LMFDB - Embedded newform 8673.2.a.ba.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8673,2,Mod(1,8673)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8673, 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("8673.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8673 = 3 \cdot 7^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8673.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:	$69.2542536731$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 17 x^{10} + 52 x^{9} + 101 x^{8} - 316 x^{7} - 260 x^{6} + 830 x^{5} + 287 x^{4} + \cdots - 61 $ x^12 - 3x^11 - 17x^10 + 52x^9 + 101x^8 - 316x^7 - 260x^6 + 830x^5 + 287x^4 - 941x^3 - 77x^2 + 360*x - 61
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 1239)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.641487$ of defining polynomial
Character	$\chi$	$=$	8673.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.641487 q^{2} +1.00000 q^{3} -1.58849 q^{4} +3.78855 q^{5} +0.641487 q^{6} -2.30197 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.641487 q^{2} +1.00000 q^{3} -1.58849 q^{4} +3.78855 q^{5} +0.641487 q^{6} -2.30197 q^{8} +1.00000 q^{9} +2.43031 q^{10} -5.01126 q^{11} -1.58849 q^{12} +0.235447 q^{13} +3.78855 q^{15} +1.70030 q^{16} -2.82782 q^{17} +0.641487 q^{18} +8.16509 q^{19} -6.01809 q^{20} -3.21466 q^{22} -1.33820 q^{23} -2.30197 q^{24} +9.35314 q^{25} +0.151036 q^{26} +1.00000 q^{27} -5.24671 q^{29} +2.43031 q^{30} -7.37377 q^{31} +5.69467 q^{32} -5.01126 q^{33} -1.81401 q^{34} -1.58849 q^{36} +7.18611 q^{37} +5.23780 q^{38} +0.235447 q^{39} -8.72115 q^{40} -3.25112 q^{41} +9.59337 q^{43} +7.96036 q^{44} +3.78855 q^{45} -0.858436 q^{46} +12.3144 q^{47} +1.70030 q^{48} +5.99992 q^{50} -2.82782 q^{51} -0.374006 q^{52} +13.2994 q^{53} +0.641487 q^{54} -18.9854 q^{55} +8.16509 q^{57} -3.36570 q^{58} +1.00000 q^{59} -6.01809 q^{60} +0.126524 q^{61} -4.73018 q^{62} +0.252457 q^{64} +0.892004 q^{65} -3.21466 q^{66} -8.50308 q^{67} +4.49197 q^{68} -1.33820 q^{69} +5.83919 q^{71} -2.30197 q^{72} -8.89116 q^{73} +4.60980 q^{74} +9.35314 q^{75} -12.9702 q^{76} +0.151036 q^{78} -9.12270 q^{79} +6.44168 q^{80} +1.00000 q^{81} -2.08555 q^{82} -5.32627 q^{83} -10.7133 q^{85} +6.15403 q^{86} -5.24671 q^{87} +11.5358 q^{88} +8.51175 q^{89} +2.43031 q^{90} +2.12572 q^{92} -7.37377 q^{93} +7.89951 q^{94} +30.9339 q^{95} +5.69467 q^{96} +10.4256 q^{97} -5.01126 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 12 q^{3} + 19 q^{4} + 4 q^{5} + 3 q^{6} + 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + 12 * q^3 + 19 * q^4 + 4 * q^5 + 3 * q^6 + 12 * q^8 + 12 * q^9	$ 12 q + 3 q^{2} + 12 q^{3} + 19 q^{4} + 4 q^{5} + 3 q^{6} + 12 q^{8} + 12 q^{9} - 2 q^{10} + 2 q^{11} + 19 q^{12} - 9 q^{13} + 4 q^{15} + 33 q^{16} + 5 q^{17} + 3 q^{18} - 7 q^{19} + 15 q^{20} + 24 q^{22} + q^{23} + 12 q^{24} + 30 q^{25} - 3 q^{26} + 12 q^{27} + 11 q^{29} - 2 q^{30} - 13 q^{31} + 22 q^{32} + 2 q^{33} - 8 q^{34} + 19 q^{36} + 7 q^{37} + 4 q^{38} - 9 q^{39} + 20 q^{40} + 21 q^{43} + 23 q^{44} + 4 q^{45} - 7 q^{46} + 18 q^{47} + 33 q^{48} + 52 q^{50} + 5 q^{51} - 23 q^{52} + 15 q^{53} + 3 q^{54} - 20 q^{55} - 7 q^{57} + 27 q^{58} + 12 q^{59} + 15 q^{60} - 30 q^{61} - q^{62} + 88 q^{64} + q^{65} + 24 q^{66} + 19 q^{67} + 25 q^{68} + q^{69} + 18 q^{71} + 12 q^{72} - 19 q^{73} + 3 q^{74} + 30 q^{75} - 62 q^{76} - 3 q^{78} + 16 q^{79} + 47 q^{80} + 12 q^{81} - 19 q^{82} + 37 q^{83} + 48 q^{85} - 8 q^{86} + 11 q^{87} + 46 q^{88} - 23 q^{89} - 2 q^{90} + 19 q^{92} - 13 q^{93} - 13 q^{94} + 20 q^{95} + 22 q^{96} - 9 q^{97} + 2 q^{99}+O(q^{100}) $ 12 * q + 3 * q^2 + 12 * q^3 + 19 * q^4 + 4 * q^5 + 3 * q^6 + 12 * q^8 + 12 * q^9 - 2 * q^10 + 2 * q^11 + 19 * q^12 - 9 * q^13 + 4 * q^15 + 33 * q^16 + 5 * q^17 + 3 * q^18 - 7 * q^19 + 15 * q^20 + 24 * q^22 + q^23 + 12 * q^24 + 30 * q^25 - 3 * q^26 + 12 * q^27 + 11 * q^29 - 2 * q^30 - 13 * q^31 + 22 * q^32 + 2 * q^33 - 8 * q^34 + 19 * q^36 + 7 * q^37 + 4 * q^38 - 9 * q^39 + 20 * q^40 + 21 * q^43 + 23 * q^44 + 4 * q^45 - 7 * q^46 + 18 * q^47 + 33 * q^48 + 52 * q^50 + 5 * q^51 - 23 * q^52 + 15 * q^53 + 3 * q^54 - 20 * q^55 - 7 * q^57 + 27 * q^58 + 12 * q^59 + 15 * q^60 - 30 * q^61 - q^62 + 88 * q^64 + q^65 + 24 * q^66 + 19 * q^67 + 25 * q^68 + q^69 + 18 * q^71 + 12 * q^72 - 19 * q^73 + 3 * q^74 + 30 * q^75 - 62 * q^76 - 3 * q^78 + 16 * q^79 + 47 * q^80 + 12 * q^81 - 19 * q^82 + 37 * q^83 + 48 * q^85 - 8 * q^86 + 11 * q^87 + 46 * q^88 - 23 * q^89 - 2 * q^90 + 19 * q^92 - 13 * q^93 - 13 * q^94 + 20 * q^95 + 22 * q^96 - 9 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.641487	0.453600	0.226800	−	0.973941i	$-0.427174\pi$
$2$	0.641487	0.453600	0.226800	+	0.973941i	$0.427174\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.58849	−0.794247
$5$	3.78855	1.69429	0.847146	−	0.531360i	$-0.178319\pi$
$5$	3.78855	1.69429	0.847146	+	0.531360i	$0.178319\pi$
$6$	0.641487	0.261886
$7$	0	0
$7$	0	0
$8$	−2.30197	−0.813871
$9$	1.00000	0.333333
$10$	2.43031	0.768531
$11$	−5.01126	−1.51095	−0.755476	−	0.655176i	$-0.772594\pi$
$11$	−5.01126	−1.51095	−0.755476	+	0.655176i	$0.772594\pi$
$12$	−1.58849	−0.458559
$13$	0.235447	0.0653013	0.0326506	−	0.999467i	$-0.489605\pi$
$13$	0.235447	0.0653013	0.0326506	+	0.999467i	$0.489605\pi$
$14$	0	0
$15$	3.78855	0.978200
$16$	1.70030	0.425075
$17$	−2.82782	−0.685846	−0.342923	−	0.939363i	$-0.611417\pi$
$17$	−2.82782	−0.685846	−0.342923	+	0.939363i	$0.611417\pi$
$18$	0.641487	0.151200
$19$	8.16509	1.87320	0.936600	−	0.350401i	$-0.113955\pi$
$19$	8.16509	1.87320	0.936600	+	0.350401i	$0.113955\pi$
$20$	−6.01809	−1.34569
$21$	0	0
$22$	−3.21466	−0.685368
$23$	−1.33820	−0.279033	−0.139517	−	0.990220i	$-0.544555\pi$
$23$	−1.33820	−0.279033	−0.139517	+	0.990220i	$0.544555\pi$
$24$	−2.30197	−0.469888
$25$	9.35314	1.87063
$26$	0.151036	0.0296207
$27$	1.00000	0.192450
$28$	0	0
