LMFDB - Embedded newform 9800.2.a.cy.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9800,2,Mod(1,9800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9800, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("9800.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9800.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:	$78.2533939809$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.239575536.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 12x^{4} + 8x^{3} + 35x^{2} - 15x - 8 $ x^6 - x^5 - 12x^4 + 8x^3 + 35x^2 - 15x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 280)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.751428$ of defining polynomial
Character	$\chi$	$=$	9800.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.751428 q^{3} -2.43536 q^{9} +O(q^{10})$	$q+0.751428 q^{3} -2.43536 q^{9} -5.27702 q^{11} -2.43536 q^{13} -6.12660 q^{17} +0.441311 q^{19} -3.18678 q^{23} -4.08428 q^{27} -1.25215 q^{29} +0.645348 q^{31} -3.96530 q^{33} +10.7511 q^{37} -1.82999 q^{39} -8.90154 q^{41} -10.4159 q^{43} +7.52994 q^{47} -4.60370 q^{51} +3.34077 q^{53} +0.331613 q^{57} +8.15535 q^{59} +3.47036 q^{61} +4.78644 q^{67} -2.39464 q^{69} +13.7064 q^{71} +5.32590 q^{73} +5.40439 q^{79} +4.23703 q^{81} -11.9379 q^{83} -0.940897 q^{87} -8.60237 q^{89} +0.484932 q^{93} +13.6714 q^{97} +12.8514 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{3} + 7 q^{9}+O(q^{10}) $ 6 * q + q^3 + 7 * q^9	$ 6 q + q^{3} + 7 q^{9} + q^{11} + 7 q^{13} + 4 q^{17} + 5 q^{19} + 6 q^{23} + 7 q^{27} - 3 q^{29} + 2 q^{31} + 16 q^{33} + 9 q^{37} + 10 q^{39} - 6 q^{41} - 3 q^{43} + 27 q^{47} - 5 q^{53} - 26 q^{57} + 24 q^{59} - 9 q^{61} + 17 q^{67} - 15 q^{69} + 4 q^{71} + 18 q^{73} - 22 q^{79} - 6 q^{81} + 9 q^{83} + 39 q^{87} - 15 q^{89} + 10 q^{93} + 12 q^{97} + 11 q^{99}+O(q^{100}) $ 6 * q + q^3 + 7 * q^9 + q^11 + 7 * q^13 + 4 * q^17 + 5 * q^19 + 6 * q^23 + 7 * q^27 - 3 * q^29 + 2 * q^31 + 16 * q^33 + 9 * q^37 + 10 * q^39 - 6 * q^41 - 3 * q^43 + 27 * q^47 - 5 * q^53 - 26 * q^57 + 24 * q^59 - 9 * q^61 + 17 * q^67 - 15 * q^69 + 4 * q^71 + 18 * q^73 - 22 * q^79 - 6 * q^81 + 9 * q^83 + 39 * q^87 - 15 * q^89 + 10 * q^93 + 12 * q^97 + 11 * q^99

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 $

$2$	0	0
$2$	0	0
$3$	0.751428	0.433837	0.216918	−	0.976190i	$-0.430399\pi$
$3$	0.751428	0.433837	0.216918	+	0.976190i	$0.430399\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	−2.43536	−0.811785
$10$	0	0
$11$	−5.27702	−1.59108	−0.795540	−	0.605901i	$-0.792813\pi$
$11$	−5.27702	−1.59108	−0.795540	+	0.605901i	$0.792813\pi$
$12$	0	0
$13$	−2.43536	−0.675446	−0.337723	−	0.941245i	$-0.609657\pi$
$13$	−2.43536	−0.675446	−0.337723	+	0.941245i	$0.609657\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−6.12660	−1.48592	−0.742959	−	0.669337i	$-0.766578\pi$
$17$	−6.12660	−1.48592	−0.742959	+	0.669337i	$0.766578\pi$
$18$	0	0
$19$	0.441311	0.101244	0.0506218	−	0.998718i	$-0.483880\pi$
$19$	0.441311	0.101244	0.0506218	+	0.998718i	$0.483880\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−3.18678	−0.664490	−0.332245	−	0.943193i	$-0.607806\pi$
$23$	−3.18678	−0.664490	−0.332245	+	0.943193i	$0.607806\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−4.08428	−0.786020
$28$	0	0
$29$	−1.25215	−0.232518	−0.116259	−	0.993219i	$-0.537090\pi$
$29$	−1.25215	−0.232518	−0.116259	+	0.993219i	$0.537090\pi$
$30$	0	0
$31$	0.645348	0.115908	0.0579539	−	0.998319i	$-0.481542\pi$
$31$	0.645348	0.115908	0.0579539	+	0.998319i	$0.481542\pi$
$32$	0	0
$33$	−3.96530	−0.690269
$34$	0	0
$35$	0	0
$36$	0	0
$37$	10.7511	1.76747	0.883737	−	0.467984i	$-0.155020\pi$
$37$	10.7511	1.76747	0.883737	+	0.467984i	$0.155020\pi$
$38$	0	0
$39$	−1.82999	−0.293034
$40$	0	0
$41$	−8.90154	−1.39019	−0.695093	−	0.718920i	$-0.744637\pi$
$41$	−8.90154	−1.39019	−0.695093	+	0.718920i	$0.744637\pi$
$42$	0	0
$43$	−10.4159	−1.58841	−0.794204	−	0.607651i	$-0.792112\pi$
$43$	−10.4159	−1.58841	−0.794204	+	0.607651i	$0.792112\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	7.52994	1.09835	0.549177	−	0.835706i	$-0.314941\pi$
$47$	7.52994	1.09835	0.549177	+	0.835706i	$0.314941\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	−4.60370	−0.644646
$52$	0	0
$53$	3.34077	0.458891	0.229445	−	0.973322i	$-0.426309\pi$
$53$	3.34077	0.458891	0.229445	+	0.973322i	$0.426309\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0.331613	0.0439232
$58$	0	0
$59$	8.15535	1.06174	0.530868	−	0.847455i	$-0.321866\pi$
$59$	8.15535	1.06174	0.530868	+	0.847455i	$0.321866\pi$
$60$	0	0
$61$	3.47036	0.444335	0.222167	−	0.975009i	$-0.428687\pi$
