LMFDB - Embedded newform 9016.2.a.bk.1.11

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			1.11
Root			$-2.32959$ 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)

$f(q)$	$=$	$q+2.32959 q^{3} +1.34069 q^{5} +2.42699 q^{9} +O(q^{10})$	$q+2.32959 q^{3} +1.34069 q^{5} +2.42699 q^{9} +0.563015 q^{11} -4.61572 q^{13} +3.12325 q^{15} -1.38686 q^{17} -2.28156 q^{19} -1.00000 q^{23} -3.20256 q^{25} -1.33487 q^{27} -0.714166 q^{29} -7.27634 q^{31} +1.31160 q^{33} +3.33097 q^{37} -10.7527 q^{39} -5.66128 q^{41} +2.57847 q^{43} +3.25384 q^{45} -4.96454 q^{47} -3.23082 q^{51} -8.82990 q^{53} +0.754827 q^{55} -5.31510 q^{57} -5.96895 q^{59} +2.37496 q^{61} -6.18823 q^{65} +0.900803 q^{67} -2.32959 q^{69} +8.18093 q^{71} -1.05727 q^{73} -7.46066 q^{75} +2.07232 q^{79} -10.3907 q^{81} -8.53166 q^{83} -1.85935 q^{85} -1.66372 q^{87} -4.65656 q^{89} -16.9509 q^{93} -3.05885 q^{95} +4.50126 q^{97} +1.36644 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.32959	1.34499	0.672495	−	0.740102i	$-0.265223\pi$
$3$	2.32959	1.34499	0.672495	+	0.740102i	$0.265223\pi$
$4$	0	0
$5$	1.34069	0.599573	0.299787	−	0.954006i	$-0.403085\pi$
$5$	1.34069	0.599573	0.299787	+	0.954006i	$0.403085\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	2.42699	0.808998
$10$	0	0
$11$	0.563015	0.169756	0.0848778	−	0.996391i	$-0.472950\pi$
$11$	0.563015	0.169756	0.0848778	+	0.996391i	$0.472950\pi$
$12$	0	0
$13$	−4.61572	−1.28017	−0.640085	−	0.768304i	$-0.721101\pi$
$13$	−4.61572	−1.28017	−0.640085	+	0.768304i	$0.721101\pi$
$14$	0	0
$15$	3.12325	0.806420
$16$	0	0
$17$	−1.38686	−0.336363	−0.168182	−	0.985756i	$-0.553789\pi$
$17$	−1.38686	−0.336363	−0.168182	+	0.985756i	$0.553789\pi$
$18$	0	0
$19$	−2.28156	−0.523425	−0.261713	−	0.965146i	$-0.584287\pi$
$19$	−2.28156	−0.523425	−0.261713	+	0.965146i	$0.584287\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0	0
$25$	−3.20256	−0.640512
$26$	0	0
$27$	−1.33487	−0.256896
$28$	0	0
$29$	−0.714166	−0.132617	−0.0663087	−	0.997799i	$-0.521122\pi$
$29$	−0.714166	−0.132617	−0.0663087	+	0.997799i	$0.521122\pi$
$30$	0	0
$31$	−7.27634	−1.30687	−0.653435	−	0.756983i	$-0.726673\pi$
$31$	−7.27634	−1.30687	−0.653435	+	0.756983i	$0.726673\pi$
$32$	0	0
$33$	1.31160	0.228320
$34$	0	0
$35$	0	0
$36$	0	0
$37$	3.33097	0.547609	0.273804	−	0.961785i	$-0.411718\pi$
$37$	3.33097	0.547609	0.273804	+	0.961785i	$0.411718\pi$
$38$	0	0
$39$	−10.7527	−1.72182
$40$	0	0
$41$	−5.66128	−0.884144	−0.442072	−	0.896980i	$-0.645756\pi$
$41$	−5.66128	−0.884144	−0.442072	+	0.896980i	$0.645756\pi$
$42$	0	0
$43$	2.57847	0.393213	0.196607	−	0.980482i	$-0.437008\pi$
$43$	2.57847	0.393213	0.196607	+	0.980482i	$0.437008\pi$
$44$	0	0
$45$	3.25384	0.485053
$46$	0	0
$47$	−4.96454	−0.724153	−0.362076	−	0.932148i	$-0.617932\pi$
$47$	−4.96454	−0.724153	−0.362076	+	0.932148i	$0.617932\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	−3.23082	−0.452405
$52$	0	0
$53$	−8.82990	−1.21288	−0.606440	−	0.795129i	$-0.707403\pi$
$53$	−8.82990	−1.21288	−0.606440	+	0.795129i	$0.707403\pi$
$54$	0	0
$55$	0.754827	0.101781
$56$	0	0
$57$	−5.31510	−0.704002
$58$	0	0
$59$	−5.96895	−0.777091	−0.388545	−	0.921430i	$-0.627022\pi$
$59$	−5.96895	−0.777091	−0.388545	+	0.921430i	$0.627022\pi$
$60$	0	0
$61$	2.37496	0.304082	0.152041	−	0.988374i	$-0.451415\pi$
$61$	2.37496	0.304082	0.152041	+	0.988374i	$0.451415\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	−6.18823	−0.767556
$66$	0	0
$67$	0.900803	0.110051	0.0550253	−	0.998485i	$-0.482476\pi$
$67$	0.900803	0.110051	0.0550253	+	0.998485i	$0.482476\pi$
$68$	0	0
$69$	−2.32959	−0.280450
$70$	0	0
$71$	8.18093	0.970898	0.485449	−	0.874265i	$-0.338656\pi$
$71$	8.18093	0.970898	0.485449	+	0.874265i	$0.338656\pi$
$72$	0	0
$73$	−1.05727	−0.123745	−0.0618723	−	0.998084i	$-0.519707\pi$
$73$	−1.05727	−0.123745	−0.0618723	+	0.998084i	$0.519707\pi$
$74$	0	0
$75$	−7.46066	−0.861482
$76$	0	0
$77$	0	0
$78$	0	0
$79$	2.07232	0.233154	0.116577	−	0.993182i	$-0.462808\pi$
$79$	2.07232	0.233154	0.116577	+	0.993182i	$0.462808\pi$
$80$	0	0
$81$	−10.3907	−1.15452
$82$	0	0
$83$	−8.53166	−0.936472	−0.468236	−	0.883604i	$-0.655110\pi$
$83$	−8.53166	−0.936472	−0.468236	+	0.883604i	$0.655110\pi$
$84$	0	0
$85$	−1.85935	−0.201674
$86$	0	0
$87$	−1.66372	−0.178369
$88$	0	0
$89$	−4.65656	−0.493595	−0.246797	−	0.969067i	$-0.579378\pi$
