LMFDB - Embedded newform 9016.2.a.bl.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} - 4x^{10} - 14x^{9} + 63x^{8} + 51x^{7} - 305x^{6} + 16x^{5} + 429x^{4} - 234x^{3} - 42x^{2} + 39x - 3 $ x^11 - 4x^10 - 14x^9 + 63x^8 + 51x^7 - 305x^6 + 16x^5 + 429x^4 - 234x^3 - 42x^2 + 39x - 3
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			$2.93595$ 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)

$f(q)$	$=$	$q-2.93595 q^{3} -2.06839 q^{5} +5.61979 q^{9} +O(q^{10})$	$q-2.93595 q^{3} -2.06839 q^{5} +5.61979 q^{9} +6.34861 q^{11} +0.551495 q^{13} +6.07270 q^{15} +1.25034 q^{17} -2.23502 q^{19} +1.00000 q^{23} -0.721750 q^{25} -7.69157 q^{27} -7.69669 q^{29} -3.78976 q^{31} -18.6392 q^{33} +9.51289 q^{37} -1.61916 q^{39} -3.26748 q^{41} -6.27717 q^{43} -11.6239 q^{45} -3.55089 q^{47} -3.67095 q^{51} +7.92272 q^{53} -13.1314 q^{55} +6.56190 q^{57} +12.1548 q^{59} +2.16576 q^{61} -1.14071 q^{65} -15.0269 q^{67} -2.93595 q^{69} -7.26256 q^{71} +2.94987 q^{73} +2.11902 q^{75} +3.06150 q^{79} +5.72268 q^{81} -1.67699 q^{83} -2.58620 q^{85} +22.5971 q^{87} -11.1616 q^{89} +11.1265 q^{93} +4.62290 q^{95} -11.7112 q^{97} +35.6779 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 4 q^{3} - q^{5} + 11 q^{9}+O(q^{10}) $ 11 * q - 4 * q^3 - q^5 + 11 * q^9	$ 11 q - 4 q^{3} - q^{5} + 11 q^{9} + 3 q^{13} - 8 q^{15} - 5 q^{17} - 12 q^{19} + 11 q^{23} + 22 q^{25} - 19 q^{27} - 15 q^{29} - 16 q^{31} - 4 q^{33} + 3 q^{37} - q^{39} - 28 q^{41} - 9 q^{43} + 19 q^{45} - 31 q^{47} - 15 q^{51} + 13 q^{53} - 35 q^{55} - 21 q^{57} - 11 q^{59} + 19 q^{61} - 7 q^{65} + 19 q^{67} - 4 q^{69} - 5 q^{71} + 5 q^{73} - 28 q^{75} - 13 q^{79} + 35 q^{81} - 17 q^{83} - 39 q^{85} - 4 q^{87} - 10 q^{89} - 6 q^{93} + 33 q^{95} - 35 q^{97} + 13 q^{99}+O(q^{100}) $ 11 * q - 4 * q^3 - q^5 + 11 * q^9 + 3 * q^13 - 8 * q^15 - 5 * q^17 - 12 * q^19 + 11 * q^23 + 22 * q^25 - 19 * q^27 - 15 * q^29 - 16 * q^31 - 4 * q^33 + 3 * q^37 - q^39 - 28 * q^41 - 9 * q^43 + 19 * q^45 - 31 * q^47 - 15 * q^51 + 13 * q^53 - 35 * q^55 - 21 * q^57 - 11 * q^59 + 19 * q^61 - 7 * q^65 + 19 * q^67 - 4 * q^69 - 5 * q^71 + 5 * q^73 - 28 * q^75 - 13 * q^79 + 35 * q^81 - 17 * q^83 - 39 * q^85 - 4 * q^87 - 10 * q^89 - 6 * q^93 + 33 * q^95 - 35 * q^97 + 13 * 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
$3$	−2.93595	−1.69507	−0.847535	−	0.530739i	$-0.821914\pi$
$3$	−2.93595	−1.69507	−0.847535	+	0.530739i	$0.821914\pi$
$4$	0	0
$5$	−2.06839	−0.925014	−0.462507	−	0.886616i	$-0.653050\pi$
$5$	−2.06839	−0.925014	−0.462507	+	0.886616i	$0.653050\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	5.61979	1.87326
$10$	0	0
$11$	6.34861	1.91418	0.957090	−	0.289792i	$-0.0935861\pi$
$11$	6.34861	1.91418	0.957090	+	0.289792i	$0.0935861\pi$
$12$	0	0
$13$	0.551495	0.152957	0.0764786	−	0.997071i	$-0.475632\pi$
$13$	0.551495	0.152957	0.0764786	+	0.997071i	$0.475632\pi$
$14$	0	0
$15$	6.07270	1.56796
$16$	0	0
$17$	1.25034	0.303253	0.151627	−	0.988438i	$-0.451549\pi$
$17$	1.25034	0.303253	0.151627	+	0.988438i	$0.451549\pi$
$18$	0	0
$19$	−2.23502	−0.512748	−0.256374	−	0.966578i	$-0.582528\pi$
$19$	−2.23502	−0.512748	−0.256374	+	0.966578i	$0.582528\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0	0
$25$	−0.721750	−0.144350
$26$	0	0
$27$	−7.69157	−1.48024
$28$	0	0
$29$	−7.69669	−1.42924	−0.714620	−	0.699513i	$-0.753400\pi$
$29$	−7.69669	−1.42924	−0.714620	+	0.699513i	$0.753400\pi$
$30$	0	0
$31$	−3.78976	−0.680661	−0.340331	−	0.940306i	$-0.610539\pi$
$31$	−3.78976	−0.680661	−0.340331	+	0.940306i	$0.610539\pi$
$32$	0	0
$33$	−18.6392	−3.24467
$34$	0	0
$35$	0	0
$36$	0	0
$37$	9.51289	1.56391	0.781955	−	0.623335i	$-0.214223\pi$
$37$	9.51289	1.56391	0.781955	+	0.623335i	$0.214223\pi$
$38$	0	0
$39$	−1.61916	−0.259273
$40$	0	0
$41$	−3.26748	−0.510295	−0.255147	−	0.966902i	$-0.582124\pi$
$41$	−3.26748	−0.510295	−0.255147	+	0.966902i	$0.582124\pi$
$42$	0	0
$43$	−6.27717	−0.957259	−0.478629	−	0.878017i	$-0.658866\pi$
$43$	−6.27717	−0.957259	−0.478629	+	0.878017i	$0.658866\pi$
$44$	0	0
$45$	−11.6239	−1.73279
$46$	0	0
$47$	−3.55089	−0.517950	−0.258975	−	0.965884i	$-0.583385\pi$
$47$	−3.55089	−0.517950	−0.258975	+	0.965884i	$0.583385\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	−3.67095	−0.514035
$52$	0	0
$53$	7.92272	1.08827	0.544135	−	0.838998i	$-0.316858\pi$
$53$	7.92272	1.08827	0.544135	+	0.838998i	$0.316858\pi$
$54$	0	0
$55$	−13.1314	−1.77064
$56$	0	0
$57$	6.56190	0.869145
$58$	0	0
$59$	12.1548	1.58241	0.791207	−	0.611548i	$-0.209453\pi$
$59$	12.1548	1.58241	0.791207	+	0.611548i	$0.209453\pi$
$60$	0	0
$61$	2.16576	0.277297	0.138649	−	0.990342i	$-0.455724\pi$
