LMFDB - Embedded newform 9702.2.a.bi.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9702,2,Mod(1,9702)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9702, 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("9702.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9702.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:	$77.4708600410$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1386)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	9702.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} -2.00000 q^{5} +1.00000 q^{8} +O(q^{10})$

$q+1.00000 q^{2} +1.00000 q^{4} -2.00000 q^{5} +1.00000 q^{8} -2.00000 q^{10} +1.00000 q^{11} +2.00000 q^{13} +1.00000 q^{16} +1.00000 q^{17} -3.00000 q^{19} -2.00000 q^{20} +1.00000 q^{22} -1.00000 q^{23} -1.00000 q^{25} +2.00000 q^{26} -1.00000 q^{29} -2.00000 q^{31} +1.00000 q^{32} +1.00000 q^{34} -5.00000 q^{37} -3.00000 q^{38} -2.00000 q^{40} -10.0000 q^{41} +1.00000 q^{43} +1.00000 q^{44} -1.00000 q^{46} +7.00000 q^{47} -1.00000 q^{50} +2.00000 q^{52} +12.0000 q^{53} -2.00000 q^{55} -1.00000 q^{58} -3.00000 q^{59} -14.0000 q^{61} -2.00000 q^{62} +1.00000 q^{64} -4.00000 q^{65} +12.0000 q^{67} +1.00000 q^{68} +5.00000 q^{71} -8.00000 q^{73} -5.00000 q^{74} -3.00000 q^{76} -2.00000 q^{80} -10.0000 q^{82} -6.00000 q^{83} -2.00000 q^{85} +1.00000 q^{86} +1.00000 q^{88} -6.00000 q^{89} -1.00000 q^{92} +7.00000 q^{94} +6.00000 q^{95} +7.00000 q^{97} +O(q^{100})$

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
$3$	0	0
$4$	1.00000	0.500000
$5$	−2.00000	−0.894427	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000	−0.894427	−0.447214	+	0.894427i	$0.647584\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	0	0
$10$	−2.00000	−0.632456
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0	0
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	1.00000	0.242536	0.121268	−	0.992620i	$-0.461304\pi$
$17$	1.00000	0.242536	0.121268	+	0.992620i	$0.461304\pi$
$18$	0	0
$19$	−3.00000	−0.688247	−0.344124	−	0.938924i	$-0.611824\pi$
$19$	−3.00000	−0.688247	−0.344124	+	0.938924i	$0.611824\pi$
$20$	−2.00000	−0.447214
$21$	0	0
$22$	1.00000	0.213201
$23$	−1.00000	−0.208514	−0.104257	−	0.994550i	$-0.533247\pi$
$23$	−1.00000	−0.208514	−0.104257	+	0.994550i	$0.533247\pi$
$24$	0	0
$25$	−1.00000	−0.200000
$26$	2.00000	0.392232
$27$	0	0
$28$	0	0
$29$	−1.00000	−0.185695	−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000	−0.185695	−0.0928477	+	0.995680i	$0.529597\pi$
$30$	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
$34$	1.00000	0.171499
$35$	0	0
$36$	0	0
$37$	−5.00000	−0.821995	−0.410997	−	0.911636i	$-0.634819\pi$
$37$	−5.00000	−0.821995	−0.410997	+	0.911636i	$0.634819\pi$
$38$	−3.00000	−0.486664
$39$	0	0
$40$	−2.00000	−0.316228
$41$	−10.0000	−1.56174	−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000	−1.56174	−0.780869	+	0.624695i	$0.785223\pi$
$42$	0	0
$43$	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
$46$	−1.00000	−0.147442
$47$	7.00000	1.02105	0.510527	−	0.859861i	$-0.329450\pi$
$47$	7.00000	1.02105	0.510527	+	0.859861i	$0.329450\pi$
$48$	0	0
$49$	0	0
$50$	−1.00000	−0.141421
$51$	0	0
$52$	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	$0.191646\pi$
$54$	0	0
$55$	−2.00000	−0.269680
$56$	0	0
$57$	0	0
$58$	−1.00000	−0.131306
$59$	−3.00000	−0.390567	−0.195283	−	0.980747i	$-0.562563\pi$
$59$	−3.00000	−0.390567	−0.195283	+	0.980747i	$0.562563\pi$
$60$	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
$63$	0	0
$64$	1.00000	0.125000
$65$	−4.00000	−0.496139
$66$	0	0
$67$	12.0000	1.46603	0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000	1.46603	0.733017	+	0.680211i	$0.238112\pi$
$68$	1.00000	0.121268
$69$	0	0
$70$	0	0
$71$	5.00000	0.593391	0.296695	−	0.954972i	$-0.404115\pi$
$71$	5.00000	0.593391	0.296695	+	0.954972i	$0.404115\pi$
$72$	0	0
$73$	−8.00000	−0.936329	−0.468165	−	0.883641i	$-0.655085\pi$
$73$	−8.00000	−0.936329	−0.468165	+	0.883641i	$0.655085\pi$
$74$	−5.00000	−0.581238
$75$	0	0
$76$	−3.00000	−0.344124
$77$	0	0
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	−2.00000	−0.223607
$81$	0	0
$82$	−10.0000	−1.10432
$83$	−6.00000	−0.658586	−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000	−0.658586	−0.329293	+	0.944228i	$0.606810\pi$
$84$	0	0
$85$	−2.00000	−0.216930
