LMFDB - Embedded newform 9555.2.a.u.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9555,2,Mod(1,9555)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9555, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("9555.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9555 = 3 \cdot 5 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9555.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:	$76.2970591313$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	9555.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+2.00000 q^{2} -1.00000 q^{3} +2.00000 q^{4} +1.00000 q^{5} -2.00000 q^{6} +1.00000 q^{9} +2.00000 q^{10} +5.00000 q^{11} -2.00000 q^{12} +1.00000 q^{13} -1.00000 q^{15} -4.00000 q^{16} +7.00000 q^{17} +2.00000 q^{18} +6.00000 q^{19} +2.00000 q^{20} +10.0000 q^{22} +3.00000 q^{23} +1.00000 q^{25} +2.00000 q^{26} -1.00000 q^{27} +2.00000 q^{29} -2.00000 q^{30} -2.00000 q^{31} -8.00000 q^{32} -5.00000 q^{33} +14.0000 q^{34} +2.00000 q^{36} +7.00000 q^{37} +12.0000 q^{38} -1.00000 q^{39} -9.00000 q^{41} -8.00000 q^{43} +10.0000 q^{44} +1.00000 q^{45} +6.00000 q^{46} -10.0000 q^{47} +4.00000 q^{48} +2.00000 q^{50} -7.00000 q^{51} +2.00000 q^{52} +5.00000 q^{53} -2.00000 q^{54} +5.00000 q^{55} -6.00000 q^{57} +4.00000 q^{58} -2.00000 q^{60} -5.00000 q^{61} -4.00000 q^{62} -8.00000 q^{64} +1.00000 q^{65} -10.0000 q^{66} -4.00000 q^{67} +14.0000 q^{68} -3.00000 q^{69} +9.00000 q^{71} +6.00000 q^{73} +14.0000 q^{74} -1.00000 q^{75} +12.0000 q^{76} -2.00000 q^{78} -3.00000 q^{79} -4.00000 q^{80} +1.00000 q^{81} -18.0000 q^{82} +4.00000 q^{83} +7.00000 q^{85} -16.0000 q^{86} -2.00000 q^{87} -11.0000 q^{89} +2.00000 q^{90} +6.00000 q^{92} +2.00000 q^{93} -20.0000 q^{94} +6.00000 q^{95} +8.00000 q^{96} +11.0000 q^{97} +5.00000 q^{99} +O(q^{100})\)

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	$-0.250000\pi$
$2$	2.00000	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.00000	1.00000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.00000	−0.816497
$7$	0	0
$7$	0	0
$8$	0	0
$9$	1.00000	0.333333
$10$	2.00000	0.632456
$11$	5.00000	1.50756	0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000	1.50756	0.753778	+	0.657129i	$0.228229\pi$
$12$	−2.00000	−0.577350
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	−1.00000	−0.258199
$16$	−4.00000	−1.00000
$17$	7.00000	1.69775	0.848875	−	0.528594i	$-0.177281\pi$
$17$	7.00000	1.69775	0.848875	+	0.528594i	$0.177281\pi$
$18$	2.00000	0.471405
$19$	6.00000	1.37649	0.688247	−	0.725476i	$-0.258380\pi$
$19$	6.00000	1.37649	0.688247	+	0.725476i	$0.258380\pi$
$20$	2.00000	0.447214
$21$	0	0
$22$	10.0000	2.13201
$23$	3.00000	0.625543	0.312772	−	0.949828i	$-0.398743\pi$
$23$	3.00000	0.625543	0.312772	+	0.949828i	$0.398743\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	2.00000	0.392232
$27$	−1.00000	−0.192450
$28$	0	0
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	−2.00000	−0.365148
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	−8.00000	−1.41421
$33$	−5.00000	−0.870388
$34$	14.0000	2.40098
$35$	0	0
$36$	2.00000	0.333333
$37$	7.00000	1.15079	0.575396	−	0.817875i	$-0.304848\pi$
$37$	7.00000	1.15079	0.575396	+	0.817875i	$0.304848\pi$
$38$	12.0000	1.94666
$39$	−1.00000	−0.160128
$40$	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
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	10.0000	1.50756
$45$	1.00000	0.149071
$46$	6.00000	0.884652
$47$	−10.0000	−1.45865	−0.729325	−	0.684167i	$-0.760166\pi$
$47$	−10.0000	−1.45865	−0.729325	+	0.684167i	$0.760166\pi$
$48$	4.00000	0.577350
$49$	0	0
$50$	2.00000	0.282843
$51$	−7.00000	−0.980196
$52$	2.00000	0.277350
$53$	5.00000	0.686803	0.343401	−	0.939189i	$-0.388421\pi$
$53$	5.00000	0.686803	0.343401	+	0.939189i	$0.388421\pi$
$54$	−2.00000	−0.272166
$55$	5.00000	0.674200
$56$	0	0
$57$	−6.00000	−0.794719
$58$	4.00000	0.525226
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	−2.00000	−0.258199
$61$	−5.00000	−0.640184	−0.320092	−	0.947386i	$-0.603714\pi$
$61$	−5.00000	−0.640184	−0.320092	+	0.947386i	$0.603714\pi$
$62$	−4.00000	−0.508001
$63$	0	0
$64$	−8.00000	−1.00000
$65$	1.00000	0.124035
$66$	−10.0000	−1.23091
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	14.0000	1.69775
$69$	−3.00000	−0.361158
$70$	0	0
$71$	9.00000	1.06810	0.534052	−	0.845452i	$-0.320669\pi$
$71$	9.00000	1.06810	0.534052	+	0.845452i	$0.320669\pi$
$72$	0	0
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	14.0000	1.62747
$75$	−1.00000	−0.115470
$76$	12.0000	1.37649
$77$	0	0
$78$	−2.00000	−0.226455
$79$	−3.00000	−0.337526	−0.168763	−	0.985657i	$-0.553977\pi$
$79$	−3.00000	−0.337526	−0.168763	+	0.985657i	$0.553977\pi$
$80$	−4.00000	−0.447214
$81$	1.00000	0.111111
$82$	−18.0000	−1.98777
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	0	0
$85$	7.00000	0.759257
$86$	−16.0000	−1.72532
