LMFDB - Embedded newform 9702.2.a.cz.1.2

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:	$2$
Coefficient field:	$\Q(\sqrt{7}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 7 $ x^2 - 7
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
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			1.2
Root			$2.64575$ of defining polynomial
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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +1.64575 q^{5} +1.00000 q^{8} +O(q^{10})$	$q+1.00000 q^{2} +1.00000 q^{4} +1.64575 q^{5} +1.00000 q^{8} +1.64575 q^{10} -1.00000 q^{11} +5.00000 q^{13} +1.00000 q^{16} -6.00000 q^{17} -5.64575 q^{19} +1.64575 q^{20} -1.00000 q^{22} -1.64575 q^{23} -2.29150 q^{25} +5.00000 q^{26} -6.29150 q^{29} -4.00000 q^{31} +1.00000 q^{32} -6.00000 q^{34} +3.64575 q^{37} -5.64575 q^{38} +1.64575 q^{40} -10.9373 q^{41} -4.00000 q^{43} -1.00000 q^{44} -1.64575 q^{46} -2.70850 q^{47} -2.29150 q^{50} +5.00000 q^{52} -1.64575 q^{53} -1.64575 q^{55} -6.29150 q^{58} -4.64575 q^{59} +14.2915 q^{61} -4.00000 q^{62} +1.00000 q^{64} +8.22876 q^{65} -11.9373 q^{67} -6.00000 q^{68} -4.35425 q^{71} +0.354249 q^{73} +3.64575 q^{74} -5.64575 q^{76} -2.64575 q^{79} +1.64575 q^{80} -10.9373 q^{82} -2.70850 q^{83} -9.87451 q^{85} -4.00000 q^{86} -1.00000 q^{88} -6.58301 q^{89} -1.64575 q^{92} -2.70850 q^{94} -9.29150 q^{95} -16.2915 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} - 2 q^{5} + 2 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^4 - 2 * q^5 + 2 * q^8	$ 2 q + 2 q^{2} + 2 q^{4} - 2 q^{5} + 2 q^{8} - 2 q^{10} - 2 q^{11} + 10 q^{13} + 2 q^{16} - 12 q^{17} - 6 q^{19} - 2 q^{20} - 2 q^{22} + 2 q^{23} + 6 q^{25} + 10 q^{26} - 2 q^{29} - 8 q^{31} + 2 q^{32} - 12 q^{34} + 2 q^{37} - 6 q^{38} - 2 q^{40} - 6 q^{41} - 8 q^{43} - 2 q^{44} + 2 q^{46} - 16 q^{47} + 6 q^{50} + 10 q^{52} + 2 q^{53} + 2 q^{55} - 2 q^{58} - 4 q^{59} + 18 q^{61} - 8 q^{62} + 2 q^{64} - 10 q^{65} - 8 q^{67} - 12 q^{68} - 14 q^{71} + 6 q^{73} + 2 q^{74} - 6 q^{76} - 2 q^{80} - 6 q^{82} - 16 q^{83} + 12 q^{85} - 8 q^{86} - 2 q^{88} + 8 q^{89} + 2 q^{92} - 16 q^{94} - 8 q^{95} - 22 q^{97}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 - 2 * q^5 + 2 * q^8 - 2 * q^10 - 2 * q^11 + 10 * q^13 + 2 * q^16 - 12 * q^17 - 6 * q^19 - 2 * q^20 - 2 * q^22 + 2 * q^23 + 6 * q^25 + 10 * q^26 - 2 * q^29 - 8 * q^31 + 2 * q^32 - 12 * q^34 + 2 * q^37 - 6 * q^38 - 2 * q^40 - 6 * q^41 - 8 * q^43 - 2 * q^44 + 2 * q^46 - 16 * q^47 + 6 * q^50 + 10 * q^52 + 2 * q^53 + 2 * q^55 - 2 * q^58 - 4 * q^59 + 18 * q^61 - 8 * q^62 + 2 * q^64 - 10 * q^65 - 8 * q^67 - 12 * q^68 - 14 * q^71 + 6 * q^73 + 2 * q^74 - 6 * q^76 - 2 * q^80 - 6 * q^82 - 16 * q^83 + 12 * q^85 - 8 * q^86 - 2 * q^88 + 8 * q^89 + 2 * q^92 - 16 * q^94 - 8 * q^95 - 22 * q^97

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
$5$	1.64575	0.736002	0.368001	−	0.929825i	$-0.380042\pi$
$5$	1.64575	0.736002	0.368001	+	0.929825i	$0.380042\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	0	0
$10$	1.64575	0.520432
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0	0
$13$	5.00000	1.38675	0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000	1.38675	0.693375	+	0.720577i	$0.256123\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	0	0
$19$	−5.64575	−1.29522	−0.647612	−	0.761970i	$-0.724232\pi$
$19$	−5.64575	−1.29522	−0.647612	+	0.761970i	$0.724232\pi$
$20$	1.64575	0.368001
$21$	0	0
$22$	−1.00000	−0.213201
$23$	−1.64575	−0.343163	−0.171581	−	0.985170i	$-0.554888\pi$
$23$	−1.64575	−0.343163	−0.171581	+	0.985170i	$0.554888\pi$
$24$	0	0
$25$	−2.29150	−0.458301
$26$	5.00000	0.980581
$27$	0	0
$28$	0	0
$29$	−6.29150	−1.16830	−0.584151	−	0.811645i	$-0.698573\pi$
$29$	−6.29150	−1.16830	−0.584151	+	0.811645i	$0.698573\pi$
$30$	0	0
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−6.00000	−1.02899
$35$	0	0
$36$	0	0
$37$	3.64575	0.599358	0.299679	−	0.954040i	$-0.403120\pi$
$37$	3.64575	0.599358	0.299679	+	0.954040i	$0.403120\pi$
$38$	−5.64575	−0.915862
$39$	0	0
$40$	1.64575	0.260216
$41$	−10.9373	−1.70811	−0.854056	−	0.520181i	$-0.825864\pi$
$41$	−10.9373	−1.70811	−0.854056	+	0.520181i	$0.825864\pi$
$42$	0	0
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	−1.64575	−0.242653
$47$	−2.70850	−0.395075	−0.197537	−	0.980295i	$-0.563294\pi$
$47$	−2.70850	−0.395075	−0.197537	+	0.980295i	$0.563294\pi$
$48$	0	0
$49$	0	0
$50$	−2.29150	−0.324067
$51$	0	0
$52$	5.00000	0.693375
$53$	−1.64575	−0.226061	−0.113031	−	0.993592i	$-0.536056\pi$
$53$	−1.64575	−0.226061	−0.113031	+	0.993592i	$0.536056\pi$
$54$	0	0
$55$	−1.64575	−0.221913
$56$	0	0
$57$	0	0
$58$	−6.29150	−0.826115
$59$	−4.64575	−0.604825	−0.302413	−	0.953177i	$-0.597792\pi$
$59$	−4.64575	−0.604825	−0.302413	+	0.953177i	$0.597792\pi$
$60$	0	0
$61$	14.2915	1.82984	0.914920	−	0.403636i	$-0.132254\pi$
$61$	14.2915	1.82984	0.914920	+	0.403636i	$0.132254\pi$
$62$	−4.00000	−0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	8.22876	1.02065
$66$	0	0
