LMFDB - Embedded newform 3850.2.a.l.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:	$0$
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	$\chi$	$=$	3850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q-1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} -2.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{11} +2.00000 q^{12} +1.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -1.00000 q^{18} -1.00000 q^{19} -2.00000 q^{21} -1.00000 q^{22} +9.00000 q^{23} -2.00000 q^{24} -1.00000 q^{26} -4.00000 q^{27} -1.00000 q^{28} -3.00000 q^{29} +5.00000 q^{31} -1.00000 q^{32} +2.00000 q^{33} +1.00000 q^{36} +4.00000 q^{37} +1.00000 q^{38} +2.00000 q^{39} +2.00000 q^{42} +1.00000 q^{43} +1.00000 q^{44} -9.00000 q^{46} +2.00000 q^{48} +1.00000 q^{49} +1.00000 q^{52} +6.00000 q^{53} +4.00000 q^{54} +1.00000 q^{56} -2.00000 q^{57} +3.00000 q^{58} +2.00000 q^{61} -5.00000 q^{62} -1.00000 q^{63} +1.00000 q^{64} -2.00000 q^{66} -2.00000 q^{67} +18.0000 q^{69} -9.00000 q^{71} -1.00000 q^{72} +4.00000 q^{73} -4.00000 q^{74} -1.00000 q^{76} -1.00000 q^{77} -2.00000 q^{78} -4.00000 q^{79} -11.0000 q^{81} +9.00000 q^{83} -2.00000 q^{84} -1.00000 q^{86} -6.00000 q^{87} -1.00000 q^{88} +15.0000 q^{89} -1.00000 q^{91} +9.00000 q^{92} +10.0000 q^{93} -2.00000 q^{96} +1.00000 q^{97} -1.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)

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
$13$	1.00000	0.277350	0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000	0.277350	0.138675	+	0.990338i	$0.455716\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	−1.00000	−0.235702
$19$	−1.00000	−0.229416	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000	−0.229416	−0.114708	+	0.993399i	$0.536593\pi$
$20$	0	0
$21$	−2.00000	−0.436436
$22$	−1.00000	−0.213201
$23$	9.00000	1.87663	0.938315	−	0.345782i	$-0.112386\pi$
$23$	9.00000	1.87663	0.938315	+	0.345782i	$0.112386\pi$
$24$	−2.00000	−0.408248
$25$	0	0
$26$	−1.00000	−0.196116
$27$	−4.00000	−0.769800
$28$	−1.00000	−0.188982
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	0	0
$31$	5.00000	0.898027	0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000	0.898027	0.449013	+	0.893525i	$0.351776\pi$
$32$	−1.00000	−0.176777
$33$	2.00000	0.348155
$34$	0	0
$35$	0	0
$36$	1.00000	0.166667
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	1.00000	0.162221
$39$	2.00000	0.320256
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	2.00000	0.308607
$43$	1.00000	0.152499	0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000	0.152499	0.0762493	+	0.997089i	$0.475706\pi$
$44$	1.00000	0.150756
$45$	0	0
$46$	−9.00000	−1.32698
$47$	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
$51$	0	0
$52$	1.00000	0.138675
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	4.00000	0.544331
$55$	0	0
$56$	1.00000	0.133631
$57$	−2.00000	−0.264906
$58$	3.00000	0.393919
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−5.00000	−0.635001
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−2.00000	−0.246183
$67$	−2.00000	−0.244339	−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000	−0.244339	−0.122169	+	0.992509i	$0.538985\pi$
$68$	0	0
$69$	18.0000	2.16695
$70$	0	0
$71$	−9.00000	−1.06810	−0.534052	−	0.845452i	$-0.679331\pi$
$71$	−9.00000	−1.06810	−0.534052	+	0.845452i	$0.679331\pi$
$72$	−1.00000	−0.117851
$73$	4.00000	0.468165	0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000	0.468165	0.234082	+	0.972217i	$0.424791\pi$
$74$	−4.00000	−0.464991
$75$	0	0
$76$	−1.00000	−0.114708
$77$	−1.00000	−0.113961
$78$	−2.00000	−0.226455
$79$	−4.00000	−0.450035	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000	−0.450035	−0.225018	+	0.974355i	$0.572244\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	0	0
$83$	9.00000	0.987878	0.493939	−	0.869496i	$-0.335557\pi$
$83$	9.00000	0.987878	0.493939	+	0.869496i	$0.335557\pi$
$84$	−2.00000	−0.218218
$85$	0	0
$86$	−1.00000	−0.107833
$87$	−6.00000	−0.643268
$88$	−1.00000	−0.106600
$89$	15.0000	1.59000	0.794998	−	0.606612i	$-0.207472\pi$
$89$	15.0000	1.59000	0.794998	+	0.606612i	$0.207472\pi$
$90$	0	0
$91$	−1.00000	−0.104828
$92$	9.00000	0.938315
$93$	10.0000	1.03695
$94$	0	0
$95$	0	0
$96$	−2.00000	−0.204124
$97$	1.00000	0.101535	0.0507673	−	0.998711i	$-0.483833\pi$
$97$	1.00000	0.101535	0.0507673	+	0.998711i	$0.483833\pi$
$98$	−1.00000	−0.101015
$99$	1.00000	0.100504
$100$	0	0
$101$	−3.00000	−0.298511	−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000	−0.298511	−0.149256	+	0.988799i	$0.547688\pi$
