LMFDB - Embedded newform 3267.2.a.q.1.2

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:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2]$
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			1.2
Root			$1.73205$ 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)

$f(q)$	$=$	$q+2.73205 q^{2} +5.46410 q^{4} +0.732051 q^{5} +3.73205 q^{7} +9.46410 q^{8} +O(q^{10})$	$q+2.73205 q^{2} +5.46410 q^{4} +0.732051 q^{5} +3.73205 q^{7} +9.46410 q^{8} +2.00000 q^{10} +0.267949 q^{13} +10.1962 q^{14} +14.9282 q^{16} -4.19615 q^{17} +5.19615 q^{19} +4.00000 q^{20} -8.00000 q^{23} -4.46410 q^{25} +0.732051 q^{26} +20.3923 q^{28} -1.26795 q^{29} +0.535898 q^{31} +21.8564 q^{32} -11.4641 q^{34} +2.73205 q^{35} -6.46410 q^{37} +14.1962 q^{38} +6.92820 q^{40} +1.46410 q^{41} -3.46410 q^{43} -21.8564 q^{46} -10.1962 q^{47} +6.92820 q^{49} -12.1962 q^{50} +1.46410 q^{52} -4.73205 q^{53} +35.3205 q^{56} -3.46410 q^{58} -10.1962 q^{59} +4.26795 q^{61} +1.46410 q^{62} +29.8564 q^{64} +0.196152 q^{65} +5.92820 q^{67} -22.9282 q^{68} +7.46410 q^{70} +13.8564 q^{71} -3.19615 q^{73} -17.6603 q^{74} +28.3923 q^{76} +5.73205 q^{79} +10.9282 q^{80} +4.00000 q^{82} -3.07180 q^{85} -9.46410 q^{86} +0.339746 q^{89} +1.00000 q^{91} -43.7128 q^{92} -27.8564 q^{94} +3.80385 q^{95} -5.39230 q^{97} +18.9282 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 4 q^{4} - 2 q^{5} + 4 q^{7} + 12 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 + 4 * q^4 - 2 * q^5 + 4 * q^7 + 12 * q^8	$ 2 q + 2 q^{2} + 4 q^{4} - 2 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{10} + 4 q^{13} + 10 q^{14} + 16 q^{16} + 2 q^{17} + 8 q^{20} - 16 q^{23} - 2 q^{25} - 2 q^{26} + 20 q^{28} - 6 q^{29} + 8 q^{31} + 16 q^{32} - 16 q^{34} + 2 q^{35} - 6 q^{37} + 18 q^{38} - 4 q^{41} - 16 q^{46} - 10 q^{47} - 14 q^{50} - 4 q^{52} - 6 q^{53} + 36 q^{56} - 10 q^{59} + 12 q^{61} - 4 q^{62} + 32 q^{64} - 10 q^{65} - 2 q^{67} - 32 q^{68} + 8 q^{70} + 4 q^{73} - 18 q^{74} + 36 q^{76} + 8 q^{79} + 8 q^{80} + 8 q^{82} - 20 q^{85} - 12 q^{86} + 18 q^{89} + 2 q^{91} - 32 q^{92} - 28 q^{94} + 18 q^{95} + 10 q^{97} + 24 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + 4 * q^4 - 2 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^10 + 4 * q^13 + 10 * q^14 + 16 * q^16 + 2 * q^17 + 8 * q^20 - 16 * q^23 - 2 * q^25 - 2 * q^26 + 20 * q^28 - 6 * q^29 + 8 * q^31 + 16 * q^32 - 16 * q^34 + 2 * q^35 - 6 * q^37 + 18 * q^38 - 4 * q^41 - 16 * q^46 - 10 * q^47 - 14 * q^50 - 4 * q^52 - 6 * q^53 + 36 * q^56 - 10 * q^59 + 12 * q^61 - 4 * q^62 + 32 * q^64 - 10 * q^65 - 2 * q^67 - 32 * q^68 + 8 * q^70 + 4 * q^73 - 18 * q^74 + 36 * q^76 + 8 * q^79 + 8 * q^80 + 8 * q^82 - 20 * q^85 - 12 * q^86 + 18 * q^89 + 2 * q^91 - 32 * q^92 - 28 * q^94 + 18 * q^95 + 10 * q^97 + 24 * q^98

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 $

$2$	2.73205	1.93185	0.965926	−	0.258819i	$-0.0833333\pi$
$2$	2.73205	1.93185	0.965926	+	0.258819i	$0.0833333\pi$
$3$	0	0
$3$	0	0
$4$	5.46410	2.73205
$5$	0.732051	0.327383	0.163692	−	0.986512i	$-0.447660\pi$
$5$	0.732051	0.327383	0.163692	+	0.986512i	$0.447660\pi$
$6$	0	0
$7$	3.73205	1.41058	0.705291	−	0.708918i	$-0.250816\pi$
$7$	3.73205	1.41058	0.705291	+	0.708918i	$0.250816\pi$
$8$	9.46410	3.34607
$9$	0	0
$10$	2.00000	0.632456
$11$	0	0
$11$	0	0
$12$	0	0
$13$	0.267949	0.0743157	0.0371579	−	0.999309i	$-0.488170\pi$
$13$	0.267949	0.0743157	0.0371579	+	0.999309i	$0.488170\pi$
$14$	10.1962	2.72504
$15$	0	0
$16$	14.9282	3.73205
$17$	−4.19615	−1.01772	−0.508858	−	0.860850i	$-0.669932\pi$
$17$	−4.19615	−1.01772	−0.508858	+	0.860850i	$0.669932\pi$
$18$	0	0
$19$	5.19615	1.19208	0.596040	−	0.802955i	$-0.296740\pi$
$19$	5.19615	1.19208	0.596040	+	0.802955i	$0.296740\pi$
$20$	4.00000	0.894427
$21$	0	0
$22$	0	0
$23$	−8.00000	−1.66812	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000	−1.66812	−0.834058	+	0.551677i	$0.813988\pi$
$24$	0	0
$25$	−4.46410	−0.892820
$26$	0.732051	0.143567
$27$	0	0
$28$	20.3923	3.85378
$29$	−1.26795	−0.235452	−0.117726	−	0.993046i	$-0.537560\pi$
$29$	−1.26795	−0.235452	−0.117726	+	0.993046i	$0.537560\pi$
$30$	0	0
$31$	0.535898	0.0962502	0.0481251	−	0.998841i	$-0.484675\pi$
$31$	0.535898	0.0962502	0.0481251	+	0.998841i	$0.484675\pi$
$32$	21.8564	3.86370
$33$	0	0
$34$	−11.4641	−1.96608
$35$	2.73205	0.461801
$36$	0	0
$37$	−6.46410	−1.06269	−0.531346	−	0.847155i	$-0.678314\pi$
$37$	−6.46410	−1.06269	−0.531346	+	0.847155i	$0.678314\pi$
$38$	14.1962	2.30292
$39$	0	0
$40$	6.92820	1.09545
$41$	1.46410	0.228654	0.114327	−	0.993443i	$-0.463529\pi$
$41$	1.46410	0.228654	0.114327	+	0.993443i	$0.463529\pi$
$42$	0	0
$43$	−3.46410	−0.528271	−0.264135	−	0.964486i	$-0.585087\pi$
$43$	−3.46410	−0.528271	−0.264135	+	0.964486i	$0.585087\pi$
$44$	0	0
$45$	0	0
$46$	−21.8564	−3.22255
$47$	−10.1962	−1.48726	−0.743631	−	0.668590i	$-0.766898\pi$
$47$	−10.1962	−1.48726	−0.743631	+	0.668590i	$0.766898\pi$
$48$	0	0
$49$	6.92820	0.989743
$50$	−12.1962	−1.72480
$51$	0	0
$52$	1.46410	0.203034
$53$	−4.73205	−0.649997	−0.324999	−	0.945715i	$-0.605364\pi$