$87$	−2.00000	−0.214423
$88$	0	0
$89$	−11.0000	−1.16600	−0.582999	−	0.812473i	$-0.698121\pi$
$89$	−11.0000	−1.16600	−0.582999	+	0.812473i	$0.698121\pi$
$90$	2.00000	0.210819
$91$	0	0
$92$	6.00000	0.625543
$93$	2.00000	0.207390
$94$	−20.0000	−2.06284
$95$	6.00000	0.615587
$96$	8.00000	0.816497
$97$	11.0000	1.11688	0.558440	−	0.829545i	$-0.311400\pi$
$97$	11.0000	1.11688	0.558440	+	0.829545i	$0.311400\pi$
$98$	0	0
$99$	5.00000	0.502519
$100$	2.00000	0.200000
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	−14.0000	−1.38621
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	0	0
$105$	0	0
$106$	10.0000	0.971286
$107$	−17.0000	−1.64345	−0.821726	−	0.569883i	$-0.806989\pi$
$107$	−17.0000	−1.64345	−0.821726	+	0.569883i	$0.806989\pi$
$108$	−2.00000	−0.192450
$109$	4.00000	0.383131	0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000	0.383131	0.191565	+	0.981480i	$0.438644\pi$
$110$	10.0000	0.953463
$111$	−7.00000	−0.664411
$112$	0	0
$113$	10.0000	0.940721	0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000	0.940721	0.470360	+	0.882474i	$0.344124\pi$
$114$	−12.0000	−1.12390
$115$	3.00000	0.279751
$116$	4.00000	0.371391
$117$	1.00000	0.0924500
$118$	0	0
$119$	0	0
$120$	0	0
$121$	14.0000	1.27273
$122$	−10.0000	−0.905357
$123$	9.00000	0.811503
$124$	−4.00000	−0.359211
$125$	1.00000	0.0894427
$126$	0	0
$127$	−2.00000	−0.177471	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000	−0.177471	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	0	0
$129$	8.00000	0.704361
$130$	2.00000	0.175412
$131$	22.0000	1.92215	0.961074	−	0.276289i	$-0.0891049\pi$
$131$	22.0000	1.92215	0.961074	+	0.276289i	$0.0891049\pi$
$132$	−10.0000	−0.870388
$133$	0	0
$134$	−8.00000	−0.691095
$135$	−1.00000	−0.0860663
$136$	0	0
$137$	−14.0000	−1.19610	−0.598050	−	0.801459i	$-0.704058\pi$
$137$	−14.0000	−1.19610	−0.598050	+	0.801459i	$0.704058\pi$
$138$	−6.00000	−0.510754
$139$	−15.0000	−1.27228	−0.636142	−	0.771572i	$-0.719471\pi$
$139$	−15.0000	−1.27228	−0.636142	+	0.771572i	$0.719471\pi$
$140$	0	0
$141$	10.0000	0.842152
$142$	18.0000	1.51053
$143$	5.00000	0.418121
$144$	−4.00000	−0.333333
$145$	2.00000	0.166091
$146$	12.0000	0.993127
$147$	0	0
$148$	14.0000	1.15079
$149$	15.0000	1.22885	0.614424	−	0.788976i	$-0.289388\pi$
$149$	15.0000	1.22885	0.614424	+	0.788976i	$0.289388\pi$
$150$	−2.00000	−0.163299
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	0	0
$153$	7.00000	0.565916
$154$	0	0
$155$	−2.00000	−0.160644
$156$	−2.00000	−0.160128
$157$	−18.0000	−1.43656	−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000	−1.43656	−0.718278	+	0.695756i	$0.755069\pi$
$158$	−6.00000	−0.477334
$159$	−5.00000	−0.396526
$160$	−8.00000	−0.632456
$161$	0	0
$162$	2.00000	0.157135
$163$	15.0000	1.17489	0.587445	−	0.809264i	$-0.300134\pi$
$163$	15.0000	1.17489	0.587445	+	0.809264i	$0.300134\pi$
$164$	−18.0000	−1.40556
$165$	−5.00000	−0.389249
$166$	8.00000	0.620920
$167$	24.0000	1.85718	0.928588	−	0.371113i	$-0.121024\pi$
$167$	24.0000	1.85718	0.928588	+	0.371113i	$0.121024\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	14.0000	1.07375
$171$	6.00000	0.458831
$172$	−16.0000	−1.21999
$173$	18.0000	1.36851	0.684257	−	0.729241i	$-0.260127\pi$
$173$	18.0000	1.36851	0.684257	+	0.729241i	$0.260127\pi$
$174$	−4.00000	−0.303239
$175$	0	0
$176$	−20.0000	−1.50756
$177$	0	0
$178$	−22.0000	−1.64897
$179$	6.00000	0.448461	0.224231	−	0.974536i	$-0.428013\pi$
$179$	6.00000	0.448461	0.224231	+	0.974536i	$0.428013\pi$
$180$	2.00000	0.149071
$181$	7.00000	0.520306	0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000	0.520306	0.260153	+	0.965567i	$0.416227\pi$
$182$	0	0
$183$	5.00000	0.369611
$184$	0	0
$185$	7.00000	0.514650
$186$	4.00000	0.293294
$187$	35.0000	2.55945
$188$	−20.0000	−1.45865
$189$	0	0
$190$	12.0000	0.870572
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	8.00000	0.577350
$193$	−17.0000	−1.22369	−0.611843	−	0.790979i	$-0.709572\pi$
$193$	−17.0000	−1.22369	−0.611843	+	0.790979i	$0.709572\pi$
$194$	22.0000	1.57951
$195$	−1.00000	−0.0716115
$196$	0	0
$197$	24.0000	1.70993	0.854965	−	0.518686i	$-0.173579\pi$
$197$	24.0000	1.70993	0.854965	+	0.518686i	$0.173579\pi$
$198$	10.0000	0.710669
$199$	28.0000	1.98487	0.992434	−	0.122782i	$-0.0391815\pi$
$199$	28.0000	1.98487	0.992434	+	0.122782i	$0.0391815\pi$
$200$	0	0
$201$	4.00000	0.282138
$202$	0	0
$203$	0	0
$204$	−14.0000	−0.980196
$205$	−9.00000	−0.628587
$206$	8.00000	0.557386
$207$	3.00000	0.208514
$208$	−4.00000	−0.277350
$209$	30.0000	2.07514
$210$	0	0
$211$	−12.0000	−0.826114	−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000	−0.826114	−0.413057	+	0.910705i	$0.635539\pi$
$212$	10.0000	0.686803
$213$	−9.00000	−0.616670
$214$	−34.0000	−2.32419
$215$	−8.00000	−0.545595
$216$	0	0
$217$	0	0
$218$	8.00000	0.541828
$219$	−6.00000	−0.405442
