LMFDB - Embedded newform 9016.2.a.bk.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:	$1$
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			1.1
Root			$3.43923$ 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)

$f(q)$	$=$	$q-3.43923 q^{3} -3.03575 q^{5} +8.82832 q^{9} +O(q^{10})$	$q-3.43923 q^{3} -3.03575 q^{5} +8.82832 q^{9} +1.03150 q^{11} +6.52747 q^{13} +10.4407 q^{15} -6.43875 q^{17} +3.24722 q^{19} -1.00000 q^{23} +4.21580 q^{25} -20.0449 q^{27} -1.55227 q^{29} -7.20354 q^{31} -3.54756 q^{33} -1.65014 q^{37} -22.4495 q^{39} +0.156612 q^{41} -1.40374 q^{43} -26.8006 q^{45} +7.75652 q^{47} +22.1444 q^{51} +7.54678 q^{53} -3.13137 q^{55} -11.1679 q^{57} -10.3247 q^{59} -1.32090 q^{61} -19.8158 q^{65} +11.3809 q^{67} +3.43923 q^{69} -2.42629 q^{71} -0.561113 q^{73} -14.4991 q^{75} -15.5668 q^{79} +42.4542 q^{81} -2.26458 q^{83} +19.5465 q^{85} +5.33861 q^{87} +2.91192 q^{89} +24.7746 q^{93} -9.85775 q^{95} +11.3280 q^{97} +9.10639 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−3.43923	−1.98564	−0.992821	−	0.119611i	$-0.961835\pi$
$3$	−3.43923	−1.98564	−0.992821	+	0.119611i	$0.961835\pi$
$4$	0	0
$5$	−3.03575	−1.35763	−0.678815	−	0.734309i	$-0.737506\pi$
$5$	−3.03575	−1.35763	−0.678815	+	0.734309i	$0.737506\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	8.82832	2.94277
$10$	0	0
$11$	1.03150	0.311008	0.155504	−	0.987835i	$-0.450300\pi$
$11$	1.03150	0.311008	0.155504	+	0.987835i	$0.450300\pi$
$12$	0	0
$13$	6.52747	1.81040	0.905198	−	0.424991i	$-0.139723\pi$
$13$	6.52747	1.81040	0.905198	+	0.424991i	$0.139723\pi$
$14$	0	0
$15$	10.4407	2.69577
$16$	0	0
$17$	−6.43875	−1.56163	−0.780813	−	0.624765i	$-0.785195\pi$
$17$	−6.43875	−1.56163	−0.780813	+	0.624765i	$0.785195\pi$
$18$	0	0
$19$	3.24722	0.744962	0.372481	−	0.928040i	$-0.378507\pi$
$19$	3.24722	0.744962	0.372481	+	0.928040i	$0.378507\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0	0
$25$	4.21580	0.843159
$26$	0	0
$27$	−20.0449	−3.85765
$28$	0	0
$29$	−1.55227	−0.288249	−0.144124	−	0.989560i	$-0.546037\pi$
$29$	−1.55227	−0.288249	−0.144124	+	0.989560i	$0.546037\pi$
$30$	0	0
$31$	−7.20354	−1.29379	−0.646897	−	0.762578i	$-0.723934\pi$
$31$	−7.20354	−1.29379	−0.646897	+	0.762578i	$0.723934\pi$
$32$	0	0
$33$	−3.54756	−0.617551
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−1.65014	−0.271281	−0.135640	−	0.990758i	$-0.543309\pi$
$37$	−1.65014	−0.271281	−0.135640	+	0.990758i	$0.543309\pi$
$38$	0	0
$39$	−22.4495	−3.59480
$40$	0	0
$41$	0.156612	0.0244587	0.0122293	−	0.999925i	$-0.496107\pi$
$41$	0.156612	0.0244587	0.0122293	+	0.999925i	$0.496107\pi$
$42$	0	0
$43$	−1.40374	−0.214068	−0.107034	−	0.994255i	$-0.534135\pi$
$43$	−1.40374	−0.214068	−0.107034	+	0.994255i	$0.534135\pi$
$44$	0	0
$45$	−26.8006	−3.99520
$46$	0	0
$47$	7.75652	1.13141	0.565703	−	0.824609i	$-0.308605\pi$
$47$	7.75652	1.13141	0.565703	+	0.824609i	$0.308605\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	22.1444	3.10083
$52$	0	0
$53$	7.54678	1.03663	0.518315	−	0.855190i	$-0.326559\pi$
$53$	7.54678	1.03663	0.518315	+	0.855190i	$0.326559\pi$
$54$	0	0
$55$	−3.13137	−0.422234
$56$	0	0
$57$	−11.1679	−1.47923
$58$	0	0
$59$	−10.3247	−1.34416	−0.672081	−	0.740478i	$-0.734599\pi$
$59$	−10.3247	−1.34416	−0.672081	+	0.740478i	$0.734599\pi$
$60$	0	0
$61$	−1.32090	−0.169123	−0.0845617	−	0.996418i	$-0.526949\pi$
$61$	−1.32090	−0.169123	−0.0845617	+	0.996418i	$0.526949\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	−19.8158	−2.45785
$66$	0	0
$67$	11.3809	1.39039	0.695197	−	0.718819i	$-0.255317\pi$
$67$	11.3809	1.39039	0.695197	+	0.718819i	$0.255317\pi$
$68$	0	0
$69$	3.43923	0.414035
$70$	0	0
$71$	−2.42629	−0.287947	−0.143974	−	0.989582i	$-0.545988\pi$
$71$	−2.42629	−0.287947	−0.143974	+	0.989582i	$0.545988\pi$
$72$	0	0
$73$	−0.561113	−0.0656734	−0.0328367	−	0.999461i	$-0.510454\pi$
$73$	−0.561113	−0.0656734	−0.0328367	+	0.999461i	$0.510454\pi$
$74$	0	0
$75$	−14.4991	−1.67421
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−15.5668	−1.75140	−0.875699	−	0.482857i	$-0.839599\pi$
$79$	−15.5668	−1.75140	−0.875699	+	0.482857i	$0.839599\pi$
$80$	0	0
$81$	42.4542	4.71714
$82$	0	0
$83$	−2.26458	−0.248570	−0.124285	−	0.992247i	$-0.539664\pi$
$83$	−2.26458	−0.248570	−0.124285	+	0.992247i	$0.539664\pi$
$84$	0	0
$85$	19.5465	2.12011
$86$	0	0
$87$	5.33861	0.572359
$88$	0	0
$89$	2.91192	0.308663	0.154332	−	0.988019i	$-0.450678\pi$
$89$	2.91192	0.308663	0.154332	+	0.988019i	$0.450678\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	24.7746	2.56901