$89$	−4.65656	−0.493595	−0.246797	+	0.969067i	$0.579378\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	−16.9509	−1.75773
$94$	0	0
$95$	−3.05885	−0.313832
$96$	0	0
$97$	4.50126	0.457034	0.228517	−	0.973540i	$-0.426612\pi$
$97$	4.50126	0.457034	0.228517	+	0.973540i	$0.426612\pi$
$98$	0	0
$99$	1.36644	0.137332
$100$	0	0
$101$	2.36281	0.235108	0.117554	−	0.993066i	$-0.462495\pi$
$101$	2.36281	0.235108	0.117554	+	0.993066i	$0.462495\pi$
$102$	0	0
$103$	17.7773	1.75165	0.875824	−	0.482631i	$-0.160319\pi$
$103$	17.7773	1.75165	0.875824	+	0.482631i	$0.160319\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−5.66976	−0.548117	−0.274058	−	0.961713i	$-0.588366\pi$
$107$	−5.66976	−0.548117	−0.274058	+	0.961713i	$0.588366\pi$
$108$	0	0
$109$	−15.6737	−1.50127	−0.750635	−	0.660717i	$-0.770252\pi$
$109$	−15.6737	−1.50127	−0.750635	+	0.660717i	$0.770252\pi$
$110$	0	0
$111$	7.75981	0.736528
$112$	0	0
$113$	5.47574	0.515115	0.257557	−	0.966263i	$-0.417082\pi$
$113$	5.47574	0.515115	0.257557	+	0.966263i	$0.417082\pi$
$114$	0	0
$115$	−1.34069	−0.125020
$116$	0	0
$117$	−11.2023	−1.03566
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−10.6830	−0.971183
$122$	0	0
$123$	−13.1885	−1.18916
$124$	0	0
$125$	−10.9971	−0.983607
$126$	0	0
$127$	0.422202	0.0374644	0.0187322	−	0.999825i	$-0.494037\pi$
$127$	0.422202	0.0374644	0.0187322	+	0.999825i	$0.494037\pi$
$128$	0	0
$129$	6.00678	0.528868
$130$	0	0
$131$	10.3827	0.907142	0.453571	−	0.891220i	$-0.350150\pi$
$131$	10.3827	0.907142	0.453571	+	0.891220i	$0.350150\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	−1.78964	−0.154028
$136$	0	0
$137$	−0.0126067	−0.00107706	−0.000538531	−	1.00000i	$-0.500171\pi$
$137$	−0.0126067	−0.00107706	−0.000538531		1.00000i	$0.500171\pi$
$138$	0	0
$139$	−1.18792	−0.100758	−0.0503790	−	0.998730i	$-0.516043\pi$
$139$	−1.18792	−0.100758	−0.0503790	+	0.998730i	$0.516043\pi$
$140$	0	0
$141$	−11.5653	−0.973978
$142$	0	0
$143$	−2.59872	−0.217316
$144$	0	0
$145$	−0.957473	−0.0795138
$146$	0	0
$147$	0	0
$148$	0	0
$149$	21.4927	1.76075	0.880377	−	0.474274i	$-0.157290\pi$
$149$	21.4927	1.76075	0.880377	+	0.474274i	$0.157290\pi$
$150$	0	0
$151$	−4.65854	−0.379107	−0.189553	−	0.981870i	$-0.560704\pi$
$151$	−4.65854	−0.379107	−0.189553	+	0.981870i	$0.560704\pi$
$152$	0	0
$153$	−3.36590	−0.272117
$154$	0	0
$155$	−9.75529	−0.783564
$156$	0	0
$157$	16.2726	1.29870	0.649349	−	0.760491i	$-0.275041\pi$
$157$	16.2726	1.29870	0.649349	+	0.760491i	$0.275041\pi$
$158$	0	0
$159$	−20.5700	−1.63131
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−17.7986	−1.39410	−0.697048	−	0.717025i	$-0.745503\pi$
$163$	−17.7986	−1.39410	−0.697048	+	0.717025i	$0.745503\pi$
$164$	0	0
$165$	1.75844	0.136894
$166$	0	0
$167$	−5.73934	−0.444123	−0.222062	−	0.975033i	$-0.571279\pi$
$167$	−5.73934	−0.444123	−0.222062	+	0.975033i	$0.571279\pi$
$168$	0	0
$169$	8.30488	0.638837
$170$	0	0
$171$	−5.53733	−0.423450
$172$	0	0
$173$	10.6003	0.805926	0.402963	−	0.915216i	$-0.367980\pi$
$173$	10.6003	0.805926	0.402963	+	0.915216i	$0.367980\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−13.9052	−1.04518
$178$	0	0
$179$	15.2570	1.14036	0.570180	−	0.821520i	$-0.306874\pi$
$179$	15.2570	1.14036	0.570180	+	0.821520i	$0.306874\pi$
$180$	0	0
$181$	−6.20485	−0.461203	−0.230601	−	0.973048i	$-0.574069\pi$
$181$	−6.20485	−0.461203	−0.230601	+	0.973048i	$0.574069\pi$
$182$	0	0
$183$	5.53269	0.408988
$184$	0	0
$185$	4.46579	0.328332
$186$	0	0
$187$	−0.780824	−0.0570995
$188$	0	0
$189$	0	0
$190$	0	0
$191$	23.3804	1.69174	0.845872	−	0.533385i	$-0.179080\pi$
$191$	23.3804	1.69174	0.845872	+	0.533385i	$0.179080\pi$
$192$	0	0
$193$	−10.5999	−0.763001	−0.381500	−	0.924369i	$-0.624593\pi$
$193$	−10.5999	−0.763001	−0.381500	+	0.924369i	$0.624593\pi$
$194$	0	0
$195$	−14.4161	−1.03235
$196$	0	0
$197$	−16.7290	−1.19189	−0.595945	−	0.803026i	$-0.703222\pi$
$197$	−16.7290	−1.19189	−0.595945	+	0.803026i	$0.703222\pi$
$198$	0	0
$199$	−19.3401	−1.37099	−0.685493	−	0.728079i	$-0.740413\pi$
$199$	−19.3401	−1.37099	−0.685493	+	0.728079i	$0.740413\pi$
$200$	0	0
$201$	2.09850	0.148017
$202$	0	0
$203$	0	0
$204$	0	0
$205$	−7.59000	−0.530109
$206$	0	0
$207$	−2.42699	−0.168688
$208$	0	0
$209$	−1.28455	−0.0888544
$210$	0	0
$211$	−8.24996	−0.567951	−0.283975	−	0.958832i	$-0.591653\pi$
$211$	−8.24996	−0.567951	−0.283975	+	0.958832i	$0.591653\pi$
$212$	0	0
$213$	19.0582	1.30585
$214$	0	0
$215$	3.45692	0.235760
$216$	0	0