$61$	3.47036	0.444335	0.222167	+	0.975009i	$0.428687\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	4.78644	0.584756	0.292378	−	0.956303i	$-0.405553\pi$
$67$	4.78644	0.584756	0.292378	+	0.956303i	$0.405553\pi$
$68$	0	0
$69$	−2.39464	−0.288281
$70$	0	0
$71$	13.7064	1.62665	0.813326	−	0.581808i	$-0.197654\pi$
$71$	13.7064	1.62665	0.813326	+	0.581808i	$0.197654\pi$
$72$	0	0
$73$	5.32590	0.623350	0.311675	−	0.950189i	$-0.399110\pi$
$73$	5.32590	0.623350	0.311675	+	0.950189i	$0.399110\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	5.40439	0.608042	0.304021	−	0.952665i	$-0.401671\pi$
$79$	5.40439	0.608042	0.304021	+	0.952665i	$0.401671\pi$
$80$	0	0
$81$	4.23703	0.470781
$82$	0	0
$83$	−11.9379	−1.31036	−0.655178	−	0.755475i	$-0.727406\pi$
$83$	−11.9379	−1.31036	−0.655178	+	0.755475i	$0.727406\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−0.940897	−0.100875
$88$	0	0
$89$	−8.60237	−0.911849	−0.455925	−	0.890018i	$-0.650691\pi$
$89$	−8.60237	−0.911849	−0.455925	+	0.890018i	$0.650691\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0.484932	0.0502851
$94$	0	0
$95$	0	0
$96$	0	0
$97$	13.6714	1.38812	0.694061	−	0.719917i	$-0.255820\pi$
$97$	13.6714	1.38812	0.694061	+	0.719917i	$0.255820\pi$
$98$	0	0
$99$	12.8514	1.29162
$100$	0	0
$101$	11.6814	1.16234	0.581172	−	0.813781i	$-0.302594\pi$
$101$	11.6814	1.16234	0.581172	+	0.813781i	$0.302594\pi$
$102$	0	0
$103$	−0.450595	−0.0443984	−0.0221992	−	0.999754i	$-0.507067\pi$
$103$	−0.450595	−0.0443984	−0.0221992	+	0.999754i	$0.507067\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−0.462608	−0.0447220	−0.0223610	−	0.999750i	$-0.507118\pi$
$107$	−0.462608	−0.0447220	−0.0223610	+	0.999750i	$0.507118\pi$
$108$	0	0
$109$	2.40606	0.230459	0.115229	−	0.993339i	$-0.463240\pi$
$109$	2.40606	0.230459	0.115229	+	0.993339i	$0.463240\pi$
$110$	0	0
$111$	8.07869	0.766795
$112$	0	0
$113$	−13.2753	−1.24884	−0.624420	−	0.781089i	$-0.714665\pi$
$113$	−13.2753	−1.24884	−0.624420	+	0.781089i	$0.714665\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	5.93096	0.548318
$118$	0	0
$119$	0	0
$120$	0	0
$121$	16.8469	1.53154
$122$	0	0
$123$	−6.68886	−0.603114
$124$	0	0
$125$	0	0
$126$	0	0
$127$	5.17855	0.459522	0.229761	−	0.973247i	$-0.426205\pi$
$127$	5.17855	0.459522	0.229761	+	0.973247i	$0.426205\pi$
$128$	0	0
$129$	−7.82679	−0.689110
$130$	0	0
$131$	−9.15344	−0.799740	−0.399870	−	0.916572i	$-0.630945\pi$
$131$	−9.15344	−0.799740	−0.399870	+	0.916572i	$0.630945\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	7.89528	0.674539	0.337270	−	0.941408i	$-0.390497\pi$
$137$	7.89528	0.674539	0.337270	+	0.941408i	$0.390497\pi$
$138$	0	0
$139$	3.92998	0.333337	0.166668	−	0.986013i	$-0.446699\pi$
$139$	3.92998	0.333337	0.166668	+	0.986013i	$0.446699\pi$
$140$	0	0
$141$	5.65820	0.476507
$142$	0	0
$143$	12.8514	1.07469
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−7.04202	−0.576904	−0.288452	−	0.957494i	$-0.593141\pi$
$149$	−7.04202	−0.576904	−0.288452	+	0.957494i	$0.593141\pi$
$150$	0	0
$151$	−0.715364	−0.0582155	−0.0291077	−	0.999576i	$-0.509267\pi$
$151$	−0.715364	−0.0582155	−0.0291077	+	0.999576i	$0.509267\pi$
$152$	0	0
$153$	14.9205	1.20625
$154$	0	0
$155$	0	0
$156$	0	0
$157$	15.7454	1.25662	0.628310	−	0.777963i	$-0.283747\pi$
$157$	15.7454	1.25662	0.628310	+	0.777963i	$0.283747\pi$
$158$	0	0
$159$	2.51035	0.199084
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−12.9431	−1.01379	−0.506893	−	0.862009i	$-0.669206\pi$
$163$	−12.9431	−1.01379	−0.506893	+	0.862009i	$0.669206\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	4.70185	0.363840	0.181920	−	0.983313i	$-0.441769\pi$
$167$	4.70185	0.363840	0.181920	+	0.983313i	$0.441769\pi$
$168$	0	0
$169$	−7.06904	−0.543772
$170$	0	0
$171$	−1.07475	−0.0821881
$172$	0	0
$173$	8.18518	0.622308	0.311154	−	0.950360i	$-0.399285\pi$
$173$	8.18518	0.622308	0.311154	+	0.950360i	$0.399285\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	6.12816	0.460620
$178$	0	0
$179$	20.1942	1.50938	0.754691	−	0.656080i	$-0.227787\pi$
$179$	20.1942	1.50938	0.754691	+	0.656080i	$0.227787\pi$
$180$	0	0
$181$	0.542841	0.0403490	0.0201745	−	0.999796i	$-0.493578\pi$
$181$	0.542841	0.0403490	0.0201745	+	0.999796i	$0.493578\pi$
$182$	0	0
$183$	2.60773	0.192769
$184$	0	0
$185$	0	0
$186$	0	0
$187$	32.3302	2.36422
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−12.9911	−0.940000	−0.470000	−	0.882666i	$-0.655746\pi$
$191$	−12.9911	−0.940000	−0.470000	+	0.882666i	$0.655746\pi$
$192$	0	0
$193$	4.83540	0.348060	0.174030	−	0.984740i	$-0.444321\pi$
$193$	4.83540	0.348060	0.174030	+	0.984740i	$0.444321\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−16.5967	−1.18246	−0.591232	−	0.806502i	$-0.701358\pi$
