LMFDB - Embedded newform 3887.2.a.p.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3887,2,Mod(1,3887)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3887, 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("3887.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3887 = 13^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3887.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:	$31.0378512657$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 19x^{8} + 18x^{7} + 127x^{6} - 109x^{5} - 357x^{4} + 252x^{3} + 400x^{2} - 192x - 128 $ x^10 - x^9 - 19x^8 + 18x^7 + 127x^6 - 109x^5 - 357x^4 + 252x^3 + 400x^2 - 192x - 128
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 299)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.76732$ of defining polynomial
Character	$\chi$	$=$	3887.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.76732 q^{2} +0.315862 q^{3} +5.65804 q^{4} +0.739140 q^{5} -0.874091 q^{6} +4.71764 q^{7} -10.1230 q^{8} -2.90023 q^{9} +O(q^{10})$	\(q-2.76732 q^{2} +0.315862 q^{3} +5.65804 q^{4} +0.739140 q^{5} -0.874091 q^{6} +4.71764 q^{7} -10.1230 q^{8} -2.90023 q^{9} -2.04543 q^{10} -4.47733 q^{11} +1.78716 q^{12} -13.0552 q^{14} +0.233466 q^{15} +16.6973 q^{16} -1.20264 q^{17} +8.02586 q^{18} +4.53243 q^{19} +4.18208 q^{20} +1.49012 q^{21} +12.3902 q^{22} +1.00000 q^{23} -3.19746 q^{24} -4.45367 q^{25} -1.86366 q^{27} +26.6926 q^{28} +1.63190 q^{29} -0.646075 q^{30} -2.02953 q^{31} -25.9609 q^{32} -1.41422 q^{33} +3.32807 q^{34} +3.48699 q^{35} -16.4096 q^{36} -1.30304 q^{37} -12.5427 q^{38} -7.48227 q^{40} -5.73626 q^{41} -4.12364 q^{42} -3.32183 q^{43} -25.3329 q^{44} -2.14368 q^{45} -2.76732 q^{46} -8.46838 q^{47} +5.27406 q^{48} +15.2561 q^{49} +12.3247 q^{50} -0.379867 q^{51} +8.80439 q^{53} +5.15734 q^{54} -3.30937 q^{55} -47.7564 q^{56} +1.43162 q^{57} -4.51598 q^{58} +13.8468 q^{59} +1.32096 q^{60} +3.37399 q^{61} +5.61634 q^{62} -13.6822 q^{63} +38.4473 q^{64} +3.91359 q^{66} +7.84742 q^{67} -6.80456 q^{68} +0.315862 q^{69} -9.64961 q^{70} +1.11829 q^{71} +29.3589 q^{72} +2.83064 q^{73} +3.60592 q^{74} -1.40675 q^{75} +25.6447 q^{76} -21.1224 q^{77} +6.85571 q^{79} +12.3417 q^{80} +8.11203 q^{81} +15.8740 q^{82} +16.8067 q^{83} +8.43118 q^{84} -0.888916 q^{85} +9.19256 q^{86} +0.515455 q^{87} +45.3238 q^{88} +6.44775 q^{89} +5.93223 q^{90} +5.65804 q^{92} -0.641051 q^{93} +23.4347 q^{94} +3.35010 q^{95} -8.20006 q^{96} -3.68806 q^{97} -42.2185 q^{98} +12.9853 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} + 3 q^{3} + 19 q^{4} - 3 q^{5} - q^{6} + 2 q^{7} + 17 q^{9}+O(q^{10}) $ 10 * q - q^2 + 3 * q^3 + 19 * q^4 - 3 * q^5 - q^6 + 2 * q^7 + 17 * q^9	\( 10 q - q^{2} + 3 q^{3} + 19 q^{4} - 3 q^{5} - q^{6} + 2 q^{7} + 17 q^{9} + 6 q^{10} - 3 q^{11} + 10 q^{12} - 15 q^{14} - 2 q^{15} + 25 q^{16} - 3 q^{17} - q^{18} - 2 q^{19} + 19 q^{20} - 21 q^{21} + 13 q^{22} + 10 q^{23} + 35 q^{24} + 33 q^{25} + 6 q^{27} + 19 q^{28} + 17 q^{29} - 47 q^{30} - 5 q^{31} + 9 q^{32} + 23 q^{33} - 23 q^{34} + 3 q^{35} + 48 q^{36} - 16 q^{37} + 5 q^{38} + 13 q^{40} + 16 q^{41} - 65 q^{42} - 9 q^{43} - 18 q^{44} - 32 q^{45} - q^{46} + 11 q^{47} + 37 q^{48} + 40 q^{49} + 30 q^{50} - 31 q^{51} + 8 q^{53} + 73 q^{54} - 14 q^{55} - 54 q^{56} + 35 q^{57} - 17 q^{58} - 2 q^{59} + 37 q^{60} + 48 q^{61} - 19 q^{62} + 15 q^{63} + 64 q^{64} - 84 q^{66} + 6 q^{67} - 62 q^{68} + 3 q^{69} + 44 q^{70} - 24 q^{71} + 89 q^{72} + 33 q^{73} - 28 q^{74} - 22 q^{75} + 53 q^{76} + 15 q^{77} + 17 q^{79} + 94 q^{80} + 30 q^{81} + 35 q^{82} + 21 q^{83} - 92 q^{84} - 58 q^{85} + 7 q^{86} + 23 q^{87} + 9 q^{88} + 16 q^{89} + 67 q^{90} + 19 q^{92} - 15 q^{93} + 12 q^{94} - 27 q^{95} + 22 q^{96} + 40 q^{97} + 34 q^{98} + 17 q^{99}+O(q^{100}) \) 10 * q - q^2 + 3 * q^3 + 19 * q^4 - 3 * q^5 - q^6 + 2 * q^7 + 17 * q^9 + 6 * q^10 - 3 * q^11 + 10 * q^12 - 15 * q^14 - 2 * q^15 + 25 * q^16 - 3 * q^17 - q^18 - 2 * q^19 + 19 * q^20 - 21 * q^21 + 13 * q^22 + 10 * q^23 + 35 * q^24 + 33 * q^25 + 6 * q^27 + 19 * q^28 + 17 * q^29 - 47 * q^30 - 5 * q^31 + 9 * q^32 + 23 * q^33 - 23 * q^34 + 3 * q^35 + 48 * q^36 - 16 * q^37 + 5 * q^38 + 13 * q^40 + 16 * q^41 - 65 * q^42 - 9 * q^43 - 18 * q^44 - 32 * q^45 - q^46 + 11 * q^47 + 37 * q^48 + 40 * q^49 + 30 * q^50 - 31 * q^51 + 8 * q^53 + 73 * q^54 - 14 * q^55 - 54 * q^56 + 35 * q^57 - 17 * q^58 - 2 * q^59 + 37 * q^60 + 48 * q^61 - 19 * q^62 + 15 * q^63 + 64 * q^64 - 84 * q^66 + 6 * q^67 - 62 * q^68 + 3 * q^69 + 44 * q^70 - 24 * q^71 + 89 * q^72 + 33 * q^73 - 28 * q^74 - 22 * q^75 + 53 * q^76 + 15 * q^77 + 17 * q^79 + 94 * q^80 + 30 * q^81 + 35 * q^82 + 21 * q^83 - 92 * q^84 - 58 * q^85 + 7 * q^86 + 23 * q^87 + 9 * q^88 + 16 * q^89 + 67 * q^90 + 19 * q^92 - 15 * q^93 + 12 * q^94 - 27 * q^95 + 22 * q^96 + 40 * q^97 + 34 * q^98 + 17 * 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 $

$2$	−2.76732	−1.95679	−0.978394	−	0.206749i	$-0.933712\pi$
$2$	−2.76732	−1.95679	−0.978394	+	0.206749i	$0.933712\pi$
$3$	0.315862	0.182363	0.0911816	−	0.995834i	$-0.470936\pi$
$3$	0.315862	0.182363	0.0911816	+	0.995834i	$0.470936\pi$
$4$	5.65804	2.82902
$5$	0.739140	0.330553	0.165277	−	0.986247i	$-0.447148\pi$
$5$	0.739140	0.330553	0.165277	+	0.986247i	$0.447148\pi$
$6$	−0.874091	−0.356846
$7$	4.71764	1.78310	0.891550	−	0.452923i	$-0.149619\pi$
$7$	4.71764	1.78310	0.891550	+	0.452923i	$0.149619\pi$
$8$	−10.1230	−3.57900
$9$	−2.90023	−0.966744
$10$	−2.04543	−0.646823
$11$	−4.47733	−1.34997	−0.674983	−	0.737833i	$-0.735849\pi$
$11$	−4.47733	−1.34997	−0.674983	+	0.737833i	$0.735849\pi$
$12$	1.78716	0.515909
$13$	0	0
$13$	0	0
$14$	−13.0552	−3.48915
$15$	0.233466	0.0602807
$16$	16.6973	4.17433
$17$	−1.20264	−0.291682	−0.145841	−	0.989308i	$-0.546589\pi$
$17$	−1.20264	−0.291682	−0.145841	+	0.989308i	$0.546589\pi$
$18$	8.02586	1.89171
$19$	4.53243	1.03981	0.519905	−	0.854224i	$-0.325967\pi$
$19$	4.53243	1.03981	0.519905	+	0.854224i	$0.325967\pi$
$20$	4.18208	0.935142
$21$	1.49012	0.325172
$22$	12.3902	2.64160
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−3.19746	−0.652678