$29$	−5.24671	−0.974290	−0.487145	−	0.873321i	$-0.661962\pi$
$29$	−5.24671	−0.974290	−0.487145	+	0.873321i	$0.661962\pi$
$30$	2.43031	0.443712
$31$	−7.37377	−1.32437	−0.662184	−	0.749341i	$-0.730370\pi$
$31$	−7.37377	−1.32437	−0.662184	+	0.749341i	$0.730370\pi$
$32$	5.69467	1.00668
$33$	−5.01126	−0.872349
$34$	−1.81401	−0.311100
$35$	0	0
$36$	−1.58849	−0.264749
$37$	7.18611	1.18139	0.590694	−	0.806895i	$-0.298854\pi$
$37$	7.18611	1.18139	0.590694	+	0.806895i	$0.298854\pi$
$38$	5.23780	0.849683
$39$	0.235447	0.0377017
$40$	−8.72115	−1.37894
$41$	−3.25112	−0.507740	−0.253870	−	0.967238i	$-0.581703\pi$
$41$	−3.25112	−0.507740	−0.253870	+	0.967238i	$0.581703\pi$
$42$	0	0
$43$	9.59337	1.46298	0.731488	−	0.681855i	$-0.238826\pi$
$43$	9.59337	1.46298	0.731488	+	0.681855i	$0.238826\pi$
$44$	7.96036	1.20007
$45$	3.78855	0.564764
$46$	−0.858436	−0.126569
$47$	12.3144	1.79623	0.898117	−	0.439756i	$-0.144935\pi$
$47$	12.3144	1.79623	0.898117	+	0.439756i	$0.144935\pi$
$48$	1.70030	0.245417
$49$	0	0
$50$	5.99992	0.848517
$51$	−2.82782	−0.395974
$52$	−0.374006	−0.0518653
$53$	13.2994	1.82681	0.913407	−	0.407047i	$-0.133442\pi$
$53$	13.2994	1.82681	0.913407	+	0.407047i	$0.133442\pi$
$54$	0.641487	0.0872954
$55$	−18.9854	−2.56000
$56$	0	0
$57$	8.16509	1.08149
$58$	−3.36570	−0.441938
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−6.01809	−0.776933
$61$	0.126524	0.0161997	0.00809986	−	0.999967i	$-0.497422\pi$
$61$	0.126524	0.0161997	0.00809986	+	0.999967i	$0.497422\pi$
$62$	−4.73018	−0.600734
$63$	0	0
$64$	0.252457	0.0315571
$65$	0.892004	0.110639
$66$	−3.21466	−0.395698
$67$	−8.50308	−1.03882	−0.519408	−	0.854526i	$-0.673848\pi$
$67$	−8.50308	−1.03882	−0.519408	+	0.854526i	$0.673848\pi$
$68$	4.49197	0.544731
$69$	−1.33820	−0.161100
$70$	0	0
$71$	5.83919	0.692985	0.346492	−	0.938053i	$-0.387373\pi$
$71$	5.83919	0.692985	0.346492	+	0.938053i	$0.387373\pi$
$72$	−2.30197	−0.271290
$73$	−8.89116	−1.04063	−0.520316	−	0.853974i	$-0.674186\pi$
$73$	−8.89116	−1.04063	−0.520316	+	0.853974i	$0.674186\pi$
$74$	4.60980	0.535878
$75$	9.35314	1.08001
$76$	−12.9702	−1.48778
$77$	0	0
$78$	0.151036	0.0171015
$79$	−9.12270	−1.02638	−0.513192	−	0.858274i	$-0.671537\pi$
$79$	−9.12270	−1.02638	−0.513192	+	0.858274i	$0.671537\pi$
$80$	6.44168	0.720202
$81$	1.00000	0.111111
$82$	−2.08555	−0.230311
$83$	−5.32627	−0.584634	−0.292317	−	0.956322i	$-0.594426\pi$
$83$	−5.32627	−0.584634	−0.292317	+	0.956322i	$0.594426\pi$
$84$	0	0
$85$	−10.7133	−1.16202
$86$	6.15403	0.663606
$87$	−5.24671	−0.562506
$88$	11.5358	1.22972
$89$	8.51175	0.902243	0.451122	−	0.892462i	$-0.351024\pi$
$89$	8.51175	0.902243	0.451122	+	0.892462i	$0.351024\pi$
$90$	2.43031	0.256177
$91$	0	0
$92$	2.12572	0.221621
$93$	−7.37377	−0.764624
$94$	7.89951	0.814772
$95$	30.9339	3.17375
$96$	5.69467	0.581210
$97$	10.4256	1.05856	0.529280	−	0.848447i	$-0.322462\pi$
$97$	10.4256	1.05856	0.529280	+	0.848447i	$0.322462\pi$
$98$	0	0
$99$	−5.01126	−0.503651
$100$	−14.8574	−1.48574
$101$	7.99225	0.795259	0.397629	−	0.917546i	$-0.369833\pi$
$101$	7.99225	0.795259	0.397629	+	0.917546i	$0.369833\pi$
$102$	−1.81401	−0.179614
$103$	7.06270	0.695908	0.347954	−	0.937512i	$-0.386876\pi$
$103$	7.06270	0.695908	0.347954	+	0.937512i	$0.386876\pi$
$104$	−0.541993	−0.0531468
$105$	0	0
$106$	8.53140	0.828643
$107$	13.8797	1.34181	0.670903	−	0.741545i	$-0.265907\pi$
$107$	13.8797	1.34181	0.670903	+	0.741545i	$0.265907\pi$
$108$	−1.58849	−0.152853
$109$	−3.05086	−0.292219	−0.146109	−	0.989268i	$-0.546675\pi$
$109$	−3.05086	−0.292219	−0.146109	+	0.989268i	$0.546675\pi$
$110$	−12.1789	−1.16121
$111$	7.18611	0.682075
$112$	0	0
$113$	20.0788	1.88886	0.944429	−	0.328715i	$-0.106616\pi$
$113$	20.0788	1.88886	0.944429	+	0.328715i	$0.106616\pi$
$114$	5.23780	0.490565
$115$	−5.06983	−0.472764
$116$	8.33437	0.773827
$117$	0.235447	0.0217671
$118$	0.641487	0.0590537
$119$	0	0
$120$	−8.72115	−0.796129
$121$	14.1128	1.28298
$122$	0.0811635	0.00734819
$123$	−3.25112	−0.293144
$124$	11.7132	1.05188
$125$	16.4921	1.47510
$126$	0	0
$127$	10.0745	0.893965	0.446983	−	0.894543i	$-0.352499\pi$
$127$	10.0745	0.893965	0.446983	+	0.894543i	$0.352499\pi$
$128$	−11.2274	−0.992370
$129$	9.59337	0.844649
$130$	0.572209	0.0501861
$131$	14.8158	1.29446	0.647232	−	0.762293i	$-0.275926\pi$
$131$	14.8158	1.29446	0.647232	+	0.762293i	$0.275926\pi$
$132$	7.96036	0.692860
$133$	0	0
$134$	−5.45462	−0.471207
$135$	3.78855	0.326067
$136$	6.50956	0.558190
$137$	−22.0396	−1.88297	−0.941485	−	0.337054i	$-0.890569\pi$
$137$	−22.0396	−1.88297	−0.941485	+	0.337054i	$0.890569\pi$
$138$	−0.858436	−0.0730749
$139$	9.12376	0.773867	0.386933	−	0.922108i	$-0.373534\pi$
$139$	9.12376	0.773867	0.386933	+	0.922108i	$0.373534\pi$
$140$	0	0
$141$	12.3144	1.03706
$142$	3.74577	0.314338
$143$	−1.17989	−0.0986671
$144$	1.70030	0.141692
$145$	−19.8774	−1.65073
$146$	−5.70357	−0.472030
$147$	0	0
$148$	−11.4151	−0.938314
$149$	−7.16312	−0.586826	−0.293413	−	0.955986i	$-0.594791\pi$
$149$	−7.16312	−0.586826	−0.293413	+	0.955986i	$0.594791\pi$
$150$	5.99992	0.489892
$151$	9.52933	0.775486	0.387743	−	0.921768i	$-0.373255\pi$
$151$	9.52933	0.775486	0.387743	+	0.921768i	$0.373255\pi$
$152$	−18.7958	−1.52454
$153$	−2.82782	−0.228615
$154$	0	0
$155$	−27.9359	−2.24387
$156$	−0.374006	−0.0299445
$157$	−22.0586	−1.76046	−0.880232	−	0.474543i	$-0.842613\pi$
$157$	−22.0586	−1.76046	−0.880232	+	0.474543i	$0.842613\pi$
$158$	−5.85210	−0.465568
$159$	13.2994	1.05471
$160$	21.5746	1.70562
$161$	0	0
$162$	0.641487	0.0504000
$163$	15.5466	1.21771	0.608853	−	0.793283i	$-0.291630\pi$
$163$	15.5466	1.21771	0.608853	+	0.793283i	$0.291630\pi$
$164$	5.16439	0.403271
$165$	−18.9854	−1.47801
$166$	−3.41673	−0.265190
$167$	6.42884	0.497478	0.248739	−	0.968571i	$-0.419984\pi$
$167$	6.42884	0.497478	0.248739	+	0.968571i	$0.419984\pi$
$168$	0	0
$169$	−12.9446	−0.995736
$170$	−6.87247	−0.527094