$197$	−16.5967	−1.18246	−0.591232	+	0.806502i	$0.701358\pi$
$198$	0	0
$199$	15.6444	1.10900	0.554502	−	0.832183i	$-0.312909\pi$
$199$	15.6444	1.10900	0.554502	+	0.832183i	$0.312909\pi$
$200$	0	0
$201$	3.59666	0.253689
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	7.76096	0.539424
$208$	0	0
$209$	−2.32880	−0.161087
$210$	0	0
$211$	−23.5521	−1.62139	−0.810697	−	0.585465i	$-0.800912\pi$
$211$	−23.5521	−1.62139	−0.810697	+	0.585465i	$0.800912\pi$
$212$	0	0
$213$	10.2994	0.705702
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	4.00203	0.270432
$220$	0	0
$221$	14.9205	1.00366
$222$	0	0
$223$	21.4669	1.43753	0.718765	−	0.695253i	$-0.244708\pi$
$223$	21.4669	1.43753	0.718765	+	0.695253i	$0.244708\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	16.6047	1.10209	0.551046	−	0.834475i	$-0.314229\pi$
$227$	16.6047	1.10209	0.551046	+	0.834475i	$0.314229\pi$
$228$	0	0
$229$	−12.7459	−0.842276	−0.421138	−	0.906997i	$-0.638369\pi$
$229$	−12.7459	−0.842276	−0.421138	+	0.906997i	$0.638369\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	15.4073	1.00937	0.504684	−	0.863304i	$-0.331609\pi$
$233$	15.4073	1.00937	0.504684	+	0.863304i	$0.331609\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	4.06101	0.263791
$238$	0	0
$239$	−1.60666	−0.103926	−0.0519631	−	0.998649i	$-0.516548\pi$
$239$	−1.60666	−0.103926	−0.0519631	+	0.998649i	$0.516548\pi$
$240$	0	0
$241$	−21.8152	−1.40524	−0.702620	−	0.711565i	$-0.747987\pi$
$241$	−21.8152	−1.40524	−0.702620	+	0.711565i	$0.747987\pi$
$242$	0	0
$243$	15.4367	0.990262
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−1.07475	−0.0683847
$248$	0	0
$249$	−8.97047	−0.568481
$250$	0	0
$251$	8.23904	0.520044	0.260022	−	0.965603i	$-0.416270\pi$
$251$	8.23904	0.520044	0.260022	+	0.965603i	$0.416270\pi$
$252$	0	0
$253$	16.8167	1.05726
$254$	0	0
$255$	0	0
$256$	0	0
$257$	7.31792	0.456479	0.228240	−	0.973605i	$-0.426703\pi$
$257$	7.31792	0.456479	0.228240	+	0.973605i	$0.426703\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	3.04942	0.188754
$262$	0	0
$263$	15.8872	0.979650	0.489825	−	0.871821i	$-0.337061\pi$
$263$	15.8872	0.979650	0.489825	+	0.871821i	$0.337061\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−6.46406	−0.395594
$268$	0	0
$269$	−11.0777	−0.675422	−0.337711	−	0.941250i	$-0.609653\pi$
$269$	−11.0777	−0.675422	−0.337711	+	0.941250i	$0.609653\pi$
$270$	0	0
$271$	2.82105	0.171366	0.0856832	−	0.996322i	$-0.472693\pi$
$271$	2.82105	0.171366	0.0856832	+	0.996322i	$0.472693\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	1.44948	0.0870908	0.0435454	−	0.999051i	$-0.486135\pi$
$277$	1.44948	0.0870908	0.0435454	+	0.999051i	$0.486135\pi$
$278$	0	0
$279$	−1.57165	−0.0940923
$280$	0	0
$281$	−20.2681	−1.20909	−0.604546	−	0.796570i	$-0.706645\pi$
$281$	−20.2681	−1.20909	−0.604546	+	0.796570i	$0.706645\pi$
$282$	0	0
$283$	1.63007	0.0968975	0.0484487	−	0.998826i	$-0.484572\pi$
$283$	1.63007	0.0968975	0.0484487	+	0.998826i	$0.484572\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	20.5352	1.20795
$290$	0	0
$291$	10.2731	0.602218
$292$	0	0
$293$	−20.5114	−1.19829	−0.599144	−	0.800641i	$-0.704493\pi$
$293$	−20.5114	−1.19829	−0.599144	+	0.800641i	$0.704493\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	21.5528	1.25062
$298$	0	0
$299$	7.76096	0.448828
$300$	0	0
$301$	0	0
$302$	0	0
$303$	8.77773	0.504268
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−1.58019	−0.0901860	−0.0450930	−	0.998983i	$-0.514358\pi$
$307$	−1.58019	−0.0901860	−0.0450930	+	0.998983i	$0.514358\pi$
$308$	0	0
$309$	−0.338589	−0.0192617
$310$	0	0
$311$	−20.8410	−1.18179	−0.590894	−	0.806749i	$-0.701225\pi$
$311$	−20.8410	−1.18179	−0.590894	+	0.806749i	$0.701225\pi$
$312$	0	0
$313$	22.9695	1.29831	0.649155	−	0.760656i	$-0.275123\pi$
$313$	22.9695	1.29831	0.649155	+	0.760656i	$0.275123\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−19.6447	−1.10336	−0.551678	−	0.834057i	$-0.686012\pi$
$317$	−19.6447	−1.10336	−0.551678	+	0.834057i	$0.686012\pi$
$318$	0	0
$319$	6.60759	0.369954
$320$	0	0
$321$	−0.347616	−0.0194021
$322$	0	0
$323$	−2.70374	−0.150440
$324$	0	0
$325$	0	0
$326$	0	0
$327$	1.80798	0.0999815
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−6.95702	−0.382393	−0.191196	−	0.981552i	$-0.561237\pi$
$331$	−6.95702	−0.382393	−0.191196	+	0.981552i	$0.561237\pi$
$332$	0	0
$333$	−26.1828	−1.43481
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−31.0168	−1.68959	−0.844796	−	0.535089i	$-0.820278\pi$
$337$	−31.0168	−1.68959	−0.844796	+	0.535089i	$0.820278\pi$
$338$	0	0
$339$	−9.97547	−0.541793
$340$	0	0
$341$	−3.40551	−0.184419
