LMFDB - Embedded newform 3850.2.a.m.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:	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)

$f(q)$

$=$

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

\(q+1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} -2.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{11} -2.00000 q^{12} -2.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} -2.00000 q^{17} +1.00000 q^{18} +6.00000 q^{19} +2.00000 q^{21} -1.00000 q^{22} -6.00000 q^{23} -2.00000 q^{24} -2.00000 q^{26} +4.00000 q^{27} -1.00000 q^{28} +4.00000 q^{29} +1.00000 q^{32} +2.00000 q^{33} -2.00000 q^{34} +1.00000 q^{36} -8.00000 q^{37} +6.00000 q^{38} +4.00000 q^{39} +2.00000 q^{42} -4.00000 q^{43} -1.00000 q^{44} -6.00000 q^{46} +4.00000 q^{47} -2.00000 q^{48} +1.00000 q^{49} +4.00000 q^{51} -2.00000 q^{52} +12.0000 q^{53} +4.00000 q^{54} -1.00000 q^{56} -12.0000 q^{57} +4.00000 q^{58} +2.00000 q^{61} -1.00000 q^{63} +1.00000 q^{64} +2.00000 q^{66} +8.00000 q^{67} -2.00000 q^{68} +12.0000 q^{69} -12.0000 q^{71} +1.00000 q^{72} +6.00000 q^{73} -8.00000 q^{74} +6.00000 q^{76} +1.00000 q^{77} +4.00000 q^{78} +10.0000 q^{79} -11.0000 q^{81} +12.0000 q^{83} +2.00000 q^{84} -4.00000 q^{86} -8.00000 q^{87} -1.00000 q^{88} +14.0000 q^{89} +2.00000 q^{91} -6.00000 q^{92} +4.00000 q^{94} -2.00000 q^{96} -4.00000 q^{97} +1.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

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	$-0.695913\pi$
$3$	−2.00000	−1.15470	−0.577350	+	0.816497i	$0.695913\pi$
$4$	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
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	1.00000	0.235702
$19$	6.00000	1.37649	0.688247	−	0.725476i	$-0.258380\pi$
$19$	6.00000	1.37649	0.688247	+	0.725476i	$0.258380\pi$
$20$	0	0
$21$	2.00000	0.436436
$22$	−1.00000	−0.213201
$23$	−6.00000	−1.25109	−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000	−1.25109	−0.625543	+	0.780189i	$0.715123\pi$
$24$	−2.00000	−0.408248
$25$	0	0
$26$	−2.00000	−0.392232
$27$	4.00000	0.769800
$28$	−1.00000	−0.188982
$29$	4.00000	0.742781	0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000	0.742781	0.371391	+	0.928477i	$0.378881\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	1.00000	0.176777
$33$	2.00000	0.348155
$34$	−2.00000	−0.342997
$35$	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	$0.728427\pi$
$38$	6.00000	0.973329
$39$	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	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	−6.00000	−0.884652
$47$	4.00000	0.583460	0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000	0.583460	0.291730	+	0.956501i	$0.405769\pi$
$48$	−2.00000	−0.288675
$49$	1.00000	0.142857
$50$	0	0
$51$	4.00000	0.560112
$52$	−2.00000	−0.277350
$53$	12.0000	1.64833	0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000	1.64833	0.824163	+	0.566352i	$0.191646\pi$
$54$	4.00000	0.544331
$55$	0	0
$56$	−1.00000	−0.133631
$57$	−12.0000	−1.58944
$58$	4.00000	0.525226
$59$	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	$0.459132\pi$
$62$	0	0
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	2.00000	0.246183
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	−2.00000	−0.242536
$69$	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
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	−8.00000	−0.929981
$75$	0	0
$76$	6.00000	0.688247
$77$	1.00000	0.113961
$78$	4.00000	0.452911
$79$	10.0000	1.12509	0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000	1.12509	0.562544	+	0.826767i	$0.309823\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	0	0
$83$	12.0000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	2.00000	0.218218
$85$	0	0
$86$	−4.00000	−0.431331
$87$	−8.00000	−0.857690
$88$	−1.00000	−0.106600
$89$	14.0000	1.48400	0.741999	−	0.670402i	$-0.233878\pi$
$89$	14.0000	1.48400	0.741999	+	0.670402i	$0.233878\pi$
$90$	0	0
$91$	2.00000	0.209657
$92$	−6.00000	−0.625543
$93$	0	0
$94$	4.00000	0.412568
$95$	0	0
$96$	−2.00000	−0.204124
$97$	−4.00000	−0.406138	−0.203069	−	0.979164i	$-0.565092\pi$
$97$	−4.00000	−0.406138	−0.203069	+	0.979164i	$0.565092\pi$
$98$	1.00000	0.101015
$99$	−1.00000	−0.100504
$100$	0	0
$101$	10.0000	0.995037	0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000	0.995037	0.497519	+	0.867453i	$0.334245\pi$
$102$	4.00000	0.396059
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	−2.00000	−0.196116
$105$	0	0