$220$	10.0000	0.674200
$221$	7.00000	0.470871
$222$	−14.0000	−0.939618
$223$	8.00000	0.535720	0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000	0.535720	0.267860	+	0.963458i	$0.413684\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	20.0000	1.33038
$227$	2.00000	0.132745	0.0663723	−	0.997795i	$-0.478857\pi$
$227$	2.00000	0.132745	0.0663723	+	0.997795i	$0.478857\pi$
$228$	−12.0000	−0.794719
$229$	−14.0000	−0.925146	−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000	−0.925146	−0.462573	+	0.886581i	$0.653074\pi$
$230$	6.00000	0.395628
$231$	0	0
$232$	0	0
$233$	19.0000	1.24473	0.622366	−	0.782727i	$-0.286172\pi$
$233$	19.0000	1.24473	0.622366	+	0.782727i	$0.286172\pi$
$234$	2.00000	0.130744
$235$	−10.0000	−0.652328
$236$	0	0
$237$	3.00000	0.194871
$238$	0	0
$239$	9.00000	0.582162	0.291081	−	0.956698i	$-0.405985\pi$
$239$	9.00000	0.582162	0.291081	+	0.956698i	$0.405985\pi$
$240$	4.00000	0.258199
$241$	−22.0000	−1.41714	−0.708572	−	0.705638i	$-0.750660\pi$
$241$	−22.0000	−1.41714	−0.708572	+	0.705638i	$0.750660\pi$
$242$	28.0000	1.79991
$243$	−1.00000	−0.0641500
$244$	−10.0000	−0.640184
$245$	0	0
$246$	18.0000	1.14764
$247$	6.00000	0.381771
$248$	0	0
$249$	−4.00000	−0.253490
$250$	2.00000	0.126491
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	15.0000	0.943042
$254$	−4.00000	−0.250982
$255$	−7.00000	−0.438357
$256$	16.0000	1.00000
$257$	−2.00000	−0.124757	−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	−2.00000	−0.124757	−0.0623783	+	0.998053i	$0.519869\pi$
$258$	16.0000	0.996116
$259$	0	0
$260$	2.00000	0.124035
$261$	2.00000	0.123797
$262$	44.0000	2.71833
$263$	−16.0000	−0.986602	−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000	−0.986602	−0.493301	+	0.869859i	$0.664210\pi$
$264$	0	0
$265$	5.00000	0.307148
$266$	0	0
$267$	11.0000	0.673189
$268$	−8.00000	−0.488678
$269$	24.0000	1.46331	0.731653	−	0.681677i	$-0.238749\pi$
$269$	24.0000	1.46331	0.731653	+	0.681677i	$0.238749\pi$
$270$	−2.00000	−0.121716
$271$	22.0000	1.33640	0.668202	−	0.743980i	$-0.267064\pi$
$271$	22.0000	1.33640	0.668202	+	0.743980i	$0.267064\pi$
$272$	−28.0000	−1.69775
$273$	0	0
$274$	−28.0000	−1.69154
$275$	5.00000	0.301511
$276$	−6.00000	−0.361158
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	−30.0000	−1.79928
$279$	−2.00000	−0.119737
$280$	0	0
$281$	18.0000	1.07379	0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000	1.07379	0.536895	+	0.843649i	$0.319597\pi$
$282$	20.0000	1.19098
$283$	−20.0000	−1.18888	−0.594438	−	0.804141i	$-0.702626\pi$
$283$	−20.0000	−1.18888	−0.594438	+	0.804141i	$0.702626\pi$
$284$	18.0000	1.06810
$285$	−6.00000	−0.355409
$286$	10.0000	0.591312
$287$	0	0
$288$	−8.00000	−0.471405
$289$	32.0000	1.88235
$290$	4.00000	0.234888
$291$	−11.0000	−0.644831
$292$	12.0000	0.702247
$293$	−4.00000	−0.233682	−0.116841	−	0.993151i	$-0.537277\pi$
$293$	−4.00000	−0.233682	−0.116841	+	0.993151i	$0.537277\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−5.00000	−0.290129
$298$	30.0000	1.73785
$299$	3.00000	0.173494
$300$	−2.00000	−0.115470
$301$	0	0
$302$	−16.0000	−0.920697
$303$	0	0
$304$	−24.0000	−1.37649
$305$	−5.00000	−0.286299
$306$	14.0000	0.800327
$307$	−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
$309$	−4.00000	−0.227552
$310$	−4.00000	−0.227185
$311$	−20.0000	−1.13410	−0.567048	−	0.823685i	$-0.691915\pi$
$311$	−20.0000	−1.13410	−0.567048	+	0.823685i	$0.691915\pi$
$312$	0	0
$313$	22.0000	1.24351	0.621757	−	0.783210i	$-0.286419\pi$
$313$	22.0000	1.24351	0.621757	+	0.783210i	$0.286419\pi$
$314$	−36.0000	−2.03160
$315$	0	0
$316$	−6.00000	−0.337526
$317$	−24.0000	−1.34797	−0.673987	−	0.738743i	$-0.735420\pi$
$317$	−24.0000	−1.34797	−0.673987	+	0.738743i	$0.735420\pi$
$318$	−10.0000	−0.560772
$319$	10.0000	0.559893
$320$	−8.00000	−0.447214
$321$	17.0000	0.948847
$322$	0	0
$323$	42.0000	2.33694
$324$	2.00000	0.111111
$325$	1.00000	0.0554700
$326$	30.0000	1.66155
$327$	−4.00000	−0.221201
$328$	0	0
$329$	0	0
$330$	−10.0000	−0.550482
$331$	0	0		−	1.00000i	$-0.5\pi$
$331$	0	0			1.00000i	$0.5\pi$
$332$	8.00000	0.439057
$333$	7.00000	0.383598
$334$	48.0000	2.62644
$335$	−4.00000	−0.218543
$336$	0	0
$337$	8.00000	0.435788	0.217894	−	0.975972i	$-0.430081\pi$
$337$	8.00000	0.435788	0.217894	+	0.975972i	$0.430081\pi$
$338$	2.00000	0.108786
$339$	−10.0000	−0.543125
$340$	14.0000	0.759257
$341$	−10.0000	−0.541530
$342$	12.0000	0.648886
$343$	0	0
$344$	0	0
$345$	−3.00000	−0.161515
$346$	36.0000	1.93537
$347$	11.0000	0.590511	0.295255	−	0.955418i	$-0.404595\pi$
$347$	11.0000	0.590511	0.295255	+	0.955418i	$0.404595\pi$
$348$	−4.00000	−0.214423
$349$	−24.0000	−1.28469	−0.642345	−	0.766415i	$-0.722038\pi$
$349$	−24.0000	−1.28469	−0.642345	+	0.766415i	$0.722038\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	−40.0000	−2.13201