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	5.81047	0.311922	0.155961	−	0.987763i	$-0.450153\pi$
$347$	5.81047	0.311922	0.155961	+	0.987763i	$0.450153\pi$
$348$	0	0
$349$	28.0316	1.50050	0.750249	−	0.661155i	$-0.229934\pi$
$349$	28.0316	1.50050	0.750249	+	0.661155i	$0.229934\pi$
$350$	0	0
$351$	9.94667	0.530914
$352$	0	0
$353$	−32.9076	−1.75150	−0.875748	−	0.482768i	$-0.839631\pi$
$353$	−32.9076	−1.75150	−0.875748	+	0.482768i	$0.839631\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−28.3368	−1.49556	−0.747778	−	0.663948i	$-0.768879\pi$
$359$	−28.3368	−1.49556	−0.747778	+	0.663948i	$0.768879\pi$
$360$	0	0
$361$	−18.8052	−0.989750
$362$	0	0
$363$	12.6592	0.664437
$364$	0	0
$365$	0	0
$366$	0	0
$367$	23.7654	1.24054	0.620271	−	0.784388i	$-0.287023\pi$
$367$	23.7654	1.24054	0.620271	+	0.784388i	$0.287023\pi$
$368$	0	0
$369$	21.6784	1.12853
$370$	0	0
$371$	0	0
$372$	0	0
$373$	9.08860	0.470590	0.235295	−	0.971924i	$-0.424394\pi$
$373$	9.08860	0.470590	0.235295	+	0.971924i	$0.424394\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	3.04942	0.157053
$378$	0	0
$379$	−8.08377	−0.415235	−0.207618	−	0.978210i	$-0.566571\pi$
$379$	−8.08377	−0.415235	−0.207618	+	0.978210i	$0.566571\pi$
$380$	0	0
$381$	3.89131	0.199358
$382$	0	0
$383$	−5.52866	−0.282501	−0.141251	−	0.989974i	$-0.545112\pi$
$383$	−5.52866	−0.282501	−0.141251	+	0.989974i	$0.545112\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	25.3664	1.28945
$388$	0	0
$389$	−22.3057	−1.13094	−0.565472	−	0.824768i	$-0.691306\pi$
$389$	−22.3057	−1.13094	−0.565472	+	0.824768i	$0.691306\pi$
$390$	0	0
$391$	19.5241	0.987379
$392$	0	0
$393$	−6.87815	−0.346957
$394$	0	0
$395$	0	0
$396$	0	0
$397$	32.2201	1.61708	0.808539	−	0.588443i	$-0.200259\pi$
$397$	32.2201	1.61708	0.808539	+	0.588443i	$0.200259\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	5.94427	0.296843	0.148421	−	0.988924i	$-0.452581\pi$
$401$	5.94427	0.296843	0.148421	+	0.988924i	$0.452581\pi$
$402$	0	0
$403$	−1.57165	−0.0782895
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−56.7338	−2.81219
$408$	0	0
$409$	−30.5234	−1.50929	−0.754643	−	0.656136i	$-0.772190\pi$
$409$	−30.5234	−1.50929	−0.754643	+	0.656136i	$0.772190\pi$
$410$	0	0
$411$	5.93273	0.292640
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	2.95310	0.144614
$418$	0	0
$419$	−4.06306	−0.198493	−0.0992466	−	0.995063i	$-0.531643\pi$
$419$	−4.06306	−0.198493	−0.0992466	+	0.995063i	$0.531643\pi$
$420$	0	0
$421$	−2.34322	−0.114201	−0.0571007	−	0.998368i	$-0.518186\pi$
$421$	−2.34322	−0.114201	−0.0571007	+	0.998368i	$0.518186\pi$
$422$	0	0
$423$	−18.3381	−0.891628
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	9.65691	0.466240
$430$	0	0
$431$	−6.43702	−0.310060	−0.155030	−	0.987910i	$-0.549547\pi$
$431$	−6.43702	−0.310060	−0.155030	+	0.987910i	$0.549547\pi$
$432$	0	0
$433$	22.4161	1.07725	0.538624	−	0.842547i	$-0.318945\pi$
$433$	22.4161	1.07725	0.538624	+	0.842547i	$0.318945\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−1.40636	−0.0672755
$438$	0	0
$439$	−17.4077	−0.830824	−0.415412	−	0.909633i	$-0.636363\pi$
$439$	−17.4077	−0.830824	−0.415412	+	0.909633i	$0.636363\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	35.6871	1.69555	0.847773	−	0.530359i	$-0.177943\pi$
$443$	35.6871	1.69555	0.847773	+	0.530359i	$0.177943\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−5.29157	−0.250282
$448$	0	0
$449$	−5.24155	−0.247364	−0.123682	−	0.992322i	$-0.539470\pi$
$449$	−5.24155	−0.247364	−0.123682	+	0.992322i	$0.539470\pi$
$450$	0	0
$451$	46.9736	2.21190
$452$	0	0
$453$	−0.537544	−0.0252560
$454$	0	0
$455$	0	0
$456$	0	0
$457$	14.9695	0.700241	0.350121	−	0.936705i	$-0.386141\pi$
$457$	14.9695	0.700241	0.350121	+	0.936705i	$0.386141\pi$
$458$	0	0
$459$	25.0227	1.16796
$460$	0	0
$461$	9.92904	0.462441	0.231221	−	0.972901i	$-0.425728\pi$
$461$	9.92904	0.462441	0.231221	+	0.972901i	$0.425728\pi$
$462$	0	0
$463$	3.07448	0.142883	0.0714415	−	0.997445i	$-0.477240\pi$
$463$	3.07448	0.142883	0.0714415	+	0.997445i	$0.477240\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−19.9442	−0.922909	−0.461455	−	0.887164i	$-0.652672\pi$
$467$	−19.9442	−0.922909	−0.461455	+	0.887164i	$0.652672\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	11.8315	0.545168
$472$	0	0
$473$	54.9648	2.52729
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−8.13598	−0.372521
$478$	0	0
$479$	40.3391	1.84314	0.921571	−	0.388209i	$-0.126906\pi$
$479$	40.3391	1.84314	0.921571	+	0.388209i	$0.126906\pi$
$480$	0	0
$481$	−26.1828	−1.19383
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	5.92314	0.268403	0.134202	−	0.990954i	$-0.457153\pi$
