LMFDB - Embedded newform 9016.2.a.bk.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9016, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("9016.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			1.7
Root			$-0.560144$ 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)

$f(q)$	$=$	$q+0.560144 q^{3} +0.521201 q^{5} -2.68624 q^{9} +O(q^{10})$	$q+0.560144 q^{3} +0.521201 q^{5} -2.68624 q^{9} -0.305932 q^{11} -2.33988 q^{13} +0.291948 q^{15} +4.89476 q^{17} -2.13751 q^{19} -1.00000 q^{23} -4.72835 q^{25} -3.18511 q^{27} +8.37454 q^{29} +7.01183 q^{31} -0.171366 q^{33} +1.83646 q^{37} -1.31067 q^{39} +2.78616 q^{41} -9.61547 q^{43} -1.40007 q^{45} -4.01465 q^{47} +2.74177 q^{51} -5.03011 q^{53} -0.159452 q^{55} -1.19731 q^{57} -1.05255 q^{59} -9.07628 q^{61} -1.21955 q^{65} +13.3081 q^{67} -0.560144 q^{69} -0.0980520 q^{71} +2.99163 q^{73} -2.64856 q^{75} -11.3048 q^{79} +6.27459 q^{81} +8.58854 q^{83} +2.55115 q^{85} +4.69095 q^{87} -3.40120 q^{89} +3.92764 q^{93} -1.11407 q^{95} +0.450608 q^{97} +0.821807 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 4 q^{3} - 3 q^{5} + 11 q^{9}+O(q^{10}) $ 11 * q - 4 * q^3 - 3 * q^5 + 11 * q^9	$ 11 q - 4 q^{3} - 3 q^{5} + 11 q^{9} + 13 q^{13} - 7 q^{17} - 8 q^{19} - 11 q^{23} + 6 q^{25} - 25 q^{27} - 3 q^{29} - 12 q^{31} + 2 q^{33} - q^{37} - 21 q^{39} - 12 q^{41} + 9 q^{43} - 19 q^{45} - 17 q^{47} + 19 q^{51} - 5 q^{53} - 21 q^{55} + 11 q^{57} - 33 q^{59} + 15 q^{61} - 9 q^{65} - 5 q^{67} + 4 q^{69} - 9 q^{71} - 5 q^{73} - 44 q^{75} + 11 q^{79} - 13 q^{81} - 51 q^{83} + 33 q^{85} - 4 q^{87} - 26 q^{89} + 6 q^{93} - 19 q^{95} - 21 q^{97} + 15 q^{99}+O(q^{100}) $ 11 * q - 4 * q^3 - 3 * q^5 + 11 * q^9 + 13 * q^13 - 7 * q^17 - 8 * q^19 - 11 * q^23 + 6 * q^25 - 25 * q^27 - 3 * q^29 - 12 * q^31 + 2 * q^33 - q^37 - 21 * q^39 - 12 * q^41 + 9 * q^43 - 19 * q^45 - 17 * q^47 + 19 * q^51 - 5 * q^53 - 21 * q^55 + 11 * q^57 - 33 * q^59 + 15 * q^61 - 9 * q^65 - 5 * q^67 + 4 * q^69 - 9 * q^71 - 5 * q^73 - 44 * q^75 + 11 * q^79 - 13 * q^81 - 51 * q^83 + 33 * q^85 - 4 * q^87 - 26 * q^89 + 6 * q^93 - 19 * q^95 - 21 * q^97 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0	0
$2$	0	0
$3$	0.560144	0.323400	0.161700	−	0.986840i	$-0.448302\pi$
$3$	0.560144	0.323400	0.161700	+	0.986840i	$0.448302\pi$
$4$	0	0
$5$	0.521201	0.233088	0.116544	−	0.993186i	$-0.462818\pi$
$5$	0.521201	0.233088	0.116544	+	0.993186i	$0.462818\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	−2.68624	−0.895413
$10$	0	0
$11$	−0.305932	−0.0922420	−0.0461210	−	0.998936i	$-0.514686\pi$
$11$	−0.305932	−0.0922420	−0.0461210	+	0.998936i	$0.514686\pi$
$12$	0	0
$13$	−2.33988	−0.648966	−0.324483	−	0.945891i	$-0.605190\pi$
$13$	−2.33988	−0.648966	−0.324483	+	0.945891i	$0.605190\pi$
$14$	0	0
$15$	0.291948	0.0753806
$16$	0	0
$17$	4.89476	1.18715	0.593577	−	0.804777i	$-0.297715\pi$
$17$	4.89476	1.18715	0.593577	+	0.804777i	$0.297715\pi$
$18$	0	0
$19$	−2.13751	−0.490378	−0.245189	−	0.969475i	$-0.578850\pi$
$19$	−2.13751	−0.490378	−0.245189	+	0.969475i	$0.578850\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0	0
$25$	−4.72835	−0.945670
$26$	0	0
$27$	−3.18511	−0.612976
$28$	0	0
$29$	8.37454	1.55511	0.777556	−	0.628813i	$-0.216459\pi$
$29$	8.37454	1.55511	0.777556	+	0.628813i	$0.216459\pi$
$30$	0	0
$31$	7.01183	1.25936	0.629681	−	0.776854i	$-0.283185\pi$
$31$	7.01183	1.25936	0.629681	+	0.776854i	$0.283185\pi$
$32$	0	0
$33$	−0.171366	−0.0298310
$34$	0	0
$35$	0	0
$36$	0	0
$37$	1.83646	0.301912	0.150956	−	0.988540i	$-0.451765\pi$
$37$	1.83646	0.301912	0.150956	+	0.988540i	$0.451765\pi$
$38$	0	0
$39$	−1.31067	−0.209875
$40$	0	0
$41$	2.78616	0.435124	0.217562	−	0.976046i	$-0.430189\pi$
$41$	2.78616	0.435124	0.217562	+	0.976046i	$0.430189\pi$
$42$	0	0
$43$	−9.61547	−1.46635	−0.733173	−	0.680043i	$-0.761961\pi$
$43$	−9.61547	−1.46635	−0.733173	+	0.680043i	$0.761961\pi$
$44$	0	0
$45$	−1.40007	−0.208710
$46$	0	0
$47$	−4.01465	−0.585597	−0.292799	−	0.956174i	$-0.594587\pi$
$47$	−4.01465	−0.585597	−0.292799	+	0.956174i	$0.594587\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	2.74177	0.383925
$52$	0	0
$53$	−5.03011	−0.690938	−0.345469	−	0.938430i	$-0.612280\pi$
$53$	−5.03011	−0.690938	−0.345469	+	0.938430i	$0.612280\pi$
$54$	0	0
$55$	−0.159452	−0.0215005
$56$	0	0
$57$	−1.19731	−0.158588
$58$	0	0
$59$	−1.05255	−0.137030	−0.0685150	−	0.997650i	$-0.521826\pi$
$59$	−1.05255	−0.137030	−0.0685150	+	0.997650i	$0.521826\pi$
$60$	0	0
$61$	−9.07628	−1.16210	−0.581050	−	0.813868i	$-0.697358\pi$
$61$	−9.07628	−1.16210	−0.581050	+	0.813868i	$0.697358\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	−1.21955	−0.151266
$66$	0	0