$53$	−4.73205	−0.649997	−0.324999	+	0.945715i	$0.605364\pi$
$54$	0	0
$55$	0	0
$56$	35.3205	4.71990
$57$	0	0
$58$	−3.46410	−0.454859
$59$	−10.1962	−1.32743	−0.663713	−	0.747987i	$-0.731020\pi$
$59$	−10.1962	−1.32743	−0.663713	+	0.747987i	$0.731020\pi$
$60$	0	0
$61$	4.26795	0.546455	0.273227	−	0.961949i	$-0.411909\pi$
$61$	4.26795	0.546455	0.273227	+	0.961949i	$0.411909\pi$
$62$	1.46410	0.185941
$63$	0	0
$64$	29.8564	3.73205
$65$	0.196152	0.0243297
$66$	0	0
$67$	5.92820	0.724245	0.362123	−	0.932130i	$-0.382052\pi$
$67$	5.92820	0.724245	0.362123	+	0.932130i	$0.382052\pi$
$68$	−22.9282	−2.78045
$69$	0	0
$70$	7.46410	0.892131
$71$	13.8564	1.64445	0.822226	−	0.569160i	$-0.192732\pi$
$71$	13.8564	1.64445	0.822226	+	0.569160i	$0.192732\pi$
$72$	0	0
$73$	−3.19615	−0.374081	−0.187041	−	0.982352i	$-0.559890\pi$
$73$	−3.19615	−0.374081	−0.187041	+	0.982352i	$0.559890\pi$
$74$	−17.6603	−2.05296
$75$	0	0
$76$	28.3923	3.25682
$77$	0	0
$78$	0	0
$79$	5.73205	0.644906	0.322453	−	0.946585i	$-0.395493\pi$
$79$	5.73205	0.644906	0.322453	+	0.946585i	$0.395493\pi$
$80$	10.9282	1.22181
$81$	0	0
$82$	4.00000	0.441726
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	−3.07180	−0.333183
$86$	−9.46410	−1.02054
$87$	0	0
$88$	0	0
$89$	0.339746	0.0360130	0.0180065	−	0.999838i	$-0.494268\pi$
$89$	0.339746	0.0360130	0.0180065	+	0.999838i	$0.494268\pi$
$90$	0	0
$91$	1.00000	0.104828
$92$	−43.7128	−4.55738
$93$	0	0
$94$	−27.8564	−2.87317
$95$	3.80385	0.390267
$96$	0	0
$97$	−5.39230	−0.547506	−0.273753	−	0.961800i	$-0.588265\pi$
$97$	−5.39230	−0.547506	−0.273753	+	0.961800i	$0.588265\pi$
$98$	18.9282	1.91204
$99$	0	0
$100$	−24.3923	−2.43923
$101$	−0.196152	−0.0195179	−0.00975895	−	0.999952i	$-0.503106\pi$
$101$	−0.196152	−0.0195179	−0.00975895	+	0.999952i	$0.503106\pi$
$102$	0	0
$103$	12.8564	1.26678	0.633390	−	0.773833i	$-0.281663\pi$
$103$	12.8564	1.26678	0.633390	+	0.773833i	$0.281663\pi$
$104$	2.53590	0.248665
$105$	0	0
$106$	−12.9282	−1.25570
$107$	5.66025	0.547197	0.273599	−	0.961844i	$-0.411786\pi$
$107$	5.66025	0.547197	0.273599	+	0.961844i	$0.411786\pi$
$108$	0	0
$109$	−11.8564	−1.13564	−0.567819	−	0.823154i	$-0.692213\pi$
$109$	−11.8564	−1.13564	−0.567819	+	0.823154i	$0.692213\pi$
$110$	0	0
$111$	0	0
$112$	55.7128	5.26437
$113$	11.6603	1.09690	0.548452	−	0.836182i	$-0.315217\pi$
$113$	11.6603	1.09690	0.548452	+	0.836182i	$0.315217\pi$
$114$	0	0
$115$	−5.85641	−0.546113
$116$	−6.92820	−0.643268
$117$	0	0
$118$	−27.8564	−2.56439
$119$	−15.6603	−1.43557
$120$	0	0
$121$	0	0
$122$	11.6603	1.05567
$123$	0	0
$124$	2.92820	0.262960
$125$	−6.92820	−0.619677
$126$	0	0
$127$	−5.46410	−0.484861	−0.242430	−	0.970169i	$-0.577945\pi$
$127$	−5.46410	−0.484861	−0.242430	+	0.970169i	$0.577945\pi$
$128$	37.8564	3.34607
$129$	0	0
$130$	0.535898	0.0470014
$131$	−15.1244	−1.32142	−0.660711	−	0.750641i	$-0.729745\pi$
$131$	−15.1244	−1.32142	−0.660711	+	0.750641i	$0.729745\pi$
$132$	0	0
$133$	19.3923	1.68153
$134$	16.1962	1.39913
$135$	0	0
$136$	−39.7128	−3.40535
$137$	8.39230	0.717003	0.358501	−	0.933529i	$-0.383288\pi$
$137$	8.39230	0.717003	0.358501	+	0.933529i	$0.383288\pi$
$138$	0	0
$139$	7.19615	0.610370	0.305185	−	0.952293i	$-0.401282\pi$
$139$	7.19615	0.610370	0.305185	+	0.952293i	$0.401282\pi$
$140$	14.9282	1.26166
$141$	0	0
$142$	37.8564	3.17684
$143$	0	0
$144$	0	0
$145$	−0.928203	−0.0770831
$146$	−8.73205	−0.722670
$147$	0	0
$148$	−35.3205	−2.90333
$149$	9.85641	0.807468	0.403734	−	0.914876i	$-0.367712\pi$
$149$	9.85641	0.807468	0.403734	+	0.914876i	$0.367712\pi$
$150$	0	0
$151$	4.80385	0.390932	0.195466	−	0.980711i	$-0.437378\pi$
$151$	4.80385	0.390932	0.195466	+	0.980711i	$0.437378\pi$
$152$	49.1769	3.98877
$153$	0	0
$154$	0	0
$155$	0.392305	0.0315107
$156$	0	0
$157$	10.5359	0.840856	0.420428	−	0.907326i	$-0.361880\pi$
$157$	10.5359	0.840856	0.420428	+	0.907326i	$0.361880\pi$
$158$	15.6603	1.24586
$159$	0	0
$160$	16.0000	1.26491
$161$	−29.8564	−2.35301
$162$	0	0
$163$	19.0000	1.48819	0.744097	−	0.668071i	$-0.232880\pi$
$163$	19.0000	1.48819	0.744097	+	0.668071i	$0.232880\pi$
$164$	8.00000	0.624695
$165$	0	0
$166$	0	0
$167$	22.7321	1.75906	0.879529	−	0.475844i	$-0.157857\pi$
$167$	22.7321	1.75906	0.879529	+	0.475844i	$0.157857\pi$
$168$	0	0
$169$	−12.9282	−0.994477
$170$	−8.39230	−0.643660
$171$	0	0
$172$	−18.9282	−1.44326
$173$	−4.39230	−0.333941	−0.166970	−	0.985962i	$-0.553398\pi$
$173$	−4.39230	−0.333941	−0.166970	+	0.985962i	$0.553398\pi$
$174$	0	0
$175$	−16.6603	−1.25940
$176$	0	0
$177$	0	0
$178$	0.928203	0.0695718
$179$	14.1962	1.06107	0.530535	−	0.847663i	$-0.321991\pi$
$179$	14.1962	1.06107	0.530535	+	0.847663i	$0.321991\pi$
$180$	0	0
$181$	−16.3205	−1.21309	−0.606547	−	0.795048i	$-0.707446\pi$
$181$	−16.3205	−1.21309	−0.606547	+	0.795048i	$0.707446\pi$
$182$	2.73205	0.202513
$183$	0	0
$184$	−75.7128	−5.58162
$185$	−4.73205	−0.347907
$186$	0	0
$187$	0	0
$188$	−55.7128	−4.06327
$189$	0	0
$190$	10.3923	0.753937
$191$	4.00000	0.289430	0.144715	−	0.989473i	$-0.453773\pi$
$191$	4.00000	0.289430	0.144715	+	0.989473i	$0.453773\pi$
$192$	0	0
