LMFDB - Embedded newform 3850.2.a.u.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 154)
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)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} +1.00000 q^{8} -3.00000 q^{9} +O(q^{10})$

$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} +1.00000 q^{8} -3.00000 q^{9} -1.00000 q^{11} -2.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} +4.00000 q^{17} -3.00000 q^{18} -6.00000 q^{19} -1.00000 q^{22} -4.00000 q^{23} -2.00000 q^{26} +1.00000 q^{28} -2.00000 q^{29} -2.00000 q^{31} +1.00000 q^{32} +4.00000 q^{34} -3.00000 q^{36} -10.0000 q^{37} -6.00000 q^{38} +4.00000 q^{41} +8.00000 q^{43} -1.00000 q^{44} -4.00000 q^{46} -2.00000 q^{47} +1.00000 q^{49} -2.00000 q^{52} -6.00000 q^{53} +1.00000 q^{56} -2.00000 q^{58} -12.0000 q^{59} -14.0000 q^{61} -2.00000 q^{62} -3.00000 q^{63} +1.00000 q^{64} +12.0000 q^{67} +4.00000 q^{68} -8.00000 q^{71} -3.00000 q^{72} -4.00000 q^{73} -10.0000 q^{74} -6.00000 q^{76} -1.00000 q^{77} +9.00000 q^{81} +4.00000 q^{82} +6.00000 q^{83} +8.00000 q^{86} -1.00000 q^{88} -6.00000 q^{89} -2.00000 q^{91} -4.00000 q^{92} -2.00000 q^{94} +14.0000 q^{97} +1.00000 q^{98} +3.00000 q^{99} +O(q^{100})$

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
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−3.00000	−1.00000
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0	0
$13$	−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
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	−3.00000	−0.707107
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	0	0
$21$	0	0
$22$	−1.00000	−0.213201
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	0	0
$25$	0	0
$26$	−2.00000	−0.392232
$27$	0	0
$28$	1.00000	0.188982
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	0	0
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	4.00000	0.685994
$35$	0	0
$36$	−3.00000	−0.500000
$37$	−10.0000	−1.64399	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000	−1.64399	−0.821995	+	0.569495i	$0.807139\pi$
$38$	−6.00000	−0.973329
$39$	0	0
$40$	0	0
$41$	4.00000	0.624695	0.312348	−	0.949968i	$-0.398885\pi$
$41$	4.00000	0.624695	0.312348	+	0.949968i	$0.398885\pi$
$42$	0	0
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	−4.00000	−0.589768
$47$	−2.00000	−0.291730	−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000	−0.291730	−0.145865	+	0.989305i	$0.546597\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	0	0
$52$	−2.00000	−0.277350
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	0	0
$55$	0	0
$56$	1.00000	0.133631
$57$	0	0
$58$	−2.00000	−0.262613
$59$	−12.0000	−1.56227	−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000	−1.56227	−0.781133	+	0.624364i	$0.785358\pi$
$60$	0	0
$61$	−14.0000	−1.79252	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000	−1.79252	−0.896258	+	0.443533i	$0.853725\pi$
$62$	−2.00000	−0.254000
$63$	−3.00000	−0.377964
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	12.0000	1.46603	0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000	1.46603	0.733017	+	0.680211i	$0.238112\pi$
$68$	4.00000	0.485071
$69$	0	0
$70$	0	0
$71$	−8.00000	−0.949425	−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000	−0.949425	−0.474713	+	0.880141i	$0.657448\pi$
$72$	−3.00000	−0.353553
$73$	−4.00000	−0.468165	−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000	−0.468165	−0.234082	+	0.972217i	$0.575209\pi$
$74$	−10.0000	−1.16248
$75$	0	0
$76$	−6.00000	−0.688247
$77$	−1.00000	−0.113961
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	4.00000	0.441726
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	0	0
$85$	0	0
$86$	8.00000	0.862662
$87$	0	0
$88$	−1.00000	−0.106600
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	0	0
$91$	−2.00000	−0.209657
$92$	−4.00000	−0.417029
$93$	0	0
$94$	−2.00000	−0.206284
$95$	0	0
$96$	0	0
$97$	14.0000	1.42148	0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000	1.42148	0.710742	+	0.703452i	$0.248359\pi$
$98$	1.00000	0.101015
$99$	3.00000	0.301511
$100$	0	0
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	0	0
$103$	−18.0000	−1.77359	−0.886796	−	0.462160i	$-0.847074\pi$
$103$	−18.0000	−1.77359	−0.886796	+	0.462160i	$0.847074\pi$
$104$	−2.00000	−0.196116
$105$	0	0
$106$	−6.00000	−0.582772
$107$	16.0000	1.54678	0.773389	−	0.633932i	$-0.218560\pi$
$107$	16.0000	1.54678	0.773389	+	0.633932i	$0.218560\pi$