$67$	13.3081	1.62585	0.812924	−	0.582370i	$-0.197875\pi$
$67$	13.3081	1.62585	0.812924	+	0.582370i	$0.197875\pi$
$68$	0	0
$69$	−0.560144	−0.0674335
$70$	0	0
$71$	−0.0980520	−0.0116366	−0.00581832	−	0.999983i	$-0.501852\pi$
$71$	−0.0980520	−0.0116366	−0.00581832	+	0.999983i	$0.501852\pi$
$72$	0	0
$73$	2.99163	0.350143	0.175072	−	0.984556i	$-0.443984\pi$
$73$	2.99163	0.350143	0.175072	+	0.984556i	$0.443984\pi$
$74$	0	0
$75$	−2.64856	−0.305829
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−11.3048	−1.27189	−0.635944	−	0.771735i	$-0.719389\pi$
$79$	−11.3048	−1.27189	−0.635944	+	0.771735i	$0.719389\pi$
$80$	0	0
$81$	6.27459	0.697177
$82$	0	0
$83$	8.58854	0.942714	0.471357	−	0.881942i	$-0.343764\pi$
$83$	8.58854	0.942714	0.471357	+	0.881942i	$0.343764\pi$
$84$	0	0
$85$	2.55115	0.276712
$86$	0	0
$87$	4.69095	0.502923
$88$	0	0
$89$	−3.40120	−0.360526	−0.180263	−	0.983618i	$-0.557695\pi$
$89$	−3.40120	−0.360526	−0.180263	+	0.983618i	$0.557695\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	3.92764	0.407277
$94$	0	0
$95$	−1.11407	−0.114301
$96$	0	0
$97$	0.450608	0.0457523	0.0228761	−	0.999738i	$-0.492718\pi$
$97$	0.450608	0.0457523	0.0228761	+	0.999738i	$0.492718\pi$
$98$	0	0
$99$	0.821807	0.0825947
$100$	0	0
$101$	−3.96110	−0.394144	−0.197072	−	0.980389i	$-0.563143\pi$
$101$	−3.96110	−0.394144	−0.197072	+	0.980389i	$0.563143\pi$
$102$	0	0
$103$	−12.0047	−1.18285	−0.591427	−	0.806359i	$-0.701435\pi$
$103$	−12.0047	−1.18285	−0.591427	+	0.806359i	$0.701435\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	1.91001	0.184647	0.0923236	−	0.995729i	$-0.470571\pi$
$107$	1.91001	0.184647	0.0923236	+	0.995729i	$0.470571\pi$
$108$	0	0
$109$	−8.24040	−0.789287	−0.394643	−	0.918834i	$-0.629132\pi$
$109$	−8.24040	−0.789287	−0.394643	+	0.918834i	$0.629132\pi$
$110$	0	0
$111$	1.02868	0.0976382
$112$	0	0
$113$	3.09028	0.290709	0.145355	−	0.989380i	$-0.453568\pi$
$113$	3.09028	0.290709	0.145355	+	0.989380i	$0.453568\pi$
$114$	0	0
$115$	−0.521201	−0.0486022
$116$	0	0
$117$	6.28548	0.581093
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−10.9064	−0.991491
$122$	0	0
$123$	1.56065	0.140719
$124$	0	0
$125$	−5.07042	−0.453513
$126$	0	0
$127$	−4.93150	−0.437600	−0.218800	−	0.975770i	$-0.570214\pi$
$127$	−4.93150	−0.437600	−0.218800	+	0.975770i	$0.570214\pi$
$128$	0	0
$129$	−5.38605	−0.474215
$130$	0	0
$131$	5.44645	0.475858	0.237929	−	0.971283i	$-0.423531\pi$
$131$	5.44645	0.475858	0.237929	+	0.971283i	$0.423531\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	−1.66008	−0.142877
$136$	0	0
$137$	−20.6034	−1.76027	−0.880134	−	0.474726i	$-0.842547\pi$
$137$	−20.6034	−1.76027	−0.880134	+	0.474726i	$0.842547\pi$
$138$	0	0
$139$	−14.4270	−1.22368	−0.611842	−	0.790980i	$-0.709571\pi$
$139$	−14.4270	−1.22368	−0.611842	+	0.790980i	$0.709571\pi$
$140$	0	0
$141$	−2.24879	−0.189382
$142$	0	0
$143$	0.715845	0.0598620
$144$	0	0
$145$	4.36482	0.362478
$146$	0	0
$147$	0	0
$148$	0	0
$149$	14.6040	1.19641	0.598203	−	0.801345i	$-0.295882\pi$
$149$	14.6040	1.19641	0.598203	+	0.801345i	$0.295882\pi$
$150$	0	0
$151$	1.99061	0.161994	0.0809968	−	0.996714i	$-0.474190\pi$
$151$	1.99061	0.161994	0.0809968	+	0.996714i	$0.474190\pi$
$152$	0	0
$153$	−13.1485	−1.06299
$154$	0	0
$155$	3.65457	0.293543
$156$	0	0
$157$	−9.43052	−0.752638	−0.376319	−	0.926490i	$-0.622810\pi$
$157$	−9.43052	−0.752638	−0.376319	+	0.926490i	$0.622810\pi$
$158$	0	0
$159$	−2.81759	−0.223449
$160$	0	0
$161$	0	0
$162$	0	0
$163$	6.06093	0.474729	0.237364	−	0.971421i	$-0.423716\pi$
$163$	6.06093	0.474729	0.237364	+	0.971421i	$0.423716\pi$
$164$	0	0
$165$	−0.0893162	−0.00695326
$166$	0	0
$167$	−20.8722	−1.61514	−0.807569	−	0.589773i	$-0.799217\pi$
$167$	−20.8722	−1.61514	−0.807569	+	0.589773i	$0.799217\pi$
$168$	0	0
$169$	−7.52496	−0.578843
$170$	0	0
$171$	5.74185	0.439091
$172$	0	0
$173$	−12.6615	−0.962633	−0.481317	−	0.876547i	$-0.659841\pi$
$173$	−12.6615	−0.962633	−0.481317	+	0.876547i	$0.659841\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−0.589579	−0.0443155
$178$	0	0
$179$	−18.0383	−1.34825	−0.674124	−	0.738618i	$-0.735479\pi$
$179$	−18.0383	−1.34825	−0.674124	+	0.738618i	$0.735479\pi$
$180$	0	0
$181$	−8.76827	−0.651740	−0.325870	−	0.945415i	$-0.605657\pi$
$181$	−8.76827	−0.651740	−0.325870	+	0.945415i	$0.605657\pi$
$182$	0	0
$183$	−5.08403	−0.375822
$184$	0	0
$185$	0.957165	0.0703721
$186$	0	0
$187$	−1.49747	−0.109506
$188$	0	0
$189$	0	0
$190$	0	0
$191$	1.85562	0.134268	0.0671339	−	0.997744i	$-0.478615\pi$
$191$	1.85562	0.134268	0.0671339	+	0.997744i	$0.478615\pi$
$192$	0	0
$193$	−22.7693	−1.63897	−0.819487	−	0.573098i	$-0.805741\pi$
$193$	−22.7693	−1.63897	−0.819487	+	0.573098i	$0.805741\pi$
$194$	0	0
