LMFDB - Embedded newform 6027.2.a.be.1.6

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:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 11x^{8} + 56x^{7} + 26x^{6} - 266x^{5} + 52x^{4} + 526x^{3} - 255x^{2} - 372x + 239 $ x^10 - 4x^9 - 11x^8 + 56x^7 + 26x^6 - 266x^5 + 52x^4 + 526x^3 - 255x^2 - 372*x + 239
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.32624$ 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)

$f(q)$	$=$	$q+1.32624 q^{2} +1.00000 q^{3} -0.241096 q^{4} -0.903630 q^{5} +1.32624 q^{6} -2.97222 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.32624 q^{2} +1.00000 q^{3} -0.241096 q^{4} -0.903630 q^{5} +1.32624 q^{6} -2.97222 q^{8} +1.00000 q^{9} -1.19843 q^{10} -0.215437 q^{11} -0.241096 q^{12} +4.39375 q^{13} -0.903630 q^{15} -3.45968 q^{16} +7.88448 q^{17} +1.32624 q^{18} -6.94919 q^{19} +0.217861 q^{20} -0.285720 q^{22} +2.86954 q^{23} -2.97222 q^{24} -4.18345 q^{25} +5.82715 q^{26} +1.00000 q^{27} -4.84470 q^{29} -1.19843 q^{30} -4.36016 q^{31} +1.35609 q^{32} -0.215437 q^{33} +10.4567 q^{34} -0.241096 q^{36} +5.19593 q^{37} -9.21627 q^{38} +4.39375 q^{39} +2.68579 q^{40} +1.00000 q^{41} +11.4746 q^{43} +0.0519408 q^{44} -0.903630 q^{45} +3.80570 q^{46} -0.643892 q^{47} -3.45968 q^{48} -5.54825 q^{50} +7.88448 q^{51} -1.05931 q^{52} -1.87995 q^{53} +1.32624 q^{54} +0.194675 q^{55} -6.94919 q^{57} -6.42523 q^{58} +9.92968 q^{59} +0.217861 q^{60} +2.61168 q^{61} -5.78261 q^{62} +8.71786 q^{64} -3.97032 q^{65} -0.285720 q^{66} +13.5451 q^{67} -1.90091 q^{68} +2.86954 q^{69} +0.978400 q^{71} -2.97222 q^{72} +9.48157 q^{73} +6.89104 q^{74} -4.18345 q^{75} +1.67542 q^{76} +5.82715 q^{78} +10.6043 q^{79} +3.12627 q^{80} +1.00000 q^{81} +1.32624 q^{82} -9.10249 q^{83} -7.12465 q^{85} +15.2180 q^{86} -4.84470 q^{87} +0.640326 q^{88} -6.38298 q^{89} -1.19843 q^{90} -0.691834 q^{92} -4.36016 q^{93} -0.853954 q^{94} +6.27950 q^{95} +1.35609 q^{96} -9.92473 q^{97} -0.215437 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 10 q^{3} + 18 q^{4} + 6 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 + 10 * q^3 + 18 * q^4 + 6 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9	$ 10 q + 4 q^{2} + 10 q^{3} + 18 q^{4} + 6 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9} + 2 q^{10} - 2 q^{11} + 18 q^{12} + 6 q^{15} + 14 q^{16} + 8 q^{17} + 4 q^{18} + 6 q^{19} + 20 q^{20} + 2 q^{22} + 12 q^{24} + 10 q^{25} + 16 q^{26} + 10 q^{27} + 16 q^{29} + 2 q^{30} + 2 q^{31} + 38 q^{32} - 2 q^{33} - 4 q^{34} + 18 q^{36} + 24 q^{37} - 26 q^{38} + 40 q^{40} + 10 q^{41} + 8 q^{43} - 8 q^{44} + 6 q^{45} + 4 q^{46} - 8 q^{47} + 14 q^{48} + 44 q^{50} + 8 q^{51} - 30 q^{52} + 24 q^{53} + 4 q^{54} + 6 q^{57} - 14 q^{58} + 6 q^{59} + 20 q^{60} - 14 q^{61} - 2 q^{62} + 86 q^{64} + 28 q^{65} + 2 q^{66} + 26 q^{67} - 6 q^{68} + 14 q^{71} + 12 q^{72} - 36 q^{73} + 18 q^{74} + 10 q^{75} - 32 q^{76} + 16 q^{78} + 20 q^{79} + 70 q^{80} + 10 q^{81} + 4 q^{82} + 40 q^{83} + 24 q^{85} - 36 q^{86} + 16 q^{87} + 14 q^{88} + 2 q^{89} + 2 q^{90} + 8 q^{92} + 2 q^{93} - 54 q^{94} - 24 q^{95} + 38 q^{96} + 16 q^{97} - 2 q^{99}+O(q^{100}) $ 10 * q + 4 * q^2 + 10 * q^3 + 18 * q^4 + 6 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9 + 2 * q^10 - 2 * q^11 + 18 * q^12 + 6 * q^15 + 14 * q^16 + 8 * q^17 + 4 * q^18 + 6 * q^19 + 20 * q^20 + 2 * q^22 + 12 * q^24 + 10 * q^25 + 16 * q^26 + 10 * q^27 + 16 * q^29 + 2 * q^30 + 2 * q^31 + 38 * q^32 - 2 * q^33 - 4 * q^34 + 18 * q^36 + 24 * q^37 - 26 * q^38 + 40 * q^40 + 10 * q^41 + 8 * q^43 - 8 * q^44 + 6 * q^45 + 4 * q^46 - 8 * q^47 + 14 * q^48 + 44 * q^50 + 8 * q^51 - 30 * q^52 + 24 * q^53 + 4 * q^54 + 6 * q^57 - 14 * q^58 + 6 * q^59 + 20 * q^60 - 14 * q^61 - 2 * q^62 + 86 * q^64 + 28 * q^65 + 2 * q^66 + 26 * q^67 - 6 * q^68 + 14 * q^71 + 12 * q^72 - 36 * q^73 + 18 * q^74 + 10 * q^75 - 32 * q^76 + 16 * q^78 + 20 * q^79 + 70 * q^80 + 10 * q^81 + 4 * q^82 + 40 * q^83 + 24 * q^85 - 36 * q^86 + 16 * q^87 + 14 * q^88 + 2 * q^89 + 2 * q^90 + 8 * q^92 + 2 * q^93 - 54 * q^94 - 24 * q^95 + 38 * q^96 + 16 * 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 $

$2$	1.32624	0.937791	0.468896	−	0.883254i	$-0.344652\pi$
$2$	1.32624	0.937791	0.468896	+	0.883254i	$0.344652\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.241096	−0.120548
$5$	−0.903630	−0.404116	−0.202058	−	0.979374i	$-0.564763\pi$
$5$	−0.903630	−0.404116	−0.202058	+	0.979374i	$0.564763\pi$
$6$	1.32624	0.541434
$7$	0	0
$7$	0	0
$8$	−2.97222	−1.05084
$9$	1.00000	0.333333
$10$	−1.19843	−0.378976
$11$	−0.215437	−0.0649566	−0.0324783	−	0.999472i	$-0.510340\pi$
$11$	−0.215437	−0.0649566	−0.0324783	+	0.999472i	$0.510340\pi$
$12$	−0.241096	−0.0695983
$13$	4.39375	1.21861	0.609303	−	0.792937i	$-0.291449\pi$
$13$	4.39375	1.21861	0.609303	+	0.792937i	$0.291449\pi$
$14$	0	0
$15$	−0.903630	−0.233316
$16$	−3.45968	−0.864920
$17$	7.88448	1.91227	0.956133	−	0.292932i	$-0.0946308\pi$
$17$	7.88448	1.91227	0.956133	+	0.292932i	$0.0946308\pi$