$106$	12.0000	1.16554
$107$	−20.0000	−1.93347	−0.966736	−	0.255774i	$-0.917670\pi$
$107$	−20.0000	−1.93347	−0.966736	+	0.255774i	$0.917670\pi$
$108$	4.00000	0.384900
$109$	4.00000	0.383131	0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000	0.383131	0.191565	+	0.981480i	$0.438644\pi$
$110$	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	$0.408930\pi$
$114$	−12.0000	−1.12390
$115$	0	0
$116$	4.00000	0.371391
$117$	−2.00000	−0.184900
$118$	0	0
$119$	2.00000	0.183340
$120$	0	0
$121$	1.00000	0.0909091
$122$	2.00000	0.181071
$123$	0	0
$124$	0	0
$125$	0	0
$126$	−1.00000	−0.0890871
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	1.00000	0.0883883
$129$	8.00000	0.704361
$130$	0	0
$131$	−6.00000	−0.524222	−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000	−0.524222	−0.262111	+	0.965038i	$0.584419\pi$
$132$	2.00000	0.174078
$133$	−6.00000	−0.520266
$134$	8.00000	0.691095
$135$	0	0
$136$	−2.00000	−0.171499
$137$	22.0000	1.87959	0.939793	−	0.341743i	$-0.111017\pi$
$137$	22.0000	1.87959	0.939793	+	0.341743i	$0.111017\pi$
$138$	12.0000	1.02151
$139$	−6.00000	−0.508913	−0.254457	−	0.967084i	$-0.581897\pi$
$139$	−6.00000	−0.508913	−0.254457	+	0.967084i	$0.581897\pi$
$140$	0	0
$141$	−8.00000	−0.673722
$142$	−12.0000	−1.00702
$143$	2.00000	0.167248
$144$	1.00000	0.0833333
$145$	0	0
$146$	6.00000	0.496564
$147$	−2.00000	−0.164957
$148$	−8.00000	−0.657596
$149$	4.00000	0.327693	0.163846	−	0.986486i	$-0.447610\pi$
$149$	4.00000	0.327693	0.163846	+	0.986486i	$0.447610\pi$
$150$	0	0
$151$	−6.00000	−0.488273	−0.244137	−	0.969741i	$-0.578505\pi$
$151$	−6.00000	−0.488273	−0.244137	+	0.969741i	$0.578505\pi$
$152$	6.00000	0.486664
$153$	−2.00000	−0.161690
$154$	1.00000	0.0805823
$155$	0	0
$156$	4.00000	0.320256
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	10.0000	0.795557
$159$	−24.0000	−1.90332
$160$	0	0
$161$	6.00000	0.472866
$162$	−11.0000	−0.864242
$163$	24.0000	1.87983	0.939913	−	0.341415i	$-0.110906\pi$
$163$	24.0000	1.87983	0.939913	+	0.341415i	$0.110906\pi$
$164$	0	0
$165$	0	0
$166$	12.0000	0.931381
$167$	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
$171$	6.00000	0.458831
$172$	−4.00000	−0.304997
$173$	18.0000	1.36851	0.684257	−	0.729241i	$-0.260127\pi$
$173$	18.0000	1.36851	0.684257	+	0.729241i	$0.260127\pi$
$174$	−8.00000	−0.606478
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	0	0
$178$	14.0000	1.04934
$179$	−4.00000	−0.298974	−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000	−0.298974	−0.149487	+	0.988764i	$0.547762\pi$
$180$	0	0
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	2.00000	0.148250
$183$	−4.00000	−0.295689
$184$	−6.00000	−0.442326
$185$	0	0
$186$	0	0
$187$	2.00000	0.146254
$188$	4.00000	0.291730
$189$	−4.00000	−0.290957
$190$	0	0
$191$	8.00000	0.578860	0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000	0.578860	0.289430	+	0.957199i	$0.406534\pi$
$192$	−2.00000	−0.144338
$193$	−2.00000	−0.143963	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000	−0.143963	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	−4.00000	−0.287183
$195$	0	0
$196$	1.00000	0.0714286
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	−1.00000	−0.0710669
$199$	16.0000	1.13421	0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000	1.13421	0.567105	+	0.823646i	$0.308063\pi$
$200$	0	0
$201$	−16.0000	−1.12855
$202$	10.0000	0.703598
$203$	−4.00000	−0.280745
$204$	4.00000	0.280056
$205$	0	0
$206$	8.00000	0.557386
$207$	−6.00000	−0.417029
$208$	−2.00000	−0.138675
$209$	−6.00000	−0.415029
$210$	0	0
$211$	−20.0000	−1.37686	−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000	−1.37686	−0.688428	+	0.725304i	$0.741699\pi$
$212$	12.0000	0.824163
$213$	24.0000	1.64445
$214$	−20.0000	−1.36717
$215$	0	0
$216$	4.00000	0.272166
$217$	0	0
$218$	4.00000	0.270914
$219$	−12.0000	−0.810885
$220$	0	0
$221$	4.00000	0.269069
$222$	16.0000	1.07385
$223$	−16.0000	−1.07144	−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000	−1.07144	−0.535720	+	0.844396i	$0.679960\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	6.00000	0.399114
$227$	24.0000	1.59294	0.796468	−	0.604681i	$-0.206699\pi$
$227$	24.0000	1.59294	0.796468	+	0.604681i	$0.206699\pi$
$228$	−12.0000	−0.794719
$229$	6.00000	0.396491	0.198246	−	0.980152i	$-0.436476\pi$
$229$	6.00000	0.396491	0.198246	+	0.980152i	$0.436476\pi$
$230$	0	0
$231$	−2.00000	−0.131590
$232$	4.00000	0.262613
$233$	26.0000	1.70332	0.851658	−	0.524097i	$-0.175597\pi$
