LMFDB - Embedded newform 9522.2.a.q.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9522,2,Mod(1,9522)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9522, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("9522.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9522 = 2 \cdot 3^{2} \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9522.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:	$76.0335528047$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 138)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	9522.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +1.23607 q^{5} +4.47214 q^{7} -1.00000 q^{8} +O(q^{10})$	$q-1.00000 q^{2} +1.00000 q^{4} +1.23607 q^{5} +4.47214 q^{7} -1.00000 q^{8} -1.23607 q^{10} -5.23607 q^{11} +4.47214 q^{13} -4.47214 q^{14} +1.00000 q^{16} -4.00000 q^{17} -5.70820 q^{19} +1.23607 q^{20} +5.23607 q^{22} -3.47214 q^{25} -4.47214 q^{26} +4.47214 q^{28} +4.47214 q^{29} -2.47214 q^{31} -1.00000 q^{32} +4.00000 q^{34} +5.52786 q^{35} -11.2361 q^{37} +5.70820 q^{38} -1.23607 q^{40} +2.00000 q^{41} +4.76393 q^{43} -5.23607 q^{44} -4.00000 q^{47} +13.0000 q^{49} +3.47214 q^{50} +4.47214 q^{52} +5.23607 q^{53} -6.47214 q^{55} -4.47214 q^{56} -4.47214 q^{58} +8.94427 q^{59} -0.763932 q^{61} +2.47214 q^{62} +1.00000 q^{64} +5.52786 q^{65} -9.70820 q^{67} -4.00000 q^{68} -5.52786 q^{70} -8.94427 q^{71} -4.47214 q^{73} +11.2361 q^{74} -5.70820 q^{76} -23.4164 q^{77} -4.47214 q^{79} +1.23607 q^{80} -2.00000 q^{82} +13.2361 q^{83} -4.94427 q^{85} -4.76393 q^{86} +5.23607 q^{88} -10.4721 q^{89} +20.0000 q^{91} +4.00000 q^{94} -7.05573 q^{95} -0.472136 q^{97} -13.0000 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 6 q^{11} + 2 q^{16} - 8 q^{17} + 2 q^{19} - 2 q^{20} + 6 q^{22} + 2 q^{25} + 4 q^{31} - 2 q^{32} + 8 q^{34} + 20 q^{35} - 18 q^{37} - 2 q^{38} + 2 q^{40} + 4 q^{41} + 14 q^{43} - 6 q^{44} - 8 q^{47} + 26 q^{49} - 2 q^{50} + 6 q^{53} - 4 q^{55} - 6 q^{61} - 4 q^{62} + 2 q^{64} + 20 q^{65} - 6 q^{67} - 8 q^{68} - 20 q^{70} + 18 q^{74} + 2 q^{76} - 20 q^{77} - 2 q^{80} - 4 q^{82} + 22 q^{83} + 8 q^{85} - 14 q^{86} + 6 q^{88} - 12 q^{89} + 40 q^{91} + 8 q^{94} - 32 q^{95} + 8 q^{97} - 26 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^5 - 2 * q^8 + 2 * q^10 - 6 * q^11 + 2 * q^16 - 8 * q^17 + 2 * q^19 - 2 * q^20 + 6 * q^22 + 2 * q^25 + 4 * q^31 - 2 * q^32 + 8 * q^34 + 20 * q^35 - 18 * q^37 - 2 * q^38 + 2 * q^40 + 4 * q^41 + 14 * q^43 - 6 * q^44 - 8 * q^47 + 26 * q^49 - 2 * q^50 + 6 * q^53 - 4 * q^55 - 6 * q^61 - 4 * q^62 + 2 * q^64 + 20 * q^65 - 6 * q^67 - 8 * q^68 - 20 * q^70 + 18 * q^74 + 2 * q^76 - 20 * q^77 - 2 * q^80 - 4 * q^82 + 22 * q^83 + 8 * q^85 - 14 * q^86 + 6 * q^88 - 12 * q^89 + 40 * q^91 + 8 * q^94 - 32 * q^95 + 8 * q^97 - 26 * q^98

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
$5$	1.23607	0.552786	0.276393	−	0.961045i	$-0.410861\pi$
$5$	1.23607	0.552786	0.276393	+	0.961045i	$0.410861\pi$
$6$	0	0
$7$	4.47214	1.69031	0.845154	−	0.534522i	$-0.179509\pi$
$7$	4.47214	1.69031	0.845154	+	0.534522i	$0.179509\pi$
$8$	−1.00000	−0.353553
$9$	0	0
$10$	−1.23607	−0.390879
$11$	−5.23607	−1.57873	−0.789367	−	0.613922i	$-0.789591\pi$
$11$	−5.23607	−1.57873	−0.789367	+	0.613922i	$0.789591\pi$
$12$	0	0
$13$	4.47214	1.24035	0.620174	−	0.784465i	$-0.287062\pi$
$13$	4.47214	1.24035	0.620174	+	0.784465i	$0.287062\pi$
$14$	−4.47214	−1.19523
$15$	0	0
$16$	1.00000	0.250000
$17$	−4.00000	−0.970143	−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000	−0.970143	−0.485071	+	0.874475i	$0.661206\pi$
$18$	0	0
$19$	−5.70820	−1.30955	−0.654776	−	0.755823i	$-0.727237\pi$
$19$	−5.70820	−1.30955	−0.654776	+	0.755823i	$0.727237\pi$
$20$	1.23607	0.276393
$21$	0	0
$22$	5.23607	1.11633
$23$	0	0
$23$	0	0
$24$	0	0
$25$	−3.47214	−0.694427
$26$	−4.47214	−0.877058
$27$	0	0
$28$	4.47214	0.845154
$29$	4.47214	0.830455	0.415227	−	0.909718i	$-0.363702\pi$
$29$	4.47214	0.830455	0.415227	+	0.909718i	$0.363702\pi$
$30$	0	0
$31$	−2.47214	−0.444009	−0.222004	−	0.975046i	$-0.571260\pi$
$31$	−2.47214	−0.444009	−0.222004	+	0.975046i	$0.571260\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	4.00000	0.685994
$35$	5.52786	0.934380
$36$	0	0
$37$	−11.2361	−1.84720	−0.923599	−	0.383360i	$-0.874767\pi$
$37$	−11.2361	−1.84720	−0.923599	+	0.383360i	$0.874767\pi$
$38$	5.70820	0.925993
$39$	0	0
$40$	−1.23607	−0.195440
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	0	0
$43$	4.76393	0.726493	0.363246	−	0.931693i	$-0.381668\pi$
$43$	4.76393	0.726493	0.363246	+	0.931693i	$0.381668\pi$
$44$	−5.23607	−0.789367
$45$	0	0
$46$	0	0
$47$	−4.00000	−0.583460	−0.291730	−	0.956501i	$-0.594231\pi$
$47$	−4.00000	−0.583460	−0.291730	+	0.956501i	$0.594231\pi$
$48$	0	0
$49$	13.0000	1.85714
$50$	3.47214	0.491034
$51$	0	0
$52$	4.47214	0.620174
$53$	5.23607	0.719229	0.359615	−	0.933101i	$-0.382908\pi$
$53$	5.23607	0.719229	0.359615	+	0.933101i	$0.382908\pi$
$54$	0	0
$55$	−6.47214	−0.872703
$56$	−4.47214	−0.597614
$57$	0	0
$58$	−4.47214	−0.587220
$59$	8.94427	1.16445	0.582223	−	0.813029i	$-0.302183\pi$
$59$	8.94427	1.16445	0.582223	+	0.813029i	$0.302183\pi$
$60$	0	0