$195$	−0.683123	−0.0489195
$196$	0	0
$197$	14.3712	1.02390	0.511952	−	0.859014i	$-0.328922\pi$
$197$	14.3712	1.02390	0.511952	+	0.859014i	$0.328922\pi$
$198$	0	0
$199$	−19.6292	−1.39148	−0.695740	−	0.718293i	$-0.744924\pi$
$199$	−19.6292	−1.39148	−0.695740	+	0.718293i	$0.744924\pi$
$200$	0	0
$201$	7.45448	0.525798
$202$	0	0
$203$	0	0
$204$	0	0
$205$	1.45215	0.101422
$206$	0	0
$207$	2.68624	0.186706
$208$	0	0
$209$	0.653932	0.0452334
$210$	0	0
$211$	17.5888	1.21086	0.605431	−	0.795898i	$-0.293001\pi$
$211$	17.5888	1.21086	0.605431	+	0.795898i	$0.293001\pi$
$212$	0	0
$213$	−0.0549233	−0.00376328
$214$	0	0
$215$	−5.01159	−0.341788
$216$	0	0
$217$	0	0
$218$	0	0
$219$	1.67574	0.113236
$220$	0	0
$221$	−11.4532	−0.770423
$222$	0	0
$223$	3.38580	0.226730	0.113365	−	0.993553i	$-0.463837\pi$
$223$	3.38580	0.226730	0.113365	+	0.993553i	$0.463837\pi$
$224$	0	0
$225$	12.7015	0.846765
$226$	0	0
$227$	−20.2610	−1.34477	−0.672384	−	0.740202i	$-0.734730\pi$
$227$	−20.2610	−1.34477	−0.672384	+	0.740202i	$0.734730\pi$
$228$	0	0
$229$	−10.4467	−0.690338	−0.345169	−	0.938541i	$-0.612178\pi$
$229$	−10.4467	−0.690338	−0.345169	+	0.938541i	$0.612178\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	14.4123	0.944182	0.472091	−	0.881550i	$-0.343499\pi$
$233$	14.4123	0.944182	0.472091	+	0.881550i	$0.343499\pi$
$234$	0	0
$235$	−2.09244	−0.136496
$236$	0	0
$237$	−6.33232	−0.411328
$238$	0	0
$239$	−6.36296	−0.411586	−0.205793	−	0.978596i	$-0.565977\pi$
$239$	−6.36296	−0.411586	−0.205793	+	0.978596i	$0.565977\pi$
$240$	0	0
$241$	17.4185	1.12202	0.561012	−	0.827807i	$-0.310412\pi$
$241$	17.4185	1.12202	0.561012	+	0.827807i	$0.310412\pi$
$242$	0	0
$243$	13.0700	0.838442
$244$	0	0
$245$	0	0
$246$	0	0
$247$	5.00151	0.318239
$248$	0	0
$249$	4.81082	0.304873
$250$	0	0
$251$	−16.2539	−1.02594	−0.512969	−	0.858407i	$-0.671454\pi$
$251$	−16.2539	−1.02594	−0.512969	+	0.858407i	$0.671454\pi$
$252$	0	0
$253$	0.305932	0.0192338
$254$	0	0
$255$	1.42901	0.0894884
$256$	0	0
$257$	25.1011	1.56576	0.782881	−	0.622172i	$-0.213750\pi$
$257$	25.1011	1.56576	0.782881	+	0.622172i	$0.213750\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−22.4960	−1.39247
$262$	0	0
$263$	15.8777	0.979058	0.489529	−	0.871987i	$-0.337169\pi$
$263$	15.8777	0.979058	0.489529	+	0.871987i	$0.337169\pi$
$264$	0	0
$265$	−2.62170	−0.161050
$266$	0	0
$267$	−1.90516	−0.116594
$268$	0	0
$269$	−10.8829	−0.663545	−0.331773	−	0.943359i	$-0.607647\pi$
$269$	−10.8829	−0.663545	−0.331773	+	0.943359i	$0.607647\pi$
$270$	0	0
$271$	−4.87160	−0.295929	−0.147964	−	0.988993i	$-0.547272\pi$
$271$	−4.87160	−0.295929	−0.147964	+	0.988993i	$0.547272\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	1.44655	0.0872305
$276$	0	0
$277$	−4.95894	−0.297954	−0.148977	−	0.988841i	$-0.547598\pi$
$277$	−4.95894	−0.297954	−0.148977	+	0.988841i	$0.547598\pi$
$278$	0	0
$279$	−18.8355	−1.12765
$280$	0	0
$281$	18.6792	1.11431	0.557155	−	0.830409i	$-0.311893\pi$
$281$	18.6792	1.11431	0.557155	+	0.830409i	$0.311893\pi$
$282$	0	0
$283$	−15.1216	−0.898886	−0.449443	−	0.893309i	$-0.648378\pi$
$283$	−15.1216	−0.898886	−0.449443	+	0.893309i	$0.648378\pi$
$284$	0	0
$285$	−0.624041	−0.0369650
$286$	0	0
$287$	0	0
$288$	0	0
$289$	6.95869	0.409335
$290$	0	0
$291$	0.252405	0.0147963
$292$	0	0
$293$	25.5354	1.49179	0.745897	−	0.666061i	$-0.232021\pi$
$293$	25.5354	1.49179	0.745897	+	0.666061i	$0.232021\pi$
$294$	0	0
$295$	−0.548589	−0.0319401
$296$	0	0
$297$	0.974429	0.0565421
$298$	0	0
$299$	2.33988	0.135319
$300$	0	0
$301$	0	0
$302$	0	0
$303$	−2.21879	−0.127466
$304$	0	0
$305$	−4.73057	−0.270872
$306$	0	0
$307$	−29.5093	−1.68419	−0.842093	−	0.539332i	$-0.818677\pi$
$307$	−29.5093	−1.68419	−0.842093	+	0.539332i	$0.818677\pi$
$308$	0	0
$309$	−6.72434	−0.382534
$310$	0	0
$311$	−25.0831	−1.42233	−0.711165	−	0.703025i	$-0.751832\pi$
$311$	−25.0831	−1.42233	−0.711165	+	0.703025i	$0.751832\pi$
$312$	0	0
$313$	5.24199	0.296295	0.148147	−	0.988965i	$-0.452669\pi$
$313$	5.24199	0.296295	0.148147	+	0.988965i	$0.452669\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	9.01670	0.506428	0.253214	−	0.967410i	$-0.418512\pi$
$317$	9.01670	0.506428	0.253214	+	0.967410i	$0.418512\pi$
$318$	0	0
$319$	−2.56204	−0.143447
$320$	0	0
$321$	1.06988	0.0597148
$322$	0	0
$323$	−10.4626	−0.582154
$324$	0	0
$325$	11.0638	0.613708
$326$	0	0
$327$	−4.61581	−0.255255
$328$	0	0
$329$	0	0
$330$	0	0
$331$	16.6305	0.914092	0.457046	−	0.889443i	$-0.348907\pi$
$331$	16.6305	0.914092	0.457046	+	0.889443i	$0.348907\pi$
$332$	0	0
$333$	−4.93317	−0.270336
$334$	0	0
$335$	6.93621	0.378966
$336$	0	0
$337$	−27.7453	−1.51138	−0.755691	−	0.654928i	$-0.772699\pi$
$337$	−27.7453	−1.51138	−0.755691	+	0.654928i	$0.772699\pi$