$18$	1.32624	0.312597
$19$	−6.94919	−1.59425	−0.797126	−	0.603812i	$-0.793648\pi$
$19$	−6.94919	−1.59425	−0.797126	+	0.603812i	$0.793648\pi$
$20$	0.217861	0.0487153
$21$	0	0
$22$	−0.285720	−0.0609157
$23$	2.86954	0.598341	0.299171	−	0.954200i	$-0.403290\pi$
$23$	2.86954	0.598341	0.299171	+	0.954200i	$0.403290\pi$
$24$	−2.97222	−0.606703
$25$	−4.18345	−0.836690
$26$	5.82715	1.14280
$27$	1.00000	0.192450
$28$	0	0
$29$	−4.84470	−0.899639	−0.449819	−	0.893119i	$-0.648512\pi$
$29$	−4.84470	−0.899639	−0.449819	+	0.893119i	$0.648512\pi$
$30$	−1.19843	−0.218802
$31$	−4.36016	−0.783108	−0.391554	−	0.920155i	$-0.628062\pi$
$31$	−4.36016	−0.783108	−0.391554	+	0.920155i	$0.628062\pi$
$32$	1.35609	0.239725
$33$	−0.215437	−0.0375027
$34$	10.4567	1.79331
$35$	0	0
$36$	−0.241096	−0.0401826
$37$	5.19593	0.854206	0.427103	−	0.904203i	$-0.359534\pi$
$37$	5.19593	0.854206	0.427103	+	0.904203i	$0.359534\pi$
$38$	−9.21627	−1.49508
$39$	4.39375	0.703563
$40$	2.68579	0.424661
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	11.4746	1.74985	0.874927	−	0.484256i	$-0.160910\pi$
$43$	11.4746	1.74985	0.874927	+	0.484256i	$0.160910\pi$
$44$	0.0519408	0.00783037
$45$	−0.903630	−0.134705
$46$	3.80570	0.561119
$47$	−0.643892	−0.0939213	−0.0469607	−	0.998897i	$-0.514954\pi$
$47$	−0.643892	−0.0939213	−0.0469607	+	0.998897i	$0.514954\pi$
$48$	−3.45968	−0.499362
$49$	0	0
$50$	−5.54825	−0.784641
$51$	7.88448	1.10405
$52$	−1.05931	−0.146900
$53$	−1.87995	−0.258232	−0.129116	−	0.991630i	$-0.541214\pi$
$53$	−1.87995	−0.258232	−0.129116	+	0.991630i	$0.541214\pi$
$54$	1.32624	0.180478
$55$	0.194675	0.0262500
$56$	0	0
$57$	−6.94919	−0.920442
$58$	−6.42523	−0.843673
$59$	9.92968	1.29273	0.646367	−	0.763026i	$-0.276287\pi$
$59$	9.92968	1.29273	0.646367	+	0.763026i	$0.276287\pi$
$60$	0.217861	0.0281258
$61$	2.61168	0.334391	0.167195	−	0.985924i	$-0.446529\pi$
$61$	2.61168	0.334391	0.167195	+	0.985924i	$0.446529\pi$
$62$	−5.78261	−0.734392
$63$	0	0
$64$	8.71786	1.08973
$65$	−3.97032	−0.492458
$66$	−0.285720	−0.0351697
$67$	13.5451	1.65480	0.827401	−	0.561611i	$-0.189818\pi$
$67$	13.5451	1.65480	0.827401	+	0.561611i	$0.189818\pi$
$68$	−1.90091	−0.230520
$69$	2.86954	0.345453
$70$	0	0
$71$	0.978400	0.116115	0.0580573	−	0.998313i	$-0.481509\pi$
$71$	0.978400	0.116115	0.0580573	+	0.998313i	$0.481509\pi$
$72$	−2.97222	−0.350280
$73$	9.48157	1.10973	0.554867	−	0.831939i	$-0.312769\pi$
$73$	9.48157	1.10973	0.554867	+	0.831939i	$0.312769\pi$
$74$	6.89104	0.801067
$75$	−4.18345	−0.483063
$76$	1.67542	0.192184
$77$	0	0
$78$	5.82715	0.659795
$79$	10.6043	1.19307	0.596536	−	0.802586i	$-0.296543\pi$
$79$	10.6043	1.19307	0.596536	+	0.802586i	$0.296543\pi$
$80$	3.12627	0.349528
$81$	1.00000	0.111111
$82$	1.32624	0.146458
$83$	−9.10249	−0.999129	−0.499564	−	0.866277i	$-0.666507\pi$
$83$	−9.10249	−0.999129	−0.499564	+	0.866277i	$0.666507\pi$
$84$	0	0
$85$	−7.12465	−0.772777
$86$	15.2180	1.64100
$87$	−4.84470	−0.519407
$88$	0.640326	0.0682590
$89$	−6.38298	−0.676595	−0.338297	−	0.941039i	$-0.609851\pi$
$89$	−6.38298	−0.676595	−0.338297	+	0.941039i	$0.609851\pi$
$90$	−1.19843	−0.126325
$91$	0	0
$92$	−0.691834	−0.0721287
$93$	−4.36016	−0.452128
$94$	−0.853954	−0.0880786
$95$	6.27950	0.644263
$96$	1.35609	0.138405
$97$	−9.92473	−1.00770	−0.503852	−	0.863790i	$-0.668084\pi$
$97$	−9.92473	−1.00770	−0.503852	+	0.863790i	$0.668084\pi$
$98$	0	0
$99$	−0.215437	−0.0216522
$100$	1.00861	0.100861
$101$	−1.26362	−0.125735	−0.0628673	−	0.998022i	$-0.520024\pi$
$101$	−1.26362	−0.125735	−0.0628673	+	0.998022i	$0.520024\pi$
$102$	10.4567	1.03537
$103$	2.98031	0.293659	0.146829	−	0.989162i	$-0.453093\pi$
$103$	2.98031	0.293659	0.146829	+	0.989162i	$0.453093\pi$
$104$	−13.0592	−1.28056
$105$	0	0
$106$	−2.49327	−0.242167
$107$	7.10706	0.687066	0.343533	−	0.939141i	$-0.388376\pi$
$107$	7.10706	0.687066	0.343533	+	0.939141i	$0.388376\pi$
$108$	−0.241096	−0.0231994
$109$	16.1938	1.55108	0.775540	−	0.631298i	$-0.217478\pi$
$109$	16.1938	1.55108	0.775540	+	0.631298i	$0.217478\pi$
$110$	0.258185	0.0246170
$111$	5.19593	0.493176
$112$	0	0
$113$	5.43547	0.511326	0.255663	−	0.966766i	$-0.417706\pi$
$113$	5.43547	0.511326	0.255663	+	0.966766i	$0.417706\pi$
$114$	−9.21627	−0.863183
$115$	−2.59301	−0.241799
$116$	1.16804	0.108449
$117$	4.39375	0.406202
$118$	13.1691	1.21232
$119$	0	0
$120$	2.68579	0.245178
$121$	−10.9536	−0.995781
$122$	3.46370	0.313589
$123$	1.00000	0.0901670
$124$	1.05122	0.0944020
$125$	8.29845	0.742236
$126$	0	0
$127$	−8.08737	−0.717638	−0.358819	−	0.933407i	$-0.616821\pi$
$127$	−8.08737	−0.717638	−0.358819	+	0.933407i	$0.616821\pi$
$128$	8.84977	0.782216
$129$	11.4746	1.01028
$130$	−5.26559	−0.461823
$131$	−2.14995	−0.187842	−0.0939208	−	0.995580i	$-0.529940\pi$
$131$	−2.14995	−0.187842	−0.0939208	+	0.995580i	$0.529940\pi$
$132$	0.0519408	0.00452087
$133$	0	0
$134$	17.9641	1.55186
$135$	−0.903630	−0.0777721
$136$	−23.4344	−2.00949
$137$	4.74993	0.405814	0.202907	−	0.979198i	$-0.434961\pi$
