01746	−0.508729	−	0.860927i	$-0.669885\pi$
$653$	−26.0000	−1.01746	−0.508729	+	0.860927i	$0.669885\pi$
$654$	−42.0000	−1.64233
$655$	14.0000	0.547025
$656$	32.0000	1.24939
$657$	60.0000	2.34082
$658$	−2.00000	−0.0779681
$659$	3.00000	0.116863	0.0584317	−	0.998291i	$-0.481390\pi$
$659$	3.00000	0.116863	0.0584317	+	0.998291i	$0.481390\pi$
$660$	−18.0000	−0.700649
$661$	−14.0000	−0.544537	−0.272268	−	0.962221i	$-0.587774\pi$
$661$	−14.0000	−0.544537	−0.272268	+	0.962221i	$0.587774\pi$
$662$	48.0000	1.86557
$663$	27.0000	1.04859
$664$	0	0
$665$	1.00000	0.0387783
$666$	48.0000	1.85996
$667$	−4.00000	−0.154881
$668$	6.00000	0.232147
$669$	−3.00000	−0.115987
$670$	−8.00000	−0.309067
$671$	18.0000	0.694882
$672$	24.0000	0.925820
$673$	−26.0000	−1.00223	−0.501113	−	0.865382i	$-0.667076\pi$
$673$	−26.0000	−1.00223	−0.501113	+	0.865382i	$0.667076\pi$
$674$	−64.0000	−2.46519
$675$	9.00000	0.346410
$676$	−8.00000	−0.307692
$677$	3.00000	0.115299	0.0576497	−	0.998337i	$-0.481639\pi$
$677$	3.00000	0.115299	0.0576497	+	0.998337i	$0.481639\pi$
$678$	120.000	4.60857
$679$	5.00000	0.191882
$680$	0	0
$681$	21.0000	0.804722
$682$	48.0000	1.83801
$683$	12.0000	0.459167	0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000	0.459167	0.229584	+	0.973289i	$0.426264\pi$
$684$	12.0000	0.458831
$685$	−12.0000	−0.458496
$686$	−2.00000	−0.0763604
$687$	48.0000	1.83131
$688$	16.0000	0.609994
$689$	−36.0000	−1.37149
$690$	24.0000	0.913664
$691$	8.00000	0.304334	0.152167	−	0.988355i	$-0.451375\pi$
$691$	8.00000	0.304334	0.152167	+	0.988355i	$0.451375\pi$
$692$	−22.0000	−0.836315
$693$	−18.0000	−0.683763
$694$	40.0000	1.51838
$695$	12.0000	0.455186
$696$	0	0
$697$	−24.0000	−0.909065
$698$	−40.0000	−1.51402
$699$	18.0000	0.680823
$700$	2.00000	0.0755929
$701$	15.0000	0.566542	0.283271	−	0.959040i	$-0.408580\pi$
$701$	15.0000	0.566542	0.283271	+	0.959040i	$0.408580\pi$
$702$	−54.0000	−2.03810
$703$	−4.00000	−0.150863
$704$	24.0000	0.904534
$705$	3.00000	0.112987
$706$	42.0000	1.58069
$707$	18.0000	0.676960
$708$	36.0000	1.35296
$709$	19.0000	0.713560	0.356780	−	0.934188i	$-0.383875\pi$
$709$	19.0000	0.713560	0.356780	+	0.934188i	$0.383875\pi$
$710$	0	0
$711$	78.0000	2.92523
$712$	0	0
$713$	−32.0000	−1.19841
$714$	−18.0000	−0.673633
$715$	−9.00000	−0.336581
$716$	−40.0000	−1.49487
$717$	69.0000	2.57685
$718$	0	0
$719$	30.0000	1.11881	0.559406	−	0.828894i	$-0.311029\pi$
$719$	30.0000	1.11881	0.559406	+	0.828894i	$0.311029\pi$
$720$	−24.0000	−0.894427
$721$	3.00000	0.111726
$722$	−2.00000	−0.0744323
$723$	−54.0000	−2.00828
$724$	−40.0000	−1.48659
$725$	1.00000	0.0371391