$86$	1.00000	0.107833
$87$	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
$91$	0	0
$92$	−1.00000	−0.104257
$93$	0	0
$94$	7.00000	0.721995
$95$	6.00000	0.615587
$96$	0	0
$97$	7.00000	0.710742	0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000	0.710742	0.355371	+	0.934725i	$0.384354\pi$
$98$	0	0
$99$	0	0
$100$	−1.00000	−0.100000
$101$	−9.00000	−0.895533	−0.447767	−	0.894150i	$-0.647781\pi$
$101$	−9.00000	−0.895533	−0.447767	+	0.894150i	$0.647781\pi$
$102$	0	0
$103$	−6.00000	−0.591198	−0.295599	−	0.955312i	$-0.595519\pi$
$103$	−6.00000	−0.591198	−0.295599	+	0.955312i	$0.595519\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	12.0000	1.16554
$107$	−2.00000	−0.193347	−0.0966736	−	0.995316i	$-0.530820\pi$
$107$	−2.00000	−0.193347	−0.0966736	+	0.995316i	$0.530820\pi$
$108$	0	0
$109$	−20.0000	−1.91565	−0.957826	−	0.287348i	$-0.907226\pi$
$109$	−20.0000	−1.91565	−0.957826	+	0.287348i	$0.907226\pi$
$110$	−2.00000	−0.190693
$111$	0	0
$112$	0	0
$113$	10.0000	0.940721	0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000	0.940721	0.470360	+	0.882474i	$0.344124\pi$
$114$	0	0
$115$	2.00000	0.186501
$116$	−1.00000	−0.0928477
$117$	0	0
$118$	−3.00000	−0.276172
$119$	0	0
$120$	0	0
$121$	1.00000	0.0909091
$122$	−14.0000	−1.26750
$123$	0	0
$124$	−2.00000	−0.179605
$125$	12.0000	1.07331
$126$	0	0
$127$	−1.00000	−0.0887357	−0.0443678	−	0.999015i	$-0.514127\pi$
$127$	−1.00000	−0.0887357	−0.0443678	+	0.999015i	$0.514127\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	−4.00000	−0.350823
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	0	0
$134$	12.0000	1.03664
$135$	0	0
$136$	1.00000	0.0857493
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	0	0
$139$	−13.0000	−1.10265	−0.551323	−	0.834292i	$-0.685877\pi$
$139$	−13.0000	−1.10265	−0.551323	+	0.834292i	$0.685877\pi$
$140$	0	0
$141$	0	0
$142$	5.00000	0.419591
$143$	2.00000	0.167248
$144$	0	0
$145$	2.00000	0.166091
$146$	−8.00000	−0.662085
$147$	0	0
$148$	−5.00000	−0.410997
$149$	−11.0000	−0.901155	−0.450578	−	0.892737i	$-0.648782\pi$
$149$	−11.0000	−0.901155	−0.450578	+	0.892737i	$0.648782\pi$
$150$	0	0
$151$	−15.0000	−1.22068	−0.610341	−	0.792139i	$-0.708968\pi$
$151$	−15.0000	−1.22068	−0.610341	+	0.792139i	$0.708968\pi$
$152$	−3.00000	−0.243332
$153$	0	0
$154$	0	0
$155$	4.00000	0.321288
$156$	0	0
$157$	1.00000	0.0798087	0.0399043	−	0.999204i	$-0.487295\pi$
$157$	1.00000	0.0798087	0.0399043	+	0.999204i	$0.487295\pi$
$158$	0	0
$159$	0	0
$160$	−2.00000	−0.158114
$161$	0	0
$162$	0	0
$163$	10.0000	0.783260	0.391630	−	0.920123i	$-0.371911\pi$
$163$	10.0000	0.783260	0.391630	+	0.920123i	$0.371911\pi$
$164$	−10.0000	−0.780869
$165$	0	0
$166$	−6.00000	−0.465690
$167$	2.00000	0.154765	0.0773823	−	0.997001i	$-0.475344\pi$
$167$	2.00000	0.154765	0.0773823	+	0.997001i	$0.475344\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	−2.00000	−0.153393
$171$	0	0
$172$	1.00000	0.0762493
$173$	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
$179$	−7.00000	−0.523205	−0.261602	−	0.965176i	$-0.584251\pi$
$179$	−7.00000	−0.523205	−0.261602	+	0.965176i	$0.584251\pi$
$180$	0	0
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	0	0
$183$	0	0
$184$	−1.00000	−0.0737210
$185$	10.0000	0.735215
$186$	0	0
$187$	1.00000	0.0731272
$188$	7.00000	0.510527
$189$	0	0
$190$	6.00000	0.435286
$191$	−8.00000	−0.578860	−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000	−0.578860	−0.289430	+	0.957199i	$0.593466\pi$
$192$	0	0
$193$	8.00000	0.575853	0.287926	−	0.957653i	$-0.407034\pi$
$193$	8.00000	0.575853	0.287926	+	0.957653i	$0.407034\pi$
$194$	7.00000	0.502571
$195$	0	0
$196$	0	0
$197$	27.0000	1.92367	0.961835	−	0.273629i	$-0.0882242\pi$
$197$	27.0000	1.92367	0.961835	+	0.273629i	$0.0882242\pi$
$198$	0	0
$199$	−2.00000	−0.141776	−0.0708881	−	0.997484i	$-0.522583\pi$
$199$	−2.00000	−0.141776	−0.0708881	+	0.997484i	$0.522583\pi$
$200$	−1.00000	−0.0707107
$201$	0	0
$202$	−9.00000	−0.633238
$203$	0	0
$204$	0	0
$205$	20.0000	1.39686
$206$	−6.00000	−0.418040
$207$	0	0
$208$	2.00000	0.138675
$209$	−3.00000	−0.207514
$210$	0	0
$211$	4.00000	0.275371	0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000	0.275371	0.137686	+	0.990476i	$0.456034\pi$
$212$	12.0000	0.824163
$213$	0	0
$214$	−2.00000	−0.136717
$215$	−2.00000	−0.136399
$216$	0	0
