LMFDB - Embedded newform 3381.2.a.bj.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3381,2,Mod(1,3381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3381, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3381 = 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3381.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:	$26.9974209234$
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} - 3x^{9} - 13x^{8} + 41x^{7} + 47x^{6} - 165x^{5} - 45x^{4} + 207x^{3} + 12x^{2} - 76x - 2 $ x^10 - 3x^9 - 13x^8 + 41x^7 + 47x^6 - 165x^5 - 45x^4 + 207x^3 + 12x^2 - 76*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 483)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$2.79962$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.79962 q^{2} +1.00000 q^{3} +5.83786 q^{4} +1.94708 q^{5} +2.79962 q^{6} +10.7446 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.79962 q^{2} +1.00000 q^{3} +5.83786 q^{4} +1.94708 q^{5} +2.79962 q^{6} +10.7446 q^{8} +1.00000 q^{9} +5.45107 q^{10} -2.68769 q^{11} +5.83786 q^{12} -4.19039 q^{13} +1.94708 q^{15} +18.4049 q^{16} +0.632396 q^{17} +2.79962 q^{18} -5.55426 q^{19} +11.3668 q^{20} -7.52450 q^{22} +1.00000 q^{23} +10.7446 q^{24} -1.20890 q^{25} -11.7315 q^{26} +1.00000 q^{27} +5.57812 q^{29} +5.45107 q^{30} +5.59818 q^{31} +30.0377 q^{32} -2.68769 q^{33} +1.77047 q^{34} +5.83786 q^{36} +4.11612 q^{37} -15.5498 q^{38} -4.19039 q^{39} +20.9205 q^{40} -5.19481 q^{41} -1.98626 q^{43} -15.6903 q^{44} +1.94708 q^{45} +2.79962 q^{46} +0.292587 q^{47} +18.4049 q^{48} -3.38445 q^{50} +0.632396 q^{51} -24.4629 q^{52} -10.1722 q^{53} +2.79962 q^{54} -5.23313 q^{55} -5.55426 q^{57} +15.6166 q^{58} -7.31960 q^{59} +11.3668 q^{60} +6.28692 q^{61} +15.6728 q^{62} +47.2842 q^{64} -8.15900 q^{65} -7.52450 q^{66} +3.14875 q^{67} +3.69184 q^{68} +1.00000 q^{69} +6.00227 q^{71} +10.7446 q^{72} -13.8625 q^{73} +11.5236 q^{74} -1.20890 q^{75} -32.4250 q^{76} -11.7315 q^{78} +15.7902 q^{79} +35.8358 q^{80} +1.00000 q^{81} -14.5435 q^{82} -12.4983 q^{83} +1.23132 q^{85} -5.56077 q^{86} +5.57812 q^{87} -28.8780 q^{88} -1.81155 q^{89} +5.45107 q^{90} +5.83786 q^{92} +5.59818 q^{93} +0.819132 q^{94} -10.8146 q^{95} +30.0377 q^{96} +2.95190 q^{97} -2.68769 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{2} + 10 q^{3} + 15 q^{4} + 5 q^{5} + 3 q^{6} + 9 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 3 * q^2 + 10 * q^3 + 15 * q^4 + 5 * q^5 + 3 * q^6 + 9 * q^8 + 10 * q^9	$ 10 q + 3 q^{2} + 10 q^{3} + 15 q^{4} + 5 q^{5} + 3 q^{6} + 9 q^{8} + 10 q^{9} - 11 q^{10} + 8 q^{11} + 15 q^{12} + 5 q^{15} + 37 q^{16} + 11 q^{17} + 3 q^{18} - q^{19} + 15 q^{20} + 6 q^{22} + 10 q^{23} + 9 q^{24} + 21 q^{25} - q^{26} + 10 q^{27} + 22 q^{29} - 11 q^{30} + 3 q^{31} + 11 q^{32} + 8 q^{33} + 3 q^{34} + 15 q^{36} - 3 q^{37} - 16 q^{38} - 39 q^{40} + 26 q^{41} + 27 q^{43} + 16 q^{44} + 5 q^{45} + 3 q^{46} - 11 q^{47} + 37 q^{48} + 2 q^{50} + 11 q^{51} - 29 q^{52} + 5 q^{53} + 3 q^{54} + 18 q^{55} - q^{57} + 16 q^{58} + 10 q^{59} + 15 q^{60} - 22 q^{61} + 32 q^{62} + 69 q^{64} - 11 q^{65} + 6 q^{66} - 2 q^{67} + 21 q^{68} + 10 q^{69} + 27 q^{71} + 9 q^{72} + 8 q^{73} + 14 q^{74} + 21 q^{75} + 22 q^{76} - q^{78} + 21 q^{79} + 53 q^{80} + 10 q^{81} - 36 q^{82} + 12 q^{83} + 23 q^{85} + 18 q^{86} + 22 q^{87} - 10 q^{88} - 6 q^{89} - 11 q^{90} + 15 q^{92} + 3 q^{93} - 35 q^{94} + 44 q^{95} + 11 q^{96} - 6 q^{97} + 8 q^{99}+O(q^{100}) $ 10 * q + 3 * q^2 + 10 * q^3 + 15 * q^4 + 5 * q^5 + 3 * q^6 + 9 * q^8 + 10 * q^9 - 11 * q^10 + 8 * q^11 + 15 * q^12 + 5 * q^15 + 37 * q^16 + 11 * q^17 + 3 * q^18 - q^19 + 15 * q^20 + 6 * q^22 + 10 * q^23 + 9 * q^24 + 21 * q^25 - q^26 + 10 * q^27 + 22 * q^29 - 11 * q^30 + 3 * q^31 + 11 * q^32 + 8 * q^33 + 3 * q^34 + 15 * q^36 - 3 * q^37 - 16 * q^38 - 39 * q^40 + 26 * q^41 + 27 * q^43 + 16 * q^44 + 5 * q^45 + 3 * q^46 - 11 * q^47 + 37 * q^48 + 2 * q^50 + 11 * q^51 - 29 * q^52 + 5 * q^53 + 3 * q^54 + 18 * q^55 - q^57 + 16 * q^58 + 10 * q^59 + 15 * q^60 - 22 * q^61 + 32 * q^62 + 69 * q^64 - 11 * q^65 + 6 * q^66 - 2 * q^67 + 21 * q^68 + 10 * q^69 + 27 * q^71 + 9 * q^72 + 8 * q^73 + 14 * q^74 + 21 * q^75 + 22 * q^76 - q^78 + 21 * q^79 + 53 * q^80 + 10 * q^81 - 36 * q^82 + 12 * q^83 + 23 * q^85 + 18 * q^86 + 22 * q^87 - 10 * q^88 - 6 * q^89 - 11 * q^90 + 15 * q^92 + 3 * q^93 - 35 * q^94 + 44 * q^95 + 11 * q^96 - 6 * q^97 + 8 * 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 $

$2$	2.79962	1.97963	0.989815	−	0.142362i	$-0.0454697\pi$
$2$	2.79962	1.97963	0.989815	+	0.142362i	$0.0454697\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.83786	2.91893
$5$	1.94708	0.870759	0.435379	−	0.900247i	$-0.356614\pi$
$5$	1.94708	0.870759	0.435379	+	0.900247i	$0.356614\pi$
$6$	2.79962	1.14294
$7$	0	0
$7$	0	0
$8$	10.7446	3.79878
$9$	1.00000	0.333333
$10$	5.45107	1.72378
$11$	−2.68769	−0.810368	−0.405184	−	0.914235i	$-0.632793\pi$
$11$	−2.68769	−0.810368	−0.405184	+	0.914235i	$0.632793\pi$
$12$	5.83786	1.68525
$13$	−4.19039	−1.16220	−0.581102	−	0.813831i	$-0.697378\pi$
$13$	−4.19039	−1.16220	−0.581102	+	0.813831i	$0.697378\pi$
$14$	0	0
$15$	1.94708	0.502733
$16$	18.4049	4.60123
$17$	0.632396	0.153379	0.0766893	−	0.997055i	$-0.475565\pi$
$17$	0.632396	0.153379	0.0766893	+	0.997055i	$0.475565\pi$
$18$	2.79962	0.659876
$19$	−5.55426	−1.27423	−0.637117	−	0.770767i	$-0.719873\pi$
$19$	−5.55426	−1.27423	−0.637117	+	0.770767i	$0.719873\pi$
$20$	11.3668	2.54169
$21$	0	0
$22$	−7.52450	−1.60423
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	10.7446	2.19322
$25$	−1.20890	−0.241779
$26$	−11.7315	−2.30073
$27$	1.00000	0.192450
$28$	0	0
$29$	5.57812	1.03583	0.517915	−	0.855432i	$-0.326708\pi$
$29$	5.57812	1.03583	0.517915	+	0.855432i	$0.326708\pi$
$30$	5.45107	0.995225
$31$	5.59818	1.00546	0.502732	−	0.864443i	$-0.332328\pi$