$233$	26.0000	1.70332	0.851658	+	0.524097i	$0.175597\pi$
$234$	−2.00000	−0.130744
$235$	0	0
$236$	0	0
$237$	−20.0000	−1.29914
$238$	2.00000	0.129641
$239$	6.00000	0.388108	0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000	0.388108	0.194054	+	0.980991i	$0.437836\pi$
$240$	0	0
$241$	−8.00000	−0.515325	−0.257663	−	0.966235i	$-0.582952\pi$
$241$	−8.00000	−0.515325	−0.257663	+	0.966235i	$0.582952\pi$
$242$	1.00000	0.0642824
$243$	10.0000	0.641500
$244$	2.00000	0.128037
$245$	0	0
$246$	0	0
$247$	−12.0000	−0.763542
$248$	0	0
$249$	−24.0000	−1.52094
$250$	0	0
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	−1.00000	−0.0629941
$253$	6.00000	0.377217
$254$	−8.00000	−0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	28.0000	1.74659	0.873296	−	0.487190i	$-0.161978\pi$
$257$	28.0000	1.74659	0.873296	+	0.487190i	$0.161978\pi$
$258$	8.00000	0.498058
$259$	8.00000	0.497096
$260$	0	0
$261$	4.00000	0.247594
$262$	−6.00000	−0.370681
$263$	−8.00000	−0.493301	−0.246651	−	0.969104i	$-0.579330\pi$
$263$	−8.00000	−0.493301	−0.246651	+	0.969104i	$0.579330\pi$
$264$	2.00000	0.123091
$265$	0	0
$266$	−6.00000	−0.367884
$267$	−28.0000	−1.71357
$268$	8.00000	0.488678
$269$	14.0000	0.853595	0.426798	−	0.904347i	$-0.359642\pi$
$269$	14.0000	0.853595	0.426798	+	0.904347i	$0.359642\pi$
$270$	0	0
$271$	28.0000	1.70088	0.850439	−	0.526073i	$-0.176336\pi$
$271$	28.0000	1.70088	0.850439	+	0.526073i	$0.176336\pi$
$272$	−2.00000	−0.121268
$273$	−4.00000	−0.242091
$274$	22.0000	1.32907
$275$	0	0
$276$	12.0000	0.722315
$277$	22.0000	1.32185	0.660926	−	0.750451i	$-0.270164\pi$
$277$	22.0000	1.32185	0.660926	+	0.750451i	$0.270164\pi$
$278$	−6.00000	−0.359856
$279$	0	0
$280$	0	0
$281$	−2.00000	−0.119310	−0.0596550	−	0.998219i	$-0.519000\pi$
$281$	−2.00000	−0.119310	−0.0596550	+	0.998219i	$0.519000\pi$
$282$	−8.00000	−0.476393
$283$	−32.0000	−1.90220	−0.951101	−	0.308879i	$-0.900046\pi$
$283$	−32.0000	−1.90220	−0.951101	+	0.308879i	$0.900046\pi$
$284$	−12.0000	−0.712069
$285$	0	0
$286$	2.00000	0.118262
$287$	0	0
$288$	1.00000	0.0589256
$289$	−13.0000	−0.764706
$290$	0	0
$291$	8.00000	0.468968
$292$	6.00000	0.351123
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	−2.00000	−0.116642
$295$	0	0
$296$	−8.00000	−0.464991
$297$	−4.00000	−0.232104
$298$	4.00000	0.231714
$299$	12.0000	0.693978
$300$	0	0
$301$	4.00000	0.230556
$302$	−6.00000	−0.345261
$303$	−20.0000	−1.14897
$304$	6.00000	0.344124
$305$	0	0
$306$	−2.00000	−0.114332
$307$	12.0000	0.684876	0.342438	−	0.939540i	$-0.388747\pi$
$307$	12.0000	0.684876	0.342438	+	0.939540i	$0.388747\pi$
$308$	1.00000	0.0569803
$309$	−16.0000	−0.910208
$310$	0	0
$311$	16.0000	0.907277	0.453638	−	0.891186i	$-0.350126\pi$
$311$	16.0000	0.907277	0.453638	+	0.891186i	$0.350126\pi$
$312$	4.00000	0.226455
$313$	12.0000	0.678280	0.339140	−	0.940736i	$-0.389864\pi$
$313$	12.0000	0.678280	0.339140	+	0.940736i	$0.389864\pi$
$314$	10.0000	0.564333
$315$	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
$319$	−4.00000	−0.223957
$320$	0	0
$321$	40.0000	2.23258
$322$	6.00000	0.334367
$323$	−12.0000	−0.667698
$324$	−11.0000	−0.611111
$325$	0	0
$326$	24.0000	1.32924
$327$	−8.00000	−0.442401
$328$	0	0
$329$	−4.00000	−0.220527
$330$	0	0
$331$	12.0000	0.659580	0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000	0.659580	0.329790	+	0.944054i	$0.393022\pi$
$332$	12.0000	0.658586
$333$	−8.00000	−0.438397
$334$	0	0
$335$	0	0
$336$	2.00000	0.109109
$337$	2.00000	0.108947	0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000	0.108947	0.0544735	+	0.998515i	$0.482652\pi$
$338$	−9.00000	−0.489535
$339$	−12.0000	−0.651751
$340$	0	0
$341$	0	0
$342$	6.00000	0.324443
$343$	−1.00000	−0.0539949
$344$	−4.00000	−0.215666
$345$	0	0
$346$	18.0000	0.967686
$347$	−20.0000	−1.07366	−0.536828	−	0.843692i	$-0.680378\pi$
$347$	−20.0000	−1.07366	−0.536828	+	0.843692i	$0.680378\pi$
$348$	−8.00000	−0.428845
$349$	6.00000	0.321173	0.160586	−	0.987022i	$-0.448662\pi$
$349$	6.00000	0.321173	0.160586	+	0.987022i	$0.448662\pi$
$350$	0	0
$351$	−8.00000	−0.427008
$352$	−1.00000	−0.0533002
$353$	−20.0000	−1.06449	−0.532246	−	0.846590i	$-0.678652\pi$
$353$	−20.0000	−1.06449	−0.532246	+	0.846590i	$0.678652\pi$
$354$	0	0
$355$	0	0
$356$	14.0000	0.741999
$357$	−4.00000	−0.211702
$358$	−4.00000	−0.211407
$359$	−6.00000	−0.316668	−0.158334	−	0.987386i	$-0.550612\pi$
$359$	−6.00000	−0.316668	−0.158334	+	0.987386i	$0.550612\pi$
$360$	0	0