$353$	6.00000	0.319348	0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000	0.319348	0.159674	+	0.987170i	$0.448956\pi$
$354$	0	0
$355$	9.00000	0.477670
$356$	−22.0000	−1.16600
$357$	0	0
$358$	12.0000	0.634220
$359$	−16.0000	−0.844448	−0.422224	−	0.906492i	$-0.638750\pi$
$359$	−16.0000	−0.844448	−0.422224	+	0.906492i	$0.638750\pi$
$360$	0	0
$361$	17.0000	0.894737
$362$	14.0000	0.735824
$363$	−14.0000	−0.734809
$364$	0	0
$365$	6.00000	0.314054
$366$	10.0000	0.522708
$367$	−4.00000	−0.208798	−0.104399	−	0.994535i	$-0.533292\pi$
$367$	−4.00000	−0.208798	−0.104399	+	0.994535i	$0.533292\pi$
$368$	−12.0000	−0.625543
$369$	−9.00000	−0.468521
$370$	14.0000	0.727825
$371$	0	0
$372$	4.00000	0.207390
$373$	−32.0000	−1.65690	−0.828449	−	0.560065i	$-0.810776\pi$
$373$	−32.0000	−1.65690	−0.828449	+	0.560065i	$0.810776\pi$
$374$	70.0000	3.61961
$375$	−1.00000	−0.0516398
$376$	0	0
$377$	2.00000	0.103005
$378$	0	0
$379$	10.0000	0.513665	0.256833	−	0.966456i	$-0.417321\pi$
$379$	10.0000	0.513665	0.256833	+	0.966456i	$0.417321\pi$
$380$	12.0000	0.615587
$381$	2.00000	0.102463
$382$	−24.0000	−1.22795
$383$	6.00000	0.306586	0.153293	−	0.988181i	$-0.451012\pi$
$383$	6.00000	0.306586	0.153293	+	0.988181i	$0.451012\pi$
$384$	0	0
$385$	0	0
$386$	−34.0000	−1.73055
$387$	−8.00000	−0.406663
$388$	22.0000	1.11688
$389$	−4.00000	−0.202808	−0.101404	−	0.994845i	$-0.532333\pi$
$389$	−4.00000	−0.202808	−0.101404	+	0.994845i	$0.532333\pi$
$390$	−2.00000	−0.101274
$391$	21.0000	1.06202
$392$	0	0
$393$	−22.0000	−1.10975
$394$	48.0000	2.41821
$395$	−3.00000	−0.150946
$396$	10.0000	0.502519
$397$	−15.0000	−0.752828	−0.376414	−	0.926451i	$-0.622843\pi$
$397$	−15.0000	−0.752828	−0.376414	+	0.926451i	$0.622843\pi$
$398$	56.0000	2.80703
$399$	0	0
$400$	−4.00000	−0.200000
$401$	−14.0000	−0.699127	−0.349563	−	0.936913i	$-0.613670\pi$
$401$	−14.0000	−0.699127	−0.349563	+	0.936913i	$0.613670\pi$
$402$	8.00000	0.399004
$403$	−2.00000	−0.0996271
$404$	0	0
$405$	1.00000	0.0496904
$406$	0	0
$407$	35.0000	1.73489
$408$	0	0
$409$	−30.0000	−1.48340	−0.741702	−	0.670729i	$-0.765981\pi$
$409$	−30.0000	−1.48340	−0.741702	+	0.670729i	$0.765981\pi$
$410$	−18.0000	−0.888957
$411$	14.0000	0.690569
$412$	8.00000	0.394132
$413$	0	0
$414$	6.00000	0.294884
$415$	4.00000	0.196352
$416$	−8.00000	−0.392232
$417$	15.0000	0.734553
$418$	60.0000	2.93470
$419$	−26.0000	−1.27018	−0.635092	−	0.772437i	$-0.719038\pi$
$419$	−26.0000	−1.27018	−0.635092	+	0.772437i	$0.719038\pi$
$420$	0	0
$421$	−20.0000	−0.974740	−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000	−0.974740	−0.487370	+	0.873195i	$0.662044\pi$
$422$	−24.0000	−1.16830
$423$	−10.0000	−0.486217
$424$	0	0
$425$	7.00000	0.339550
$426$	−18.0000	−0.872103
$427$	0	0
$428$	−34.0000	−1.64345
$429$	−5.00000	−0.241402
$430$	−16.0000	−0.771589
$431$	−40.0000	−1.92673	−0.963366	−	0.268190i	$-0.913575\pi$
$431$	−40.0000	−1.92673	−0.963366	+	0.268190i	$0.913575\pi$
$432$	4.00000	0.192450
$433$	20.0000	0.961139	0.480569	−	0.876957i	$-0.340430\pi$
$433$	20.0000	0.961139	0.480569	+	0.876957i	$0.340430\pi$
$434$	0	0
$435$	−2.00000	−0.0958927
$436$	8.00000	0.383131
$437$	18.0000	0.861057
$438$	−12.0000	−0.573382
$439$	−15.0000	−0.715911	−0.357955	−	0.933739i	$-0.616526\pi$
$439$	−15.0000	−0.715911	−0.357955	+	0.933739i	$0.616526\pi$
$440$	0	0
$441$	0	0
$442$	14.0000	0.665912
$443$	−1.00000	−0.0475114	−0.0237557	−	0.999718i	$-0.507562\pi$
$443$	−1.00000	−0.0475114	−0.0237557	+	0.999718i	$0.507562\pi$
$444$	−14.0000	−0.664411
$445$	−11.0000	−0.521450
$446$	16.0000	0.757622
$447$	−15.0000	−0.709476
$448$	0	0
$449$	9.00000	0.424736	0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000	0.424736	0.212368	+	0.977190i	$0.431882\pi$
$450$	2.00000	0.0942809
$451$	−45.0000	−2.11897
$452$	20.0000	0.940721
$453$	8.00000	0.375873
$454$	4.00000	0.187729
$455$	0	0
$456$	0	0
$457$	−7.00000	−0.327446	−0.163723	−	0.986506i	$-0.552350\pi$
$457$	−7.00000	−0.327446	−0.163723	+	0.986506i	$0.552350\pi$
$458$	−28.0000	−1.30835
$459$	−7.00000	−0.326732
$460$	6.00000	0.279751
$461$	−37.0000	−1.72326	−0.861631	−	0.507535i	$-0.830557\pi$
$461$	−37.0000	−1.72326	−0.861631	+	0.507535i	$0.830557\pi$
$462$	0	0
$463$	15.0000	0.697109	0.348555	−	0.937288i	$-0.386673\pi$
$463$	15.0000	0.697109	0.348555	+	0.937288i	$0.386673\pi$
$464$	−8.00000	−0.371391
$465$	2.00000	0.0927478
$466$	38.0000	1.76032
$467$	1.00000	0.0462745	0.0231372	−	0.999732i	$-0.492635\pi$
$467$	1.00000	0.0462745	0.0231372	+	0.999732i	$0.492635\pi$
$468$	2.00000	0.0924500
$469$	0	0
$470$	−20.0000	−0.922531
$471$	18.0000	0.829396
$472$	0	0
$473$	−40.0000	−1.83920
$474$	6.00000	0.275589
$475$	6.00000	0.275299
$476$	0	0
$477$	5.00000	0.228934
$478$	18.0000	0.823301
$479$	−3.00000	−0.137073	−0.0685367	−	0.997649i	$-0.521833\pi$
$479$	−3.00000	−0.137073	−0.0685367	+	0.997649i	$0.521833\pi$