$67$	−11.9373	−1.45837	−0.729184	−	0.684318i	$-0.760100\pi$
$67$	−11.9373	−1.45837	−0.729184	+	0.684318i	$0.760100\pi$
$68$	−6.00000	−0.727607
$69$	0	0
$70$	0	0
$71$	−4.35425	−0.516754	−0.258377	−	0.966044i	$-0.583188\pi$
$71$	−4.35425	−0.516754	−0.258377	+	0.966044i	$0.583188\pi$
$72$	0	0
$73$	0.354249	0.0414617	0.0207308	−	0.999785i	$-0.493401\pi$
$73$	0.354249	0.0414617	0.0207308	+	0.999785i	$0.493401\pi$
$74$	3.64575	0.423810
$75$	0	0
$76$	−5.64575	−0.647612
$77$	0	0
$78$	0	0
$79$	−2.64575	−0.297670	−0.148835	−	0.988862i	$-0.547552\pi$
$79$	−2.64575	−0.297670	−0.148835	+	0.988862i	$0.547552\pi$
$80$	1.64575	0.184001
$81$	0	0
$82$	−10.9373	−1.20782
$83$	−2.70850	−0.297296	−0.148648	−	0.988890i	$-0.547492\pi$
$83$	−2.70850	−0.297296	−0.148648	+	0.988890i	$0.547492\pi$
$84$	0	0
$85$	−9.87451	−1.07104
$86$	−4.00000	−0.431331
$87$	0	0
$88$	−1.00000	−0.106600
$89$	−6.58301	−0.697797	−0.348899	−	0.937160i	$-0.613444\pi$
$89$	−6.58301	−0.697797	−0.348899	+	0.937160i	$0.613444\pi$
$90$	0	0
$91$	0	0
$92$	−1.64575	−0.171581
$93$	0	0
$94$	−2.70850	−0.279360
$95$	−9.29150	−0.953288
$96$	0	0
$97$	−16.2915	−1.65415	−0.827076	−	0.562090i	$-0.809997\pi$
$97$	−16.2915	−1.65415	−0.827076	+	0.562090i	$0.809997\pi$
$98$	0	0
$99$	0	0
$100$	−2.29150	−0.229150
$101$	−3.00000	−0.298511	−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000	−0.298511	−0.149256	+	0.988799i	$0.547688\pi$
$102$	0	0
$103$	−2.93725	−0.289416	−0.144708	−	0.989474i	$-0.546224\pi$
$103$	−2.93725	−0.289416	−0.144708	+	0.989474i	$0.546224\pi$
$104$	5.00000	0.490290
$105$	0	0
$106$	−1.64575	−0.159849
$107$	10.9373	1.05734	0.528672	−	0.848826i	$-0.322690\pi$
$107$	10.9373	1.05734	0.528672	+	0.848826i	$0.322690\pi$
$108$	0	0
$109$	−10.5830	−1.01367	−0.506834	−	0.862044i	$-0.669184\pi$
$109$	−10.5830	−1.01367	−0.506834	+	0.862044i	$0.669184\pi$
$110$	−1.64575	−0.156916
$111$	0	0
$112$	0	0
$113$	18.2915	1.72072	0.860360	−	0.509687i	$-0.170239\pi$
$113$	18.2915	1.72072	0.860360	+	0.509687i	$0.170239\pi$
$114$	0	0
$115$	−2.70850	−0.252569
$116$	−6.29150	−0.584151
$117$	0	0
$118$	−4.64575	−0.427676
$119$	0	0
$120$	0	0
$121$	1.00000	0.0909091
$122$	14.2915	1.29389
$123$	0	0
$124$	−4.00000	−0.359211
$125$	−12.0000	−1.07331
$126$	0	0
$127$	15.9373	1.41420	0.707101	−	0.707112i	$-0.250002\pi$
$127$	15.9373	1.41420	0.707101	+	0.707112i	$0.250002\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	8.22876	0.721710
$131$	−10.3542	−0.904655	−0.452327	−	0.891852i	$-0.649406\pi$
$131$	−10.3542	−0.904655	−0.452327	+	0.891852i	$0.649406\pi$
$132$	0	0
$133$	0	0
$134$	−11.9373	−1.03122
$135$	0	0
$136$	−6.00000	−0.514496
$137$	12.8745	1.09994	0.549972	−	0.835183i	$-0.314638\pi$
$137$	12.8745	1.09994	0.549972	+	0.835183i	$0.314638\pi$
$138$	0	0
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	0	0
$141$	0	0
$142$	−4.35425	−0.365400
$143$	−5.00000	−0.418121
$144$	0	0
$145$	−10.3542	−0.859874
$146$	0.354249	0.0293178
$147$	0	0
$148$	3.64575	0.299679
$149$	15.2915	1.25273	0.626364	−	0.779530i	$-0.284542\pi$
$149$	15.2915	1.25273	0.626364	+	0.779530i	$0.284542\pi$
$150$	0	0
$151$	−8.64575	−0.703581	−0.351791	−	0.936079i	$-0.614427\pi$
$151$	−8.64575	−0.703581	−0.351791	+	0.936079i	$0.614427\pi$
$152$	−5.64575	−0.457931
$153$	0	0
$154$	0	0
$155$	−6.58301	−0.528760
$156$	0	0
$157$	21.1660	1.68923	0.844616	−	0.535373i	$-0.179829\pi$
$157$	21.1660	1.68923	0.844616	+	0.535373i	$0.179829\pi$
$158$	−2.64575	−0.210485
$159$	0	0
$160$	1.64575	0.130108
$161$	0	0
$162$	0	0
$163$	0.645751	0.0505791	0.0252896	−	0.999680i	$-0.491949\pi$
$163$	0.645751	0.0505791	0.0252896	+	0.999680i	$0.491949\pi$
$164$	−10.9373	−0.854056
$165$	0	0
$166$	−2.70850	−0.210220
$167$	11.2288	0.868907	0.434454	−	0.900694i	$-0.356941\pi$
$167$	11.2288	0.868907	0.434454	+	0.900694i	$0.356941\pi$
$168$	0	0
$169$	12.0000	0.923077
$170$	−9.87451	−0.757340
$171$	0	0
$172$	−4.00000	−0.304997
$173$	0.291503	0.0221625	0.0110813	−	0.999939i	$-0.496473\pi$
$173$	0.291503	0.0221625	0.0110813	+	0.999939i	$0.496473\pi$
$174$	0	0
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	0	0
$178$	−6.58301	−0.493417
$179$	19.9373	1.49018	0.745090	−	0.666964i	$-0.232406\pi$
$179$	19.9373	1.49018	0.745090	+	0.666964i	$0.232406\pi$
$180$	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
$184$	−1.64575	−0.121326
$185$	6.00000	0.441129
$186$	0	0
$187$	6.00000	0.438763
$188$	−2.70850	−0.197537
$189$	0	0
$190$	−9.29150	−0.674076
$191$	2.70850	0.195980	0.0979900	−	0.995187i	$-0.468759\pi$
$191$	2.70850	0.195980	0.0979900	+	0.995187i	$0.468759\pi$
$192$	0	0
$193$	25.5203	1.83699	0.918494	−	0.395434i	$-0.129406\pi$
$193$	25.5203	1.83699	0.918494	+	0.395434i	$0.129406\pi$
$194$	−16.2915	−1.16966
$195$	0	0
$196$	0	0
$197$	12.8745	0.917271	0.458635	−	0.888625i	$-0.348338\pi$
$197$	12.8745	0.917271	0.458635	+	0.888625i	$0.348338\pi$
$198$	0	0
$199$	4.22876	0.299769	0.149884	−	0.988704i	$-0.452110\pi$
$199$	4.22876	0.299769	0.149884	+	0.988704i	$0.452110\pi$