$217$	0	0
$218$	0	0
$219$	−2.46302	−0.166435
$220$	0	0
$221$	6.40136	0.430602
$222$	0	0
$223$	−17.7244	−1.18692	−0.593458	−	0.804865i	$-0.702238\pi$
$223$	−17.7244	−1.18692	−0.593458	+	0.804865i	$0.702238\pi$
$224$	0	0
$225$	−7.77260	−0.518173
$226$	0	0
$227$	20.9600	1.39116	0.695582	−	0.718447i	$-0.255147\pi$
$227$	20.9600	1.39116	0.695582	+	0.718447i	$0.255147\pi$
$228$	0	0
$229$	2.88647	0.190744	0.0953718	−	0.995442i	$-0.469596\pi$
$229$	2.88647	0.190744	0.0953718	+	0.995442i	$0.469596\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	23.6911	1.55206	0.776028	−	0.630699i	$-0.217232\pi$
$233$	23.6911	1.55206	0.776028	+	0.630699i	$0.217232\pi$
$234$	0	0
$235$	−6.65589	−0.434182
$236$	0	0
$237$	4.82766	0.313590
$238$	0	0
$239$	−3.89225	−0.251769	−0.125884	−	0.992045i	$-0.540177\pi$
$239$	−3.89225	−0.251769	−0.125884	+	0.992045i	$0.540177\pi$
$240$	0	0
$241$	2.19702	0.141523	0.0707614	−	0.997493i	$-0.477457\pi$
$241$	2.19702	0.141523	0.0707614	+	0.997493i	$0.477457\pi$
$242$	0	0
$243$	−20.2014	−1.29592
$244$	0	0
$245$	0	0
$246$	0	0
$247$	10.5310	0.670074
$248$	0	0
$249$	−19.8753	−1.25955
$250$	0	0
$251$	−15.5335	−0.980464	−0.490232	−	0.871592i	$-0.663088\pi$
$251$	−15.5335	−0.980464	−0.490232	+	0.871592i	$0.663088\pi$
$252$	0	0
$253$	−0.563015	−0.0353965
$254$	0	0
$255$	−4.33151	−0.271250
$256$	0	0
$257$	2.23550	0.139447	0.0697235	−	0.997566i	$-0.477788\pi$
$257$	2.23550	0.139447	0.0697235	+	0.997566i	$0.477788\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−1.73328	−0.107287
$262$	0	0
$263$	13.7931	0.850518	0.425259	−	0.905072i	$-0.360183\pi$
$263$	13.7931	0.850518	0.425259	+	0.905072i	$0.360183\pi$
$264$	0	0
$265$	−11.8381	−0.727210
$266$	0	0
$267$	−10.8479	−0.663880
$268$	0	0
$269$	19.2807	1.17557	0.587783	−	0.809019i	$-0.300001\pi$
$269$	19.2807	1.17557	0.587783	+	0.809019i	$0.300001\pi$
$270$	0	0
$271$	25.3745	1.54139	0.770697	−	0.637202i	$-0.219908\pi$
$271$	25.3745	1.54139	0.770697	+	0.637202i	$0.219908\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	−1.80309	−0.108730
$276$	0	0
$277$	−0.704181	−0.0423101	−0.0211551	−	0.999776i	$-0.506734\pi$
$277$	−0.704181	−0.0423101	−0.0211551	+	0.999776i	$0.506734\pi$
$278$	0	0
$279$	−17.6596	−1.05725
$280$	0	0
$281$	−1.79076	−0.106828	−0.0534138	−	0.998572i	$-0.517010\pi$
$281$	−1.79076	−0.106828	−0.0534138	+	0.998572i	$0.517010\pi$
$282$	0	0
$283$	2.72351	0.161896	0.0809480	−	0.996718i	$-0.474205\pi$
$283$	2.72351	0.161896	0.0809480	+	0.996718i	$0.474205\pi$
$284$	0	0
$285$	−7.12588	−0.422101
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−15.0766	−0.886860
$290$	0	0
$291$	10.4861	0.614706
$292$	0	0
$293$	−20.9919	−1.22636	−0.613180	−	0.789943i	$-0.710110\pi$
$293$	−20.9919	−1.22636	−0.613180	+	0.789943i	$0.710110\pi$
$294$	0	0
$295$	−8.00248	−0.465923
$296$	0	0
$297$	−0.751552	−0.0436095
$298$	0	0
$299$	4.61572	0.266934
$300$	0	0
$301$	0	0
$302$	0	0
$303$	5.50437	0.316218
$304$	0	0
$305$	3.18408	0.182320
$306$	0	0
$307$	−29.7415	−1.69744	−0.848720	−	0.528843i	$-0.822626\pi$
$307$	−29.7415	−1.69744	−0.848720	+	0.528843i	$0.822626\pi$
$308$	0	0
$309$	41.4138	2.35595
$310$	0	0
$311$	6.93179	0.393066	0.196533	−	0.980497i	$-0.437032\pi$
$311$	6.93179	0.393066	0.196533	+	0.980497i	$0.437032\pi$
$312$	0	0
$313$	−10.4988	−0.593430	−0.296715	−	0.954966i	$-0.595891\pi$
$313$	−10.4988	−0.593430	−0.296715	+	0.954966i	$0.595891\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	20.8489	1.17099	0.585495	−	0.810676i	$-0.300900\pi$
$317$	20.8489	1.17099	0.585495	+	0.810676i	$0.300900\pi$
$318$	0	0
$319$	−0.402087	−0.0225125
$320$	0	0
$321$	−13.2082	−0.737211
$322$	0	0
$323$	3.16420	0.176061
$324$	0	0
$325$	14.7821	0.819965
$326$	0	0
$327$	−36.5134	−2.01919
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−13.4066	−0.736895	−0.368447	−	0.929649i	$-0.620111\pi$
$331$	−13.4066	−0.736895	−0.368447	+	0.929649i	$0.620111\pi$
$332$	0	0
$333$	8.08426	0.443015
$334$	0	0
$335$	1.20769	0.0659834
$336$	0	0
$337$	30.5812	1.66586	0.832931	−	0.553377i	$-0.186661\pi$
$337$	30.5812	1.66586	0.832931	+	0.553377i	$0.186661\pi$
$338$	0	0
$339$	12.7562	0.692824
$340$	0	0
$341$	−4.09669	−0.221848
$342$	0	0
$343$	0	0
$344$	0	0
$345$	−3.12325	−0.168150
$346$	0	0
$347$	17.0814	0.916978	0.458489	−	0.888700i	$-0.348391\pi$
$347$	17.0814	0.916978	0.458489	+	0.888700i	$0.348391\pi$
$348$	0	0
$349$	22.1142	1.18375	0.591874	−	0.806030i	$-0.298388\pi$