$25$	−4.45367	−0.890735
$26$	0	0
$27$	−1.86366	−0.358662
$28$	26.6926	5.04442
$29$	1.63190	0.303036	0.151518	−	0.988454i	$-0.451584\pi$
$29$	1.63190	0.303036	0.151518	+	0.988454i	$0.451584\pi$
$30$	−0.646075	−0.117957
$31$	−2.02953	−0.364514	−0.182257	−	0.983251i	$-0.558340\pi$
$31$	−2.02953	−0.364514	−0.182257	+	0.983251i	$0.558340\pi$
$32$	−25.9609	−4.58928
$33$	−1.41422	−0.246184
$34$	3.32807	0.570760
$35$	3.48699	0.589409
$36$	−16.4096	−2.73494
$37$	−1.30304	−0.214218	−0.107109	−	0.994247i	$-0.534159\pi$
$37$	−1.30304	−0.214218	−0.107109	+	0.994247i	$0.534159\pi$
$38$	−12.5427	−2.03469
$39$	0	0
$40$	−7.48227	−1.18305
$41$	−5.73626	−0.895853	−0.447926	−	0.894070i	$-0.647837\pi$
$41$	−5.73626	−0.895853	−0.447926	+	0.894070i	$0.647837\pi$
$42$	−4.12364	−0.636292
$43$	−3.32183	−0.506575	−0.253287	−	0.967391i	$-0.581512\pi$
$43$	−3.32183	−0.506575	−0.253287	+	0.967391i	$0.581512\pi$
$44$	−25.3329	−3.81908
$45$	−2.14368	−0.319560
$46$	−2.76732	−0.408019
$47$	−8.46838	−1.23524	−0.617620	−	0.786477i	$-0.711903\pi$
$47$	−8.46838	−1.23524	−0.617620	+	0.786477i	$0.711903\pi$
$48$	5.27406	0.761244
$49$	15.2561	2.17944
$50$	12.3247	1.74298
$51$	−0.379867	−0.0531920
$52$	0	0
$53$	8.80439	1.20938	0.604688	−	0.796463i	$-0.293298\pi$
$53$	8.80439	1.20938	0.604688	+	0.796463i	$0.293298\pi$
$54$	5.15734	0.701825
$55$	−3.30937	−0.446236
$56$	−47.7564	−6.38172
$57$	1.43162	0.189623
$58$	−4.51598	−0.592977
$59$	13.8468	1.80270	0.901349	−	0.433093i	$-0.142578\pi$
$59$	13.8468	1.80270	0.901349	+	0.433093i	$0.142578\pi$
$60$	1.32096	0.170535
$61$	3.37399	0.431995	0.215998	−	0.976394i	$-0.430700\pi$
$61$	3.37399	0.431995	0.215998	+	0.976394i	$0.430700\pi$
$62$	5.61634	0.713276
$63$	−13.6822	−1.72380
$64$	38.4473	4.80592
$65$	0	0
$66$	3.91359	0.481730
$67$	7.84742	0.958715	0.479358	−	0.877620i	$-0.340870\pi$
$67$	7.84742	0.958715	0.479358	+	0.877620i	$0.340870\pi$
$68$	−6.80456	−0.825174
$69$	0.315862	0.0380254
$70$	−9.64961	−1.15335
$71$	1.11829	0.132717	0.0663584	−	0.997796i	$-0.478862\pi$
$71$	1.11829	0.132717	0.0663584	+	0.997796i	$0.478862\pi$
$72$	29.3589	3.45998
$73$	2.83064	0.331302	0.165651	−	0.986184i	$-0.447028\pi$
$73$	2.83064	0.331302	0.165651	+	0.986184i	$0.447028\pi$
$74$	3.60592	0.419179
$75$	−1.40675	−0.162437
$76$	25.6447	2.94164
$77$	−21.1224	−2.40712
$78$	0	0
$79$	6.85571	0.771328	0.385664	−	0.922639i	$-0.373972\pi$
$79$	6.85571	0.771328	0.385664	+	0.922639i	$0.373972\pi$
$80$	12.3417	1.37984
$81$	8.11203	0.901337
$82$	15.8740	1.75299
$83$	16.8067	1.84477	0.922386	−	0.386271i	$-0.126237\pi$
$83$	16.8067	1.84477	0.922386	+	0.386271i	$0.126237\pi$
$84$	8.43118	0.919917
$85$	−0.888916	−0.0964164
$86$	9.19256	0.991259
$87$	0.515455	0.0552626
$88$	45.3238	4.83153
$89$	6.44775	0.683460	0.341730	−	0.939798i	$-0.388987\pi$
$89$	6.44775	0.683460	0.341730	+	0.939798i	$0.388987\pi$
$90$	5.93223	0.625312
$91$	0	0
$92$	5.65804	0.589891
$93$	−0.641051	−0.0664739
$94$	23.4347	2.41710
$95$	3.35010	0.343713
$96$	−8.20006	−0.836916
$97$	−3.68806	−0.374466	−0.187233	−	0.982316i	$-0.559952\pi$
$97$	−3.68806	−0.374466	−0.187233	+	0.982316i	$0.559952\pi$
$98$	−42.2185	−4.26471
$99$	12.9853	1.30507
$100$	−25.1991	−2.51991
$101$	7.21502	0.717921	0.358961	−	0.933353i	$-0.383131\pi$
$101$	7.21502	0.717921	0.358961	+	0.933353i	$0.383131\pi$
$102$	1.05121	0.104086
$103$	9.46737	0.932847	0.466424	−	0.884561i	$-0.345542\pi$
$103$	9.46737	0.932847	0.466424	+	0.884561i	$0.345542\pi$
$104$	0	0
$105$	1.10141	0.107487
$106$	−24.3645	−2.36649
$107$	11.1501	1.07792	0.538962	−	0.842330i	$-0.318816\pi$
$107$	11.1501	1.07792	0.538962	+	0.842330i	$0.318816\pi$
$108$	−10.5447	−1.01466
$109$	−10.4253	−0.998558	−0.499279	−	0.866441i	$-0.666402\pi$
$109$	−10.4253	−0.998558	−0.499279	+	0.866441i	$0.666402\pi$
$110$	9.15808	0.873189
$111$	−0.411581	−0.0390655
$112$	78.7719	7.44325
$113$	1.66658	0.156778	0.0783891	−	0.996923i	$-0.475022\pi$
$113$	1.66658	0.156778	0.0783891	+	0.996923i	$0.475022\pi$
$114$	−3.96176	−0.371052
$115$	0.739140	0.0689251
$116$	9.23335	0.857295
$117$	0	0
$118$	−38.3184	−3.52750
$119$	−5.67360	−0.520098
$120$	−2.36337	−0.215745
$121$	9.04650	0.822409
$122$	−9.33690	−0.845323
$123$	−1.81187	−0.163371
$124$	−11.4831	−1.03122
$125$	−6.98758	−0.624989
$126$	37.8631	3.37311
$127$	−18.4947	−1.64114	−0.820568	−	0.571548i	$-0.806343\pi$
$127$	−18.4947	−1.64114	−0.820568	+	0.571548i	$0.806343\pi$
$128$	−54.4741	−4.81488
$129$	−1.04924	−0.0923806
$130$	0	0
$131$	10.7151	0.936185	0.468093	−	0.883679i	$-0.344941\pi$
$131$	10.7151	0.936185	0.468093	+	0.883679i	$0.344941\pi$
$132$	−8.00171	−0.696460
$133$	21.3824	1.85409
$134$	−21.7163	−1.87600
$135$	−1.37751	−0.118557
$136$	12.1742	1.04393
$137$	12.7263	1.08729	0.543643	−	0.839317i	$-0.317045\pi$
$137$	12.7263	1.08729	0.543643	+	0.839317i	$0.317045\pi$
$138$	−0.874091	−0.0744076
$139$	−6.55662	−0.556126	−0.278063	−	0.960563i	$-0.589692\pi$
$139$	−6.55662	−0.556126	−0.278063	+	0.960563i	$0.589692\pi$
$140$	19.7295	1.66745
$141$	−2.67484	−0.225262
$142$	−3.09467	−0.259699
$143$	0	0
$144$	−48.4261	−4.03551
$145$	1.20620	0.100170
$146$	−7.83328	−0.648287
$147$	4.81883	0.397450
$148$	−7.37264	−0.606027
$149$	1.88624	0.154527	0.0772634	−	0.997011i	$-0.475382\pi$
$149$	1.88624	0.154527	0.0772634	+	0.997011i	$0.475382\pi$
$150$	3.89291	0.317855
$151$	7.99050	0.650257	0.325129	−	0.945670i	$-0.394592\pi$
$151$	7.99050	0.650257	0.325129	+	0.945670i	$0.394592\pi$
$152$	−45.8816	−3.72149
$153$	3.48792	0.281982
$154$	58.4524	4.71023
$155$	−1.50010	−0.120491
$156$	0	0
$157$	2.23976	0.178752	0.0893762	−	0.995998i	$-0.471513\pi$
$157$	2.23976	0.178752	0.0893762	+	0.995998i	$0.471513\pi$
$158$	−18.9719	−1.50932
$159$	2.78097	0.220546
$160$	−19.1887	−1.51700
$161$	4.71764	0.371802
$162$	−22.4486	−1.76373
$163$	16.5130	1.29340	0.646699	−	0.762746i	$-0.276149\pi$
$163$	16.5130	1.29340	0.646699	+	0.762746i	$0.276149\pi$
$164$	−32.4560	−2.53439
$165$	−1.04531	−0.0813770
$166$	−46.5094	−3.60983
$167$	9.90853	0.766745	0.383372	−	0.923594i	$-0.374763\pi$