$200$	−2.29150	−0.162034
$201$	0	0
$202$	−3.00000	−0.211079
$203$	0	0
$204$	0	0
$205$	−18.0000	−1.25717
$206$	−2.93725	−0.204648
$207$	0	0
$208$	5.00000	0.346688
$209$	5.64575	0.390525
$210$	0	0
$211$	0.937254	0.0645232	0.0322616	−	0.999479i	$-0.489729\pi$
$211$	0.937254	0.0645232	0.0322616	+	0.999479i	$0.489729\pi$
$212$	−1.64575	−0.113031
$213$	0	0
$214$	10.9373	0.747655
$215$	−6.58301	−0.448957
$216$	0	0
$217$	0	0
$218$	−10.5830	−0.716772
$219$	0	0
$220$	−1.64575	−0.110957
$221$	−30.0000	−2.01802
$222$	0	0
$223$	−17.6458	−1.18165	−0.590823	−	0.806801i	$-0.701197\pi$
$223$	−17.6458	−1.18165	−0.590823	+	0.806801i	$0.701197\pi$
$224$	0	0
$225$	0	0
$226$	18.2915	1.21673
$227$	2.70850	0.179769	0.0898846	−	0.995952i	$-0.471350\pi$
$227$	2.70850	0.179769	0.0898846	+	0.995952i	$0.471350\pi$
$228$	0	0
$229$	−16.0000	−1.05731	−0.528655	−	0.848837i	$-0.677303\pi$
$229$	−16.0000	−1.05731	−0.528655	+	0.848837i	$0.677303\pi$
$230$	−2.70850	−0.178593
$231$	0	0
$232$	−6.29150	−0.413057
$233$	−1.06275	−0.0696228	−0.0348114	−	0.999394i	$-0.511083\pi$
$233$	−1.06275	−0.0696228	−0.0348114	+	0.999394i	$0.511083\pi$
$234$	0	0
$235$	−4.45751	−0.290776
$236$	−4.64575	−0.302413
$237$	0	0
$238$	0	0
$239$	17.2288	1.11444	0.557218	−	0.830366i	$-0.311869\pi$
$239$	17.2288	1.11444	0.557218	+	0.830366i	$0.311869\pi$
$240$	0	0
$241$	−24.8118	−1.59827	−0.799133	−	0.601154i	$-0.794708\pi$
$241$	−24.8118	−1.59827	−0.799133	+	0.601154i	$0.794708\pi$
$242$	1.00000	0.0642824
$243$	0	0
$244$	14.2915	0.914920
$245$	0	0
$246$	0	0
$247$	−28.2288	−1.79615
$248$	−4.00000	−0.254000
$249$	0	0
$250$	−12.0000	−0.758947
$251$	3.29150	0.207758	0.103879	−	0.994590i	$-0.466875\pi$
$251$	3.29150	0.207758	0.103879	+	0.994590i	$0.466875\pi$
$252$	0	0
$253$	1.64575	0.103467
$254$	15.9373	0.999992
$255$	0	0
$256$	1.00000	0.0625000
$257$	21.5830	1.34631	0.673155	−	0.739501i	$-0.264938\pi$
$257$	21.5830	1.34631	0.673155	+	0.739501i	$0.264938\pi$
$258$	0	0
$259$	0	0
$260$	8.22876	0.510326
$261$	0	0
$262$	−10.3542	−0.639688
$263$	−19.9373	−1.22938	−0.614692	−	0.788767i	$-0.710720\pi$
$263$	−19.9373	−1.22938	−0.614692	+	0.788767i	$0.710720\pi$
$264$	0	0
$265$	−2.70850	−0.166382
$266$	0	0
$267$	0	0
$268$	−11.9373	−0.729184
$269$	−5.41699	−0.330280	−0.165140	−	0.986270i	$-0.552808\pi$
$269$	−5.41699	−0.330280	−0.165140	+	0.986270i	$0.552808\pi$
$270$	0	0
$271$	−2.06275	−0.125303	−0.0626514	−	0.998035i	$-0.519956\pi$
$271$	−2.06275	−0.125303	−0.0626514	+	0.998035i	$0.519956\pi$
$272$	−6.00000	−0.363803
$273$	0	0
$274$	12.8745	0.777777
$275$	2.29150	0.138183
$276$	0	0
$277$	−22.2915	−1.33937	−0.669683	−	0.742647i	$-0.733570\pi$
$277$	−22.2915	−1.33937	−0.669683	+	0.742647i	$0.733570\pi$
$278$	−4.00000	−0.239904
$279$	0	0
$280$	0	0
$281$	22.9373	1.36832	0.684161	−	0.729331i	$-0.260169\pi$
$281$	22.9373	1.36832	0.684161	+	0.729331i	$0.260169\pi$
$282$	0	0
$283$	−2.35425	−0.139946	−0.0699728	−	0.997549i	$-0.522291\pi$
$283$	−2.35425	−0.139946	−0.0699728	+	0.997549i	$0.522291\pi$
$284$	−4.35425	−0.258377
$285$	0	0
$286$	−5.00000	−0.295656
$287$	0	0
$288$	0	0
$289$	19.0000	1.11765
$290$	−10.3542	−0.608022
$291$	0	0
$292$	0.354249	0.0207308
$293$	−12.0000	−0.701047	−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000	−0.701047	−0.350524	+	0.936554i	$0.613996\pi$
$294$	0	0
$295$	−7.64575	−0.445153
$296$	3.64575	0.211905
$297$	0	0
$298$	15.2915	0.885813
$299$	−8.22876	−0.475881
$300$	0	0
$301$	0	0
$302$	−8.64575	−0.497507
$303$	0	0
$304$	−5.64575	−0.323806
$305$	23.5203	1.34677
$306$	0	0
$307$	22.2288	1.26866	0.634331	−	0.773062i	$-0.281276\pi$
$307$	22.2288	1.26866	0.634331	+	0.773062i	$0.281276\pi$
$308$	0	0
$309$	0	0
$310$	−6.58301	−0.373890
$311$	−1.06275	−0.0602628	−0.0301314	−	0.999546i	$-0.509593\pi$
$311$	−1.06275	−0.0602628	−0.0301314	+	0.999546i	$0.509593\pi$
$312$	0	0
$313$	23.5830	1.33299	0.666495	−	0.745509i	$-0.267794\pi$
$313$	23.5830	1.33299	0.666495	+	0.745509i	$0.267794\pi$
$314$	21.1660	1.19447
$315$	0	0
$316$	−2.64575	−0.148835
$317$	−12.0000	−0.673987	−0.336994	−	0.941507i	$-0.609410\pi$
$317$	−12.0000	−0.673987	−0.336994	+	0.941507i	$0.609410\pi$
$318$	0	0
$319$	6.29150	0.352257
$320$	1.64575	0.0920003
$321$	0	0
$322$	0	0
$323$	33.8745	1.88483
$324$	0	0
$325$	−11.4575	−0.635548
$326$	0.645751	0.0357649
$327$	0	0
$328$	−10.9373	−0.603909
$329$	0	0
$330$	0	0
$331$	−20.6458	−1.13479	−0.567397	−	0.823445i	$-0.692049\pi$
$331$	−20.6458	−1.13479	−0.567397	+	0.823445i	$0.692049\pi$
$332$	−2.70850	−0.148648
$333$	0	0
$334$	11.2288	0.614410
$335$	−19.6458	−1.07336
$336$	0	0
$337$	9.06275	0.493679	0.246840	−	0.969056i	$-0.420608\pi$
$337$	9.06275	0.493679	0.246840	+	0.969056i	$0.420608\pi$
$338$	12.0000	0.652714
$339$	0	0
$340$	−9.87451	−0.535520
$341$	4.00000	0.216612
$342$	0	0
$343$	0	0
$344$	−4.00000	−0.215666
$345$	0	0
$346$	0.291503	0.0156713
$347$	20.8118	1.11723	0.558617	−	0.829426i	$-0.311332\pi$
$347$	20.8118	1.11723	0.558617	+	0.829426i	$0.311332\pi$
$348$	0	0
