LMFDB - Embedded newform 9016.2.a.bl.1.3

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			1.3
Root			$2.85830$ 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)

$f(q)$	$=$	$q-2.85830 q^{3} +3.84386 q^{5} +5.16987 q^{9} +O(q^{10})$	$q-2.85830 q^{3} +3.84386 q^{5} +5.16987 q^{9} -4.51405 q^{11} +7.14597 q^{13} -10.9869 q^{15} -3.05130 q^{17} -0.215304 q^{19} +1.00000 q^{23} +9.77525 q^{25} -6.20213 q^{27} -6.20805 q^{29} +1.56658 q^{31} +12.9025 q^{33} -3.45591 q^{37} -20.4253 q^{39} -6.19578 q^{41} -2.28022 q^{43} +19.8722 q^{45} -7.25389 q^{47} +8.72153 q^{51} +2.93642 q^{53} -17.3514 q^{55} +0.615402 q^{57} -7.56242 q^{59} +3.29684 q^{61} +27.4681 q^{65} +7.39128 q^{67} -2.85830 q^{69} +3.82031 q^{71} -11.0552 q^{73} -27.9406 q^{75} +12.7130 q^{79} +2.21793 q^{81} -15.4285 q^{83} -11.7288 q^{85} +17.7445 q^{87} -4.73777 q^{89} -4.47774 q^{93} -0.827596 q^{95} -12.0976 q^{97} -23.3371 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.85830	−1.65024	−0.825120	−	0.564958i	$-0.808892\pi$
$3$	−2.85830	−1.65024	−0.825120	+	0.564958i	$0.808892\pi$
$4$	0	0
$5$	3.84386	1.71903	0.859513	−	0.511114i	$-0.170767\pi$
$5$	3.84386	1.71903	0.859513	+	0.511114i	$0.170767\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	5.16987	1.72329
$10$	0	0
$11$	−4.51405	−1.36104	−0.680519	−	0.732730i	$-0.738246\pi$
$11$	−4.51405	−1.36104	−0.680519	+	0.732730i	$0.738246\pi$
$12$	0	0
$13$	7.14597	1.98194	0.990968	−	0.134101i	$-0.0428147\pi$
$13$	7.14597	1.98194	0.990968	+	0.134101i	$0.0428147\pi$
$14$	0	0
$15$	−10.9869	−2.83680
$16$	0	0
$17$	−3.05130	−0.740049	−0.370025	−	0.929022i	$-0.620651\pi$
$17$	−3.05130	−0.740049	−0.370025	+	0.929022i	$0.620651\pi$
$18$	0	0
$19$	−0.215304	−0.0493940	−0.0246970	−	0.999695i	$-0.507862\pi$
$19$	−0.215304	−0.0493940	−0.0246970	+	0.999695i	$0.507862\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0	0
$25$	9.77525	1.95505
$26$	0	0
$27$	−6.20213	−1.19360
$28$	0	0
$29$	−6.20805	−1.15281	−0.576403	−	0.817165i	$-0.695544\pi$
$29$	−6.20805	−1.15281	−0.576403	+	0.817165i	$0.695544\pi$
$30$	0	0
$31$	1.56658	0.281365	0.140683	−	0.990055i	$-0.455070\pi$
$31$	1.56658	0.281365	0.140683	+	0.990055i	$0.455070\pi$
$32$	0	0
$33$	12.9025	2.24604
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−3.45591	−0.568148	−0.284074	−	0.958802i	$-0.591686\pi$
$37$	−3.45591	−0.568148	−0.284074	+	0.958802i	$0.591686\pi$
$38$	0	0
$39$	−20.4253	−3.27067
$40$	0	0
$41$	−6.19578	−0.967619	−0.483809	−	0.875173i	$-0.660747\pi$
$41$	−6.19578	−0.967619	−0.483809	+	0.875173i	$0.660747\pi$
$42$	0	0
$43$	−2.28022	−0.347730	−0.173865	−	0.984770i	$-0.555626\pi$
$43$	−2.28022	−0.347730	−0.173865	+	0.984770i	$0.555626\pi$
$44$	0	0
$45$	19.8722	2.96238
$46$	0	0
$47$	−7.25389	−1.05809	−0.529045	−	0.848594i	$-0.677450\pi$
$47$	−7.25389	−1.05809	−0.529045	+	0.848594i	$0.677450\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	8.72153	1.22126
$52$	0	0
$53$	2.93642	0.403348	0.201674	−	0.979453i	$-0.435362\pi$
$53$	2.93642	0.403348	0.201674	+	0.979453i	$0.435362\pi$
$54$	0	0
$55$	−17.3514	−2.33966
$56$	0	0
$57$	0.615402	0.0815119
$58$	0	0
$59$	−7.56242	−0.984543	−0.492272	−	0.870442i	$-0.663833\pi$
$59$	−7.56242	−0.984543	−0.492272	+	0.870442i	$0.663833\pi$
$60$	0	0
$61$	3.29684	0.422117	0.211059	−	0.977473i	$-0.432309\pi$
$61$	3.29684	0.422117	0.211059	+	0.977473i	$0.432309\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	27.4681	3.40700
$66$	0	0
$67$	7.39128	0.902989	0.451494	−	0.892274i	$-0.350891\pi$
$67$	7.39128	0.902989	0.451494	+	0.892274i	$0.350891\pi$
$68$	0	0
$69$	−2.85830	−0.344099
$70$	0	0
$71$	3.82031	0.453388	0.226694	−	0.973966i	$-0.427208\pi$
$71$	3.82031	0.453388	0.226694	+	0.973966i	$0.427208\pi$
$72$	0	0
$73$	−11.0552	−1.29391	−0.646955	−	0.762528i	$-0.723958\pi$
$73$	−11.0552	−1.29391	−0.646955	+	0.762528i	$0.723958\pi$
$74$	0	0
$75$	−27.9406	−3.22630
$76$	0	0
$77$	0	0
$78$	0	0
$79$	12.7130	1.43032	0.715160	−	0.698961i	$-0.246354\pi$
$79$	12.7130	1.43032	0.715160	+	0.698961i	$0.246354\pi$
$80$	0	0
$81$	2.21793	0.246437
$82$	0	0
$83$	−15.4285	−1.69350	−0.846748	−	0.531994i	$-0.821443\pi$
$83$	−15.4285	−1.69350	−0.846748	+	0.531994i	$0.821443\pi$
$84$	0	0
$85$	−11.7288	−1.27216
$86$	0	0
$87$	17.7445	1.90241
$88$	0	0
$89$	−4.73777	−0.502202	−0.251101	−	0.967961i	$-0.580793\pi$