$361$	17.0000	0.894737
$362$	2.00000	0.105118
$363$	−2.00000	−0.104973
$364$	2.00000	0.104828
$365$	0	0
$366$	−4.00000	−0.209083
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	−6.00000	−0.312772
$369$	0	0
$370$	0	0
$371$	−12.0000	−0.623009
$372$	0	0
$373$	26.0000	1.34623	0.673114	−	0.739538i	$-0.264956\pi$
$373$	26.0000	1.34623	0.673114	+	0.739538i	$0.264956\pi$
$374$	2.00000	0.103418
$375$	0	0
$376$	4.00000	0.206284
$377$	−8.00000	−0.412021
$378$	−4.00000	−0.205738
$379$	4.00000	0.205466	0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000	0.205466	0.102733	+	0.994709i	$0.467241\pi$
$380$	0	0
$381$	16.0000	0.819705
$382$	8.00000	0.409316
$383$	−16.0000	−0.817562	−0.408781	−	0.912633i	$-0.634046\pi$
$383$	−16.0000	−0.817562	−0.408781	+	0.912633i	$0.634046\pi$
$384$	−2.00000	−0.102062
$385$	0	0
$386$	−2.00000	−0.101797
$387$	−4.00000	−0.203331
$388$	−4.00000	−0.203069
$389$	18.0000	0.912636	0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000	0.912636	0.456318	+	0.889817i	$0.349168\pi$
$390$	0	0
$391$	12.0000	0.606866
$392$	1.00000	0.0505076
$393$	12.0000	0.605320
$394$	2.00000	0.100759
$395$	0	0
$396$	−1.00000	−0.0502519
$397$	−14.0000	−0.702640	−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000	−0.702640	−0.351320	+	0.936255i	$0.614267\pi$
$398$	16.0000	0.802008
$399$	12.0000	0.600751
$400$	0	0
$401$	−34.0000	−1.69788	−0.848939	−	0.528490i	$-0.822758\pi$
$401$	−34.0000	−1.69788	−0.848939	+	0.528490i	$0.822758\pi$
$402$	−16.0000	−0.798007
$403$	0	0
$404$	10.0000	0.497519
$405$	0	0
$406$	−4.00000	−0.198517
$407$	8.00000	0.396545
$408$	4.00000	0.198030
$409$	0	0		−	1.00000i	$-0.5\pi$
$409$	0	0			1.00000i	$0.5\pi$
$410$	0	0
$411$	−44.0000	−2.17036
$412$	8.00000	0.394132
$413$	0	0
$414$	−6.00000	−0.294884
$415$	0	0
$416$	−2.00000	−0.0980581
$417$	12.0000	0.587643
$418$	−6.00000	−0.293470
$419$	−16.0000	−0.781651	−0.390826	−	0.920465i	$-0.627810\pi$
$419$	−16.0000	−0.781651	−0.390826	+	0.920465i	$0.627810\pi$
$420$	0	0
$421$	−26.0000	−1.26716	−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000	−1.26716	−0.633581	+	0.773676i	$0.718416\pi$
$422$	−20.0000	−0.973585
$423$	4.00000	0.194487
$424$	12.0000	0.582772
$425$	0	0
$426$	24.0000	1.16280
$427$	−2.00000	−0.0967868
$428$	−20.0000	−0.966736
$429$	−4.00000	−0.193122
$430$	0	0
$431$	−22.0000	−1.05970	−0.529851	−	0.848091i	$-0.677752\pi$
$431$	−22.0000	−1.05970	−0.529851	+	0.848091i	$0.677752\pi$
$432$	4.00000	0.192450
$433$	−16.0000	−0.768911	−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000	−0.768911	−0.384455	+	0.923144i	$0.625611\pi$
$434$	0	0
$435$	0	0
$436$	4.00000	0.191565
$437$	−36.0000	−1.72211
$438$	−12.0000	−0.573382
$439$	12.0000	0.572729	0.286364	−	0.958121i	$-0.407553\pi$
$439$	12.0000	0.572729	0.286364	+	0.958121i	$0.407553\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	4.00000	0.190261
$443$	−40.0000	−1.90046	−0.950229	−	0.311553i	$-0.899151\pi$
$443$	−40.0000	−1.90046	−0.950229	+	0.311553i	$0.899151\pi$
$444$	16.0000	0.759326
$445$	0	0
$446$	−16.0000	−0.757622
$447$	−8.00000	−0.378387
$448$	−1.00000	−0.0472456
$449$	14.0000	0.660701	0.330350	−	0.943858i	$-0.392833\pi$
$449$	14.0000	0.660701	0.330350	+	0.943858i	$0.392833\pi$
$450$	0	0
$451$	0	0
$452$	6.00000	0.282216
$453$	12.0000	0.563809
$454$	24.0000	1.12638
$455$	0	0
$456$	−12.0000	−0.561951
$457$	−22.0000	−1.02912	−0.514558	−	0.857455i	$-0.672044\pi$
$457$	−22.0000	−1.02912	−0.514558	+	0.857455i	$0.672044\pi$
$458$	6.00000	0.280362
$459$	−8.00000	−0.373408
$460$	0	0
$461$	−26.0000	−1.21094	−0.605470	−	0.795868i	$-0.707015\pi$
$461$	−26.0000	−1.21094	−0.605470	+	0.795868i	$0.707015\pi$
$462$	−2.00000	−0.0930484
$463$	10.0000	0.464739	0.232370	−	0.972628i	$-0.425352\pi$
$463$	10.0000	0.464739	0.232370	+	0.972628i	$0.425352\pi$
$464$	4.00000	0.185695
$465$	0	0
$466$	26.0000	1.20443
$467$	−38.0000	−1.75843	−0.879215	−	0.476425i	$-0.841932\pi$
$467$	−38.0000	−1.75843	−0.879215	+	0.476425i	$0.841932\pi$
$468$	−2.00000	−0.0924500
$469$	−8.00000	−0.369406
$470$	0	0
$471$	−20.0000	−0.921551
$472$	0	0
$473$	4.00000	0.183920
$474$	−20.0000	−0.918630
$475$	0	0
$476$	2.00000	0.0916698
$477$	12.0000	0.549442
$478$	6.00000	0.274434
$479$	8.00000	0.365529	0.182765	−	0.983157i	$-0.441495\pi$
$479$	8.00000	0.365529	0.182765	+	0.983157i	$0.441495\pi$
$480$	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
$487$	18.0000	0.815658	0.407829	−	0.913058i	$-0.366286\pi$
