LMFDB - Embedded newform 9016.2.a.bk.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9016,2,Mod(1,9016)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9016, 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("9016.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9016 = 2^{3} \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9016.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:	$71.9931224624$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 4 x^{10} - 14 x^{9} + 61 x^{8} + 71 x^{7} - 343 x^{6} - 152 x^{5} + 867 x^{4} + 102 x^{3} + \cdots + 243 $ x^11 - 4x^10 - 14x^9 + 61x^8 + 71x^7 - 343x^6 - 152x^5 + 867x^4 + 102x^3 - 918x^2 + 35x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1288)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.73452$ of defining polynomial
Character	$\chi$	$=$	9016.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.73452 q^{3} +3.07461 q^{5} +4.47758 q^{9} +O(q^{10})$	$q-2.73452 q^{3} +3.07461 q^{5} +4.47758 q^{9} -0.693180 q^{11} -1.77506 q^{13} -8.40757 q^{15} -1.86686 q^{17} -2.98886 q^{19} -1.00000 q^{23} +4.45322 q^{25} -4.04046 q^{27} +2.84122 q^{29} +1.48846 q^{31} +1.89551 q^{33} +1.47714 q^{37} +4.85394 q^{39} +10.3594 q^{41} +0.231614 q^{43} +13.7668 q^{45} -7.58091 q^{47} +5.10497 q^{51} +4.64827 q^{53} -2.13126 q^{55} +8.17309 q^{57} -8.95999 q^{59} +2.24477 q^{61} -5.45762 q^{65} +2.85893 q^{67} +2.73452 q^{69} -11.1511 q^{71} -3.50272 q^{73} -12.1774 q^{75} +7.42715 q^{79} -2.38404 q^{81} -5.90127 q^{83} -5.73987 q^{85} -7.76935 q^{87} -17.1563 q^{89} -4.07022 q^{93} -9.18958 q^{95} -4.64667 q^{97} -3.10377 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 4 q^{3} - 3 q^{5} + 11 q^{9}+O(q^{10}) $ 11 * q - 4 * q^3 - 3 * q^5 + 11 * q^9	$ 11 q - 4 q^{3} - 3 q^{5} + 11 q^{9} + 13 q^{13} - 7 q^{17} - 8 q^{19} - 11 q^{23} + 6 q^{25} - 25 q^{27} - 3 q^{29} - 12 q^{31} + 2 q^{33} - q^{37} - 21 q^{39} - 12 q^{41} + 9 q^{43} - 19 q^{45} - 17 q^{47} + 19 q^{51} - 5 q^{53} - 21 q^{55} + 11 q^{57} - 33 q^{59} + 15 q^{61} - 9 q^{65} - 5 q^{67} + 4 q^{69} - 9 q^{71} - 5 q^{73} - 44 q^{75} + 11 q^{79} - 13 q^{81} - 51 q^{83} + 33 q^{85} - 4 q^{87} - 26 q^{89} + 6 q^{93} - 19 q^{95} - 21 q^{97} + 15 q^{99}+O(q^{100}) $ 11 * q - 4 * q^3 - 3 * q^5 + 11 * q^9 + 13 * q^13 - 7 * q^17 - 8 * q^19 - 11 * q^23 + 6 * q^25 - 25 * q^27 - 3 * q^29 - 12 * q^31 + 2 * q^33 - q^37 - 21 * q^39 - 12 * q^41 + 9 * q^43 - 19 * q^45 - 17 * q^47 + 19 * q^51 - 5 * q^53 - 21 * q^55 + 11 * q^57 - 33 * q^59 + 15 * q^61 - 9 * q^65 - 5 * q^67 + 4 * q^69 - 9 * q^71 - 5 * q^73 - 44 * q^75 + 11 * q^79 - 13 * q^81 - 51 * q^83 + 33 * q^85 - 4 * q^87 - 26 * q^89 + 6 * q^93 - 19 * q^95 - 21 * q^97 + 15 * 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
$3$	−2.73452	−1.57877	−0.789387	−	0.613896i	$-0.789601\pi$
$3$	−2.73452	−1.57877	−0.789387	+	0.613896i	$0.789601\pi$
$4$	0	0
$5$	3.07461	1.37501	0.687503	−	0.726181i	$-0.258707\pi$
$5$	3.07461	1.37501	0.687503	+	0.726181i	$0.258707\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	4.47758	1.49253
$10$	0	0
$11$	−0.693180	−0.209002	−0.104501	−	0.994525i	$-0.533324\pi$
$11$	−0.693180	−0.209002	−0.104501	+	0.994525i	$0.533324\pi$
$12$	0	0
$13$	−1.77506	−0.492314	−0.246157	−	0.969230i	$-0.579168\pi$
$13$	−1.77506	−0.492314	−0.246157	+	0.969230i	$0.579168\pi$
$14$	0	0
$15$	−8.40757	−2.17082
$16$	0	0
$17$	−1.86686	−0.452781	−0.226390	−	0.974037i	$-0.572693\pi$
$17$	−1.86686	−0.452781	−0.226390	+	0.974037i	$0.572693\pi$
$18$	0	0
$19$	−2.98886	−0.685692	−0.342846	−	0.939392i	$-0.611391\pi$
$19$	−2.98886	−0.685692	−0.342846	+	0.939392i	$0.611391\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0	0
$25$	4.45322	0.890643
$26$	0	0
$27$	−4.04046	−0.777586
$28$	0	0
$29$	2.84122	0.527601	0.263800	−	0.964577i	$-0.415024\pi$
$29$	2.84122	0.527601	0.263800	+	0.964577i	$0.415024\pi$
$30$	0	0
$31$	1.48846	0.267336	0.133668	−	0.991026i	$-0.457324\pi$
$31$	1.48846	0.267336	0.133668	+	0.991026i	$0.457324\pi$
$32$	0	0
$33$	1.89551	0.329966
$34$	0	0
$35$	0	0
$36$	0	0
$37$	1.47714	0.242840	0.121420	−	0.992601i	$-0.461255\pi$
$37$	1.47714	0.242840	0.121420	+	0.992601i	$0.461255\pi$
$38$	0	0
$39$	4.85394	0.777252
$40$	0	0
$41$	10.3594	1.61787	0.808935	−	0.587898i	$-0.200044\pi$
$41$	10.3594	1.61787	0.808935	+	0.587898i	$0.200044\pi$
$42$	0	0
$43$	0.231614	0.0353208	0.0176604	−	0.999844i	$-0.494378\pi$
$43$	0.231614	0.0353208	0.0176604	+	0.999844i	$0.494378\pi$
$44$	0	0
$45$	13.7668	2.05223
$46$	0	0
$47$	−7.58091	−1.10579	−0.552894	−	0.833251i	$-0.686477\pi$
$47$	−7.58091	−1.10579	−0.552894	+	0.833251i	$0.686477\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	5.10497	0.714838
$52$	0	0
$53$	4.64827	0.638489	0.319244	−	0.947672i	$-0.396571\pi$