$137$	4.74993	0.405814	0.202907	+	0.979198i	$0.434961\pi$
$138$	3.80570	0.323962
$139$	4.62192	0.392026	0.196013	−	0.980601i	$-0.437200\pi$
$139$	4.62192	0.392026	0.196013	+	0.980601i	$0.437200\pi$
$140$	0	0
$141$	−0.643892	−0.0542255
$142$	1.29759	0.108891
$143$	−0.946574	−0.0791565
$144$	−3.45968	−0.288307
$145$	4.37782	0.363558
$146$	12.5748	1.04070
$147$	0	0
$148$	−1.25272	−0.102973
$149$	−16.9602	−1.38944	−0.694718	−	0.719282i	$-0.744471\pi$
$149$	−16.9602	−1.38944	−0.694718	+	0.719282i	$0.744471\pi$
$150$	−5.54825	−0.453013
$151$	17.0675	1.38894	0.694468	−	0.719523i	$-0.255640\pi$
$151$	17.0675	1.38894	0.694468	+	0.719523i	$0.255640\pi$
$152$	20.6545	1.67530
$153$	7.88448	0.637422
$154$	0	0
$155$	3.93997	0.316466
$156$	−1.05931	−0.0848129
$157$	−17.6287	−1.40693	−0.703463	−	0.710732i	$-0.748364\pi$
$157$	−17.6287	−1.40693	−0.703463	+	0.710732i	$0.748364\pi$
$158$	14.0638	1.11885
$159$	−1.87995	−0.149090
$160$	−1.22540	−0.0968767
$161$	0	0
$162$	1.32624	0.104199
$163$	1.57864	0.123649	0.0618243	−	0.998087i	$-0.480308\pi$
$163$	1.57864	0.123649	0.0618243	+	0.998087i	$0.480308\pi$
$164$	−0.241096	−0.0188264
$165$	0.194675	0.0151554
$166$	−12.0721	−0.936974
$167$	−2.38357	−0.184446	−0.0922230	−	0.995738i	$-0.529397\pi$
$167$	−2.38357	−0.184446	−0.0922230	+	0.995738i	$0.529397\pi$
$168$	0	0
$169$	6.30501	0.485001
$170$	−9.44898	−0.724704
$171$	−6.94919	−0.531418
$172$	−2.76646	−0.210941
$173$	25.3677	1.92867	0.964335	−	0.264686i	$-0.0852685\pi$
$173$	25.3677	1.92867	0.964335	+	0.264686i	$0.0852685\pi$
$174$	−6.42523	−0.487095
$175$	0	0
$176$	0.745342	0.0561823
$177$	9.92968	0.746361
$178$	−8.46534	−0.634504
$179$	−7.55216	−0.564475	−0.282237	−	0.959345i	$-0.591077\pi$
$179$	−7.55216	−0.564475	−0.282237	+	0.959345i	$0.591077\pi$
$180$	0.217861	0.0162384
$181$	6.02737	0.448011	0.224005	−	0.974588i	$-0.428087\pi$
$181$	6.02737	0.448011	0.224005	+	0.974588i	$0.428087\pi$
$182$	0	0
$183$	2.61168	0.193061
$184$	−8.52893	−0.628761
$185$	−4.69520	−0.345198
$186$	−5.78261	−0.424001
$187$	−1.69861	−0.124214
$188$	0.155240	0.0113220
$189$	0	0
$190$	8.32810	0.604184
$191$	9.74507	0.705128	0.352564	−	0.935788i	$-0.385310\pi$
$191$	9.74507	0.705128	0.352564	+	0.935788i	$0.385310\pi$
$192$	8.71786	0.629157
$193$	25.0321	1.80185	0.900923	−	0.433978i	$-0.142891\pi$
$193$	25.0321	1.80185	0.900923	+	0.433978i	$0.142891\pi$
$194$	−13.1625	−0.945016
$195$	−3.97032	−0.284321
$196$	0	0
$197$	19.1663	1.36554	0.682772	−	0.730631i	$-0.260774\pi$
$197$	19.1663	1.36554	0.682772	+	0.730631i	$0.260774\pi$
$198$	−0.285720	−0.0203052
$199$	−10.3001	−0.730152	−0.365076	−	0.930978i	$-0.618957\pi$
$199$	−10.3001	−0.730152	−0.365076	+	0.930978i	$0.618957\pi$
$200$	12.4342	0.879228
$201$	13.5451	0.955400
$202$	−1.67586	−0.117913
$203$	0	0
$204$	−1.90091	−0.133091
$205$	−0.903630	−0.0631123
$206$	3.95260	0.275390
$207$	2.86954	0.199447
$208$	−15.2010	−1.05400
$209$	1.49711	0.103557
$210$	0	0
$211$	−23.1371	−1.59282	−0.796411	−	0.604756i	$-0.793271\pi$
$211$	−23.1371	−1.59282	−0.796411	+	0.604756i	$0.793271\pi$
$212$	0.453249	0.0311293
$213$	0.978400	0.0670388
$214$	9.42565	0.644324
$215$	−10.3688	−0.707143
$216$	−2.97222	−0.202234
$217$	0	0
$218$	21.4768	1.45459
$219$	9.48157	0.640705
$220$	−0.0469353	−0.00316438
$221$	34.6424	2.33030
$222$	6.89104	0.462496
$223$	18.4257	1.23388	0.616938	−	0.787012i	$-0.288373\pi$
$223$	18.4257	1.23388	0.616938	+	0.787012i	$0.288373\pi$
$224$	0	0
$225$	−4.18345	−0.278897
$226$	7.20872	0.479517
$227$	4.13746	0.274613	0.137307	−	0.990529i	$-0.456155\pi$
$227$	4.13746	0.274613	0.137307	+	0.990529i	$0.456155\pi$
$228$	1.67542	0.110957
$229$	−8.10981	−0.535912	−0.267956	−	0.963431i	$-0.586348\pi$
$229$	−8.10981	−0.535912	−0.267956	+	0.963431i	$0.586348\pi$
$230$	−3.43894	−0.226757
$231$	0	0
$232$	14.3995	0.945376
$233$	5.35817	0.351025	0.175513	−	0.984477i	$-0.443842\pi$
$233$	5.35817	0.351025	0.175513	+	0.984477i	$0.443842\pi$
$234$	5.82715	0.380933
$235$	0.581840	0.0379551
$236$	−2.39400	−0.155836
$237$	10.6043	0.688821
$238$	0	0
$239$	28.6504	1.85324	0.926621	−	0.375996i	$-0.122699\pi$
$239$	28.6504	1.85324	0.926621	+	0.375996i	$0.122699\pi$
$240$	3.12627	0.201800
$241$	18.5866	1.19727	0.598636	−	0.801021i	$-0.295710\pi$
$241$	18.5866	1.19727	0.598636	+	0.801021i	$0.295710\pi$
$242$	−14.5271	−0.933834
$243$	1.00000	0.0641500
$244$	−0.629664	−0.0403101
$245$	0	0
$246$	1.32624	0.0845578
$247$	−30.5330	−1.94277
$248$	12.9594	0.822921
$249$	−9.10249	−0.576847
$250$	11.0057	0.696062
$251$	−5.97228	−0.376967	−0.188484	−	0.982076i	$-0.560357\pi$
$251$	−5.97228	−0.376967	−0.188484	+	0.982076i	$0.560357\pi$
$252$	0	0
$253$	−0.618205	−0.0388662
$254$	−10.7258	−0.672995
$255$	−7.12465	−0.446163
$256$	−5.69883	−0.356177
$257$	−10.2788	−0.641175	−0.320587	−	0.947219i	$-0.603880\pi$
$257$	−10.2788	−0.641175	−0.320587	+	0.947219i	$0.603880\pi$
$258$	15.2180	0.947430
$259$	0	0
$260$	0.957227	0.0593647
$261$	−4.84470	−0.299880
$262$	−2.85134	−0.176156
