LMFDB - Embedded newform 8673.2.a.ba.1.9

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			1.9
Root			$1.58626$ 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)

$f(q)$	$=$	$q+1.58626 q^{2} +1.00000 q^{3} +0.516213 q^{4} -3.36773 q^{5} +1.58626 q^{6} -2.35367 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.58626 q^{2} +1.00000 q^{3} +0.516213 q^{4} -3.36773 q^{5} +1.58626 q^{6} -2.35367 q^{8} +1.00000 q^{9} -5.34209 q^{10} -2.28178 q^{11} +0.516213 q^{12} -5.46493 q^{13} -3.36773 q^{15} -4.76595 q^{16} -0.821461 q^{17} +1.58626 q^{18} -6.52704 q^{19} -1.73847 q^{20} -3.61950 q^{22} -3.49067 q^{23} -2.35367 q^{24} +6.34161 q^{25} -8.66878 q^{26} +1.00000 q^{27} +3.18314 q^{29} -5.34209 q^{30} -0.597837 q^{31} -2.85269 q^{32} -2.28178 q^{33} -1.30305 q^{34} +0.516213 q^{36} +6.68959 q^{37} -10.3536 q^{38} -5.46493 q^{39} +7.92652 q^{40} +9.93409 q^{41} +0.228372 q^{43} -1.17789 q^{44} -3.36773 q^{45} -5.53710 q^{46} +0.251356 q^{47} -4.76595 q^{48} +10.0594 q^{50} -0.821461 q^{51} -2.82107 q^{52} +11.4182 q^{53} +1.58626 q^{54} +7.68443 q^{55} -6.52704 q^{57} +5.04928 q^{58} +1.00000 q^{59} -1.73847 q^{60} +4.90221 q^{61} -0.948324 q^{62} +5.00680 q^{64} +18.4044 q^{65} -3.61950 q^{66} +7.76550 q^{67} -0.424049 q^{68} -3.49067 q^{69} -5.92867 q^{71} -2.35367 q^{72} -1.75521 q^{73} +10.6114 q^{74} +6.34161 q^{75} -3.36934 q^{76} -8.66878 q^{78} -10.9979 q^{79} +16.0504 q^{80} +1.00000 q^{81} +15.7580 q^{82} -3.74597 q^{83} +2.76646 q^{85} +0.362256 q^{86} +3.18314 q^{87} +5.37056 q^{88} -7.11552 q^{89} -5.34209 q^{90} -1.80193 q^{92} -0.597837 q^{93} +0.398715 q^{94} +21.9813 q^{95} -2.85269 q^{96} +5.99737 q^{97} -2.28178 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.58626	1.12165	0.560827	−	0.827933i	$-0.310483\pi$
$2$	1.58626	1.12165	0.560827	+	0.827933i	$0.310483\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.516213	0.258107
$5$	−3.36773	−1.50610	−0.753048	−	0.657966i	$-0.771417\pi$
$5$	−3.36773	−1.50610	−0.753048	+	0.657966i	$0.771417\pi$
$6$	1.58626	0.647587
$7$	0	0
$7$	0	0
$8$	−2.35367	−0.832147
$9$	1.00000	0.333333
$10$	−5.34209	−1.68932
$11$	−2.28178	−0.687984	−0.343992	−	0.938973i	$-0.611779\pi$
$11$	−2.28178	−0.687984	−0.343992	+	0.938973i	$0.611779\pi$
$12$	0.516213	0.149018
$13$	−5.46493	−1.51570	−0.757849	−	0.652430i	$-0.773750\pi$
$13$	−5.46493	−1.51570	−0.757849	+	0.652430i	$0.773750\pi$
$14$	0	0
$15$	−3.36773	−0.869544
$16$	−4.76595	−1.19149
$17$	−0.821461	−0.199234	−0.0996168	−	0.995026i	$-0.531762\pi$
$17$	−0.821461	−0.199234	−0.0996168	+	0.995026i	$0.531762\pi$
$18$	1.58626	0.373884
$19$	−6.52704	−1.49741	−0.748703	−	0.662906i	$-0.769323\pi$
$19$	−6.52704	−1.49741	−0.748703	+	0.662906i	$0.769323\pi$
$20$	−1.73847	−0.388733
$21$	0	0
$22$	−3.61950	−0.771679
$23$	−3.49067	−0.727855	−0.363928	−	0.931427i	$-0.618564\pi$
$23$	−3.49067	−0.727855	−0.363928	+	0.931427i	$0.618564\pi$
$24$	−2.35367	−0.480441
$25$	6.34161	1.26832
$26$	−8.66878	−1.70009
$27$	1.00000	0.192450
$28$	0	0
$29$	3.18314	0.591095	0.295547	−	0.955328i	$-0.404498\pi$
$29$	3.18314	0.591095	0.295547	+	0.955328i	$0.404498\pi$
$30$	−5.34209	−0.975328
$31$	−0.597837	−0.107375	−0.0536874	−	0.998558i	$-0.517097\pi$
$31$	−0.597837	−0.107375	−0.0536874	+	0.998558i	$0.517097\pi$
$32$	−2.85269	−0.504289
$33$	−2.28178	−0.397208
$34$	−1.30305	−0.223471
$35$	0	0
$36$	0.516213	0.0860355
$37$	6.68959	1.09976	0.549881	−	0.835243i	$-0.314673\pi$
$37$	6.68959	1.09976	0.549881	+	0.835243i	$0.314673\pi$
$38$	−10.3536	−1.67957
$39$	−5.46493	−0.875088
$40$	7.92652	1.25329
$41$	9.93409	1.55144	0.775722	−	0.631075i	$-0.217386\pi$
$41$	9.93409	1.55144	0.775722	+	0.631075i	$0.217386\pi$
$42$	0	0
$43$	0.228372	0.0348263	0.0174132	−	0.999848i	$-0.494457\pi$
$43$	0.228372	0.0348263	0.0174132	+	0.999848i	$0.494457\pi$
$44$	−1.17789	−0.177573
$45$	−3.36773	−0.502032
$46$	−5.53710	−0.816401
$47$	0.251356	0.0366640	0.0183320	−	0.999832i	$-0.494164\pi$
$47$	0.251356	0.0366640	0.0183320	+	0.999832i	$0.494164\pi$
$48$	−4.76595	−0.687906
$49$	0	0
$50$	10.0594	1.42262
$51$	−0.821461	−0.115028
$52$	−2.82107	−0.391211
$53$	11.4182	1.56841	0.784203	−	0.620505i	$-0.213072\pi$
$53$	11.4182	1.56841	0.784203	+	0.620505i	$0.213072\pi$
$54$	1.58626	0.215862
$55$	7.68443	1.03617
$56$	0	0
$57$	−6.52704	−0.864527
$58$	5.04928	0.663003
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−1.73847	−0.224435
$61$	4.90221	0.627664	0.313832	−	0.949479i	$-0.398387\pi$
$61$	4.90221	0.627664	0.313832	+	0.949479i	$0.398387\pi$
$62$	−0.948324	−0.120437
$63$	0	0
$64$	5.00680	0.625850
$65$	18.4044	2.28278
$66$	−3.61950	−0.445529
$67$	7.76550	0.948707	0.474353	−	0.880334i	$-0.342682\pi$
$67$	7.76550	0.948707	0.474353	+	0.880334i	$0.342682\pi$
$68$	−0.424049	−0.0514235
$69$	−3.49067	−0.420227
$70$	0	0
$71$	−5.92867	−0.703603	−0.351802	−	0.936075i	$-0.614431\pi$
$71$	−5.92867	−0.703603	−0.351802	+	0.936075i	$0.614431\pi$
$72$	−2.35367	−0.277382
$73$	−1.75521	−0.205431	−0.102716	−	0.994711i	$-0.532753\pi$
$73$	−1.75521	−0.205431	−0.102716	+	0.994711i	$0.532753\pi$
$74$	10.6114	1.23355
$75$	6.34161	0.732266
$76$	−3.36934	−0.386490
$77$	0	0
$78$	−8.66878	−0.981546
$79$	−10.9979	−1.23736	−0.618682	−	0.785641i	$-0.712333\pi$