$53$	4.64827	0.638489	0.319244	+	0.947672i	$0.396571\pi$
$54$	0	0
$55$	−2.13126	−0.287379
$56$	0	0
$57$	8.17309	1.08255
$58$	0	0
$59$	−8.95999	−1.16649	−0.583246	−	0.812296i	$-0.698217\pi$
$59$	−8.95999	−1.16649	−0.583246	+	0.812296i	$0.698217\pi$
$60$	0	0
$61$	2.24477	0.287413	0.143706	−	0.989620i	$-0.454098\pi$
$61$	2.24477	0.287413	0.143706	+	0.989620i	$0.454098\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	−5.45762	−0.676935
$66$	0	0
$67$	2.85893	0.349274	0.174637	−	0.984633i	$-0.444125\pi$
$67$	2.85893	0.349274	0.174637	+	0.984633i	$0.444125\pi$
$68$	0	0
$69$	2.73452	0.329197
$70$	0	0
$71$	−11.1511	−1.32340	−0.661698	−	0.749771i	$-0.730164\pi$
$71$	−11.1511	−1.32340	−0.661698	+	0.749771i	$0.730164\pi$
$72$	0	0
$73$	−3.50272	−0.409962	−0.204981	−	0.978766i	$-0.565713\pi$
$73$	−3.50272	−0.409962	−0.204981	+	0.978766i	$0.565713\pi$
$74$	0	0
$75$	−12.1774	−1.40612
$76$	0	0
$77$	0	0
$78$	0	0
$79$	7.42715	0.835619	0.417810	−	0.908535i	$-0.362798\pi$
$79$	7.42715	0.835619	0.417810	+	0.908535i	$0.362798\pi$
$80$	0	0
$81$	−2.38404	−0.264893
$82$	0	0
$83$	−5.90127	−0.647749	−0.323874	−	0.946100i	$-0.604986\pi$
$83$	−5.90127	−0.647749	−0.323874	+	0.946100i	$0.604986\pi$
$84$	0	0
$85$	−5.73987	−0.622577
$86$	0	0
$87$	−7.76935	−0.832962
$88$	0	0
$89$	−17.1563	−1.81856	−0.909280	−	0.416184i	$-0.863367\pi$
$89$	−17.1563	−1.81856	−0.909280	+	0.416184i	$0.863367\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	−4.07022	−0.422063
$94$	0	0
$95$	−9.18958	−0.942831
$96$	0	0
$97$	−4.64667	−0.471798	−0.235899	−	0.971778i	$-0.575804\pi$
$97$	−4.64667	−0.471798	−0.235899	+	0.971778i	$0.575804\pi$
$98$	0	0
$99$	−3.10377	−0.311940
$100$	0	0
$101$	3.38797	0.337116	0.168558	−	0.985692i	$-0.446089\pi$
$101$	3.38797	0.337116	0.168558	+	0.985692i	$0.446089\pi$
$102$	0	0
$103$	5.76358	0.567902	0.283951	−	0.958839i	$-0.408355\pi$
$103$	5.76358	0.567902	0.283951	+	0.958839i	$0.408355\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	19.1117	1.84760	0.923799	−	0.382877i	$-0.125067\pi$
$107$	19.1117	1.84760	0.923799	+	0.382877i	$0.125067\pi$
$108$	0	0
$109$	−18.9503	−1.81511	−0.907555	−	0.419934i	$-0.862053\pi$
$109$	−18.9503	−1.81511	−0.907555	+	0.419934i	$0.862053\pi$
$110$	0	0
$111$	−4.03927	−0.383390
$112$	0	0
$113$	13.1480	1.23686	0.618430	−	0.785840i	$-0.287769\pi$
$113$	13.1480	1.23686	0.618430	+	0.785840i	$0.287769\pi$
$114$	0	0
$115$	−3.07461	−0.286709
$116$	0	0
$117$	−7.94798	−0.734791
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−10.5195	−0.956318
$122$	0	0
$123$	−28.3280	−2.55425
$124$	0	0
$125$	−1.68115	−0.150366
$126$	0	0
$127$	−14.7795	−1.31147	−0.655735	−	0.754991i	$-0.727641\pi$
$127$	−14.7795	−1.31147	−0.655735	+	0.754991i	$0.727641\pi$
$128$	0	0
$129$	−0.633353	−0.0557636
$130$	0	0
$131$	−21.0852	−1.84222	−0.921112	−	0.389298i	$-0.872718\pi$
$131$	−21.0852	−1.84222	−0.921112	+	0.389298i	$0.872718\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	−12.4228	−1.06919
$136$	0	0
$137$	18.4345	1.57496	0.787482	−	0.616337i	$-0.211384\pi$
$137$	18.4345	1.57496	0.787482	+	0.616337i	$0.211384\pi$
$138$	0	0
$139$	9.44182	0.800845	0.400422	−	0.916331i	$-0.368863\pi$
$139$	9.44182	0.800845	0.400422	+	0.916331i	$0.368863\pi$
$140$	0	0
$141$	20.7301	1.74579
$142$	0	0
$143$	1.23044	0.102894
$144$	0	0
$145$	8.73563	0.725454
$146$	0	0
$147$	0	0
$148$	0	0
$149$	16.7357	1.37104	0.685519	−	0.728054i	$-0.259575\pi$
$149$	16.7357	1.37104	0.685519	+	0.728054i	$0.259575\pi$
$150$	0	0
$151$	−1.29907	−0.105716	−0.0528582	−	0.998602i	$-0.516833\pi$
$151$	−1.29907	−0.105716	−0.0528582	+	0.998602i	$0.516833\pi$
$152$	0	0
$153$	−8.35902	−0.675787
$154$	0	0
$155$	4.57644	0.367588
$156$	0	0
$157$	−5.09377	−0.406527	−0.203264	−	0.979124i	$-0.565155\pi$
$157$	−5.09377	−0.406527	−0.203264	+	0.979124i	$0.565155\pi$
$158$	0	0
$159$	−12.7108	−1.00803
$160$	0	0
$161$	0	0
$162$	0	0
$163$	19.3829	1.51818	0.759091	−	0.650985i	$-0.225644\pi$
$163$	19.3829	1.51818	0.759091	+	0.650985i	$0.225644\pi$
$164$	0	0
$165$	5.82795	0.453706
$166$	0	0
$167$	2.76998	0.214348	0.107174	−	0.994240i	$-0.465820\pi$
$167$	2.76998	0.214348	0.107174	+	0.994240i	$0.465820\pi$
$168$	0	0
$169$	−9.84915	−0.757627
$170$	0	0
$171$	−13.3829	−1.02341
$172$	0	0
$173$	−10.7104	−0.814296	−0.407148	−	0.913362i	$-0.633477\pi$
$173$	−10.7104	−0.814296	−0.407148	+	0.913362i	$0.633477\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	24.5012	1.84163
$178$	0	0
$179$	−20.9897	−1.56884	−0.784422	−	0.620228i	$-0.787040\pi$
$179$	−20.9897	−1.56884	−0.784422	+	0.620228i	$0.787040\pi$
$180$	0	0
$181$	2.47965	0.184311	0.0921555	−	0.995745i	$-0.470624\pi$
$181$	2.47965	0.184311	0.0921555	+	0.995745i	$0.470624\pi$
$182$	0	0
$183$	−6.13835	−0.453760
$184$	0	0
