LMFDB - Embedded newform 9016.2.a.bq.1.1

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:	$0$
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			1.1
Root			$-2.69483$ 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)

$f(q)$	$=$	$q-2.69483 q^{3} +0.987745 q^{5} +4.26210 q^{9} +O(q^{10})$	$q-2.69483 q^{3} +0.987745 q^{5} +4.26210 q^{9} +2.37013 q^{11} -4.07929 q^{13} -2.66180 q^{15} +7.58866 q^{17} +1.98174 q^{19} +1.00000 q^{23} -4.02436 q^{25} -3.40115 q^{27} -9.65576 q^{29} +6.17029 q^{31} -6.38709 q^{33} +0.0640261 q^{37} +10.9930 q^{39} +11.2783 q^{41} -5.61229 q^{43} +4.20987 q^{45} +11.3526 q^{47} -20.4501 q^{51} -7.57754 q^{53} +2.34108 q^{55} -5.34044 q^{57} +4.78879 q^{59} +9.53051 q^{61} -4.02930 q^{65} +10.8562 q^{67} -2.69483 q^{69} +7.82290 q^{71} -6.95332 q^{73} +10.8450 q^{75} +2.96992 q^{79} -3.62078 q^{81} -15.8626 q^{83} +7.49566 q^{85} +26.0206 q^{87} -4.81027 q^{89} -16.6279 q^{93} +1.95745 q^{95} +2.63923 q^{97} +10.1017 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.69483	−1.55586	−0.777930	−	0.628351i	$-0.783730\pi$
$3$	−2.69483	−1.55586	−0.777930	+	0.628351i	$0.783730\pi$
$4$	0	0
$5$	0.987745	0.441733	0.220866	−	0.975304i	$-0.429112\pi$
$5$	0.987745	0.441733	0.220866	+	0.975304i	$0.429112\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	4.26210	1.42070
$10$	0	0
$11$	2.37013	0.714620	0.357310	−	0.933986i	$-0.383694\pi$
$11$	2.37013	0.714620	0.357310	+	0.933986i	$0.383694\pi$
$12$	0	0
$13$	−4.07929	−1.13139	−0.565696	−	0.824614i	$-0.691393\pi$
$13$	−4.07929	−1.13139	−0.565696	+	0.824614i	$0.691393\pi$
$14$	0	0
$15$	−2.66180	−0.687275
$16$	0	0
$17$	7.58866	1.84052	0.920260	−	0.391307i	$-0.127977\pi$
$17$	7.58866	1.84052	0.920260	+	0.391307i	$0.127977\pi$
$18$	0	0
$19$	1.98174	0.454641	0.227321	−	0.973820i	$-0.427003\pi$
$19$	1.98174	0.454641	0.227321	+	0.973820i	$0.427003\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0	0
$25$	−4.02436	−0.804872
$26$	0	0
$27$	−3.40115	−0.654552
$28$	0	0
$29$	−9.65576	−1.79303	−0.896515	−	0.443013i	$-0.853909\pi$
$29$	−9.65576	−1.79303	−0.896515	+	0.443013i	$0.853909\pi$
$30$	0	0
$31$	6.17029	1.10822	0.554108	−	0.832445i	$-0.313059\pi$
$31$	6.17029	1.10822	0.554108	+	0.832445i	$0.313059\pi$
$32$	0	0
$33$	−6.38709	−1.11185
$34$	0	0
$35$	0	0
$36$	0	0
$37$	0.0640261	0.0105258	0.00526292	−	0.999986i	$-0.498325\pi$
$37$	0.0640261	0.0105258	0.00526292	+	0.999986i	$0.498325\pi$
$38$	0	0
$39$	10.9930	1.76029
$40$	0	0
$41$	11.2783	1.76137	0.880685	−	0.473702i	$-0.157082\pi$
$41$	11.2783	1.76137	0.880685	+	0.473702i	$0.157082\pi$
$42$	0	0
$43$	−5.61229	−0.855866	−0.427933	−	0.903810i	$-0.640758\pi$
$43$	−5.61229	−0.855866	−0.427933	+	0.903810i	$0.640758\pi$
$44$	0	0
$45$	4.20987	0.627571
$46$	0	0
$47$	11.3526	1.65595	0.827975	−	0.560765i	$-0.189493\pi$
$47$	11.3526	1.65595	0.827975	+	0.560765i	$0.189493\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	−20.4501	−2.86359
$52$	0	0
$53$	−7.57754	−1.04086	−0.520428	−	0.853906i	$-0.674228\pi$
$53$	−7.57754	−1.04086	−0.520428	+	0.853906i	$0.674228\pi$
$54$	0	0
$55$	2.34108	0.315671
$56$	0	0
$57$	−5.34044	−0.707359
$58$	0	0
$59$	4.78879	0.623447	0.311723	−	0.950173i	$-0.399094\pi$
$59$	4.78879	0.623447	0.311723	+	0.950173i	$0.399094\pi$
$60$	0	0
$61$	9.53051	1.22026	0.610129	−	0.792302i	$-0.291118\pi$
$61$	9.53051	1.22026	0.610129	+	0.792302i	$0.291118\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	−4.02930	−0.499773
$66$	0	0
$67$	10.8562	1.32630	0.663148	−	0.748488i	$-0.269220\pi$
$67$	10.8562	1.32630	0.663148	+	0.748488i	$0.269220\pi$
$68$	0	0
$69$	−2.69483	−0.324419
$70$	0	0
$71$	7.82290	0.928408	0.464204	−	0.885728i	$-0.346340\pi$
$71$	7.82290	0.928408	0.464204	+	0.885728i	$0.346340\pi$
$72$	0	0
$73$	−6.95332	−0.813825	−0.406912	−	0.913467i	$-0.633395\pi$
$73$	−6.95332	−0.813825	−0.406912	+	0.913467i	$0.633395\pi$
$74$	0	0
$75$	10.8450	1.25227
$76$	0	0
$77$	0	0
$78$	0	0
$79$	2.96992	0.334142	0.167071	−	0.985945i	$-0.446569\pi$
$79$	2.96992	0.334142	0.167071	+	0.985945i	$0.446569\pi$
$80$	0	0
$81$	−3.62078	−0.402309
$82$	0	0
$83$	−15.8626	−1.74115	−0.870575	−	0.492036i	$-0.836253\pi$
$83$	−15.8626	−1.74115	−0.870575	+	0.492036i	$0.836253\pi$
$84$	0	0
$85$	7.49566	0.813018
$86$	0	0
$87$	26.0206	2.78970
$88$	0	0
$89$	−4.81027	−0.509887	−0.254944	−	0.966956i	$-0.582057\pi$
