LMFDB - Embedded newform 9702.2.a.u.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:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

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

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	$-0.352416\pi$
$5$	2.00000	0.894427	0.447214	+	0.894427i	$0.352416\pi$
$6$	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
$17$	6.00000	1.45521	0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000	1.45521	0.727607	+	0.685994i	$0.240633\pi$
$18$	0	0
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	2.00000	0.447214
$21$	0	0
$22$	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	$0.715123\pi$
$24$	0	0
$25$	−1.00000	−0.200000
$26$	−2.00000	−0.392232
$27$	0	0
$28$	0	0
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	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
$34$	−6.00000	−1.02899
$35$	0	0
$36$	0	0
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	−4.00000	−0.648886
$39$	0	0
$40$	−2.00000	−0.316228
$41$	10.0000	1.56174	0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000	1.56174	0.780869	+	0.624695i	$0.214777\pi$
$42$	0	0
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	6.00000	0.884652
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	0	0
$50$	1.00000	0.141421
$51$	0	0
$52$	2.00000	0.277350
$53$	2.00000	0.274721	0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000	0.274721	0.137361	+	0.990521i	$0.456138\pi$
$54$	0	0
$55$	−2.00000	−0.269680
$56$	0	0
$57$	0	0
$58$	6.00000	0.787839
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	0	0
$61$	14.0000	1.79252	0.896258	−	0.443533i	$-0.146275\pi$
$61$	14.0000	1.79252	0.896258	+	0.443533i	$0.146275\pi$
$62$	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	$0.238112\pi$
$68$	6.00000	0.727607
$69$	0	0
$70$	0	0
$71$	2.00000	0.237356	0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000	0.237356	0.118678	+	0.992933i	$0.462134\pi$
$72$	0	0
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	−2.00000	−0.232495
$75$	0	0
$76$	4.00000	0.458831
$77$	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	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	0	0
$85$	12.0000	1.30158
$86$	6.00000	0.646997
$87$	0	0
$88$	1.00000	0.106600
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	0	0
$91$	0	0
$92$	−6.00000	−0.625543
$93$	0	0
$94$	0	0
$95$	8.00000	0.820783
$96$	0	0
$97$	0	0		−	1.00000i	$-0.5\pi$
$97$	0	0			1.00000i	$0.5\pi$
$98$	0	0
$99$	0	0
$100$	−1.00000	−0.100000
$101$	−12.0000	−1.19404	−0.597022	−	0.802225i	$-0.703650\pi$
$101$	−12.0000	−1.19404	−0.597022	+	0.802225i	$0.703650\pi$
$102$	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
$106$	−2.00000	−0.194257
$107$	−12.0000	−1.16008	−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000	−1.16008	−0.580042	+	0.814587i	$0.696964\pi$
$108$	0	0
$109$	8.00000	0.766261	0.383131	−	0.923694i	$-0.374846\pi$
$109$	8.00000	0.766261	0.383131	+	0.923694i	$0.374846\pi$
$110$	2.00000	0.190693
$111$	0	0
$112$	0	0
$113$	4.00000	0.376288	0.188144	−	0.982141i	$-0.439753\pi$
$113$	4.00000	0.376288	0.188144	+	0.982141i	$0.439753\pi$
$114$	0	0
$115$	−12.0000	−1.11901
$116$	−6.00000	−0.557086
$117$	0	0
$118$	4.00000	0.368230
$119$	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
$127$	−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
$130$	−4.00000	−0.350823
$131$	14.0000	1.22319	0.611593	−	0.791173i	$-0.290529\pi$
$131$	14.0000	1.22319	0.611593	+	0.791173i	$0.290529\pi$
$132$	0	0
$133$	0	0
$134$	−12.0000	−1.03664
$135$	0	0
$136$	−6.00000	−0.514496
$137$	8.00000	0.683486	0.341743	−	0.939793i	$-0.388983\pi$
$137$	8.00000	0.683486	0.341743	+	0.939793i	$0.388983\pi$
$138$	0	0
$139$	−20.0000	−1.69638	−0.848189	−	0.529694i	$-0.822307\pi$
$139$	−20.0000	−1.69638	−0.848189	+	0.529694i	$0.822307\pi$
$140$	0	0
$141$	0	0
$142$	−2.00000	−0.167836
$143$	−2.00000	−0.167248
$144$	0	0