$217$	0	0
$218$	−20.0000	−1.35457
$219$	0	0
$220$	−2.00000	−0.134840
$221$	2.00000	0.134535
$222$	0	0
$223$	−26.0000	−1.74109	−0.870544	−	0.492090i	$-0.836233\pi$
$223$	−26.0000	−1.74109	−0.870544	+	0.492090i	$0.836233\pi$
$224$	0	0
$225$	0	0
$226$	10.0000	0.665190
$227$	−10.0000	−0.663723	−0.331862	−	0.943328i	$-0.607677\pi$
$227$	−10.0000	−0.663723	−0.331862	+	0.943328i	$0.607677\pi$
$228$	0	0
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	2.00000	0.131876
$231$	0	0
$232$	−1.00000	−0.0656532
$233$	−21.0000	−1.37576	−0.687878	−	0.725826i	$-0.741458\pi$
$233$	−21.0000	−1.37576	−0.687878	+	0.725826i	$0.741458\pi$
$234$	0	0
$235$	−14.0000	−0.913259
$236$	−3.00000	−0.195283
$237$	0	0
$238$	0	0
$239$	−22.0000	−1.42306	−0.711531	−	0.702655i	$-0.751998\pi$
$239$	−22.0000	−1.42306	−0.711531	+	0.702655i	$0.751998\pi$
$240$	0	0
$241$	−12.0000	−0.772988	−0.386494	−	0.922292i	$-0.626314\pi$
$241$	−12.0000	−0.772988	−0.386494	+	0.922292i	$0.626314\pi$
$242$	1.00000	0.0642824
$243$	0	0
$244$	−14.0000	−0.896258
$245$	0	0
$246$	0	0
$247$	−6.00000	−0.381771
$248$	−2.00000	−0.127000
$249$	0	0
$250$	12.0000	0.758947
$251$	−21.0000	−1.32551	−0.662754	−	0.748837i	$-0.730613\pi$
$251$	−21.0000	−1.32551	−0.662754	+	0.748837i	$0.730613\pi$
$252$	0	0
$253$	−1.00000	−0.0628695
$254$	−1.00000	−0.0627456
$255$	0	0
$256$	1.00000	0.0625000
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	0	0
$259$	0	0
$260$	−4.00000	−0.248069
$261$	0	0
$262$	0	0
$263$	−6.00000	−0.369976	−0.184988	−	0.982741i	$-0.559225\pi$
$263$	−6.00000	−0.369976	−0.184988	+	0.982741i	$0.559225\pi$
$264$	0	0
$265$	−24.0000	−1.47431
$266$	0	0
$267$	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
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	1.00000	0.0606339
$273$	0	0
$274$	6.00000	0.362473
$275$	−1.00000	−0.0603023
$276$	0	0
$277$	−24.0000	−1.44202	−0.721010	−	0.692925i	$-0.756322\pi$
$277$	−24.0000	−1.44202	−0.721010	+	0.692925i	$0.756322\pi$
$278$	−13.0000	−0.779688
$279$	0	0
$280$	0	0
$281$	7.00000	0.417585	0.208792	−	0.977960i	$-0.433047\pi$
$281$	7.00000	0.417585	0.208792	+	0.977960i	$0.433047\pi$
$282$	0	0
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	5.00000	0.296695
$285$	0	0
$286$	2.00000	0.118262
$287$	0	0
$288$	0	0
$289$	−16.0000	−0.941176
$290$	2.00000	0.117444
$291$	0	0
$292$	−8.00000	−0.468165
$293$	9.00000	0.525786	0.262893	−	0.964825i	$-0.415323\pi$
$293$	9.00000	0.525786	0.262893	+	0.964825i	$0.415323\pi$
$294$	0	0
$295$	6.00000	0.349334
$296$	−5.00000	−0.290619
$297$	0	0
$298$	−11.0000	−0.637213
$299$	−2.00000	−0.115663
$300$	0	0
$301$	0	0
$302$	−15.0000	−0.863153
$303$	0	0
$304$	−3.00000	−0.172062
$305$	28.0000	1.60328
$306$	0	0
$307$	−4.00000	−0.228292	−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000	−0.228292	−0.114146	+	0.993464i	$0.536413\pi$
$308$	0	0
$309$	0	0
$310$	4.00000	0.227185
$311$	13.0000	0.737162	0.368581	−	0.929596i	$-0.379844\pi$
$311$	13.0000	0.737162	0.368581	+	0.929596i	$0.379844\pi$
$312$	0	0
$313$	7.00000	0.395663	0.197832	−	0.980236i	$-0.436610\pi$
$313$	7.00000	0.395663	0.197832	+	0.980236i	$0.436610\pi$
$314$	1.00000	0.0564333
$315$	0	0
$316$	0	0
$317$	6.00000	0.336994	0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000	0.336994	0.168497	+	0.985702i	$0.446109\pi$
$318$	0	0
$319$	−1.00000	−0.0559893
$320$	−2.00000	−0.111803
$321$	0	0
$322$	0	0
$323$	−3.00000	−0.166924
$324$	0	0
$325$	−2.00000	−0.110940
$326$	10.0000	0.553849
$327$	0	0
$328$	−10.0000	−0.552158
$329$	0	0
$330$	0	0
$331$	−2.00000	−0.109930	−0.0549650	−	0.998488i	$-0.517505\pi$
$331$	−2.00000	−0.109930	−0.0549650	+	0.998488i	$0.517505\pi$
$332$	−6.00000	−0.329293
$333$	0	0
$334$	2.00000	0.109435
$335$	−24.0000	−1.31126
$336$	0	0
$337$	0	0		−	1.00000i	$-0.5\pi$
$337$	0	0			1.00000i	$0.5\pi$
$338$	−9.00000	−0.489535
$339$	0	0
$340$	−2.00000	−0.108465
$341$	−2.00000	−0.108306
$342$	0	0
$343$	0	0
$344$	1.00000	0.0539164
$345$	0	0
$346$	14.0000	0.752645
$347$	−32.0000	−1.71785	−0.858925	−	0.512101i	$-0.828867\pi$
$347$	−32.0000	−1.71785	−0.858925	+	0.512101i	$0.828867\pi$
$348$	0	0
$349$	−16.0000	−0.856460	−0.428230	−	0.903670i	$-0.640863\pi$
$349$	−16.0000	−0.856460	−0.428230	+	0.903670i	$0.640863\pi$
$350$	0	0
$351$	0	0
$352$	1.00000	0.0533002