$480$	8.00000	0.365148
$481$	7.00000	0.319173
$482$	−44.0000	−2.00415
$483$	0	0
$484$	28.0000	1.27273
$485$	11.0000	0.499484
$486$	−2.00000	−0.0907218
$487$	5.00000	0.226572	0.113286	−	0.993562i	$-0.463862\pi$
$487$	5.00000	0.226572	0.113286	+	0.993562i	$0.463862\pi$
$488$	0	0
$489$	−15.0000	−0.678323
$490$	0	0
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	18.0000	0.811503
$493$	14.0000	0.630528
$494$	12.0000	0.539906
$495$	5.00000	0.224733
$496$	8.00000	0.359211
$497$	0	0
$498$	−8.00000	−0.358489
$499$	−14.0000	−0.626726	−0.313363	−	0.949633i	$-0.601456\pi$
$499$	−14.0000	−0.626726	−0.313363	+	0.949633i	$0.601456\pi$
$500$	2.00000	0.0894427
$501$	−24.0000	−1.07224
$502$	0	0
$503$	−36.0000	−1.60516	−0.802580	−	0.596544i	$-0.796540\pi$
$503$	−36.0000	−1.60516	−0.802580	+	0.596544i	$0.796540\pi$
$504$	0	0
$505$	0	0
$506$	30.0000	1.33366
$507$	−1.00000	−0.0444116
$508$	−4.00000	−0.177471
$509$	−27.0000	−1.19675	−0.598377	−	0.801215i	$-0.704187\pi$
$509$	−27.0000	−1.19675	−0.598377	+	0.801215i	$0.704187\pi$
$510$	−14.0000	−0.619930
$511$	0	0
$512$	32.0000	1.41421
$513$	−6.00000	−0.264906
$514$	−4.00000	−0.176432
$515$	4.00000	0.176261
$516$	16.0000	0.704361
$517$	−50.0000	−2.19900
$518$	0	0
$519$	−18.0000	−0.790112
$520$	0	0
$521$	18.0000	0.788594	0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000	0.788594	0.394297	+	0.918983i	$0.370988\pi$
$522$	4.00000	0.175075
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	44.0000	1.92215
$525$	0	0
$526$	−32.0000	−1.39527
$527$	−14.0000	−0.609850
$528$	20.0000	0.870388
$529$	−14.0000	−0.608696
$530$	10.0000	0.434372
$531$	0	0
$532$	0	0
$533$	−9.00000	−0.389833
$534$	22.0000	0.952033
$535$	−17.0000	−0.734974
$536$	0	0
$537$	−6.00000	−0.258919
$538$	48.0000	2.06943
$539$	0	0
$540$	−2.00000	−0.0860663
$541$	38.0000	1.63375	0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000	1.63375	0.816874	+	0.576816i	$0.195705\pi$
$542$	44.0000	1.88996
$543$	−7.00000	−0.300399
$544$	−56.0000	−2.40098
$545$	4.00000	0.171341
$546$	0	0
$547$	36.0000	1.53925	0.769624	−	0.638497i	$-0.220443\pi$
$547$	36.0000	1.53925	0.769624	+	0.638497i	$0.220443\pi$
$548$	−28.0000	−1.19610
$549$	−5.00000	−0.213395
$550$	10.0000	0.426401
$551$	12.0000	0.511217
$552$	0	0
$553$	0	0
$554$	−4.00000	−0.169944
$555$	−7.00000	−0.297133
$556$	−30.0000	−1.27228
$557$	−2.00000	−0.0847427	−0.0423714	−	0.999102i	$-0.513491\pi$
$557$	−2.00000	−0.0847427	−0.0423714	+	0.999102i	$0.513491\pi$
$558$	−4.00000	−0.169334
$559$	−8.00000	−0.338364
$560$	0	0
$561$	−35.0000	−1.47770
$562$	36.0000	1.51857
$563$	−11.0000	−0.463595	−0.231797	−	0.972764i	$-0.574461\pi$
$563$	−11.0000	−0.463595	−0.231797	+	0.972764i	$0.574461\pi$
$564$	20.0000	0.842152
$565$	10.0000	0.420703
$566$	−40.0000	−1.68133
$567$	0	0
$568$	0	0
$569$	−20.0000	−0.838444	−0.419222	−	0.907884i	$-0.637697\pi$
$569$	−20.0000	−0.838444	−0.419222	+	0.907884i	$0.637697\pi$
$570$	−12.0000	−0.502625
$571$	−39.0000	−1.63210	−0.816050	−	0.577982i	$-0.803840\pi$
$571$	−39.0000	−1.63210	−0.816050	+	0.577982i	$0.803840\pi$
$572$	10.0000	0.418121
$573$	12.0000	0.501307
$574$	0	0
$575$	3.00000	0.125109
$576$	−8.00000	−0.333333
$577$	7.00000	0.291414	0.145707	−	0.989328i	$-0.453454\pi$
$577$	7.00000	0.291414	0.145707	+	0.989328i	$0.453454\pi$
$578$	64.0000	2.66205
$579$	17.0000	0.706496
$580$	4.00000	0.166091
$581$	0	0
$582$	−22.0000	−0.911929
$583$	25.0000	1.03539
$584$	0	0
$585$	1.00000	0.0413449
$586$	−8.00000	−0.330477
$587$	2.00000	0.0825488	0.0412744	−	0.999148i	$-0.486858\pi$
$587$	2.00000	0.0825488	0.0412744	+	0.999148i	$0.486858\pi$
$588$	0	0
$589$	−12.0000	−0.494451
$590$	0	0
$591$	−24.0000	−0.987228
$592$	−28.0000	−1.15079
$593$	16.0000	0.657041	0.328521	−	0.944497i	$-0.393450\pi$
$593$	16.0000	0.657041	0.328521	+	0.944497i	$0.393450\pi$
$594$	−10.0000	−0.410305
$595$	0	0
$596$	30.0000	1.22885
$597$	−28.0000	−1.14596
$598$	6.00000	0.245358
$599$	20.0000	0.817178	0.408589	−	0.912719i	$-0.366021\pi$
$599$	20.0000	0.817178	0.408589	+	0.912719i	$0.366021\pi$
$600$	0	0
$601$	5.00000	0.203954	0.101977	−	0.994787i	$-0.467483\pi$
$601$	5.00000	0.203954	0.101977	+	0.994787i	$0.467483\pi$
$602$	0	0
$603$	−4.00000	−0.162893
$604$	−16.0000	−0.651031
$605$	14.0000	0.569181
$606$	0	0
$607$	32.0000	1.29884	0.649420	−	0.760430i	$-0.275012\pi$
$607$	32.0000	1.29884	0.649420	+	0.760430i	$0.275012\pi$
$608$	−48.0000	−1.94666
$609$	0	0
$610$	−10.0000	−0.404888
$611$	−10.0000	−0.404557
$612$	14.0000	0.565916
$613$	9.00000	0.363507	0.181753	−	0.983344i	$-0.441823\pi$
$613$	9.00000	0.363507	0.181753	+	0.983344i	$0.441823\pi$
$614$	−46.0000	−1.85641
$615$	9.00000	0.362915
$616$	0	0
$617$	18.0000	0.724653	0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000	0.724653	0.362326	+	0.932051i	$0.381983\pi$
$618$	−8.00000	−0.321807
