LMFDB - Embedded newform 3850.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3850,2,Mod(1,3850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3850, 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("3850.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3850.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:	$30.7424047782$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 770)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	3850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -2.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -2.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{11} +2.00000 q^{12} -2.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -6.00000 q^{17} -1.00000 q^{18} +2.00000 q^{19} -2.00000 q^{21} +1.00000 q^{22} +6.00000 q^{23} -2.00000 q^{24} +2.00000 q^{26} -4.00000 q^{27} -1.00000 q^{28} +8.00000 q^{31} -1.00000 q^{32} -2.00000 q^{33} +6.00000 q^{34} +1.00000 q^{36} -8.00000 q^{37} -2.00000 q^{38} -4.00000 q^{39} +2.00000 q^{42} +4.00000 q^{43} -1.00000 q^{44} -6.00000 q^{46} +2.00000 q^{48} +1.00000 q^{49} -12.0000 q^{51} -2.00000 q^{52} -12.0000 q^{53} +4.00000 q^{54} +1.00000 q^{56} +4.00000 q^{57} +12.0000 q^{59} -10.0000 q^{61} -8.00000 q^{62} -1.00000 q^{63} +1.00000 q^{64} +2.00000 q^{66} +4.00000 q^{67} -6.00000 q^{68} +12.0000 q^{69} -12.0000 q^{71} -1.00000 q^{72} -14.0000 q^{73} +8.00000 q^{74} +2.00000 q^{76} +1.00000 q^{77} +4.00000 q^{78} -10.0000 q^{79} -11.0000 q^{81} -2.00000 q^{84} -4.00000 q^{86} +1.00000 q^{88} -18.0000 q^{89} +2.00000 q^{91} +6.00000 q^{92} +16.0000 q^{93} -2.00000 q^{96} -8.00000 q^{97} -1.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.00000	1.15470	0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−2.00000	−0.816497
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.00000	0.577350
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	−1.00000	−0.235702
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	0	0
$21$	−2.00000	−0.436436
$22$	1.00000	0.213201
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	−2.00000	−0.408248
$25$	0	0
$26$	2.00000	0.392232
$27$	−4.00000	−0.769800
$28$	−1.00000	−0.188982
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	8.00000	1.43684	0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$32$	−1.00000	−0.176777
$33$	−2.00000	−0.348155
$34$	6.00000	1.02899
$35$	0	0
$36$	1.00000	0.166667
$37$	−8.00000	−1.31519	−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000	−1.31519	−0.657596	+	0.753371i	$0.728427\pi$
$38$	−2.00000	−0.324443
$39$	−4.00000	−0.640513
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	2.00000	0.308607
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	−6.00000	−0.884652
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	2.00000	0.288675
$49$	1.00000	0.142857
$50$	0	0
$51$	−12.0000	−1.68034
$52$	−2.00000	−0.277350
$53$	−12.0000	−1.64833	−0.824163	−	0.566352i	$-0.808354\pi$
$53$	−12.0000	−1.64833	−0.824163	+	0.566352i	$0.808354\pi$
$54$	4.00000	0.544331
$55$	0	0
$56$	1.00000	0.133631
$57$	4.00000	0.529813
$58$	0	0
$59$	12.0000	1.56227	0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000	1.56227	0.781133	+	0.624364i	$0.214642\pi$
$60$	0	0
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	−8.00000	−1.01600
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	2.00000	0.246183
$67$	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
$70$	0	0
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	−1.00000	−0.117851
$73$	−14.0000	−1.63858	−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000	−1.63858	−0.819288	+	0.573382i	$0.805631\pi$
$74$	8.00000	0.929981
$75$	0	0
$76$	2.00000	0.229416
$77$	1.00000	0.113961
$78$	4.00000	0.452911
$79$	−10.0000	−1.12509	−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000	−1.12509	−0.562544	+	0.826767i	$0.690177\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	0	0
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	−2.00000	−0.218218
$85$	0	0
$86$	−4.00000	−0.431331
$87$	0	0
$88$	1.00000	0.106600
$89$	−18.0000	−1.90800	−0.953998	−	0.299813i	$-0.903076\pi$
$89$	−18.0000	−1.90800	−0.953998	+	0.299813i	$0.903076\pi$
$90$	0	0
$91$	2.00000	0.209657
$92$	6.00000	0.625543
$93$	16.0000	1.65912
$94$	0	0
$95$	0	0
$96$	−2.00000	−0.204124
$97$	−8.00000	−0.812277	−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000	−0.812277	−0.406138	+	0.913812i	$0.633125\pi$