$349$	−1.87451	−0.100340	−0.0501701	−	0.998741i	$-0.515976\pi$
$349$	−1.87451	−0.100340	−0.0501701	+	0.998741i	$0.515976\pi$
$350$	0	0
$351$	0	0
$352$	−1.00000	−0.0533002
$353$	−7.16601	−0.381408	−0.190704	−	0.981648i	$-0.561077\pi$
$353$	−7.16601	−0.381408	−0.190704	+	0.981648i	$0.561077\pi$
$354$	0	0
$355$	−7.16601	−0.380332
$356$	−6.58301	−0.348899
$357$	0	0
$358$	19.9373	1.05372
$359$	25.9373	1.36892	0.684458	−	0.729052i	$-0.260039\pi$
$359$	25.9373	1.36892	0.684458	+	0.729052i	$0.260039\pi$
$360$	0	0
$361$	12.8745	0.677606
$362$	−10.0000	−0.525588
$363$	0	0
$364$	0	0
$365$	0.583005	0.0305159
$366$	0	0
$367$	−36.2288	−1.89113	−0.945563	−	0.325440i	$-0.894488\pi$
$367$	−36.2288	−1.89113	−0.945563	+	0.325440i	$0.894488\pi$
$368$	−1.64575	−0.0857907
$369$	0	0
$370$	6.00000	0.311925
$371$	0	0
$372$	0	0
$373$	20.8745	1.08084	0.540421	−	0.841395i	$-0.318265\pi$
$373$	20.8745	1.08084	0.540421	+	0.841395i	$0.318265\pi$
$374$	6.00000	0.310253
$375$	0	0
$376$	−2.70850	−0.139680
$377$	−31.4575	−1.62014
$378$	0	0
$379$	6.06275	0.311422	0.155711	−	0.987803i	$-0.450233\pi$
$379$	6.06275	0.311422	0.155711	+	0.987803i	$0.450233\pi$
$380$	−9.29150	−0.476644
$381$	0	0
$382$	2.70850	0.138579
$383$	−24.1033	−1.23162	−0.615810	−	0.787895i	$-0.711171\pi$
$383$	−24.1033	−1.23162	−0.615810	+	0.787895i	$0.711171\pi$
$384$	0	0
$385$	0	0
$386$	25.5203	1.29895
$387$	0	0
$388$	−16.2915	−0.827076
$389$	−26.8118	−1.35941	−0.679705	−	0.733485i	$-0.737892\pi$
$389$	−26.8118	−1.35941	−0.679705	+	0.733485i	$0.737892\pi$
$390$	0	0
$391$	9.87451	0.499375
$392$	0	0
$393$	0	0
$394$	12.8745	0.648608
$395$	−4.35425	−0.219086
$396$	0	0
$397$	−11.1660	−0.560406	−0.280203	−	0.959941i	$-0.590402\pi$
$397$	−11.1660	−0.560406	−0.280203	+	0.959941i	$0.590402\pi$
$398$	4.22876	0.211968
$399$	0	0
$400$	−2.29150	−0.114575
$401$	−21.5830	−1.07780	−0.538902	−	0.842369i	$-0.681161\pi$
$401$	−21.5830	−1.07780	−0.538902	+	0.842369i	$0.681161\pi$
$402$	0	0
$403$	−20.0000	−0.996271
$404$	−3.00000	−0.149256
$405$	0	0
$406$	0	0
$407$	−3.64575	−0.180713
$408$	0	0
$409$	3.06275	0.151443	0.0757215	−	0.997129i	$-0.475874\pi$
$409$	3.06275	0.151443	0.0757215	+	0.997129i	$0.475874\pi$
$410$	−18.0000	−0.888957
$411$	0	0
$412$	−2.93725	−0.144708
$413$	0	0
$414$	0	0
$415$	−4.45751	−0.218811
$416$	5.00000	0.245145
$417$	0	0
$418$	5.64575	0.276143
$419$	9.87451	0.482401	0.241201	−	0.970475i	$-0.422459\pi$
$419$	9.87451	0.482401	0.241201	+	0.970475i	$0.422459\pi$
$420$	0	0
$421$	9.16601	0.446724	0.223362	−	0.974736i	$-0.428297\pi$
$421$	9.16601	0.446724	0.223362	+	0.974736i	$0.428297\pi$
$422$	0.937254	0.0456248
$423$	0	0
$424$	−1.64575	−0.0799247
$425$	13.7490	0.666925
$426$	0	0
$427$	0	0
$428$	10.9373	0.528672
$429$	0	0
$430$	−6.58301	−0.317461
$431$	−29.2288	−1.40790	−0.703950	−	0.710250i	$-0.748582\pi$
$431$	−29.2288	−1.40790	−0.703950	+	0.710250i	$0.748582\pi$
$432$	0	0
$433$	−16.0000	−0.768911	−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000	−0.768911	−0.384455	+	0.923144i	$0.625611\pi$
$434$	0	0
$435$	0	0
$436$	−10.5830	−0.506834
$437$	9.29150	0.444473
$438$	0	0
$439$	3.93725	0.187915	0.0939574	−	0.995576i	$-0.470048\pi$
$439$	3.93725	0.187915	0.0939574	+	0.995576i	$0.470048\pi$
$440$	−1.64575	−0.0784581
$441$	0	0
$442$	−30.0000	−1.42695
$443$	−34.4575	−1.63713	−0.818563	−	0.574417i	$-0.805229\pi$
$443$	−34.4575	−1.63713	−0.818563	+	0.574417i	$0.805229\pi$
$444$	0	0
$445$	−10.8340	−0.513580
$446$	−17.6458	−0.835551
$447$	0	0
$448$	0	0
$449$	21.8745	1.03232	0.516161	−	0.856492i	$-0.327361\pi$
$449$	21.8745	1.03232	0.516161	+	0.856492i	$0.327361\pi$
$450$	0	0
$451$	10.9373	0.515015
$452$	18.2915	0.860360
$453$	0	0
$454$	2.70850	0.127116
$455$	0	0
$456$	0	0
$457$	3.16601	0.148100	0.0740499	−	0.997255i	$-0.476408\pi$
$457$	3.16601	0.148100	0.0740499	+	0.997255i	$0.476408\pi$
$458$	−16.0000	−0.747631
$459$	0	0
$460$	−2.70850	−0.126284
$461$	−10.1660	−0.473478	−0.236739	−	0.971573i	$-0.576079\pi$
$461$	−10.1660	−0.473478	−0.236739	+	0.971573i	$0.576079\pi$
$462$	0	0
$463$	30.4575	1.41548	0.707740	−	0.706473i	$-0.249715\pi$
$463$	30.4575	1.41548	0.707740	+	0.706473i	$0.249715\pi$
$464$	−6.29150	−0.292076
$465$	0	0
$466$	−1.06275	−0.0492308
$467$	−21.2915	−0.985253	−0.492627	−	0.870241i	$-0.663963\pi$
$467$	−21.2915	−0.985253	−0.492627	+	0.870241i	$0.663963\pi$
$468$	0	0
$469$	0	0
$470$	−4.45751	−0.205610
$471$	0	0
$472$	−4.64575	−0.213838
$473$	4.00000	0.183920
$474$	0	0
$475$	12.9373	0.593602
$476$	0	0
$477$	0	0
$478$	17.2288	0.788025
$479$	10.0627	0.459779	0.229889	−	0.973217i	$-0.426164\pi$
$479$	10.0627	0.459779	0.229889	+	0.973217i	$0.426164\pi$
$480$	0	0
$481$	18.2288	0.831160
$482$	−24.8118	−1.13014
$483$	0	0
$484$	1.00000	0.0454545
$485$	−26.8118	−1.21746
$486$	0	0
$487$	−9.41699	−0.426725	−0.213362	−	0.976973i	$-0.568441\pi$
$487$	−9.41699	−0.426725	−0.213362	+	0.976973i	$0.568441\pi$
$488$	14.2915	0.646946
$489$	0	0
$490$	0	0
$491$	−21.2915	−0.960872	−0.480436	−	0.877030i	$-0.659522\pi$