$31$	5.59818	1.00546	0.502732	+	0.864443i	$0.332328\pi$
$32$	30.0377	5.30996
$33$	−2.68769	−0.467866
$34$	1.77047	0.303633
$35$	0	0
$36$	5.83786	0.972977
$37$	4.11612	0.676686	0.338343	−	0.941023i	$-0.390134\pi$
$37$	4.11612	0.676686	0.338343	+	0.941023i	$0.390134\pi$
$38$	−15.5498	−2.52251
$39$	−4.19039	−0.670999
$40$	20.9205	3.30782
$41$	−5.19481	−0.811293	−0.405647	−	0.914030i	$-0.632954\pi$
$41$	−5.19481	−0.811293	−0.405647	+	0.914030i	$0.632954\pi$
$42$	0	0
$43$	−1.98626	−0.302902	−0.151451	−	0.988465i	$-0.548395\pi$
$43$	−1.98626	−0.302902	−0.151451	+	0.988465i	$0.548395\pi$
$44$	−15.6903	−2.36541
$45$	1.94708	0.290253
$46$	2.79962	0.412781
$47$	0.292587	0.0426782	0.0213391	−	0.999772i	$-0.493207\pi$
$47$	0.292587	0.0426782	0.0213391	+	0.999772i	$0.493207\pi$
$48$	18.4049	2.65652
$49$	0	0
$50$	−3.38445	−0.478633
$51$	0.632396	0.0885532
$52$	−24.4629	−3.39240
$53$	−10.1722	−1.39725	−0.698627	−	0.715486i	$-0.746205\pi$
$53$	−10.1722	−1.39725	−0.698627	+	0.715486i	$0.746205\pi$
$54$	2.79962	0.380980
$55$	−5.23313	−0.705635
$56$	0	0
$57$	−5.55426	−0.735679
$58$	15.6166	2.05056
$59$	−7.31960	−0.952931	−0.476466	−	0.879193i	$-0.658082\pi$
$59$	−7.31960	−0.952931	−0.476466	+	0.879193i	$0.658082\pi$
$60$	11.3668	1.46744
$61$	6.28692	0.804958	0.402479	−	0.915429i	$-0.368149\pi$
$61$	6.28692	0.804958	0.402479	+	0.915429i	$0.368149\pi$
$62$	15.6728	1.99044
$63$	0	0
$64$	47.2842	5.91053
$65$	−8.15900	−1.01200
$66$	−7.52450	−0.926201
$67$	3.14875	0.384681	0.192340	−	0.981328i	$-0.438392\pi$
$67$	3.14875	0.384681	0.192340	+	0.981328i	$0.438392\pi$
$68$	3.69184	0.447702
$69$	1.00000	0.120386
$70$	0	0
$71$	6.00227	0.712338	0.356169	−	0.934422i	$-0.384083\pi$
$71$	6.00227	0.712338	0.356169	+	0.934422i	$0.384083\pi$
$72$	10.7446	1.26626
$73$	−13.8625	−1.62249	−0.811243	−	0.584709i	$-0.801209\pi$
$73$	−13.8625	−1.62249	−0.811243	+	0.584709i	$0.801209\pi$
$74$	11.5236	1.33959
$75$	−1.20890	−0.139591
$76$	−32.4250	−3.71940
$77$	0	0
$78$	−11.7315	−1.32833
$79$	15.7902	1.77654	0.888268	−	0.459326i	$-0.151909\pi$
$79$	15.7902	1.77654	0.888268	+	0.459326i	$0.151909\pi$
$80$	35.8358	4.00656
$81$	1.00000	0.111111
$82$	−14.5435	−1.60606
$83$	−12.4983	−1.37186	−0.685931	−	0.727666i	$-0.740605\pi$
$83$	−12.4983	−1.37186	−0.685931	+	0.727666i	$0.740605\pi$
$84$	0	0
$85$	1.23132	0.133556
$86$	−5.56077	−0.599633
$87$	5.57812	0.598037
$88$	−28.8780	−3.07841
$89$	−1.81155	−0.192024	−0.0960119	−	0.995380i	$-0.530609\pi$
$89$	−1.81155	−0.192024	−0.0960119	+	0.995380i	$0.530609\pi$
$90$	5.45107	0.574593
$91$	0	0
$92$	5.83786	0.608639
$93$	5.59818	0.580504
$94$	0.819132	0.0844870
$95$	−10.8146	−1.10955
$96$	30.0377	3.06571
$97$	2.95190	0.299720	0.149860	−	0.988707i	$-0.452118\pi$
$97$	2.95190	0.299720	0.149860	+	0.988707i	$0.452118\pi$
$98$	0	0
$99$	−2.68769	−0.270123
$100$	−7.05738	−0.705738
$101$	12.8013	1.27378	0.636889	−	0.770955i	$-0.280221\pi$
$101$	12.8013	1.27378	0.636889	+	0.770955i	$0.280221\pi$
$102$	1.77047	0.175302
$103$	−13.0581	−1.28665	−0.643325	−	0.765593i	$-0.722446\pi$
$103$	−13.0581	−1.28665	−0.643325	+	0.765593i	$0.722446\pi$
$104$	−45.0239	−4.41495
$105$	0	0
$106$	−28.4782	−2.76605
$107$	−13.7217	−1.32653	−0.663263	−	0.748387i	$-0.730829\pi$
$107$	−13.7217	−1.32653	−0.663263	+	0.748387i	$0.730829\pi$
$108$	5.83786	0.561749
$109$	−4.50591	−0.431588	−0.215794	−	0.976439i	$-0.569234\pi$
$109$	−4.50591	−0.431588	−0.215794	+	0.976439i	$0.569234\pi$
$110$	−14.6508	−1.39690
$111$	4.11612	0.390685
$112$	0	0
$113$	−16.4013	−1.54290	−0.771451	−	0.636288i	$-0.780469\pi$
$113$	−16.4013	−1.54290	−0.771451	+	0.636288i	$0.780469\pi$
$114$	−15.5498	−1.45637
$115$	1.94708	0.181566
$116$	32.5643	3.02352
$117$	−4.19039	−0.387401
$118$	−20.4921	−1.88645
$119$	0	0
$120$	20.9205	1.90977
$121$	−3.77634	−0.343304
$122$	17.6010	1.59352
$123$	−5.19481	−0.468400
$124$	32.6814	2.93488
$125$	−12.0892	−1.08129
$126$	0	0
$127$	−18.2031	−1.61527	−0.807634	−	0.589685i	$-0.799252\pi$
$127$	−18.2031	−1.61527	−0.807634	+	0.589685i	$0.799252\pi$
$128$	72.3024	6.39069
$129$	−1.98626	−0.174880
$130$	−22.8421	−2.00338
$131$	8.32841	0.727656	0.363828	−	0.931466i	$-0.381470\pi$
$131$	8.32841	0.727656	0.363828	+	0.931466i	$0.381470\pi$
$132$	−15.6903	−1.36567
$133$	0	0
$134$	8.81530	0.761526
$135$	1.94708	0.167578
$136$	6.79482	0.582651
$137$	−13.3043	−1.13667	−0.568333	−	0.822798i	$-0.692412\pi$
$137$	−13.3043	−1.13667	−0.568333	+	0.822798i	$0.692412\pi$
$138$	2.79962	0.238319
$139$	5.93319	0.503247	0.251623	−	0.967825i	$-0.419036\pi$
$139$	5.93319	0.503247	0.251623	+	0.967825i	$0.419036\pi$
$140$	0	0
$141$	0.292587	0.0246403
$142$	16.8041	1.41017
$143$	11.2624	0.941813
$144$	18.4049	1.53374
$145$	10.8610	0.901959
$146$	−38.8098	−3.21192
$147$	0	0
$148$	24.0293	1.97520
$149$	−4.83066	−0.395743	−0.197872	−	0.980228i	$-0.563403\pi$
$149$	−4.83066	−0.395743	−0.197872	+	0.980228i	$0.563403\pi$
$150$	−3.38445	−0.276339
$151$	20.9847	1.70771	0.853854	−	0.520513i	$-0.174259\pi$
$151$	20.9847	1.70771	0.853854	+	0.520513i	$0.174259\pi$
$152$	−59.6780	−4.84053
$153$	0.632396	0.0511262
$154$	0	0
$155$	10.9001	0.875516
$156$	−24.4629	−1.95860
$157$	−1.59444	−0.127250	−0.0636250	−	0.997974i	$-0.520266\pi$
$157$	−1.59444	−0.127250	−0.0636250	+	0.997974i	$0.520266\pi$
$158$	44.2065	3.51688
$159$	−10.1722	−0.806705
$160$	58.4857	4.62370
$161$	0	0
$162$	2.79962	0.219959
$163$	−10.8977	−0.853571	−0.426786	−	0.904353i	$-0.640354\pi$
$163$	−10.8977	−0.853571	−0.426786	+	0.904353i	$0.640354\pi$
$164$	−30.3266	−2.36811
$165$	−5.23313	−0.407398
$166$	−34.9904	−2.71578
$167$	15.5931	1.20663	0.603313	−	0.797504i	$-0.293847\pi$
$167$	15.5931	1.20663	0.603313	+	0.797504i	$0.293847\pi$
$168$	0	0
$169$	4.55935	0.350719
$170$	3.44723	0.264391
$171$	−5.55426	−0.424745
$172$	−11.5955	−0.884149