$61$	−0.763932	−0.0978115	−0.0489057	−	0.998803i	$-0.515573\pi$
$61$	−0.763932	−0.0978115	−0.0489057	+	0.998803i	$0.515573\pi$
$62$	2.47214	0.313962
$63$	0	0
$64$	1.00000	0.125000
$65$	5.52786	0.685647
$66$	0	0
$67$	−9.70820	−1.18605	−0.593023	−	0.805186i	$-0.702066\pi$
$67$	−9.70820	−1.18605	−0.593023	+	0.805186i	$0.702066\pi$
$68$	−4.00000	−0.485071
$69$	0	0
$70$	−5.52786	−0.660706
$71$	−8.94427	−1.06149	−0.530745	−	0.847532i	$-0.678088\pi$
$71$	−8.94427	−1.06149	−0.530745	+	0.847532i	$0.678088\pi$
$72$	0	0
$73$	−4.47214	−0.523424	−0.261712	−	0.965146i	$-0.584287\pi$
$73$	−4.47214	−0.523424	−0.261712	+	0.965146i	$0.584287\pi$
$74$	11.2361	1.30617
$75$	0	0
$76$	−5.70820	−0.654776
$77$	−23.4164	−2.66855
$78$	0	0
$79$	−4.47214	−0.503155	−0.251577	−	0.967837i	$-0.580949\pi$
$79$	−4.47214	−0.503155	−0.251577	+	0.967837i	$0.580949\pi$
$80$	1.23607	0.138197
$81$	0	0
$82$	−2.00000	−0.220863
$83$	13.2361	1.45285	0.726424	−	0.687247i	$-0.241181\pi$
$83$	13.2361	1.45285	0.726424	+	0.687247i	$0.241181\pi$
$84$	0	0
$85$	−4.94427	−0.536282
$86$	−4.76393	−0.513708
$87$	0	0
$88$	5.23607	0.558167
$89$	−10.4721	−1.11004	−0.555022	−	0.831836i	$-0.687290\pi$
$89$	−10.4721	−1.11004	−0.555022	+	0.831836i	$0.687290\pi$
$90$	0	0
$91$	20.0000	2.09657
$92$	0	0
$93$	0	0
$94$	4.00000	0.412568
$95$	−7.05573	−0.723902
$96$	0	0
$97$	−0.472136	−0.0479381	−0.0239691	−	0.999713i	$-0.507630\pi$
$97$	−0.472136	−0.0479381	−0.0239691	+	0.999713i	$0.507630\pi$
$98$	−13.0000	−1.31320
$99$	0	0
$100$	−3.47214	−0.347214
$101$	−4.47214	−0.444994	−0.222497	−	0.974933i	$-0.571421\pi$
$101$	−4.47214	−0.444994	−0.222497	+	0.974933i	$0.571421\pi$
$102$	0	0
$103$	6.00000	0.591198	0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000	0.591198	0.295599	+	0.955312i	$0.404481\pi$
$104$	−4.47214	−0.438529
$105$	0	0
$106$	−5.23607	−0.508572
$107$	−12.6525	−1.22316	−0.611581	−	0.791182i	$-0.709466\pi$
$107$	−12.6525	−1.22316	−0.611581	+	0.791182i	$0.709466\pi$
$108$	0	0
$109$	−4.76393	−0.456302	−0.228151	−	0.973626i	$-0.573268\pi$
$109$	−4.76393	−0.456302	−0.228151	+	0.973626i	$0.573268\pi$
$110$	6.47214	0.617094
$111$	0	0
$112$	4.47214	0.422577
$113$	−5.52786	−0.520018	−0.260009	−	0.965606i	$-0.583725\pi$
$113$	−5.52786	−0.520018	−0.260009	+	0.965606i	$0.583725\pi$
$114$	0	0
$115$	0	0
$116$	4.47214	0.415227
$117$	0	0
$118$	−8.94427	−0.823387
$119$	−17.8885	−1.63984
$120$	0	0
$121$	16.4164	1.49240
$122$	0.763932	0.0691632
$123$	0	0
$124$	−2.47214	−0.222004
$125$	−10.4721	−0.936656
$126$	0	0
$127$	−4.00000	−0.354943	−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	−5.52786	−0.484826
$131$	9.52786	0.832453	0.416227	−	0.909261i	$-0.363352\pi$
$131$	9.52786	0.832453	0.416227	+	0.909261i	$0.363352\pi$
$132$	0	0
$133$	−25.5279	−2.21355
$134$	9.70820	0.838661
$135$	0	0
$136$	4.00000	0.342997
$137$	3.05573	0.261068	0.130534	−	0.991444i	$-0.458331\pi$
$137$	3.05573	0.261068	0.130534	+	0.991444i	$0.458331\pi$
$138$	0	0
$139$	−16.9443	−1.43719	−0.718597	−	0.695427i	$-0.755215\pi$
$139$	−16.9443	−1.43719	−0.718597	+	0.695427i	$0.755215\pi$
$140$	5.52786	0.467190
$141$	0	0
$142$	8.94427	0.750587
$143$	−23.4164	−1.95818
$144$	0	0
$145$	5.52786	0.459064
$146$	4.47214	0.370117
$147$	0	0
$148$	−11.2361	−0.923599
$149$	−11.7082	−0.959173	−0.479587	−	0.877494i	$-0.659213\pi$
$149$	−11.7082	−0.959173	−0.479587	+	0.877494i	$0.659213\pi$
$150$	0	0
$151$	−14.4721	−1.17773	−0.588863	−	0.808233i	$-0.700424\pi$
$151$	−14.4721	−1.17773	−0.588863	+	0.808233i	$0.700424\pi$
$152$	5.70820	0.462996
$153$	0	0
$154$	23.4164	1.88695
$155$	−3.05573	−0.245442
$156$	0	0
$157$	6.65248	0.530925	0.265463	−	0.964121i	$-0.414475\pi$
$157$	6.65248	0.530925	0.265463	+	0.964121i	$0.414475\pi$
$158$	4.47214	0.355784
$159$	0	0
$160$	−1.23607	−0.0977198
$161$	0	0
$162$	0	0
$163$	−2.47214	−0.193633	−0.0968163	−	0.995302i	$-0.530866\pi$
$163$	−2.47214	−0.193633	−0.0968163	+	0.995302i	$0.530866\pi$
$164$	2.00000	0.156174
$165$	0	0
$166$	−13.2361	−1.02732
$167$	−16.9443	−1.31119	−0.655594	−	0.755114i	$-0.727582\pi$
$167$	−16.9443	−1.31119	−0.655594	+	0.755114i	$0.727582\pi$
$168$	0	0
$169$	7.00000	0.538462
$170$	4.94427	0.379208
$171$	0	0
$172$	4.76393	0.363246
$173$	17.4164	1.32414	0.662072	−	0.749440i	$-0.269677\pi$
$173$	17.4164	1.32414	0.662072	+	0.749440i	$0.269677\pi$
$174$	0	0
$175$	−15.5279	−1.17380
$176$	−5.23607	−0.394683
$177$	0	0
$178$	10.4721	0.784920
$179$	−19.4164	−1.45125	−0.725625	−	0.688090i	$-0.758449\pi$
$179$	−19.4164	−1.45125	−0.725625	+	0.688090i	$0.758449\pi$
$180$	0	0
$181$	11.2361	0.835170	0.417585	−	0.908638i	$-0.362877\pi$
$181$	11.2361	0.835170	0.417585	+	0.908638i	$0.362877\pi$
$182$	−20.0000	−1.48250
$183$	0	0
$184$	0	0
$185$	−13.8885	−1.02111
$186$	0	0
$187$	20.9443	1.53160
$188$	−4.00000	−0.291730
$189$	0	0
$190$	7.05573	0.511876
$191$	6.47214	0.468307	0.234154	−	0.972200i	$-0.424768\pi$
$191$	6.47214	0.468307	0.234154	+	0.972200i	$0.424768\pi$
$192$	0	0
$193$	23.8885	1.71954	0.859768	−	0.510686i	$-0.170608\pi$
$193$	23.8885	1.71954	0.859768	+	0.510686i	$0.170608\pi$
$194$	0.472136	0.0338974
$195$	0	0
$196$	13.0000	0.928571