$487$	5.92314	0.268403	0.134202	+	0.990954i	$0.457153\pi$
$488$	0	0
$489$	−9.72584	−0.439818
$490$	0	0
$491$	−26.3855	−1.19076	−0.595380	−	0.803444i	$-0.702999\pi$
$491$	−26.3855	−1.19076	−0.595380	+	0.803444i	$0.702999\pi$
$492$	0	0
$493$	7.67139	0.345502
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−6.02895	−0.269893	−0.134946	−	0.990853i	$-0.543086\pi$
$499$	−6.02895	−0.269893	−0.134946	+	0.990853i	$0.543086\pi$
$500$	0	0
$501$	3.53310	0.157847
$502$	0	0
$503$	−37.5173	−1.67281	−0.836407	−	0.548109i	$-0.815348\pi$
$503$	−37.5173	−1.67281	−0.836407	+	0.548109i	$0.815348\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−5.31187	−0.235908
$508$	0	0
$509$	15.9162	0.705472	0.352736	−	0.935723i	$-0.385251\pi$
$509$	15.9162	0.705472	0.352736	+	0.935723i	$0.385251\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−1.80244	−0.0795795
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−39.7356	−1.74757
$518$	0	0
$519$	6.15057	0.269980
$520$	0	0
$521$	−19.3893	−0.849460	−0.424730	−	0.905320i	$-0.639631\pi$
$521$	−19.3893	−0.849460	−0.424730	+	0.905320i	$0.639631\pi$
$522$	0	0
$523$	5.92314	0.259001	0.129500	−	0.991579i	$-0.458663\pi$
$523$	5.92314	0.259001	0.129500	+	0.991579i	$0.458663\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−3.95379	−0.172230
$528$	0	0
$529$	−12.8444	−0.558452
$530$	0	0
$531$	−19.8612	−0.861902
$532$	0	0
$533$	21.6784	0.938996
$534$	0	0
$535$	0	0
$536$	0	0
$537$	15.1744	0.654826
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−23.4343	−1.00752	−0.503759	−	0.863844i	$-0.668050\pi$
$541$	−23.4343	−1.00752	−0.503759	+	0.863844i	$0.668050\pi$
$542$	0	0
$543$	0.407905	0.0175049
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−40.9760	−1.75201	−0.876003	−	0.482306i	$-0.839799\pi$
$547$	−40.9760	−1.75201	−0.876003	+	0.482306i	$0.839799\pi$
$548$	0	0
$549$	−8.45157	−0.360704
$550$	0	0
$551$	−0.552586	−0.0235409
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−7.69824	−0.326185	−0.163092	−	0.986611i	$-0.552147\pi$
$557$	−7.69824	−0.326185	−0.163092	+	0.986611i	$0.552147\pi$
$558$	0	0
$559$	25.3664	1.07288
$560$	0	0
$561$	24.2938	1.02568
$562$	0	0
$563$	24.1993	1.01988	0.509939	−	0.860211i	$-0.329668\pi$
$563$	24.1993	1.01988	0.509939	+	0.860211i	$0.329668\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	16.3014	0.683392	0.341696	−	0.939811i	$-0.388999\pi$
$569$	16.3014	0.683392	0.341696	+	0.939811i	$0.388999\pi$
$570$	0	0
$571$	31.0604	1.29984	0.649918	−	0.760005i	$-0.274803\pi$
$571$	31.0604	1.29984	0.649918	+	0.760005i	$0.274803\pi$
$572$	0	0
$573$	−9.76184	−0.407807
$574$	0	0
$575$	0	0
$576$	0	0
$577$	6.33948	0.263916	0.131958	−	0.991255i	$-0.457874\pi$
$577$	6.33948	0.263916	0.131958	+	0.991255i	$0.457874\pi$
$578$	0	0
$579$	3.63345	0.151001
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−17.6293	−0.730132
$584$	0	0
$585$	0	0
$586$	0	0
$587$	14.8548	0.613122	0.306561	−	0.951851i	$-0.400822\pi$
$587$	14.8548	0.613122	0.306561	+	0.951851i	$0.400822\pi$
$588$	0	0
$589$	0.284799	0.0117349
$590$	0	0
$591$	−12.4712	−0.512996
$592$	0	0
$593$	12.2841	0.504446	0.252223	−	0.967669i	$-0.418838\pi$
$593$	12.2841	0.504446	0.252223	+	0.967669i	$0.418838\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	11.7556	0.481127
$598$	0	0
$599$	−22.8175	−0.932296	−0.466148	−	0.884707i	$-0.654359\pi$
$599$	−22.8175	−0.932296	−0.466148	+	0.884707i	$0.654359\pi$
$600$	0	0
$601$	−25.8612	−1.05490	−0.527450	−	0.849586i	$-0.676852\pi$
$601$	−25.8612	−1.05490	−0.527450	+	0.849586i	$0.676852\pi$
$602$	0	0
$603$	−11.6567	−0.474697
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−2.23081	−0.0905459	−0.0452730	−	0.998975i	$-0.514416\pi$
$607$	−2.23081	−0.0905459	−0.0452730	+	0.998975i	$0.514416\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−18.3381	−0.741880
$612$	0	0
$613$	−19.9320	−0.805047	−0.402524	−	0.915410i	$-0.631867\pi$
$613$	−19.9320	−0.805047	−0.402524	+	0.915410i	$0.631867\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	12.1435	0.488880	0.244440	−	0.969664i	$-0.421396\pi$
$617$	12.1435	0.488880	0.244440	+	0.969664i	$0.421396\pi$
$618$	0	0
$619$	−0.930105	−0.0373841	−0.0186920	−	0.999825i	$-0.505950\pi$
$619$	−0.930105	−0.0373841	−0.0186920	+	0.999825i	$0.505950\pi$
$620$	0	0
$621$	13.0157	0.522302
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−1.74993	−0.0698854
$628$	0	0
$629$	−65.8678	−2.62632
$630$	0	0
$631$	35.8314	1.42643	0.713214	−	0.700947i	$-0.247239\pi$
$631$	35.8314	1.42643	0.713214	+	0.700947i	$0.247239\pi$
$632$	0	0
$633$	−17.6977	−0.703421
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	−33.3800	−1.32049