$349$	22.1142	1.18375	0.591874	+	0.806030i	$0.298388\pi$
$350$	0	0
$351$	6.16139	0.328870
$352$	0	0
$353$	−26.2873	−1.39913	−0.699567	−	0.714567i	$-0.746624\pi$
$353$	−26.2873	−1.39913	−0.699567	+	0.714567i	$0.746624\pi$
$354$	0	0
$355$	10.9681	0.582124
$356$	0	0
$357$	0	0
$358$	0	0
$359$	7.18002	0.378947	0.189474	−	0.981886i	$-0.439322\pi$
$359$	7.18002	0.378947	0.189474	+	0.981886i	$0.439322\pi$
$360$	0	0
$361$	−13.7945	−0.726026
$362$	0	0
$363$	−24.8871	−1.30623
$364$	0	0
$365$	−1.41747	−0.0741939
$366$	0	0
$367$	−26.5046	−1.38353	−0.691764	−	0.722123i	$-0.743166\pi$
$367$	−26.5046	−1.38353	−0.691764	+	0.722123i	$0.743166\pi$
$368$	0	0
$369$	−13.7399	−0.715270
$370$	0	0
$371$	0	0
$372$	0	0
$373$	28.2535	1.46291	0.731456	−	0.681889i	$-0.238841\pi$
$373$	28.2535	1.46291	0.731456	+	0.681889i	$0.238841\pi$
$374$	0	0
$375$	−25.6187	−1.32294
$376$	0	0
$377$	3.29639	0.169773
$378$	0	0
$379$	28.0829	1.44252	0.721262	−	0.692662i	$-0.243562\pi$
$379$	28.0829	1.44252	0.721262	+	0.692662i	$0.243562\pi$
$380$	0	0
$381$	0.983558	0.0503892
$382$	0	0
$383$	−28.4944	−1.45600	−0.727999	−	0.685578i	$-0.759550\pi$
$383$	−28.4944	−1.45600	−0.727999	+	0.685578i	$0.759550\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	6.25793	0.318109
$388$	0	0
$389$	−28.8924	−1.46490	−0.732452	−	0.680819i	$-0.761624\pi$
$389$	−28.8924	−1.46490	−0.732452	+	0.680819i	$0.761624\pi$
$390$	0	0
$391$	1.38686	0.0701366
$392$	0	0
$393$	24.1875	1.22010
$394$	0	0
$395$	2.77833	0.139793
$396$	0	0
$397$	−24.9070	−1.25005	−0.625024	−	0.780606i	$-0.714911\pi$
$397$	−24.9070	−1.25005	−0.625024	+	0.780606i	$0.714911\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	4.77959	0.238682	0.119341	−	0.992853i	$-0.461922\pi$
$401$	4.77959	0.238682	0.119341	+	0.992853i	$0.461922\pi$
$402$	0	0
$403$	33.5856	1.67302
$404$	0	0
$405$	−13.9306	−0.692219
$406$	0	0
$407$	1.87539	0.0929597
$408$	0	0
$409$	−19.8035	−0.979220	−0.489610	−	0.871942i	$-0.662861\pi$
$409$	−19.8035	−0.979220	−0.489610	+	0.871942i	$0.662861\pi$
$410$	0	0
$411$	−0.0293684	−0.00144864
$412$	0	0
$413$	0	0
$414$	0	0
$415$	−11.4383	−0.561483
$416$	0	0
$417$	−2.76737	−0.135519
$418$	0	0
$419$	12.1574	0.593930	0.296965	−	0.954888i	$-0.404026\pi$
$419$	12.1574	0.593930	0.296965	+	0.954888i	$0.404026\pi$
$420$	0	0
$421$	3.97012	0.193492	0.0967458	−	0.995309i	$-0.469157\pi$
$421$	3.97012	0.193492	0.0967458	+	0.995309i	$0.469157\pi$
$422$	0	0
$423$	−12.0489	−0.585838
$424$	0	0
$425$	4.44151	0.215445
$426$	0	0
$427$	0	0
$428$	0	0
$429$	−6.05396	−0.292288
$430$	0	0
$431$	−4.76062	−0.229311	−0.114655	−	0.993405i	$-0.536576\pi$
$431$	−4.76062	−0.229311	−0.114655	+	0.993405i	$0.536576\pi$
$432$	0	0
$433$	21.0796	1.01302	0.506509	−	0.862234i	$-0.330936\pi$
$433$	21.0796	1.01302	0.506509	+	0.862234i	$0.330936\pi$
$434$	0	0
$435$	−2.23052	−0.106945
$436$	0	0
$437$	2.28156	0.109142
$438$	0	0
$439$	−25.8689	−1.23465	−0.617326	−	0.786707i	$-0.711784\pi$
$439$	−25.8689	−1.23465	−0.617326	+	0.786707i	$0.711784\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−1.40828	−0.0669092	−0.0334546	−	0.999440i	$-0.510651\pi$
$443$	−1.40828	−0.0669092	−0.0334546	+	0.999440i	$0.510651\pi$
$444$	0	0
$445$	−6.24299	−0.295946
$446$	0	0
$447$	50.0693	2.36820
$448$	0	0
$449$	4.94932	0.233573	0.116786	−	0.993157i	$-0.462741\pi$
$449$	4.94932	0.233573	0.116786	+	0.993157i	$0.462741\pi$
$450$	0	0
$451$	−3.18739	−0.150088
$452$	0	0
$453$	−10.8525	−0.509895
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−26.4184	−1.23580	−0.617901	−	0.786256i	$-0.712017\pi$
$457$	−26.4184	−1.23580	−0.617901	+	0.786256i	$0.712017\pi$
$458$	0	0
$459$	1.85128	0.0864103
$460$	0	0
$461$	29.3699	1.36789	0.683947	−	0.729532i	$-0.260262\pi$
$461$	29.3699	1.36789	0.683947	+	0.729532i	$0.260262\pi$
$462$	0	0
$463$	−14.4457	−0.671346	−0.335673	−	0.941979i	$-0.608964\pi$
$463$	−14.4457	−0.671346	−0.335673	+	0.941979i	$0.608964\pi$
$464$	0	0
$465$	−22.7258	−1.05389
$466$	0	0
$467$	−0.208861	−0.00966492	−0.00483246	−	0.999988i	$-0.501538\pi$
$467$	−0.208861	−0.00966492	−0.00483246	+	0.999988i	$0.501538\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	37.9086	1.74674
$472$	0	0
$473$	1.45172	0.0667501
$474$	0	0
$475$	7.30683	0.335260
$476$	0	0
$477$	−21.4301	−0.981217
$478$	0	0
$479$	1.37801	0.0629627	0.0314814	−	0.999504i	$-0.489978\pi$
$479$	1.37801	0.0629627	0.0314814	+	0.999504i	$0.489978\pi$