$61$	2.16576	0.277297	0.138649	+	0.990342i	$0.455724\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	−1.14071	−0.141487
$66$	0	0
$67$	−15.0269	−1.83583	−0.917915	−	0.396776i	$-0.870129\pi$
$67$	−15.0269	−1.83583	−0.917915	+	0.396776i	$0.870129\pi$
$68$	0	0
$69$	−2.93595	−0.353447
$70$	0	0
$71$	−7.26256	−0.861907	−0.430954	−	0.902374i	$-0.641823\pi$
$71$	−7.26256	−0.861907	−0.430954	+	0.902374i	$0.641823\pi$
$72$	0	0
$73$	2.94987	0.345256	0.172628	−	0.984987i	$-0.444774\pi$
$73$	2.94987	0.345256	0.172628	+	0.984987i	$0.444774\pi$
$74$	0	0
$75$	2.11902	0.244683
$76$	0	0
$77$	0	0
$78$	0	0
$79$	3.06150	0.344446	0.172223	−	0.985058i	$-0.444905\pi$
$79$	3.06150	0.344446	0.172223	+	0.985058i	$0.444905\pi$
$80$	0	0
$81$	5.72268	0.635854
$82$	0	0
$83$	−1.67699	−0.184074	−0.0920370	−	0.995756i	$-0.529338\pi$
$83$	−1.67699	−0.184074	−0.0920370	+	0.995756i	$0.529338\pi$
$84$	0	0
$85$	−2.58620	−0.280513
$86$	0	0
$87$	22.5971	2.42266
$88$	0	0
$89$	−11.1616	−1.18313	−0.591565	−	0.806258i	$-0.701490\pi$
$89$	−11.1616	−1.18313	−0.591565	+	0.806258i	$0.701490\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	11.1265	1.15377
$94$	0	0
$95$	4.62290	0.474299
$96$	0	0
$97$	−11.7112	−1.18910	−0.594548	−	0.804060i	$-0.702669\pi$
$97$	−11.7112	−1.18910	−0.594548	+	0.804060i	$0.702669\pi$
$98$	0	0
$99$	35.6779	3.58576
$100$	0	0
$101$	−1.85311	−0.184391	−0.0921957	−	0.995741i	$-0.529389\pi$
$101$	−1.85311	−0.184391	−0.0921957	+	0.995741i	$0.529389\pi$
$102$	0	0
$103$	4.60136	0.453385	0.226693	−	0.973966i	$-0.427209\pi$
$103$	4.60136	0.453385	0.226693	+	0.973966i	$0.427209\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	10.7763	1.04178	0.520891	−	0.853623i	$-0.325600\pi$
$107$	10.7763	1.04178	0.520891	+	0.853623i	$0.325600\pi$
$108$	0	0
$109$	−7.02350	−0.672729	−0.336364	−	0.941732i	$-0.609197\pi$
$109$	−7.02350	−0.672729	−0.336364	+	0.941732i	$0.609197\pi$
$110$	0	0
$111$	−27.9294	−2.65094
$112$	0	0
$113$	2.88694	0.271581	0.135790	−	0.990738i	$-0.456643\pi$
$113$	2.88694	0.271581	0.135790	+	0.990738i	$0.456643\pi$
$114$	0	0
$115$	−2.06839	−0.192879
$116$	0	0
$117$	3.09929	0.286529
$118$	0	0
$119$	0	0
$120$	0	0
$121$	29.3049	2.66408
$122$	0	0
$123$	9.59315	0.864985
$124$	0	0
$125$	11.8348	1.05854
$126$	0	0
$127$	−15.9834	−1.41830	−0.709149	−	0.705059i	$-0.750921\pi$
$127$	−15.9834	−1.41830	−0.709149	+	0.705059i	$0.750921\pi$
$128$	0	0
$129$	18.4294	1.62262
$130$	0	0
$131$	3.69471	0.322809	0.161404	−	0.986888i	$-0.448398\pi$
$131$	3.69471	0.322809	0.161404	+	0.986888i	$0.448398\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	15.9092	1.36925
$136$	0	0
$137$	18.6901	1.59680	0.798401	−	0.602126i	$-0.205679\pi$
$137$	18.6901	1.59680	0.798401	+	0.602126i	$0.205679\pi$
$138$	0	0
$139$	−3.59952	−0.305307	−0.152654	−	0.988280i	$-0.548782\pi$
$139$	−3.59952	−0.305307	−0.152654	+	0.988280i	$0.548782\pi$
$140$	0	0
$141$	10.4252	0.877962
$142$	0	0
$143$	3.50123	0.292788
$144$	0	0
$145$	15.9198	1.32207
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−4.45987	−0.365366	−0.182683	−	0.983172i	$-0.558478\pi$
$149$	−4.45987	−0.365366	−0.182683	+	0.983172i	$0.558478\pi$
$150$	0	0
$151$	12.2119	0.993786	0.496893	−	0.867812i	$-0.334474\pi$
$151$	12.2119	0.993786	0.496893	+	0.867812i	$0.334474\pi$
$152$	0	0
$153$	7.02668	0.568073
$154$	0	0
$155$	7.83872	0.629621
$156$	0	0
$157$	22.2310	1.77423	0.887115	−	0.461549i	$-0.152706\pi$
$157$	22.2310	1.77423	0.887115	+	0.461549i	$0.152706\pi$
$158$	0	0
$159$	−23.2607	−1.84469
$160$	0	0
$161$	0	0
$162$	0	0
$163$	2.84250	0.222641	0.111321	−	0.993785i	$-0.464492\pi$
$163$	2.84250	0.222641	0.111321	+	0.993785i	$0.464492\pi$
$164$	0	0
$165$	38.5532	3.00136
$166$	0	0
$167$	14.2845	1.10537	0.552683	−	0.833392i	$-0.313604\pi$
$167$	14.2845	1.10537	0.552683	+	0.833392i	$0.313604\pi$
$168$	0	0
$169$	−12.6959	−0.976604
$170$	0	0
$171$	−12.5603	−0.960513
$172$	0	0
$173$	19.6354	1.49286	0.746428	−	0.665467i	$-0.231767\pi$
$173$	19.6354	1.49286	0.746428	+	0.665467i	$0.231767\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−35.6857	−2.68230
$178$	0	0
$179$	−4.79361	−0.358291	−0.179145	−	0.983823i	$-0.557333\pi$
$179$	−4.79361	−0.358291	−0.179145	+	0.983823i	$0.557333\pi$
$180$	0	0
$181$	16.8379	1.25155	0.625775	−	0.780004i	$-0.284783\pi$
$181$	16.8379	1.25155	0.625775	+	0.780004i	$0.284783\pi$
$182$	0	0
$183$	−6.35856	−0.470038
$184$	0	0
$185$	−19.6764	−1.44664
$186$	0	0
$187$	7.93796	0.580481
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−19.1466	−1.38540	−0.692701	−	0.721225i	$-0.743579\pi$
$191$	−19.1466	−1.38540	−0.692701	+	0.721225i	$0.743579\pi$
$192$	0	0
$193$	17.1942	1.23767	0.618834	−	0.785522i	$-0.287605\pi$