$491$	−21.2915	−0.960872	−0.480436	+	0.877030i	$0.659522\pi$
$492$	0	0
$493$	37.7490	1.70013
$494$	−28.2288	−1.27007
$495$	0	0
$496$	−4.00000	−0.179605
$497$	0	0
$498$	0	0
$499$	−13.8745	−0.621108	−0.310554	−	0.950556i	$-0.600515\pi$
$499$	−13.8745	−0.621108	−0.310554	+	0.950556i	$0.600515\pi$
$500$	−12.0000	−0.536656
$501$	0	0
$502$	3.29150	0.146907
$503$	4.06275	0.181149	0.0905744	−	0.995890i	$-0.471130\pi$
$503$	4.06275	0.181149	0.0905744	+	0.995890i	$0.471130\pi$
$504$	0	0
$505$	−4.93725	−0.219705
$506$	1.64575	0.0731626
$507$	0	0
$508$	15.9373	0.707101
$509$	0.583005	0.0258413	0.0129206	−	0.999917i	$-0.495887\pi$
$509$	0.583005	0.0258413	0.0129206	+	0.999917i	$0.495887\pi$
$510$	0	0
$511$	0	0
$512$	1.00000	0.0441942
$513$	0	0
$514$	21.5830	0.951986
$515$	−4.83399	−0.213011
$516$	0	0
$517$	2.70850	0.119120
$518$	0	0
$519$	0	0
$520$	8.22876	0.360855
$521$	33.8745	1.48407	0.742035	−	0.670362i	$-0.233861\pi$
$521$	33.8745	1.48407	0.742035	+	0.670362i	$0.233861\pi$
$522$	0	0
$523$	−21.5203	−0.941015	−0.470508	−	0.882396i	$-0.655929\pi$
$523$	−21.5203	−0.941015	−0.470508	+	0.882396i	$0.655929\pi$
$524$	−10.3542	−0.452327
$525$	0	0
$526$	−19.9373	−0.869306
$527$	24.0000	1.04546
$528$	0	0
$529$	−20.2915	−0.882239
$530$	−2.70850	−0.117650
$531$	0	0
$532$	0	0
$533$	−54.6863	−2.36873
$534$	0	0
$535$	18.0000	0.778208
$536$	−11.9373	−0.515611
$537$	0	0
$538$	−5.41699	−0.233543
$539$	0	0
$540$	0	0
$541$	2.29150	0.0985194	0.0492597	−	0.998786i	$-0.484314\pi$
$541$	2.29150	0.0985194	0.0492597	+	0.998786i	$0.484314\pi$
$542$	−2.06275	−0.0886025
$543$	0	0
$544$	−6.00000	−0.257248
$545$	−17.4170	−0.746062
$546$	0	0
$547$	−9.52026	−0.407057	−0.203528	−	0.979069i	$-0.565241\pi$
$547$	−9.52026	−0.407057	−0.203528	+	0.979069i	$0.565241\pi$
$548$	12.8745	0.549972
$549$	0	0
$550$	2.29150	0.0977100
$551$	35.5203	1.51321
$552$	0	0
$553$	0	0
$554$	−22.2915	−0.947075
$555$	0	0
$556$	−4.00000	−0.169638
$557$	31.7490	1.34525	0.672624	−	0.739984i	$-0.265167\pi$
$557$	31.7490	1.34525	0.672624	+	0.739984i	$0.265167\pi$
$558$	0	0
$559$	−20.0000	−0.845910
$560$	0	0
$561$	0	0
$562$	22.9373	0.967550
$563$	−28.9373	−1.21956	−0.609780	−	0.792571i	$-0.708742\pi$
$563$	−28.9373	−1.21956	−0.609780	+	0.792571i	$0.708742\pi$
$564$	0	0
$565$	30.1033	1.26645
$566$	−2.35425	−0.0989565
$567$	0	0
$568$	−4.35425	−0.182700
$569$	−1.16601	−0.0488817	−0.0244409	−	0.999701i	$-0.507781\pi$
$569$	−1.16601	−0.0488817	−0.0244409	+	0.999701i	$0.507781\pi$
$570$	0	0
$571$	−29.0627	−1.21624	−0.608119	−	0.793846i	$-0.708076\pi$
$571$	−29.0627	−1.21624	−0.608119	+	0.793846i	$0.708076\pi$
$572$	−5.00000	−0.209061
$573$	0	0
$574$	0	0
$575$	3.77124	0.157272
$576$	0	0
$577$	27.4575	1.14307	0.571536	−	0.820577i	$-0.306348\pi$
$577$	27.4575	1.14307	0.571536	+	0.820577i	$0.306348\pi$
$578$	19.0000	0.790296
$579$	0	0
$580$	−10.3542	−0.429937
$581$	0	0
$582$	0	0
$583$	1.64575	0.0681601
$584$	0.354249	0.0146589
$585$	0	0
$586$	−12.0000	−0.495715
$587$	−7.93725	−0.327606	−0.163803	−	0.986493i	$-0.552376\pi$
$587$	−7.93725	−0.327606	−0.163803	+	0.986493i	$0.552376\pi$
$588$	0	0
$589$	22.5830	0.930517
$590$	−7.64575	−0.314771
$591$	0	0
$592$	3.64575	0.149839
$593$	−7.06275	−0.290032	−0.145016	−	0.989429i	$-0.546323\pi$
$593$	−7.06275	−0.290032	−0.145016	+	0.989429i	$0.546323\pi$
$594$	0	0
$595$	0	0
$596$	15.2915	0.626364
$597$	0	0
$598$	−8.22876	−0.336499
$599$	−43.7490	−1.78754	−0.893768	−	0.448529i	$-0.851948\pi$
$599$	−43.7490	−1.78754	−0.893768	+	0.448529i	$0.851948\pi$
$600$	0	0
$601$	−3.41699	−0.139382	−0.0696911	−	0.997569i	$-0.522201\pi$
$601$	−3.41699	−0.139382	−0.0696911	+	0.997569i	$0.522201\pi$
$602$	0	0
$603$	0	0
$604$	−8.64575	−0.351791
$605$	1.64575	0.0669093
$606$	0	0
$607$	10.7085	0.434645	0.217322	−	0.976100i	$-0.430268\pi$
$607$	10.7085	0.434645	0.217322	+	0.976100i	$0.430268\pi$
$608$	−5.64575	−0.228965
$609$	0	0
$610$	23.5203	0.952307
$611$	−13.5425	−0.547870
$612$	0	0
$613$	2.00000	0.0807792	0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000	0.0807792	0.0403896	+	0.999184i	$0.487140\pi$
$614$	22.2288	0.897080
$615$	0	0
$616$	0	0
$617$	5.70850	0.229815	0.114908	−	0.993376i	$-0.463343\pi$
$617$	5.70850	0.229815	0.114908	+	0.993376i	$0.463343\pi$
$618$	0	0
$619$	13.4170	0.539275	0.269637	−	0.962962i	$-0.413096\pi$
$619$	13.4170	0.539275	0.269637	+	0.962962i	$0.413096\pi$
$620$	−6.58301	−0.264380
$621$	0	0
$622$	−1.06275	−0.0426122
$623$	0	0
$624$	0	0
$625$	−8.29150	−0.331660
$626$	23.5830	0.942566
$627$	0	0
$628$	21.1660	0.844616
$629$	−21.8745	−0.872194
$630$	0	0
$631$	−12.8118	−0.510028	−0.255014	−	0.966937i	$-0.582080\pi$
$631$	−12.8118	−0.510028	−0.255014	+	0.966937i	$0.582080\pi$
$632$	−2.64575	−0.105242
$633$	0	0
$634$	−12.0000	−0.476581
$635$	26.2288	1.04086
$636$	0	0
$637$	0	0
$638$	6.29150	0.249083
$639$	0	0
$640$	1.64575	0.0650540
$641$	−12.8745	−0.508512	−0.254256	−	0.967137i	$-0.581831\pi$
$641$	−12.8745	−0.508512	−0.254256	+	0.967137i	$0.581831\pi$
$642$	0	0