$89$	−4.73777	−0.502202	−0.251101	+	0.967961i	$0.580793\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	−4.47774	−0.464320
$94$	0	0
$95$	−0.827596	−0.0849096
$96$	0	0
$97$	−12.0976	−1.22832	−0.614161	−	0.789180i	$-0.710506\pi$
$97$	−12.0976	−1.22832	−0.614161	+	0.789180i	$0.710506\pi$
$98$	0	0
$99$	−23.3371	−2.34546
$100$	0	0
$101$	−14.7607	−1.46874	−0.734372	−	0.678747i	$-0.762523\pi$
$101$	−14.7607	−1.46874	−0.734372	+	0.678747i	$0.762523\pi$
$102$	0	0
$103$	6.22336	0.613206	0.306603	−	0.951838i	$-0.400808\pi$
$103$	6.22336	0.613206	0.306603	+	0.951838i	$0.400808\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−16.5687	−1.60175	−0.800877	−	0.598829i	$-0.795633\pi$
$107$	−16.5687	−1.60175	−0.800877	+	0.598829i	$0.795633\pi$
$108$	0	0
$109$	3.90163	0.373708	0.186854	−	0.982388i	$-0.440171\pi$
$109$	3.90163	0.373708	0.186854	+	0.982388i	$0.440171\pi$
$110$	0	0
$111$	9.87802	0.937580
$112$	0	0
$113$	−19.0532	−1.79237	−0.896186	−	0.443679i	$-0.853673\pi$
$113$	−19.0532	−1.79237	−0.896186	+	0.443679i	$0.853673\pi$
$114$	0	0
$115$	3.84386	0.358442
$116$	0	0
$117$	36.9437	3.41545
$118$	0	0
$119$	0	0
$120$	0	0
$121$	9.37668	0.852426
$122$	0	0
$123$	17.7094	1.59680
$124$	0	0
$125$	18.3554	1.64176
$126$	0	0
$127$	8.73623	0.775215	0.387608	−	0.921824i	$-0.373302\pi$
$127$	8.73623	0.775215	0.387608	+	0.921824i	$0.373302\pi$
$128$	0	0
$129$	6.51754	0.573837
$130$	0	0
$131$	15.7676	1.37762	0.688812	−	0.724940i	$-0.258133\pi$
$131$	15.7676	1.37762	0.688812	+	0.724940i	$0.258133\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	−23.8401	−2.05183
$136$	0	0
$137$	−13.1302	−1.12179	−0.560894	−	0.827887i	$-0.689543\pi$
$137$	−13.1302	−1.12179	−0.560894	+	0.827887i	$0.689543\pi$
$138$	0	0
$139$	−11.8971	−1.00910	−0.504549	−	0.863383i	$-0.668341\pi$
$139$	−11.8971	−1.00910	−0.504549	+	0.863383i	$0.668341\pi$
$140$	0	0
$141$	20.7338	1.74610
$142$	0	0
$143$	−32.2573	−2.69749
$144$	0	0
$145$	−23.8629	−1.98170
$146$	0	0
$147$	0	0
$148$	0	0
$149$	5.59321	0.458214	0.229107	−	0.973401i	$-0.426419\pi$
$149$	5.59321	0.458214	0.229107	+	0.973401i	$0.426419\pi$
$150$	0	0
$151$	−15.0760	−1.22687	−0.613435	−	0.789745i	$-0.710213\pi$
$151$	−15.0760	−1.22687	−0.613435	+	0.789745i	$0.710213\pi$
$152$	0	0
$153$	−15.7748	−1.27532
$154$	0	0
$155$	6.02170	0.483674
$156$	0	0
$157$	11.9650	0.954914	0.477457	−	0.878655i	$-0.341559\pi$
$157$	11.9650	0.954914	0.477457	+	0.878655i	$0.341559\pi$
$158$	0	0
$159$	−8.39315	−0.665620
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−6.24986	−0.489526	−0.244763	−	0.969583i	$-0.578710\pi$
$163$	−6.24986	−0.489526	−0.244763	+	0.969583i	$0.578710\pi$
$164$	0	0
$165$	49.5954	3.86100
$166$	0	0
$167$	−1.56364	−0.120998	−0.0604990	−	0.998168i	$-0.519269\pi$
$167$	−1.56364	−0.120998	−0.0604990	+	0.998168i	$0.519269\pi$
$168$	0	0
$169$	38.0649	2.92807
$170$	0	0
$171$	−1.11309	−0.0851202
$172$	0	0
$173$	−14.9764	−1.13864	−0.569318	−	0.822117i	$-0.692793\pi$
$173$	−14.9764	−1.13864	−0.569318	+	0.822117i	$0.692793\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	21.6157	1.62473
$178$	0	0
$179$	8.25214	0.616794	0.308397	−	0.951258i	$-0.400208\pi$
$179$	8.25214	0.616794	0.308397	+	0.951258i	$0.400208\pi$
$180$	0	0
$181$	4.32852	0.321736	0.160868	−	0.986976i	$-0.448571\pi$
$181$	4.32852	0.321736	0.160868	+	0.986976i	$0.448571\pi$
$182$	0	0
$183$	−9.42335	−0.696594
$184$	0	0
$185$	−13.2840	−0.976661
$186$	0	0
$187$	13.7737	1.00724
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−1.09655	−0.0793435	−0.0396718	−	0.999213i	$-0.512631\pi$
$191$	−1.09655	−0.0793435	−0.0396718	+	0.999213i	$0.512631\pi$
$192$	0	0
$193$	18.6549	1.34281	0.671404	−	0.741091i	$-0.265691\pi$
$193$	18.6549	1.34281	0.671404	+	0.741091i	$0.265691\pi$
$194$	0	0
$195$	−78.5120	−5.62236
$196$	0	0
$197$	15.4343	1.09965	0.549823	−	0.835281i	$-0.314695\pi$
$197$	15.4343	1.09965	0.549823	+	0.835281i	$0.314695\pi$
$198$	0	0
$199$	20.1239	1.42655	0.713274	−	0.700885i	$-0.247212\pi$
$199$	20.1239	1.42655	0.713274	+	0.700885i	$0.247212\pi$
$200$	0	0
$201$	−21.1265	−1.49015
$202$	0	0
$203$	0	0
$204$	0	0
$205$	−23.8157	−1.66336
$206$	0	0
$207$	5.16987	0.359331
$208$	0	0
$209$	0.971892	0.0672272
$210$	0	0
$211$	−11.8833	−0.818077	−0.409038	−	0.912517i	$-0.634136\pi$
$211$	−11.8833	−0.818077	−0.409038	+	0.912517i	$0.634136\pi$
$212$	0	0
$213$	−10.9196	−0.748198
$214$	0	0
$215$	−8.76483	−0.597757
$216$	0	0
$217$	0	0