$79$	−10.9979	−1.23736	−0.618682	+	0.785641i	$0.712333\pi$
$80$	16.0504	1.79449
$81$	1.00000	0.111111
$82$	15.7580	1.74018
$83$	−3.74597	−0.411173	−0.205587	−	0.978639i	$-0.565910\pi$
$83$	−3.74597	−0.411173	−0.205587	+	0.978639i	$0.565910\pi$
$84$	0	0
$85$	2.76646	0.300065
$86$	0.362256	0.0390631
$87$	3.18314	0.341269
$88$	5.37056	0.572504
$89$	−7.11552	−0.754244	−0.377122	−	0.926164i	$-0.623086\pi$
$89$	−7.11552	−0.754244	−0.377122	+	0.926164i	$0.623086\pi$
$90$	−5.34209	−0.563106
$91$	0	0
$92$	−1.80193	−0.187864
$93$	−0.597837	−0.0619928
$94$	0.398715	0.0411243
$95$	21.9813	2.25523
$96$	−2.85269	−0.291151
$97$	5.99737	0.608941	0.304470	−	0.952522i	$-0.401521\pi$
$97$	5.99737	0.608941	0.304470	+	0.952522i	$0.401521\pi$
$98$	0	0
$99$	−2.28178	−0.229328
$100$	3.27362	0.327362
$101$	−4.57698	−0.455427	−0.227713	−	0.973728i	$-0.573125\pi$
$101$	−4.57698	−0.455427	−0.227713	+	0.973728i	$0.573125\pi$
$102$	−1.30305	−0.129021
$103$	17.0296	1.67797	0.838987	−	0.544151i	$-0.183148\pi$
$103$	17.0296	1.67797	0.838987	+	0.544151i	$0.183148\pi$
$104$	12.8626	1.26128
$105$	0	0
$106$	18.1121	1.75921
$107$	7.52734	0.727695	0.363847	−	0.931459i	$-0.381463\pi$
$107$	7.52734	0.727695	0.363847	+	0.931459i	$0.381463\pi$
$108$	0.516213	0.0496726
$109$	2.40811	0.230655	0.115327	−	0.993328i	$-0.463208\pi$
$109$	2.40811	0.230655	0.115327	+	0.993328i	$0.463208\pi$
$110$	12.1895	1.16222
$111$	6.68959	0.634948
$112$	0	0
$113$	−18.9656	−1.78413	−0.892065	−	0.451908i	$-0.850744\pi$
$113$	−18.9656	−1.78413	−0.892065	+	0.451908i	$0.850744\pi$
$114$	−10.3536	−0.969700
$115$	11.7556	1.09622
$116$	1.64318	0.152565
$117$	−5.46493	−0.505233
$118$	1.58626	0.146027
$119$	0	0
$120$	7.92652	0.723589
$121$	−5.79346	−0.526678
$122$	7.77617	0.704021
$123$	9.93409	0.895726
$124$	−0.308611	−0.0277141
$125$	−4.51819	−0.404119
$126$	0	0
$127$	−9.68829	−0.859697	−0.429849	−	0.902901i	$-0.641433\pi$
$127$	−9.68829	−0.859697	−0.429849	+	0.902901i	$0.641433\pi$
$128$	13.6475	1.20628
$129$	0.228372	0.0201070
$130$	29.1941	2.56049
$131$	4.76789	0.416573	0.208286	−	0.978068i	$-0.433211\pi$
$131$	4.76789	0.416573	0.208286	+	0.978068i	$0.433211\pi$
$132$	−1.17789	−0.102522
$133$	0	0
$134$	12.3181	1.06412
$135$	−3.36773	−0.289848
$136$	1.93345	0.165792
$137$	−6.97951	−0.596299	−0.298150	−	0.954519i	$-0.596369\pi$
$137$	−6.97951	−0.596299	−0.298150	+	0.954519i	$0.596369\pi$
$138$	−5.53710	−0.471349
$139$	0.515718	0.0437426	0.0218713	−	0.999761i	$-0.493038\pi$
$139$	0.515718	0.0437426	0.0218713	+	0.999761i	$0.493038\pi$
$140$	0	0
$141$	0.251356	0.0211680
$142$	−9.40439	−0.789199
$143$	12.4698	1.04278
$144$	−4.76595	−0.397163
$145$	−10.7200	−0.890245
$146$	−2.78421	−0.230423
$147$	0	0
$148$	3.45325	0.283856
$149$	−9.39223	−0.769442	−0.384721	−	0.923033i	$-0.625702\pi$
$149$	−9.39223	−0.769442	−0.384721	+	0.923033i	$0.625702\pi$
$150$	10.0594	0.821349
$151$	22.5101	1.83184	0.915921	−	0.401358i	$-0.131462\pi$
$151$	22.5101	1.83184	0.915921	+	0.401358i	$0.131462\pi$
$152$	15.3625	1.24606
$153$	−0.821461	−0.0664112
$154$	0	0
$155$	2.01335	0.161717
$156$	−2.82107	−0.225866
$157$	−17.1306	−1.36717	−0.683587	−	0.729869i	$-0.739581\pi$
$157$	−17.1306	−1.36717	−0.683587	+	0.729869i	$0.739581\pi$
$158$	−17.4456	−1.38789
$159$	11.4182	0.905519
$160$	9.60709	0.759507
$161$	0	0
$162$	1.58626	0.124628
$163$	−22.6970	−1.77777	−0.888884	−	0.458132i	$-0.848519\pi$
$163$	−22.6970	−1.77777	−0.888884	+	0.458132i	$0.848519\pi$
$164$	5.12810	0.400438
$165$	7.68443	0.598232
$166$	−5.94207	−0.461194
$167$	21.7868	1.68591	0.842956	−	0.537982i	$-0.180813\pi$
$167$	21.7868	1.68591	0.842956	+	0.537982i	$0.180813\pi$
$168$	0	0
$169$	16.8654	1.29734
$170$	4.38832	0.336569
$171$	−6.52704	−0.499135
$172$	0.117888	0.00898891
$173$	−10.2246	−0.777359	−0.388679	−	0.921373i	$-0.627069\pi$
$173$	−10.2246	−0.777359	−0.388679	+	0.921373i	$0.627069\pi$
$174$	5.04928	0.382785
$175$	0	0
$176$	10.8749	0.819724
$177$	1.00000	0.0751646
$178$	−11.2871	−0.846000
$179$	−22.6004	−1.68923	−0.844616	−	0.535372i	$-0.820171\pi$
$179$	−22.6004	−1.68923	−0.844616	+	0.535372i	$0.820171\pi$
$180$	−1.73847	−0.129578
$181$	10.0541	0.747314	0.373657	−	0.927567i	$-0.378104\pi$
$181$	10.0541	0.747314	0.373657	+	0.927567i	$0.378104\pi$
$182$	0	0
$183$	4.90221	0.362382
$184$	8.21588	0.605683
$185$	−22.5287	−1.65635
$186$	−0.948324	−0.0695345
$187$	1.87440	0.137069
$188$	0.129753	0.00946323
$189$	0	0
$190$	34.8680	2.52959
$191$	9.44083	0.683114	0.341557	−	0.939861i	$-0.389046\pi$
$191$	9.44083	0.683114	0.341557	+	0.939861i	$0.389046\pi$
$192$	5.00680	0.361335
$193$	12.6514	0.910667	0.455333	−	0.890321i	$-0.349520\pi$
$193$	12.6514	0.910667	0.455333	+	0.890321i	$0.349520\pi$
$194$	9.51338	0.683021
$195$	18.4044	1.31797
$196$	0	0
$197$	−20.6234	−1.46936	−0.734678	−	0.678416i	$-0.762667\pi$
$197$	−20.6234	−1.46936	−0.734678	+	0.678416i	$0.762667\pi$
$198$	−3.61950	−0.257226
$199$	−0.247939	−0.0175759	−0.00878795	−	0.999961i	$-0.502797\pi$
$199$	−0.247939	−0.0175759	−0.00878795	+	0.999961i	$0.502797\pi$
$200$	−14.9261	−1.05543
$201$	7.76550	0.547736
$202$	−7.26027	−0.510831
$203$	0	0
$204$	−0.424049	−0.0296894
$205$	−33.4553	−2.33662
$206$	27.0133	1.88211
$207$	−3.49067	−0.242618
$208$	26.0456	1.80593