$193$	2.80385	0.201825	0.100913	−	0.994895i	$-0.467824\pi$
$193$	2.80385	0.201825	0.100913	+	0.994895i	$0.467824\pi$
$194$	−14.7321	−1.05770
$195$	0	0
$196$	37.8564	2.70403
$197$	9.66025	0.688265	0.344132	−	0.938921i	$-0.388173\pi$
$197$	9.66025	0.688265	0.344132	+	0.938921i	$0.388173\pi$
$198$	0	0
$199$	−15.0000	−1.06332	−0.531661	−	0.846957i	$-0.678432\pi$
$199$	−15.0000	−1.06332	−0.531661	+	0.846957i	$0.678432\pi$
$200$	−42.2487	−2.98744
$201$	0	0
$202$	−0.535898	−0.0377057
$203$	−4.73205	−0.332125
$204$	0	0
$205$	1.07180	0.0748575
$206$	35.1244	2.44723
$207$	0	0
$208$	4.00000	0.277350
$209$	0	0
$210$	0	0
$211$	9.33975	0.642975	0.321487	−	0.946914i	$-0.395817\pi$
$211$	9.33975	0.642975	0.321487	+	0.946914i	$0.395817\pi$
$212$	−25.8564	−1.77583
$213$	0	0
$214$	15.4641	1.05710
$215$	−2.53590	−0.172947
$216$	0	0
$217$	2.00000	0.135769
$218$	−32.3923	−2.19388
$219$	0	0
$220$	0	0
$221$	−1.12436	−0.0756323
$222$	0	0
$223$	17.8564	1.19575	0.597877	−	0.801588i	$-0.296011\pi$
$223$	17.8564	1.19575	0.597877	+	0.801588i	$0.296011\pi$
$224$	81.5692	5.45007
$225$	0	0
$226$	31.8564	2.11906
$227$	−29.6603	−1.96862	−0.984310	−	0.176447i	$-0.943540\pi$
$227$	−29.6603	−1.96862	−0.984310	+	0.176447i	$0.943540\pi$
$228$	0	0
$229$	−16.3923	−1.08323	−0.541617	−	0.840625i	$-0.682188\pi$
$229$	−16.3923	−1.08323	−0.541617	+	0.840625i	$0.682188\pi$
$230$	−16.0000	−1.05501
$231$	0	0
$232$	−12.0000	−0.787839
$233$	−6.33975	−0.415331	−0.207665	−	0.978200i	$-0.566586\pi$
$233$	−6.33975	−0.415331	−0.207665	+	0.978200i	$0.566586\pi$
$234$	0	0
$235$	−7.46410	−0.486904
$236$	−55.7128	−3.62660
$237$	0	0
$238$	−42.7846	−2.77331
$239$	16.3923	1.06033	0.530165	−	0.847894i	$-0.322130\pi$
$239$	16.3923	1.06033	0.530165	+	0.847894i	$0.322130\pi$
$240$	0	0
$241$	−15.1962	−0.978870	−0.489435	−	0.872040i	$-0.662797\pi$
$241$	−15.1962	−0.978870	−0.489435	+	0.872040i	$0.662797\pi$
$242$	0	0
$243$	0	0
$244$	23.3205	1.49294
$245$	5.07180	0.324025
$246$	0	0
$247$	1.39230	0.0885902
$248$	5.07180	0.322059
$249$	0	0
$250$	−18.9282	−1.19712
$251$	−10.5885	−0.668337	−0.334169	−	0.942513i	$-0.608456\pi$
$251$	−10.5885	−0.668337	−0.334169	+	0.942513i	$0.608456\pi$
$252$	0	0
$253$	0	0
$254$	−14.9282	−0.936679
$255$	0	0
$256$	43.7128	2.73205
$257$	12.7321	0.794204	0.397102	−	0.917775i	$-0.370016\pi$
$257$	12.7321	0.794204	0.397102	+	0.917775i	$0.370016\pi$
$258$	0	0
$259$	−24.1244	−1.49901
$260$	1.07180	0.0664700
$261$	0	0
$262$	−41.3205	−2.55279
$263$	4.87564	0.300645	0.150323	−	0.988637i	$-0.451969\pi$
$263$	4.87564	0.300645	0.150323	+	0.988637i	$0.451969\pi$
$264$	0	0
$265$	−3.46410	−0.212798
$266$	52.9808	3.24846
$267$	0	0
$268$	32.3923	1.97867
$269$	26.9282	1.64184	0.820921	−	0.571042i	$-0.193461\pi$
$269$	26.9282	1.64184	0.820921	+	0.571042i	$0.193461\pi$
$270$	0	0
$271$	2.26795	0.137768	0.0688841	−	0.997625i	$-0.478056\pi$
$271$	2.26795	0.137768	0.0688841	+	0.997625i	$0.478056\pi$
$272$	−62.6410	−3.79817
$273$	0	0
$274$	22.9282	1.38514
$275$	0	0
$276$	0	0
$277$	9.85641	0.592214	0.296107	−	0.955155i	$-0.404311\pi$
$277$	9.85641	0.592214	0.296107	+	0.955155i	$0.404311\pi$
$278$	19.6603	1.17914
$279$	0	0
$280$	25.8564	1.54522
$281$	0	0		−	1.00000i	$-0.5\pi$
$281$	0	0			1.00000i	$0.5\pi$
$282$	0	0
$283$	26.2487	1.56032	0.780162	−	0.625578i	$-0.215137\pi$
$283$	26.2487	1.56032	0.780162	+	0.625578i	$0.215137\pi$
$284$	75.7128	4.49273
$285$	0	0
$286$	0	0
$287$	5.46410	0.322536
$288$	0	0
$289$	0.607695	0.0357468
$290$	−2.53590	−0.148913
$291$	0	0
$292$	−17.4641	−1.02201
$293$	−27.1244	−1.58462	−0.792311	−	0.610118i	$-0.791122\pi$
$293$	−27.1244	−1.58462	−0.792311	+	0.610118i	$0.791122\pi$
$294$	0	0
$295$	−7.46410	−0.434577
$296$	−61.1769	−3.55584
$297$	0	0
$298$	26.9282	1.55991
$299$	−2.14359	−0.123967
$300$	0	0
$301$	−12.9282	−0.745169
$302$	13.1244	0.755222
$303$	0	0
$304$	77.5692	4.44890
$305$	3.12436	0.178900
$306$	0	0
$307$	27.3205	1.55926	0.779632	−	0.626238i	$-0.215406\pi$
$307$	27.3205	1.55926	0.779632	+	0.626238i	$0.215406\pi$
$308$	0	0
$309$	0	0
$310$	1.07180	0.0608740
$311$	−30.5885	−1.73451	−0.867256	−	0.497862i	$-0.834119\pi$
$311$	−30.5885	−1.73451	−0.867256	+	0.497862i	$0.834119\pi$
$312$	0	0
$313$	−1.92820	−0.108988	−0.0544942	−	0.998514i	$-0.517355\pi$
$313$	−1.92820	−0.108988	−0.0544942	+	0.998514i	$0.517355\pi$
$314$	28.7846	1.62441
$315$	0	0
$316$	31.3205	1.76192
$317$	−10.5885	−0.594707	−0.297354	−	0.954767i	$-0.596104\pi$
$317$	−10.5885	−0.594707	−0.297354	+	0.954767i	$0.596104\pi$
$318$	0	0
$319$	0	0
$320$	21.8564	1.22181
$321$	0	0
$322$	−81.5692	−4.54567
$323$	−21.8038	−1.21320
$324$	0	0
$325$	−1.19615	−0.0663506
$326$	51.9090	2.87497
$327$	0	0
$328$	13.8564	0.765092
$329$	−38.0526	−2.09791
$330$	0	0
$331$	−27.3923	−1.50562	−0.752809	−	0.658239i	$-0.771301\pi$
$331$	−27.3923	−1.50562	−0.752809	+	0.658239i	$0.771301\pi$
$332$	0	0
$333$	0	0
$334$	62.1051	3.39824
$335$	4.33975	0.237106
$336$	0	0
$337$	29.9808	1.63316	0.816578	−	0.577235i	$-0.195868\pi$
$337$	29.9808	1.63316	0.816578	+	0.577235i	$0.195868\pi$
$338$	−35.3205	−1.92118
$339$	0	0
$340$	−16.7846	−0.910273
$341$	0	0