$94$	0	0
$95$	−9.85775	−1.01138
$96$	0	0
$97$	11.3280	1.15019	0.575094	−	0.818087i	$-0.304965\pi$
$97$	11.3280	1.15019	0.575094	+	0.818087i	$0.304965\pi$
$98$	0	0
$99$	9.10639	0.915226
$100$	0	0
$101$	2.55234	0.253967	0.126983	−	0.991905i	$-0.459470\pi$
$101$	2.55234	0.253967	0.126983	+	0.991905i	$0.459470\pi$
$102$	0	0
$103$	−4.12412	−0.406361	−0.203181	−	0.979141i	$-0.565128\pi$
$103$	−4.12412	−0.406361	−0.203181	+	0.979141i	$0.565128\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−4.84487	−0.468371	−0.234186	−	0.972192i	$-0.575242\pi$
$107$	−4.84487	−0.468371	−0.234186	+	0.972192i	$0.575242\pi$
$108$	0	0
$109$	7.68879	0.736452	0.368226	−	0.929736i	$-0.379965\pi$
$109$	7.68879	0.736452	0.368226	+	0.929736i	$0.379965\pi$
$110$	0	0
$111$	5.67520	0.538666
$112$	0	0
$113$	0.717498	0.0674965	0.0337482	−	0.999430i	$-0.489256\pi$
$113$	0.717498	0.0674965	0.0337482	+	0.999430i	$0.489256\pi$
$114$	0	0
$115$	3.03575	0.283085
$116$	0	0
$117$	57.6266	5.32758
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−9.93601	−0.903274
$122$	0	0
$123$	−0.538625	−0.0485662
$124$	0	0
$125$	2.38065	0.212932
$126$	0	0
$127$	5.49222	0.487355	0.243678	−	0.969856i	$-0.421646\pi$
$127$	5.49222	0.487355	0.243678	+	0.969856i	$0.421646\pi$
$128$	0	0
$129$	4.82778	0.425062
$130$	0	0
$131$	−12.6216	−1.10276	−0.551378	−	0.834255i	$-0.685898\pi$
$131$	−12.6216	−1.10276	−0.551378	+	0.834255i	$0.685898\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	60.8515	5.23726
$136$	0	0
$137$	−6.62914	−0.566366	−0.283183	−	0.959066i	$-0.591390\pi$
$137$	−6.62914	−0.566366	−0.283183	+	0.959066i	$0.591390\pi$
$138$	0	0
$139$	11.4845	0.974105	0.487053	−	0.873373i	$-0.338072\pi$
$139$	11.4845	0.974105	0.487053	+	0.873373i	$0.338072\pi$
$140$	0	0
$141$	−26.6765	−2.24657
$142$	0	0
$143$	6.73307	0.563048
$144$	0	0
$145$	4.71230	0.391335
$146$	0	0
$147$	0	0
$148$	0	0
$149$	10.7585	0.881368	0.440684	−	0.897662i	$-0.354736\pi$
$149$	10.7585	0.881368	0.440684	+	0.897662i	$0.354736\pi$
$150$	0	0
$151$	−1.42374	−0.115862	−0.0579311	−	0.998321i	$-0.518450\pi$
$151$	−1.42374	−0.115862	−0.0579311	+	0.998321i	$0.518450\pi$
$152$	0	0
$153$	−56.8433	−4.59551
$154$	0	0
$155$	21.8682	1.75649
$156$	0	0
$157$	19.4095	1.54905	0.774525	−	0.632543i	$-0.217989\pi$
$157$	19.4095	1.54905	0.774525	+	0.632543i	$0.217989\pi$
$158$	0	0
$159$	−25.9551	−2.05838
$160$	0	0
$161$	0	0
$162$	0	0
$163$	12.3182	0.964837	0.482418	−	0.875941i	$-0.339759\pi$
$163$	12.3182	0.964837	0.482418	+	0.875941i	$0.339759\pi$
$164$	0	0
$165$	10.7695	0.838405
$166$	0	0
$167$	−1.47237	−0.113935	−0.0569676	−	0.998376i	$-0.518143\pi$
$167$	−1.47237	−0.113935	−0.0569676	+	0.998376i	$0.518143\pi$
$168$	0	0
$169$	29.6079	2.27753
$170$	0	0
$171$	28.6675	2.19226
$172$	0	0
$173$	3.03478	0.230730	0.115365	−	0.993323i	$-0.463196\pi$
$173$	3.03478	0.230730	0.115365	+	0.993323i	$0.463196\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	35.5090	2.66902
$178$	0	0
$179$	23.9739	1.79189	0.895947	−	0.444162i	$-0.146498\pi$
$179$	23.9739	1.79189	0.895947	+	0.444162i	$0.146498\pi$
$180$	0	0
$181$	2.76855	0.205784	0.102892	−	0.994693i	$-0.467190\pi$
$181$	2.76855	0.205784	0.102892	+	0.994693i	$0.467190\pi$
$182$	0	0
$183$	4.54287	0.335818
$184$	0	0
$185$	5.00941	0.368299
$186$	0	0
$187$	−6.64155	−0.485679
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−5.55498	−0.401944	−0.200972	−	0.979597i	$-0.564410\pi$
$191$	−5.55498	−0.401944	−0.200972	+	0.979597i	$0.564410\pi$
$192$	0	0
$193$	−5.48354	−0.394714	−0.197357	−	0.980332i	$-0.563236\pi$
$193$	−5.48354	−0.394714	−0.197357	+	0.980332i	$0.563236\pi$
$194$	0	0
$195$	68.1511	4.88040
$196$	0	0
$197$	−7.16820	−0.510713	−0.255357	−	0.966847i	$-0.582193\pi$
$197$	−7.16820	−0.510713	−0.255357	+	0.966847i	$0.582193\pi$
$198$	0	0
$199$	−15.2222	−1.07907	−0.539535	−	0.841963i	$-0.681400\pi$
$199$	−15.2222	−1.07907	−0.539535	+	0.841963i	$0.681400\pi$
$200$	0	0
$201$	−39.1414	−2.76082
$202$	0	0
$203$	0	0
$204$	0	0
$205$	−0.475435	−0.0332058
$206$	0	0
$207$	−8.82832	−0.613611
$208$	0	0
$209$	3.34949	0.231689
$210$	0	0
$211$	−13.7696	−0.947936	−0.473968	−	0.880542i	$-0.657179\pi$
$211$	−13.7696	−0.947936	−0.473968	+	0.880542i	$0.657179\pi$
$212$	0	0
$213$	8.34456	0.571760
$214$	0	0
$215$	4.26140	0.290625
$216$	0	0
$217$	0	0
$218$	0	0
$219$	1.92980	0.130404
$220$	0	0
$221$	−42.0288	−2.82716
$222$	0	0
$223$	6.84027	0.458059	0.229029	−	0.973420i	$-0.426445\pi$