$197$	−2.94427	−0.209771	−0.104885	−	0.994484i	$-0.533448\pi$
$197$	−2.94427	−0.209771	−0.104885	+	0.994484i	$0.533448\pi$
$198$	0	0
$199$	−17.4164	−1.23462	−0.617308	−	0.786721i	$-0.711777\pi$
$199$	−17.4164	−1.23462	−0.617308	+	0.786721i	$0.711777\pi$
$200$	3.47214	0.245517
$201$	0	0
$202$	4.47214	0.314658
$203$	20.0000	1.40372
$204$	0	0
$205$	2.47214	0.172661
$206$	−6.00000	−0.418040
$207$	0	0
$208$	4.47214	0.310087
$209$	29.8885	2.06743
$210$	0	0
$211$	−23.4164	−1.61205	−0.806026	−	0.591880i	$-0.798386\pi$
$211$	−23.4164	−1.61205	−0.806026	+	0.591880i	$0.798386\pi$
$212$	5.23607	0.359615
$213$	0	0
$214$	12.6525	0.864905
$215$	5.88854	0.401595
$216$	0	0
$217$	−11.0557	−0.750512
$218$	4.76393	0.322654
$219$	0	0
$220$	−6.47214	−0.436351
$221$	−17.8885	−1.20331
$222$	0	0
$223$	19.4164	1.30022	0.650109	−	0.759841i	$-0.274723\pi$
$223$	19.4164	1.30022	0.650109	+	0.759841i	$0.274723\pi$
$224$	−4.47214	−0.298807
$225$	0	0
$226$	5.52786	0.367708
$227$	−9.23607	−0.613019	−0.306510	−	0.951868i	$-0.599161\pi$
$227$	−9.23607	−0.613019	−0.306510	+	0.951868i	$0.599161\pi$
$228$	0	0
$229$	−17.7082	−1.17019	−0.585096	−	0.810964i	$-0.698943\pi$
$229$	−17.7082	−1.17019	−0.585096	+	0.810964i	$0.698943\pi$
$230$	0	0
$231$	0	0
$232$	−4.47214	−0.293610
$233$	−19.8885	−1.30294	−0.651471	−	0.758674i	$-0.725848\pi$
$233$	−19.8885	−1.30294	−0.651471	+	0.758674i	$0.725848\pi$
$234$	0	0
$235$	−4.94427	−0.322529
$236$	8.94427	0.582223
$237$	0	0
$238$	17.8885	1.15954
$239$	4.94427	0.319818	0.159909	−	0.987132i	$-0.448880\pi$
$239$	4.94427	0.319818	0.159909	+	0.987132i	$0.448880\pi$
$240$	0	0
$241$	12.4721	0.803401	0.401700	−	0.915771i	$-0.368419\pi$
$241$	12.4721	0.803401	0.401700	+	0.915771i	$0.368419\pi$
$242$	−16.4164	−1.05529
$243$	0	0
$244$	−0.763932	−0.0489057
$245$	16.0689	1.02660
$246$	0	0
$247$	−25.5279	−1.62430
$248$	2.47214	0.156981
$249$	0	0
$250$	10.4721	0.662316
$251$	−19.7082	−1.24397	−0.621985	−	0.783029i	$-0.713674\pi$
$251$	−19.7082	−1.24397	−0.621985	+	0.783029i	$0.713674\pi$
$252$	0	0
$253$	0	0
$254$	4.00000	0.250982
$255$	0	0
$256$	1.00000	0.0625000
$257$	11.8885	0.741587	0.370793	−	0.928715i	$-0.379086\pi$
$257$	11.8885	0.741587	0.370793	+	0.928715i	$0.379086\pi$
$258$	0	0
$259$	−50.2492	−3.12233
$260$	5.52786	0.342824
$261$	0	0
$262$	−9.52786	−0.588633
$263$	24.9443	1.53813	0.769065	−	0.639171i	$-0.220722\pi$
$263$	24.9443	1.53813	0.769065	+	0.639171i	$0.220722\pi$
$264$	0	0
$265$	6.47214	0.397580
$266$	25.5279	1.56521
$267$	0	0
$268$	−9.70820	−0.593023
$269$	13.0557	0.796022	0.398011	−	0.917381i	$-0.369701\pi$
$269$	13.0557	0.796022	0.398011	+	0.917381i	$0.369701\pi$
$270$	0	0
$271$	−16.9443	−1.02929	−0.514646	−	0.857403i	$-0.672076\pi$
$271$	−16.9443	−1.02929	−0.514646	+	0.857403i	$0.672076\pi$
$272$	−4.00000	−0.242536
$273$	0	0
$274$	−3.05573	−0.184603
$275$	18.1803	1.09632
$276$	0	0
$277$	−20.4721	−1.23005	−0.615026	−	0.788507i	$-0.710854\pi$
$277$	−20.4721	−1.23005	−0.615026	+	0.788507i	$0.710854\pi$
$278$	16.9443	1.01625
$279$	0	0
$280$	−5.52786	−0.330353
$281$	−13.5279	−0.807005	−0.403502	−	0.914979i	$-0.632207\pi$
$281$	−13.5279	−0.807005	−0.403502	+	0.914979i	$0.632207\pi$
$282$	0	0
$283$	3.81966	0.227055	0.113528	−	0.993535i	$-0.463785\pi$
$283$	3.81966	0.227055	0.113528	+	0.993535i	$0.463785\pi$
$284$	−8.94427	−0.530745
$285$	0	0
$286$	23.4164	1.38464
$287$	8.94427	0.527964
$288$	0	0
$289$	−1.00000	−0.0588235
$290$	−5.52786	−0.324607
$291$	0	0
$292$	−4.47214	−0.261712
$293$	0.291796	0.0170469	0.00852345	−	0.999964i	$-0.497287\pi$
$293$	0.291796	0.0170469	0.00852345	+	0.999964i	$0.497287\pi$
$294$	0	0
$295$	11.0557	0.643689
$296$	11.2361	0.653083
$297$	0	0
$298$	11.7082	0.678238
$299$	0	0
$300$	0	0
$301$	21.3050	1.22800
$302$	14.4721	0.832778
$303$	0	0
$304$	−5.70820	−0.327388
$305$	−0.944272	−0.0540689
$306$	0	0
$307$	15.4164	0.879861	0.439930	−	0.898032i	$-0.355003\pi$
$307$	15.4164	0.879861	0.439930	+	0.898032i	$0.355003\pi$
$308$	−23.4164	−1.33427
$309$	0	0
$310$	3.05573	0.173554
$311$	20.9443	1.18764	0.593820	−	0.804598i	$-0.297619\pi$
$311$	20.9443	1.18764	0.593820	+	0.804598i	$0.297619\pi$
$312$	0	0
$313$	−15.5279	−0.877687	−0.438843	−	0.898564i	$-0.644612\pi$
$313$	−15.5279	−0.877687	−0.438843	+	0.898564i	$0.644612\pi$
$314$	−6.65248	−0.375421
$315$	0	0
$316$	−4.47214	−0.251577
$317$	−19.5279	−1.09679	−0.548397	−	0.836218i	$-0.684762\pi$
$317$	−19.5279	−1.09679	−0.548397	+	0.836218i	$0.684762\pi$
$318$	0	0
$319$	−23.4164	−1.31107
$320$	1.23607	0.0690983
$321$	0	0
$322$	0	0
$323$	22.8328	1.27045
$324$	0	0
$325$	−15.5279	−0.861331
$326$	2.47214	0.136919
$327$	0	0
$328$	−2.00000	−0.110432
$329$	−17.8885	−0.986227
$330$	0	0
$331$	−10.4721	−0.575601	−0.287800	−	0.957690i	$-0.592924\pi$
$331$	−10.4721	−0.575601	−0.287800	+	0.957690i	$0.592924\pi$
$332$	13.2361	0.726424
$333$	0	0
$334$	16.9443	0.927149
$335$	−12.0000	−0.655630
$336$	0	0
$337$	19.8885	1.08340	0.541699	−	0.840573i	$-0.317781\pi$
$337$	19.8885	1.08340	0.541699	+	0.840573i	$0.317781\pi$
$338$	−7.00000	−0.380750
$339$	0	0
$340$	−4.94427	−0.268141
$341$	12.9443	0.700972
$342$	0	0
$343$	26.8328	1.44884
$344$	−4.76393	−0.256854
