LMFDB - Embedded newform 6027.2.a.bi.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, 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("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$1$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 4 x^{12} - 11 x^{11} + 56 x^{10} + 26 x^{9} - 263 x^{8} + 50 x^{7} + 478 x^{6} - 174 x^{5} + \cdots - 4 $ x^13 - 4x^12 - 11x^11 + 56x^10 + 26x^9 - 263x^8 + 50x^7 + 478x^6 - 174x^5 - 311x^4 + 84x^3 + 69x^2 - 12x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.73393$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.73393 q^{2} +1.00000 q^{3} +5.47440 q^{4} +2.29019 q^{5} -2.73393 q^{6} -9.49877 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.73393 q^{2} +1.00000 q^{3} +5.47440 q^{4} +2.29019 q^{5} -2.73393 q^{6} -9.49877 q^{8} +1.00000 q^{9} -6.26122 q^{10} -0.920136 q^{11} +5.47440 q^{12} -6.70791 q^{13} +2.29019 q^{15} +15.0202 q^{16} +3.80909 q^{17} -2.73393 q^{18} +6.56558 q^{19} +12.5374 q^{20} +2.51559 q^{22} -6.79688 q^{23} -9.49877 q^{24} +0.244953 q^{25} +18.3390 q^{26} +1.00000 q^{27} -4.96509 q^{29} -6.26122 q^{30} +1.14250 q^{31} -22.0668 q^{32} -0.920136 q^{33} -10.4138 q^{34} +5.47440 q^{36} -10.4608 q^{37} -17.9499 q^{38} -6.70791 q^{39} -21.7540 q^{40} +1.00000 q^{41} +3.89955 q^{43} -5.03719 q^{44} +2.29019 q^{45} +18.5822 q^{46} -11.0064 q^{47} +15.0202 q^{48} -0.669685 q^{50} +3.80909 q^{51} -36.7217 q^{52} +7.81643 q^{53} -2.73393 q^{54} -2.10728 q^{55} +6.56558 q^{57} +13.5742 q^{58} +0.168195 q^{59} +12.5374 q^{60} +14.4855 q^{61} -3.12352 q^{62} +30.2886 q^{64} -15.3624 q^{65} +2.51559 q^{66} +1.48503 q^{67} +20.8525 q^{68} -6.79688 q^{69} -6.79705 q^{71} -9.49877 q^{72} +4.20182 q^{73} +28.5991 q^{74} +0.244953 q^{75} +35.9426 q^{76} +18.3390 q^{78} +4.67401 q^{79} +34.3991 q^{80} +1.00000 q^{81} -2.73393 q^{82} -6.73979 q^{83} +8.72353 q^{85} -10.6611 q^{86} -4.96509 q^{87} +8.74016 q^{88} -8.78706 q^{89} -6.26122 q^{90} -37.2088 q^{92} +1.14250 q^{93} +30.0907 q^{94} +15.0364 q^{95} -22.0668 q^{96} +1.94754 q^{97} -0.920136 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 4 q^{2} + 13 q^{3} + 12 q^{4} - 8 q^{5} - 4 q^{6} - 12 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q - 4 * q^2 + 13 * q^3 + 12 * q^4 - 8 * q^5 - 4 * q^6 - 12 * q^8 + 13 * q^9	$ 13 q - 4 q^{2} + 13 q^{3} + 12 q^{4} - 8 q^{5} - 4 q^{6} - 12 q^{8} + 13 q^{9} - q^{10} - 10 q^{11} + 12 q^{12} - 16 q^{13} - 8 q^{15} + 26 q^{16} - 12 q^{17} - 4 q^{18} - 11 q^{19} - 6 q^{20} + q^{22} - 15 q^{23} - 12 q^{24} + 15 q^{25} - 18 q^{26} + 13 q^{27} - 8 q^{29} - q^{30} - 9 q^{31} - 23 q^{32} - 10 q^{33} + 7 q^{34} + 12 q^{36} - 2 q^{37} - 20 q^{38} - 16 q^{39} - 49 q^{40} + 13 q^{41} - 7 q^{43} - 22 q^{44} - 8 q^{45} - 4 q^{46} - 26 q^{47} + 26 q^{48} - 15 q^{50} - 12 q^{51} - 24 q^{52} + 4 q^{53} - 4 q^{54} - q^{55} - 11 q^{57} + 39 q^{58} + 3 q^{59} - 6 q^{60} - 28 q^{61} - 7 q^{62} + 2 q^{64} - 20 q^{65} + q^{66} + 7 q^{67} - 55 q^{68} - 15 q^{69} - 40 q^{71} - 12 q^{72} + 2 q^{73} + q^{74} + 15 q^{75} + 26 q^{76} - 18 q^{78} + 13 q^{79} - 22 q^{80} + 13 q^{81} - 4 q^{82} - 14 q^{83} + 48 q^{85} - 49 q^{86} - 8 q^{87} + 20 q^{88} - 35 q^{89} - q^{90} - 105 q^{92} - 9 q^{93} + 2 q^{94} + 7 q^{95} - 23 q^{96} - 64 q^{97} - 10 q^{99}+O(q^{100}) $ 13 * q - 4 * q^2 + 13 * q^3 + 12 * q^4 - 8 * q^5 - 4 * q^6 - 12 * q^8 + 13 * q^9 - q^10 - 10 * q^11 + 12 * q^12 - 16 * q^13 - 8 * q^15 + 26 * q^16 - 12 * q^17 - 4 * q^18 - 11 * q^19 - 6 * q^20 + q^22 - 15 * q^23 - 12 * q^24 + 15 * q^25 - 18 * q^26 + 13 * q^27 - 8 * q^29 - q^30 - 9 * q^31 - 23 * q^32 - 10 * q^33 + 7 * q^34 + 12 * q^36 - 2 * q^37 - 20 * q^38 - 16 * q^39 - 49 * q^40 + 13 * q^41 - 7 * q^43 - 22 * q^44 - 8 * q^45 - 4 * q^46 - 26 * q^47 + 26 * q^48 - 15 * q^50 - 12 * q^51 - 24 * q^52 + 4 * q^53 - 4 * q^54 - q^55 - 11 * q^57 + 39 * q^58 + 3 * q^59 - 6 * q^60 - 28 * q^61 - 7 * q^62 + 2 * q^64 - 20 * q^65 + q^66 + 7 * q^67 - 55 * q^68 - 15 * q^69 - 40 * q^71 - 12 * q^72 + 2 * q^73 + q^74 + 15 * q^75 + 26 * q^76 - 18 * q^78 + 13 * q^79 - 22 * q^80 + 13 * q^81 - 4 * q^82 - 14 * q^83 + 48 * q^85 - 49 * q^86 - 8 * q^87 + 20 * q^88 - 35 * q^89 - q^90 - 105 * q^92 - 9 * q^93 + 2 * q^94 + 7 * q^95 - 23 * q^96 - 64 * q^97 - 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.73393	−1.93318	−0.966592	−	0.256321i	$-0.917490\pi$
$2$	−2.73393	−1.93318	−0.966592	+	0.256321i	$0.917490\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.47440	2.73720
$5$	2.29019	1.02420	0.512101	−	0.858925i	$-0.328867\pi$
$5$	2.29019	1.02420	0.512101	+	0.858925i	$0.328867\pi$
$6$	−2.73393	−1.11612
$7$	0	0
$7$	0	0
$8$	−9.49877	−3.35832
$9$	1.00000	0.333333
$10$	−6.26122	−1.97997
$11$	−0.920136	−0.277431	−0.138716	−	0.990332i	$-0.544297\pi$
$11$	−0.920136	−0.277431	−0.138716	+	0.990332i	$0.544297\pi$
$12$	5.47440	1.58032
$13$	−6.70791	−1.86044	−0.930219	−	0.367005i	$-0.880383\pi$
$13$	−6.70791	−1.86044	−0.930219	+	0.367005i	$0.880383\pi$
$14$	0	0
$15$	2.29019	0.591324
$16$	15.0202	3.75506
$17$	3.80909	0.923840	0.461920	−	0.886922i	$-0.347161\pi$
$17$	3.80909	0.923840	0.461920	+	0.886922i	$0.347161\pi$
$18$	−2.73393	−0.644394
$19$	6.56558	1.50625	0.753123	−	0.657879i	$-0.228546\pi$
$19$	6.56558	1.50625	0.753123	+	0.657879i	$0.228546\pi$
$20$	12.5374	2.80344
$21$	0	0
$22$	2.51559	0.536326
$23$	−6.79688	−1.41725	−0.708624	−	0.705587i	$-0.750684\pi$
$23$	−6.79688	−1.41725	−0.708624	+	0.705587i	$0.750684\pi$
$24$	−9.49877	−1.93893
$25$	0.244953	0.0489906
$26$	18.3390	3.59657
$27$	1.00000	0.192450
$28$	0	0
$29$	−4.96509	−0.921994	−0.460997	−	0.887402i	$-0.652508\pi$
$29$	−4.96509	−0.921994	−0.460997	+	0.887402i	$0.652508\pi$
$30$	−6.26122	−1.14314
$31$	1.14250	0.205199	0.102599	−	0.994723i	$-0.467284\pi$
$31$	1.14250	0.205199	0.102599	+	0.994723i	$0.467284\pi$