$171$	8.16509	0.624400
$172$	−15.2390	−1.16196
$173$	3.39872	0.258400	0.129200	−	0.991619i	$-0.458759\pi$
$173$	3.39872	0.258400	0.129200	+	0.991619i	$0.458759\pi$
$174$	−3.36570	−0.255153
$175$	0	0
$176$	−8.52065	−0.642268
$177$	1.00000	0.0751646
$178$	5.46018	0.409258
$179$	−1.59969	−0.119566	−0.0597832	−	0.998211i	$-0.519041\pi$
$179$	−1.59969	−0.119566	−0.0597832	+	0.998211i	$0.519041\pi$
$180$	−6.01809	−0.448562
$181$	9.23974	0.686785	0.343392	−	0.939192i	$-0.388424\pi$
$181$	9.23974	0.686785	0.343392	+	0.939192i	$0.388424\pi$
$182$	0	0
$183$	0.126524	0.00935291
$184$	3.08049	0.227097
$185$	27.2250	2.00162
$186$	−4.73018	−0.346834
$187$	14.1709	1.03628
$188$	−19.5613	−1.42665
$189$	0	0
$190$	19.8437	1.43961
$191$	4.07757	0.295043	0.147521	−	0.989059i	$-0.452871\pi$
$191$	4.07757	0.295043	0.147521	+	0.989059i	$0.452871\pi$
$192$	0.252457	0.0182195
$193$	1.41320	0.101724	0.0508622	−	0.998706i	$-0.483803\pi$
$193$	1.41320	0.101724	0.0508622	+	0.998706i	$0.483803\pi$
$194$	6.68789	0.480163
$195$	0.892004	0.0638777
$196$	0	0
$197$	−5.02224	−0.357820	−0.178910	−	0.983865i	$-0.557257\pi$
$197$	−5.02224	−0.357820	−0.178910	+	0.983865i	$0.557257\pi$
$198$	−3.21466	−0.228456
$199$	0.00858483	0.000608562 0	0.000304281	−	1.00000i	$-0.499903\pi$
$199$	0.00858483	0.000608562 0	0.000304281		1.00000i	$0.499903\pi$
$200$	−21.5307	−1.52245
$201$	−8.50308	−0.599761
$202$	5.12693	0.360729
$203$	0	0
$204$	4.49197	0.314501
$205$	−12.3170	−0.860260
$206$	4.53063	0.315664
$207$	−1.33820	−0.0930111
$208$	0.400331	0.0277579
$209$	−40.9174	−2.83032
$210$	0	0
$211$	19.1738	1.31998	0.659991	−	0.751274i	$-0.270560\pi$
$211$	19.1738	1.31998	0.659991	+	0.751274i	$0.270560\pi$
$212$	−21.1260	−1.45094
$213$	5.83919	0.400095
$214$	8.90368	0.608643
$215$	36.3450	2.47871
$216$	−2.30197	−0.156629
$217$	0	0
$218$	−1.95709	−0.132551
$219$	−8.89116	−0.600809
$220$	30.1583	2.03327
$221$	−0.665801	−0.0447866
$222$	4.60980	0.309389
$223$	−11.7982	−0.790067	−0.395033	−	0.918667i	$-0.629267\pi$
$223$	−11.7982	−0.790067	−0.395033	+	0.918667i	$0.629267\pi$
$224$	0	0
$225$	9.35314	0.623543
$226$	12.8803	0.856786
$227$	3.17897	0.210996	0.105498	−	0.994420i	$-0.466356\pi$
$227$	3.17897	0.210996	0.105498	+	0.994420i	$0.466356\pi$
$228$	−12.9702	−0.858972
$229$	−24.6454	−1.62861	−0.814307	−	0.580435i	$-0.802883\pi$
$229$	−24.6454	−1.62861	−0.814307	+	0.580435i	$0.802883\pi$
$230$	−3.25223	−0.214446
$231$	0	0
$232$	12.0778	0.792946
$233$	21.0830	1.38120	0.690598	−	0.723239i	$-0.257348\pi$
$233$	21.0830	1.38120	0.690598	+	0.723239i	$0.257348\pi$
$234$	0.151036	0.00987355
$235$	46.6536	3.04335
$236$	−1.58849	−0.103402
$237$	−9.12270	−0.592583
$238$	0	0
$239$	14.8270	0.959078	0.479539	−	0.877521i	$-0.340804\pi$
$239$	14.8270	0.959078	0.479539	+	0.877521i	$0.340804\pi$
$240$	6.44168	0.415809
$241$	4.78095	0.307968	0.153984	−	0.988073i	$-0.450790\pi$
$241$	4.78095	0.307968	0.153984	+	0.988073i	$0.450790\pi$
$242$	9.05316	0.581959
$243$	1.00000	0.0641500
$244$	−0.200982	−0.0128666
$245$	0	0
$246$	−2.08555	−0.132970
$247$	1.92245	0.122322
$248$	16.9742	1.07786
$249$	−5.32627	−0.337538
$250$	10.5795	0.669105
$251$	−9.07951	−0.573094	−0.286547	−	0.958066i	$-0.592507\pi$
$251$	−9.07951	−0.573094	−0.286547	+	0.958066i	$0.592507\pi$
$252$	0	0
$253$	6.70605	0.421606
$254$	6.46265	0.405503
$255$	−10.7133	−0.670895
$256$	−7.70714	−0.481696
$257$	−16.8421	−1.05058	−0.525289	−	0.850924i	$-0.676043\pi$
$257$	−16.8421	−1.05058	−0.525289	+	0.850924i	$0.676043\pi$
$258$	6.15403	0.383133
$259$	0	0
$260$	−1.41694	−0.0878751
$261$	−5.24671	−0.324763
$262$	9.50416	0.587169
$263$	11.1038	0.684688	0.342344	−	0.939575i	$-0.388779\pi$
$263$	11.1038	0.684688	0.342344	+	0.939575i	$0.388779\pi$
$264$	11.5358	0.709979
$265$	50.3855	3.09516
$266$	0	0
$267$	8.51175	0.520910
$268$	13.5071	0.825076
$269$	−3.51499	−0.214313	−0.107156	−	0.994242i	$-0.534175\pi$
$269$	−3.51499	−0.214313	−0.107156	+	0.994242i	$0.534175\pi$
$270$	2.43031	0.147904
$271$	−14.7628	−0.896774	−0.448387	−	0.893839i	$-0.648001\pi$
$271$	−14.7628	−0.896774	−0.448387	+	0.893839i	$0.648001\pi$
$272$	−4.80814	−0.291536
$273$	0	0
$274$	−14.1381	−0.854116
$275$	−46.8710	−2.82643
$276$	2.12572	0.127953
$277$	4.09223	0.245878	0.122939	−	0.992414i	$-0.460768\pi$
$277$	4.09223	0.245878	0.122939	+	0.992414i	$0.460768\pi$
$278$	5.85277	0.351026
$279$	−7.37377	−0.441456
$280$	0	0
$281$	30.8418	1.83987	0.919934	−	0.392072i	$-0.128242\pi$
$281$	30.8418	1.83987	0.919934	+	0.392072i	$0.128242\pi$
$282$	7.89951	0.470409
$283$	−9.57858	−0.569388	−0.284694	−	0.958618i	$-0.591892\pi$
$283$	−9.57858	−0.569388	−0.284694	+	0.958618i	$0.591892\pi$
$284$	−9.27552	−0.550401
$285$	30.9339	1.83236
$286$	−0.756883	−0.0447554
$287$	0	0
$288$	5.69467	0.335562
$289$	−9.00345	−0.529615
$290$	−12.7511	−0.748772
$291$	10.4256	0.611160
$292$	14.1236	0.826518
$293$	0.653868	0.0381994	0.0190997	−	0.999818i	$-0.493920\pi$
$293$	0.653868	0.0381994	0.0190997	+	0.999818i	$0.493920\pi$
$294$	0	0
$295$	3.78855	0.220578
$296$	−16.5422	−0.961497
$297$	−5.01126	−0.290783
$298$	−4.59505	−0.266184
$299$	−0.315074	−0.0182212
$300$	−14.8574	−0.857793
$301$	0	0
$302$	6.11294	0.351760
$303$	7.99225	0.459143
$304$	13.8831	0.796251
$305$	0.479342	0.0274471
$306$	−1.81401	−0.103700
$307$	0.782729	0.0446727	0.0223363	−	0.999751i	$-0.492890\pi$
$307$	0.782729	0.0446727	0.0223363	+	0.999751i	$0.492890\pi$
$308$	0	0
$309$	7.06270	0.401783
$310$	−17.9205	−1.01782
$311$	19.5710	1.10977	0.554885	−	0.831927i	$-0.312762\pi$
$311$	19.5710	1.10977	0.554885	+	0.831927i	$0.312762\pi$
$312$	−0.541993	−0.0306843
$313$	−22.5489	−1.27454	−0.637269	−	0.770642i	$-0.719936\pi$
$313$	−22.5489	−1.27454	−0.637269	+	0.770642i	$0.719936\pi$
$314$	−14.1503	−0.798547
$315$	0	0
$316$	14.4914	0.815202
$317$	−10.3753	−0.582737	−0.291369	−	0.956611i	$-0.594111\pi$
$317$	−10.3753	−0.582737	−0.291369	+	0.956611i	$0.594111\pi$