$89$	−4.81027	−0.509887	−0.254944	+	0.966956i	$0.582057\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	−16.6279	−1.72423
$94$	0	0
$95$	1.95745	0.200830
$96$	0	0
$97$	2.63923	0.267973	0.133987	−	0.990983i	$-0.457222\pi$
$97$	2.63923	0.267973	0.133987	+	0.990983i	$0.457222\pi$
$98$	0	0
$99$	10.1017	1.01526
$100$	0	0
$101$	−10.4154	−1.03637	−0.518186	−	0.855268i	$-0.673392\pi$
$101$	−10.4154	−1.03637	−0.518186	+	0.855268i	$0.673392\pi$
$102$	0	0
$103$	−3.81381	−0.375786	−0.187893	−	0.982189i	$-0.560166\pi$
$103$	−3.81381	−0.375786	−0.187893	+	0.982189i	$0.560166\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−13.3838	−1.29386	−0.646931	−	0.762548i	$-0.723948\pi$
$107$	−13.3838	−1.29386	−0.646931	+	0.762548i	$0.723948\pi$
$108$	0	0
$109$	13.1577	1.26028	0.630142	−	0.776480i	$-0.282997\pi$
$109$	13.1577	1.26028	0.630142	+	0.776480i	$0.282997\pi$
$110$	0	0
$111$	−0.172540	−0.0163767
$112$	0	0
$113$	10.7207	1.00852	0.504259	−	0.863552i	$-0.331766\pi$
$113$	10.7207	1.00852	0.504259	+	0.863552i	$0.331766\pi$
$114$	0	0
$115$	0.987745	0.0921077
$116$	0	0
$117$	−17.3864	−1.60737
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−5.38250	−0.489318
$122$	0	0
$123$	−30.3930	−2.74045
$124$	0	0
$125$	−8.91376	−0.797271
$126$	0	0
$127$	1.10959	0.0984604	0.0492302	−	0.998787i	$-0.484323\pi$
$127$	1.10959	0.0984604	0.0492302	+	0.998787i	$0.484323\pi$
$128$	0	0
$129$	15.1242	1.33161
$130$	0	0
$131$	18.3702	1.60501	0.802504	−	0.596647i	$-0.203501\pi$
$131$	18.3702	1.60501	0.802504	+	0.596647i	$0.203501\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	−3.35947	−0.289137
$136$	0	0
$137$	−16.0068	−1.36755	−0.683776	−	0.729692i	$-0.739663\pi$
$137$	−16.0068	−1.36755	−0.683776	+	0.729692i	$0.739663\pi$
$138$	0	0
$139$	4.19528	0.355839	0.177920	−	0.984045i	$-0.443063\pi$
$139$	4.19528	0.355839	0.177920	+	0.984045i	$0.443063\pi$
$140$	0	0
$141$	−30.5934	−2.57643
$142$	0	0
$143$	−9.66845	−0.808516
$144$	0	0
$145$	−9.53743	−0.792040
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−9.21653	−0.755048	−0.377524	−	0.926000i	$-0.623224\pi$
$149$	−9.21653	−0.755048	−0.377524	+	0.926000i	$0.623224\pi$
$150$	0	0
$151$	21.6426	1.76125	0.880625	−	0.473813i	$-0.157123\pi$
$151$	21.6426	1.76125	0.880625	+	0.473813i	$0.157123\pi$
$152$	0	0
$153$	32.3437	2.61483
$154$	0	0
$155$	6.09467	0.489535
$156$	0	0
$157$	6.50023	0.518774	0.259387	−	0.965773i	$-0.416479\pi$
$157$	6.50023	0.518774	0.259387	+	0.965773i	$0.416479\pi$
$158$	0	0
$159$	20.4202	1.61943
$160$	0	0
$161$	0	0
$162$	0	0
$163$	15.7470	1.23340	0.616701	−	0.787198i	$-0.288469\pi$
$163$	15.7470	1.23340	0.616701	+	0.787198i	$0.288469\pi$
$164$	0	0
$165$	−6.30881	−0.491140
$166$	0	0
$167$	−23.2107	−1.79610	−0.898049	−	0.439896i	$-0.855015\pi$
$167$	−23.2107	−1.79610	−0.898049	+	0.439896i	$0.855015\pi$
$168$	0	0
$169$	3.64065	0.280050
$170$	0	0
$171$	8.44636	0.645910
$172$	0	0
$173$	2.68879	0.204425	0.102213	−	0.994763i	$-0.467408\pi$
$173$	2.68879	0.204425	0.102213	+	0.994763i	$0.467408\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−12.9050	−0.969996
$178$	0	0
$179$	18.5089	1.38342	0.691709	−	0.722176i	$-0.256858\pi$
$179$	18.5089	1.38342	0.691709	+	0.722176i	$0.256858\pi$
$180$	0	0
$181$	−24.9626	−1.85545	−0.927726	−	0.373262i	$-0.878239\pi$
$181$	−24.9626	−1.85545	−0.927726	+	0.373262i	$0.878239\pi$
$182$	0	0
$183$	−25.6831	−1.89855
$184$	0	0
$185$	0.0632415	0.00464961
$186$	0	0
$187$	17.9861	1.31527
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−13.5132	−0.977781	−0.488890	−	0.872345i	$-0.662598\pi$
$191$	−13.5132	−0.977781	−0.488890	+	0.872345i	$0.662598\pi$
$192$	0	0
$193$	5.02075	0.361402	0.180701	−	0.983538i	$-0.442163\pi$
$193$	5.02075	0.361402	0.180701	+	0.983538i	$0.442163\pi$
$194$	0	0
$195$	10.8583	0.777578
$196$	0	0
$197$	2.03479	0.144973	0.0724865	−	0.997369i	$-0.476907\pi$
$197$	2.03479	0.144973	0.0724865	+	0.997369i	$0.476907\pi$
$198$	0	0
$199$	−8.77058	−0.621730	−0.310865	−	0.950454i	$-0.600619\pi$
$199$	−8.77058	−0.621730	−0.310865	+	0.950454i	$0.600619\pi$
$200$	0	0
$201$	−29.2556	−2.06353
$202$	0	0
$203$	0	0
$204$	0	0
$205$	11.1401	0.778055
$206$	0	0
$207$	4.26210	0.296237
$208$	0	0
$209$	4.69697	0.324896
$210$	0	0
$211$	−18.6551	−1.28427	−0.642136	−	0.766590i	$-0.721952\pi$
$211$	−18.6551	−1.28427	−0.642136	+	0.766590i	$0.721952\pi$
$212$	0	0
$213$	−21.0814	−1.44447
$214$	0	0
$215$	−5.54351	−0.378064
$216$	0	0
$217$	0	0