$218$	0	0
$219$	31.5990	2.13526
$220$	0	0
$221$	−21.8045	−1.46673
$222$	0	0
$223$	4.60279	0.308226	0.154113	−	0.988053i	$-0.450748\pi$
$223$	4.60279	0.308226	0.154113	+	0.988053i	$0.450748\pi$
$224$	0	0
$225$	50.5368	3.36912
$226$	0	0
$227$	−20.2406	−1.34342	−0.671708	−	0.740816i	$-0.734439\pi$
$227$	−20.2406	−1.34342	−0.671708	+	0.740816i	$0.734439\pi$
$228$	0	0
$229$	−2.96940	−0.196224	−0.0981119	−	0.995175i	$-0.531280\pi$
$229$	−2.96940	−0.196224	−0.0981119	+	0.995175i	$0.531280\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−24.8709	−1.62934	−0.814672	−	0.579922i	$-0.803083\pi$
$233$	−24.8709	−1.62934	−0.814672	+	0.579922i	$0.803083\pi$
$234$	0	0
$235$	−27.8829	−1.81888
$236$	0	0
$237$	−36.3374	−2.36037
$238$	0	0
$239$	11.7151	0.757785	0.378892	−	0.925441i	$-0.376305\pi$
$239$	11.7151	0.757785	0.378892	+	0.925441i	$0.376305\pi$
$240$	0	0
$241$	−2.89902	−0.186743	−0.0933713	−	0.995631i	$-0.529764\pi$
$241$	−2.89902	−0.186743	−0.0933713	+	0.995631i	$0.529764\pi$
$242$	0	0
$243$	12.2669	0.786921
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−1.53855	−0.0978957
$248$	0	0
$249$	44.0992	2.79467
$250$	0	0
$251$	27.3168	1.72422	0.862111	−	0.506720i	$-0.169142\pi$
$251$	27.3168	1.72422	0.862111	+	0.506720i	$0.169142\pi$
$252$	0	0
$253$	−4.51405	−0.283796
$254$	0	0
$255$	33.5243	2.09937
$256$	0	0
$257$	19.3689	1.20820	0.604101	−	0.796908i	$-0.293532\pi$
$257$	19.3689	1.20820	0.604101	+	0.796908i	$0.293532\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−32.0948	−1.98662
$262$	0	0
$263$	1.45070	0.0894540	0.0447270	−	0.998999i	$-0.485758\pi$
$263$	1.45070	0.0894540	0.0447270	+	0.998999i	$0.485758\pi$
$264$	0	0
$265$	11.2872	0.693365
$266$	0	0
$267$	13.5419	0.828754
$268$	0	0
$269$	−25.4016	−1.54876	−0.774381	−	0.632720i	$-0.781939\pi$
$269$	−25.4016	−1.54876	−0.774381	+	0.632720i	$0.781939\pi$
$270$	0	0
$271$	2.33147	0.141627	0.0708133	−	0.997490i	$-0.477441\pi$
$271$	2.33147	0.141627	0.0708133	+	0.997490i	$0.477441\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	−44.1260	−2.66090
$276$	0	0
$277$	19.5077	1.17211	0.586053	−	0.810273i	$-0.300681\pi$
$277$	19.5077	1.17211	0.586053	+	0.810273i	$0.300681\pi$
$278$	0	0
$279$	8.09899	0.484874
$280$	0	0
$281$	17.5731	1.04832	0.524161	−	0.851619i	$-0.324379\pi$
$281$	17.5731	1.04832	0.524161	+	0.851619i	$0.324379\pi$
$282$	0	0
$283$	21.9695	1.30595	0.652977	−	0.757378i	$-0.273520\pi$
$283$	21.9695	1.30595	0.652977	+	0.757378i	$0.273520\pi$
$284$	0	0
$285$	2.36552	0.140121
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−7.68957	−0.452327
$290$	0	0
$291$	34.5785	2.02703
$292$	0	0
$293$	−10.0326	−0.586112	−0.293056	−	0.956095i	$-0.594672\pi$
$293$	−10.0326	−0.586112	−0.293056	+	0.956095i	$0.594672\pi$
$294$	0	0
$295$	−29.0689	−1.69246
$296$	0	0
$297$	27.9967	1.62454
$298$	0	0
$299$	7.14597	0.413262
$300$	0	0
$301$	0	0
$302$	0	0
$303$	42.1905	2.42378
$304$	0	0
$305$	12.6726	0.725630
$306$	0	0
$307$	9.91159	0.565685	0.282842	−	0.959166i	$-0.408723\pi$
$307$	9.91159	0.565685	0.282842	+	0.959166i	$0.408723\pi$
$308$	0	0
$309$	−17.7882	−1.01194
$310$	0	0
$311$	−25.5776	−1.45037	−0.725185	−	0.688554i	$-0.758246\pi$
$311$	−25.5776	−1.45037	−0.725185	+	0.688554i	$0.758246\pi$
$312$	0	0
$313$	−5.37576	−0.303856	−0.151928	−	0.988392i	$-0.548548\pi$
$313$	−5.37576	−0.303856	−0.151928	+	0.988392i	$0.548548\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	0.734486	0.0412528	0.0206264	−	0.999787i	$-0.493434\pi$
$317$	0.734486	0.0412528	0.0206264	+	0.999787i	$0.493434\pi$
$318$	0	0
$319$	28.0235	1.56901
$320$	0	0
$321$	47.3582	2.64328
$322$	0	0
$323$	0.656956	0.0365540
$324$	0	0
$325$	69.8536	3.87478
$326$	0	0
$327$	−11.1520	−0.616708
$328$	0	0
$329$	0	0
$330$	0	0
$331$	7.70116	0.423294	0.211647	−	0.977346i	$-0.432117\pi$
$331$	7.70116	0.423294	0.211647	+	0.977346i	$0.432117\pi$
$332$	0	0
$333$	−17.8666	−0.979083
$334$	0	0
$335$	28.4110	1.55226
$336$	0	0
$337$	11.7441	0.639741	0.319870	−	0.947461i	$-0.396361\pi$
$337$	11.7441	0.639741	0.319870	+	0.947461i	$0.396361\pi$
$338$	0	0
$339$	54.4596	2.95784
$340$	0	0
$341$	−7.07161	−0.382949
$342$	0	0
$343$	0	0
$344$	0	0
$345$	−10.9869	−0.591515
$346$	0	0
$347$	21.0362	1.12928	0.564640	−	0.825337i	$-0.309015\pi$
$347$	21.0362	1.12928	0.564640	+	0.825337i	$0.309015\pi$
$348$	0	0
$349$	3.32688	0.178084	0.0890420	−	0.996028i	$-0.471619\pi$