$185$	4.54163	0.333907
$186$	0	0
$187$	1.29407	0.0946319
$188$	0	0
$189$	0	0
$190$	0	0
$191$	16.2921	1.17886	0.589428	−	0.807821i	$-0.299353\pi$
$191$	16.2921	1.17886	0.589428	+	0.807821i	$0.299353\pi$
$192$	0	0
$193$	15.5476	1.11914	0.559569	−	0.828784i	$-0.310967\pi$
$193$	15.5476	1.11914	0.559569	+	0.828784i	$0.310967\pi$
$194$	0	0
$195$	14.9240	1.06873
$196$	0	0
$197$	12.6426	0.900746	0.450373	−	0.892841i	$-0.351291\pi$
$197$	12.6426	0.900746	0.450373	+	0.892841i	$0.351291\pi$
$198$	0	0
$199$	0.0160594	0.00113842	0.000569212	−	1.00000i	$-0.499819\pi$
$199$	0.0160594	0.00113842	0.000569212		1.00000i	$0.499819\pi$
$200$	0	0
$201$	−7.81778	−0.551424
$202$	0	0
$203$	0	0
$204$	0	0
$205$	31.8512	2.22458
$206$	0	0
$207$	−4.47758	−0.311213
$208$	0	0
$209$	2.07182	0.143311
$210$	0	0
$211$	−15.0228	−1.03421	−0.517107	−	0.855921i	$-0.672991\pi$
$211$	−15.0228	−1.03421	−0.517107	+	0.855921i	$0.672991\pi$
$212$	0	0
$213$	30.4929	2.08934
$214$	0	0
$215$	0.712123	0.0485664
$216$	0	0
$217$	0	0
$218$	0	0
$219$	9.57824	0.647237
$220$	0	0
$221$	3.31380	0.222910
$222$	0	0
$223$	−2.76518	−0.185170	−0.0925852	−	0.995705i	$-0.529513\pi$
$223$	−2.76518	−0.185170	−0.0925852	+	0.995705i	$0.529513\pi$
$224$	0	0
$225$	19.9396	1.32931
$226$	0	0
$227$	−12.0027	−0.796646	−0.398323	−	0.917245i	$-0.630408\pi$
$227$	−12.0027	−0.796646	−0.398323	+	0.917245i	$0.630408\pi$
$228$	0	0
$229$	17.0070	1.12385	0.561927	−	0.827187i	$-0.310060\pi$
$229$	17.0070	1.12385	0.561927	+	0.827187i	$0.310060\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−16.0758	−1.05316	−0.526580	−	0.850126i	$-0.676526\pi$
$233$	−16.0758	−1.05316	−0.526580	+	0.850126i	$0.676526\pi$
$234$	0	0
$235$	−23.3083	−1.52047
$236$	0	0
$237$	−20.3096	−1.31925
$238$	0	0
$239$	−7.93261	−0.513118	−0.256559	−	0.966529i	$-0.582589\pi$
$239$	−7.93261	−0.513118	−0.256559	+	0.966529i	$0.582589\pi$
$240$	0	0
$241$	−26.7362	−1.72223	−0.861116	−	0.508408i	$-0.830234\pi$
$241$	−26.7362	−1.72223	−0.861116	+	0.508408i	$0.830234\pi$
$242$	0	0
$243$	18.6406	1.19579
$244$	0	0
$245$	0	0
$246$	0	0
$247$	5.30542	0.337576
$248$	0	0
$249$	16.1371	1.02265
$250$	0	0
$251$	7.37655	0.465604	0.232802	−	0.972524i	$-0.425211\pi$
$251$	7.37655	0.465604	0.232802	+	0.972524i	$0.425211\pi$
$252$	0	0
$253$	0.693180	0.0435798
$254$	0	0
$255$	15.6958	0.982908
$256$	0	0
$257$	−15.5004	−0.966888	−0.483444	−	0.875375i	$-0.660614\pi$
$257$	−15.5004	−0.966888	−0.483444	+	0.875375i	$0.660614\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	12.7218	0.787458
$262$	0	0
$263$	−5.64590	−0.348141	−0.174071	−	0.984733i	$-0.555692\pi$
$263$	−5.64590	−0.348141	−0.174071	+	0.984733i	$0.555692\pi$
$264$	0	0
$265$	14.2916	0.877926
$266$	0	0
$267$	46.9141	2.87110
$268$	0	0
$269$	−29.4641	−1.79646	−0.898229	−	0.439527i	$-0.855146\pi$
$269$	−29.4641	−1.79646	−0.898229	+	0.439527i	$0.855146\pi$
$270$	0	0
$271$	−21.0757	−1.28026	−0.640130	−	0.768266i	$-0.721120\pi$
$271$	−21.0757	−1.28026	−0.640130	+	0.768266i	$0.721120\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	−3.08688	−0.186146
$276$	0	0
$277$	0.727357	0.0437026	0.0218513	−	0.999761i	$-0.493044\pi$
$277$	0.727357	0.0437026	0.0218513	+	0.999761i	$0.493044\pi$
$278$	0	0
$279$	6.66470	0.399005
$280$	0	0
$281$	24.5291	1.46328	0.731642	−	0.681689i	$-0.238754\pi$
$281$	24.5291	1.46328	0.731642	+	0.681689i	$0.238754\pi$
$282$	0	0
$283$	2.15836	0.128301	0.0641507	−	0.997940i	$-0.479566\pi$
$283$	2.15836	0.128301	0.0641507	+	0.997940i	$0.479566\pi$
$284$	0	0
$285$	25.1290	1.48852
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−13.5148	−0.794989
$290$	0	0
$291$	12.7064	0.744863
$292$	0	0
$293$	19.2860	1.12670	0.563350	−	0.826218i	$-0.309512\pi$
$293$	19.2860	1.12670	0.563350	+	0.826218i	$0.309512\pi$
$294$	0	0
$295$	−27.5485	−1.60393
$296$	0	0
$297$	2.80076	0.162517
$298$	0	0
$299$	1.77506	0.102655
$300$	0	0
$301$	0	0
$302$	0	0
$303$	−9.26446	−0.532229
$304$	0	0
$305$	6.90178	0.395195
$306$	0	0
$307$	−19.4602	−1.11065	−0.555327	−	0.831632i	$-0.687407\pi$
$307$	−19.4602	−1.11065	−0.555327	+	0.831632i	$0.687407\pi$
$308$	0	0
$309$	−15.7606	−0.896589
$310$	0	0
$311$	28.8979	1.63865	0.819326	−	0.573328i	$-0.194348\pi$
$311$	28.8979	1.63865	0.819326	+	0.573328i	$0.194348\pi$
$312$	0	0
$313$	−8.48074	−0.479360	−0.239680	−	0.970852i	$-0.577042\pi$
$313$	−8.48074	−0.479360	−0.239680	+	0.970852i	$0.577042\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	4.59314	0.257976	0.128988	−	0.991646i	$-0.458827\pi$
$317$	4.59314	0.257976	0.128988	+	0.991646i	$0.458827\pi$
$318$	0	0
$319$	−1.96947	−0.110269
$320$	0	0
$321$	−52.2613	−2.91694
$322$	0	0
$323$	5.57980	0.310468
$324$	0	0
$325$	−7.90474	−0.438476
$326$	0	0
$327$	51.8199	2.86565