$173$	11.2721	0.857002	0.428501	−	0.903541i	$-0.359042\pi$
$173$	11.2721	0.857002	0.428501	+	0.903541i	$0.359042\pi$
$174$	15.6166	1.18389
$175$	0	0
$176$	−49.4667	−3.72869
$177$	−7.31960	−0.550175
$178$	−5.07165	−0.380136
$179$	8.17508	0.611034	0.305517	−	0.952187i	$-0.401171\pi$
$179$	8.17508	0.611034	0.305517	+	0.952187i	$0.401171\pi$
$180$	11.3668	0.847229
$181$	3.00094	0.223058	0.111529	−	0.993761i	$-0.464425\pi$
$181$	3.00094	0.223058	0.111529	+	0.993761i	$0.464425\pi$
$182$	0	0
$183$	6.28692	0.464743
$184$	10.7446	0.792099
$185$	8.01439	0.589230
$186$	15.6728	1.14918
$187$	−1.69968	−0.124293
$188$	1.70808	0.124575
$189$	0	0
$190$	−30.2766	−2.19650
$191$	−11.5788	−0.837814	−0.418907	−	0.908029i	$-0.637587\pi$
$191$	−11.5788	−0.837814	−0.418907	+	0.908029i	$0.637587\pi$
$192$	47.2842	3.41244
$193$	5.69929	0.410244	0.205122	−	0.978736i	$-0.434241\pi$
$193$	5.69929	0.410244	0.205122	+	0.978736i	$0.434241\pi$
$194$	8.26419	0.593334
$195$	−8.15900	−0.584278
$196$	0	0
$197$	−12.9883	−0.925379	−0.462689	−	0.886521i	$-0.653115\pi$
$197$	−12.9883	−0.925379	−0.462689	+	0.886521i	$0.653115\pi$
$198$	−7.52450	−0.534743
$199$	21.3255	1.51173	0.755864	−	0.654729i	$-0.227217\pi$
$199$	21.3255	1.51173	0.755864	+	0.654729i	$0.227217\pi$
$200$	−12.9891	−0.918465
$201$	3.14875	0.222096
$202$	35.8388	2.52161
$203$	0	0
$204$	3.69184	0.258481
$205$	−10.1147	−0.706441
$206$	−36.5576	−2.54709
$207$	1.00000	0.0695048
$208$	−77.1238	−5.34758
$209$	14.9281	1.03260
$210$	0	0
$211$	7.69191	0.529533	0.264766	−	0.964313i	$-0.414705\pi$
$211$	7.69191	0.529533	0.264766	+	0.964313i	$0.414705\pi$
$212$	−59.3837	−4.07849
$213$	6.00227	0.411269
$214$	−38.4155	−2.62603
$215$	−3.86740	−0.263754
$216$	10.7446	0.731075
$217$	0	0
$218$	−12.6148	−0.854384
$219$	−13.8625	−0.936743
$220$	−30.5503	−2.05970
$221$	−2.64998	−0.178257
$222$	11.5236	0.773411
$223$	−20.9689	−1.40418	−0.702091	−	0.712087i	$-0.747750\pi$
$223$	−20.9689	−1.40418	−0.702091	+	0.712087i	$0.747750\pi$
$224$	0	0
$225$	−1.20890	−0.0805931
$226$	−45.9173	−3.05438
$227$	24.1758	1.60460	0.802302	−	0.596918i	$-0.203608\pi$
$227$	24.1758	1.60460	0.802302	+	0.596918i	$0.203608\pi$
$228$	−32.4250	−2.14740
$229$	8.67855	0.573495	0.286747	−	0.958006i	$-0.407426\pi$
$229$	8.67855	0.573495	0.286747	+	0.958006i	$0.407426\pi$
$230$	5.45107	0.359433
$231$	0	0
$232$	59.9344	3.93489
$233$	2.69180	0.176346	0.0881729	−	0.996105i	$-0.471897\pi$
$233$	2.69180	0.176346	0.0881729	+	0.996105i	$0.471897\pi$
$234$	−11.7315	−0.766911
$235$	0.569689	0.0371624
$236$	−42.7308	−2.78154
$237$	15.7902	1.02568
$238$	0	0
$239$	−0.0523580	−0.00338675	−0.00169338	−	0.999999i	$-0.500539\pi$
$239$	−0.0523580	−0.00338675	−0.00169338	+	0.999999i	$0.500539\pi$
$240$	35.8358	2.31319
$241$	0.299551	0.0192958	0.00964789	−	0.999953i	$-0.496929\pi$
$241$	0.299551	0.0192958	0.00964789	+	0.999953i	$0.496929\pi$
$242$	−10.5723	−0.679615
$243$	1.00000	0.0641500
$244$	36.7022	2.34962
$245$	0	0
$246$	−14.5435	−0.927259
$247$	23.2745	1.48092
$248$	60.1500	3.81953
$249$	−12.4983	−0.792045
$250$	−33.8451	−2.14055
$251$	5.72848	0.361579	0.180789	−	0.983522i	$-0.442135\pi$
$251$	5.72848	0.361579	0.180789	+	0.983522i	$0.442135\pi$
$252$	0	0
$253$	−2.68769	−0.168973
$254$	−50.9618	−3.19763
$255$	1.23132	0.0771084
$256$	107.851	6.74066
$257$	17.2297	1.07476	0.537379	−	0.843341i	$-0.319415\pi$
$257$	17.2297	1.07476	0.537379	+	0.843341i	$0.319415\pi$
$258$	−5.56077	−0.346198
$259$	0	0
$260$	−47.6312	−2.95396
$261$	5.57812	0.345277
$262$	23.3164	1.44049
$263$	23.5216	1.45040	0.725202	−	0.688537i	$-0.241747\pi$
$263$	23.5216	1.45040	0.725202	+	0.688537i	$0.241747\pi$
$264$	−28.8780	−1.77732
$265$	−19.8060	−1.21667
$266$	0	0
$267$	−1.81155	−0.110865
$268$	18.3820	1.12286
$269$	13.8092	0.841965	0.420982	−	0.907069i	$-0.361685\pi$
$269$	13.8092	0.841965	0.420982	+	0.907069i	$0.361685\pi$
$270$	5.45107	0.331742
$271$	22.4422	1.36327	0.681634	−	0.731693i	$-0.261270\pi$
$271$	22.4422	1.36327	0.681634	+	0.731693i	$0.261270\pi$
$272$	11.6392	0.705731
$273$	0	0
$274$	−37.2471	−2.25018
$275$	3.24913	0.195930
$276$	5.83786	0.351398
$277$	22.2276	1.33553	0.667765	−	0.744373i	$-0.267251\pi$
$277$	22.2276	1.33553	0.667765	+	0.744373i	$0.267251\pi$
$278$	16.6107	0.996242
$279$	5.59818	0.335154
$280$	0	0
$281$	6.99680	0.417394	0.208697	−	0.977980i	$-0.433078\pi$
$281$	6.99680	0.417394	0.208697	+	0.977980i	$0.433078\pi$
$282$	0.819132	0.0487786
$283$	−8.06377	−0.479341	−0.239671	−	0.970854i	$-0.577039\pi$
$283$	−8.06377	−0.479341	−0.239671	+	0.970854i	$0.577039\pi$
$284$	35.0404	2.07927
$285$	−10.8146	−0.640599
$286$	31.5306	1.86444
$287$	0	0
$288$	30.0377	1.76999
$289$	−16.6001	−0.976475
$290$	30.4067	1.78554
$291$	2.95190	0.173043
$292$	−80.9276	−4.73593
$293$	13.1458	0.767986	0.383993	−	0.923336i	$-0.374549\pi$
$293$	13.1458	0.767986	0.383993	+	0.923336i	$0.374549\pi$
$294$	0	0
$295$	−14.2518	−0.829773
$296$	44.2259	2.57058
$297$	−2.68769	−0.155955
$298$	−13.5240	−0.783425
$299$	−4.19039	−0.242336
$300$	−7.05738	−0.407458
$301$	0	0
$302$	58.7490	3.38063
$303$	12.8013	0.735416
$304$	−102.226	−5.86305
$305$	12.2411	0.700924
$306$	1.77047	0.101211
$307$	−15.1086	−0.862293	−0.431147	−	0.902282i	$-0.641891\pi$
$307$	−15.1086	−0.862293	−0.431147	+	0.902282i	$0.641891\pi$
$308$	0	0
$309$	−13.0581	−0.742848
$310$	30.5161	1.73320
$311$	21.4828	1.21818	0.609090	−	0.793101i	$-0.291535\pi$
$311$	21.4828	1.21818	0.609090	+	0.793101i	$0.291535\pi$
$312$	−45.0239	−2.54897
$313$	−14.8382	−0.838707	−0.419353	−	0.907823i	$-0.637743\pi$
$313$	−14.8382	−0.838707	−0.419353	+	0.907823i	$0.637743\pi$
$314$	−4.46382	−0.251908
$315$	0	0
$316$	92.1810	5.18559
$317$	−4.70173	−0.264075	−0.132038	−	0.991245i	$-0.542152\pi$
$317$	−4.70173	−0.264075	−0.132038	+	0.991245i	$0.542152\pi$