$263$	26.7187	1.64755	0.823773	−	0.566920i	$-0.191865\pi$
$263$	26.7187	1.64755	0.823773	+	0.566920i	$0.191865\pi$
$264$	0.640326	0.0394093
$265$	1.69878	0.104355
$266$	0	0
$267$	−6.38298	−0.390632
$268$	−3.26567	−0.199483
$269$	30.4667	1.85759	0.928794	−	0.370597i	$-0.120847\pi$
$269$	30.4667	1.85759	0.928794	+	0.370597i	$0.120847\pi$
$270$	−1.19843	−0.0729340
$271$	−10.8647	−0.659985	−0.329992	−	0.943984i	$-0.607046\pi$
$271$	−10.8647	−0.659985	−0.329992	+	0.943984i	$0.607046\pi$
$272$	−27.2778	−1.65396
$273$	0	0
$274$	6.29953	0.380568
$275$	0.901269	0.0543485
$276$	−0.691834	−0.0416435
$277$	3.89451	0.233999	0.116999	−	0.993132i	$-0.462672\pi$
$277$	3.89451	0.233999	0.116999	+	0.993132i	$0.462672\pi$
$278$	6.12976	0.367639
$279$	−4.36016	−0.261036
$280$	0	0
$281$	9.57428	0.571154	0.285577	−	0.958356i	$-0.407815\pi$
$281$	9.57428	0.571154	0.285577	+	0.958356i	$0.407815\pi$
$282$	−0.853954	−0.0508522
$283$	11.9864	0.712520	0.356260	−	0.934387i	$-0.384052\pi$
$283$	11.9864	0.712520	0.356260	+	0.934387i	$0.384052\pi$
$284$	−0.235888	−0.0139974
$285$	6.27950	0.371965
$286$	−1.25538	−0.0742322
$287$	0	0
$288$	1.35609	0.0799084
$289$	45.1650	2.65676
$290$	5.80603	0.340942
$291$	−9.92473	−0.581798
$292$	−2.28596	−0.133776
$293$	−6.71477	−0.392281	−0.196140	−	0.980576i	$-0.562841\pi$
$293$	−6.71477	−0.392281	−0.196140	+	0.980576i	$0.562841\pi$
$294$	0	0
$295$	−8.97276	−0.522414
$296$	−15.4435	−0.897634
$297$	−0.215437	−0.0125009
$298$	−22.4933	−1.30300
$299$	12.6081	0.729142
$300$	1.00861	0.0582322
$301$	0	0
$302$	22.6356	1.30253
$303$	−1.26362	−0.0725929
$304$	24.0420	1.37890
$305$	−2.35999	−0.135133
$306$	10.4567	0.597769
$307$	−29.8411	−1.70312	−0.851562	−	0.524255i	$-0.824344\pi$
$307$	−29.8411	−1.70312	−0.851562	+	0.524255i	$0.824344\pi$
$308$	0	0
$309$	2.98031	0.169544
$310$	5.22534	0.296779
$311$	−13.2611	−0.751970	−0.375985	−	0.926626i	$-0.622696\pi$
$311$	−13.2611	−0.751970	−0.375985	+	0.926626i	$0.622696\pi$
$312$	−13.0592	−0.739332
$313$	−26.2366	−1.48298	−0.741489	−	0.670965i	$-0.765880\pi$
$313$	−26.2366	−1.48298	−0.741489	+	0.670965i	$0.765880\pi$
$314$	−23.3799	−1.31940
$315$	0	0
$316$	−2.55664	−0.143822
$317$	−6.00428	−0.337234	−0.168617	−	0.985682i	$-0.553930\pi$
$317$	−6.00428	−0.337234	−0.168617	+	0.985682i	$0.553930\pi$
$318$	−2.49327	−0.139815
$319$	1.04373	0.0584375
$320$	−7.87772	−0.440378
$321$	7.10706	0.396678
$322$	0	0
$323$	−54.7907	−3.04864
$324$	−0.241096	−0.0133942
$325$	−18.3810	−1.01960
$326$	2.09365	0.115957
$327$	16.1938	0.895517
$328$	−2.97222	−0.164114
$329$	0	0
$330$	0.258185	0.0142126
$331$	−20.4201	−1.12239	−0.561194	−	0.827684i	$-0.689658\pi$
$331$	−20.4201	−1.12239	−0.561194	+	0.827684i	$0.689658\pi$
$332$	2.19457	0.120443
$333$	5.19593	0.284735
$334$	−3.16117	−0.172972
$335$	−12.2398	−0.668732
$336$	0	0
$337$	−20.0542	−1.09242	−0.546211	−	0.837647i	$-0.683930\pi$
$337$	−20.0542	−1.09242	−0.546211	+	0.837647i	$0.683930\pi$
$338$	8.36194	0.454829
$339$	5.43547	0.295214
$340$	1.71772	0.0931566
$341$	0.939338	0.0508680
$342$	−9.21627	−0.498359
$343$	0	0
$344$	−34.1049	−1.83882
$345$	−2.59301	−0.139603
$346$	33.6436	1.80869
$347$	32.7373	1.75743	0.878715	−	0.477347i	$-0.158402\pi$
$347$	32.7373	1.75743	0.878715	+	0.477347i	$0.158402\pi$
$348$	1.16804	0.0626133
$349$	−0.0574302	−0.00307417	−0.00153708	−	0.999999i	$-0.500489\pi$
$349$	−0.0574302	−0.00307417	−0.00153708	+	0.999999i	$0.500489\pi$
$350$	0	0
$351$	4.39375	0.234521
$352$	−0.292151	−0.0155717
$353$	−0.486551	−0.0258965	−0.0129483	−	0.999916i	$-0.504122\pi$
$353$	−0.486551	−0.0258965	−0.0129483	+	0.999916i	$0.504122\pi$
$354$	13.1691	0.699931
$355$	−0.884111	−0.0469238
$356$	1.53891	0.0815620
$357$	0	0
$358$	−10.0160	−0.529360
$359$	−11.9174	−0.628978	−0.314489	−	0.949261i	$-0.601833\pi$
$359$	−11.9174	−0.628978	−0.314489	+	0.949261i	$0.601833\pi$
$360$	2.68579	0.141554
$361$	29.2912	1.54164
$362$	7.99372	0.420141
$363$	−10.9536	−0.574914
$364$	0	0
$365$	−8.56783	−0.448461
$366$	3.46370	0.181051
$367$	−28.8901	−1.50805	−0.754026	−	0.656845i	$-0.771891\pi$
$367$	−28.8901	−1.50805	−0.754026	+	0.656845i	$0.771891\pi$
$368$	−9.92771	−0.517518
$369$	1.00000	0.0520579
$370$	−6.22695	−0.323724
$371$	0	0
$372$	1.05122	0.0545030
$373$	5.71033	0.295670	0.147835	−	0.989012i	$-0.452770\pi$
$373$	5.71033	0.295670	0.147835	+	0.989012i	$0.452770\pi$
$374$	−2.25275	−0.116487
$375$	8.29845	0.428530
$376$	1.91379	0.0986963
$377$	−21.2864	−1.09631
$378$	0	0
$379$	15.1130	0.776302	0.388151	−	0.921596i	$-0.373114\pi$
$379$	15.1130	0.776302	0.388151	+	0.921596i	$0.373114\pi$
$380$	−1.51396	−0.0776644
$381$	−8.08737	−0.414329
$382$	12.9243	0.661263
$383$	−35.7518	−1.82683	−0.913416	−	0.407027i	$-0.866565\pi$
$383$	−35.7518	−1.82683	−0.913416	+	0.407027i	$0.866565\pi$
$384$	8.84977	0.451613
$385$	0	0
$386$	33.1984	1.68976
$387$	11.4746	0.583284
$388$	2.39281	0.121476
$389$	−32.5460	−1.65015	−0.825074	−	0.565025i	$-0.808867\pi$
$389$	−32.5460	−1.65015	−0.825074	+	0.565025i	$0.808867\pi$