$108$	0	0
$109$	−14.0000	−1.34096	−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000	−1.34096	−0.670478	+	0.741929i	$0.733911\pi$
$110$	0	0
$111$	0	0
$112$	1.00000	0.0944911
$113$	−14.0000	−1.31701	−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000	−1.31701	−0.658505	+	0.752577i	$0.728811\pi$
$114$	0	0
$115$	0	0
$116$	−2.00000	−0.185695
$117$	6.00000	0.554700
$118$	−12.0000	−1.10469
$119$	4.00000	0.366679
$120$	0	0
$121$	1.00000	0.0909091
$122$	−14.0000	−1.26750
$123$	0	0
$124$	−2.00000	−0.179605
$125$	0	0
$126$	−3.00000	−0.267261
$127$	−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
$129$	0	0
$130$	0	0
$131$	6.00000	0.524222	0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000	0.524222	0.262111	+	0.965038i	$0.415581\pi$
$132$	0	0
$133$	−6.00000	−0.520266
$134$	12.0000	1.03664
$135$	0	0
$136$	4.00000	0.342997
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	0	0
$139$	14.0000	1.18746	0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000	1.18746	0.593732	+	0.804663i	$0.297654\pi$
$140$	0	0
$141$	0	0
$142$	−8.00000	−0.671345
$143$	2.00000	0.167248
$144$	−3.00000	−0.250000
$145$	0	0
$146$	−4.00000	−0.331042
$147$	0	0
$148$	−10.0000	−0.821995
$149$	2.00000	0.163846	0.0819232	−	0.996639i	$-0.473894\pi$
$149$	2.00000	0.163846	0.0819232	+	0.996639i	$0.473894\pi$
$150$	0	0
$151$	−24.0000	−1.95309	−0.976546	−	0.215308i	$-0.930924\pi$
$151$	−24.0000	−1.95309	−0.976546	+	0.215308i	$0.930924\pi$
$152$	−6.00000	−0.486664
$153$	−12.0000	−0.970143
$154$	−1.00000	−0.0805823
$155$	0	0
$156$	0	0
$157$	8.00000	0.638470	0.319235	−	0.947676i	$-0.396574\pi$
$157$	8.00000	0.638470	0.319235	+	0.947676i	$0.396574\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	−4.00000	−0.315244
$162$	9.00000	0.707107
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	4.00000	0.312348
$165$	0	0
$166$	6.00000	0.465690
$167$	−4.00000	−0.309529	−0.154765	−	0.987951i	$-0.549462\pi$
$167$	−4.00000	−0.309529	−0.154765	+	0.987951i	$0.549462\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	0	0
$171$	18.0000	1.37649
$172$	8.00000	0.609994
$173$	14.0000	1.06440	0.532200	−	0.846619i	$-0.321365\pi$
$173$	14.0000	1.06440	0.532200	+	0.846619i	$0.321365\pi$
$174$	0	0
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	0	0
$178$	−6.00000	−0.449719
$179$	4.00000	0.298974	0.149487	−	0.988764i	$-0.452238\pi$
$179$	4.00000	0.298974	0.149487	+	0.988764i	$0.452238\pi$
$180$	0	0
$181$	20.0000	1.48659	0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000	1.48659	0.743294	+	0.668965i	$0.233262\pi$
$182$	−2.00000	−0.148250
$183$	0	0
$184$	−4.00000	−0.294884
$185$	0	0
$186$	0	0
$187$	−4.00000	−0.292509
$188$	−2.00000	−0.145865
$189$	0	0
$190$	0	0
$191$	−4.00000	−0.289430	−0.144715	−	0.989473i	$-0.546227\pi$
$191$	−4.00000	−0.289430	−0.144715	+	0.989473i	$0.546227\pi$
$192$	0	0
$193$	−2.00000	−0.143963	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000	−0.143963	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	14.0000	1.00514
$195$	0	0
$196$	1.00000	0.0714286
$197$	−6.00000	−0.427482	−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000	−0.427482	−0.213741	+	0.976890i	$0.568565\pi$
$198$	3.00000	0.213201
$199$	−14.0000	−0.992434	−0.496217	−	0.868199i	$-0.665278\pi$
$199$	−14.0000	−0.992434	−0.496217	+	0.868199i	$0.665278\pi$
$200$	0	0
$201$	0	0
$202$	6.00000	0.422159
$203$	−2.00000	−0.140372
$204$	0	0
$205$	0	0
$206$	−18.0000	−1.25412
$207$	12.0000	0.834058
$208$	−2.00000	−0.138675
$209$	6.00000	0.415029
$210$	0	0
$211$	−8.00000	−0.550743	−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000	−0.550743	−0.275371	+	0.961338i	$0.588801\pi$
$212$	−6.00000	−0.412082
$213$	0	0
$214$	16.0000	1.09374
$215$	0	0
$216$	0	0
$217$	−2.00000	−0.135769
$218$	−14.0000	−0.948200
$219$	0	0
$220$	0	0
$221$	−8.00000	−0.538138
$222$	0	0
$223$	2.00000	0.133930	0.0669650	−	0.997755i	$-0.478668\pi$
$223$	2.00000	0.133930	0.0669650	+	0.997755i	$0.478668\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	−14.0000	−0.931266
$227$	2.00000	0.132745	0.0663723	−	0.997795i	$-0.478857\pi$
$227$	2.00000	0.132745	0.0663723	+	0.997795i	$0.478857\pi$
$228$	0	0
$229$	20.0000	1.32164	0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000	1.32164	0.660819	+	0.750546i	$0.270209\pi$
$230$	0	0
$231$	0	0
$232$	−2.00000	−0.131306
$233$	−30.0000	−1.96537	−0.982683	−	0.185296i	$-0.940675\pi$