$318$	−28.4782	−1.59698
$319$	−14.9922	−0.839404
$320$	92.0659	5.14664
$321$	−13.7217	−0.765870
$322$	0	0
$323$	−3.51249	−0.195440
$324$	5.83786	0.324326
$325$	5.06575	0.280997
$326$	−30.5093	−1.68975
$327$	−4.50591	−0.249177
$328$	−55.8160	−3.08192
$329$	0	0
$330$	−14.6508	−0.806498
$331$	−7.87864	−0.433049	−0.216524	−	0.976277i	$-0.569472\pi$
$331$	−7.87864	−0.433049	−0.216524	+	0.976277i	$0.569472\pi$
$332$	−72.9632	−4.00437
$333$	4.11612	0.225562
$334$	43.6546	2.38867
$335$	6.13085	0.334964
$336$	0	0
$337$	−18.3857	−1.00153	−0.500767	−	0.865582i	$-0.666949\pi$
$337$	−18.3857	−1.00153	−0.500767	+	0.865582i	$0.666949\pi$
$338$	12.7644	0.694294
$339$	−16.4013	−0.890795
$340$	7.18830	0.389840
$341$	−15.0462	−0.814795
$342$	−15.5498	−0.840837
$343$	0	0
$344$	−21.3415	−1.15066
$345$	1.94708	0.104827
$346$	31.5576	1.69655
$347$	6.02078	0.323212	0.161606	−	0.986855i	$-0.448333\pi$
$347$	6.02078	0.323212	0.161606	+	0.986855i	$0.448333\pi$
$348$	32.5643	1.74563
$349$	−13.3378	−0.713956	−0.356978	−	0.934113i	$-0.616193\pi$
$349$	−13.3378	−0.713956	−0.356978	+	0.934113i	$0.616193\pi$
$350$	0	0
$351$	−4.19039	−0.223666
$352$	−80.7319	−4.30302
$353$	−17.4870	−0.930739	−0.465369	−	0.885117i	$-0.654078\pi$
$353$	−17.4870	−0.930739	−0.465369	+	0.885117i	$0.654078\pi$
$354$	−20.4921	−1.08914
$355$	11.6869	0.620275
$356$	−10.5756	−0.560505
$357$	0	0
$358$	22.8871	1.20962
$359$	−8.56723	−0.452161	−0.226081	−	0.974109i	$-0.572591\pi$
$359$	−8.56723	−0.452161	−0.226081	+	0.974109i	$0.572591\pi$
$360$	20.9205	1.10261
$361$	11.8498	0.623671
$362$	8.40150	0.441573
$363$	−3.77634	−0.198207
$364$	0	0
$365$	−26.9914	−1.41279
$366$	17.6010	0.920018
$367$	19.7115	1.02893	0.514467	−	0.857510i	$-0.327990\pi$
$367$	19.7115	1.02893	0.514467	+	0.857510i	$0.327990\pi$
$368$	18.4049	0.959424
$369$	−5.19481	−0.270431
$370$	22.4372	1.16646
$371$	0	0
$372$	32.6814	1.69445
$373$	21.9259	1.13528	0.567639	−	0.823278i	$-0.307857\pi$
$373$	21.9259	1.13528	0.567639	+	0.823278i	$0.307857\pi$
$374$	−4.75846	−0.246054
$375$	−12.0892	−0.624283
$376$	3.14372	0.162125
$377$	−23.3745	−1.20385
$378$	0	0
$379$	9.89943	0.508500	0.254250	−	0.967139i	$-0.418171\pi$
$379$	9.89943	0.508500	0.254250	+	0.967139i	$0.418171\pi$
$380$	−63.1339	−3.23870
$381$	−18.2031	−0.932575
$382$	−32.4163	−1.65856
$383$	17.5379	0.896143	0.448071	−	0.893998i	$-0.352111\pi$
$383$	17.5379	0.896143	0.448071	+	0.893998i	$0.352111\pi$
$384$	72.3024	3.68966
$385$	0	0
$386$	15.9558	0.812131
$387$	−1.98626	−0.100967
$388$	17.2328	0.874862
$389$	19.2476	0.975894	0.487947	−	0.872873i	$-0.337746\pi$
$389$	19.2476	0.975894	0.487947	+	0.872873i	$0.337746\pi$
$390$	−22.8421	−1.15665
$391$	0.632396	0.0319816
$392$	0	0
$393$	8.32841	0.420113
$394$	−36.3623	−1.83191
$395$	30.7447	1.54693
$396$	−15.6903	−0.788470
$397$	24.5994	1.23461	0.617304	−	0.786724i	$-0.288225\pi$
$397$	24.5994	1.23461	0.617304	+	0.786724i	$0.288225\pi$
$398$	59.7034	2.99266
$399$	0	0
$400$	−22.2497	−1.11248
$401$	−7.88512	−0.393764	−0.196882	−	0.980427i	$-0.563082\pi$
$401$	−7.88512	−0.393764	−0.196882	+	0.980427i	$0.563082\pi$
$402$	8.81530	0.439667
$403$	−23.4586	−1.16855
$404$	74.7323	3.71807
$405$	1.94708	0.0967510
$406$	0	0
$407$	−11.0628	−0.548364
$408$	6.79482	0.336394
$409$	−4.80677	−0.237680	−0.118840	−	0.992913i	$-0.537917\pi$
$409$	−4.80677	−0.237680	−0.118840	+	0.992913i	$0.537917\pi$
$410$	−28.3173	−1.39849
$411$	−13.3043	−0.656255
$412$	−76.2313	−3.75565
$413$	0	0
$414$	2.79962	0.137594
$415$	−24.3351	−1.19456
$416$	−125.870	−6.17126
$417$	5.93319	0.290550
$418$	41.7930	2.04416
$419$	−4.37312	−0.213641	−0.106820	−	0.994278i	$-0.534067\pi$
$419$	−4.37312	−0.213641	−0.106820	+	0.994278i	$0.534067\pi$
$420$	0	0
$421$	−15.6894	−0.764655	−0.382327	−	0.924027i	$-0.624877\pi$
$421$	−15.6894	−0.764655	−0.382327	+	0.924027i	$0.624877\pi$
$422$	21.5344	1.04828
$423$	0.292587	0.0142261
$424$	−109.295	−5.30785
$425$	−0.764501	−0.0370838
$426$	16.8041	0.814159
$427$	0	0
$428$	−80.1053	−3.87204
$429$	11.2624	0.543756
$430$	−10.8272	−0.522136
$431$	−3.34633	−0.161187	−0.0805935	−	0.996747i	$-0.525682\pi$
$431$	−3.34633	−0.161187	−0.0805935	+	0.996747i	$0.525682\pi$
$432$	18.4049	0.885508
$433$	15.2273	0.731779	0.365889	−	0.930658i	$-0.380765\pi$
$433$	15.2273	0.731779	0.365889	+	0.930658i	$0.380765\pi$
$434$	0	0
$435$	10.8610	0.520746
$436$	−26.3049	−1.25978
$437$	−5.55426	−0.265696
$438$	−38.8098	−1.85440
$439$	−21.4914	−1.02573	−0.512865	−	0.858469i	$-0.671416\pi$
$439$	−21.4914	−1.02573	−0.512865	+	0.858469i	$0.671416\pi$
$440$	−56.2276	−2.68055
$441$	0	0
$442$	−7.41895	−0.352883
$443$	23.7846	1.13004	0.565019	−	0.825078i	$-0.308869\pi$
$443$	23.7846	1.13004	0.565019	+	0.825078i	$0.308869\pi$
$444$	24.0293	1.14038
$445$	−3.52722	−0.167206
$446$	−58.7050	−2.77976
$447$	−4.83066	−0.228482
$448$	0	0
$449$	−8.36232	−0.394642	−0.197321	−	0.980339i	$-0.563224\pi$
$449$	−8.36232	−0.394642	−0.197321	+	0.980339i	$0.563224\pi$
$450$	−3.38445	−0.159544
$451$	13.9620	0.657446
$452$	−95.7485	−4.50363
$453$	20.9847	0.985945
$454$	67.6831	3.17652
$455$	0	0
$456$	−59.6780	−2.79468
$457$	−15.9314	−0.745238	−0.372619	−	0.927984i	$-0.621540\pi$
$457$	−15.9314	−0.745238	−0.372619	+	0.927984i	$0.621540\pi$
$458$	24.2966	1.13531
$459$	0.632396	0.0295177
$460$	11.3668	0.529978
$461$	11.6774	0.543873	0.271936	−	0.962315i	$-0.412336\pi$
$461$	11.6774	0.543873	0.271936	+	0.962315i	$0.412336\pi$
$462$	0	0
$463$	−6.74188	−0.313322	−0.156661	−	0.987652i	$-0.550073\pi$
$463$	−6.74188	−0.313322	−0.156661	+	0.987652i	$0.550073\pi$
$464$	102.665	4.76610
$465$	10.9001	0.505479
$466$	7.53602	0.349099
$467$	−15.4800	−0.716328	−0.358164	−	0.933659i	$-0.616597\pi$
$467$	−15.4800	−0.716328	−0.358164	+	0.933659i	$0.616597\pi$
$468$	−24.4629	−1.13080
$469$	0	0
$470$	1.59491	0.0735678