$726$	12.0000	0.445362
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	−20.0000	−0.740233
$731$	−12.0000	−0.443836
$732$	−36.0000	−1.33060
$733$	13.0000	0.480166	0.240083	−	0.970752i	$-0.422825\pi$
$733$	13.0000	0.480166	0.240083	+	0.970752i	$0.422825\pi$
$734$	−26.0000	−0.959678
$735$	3.00000	0.110657
$736$	−32.0000	−1.17954
$737$	−12.0000	−0.442026
$738$	96.0000	3.53381
$739$	29.0000	1.06678	0.533391	−	0.845869i	$-0.320917\pi$
$739$	29.0000	1.06678	0.533391	+	0.845869i	$0.320917\pi$
$740$	−8.00000	−0.294086
$741$	9.00000	0.330623
$742$	24.0000	0.881068
$743$	26.0000	0.953847	0.476924	−	0.878945i	$-0.341752\pi$
$743$	26.0000	0.953847	0.476924	+	0.878945i	$0.341752\pi$
$744$	0	0
$745$	−6.00000	−0.219823
$746$	−8.00000	−0.292901
$747$	24.0000	0.878114
$748$	−18.0000	−0.658145
$749$	−20.0000	−0.730784
$750$	−6.00000	−0.219089
$751$	21.0000	0.766301	0.383150	−	0.923686i	$-0.374839\pi$
$751$	21.0000	0.766301	0.383150	+	0.923686i	$0.374839\pi$
$752$	−4.00000	−0.145865
$753$	54.0000	1.96787
$754$	−6.00000	−0.218507
$755$	13.0000	0.473118
$756$	18.0000	0.654654
$757$	−42.0000	−1.52652	−0.763258	−	0.646094i	$-0.776401\pi$
$757$	−42.0000	−1.52652	−0.763258	+	0.646094i	$0.776401\pi$
$758$	8.00000	0.290573
$759$	36.0000	1.30672
$760$	0	0
$761$	−20.0000	−0.724999	−0.362500	−	0.931984i	$-0.618077\pi$
$761$	−20.0000	−0.724999	−0.362500	+	0.931984i	$0.618077\pi$
$762$	48.0000	1.73886
$763$	7.00000	0.253417
$764$	−54.0000	−1.95365
$765$	18.0000	0.650791
$766$	0	0
$767$	18.0000	0.649942
$768$	48.0000	1.73205
$769$	16.0000	0.576975	0.288487	−	0.957484i	$-0.406848\pi$
$769$	16.0000	0.576975	0.288487	+	0.957484i	$0.406848\pi$
$770$	6.00000	0.216225
$771$	78.0000	2.80910
$772$	40.0000	1.43963
$773$	7.00000	0.251773	0.125886	−	0.992045i	$-0.459823\pi$
$773$	7.00000	0.251773	0.125886	+	0.992045i	$0.459823\pi$
$774$	48.0000	1.72532
$775$	8.00000	0.287368
$776$	0	0
$777$	−12.0000	−0.430498
$778$	−18.0000	−0.645331
$779$	−8.00000	−0.286630
$780$	18.0000	0.644503
$781$	0	0
$782$	24.0000	0.858238
$783$	9.00000	0.321634
$784$	−4.00000	−0.142857
$785$	−18.0000	−0.642448
$786$	−84.0000	−2.99618
$787$	−5.00000	−0.178231	−0.0891154	−	0.996021i	$-0.528404\pi$
$787$	−5.00000	−0.178231	−0.0891154	+	0.996021i	$0.528404\pi$
$788$	−12.0000	−0.427482
$789$	36.0000	1.28163
$790$	−26.0000	−0.925038
$791$	−20.0000	−0.711118
$792$	0	0
$793$	−18.0000	−0.639199
$794$	−62.0000	−2.20030
$795$	−36.0000	−1.27679
$796$	36.0000	1.27599
$797$	37.0000	1.31061	0.655304	−	0.755366i	$-0.272541\pi$
$797$	37.0000	1.31061	0.655304	+	0.755366i	$0.272541\pi$
$798$	−6.00000	−0.212398
$799$	3.00000	0.106132