$233$	−30.0000	−1.96537	−0.982683	+	0.185296i	$0.940675\pi$
$234$	6.00000	0.392232
$235$	0	0
$236$	−12.0000	−0.781133
$237$	0	0
$238$	4.00000	0.259281
$239$	16.0000	1.03495	0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000	1.03495	0.517477	+	0.855697i	$0.326871\pi$
$240$	0	0
$241$	12.0000	0.772988	0.386494	−	0.922292i	$-0.373686\pi$
$241$	12.0000	0.772988	0.386494	+	0.922292i	$0.373686\pi$
$242$	1.00000	0.0642824
$243$	0	0
$244$	−14.0000	−0.896258
$245$	0	0
$246$	0	0
$247$	12.0000	0.763542
$248$	−2.00000	−0.127000
$249$	0	0
$250$	0	0
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	−3.00000	−0.188982
$253$	4.00000	0.251478
$254$	−8.00000	−0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	6.00000	0.374270	0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000	0.374270	0.187135	+	0.982334i	$0.440080\pi$
$258$	0	0
$259$	−10.0000	−0.621370
$260$	0	0
$261$	6.00000	0.371391
$262$	6.00000	0.370681
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	0	0
$266$	−6.00000	−0.367884
$267$	0	0
$268$	12.0000	0.733017
$269$	12.0000	0.731653	0.365826	−	0.930683i	$-0.380786\pi$
$269$	12.0000	0.731653	0.365826	+	0.930683i	$0.380786\pi$
$270$	0	0
$271$	−20.0000	−1.21491	−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000	−1.21491	−0.607457	+	0.794353i	$0.707810\pi$
$272$	4.00000	0.242536
$273$	0	0
$274$	−6.00000	−0.362473
$275$	0	0
$276$	0	0
$277$	30.0000	1.80253	0.901263	−	0.433273i	$-0.142641\pi$
$277$	30.0000	1.80253	0.901263	+	0.433273i	$0.142641\pi$
$278$	14.0000	0.839664
$279$	6.00000	0.359211
$280$	0	0
$281$	−10.0000	−0.596550	−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000	−0.596550	−0.298275	+	0.954480i	$0.596411\pi$
$282$	0	0
$283$	−6.00000	−0.356663	−0.178331	−	0.983970i	$-0.557070\pi$
$283$	−6.00000	−0.356663	−0.178331	+	0.983970i	$0.557070\pi$
$284$	−8.00000	−0.474713
$285$	0	0
$286$	2.00000	0.118262
$287$	4.00000	0.236113
$288$	−3.00000	−0.176777
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	0	0
$292$	−4.00000	−0.234082
$293$	−18.0000	−1.05157	−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000	−1.05157	−0.525786	+	0.850617i	$0.676229\pi$
$294$	0	0
$295$	0	0
$296$	−10.0000	−0.581238
$297$	0	0
$298$	2.00000	0.115857
$299$	8.00000	0.462652
$300$	0	0
$301$	8.00000	0.461112
$302$	−24.0000	−1.38104
$303$	0	0
$304$	−6.00000	−0.344124
$305$	0	0
$306$	−12.0000	−0.685994
$307$	10.0000	0.570730	0.285365	−	0.958419i	$-0.407885\pi$
$307$	10.0000	0.570730	0.285365	+	0.958419i	$0.407885\pi$
$308$	−1.00000	−0.0569803
$309$	0	0
$310$	0	0
$311$	14.0000	0.793867	0.396934	−	0.917847i	$-0.370074\pi$
$311$	14.0000	0.793867	0.396934	+	0.917847i	$0.370074\pi$
$312$	0	0
$313$	2.00000	0.113047	0.0565233	−	0.998401i	$-0.481998\pi$
$313$	2.00000	0.113047	0.0565233	+	0.998401i	$0.481998\pi$
$314$	8.00000	0.451466
$315$	0	0
$316$	0	0
$317$	−6.00000	−0.336994	−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000	−0.336994	−0.168497	+	0.985702i	$0.553891\pi$
$318$	0	0
$319$	2.00000	0.111979
$320$	0	0
$321$	0	0
$322$	−4.00000	−0.222911
$323$	−24.0000	−1.33540
$324$	9.00000	0.500000
$325$	0	0
$326$	−4.00000	−0.221540
$327$	0	0
$328$	4.00000	0.220863
$329$	−2.00000	−0.110264
$330$	0	0
$331$	−20.0000	−1.09930	−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000	−1.09930	−0.549650	+	0.835395i	$0.685239\pi$
$332$	6.00000	0.329293
$333$	30.0000	1.64399
$334$	−4.00000	−0.218870
$335$	0	0
$336$	0	0
$337$	18.0000	0.980522	0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000	0.980522	0.490261	+	0.871576i	$0.336901\pi$
$338$	−9.00000	−0.489535
$339$	0	0
$340$	0	0
$341$	2.00000	0.108306
$342$	18.0000	0.973329
$343$	1.00000	0.0539949
$344$	8.00000	0.431331
$345$	0	0
$346$	14.0000	0.752645
$347$	−8.00000	−0.429463	−0.214731	−	0.976673i	$-0.568888\pi$
$347$	−8.00000	−0.429463	−0.214731	+	0.976673i	$0.568888\pi$
$348$	0	0
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	0	0
$351$	0	0
$352$	−1.00000	−0.0533002
$353$	6.00000	0.319348	0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000	0.319348	0.159674	+	0.987170i	$0.448956\pi$
$354$	0	0
$355$	0	0
$356$	−6.00000	−0.317999
$357$	0	0
$358$	4.00000	0.211407
$359$	−16.0000	−0.844448	−0.422224	−	0.906492i	$-0.638750\pi$
$359$	−16.0000	−0.844448	−0.422224	+	0.906492i	$0.638750\pi$
$360$	0	0
$361$	17.0000	0.894737
$362$	20.0000	1.05118
$363$	0	0
$364$	−2.00000	−0.104828
$365$	0	0