$98$	−1.00000	−0.101015
$99$	−1.00000	−0.100504
$100$	0	0
$101$	−18.0000	−1.79107	−0.895533	−	0.444994i	$-0.853206\pi$
$101$	−18.0000	−1.79107	−0.895533	+	0.444994i	$0.853206\pi$
$102$	12.0000	1.18818
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	12.0000	1.16554
$107$	−12.0000	−1.16008	−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000	−1.16008	−0.580042	+	0.814587i	$0.696964\pi$
$108$	−4.00000	−0.384900
$109$	8.00000	0.766261	0.383131	−	0.923694i	$-0.374846\pi$
$109$	8.00000	0.766261	0.383131	+	0.923694i	$0.374846\pi$
$110$	0	0
$111$	−16.0000	−1.51865
$112$	−1.00000	−0.0944911
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	−4.00000	−0.374634
$115$	0	0
$116$	0	0
$117$	−2.00000	−0.184900
$118$	−12.0000	−1.10469
$119$	6.00000	0.550019
$120$	0	0
$121$	1.00000	0.0909091
$122$	10.0000	0.905357
$123$	0	0
$124$	8.00000	0.718421
$125$	0	0
$126$	1.00000	0.0890871
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	−1.00000	−0.0883883
$129$	8.00000	0.704361
$130$	0	0
$131$	−18.0000	−1.57267	−0.786334	−	0.617802i	$-0.788023\pi$
$131$	−18.0000	−1.57267	−0.786334	+	0.617802i	$0.788023\pi$
$132$	−2.00000	−0.174078
$133$	−2.00000	−0.173422
$134$	−4.00000	−0.345547
$135$	0	0
$136$	6.00000	0.514496
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	−12.0000	−1.02151
$139$	−10.0000	−0.848189	−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000	−0.848189	−0.424094	+	0.905618i	$0.639408\pi$
$140$	0	0
$141$	0	0
$142$	12.0000	1.00702
$143$	2.00000	0.167248
$144$	1.00000	0.0833333
$145$	0	0
$146$	14.0000	1.15865
$147$	2.00000	0.164957
$148$	−8.00000	−0.657596
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	−10.0000	−0.813788	−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000	−0.813788	−0.406894	+	0.913475i	$0.633388\pi$
$152$	−2.00000	−0.162221
$153$	−6.00000	−0.485071
$154$	−1.00000	−0.0805823
$155$	0	0
$156$	−4.00000	−0.320256
$157$	−2.00000	−0.159617	−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000	−0.159617	−0.0798087	+	0.996810i	$0.525431\pi$
$158$	10.0000	0.795557
$159$	−24.0000	−1.90332
$160$	0	0
$161$	−6.00000	−0.472866
$162$	11.0000	0.864242
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	2.00000	0.154303
$169$	−9.00000	−0.692308
$170$	0	0
$171$	2.00000	0.152944
$172$	4.00000	0.304997
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	0	0
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	24.0000	1.80395
$178$	18.0000	1.34916
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	0	0
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	−2.00000	−0.148250
$183$	−20.0000	−1.47844
$184$	−6.00000	−0.442326
$185$	0	0
$186$	−16.0000	−1.17318
$187$	6.00000	0.438763
$188$	0	0
$189$	4.00000	0.290957
$190$	0	0
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	2.00000	0.144338
$193$	−14.0000	−1.00774	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000	−1.00774	−0.503871	+	0.863779i	$0.668091\pi$
$194$	8.00000	0.574367
$195$	0	0
$196$	1.00000	0.0714286
$197$	−18.0000	−1.28245	−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000	−1.28245	−0.641223	+	0.767354i	$0.721573\pi$
$198$	1.00000	0.0710669
$199$	8.00000	0.567105	0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000	0.567105	0.283552	+	0.958957i	$0.408487\pi$
$200$	0	0
$201$	8.00000	0.564276
$202$	18.0000	1.26648
$203$	0	0
$204$	−12.0000	−0.840168
$205$	0	0
$206$	−4.00000	−0.278693
$207$	6.00000	0.417029
$208$	−2.00000	−0.138675
$209$	−2.00000	−0.138343
$210$	0	0
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	−12.0000	−0.824163
$213$	−24.0000	−1.64445
$214$	12.0000	0.820303
$215$	0	0
$216$	4.00000	0.272166
$217$	−8.00000	−0.543075
$218$	−8.00000	−0.541828
$219$	−28.0000	−1.89206
$220$	0	0
$221$	12.0000	0.807207
$222$	16.0000	1.07385
$223$	4.00000	0.267860	0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000	0.267860	0.133930	+	0.990991i	$0.457240\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	−6.00000	−0.399114
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	4.00000	0.264906
$229$	26.0000	1.71813	0.859064	−	0.511868i	$-0.171046\pi$
$229$	26.0000	1.71813	0.859064	+	0.511868i	$0.171046\pi$
$230$	0	0
$231$	2.00000	0.131590
$232$	0	0
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	2.00000	0.130744
$235$	0	0
$236$	12.0000	0.781133
$237$	−20.0000	−1.29914
$238$	−6.00000	−0.388922
$239$	18.0000	1.16432	0.582162	−	0.813073i	$-0.302207\pi$