$102$	0	0
$103$	7.00000	0.689730	0.344865	−	0.938652i	$-0.387925\pi$
$103$	7.00000	0.689730	0.344865	+	0.938652i	$0.387925\pi$
$104$	−1.00000	−0.0980581
$105$	0	0
$106$	−6.00000	−0.582772
$107$	3.00000	0.290021	0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000	0.290021	0.145010	+	0.989430i	$0.453678\pi$
$108$	−4.00000	−0.384900
$109$	11.0000	1.05361	0.526804	−	0.849987i	$-0.323390\pi$
$109$	11.0000	1.05361	0.526804	+	0.849987i	$0.323390\pi$
$110$	0	0
$111$	8.00000	0.759326
$112$	−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	$0.408930\pi$
$114$	2.00000	0.187317
$115$	0	0
$116$	−3.00000	−0.278543
$117$	1.00000	0.0924500
$118$	0	0
$119$	0	0
$120$	0	0
$121$	1.00000	0.0909091
$122$	−2.00000	−0.181071
$123$	0	0
$124$	5.00000	0.449013
$125$	0	0
$126$	1.00000	0.0890871
$127$	4.00000	0.354943	0.177471	−	0.984126i	$-0.443208\pi$
$127$	4.00000	0.354943	0.177471	+	0.984126i	$0.443208\pi$
$128$	−1.00000	−0.0883883
$129$	2.00000	0.176090
$130$	0	0
$131$	3.00000	0.262111	0.131056	−	0.991375i	$-0.458163\pi$
$131$	3.00000	0.262111	0.131056	+	0.991375i	$0.458163\pi$
$132$	2.00000	0.174078
$133$	1.00000	0.0867110
$134$	2.00000	0.172774
$135$	0	0
$136$	0	0
$137$	21.0000	1.79415	0.897076	−	0.441877i	$-0.145687\pi$
$137$	21.0000	1.79415	0.897076	+	0.441877i	$0.145687\pi$
$138$	−18.0000	−1.53226
$139$	5.00000	0.424094	0.212047	−	0.977259i	$-0.431987\pi$
$139$	5.00000	0.424094	0.212047	+	0.977259i	$0.431987\pi$
$140$	0	0
$141$	0	0
$142$	9.00000	0.755263
$143$	1.00000	0.0836242
$144$	1.00000	0.0833333
$145$	0	0
$146$	−4.00000	−0.331042
$147$	2.00000	0.164957
$148$	4.00000	0.328798
$149$	−18.0000	−1.47462	−0.737309	−	0.675556i	$-0.763904\pi$
$149$	−18.0000	−1.47462	−0.737309	+	0.675556i	$0.763904\pi$
$150$	0	0
$151$	−4.00000	−0.325515	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	−4.00000	−0.325515	−0.162758	+	0.986666i	$0.552039\pi$
$152$	1.00000	0.0811107
$153$	0	0
$154$	1.00000	0.0805823
$155$	0	0
$156$	2.00000	0.160128
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	4.00000	0.318223
$159$	12.0000	0.951662
$160$	0	0
$161$	−9.00000	−0.709299
$162$	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
$166$	−9.00000	−0.698535
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	2.00000	0.154303
$169$	−12.0000	−0.923077
$170$	0	0
$171$	−1.00000	−0.0764719
$172$	1.00000	0.0762493
$173$	9.00000	0.684257	0.342129	−	0.939653i	$-0.388852\pi$
$173$	9.00000	0.684257	0.342129	+	0.939653i	$0.388852\pi$
$174$	6.00000	0.454859
$175$	0	0
$176$	1.00000	0.0753778
$177$	0	0
$178$	−15.0000	−1.12430
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	0	0
$181$	−16.0000	−1.18927	−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000	−1.18927	−0.594635	+	0.803996i	$0.702704\pi$
$182$	1.00000	0.0741249
$183$	4.00000	0.295689
$184$	−9.00000	−0.663489
$185$	0	0
$186$	−10.0000	−0.733236
$187$	0	0
$188$	0	0
$189$	4.00000	0.290957
$190$	0	0
$191$	3.00000	0.217072	0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000	0.217072	0.108536	+	0.994092i	$0.465384\pi$
$192$	2.00000	0.144338
$193$	4.00000	0.287926	0.143963	−	0.989583i	$-0.454015\pi$
$193$	4.00000	0.287926	0.143963	+	0.989583i	$0.454015\pi$
$194$	−1.00000	−0.0717958
$195$	0	0
$196$	1.00000	0.0714286
$197$	27.0000	1.92367	0.961835	−	0.273629i	$-0.0882242\pi$
$197$	27.0000	1.92367	0.961835	+	0.273629i	$0.0882242\pi$
$198$	−1.00000	−0.0710669
$199$	11.0000	0.779769	0.389885	−	0.920864i	$-0.372515\pi$
$199$	11.0000	0.779769	0.389885	+	0.920864i	$0.372515\pi$
$200$	0	0
$201$	−4.00000	−0.282138
$202$	3.00000	0.211079
$203$	3.00000	0.210559
$204$	0	0
$205$	0	0
$206$	−7.00000	−0.487713
$207$	9.00000	0.625543
$208$	1.00000	0.0693375
$209$	−1.00000	−0.0691714
$210$	0	0
$211$	−4.00000	−0.275371	−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000	−0.275371	−0.137686	+	0.990476i	$0.543966\pi$
$212$	6.00000	0.412082
$213$	−18.0000	−1.23334
$214$	−3.00000	−0.205076
$215$	0	0
$216$	4.00000	0.272166
$217$	−5.00000	−0.339422
$218$	−11.0000	−0.745014
$219$	8.00000	0.540590
$220$	0	0
$221$	0	0
$222$	−8.00000	−0.536925
$223$	16.0000	1.07144	0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000	1.07144	0.535720	+	0.844396i	$0.320040\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	−6.00000	−0.399114
$227$	−27.0000	−1.79205	−0.896026	−	0.444001i	$-0.853559\pi$
$227$	−27.0000	−1.79205	−0.896026	+	0.444001i	$0.853559\pi$
$228$	−2.00000	−0.132453
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	0	0