$390$	−5.26559	−0.266633
$391$	22.6249	1.14419
$392$	0	0
$393$	−2.14995	−0.108450
$394$	25.4191	1.28060
$395$	−9.58233	−0.482140
$396$	0.0519408	0.00261012
$397$	26.1714	1.31351	0.656753	−	0.754106i	$-0.271929\pi$
$397$	26.1714	1.31351	0.656753	+	0.754106i	$0.271929\pi$
$398$	−13.6603	−0.684730
$399$	0	0
$400$	14.4734	0.723671
$401$	24.2772	1.21234	0.606172	−	0.795333i	$-0.292704\pi$
$401$	24.2772	1.21234	0.606172	+	0.795333i	$0.292704\pi$
$402$	17.9641	0.895966
$403$	−19.1574	−0.954300
$404$	0.304653	0.0151570
$405$	−0.903630	−0.0449017
$406$	0	0
$407$	−1.11939	−0.0554863
$408$	−23.4344	−1.16018
$409$	−2.40378	−0.118859	−0.0594296	−	0.998232i	$-0.518928\pi$
$409$	−2.40378	−0.118859	−0.0594296	+	0.998232i	$0.518928\pi$
$410$	−1.19843	−0.0591861
$411$	4.74993	0.234297
$412$	−0.718540	−0.0353999
$413$	0	0
$414$	3.80570	0.187040
$415$	8.22529	0.403764
$416$	5.95831	0.292130
$417$	4.62192	0.226336
$418$	1.98552	0.0971150
$419$	−13.1533	−0.642579	−0.321289	−	0.946981i	$-0.604116\pi$
$419$	−13.1533	−0.642579	−0.321289	+	0.946981i	$0.604116\pi$
$420$	0	0
$421$	30.7974	1.50097	0.750486	−	0.660886i	$-0.229819\pi$
$421$	30.7974	1.50097	0.750486	+	0.660886i	$0.229819\pi$
$422$	−30.6852	−1.49373
$423$	−0.643892	−0.0313071
$424$	5.58765	0.271360
$425$	−32.9843	−1.59998
$426$	1.29759	0.0628684
$427$	0	0
$428$	−1.71348	−0.0828242
$429$	−0.946574	−0.0457010
$430$	−13.7514	−0.663153
$431$	9.41915	0.453705	0.226852	−	0.973929i	$-0.427157\pi$
$431$	9.41915	0.453705	0.226852	+	0.973929i	$0.427157\pi$
$432$	−3.45968	−0.166454
$433$	0.269336	0.0129434	0.00647172	−	0.999979i	$-0.497940\pi$
$433$	0.269336	0.0129434	0.00647172	+	0.999979i	$0.497940\pi$
$434$	0	0
$435$	4.37782	0.209900
$436$	−3.90424	−0.186979
$437$	−19.9410	−0.953907
$438$	12.5748	0.600848
$439$	−29.4106	−1.40369	−0.701845	−	0.712330i	$-0.747640\pi$
$439$	−29.4106	−1.40369	−0.701845	+	0.712330i	$0.747640\pi$
$440$	−0.578618	−0.0275845
$441$	0	0
$442$	45.9440	2.18533
$443$	−16.2242	−0.770833	−0.385417	−	0.922743i	$-0.625942\pi$
$443$	−16.2242	−0.770833	−0.385417	+	0.922743i	$0.625942\pi$
$444$	−1.25272	−0.0594513
$445$	5.76785	0.273422
$446$	24.4368	1.15712
$447$	−16.9602	−0.802191
$448$	0	0
$449$	11.2100	0.529031	0.264516	−	0.964381i	$-0.414788\pi$
$449$	11.2100	0.529031	0.264516	+	0.964381i	$0.414788\pi$
$450$	−5.54825	−0.261547
$451$	−0.215437	−0.0101445
$452$	−1.31047	−0.0616392
$453$	17.0675	0.801903
$454$	5.48726	0.257530
$455$	0	0
$456$	20.6545	0.967237
$457$	−33.0572	−1.54635	−0.773174	−	0.634193i	$-0.781332\pi$
$457$	−33.0572	−1.54635	−0.773174	+	0.634193i	$0.781332\pi$
$458$	−10.7555	−0.502573
$459$	7.88448	0.368016
$460$	0.625162	0.0291484
$461$	−3.50480	−0.163235	−0.0816174	−	0.996664i	$-0.526009\pi$
$461$	−3.50480	−0.163235	−0.0816174	+	0.996664i	$0.526009\pi$
$462$	0	0
$463$	−18.2762	−0.849368	−0.424684	−	0.905342i	$-0.639615\pi$
$463$	−18.2762	−0.849368	−0.424684	+	0.905342i	$0.639615\pi$
$464$	16.7611	0.778116
$465$	3.93997	0.182712
$466$	7.10620	0.329189
$467$	−41.1735	−1.90528	−0.952642	−	0.304093i	$-0.901647\pi$
$467$	−41.1735	−1.90528	−0.952642	+	0.304093i	$0.901647\pi$
$468$	−1.05931	−0.0489668
$469$	0	0
$470$	0.771658	0.0355939
$471$	−17.6287	−0.812289
$472$	−29.5132	−1.35846
$473$	−2.47204	−0.113664
$474$	14.0638	0.645970
$475$	29.0716	1.33390
$476$	0	0
$477$	−1.87995	−0.0860772
$478$	37.9973	1.73795
$479$	39.0025	1.78207	0.891036	−	0.453933i	$-0.149979\pi$
$479$	39.0025	1.78207	0.891036	+	0.453933i	$0.149979\pi$
$480$	−1.22540	−0.0559318
$481$	22.8296	1.04094
$482$	24.6503	1.12279
$483$	0	0
$484$	2.64086	0.120039
$485$	8.96829	0.407229
$486$	1.32624	0.0601593
$487$	−13.4915	−0.611356	−0.305678	−	0.952135i	$-0.598883\pi$
$487$	−13.4915	−0.611356	−0.305678	+	0.952135i	$0.598883\pi$
$488$	−7.76249	−0.351391
$489$	1.57864	0.0713886
$490$	0	0
$491$	−26.1720	−1.18113	−0.590563	−	0.806992i	$-0.701094\pi$
$491$	−26.1720	−1.18113	−0.590563	+	0.806992i	$0.701094\pi$
$492$	−0.241096	−0.0108694
$493$	−38.1980	−1.72035
$494$	−40.4939	−1.82191
$495$	0.194675	0.00874999
$496$	15.0848	0.677326
$497$	0	0
$498$	−12.0721	−0.540962
$499$	−28.9355	−1.29533	−0.647666	−	0.761924i	$-0.724255\pi$
$499$	−28.9355	−1.29533	−0.647666	+	0.761924i	$0.724255\pi$
$500$	−2.00072	−0.0894749
$501$	−2.38357	−0.106490
$502$	−7.92066	−0.353516
$503$	4.58143	0.204276	0.102138	−	0.994770i	$-0.467432\pi$
$503$	4.58143	0.204276	0.102138	+	0.994770i	$0.467432\pi$
$504$	0	0
$505$	1.14184	0.0508114
$506$	−0.819886	−0.0364484
$507$	6.30501	0.280015
$508$	1.94983	0.0865097
$509$	−27.1220	−1.20216	−0.601080	−	0.799189i	$-0.705263\pi$
$509$	−27.1220	−1.20216	−0.601080	+	0.799189i	$0.705263\pi$
$510$	−9.44898	−0.418408
$511$	0	0
$512$	−25.2575	−1.11624
$513$	−6.94919	−0.306814
$514$	−13.6321	−0.601288
$515$	−2.69310	−0.118672
$516$	−2.76646	−0.121787
$517$	0.138718	0.00610081
$518$	0	0
$519$	25.3677	1.11352
$520$	11.8007	0.517494
$521$	23.2148	1.01706	0.508529	−	0.861045i	$-0.330190\pi$