$487$	18.0000	0.815658	0.407829	+	0.913058i	$0.366286\pi$
$488$	2.00000	0.0905357
$489$	−48.0000	−2.17064
$490$	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
$493$	−8.00000	−0.360302
$494$	−12.0000	−0.539906
$495$	0	0
$496$	0	0
$497$	12.0000	0.538274
$498$	−24.0000	−1.07547
$499$	−28.0000	−1.25345	−0.626726	−	0.779240i	$-0.715605\pi$
$499$	−28.0000	−1.25345	−0.626726	+	0.779240i	$0.715605\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	−16.0000	−0.713405	−0.356702	−	0.934218i	$-0.616099\pi$
$503$	−16.0000	−0.713405	−0.356702	+	0.934218i	$0.616099\pi$
$504$	−1.00000	−0.0445435
$505$	0	0
$506$	6.00000	0.266733
$507$	18.0000	0.799408
$508$	−8.00000	−0.354943
$509$	2.00000	0.0886484	0.0443242	−	0.999017i	$-0.485887\pi$
$509$	2.00000	0.0886484	0.0443242	+	0.999017i	$0.485887\pi$
$510$	0	0
$511$	−6.00000	−0.265424
$512$	1.00000	0.0441942
$513$	24.0000	1.05963
$514$	28.0000	1.23503
$515$	0	0
$516$	8.00000	0.352180
$517$	−4.00000	−0.175920
$518$	8.00000	0.351500
$519$	−36.0000	−1.58022
$520$	0	0
$521$	−10.0000	−0.438108	−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000	−0.438108	−0.219054	+	0.975713i	$0.570297\pi$
$522$	4.00000	0.175075
$523$	−4.00000	−0.174908	−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000	−0.174908	−0.0874539	+	0.996169i	$0.527873\pi$
$524$	−6.00000	−0.262111
$525$	0	0
$526$	−8.00000	−0.348817
$527$	0	0
$528$	2.00000	0.0870388
$529$	13.0000	0.565217
$530$	0	0
$531$	0	0
$532$	−6.00000	−0.260133
$533$	0	0
$534$	−28.0000	−1.21168
$535$	0	0
$536$	8.00000	0.345547
$537$	8.00000	0.345225
$538$	14.0000	0.603583
$539$	−1.00000	−0.0430730
$540$	0	0
$541$	−16.0000	−0.687894	−0.343947	−	0.938989i	$-0.611764\pi$
$541$	−16.0000	−0.687894	−0.343947	+	0.938989i	$0.611764\pi$
$542$	28.0000	1.20270
$543$	−4.00000	−0.171656
$544$	−2.00000	−0.0857493
$545$	0	0
$546$	−4.00000	−0.171184
$547$	−20.0000	−0.855138	−0.427569	−	0.903983i	$-0.640630\pi$
$547$	−20.0000	−0.855138	−0.427569	+	0.903983i	$0.640630\pi$
$548$	22.0000	0.939793
$549$	2.00000	0.0853579
$550$	0	0
$551$	24.0000	1.02243
$552$	12.0000	0.510754
$553$	−10.0000	−0.425243
$554$	22.0000	0.934690
$555$	0	0
$556$	−6.00000	−0.254457
$557$	18.0000	0.762684	0.381342	−	0.924434i	$-0.375462\pi$
$557$	18.0000	0.762684	0.381342	+	0.924434i	$0.375462\pi$
$558$	0	0
$559$	8.00000	0.338364
$560$	0	0
$561$	−4.00000	−0.168880
$562$	−2.00000	−0.0843649
$563$	24.0000	1.01148	0.505740	−	0.862686i	$-0.331220\pi$
$563$	24.0000	1.01148	0.505740	+	0.862686i	$0.331220\pi$
$564$	−8.00000	−0.336861
$565$	0	0
$566$	−32.0000	−1.34506
$567$	11.0000	0.461957
$568$	−12.0000	−0.503509
$569$	26.0000	1.08998	0.544988	−	0.838444i	$-0.316534\pi$
$569$	26.0000	1.08998	0.544988	+	0.838444i	$0.316534\pi$
$570$	0	0
$571$	−40.0000	−1.67395	−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000	−1.67395	−0.836974	+	0.547243i	$0.815677\pi$
$572$	2.00000	0.0836242
$573$	−16.0000	−0.668410
$574$	0	0
$575$	0	0
$576$	1.00000	0.0416667
$577$	−4.00000	−0.166522	−0.0832611	−	0.996528i	$-0.526534\pi$
$577$	−4.00000	−0.166522	−0.0832611	+	0.996528i	$0.526534\pi$
$578$	−13.0000	−0.540729
$579$	4.00000	0.166234
$580$	0	0
$581$	−12.0000	−0.497844
$582$	8.00000	0.331611
$583$	−12.0000	−0.496989
$584$	6.00000	0.248282
$585$	0	0
$586$	6.00000	0.247858
$587$	2.00000	0.0825488	0.0412744	−	0.999148i	$-0.486858\pi$
$587$	2.00000	0.0825488	0.0412744	+	0.999148i	$0.486858\pi$
$588$	−2.00000	−0.0824786
$589$	0	0
$590$	0	0
$591$	−4.00000	−0.164538
$592$	−8.00000	−0.328798
$593$	−26.0000	−1.06769	−0.533846	−	0.845582i	$-0.679254\pi$
$593$	−26.0000	−1.06769	−0.533846	+	0.845582i	$0.679254\pi$
$594$	−4.00000	−0.164122
$595$	0	0
$596$	4.00000	0.163846
$597$	−32.0000	−1.30967
$598$	12.0000	0.490716
$599$	44.0000	1.79779	0.898896	−	0.438163i	$-0.144371\pi$
$599$	44.0000	1.79779	0.898896	+	0.438163i	$0.144371\pi$
$600$	0	0
$601$	44.0000	1.79480	0.897399	−	0.441221i	$-0.145454\pi$
$601$	44.0000	1.79480	0.897399	+	0.441221i	$0.145454\pi$
$602$	4.00000	0.163028
$603$	8.00000	0.325785
$604$	−6.00000	−0.244137
$605$	0	0
$606$	−20.0000	−0.812444
$607$	−16.0000	−0.649420	−0.324710	−	0.945814i	$-0.605267\pi$
$607$	−16.0000	−0.649420	−0.324710	+	0.945814i	$0.605267\pi$
$608$	6.00000	0.243332
$609$	8.00000	0.324176
$610$	0	0
$611$	−8.00000	−0.323645
$612$	−2.00000	−0.0808452
$613$	26.0000	1.05013	0.525065	−	0.851062i	$-0.324041\pi$
$613$	26.0000	1.05013	0.525065	+	0.851062i	$0.324041\pi$
$614$	12.0000	0.484281
$615$	0	0
$616$	1.00000	0.0402911