$366$	0	0
$367$	−22.0000	−1.14839	−0.574195	−	0.818718i	$-0.694685\pi$
$367$	−22.0000	−1.14839	−0.574195	+	0.818718i	$0.694685\pi$
$368$	−4.00000	−0.208514
$369$	−12.0000	−0.624695
$370$	0	0
$371$	−6.00000	−0.311504
$372$	0	0
$373$	10.0000	0.517780	0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000	0.517780	0.258890	+	0.965907i	$0.416643\pi$
$374$	−4.00000	−0.206835
$375$	0	0
$376$	−2.00000	−0.103142
$377$	4.00000	0.206010
$378$	0	0
$379$	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
$381$	0	0
$382$	−4.00000	−0.204658
$383$	10.0000	0.510976	0.255488	−	0.966812i	$-0.417764\pi$
$383$	10.0000	0.510976	0.255488	+	0.966812i	$0.417764\pi$
$384$	0	0
$385$	0	0
$386$	−2.00000	−0.101797
$387$	−24.0000	−1.21999
$388$	14.0000	0.710742
$389$	−30.0000	−1.52106	−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000	−1.52106	−0.760530	+	0.649303i	$0.775061\pi$
$390$	0	0
$391$	−16.0000	−0.809155
$392$	1.00000	0.0505076
$393$	0	0
$394$	−6.00000	−0.302276
$395$	0	0
$396$	3.00000	0.150756
$397$	−24.0000	−1.20453	−0.602263	−	0.798298i	$-0.705734\pi$
$397$	−24.0000	−1.20453	−0.602263	+	0.798298i	$0.705734\pi$
$398$	−14.0000	−0.701757
$399$	0	0
$400$	0	0
$401$	−18.0000	−0.898877	−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000	−0.898877	−0.449439	+	0.893311i	$0.648376\pi$
$402$	0	0
$403$	4.00000	0.199254
$404$	6.00000	0.298511
$405$	0	0
$406$	−2.00000	−0.0992583
$407$	10.0000	0.495682
$408$	0	0
$409$	16.0000	0.791149	0.395575	−	0.918434i	$-0.370545\pi$
$409$	16.0000	0.791149	0.395575	+	0.918434i	$0.370545\pi$
$410$	0	0
$411$	0	0
$412$	−18.0000	−0.886796
$413$	−12.0000	−0.590481
$414$	12.0000	0.589768
$415$	0	0
$416$	−2.00000	−0.0980581
$417$	0	0
$418$	6.00000	0.293470
$419$	−32.0000	−1.56330	−0.781651	−	0.623716i	$-0.785622\pi$
$419$	−32.0000	−1.56330	−0.781651	+	0.623716i	$0.785622\pi$
$420$	0	0
$421$	−2.00000	−0.0974740	−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000	−0.0974740	−0.0487370	+	0.998812i	$0.515520\pi$
$422$	−8.00000	−0.389434
$423$	6.00000	0.291730
$424$	−6.00000	−0.291386
$425$	0	0
$426$	0	0
$427$	−14.0000	−0.677507
$428$	16.0000	0.773389
$429$	0	0
$430$	0	0
$431$	16.0000	0.770693	0.385346	−	0.922772i	$-0.374082\pi$
$431$	16.0000	0.770693	0.385346	+	0.922772i	$0.374082\pi$
$432$	0	0
$433$	−2.00000	−0.0961139	−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000	−0.0961139	−0.0480569	+	0.998845i	$0.515303\pi$
$434$	−2.00000	−0.0960031
$435$	0	0
$436$	−14.0000	−0.670478
$437$	24.0000	1.14808
$438$	0	0
$439$	28.0000	1.33637	0.668184	−	0.743996i	$-0.267072\pi$
$439$	28.0000	1.33637	0.668184	+	0.743996i	$0.267072\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	−8.00000	−0.380521
$443$	36.0000	1.71041	0.855206	−	0.518289i	$-0.173431\pi$
$443$	36.0000	1.71041	0.855206	+	0.518289i	$0.173431\pi$
$444$	0	0
$445$	0	0
$446$	2.00000	0.0947027
$447$	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
$451$	−4.00000	−0.188353
$452$	−14.0000	−0.658505
$453$	0	0
$454$	2.00000	0.0938647
$455$	0	0
$456$	0	0
$457$	−2.00000	−0.0935561	−0.0467780	−	0.998905i	$-0.514895\pi$
$457$	−2.00000	−0.0935561	−0.0467780	+	0.998905i	$0.514895\pi$
$458$	20.0000	0.934539
$459$	0	0
$460$	0	0
$461$	30.0000	1.39724	0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000	1.39724	0.698620	+	0.715493i	$0.253798\pi$
$462$	0	0
$463$	32.0000	1.48717	0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000	1.48717	0.743583	+	0.668644i	$0.233125\pi$
$464$	−2.00000	−0.0928477
$465$	0	0
$466$	−30.0000	−1.38972
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	6.00000	0.277350
$469$	12.0000	0.554109
$470$	0	0
$471$	0	0
$472$	−12.0000	−0.552345
$473$	−8.00000	−0.367840
$474$	0	0
$475$	0	0
$476$	4.00000	0.183340
$477$	18.0000	0.824163
$478$	16.0000	0.731823
$479$	−16.0000	−0.731059	−0.365529	−	0.930800i	$-0.619112\pi$
$479$	−16.0000	−0.731059	−0.365529	+	0.930800i	$0.619112\pi$
$480$	0	0
$481$	20.0000	0.911922
$482$	12.0000	0.546585
$483$	0	0
$484$	1.00000	0.0454545
$485$	0	0
$486$	0	0
$487$	28.0000	1.26880	0.634401	−	0.773004i	$-0.281247\pi$
$487$	28.0000	1.26880	0.634401	+	0.773004i	$0.281247\pi$
$488$	−14.0000	−0.633750
$489$	0	0
$490$	0	0
$491$	−36.0000	−1.62466	−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000	−1.62466	−0.812329	+	0.583200i	$0.801800\pi$
$492$	0	0
$493$	−8.00000	−0.360302
$494$	12.0000	0.539906
$495$	0	0
$496$	−2.00000	−0.0898027