$521$	23.2148	1.01706	0.508529	+	0.861045i	$0.330190\pi$
$522$	−6.42523	−0.281224
$523$	−24.2559	−1.06063	−0.530317	−	0.847799i	$-0.677927\pi$
$523$	−24.2559	−1.06063	−0.530317	+	0.847799i	$0.677927\pi$
$524$	0.518342	0.0226439
$525$	0	0
$526$	35.4353	1.54505
$527$	−34.3776	−1.49751
$528$	0.745342	0.0324368
$529$	−14.7657	−0.641988
$530$	2.25299	0.0978636
$531$	9.92968	0.430912
$532$	0	0
$533$	4.39375	0.190314
$534$	−8.46534	−0.366331
$535$	−6.42216	−0.277654
$536$	−40.2592	−1.73893
$537$	−7.55216	−0.325900
$538$	40.4061	1.74203
$539$	0	0
$540$	0.217861	0.00937526
$541$	−14.4341	−0.620571	−0.310286	−	0.950643i	$-0.600425\pi$
$541$	−14.4341	−0.620571	−0.310286	+	0.950643i	$0.600425\pi$
$542$	−14.4092	−0.618928
$543$	6.02737	0.258659
$544$	10.6921	0.458418
$545$	−14.6332	−0.626816
$546$	0	0
$547$	−32.1515	−1.37470	−0.687350	−	0.726326i	$-0.741226\pi$
$547$	−32.1515	−1.37470	−0.687350	+	0.726326i	$0.741226\pi$
$548$	−1.14519	−0.0489199
$549$	2.61168	0.111464
$550$	1.19530	0.0509676
$551$	33.6668	1.43425
$552$	−8.52893	−0.363015
$553$	0	0
$554$	5.16504	0.219442
$555$	−4.69520	−0.199300
$556$	−1.11432	−0.0472579
$557$	−19.0479	−0.807084	−0.403542	−	0.914961i	$-0.632221\pi$
$557$	−19.0479	−0.807084	−0.403542	+	0.914961i	$0.632221\pi$
$558$	−5.78261	−0.244797
$559$	50.4163	2.13238
$560$	0	0
$561$	−1.69861	−0.0717152
$562$	12.6978	0.535623
$563$	36.8047	1.55113	0.775566	−	0.631267i	$-0.217465\pi$
$563$	36.8047	1.55113	0.775566	+	0.631267i	$0.217465\pi$
$564$	0.155240	0.00653677
$565$	−4.91165	−0.206635
$566$	15.8969	0.668195
$567$	0	0
$568$	−2.90802	−0.122018
$569$	2.62085	0.109872	0.0549359	−	0.998490i	$-0.482505\pi$
$569$	2.62085	0.109872	0.0549359	+	0.998490i	$0.482505\pi$
$570$	8.32810	0.348826
$571$	−21.1316	−0.884330	−0.442165	−	0.896934i	$-0.645789\pi$
$571$	−21.1316	−0.884330	−0.442165	+	0.896934i	$0.645789\pi$
$572$	0.228215	0.00954214
$573$	9.74507	0.407106
$574$	0	0
$575$	−12.0046	−0.500626
$576$	8.71786	0.363244
$577$	4.01140	0.166997	0.0834983	−	0.996508i	$-0.473391\pi$
$577$	4.01140	0.166997	0.0834983	+	0.996508i	$0.473391\pi$
$578$	59.8995	2.49149
$579$	25.0321	1.04030
$580$	−1.05547	−0.0438261
$581$	0	0
$582$	−13.1625	−0.545605
$583$	0.405011	0.0167738
$584$	−28.1814	−1.16615
$585$	−3.97032	−0.164153
$586$	−8.90537	−0.367877
$587$	−5.11753	−0.211223	−0.105612	−	0.994407i	$-0.533680\pi$
$587$	−5.11753	−0.211223	−0.105612	+	0.994407i	$0.533680\pi$
$588$	0	0
$589$	30.2996	1.24847
$590$	−11.9000	−0.489916
$591$	19.1663	0.788397
$592$	−17.9763	−0.738820
$593$	13.1478	0.539915	0.269957	−	0.962872i	$-0.412990\pi$
$593$	13.1478	0.539915	0.269957	+	0.962872i	$0.412990\pi$
$594$	−0.285720	−0.0117232
$595$	0	0
$596$	4.08904	0.167493
$597$	−10.3001	−0.421553
$598$	16.7213	0.683783
$599$	−30.0137	−1.22633	−0.613164	−	0.789956i	$-0.710103\pi$
$599$	−30.0137	−1.22633	−0.613164	+	0.789956i	$0.710103\pi$
$600$	12.4342	0.507622
$601$	−6.10032	−0.248837	−0.124419	−	0.992230i	$-0.539707\pi$
$601$	−6.10032	−0.248837	−0.124419	+	0.992230i	$0.539707\pi$
$602$	0	0
$603$	13.5451	0.551601
$604$	−4.11491	−0.167433
$605$	9.89799	0.402411
$606$	−1.67586	−0.0680770
$607$	−13.5283	−0.549097	−0.274548	−	0.961573i	$-0.588528\pi$
$607$	−13.5283	−0.549097	−0.274548	+	0.961573i	$0.588528\pi$
$608$	−9.42372	−0.382182
$609$	0	0
$610$	−3.12991	−0.126726
$611$	−2.82910	−0.114453
$612$	−1.90091	−0.0768398
$613$	9.77539	0.394824	0.197412	−	0.980321i	$-0.436746\pi$
$613$	9.77539	0.394824	0.197412	+	0.980321i	$0.436746\pi$
$614$	−39.5764	−1.59717
$615$	−0.903630	−0.0364379
$616$	0	0
$617$	19.6651	0.791686	0.395843	−	0.918318i	$-0.370452\pi$
$617$	19.6651	0.791686	0.395843	+	0.918318i	$0.370452\pi$
$618$	3.95260	0.158997
$619$	−19.1835	−0.771050	−0.385525	−	0.922697i	$-0.625980\pi$
$619$	−19.1835	−0.771050	−0.385525	+	0.922697i	$0.625980\pi$
$620$	−0.949910	−0.0381493
$621$	2.86954	0.115151
$622$	−17.5874	−0.705190
$623$	0	0
$624$	−15.2010	−0.608526
$625$	13.4185	0.536741
$626$	−34.7959	−1.39072
$627$	1.49711	0.0597888
$628$	4.25021	0.169602
$629$	40.9672	1.63347
$630$	0	0
$631$	5.84041	0.232503	0.116252	−	0.993220i	$-0.462912\pi$
$631$	5.84041	0.232503	0.116252	+	0.993220i	$0.462912\pi$
$632$	−31.5182	−1.25373
$633$	−23.1371	−0.919616
$634$	−7.96309	−0.316255
$635$	7.30799	0.290009
$636$	0.453249	0.0179725
$637$	0	0
$638$	1.38423	0.0548021
$639$	0.978400	0.0387049
$640$	−7.99692	−0.316106
$641$	−25.9972	−1.02683	−0.513414	−	0.858141i	$-0.671620\pi$
$641$	−25.9972	−1.02683	−0.513414	+	0.858141i	$0.671620\pi$
$642$	9.42565	0.372001
$643$	−48.8910	−1.92807	−0.964036	−	0.265770i	$-0.914374\pi$
$643$	−48.8910	−1.92807	−0.964036	+	0.265770i	$0.914374\pi$
$644$	0	0
$645$	−10.3688	−0.408269
$646$	−72.6655	−2.85898
$647$	24.2591	0.953724	0.476862	−	0.878978i	$-0.341774\pi$
$647$	24.2591	0.953724	0.476862	+	0.878978i	$0.341774\pi$
$648$	−2.97222	−0.116760
$649$	−2.13922	−0.0839716
$650$	−24.3776	−0.956168
$651$	0	0
$652$	−0.380603	−0.0149056
$653$	32.6271	1.27680	0.638398	−	0.769707i	$-0.279597\pi$