$617$	42.0000	1.69086	0.845428	−	0.534089i	$-0.179345\pi$
$617$	42.0000	1.69086	0.845428	+	0.534089i	$0.179345\pi$
$618$	−16.0000	−0.643614
$619$	−32.0000	−1.28619	−0.643094	−	0.765787i	$-0.722350\pi$
$619$	−32.0000	−1.28619	−0.643094	+	0.765787i	$0.722350\pi$
$620$	0	0
$621$	−24.0000	−0.963087
$622$	16.0000	0.641542
$623$	−14.0000	−0.560898
$624$	4.00000	0.160128
$625$	0	0
$626$	12.0000	0.479616
$627$	12.0000	0.479234
$628$	10.0000	0.399043
$629$	16.0000	0.637962
$630$	0	0
$631$	−8.00000	−0.318475	−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000	−0.318475	−0.159237	+	0.987240i	$0.550904\pi$
$632$	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
$638$	−4.00000	−0.158362
$639$	−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	$0.701845\pi$
$642$	40.0000	1.57867
$643$	−34.0000	−1.34083	−0.670415	−	0.741987i	$-0.733884\pi$
$643$	−34.0000	−1.34083	−0.670415	+	0.741987i	$0.733884\pi$
$644$	6.00000	0.236433
$645$	0	0
$646$	−12.0000	−0.472134
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	−11.0000	−0.432121
$649$	0	0
$650$	0	0
$651$	0	0
$652$	24.0000	0.939913
$653$	36.0000	1.40879	0.704394	−	0.709809i	$-0.251219\pi$
$653$	36.0000	1.40879	0.704394	+	0.709809i	$0.251219\pi$
$654$	−8.00000	−0.312825
$655$	0	0
$656$	0	0
$657$	6.00000	0.234082
$658$	−4.00000	−0.155936
$659$	8.00000	0.311636	0.155818	−	0.987786i	$-0.450199\pi$
$659$	8.00000	0.311636	0.155818	+	0.987786i	$0.450199\pi$
$660$	0	0
$661$	42.0000	1.63361	0.816805	−	0.576913i	$-0.195743\pi$
$661$	42.0000	1.63361	0.816805	+	0.576913i	$0.195743\pi$
$662$	12.0000	0.466393
$663$	−8.00000	−0.310694
$664$	12.0000	0.465690
$665$	0	0
$666$	−8.00000	−0.309994
$667$	−24.0000	−0.929284
$668$	0	0
$669$	32.0000	1.23719
$670$	0	0
$671$	−2.00000	−0.0772091
$672$	2.00000	0.0771517
$673$	42.0000	1.61898	0.809491	−	0.587133i	$-0.199743\pi$
$673$	42.0000	1.61898	0.809491	+	0.587133i	$0.199743\pi$
$674$	2.00000	0.0770371
$675$	0	0
$676$	−9.00000	−0.346154
$677$	−38.0000	−1.46046	−0.730229	−	0.683202i	$-0.760587\pi$
$677$	−38.0000	−1.46046	−0.730229	+	0.683202i	$0.760587\pi$
$678$	−12.0000	−0.460857
$679$	4.00000	0.153506
$680$	0	0
$681$	−48.0000	−1.83936
$682$	0	0
$683$	4.00000	0.153056	0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000	0.153056	0.0765279	+	0.997067i	$0.475617\pi$
$684$	6.00000	0.229416
$685$	0	0
$686$	−1.00000	−0.0381802
$687$	−12.0000	−0.457829
$688$	−4.00000	−0.152499
$689$	−24.0000	−0.914327
$690$	0	0
$691$	12.0000	0.456502	0.228251	−	0.973602i	$-0.426699\pi$
$691$	12.0000	0.456502	0.228251	+	0.973602i	$0.426699\pi$
$692$	18.0000	0.684257
$693$	1.00000	0.0379869
$694$	−20.0000	−0.759190
$695$	0	0
$696$	−8.00000	−0.303239
$697$	0	0
$698$	6.00000	0.227103
$699$	−52.0000	−1.96682
$700$	0	0
$701$	−8.00000	−0.302156	−0.151078	−	0.988522i	$-0.548274\pi$
$701$	−8.00000	−0.302156	−0.151078	+	0.988522i	$0.548274\pi$
$702$	−8.00000	−0.301941
$703$	−48.0000	−1.81035
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	−20.0000	−0.752710
$707$	−10.0000	−0.376089
$708$	0	0
$709$	−30.0000	−1.12667	−0.563337	−	0.826227i	$-0.690483\pi$
$709$	−30.0000	−1.12667	−0.563337	+	0.826227i	$0.690483\pi$
$710$	0	0
$711$	10.0000	0.375029
$712$	14.0000	0.524672
$713$	0	0
$714$	−4.00000	−0.149696
$715$	0	0
$716$	−4.00000	−0.149487
$717$	−12.0000	−0.448148
$718$	−6.00000	−0.223918
$719$	48.0000	1.79010	0.895049	−	0.445968i	$-0.147140\pi$
$719$	48.0000	1.79010	0.895049	+	0.445968i	$0.147140\pi$
$720$	0	0
$721$	−8.00000	−0.297936
$722$	17.0000	0.632674
$723$	16.0000	0.595046
$724$	2.00000	0.0743294
$725$	0	0
$726$	−2.00000	−0.0742270
$727$	44.0000	1.63187	0.815935	−	0.578144i	$-0.196223\pi$
$727$	44.0000	1.63187	0.815935	+	0.578144i	$0.196223\pi$
$728$	2.00000	0.0741249
$729$	13.0000	0.481481
$730$	0	0
$731$	8.00000	0.295891
$732$	−4.00000	−0.147844
$733$	2.00000	0.0738717	0.0369358	−	0.999318i	$-0.488240\pi$
$733$	2.00000	0.0738717	0.0369358	+	0.999318i	$0.488240\pi$
$734$	0	0
$735$	0	0
$736$	−6.00000	−0.221163
$737$	−8.00000	−0.294684
$738$	0	0
$739$	−36.0000	−1.32428	−0.662141	−	0.749380i	$-0.730352\pi$
$739$	−36.0000	−1.32428	−0.662141	+	0.749380i	$0.730352\pi$
$740$	0	0
$741$	24.0000	0.881662
$742$	−12.0000	−0.440534
$743$	−48.0000	−1.76095	−0.880475	−	0.474093i	$-0.842776\pi$
$743$	−48.0000	−1.76095	−0.880475	+	0.474093i	$0.842776\pi$
$744$	0	0
$745$	0	0
$746$	26.0000	0.951928
$747$	12.0000	0.439057
$748$	2.00000	0.0731272
$749$	20.0000	0.730784
$750$	0	0