$338$	0	0
$339$	1.73100	0.0940152
$340$	0	0
$341$	−2.14515	−0.116166
$342$	0	0
$343$	0	0
$344$	0	0
$345$	−0.291948	−0.0157179
$346$	0	0
$347$	−20.0208	−1.07477	−0.537386	−	0.843337i	$-0.680588\pi$
$347$	−20.0208	−1.07477	−0.537386	+	0.843337i	$0.680588\pi$
$348$	0	0
$349$	−0.0188589	−0.00100950	−0.000504748	−	1.00000i	$-0.500161\pi$
$349$	−0.0188589	−0.00100950	−0.000504748		1.00000i	$0.500161\pi$
$350$	0	0
$351$	7.45279	0.397801
$352$	0	0
$353$	10.5365	0.560802	0.280401	−	0.959883i	$-0.409533\pi$
$353$	10.5365	0.560802	0.280401	+	0.959883i	$0.409533\pi$
$354$	0	0
$355$	−0.0511048	−0.00271236
$356$	0	0
$357$	0	0
$358$	0	0
$359$	9.67213	0.510475	0.255238	−	0.966878i	$-0.417846\pi$
$359$	9.67213	0.510475	0.255238	+	0.966878i	$0.417846\pi$
$360$	0	0
$361$	−14.4311	−0.759530
$362$	0	0
$363$	−6.10916	−0.320648
$364$	0	0
$365$	1.55924	0.0816142
$366$	0	0
$367$	20.8136	1.08646	0.543231	−	0.839583i	$-0.317201\pi$
$367$	20.8136	1.08646	0.543231	+	0.839583i	$0.317201\pi$
$368$	0	0
$369$	−7.48428	−0.389616
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−15.0931	−0.781493	−0.390746	−	0.920498i	$-0.627783\pi$
$373$	−15.0931	−0.781493	−0.390746	+	0.920498i	$0.627783\pi$
$374$	0	0
$375$	−2.84017	−0.146666
$376$	0	0
$377$	−19.5954	−1.00922
$378$	0	0
$379$	−10.3474	−0.531509	−0.265754	−	0.964041i	$-0.585621\pi$
$379$	−10.3474	−0.531509	−0.265754	+	0.964041i	$0.585621\pi$
$380$	0	0
$381$	−2.76235	−0.141520
$382$	0	0
$383$	−26.2452	−1.34107	−0.670534	−	0.741878i	$-0.733935\pi$
$383$	−26.2452	−1.34107	−0.670534	+	0.741878i	$0.733935\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	25.8294	1.31298
$388$	0	0
$389$	24.6422	1.24941	0.624705	−	0.780861i	$-0.285219\pi$
$389$	24.6422	1.24941	0.624705	+	0.780861i	$0.285219\pi$
$390$	0	0
$391$	−4.89476	−0.247539
$392$	0	0
$393$	3.05080	0.153892
$394$	0	0
$395$	−5.89207	−0.296462
$396$	0	0
$397$	28.4790	1.42932	0.714660	−	0.699472i	$-0.246581\pi$
$397$	28.4790	1.42932	0.714660	+	0.699472i	$0.246581\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	18.3977	0.918736	0.459368	−	0.888246i	$-0.348076\pi$
$401$	18.3977	0.918736	0.459368	+	0.888246i	$0.348076\pi$
$402$	0	0
$403$	−16.4069	−0.817284
$404$	0	0
$405$	3.27032	0.162504
$406$	0	0
$407$	−0.561832	−0.0278490
$408$	0	0
$409$	−37.8921	−1.87364	−0.936822	−	0.349806i	$-0.886248\pi$
$409$	−37.8921	−1.87364	−0.936822	+	0.349806i	$0.886248\pi$
$410$	0	0
$411$	−11.5409	−0.569270
$412$	0	0
$413$	0	0
$414$	0	0
$415$	4.47635	0.219736
$416$	0	0
$417$	−8.08122	−0.395739
$418$	0	0
$419$	−20.2937	−0.991412	−0.495706	−	0.868491i	$-0.665091\pi$
$419$	−20.2937	−0.991412	−0.495706	+	0.868491i	$0.665091\pi$
$420$	0	0
$421$	23.5134	1.14597	0.572986	−	0.819565i	$-0.305785\pi$
$421$	23.5134	1.14597	0.572986	+	0.819565i	$0.305785\pi$
$422$	0	0
$423$	10.7843	0.524351
$424$	0	0
$425$	−23.1441	−1.12266
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0.400977	0.0193593
$430$	0	0
$431$	−4.01494	−0.193393	−0.0966965	−	0.995314i	$-0.530828\pi$
$431$	−4.01494	−0.193393	−0.0966965	+	0.995314i	$0.530828\pi$
$432$	0	0
$433$	−41.0228	−1.97143	−0.985714	−	0.168427i	$-0.946131\pi$
$433$	−41.0228	−1.97143	−0.985714	+	0.168427i	$0.946131\pi$
$434$	0	0
$435$	2.44493	0.117225
$436$	0	0
$437$	2.13751	0.102251
$438$	0	0
$439$	−12.3640	−0.590102	−0.295051	−	0.955481i	$-0.595337\pi$
$439$	−12.3640	−0.590102	−0.295051	+	0.955481i	$0.595337\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	15.7005	0.745953	0.372977	−	0.927841i	$-0.378337\pi$
$443$	15.7005	0.745953	0.372977	+	0.927841i	$0.378337\pi$
$444$	0	0
$445$	−1.77271	−0.0840344
$446$	0	0
$447$	8.18034	0.386917
$448$	0	0
$449$	25.0706	1.18316	0.591578	−	0.806248i	$-0.298505\pi$
$449$	25.0706	1.18316	0.591578	+	0.806248i	$0.298505\pi$
$450$	0	0
$451$	−0.852375	−0.0401368
$452$	0	0
$453$	1.11503	0.0523886
$454$	0	0
$455$	0	0
$456$	0	0
$457$	9.52208	0.445424	0.222712	−	0.974884i	$-0.428509\pi$
$457$	9.52208	0.445424	0.222712	+	0.974884i	$0.428509\pi$
$458$	0	0
$459$	−15.5904	−0.727696
$460$	0	0
$461$	−10.2801	−0.478792	−0.239396	−	0.970922i	$-0.576949\pi$
$461$	−10.2801	−0.478792	−0.239396	+	0.970922i	$0.576949\pi$
$462$	0	0
$463$	22.6791	1.05399	0.526995	−	0.849869i	$-0.323319\pi$
$463$	22.6791	1.05399	0.526995	+	0.849869i	$0.323319\pi$
$464$	0	0
$465$	2.04709	0.0949315
$466$	0	0
$467$	−23.1175	−1.06975	−0.534876	−	0.844931i	$-0.679642\pi$
$467$	−23.1175	−1.06975	−0.534876	+	0.844931i	$0.679642\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	−5.28246	−0.243403
$472$	0	0
$473$	2.94168	0.135259
$474$	0	0
$475$	10.1069	0.463736
$476$	0	0
$477$	13.5121	0.618675
$478$	0	0
$479$	7.20489	0.329200	0.164600	−	0.986360i	$-0.447367\pi$