$239$	18.0000	1.16432	0.582162	+	0.813073i	$0.302207\pi$
$240$	0	0
$241$	8.00000	0.515325	0.257663	−	0.966235i	$-0.417048\pi$
$241$	8.00000	0.515325	0.257663	+	0.966235i	$0.417048\pi$
$242$	−1.00000	−0.0642824
$243$	−10.0000	−0.641500
$244$	−10.0000	−0.640184
$245$	0	0
$246$	0	0
$247$	−4.00000	−0.254514
$248$	−8.00000	−0.508001
$249$	0	0
$250$	0	0
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	−1.00000	−0.0629941
$253$	−6.00000	−0.377217
$254$	−16.0000	−1.00393
$255$	0	0
$256$	1.00000	0.0625000
$257$	24.0000	1.49708	0.748539	−	0.663090i	$-0.230755\pi$
$257$	24.0000	1.49708	0.748539	+	0.663090i	$0.230755\pi$
$258$	−8.00000	−0.498058
$259$	8.00000	0.497096
$260$	0	0
$261$	0	0
$262$	18.0000	1.11204
$263$	24.0000	1.47990	0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000	1.47990	0.739952	+	0.672660i	$0.234848\pi$
$264$	2.00000	0.123091
$265$	0	0
$266$	2.00000	0.122628
$267$	−36.0000	−2.20316
$268$	4.00000	0.244339
$269$	18.0000	1.09748	0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000	1.09748	0.548740	+	0.835993i	$0.315108\pi$
$270$	0	0
$271$	20.0000	1.21491	0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000	1.21491	0.607457	+	0.794353i	$0.292190\pi$
$272$	−6.00000	−0.363803
$273$	4.00000	0.242091
$274$	−6.00000	−0.362473
$275$	0	0
$276$	12.0000	0.722315
$277$	10.0000	0.600842	0.300421	−	0.953807i	$-0.402873\pi$
$277$	10.0000	0.600842	0.300421	+	0.953807i	$0.402873\pi$
$278$	10.0000	0.599760
$279$	8.00000	0.478947
$280$	0	0
$281$	6.00000	0.357930	0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000	0.357930	0.178965	+	0.983855i	$0.442725\pi$
$282$	0	0
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	−12.0000	−0.712069
$285$	0	0
$286$	−2.00000	−0.118262
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	19.0000	1.11765
$290$	0	0
$291$	−16.0000	−0.937937
$292$	−14.0000	−0.819288
$293$	−18.0000	−1.05157	−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000	−1.05157	−0.525786	+	0.850617i	$0.676229\pi$
$294$	−2.00000	−0.116642
$295$	0	0
$296$	8.00000	0.464991
$297$	4.00000	0.232104
$298$	0	0
$299$	−12.0000	−0.693978
$300$	0	0
$301$	−4.00000	−0.230556
$302$	10.0000	0.575435
$303$	−36.0000	−2.06815
$304$	2.00000	0.114708
$305$	0	0
$306$	6.00000	0.342997
$307$	−32.0000	−1.82634	−0.913168	−	0.407583i	$-0.866372\pi$
$307$	−32.0000	−1.82634	−0.913168	+	0.407583i	$0.866372\pi$
$308$	1.00000	0.0569803
$309$	8.00000	0.455104
$310$	0	0
$311$	24.0000	1.36092	0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000	1.36092	0.680458	+	0.732787i	$0.261781\pi$
$312$	4.00000	0.226455
$313$	16.0000	0.904373	0.452187	−	0.891923i	$-0.350644\pi$
$313$	16.0000	0.904373	0.452187	+	0.891923i	$0.350644\pi$
$314$	2.00000	0.112867
$315$	0	0
$316$	−10.0000	−0.562544
$317$	0	0		−	1.00000i	$-0.5\pi$
$317$	0	0			1.00000i	$0.5\pi$
$318$	24.0000	1.34585
$319$	0	0
$320$	0	0
$321$	−24.0000	−1.33955
$322$	6.00000	0.334367
$323$	−12.0000	−0.667698
$324$	−11.0000	−0.611111
$325$	0	0
$326$	−4.00000	−0.221540
$327$	16.0000	0.884802
$328$	0	0
$329$	0	0
$330$	0	0
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	0	0
$333$	−8.00000	−0.438397
$334$	0	0
$335$	0	0
$336$	−2.00000	−0.109109
$337$	22.0000	1.19842	0.599208	−	0.800593i	$-0.295482\pi$
$337$	22.0000	1.19842	0.599208	+	0.800593i	$0.295482\pi$
$338$	9.00000	0.489535
$339$	12.0000	0.651751
$340$	0	0
$341$	−8.00000	−0.433224
$342$	−2.00000	−0.108148
$343$	−1.00000	−0.0539949
$344$	−4.00000	−0.215666
$345$	0	0
$346$	6.00000	0.322562
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	0	0
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	0	0
$351$	8.00000	0.427008
$352$	1.00000	0.0533002
$353$	24.0000	1.27739	0.638696	−	0.769460i	$-0.279474\pi$
$353$	24.0000	1.27739	0.638696	+	0.769460i	$0.279474\pi$
$354$	−24.0000	−1.27559
$355$	0	0
$356$	−18.0000	−0.953998
$357$	12.0000	0.635107
$358$	12.0000	0.634220
$359$	−18.0000	−0.950004	−0.475002	−	0.879985i	$-0.657553\pi$
$359$	−18.0000	−0.950004	−0.475002	+	0.879985i	$0.657553\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	10.0000	0.525588
$363$	2.00000	0.104973
$364$	2.00000	0.104828
$365$	0	0
$366$	20.0000	1.04542
$367$	−20.0000	−1.04399	−0.521996	−	0.852948i	$-0.674812\pi$
$367$	−20.0000	−1.04399	−0.521996	+	0.852948i	$0.674812\pi$
$368$	6.00000	0.312772
$369$	0	0
$370$	0	0
$371$	12.0000	0.623009
$372$	16.0000	0.829561
$373$	22.0000	1.13912	0.569558	−	0.821951i	$-0.307114\pi$