$471$	−1.59444	−0.0734679
$472$	−78.6459	−3.61997
$473$	5.33844	0.245462
$474$	44.2065	2.03047
$475$	6.71452	0.308083
$476$	0	0
$477$	−10.1722	−0.465751
$478$	−0.146582	−0.00670452
$479$	−18.5720	−0.848574	−0.424287	−	0.905528i	$-0.639475\pi$
$479$	−18.5720	−0.848574	−0.424287	+	0.905528i	$0.639475\pi$
$480$	58.4857	2.66949
$481$	−17.2481	−0.786447
$482$	0.838629	0.0381985
$483$	0	0
$484$	−22.0458	−1.00208
$485$	5.74757	0.260984
$486$	2.79962	0.126993
$487$	18.1617	0.822984	0.411492	−	0.911413i	$-0.365008\pi$
$487$	18.1617	0.822984	0.411492	+	0.911413i	$0.365008\pi$
$488$	67.5502	3.05785
$489$	−10.8977	−0.492810
$490$	0	0
$491$	14.1905	0.640410	0.320205	−	0.947348i	$-0.396248\pi$
$491$	14.1905	0.640410	0.320205	+	0.947348i	$0.396248\pi$
$492$	−30.3266	−1.36723
$493$	3.52758	0.158874
$494$	65.1597	2.93167
$495$	−5.23313	−0.235212
$496$	103.034	4.62637
$497$	0	0
$498$	−34.9904	−1.56796
$499$	14.3387	0.641890	0.320945	−	0.947098i	$-0.396000\pi$
$499$	14.3387	0.641890	0.320945	+	0.947098i	$0.396000\pi$
$500$	−70.5751	−3.15621
$501$	15.5931	0.696646
$502$	16.0376	0.715791
$503$	−10.8254	−0.482681	−0.241341	−	0.970440i	$-0.577587\pi$
$503$	−10.8254	−0.482681	−0.241341	+	0.970440i	$0.577587\pi$
$504$	0	0
$505$	24.9251	1.10915
$506$	−7.52450	−0.334505
$507$	4.55935	0.202488
$508$	−106.267	−4.71486
$509$	−27.5502	−1.22114	−0.610570	−	0.791962i	$-0.709060\pi$
$509$	−27.5502	−1.22114	−0.610570	+	0.791962i	$0.709060\pi$
$510$	3.44723	0.152646
$511$	0	0
$512$	157.336	6.95333
$513$	−5.55426	−0.245226
$514$	48.2365	2.12762
$515$	−25.4251	−1.12036
$516$	−11.5955	−0.510464
$517$	−0.786382	−0.0345850
$518$	0	0
$519$	11.2721	0.494791
$520$	−87.6649	−3.84436
$521$	13.6364	0.597423	0.298712	−	0.954343i	$-0.403443\pi$
$521$	13.6364	0.597423	0.298712	+	0.954343i	$0.403443\pi$
$522$	15.6166	0.683520
$523$	10.5636	0.461912	0.230956	−	0.972964i	$-0.425815\pi$
$523$	10.5636	0.461912	0.230956	+	0.972964i	$0.425815\pi$
$524$	48.6201	2.12398
$525$	0	0
$526$	65.8515	2.87126
$527$	3.54027	0.154217
$528$	−49.4667	−2.15276
$529$	1.00000	0.0434783
$530$	−55.4492	−2.40856
$531$	−7.31960	−0.317644
$532$	0	0
$533$	21.7683	0.942889
$534$	−5.07165	−0.219472
$535$	−26.7172	−1.15508
$536$	33.8319	1.46132
$537$	8.17508	0.352781
$538$	38.6606	1.66678
$539$	0	0
$540$	11.3668	0.489148
$541$	31.6652	1.36139	0.680696	−	0.732566i	$-0.261677\pi$
$541$	31.6652	1.36139	0.680696	+	0.732566i	$0.261677\pi$
$542$	62.8297	2.69877
$543$	3.00094	0.128783
$544$	18.9957	0.814435
$545$	−8.77335	−0.375809
$546$	0	0
$547$	−30.4882	−1.30358	−0.651792	−	0.758398i	$-0.725982\pi$
$547$	−30.4882	−1.30358	−0.651792	+	0.758398i	$0.725982\pi$
$548$	−77.6689	−3.31785
$549$	6.28692	0.268319
$550$	9.09634	0.387869
$551$	−30.9823	−1.31989
$552$	10.7446	0.457319
$553$	0	0
$554$	62.2289	2.64385
$555$	8.01439	0.340192
$556$	34.6372	1.46894
$557$	14.1228	0.598401	0.299200	−	0.954190i	$-0.403280\pi$
$557$	14.1228	0.598401	0.299200	+	0.954190i	$0.403280\pi$
$558$	15.6728	0.663482
$559$	8.32319	0.352034
$560$	0	0
$561$	−1.69968	−0.0717606
$562$	19.5884	0.826285
$563$	17.2841	0.728437	0.364219	−	0.931313i	$-0.381336\pi$
$563$	17.2841	0.728437	0.364219	+	0.931313i	$0.381336\pi$
$564$	1.70808	0.0719233
$565$	−31.9345	−1.34350
$566$	−22.5755	−0.948918
$567$	0	0
$568$	64.4917	2.70601
$569$	2.74157	0.114932	0.0574662	−	0.998347i	$-0.481698\pi$
$569$	2.74157	0.114932	0.0574662	+	0.998347i	$0.481698\pi$
$570$	−30.2766	−1.26815
$571$	31.1908	1.30529	0.652647	−	0.757662i	$-0.273659\pi$
$571$	31.1908	1.30529	0.652647	+	0.757662i	$0.273659\pi$
$572$	65.7486	2.74909
$573$	−11.5788	−0.483712
$574$	0	0
$575$	−1.20890	−0.0504145
$576$	47.2842	1.97018
$577$	4.24819	0.176855	0.0884273	−	0.996083i	$-0.471816\pi$
$577$	4.24819	0.176855	0.0884273	+	0.996083i	$0.471816\pi$
$578$	−46.4739	−1.93306
$579$	5.69929	0.236854
$580$	63.4052	2.63276
$581$	0	0
$582$	8.26419	0.342562
$583$	27.3396	1.13229
$584$	−148.947	−6.16346
$585$	−8.15900	−0.337333
$586$	36.8032	1.52033
$587$	27.9648	1.15423	0.577116	−	0.816662i	$-0.304178\pi$
$587$	27.9648	1.15423	0.577116	+	0.816662i	$0.304178\pi$
$588$	0	0
$589$	−31.0937	−1.28119
$590$	−39.8997	−1.64264
$591$	−12.9883	−0.534268
$592$	75.7569	3.11359
$593$	24.4826	1.00538	0.502690	−	0.864467i	$-0.332344\pi$
$593$	24.4826	1.00538	0.502690	+	0.864467i	$0.332344\pi$
$594$	−7.52450	−0.308734
$595$	0	0
$596$	−28.2007	−1.15515
$597$	21.3255	0.872796
$598$	−11.7315	−0.479736
$599$	−43.9902	−1.79739	−0.898696	−	0.438573i	$-0.855484\pi$
$599$	−43.9902	−1.79739	−0.898696	+	0.438573i	$0.855484\pi$
$600$	−12.9891	−0.530276
$601$	−9.57098	−0.390408	−0.195204	−	0.980763i	$-0.562537\pi$
$601$	−9.57098	−0.390408	−0.195204	+	0.980763i	$0.562537\pi$
$602$	0	0
$603$	3.14875	0.128227
$604$	122.506	4.98468
$605$	−7.35283	−0.298935
$606$	35.8388	1.45585
$607$	1.59084	0.0645701	0.0322851	−	0.999479i	$-0.489722\pi$
$607$	1.59084	0.0645701	0.0322851	+	0.999479i	$0.489722\pi$
$608$	−166.837	−6.76613
$609$	0	0
$610$	34.2705	1.38757
$611$	−1.22605	−0.0496008
$612$	3.69184	0.149234
$613$	17.2292	0.695881	0.347941	−	0.937517i	$-0.386881\pi$
$613$	17.2292	0.695881	0.347941	+	0.937517i	$0.386881\pi$
$614$	−42.2983	−1.70702
$615$	−10.1147	−0.407864
$616$	0	0
$617$	−28.9242	−1.16444	−0.582222	−	0.813030i	$-0.697817\pi$
$617$	−28.9242	−1.16444	−0.582222	+	0.813030i	$0.697817\pi$
$618$	−36.5576	−1.47056
$619$	21.8645	0.878809	0.439404	−	0.898289i	$-0.355190\pi$
$619$	21.8645	0.878809	0.439404	+	0.898289i	$0.355190\pi$
$620$	63.6332	2.55557
$621$	1.00000	0.0401286
$622$	60.1438	2.41154
$623$	0	0
$624$	−77.1238	−3.08742
$625$	−17.4941	−0.699763
$626$	−41.5414	−1.66033
$627$	14.9281	0.596171
$628$	−9.30812	−0.371434
$629$	2.60302	0.103789
$630$	0	0
$631$	−11.5152	−0.458412	−0.229206	−	0.973378i	$-0.573613\pi$