$209$	14.8933	1.03019
$210$	0	0
$211$	1.22418	0.0842760	0.0421380	−	0.999112i	$-0.486583\pi$
$211$	1.22418	0.0842760	0.0421380	+	0.999112i	$0.486583\pi$
$212$	5.89420	0.404816
$213$	−5.92867	−0.406226
$214$	11.9403	0.816222
$215$	−0.769094	−0.0524518
$216$	−2.35367	−0.160147
$217$	0	0
$218$	3.81987	0.258715
$219$	−1.75521	−0.118606
$220$	3.96681	0.267442
$221$	4.48923	0.301978
$222$	10.6114	0.712191
$223$	11.6756	0.781853	0.390927	−	0.920422i	$-0.372155\pi$
$223$	11.6756	0.781853	0.390927	+	0.920422i	$0.372155\pi$
$224$	0	0
$225$	6.34161	0.422774
$226$	−30.0843	−2.00118
$227$	20.6450	1.37026	0.685128	−	0.728422i	$-0.259746\pi$
$227$	20.6450	1.37026	0.685128	+	0.728422i	$0.259746\pi$
$228$	−3.36934	−0.223140
$229$	−7.42657	−0.490761	−0.245381	−	0.969427i	$-0.578913\pi$
$229$	−7.42657	−0.490761	−0.245381	+	0.969427i	$0.578913\pi$
$230$	18.6475	1.22958
$231$	0	0
$232$	−7.49206	−0.491878
$233$	−1.96999	−0.129058	−0.0645292	−	0.997916i	$-0.520555\pi$
$233$	−1.96999	−0.129058	−0.0645292	+	0.997916i	$0.520555\pi$
$234$	−8.66878	−0.566696
$235$	−0.846499	−0.0552195
$236$	0.516213	0.0336026
$237$	−10.9979	−0.714392
$238$	0	0
$239$	−25.0695	−1.62161	−0.810806	−	0.585315i	$-0.800971\pi$
$239$	−25.0695	−1.62161	−0.810806	+	0.585315i	$0.800971\pi$
$240$	16.0504	1.03605
$241$	17.3721	1.11903	0.559516	−	0.828819i	$-0.310987\pi$
$241$	17.3721	1.11903	0.559516	+	0.828819i	$0.310987\pi$
$242$	−9.18992	−0.590751
$243$	1.00000	0.0641500
$244$	2.53058	0.162004
$245$	0	0
$246$	15.7580	1.00469
$247$	35.6698	2.26961
$248$	1.40711	0.0893516
$249$	−3.74597	−0.237391
$250$	−7.16701	−0.453282
$251$	−9.52729	−0.601357	−0.300679	−	0.953725i	$-0.597213\pi$
$251$	−9.52729	−0.601357	−0.300679	+	0.953725i	$0.597213\pi$
$252$	0	0
$253$	7.96496	0.500752
$254$	−15.3681	−0.964282
$255$	2.76646	0.173242
$256$	11.6348	0.727173
$257$	21.1052	1.31650	0.658252	−	0.752798i	$-0.271296\pi$
$257$	21.1052	1.31650	0.658252	+	0.752798i	$0.271296\pi$
$258$	0.362256	0.0225531
$259$	0	0
$260$	9.50059	0.589202
$261$	3.18314	0.197032
$262$	7.56311	0.467250
$263$	22.3200	1.37631	0.688156	−	0.725563i	$-0.258420\pi$
$263$	22.3200	1.37631	0.688156	+	0.725563i	$0.258420\pi$
$264$	5.37056	0.330535
$265$	−38.4533	−2.36217
$266$	0	0
$267$	−7.11552	−0.435463
$268$	4.00865	0.244867
$269$	26.3019	1.60365	0.801827	−	0.597556i	$-0.203862\pi$
$269$	26.3019	1.60365	0.801827	+	0.597556i	$0.203862\pi$
$270$	−5.34209	−0.325109
$271$	3.11791	0.189400	0.0946998	−	0.995506i	$-0.469811\pi$
$271$	3.11791	0.189400	0.0946998	+	0.995506i	$0.469811\pi$
$272$	3.91504	0.237384
$273$	0	0
$274$	−11.0713	−0.668841
$275$	−14.4702	−0.872585
$276$	−1.80193	−0.108463
$277$	−26.1809	−1.57306	−0.786528	−	0.617555i	$-0.788123\pi$
$277$	−26.1809	−1.57306	−0.786528	+	0.617555i	$0.788123\pi$
$278$	0.818061	0.0490641
$279$	−0.597837	−0.0357916
$280$	0	0
$281$	−2.24346	−0.133834	−0.0669169	−	0.997759i	$-0.521316\pi$
$281$	−2.24346	−0.133834	−0.0669169	+	0.997759i	$0.521316\pi$
$282$	0.398715	0.0237432
$283$	−1.77185	−0.105325	−0.0526626	−	0.998612i	$-0.516771\pi$
$283$	−1.77185	−0.105325	−0.0526626	+	0.998612i	$0.516771\pi$
$284$	−3.06045	−0.181605
$285$	21.9813	1.30206
$286$	19.7803	1.16963
$287$	0	0
$288$	−2.85269	−0.168096
$289$	−16.3252	−0.960306
$290$	−17.0046	−0.998546
$291$	5.99737	0.351572
$292$	−0.906061	−0.0530232
$293$	−25.3513	−1.48104	−0.740520	−	0.672034i	$-0.765421\pi$
$293$	−25.3513	−1.48104	−0.740520	+	0.672034i	$0.765421\pi$
$294$	0	0
$295$	−3.36773	−0.196077
$296$	−15.7451	−0.915164
$297$	−2.28178	−0.132403
$298$	−14.8985	−0.863047
$299$	19.0763	1.10321
$300$	3.27362	0.189003
$301$	0	0
$302$	35.7068	2.05469
$303$	−4.57698	−0.262941
$304$	31.1075	1.78414
$305$	−16.5093	−0.945321
$306$	−1.30305	−0.0744904
$307$	−14.8171	−0.845658	−0.422829	−	0.906209i	$-0.638963\pi$
$307$	−14.8171	−0.845658	−0.422829	+	0.906209i	$0.638963\pi$
$308$	0	0
$309$	17.0296	0.968779
$310$	3.19370	0.181390
$311$	13.0078	0.737603	0.368802	−	0.929508i	$-0.379768\pi$
$311$	13.0078	0.737603	0.368802	+	0.929508i	$0.379768\pi$
$312$	12.8626	0.728203
$313$	−18.9634	−1.07188	−0.535938	−	0.844257i	$-0.680042\pi$
$313$	−18.9634	−1.07188	−0.535938	+	0.844257i	$0.680042\pi$
$314$	−27.1736	−1.53350
$315$	0	0
$316$	−5.67728	−0.319372
$317$	25.9866	1.45955	0.729777	−	0.683685i	$-0.239624\pi$
$317$	25.9866	1.45955	0.729777	+	0.683685i	$0.239624\pi$
$318$	18.1121	1.01568
$319$	−7.26324	−0.406663
$320$	−16.8616	−0.942590
$321$	7.52734	0.420135
$322$	0	0
$323$	5.36171	0.298333
$324$	0.516213	0.0286785
$325$	−34.6564	−1.92239
$326$	−36.0033	−1.99404
$327$	2.40811	0.133169
$328$	−23.3815	−1.29103
$329$	0	0
$330$	12.1895	0.671009
$331$	21.1733	1.16379	0.581896	−	0.813263i	$-0.302311\pi$
$331$	21.1733	1.16379	0.581896	+	0.813263i	$0.302311\pi$
$332$	−1.93372	−0.106127
$333$	6.68959	0.366587
$334$	34.5595	1.89101
$335$	−26.1521	−1.42884
$336$	0	0
$337$	0.130351	0.00710065	0.00355033	−	0.999994i	$-0.498870\pi$
$337$	0.130351	0.00710065	0.00355033	+	0.999994i	$0.498870\pi$
$338$	26.7529	1.45517
$339$	−18.9656	−1.03007
$340$	1.42808	0.0774487
$341$	1.36413	0.0738720
$342$	−10.3536	−0.559857
$343$	0	0
$344$	−0.537511	−0.0289806
$345$	11.7556	0.632902
$346$	−16.2188	−0.871927
$347$	18.9141	1.01536	0.507682	−	0.861545i	$-0.330503\pi$