$479$	7.20489	0.329200	0.164600	+	0.986360i	$0.447367\pi$
$480$	0	0
$481$	−4.29710	−0.195931
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0.234857	0.0106643
$486$	0	0
$487$	−3.47336	−0.157393	−0.0786965	−	0.996899i	$-0.525076\pi$
$487$	−3.47336	−0.157393	−0.0786965	+	0.996899i	$0.525076\pi$
$488$	0	0
$489$	3.39500	0.153527
$490$	0	0
$491$	−18.0734	−0.815643	−0.407821	−	0.913062i	$-0.633711\pi$
$491$	−18.0734	−0.815643	−0.407821	+	0.913062i	$0.633711\pi$
$492$	0	0
$493$	40.9914	1.84616
$494$	0	0
$495$	0.428326	0.0192518
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−19.8936	−0.890558	−0.445279	−	0.895392i	$-0.646896\pi$
$499$	−19.8936	−0.890558	−0.445279	+	0.895392i	$0.646896\pi$
$500$	0	0
$501$	−11.6914	−0.522335
$502$	0	0
$503$	8.99553	0.401091	0.200545	−	0.979684i	$-0.435729\pi$
$503$	8.99553	0.401091	0.200545	+	0.979684i	$0.435729\pi$
$504$	0	0
$505$	−2.06453	−0.0918704
$506$	0	0
$507$	−4.21506	−0.187197
$508$	0	0
$509$	5.58326	0.247474	0.123737	−	0.992315i	$-0.460512\pi$
$509$	5.58326	0.247474	0.123737	+	0.992315i	$0.460512\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	6.80821	0.300590
$514$	0	0
$515$	−6.25684	−0.275709
$516$	0	0
$517$	1.22821	0.0540167
$518$	0	0
$519$	−7.09225	−0.311315
$520$	0	0
$521$	11.5068	0.504121	0.252061	−	0.967711i	$-0.418892\pi$
$521$	11.5068	0.504121	0.252061	+	0.967711i	$0.418892\pi$
$522$	0	0
$523$	24.0958	1.05364	0.526818	−	0.849978i	$-0.323385\pi$
$523$	24.0958	1.05364	0.526818	+	0.849978i	$0.323385\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	34.3213	1.49506
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	2.82739	0.122698
$532$	0	0
$533$	−6.51927	−0.282381
$534$	0	0
$535$	0.995497	0.0430391
$536$	0	0
$537$	−10.1041	−0.436023
$538$	0	0
$539$	0	0
$540$	0	0
$541$	6.49186	0.279107	0.139553	−	0.990215i	$-0.455433\pi$
$541$	6.49186	0.279107	0.139553	+	0.990215i	$0.455433\pi$
$542$	0	0
$543$	−4.91150	−0.210773
$544$	0	0
$545$	−4.29490	−0.183973
$546$	0	0
$547$	35.4433	1.51545	0.757723	−	0.652576i	$-0.226312\pi$
$547$	35.4433	1.51545	0.757723	+	0.652576i	$0.226312\pi$
$548$	0	0
$549$	24.3811	1.04056
$550$	0	0
$551$	−17.9006	−0.762593
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0.536150	0.0227583
$556$	0	0
$557$	32.2288	1.36558	0.682789	−	0.730616i	$-0.260767\pi$
$557$	32.2288	1.36558	0.682789	+	0.730616i	$0.260767\pi$
$558$	0	0
$559$	22.4991	0.951609
$560$	0	0
$561$	−0.838797	−0.0354140
$562$	0	0
$563$	−46.8312	−1.97370	−0.986850	−	0.161640i	$-0.948322\pi$
$563$	−46.8312	−1.97370	−0.986850	+	0.161640i	$0.948322\pi$
$564$	0	0
$565$	1.61066	0.0677609
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−22.9288	−0.961224	−0.480612	−	0.876933i	$-0.659585\pi$
$569$	−22.9288	−0.961224	−0.480612	+	0.876933i	$0.659585\pi$
$570$	0	0
$571$	−27.7500	−1.16130	−0.580650	−	0.814153i	$-0.697201\pi$
$571$	−27.7500	−1.16130	−0.580650	+	0.814153i	$0.697201\pi$
$572$	0	0
$573$	1.03941	0.0434221
$574$	0	0
$575$	4.72835	0.197186
$576$	0	0
$577$	27.4681	1.14351	0.571755	−	0.820424i	$-0.306263\pi$
$577$	27.4681	1.14351	0.571755	+	0.820424i	$0.306263\pi$
$578$	0	0
$579$	−12.7541	−0.530043
$580$	0	0
$581$	0	0
$582$	0	0
$583$	1.53887	0.0637335
$584$	0	0
$585$	3.27600	0.135446
$586$	0	0
$587$	7.04626	0.290830	0.145415	−	0.989371i	$-0.453548\pi$
$587$	7.04626	0.290830	0.145415	+	0.989371i	$0.453548\pi$
$588$	0	0
$589$	−14.9878	−0.617564
$590$	0	0
$591$	8.04994	0.331130
$592$	0	0
$593$	−5.19578	−0.213365	−0.106683	−	0.994293i	$-0.534023\pi$
$593$	−5.19578	−0.213365	−0.106683	+	0.994293i	$0.534023\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−10.9952	−0.450004
$598$	0	0
$599$	14.8840	0.608144	0.304072	−	0.952649i	$-0.401654\pi$
$599$	14.8840	0.608144	0.304072	+	0.952649i	$0.401654\pi$
$600$	0	0
$601$	47.9465	1.95578	0.977890	−	0.209119i	$-0.0670597\pi$
$601$	47.9465	1.95578	0.977890	+	0.209119i	$0.0670597\pi$
$602$	0	0
$603$	−35.7488	−1.45580
$604$	0	0
$605$	−5.68443	−0.231105
$606$	0	0
$607$	−39.0936	−1.58676	−0.793380	−	0.608727i	$-0.791680\pi$
$607$	−39.0936	−1.58676	−0.793380	+	0.608727i	$0.791680\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	9.39381	0.380033
$612$	0	0
$613$	35.7773	1.44503	0.722515	−	0.691355i	$-0.242986\pi$
$613$	35.7773	1.44503	0.722515	+	0.691355i	$0.242986\pi$
$614$	0	0
$615$	0.813412	0.0327999
$616$	0	0
$617$	15.1119	0.608383	0.304191	−	0.952611i	$-0.401614\pi$
$617$	15.1119	0.608383	0.304191	+	0.952611i	$0.401614\pi$
$618$	0	0
$619$	−6.18895	−0.248755	−0.124377	−	0.992235i	$-0.539693\pi$
$619$	−6.18895	−0.248755	−0.124377	+	0.992235i	$0.539693\pi$
$620$	0	0
$621$	3.18511	0.127814
$622$	0	0
$623$	0	0
$624$	0	0
$625$	20.9990	0.839962