$223$	6.84027	0.458059	0.229029	+	0.973420i	$0.426445\pi$
$224$	0	0
$225$	37.2184	2.48123
$226$	0	0
$227$	11.5796	0.768566	0.384283	−	0.923215i	$-0.374449\pi$
$227$	11.5796	0.768566	0.384283	+	0.923215i	$0.374449\pi$
$228$	0	0
$229$	−13.2568	−0.876035	−0.438017	−	0.898967i	$-0.644319\pi$
$229$	−13.2568	−0.876035	−0.438017	+	0.898967i	$0.644319\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−8.69239	−0.569458	−0.284729	−	0.958608i	$-0.591904\pi$
$233$	−8.69239	−0.569458	−0.284729	+	0.958608i	$0.591904\pi$
$234$	0	0
$235$	−23.5469	−1.53603
$236$	0	0
$237$	53.5377	3.47765
$238$	0	0
$239$	−13.4576	−0.870502	−0.435251	−	0.900309i	$-0.643340\pi$
$239$	−13.4576	−0.870502	−0.435251	+	0.900309i	$0.643340\pi$
$240$	0	0
$241$	5.30777	0.341904	0.170952	−	0.985279i	$-0.445316\pi$
$241$	5.30777	0.341904	0.170952	+	0.985279i	$0.445316\pi$
$242$	0	0
$243$	−85.8752	−5.50890
$244$	0	0
$245$	0	0
$246$	0	0
$247$	21.1961	1.34868
$248$	0	0
$249$	7.78843	0.493572
$250$	0	0
$251$	15.9884	1.00918	0.504589	−	0.863360i	$-0.331644\pi$
$251$	15.9884	1.00918	0.504589	+	0.863360i	$0.331644\pi$
$252$	0	0
$253$	−1.03150	−0.0648497
$254$	0	0
$255$	−67.2248	−4.20978
$256$	0	0
$257$	20.9250	1.30526	0.652632	−	0.757675i	$-0.273665\pi$
$257$	20.9250	1.30526	0.652632	+	0.757675i	$0.273665\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−13.7039	−0.848251
$262$	0	0
$263$	−26.5346	−1.63620	−0.818098	−	0.575079i	$-0.804971\pi$
$263$	−26.5346	−1.63620	−0.818098	+	0.575079i	$0.804971\pi$
$264$	0	0
$265$	−22.9102	−1.40736
$266$	0	0
$267$	−10.0148	−0.612895
$268$	0	0
$269$	15.8025	0.963494	0.481747	−	0.876310i	$-0.340002\pi$
$269$	15.8025	0.963494	0.481747	+	0.876310i	$0.340002\pi$
$270$	0	0
$271$	−12.7434	−0.774104	−0.387052	−	0.922058i	$-0.626507\pi$
$271$	−12.7434	−0.774104	−0.387052	+	0.922058i	$0.626507\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	4.34858	0.262229
$276$	0	0
$277$	12.0065	0.721404	0.360702	−	0.932681i	$-0.382537\pi$
$277$	12.0065	0.721404	0.360702	+	0.932681i	$0.382537\pi$
$278$	0	0
$279$	−63.5951	−3.80734
$280$	0	0
$281$	−30.4505	−1.81653	−0.908263	−	0.418400i	$-0.862591\pi$
$281$	−30.4505	−1.81653	−0.908263	+	0.418400i	$0.862591\pi$
$282$	0	0
$283$	2.11302	0.125606	0.0628030	−	0.998026i	$-0.479996\pi$
$283$	2.11302	0.125606	0.0628030	+	0.998026i	$0.479996\pi$
$284$	0	0
$285$	33.9031	2.00824
$286$	0	0
$287$	0	0
$288$	0	0
$289$	24.4575	1.43868
$290$	0	0
$291$	−38.9598	−2.28386
$292$	0	0
$293$	−8.52028	−0.497760	−0.248880	−	0.968534i	$-0.580063\pi$
$293$	−8.52028	−0.497760	−0.248880	+	0.968534i	$0.580063\pi$
$294$	0	0
$295$	31.3432	1.82487
$296$	0	0
$297$	−20.6763	−1.19976
$298$	0	0
$299$	−6.52747	−0.377494
$300$	0	0
$301$	0	0
$302$	0	0
$303$	−8.77808	−0.504287
$304$	0	0
$305$	4.00991	0.229607
$306$	0	0
$307$	−17.2994	−0.987327	−0.493664	−	0.869653i	$-0.664343\pi$
$307$	−17.2994	−0.987327	−0.493664	+	0.869653i	$0.664343\pi$
$308$	0	0
$309$	14.1838	0.806888
$310$	0	0
$311$	−6.50405	−0.368811	−0.184406	−	0.982850i	$-0.559036\pi$
$311$	−6.50405	−0.368811	−0.184406	+	0.982850i	$0.559036\pi$
$312$	0	0
$313$	−2.41724	−0.136630	−0.0683152	−	0.997664i	$-0.521762\pi$
$313$	−2.41724	−0.136630	−0.0683152	+	0.997664i	$0.521762\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−32.6257	−1.83244	−0.916221	−	0.400673i	$-0.868776\pi$
$317$	−32.6257	−1.83244	−0.916221	+	0.400673i	$0.868776\pi$
$318$	0	0
$319$	−1.60116	−0.0896478
$320$	0	0
$321$	16.6626	0.930017
$322$	0	0
$323$	−20.9080	−1.16335
$324$	0	0
$325$	27.5185	1.52645
$326$	0	0
$327$	−26.4435	−1.46233
$328$	0	0
$329$	0	0
$330$	0	0
$331$	4.95182	0.272177	0.136088	−	0.990697i	$-0.456547\pi$
$331$	4.95182	0.272177	0.136088	+	0.990697i	$0.456547\pi$
$332$	0	0
$333$	−14.5679	−0.798318
$334$	0	0
$335$	−34.5495	−1.88764
$336$	0	0
$337$	26.7873	1.45920	0.729599	−	0.683876i	$-0.239707\pi$
$337$	26.7873	1.45920	0.729599	+	0.683876i	$0.239707\pi$
$338$	0	0
$339$	−2.46764	−0.134024
$340$	0	0
$341$	−7.43043	−0.402380
$342$	0	0
$343$	0	0
$344$	0	0
$345$	−10.4407	−0.562106
$346$	0	0
$347$	24.1951	1.29886	0.649430	−	0.760421i	$-0.275007\pi$
$347$	24.1951	1.29886	0.649430	+	0.760421i	$0.275007\pi$
$348$	0	0
$349$	12.7374	0.681817	0.340908	−	0.940097i	$-0.389265\pi$
$349$	12.7374	0.681817	0.340908	+	0.940097i	$0.389265\pi$
$350$	0	0
$351$	−130.843	−6.98387
$352$	0	0
$353$	2.60866	0.138845	0.0694224	−	0.997587i	$-0.477884\pi$
$353$	2.60866	0.138845	0.0694224	+	0.997587i	$0.477884\pi$
$354$	0	0
$355$	7.36561	0.390926