$353$	−6.00000	−0.319348	−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000	−0.319348	−0.159674	+	0.987170i	$0.551044\pi$
$354$	0	0
$355$	−10.0000	−0.530745
$356$	−6.00000	−0.317999
$357$	0	0
$358$	−7.00000	−0.369961
$359$	10.0000	0.527780	0.263890	−	0.964553i	$-0.414994\pi$
$359$	10.0000	0.527780	0.263890	+	0.964553i	$0.414994\pi$
$360$	0	0
$361$	−10.0000	−0.526316
$362$	−10.0000	−0.525588
$363$	0	0
$364$	0	0
$365$	16.0000	0.837478
$366$	0	0
$367$	−32.0000	−1.67039	−0.835193	−	0.549957i	$-0.814644\pi$
$367$	−32.0000	−1.67039	−0.835193	+	0.549957i	$0.814644\pi$
$368$	−1.00000	−0.0521286
$369$	0	0
$370$	10.0000	0.519875
$371$	0	0
$372$	0	0
$373$	26.0000	1.34623	0.673114	−	0.739538i	$-0.264956\pi$
$373$	26.0000	1.34623	0.673114	+	0.739538i	$0.264956\pi$
$374$	1.00000	0.0517088
$375$	0	0
$376$	7.00000	0.360997
$377$	−2.00000	−0.103005
$378$	0	0
$379$	−8.00000	−0.410932	−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000	−0.410932	−0.205466	+	0.978664i	$0.565871\pi$
$380$	6.00000	0.307794
$381$	0	0
$382$	−8.00000	−0.409316
$383$	25.0000	1.27744	0.638720	−	0.769439i	$-0.279464\pi$
$383$	25.0000	1.27744	0.638720	+	0.769439i	$0.279464\pi$
$384$	0	0
$385$	0	0
$386$	8.00000	0.407189
$387$	0	0
$388$	7.00000	0.355371
$389$	−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
$391$	−1.00000	−0.0505722
$392$	0	0
$393$	0	0
$394$	27.0000	1.36024
$395$	0	0
$396$	0	0
$397$	−27.0000	−1.35509	−0.677546	−	0.735481i	$-0.736956\pi$
$397$	−27.0000	−1.35509	−0.677546	+	0.735481i	$0.736956\pi$
$398$	−2.00000	−0.100251
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	−24.0000	−1.19850	−0.599251	−	0.800561i	$-0.704535\pi$
$401$	−24.0000	−1.19850	−0.599251	+	0.800561i	$0.704535\pi$
$402$	0	0
$403$	−4.00000	−0.199254
$404$	−9.00000	−0.447767
$405$	0	0
$406$	0	0
$407$	−5.00000	−0.247841
$408$	0	0
$409$	16.0000	0.791149	0.395575	−	0.918434i	$-0.370545\pi$
$409$	16.0000	0.791149	0.395575	+	0.918434i	$0.370545\pi$
$410$	20.0000	0.987730
$411$	0	0
$412$	−6.00000	−0.295599
$413$	0	0
$414$	0	0
$415$	12.0000	0.589057
$416$	2.00000	0.0980581
$417$	0	0
$418$	−3.00000	−0.146735
$419$	29.0000	1.41674	0.708371	−	0.705840i	$-0.249430\pi$
$419$	29.0000	1.41674	0.708371	+	0.705840i	$0.249430\pi$
$420$	0	0
$421$	−17.0000	−0.828529	−0.414265	−	0.910156i	$-0.635961\pi$
$421$	−17.0000	−0.828529	−0.414265	+	0.910156i	$0.635961\pi$
$422$	4.00000	0.194717
$423$	0	0
$424$	12.0000	0.582772
$425$	−1.00000	−0.0485071
$426$	0	0
$427$	0	0
$428$	−2.00000	−0.0966736
$429$	0	0
$430$	−2.00000	−0.0964486
$431$	−16.0000	−0.770693	−0.385346	−	0.922772i	$-0.625918\pi$
$431$	−16.0000	−0.770693	−0.385346	+	0.922772i	$0.625918\pi$
$432$	0	0
$433$	−19.0000	−0.913082	−0.456541	−	0.889702i	$-0.650912\pi$
$433$	−19.0000	−0.913082	−0.456541	+	0.889702i	$0.650912\pi$
$434$	0	0
$435$	0	0
$436$	−20.0000	−0.957826
$437$	3.00000	0.143509
$438$	0	0
$439$	31.0000	1.47955	0.739775	−	0.672855i	$-0.234932\pi$
$439$	31.0000	1.47955	0.739775	+	0.672855i	$0.234932\pi$
$440$	−2.00000	−0.0953463
$441$	0	0
$442$	2.00000	0.0951303
$443$	15.0000	0.712672	0.356336	−	0.934358i	$-0.384026\pi$
$443$	15.0000	0.712672	0.356336	+	0.934358i	$0.384026\pi$
$444$	0	0
$445$	12.0000	0.568855
$446$	−26.0000	−1.23114
$447$	0	0
$448$	0	0
$449$	−12.0000	−0.566315	−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000	−0.566315	−0.283158	+	0.959073i	$0.591382\pi$
$450$	0	0
$451$	−10.0000	−0.470882
$452$	10.0000	0.470360
$453$	0	0
$454$	−10.0000	−0.469323
$455$	0	0
$456$	0	0
$457$	32.0000	1.49690	0.748448	−	0.663193i	$-0.230799\pi$
$457$	32.0000	1.49690	0.748448	+	0.663193i	$0.230799\pi$
$458$	−10.0000	−0.467269
$459$	0	0
$460$	2.00000	0.0932505
$461$	33.0000	1.53696	0.768482	−	0.639872i	$-0.221013\pi$
$461$	33.0000	1.53696	0.768482	+	0.639872i	$0.221013\pi$
$462$	0	0
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	−1.00000	−0.0464238
$465$	0	0
$466$	−21.0000	−0.972806
$467$	27.0000	1.24941	0.624705	−	0.780860i	$-0.285219\pi$
$467$	27.0000	1.24941	0.624705	+	0.780860i	$0.285219\pi$
$468$	0	0
$469$	0	0
$470$	−14.0000	−0.645772
$471$	0	0
$472$	−3.00000	−0.138086
$473$	1.00000	0.0459800
$474$	0	0
$475$	3.00000	0.137649
$476$	0	0
$477$	0	0
$478$	−22.0000	−1.00626
$479$	−26.0000	−1.18797	−0.593985	−	0.804476i	$-0.702446\pi$
$479$	−26.0000	−1.18797	−0.593985	+	0.804476i	$0.702446\pi$
$480$	0	0