$497$	−8.00000	−0.358849
$498$	0	0
$499$	44.0000	1.96971	0.984855	−	0.173379i	$-0.0554684\pi$
$499$	44.0000	1.96971	0.984855	+	0.173379i	$0.0554684\pi$
$500$	0	0
$501$	0	0
$502$	12.0000	0.535586
$503$	36.0000	1.60516	0.802580	−	0.596544i	$-0.203460\pi$
$503$	36.0000	1.60516	0.802580	+	0.596544i	$0.203460\pi$
$504$	−3.00000	−0.133631
$505$	0	0
$506$	4.00000	0.177822
$507$	0	0
$508$	−8.00000	−0.354943
$509$	−28.0000	−1.24108	−0.620539	−	0.784176i	$-0.713086\pi$
$509$	−28.0000	−1.24108	−0.620539	+	0.784176i	$0.713086\pi$
$510$	0	0
$511$	−4.00000	−0.176950
$512$	1.00000	0.0441942
$513$	0	0
$514$	6.00000	0.264649
$515$	0	0
$516$	0	0
$517$	2.00000	0.0879599
$518$	−10.0000	−0.439375
$519$	0	0
$520$	0	0
$521$	10.0000	0.438108	0.219054	−	0.975713i	$-0.429703\pi$
$521$	10.0000	0.438108	0.219054	+	0.975713i	$0.429703\pi$
$522$	6.00000	0.262613
$523$	34.0000	1.48672	0.743358	−	0.668894i	$-0.233232\pi$
$523$	34.0000	1.48672	0.743358	+	0.668894i	$0.233232\pi$
$524$	6.00000	0.262111
$525$	0	0
$526$	0	0
$527$	−8.00000	−0.348485
$528$	0	0
$529$	−7.00000	−0.304348
$530$	0	0
$531$	36.0000	1.56227
$532$	−6.00000	−0.260133
$533$	−8.00000	−0.346518
$534$	0	0
$535$	0	0
$536$	12.0000	0.518321
$537$	0	0
$538$	12.0000	0.517357
$539$	−1.00000	−0.0430730
$540$	0	0
$541$	14.0000	0.601907	0.300954	−	0.953639i	$-0.402695\pi$
$541$	14.0000	0.601907	0.300954	+	0.953639i	$0.402695\pi$
$542$	−20.0000	−0.859074
$543$	0	0
$544$	4.00000	0.171499
$545$	0	0
$546$	0	0
$547$	12.0000	0.513083	0.256541	−	0.966533i	$-0.417417\pi$
$547$	12.0000	0.513083	0.256541	+	0.966533i	$0.417417\pi$
$548$	−6.00000	−0.256307
$549$	42.0000	1.79252
$550$	0	0
$551$	12.0000	0.511217
$552$	0	0
$553$	0	0
$554$	30.0000	1.27458
$555$	0	0
$556$	14.0000	0.593732
$557$	−14.0000	−0.593199	−0.296600	−	0.955002i	$-0.595853\pi$
$557$	−14.0000	−0.593199	−0.296600	+	0.955002i	$0.595853\pi$
$558$	6.00000	0.254000
$559$	−16.0000	−0.676728
$560$	0	0
$561$	0	0
$562$	−10.0000	−0.421825
$563$	34.0000	1.43293	0.716465	−	0.697623i	$-0.245759\pi$
$563$	34.0000	1.43293	0.716465	+	0.697623i	$0.245759\pi$
$564$	0	0
$565$	0	0
$566$	−6.00000	−0.252199
$567$	9.00000	0.377964
$568$	−8.00000	−0.335673
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	0	0
$571$	28.0000	1.17176	0.585882	−	0.810397i	$-0.300748\pi$
$571$	28.0000	1.17176	0.585882	+	0.810397i	$0.300748\pi$
$572$	2.00000	0.0836242
$573$	0	0
$574$	4.00000	0.166957
$575$	0	0
$576$	−3.00000	−0.125000
$577$	−14.0000	−0.582828	−0.291414	−	0.956597i	$-0.594126\pi$
$577$	−14.0000	−0.582828	−0.291414	+	0.956597i	$0.594126\pi$
$578$	−1.00000	−0.0415945
$579$	0	0
$580$	0	0
$581$	6.00000	0.248922
$582$	0	0
$583$	6.00000	0.248495
$584$	−4.00000	−0.165521
$585$	0	0
$586$	−18.0000	−0.743573
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	0	0
$589$	12.0000	0.494451
$590$	0	0
$591$	0	0
$592$	−10.0000	−0.410997
$593$	12.0000	0.492781	0.246390	−	0.969171i	$-0.420755\pi$
$593$	12.0000	0.492781	0.246390	+	0.969171i	$0.420755\pi$
$594$	0	0
$595$	0	0
$596$	2.00000	0.0819232
$597$	0	0
$598$	8.00000	0.327144
$599$	24.0000	0.980613	0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000	0.980613	0.490307	+	0.871550i	$0.336885\pi$
$600$	0	0
$601$	8.00000	0.326327	0.163163	−	0.986599i	$-0.447830\pi$
$601$	8.00000	0.326327	0.163163	+	0.986599i	$0.447830\pi$
$602$	8.00000	0.326056
$603$	−36.0000	−1.46603
$604$	−24.0000	−0.976546
$605$	0	0
$606$	0	0
$607$	−8.00000	−0.324710	−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000	−0.324710	−0.162355	+	0.986732i	$0.551909\pi$
$608$	−6.00000	−0.243332
$609$	0	0
$610$	0	0
$611$	4.00000	0.161823
$612$	−12.0000	−0.485071
$613$	−46.0000	−1.85792	−0.928961	−	0.370177i	$-0.879297\pi$
$613$	−46.0000	−1.85792	−0.928961	+	0.370177i	$0.879297\pi$
$614$	10.0000	0.403567
$615$	0	0
$616$	−1.00000	−0.0402911
$617$	−18.0000	−0.724653	−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000	−0.724653	−0.362326	+	0.932051i	$0.618017\pi$
$618$	0	0
$619$	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
$621$	0	0
$622$	14.0000	0.561349
$623$	−6.00000	−0.240385
$624$	0	0
$625$	0	0
$626$	2.00000	0.0799361
$627$	0	0
$628$	8.00000	0.319235
$629$	−40.0000	−1.59490
$630$	0	0
$631$	−12.0000	−0.477712	−0.238856	−	0.971055i	$-0.576772\pi$
$631$	−12.0000	−0.477712	−0.238856	+	0.971055i	$0.576772\pi$
$632$	0	0
$633$	0	0
$634$	−6.00000	−0.238290
$635$	0	0
$636$	0	0