$167$	9.90853	0.766745	0.383372	+	0.923594i	$0.374763\pi$
$168$	−15.0844	−1.16379
$169$	0	0
$170$	2.45991	0.188667
$171$	−13.1451	−1.00523
$172$	−18.7951	−1.43311
$173$	−5.29688	−0.402714	−0.201357	−	0.979518i	$-0.564535\pi$
$173$	−5.29688	−0.402714	−0.201357	+	0.979518i	$0.564535\pi$
$174$	−1.42643	−0.108137
$175$	−21.0108	−1.58827
$176$	−74.7595	−5.63521
$177$	4.37368	0.328746
$178$	−17.8430	−1.33739
$179$	−8.11304	−0.606397	−0.303199	−	0.952927i	$-0.598055\pi$
$179$	−8.11304	−0.606397	−0.303199	+	0.952927i	$0.598055\pi$
$180$	−12.1290	−0.904042
$181$	7.44088	0.553076	0.276538	−	0.961003i	$-0.410813\pi$
$181$	7.44088	0.553076	0.276538	+	0.961003i	$0.410813\pi$
$182$	0	0
$183$	1.06572	0.0787800
$184$	−10.1230	−0.746274
$185$	−0.963127	−0.0708105
$186$	1.77399	0.130075
$187$	5.38460	0.393761
$188$	−47.9144	−3.49452
$189$	−8.79207	−0.639529
$190$	−9.27078	−0.672573
$191$	6.65101	0.481250	0.240625	−	0.970618i	$-0.422648\pi$
$191$	6.65101	0.481250	0.240625	+	0.970618i	$0.422648\pi$
$192$	12.1441	0.876422
$193$	−6.64937	−0.478632	−0.239316	−	0.970942i	$-0.576923\pi$
$193$	−6.64937	−0.478632	−0.239316	+	0.970942i	$0.576923\pi$
$194$	10.2060	0.732750
$195$	0	0
$196$	86.3196	6.16569
$197$	17.5570	1.25088	0.625442	−	0.780271i	$-0.284919\pi$
$197$	17.5570	1.25088	0.625442	+	0.780271i	$0.284919\pi$
$198$	−35.9344	−2.55375
$199$	24.3992	1.72962	0.864808	−	0.502103i	$-0.167440\pi$
$199$	24.3992	1.72962	0.864808	+	0.502103i	$0.167440\pi$
$200$	45.0843	3.18794
$201$	2.47870	0.174834
$202$	−19.9662	−1.40482
$203$	7.69871	0.540343
$204$	−2.14930	−0.150481
$205$	−4.23990	−0.296127
$206$	−26.1992	−1.82538
$207$	−2.90023	−0.201580
$208$	0	0
$209$	−20.2932	−1.40371
$210$	−3.04795	−0.210328
$211$	−3.37894	−0.232616	−0.116308	−	0.993213i	$-0.537106\pi$
$211$	−3.37894	−0.232616	−0.116308	+	0.993213i	$0.537106\pi$
$212$	49.8156	3.42135
$213$	0.353226	0.0242027
$214$	−30.8560	−2.10927
$215$	−2.45530	−0.167450
$216$	18.8657	1.28365
$217$	−9.57457	−0.649964
$218$	28.8500	1.95397
$219$	0.894093	0.0604172
$220$	−18.7246	−1.26241
$221$	0	0
$222$	1.13897	0.0764429
$223$	13.3122	0.891450	0.445725	−	0.895170i	$-0.352946\pi$
$223$	13.3122	0.891450	0.445725	+	0.895170i	$0.352946\pi$
$224$	−122.474	−8.18314
$225$	12.9167	0.861112
$226$	−4.61194	−0.306782
$227$	16.0945	1.06823	0.534116	−	0.845411i	$-0.320645\pi$
$227$	16.0945	1.06823	0.534116	+	0.845411i	$0.320645\pi$
$228$	8.10018	0.536448
$229$	−12.8152	−0.846849	−0.423425	−	0.905931i	$-0.639172\pi$
$229$	−12.8152	−0.846849	−0.423425	+	0.905931i	$0.639172\pi$
$230$	−2.04543	−0.134872
$231$	−6.67178	−0.438971
$232$	−16.5196	−1.08457
$233$	−14.1688	−0.928232	−0.464116	−	0.885774i	$-0.653628\pi$
$233$	−14.1688	−0.928232	−0.464116	+	0.885774i	$0.653628\pi$
$234$	0	0
$235$	−6.25931	−0.408313
$236$	78.3457	5.09987
$237$	2.16546	0.140662
$238$	15.7006	1.01772
$239$	−8.09455	−0.523593	−0.261796	−	0.965123i	$-0.584315\pi$
$239$	−8.09455	−0.523593	−0.261796	+	0.965123i	$0.584315\pi$
$240$	3.89826	0.251632
$241$	−11.1249	−0.716619	−0.358309	−	0.933603i	$-0.616647\pi$
$241$	−11.1249	−0.716619	−0.358309	+	0.933603i	$0.616647\pi$
$242$	−25.0345	−1.60928
$243$	8.15327	0.523032
$244$	19.0902	1.22212
$245$	11.2764	0.720422
$246$	5.01401	0.319682
$247$	0	0
$248$	20.5448	1.30460
$249$	5.30859	0.336418
$250$	19.3369	1.22297
$251$	3.50892	0.221481	0.110740	−	0.993849i	$-0.464678\pi$
$251$	3.50892	0.221481	0.110740	+	0.993849i	$0.464678\pi$
$252$	−77.4146	−4.87666
$253$	−4.47733	−0.281487
$254$	51.1806	3.21136
$255$	−0.280775	−0.0175828
$256$	73.8525	4.61578
$257$	0.291931	0.0182101	0.00910507	−	0.999959i	$-0.497102\pi$
$257$	0.291931	0.0182101	0.00910507	+	0.999959i	$0.497102\pi$
$258$	2.90358	0.180769
$259$	−6.14726	−0.381972
$260$	0	0
$261$	−4.73288	−0.292958
$262$	−29.6521	−1.83192
$263$	8.63454	0.532429	0.266214	−	0.963914i	$-0.414227\pi$
$263$	8.63454	0.532429	0.266214	+	0.963914i	$0.414227\pi$
$264$	14.3161	0.881094
$265$	6.50767	0.399763
$266$	−59.1718	−3.62805
$267$	2.03660	0.124638
$268$	44.4010	2.71222
$269$	−1.60114	−0.0976231	−0.0488115	−	0.998808i	$-0.515543\pi$
$269$	−1.60114	−0.0976231	−0.0488115	+	0.998808i	$0.515543\pi$
$270$	3.81199	0.231990
$271$	24.3492	1.47911	0.739554	−	0.673097i	$-0.235036\pi$
$271$	24.3492	1.47911	0.739554	+	0.673097i	$0.235036\pi$
$272$	−20.0808	−1.21758
$273$	0	0
$274$	−35.2178	−2.12759
$275$	19.9406	1.20246
$276$	1.78716	0.107574
$277$	7.17360	0.431020	0.215510	−	0.976502i	$-0.430859\pi$
$277$	7.17360	0.431020	0.215510	+	0.976502i	$0.430859\pi$
$278$	18.1443	1.08822
$279$	5.88610	0.352391
$280$	−35.2987	−2.10950
$281$	−0.142062	−0.00847473	−0.00423736	−	0.999991i	$-0.501349\pi$
$281$	−0.142062	−0.00847473	−0.00423736	+	0.999991i	$0.501349\pi$
$282$	7.40213	0.440791
$283$	−22.9584	−1.36474	−0.682368	−	0.731009i	$-0.739050\pi$
$283$	−22.9584	−1.36474	−0.682368	+	0.731009i	$0.739050\pi$
$284$	6.32734	0.375459
$285$	1.05817	0.0626806
$286$	0	0
$287$	−27.0616	−1.59739
$288$	75.2926	4.43666
$289$	−15.5537	−0.914922
$290$	−3.33794	−0.196011
$291$	−1.16492	−0.0682888
$292$	16.0159	0.937259
$293$	14.9983	0.876208	0.438104	−	0.898924i	$-0.355650\pi$
$293$	14.9983	0.876208	0.438104	+	0.898924i	$0.355650\pi$
$294$	−13.3352	−0.777726
$295$	10.2347	0.595888
$296$	13.1906	0.766687
$297$	8.34423	0.484181
$298$	−5.21982	−0.302376
$299$	0	0
$300$	−7.95943	−0.459538
$301$	−15.6712	−0.903273
$302$	−22.1122	−1.27242
$303$	2.27895	0.130922
$304$	75.6795	4.34052
$305$	2.49385	0.142797
$306$	−9.65218	−0.551778
$307$	−8.33251	−0.475561	−0.237781	−	0.971319i	$-0.576420\pi$
$307$	−8.33251	−0.475561	−0.237781	+	0.971319i	$0.576420\pi$
$308$	−119.512	−6.80980
$309$	2.99038	0.170117
$310$	4.15126	0.235776
$311$	−30.0858	−1.70601	−0.853005	−	0.521902i	$-0.825222\pi$
$311$	−30.0858	−1.70601	−0.853005	+	0.521902i	$0.825222\pi$
$312$	0	0
$313$	15.5699	0.880066	0.440033	−	0.897982i	$-0.354967\pi$
$313$	15.5699	0.880066	0.440033	+	0.897982i	$0.354967\pi$
$314$	−6.19813	−0.349781
$315$	−10.1131	−0.569808
$316$	38.7899	2.18210
$317$	−25.3517	−1.42389	−0.711945	−	0.702235i	$-0.752186\pi$