$342$	0	0
$343$	−0.267949	−0.0144679
$344$	−32.7846	−1.76763
$345$	0	0
$346$	−12.0000	−0.645124
$347$	10.3397	0.555067	0.277533	−	0.960716i	$-0.410483\pi$
$347$	10.3397	0.555067	0.277533	+	0.960716i	$0.410483\pi$
$348$	0	0
$349$	5.87564	0.314516	0.157258	−	0.987558i	$-0.449735\pi$
$349$	5.87564	0.314516	0.157258	+	0.987558i	$0.449735\pi$
$350$	−45.5167	−2.43297
$351$	0	0
$352$	0	0
$353$	−21.1244	−1.12434	−0.562168	−	0.827023i	$-0.690033\pi$
$353$	−21.1244	−1.12434	−0.562168	+	0.827023i	$0.690033\pi$
$354$	0	0
$355$	10.1436	0.538366
$356$	1.85641	0.0983893
$357$	0	0
$358$	38.7846	2.04983
$359$	6.53590	0.344952	0.172476	−	0.985014i	$-0.444823\pi$
$359$	6.53590	0.344952	0.172476	+	0.985014i	$0.444823\pi$
$360$	0	0
$361$	8.00000	0.421053
$362$	−44.5885	−2.34352
$363$	0	0
$364$	5.46410	0.286397
$365$	−2.33975	−0.122468
$366$	0	0
$367$	13.9282	0.727046	0.363523	−	0.931585i	$-0.381574\pi$
$367$	13.9282	0.727046	0.363523	+	0.931585i	$0.381574\pi$
$368$	−119.426	−6.22549
$369$	0	0
$370$	−12.9282	−0.672105
$371$	−17.6603	−0.916875
$372$	0	0
$373$	20.1244	1.04200	0.521000	−	0.853557i	$-0.325559\pi$
$373$	20.1244	1.04200	0.521000	+	0.853557i	$0.325559\pi$
$374$	0	0
$375$	0	0
$376$	−96.4974	−4.97647
$377$	−0.339746	−0.0174978
$378$	0	0
$379$	14.8564	0.763122	0.381561	−	0.924344i	$-0.375387\pi$
$379$	14.8564	0.763122	0.381561	+	0.924344i	$0.375387\pi$
$380$	20.7846	1.06623
$381$	0	0
$382$	10.9282	0.559136
$383$	−24.7321	−1.26375	−0.631874	−	0.775071i	$-0.717714\pi$
$383$	−24.7321	−1.26375	−0.631874	+	0.775071i	$0.717714\pi$
$384$	0	0
$385$	0	0
$386$	7.66025	0.389897
$387$	0	0
$388$	−29.4641	−1.49581
$389$	−21.4641	−1.08827	−0.544137	−	0.838997i	$-0.683143\pi$
$389$	−21.4641	−1.08827	−0.544137	+	0.838997i	$0.683143\pi$
$390$	0	0
$391$	33.5692	1.69767
$392$	65.5692	3.31175
$393$	0	0
$394$	26.3923	1.32963
$395$	4.19615	0.211131
$396$	0	0
$397$	20.3923	1.02346	0.511730	−	0.859146i	$-0.329005\pi$
$397$	20.3923	1.02346	0.511730	+	0.859146i	$0.329005\pi$
$398$	−40.9808	−2.05418
$399$	0	0
$400$	−66.6410	−3.33205
$401$	6.53590	0.326387	0.163194	−	0.986594i	$-0.447820\pi$
$401$	6.53590	0.326387	0.163194	+	0.986594i	$0.447820\pi$
$402$	0	0
$403$	0.143594	0.00715290
$404$	−1.07180	−0.0533239
$405$	0	0
$406$	−12.9282	−0.641616
$407$	0	0
$408$	0	0
$409$	−32.9090	−1.62724	−0.813622	−	0.581394i	$-0.802507\pi$
$409$	−32.9090	−1.62724	−0.813622	+	0.581394i	$0.802507\pi$
$410$	2.92820	0.144614
$411$	0	0
$412$	70.2487	3.46091
$413$	−38.0526	−1.87244
$414$	0	0
$415$	0	0
$416$	5.85641	0.287134
$417$	0	0
$418$	0	0
$419$	−23.7128	−1.15845	−0.579223	−	0.815169i	$-0.696644\pi$
$419$	−23.7128	−1.15845	−0.579223	+	0.815169i	$0.696644\pi$
$420$	0	0
$421$	20.8564	1.01648	0.508240	−	0.861216i	$-0.330296\pi$
$421$	20.8564	1.01648	0.508240	+	0.861216i	$0.330296\pi$
$422$	25.5167	1.24213
$423$	0	0
$424$	−44.7846	−2.17493
$425$	18.7321	0.908638
$426$	0	0
$427$	15.9282	0.770820
$428$	30.9282	1.49497
$429$	0	0
$430$	−6.92820	−0.334108
$431$	14.5359	0.700170	0.350085	−	0.936718i	$-0.386153\pi$
$431$	14.5359	0.700170	0.350085	+	0.936718i	$0.386153\pi$
$432$	0	0
$433$	−3.60770	−0.173375	−0.0866874	−	0.996236i	$-0.527628\pi$
$433$	−3.60770	−0.173375	−0.0866874	+	0.996236i	$0.527628\pi$
$434$	5.46410	0.262285
$435$	0	0
$436$	−64.7846	−3.10262
$437$	−41.5692	−1.98853
$438$	0	0
$439$	−30.5359	−1.45740	−0.728699	−	0.684834i	$-0.759875\pi$
$439$	−30.5359	−1.45740	−0.728699	+	0.684834i	$0.759875\pi$
$440$	0	0
$441$	0	0
$442$	−3.07180	−0.146110
$443$	3.26795	0.155265	0.0776325	−	0.996982i	$-0.475264\pi$
$443$	3.26795	0.155265	0.0776325	+	0.996982i	$0.475264\pi$
$444$	0	0
$445$	0.248711	0.0117900
$446$	48.7846	2.31002
$447$	0	0
$448$	111.426	5.26437
$449$	10.2487	0.483667	0.241833	−	0.970318i	$-0.422251\pi$
$449$	10.2487	0.483667	0.241833	+	0.970318i	$0.422251\pi$
$450$	0	0
$451$	0	0
$452$	63.7128	2.99680
$453$	0	0
$454$	−81.0333	−3.80308
$455$	0.732051	0.0343191
$456$	0	0
$457$	11.0718	0.517917	0.258958	−	0.965888i	$-0.416621\pi$
$457$	11.0718	0.517917	0.258958	+	0.965888i	$0.416621\pi$
$458$	−44.7846	−2.09265
$459$	0	0
$460$	−32.0000	−1.49201
$461$	−29.6603	−1.38142	−0.690708	−	0.723134i	$-0.742701\pi$
$461$	−29.6603	−1.38142	−0.690708	+	0.723134i	$0.742701\pi$
$462$	0	0
$463$	−25.7846	−1.19831	−0.599156	−	0.800632i	$-0.704497\pi$
$463$	−25.7846	−1.19831	−0.599156	+	0.800632i	$0.704497\pi$
$464$	−18.9282	−0.878720
$465$	0	0
$466$	−17.3205	−0.802357
$467$	18.9282	0.875893	0.437946	−	0.899001i	$-0.355706\pi$
$467$	18.9282	0.875893	0.437946	+	0.899001i	$0.355706\pi$
$468$	0	0
$469$	22.1244	1.02161
$470$	−20.3923	−0.940627
$471$	0	0
$472$	−96.4974	−4.44165
$473$	0	0
$474$	0	0
$475$	−23.1962	−1.06431
$476$	−85.5692	−3.92206
$477$	0	0
$478$	44.7846	2.04840
$479$	−11.5167	−0.526210	−0.263105	−	0.964767i	$-0.584747\pi$
$479$	−11.5167	−0.526210	−0.263105	+	0.964767i	$0.584747\pi$
$480$	0	0
$481$	−1.73205	−0.0789747
$482$	−41.5167	−1.89103
$483$	0	0
$484$	0	0
$485$	−3.94744	−0.179244
$486$	0	0
$487$	18.8564	0.854465	0.427233	−	0.904142i	$-0.359489\pi$
$487$	18.8564	0.854465	0.427233	+	0.904142i	$0.359489\pi$