$193$	17.1942	1.23767	0.618834	+	0.785522i	$0.287605\pi$
$194$	0	0
$195$	3.34906	0.239831
$196$	0	0
$197$	−11.5331	−0.821703	−0.410851	−	0.911702i	$-0.634768\pi$
$197$	−11.5331	−0.821703	−0.410851	+	0.911702i	$0.634768\pi$
$198$	0	0
$199$	−10.1556	−0.719915	−0.359957	−	0.932969i	$-0.617209\pi$
$199$	−10.1556	−0.719915	−0.359957	+	0.932969i	$0.617209\pi$
$200$	0	0
$201$	44.1183	3.11186
$202$	0	0
$203$	0	0
$204$	0	0
$205$	6.75843	0.472029
$206$	0	0
$207$	5.61979	0.390603
$208$	0	0
$209$	−14.1893	−0.981492
$210$	0	0
$211$	−4.55937	−0.313880	−0.156940	−	0.987608i	$-0.550163\pi$
$211$	−4.55937	−0.313880	−0.156940	+	0.987608i	$0.550163\pi$
$212$	0	0
$213$	21.3225	1.46099
$214$	0	0
$215$	12.9836	0.885477
$216$	0	0
$217$	0	0
$218$	0	0
$219$	−8.66066	−0.585233
$220$	0	0
$221$	0.689559	0.0463847
$222$	0	0
$223$	−6.55814	−0.439166	−0.219583	−	0.975594i	$-0.570470\pi$
$223$	−6.55814	−0.439166	−0.219583	+	0.975594i	$0.570470\pi$
$224$	0	0
$225$	−4.05608	−0.270406
$226$	0	0
$227$	−27.1171	−1.79983	−0.899914	−	0.436068i	$-0.856371\pi$
$227$	−27.1171	−1.79983	−0.899914	+	0.436068i	$0.856371\pi$
$228$	0	0
$229$	−11.5573	−0.763729	−0.381865	−	0.924218i	$-0.624718\pi$
$229$	−11.5573	−0.763729	−0.381865	+	0.924218i	$0.624718\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	16.4113	1.07514	0.537570	−	0.843219i	$-0.319342\pi$
$233$	16.4113	1.07514	0.537570	+	0.843219i	$0.319342\pi$
$234$	0	0
$235$	7.34463	0.479111
$236$	0	0
$237$	−8.98840	−0.583860
$238$	0	0
$239$	−18.7816	−1.21488	−0.607440	−	0.794366i	$-0.707803\pi$
$239$	−18.7816	−1.21488	−0.607440	+	0.794366i	$0.707803\pi$
$240$	0	0
$241$	28.0261	1.80532	0.902659	−	0.430357i	$-0.141612\pi$
$241$	28.0261	1.80532	0.902659	+	0.430357i	$0.141612\pi$
$242$	0	0
$243$	6.27321	0.402427
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−1.23260	−0.0784286
$248$	0	0
$249$	4.92357	0.312018
$250$	0	0
$251$	−10.3675	−0.654394	−0.327197	−	0.944956i	$-0.606104\pi$
$251$	−10.3675	−0.654394	−0.327197	+	0.944956i	$0.606104\pi$
$252$	0	0
$253$	6.34861	0.399134
$254$	0	0
$255$	7.59296	0.475490
$256$	0	0
$257$	−23.7395	−1.48083	−0.740413	−	0.672152i	$-0.765370\pi$
$257$	−23.7395	−1.48083	−0.740413	+	0.672152i	$0.765370\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−43.2538	−2.67734
$262$	0	0
$263$	8.09431	0.499117	0.249558	−	0.968360i	$-0.419715\pi$
$263$	8.09431	0.499117	0.249558	+	0.968360i	$0.419715\pi$
$264$	0	0
$265$	−16.3873	−1.00666
$266$	0	0
$267$	32.7699	2.00549
$268$	0	0
$269$	19.9892	1.21876	0.609381	−	0.792878i	$-0.291418\pi$
$269$	19.9892	1.21876	0.609381	+	0.792878i	$0.291418\pi$
$270$	0	0
$271$	−21.2861	−1.29304	−0.646519	−	0.762898i	$-0.723776\pi$
$271$	−21.2861	−1.29304	−0.646519	+	0.762898i	$0.723776\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	−4.58211	−0.276312
$276$	0	0
$277$	16.8975	1.01527	0.507636	−	0.861572i	$-0.330520\pi$
$277$	16.8975	1.01527	0.507636	+	0.861572i	$0.330520\pi$
$278$	0	0
$279$	−21.2977	−1.27506
$280$	0	0
$281$	−27.2088	−1.62314	−0.811571	−	0.584254i	$-0.801387\pi$
$281$	−27.2088	−1.62314	−0.811571	+	0.584254i	$0.801387\pi$
$282$	0	0
$283$	−25.8263	−1.53522	−0.767608	−	0.640919i	$-0.778553\pi$
$283$	−25.8263	−1.53522	−0.767608	+	0.640919i	$0.778553\pi$
$284$	0	0
$285$	−13.5726	−0.803971
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−15.4366	−0.908038
$290$	0	0
$291$	34.3836	2.01560
$292$	0	0
$293$	1.06129	0.0620014	0.0310007	−	0.999519i	$-0.490131\pi$
$293$	1.06129	0.0620014	0.0310007	+	0.999519i	$0.490131\pi$
$294$	0	0
$295$	−25.1408	−1.46375
$296$	0	0
$297$	−48.8308	−2.83345
$298$	0	0
$299$	0.551495	0.0318938
$300$	0	0
$301$	0	0
$302$	0	0
$303$	5.44064	0.312556
$304$	0	0
$305$	−4.47965	−0.256504
$306$	0	0
$307$	−5.21889	−0.297858	−0.148929	−	0.988848i	$-0.547583\pi$
$307$	−5.21889	−0.297858	−0.148929	+	0.988848i	$0.547583\pi$
$308$	0	0
$309$	−13.5093	−0.768520
$310$	0	0
$311$	0.518625	0.0294085	0.0147043	−	0.999892i	$-0.495319\pi$
$311$	0.518625	0.0294085	0.0147043	+	0.999892i	$0.495319\pi$
$312$	0	0
$313$	−20.8005	−1.17572	−0.587858	−	0.808964i	$-0.700028\pi$
$313$	−20.8005	−1.17572	−0.587858	+	0.808964i	$0.700028\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−30.4841	−1.71216	−0.856079	−	0.516844i	$-0.827107\pi$
$317$	−30.4841	−1.71216	−0.856079	+	0.516844i	$0.827107\pi$
$318$	0	0
$319$	−48.8633	−2.73582
$320$	0	0
$321$	−31.6386	−1.76589
$322$	0	0
$323$	−2.79454	−0.155493
$324$	0	0
$325$	−0.398041	−0.0220794
$326$	0	0
$327$	20.6206	1.14032
$328$	0	0
$329$	0	0
$330$	0	0
$331$	10.7340	0.589996	0.294998	−	0.955498i	$-0.404681\pi$
$331$	10.7340	0.589996	0.294998	+	0.955498i	$0.404681\pi$
$332$	0	0
$333$	53.4605	2.92962
$334$	0	0
$335$	31.0816	1.69817