$317$	−25.3517	−1.42389	−0.711945	+	0.702235i	$0.752186\pi$
$318$	−7.69583	−0.431561
$319$	−7.30655	−0.409088
$320$	28.4179	1.58861
$321$	3.52191	0.196574
$322$	−13.0552	−0.727538
$323$	−5.45086	−0.303294
$324$	45.8982	2.54990
$325$	0	0
$326$	−45.6967	−2.53090
$327$	−3.29294	−0.182100
$328$	58.0679	3.20626
$329$	−39.9507	−2.20256
$330$	2.89269	0.159237
$331$	−29.5940	−1.62664	−0.813318	−	0.581820i	$-0.802341\pi$
$331$	−29.5940	−1.62664	−0.813318	+	0.581820i	$0.802341\pi$
$332$	95.0928	5.21889
$333$	3.77911	0.207094
$334$	−27.4200	−1.50036
$335$	5.80034	0.316906
$336$	24.8811	1.35737
$337$	−8.19556	−0.446441	−0.223220	−	0.974768i	$-0.571657\pi$
$337$	−8.19556	−0.446441	−0.223220	+	0.974768i	$0.571657\pi$
$338$	0	0
$339$	0.526409	0.0285906
$340$	−5.02952	−0.272764
$341$	9.08687	0.492081
$342$	36.3766	1.96702
$343$	38.9493	2.10306
$344$	33.6267	1.81303
$345$	0.233466	0.0125694
$346$	14.6581	0.788026
$347$	19.7991	1.06287	0.531436	−	0.847099i	$-0.321653\pi$
$347$	19.7991	1.06287	0.531436	+	0.847099i	$0.321653\pi$
$348$	2.91647	0.156339
$349$	−10.9383	−0.585516	−0.292758	−	0.956187i	$-0.594573\pi$
$349$	−10.9383	−0.585516	−0.292758	+	0.956187i	$0.594573\pi$
$350$	58.1436	3.10790
$351$	0	0
$352$	116.235	6.19537
$353$	−32.4419	−1.72671	−0.863355	−	0.504597i	$-0.831641\pi$
$353$	−32.4419	−1.72671	−0.863355	+	0.504597i	$0.831641\pi$
$354$	−12.1033	−0.643286
$355$	0.826574	0.0438700
$356$	36.4816	1.93352
$357$	−1.79208	−0.0948467
$358$	22.4513	1.18659
$359$	7.04035	0.371575	0.185788	−	0.982590i	$-0.440516\pi$
$359$	7.04035	0.371575	0.185788	+	0.982590i	$0.440516\pi$
$360$	21.7003	1.14371
$361$	1.54292	0.0812063
$362$	−20.5913	−1.08225
$363$	2.85745	0.149977
$364$	0	0
$365$	2.09224	0.109513
$366$	−2.94917	−0.154156
$367$	−29.0402	−1.51589	−0.757944	−	0.652320i	$-0.773796\pi$
$367$	−29.0402	−1.51589	−0.757944	+	0.652320i	$0.773796\pi$
$368$	16.6973	0.870408
$369$	16.6365	0.866060
$370$	2.66528	0.138561
$371$	41.5359	2.15644
$372$	−3.62709	−0.188056
$373$	20.8084	1.07742	0.538709	−	0.842492i	$-0.318912\pi$
$373$	20.8084	1.07742	0.538709	+	0.842492i	$0.318912\pi$
$374$	−14.9009	−0.770506
$375$	−2.20711	−0.113975
$376$	85.7250	4.42093
$377$	0	0
$378$	24.3305	1.25142
$379$	15.5821	0.800396	0.400198	−	0.916429i	$-0.368941\pi$
$379$	15.5821	0.800396	0.400198	+	0.916429i	$0.368941\pi$
$380$	18.9550	0.972370
$381$	−5.84177	−0.299283
$382$	−18.4054	−0.941704
$383$	19.6830	1.00576	0.502878	−	0.864357i	$-0.332274\pi$
$383$	19.6830	1.00576	0.502878	+	0.864357i	$0.332274\pi$
$384$	−17.2063	−0.878056
$385$	−15.6124	−0.795683
$386$	18.4009	0.936581
$387$	9.63408	0.489728
$388$	−20.8672	−1.05937
$389$	−25.0150	−1.26831	−0.634156	−	0.773205i	$-0.718652\pi$
$389$	−25.0150	−1.26831	−0.634156	+	0.773205i	$0.718652\pi$
$390$	0	0
$391$	−1.20264	−0.0608199
$392$	−154.437	−7.80024
$393$	3.38451	0.170726
$394$	−48.5858	−2.44772
$395$	5.06733	0.254965
$396$	73.4713	3.69207
$397$	−20.3974	−1.02372	−0.511858	−	0.859070i	$-0.671042\pi$
$397$	−20.3974	−1.02372	−0.511858	+	0.859070i	$0.671042\pi$
$398$	−67.5204	−3.38449
$399$	6.75388	0.338117
$400$	−74.3644	−3.71822
$401$	7.47619	0.373343	0.186672	−	0.982422i	$-0.440230\pi$
$401$	7.47619	0.373343	0.186672	+	0.982422i	$0.440230\pi$
$402$	−6.85936	−0.342114
$403$	0	0
$404$	40.8229	2.03101
$405$	5.99592	0.297940
$406$	−21.3048	−1.05734
$407$	5.83413	0.289187
$408$	3.84538	0.190375
$409$	−7.80144	−0.385756	−0.192878	−	0.981223i	$-0.561782\pi$
$409$	−7.80144	−0.385756	−0.192878	+	0.981223i	$0.561782\pi$
$410$	11.7331	0.579458
$411$	4.01977	0.198281
$412$	53.5667	2.63904
$413$	65.3241	3.21439
$414$	8.02586	0.394449
$415$	12.4225	0.609795
$416$	0	0
$417$	−2.07099	−0.101417
$418$	56.1577	2.74676
$419$	19.3521	0.945410	0.472705	−	0.881221i	$-0.343278\pi$
$419$	19.3521	0.945410	0.472705	+	0.881221i	$0.343278\pi$
$420$	6.23182	0.304082
$421$	20.2313	0.986011	0.493006	−	0.870026i	$-0.335898\pi$
$421$	20.2313	0.986011	0.493006	+	0.870026i	$0.335898\pi$
$422$	9.35059	0.455180
$423$	24.5603	1.19416
$424$	−89.1264	−4.32836
$425$	5.35614	0.259811
$426$	−0.977489	−0.0473595
$427$	15.9173	0.770290
$428$	63.0879	3.04947
$429$	0	0
$430$	6.79459	0.327664
$431$	−4.62928	−0.222985	−0.111492	−	0.993765i	$-0.535563\pi$
$431$	−4.62928	−0.222985	−0.111492	+	0.993765i	$0.535563\pi$
$432$	−31.1182	−1.49717
$433$	34.8591	1.67522	0.837610	−	0.546269i	$-0.183952\pi$
$433$	34.8591	1.67522	0.837610	+	0.546269i	$0.183952\pi$
$434$	26.4959	1.27184
$435$	0.380993	0.0182672
$436$	−58.9865	−2.82494
$437$	4.53243	0.216816
$438$	−2.47424	−0.118224
$439$	−28.3163	−1.35146	−0.675731	−	0.737148i	$-0.736172\pi$
$439$	−28.3163	−1.35146	−0.675731	+	0.737148i	$0.736172\pi$
$440$	33.5006	1.59708
$441$	−44.2462	−2.10696
$442$	0	0
$443$	25.9668	1.23372	0.616859	−	0.787074i	$-0.288405\pi$
$443$	25.9668	1.23372	0.616859	+	0.787074i	$0.288405\pi$
$444$	−2.32874	−0.110517
$445$	4.76579	0.225920
$446$	−36.8390	−1.74438
$447$	0.595792	0.0281800
$448$	181.381	8.56942
$449$	−15.2511	−0.719743	−0.359871	−	0.933002i	$-0.617179\pi$
$449$	−15.2511	−0.719743	−0.359871	+	0.933002i	$0.617179\pi$
$450$	−35.7445	−1.68501
$451$	25.6831	1.20937
$452$	9.42955	0.443529
$453$	2.52390	0.118583
$454$	−44.5387	−2.09030
$455$	0	0
$456$	−14.4923	−0.678662
$457$	−27.0869	−1.26707	−0.633535	−	0.773714i	$-0.718397\pi$
$457$	−27.0869	−1.26707	−0.633535	+	0.773714i	$0.718397\pi$
$458$	35.4636	1.65710
$459$	2.24130	0.104615
$460$	4.18208	0.194991
$461$	23.7791	1.10750	0.553750	−	0.832683i	$-0.313196\pi$
$461$	23.7791	1.10750	0.553750	+	0.832683i	$0.313196\pi$
$462$	18.4629	0.858973
$463$	19.2629	0.895224	0.447612	−	0.894228i	$-0.352275\pi$
$463$	19.2629	0.895224	0.447612	+	0.894228i	$0.352275\pi$
$464$	27.2484	1.26497
$465$	−0.473826	−0.0219732
$466$	39.2097	1.81635
$467$	−26.6943	−1.23526	−0.617632	−	0.786467i	$-0.711908\pi$
$467$	−26.6943	−1.23526	−0.617632	+	0.786467i	$0.711908\pi$
$468$	0	0
$469$	37.0213	1.70948
$470$	17.3215	0.798981
$471$	0.707456	0.0325979
$472$	−140.170	−6.45186
$473$	14.8729	0.683859
$474$	−5.99251	−0.275245
$475$	−20.1860	−0.926195