$231$	−2.00000	−0.131590
$232$	3.00000	0.196960
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	−1.00000	−0.0653720
$235$	0	0
$236$	0	0
$237$	−8.00000	−0.519656
$238$	0	0
$239$	−18.0000	−1.16432	−0.582162	−	0.813073i	$-0.697793\pi$
$239$	−18.0000	−1.16432	−0.582162	+	0.813073i	$0.697793\pi$
$240$	0	0
$241$	−22.0000	−1.41714	−0.708572	−	0.705638i	$-0.750660\pi$
$241$	−22.0000	−1.41714	−0.708572	+	0.705638i	$0.750660\pi$
$242$	−1.00000	−0.0642824
$243$	−10.0000	−0.641500
$244$	2.00000	0.128037
$245$	0	0
$246$	0	0
$247$	−1.00000	−0.0636285
$248$	−5.00000	−0.317500
$249$	18.0000	1.14070
$250$	0	0
$251$	24.0000	1.51487	0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000	1.51487	0.757433	+	0.652913i	$0.226453\pi$
$252$	−1.00000	−0.0629941
$253$	9.00000	0.565825
$254$	−4.00000	−0.250982
$255$	0	0
$256$	1.00000	0.0625000
$257$	−3.00000	−0.187135	−0.0935674	−	0.995613i	$-0.529827\pi$
$257$	−3.00000	−0.187135	−0.0935674	+	0.995613i	$0.529827\pi$
$258$	−2.00000	−0.124515
$259$	−4.00000	−0.248548
$260$	0	0
$261$	−3.00000	−0.185695
$262$	−3.00000	−0.185341
$263$	−24.0000	−1.47990	−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000	−1.47990	−0.739952	+	0.672660i	$0.765152\pi$
$264$	−2.00000	−0.123091
$265$	0	0
$266$	−1.00000	−0.0613139
$267$	30.0000	1.83597
$268$	−2.00000	−0.122169
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	0	0
$271$	2.00000	0.121491	0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000	0.121491	0.0607457	+	0.998153i	$0.480652\pi$
$272$	0	0
$273$	−2.00000	−0.121046
$274$	−21.0000	−1.26866
$275$	0	0
$276$	18.0000	1.08347
$277$	−14.0000	−0.841178	−0.420589	−	0.907251i	$-0.638177\pi$
$277$	−14.0000	−0.841178	−0.420589	+	0.907251i	$0.638177\pi$
$278$	−5.00000	−0.299880
$279$	5.00000	0.299342
$280$	0	0
$281$	0	0		−	1.00000i	$-0.5\pi$
$281$	0	0			1.00000i	$0.5\pi$
$282$	0	0
$283$	−20.0000	−1.18888	−0.594438	−	0.804141i	$-0.702626\pi$
$283$	−20.0000	−1.18888	−0.594438	+	0.804141i	$0.702626\pi$
$284$	−9.00000	−0.534052
$285$	0	0
$286$	−1.00000	−0.0591312
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	−17.0000	−1.00000
$290$	0	0
$291$	2.00000	0.117242
$292$	4.00000	0.234082
$293$	30.0000	1.75262	0.876309	−	0.481749i	$-0.159998\pi$
$293$	30.0000	1.75262	0.876309	+	0.481749i	$0.159998\pi$
$294$	−2.00000	−0.116642
$295$	0	0
$296$	−4.00000	−0.232495
$297$	−4.00000	−0.232104
$298$	18.0000	1.04271
$299$	9.00000	0.520483
$300$	0	0
$301$	−1.00000	−0.0576390
$302$	4.00000	0.230174
$303$	−6.00000	−0.344691
$304$	−1.00000	−0.0573539
$305$	0	0
$306$	0	0
$307$	16.0000	0.913168	0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000	0.913168	0.456584	+	0.889680i	$0.349073\pi$
$308$	−1.00000	−0.0569803
$309$	14.0000	0.796432
$310$	0	0
$311$	−21.0000	−1.19080	−0.595400	−	0.803429i	$-0.703007\pi$
$311$	−21.0000	−1.19080	−0.595400	+	0.803429i	$0.703007\pi$
$312$	−2.00000	−0.113228
$313$	−26.0000	−1.46961	−0.734803	−	0.678280i	$-0.762726\pi$
$313$	−26.0000	−1.46961	−0.734803	+	0.678280i	$0.762726\pi$
$314$	−10.0000	−0.564333
$315$	0	0
$316$	−4.00000	−0.225018
$317$	12.0000	0.673987	0.336994	−	0.941507i	$-0.390590\pi$
$317$	12.0000	0.673987	0.336994	+	0.941507i	$0.390590\pi$
$318$	−12.0000	−0.672927
$319$	−3.00000	−0.167968
$320$	0	0
$321$	6.00000	0.334887
$322$	9.00000	0.501550
$323$	0	0
$324$	−11.0000	−0.611111
$325$	0	0
$326$	−4.00000	−0.221540
$327$	22.0000	1.21660
$328$	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	$0.314761\pi$
$332$	9.00000	0.493939
$333$	4.00000	0.219199
$334$	−12.0000	−0.656611
$335$	0	0
$336$	−2.00000	−0.109109
$337$	−14.0000	−0.762629	−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000	−0.762629	−0.381314	+	0.924445i	$0.624528\pi$
$338$	12.0000	0.652714
$339$	12.0000	0.651751
$340$	0	0
$341$	5.00000	0.270765
$342$	1.00000	0.0540738
$343$	−1.00000	−0.0539949
$344$	−1.00000	−0.0539164
$345$	0	0
$346$	−9.00000	−0.483843
$347$	−12.0000	−0.644194	−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000	−0.644194	−0.322097	+	0.946707i	$0.604388\pi$
$348$	−6.00000	−0.321634
$349$	17.0000	0.909989	0.454995	−	0.890494i	$-0.349641\pi$
$349$	17.0000	0.909989	0.454995	+	0.890494i	$0.349641\pi$
$350$	0	0
$351$	−4.00000	−0.213504
$352$	−1.00000	−0.0533002
$353$	−3.00000	−0.159674	−0.0798369	−	0.996808i	$-0.525440\pi$
$353$	−3.00000	−0.159674	−0.0798369	+	0.996808i	$0.525440\pi$
$354$	0	0
$355$	0	0
$356$	15.0000	0.794998
$357$	0	0
$358$	−12.0000	−0.634220
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	16.0000	0.840941