$751$	4.00000	0.145962	0.0729810	−	0.997333i	$-0.476749\pi$
$751$	4.00000	0.145962	0.0729810	+	0.997333i	$0.476749\pi$
$752$	4.00000	0.145865
$753$	0	0
$754$	−8.00000	−0.291343
$755$	0	0
$756$	−4.00000	−0.145479
$757$	−52.0000	−1.88997	−0.944986	−	0.327111i	$-0.893925\pi$
$757$	−52.0000	−1.88997	−0.944986	+	0.327111i	$0.893925\pi$
$758$	4.00000	0.145287
$759$	−12.0000	−0.435572
$760$	0	0
$761$	−24.0000	−0.869999	−0.435000	−	0.900431i	$-0.643252\pi$
$761$	−24.0000	−0.869999	−0.435000	+	0.900431i	$0.643252\pi$
$762$	16.0000	0.579619
$763$	−4.00000	−0.144810
$764$	8.00000	0.289430
$765$	0	0
$766$	−16.0000	−0.578103
$767$	0	0
$768$	−2.00000	−0.0721688
$769$	−28.0000	−1.00971	−0.504853	−	0.863205i	$-0.668453\pi$
$769$	−28.0000	−1.00971	−0.504853	+	0.863205i	$0.668453\pi$
$770$	0	0
$771$	−56.0000	−2.01679
$772$	−2.00000	−0.0719816
$773$	6.00000	0.215805	0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000	0.215805	0.107903	+	0.994161i	$0.465587\pi$
$774$	−4.00000	−0.143777
$775$	0	0
$776$	−4.00000	−0.143592
$777$	−16.0000	−0.573997
$778$	18.0000	0.645331
$779$	0	0
$780$	0	0
$781$	12.0000	0.429394
$782$	12.0000	0.429119
$783$	16.0000	0.571793
$784$	1.00000	0.0357143
$785$	0	0
$786$	12.0000	0.428026
$787$	48.0000	1.71102	0.855508	−	0.517790i	$-0.173245\pi$
$787$	48.0000	1.71102	0.855508	+	0.517790i	$0.173245\pi$
$788$	2.00000	0.0712470
$789$	16.0000	0.569615
$790$	0	0
$791$	−6.00000	−0.213335
$792$	−1.00000	−0.0355335
$793$	−4.00000	−0.142044
$794$	−14.0000	−0.496841
$795$	0	0
$796$	16.0000	0.567105
$797$	−30.0000	−1.06265	−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000	−1.06265	−0.531327	+	0.847167i	$0.678307\pi$
$798$	12.0000	0.424795
$799$	−8.00000	−0.283020
$800$	0	0
$801$	14.0000	0.494666
$802$	−34.0000	−1.20058
$803$	−6.00000	−0.211735
$804$	−16.0000	−0.564276
$805$	0	0
$806$	0	0
$807$	−28.0000	−0.985647
$808$	10.0000	0.351799
$809$	54.0000	1.89854	0.949269	−	0.314464i	$-0.101825\pi$
$809$	54.0000	1.89854	0.949269	+	0.314464i	$0.101825\pi$
$810$	0	0
$811$	−30.0000	−1.05344	−0.526721	−	0.850038i	$-0.676579\pi$
$811$	−30.0000	−1.05344	−0.526721	+	0.850038i	$0.676579\pi$
$812$	−4.00000	−0.140372
$813$	−56.0000	−1.96401
$814$	8.00000	0.280400
$815$	0	0
$816$	4.00000	0.140028
$817$	−24.0000	−0.839654
$818$	0	0
$819$	2.00000	0.0698857
$820$	0	0
$821$	−8.00000	−0.279202	−0.139601	−	0.990208i	$-0.544582\pi$
$821$	−8.00000	−0.279202	−0.139601	+	0.990208i	$0.544582\pi$
$822$	−44.0000	−1.53468
$823$	−14.0000	−0.488009	−0.244005	−	0.969774i	$-0.578461\pi$
$823$	−14.0000	−0.488009	−0.244005	+	0.969774i	$0.578461\pi$
$824$	8.00000	0.278693
$825$	0	0
$826$	0	0
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	−6.00000	−0.208514
$829$	−26.0000	−0.903017	−0.451509	−	0.892267i	$-0.649114\pi$
$829$	−26.0000	−0.903017	−0.451509	+	0.892267i	$0.649114\pi$
$830$	0	0
$831$	−44.0000	−1.52634
$832$	−2.00000	−0.0693375
$833$	−2.00000	−0.0692959
$834$	12.0000	0.415526
$835$	0	0
$836$	−6.00000	−0.207514
$837$	0	0
$838$	−16.0000	−0.552711
$839$	−40.0000	−1.38095	−0.690477	−	0.723355i	$-0.742599\pi$
$839$	−40.0000	−1.38095	−0.690477	+	0.723355i	$0.742599\pi$
$840$	0	0
$841$	−13.0000	−0.448276
$842$	−26.0000	−0.896019
$843$	4.00000	0.137767
$844$	−20.0000	−0.688428
$845$	0	0
$846$	4.00000	0.137523
$847$	−1.00000	−0.0343604
$848$	12.0000	0.412082
$849$	64.0000	2.19647
$850$	0	0
$851$	48.0000	1.64542
$852$	24.0000	0.822226
$853$	−22.0000	−0.753266	−0.376633	−	0.926363i	$-0.622918\pi$
$853$	−22.0000	−0.753266	−0.376633	+	0.926363i	$0.622918\pi$
$854$	−2.00000	−0.0684386
$855$	0	0
$856$	−20.0000	−0.683586
$857$	30.0000	1.02478	0.512390	−	0.858753i	$-0.328760\pi$
$857$	30.0000	1.02478	0.512390	+	0.858753i	$0.328760\pi$
$858$	−4.00000	−0.136558
$859$	48.0000	1.63774	0.818869	−	0.573980i	$-0.194601\pi$
$859$	48.0000	1.63774	0.818869	+	0.573980i	$0.194601\pi$
$860$	0	0
$861$	0	0
$862$	−22.0000	−0.749323
$863$	−30.0000	−1.02121	−0.510606	−	0.859815i	$-0.670579\pi$
$863$	−30.0000	−1.02121	−0.510606	+	0.859815i	$0.670579\pi$
$864$	4.00000	0.136083
$865$	0	0
$866$	−16.0000	−0.543702
$867$	26.0000	0.883006
$868$	0	0
$869$	−10.0000	−0.339227
$870$	0	0
$871$	−16.0000	−0.542139
$872$	4.00000	0.135457
$873$	−4.00000	−0.135379
$874$	−36.0000	−1.21772
$875$	0	0
$876$	−12.0000	−0.405442
$877$	−14.0000	−0.472746	−0.236373	−	0.971662i	$-0.575959\pi$
$877$	−14.0000	−0.472746	−0.236373	+	0.971662i	$0.575959\pi$
$878$	12.0000	0.404980
$879$	−12.0000	−0.404750