$640$	0	0
$641$	−6.19676	−0.244757	−0.122379	−	0.992483i	$-0.539052\pi$
$641$	−6.19676	−0.244757	−0.122379	+	0.992483i	$0.539052\pi$
$642$	0	0
$643$	20.2885	0.800102	0.400051	−	0.916493i	$-0.368992\pi$
$643$	20.2885	0.800102	0.400051	+	0.916493i	$0.368992\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	23.8180	0.936381	0.468191	−	0.883627i	$-0.344906\pi$
$647$	23.8180	0.936381	0.468191	+	0.883627i	$0.344906\pi$
$648$	0	0
$649$	−43.0359	−1.68931
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−9.93646	−0.388844	−0.194422	−	0.980918i	$-0.562283\pi$
$653$	−9.93646	−0.388844	−0.194422	+	0.980918i	$0.562283\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−12.9705	−0.506026
$658$	0	0
$659$	45.4504	1.77050	0.885249	−	0.465118i	$-0.153988\pi$
$659$	45.4504	1.77050	0.885249	+	0.465118i	$0.153988\pi$
$660$	0	0
$661$	−5.54038	−0.215496	−0.107748	−	0.994178i	$-0.534364\pi$
$661$	−5.54038	−0.215496	−0.107748	+	0.994178i	$0.534364\pi$
$662$	0	0
$663$	11.2116	0.435424
$664$	0	0
$665$	0	0
$666$	0	0
$667$	3.99032	0.154506
$668$	0	0
$669$	16.1308	0.623654
$670$	0	0
$671$	−18.3132	−0.706972
$672$	0	0
$673$	−9.34880	−0.360370	−0.180185	−	0.983633i	$-0.557670\pi$
$673$	−9.34880	−0.360370	−0.180185	+	0.983633i	$0.557670\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	32.8344	1.26193	0.630965	−	0.775811i	$-0.282659\pi$
$677$	32.8344	1.26193	0.630965	+	0.775811i	$0.282659\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	12.4772	0.478128
$682$	0	0
$683$	13.0893	0.500847	0.250424	−	0.968136i	$-0.419430\pi$
$683$	13.0893	0.500847	0.250424	+	0.968136i	$0.419430\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	−9.57766	−0.365410
$688$	0	0
$689$	−8.13598	−0.309956
$690$	0	0
$691$	22.9796	0.874186	0.437093	−	0.899416i	$-0.356008\pi$
$691$	22.9796	0.874186	0.437093	+	0.899416i	$0.356008\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	54.5362	2.06570
$698$	0	0
$699$	11.5775	0.437901
$700$	0	0
$701$	3.12916	0.118187	0.0590934	−	0.998252i	$-0.481179\pi$
$701$	3.12916	0.118187	0.0590934	+	0.998252i	$0.481179\pi$
$702$	0	0
$703$	4.74459	0.178946
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	37.8712	1.42228	0.711141	−	0.703049i	$-0.248179\pi$
$709$	37.8712	1.42228	0.711141	+	0.703049i	$0.248179\pi$
$710$	0	0
$711$	−13.1616	−0.493599
$712$	0	0
$713$	−2.05658	−0.0770196
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−1.20729	−0.0450870
$718$	0	0
$719$	25.8182	0.962855	0.481427	−	0.876486i	$-0.340118\pi$
$719$	25.8182	0.962855	0.481427	+	0.876486i	$0.340118\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	−16.3925	−0.609645
$724$	0	0
$725$	0	0
$726$	0	0
$727$	24.1385	0.895248	0.447624	−	0.894222i	$-0.352270\pi$
$727$	24.1385	0.895248	0.447624	+	0.894222i	$0.352270\pi$
$728$	0	0
$729$	−1.11156	−0.0411690
$730$	0	0
$731$	63.8140	2.36025
$732$	0	0
$733$	10.9064	0.402837	0.201418	−	0.979505i	$-0.435445\pi$
$733$	10.9064	0.402837	0.201418	+	0.979505i	$0.435445\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−25.2581	−0.930394
$738$	0	0
$739$	−43.6153	−1.60442	−0.802208	−	0.597045i	$-0.796341\pi$
$739$	−43.6153	−1.60442	−0.802208	+	0.597045i	$0.796341\pi$
$740$	0	0
$741$	−0.807597	−0.0296678
$742$	0	0
$743$	−36.1676	−1.32686	−0.663431	−	0.748238i	$-0.730900\pi$
$743$	−36.1676	−1.32686	−0.663431	+	0.748238i	$0.730900\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	29.0731	1.06373
$748$	0	0
$749$	0	0
$750$	0	0
$751$	41.9165	1.52955	0.764777	−	0.644295i	$-0.222849\pi$
$751$	41.9165	1.52955	0.764777	+	0.644295i	$0.222849\pi$
$752$	0	0
$753$	6.19105	0.225614
$754$	0	0
$755$	0	0
$756$	0	0
$757$	27.3777	0.995060	0.497530	−	0.867447i	$-0.334241\pi$
$757$	27.3777	0.995060	0.497530	+	0.867447i	$0.334241\pi$
$758$	0	0
$759$	12.6365	0.458677
$760$	0	0
$761$	14.2133	0.515232	0.257616	−	0.966247i	$-0.417063\pi$
$761$	14.2133	0.515232	0.257616	+	0.966247i	$0.417063\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−19.8612	−0.717146
$768$	0	0
$769$	−38.1788	−1.37676	−0.688381	−	0.725349i	$-0.741678\pi$
$769$	−38.1788	−1.37676	−0.688381	+	0.725349i	$0.741678\pi$
$770$	0	0
$771$	5.49889	0.198038
$772$	0	0
$773$	29.9828	1.07841	0.539203	−	0.842176i	$-0.318726\pi$
$773$	29.9828	1.07841	0.539203	+	0.842176i	$0.318726\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	−3.92835	−0.140748
$780$	0	0
$781$	−72.3290	−2.58813
$782$	0	0
$783$	5.11411	0.182763
$784$	0	0
$785$	0	0
$786$	0	0
$787$	29.0783	1.03653	0.518265	−	0.855220i	$-0.326578\pi$
$787$	29.0783	1.03653	0.518265	+	0.855220i	$0.326578\pi$
$788$	0	0
$789$	11.9381	0.425008
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−8.45157	−0.300124