$481$	−10.0000	−0.455961
$482$	−12.0000	−0.546585
$483$	0	0
$484$	1.00000	0.0454545
$485$	−14.0000	−0.635707
$486$	0	0
$487$	−34.0000	−1.54069	−0.770344	−	0.637629i	$-0.779915\pi$
$487$	−34.0000	−1.54069	−0.770344	+	0.637629i	$0.779915\pi$
$488$	−14.0000	−0.633750
$489$	0	0
$490$	0	0
$491$	−6.00000	−0.270776	−0.135388	−	0.990793i	$-0.543228\pi$
$491$	−6.00000	−0.270776	−0.135388	+	0.990793i	$0.543228\pi$
$492$	0	0
$493$	−1.00000	−0.0450377
$494$	−6.00000	−0.269953
$495$	0	0
$496$	−2.00000	−0.0898027
$497$	0	0
$498$	0	0
$499$	8.00000	0.358129	0.179065	−	0.983837i	$-0.442693\pi$
$499$	8.00000	0.358129	0.179065	+	0.983837i	$0.442693\pi$
$500$	12.0000	0.536656
$501$	0	0
$502$	−21.0000	−0.937276
$503$	−42.0000	−1.87269	−0.936344	−	0.351085i	$-0.885813\pi$
$503$	−42.0000	−1.87269	−0.936344	+	0.351085i	$0.885813\pi$
$504$	0	0
$505$	18.0000	0.800989
$506$	−1.00000	−0.0444554
$507$	0	0
$508$	−1.00000	−0.0443678
$509$	−20.0000	−0.886484	−0.443242	−	0.896402i	$-0.646172\pi$
$509$	−20.0000	−0.886484	−0.443242	+	0.896402i	$0.646172\pi$
$510$	0	0
$511$	0	0
$512$	1.00000	0.0441942
$513$	0	0
$514$	−6.00000	−0.264649
$515$	12.0000	0.528783
$516$	0	0
$517$	7.00000	0.307860
$518$	0	0
$519$	0	0
$520$	−4.00000	−0.175412
$521$	14.0000	0.613351	0.306676	−	0.951814i	$-0.400783\pi$
$521$	14.0000	0.613351	0.306676	+	0.951814i	$0.400783\pi$
$522$	0	0
$523$	−4.00000	−0.174908	−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000	−0.174908	−0.0874539	+	0.996169i	$0.527873\pi$
$524$	0	0
$525$	0	0
$526$	−6.00000	−0.261612
$527$	−2.00000	−0.0871214
$528$	0	0
$529$	−22.0000	−0.956522
$530$	−24.0000	−1.04249
$531$	0	0
$532$	0	0
$533$	−20.0000	−0.866296
$534$	0	0
$535$	4.00000	0.172935
$536$	12.0000	0.518321
$537$	0	0
$538$	12.0000	0.517357
$539$	0	0
$540$	0	0
$541$	−16.0000	−0.687894	−0.343947	−	0.938989i	$-0.611764\pi$
$541$	−16.0000	−0.687894	−0.343947	+	0.938989i	$0.611764\pi$
$542$	16.0000	0.687259
$543$	0	0
$544$	1.00000	0.0428746
$545$	40.0000	1.71341
$546$	0	0
$547$	39.0000	1.66752	0.833760	−	0.552127i	$-0.186184\pi$
$547$	39.0000	1.66752	0.833760	+	0.552127i	$0.186184\pi$
$548$	6.00000	0.256307
$549$	0	0
$550$	−1.00000	−0.0426401
$551$	3.00000	0.127804
$552$	0	0
$553$	0	0
$554$	−24.0000	−1.01966
$555$	0	0
$556$	−13.0000	−0.551323
$557$	−35.0000	−1.48300	−0.741499	−	0.670954i	$-0.765885\pi$
$557$	−35.0000	−1.48300	−0.741499	+	0.670954i	$0.765885\pi$
$558$	0	0
$559$	2.00000	0.0845910
$560$	0	0
$561$	0	0
$562$	7.00000	0.295277
$563$	−38.0000	−1.60151	−0.800755	−	0.598993i	$-0.795568\pi$
$563$	−38.0000	−1.60151	−0.800755	+	0.598993i	$0.795568\pi$
$564$	0	0
$565$	−20.0000	−0.841406
$566$	0	0
$567$	0	0
$568$	5.00000	0.209795
$569$	−15.0000	−0.628833	−0.314416	−	0.949285i	$-0.601809\pi$
$569$	−15.0000	−0.628833	−0.314416	+	0.949285i	$0.601809\pi$
$570$	0	0
$571$	7.00000	0.292941	0.146470	−	0.989215i	$-0.453209\pi$
$571$	7.00000	0.292941	0.146470	+	0.989215i	$0.453209\pi$
$572$	2.00000	0.0836242
$573$	0	0
$574$	0	0
$575$	1.00000	0.0417029
$576$	0	0
$577$	14.0000	0.582828	0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000	0.582828	0.291414	+	0.956597i	$0.405874\pi$
$578$	−16.0000	−0.665512
$579$	0	0
$580$	2.00000	0.0830455
$581$	0	0
$582$	0	0
$583$	12.0000	0.496989
$584$	−8.00000	−0.331042
$585$	0	0
$586$	9.00000	0.371787
$587$	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
$589$	6.00000	0.247226
$590$	6.00000	0.247016
$591$	0	0
$592$	−5.00000	−0.205499
$593$	15.0000	0.615976	0.307988	−	0.951390i	$-0.400344\pi$
$593$	15.0000	0.615976	0.307988	+	0.951390i	$0.400344\pi$
$594$	0	0
$595$	0	0
$596$	−11.0000	−0.450578
$597$	0	0
$598$	−2.00000	−0.0817861
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	8.00000	0.326327	0.163163	−	0.986599i	$-0.447830\pi$
$601$	8.00000	0.326327	0.163163	+	0.986599i	$0.447830\pi$
$602$	0	0
$603$	0	0
$604$	−15.0000	−0.610341
$605$	−2.00000	−0.0813116
$606$	0	0
$607$	−28.0000	−1.13648	−0.568242	−	0.822861i	$-0.692376\pi$
$607$	−28.0000	−1.13648	−0.568242	+	0.822861i	$0.692376\pi$
$608$	−3.00000	−0.121666
$609$	0	0
$610$	28.0000	1.13369
$611$	14.0000	0.566379
$612$	0	0
$613$	−14.0000	−0.565455	−0.282727	−	0.959200i	$-0.591239\pi$
$613$	−14.0000	−0.565455	−0.282727	+	0.959200i	$0.591239\pi$
$614$	−4.00000	−0.161427
$615$	0	0
$616$	0	0
$617$	36.0000	1.44931	0.724653	−	0.689114i	$-0.242000\pi$
