LMFDB - Embedded newform 3267.2.a.bi.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3267,2,Mod(1,3267)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3267, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("3267.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3267 = 3^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3267.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:	$26.0871263404$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	8.8.234144800000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 13x^{6} + 51x^{4} - 55x^{2} + 5 $ x^8 - 13x^6 + 51x^4 - 55*x^2 + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 297)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$2.46033$ of defining polynomial
Character	$\chi$	$=$	3267.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.46033 q^{2} +4.05323 q^{4} -0.989783 q^{5} -4.32219 q^{7} +5.05161 q^{8} -2.43519 q^{10} -3.61803 q^{13} -10.6340 q^{14} +4.32219 q^{16} +2.64130 q^{17} +3.82722 q^{19} -4.01181 q^{20} -3.45011 q^{23} -4.02033 q^{25} -8.90156 q^{26} -17.5188 q^{28} -10.4221 q^{29} -1.68787 q^{31} +0.530785 q^{32} +6.49848 q^{34} +4.27803 q^{35} +3.23607 q^{37} +9.41623 q^{38} -5.00000 q^{40} -11.9075 q^{41} +2.12307 q^{43} -8.48842 q^{46} -4.29980 q^{47} +11.6813 q^{49} -9.89134 q^{50} -14.6647 q^{52} +9.48236 q^{53} -21.8340 q^{56} -25.6419 q^{58} -6.47214 q^{59} +4.81061 q^{61} -4.15273 q^{62} -7.33847 q^{64} +3.58107 q^{65} +0.854102 q^{67} +10.7058 q^{68} +10.5254 q^{70} +3.77816 q^{71} -11.4083 q^{73} +7.96180 q^{74} +15.5126 q^{76} -6.14340 q^{79} -4.27803 q^{80} -29.2963 q^{82} +3.36003 q^{83} -2.61432 q^{85} +5.22344 q^{86} +13.2605 q^{89} +15.6378 q^{91} -13.9841 q^{92} -10.5789 q^{94} -3.78812 q^{95} -0.371367 q^{97} +28.7399 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 10 q^{4} - 10 q^{7} - 6 q^{10} - 20 q^{13} + 10 q^{16} - 14 q^{19} + 6 q^{25} - 26 q^{28} + 2 q^{31} - 24 q^{34} + 8 q^{37} - 40 q^{40} - 12 q^{43} - 32 q^{46} + 22 q^{49} - 30 q^{52} - 62 q^{58}+ \cdots + 6 q^{97}+O(q^{100}) $ 8 * q + 10 * q^4 - 10 * q^7 - 6 * q^10 - 20 * q^13 + 10 * q^16 - 14 * q^19 + 6 * q^25 - 26 * q^28 + 2 * q^31 - 24 * q^34 + 8 * q^37 - 40 * q^40 - 12 * q^43 - 32 * q^46 + 22 * q^49 - 30 * q^52 - 62 * q^58 - 22 * q^61 - 34 * q^64 - 20 * q^67 + 26 * q^70 - 60 * q^73 - 30 * q^76 + 18 * q^79 - 2 * q^82 - 66 * q^85 + 20 * q^91 - 20 * q^94 + 6 * q^97

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 $

$2$	2.46033	1.73972	0.869858	−	0.493302i	$-0.164210\pi$
$2$	2.46033	1.73972	0.869858	+	0.493302i	$0.164210\pi$
$3$	0	0
$3$	0	0
$4$	4.05323	2.02661
$5$	−0.989783	−0.442644	−0.221322	−	0.975201i	$-0.571037\pi$
$5$	−0.989783	−0.442644	−0.221322	+	0.975201i	$0.571037\pi$
$6$	0	0
$7$	−4.32219	−1.63363	−0.816817	−	0.576897i	$-0.804263\pi$
$7$	−4.32219	−1.63363	−0.816817	+	0.576897i	$0.804263\pi$
$8$	5.05161	1.78602
$9$	0	0
$10$	−2.43519	−0.770075
$11$	0	0
$11$	0	0
$12$	0	0
$13$	−3.61803	−1.00346	−0.501731	−	0.865024i	$-0.667303\pi$
$13$	−3.61803	−1.00346	−0.501731	+	0.865024i	$0.667303\pi$
$14$	−10.6340	−2.84206
$15$	0	0
$16$	4.32219	1.08055
$17$	2.64130	0.640610	0.320305	−	0.947314i	$-0.396215\pi$
$17$	2.64130	0.640610	0.320305	+	0.947314i	$0.396215\pi$
$18$	0	0
$19$	3.82722	0.878025	0.439012	−	0.898481i	$-0.355328\pi$
$19$	3.82722	0.878025	0.439012	+	0.898481i	$0.355328\pi$
$20$	−4.01181	−0.897069
$21$	0	0
$22$	0	0
$23$	−3.45011	−0.719398	−0.359699	−	0.933068i	$-0.617121\pi$
$23$	−3.45011	−0.719398	−0.359699	+	0.933068i	$0.617121\pi$
$24$	0	0
$25$	−4.02033	−0.804066
$26$	−8.90156	−1.74574
$27$	0	0
$28$	−17.5188	−3.31074
$29$	−10.4221	−1.93534	−0.967670	−	0.252219i	$-0.918840\pi$
$29$	−10.4221	−1.93534	−0.967670	+	0.252219i	$0.918840\pi$
$30$	0	0
$31$	−1.68787	−0.303151	−0.151576	−	0.988446i	$-0.548435\pi$
$31$	−1.68787	−0.303151	−0.151576	+	0.988446i	$0.548435\pi$
$32$	0.530785	0.0938305
$33$	0	0
$34$	6.49848	1.11448
$35$	4.27803	0.723119
$36$	0	0
$37$	3.23607	0.532006	0.266003	−	0.963972i	$-0.414297\pi$
$37$	3.23607	0.532006	0.266003	+	0.963972i	$0.414297\pi$
$38$	9.41623	1.52751
$39$	0	0
$40$	−5.00000	−0.790569
$41$	−11.9075	−1.85963	−0.929817	−	0.368021i	$-0.880035\pi$
$41$	−11.9075	−1.85963	−0.929817	+	0.368021i	$0.880035\pi$
$42$	0	0
$43$	2.12307	0.323764	0.161882	−	0.986810i	$-0.448244\pi$
$43$	2.12307	0.323764	0.161882	+	0.986810i	$0.448244\pi$
$44$	0	0
$45$	0	0
$46$	−8.48842	−1.25155
$47$	−4.29980	−0.627190	−0.313595	−	0.949557i	$-0.601533\pi$
$47$	−4.29980	−0.627190	−0.313595	+	0.949557i	$0.601533\pi$
$48$	0	0
$49$	11.6813	1.66876
$50$	−9.89134	−1.39885
$51$	0	0
$52$	−14.6647	−2.03363
$53$	9.48236	1.30250	0.651251	−	0.758862i	$-0.274244\pi$
$53$	9.48236	1.30250	0.651251	+	0.758862i	$0.274244\pi$
$54$	0	0
$55$	0	0
$56$	−21.8340	−2.91770
$57$	0	0
$58$	−25.6419	−3.36694
$59$	−6.47214	−0.842601	−0.421301	−	0.906921i	$-0.638426\pi$
$59$	−6.47214	−0.842601	−0.421301	+	0.906921i	$0.638426\pi$
$60$	0	0
$61$	4.81061	0.615935	0.307968	−	0.951397i	$-0.400351\pi$