$643$	−30.5203	−1.20360	−0.601801	−	0.798646i	$-0.705550\pi$
$643$	−30.5203	−1.20360	−0.601801	+	0.798646i	$0.705550\pi$
$644$	0	0
$645$	0	0
$646$	33.8745	1.33277
$647$	8.81176	0.346426	0.173213	−	0.984884i	$-0.444585\pi$
$647$	8.81176	0.346426	0.173213	+	0.984884i	$0.444585\pi$
$648$	0	0
$649$	4.64575	0.182362
$650$	−11.4575	−0.449401
$651$	0	0
$652$	0.645751	0.0252896
$653$	−7.64575	−0.299201	−0.149601	−	0.988746i	$-0.547799\pi$
$653$	−7.64575	−0.299201	−0.149601	+	0.988746i	$0.547799\pi$
$654$	0	0
$655$	−17.0405	−0.665828
$656$	−10.9373	−0.427028
$657$	0	0
$658$	0	0
$659$	6.58301	0.256437	0.128219	−	0.991746i	$-0.459074\pi$
$659$	6.58301	0.256437	0.128219	+	0.991746i	$0.459074\pi$
$660$	0	0
$661$	7.41699	0.288488	0.144244	−	0.989542i	$-0.453925\pi$
$661$	7.41699	0.288488	0.144244	+	0.989542i	$0.453925\pi$
$662$	−20.6458	−0.802420
$663$	0	0
$664$	−2.70850	−0.105110
$665$	0	0
$666$	0	0
$667$	10.3542	0.400918
$668$	11.2288	0.434454
$669$	0	0
$670$	−19.6458	−0.758982
$671$	−14.2915	−0.551717
$672$	0	0
$673$	0.937254	0.0361285	0.0180642	−	0.999837i	$-0.494250\pi$
$673$	0.937254	0.0361285	0.0180642	+	0.999837i	$0.494250\pi$
$674$	9.06275	0.349084
$675$	0	0
$676$	12.0000	0.461538
$677$	33.8745	1.30190	0.650952	−	0.759119i	$-0.274370\pi$
$677$	33.8745	1.30190	0.650952	+	0.759119i	$0.274370\pi$
$678$	0	0
$679$	0	0
$680$	−9.87451	−0.378670
$681$	0	0
$682$	4.00000	0.153168
$683$	−1.93725	−0.0741270	−0.0370635	−	0.999313i	$-0.511800\pi$
$683$	−1.93725	−0.0741270	−0.0370635	+	0.999313i	$0.511800\pi$
$684$	0	0
$685$	21.1882	0.809561
$686$	0	0
$687$	0	0
$688$	−4.00000	−0.152499
$689$	−8.22876	−0.313491
$690$	0	0
$691$	−45.2288	−1.72058	−0.860291	−	0.509802i	$-0.829718\pi$
$691$	−45.2288	−1.72058	−0.860291	+	0.509802i	$0.829718\pi$
$692$	0.291503	0.0110813
$693$	0	0
$694$	20.8118	0.790004
$695$	−6.58301	−0.249708
$696$	0	0
$697$	65.6235	2.48567
$698$	−1.87451	−0.0709512
$699$	0	0
$700$	0	0
$701$	−24.8745	−0.939497	−0.469749	−	0.882800i	$-0.655655\pi$
$701$	−24.8745	−0.939497	−0.469749	+	0.882800i	$0.655655\pi$
$702$	0	0
$703$	−20.5830	−0.776303
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	−7.16601	−0.269696
$707$	0	0
$708$	0	0
$709$	40.8118	1.53272	0.766359	−	0.642413i	$-0.222066\pi$
$709$	40.8118	1.53272	0.766359	+	0.642413i	$0.222066\pi$
$710$	−7.16601	−0.268936
$711$	0	0
$712$	−6.58301	−0.246709
$713$	6.58301	0.246535
$714$	0	0
$715$	−8.22876	−0.307738
$716$	19.9373	0.745090
$717$	0	0
$718$	25.9373	0.967970
$719$	−27.8745	−1.03954	−0.519772	−	0.854305i	$-0.673983\pi$
$719$	−27.8745	−1.03954	−0.519772	+	0.854305i	$0.673983\pi$
$720$	0	0
$721$	0	0
$722$	12.8745	0.479140
$723$	0	0
$724$	−10.0000	−0.371647
$725$	14.4170	0.535434
$726$	0	0
$727$	−6.70850	−0.248804	−0.124402	−	0.992232i	$-0.539701\pi$
$727$	−6.70850	−0.248804	−0.124402	+	0.992232i	$0.539701\pi$
$728$	0	0
$729$	0	0
$730$	0.583005	0.0215780
$731$	24.0000	0.887672
$732$	0	0
$733$	−11.4575	−0.423193	−0.211596	−	0.977357i	$-0.567866\pi$
$733$	−11.4575	−0.423193	−0.211596	+	0.977357i	$0.567866\pi$
$734$	−36.2288	−1.33723
$735$	0	0
$736$	−1.64575	−0.0606632
$737$	11.9373	0.439714
$738$	0	0
$739$	23.8745	0.878238	0.439119	−	0.898429i	$-0.355291\pi$
$739$	23.8745	0.878238	0.439119	+	0.898429i	$0.355291\pi$
$740$	6.00000	0.220564
$741$	0	0
$742$	0	0
$743$	45.2915	1.66158	0.830792	−	0.556583i	$-0.187888\pi$
$743$	45.2915	1.66158	0.830792	+	0.556583i	$0.187888\pi$
$744$	0	0
$745$	25.1660	0.922011
$746$	20.8745	0.764270
$747$	0	0
$748$	6.00000	0.219382
$749$	0	0
$750$	0	0
$751$	−16.0000	−0.583848	−0.291924	−	0.956441i	$-0.594295\pi$
$751$	−16.0000	−0.583848	−0.291924	+	0.956441i	$0.594295\pi$
$752$	−2.70850	−0.0987687
$753$	0	0
$754$	−31.4575	−1.14562
$755$	−14.2288	−0.517837
$756$	0	0
$757$	−23.1660	−0.841983	−0.420991	−	0.907065i	$-0.638318\pi$
$757$	−23.1660	−0.841983	−0.420991	+	0.907065i	$0.638318\pi$
$758$	6.06275	0.220209
$759$	0	0
$760$	−9.29150	−0.337038
$761$	6.00000	0.217500	0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000	0.217500	0.108750	+	0.994069i	$0.465315\pi$
$762$	0	0
$763$	0	0
$764$	2.70850	0.0979900
$765$	0	0
$766$	−24.1033	−0.870886
$767$	−23.2288	−0.838742
$768$	0	0
$769$	27.1660	0.979631	0.489816	−	0.871826i	$-0.337064\pi$
$769$	27.1660	0.979631	0.489816	+	0.871826i	$0.337064\pi$
$770$	0	0
$771$	0	0
$772$	25.5203	0.918494
$773$	18.5830	0.668384	0.334192	−	0.942505i	$-0.391537\pi$
$773$	18.5830	0.668384	0.334192	+	0.942505i	$0.391537\pi$
$774$	0	0
$775$	9.16601	0.329253
$776$	−16.2915	−0.584831
$777$	0	0
$778$	−26.8118	−0.961248
$779$	61.7490	2.21239
$780$	0	0
$781$	4.35425	0.155807
$782$	9.87451	0.353112
$783$	0	0
$784$	0	0
$785$	34.8340	1.24328
$786$	0	0
$787$	46.8118	1.66866	0.834330	−	0.551266i	$-0.185855\pi$
$787$	46.8118	1.66866	0.834330	+	0.551266i	$0.185855\pi$
$788$	12.8745	0.458635
$789$	0	0
$790$	−4.35425	−0.154917
$791$	0	0
$792$	0	0
$793$	71.4575	2.53753
$794$	−11.1660	−0.396267
$795$	0	0
$796$	4.22876	0.149884
$797$	−7.16601	−0.253833	−0.126917	−	0.991913i	$-0.540508\pi$