$619$	38.0000	1.52735	0.763674	−	0.645601i	$-0.223393\pi$
$619$	38.0000	1.52735	0.763674	+	0.645601i	$0.223393\pi$
$620$	−4.00000	−0.160644
$621$	−3.00000	−0.120386
$622$	−40.0000	−1.60385
$623$	0	0
$624$	4.00000	0.160128
$625$	1.00000	0.0400000
$626$	44.0000	1.75859
$627$	−30.0000	−1.19808
$628$	−36.0000	−1.43656
$629$	49.0000	1.95376
$630$	0	0
$631$	−20.0000	−0.796187	−0.398094	−	0.917345i	$-0.630328\pi$
$631$	−20.0000	−0.796187	−0.398094	+	0.917345i	$0.630328\pi$
$632$	0	0
$633$	12.0000	0.476957
$634$	−48.0000	−1.90632
$635$	−2.00000	−0.0793676
$636$	−10.0000	−0.396526
$637$	0	0
$638$	20.0000	0.791808
$639$	9.00000	0.356034
$640$	0	0
$641$	20.0000	0.789953	0.394976	−	0.918691i	$-0.370753\pi$
$641$	20.0000	0.789953	0.394976	+	0.918691i	$0.370753\pi$
$642$	34.0000	1.34187
$643$	37.0000	1.45914	0.729569	−	0.683907i	$-0.239721\pi$
$643$	37.0000	1.45914	0.729569	+	0.683907i	$0.239721\pi$
$644$	0	0
$645$	8.00000	0.315000
$646$	84.0000	3.30494
$647$	−17.0000	−0.668339	−0.334169	−	0.942513i	$-0.608456\pi$
$647$	−17.0000	−0.668339	−0.334169	+	0.942513i	$0.608456\pi$
$648$	0	0
$649$	0	0
$650$	2.00000	0.0784465
$651$	0	0
$652$	30.0000	1.17489
$653$	18.0000	0.704394	0.352197	−	0.935926i	$-0.385435\pi$
$653$	18.0000	0.704394	0.352197	+	0.935926i	$0.385435\pi$
$654$	−8.00000	−0.312825
$655$	22.0000	0.859611
$656$	36.0000	1.40556
$657$	6.00000	0.234082
$658$	0	0
$659$	24.0000	0.934907	0.467454	−	0.884018i	$-0.345171\pi$
$659$	24.0000	0.934907	0.467454	+	0.884018i	$0.345171\pi$
$660$	−10.0000	−0.389249
$661$	40.0000	1.55582	0.777910	−	0.628376i	$-0.216280\pi$
$661$	40.0000	1.55582	0.777910	+	0.628376i	$0.216280\pi$
$662$	0	0
$663$	−7.00000	−0.271857
$664$	0	0
$665$	0	0
$666$	14.0000	0.542489
$667$	6.00000	0.232321
$668$	48.0000	1.85718
$669$	−8.00000	−0.309298
$670$	−8.00000	−0.309067
$671$	−25.0000	−0.965114
$672$	0	0
$673$	42.0000	1.61898	0.809491	−	0.587133i	$-0.199743\pi$
$673$	42.0000	1.61898	0.809491	+	0.587133i	$0.199743\pi$
$674$	16.0000	0.616297
$675$	−1.00000	−0.0384900
$676$	2.00000	0.0769231
$677$	−21.0000	−0.807096	−0.403548	−	0.914959i	$-0.632223\pi$
$677$	−21.0000	−0.807096	−0.403548	+	0.914959i	$0.632223\pi$
$678$	−20.0000	−0.768095
$679$	0	0
$680$	0	0
$681$	−2.00000	−0.0766402
$682$	−20.0000	−0.765840
$683$	16.0000	0.612223	0.306111	−	0.951996i	$-0.400972\pi$
$683$	16.0000	0.612223	0.306111	+	0.951996i	$0.400972\pi$
$684$	12.0000	0.458831
$685$	−14.0000	−0.534913
$686$	0	0
$687$	14.0000	0.534133
$688$	32.0000	1.21999
$689$	5.00000	0.190485
$690$	−6.00000	−0.228416
$691$	−10.0000	−0.380418	−0.190209	−	0.981744i	$-0.560917\pi$
$691$	−10.0000	−0.380418	−0.190209	+	0.981744i	$0.560917\pi$
$692$	36.0000	1.36851
$693$	0	0
$694$	22.0000	0.835109
$695$	−15.0000	−0.568982
$696$	0	0
$697$	−63.0000	−2.38630
$698$	−48.0000	−1.81683
$699$	−19.0000	−0.718646
$700$	0	0
$701$	28.0000	1.05755	0.528773	−	0.848763i	$-0.322652\pi$
$701$	28.0000	1.05755	0.528773	+	0.848763i	$0.322652\pi$
$702$	−2.00000	−0.0754851
$703$	42.0000	1.58406
$704$	−40.0000	−1.50756
$705$	10.0000	0.376622
$706$	12.0000	0.451626
$707$	0	0
$708$	0	0
$709$	−44.0000	−1.65245	−0.826227	−	0.563337i	$-0.809517\pi$
$709$	−44.0000	−1.65245	−0.826227	+	0.563337i	$0.809517\pi$
$710$	18.0000	0.675528
$711$	−3.00000	−0.112509
$712$	0	0
$713$	−6.00000	−0.224702
$714$	0	0
$715$	5.00000	0.186989
$716$	12.0000	0.448461
$717$	−9.00000	−0.336111
$718$	−32.0000	−1.19423
$719$	−16.0000	−0.596699	−0.298350	−	0.954457i	$-0.596436\pi$
$719$	−16.0000	−0.596699	−0.298350	+	0.954457i	$0.596436\pi$
$720$	−4.00000	−0.149071
$721$	0	0
$722$	34.0000	1.26535
$723$	22.0000	0.818189
$724$	14.0000	0.520306
$725$	2.00000	0.0742781
$726$	−28.0000	−1.03918
$727$	18.0000	0.667583	0.333792	−	0.942647i	$-0.391672\pi$
$727$	18.0000	0.667583	0.333792	+	0.942647i	$0.391672\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	12.0000	0.444140
$731$	−56.0000	−2.07123
$732$	10.0000	0.369611
$733$	−43.0000	−1.58824	−0.794121	−	0.607760i	$-0.792068\pi$
$733$	−43.0000	−1.58824	−0.794121	+	0.607760i	$0.792068\pi$
$734$	−8.00000	−0.295285
$735$	0	0
$736$	−24.0000	−0.884652
$737$	−20.0000	−0.736709
$738$	−18.0000	−0.662589
$739$	−6.00000	−0.220714	−0.110357	−	0.993892i	$-0.535199\pi$
$739$	−6.00000	−0.220714	−0.110357	+	0.993892i	$0.535199\pi$
$740$	14.0000	0.514650
$741$	−6.00000	−0.220416
$742$	0	0
$743$	30.0000	1.10059	0.550297	−	0.834969i	$-0.314515\pi$
$743$	30.0000	1.10059	0.550297	+	0.834969i	$0.314515\pi$
$744$	0	0
$745$	15.0000	0.549557
$746$	−64.0000	−2.34321
$747$	4.00000	0.146352
$748$	70.0000	2.55945
$749$	0	0
$750$	−2.00000	−0.0730297
$751$	−13.0000	−0.474377	−0.237188	−	0.971464i	$-0.576226\pi$
$751$	−13.0000	−0.474377	−0.237188	+	0.971464i	$0.576226\pi$
$752$	40.0000	1.45865
$753$	0	0
$754$	4.00000	0.145671
$755$	−8.00000	−0.291150
$756$	0	0
$757$	20.0000	0.726912	0.363456	−	0.931611i	$-0.381597\pi$