$145$	−12.0000	−0.996546
$146$	−6.00000	−0.496564
$147$	0	0
$148$	2.00000	0.164399
$149$	−10.0000	−0.819232	−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000	−0.819232	−0.409616	+	0.912258i	$0.634337\pi$
$150$	0	0
$151$	20.0000	1.62758	0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000	1.62758	0.813788	+	0.581161i	$0.197401\pi$
$152$	−4.00000	−0.324443
$153$	0	0
$154$	0	0
$155$	−4.00000	−0.321288
$156$	0	0
$157$	22.0000	1.75579	0.877896	−	0.478852i	$-0.158947\pi$
$157$	22.0000	1.75579	0.877896	+	0.478852i	$0.158947\pi$
$158$	0	0
$159$	0	0
$160$	−2.00000	−0.158114
$161$	0	0
$162$	0	0
$163$	24.0000	1.87983	0.939913	−	0.341415i	$-0.110906\pi$
$163$	24.0000	1.87983	0.939913	+	0.341415i	$0.110906\pi$
$164$	10.0000	0.780869
$165$	0	0
$166$	−6.00000	−0.465690
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	−12.0000	−0.920358
$171$	0	0
$172$	−6.00000	−0.457496
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	0	0
$178$	−6.00000	−0.449719
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	18.0000	1.33793	0.668965	−	0.743294i	$-0.266738\pi$
$181$	18.0000	1.33793	0.668965	+	0.743294i	$0.266738\pi$
$182$	0	0
$183$	0	0
$184$	6.00000	0.442326
$185$	4.00000	0.294086
$186$	0	0
$187$	−6.00000	−0.438763
$188$	0	0
$189$	0	0
$190$	−8.00000	−0.580381
$191$	−6.00000	−0.434145	−0.217072	−	0.976156i	$-0.569651\pi$
$191$	−6.00000	−0.434145	−0.217072	+	0.976156i	$0.569651\pi$
$192$	0	0
$193$	22.0000	1.58359	0.791797	−	0.610784i	$-0.209146\pi$
$193$	22.0000	1.58359	0.791797	+	0.610784i	$0.209146\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−6.00000	−0.427482	−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000	−0.427482	−0.213741	+	0.976890i	$0.568565\pi$
$198$	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
$202$	12.0000	0.844317
$203$	0	0
$204$	0	0
$205$	20.0000	1.39686
$206$	6.00000	0.418040
$207$	0	0
$208$	2.00000	0.138675
$209$	−4.00000	−0.276686
$210$	0	0
$211$	−10.0000	−0.688428	−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000	−0.688428	−0.344214	+	0.938891i	$0.611855\pi$
$212$	2.00000	0.137361
$213$	0	0
$214$	12.0000	0.820303
$215$	−12.0000	−0.818393
$216$	0	0
$217$	0	0
$218$	−8.00000	−0.541828
$219$	0	0
$220$	−2.00000	−0.134840
$221$	12.0000	0.807207
$222$	0	0
$223$	2.00000	0.133930	0.0669650	−	0.997755i	$-0.478668\pi$
$223$	2.00000	0.133930	0.0669650	+	0.997755i	$0.478668\pi$
$224$	0	0
$225$	0	0
$226$	−4.00000	−0.266076
$227$	−18.0000	−1.19470	−0.597351	−	0.801980i	$-0.703780\pi$
$227$	−18.0000	−1.19470	−0.597351	+	0.801980i	$0.703780\pi$
$228$	0	0
$229$	18.0000	1.18947	0.594737	−	0.803921i	$-0.297256\pi$
$229$	18.0000	1.18947	0.594737	+	0.803921i	$0.297256\pi$
$230$	12.0000	0.791257
$231$	0	0
$232$	6.00000	0.393919
$233$	−14.0000	−0.917170	−0.458585	−	0.888650i	$-0.651644\pi$
$233$	−14.0000	−0.917170	−0.458585	+	0.888650i	$0.651644\pi$
$234$	0	0
$235$	0	0
$236$	−4.00000	−0.260378
$237$	0	0
$238$	0	0
$239$	−20.0000	−1.29369	−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000	−1.29369	−0.646846	+	0.762620i	$0.723912\pi$
$240$	0	0
$241$	2.00000	0.128831	0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000	0.128831	0.0644157	+	0.997923i	$0.479482\pi$
$242$	−1.00000	−0.0642824
$243$	0	0
$244$	14.0000	0.896258
$245$	0	0
$246$	0	0
$247$	8.00000	0.509028
$248$	2.00000	0.127000
$249$	0	0
$250$	12.0000	0.758947
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	6.00000	0.377217
$254$	8.00000	0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	−22.0000	−1.37232	−0.686161	−	0.727450i	$-0.740706\pi$
$257$	−22.0000	−1.37232	−0.686161	+	0.727450i	$0.740706\pi$
$258$	0	0
$259$	0	0
$260$	4.00000	0.248069
$261$	0	0
$262$	−14.0000	−0.864923
$263$	20.0000	1.23325	0.616626	−	0.787256i	$-0.288499\pi$
$263$	20.0000	1.23325	0.616626	+	0.787256i	$0.288499\pi$
$264$	0	0
$265$	4.00000	0.245718
$266$	0	0
$267$	0	0
$268$	12.0000	0.733017