$363$	2.00000	0.104973
$364$	−1.00000	−0.0524142
$365$	0	0
$366$	−4.00000	−0.209083
$367$	−17.0000	−0.887393	−0.443696	−	0.896177i	$-0.646333\pi$
$367$	−17.0000	−0.887393	−0.443696	+	0.896177i	$0.646333\pi$
$368$	9.00000	0.469157
$369$	0	0
$370$	0	0
$371$	−6.00000	−0.311504
$372$	10.0000	0.518476
$373$	−14.0000	−0.724893	−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000	−0.724893	−0.362446	+	0.932005i	$0.618058\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−3.00000	−0.154508
$378$	−4.00000	−0.205738
$379$	−22.0000	−1.13006	−0.565032	−	0.825069i	$-0.691136\pi$
$379$	−22.0000	−1.13006	−0.565032	+	0.825069i	$0.691136\pi$
$380$	0	0
$381$	8.00000	0.409852
$382$	−3.00000	−0.153493
$383$	−21.0000	−1.07305	−0.536525	−	0.843884i	$-0.680263\pi$
$383$	−21.0000	−1.07305	−0.536525	+	0.843884i	$0.680263\pi$
$384$	−2.00000	−0.102062
$385$	0	0
$386$	−4.00000	−0.203595
$387$	1.00000	0.0508329
$388$	1.00000	0.0507673
$389$	12.0000	0.608424	0.304212	−	0.952604i	$-0.401607\pi$
$389$	12.0000	0.608424	0.304212	+	0.952604i	$0.401607\pi$
$390$	0	0
$391$	0	0
$392$	−1.00000	−0.0505076
$393$	6.00000	0.302660
$394$	−27.0000	−1.36024
$395$	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	$0.515982\pi$
$398$	−11.0000	−0.551380
$399$	2.00000	0.100125
$400$	0	0
$401$	15.0000	0.749064	0.374532	−	0.927214i	$-0.377803\pi$
$401$	15.0000	0.749064	0.374532	+	0.927214i	$0.377803\pi$
$402$	4.00000	0.199502
$403$	5.00000	0.249068
$404$	−3.00000	−0.149256
$405$	0	0
$406$	−3.00000	−0.148888
$407$	4.00000	0.198273
$408$	0	0
$409$	−4.00000	−0.197787	−0.0988936	−	0.995098i	$-0.531530\pi$
$409$	−4.00000	−0.197787	−0.0988936	+	0.995098i	$0.531530\pi$
$410$	0	0
$411$	42.0000	2.07171
$412$	7.00000	0.344865
$413$	0	0
$414$	−9.00000	−0.442326
$415$	0	0
$416$	−1.00000	−0.0490290
$417$	10.0000	0.489702
$418$	1.00000	0.0489116
$419$	30.0000	1.46560	0.732798	−	0.680446i	$-0.238214\pi$
$419$	30.0000	1.46560	0.732798	+	0.680446i	$0.238214\pi$
$420$	0	0
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	4.00000	0.194717
$423$	0	0
$424$	−6.00000	−0.291386
$425$	0	0
$426$	18.0000	0.872103
$427$	−2.00000	−0.0967868
$428$	3.00000	0.145010
$429$	2.00000	0.0965609
$430$	0	0
$431$	24.0000	1.15604	0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000	1.15604	0.578020	+	0.816023i	$0.303826\pi$
$432$	−4.00000	−0.192450
$433$	25.0000	1.20142	0.600712	−	0.799466i	$-0.294884\pi$
$433$	25.0000	1.20142	0.600712	+	0.799466i	$0.294884\pi$
$434$	5.00000	0.240008
$435$	0	0
$436$	11.0000	0.526804
$437$	−9.00000	−0.430528
$438$	−8.00000	−0.382255
$439$	−28.0000	−1.33637	−0.668184	−	0.743996i	$-0.732928\pi$
$439$	−28.0000	−1.33637	−0.668184	+	0.743996i	$0.732928\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	0	0
$443$	24.0000	1.14027	0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000	1.14027	0.570137	+	0.821549i	$0.306890\pi$
$444$	8.00000	0.379663
$445$	0	0
$446$	−16.0000	−0.757622
$447$	−36.0000	−1.70274
$448$	−1.00000	−0.0472456
$449$	21.0000	0.991051	0.495526	−	0.868593i	$-0.334975\pi$
$449$	21.0000	0.991051	0.495526	+	0.868593i	$0.334975\pi$
$450$	0	0
$451$	0	0
$452$	6.00000	0.282216
$453$	−8.00000	−0.375873
$454$	27.0000	1.26717
$455$	0	0
$456$	2.00000	0.0936586
$457$	−8.00000	−0.374224	−0.187112	−	0.982339i	$-0.559913\pi$
$457$	−8.00000	−0.374224	−0.187112	+	0.982339i	$0.559913\pi$
$458$	10.0000	0.467269
$459$	0	0
$460$	0	0
$461$	−18.0000	−0.838344	−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000	−0.838344	−0.419172	+	0.907907i	$0.637680\pi$
$462$	2.00000	0.0930484
$463$	−23.0000	−1.06890	−0.534450	−	0.845200i	$-0.679481\pi$
$463$	−23.0000	−1.06890	−0.534450	+	0.845200i	$0.679481\pi$
$464$	−3.00000	−0.139272
$465$	0	0
$466$	−6.00000	−0.277945
$467$	−6.00000	−0.277647	−0.138823	−	0.990317i	$-0.544332\pi$
$467$	−6.00000	−0.277647	−0.138823	+	0.990317i	$0.544332\pi$
$468$	1.00000	0.0462250
$469$	2.00000	0.0923514
$470$	0	0
$471$	20.0000	0.921551
$472$	0	0
$473$	1.00000	0.0459800
$474$	8.00000	0.367452
$475$	0	0
$476$	0	0
$477$	6.00000	0.274721
$478$	18.0000	0.823301
$479$	−18.0000	−0.822441	−0.411220	−	0.911536i	$-0.634897\pi$
$479$	−18.0000	−0.822441	−0.411220	+	0.911536i	$0.634897\pi$
$480$	0	0
$481$	4.00000	0.182384
$482$	22.0000	1.00207
$483$	−18.0000	−0.819028
$484$	1.00000	0.0454545
$485$	0	0
$486$	10.0000	0.453609
$487$	7.00000	0.317200	0.158600	−	0.987343i	$-0.449302\pi$
$487$	7.00000	0.317200	0.158600	+	0.987343i	$0.449302\pi$
$488$	−2.00000	−0.0905357
$489$	8.00000	0.361773