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−34.0726	−1.79828	−0.899141	−	0.437660i	$-0.855807\pi$
$359$	−34.0726	−1.79828	−0.899141	+	0.437660i	$0.855807\pi$
$360$	0	0
$361$	−8.45559	−0.445031
$362$	0	0
$363$	34.1723	1.79358
$364$	0	0
$365$	1.70340	0.0891601
$366$	0	0
$367$	13.8724	0.724135	0.362068	−	0.932152i	$-0.382071\pi$
$367$	13.8724	0.724135	0.362068	+	0.932152i	$0.382071\pi$
$368$	0	0
$369$	1.38262	0.0719763
$370$	0	0
$371$	0	0
$372$	0	0
$373$	25.0702	1.29809	0.649043	−	0.760752i	$-0.275170\pi$
$373$	25.0702	1.29809	0.649043	+	0.760752i	$0.275170\pi$
$374$	0	0
$375$	−8.18761	−0.422807
$376$	0	0
$377$	−10.1324	−0.521845
$378$	0	0
$379$	−3.84775	−0.197646	−0.0988228	−	0.995105i	$-0.531508\pi$
$379$	−3.84775	−0.197646	−0.0988228	+	0.995105i	$0.531508\pi$
$380$	0	0
$381$	−18.8890	−0.967713
$382$	0	0
$383$	−19.0026	−0.970986	−0.485493	−	0.874240i	$-0.661360\pi$
$383$	−19.0026	−0.970986	−0.485493	+	0.874240i	$0.661360\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−12.3926	−0.629953
$388$	0	0
$389$	−18.4835	−0.937152	−0.468576	−	0.883423i	$-0.655233\pi$
$389$	−18.4835	−0.937152	−0.468576	+	0.883423i	$0.655233\pi$
$390$	0	0
$391$	6.43875	0.325622
$392$	0	0
$393$	43.4087	2.18968
$394$	0	0
$395$	47.2569	2.37775
$396$	0	0
$397$	24.2859	1.21888	0.609438	−	0.792834i	$-0.291395\pi$
$397$	24.2859	1.21888	0.609438	+	0.792834i	$0.291395\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	11.7584	0.587189	0.293594	−	0.955930i	$-0.405149\pi$
$401$	11.7584	0.587189	0.293594	+	0.955930i	$0.405149\pi$
$402$	0	0
$403$	−47.0209	−2.34228
$404$	0	0
$405$	−128.881	−6.40413
$406$	0	0
$407$	−1.70211	−0.0843705
$408$	0	0
$409$	−26.7230	−1.32137	−0.660683	−	0.750665i	$-0.729733\pi$
$409$	−26.7230	−1.32137	−0.660683	+	0.750665i	$0.729733\pi$
$410$	0	0
$411$	22.7992	1.12460
$412$	0	0
$413$	0	0
$414$	0	0
$415$	6.87472	0.337467
$416$	0	0
$417$	−39.4980	−1.93422
$418$	0	0
$419$	19.4590	0.950636	0.475318	−	0.879814i	$-0.342333\pi$
$419$	19.4590	0.950636	0.475318	+	0.879814i	$0.342333\pi$
$420$	0	0
$421$	15.2400	0.742754	0.371377	−	0.928482i	$-0.378886\pi$
$421$	15.2400	0.742754	0.371377	+	0.928482i	$0.378886\pi$
$422$	0	0
$423$	68.4771	3.32947
$424$	0	0
$425$	−27.1445	−1.31670
$426$	0	0
$427$	0	0
$428$	0	0
$429$	−23.1566	−1.11801
$430$	0	0
$431$	2.61438	0.125930	0.0629652	−	0.998016i	$-0.479944\pi$
$431$	2.61438	0.125930	0.0629652	+	0.998016i	$0.479944\pi$
$432$	0	0
$433$	9.41184	0.452304	0.226152	−	0.974092i	$-0.427385\pi$
$433$	9.41184	0.452304	0.226152	+	0.974092i	$0.427385\pi$
$434$	0	0
$435$	−16.2067	−0.777052
$436$	0	0
$437$	−3.24722	−0.155335
$438$	0	0
$439$	25.5107	1.21756	0.608779	−	0.793340i	$-0.291660\pi$
$439$	25.5107	1.21756	0.608779	+	0.793340i	$0.291660\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−24.1864	−1.14913	−0.574566	−	0.818458i	$-0.694829\pi$
$443$	−24.1864	−1.14913	−0.574566	+	0.818458i	$0.694829\pi$
$444$	0	0
$445$	−8.83988	−0.419051
$446$	0	0
$447$	−37.0009	−1.75008
$448$	0	0
$449$	−32.4384	−1.53086	−0.765431	−	0.643518i	$-0.777474\pi$
$449$	−32.4384	−1.53086	−0.765431	+	0.643518i	$0.777474\pi$
$450$	0	0
$451$	0.161545	0.00760685
$452$	0	0
$453$	4.89657	0.230061
$454$	0	0
$455$	0	0
$456$	0	0
$457$	21.9051	1.02468	0.512339	−	0.858783i	$-0.328779\pi$
$457$	21.9051	1.02468	0.512339	+	0.858783i	$0.328779\pi$
$458$	0	0
$459$	129.064	6.02421
$460$	0	0
$461$	−12.1889	−0.567694	−0.283847	−	0.958870i	$-0.591611\pi$
$461$	−12.1889	−0.567694	−0.283847	+	0.958870i	$0.591611\pi$
$462$	0	0
$463$	38.7588	1.80127	0.900637	−	0.434571i	$-0.143100\pi$
$463$	38.7588	1.80127	0.900637	+	0.434571i	$0.143100\pi$
$464$	0	0
$465$	−75.2097	−3.48777
$466$	0	0
$467$	−1.62696	−0.0752867	−0.0376433	−	0.999291i	$-0.511985\pi$
$467$	−1.62696	−0.0752867	−0.0376433	+	0.999291i	$0.511985\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	−66.7539	−3.07586
$472$	0	0
$473$	−1.44795	−0.0665769
$474$	0	0
$475$	13.6896	0.628122
$476$	0	0
$477$	66.6254	3.05057
$478$	0	0
$479$	22.9513	1.04867	0.524335	−	0.851512i	$-0.324314\pi$
$479$	22.9513	1.04867	0.524335	+	0.851512i	$0.324314\pi$
$480$	0	0
$481$	−10.7712	−0.491125
$482$	0	0
$483$	0	0
$484$	0	0
$485$	−34.3891	−1.56153
$486$	0	0
$487$	−30.8768	−1.39916	−0.699580	−	0.714554i	$-0.746630\pi$
$487$	−30.8768	−1.39916	−0.699580	+	0.714554i	$0.746630\pi$
$488$	0	0
$489$	−42.3652	−1.91582
$490$	0	0
$491$	−11.9455	−0.539093	−0.269547	−	0.962987i	$-0.586874\pi$
$491$	−11.9455	−0.539093	−0.269547	+	0.962987i	$0.586874\pi$