$345$	0	0
$346$	−17.4164	−0.936312
$347$	−30.4721	−1.63583	−0.817915	−	0.575339i	$-0.804870\pi$
$347$	−30.4721	−1.63583	−0.817915	+	0.575339i	$0.804870\pi$
$348$	0	0
$349$	3.88854	0.208149	0.104074	−	0.994570i	$-0.466812\pi$
$349$	3.88854	0.208149	0.104074	+	0.994570i	$0.466812\pi$
$350$	15.5279	0.829999
$351$	0	0
$352$	5.23607	0.279083
$353$	3.88854	0.206966	0.103483	−	0.994631i	$-0.467001\pi$
$353$	3.88854	0.206966	0.103483	+	0.994631i	$0.467001\pi$
$354$	0	0
$355$	−11.0557	−0.586777
$356$	−10.4721	−0.555022
$357$	0	0
$358$	19.4164	1.02619
$359$	29.3050	1.54666	0.773328	−	0.634006i	$-0.218591\pi$
$359$	29.3050	1.54666	0.773328	+	0.634006i	$0.218591\pi$
$360$	0	0
$361$	13.5836	0.714926
$362$	−11.2361	−0.590555
$363$	0	0
$364$	20.0000	1.04828
$365$	−5.52786	−0.289342
$366$	0	0
$367$	−9.41641	−0.491532	−0.245766	−	0.969329i	$-0.579040\pi$
$367$	−9.41641	−0.491532	−0.245766	+	0.969329i	$0.579040\pi$
$368$	0	0
$369$	0	0
$370$	13.8885	0.722031
$371$	23.4164	1.21572
$372$	0	0
$373$	35.5967	1.84313	0.921565	−	0.388224i	$-0.126911\pi$
$373$	35.5967	1.84313	0.921565	+	0.388224i	$0.126911\pi$
$374$	−20.9443	−1.08300
$375$	0	0
$376$	4.00000	0.206284
$377$	20.0000	1.03005
$378$	0	0
$379$	−13.7082	−0.704143	−0.352072	−	0.935973i	$-0.614523\pi$
$379$	−13.7082	−0.704143	−0.352072	+	0.935973i	$0.614523\pi$
$380$	−7.05573	−0.361951
$381$	0	0
$382$	−6.47214	−0.331143
$383$	7.05573	0.360531	0.180265	−	0.983618i	$-0.442304\pi$
$383$	7.05573	0.360531	0.180265	+	0.983618i	$0.442304\pi$
$384$	0	0
$385$	−28.9443	−1.47514
$386$	−23.8885	−1.21589
$387$	0	0
$388$	−0.472136	−0.0239691
$389$	23.7082	1.20205	0.601027	−	0.799229i	$-0.294758\pi$
$389$	23.7082	1.20205	0.601027	+	0.799229i	$0.294758\pi$
$390$	0	0
$391$	0	0
$392$	−13.0000	−0.656599
$393$	0	0
$394$	2.94427	0.148330
$395$	−5.52786	−0.278137
$396$	0	0
$397$	26.9443	1.35229	0.676147	−	0.736767i	$-0.263648\pi$
$397$	26.9443	1.35229	0.676147	+	0.736767i	$0.263648\pi$
$398$	17.4164	0.873006
$399$	0	0
$400$	−3.47214	−0.173607
$401$	8.94427	0.446656	0.223328	−	0.974743i	$-0.428308\pi$
$401$	8.94427	0.446656	0.223328	+	0.974743i	$0.428308\pi$
$402$	0	0
$403$	−11.0557	−0.550725
$404$	−4.47214	−0.222497
$405$	0	0
$406$	−20.0000	−0.992583
$407$	58.8328	2.91623
$408$	0	0
$409$	−35.8885	−1.77457	−0.887287	−	0.461217i	$-0.847413\pi$
$409$	−35.8885	−1.77457	−0.887287	+	0.461217i	$0.847413\pi$
$410$	−2.47214	−0.122090
$411$	0	0
$412$	6.00000	0.295599
$413$	40.0000	1.96827
$414$	0	0
$415$	16.3607	0.803114
$416$	−4.47214	−0.219265
$417$	0	0
$418$	−29.8885	−1.46190
$419$	28.0689	1.37125	0.685627	−	0.727953i	$-0.259528\pi$
$419$	28.0689	1.37125	0.685627	+	0.727953i	$0.259528\pi$
$420$	0	0
$421$	0.763932	0.0372318	0.0186159	−	0.999827i	$-0.494074\pi$
$421$	0.763932	0.0372318	0.0186159	+	0.999827i	$0.494074\pi$
$422$	23.4164	1.13989
$423$	0	0
$424$	−5.23607	−0.254286
$425$	13.8885	0.673693
$426$	0	0
$427$	−3.41641	−0.165332
$428$	−12.6525	−0.611581
$429$	0	0
$430$	−5.88854	−0.283971
$431$	−23.4164	−1.12793	−0.563964	−	0.825799i	$-0.690724\pi$
$431$	−23.4164	−1.12793	−0.563964	+	0.825799i	$0.690724\pi$
$432$	0	0
$433$	21.4164	1.02921	0.514603	−	0.857428i	$-0.327939\pi$
$433$	21.4164	1.02921	0.514603	+	0.857428i	$0.327939\pi$
$434$	11.0557	0.530692
$435$	0	0
$436$	−4.76393	−0.228151
$437$	0	0
$438$	0	0
$439$	19.0557	0.909480	0.454740	−	0.890624i	$-0.349732\pi$
$439$	19.0557	0.909480	0.454740	+	0.890624i	$0.349732\pi$
$440$	6.47214	0.308547
$441$	0	0
$442$	17.8885	0.850871
$443$	15.0557	0.715319	0.357660	−	0.933852i	$-0.383575\pi$
$443$	15.0557	0.715319	0.357660	+	0.933852i	$0.383575\pi$
$444$	0	0
$445$	−12.9443	−0.613617
$446$	−19.4164	−0.919394
$447$	0	0
$448$	4.47214	0.211289
$449$	−15.8885	−0.749827	−0.374913	−	0.927060i	$-0.622328\pi$
$449$	−15.8885	−0.749827	−0.374913	+	0.927060i	$0.622328\pi$
$450$	0	0
$451$	−10.4721	−0.493114
$452$	−5.52786	−0.260009
$453$	0	0
$454$	9.23607	0.433470
$455$	24.7214	1.15896
$456$	0	0
$457$	−27.5279	−1.28770	−0.643850	−	0.765152i	$-0.722664\pi$
$457$	−27.5279	−1.28770	−0.643850	+	0.765152i	$0.722664\pi$
$458$	17.7082	0.827450
$459$	0	0
$460$	0	0
$461$	−22.0000	−1.02464	−0.512321	−	0.858794i	$-0.671214\pi$
$461$	−22.0000	−1.02464	−0.512321	+	0.858794i	$0.671214\pi$
$462$	0	0
$463$	24.0000	1.11537	0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000	1.11537	0.557687	+	0.830051i	$0.311689\pi$
$464$	4.47214	0.207614
$465$	0	0
$466$	19.8885	0.921319
$467$	−17.8197	−0.824596	−0.412298	−	0.911049i	$-0.635274\pi$
$467$	−17.8197	−0.824596	−0.412298	+	0.911049i	$0.635274\pi$
$468$	0	0
$469$	−43.4164	−2.00478
$470$	4.94427	0.228062
$471$	0	0
$472$	−8.94427	−0.411693
$473$	−24.9443	−1.14694
$474$	0	0
$475$	19.8197	0.909388
$476$	−17.8885	−0.819920
$477$	0	0
$478$	−4.94427	−0.226146
$479$	−28.9443	−1.32250	−0.661249	−	0.750167i	$-0.729973\pi$
$479$	−28.9443	−1.32250	−0.661249	+	0.750167i	$0.729973\pi$
$480$	0	0
$481$	−50.2492	−2.29117
$482$	−12.4721	−0.568090
$483$	0	0
$484$	16.4164	0.746200
$485$	−0.583592	−0.0264996
$486$	0	0
$487$	9.88854	0.448093	0.224046	−	0.974578i	$-0.428073\pi$
$487$	9.88854	0.448093	0.224046	+	0.974578i	$0.428073\pi$