$490$	0	0
$491$	27.0000	1.21849	0.609246	−	0.792981i	$-0.291472\pi$
$491$	27.0000	1.21849	0.609246	+	0.792981i	$0.291472\pi$
$492$	0	0
$493$	0	0
$494$	1.00000	0.0449921
$495$	0	0
$496$	5.00000	0.224507
$497$	9.00000	0.403705
$498$	−18.0000	−0.806599
$499$	14.0000	0.626726	0.313363	−	0.949633i	$-0.398544\pi$
$499$	14.0000	0.626726	0.313363	+	0.949633i	$0.398544\pi$
$500$	0	0
$501$	24.0000	1.07224
$502$	−24.0000	−1.07117
$503$	42.0000	1.87269	0.936344	−	0.351085i	$-0.114187\pi$
$503$	42.0000	1.87269	0.936344	+	0.351085i	$0.114187\pi$
$504$	1.00000	0.0445435
$505$	0	0
$506$	−9.00000	−0.400099
$507$	−24.0000	−1.06588
$508$	4.00000	0.177471
$509$	18.0000	0.797836	0.398918	−	0.916987i	$-0.369386\pi$
$509$	18.0000	0.797836	0.398918	+	0.916987i	$0.369386\pi$
$510$	0	0
$511$	−4.00000	−0.176950
$512$	−1.00000	−0.0441942
$513$	4.00000	0.176604
$514$	3.00000	0.132324
$515$	0	0
$516$	2.00000	0.0880451
$517$	0	0
$518$	4.00000	0.175750
$519$	18.0000	0.790112
$520$	0	0
$521$	3.00000	0.131432	0.0657162	−	0.997838i	$-0.479067\pi$
$521$	3.00000	0.131432	0.0657162	+	0.997838i	$0.479067\pi$
$522$	3.00000	0.131306
$523$	−29.0000	−1.26808	−0.634041	−	0.773300i	$-0.718605\pi$
$523$	−29.0000	−1.26808	−0.634041	+	0.773300i	$0.718605\pi$
$524$	3.00000	0.131056
$525$	0	0
$526$	24.0000	1.04645
$527$	0	0
$528$	2.00000	0.0870388
$529$	58.0000	2.52174
$530$	0	0
$531$	0	0
$532$	1.00000	0.0433555
$533$	0	0
$534$	−30.0000	−1.29823
$535$	0	0
$536$	2.00000	0.0863868
$537$	24.0000	1.03568
$538$	6.00000	0.258678
$539$	1.00000	0.0430730
$540$	0	0
$541$	23.0000	0.988847	0.494424	−	0.869221i	$-0.335379\pi$
$541$	23.0000	0.988847	0.494424	+	0.869221i	$0.335379\pi$
$542$	−2.00000	−0.0859074
$543$	−32.0000	−1.37325
$544$	0	0
$545$	0	0
$546$	2.00000	0.0855921
$547$	19.0000	0.812381	0.406191	−	0.913788i	$-0.366857\pi$
$547$	19.0000	0.812381	0.406191	+	0.913788i	$0.366857\pi$
$548$	21.0000	0.897076
$549$	2.00000	0.0853579
$550$	0	0
$551$	3.00000	0.127804
$552$	−18.0000	−0.766131
$553$	4.00000	0.170097
$554$	14.0000	0.594803
$555$	0	0
$556$	5.00000	0.212047
$557$	−45.0000	−1.90671	−0.953356	−	0.301849i	$-0.902396\pi$
$557$	−45.0000	−1.90671	−0.953356	+	0.301849i	$0.902396\pi$
$558$	−5.00000	−0.211667
$559$	1.00000	0.0422955
$560$	0	0
$561$	0	0
$562$	0	0
$563$	12.0000	0.505740	0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000	0.505740	0.252870	+	0.967500i	$0.418626\pi$
$564$	0	0
$565$	0	0
$566$	20.0000	0.840663
$567$	11.0000	0.461957
$568$	9.00000	0.377632
$569$	−36.0000	−1.50920	−0.754599	−	0.656186i	$-0.772169\pi$
$569$	−36.0000	−1.50920	−0.754599	+	0.656186i	$0.772169\pi$
$570$	0	0
$571$	−13.0000	−0.544033	−0.272017	−	0.962293i	$-0.587691\pi$
$571$	−13.0000	−0.544033	−0.272017	+	0.962293i	$0.587691\pi$
$572$	1.00000	0.0418121
$573$	6.00000	0.250654
$574$	0	0
$575$	0	0
$576$	1.00000	0.0416667
$577$	−2.00000	−0.0832611	−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	−2.00000	−0.0832611	−0.0416305	+	0.999133i	$0.513255\pi$
$578$	17.0000	0.707107
$579$	8.00000	0.332469
$580$	0	0
$581$	−9.00000	−0.373383
$582$	−2.00000	−0.0829027
$583$	6.00000	0.248495
$584$	−4.00000	−0.165521
$585$	0	0
$586$	−30.0000	−1.23929
$587$	−12.0000	−0.495293	−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000	−0.495293	−0.247647	+	0.968850i	$0.579657\pi$
$588$	2.00000	0.0824786
$589$	−5.00000	−0.206021
$590$	0	0
$591$	54.0000	2.22126
$592$	4.00000	0.164399
$593$	42.0000	1.72473	0.862367	−	0.506284i	$-0.168981\pi$
$593$	42.0000	1.72473	0.862367	+	0.506284i	$0.168981\pi$
$594$	4.00000	0.164122
$595$	0	0
$596$	−18.0000	−0.737309
$597$	22.0000	0.900400
$598$	−9.00000	−0.368037
$599$	−12.0000	−0.490307	−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000	−0.490307	−0.245153	+	0.969484i	$0.578838\pi$
$600$	0	0
$601$	−4.00000	−0.163163	−0.0815817	−	0.996667i	$-0.525997\pi$
$601$	−4.00000	−0.163163	−0.0815817	+	0.996667i	$0.525997\pi$
$602$	1.00000	0.0407570
$603$	−2.00000	−0.0814463
$604$	−4.00000	−0.162758
$605$	0	0
$606$	6.00000	0.243733
$607$	−14.0000	−0.568242	−0.284121	−	0.958788i	$-0.591702\pi$
$607$	−14.0000	−0.568242	−0.284121	+	0.958788i	$0.591702\pi$
$608$	1.00000	0.0405554
$609$	6.00000	0.243132
$610$	0	0
$611$	0	0
$612$	0	0
$613$	−38.0000	−1.53481	−0.767403	−	0.641165i	$-0.778451\pi$
$613$	−38.0000	−1.53481	−0.767403	+	0.641165i	$0.778451\pi$
$614$	−16.0000	−0.645707
$615$	0	0
$616$	1.00000	0.0402911
$617$	3.00000	0.120775	0.0603877	−	0.998175i	$-0.480766\pi$
$617$	3.00000	0.120775	0.0603877	+	0.998175i	$0.480766\pi$