$61$	4.81061	0.615935	0.307968	+	0.951397i	$0.400351\pi$
$62$	−4.15273	−0.527397
$63$	0	0
$64$	−7.33847	−0.917309
$65$	3.58107	0.444177
$66$	0	0
$67$	0.854102	0.104345	0.0521726	−	0.998638i	$-0.483385\pi$
$67$	0.854102	0.104345	0.0521726	+	0.998638i	$0.483385\pi$
$68$	10.7058	1.29827
$69$	0	0
$70$	10.5254	1.25802
$71$	3.77816	0.448385	0.224192	−	0.974545i	$-0.428026\pi$
$71$	3.77816	0.448385	0.224192	+	0.974545i	$0.428026\pi$
$72$	0	0
$73$	−11.4083	−1.33524	−0.667621	−	0.744501i	$-0.732687\pi$
$73$	−11.4083	−1.33524	−0.667621	+	0.744501i	$0.732687\pi$
$74$	7.96180	0.925540
$75$	0	0
$76$	15.5126	1.77942
$77$	0	0
$78$	0	0
$79$	−6.14340	−0.691186	−0.345593	−	0.938384i	$-0.612322\pi$
$79$	−6.14340	−0.691186	−0.345593	+	0.938384i	$0.612322\pi$
$80$	−4.27803	−0.478298
$81$	0	0
$82$	−29.2963	−3.23524
$83$	3.36003	0.368812	0.184406	−	0.982850i	$-0.440964\pi$
$83$	3.36003	0.368812	0.184406	+	0.982850i	$0.440964\pi$
$84$	0	0
$85$	−2.61432	−0.283562
$86$	5.22344	0.563258
$87$	0	0
$88$	0	0
$89$	13.2605	1.40561	0.702806	−	0.711381i	$-0.251930\pi$
$89$	13.2605	1.40561	0.702806	+	0.711381i	$0.251930\pi$
$90$	0	0
$91$	15.6378	1.63929
$92$	−13.9841	−1.45794
$93$	0	0
$94$	−10.5789	−1.09113
$95$	−3.78812	−0.388653
$96$	0	0
$97$	−0.371367	−0.0377066	−0.0188533	−	0.999822i	$-0.506002\pi$
$97$	−0.371367	−0.0377066	−0.0188533	+	0.999822i	$0.506002\pi$
$98$	28.7399	2.90317
$99$	0	0
$100$	−16.2953	−1.62953
$101$	12.9943	1.29298	0.646491	−	0.762922i	$-0.276236\pi$
$101$	12.9943	1.29298	0.646491	+	0.762922i	$0.276236\pi$
$102$	0	0
$103$	−11.8041	−1.16309	−0.581544	−	0.813515i	$-0.697551\pi$
$103$	−11.8041	−1.16309	−0.581544	+	0.813515i	$0.697551\pi$
$104$	−18.2769	−1.79220
$105$	0	0
$106$	23.3298	2.26599
$107$	−4.72788	−0.457061	−0.228531	−	0.973537i	$-0.573392\pi$
$107$	−4.72788	−0.457061	−0.228531	+	0.973537i	$0.573392\pi$
$108$	0	0
$109$	−16.1864	−1.55037	−0.775186	−	0.631733i	$-0.782344\pi$
$109$	−16.1864	−1.55037	−0.775186	+	0.631733i	$0.782344\pi$
$110$	0	0
$111$	0	0
$112$	−18.6813	−1.76522
$113$	−0.849683	−0.0799315	−0.0399657	−	0.999201i	$-0.512725\pi$
$113$	−0.849683	−0.0799315	−0.0399657	+	0.999201i	$0.512725\pi$
$114$	0	0
$115$	3.41486	0.318437
$116$	−42.2432	−3.92219
$117$	0	0
$118$	−15.9236	−1.46589
$119$	−11.4162	−1.04652
$120$	0	0
$121$	0	0
$122$	11.8357	1.07155
$123$	0	0
$124$	−6.84133	−0.614370
$125$	8.92817	0.798559
$126$	0	0
$127$	−11.6546	−1.03418	−0.517091	−	0.855930i	$-0.672985\pi$
$127$	−11.6546	−1.03418	−0.517091	+	0.855930i	$0.672985\pi$
$128$	−19.1166	−1.68969
$129$	0	0
$130$	8.81061	0.772741
$131$	−0.242802	−0.0212137	−0.0106068	−	0.999944i	$-0.503376\pi$
$131$	−0.242802	−0.0212137	−0.0106068	+	0.999944i	$0.503376\pi$
$132$	0	0
$133$	−16.5420	−1.43437
$134$	2.10137	0.181531
$135$	0	0
$136$	13.3429	1.14414
$137$	−0.454689	−0.0388467	−0.0194234	−	0.999811i	$-0.506183\pi$
$137$	−0.454689	−0.0388467	−0.0194234	+	0.999811i	$0.506183\pi$
$138$	0	0
$139$	17.8410	1.51325	0.756627	−	0.653847i	$-0.226846\pi$
$139$	17.8410	1.51325	0.756627	+	0.653847i	$0.226846\pi$
$140$	17.3398	1.46548
$141$	0	0
$142$	9.29551	0.780062
$143$	0	0
$144$	0	0
$145$	10.3156	0.856667
$146$	−28.0682	−2.32294
$147$	0	0
$148$	13.1165	1.07817
$149$	15.9384	1.30572	0.652862	−	0.757477i	$-0.273568\pi$
$149$	15.9384	1.30572	0.652862	+	0.757477i	$0.273568\pi$
$150$	0	0
$151$	−6.05356	−0.492631	−0.246316	−	0.969190i	$-0.579220\pi$
$151$	−6.05356	−0.492631	−0.246316	+	0.969190i	$0.579220\pi$
$152$	19.3336	1.56817
$153$	0	0
$154$	0	0
$155$	1.67063	0.134188
$156$	0	0
$157$	7.48187	0.597118	0.298559	−	0.954391i	$-0.403494\pi$
$157$	7.48187	0.597118	0.298559	+	0.954391i	$0.403494\pi$
$158$	−15.1148	−1.20247
$159$	0	0
$160$	−0.525362	−0.0415335
$161$	14.9120	1.17523
$162$	0	0
$163$	13.9766	1.09473	0.547367	−	0.836893i	$-0.315630\pi$
$163$	13.9766	1.09473	0.547367	+	0.836893i	$0.315630\pi$
$164$	−48.2637	−3.76876
$165$	0	0
$166$	8.26679	0.641628
$167$	6.39121	0.494567	0.247283	−	0.968943i	$-0.420462\pi$
$167$	6.39121	0.494567	0.247283	+	0.968943i	$0.420462\pi$
$168$	0	0
$169$	0.0901699	0.00693615
$170$	−6.43208	−0.493318
$171$	0	0
$172$	8.60526	0.656145
$173$	7.84564	0.596493	0.298247	−	0.954489i	$-0.403598\pi$
$173$	7.84564	0.596493	0.298247	+	0.954489i	$0.403598\pi$
$174$	0	0
$175$	17.3766	1.31355
$176$	0	0
$177$	0	0
$178$	32.6253	2.44537
$179$	4.87495	0.364371	0.182185	−	0.983264i	$-0.441683\pi$
$179$	4.87495	0.364371	0.182185	+	0.983264i	$0.441683\pi$
$180$	0	0
$181$	9.04668	0.672434	0.336217	−	0.941785i	$-0.390852\pi$
$181$	9.04668	0.672434	0.336217	+	0.941785i	$0.390852\pi$
$182$	38.4742	2.85190
$183$	0	0
$184$	−17.4286	−1.28486
$185$	−3.20300	−0.235490
$186$	0	0
$187$	0	0
$188$	−17.4280	−1.27107
$189$	0	0
$190$	−9.32002	−0.676145
$191$	18.7676	1.35798	0.678989	−	0.734148i	$-0.262418\pi$
$191$	18.7676	1.35798	0.678989	+	0.734148i	$0.262418\pi$
$192$	0	0
$193$	17.3025	1.24546	0.622732	−	0.782435i	$-0.286023\pi$
$193$	17.3025	1.24546	0.622732	+	0.782435i	$0.286023\pi$
$194$	−0.913687	−0.0655989