$32$	−22.0668	−3.90089
$33$	−0.920136	−0.160175
$34$	−10.4138	−1.78595
$35$	0	0
$36$	5.47440	0.912399
$37$	−10.4608	−1.71974	−0.859870	−	0.510513i	$-0.829456\pi$
$37$	−10.4608	−1.71974	−0.859870	+	0.510513i	$0.829456\pi$
$38$	−17.9499	−2.91185
$39$	−6.70791	−1.07412
$40$	−21.7540	−3.43960
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	3.89955	0.594676	0.297338	−	0.954772i	$-0.403901\pi$
$43$	3.89955	0.594676	0.297338	+	0.954772i	$0.403901\pi$
$44$	−5.03719	−0.759385
$45$	2.29019	0.341401
$46$	18.5822	2.73980
$47$	−11.0064	−1.60545	−0.802724	−	0.596351i	$-0.796617\pi$
$47$	−11.0064	−1.60545	−0.802724	+	0.596351i	$0.796617\pi$
$48$	15.0202	2.16798
$49$	0	0
$50$	−0.669685	−0.0947078
$51$	3.80909	0.533379
$52$	−36.7217	−5.09239
$53$	7.81643	1.07367	0.536834	−	0.843688i	$-0.319620\pi$
$53$	7.81643	1.07367	0.536834	+	0.843688i	$0.319620\pi$
$54$	−2.73393	−0.372041
$55$	−2.10728	−0.284146
$56$	0	0
$57$	6.56558	0.869632
$58$	13.5742	1.78238
$59$	0.168195	0.0218972	0.0109486	−	0.999940i	$-0.496515\pi$
$59$	0.168195	0.0218972	0.0109486	+	0.999940i	$0.496515\pi$
$60$	12.5374	1.61857
$61$	14.4855	1.85468	0.927342	−	0.374216i	$-0.122088\pi$
$61$	14.4855	1.85468	0.927342	+	0.374216i	$0.122088\pi$
$62$	−3.12352	−0.396687
$63$	0	0
$64$	30.2886	3.78608
$65$	−15.3624	−1.90547
$66$	2.51559	0.309648
$67$	1.48503	0.181426	0.0907128	−	0.995877i	$-0.471085\pi$
$67$	1.48503	0.181426	0.0907128	+	0.995877i	$0.471085\pi$
$68$	20.8525	2.52873
$69$	−6.79688	−0.818248
$70$	0	0
$71$	−6.79705	−0.806662	−0.403331	−	0.915054i	$-0.632148\pi$
$71$	−6.79705	−0.806662	−0.403331	+	0.915054i	$0.632148\pi$
$72$	−9.49877	−1.11944
$73$	4.20182	0.491786	0.245893	−	0.969297i	$-0.420919\pi$
$73$	4.20182	0.491786	0.245893	+	0.969297i	$0.420919\pi$
$74$	28.5991	3.32457
$75$	0.244953	0.0282847
$76$	35.9426	4.12289
$77$	0	0
$78$	18.3390	2.07648
$79$	4.67401	0.525867	0.262933	−	0.964814i	$-0.415310\pi$
$79$	4.67401	0.525867	0.262933	+	0.964814i	$0.415310\pi$
$80$	34.3991	3.84594
$81$	1.00000	0.111111
$82$	−2.73393	−0.301913
$83$	−6.73979	−0.739788	−0.369894	−	0.929074i	$-0.620606\pi$
$83$	−6.73979	−0.739788	−0.369894	+	0.929074i	$0.620606\pi$
$84$	0	0
$85$	8.72353	0.946199
$86$	−10.6611	−1.14962
$87$	−4.96509	−0.532313
$88$	8.74016	0.931704
$89$	−8.78706	−0.931426	−0.465713	−	0.884936i	$-0.654202\pi$
$89$	−8.78706	−0.931426	−0.465713	+	0.884936i	$0.654202\pi$
$90$	−6.26122	−0.659990
$91$	0	0
$92$	−37.2088	−3.87929
$93$	1.14250	0.118472
$94$	30.0907	3.10362
$95$	15.0364	1.54270
$96$	−22.0668	−2.25218
$97$	1.94754	0.197742	0.0988711	−	0.995100i	$-0.468477\pi$
$97$	1.94754	0.197742	0.0988711	+	0.995100i	$0.468477\pi$
$98$	0	0
$99$	−0.920136	−0.0924772
$100$	1.34097	0.134097
$101$	1.27704	0.127071	0.0635353	−	0.997980i	$-0.479762\pi$
$101$	1.27704	0.127071	0.0635353	+	0.997980i	$0.479762\pi$
$102$	−10.4138	−1.03112
$103$	−4.42261	−0.435773	−0.217886	−	0.975974i	$-0.569916\pi$
$103$	−4.42261	−0.435773	−0.217886	+	0.975974i	$0.569916\pi$
$104$	63.7169	6.24795
$105$	0	0
$106$	−21.3696	−2.07560
$107$	−2.72192	−0.263138	−0.131569	−	0.991307i	$-0.542002\pi$
$107$	−2.72192	−0.263138	−0.131569	+	0.991307i	$0.542002\pi$
$108$	5.47440	0.526774
$109$	−8.27489	−0.792591	−0.396295	−	0.918123i	$-0.629704\pi$
$109$	−8.27489	−0.792591	−0.396295	+	0.918123i	$0.629704\pi$
$110$	5.76117	0.549306
$111$	−10.4608	−0.992893
$112$	0	0
$113$	−14.9047	−1.40212	−0.701060	−	0.713102i	$-0.747289\pi$
$113$	−14.9047	−1.40212	−0.701060	+	0.713102i	$0.747289\pi$
$114$	−17.9499	−1.68116
$115$	−15.5661	−1.45155
$116$	−27.1809	−2.52368
$117$	−6.70791	−0.620146
$118$	−0.459835	−0.0423312
$119$	0	0
$120$	−21.7540	−1.98586
$121$	−10.1533	−0.923032
$122$	−39.6025	−3.58544
$123$	1.00000	0.0901670
$124$	6.25449	0.561670
$125$	−10.8899	−0.974026
$126$	0	0
$127$	−9.15904	−0.812734	−0.406367	−	0.913710i	$-0.633204\pi$
$127$	−9.15904	−0.812734	−0.406367	+	0.913710i	$0.633204\pi$
$128$	−38.6736	−3.41829
$129$	3.89955	0.343337
$130$	41.9997	3.68361
$131$	−4.70020	−0.410658	−0.205329	−	0.978693i	$-0.565827\pi$
$131$	−4.70020	−0.410658	−0.205329	+	0.978693i	$0.565827\pi$
$132$	−5.03719	−0.438431
$133$	0	0
$134$	−4.05998	−0.350729
$135$	2.29019	0.197108
$136$	−36.1817	−3.10255
$137$	−0.592614	−0.0506305	−0.0253152	−	0.999680i	$-0.508059\pi$
$137$	−0.592614	−0.0506305	−0.0253152	+	0.999680i	$0.508059\pi$
$138$	18.5822	1.58182
$139$	16.3539	1.38712	0.693558	−	0.720401i	$-0.256042\pi$
$139$	16.3539	1.38712	0.693558	+	0.720401i	$0.256042\pi$
$140$	0	0
$141$	−11.0064	−0.926905
$142$	18.5827	1.55942
$143$	6.17219	0.516144
$144$	15.0202	1.25169
$145$	−11.3710	−0.944308
$146$	−11.4875	−0.950713
$147$	0	0
$148$	−57.2664	−4.70727
$149$	5.86805	0.480730	0.240365	−	0.970683i	$-0.422733\pi$
$149$	5.86805	0.480730	0.240365	+	0.970683i	$0.422733\pi$
$150$	−0.669685	−0.0546796
$151$	−2.15284	−0.175196	−0.0875979	−	0.996156i	$-0.527919\pi$
$151$	−2.15284	−0.175196	−0.0875979	+	0.996156i	$0.527919\pi$
$152$	−62.3649	−5.05846
$153$	3.80909	0.307947
$154$	0	0
$155$	2.61653	0.210165
$156$	−36.7217	−2.94009
$157$	3.14404	0.250921	0.125461	−	0.992099i	$-0.459959\pi$
$157$	3.14404	0.250921	0.125461	+	0.992099i	$0.459959\pi$
$158$	−12.7784	−1.01660
$159$	7.81643	0.619883
$160$	−50.5370	−3.99530
$161$	0	0
$162$	−2.73393	−0.214798
$163$	1.17623	0.0921293	0.0460647	−	0.998938i	$-0.485332\pi$
$163$	1.17623	0.0921293	0.0460647	+	0.998938i	$0.485332\pi$
$164$	5.47440	0.427479
$165$	−2.10728	−0.164052
$166$	18.4261	1.43015
$167$	−3.91921	−0.303278	−0.151639	−	0.988436i	$-0.548455\pi$
$167$	−3.91921	−0.303278	−0.151639	+	0.988436i	$0.548455\pi$
$168$	0	0
$169$	31.9960	2.46123
$170$	−23.8496	−1.82918
$171$	6.56558	0.502082
$172$	21.3477	1.62775
$173$	−19.2921	−1.46675	−0.733375	−	0.679824i	$-0.762056\pi$
$173$	−19.2921	−1.46675	−0.733375	+	0.679824i	$0.762056\pi$