$373$	22.0000	1.13912	0.569558	+	0.821951i	$0.307114\pi$
$374$	−6.00000	−0.310253
$375$	0	0
$376$	0	0
$377$	0	0
$378$	−4.00000	−0.205738
$379$	−28.0000	−1.43826	−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000	−1.43826	−0.719132	+	0.694874i	$0.755460\pi$
$380$	0	0
$381$	32.0000	1.63941
$382$	0	0
$383$	12.0000	0.613171	0.306586	−	0.951843i	$-0.400813\pi$
$383$	12.0000	0.613171	0.306586	+	0.951843i	$0.400813\pi$
$384$	−2.00000	−0.102062
$385$	0	0
$386$	14.0000	0.712581
$387$	4.00000	0.203331
$388$	−8.00000	−0.406138
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	0	0
$391$	−36.0000	−1.82060
$392$	−1.00000	−0.0505076
$393$	−36.0000	−1.81596
$394$	18.0000	0.906827
$395$	0	0
$396$	−1.00000	−0.0502519
$397$	−2.00000	−0.100377	−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000	−0.100377	−0.0501886	+	0.998740i	$0.515982\pi$
$398$	−8.00000	−0.401004
$399$	−4.00000	−0.200250
$400$	0	0
$401$	−18.0000	−0.898877	−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000	−0.898877	−0.449439	+	0.893311i	$0.648376\pi$
$402$	−8.00000	−0.399004
$403$	−16.0000	−0.797017
$404$	−18.0000	−0.895533
$405$	0	0
$406$	0	0
$407$	8.00000	0.396545
$408$	12.0000	0.594089
$409$	8.00000	0.395575	0.197787	−	0.980245i	$-0.436624\pi$
$409$	8.00000	0.395575	0.197787	+	0.980245i	$0.436624\pi$
$410$	0	0
$411$	12.0000	0.591916
$412$	4.00000	0.197066
$413$	−12.0000	−0.590481
$414$	−6.00000	−0.294884
$415$	0	0
$416$	2.00000	0.0980581
$417$	−20.0000	−0.979404
$418$	2.00000	0.0978232
$419$	−12.0000	−0.586238	−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000	−0.586238	−0.293119	+	0.956076i	$0.594693\pi$
$420$	0	0
$421$	14.0000	0.682318	0.341159	−	0.940006i	$-0.389181\pi$
$421$	14.0000	0.682318	0.341159	+	0.940006i	$0.389181\pi$
$422$	−20.0000	−0.973585
$423$	0	0
$424$	12.0000	0.582772
$425$	0	0
$426$	24.0000	1.16280
$427$	10.0000	0.483934
$428$	−12.0000	−0.580042
$429$	4.00000	0.193122
$430$	0	0
$431$	−18.0000	−0.867029	−0.433515	−	0.901146i	$-0.642727\pi$
$431$	−18.0000	−0.867029	−0.433515	+	0.901146i	$0.642727\pi$
$432$	−4.00000	−0.192450
$433$	4.00000	0.192228	0.0961139	−	0.995370i	$-0.469359\pi$
$433$	4.00000	0.192228	0.0961139	+	0.995370i	$0.469359\pi$
$434$	8.00000	0.384012
$435$	0	0
$436$	8.00000	0.383131
$437$	12.0000	0.574038
$438$	28.0000	1.33789
$439$	20.0000	0.954548	0.477274	−	0.878755i	$-0.341625\pi$
$439$	20.0000	0.954548	0.477274	+	0.878755i	$0.341625\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	−12.0000	−0.570782
$443$	−12.0000	−0.570137	−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000	−0.570137	−0.285069	+	0.958507i	$0.592016\pi$
$444$	−16.0000	−0.759326
$445$	0	0
$446$	−4.00000	−0.189405
$447$	0	0
$448$	−1.00000	−0.0472456
$449$	−18.0000	−0.849473	−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000	−0.849473	−0.424736	+	0.905317i	$0.639633\pi$
$450$	0	0
$451$	0	0
$452$	6.00000	0.282216
$453$	−20.0000	−0.939682
$454$	−12.0000	−0.563188
$455$	0	0
$456$	−4.00000	−0.187317
$457$	−26.0000	−1.21623	−0.608114	−	0.793849i	$-0.708074\pi$
$457$	−26.0000	−1.21623	−0.608114	+	0.793849i	$0.708074\pi$
$458$	−26.0000	−1.21490
$459$	24.0000	1.12022
$460$	0	0
$461$	−30.0000	−1.39724	−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000	−1.39724	−0.698620	+	0.715493i	$0.746202\pi$
$462$	−2.00000	−0.0930484
$463$	−2.00000	−0.0929479	−0.0464739	−	0.998920i	$-0.514798\pi$
$463$	−2.00000	−0.0929479	−0.0464739	+	0.998920i	$0.514798\pi$
$464$	0	0
$465$	0	0
$466$	−6.00000	−0.277945
$467$	−18.0000	−0.832941	−0.416470	−	0.909149i	$-0.636733\pi$
$467$	−18.0000	−0.832941	−0.416470	+	0.909149i	$0.636733\pi$
$468$	−2.00000	−0.0924500
$469$	−4.00000	−0.184703
$470$	0	0
$471$	−4.00000	−0.184310
$472$	−12.0000	−0.552345
$473$	−4.00000	−0.183920
$474$	20.0000	0.918630
$475$	0	0
$476$	6.00000	0.275010
$477$	−12.0000	−0.549442
$478$	−18.0000	−0.823301
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	16.0000	0.729537
$482$	−8.00000	−0.364390
$483$	−12.0000	−0.546019
$484$	1.00000	0.0454545
$485$	0	0
$486$	10.0000	0.453609
$487$	22.0000	0.996915	0.498458	−	0.866914i	$-0.333900\pi$
$487$	22.0000	0.996915	0.498458	+	0.866914i	$0.333900\pi$
$488$	10.0000	0.452679
$489$	8.00000	0.361773
$490$	0	0
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	0	0
$493$	0	0
$494$	4.00000	0.179969
$495$	0	0
$496$	8.00000	0.359211
$497$	12.0000	0.538274
$498$	0	0
$499$	20.0000	0.895323	0.447661	−	0.894203i	$-0.352257\pi$