$492$	0	0
$493$	9.99467	0.450137
$494$	0	0
$495$	−27.6447	−1.24254
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−25.6148	−1.14667	−0.573337	−	0.819319i	$-0.694352\pi$
$499$	−25.6148	−1.14667	−0.573337	+	0.819319i	$0.694352\pi$
$500$	0	0
$501$	5.06382	0.226235
$502$	0	0
$503$	−12.5141	−0.557977	−0.278988	−	0.960294i	$-0.589999\pi$
$503$	−12.5141	−0.557977	−0.278988	+	0.960294i	$0.589999\pi$
$504$	0	0
$505$	−7.74826	−0.344793
$506$	0	0
$507$	−101.828	−4.52236
$508$	0	0
$509$	−25.8495	−1.14576	−0.572879	−	0.819640i	$-0.694174\pi$
$509$	−25.8495	−1.14576	−0.572879	+	0.819640i	$0.694174\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−65.0903	−2.87380
$514$	0	0
$515$	12.5198	0.551688
$516$	0	0
$517$	8.00083	0.351876
$518$	0	0
$519$	−10.4373	−0.458147
$520$	0	0
$521$	−6.78988	−0.297470	−0.148735	−	0.988877i	$-0.547520\pi$
$521$	−6.78988	−0.297470	−0.148735	+	0.988877i	$0.547520\pi$
$522$	0	0
$523$	−5.59548	−0.244673	−0.122337	−	0.992489i	$-0.539039\pi$
$523$	−5.59548	−0.244673	−0.122337	+	0.992489i	$0.539039\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	46.3818	2.02042
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	−91.1497	−3.95556
$532$	0	0
$533$	1.02228	0.0442799
$534$	0	0
$535$	14.7078	0.635875
$536$	0	0
$537$	−82.4518	−3.55806
$538$	0	0
$539$	0	0
$540$	0	0
$541$	16.7304	0.719294	0.359647	−	0.933088i	$-0.382897\pi$
$541$	16.7304	0.719294	0.359647	+	0.933088i	$0.382897\pi$
$542$	0	0
$543$	−9.52167	−0.408614
$544$	0	0
$545$	−23.3413	−0.999829
$546$	0	0
$547$	−26.2217	−1.12116	−0.560580	−	0.828100i	$-0.689422\pi$
$547$	−26.2217	−1.12116	−0.560580	+	0.828100i	$0.689422\pi$
$548$	0	0
$549$	−11.6613	−0.497692
$550$	0	0
$551$	−5.04055	−0.214735
$552$	0	0
$553$	0	0
$554$	0	0
$555$	−17.2285	−0.731309
$556$	0	0
$557$	1.34474	0.0569783	0.0284891	−	0.999594i	$-0.490930\pi$
$557$	1.34474	0.0569783	0.0284891	+	0.999594i	$0.490930\pi$
$558$	0	0
$559$	−9.16286	−0.387548
$560$	0	0
$561$	22.8418	0.964383
$562$	0	0
$563$	−11.7752	−0.496265	−0.248132	−	0.968726i	$-0.579817\pi$
$563$	−11.7752	−0.496265	−0.248132	+	0.968726i	$0.579817\pi$
$564$	0	0
$565$	−2.17815	−0.0916353
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−8.00369	−0.335532	−0.167766	−	0.985827i	$-0.553655\pi$
$569$	−8.00369	−0.335532	−0.167766	+	0.985827i	$0.553655\pi$
$570$	0	0
$571$	−19.5529	−0.818264	−0.409132	−	0.912475i	$-0.634168\pi$
$571$	−19.5529	−0.818264	−0.409132	+	0.912475i	$0.634168\pi$
$572$	0	0
$573$	19.1049	0.798117
$574$	0	0
$575$	−4.21580	−0.175811
$576$	0	0
$577$	29.2312	1.21691	0.608454	−	0.793589i	$-0.291790\pi$
$577$	29.2312	1.21691	0.608454	+	0.793589i	$0.291790\pi$
$578$	0	0
$579$	18.8592	0.783761
$580$	0	0
$581$	0	0
$582$	0	0
$583$	7.78449	0.322400
$584$	0	0
$585$	−174.940	−7.23289
$586$	0	0
$587$	12.1528	0.501601	0.250800	−	0.968039i	$-0.419306\pi$
$587$	12.1528	0.501601	0.250800	+	0.968039i	$0.419306\pi$
$588$	0	0
$589$	−23.3914	−0.963828
$590$	0	0
$591$	24.6531	1.01409
$592$	0	0
$593$	26.8847	1.10402	0.552011	−	0.833837i	$-0.313860\pi$
$593$	26.8847	1.10402	0.552011	+	0.833837i	$0.313860\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	52.3526	2.14265
$598$	0	0
$599$	38.8743	1.58836	0.794180	−	0.607683i	$-0.207901\pi$
$599$	38.8743	1.58836	0.794180	+	0.607683i	$0.207901\pi$
$600$	0	0
$601$	36.5539	1.49106	0.745532	−	0.666470i	$-0.232195\pi$
$601$	36.5539	1.49106	0.745532	+	0.666470i	$0.232195\pi$
$602$	0	0
$603$	100.474	4.09161
$604$	0	0
$605$	30.1633	1.22631
$606$	0	0
$607$	22.5945	0.917083	0.458542	−	0.888673i	$-0.348372\pi$
$607$	22.5945	0.917083	0.458542	+	0.888673i	$0.348372\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	50.6305	2.04829
$612$	0	0
$613$	31.7112	1.28080	0.640402	−	0.768040i	$-0.278768\pi$
$613$	31.7112	1.28080	0.640402	+	0.768040i	$0.278768\pi$
$614$	0	0
$615$	1.63513	0.0659349
$616$	0	0
$617$	−34.4966	−1.38878	−0.694390	−	0.719599i	$-0.744326\pi$
$617$	−34.4966	−1.38878	−0.694390	+	0.719599i	$0.744326\pi$
$618$	0	0
$619$	−28.6438	−1.15129	−0.575646	−	0.817699i	$-0.695249\pi$
$619$	−28.6438	−1.15129	−0.575646	+	0.817699i	$0.695249\pi$
$620$	0	0
$621$	20.0449	0.804376
$622$	0	0
$623$	0	0
$624$	0	0
$625$	−28.3060	−1.13224
$626$	0	0
$627$	−11.5197	−0.460052
$628$	0	0
$629$	10.6248	0.423639
$630$	0	0
$631$	28.2682	1.12534	0.562671	−	0.826681i	$-0.309774\pi$
$631$	28.2682	1.12534	0.562671	+	0.826681i	$0.309774\pi$
$632$	0	0
$633$	47.3567	1.88226
$634$	0	0
$635$	−16.6730	−0.661648
$636$	0	0