$349$	3.32688	0.178084	0.0890420	+	0.996028i	$0.471619\pi$
$350$	0	0
$351$	−44.3202	−2.36564
$352$	0	0
$353$	−19.5880	−1.04256	−0.521281	−	0.853385i	$-0.674546\pi$
$353$	−19.5880	−1.04256	−0.521281	+	0.853385i	$0.674546\pi$
$354$	0	0
$355$	14.6847	0.779385
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−3.32906	−0.175701	−0.0878504	−	0.996134i	$-0.528000\pi$
$359$	−3.32906	−0.175701	−0.0878504	+	0.996134i	$0.528000\pi$
$360$	0	0
$361$	−18.9536	−0.997560
$362$	0	0
$363$	−26.8013	−1.40671
$364$	0	0
$365$	−42.4946	−2.22427
$366$	0	0
$367$	−19.2235	−1.00346	−0.501730	−	0.865024i	$-0.667303\pi$
$367$	−19.2235	−1.00346	−0.501730	+	0.865024i	$0.667303\pi$
$368$	0	0
$369$	−32.0314	−1.66749
$370$	0	0
$371$	0	0
$372$	0	0
$373$	3.48632	0.180515	0.0902573	−	0.995918i	$-0.471231\pi$
$373$	3.48632	0.180515	0.0902573	+	0.995918i	$0.471231\pi$
$374$	0	0
$375$	−52.4652	−2.70929
$376$	0	0
$377$	−44.3625	−2.28479
$378$	0	0
$379$	−20.5501	−1.05559	−0.527795	−	0.849372i	$-0.676981\pi$
$379$	−20.5501	−1.05559	−0.527795	+	0.849372i	$0.676981\pi$
$380$	0	0
$381$	−24.9708	−1.27929
$382$	0	0
$383$	−18.0640	−0.923025	−0.461512	−	0.887134i	$-0.652693\pi$
$383$	−18.0640	−0.923025	−0.461512	+	0.887134i	$0.652693\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−11.7884	−0.599239
$388$	0	0
$389$	15.5461	0.788220	0.394110	−	0.919063i	$-0.371053\pi$
$389$	15.5461	0.788220	0.394110	+	0.919063i	$0.371053\pi$
$390$	0	0
$391$	−3.05130	−0.154311
$392$	0	0
$393$	−45.0686	−2.27341
$394$	0	0
$395$	48.8668	2.45876
$396$	0	0
$397$	−4.01340	−0.201427	−0.100713	−	0.994915i	$-0.532113\pi$
$397$	−4.01340	−0.201427	−0.100713	+	0.994915i	$0.532113\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	17.4347	0.870649	0.435325	−	0.900274i	$-0.356634\pi$
$401$	17.4347	0.870649	0.435325	+	0.900274i	$0.356634\pi$
$402$	0	0
$403$	11.1947	0.557648
$404$	0	0
$405$	8.52541	0.423631
$406$	0	0
$407$	15.6002	0.773271
$408$	0	0
$409$	11.4659	0.566950	0.283475	−	0.958980i	$-0.408513\pi$
$409$	11.4659	0.566950	0.283475	+	0.958980i	$0.408513\pi$
$410$	0	0
$411$	37.5300	1.85122
$412$	0	0
$413$	0	0
$414$	0	0
$415$	−59.3049	−2.91116
$416$	0	0
$417$	34.0055	1.66525
$418$	0	0
$419$	−25.9484	−1.26766	−0.633830	−	0.773472i	$-0.718518\pi$
$419$	−25.9484	−1.26766	−0.633830	+	0.773472i	$0.718518\pi$
$420$	0	0
$421$	−25.7409	−1.25453	−0.627267	−	0.778805i	$-0.715826\pi$
$421$	−25.7409	−1.25453	−0.627267	+	0.778805i	$0.715826\pi$
$422$	0	0
$423$	−37.5017	−1.82339
$424$	0	0
$425$	−29.8272	−1.44683
$426$	0	0
$427$	0	0
$428$	0	0
$429$	92.2009	4.45150
$430$	0	0
$431$	−32.9568	−1.58747	−0.793736	−	0.608263i	$-0.791867\pi$
$431$	−32.9568	−1.58747	−0.793736	+	0.608263i	$0.791867\pi$
$432$	0	0
$433$	−19.3004	−0.927519	−0.463759	−	0.885961i	$-0.653500\pi$
$433$	−19.3004	−0.927519	−0.463759	+	0.885961i	$0.653500\pi$
$434$	0	0
$435$	68.2072	3.27029
$436$	0	0
$437$	−0.215304	−0.0102994
$438$	0	0
$439$	−7.82525	−0.373479	−0.186739	−	0.982410i	$-0.559792\pi$
$439$	−7.82525	−0.373479	−0.186739	+	0.982410i	$0.559792\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	0.289320	0.0137460	0.00687300	−	0.999976i	$-0.497812\pi$
$443$	0.289320	0.0137460	0.00687300	+	0.999976i	$0.497812\pi$
$444$	0	0
$445$	−18.2113	−0.863299
$446$	0	0
$447$	−15.9871	−0.756162
$448$	0	0
$449$	14.6632	0.691998	0.345999	−	0.938235i	$-0.387540\pi$
$449$	14.6632	0.691998	0.345999	+	0.938235i	$0.387540\pi$
$450$	0	0
$451$	27.9681	1.31697
$452$	0	0
$453$	43.0918	2.02463
$454$	0	0
$455$	0	0
$456$	0	0
$457$	11.0440	0.516617	0.258309	−	0.966062i	$-0.416835\pi$
$457$	11.0440	0.516617	0.258309	+	0.966062i	$0.416835\pi$
$458$	0	0
$459$	18.9246	0.883323
$460$	0	0
$461$	−20.7850	−0.968054	−0.484027	−	0.875053i	$-0.660826\pi$
$461$	−20.7850	−0.968054	−0.484027	+	0.875053i	$0.660826\pi$
$462$	0	0
$463$	21.0593	0.978707	0.489353	−	0.872086i	$-0.337233\pi$
$463$	21.0593	0.978707	0.489353	+	0.872086i	$0.337233\pi$
$464$	0	0
$465$	−17.2118	−0.798178
$466$	0	0
$467$	21.5409	0.996796	0.498398	−	0.866948i	$-0.333922\pi$
$467$	21.5409	0.996796	0.498398	+	0.866948i	$0.333922\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	−34.1996	−1.57584
$472$	0	0
$473$	10.2930	0.473274
$474$	0	0
$475$	−2.10465	−0.0965678
$476$	0	0
$477$	15.1809	0.695085
$478$	0	0
$479$	−9.53169	−0.435514	−0.217757	−	0.976003i	$-0.569874\pi$
$479$	−9.53169	−0.435514	−0.217757	+	0.976003i	$0.569874\pi$