$618$	−14.0000	−0.563163
$619$	8.00000	0.321547	0.160774	−	0.986991i	$-0.448601\pi$
$619$	8.00000	0.321547	0.160774	+	0.986991i	$0.448601\pi$
$620$	0	0
$621$	−36.0000	−1.44463
$622$	21.0000	0.842023
$623$	−15.0000	−0.600962
$624$	2.00000	0.0800641
$625$	0	0
$626$	26.0000	1.03917
$627$	−2.00000	−0.0798723
$628$	10.0000	0.399043
$629$	0	0
$630$	0	0
$631$	8.00000	0.318475	0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000	0.318475	0.159237	+	0.987240i	$0.449096\pi$
$632$	4.00000	0.159111
$633$	−8.00000	−0.317971
$634$	−12.0000	−0.476581
$635$	0	0
$636$	12.0000	0.475831
$637$	1.00000	0.0396214
$638$	3.00000	0.118771
$639$	−9.00000	−0.356034
$640$	0	0
$641$	−3.00000	−0.118493	−0.0592464	−	0.998243i	$-0.518870\pi$
$641$	−3.00000	−0.118493	−0.0592464	+	0.998243i	$0.518870\pi$
$642$	−6.00000	−0.236801
$643$	−8.00000	−0.315489	−0.157745	−	0.987480i	$-0.550422\pi$
$643$	−8.00000	−0.315489	−0.157745	+	0.987480i	$0.550422\pi$
$644$	−9.00000	−0.354650
$645$	0	0
$646$	0	0
$647$	−24.0000	−0.943537	−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000	−0.943537	−0.471769	+	0.881722i	$0.656384\pi$
$648$	11.0000	0.432121
$649$	0	0
$650$	0	0
$651$	−10.0000	−0.391931
$652$	4.00000	0.156652
$653$	6.00000	0.234798	0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000	0.234798	0.117399	+	0.993085i	$0.462544\pi$
$654$	−22.0000	−0.860268
$655$	0	0
$656$	0	0
$657$	4.00000	0.156055
$658$	0	0
$659$	−15.0000	−0.584317	−0.292159	−	0.956370i	$-0.594373\pi$
$659$	−15.0000	−0.584317	−0.292159	+	0.956370i	$0.594373\pi$
$660$	0	0
$661$	−28.0000	−1.08907	−0.544537	−	0.838737i	$-0.683295\pi$
$661$	−28.0000	−1.08907	−0.544537	+	0.838737i	$0.683295\pi$
$662$	−20.0000	−0.777322
$663$	0	0
$664$	−9.00000	−0.349268
$665$	0	0
$666$	−4.00000	−0.154997
$667$	−27.0000	−1.04544
$668$	12.0000	0.464294
$669$	32.0000	1.23719
$670$	0	0
$671$	2.00000	0.0772091
$672$	2.00000	0.0771517
$673$	−20.0000	−0.770943	−0.385472	−	0.922720i	$-0.625961\pi$
$673$	−20.0000	−0.770943	−0.385472	+	0.922720i	$0.625961\pi$
$674$	14.0000	0.539260
$675$	0	0
$676$	−12.0000	−0.461538
$677$	−3.00000	−0.115299	−0.0576497	−	0.998337i	$-0.518361\pi$
$677$	−3.00000	−0.115299	−0.0576497	+	0.998337i	$0.518361\pi$
$678$	−12.0000	−0.460857
$679$	−1.00000	−0.0383765
$680$	0	0
$681$	−54.0000	−2.06928
$682$	−5.00000	−0.191460
$683$	12.0000	0.459167	0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000	0.459167	0.229584	+	0.973289i	$0.426264\pi$
$684$	−1.00000	−0.0382360
$685$	0	0
$686$	1.00000	0.0381802
$687$	−20.0000	−0.763048
$688$	1.00000	0.0381246
$689$	6.00000	0.228582
$690$	0	0
$691$	32.0000	1.21734	0.608669	−	0.793424i	$-0.291704\pi$
$691$	32.0000	1.21734	0.608669	+	0.793424i	$0.291704\pi$
$692$	9.00000	0.342129
$693$	−1.00000	−0.0379869
$694$	12.0000	0.455514
$695$	0	0
$696$	6.00000	0.227429
$697$	0	0
$698$	−17.0000	−0.643459
$699$	12.0000	0.453882
$700$	0	0
$701$	−21.0000	−0.793159	−0.396580	−	0.918000i	$-0.629803\pi$
$701$	−21.0000	−0.793159	−0.396580	+	0.918000i	$0.629803\pi$
$702$	4.00000	0.150970
$703$	−4.00000	−0.150863
$704$	1.00000	0.0376889
$705$	0	0
$706$	3.00000	0.112906
$707$	3.00000	0.112827
$708$	0	0
$709$	−40.0000	−1.50223	−0.751116	−	0.660171i	$-0.770484\pi$
$709$	−40.0000	−1.50223	−0.751116	+	0.660171i	$0.770484\pi$
$710$	0	0
$711$	−4.00000	−0.150012
$712$	−15.0000	−0.562149
$713$	45.0000	1.68526
$714$	0	0
$715$	0	0
$716$	12.0000	0.448461
$717$	−36.0000	−1.34444
$718$	0	0
$719$	−24.0000	−0.895049	−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000	−0.895049	−0.447524	+	0.894272i	$0.647694\pi$
$720$	0	0
$721$	−7.00000	−0.260694
$722$	18.0000	0.669891
$723$	−44.0000	−1.63638
$724$	−16.0000	−0.594635
$725$	0	0
$726$	−2.00000	−0.0742270
$727$	−29.0000	−1.07555	−0.537775	−	0.843088i	$-0.680735\pi$
$727$	−29.0000	−1.07555	−0.537775	+	0.843088i	$0.680735\pi$
$728$	1.00000	0.0370625
$729$	13.0000	0.481481
$730$	0	0
$731$	0	0
$732$	4.00000	0.147844
$733$	−23.0000	−0.849524	−0.424762	−	0.905305i	$-0.639642\pi$
$733$	−23.0000	−0.849524	−0.424762	+	0.905305i	$0.639642\pi$
$734$	17.0000	0.627481
$735$	0	0
$736$	−9.00000	−0.331744
$737$	−2.00000	−0.0736709
$738$	0	0
$739$	8.00000	0.294285	0.147142	−	0.989115i	$-0.452992\pi$
$739$	8.00000	0.294285	0.147142	+	0.989115i	$0.452992\pi$
$740$	0	0
$741$	−2.00000	−0.0734718
$742$	6.00000	0.220267
$743$	6.00000	0.220119	0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000	0.220119	0.110059	+	0.993925i	$0.464896\pi$
$744$	−10.0000	−0.366618
$745$	0	0
$746$	14.0000	0.512576