$794$	0	0
$795$	0	0
$796$	0	0
$797$	42.5726	1.50800	0.753999	−	0.656875i	$-0.228122\pi$
$797$	42.5726	1.50800	0.753999	+	0.656875i	$0.228122\pi$
$798$	0	0
$799$	−46.1329	−1.63207
$800$	0	0
$801$	20.9498	0.740226
$802$	0	0
$803$	−28.1049	−0.991799
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−8.32412	−0.293023
$808$	0	0
$809$	21.3774	0.751589	0.375794	−	0.926703i	$-0.377370\pi$
$809$	21.3774	0.751589	0.375794	+	0.926703i	$0.377370\pi$
$810$	0	0
$811$	−23.3902	−0.821342	−0.410671	−	0.911784i	$-0.634706\pi$
$811$	−23.3902	−0.821342	−0.410671	+	0.911784i	$0.634706\pi$
$812$	0	0
$813$	2.11981	0.0743451
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−4.59665	−0.160816
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−2.59645	−0.0906166	−0.0453083	−	0.998973i	$-0.514427\pi$
$821$	−2.59645	−0.0906166	−0.0453083	+	0.998973i	$0.514427\pi$
$822$	0	0
$823$	−11.3513	−0.395681	−0.197840	−	0.980234i	$-0.563393\pi$
$823$	−11.3513	−0.395681	−0.197840	+	0.980234i	$0.563393\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	28.8025	1.00156	0.500781	−	0.865574i	$-0.333046\pi$
$827$	28.8025	1.00156	0.500781	+	0.865574i	$0.333046\pi$
$828$	0	0
$829$	3.33167	0.115714	0.0578569	−	0.998325i	$-0.481573\pi$
$829$	3.33167	0.115714	0.0578569	+	0.998325i	$0.481573\pi$
$830$	0	0
$831$	1.08918	0.0377832
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−2.63578	−0.0911058
$838$	0	0
$839$	30.6414	1.05786	0.528929	−	0.848666i	$-0.322594\pi$
$839$	30.6414	1.05786	0.528929	+	0.848666i	$0.322594\pi$
$840$	0	0
$841$	−27.4321	−0.945936
$842$	0	0
$843$	−15.2300	−0.524549
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0	0
$848$	0	0
$849$	1.22488	0.0420377
$850$	0	0
$851$	−34.2615	−1.17447
$852$	0	0
$853$	11.0513	0.378390	0.189195	−	0.981940i	$-0.439412\pi$
$853$	11.0513	0.378390	0.189195	+	0.981940i	$0.439412\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−11.4894	−0.392469	−0.196235	−	0.980557i	$-0.562871\pi$
$857$	−11.4894	−0.392469	−0.196235	+	0.980557i	$0.562871\pi$
$858$	0	0
$859$	50.6348	1.72764	0.863819	−	0.503802i	$-0.168066\pi$
$859$	50.6348	1.72764	0.863819	+	0.503802i	$0.168066\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	51.3958	1.74953	0.874766	−	0.484545i	$-0.161015\pi$
$863$	51.3958	1.74953	0.874766	+	0.484545i	$0.161015\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	15.4307	0.524055
$868$	0	0
$869$	−28.5191	−0.967443
$870$	0	0
$871$	−11.6567	−0.394971
$872$	0	0
$873$	−33.2948	−1.12686
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−6.16086	−0.208038	−0.104019	−	0.994575i	$-0.533170\pi$
$877$	−6.16086	−0.208038	−0.104019	+	0.994575i	$0.533170\pi$
$878$	0	0
$879$	−15.4128	−0.519862
$880$	0	0
$881$	5.10894	0.172124	0.0860622	−	0.996290i	$-0.472572\pi$
$881$	5.10894	0.172124	0.0860622	+	0.996290i	$0.472572\pi$
$882$	0	0
$883$	7.26283	0.244414	0.122207	−	0.992505i	$-0.461003\pi$
$883$	7.26283	0.244414	0.122207	+	0.992505i	$0.461003\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	31.2210	1.04830	0.524150	−	0.851626i	$-0.324383\pi$
$887$	31.2210	1.04830	0.524150	+	0.851626i	$0.324383\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−22.3589	−0.749051
$892$	0	0
$893$	3.32304	0.111201
$894$	0	0
$895$	0	0
$896$	0	0
$897$	5.83180	0.194718
$898$	0	0
$899$	−0.808069	−0.0269506
$900$	0	0
$901$	−20.4676	−0.681874
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	28.2350	0.937526	0.468763	−	0.883324i	$-0.344700\pi$
$907$	28.2350	0.937526	0.468763	+	0.883324i	$0.344700\pi$
$908$	0	0
$909$	−28.4484	−0.943574
$910$	0	0
$911$	48.7700	1.61582	0.807911	−	0.589304i	$-0.200598\pi$
$911$	48.7700	1.61582	0.807911	+	0.589304i	$0.200598\pi$
$912$	0	0
$913$	62.9965	2.08488
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−43.8963	−1.44800	−0.724002	−	0.689797i	$-0.757700\pi$
$919$	−43.8963	−1.44800	−0.724002	+	0.689797i	$0.757700\pi$
$920$	0	0
$921$	−1.18740	−0.0391260
$922$	0	0
$923$	−33.3800	−1.09872
$924$	0	0
$925$	0	0
$926$	0	0
$927$	1.09736	0.0360420
$928$	0	0
$929$	33.9542	1.11400	0.557000	−	0.830513i	$-0.311952\pi$
$929$	33.9542	1.11400	0.557000	+	0.830513i	$0.311952\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	−15.6605	−0.512703
$934$	0	0
$935$	0	0
$936$	0	0
$937$	16.4081	0.536028	0.268014	−	0.963415i	$-0.413633\pi$
$937$	16.4081	0.536028	0.268014	+	0.963415i	$0.413633\pi$
$938$	0	0
$939$	17.2599	0.563255
$940$	0	0
$941$	−28.7404	−0.936912	−0.468456	−	0.883487i	$-0.655190\pi$
$941$	−28.7404	−0.936912	−0.468456	+	0.883487i	$0.655190\pi$
$942$	0	0
$943$	28.3673	0.923766
$944$	0	0
$945$	0	0
$946$	0	0
$947$	6.44139	0.209317	0.104659	−	0.994508i	$-0.466625\pi$