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−27.0259	−1.48548	−0.742740	−	0.669580i	$-0.766474\pi$
$331$	−27.0259	−1.48548	−0.742740	+	0.669580i	$0.766474\pi$
$332$	0	0
$333$	6.61401	0.362446
$334$	0	0
$335$	8.79008	0.480254
$336$	0	0
$337$	−2.66076	−0.144941	−0.0724703	−	0.997371i	$-0.523088\pi$
$337$	−2.66076	−0.144941	−0.0724703	+	0.997371i	$0.523088\pi$
$338$	0	0
$339$	−35.9534	−1.95272
$340$	0	0
$341$	−1.03177	−0.0558736
$342$	0	0
$343$	0	0
$344$	0	0
$345$	8.40757	0.452648
$346$	0	0
$347$	25.6545	1.37721	0.688603	−	0.725138i	$-0.258224\pi$
$347$	25.6545	1.37721	0.688603	+	0.725138i	$0.258224\pi$
$348$	0	0
$349$	21.1851	1.13401	0.567007	−	0.823713i	$-0.308101\pi$
$349$	21.1851	1.13401	0.567007	+	0.823713i	$0.308101\pi$
$350$	0	0
$351$	7.17206	0.382816
$352$	0	0
$353$	−5.20753	−0.277169	−0.138584	−	0.990351i	$-0.544255\pi$
$353$	−5.20753	−0.277169	−0.138584	+	0.990351i	$0.544255\pi$
$354$	0	0
$355$	−34.2854	−1.81968
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−30.5853	−1.61423	−0.807116	−	0.590392i	$-0.798973\pi$
$359$	−30.5853	−1.61423	−0.807116	+	0.590392i	$0.798973\pi$
$360$	0	0
$361$	−10.0667	−0.529827
$362$	0	0
$363$	28.7657	1.50981
$364$	0	0
$365$	−10.7695	−0.563701
$366$	0	0
$367$	−15.3892	−0.803311	−0.401655	−	0.915791i	$-0.631565\pi$
$367$	−15.3892	−0.803311	−0.401655	+	0.915791i	$0.631565\pi$
$368$	0	0
$369$	46.3851	2.41471
$370$	0	0
$371$	0	0
$372$	0	0
$373$	4.01079	0.207671	0.103835	−	0.994595i	$-0.466889\pi$
$373$	4.01079	0.207671	0.103835	+	0.994595i	$0.466889\pi$
$374$	0	0
$375$	4.59712	0.237394
$376$	0	0
$377$	−5.04334	−0.259745
$378$	0	0
$379$	31.5721	1.62175	0.810876	−	0.585218i	$-0.198991\pi$
$379$	31.5721	1.62175	0.810876	+	0.585218i	$0.198991\pi$
$380$	0	0
$381$	40.4148	2.07051
$382$	0	0
$383$	−16.8450	−0.860739	−0.430369	−	0.902653i	$-0.641617\pi$
$383$	−16.8450	−0.860739	−0.430369	+	0.902653i	$0.641617\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	1.03707	0.0527172
$388$	0	0
$389$	−18.2527	−0.925448	−0.462724	−	0.886502i	$-0.653128\pi$
$389$	−18.2527	−0.925448	−0.462724	+	0.886502i	$0.653128\pi$
$390$	0	0
$391$	1.86686	0.0944113
$392$	0	0
$393$	57.6579	2.90845
$394$	0	0
$395$	22.8356	1.14898
$396$	0	0
$397$	5.82087	0.292141	0.146071	−	0.989274i	$-0.453337\pi$
$397$	5.82087	0.292141	0.146071	+	0.989274i	$0.453337\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−3.24590	−0.162093	−0.0810463	−	0.996710i	$-0.525826\pi$
$401$	−3.24590	−0.162093	−0.0810463	+	0.996710i	$0.525826\pi$
$402$	0	0
$403$	−2.64211	−0.131613
$404$	0	0
$405$	−7.32998	−0.364230
$406$	0	0
$407$	−1.02392	−0.0507540
$408$	0	0
$409$	−17.8913	−0.884670	−0.442335	−	0.896850i	$-0.645850\pi$
$409$	−17.8913	−0.884670	−0.442335	+	0.896850i	$0.645850\pi$
$410$	0	0
$411$	−50.4094	−2.48651
$412$	0	0
$413$	0	0
$414$	0	0
$415$	−18.1441	−0.890659
$416$	0	0
$417$	−25.8188	−1.26435
$418$	0	0
$419$	1.97879	0.0966703	0.0483352	−	0.998831i	$-0.484608\pi$
$419$	1.97879	0.0966703	0.0483352	+	0.998831i	$0.484608\pi$
$420$	0	0
$421$	6.63548	0.323394	0.161697	−	0.986840i	$-0.448303\pi$
$421$	6.63548	0.323394	0.161697	+	0.986840i	$0.448303\pi$
$422$	0	0
$423$	−33.9441	−1.65042
$424$	0	0
$425$	−8.31355	−0.403266
$426$	0	0
$427$	0	0
$428$	0	0
$429$	−3.36465	−0.162447
$430$	0	0
$431$	−15.7921	−0.760678	−0.380339	−	0.924847i	$-0.624193\pi$
$431$	−15.7921	−0.760678	−0.380339	+	0.924847i	$0.624193\pi$
$432$	0	0
$433$	−18.8432	−0.905546	−0.452773	−	0.891626i	$-0.649565\pi$
$433$	−18.8432	−0.905546	−0.452773	+	0.891626i	$0.649565\pi$
$434$	0	0
$435$	−23.8877	−1.14533
$436$	0	0
$437$	2.98886	0.142977
$438$	0	0
$439$	−19.6058	−0.935732	−0.467866	−	0.883799i	$-0.654977\pi$
$439$	−19.6058	−0.935732	−0.467866	+	0.883799i	$0.654977\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	0.896249	0.0425821	0.0212910	−	0.999773i	$-0.493222\pi$
$443$	0.896249	0.0425821	0.0212910	+	0.999773i	$0.493222\pi$
$444$	0	0
$445$	−52.7488	−2.50053
$446$	0	0
$447$	−45.7639	−2.16456
$448$	0	0
$449$	38.2519	1.80522	0.902610	−	0.430460i	$-0.141649\pi$
$449$	38.2519	1.80522	0.902610	+	0.430460i	$0.141649\pi$
$450$	0	0
$451$	−7.18094	−0.338137
$452$	0	0
$453$	3.55231	0.166902
$454$	0	0
$455$	0	0
$456$	0	0
$457$	10.2733	0.480565	0.240282	−	0.970703i	$-0.422760\pi$
$457$	10.2733	0.480565	0.240282	+	0.970703i	$0.422760\pi$
$458$	0	0
$459$	7.54298	0.352076
$460$	0	0
$461$	−0.596189	−0.0277673	−0.0138836	−	0.999904i	$-0.504419\pi$
$461$	−0.596189	−0.0277673	−0.0138836	+	0.999904i	$0.504419\pi$
$462$	0	0
$463$	−4.00903	−0.186316	−0.0931578	−	0.995651i	$-0.529696\pi$
$463$	−4.00903	−0.186316	−0.0931578	+	0.995651i	$0.529696\pi$
$464$	0	0
$465$	−12.5143	−0.580339
$466$	0	0
$467$	−27.0273	−1.25067	−0.625337	−	0.780355i	$-0.715039\pi$