$626$	0	0
$627$	0.366297	0.0146285
$628$	0	0
$629$	8.98903	0.358416
$630$	0	0
$631$	18.5256	0.737493	0.368747	−	0.929530i	$-0.379787\pi$
$631$	18.5256	0.737493	0.368747	+	0.929530i	$0.379787\pi$
$632$	0	0
$633$	9.85226	0.391592
$634$	0	0
$635$	−2.57030	−0.101999
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0.263391	0.0104196
$640$	0	0
$641$	−4.42647	−0.174835	−0.0874175	−	0.996172i	$-0.527861\pi$
$641$	−4.42647	−0.174835	−0.0874175	+	0.996172i	$0.527861\pi$
$642$	0	0
$643$	−8.79724	−0.346929	−0.173465	−	0.984840i	$-0.555496\pi$
$643$	−8.79724	−0.346929	−0.173465	+	0.984840i	$0.555496\pi$
$644$	0	0
$645$	−2.80721	−0.110534
$646$	0	0
$647$	−40.4973	−1.59211	−0.796057	−	0.605222i	$-0.793084\pi$
$647$	−40.4973	−1.59211	−0.796057	+	0.605222i	$0.793084\pi$
$648$	0	0
$649$	0.322008	0.0126399
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−29.8079	−1.16648	−0.583238	−	0.812302i	$-0.698214\pi$
$653$	−29.8079	−1.16648	−0.583238	+	0.812302i	$0.698214\pi$
$654$	0	0
$655$	2.83869	0.110917
$656$	0	0
$657$	−8.03622	−0.313523
$658$	0	0
$659$	−21.6800	−0.844532	−0.422266	−	0.906472i	$-0.638765\pi$
$659$	−21.6800	−0.844532	−0.422266	+	0.906472i	$0.638765\pi$
$660$	0	0
$661$	3.72146	0.144748	0.0723739	−	0.997378i	$-0.476943\pi$
$661$	3.72146	0.144748	0.0723739	+	0.997378i	$0.476943\pi$
$662$	0	0
$663$	−6.41542	−0.249154
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−8.37454	−0.324263
$668$	0	0
$669$	1.89654	0.0733244
$670$	0	0
$671$	2.77673	0.107194
$672$	0	0
$673$	−0.934516	−0.0360230	−0.0180115	−	0.999838i	$-0.505734\pi$
$673$	−0.934516	−0.0360230	−0.0180115	+	0.999838i	$0.505734\pi$
$674$	0	0
$675$	15.0603	0.579673
$676$	0	0
$677$	31.7944	1.22196	0.610979	−	0.791647i	$-0.290776\pi$
$677$	31.7944	1.22196	0.610979	+	0.791647i	$0.290776\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	−11.3491	−0.434898
$682$	0	0
$683$	18.4056	0.704269	0.352134	−	0.935949i	$-0.385456\pi$
$683$	18.4056	0.704269	0.352134	+	0.935949i	$0.385456\pi$
$684$	0	0
$685$	−10.7385	−0.410298
$686$	0	0
$687$	−5.85167	−0.223255
$688$	0	0
$689$	11.7699	0.448396
$690$	0	0
$691$	12.0053	0.456704	0.228352	−	0.973579i	$-0.426666\pi$
$691$	12.0053	0.456704	0.228352	+	0.973579i	$0.426666\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	−7.51938	−0.285226
$696$	0	0
$697$	13.6376	0.516560
$698$	0	0
$699$	8.07297	0.305348
$700$	0	0
$701$	31.5341	1.19103	0.595513	−	0.803346i	$-0.296949\pi$
$701$	31.5341	1.19103	0.595513	+	0.803346i	$0.296949\pi$
$702$	0	0
$703$	−3.92545	−0.148051
$704$	0	0
$705$	−1.17207	−0.0441427
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−4.47085	−0.167906	−0.0839532	−	0.996470i	$-0.526755\pi$
$709$	−4.47085	−0.167906	−0.0839532	+	0.996470i	$0.526755\pi$
$710$	0	0
$711$	30.3674	1.13887
$712$	0	0
$713$	−7.01183	−0.262595
$714$	0	0
$715$	0.373099	0.0139531
$716$	0	0
$717$	−3.56418	−0.133107
$718$	0	0
$719$	−9.77964	−0.364719	−0.182360	−	0.983232i	$-0.558373\pi$
$719$	−9.77964	−0.364719	−0.182360	+	0.983232i	$0.558373\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	9.75688	0.362862
$724$	0	0
$725$	−39.5977	−1.47062
$726$	0	0
$727$	19.1375	0.709770	0.354885	−	0.934910i	$-0.384520\pi$
$727$	19.1375	0.709770	0.354885	+	0.934910i	$0.384520\pi$
$728$	0	0
$729$	−11.5027	−0.426025
$730$	0	0
$731$	−47.0654	−1.74078
$732$	0	0
$733$	36.7493	1.35736	0.678682	−	0.734432i	$-0.262551\pi$
$733$	36.7493	1.35736	0.678682	+	0.734432i	$0.262551\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−4.07139	−0.149971
$738$	0	0
$739$	−2.70284	−0.0994257	−0.0497129	−	0.998764i	$-0.515831\pi$
$739$	−2.70284	−0.0994257	−0.0497129	+	0.998764i	$0.515831\pi$
$740$	0	0
$741$	2.80157	0.102918
$742$	0	0
$743$	10.8814	0.399202	0.199601	−	0.979877i	$-0.436035\pi$
$743$	10.8814	0.399202	0.199601	+	0.979877i	$0.436035\pi$
$744$	0	0
$745$	7.61161	0.278868
$746$	0	0
$747$	−23.0709	−0.844118
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−11.8312	−0.431727	−0.215863	−	0.976424i	$-0.569257\pi$
$751$	−11.8312	−0.431727	−0.215863	+	0.976424i	$0.569257\pi$
$752$	0	0
$753$	−9.10454	−0.331788
$754$	0	0
$755$	1.03751	0.0377588
$756$	0	0
$757$	−39.1119	−1.42155	−0.710774	−	0.703421i	$-0.751655\pi$
$757$	−39.1119	−1.42155	−0.710774	+	0.703421i	$0.751655\pi$
$758$	0	0
$759$	0.171366	0.00622020
$760$	0	0
$761$	−53.2369	−1.92984	−0.964918	−	0.262551i	$-0.915436\pi$
$761$	−53.2369	−1.92984	−0.964918	+	0.262551i	$0.915436\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	−6.85301	−0.247771
$766$	0	0
$767$	2.46284	0.0889279
$768$	0	0
$769$	−39.8594	−1.43737	−0.718683	−	0.695338i	$-0.755255\pi$
$769$	−39.8594	−1.43737	−0.718683	+	0.695338i	$0.755255\pi$
$770$	0	0