$174$	13.5742	1.02906
$175$	0	0
$176$	−13.8206	−1.04177
$177$	0.168195	0.0126423
$178$	24.0232	1.80062
$179$	−11.2833	−0.843351	−0.421676	−	0.906747i	$-0.638558\pi$
$179$	−11.2833	−0.843351	−0.421676	+	0.906747i	$0.638558\pi$
$180$	12.5374	0.934482
$181$	−0.973827	−0.0723840	−0.0361920	−	0.999345i	$-0.511523\pi$
$181$	−0.973827	−0.0723840	−0.0361920	+	0.999345i	$0.511523\pi$
$182$	0	0
$183$	14.4855	1.07080
$184$	64.5620	4.75957
$185$	−23.9571	−1.76136
$186$	−3.12352	−0.229027
$187$	−3.50488	−0.256302
$188$	−60.2533	−4.39443
$189$	0	0
$190$	−41.1085	−2.98232
$191$	−18.1333	−1.31208	−0.656040	−	0.754726i	$-0.727770\pi$
$191$	−18.1333	−1.31208	−0.656040	+	0.754726i	$0.727770\pi$
$192$	30.2886	2.18589
$193$	−10.3872	−0.747684	−0.373842	−	0.927492i	$-0.621960\pi$
$193$	−10.3872	−0.747684	−0.373842	+	0.927492i	$0.621960\pi$
$194$	−5.32443	−0.382272
$195$	−15.3624	−1.10012
$196$	0	0
$197$	16.6319	1.18497	0.592487	−	0.805580i	$-0.298146\pi$
$197$	16.6319	1.18497	0.592487	+	0.805580i	$0.298146\pi$
$198$	2.51559	0.178775
$199$	−7.52775	−0.533628	−0.266814	−	0.963748i	$-0.585971\pi$
$199$	−7.52775	−0.533628	−0.266814	+	0.963748i	$0.585971\pi$
$200$	−2.32675	−0.164526
$201$	1.48503	0.104746
$202$	−3.49136	−0.245651
$203$	0	0
$204$	20.8525	1.45997
$205$	2.29019	0.159954
$206$	12.0911	0.842429
$207$	−6.79688	−0.472416
$208$	−100.754	−6.98605
$209$	−6.04122	−0.417880
$210$	0	0
$211$	−16.6359	−1.14526	−0.572632	−	0.819812i	$-0.694078\pi$
$211$	−16.6359	−1.14526	−0.572632	+	0.819812i	$0.694078\pi$
$212$	42.7902	2.93884
$213$	−6.79705	−0.465726
$214$	7.44156	0.508695
$215$	8.93071	0.609069
$216$	−9.49877	−0.646309
$217$	0	0
$218$	22.6230	1.53222
$219$	4.20182	0.283933
$220$	−11.5361	−0.777764
$221$	−25.5510	−1.71875
$222$	28.5991	1.91944
$223$	8.51137	0.569964	0.284982	−	0.958533i	$-0.408012\pi$
$223$	8.51137	0.569964	0.284982	+	0.958533i	$0.408012\pi$
$224$	0	0
$225$	0.244953	0.0163302
$226$	40.7486	2.71055
$227$	9.94786	0.660263	0.330131	−	0.943935i	$-0.392907\pi$
$227$	9.94786	0.660263	0.330131	+	0.943935i	$0.392907\pi$
$228$	35.9426	2.38035
$229$	−9.27228	−0.612729	−0.306365	−	0.951914i	$-0.599113\pi$
$229$	−9.27228	−0.612729	−0.306365	+	0.951914i	$0.599113\pi$
$230$	42.5567	2.80611
$231$	0	0
$232$	47.1622	3.09635
$233$	−1.53898	−0.100822	−0.0504109	−	0.998729i	$-0.516053\pi$
$233$	−1.53898	−0.100822	−0.0504109	+	0.998729i	$0.516053\pi$
$234$	18.3390	1.19886
$235$	−25.2067	−1.64430
$236$	0.920767	0.0599369
$237$	4.67401	0.303609
$238$	0	0
$239$	−23.6779	−1.53159	−0.765797	−	0.643082i	$-0.777655\pi$
$239$	−23.6779	−1.53159	−0.765797	+	0.643082i	$0.777655\pi$
$240$	34.3991	2.22045
$241$	−26.3182	−1.69530	−0.847652	−	0.530553i	$-0.821984\pi$
$241$	−26.3182	−1.69530	−0.847652	+	0.530553i	$0.821984\pi$
$242$	27.7586	1.78439
$243$	1.00000	0.0641500
$244$	79.2996	5.07664
$245$	0	0
$246$	−2.73393	−0.174309
$247$	−44.0413	−2.80228
$248$	−10.8523	−0.689124
$249$	−6.73979	−0.427117
$250$	29.7724	1.88297
$251$	4.25241	0.268410	0.134205	−	0.990954i	$-0.457152\pi$
$251$	4.25241	0.268410	0.134205	+	0.990954i	$0.457152\pi$
$252$	0	0
$253$	6.25405	0.393189
$254$	25.0402	1.57116
$255$	8.72353	0.546288
$256$	45.1538	2.82211
$257$	−11.4453	−0.713941	−0.356970	−	0.934116i	$-0.616190\pi$
$257$	−11.4453	−0.713941	−0.356970	+	0.934116i	$0.616190\pi$
$258$	−10.6611	−0.663733
$259$	0	0
$260$	−84.0996	−5.21564
$261$	−4.96509	−0.307331
$262$	12.8500	0.793878
$263$	−23.1262	−1.42602	−0.713011	−	0.701152i	$-0.752669\pi$
$263$	−23.1262	−1.42602	−0.713011	+	0.701152i	$0.752669\pi$
$264$	8.74016	0.537920
$265$	17.9011	1.09965
$266$	0	0
$267$	−8.78706	−0.537759
$268$	8.12965	0.496598
$269$	11.0495	0.673699	0.336849	−	0.941559i	$-0.390639\pi$
$269$	11.0495	0.673699	0.336849	+	0.941559i	$0.390639\pi$
$270$	−6.26122	−0.381046
$271$	−1.89289	−0.114985	−0.0574925	−	0.998346i	$-0.518311\pi$
$271$	−1.89289	−0.114985	−0.0574925	+	0.998346i	$0.518311\pi$
$272$	57.2134	3.46907
$273$	0	0
$274$	1.62017	0.0978780
$275$	−0.225390	−0.0135915
$276$	−37.2088	−2.23971
$277$	20.0397	1.20407	0.602035	−	0.798470i	$-0.294357\pi$
$277$	20.0397	1.20407	0.602035	+	0.798470i	$0.294357\pi$
$278$	−44.7104	−2.68155
$279$	1.14250	0.0683996
$280$	0	0
$281$	13.2150	0.788338	0.394169	−	0.919038i	$-0.371032\pi$
$281$	13.2150	0.788338	0.394169	+	0.919038i	$0.371032\pi$
$282$	30.0907	1.79188
$283$	9.83784	0.584799	0.292400	−	0.956296i	$-0.405546\pi$
$283$	9.83784	0.584799	0.292400	+	0.956296i	$0.405546\pi$
$284$	−37.2098	−2.20799
$285$	15.0364	0.890679
$286$	−16.8743	−0.997801
$287$	0	0
$288$	−22.0668	−1.30030
$289$	−2.49083	−0.146519
$290$	31.0875	1.82552
$291$	1.94754	0.114167
$292$	23.0024	1.34612
$293$	−4.28195	−0.250154	−0.125077	−	0.992147i	$-0.539918\pi$
$293$	−4.28195	−0.250154	−0.125077	+	0.992147i	$0.539918\pi$
$294$	0	0
$295$	0.385198	0.0224271
$296$	99.3645	5.77544
$297$	−0.920136	−0.0533917
$298$	−16.0429	−0.929339
$299$	45.5928	2.63670
$300$	1.34097	0.0774209
$301$	0	0
$302$	5.88573	0.338686
$303$	1.27704	0.0733643
$304$	98.6164	5.65604
$305$	33.1746	1.89957
$306$	−10.4138	−0.595318
$307$	−15.3385	−0.875413	−0.437707	−	0.899118i	$-0.644209\pi$
$307$	−15.3385	−0.875413	−0.437707	+	0.899118i	$0.644209\pi$
$308$	0	0
$309$	−4.42261	−0.251594
$310$	−7.15343	−0.406288
$311$	18.3369	1.03979	0.519896	−	0.854230i	$-0.325971\pi$
$311$	18.3369	1.03979	0.519896	+	0.854230i	$0.325971\pi$
$312$	63.7169	3.60726
$313$	18.4991	1.04563	0.522815	−	0.852446i	$-0.324882\pi$
$313$	18.4991	1.04563	0.522815	+	0.852446i	$0.324882\pi$
$314$	−8.59559	−0.485077
$315$	0	0
$316$	25.5874	1.43940
$317$	−0.786740	−0.0441877	−0.0220939	−	0.999756i	$-0.507033\pi$
$317$	−0.786740	−0.0441877	−0.0220939	+	0.999756i	$0.507033\pi$
$318$	−21.3696	−1.19835
$319$	4.56856	0.255790
$320$	69.3666	3.87771
$321$	−2.72192	−0.151923