$800$	8.00000	0.282843
$801$	−36.0000	−1.27200
$802$	10.0000	0.353112
$803$	−30.0000	−1.05868
$804$	24.0000	0.846415
$805$	−4.00000	−0.140981
$806$	−48.0000	−1.69073
$807$	−30.0000	−1.05605
$808$	0	0
$809$	9.00000	0.316423	0.158212	−	0.987405i	$-0.449427\pi$
$809$	9.00000	0.316423	0.158212	+	0.987405i	$0.449427\pi$
$810$	−18.0000	−0.632456
$811$	−22.0000	−0.772524	−0.386262	−	0.922389i	$-0.626234\pi$
$811$	−22.0000	−0.772524	−0.386262	+	0.922389i	$0.626234\pi$
$812$	2.00000	0.0701862
$813$	−60.0000	−2.10429
$814$	−24.0000	−0.841200
$815$	−22.0000	−0.770626
$816$	−36.0000	−1.26025
$817$	−4.00000	−0.139942
$818$	56.0000	1.95799
$819$	18.0000	0.628971
$820$	−16.0000	−0.558744
$821$	25.0000	0.872506	0.436253	−	0.899824i	$-0.356305\pi$
$821$	25.0000	0.872506	0.436253	+	0.899824i	$0.356305\pi$
$822$	72.0000	2.51129
$823$	10.0000	0.348578	0.174289	−	0.984695i	$-0.444237\pi$
$823$	10.0000	0.348578	0.174289	+	0.984695i	$0.444237\pi$
$824$	0	0
$825$	−9.00000	−0.313340
$826$	−12.0000	−0.417533
$827$	−52.0000	−1.80822	−0.904109	−	0.427303i	$-0.859464\pi$
$827$	−52.0000	−1.80822	−0.904109	+	0.427303i	$0.859464\pi$
$828$	−48.0000	−1.66812
$829$	−14.0000	−0.486240	−0.243120	−	0.969996i	$-0.578171\pi$
$829$	−14.0000	−0.486240	−0.243120	+	0.969996i	$0.578171\pi$
$830$	−8.00000	−0.277684
$831$	−48.0000	−1.66510
$832$	−24.0000	−0.832050
$833$	3.00000	0.103944
$834$	−72.0000	−2.49316
$835$	3.00000	0.103819
$836$	−6.00000	−0.207514
$837$	72.0000	2.48868
$838$	12.0000	0.414533
$839$	42.0000	1.45000	0.725001	−	0.688748i	$-0.241839\pi$
$839$	42.0000	1.45000	0.725001	+	0.688748i	$0.241839\pi$
$840$	0	0
$841$	−28.0000	−0.965517
$842$	26.0000	0.896019
$843$	−81.0000	−2.78979
$844$	−54.0000	−1.85876
$845$	−4.00000	−0.137604
$846$	−12.0000	−0.412568
$847$	−2.00000	−0.0687208
$848$	48.0000	1.64833
$849$	−51.0000	−1.75032
$850$	−6.00000	−0.205798
$851$	16.0000	0.548473
$852$	0	0
$853$	−26.0000	−0.890223	−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000	−0.890223	−0.445112	+	0.895475i	$0.646836\pi$
$854$	12.0000	0.410632
$855$	6.00000	0.205196
$856$	0	0
$857$	6.00000	0.204956	0.102478	−	0.994735i	$-0.467323\pi$
$857$	6.00000	0.204956	0.102478	+	0.994735i	$0.467323\pi$
$858$	54.0000	1.84353
$859$	2.00000	0.0682391	0.0341196	−	0.999418i	$-0.489137\pi$
$859$	2.00000	0.0682391	0.0341196	+	0.999418i	$0.489137\pi$
$860$	−8.00000	−0.272798
$861$	−24.0000	−0.817918
$862$	−38.0000	−1.29429
$863$	6.00000	0.204242	0.102121	−	0.994772i	$-0.467437\pi$
$863$	6.00000	0.204242	0.102121	+	0.994772i	$0.467437\pi$
$864$	72.0000	2.44949
$865$	−11.0000	−0.374011
$866$	68.0000	2.31073