$771$	14.0602	0.506366
$772$	0	0
$773$	−39.3171	−1.41414	−0.707068	−	0.707145i	$-0.749983\pi$
$773$	−39.3171	−1.41414	−0.707068	+	0.707145i	$0.749983\pi$
$774$	0	0
$775$	−33.1544	−1.19094
$776$	0	0
$777$	0	0
$778$	0	0
$779$	−5.95543	−0.213375
$780$	0	0
$781$	0.0299973	0.00107339
$782$	0	0
$783$	−26.6739	−0.953246
$784$	0	0
$785$	−4.91520	−0.175431
$786$	0	0
$787$	28.0588	1.00019	0.500093	−	0.865971i	$-0.333299\pi$
$787$	28.0588	1.00019	0.500093	+	0.865971i	$0.333299\pi$
$788$	0	0
$789$	8.89378	0.316627
$790$	0	0
$791$	0	0
$792$	0	0
$793$	21.2374	0.754163
$794$	0	0
$795$	−1.46853	−0.0520833
$796$	0	0
$797$	18.4008	0.651790	0.325895	−	0.945406i	$-0.394334\pi$
$797$	18.4008	0.651790	0.325895	+	0.945406i	$0.394334\pi$
$798$	0	0
$799$	−19.6508	−0.695194
$800$	0	0
$801$	9.13643	0.322820
$802$	0	0
$803$	−0.915234	−0.0322979
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−6.09602	−0.214590
$808$	0	0
$809$	−34.7925	−1.22324	−0.611620	−	0.791152i	$-0.709482\pi$
$809$	−34.7925	−1.22324	−0.611620	+	0.791152i	$0.709482\pi$
$810$	0	0
$811$	−14.6315	−0.513780	−0.256890	−	0.966441i	$-0.582698\pi$
$811$	−14.6315	−0.513780	−0.256890	+	0.966441i	$0.582698\pi$
$812$	0	0
$813$	−2.72880	−0.0957032
$814$	0	0
$815$	3.15896	0.110654
$816$	0	0
$817$	20.5531	0.719063
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−23.0488	−0.804408	−0.402204	−	0.915550i	$-0.631756\pi$
$821$	−23.0488	−0.804408	−0.402204	+	0.915550i	$0.631756\pi$
$822$	0	0
$823$	−16.3464	−0.569801	−0.284900	−	0.958557i	$-0.591960\pi$
$823$	−16.3464	−0.569801	−0.284900	+	0.958557i	$0.591960\pi$
$824$	0	0
$825$	0.810279	0.0282103
$826$	0	0
$827$	−13.0015	−0.452106	−0.226053	−	0.974115i	$-0.572582\pi$
$827$	−13.0015	−0.452106	−0.226053	+	0.974115i	$0.572582\pi$
$828$	0	0
$829$	49.8380	1.73094	0.865472	−	0.500957i	$-0.167018\pi$
$829$	49.8380	1.73094	0.865472	+	0.500957i	$0.167018\pi$
$830$	0	0
$831$	−2.77772	−0.0963582
$832$	0	0
$833$	0	0
$834$	0	0
$835$	−10.8786	−0.376470
$836$	0	0
$837$	−22.3335	−0.771959
$838$	0	0
$839$	−38.0603	−1.31399	−0.656993	−	0.753897i	$-0.728172\pi$
$839$	−38.0603	−1.31399	−0.656993	+	0.753897i	$0.728172\pi$
$840$	0	0
$841$	41.1329	1.41838
$842$	0	0
$843$	10.4631	0.360367
$844$	0	0
$845$	−3.92201	−0.134921
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−8.47028	−0.290699
$850$	0	0
$851$	−1.83646	−0.0629530
$852$	0	0
$853$	−25.9595	−0.888836	−0.444418	−	0.895820i	$-0.646590\pi$
$853$	−25.9595	−0.888836	−0.444418	+	0.895820i	$0.646590\pi$
$854$	0	0
$855$	2.99266	0.102347
$856$	0	0
$857$	−53.2096	−1.81761	−0.908803	−	0.417225i	$-0.863003\pi$
$857$	−53.2096	−1.81761	−0.908803	+	0.417225i	$0.863003\pi$
$858$	0	0
$859$	−20.4853	−0.698950	−0.349475	−	0.936946i	$-0.613640\pi$
$859$	−20.4853	−0.698950	−0.349475	+	0.936946i	$0.613640\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−3.34268	−0.113786	−0.0568931	−	0.998380i	$-0.518119\pi$
$863$	−3.34268	−0.113786	−0.0568931	+	0.998380i	$0.518119\pi$
$864$	0	0
$865$	−6.59917	−0.224378
$866$	0	0
$867$	3.89787	0.132379
$868$	0	0
$869$	3.45850	0.117322
$870$	0	0
$871$	−31.1395	−1.05512
$872$	0	0
$873$	−1.21044	−0.0409672
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−21.4327	−0.723730	−0.361865	−	0.932230i	$-0.617860\pi$
$877$	−21.4327	−0.723730	−0.361865	+	0.932230i	$0.617860\pi$
$878$	0	0
$879$	14.3035	0.482446
$880$	0	0
$881$	−29.2671	−0.986033	−0.493017	−	0.870020i	$-0.664106\pi$
$881$	−29.2671	−0.986033	−0.493017	+	0.870020i	$0.664106\pi$
$882$	0	0
$883$	−4.84428	−0.163023	−0.0815115	−	0.996672i	$-0.525975\pi$
$883$	−4.84428	−0.163023	−0.0815115	+	0.996672i	$0.525975\pi$
$884$	0	0
$885$	−0.307289	−0.0103294
$886$	0	0
$887$	35.6112	1.19571	0.597853	−	0.801606i	$-0.296021\pi$
$887$	35.6112	1.19571	0.597853	+	0.801606i	$0.296021\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−1.91960	−0.0643090
$892$	0	0
$893$	8.58135	0.287164
$894$	0	0
$895$	−9.40160	−0.314261
$896$	0	0
$897$	1.31067	0.0437620
$898$	0	0
$899$	58.7209	1.95845
$900$	0	0
$901$	−24.6212	−0.820250
$902$	0	0
$903$	0	0
$904$	0	0
$905$	−4.57003	−0.151913
$906$	0	0
$907$	50.7607	1.68548	0.842741	−	0.538320i	$-0.180941\pi$
$907$	50.7607	1.68548	0.842741	+	0.538320i	$0.180941\pi$
$908$	0	0
$909$	10.6405	0.352922
$910$	0	0
$911$	44.5029	1.47445	0.737224	−	0.675649i	$-0.236136\pi$
$911$	44.5029	1.47445	0.737224	+	0.675649i	$0.236136\pi$
$912$	0	0
$913$	−2.62751	−0.0869579
$914$	0	0
$915$	−2.64980	−0.0875997
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−4.73893	−0.156323	−0.0781615	−	0.996941i	$-0.524905\pi$
$919$	−4.73893	−0.156323	−0.0781615	+	0.996941i	$0.524905\pi$
$920$	0	0
$921$	−16.5295	−0.544665
$922$	0	0
$923$	0.229430	0.00755178