$797$	−7.16601	−0.253833	−0.126917	+	0.991913i	$0.540508\pi$
$798$	0	0
$799$	16.2510	0.574918
$800$	−2.29150	−0.0810169
$801$	0	0
$802$	−21.5830	−0.762122
$803$	−0.354249	−0.0125012
$804$	0	0
$805$	0	0
$806$	−20.0000	−0.704470
$807$	0	0
$808$	−3.00000	−0.105540
$809$	−29.4170	−1.03425	−0.517123	−	0.855911i	$-0.672997\pi$
$809$	−29.4170	−1.03425	−0.517123	+	0.855911i	$0.672997\pi$
$810$	0	0
$811$	−35.7490	−1.25532	−0.627659	−	0.778489i	$-0.715987\pi$
$811$	−35.7490	−1.25532	−0.627659	+	0.778489i	$0.715987\pi$
$812$	0	0
$813$	0	0
$814$	−3.64575	−0.127784
$815$	1.06275	0.0372264
$816$	0	0
$817$	22.5830	0.790079
$818$	3.06275	0.107086
$819$	0	0
$820$	−18.0000	−0.628587
$821$	18.2915	0.638378	0.319189	−	0.947691i	$-0.396590\pi$
$821$	18.2915	0.638378	0.319189	+	0.947691i	$0.396590\pi$
$822$	0	0
$823$	−12.1255	−0.422668	−0.211334	−	0.977414i	$-0.567781\pi$
$823$	−12.1255	−0.422668	−0.211334	+	0.977414i	$0.567781\pi$
$824$	−2.93725	−0.102324
$825$	0	0
$826$	0	0
$827$	−33.3948	−1.16125	−0.580625	−	0.814171i	$-0.697192\pi$
$827$	−33.3948	−1.16125	−0.580625	+	0.814171i	$0.697192\pi$
$828$	0	0
$829$	−25.3948	−0.881997	−0.440998	−	0.897508i	$-0.645376\pi$
$829$	−25.3948	−0.881997	−0.440998	+	0.897508i	$0.645376\pi$
$830$	−4.45751	−0.154723
$831$	0	0
$832$	5.00000	0.173344
$833$	0	0
$834$	0	0
$835$	18.4797	0.639518
$836$	5.64575	0.195262
$837$	0	0
$838$	9.87451	0.341109
$839$	3.87451	0.133763	0.0668814	−	0.997761i	$-0.478695\pi$
$839$	3.87451	0.133763	0.0668814	+	0.997761i	$0.478695\pi$
$840$	0	0
$841$	10.5830	0.364931
$842$	9.16601	0.315882
$843$	0	0
$844$	0.937254	0.0322616
$845$	19.7490	0.679387
$846$	0	0
$847$	0	0
$848$	−1.64575	−0.0565153
$849$	0	0
$850$	13.7490	0.471587
$851$	−6.00000	−0.205677
$852$	0	0
$853$	39.1660	1.34102	0.670509	−	0.741901i	$-0.266076\pi$
$853$	39.1660	1.34102	0.670509	+	0.741901i	$0.266076\pi$
$854$	0	0
$855$	0	0
$856$	10.9373	0.373828
$857$	−36.0000	−1.22974	−0.614868	−	0.788630i	$-0.710791\pi$
$857$	−36.0000	−1.22974	−0.614868	+	0.788630i	$0.710791\pi$
$858$	0	0
$859$	−9.81176	−0.334773	−0.167386	−	0.985891i	$-0.553533\pi$
$859$	−9.81176	−0.334773	−0.167386	+	0.985891i	$0.553533\pi$
$860$	−6.58301	−0.224479
$861$	0	0
$862$	−29.2288	−0.995535
$863$	12.4797	0.424815	0.212408	−	0.977181i	$-0.431870\pi$
$863$	12.4797	0.424815	0.212408	+	0.977181i	$0.431870\pi$
$864$	0	0
$865$	0.479741	0.0163117
$866$	−16.0000	−0.543702
$867$	0	0
$868$	0	0
$869$	2.64575	0.0897510
$870$	0	0
$871$	−59.6863	−2.02239
$872$	−10.5830	−0.358386
$873$	0	0
$874$	9.29150	0.314290
$875$	0	0
$876$	0	0
$877$	−22.8745	−0.772417	−0.386209	−	0.922411i	$-0.626216\pi$
$877$	−22.8745	−0.772417	−0.386209	+	0.922411i	$0.626216\pi$
$878$	3.93725	0.132876
$879$	0	0
$880$	−1.64575	−0.0554783
$881$	24.8745	0.838043	0.419022	−	0.907976i	$-0.362373\pi$
$881$	24.8745	0.838043	0.419022	+	0.907976i	$0.362373\pi$
$882$	0	0
$883$	21.9373	0.738247	0.369124	−	0.929380i	$-0.379658\pi$
$883$	21.9373	0.738247	0.369124	+	0.929380i	$0.379658\pi$
$884$	−30.0000	−1.00901
$885$	0	0
$886$	−34.4575	−1.15762
$887$	−45.1033	−1.51442	−0.757210	−	0.653172i	$-0.773438\pi$
$887$	−45.1033	−1.51442	−0.757210	+	0.653172i	$0.773438\pi$
$888$	0	0
$889$	0	0
$890$	−10.8340	−0.363156
$891$	0	0
$892$	−17.6458	−0.590823
$893$	15.2915	0.511711
$894$	0	0
$895$	32.8118	1.09678
$896$	0	0
$897$	0	0
$898$	21.8745	0.729962
$899$	25.1660	0.839333
$900$	0	0
$901$	9.87451	0.328968
$902$	10.9373	0.364171
$903$	0	0
$904$	18.2915	0.608366
$905$	−16.4575	−0.547066
$906$	0	0
$907$	42.4575	1.40978	0.704889	−	0.709317i	$-0.250997\pi$
$907$	42.4575	1.40978	0.704889	+	0.709317i	$0.250997\pi$
$908$	2.70850	0.0898846
$909$	0	0
$910$	0	0
$911$	−9.29150	−0.307841	−0.153921	−	0.988083i	$-0.549190\pi$
$911$	−9.29150	−0.307841	−0.153921	+	0.988083i	$0.549190\pi$
$912$	0	0
$913$	2.70850	0.0896382
$914$	3.16601	0.104722
$915$	0	0
$916$	−16.0000	−0.528655
$917$	0	0
$918$	0	0
$919$	−24.7085	−0.815058	−0.407529	−	0.913192i	$-0.633609\pi$
$919$	−24.7085	−0.815058	−0.407529	+	0.913192i	$0.633609\pi$
$920$	−2.70850	−0.0892965
$921$	0	0
$922$	−10.1660	−0.334800
$923$	−21.7712	−0.716609
$924$	0	0
$925$	−8.35425	−0.274686
$926$	30.4575	1.00090
$927$	0	0
$928$	−6.29150	−0.206529
$929$	−14.4170	−0.473006	−0.236503	−	0.971631i	$-0.576001\pi$
$929$	−14.4170	−0.473006	−0.236503	+	0.971631i	$0.576001\pi$
$930$	0	0
$931$	0	0
$932$	−1.06275	−0.0348114
$933$	0	0
$934$	−21.2915	−0.696679
$935$	9.87451	0.322931
$936$	0	0
$937$	32.6863	1.06781	0.533907	−	0.845543i	$-0.320723\pi$
$937$	32.6863	1.06781	0.533907	+	0.845543i	$0.320723\pi$
$938$	0	0
$939$	0	0
$940$	−4.45751	−0.145388
$941$	−50.6235	−1.65028	−0.825140	−	0.564929i	$-0.808904\pi$
$941$	−50.6235	−1.65028	−0.825140	+	0.564929i	$0.808904\pi$
$942$	0	0
$943$	18.0000	0.586161
$944$	−4.64575	−0.151206
$945$	0	0
$946$	4.00000	0.130051
$947$	2.12549	0.0690692	0.0345346	−	0.999404i	$-0.489005\pi$
$947$	2.12549	0.0690692	0.0345346	+	0.999404i	$0.489005\pi$
$948$	0	0
$949$	1.77124	0.0574970