$637$	−2.00000	−0.0792429
$638$	2.00000	0.0791808
$639$	24.0000	0.949425
$640$	0	0
$641$	−6.00000	−0.236986	−0.118493	−	0.992955i	$-0.537806\pi$
$641$	−6.00000	−0.236986	−0.118493	+	0.992955i	$0.537806\pi$
$642$	0	0
$643$	−4.00000	−0.157745	−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000	−0.157745	−0.0788723	+	0.996885i	$0.525132\pi$
$644$	−4.00000	−0.157622
$645$	0	0
$646$	−24.0000	−0.944267
$647$	−6.00000	−0.235884	−0.117942	−	0.993020i	$-0.537630\pi$
$647$	−6.00000	−0.235884	−0.117942	+	0.993020i	$0.537630\pi$
$648$	9.00000	0.353553
$649$	12.0000	0.471041
$650$	0	0
$651$	0	0
$652$	−4.00000	−0.156652
$653$	−10.0000	−0.391330	−0.195665	−	0.980671i	$-0.562687\pi$
$653$	−10.0000	−0.391330	−0.195665	+	0.980671i	$0.562687\pi$
$654$	0	0
$655$	0	0
$656$	4.00000	0.156174
$657$	12.0000	0.468165
$658$	−2.00000	−0.0779681
$659$	−8.00000	−0.311636	−0.155818	−	0.987786i	$-0.549801\pi$
$659$	−8.00000	−0.311636	−0.155818	+	0.987786i	$0.549801\pi$
$660$	0	0
$661$	20.0000	0.777910	0.388955	−	0.921257i	$-0.372836\pi$
$661$	20.0000	0.777910	0.388955	+	0.921257i	$0.372836\pi$
$662$	−20.0000	−0.777322
$663$	0	0
$664$	6.00000	0.232845
$665$	0	0
$666$	30.0000	1.16248
$667$	8.00000	0.309761
$668$	−4.00000	−0.154765
$669$	0	0
$670$	0	0
$671$	14.0000	0.540464
$672$	0	0
$673$	−22.0000	−0.848038	−0.424019	−	0.905653i	$-0.639381\pi$
$673$	−22.0000	−0.848038	−0.424019	+	0.905653i	$0.639381\pi$
$674$	18.0000	0.693334
$675$	0	0
$676$	−9.00000	−0.346154
$677$	−26.0000	−0.999261	−0.499631	−	0.866239i	$-0.666531\pi$
$677$	−26.0000	−0.999261	−0.499631	+	0.866239i	$0.666531\pi$
$678$	0	0
$679$	14.0000	0.537271
$680$	0	0
$681$	0	0
$682$	2.00000	0.0765840
$683$	−36.0000	−1.37750	−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000	−1.37750	−0.688751	+	0.724998i	$0.741841\pi$
$684$	18.0000	0.688247
$685$	0	0
$686$	1.00000	0.0381802
$687$	0	0
$688$	8.00000	0.304997
$689$	12.0000	0.457164
$690$	0	0
$691$	36.0000	1.36950	0.684752	−	0.728776i	$-0.259910\pi$
$691$	36.0000	1.36950	0.684752	+	0.728776i	$0.259910\pi$
$692$	14.0000	0.532200
$693$	3.00000	0.113961
$694$	−8.00000	−0.303676
$695$	0	0
$696$	0	0
$697$	16.0000	0.606043
$698$	−10.0000	−0.378506
$699$	0	0
$700$	0	0
$701$	−30.0000	−1.13308	−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000	−1.13308	−0.566542	+	0.824033i	$0.691719\pi$
$702$	0	0
$703$	60.0000	2.26294
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	6.00000	0.225813
$707$	6.00000	0.225653
$708$	0	0
$709$	18.0000	0.676004	0.338002	−	0.941145i	$-0.390249\pi$
$709$	18.0000	0.676004	0.338002	+	0.941145i	$0.390249\pi$
$710$	0	0
$711$	0	0
$712$	−6.00000	−0.224860
$713$	8.00000	0.299602
$714$	0	0
$715$	0	0
$716$	4.00000	0.149487
$717$	0	0
$718$	−16.0000	−0.597115
$719$	−26.0000	−0.969636	−0.484818	−	0.874615i	$-0.661114\pi$
$719$	−26.0000	−0.969636	−0.484818	+	0.874615i	$0.661114\pi$
$720$	0	0
$721$	−18.0000	−0.670355
$722$	17.0000	0.632674
$723$	0	0
$724$	20.0000	0.743294
$725$	0	0
$726$	0	0
$727$	10.0000	0.370879	0.185440	−	0.982656i	$-0.440629\pi$
$727$	10.0000	0.370879	0.185440	+	0.982656i	$0.440629\pi$
$728$	−2.00000	−0.0741249
$729$	−27.0000	−1.00000
$730$	0	0
$731$	32.0000	1.18356
$732$	0	0
$733$	22.0000	0.812589	0.406294	−	0.913742i	$-0.366821\pi$
$733$	22.0000	0.812589	0.406294	+	0.913742i	$0.366821\pi$
$734$	−22.0000	−0.812035
$735$	0	0
$736$	−4.00000	−0.147442
$737$	−12.0000	−0.442026
$738$	−12.0000	−0.441726
$739$	−12.0000	−0.441427	−0.220714	−	0.975339i	$-0.570839\pi$
$739$	−12.0000	−0.441427	−0.220714	+	0.975339i	$0.570839\pi$
$740$	0	0
$741$	0	0
$742$	−6.00000	−0.220267
$743$	24.0000	0.880475	0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000	0.880475	0.440237	+	0.897881i	$0.354894\pi$
$744$	0	0
$745$	0	0
$746$	10.0000	0.366126
$747$	−18.0000	−0.658586
$748$	−4.00000	−0.146254
$749$	16.0000	0.584627
$750$	0	0
$751$	28.0000	1.02173	0.510867	−	0.859660i	$-0.329324\pi$
$751$	28.0000	1.02173	0.510867	+	0.859660i	$0.329324\pi$
$752$	−2.00000	−0.0729325
$753$	0	0
$754$	4.00000	0.145671
$755$	0	0
$756$	0	0
$757$	−26.0000	−0.944986	−0.472493	−	0.881334i	$-0.656646\pi$
$757$	−26.0000	−0.944986	−0.472493	+	0.881334i	$0.656646\pi$
$758$	4.00000	0.145287
$759$	0	0
$760$	0	0
$761$	−48.0000	−1.74000	−0.869999	−	0.493053i	$-0.835881\pi$
$761$	−48.0000	−1.74000	−0.869999	+	0.493053i	$0.835881\pi$
$762$	0	0
$763$	−14.0000	−0.506834
$764$	−4.00000	−0.144715
$765$	0	0