$480$	0	0
$481$	−15.3749	−0.701033
$482$	0	0
$483$	0	0
$484$	0	0
$485$	6.03478	0.274025
$486$	0	0
$487$	35.0372	1.58769	0.793845	−	0.608121i	$-0.208076\pi$
$487$	35.0372	1.58769	0.793845	+	0.608121i	$0.208076\pi$
$488$	0	0
$489$	−41.4635	−1.87504
$490$	0	0
$491$	−5.92284	−0.267294	−0.133647	−	0.991029i	$-0.542669\pi$
$491$	−5.92284	−0.267294	−0.133647	+	0.991029i	$0.542669\pi$
$492$	0	0
$493$	0.990449	0.0446076
$494$	0	0
$495$	1.83196	0.0823405
$496$	0	0
$497$	0	0
$498$	0	0
$499$	15.3826	0.688618	0.344309	−	0.938856i	$-0.388113\pi$
$499$	15.3826	0.688618	0.344309	+	0.938856i	$0.388113\pi$
$500$	0	0
$501$	−13.3703	−0.597341
$502$	0	0
$503$	−11.4778	−0.511771	−0.255886	−	0.966707i	$-0.582367\pi$
$503$	−11.4778	−0.511771	−0.255886	+	0.966707i	$0.582367\pi$
$504$	0	0
$505$	3.16778	0.140964
$506$	0	0
$507$	19.3470	0.859229
$508$	0	0
$509$	12.5718	0.557236	0.278618	−	0.960402i	$-0.410124\pi$
$509$	12.5718	0.557236	0.278618	+	0.960402i	$0.410124\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	3.04558	0.134466
$514$	0	0
$515$	23.8337	1.05024
$516$	0	0
$517$	−2.79511	−0.122929
$518$	0	0
$519$	24.6944	1.08396
$520$	0	0
$521$	−33.9302	−1.48651	−0.743254	−	0.669009i	$-0.766719\pi$
$521$	−33.9302	−1.48651	−0.743254	+	0.669009i	$0.766719\pi$
$522$	0	0
$523$	25.6207	1.12032	0.560158	−	0.828386i	$-0.310740\pi$
$523$	25.6207	1.12032	0.560158	+	0.828386i	$0.310740\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	10.0913	0.439583
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	−14.4866	−0.628665
$532$	0	0
$533$	26.1309	1.13185
$534$	0	0
$535$	−7.60137	−0.328636
$536$	0	0
$537$	35.5425	1.53377
$538$	0	0
$539$	0	0
$540$	0	0
$541$	21.4057	0.920304	0.460152	−	0.887840i	$-0.347795\pi$
$541$	21.4057	0.920304	0.460152	+	0.887840i	$0.347795\pi$
$542$	0	0
$543$	−14.4548	−0.620313
$544$	0	0
$545$	−21.0135	−0.900121
$546$	0	0
$547$	−39.8808	−1.70518	−0.852591	−	0.522579i	$-0.824970\pi$
$547$	−39.8808	−1.70518	−0.852591	+	0.522579i	$0.824970\pi$
$548$	0	0
$549$	5.76401	0.246002
$550$	0	0
$551$	1.62941	0.0694153
$552$	0	0
$553$	0	0
$554$	0	0
$555$	10.4035	0.441603
$556$	0	0
$557$	−8.89360	−0.376834	−0.188417	−	0.982089i	$-0.560336\pi$
$557$	−8.89360	−0.376834	−0.188417	+	0.982089i	$0.560336\pi$
$558$	0	0
$559$	−11.9015	−0.503380
$560$	0	0
$561$	−1.81900	−0.0767983
$562$	0	0
$563$	−30.0254	−1.26542	−0.632710	−	0.774389i	$-0.718057\pi$
$563$	−30.0254	−1.26542	−0.632710	+	0.774389i	$0.718057\pi$
$564$	0	0
$565$	7.34125	0.308849
$566$	0	0
$567$	0	0
$568$	0	0
$569$	34.2965	1.43779	0.718893	−	0.695121i	$-0.244649\pi$
$569$	34.2965	1.43779	0.718893	+	0.695121i	$0.244649\pi$
$570$	0	0
$571$	−19.6215	−0.821133	−0.410566	−	0.911831i	$-0.634669\pi$
$571$	−19.6215	−0.821133	−0.410566	+	0.911831i	$0.634669\pi$
$572$	0	0
$573$	54.4667	2.27538
$574$	0	0
$575$	3.20256	0.133556
$576$	0	0
$577$	43.9678	1.83040	0.915202	−	0.402996i	$-0.132031\pi$
$577$	43.9678	1.83040	0.915202	+	0.402996i	$0.132031\pi$
$578$	0	0
$579$	−24.6935	−1.02623
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−4.97137	−0.205893
$584$	0	0
$585$	−15.0188	−0.620951
$586$	0	0
$587$	−38.8133	−1.60200	−0.800998	−	0.598666i	$-0.795698\pi$
$587$	−38.8133	−1.60200	−0.800998	+	0.598666i	$0.795698\pi$
$588$	0	0
$589$	16.6014	0.684049
$590$	0	0
$591$	−38.9716	−1.60308
$592$	0	0
$593$	20.4169	0.838421	0.419210	−	0.907889i	$-0.362307\pi$
$593$	20.4169	0.838421	0.419210	+	0.907889i	$0.362307\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−45.0546	−1.84396
$598$	0	0
$599$	20.9594	0.856380	0.428190	−	0.903689i	$-0.359151\pi$
$599$	20.9594	0.856380	0.428190	+	0.903689i	$0.359151\pi$
$600$	0	0
$601$	−4.02772	−0.164294	−0.0821471	−	0.996620i	$-0.526178\pi$
$601$	−4.02772	−0.164294	−0.0821471	+	0.996620i	$0.526178\pi$
$602$	0	0
$603$	2.18624	0.0890307
$604$	0	0
$605$	−14.3226	−0.582295
$606$	0	0
$607$	35.3693	1.43560	0.717798	−	0.696251i	$-0.245150\pi$
$607$	35.3693	1.43560	0.717798	+	0.696251i	$0.245150\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	22.9149	0.927039
$612$	0	0
$613$	−20.5906	−0.831646	−0.415823	−	0.909445i	$-0.636506\pi$
$613$	−20.5906	−0.831646	−0.415823	+	0.909445i	$0.636506\pi$
$614$	0	0
$615$	−17.6816	−0.712991
$616$	0	0
$617$	−10.9336	−0.440170	−0.220085	−	0.975481i	$-0.570633\pi$
$617$	−10.9336	−0.440170	−0.220085	+	0.975481i	$0.570633\pi$
$618$	0	0