$467$	−27.0273	−1.25067	−0.625337	+	0.780355i	$0.715039\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	13.9290	0.641814
$472$	0	0
$473$	−0.160550	−0.00738211
$474$	0	0
$475$	−13.3100	−0.610707
$476$	0	0
$477$	20.8130	0.952961
$478$	0	0
$479$	1.30881	0.0598008	0.0299004	−	0.999553i	$-0.490481\pi$
$479$	1.30881	0.0598008	0.0299004	+	0.999553i	$0.490481\pi$
$480$	0	0
$481$	−2.62202	−0.119554
$482$	0	0
$483$	0	0
$484$	0	0
$485$	−14.2867	−0.648726
$486$	0	0
$487$	20.9026	0.947187	0.473593	−	0.880744i	$-0.342957\pi$
$487$	20.9026	0.947187	0.473593	+	0.880744i	$0.342957\pi$
$488$	0	0
$489$	−53.0027	−2.39687
$490$	0	0
$491$	−20.3940	−0.920370	−0.460185	−	0.887823i	$-0.652217\pi$
$491$	−20.3940	−0.920370	−0.460185	+	0.887823i	$0.652217\pi$
$492$	0	0
$493$	−5.30416	−0.238888
$494$	0	0
$495$	−9.54286	−0.428920
$496$	0	0
$497$	0	0
$498$	0	0
$499$	5.32244	0.238265	0.119133	−	0.992878i	$-0.461989\pi$
$499$	5.32244	0.238265	0.119133	+	0.992878i	$0.461989\pi$
$500$	0	0
$501$	−7.57456	−0.338406
$502$	0	0
$503$	−34.7932	−1.55135	−0.775676	−	0.631131i	$-0.782591\pi$
$503$	−34.7932	−1.55135	−0.775676	+	0.631131i	$0.782591\pi$
$504$	0	0
$505$	10.4167	0.463536
$506$	0	0
$507$	26.9327	1.19612
$508$	0	0
$509$	−43.2078	−1.91515	−0.957577	−	0.288178i	$-0.906951\pi$
$509$	−43.2078	−1.91515	−0.957577	+	0.288178i	$0.906951\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	12.0764	0.533185
$514$	0	0
$515$	17.7207	0.780869
$516$	0	0
$517$	5.25493	0.231112
$518$	0	0
$519$	29.2877	1.28559
$520$	0	0
$521$	−2.14891	−0.0941454	−0.0470727	−	0.998891i	$-0.514989\pi$
$521$	−2.14891	−0.0941454	−0.0470727	+	0.998891i	$0.514989\pi$
$522$	0	0
$523$	33.3093	1.45651	0.728257	−	0.685304i	$-0.240331\pi$
$523$	33.3093	1.45651	0.728257	+	0.685304i	$0.240331\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−2.77876	−0.121045
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	−40.1190	−1.74102
$532$	0	0
$533$	−18.3886	−0.796500
$534$	0	0
$535$	58.7610	2.54046
$536$	0	0
$537$	57.3967	2.47685
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−25.3682	−1.09066	−0.545332	−	0.838220i	$-0.683596\pi$
$541$	−25.3682	−1.09066	−0.545332	+	0.838220i	$0.683596\pi$
$542$	0	0
$543$	−6.78065	−0.290985
$544$	0	0
$545$	−58.2647	−2.49579
$546$	0	0
$547$	−38.1137	−1.62962	−0.814812	−	0.579725i	$-0.803160\pi$
$547$	−38.1137	−1.62962	−0.814812	+	0.579725i	$0.803160\pi$
$548$	0	0
$549$	10.0511	0.428971
$550$	0	0
$551$	−8.49200	−0.361772
$552$	0	0
$553$	0	0
$554$	0	0
$555$	−12.4192	−0.527164
$556$	0	0
$557$	9.26563	0.392597	0.196299	−	0.980544i	$-0.437108\pi$
$557$	9.26563	0.392597	0.196299	+	0.980544i	$0.437108\pi$
$558$	0	0
$559$	−0.411130	−0.0173889
$560$	0	0
$561$	−3.53866	−0.149402
$562$	0	0
$563$	10.0328	0.422834	0.211417	−	0.977396i	$-0.432192\pi$
$563$	10.0328	0.422834	0.211417	+	0.977396i	$0.432192\pi$
$564$	0	0
$565$	40.4249	1.70069
$566$	0	0
$567$	0	0
$568$	0	0
$569$	2.39151	0.100257	0.0501286	−	0.998743i	$-0.484037\pi$
$569$	2.39151	0.100257	0.0501286	+	0.998743i	$0.484037\pi$
$570$	0	0
$571$	41.9257	1.75453	0.877267	−	0.480002i	$-0.159364\pi$
$571$	41.9257	1.75453	0.877267	+	0.480002i	$0.159364\pi$
$572$	0	0
$573$	−44.5511	−1.86115
$574$	0	0
$575$	−4.45322	−0.185712
$576$	0	0
$577$	−29.7657	−1.23916	−0.619580	−	0.784933i	$-0.712697\pi$
$577$	−29.7657	−1.23916	−0.619580	+	0.784933i	$0.712697\pi$
$578$	0	0
$579$	−42.5150	−1.76686
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−3.22209	−0.133445
$584$	0	0
$585$	−24.4369	−1.01034
$586$	0	0
$587$	−19.5121	−0.805352	−0.402676	−	0.915342i	$-0.631920\pi$
$587$	−19.5121	−0.805352	−0.402676	+	0.915342i	$0.631920\pi$
$588$	0	0
$589$	−4.44881	−0.183310
$590$	0	0
$591$	−34.5713	−1.42207
$592$	0	0
$593$	42.0654	1.72742	0.863709	−	0.503991i	$-0.168136\pi$
$593$	42.0654	1.72742	0.863709	+	0.503991i	$0.168136\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−0.0439148	−0.00179731
$598$	0	0
$599$	−13.3718	−0.546358	−0.273179	−	0.961963i	$-0.588075\pi$
$599$	−13.3718	−0.546358	−0.273179	+	0.961963i	$0.588075\pi$
$600$	0	0
$601$	−27.5646	−1.12438	−0.562191	−	0.827007i	$-0.690042\pi$
$601$	−27.5646	−1.12438	−0.562191	+	0.827007i	$0.690042\pi$
$602$	0	0
$603$	12.8011	0.521300
$604$	0	0
$605$	−32.3433	−1.31494
$606$	0	0
$607$	18.5390	0.752475	0.376238	−	0.926523i	$-0.377218\pi$
$607$	18.5390	0.752475	0.376238	+	0.926523i	$0.377218\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	13.4566	0.544395
$612$	0	0
$613$	−38.9542	−1.57334	−0.786672	−	0.617372i	$-0.788198\pi$
$613$	−38.9542	−1.57334	−0.786672	+	0.617372i	$0.788198\pi$
$614$	0	0
$615$	−87.0975	−3.51211
$616$	0	0
$617$	−23.2489	−0.935965	−0.467983	−	0.883738i	$-0.655019\pi$
$617$	−23.2489	−0.935965	−0.467983	+	0.883738i	$0.655019\pi$
$618$	0	0
$619$	−22.6145	−0.908952	−0.454476	−	0.890759i	$-0.650174\pi$