$766$	10.0000	0.361315
$767$	24.0000	0.866590
$768$	0	0
$769$	16.0000	0.576975	0.288487	−	0.957484i	$-0.406848\pi$
$769$	16.0000	0.576975	0.288487	+	0.957484i	$0.406848\pi$
$770$	0	0
$771$	0	0
$772$	−2.00000	−0.0719816
$773$	48.0000	1.72644	0.863220	−	0.504828i	$-0.168444\pi$
$773$	48.0000	1.72644	0.863220	+	0.504828i	$0.168444\pi$
$774$	−24.0000	−0.862662
$775$	0	0
$776$	14.0000	0.502571
$777$	0	0
$778$	−30.0000	−1.07555
$779$	−24.0000	−0.859889
$780$	0	0
$781$	8.00000	0.286263
$782$	−16.0000	−0.572159
$783$	0	0
$784$	1.00000	0.0357143
$785$	0	0
$786$	0	0
$787$	22.0000	0.784215	0.392108	−	0.919919i	$-0.371746\pi$
$787$	22.0000	0.784215	0.392108	+	0.919919i	$0.371746\pi$
$788$	−6.00000	−0.213741
$789$	0	0
$790$	0	0
$791$	−14.0000	−0.497783
$792$	3.00000	0.106600
$793$	28.0000	0.994309
$794$	−24.0000	−0.851728
$795$	0	0
$796$	−14.0000	−0.496217
$797$	16.0000	0.566749	0.283375	−	0.959009i	$-0.408546\pi$
$797$	16.0000	0.566749	0.283375	+	0.959009i	$0.408546\pi$
$798$	0	0
$799$	−8.00000	−0.283020
$800$	0	0
$801$	18.0000	0.635999
$802$	−18.0000	−0.635602
$803$	4.00000	0.141157
$804$	0	0
$805$	0	0
$806$	4.00000	0.140894
$807$	0	0
$808$	6.00000	0.211079
$809$	−30.0000	−1.05474	−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000	−1.05474	−0.527372	+	0.849635i	$0.676823\pi$
$810$	0	0
$811$	38.0000	1.33436	0.667180	−	0.744896i	$-0.267501\pi$
$811$	38.0000	1.33436	0.667180	+	0.744896i	$0.267501\pi$
$812$	−2.00000	−0.0701862
$813$	0	0
$814$	10.0000	0.350500
$815$	0	0
$816$	0	0
$817$	−48.0000	−1.67931
$818$	16.0000	0.559427
$819$	6.00000	0.209657
$820$	0	0
$821$	18.0000	0.628204	0.314102	−	0.949389i	$-0.398297\pi$
$821$	18.0000	0.628204	0.314102	+	0.949389i	$0.398297\pi$
$822$	0	0
$823$	4.00000	0.139431	0.0697156	−	0.997567i	$-0.477791\pi$
$823$	4.00000	0.139431	0.0697156	+	0.997567i	$0.477791\pi$
$824$	−18.0000	−0.627060
$825$	0	0
$826$	−12.0000	−0.417533
$827$	−20.0000	−0.695468	−0.347734	−	0.937593i	$-0.613049\pi$
$827$	−20.0000	−0.695468	−0.347734	+	0.937593i	$0.613049\pi$
$828$	12.0000	0.417029
$829$	−20.0000	−0.694629	−0.347314	−	0.937749i	$-0.612906\pi$
$829$	−20.0000	−0.694629	−0.347314	+	0.937749i	$0.612906\pi$
$830$	0	0
$831$	0	0
$832$	−2.00000	−0.0693375
$833$	4.00000	0.138592
$834$	0	0
$835$	0	0
$836$	6.00000	0.207514
$837$	0	0
$838$	−32.0000	−1.10542
$839$	30.0000	1.03572	0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000	1.03572	0.517858	+	0.855467i	$0.326730\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	−2.00000	−0.0689246
$843$	0	0
$844$	−8.00000	−0.275371
$845$	0	0
$846$	6.00000	0.206284
$847$	1.00000	0.0343604
$848$	−6.00000	−0.206041
$849$	0	0
$850$	0	0
$851$	40.0000	1.37118
$852$	0	0
$853$	−2.00000	−0.0684787	−0.0342393	−	0.999414i	$-0.510901\pi$
$853$	−2.00000	−0.0684787	−0.0342393	+	0.999414i	$0.510901\pi$
$854$	−14.0000	−0.479070
$855$	0	0
$856$	16.0000	0.546869
$857$	−32.0000	−1.09310	−0.546550	−	0.837427i	$-0.684059\pi$
$857$	−32.0000	−1.09310	−0.546550	+	0.837427i	$0.684059\pi$
$858$	0	0
$859$	28.0000	0.955348	0.477674	−	0.878537i	$-0.341480\pi$
$859$	28.0000	0.955348	0.477674	+	0.878537i	$0.341480\pi$
$860$	0	0
$861$	0	0
$862$	16.0000	0.544962
$863$	44.0000	1.49778	0.748889	−	0.662696i	$-0.230588\pi$
$863$	44.0000	1.49778	0.748889	+	0.662696i	$0.230588\pi$
$864$	0	0
$865$	0	0
$866$	−2.00000	−0.0679628
$867$	0	0
$868$	−2.00000	−0.0678844
$869$	0	0
$870$	0	0
$871$	−24.0000	−0.813209
$872$	−14.0000	−0.474100
$873$	−42.0000	−1.42148
$874$	24.0000	0.811812
$875$	0	0
$876$	0	0
$877$	−34.0000	−1.14810	−0.574049	−	0.818821i	$-0.694628\pi$
$877$	−34.0000	−1.14810	−0.574049	+	0.818821i	$0.694628\pi$
$878$	28.0000	0.944954
$879$	0	0
$880$	0	0
$881$	30.0000	1.01073	0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000	1.01073	0.505363	+	0.862907i	$0.331359\pi$
$882$	−3.00000	−0.101015
$883$	44.0000	1.48072	0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000	1.48072	0.740359	+	0.672212i	$0.234656\pi$
$884$	−8.00000	−0.269069
$885$	0	0
$886$	36.0000	1.20944
$887$	−16.0000	−0.537227	−0.268614	−	0.963248i	$-0.586566\pi$
$887$	−16.0000	−0.537227	−0.268614	+	0.963248i	$0.586566\pi$
$888$	0	0
$889$	−8.00000	−0.268311
$890$	0	0
$891$	−9.00000	−0.301511
$892$	2.00000	0.0669650
$893$	12.0000	0.401565
$894$	0	0
$895$	0	0
$896$	1.00000	0.0334077
$897$	0	0
$898$	−18.0000	−0.600668
$899$	4.00000	0.133407
$900$	0	0
$901$	−24.0000	−0.799556