$336$	0	0
$337$	2.69258	0.146674	0.0733370	−	0.997307i	$-0.476635\pi$
$337$	2.69258	0.146674	0.0733370	+	0.997307i	$0.476635\pi$
$338$	0	0
$339$	−8.47591	−0.460348
$340$	0	0
$341$	−24.0597	−1.30291
$342$	0	0
$343$	0	0
$344$	0	0
$345$	6.07270	0.326943
$346$	0	0
$347$	−20.1187	−1.08003	−0.540014	−	0.841656i	$-0.681581\pi$
$347$	−20.1187	−1.08003	−0.540014	+	0.841656i	$0.681581\pi$
$348$	0	0
$349$	25.4293	1.36120	0.680601	−	0.732654i	$-0.261719\pi$
$349$	25.4293	1.36120	0.680601	+	0.732654i	$0.261719\pi$
$350$	0	0
$351$	−4.24186	−0.226414
$352$	0	0
$353$	24.7628	1.31799	0.658996	−	0.752147i	$-0.270982\pi$
$353$	24.7628	1.31799	0.658996	+	0.752147i	$0.270982\pi$
$354$	0	0
$355$	15.0218	0.797276
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−23.9752	−1.26536	−0.632682	−	0.774412i	$-0.718046\pi$
$359$	−23.9752	−1.26536	−0.632682	+	0.774412i	$0.718046\pi$
$360$	0	0
$361$	−14.0047	−0.737089
$362$	0	0
$363$	−86.0377	−4.51581
$364$	0	0
$365$	−6.10149	−0.319366
$366$	0	0
$367$	−34.9516	−1.82446	−0.912229	−	0.409682i	$-0.865640\pi$
$367$	−34.9516	−1.82446	−0.912229	+	0.409682i	$0.865640\pi$
$368$	0	0
$369$	−18.3626	−0.955916
$370$	0	0
$371$	0	0
$372$	0	0
$373$	6.23666	0.322922	0.161461	−	0.986879i	$-0.448379\pi$
$373$	6.23666	0.322922	0.161461	+	0.986879i	$0.448379\pi$
$374$	0	0
$375$	−34.7464	−1.79430
$376$	0	0
$377$	−4.24469	−0.218613
$378$	0	0
$379$	10.4383	0.536181	0.268091	−	0.963394i	$-0.413607\pi$
$379$	10.4383	0.536181	0.268091	+	0.963394i	$0.413607\pi$
$380$	0	0
$381$	46.9264	2.40411
$382$	0	0
$383$	28.1576	1.43879	0.719393	−	0.694603i	$-0.244420\pi$
$383$	28.1576	1.43879	0.719393	+	0.694603i	$0.244420\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−35.2764	−1.79320
$388$	0	0
$389$	24.5888	1.24670	0.623350	−	0.781943i	$-0.285771\pi$
$389$	24.5888	1.24670	0.623350	+	0.781943i	$0.285771\pi$
$390$	0	0
$391$	1.25034	0.0632326
$392$	0	0
$393$	−10.8475	−0.547183
$394$	0	0
$395$	−6.33238	−0.318617
$396$	0	0
$397$	33.5961	1.68614	0.843069	−	0.537806i	$-0.180747\pi$
$397$	33.5961	1.68614	0.843069	+	0.537806i	$0.180747\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	23.7193	1.18449	0.592244	−	0.805759i	$-0.298242\pi$
$401$	23.7193	1.18449	0.592244	+	0.805759i	$0.298242\pi$
$402$	0	0
$403$	−2.09003	−0.104112
$404$	0	0
$405$	−11.8368	−0.588173
$406$	0	0
$407$	60.3937	2.99360
$408$	0	0
$409$	−25.0622	−1.23924	−0.619622	−	0.784900i	$-0.712714\pi$
$409$	−25.0622	−1.23924	−0.619622	+	0.784900i	$0.712714\pi$
$410$	0	0
$411$	−54.8731	−2.70669
$412$	0	0
$413$	0	0
$414$	0	0
$415$	3.46868	0.170271
$416$	0	0
$417$	10.5680	0.517517
$418$	0	0
$419$	−14.5270	−0.709693	−0.354846	−	0.934925i	$-0.615467\pi$
$419$	−14.5270	−0.709693	−0.354846	+	0.934925i	$0.615467\pi$
$420$	0	0
$421$	26.9894	1.31538	0.657691	−	0.753288i	$-0.271533\pi$
$421$	26.9894	1.31538	0.657691	+	0.753288i	$0.271533\pi$
$422$	0	0
$423$	−19.9553	−0.970258
$424$	0	0
$425$	−0.902436	−0.0437746
$426$	0	0
$427$	0	0
$428$	0	0
$429$	−10.2794	−0.496296
$430$	0	0
$431$	−33.2874	−1.60340	−0.801700	−	0.597727i	$-0.796071\pi$
$431$	−33.2874	−1.60340	−0.801700	+	0.597727i	$0.796071\pi$
$432$	0	0
$433$	−40.7744	−1.95949	−0.979746	−	0.200244i	$-0.935826\pi$
$433$	−40.7744	−1.95949	−0.979746	+	0.200244i	$0.935826\pi$
$434$	0	0
$435$	−46.7397	−2.24100
$436$	0	0
$437$	−2.23502	−0.106915
$438$	0	0
$439$	6.36980	0.304014	0.152007	−	0.988379i	$-0.451426\pi$
$439$	6.36980	0.304014	0.152007	+	0.988379i	$0.451426\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	6.96736	0.331029	0.165515	−	0.986207i	$-0.447071\pi$
$443$	6.96736	0.331029	0.165515	+	0.986207i	$0.447071\pi$
$444$	0	0
$445$	23.0866	1.09441
$446$	0	0
$447$	13.0939	0.619322
$448$	0	0
$449$	7.78042	0.367181	0.183590	−	0.983003i	$-0.441228\pi$
$449$	7.78042	0.367181	0.183590	+	0.983003i	$0.441228\pi$
$450$	0	0
$451$	−20.7440	−0.976795
$452$	0	0
$453$	−35.8534	−1.68454
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−14.3083	−0.669316	−0.334658	−	0.942340i	$-0.608621\pi$
$457$	−14.3083	−0.669316	−0.334658	+	0.942340i	$0.608621\pi$
$458$	0	0
$459$	−9.61712	−0.448889
$460$	0	0
$461$	10.5537	0.491534	0.245767	−	0.969329i	$-0.420960\pi$
$461$	10.5537	0.491534	0.245767	+	0.969329i	$0.420960\pi$
$462$	0	0
$463$	5.42674	0.252202	0.126101	−	0.992017i	$-0.459754\pi$
$463$	5.42674	0.252202	0.126101	+	0.992017i	$0.459754\pi$
$464$	0	0
$465$	−23.0141	−1.06725
$466$	0	0
$467$	1.09634	0.0507327	0.0253664	−	0.999678i	$-0.491925\pi$
$467$	1.09634	0.0507327	0.0253664	+	0.999678i	$0.491925\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	−65.2691	−3.00744
$472$	0	0
$473$	−39.8513	−1.83236
$474$	0	0
$475$	1.61312	0.0740152
$476$	0	0