$318$	8.53140	0.478417
$319$	26.2926	1.47211
$320$	0.956446	0.0534670
$321$	13.8797	0.774692
$322$	0	0
$323$	−23.0894	−1.28473
$324$	−1.58849	−0.0882497
$325$	2.20217	0.122154
$326$	9.97296	0.552351
$327$	−3.05086	−0.168713
$328$	7.48399	0.413234
$329$	0	0
$330$	−12.1789	−0.670428
$331$	−23.7371	−1.30471	−0.652355	−	0.757913i	$-0.726219\pi$
$331$	−23.7371	−1.30471	−0.652355	+	0.757913i	$0.726219\pi$
$332$	8.46074	0.464344
$333$	7.18611	0.393796
$334$	4.12402	0.225656
$335$	−32.2144	−1.76006
$336$	0	0
$337$	−10.9496	−0.596461	−0.298231	−	0.954494i	$-0.596396\pi$
$337$	−10.9496	−0.596461	−0.298231	+	0.954494i	$0.596396\pi$
$338$	−8.30378	−0.451666
$339$	20.0788	1.09053
$340$	17.0181	0.922934
$341$	36.9519	2.00106
$342$	5.23780	0.283228
$343$	0	0
$344$	−22.0837	−1.19067
$345$	−5.06983	−0.272950
$346$	2.18023	0.117210
$347$	−14.2360	−0.764227	−0.382113	−	0.924115i	$-0.624804\pi$
$347$	−14.2360	−0.764227	−0.382113	+	0.924115i	$0.624804\pi$
$348$	8.33437	0.446769
$349$	20.9115	1.11937	0.559684	−	0.828706i	$-0.310923\pi$
$349$	20.9115	1.11937	0.559684	+	0.828706i	$0.310923\pi$
$350$	0	0
$351$	0.235447	0.0125672
$352$	−28.5375	−1.52105
$353$	−20.6307	−1.09806	−0.549032	−	0.835801i	$-0.685003\pi$
$353$	−20.6307	−1.09806	−0.549032	+	0.835801i	$0.685003\pi$
$354$	0.641487	0.0340947
$355$	22.1221	1.17412
$356$	−13.5209	−0.716604
$357$	0	0
$358$	−1.02618	−0.0542354
$359$	10.4773	0.552971	0.276485	−	0.961018i	$-0.410830\pi$
$359$	10.4773	0.552971	0.276485	+	0.961018i	$0.410830\pi$
$360$	−8.72115	−0.459645
$361$	47.6686	2.50888
$362$	5.92718	0.311526
$363$	14.1128	0.740728
$364$	0	0
$365$	−33.6846	−1.76313
$366$	0.0811635	0.00424248
$367$	−29.4204	−1.53573	−0.767865	−	0.640611i	$-0.778681\pi$
$367$	−29.4204	−1.53573	−0.767865	+	0.640611i	$0.778681\pi$
$368$	−2.27534	−0.118610
$369$	−3.25112	−0.169247
$370$	17.4645	0.907934
$371$	0	0
$372$	11.7132	0.607301
$373$	−28.6260	−1.48220	−0.741098	−	0.671396i	$-0.765695\pi$
$373$	−28.6260	−1.48220	−0.741098	+	0.671396i	$0.765695\pi$
$374$	9.09048	0.470057
$375$	16.4921	0.851649
$376$	−28.3473	−1.46190
$377$	−1.23532	−0.0636223
$378$	0	0
$379$	−18.5220	−0.951412	−0.475706	−	0.879604i	$-0.657807\pi$
$379$	−18.5220	−0.951412	−0.475706	+	0.879604i	$0.657807\pi$
$380$	−49.1383	−2.52074
$381$	10.0745	0.516131
$382$	2.61571	0.133831
$383$	8.98229	0.458973	0.229487	−	0.973312i	$-0.426295\pi$
$383$	8.98229	0.458973	0.229487	+	0.973312i	$0.426295\pi$
$384$	−11.2274	−0.572945
$385$	0	0
$386$	0.906550	0.0461422
$387$	9.59337	0.487658
$388$	−16.5610	−0.840758
$389$	37.2171	1.88698	0.943492	−	0.331395i	$-0.107519\pi$
$389$	37.2171	1.88698	0.943492	+	0.331395i	$0.107519\pi$
$390$	0.572209	0.0289749
$391$	3.78417	0.191374
$392$	0	0
$393$	14.8158	0.747359
$394$	−3.22170	−0.162307
$395$	−34.5618	−1.73899
$396$	7.96036	0.400023
$397$	−5.45453	−0.273755	−0.136878	−	0.990588i	$-0.543707\pi$
$397$	−5.45453	−0.273755	−0.136878	+	0.990588i	$0.543707\pi$
$398$	0.00550706	0.000276044 0
$399$	0	0
$400$	15.9032	0.795158
$401$	5.68029	0.283660	0.141830	−	0.989891i	$-0.454701\pi$
$401$	5.68029	0.283660	0.141830	+	0.989891i	$0.454701\pi$
$402$	−5.45462	−0.272052
$403$	−1.73613	−0.0864829
$404$	−12.6956	−0.631632
$405$	3.78855	0.188255
$406$	0	0
$407$	−36.0115	−1.78502
$408$	6.50956	0.322271
$409$	5.98038	0.295711	0.147855	−	0.989009i	$-0.452763\pi$
$409$	5.98038	0.295711	0.147855	+	0.989009i	$0.452763\pi$
$410$	−7.90123	−0.390214
$411$	−22.0396	−1.08713
$412$	−11.2191	−0.552723
$413$	0	0
$414$	−0.858436	−0.0421898
$415$	−20.1788	−0.990541
$416$	1.34079	0.0657378
$417$	9.12376	0.446792
$418$	−26.2480	−1.28383
$419$	4.99917	0.244225	0.122113	−	0.992516i	$-0.461033\pi$
$419$	4.99917	0.244225	0.122113	+	0.992516i	$0.461033\pi$
$420$	0	0
$421$	32.6231	1.58995	0.794976	−	0.606641i	$-0.207483\pi$
$421$	32.6231	1.58995	0.794976	+	0.606641i	$0.207483\pi$
$422$	12.2998	0.598744
$423$	12.3144	0.598745
$424$	−30.6149	−1.48679
$425$	−26.4490	−1.28296
$426$	3.74577	0.181483
$427$	0	0
$428$	−22.0479	−1.06573
$429$	−1.17989	−0.0569655
$430$	23.3149	1.12434
$431$	−20.9225	−1.00780	−0.503900	−	0.863762i	$-0.668102\pi$
$431$	−20.9225	−1.00780	−0.503900	+	0.863762i	$0.668102\pi$
$432$	1.70030	0.0818058
$433$	−19.5348	−0.938783	−0.469392	−	0.882990i	$-0.655527\pi$
$433$	−19.5348	−0.938783	−0.469392	+	0.882990i	$0.655527\pi$
$434$	0	0
$435$	−19.8774	−0.953050
$436$	4.84627	0.232094
$437$	−10.9265	−0.522685
$438$	−5.70357	−0.272527
$439$	−30.5570	−1.45840	−0.729202	−	0.684298i	$-0.760109\pi$
$439$	−30.5570	−1.45840	−0.729202	+	0.684298i	$0.760109\pi$
$440$	43.7040	2.08351
$441$	0	0
$442$	−0.427103	−0.0203152
$443$	−12.5897	−0.598157	−0.299078	−	0.954229i	$-0.596679\pi$
$443$	−12.5897	−0.598157	−0.299078	+	0.954229i	$0.596679\pi$
$444$	−11.4151	−0.541736
$445$	32.2472	1.52866
$446$	−7.56841	−0.358374
$447$	−7.16312	−0.338804
$448$	0	0
$449$	28.9707	1.36721	0.683606	−	0.729852i	$-0.260411\pi$
$449$	28.9707	1.36721	0.683606	+	0.729852i	$0.260411\pi$
$450$	5.99992	0.282839
$451$	16.2922	0.767171
$452$	−31.8951	−1.50022
$453$	9.52933	0.447727
$454$	2.03927	0.0957076
$455$	0	0
$456$	−18.7958	−0.880195
$457$	−36.9974	−1.73066	−0.865332	−	0.501199i	$-0.832892\pi$
$457$	−36.9974	−1.73066	−0.865332	+	0.501199i	$0.832892\pi$
$458$	−15.8097	−0.738739
$459$	−2.82782	−0.131991
$460$	8.05339	0.375491
$461$	3.18625	0.148398	0.0741991	−	0.997243i	$-0.476360\pi$
$461$	3.18625	0.148398	0.0741991	+	0.997243i	$0.476360\pi$
$462$	0	0
$463$	6.58591	0.306073	0.153037	−	0.988221i	$-0.451095\pi$
$463$	6.58591	0.306073	0.153037	+	0.988221i	$0.451095\pi$
$464$	−8.92099	−0.414146
$465$	−27.9359	−1.29550
$466$	13.5245	0.626510
$467$	17.8936	0.828018	0.414009	−	0.910273i	$-0.364128\pi$
$467$	17.8936	0.828018	0.414009	+	0.910273i	$0.364128\pi$
$468$	−0.374006	−0.0172884
$469$	0	0
$470$	29.9277	1.38046
$471$	−22.0586	−1.01640