$867$	−24.0000	−0.815083
$868$	16.0000	0.543075
$869$	−39.0000	−1.32298
$870$	−6.00000	−0.203419
$871$	12.0000	0.406604
$872$	0	0
$873$	30.0000	1.01535
$874$	8.00000	0.270604
$875$	1.00000	0.0338062
$876$	60.0000	2.02721
$877$	0	0		−	1.00000i	$-0.5\pi$
$877$	0	0			1.00000i	$0.5\pi$
$878$	−56.0000	−1.88991
$879$	−69.0000	−2.32731
$880$	12.0000	0.404520
$881$	−58.0000	−1.95407	−0.977035	−	0.213080i	$-0.931651\pi$
$881$	−58.0000	−1.95407	−0.977035	+	0.213080i	$0.931651\pi$
$882$	−12.0000	−0.404061
$883$	26.0000	0.874970	0.437485	−	0.899226i	$-0.355869\pi$
$883$	26.0000	0.874970	0.437485	+	0.899226i	$0.355869\pi$
$884$	18.0000	0.605406
$885$	18.0000	0.605063
$886$	−48.0000	−1.61259
$887$	−24.0000	−0.805841	−0.402921	−	0.915235i	$-0.632005\pi$
$887$	−24.0000	−0.805841	−0.402921	+	0.915235i	$0.632005\pi$
$888$	0	0
$889$	−8.00000	−0.268311
$890$	12.0000	0.402241
$891$	−27.0000	−0.904534
$892$	−2.00000	−0.0669650
$893$	1.00000	0.0334637
$894$	36.0000	1.20402
$895$	−20.0000	−0.668526
$896$	0	0
$897$	−36.0000	−1.20201
$898$	−26.0000	−0.867631
$899$	8.00000	0.266815
$900$	12.0000	0.400000
$901$	−36.0000	−1.19933
$902$	−48.0000	−1.59823
$903$	−12.0000	−0.399335
$904$	0	0
$905$	−20.0000	−0.664822
$906$	−78.0000	−2.59138
$907$	22.0000	0.730498	0.365249	−	0.930910i	$-0.380984\pi$
$907$	22.0000	0.730498	0.365249	+	0.930910i	$0.380984\pi$
$908$	14.0000	0.464606
$909$	108.000	3.58213
$910$	−6.00000	−0.198898
$911$	−8.00000	−0.265052	−0.132526	−	0.991180i	$-0.542309\pi$
$911$	−8.00000	−0.265052	−0.132526	+	0.991180i	$0.542309\pi$
$912$	−12.0000	−0.397360
$913$	−12.0000	−0.397142
$914$	48.0000	1.58770
$915$	−18.0000	−0.595062
$916$	32.0000	1.05731
$917$	14.0000	0.462321
$918$	−54.0000	−1.78227
$919$	35.0000	1.15454	0.577272	−	0.816552i	$-0.304117\pi$
$919$	35.0000	1.15454	0.577272	+	0.816552i	$0.304117\pi$
$920$	0	0
$921$	−9.00000	−0.296560
$922$	−68.0000	−2.23946
$923$	0	0
$924$	−18.0000	−0.592157
$925$	−4.00000	−0.131519
$926$	−12.0000	−0.394344
$927$	18.0000	0.591198
$928$	8.00000	0.262613
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	−48.0000	−1.57398
$931$	1.00000	0.0327737
$932$	12.0000	0.393073
$933$	42.0000	1.37502
$934$	−6.00000	−0.196326
$935$	−9.00000	−0.294331
$936$	0	0
$937$	−37.0000	−1.20874	−0.604369	−	0.796705i	$-0.706575\pi$
$937$	−37.0000	−1.20874	−0.604369	+	0.796705i	$0.706575\pi$
$938$	−8.00000	−0.261209
$939$	27.0000	0.881112
$940$	2.00000	0.0652328
$941$	38.0000	1.23876	0.619382	−	0.785090i	$-0.287383\pi$
$941$	38.0000	1.23876	0.619382	+	0.785090i	$0.287383\pi$
$942$	108.000	3.51883
$943$	32.0000	1.04206
$944$	−24.0000	−0.781133