$269$	30.0000	1.82913	0.914566	−	0.404436i	$-0.132532\pi$
$269$	30.0000	1.82913	0.914566	+	0.404436i	$0.132532\pi$
$270$	0	0
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	6.00000	0.363803
$273$	0	0
$274$	−8.00000	−0.483298
$275$	1.00000	0.0603023
$276$	0	0
$277$	4.00000	0.240337	0.120168	−	0.992754i	$-0.461657\pi$
$277$	4.00000	0.240337	0.120168	+	0.992754i	$0.461657\pi$
$278$	20.0000	1.19952
$279$	0	0
$280$	0	0
$281$	−14.0000	−0.835170	−0.417585	−	0.908638i	$-0.637123\pi$
$281$	−14.0000	−0.835170	−0.417585	+	0.908638i	$0.637123\pi$
$282$	0	0
$283$	28.0000	1.66443	0.832214	−	0.554455i	$-0.187073\pi$
$283$	28.0000	1.66443	0.832214	+	0.554455i	$0.187073\pi$
$284$	2.00000	0.118678
$285$	0	0
$286$	2.00000	0.118262
$287$	0	0
$288$	0	0
$289$	19.0000	1.11765
$290$	12.0000	0.704664
$291$	0	0
$292$	6.00000	0.351123
$293$	−16.0000	−0.934730	−0.467365	−	0.884064i	$-0.654797\pi$
$293$	−16.0000	−0.934730	−0.467365	+	0.884064i	$0.654797\pi$
$294$	0	0
$295$	−8.00000	−0.465778
$296$	−2.00000	−0.116248
$297$	0	0
$298$	10.0000	0.579284
$299$	−12.0000	−0.693978
$300$	0	0
$301$	0	0
$302$	−20.0000	−1.15087
$303$	0	0
$304$	4.00000	0.229416
$305$	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
$311$	8.00000	0.453638	0.226819	−	0.973937i	$-0.427167\pi$
$311$	8.00000	0.453638	0.226819	+	0.973937i	$0.427167\pi$
$312$	0	0
$313$	−28.0000	−1.58265	−0.791327	−	0.611393i	$-0.790609\pi$
$313$	−28.0000	−1.58265	−0.791327	+	0.611393i	$0.790609\pi$
$314$	−22.0000	−1.24153
$315$	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
$319$	6.00000	0.335936
$320$	2.00000	0.111803
$321$	0	0
$322$	0	0
$323$	24.0000	1.33540
$324$	0	0
$325$	−2.00000	−0.110940
$326$	−24.0000	−1.32924
$327$	0	0
$328$	−10.0000	−0.552158
$329$	0	0
$330$	0	0
$331$	12.0000	0.659580	0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000	0.659580	0.329790	+	0.944054i	$0.393022\pi$
$332$	6.00000	0.329293
$333$	0	0
$334$	−12.0000	−0.656611
$335$	24.0000	1.31126
$336$	0	0
$337$	−14.0000	−0.762629	−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000	−0.762629	−0.381314	+	0.924445i	$0.624528\pi$
$338$	9.00000	0.489535
$339$	0	0
$340$	12.0000	0.650791
$341$	2.00000	0.108306
$342$	0	0
$343$	0	0
$344$	6.00000	0.323498
$345$	0	0
$346$	0	0
$347$	4.00000	0.214731	0.107366	−	0.994220i	$-0.465758\pi$
$347$	4.00000	0.214731	0.107366	+	0.994220i	$0.465758\pi$
$348$	0	0
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	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
$355$	4.00000	0.212298
$356$	6.00000	0.317999
$357$	0	0
$358$	0	0
$359$	4.00000	0.211112	0.105556	−	0.994413i	$-0.466338\pi$
$359$	4.00000	0.211112	0.105556	+	0.994413i	$0.466338\pi$
$360$	0	0
$361$	−3.00000	−0.157895
$362$	−18.0000	−0.946059
$363$	0	0
$364$	0	0
$365$	12.0000	0.628109
$366$	0	0
$367$	10.0000	0.521996	0.260998	−	0.965339i	$-0.415948\pi$
$367$	10.0000	0.521996	0.260998	+	0.965339i	$0.415948\pi$
$368$	−6.00000	−0.312772
$369$	0	0
$370$	−4.00000	−0.207950
$371$	0	0
$372$	0	0
$373$	12.0000	0.621336	0.310668	−	0.950518i	$-0.399447\pi$
$373$	12.0000	0.621336	0.310668	+	0.950518i	$0.399447\pi$
$374$	6.00000	0.310253
$375$	0	0
$376$	0	0
$377$	−12.0000	−0.618031
$378$	0	0
$379$	−8.00000	−0.410932	−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000	−0.410932	−0.205466	+	0.978664i	$0.565871\pi$
$380$	8.00000	0.410391
$381$	0	0
$382$	6.00000	0.306987
$383$	24.0000	1.22634	0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000	1.22634	0.613171	+	0.789950i	$0.289894\pi$
$384$	0	0
$385$	0	0
$386$	−22.0000	−1.11977
$387$	0	0
$388$	0	0
$389$	2.00000	0.101404	0.0507020	−	0.998714i	$-0.483854\pi$
$389$	2.00000	0.101404	0.0507020	+	0.998714i	$0.483854\pi$
$390$	0	0
$391$	−36.0000	−1.82060
$392$	0	0
$393$	0	0
$394$	6.00000	0.302276
$395$	0	0
$396$	0	0
$397$	22.0000	1.10415	0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000	1.10415	0.552074	+	0.833795i	$0.313837\pi$