$195$	0	0
$196$	47.3470	3.38193
$197$	−6.06800	−0.432327	−0.216164	−	0.976357i	$-0.569354\pi$
$197$	−6.06800	−0.432327	−0.216164	+	0.976357i	$0.569354\pi$
$198$	0	0
$199$	−10.1108	−0.716738	−0.358369	−	0.933580i	$-0.616667\pi$
$199$	−10.1108	−0.716738	−0.358369	+	0.933580i	$0.616667\pi$
$200$	−20.3092	−1.43607
$201$	0	0
$202$	31.9703	2.24942
$203$	45.0464	3.16164
$204$	0	0
$205$	11.7858	0.823157
$206$	−29.0419	−2.02344
$207$	0	0
$208$	−15.6378	−1.08429
$209$	0	0
$210$	0	0
$211$	−14.7414	−1.01484	−0.507421	−	0.861698i	$-0.669401\pi$
$211$	−14.7414	−1.01484	−0.507421	+	0.861698i	$0.669401\pi$
$212$	38.4342	2.63967
$213$	0	0
$214$	−11.6321	−0.795157
$215$	−2.10137	−0.143312
$216$	0	0
$217$	7.29531	0.495238
$218$	−39.8238	−2.69721
$219$	0	0
$220$	0	0
$221$	−9.55633	−0.642828
$222$	0	0
$223$	0.613986	0.0411155	0.0205578	−	0.999789i	$-0.493456\pi$
$223$	0.613986	0.0411155	0.0205578	+	0.999789i	$0.493456\pi$
$224$	−2.29415	−0.153285
$225$	0	0
$226$	−2.09050	−0.139058
$227$	11.6103	0.770606	0.385303	−	0.922790i	$-0.374097\pi$
$227$	11.6103	0.770606	0.385303	+	0.922790i	$0.374097\pi$
$228$	0	0
$229$	0.813441	0.0537537	0.0268768	−	0.999639i	$-0.491444\pi$
$229$	0.813441	0.0537537	0.0268768	+	0.999639i	$0.491444\pi$
$230$	8.40169	0.553991
$231$	0	0
$232$	−52.6486	−3.45655
$233$	−17.2514	−1.13018	−0.565088	−	0.825031i	$-0.691158\pi$
$233$	−17.2514	−1.13018	−0.565088	+	0.825031i	$0.691158\pi$
$234$	0	0
$235$	4.25586	0.277622
$236$	−26.2331	−1.70763
$237$	0	0
$238$	−28.0877	−1.82065
$239$	−0.199752	−0.0129209	−0.00646044	−	0.999979i	$-0.502056\pi$
$239$	−0.199752	−0.0129209	−0.00646044	+	0.999979i	$0.502056\pi$
$240$	0	0
$241$	−14.8309	−0.955345	−0.477672	−	0.878538i	$-0.658519\pi$
$241$	−14.8309	−0.955345	−0.477672	+	0.878538i	$0.658519\pi$
$242$	0	0
$243$	0	0
$244$	19.4985	1.24826
$245$	−11.5620	−0.738667
$246$	0	0
$247$	−13.8470	−0.881065
$248$	−8.52649	−0.541432
$249$	0	0
$250$	21.9662	1.38927
$251$	−8.52649	−0.538187	−0.269094	−	0.963114i	$-0.586724\pi$
$251$	−8.52649	−0.538187	−0.269094	+	0.963114i	$0.586724\pi$
$252$	0	0
$253$	0	0
$254$	−28.6743	−1.79918
$255$	0	0
$256$	−32.3563	−2.02227
$257$	12.9986	0.810831	0.405416	−	0.914132i	$-0.367127\pi$
$257$	12.9986	0.810831	0.405416	+	0.914132i	$0.367127\pi$
$258$	0	0
$259$	−13.9869	−0.869104
$260$	14.5149	0.900174
$261$	0	0
$262$	−0.597372	−0.0369058
$263$	−14.8529	−0.915868	−0.457934	−	0.888986i	$-0.651410\pi$
$263$	−14.8529	−0.915868	−0.457934	+	0.888986i	$0.651410\pi$
$264$	0	0
$265$	−9.38548	−0.576545
$266$	−40.6987	−2.49540
$267$	0	0
$268$	3.46187	0.211467
$269$	3.81173	0.232405	0.116203	−	0.993226i	$-0.462928\pi$
$269$	3.81173	0.232405	0.116203	+	0.993226i	$0.462928\pi$
$270$	0	0
$271$	13.8375	0.840568	0.420284	−	0.907393i	$-0.361931\pi$
$271$	13.8375	0.840568	0.420284	+	0.907393i	$0.361931\pi$
$272$	11.4162	0.692210
$273$	0	0
$274$	−1.11869	−0.0675823
$275$	0	0
$276$	0	0
$277$	−2.45802	−0.147688	−0.0738442	−	0.997270i	$-0.523527\pi$
$277$	−2.45802	−0.147688	−0.0738442	+	0.997270i	$0.523527\pi$
$278$	43.8948	2.63263
$279$	0	0
$280$	21.6109	1.29150
$281$	19.9206	1.18836	0.594182	−	0.804331i	$-0.297476\pi$
$281$	19.9206	1.18836	0.594182	+	0.804331i	$0.297476\pi$
$282$	0	0
$283$	−7.18853	−0.427313	−0.213657	−	0.976909i	$-0.568537\pi$
$283$	−7.18853	−0.427313	−0.213657	+	0.976909i	$0.568537\pi$
$284$	15.3137	0.908702
$285$	0	0
$286$	0	0
$287$	51.4664	3.03796
$288$	0	0
$289$	−10.0235	−0.589618
$290$	25.3799	1.49036
$291$	0	0
$292$	−46.2405	−2.70602
$293$	−17.0618	−0.996760	−0.498380	−	0.866959i	$-0.666072\pi$
$293$	−17.0618	−0.996760	−0.498380	+	0.866959i	$0.666072\pi$
$294$	0	0
$295$	6.40601	0.372973
$296$	16.3474	0.950172
$297$	0	0
$298$	39.2137	2.27159
$299$	12.4826	0.721889
$300$	0	0
$301$	−9.17629	−0.528913
$302$	−14.8938	−0.857039
$303$	0	0
$304$	16.5420	0.948747
$305$	−4.76146	−0.272640
$306$	0	0
$307$	−7.48842	−0.427387	−0.213693	−	0.976901i	$-0.568549\pi$
$307$	−7.48842	−0.427387	−0.213693	+	0.976901i	$0.568549\pi$
$308$	0	0
$309$	0	0
$310$	4.11030	0.233449
$311$	−10.5208	−0.596583	−0.298291	−	0.954475i	$-0.596417\pi$
$311$	−10.5208	−0.596583	−0.298291	+	0.954475i	$0.596417\pi$
$312$	0	0
$313$	−10.4347	−0.589802	−0.294901	−	0.955528i	$-0.595287\pi$
$313$	−10.4347	−0.589802	−0.294901	+	0.955528i	$0.595287\pi$
$314$	18.4079	1.03882
$315$	0	0
$316$	−24.9006	−1.40077
$317$	−12.7881	−0.718250	−0.359125	−	0.933290i	$-0.616925\pi$
$317$	−12.7881	−0.718250	−0.359125	+	0.933290i	$0.616925\pi$
$318$	0	0
$319$	0	0
$320$	7.26349	0.406042
$321$	0	0
$322$	36.6886	2.04457
$323$	10.1089	0.562472
$324$	0	0
$325$	14.5457	0.806850
$326$	34.3871	1.90453
$327$	0	0
$328$	−60.1520	−3.32134
$329$	18.5845	1.02460
$330$	0	0
$331$	16.3849	0.900598	0.450299	−	0.892878i	$-0.351317\pi$
$331$	16.3849	0.900598	0.450299	+	0.892878i	$0.351317\pi$
$332$	13.6190	0.747438
$333$	0	0
$334$	15.7245	0.860406
$335$	−0.845375	−0.0461878
$336$	0	0
$337$	−29.0673	−1.58340	−0.791699	−	0.610911i	$-0.790803\pi$
$337$	−29.0673	−1.58340	−0.791699	+	0.610911i	$0.790803\pi$