$499$	20.0000	0.895323	0.447661	+	0.894203i	$0.352257\pi$
$500$	0	0
$501$	0	0
$502$	12.0000	0.535586
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	1.00000	0.0445435
$505$	0	0
$506$	6.00000	0.266733
$507$	−18.0000	−0.799408
$508$	16.0000	0.709885
$509$	−42.0000	−1.86162	−0.930809	−	0.365507i	$-0.880896\pi$
$509$	−42.0000	−1.86162	−0.930809	+	0.365507i	$0.880896\pi$
$510$	0	0
$511$	14.0000	0.619324
$512$	−1.00000	−0.0441942
$513$	−8.00000	−0.353209
$514$	−24.0000	−1.05859
$515$	0	0
$516$	8.00000	0.352180
$517$	0	0
$518$	−8.00000	−0.351500
$519$	−12.0000	−0.526742
$520$	0	0
$521$	6.00000	0.262865	0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000	0.262865	0.131432	+	0.991325i	$0.458042\pi$
$522$	0	0
$523$	16.0000	0.699631	0.349816	−	0.936819i	$-0.386244\pi$
$523$	16.0000	0.699631	0.349816	+	0.936819i	$0.386244\pi$
$524$	−18.0000	−0.786334
$525$	0	0
$526$	−24.0000	−1.04645
$527$	−48.0000	−2.09091
$528$	−2.00000	−0.0870388
$529$	13.0000	0.565217
$530$	0	0
$531$	12.0000	0.520756
$532$	−2.00000	−0.0867110
$533$	0	0
$534$	36.0000	1.55787
$535$	0	0
$536$	−4.00000	−0.172774
$537$	−24.0000	−1.03568
$538$	−18.0000	−0.776035
$539$	−1.00000	−0.0430730
$540$	0	0
$541$	20.0000	0.859867	0.429934	−	0.902861i	$-0.358537\pi$
$541$	20.0000	0.859867	0.429934	+	0.902861i	$0.358537\pi$
$542$	−20.0000	−0.859074
$543$	−20.0000	−0.858282
$544$	6.00000	0.257248
$545$	0	0
$546$	−4.00000	−0.171184
$547$	−44.0000	−1.88130	−0.940652	−	0.339372i	$-0.889785\pi$
$547$	−44.0000	−1.88130	−0.940652	+	0.339372i	$0.889785\pi$
$548$	6.00000	0.256307
$549$	−10.0000	−0.426790
$550$	0	0
$551$	0	0
$552$	−12.0000	−0.510754
$553$	10.0000	0.425243
$554$	−10.0000	−0.424859
$555$	0	0
$556$	−10.0000	−0.424094
$557$	6.00000	0.254228	0.127114	−	0.991888i	$-0.459429\pi$
$557$	6.00000	0.254228	0.127114	+	0.991888i	$0.459429\pi$
$558$	−8.00000	−0.338667
$559$	−8.00000	−0.338364
$560$	0	0
$561$	12.0000	0.506640
$562$	−6.00000	−0.253095
$563$	36.0000	1.51722	0.758610	−	0.651546i	$-0.225879\pi$
$563$	36.0000	1.51722	0.758610	+	0.651546i	$0.225879\pi$
$564$	0	0
$565$	0	0
$566$	−4.00000	−0.168133
$567$	11.0000	0.461957
$568$	12.0000	0.503509
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	0	0
$571$	32.0000	1.33916	0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000	1.33916	0.669579	+	0.742741i	$0.266474\pi$
$572$	2.00000	0.0836242
$573$	0	0
$574$	0	0
$575$	0	0
$576$	1.00000	0.0416667
$577$	16.0000	0.666089	0.333044	−	0.942911i	$-0.391924\pi$
$577$	16.0000	0.666089	0.333044	+	0.942911i	$0.391924\pi$
$578$	−19.0000	−0.790296
$579$	−28.0000	−1.16364
$580$	0	0
$581$	0	0
$582$	16.0000	0.663221
$583$	12.0000	0.496989
$584$	14.0000	0.579324
$585$	0	0
$586$	18.0000	0.743573
$587$	−18.0000	−0.742940	−0.371470	−	0.928445i	$-0.621146\pi$
$587$	−18.0000	−0.742940	−0.371470	+	0.928445i	$0.621146\pi$
$588$	2.00000	0.0824786
$589$	16.0000	0.659269
$590$	0	0
$591$	−36.0000	−1.48084
$592$	−8.00000	−0.328798
$593$	−30.0000	−1.23195	−0.615976	−	0.787765i	$-0.711238\pi$
$593$	−30.0000	−1.23195	−0.615976	+	0.787765i	$0.711238\pi$
$594$	−4.00000	−0.164122
$595$	0	0
$596$	0	0
$597$	16.0000	0.654836
$598$	12.0000	0.490716
$599$	−36.0000	−1.47092	−0.735460	−	0.677568i	$-0.763034\pi$
$599$	−36.0000	−1.47092	−0.735460	+	0.677568i	$0.763034\pi$
$600$	0	0
$601$	−28.0000	−1.14214	−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000	−1.14214	−0.571072	+	0.820900i	$0.693472\pi$
$602$	4.00000	0.163028
$603$	4.00000	0.162893
$604$	−10.0000	−0.406894
$605$	0	0
$606$	36.0000	1.46240
$607$	16.0000	0.649420	0.324710	−	0.945814i	$-0.394733\pi$
$607$	16.0000	0.649420	0.324710	+	0.945814i	$0.394733\pi$
$608$	−2.00000	−0.0811107
$609$	0	0
$610$	0	0
$611$	0	0
$612$	−6.00000	−0.242536
$613$	−26.0000	−1.05013	−0.525065	−	0.851062i	$-0.675959\pi$
$613$	−26.0000	−1.05013	−0.525065	+	0.851062i	$0.675959\pi$
$614$	32.0000	1.29141
$615$	0	0
$616$	−1.00000	−0.0402911
$617$	−30.0000	−1.20775	−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000	−1.20775	−0.603877	+	0.797077i	$0.706378\pi$
$618$	−8.00000	−0.321807
$619$	44.0000	1.76851	0.884255	−	0.467005i	$-0.154667\pi$
$619$	44.0000	1.76851	0.884255	+	0.467005i	$0.154667\pi$
$620$	0	0
$621$	−24.0000	−0.963087
$622$	−24.0000	−0.962312
$623$	18.0000	0.721155
$624$	−4.00000	−0.160128
$625$	0	0
$626$	−16.0000	−0.639489
$627$	−4.00000	−0.159745
$628$	−2.00000	−0.0798087
$629$	48.0000	1.91389
$630$	0	0