$653$	32.6271	1.27680	0.638398	+	0.769707i	$0.279597\pi$
$654$	21.4768	0.839808
$655$	1.94276	0.0759098
$656$	−3.45968	−0.135078
$657$	9.48157	0.369911
$658$	0	0
$659$	45.8123	1.78459	0.892296	−	0.451450i	$-0.149093\pi$
$659$	45.8123	1.78459	0.892296	+	0.451450i	$0.149093\pi$
$660$	−0.0469353	−0.00182695
$661$	47.1834	1.83522	0.917610	−	0.397482i	$-0.130116\pi$
$661$	47.1834	1.83522	0.917610	+	0.397482i	$0.130116\pi$
$662$	−27.0819	−1.05257
$663$	34.6424	1.34540
$664$	27.0546	1.04992
$665$	0	0
$666$	6.89104	0.267022
$667$	−13.9021	−0.538291
$668$	0.574668	0.0222346
$669$	18.4257	0.712378
$670$	−16.2329	−0.627131
$671$	−0.562651	−0.0217209
$672$	0	0
$673$	−21.5537	−0.830833	−0.415417	−	0.909631i	$-0.636364\pi$
$673$	−21.5537	−0.830833	−0.415417	+	0.909631i	$0.636364\pi$
$674$	−26.5966	−1.02446
$675$	−4.18345	−0.161021
$676$	−1.52011	−0.0584658
$677$	11.7677	0.452271	0.226136	−	0.974096i	$-0.427391\pi$
$677$	11.7677	0.452271	0.226136	+	0.974096i	$0.427391\pi$
$678$	7.20872	0.276849
$679$	0	0
$680$	21.1761	0.812065
$681$	4.13746	0.158548
$682$	1.24579	0.0477036
$683$	46.5738	1.78210	0.891048	−	0.453909i	$-0.149971\pi$
$683$	46.5738	1.78210	0.891048	+	0.453909i	$0.149971\pi$
$684$	1.67542	0.0640612
$685$	−4.29218	−0.163996
$686$	0	0
$687$	−8.10981	−0.309409
$688$	−39.6983	−1.51348
$689$	−8.26005	−0.314683
$690$	−3.43894	−0.130918
$691$	11.6480	0.443110	0.221555	−	0.975148i	$-0.428887\pi$
$691$	11.6480	0.443110	0.221555	+	0.975148i	$0.428887\pi$
$692$	−6.11604	−0.232497
$693$	0	0
$694$	43.4174	1.64810
$695$	−4.17651	−0.158424
$696$	14.3995	0.545813
$697$	7.88448	0.298646
$698$	−0.0761661	−0.00288293
$699$	5.35817	0.202665
$700$	0	0
$701$	−28.2051	−1.06529	−0.532646	−	0.846338i	$-0.678802\pi$
$701$	−28.2051	−1.06529	−0.532646	+	0.846338i	$0.678802\pi$
$702$	5.82715	0.219932
$703$	−36.1075	−1.36182
$704$	−1.87815	−0.0707853
$705$	0.581840	0.0219134
$706$	−0.645282	−0.0242855
$707$	0	0
$708$	−2.39400	−0.0899721
$709$	−11.5566	−0.434017	−0.217008	−	0.976170i	$-0.569630\pi$
$709$	−11.5566	−0.434017	−0.217008	+	0.976170i	$0.569630\pi$
$710$	−1.17254	−0.0440047
$711$	10.6043	0.397691
$712$	18.9716	0.710992
$713$	−12.5117	−0.468566
$714$	0	0
$715$	0.855353	0.0319884
$716$	1.82079	0.0680462
$717$	28.6504	1.06997
$718$	−15.8053	−0.589850
$719$	−13.5921	−0.506898	−0.253449	−	0.967349i	$-0.581565\pi$
$719$	−13.5921	−0.506898	−0.253449	+	0.967349i	$0.581565\pi$
$720$	3.12627	0.116509
$721$	0	0
$722$	38.8471	1.44574
$723$	18.5866	0.691245
$724$	−1.45317	−0.0540067
$725$	20.2676	0.752719
$726$	−14.5271	−0.539149
$727$	−8.32332	−0.308695	−0.154348	−	0.988017i	$-0.549328\pi$
$727$	−8.32332	−0.308695	−0.154348	+	0.988017i	$0.549328\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−11.3630	−0.420563
$731$	90.4709	3.34619
$732$	−0.629664	−0.0232730
$733$	−30.0076	−1.10835	−0.554177	−	0.832399i	$-0.686967\pi$
$733$	−30.0076	−1.10835	−0.554177	+	0.832399i	$0.686967\pi$
$734$	−38.3151	−1.41424
$735$	0	0
$736$	3.89136	0.143437
$737$	−2.91812	−0.107490
$738$	1.32624	0.0488195
$739$	−28.2466	−1.03907	−0.519533	−	0.854450i	$-0.673894\pi$
$739$	−28.2466	−1.03907	−0.519533	+	0.854450i	$0.673894\pi$
$740$	1.13199	0.0416129
$741$	−30.5330	−1.12166
$742$	0	0
$743$	−45.2535	−1.66019	−0.830095	−	0.557623i	$-0.811714\pi$
$743$	−45.2535	−1.66019	−0.830095	+	0.557623i	$0.811714\pi$
$744$	12.9594	0.475114
$745$	15.3258	0.561493
$746$	7.57325	0.277277
$747$	−9.10249	−0.333043
$748$	0.409526	0.0149738
$749$	0	0
$750$	11.0057	0.401872
$751$	−17.3412	−0.632791	−0.316395	−	0.948627i	$-0.602473\pi$
$751$	−17.3412	−0.632791	−0.316395	+	0.948627i	$0.602473\pi$
$752$	2.22766	0.0812345
$753$	−5.97228	−0.217642
$754$	−28.2308	−1.02811
$755$	−15.4227	−0.561291
$756$	0	0
$757$	−14.9879	−0.544744	−0.272372	−	0.962192i	$-0.587808\pi$
$757$	−14.9879	−0.544744	−0.272372	+	0.962192i	$0.587808\pi$
$758$	20.0434	0.728010
$759$	−0.618205	−0.0224394
$760$	−18.6641	−0.677017
$761$	23.7391	0.860543	0.430272	−	0.902699i	$-0.358418\pi$
$761$	23.7391	0.860543	0.430272	+	0.902699i	$0.358418\pi$
$762$	−10.7258	−0.388554
$763$	0	0
$764$	−2.34949	−0.0850016
$765$	−7.12465	−0.257592
$766$	−47.4154	−1.71319
$767$	43.6285	1.57533
$768$	−5.69883	−0.205639
$769$	16.3470	0.589488	0.294744	−	0.955576i	$-0.404766\pi$
$769$	16.3470	0.589488	0.294744	+	0.955576i	$0.404766\pi$
$770$	0	0
$771$	−10.2788	−0.370183
$772$	−6.03512	−0.217209
$773$	−29.9422	−1.07695	−0.538473	−	0.842643i	$-0.680999\pi$
$773$	−29.9422	−1.07695	−0.538473	+	0.842643i	$0.680999\pi$
$774$	15.2180	0.546999
$775$	18.2405	0.655219
$776$	29.4985	1.05894
$777$	0	0
$778$	−43.1637	−1.54749
$779$	−6.94919	−0.248980
$780$	0.957227	0.0342742
$781$	−0.210783	−0.00754241
$782$	30.0059	1.07301
$783$	−4.84470	−0.173136
$784$	0	0
$785$	15.9298	0.568561
$786$	−2.85134	−0.101704
$787$	7.83527	0.279297	0.139649	−	0.990201i	$-0.455403\pi$
$787$	7.83527	0.279297	0.139649	+	0.990201i	$0.455403\pi$
$788$	−4.62092	−0.164613
$789$	26.7187	0.951211