$218$	0	0
$219$	18.7380	1.26620
$220$	0	0
$221$	−30.9564	−2.08235
$222$	0	0
$223$	−5.65726	−0.378838	−0.189419	−	0.981896i	$-0.560660\pi$
$223$	−5.65726	−0.378838	−0.189419	+	0.981896i	$0.560660\pi$
$224$	0	0
$225$	−17.1522	−1.14348
$226$	0	0
$227$	−11.5286	−0.765180	−0.382590	−	0.923918i	$-0.624968\pi$
$227$	−11.5286	−0.765180	−0.382590	+	0.923918i	$0.624968\pi$
$228$	0	0
$229$	14.3831	0.950460	0.475230	−	0.879862i	$-0.342365\pi$
$229$	14.3831	0.950460	0.475230	+	0.879862i	$0.342365\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−5.10030	−0.334132	−0.167066	−	0.985946i	$-0.553429\pi$
$233$	−5.10030	−0.334132	−0.167066	+	0.985946i	$0.553429\pi$
$234$	0	0
$235$	11.2135	0.731488
$236$	0	0
$237$	−8.00343	−0.519879
$238$	0	0
$239$	21.8025	1.41029	0.705143	−	0.709065i	$-0.250883\pi$
$239$	21.8025	1.41029	0.705143	+	0.709065i	$0.250883\pi$
$240$	0	0
$241$	−13.7370	−0.884879	−0.442440	−	0.896798i	$-0.645887\pi$
$241$	−13.7370	−0.884879	−0.442440	+	0.896798i	$0.645887\pi$
$242$	0	0
$243$	19.9609	1.28049
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−8.08409	−0.514378
$248$	0	0
$249$	42.7471	2.70898
$250$	0	0
$251$	3.89434	0.245809	0.122904	−	0.992419i	$-0.460779\pi$
$251$	3.89434	0.245809	0.122904	+	0.992419i	$0.460779\pi$
$252$	0	0
$253$	2.37013	0.149009
$254$	0	0
$255$	−20.1995	−1.26494
$256$	0	0
$257$	17.3661	1.08327	0.541634	−	0.840614i	$-0.317806\pi$
$257$	17.3661	1.08327	0.541634	+	0.840614i	$0.317806\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−41.1539	−2.54736
$262$	0	0
$263$	3.78239	0.233232	0.116616	−	0.993177i	$-0.462795\pi$
$263$	3.78239	0.233232	0.116616	+	0.993177i	$0.462795\pi$
$264$	0	0
$265$	−7.48468	−0.459780
$266$	0	0
$267$	12.9628	0.793313
$268$	0	0
$269$	−6.05445	−0.369147	−0.184573	−	0.982819i	$-0.559090\pi$
$269$	−6.05445	−0.369147	−0.184573	+	0.982819i	$0.559090\pi$
$270$	0	0
$271$	3.35742	0.203948	0.101974	−	0.994787i	$-0.467484\pi$
$271$	3.35742	0.203948	0.101974	+	0.994787i	$0.467484\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	−9.53825	−0.575178
$276$	0	0
$277$	6.95480	0.417874	0.208937	−	0.977929i	$-0.433000\pi$
$277$	6.95480	0.417874	0.208937	+	0.977929i	$0.433000\pi$
$278$	0	0
$279$	26.2984	1.57444
$280$	0	0
$281$	11.9204	0.711109	0.355555	−	0.934656i	$-0.384292\pi$
$281$	11.9204	0.711109	0.355555	+	0.934656i	$0.384292\pi$
$282$	0	0
$283$	13.2946	0.790280	0.395140	−	0.918621i	$-0.370696\pi$
$283$	13.2946	0.790280	0.395140	+	0.918621i	$0.370696\pi$
$284$	0	0
$285$	−5.27499	−0.312464
$286$	0	0
$287$	0	0
$288$	0	0
$289$	40.5878	2.38752
$290$	0	0
$291$	−7.11228	−0.416929
$292$	0	0
$293$	7.09325	0.414392	0.207196	−	0.978299i	$-0.433566\pi$
$293$	7.09325	0.414392	0.207196	+	0.978299i	$0.433566\pi$
$294$	0	0
$295$	4.73010	0.275397
$296$	0	0
$297$	−8.06117	−0.467756
$298$	0	0
$299$	−4.07929	−0.235912
$300$	0	0
$301$	0	0
$302$	0	0
$303$	28.0677	1.61245
$304$	0	0
$305$	9.41371	0.539028
$306$	0	0
$307$	6.71310	0.383137	0.191569	−	0.981479i	$-0.438643\pi$
$307$	6.71310	0.383137	0.191569	+	0.981479i	$0.438643\pi$
$308$	0	0
$309$	10.2776	0.584671
$310$	0	0
$311$	−3.29794	−0.187009	−0.0935044	−	0.995619i	$-0.529807\pi$
$311$	−3.29794	−0.187009	−0.0935044	+	0.995619i	$0.529807\pi$
$312$	0	0
$313$	9.19958	0.519991	0.259996	−	0.965610i	$-0.416279\pi$
$313$	9.19958	0.519991	0.259996	+	0.965610i	$0.416279\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−30.6963	−1.72407	−0.862037	−	0.506845i	$-0.830812\pi$
$317$	−30.6963	−1.72407	−0.862037	+	0.506845i	$0.830812\pi$
$318$	0	0
$319$	−22.8854	−1.28134
$320$	0	0
$321$	36.0671	2.01307
$322$	0	0
$323$	15.0387	0.836777
$324$	0	0
$325$	16.4166	0.910626
$326$	0	0
$327$	−35.4579	−1.96082
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−3.84446	−0.211310	−0.105655	−	0.994403i	$-0.533694\pi$
$331$	−3.84446	−0.211310	−0.105655	+	0.994403i	$0.533694\pi$
$332$	0	0
$333$	0.272886	0.0149541
$334$	0	0
$335$	10.7232	0.585869
$336$	0	0
$337$	−15.1802	−0.826916	−0.413458	−	0.910523i	$-0.635679\pi$
$337$	−15.1802	−0.826916	−0.413458	+	0.910523i	$0.635679\pi$
$338$	0	0
$339$	−28.8904	−1.56911
$340$	0	0
$341$	14.6244	0.791954
$342$	0	0
$343$	0	0
$344$	0	0
$345$	−2.66180	−0.143307
$346$	0	0
$347$	−4.87353	−0.261625	−0.130813	−	0.991407i	$-0.541759\pi$
$347$	−4.87353	−0.261625	−0.130813	+	0.991407i	$0.541759\pi$
$348$	0	0
$349$	13.4939	0.722313	0.361157	−	0.932505i	$-0.382382\pi$