$947$	6.44139	0.209317	0.104659	+	0.994508i	$0.466625\pi$
$948$	0	0
$949$	−12.9705	−0.421039
$950$	0	0
$951$	−14.7616	−0.478677
$952$	0	0
$953$	−17.4655	−0.565762	−0.282881	−	0.959155i	$-0.591290\pi$
$953$	−17.4655	−0.565762	−0.282881	+	0.959155i	$0.591290\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	4.96513	0.160500
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−30.5835	−0.986565
$962$	0	0
$963$	1.12662	0.0363047
$964$	0	0
$965$	0	0
$966$	0	0
$967$	43.5117	1.39924	0.699620	−	0.714515i	$-0.253352\pi$
$967$	43.5117	1.39924	0.699620	+	0.714515i	$0.253352\pi$
$968$	0	0
$969$	−2.03166	−0.0652664
$970$	0	0
$971$	43.8608	1.40756	0.703780	−	0.710418i	$-0.251494\pi$
$971$	43.8608	1.40756	0.703780	+	0.710418i	$0.251494\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−1.91400	−0.0612343	−0.0306171	−	0.999531i	$-0.509747\pi$
$977$	−1.91400	−0.0612343	−0.0306171	+	0.999531i	$0.509747\pi$
$978$	0	0
$979$	45.3948	1.45083
$980$	0	0
$981$	−5.85961	−0.187083
$982$	0	0
$983$	4.03107	0.128571	0.0642855	−	0.997932i	$-0.479523\pi$
$983$	4.03107	0.128571	0.0642855	+	0.997932i	$0.479523\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	33.1932	1.05548
$990$	0	0
$991$	36.8258	1.16981	0.584905	−	0.811102i	$-0.301132\pi$
$991$	36.8258	1.16981	0.584905	+	0.811102i	$0.301132\pi$
$992$	0	0
$993$	−5.22770	−0.165896
$994$	0	0
$995$	0	0
$996$	0	0
$997$	39.7812	1.25988	0.629942	−	0.776642i	$-0.283079\pi$
$997$	39.7812	1.25988	0.629942	+	0.776642i	$0.283079\pi$
$998$	0	0
$999$	−43.9106	−1.38927

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9800.2.a.cy.1.4		6
5.2	odd	4		1960.2.g.e.1569.5		12
5.3	odd	4		1960.2.g.e.1569.8		12
5.4	even	2		9800.2.a.cw.1.3		6
7.3	odd	6		1400.2.q.o.401.4		12
7.5	odd	6		1400.2.q.o.1201.4		12
7.6	odd	2		9800.2.a.cv.1.3		6
35.3	even	12		280.2.bg.a.9.5	✓	24
35.12	even	12		280.2.bg.a.249.5	yes	24
35.13	even	4		1960.2.g.f.1569.5		12
35.17	even	12		280.2.bg.a.9.8	yes	24
35.19	odd	6		1400.2.q.n.1201.3		12
35.24	odd	6		1400.2.q.n.401.3		12
35.27	even	4		1960.2.g.f.1569.8		12
35.33	even	12		280.2.bg.a.249.8	yes	24
35.34	odd	2		9800.2.a.cx.1.4		6
140.3	odd	12		560.2.bw.f.289.8		24
140.47	odd	12		560.2.bw.f.529.8		24
140.87	odd	12		560.2.bw.f.289.5		24
140.103	odd	12		560.2.bw.f.529.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bg.a.9.5	✓	24	35.3	even	12
280.2.bg.a.9.8	yes	24	35.17	even	12
280.2.bg.a.249.5	yes	24	35.12	even	12
280.2.bg.a.249.8	yes	24	35.33	even	12
560.2.bw.f.289.5		24	140.87	odd	12
560.2.bw.f.289.8		24	140.3	odd	12
560.2.bw.f.529.5		24	140.103	odd	12
560.2.bw.f.529.8		24	140.47	odd	12
1400.2.q.n.401.3		12	35.24	odd	6
1400.2.q.n.1201.3		12	35.19	odd	6
1400.2.q.o.401.4		12	7.3	odd	6
1400.2.q.o.1201.4		12	7.5	odd	6
1960.2.g.e.1569.5		12	5.2	odd	4
1960.2.g.e.1569.8		12	5.3	odd	4
1960.2.g.f.1569.5		12	35.13	even	4
1960.2.g.f.1569.8		12	35.27	even	4
9800.2.a.cv.1.3		6	7.6	odd	2
9800.2.a.cw.1.3		6	5.4	even	2
9800.2.a.cx.1.4		6	35.34	odd	2
9800.2.a.cy.1.4		6	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:	\( N \)	\(=\)	\( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9800.a (trivial)

\(f(q)\)	\(=\)	\(q+0.751428 q^{3} -2.43536 q^{9} +O(q^{10})\)	\(q+0.751428 q^{3} -2.43536 q^{9} -5.27702 q^{11} -2.43536 q^{13} -6.12660 q^{17} +0.441311 q^{19} -3.18678 q^{23} -4.08428 q^{27} -1.25215 q^{29} +0.645348 q^{31} -3.96530 q^{33} +10.7511 q^{37} -1.82999 q^{39} -8.90154 q^{41} -10.4159 q^{43} +7.52994 q^{47} -4.60370 q^{51} +3.34077 q^{53} +0.331613 q^{57} +8.15535 q^{59} +3.47036 q^{61} +4.78644 q^{67} -2.39464 q^{69} +13.7064 q^{71} +5.32590 q^{73} +5.40439 q^{79} +4.23703 q^{81} -11.9379 q^{83} -0.940897 q^{87} -8.60237 q^{89} +0.484932 q^{93} +13.6714 q^{97} +12.8514 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{3} + 7 q^{9}+O(q^{10}) \) 6 * q + q^3 + 7 * q^9	\( 6 q + q^{3} + 7 q^{9} + q^{11} + 7 q^{13} + 4 q^{17} + 5 q^{19} + 6 q^{23} + 7 q^{27} - 3 q^{29} + 2 q^{31} + 16 q^{33} + 9 q^{37} + 10 q^{39} - 6 q^{41} - 3 q^{43} + 27 q^{47} - 5 q^{53} - 26 q^{57} + 24 q^{59} - 9 q^{61} + 17 q^{67} - 15 q^{69} + 4 q^{71} + 18 q^{73} - 22 q^{79} - 6 q^{81} + 9 q^{83} + 39 q^{87} - 15 q^{89} + 10 q^{93} + 12 q^{97} + 11 q^{99}+O(q^{100}) \) 6 * q + q^3 + 7 * q^9 + q^11 + 7 * q^13 + 4 * q^17 + 5 * q^19 + 6 * q^23 + 7 * q^27 - 3 * q^29 + 2 * q^31 + 16 * q^33 + 9 * q^37 + 10 * q^39 - 6 * q^41 - 3 * q^43 + 27 * q^47 - 5 * q^53 - 26 * q^57 + 24 * q^59 - 9 * q^61 + 17 * q^67 - 15 * q^69 + 4 * q^71 + 18 * q^73 - 22 * q^79 - 6 * q^81 + 9 * q^83 + 39 * q^87 - 15 * q^89 + 10 * q^93 + 12 * q^97 + 11 * q^99

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