$619$	−12.3137	−0.494930	−0.247465	−	0.968897i	$-0.579597\pi$
$619$	−12.3137	−0.494930	−0.247465	+	0.968897i	$0.579597\pi$
$620$	0	0
$621$	1.33487	0.0535665
$622$	0	0
$623$	0	0
$624$	0	0
$625$	1.26920	0.0507679
$626$	0	0
$627$	−2.99248	−0.119508
$628$	0	0
$629$	−4.61960	−0.184195
$630$	0	0
$631$	35.3258	1.40630	0.703150	−	0.711042i	$-0.251776\pi$
$631$	35.3258	1.40630	0.703150	+	0.711042i	$0.251776\pi$
$632$	0	0
$633$	−19.2190	−0.763888
$634$	0	0
$635$	0.566040	0.0224626
$636$	0	0
$637$	0	0
$638$	0	0
$639$	19.8551	0.785454
$640$	0	0
$641$	15.1695	0.599159	0.299579	−	0.954071i	$-0.403154\pi$
$641$	15.1695	0.599159	0.299579	+	0.954071i	$0.403154\pi$
$642$	0	0
$643$	2.16152	0.0852420	0.0426210	−	0.999091i	$-0.486429\pi$
$643$	2.16152	0.0852420	0.0426210	+	0.999091i	$0.486429\pi$
$644$	0	0
$645$	8.05321	0.317095
$646$	0	0
$647$	−18.9559	−0.745234	−0.372617	−	0.927985i	$-0.621540\pi$
$647$	−18.9559	−0.745234	−0.372617	+	0.927985i	$0.621540\pi$
$648$	0	0
$649$	−3.36061	−0.131915
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−25.9293	−1.01469	−0.507346	−	0.861742i	$-0.669374\pi$
$653$	−25.9293	−1.01469	−0.507346	+	0.861742i	$0.669374\pi$
$654$	0	0
$655$	13.9200	0.543898
$656$	0	0
$657$	−2.56600	−0.100109
$658$	0	0
$659$	−34.1732	−1.33120	−0.665599	−	0.746310i	$-0.731824\pi$
$659$	−34.1732	−1.33120	−0.665599	+	0.746310i	$0.731824\pi$
$660$	0	0
$661$	−45.0769	−1.75329	−0.876645	−	0.481138i	$-0.840224\pi$
$661$	−45.0769	−1.75329	−0.876645	+	0.481138i	$0.840224\pi$
$662$	0	0
$663$	14.9126	0.579156
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0.714166	0.0276526
$668$	0	0
$669$	−41.2907	−1.59639
$670$	0	0
$671$	1.33714	0.0516197
$672$	0	0
$673$	−4.33674	−0.167169	−0.0835845	−	0.996501i	$-0.526637\pi$
$673$	−4.33674	−0.167169	−0.0835845	+	0.996501i	$0.526637\pi$
$674$	0	0
$675$	4.27500	0.164545
$676$	0	0
$677$	−28.1146	−1.08053	−0.540265	−	0.841495i	$-0.681676\pi$
$677$	−28.1146	−1.08053	−0.540265	+	0.841495i	$0.681676\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	48.8282	1.87110
$682$	0	0
$683$	−34.8171	−1.33224	−0.666120	−	0.745845i	$-0.732046\pi$
$683$	−34.8171	−1.33224	−0.666120	+	0.745845i	$0.732046\pi$
$684$	0	0
$685$	−0.0169016	−0.000645777 0
$686$	0	0
$687$	6.72430	0.256548
$688$	0	0
$689$	40.7563	1.55269
$690$	0	0
$691$	−27.0693	−1.02976	−0.514882	−	0.857261i	$-0.672164\pi$
$691$	−27.0693	−1.02976	−0.514882	+	0.857261i	$0.672164\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	−1.59263	−0.0604118
$696$	0	0
$697$	7.85141	0.297393
$698$	0	0
$699$	55.1906	2.08750
$700$	0	0
$701$	−19.2340	−0.726457	−0.363229	−	0.931700i	$-0.618326\pi$
$701$	−19.2340	−0.726457	−0.363229	+	0.931700i	$0.618326\pi$
$702$	0	0
$703$	−7.59981	−0.286632
$704$	0	0
$705$	−15.5055	−0.583971
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−14.7178	−0.552738	−0.276369	−	0.961052i	$-0.589131\pi$
$709$	−14.7178	−0.552738	−0.276369	+	0.961052i	$0.589131\pi$
$710$	0	0
$711$	5.02951	0.188621
$712$	0	0
$713$	7.27634	0.272501
$714$	0	0
$715$	−3.48407	−0.130297
$716$	0	0
$717$	−9.06735	−0.338626
$718$	0	0
$719$	−41.3474	−1.54200	−0.770998	−	0.636837i	$-0.780242\pi$
$719$	−41.3474	−1.54200	−0.770998	+	0.636837i	$0.780242\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	5.11817	0.190347
$724$	0	0
$725$	2.28716	0.0849430
$726$	0	0
$727$	14.2122	0.527103	0.263552	−	0.964645i	$-0.415106\pi$
$727$	14.2122	0.527103	0.263552	+	0.964645i	$0.415106\pi$
$728$	0	0
$729$	−15.8890	−0.588482
$730$	0	0
$731$	−3.57598	−0.132262
$732$	0	0
$733$	21.0790	0.778569	0.389285	−	0.921117i	$-0.372722\pi$
$733$	21.0790	0.778569	0.389285	+	0.921117i	$0.372722\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0.507166	0.0186817
$738$	0	0
$739$	13.3180	0.489911	0.244955	−	0.969534i	$-0.421227\pi$
$739$	13.3180	0.489911	0.244955	+	0.969534i	$0.421227\pi$
$740$	0	0
$741$	24.5330	0.901243
$742$	0	0
$743$	−25.4715	−0.934459	−0.467230	−	0.884136i	$-0.654748\pi$
$743$	−25.4715	−0.934459	−0.467230	+	0.884136i	$0.654748\pi$
$744$	0	0
$745$	28.8150	1.05570
$746$	0	0
$747$	−20.7063	−0.757604
$748$	0	0
$749$	0	0
$750$	0	0
$751$	40.0809	1.46257	0.731286	−	0.682071i	$-0.238920\pi$
$751$	40.0809	1.46257	0.731286	+	0.682071i	$0.238920\pi$
$752$	0	0
$753$	−36.1866	−1.31871
$754$	0	0
$755$	−6.24564	−0.227302
$756$	0	0
$757$	34.0731	1.23841	0.619204	−	0.785230i	$-0.287455\pi$
$757$	34.0731	1.23841	0.619204	+	0.785230i	$0.287455\pi$