$950$	12.9373	0.419740
$951$	0	0
$952$	0	0
$953$	−11.5203	−0.373178	−0.186589	−	0.982438i	$-0.559743\pi$
$953$	−11.5203	−0.373178	−0.186589	+	0.982438i	$0.559743\pi$
$954$	0	0
$955$	4.45751	0.144242
$956$	17.2288	0.557218
$957$	0	0
$958$	10.0627	0.325113
$959$	0	0
$960$	0	0
$961$	−15.0000	−0.483871
$962$	18.2288	0.587719
$963$	0	0
$964$	−24.8118	−0.799133
$965$	42.0000	1.35203
$966$	0	0
$967$	58.3320	1.87583	0.937916	−	0.346863i	$-0.112753\pi$
$967$	58.3320	1.87583	0.937916	+	0.346863i	$0.112753\pi$
$968$	1.00000	0.0321412
$969$	0	0
$970$	−26.8118	−0.860874
$971$	10.0627	0.322929	0.161464	−	0.986879i	$-0.448378\pi$
$971$	10.0627	0.322929	0.161464	+	0.986879i	$0.448378\pi$
$972$	0	0
$973$	0	0
$974$	−9.41699	−0.301740
$975$	0	0
$976$	14.2915	0.457460
$977$	16.4575	0.526522	0.263261	−	0.964725i	$-0.415202\pi$
$977$	16.4575	0.526522	0.263261	+	0.964725i	$0.415202\pi$
$978$	0	0
$979$	6.58301	0.210394
$980$	0	0
$981$	0	0
$982$	−21.2915	−0.679439
$983$	26.7085	0.851869	0.425934	−	0.904754i	$-0.359945\pi$
$983$	26.7085	0.851869	0.425934	+	0.904754i	$0.359945\pi$
$984$	0	0
$985$	21.1882	0.675113
$986$	37.7490	1.20217
$987$	0	0
$988$	−28.2288	−0.898076
$989$	6.58301	0.209327
$990$	0	0
$991$	−22.6863	−0.720653	−0.360327	−	0.932826i	$-0.617335\pi$
$991$	−22.6863	−0.720653	−0.360327	+	0.932826i	$0.617335\pi$
$992$	−4.00000	−0.127000
$993$	0	0
$994$	0	0
$995$	6.95948	0.220630
$996$	0	0
$997$	−21.4170	−0.678283	−0.339142	−	0.940735i	$-0.610137\pi$
$997$	−21.4170	−0.678283	−0.339142	+	0.940735i	$0.610137\pi$
$998$	−13.8745	−0.439190
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9702.2.a.cz.1.2		2
3.2	odd	2		1078.2.a.s.1.2		2
7.2	even	3		1386.2.k.s.991.1		4
7.4	even	3		1386.2.k.s.793.1		4
7.6	odd	2		9702.2.a.dr.1.1		2
12.11	even	2		8624.2.a.ca.1.1		2
21.2	odd	6		154.2.e.f.67.1	yes	4
21.5	even	6		1078.2.e.v.67.2		4
21.11	odd	6		154.2.e.f.23.1	✓	4
21.17	even	6		1078.2.e.v.177.2		4
21.20	even	2		1078.2.a.n.1.1		2
84.11	even	6		1232.2.q.g.177.2		4
84.23	even	6		1232.2.q.g.529.2		4
84.83	odd	2		8624.2.a.bk.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.e.f.23.1	✓	4	21.11	odd	6
154.2.e.f.67.1	yes	4	21.2	odd	6
1078.2.a.n.1.1		2	21.20	even	2
1078.2.a.s.1.2		2	3.2	odd	2
1078.2.e.v.67.2		4	21.5	even	6
1078.2.e.v.177.2		4	21.17	even	6
1232.2.q.g.177.2		4	84.11	even	6
1232.2.q.g.529.2		4	84.23	even	6
1386.2.k.s.793.1		4	7.4	even	3
1386.2.k.s.991.1		4	7.2	even	3
8624.2.a.bk.1.2		2	84.83	odd	2
8624.2.a.ca.1.1		2	12.11	even	2
9702.2.a.cz.1.2		2	1.1	even	1	trivial
9702.2.a.dr.1.1		2	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +1.64575 q^{5} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +1.64575 q^{5} +1.00000 q^{8} +1.64575 q^{10} -1.00000 q^{11} +5.00000 q^{13} +1.00000 q^{16} -6.00000 q^{17} -5.64575 q^{19} +1.64575 q^{20} -1.00000 q^{22} -1.64575 q^{23} -2.29150 q^{25} +5.00000 q^{26} -6.29150 q^{29} -4.00000 q^{31} +1.00000 q^{32} -6.00000 q^{34} +3.64575 q^{37} -5.64575 q^{38} +1.64575 q^{40} -10.9373 q^{41} -4.00000 q^{43} -1.00000 q^{44} -1.64575 q^{46} -2.70850 q^{47} -2.29150 q^{50} +5.00000 q^{52} -1.64575 q^{53} -1.64575 q^{55} -6.29150 q^{58} -4.64575 q^{59} +14.2915 q^{61} -4.00000 q^{62} +1.00000 q^{64} +8.22876 q^{65} -11.9373 q^{67} -6.00000 q^{68} -4.35425 q^{71} +0.354249 q^{73} +3.64575 q^{74} -5.64575 q^{76} -2.64575 q^{79} +1.64575 q^{80} -10.9373 q^{82} -2.70850 q^{83} -9.87451 q^{85} -4.00000 q^{86} -1.00000 q^{88} -6.58301 q^{89} -1.64575 q^{92} -2.70850 q^{94} -9.29150 q^{95} -16.2915 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} - 2 q^{5} + 2 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^4 - 2 * q^5 + 2 * q^8	\( 2 q + 2 q^{2} + 2 q^{4} - 2 q^{5} + 2 q^{8} - 2 q^{10} - 2 q^{11} + 10 q^{13} + 2 q^{16} - 12 q^{17} - 6 q^{19} - 2 q^{20} - 2 q^{22} + 2 q^{23} + 6 q^{25} + 10 q^{26} - 2 q^{29} - 8 q^{31} + 2 q^{32} - 12 q^{34} + 2 q^{37} - 6 q^{38} - 2 q^{40} - 6 q^{41} - 8 q^{43} - 2 q^{44} + 2 q^{46} - 16 q^{47} + 6 q^{50} + 10 q^{52} + 2 q^{53} + 2 q^{55} - 2 q^{58} - 4 q^{59} + 18 q^{61} - 8 q^{62} + 2 q^{64} - 10 q^{65} - 8 q^{67} - 12 q^{68} - 14 q^{71} + 6 q^{73} + 2 q^{74} - 6 q^{76} - 2 q^{80} - 6 q^{82} - 16 q^{83} + 12 q^{85} - 8 q^{86} - 2 q^{88} + 8 q^{89} + 2 q^{92} - 16 q^{94} - 8 q^{95} - 22 q^{97}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 - 2 * q^5 + 2 * q^8 - 2 * q^10 - 2 * q^11 + 10 * q^13 + 2 * q^16 - 12 * q^17 - 6 * q^19 - 2 * q^20 - 2 * q^22 + 2 * q^23 + 6 * q^25 + 10 * q^26 - 2 * q^29 - 8 * q^31 + 2 * q^32 - 12 * q^34 + 2 * q^37 - 6 * q^38 - 2 * q^40 - 6 * q^41 - 8 * q^43 - 2 * q^44 + 2 * q^46 - 16 * q^47 + 6 * q^50 + 10 * q^52 + 2 * q^53 + 2 * q^55 - 2 * q^58 - 4 * q^59 + 18 * q^61 - 8 * q^62 + 2 * q^64 - 10 * q^65 - 8 * q^67 - 12 * q^68 - 14 * q^71 + 6 * q^73 + 2 * q^74 - 6 * q^76 - 2 * q^80 - 6 * q^82 - 16 * q^83 + 12 * q^85 - 8 * q^86 - 2 * q^88 + 8 * q^89 + 2 * q^92 - 16 * q^94 - 8 * q^95 - 22 * q^97

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