$477$	44.5240	2.03862
$478$	0	0
$479$	−19.4326	−0.887898	−0.443949	−	0.896052i	$-0.646423\pi$
$479$	−19.4326	−0.887898	−0.443949	+	0.896052i	$0.646423\pi$
$480$	0	0
$481$	5.24631	0.239211
$482$	0	0
$483$	0	0
$484$	0	0
$485$	24.2234	1.09993
$486$	0	0
$487$	3.23406	0.146549	0.0732746	−	0.997312i	$-0.476655\pi$
$487$	3.23406	0.146549	0.0732746	+	0.997312i	$0.476655\pi$
$488$	0	0
$489$	−8.34542	−0.377393
$490$	0	0
$491$	−8.64754	−0.390258	−0.195129	−	0.980778i	$-0.562513\pi$
$491$	−8.64754	−0.390258	−0.195129	+	0.980778i	$0.562513\pi$
$492$	0	0
$493$	−9.62352	−0.433421
$494$	0	0
$495$	−73.7959	−3.31688
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−1.43001	−0.0640162	−0.0320081	−	0.999488i	$-0.510190\pi$
$499$	−1.43001	−0.0640162	−0.0320081	+	0.999488i	$0.510190\pi$
$500$	0	0
$501$	−41.9385	−1.87367
$502$	0	0
$503$	11.2804	0.502967	0.251484	−	0.967862i	$-0.419082\pi$
$503$	11.2804	0.502967	0.251484	+	0.967862i	$0.419082\pi$
$504$	0	0
$505$	3.83296	0.170565
$506$	0	0
$507$	37.2744	1.65541
$508$	0	0
$509$	−24.0546	−1.06620	−0.533101	−	0.846051i	$-0.678974\pi$
$509$	−24.0546	−1.06620	−0.533101	+	0.846051i	$0.678974\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	17.1908	0.758993
$514$	0	0
$515$	−9.51741	−0.419387
$516$	0	0
$517$	−22.5432	−0.991450
$518$	0	0
$519$	−57.6487	−2.53049
$520$	0	0
$521$	−20.7137	−0.907483	−0.453741	−	0.891133i	$-0.649911\pi$
$521$	−20.7137	−0.907483	−0.453741	+	0.891133i	$0.649911\pi$
$522$	0	0
$523$	33.9765	1.48569	0.742844	−	0.669465i	$-0.233477\pi$
$523$	33.9765	1.48569	0.742844	+	0.669465i	$0.233477\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−4.73851	−0.206413
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	68.3072	2.96428
$532$	0	0
$533$	−1.80200	−0.0780532
$534$	0	0
$535$	−22.2896	−0.963662
$536$	0	0
$537$	14.0738	0.607328
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−1.32392	−0.0569196	−0.0284598	−	0.999595i	$-0.509060\pi$
$541$	−1.32392	−0.0569196	−0.0284598	+	0.999595i	$0.509060\pi$
$542$	0	0
$543$	−49.4352	−2.12147
$544$	0	0
$545$	14.5274	0.622283
$546$	0	0
$547$	30.9173	1.32193	0.660964	−	0.750418i	$-0.270148\pi$
$547$	30.9173	1.32193	0.660964	+	0.750418i	$0.270148\pi$
$548$	0	0
$549$	12.1711	0.519451
$550$	0	0
$551$	17.2023	0.732841
$552$	0	0
$553$	0	0
$554$	0	0
$555$	57.7689	2.45215
$556$	0	0
$557$	−8.04495	−0.340876	−0.170438	−	0.985368i	$-0.554518\pi$
$557$	−8.04495	−0.340876	−0.170438	+	0.985368i	$0.554518\pi$
$558$	0	0
$559$	−3.46183	−0.146420
$560$	0	0
$561$	−23.3054	−0.983956
$562$	0	0
$563$	−27.3348	−1.15203	−0.576013	−	0.817441i	$-0.695392\pi$
$563$	−27.3348	−1.15203	−0.576013	+	0.817441i	$0.695392\pi$
$564$	0	0
$565$	−5.97133	−0.251216
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−28.4334	−1.19199	−0.595996	−	0.802987i	$-0.703243\pi$
$569$	−28.4334	−1.19199	−0.595996	+	0.802987i	$0.703243\pi$
$570$	0	0
$571$	−1.46470	−0.0612958	−0.0306479	−	0.999530i	$-0.509757\pi$
$571$	−1.46470	−0.0612958	−0.0306479	+	0.999530i	$0.509757\pi$
$572$	0	0
$573$	56.2135	2.34835
$574$	0	0
$575$	−0.721750	−0.0300990
$576$	0	0
$577$	−15.2246	−0.633808	−0.316904	−	0.948458i	$-0.602643\pi$
$577$	−15.2246	−0.633808	−0.316904	+	0.948458i	$0.602643\pi$
$578$	0	0
$579$	−50.4814	−2.09793
$580$	0	0
$581$	0	0
$582$	0	0
$583$	50.2983	2.08314
$584$	0	0
$585$	−6.41055	−0.265043
$586$	0	0
$587$	8.36744	0.345361	0.172681	−	0.984978i	$-0.444757\pi$
$587$	8.36744	0.345361	0.172681	+	0.984978i	$0.444757\pi$
$588$	0	0
$589$	8.47019	0.349008
$590$	0	0
$591$	33.8607	1.39284
$592$	0	0
$593$	12.4620	0.511753	0.255876	−	0.966709i	$-0.417636\pi$
$593$	12.4620	0.511753	0.255876	+	0.966709i	$0.417636\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	29.8165	1.22031
$598$	0	0
$599$	36.7397	1.50114	0.750571	−	0.660790i	$-0.229779\pi$
$599$	36.7397	1.50114	0.750571	+	0.660790i	$0.229779\pi$
$600$	0	0
$601$	−13.7878	−0.562418	−0.281209	−	0.959647i	$-0.590735\pi$
$601$	−13.7878	−0.562418	−0.281209	+	0.959647i	$0.590735\pi$
$602$	0	0
$603$	−84.4482	−3.43900
$604$	0	0
$605$	−60.6141	−2.46431
$606$	0	0
$607$	−34.3426	−1.39392	−0.696961	−	0.717109i	$-0.745465\pi$
$607$	−34.3426	−1.39392	−0.696961	+	0.717109i	$0.745465\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−1.95830	−0.0792243
$612$	0	0
$613$	−35.9235	−1.45093	−0.725467	−	0.688257i	$-0.758376\pi$
$613$	−35.9235	−1.45093	−0.725467	+	0.688257i	$0.758376\pi$
$614$	0	0
$615$	−19.8424	−0.800123
$616$	0	0
$617$	−47.9263	−1.92944	−0.964719	−	0.263280i	$-0.915196\pi$
$617$	−47.9263	−1.92944	−0.964719	+	0.263280i	$0.915196\pi$
$618$	0	0
$619$	−1.55838	−0.0626366	−0.0313183	−	0.999509i	$-0.509971\pi$