$945$	9.00000	0.292770
$946$	−24.0000	−0.780307
$947$	−48.0000	−1.55979	−0.779895	−	0.625910i	$-0.784728\pi$
$947$	−48.0000	−1.55979	−0.779895	+	0.625910i	$0.784728\pi$
$948$	78.0000	2.53332
$949$	30.0000	0.973841
$950$	−2.00000	−0.0648886
$951$	30.0000	0.972817
$952$	0	0
$953$	22.0000	0.712650	0.356325	−	0.934362i	$-0.384030\pi$
$953$	22.0000	0.712650	0.356325	+	0.934362i	$0.384030\pi$
$954$	144.000	4.66217
$955$	−27.0000	−0.873699
$956$	46.0000	1.48775
$957$	−9.00000	−0.290929
$958$	−80.0000	−2.58468
$959$	−12.0000	−0.387500
$960$	−24.0000	−0.774597
$961$	33.0000	1.06452
$962$	24.0000	0.773791
$963$	−120.000	−3.86695
$964$	−36.0000	−1.15948
$965$	20.0000	0.643823
$966$	24.0000	0.772187
$967$	24.0000	0.771788	0.385894	−	0.922543i	$-0.373893\pi$
$967$	24.0000	0.771788	0.385894	+	0.922543i	$0.373893\pi$
$968$	0	0
$969$	9.00000	0.289122
$970$	−10.0000	−0.321081
$971$	−6.00000	−0.192549	−0.0962746	−	0.995355i	$-0.530693\pi$
$971$	−6.00000	−0.192549	−0.0962746	+	0.995355i	$0.530693\pi$
$972$	0	0
$973$	12.0000	0.384702
$974$	40.0000	1.28168
$975$	9.00000	0.288231
$976$	24.0000	0.768221
$977$	56.0000	1.79160	0.895799	−	0.444459i	$-0.146604\pi$
$977$	56.0000	1.79160	0.895799	+	0.444459i	$0.146604\pi$
$978$	132.000	4.22089
$979$	18.0000	0.575282
$980$	2.00000	0.0638877
$981$	42.0000	1.34096
$982$	−54.0000	−1.72321
$983$	9.00000	0.287055	0.143528	−	0.989646i	$-0.454155\pi$
$983$	9.00000	0.287055	0.143528	+	0.989646i	$0.454155\pi$
$984$	0	0
$985$	−6.00000	−0.191176
$986$	−6.00000	−0.191079
$987$	3.00000	0.0954911
$988$	6.00000	0.190885
$989$	16.0000	0.508770
$990$	36.0000	1.14416
$991$	−16.0000	−0.508257	−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000	−0.508257	−0.254128	+	0.967170i	$0.581789\pi$
$992$	64.0000	2.03200
$993$	−72.0000	−2.28485
$994$	0	0
$995$	18.0000	0.570638
$996$	24.0000	0.760469
$997$	43.0000	1.36182	0.680912	−	0.732365i	$-0.261584\pi$
$997$	43.0000	1.36182	0.680912	+	0.732365i	$0.261584\pi$
$998$	−50.0000	−1.58272
$999$	−36.0000	−1.13899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	665.2.a.b.1.1	✓	1
3.2	odd	2		5985.2.a.r.1.1		1
5.4	even	2		3325.2.a.i.1.1		1
7.6	odd	2		4655.2.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
665.2.a.b.1.1	✓	1	1.1	even	1	trivial
3325.2.a.i.1.1		1	5.4	even	2
4655.2.a.a.1.1		1	7.6	odd	2
5985.2.a.r.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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 665 = 5 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	665.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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