$338$	0.221848	0.0120669
$339$	0	0
$340$	−10.5964	−0.574671
$341$	0	0
$342$	0	0
$343$	−20.2336	−1.09251
$344$	10.7249	0.578248
$345$	0	0
$346$	19.3029	1.03773
$347$	−21.5826	−1.15862	−0.579308	−	0.815109i	$-0.696677\pi$
$347$	−21.5826	−1.15862	−0.579308	+	0.815109i	$0.696677\pi$
$348$	0	0
$349$	−24.2003	−1.29541	−0.647707	−	0.761889i	$-0.724272\pi$
$349$	−24.2003	−1.29541	−0.647707	+	0.761889i	$0.724272\pi$
$350$	42.7523	2.28520
$351$	0	0
$352$	0	0
$353$	20.9800	1.11666	0.558328	−	0.829621i	$-0.311443\pi$
$353$	20.9800	1.11666	0.558328	+	0.829621i	$0.311443\pi$
$354$	0	0
$355$	−3.73955	−0.198475
$356$	53.7479	2.84863
$357$	0	0
$358$	11.9940	0.633902
$359$	15.6835	0.827741	0.413871	−	0.910336i	$-0.364177\pi$
$359$	15.6835	0.827741	0.413871	+	0.910336i	$0.364177\pi$
$360$	0	0
$361$	−4.35238	−0.229073
$362$	22.2578	1.16984
$363$	0	0
$364$	63.3837	3.32221
$365$	11.2917	0.591037
$366$	0	0
$367$	−8.19454	−0.427752	−0.213876	−	0.976861i	$-0.568609\pi$
$367$	−8.19454	−0.427752	−0.213876	+	0.976861i	$0.568609\pi$
$368$	−14.9120	−0.777344
$369$	0	0
$370$	−7.88045	−0.409685
$371$	−40.9846	−2.12781
$372$	0	0
$373$	−30.8172	−1.59565	−0.797826	−	0.602888i	$-0.794017\pi$
$373$	−30.8172	−1.59565	−0.797826	+	0.602888i	$0.794017\pi$
$374$	0	0
$375$	0	0
$376$	−21.7209	−1.12017
$377$	37.7076	1.94204
$378$	0	0
$379$	19.8170	1.01793	0.508964	−	0.860788i	$-0.330029\pi$
$379$	19.8170	1.01793	0.508964	+	0.860788i	$0.330029\pi$
$380$	−15.3541	−0.787648
$381$	0	0
$382$	46.1746	2.36250
$383$	23.6757	1.20977	0.604885	−	0.796313i	$-0.293219\pi$
$383$	23.6757	1.20977	0.604885	+	0.796313i	$0.293219\pi$
$384$	0	0
$385$	0	0
$386$	42.5700	2.16675
$387$	0	0
$388$	−1.50524	−0.0764168
$389$	−8.51653	−0.431805	−0.215903	−	0.976415i	$-0.569269\pi$
$389$	−8.51653	−0.431805	−0.215903	+	0.976415i	$0.569269\pi$
$390$	0	0
$391$	−9.11280	−0.460854
$392$	59.0095	2.98043
$393$	0	0
$394$	−14.9293	−0.752127
$395$	6.08063	0.305949
$396$	0	0
$397$	−3.78373	−0.189900	−0.0949499	−	0.995482i	$-0.530269\pi$
$397$	−3.78373	−0.189900	−0.0949499	+	0.995482i	$0.530269\pi$
$398$	−24.8760	−1.24692
$399$	0	0
$400$	−17.3766	−0.868832
$401$	−17.5533	−0.876572	−0.438286	−	0.898835i	$-0.644414\pi$
$401$	−17.5533	−0.876572	−0.438286	+	0.898835i	$0.644414\pi$
$402$	0	0
$403$	6.10678	0.304201
$404$	52.6689	2.62037
$405$	0	0
$406$	110.829	5.50035
$407$	0	0
$408$	0	0
$409$	−28.2905	−1.39888	−0.699438	−	0.714693i	$-0.746566\pi$
$409$	−28.2905	−1.39888	−0.699438	+	0.714693i	$0.746566\pi$
$410$	28.9970	1.43206
$411$	0	0
$412$	−47.8445	−2.35713
$413$	27.9738	1.37650
$414$	0	0
$415$	−3.32570	−0.163252
$416$	−1.92040	−0.0941553
$417$	0	0
$418$	0	0
$419$	32.2357	1.57482	0.787409	−	0.616430i	$-0.211422\pi$
$419$	32.2357	1.57482	0.787409	+	0.616430i	$0.211422\pi$
$420$	0	0
$421$	−28.4419	−1.38617	−0.693086	−	0.720855i	$-0.743750\pi$
$421$	−28.4419	−1.38617	−0.693086	+	0.720855i	$0.743750\pi$
$422$	−36.2688	−1.76554
$423$	0	0
$424$	47.9013	2.32629
$425$	−10.6189	−0.515093
$426$	0	0
$427$	−20.7924	−1.00621
$428$	−19.1632	−0.926286
$429$	0	0
$430$	−5.17007	−0.249323
$431$	−26.7921	−1.29053	−0.645265	−	0.763959i	$-0.723253\pi$
$431$	−26.7921	−1.29053	−0.645265	+	0.763959i	$0.723253\pi$
$432$	0	0
$433$	−9.40242	−0.451852	−0.225926	−	0.974145i	$-0.572541\pi$
$433$	−9.40242	−0.451852	−0.225926	+	0.974145i	$0.572541\pi$
$434$	17.9489	0.861573
$435$	0	0
$436$	−65.6070	−3.14200
$437$	−13.2043	−0.631649
$438$	0	0
$439$	17.8962	0.854139	0.427069	−	0.904219i	$-0.359546\pi$
$439$	17.8962	0.854139	0.427069	+	0.904219i	$0.359546\pi$
$440$	0	0
$441$	0	0
$442$	−23.5117	−1.11834
$443$	18.3813	0.873320	0.436660	−	0.899627i	$-0.356161\pi$
$443$	18.3813	0.873320	0.436660	+	0.899627i	$0.356161\pi$
$444$	0	0
$445$	−13.1250	−0.622186
$446$	1.51061	0.0715293
$447$	0	0
$448$	31.7183	1.49855
$449$	−5.99650	−0.282992	−0.141496	−	0.989939i	$-0.545191\pi$
$449$	−5.99650	−0.282992	−0.141496	+	0.989939i	$0.545191\pi$
$450$	0	0
$451$	0	0
$452$	−3.44396	−0.161990
$453$	0	0
$454$	28.5653	1.34064
$455$	−15.4780	−0.725622
$456$	0	0
$457$	−25.5348	−1.19447	−0.597233	−	0.802068i	$-0.703733\pi$
$457$	−25.5348	−1.19447	−0.597233	+	0.802068i	$0.703733\pi$
$458$	2.00133	0.0935162
$459$	0	0
$460$	13.8412	0.645350
$461$	−31.5683	−1.47028	−0.735142	−	0.677913i	$-0.762885\pi$
$461$	−31.5683	−1.47028	−0.735142	+	0.677913i	$0.762885\pi$
$462$	0	0
$463$	3.76414	0.174934	0.0874671	−	0.996167i	$-0.472123\pi$
$463$	3.76414	0.174934	0.0874671	+	0.996167i	$0.472123\pi$
$464$	−45.0464	−2.09123
$465$	0	0
$466$	−42.4441	−1.96618
$467$	−5.85161	−0.270780	−0.135390	−	0.990792i	$-0.543229\pi$
$467$	−5.85161	−0.270780	−0.135390	+	0.990792i	$0.543229\pi$
$468$	0	0
$469$	−3.69159	−0.170462
$470$	10.4708	0.482983
$471$	0	0
$472$	−32.6948	−1.50490
$473$	0	0
$474$	0	0
$475$	−15.3867	−0.705990
$476$	−46.2725	−2.12090
$477$	0	0
$478$	−0.491456	−0.0224787
$479$	25.6896	1.17379	0.586895	−	0.809663i	$-0.300350\pi$
$479$	25.6896	1.17379	0.586895	+	0.809663i	$0.300350\pi$
$480$	0	0
$481$	−11.7082	−0.533848