$488$	40.3923	1.82847
$489$	0	0
$490$	13.8564	0.625969
$491$	−30.0526	−1.35625	−0.678126	−	0.734945i	$-0.737208\pi$
$491$	−30.0526	−1.35625	−0.678126	+	0.734945i	$0.737208\pi$
$492$	0	0
$493$	5.32051	0.239624
$494$	3.80385	0.171143
$495$	0	0
$496$	8.00000	0.359211
$497$	51.7128	2.31964
$498$	0	0
$499$	−19.4641	−0.871333	−0.435666	−	0.900108i	$-0.643487\pi$
$499$	−19.4641	−0.871333	−0.435666	+	0.900108i	$0.643487\pi$
$500$	−37.8564	−1.69299
$501$	0	0
$502$	−28.9282	−1.29113
$503$	22.9282	1.02232	0.511159	−	0.859486i	$-0.329216\pi$
$503$	22.9282	1.02232	0.511159	+	0.859486i	$0.329216\pi$
$504$	0	0
$505$	−0.143594	−0.00638983
$506$	0	0
$507$	0	0
$508$	−29.8564	−1.32466
$509$	−16.0526	−0.711517	−0.355759	−	0.934578i	$-0.615777\pi$
$509$	−16.0526	−0.711517	−0.355759	+	0.934578i	$0.615777\pi$
$510$	0	0
$511$	−11.9282	−0.527673
$512$	43.7128	1.93185
$513$	0	0
$514$	34.7846	1.53428
$515$	9.41154	0.414722
$516$	0	0
$517$	0	0
$518$	−65.9090	−2.89587
$519$	0	0
$520$	1.85641	0.0814088
$521$	−20.7846	−0.910590	−0.455295	−	0.890341i	$-0.650466\pi$
$521$	−20.7846	−0.910590	−0.455295	+	0.890341i	$0.650466\pi$
$522$	0	0
$523$	−39.9808	−1.74824	−0.874118	−	0.485713i	$-0.838560\pi$
$523$	−39.9808	−1.74824	−0.874118	+	0.485713i	$0.838560\pi$
$524$	−82.6410	−3.61019
$525$	0	0
$526$	13.3205	0.580802
$527$	−2.24871	−0.0979554
$528$	0	0
$529$	41.0000	1.78261
$530$	−9.46410	−0.411094
$531$	0	0
$532$	105.962	4.59401
$533$	0.392305	0.0169926
$534$	0	0
$535$	4.14359	0.179143
$536$	56.1051	2.42337
$537$	0	0
$538$	73.5692	3.17179
$539$	0	0
$540$	0	0
$541$	23.5885	1.01415	0.507073	−	0.861903i	$-0.330727\pi$
$541$	23.5885	1.01415	0.507073	+	0.861903i	$0.330727\pi$
$542$	6.19615	0.266148
$543$	0	0
$544$	−91.7128	−3.93215
$545$	−8.67949	−0.371789
$546$	0	0
$547$	16.8038	0.718481	0.359240	−	0.933245i	$-0.383036\pi$
$547$	16.8038	0.718481	0.359240	+	0.933245i	$0.383036\pi$
$548$	45.8564	1.95889
$549$	0	0
$550$	0	0
$551$	−6.58846	−0.280678
$552$	0	0
$553$	21.3923	0.909693
$554$	26.9282	1.14407
$555$	0	0
$556$	39.3205	1.66756
$557$	29.2679	1.24012	0.620061	−	0.784553i	$-0.287108\pi$
$557$	29.2679	1.24012	0.620061	+	0.784553i	$0.287108\pi$
$558$	0	0
$559$	−0.928203	−0.0392588
$560$	40.7846	1.72346
$561$	0	0
$562$	0	0
$563$	−35.7128	−1.50512	−0.752558	−	0.658526i	$-0.771180\pi$
$563$	−35.7128	−1.50512	−0.752558	+	0.658526i	$0.771180\pi$
$564$	0	0
$565$	8.53590	0.359108
$566$	71.7128	3.01431
$567$	0	0
$568$	131.138	5.50245
$569$	35.3205	1.48071	0.740356	−	0.672215i	$-0.234657\pi$
$569$	35.3205	1.48071	0.740356	+	0.672215i	$0.234657\pi$
$570$	0	0
$571$	−32.1244	−1.34436	−0.672181	−	0.740387i	$-0.734642\pi$
$571$	−32.1244	−1.34436	−0.672181	+	0.740387i	$0.734642\pi$
$572$	0	0
$573$	0	0
$574$	14.9282	0.623091
$575$	35.7128	1.48933
$576$	0	0
$577$	−3.00000	−0.124892	−0.0624458	−	0.998048i	$-0.519890\pi$
$577$	−3.00000	−0.124892	−0.0624458	+	0.998048i	$0.519890\pi$
$578$	1.66025	0.0690575
$579$	0	0
$580$	−5.07180	−0.210595
$581$	0	0
$582$	0	0
$583$	0	0
$584$	−30.2487	−1.25170
$585$	0	0
$586$	−74.1051	−3.06125
$587$	1.41154	0.0582606	0.0291303	−	0.999576i	$-0.490726\pi$
$587$	1.41154	0.0582606	0.0291303	+	0.999576i	$0.490726\pi$
$588$	0	0
$589$	2.78461	0.114738
$590$	−20.3923	−0.839538
$591$	0	0
$592$	−96.4974	−3.96602
$593$	47.7128	1.95933	0.979665	−	0.200639i	$-0.0643019\pi$
$593$	47.7128	1.95933	0.979665	+	0.200639i	$0.0643019\pi$
$594$	0	0
$595$	−11.4641	−0.469982
$596$	53.8564	2.20604
$597$	0	0
$598$	−5.85641	−0.239486
$599$	−46.2487	−1.88967	−0.944836	−	0.327545i	$-0.893779\pi$
$599$	−46.2487	−1.88967	−0.944836	+	0.327545i	$0.893779\pi$
$600$	0	0
$601$	−3.85641	−0.157306	−0.0786531	−	0.996902i	$-0.525062\pi$
$601$	−3.85641	−0.157306	−0.0786531	+	0.996902i	$0.525062\pi$
$602$	−35.3205	−1.43956
$603$	0	0
$604$	26.2487	1.06804
$605$	0	0
$606$	0	0
$607$	37.5885	1.52567	0.762834	−	0.646594i	$-0.223807\pi$
$607$	37.5885	1.52567	0.762834	+	0.646594i	$0.223807\pi$
$608$	113.569	4.60584
$609$	0	0
$610$	8.53590	0.345608
$611$	−2.73205	−0.110527
$612$	0	0
$613$	−22.9090	−0.925284	−0.462642	−	0.886545i	$-0.653099\pi$
$613$	−22.9090	−0.925284	−0.462642	+	0.886545i	$0.653099\pi$
$614$	74.6410	3.01227
$615$	0	0
$616$	0	0
$617$	−37.8564	−1.52404	−0.762021	−	0.647553i	$-0.775793\pi$
$617$	−37.8564	−1.52404	−0.762021	+	0.647553i	$0.775793\pi$
$618$	0	0
$619$	20.4641	0.822522	0.411261	−	0.911518i	$-0.365089\pi$
$619$	20.4641	0.822522	0.411261	+	0.911518i	$0.365089\pi$
$620$	2.14359	0.0860888
$621$	0	0
$622$	−83.5692	−3.35082
$623$	1.26795	0.0507993
$624$	0	0
$625$	17.2487	0.689948
$626$	−5.26795	−0.210550
$627$	0	0
$628$	57.5692	2.29726
$629$	27.1244	1.08152
$630$	0	0
$631$	−3.39230	−0.135046	−0.0675228	−	0.997718i	$-0.521510\pi$
$631$	−3.39230	−0.135046	−0.0675228	+	0.997718i	$0.521510\pi$
$632$	54.2487	2.15790
$633$	0	0
$634$	−28.9282	−1.14889
$635$	−4.00000	−0.158735
$636$	0	0
$637$	1.85641	0.0735535
$638$	0	0
$639$	0	0
$640$	27.7128	1.09545
$641$	−2.87564	−0.113581	−0.0567906	−	0.998386i	$-0.518087\pi$
$641$	−2.87564	−0.113581	−0.0567906	+	0.998386i	$0.518087\pi$