$488$	0.763932	0.0345816
$489$	0	0
$490$	−16.0689	−0.725918
$491$	−29.3050	−1.32251	−0.661257	−	0.750159i	$-0.729977\pi$
$491$	−29.3050	−1.32251	−0.661257	+	0.750159i	$0.729977\pi$
$492$	0	0
$493$	−17.8885	−0.805659
$494$	25.5279	1.14855
$495$	0	0
$496$	−2.47214	−0.111002
$497$	−40.0000	−1.79425
$498$	0	0
$499$	0.583592	0.0261252	0.0130626	−	0.999915i	$-0.495842\pi$
$499$	0.583592	0.0261252	0.0130626	+	0.999915i	$0.495842\pi$
$500$	−10.4721	−0.468328
$501$	0	0
$502$	19.7082	0.879620
$503$	10.4721	0.466929	0.233465	−	0.972365i	$-0.424994\pi$
$503$	10.4721	0.466929	0.233465	+	0.972365i	$0.424994\pi$
$504$	0	0
$505$	−5.52786	−0.245987
$506$	0	0
$507$	0	0
$508$	−4.00000	−0.177471
$509$	33.4164	1.48116	0.740578	−	0.671970i	$-0.234552\pi$
$509$	33.4164	1.48116	0.740578	+	0.671970i	$0.234552\pi$
$510$	0	0
$511$	−20.0000	−0.884748
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−11.8885	−0.524381
$515$	7.41641	0.326806
$516$	0	0
$517$	20.9443	0.921128
$518$	50.2492	2.20782
$519$	0	0
$520$	−5.52786	−0.242413
$521$	16.0000	0.700973	0.350486	−	0.936568i	$-0.386016\pi$
$521$	16.0000	0.700973	0.350486	+	0.936568i	$0.386016\pi$
$522$	0	0
$523$	−25.7082	−1.12414	−0.562071	−	0.827089i	$-0.689995\pi$
$523$	−25.7082	−1.12414	−0.562071	+	0.827089i	$0.689995\pi$
$524$	9.52786	0.416227
$525$	0	0
$526$	−24.9443	−1.08762
$527$	9.88854	0.430752
$528$	0	0
$529$	0	0
$530$	−6.47214	−0.281132
$531$	0	0
$532$	−25.5279	−1.10677
$533$	8.94427	0.387419
$534$	0	0
$535$	−15.6393	−0.676147
$536$	9.70820	0.419331
$537$	0	0
$538$	−13.0557	−0.562872
$539$	−68.0689	−2.93193
$540$	0	0
$541$	8.11146	0.348739	0.174369	−	0.984680i	$-0.444211\pi$
$541$	8.11146	0.348739	0.174369	+	0.984680i	$0.444211\pi$
$542$	16.9443	0.727819
$543$	0	0
$544$	4.00000	0.171499
$545$	−5.88854	−0.252238
$546$	0	0
$547$	41.3050	1.76607	0.883036	−	0.469305i	$-0.155496\pi$
$547$	41.3050	1.76607	0.883036	+	0.469305i	$0.155496\pi$
$548$	3.05573	0.130534
$549$	0	0
$550$	−18.1803	−0.775212
$551$	−25.5279	−1.08752
$552$	0	0
$553$	−20.0000	−0.850487
$554$	20.4721	0.869778
$555$	0	0
$556$	−16.9443	−0.718597
$557$	−15.1246	−0.640850	−0.320425	−	0.947274i	$-0.603826\pi$
$557$	−15.1246	−0.640850	−0.320425	+	0.947274i	$0.603826\pi$
$558$	0	0
$559$	21.3050	0.901103
$560$	5.52786	0.233595
$561$	0	0
$562$	13.5279	0.570639
$563$	24.6525	1.03898	0.519489	−	0.854477i	$-0.326122\pi$
$563$	24.6525	1.03898	0.519489	+	0.854477i	$0.326122\pi$
$564$	0	0
$565$	−6.83282	−0.287459
$566$	−3.81966	−0.160552
$567$	0	0
$568$	8.94427	0.375293
$569$	20.0000	0.838444	0.419222	−	0.907884i	$-0.362303\pi$
$569$	20.0000	0.838444	0.419222	+	0.907884i	$0.362303\pi$
$570$	0	0
$571$	14.2918	0.598093	0.299047	−	0.954239i	$-0.403331\pi$
$571$	14.2918	0.598093	0.299047	+	0.954239i	$0.403331\pi$
$572$	−23.4164	−0.979089
$573$	0	0
$574$	−8.94427	−0.373327
$575$	0	0
$576$	0	0
$577$	−34.3607	−1.43045	−0.715227	−	0.698892i	$-0.753677\pi$
$577$	−34.3607	−1.43045	−0.715227	+	0.698892i	$0.753677\pi$
$578$	1.00000	0.0415945
$579$	0	0
$580$	5.52786	0.229532
$581$	59.1935	2.45576
$582$	0	0
$583$	−27.4164	−1.13547
$584$	4.47214	0.185058
$585$	0	0
$586$	−0.291796	−0.0120540
$587$	−6.47214	−0.267134	−0.133567	−	0.991040i	$-0.542643\pi$
$587$	−6.47214	−0.267134	−0.133567	+	0.991040i	$0.542643\pi$
$588$	0	0
$589$	14.1115	0.581452
$590$	−11.0557	−0.455157
$591$	0	0
$592$	−11.2361	−0.461800
$593$	−33.7771	−1.38706	−0.693529	−	0.720428i	$-0.743945\pi$
$593$	−33.7771	−1.38706	−0.693529	+	0.720428i	$0.743945\pi$
$594$	0	0
$595$	−22.1115	−0.906481
$596$	−11.7082	−0.479587
$597$	0	0
$598$	0	0
$599$	−33.8885	−1.38465	−0.692324	−	0.721587i	$-0.743413\pi$
$599$	−33.8885	−1.38465	−0.692324	+	0.721587i	$0.743413\pi$
$600$	0	0
$601$	−10.3607	−0.422621	−0.211310	−	0.977419i	$-0.567773\pi$
$601$	−10.3607	−0.422621	−0.211310	+	0.977419i	$0.567773\pi$
$602$	−21.3050	−0.868325
$603$	0	0
$604$	−14.4721	−0.588863
$605$	20.2918	0.824979
$606$	0	0
$607$	−17.5279	−0.711434	−0.355717	−	0.934594i	$-0.615763\pi$
$607$	−17.5279	−0.711434	−0.355717	+	0.934594i	$0.615763\pi$
$608$	5.70820	0.231498
$609$	0	0
$610$	0.944272	0.0382325
$611$	−17.8885	−0.723693
$612$	0	0
$613$	25.1246	1.01477	0.507387	−	0.861718i	$-0.330612\pi$
$613$	25.1246	1.01477	0.507387	+	0.861718i	$0.330612\pi$
$614$	−15.4164	−0.622156
$615$	0	0
$616$	23.4164	0.943474
$617$	20.3607	0.819690	0.409845	−	0.912155i	$-0.365583\pi$
$617$	20.3607	0.819690	0.409845	+	0.912155i	$0.365583\pi$
$618$	0	0
$619$	−18.2918	−0.735209	−0.367605	−	0.929982i	$-0.619822\pi$
$619$	−18.2918	−0.735209	−0.367605	+	0.929982i	$0.619822\pi$
$620$	−3.05573	−0.122721
$621$	0	0
$622$	−20.9443	−0.839789
$623$	−46.8328	−1.87632
$624$	0	0
$625$	4.41641	0.176656
$626$	15.5279	0.620618
$627$	0	0
$628$	6.65248	0.265463
$629$	44.9443	1.79205
$630$	0	0
$631$	6.00000	0.238856	0.119428	−	0.992843i	$-0.461894\pi$
$631$	6.00000	0.238856	0.119428	+	0.992843i	$0.461894\pi$
$632$	4.47214	0.177892
$633$	0	0
$634$	19.5279	0.775551
$635$	−4.94427	−0.196207
$636$	0	0
$637$	58.1378	2.30350
$638$	23.4164	0.927064
$639$	0	0
$640$	−1.23607	−0.0488599
$641$	4.00000	0.157991	0.0789953	−	0.996875i	$-0.474829\pi$