$482$	−36.4890	−1.66203
$483$	0	0
$484$	0	0
$485$	0.367573	0.0166906
$486$	0	0
$487$	−5.31409	−0.240805	−0.120402	−	0.992725i	$-0.538418\pi$
$487$	−5.31409	−0.240805	−0.120402	+	0.992725i	$0.538418\pi$
$488$	24.3013	1.10007
$489$	0	0
$490$	−28.4463	−1.28507
$491$	−2.46464	−0.111228	−0.0556138	−	0.998452i	$-0.517712\pi$
$491$	−2.46464	−0.111228	−0.0556138	+	0.998452i	$0.517712\pi$
$492$	0	0
$493$	−27.5280	−1.23980
$494$	−34.0682	−1.53280
$495$	0	0
$496$	−7.29531	−0.327569
$497$	−16.3299	−0.732496
$498$	0	0
$499$	22.3025	0.998399	0.499199	−	0.866487i	$-0.333628\pi$
$499$	22.3025	0.998399	0.499199	+	0.866487i	$0.333628\pi$
$500$	36.1879	1.61837
$501$	0	0
$502$	−20.9780	−0.936293
$503$	−25.9733	−1.15809	−0.579047	−	0.815294i	$-0.696575\pi$
$503$	−25.9733	−1.15809	−0.579047	+	0.815294i	$0.696575\pi$
$504$	0	0
$505$	−12.8615	−0.572331
$506$	0	0
$507$	0	0
$508$	−47.2389	−2.09589
$509$	−27.8741	−1.23550	−0.617749	−	0.786376i	$-0.711955\pi$
$509$	−27.8741	−1.23550	−0.617749	+	0.786376i	$0.711955\pi$
$510$	0	0
$511$	49.3089	2.18130
$512$	−41.3739	−1.82849
$513$	0	0
$514$	31.9809	1.41062
$515$	11.6834	0.514834
$516$	0	0
$517$	0	0
$518$	−34.4124	−1.51199
$519$	0	0
$520$	18.0902	0.793306
$521$	25.8693	1.13335	0.566676	−	0.823940i	$-0.308229\pi$
$521$	25.8693	1.13335	0.566676	+	0.823940i	$0.308229\pi$
$522$	0	0
$523$	27.2640	1.19217	0.596085	−	0.802921i	$-0.296722\pi$
$523$	27.2640	1.19217	0.596085	+	0.802921i	$0.296722\pi$
$524$	−0.984130	−0.0429919
$525$	0	0
$526$	−36.5430	−1.59335
$527$	−4.45819	−0.194202
$528$	0	0
$529$	−11.0967	−0.482466
$530$	−23.0914	−1.00303
$531$	0	0
$532$	−67.0484	−2.90692
$533$	43.0816	1.86607
$534$	0	0
$535$	4.67957	0.202316
$536$	4.31459	0.186362
$537$	0	0
$538$	9.37812	0.404320
$539$	0	0
$540$	0	0
$541$	23.3832	1.00532	0.502661	−	0.864484i	$-0.332354\pi$
$541$	23.3832	1.00532	0.502661	+	0.864484i	$0.332354\pi$
$542$	34.0448	1.46235
$543$	0	0
$544$	1.40197	0.0601088
$545$	16.0210	0.686263
$546$	0	0
$547$	−15.2829	−0.653452	−0.326726	−	0.945119i	$-0.605945\pi$
$547$	−15.2829	−0.653452	−0.326726	+	0.945119i	$0.605945\pi$
$548$	−1.84296	−0.0787273
$549$	0	0
$550$	0	0
$551$	−39.8878	−1.69928
$552$	0	0
$553$	26.5529	1.12915
$554$	−6.04755	−0.256936
$555$	0	0
$556$	72.3136	3.06678
$557$	−7.24041	−0.306786	−0.153393	−	0.988165i	$-0.549020\pi$
$557$	−7.24041	−0.306786	−0.153393	+	0.988165i	$0.549020\pi$
$558$	0	0
$559$	−7.68132	−0.324885
$560$	18.4904	0.781364
$561$	0	0
$562$	49.0113	2.06742
$563$	31.5401	1.32926	0.664628	−	0.747174i	$-0.268590\pi$
$563$	31.5401	1.32926	0.664628	+	0.747174i	$0.268590\pi$
$564$	0	0
$565$	0.841001	0.0353812
$566$	−17.6861	−0.743404
$567$	0	0
$568$	19.0858	0.800822
$569$	11.1823	0.468785	0.234392	−	0.972142i	$-0.424690\pi$
$569$	11.1823	0.468785	0.234392	+	0.972142i	$0.424690\pi$
$570$	0	0
$571$	−11.5906	−0.485052	−0.242526	−	0.970145i	$-0.577976\pi$
$571$	−11.5906	−0.485052	−0.242526	+	0.970145i	$0.577976\pi$
$572$	0	0
$573$	0	0
$574$	126.624	5.28519
$575$	13.8706	0.578444
$576$	0	0
$577$	16.9358	0.705045	0.352522	−	0.935803i	$-0.385324\pi$
$577$	16.9358	0.705045	0.352522	+	0.935803i	$0.385324\pi$
$578$	−24.6612	−1.02577
$579$	0	0
$580$	41.8116	1.73613
$581$	−14.5227	−0.602503
$582$	0	0
$583$	0	0
$584$	−57.6304	−2.38476
$585$	0	0
$586$	−41.9776	−1.73408
$587$	−9.04678	−0.373401	−0.186700	−	0.982417i	$-0.559779\pi$
$587$	−9.04678	−0.373401	−0.186700	+	0.982417i	$0.559779\pi$
$588$	0	0
$589$	−6.45986	−0.266174
$590$	15.7609	0.648866
$591$	0	0
$592$	13.9869	0.574858
$593$	−20.4127	−0.838248	−0.419124	−	0.907929i	$-0.637663\pi$
$593$	−20.4127	−0.838248	−0.419124	+	0.907929i	$0.637663\pi$
$594$	0	0
$595$	11.2996	0.463237
$596$	64.6019	2.64620
$597$	0	0
$598$	30.7114	1.25588
$599$	−42.0219	−1.71697	−0.858485	−	0.512839i	$-0.828594\pi$
$599$	−42.0219	−1.71697	−0.858485	+	0.512839i	$0.828594\pi$
$600$	0	0
$601$	10.6951	0.436262	0.218131	−	0.975919i	$-0.430004\pi$
$601$	10.6951	0.436262	0.218131	+	0.975919i	$0.430004\pi$
$602$	−22.5767	−0.920158
$603$	0	0
$604$	−24.5364	−0.998373
$605$	0	0
$606$	0	0
$607$	45.5994	1.85082	0.925411	−	0.378965i	$-0.123720\pi$
$607$	45.5994	1.85082	0.925411	+	0.378965i	$0.123720\pi$
$608$	2.03143	0.0823855
$609$	0	0
$610$	−11.7148	−0.474317
$611$	15.5568	0.629361
$612$	0	0
$613$	−27.1676	−1.09729	−0.548644	−	0.836056i	$-0.684856\pi$
$613$	−27.1676	−1.09729	−0.548644	+	0.836056i	$0.684856\pi$
$614$	−18.4240	−0.743531
$615$	0	0
$616$	0	0
$617$	7.83117	0.315271	0.157636	−	0.987497i	$-0.449613\pi$
$617$	7.83117	0.315271	0.157636	+	0.987497i	$0.449613\pi$
$618$	0	0
$619$	37.9269	1.52441	0.762206	−	0.647335i	$-0.224116\pi$
$619$	37.9269	1.52441	0.762206	+	0.647335i	$0.224116\pi$
$620$	6.77143	0.271947
$621$	0	0
$622$	−25.8848	−1.03788
$623$	−57.3145	−2.29626
$624$	0	0
$625$	11.2647	0.450588
$626$	−25.6727	−1.02609
$627$	0	0
$628$	30.3257	1.21013
$629$	8.54744	0.340809
$630$	0	0
$631$	−27.6177	−1.09944	−0.549722	−	0.835348i	$-0.685266\pi$
$631$	−27.6177	−1.09944	−0.549722	+	0.835348i	$0.685266\pi$