$757$	20.0000	0.726912	0.363456	+	0.931611i	$0.381597\pi$
$758$	20.0000	0.726433
$759$	−15.0000	−0.544466
$760$	0	0
$761$	42.0000	1.52250	0.761249	−	0.648459i	$-0.224586\pi$
$761$	42.0000	1.52250	0.761249	+	0.648459i	$0.224586\pi$
$762$	4.00000	0.144905
$763$	0	0
$764$	−24.0000	−0.868290
$765$	7.00000	0.253086
$766$	12.0000	0.433578
$767$	0	0
$768$	−16.0000	−0.577350
$769$	28.0000	1.00971	0.504853	−	0.863205i	$-0.331547\pi$
$769$	28.0000	1.00971	0.504853	+	0.863205i	$0.331547\pi$
$770$	0	0
$771$	2.00000	0.0720282
$772$	−34.0000	−1.22369
$773$	20.0000	0.719350	0.359675	−	0.933078i	$-0.382888\pi$
$773$	20.0000	0.719350	0.359675	+	0.933078i	$0.382888\pi$
$774$	−16.0000	−0.575108
$775$	−2.00000	−0.0718421
$776$	0	0
$777$	0	0
$778$	−8.00000	−0.286814
$779$	−54.0000	−1.93475
$780$	−2.00000	−0.0716115
$781$	45.0000	1.61023
$782$	42.0000	1.50192
$783$	−2.00000	−0.0714742
$784$	0	0
$785$	−18.0000	−0.642448
$786$	−44.0000	−1.56943
$787$	−44.0000	−1.56843	−0.784215	−	0.620489i	$-0.786934\pi$
$787$	−44.0000	−1.56843	−0.784215	+	0.620489i	$0.786934\pi$
$788$	48.0000	1.70993
$789$	16.0000	0.569615
$790$	−6.00000	−0.213470
$791$	0	0
$792$	0	0
$793$	−5.00000	−0.177555
$794$	−30.0000	−1.06466
$795$	−5.00000	−0.177332
$796$	56.0000	1.98487
$797$	−39.0000	−1.38145	−0.690725	−	0.723117i	$-0.742709\pi$
$797$	−39.0000	−1.38145	−0.690725	+	0.723117i	$0.742709\pi$
$798$	0	0
$799$	−70.0000	−2.47642
$800$	−8.00000	−0.282843
$801$	−11.0000	−0.388666
$802$	−28.0000	−0.988714
$803$	30.0000	1.05868
$804$	8.00000	0.282138
$805$	0	0
$806$	−4.00000	−0.140894
$807$	−24.0000	−0.844840
$808$	0	0
$809$	−50.0000	−1.75791	−0.878953	−	0.476908i	$-0.841757\pi$
$809$	−50.0000	−1.75791	−0.878953	+	0.476908i	$0.841757\pi$
$810$	2.00000	0.0702728
$811$	−24.0000	−0.842754	−0.421377	−	0.906886i	$-0.638453\pi$
$811$	−24.0000	−0.842754	−0.421377	+	0.906886i	$0.638453\pi$
$812$	0	0
$813$	−22.0000	−0.771574
$814$	70.0000	2.45350
$815$	15.0000	0.525427
$816$	28.0000	0.980196
$817$	−48.0000	−1.67931
$818$	−60.0000	−2.09785
$819$	0	0
$820$	−18.0000	−0.628587
$821$	17.0000	0.593304	0.296652	−	0.954986i	$-0.404130\pi$
$821$	17.0000	0.593304	0.296652	+	0.954986i	$0.404130\pi$
$822$	28.0000	0.976612
$823$	−4.00000	−0.139431	−0.0697156	−	0.997567i	$-0.522209\pi$
$823$	−4.00000	−0.139431	−0.0697156	+	0.997567i	$0.522209\pi$
$824$	0	0
$825$	−5.00000	−0.174078
$826$	0	0
$827$	−26.0000	−0.904109	−0.452054	−	0.891990i	$-0.649309\pi$
$827$	−26.0000	−0.904109	−0.452054	+	0.891990i	$0.649309\pi$
$828$	6.00000	0.208514
$829$	2.00000	0.0694629	0.0347314	−	0.999397i	$-0.488942\pi$
$829$	2.00000	0.0694629	0.0347314	+	0.999397i	$0.488942\pi$
$830$	8.00000	0.277684
$831$	2.00000	0.0693792
$832$	−8.00000	−0.277350
$833$	0	0
$834$	30.0000	1.03882
$835$	24.0000	0.830554
$836$	60.0000	2.07514
$837$	2.00000	0.0691301
$838$	−52.0000	−1.79631
$839$	−17.0000	−0.586905	−0.293453	−	0.955974i	$-0.594804\pi$
$839$	−17.0000	−0.586905	−0.293453	+	0.955974i	$0.594804\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	−40.0000	−1.37849
$843$	−18.0000	−0.619953
$844$	−24.0000	−0.826114
$845$	1.00000	0.0344010
$846$	−20.0000	−0.687614
$847$	0	0
$848$	−20.0000	−0.686803
$849$	20.0000	0.686398
$850$	14.0000	0.480196
$851$	21.0000	0.719871
$852$	−18.0000	−0.616670
$853$	39.0000	1.33533	0.667667	−	0.744460i	$-0.267293\pi$
$853$	39.0000	1.33533	0.667667	+	0.744460i	$0.267293\pi$
$854$	0	0
$855$	6.00000	0.205196
$856$	0	0
$857$	45.0000	1.53717	0.768585	−	0.639747i	$-0.220961\pi$
$857$	45.0000	1.53717	0.768585	+	0.639747i	$0.220961\pi$
$858$	−10.0000	−0.341394
$859$	−19.0000	−0.648272	−0.324136	−	0.946011i	$-0.605073\pi$
$859$	−19.0000	−0.648272	−0.324136	+	0.946011i	$0.605073\pi$
$860$	−16.0000	−0.545595
$861$	0	0
$862$	−80.0000	−2.72481
$863$	6.00000	0.204242	0.102121	−	0.994772i	$-0.467437\pi$
$863$	6.00000	0.204242	0.102121	+	0.994772i	$0.467437\pi$
$864$	8.00000	0.272166
$865$	18.0000	0.612018
$866$	40.0000	1.35926
$867$	−32.0000	−1.08678
$868$	0	0
$869$	−15.0000	−0.508840
$870$	−4.00000	−0.135613
$871$	−4.00000	−0.135535
$872$	0	0
$873$	11.0000	0.372294
$874$	36.0000	1.21772
$875$	0	0
$876$	−12.0000	−0.405442
$877$	18.0000	0.607817	0.303908	−	0.952701i	$-0.401708\pi$
$877$	18.0000	0.607817	0.303908	+	0.952701i	$0.401708\pi$
$878$	−30.0000	−1.01245
$879$	4.00000	0.134917
$880$	−20.0000	−0.674200
$881$	−14.0000	−0.471672	−0.235836	−	0.971793i	$-0.575783\pi$
$881$	−14.0000	−0.471672	−0.235836	+	0.971793i	$0.575783\pi$
$882$	0	0
$883$	44.0000	1.48072	0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000	1.48072	0.740359	+	0.672212i	$0.234656\pi$
$884$	14.0000	0.470871
$885$	0	0
$886$	−2.00000	−0.0671913
$887$	−13.0000	−0.436497	−0.218249	−	0.975893i	$-0.570034\pi$
$887$	−13.0000	−0.436497	−0.218249	+	0.975893i	$0.570034\pi$
$888$	0	0
$889$	0	0
$890$	−22.0000	−0.737442