$322$	0	0
$323$	25.0089	1.39153
$324$	5.47440	0.304133
$325$	−1.64312	−0.0911439
$326$	−3.21573	−0.178103
$327$	−8.27489	−0.457602
$328$	−9.49877	−0.524482
$329$	0	0
$330$	5.76117	0.317142
$331$	−19.3618	−1.06422	−0.532109	−	0.846676i	$-0.678600\pi$
$331$	−19.3618	−1.06422	−0.532109	+	0.846676i	$0.678600\pi$
$332$	−36.8963	−2.02495
$333$	−10.4608	−0.573247
$334$	10.7149	0.586292
$335$	3.40100	0.185816
$336$	0	0
$337$	−13.8230	−0.752988	−0.376494	−	0.926419i	$-0.622871\pi$
$337$	−13.8230	−0.752988	−0.376494	+	0.926419i	$0.622871\pi$
$338$	−87.4749	−4.75801
$339$	−14.9047	−0.809514
$340$	47.7560	2.58994
$341$	−1.05125	−0.0569286
$342$	−17.9499	−0.970617
$343$	0	0
$344$	−37.0410	−1.99712
$345$	−15.5661	−0.838052
$346$	52.7433	2.83550
$347$	25.5990	1.37423	0.687114	−	0.726550i	$-0.258877\pi$
$347$	25.5990	1.37423	0.687114	+	0.726550i	$0.258877\pi$
$348$	−27.1809	−1.45705
$349$	19.7632	1.05790	0.528949	−	0.848654i	$-0.322586\pi$
$349$	19.7632	1.05790	0.528949	+	0.848654i	$0.322586\pi$
$350$	0	0
$351$	−6.70791	−0.358041
$352$	20.3044	1.08223
$353$	−18.2796	−0.972924	−0.486462	−	0.873702i	$-0.661713\pi$
$353$	−18.2796	−0.972924	−0.486462	+	0.873702i	$0.661713\pi$
$354$	−0.459835	−0.0244399
$355$	−15.5665	−0.826185
$356$	−48.1038	−2.54950
$357$	0	0
$358$	30.8477	1.63035
$359$	−21.6768	−1.14406	−0.572028	−	0.820234i	$-0.693843\pi$
$359$	−21.6768	−1.14406	−0.572028	+	0.820234i	$0.693843\pi$
$360$	−21.7540	−1.14653
$361$	24.1068	1.26878
$362$	2.66238	0.139932
$363$	−10.1533	−0.532913
$364$	0	0
$365$	9.62296	0.503689
$366$	−39.6025	−2.07006
$367$	−28.0575	−1.46459	−0.732296	−	0.680987i	$-0.761551\pi$
$367$	−28.0575	−1.46459	−0.732296	+	0.680987i	$0.761551\pi$
$368$	−102.091	−5.32184
$369$	1.00000	0.0520579
$370$	65.4972	3.40504
$371$	0	0
$372$	6.25449	0.324280
$373$	8.51841	0.441066	0.220533	−	0.975379i	$-0.429220\pi$
$373$	8.51841	0.441066	0.220533	+	0.975379i	$0.429220\pi$
$374$	9.58212	0.495479
$375$	−10.8899	−0.562354
$376$	104.547	5.39161
$377$	33.3053	1.71531
$378$	0	0
$379$	21.0962	1.08364	0.541820	−	0.840495i	$-0.317735\pi$
$379$	21.0962	1.08364	0.541820	+	0.840495i	$0.317735\pi$
$380$	82.3152	4.22268
$381$	−9.15904	−0.469232
$382$	49.5753	2.53649
$383$	−16.9365	−0.865415	−0.432707	−	0.901534i	$-0.642442\pi$
$383$	−16.9365	−0.865415	−0.432707	+	0.901534i	$0.642442\pi$
$384$	−38.6736	−1.97355
$385$	0	0
$386$	28.3978	1.44541
$387$	3.89955	0.198225
$388$	10.6616	0.541260
$389$	−20.4330	−1.03599	−0.517997	−	0.855382i	$-0.673322\pi$
$389$	−20.4330	−1.03599	−0.517997	+	0.855382i	$0.673322\pi$
$390$	41.9997	2.12674
$391$	−25.8899	−1.30931
$392$	0	0
$393$	−4.70020	−0.237094
$394$	−45.4705	−2.29077
$395$	10.7043	0.538594
$396$	−5.03719	−0.253128
$397$	−12.3328	−0.618965	−0.309482	−	0.950905i	$-0.600156\pi$
$397$	−12.3328	−0.618965	−0.309482	+	0.950905i	$0.600156\pi$
$398$	20.5804	1.03160
$399$	0	0
$400$	3.67925	0.183962
$401$	−9.88468	−0.493618	−0.246809	−	0.969064i	$-0.579382\pi$
$401$	−9.88468	−0.493618	−0.246809	+	0.969064i	$0.579382\pi$
$402$	−4.05998	−0.202493
$403$	−7.66377	−0.381760
$404$	6.99105	0.347818
$405$	2.29019	0.113800
$406$	0	0
$407$	9.62533	0.477110
$408$	−36.1817	−1.79126
$409$	−18.9705	−0.938030	−0.469015	−	0.883190i	$-0.655391\pi$
$409$	−18.9705	−0.938030	−0.469015	+	0.883190i	$0.655391\pi$
$410$	−6.26122	−0.309220
$411$	−0.592614	−0.0292315
$412$	−24.2111	−1.19280
$413$	0	0
$414$	18.5822	0.913266
$415$	−15.4354	−0.757692
$416$	148.022	7.25736
$417$	16.3539	0.800852
$418$	16.5163	0.807839
$419$	−12.3097	−0.601366	−0.300683	−	0.953724i	$-0.597215\pi$
$419$	−12.3097	−0.601366	−0.300683	+	0.953724i	$0.597215\pi$
$420$	0	0
$421$	4.56505	0.222487	0.111243	−	0.993793i	$-0.464517\pi$
$421$	4.56505	0.222487	0.111243	+	0.993793i	$0.464517\pi$
$422$	45.4815	2.21401
$423$	−11.0064	−0.535149
$424$	−74.2464	−3.60573
$425$	0.933048	0.0452595
$426$	18.5827	0.900334
$427$	0	0
$428$	−14.9009	−0.720262
$429$	6.17219	0.297996
$430$	−24.4160	−1.17744
$431$	0.917377	0.0441885	0.0220942	−	0.999756i	$-0.492967\pi$
$431$	0.917377	0.0441885	0.0220942	+	0.999756i	$0.492967\pi$
$432$	15.0202	0.722661
$433$	−10.4324	−0.501348	−0.250674	−	0.968072i	$-0.580652\pi$
$433$	−10.4324	−0.501348	−0.250674	+	0.968072i	$0.580652\pi$
$434$	0	0
$435$	−11.3710	−0.545197
$436$	−45.3000	−2.16948
$437$	−44.6254	−2.13472
$438$	−11.4875	−0.548894
$439$	2.67093	0.127476	0.0637382	−	0.997967i	$-0.479698\pi$
$439$	2.67093	0.127476	0.0637382	+	0.997967i	$0.479698\pi$
$440$	20.0166	0.954254
$441$	0	0
$442$	69.8548	3.32265
$443$	0.938028	0.0445671	0.0222835	−	0.999752i	$-0.492906\pi$
$443$	0.938028	0.0445671	0.0222835	+	0.999752i	$0.492906\pi$
$444$	−57.2664	−2.71774
$445$	−20.1240	−0.953969
$446$	−23.2695	−1.10184
$447$	5.86805	0.277549
$448$	0	0
$449$	−2.87202	−0.135539	−0.0677695	−	0.997701i	$-0.521588\pi$
$449$	−2.87202	−0.135539	−0.0677695	+	0.997701i	$0.521588\pi$
$450$	−0.669685	−0.0315693
$451$	−0.920136	−0.0433275
$452$	−81.5944	−3.83788
$453$	−2.15284	−0.101149
$454$	−27.1968	−1.27641
$455$	0	0
$456$	−62.3649	−2.92050
$457$	38.8784	1.81865	0.909327	−	0.416083i	$-0.136597\pi$
$457$	38.8784	1.81865	0.909327	+	0.416083i	$0.136597\pi$
$458$	25.3498	1.18452
$459$	3.80909	0.177793
$460$	−85.2151	−3.97317
$461$	−14.2660	−0.664435	−0.332217	−	0.943203i	$-0.607797\pi$
$461$	−14.2660	−0.664435	−0.332217	+	0.943203i	$0.607797\pi$
$462$	0	0
$463$	18.1411	0.843088	0.421544	−	0.906808i	$-0.361488\pi$
$463$	18.1411	0.843088	0.421544	+	0.906808i	$0.361488\pi$
$464$	−74.5767	−3.46214
$465$	2.61653	0.121339
$466$	4.20746	0.194907
$467$	−7.99012	−0.369739	−0.184869	−	0.982763i	$-0.559186\pi$
$467$	−7.99012	−0.369739	−0.184869	+	0.982763i	$0.559186\pi$
$468$	−36.7217	−1.69746
$469$	0	0
$470$	68.9134	3.17874
$471$	3.14404	0.144870
$472$	−1.59765	−0.0735377
$473$	−3.58812	−0.164982