$902$	−4.00000	−0.133185
$903$	0	0
$904$	−14.0000	−0.465633
$905$	0	0
$906$	0	0
$907$	52.0000	1.72663	0.863316	−	0.504664i	$-0.168384\pi$
$907$	52.0000	1.72663	0.863316	+	0.504664i	$0.168384\pi$
$908$	2.00000	0.0663723
$909$	−18.0000	−0.597022
$910$	0	0
$911$	−36.0000	−1.19273	−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000	−1.19273	−0.596367	+	0.802712i	$0.703390\pi$
$912$	0	0
$913$	−6.00000	−0.198571
$914$	−2.00000	−0.0661541
$915$	0	0
$916$	20.0000	0.660819
$917$	6.00000	0.198137
$918$	0	0
$919$	24.0000	0.791687	0.395843	−	0.918318i	$-0.370452\pi$
$919$	24.0000	0.791687	0.395843	+	0.918318i	$0.370452\pi$
$920$	0	0
$921$	0	0
$922$	30.0000	0.987997
$923$	16.0000	0.526646
$924$	0	0
$925$	0	0
$926$	32.0000	1.05159
$927$	54.0000	1.77359
$928$	−2.00000	−0.0656532
$929$	−30.0000	−0.984268	−0.492134	−	0.870519i	$-0.663783\pi$
$929$	−30.0000	−0.984268	−0.492134	+	0.870519i	$0.663783\pi$
$930$	0	0
$931$	−6.00000	−0.196642
$932$	−30.0000	−0.982683
$933$	0	0
$934$	0	0
$935$	0	0
$936$	6.00000	0.196116
$937$	−12.0000	−0.392023	−0.196011	−	0.980602i	$-0.562799\pi$
$937$	−12.0000	−0.392023	−0.196011	+	0.980602i	$0.562799\pi$
$938$	12.0000	0.391814
$939$	0	0
$940$	0	0
$941$	−14.0000	−0.456387	−0.228193	−	0.973616i	$-0.573282\pi$
$941$	−14.0000	−0.456387	−0.228193	+	0.973616i	$0.573282\pi$
$942$	0	0
$943$	−16.0000	−0.521032
$944$	−12.0000	−0.390567
$945$	0	0
$946$	−8.00000	−0.260102
$947$	4.00000	0.129983	0.0649913	−	0.997886i	$-0.479298\pi$
$947$	4.00000	0.129983	0.0649913	+	0.997886i	$0.479298\pi$
$948$	0	0
$949$	8.00000	0.259691
$950$	0	0
$951$	0	0
$952$	4.00000	0.129641
$953$	22.0000	0.712650	0.356325	−	0.934362i	$-0.384030\pi$
$953$	22.0000	0.712650	0.356325	+	0.934362i	$0.384030\pi$
$954$	18.0000	0.582772
$955$	0	0
$956$	16.0000	0.517477
$957$	0	0
$958$	−16.0000	−0.516937
$959$	−6.00000	−0.193750
$960$	0	0
$961$	−27.0000	−0.870968
$962$	20.0000	0.644826
$963$	−48.0000	−1.54678
$964$	12.0000	0.386494
$965$	0	0
$966$	0	0
$967$	−32.0000	−1.02905	−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000	−1.02905	−0.514525	+	0.857475i	$0.672032\pi$
$968$	1.00000	0.0321412
$969$	0	0
$970$	0	0
$971$	56.0000	1.79713	0.898563	−	0.438845i	$-0.144612\pi$
$971$	56.0000	1.79713	0.898563	+	0.438845i	$0.144612\pi$
$972$	0	0
$973$	14.0000	0.448819
$974$	28.0000	0.897178
$975$	0	0
$976$	−14.0000	−0.448129
$977$	−2.00000	−0.0639857	−0.0319928	−	0.999488i	$-0.510185\pi$
$977$	−2.00000	−0.0639857	−0.0319928	+	0.999488i	$0.510185\pi$
$978$	0	0
$979$	6.00000	0.191761
$980$	0	0
$981$	42.0000	1.34096
$982$	−36.0000	−1.14881
$983$	−18.0000	−0.574111	−0.287055	−	0.957914i	$-0.592676\pi$
$983$	−18.0000	−0.574111	−0.287055	+	0.957914i	$0.592676\pi$
$984$	0	0
$985$	0	0
$986$	−8.00000	−0.254772
$987$	0	0
$988$	12.0000	0.381771
$989$	−32.0000	−1.01754
$990$	0	0
$991$	16.0000	0.508257	0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000	0.508257	0.254128	+	0.967170i	$0.418211\pi$
$992$	−2.00000	−0.0635001
$993$	0	0
$994$	−8.00000	−0.253745
$995$	0	0
$996$	0	0
$997$	42.0000	1.33015	0.665077	−	0.746775i	$-0.268399\pi$
$997$	42.0000	1.33015	0.665077	+	0.746775i	$0.268399\pi$
$998$	44.0000	1.39280
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3850.2.a.u.1.1		1
5.2	odd	4		3850.2.c.j.1849.2		2
5.3	odd	4		3850.2.c.j.1849.1		2
5.4	even	2		154.2.a.a.1.1	✓	1
15.14	odd	2		1386.2.a.l.1.1		1
20.19	odd	2		1232.2.a.e.1.1		1
35.4	even	6		1078.2.e.j.177.1		2
35.9	even	6		1078.2.e.j.67.1		2
35.19	odd	6		1078.2.e.i.67.1		2
35.24	odd	6		1078.2.e.i.177.1		2
35.34	odd	2		1078.2.a.d.1.1		1
40.19	odd	2		4928.2.a.w.1.1		1
40.29	even	2		4928.2.a.v.1.1		1
55.54	odd	2		1694.2.a.g.1.1		1
105.104	even	2		9702.2.a.ba.1.1		1
140.139	even	2		8624.2.a.r.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.a.a.1.1	✓	1	5.4	even	2
1078.2.a.d.1.1		1	35.34	odd	2
1078.2.e.i.67.1		2	35.19	odd	6
1078.2.e.i.177.1		2	35.24	odd	6
1078.2.e.j.67.1		2	35.9	even	6
1078.2.e.j.177.1		2	35.4	even	6
1232.2.a.e.1.1		1	20.19	odd	2
1386.2.a.l.1.1		1	15.14	odd	2
1694.2.a.g.1.1		1	55.54	odd	2
3850.2.a.u.1.1		1	1.1	even	1	trivial
3850.2.c.j.1849.1		2	5.3	odd	4
3850.2.c.j.1849.2		2	5.2	odd	4
4928.2.a.v.1.1		1	40.29	even	2
4928.2.a.w.1.1		1	40.19	odd	2
8624.2.a.r.1.1		1	140.139	even	2
9702.2.a.ba.1.1		1	105.104	even	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)

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