$349$	13.4939	0.722313	0.361157	+	0.932505i	$0.382382\pi$
$350$	0	0
$351$	13.8743	0.740556
$352$	0	0
$353$	28.5154	1.51772	0.758860	−	0.651254i	$-0.225757\pi$
$353$	28.5154	1.51772	0.758860	+	0.651254i	$0.225757\pi$
$354$	0	0
$355$	7.72703	0.410108
$356$	0	0
$357$	0	0
$358$	0	0
$359$	15.6781	0.827458	0.413729	−	0.910400i	$-0.364226\pi$
$359$	15.6781	0.827458	0.413729	+	0.910400i	$0.364226\pi$
$360$	0	0
$361$	−15.0727	−0.793301
$362$	0	0
$363$	14.5049	0.761310
$364$	0	0
$365$	−6.86811	−0.359493
$366$	0	0
$367$	2.96664	0.154857	0.0774286	−	0.996998i	$-0.475329\pi$
$367$	2.96664	0.154857	0.0774286	+	0.996998i	$0.475329\pi$
$368$	0	0
$369$	48.0692	2.50238
$370$	0	0
$371$	0	0
$372$	0	0
$373$	0.276321	0.0143074	0.00715368	−	0.999974i	$-0.497723\pi$
$373$	0.276321	0.0143074	0.00715368	+	0.999974i	$0.497723\pi$
$374$	0	0
$375$	24.0211	1.24044
$376$	0	0
$377$	39.3887	2.02862
$378$	0	0
$379$	2.76290	0.141921	0.0709603	−	0.997479i	$-0.477394\pi$
$379$	2.76290	0.141921	0.0709603	+	0.997479i	$0.477394\pi$
$380$	0	0
$381$	−2.99016	−0.153191
$382$	0	0
$383$	−13.8062	−0.705465	−0.352732	−	0.935724i	$-0.614747\pi$
$383$	−13.8062	−0.705465	−0.352732	+	0.935724i	$0.614747\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−23.9202	−1.21593
$388$	0	0
$389$	−18.8648	−0.956484	−0.478242	−	0.878228i	$-0.658726\pi$
$389$	−18.8648	−0.956484	−0.478242	+	0.878228i	$0.658726\pi$
$390$	0	0
$391$	7.58866	0.383775
$392$	0	0
$393$	−49.5044	−2.49717
$394$	0	0
$395$	2.93352	0.147602
$396$	0	0
$397$	26.4233	1.32615	0.663075	−	0.748553i	$-0.269251\pi$
$397$	26.4233	1.32615	0.663075	+	0.748553i	$0.269251\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−8.33152	−0.416056	−0.208028	−	0.978123i	$-0.566705\pi$
$401$	−8.33152	−0.416056	−0.208028	+	0.978123i	$0.566705\pi$
$402$	0	0
$403$	−25.1704	−1.25383
$404$	0	0
$405$	−3.57641	−0.177713
$406$	0	0
$407$	0.151750	0.00752197
$408$	0	0
$409$	7.33363	0.362625	0.181312	−	0.983426i	$-0.441965\pi$
$409$	7.33363	0.362625	0.181312	+	0.983426i	$0.441965\pi$
$410$	0	0
$411$	43.1356	2.12772
$412$	0	0
$413$	0	0
$414$	0	0
$415$	−15.6682	−0.769123
$416$	0	0
$417$	−11.3056	−0.553636
$418$	0	0
$419$	11.3626	0.555098	0.277549	−	0.960711i	$-0.410478\pi$
$419$	11.3626	0.555098	0.277549	+	0.960711i	$0.410478\pi$
$420$	0	0
$421$	12.3418	0.601500	0.300750	−	0.953703i	$-0.402763\pi$
$421$	12.3418	0.601500	0.300750	+	0.953703i	$0.402763\pi$
$422$	0	0
$423$	48.3860	2.35261
$424$	0	0
$425$	−30.5395	−1.48138
$426$	0	0
$427$	0	0
$428$	0	0
$429$	26.0548	1.25794
$430$	0	0
$431$	7.06925	0.340514	0.170257	−	0.985400i	$-0.445540\pi$
$431$	7.06925	0.340514	0.170257	+	0.985400i	$0.445540\pi$
$432$	0	0
$433$	1.71716	0.0825213	0.0412606	−	0.999148i	$-0.486863\pi$
$433$	1.71716	0.0825213	0.0412606	+	0.999148i	$0.486863\pi$
$434$	0	0
$435$	25.7017	1.23230
$436$	0	0
$437$	1.98174	0.0947993
$438$	0	0
$439$	−21.0074	−1.00263	−0.501314	−	0.865266i	$-0.667150\pi$
$439$	−21.0074	−1.00263	−0.501314	+	0.865266i	$0.667150\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	2.13482	0.101428	0.0507141	−	0.998713i	$-0.483850\pi$
$443$	2.13482	0.101428	0.0507141	+	0.998713i	$0.483850\pi$
$444$	0	0
$445$	−4.75132	−0.225234
$446$	0	0
$447$	24.8370	1.17475
$448$	0	0
$449$	−8.98723	−0.424133	−0.212067	−	0.977255i	$-0.568019\pi$
$449$	−8.98723	−0.424133	−0.212067	+	0.977255i	$0.568019\pi$
$450$	0	0
$451$	26.7310	1.25871
$452$	0	0
$453$	−58.3231	−2.74026
$454$	0	0
$455$	0	0
$456$	0	0
$457$	32.1059	1.50185	0.750925	−	0.660387i	$-0.229608\pi$
$457$	32.1059	1.50185	0.750925	+	0.660387i	$0.229608\pi$
$458$	0	0
$459$	−25.8102	−1.20472
$460$	0	0
$461$	20.1388	0.937956	0.468978	−	0.883210i	$-0.344622\pi$
$461$	20.1388	0.937956	0.468978	+	0.883210i	$0.344622\pi$
$462$	0	0
$463$	−14.8725	−0.691186	−0.345593	−	0.938385i	$-0.612322\pi$
$463$	−14.8725	−0.691186	−0.345593	+	0.938385i	$0.612322\pi$
$464$	0	0
$465$	−16.4241	−0.761649
$466$	0	0
$467$	32.8511	1.52017	0.760084	−	0.649825i	$-0.225158\pi$
$467$	32.8511	1.52017	0.760084	+	0.649825i	$0.225158\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	−17.5170	−0.807141
$472$	0	0
$473$	−13.3018	−0.611619
$474$	0	0
$475$	−7.97522	−0.365928
$476$	0	0
$477$	−32.2963	−1.47874
$478$	0	0
$479$	−23.7914	−1.08706	−0.543528	−	0.839391i	$-0.682912\pi$
$479$	−23.7914	−1.08706	−0.543528	+	0.839391i	$0.682912\pi$
$480$	0	0
$481$	−0.261182	−0.0119089
$482$	0	0