$619$	−22.6145	−0.908952	−0.454476	+	0.890759i	$0.650174\pi$
$620$	0	0
$621$	4.04046	0.162138
$622$	0	0
$623$	0	0
$624$	0	0
$625$	−27.4349	−1.09740
$626$	0	0
$627$	−5.66542	−0.226255
$628$	0	0
$629$	−2.75762	−0.109954
$630$	0	0
$631$	−31.8681	−1.26865	−0.634325	−	0.773066i	$-0.718722\pi$
$631$	−31.8681	−1.26865	−0.634325	+	0.773066i	$0.718722\pi$
$632$	0	0
$633$	41.0802	1.63279
$634$	0	0
$635$	−45.4412	−1.80328
$636$	0	0
$637$	0	0
$638$	0	0
$639$	−49.9300	−1.97520
$640$	0	0
$641$	−7.66081	−0.302584	−0.151292	−	0.988489i	$-0.548343\pi$
$641$	−7.66081	−0.302584	−0.151292	+	0.988489i	$0.548343\pi$
$642$	0	0
$643$	38.1653	1.50509	0.752547	−	0.658539i	$-0.228825\pi$
$643$	38.1653	1.50509	0.752547	+	0.658539i	$0.228825\pi$
$644$	0	0
$645$	−1.94731	−0.0766753
$646$	0	0
$647$	1.28293	0.0504372	0.0252186	−	0.999682i	$-0.491972\pi$
$647$	1.28293	0.0504372	0.0252186	+	0.999682i	$0.491972\pi$
$648$	0	0
$649$	6.21088	0.243798
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−26.3467	−1.03103	−0.515513	−	0.856881i	$-0.672399\pi$
$653$	−26.3467	−1.03103	−0.515513	+	0.856881i	$0.672399\pi$
$654$	0	0
$655$	−64.8288	−2.53307
$656$	0	0
$657$	−15.6837	−0.611879
$658$	0	0
$659$	−20.7693	−0.809056	−0.404528	−	0.914526i	$-0.632564\pi$
$659$	−20.7693	−0.809056	−0.404528	+	0.914526i	$0.632564\pi$
$660$	0	0
$661$	1.28146	0.0498430	0.0249215	−	0.999689i	$-0.492066\pi$
$661$	1.28146	0.0498430	0.0249215	+	0.999689i	$0.492066\pi$
$662$	0	0
$663$	−9.06164	−0.351925
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−2.84122	−0.110012
$668$	0	0
$669$	7.56144	0.292342
$670$	0	0
$671$	−1.55603	−0.0600697
$672$	0	0
$673$	12.6810	0.488816	0.244408	−	0.969672i	$-0.421406\pi$
$673$	12.6810	0.488816	0.244408	+	0.969672i	$0.421406\pi$
$674$	0	0
$675$	−17.9930	−0.692552
$676$	0	0
$677$	−13.8828	−0.533559	−0.266780	−	0.963758i	$-0.585960\pi$
$677$	−13.8828	−0.533559	−0.266780	+	0.963758i	$0.585960\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	32.8215	1.25772
$682$	0	0
$683$	−23.6000	−0.903029	−0.451515	−	0.892264i	$-0.649116\pi$
$683$	−23.6000	−0.903029	−0.451515	+	0.892264i	$0.649116\pi$
$684$	0	0
$685$	56.6788	2.16559
$686$	0	0
$687$	−46.5059	−1.77431
$688$	0	0
$689$	−8.25097	−0.314337
$690$	0	0
$691$	31.7398	1.20744	0.603720	−	0.797197i	$-0.293685\pi$
$691$	31.7398	1.20744	0.603720	+	0.797197i	$0.293685\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	29.0299	1.10117
$696$	0	0
$697$	−19.3396	−0.732541
$698$	0	0
$699$	43.9595	1.66270
$700$	0	0
$701$	−42.2380	−1.59531	−0.797655	−	0.603115i	$-0.793926\pi$
$701$	−42.2380	−1.59531	−0.797655	+	0.603115i	$0.793926\pi$
$702$	0	0
$703$	−4.41497	−0.166514
$704$	0	0
$705$	63.7370	2.40047
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−0.0201167	−0.000755499 0	−0.000377749	−	1.00000i	$-0.500120\pi$
$709$	−0.0201167	−0.000755499 0	−0.000377749		1.00000i	$0.500120\pi$
$710$	0	0
$711$	33.2556	1.24718
$712$	0	0
$713$	−1.48846	−0.0557434
$714$	0	0
$715$	3.78311	0.141480
$716$	0	0
$717$	21.6919	0.810097
$718$	0	0
$719$	9.83255	0.366692	0.183346	−	0.983048i	$-0.441307\pi$
$719$	9.83255	0.366692	0.183346	+	0.983048i	$0.441307\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	73.1107	2.71901
$724$	0	0
$725$	12.6526	0.469904
$726$	0	0
$727$	−27.5037	−1.02006	−0.510029	−	0.860157i	$-0.670365\pi$
$727$	−27.5037	−1.02006	−0.510029	+	0.860157i	$0.670365\pi$
$728$	0	0
$729$	−43.8208	−1.62299
$730$	0	0
$731$	−0.432392	−0.0159926
$732$	0	0
$733$	−14.8808	−0.549637	−0.274818	−	0.961496i	$-0.588618\pi$
$733$	−14.8808	−0.549637	−0.274818	+	0.961496i	$0.588618\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−1.98175	−0.0729987
$738$	0	0
$739$	3.36070	0.123625	0.0618126	−	0.998088i	$-0.480312\pi$
$739$	3.36070	0.123625	0.0618126	+	0.998088i	$0.480312\pi$
$740$	0	0
$741$	−14.5077	−0.532955
$742$	0	0
$743$	42.4398	1.55697	0.778483	−	0.627666i	$-0.215990\pi$
$743$	42.4398	1.55697	0.778483	+	0.627666i	$0.215990\pi$
$744$	0	0
$745$	51.4556	1.88519
$746$	0	0
$747$	−26.4234	−0.966782
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−15.3797	−0.561212	−0.280606	−	0.959823i	$-0.590535\pi$
$751$	−15.3797	−0.561212	−0.280606	+	0.959823i	$0.590535\pi$
$752$	0	0
$753$	−20.1713	−0.735083
$754$	0	0
$755$	−3.99412	−0.145361
$756$	0	0
$757$	−35.0297	−1.27317	−0.636587	−	0.771205i	$-0.719655\pi$
$757$	−35.0297	−1.27317	−0.636587	+	0.771205i	$0.719655\pi$
$758$	0	0
$759$	−1.89551	−0.0688027
$760$	0	0
$761$	−8.32742	−0.301869	−0.150934	−	0.988544i	$-0.548228\pi$
$761$	−8.32742	−0.301869	−0.150934	+	0.988544i	$0.548228\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	−25.7007	−0.929212
$766$	0	0
$767$	15.9045	0.574280
$768$	0	0
$769$	−23.5183	−0.848093	−0.424047	−	0.905640i	$-0.639391\pi$