$472$	−2.30197	−0.105957
$473$	−48.0749	−2.21049
$474$	−5.85210	−0.268796
$475$	76.3692	3.50406
$476$	0	0
$477$	13.2994	0.608938
$478$	9.51132	0.435038
$479$	36.8348	1.68302	0.841512	−	0.540239i	$-0.181666\pi$
$479$	36.8348	1.68302	0.841512	+	0.540239i	$0.181666\pi$
$480$	21.5746	0.984739
$481$	1.69195	0.0771462
$482$	3.06692	0.139694
$483$	0	0
$484$	−22.4180	−1.01900
$485$	39.4979	1.79351
$486$	0.641487	0.0290985
$487$	−6.57559	−0.297969	−0.148984	−	0.988840i	$-0.547600\pi$
$487$	−6.57559	−0.297969	−0.148984	+	0.988840i	$0.547600\pi$
$488$	−0.291255	−0.0131845
$489$	15.5466	0.703043
$490$	0	0
$491$	9.23002	0.416545	0.208272	−	0.978071i	$-0.433216\pi$
$491$	9.23002	0.416545	0.208272	+	0.978071i	$0.433216\pi$
$492$	5.16439	0.232828
$493$	14.8367	0.668213
$494$	1.23322	0.0554854
$495$	−18.9854	−0.853332
$496$	−12.5376	−0.562956
$497$	0	0
$498$	−3.41673	−0.153107
$499$	36.5703	1.63711	0.818555	−	0.574428i	$-0.194775\pi$
$499$	36.5703	1.63711	0.818555	+	0.574428i	$0.194775\pi$
$500$	−26.1976	−1.17159
$501$	6.42884	0.287219
$502$	−5.82439	−0.259955
$503$	35.7378	1.59347	0.796736	−	0.604328i	$-0.206558\pi$
$503$	35.7378	1.59347	0.796736	+	0.604328i	$0.206558\pi$
$504$	0	0
$505$	30.2791	1.34740
$506$	4.30185	0.191240
$507$	−12.9446	−0.574888
$508$	−16.0032	−0.710029
$509$	−17.4178	−0.772028	−0.386014	−	0.922493i	$-0.626148\pi$
$509$	−17.4178	−0.772028	−0.386014	+	0.922493i	$0.626148\pi$
$510$	−6.87247	−0.304318
$511$	0	0
$512$	17.5107	0.773873
$513$	8.16509	0.360497
$514$	−10.8040	−0.476543
$515$	26.7574	1.17907
$516$	−15.2390	−0.670860
$517$	−61.7105	−2.71403
$518$	0	0
$519$	3.39872	0.149187
$520$	−2.05337	−0.0900462
$521$	20.3257	0.890484	0.445242	−	0.895410i	$-0.353118\pi$
$521$	20.3257	0.890484	0.445242	+	0.895410i	$0.353118\pi$
$522$	−3.36570	−0.147313
$523$	9.66375	0.422566	0.211283	−	0.977425i	$-0.432236\pi$
$523$	9.66375	0.422566	0.211283	+	0.977425i	$0.432236\pi$
$524$	−23.5348	−1.02812
$525$	0	0
$526$	7.12293	0.310575
$527$	20.8517	0.908313
$528$	−8.52065	−0.370814
$529$	−21.2092	−0.922140
$530$	32.3217	1.40396
$531$	1.00000	0.0433963
$532$	0	0
$533$	−0.765467	−0.0331560
$534$	5.46018	0.236285
$535$	52.5842	2.27341
$536$	19.5739	0.845462
$537$	−1.59969	−0.0690317
$538$	−2.25482	−0.0972124
$539$	0	0
$540$	−6.01809	−0.258978
$541$	−5.08795	−0.218748	−0.109374	−	0.994001i	$-0.534885\pi$
$541$	−5.08795	−0.218748	−0.109374	+	0.994001i	$0.534885\pi$
$542$	−9.47013	−0.406777
$543$	9.23974	0.396515
$544$	−16.1035	−0.690431
$545$	−11.5583	−0.495105
$546$	0	0
$547$	8.30596	0.355137	0.177569	−	0.984108i	$-0.443177\pi$
$547$	8.30596	0.355137	0.177569	+	0.984108i	$0.443177\pi$
$548$	35.0098	1.49554
$549$	0.126524	0.00539991
$550$	−30.0672	−1.28207
$551$	−42.8398	−1.82504
$552$	3.08049	0.131114
$553$	0	0
$554$	2.62512	0.111530
$555$	27.2250	1.15563
$556$	−14.4930	−0.614641
$557$	22.6742	0.960738	0.480369	−	0.877066i	$-0.340503\pi$
$557$	22.6742	0.960738	0.480369	+	0.877066i	$0.340503\pi$
$558$	−4.73018	−0.200245
$559$	2.25873	0.0955341
$560$	0	0
$561$	14.1709	0.598297
$562$	19.7846	0.834565
$563$	−32.1953	−1.35687	−0.678434	−	0.734661i	$-0.737341\pi$
$563$	−32.1953	−1.35687	−0.678434	+	0.734661i	$0.737341\pi$
$564$	−19.5613	−0.823679
$565$	76.0698	3.20028
$566$	−6.14454	−0.258274
$567$	0	0
$568$	−13.4417	−0.564000
$569$	−5.06122	−0.212177	−0.106089	−	0.994357i	$-0.533833\pi$
$569$	−5.06122	−0.212177	−0.106089	+	0.994357i	$0.533833\pi$
$570$	19.8437	0.831161
$571$	−22.0904	−0.924453	−0.462227	−	0.886762i	$-0.652949\pi$
$571$	−22.0904	−0.924453	−0.462227	+	0.886762i	$0.652949\pi$
$572$	1.87424	0.0783661
$573$	4.07757	0.170343
$574$	0	0
$575$	−12.5163	−0.521967
$576$	0.252457	0.0105190
$577$	−20.6841	−0.861091	−0.430545	−	0.902569i	$-0.641679\pi$
$577$	−20.6841	−0.861091	−0.430545	+	0.902569i	$0.641679\pi$
$578$	−5.77560	−0.240233
$579$	1.41320	0.0587306
$580$	31.5752	1.31109
$581$	0	0
$582$	6.68789	0.277222
$583$	−66.6468	−2.76023
$584$	20.4672	0.846939
$585$	0.892004	0.0368798
$586$	0.419448	0.0173272
$587$	−32.9763	−1.36108	−0.680538	−	0.732713i	$-0.738254\pi$
$587$	−32.9763	−1.36108	−0.680538	+	0.732713i	$0.738254\pi$
$588$	0	0
$589$	−60.2075	−2.48081
$590$	2.43031	0.100054
$591$	−5.02224	−0.206587
$592$	12.2185	0.502179
$593$	−37.0052	−1.51962	−0.759811	−	0.650144i	$-0.774709\pi$
$593$	−37.0052	−1.51962	−0.759811	+	0.650144i	$0.774709\pi$
$594$	−3.21466	−0.131899
$595$	0	0
$596$	11.3786	0.466085
$597$	0.00858483	0.000351354 0
$598$	−0.202116	−0.00826515
$599$	−1.36518	−0.0557797	−0.0278898	−	0.999611i	$-0.508879\pi$
$599$	−1.36518	−0.0557797	−0.0278898	+	0.999611i	$0.508879\pi$
$600$	−21.5307	−0.878986
$601$	−39.6537	−1.61751	−0.808755	−	0.588146i	$-0.799858\pi$
$601$	−39.6537	−1.61751	−0.808755	+	0.588146i	$0.799858\pi$
$602$	0	0
$603$	−8.50308	−0.346272
$604$	−15.1373	−0.615927
$605$	53.4669	2.17374
$606$	5.12693	0.208267
$607$	−4.65277	−0.188850	−0.0944250	−	0.995532i	$-0.530101\pi$
$607$	−4.65277	−0.188850	−0.0944250	+	0.995532i	$0.530101\pi$
$608$	46.4975	1.88572
$609$	0	0
$610$	0.307492	0.0124500
$611$	2.89938	0.117296
$612$	4.49197	0.181577
$613$	6.40908	0.258860	0.129430	−	0.991589i	$-0.458685\pi$
$613$	6.40908	0.258860	0.129430	+	0.991589i	$0.458685\pi$
$614$	0.502111	0.0202635
$615$	−12.3170	−0.496671
$616$	0	0
$617$	16.5538	0.666431	0.333216	−	0.942851i	$-0.391866\pi$
$617$	16.5538	0.666431	0.333216	+	0.942851i	$0.391866\pi$
$618$	4.53063	0.182249
$619$	29.9530	1.20391	0.601956	−	0.798530i	$-0.294388\pi$
$619$	29.9530	1.20391	0.601956	+	0.798530i	$0.294388\pi$
$620$	44.3761	1.78219
$621$	−1.33820	−0.0537000
$622$	12.5545	0.503391
$623$	0	0
$624$	0.400331	0.0160261
$625$	15.7155	0.628621
$626$	−14.4648	−0.578130
$627$	−40.9174	−1.63408
$628$	35.0399	1.39824
$629$	−20.3210	−0.810251
$630$	0	0
$631$	25.5285	1.01627	0.508137	−	0.861276i	$-0.330334\pi$
$631$	25.5285	1.01627	0.508137	+	0.861276i	$0.330334\pi$