$480$	0	0
$481$	−24.6958	−1.12603
$482$	0	0
$483$	0	0
$484$	0	0
$485$	−46.5014	−2.11152
$486$	0	0
$487$	−23.8340	−1.08002	−0.540010	−	0.841659i	$-0.681579\pi$
$487$	−23.8340	−1.08002	−0.540010	+	0.841659i	$0.681579\pi$
$488$	0	0
$489$	17.8639	0.807836
$490$	0	0
$491$	7.42228	0.334963	0.167481	−	0.985875i	$-0.446437\pi$
$491$	7.42228	0.334963	0.167481	+	0.985875i	$0.446437\pi$
$492$	0	0
$493$	18.9426	0.853133
$494$	0	0
$495$	−89.7044	−4.03191
$496$	0	0
$497$	0	0
$498$	0	0
$499$	7.53032	0.337104	0.168552	−	0.985693i	$-0.446091\pi$
$499$	7.53032	0.337104	0.168552	+	0.985693i	$0.446091\pi$
$500$	0	0
$501$	4.46934	0.199675
$502$	0	0
$503$	42.5124	1.89554	0.947768	−	0.318961i	$-0.103334\pi$
$503$	42.5124	1.89554	0.947768	+	0.318961i	$0.103334\pi$
$504$	0	0
$505$	−56.7380	−2.52481
$506$	0	0
$507$	−108.801	−4.83201
$508$	0	0
$509$	−21.1615	−0.937967	−0.468984	−	0.883207i	$-0.655380\pi$
$509$	−21.1615	−0.937967	−0.468984	+	0.883207i	$0.655380\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	1.33534	0.0589567
$514$	0	0
$515$	23.9217	1.05412
$516$	0	0
$517$	32.7445	1.44010
$518$	0	0
$519$	42.8071	1.87902
$520$	0	0
$521$	−39.5748	−1.73380	−0.866902	−	0.498478i	$-0.833892\pi$
$521$	−39.5748	−1.73380	−0.866902	+	0.498478i	$0.833892\pi$
$522$	0	0
$523$	−26.0760	−1.14022	−0.570112	−	0.821567i	$-0.693100\pi$
$523$	−26.0760	−1.14022	−0.570112	+	0.821567i	$0.693100\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−4.78009	−0.208224
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	−39.0967	−1.69665
$532$	0	0
$533$	−44.2749	−1.91776
$534$	0	0
$535$	−63.6876	−2.75346
$536$	0	0
$537$	−23.5871	−1.01786
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−11.7151	−0.503673	−0.251836	−	0.967770i	$-0.581034\pi$
$541$	−11.7151	−0.503673	−0.251836	+	0.967770i	$0.581034\pi$
$542$	0	0
$543$	−12.3722	−0.530942
$544$	0	0
$545$	14.9973	0.642414
$546$	0	0
$547$	13.4435	0.574802	0.287401	−	0.957810i	$-0.407209\pi$
$547$	13.4435	0.574802	0.287401	+	0.957810i	$0.407209\pi$
$548$	0	0
$549$	17.0442	0.727430
$550$	0	0
$551$	1.33662	0.0569417
$552$	0	0
$553$	0	0
$554$	0	0
$555$	37.9697	1.61172
$556$	0	0
$557$	−8.76742	−0.371487	−0.185744	−	0.982598i	$-0.559469\pi$
$557$	−8.76742	−0.371487	−0.185744	+	0.982598i	$0.559469\pi$
$558$	0	0
$559$	−16.2944	−0.689178
$560$	0	0
$561$	−39.3694	−1.66218
$562$	0	0
$563$	−0.289797	−0.0122135	−0.00610675	−	0.999981i	$-0.501944\pi$
$563$	−0.289797	−0.0122135	−0.00610675	+	0.999981i	$0.501944\pi$
$564$	0	0
$565$	−73.2377	−3.08113
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−20.1211	−0.843520	−0.421760	−	0.906707i	$-0.638588\pi$
$569$	−20.1211	−0.843520	−0.421760	+	0.906707i	$0.638588\pi$
$570$	0	0
$571$	−33.3534	−1.39579	−0.697897	−	0.716198i	$-0.745881\pi$
$571$	−33.3534	−1.39579	−0.697897	+	0.716198i	$0.745881\pi$
$572$	0	0
$573$	3.13426	0.130936
$574$	0	0
$575$	9.77525	0.407656
$576$	0	0
$577$	−1.53560	−0.0639280	−0.0319640	−	0.999489i	$-0.510176\pi$
$577$	−1.53560	−0.0639280	−0.0319640	+	0.999489i	$0.510176\pi$
$578$	0	0
$579$	−53.3212	−2.21596
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−13.2551	−0.548972
$584$	0	0
$585$	142.006	5.87124
$586$	0	0
$587$	8.48008	0.350010	0.175005	−	0.984568i	$-0.444006\pi$
$587$	8.48008	0.350010	0.175005	+	0.984568i	$0.444006\pi$
$588$	0	0
$589$	−0.337289	−0.0138978
$590$	0	0
$591$	−44.1157	−1.81468
$592$	0	0
$593$	−23.8339	−0.978740	−0.489370	−	0.872076i	$-0.662773\pi$
$593$	−23.8339	−0.978740	−0.489370	+	0.872076i	$0.662773\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−57.5202	−2.35415
$598$	0	0
$599$	−25.3432	−1.03549	−0.517747	−	0.855534i	$-0.673229\pi$
$599$	−25.3432	−1.03549	−0.517747	+	0.855534i	$0.673229\pi$
$600$	0	0
$601$	−27.3978	−1.11758	−0.558790	−	0.829309i	$-0.688734\pi$
$601$	−27.3978	−1.11758	−0.558790	+	0.829309i	$0.688734\pi$
$602$	0	0
$603$	38.2119	1.55611
$604$	0	0
$605$	36.0426	1.46534
$606$	0	0
$607$	−23.9094	−0.970454	−0.485227	−	0.874388i	$-0.661263\pi$
$607$	−23.9094	−0.970454	−0.485227	+	0.874388i	$0.661263\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−51.8361	−2.09706
$612$	0	0
$613$	−45.5812	−1.84101	−0.920504	−	0.390734i	$-0.872221\pi$
$613$	−45.5812	−1.84101	−0.920504	+	0.390734i	$0.872221\pi$
$614$	0	0
$615$	68.0724	2.74495
$616$	0	0
$617$	−11.1724	−0.449785	−0.224893	−	0.974384i	$-0.572203\pi$