$924$	0	0
$925$	−8.68342	−0.285509
$926$	0	0
$927$	32.2474	1.05914
$928$	0	0
$929$	1.12842	0.0370222	0.0185111	−	0.999829i	$-0.494107\pi$
$929$	1.12842	0.0370222	0.0185111	+	0.999829i	$0.494107\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	−14.0501	−0.459981
$934$	0	0
$935$	−0.780480	−0.0255244
$936$	0	0
$937$	−7.59738	−0.248196	−0.124098	−	0.992270i	$-0.539604\pi$
$937$	−7.59738	−0.248196	−0.124098	+	0.992270i	$0.539604\pi$
$938$	0	0
$939$	2.93627	0.0958215
$940$	0	0
$941$	22.1590	0.722361	0.361181	−	0.932496i	$-0.382374\pi$
$941$	22.1590	0.722361	0.361181	+	0.932496i	$0.382374\pi$
$942$	0	0
$943$	−2.78616	−0.0907297
$944$	0	0
$945$	0	0
$946$	0	0
$947$	37.8090	1.22863	0.614314	−	0.789062i	$-0.289433\pi$
$947$	37.8090	1.22863	0.614314	+	0.789062i	$0.289433\pi$
$948$	0	0
$949$	−7.00005	−0.227231
$950$	0	0
$951$	5.05065	0.163779
$952$	0	0
$953$	13.3563	0.432654	0.216327	−	0.976321i	$-0.430592\pi$
$953$	13.3563	0.432654	0.216327	+	0.976321i	$0.430592\pi$
$954$	0	0
$955$	0.967150	0.0312962
$956$	0	0
$957$	−1.43511	−0.0463906
$958$	0	0
$959$	0	0
$960$	0	0
$961$	18.1658	0.585994
$962$	0	0
$963$	−5.13073	−0.165335
$964$	0	0
$965$	−11.8674	−0.382025
$966$	0	0
$967$	−32.6825	−1.05100	−0.525500	−	0.850794i	$-0.676122\pi$
$967$	−32.6825	−1.05100	−0.525500	+	0.850794i	$0.676122\pi$
$968$	0	0
$969$	−5.86056	−0.188268
$970$	0	0
$971$	−51.4378	−1.65072	−0.825359	−	0.564608i	$-0.809028\pi$
$971$	−51.4378	−1.65072	−0.825359	+	0.564608i	$0.809028\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	6.19731	0.198473
$976$	0	0
$977$	−7.03143	−0.224955	−0.112478	−	0.993654i	$-0.535879\pi$
$977$	−7.03143	−0.224955	−0.112478	+	0.993654i	$0.535879\pi$
$978$	0	0
$979$	1.04054	0.0332557
$980$	0	0
$981$	22.1357	0.706737
$982$	0	0
$983$	−35.0052	−1.11649	−0.558246	−	0.829675i	$-0.688526\pi$
$983$	−35.0052	−1.11649	−0.558246	+	0.829675i	$0.688526\pi$
$984$	0	0
$985$	7.49027	0.238660
$986$	0	0
$987$	0	0
$988$	0	0
$989$	9.61547	0.305754
$990$	0	0
$991$	33.7152	1.07100	0.535500	−	0.844535i	$-0.320123\pi$
$991$	33.7152	1.07100	0.535500	+	0.844535i	$0.320123\pi$
$992$	0	0
$993$	9.31545	0.295617
$994$	0	0
$995$	−10.2308	−0.324338
$996$	0	0
$997$	2.61207	0.0827250	0.0413625	−	0.999144i	$-0.486830\pi$
$997$	2.61207	0.0827250	0.0413625	+	0.999144i	$0.486830\pi$
$998$	0	0
$999$	−5.84933	−0.185065

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9016.2.a.bk.1.7		11
7.2	even	3		1288.2.q.d.921.5	yes	22
7.4	even	3		1288.2.q.d.737.5	✓	22
7.6	odd	2		9016.2.a.br.1.5		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1288.2.q.d.737.5	✓	22	7.4	even	3
1288.2.q.d.921.5	yes	22	7.2	even	3
9016.2.a.bk.1.7		11	1.1	even	1	trivial
9016.2.a.br.1.5		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)

\(f(q)\)	\(=\)	\(q+0.560144 q^{3} +0.521201 q^{5} -2.68624 q^{9} +O(q^{10})\)	\(q+0.560144 q^{3} +0.521201 q^{5} -2.68624 q^{9} -0.305932 q^{11} -2.33988 q^{13} +0.291948 q^{15} +4.89476 q^{17} -2.13751 q^{19} -1.00000 q^{23} -4.72835 q^{25} -3.18511 q^{27} +8.37454 q^{29} +7.01183 q^{31} -0.171366 q^{33} +1.83646 q^{37} -1.31067 q^{39} +2.78616 q^{41} -9.61547 q^{43} -1.40007 q^{45} -4.01465 q^{47} +2.74177 q^{51} -5.03011 q^{53} -0.159452 q^{55} -1.19731 q^{57} -1.05255 q^{59} -9.07628 q^{61} -1.21955 q^{65} +13.3081 q^{67} -0.560144 q^{69} -0.0980520 q^{71} +2.99163 q^{73} -2.64856 q^{75} -11.3048 q^{79} +6.27459 q^{81} +8.58854 q^{83} +2.55115 q^{85} +4.69095 q^{87} -3.40120 q^{89} +3.92764 q^{93} -1.11407 q^{95} +0.450608 q^{97} +0.821807 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 4 q^{3} - 3 q^{5} + 11 q^{9}+O(q^{10}) \) 11 * q - 4 * q^3 - 3 * q^5 + 11 * q^9	\( 11 q - 4 q^{3} - 3 q^{5} + 11 q^{9} + 13 q^{13} - 7 q^{17} - 8 q^{19} - 11 q^{23} + 6 q^{25} - 25 q^{27} - 3 q^{29} - 12 q^{31} + 2 q^{33} - q^{37} - 21 q^{39} - 12 q^{41} + 9 q^{43} - 19 q^{45} - 17 q^{47} + 19 q^{51} - 5 q^{53} - 21 q^{55} + 11 q^{57} - 33 q^{59} + 15 q^{61} - 9 q^{65} - 5 q^{67} + 4 q^{69} - 9 q^{71} - 5 q^{73} - 44 q^{75} + 11 q^{79} - 13 q^{81} - 51 q^{83} + 33 q^{85} - 4 q^{87} - 26 q^{89} + 6 q^{93} - 19 q^{95} - 21 q^{97} + 15 q^{99}+O(q^{100}) \) 11 * q - 4 * q^3 - 3 * q^5 + 11 * q^9 + 13 * q^13 - 7 * q^17 - 8 * q^19 - 11 * q^23 + 6 * q^25 - 25 * q^27 - 3 * q^29 - 12 * q^31 + 2 * q^33 - q^37 - 21 * q^39 - 12 * q^41 + 9 * q^43 - 19 * q^45 - 17 * q^47 + 19 * q^51 - 5 * q^53 - 21 * q^55 + 11 * q^57 - 33 * q^59 + 15 * q^61 - 9 * q^65 - 5 * q^67 + 4 * q^69 - 9 * q^71 - 5 * q^73 - 44 * q^75 + 11 * q^79 - 13 * q^81 - 51 * q^83 + 33 * q^85 - 4 * q^87 - 26 * q^89 + 6 * q^93 - 19 * q^95 - 21 * q^97 + 15 * q^99

Introduction

L-functions

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