$632$	21.0002	0.835344
$633$	19.1738	0.762091
$634$	−6.65565	−0.264330
$635$	38.1677	1.51464
$636$	−21.1260	−0.837702
$637$	0	0
$638$	16.8664	0.667747
$639$	5.83919	0.230995
$640$	−42.5356	−1.68137
$641$	−18.7947	−0.742347	−0.371173	−	0.928564i	$-0.621044\pi$
$641$	−18.7947	−0.742347	−0.371173	+	0.928564i	$0.621044\pi$
$642$	8.90368	0.351400
$643$	13.0366	0.514112	0.257056	−	0.966397i	$-0.417248\pi$
$643$	13.0366	0.514112	0.257056	+	0.966397i	$0.417248\pi$
$644$	0	0
$645$	36.3450	1.43108
$646$	−14.8115	−0.582752
$647$	−7.06169	−0.277624	−0.138812	−	0.990319i	$-0.544328\pi$
$647$	−7.06169	−0.277624	−0.138812	+	0.990319i	$0.544328\pi$
$648$	−2.30197	−0.0904301
$649$	−5.01126	−0.196709
$650$	1.41266	0.0554092
$651$	0	0
$652$	−24.6957	−0.967159
$653$	−18.8090	−0.736054	−0.368027	−	0.929815i	$-0.619967\pi$
$653$	−18.8090	−0.736054	−0.368027	+	0.929815i	$0.619967\pi$
$654$	−1.95709	−0.0765281
$655$	56.1305	2.19320
$656$	−5.52788	−0.215828
$657$	−8.89116	−0.346877
$658$	0	0
$659$	31.9839	1.24592	0.622958	−	0.782255i	$-0.285931\pi$
$659$	31.9839	1.24592	0.622958	+	0.782255i	$0.285931\pi$
$660$	30.1583	1.17391
$661$	−34.3778	−1.33714	−0.668571	−	0.743649i	$-0.733094\pi$
$661$	−34.3778	−1.33714	−0.668571	+	0.743649i	$0.733094\pi$
$662$	−15.2271	−0.591817
$663$	−0.665801	−0.0258576
$664$	12.2609	0.475816
$665$	0	0
$666$	4.60980	0.178626
$667$	7.02113	0.271859
$668$	−10.2122	−0.395121
$669$	−11.7982	−0.456145
$670$	−20.6651	−0.798363
$671$	−0.634044	−0.0244770
$672$	0	0
$673$	−14.0277	−0.540727	−0.270364	−	0.962758i	$-0.587144\pi$
$673$	−14.0277	−0.540727	−0.270364	+	0.962758i	$0.587144\pi$
$674$	−7.02401	−0.270555
$675$	9.35314	0.360003
$676$	20.5624	0.790860
$677$	−13.4274	−0.516059	−0.258029	−	0.966137i	$-0.583073\pi$
$677$	−13.4274	−0.516059	−0.258029	+	0.966137i	$0.583073\pi$
$678$	12.8803	0.494666
$679$	0	0
$680$	24.6618	0.945738
$681$	3.17897	0.121818
$682$	23.7042	0.907680
$683$	−19.0191	−0.727744	−0.363872	−	0.931449i	$-0.618545\pi$
$683$	−19.0191	−0.727744	−0.363872	+	0.931449i	$0.618545\pi$
$684$	−12.9702	−0.495928
$685$	−83.4982	−3.19030
$686$	0	0
$687$	−24.6454	−0.940281
$688$	16.3116	0.621874
$689$	3.13131	0.119293
$690$	−3.25223	−0.123810
$691$	11.0745	0.421294	0.210647	−	0.977562i	$-0.432443\pi$
$691$	11.0745	0.421294	0.210647	+	0.977562i	$0.432443\pi$
$692$	−5.39884	−0.205233
$693$	0	0
$694$	−9.13219	−0.346653
$695$	34.5658	1.31116
$696$	12.0778	0.457807
$697$	9.19357	0.348231
$698$	13.4145	0.507745
$699$	21.0830	0.797434
$700$	0	0
$701$	−7.87037	−0.297260	−0.148630	−	0.988893i	$-0.547486\pi$
$701$	−7.87037	−0.297260	−0.148630	+	0.988893i	$0.547486\pi$
$702$	0.151036	0.00570050
$703$	58.6752	2.21298
$704$	−1.26513	−0.0476813
$705$	46.6536	1.75708
$706$	−13.2344	−0.498082
$707$	0	0
$708$	−1.58849	−0.0596993
$709$	34.4465	1.29366	0.646832	−	0.762633i	$-0.276093\pi$
$709$	34.4465	1.29366	0.646832	+	0.762633i	$0.276093\pi$
$710$	14.1910	0.532580
$711$	−9.12270	−0.342128
$712$	−19.5938	−0.734309
$713$	9.86755	0.369543
$714$	0	0
$715$	−4.47007	−0.167171
$716$	2.54110	0.0949653
$717$	14.8270	0.553724
$718$	6.72105	0.250828
$719$	−2.64831	−0.0987652	−0.0493826	−	0.998780i	$-0.515725\pi$
$719$	−2.64831	−0.0987652	−0.0493826	+	0.998780i	$0.515725\pi$
$720$	6.44168	0.240067
$721$	0	0
$722$	30.5788	1.13803
$723$	4.78095	0.177805
$724$	−14.6773	−0.545477
$725$	−49.0732	−1.82253
$726$	9.05316	0.335994
$727$	27.5870	1.02315	0.511573	−	0.859240i	$-0.329063\pi$
$727$	27.5870	1.02315	0.511573	+	0.859240i	$0.329063\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−21.6083	−0.799758
$731$	−27.1283	−1.00338
$732$	−0.200982	−0.00742852
$733$	10.9848	0.405732	0.202866	−	0.979207i	$-0.434974\pi$
$733$	10.9848	0.405732	0.202866	+	0.979207i	$0.434974\pi$
$734$	−18.8728	−0.696607
$735$	0	0
$736$	−7.62058	−0.280898
$737$	42.6111	1.56960
$738$	−2.08555	−0.0767703
$739$	21.8625	0.804225	0.402112	−	0.915590i	$-0.368276\pi$
$739$	21.8625	0.804225	0.402112	+	0.915590i	$0.368276\pi$
$740$	−43.2467	−1.58978
$741$	1.92245	0.0706228
$742$	0	0
$743$	−24.6957	−0.905998	−0.452999	−	0.891511i	$-0.649646\pi$
$743$	−24.6957	−0.905998	−0.452999	+	0.891511i	$0.649646\pi$
$744$	16.9742	0.622305
$745$	−27.1379	−0.994255
$746$	−18.3632	−0.672325
$747$	−5.32627	−0.194878
$748$	−22.5104	−0.823063
$749$	0	0
$750$	10.5795	0.386308
$751$	−23.6309	−0.862303	−0.431152	−	0.902279i	$-0.641893\pi$
$751$	−23.6309	−0.862303	−0.431152	+	0.902279i	$0.641893\pi$
$752$	20.9381	0.763535
$753$	−9.07951	−0.330876
$754$	−0.792444	−0.0288591
$755$	36.1024	1.31390
$756$	0	0
$757$	18.4855	0.671866	0.335933	−	0.941886i	$-0.390949\pi$
$757$	18.4855	0.671866	0.335933	+	0.941886i	$0.390949\pi$
$758$	−11.8816	−0.431560
$759$	6.70605	0.243414
$760$	−71.2090	−2.58302
$761$	−8.41271	−0.304961	−0.152480	−	0.988307i	$-0.548726\pi$
$761$	−8.41271	−0.304961	−0.152480	+	0.988307i	$0.548726\pi$
$762$	6.46265	0.234117
$763$	0	0
$764$	−6.47720	−0.234337
$765$	−10.7133	−0.387342
$766$	5.76202	0.208190
$767$	0.235447	0.00850150
$768$	−7.70714	−0.278108
$769$	−7.08992	−0.255669	−0.127835	−	0.991796i	$-0.540803\pi$
$769$	−7.08992	−0.255669	−0.127835	+	0.991796i	$0.540803\pi$
$770$	0	0
$771$	−16.8421	−0.606552
$772$	−2.24486	−0.0807943
$773$	−5.86695	−0.211019	−0.105510	−	0.994418i	$-0.533647\pi$
$773$	−5.86695	−0.211019	−0.105510	+	0.994418i	$0.533647\pi$
$774$	6.15403	0.221202
$775$	−68.9679	−2.47740
$776$	−23.9995	−0.861530
$777$	0	0
$778$	23.8743	0.855936
$779$	−26.5457	−0.951098
$780$	−1.41694	−0.0507347
$781$	−29.2617	−1.04707
$782$	2.42750	0.0868072
$783$	−5.24671	−0.187502
$784$	0	0
$785$	−83.5700	−2.98274
$786$	9.50416	0.339002
$787$	32.7764	1.16835	0.584176	−	0.811627i	$-0.301418\pi$
$787$	32.7764	1.16835	0.584176	+	0.811627i	$0.301418\pi$
$788$	7.97780	0.284197
$789$	11.1038	0.395305
$790$	−22.1710	−0.788808
$791$	0	0
$792$	11.5358	0.409907
$793$	0.0297897	0.00105786