$619$	−1.55838	−0.0626366	−0.0313183	+	0.999509i	$0.509971\pi$
$620$	0	0
$621$	−7.69157	−0.308652
$622$	0	0
$623$	0	0
$624$	0	0
$625$	−20.8703	−0.834813
$626$	0	0
$627$	41.6590	1.66370
$628$	0	0
$629$	11.8944	0.474261
$630$	0	0
$631$	10.7930	0.429662	0.214831	−	0.976651i	$-0.431080\pi$
$631$	10.7930	0.429662	0.214831	+	0.976651i	$0.431080\pi$
$632$	0	0
$633$	13.3861	0.532048
$634$	0	0
$635$	33.0600	1.31194
$636$	0	0
$637$	0	0
$638$	0	0
$639$	−40.8141	−1.61458
$640$	0	0
$641$	−3.93355	−0.155366	−0.0776830	−	0.996978i	$-0.524752\pi$
$641$	−3.93355	−0.155366	−0.0776830	+	0.996978i	$0.524752\pi$
$642$	0	0
$643$	6.19678	0.244377	0.122189	−	0.992507i	$-0.461009\pi$
$643$	6.19678	0.244377	0.122189	+	0.992507i	$0.461009\pi$
$644$	0	0
$645$	−38.1193	−1.50095
$646$	0	0
$647$	27.3845	1.07660	0.538298	−	0.842755i	$-0.319067\pi$
$647$	27.3845	1.07660	0.538298	+	0.842755i	$0.319067\pi$
$648$	0	0
$649$	77.1659	3.02903
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−5.34102	−0.209010	−0.104505	−	0.994524i	$-0.533326\pi$
$653$	−5.34102	−0.209010	−0.104505	+	0.994524i	$0.533326\pi$
$654$	0	0
$655$	−7.64212	−0.298602
$656$	0	0
$657$	16.5776	0.646756
$658$	0	0
$659$	−23.5086	−0.915766	−0.457883	−	0.889012i	$-0.651392\pi$
$659$	−23.5086	−0.915766	−0.457883	+	0.889012i	$0.651392\pi$
$660$	0	0
$661$	5.48028	0.213158	0.106579	−	0.994304i	$-0.466010\pi$
$661$	5.48028	0.213158	0.106579	+	0.994304i	$0.466010\pi$
$662$	0	0
$663$	−2.02451	−0.0786254
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−7.69669	−0.298017
$668$	0	0
$669$	19.2544	0.744417
$670$	0	0
$671$	13.7496	0.530797
$672$	0	0
$673$	−14.7900	−0.570113	−0.285056	−	0.958511i	$-0.592012\pi$
$673$	−14.7900	−0.570113	−0.285056	+	0.958511i	$0.592012\pi$
$674$	0	0
$675$	5.55139	0.213673
$676$	0	0
$677$	2.80804	0.107922	0.0539609	−	0.998543i	$-0.482815\pi$
$677$	2.80804	0.107922	0.0539609	+	0.998543i	$0.482815\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	79.6145	3.05083
$682$	0	0
$683$	−7.64172	−0.292402	−0.146201	−	0.989255i	$-0.546705\pi$
$683$	−7.64172	−0.292402	−0.146201	+	0.989255i	$0.546705\pi$
$684$	0	0
$685$	−38.6585	−1.47706
$686$	0	0
$687$	33.9317	1.29458
$688$	0	0
$689$	4.36934	0.166459
$690$	0	0
$691$	−11.8988	−0.452651	−0.226325	−	0.974052i	$-0.572671\pi$
$691$	−11.8988	−0.452651	−0.226325	+	0.974052i	$0.572671\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	7.44522	0.282413
$696$	0	0
$697$	−4.08548	−0.154748
$698$	0	0
$699$	−48.1827	−1.82244
$700$	0	0
$701$	27.7282	1.04728	0.523640	−	0.851940i	$-0.324574\pi$
$701$	27.7282	1.04728	0.523640	+	0.851940i	$0.324574\pi$
$702$	0	0
$703$	−21.2615	−0.801892
$704$	0	0
$705$	−21.5635	−0.812127
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−37.6152	−1.41267	−0.706334	−	0.707879i	$-0.749652\pi$
$709$	−37.6152	−1.41267	−0.706334	+	0.707879i	$0.749652\pi$
$710$	0	0
$711$	17.2050	0.645238
$712$	0	0
$713$	−3.78976	−0.141928
$714$	0	0
$715$	−7.24192	−0.270832
$716$	0	0
$717$	55.1417	2.05931
$718$	0	0
$719$	−45.9181	−1.71246	−0.856229	−	0.516596i	$-0.827199\pi$
$719$	−45.9181	−1.71246	−0.856229	+	0.516596i	$0.827199\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	−82.2831	−3.06014
$724$	0	0
$725$	5.55509	0.206311
$726$	0	0
$727$	12.0488	0.446864	0.223432	−	0.974720i	$-0.428274\pi$
$727$	12.0488	0.446864	0.223432	+	0.974720i	$0.428274\pi$
$728$	0	0
$729$	−35.5859	−1.31800
$730$	0	0
$731$	−7.84862	−0.290292
$732$	0	0
$733$	2.89618	0.106973	0.0534865	−	0.998569i	$-0.482967\pi$
$733$	2.89618	0.106973	0.0534865	+	0.998569i	$0.482967\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−95.4001	−3.51411
$738$	0	0
$739$	−24.3297	−0.894984	−0.447492	−	0.894288i	$-0.647683\pi$
$739$	−24.3297	−0.894984	−0.447492	+	0.894288i	$0.647683\pi$
$740$	0	0
$741$	3.61885	0.132942
$742$	0	0
$743$	2.03059	0.0744952	0.0372476	−	0.999306i	$-0.488141\pi$
$743$	2.03059	0.0744952	0.0372476	+	0.999306i	$0.488141\pi$
$744$	0	0
$745$	9.22475	0.337969
$746$	0	0
$747$	−9.42435	−0.344819
$748$	0	0
$749$	0	0
$750$	0	0
$751$	11.5820	0.422633	0.211317	−	0.977418i	$-0.432225\pi$
$751$	11.5820	0.422633	0.211317	+	0.977418i	$0.432225\pi$
$752$	0	0
$753$	30.4386	1.10924
$754$	0	0
$755$	−25.2589	−0.919266
$756$	0	0
$757$	4.68941	0.170439	0.0852197	−	0.996362i	$-0.472841\pi$
$757$	4.68941	0.170439	0.0852197	+	0.996362i	$0.472841\pi$
$758$	0	0
$759$	−18.6392	−0.676560
$760$	0	0
$761$	−47.2363	−1.71231	−0.856157	−	0.516716i	$-0.827154\pi$
$761$	−47.2363	−1.71231	−0.856157	+	0.516716i	$0.827154\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	−14.5339	−0.525475
$766$	0	0
$767$	6.70329	0.242042
$768$	0	0
$769$	43.0870	1.55376	0.776878	−	0.629651i	$-0.216802\pi$