$476$	−32.1014	−1.47137
$477$	−25.5348	−1.16916
$478$	22.4002	1.02456
$479$	−10.3682	−0.473734	−0.236867	−	0.971542i	$-0.576121\pi$
$479$	−10.3682	−0.473734	−0.236867	+	0.971542i	$0.576121\pi$
$480$	−6.06099	−0.276645
$481$	0	0
$482$	30.7861	1.40227
$483$	1.49012	0.0678030
$484$	51.1854	2.32661
$485$	−2.72599	−0.123781
$486$	−22.5627	−1.02346
$487$	39.9599	1.81075	0.905377	−	0.424608i	$-0.139588\pi$
$487$	39.9599	1.81075	0.905377	+	0.424608i	$0.139588\pi$
$488$	−34.1547	−1.54611
$489$	5.21583	0.235868
$490$	−31.2053	−1.40971
$491$	−3.43296	−0.154927	−0.0774636	−	0.996995i	$-0.524682\pi$
$491$	−3.43296	−0.154927	−0.0774636	+	0.996995i	$0.524682\pi$
$492$	−10.2516	−0.462179
$493$	−1.96258	−0.0883901
$494$	0	0
$495$	9.59795	0.431396
$496$	−33.8877	−1.52160
$497$	5.27570	0.236647
$498$	−14.6906	−0.658299
$499$	−30.5911	−1.36945	−0.684724	−	0.728803i	$-0.740077\pi$
$499$	−30.5911	−1.36945	−0.684724	+	0.728803i	$0.740077\pi$
$500$	−39.5360	−1.76810
$501$	3.12973	0.139826
$502$	−9.71028	−0.433391
$503$	15.6823	0.699241	0.349620	−	0.936891i	$-0.386311\pi$
$503$	15.6823	0.699241	0.349620	+	0.936891i	$0.386311\pi$
$504$	138.505	6.16949
$505$	5.33291	0.237311
$506$	12.3902	0.550811
$507$	0	0
$508$	−104.644	−4.64281
$509$	5.03697	0.223260	0.111630	−	0.993750i	$-0.464393\pi$
$509$	5.03697	0.223260	0.111630	+	0.993750i	$0.464393\pi$
$510$	0.776993	0.0344058
$511$	13.3539	0.590744
$512$	−95.4249	−4.21723
$513$	−8.44691	−0.372940
$514$	−0.807865	−0.0356334
$515$	6.99771	0.308356
$516$	−5.93665	−0.261346
$517$	37.9157	1.66753
$518$	17.0114	0.747439
$519$	−1.67308	−0.0734402
$520$	0	0
$521$	−4.32751	−0.189591	−0.0947957	−	0.995497i	$-0.530220\pi$
$521$	−4.32751	−0.189591	−0.0947957	+	0.995497i	$0.530220\pi$
$522$	13.0974	0.573257
$523$	24.7682	1.08304	0.541518	−	0.840689i	$-0.317850\pi$
$523$	24.7682	1.08304	0.541518	+	0.840689i	$0.317850\pi$
$524$	60.6266	2.64849
$525$	−6.63652	−0.289642
$526$	−23.8945	−1.04185
$527$	2.44078	0.106322
$528$	−23.6137	−1.02765
$529$	1.00000	0.0434783
$530$	−18.0088	−0.782252
$531$	−40.1589	−1.74275
$532$	120.982	5.24524
$533$	0	0
$534$	−5.63592	−0.243890
$535$	8.24151	0.356312
$536$	−79.4391	−3.43125
$537$	−2.56260	−0.110584
$538$	4.43085	0.191028
$539$	−68.3066	−2.94217
$540$	−7.79398	−0.335399
$541$	−41.8800	−1.80056	−0.900281	−	0.435308i	$-0.856639\pi$
$541$	−41.8800	−1.80056	−0.900281	+	0.435308i	$0.856639\pi$
$542$	−67.3819	−2.89430
$543$	2.35029	0.100861
$544$	31.2215	1.33861
$545$	−7.70572	−0.330077
$546$	0	0
$547$	0.0671370	0.00287057	0.00143529	−	0.999999i	$-0.499543\pi$
$547$	0.0671370	0.00287057	0.00143529	+	0.999999i	$0.499543\pi$
$548$	72.0062	3.07595
$549$	−9.78535	−0.417629
$550$	−55.1819	−2.35296
$551$	7.39647	0.315100
$552$	−3.19746	−0.136093
$553$	32.3427	1.37535
$554$	−19.8516	−0.843415
$555$	−0.304215	−0.0129132
$556$	−37.0976	−1.57329
$557$	35.5575	1.50662	0.753309	−	0.657667i	$-0.228457\pi$
$557$	35.5575	1.50662	0.753309	+	0.657667i	$0.228457\pi$
$558$	−16.2887	−0.689555
$559$	0	0
$560$	58.2235	2.46039
$561$	1.70079	0.0718075
$562$	0.393131	0.0165832
$563$	−9.57093	−0.403366	−0.201683	−	0.979451i	$-0.564641\pi$
$563$	−9.57093	−0.403366	−0.201683	+	0.979451i	$0.564641\pi$
$564$	−15.1344	−0.637271
$565$	1.23183	0.0518236
$566$	63.5332	2.67050
$567$	38.2696	1.60717
$568$	−11.3204	−0.474994
$569$	−13.3552	−0.559878	−0.279939	−	0.960018i	$-0.590314\pi$
$569$	−13.3552	−0.559878	−0.279939	+	0.960018i	$0.590314\pi$
$570$	−2.92829	−0.122653
$571$	−24.9223	−1.04296	−0.521482	−	0.853262i	$-0.674621\pi$
$571$	−24.9223	−1.04296	−0.521482	+	0.853262i	$0.674621\pi$
$572$	0	0
$573$	2.10080	0.0877623
$574$	74.8880	3.12576
$575$	−4.45367	−0.185731
$576$	−111.506	−4.64609
$577$	11.3415	0.472151	0.236075	−	0.971735i	$-0.424139\pi$
$577$	11.3415	0.472151	0.236075	+	0.971735i	$0.424139\pi$
$578$	43.0419	1.79031
$579$	−2.10028	−0.0872848
$580$	6.82473	0.283382
$581$	79.2877	3.28941
$582$	3.22370	0.133627
$583$	−39.4202	−1.63262
$584$	−28.6545	−1.18573
$585$	0	0
$586$	−41.5049	−1.71455
$587$	−35.6803	−1.47268	−0.736342	−	0.676609i	$-0.763449\pi$
$587$	−35.6803	−1.47268	−0.736342	+	0.676609i	$0.763449\pi$
$588$	27.2651	1.12439
$589$	−9.19869	−0.379025
$590$	−28.3227	−1.16603
$591$	5.54559	0.228115
$592$	−21.7573	−0.894217
$593$	6.38579	0.262233	0.131116	−	0.991367i	$-0.458144\pi$
$593$	6.38579	0.262233	0.131116	+	0.991367i	$0.458144\pi$
$594$	−23.0911	−0.947440
$595$	−4.19358	−0.171920
$596$	10.6724	0.437159
$597$	7.70680	0.315418
$598$	0	0
$599$	36.8695	1.50645	0.753223	−	0.657765i	$-0.228498\pi$
$599$	36.8695	1.50645	0.753223	+	0.657765i	$0.228498\pi$
$600$	14.2404	0.581363
$601$	27.9559	1.14035	0.570173	−	0.821524i	$-0.306876\pi$
$601$	27.9559	1.14035	0.570173	+	0.821524i	$0.306876\pi$
$602$	43.3672	1.76751
$603$	−22.7593	−0.926832
$604$	45.2105	1.83959
$605$	6.68663	0.271850
$606$	−6.30658	−0.256187
$607$	44.7084	1.81466	0.907329	−	0.420421i	$-0.138118\pi$
$607$	44.7084	1.81466	0.907329	+	0.420421i	$0.138118\pi$
$608$	−117.666	−4.77198
$609$	2.43173	0.0985387
$610$	−6.90127	−0.279424
$611$	0	0
$612$	19.7348	0.797732
$613$	26.5714	1.07321	0.536604	−	0.843834i	$-0.319707\pi$
$613$	26.5714	1.07321	0.536604	+	0.843834i	$0.319707\pi$
$614$	23.0587	0.930573
$615$	−1.33922	−0.0540027
$616$	213.821	8.61511
$617$	40.8206	1.64337	0.821687	−	0.569938i	$-0.193033\pi$
$617$	40.8206	1.64337	0.821687	+	0.569938i	$0.193033\pi$
$618$	−8.27534	−0.332883
$619$	−6.76143	−0.271765	−0.135882	−	0.990725i	$-0.543387\pi$
$619$	−6.76143	−0.271765	−0.135882	+	0.990725i	$0.543387\pi$
$620$	−8.48765	−0.340872
$621$	−1.86366	−0.0747861
$622$	83.2570	3.33830
$623$	30.4181	1.21868
$624$	0	0
$625$	17.1036	0.684143
$626$	−43.0870	−1.72210
$627$	−6.40985	−0.255985
$628$	12.6727	0.505694
$629$	1.56708	0.0624836
$630$	27.9861	1.11499
$631$	−26.6338	−1.06028	−0.530138	−	0.847912i	$-0.677860\pi$
$631$	−26.6338	−1.06028	−0.530138	+	0.847912i	$0.677860\pi$
$632$	−69.4000	−2.76058
$633$	−1.06728	−0.0424206
$634$	70.1561	2.78625
$635$	−13.6701	−0.542483
$636$	15.7349	0.623928
$637$	0	0
$638$	20.2195	0.800499