$483$	0	0
$484$	0	0
$485$	2.60689	0.118373
$486$	0	0
$487$	18.4468	0.835904	0.417952	−	0.908469i	$-0.362748\pi$
$487$	18.4468	0.835904	0.417952	+	0.908469i	$0.362748\pi$
$488$	0	0
$489$	−42.4355	−1.91900
$490$	0	0
$491$	25.0803	1.13186	0.565930	−	0.824453i	$-0.308517\pi$
$491$	25.0803	1.13186	0.565930	+	0.824453i	$0.308517\pi$
$492$	0	0
$493$	−73.2743	−3.30011
$494$	0	0
$495$	9.97793	0.448475
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−19.4790	−0.872000	−0.436000	−	0.899947i	$-0.643605\pi$
$499$	−19.4790	−0.872000	−0.436000	+	0.899947i	$0.643605\pi$
$500$	0	0
$501$	62.5489	2.79448
$502$	0	0
$503$	−5.49658	−0.245080	−0.122540	−	0.992464i	$-0.539104\pi$
$503$	−5.49658	−0.245080	−0.122540	+	0.992464i	$0.539104\pi$
$504$	0	0
$505$	−10.2878	−0.457799
$506$	0	0
$507$	−9.81092	−0.435718
$508$	0	0
$509$	−23.0812	−1.02306	−0.511529	−	0.859266i	$-0.670921\pi$
$509$	−23.0812	−1.02306	−0.511529	+	0.859266i	$0.670921\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−6.74019	−0.297587
$514$	0	0
$515$	−3.76707	−0.165997
$516$	0	0
$517$	26.9072	1.18338
$518$	0	0
$519$	−7.24584	−0.318057
$520$	0	0
$521$	−9.36861	−0.410446	−0.205223	−	0.978715i	$-0.565792\pi$
$521$	−9.36861	−0.410446	−0.205223	+	0.978715i	$0.565792\pi$
$522$	0	0
$523$	12.5537	0.548933	0.274467	−	0.961597i	$-0.411499\pi$
$523$	12.5537	0.548933	0.274467	+	0.961597i	$0.411499\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	46.8242	2.03969
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	20.4103	0.885732
$532$	0	0
$533$	−46.0074	−1.99280
$534$	0	0
$535$	−13.2198	−0.571541
$536$	0	0
$537$	−49.8782	−2.15240
$538$	0	0
$539$	0	0
$540$	0	0
$541$	5.25060	0.225741	0.112870	−	0.993610i	$-0.463995\pi$
$541$	5.25060	0.225741	0.112870	+	0.993610i	$0.463995\pi$
$542$	0	0
$543$	67.2698	2.88682
$544$	0	0
$545$	12.9965	0.556709
$546$	0	0
$547$	0.598591	0.0255939	0.0127969	−	0.999918i	$-0.495926\pi$
$547$	0.598591	0.0255939	0.0127969	+	0.999918i	$0.495926\pi$
$548$	0	0
$549$	40.6200	1.73362
$550$	0	0
$551$	−19.1352	−0.815186
$552$	0	0
$553$	0	0
$554$	0	0
$555$	−0.170425	−0.00723414
$556$	0	0
$557$	33.0121	1.39877	0.699384	−	0.714746i	$-0.253458\pi$
$557$	33.0121	1.39877	0.699384	+	0.714746i	$0.253458\pi$
$558$	0	0
$559$	22.8942	0.968320
$560$	0	0
$561$	−48.4694	−2.04638
$562$	0	0
$563$	39.7182	1.67392	0.836961	−	0.547262i	$-0.184330\pi$
$563$	39.7182	1.67392	0.836961	+	0.547262i	$0.184330\pi$
$564$	0	0
$565$	10.5893	0.445496
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−4.11738	−0.172610	−0.0863048	−	0.996269i	$-0.527506\pi$
$569$	−4.11738	−0.172610	−0.0863048	+	0.996269i	$0.527506\pi$
$570$	0	0
$571$	38.6733	1.61843	0.809215	−	0.587513i	$-0.199893\pi$
$571$	38.6733	1.61843	0.809215	+	0.587513i	$0.199893\pi$
$572$	0	0
$573$	36.4158	1.52129
$574$	0	0
$575$	−4.02436	−0.167827
$576$	0	0
$577$	37.4095	1.55738	0.778688	−	0.627411i	$-0.215885\pi$
$577$	37.4095	1.55738	0.778688	+	0.627411i	$0.215885\pi$
$578$	0	0
$579$	−13.5301	−0.562290
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−17.9597	−0.743817
$584$	0	0
$585$	−17.1733	−0.710029
$586$	0	0
$587$	25.7805	1.06408	0.532038	−	0.846721i	$-0.321427\pi$
$587$	25.7805	1.06408	0.532038	+	0.846721i	$0.321427\pi$
$588$	0	0
$589$	12.2279	0.503841
$590$	0	0
$591$	−5.48342	−0.225558
$592$	0	0
$593$	30.6506	1.25867	0.629334	−	0.777135i	$-0.283328\pi$
$593$	30.6506	1.25867	0.629334	+	0.777135i	$0.283328\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	23.6352	0.967325
$598$	0	0
$599$	−3.93269	−0.160686	−0.0803428	−	0.996767i	$-0.525601\pi$
$599$	−3.93269	−0.160686	−0.0803428	+	0.996767i	$0.525601\pi$
$600$	0	0
$601$	−27.4423	−1.11940	−0.559698	−	0.828697i	$-0.689083\pi$
$601$	−27.4423	−1.11940	−0.559698	+	0.828697i	$0.689083\pi$
$602$	0	0
$603$	46.2703	1.88427
$604$	0	0
$605$	−5.31653	−0.216148
$606$	0	0
$607$	38.0293	1.54356	0.771781	−	0.635888i	$-0.219366\pi$
$607$	38.0293	1.54356	0.771781	+	0.635888i	$0.219366\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−46.3107	−1.87353
$612$	0	0
$613$	11.7113	0.473013	0.236506	−	0.971630i	$-0.423998\pi$
$613$	11.7113	0.473013	0.236506	+	0.971630i	$0.423998\pi$
$614$	0	0
$615$	−30.0206	−1.21055
$616$	0	0
$617$	35.0965	1.41293	0.706466	−	0.707747i	$-0.250288\pi$
$617$	35.0965	1.41293	0.706466	+	0.707747i	$0.250288\pi$
$618$	0	0
$619$	17.5605	0.705815	0.352908	−	0.935658i	$-0.385193\pi$