$642$	0	0
$643$	30.3923	1.19856	0.599278	−	0.800541i	$-0.295455\pi$
$643$	30.3923	1.19856	0.599278	+	0.800541i	$0.295455\pi$
$644$	−163.138	−6.42856
$645$	0	0
$646$	−59.5692	−2.34372
$647$	−26.2487	−1.03194	−0.515972	−	0.856606i	$-0.672569\pi$
$647$	−26.2487	−1.03194	−0.515972	+	0.856606i	$0.672569\pi$
$648$	0	0
$649$	0	0
$650$	−3.26795	−0.128180
$651$	0	0
$652$	103.818	4.06582
$653$	29.4641	1.15302	0.576510	−	0.817090i	$-0.304414\pi$
$653$	29.4641	1.15302	0.576510	+	0.817090i	$0.304414\pi$
$654$	0	0
$655$	−11.0718	−0.432611
$656$	21.8564	0.853349
$657$	0	0
$658$	−103.962	−4.05284
$659$	−37.6603	−1.46704	−0.733518	−	0.679670i	$-0.762123\pi$
$659$	−37.6603	−1.46704	−0.733518	+	0.679670i	$0.762123\pi$
$660$	0	0
$661$	2.60770	0.101428	0.0507138	−	0.998713i	$-0.483850\pi$
$661$	2.60770	0.101428	0.0507138	+	0.998713i	$0.483850\pi$
$662$	−74.8372	−2.90863
$663$	0	0
$664$	0	0
$665$	14.1962	0.550503
$666$	0	0
$667$	10.1436	0.392762
$668$	124.210	4.80584
$669$	0	0
$670$	11.8564	0.458053
$671$	0	0
$672$	0	0
$673$	9.44486	0.364073	0.182036	−	0.983292i	$-0.441731\pi$
$673$	9.44486	0.364073	0.182036	+	0.983292i	$0.441731\pi$
$674$	81.9090	3.15502
$675$	0	0
$676$	−70.6410	−2.71696
$677$	30.2487	1.16255	0.581276	−	0.813706i	$-0.302554\pi$
$677$	30.2487	1.16255	0.581276	+	0.813706i	$0.302554\pi$
$678$	0	0
$679$	−20.1244	−0.772302
$680$	−29.0718	−1.11485
$681$	0	0
$682$	0	0
$683$	22.5885	0.864323	0.432162	−	0.901796i	$-0.357751\pi$
$683$	22.5885	0.864323	0.432162	+	0.901796i	$0.357751\pi$
$684$	0	0
$685$	6.14359	0.234735
$686$	−0.732051	−0.0279498
$687$	0	0
$688$	−51.7128	−1.97153
$689$	−1.26795	−0.0483050
$690$	0	0
$691$	−7.21539	−0.274486	−0.137243	−	0.990537i	$-0.543824\pi$
$691$	−7.21539	−0.274486	−0.137243	+	0.990537i	$0.543824\pi$
$692$	−24.0000	−0.912343
$693$	0	0
$694$	28.2487	1.07231
$695$	5.26795	0.199825
$696$	0	0
$697$	−6.14359	−0.232705
$698$	16.0526	0.607598
$699$	0	0
$700$	−91.0333	−3.44074
$701$	9.94744	0.375710	0.187855	−	0.982197i	$-0.439847\pi$
$701$	9.94744	0.375710	0.187855	+	0.982197i	$0.439847\pi$
$702$	0	0
$703$	−33.5885	−1.26681
$704$	0	0
$705$	0	0
$706$	−57.7128	−2.17205
$707$	−0.732051	−0.0275316
$708$	0	0
$709$	−35.3923	−1.32919	−0.664593	−	0.747206i	$-0.731395\pi$
$709$	−35.3923	−1.32919	−0.664593	+	0.747206i	$0.731395\pi$
$710$	27.7128	1.04004
$711$	0	0
$712$	3.21539	0.120502
$713$	−4.28719	−0.160556
$714$	0	0
$715$	0	0
$716$	77.5692	2.89890
$717$	0	0
$718$	17.8564	0.666395
$719$	−22.9808	−0.857038	−0.428519	−	0.903533i	$-0.640964\pi$
$719$	−22.9808	−0.857038	−0.428519	+	0.903533i	$0.640964\pi$
$720$	0	0
$721$	47.9808	1.78690
$722$	21.8564	0.813411
$723$	0	0
$724$	−89.1769	−3.31423
$725$	5.66025	0.210217
$726$	0	0
$727$	−29.3205	−1.08744	−0.543719	−	0.839268i	$-0.682984\pi$
$727$	−29.3205	−1.08744	−0.543719	+	0.839268i	$0.682984\pi$
$728$	9.46410	0.350763
$729$	0	0
$730$	−6.39230	−0.236590
$731$	14.5359	0.537630
$732$	0	0
$733$	−24.9282	−0.920744	−0.460372	−	0.887726i	$-0.652284\pi$
$733$	−24.9282	−0.920744	−0.460372	+	0.887726i	$0.652284\pi$
$734$	38.0526	1.40455
$735$	0	0
$736$	−174.851	−6.44510
$737$	0	0
$738$	0	0
$739$	34.2487	1.25986	0.629930	−	0.776652i	$-0.283084\pi$
$739$	34.2487	1.25986	0.629930	+	0.776652i	$0.283084\pi$
$740$	−25.8564	−0.950500
$741$	0	0
$742$	−48.2487	−1.77127
$743$	28.5885	1.04881	0.524404	−	0.851469i	$-0.324288\pi$
$743$	28.5885	1.04881	0.524404	+	0.851469i	$0.324288\pi$
$744$	0	0
$745$	7.21539	0.264351
$746$	54.9808	2.01299
$747$	0	0
$748$	0	0
$749$	21.1244	0.771867
$750$	0	0
$751$	−22.3205	−0.814487	−0.407243	−	0.913320i	$-0.633510\pi$
$751$	−22.3205	−0.814487	−0.407243	+	0.913320i	$0.633510\pi$
$752$	−152.210	−5.55054
$753$	0	0
$754$	−0.928203	−0.0338032
$755$	3.51666	0.127984
$756$	0	0
$757$	28.3205	1.02933	0.514663	−	0.857392i	$-0.327917\pi$
$757$	28.3205	1.02933	0.514663	+	0.857392i	$0.327917\pi$
$758$	40.5885	1.47424
$759$	0	0
$760$	36.0000	1.30586
$761$	−0.679492	−0.0246316	−0.0123158	−	0.999924i	$-0.503920\pi$
$761$	−0.679492	−0.0246316	−0.0123158	+	0.999924i	$0.503920\pi$
$762$	0	0
$763$	−44.2487	−1.60191
$764$	21.8564	0.790737
$765$	0	0
$766$	−67.5692	−2.44138
$767$	−2.73205	−0.0986486
$768$	0	0
$769$	25.5885	0.922743	0.461372	−	0.887207i	$-0.347357\pi$
$769$	25.5885	0.922743	0.461372	+	0.887207i	$0.347357\pi$
$770$	0	0
$771$	0	0
$772$	15.3205	0.551397
$773$	−21.1244	−0.759790	−0.379895	−	0.925030i	$-0.624040\pi$
$773$	−21.1244	−0.759790	−0.379895	+	0.925030i	$0.624040\pi$
$774$	0	0
$775$	−2.39230	−0.0859341
$776$	−51.0333	−1.83199
$777$	0	0
$778$	−58.6410	−2.10238
$779$	7.60770	0.272574
$780$	0	0
$781$	0	0
$782$	91.7128	3.27964
$783$	0	0
$784$	103.426	3.69377
$785$	7.71281	0.275282
$786$	0	0
$787$	−23.0526	−0.821735	−0.410867	−	0.911695i	$-0.634774\pi$
$787$	−23.0526	−0.821735	−0.410867	+	0.911695i	$0.634774\pi$
$788$	52.7846	1.88037
$789$	0	0
$790$	11.4641	0.407874
$791$	43.5167	1.54727
$792$	0	0
$793$	1.14359	0.0406102
$794$	55.7128	1.97717
$795$	0	0
$796$	−81.9615	−2.90505
$797$	−8.00000	−0.283375	−0.141687	−	0.989911i	$-0.545253\pi$