$617$	−11.1724	−0.449785	−0.224893	+	0.974384i	$0.572203\pi$
$618$	0	0
$619$	−20.8426	−0.837734	−0.418867	−	0.908048i	$-0.637573\pi$
$619$	−20.8426	−0.837734	−0.418867	+	0.908048i	$0.637573\pi$
$620$	0	0
$621$	−6.20213	−0.248883
$622$	0	0
$623$	0	0
$624$	0	0
$625$	21.6793	0.867171
$626$	0	0
$627$	−2.77796	−0.110941
$628$	0	0
$629$	10.5450	0.420457
$630$	0	0
$631$	−10.7312	−0.427201	−0.213601	−	0.976921i	$-0.568519\pi$
$631$	−10.7312	−0.427201	−0.213601	+	0.976921i	$0.568519\pi$
$632$	0	0
$633$	33.9659	1.35002
$634$	0	0
$635$	33.5808	1.33262
$636$	0	0
$637$	0	0
$638$	0	0
$639$	19.7505	0.781318
$640$	0	0
$641$	6.42616	0.253818	0.126909	−	0.991914i	$-0.459494\pi$
$641$	6.42616	0.253818	0.126909	+	0.991914i	$0.459494\pi$
$642$	0	0
$643$	−0.578241	−0.0228036	−0.0114018	−	0.999935i	$-0.503629\pi$
$643$	−0.578241	−0.0228036	−0.0114018	+	0.999935i	$0.503629\pi$
$644$	0	0
$645$	25.0525	0.986441
$646$	0	0
$647$	−23.5322	−0.925146	−0.462573	−	0.886581i	$-0.653074\pi$
$647$	−23.5322	−0.925146	−0.462573	+	0.886581i	$0.653074\pi$
$648$	0	0
$649$	34.1372	1.34000
$650$	0	0
$651$	0	0
$652$	0	0
$653$	38.8805	1.52151	0.760756	−	0.649038i	$-0.224829\pi$
$653$	38.8805	1.52151	0.760756	+	0.649038i	$0.224829\pi$
$654$	0	0
$655$	60.6085	2.36817
$656$	0	0
$657$	−57.1538	−2.22978
$658$	0	0
$659$	17.8016	0.693450	0.346725	−	0.937967i	$-0.387294\pi$
$659$	17.8016	0.693450	0.346725	+	0.937967i	$0.387294\pi$
$660$	0	0
$661$	12.4348	0.483658	0.241829	−	0.970319i	$-0.422253\pi$
$661$	12.4348	0.483658	0.241829	+	0.970319i	$0.422253\pi$
$662$	0	0
$663$	62.3238	2.42045
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−6.20805	−0.240377
$668$	0	0
$669$	−13.1561	−0.508646
$670$	0	0
$671$	−14.8821	−0.574518
$672$	0	0
$673$	−46.4810	−1.79171	−0.895855	−	0.444347i	$-0.853436\pi$
$673$	−46.4810	−1.79171	−0.895855	+	0.444347i	$0.853436\pi$
$674$	0	0
$675$	−60.6274	−2.33355
$676$	0	0
$677$	27.8424	1.07007	0.535035	−	0.844830i	$-0.320298\pi$
$677$	27.8424	1.07007	0.535035	+	0.844830i	$0.320298\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	57.8537	2.21696
$682$	0	0
$683$	27.9906	1.07103	0.535516	−	0.844525i	$-0.320117\pi$
$683$	27.9906	1.07103	0.535516	+	0.844525i	$0.320117\pi$
$684$	0	0
$685$	−50.4706	−1.92838
$686$	0	0
$687$	8.48744	0.323816
$688$	0	0
$689$	20.9835	0.799409
$690$	0	0
$691$	−41.6480	−1.58436	−0.792182	−	0.610284i	$-0.791055\pi$
$691$	−41.6480	−1.58436	−0.792182	+	0.610284i	$0.791055\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	−45.7308	−1.73467
$696$	0	0
$697$	18.9052	0.716085
$698$	0	0
$699$	71.0883	2.68881
$700$	0	0
$701$	30.9429	1.16870	0.584349	−	0.811502i	$-0.301350\pi$
$701$	30.9429	1.16870	0.584349	+	0.811502i	$0.301350\pi$
$702$	0	0
$703$	0.744069	0.0280631
$704$	0	0
$705$	79.6978	3.00159
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−42.2060	−1.58508	−0.792539	−	0.609821i	$-0.791241\pi$
$709$	−42.2060	−1.58508	−0.792539	+	0.609821i	$0.791241\pi$
$710$	0	0
$711$	65.7244	2.46486
$712$	0	0
$713$	1.56658	0.0586687
$714$	0	0
$715$	−123.992	−4.63706
$716$	0	0
$717$	−33.4852	−1.25053
$718$	0	0
$719$	−33.6077	−1.25335	−0.626677	−	0.779279i	$-0.715585\pi$
$719$	−33.6077	−1.25335	−0.626677	+	0.779279i	$0.715585\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	8.28627	0.308170
$724$	0	0
$725$	−60.6853	−2.25379
$726$	0	0
$727$	−6.95629	−0.257995	−0.128997	−	0.991645i	$-0.541176\pi$
$727$	−6.95629	−0.257995	−0.128997	+	0.991645i	$0.541176\pi$
$728$	0	0
$729$	−41.7162	−1.54504
$730$	0	0
$731$	6.95763	0.257337
$732$	0	0
$733$	33.7756	1.24753	0.623765	−	0.781612i	$-0.285602\pi$
$733$	33.7756	1.24753	0.623765	+	0.781612i	$0.285602\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−33.3646	−1.22900
$738$	0	0
$739$	−46.2043	−1.69965	−0.849826	−	0.527063i	$-0.823293\pi$
$739$	−46.2043	−1.69965	−0.849826	+	0.527063i	$0.823293\pi$
$740$	0	0
$741$	4.39764	0.161551
$742$	0	0
$743$	5.07302	0.186111	0.0930555	−	0.995661i	$-0.470337\pi$
$743$	5.07302	0.186111	0.0930555	+	0.995661i	$0.470337\pi$
$744$	0	0
$745$	21.4995	0.787682
$746$	0	0
$747$	−79.7632	−2.91838
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−6.99162	−0.255128	−0.127564	−	0.991830i	$-0.540716\pi$
$751$	−6.99162	−0.255128	−0.127564	+	0.991830i	$0.540716\pi$
$752$	0	0
$753$	−78.0796	−2.84538
$754$	0	0
$755$	−57.9502	−2.10902
$756$	0	0
$757$	13.1910	0.479436	0.239718	−	0.970843i	$-0.422945\pi$