$747$	9.00000	0.329293
$748$	0	0
$749$	−3.00000	−0.109618
$750$	0	0
$751$	35.0000	1.27717	0.638584	−	0.769552i	$-0.279520\pi$
$751$	35.0000	1.27717	0.638584	+	0.769552i	$0.279520\pi$
$752$	0	0
$753$	48.0000	1.74922
$754$	3.00000	0.109254
$755$	0	0
$756$	4.00000	0.145479
$757$	−20.0000	−0.726912	−0.363456	−	0.931611i	$-0.618403\pi$
$757$	−20.0000	−0.726912	−0.363456	+	0.931611i	$0.618403\pi$
$758$	22.0000	0.799076
$759$	18.0000	0.653359
$760$	0	0
$761$	48.0000	1.74000	0.869999	−	0.493053i	$-0.164119\pi$
$761$	48.0000	1.74000	0.869999	+	0.493053i	$0.164119\pi$
$762$	−8.00000	−0.289809
$763$	−11.0000	−0.398227
$764$	3.00000	0.108536
$765$	0	0
$766$	21.0000	0.758761
$767$	0	0
$768$	2.00000	0.0721688
$769$	14.0000	0.504853	0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000	0.504853	0.252426	+	0.967616i	$0.418771\pi$
$770$	0	0
$771$	−6.00000	−0.216085
$772$	4.00000	0.143963
$773$	36.0000	1.29483	0.647415	−	0.762138i	$-0.275850\pi$
$773$	36.0000	1.29483	0.647415	+	0.762138i	$0.275850\pi$
$774$	−1.00000	−0.0359443
$775$	0	0
$776$	−1.00000	−0.0358979
$777$	−8.00000	−0.286998
$778$	−12.0000	−0.430221
$779$	0	0
$780$	0	0
$781$	−9.00000	−0.322045
$782$	0	0
$783$	12.0000	0.428845
$784$	1.00000	0.0357143
$785$	0	0
$786$	−6.00000	−0.214013
$787$	−20.0000	−0.712923	−0.356462	−	0.934310i	$-0.616017\pi$
$787$	−20.0000	−0.712923	−0.356462	+	0.934310i	$0.616017\pi$
$788$	27.0000	0.961835
$789$	−48.0000	−1.70885
$790$	0	0
$791$	−6.00000	−0.213335
$792$	−1.00000	−0.0355335
$793$	2.00000	0.0710221
$794$	2.00000	0.0709773
$795$	0	0
$796$	11.0000	0.389885
$797$	−24.0000	−0.850124	−0.425062	−	0.905164i	$-0.639748\pi$
$797$	−24.0000	−0.850124	−0.425062	+	0.905164i	$0.639748\pi$
$798$	−2.00000	−0.0707992
$799$	0	0
$800$	0	0
$801$	15.0000	0.529999
$802$	−15.0000	−0.529668
$803$	4.00000	0.141157
$804$	−4.00000	−0.141069
$805$	0	0
$806$	−5.00000	−0.176117
$807$	−12.0000	−0.422420
$808$	3.00000	0.105540
$809$	6.00000	0.210949	0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000	0.210949	0.105474	+	0.994422i	$0.466364\pi$
$810$	0	0
$811$	20.0000	0.702295	0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000	0.702295	0.351147	+	0.936320i	$0.385792\pi$
$812$	3.00000	0.105279
$813$	4.00000	0.140286
$814$	−4.00000	−0.140200
$815$	0	0
$816$	0	0
$817$	−1.00000	−0.0349856
$818$	4.00000	0.139857
$819$	−1.00000	−0.0349428
$820$	0	0
$821$	−15.0000	−0.523504	−0.261752	−	0.965135i	$-0.584300\pi$
$821$	−15.0000	−0.523504	−0.261752	+	0.965135i	$0.584300\pi$
$822$	−42.0000	−1.46492
$823$	−32.0000	−1.11545	−0.557725	−	0.830026i	$-0.688326\pi$
$823$	−32.0000	−1.11545	−0.557725	+	0.830026i	$0.688326\pi$
$824$	−7.00000	−0.243857
$825$	0	0
$826$	0	0
$827$	−15.0000	−0.521601	−0.260801	−	0.965393i	$-0.583986\pi$
$827$	−15.0000	−0.521601	−0.260801	+	0.965393i	$0.583986\pi$
$828$	9.00000	0.312772
$829$	26.0000	0.903017	0.451509	−	0.892267i	$-0.350886\pi$
$829$	26.0000	0.903017	0.451509	+	0.892267i	$0.350886\pi$
$830$	0	0
$831$	−28.0000	−0.971309
$832$	1.00000	0.0346688
$833$	0	0
$834$	−10.0000	−0.346272
$835$	0	0
$836$	−1.00000	−0.0345857
$837$	−20.0000	−0.691301
$838$	−30.0000	−1.03633
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	10.0000	0.344623
$843$	0	0
$844$	−4.00000	−0.137686
$845$	0	0
$846$	0	0
$847$	−1.00000	−0.0343604
$848$	6.00000	0.206041
$849$	−40.0000	−1.37280
$850$	0	0
$851$	36.0000	1.23406
$852$	−18.0000	−0.616670
$853$	−26.0000	−0.890223	−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000	−0.890223	−0.445112	+	0.895475i	$0.646836\pi$
$854$	2.00000	0.0684386
$855$	0	0
$856$	−3.00000	−0.102538
$857$	−48.0000	−1.63965	−0.819824	−	0.572615i	$-0.805929\pi$
$857$	−48.0000	−1.63965	−0.819824	+	0.572615i	$0.805929\pi$
$858$	−2.00000	−0.0682789
$859$	14.0000	0.477674	0.238837	−	0.971060i	$-0.423234\pi$
$859$	14.0000	0.477674	0.238837	+	0.971060i	$0.423234\pi$
$860$	0	0
$861$	0	0
$862$	−24.0000	−0.817443
$863$	−45.0000	−1.53182	−0.765909	−	0.642949i	$-0.777711\pi$
$863$	−45.0000	−1.53182	−0.765909	+	0.642949i	$0.777711\pi$
$864$	4.00000	0.136083
$865$	0	0
$866$	−25.0000	−0.849535
$867$	−34.0000	−1.15470
$868$	−5.00000	−0.169711
$869$	−4.00000	−0.135691
$870$	0	0
$871$	−2.00000	−0.0677674
$872$	−11.0000	−0.372507
$873$	1.00000	0.0338449
$874$	9.00000	0.304430
$875$	0	0
$876$	8.00000	0.270295
$877$	−17.0000	−0.574049	−0.287025	−	0.957923i	$-0.592666\pi$
$877$	−17.0000	−0.574049	−0.287025	+	0.957923i	$0.592666\pi$
$878$	28.0000	0.944954
$879$	60.0000	2.02375
$880$	0	0