$398$	2.00000	0.100251
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	24.0000	1.19850	0.599251	−	0.800561i	$-0.295465\pi$
$401$	24.0000	1.19850	0.599251	+	0.800561i	$0.295465\pi$
$402$	0	0
$403$	−4.00000	−0.199254
$404$	−12.0000	−0.597022
$405$	0	0
$406$	0	0
$407$	−2.00000	−0.0991363
$408$	0	0
$409$	−26.0000	−1.28562	−0.642809	−	0.766027i	$-0.722231\pi$
$409$	−26.0000	−1.28562	−0.642809	+	0.766027i	$0.722231\pi$
$410$	−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
$418$	4.00000	0.195646
$419$	−36.0000	−1.75872	−0.879358	−	0.476162i	$-0.842028\pi$
$419$	−36.0000	−1.75872	−0.879358	+	0.476162i	$0.842028\pi$
$420$	0	0
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	10.0000	0.486792
$423$	0	0
$424$	−2.00000	−0.0971286
$425$	−6.00000	−0.291043
$426$	0	0
$427$	0	0
$428$	−12.0000	−0.580042
$429$	0	0
$430$	12.0000	0.578691
$431$	−12.0000	−0.578020	−0.289010	−	0.957326i	$-0.593326\pi$
$431$	−12.0000	−0.578020	−0.289010	+	0.957326i	$0.593326\pi$
$432$	0	0
$433$	16.0000	0.768911	0.384455	−	0.923144i	$-0.374389\pi$
$433$	16.0000	0.768911	0.384455	+	0.923144i	$0.374389\pi$
$434$	0	0
$435$	0	0
$436$	8.00000	0.383131
$437$	−24.0000	−1.14808
$438$	0	0
$439$	−4.00000	−0.190910	−0.0954548	−	0.995434i	$-0.530431\pi$
$439$	−4.00000	−0.190910	−0.0954548	+	0.995434i	$0.530431\pi$
$440$	2.00000	0.0953463
$441$	0	0
$442$	−12.0000	−0.570782
$443$	−36.0000	−1.71041	−0.855206	−	0.518289i	$-0.826569\pi$
$443$	−36.0000	−1.71041	−0.855206	+	0.518289i	$0.826569\pi$
$444$	0	0
$445$	12.0000	0.568855
$446$	−2.00000	−0.0947027
$447$	0	0
$448$	0	0
$449$	12.0000	0.566315	0.283158	−	0.959073i	$-0.408618\pi$
$449$	12.0000	0.566315	0.283158	+	0.959073i	$0.408618\pi$
$450$	0	0
$451$	−10.0000	−0.470882
$452$	4.00000	0.188144
$453$	0	0
$454$	18.0000	0.844782
$455$	0	0
$456$	0	0
$457$	18.0000	0.842004	0.421002	−	0.907060i	$-0.361678\pi$
$457$	18.0000	0.842004	0.421002	+	0.907060i	$0.361678\pi$
$458$	−18.0000	−0.841085
$459$	0	0
$460$	−12.0000	−0.559503
$461$	−12.0000	−0.558896	−0.279448	−	0.960161i	$-0.590151\pi$
$461$	−12.0000	−0.558896	−0.279448	+	0.960161i	$0.590151\pi$
$462$	0	0
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	−6.00000	−0.278543
$465$	0	0
$466$	14.0000	0.648537
$467$	−20.0000	−0.925490	−0.462745	−	0.886492i	$-0.653135\pi$
$467$	−20.0000	−0.925490	−0.462745	+	0.886492i	$0.653135\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	4.00000	0.184115
$473$	6.00000	0.275880
$474$	0	0
$475$	−4.00000	−0.183533
$476$	0	0
$477$	0	0
$478$	20.0000	0.914779
$479$	12.0000	0.548294	0.274147	−	0.961688i	$-0.411605\pi$
$479$	12.0000	0.548294	0.274147	+	0.961688i	$0.411605\pi$
$480$	0	0
$481$	4.00000	0.182384
$482$	−2.00000	−0.0910975
$483$	0	0
$484$	1.00000	0.0454545
$485$	0	0
$486$	0	0
$487$	8.00000	0.362515	0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000	0.362515	0.181257	+	0.983436i	$0.441983\pi$
$488$	−14.0000	−0.633750
$489$	0	0
$490$	0	0
$491$	20.0000	0.902587	0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000	0.902587	0.451294	+	0.892375i	$0.350963\pi$
$492$	0	0
$493$	−36.0000	−1.62136
$494$	−8.00000	−0.359937
$495$	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
$502$	0	0
$503$	−28.0000	−1.24846	−0.624229	−	0.781241i	$-0.714587\pi$
$503$	−28.0000	−1.24846	−0.624229	+	0.781241i	$0.714587\pi$
$504$	0	0
$505$	−24.0000	−1.06799
$506$	−6.00000	−0.266733
$507$	0	0
$508$	−8.00000	−0.354943
$509$	6.00000	0.265945	0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$510$	0	0
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	22.0000	0.970378
$515$	−12.0000	−0.528783
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	−4.00000	−0.175412
$521$	−14.0000	−0.613351	−0.306676	−	0.951814i	$-0.599217\pi$
$521$	−14.0000	−0.613351	−0.306676	+	0.951814i	$0.599217\pi$
$522$	0	0
$523$	−4.00000	−0.174908	−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000	−0.174908	−0.0874539	+	0.996169i	$0.527873\pi$