$632$	−31.0341	−1.23447
$633$	0	0
$634$	−31.4629	−1.24955
$635$	11.5356	0.457775
$636$	0	0
$637$	−42.2634	−1.67454
$638$	0	0
$639$	0	0
$640$	18.9213	0.747931
$641$	4.47215	0.176639	0.0883197	−	0.996092i	$-0.471850\pi$
$641$	4.47215	0.176639	0.0883197	+	0.996092i	$0.471850\pi$
$642$	0	0
$643$	−7.47160	−0.294651	−0.147326	−	0.989088i	$-0.547067\pi$
$643$	−7.47160	−0.294651	−0.147326	+	0.989088i	$0.547067\pi$
$644$	60.4419	2.38174
$645$	0	0
$646$	24.8711	0.978541
$647$	11.5159	0.452738	0.226369	−	0.974042i	$-0.427314\pi$
$647$	11.5159	0.452738	0.226369	+	0.974042i	$0.427314\pi$
$648$	0	0
$649$	0	0
$650$	35.7872	1.40369
$651$	0	0
$652$	56.6504	2.21860
$653$	−21.1384	−0.827209	−0.413605	−	0.910457i	$-0.635730\pi$
$653$	−21.1384	−0.827209	−0.413605	+	0.910457i	$0.635730\pi$
$654$	0	0
$655$	0.240321	0.00939011
$656$	−51.4664	−2.00942
$657$	0	0
$658$	45.7241	1.78251
$659$	27.0354	1.05315	0.526575	−	0.850129i	$-0.323476\pi$
$659$	27.0354	1.05315	0.526575	+	0.850129i	$0.323476\pi$
$660$	0	0
$661$	−26.7618	−1.04091	−0.520456	−	0.853888i	$-0.674238\pi$
$661$	−26.7618	−1.04091	−0.520456	+	0.853888i	$0.674238\pi$
$662$	40.3124	1.56678
$663$	0	0
$664$	16.9736	0.658703
$665$	16.3730	0.634916
$666$	0	0
$667$	35.9575	1.39228
$668$	25.9050	1.00230
$669$	0	0
$670$	−2.07990	−0.0803536
$671$	0	0
$672$	0	0
$673$	−49.1382	−1.89414	−0.947069	−	0.321030i	$-0.895971\pi$
$673$	−49.1382	−1.89414	−0.947069	+	0.321030i	$0.895971\pi$
$674$	−71.5153	−2.75466
$675$	0	0
$676$	0.365479	0.0140569
$677$	−45.6872	−1.75590	−0.877950	−	0.478752i	$-0.841089\pi$
$677$	−45.6872	−1.75590	−0.877950	+	0.478752i	$0.841089\pi$
$678$	0	0
$679$	1.60512	0.0615989
$680$	−13.2065	−0.506447
$681$	0	0
$682$	0	0
$683$	−47.1991	−1.80602	−0.903012	−	0.429615i	$-0.858649\pi$
$683$	−47.1991	−1.80602	−0.903012	+	0.429615i	$0.858649\pi$
$684$	0	0
$685$	0.450044	0.0171953
$686$	−49.7813	−1.90066
$687$	0	0
$688$	9.17629	0.349843
$689$	−34.3075	−1.30701
$690$	0	0
$691$	29.7835	1.13302	0.566509	−	0.824055i	$-0.308294\pi$
$691$	29.7835	1.13302	0.566509	+	0.824055i	$0.308294\pi$
$692$	31.8002	1.20886
$693$	0	0
$694$	−53.1004	−2.01566
$695$	−17.6587	−0.669833
$696$	0	0
$697$	−31.4513	−1.19130
$698$	−59.5408	−2.25365
$699$	0	0
$700$	70.4314	2.66206
$701$	−0.592613	−0.0223827	−0.0111913	−	0.999937i	$-0.503562\pi$
$701$	−0.592613	−0.0223827	−0.0111913	+	0.999937i	$0.503562\pi$
$702$	0	0
$703$	12.3851	0.467115
$704$	0	0
$705$	0	0
$706$	51.6178	1.94266
$707$	−56.1639	−2.11226
$708$	0	0
$709$	−33.8353	−1.27071	−0.635356	−	0.772219i	$-0.719147\pi$
$709$	−33.8353	−1.27071	−0.635356	+	0.772219i	$0.719147\pi$
$710$	−9.20054	−0.345290
$711$	0	0
$712$	66.9870	2.51045
$713$	5.82335	0.218086
$714$	0	0
$715$	0	0
$716$	19.7593	0.738439
$717$	0	0
$718$	38.5865	1.44003
$719$	48.6923	1.81592	0.907958	−	0.419061i	$-0.137641\pi$
$719$	48.6923	1.81592	0.907958	+	0.419061i	$0.137641\pi$
$720$	0	0
$721$	51.0194	1.90006
$722$	−10.7083	−0.398521
$723$	0	0
$724$	36.6682	1.36276
$725$	41.9004	1.55614
$726$	0	0
$727$	−38.4706	−1.42680	−0.713399	−	0.700758i	$-0.752845\pi$
$727$	−38.4706	−1.42680	−0.713399	+	0.700758i	$0.752845\pi$
$728$	78.9963	2.92780
$729$	0	0
$730$	27.7814	1.02824
$731$	5.60766	0.207407
$732$	0	0
$733$	−9.55224	−0.352820	−0.176410	−	0.984317i	$-0.556448\pi$
$733$	−9.55224	−0.352820	−0.176410	+	0.984317i	$0.556448\pi$
$734$	−20.1613	−0.744166
$735$	0	0
$736$	−1.83127	−0.0675015
$737$	0	0
$738$	0	0
$739$	−19.0274	−0.699933	−0.349966	−	0.936762i	$-0.613807\pi$
$739$	−19.0274	−0.699933	−0.349966	+	0.936762i	$0.613807\pi$
$740$	−12.9825	−0.477246
$741$	0	0
$742$	−100.836	−3.70179
$743$	−12.7149	−0.466466	−0.233233	−	0.972421i	$-0.574930\pi$
$743$	−12.7149	−0.466466	−0.233233	+	0.972421i	$0.574930\pi$
$744$	0	0
$745$	−15.7755	−0.577971
$746$	−75.8204	−2.77598
$747$	0	0
$748$	0	0
$749$	20.4348	0.746671
$750$	0	0
$751$	−38.1521	−1.39219	−0.696094	−	0.717950i	$-0.745080\pi$
$751$	−38.1521	−1.39219	−0.696094	+	0.717950i	$0.745080\pi$
$752$	−18.5845	−0.677708
$753$	0	0
$754$	92.7732	3.37860
$755$	5.99171	0.218060
$756$	0	0
$757$	6.51456	0.236776	0.118388	−	0.992967i	$-0.462227\pi$
$757$	6.51456	0.236776	0.118388	+	0.992967i	$0.462227\pi$
$758$	48.7563	1.77091
$759$	0	0
$760$	−19.1361	−0.694140
$761$	44.9281	1.62864	0.814321	−	0.580415i	$-0.197110\pi$
$761$	44.9281	1.62864	0.814321	+	0.580415i	$0.197110\pi$
$762$	0	0
$763$	69.9605	2.53274
$764$	76.0695	2.75210
$765$	0	0
$766$	58.2500	2.10466
$767$	23.4164	0.845518
$768$	0	0
$769$	0.0822779	0.00296702	0.00148351	−	0.999999i	$-0.499528\pi$
$769$	0.0822779	0.00296702	0.00148351	+	0.999999i	$0.499528\pi$
$770$	0	0
$771$	0	0
$772$	70.1311	2.52407
$773$	19.0169	0.683991	0.341996	−	0.939702i	$-0.388897\pi$
$773$	19.0169	0.683991	0.341996	+	0.939702i	$0.388897\pi$
$774$	0	0
$775$	6.78581	0.243753
$776$	−1.87601	−0.0673447
$777$	0	0
$778$	−20.9535	−0.751218
$779$	−45.5725	−1.63281
$780$	0	0
$781$	0	0
$782$	−22.4205	−0.801755
$783$	0	0
$784$	50.4889	1.80317
$785$	−7.40542	−0.264311
$786$	0	0