$769$	43.0870	1.55376	0.776878	+	0.629651i	$0.216802\pi$
$770$	0	0
$771$	69.6978	2.51011
$772$	0	0
$773$	19.7072	0.708817	0.354409	−	0.935091i	$-0.384682\pi$
$773$	19.7072	0.708817	0.354409	+	0.935091i	$0.384682\pi$
$774$	0	0
$775$	2.73526	0.0982534
$776$	0	0
$777$	0	0
$778$	0	0
$779$	7.30288	0.261653
$780$	0	0
$781$	−46.1072	−1.64985
$782$	0	0
$783$	59.1997	2.11562
$784$	0	0
$785$	−45.9825	−1.64119
$786$	0	0
$787$	−18.0730	−0.644233	−0.322117	−	0.946700i	$-0.604394\pi$
$787$	−18.0730	−0.644233	−0.322117	+	0.946700i	$0.604394\pi$
$788$	0	0
$789$	−23.7645	−0.846038
$790$	0	0
$791$	0	0
$792$	0	0
$793$	1.19441	0.0424146
$794$	0	0
$795$	48.1123	1.70637
$796$	0	0
$797$	26.0968	0.924394	0.462197	−	0.886777i	$-0.347061\pi$
$797$	26.0968	0.924394	0.462197	+	0.886777i	$0.347061\pi$
$798$	0	0
$799$	−4.43983	−0.157070
$800$	0	0
$801$	−62.7260	−2.21631
$802$	0	0
$803$	18.7276	0.660882
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−58.6872	−2.06589
$808$	0	0
$809$	7.47710	0.262881	0.131440	−	0.991324i	$-0.458040\pi$
$809$	7.47710	0.262881	0.131440	+	0.991324i	$0.458040\pi$
$810$	0	0
$811$	25.9550	0.911402	0.455701	−	0.890133i	$-0.349389\pi$
$811$	25.9550	0.911402	0.455701	+	0.890133i	$0.349389\pi$
$812$	0	0
$813$	62.4949	2.19179
$814$	0	0
$815$	−5.87940	−0.205946
$816$	0	0
$817$	14.0296	0.490833
$818$	0	0
$819$	0	0
$820$	0	0
$821$	31.0895	1.08503	0.542516	−	0.840045i	$-0.317472\pi$
$821$	31.0895	1.08503	0.542516	+	0.840045i	$0.317472\pi$
$822$	0	0
$823$	38.4131	1.33900	0.669498	−	0.742814i	$-0.266509\pi$
$823$	38.4131	1.33900	0.669498	+	0.742814i	$0.266509\pi$
$824$	0	0
$825$	13.4528	0.468368
$826$	0	0
$827$	−44.2575	−1.53899	−0.769493	−	0.638655i	$-0.779491\pi$
$827$	−44.2575	−1.53899	−0.769493	+	0.638655i	$0.779491\pi$
$828$	0	0
$829$	24.2825	0.843366	0.421683	−	0.906743i	$-0.361440\pi$
$829$	24.2825	0.843366	0.421683	+	0.906743i	$0.361440\pi$
$830$	0	0
$831$	−49.6102	−1.72096
$832$	0	0
$833$	0	0
$834$	0	0
$835$	−29.5459	−1.02248
$836$	0	0
$837$	29.1492	1.00754
$838$	0	0
$839$	−15.2155	−0.525296	−0.262648	−	0.964892i	$-0.584596\pi$
$839$	−15.2155	−0.525296	−0.262648	+	0.964892i	$0.584596\pi$
$840$	0	0
$841$	30.2391	1.04273
$842$	0	0
$843$	79.8836	2.75134
$844$	0	0
$845$	26.2600	0.903372
$846$	0	0
$847$	0	0
$848$	0	0
$849$	75.8248	2.60230
$850$	0	0
$851$	9.51289	0.326098
$852$	0	0
$853$	−45.1480	−1.54584	−0.772920	−	0.634504i	$-0.781205\pi$
$853$	−45.1480	−1.54584	−0.772920	+	0.634504i	$0.781205\pi$
$854$	0	0
$855$	25.9797	0.888488
$856$	0	0
$857$	40.2138	1.37368	0.686839	−	0.726809i	$-0.258998\pi$
$857$	40.2138	1.37368	0.686839	+	0.726809i	$0.258998\pi$
$858$	0	0
$859$	−51.3564	−1.75226	−0.876129	−	0.482078i	$-0.839882\pi$
$859$	−51.3564	−1.75226	−0.876129	+	0.482078i	$0.839882\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	23.2067	0.789964	0.394982	−	0.918689i	$-0.370751\pi$
$863$	23.2067	0.789964	0.394982	+	0.918689i	$0.370751\pi$
$864$	0	0
$865$	−40.6138	−1.38091
$866$	0	0
$867$	45.3212	1.53919
$868$	0	0
$869$	19.4363	0.659331
$870$	0	0
$871$	−8.28727	−0.280804
$872$	0	0
$873$	−65.8147	−2.22749
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−2.37924	−0.0803413	−0.0401707	−	0.999193i	$-0.512790\pi$
$877$	−2.37924	−0.0803413	−0.0401707	+	0.999193i	$0.512790\pi$
$878$	0	0
$879$	−3.11590	−0.105097
$880$	0	0
$881$	−39.7507	−1.33923	−0.669617	−	0.742707i	$-0.733542\pi$
$881$	−39.7507	−1.33923	−0.669617	+	0.742707i	$0.733542\pi$
$882$	0	0
$883$	−13.1182	−0.441463	−0.220731	−	0.975335i	$-0.570844\pi$
$883$	−13.1182	−0.441463	−0.220731	+	0.975335i	$0.570844\pi$
$884$	0	0
$885$	73.8121	2.48117
$886$	0	0
$887$	38.1150	1.27977	0.639887	−	0.768469i	$-0.278981\pi$
$887$	38.1150	1.27977	0.639887	+	0.768469i	$0.278981\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	36.3311	1.21714
$892$	0	0
$893$	7.93630	0.265578
$894$	0	0
$895$	9.91506	0.331424
$896$	0	0
$897$	−1.61916	−0.0540622
$898$	0	0
$899$	29.1686	0.972828
$900$	0	0
$901$	9.90613	0.330021
$902$	0	0
$903$	0	0
$904$	0	0
$905$	−34.8274	−1.15770
$906$	0	0
$907$	34.2260	1.13646	0.568228	−	0.822871i	$-0.307629\pi$
$907$	34.2260	1.13646	0.568228	+	0.822871i	$0.307629\pi$
$908$	0	0
$909$	−10.4141	−0.345414
$910$	0	0
$911$	−16.5863	−0.549528	−0.274764	−	0.961512i	$-0.588600\pi$
$911$	−16.5863	−0.549528	−0.274764	+	0.961512i	$0.588600\pi$
$912$	0	0
$913$	−10.6466	−0.352351
$914$	0	0
$915$	13.1520	0.434792
$916$	0	0
$917$	0	0
$918$	0	0
$919$	0.100570	0.00331751	0.00165875	−	0.999999i	$-0.499472\pi$
$919$	0.100570	0.00331751	0.00165875	+	0.999999i	$0.499472\pi$
$920$	0	0
$921$	15.3224	0.504890
$922$	0	0
$923$	−4.00527	−0.131835
$924$	0	0
$925$	−6.86593	−0.225750
$926$	0	0
$927$	25.8587	0.849310