$524$	14.0000	0.611593
$525$	0	0
$526$	−20.0000	−0.872041
$527$	−12.0000	−0.522728
$528$	0	0
$529$	13.0000	0.565217
$530$	−4.00000	−0.173749
$531$	0	0
$532$	0	0
$533$	20.0000	0.866296
$534$	0	0
$535$	−24.0000	−1.03761
$536$	−12.0000	−0.518321
$537$	0	0
$538$	−30.0000	−1.29339
$539$	0	0
$540$	0	0
$541$	40.0000	1.71973	0.859867	−	0.510518i	$-0.170546\pi$
$541$	40.0000	1.71973	0.859867	+	0.510518i	$0.170546\pi$
$542$	−16.0000	−0.687259
$543$	0	0
$544$	−6.00000	−0.257248
$545$	16.0000	0.685365
$546$	0	0
$547$	−38.0000	−1.62476	−0.812381	−	0.583127i	$-0.801829\pi$
$547$	−38.0000	−1.62476	−0.812381	+	0.583127i	$0.801829\pi$
$548$	8.00000	0.341743
$549$	0	0
$550$	−1.00000	−0.0426401
$551$	−24.0000	−1.02243
$552$	0	0
$553$	0	0
$554$	−4.00000	−0.169944
$555$	0	0
$556$	−20.0000	−0.848189
$557$	14.0000	0.593199	0.296600	−	0.955002i	$-0.404147\pi$
$557$	14.0000	0.593199	0.296600	+	0.955002i	$0.404147\pi$
$558$	0	0
$559$	−12.0000	−0.507546
$560$	0	0
$561$	0	0
$562$	14.0000	0.590554
$563$	10.0000	0.421450	0.210725	−	0.977545i	$-0.432418\pi$
$563$	10.0000	0.421450	0.210725	+	0.977545i	$0.432418\pi$
$564$	0	0
$565$	8.00000	0.336563
$566$	−28.0000	−1.17693
$567$	0	0
$568$	−2.00000	−0.0839181
$569$	−34.0000	−1.42535	−0.712677	−	0.701492i	$-0.752517\pi$
$569$	−34.0000	−1.42535	−0.712677	+	0.701492i	$0.752517\pi$
$570$	0	0
$571$	−14.0000	−0.585882	−0.292941	−	0.956131i	$-0.594634\pi$
$571$	−14.0000	−0.585882	−0.292941	+	0.956131i	$0.594634\pi$
$572$	−2.00000	−0.0836242
$573$	0	0
$574$	0	0
$575$	6.00000	0.250217
$576$	0	0
$577$	28.0000	1.16566	0.582828	−	0.812596i	$-0.301946\pi$
$577$	28.0000	1.16566	0.582828	+	0.812596i	$0.301946\pi$
$578$	−19.0000	−0.790296
$579$	0	0
$580$	−12.0000	−0.498273
$581$	0	0
$582$	0	0
$583$	−2.00000	−0.0828315
$584$	−6.00000	−0.248282
$585$	0	0
$586$	16.0000	0.660954
$587$	−12.0000	−0.495293	−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000	−0.495293	−0.247647	+	0.968850i	$0.579657\pi$
$588$	0	0
$589$	−8.00000	−0.329634
$590$	8.00000	0.329355
$591$	0	0
$592$	2.00000	0.0821995
$593$	34.0000	1.39621	0.698106	−	0.715994i	$-0.254026\pi$
$593$	34.0000	1.39621	0.698106	+	0.715994i	$0.254026\pi$
$594$	0	0
$595$	0	0
$596$	−10.0000	−0.409616
$597$	0	0
$598$	12.0000	0.490716
$599$	14.0000	0.572024	0.286012	−	0.958226i	$-0.407670\pi$
$599$	14.0000	0.572024	0.286012	+	0.958226i	$0.407670\pi$
$600$	0	0
$601$	22.0000	0.897399	0.448699	−	0.893683i	$-0.351887\pi$
$601$	22.0000	0.897399	0.448699	+	0.893683i	$0.351887\pi$
$602$	0	0
$603$	0	0
$604$	20.0000	0.813788
$605$	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	$0.692376\pi$
$608$	−4.00000	−0.162221
$609$	0	0
$610$	−28.0000	−1.13369
$611$	0	0
$612$	0	0
$613$	0	0		−	1.00000i	$-0.5\pi$
$613$	0	0			1.00000i	$0.5\pi$
$614$	4.00000	0.161427
$615$	0	0
$616$	0	0
$617$	−36.0000	−1.44931	−0.724653	−	0.689114i	$-0.758000\pi$
$617$	−36.0000	−1.44931	−0.724653	+	0.689114i	$0.758000\pi$
$618$	0	0
$619$	40.0000	1.60774	0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000	1.60774	0.803868	+	0.594808i	$0.202772\pi$
$620$	−4.00000	−0.160644
$621$	0	0
$622$	−8.00000	−0.320771
$623$	0	0
$624$	0	0
$625$	−19.0000	−0.760000
$626$	28.0000	1.11911
$627$	0	0
$628$	22.0000	0.877896
$629$	12.0000	0.478471
$630$	0	0
$631$	32.0000	1.27390	0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000	1.27390	0.636950	+	0.770905i	$0.280196\pi$
$632$	0	0
$633$	0	0
$634$	6.00000	0.238290
$635$	−16.0000	−0.634941
$636$	0	0
$637$	0	0
$638$	−6.00000	−0.237542
$639$	0	0
$640$	−2.00000	−0.0790569
$641$	12.0000	0.473972	0.236986	−	0.971513i	$-0.423841\pi$
$641$	12.0000	0.473972	0.236986	+	0.971513i	$0.423841\pi$
$642$	0	0
$643$	−4.00000	−0.157745	−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000	−0.157745	−0.0788723	+	0.996885i	$0.525132\pi$
$644$	0	0
$645$	0	0
$646$	−24.0000	−0.944267