$639$	−3.24331	−0.128303
$640$	−40.2640	−1.59157
$641$	42.8339	1.69184	0.845920	−	0.533310i	$-0.179052\pi$
$641$	42.8339	1.69184	0.845920	+	0.533310i	$0.179052\pi$
$642$	−9.74624	−0.384653
$643$	−44.5719	−1.75775	−0.878873	−	0.477056i	$-0.841704\pi$
$643$	−44.5719	−1.75775	−0.878873	+	0.477056i	$0.841704\pi$
$644$	26.6926	1.05183
$645$	−0.775536	−0.0305367
$646$	15.0843	0.593482
$647$	−8.45715	−0.332485	−0.166242	−	0.986085i	$-0.553163\pi$
$647$	−8.45715	−0.332485	−0.166242	+	0.986085i	$0.553163\pi$
$648$	−82.1177	−3.22589
$649$	−61.9967	−2.43358
$650$	0	0
$651$	−3.02425	−0.118530
$652$	93.4311	3.65905
$653$	−10.6991	−0.418690	−0.209345	−	0.977842i	$-0.567133\pi$
$653$	−10.6991	−0.418690	−0.209345	+	0.977842i	$0.567133\pi$
$654$	9.11262	0.356332
$655$	7.91998	0.309459
$656$	−95.7802	−3.73959
$657$	−8.20952	−0.320284
$658$	110.556	4.30993
$659$	11.8966	0.463425	0.231712	−	0.972784i	$-0.425567\pi$
$659$	11.8966	0.463425	0.231712	+	0.972784i	$0.425567\pi$
$660$	−5.91438	−0.230217
$661$	−15.6606	−0.609125	−0.304562	−	0.952492i	$-0.598510\pi$
$661$	−15.6606	−0.609125	−0.304562	+	0.952492i	$0.598510\pi$
$662$	81.8961	3.18298
$663$	0	0
$664$	−170.133	−6.60244
$665$	15.8045	0.612874
$666$	−10.4580	−0.405239
$667$	1.63190	0.0631874
$668$	56.0628	2.16914
$669$	4.20482	0.162568
$670$	−16.0514	−0.620119
$671$	−15.1065	−0.583179
$672$	−38.6849	−1.49230
$673$	−8.48113	−0.326923	−0.163462	−	0.986550i	$-0.552266\pi$
$673$	−8.48113	−0.326923	−0.163462	+	0.986550i	$0.552266\pi$
$674$	22.6797	0.873590
$675$	8.30013	0.319472
$676$	0	0
$677$	29.6898	1.14107	0.570536	−	0.821272i	$-0.306735\pi$
$677$	29.6898	1.14107	0.570536	+	0.821272i	$0.306735\pi$
$678$	−1.45674	−0.0559457
$679$	−17.3989	−0.667710
$680$	8.99845	0.345075
$681$	5.08366	0.194806
$682$	−25.1462	−0.962899
$683$	21.8094	0.834514	0.417257	−	0.908789i	$-0.362991\pi$
$683$	21.8094	0.834514	0.417257	+	0.908789i	$0.362991\pi$
$684$	−74.3755	−2.84382
$685$	9.40655	0.359406
$686$	−107.785	−4.11525
$687$	−4.04782	−0.154434
$688$	−55.4657	−2.11461
$689$	0	0
$690$	−0.646075	−0.0245957
$691$	−41.7281	−1.58741	−0.793706	−	0.608301i	$-0.791851\pi$
$691$	−41.7281	−1.58741	−0.793706	+	0.608301i	$0.791851\pi$
$692$	−29.9699	−1.13929
$693$	61.2599	2.32707
$694$	−54.7904	−2.07981
$695$	−4.84626	−0.183829
$696$	−5.21793	−0.197785
$697$	6.89863	0.261304
$698$	30.2699	1.14573
$699$	−4.47540	−0.169275
$700$	−118.880	−4.49324
$701$	10.4663	0.395306	0.197653	−	0.980272i	$-0.436668\pi$
$701$	10.4663	0.395306	0.197653	+	0.980272i	$0.436668\pi$
$702$	0	0
$703$	−5.90593	−0.222746
$704$	−172.141	−6.48782
$705$	−1.97708	−0.0744612
$706$	89.7771	3.37880
$707$	34.0378	1.28013
$708$	24.7464	0.930028
$709$	8.52804	0.320277	0.160139	−	0.987095i	$-0.448806\pi$
$709$	8.52804	0.320277	0.160139	+	0.987095i	$0.448806\pi$
$710$	−2.28739	−0.0858443
$711$	−19.8831	−0.745676
$712$	−65.2702	−2.44611
$713$	−2.02953	−0.0760064
$714$	4.95924	0.185595
$715$	0	0
$716$	−45.9039	−1.71551
$717$	−2.55676	−0.0954840
$718$	−19.4829	−0.727094
$719$	1.58809	0.0592259	0.0296130	−	0.999561i	$-0.490573\pi$
$719$	1.58809	0.0592259	0.0296130	+	0.999561i	$0.490573\pi$
$720$	−35.7937	−1.33395
$721$	44.6636	1.66336
$722$	−4.26975	−0.158904
$723$	−3.51394	−0.130685
$724$	42.1008	1.56466
$725$	−7.26794	−0.269925
$726$	−7.90746	−0.293473
$727$	44.7350	1.65913	0.829564	−	0.558411i	$-0.188589\pi$
$727$	44.7350	1.65913	0.829564	+	0.558411i	$0.188589\pi$
$728$	0	0
$729$	−21.7608	−0.805955
$730$	−5.78989	−0.214293
$731$	3.99495	0.147759
$732$	6.02987	0.222870
$733$	39.6658	1.46509	0.732545	−	0.680718i	$-0.238332\pi$
$733$	39.6658	1.46509	0.732545	+	0.680718i	$0.238332\pi$
$734$	80.3635	2.96627
$735$	3.56179	0.131378
$736$	−25.9609	−0.956931
$737$	−35.1355	−1.29423
$738$	−46.0384	−1.69470
$739$	4.76346	0.175227	0.0876134	−	0.996155i	$-0.472076\pi$
$739$	4.76346	0.175227	0.0876134	+	0.996155i	$0.472076\pi$
$740$	−5.44941	−0.200324
$741$	0	0
$742$	−114.943	−4.21969
$743$	5.52606	0.202732	0.101366	−	0.994849i	$-0.467679\pi$
$743$	5.52606	0.202732	0.101366	+	0.994849i	$0.467679\pi$
$744$	6.48933	0.237910
$745$	1.39419	0.0510793
$746$	−57.5834	−2.10828
$747$	−48.7432	−1.78342
$748$	30.4663	1.11396
$749$	52.6023	1.92205
$750$	6.10778	0.223025
$751$	39.1777	1.42962	0.714808	−	0.699321i	$-0.246514\pi$
$751$	39.1777	1.42962	0.714808	+	0.699321i	$0.246514\pi$
$752$	−141.399	−5.15630
$753$	1.10833	0.0403899
$754$	0	0
$755$	5.90609	0.214945
$756$	−49.7459	−1.80924
$757$	0.504282	0.0183285	0.00916423	−	0.999958i	$-0.497083\pi$
$757$	0.504282	0.0183285	0.00916423	+	0.999958i	$0.497083\pi$
$758$	−43.1205	−1.56621
$759$	−1.41422	−0.0513329
$760$	−33.9129	−1.23015
$761$	−30.0132	−1.08798	−0.543988	−	0.839093i	$-0.683086\pi$
$761$	−30.0132	−1.08798	−0.543988	+	0.839093i	$0.683086\pi$
$762$	16.1660	0.585633
$763$	−49.1826	−1.78053
$764$	37.6317	1.36147
$765$	2.57806	0.0932100
$766$	−54.4692	−1.96805
$767$	0	0
$768$	23.3272	0.841748
$769$	49.7409	1.79370	0.896852	−	0.442331i	$-0.145848\pi$
$769$	49.7409	1.79370	0.896852	+	0.442331i	$0.145848\pi$
$770$	43.2045	1.55698
$771$	0.0922099	0.00332086
$772$	−37.6224	−1.35406
$773$	−53.2039	−1.91361	−0.956805	−	0.290730i	$-0.906102\pi$
$773$	−53.2039	−1.91361	−0.956805	+	0.290730i	$0.906102\pi$
$774$	−26.6605	−0.958294
$775$	9.03885	0.324685
$776$	37.3341	1.34021
$777$	−1.94169	−0.0696577
$778$	69.2245	2.48182
$779$	−25.9992	−0.931517
$780$	0	0
$781$	−5.00697	−0.179163
$782$	3.32807	0.119012
$783$	−3.04131	−0.108687
$784$	254.736	9.09772
$785$	1.65550	0.0590872
$786$	−9.36600	−0.334074
$787$	40.3456	1.43817	0.719083	−	0.694924i	$-0.244562\pi$
$787$	40.3456	1.43817	0.719083	+	0.694924i	$0.244562\pi$
$788$	99.3382	3.53878
$789$	2.72733	0.0970954
$790$	−14.0229	−0.498912
$791$	7.86230	0.279551
$792$	−131.450	−4.67086
$793$	0	0
$794$	56.4460	2.00319
$795$	2.05553	0.0729021
$796$	138.052	4.89312
$797$	−20.7329	−0.734396	−0.367198	−	0.930143i	$-0.619683\pi$
$797$	−20.7329	−0.734396	−0.367198	+	0.930143i	$0.619683\pi$
$798$	−18.6901	−0.661623
$799$	10.1844	0.360297
$800$	115.621	4.08783