$347$	18.9141	1.01536	0.507682	+	0.861545i	$0.330503\pi$
$348$	1.64318	0.0880837
$349$	−29.4722	−1.57761	−0.788806	−	0.614642i	$-0.789301\pi$
$349$	−29.4722	−1.57761	−0.788806	+	0.614642i	$0.789301\pi$
$350$	0	0
$351$	−5.46493	−0.291696
$352$	6.50922	0.346942
$353$	18.6749	0.993965	0.496983	−	0.867761i	$-0.334441\pi$
$353$	18.6749	0.993965	0.496983	+	0.867761i	$0.334441\pi$
$354$	1.58626	0.0843086
$355$	19.9662	1.05969
$356$	−3.67313	−0.194675
$357$	0	0
$358$	−35.8500	−1.89473
$359$	21.7462	1.14772	0.573861	−	0.818953i	$-0.305445\pi$
$359$	21.7462	1.14772	0.573861	+	0.818953i	$0.305445\pi$
$360$	7.92652	0.417764
$361$	23.6022	1.24222
$362$	15.9484	0.838227
$363$	−5.79346	−0.304078
$364$	0	0
$365$	5.91107	0.309399
$366$	7.77617	0.406467
$367$	−7.93246	−0.414071	−0.207035	−	0.978333i	$-0.566382\pi$
$367$	−7.93246	−0.414071	−0.207035	+	0.978333i	$0.566382\pi$
$368$	16.6364	0.867230
$369$	9.93409	0.517148
$370$	−35.7364	−1.85785
$371$	0	0
$372$	−0.308611	−0.0160008
$373$	−20.4040	−1.05648	−0.528240	−	0.849095i	$-0.677148\pi$
$373$	−20.4040	−1.05648	−0.528240	+	0.849095i	$0.677148\pi$
$374$	2.97328	0.153744
$375$	−4.51819	−0.233318
$376$	−0.591609	−0.0305099
$377$	−17.3956	−0.895921
$378$	0	0
$379$	−21.9499	−1.12749	−0.563746	−	0.825948i	$-0.690640\pi$
$379$	−21.9499	−1.12749	−0.563746	+	0.825948i	$0.690640\pi$
$380$	11.3470	0.582091
$381$	−9.68829	−0.496346
$382$	14.9756	0.766217
$383$	−9.88417	−0.505057	−0.252529	−	0.967589i	$-0.581262\pi$
$383$	−9.88417	−0.505057	−0.252529	+	0.967589i	$0.581262\pi$
$384$	13.6475	0.696444
$385$	0	0
$386$	20.0684	1.02145
$387$	0.228372	0.0116088
$388$	3.09592	0.157172
$389$	23.6400	1.19860	0.599298	−	0.800526i	$-0.295446\pi$
$389$	23.6400	1.19860	0.599298	+	0.800526i	$0.295446\pi$
$390$	29.1941	1.47830
$391$	2.86745	0.145013
$392$	0	0
$393$	4.76789	0.240508
$394$	−32.7140	−1.64811
$395$	37.0381	1.86359
$396$	−1.17789	−0.0591910
$397$	−32.2898	−1.62058	−0.810288	−	0.586031i	$-0.800690\pi$
$397$	−32.2898	−1.62058	−0.810288	+	0.586031i	$0.800690\pi$
$398$	−0.393294	−0.0197141
$399$	0	0
$400$	−30.2238	−1.51119
$401$	8.70332	0.434623	0.217312	−	0.976102i	$-0.430271\pi$
$401$	8.70332	0.434623	0.217312	+	0.976102i	$0.430271\pi$
$402$	12.3181	0.614370
$403$	3.26714	0.162748
$404$	−2.36270	−0.117549
$405$	−3.36773	−0.167344
$406$	0	0
$407$	−15.2642	−0.756618
$408$	1.93345	0.0957199
$409$	22.2211	1.09876	0.549382	−	0.835571i	$-0.314863\pi$
$409$	22.2211	1.09876	0.549382	+	0.835571i	$0.314863\pi$
$410$	−53.0688	−2.62088
$411$	−6.97951	−0.344274
$412$	8.79089	0.433096
$413$	0	0
$414$	−5.53710	−0.272134
$415$	12.6154	0.619266
$416$	15.5897	0.764349
$417$	0.515718	0.0252548
$418$	23.6246	1.15552
$419$	5.70294	0.278607	0.139304	−	0.990250i	$-0.455514\pi$
$419$	5.70294	0.278607	0.139304	+	0.990250i	$0.455514\pi$
$420$	0	0
$421$	20.1419	0.981655	0.490828	−	0.871257i	$-0.336694\pi$
$421$	20.1419	0.981655	0.490828	+	0.871257i	$0.336694\pi$
$422$	1.94186	0.0945285
$423$	0.251356	0.0122213
$424$	−26.8746	−1.30514
$425$	−5.20939	−0.252692
$426$	−9.40439	−0.455644
$427$	0	0
$428$	3.88571	0.187823
$429$	12.4698	0.602047
$430$	−1.21998	−0.0588327
$431$	34.6661	1.66981	0.834904	−	0.550395i	$-0.185523\pi$
$431$	34.6661	1.66981	0.834904	+	0.550395i	$0.185523\pi$
$432$	−4.76595	−0.229302
$433$	−25.4119	−1.22122	−0.610609	−	0.791932i	$-0.709075\pi$
$433$	−25.4119	−1.22122	−0.610609	+	0.791932i	$0.709075\pi$
$434$	0	0
$435$	−10.7200	−0.513983
$436$	1.24310	0.0595335
$437$	22.7837	1.08989
$438$	−2.78421	−0.133035
$439$	−11.3234	−0.540438	−0.270219	−	0.962799i	$-0.587096\pi$
$439$	−11.3234	−0.540438	−0.270219	+	0.962799i	$0.587096\pi$
$440$	−18.0866	−0.862245
$441$	0	0
$442$	7.12107	0.338715
$443$	28.9527	1.37558	0.687792	−	0.725908i	$-0.258580\pi$
$443$	28.9527	1.37558	0.687792	+	0.725908i	$0.258580\pi$
$444$	3.45325	0.163884
$445$	23.9632	1.13596
$446$	18.5204	0.876968
$447$	−9.39223	−0.444237
$448$	0	0
$449$	0.602245	0.0284217	0.0142108	−	0.999899i	$-0.495476\pi$
$449$	0.602245	0.0284217	0.0142108	+	0.999899i	$0.495476\pi$
$450$	10.0594	0.474206
$451$	−22.6674	−1.06737
$452$	−9.79027	−0.460495
$453$	22.5101	1.05761
$454$	32.7483	1.53695
$455$	0	0
$456$	15.3625	0.719414
$457$	27.7934	1.30012	0.650061	−	0.759882i	$-0.274743\pi$
$457$	27.7934	1.30012	0.650061	+	0.759882i	$0.274743\pi$
$458$	−11.7804	−0.550464
$459$	−0.821461	−0.0383425
$460$	6.06841	0.282941
$461$	14.8854	0.693282	0.346641	−	0.937998i	$-0.387322\pi$
$461$	14.8854	0.693282	0.346641	+	0.937998i	$0.387322\pi$
$462$	0	0
$463$	−4.94909	−0.230004	−0.115002	−	0.993365i	$-0.536687\pi$
$463$	−4.94909	−0.230004	−0.115002	+	0.993365i	$0.536687\pi$
$464$	−15.1707	−0.704282
$465$	2.01335	0.0933671
$466$	−3.12491	−0.144759
$467$	3.68277	0.170418	0.0852090	−	0.996363i	$-0.472844\pi$
$467$	3.68277	0.170418	0.0852090	+	0.996363i	$0.472844\pi$
$468$	−2.82107	−0.130404
$469$	0	0
$470$	−1.34277	−0.0619372
$471$	−17.1306	−0.789338
$472$	−2.35367	−0.108336
$473$	−0.521095	−0.0239600
$474$	−17.4456	−0.801301
$475$	−41.3919	−1.89919
$476$	0	0
$477$	11.4182	0.522802
$478$	−39.7667	−1.81889
$479$	−7.86046	−0.359154	−0.179577	−	0.983744i	$-0.557473\pi$
$479$	−7.86046	−0.359154	−0.179577	+	0.983744i	$0.557473\pi$