$647$	8.00000	0.314512	0.157256	−	0.987558i	$-0.449735\pi$
$647$	8.00000	0.314512	0.157256	+	0.987558i	$0.449735\pi$
$648$	0	0
$649$	4.00000	0.157014
$650$	2.00000	0.0784465
$651$	0	0
$652$	24.0000	0.939913
$653$	42.0000	1.64359	0.821794	−	0.569785i	$-0.192974\pi$
$653$	42.0000	1.64359	0.821794	+	0.569785i	$0.192974\pi$
$654$	0	0
$655$	28.0000	1.09405
$656$	10.0000	0.390434
$657$	0	0
$658$	0	0
$659$	12.0000	0.467454	0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000	0.467454	0.233727	+	0.972302i	$0.424908\pi$
$660$	0	0
$661$	−30.0000	−1.16686	−0.583432	−	0.812162i	$-0.698291\pi$
$661$	−30.0000	−1.16686	−0.583432	+	0.812162i	$0.698291\pi$
$662$	−12.0000	−0.466393
$663$	0	0
$664$	−6.00000	−0.232845
$665$	0	0
$666$	0	0
$667$	36.0000	1.39393
$668$	12.0000	0.464294
$669$	0	0
$670$	−24.0000	−0.927201
$671$	−14.0000	−0.540464
$672$	0	0
$673$	−6.00000	−0.231283	−0.115642	−	0.993291i	$-0.536892\pi$
$673$	−6.00000	−0.231283	−0.115642	+	0.993291i	$0.536892\pi$
$674$	14.0000	0.539260
$675$	0	0
$676$	−9.00000	−0.346154
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	0	0
$680$	−12.0000	−0.460179
$681$	0	0
$682$	−2.00000	−0.0765840
$683$	32.0000	1.22445	0.612223	−	0.790685i	$-0.290275\pi$
$683$	32.0000	1.22445	0.612223	+	0.790685i	$0.290275\pi$
$684$	0	0
$685$	16.0000	0.611329
$686$	0	0
$687$	0	0
$688$	−6.00000	−0.228748
$689$	4.00000	0.152388
$690$	0	0
$691$	−4.00000	−0.152167	−0.0760836	−	0.997101i	$-0.524242\pi$
$691$	−4.00000	−0.152167	−0.0760836	+	0.997101i	$0.524242\pi$
$692$	0	0
$693$	0	0
$694$	−4.00000	−0.151838
$695$	−40.0000	−1.51729
$696$	0	0
$697$	60.0000	2.27266
$698$	2.00000	0.0757011
$699$	0	0
$700$	0	0
$701$	−2.00000	−0.0755390	−0.0377695	−	0.999286i	$-0.512025\pi$
$701$	−2.00000	−0.0755390	−0.0377695	+	0.999286i	$0.512025\pi$
$702$	0	0
$703$	8.00000	0.301726
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	−6.00000	−0.225813
$707$	0	0
$708$	0	0
$709$	−26.0000	−0.976450	−0.488225	−	0.872718i	$-0.662356\pi$
$709$	−26.0000	−0.976450	−0.488225	+	0.872718i	$0.662356\pi$
$710$	−4.00000	−0.150117
$711$	0	0
$712$	−6.00000	−0.224860
$713$	12.0000	0.449404
$714$	0	0
$715$	−4.00000	−0.149592
$716$	0	0
$717$	0	0
$718$	−4.00000	−0.149279
$719$	40.0000	1.49175	0.745874	−	0.666087i	$-0.232032\pi$
$719$	40.0000	1.49175	0.745874	+	0.666087i	$0.232032\pi$
$720$	0	0
$721$	0	0
$722$	3.00000	0.111648
$723$	0	0
$724$	18.0000	0.668965
$725$	6.00000	0.222834
$726$	0	0
$727$	42.0000	1.55769	0.778847	−	0.627214i	$-0.215805\pi$
$727$	42.0000	1.55769	0.778847	+	0.627214i	$0.215805\pi$
$728$	0	0
$729$	0	0
$730$	−12.0000	−0.444140
$731$	−36.0000	−1.33151
$732$	0	0
$733$	18.0000	0.664845	0.332423	−	0.943131i	$-0.392134\pi$
$733$	18.0000	0.664845	0.332423	+	0.943131i	$0.392134\pi$
$734$	−10.0000	−0.369107
$735$	0	0
$736$	6.00000	0.221163
$737$	−12.0000	−0.442026
$738$	0	0
$739$	−34.0000	−1.25071	−0.625355	−	0.780340i	$-0.715046\pi$
$739$	−34.0000	−1.25071	−0.625355	+	0.780340i	$0.715046\pi$
$740$	4.00000	0.147043
$741$	0	0
$742$	0	0
$743$	48.0000	1.76095	0.880475	−	0.474093i	$-0.157224\pi$
$743$	48.0000	1.76095	0.880475	+	0.474093i	$0.157224\pi$
$744$	0	0
$745$	−20.0000	−0.732743
$746$	−12.0000	−0.439351
$747$	0	0
$748$	−6.00000	−0.219382
$749$	0	0
$750$	0	0
$751$	24.0000	0.875772	0.437886	−	0.899030i	$-0.355727\pi$
$751$	24.0000	0.875772	0.437886	+	0.899030i	$0.355727\pi$
$752$	0	0
$753$	0	0
$754$	12.0000	0.437014
$755$	40.0000	1.45575
$756$	0	0
$757$	−30.0000	−1.09037	−0.545184	−	0.838316i	$-0.683540\pi$
$757$	−30.0000	−1.09037	−0.545184	+	0.838316i	$0.683540\pi$
$758$	8.00000	0.290573
$759$	0	0
$760$	−8.00000	−0.290191
$761$	10.0000	0.362500	0.181250	−	0.983437i	$-0.441986\pi$
$761$	10.0000	0.362500	0.181250	+	0.983437i	$0.441986\pi$
$762$	0	0
$763$	0	0
$764$	−6.00000	−0.217072
$765$	0	0
$766$	−24.0000	−0.867155
$767$	−8.00000	−0.288863
$768$	0	0
$769$	50.0000	1.80305	0.901523	−	0.432731i	$-0.142450\pi$