$787$	−8.62985	−0.307621	−0.153810	−	0.988100i	$-0.549155\pi$
$787$	−8.62985	−0.307621	−0.153810	+	0.988100i	$0.549155\pi$
$788$	−24.5950	−0.876160
$789$	0	0
$790$	14.9603	0.532265
$791$	3.67249	0.130579
$792$	0	0
$793$	−17.4049	−0.618068
$794$	−9.30922	−0.330372
$795$	0	0
$796$	−40.9815	−1.45255
$797$	16.5737	0.587072	0.293536	−	0.955948i	$-0.405168\pi$
$797$	16.5737	0.587072	0.293536	+	0.955948i	$0.405168\pi$
$798$	0	0
$799$	−11.3571	−0.401784
$800$	−2.13393	−0.0754459
$801$	0	0
$802$	−43.1870	−1.52499
$803$	0	0
$804$	0	0
$805$	−14.7597	−0.520210
$806$	15.0247	0.529223
$807$	0	0
$808$	65.6422	2.30929
$809$	−22.6429	−0.796081	−0.398041	−	0.917368i	$-0.630310\pi$
$809$	−22.6429	−0.796081	−0.398041	+	0.917368i	$0.630310\pi$
$810$	0	0
$811$	56.5839	1.98693	0.993464	−	0.114147i	$-0.0364134\pi$
$811$	56.5839	1.98693	0.993464	+	0.114147i	$0.0364134\pi$
$812$	182.583	6.40742
$813$	0	0
$814$	0	0
$815$	−13.8338	−0.484578
$816$	0	0
$817$	8.12544	0.284273
$818$	−69.6040	−2.43365
$819$	0	0
$820$	47.7705	1.66822
$821$	47.3494	1.65250	0.826252	−	0.563300i	$-0.190468\pi$
$821$	47.3494	1.65250	0.826252	+	0.563300i	$0.190468\pi$
$822$	0	0
$823$	−6.98088	−0.243338	−0.121669	−	0.992571i	$-0.538825\pi$
$823$	−6.98088	−0.243338	−0.121669	+	0.992571i	$0.538825\pi$
$824$	−59.6296	−2.07729
$825$	0	0
$826$	68.8249	2.39472
$827$	−39.8238	−1.38481	−0.692404	−	0.721510i	$-0.743449\pi$
$827$	−39.8238	−1.38481	−0.692404	+	0.721510i	$0.743449\pi$
$828$	0	0
$829$	−33.0813	−1.14896	−0.574481	−	0.818518i	$-0.694796\pi$
$829$	−33.0813	−1.14896	−0.574481	+	0.818518i	$0.694796\pi$
$830$	−8.18233	−0.284013
$831$	0	0
$832$	26.5508	0.920485
$833$	30.8539	1.06903
$834$	0	0
$835$	−6.32591	−0.218917
$836$	0	0
$837$	0	0
$838$	79.3106	2.73974
$839$	−34.1940	−1.18051	−0.590254	−	0.807217i	$-0.700973\pi$
$839$	−34.1940	−1.18051	−0.590254	+	0.807217i	$0.700973\pi$
$840$	0	0
$841$	79.6207	2.74554
$842$	−69.9764	−2.41155
$843$	0	0
$844$	−59.7504	−2.05669
$845$	−0.0892486	−0.00307025
$846$	0	0
$847$	0	0
$848$	40.9846	1.40742
$849$	0	0
$850$	−26.1260	−0.896116
$851$	−11.1648	−0.382724
$852$	0	0
$853$	7.64122	0.261630	0.130815	−	0.991407i	$-0.458241\pi$
$853$	7.64122	0.261630	0.130815	+	0.991407i	$0.458241\pi$
$854$	−51.1561	−1.75052
$855$	0	0
$856$	−23.8834	−0.816319
$857$	27.6052	0.942976	0.471488	−	0.881873i	$-0.343717\pi$
$857$	27.6052	0.942976	0.471488	+	0.881873i	$0.343717\pi$
$858$	0	0
$859$	−17.0244	−0.580864	−0.290432	−	0.956896i	$-0.593799\pi$
$859$	−17.0244	−0.580864	−0.290432	+	0.956896i	$0.593799\pi$
$860$	−8.51734	−0.290439
$861$	0	0
$862$	−65.9174	−2.24516
$863$	−10.2621	−0.349326	−0.174663	−	0.984628i	$-0.555884\pi$
$863$	−10.2621	−0.349326	−0.174663	+	0.984628i	$0.555884\pi$
$864$	0	0
$865$	−7.76548	−0.264034
$866$	−23.1331	−0.786094
$867$	0	0
$868$	29.5695	1.00366
$869$	0	0
$870$	0	0
$871$	−3.09017	−0.104706
$872$	−81.7672	−2.76899
$873$	0	0
$874$	−32.4871	−1.09889
$875$	−38.5892	−1.30455
$876$	0	0
$877$	22.2626	0.751753	0.375877	−	0.926670i	$-0.377342\pi$
$877$	22.2626	0.751753	0.375877	+	0.926670i	$0.377342\pi$
$878$	44.0306	1.48596
$879$	0	0
$880$	0	0
$881$	3.58540	0.120795	0.0603976	−	0.998174i	$-0.480763\pi$
$881$	3.58540	0.120795	0.0603976	+	0.998174i	$0.480763\pi$
$882$	0	0
$883$	44.9895	1.51402	0.757008	−	0.653406i	$-0.226660\pi$
$883$	44.9895	1.51402	0.757008	+	0.653406i	$0.226660\pi$
$884$	−38.7340	−1.30276
$885$	0	0
$886$	45.2240	1.51933
$887$	14.8037	0.497059	0.248530	−	0.968624i	$-0.420053\pi$
$887$	14.8037	0.497059	0.248530	+	0.968624i	$0.420053\pi$
$888$	0	0
$889$	50.3736	1.68948
$890$	−32.2919	−1.08243
$891$	0	0
$892$	2.48862	0.0833253
$893$	−16.4563	−0.550688
$894$	0	0
$895$	−4.82514	−0.161287
$896$	82.6257	2.76033
$897$	0	0
$898$	−14.7534	−0.492326
$899$	17.5912	0.586700
$900$	0	0
$901$	25.0458	0.834397
$902$	0	0
$903$	0	0
$904$	−4.29227	−0.142759
$905$	−8.95424	−0.297649
$906$	0	0
$907$	23.9740	0.796044	0.398022	−	0.917376i	$-0.369697\pi$
$907$	23.9740	0.796044	0.398022	+	0.917376i	$0.369697\pi$
$908$	47.0593	1.56172
$909$	0	0
$910$	−38.0811	−1.26238
$911$	22.4487	0.743760	0.371880	−	0.928281i	$-0.378713\pi$
$911$	22.4487	0.743760	0.371880	+	0.928281i	$0.378713\pi$
$912$	0	0
$913$	0	0
$914$	−62.8240	−2.07803
$915$	0	0
$916$	3.29706	0.108938
$917$	1.04943	0.0346554
$918$	0	0
$919$	−18.9294	−0.624424	−0.312212	−	0.950012i	$-0.601070\pi$
$919$	−18.9294	−0.624424	−0.312212	+	0.950012i	$0.601070\pi$
$920$	17.2506	0.568734
$921$	0	0
$922$	−77.6686	−2.55788
$923$	−13.6695	−0.449937
$924$	0	0
$925$	−13.0101	−0.427768
$926$	9.26102	0.304336
$927$	0	0
$928$	−5.53191	−0.181594
$929$	−22.0833	−0.724530	−0.362265	−	0.932075i	$-0.617997\pi$
$929$	−22.0833	−0.724530	−0.362265	+	0.932075i	$0.617997\pi$
$930$	0	0
$931$	44.7070	1.46521
$932$	−69.9237	−2.29043
$933$	0	0
$934$	−14.3969	−0.471080
$935$	0	0
$936$	0	0
$937$	−12.0955	−0.395143	−0.197572	−	0.980288i	$-0.563306\pi$
$937$	−12.0955	−0.395143	−0.197572	+	0.980288i	$0.563306\pi$
$938$	−9.08253	−0.296555
$939$	0	0
$940$	17.2500	0.562632