$480$	9.60709	0.438501
$481$	−36.5581	−1.66691
$482$	27.5566	1.25517
$483$	0	0
$484$	−2.99066	−0.135939
$485$	−20.1975	−0.917123
$486$	1.58626	0.0719541
$487$	−11.6310	−0.527050	−0.263525	−	0.964653i	$-0.584885\pi$
$487$	−11.6310	−0.527050	−0.263525	+	0.964653i	$0.584885\pi$
$488$	−11.5382	−0.522309
$489$	−22.6970	−1.02640
$490$	0	0
$491$	23.3795	1.05510	0.527551	−	0.849523i	$-0.323110\pi$
$491$	23.3795	1.05510	0.527551	+	0.849523i	$0.323110\pi$
$492$	5.12810	0.231193
$493$	−2.61483	−0.117766
$494$	56.5814	2.54572
$495$	7.68443	0.345390
$496$	2.84926	0.127936
$497$	0	0
$498$	−5.94207	−0.266270
$499$	13.5131	0.604929	0.302464	−	0.953161i	$-0.402191\pi$
$499$	13.5131	0.604929	0.302464	+	0.953161i	$0.402191\pi$
$500$	−2.33235	−0.104306
$501$	21.7868	0.973362
$502$	−15.1127	−0.674515
$503$	12.6659	0.564743	0.282371	−	0.959305i	$-0.408879\pi$
$503$	12.6659	0.564743	0.282371	+	0.959305i	$0.408879\pi$
$504$	0	0
$505$	15.4140	0.685916
$506$	12.6345	0.561671
$507$	16.8654	0.749019
$508$	−5.00122	−0.221893
$509$	28.0248	1.24218	0.621089	−	0.783740i	$-0.286690\pi$
$509$	28.0248	1.24218	0.621089	+	0.783740i	$0.286690\pi$
$510$	4.38832	0.194318
$511$	0	0
$512$	−8.83916	−0.390639
$513$	−6.52704	−0.288176
$514$	33.4782	1.47666
$515$	−57.3510	−2.52719
$516$	0.117888	0.00518975
$517$	−0.573540	−0.0252243
$518$	0	0
$519$	−10.2246	−0.448808
$520$	−43.3179	−1.89961
$521$	8.78465	0.384862	0.192431	−	0.981310i	$-0.438363\pi$
$521$	8.78465	0.384862	0.192431	+	0.981310i	$0.438363\pi$
$522$	5.04928	0.221001
$523$	0.599973	0.0262350	0.0131175	−	0.999914i	$-0.495824\pi$
$523$	0.599973	0.0262350	0.0131175	+	0.999914i	$0.495824\pi$
$524$	2.46125	0.107520
$525$	0	0
$526$	35.4053	1.54375
$527$	0.491100	0.0213927
$528$	10.8749	0.473268
$529$	−10.8152	−0.470227
$530$	−60.9968	−2.64953
$531$	1.00000	0.0433963
$532$	0	0
$533$	−54.2890	−2.35152
$534$	−11.2871	−0.488439
$535$	−25.3500	−1.09598
$536$	−18.2774	−0.789464
$537$	−22.6004	−0.975279
$538$	41.7216	1.79874
$539$	0	0
$540$	−1.73847	−0.0748117
$541$	44.0617	1.89436	0.947180	−	0.320703i	$-0.103919\pi$
$541$	44.0617	1.89436	0.947180	+	0.320703i	$0.103919\pi$
$542$	4.94581	0.212441
$543$	10.0541	0.431462
$544$	2.34337	0.100471
$545$	−8.10985	−0.347388
$546$	0	0
$547$	16.1270	0.689542	0.344771	−	0.938687i	$-0.387957\pi$
$547$	16.1270	0.689542	0.344771	+	0.938687i	$0.387957\pi$
$548$	−3.60291	−0.153909
$549$	4.90221	0.209221
$550$	−22.9534	−0.978738
$551$	−20.7765	−0.885108
$552$	8.21588	0.349691
$553$	0	0
$554$	−41.5296	−1.76442
$555$	−22.5287	−0.956291
$556$	0.266220	0.0112903
$557$	20.7482	0.879130	0.439565	−	0.898211i	$-0.355133\pi$
$557$	20.7482	0.879130	0.439565	+	0.898211i	$0.355133\pi$
$558$	−0.948324	−0.0401457
$559$	−1.24803	−0.0527862
$560$	0	0
$561$	1.87440	0.0791371
$562$	−3.55871	−0.150115
$563$	36.8833	1.55444	0.777222	−	0.629226i	$-0.216628\pi$
$563$	36.8833	1.55444	0.777222	+	0.629226i	$0.216628\pi$
$564$	0.129753	0.00546360
$565$	63.8709	2.68707
$566$	−2.81060	−0.118138
$567$	0	0
$568$	13.9541	0.585502
$569$	−3.30886	−0.138715	−0.0693574	−	0.997592i	$-0.522095\pi$
$569$	−3.30886	−0.138715	−0.0693574	+	0.997592i	$0.522095\pi$
$570$	34.8680	1.46046
$571$	−38.5494	−1.61324	−0.806622	−	0.591068i	$-0.798706\pi$
$571$	−38.5494	−1.61324	−0.806622	+	0.591068i	$0.798706\pi$
$572$	6.43706	0.269147
$573$	9.44083	0.394396
$574$	0	0
$575$	−22.1365	−0.923155
$576$	5.00680	0.208617
$577$	8.31098	0.345991	0.172995	−	0.984923i	$-0.444655\pi$
$577$	8.31098	0.345991	0.172995	+	0.984923i	$0.444655\pi$
$578$	−25.8960	−1.07713
$579$	12.6514	0.525774
$580$	−5.53379	−0.229778
$581$	0	0
$582$	9.51338	0.394342
$583$	−26.0538	−1.07904
$584$	4.13118	0.170949
$585$	18.4044	0.760928
$586$	−40.2137	−1.66121
$587$	4.78654	0.197562	0.0987809	−	0.995109i	$-0.468506\pi$
$587$	4.78654	0.197562	0.0987809	+	0.995109i	$0.468506\pi$
$588$	0	0
$589$	3.90210	0.160783
$590$	−5.34209	−0.219930
$591$	−20.6234	−0.848333
$592$	−31.8822	−1.31035
$593$	39.5039	1.62223	0.811115	−	0.584887i	$-0.198861\pi$
$593$	39.5039	1.62223	0.811115	+	0.584887i	$0.198861\pi$
$594$	−3.61950	−0.148510
$595$	0	0
$596$	−4.84839	−0.198598
$597$	−0.247939	−0.0101474
$598$	30.2599	1.23742
$599$	23.3088	0.952373	0.476187	−	0.879344i	$-0.342019\pi$
$599$	23.3088	0.952373	0.476187	+	0.879344i	$0.342019\pi$
$600$	−14.9261	−0.609353
$601$	−6.23513	−0.254336	−0.127168	−	0.991881i	$-0.540589\pi$
$601$	−6.23513	−0.254336	−0.127168	+	0.991881i	$0.540589\pi$
$602$	0	0
$603$	7.76550	0.316236
$604$	11.6200	0.472811
$605$	19.5108	0.793228
$606$	−7.26027	−0.294928
$607$	−19.2608	−0.781773	−0.390886	−	0.920439i	$-0.627831\pi$
$607$	−19.2608	−0.781773	−0.390886	+	0.920439i	$0.627831\pi$
$608$	18.6196	0.755125
$609$	0	0
$610$	−26.1880	−1.06032
$611$	−1.37364	−0.0555716
$612$	−0.424049	−0.0171412
$613$	32.2240	1.30152	0.650758	−	0.759286i	$-0.274451\pi$
$613$	32.2240	1.30152	0.650758	+	0.759286i	$0.274451\pi$
$614$	−23.5038	−0.948535
$615$	−33.4553	−1.34905
$616$	0	0
$617$	−48.1670	−1.93913	−0.969566	−	0.244830i	$-0.921268\pi$
$617$	−48.1670	−1.93913	−0.969566	+	0.244830i	$0.921268\pi$
$618$	27.0133	1.08663
$619$	−20.2989	−0.815883	−0.407942	−	0.913008i	$-0.633753\pi$
$619$	−20.2989	−0.815883	−0.407942	+	0.913008i	$0.633753\pi$
$620$	1.03932	0.0417401