$769$	50.0000	1.80305	0.901523	+	0.432731i	$0.142450\pi$
$770$	0	0
$771$	0	0
$772$	22.0000	0.791797
$773$	34.0000	1.22290	0.611448	−	0.791285i	$-0.290588\pi$
$773$	34.0000	1.22290	0.611448	+	0.791285i	$0.290588\pi$
$774$	0	0
$775$	2.00000	0.0718421
$776$	0	0
$777$	0	0
$778$	−2.00000	−0.0717035
$779$	40.0000	1.43315
$780$	0	0
$781$	−2.00000	−0.0715656
$782$	36.0000	1.28736
$783$	0	0
$784$	0	0
$785$	44.0000	1.57043
$786$	0	0
$787$	−52.0000	−1.85360	−0.926800	−	0.375555i	$-0.877452\pi$
$787$	−52.0000	−1.85360	−0.926800	+	0.375555i	$0.877452\pi$
$788$	−6.00000	−0.213741
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	28.0000	0.994309
$794$	−22.0000	−0.780751
$795$	0	0
$796$	−2.00000	−0.0708881
$797$	6.00000	0.212531	0.106265	−	0.994338i	$-0.466111\pi$
$797$	6.00000	0.212531	0.106265	+	0.994338i	$0.466111\pi$
$798$	0	0
$799$	0	0
$800$	1.00000	0.0353553
$801$	0	0
$802$	−24.0000	−0.847469
$803$	−6.00000	−0.211735
$804$	0	0
$805$	0	0
$806$	4.00000	0.140894
$807$	0	0
$808$	12.0000	0.422159
$809$	10.0000	0.351581	0.175791	−	0.984428i	$-0.443752\pi$
$809$	10.0000	0.351581	0.175791	+	0.984428i	$0.443752\pi$
$810$	0	0
$811$	28.0000	0.983213	0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000	0.983213	0.491606	+	0.870817i	$0.336410\pi$
$812$	0	0
$813$	0	0
$814$	2.00000	0.0701000
$815$	48.0000	1.68137
$816$	0	0
$817$	−24.0000	−0.839654
$818$	26.0000	0.909069
$819$	0	0
$820$	20.0000	0.698430
$821$	30.0000	1.04701	0.523504	−	0.852023i	$-0.324625\pi$
$821$	30.0000	1.04701	0.523504	+	0.852023i	$0.324625\pi$
$822$	0	0
$823$	16.0000	0.557725	0.278862	−	0.960331i	$-0.410043\pi$
$823$	16.0000	0.557725	0.278862	+	0.960331i	$0.410043\pi$
$824$	6.00000	0.209020
$825$	0	0
$826$	0	0
$827$	36.0000	1.25184	0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000	1.25184	0.625921	+	0.779886i	$0.284723\pi$
$828$	0	0
$829$	14.0000	0.486240	0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000	0.486240	0.243120	+	0.969996i	$0.421829\pi$
$830$	−12.0000	−0.416526
$831$	0	0
$832$	2.00000	0.0693375
$833$	0	0
$834$	0	0
$835$	24.0000	0.830554
$836$	−4.00000	−0.138343
$837$	0	0
$838$	36.0000	1.24360
$839$	24.0000	0.828572	0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000	0.828572	0.414286	+	0.910147i	$0.364031\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	10.0000	0.344623
$843$	0	0
$844$	−10.0000	−0.344214
$845$	−18.0000	−0.619219
$846$	0	0
$847$	0	0
$848$	2.00000	0.0686803
$849$	0	0
$850$	6.00000	0.205798
$851$	−12.0000	−0.411355
$852$	0	0
$853$	−42.0000	−1.43805	−0.719026	−	0.694983i	$-0.755412\pi$
$853$	−42.0000	−1.43805	−0.719026	+	0.694983i	$0.755412\pi$
$854$	0	0
$855$	0	0
$856$	12.0000	0.410152
$857$	−30.0000	−1.02478	−0.512390	−	0.858753i	$-0.671240\pi$
$857$	−30.0000	−1.02478	−0.512390	+	0.858753i	$0.671240\pi$
$858$	0	0
$859$	−40.0000	−1.36478	−0.682391	−	0.730987i	$-0.739060\pi$
$859$	−40.0000	−1.36478	−0.682391	+	0.730987i	$0.739060\pi$
$860$	−12.0000	−0.409197
$861$	0	0
$862$	12.0000	0.408722
$863$	−2.00000	−0.0680808	−0.0340404	−	0.999420i	$-0.510837\pi$
$863$	−2.00000	−0.0680808	−0.0340404	+	0.999420i	$0.510837\pi$
$864$	0	0
$865$	0	0
$866$	−16.0000	−0.543702
$867$	0	0
$868$	0	0
$869$	0	0
$870$	0	0
$871$	24.0000	0.813209
$872$	−8.00000	−0.270914
$873$	0	0
$874$	24.0000	0.811812
$875$	0	0
$876$	0	0
$877$	28.0000	0.945493	0.472746	−	0.881199i	$-0.343263\pi$
$877$	28.0000	0.945493	0.472746	+	0.881199i	$0.343263\pi$
$878$	4.00000	0.134993
$879$	0	0
$880$	−2.00000	−0.0674200
$881$	30.0000	1.01073	0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000	1.01073	0.505363	+	0.862907i	$0.331359\pi$
$882$	0	0
$883$	−16.0000	−0.538443	−0.269221	−	0.963078i	$-0.586766\pi$
$883$	−16.0000	−0.538443	−0.269221	+	0.963078i	$0.586766\pi$
$884$	12.0000	0.403604
$885$	0	0
$886$	36.0000	1.20944
$887$	−44.0000	−1.47738	−0.738688	−	0.674048i	$-0.764554\pi$