$631$	−11.5152	−0.458412	−0.229206	+	0.973378i	$0.573613\pi$
$632$	169.659	6.74866
$633$	7.69191	0.305726
$634$	−13.1630	−0.522771
$635$	−35.4429	−1.40651
$636$	−59.3837	−2.35472
$637$	0	0
$638$	−41.9725	−1.66171
$639$	6.00227	0.237446
$640$	140.778	5.56475
$641$	9.26801	0.366064	0.183032	−	0.983107i	$-0.441409\pi$
$641$	9.26801	0.366064	0.183032	+	0.983107i	$0.441409\pi$
$642$	−38.4155	−1.51614
$643$	−13.8712	−0.547025	−0.273513	−	0.961868i	$-0.588186\pi$
$643$	−13.8712	−0.547025	−0.273513	+	0.961868i	$0.588186\pi$
$644$	0	0
$645$	−3.86740	−0.152279
$646$	−9.83363	−0.386899
$647$	7.30063	0.287017	0.143509	−	0.989649i	$-0.454162\pi$
$647$	7.30063	0.287017	0.143509	+	0.989649i	$0.454162\pi$
$648$	10.7446	0.422086
$649$	19.6728	0.772225
$650$	14.1822	0.556270
$651$	0	0
$652$	−63.6191	−2.49152
$653$	−28.2777	−1.10659	−0.553296	−	0.832984i	$-0.686630\pi$
$653$	−28.2777	−1.10659	−0.553296	+	0.832984i	$0.686630\pi$
$654$	−12.6148	−0.493279
$655$	16.2160	0.633613
$656$	−95.6102	−3.73295
$657$	−13.8625	−0.540829
$658$	0	0
$659$	26.3606	1.02686	0.513431	−	0.858131i	$-0.328374\pi$
$659$	26.3606	1.02686	0.513431	+	0.858131i	$0.328374\pi$
$660$	−30.5503	−1.18917
$661$	16.9293	0.658474	0.329237	−	0.944247i	$-0.393208\pi$
$661$	16.9293	0.658474	0.329237	+	0.944247i	$0.393208\pi$
$662$	−22.0572	−0.857276
$663$	−2.64998	−0.102917
$664$	−134.288	−5.21140
$665$	0	0
$666$	11.5236	0.446529
$667$	5.57812	0.215986
$668$	91.0302	3.52206
$669$	−20.9689	−0.810705
$670$	17.1640	0.663105
$671$	−16.8973	−0.652312
$672$	0	0
$673$	−23.7746	−0.916444	−0.458222	−	0.888838i	$-0.651513\pi$
$673$	−23.7746	−0.916444	−0.458222	+	0.888838i	$0.651513\pi$
$674$	−51.4730	−1.98267
$675$	−1.20890	−0.0465305
$676$	26.6169	1.02373
$677$	−22.7084	−0.872755	−0.436377	−	0.899764i	$-0.643739\pi$
$677$	−22.7084	−0.872755	−0.436377	+	0.899764i	$0.643739\pi$
$678$	−45.9173	−1.76344
$679$	0	0
$680$	13.2300	0.507348
$681$	24.1758	0.926419
$682$	−42.1235	−1.61299
$683$	10.8416	0.414841	0.207421	−	0.978252i	$-0.433493\pi$
$683$	10.8416	0.414841	0.207421	+	0.978252i	$0.433493\pi$
$684$	−32.4250	−1.23980
$685$	−25.9046	−0.989762
$686$	0	0
$687$	8.67855	0.331107
$688$	−36.5570	−1.39372
$689$	42.6253	1.62390
$690$	5.45107	0.207519
$691$	−15.0020	−0.570704	−0.285352	−	0.958423i	$-0.592111\pi$
$691$	−15.0020	−0.570704	−0.285352	+	0.958423i	$0.592111\pi$
$692$	65.8050	2.50153
$693$	0	0
$694$	16.8559	0.639841
$695$	11.5524	0.438207
$696$	59.9344	2.27181
$697$	−3.28518	−0.124435
$698$	−37.3408	−1.41337
$699$	2.69180	0.101813
$700$	0	0
$701$	−8.60412	−0.324973	−0.162486	−	0.986711i	$-0.551951\pi$
$701$	−8.60412	−0.324973	−0.162486	+	0.986711i	$0.551951\pi$
$702$	−11.7315	−0.442776
$703$	−22.8620	−0.862256
$704$	−127.085	−4.78970
$705$	0.569689	0.0214557
$706$	−48.9569	−1.84252
$707$	0	0
$708$	−42.7308	−1.60592
$709$	−29.1209	−1.09366	−0.546829	−	0.837244i	$-0.684165\pi$
$709$	−29.1209	−1.09366	−0.546829	+	0.837244i	$0.684165\pi$
$710$	32.7188	1.22791
$711$	15.7902	0.592178
$712$	−19.4643	−0.729455
$713$	5.59818	0.209654
$714$	0	0
$715$	21.9288	0.820092
$716$	47.7250	1.78357
$717$	−0.0523580	−0.00195534
$718$	−23.9850	−0.895112
$719$	15.3158	0.571182	0.285591	−	0.958352i	$-0.407810\pi$
$719$	15.3158	0.571182	0.285591	+	0.958352i	$0.407810\pi$
$720$	35.8358	1.33552
$721$	0	0
$722$	33.1748	1.23464
$723$	0.299551	0.0111404
$724$	17.5191	0.651093
$725$	−6.74337	−0.250443
$726$	−10.5723	−0.392376
$727$	−32.6484	−1.21086	−0.605432	−	0.795897i	$-0.707000\pi$
$727$	−32.6484	−1.21086	−0.605432	+	0.795897i	$0.707000\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−75.5656	−2.79681
$731$	−1.25610	−0.0464586
$732$	36.7022	1.35655
$733$	43.4532	1.60498	0.802490	−	0.596665i	$-0.203508\pi$
$733$	43.4532	1.60498	0.802490	+	0.596665i	$0.203508\pi$
$734$	55.1848	2.03691
$735$	0	0
$736$	30.0377	1.10720
$737$	−8.46285	−0.311733
$738$	−14.5435	−0.535353
$739$	3.48869	0.128333	0.0641667	−	0.997939i	$-0.479561\pi$
$739$	3.48869	0.128333	0.0641667	+	0.997939i	$0.479561\pi$
$740$	46.7869	1.71992
$741$	23.2745	0.855010
$742$	0	0
$743$	22.0130	0.807577	0.403789	−	0.914852i	$-0.367693\pi$
$743$	22.0130	0.807577	0.403789	+	0.914852i	$0.367693\pi$
$744$	60.1500	2.20521
$745$	−9.40566	−0.344597
$746$	61.3840	2.24743
$747$	−12.4983	−0.457288
$748$	−9.92251	−0.362803
$749$	0	0
$750$	−33.8451	−1.23585
$751$	15.4339	0.563192	0.281596	−	0.959533i	$-0.409136\pi$
$751$	15.4339	0.563192	0.281596	+	0.959533i	$0.409136\pi$
$752$	5.38504	0.196372
$753$	5.72848	0.208757
$754$	−65.4397	−2.38317
$755$	40.8587	1.48700
$756$	0	0
$757$	−13.1778	−0.478955	−0.239478	−	0.970902i	$-0.576976\pi$
$757$	−13.1778	−0.478955	−0.239478	+	0.970902i	$0.576976\pi$
$758$	27.7146	1.00664
$759$	−2.68769	−0.0975568
$760$	−116.198	−4.21493
$761$	−10.7069	−0.388123	−0.194062	−	0.980989i	$-0.562166\pi$
$761$	−10.7069	−0.388123	−0.194062	+	0.980989i	$0.562166\pi$
$762$	−50.9618	−1.84615
$763$	0	0
$764$	−67.5956	−2.44552
$765$	1.23132	0.0445186
$766$	49.0993	1.77403
$767$	30.6720	1.10750
$768$	107.851	3.89172
$769$	−30.1544	−1.08739	−0.543697	−	0.839282i	$-0.682976\pi$
$769$	−30.1544	−1.08739	−0.543697	+	0.839282i	$0.682976\pi$
$770$	0	0
$771$	17.2297	0.620512
$772$	33.2717	1.19747
$773$	−46.2383	−1.66307	−0.831537	−	0.555469i	$-0.812539\pi$
$773$	−46.2383	−1.66307	−0.831537	+	0.555469i	$0.812539\pi$
$774$	−5.56077	−0.199878
$775$	−6.76762	−0.243100
$776$	31.7169	1.13857
$777$	0	0
$778$	53.8860	1.93191
$779$	28.8533	1.03378
$780$	−47.6312	−1.70547
$781$	−16.1322	−0.577256
$782$	1.77047	0.0633118
$783$	5.57812	0.199346
$784$	0	0
$785$	−3.10449	−0.110804
$786$	23.3164	0.831667
$787$	−36.7305	−1.30930	−0.654651	−	0.755931i	$-0.727184\pi$
$787$	−36.7305	−1.30930	−0.654651	+	0.755931i	$0.727184\pi$
$788$	−75.8240	−2.70112
$789$	23.5216	0.837391
$790$	86.0734	3.06236
$791$	0	0