$617$	36.0000	1.44931	0.724653	+	0.689114i	$0.242000\pi$
$618$	0	0
$619$	26.0000	1.04503	0.522514	−	0.852631i	$-0.324994\pi$
$619$	26.0000	1.04503	0.522514	+	0.852631i	$0.324994\pi$
$620$	4.00000	0.160644
$621$	0	0
$622$	13.0000	0.521253
$623$	0	0
$624$	0	0
$625$	−19.0000	−0.760000
$626$	7.00000	0.279776
$627$	0	0
$628$	1.00000	0.0399043
$629$	−5.00000	−0.199363
$630$	0	0
$631$	18.0000	0.716569	0.358284	−	0.933613i	$-0.383362\pi$
$631$	18.0000	0.716569	0.358284	+	0.933613i	$0.383362\pi$
$632$	0	0
$633$	0	0
$634$	6.00000	0.238290
$635$	2.00000	0.0793676
$636$	0	0
$637$	0	0
$638$	−1.00000	−0.0395904
$639$	0	0
$640$	−2.00000	−0.0790569
$641$	−12.0000	−0.473972	−0.236986	−	0.971513i	$-0.576159\pi$
$641$	−12.0000	−0.473972	−0.236986	+	0.971513i	$0.576159\pi$
$642$	0	0
$643$	−32.0000	−1.26196	−0.630978	−	0.775800i	$-0.717346\pi$
$643$	−32.0000	−1.26196	−0.630978	+	0.775800i	$0.717346\pi$
$644$	0	0
$645$	0	0
$646$	−3.00000	−0.118033
$647$	48.0000	1.88707	0.943537	−	0.331266i	$-0.107476\pi$
$647$	48.0000	1.88707	0.943537	+	0.331266i	$0.107476\pi$
$648$	0	0
$649$	−3.00000	−0.117760
$650$	−2.00000	−0.0784465
$651$	0	0
$652$	10.0000	0.391630
$653$	14.0000	0.547862	0.273931	−	0.961749i	$-0.411676\pi$
$653$	14.0000	0.547862	0.273931	+	0.961749i	$0.411676\pi$
$654$	0	0
$655$	0	0
$656$	−10.0000	−0.390434
$657$	0	0
$658$	0	0
$659$	44.0000	1.71400	0.856998	−	0.515319i	$-0.172327\pi$
$659$	44.0000	1.71400	0.856998	+	0.515319i	$0.172327\pi$
$660$	0	0
$661$	5.00000	0.194477	0.0972387	−	0.995261i	$-0.468999\pi$
$661$	5.00000	0.194477	0.0972387	+	0.995261i	$0.468999\pi$
$662$	−2.00000	−0.0777322
$663$	0	0
$664$	−6.00000	−0.232845
$665$	0	0
$666$	0	0
$667$	1.00000	0.0387202
$668$	2.00000	0.0773823
$669$	0	0
$670$	−24.0000	−0.927201
$671$	−14.0000	−0.540464
$672$	0	0
$673$	22.0000	0.848038	0.424019	−	0.905653i	$-0.360619\pi$
$673$	22.0000	0.848038	0.424019	+	0.905653i	$0.360619\pi$
$674$	0	0
$675$	0	0
$676$	−9.00000	−0.346154
$677$	7.00000	0.269032	0.134516	−	0.990911i	$-0.457052\pi$
$677$	7.00000	0.269032	0.134516	+	0.990911i	$0.457052\pi$
$678$	0	0
$679$	0	0
$680$	−2.00000	−0.0766965
$681$	0	0
$682$	−2.00000	−0.0765840
$683$	−39.0000	−1.49229	−0.746147	−	0.665782i	$-0.768098\pi$
$683$	−39.0000	−1.49229	−0.746147	+	0.665782i	$0.768098\pi$
$684$	0	0
$685$	−12.0000	−0.458496
$686$	0	0
$687$	0	0
$688$	1.00000	0.0381246
$689$	24.0000	0.914327
$690$	0	0
$691$	−18.0000	−0.684752	−0.342376	−	0.939563i	$-0.611232\pi$
$691$	−18.0000	−0.684752	−0.342376	+	0.939563i	$0.611232\pi$
$692$	14.0000	0.532200
$693$	0	0
$694$	−32.0000	−1.21470
$695$	26.0000	0.986236
$696$	0	0
$697$	−10.0000	−0.378777
$698$	−16.0000	−0.605609
$699$	0	0
$700$	0	0
$701$	9.00000	0.339925	0.169963	−	0.985451i	$-0.445635\pi$
$701$	9.00000	0.339925	0.169963	+	0.985451i	$0.445635\pi$
$702$	0	0
$703$	15.0000	0.565736
$704$	1.00000	0.0376889
$705$	0	0
$706$	−6.00000	−0.225813
$707$	0	0
$708$	0	0
$709$	9.00000	0.338002	0.169001	−	0.985616i	$-0.445946\pi$
$709$	9.00000	0.338002	0.169001	+	0.985616i	$0.445946\pi$
$710$	−10.0000	−0.375293
$711$	0	0
$712$	−6.00000	−0.224860
$713$	2.00000	0.0749006
$714$	0	0
$715$	−4.00000	−0.149592
$716$	−7.00000	−0.261602
$717$	0	0
$718$	10.0000	0.373197
$719$	23.0000	0.857755	0.428878	−	0.903363i	$-0.358909\pi$
$719$	23.0000	0.857755	0.428878	+	0.903363i	$0.358909\pi$
$720$	0	0
$721$	0	0
$722$	−10.0000	−0.372161
$723$	0	0
$724$	−10.0000	−0.371647
$725$	1.00000	0.0371391
$726$	0	0
$727$	14.0000	0.519231	0.259616	−	0.965712i	$-0.416404\pi$
$727$	14.0000	0.519231	0.259616	+	0.965712i	$0.416404\pi$
$728$	0	0
$729$	0	0
$730$	16.0000	0.592187
$731$	1.00000	0.0369863
$732$	0	0
$733$	−10.0000	−0.369358	−0.184679	−	0.982799i	$-0.559125\pi$
$733$	−10.0000	−0.369358	−0.184679	+	0.982799i	$0.559125\pi$
$734$	−32.0000	−1.18114
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	12.0000	0.442026
$738$	0	0
$739$	36.0000	1.32428	0.662141	−	0.749380i	$-0.269648\pi$
$739$	36.0000	1.32428	0.662141	+	0.749380i	$0.269648\pi$
$740$	10.0000	0.367607
$741$	0	0
$742$	0	0
$743$	36.0000	1.32071	0.660356	−	0.750953i	$-0.270405\pi$
$743$	36.0000	1.32071	0.660356	+	0.750953i	$0.270405\pi$
$744$	0	0
$745$	22.0000	0.806018
$746$	26.0000	0.951928
$747$	0	0
$748$	1.00000	0.0365636
$749$	0	0
$750$	0	0