$474$	−12.7784	−0.586933
$475$	1.60826	0.0737919
$476$	0	0
$477$	7.81643	0.357890
$478$	64.7338	2.96085
$479$	8.37792	0.382797	0.191398	−	0.981512i	$-0.438698\pi$
$479$	8.37792	0.382797	0.191398	+	0.981512i	$0.438698\pi$
$480$	−50.5370	−2.30669
$481$	70.1699	3.19947
$482$	71.9522	3.27733
$483$	0	0
$484$	−55.5835	−2.52652
$485$	4.46022	0.202528
$486$	−2.73393	−0.124014
$487$	28.2457	1.27993	0.639967	−	0.768402i	$-0.278948\pi$
$487$	28.2457	1.27993	0.639967	+	0.768402i	$0.278948\pi$
$488$	−137.595	−6.22862
$489$	1.17623	0.0531909
$490$	0	0
$491$	24.9382	1.12545	0.562723	−	0.826645i	$-0.309754\pi$
$491$	24.9382	1.12545	0.562723	+	0.826645i	$0.309754\pi$
$492$	5.47440	0.246805
$493$	−18.9125	−0.851775
$494$	120.406	5.41732
$495$	−2.10728	−0.0947153
$496$	17.1606	0.770533
$497$	0	0
$498$	18.4261	0.825695
$499$	41.1428	1.84181	0.920903	−	0.389792i	$-0.127453\pi$
$499$	41.1428	1.84181	0.920903	+	0.389792i	$0.127453\pi$
$500$	−59.6159	−2.66610
$501$	−3.91921	−0.175098
$502$	−11.6258	−0.518885
$503$	31.1684	1.38973	0.694864	−	0.719141i	$-0.255464\pi$
$503$	31.1684	1.38973	0.694864	+	0.719141i	$0.255464\pi$
$504$	0	0
$505$	2.92467	0.130146
$506$	−17.0982	−0.760106
$507$	31.9960	1.42099
$508$	−50.1402	−2.22461
$509$	13.6377	0.604482	0.302241	−	0.953232i	$-0.402265\pi$
$509$	13.6377	0.604482	0.302241	+	0.953232i	$0.402265\pi$
$510$	−23.8496	−1.05608
$511$	0	0
$512$	−46.1003	−2.03736
$513$	6.56558	0.289877
$514$	31.2908	1.38018
$515$	−10.1286	−0.446320
$516$	21.3477	0.939780
$517$	10.1274	0.445402
$518$	0	0
$519$	−19.2921	−0.846828
$520$	145.923	6.39917
$521$	11.2007	0.490710	0.245355	−	0.969433i	$-0.421095\pi$
$521$	11.2007	0.490710	0.245355	+	0.969433i	$0.421095\pi$
$522$	13.5742	0.594128
$523$	21.7294	0.950162	0.475081	−	0.879942i	$-0.342419\pi$
$523$	21.7294	0.950162	0.475081	+	0.879942i	$0.342419\pi$
$524$	−25.7308	−1.12405
$525$	0	0
$526$	63.2255	2.75676
$527$	4.35188	0.189571
$528$	−13.8206	−0.601466
$529$	23.1976	1.00859
$530$	−48.9403	−2.12583
$531$	0.168195	0.00729905
$532$	0	0
$533$	−6.70791	−0.290552
$534$	24.0232	1.03959
$535$	−6.23371	−0.269507
$536$	−14.1060	−0.609285
$537$	−11.2833	−0.486909
$538$	−30.2086	−1.30238
$539$	0	0
$540$	12.5374	0.539523
$541$	−23.7323	−1.02033	−0.510166	−	0.860076i	$-0.670416\pi$
$541$	−23.7323	−1.02033	−0.510166	+	0.860076i	$0.670416\pi$
$542$	5.17504	0.222287
$543$	−0.973827	−0.0417909
$544$	−84.0543	−3.60380
$545$	−18.9510	−0.811773
$546$	0	0
$547$	−24.9288	−1.06588	−0.532939	−	0.846154i	$-0.678912\pi$
$547$	−24.9288	−1.06588	−0.532939	+	0.846154i	$0.678912\pi$
$548$	−3.24421	−0.138586
$549$	14.4855	0.618228
$550$	0.616201	0.0262749
$551$	−32.5987	−1.38875
$552$	64.5620	2.74794
$553$	0	0
$554$	−54.7872	−2.32769
$555$	−23.9571	−1.01692
$556$	89.5275	3.79681
$557$	−17.5708	−0.744498	−0.372249	−	0.928133i	$-0.621413\pi$
$557$	−17.5708	−0.744498	−0.372249	+	0.928133i	$0.621413\pi$
$558$	−3.12352	−0.132229
$559$	−26.1578	−1.10636
$560$	0	0
$561$	−3.50488	−0.147976
$562$	−36.1288	−1.52400
$563$	40.8438	1.72136	0.860681	−	0.509144i	$-0.170038\pi$
$563$	40.8438	1.72136	0.860681	+	0.509144i	$0.170038\pi$
$564$	−60.2533	−2.53712
$565$	−34.1346	−1.43605
$566$	−26.8960	−1.13052
$567$	0	0
$568$	64.5636	2.70903
$569$	34.2876	1.43741	0.718706	−	0.695314i	$-0.244735\pi$
$569$	34.2876	1.43741	0.718706	+	0.695314i	$0.244735\pi$
$570$	−41.1085	−1.72185
$571$	−24.4051	−1.02132	−0.510661	−	0.859782i	$-0.670599\pi$
$571$	−24.4051	−1.02132	−0.510661	+	0.859782i	$0.670599\pi$
$572$	33.7890	1.41279
$573$	−18.1333	−0.757530
$574$	0	0
$575$	−1.66492	−0.0694318
$576$	30.2886	1.26203
$577$	−19.7937	−0.824022	−0.412011	−	0.911179i	$-0.635173\pi$
$577$	−19.7937	−0.824022	−0.412011	+	0.911179i	$0.635173\pi$
$578$	6.80975	0.283248
$579$	−10.3872	−0.431676
$580$	−62.2492	−2.58476
$581$	0	0
$582$	−5.32443	−0.220705
$583$	−7.19218	−0.297869
$584$	−39.9122	−1.65158
$585$	−15.3624	−0.635155
$586$	11.7066	0.483593
$587$	25.9454	1.07088	0.535441	−	0.844572i	$-0.320145\pi$
$587$	25.9454	1.07088	0.535441	+	0.844572i	$0.320145\pi$
$588$	0	0
$589$	7.50116	0.309080
$590$	−1.05311	−0.0433557
$591$	16.6319	0.684145
$592$	−157.123	−6.45772
$593$	20.4811	0.841059	0.420530	−	0.907279i	$-0.361844\pi$
$593$	20.4811	0.841059	0.420530	+	0.907279i	$0.361844\pi$
$594$	2.51559	0.103216
$595$	0	0
$596$	32.1241	1.31585
$597$	−7.52775	−0.308090
$598$	−124.648	−5.09723
$599$	−12.9864	−0.530609	−0.265305	−	0.964165i	$-0.585473\pi$
$599$	−12.9864	−0.530609	−0.265305	+	0.964165i	$0.585473\pi$
$600$	−2.32675	−0.0949892
$601$	−15.2261	−0.621085	−0.310543	−	0.950559i	$-0.600511\pi$
$601$	−15.2261	−0.621085	−0.310543	+	0.950559i	$0.600511\pi$
$602$	0	0
$603$	1.48503	0.0604752
$604$	−11.7855	−0.479546
$605$	−23.2531	−0.945371
$606$	−3.49136	−0.141827
$607$	−6.86266	−0.278547	−0.139273	−	0.990254i	$-0.544477\pi$
$607$	−6.86266	−0.278547	−0.139273	+	0.990254i	$0.544477\pi$
$608$	−144.881	−5.87570
$609$	0	0
$610$	−90.6971	−3.67222
$611$	73.8298	2.98683
$612$	20.8525	0.842911
$613$	20.8353	0.841530	0.420765	−	0.907170i	$-0.361762\pi$
$613$	20.8353	0.841530	0.420765	+	0.907170i	$0.361762\pi$
$614$	41.9344	1.69233
$615$	2.29019	0.0923492
$616$	0	0
$617$	8.59189	0.345897	0.172948	−	0.984931i	$-0.444671\pi$
$617$	8.59189	0.345897	0.172948	+	0.984931i	$0.444671\pi$
$618$	12.0911	0.486377
$619$	−37.1170	−1.49186	−0.745929	−	0.666025i	$-0.767994\pi$
$619$	−37.1170	−1.49186	−0.745929	+	0.666025i	$0.767994\pi$
$620$	14.3239	0.575264
$621$	−6.79688	−0.272749
$622$	−50.1319	−2.01011
$623$	0	0
$624$	−100.754	−4.03340
$625$	−26.1648	−1.04659
$626$	−50.5753	−2.02140
$627$	−6.04122	−0.241263
$628$	17.2117	0.686822
$629$	−39.8460	−1.58877
$630$	0	0
$631$	−26.0046	−1.03523	−0.517614	−	0.855614i	$-0.673180\pi$
$631$	−26.0046	−1.03523	−0.517614	+	0.855614i	$0.673180\pi$