$887$	−44.0000	−1.47738	−0.738688	+	0.674048i	$0.764554\pi$
$888$	0	0
$889$	0	0
$890$	−12.0000	−0.402241
$891$	0	0
$892$	2.00000	0.0669650
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	−12.0000	−0.400445
$899$	12.0000	0.400222
$900$	0	0
$901$	12.0000	0.399778
$902$	10.0000	0.332964
$903$	0	0
$904$	−4.00000	−0.133038
$905$	36.0000	1.19668
$906$	0	0
$907$	16.0000	0.531271	0.265636	−	0.964073i	$-0.414418\pi$
$907$	16.0000	0.531271	0.265636	+	0.964073i	$0.414418\pi$
$908$	−18.0000	−0.597351
$909$	0	0
$910$	0	0
$911$	38.0000	1.25900	0.629498	−	0.777002i	$-0.283261\pi$
$911$	38.0000	1.25900	0.629498	+	0.777002i	$0.283261\pi$
$912$	0	0
$913$	−6.00000	−0.198571
$914$	−18.0000	−0.595387
$915$	0	0
$916$	18.0000	0.594737
$917$	0	0
$918$	0	0
$919$	−20.0000	−0.659739	−0.329870	−	0.944027i	$-0.607005\pi$
$919$	−20.0000	−0.659739	−0.329870	+	0.944027i	$0.607005\pi$
$920$	12.0000	0.395628
$921$	0	0
$922$	12.0000	0.395199
$923$	4.00000	0.131662
$924$	0	0
$925$	−2.00000	−0.0657596
$926$	−16.0000	−0.525793
$927$	0	0
$928$	6.00000	0.196960
$929$	34.0000	1.11550	0.557752	−	0.830008i	$-0.311664\pi$
$929$	34.0000	1.11550	0.557752	+	0.830008i	$0.311664\pi$
$930$	0	0
$931$	0	0
$932$	−14.0000	−0.458585
$933$	0	0
$934$	20.0000	0.654420
$935$	−12.0000	−0.392442
$936$	0	0
$937$	−38.0000	−1.24141	−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000	−1.24141	−0.620703	+	0.784046i	$0.713153\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	0	0		−	1.00000i	$-0.5\pi$
$941$	0	0			1.00000i	$0.5\pi$
$942$	0	0
$943$	−60.0000	−1.95387
$944$	−4.00000	−0.130189
$945$	0	0
$946$	−6.00000	−0.195077
$947$	−24.0000	−0.779895	−0.389948	−	0.920837i	$-0.627507\pi$
$947$	−24.0000	−0.779895	−0.389948	+	0.920837i	$0.627507\pi$
$948$	0	0
$949$	12.0000	0.389536
$950$	4.00000	0.129777
$951$	0	0
$952$	0	0
$953$	26.0000	0.842223	0.421111	−	0.907009i	$-0.361640\pi$
$953$	26.0000	0.842223	0.421111	+	0.907009i	$0.361640\pi$
$954$	0	0
$955$	−12.0000	−0.388311
$956$	−20.0000	−0.646846
$957$	0	0
$958$	−12.0000	−0.387702
$959$	0	0
$960$	0	0
$961$	−27.0000	−0.870968
$962$	−4.00000	−0.128965
$963$	0	0
$964$	2.00000	0.0644157
$965$	44.0000	1.41641
$966$	0	0
$967$	20.0000	0.643157	0.321578	−	0.946883i	$-0.395787\pi$
$967$	20.0000	0.643157	0.321578	+	0.946883i	$0.395787\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	0	0
$971$	24.0000	0.770197	0.385098	−	0.922876i	$-0.374168\pi$
$971$	24.0000	0.770197	0.385098	+	0.922876i	$0.374168\pi$
$972$	0	0
$973$	0	0
$974$	−8.00000	−0.256337
$975$	0	0
$976$	14.0000	0.448129
$977$	56.0000	1.79160	0.895799	−	0.444459i	$-0.146604\pi$
$977$	56.0000	1.79160	0.895799	+	0.444459i	$0.146604\pi$
$978$	0	0
$979$	−6.00000	−0.191761
$980$	0	0
$981$	0	0
$982$	−20.0000	−0.638226
$983$	−32.0000	−1.02064	−0.510321	−	0.859984i	$-0.670473\pi$
$983$	−32.0000	−1.02064	−0.510321	+	0.859984i	$0.670473\pi$
$984$	0	0
$985$	−12.0000	−0.382352
$986$	36.0000	1.14647
$987$	0	0
$988$	8.00000	0.254514
$989$	36.0000	1.14473
$990$	0	0
$991$	−40.0000	−1.27064	−0.635321	−	0.772248i	$-0.719132\pi$
$991$	−40.0000	−1.27064	−0.635321	+	0.772248i	$0.719132\pi$
$992$	2.00000	0.0635001
$993$	0	0
$994$	0	0
$995$	−4.00000	−0.126809
$996$	0	0
$997$	14.0000	0.443384	0.221692	−	0.975117i	$-0.428842\pi$
$997$	14.0000	0.443384	0.221692	+	0.975117i	$0.428842\pi$
$998$	−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.u.1.1	yes	1
3.2	odd	2		9702.2.a.bh.1.1	yes	1
7.6	odd	2		9702.2.a.d.1.1	✓	1
21.20	even	2		9702.2.a.cb.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9702.2.a.d.1.1	✓	1	7.6	odd	2
9702.2.a.u.1.1	yes	1	1.1	even	1	trivial
9702.2.a.bh.1.1	yes	1	3.2	odd	2
9702.2.a.cb.1.1	yes	1	21.20	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:	\( N \)	\(=\)	\( 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9702.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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