$794$	−3.49901	−0.124175
$795$	50.3855	1.78699
$796$	−0.0136369	−0.000483349 0
$797$	−13.4127	−0.475103	−0.237551	−	0.971375i	$-0.576345\pi$
$797$	−13.4127	−0.475103	−0.237551	+	0.971375i	$0.576345\pi$
$798$	0	0
$799$	−34.8228	−1.23194
$800$	53.2630	1.88313
$801$	8.51175	0.300748
$802$	3.64384	0.128668
$803$	44.5559	1.57234
$804$	13.5071	0.476358
$805$	0	0
$806$	−1.11371	−0.0392287
$807$	−3.51499	−0.123734
$808$	−18.3980	−0.647238
$809$	4.98493	0.175261	0.0876304	−	0.996153i	$-0.472071\pi$
$809$	4.98493	0.175261	0.0876304	+	0.996153i	$0.472071\pi$
$810$	2.43031	0.0853924
$811$	9.74181	0.342081	0.171041	−	0.985264i	$-0.445287\pi$
$811$	9.74181	0.342081	0.171041	+	0.985264i	$0.445287\pi$
$812$	0	0
$813$	−14.7628	−0.517753
$814$	−23.1009	−0.809686
$815$	58.8992	2.06315
$816$	−4.80814	−0.168319
$817$	78.3307	2.74044
$818$	3.83634	0.134134
$819$	0	0
$820$	19.5656	0.683259
$821$	37.7959	1.31908	0.659542	−	0.751667i	$-0.270750\pi$
$821$	37.7959	1.31908	0.659542	+	0.751667i	$0.270750\pi$
$822$	−14.1381	−0.493124
$823$	−9.08657	−0.316738	−0.158369	−	0.987380i	$-0.550624\pi$
$823$	−9.08657	−0.316738	−0.158369	+	0.987380i	$0.550624\pi$
$824$	−16.2581	−0.566379
$825$	−46.8710	−1.63184
$826$	0	0
$827$	27.5874	0.959310	0.479655	−	0.877457i	$-0.340762\pi$
$827$	27.5874	0.959310	0.479655	+	0.877457i	$0.340762\pi$
$828$	2.12572	0.0738737
$829$	−9.56132	−0.332078	−0.166039	−	0.986119i	$-0.553098\pi$
$829$	−9.56132	−0.332078	−0.166039	+	0.986119i	$0.553098\pi$
$830$	−12.9445	−0.449309
$831$	4.09223	0.141958
$832$	0.0594402	0.00206072
$833$	0	0
$834$	5.85277	0.202665
$835$	24.3560	0.842874
$836$	64.9970	2.24797
$837$	−7.37377	−0.254875
$838$	3.20690	0.110781
$839$	11.2463	0.388265	0.194133	−	0.980975i	$-0.437811\pi$
$839$	11.2463	0.388265	0.194133	+	0.980975i	$0.437811\pi$
$840$	0	0
$841$	−1.47203	−0.0507597
$842$	20.9273	0.721202
$843$	30.8418	1.06225
$844$	−30.4575	−1.04839
$845$	−49.0412	−1.68707
$846$	7.89951	0.271591
$847$	0	0
$848$	22.6130	0.776533
$849$	−9.57858	−0.328736
$850$	−16.9667	−0.581952
$851$	−9.61642	−0.329647
$852$	−9.27552	−0.317774
$853$	47.9377	1.64135	0.820677	−	0.571392i	$-0.193597\pi$
$853$	47.9377	1.64135	0.820677	+	0.571392i	$0.193597\pi$
$854$	0	0
$855$	30.9339	1.05792
$856$	−31.9508	−1.09206
$857$	−3.09429	−0.105699	−0.0528495	−	0.998602i	$-0.516830\pi$
$857$	−3.09429	−0.105699	−0.0528495	+	0.998602i	$0.516830\pi$
$858$	−0.756883	−0.0258396
$859$	−28.9494	−0.987742	−0.493871	−	0.869535i	$-0.664419\pi$
$859$	−28.9494	−0.987742	−0.493871	+	0.869535i	$0.664419\pi$
$860$	−57.7338	−1.96871
$861$	0	0
$862$	−13.4215	−0.457138
$863$	−35.1914	−1.19793	−0.598964	−	0.800776i	$-0.704421\pi$
$863$	−35.1914	−1.19793	−0.598964	+	0.800776i	$0.704421\pi$
$864$	5.69467	0.193737
$865$	12.8762	0.437805
$866$	−12.5313	−0.425832
$867$	−9.00345	−0.305773
$868$	0	0
$869$	45.7163	1.55082
$870$	−12.7511	−0.432304
$871$	−2.00202	−0.0678360
$872$	7.02299	0.237828
$873$	10.4256	0.352853
$874$	−7.00920	−0.237090
$875$	0	0
$876$	14.1236	0.477191
$877$	34.3715	1.16064	0.580321	−	0.814388i	$-0.302927\pi$
$877$	34.3715	1.16064	0.580321	+	0.814388i	$0.302927\pi$
$878$	−19.6019	−0.661532
$879$	0.653868	0.0220544
$880$	−32.2810	−1.08819
$881$	−53.2445	−1.79385	−0.896926	−	0.442180i	$-0.854205\pi$
$881$	−53.2445	−1.79385	−0.896926	+	0.442180i	$0.854205\pi$
$882$	0	0
$883$	14.7269	0.495600	0.247800	−	0.968811i	$-0.420292\pi$
$883$	14.7269	0.495600	0.247800	+	0.968811i	$0.420292\pi$
$884$	1.05762	0.0355717
$885$	3.78855	0.127351
$886$	−8.07616	−0.271324
$887$	1.24479	0.0417961	0.0208980	−	0.999782i	$-0.493347\pi$
$887$	1.24479	0.0417961	0.0208980	+	0.999782i	$0.493347\pi$
$888$	−16.5422	−0.555121
$889$	0	0
$890$	20.6862	0.693402
$891$	−5.01126	−0.167884
$892$	18.7414	0.627508
$893$	100.548	3.36471
$894$	−4.59505	−0.153682
$895$	−6.06051	−0.202581
$896$	0	0
$897$	−0.315074	−0.0105200
$898$	18.5843	0.620167
$899$	38.6880	1.29032
$900$	−14.8574	−0.495247
$901$	−37.6083	−1.25291
$902$	10.4513	0.347989
$903$	0	0
$904$	−46.2210	−1.53729
$905$	35.0053	1.16361
$906$	6.11294	0.203089
$907$	57.5809	1.91194	0.955971	−	0.293463i	$-0.0948077\pi$
$907$	57.5809	1.91194	0.955971	+	0.293463i	$0.0948077\pi$
$908$	−5.04977	−0.167583
$909$	7.99225	0.265086
$910$	0	0
$911$	−45.4569	−1.50605	−0.753027	−	0.657990i	$-0.771407\pi$
$911$	−45.4569	−1.50605	−0.753027	+	0.657990i	$0.771407\pi$
$912$	13.8831	0.459715
$913$	26.6913	0.883354
$914$	−23.7333	−0.785029
$915$	0.479342	0.0158466
$916$	39.1491	1.29352
$917$	0	0
$918$	−1.81401	−0.0598712
$919$	17.1230	0.564837	0.282419	−	0.959291i	$-0.408863\pi$
$919$	17.1230	0.564837	0.282419	+	0.959291i	$0.408863\pi$
$920$	11.6706	0.384769
$921$	0.782729	0.0257918
$922$	2.04394	0.0673135
$923$	1.37482	0.0452528
$924$	0	0
$925$	67.2127	2.20994
$926$	4.22478	0.138835
$927$	7.06270	0.231969
$928$	−29.8783	−0.980802
$929$	27.4460	0.900473	0.450236	−	0.892909i	$-0.351340\pi$
$929$	27.4460	0.900473	0.450236	+	0.892909i	$0.351340\pi$
$930$	−17.9205	−0.587638
$931$	0	0
$932$	−33.4903	−1.09701
$933$	19.5710	0.640726
$934$	11.4785	0.375589
$935$	53.6874	1.75576
$936$	−0.541993	−0.0177156
$937$	−13.6188	−0.444908	−0.222454	−	0.974943i	$-0.571407\pi$
$937$	−13.6188	−0.444908	−0.222454	+	0.974943i	$0.571407\pi$
$938$	0	0
$939$	−22.5489	−0.735855
$940$	−74.1090	−2.41717
$941$	30.6516	0.999215	0.499607	−	0.866252i	$-0.333478\pi$
$941$	30.6516	0.999215	0.499607	+	0.866252i	$0.333478\pi$
$942$	−14.1503	−0.461041
$943$	4.35064	0.141676
$944$	1.70030	0.0553401
$945$	0	0
$946$	−30.8394	−1.00268
$947$	44.5128	1.44647	0.723235	−	0.690602i	$-0.242654\pi$
$947$	44.5128	1.44647	0.723235	+	0.690602i	$0.242654\pi$
$948$	14.4914	0.470657
$949$	−2.09340	−0.0679546
$950$	48.9899	1.58944
$951$	−10.3753	−0.336443
$952$	0	0
$953$	30.9896	1.00385	0.501925	−	0.864911i	$-0.332625\pi$
$953$	30.9896	1.00385	0.501925	+	0.864911i	$0.332625\pi$
$954$	8.53140	0.276214