$632$	−44.3973	−1.76603
$633$	−16.6359	−0.661219
$634$	2.15090	0.0854230
$635$	−20.9759	−0.832404
$636$	42.7902	1.69674
$637$	0	0
$638$	−12.4901	−0.494489
$639$	−6.79705	−0.268887
$640$	−88.5697	−3.50102
$641$	−38.1624	−1.50732	−0.753661	−	0.657263i	$-0.771714\pi$
$641$	−38.1624	−1.50732	−0.753661	+	0.657263i	$0.771714\pi$
$642$	7.44156	0.293695
$643$	−21.5892	−0.851395	−0.425698	−	0.904865i	$-0.639971\pi$
$643$	−21.5892	−0.851395	−0.425698	+	0.904865i	$0.639971\pi$
$644$	0	0
$645$	8.93071	0.351646
$646$	−68.3726	−2.69008
$647$	−8.98456	−0.353220	−0.176610	−	0.984281i	$-0.556513\pi$
$647$	−8.98456	−0.353220	−0.176610	+	0.984281i	$0.556513\pi$
$648$	−9.49877	−0.373147
$649$	−0.154763	−0.00607496
$650$	4.49218	0.176198
$651$	0	0
$652$	6.43914	0.252176
$653$	30.8365	1.20673	0.603363	−	0.797466i	$-0.293827\pi$
$653$	30.8365	1.20673	0.603363	+	0.797466i	$0.293827\pi$
$654$	22.6230	0.884629
$655$	−10.7643	−0.420597
$656$	15.0202	0.586441
$657$	4.20182	0.163929
$658$	0	0
$659$	10.7668	0.419417	0.209708	−	0.977764i	$-0.432749\pi$
$659$	10.7668	0.419417	0.209708	+	0.977764i	$0.432749\pi$
$660$	−11.5361	−0.449042
$661$	22.4119	0.871722	0.435861	−	0.900014i	$-0.356444\pi$
$661$	22.4119	0.871722	0.435861	+	0.900014i	$0.356444\pi$
$662$	52.9338	2.05733
$663$	−25.5510	−0.992319
$664$	64.0197	2.48445
$665$	0	0
$666$	28.5991	1.10819
$667$	33.7471	1.30669
$668$	−21.4553	−0.830131
$669$	8.51137	0.329069
$670$	−9.29811	−0.359217
$671$	−13.3287	−0.514548
$672$	0	0
$673$	1.06312	0.0409804	0.0204902	−	0.999790i	$-0.493477\pi$
$673$	1.06312	0.0409804	0.0204902	+	0.999790i	$0.493477\pi$
$674$	37.7913	1.45566
$675$	0.244953	0.00942824
$676$	175.159	6.73687
$677$	−43.6076	−1.67598	−0.837989	−	0.545688i	$-0.816268\pi$
$677$	−43.6076	−1.67598	−0.837989	+	0.545688i	$0.816268\pi$
$678$	40.7486	1.56494
$679$	0	0
$680$	−82.8628	−3.17764
$681$	9.94786	0.381203
$682$	2.87406	0.110053
$683$	33.0798	1.26576	0.632882	−	0.774248i	$-0.281872\pi$
$683$	33.0798	1.26576	0.632882	+	0.774248i	$0.281872\pi$
$684$	35.9426	1.37430
$685$	−1.35720	−0.0518558
$686$	0	0
$687$	−9.27228	−0.353759
$688$	58.5722	2.23304
$689$	−52.4318	−1.99749
$690$	42.5567	1.62011
$691$	−10.8717	−0.413578	−0.206789	−	0.978386i	$-0.566301\pi$
$691$	−10.8717	−0.413578	−0.206789	+	0.978386i	$0.566301\pi$
$692$	−105.612	−4.01478
$693$	0	0
$694$	−69.9861	−2.65663
$695$	37.4534	1.42069
$696$	47.1622	1.78768
$697$	3.80909	0.144280
$698$	−54.0312	−2.04511
$699$	−1.53898	−0.0582094
$700$	0	0
$701$	36.1667	1.36600	0.682998	−	0.730420i	$-0.260676\pi$
$701$	36.1667	1.36600	0.682998	+	0.730420i	$0.260676\pi$
$702$	18.3390	0.692160
$703$	−68.6810	−2.59035
$704$	−27.8696	−1.05038
$705$	−25.2067	−0.949339
$706$	49.9751	1.88084
$707$	0	0
$708$	0.920767	0.0346046
$709$	−44.4927	−1.67096	−0.835480	−	0.549521i	$-0.814810\pi$
$709$	−44.4927	−1.67096	−0.835480	+	0.549521i	$0.814810\pi$
$710$	42.5578	1.59717
$711$	4.67401	0.175289
$712$	83.4662	3.12803
$713$	−7.76543	−0.290817
$714$	0	0
$715$	14.1355	0.528636
$716$	−61.7691	−2.30842
$717$	−23.6779	−0.884266
$718$	59.2629	2.21167
$719$	14.0486	0.523925	0.261962	−	0.965078i	$-0.415630\pi$
$719$	14.0486	0.523925	0.261962	+	0.965078i	$0.415630\pi$
$720$	34.3991	1.28198
$721$	0	0
$722$	−65.9064	−2.45278
$723$	−26.3182	−0.978784
$724$	−5.33112	−0.198129
$725$	−1.21621	−0.0451690
$726$	27.7586	1.03022
$727$	−10.5472	−0.391174	−0.195587	−	0.980686i	$-0.562661\pi$
$727$	−10.5472	−0.391174	−0.195587	+	0.980686i	$0.562661\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−26.3085	−0.973723
$731$	14.8538	0.549386
$732$	79.2996	2.93100
$733$	−30.1491	−1.11358	−0.556791	−	0.830652i	$-0.687968\pi$
$733$	−30.1491	−1.11358	−0.556791	+	0.830652i	$0.687968\pi$
$734$	76.7074	2.83132
$735$	0	0
$736$	149.985	5.52852
$737$	−1.36643	−0.0503331
$738$	−2.73393	−0.100638
$739$	14.9843	0.551208	0.275604	−	0.961271i	$-0.411122\pi$
$739$	14.9843	0.551208	0.275604	+	0.961271i	$0.411122\pi$
$740$	−131.151	−4.82120
$741$	−44.0413	−1.61790
$742$	0	0
$743$	13.0072	0.477187	0.238593	−	0.971120i	$-0.423314\pi$
$743$	13.0072	0.477187	0.238593	+	0.971120i	$0.423314\pi$
$744$	−10.8523	−0.397866
$745$	13.4389	0.492365
$746$	−23.2888	−0.852662
$747$	−6.73979	−0.246596
$748$	−19.1871	−0.701550
$749$	0	0
$750$	29.7724	1.08713
$751$	45.5335	1.66154	0.830770	−	0.556616i	$-0.187901\pi$
$751$	45.5335	1.66154	0.830770	+	0.556616i	$0.187901\pi$
$752$	−165.318	−6.02854
$753$	4.25241	0.154966
$754$	−91.0546	−3.31601
$755$	−4.93041	−0.179436
$756$	0	0
$757$	29.0005	1.05404	0.527020	−	0.849853i	$-0.323309\pi$
$757$	29.0005	1.05404	0.527020	+	0.849853i	$0.323309\pi$
$758$	−57.6757	−2.09487
$759$	6.25405	0.227008
$760$	−142.827	−5.18089
$761$	−32.1728	−1.16626	−0.583131	−	0.812378i	$-0.698173\pi$
$761$	−32.1728	−1.16626	−0.583131	+	0.812378i	$0.698173\pi$
$762$	25.0402	0.907112
$763$	0	0
$764$	−99.2689	−3.59142
$765$	8.72353	0.315400
$766$	46.3033	1.67301
$767$	−1.12824	−0.0407383
$768$	45.1538	1.62935
$769$	−19.0933	−0.688523	−0.344262	−	0.938874i	$-0.611871\pi$
$769$	−19.0933	−0.688523	−0.344262	+	0.938874i	$0.611871\pi$
$770$	0	0
$771$	−11.4453	−0.412194
$772$	−56.8635	−2.04656
$773$	7.51351	0.270242	0.135121	−	0.990829i	$-0.456858\pi$
$773$	7.51351	0.270242	0.135121	+	0.990829i	$0.456858\pi$
$774$	−10.6611	−0.383206
$775$	0.279858	0.0100528
$776$	−18.4992	−0.664082
$777$	0	0
$778$	55.8625	2.00277
$779$	6.56558	0.235236
$780$	−84.0996	−3.01125
$781$	6.25421	0.223793
$782$	70.7814	2.53114
$783$	−4.96509	−0.177438
$784$	0	0
$785$	7.20043	0.256994
$786$	12.8500	0.458346
$787$	5.80038	0.206761	0.103381	−	0.994642i	$-0.467034\pi$
$787$	5.80038	0.206761	0.103381	+	0.994642i	$0.467034\pi$
$788$	91.0496	3.24351
$789$	−23.1262	−0.823315
$790$	−29.2650	−1.04120
$791$	0	0
$792$	8.74016	0.310568
$793$	−97.1676	−3.45052
$794$	33.7170	1.19657