$801$	−18.7000	−0.660731
$802$	−20.6890	−0.730553
$803$	−12.6737	−0.447246
$804$	14.0246	0.494610
$805$	3.48699	0.122900
$806$	0	0
$807$	−0.505739	−0.0178029
$808$	−73.0373	−2.56944
$809$	−0.978821	−0.0344135	−0.0172068	−	0.999852i	$-0.505477\pi$
$809$	−0.978821	−0.0344135	−0.0172068	+	0.999852i	$0.505477\pi$
$810$	−16.5926	−0.583005
$811$	−5.02687	−0.176517	−0.0882586	−	0.996098i	$-0.528130\pi$
$811$	−5.02687	−0.176517	−0.0882586	+	0.996098i	$0.528130\pi$
$812$	43.5596	1.52864
$813$	7.69099	0.269735
$814$	−16.1449	−0.565878
$815$	12.2054	0.427537
$816$	−6.34277	−0.222041
$817$	−15.0560	−0.526742
$818$	21.5890	0.754843
$819$	0	0
$820$	−23.9895	−0.837749
$821$	−15.1356	−0.528235	−0.264117	−	0.964491i	$-0.585081\pi$
$821$	−15.1356	−0.528235	−0.264117	+	0.964491i	$0.585081\pi$
$822$	−11.1240	−0.387994
$823$	5.51966	0.192403	0.0962017	−	0.995362i	$-0.469331\pi$
$823$	5.51966	0.192403	0.0962017	+	0.995362i	$0.469331\pi$
$824$	−95.8377	−3.33866
$825$	6.29847	0.219285
$826$	−180.772	−6.28988
$827$	3.06575	0.106607	0.0533033	−	0.998578i	$-0.483025\pi$
$827$	3.06575	0.106607	0.0533033	+	0.998578i	$0.483025\pi$
$828$	−16.4096	−0.570274
$829$	22.1285	0.768553	0.384277	−	0.923218i	$-0.374451\pi$
$829$	22.1285	0.768553	0.384277	+	0.923218i	$0.374451\pi$
$830$	−34.3769	−1.19324
$831$	2.26587	0.0786022
$832$	0	0
$833$	−18.3475	−0.635704
$834$	5.73108	0.198451
$835$	7.32378	0.253450
$836$	−114.820	−3.97112
$837$	3.78235	0.130737
$838$	−53.5533	−1.84997
$839$	−24.3377	−0.840231	−0.420116	−	0.907471i	$-0.638010\pi$
$839$	−24.3377	−0.840231	−0.420116	+	0.907471i	$0.638010\pi$
$840$	−11.1495	−0.384695
$841$	−26.3369	−0.908169
$842$	−55.9863	−1.92942
$843$	−0.0448721	−0.00154548
$844$	−19.1182	−0.658075
$845$	0	0
$846$	−67.9660	−2.33672
$847$	42.6781	1.46644
$848$	147.010	5.04833
$849$	−7.25170	−0.248878
$850$	−14.8221	−0.508395
$851$	−1.30304	−0.0446676
$852$	1.99857	0.0684698
$853$	−2.47096	−0.0846041	−0.0423020	−	0.999105i	$-0.513469\pi$
$853$	−2.47096	−0.0846041	−0.0423020	+	0.999105i	$0.513469\pi$
$854$	−44.0481	−1.50730
$855$	−9.71606	−0.332282
$856$	−112.872	−3.85790
$857$	38.5016	1.31519	0.657595	−	0.753371i	$-0.271574\pi$
$857$	38.5016	1.31519	0.657595	+	0.753371i	$0.271574\pi$
$858$	0	0
$859$	30.9439	1.05579	0.527897	−	0.849309i	$-0.322981\pi$
$859$	30.9439	1.05579	0.527897	+	0.849309i	$0.322981\pi$
$860$	−13.8922	−0.473719
$861$	−8.54773	−0.291306
$862$	12.8107	0.436334
$863$	−15.7394	−0.535774	−0.267887	−	0.963450i	$-0.586325\pi$
$863$	−15.7394	−0.535774	−0.267887	+	0.963450i	$0.586325\pi$
$864$	48.3823	1.64600
$865$	−3.91513	−0.133119
$866$	−96.4661	−3.27805
$867$	−4.91282	−0.166848
$868$	−54.1733	−1.83876
$869$	−30.6953	−1.04127
$870$	−1.05433	−0.0357451
$871$	0	0
$872$	105.534	3.57384
$873$	10.6962	0.362013
$874$	−12.5427	−0.424262
$875$	−32.9649	−1.11442
$876$	5.05881	0.170921
$877$	34.4601	1.16364	0.581818	−	0.813319i	$-0.302342\pi$
$877$	34.4601	1.16364	0.581818	+	0.813319i	$0.302342\pi$
$878$	78.3601	2.64452
$879$	4.73739	0.159788
$880$	−55.2577	−1.86274
$881$	−35.7138	−1.20323	−0.601615	−	0.798786i	$-0.705476\pi$
$881$	−35.7138	−1.20323	−0.601615	+	0.798786i	$0.705476\pi$
$882$	122.443	4.12288
$883$	−17.3046	−0.582348	−0.291174	−	0.956670i	$-0.594046\pi$
$883$	−17.3046	−0.582348	−0.291174	+	0.956670i	$0.594046\pi$
$884$	0	0
$885$	3.23276	0.108668
$886$	−71.8583	−2.41413
$887$	−38.2474	−1.28422	−0.642111	−	0.766612i	$-0.721941\pi$
$887$	−38.2474	−1.28422	−0.642111	+	0.766612i	$0.721941\pi$
$888$	4.16641	0.139816
$889$	−87.2512	−2.92631
$890$	−13.1884	−0.442077
$891$	−36.3203	−1.21677
$892$	75.3209	2.52193
$893$	−38.3823	−1.28442
$894$	−1.64874	−0.0551423
$895$	−5.99667	−0.200447
$896$	−256.989	−8.58541
$897$	0	0
$898$	42.2045	1.40838
$899$	−3.31198	−0.110461
$900$	73.0831	2.43610
$901$	−10.5885	−0.352753
$902$	−71.0733	−2.36648
$903$	−4.94994	−0.164724
$904$	−16.8707	−0.561110
$905$	5.49985	0.182821
$906$	−6.98442	−0.232042
$907$	−4.44990	−0.147756	−0.0738782	−	0.997267i	$-0.523538\pi$
$907$	−4.44990	−0.147756	−0.0738782	+	0.997267i	$0.523538\pi$
$908$	91.0635	3.02205
$909$	−20.9252	−0.694046
$910$	0	0
$911$	−27.7686	−0.920016	−0.460008	−	0.887915i	$-0.652153\pi$
$911$	−27.7686	−0.920016	−0.460008	+	0.887915i	$0.652153\pi$
$912$	23.9043	0.791550
$913$	−75.2490	−2.49038
$914$	74.9579	2.47939
$915$	0.787713	0.0260410
$916$	−72.5087	−2.39575
$917$	50.5501	1.66931
$918$	−6.20240	−0.204710
$919$	8.30967	0.274111	0.137055	−	0.990563i	$-0.456236\pi$
$919$	8.30967	0.274111	0.137055	+	0.990563i	$0.456236\pi$
$920$	−7.48227	−0.246683
$921$	−2.63193	−0.0867249
$922$	−65.8042	−2.16714
$923$	0	0
$924$	−37.7492	−1.24186
$925$	5.80330	0.190811
$926$	−53.3066	−1.75176
$927$	−27.4576	−0.901824
$928$	−42.3655	−1.39072
$929$	−29.4176	−0.965159	−0.482580	−	0.875852i	$-0.660300\pi$
$929$	−29.4176	−0.965159	−0.482580	+	0.875852i	$0.660300\pi$
$930$	1.31123	0.0429968
$931$	69.1472	2.26621
$932$	−80.1679	−2.62599
$933$	−9.50298	−0.311113
$934$	73.8715	2.41715
$935$	3.97997	0.130159
$936$	0	0
$937$	43.3617	1.41656	0.708282	−	0.705929i	$-0.249470\pi$
$937$	43.3617	1.41656	0.708282	+	0.705929i	$0.249470\pi$
$938$	−102.450	−3.34510
$939$	4.91796	0.160492
$940$	−35.4154	−1.15512
$941$	−31.6000	−1.03013	−0.515065	−	0.857151i	$-0.672232\pi$
$941$	−31.6000	−1.03013	−0.515065	+	0.857151i	$0.672232\pi$
$942$	−1.95776	−0.0637871
$943$	−5.73626	−0.186798
$944$	231.204	7.52506
$945$	−6.49857	−0.211399
$946$	−41.1581	−1.33817
$947$	−12.6783	−0.411991	−0.205995	−	0.978553i	$-0.566043\pi$
$947$	−12.6783	−0.411991	−0.205995	+	0.978553i	$0.566043\pi$
$948$	12.2523	0.397935
$949$	0	0
$950$	55.8609	1.81237
$951$	−8.00763	−0.259665
$952$	57.4336	1.86143
$953$	−11.4162	−0.369808	−0.184904	−	0.982757i	$-0.559197\pi$
$953$	−11.4162	−0.369808	−0.184904	+	0.982757i	$0.559197\pi$
$954$	70.6627	2.28779
$955$	4.91602	0.159079
$956$	−45.7993	−1.48125
$957$	−2.30786	−0.0746027
$958$	28.6920	0.926997
$959$	60.0383	1.93874
$960$	8.97616	0.289704
$961$	−26.8810	−0.867130
$962$	0	0
$963$	−32.3380	−1.04208
$964$	−62.9452	−2.02733