$955$	15.4481	0.499889
$956$	−23.5526	−0.761745
$957$	26.2926	0.849920
$958$	23.6290	0.763420
$959$	0	0
$960$	0.956446	0.0308692
$961$	23.3725	0.753951
$962$	1.08536	0.0349935
$963$	13.8797	0.447269
$964$	−7.59451	−0.244603
$965$	5.35399	0.172351
$966$	0	0
$967$	−21.6137	−0.695048	−0.347524	−	0.937671i	$-0.612978\pi$
$967$	−21.6137	−0.695048	−0.347524	+	0.937671i	$0.612978\pi$
$968$	−32.4872	−1.04418
$969$	−23.0894	−0.741737
$970$	25.3374	0.813536
$971$	−41.0521	−1.31743	−0.658713	−	0.752394i	$-0.728899\pi$
$971$	−41.0521	−1.31743	−0.658713	+	0.752394i	$0.728899\pi$
$972$	−1.58849	−0.0509510
$973$	0	0
$974$	−4.21816	−0.135159
$975$	2.20217	0.0705259
$976$	0.215129	0.00688610
$977$	34.9785	1.11906	0.559531	−	0.828810i	$-0.310981\pi$
$977$	34.9785	1.11906	0.559531	+	0.828810i	$0.310981\pi$
$978$	9.97296	0.318900
$979$	−42.6546	−1.36325
$980$	0	0
$981$	−3.05086	−0.0974063
$982$	5.92094	0.188945
$983$	1.97117	0.0628705	0.0314353	−	0.999506i	$-0.489992\pi$
$983$	1.97117	0.0628705	0.0314353	+	0.999506i	$0.489992\pi$
$984$	7.48399	0.238581
$985$	−19.0270	−0.606251
$986$	9.51758	0.303101
$987$	0	0
$988$	−3.05379	−0.0971541
$989$	−12.8378	−0.408219
$990$	−12.1789	−0.387072
$991$	−50.6897	−1.61021	−0.805105	−	0.593132i	$-0.797891\pi$
$991$	−50.6897	−1.61021	−0.805105	+	0.593132i	$0.797891\pi$
$992$	−41.9912	−1.33322
$993$	−23.7371	−0.753275
$994$	0	0
$995$	0.0325241	0.00103108
$996$	8.46074	0.268089
$997$	37.4271	1.18533	0.592665	−	0.805449i	$-0.298076\pi$
$997$	37.4271	1.18533	0.592665	+	0.805449i	$0.298076\pi$
$998$	23.4594	0.742593
$999$	7.18611	0.227358

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8673.2.a.ba.1.7		12
7.6	odd	2		1239.2.a.i.1.7	✓	12
21.20	even	2		3717.2.a.q.1.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1239.2.a.i.1.7	✓	12	7.6	odd	2
3717.2.a.q.1.6		12	21.20	even	2
8673.2.a.ba.1.7		12	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:	\( N \)	\(=\)	\( 8673 = 3 \cdot 7^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8673.a (trivial)

\(f(q)\)	\(=\)	\(q+0.641487 q^{2} +1.00000 q^{3} -1.58849 q^{4} +3.78855 q^{5} +0.641487 q^{6} -2.30197 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.641487 q^{2} +1.00000 q^{3} -1.58849 q^{4} +3.78855 q^{5} +0.641487 q^{6} -2.30197 q^{8} +1.00000 q^{9} +2.43031 q^{10} -5.01126 q^{11} -1.58849 q^{12} +0.235447 q^{13} +3.78855 q^{15} +1.70030 q^{16} -2.82782 q^{17} +0.641487 q^{18} +8.16509 q^{19} -6.01809 q^{20} -3.21466 q^{22} -1.33820 q^{23} -2.30197 q^{24} +9.35314 q^{25} +0.151036 q^{26} +1.00000 q^{27} -5.24671 q^{29} +2.43031 q^{30} -7.37377 q^{31} +5.69467 q^{32} -5.01126 q^{33} -1.81401 q^{34} -1.58849 q^{36} +7.18611 q^{37} +5.23780 q^{38} +0.235447 q^{39} -8.72115 q^{40} -3.25112 q^{41} +9.59337 q^{43} +7.96036 q^{44} +3.78855 q^{45} -0.858436 q^{46} +12.3144 q^{47} +1.70030 q^{48} +5.99992 q^{50} -2.82782 q^{51} -0.374006 q^{52} +13.2994 q^{53} +0.641487 q^{54} -18.9854 q^{55} +8.16509 q^{57} -3.36570 q^{58} +1.00000 q^{59} -6.01809 q^{60} +0.126524 q^{61} -4.73018 q^{62} +0.252457 q^{64} +0.892004 q^{65} -3.21466 q^{66} -8.50308 q^{67} +4.49197 q^{68} -1.33820 q^{69} +5.83919 q^{71} -2.30197 q^{72} -8.89116 q^{73} +4.60980 q^{74} +9.35314 q^{75} -12.9702 q^{76} +0.151036 q^{78} -9.12270 q^{79} +6.44168 q^{80} +1.00000 q^{81} -2.08555 q^{82} -5.32627 q^{83} -10.7133 q^{85} +6.15403 q^{86} -5.24671 q^{87} +11.5358 q^{88} +8.51175 q^{89} +2.43031 q^{90} +2.12572 q^{92} -7.37377 q^{93} +7.89951 q^{94} +30.9339 q^{95} +5.69467 q^{96} +10.4256 q^{97} -5.01126 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 12 q^{3} + 19 q^{4} + 4 q^{5} + 3 q^{6} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + 12 * q^3 + 19 * q^4 + 4 * q^5 + 3 * q^6 + 12 * q^8 + 12 * q^9	\( 12 q + 3 q^{2} + 12 q^{3} + 19 q^{4} + 4 q^{5} + 3 q^{6} + 12 q^{8} + 12 q^{9} - 2 q^{10} + 2 q^{11} + 19 q^{12} - 9 q^{13} + 4 q^{15} + 33 q^{16} + 5 q^{17} + 3 q^{18} - 7 q^{19} + 15 q^{20} + 24 q^{22} + q^{23} + 12 q^{24} + 30 q^{25} - 3 q^{26} + 12 q^{27} + 11 q^{29} - 2 q^{30} - 13 q^{31} + 22 q^{32} + 2 q^{33} - 8 q^{34} + 19 q^{36} + 7 q^{37} + 4 q^{38} - 9 q^{39} + 20 q^{40} + 21 q^{43} + 23 q^{44} + 4 q^{45} - 7 q^{46} + 18 q^{47} + 33 q^{48} + 52 q^{50} + 5 q^{51} - 23 q^{52} + 15 q^{53} + 3 q^{54} - 20 q^{55} - 7 q^{57} + 27 q^{58} + 12 q^{59} + 15 q^{60} - 30 q^{61} - q^{62} + 88 q^{64} + q^{65} + 24 q^{66} + 19 q^{67} + 25 q^{68} + q^{69} + 18 q^{71} + 12 q^{72} - 19 q^{73} + 3 q^{74} + 30 q^{75} - 62 q^{76} - 3 q^{78} + 16 q^{79} + 47 q^{80} + 12 q^{81} - 19 q^{82} + 37 q^{83} + 48 q^{85} - 8 q^{86} + 11 q^{87} + 46 q^{88} - 23 q^{89} - 2 q^{90} + 19 q^{92} - 13 q^{93} - 13 q^{94} + 20 q^{95} + 22 q^{96} - 9 q^{97} + 2 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 12 * q^3 + 19 * q^4 + 4 * q^5 + 3 * q^6 + 12 * q^8 + 12 * q^9 - 2 * q^10 + 2 * q^11 + 19 * q^12 - 9 * q^13 + 4 * q^15 + 33 * q^16 + 5 * q^17 + 3 * q^18 - 7 * q^19 + 15 * q^20 + 24 * q^22 + q^23 + 12 * q^24 + 30 * q^25 - 3 * q^26 + 12 * q^27 + 11 * q^29 - 2 * q^30 - 13 * q^31 + 22 * q^32 + 2 * q^33 - 8 * q^34 + 19 * q^36 + 7 * q^37 + 4 * q^38 - 9 * q^39 + 20 * q^40 + 21 * q^43 + 23 * q^44 + 4 * q^45 - 7 * q^46 + 18 * q^47 + 33 * q^48 + 52 * q^50 + 5 * q^51 - 23 * q^52 + 15 * q^53 + 3 * q^54 - 20 * q^55 - 7 * q^57 + 27 * q^58 + 12 * q^59 + 15 * q^60 - 30 * q^61 - q^62 + 88 * q^64 + q^65 + 24 * q^66 + 19 * q^67 + 25 * q^68 + q^69 + 18 * q^71 + 12 * q^72 - 19 * q^73 + 3 * q^74 + 30 * q^75 - 62 * q^76 - 3 * q^78 + 16 * q^79 + 47 * q^80 + 12 * q^81 - 19 * q^82 + 37 * q^83 + 48 * q^85 - 8 * q^86 + 11 * q^87 + 46 * q^88 - 23 * q^89 - 2 * q^90 + 19 * q^92 - 13 * q^93 - 13 * q^94 + 20 * q^95 + 22 * q^96 - 9 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

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Database

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