$641$	4.00000	0.157991	0.0789953	+	0.996875i	$0.474829\pi$
$642$	0	0
$643$	32.5410	1.28329	0.641646	−	0.767001i	$-0.278252\pi$
$643$	32.5410	1.28329	0.641646	+	0.767001i	$0.278252\pi$
$644$	0	0
$645$	0	0
$646$	−22.8328	−0.898345
$647$	−12.9443	−0.508892	−0.254446	−	0.967087i	$-0.581893\pi$
$647$	−12.9443	−0.508892	−0.254446	+	0.967087i	$0.581893\pi$
$648$	0	0
$649$	−46.8328	−1.83835
$650$	15.5279	0.609053
$651$	0	0
$652$	−2.47214	−0.0968163
$653$	−9.41641	−0.368493	−0.184246	−	0.982880i	$-0.558984\pi$
$653$	−9.41641	−0.368493	−0.184246	+	0.982880i	$0.558984\pi$
$654$	0	0
$655$	11.7771	0.460169
$656$	2.00000	0.0780869
$657$	0	0
$658$	17.8885	0.697368
$659$	−32.6525	−1.27196	−0.635980	−	0.771706i	$-0.719404\pi$
$659$	−32.6525	−1.27196	−0.635980	+	0.771706i	$0.719404\pi$
$660$	0	0
$661$	−3.81966	−0.148568	−0.0742838	−	0.997237i	$-0.523667\pi$
$661$	−3.81966	−0.148568	−0.0742838	+	0.997237i	$0.523667\pi$
$662$	10.4721	0.407011
$663$	0	0
$664$	−13.2361	−0.513659
$665$	−31.5542	−1.22362
$666$	0	0
$667$	0	0
$668$	−16.9443	−0.655594
$669$	0	0
$670$	12.0000	0.463600
$671$	4.00000	0.154418
$672$	0	0
$673$	4.47214	0.172388	0.0861941	−	0.996278i	$-0.472529\pi$
$673$	4.47214	0.172388	0.0861941	+	0.996278i	$0.472529\pi$
$674$	−19.8885	−0.766078
$675$	0	0
$676$	7.00000	0.269231
$677$	19.1246	0.735019	0.367509	−	0.930020i	$-0.380211\pi$
$677$	19.1246	0.735019	0.367509	+	0.930020i	$0.380211\pi$
$678$	0	0
$679$	−2.11146	−0.0810303
$680$	4.94427	0.189604
$681$	0	0
$682$	−12.9443	−0.495662
$683$	−14.4721	−0.553761	−0.276880	−	0.960904i	$-0.589301\pi$
$683$	−14.4721	−0.553761	−0.276880	+	0.960904i	$0.589301\pi$
$684$	0	0
$685$	3.77709	0.144315
$686$	−26.8328	−1.02448
$687$	0	0
$688$	4.76393	0.181623
$689$	23.4164	0.892094
$690$	0	0
$691$	16.5836	0.630870	0.315435	−	0.948947i	$-0.397850\pi$
$691$	16.5836	0.630870	0.315435	+	0.948947i	$0.397850\pi$
$692$	17.4164	0.662072
$693$	0	0
$694$	30.4721	1.15671
$695$	−20.9443	−0.794462
$696$	0	0
$697$	−8.00000	−0.303022
$698$	−3.88854	−0.147184
$699$	0	0
$700$	−15.5279	−0.586898
$701$	−3.12461	−0.118015	−0.0590075	−	0.998258i	$-0.518794\pi$
$701$	−3.12461	−0.118015	−0.0590075	+	0.998258i	$0.518794\pi$
$702$	0	0
$703$	64.1378	2.41900
$704$	−5.23607	−0.197342
$705$	0	0
$706$	−3.88854	−0.146347
$707$	−20.0000	−0.752177
$708$	0	0
$709$	−35.0132	−1.31495	−0.657473	−	0.753478i	$-0.728375\pi$
$709$	−35.0132	−1.31495	−0.657473	+	0.753478i	$0.728375\pi$
$710$	11.0557	0.414914
$711$	0	0
$712$	10.4721	0.392460
$713$	0	0
$714$	0	0
$715$	−28.9443	−1.08245
$716$	−19.4164	−0.725625
$717$	0	0
$718$	−29.3050	−1.09365
$719$	3.05573	0.113959	0.0569797	−	0.998375i	$-0.481853\pi$
$719$	3.05573	0.113959	0.0569797	+	0.998375i	$0.481853\pi$
$720$	0	0
$721$	26.8328	0.999306
$722$	−13.5836	−0.505529
$723$	0	0
$724$	11.2361	0.417585
$725$	−15.5279	−0.576690
$726$	0	0
$727$	19.3050	0.715981	0.357991	−	0.933725i	$-0.383462\pi$
$727$	19.3050	0.715981	0.357991	+	0.933725i	$0.383462\pi$
$728$	−20.0000	−0.741249
$729$	0	0
$730$	5.52786	0.204595
$731$	−19.0557	−0.704802
$732$	0	0
$733$	21.7082	0.801811	0.400905	−	0.916119i	$-0.368696\pi$
$733$	21.7082	0.801811	0.400905	+	0.916119i	$0.368696\pi$
$734$	9.41641	0.347566
$735$	0	0
$736$	0	0
$737$	50.8328	1.87245
$738$	0	0
$739$	−32.9443	−1.21187	−0.605937	−	0.795512i	$-0.707202\pi$
$739$	−32.9443	−1.21187	−0.605937	+	0.795512i	$0.707202\pi$
$740$	−13.8885	−0.510553
$741$	0	0
$742$	−23.4164	−0.859643
$743$	−4.00000	−0.146746	−0.0733729	−	0.997305i	$-0.523376\pi$
$743$	−4.00000	−0.146746	−0.0733729	+	0.997305i	$0.523376\pi$
$744$	0	0
$745$	−14.4721	−0.530218
$746$	−35.5967	−1.30329
$747$	0	0
$748$	20.9443	0.765798
$749$	−56.5836	−2.06752
$750$	0	0
$751$	18.0000	0.656829	0.328415	−	0.944534i	$-0.393486\pi$
$751$	18.0000	0.656829	0.328415	+	0.944534i	$0.393486\pi$
$752$	−4.00000	−0.145865
$753$	0	0
$754$	−20.0000	−0.728357
$755$	−17.8885	−0.651031
$756$	0	0
$757$	1.34752	0.0489766	0.0244883	−	0.999700i	$-0.492204\pi$
$757$	1.34752	0.0489766	0.0244883	+	0.999700i	$0.492204\pi$
$758$	13.7082	0.497904
$759$	0	0
$760$	7.05573	0.255938
$761$	5.05573	0.183270	0.0916350	−	0.995793i	$-0.470791\pi$
$761$	5.05573	0.183270	0.0916350	+	0.995793i	$0.470791\pi$
$762$	0	0
$763$	−21.3050	−0.771291
$764$	6.47214	0.234154
$765$	0	0
$766$	−7.05573	−0.254934
$767$	40.0000	1.44432
$768$	0	0
$769$	−12.4721	−0.449757	−0.224878	−	0.974387i	$-0.572198\pi$
$769$	−12.4721	−0.449757	−0.224878	+	0.974387i	$0.572198\pi$
$770$	28.9443	1.04308
$771$	0	0
$772$	23.8885	0.859768
$773$	−38.1803	−1.37325	−0.686626	−	0.727011i	$-0.740909\pi$
$773$	−38.1803	−1.37325	−0.686626	+	0.727011i	$0.740909\pi$
$774$	0	0
$775$	8.58359	0.308332
$776$	0.472136	0.0169487
$777$	0	0
$778$	−23.7082	−0.849980
$779$	−11.4164	−0.409035
$780$	0	0
$781$	46.8328	1.67581
$782$	0	0
$783$	0	0
$784$	13.0000	0.464286
$785$	8.22291	0.293488
$786$	0	0
$787$	−35.2361	−1.25603	−0.628015	−	0.778201i	$-0.716132\pi$
$787$	−35.2361	−1.25603	−0.628015	+	0.778201i	$0.716132\pi$
$788$	−2.94427	−0.104885
$789$	0	0
$790$	5.52786	0.196673
$791$	−24.7214	−0.878990
$792$	0	0
$793$	−3.41641	−0.121320