$637$	0	0
$638$	0	0
$639$	−21.4200	−0.847363
$640$	0	0
$641$	14.2980	0.564737	0.282368	−	0.959306i	$-0.408880\pi$
$641$	14.2980	0.564737	0.282368	+	0.959306i	$0.408880\pi$
$642$	0	0
$643$	4.36419	0.172107	0.0860535	−	0.996291i	$-0.472574\pi$
$643$	4.36419	0.172107	0.0860535	+	0.996291i	$0.472574\pi$
$644$	0	0
$645$	−14.6559	−0.577077
$646$	0	0
$647$	−20.4246	−0.802974	−0.401487	−	0.915865i	$-0.631507\pi$
$647$	−20.4246	−0.802974	−0.401487	+	0.915865i	$0.631507\pi$
$648$	0	0
$649$	−10.6499	−0.418045
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−29.2507	−1.14467	−0.572335	−	0.820020i	$-0.693962\pi$
$653$	−29.2507	−1.14467	−0.572335	+	0.820020i	$0.693962\pi$
$654$	0	0
$655$	38.3161	1.49714
$656$	0	0
$657$	−4.95369	−0.193262
$658$	0	0
$659$	−47.0016	−1.83092	−0.915461	−	0.402406i	$-0.868174\pi$
$659$	−47.0016	−1.83092	−0.915461	+	0.402406i	$0.868174\pi$
$660$	0	0
$661$	−33.6299	−1.30805	−0.654025	−	0.756473i	$-0.726921\pi$
$661$	−33.6299	−1.30805	−0.654025	+	0.756473i	$0.726921\pi$
$662$	0	0
$663$	144.547	5.61373
$664$	0	0
$665$	0	0
$666$	0	0
$667$	1.55227	0.0601041
$668$	0	0
$669$	−23.5253	−0.909540
$670$	0	0
$671$	−1.36250	−0.0525987
$672$	0	0
$673$	22.3988	0.863410	0.431705	−	0.902015i	$-0.357912\pi$
$673$	22.3988	0.863410	0.431705	+	0.902015i	$0.357912\pi$
$674$	0	0
$675$	−84.5054	−3.25261
$676$	0	0
$677$	24.7092	0.949651	0.474825	−	0.880080i	$-0.342511\pi$
$677$	24.7092	0.949651	0.474825	+	0.880080i	$0.342511\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	−39.8250	−1.52610
$682$	0	0
$683$	−17.7486	−0.679129	−0.339565	−	0.940583i	$-0.610280\pi$
$683$	−17.7486	−0.679129	−0.339565	+	0.940583i	$0.610280\pi$
$684$	0	0
$685$	20.1244	0.768915
$686$	0	0
$687$	45.5932	1.73949
$688$	0	0
$689$	49.2614	1.87671
$690$	0	0
$691$	18.4937	0.703533	0.351767	−	0.936088i	$-0.385581\pi$
$691$	18.4937	0.703533	0.351767	+	0.936088i	$0.385581\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	−34.8642	−1.32247
$696$	0	0
$697$	−1.00839	−0.0381953
$698$	0	0
$699$	29.8952	1.13074
$700$	0	0
$701$	−49.2378	−1.85968	−0.929842	−	0.367959i	$-0.880057\pi$
$701$	−49.2378	−1.85968	−0.929842	+	0.367959i	$0.880057\pi$
$702$	0	0
$703$	−5.35835	−0.202094
$704$	0	0
$705$	80.9832	3.05000
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−28.3647	−1.06526	−0.532628	−	0.846349i	$-0.678796\pi$
$709$	−28.3647	−1.06526	−0.532628	+	0.846349i	$0.678796\pi$
$710$	0	0
$711$	−137.428	−5.15397
$712$	0	0
$713$	7.20354	0.269775
$714$	0	0
$715$	−20.4399	−0.764410
$716$	0	0
$717$	46.2839	1.72850
$718$	0	0
$719$	−14.2178	−0.530236	−0.265118	−	0.964216i	$-0.585411\pi$
$719$	−14.2178	−0.530236	−0.265118	+	0.964216i	$0.585411\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	−18.2547	−0.678898
$724$	0	0
$725$	−6.54405	−0.243040
$726$	0	0
$727$	−53.3242	−1.97769	−0.988843	−	0.148961i	$-0.952407\pi$
$727$	−53.3242	−1.97769	−0.988843	+	0.148961i	$0.952407\pi$
$728$	0	0
$729$	167.982	6.22156
$730$	0	0
$731$	9.03832	0.334294
$732$	0	0
$733$	13.9599	0.515622	0.257811	−	0.966195i	$-0.416999\pi$
$733$	13.9599	0.515622	0.257811	+	0.966195i	$0.416999\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	11.7393	0.432424
$738$	0	0
$739$	4.00237	0.147230	0.0736148	−	0.997287i	$-0.476546\pi$
$739$	4.00237	0.147230	0.0736148	+	0.997287i	$0.476546\pi$
$740$	0	0
$741$	−72.8984	−2.67799
$742$	0	0
$743$	23.6893	0.869077	0.434538	−	0.900653i	$-0.356912\pi$
$743$	23.6893	0.869077	0.434538	+	0.900653i	$0.356912\pi$
$744$	0	0
$745$	−32.6600	−1.19657
$746$	0	0
$747$	−19.9925	−0.731486
$748$	0	0
$749$	0	0
$750$	0	0
$751$	3.78680	0.138182	0.0690912	−	0.997610i	$-0.477990\pi$
$751$	3.78680	0.138182	0.0690912	+	0.997610i	$0.477990\pi$
$752$	0	0
$753$	−54.9877	−2.00386
$754$	0	0
$755$	4.32212	0.157298
$756$	0	0
$757$	−20.6335	−0.749937	−0.374968	−	0.927038i	$-0.622346\pi$
$757$	−20.6335	−0.749937	−0.374968	+	0.927038i	$0.622346\pi$
$758$	0	0
$759$	3.54756	0.128768
$760$	0	0
$761$	−29.9661	−1.08627	−0.543134	−	0.839646i	$-0.682763\pi$
$761$	−29.9661	−1.08627	−0.543134	+	0.839646i	$0.682763\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	172.562	6.23900
$766$	0	0
$767$	−67.3942	−2.43346
$768$	0	0
$769$	−39.4536	−1.42273	−0.711366	−	0.702822i	$-0.751923\pi$
$769$	−39.4536	−1.42273	−0.711366	+	0.702822i	$0.751923\pi$
$770$	0	0
$771$	−71.9659	−2.59179
$772$	0	0
$773$	−20.8461	−0.749783	−0.374892	−	0.927069i	$-0.622320\pi$
$773$	−20.8461	−0.749783	−0.374892	+	0.927069i	$0.622320\pi$
$774$	0	0