$965$	−4.91481	−0.158213
$966$	−4.12364	−0.132676
$967$	12.4165	0.399287	0.199644	−	0.979869i	$-0.436022\pi$
$967$	12.4165	0.399287	0.199644	+	0.979869i	$0.436022\pi$
$968$	−91.5773	−2.94340
$969$	−1.72172	−0.0553097
$970$	7.54368	0.242213
$971$	−11.0123	−0.353400	−0.176700	−	0.984265i	$-0.556542\pi$
$971$	−11.0123	−0.353400	−0.176700	+	0.984265i	$0.556542\pi$
$972$	46.1315	1.47967
$973$	−30.9318	−0.991627
$974$	−110.582	−3.54326
$975$	0	0
$976$	56.3366	1.80329
$977$	21.3657	0.683550	0.341775	−	0.939782i	$-0.388972\pi$
$977$	21.3657	0.683550	0.341775	+	0.939782i	$0.388972\pi$
$978$	−14.4339	−0.461544
$979$	−28.8687	−0.922648
$980$	63.8023	2.03809
$981$	30.2356	0.965350
$982$	9.50008	0.303160
$983$	−0.313237	−0.00999070	−0.00499535	−	0.999988i	$-0.501590\pi$
$983$	−0.313237	−0.00999070	−0.00499535	+	0.999988i	$0.501590\pi$
$984$	18.3414	0.584704
$985$	12.9771	0.413484
$986$	5.43108	0.172961
$987$	−12.6189	−0.401665
$988$	0	0
$989$	−3.32183	−0.105628
$990$	−26.5606	−0.844150
$991$	7.96997	0.253174	0.126587	−	0.991955i	$-0.459598\pi$
$991$	7.96997	0.253174	0.126587	+	0.991955i	$0.459598\pi$
$992$	52.6883	1.67286
$993$	−9.34764	−0.296638
$994$	−14.5995	−0.463069
$995$	18.0344	0.571730
$996$	30.0362	0.951734
$997$	−37.2832	−1.18077	−0.590385	−	0.807122i	$-0.701024\pi$
$997$	−37.2832	−1.18077	−0.590385	+	0.807122i	$0.701024\pi$
$998$	84.6553	2.67972
$999$	2.42842	0.0768318

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3887.2.a.p.1.1		10
13.12	even	2		299.2.a.g.1.10	✓	10
39.38	odd	2		2691.2.a.bc.1.1		10
52.51	odd	2		4784.2.a.bh.1.6		10
65.64	even	2		7475.2.a.w.1.1		10
299.298	odd	2		6877.2.a.o.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
299.2.a.g.1.10	✓	10	13.12	even	2
2691.2.a.bc.1.1		10	39.38	odd	2
3887.2.a.p.1.1		10	1.1	even	1	trivial
4784.2.a.bh.1.6		10	52.51	odd	2
6877.2.a.o.1.10		10	299.298	odd	2
7475.2.a.w.1.1		10	65.64	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:	\( N \)	\(=\)	\( 3887 = 13^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3887.a (trivial)

\(f(q)\)	\(=\)	\(q-2.76732 q^{2} +0.315862 q^{3} +5.65804 q^{4} +0.739140 q^{5} -0.874091 q^{6} +4.71764 q^{7} -10.1230 q^{8} -2.90023 q^{9} +O(q^{10})\)	\(q-2.76732 q^{2} +0.315862 q^{3} +5.65804 q^{4} +0.739140 q^{5} -0.874091 q^{6} +4.71764 q^{7} -10.1230 q^{8} -2.90023 q^{9} -2.04543 q^{10} -4.47733 q^{11} +1.78716 q^{12} -13.0552 q^{14} +0.233466 q^{15} +16.6973 q^{16} -1.20264 q^{17} +8.02586 q^{18} +4.53243 q^{19} +4.18208 q^{20} +1.49012 q^{21} +12.3902 q^{22} +1.00000 q^{23} -3.19746 q^{24} -4.45367 q^{25} -1.86366 q^{27} +26.6926 q^{28} +1.63190 q^{29} -0.646075 q^{30} -2.02953 q^{31} -25.9609 q^{32} -1.41422 q^{33} +3.32807 q^{34} +3.48699 q^{35} -16.4096 q^{36} -1.30304 q^{37} -12.5427 q^{38} -7.48227 q^{40} -5.73626 q^{41} -4.12364 q^{42} -3.32183 q^{43} -25.3329 q^{44} -2.14368 q^{45} -2.76732 q^{46} -8.46838 q^{47} +5.27406 q^{48} +15.2561 q^{49} +12.3247 q^{50} -0.379867 q^{51} +8.80439 q^{53} +5.15734 q^{54} -3.30937 q^{55} -47.7564 q^{56} +1.43162 q^{57} -4.51598 q^{58} +13.8468 q^{59} +1.32096 q^{60} +3.37399 q^{61} +5.61634 q^{62} -13.6822 q^{63} +38.4473 q^{64} +3.91359 q^{66} +7.84742 q^{67} -6.80456 q^{68} +0.315862 q^{69} -9.64961 q^{70} +1.11829 q^{71} +29.3589 q^{72} +2.83064 q^{73} +3.60592 q^{74} -1.40675 q^{75} +25.6447 q^{76} -21.1224 q^{77} +6.85571 q^{79} +12.3417 q^{80} +8.11203 q^{81} +15.8740 q^{82} +16.8067 q^{83} +8.43118 q^{84} -0.888916 q^{85} +9.19256 q^{86} +0.515455 q^{87} +45.3238 q^{88} +6.44775 q^{89} +5.93223 q^{90} +5.65804 q^{92} -0.641051 q^{93} +23.4347 q^{94} +3.35010 q^{95} -8.20006 q^{96} -3.68806 q^{97} -42.2185 q^{98} +12.9853 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} + 3 q^{3} + 19 q^{4} - 3 q^{5} - q^{6} + 2 q^{7} + 17 q^{9}+O(q^{10}) \) 10 * q - q^2 + 3 * q^3 + 19 * q^4 - 3 * q^5 - q^6 + 2 * q^7 + 17 * q^9	\( 10 q - q^{2} + 3 q^{3} + 19 q^{4} - 3 q^{5} - q^{6} + 2 q^{7} + 17 q^{9} + 6 q^{10} - 3 q^{11} + 10 q^{12} - 15 q^{14} - 2 q^{15} + 25 q^{16} - 3 q^{17} - q^{18} - 2 q^{19} + 19 q^{20} - 21 q^{21} + 13 q^{22} + 10 q^{23} + 35 q^{24} + 33 q^{25} + 6 q^{27} + 19 q^{28} + 17 q^{29} - 47 q^{30} - 5 q^{31} + 9 q^{32} + 23 q^{33} - 23 q^{34} + 3 q^{35} + 48 q^{36} - 16 q^{37} + 5 q^{38} + 13 q^{40} + 16 q^{41} - 65 q^{42} - 9 q^{43} - 18 q^{44} - 32 q^{45} - q^{46} + 11 q^{47} + 37 q^{48} + 40 q^{49} + 30 q^{50} - 31 q^{51} + 8 q^{53} + 73 q^{54} - 14 q^{55} - 54 q^{56} + 35 q^{57} - 17 q^{58} - 2 q^{59} + 37 q^{60} + 48 q^{61} - 19 q^{62} + 15 q^{63} + 64 q^{64} - 84 q^{66} + 6 q^{67} - 62 q^{68} + 3 q^{69} + 44 q^{70} - 24 q^{71} + 89 q^{72} + 33 q^{73} - 28 q^{74} - 22 q^{75} + 53 q^{76} + 15 q^{77} + 17 q^{79} + 94 q^{80} + 30 q^{81} + 35 q^{82} + 21 q^{83} - 92 q^{84} - 58 q^{85} + 7 q^{86} + 23 q^{87} + 9 q^{88} + 16 q^{89} + 67 q^{90} + 19 q^{92} - 15 q^{93} + 12 q^{94} - 27 q^{95} + 22 q^{96} + 40 q^{97} + 34 q^{98} + 17 q^{99}+O(q^{100}) \) 10 * q - q^2 + 3 * q^3 + 19 * q^4 - 3 * q^5 - q^6 + 2 * q^7 + 17 * q^9 + 6 * q^10 - 3 * q^11 + 10 * q^12 - 15 * q^14 - 2 * q^15 + 25 * q^16 - 3 * q^17 - q^18 - 2 * q^19 + 19 * q^20 - 21 * q^21 + 13 * q^22 + 10 * q^23 + 35 * q^24 + 33 * q^25 + 6 * q^27 + 19 * q^28 + 17 * q^29 - 47 * q^30 - 5 * q^31 + 9 * q^32 + 23 * q^33 - 23 * q^34 + 3 * q^35 + 48 * q^36 - 16 * q^37 + 5 * q^38 + 13 * q^40 + 16 * q^41 - 65 * q^42 - 9 * q^43 - 18 * q^44 - 32 * q^45 - q^46 + 11 * q^47 + 37 * q^48 + 40 * q^49 + 30 * q^50 - 31 * q^51 + 8 * q^53 + 73 * q^54 - 14 * q^55 - 54 * q^56 + 35 * q^57 - 17 * q^58 - 2 * q^59 + 37 * q^60 + 48 * q^61 - 19 * q^62 + 15 * q^63 + 64 * q^64 - 84 * q^66 + 6 * q^67 - 62 * q^68 + 3 * q^69 + 44 * q^70 - 24 * q^71 + 89 * q^72 + 33 * q^73 - 28 * q^74 - 22 * q^75 + 53 * q^76 + 15 * q^77 + 17 * q^79 + 94 * q^80 + 30 * q^81 + 35 * q^82 + 21 * q^83 - 92 * q^84 - 58 * q^85 + 7 * q^86 + 23 * q^87 + 9 * q^88 + 16 * q^89 + 67 * q^90 + 19 * q^92 - 15 * q^93 + 12 * q^94 - 27 * q^95 + 22 * q^96 + 40 * q^97 + 34 * q^98 + 17 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more