$621$	−3.49067	−0.140076
$622$	20.6337	0.827335
$623$	0	0
$624$	26.0456	1.04266
$625$	−16.4920	−0.659681
$626$	−30.0809	−1.20227
$627$	14.8933	0.594781
$628$	−8.84306	−0.352876
$629$	−5.49524	−0.219109
$630$	0	0
$631$	8.63085	0.343589	0.171794	−	0.985133i	$-0.445044\pi$
$631$	8.63085	0.343589	0.171794	+	0.985133i	$0.445044\pi$
$632$	25.8855	1.02967
$633$	1.22418	0.0486568
$634$	41.2215	1.63711
$635$	32.6276	1.29479
$636$	5.89420	0.233720
$637$	0	0
$638$	−11.5214	−0.456135
$639$	−5.92867	−0.234534
$640$	−45.9610	−1.81677
$641$	44.8985	1.77339	0.886693	−	0.462360i	$-0.152997\pi$
$641$	44.8985	1.77339	0.886693	+	0.462360i	$0.152997\pi$
$642$	11.9403	0.471246
$643$	41.5688	1.63932	0.819658	−	0.572854i	$-0.194164\pi$
$643$	41.5688	1.63932	0.819658	+	0.572854i	$0.194164\pi$
$644$	0	0
$645$	−0.769094	−0.0302830
$646$	8.50505	0.334627
$647$	34.1129	1.34112	0.670559	−	0.741857i	$-0.266055\pi$
$647$	34.1129	1.34112	0.670559	+	0.741857i	$0.266055\pi$
$648$	−2.35367	−0.0924608
$649$	−2.28178	−0.0895679
$650$	−54.9740	−2.15626
$651$	0	0
$652$	−11.7165	−0.458854
$653$	25.7716	1.00852	0.504260	−	0.863552i	$-0.331765\pi$
$653$	25.7716	1.00852	0.504260	+	0.863552i	$0.331765\pi$
$654$	3.81987	0.149369
$655$	−16.0570	−0.627398
$656$	−47.3454	−1.84853
$657$	−1.75521	−0.0684771
$658$	0	0
$659$	−19.6037	−0.763650	−0.381825	−	0.924235i	$-0.624704\pi$
$659$	−19.6037	−0.763650	−0.381825	+	0.924235i	$0.624704\pi$
$660$	3.96681	0.154408
$661$	16.3879	0.637415	0.318708	−	0.947853i	$-0.396751\pi$
$661$	16.3879	0.637415	0.318708	+	0.947853i	$0.396751\pi$
$662$	33.5864	1.30537
$663$	4.48923	0.174347
$664$	8.81676	0.342157
$665$	0	0
$666$	10.6114	0.411184
$667$	−11.1113	−0.430231
$668$	11.2466	0.435145
$669$	11.6756	0.451403
$670$	−41.4840	−1.60267
$671$	−11.1858	−0.431822
$672$	0	0
$673$	−16.0570	−0.618951	−0.309475	−	0.950907i	$-0.600153\pi$
$673$	−16.0570	−0.618951	−0.309475	+	0.950907i	$0.600153\pi$
$674$	0.206770	0.00796447
$675$	6.34161	0.244089
$676$	8.70615	0.334852
$677$	35.2693	1.35551	0.677754	−	0.735289i	$-0.262953\pi$
$677$	35.2693	1.35551	0.677754	+	0.735289i	$0.262953\pi$
$678$	−30.0843	−1.15538
$679$	0	0
$680$	−6.51133	−0.249698
$681$	20.6450	0.791118
$682$	2.16387	0.0828588
$683$	1.20048	0.0459352	0.0229676	−	0.999736i	$-0.492689\pi$
$683$	1.20048	0.0459352	0.0229676	+	0.999736i	$0.492689\pi$
$684$	−3.36934	−0.128830
$685$	23.5051	0.898084
$686$	0	0
$687$	−7.42657	−0.283341
$688$	−1.08841	−0.0414951
$689$	−62.3994	−2.37723
$690$	18.6475	0.709897
$691$	−16.7569	−0.637462	−0.318731	−	0.947845i	$-0.603257\pi$
$691$	−16.7569	−0.637462	−0.318731	+	0.947845i	$0.603257\pi$
$692$	−5.27805	−0.200641
$693$	0	0
$694$	30.0027	1.13889
$695$	−1.73680	−0.0658805
$696$	−7.49206	−0.283986
$697$	−8.16047	−0.309100
$698$	−46.7506	−1.76953
$699$	−1.96999	−0.0745119
$700$	0	0
$701$	1.31899	0.0498176	0.0249088	−	0.999690i	$-0.492070\pi$
$701$	1.31899	0.0498176	0.0249088	+	0.999690i	$0.492070\pi$
$702$	−8.66878	−0.327182
$703$	−43.6632	−1.64679
$704$	−11.4244	−0.430575
$705$	−0.846499	−0.0318810
$706$	29.6232	1.11488
$707$	0	0
$708$	0.516213	0.0194005
$709$	−30.2122	−1.13464	−0.567322	−	0.823496i	$-0.692021\pi$
$709$	−30.2122	−1.13464	−0.567322	+	0.823496i	$0.692021\pi$
$710$	31.6715	1.18861
$711$	−10.9979	−0.412455
$712$	16.7476	0.627642
$713$	2.08685	0.0781532
$714$	0	0
$715$	−41.9949	−1.57052
$716$	−11.6666	−0.436002
$717$	−25.0695	−0.936238
$718$	34.4951	1.28735
$719$	−20.3895	−0.760399	−0.380200	−	0.924904i	$-0.624145\pi$
$719$	−20.3895	−0.760399	−0.380200	+	0.924904i	$0.624145\pi$
$720$	16.0504	0.598165
$721$	0	0
$722$	37.4392	1.39334
$723$	17.3721	0.646074
$724$	5.19005	0.192887
$725$	20.1863	0.749699
$726$	−9.18992	−0.341070
$727$	34.9671	1.29686	0.648428	−	0.761276i	$-0.275427\pi$
$727$	34.9671	1.29686	0.648428	+	0.761276i	$0.275427\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	9.37647	0.347039
$731$	−0.187598	−0.00693858
$732$	2.53058	0.0935331
$733$	−26.5274	−0.979812	−0.489906	−	0.871775i	$-0.662969\pi$
$733$	−26.5274	−0.979812	−0.489906	+	0.871775i	$0.662969\pi$
$734$	−12.5829	−0.464444
$735$	0	0
$736$	9.95779	0.367049
$737$	−17.7192	−0.652695
$738$	15.7580	0.580061
$739$	17.9180	0.659124	0.329562	−	0.944134i	$-0.393099\pi$
$739$	17.9180	0.659124	0.329562	+	0.944134i	$0.393099\pi$
$740$	−11.6296	−0.427514
$741$	35.6698	1.31036
$742$	0	0
$743$	44.5607	1.63477	0.817387	−	0.576089i	$-0.195422\pi$
$743$	44.5607	1.63477	0.817387	+	0.576089i	$0.195422\pi$
$744$	1.40711	0.0515872
$745$	31.6305	1.15885
$746$	−32.3660	−1.18500
$747$	−3.74597	−0.137058
$748$	0.967588	0.0353785
$749$	0	0
$750$	−7.16701	−0.261702
$751$	13.0076	0.474655	0.237328	−	0.971430i	$-0.423729\pi$
$751$	13.0076	0.474655	0.237328	+	0.971430i	$0.423729\pi$
$752$	−1.19795	−0.0436847
$753$	−9.52729	−0.347194
$754$	−27.5940	−1.00491
$755$	−75.8078	−2.75893
$756$	0	0
$757$	7.65973	0.278398	0.139199	−	0.990264i	$-0.455547\pi$
$757$	7.65973	0.278398	0.139199	+	0.990264i	$0.455547\pi$
$758$	−34.8182	−1.26466
$759$	7.96496	0.289110
$760$	−51.7367	−1.87669
$761$	32.3641	1.17320	0.586600	−	0.809877i	$-0.300466\pi$
$761$	32.3641	1.17320	0.586600	+	0.809877i	$0.300466\pi$
$762$	−15.3681	−0.556729
$763$	0	0
$764$	4.87348	0.176316