$757$	13.1910	0.479436	0.239718	+	0.970843i	$0.422945\pi$
$758$	0	0
$759$	12.9025	0.468331
$760$	0	0
$761$	28.2475	1.02397	0.511986	−	0.858994i	$-0.328910\pi$
$761$	28.2475	1.02397	0.511986	+	0.858994i	$0.328910\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	−60.6362	−2.19231
$766$	0	0
$767$	−54.0408	−1.95130
$768$	0	0
$769$	32.7859	1.18229	0.591145	−	0.806565i	$-0.298676\pi$
$769$	32.7859	1.18229	0.591145	+	0.806565i	$0.298676\pi$
$770$	0	0
$771$	−55.3622	−1.99382
$772$	0	0
$773$	−12.4192	−0.446686	−0.223343	−	0.974740i	$-0.571697\pi$
$773$	−12.4192	−0.446686	−0.223343	+	0.974740i	$0.571697\pi$
$774$	0	0
$775$	15.3137	0.550083
$776$	0	0
$777$	0	0
$778$	0	0
$779$	1.33397	0.0477946
$780$	0	0
$781$	−17.2451	−0.617078
$782$	0	0
$783$	38.5031	1.37599
$784$	0	0
$785$	45.9919	1.64152
$786$	0	0
$787$	19.5328	0.696269	0.348134	−	0.937445i	$-0.386815\pi$
$787$	19.5328	0.696269	0.348134	+	0.937445i	$0.386815\pi$
$788$	0	0
$789$	−4.14653	−0.147620
$790$	0	0
$791$	0	0
$792$	0	0
$793$	23.5591	0.836609
$794$	0	0
$795$	−32.2621	−1.14422
$796$	0	0
$797$	13.4836	0.477613	0.238806	−	0.971067i	$-0.423244\pi$
$797$	13.4836	0.477613	0.238806	+	0.971067i	$0.423244\pi$
$798$	0	0
$799$	22.1338	0.783038
$800$	0	0
$801$	−24.4936	−0.865440
$802$	0	0
$803$	49.9037	1.76106
$804$	0	0
$805$	0	0
$806$	0	0
$807$	72.6053	2.55583
$808$	0	0
$809$	27.1918	0.956014	0.478007	−	0.878356i	$-0.341359\pi$
$809$	27.1918	0.956014	0.478007	+	0.878356i	$0.341359\pi$
$810$	0	0
$811$	−18.6096	−0.653470	−0.326735	−	0.945116i	$-0.605949\pi$
$811$	−18.6096	−0.653470	−0.326735	+	0.945116i	$0.605949\pi$
$812$	0	0
$813$	−6.66403	−0.233718
$814$	0	0
$815$	−24.0236	−0.841509
$816$	0	0
$817$	0.490939	0.0171758
$818$	0	0
$819$	0	0
$820$	0	0
$821$	40.0490	1.39772	0.698860	−	0.715258i	$-0.253691\pi$
$821$	40.0490	1.39772	0.698860	+	0.715258i	$0.253691\pi$
$822$	0	0
$823$	−0.388160	−0.0135304	−0.00676521	−	0.999977i	$-0.502153\pi$
$823$	−0.388160	−0.0135304	−0.00676521	+	0.999977i	$0.502153\pi$
$824$	0	0
$825$	126.125	4.39112
$826$	0	0
$827$	23.2486	0.808433	0.404217	−	0.914663i	$-0.367544\pi$
$827$	23.2486	0.808433	0.404217	+	0.914663i	$0.367544\pi$
$828$	0	0
$829$	−45.7481	−1.58890	−0.794449	−	0.607331i	$-0.792240\pi$
$829$	−45.7481	−1.58890	−0.794449	+	0.607331i	$0.792240\pi$
$830$	0	0
$831$	−55.7589	−1.93425
$832$	0	0
$833$	0	0
$834$	0	0
$835$	−6.01040	−0.207999
$836$	0	0
$837$	−9.71610	−0.335838
$838$	0	0
$839$	−6.09309	−0.210357	−0.105178	−	0.994453i	$-0.533541\pi$
$839$	−6.09309	−0.210357	−0.105178	+	0.994453i	$0.533541\pi$
$840$	0	0
$841$	9.53990	0.328962
$842$	0	0
$843$	−50.2291	−1.72998
$844$	0	0
$845$	146.316	5.03342
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−62.7955	−2.15514
$850$	0	0
$851$	−3.45591	−0.118467
$852$	0	0
$853$	21.2850	0.728785	0.364392	−	0.931246i	$-0.381277\pi$
$853$	21.2850	0.728785	0.364392	+	0.931246i	$0.381277\pi$
$854$	0	0
$855$	−4.27856	−0.146324
$856$	0	0
$857$	48.1521	1.64484	0.822421	−	0.568879i	$-0.192623\pi$
$857$	48.1521	1.64484	0.822421	+	0.568879i	$0.192623\pi$
$858$	0	0
$859$	5.85919	0.199913	0.0999566	−	0.994992i	$-0.468130\pi$
$859$	5.85919	0.199913	0.0999566	+	0.994992i	$0.468130\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	19.6055	0.667380	0.333690	−	0.942683i	$-0.391706\pi$
$863$	19.6055	0.667380	0.333690	+	0.942683i	$0.391706\pi$
$864$	0	0
$865$	−57.5672	−1.95734
$866$	0	0
$867$	21.9791	0.746448
$868$	0	0
$869$	−57.3870	−1.94672
$870$	0	0
$871$	52.8179	1.78967
$872$	0	0
$873$	−62.5429	−2.11676
$874$	0	0
$875$	0	0
$876$	0	0
$877$	6.68391	0.225699	0.112850	−	0.993612i	$-0.464002\pi$
$877$	6.68391	0.225699	0.112850	+	0.993612i	$0.464002\pi$
$878$	0	0
$879$	28.6762	0.967224
$880$	0	0
$881$	−12.4925	−0.420884	−0.210442	−	0.977606i	$-0.567490\pi$
$881$	−12.4925	−0.420884	−0.210442	+	0.977606i	$0.567490\pi$
$882$	0	0
$883$	53.3884	1.79666	0.898332	−	0.439318i	$-0.144780\pi$
$883$	53.3884	1.79666	0.898332	+	0.439318i	$0.144780\pi$
$884$	0	0
$885$	83.0875	2.79296
$886$	0	0
$887$	−30.6495	−1.02911	−0.514555	−	0.857457i	$-0.672043\pi$
$887$	−30.6495	−1.02911	−0.514555	+	0.857457i	$0.672043\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−10.0119	−0.335410
$892$	0	0
$893$	1.56179	0.0522633
$894$	0	0
$895$	31.7201	1.06028
$896$	0	0
$897$	−20.4253	−0.681981
$898$	0	0
$899$	−9.72538	−0.324360
$900$	0	0
$901$	−8.95989	−0.298497
$902$	0	0