$775$	−30.3686	−1.09087
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0.508553	0.0182208
$780$	0	0
$781$	−2.50271	−0.0895539
$782$	0	0
$783$	31.1151	1.11196
$784$	0	0
$785$	−58.9226	−2.10304
$786$	0	0
$787$	16.0884	0.573488	0.286744	−	0.958007i	$-0.407427\pi$
$787$	16.0884	0.573488	0.286744	+	0.958007i	$0.407427\pi$
$788$	0	0
$789$	91.2588	3.24890
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−8.62211	−0.306180
$794$	0	0
$795$	78.7934	2.79451
$796$	0	0
$797$	27.6600	0.979769	0.489884	−	0.871787i	$-0.337039\pi$
$797$	27.6600	0.979769	0.489884	+	0.871787i	$0.337039\pi$
$798$	0	0
$799$	−49.9423	−1.76683
$800$	0	0
$801$	25.7074	0.908326
$802$	0	0
$803$	−0.578787	−0.0204249
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−54.3484	−1.91315
$808$	0	0
$809$	−15.5696	−0.547397	−0.273698	−	0.961816i	$-0.588247\pi$
$809$	−15.5696	−0.547397	−0.273698	+	0.961816i	$0.588247\pi$
$810$	0	0
$811$	−17.3349	−0.608712	−0.304356	−	0.952558i	$-0.598441\pi$
$811$	−17.3349	−0.608712	−0.304356	+	0.952558i	$0.598441\pi$
$812$	0	0
$813$	43.8274	1.53709
$814$	0	0
$815$	−37.3950	−1.30989
$816$	0	0
$817$	−4.55824	−0.159473
$818$	0	0
$819$	0	0
$820$	0	0
$821$	46.0957	1.60875	0.804375	−	0.594122i	$-0.202500\pi$
$821$	46.0957	1.60875	0.804375	+	0.594122i	$0.202500\pi$
$822$	0	0
$823$	1.54557	0.0538753	0.0269377	−	0.999637i	$-0.491424\pi$
$823$	1.54557	0.0538753	0.0269377	+	0.999637i	$0.491424\pi$
$824$	0	0
$825$	−14.9558	−0.520694
$826$	0	0
$827$	9.10286	0.316537	0.158269	−	0.987396i	$-0.449409\pi$
$827$	9.10286	0.316537	0.158269	+	0.987396i	$0.449409\pi$
$828$	0	0
$829$	41.3578	1.43642	0.718209	−	0.695828i	$-0.244962\pi$
$829$	41.3578	1.43642	0.718209	+	0.695828i	$0.244962\pi$
$830$	0	0
$831$	−41.2933	−1.43245
$832$	0	0
$833$	0	0
$834$	0	0
$835$	4.46975	0.154682
$836$	0	0
$837$	144.394	4.99100
$838$	0	0
$839$	−23.5488	−0.812994	−0.406497	−	0.913652i	$-0.633250\pi$
$839$	−23.5488	−0.812994	−0.406497	+	0.913652i	$0.633250\pi$
$840$	0	0
$841$	−26.5905	−0.916913
$842$	0	0
$843$	104.726	3.60697
$844$	0	0
$845$	−89.8823	−3.09205
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−7.26717	−0.249409
$850$	0	0
$851$	1.65014	0.0565659
$852$	0	0
$853$	21.3195	0.729965	0.364983	−	0.931014i	$-0.381075\pi$
$853$	21.3195	0.729965	0.364983	+	0.931014i	$0.381075\pi$
$854$	0	0
$855$	−87.0273	−2.97627
$856$	0	0
$857$	−34.5708	−1.18091	−0.590457	−	0.807069i	$-0.701053\pi$
$857$	−34.5708	−1.18091	−0.590457	+	0.807069i	$0.701053\pi$
$858$	0	0
$859$	−39.3467	−1.34249	−0.671246	−	0.741235i	$-0.734240\pi$
$859$	−39.3467	−1.34249	−0.671246	+	0.741235i	$0.734240\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	44.3941	1.51119	0.755596	−	0.655038i	$-0.227348\pi$
$863$	44.3941	1.51119	0.755596	+	0.655038i	$0.227348\pi$
$864$	0	0
$865$	−9.21284	−0.313246
$866$	0	0
$867$	−84.1150	−2.85670
$868$	0	0
$869$	−16.0571	−0.544699
$870$	0	0
$871$	74.2883	2.51716
$872$	0	0
$873$	100.008	3.38474
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−42.8446	−1.44676	−0.723380	−	0.690450i	$-0.757413\pi$
$877$	−42.8446	−1.44676	−0.723380	+	0.690450i	$0.757413\pi$
$878$	0	0
$879$	29.3032	0.988373
$880$	0	0
$881$	−37.5740	−1.26590	−0.632950	−	0.774192i	$-0.718156\pi$
$881$	−37.5740	−1.26590	−0.632950	+	0.774192i	$0.718156\pi$
$882$	0	0
$883$	5.71163	0.192212	0.0961059	−	0.995371i	$-0.469361\pi$
$883$	5.71163	0.192212	0.0961059	+	0.995371i	$0.469361\pi$
$884$	0	0
$885$	−107.797	−3.62354
$886$	0	0
$887$	−2.78979	−0.0936719	−0.0468359	−	0.998903i	$-0.514914\pi$
$887$	−2.78979	−0.0936719	−0.0468359	+	0.998903i	$0.514914\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	43.7914	1.46707
$892$	0	0
$893$	25.1871	0.842854
$894$	0	0
$895$	−72.7788	−2.43273
$896$	0	0
$897$	22.4495	0.749567
$898$	0	0
$899$	11.1818	0.372935
$900$	0	0
$901$	−48.5918	−1.61883
$902$	0	0
$903$	0	0
$904$	0	0
$905$	−8.40462	−0.279379
$906$	0	0
$907$	−29.2201	−0.970238	−0.485119	−	0.874448i	$-0.661224\pi$
$907$	−29.2201	−0.970238	−0.485119	+	0.874448i	$0.661224\pi$
$908$	0	0
$909$	22.5328	0.747367
$910$	0	0
$911$	31.3098	1.03734	0.518669	−	0.854975i	$-0.326428\pi$
$911$	31.3098	1.03734	0.518669	+	0.854975i	$0.326428\pi$
$912$	0	0
$913$	−2.33591	−0.0773074
$914$	0	0
$915$	−13.7910	−0.455917
$916$	0	0
$917$	0	0
$918$	0	0
$919$	1.25540	0.0414119	0.0207059	−	0.999786i	$-0.493409\pi$
$919$	1.25540	0.0414119	0.0207059	+	0.999786i	$0.493409\pi$
$920$	0	0
$921$	59.4965	1.96048
$922$	0	0
$923$	−15.8375	−0.521298
$924$	0	0