$797$	−8.00000	−0.283375	−0.141687	+	0.989911i	$0.545253\pi$
$798$	0	0
$799$	42.7846	1.51361
$800$	−97.5692	−3.44959
$801$	0	0
$802$	17.8564	0.630532
$803$	0	0
$804$	0	0
$805$	−21.8564	−0.770337
$806$	0.392305	0.0138183
$807$	0	0
$808$	−1.85641	−0.0653082
$809$	23.4115	0.823106	0.411553	−	0.911386i	$-0.364987\pi$
$809$	23.4115	0.823106	0.411553	+	0.911386i	$0.364987\pi$
$810$	0	0
$811$	−20.3923	−0.716071	−0.358035	−	0.933708i	$-0.616553\pi$
$811$	−20.3923	−0.716071	−0.358035	+	0.933708i	$0.616553\pi$
$812$	−25.8564	−0.907382
$813$	0	0
$814$	0	0
$815$	13.9090	0.487210
$816$	0	0
$817$	−18.0000	−0.629740
$818$	−89.9090	−3.14359
$819$	0	0
$820$	5.85641	0.204515
$821$	−12.3923	−0.432494	−0.216247	−	0.976339i	$-0.569382\pi$
$821$	−12.3923	−0.432494	−0.216247	+	0.976339i	$0.569382\pi$
$822$	0	0
$823$	48.7128	1.69802	0.849011	−	0.528375i	$-0.177199\pi$
$823$	48.7128	1.69802	0.849011	+	0.528375i	$0.177199\pi$
$824$	121.674	4.23873
$825$	0	0
$826$	−103.962	−3.61728
$827$	−44.9808	−1.56413	−0.782067	−	0.623194i	$-0.785835\pi$
$827$	−44.9808	−1.56413	−0.782067	+	0.623194i	$0.785835\pi$
$828$	0	0
$829$	−0.607695	−0.0211061	−0.0105531	−	0.999944i	$-0.503359\pi$
$829$	−0.607695	−0.0211061	−0.0105531	+	0.999944i	$0.503359\pi$
$830$	0	0
$831$	0	0
$832$	8.00000	0.277350
$833$	−29.0718	−1.00728
$834$	0	0
$835$	16.6410	0.575886
$836$	0	0
$837$	0	0
$838$	−64.7846	−2.23795
$839$	35.0333	1.20948	0.604742	−	0.796421i	$-0.293276\pi$
$839$	35.0333	1.20948	0.604742	+	0.796421i	$0.293276\pi$
$840$	0	0
$841$	−27.3923	−0.944562
$842$	56.9808	1.96369
$843$	0	0
$844$	51.0333	1.75664
$845$	−9.46410	−0.325575
$846$	0	0
$847$	0	0
$848$	−70.6410	−2.42582
$849$	0	0
$850$	51.1769	1.75535
$851$	51.7128	1.77269
$852$	0	0
$853$	−12.2679	−0.420047	−0.210023	−	0.977696i	$-0.567354\pi$
$853$	−12.2679	−0.420047	−0.210023	+	0.977696i	$0.567354\pi$
$854$	43.5167	1.48911
$855$	0	0
$856$	53.5692	1.83096
$857$	23.8038	0.813124	0.406562	−	0.913623i	$-0.366728\pi$
$857$	23.8038	0.813124	0.406562	+	0.913623i	$0.366728\pi$
$858$	0	0
$859$	28.8564	0.984568	0.492284	−	0.870435i	$-0.336162\pi$
$859$	28.8564	0.984568	0.492284	+	0.870435i	$0.336162\pi$
$860$	−13.8564	−0.472500
$861$	0	0
$862$	39.7128	1.35262
$863$	17.9090	0.609628	0.304814	−	0.952412i	$-0.401406\pi$
$863$	17.9090	0.609628	0.304814	+	0.952412i	$0.401406\pi$
$864$	0	0
$865$	−3.21539	−0.109327
$866$	−9.85641	−0.334934
$867$	0	0
$868$	10.9282	0.370927
$869$	0	0
$870$	0	0
$871$	1.58846	0.0538228
$872$	−112.210	−3.79992
$873$	0	0
$874$	−113.569	−3.84154
$875$	−25.8564	−0.874106
$876$	0	0
$877$	11.1962	0.378067	0.189034	−	0.981971i	$-0.439464\pi$
$877$	11.1962	0.378067	0.189034	+	0.981971i	$0.439464\pi$
$878$	−83.4256	−2.81548
$879$	0	0
$880$	0	0
$881$	51.3205	1.72903	0.864516	−	0.502605i	$-0.167625\pi$
$881$	51.3205	1.72903	0.864516	+	0.502605i	$0.167625\pi$
$882$	0	0
$883$	−5.67949	−0.191130	−0.0955651	−	0.995423i	$-0.530466\pi$
$883$	−5.67949	−0.191130	−0.0955651	+	0.995423i	$0.530466\pi$
$884$	−6.14359	−0.206631
$885$	0	0
$886$	8.92820	0.299949
$887$	6.73205	0.226040	0.113020	−	0.993593i	$-0.463948\pi$
$887$	6.73205	0.226040	0.113020	+	0.993593i	$0.463948\pi$
$888$	0	0
$889$	−20.3923	−0.683936
$890$	0.679492	0.0227766
$891$	0	0
$892$	97.5692	3.26686
$893$	−52.9808	−1.77293
$894$	0	0
$895$	10.3923	0.347376
$896$	141.282	4.71990
$897$	0	0
$898$	28.0000	0.934372
$899$	−0.679492	−0.0226623
$900$	0	0
$901$	19.8564	0.661513
$902$	0	0
$903$	0	0
$904$	110.354	3.67031
$905$	−11.9474	−0.397146
$906$	0	0
$907$	12.4641	0.413864	0.206932	−	0.978355i	$-0.433652\pi$
$907$	12.4641	0.413864	0.206932	+	0.978355i	$0.433652\pi$
$908$	−162.067	−5.37837
$909$	0	0
$910$	2.00000	0.0662994
$911$	9.46410	0.313560	0.156780	−	0.987634i	$-0.449889\pi$
$911$	9.46410	0.313560	0.156780	+	0.987634i	$0.449889\pi$
$912$	0	0
$913$	0	0
$914$	30.2487	1.00054
$915$	0	0
$916$	−89.5692	−2.95945
$917$	−56.4449	−1.86397
$918$	0	0
$919$	43.3205	1.42901	0.714506	−	0.699629i	$-0.246652\pi$
$919$	43.3205	1.42901	0.714506	+	0.699629i	$0.246652\pi$
$920$	−55.4256	−1.82733
$921$	0	0
$922$	−81.0333	−2.66869
$923$	3.71281	0.122209
$924$	0	0
$925$	28.8564	0.948793
$926$	−70.4449	−2.31496
$927$	0	0
$928$	−27.7128	−0.909718
$929$	−43.2679	−1.41958	−0.709788	−	0.704416i	$-0.751209\pi$
$929$	−43.2679	−1.41958	−0.709788	+	0.704416i	$0.751209\pi$
$930$	0	0
$931$	36.0000	1.17985
$932$	−34.6410	−1.13470
$933$	0	0
$934$	51.7128	1.69209
$935$	0	0
$936$	0	0
$937$	45.1962	1.47649	0.738247	−	0.674531i	$-0.235654\pi$
$937$	45.1962	1.47649	0.738247	+	0.674531i	$0.235654\pi$
$938$	60.4449	1.97359
$939$	0	0
$940$	−40.7846	−1.33025
$941$	26.5359	0.865046	0.432523	−	0.901623i	$-0.357624\pi$
$941$	26.5359	0.865046	0.432523	+	0.901623i	$0.357624\pi$
$942$	0	0
$943$	−11.7128	−0.381422
$944$	−152.210	−4.95402
$945$	0	0
$946$	0	0
$947$	23.6603	0.768855	0.384427	−	0.923155i	$-0.374399\pi$
$947$	23.6603	0.768855	0.384427	+	0.923155i	$0.374399\pi$
$948$	0	0
$949$	−0.856406	−0.0278001
$950$	−63.3731	−2.05609
$951$	0	0
$952$	−148.210	−4.80352
$953$	−6.14359	−0.199011	−0.0995053	−	0.995037i	$-0.531726\pi$