$619$	17.5605	0.705815	0.352908	+	0.935658i	$0.385193\pi$
$620$	0	0
$621$	−3.40115	−0.136484
$622$	0	0
$623$	0	0
$624$	0	0
$625$	11.3173	0.452691
$626$	0	0
$627$	−12.6575	−0.505493
$628$	0	0
$629$	0.485873	0.0193730
$630$	0	0
$631$	−1.36226	−0.0542307	−0.0271154	−	0.999632i	$-0.508632\pi$
$631$	−1.36226	−0.0542307	−0.0271154	+	0.999632i	$0.508632\pi$
$632$	0	0
$633$	50.2724	1.99815
$634$	0	0
$635$	1.09599	0.0434932
$636$	0	0
$637$	0	0
$638$	0	0
$639$	33.3420	1.31899
$640$	0	0
$641$	14.6027	0.576771	0.288385	−	0.957514i	$-0.406882\pi$
$641$	14.6027	0.576771	0.288385	+	0.957514i	$0.406882\pi$
$642$	0	0
$643$	−18.3215	−0.722529	−0.361265	−	0.932463i	$-0.617655\pi$
$643$	−18.3215	−0.722529	−0.361265	+	0.932463i	$0.617655\pi$
$644$	0	0
$645$	14.9388	0.588215
$646$	0	0
$647$	45.2648	1.77954	0.889772	−	0.456405i	$-0.150863\pi$
$647$	45.2648	1.77954	0.889772	+	0.456405i	$0.150863\pi$
$648$	0	0
$649$	11.3500	0.445528
$650$	0	0
$651$	0	0
$652$	0	0
$653$	6.93885	0.271538	0.135769	−	0.990741i	$-0.456649\pi$
$653$	6.93885	0.271538	0.135769	+	0.990741i	$0.456649\pi$
$654$	0	0
$655$	18.1450	0.708985
$656$	0	0
$657$	−29.6358	−1.15620
$658$	0	0
$659$	36.8233	1.43443	0.717215	−	0.696852i	$-0.245416\pi$
$659$	36.8233	1.43443	0.717215	+	0.696852i	$0.245416\pi$
$660$	0	0
$661$	42.6351	1.65831	0.829157	−	0.559015i	$-0.188821\pi$
$661$	42.6351	1.65831	0.829157	+	0.559015i	$0.188821\pi$
$662$	0	0
$663$	83.4222	3.23985
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−9.65576	−0.373873
$668$	0	0
$669$	15.2453	0.589419
$670$	0	0
$671$	22.5885	0.872020
$672$	0	0
$673$	−29.5976	−1.14090	−0.570452	−	0.821331i	$-0.693232\pi$
$673$	−29.5976	−1.14090	−0.570452	+	0.821331i	$0.693232\pi$
$674$	0	0
$675$	13.6875	0.526831
$676$	0	0
$677$	−26.1886	−1.00651	−0.503255	−	0.864138i	$-0.667864\pi$
$677$	−26.1886	−1.00651	−0.503255	+	0.864138i	$0.667864\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	31.0676	1.19051
$682$	0	0
$683$	−1.94336	−0.0743606	−0.0371803	−	0.999309i	$-0.511838\pi$
$683$	−1.94336	−0.0743606	−0.0371803	+	0.999309i	$0.511838\pi$
$684$	0	0
$685$	−15.8106	−0.604093
$686$	0	0
$687$	−38.7599	−1.47878
$688$	0	0
$689$	30.9110	1.17762
$690$	0	0
$691$	26.7475	1.01752	0.508761	−	0.860908i	$-0.330104\pi$
$691$	26.7475	1.01752	0.508761	+	0.860908i	$0.330104\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	4.14387	0.157186
$696$	0	0
$697$	85.5870	3.24184
$698$	0	0
$699$	13.7444	0.519862
$700$	0	0
$701$	2.10164	0.0793779	0.0396890	−	0.999212i	$-0.487363\pi$
$701$	2.10164	0.0793779	0.0396890	+	0.999212i	$0.487363\pi$
$702$	0	0
$703$	0.126883	0.00478548
$704$	0	0
$705$	−30.2184	−1.13809
$706$	0	0
$707$	0	0
$708$	0	0
$709$	51.3222	1.92745	0.963723	−	0.266906i	$-0.0860012\pi$
$709$	51.3222	1.92745	0.963723	+	0.266906i	$0.0860012\pi$
$710$	0	0
$711$	12.6581	0.474716
$712$	0	0
$713$	6.17029	0.231079
$714$	0	0
$715$	−9.54996	−0.357148
$716$	0	0
$717$	−58.7540	−2.19421
$718$	0	0
$719$	46.4316	1.73161	0.865804	−	0.500384i	$-0.166808\pi$
$719$	46.4316	1.73161	0.865804	+	0.500384i	$0.166808\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	37.0189	1.37675
$724$	0	0
$725$	38.8583	1.44316
$726$	0	0
$727$	−29.0942	−1.07904	−0.539521	−	0.841972i	$-0.681395\pi$
$727$	−29.0942	−1.07904	−0.539521	+	0.841972i	$0.681395\pi$
$728$	0	0
$729$	−42.9287	−1.58995
$730$	0	0
$731$	−42.5897	−1.57524
$732$	0	0
$733$	−45.8319	−1.69284	−0.846420	−	0.532516i	$-0.821247\pi$
$733$	−45.8319	−1.69284	−0.846420	+	0.532516i	$0.821247\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	25.7306	0.947798
$738$	0	0
$739$	−26.0618	−0.958700	−0.479350	−	0.877624i	$-0.659128\pi$
$739$	−26.0618	−0.958700	−0.479350	+	0.877624i	$0.659128\pi$
$740$	0	0
$741$	21.7852	0.800300
$742$	0	0
$743$	2.87154	0.105347	0.0526733	−	0.998612i	$-0.483226\pi$
$743$	2.87154	0.105347	0.0526733	+	0.998612i	$0.483226\pi$
$744$	0	0
$745$	−9.10358	−0.333529
$746$	0	0
$747$	−67.6082	−2.47365
$748$	0	0
$749$	0	0
$750$	0	0
$751$	8.21840	0.299894	0.149947	−	0.988694i	$-0.452090\pi$
$751$	8.21840	0.299894	0.149947	+	0.988694i	$0.452090\pi$
$752$	0	0
$753$	−10.4946	−0.382444
$754$	0	0
$755$	21.3774	0.778002
$756$	0	0
$757$	10.8844	0.395602	0.197801	−	0.980242i	$-0.436620\pi$
$757$	10.8844	0.395602	0.197801	+	0.980242i	$0.436620\pi$
$758$	0	0
$759$	−6.38709	−0.231837
$760$	0	0
$761$	24.5739	0.890804	0.445402	−	0.895331i	$-0.353061\pi$