$925$	−6.95664	−0.228733
$926$	0	0
$927$	−36.4090	−1.19583
$928$	0	0
$929$	32.1615	1.05519	0.527593	−	0.849497i	$-0.323095\pi$
$929$	32.1615	1.05519	0.527593	+	0.849497i	$0.323095\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	22.3690	0.732327
$934$	0	0
$935$	20.1621	0.659372
$936$	0	0
$937$	−37.2225	−1.21601	−0.608004	−	0.793934i	$-0.708029\pi$
$937$	−37.2225	−1.21601	−0.608004	+	0.793934i	$0.708029\pi$
$938$	0	0
$939$	8.31345	0.271299
$940$	0	0
$941$	−5.18668	−0.169081	−0.0845404	−	0.996420i	$-0.526942\pi$
$941$	−5.18668	−0.169081	−0.0845404	+	0.996420i	$0.526942\pi$
$942$	0	0
$943$	−0.156612	−0.00509999
$944$	0	0
$945$	0	0
$946$	0	0
$947$	42.4348	1.37894	0.689472	−	0.724312i	$-0.257843\pi$
$947$	42.4348	1.37894	0.689472	+	0.724312i	$0.257843\pi$
$948$	0	0
$949$	−3.66265	−0.118895
$950$	0	0
$951$	112.207	3.63857
$952$	0	0
$953$	−9.80129	−0.317495	−0.158748	−	0.987319i	$-0.550746\pi$
$953$	−9.80129	−0.317495	−0.158748	+	0.987319i	$0.550746\pi$
$954$	0	0
$955$	16.8635	0.545691
$956$	0	0
$957$	5.50676	0.178008
$958$	0	0
$959$	0	0
$960$	0	0
$961$	20.8910	0.673902
$962$	0	0
$963$	−42.7720	−1.37831
$964$	0	0
$965$	16.6467	0.535876
$966$	0	0
$967$	−4.14507	−0.133297	−0.0666483	−	0.997777i	$-0.521231\pi$
$967$	−4.14507	−0.133297	−0.0666483	+	0.997777i	$0.521231\pi$
$968$	0	0
$969$	71.9075	2.31000
$970$	0	0
$971$	−10.5711	−0.339243	−0.169621	−	0.985509i	$-0.554255\pi$
$971$	−10.5711	−0.339243	−0.169621	+	0.985509i	$0.554255\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	−94.6425	−3.03099
$976$	0	0
$977$	−2.02363	−0.0647418	−0.0323709	−	0.999476i	$-0.510306\pi$
$977$	−2.02363	−0.0647418	−0.0323709	+	0.999476i	$0.510306\pi$
$978$	0	0
$979$	3.00364	0.0959968
$980$	0	0
$981$	67.8790	2.16721
$982$	0	0
$983$	−12.0404	−0.384028	−0.192014	−	0.981392i	$-0.561502\pi$
$983$	−12.0404	−0.384028	−0.192014	+	0.981392i	$0.561502\pi$
$984$	0	0
$985$	21.7609	0.693359
$986$	0	0
$987$	0	0
$988$	0	0
$989$	1.40374	0.0446363
$990$	0	0
$991$	−8.65751	−0.275015	−0.137507	−	0.990501i	$-0.543909\pi$
$991$	−8.65751	−0.275015	−0.137507	+	0.990501i	$0.543909\pi$
$992$	0	0
$993$	−17.0305	−0.540446
$994$	0	0
$995$	46.2107	1.46498
$996$	0	0
$997$	14.1331	0.447600	0.223800	−	0.974635i	$-0.428154\pi$
$997$	14.1331	0.447600	0.223800	+	0.974635i	$0.428154\pi$
$998$	0	0
$999$	33.0769	1.04651

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1288.2.q.d.737.11	✓	22	7.4	even	3
1288.2.q.d.921.11	yes	22	7.2	even	3
9016.2.a.bk.1.1		11	1.1	even	1	trivial
9016.2.a.br.1.11		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)

\(f(q)\)	\(=\)	\(q-3.43923 q^{3} -3.03575 q^{5} +8.82832 q^{9} +O(q^{10})\)	\(q-3.43923 q^{3} -3.03575 q^{5} +8.82832 q^{9} +1.03150 q^{11} +6.52747 q^{13} +10.4407 q^{15} -6.43875 q^{17} +3.24722 q^{19} -1.00000 q^{23} +4.21580 q^{25} -20.0449 q^{27} -1.55227 q^{29} -7.20354 q^{31} -3.54756 q^{33} -1.65014 q^{37} -22.4495 q^{39} +0.156612 q^{41} -1.40374 q^{43} -26.8006 q^{45} +7.75652 q^{47} +22.1444 q^{51} +7.54678 q^{53} -3.13137 q^{55} -11.1679 q^{57} -10.3247 q^{59} -1.32090 q^{61} -19.8158 q^{65} +11.3809 q^{67} +3.43923 q^{69} -2.42629 q^{71} -0.561113 q^{73} -14.4991 q^{75} -15.5668 q^{79} +42.4542 q^{81} -2.26458 q^{83} +19.5465 q^{85} +5.33861 q^{87} +2.91192 q^{89} +24.7746 q^{93} -9.85775 q^{95} +11.3280 q^{97} +9.10639 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 4 q^{3} - 3 q^{5} + 11 q^{9}+O(q^{10}) \) 11 * q - 4 * q^3 - 3 * q^5 + 11 * q^9	\( 11 q - 4 q^{3} - 3 q^{5} + 11 q^{9} + 13 q^{13} - 7 q^{17} - 8 q^{19} - 11 q^{23} + 6 q^{25} - 25 q^{27} - 3 q^{29} - 12 q^{31} + 2 q^{33} - q^{37} - 21 q^{39} - 12 q^{41} + 9 q^{43} - 19 q^{45} - 17 q^{47} + 19 q^{51} - 5 q^{53} - 21 q^{55} + 11 q^{57} - 33 q^{59} + 15 q^{61} - 9 q^{65} - 5 q^{67} + 4 q^{69} - 9 q^{71} - 5 q^{73} - 44 q^{75} + 11 q^{79} - 13 q^{81} - 51 q^{83} + 33 q^{85} - 4 q^{87} - 26 q^{89} + 6 q^{93} - 19 q^{95} - 21 q^{97} + 15 q^{99}+O(q^{100}) \) 11 * q - 4 * q^3 - 3 * q^5 + 11 * q^9 + 13 * q^13 - 7 * q^17 - 8 * q^19 - 11 * q^23 + 6 * q^25 - 25 * q^27 - 3 * q^29 - 12 * q^31 + 2 * q^33 - q^37 - 21 * q^39 - 12 * q^41 + 9 * q^43 - 19 * q^45 - 17 * q^47 + 19 * q^51 - 5 * q^53 - 21 * q^55 + 11 * q^57 - 33 * q^59 + 15 * q^61 - 9 * q^65 - 5 * q^67 + 4 * q^69 - 9 * q^71 - 5 * q^73 - 44 * q^75 + 11 * q^79 - 13 * q^81 - 51 * q^83 + 33 * q^85 - 4 * q^87 - 26 * q^89 + 6 * q^93 - 19 * q^95 - 21 * q^97 + 15 * q^99

Introduction

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