$880$	0	0
$881$	−14.0000	−0.471672	−0.235836	−	0.971793i	$-0.575783\pi$
$881$	−14.0000	−0.471672	−0.235836	+	0.971793i	$0.575783\pi$
$882$	1.00000	0.0336718
$883$	−28.0000	−0.942275	−0.471138	−	0.882060i	$-0.656156\pi$
$883$	−28.0000	−0.942275	−0.471138	+	0.882060i	$0.656156\pi$
$884$	4.00000	0.134535
$885$	0	0
$886$	−40.0000	−1.34383
$887$	−48.0000	−1.61168	−0.805841	−	0.592132i	$-0.798286\pi$
$887$	−48.0000	−1.61168	−0.805841	+	0.592132i	$0.798286\pi$
$888$	16.0000	0.536925
$889$	8.00000	0.268311
$890$	0	0
$891$	11.0000	0.368514
$892$	−16.0000	−0.535720
$893$	24.0000	0.803129
$894$	−8.00000	−0.267560
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	−24.0000	−0.801337
$898$	14.0000	0.467186
$899$	0	0
$900$	0	0
$901$	−24.0000	−0.799556
$902$	0	0
$903$	−8.00000	−0.266223
$904$	6.00000	0.199557
$905$	0	0
$906$	12.0000	0.398673
$907$	4.00000	0.132818	0.0664089	−	0.997792i	$-0.478846\pi$
$907$	4.00000	0.132818	0.0664089	+	0.997792i	$0.478846\pi$
$908$	24.0000	0.796468
$909$	10.0000	0.331679
$910$	0	0
$911$	−12.0000	−0.397578	−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000	−0.397578	−0.198789	+	0.980042i	$0.563701\pi$
$912$	−12.0000	−0.397360
$913$	−12.0000	−0.397142
$914$	−22.0000	−0.727695
$915$	0	0
$916$	6.00000	0.198246
$917$	6.00000	0.198137
$918$	−8.00000	−0.264039
$919$	26.0000	0.857661	0.428830	−	0.903385i	$-0.358926\pi$
$919$	26.0000	0.857661	0.428830	+	0.903385i	$0.358926\pi$
$920$	0	0
$921$	−24.0000	−0.790827
$922$	−26.0000	−0.856264
$923$	24.0000	0.789970
$924$	−2.00000	−0.0657952
$925$	0	0
$926$	10.0000	0.328620
$927$	8.00000	0.262754
$928$	4.00000	0.131306
$929$	30.0000	0.984268	0.492134	−	0.870519i	$-0.336217\pi$
$929$	30.0000	0.984268	0.492134	+	0.870519i	$0.336217\pi$
$930$	0	0
$931$	6.00000	0.196642
$932$	26.0000	0.851658
$933$	−32.0000	−1.04763
$934$	−38.0000	−1.24340
$935$	0	0
$936$	−2.00000	−0.0653720
$937$	−6.00000	−0.196011	−0.0980057	−	0.995186i	$-0.531246\pi$
$937$	−6.00000	−0.196011	−0.0980057	+	0.995186i	$0.531246\pi$
$938$	−8.00000	−0.261209
$939$	−24.0000	−0.783210
$940$	0	0
$941$	18.0000	0.586783	0.293392	−	0.955992i	$-0.405216\pi$
$941$	18.0000	0.586783	0.293392	+	0.955992i	$0.405216\pi$
$942$	−20.0000	−0.651635
$943$	0	0
$944$	0	0
$945$	0	0
$946$	4.00000	0.130051
$947$	52.0000	1.68977	0.844886	−	0.534946i	$-0.179668\pi$
$947$	52.0000	1.68977	0.844886	+	0.534946i	$0.179668\pi$
$948$	−20.0000	−0.649570
$949$	−12.0000	−0.389536
$950$	0	0
$951$	0	0
$952$	2.00000	0.0648204
$953$	−18.0000	−0.583077	−0.291539	−	0.956559i	$-0.594167\pi$
$953$	−18.0000	−0.583077	−0.291539	+	0.956559i	$0.594167\pi$
$954$	12.0000	0.388514
$955$	0	0
$956$	6.00000	0.194054
$957$	8.00000	0.258603
$958$	8.00000	0.258468
$959$	−22.0000	−0.710417
$960$	0	0
$961$	−31.0000	−1.00000
$962$	16.0000	0.515861
$963$	−20.0000	−0.644491
$964$	−8.00000	−0.257663
$965$	0	0
$966$	−12.0000	−0.386094
$967$	56.0000	1.80084	0.900419	−	0.435023i	$-0.143260\pi$
$967$	56.0000	1.80084	0.900419	+	0.435023i	$0.143260\pi$
$968$	1.00000	0.0321412
$969$	24.0000	0.770991
$970$	0	0
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	10.0000	0.320750
$973$	6.00000	0.192351
$974$	18.0000	0.576757
$975$	0	0
$976$	2.00000	0.0640184
$977$	54.0000	1.72761	0.863807	−	0.503824i	$-0.168074\pi$
$977$	54.0000	1.72761	0.863807	+	0.503824i	$0.168074\pi$
$978$	−48.0000	−1.53487
$979$	−14.0000	−0.447442
$980$	0	0
$981$	4.00000	0.127710
$982$	12.0000	0.382935
$983$	56.0000	1.78612	0.893061	−	0.449935i	$-0.148553\pi$
$983$	56.0000	1.78612	0.893061	+	0.449935i	$0.148553\pi$
$984$	0	0
$985$	0	0
$986$	−8.00000	−0.254772
$987$	8.00000	0.254643
$988$	−12.0000	−0.381771
$989$	24.0000	0.763156
$990$	0	0
$991$	16.0000	0.508257	0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000	0.508257	0.254128	+	0.967170i	$0.418211\pi$
$992$	0	0
$993$	−24.0000	−0.761617
$994$	12.0000	0.380617
$995$	0	0
$996$	−24.0000	−0.760469
$997$	42.0000	1.33015	0.665077	−	0.746775i	$-0.268399\pi$
$997$	42.0000	1.33015	0.665077	+	0.746775i	$0.268399\pi$
$998$	−28.0000	−0.886325
$999$	−32.0000	−1.01244

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.a.e.1.1	✓	1	5.4	even	2
3850.2.a.m.1.1		1	1.1	even	1	trivial
3850.2.c.c.1849.1		2	5.3	odd	4
3850.2.c.c.1849.2		2	5.2	odd	4
5390.2.a.c.1.1		1	35.34	odd	2
6160.2.a.a.1.1		1	20.19	odd	2
6930.2.a.bk.1.1		1	15.14	odd	2
8470.2.a.bg.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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