$769$	−23.5183	−0.848093	−0.424047	+	0.905640i	$0.639391\pi$
$770$	0	0
$771$	42.3861	1.52650
$772$	0	0
$773$	46.0971	1.65800	0.828998	−	0.559251i	$-0.188911\pi$
$773$	46.0971	1.65800	0.828998	+	0.559251i	$0.188911\pi$
$774$	0	0
$775$	6.62845	0.238101
$776$	0	0
$777$	0	0
$778$	0	0
$779$	−30.9629	−1.10936
$780$	0	0
$781$	7.72974	0.276592
$782$	0	0
$783$	−11.4798	−0.410255
$784$	0	0
$785$	−15.6614	−0.558978
$786$	0	0
$787$	−5.30434	−0.189079	−0.0945397	−	0.995521i	$-0.530138\pi$
$787$	−5.30434	−0.189079	−0.0945397	+	0.995521i	$0.530138\pi$
$788$	0	0
$789$	15.4388	0.549636
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−3.98460	−0.141497
$794$	0	0
$795$	−39.0806	−1.38605
$796$	0	0
$797$	26.3785	0.934375	0.467188	−	0.884158i	$-0.345267\pi$
$797$	26.3785	0.934375	0.467188	+	0.884158i	$0.345267\pi$
$798$	0	0
$799$	14.1525	0.500680
$800$	0	0
$801$	−76.8185	−2.71425
$802$	0	0
$803$	2.42801	0.0856827
$804$	0	0
$805$	0	0
$806$	0	0
$807$	80.5701	2.83620
$808$	0	0
$809$	−16.0211	−0.563271	−0.281635	−	0.959522i	$-0.590877\pi$
$809$	−16.0211	−0.563271	−0.281635	+	0.959522i	$0.590877\pi$
$810$	0	0
$811$	28.9052	1.01500	0.507499	−	0.861652i	$-0.330570\pi$
$811$	28.9052	1.01500	0.507499	+	0.861652i	$0.330570\pi$
$812$	0	0
$813$	57.6320	2.02124
$814$	0	0
$815$	59.5947	2.08751
$816$	0	0
$817$	−0.692263	−0.0242192
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−35.1969	−1.22838	−0.614190	−	0.789158i	$-0.710517\pi$
$821$	−35.1969	−1.22838	−0.614190	+	0.789158i	$0.710517\pi$
$822$	0	0
$823$	34.3185	1.19627	0.598134	−	0.801396i	$-0.295909\pi$
$823$	34.3185	1.19627	0.598134	+	0.801396i	$0.295909\pi$
$824$	0	0
$825$	8.44112	0.293882
$826$	0	0
$827$	−13.7463	−0.478006	−0.239003	−	0.971019i	$-0.576821\pi$
$827$	−13.7463	−0.478006	−0.239003	+	0.971019i	$0.576821\pi$
$828$	0	0
$829$	7.16505	0.248852	0.124426	−	0.992229i	$-0.460291\pi$
$829$	7.16505	0.248852	0.124426	+	0.992229i	$0.460291\pi$
$830$	0	0
$831$	−1.98897	−0.0689966
$832$	0	0
$833$	0	0
$834$	0	0
$835$	8.51661	0.294729
$836$	0	0
$837$	−6.01407	−0.207877
$838$	0	0
$839$	28.2774	0.976243	0.488121	−	0.872776i	$-0.337682\pi$
$839$	28.2774	0.976243	0.488121	+	0.872776i	$0.337682\pi$
$840$	0	0
$841$	−20.9275	−0.721638
$842$	0	0
$843$	−67.0752	−2.31019
$844$	0	0
$845$	−30.2823	−1.04174
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−5.90208	−0.202559
$850$	0	0
$851$	−1.47714	−0.0506357
$852$	0	0
$853$	−31.1638	−1.06703	−0.533514	−	0.845791i	$-0.679129\pi$
$853$	−31.1638	−1.06703	−0.533514	+	0.845791i	$0.679129\pi$
$854$	0	0
$855$	−41.1470	−1.40720
$856$	0	0
$857$	45.3426	1.54887	0.774437	−	0.632652i	$-0.218033\pi$
$857$	45.3426	1.54887	0.774437	+	0.632652i	$0.218033\pi$
$858$	0	0
$859$	1.33930	0.0456963	0.0228481	−	0.999739i	$-0.492727\pi$
$859$	1.33930	0.0456963	0.0228481	+	0.999739i	$0.492727\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	1.78721	0.0608372	0.0304186	−	0.999537i	$-0.490316\pi$
$863$	1.78721	0.0608372	0.0304186	+	0.999537i	$0.490316\pi$
$864$	0	0
$865$	−32.9303	−1.11966
$866$	0	0
$867$	36.9565	1.25511
$868$	0	0
$869$	−5.14835	−0.174646
$870$	0	0
$871$	−5.07477	−0.171952
$872$	0	0
$873$	−20.8058	−0.704171
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−39.6271	−1.33811	−0.669055	−	0.743213i	$-0.733301\pi$
$877$	−39.6271	−1.33811	−0.669055	+	0.743213i	$0.733301\pi$
$878$	0	0
$879$	−52.7379	−1.77881
$880$	0	0
$881$	28.8863	0.973205	0.486602	−	0.873624i	$-0.338236\pi$
$881$	28.8863	0.973205	0.486602	+	0.873624i	$0.338236\pi$
$882$	0	0
$883$	30.2973	1.01959	0.509793	−	0.860297i	$-0.329722\pi$
$883$	30.2973	1.01959	0.509793	+	0.860297i	$0.329722\pi$
$884$	0	0
$885$	75.3317	2.53225
$886$	0	0
$887$	−57.3998	−1.92730	−0.963648	−	0.267174i	$-0.913910\pi$
$887$	−57.3998	−1.92730	−0.963648	+	0.267174i	$0.913910\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	1.65257	0.0553630
$892$	0	0
$893$	22.6583	0.758230
$894$	0	0
$895$	−64.5351	−2.15717
$896$	0	0
$897$	−4.85394	−0.162068
$898$	0	0
$899$	4.22904	0.141047
$900$	0	0
$901$	−8.67768	−0.289096
$902$	0	0
$903$	0	0
$904$	0	0
$905$	7.62396	0.253429
$906$	0	0
$907$	−42.6832	−1.41727	−0.708637	−	0.705573i	$-0.750690\pi$
$907$	−42.6832	−1.41727	−0.708637	+	0.705573i	$0.750690\pi$
$908$	0	0
$909$	15.1699	0.503154
$910$	0	0
$911$	38.1007	1.26233	0.631166	−	0.775647i	$-0.282576\pi$
$911$	38.1007	1.26233	0.631166	+	0.775647i	$0.282576\pi$
$912$	0	0
$913$	4.09064	0.135381
$914$	0	0
$915$	−18.8730	−0.623923
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−46.6525	−1.53892	−0.769462	−	0.638693i	$-0.779475\pi$
$919$	−46.6525	−1.53892	−0.769462	+	0.638693i	$0.779475\pi$
$920$	0	0
$921$	53.2143	1.75347
$922$	0	0
$923$	19.7940	0.651526
$924$	0	0
$925$	6.57803	0.216284