$761$	24.5739	0.890804	0.445402	+	0.895331i	$0.353061\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	31.9473	1.15506
$766$	0	0
$767$	−19.5349	−0.705363
$768$	0	0
$769$	48.6181	1.75321	0.876607	−	0.481206i	$-0.159801\pi$
$769$	48.6181	1.75321	0.876607	+	0.481206i	$0.159801\pi$
$770$	0	0
$771$	−46.7987	−1.68541
$772$	0	0
$773$	−40.9021	−1.47115	−0.735573	−	0.677445i	$-0.763087\pi$
$773$	−40.9021	−1.47115	−0.735573	+	0.677445i	$0.763087\pi$
$774$	0	0
$775$	−24.8315	−0.891972
$776$	0	0
$777$	0	0
$778$	0	0
$779$	22.3506	0.800792
$780$	0	0
$781$	18.5413	0.663459
$782$	0	0
$783$	32.8407	1.17363
$784$	0	0
$785$	6.42056	0.229160
$786$	0	0
$787$	13.7819	0.491272	0.245636	−	0.969362i	$-0.421003\pi$
$787$	13.7819	0.491272	0.245636	+	0.969362i	$0.421003\pi$
$788$	0	0
$789$	−10.1929	−0.362877
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−38.8778	−1.38059
$794$	0	0
$795$	20.1699	0.715354
$796$	0	0
$797$	−19.8832	−0.704299	−0.352150	−	0.935944i	$-0.614549\pi$
$797$	−19.8832	−0.704299	−0.352150	+	0.935944i	$0.614549\pi$
$798$	0	0
$799$	86.1512	3.04781
$800$	0	0
$801$	−20.5019	−0.724398
$802$	0	0
$803$	−16.4803	−0.581576
$804$	0	0
$805$	0	0
$806$	0	0
$807$	16.3157	0.574340
$808$	0	0
$809$	52.9515	1.86167	0.930837	−	0.365435i	$-0.119080\pi$
$809$	52.9515	1.86167	0.930837	+	0.365435i	$0.119080\pi$
$810$	0	0
$811$	21.0859	0.740427	0.370213	−	0.928947i	$-0.379285\pi$
$811$	21.0859	0.740427	0.370213	+	0.928947i	$0.379285\pi$
$812$	0	0
$813$	−9.04766	−0.317315
$814$	0	0
$815$	15.5540	0.544834
$816$	0	0
$817$	−11.1221	−0.389112
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−12.0104	−0.419164	−0.209582	−	0.977791i	$-0.567210\pi$
$821$	−12.0104	−0.419164	−0.209582	+	0.977791i	$0.567210\pi$
$822$	0	0
$823$	−8.52381	−0.297121	−0.148561	−	0.988903i	$-0.547464\pi$
$823$	−8.52381	−0.297121	−0.148561	+	0.988903i	$0.547464\pi$
$824$	0	0
$825$	25.7039	0.894896
$826$	0	0
$827$	−41.3301	−1.43719	−0.718594	−	0.695430i	$-0.755214\pi$
$827$	−41.3301	−1.43719	−0.718594	+	0.695430i	$0.755214\pi$
$828$	0	0
$829$	7.50736	0.260741	0.130371	−	0.991465i	$-0.458383\pi$
$829$	7.50736	0.260741	0.130371	+	0.991465i	$0.458383\pi$
$830$	0	0
$831$	−18.7420	−0.650153
$832$	0	0
$833$	0	0
$834$	0	0
$835$	−22.9262	−0.793395
$836$	0	0
$837$	−20.9861	−0.725386
$838$	0	0
$839$	56.2893	1.94332	0.971662	−	0.236374i	$-0.0759592\pi$
$839$	56.2893	1.94332	0.971662	+	0.236374i	$0.0759592\pi$
$840$	0	0
$841$	64.2338	2.21496
$842$	0	0
$843$	−32.1233	−1.10639
$844$	0	0
$845$	3.59603	0.123707
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−35.8266	−1.22956
$850$	0	0
$851$	0.0640261	0.00219479
$852$	0	0
$853$	−2.83615	−0.0971081	−0.0485540	−	0.998821i	$-0.515461\pi$
$853$	−2.83615	−0.0971081	−0.0485540	+	0.998821i	$0.515461\pi$
$854$	0	0
$855$	8.34285	0.285320
$856$	0	0
$857$	−6.25343	−0.213613	−0.106806	−	0.994280i	$-0.534063\pi$
$857$	−6.25343	−0.213613	−0.106806	+	0.994280i	$0.534063\pi$
$858$	0	0
$859$	−48.9497	−1.67014	−0.835071	−	0.550142i	$-0.814574\pi$
$859$	−48.9497	−1.67014	−0.835071	+	0.550142i	$0.814574\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−35.7758	−1.21782	−0.608911	−	0.793238i	$-0.708394\pi$
$863$	−35.7758	−1.21782	−0.608911	+	0.793238i	$0.708394\pi$
$864$	0	0
$865$	2.65584	0.0903013
$866$	0	0
$867$	−109.377	−3.71464
$868$	0	0
$869$	7.03909	0.238785
$870$	0	0
$871$	−44.2857	−1.50056
$872$	0	0
$873$	11.2487	0.380710
$874$	0	0
$875$	0	0
$876$	0	0
$877$	11.1606	0.376867	0.188434	−	0.982086i	$-0.439659\pi$
$877$	11.1606	0.376867	0.188434	+	0.982086i	$0.439659\pi$
$878$	0	0
$879$	−19.1151	−0.644737
$880$	0	0
$881$	1.96039	0.0660473	0.0330237	−	0.999455i	$-0.489486\pi$
$881$	1.96039	0.0660473	0.0330237	+	0.999455i	$0.489486\pi$
$882$	0	0
$883$	−3.79898	−0.127846	−0.0639229	−	0.997955i	$-0.520361\pi$
$883$	−3.79898	−0.127846	−0.0639229	+	0.997955i	$0.520361\pi$
$884$	0	0
$885$	−12.7468	−0.428479
$886$	0	0
$887$	−23.2012	−0.779021	−0.389511	−	0.921022i	$-0.627356\pi$
$887$	−23.2012	−0.779021	−0.389511	+	0.921022i	$0.627356\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−8.58171	−0.287498
$892$	0	0
$893$	22.4979	0.752863
$894$	0	0
$895$	18.2820	0.611101
$896$	0	0
$897$	10.9930	0.367046
$898$	0	0
$899$	−59.5788	−1.98706
$900$	0	0
$901$	−57.5034	−1.91572
$902$	0	0
$903$	0	0
$904$	0	0
$905$	−24.6566	−0.819614
$906$	0	0
$907$	−26.7518	−0.888279	−0.444139	−	0.895958i	$-0.646490\pi$