$795$	17.9011	0.634886
$796$	−41.2099	−1.46065
$797$	−45.1366	−1.59882	−0.799411	−	0.600785i	$-0.794855\pi$
$797$	−45.1366	−1.59882	−0.799411	+	0.600785i	$0.794855\pi$
$798$	0	0
$799$	−41.9243	−1.48318
$800$	−5.40532	−0.191107
$801$	−8.78706	−0.310475
$802$	27.0241	0.954253
$803$	−3.86625	−0.136437
$804$	8.12965	0.286711
$805$	0	0
$806$	20.9523	0.738012
$807$	11.0495	0.388960
$808$	−12.1304	−0.426744
$809$	30.3818	1.06817	0.534084	−	0.845432i	$-0.320657\pi$
$809$	30.3818	1.06817	0.534084	+	0.845432i	$0.320657\pi$
$810$	−6.26122	−0.219997
$811$	16.1134	0.565818	0.282909	−	0.959147i	$-0.408701\pi$
$811$	16.1134	0.565818	0.282909	+	0.959147i	$0.408701\pi$
$812$	0	0
$813$	−1.89289	−0.0663866
$814$	−26.3150	−0.922341
$815$	2.69378	0.0943591
$816$	57.2134	2.00287
$817$	25.6028	0.895729
$818$	51.8641	1.81338
$819$	0	0
$820$	12.5374	0.437825
$821$	−24.0040	−0.837745	−0.418873	−	0.908045i	$-0.637575\pi$
$821$	−24.0040	−0.837745	−0.418873	+	0.908045i	$0.637575\pi$
$822$	1.62017	0.0565099
$823$	3.43559	0.119757	0.0598786	−	0.998206i	$-0.480929\pi$
$823$	3.43559	0.119757	0.0598786	+	0.998206i	$0.480929\pi$
$824$	42.0094	1.46347
$825$	−0.225390	−0.00784707
$826$	0	0
$827$	−31.0481	−1.07965	−0.539825	−	0.841778i	$-0.681509\pi$
$827$	−31.0481	−1.07965	−0.539825	+	0.841778i	$0.681509\pi$
$828$	−37.2088	−1.29310
$829$	40.4112	1.40354	0.701769	−	0.712404i	$-0.252394\pi$
$829$	40.4112	1.40354	0.701769	+	0.712404i	$0.252394\pi$
$830$	42.1993	1.46476
$831$	20.0397	0.695170
$832$	−203.173	−7.04376
$833$	0	0
$834$	−44.7104	−1.54819
$835$	−8.97573	−0.310618
$836$	−33.0721	−1.14382
$837$	1.14250	0.0394905
$838$	33.6538	1.16255
$839$	−31.9055	−1.10150	−0.550749	−	0.834671i	$-0.685658\pi$
$839$	−31.9055	−1.10150	−0.550749	+	0.834671i	$0.685658\pi$
$840$	0	0
$841$	−4.34789	−0.149927
$842$	−12.4805	−0.430108
$843$	13.2150	0.455147
$844$	−91.0717	−3.13482
$845$	73.2768	2.52080
$846$	30.0907	1.03454
$847$	0	0
$848$	117.404	4.03169
$849$	9.83784	0.337634
$850$	−2.55089	−0.0874949
$851$	71.1006	2.43730
$852$	−37.2098	−1.27479
$853$	−35.9675	−1.23150	−0.615751	−	0.787941i	$-0.711147\pi$
$853$	−35.9675	−1.23150	−0.615751	+	0.787941i	$0.711147\pi$
$854$	0	0
$855$	15.0364	0.514234
$856$	25.8549	0.883703
$857$	48.5172	1.65732	0.828658	−	0.559755i	$-0.189105\pi$
$857$	48.5172	1.65732	0.828658	+	0.559755i	$0.189105\pi$
$858$	−16.8743	−0.576081
$859$	−23.9749	−0.818014	−0.409007	−	0.912531i	$-0.634125\pi$
$859$	−23.9749	−0.818014	−0.409007	+	0.912531i	$0.634125\pi$
$860$	48.8902	1.66714
$861$	0	0
$862$	−2.50805	−0.0854244
$863$	−6.69716	−0.227974	−0.113987	−	0.993482i	$-0.536362\pi$
$863$	−6.69716	−0.227974	−0.113987	+	0.993482i	$0.536362\pi$
$864$	−22.0668	−0.750726
$865$	−44.1825	−1.50225
$866$	28.5214	0.969198
$867$	−2.49083	−0.0845929
$868$	0	0
$869$	−4.30072	−0.145892
$870$	31.0875	1.05397
$871$	−9.96145	−0.337531
$872$	78.6013	2.66177
$873$	1.94754	0.0659141
$874$	122.003	4.12681
$875$	0	0
$876$	23.0024	0.777181
$877$	0.419497	0.0141654	0.00708270	−	0.999975i	$-0.497745\pi$
$877$	0.419497	0.0141654	0.00708270	+	0.999975i	$0.497745\pi$
$878$	−7.30214	−0.246435
$879$	−4.28195	−0.144426
$880$	−31.6519	−1.06698
$881$	−9.00618	−0.303426	−0.151713	−	0.988425i	$-0.548479\pi$
$881$	−9.00618	−0.303426	−0.151713	+	0.988425i	$0.548479\pi$
$882$	0	0
$883$	−7.98290	−0.268646	−0.134323	−	0.990938i	$-0.542886\pi$
$883$	−7.98290	−0.268646	−0.134323	+	0.990938i	$0.542886\pi$
$884$	−139.876	−4.70455
$885$	0.385198	0.0129483
$886$	−2.56451	−0.0861563
$887$	14.6135	0.490674	0.245337	−	0.969438i	$-0.421101\pi$
$887$	14.6135	0.490674	0.245337	+	0.969438i	$0.421101\pi$
$888$	99.3645	3.33445
$889$	0	0
$890$	55.0177	1.84420
$891$	−0.920136	−0.0308257
$892$	46.5946	1.56010
$893$	−72.2633	−2.41820
$894$	−16.0429	−0.536554
$895$	−25.8408	−0.863762
$896$	0	0
$897$	45.5928	1.52230
$898$	7.85191	0.262022
$899$	−5.67261	−0.189192
$900$	1.34097	0.0446990
$901$	29.7735	0.991898
$902$	2.51559	0.0837600
$903$	0	0
$904$	141.577	4.70877
$905$	−2.23025	−0.0741359
$906$	5.88573	0.195540
$907$	−46.2582	−1.53598	−0.767989	−	0.640463i	$-0.778743\pi$
$907$	−46.2582	−1.53598	−0.767989	+	0.640463i	$0.778743\pi$
$908$	54.4586	1.80727
$909$	1.27704	0.0423569
$910$	0	0
$911$	19.9858	0.662158	0.331079	−	0.943603i	$-0.392587\pi$
$911$	19.9858	0.662158	0.331079	+	0.943603i	$0.392587\pi$
$912$	98.6164	3.26552
$913$	6.20152	0.205240
$914$	−106.291	−3.51579
$915$	33.1746	1.09672
$916$	−50.7601	−1.67716
$917$	0	0
$918$	−10.4138	−0.343707
$919$	31.1575	1.02779	0.513895	−	0.857853i	$-0.328202\pi$
$919$	31.1575	1.02779	0.513895	+	0.857853i	$0.328202\pi$
$920$	147.859	4.87477
$921$	−15.3385	−0.505420
$922$	39.0024	1.28447
$923$	45.5940	1.50074
$924$	0	0
$925$	−2.56240	−0.0842511
$926$	−49.5966	−1.62984
$927$	−4.42261	−0.145258
$928$	109.563	3.59660
$929$	−22.1258	−0.725924	−0.362962	−	0.931804i	$-0.618235\pi$
$929$	−22.1258	−0.725924	−0.362962	+	0.931804i	$0.618235\pi$
$930$	−7.15343	−0.234570
$931$	0	0
$932$	−8.42497	−0.275969
$933$	18.3369	0.600324
$934$	21.8445	0.714773
$935$	−8.02683	−0.262505
$936$	63.7169	2.08265
$937$	−38.4236	−1.25525	−0.627623	−	0.778518i	$-0.715972\pi$
$937$	−38.4236	−1.25525	−0.627623	+	0.778518i	$0.715972\pi$
$938$	0	0
$939$	18.4991	0.603695
$940$	−137.991	−4.50078
$941$	−37.6411	−1.22706	−0.613532	−	0.789670i	$-0.710252\pi$
$941$	−37.6411	−1.22706	−0.613532	+	0.789670i	$0.710252\pi$
$942$	−8.59559	−0.280059
$943$	−6.79688	−0.221337
$944$	2.52633	0.0822250
$945$	0	0
$946$	9.80969	0.318940
$947$	11.0615	0.359451	0.179725	−	0.983717i	$-0.442479\pi$
$947$	11.0615	0.359451	0.179725	+	0.983717i	$0.442479\pi$
$948$	25.5874	0.831039
$949$	−28.1854	−0.914938
$950$	−4.39687	−0.142653
$951$	−0.786740	−0.0255118
$952$	0	0
$953$	23.5602	0.763190	0.381595	−	0.924330i	$-0.375375\pi$