$926$	0	0
$927$	25.8069	0.847608
$928$	0	0
$929$	21.0973	0.692181	0.346091	−	0.938201i	$-0.387509\pi$
$929$	21.0973	0.692181	0.346091	+	0.938201i	$0.387509\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	−79.0219	−2.58706
$934$	0	0
$935$	3.97876	0.130120
$936$	0	0
$937$	27.0602	0.884020	0.442010	−	0.897010i	$-0.354266\pi$
$937$	27.0602	0.884020	0.442010	+	0.897010i	$0.354266\pi$
$938$	0	0
$939$	23.1907	0.756800
$940$	0	0
$941$	23.7942	0.775669	0.387835	−	0.921729i	$-0.373223\pi$
$941$	23.7942	0.775669	0.387835	+	0.921729i	$0.373223\pi$
$942$	0	0
$943$	−10.3594	−0.337349
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−18.6159	−0.604934	−0.302467	−	0.953160i	$-0.597810\pi$
$947$	−18.6159	−0.604934	−0.302467	+	0.953160i	$0.597810\pi$
$948$	0	0
$949$	6.21754	0.201830
$950$	0	0
$951$	−12.5600	−0.407286
$952$	0	0
$953$	−55.1166	−1.78540	−0.892701	−	0.450650i	$-0.851192\pi$
$953$	−55.1166	−1.78540	−0.892701	+	0.450650i	$0.851192\pi$
$954$	0	0
$955$	50.0919	1.62094
$956$	0	0
$957$	5.38556	0.174090
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−28.7845	−0.928532
$962$	0	0
$963$	85.5742	2.75759
$964$	0	0
$965$	47.8026	1.53882
$966$	0	0
$967$	13.4575	0.432764	0.216382	−	0.976309i	$-0.430574\pi$
$967$	13.4575	0.432764	0.216382	+	0.976309i	$0.430574\pi$
$968$	0	0
$969$	−15.2580	−0.490159
$970$	0	0
$971$	51.8741	1.66472	0.832359	−	0.554237i	$-0.186990\pi$
$971$	51.8741	1.66472	0.832359	+	0.554237i	$0.186990\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	21.6156	0.692254
$976$	0	0
$977$	−24.9979	−0.799752	−0.399876	−	0.916569i	$-0.630947\pi$
$977$	−24.9979	−0.799752	−0.399876	+	0.916569i	$0.630947\pi$
$978$	0	0
$979$	11.8924	0.380082
$980$	0	0
$981$	−84.8514	−2.70910
$982$	0	0
$983$	4.20080	0.133985	0.0669923	−	0.997753i	$-0.478660\pi$
$983$	4.20080	0.133985	0.0669923	+	0.997753i	$0.478660\pi$
$984$	0	0
$985$	38.8710	1.23853
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−0.231614	−0.00736490
$990$	0	0
$991$	37.3375	1.18607	0.593033	−	0.805178i	$-0.297930\pi$
$991$	37.3375	1.18607	0.593033	+	0.805178i	$0.297930\pi$
$992$	0	0
$993$	73.9028	2.34524
$994$	0	0
$995$	0.0493765	0.00156534
$996$	0	0
$997$	31.0689	0.983963	0.491982	−	0.870606i	$-0.336273\pi$
$997$	31.0689	0.983963	0.491982	+	0.870606i	$0.336273\pi$
$998$	0	0
$999$	−5.96832	−0.188829

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9016.2.a.bk.1.2		11
7.2	even	3		1288.2.q.d.921.10	yes	22
7.4	even	3		1288.2.q.d.737.10	✓	22
7.6	odd	2		9016.2.a.br.1.10		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1288.2.q.d.737.10	✓	22	7.4	even	3
1288.2.q.d.921.10	yes	22	7.2	even	3
9016.2.a.bk.1.2		11	1.1	even	1	trivial
9016.2.a.br.1.10		11	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:	\( N \)	\(=\)	\( 9016 = 2^{3} \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9016.a (trivial)

\(f(q)\)	\(=\)	\(q-2.73452 q^{3} +3.07461 q^{5} +4.47758 q^{9} +O(q^{10})\)	\(q-2.73452 q^{3} +3.07461 q^{5} +4.47758 q^{9} -0.693180 q^{11} -1.77506 q^{13} -8.40757 q^{15} -1.86686 q^{17} -2.98886 q^{19} -1.00000 q^{23} +4.45322 q^{25} -4.04046 q^{27} +2.84122 q^{29} +1.48846 q^{31} +1.89551 q^{33} +1.47714 q^{37} +4.85394 q^{39} +10.3594 q^{41} +0.231614 q^{43} +13.7668 q^{45} -7.58091 q^{47} +5.10497 q^{51} +4.64827 q^{53} -2.13126 q^{55} +8.17309 q^{57} -8.95999 q^{59} +2.24477 q^{61} -5.45762 q^{65} +2.85893 q^{67} +2.73452 q^{69} -11.1511 q^{71} -3.50272 q^{73} -12.1774 q^{75} +7.42715 q^{79} -2.38404 q^{81} -5.90127 q^{83} -5.73987 q^{85} -7.76935 q^{87} -17.1563 q^{89} -4.07022 q^{93} -9.18958 q^{95} -4.64667 q^{97} -3.10377 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 4 q^{3} - 3 q^{5} + 11 q^{9}+O(q^{10}) \) 11 * q - 4 * q^3 - 3 * q^5 + 11 * q^9	\( 11 q - 4 q^{3} - 3 q^{5} + 11 q^{9} + 13 q^{13} - 7 q^{17} - 8 q^{19} - 11 q^{23} + 6 q^{25} - 25 q^{27} - 3 q^{29} - 12 q^{31} + 2 q^{33} - q^{37} - 21 q^{39} - 12 q^{41} + 9 q^{43} - 19 q^{45} - 17 q^{47} + 19 q^{51} - 5 q^{53} - 21 q^{55} + 11 q^{57} - 33 q^{59} + 15 q^{61} - 9 q^{65} - 5 q^{67} + 4 q^{69} - 9 q^{71} - 5 q^{73} - 44 q^{75} + 11 q^{79} - 13 q^{81} - 51 q^{83} + 33 q^{85} - 4 q^{87} - 26 q^{89} + 6 q^{93} - 19 q^{95} - 21 q^{97} + 15 q^{99}+O(q^{100}) \) 11 * q - 4 * q^3 - 3 * q^5 + 11 * q^9 + 13 * q^13 - 7 * q^17 - 8 * q^19 - 11 * q^23 + 6 * q^25 - 25 * q^27 - 3 * q^29 - 12 * q^31 + 2 * q^33 - q^37 - 21 * q^39 - 12 * q^41 + 9 * q^43 - 19 * q^45 - 17 * q^47 + 19 * q^51 - 5 * q^53 - 21 * q^55 + 11 * q^57 - 33 * q^59 + 15 * q^61 - 9 * q^65 - 5 * q^67 + 4 * q^69 - 9 * q^71 - 5 * q^73 - 44 * q^75 + 11 * q^79 - 13 * q^81 - 51 * q^83 + 33 * q^85 - 4 * q^87 - 26 * q^89 + 6 * q^93 - 19 * q^95 - 21 * q^97 + 15 * q^99

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