$758$	0	0
$759$	−1.31160	−0.0476079
$760$	0	0
$761$	0.368393	0.0133542	0.00667712	−	0.999978i	$-0.497875\pi$
$761$	0.368393	0.0133542	0.00667712	+	0.999978i	$0.497875\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	−4.51262	−0.163154
$766$	0	0
$767$	27.5510	0.994809
$768$	0	0
$769$	3.28687	0.118528	0.0592639	−	0.998242i	$-0.481125\pi$
$769$	3.28687	0.118528	0.0592639	+	0.998242i	$0.481125\pi$
$770$	0	0
$771$	5.20781	0.187555
$772$	0	0
$773$	11.8387	0.425807	0.212904	−	0.977073i	$-0.431708\pi$
$773$	11.8387	0.425807	0.212904	+	0.977073i	$0.431708\pi$
$774$	0	0
$775$	23.3029	0.837066
$776$	0	0
$777$	0	0
$778$	0	0
$779$	12.9165	0.462783
$780$	0	0
$781$	4.60599	0.164815
$782$	0	0
$783$	0.953319	0.0340688
$784$	0	0
$785$	21.8165	0.778664
$786$	0	0
$787$	−19.5150	−0.695635	−0.347818	−	0.937562i	$-0.613077\pi$
$787$	−19.5150	−0.695635	−0.347818	+	0.937562i	$0.613077\pi$
$788$	0	0
$789$	32.1322	1.14394
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−10.9622	−0.389277
$794$	0	0
$795$	−27.5780	−0.978090
$796$	0	0
$797$	34.2842	1.21441	0.607204	−	0.794546i	$-0.292291\pi$
$797$	34.2842	1.21441	0.607204	+	0.794546i	$0.292291\pi$
$798$	0	0
$799$	6.88513	0.243578
$800$	0	0
$801$	−11.3014	−0.399317
$802$	0	0
$803$	−0.595262	−0.0210063
$804$	0	0
$805$	0	0
$806$	0	0
$807$	44.9162	1.58112
$808$	0	0
$809$	47.1042	1.65610	0.828048	−	0.560658i	$-0.189452\pi$
$809$	47.1042	1.65610	0.828048	+	0.560658i	$0.189452\pi$
$810$	0	0
$811$	−1.04287	−0.0366202	−0.0183101	−	0.999832i	$-0.505829\pi$
$811$	−1.04287	−0.0366202	−0.0183101	+	0.999832i	$0.505829\pi$
$812$	0	0
$813$	59.1123	2.07316
$814$	0	0
$815$	−23.8624	−0.835862
$816$	0	0
$817$	−5.88293	−0.205818
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−27.9538	−0.975594	−0.487797	−	0.872957i	$-0.662199\pi$
$821$	−27.9538	−0.975594	−0.487797	+	0.872957i	$0.662199\pi$
$822$	0	0
$823$	20.5409	0.716011	0.358005	−	0.933720i	$-0.383457\pi$
$823$	20.5409	0.716011	0.358005	+	0.933720i	$0.383457\pi$
$824$	0	0
$825$	−4.20046	−0.146241
$826$	0	0
$827$	3.71969	0.129346	0.0646732	−	0.997906i	$-0.479400\pi$
$827$	3.71969	0.129346	0.0646732	+	0.997906i	$0.479400\pi$
$828$	0	0
$829$	−11.4649	−0.398193	−0.199097	−	0.979980i	$-0.563801\pi$
$829$	−11.4649	−0.398193	−0.199097	+	0.979980i	$0.563801\pi$
$830$	0	0
$831$	−1.64045	−0.0569067
$832$	0	0
$833$	0	0
$834$	0	0
$835$	−7.69465	−0.266284
$836$	0	0
$837$	9.71297	0.335729
$838$	0	0
$839$	13.9717	0.482356	0.241178	−	0.970481i	$-0.422466\pi$
$839$	13.9717	0.482356	0.241178	+	0.970481i	$0.422466\pi$
$840$	0	0
$841$	−28.4900	−0.982413
$842$	0	0
$843$	−4.17173	−0.143682
$844$	0	0
$845$	11.1342	0.383029
$846$	0	0
$847$	0	0
$848$	0	0
$849$	6.34467	0.217749
$850$	0	0
$851$	−3.33097	−0.114184
$852$	0	0
$853$	57.1335	1.95621	0.978107	−	0.208103i	$-0.0667288\pi$
$853$	57.1335	1.95621	0.978107	+	0.208103i	$0.0667288\pi$
$854$	0	0
$855$	−7.42382	−0.253889
$856$	0	0
$857$	−19.1996	−0.655847	−0.327923	−	0.944704i	$-0.606349\pi$
$857$	−19.1996	−0.655847	−0.327923	+	0.944704i	$0.606349\pi$
$858$	0	0
$859$	−51.6269	−1.76149	−0.880743	−	0.473595i	$-0.842956\pi$
$859$	−51.6269	−1.76149	−0.880743	+	0.473595i	$0.842956\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	8.14904	0.277397	0.138698	−	0.990335i	$-0.455708\pi$
$863$	8.14904	0.277397	0.138698	+	0.990335i	$0.455708\pi$
$864$	0	0
$865$	14.2117	0.483212
$866$	0	0
$867$	−35.1224	−1.19282
$868$	0	0
$869$	1.16675	0.0395792
$870$	0	0
$871$	−4.15786	−0.140884
$872$	0	0
$873$	10.9245	0.369739
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−5.15951	−0.174224	−0.0871121	−	0.996199i	$-0.527764\pi$
$877$	−5.15951	−0.174224	−0.0871121	+	0.996199i	$0.527764\pi$
$878$	0	0
$879$	−48.9026	−1.64944
$880$	0	0
$881$	−16.3049	−0.549327	−0.274664	−	0.961540i	$-0.588566\pi$
$881$	−16.3049	−0.549327	−0.274664	+	0.961540i	$0.588566\pi$
$882$	0	0
$883$	7.33836	0.246955	0.123478	−	0.992347i	$-0.460595\pi$
$883$	7.33836	0.246955	0.123478	+	0.992347i	$0.460595\pi$
$884$	0	0
$885$	−18.6425	−0.626661
$886$	0	0
$887$	−54.4522	−1.82832	−0.914162	−	0.405348i	$-0.867150\pi$
$887$	−54.4522	−1.82832	−0.914162	+	0.405348i	$0.867150\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−5.85012	−0.195986
$892$	0	0
$893$	11.3269	0.379040
$894$	0	0
$895$	20.4548	0.683729
$896$	0	0
$897$	10.7527	0.359024
$898$	0	0
$899$	5.19652	0.173314
$900$	0	0
$901$	12.2458	0.407968
$902$	0	0