$792$	−28.8780	−1.02614
$793$	−26.3446	−0.935526
$794$	68.8690	2.44407
$795$	−19.8060	−0.702445
$796$	124.496	4.41263
$797$	32.2468	1.14224	0.571120	−	0.820867i	$-0.306509\pi$
$797$	32.2468	1.14224	0.571120	+	0.820867i	$0.306509\pi$
$798$	0	0
$799$	0.185031	0.00654592
$800$	−36.3125	−1.28384
$801$	−1.81155	−0.0640080
$802$	−22.0753	−0.779507
$803$	37.2581	1.31481
$804$	18.3820	0.648282
$805$	0	0
$806$	−65.6750	−2.31330
$807$	13.8092	0.486108
$808$	137.544	4.83880
$809$	6.80062	0.239097	0.119548	−	0.992828i	$-0.461855\pi$
$809$	6.80062	0.239097	0.119548	+	0.992828i	$0.461855\pi$
$810$	5.45107	0.191531
$811$	32.1358	1.12844	0.564220	−	0.825625i	$-0.309177\pi$
$811$	32.1358	1.12844	0.564220	+	0.825625i	$0.309177\pi$
$812$	0	0
$813$	22.4422	0.787083
$814$	−30.9717	−1.08556
$815$	−21.2186	−0.743255
$816$	11.6392	0.407454
$817$	11.0322	0.385967
$818$	−13.4571	−0.470517
$819$	0	0
$820$	−59.0482	−2.06205
$821$	−30.7924	−1.07466	−0.537331	−	0.843372i	$-0.680567\pi$
$821$	−30.7924	−1.07466	−0.537331	+	0.843372i	$0.680567\pi$
$822$	−37.2471	−1.29914
$823$	−55.2351	−1.92537	−0.962687	−	0.270618i	$-0.912772\pi$
$823$	−55.2351	−1.92537	−0.962687	+	0.270618i	$0.912772\pi$
$824$	−140.303	−4.88770
$825$	3.24913	0.113120
$826$	0	0
$827$	25.1429	0.874303	0.437152	−	0.899388i	$-0.355987\pi$
$827$	25.1429	0.874303	0.437152	+	0.899388i	$0.355987\pi$
$828$	5.83786	0.202880
$829$	−19.7977	−0.687604	−0.343802	−	0.939042i	$-0.611715\pi$
$829$	−19.7977	−0.687604	−0.343802	+	0.939042i	$0.611715\pi$
$830$	−68.1289	−2.36479
$831$	22.2276	0.771068
$832$	−198.139	−6.86924
$833$	0	0
$834$	16.6107	0.575181
$835$	30.3609	1.05068
$836$	87.1482	3.01408
$837$	5.59818	0.193501
$838$	−12.2431	−0.422930
$839$	−32.6430	−1.12696	−0.563480	−	0.826130i	$-0.690538\pi$
$839$	−32.6430	−1.12696	−0.563480	+	0.826130i	$0.690538\pi$
$840$	0	0
$841$	2.11543	0.0729458
$842$	−43.9243	−1.51373
$843$	6.99680	0.240982
$844$	44.9043	1.54567
$845$	8.87740	0.305392
$846$	0.819132	0.0281623
$847$	0	0
$848$	−187.218	−6.42909
$849$	−8.06377	−0.276748
$850$	−2.14031	−0.0734121
$851$	4.11612	0.141099
$852$	35.0404	1.20047
$853$	−50.0984	−1.71534	−0.857668	−	0.514204i	$-0.828087\pi$
$853$	−50.0984	−1.71534	−0.857668	+	0.514204i	$0.828087\pi$
$854$	0	0
$855$	−10.8146	−0.369850
$856$	−147.433	−5.03917
$857$	−3.60431	−0.123121	−0.0615605	−	0.998103i	$-0.519608\pi$
$857$	−3.60431	−0.123121	−0.0615605	+	0.998103i	$0.519608\pi$
$858$	31.5306	1.07644
$859$	−4.40656	−0.150350	−0.0751749	−	0.997170i	$-0.523952\pi$
$859$	−4.40656	−0.150350	−0.0751749	+	0.997170i	$0.523952\pi$
$860$	−22.5773	−0.769881
$861$	0	0
$862$	−9.36845	−0.319091
$863$	47.1708	1.60571	0.802857	−	0.596172i	$-0.203312\pi$
$863$	47.1708	1.60571	0.802857	+	0.596172i	$0.203312\pi$
$864$	30.0377	1.02190
$865$	21.9476	0.746242
$866$	42.6307	1.44865
$867$	−16.6001	−0.563768
$868$	0	0
$869$	−42.4391	−1.43965
$870$	30.4067	1.03088
$871$	−13.1945	−0.447078
$872$	−48.4140	−1.63951
$873$	2.95190	0.0999066
$874$	−15.5498	−0.525980
$875$	0	0
$876$	−80.9276	−2.73429
$877$	41.0405	1.38584	0.692920	−	0.721014i	$-0.256324\pi$
$877$	41.0405	1.38584	0.692920	+	0.721014i	$0.256324\pi$
$878$	−60.1678	−2.03057
$879$	13.1458	0.443397
$880$	−96.3154	−3.24679
$881$	−50.3825	−1.69743	−0.848715	−	0.528851i	$-0.822623\pi$
$881$	−50.3825	−1.69743	−0.848715	+	0.528851i	$0.822623\pi$
$882$	0	0
$883$	7.65081	0.257470	0.128735	−	0.991679i	$-0.458908\pi$
$883$	7.65081	0.257470	0.128735	+	0.991679i	$0.458908\pi$
$884$	−15.4703	−0.520321
$885$	−14.2518	−0.479070
$886$	66.5877	2.23706
$887$	37.3128	1.25284	0.626421	−	0.779485i	$-0.284519\pi$
$887$	37.3128	1.25284	0.626421	+	0.779485i	$0.284519\pi$
$888$	44.2259	1.48412
$889$	0	0
$890$	−9.87488	−0.331007
$891$	−2.68769	−0.0900409
$892$	−122.414	−4.09871
$893$	−1.62510	−0.0543820
$894$	−13.5240	−0.452311
$895$	15.9175	0.532064
$896$	0	0
$897$	−4.19039	−0.139913
$898$	−23.4113	−0.781245
$899$	31.2273	1.04149
$900$	−7.05738	−0.235246
$901$	−6.43284	−0.214309
$902$	39.0883	1.30150
$903$	0	0
$904$	−176.225	−5.86114
$905$	5.84307	0.194230
$906$	58.7490	1.95181
$907$	50.1224	1.66429	0.832144	−	0.554560i	$-0.187113\pi$
$907$	50.1224	1.66429	0.832144	+	0.554560i	$0.187113\pi$
$908$	141.135	4.68373
$909$	12.8013	0.424593
$910$	0	0
$911$	33.1001	1.09666	0.548328	−	0.836264i	$-0.315265\pi$
$911$	33.1001	1.09666	0.548328	+	0.836264i	$0.315265\pi$
$912$	−102.226	−3.38503
$913$	33.5914	1.11171
$914$	−44.6018	−1.47530
$915$	12.2411	0.404679
$916$	50.6642	1.67399
$917$	0	0
$918$	1.77047	0.0584341
$919$	−45.9534	−1.51586	−0.757931	−	0.652334i	$-0.773790\pi$
$919$	−45.9534	−1.51586	−0.757931	+	0.652334i	$0.773790\pi$
$920$	20.9205	0.689727
$921$	−15.1086	−0.497845
$922$	32.6924	1.07667
$923$	−25.1518	−0.827883
$924$	0	0
$925$	−4.97596	−0.163609
$926$	−18.8747	−0.620261
$927$	−13.0581	−0.428884
$928$	167.554	5.50022
$929$	22.5360	0.739383	0.369692	−	0.929155i	$-0.379463\pi$
$929$	22.5360	0.739383	0.369692	+	0.929155i	$0.379463\pi$
$930$	30.5161	1.00066
$931$	0	0
$932$	15.7144	0.514741
$933$	21.4828	0.703317
$934$	−43.3381	−1.41806
$935$	−3.30941	−0.108229
$936$	−45.0239	−1.47165
$937$	20.5555	0.671520	0.335760	−	0.941948i	$-0.391007\pi$
$937$	20.5555	0.671520	0.335760	+	0.941948i	$0.391007\pi$
$938$	0	0
$939$	−14.8382	−0.484227
$940$	3.32577	0.108475
$941$	39.8841	1.30019	0.650093	−	0.759855i	$-0.274730\pi$
$941$	39.8841	1.30019	0.650093	+	0.759855i	$0.274730\pi$
$942$	−4.46382	−0.145439
$943$	−5.19481	−0.169166
$944$	−134.717	−4.38466
$945$	0	0
$946$	14.9456	0.485923
$947$	2.73802	0.0889738	0.0444869	−	0.999010i	$-0.485835\pi$
$947$	2.73802	0.0889738	0.0444869	+	0.999010i	$0.485835\pi$
$948$	92.1810	2.99390
$949$	58.0894	1.88566
$950$	18.7981	0.609891
$951$	−4.70173	−0.152464
$952$	0	0
$953$	20.6225	0.668027	0.334014	−	0.942568i	$-0.391597\pi$