$631$	−16.0000	−0.636950	−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000	−0.636950	−0.318475	+	0.947931i	$0.603171\pi$
$632$	10.0000	0.397779
$633$	40.0000	1.58986
$634$	0	0
$635$	0	0
$636$	−24.0000	−0.951662
$637$	−2.00000	−0.0792429
$638$	0	0
$639$	−12.0000	−0.474713
$640$	0	0
$641$	−30.0000	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$642$	24.0000	0.947204
$643$	−14.0000	−0.552106	−0.276053	−	0.961142i	$-0.589027\pi$
$643$	−14.0000	−0.552106	−0.276053	+	0.961142i	$0.589027\pi$
$644$	−6.00000	−0.236433
$645$	0	0
$646$	12.0000	0.472134
$647$	−12.0000	−0.471769	−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000	−0.471769	−0.235884	+	0.971781i	$0.575799\pi$
$648$	11.0000	0.432121
$649$	−12.0000	−0.471041
$650$	0	0
$651$	−16.0000	−0.627089
$652$	4.00000	0.156652
$653$	36.0000	1.40879	0.704394	−	0.709809i	$-0.251219\pi$
$653$	36.0000	1.40879	0.704394	+	0.709809i	$0.251219\pi$
$654$	−16.0000	−0.625650
$655$	0	0
$656$	0	0
$657$	−14.0000	−0.546192
$658$	0	0
$659$	24.0000	0.934907	0.467454	−	0.884018i	$-0.345171\pi$
$659$	24.0000	0.934907	0.467454	+	0.884018i	$0.345171\pi$
$660$	0	0
$661$	−10.0000	−0.388955	−0.194477	−	0.980907i	$-0.562301\pi$
$661$	−10.0000	−0.388955	−0.194477	+	0.980907i	$0.562301\pi$
$662$	−20.0000	−0.777322
$663$	24.0000	0.932083
$664$	0	0
$665$	0	0
$666$	8.00000	0.309994
$667$	0	0
$668$	0	0
$669$	8.00000	0.309298
$670$	0	0
$671$	10.0000	0.386046
$672$	2.00000	0.0771517
$673$	−2.00000	−0.0770943	−0.0385472	−	0.999257i	$-0.512273\pi$
$673$	−2.00000	−0.0770943	−0.0385472	+	0.999257i	$0.512273\pi$
$674$	−22.0000	−0.847408
$675$	0	0
$676$	−9.00000	−0.346154
$677$	−6.00000	−0.230599	−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000	−0.230599	−0.115299	+	0.993331i	$0.536783\pi$
$678$	−12.0000	−0.460857
$679$	8.00000	0.307012
$680$	0	0
$681$	24.0000	0.919682
$682$	8.00000	0.306336
$683$	24.0000	0.918334	0.459167	−	0.888350i	$-0.348148\pi$
$683$	24.0000	0.918334	0.459167	+	0.888350i	$0.348148\pi$
$684$	2.00000	0.0764719
$685$	0	0
$686$	1.00000	0.0381802
$687$	52.0000	1.98392
$688$	4.00000	0.152499
$689$	24.0000	0.914327
$690$	0	0
$691$	8.00000	0.304334	0.152167	−	0.988355i	$-0.451375\pi$
$691$	8.00000	0.304334	0.152167	+	0.988355i	$0.451375\pi$
$692$	−6.00000	−0.228086
$693$	1.00000	0.0379869
$694$	−12.0000	−0.455514
$695$	0	0
$696$	0	0
$697$	0	0
$698$	−2.00000	−0.0757011
$699$	12.0000	0.453882
$700$	0	0
$701$	−36.0000	−1.35970	−0.679851	−	0.733351i	$-0.737955\pi$
$701$	−36.0000	−1.35970	−0.679851	+	0.733351i	$0.737955\pi$
$702$	−8.00000	−0.301941
$703$	−16.0000	−0.603451
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	−24.0000	−0.903252
$707$	18.0000	0.676960
$708$	24.0000	0.901975
$709$	−46.0000	−1.72757	−0.863783	−	0.503864i	$-0.831911\pi$
$709$	−46.0000	−1.72757	−0.863783	+	0.503864i	$0.831911\pi$
$710$	0	0
$711$	−10.0000	−0.375029
$712$	18.0000	0.674579
$713$	48.0000	1.79761
$714$	−12.0000	−0.449089
$715$	0	0
$716$	−12.0000	−0.448461
$717$	36.0000	1.34444
$718$	18.0000	0.671754
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	−4.00000	−0.148968
$722$	15.0000	0.558242
$723$	16.0000	0.595046
$724$	−10.0000	−0.371647
$725$	0	0
$726$	−2.00000	−0.0742270
$727$	16.0000	0.593407	0.296704	−	0.954970i	$-0.404113\pi$
$727$	16.0000	0.593407	0.296704	+	0.954970i	$0.404113\pi$
$728$	−2.00000	−0.0741249
$729$	13.0000	0.481481
$730$	0	0
$731$	−24.0000	−0.887672
$732$	−20.0000	−0.739221
$733$	−14.0000	−0.517102	−0.258551	−	0.965998i	$-0.583245\pi$
$733$	−14.0000	−0.517102	−0.258551	+	0.965998i	$0.583245\pi$
$734$	20.0000	0.738213
$735$	0	0
$736$	−6.00000	−0.221163
$737$	−4.00000	−0.147342
$738$	0	0
$739$	20.0000	0.735712	0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000	0.735712	0.367856	+	0.929883i	$0.380092\pi$
$740$	0	0
$741$	−8.00000	−0.293887
$742$	−12.0000	−0.440534
$743$	24.0000	0.880475	0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000	0.880475	0.440237	+	0.897881i	$0.354894\pi$
$744$	−16.0000	−0.586588
$745$	0	0
$746$	−22.0000	−0.805477
$747$	0	0
$748$	6.00000	0.219382
$749$	12.0000	0.438470
$750$	0	0
$751$	44.0000	1.60558	0.802791	−	0.596260i	$-0.203347\pi$
$751$	44.0000	1.60558	0.802791	+	0.596260i	$0.203347\pi$
$752$	0	0
$753$	−24.0000	−0.874609
$754$	0	0
$755$	0	0
$756$	4.00000	0.145479
$757$	52.0000	1.88997	0.944986	−	0.327111i	$-0.106075\pi$
$757$	52.0000	1.88997	0.944986	+	0.327111i	$0.106075\pi$
$758$	28.0000	1.01701
$759$	−12.0000	−0.435572
$760$	0	0