$881$	33.0000	1.11180	0.555899	−	0.831250i	$-0.312374\pi$
$881$	33.0000	1.11180	0.555899	+	0.831250i	$0.312374\pi$
$882$	−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	$0.413234\pi$
$884$	0	0
$885$	0	0
$886$	−24.0000	−0.806296
$887$	−18.0000	−0.604381	−0.302190	−	0.953248i	$-0.597718\pi$
$887$	−18.0000	−0.604381	−0.302190	+	0.953248i	$0.597718\pi$
$888$	−8.00000	−0.268462
$889$	−4.00000	−0.134156
$890$	0	0
$891$	−11.0000	−0.368514
$892$	16.0000	0.535720
$893$	0	0
$894$	36.0000	1.20402
$895$	0	0
$896$	1.00000	0.0334077
$897$	18.0000	0.601003
$898$	−21.0000	−0.700779
$899$	−15.0000	−0.500278
$900$	0	0
$901$	0	0
$902$	0	0
$903$	−2.00000	−0.0665558
$904$	−6.00000	−0.199557
$905$	0	0
$906$	8.00000	0.265782
$907$	−2.00000	−0.0664089	−0.0332045	−	0.999449i	$-0.510571\pi$
$907$	−2.00000	−0.0664089	−0.0332045	+	0.999449i	$0.510571\pi$
$908$	−27.0000	−0.896026
$909$	−3.00000	−0.0995037
$910$	0	0
$911$	−24.0000	−0.795155	−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000	−0.795155	−0.397578	+	0.917568i	$0.630149\pi$
$912$	−2.00000	−0.0662266
$913$	9.00000	0.297857
$914$	8.00000	0.264616
$915$	0	0
$916$	−10.0000	−0.330409
$917$	−3.00000	−0.0990687
$918$	0	0
$919$	−16.0000	−0.527791	−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000	−0.527791	−0.263896	+	0.964551i	$0.585007\pi$
$920$	0	0
$921$	32.0000	1.05444
$922$	18.0000	0.592798
$923$	−9.00000	−0.296239
$924$	−2.00000	−0.0657952
$925$	0	0
$926$	23.0000	0.755827
$927$	7.00000	0.229910
$928$	3.00000	0.0984798
$929$	−45.0000	−1.47640	−0.738201	−	0.674581i	$-0.764324\pi$
$929$	−45.0000	−1.47640	−0.738201	+	0.674581i	$0.764324\pi$
$930$	0	0
$931$	−1.00000	−0.0327737
$932$	6.00000	0.196537
$933$	−42.0000	−1.37502
$934$	6.00000	0.196326
$935$	0	0
$936$	−1.00000	−0.0326860
$937$	−2.00000	−0.0653372	−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000	−0.0653372	−0.0326686	+	0.999466i	$0.510401\pi$
$938$	−2.00000	−0.0653023
$939$	−52.0000	−1.69696
$940$	0	0
$941$	−30.0000	−0.977972	−0.488986	−	0.872292i	$-0.662633\pi$
$941$	−30.0000	−0.977972	−0.488986	+	0.872292i	$0.662633\pi$
$942$	−20.0000	−0.651635
$943$	0	0
$944$	0	0
$945$	0	0
$946$	−1.00000	−0.0325128
$947$	−18.0000	−0.584921	−0.292461	−	0.956278i	$-0.594474\pi$
$947$	−18.0000	−0.584921	−0.292461	+	0.956278i	$0.594474\pi$
$948$	−8.00000	−0.259828
$949$	4.00000	0.129845
$950$	0	0
$951$	24.0000	0.778253
$952$	0	0
$953$	54.0000	1.74923	0.874616	−	0.484817i	$-0.161114\pi$
$953$	54.0000	1.74923	0.874616	+	0.484817i	$0.161114\pi$
$954$	−6.00000	−0.194257
$955$	0	0
$956$	−18.0000	−0.582162
$957$	−6.00000	−0.193952
$958$	18.0000	0.581554
$959$	−21.0000	−0.678125
$960$	0	0
$961$	−6.00000	−0.193548
$962$	−4.00000	−0.128965
$963$	3.00000	0.0966736
$964$	−22.0000	−0.708572
$965$	0	0
$966$	18.0000	0.579141
$967$	46.0000	1.47926	0.739630	−	0.673014i	$-0.235000\pi$
$967$	46.0000	1.47926	0.739630	+	0.673014i	$0.235000\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	0	0
$971$	−30.0000	−0.962746	−0.481373	−	0.876516i	$-0.659862\pi$
$971$	−30.0000	−0.962746	−0.481373	+	0.876516i	$0.659862\pi$
$972$	−10.0000	−0.320750
$973$	−5.00000	−0.160293
$974$	−7.00000	−0.224294
$975$	0	0
$976$	2.00000	0.0640184
$977$	18.0000	0.575871	0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000	0.575871	0.287936	+	0.957650i	$0.407031\pi$
$978$	−8.00000	−0.255812
$979$	15.0000	0.479402
$980$	0	0
$981$	11.0000	0.351203
$982$	−27.0000	−0.861605
$983$	−39.0000	−1.24391	−0.621953	−	0.783054i	$-0.713661\pi$
$983$	−39.0000	−1.24391	−0.621953	+	0.783054i	$0.713661\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	−1.00000	−0.0318142
$989$	9.00000	0.286183
$990$	0	0
$991$	56.0000	1.77890	0.889449	−	0.457034i	$-0.151088\pi$
$991$	56.0000	1.77890	0.889449	+	0.457034i	$0.151088\pi$
$992$	−5.00000	−0.158750
$993$	40.0000	1.26936
$994$	−9.00000	−0.285463
$995$	0	0
$996$	18.0000	0.570352
$997$	−14.0000	−0.443384	−0.221692	−	0.975117i	$-0.571158\pi$
$997$	−14.0000	−0.443384	−0.221692	+	0.975117i	$0.571158\pi$
$998$	−14.0000	−0.443162
$999$	−16.0000	−0.506218

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3850.2.a.l.1.1	✓	1
5.2	odd	4		3850.2.c.e.1849.1		2
5.3	odd	4		3850.2.c.e.1849.2		2
5.4	even	2		3850.2.a.n.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3850.2.a.l.1.1	✓	1	1.1	even	1	trivial
3850.2.a.n.1.1	yes	1	5.4	even	2
3850.2.c.e.1849.1		2	5.2	odd	4
3850.2.c.e.1849.2		2	5.3	odd	4

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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