$941$	−20.6359	−0.672710	−0.336355	−	0.941735i	$-0.609194\pi$
$941$	−20.6359	−0.672710	−0.336355	+	0.941735i	$0.609194\pi$
$942$	0	0
$943$	41.0821	1.33782
$944$	−27.9738	−0.910471
$945$	0	0
$946$	0	0
$947$	5.27445	0.171397	0.0856983	−	0.996321i	$-0.472688\pi$
$947$	5.27445	0.171397	0.0856983	+	0.996321i	$0.472688\pi$
$948$	0	0
$949$	41.2757	1.33986
$950$	−37.8564	−1.22822
$951$	0	0
$952$	−57.6703	−1.86911
$953$	53.4076	1.73004	0.865020	−	0.501737i	$-0.167306\pi$
$953$	53.4076	1.73004	0.865020	+	0.501737i	$0.167306\pi$
$954$	0	0
$955$	−18.5759	−0.601101
$956$	−0.809640	−0.0261856
$957$	0	0
$958$	63.2050	2.04206
$959$	1.96525	0.0634614
$960$	0	0
$961$	−28.1511	−0.908099
$962$	−28.8061	−0.928744
$963$	0	0
$964$	−60.1131	−1.93611
$965$	−17.1258	−0.551297
$966$	0	0
$967$	−44.5529	−1.43273	−0.716363	−	0.697728i	$-0.754194\pi$
$967$	−44.5529	−1.43273	−0.716363	+	0.697728i	$0.754194\pi$
$968$	0	0
$969$	0	0
$970$	0.904351	0.0290370
$971$	39.6181	1.27140	0.635702	−	0.771934i	$-0.280711\pi$
$971$	39.6181	1.27140	0.635702	+	0.771934i	$0.280711\pi$
$972$	0	0
$973$	−77.1122	−2.47210
$974$	−13.0744	−0.418932
$975$	0	0
$976$	20.7924	0.665547
$977$	56.8503	1.81880	0.909402	−	0.415918i	$-0.136540\pi$
$977$	56.8503	1.81880	0.909402	+	0.415918i	$0.136540\pi$
$978$	0	0
$979$	0	0
$980$	−46.8633	−1.49699
$981$	0	0
$982$	−6.06382	−0.193504
$983$	−11.1761	−0.356462	−0.178231	−	0.983989i	$-0.557037\pi$
$983$	−11.1761	−0.356462	−0.178231	+	0.983989i	$0.557037\pi$
$984$	0	0
$985$	6.00600	0.191367
$986$	−67.7280	−2.15690
$987$	0	0
$988$	−56.1251	−1.78558
$989$	−7.32482	−0.232916
$990$	0	0
$991$	−37.0475	−1.17685	−0.588426	−	0.808551i	$-0.700252\pi$
$991$	−37.0475	−1.17685	−0.588426	+	0.808551i	$0.700252\pi$
$992$	−0.895898	−0.0284448
$993$	0	0
$994$	−40.1770	−1.27434
$995$	10.0075	0.317260
$996$	0	0
$997$	−43.0930	−1.36477	−0.682385	−	0.730993i	$-0.739057\pi$
$997$	−43.0930	−1.36477	−0.682385	+	0.730993i	$0.739057\pi$
$998$	54.8716	1.73693
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3267.2.a.bi.1.8		8
3.2	odd	2	inner	3267.2.a.bi.1.1		8
11.7	odd	10		297.2.f.b.82.1	✓	16
11.8	odd	10		297.2.f.b.163.1	yes	16
11.10	odd	2		3267.2.a.bj.1.1		8
33.8	even	10		297.2.f.b.163.4	yes	16
33.29	even	10		297.2.f.b.82.4	yes	16
33.32	even	2		3267.2.a.bj.1.8		8
99.7	odd	30		891.2.n.h.676.1		32
99.29	even	30		891.2.n.h.676.4		32
99.40	odd	30		891.2.n.h.379.4		32
99.41	even	30		891.2.n.h.460.4		32
99.52	odd	30		891.2.n.h.757.4		32
99.74	even	30		891.2.n.h.757.1		32
99.85	odd	30		891.2.n.h.460.1		32
99.95	even	30		891.2.n.h.379.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.f.b.82.1	✓	16	11.7	odd	10
297.2.f.b.82.4	yes	16	33.29	even	10
297.2.f.b.163.1	yes	16	11.8	odd	10
297.2.f.b.163.4	yes	16	33.8	even	10
891.2.n.h.379.1		32	99.95	even	30
891.2.n.h.379.4		32	99.40	odd	30
891.2.n.h.460.1		32	99.85	odd	30
891.2.n.h.460.4		32	99.41	even	30
891.2.n.h.676.1		32	99.7	odd	30
891.2.n.h.676.4		32	99.29	even	30
891.2.n.h.757.1		32	99.74	even	30
891.2.n.h.757.4		32	99.52	odd	30
3267.2.a.bi.1.1		8	3.2	odd	2	inner
3267.2.a.bi.1.8		8	1.1	even	1	trivial
3267.2.a.bj.1.1		8	11.10	odd	2
3267.2.a.bj.1.8		8	33.32	even	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:	\( N \)	\(=\)	\( 3267 = 3^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3267.a (trivial)

\(f(q)\)	\(=\)	\(q+2.46033 q^{2} +4.05323 q^{4} -0.989783 q^{5} -4.32219 q^{7} +5.05161 q^{8} -2.43519 q^{10} -3.61803 q^{13} -10.6340 q^{14} +4.32219 q^{16} +2.64130 q^{17} +3.82722 q^{19} -4.01181 q^{20} -3.45011 q^{23} -4.02033 q^{25} -8.90156 q^{26} -17.5188 q^{28} -10.4221 q^{29} -1.68787 q^{31} +0.530785 q^{32} +6.49848 q^{34} +4.27803 q^{35} +3.23607 q^{37} +9.41623 q^{38} -5.00000 q^{40} -11.9075 q^{41} +2.12307 q^{43} -8.48842 q^{46} -4.29980 q^{47} +11.6813 q^{49} -9.89134 q^{50} -14.6647 q^{52} +9.48236 q^{53} -21.8340 q^{56} -25.6419 q^{58} -6.47214 q^{59} +4.81061 q^{61} -4.15273 q^{62} -7.33847 q^{64} +3.58107 q^{65} +0.854102 q^{67} +10.7058 q^{68} +10.5254 q^{70} +3.77816 q^{71} -11.4083 q^{73} +7.96180 q^{74} +15.5126 q^{76} -6.14340 q^{79} -4.27803 q^{80} -29.2963 q^{82} +3.36003 q^{83} -2.61432 q^{85} +5.22344 q^{86} +13.2605 q^{89} +15.6378 q^{91} -13.9841 q^{92} -10.5789 q^{94} -3.78812 q^{95} -0.371367 q^{97} +28.7399 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 10 q^{4} - 10 q^{7} - 6 q^{10} - 20 q^{13} + 10 q^{16} - 14 q^{19} + 6 q^{25} - 26 q^{28} + 2 q^{31} - 24 q^{34} + 8 q^{37} - 40 q^{40} - 12 q^{43} - 32 q^{46} + 22 q^{49} - 30 q^{52} - 62 q^{58}+ \cdots + 6 q^{97}+O(q^{100}) \) 8 * q + 10 * q^4 - 10 * q^7 - 6 * q^10 - 20 * q^13 + 10 * q^16 - 14 * q^19 + 6 * q^25 - 26 * q^28 + 2 * q^31 - 24 * q^34 + 8 * q^37 - 40 * q^40 - 12 * q^43 - 32 * q^46 + 22 * q^49 - 30 * q^52 - 62 * q^58 - 22 * q^61 - 34 * q^64 - 20 * q^67 + 26 * q^70 - 60 * q^73 - 30 * q^76 + 18 * q^79 - 2 * q^82 - 66 * q^85 + 20 * q^91 - 20 * q^94 + 6 * q^97

Introduction

L-functions

Modular forms

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