$761$	−48.0000	−1.74000	−0.869999	−	0.493053i	$-0.835881\pi$
$761$	−48.0000	−1.74000	−0.869999	+	0.493053i	$0.835881\pi$
$762$	−32.0000	−1.15924
$763$	−8.00000	−0.289619
$764$	0	0
$765$	0	0
$766$	−12.0000	−0.433578
$767$	−24.0000	−0.866590
$768$	2.00000	0.0721688
$769$	20.0000	0.721218	0.360609	−	0.932717i	$-0.382569\pi$
$769$	20.0000	0.721218	0.360609	+	0.932717i	$0.382569\pi$
$770$	0	0
$771$	48.0000	1.72868
$772$	−14.0000	−0.503871
$773$	42.0000	1.51064	0.755318	−	0.655359i	$-0.227483\pi$
$773$	42.0000	1.51064	0.755318	+	0.655359i	$0.227483\pi$
$774$	−4.00000	−0.143777
$775$	0	0
$776$	8.00000	0.287183
$777$	16.0000	0.573997
$778$	6.00000	0.215110
$779$	0	0
$780$	0	0
$781$	12.0000	0.429394
$782$	36.0000	1.28736
$783$	0	0
$784$	1.00000	0.0357143
$785$	0	0
$786$	36.0000	1.28408
$787$	4.00000	0.142585	0.0712923	−	0.997455i	$-0.477288\pi$
$787$	4.00000	0.142585	0.0712923	+	0.997455i	$0.477288\pi$
$788$	−18.0000	−0.641223
$789$	48.0000	1.70885
$790$	0	0
$791$	−6.00000	−0.213335
$792$	1.00000	0.0355335
$793$	20.0000	0.710221
$794$	2.00000	0.0709773
$795$	0	0
$796$	8.00000	0.283552
$797$	−42.0000	−1.48772	−0.743858	−	0.668338i	$-0.767006\pi$
$797$	−42.0000	−1.48772	−0.743858	+	0.668338i	$0.767006\pi$
$798$	4.00000	0.141598
$799$	0	0
$800$	0	0
$801$	−18.0000	−0.635999
$802$	18.0000	0.635602
$803$	14.0000	0.494049
$804$	8.00000	0.282138
$805$	0	0
$806$	16.0000	0.563576
$807$	36.0000	1.26726
$808$	18.0000	0.633238
$809$	30.0000	1.05474	0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000	1.05474	0.527372	+	0.849635i	$0.323177\pi$
$810$	0	0
$811$	14.0000	0.491606	0.245803	−	0.969320i	$-0.420948\pi$
$811$	14.0000	0.491606	0.245803	+	0.969320i	$0.420948\pi$
$812$	0	0
$813$	40.0000	1.40286
$814$	−8.00000	−0.280400
$815$	0	0
$816$	−12.0000	−0.420084
$817$	8.00000	0.279885
$818$	−8.00000	−0.279713
$819$	2.00000	0.0698857
$820$	0	0
$821$	36.0000	1.25641	0.628204	−	0.778048i	$-0.283790\pi$
$821$	36.0000	1.25641	0.628204	+	0.778048i	$0.283790\pi$
$822$	−12.0000	−0.418548
$823$	−2.00000	−0.0697156	−0.0348578	−	0.999392i	$-0.511098\pi$
$823$	−2.00000	−0.0697156	−0.0348578	+	0.999392i	$0.511098\pi$
$824$	−4.00000	−0.139347
$825$	0	0
$826$	12.0000	0.417533
$827$	−36.0000	−1.25184	−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000	−1.25184	−0.625921	+	0.779886i	$0.715277\pi$
$828$	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	$0.488942\pi$
$830$	0	0
$831$	20.0000	0.693792
$832$	−2.00000	−0.0693375
$833$	−6.00000	−0.207888
$834$	20.0000	0.692543
$835$	0	0
$836$	−2.00000	−0.0691714
$837$	−32.0000	−1.10608
$838$	12.0000	0.414533
$839$	−48.0000	−1.65714	−0.828572	−	0.559883i	$-0.810846\pi$
$839$	−48.0000	−1.65714	−0.828572	+	0.559883i	$0.810846\pi$
$840$	0	0
$841$	−29.0000	−1.00000
$842$	−14.0000	−0.482472
$843$	12.0000	0.413302
$844$	20.0000	0.688428
$845$	0	0
$846$	0	0
$847$	−1.00000	−0.0343604
$848$	−12.0000	−0.412082
$849$	8.00000	0.274559
$850$	0	0
$851$	−48.0000	−1.64542
$852$	−24.0000	−0.822226
$853$	−14.0000	−0.479351	−0.239675	−	0.970853i	$-0.577041\pi$
$853$	−14.0000	−0.479351	−0.239675	+	0.970853i	$0.577041\pi$
$854$	−10.0000	−0.342193
$855$	0	0
$856$	12.0000	0.410152
$857$	−30.0000	−1.02478	−0.512390	−	0.858753i	$-0.671240\pi$
$857$	−30.0000	−1.02478	−0.512390	+	0.858753i	$0.671240\pi$
$858$	−4.00000	−0.136558
$859$	−28.0000	−0.955348	−0.477674	−	0.878537i	$-0.658520\pi$
$859$	−28.0000	−0.955348	−0.477674	+	0.878537i	$0.658520\pi$
$860$	0	0
$861$	0	0
$862$	18.0000	0.613082
$863$	30.0000	1.02121	0.510606	−	0.859815i	$-0.329421\pi$
$863$	30.0000	1.02121	0.510606	+	0.859815i	$0.329421\pi$
$864$	4.00000	0.136083
$865$	0	0
$866$	−4.00000	−0.135926
$867$	38.0000	1.29055
$868$	−8.00000	−0.271538
$869$	10.0000	0.339227
$870$	0	0
$871$	−8.00000	−0.271070
$872$	−8.00000	−0.270914
$873$	−8.00000	−0.270759
$874$	−12.0000	−0.405906
$875$	0	0
$876$	−28.0000	−0.946032
$877$	22.0000	0.742887	0.371444	−	0.928456i	$-0.378863\pi$
$877$	22.0000	0.742887	0.371444	+	0.928456i	$0.378863\pi$
$878$	−20.0000	−0.674967
$879$	−36.0000	−1.21425
$880$	0	0
$881$	−30.0000	−1.01073	−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000	−1.01073	−0.505363	+	0.862907i	$0.668641\pi$
$882$	−1.00000	−0.0336718
$883$	16.0000	0.538443	0.269221	−	0.963078i	$-0.413234\pi$
$883$	16.0000	0.538443	0.269221	+	0.963078i	$0.413234\pi$
$884$	12.0000	0.403604
$885$	0	0
$886$	12.0000	0.403148
$887$	0	0		−	1.00000i	$-0.5\pi$