$751$	−32.0000	−1.16770	−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000	−1.16770	−0.583848	+	0.811863i	$0.698454\pi$
$752$	7.00000	0.255264
$753$	0	0
$754$	−2.00000	−0.0728357
$755$	30.0000	1.09181
$756$	0	0
$757$	47.0000	1.70824	0.854122	−	0.520073i	$-0.174095\pi$
$757$	47.0000	1.70824	0.854122	+	0.520073i	$0.174095\pi$
$758$	−8.00000	−0.290573
$759$	0	0
$760$	6.00000	0.217643
$761$	18.0000	0.652499	0.326250	−	0.945284i	$-0.394215\pi$
$761$	18.0000	0.652499	0.326250	+	0.945284i	$0.394215\pi$
$762$	0	0
$763$	0	0
$764$	−8.00000	−0.289430
$765$	0	0
$766$	25.0000	0.903287
$767$	−6.00000	−0.216647
$768$	0	0
$769$	−20.0000	−0.721218	−0.360609	−	0.932717i	$-0.617431\pi$
$769$	−20.0000	−0.721218	−0.360609	+	0.932717i	$0.617431\pi$
$770$	0	0
$771$	0	0
$772$	8.00000	0.287926
$773$	36.0000	1.29483	0.647415	−	0.762138i	$-0.275850\pi$
$773$	36.0000	1.29483	0.647415	+	0.762138i	$0.275850\pi$
$774$	0	0
$775$	2.00000	0.0718421
$776$	7.00000	0.251285
$777$	0	0
$778$	−30.0000	−1.07555
$779$	30.0000	1.07486
$780$	0	0
$781$	5.00000	0.178914
$782$	−1.00000	−0.0357599
$783$	0	0
$784$	0	0
$785$	−2.00000	−0.0713831
$786$	0	0
$787$	−31.0000	−1.10503	−0.552515	−	0.833503i	$-0.686332\pi$
$787$	−31.0000	−1.10503	−0.552515	+	0.833503i	$0.686332\pi$
$788$	27.0000	0.961835
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−28.0000	−0.994309
$794$	−27.0000	−0.958194
$795$	0	0
$796$	−2.00000	−0.0708881
$797$	22.0000	0.779280	0.389640	−	0.920967i	$-0.372599\pi$
$797$	22.0000	0.779280	0.389640	+	0.920967i	$0.372599\pi$
$798$	0	0
$799$	7.00000	0.247642
$800$	−1.00000	−0.0353553
$801$	0	0
$802$	−24.0000	−0.847469
$803$	−8.00000	−0.282314
$804$	0	0
$805$	0	0
$806$	−4.00000	−0.140894
$807$	0	0
$808$	−9.00000	−0.316619
$809$	18.0000	0.632846	0.316423	−	0.948618i	$-0.397518\pi$
$809$	18.0000	0.632846	0.316423	+	0.948618i	$0.397518\pi$
$810$	0	0
$811$	−28.0000	−0.983213	−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000	−0.983213	−0.491606	+	0.870817i	$0.663590\pi$
$812$	0	0
$813$	0	0
$814$	−5.00000	−0.175250
$815$	−20.0000	−0.700569
$816$	0	0
$817$	−3.00000	−0.104957
$818$	16.0000	0.559427
$819$	0	0
$820$	20.0000	0.698430
$821$	−30.0000	−1.04701	−0.523504	−	0.852023i	$-0.675375\pi$
$821$	−30.0000	−1.04701	−0.523504	+	0.852023i	$0.675375\pi$
$822$	0	0
$823$	44.0000	1.53374	0.766872	−	0.641800i	$-0.221812\pi$
$823$	44.0000	1.53374	0.766872	+	0.641800i	$0.221812\pi$
$824$	−6.00000	−0.209020
$825$	0	0
$826$	0	0
$827$	34.0000	1.18230	0.591148	−	0.806563i	$-0.298675\pi$
$827$	34.0000	1.18230	0.591148	+	0.806563i	$0.298675\pi$
$828$	0	0
$829$	7.00000	0.243120	0.121560	−	0.992584i	$-0.461210\pi$
$829$	7.00000	0.243120	0.121560	+	0.992584i	$0.461210\pi$
$830$	12.0000	0.416526
$831$	0	0
$832$	2.00000	0.0693375
$833$	0	0
$834$	0	0
$835$	−4.00000	−0.138426
$836$	−3.00000	−0.103757
$837$	0	0
$838$	29.0000	1.00179
$839$	−24.0000	−0.828572	−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000	−0.828572	−0.414286	+	0.910147i	$0.635969\pi$
$840$	0	0
$841$	−28.0000	−0.965517
$842$	−17.0000	−0.585859
$843$	0	0
$844$	4.00000	0.137686
$845$	18.0000	0.619219
$846$	0	0
$847$	0	0
$848$	12.0000	0.412082
$849$	0	0
$850$	−1.00000	−0.0342997
$851$	5.00000	0.171398
$852$	0	0
$853$	14.0000	0.479351	0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000	0.479351	0.239675	+	0.970853i	$0.422959\pi$
$854$	0	0
$855$	0	0
$856$	−2.00000	−0.0683586
$857$	−47.0000	−1.60549	−0.802745	−	0.596323i	$-0.796628\pi$
$857$	−47.0000	−1.60549	−0.802745	+	0.596323i	$0.796628\pi$
$858$	0	0
$859$	−26.0000	−0.887109	−0.443554	−	0.896248i	$-0.646283\pi$
$859$	−26.0000	−0.887109	−0.443554	+	0.896248i	$0.646283\pi$
$860$	−2.00000	−0.0681994
$861$	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
$865$	−28.0000	−0.952029
$866$	−19.0000	−0.645646
$867$	0	0
$868$	0	0
$869$	0	0
$870$	0	0
$871$	24.0000	0.813209
$872$	−20.0000	−0.677285
$873$	0	0
$874$	3.00000	0.101477
$875$	0	0
$876$	0	0
$877$	−14.0000	−0.472746	−0.236373	−	0.971662i	$-0.575959\pi$
$877$	−14.0000	−0.472746	−0.236373	+	0.971662i	$0.575959\pi$
$878$	31.0000	1.04620
$879$	0	0
$880$	−2.00000	−0.0674200
$881$	12.0000	0.404290	0.202145	−	0.979356i	$-0.435209\pi$
$881$	12.0000	0.404290	0.202145	+	0.979356i	$0.435209\pi$
$882$	0	0
$883$	40.0000	1.34611	0.673054	−	0.739594i	$-0.264982\pi$