$891$	5.00000	0.167506
$892$	16.0000	0.535720
$893$	−60.0000	−2.00782
$894$	−30.0000	−1.00335
$895$	6.00000	0.200558
$896$	0	0
$897$	−3.00000	−0.100167
$898$	18.0000	0.600668
$899$	−4.00000	−0.133407
$900$	2.00000	0.0666667
$901$	35.0000	1.16602
$902$	−90.0000	−2.99667
$903$	0	0
$904$	0	0
$905$	7.00000	0.232688
$906$	16.0000	0.531564
$907$	38.0000	1.26177	0.630885	−	0.775877i	$-0.282692\pi$
$907$	38.0000	1.26177	0.630885	+	0.775877i	$0.282692\pi$
$908$	4.00000	0.132745
$909$	0	0
$910$	0	0
$911$	−12.0000	−0.397578	−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000	−0.397578	−0.198789	+	0.980042i	$0.563701\pi$
$912$	24.0000	0.794719
$913$	20.0000	0.661903
$914$	−14.0000	−0.463079
$915$	5.00000	0.165295
$916$	−28.0000	−0.925146
$917$	0	0
$918$	−14.0000	−0.462069
$919$	−19.0000	−0.626752	−0.313376	−	0.949629i	$-0.601460\pi$
$919$	−19.0000	−0.626752	−0.313376	+	0.949629i	$0.601460\pi$
$920$	0	0
$921$	23.0000	0.757876
$922$	−74.0000	−2.43706
$923$	9.00000	0.296239
$924$	0	0
$925$	7.00000	0.230159
$926$	30.0000	0.985861
$927$	4.00000	0.131377
$928$	−16.0000	−0.525226
$929$	29.0000	0.951459	0.475730	−	0.879592i	$-0.342184\pi$
$929$	29.0000	0.951459	0.475730	+	0.879592i	$0.342184\pi$
$930$	4.00000	0.131165
$931$	0	0
$932$	38.0000	1.24473
$933$	20.0000	0.654771
$934$	2.00000	0.0654420
$935$	35.0000	1.14462
$936$	0	0
$937$	6.00000	0.196011	0.0980057	−	0.995186i	$-0.468754\pi$
$937$	6.00000	0.196011	0.0980057	+	0.995186i	$0.468754\pi$
$938$	0	0
$939$	−22.0000	−0.717943
$940$	−20.0000	−0.652328
$941$	−15.0000	−0.488986	−0.244493	−	0.969651i	$-0.578622\pi$
$941$	−15.0000	−0.488986	−0.244493	+	0.969651i	$0.578622\pi$
$942$	36.0000	1.17294
$943$	−27.0000	−0.879241
$944$	0	0
$945$	0	0
$946$	−80.0000	−2.60102
$947$	12.0000	0.389948	0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000	0.389948	0.194974	+	0.980808i	$0.437538\pi$
$948$	6.00000	0.194871
$949$	6.00000	0.194768
$950$	12.0000	0.389331
$951$	24.0000	0.778253
$952$	0	0
$953$	−15.0000	−0.485898	−0.242949	−	0.970039i	$-0.578115\pi$
$953$	−15.0000	−0.485898	−0.242949	+	0.970039i	$0.578115\pi$
$954$	10.0000	0.323762
$955$	−12.0000	−0.388311
$956$	18.0000	0.582162
$957$	−10.0000	−0.323254
$958$	−6.00000	−0.193851
$959$	0	0
$960$	8.00000	0.258199
$961$	−27.0000	−0.870968
$962$	14.0000	0.451378
$963$	−17.0000	−0.547817
$964$	−44.0000	−1.41714
$965$	−17.0000	−0.547249
$966$	0	0
$967$	−8.00000	−0.257263	−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000	−0.257263	−0.128631	+	0.991692i	$0.541058\pi$
$968$	0	0
$969$	−42.0000	−1.34923
$970$	22.0000	0.706377
$971$	28.0000	0.898563	0.449281	−	0.893390i	$-0.351680\pi$
$971$	28.0000	0.898563	0.449281	+	0.893390i	$0.351680\pi$
$972$	−2.00000	−0.0641500
$973$	0	0
$974$	10.0000	0.320421
$975$	−1.00000	−0.0320256
$976$	20.0000	0.640184
$977$	−12.0000	−0.383914	−0.191957	−	0.981403i	$-0.561483\pi$
$977$	−12.0000	−0.383914	−0.191957	+	0.981403i	$0.561483\pi$
$978$	−30.0000	−0.959294
$979$	−55.0000	−1.75781
$980$	0	0
$981$	4.00000	0.127710
$982$	0	0
$983$	4.00000	0.127580	0.0637901	−	0.997963i	$-0.479681\pi$
$983$	4.00000	0.127580	0.0637901	+	0.997963i	$0.479681\pi$
$984$	0	0
$985$	24.0000	0.764704
$986$	28.0000	0.891702
$987$	0	0
$988$	12.0000	0.381771
$989$	−24.0000	−0.763156
$990$	10.0000	0.317821
$991$	−57.0000	−1.81066	−0.905332	−	0.424704i	$-0.860378\pi$
$991$	−57.0000	−1.81066	−0.905332	+	0.424704i	$0.860378\pi$
$992$	16.0000	0.508001
$993$	0	0
$994$	0	0
$995$	28.0000	0.887660
$996$	−8.00000	−0.253490
$997$	−8.00000	−0.253363	−0.126681	−	0.991943i	$-0.540433\pi$
$997$	−8.00000	−0.253363	−0.126681	+	0.991943i	$0.540433\pi$
$998$	−28.0000	−0.886325
$999$	−7.00000	−0.221470

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9555.2.a.u.1.1		1
7.6	odd	2		195.2.a.c.1.1	✓	1
21.20	even	2		585.2.a.c.1.1		1
28.27	even	2		3120.2.a.d.1.1		1
35.13	even	4		975.2.c.c.274.1		2
35.27	even	4		975.2.c.c.274.2		2
35.34	odd	2		975.2.a.a.1.1		1
84.83	odd	2		9360.2.a.bv.1.1		1
91.90	odd	2		2535.2.a.d.1.1		1
105.62	odd	4		2925.2.c.a.2224.1		2
105.83	odd	4		2925.2.c.a.2224.2		2
105.104	even	2		2925.2.a.s.1.1		1
273.272	even	2		7605.2.a.t.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.a.c.1.1	✓	1	7.6	odd	2
585.2.a.c.1.1		1	21.20	even	2
975.2.a.a.1.1		1	35.34	odd	2
975.2.c.c.274.1		2	35.13	even	4
975.2.c.c.274.2		2	35.27	even	4
2535.2.a.d.1.1		1	91.90	odd	2
2925.2.a.s.1.1		1	105.104	even	2
2925.2.c.a.2224.1		2	105.62	odd	4
2925.2.c.a.2224.2		2	105.83	odd	4
3120.2.a.d.1.1		1	28.27	even	2
7605.2.a.t.1.1		1	273.272	even	2
9360.2.a.bv.1.1		1	84.83	odd	2
9555.2.a.u.1.1		1	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 9555 = 3 \cdot 5 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9555.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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