$887$	0	0			1.00000i	$0.5\pi$
$888$	16.0000	0.536925
$889$	−16.0000	−0.536623
$890$	0	0
$891$	11.0000	0.368514
$892$	4.00000	0.133930
$893$	0	0
$894$	0	0
$895$	0	0
$896$	1.00000	0.0334077
$897$	−24.0000	−0.801337
$898$	18.0000	0.600668
$899$	0	0
$900$	0	0
$901$	72.0000	2.39867
$902$	0	0
$903$	−8.00000	−0.266223
$904$	−6.00000	−0.199557
$905$	0	0
$906$	20.0000	0.664455
$907$	−32.0000	−1.06254	−0.531271	−	0.847202i	$-0.678286\pi$
$907$	−32.0000	−1.06254	−0.531271	+	0.847202i	$0.678286\pi$
$908$	12.0000	0.398234
$909$	−18.0000	−0.597022
$910$	0	0
$911$	12.0000	0.397578	0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000	0.397578	0.198789	+	0.980042i	$0.436299\pi$
$912$	4.00000	0.132453
$913$	0	0
$914$	26.0000	0.860004
$915$	0	0
$916$	26.0000	0.859064
$917$	18.0000	0.594412
$918$	−24.0000	−0.792118
$919$	−34.0000	−1.12156	−0.560778	−	0.827966i	$-0.689498\pi$
$919$	−34.0000	−1.12156	−0.560778	+	0.827966i	$0.689498\pi$
$920$	0	0
$921$	−64.0000	−2.10887
$922$	30.0000	0.987997
$923$	24.0000	0.789970
$924$	2.00000	0.0657952
$925$	0	0
$926$	2.00000	0.0657241
$927$	4.00000	0.131377
$928$	0	0
$929$	−18.0000	−0.590561	−0.295280	−	0.955411i	$-0.595413\pi$
$929$	−18.0000	−0.590561	−0.295280	+	0.955411i	$0.595413\pi$
$930$	0	0
$931$	2.00000	0.0655474
$932$	6.00000	0.196537
$933$	48.0000	1.57145
$934$	18.0000	0.588978
$935$	0	0
$936$	2.00000	0.0653720
$937$	−2.00000	−0.0653372	−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000	−0.0653372	−0.0326686	+	0.999466i	$0.510401\pi$
$938$	4.00000	0.130605
$939$	32.0000	1.04428
$940$	0	0
$941$	−18.0000	−0.586783	−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000	−0.586783	−0.293392	+	0.955992i	$0.594784\pi$
$942$	4.00000	0.130327
$943$	0	0
$944$	12.0000	0.390567
$945$	0	0
$946$	4.00000	0.130051
$947$	48.0000	1.55979	0.779895	−	0.625910i	$-0.215272\pi$
$947$	48.0000	1.55979	0.779895	+	0.625910i	$0.215272\pi$
$948$	−20.0000	−0.649570
$949$	28.0000	0.908918
$950$	0	0
$951$	0	0
$952$	−6.00000	−0.194461
$953$	−6.00000	−0.194359	−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000	−0.194359	−0.0971795	+	0.995267i	$0.530982\pi$
$954$	12.0000	0.388514
$955$	0	0
$956$	18.0000	0.582162
$957$	0	0
$958$	0	0
$959$	−6.00000	−0.193750
$960$	0	0
$961$	33.0000	1.06452
$962$	−16.0000	−0.515861
$963$	−12.0000	−0.386695
$964$	8.00000	0.257663
$965$	0	0
$966$	12.0000	0.386094
$967$	16.0000	0.514525	0.257263	−	0.966342i	$-0.417179\pi$
$967$	16.0000	0.514525	0.257263	+	0.966342i	$0.417179\pi$
$968$	−1.00000	−0.0321412
$969$	−24.0000	−0.770991
$970$	0	0
$971$	60.0000	1.92549	0.962746	−	0.270408i	$-0.0871586\pi$
$971$	60.0000	1.92549	0.962746	+	0.270408i	$0.0871586\pi$
$972$	−10.0000	−0.320750
$973$	10.0000	0.320585
$974$	−22.0000	−0.704925
$975$	0	0
$976$	−10.0000	−0.320092
$977$	−42.0000	−1.34370	−0.671850	−	0.740688i	$-0.734500\pi$
$977$	−42.0000	−1.34370	−0.671850	+	0.740688i	$0.734500\pi$
$978$	−8.00000	−0.255812
$979$	18.0000	0.575282
$980$	0	0
$981$	8.00000	0.255420
$982$	−12.0000	−0.382935
$983$	−12.0000	−0.382741	−0.191370	−	0.981518i	$-0.561293\pi$
$983$	−12.0000	−0.382741	−0.191370	+	0.981518i	$0.561293\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	−4.00000	−0.127257
$989$	24.0000	0.763156
$990$	0	0
$991$	56.0000	1.77890	0.889449	−	0.457034i	$-0.151088\pi$
$991$	56.0000	1.77890	0.889449	+	0.457034i	$0.151088\pi$
$992$	−8.00000	−0.254000
$993$	40.0000	1.26936
$994$	−12.0000	−0.380617
$995$	0	0
$996$	0	0
$997$	10.0000	0.316703	0.158352	−	0.987383i	$-0.449382\pi$
$997$	10.0000	0.316703	0.158352	+	0.987383i	$0.449382\pi$
$998$	−20.0000	−0.633089
$999$	32.0000	1.01244

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3850.2.a.j.1.1		1
5.2	odd	4		3850.2.c.a.1849.1		2
5.3	odd	4		3850.2.c.a.1849.2		2
5.4	even	2		770.2.a.g.1.1	✓	1
15.14	odd	2		6930.2.a.f.1.1		1
20.19	odd	2		6160.2.a.n.1.1		1
35.34	odd	2		5390.2.a.bh.1.1		1
55.54	odd	2		8470.2.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.a.g.1.1	✓	1	5.4	even	2
3850.2.a.j.1.1		1	1.1	even	1	trivial
3850.2.c.a.1849.1		2	5.2	odd	4
3850.2.c.a.1849.2		2	5.3	odd	4
5390.2.a.bh.1.1		1	35.34	odd	2
6160.2.a.n.1.1		1	20.19	odd	2
6930.2.a.f.1.1		1	15.14	odd	2
8470.2.a.e.1.1		1	55.54	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:	\( N \)	\(=\)	\( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3850.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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