$953$	23.5602	0.763190	0.381595	+	0.924330i	$0.375375\pi$
$954$	−21.3696	−0.691866
$955$	−41.5287	−1.34384
$956$	−129.622	−4.19228
$957$	4.56856	0.147681
$958$	−22.9047	−0.740016
$959$	0	0
$960$	69.3666	2.23880
$961$	−29.6947	−0.957893
$962$	−191.840	−6.18516
$963$	−2.72192	−0.0877128
$964$	−144.076	−4.64038
$965$	−23.7885	−0.765780
$966$	0	0
$967$	−51.6037	−1.65946	−0.829732	−	0.558162i	$-0.811507\pi$
$967$	−51.6037	−1.65946	−0.829732	+	0.558162i	$0.811507\pi$
$968$	96.4443	3.09984
$969$	25.0089	0.803401
$970$	−12.1939	−0.391524
$971$	38.0921	1.22243	0.611216	−	0.791464i	$-0.290681\pi$
$971$	38.0921	1.22243	0.611216	+	0.791464i	$0.290681\pi$
$972$	5.47440	0.175591
$973$	0	0
$974$	−77.2219	−2.47435
$975$	−1.64312	−0.0526220
$976$	217.576	6.96444
$977$	41.7688	1.33630	0.668151	−	0.744025i	$-0.267086\pi$
$977$	41.7688	1.33630	0.668151	+	0.744025i	$0.267086\pi$
$978$	−3.21573	−0.102828
$979$	8.08529	0.258407
$980$	0	0
$981$	−8.27489	−0.264197
$982$	−68.1795	−2.17569
$983$	49.4080	1.57587	0.787935	−	0.615758i	$-0.211150\pi$
$983$	49.4080	1.57587	0.787935	+	0.615758i	$0.211150\pi$
$984$	−9.49877	−0.302810
$985$	38.0901	1.21365
$986$	51.7055	1.64664
$987$	0	0
$988$	−241.099	−7.67039
$989$	−26.5048	−0.842804
$990$	5.76117	0.183102
$991$	−7.25462	−0.230451	−0.115225	−	0.993339i	$-0.536759\pi$
$991$	−7.25462	−0.230451	−0.115225	+	0.993339i	$0.536759\pi$
$992$	−25.2112	−0.800458
$993$	−19.3618	−0.614427
$994$	0	0
$995$	−17.2400	−0.546543
$996$	−36.8963	−1.16910
$997$	39.6994	1.25729	0.628646	−	0.777692i	$-0.283610\pi$
$997$	39.6994	1.25729	0.628646	+	0.777692i	$0.283610\pi$
$998$	−112.482	−3.56055
$999$	−10.4608	−0.330964

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bi.1.1		13
7.2	even	3		861.2.i.f.739.13	yes	26
7.4	even	3		861.2.i.f.247.13	✓	26
7.6	odd	2		6027.2.a.bh.1.1		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.f.247.13	✓	26	7.4	even	3
861.2.i.f.739.13	yes	26	7.2	even	3
6027.2.a.bh.1.1		13	7.6	odd	2
6027.2.a.bi.1.1		13	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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.73393 q^{2} +1.00000 q^{3} +5.47440 q^{4} +2.29019 q^{5} -2.73393 q^{6} -9.49877 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.73393 q^{2} +1.00000 q^{3} +5.47440 q^{4} +2.29019 q^{5} -2.73393 q^{6} -9.49877 q^{8} +1.00000 q^{9} -6.26122 q^{10} -0.920136 q^{11} +5.47440 q^{12} -6.70791 q^{13} +2.29019 q^{15} +15.0202 q^{16} +3.80909 q^{17} -2.73393 q^{18} +6.56558 q^{19} +12.5374 q^{20} +2.51559 q^{22} -6.79688 q^{23} -9.49877 q^{24} +0.244953 q^{25} +18.3390 q^{26} +1.00000 q^{27} -4.96509 q^{29} -6.26122 q^{30} +1.14250 q^{31} -22.0668 q^{32} -0.920136 q^{33} -10.4138 q^{34} +5.47440 q^{36} -10.4608 q^{37} -17.9499 q^{38} -6.70791 q^{39} -21.7540 q^{40} +1.00000 q^{41} +3.89955 q^{43} -5.03719 q^{44} +2.29019 q^{45} +18.5822 q^{46} -11.0064 q^{47} +15.0202 q^{48} -0.669685 q^{50} +3.80909 q^{51} -36.7217 q^{52} +7.81643 q^{53} -2.73393 q^{54} -2.10728 q^{55} +6.56558 q^{57} +13.5742 q^{58} +0.168195 q^{59} +12.5374 q^{60} +14.4855 q^{61} -3.12352 q^{62} +30.2886 q^{64} -15.3624 q^{65} +2.51559 q^{66} +1.48503 q^{67} +20.8525 q^{68} -6.79688 q^{69} -6.79705 q^{71} -9.49877 q^{72} +4.20182 q^{73} +28.5991 q^{74} +0.244953 q^{75} +35.9426 q^{76} +18.3390 q^{78} +4.67401 q^{79} +34.3991 q^{80} +1.00000 q^{81} -2.73393 q^{82} -6.73979 q^{83} +8.72353 q^{85} -10.6611 q^{86} -4.96509 q^{87} +8.74016 q^{88} -8.78706 q^{89} -6.26122 q^{90} -37.2088 q^{92} +1.14250 q^{93} +30.0907 q^{94} +15.0364 q^{95} -22.0668 q^{96} +1.94754 q^{97} -0.920136 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 4 q^{2} + 13 q^{3} + 12 q^{4} - 8 q^{5} - 4 q^{6} - 12 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q - 4 * q^2 + 13 * q^3 + 12 * q^4 - 8 * q^5 - 4 * q^6 - 12 * q^8 + 13 * q^9	\( 13 q - 4 q^{2} + 13 q^{3} + 12 q^{4} - 8 q^{5} - 4 q^{6} - 12 q^{8} + 13 q^{9} - q^{10} - 10 q^{11} + 12 q^{12} - 16 q^{13} - 8 q^{15} + 26 q^{16} - 12 q^{17} - 4 q^{18} - 11 q^{19} - 6 q^{20} + q^{22} - 15 q^{23} - 12 q^{24} + 15 q^{25} - 18 q^{26} + 13 q^{27} - 8 q^{29} - q^{30} - 9 q^{31} - 23 q^{32} - 10 q^{33} + 7 q^{34} + 12 q^{36} - 2 q^{37} - 20 q^{38} - 16 q^{39} - 49 q^{40} + 13 q^{41} - 7 q^{43} - 22 q^{44} - 8 q^{45} - 4 q^{46} - 26 q^{47} + 26 q^{48} - 15 q^{50} - 12 q^{51} - 24 q^{52} + 4 q^{53} - 4 q^{54} - q^{55} - 11 q^{57} + 39 q^{58} + 3 q^{59} - 6 q^{60} - 28 q^{61} - 7 q^{62} + 2 q^{64} - 20 q^{65} + q^{66} + 7 q^{67} - 55 q^{68} - 15 q^{69} - 40 q^{71} - 12 q^{72} + 2 q^{73} + q^{74} + 15 q^{75} + 26 q^{76} - 18 q^{78} + 13 q^{79} - 22 q^{80} + 13 q^{81} - 4 q^{82} - 14 q^{83} + 48 q^{85} - 49 q^{86} - 8 q^{87} + 20 q^{88} - 35 q^{89} - q^{90} - 105 q^{92} - 9 q^{93} + 2 q^{94} + 7 q^{95} - 23 q^{96} - 64 q^{97} - 10 q^{99}+O(q^{100}) \) 13 * q - 4 * q^2 + 13 * q^3 + 12 * q^4 - 8 * q^5 - 4 * q^6 - 12 * q^8 + 13 * q^9 - q^10 - 10 * q^11 + 12 * q^12 - 16 * q^13 - 8 * q^15 + 26 * q^16 - 12 * q^17 - 4 * q^18 - 11 * q^19 - 6 * q^20 + q^22 - 15 * q^23 - 12 * q^24 + 15 * q^25 - 18 * q^26 + 13 * q^27 - 8 * q^29 - q^30 - 9 * q^31 - 23 * q^32 - 10 * q^33 + 7 * q^34 + 12 * q^36 - 2 * q^37 - 20 * q^38 - 16 * q^39 - 49 * q^40 + 13 * q^41 - 7 * q^43 - 22 * q^44 - 8 * q^45 - 4 * q^46 - 26 * q^47 + 26 * q^48 - 15 * q^50 - 12 * q^51 - 24 * q^52 + 4 * q^53 - 4 * q^54 - q^55 - 11 * q^57 + 39 * q^58 + 3 * q^59 - 6 * q^60 - 28 * q^61 - 7 * q^62 + 2 * q^64 - 20 * q^65 + q^66 + 7 * q^67 - 55 * q^68 - 15 * q^69 - 40 * q^71 - 12 * q^72 + 2 * q^73 + q^74 + 15 * q^75 + 26 * q^76 - 18 * q^78 + 13 * q^79 - 22 * q^80 + 13 * q^81 - 4 * q^82 - 14 * q^83 + 48 * q^85 - 49 * q^86 - 8 * q^87 + 20 * q^88 - 35 * q^89 - q^90 - 105 * q^92 - 9 * q^93 + 2 * q^94 + 7 * q^95 - 23 * q^96 - 64 * q^97 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more