$794$	−26.9443	−0.956216
$795$	0	0
$796$	−17.4164	−0.617308
$797$	41.5967	1.47343	0.736716	−	0.676202i	$-0.236375\pi$
$797$	41.5967	1.47343	0.736716	+	0.676202i	$0.236375\pi$
$798$	0	0
$799$	16.0000	0.566039
$800$	3.47214	0.122759
$801$	0	0
$802$	−8.94427	−0.315833
$803$	23.4164	0.826347
$804$	0	0
$805$	0	0
$806$	11.0557	0.389421
$807$	0	0
$808$	4.47214	0.157329
$809$	−42.9443	−1.50984	−0.754920	−	0.655817i	$-0.772324\pi$
$809$	−42.9443	−1.50984	−0.754920	+	0.655817i	$0.772324\pi$
$810$	0	0
$811$	41.3050	1.45041	0.725207	−	0.688531i	$-0.241744\pi$
$811$	41.3050	1.45041	0.725207	+	0.688531i	$0.241744\pi$
$812$	20.0000	0.701862
$813$	0	0
$814$	−58.8328	−2.06209
$815$	−3.05573	−0.107037
$816$	0	0
$817$	−27.1935	−0.951380
$818$	35.8885	1.25481
$819$	0	0
$820$	2.47214	0.0863307
$821$	−39.5279	−1.37953	−0.689766	−	0.724032i	$-0.742287\pi$
$821$	−39.5279	−1.37953	−0.689766	+	0.724032i	$0.742287\pi$
$822$	0	0
$823$	−52.3607	−1.82518	−0.912589	−	0.408877i	$-0.865920\pi$
$823$	−52.3607	−1.82518	−0.912589	+	0.408877i	$0.865920\pi$
$824$	−6.00000	−0.209020
$825$	0	0
$826$	−40.0000	−1.39178
$827$	−21.5967	−0.750993	−0.375496	−	0.926824i	$-0.622528\pi$
$827$	−21.5967	−0.750993	−0.375496	+	0.926824i	$0.622528\pi$
$828$	0	0
$829$	−6.00000	−0.208389	−0.104194	−	0.994557i	$-0.533226\pi$
$829$	−6.00000	−0.208389	−0.104194	+	0.994557i	$0.533226\pi$
$830$	−16.3607	−0.567887
$831$	0	0
$832$	4.47214	0.155043
$833$	−52.0000	−1.80169
$834$	0	0
$835$	−20.9443	−0.724806
$836$	29.8885	1.03372
$837$	0	0
$838$	−28.0689	−0.969623
$839$	−45.8885	−1.58425	−0.792124	−	0.610360i	$-0.791025\pi$
$839$	−45.8885	−1.58425	−0.792124	+	0.610360i	$0.791025\pi$
$840$	0	0
$841$	−9.00000	−0.310345
$842$	−0.763932	−0.0263268
$843$	0	0
$844$	−23.4164	−0.806026
$845$	8.65248	0.297654
$846$	0	0
$847$	73.4164	2.52262
$848$	5.23607	0.179807
$849$	0	0
$850$	−13.8885	−0.476373
$851$	0	0
$852$	0	0
$853$	−26.0000	−0.890223	−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000	−0.890223	−0.445112	+	0.895475i	$0.646836\pi$
$854$	3.41641	0.116907
$855$	0	0
$856$	12.6525	0.432453
$857$	22.0000	0.751506	0.375753	−	0.926720i	$-0.377384\pi$
$857$	22.0000	0.751506	0.375753	+	0.926720i	$0.377384\pi$
$858$	0	0
$859$	−20.0000	−0.682391	−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000	−0.682391	−0.341196	+	0.939992i	$0.610832\pi$
$860$	5.88854	0.200798
$861$	0	0
$862$	23.4164	0.797566
$863$	−14.8328	−0.504915	−0.252457	−	0.967608i	$-0.581239\pi$
$863$	−14.8328	−0.504915	−0.252457	+	0.967608i	$0.581239\pi$
$864$	0	0
$865$	21.5279	0.731969
$866$	−21.4164	−0.727759
$867$	0	0
$868$	−11.0557	−0.375256
$869$	23.4164	0.794347
$870$	0	0
$871$	−43.4164	−1.47111
$872$	4.76393	0.161327
$873$	0	0
$874$	0	0
$875$	−46.8328	−1.58324
$876$	0	0
$877$	−48.2492	−1.62926	−0.814630	−	0.579981i	$-0.803060\pi$
$877$	−48.2492	−1.62926	−0.814630	+	0.579981i	$0.803060\pi$
$878$	−19.0557	−0.643100
$879$	0	0
$880$	−6.47214	−0.218176
$881$	39.4164	1.32797	0.663986	−	0.747745i	$-0.268863\pi$
$881$	39.4164	1.32797	0.663986	+	0.747745i	$0.268863\pi$
$882$	0	0
$883$	13.5279	0.455249	0.227624	−	0.973749i	$-0.426904\pi$
$883$	13.5279	0.455249	0.227624	+	0.973749i	$0.426904\pi$
$884$	−17.8885	−0.601657
$885$	0	0
$886$	−15.0557	−0.505807
$887$	16.9443	0.568933	0.284466	−	0.958686i	$-0.408184\pi$
$887$	16.9443	0.568933	0.284466	+	0.958686i	$0.408184\pi$
$888$	0	0
$889$	−17.8885	−0.599963
$890$	12.9443	0.433893
$891$	0	0
$892$	19.4164	0.650109
$893$	22.8328	0.764071
$894$	0	0
$895$	−24.0000	−0.802232
$896$	−4.47214	−0.149404
$897$	0	0
$898$	15.8885	0.530208
$899$	−11.0557	−0.368729
$900$	0	0
$901$	−20.9443	−0.697755
$902$	10.4721	0.348684
$903$	0	0
$904$	5.52786	0.183854
$905$	13.8885	0.461671
$906$	0	0
$907$	−4.18034	−0.138806	−0.0694030	−	0.997589i	$-0.522109\pi$
$907$	−4.18034	−0.138806	−0.0694030	+	0.997589i	$0.522109\pi$
$908$	−9.23607	−0.306510
$909$	0	0
$910$	−24.7214	−0.819505
$911$	16.5836	0.549439	0.274719	−	0.961524i	$-0.411415\pi$
$911$	16.5836	0.549439	0.274719	+	0.961524i	$0.411415\pi$
$912$	0	0
$913$	−69.3050	−2.29366
$914$	27.5279	0.910541
$915$	0	0
$916$	−17.7082	−0.585096
$917$	42.6099	1.40710
$918$	0	0
$919$	16.4721	0.543366	0.271683	−	0.962387i	$-0.412420\pi$
$919$	16.4721	0.543366	0.271683	+	0.962387i	$0.412420\pi$
$920$	0	0
$921$	0	0
$922$	22.0000	0.724531
$923$	−40.0000	−1.31662
$924$	0	0
$925$	39.0132	1.28274
$926$	−24.0000	−0.788689
$927$	0	0
$928$	−4.47214	−0.146805
$929$	24.8328	0.814738	0.407369	−	0.913264i	$-0.366446\pi$
$929$	24.8328	0.814738	0.407369	+	0.913264i	$0.366446\pi$
$930$	0	0
$931$	−74.2067	−2.43202
$932$	−19.8885	−0.651471
$933$	0	0
$934$	17.8197	0.583077
$935$	25.8885	0.846646
$936$	0	0
$937$	30.0000	0.980057	0.490029	−	0.871706i	$-0.336986\pi$
$937$	30.0000	0.980057	0.490029	+	0.871706i	$0.336986\pi$
$938$	43.4164	1.41760
$939$	0	0
$940$	−4.94427	−0.161264
$941$	38.1803	1.24464	0.622322	−	0.782762i	$-0.286190\pi$
$941$	38.1803	1.24464	0.622322	+	0.782762i	$0.286190\pi$
$942$	0	0
$943$	0	0
$944$	8.94427	0.291111
$945$	0	0
$946$	24.9443	0.811008
$947$	47.1935	1.53358	0.766791	−	0.641897i	$-0.221852\pi$
$947$	47.1935	1.53358	0.766791	+	0.641897i	$0.221852\pi$