$907$	−26.7518	−0.888279	−0.444139	+	0.895958i	$0.646490\pi$
$908$	0	0
$909$	−44.3915	−1.47237
$910$	0	0
$911$	16.0286	0.531050	0.265525	−	0.964104i	$-0.414455\pi$
$911$	16.0286	0.531050	0.265525	+	0.964104i	$0.414455\pi$
$912$	0	0
$913$	−37.5964	−1.24426
$914$	0	0
$915$	−25.3684	−0.838652
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−19.1809	−0.632719	−0.316360	−	0.948639i	$-0.602461\pi$
$919$	−19.1809	−0.632719	−0.316360	+	0.948639i	$0.602461\pi$
$920$	0	0
$921$	−18.0907	−0.596108
$922$	0	0
$923$	−31.9119	−1.05039
$924$	0	0
$925$	−0.257664	−0.00847195
$926$	0	0
$927$	−16.2549	−0.533880
$928$	0	0
$929$	20.9710	0.688036	0.344018	−	0.938963i	$-0.388212\pi$
$929$	20.9710	0.688036	0.344018	+	0.938963i	$0.388212\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	8.88737	0.290959
$934$	0	0
$935$	17.7657	0.580999
$936$	0	0
$937$	−45.6522	−1.49139	−0.745697	−	0.666285i	$-0.767883\pi$
$937$	−45.6522	−1.49139	−0.745697	+	0.666285i	$0.767883\pi$
$938$	0	0
$939$	−24.7913	−0.809034
$940$	0	0
$941$	0.160121	0.00521980	0.00260990	−	0.999997i	$-0.499169\pi$
$941$	0.160121	0.00521980	0.00260990	+	0.999997i	$0.499169\pi$
$942$	0	0
$943$	11.2783	0.367271
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−5.31824	−0.172820	−0.0864099	−	0.996260i	$-0.527539\pi$
$947$	−5.31824	−0.172820	−0.0864099	+	0.996260i	$0.527539\pi$
$948$	0	0
$949$	28.3646	0.920755
$950$	0	0
$951$	82.7212	2.68242
$952$	0	0
$953$	3.05836	0.0990699	0.0495349	−	0.998772i	$-0.484226\pi$
$953$	3.05836	0.0990699	0.0495349	+	0.998772i	$0.484226\pi$
$954$	0	0
$955$	−13.3476	−0.431918
$956$	0	0
$957$	61.6722	1.99358
$958$	0	0
$959$	0	0
$960$	0	0
$961$	7.07243	0.228143
$962$	0	0
$963$	−57.0432	−1.83819
$964$	0	0
$965$	4.95922	0.159643
$966$	0	0
$967$	−3.96793	−0.127600	−0.0638001	−	0.997963i	$-0.520322\pi$
$967$	−3.96793	−0.127600	−0.0638001	+	0.997963i	$0.520322\pi$
$968$	0	0
$969$	−40.5268	−1.30191
$970$	0	0
$971$	42.3548	1.35923	0.679615	−	0.733569i	$-0.262147\pi$
$971$	42.3548	1.35923	0.679615	+	0.733569i	$0.262147\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	−44.2398	−1.41681
$976$	0	0
$977$	9.77393	0.312696	0.156348	−	0.987702i	$-0.450028\pi$
$977$	9.77393	0.312696	0.156348	+	0.987702i	$0.450028\pi$
$978$	0	0
$979$	−11.4009	−0.364376
$980$	0	0
$981$	56.0797	1.79049
$982$	0	0
$983$	4.20960	0.134265	0.0671326	−	0.997744i	$-0.478615\pi$
$983$	4.20960	0.134265	0.0671326	+	0.997744i	$0.478615\pi$
$984$	0	0
$985$	2.00986	0.0640394
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−5.61229	−0.178460
$990$	0	0
$991$	41.1486	1.30713	0.653564	−	0.756871i	$-0.273273\pi$
$991$	41.1486	1.30713	0.653564	+	0.756871i	$0.273273\pi$
$992$	0	0
$993$	10.3602	0.328770
$994$	0	0
$995$	−8.66310	−0.274639
$996$	0	0
$997$	−32.6805	−1.03500	−0.517501	−	0.855682i	$-0.673138\pi$
$997$	−32.6805	−1.03500	−0.517501	+	0.855682i	$0.673138\pi$
$998$	0	0
$999$	−0.217763	−0.00688971

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9016.2.a.bq.1.1		11
7.2	even	3		1288.2.q.a.921.11	yes	22
7.4	even	3		1288.2.q.a.737.11	✓	22
7.6	odd	2		9016.2.a.bl.1.11		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1288.2.q.a.737.11	✓	22	7.4	even	3
1288.2.q.a.921.11	yes	22	7.2	even	3
9016.2.a.bl.1.11		11	7.6	odd	2
9016.2.a.bq.1.1		11	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 9016 = 2^{3} \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9016.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69483 q^{3} +0.987745 q^{5} +4.26210 q^{9} +O(q^{10})\)	\(q-2.69483 q^{3} +0.987745 q^{5} +4.26210 q^{9} +2.37013 q^{11} -4.07929 q^{13} -2.66180 q^{15} +7.58866 q^{17} +1.98174 q^{19} +1.00000 q^{23} -4.02436 q^{25} -3.40115 q^{27} -9.65576 q^{29} +6.17029 q^{31} -6.38709 q^{33} +0.0640261 q^{37} +10.9930 q^{39} +11.2783 q^{41} -5.61229 q^{43} +4.20987 q^{45} +11.3526 q^{47} -20.4501 q^{51} -7.57754 q^{53} +2.34108 q^{55} -5.34044 q^{57} +4.78879 q^{59} +9.53051 q^{61} -4.02930 q^{65} +10.8562 q^{67} -2.69483 q^{69} +7.82290 q^{71} -6.95332 q^{73} +10.8450 q^{75} +2.96992 q^{79} -3.62078 q^{81} -15.8626 q^{83} +7.49566 q^{85} +26.0206 q^{87} -4.81027 q^{89} -16.6279 q^{93} +1.95745 q^{95} +2.63923 q^{97} +10.1017 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 4 q^{3} + q^{5} + 11 q^{9}+O(q^{10}) \) 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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