$765$	2.76646	0.100022
$766$	−15.6788	−0.566499
$767$	−5.46493	−0.197327
$768$	11.6348	0.419834
$769$	32.6770	1.17836	0.589182	−	0.808001i	$-0.299450\pi$
$769$	32.6770	1.17836	0.589182	+	0.808001i	$0.299450\pi$
$770$	0	0
$771$	21.1052	0.760084
$772$	6.53081	0.235049
$773$	−54.9721	−1.97721	−0.988604	−	0.150539i	$-0.951899\pi$
$773$	−54.9721	−1.97721	−0.988604	+	0.150539i	$0.951899\pi$
$774$	0.362256	0.0130210
$775$	−3.79125	−0.136186
$776$	−14.1158	−0.506729
$777$	0	0
$778$	37.4991	1.34441
$779$	−64.8402	−2.32314
$780$	9.50059	0.340176
$781$	13.5279	0.484068
$782$	4.54852	0.162655
$783$	3.18314	0.113756
$784$	0	0
$785$	57.6914	2.05909
$786$	7.56311	0.269767
$787$	11.9074	0.424453	0.212227	−	0.977220i	$-0.431928\pi$
$787$	11.9074	0.424453	0.212227	+	0.977220i	$0.431928\pi$
$788$	−10.6461	−0.379250
$789$	22.3200	0.794614
$790$	58.7519	2.09030
$791$	0	0
$792$	5.37056	0.190835
$793$	−26.7902	−0.951348
$794$	−51.2199	−1.81773
$795$	−38.4533	−1.36380
$796$	−0.127989	−0.00453645
$797$	1.81830	0.0644074	0.0322037	−	0.999481i	$-0.489747\pi$
$797$	1.81830	0.0644074	0.0322037	+	0.999481i	$0.489747\pi$
$798$	0	0
$799$	−0.206479	−0.00730471
$800$	−18.0906	−0.639601
$801$	−7.11552	−0.251415
$802$	13.8057	0.487497
$803$	4.00500	0.141333
$804$	4.00865	0.141374
$805$	0	0
$806$	5.18252	0.182546
$807$	26.3019	0.925870
$808$	10.7727	0.378982
$809$	−13.2669	−0.466440	−0.233220	−	0.972424i	$-0.574926\pi$
$809$	−13.2669	−0.466440	−0.233220	+	0.972424i	$0.574926\pi$
$810$	−5.34209	−0.187702
$811$	−18.1776	−0.638301	−0.319151	−	0.947704i	$-0.603398\pi$
$811$	−18.1776	−0.638301	−0.319151	+	0.947704i	$0.603398\pi$
$812$	0	0
$813$	3.11791	0.109350
$814$	−24.2129	−0.848663
$815$	76.4375	2.67749
$816$	3.91504	0.137054
$817$	−1.49059	−0.0521491
$818$	35.2484	1.23243
$819$	0	0
$820$	−17.2701	−0.603097
$821$	−2.67820	−0.0934700	−0.0467350	−	0.998907i	$-0.514882\pi$
$821$	−2.67820	−0.0934700	−0.0467350	+	0.998907i	$0.514882\pi$
$822$	−11.0713	−0.386156
$823$	−21.2654	−0.741264	−0.370632	−	0.928780i	$-0.620859\pi$
$823$	−21.2654	−0.741264	−0.370632	+	0.928780i	$0.620859\pi$
$824$	−40.0820	−1.39632
$825$	−14.4702	−0.503787
$826$	0	0
$827$	−7.02240	−0.244193	−0.122096	−	0.992518i	$-0.538962\pi$
$827$	−7.02240	−0.244193	−0.122096	+	0.992518i	$0.538962\pi$
$828$	−1.80193	−0.0626214
$829$	44.3719	1.54110	0.770550	−	0.637379i	$-0.219982\pi$
$829$	44.3719	1.54110	0.770550	+	0.637379i	$0.219982\pi$
$830$	20.0113	0.694602
$831$	−26.1809	−0.908204
$832$	−27.3618	−0.948600
$833$	0	0
$834$	0.818061	0.0283271
$835$	−73.3721	−2.53914
$836$	7.68811	0.265899
$837$	−0.597837	−0.0206643
$838$	9.04634	0.312501
$839$	−7.06272	−0.243832	−0.121916	−	0.992540i	$-0.538904\pi$
$839$	−7.06272	−0.243832	−0.121916	+	0.992540i	$0.538904\pi$
$840$	0	0
$841$	−18.8676	−0.650607
$842$	31.9502	1.10108
$843$	−2.24346	−0.0772689
$844$	0.631937	0.0217522
$845$	−56.7982	−1.95392
$846$	0.398715	0.0137081
$847$	0	0
$848$	−54.4184	−1.86874
$849$	−1.77185	−0.0608096
$850$	−8.26343	−0.283433
$851$	−23.3511	−0.800467
$852$	−3.06045	−0.104849
$853$	−34.0279	−1.16509	−0.582546	−	0.812798i	$-0.697943\pi$
$853$	−34.0279	−1.16509	−0.582546	+	0.812798i	$0.697943\pi$
$854$	0	0
$855$	21.9813	0.751745
$856$	−17.7168	−0.605549
$857$	−14.5400	−0.496676	−0.248338	−	0.968673i	$-0.579884\pi$
$857$	−14.5400	−0.496676	−0.248338	+	0.968673i	$0.579884\pi$
$858$	19.7803	0.675288
$859$	−9.20460	−0.314057	−0.157028	−	0.987594i	$-0.550191\pi$
$859$	−9.20460	−0.314057	−0.157028	+	0.987594i	$0.550191\pi$
$860$	−0.397016	−0.0135381
$861$	0	0
$862$	54.9894	1.87295
$863$	−23.2959	−0.793002	−0.396501	−	0.918034i	$-0.629776\pi$
$863$	−23.2959	−0.793002	−0.396501	+	0.918034i	$0.629776\pi$
$864$	−2.85269	−0.0970504
$865$	34.4336	1.17078
$866$	−40.3098	−1.36978
$867$	−16.3252	−0.554433
$868$	0	0
$869$	25.0949	0.851286
$870$	−17.0046	−0.576511
$871$	−42.4379	−1.43795
$872$	−5.66788	−0.191939
$873$	5.99737	0.202980
$874$	36.1409	1.22248
$875$	0	0
$876$	−0.906061	−0.0306130
$877$	−1.38736	−0.0468480	−0.0234240	−	0.999726i	$-0.507457\pi$
$877$	−1.38736	−0.0468480	−0.0234240	+	0.999726i	$0.507457\pi$
$878$	−17.9619	−0.606185
$879$	−25.3513	−0.855079
$880$	−36.6236	−1.23458
$881$	−45.3486	−1.52783	−0.763917	−	0.645314i	$-0.776727\pi$
$881$	−45.3486	−1.52783	−0.763917	+	0.645314i	$0.776727\pi$
$882$	0	0
$883$	26.8464	0.903454	0.451727	−	0.892156i	$-0.350808\pi$
$883$	26.8464	0.903454	0.451727	+	0.892156i	$0.350808\pi$
$884$	2.31740	0.0779425
$885$	−3.36773	−0.113205
$886$	45.9264	1.54293
$887$	37.3592	1.25440	0.627200	−	0.778858i	$-0.284201\pi$
$887$	37.3592	1.25440	0.627200	+	0.778858i	$0.284201\pi$
$888$	−15.7451	−0.528370
$889$	0	0
$890$	38.0118	1.27416
$891$	−2.28178	−0.0764426
$892$	6.02707	0.201801
$893$	−1.64061	−0.0549009
$894$	−14.8985	−0.498280
$895$	76.1120	2.54414
$896$	0	0
$897$	19.0763	0.636938
$898$	0.955315	0.0318793
$899$	−1.90300	−0.0634686
$900$	3.27362	0.109121
$901$	−9.37958	−0.312479
$902$	−35.9564	−1.19722
$903$	0	0
$904$	44.6386	1.48466
$905$	−33.8594	−1.12553
$906$	35.7068	1.18628
$907$	−38.2404	−1.26975	−0.634875	−	0.772615i	$-0.718949\pi$
$907$	−38.2404	−1.26975	−0.634875	+	0.772615i	$0.718949\pi$
$908$	10.6572	0.353672
$909$	−4.57698	−0.151809
$910$	0	0