$948$	0	0
$949$	−20.0000	−0.649227
$950$	−19.8197	−0.643035
$951$	0	0
$952$	17.8885	0.579771
$953$	−47.7771	−1.54765	−0.773826	−	0.633398i	$-0.781659\pi$
$953$	−47.7771	−1.54765	−0.773826	+	0.633398i	$0.781659\pi$
$954$	0	0
$955$	8.00000	0.258874
$956$	4.94427	0.159909
$957$	0	0
$958$	28.9443	0.935147
$959$	13.6656	0.441286
$960$	0	0
$961$	−24.8885	−0.802856
$962$	50.2492	1.62010
$963$	0	0
$964$	12.4721	0.401700
$965$	29.5279	0.950536
$966$	0	0
$967$	15.4164	0.495758	0.247879	−	0.968791i	$-0.420266\pi$
$967$	15.4164	0.495758	0.247879	+	0.968791i	$0.420266\pi$
$968$	−16.4164	−0.527643
$969$	0	0
$970$	0.583592	0.0187380
$971$	−19.1246	−0.613738	−0.306869	−	0.951752i	$-0.599281\pi$
$971$	−19.1246	−0.613738	−0.306869	+	0.951752i	$0.599281\pi$
$972$	0	0
$973$	−75.7771	−2.42930
$974$	−9.88854	−0.316849
$975$	0	0
$976$	−0.763932	−0.0244529
$977$	1.16718	0.0373415	0.0186708	−	0.999826i	$-0.494057\pi$
$977$	1.16718	0.0373415	0.0186708	+	0.999826i	$0.494057\pi$
$978$	0	0
$979$	54.8328	1.75246
$980$	16.0689	0.513302
$981$	0	0
$982$	29.3050	0.935159
$983$	0.583592	0.0186137	0.00930685	−	0.999957i	$-0.497037\pi$
$983$	0.583592	0.0186137	0.00930685	+	0.999957i	$0.497037\pi$
$984$	0	0
$985$	−3.63932	−0.115958
$986$	17.8885	0.569687
$987$	0	0
$988$	−25.5279	−0.812150
$989$	0	0
$990$	0	0
$991$	−10.4721	−0.332658	−0.166329	−	0.986070i	$-0.553191\pi$
$991$	−10.4721	−0.332658	−0.166329	+	0.986070i	$0.553191\pi$
$992$	2.47214	0.0784904
$993$	0	0
$994$	40.0000	1.26872
$995$	−21.5279	−0.682479
$996$	0	0
$997$	5.05573	0.160117	0.0800583	−	0.996790i	$-0.474489\pi$
$997$	5.05573	0.160117	0.0800583	+	0.996790i	$0.474489\pi$
$998$	−0.583592	−0.0184733
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9522.2.a.q.1.2		2
3.2	odd	2		3174.2.a.s.1.1		2
23.22	odd	2		414.2.a.f.1.1		2
69.68	even	2		138.2.a.d.1.2	✓	2
92.91	even	2		3312.2.a.bc.1.1		2
276.275	odd	2		1104.2.a.j.1.2		2
345.68	odd	4		3450.2.d.x.2899.2		4
345.137	odd	4		3450.2.d.x.2899.3		4
345.344	even	2		3450.2.a.be.1.2		2
483.482	odd	2		6762.2.a.cb.1.1		2
552.275	odd	2		4416.2.a.bl.1.1		2
552.413	even	2		4416.2.a.bh.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.a.d.1.2	✓	2	69.68	even	2
414.2.a.f.1.1		2	23.22	odd	2
1104.2.a.j.1.2		2	276.275	odd	2
3174.2.a.s.1.1		2	3.2	odd	2
3312.2.a.bc.1.1		2	92.91	even	2
3450.2.a.be.1.2		2	345.344	even	2
3450.2.d.x.2899.2		4	345.68	odd	4
3450.2.d.x.2899.3		4	345.137	odd	4
4416.2.a.bh.1.1		2	552.413	even	2
4416.2.a.bl.1.1		2	552.275	odd	2
6762.2.a.cb.1.1		2	483.482	odd	2
9522.2.a.q.1.2		2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 9522 = 2 \cdot 3^{2} \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9522.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +1.23607 q^{5} +4.47214 q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +1.23607 q^{5} +4.47214 q^{7} -1.00000 q^{8} -1.23607 q^{10} -5.23607 q^{11} +4.47214 q^{13} -4.47214 q^{14} +1.00000 q^{16} -4.00000 q^{17} -5.70820 q^{19} +1.23607 q^{20} +5.23607 q^{22} -3.47214 q^{25} -4.47214 q^{26} +4.47214 q^{28} +4.47214 q^{29} -2.47214 q^{31} -1.00000 q^{32} +4.00000 q^{34} +5.52786 q^{35} -11.2361 q^{37} +5.70820 q^{38} -1.23607 q^{40} +2.00000 q^{41} +4.76393 q^{43} -5.23607 q^{44} -4.00000 q^{47} +13.0000 q^{49} +3.47214 q^{50} +4.47214 q^{52} +5.23607 q^{53} -6.47214 q^{55} -4.47214 q^{56} -4.47214 q^{58} +8.94427 q^{59} -0.763932 q^{61} +2.47214 q^{62} +1.00000 q^{64} +5.52786 q^{65} -9.70820 q^{67} -4.00000 q^{68} -5.52786 q^{70} -8.94427 q^{71} -4.47214 q^{73} +11.2361 q^{74} -5.70820 q^{76} -23.4164 q^{77} -4.47214 q^{79} +1.23607 q^{80} -2.00000 q^{82} +13.2361 q^{83} -4.94427 q^{85} -4.76393 q^{86} +5.23607 q^{88} -10.4721 q^{89} +20.0000 q^{91} +4.00000 q^{94} -7.05573 q^{95} -0.472136 q^{97} -13.0000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} - 2 q^{5} - 2 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^5 - 2 * q^8	\( 2 q - 2 q^{2} + 2 q^{4} - 2 q^{5} - 2 q^{8} + 2 q^{10} - 6 q^{11} + 2 q^{16} - 8 q^{17} + 2 q^{19} - 2 q^{20} + 6 q^{22} + 2 q^{25} + 4 q^{31} - 2 q^{32} + 8 q^{34} + 20 q^{35} - 18 q^{37} - 2 q^{38} + 2 q^{40} + 4 q^{41} + 14 q^{43} - 6 q^{44} - 8 q^{47} + 26 q^{49} - 2 q^{50} + 6 q^{53} - 4 q^{55} - 6 q^{61} - 4 q^{62} + 2 q^{64} + 20 q^{65} - 6 q^{67} - 8 q^{68} - 20 q^{70} + 18 q^{74} + 2 q^{76} - 20 q^{77} - 2 q^{80} - 4 q^{82} + 22 q^{83} + 8 q^{85} - 14 q^{86} + 6 q^{88} - 12 q^{89} + 40 q^{91} + 8 q^{94} - 32 q^{95} + 8 q^{97} - 26 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^5 - 2 * q^8 + 2 * q^10 - 6 * q^11 + 2 * q^16 - 8 * q^17 + 2 * q^19 - 2 * q^20 + 6 * q^22 + 2 * q^25 + 4 * q^31 - 2 * q^32 + 8 * q^34 + 20 * q^35 - 18 * q^37 - 2 * q^38 + 2 * q^40 + 4 * q^41 + 14 * q^43 - 6 * q^44 - 8 * q^47 + 26 * q^49 - 2 * q^50 + 6 * q^53 - 4 * q^55 - 6 * q^61 - 4 * q^62 + 2 * q^64 + 20 * q^65 - 6 * q^67 - 8 * q^68 - 20 * q^70 + 18 * q^74 + 2 * q^76 - 20 * q^77 - 2 * q^80 - 4 * q^82 + 22 * q^83 + 8 * q^85 - 14 * q^86 + 6 * q^88 - 12 * q^89 + 40 * q^91 + 8 * q^94 - 32 * q^95 + 8 * q^97 - 26 * q^98

Introduction

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