$903$	0	0
$904$	0	0
$905$	−8.31875	−0.276525
$906$	0	0
$907$	−49.3783	−1.63958	−0.819790	−	0.572664i	$-0.805910\pi$
$907$	−49.3783	−1.63958	−0.819790	+	0.572664i	$0.805910\pi$
$908$	0	0
$909$	5.73451	0.190202
$910$	0	0
$911$	−46.5200	−1.54128	−0.770638	−	0.637273i	$-0.780063\pi$
$911$	−46.5200	−1.54128	−0.770638	+	0.637273i	$0.780063\pi$
$912$	0	0
$913$	−4.80346	−0.158971
$914$	0	0
$915$	7.41759	0.245218
$916$	0	0
$917$	0	0
$918$	0	0
$919$	45.6308	1.50522	0.752611	−	0.658466i	$-0.228794\pi$
$919$	45.6308	1.50522	0.752611	+	0.658466i	$0.228794\pi$
$920$	0	0
$921$	−69.2856	−2.28304
$922$	0	0
$923$	−37.7609	−1.24291
$924$	0	0
$925$	−10.6676	−0.350750
$926$	0	0
$927$	43.1453	1.41708
$928$	0	0
$929$	−35.0901	−1.15127	−0.575634	−	0.817708i	$-0.695245\pi$
$929$	−35.0901	−1.15127	−0.575634	+	0.817708i	$0.695245\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	16.1482	0.528669
$934$	0	0
$935$	−1.04684	−0.0342353
$936$	0	0
$937$	1.90708	0.0623015	0.0311508	−	0.999515i	$-0.490083\pi$
$937$	1.90708	0.0623015	0.0311508	+	0.999515i	$0.490083\pi$
$938$	0	0
$939$	−24.4580	−0.798157
$940$	0	0
$941$	−6.44205	−0.210005	−0.105002	−	0.994472i	$-0.533485\pi$
$941$	−6.44205	−0.210005	−0.105002	+	0.994472i	$0.533485\pi$
$942$	0	0
$943$	5.66128	0.184357
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−3.93767	−0.127957	−0.0639786	−	0.997951i	$-0.520379\pi$
$947$	−3.93767	−0.127957	−0.0639786	+	0.997951i	$0.520379\pi$
$948$	0	0
$949$	4.88008	0.158414
$950$	0	0
$951$	48.5694	1.57497
$952$	0	0
$953$	45.5709	1.47618	0.738092	−	0.674700i	$-0.235727\pi$
$953$	45.5709	1.47618	0.738092	+	0.674700i	$0.235727\pi$
$954$	0	0
$955$	31.3458	1.01432
$956$	0	0
$957$	−0.936697	−0.0302791
$958$	0	0
$959$	0	0
$960$	0	0
$961$	21.9451	0.707907
$962$	0	0
$963$	−13.7605	−0.443425
$964$	0	0
$965$	−14.2112	−0.457475
$966$	0	0
$967$	21.7441	0.699244	0.349622	−	0.936891i	$-0.386310\pi$
$967$	21.7441	0.699244	0.349622	+	0.936891i	$0.386310\pi$
$968$	0	0
$969$	7.37130	0.236800
$970$	0	0
$971$	−45.7017	−1.46664	−0.733318	−	0.679885i	$-0.762030\pi$
$971$	−45.7017	−1.46664	−0.733318	+	0.679885i	$0.762030\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	34.4363	1.10284
$976$	0	0
$977$	56.7452	1.81544	0.907720	−	0.419576i	$-0.137821\pi$
$977$	56.7452	1.81544	0.907720	+	0.419576i	$0.137821\pi$
$978$	0	0
$979$	−2.62172	−0.0837904
$980$	0	0
$981$	−38.0400	−1.21452
$982$	0	0
$983$	23.6014	0.752767	0.376383	−	0.926464i	$-0.377168\pi$
$983$	23.6014	0.752767	0.376383	+	0.926464i	$0.377168\pi$
$984$	0	0
$985$	−22.4283	−0.714625
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−2.57847	−0.0819906
$990$	0	0
$991$	−5.49894	−0.174679	−0.0873397	−	0.996179i	$-0.527837\pi$
$991$	−5.49894	−0.174679	−0.0873397	+	0.996179i	$0.527837\pi$
$992$	0	0
$993$	−31.2320	−0.991116
$994$	0	0
$995$	−25.9291	−0.822006
$996$	0	0
$997$	8.64545	0.273804	0.136902	−	0.990585i	$-0.456285\pi$
$997$	8.64545	0.273804	0.136902	+	0.990585i	$0.456285\pi$
$998$	0	0
$999$	−4.44642	−0.140678

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9016.2.a.bk.1.11		11
7.2	even	3		1288.2.q.d.921.1	yes	22
7.4	even	3		1288.2.q.d.737.1	✓	22
7.6	odd	2		9016.2.a.br.1.1		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1288.2.q.d.737.1	✓	22	7.4	even	3
1288.2.q.d.921.1	yes	22	7.2	even	3
9016.2.a.bk.1.11		11	1.1	even	1	trivial
9016.2.a.br.1.1		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)

\(f(q)\)	\(=\)	\(q+2.32959 q^{3} +1.34069 q^{5} +2.42699 q^{9} +O(q^{10})\)	\(q+2.32959 q^{3} +1.34069 q^{5} +2.42699 q^{9} +0.563015 q^{11} -4.61572 q^{13} +3.12325 q^{15} -1.38686 q^{17} -2.28156 q^{19} -1.00000 q^{23} -3.20256 q^{25} -1.33487 q^{27} -0.714166 q^{29} -7.27634 q^{31} +1.31160 q^{33} +3.33097 q^{37} -10.7527 q^{39} -5.66128 q^{41} +2.57847 q^{43} +3.25384 q^{45} -4.96454 q^{47} -3.23082 q^{51} -8.82990 q^{53} +0.754827 q^{55} -5.31510 q^{57} -5.96895 q^{59} +2.37496 q^{61} -6.18823 q^{65} +0.900803 q^{67} -2.32959 q^{69} +8.18093 q^{71} -1.05727 q^{73} -7.46066 q^{75} +2.07232 q^{79} -10.3907 q^{81} -8.53166 q^{83} -1.85935 q^{85} -1.66372 q^{87} -4.65656 q^{89} -16.9509 q^{93} -3.05885 q^{95} +4.50126 q^{97} +1.36644 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 4 q^{3} - 3 q^{5} + 11 q^{9}+O(q^{10}) \) 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

Introduction

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