$953$	−6.14359	−0.199011	−0.0995053	+	0.995037i	$0.531726\pi$
$954$	0	0
$955$	2.92820	0.0947544
$956$	89.5692	2.89688
$957$	0	0
$958$	−31.4641	−1.01656
$959$	31.3205	1.01139
$960$	0	0
$961$	−30.7128	−0.990736
$962$	−4.73205	−0.152567
$963$	0	0
$964$	−83.0333	−2.67432
$965$	2.05256	0.0660742
$966$	0	0
$967$	−30.4115	−0.977969	−0.488985	−	0.872292i	$-0.662633\pi$
$967$	−30.4115	−0.977969	−0.488985	+	0.872292i	$0.662633\pi$
$968$	0	0
$969$	0	0
$970$	−10.7846	−0.346273
$971$	−2.58846	−0.0830675	−0.0415338	−	0.999137i	$-0.513224\pi$
$971$	−2.58846	−0.0830675	−0.0415338	+	0.999137i	$0.513224\pi$
$972$	0	0
$973$	26.8564	0.860977
$974$	51.5167	1.65070
$975$	0	0
$976$	63.7128	2.03940
$977$	35.6603	1.14087	0.570436	−	0.821342i	$-0.306774\pi$
$977$	35.6603	1.14087	0.570436	+	0.821342i	$0.306774\pi$
$978$	0	0
$979$	0	0
$980$	27.7128	0.885253
$981$	0	0
$982$	−82.1051	−2.62008
$983$	16.0526	0.511997	0.255999	−	0.966677i	$-0.417596\pi$
$983$	16.0526	0.511997	0.255999	+	0.966677i	$0.417596\pi$
$984$	0	0
$985$	7.07180	0.225326
$986$	14.5359	0.462917
$987$	0	0
$988$	7.60770	0.242033
$989$	27.7128	0.881216
$990$	0	0
$991$	−26.4641	−0.840660	−0.420330	−	0.907371i	$-0.638086\pi$
$991$	−26.4641	−0.840660	−0.420330	+	0.907371i	$0.638086\pi$
$992$	11.7128	0.371882
$993$	0	0
$994$	141.282	4.48119
$995$	−10.9808	−0.348114
$996$	0	0
$997$	−0.143594	−0.00454765	−0.00227383	−	0.999997i	$-0.500724\pi$
$997$	−0.143594	−0.00454765	−0.00227383	+	0.999997i	$0.500724\pi$
$998$	−53.1769	−1.68329
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3267.2.a.q.1.2		2
3.2	odd	2		3267.2.a.l.1.1		2
11.10	odd	2		297.2.a.e.1.1	✓	2
33.32	even	2		297.2.a.f.1.2	yes	2
44.43	even	2		4752.2.a.w.1.2		2
55.54	odd	2		7425.2.a.bl.1.2		2
99.32	even	6		891.2.e.m.298.1		4
99.43	odd	6		891.2.e.p.595.2		4
99.65	even	6		891.2.e.m.595.1		4
99.76	odd	6		891.2.e.p.298.2		4
132.131	odd	2		4752.2.a.bf.1.1		2
165.164	even	2		7425.2.a.z.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.a.e.1.1	✓	2	11.10	odd	2
297.2.a.f.1.2	yes	2	33.32	even	2
891.2.e.m.298.1		4	99.32	even	6
891.2.e.m.595.1		4	99.65	even	6
891.2.e.p.298.2		4	99.76	odd	6
891.2.e.p.595.2		4	99.43	odd	6
3267.2.a.l.1.1		2	3.2	odd	2
3267.2.a.q.1.2		2	1.1	even	1	trivial
4752.2.a.w.1.2		2	44.43	even	2
4752.2.a.bf.1.1		2	132.131	odd	2
7425.2.a.z.1.1		2	165.164	even	2
7425.2.a.bl.1.2		2	55.54	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:	\( N \)	\(=\)	\( 3267 = 3^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3267.a (trivial)

\(f(q)\)	\(=\)	\(q+2.73205 q^{2} +5.46410 q^{4} +0.732051 q^{5} +3.73205 q^{7} +9.46410 q^{8} +O(q^{10})\)	\(q+2.73205 q^{2} +5.46410 q^{4} +0.732051 q^{5} +3.73205 q^{7} +9.46410 q^{8} +2.00000 q^{10} +0.267949 q^{13} +10.1962 q^{14} +14.9282 q^{16} -4.19615 q^{17} +5.19615 q^{19} +4.00000 q^{20} -8.00000 q^{23} -4.46410 q^{25} +0.732051 q^{26} +20.3923 q^{28} -1.26795 q^{29} +0.535898 q^{31} +21.8564 q^{32} -11.4641 q^{34} +2.73205 q^{35} -6.46410 q^{37} +14.1962 q^{38} +6.92820 q^{40} +1.46410 q^{41} -3.46410 q^{43} -21.8564 q^{46} -10.1962 q^{47} +6.92820 q^{49} -12.1962 q^{50} +1.46410 q^{52} -4.73205 q^{53} +35.3205 q^{56} -3.46410 q^{58} -10.1962 q^{59} +4.26795 q^{61} +1.46410 q^{62} +29.8564 q^{64} +0.196152 q^{65} +5.92820 q^{67} -22.9282 q^{68} +7.46410 q^{70} +13.8564 q^{71} -3.19615 q^{73} -17.6603 q^{74} +28.3923 q^{76} +5.73205 q^{79} +10.9282 q^{80} +4.00000 q^{82} -3.07180 q^{85} -9.46410 q^{86} +0.339746 q^{89} +1.00000 q^{91} -43.7128 q^{92} -27.8564 q^{94} +3.80385 q^{95} -5.39230 q^{97} +18.9282 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 4 q^{4} - 2 q^{5} + 4 q^{7} + 12 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 + 4 * q^4 - 2 * q^5 + 4 * q^7 + 12 * q^8	\( 2 q + 2 q^{2} + 4 q^{4} - 2 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{10} + 4 q^{13} + 10 q^{14} + 16 q^{16} + 2 q^{17} + 8 q^{20} - 16 q^{23} - 2 q^{25} - 2 q^{26} + 20 q^{28} - 6 q^{29} + 8 q^{31} + 16 q^{32} - 16 q^{34} + 2 q^{35} - 6 q^{37} + 18 q^{38} - 4 q^{41} - 16 q^{46} - 10 q^{47} - 14 q^{50} - 4 q^{52} - 6 q^{53} + 36 q^{56} - 10 q^{59} + 12 q^{61} - 4 q^{62} + 32 q^{64} - 10 q^{65} - 2 q^{67} - 32 q^{68} + 8 q^{70} + 4 q^{73} - 18 q^{74} + 36 q^{76} + 8 q^{79} + 8 q^{80} + 8 q^{82} - 20 q^{85} - 12 q^{86} + 18 q^{89} + 2 q^{91} - 32 q^{92} - 28 q^{94} + 18 q^{95} + 10 q^{97} + 24 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + 4 * q^4 - 2 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^10 + 4 * q^13 + 10 * q^14 + 16 * q^16 + 2 * q^17 + 8 * q^20 - 16 * q^23 - 2 * q^25 - 2 * q^26 + 20 * q^28 - 6 * q^29 + 8 * q^31 + 16 * q^32 - 16 * q^34 + 2 * q^35 - 6 * q^37 + 18 * q^38 - 4 * q^41 - 16 * q^46 - 10 * q^47 - 14 * q^50 - 4 * q^52 - 6 * q^53 + 36 * q^56 - 10 * q^59 + 12 * q^61 - 4 * q^62 + 32 * q^64 - 10 * q^65 - 2 * q^67 - 32 * q^68 + 8 * q^70 + 4 * q^73 - 18 * q^74 + 36 * q^76 + 8 * q^79 + 8 * q^80 + 8 * q^82 - 20 * q^85 - 12 * q^86 + 18 * q^89 + 2 * q^91 - 32 * q^92 - 28 * q^94 + 18 * q^95 + 10 * q^97 + 24 * q^98

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