$928$	0	0
$929$	−13.4833	−0.442372	−0.221186	−	0.975232i	$-0.570993\pi$
$929$	−13.4833	−0.442372	−0.221186	+	0.975232i	$0.570993\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	−1.52266	−0.0498495
$934$	0	0
$935$	−16.4188	−0.536953
$936$	0	0
$937$	54.6060	1.78390	0.891951	−	0.452133i	$-0.149337\pi$
$937$	54.6060	1.78390	0.891951	+	0.452133i	$0.149337\pi$
$938$	0	0
$939$	61.0693	1.99292
$940$	0	0
$941$	−22.9348	−0.747654	−0.373827	−	0.927498i	$-0.621955\pi$
$941$	−22.9348	−0.747654	−0.373827	+	0.927498i	$0.621955\pi$
$942$	0	0
$943$	−3.26748	−0.106404
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−6.84874	−0.222554	−0.111277	−	0.993789i	$-0.535494\pi$
$947$	−6.84874	−0.222554	−0.111277	+	0.993789i	$0.535494\pi$
$948$	0	0
$949$	1.62684	0.0528094
$950$	0	0
$951$	89.4998	2.90223
$952$	0	0
$953$	42.1107	1.36410	0.682049	−	0.731306i	$-0.261089\pi$
$953$	42.1107	1.36410	0.682049	+	0.731306i	$0.261089\pi$
$954$	0	0
$955$	39.6027	1.28151
$956$	0	0
$957$	143.460	4.63741
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−16.6377	−0.536700
$962$	0	0
$963$	60.5604	1.95153
$964$	0	0
$965$	−35.5644	−1.14486
$966$	0	0
$967$	−27.2233	−0.875441	−0.437721	−	0.899111i	$-0.644214\pi$
$967$	−27.2233	−0.875441	−0.437721	+	0.899111i	$0.644214\pi$
$968$	0	0
$969$	8.20463	0.263571
$970$	0	0
$971$	−48.7620	−1.56485	−0.782423	−	0.622748i	$-0.786016\pi$
$971$	−48.7620	−1.56485	−0.782423	+	0.622748i	$0.786016\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	1.16863	0.0374261
$976$	0	0
$977$	3.28324	0.105040	0.0525200	−	0.998620i	$-0.483275\pi$
$977$	3.28324	0.105040	0.0525200	+	0.998620i	$0.483275\pi$
$978$	0	0
$979$	−70.8608	−2.26472
$980$	0	0
$981$	−39.4706	−1.26020
$982$	0	0
$983$	13.0907	0.417528	0.208764	−	0.977966i	$-0.433056\pi$
$983$	13.0907	0.417528	0.208764	+	0.977966i	$0.433056\pi$
$984$	0	0
$985$	23.8551	0.760086
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−6.27717	−0.199602
$990$	0	0
$991$	−2.58348	−0.0820669	−0.0410335	−	0.999158i	$-0.513065\pi$
$991$	−2.58348	−0.0820669	−0.0410335	+	0.999158i	$0.513065\pi$
$992$	0	0
$993$	−31.5146	−1.00008
$994$	0	0
$995$	21.0059	0.665931
$996$	0	0
$997$	−0.663626	−0.0210172	−0.0105086	−	0.999945i	$-0.503345\pi$
$997$	−0.663626	−0.0210172	−0.0105086	+	0.999945i	$0.503345\pi$
$998$	0	0
$999$	−73.1691	−2.31497

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9016.2.a.bl.1.2		11
7.3	odd	6		1288.2.q.a.737.2	✓	22
7.5	odd	6		1288.2.q.a.921.2	yes	22
7.6	odd	2		9016.2.a.bq.1.10		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1288.2.q.a.737.2	✓	22	7.3	odd	6
1288.2.q.a.921.2	yes	22	7.5	odd	6
9016.2.a.bl.1.2		11	1.1	even	1	trivial
9016.2.a.bq.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)

\(f(q)\)	\(=\)	\(q-2.93595 q^{3} -2.06839 q^{5} +5.61979 q^{9} +O(q^{10})\)	\(q-2.93595 q^{3} -2.06839 q^{5} +5.61979 q^{9} +6.34861 q^{11} +0.551495 q^{13} +6.07270 q^{15} +1.25034 q^{17} -2.23502 q^{19} +1.00000 q^{23} -0.721750 q^{25} -7.69157 q^{27} -7.69669 q^{29} -3.78976 q^{31} -18.6392 q^{33} +9.51289 q^{37} -1.61916 q^{39} -3.26748 q^{41} -6.27717 q^{43} -11.6239 q^{45} -3.55089 q^{47} -3.67095 q^{51} +7.92272 q^{53} -13.1314 q^{55} +6.56190 q^{57} +12.1548 q^{59} +2.16576 q^{61} -1.14071 q^{65} -15.0269 q^{67} -2.93595 q^{69} -7.26256 q^{71} +2.94987 q^{73} +2.11902 q^{75} +3.06150 q^{79} +5.72268 q^{81} -1.67699 q^{83} -2.58620 q^{85} +22.5971 q^{87} -11.1616 q^{89} +11.1265 q^{93} +4.62290 q^{95} -11.7112 q^{97} +35.6779 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 4 q^{3} - q^{5} + 11 q^{9}+O(q^{10}) \) 11 * q - 4 * q^3 - q^5 + 11 * q^9	\( 11 q - 4 q^{3} - q^{5} + 11 q^{9} + 3 q^{13} - 8 q^{15} - 5 q^{17} - 12 q^{19} + 11 q^{23} + 22 q^{25} - 19 q^{27} - 15 q^{29} - 16 q^{31} - 4 q^{33} + 3 q^{37} - q^{39} - 28 q^{41} - 9 q^{43} + 19 q^{45} - 31 q^{47} - 15 q^{51} + 13 q^{53} - 35 q^{55} - 21 q^{57} - 11 q^{59} + 19 q^{61} - 7 q^{65} + 19 q^{67} - 4 q^{69} - 5 q^{71} + 5 q^{73} - 28 q^{75} - 13 q^{79} + 35 q^{81} - 17 q^{83} - 39 q^{85} - 4 q^{87} - 10 q^{89} - 6 q^{93} + 33 q^{95} - 35 q^{97} + 13 q^{99}+O(q^{100}) \) 11 * q - 4 * q^3 - q^5 + 11 * q^9 + 3 * q^13 - 8 * q^15 - 5 * q^17 - 12 * q^19 + 11 * q^23 + 22 * q^25 - 19 * q^27 - 15 * q^29 - 16 * q^31 - 4 * q^33 + 3 * q^37 - q^39 - 28 * q^41 - 9 * q^43 + 19 * q^45 - 31 * q^47 - 15 * q^51 + 13 * q^53 - 35 * q^55 - 21 * q^57 - 11 * q^59 + 19 * q^61 - 7 * q^65 + 19 * q^67 - 4 * q^69 - 5 * q^71 + 5 * q^73 - 28 * q^75 - 13 * q^79 + 35 * q^81 - 17 * q^83 - 39 * q^85 - 4 * q^87 - 10 * q^89 - 6 * q^93 + 33 * q^95 - 35 * q^97 + 13 * q^99

Introduction

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