$911$	32.4438	1.07491	0.537455	−	0.843292i	$-0.319386\pi$
$911$	32.4438	1.07491	0.537455	+	0.843292i	$0.319386\pi$
$912$	31.1075	1.03007
$913$	8.54749	0.282881
$914$	44.0875	1.45829
$915$	−16.5093	−0.545781
$916$	−3.83369	−0.126669
$917$	0	0
$918$	−1.30305	−0.0430070
$919$	38.3584	1.26533	0.632664	−	0.774427i	$-0.281962\pi$
$919$	38.3584	1.26533	0.632664	+	0.774427i	$0.281962\pi$
$920$	−27.6689	−0.912216
$921$	−14.8171	−0.488241
$922$	23.6121	0.777622
$923$	32.3997	1.06645
$924$	0	0
$925$	42.4228	1.39485
$926$	−7.85053	−0.257984
$927$	17.0296	0.559325
$928$	−9.08051	−0.298082
$929$	−34.1113	−1.11916	−0.559578	−	0.828778i	$-0.689037\pi$
$929$	−34.1113	−1.11916	−0.559578	+	0.828778i	$0.689037\pi$
$930$	3.19370	0.104726
$931$	0	0
$932$	−1.01694	−0.0333108
$933$	13.0078	0.425855
$934$	5.84182	0.191150
$935$	−6.31247	−0.206440
$936$	12.8626	0.420428
$937$	−5.67738	−0.185472	−0.0927359	−	0.995691i	$-0.529561\pi$
$937$	−5.67738	−0.185472	−0.0927359	+	0.995691i	$0.529561\pi$
$938$	0	0
$939$	−18.9634	−0.618848
$940$	−0.436974	−0.0142525
$941$	39.1504	1.27627	0.638133	−	0.769926i	$-0.279707\pi$
$941$	39.1504	1.27627	0.638133	+	0.769926i	$0.279707\pi$
$942$	−27.1736	−0.885364
$943$	−34.6766	−1.12923
$944$	−4.76595	−0.155118
$945$	0	0
$946$	−0.826590	−0.0268748
$947$	−49.6104	−1.61212	−0.806060	−	0.591833i	$-0.798404\pi$
$947$	−49.6104	−1.61212	−0.806060	+	0.591833i	$0.798404\pi$
$948$	−5.67728	−0.184389
$949$	9.59208	0.311372
$950$	−65.6583	−2.13024
$951$	25.9866	0.842674
$952$	0	0
$953$	−32.9552	−1.06752	−0.533762	−	0.845635i	$-0.679222\pi$
$953$	−32.9552	−1.06752	−0.533762	+	0.845635i	$0.679222\pi$
$954$	18.1121	0.586402
$955$	−31.7942	−1.02883
$956$	−12.9412	−0.418549
$957$	−7.26324	−0.234787
$958$	−12.4687	−0.402846
$959$	0	0
$960$	−16.8616	−0.544205
$961$	−30.6426	−0.988471
$962$	−57.9906	−1.86969
$963$	7.52734	0.242565
$964$	8.96768	0.288830
$965$	−42.6065	−1.37155
$966$	0	0
$967$	−2.16390	−0.0695865	−0.0347932	−	0.999395i	$-0.511077\pi$
$967$	−2.16390	−0.0695865	−0.0347932	+	0.999395i	$0.511077\pi$
$968$	13.6359	0.438274
$969$	5.36171	0.172243
$970$	−32.0385	−1.02869
$971$	−5.84189	−0.187475	−0.0937377	−	0.995597i	$-0.529881\pi$
$971$	−5.84189	−0.187475	−0.0937377	+	0.995597i	$0.529881\pi$
$972$	0.516213	0.0165575
$973$	0	0
$974$	−18.4497	−0.591167
$975$	−34.6564	−1.10989
$976$	−23.3637	−0.747853
$977$	17.5599	0.561792	0.280896	−	0.959738i	$-0.409368\pi$
$977$	17.5599	0.561792	0.280896	+	0.959738i	$0.409368\pi$
$978$	−36.0033	−1.15126
$979$	16.2361	0.518908
$980$	0	0
$981$	2.40811	0.0768849
$982$	37.0859	1.18346
$983$	−6.33329	−0.202001	−0.101000	−	0.994886i	$-0.532204\pi$
$983$	−6.33329	−0.202001	−0.101000	+	0.994886i	$0.532204\pi$
$984$	−23.3815	−0.745376
$985$	69.4541	2.21299
$986$	−4.14779	−0.132093
$987$	0	0
$988$	18.4132	0.585802
$989$	−0.797170	−0.0253485
$990$	12.1895	0.387407
$991$	48.7435	1.54839	0.774194	−	0.632949i	$-0.218156\pi$
$991$	48.7435	1.54839	0.774194	+	0.632949i	$0.218156\pi$
$992$	1.70544	0.0541479
$993$	21.1733	0.671915
$994$	0	0
$995$	0.834990	0.0264710
$996$	−1.93372	−0.0612722
$997$	−41.1104	−1.30198	−0.650989	−	0.759087i	$-0.725646\pi$
$997$	−41.1104	−1.30198	−0.650989	+	0.759087i	$0.725646\pi$
$998$	21.4352	0.678520
$999$	6.68959	0.211649

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8673.2.a.ba.1.9		12
7.6	odd	2		1239.2.a.i.1.9	✓	12
21.20	even	2		3717.2.a.q.1.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1239.2.a.i.1.9	✓	12	7.6	odd	2
3717.2.a.q.1.4		12	21.20	even	2
8673.2.a.ba.1.9		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)

\(f(q)\)	\(=\)	\(q+1.58626 q^{2} +1.00000 q^{3} +0.516213 q^{4} -3.36773 q^{5} +1.58626 q^{6} -2.35367 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.58626 q^{2} +1.00000 q^{3} +0.516213 q^{4} -3.36773 q^{5} +1.58626 q^{6} -2.35367 q^{8} +1.00000 q^{9} -5.34209 q^{10} -2.28178 q^{11} +0.516213 q^{12} -5.46493 q^{13} -3.36773 q^{15} -4.76595 q^{16} -0.821461 q^{17} +1.58626 q^{18} -6.52704 q^{19} -1.73847 q^{20} -3.61950 q^{22} -3.49067 q^{23} -2.35367 q^{24} +6.34161 q^{25} -8.66878 q^{26} +1.00000 q^{27} +3.18314 q^{29} -5.34209 q^{30} -0.597837 q^{31} -2.85269 q^{32} -2.28178 q^{33} -1.30305 q^{34} +0.516213 q^{36} +6.68959 q^{37} -10.3536 q^{38} -5.46493 q^{39} +7.92652 q^{40} +9.93409 q^{41} +0.228372 q^{43} -1.17789 q^{44} -3.36773 q^{45} -5.53710 q^{46} +0.251356 q^{47} -4.76595 q^{48} +10.0594 q^{50} -0.821461 q^{51} -2.82107 q^{52} +11.4182 q^{53} +1.58626 q^{54} +7.68443 q^{55} -6.52704 q^{57} +5.04928 q^{58} +1.00000 q^{59} -1.73847 q^{60} +4.90221 q^{61} -0.948324 q^{62} +5.00680 q^{64} +18.4044 q^{65} -3.61950 q^{66} +7.76550 q^{67} -0.424049 q^{68} -3.49067 q^{69} -5.92867 q^{71} -2.35367 q^{72} -1.75521 q^{73} +10.6114 q^{74} +6.34161 q^{75} -3.36934 q^{76} -8.66878 q^{78} -10.9979 q^{79} +16.0504 q^{80} +1.00000 q^{81} +15.7580 q^{82} -3.74597 q^{83} +2.76646 q^{85} +0.362256 q^{86} +3.18314 q^{87} +5.37056 q^{88} -7.11552 q^{89} -5.34209 q^{90} -1.80193 q^{92} -0.597837 q^{93} +0.398715 q^{94} +21.9813 q^{95} -2.85269 q^{96} +5.99737 q^{97} -2.28178 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 12 q^{3} + 19 q^{4} + 4 q^{5} + 3 q^{6} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more