$953$	20.6225	0.668027	0.334014	+	0.942568i	$0.391597\pi$
$954$	−28.4782	−0.922015
$955$	−22.5448	−0.729534
$956$	−0.305659	−0.00988571
$957$	−14.9922	−0.484630
$958$	−51.9944	−1.67986
$959$	0	0
$960$	92.0659	2.97141
$961$	0.339647	0.0109563
$962$	−48.2882	−1.55687
$963$	−13.7217	−0.442175
$964$	1.74874	0.0563231
$965$	11.0969	0.357223
$966$	0	0
$967$	46.6896	1.50144	0.750719	−	0.660622i	$-0.229707\pi$
$967$	46.6896	1.50144	0.750719	+	0.660622i	$0.229707\pi$
$968$	−40.5752	−1.30413
$969$	−3.51249	−0.112837
$970$	16.0910	0.516651
$971$	39.8063	1.27745	0.638723	−	0.769437i	$-0.279463\pi$
$971$	39.8063	1.27745	0.638723	+	0.769437i	$0.279463\pi$
$972$	5.83786	0.187250
$973$	0	0
$974$	50.8458	1.62920
$975$	5.06575	0.162234
$976$	115.710	3.70380
$977$	−32.2999	−1.03337	−0.516683	−	0.856177i	$-0.672833\pi$
$977$	−32.2999	−1.03337	−0.516683	+	0.856177i	$0.672833\pi$
$978$	−30.5093	−0.975580
$979$	4.86888	0.155610
$980$	0	0
$981$	−4.50591	−0.143863
$982$	39.7281	1.26777
$983$	−57.0785	−1.82052	−0.910261	−	0.414035i	$-0.864119\pi$
$983$	−57.0785	−1.82052	−0.910261	+	0.414035i	$0.864119\pi$
$984$	−55.8160	−1.77935
$985$	−25.2892	−0.805781
$986$	9.87588	0.314512
$987$	0	0
$988$	135.873	4.32271
$989$	−1.98626	−0.0631594
$990$	−14.6508	−0.465632
$991$	−37.0328	−1.17639	−0.588193	−	0.808721i	$-0.700160\pi$
$991$	−37.0328	−1.17639	−0.588193	+	0.808721i	$0.700160\pi$
$992$	168.156	5.33897
$993$	−7.87864	−0.250021
$994$	0	0
$995$	41.5224	1.31635
$996$	−72.9632	−2.31193
$997$	47.0188	1.48910	0.744550	−	0.667567i	$-0.232664\pi$
$997$	47.0188	1.48910	0.744550	+	0.667567i	$0.232664\pi$
$998$	40.1430	1.27070
$999$	4.11612	0.130228

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bj.1.10		10
7.3	odd	6		483.2.i.h.415.1	yes	20
7.5	odd	6		483.2.i.h.277.1	✓	20
7.6	odd	2		3381.2.a.bi.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.h.277.1	✓	20	7.5	odd	6
483.2.i.h.415.1	yes	20	7.3	odd	6
3381.2.a.bi.1.10		10	7.6	odd	2
3381.2.a.bj.1.10		10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q+2.79962 q^{2} +1.00000 q^{3} +5.83786 q^{4} +1.94708 q^{5} +2.79962 q^{6} +10.7446 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.79962 q^{2} +1.00000 q^{3} +5.83786 q^{4} +1.94708 q^{5} +2.79962 q^{6} +10.7446 q^{8} +1.00000 q^{9} +5.45107 q^{10} -2.68769 q^{11} +5.83786 q^{12} -4.19039 q^{13} +1.94708 q^{15} +18.4049 q^{16} +0.632396 q^{17} +2.79962 q^{18} -5.55426 q^{19} +11.3668 q^{20} -7.52450 q^{22} +1.00000 q^{23} +10.7446 q^{24} -1.20890 q^{25} -11.7315 q^{26} +1.00000 q^{27} +5.57812 q^{29} +5.45107 q^{30} +5.59818 q^{31} +30.0377 q^{32} -2.68769 q^{33} +1.77047 q^{34} +5.83786 q^{36} +4.11612 q^{37} -15.5498 q^{38} -4.19039 q^{39} +20.9205 q^{40} -5.19481 q^{41} -1.98626 q^{43} -15.6903 q^{44} +1.94708 q^{45} +2.79962 q^{46} +0.292587 q^{47} +18.4049 q^{48} -3.38445 q^{50} +0.632396 q^{51} -24.4629 q^{52} -10.1722 q^{53} +2.79962 q^{54} -5.23313 q^{55} -5.55426 q^{57} +15.6166 q^{58} -7.31960 q^{59} +11.3668 q^{60} +6.28692 q^{61} +15.6728 q^{62} +47.2842 q^{64} -8.15900 q^{65} -7.52450 q^{66} +3.14875 q^{67} +3.69184 q^{68} +1.00000 q^{69} +6.00227 q^{71} +10.7446 q^{72} -13.8625 q^{73} +11.5236 q^{74} -1.20890 q^{75} -32.4250 q^{76} -11.7315 q^{78} +15.7902 q^{79} +35.8358 q^{80} +1.00000 q^{81} -14.5435 q^{82} -12.4983 q^{83} +1.23132 q^{85} -5.56077 q^{86} +5.57812 q^{87} -28.8780 q^{88} -1.81155 q^{89} +5.45107 q^{90} +5.83786 q^{92} +5.59818 q^{93} +0.819132 q^{94} -10.8146 q^{95} +30.0377 q^{96} +2.95190 q^{97} -2.68769 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} + 10 q^{3} + 15 q^{4} + 5 q^{5} + 3 q^{6} + 9 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 3 * q^2 + 10 * q^3 + 15 * q^4 + 5 * q^5 + 3 * q^6 + 9 * q^8 + 10 * q^9	\( 10 q + 3 q^{2} + 10 q^{3} + 15 q^{4} + 5 q^{5} + 3 q^{6} + 9 q^{8} + 10 q^{9} - 11 q^{10} + 8 q^{11} + 15 q^{12} + 5 q^{15} + 37 q^{16} + 11 q^{17} + 3 q^{18} - q^{19} + 15 q^{20} + 6 q^{22} + 10 q^{23} + 9 q^{24} + 21 q^{25} - q^{26} + 10 q^{27} + 22 q^{29} - 11 q^{30} + 3 q^{31} + 11 q^{32} + 8 q^{33} + 3 q^{34} + 15 q^{36} - 3 q^{37} - 16 q^{38} - 39 q^{40} + 26 q^{41} + 27 q^{43} + 16 q^{44} + 5 q^{45} + 3 q^{46} - 11 q^{47} + 37 q^{48} + 2 q^{50} + 11 q^{51} - 29 q^{52} + 5 q^{53} + 3 q^{54} + 18 q^{55} - q^{57} + 16 q^{58} + 10 q^{59} + 15 q^{60} - 22 q^{61} + 32 q^{62} + 69 q^{64} - 11 q^{65} + 6 q^{66} - 2 q^{67} + 21 q^{68} + 10 q^{69} + 27 q^{71} + 9 q^{72} + 8 q^{73} + 14 q^{74} + 21 q^{75} + 22 q^{76} - q^{78} + 21 q^{79} + 53 q^{80} + 10 q^{81} - 36 q^{82} + 12 q^{83} + 23 q^{85} + 18 q^{86} + 22 q^{87} - 10 q^{88} - 6 q^{89} - 11 q^{90} + 15 q^{92} + 3 q^{93} - 35 q^{94} + 44 q^{95} + 11 q^{96} - 6 q^{97} + 8 q^{99}+O(q^{100}) \) 10 * q + 3 * q^2 + 10 * q^3 + 15 * q^4 + 5 * q^5 + 3 * q^6 + 9 * q^8 + 10 * q^9 - 11 * q^10 + 8 * q^11 + 15 * q^12 + 5 * q^15 + 37 * q^16 + 11 * q^17 + 3 * q^18 - q^19 + 15 * q^20 + 6 * q^22 + 10 * q^23 + 9 * q^24 + 21 * q^25 - q^26 + 10 * q^27 + 22 * q^29 - 11 * q^30 + 3 * q^31 + 11 * q^32 + 8 * q^33 + 3 * q^34 + 15 * q^36 - 3 * q^37 - 16 * q^38 - 39 * q^40 + 26 * q^41 + 27 * q^43 + 16 * q^44 + 5 * q^45 + 3 * q^46 - 11 * q^47 + 37 * q^48 + 2 * q^50 + 11 * q^51 - 29 * q^52 + 5 * q^53 + 3 * q^54 + 18 * q^55 - q^57 + 16 * q^58 + 10 * q^59 + 15 * q^60 - 22 * q^61 + 32 * q^62 + 69 * q^64 - 11 * q^65 + 6 * q^66 - 2 * q^67 + 21 * q^68 + 10 * q^69 + 27 * q^71 + 9 * q^72 + 8 * q^73 + 14 * q^74 + 21 * q^75 + 22 * q^76 - q^78 + 21 * q^79 + 53 * q^80 + 10 * q^81 - 36 * q^82 + 12 * q^83 + 23 * q^85 + 18 * q^86 + 22 * q^87 - 10 * q^88 - 6 * q^89 - 11 * q^90 + 15 * q^92 + 3 * q^93 - 35 * q^94 + 44 * q^95 + 11 * q^96 - 6 * q^97 + 8 * q^99

Introduction

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Database

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