$883$	40.0000	1.34611	0.673054	+	0.739594i	$0.264982\pi$
$884$	2.00000	0.0672673
$885$	0	0
$886$	15.0000	0.503935
$887$	44.0000	1.47738	0.738688	−	0.674048i	$-0.235446\pi$
$887$	44.0000	1.47738	0.738688	+	0.674048i	$0.235446\pi$
$888$	0	0
$889$	0	0
$890$	12.0000	0.402241
$891$	0	0
$892$	−26.0000	−0.870544
$893$	−21.0000	−0.702738
$894$	0	0
$895$	14.0000	0.467968
$896$	0	0
$897$	0	0
$898$	−12.0000	−0.400445
$899$	2.00000	0.0667037
$900$	0	0
$901$	12.0000	0.399778
$902$	−10.0000	−0.332964
$903$	0	0
$904$	10.0000	0.332595
$905$	20.0000	0.664822
$906$	0	0
$907$	−40.0000	−1.32818	−0.664089	−	0.747653i	$-0.731180\pi$
$907$	−40.0000	−1.32818	−0.664089	+	0.747653i	$0.731180\pi$
$908$	−10.0000	−0.331862
$909$	0	0
$910$	0	0
$911$	−45.0000	−1.49092	−0.745458	−	0.666552i	$-0.767769\pi$
$911$	−45.0000	−1.49092	−0.745458	+	0.666552i	$0.767769\pi$
$912$	0	0
$913$	−6.00000	−0.198571
$914$	32.0000	1.05847
$915$	0	0
$916$	−10.0000	−0.330409
$917$	0	0
$918$	0	0
$919$	57.0000	1.88026	0.940128	−	0.340821i	$-0.110705\pi$
$919$	57.0000	1.88026	0.940128	+	0.340821i	$0.110705\pi$
$920$	2.00000	0.0659380
$921$	0	0
$922$	33.0000	1.08680
$923$	10.0000	0.329154
$924$	0	0
$925$	5.00000	0.164399
$926$	16.0000	0.525793
$927$	0	0
$928$	−1.00000	−0.0328266
$929$	36.0000	1.18112	0.590561	−	0.806993i	$-0.298907\pi$
$929$	36.0000	1.18112	0.590561	+	0.806993i	$0.298907\pi$
$930$	0	0
$931$	0	0
$932$	−21.0000	−0.687878
$933$	0	0
$934$	27.0000	0.883467
$935$	−2.00000	−0.0654070
$936$	0	0
$937$	18.0000	0.588034	0.294017	−	0.955800i	$-0.405008\pi$
$937$	18.0000	0.588034	0.294017	+	0.955800i	$0.405008\pi$
$938$	0	0
$939$	0	0
$940$	−14.0000	−0.456630
$941$	35.0000	1.14097	0.570484	−	0.821309i	$-0.306756\pi$
$941$	35.0000	1.14097	0.570484	+	0.821309i	$0.306756\pi$
$942$	0	0
$943$	10.0000	0.325645
$944$	−3.00000	−0.0976417
$945$	0	0
$946$	1.00000	0.0325128
$947$	−53.0000	−1.72227	−0.861134	−	0.508378i	$-0.830245\pi$
$947$	−53.0000	−1.72227	−0.861134	+	0.508378i	$0.830245\pi$
$948$	0	0
$949$	−16.0000	−0.519382
$950$	3.00000	0.0973329
$951$	0	0
$952$	0	0
$953$	−26.0000	−0.842223	−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000	−0.842223	−0.421111	+	0.907009i	$0.638360\pi$
$954$	0	0
$955$	16.0000	0.517748
$956$	−22.0000	−0.711531
$957$	0	0
$958$	−26.0000	−0.840022
$959$	0	0
$960$	0	0
$961$	−27.0000	−0.870968
$962$	−10.0000	−0.322413
$963$	0	0
$964$	−12.0000	−0.386494
$965$	−16.0000	−0.515058
$966$	0	0
$967$	−1.00000	−0.0321578	−0.0160789	−	0.999871i	$-0.505118\pi$
$967$	−1.00000	−0.0321578	−0.0160789	+	0.999871i	$0.505118\pi$
$968$	1.00000	0.0321412
$969$	0	0
$970$	−14.0000	−0.449513
$971$	4.00000	0.128366	0.0641831	−	0.997938i	$-0.479556\pi$
$971$	4.00000	0.128366	0.0641831	+	0.997938i	$0.479556\pi$
$972$	0	0
$973$	0	0
$974$	−34.0000	−1.08943
$975$	0	0
$976$	−14.0000	−0.448129
$977$	28.0000	0.895799	0.447900	−	0.894084i	$-0.352172\pi$
$977$	28.0000	0.895799	0.447900	+	0.894084i	$0.352172\pi$
$978$	0	0
$979$	−6.00000	−0.191761
$980$	0	0
$981$	0	0
$982$	−6.00000	−0.191468
$983$	39.0000	1.24391	0.621953	−	0.783054i	$-0.286339\pi$
$983$	39.0000	1.24391	0.621953	+	0.783054i	$0.286339\pi$
$984$	0	0
$985$	−54.0000	−1.72058
$986$	−1.00000	−0.0318465
$987$	0	0
$988$	−6.00000	−0.190885
$989$	−1.00000	−0.0317982
$990$	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
$994$	0	0
$995$	4.00000	0.126809
$996$	0	0
$997$	−42.0000	−1.33015	−0.665077	−	0.746775i	$-0.731601\pi$
$997$	−42.0000	−1.33015	−0.665077	+	0.746775i	$0.731601\pi$
$998$	8.00000	0.253236
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9702.2.a.bi.1.1		1
3.2	odd	2		9702.2.a.s.1.1		1
7.2	even	3		1386.2.k.h.991.1	yes	2
7.4	even	3		1386.2.k.h.793.1	✓	2
7.6	odd	2		9702.2.a.ca.1.1		1
21.2	odd	6		1386.2.k.l.991.1	yes	2
21.11	odd	6		1386.2.k.l.793.1	yes	2
21.20	even	2		9702.2.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.k.h.793.1	✓	2	7.4	even	3
1386.2.k.h.991.1	yes	2	7.2	even	3
1386.2.k.l.793.1	yes	2	21.11	odd	6
1386.2.k.l.991.1	yes	2	21.2	odd	6
9702.2.a.f.1.1		1	21.20	even	2
9702.2.a.s.1.1		1	3.2	odd	2
9702.2.a.bi.1.1		1	1.1	even	1	trivial
9702.2.a.ca.1.1		1	7.6	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:	\( N \)	\(=\)	\( 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9702.a (trivial)

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