$903$	0	0
$904$	0	0
$905$	16.6382	0.553073
$906$	0	0
$907$	−1.36416	−0.0452963	−0.0226481	−	0.999743i	$-0.507210\pi$
$907$	−1.36416	−0.0452963	−0.0226481	+	0.999743i	$0.507210\pi$
$908$	0	0
$909$	−76.3108	−2.53107
$910$	0	0
$911$	21.0681	0.698017	0.349008	−	0.937120i	$-0.386519\pi$
$911$	21.0681	0.698017	0.349008	+	0.937120i	$0.386519\pi$
$912$	0	0
$913$	69.6450	2.30491
$914$	0	0
$915$	−36.2220	−1.19746
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−6.26594	−0.206694	−0.103347	−	0.994645i	$-0.532955\pi$
$919$	−6.26594	−0.206694	−0.103347	+	0.994645i	$0.532955\pi$
$920$	0	0
$921$	−28.3303	−0.933515
$922$	0	0
$923$	27.2998	0.898585
$924$	0	0
$925$	−33.7824	−1.11076
$926$	0	0
$927$	32.1739	1.05673
$928$	0	0
$929$	0.624582	0.0204919	0.0102459	−	0.999948i	$-0.496739\pi$
$929$	0.624582	0.0204919	0.0102459	+	0.999948i	$0.496739\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	73.1083	2.39346
$934$	0	0
$935$	52.9443	1.73146
$936$	0	0
$937$	−52.0278	−1.69967	−0.849836	−	0.527046i	$-0.823299\pi$
$937$	−52.0278	−1.69967	−0.849836	+	0.527046i	$0.823299\pi$
$938$	0	0
$939$	15.3655	0.501435
$940$	0	0
$941$	0.181538	0.00591798	0.00295899	−	0.999996i	$-0.499058\pi$
$941$	0.181538	0.00591798	0.00295899	+	0.999996i	$0.499058\pi$
$942$	0	0
$943$	−6.19578	−0.201762
$944$	0	0
$945$	0	0
$946$	0	0
$947$	22.7933	0.740682	0.370341	−	0.928896i	$-0.379241\pi$
$947$	22.7933	0.740682	0.370341	+	0.928896i	$0.379241\pi$
$948$	0	0
$949$	−79.0000	−2.56445
$950$	0	0
$951$	−2.09938	−0.0680770
$952$	0	0
$953$	50.0851	1.62242	0.811208	−	0.584758i	$-0.198810\pi$
$953$	50.0851	1.62242	0.811208	+	0.584758i	$0.198810\pi$
$954$	0	0
$955$	−4.21498	−0.136394
$956$	0	0
$957$	−80.0995	−2.58925
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−28.5458	−0.920834
$962$	0	0
$963$	−85.6578	−2.76028
$964$	0	0
$965$	71.7068	2.30832
$966$	0	0
$967$	−25.9323	−0.833927	−0.416964	−	0.908923i	$-0.636906\pi$
$967$	−25.9323	−0.833927	−0.416964	+	0.908923i	$0.636906\pi$
$968$	0	0
$969$	−1.87778	−0.0603228
$970$	0	0
$971$	9.25590	0.297036	0.148518	−	0.988910i	$-0.452550\pi$
$971$	9.25590	0.297036	0.148518	+	0.988910i	$0.452550\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	−199.663	−6.39432
$976$	0	0
$977$	34.2678	1.09632	0.548162	−	0.836372i	$-0.315328\pi$
$977$	34.2678	1.09632	0.548162	+	0.836372i	$0.315328\pi$
$978$	0	0
$979$	21.3865	0.683516
$980$	0	0
$981$	20.1709	0.644007
$982$	0	0
$983$	−47.7710	−1.52366	−0.761829	−	0.647779i	$-0.775698\pi$
$983$	−47.7710	−1.52366	−0.761829	+	0.647779i	$0.775698\pi$
$984$	0	0
$985$	59.3271	1.89032
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−2.28022	−0.0725067
$990$	0	0
$991$	−32.3210	−1.02671	−0.513355	−	0.858176i	$-0.671598\pi$
$991$	−32.3210	−1.02671	−0.513355	+	0.858176i	$0.671598\pi$
$992$	0	0
$993$	−22.0122	−0.698537
$994$	0	0
$995$	77.3536	2.45227
$996$	0	0
$997$	50.1408	1.58798	0.793988	−	0.607933i	$-0.208001\pi$
$997$	50.1408	1.58798	0.793988	+	0.607933i	$0.208001\pi$
$998$	0	0
$999$	21.4340	0.678142

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9016.2.a.bl.1.3		11
7.3	odd	6		1288.2.q.a.737.3	✓	22
7.5	odd	6		1288.2.q.a.921.3	yes	22
7.6	odd	2		9016.2.a.bq.1.9		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1288.2.q.a.737.3	✓	22	7.3	odd	6
1288.2.q.a.921.3	yes	22	7.5	odd	6
9016.2.a.bl.1.3		11	1.1	even	1	trivial
9016.2.a.bq.1.9		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)

\(f(q)\)	\(=\)	\(q-2.85830 q^{3} +3.84386 q^{5} +5.16987 q^{9} +O(q^{10})\)	\(q-2.85830 q^{3} +3.84386 q^{5} +5.16987 q^{9} -4.51405 q^{11} +7.14597 q^{13} -10.9869 q^{15} -3.05130 q^{17} -0.215304 q^{19} +1.00000 q^{23} +9.77525 q^{25} -6.20213 q^{27} -6.20805 q^{29} +1.56658 q^{31} +12.9025 q^{33} -3.45591 q^{37} -20.4253 q^{39} -6.19578 q^{41} -2.28022 q^{43} +19.8722 q^{45} -7.25389 q^{47} +8.72153 q^{51} +2.93642 q^{53} -17.3514 q^{55} +0.615402 q^{57} -7.56242 q^{59} +3.29684 q^{61} +27.4681 q^{65} +7.39128 q^{67} -2.85830 q^{69} +3.82031 q^{71} -11.0552 q^{73} -27.9406 q^{75} +12.7130 q^{79} +2.21793 q^{81} -15.4285 q^{83} -11.7288 q^{85} +17.7445 q^{87} -4.73777 q^{89} -4.47774 q^{93} -0.827596 q^{95} -12.0976 q^{97} -23.3371 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 4 q^{3} - q^{5} + 11 q^{9}+O(q^{10}) \) 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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