$790$	−12.7084	−0.452146
$791$	0	0
$792$	0.640326	0.0227530
$793$	11.4750	0.407491
$794$	34.7095	1.23179
$795$	1.69878	0.0602497
$796$	2.48330	0.0880182
$797$	1.40098	0.0496254	0.0248127	−	0.999692i	$-0.492101\pi$
$797$	1.40098	0.0496254	0.0248127	+	0.999692i	$0.492101\pi$
$798$	0	0
$799$	−5.07675	−0.179603
$800$	−5.67314	−0.200576
$801$	−6.38298	−0.225532
$802$	32.1973	1.13693
$803$	−2.04268	−0.0720845
$804$	−3.26567	−0.115171
$805$	0	0
$806$	−25.4073	−0.894934
$807$	30.4667	1.07248
$808$	3.75575	0.132127
$809$	18.1826	0.639265	0.319633	−	0.947542i	$-0.396440\pi$
$809$	18.1826	0.639265	0.319633	+	0.947542i	$0.396440\pi$
$810$	−1.19843	−0.0421085
$811$	−49.1139	−1.72462	−0.862310	−	0.506380i	$-0.830983\pi$
$811$	−49.1139	−1.72462	−0.862310	+	0.506380i	$0.830983\pi$
$812$	0	0
$813$	−10.8647	−0.381042
$814$	−1.48458	−0.0520346
$815$	−1.42651	−0.0499684
$816$	−27.2778	−0.954913
$817$	−79.7388	−2.78971
$818$	−3.18798	−0.111465
$819$	0	0
$820$	0.217861	0.00760805
$821$	11.8200	0.412521	0.206260	−	0.978497i	$-0.433871\pi$
$821$	11.8200	0.412521	0.206260	+	0.978497i	$0.433871\pi$
$822$	6.29953	0.219721
$823$	−18.2077	−0.634680	−0.317340	−	0.948312i	$-0.602790\pi$
$823$	−18.2077	−0.634680	−0.317340	+	0.948312i	$0.602790\pi$
$824$	−8.85815	−0.308588
$825$	0.901269	0.0313781
$826$	0	0
$827$	−29.3741	−1.02144	−0.510718	−	0.859748i	$-0.670620\pi$
$827$	−29.3741	−1.02144	−0.510718	+	0.859748i	$0.670620\pi$
$828$	−0.691834	−0.0240429
$829$	−39.7415	−1.38028	−0.690140	−	0.723676i	$-0.742451\pi$
$829$	−39.7415	−1.38028	−0.690140	+	0.723676i	$0.742451\pi$
$830$	10.9087	0.378646
$831$	3.89451	0.135099
$832$	38.3041	1.32795
$833$	0	0
$834$	6.12976	0.212256
$835$	2.15386	0.0745375
$836$	−0.360946	−0.0124836
$837$	−4.36016	−0.150709
$838$	−17.4443	−0.602605
$839$	8.72265	0.301139	0.150570	−	0.988599i	$-0.451889\pi$
$839$	8.72265	0.301139	0.150570	+	0.988599i	$0.451889\pi$
$840$	0	0
$841$	−5.52884	−0.190650
$842$	40.8446	1.40760
$843$	9.57428	0.329756
$844$	5.57824	0.192011
$845$	−5.69740	−0.195996
$846$	−0.853954	−0.0293595
$847$	0	0
$848$	6.50405	0.223350
$849$	11.9864	0.411374
$850$	−43.7450	−1.50044
$851$	14.9100	0.511107
$852$	−0.235888	−0.00808138
$853$	−3.60943	−0.123585	−0.0617923	−	0.998089i	$-0.519682\pi$
$853$	−3.60943	−0.123585	−0.0617923	+	0.998089i	$0.519682\pi$
$854$	0	0
$855$	6.27950	0.214754
$856$	−21.1238	−0.721996
$857$	−35.4588	−1.21125	−0.605625	−	0.795750i	$-0.707077\pi$
$857$	−35.4588	−1.21125	−0.605625	+	0.795750i	$0.707077\pi$
$858$	−1.25538	−0.0428580
$859$	10.0643	0.343391	0.171695	−	0.985150i	$-0.445076\pi$
$859$	10.0643	0.343391	0.171695	+	0.985150i	$0.445076\pi$
$860$	2.49986	0.0852445
$861$	0	0
$862$	12.4920	0.425480
$863$	11.1068	0.378080	0.189040	−	0.981969i	$-0.439462\pi$
$863$	11.1068	0.378080	0.189040	+	0.981969i	$0.439462\pi$
$864$	1.35609	0.0461351
$865$	−22.9230	−0.779406
$866$	0.357203	0.0121382
$867$	45.1650	1.53388
$868$	0	0
$869$	−2.28455	−0.0774979
$870$	5.80603	0.196843
$871$	59.5139	2.01655
$872$	−48.1315	−1.62994
$873$	−9.92473	−0.335901
$874$	−26.4465	−0.894566
$875$	0	0
$876$	−2.28596	−0.0772356
$877$	13.9721	0.471806	0.235903	−	0.971777i	$-0.424195\pi$
$877$	13.9721	0.471806	0.235903	+	0.971777i	$0.424195\pi$
$878$	−39.0054	−1.31637
$879$	−6.71477	−0.226483
$880$	−0.673514	−0.0227041
$881$	51.0123	1.71865	0.859323	−	0.511433i	$-0.170885\pi$
$881$	51.0123	1.71865	0.859323	+	0.511433i	$0.170885\pi$
$882$	0	0
$883$	30.7434	1.03460	0.517299	−	0.855805i	$-0.326938\pi$
$883$	30.7434	1.03460	0.517299	+	0.855805i	$0.326938\pi$
$884$	−8.35213	−0.280913
$885$	−8.97276	−0.301616
$886$	−21.5171	−0.722881
$887$	20.6989	0.695002	0.347501	−	0.937680i	$-0.387030\pi$
$887$	20.6989	0.695002	0.347501	+	0.937680i	$0.387030\pi$
$888$	−15.4435	−0.518249
$889$	0	0
$890$	7.64954	0.256413
$891$	−0.215437	−0.00721740
$892$	−4.44235	−0.148741
$893$	4.47453	0.149734
$894$	−22.4933	−0.752288
$895$	6.82436	0.228113
$896$	0	0
$897$	12.6081	0.420971
$898$	14.8671	0.496121
$899$	21.1237	0.704515
$900$	1.00861	0.0336204
$901$	−14.8225	−0.493808
$902$	−0.285720	−0.00951343
$903$	0	0
$904$	−16.1554	−0.537322
$905$	−5.44651	−0.181048
$906$	22.6356	0.752018
$907$	−8.10539	−0.269135	−0.134568	−	0.990904i	$-0.542965\pi$
$907$	−8.10539	−0.269135	−0.134568	+	0.990904i	$0.542965\pi$
$908$	−0.997524	−0.0331040
$909$	−1.26362	−0.0419116
$910$	0	0
$911$	−46.1116	−1.52775	−0.763873	−	0.645366i	$-0.776705\pi$
$911$	−46.1116	−1.52775	−0.763873	+	0.645366i	$0.776705\pi$
$912$	24.0420	0.796109
$913$	1.96101	0.0649000
$914$	−43.8416	−1.45015
$915$	−2.35999	−0.0780189
$916$	1.95524	0.0646030
$917$	0	0
$918$	10.4567	0.345122
$919$	1.04637	0.0345167	0.0172583	−	0.999851i	$-0.494506\pi$
$919$	1.04637	0.0345167	0.0172583	+	0.999851i	$0.494506\pi$
$920$	7.70700	0.254092
$921$	−29.8411	−0.983299
$922$	−4.64819	−0.153080
$923$	4.29884	0.141498
$924$	0	0
$925$	−21.7369	−0.714706
$926$	−24.2386	−0.796529
$927$	2.98031	0.0978862
$928$	−6.56985	−0.215666
$929$	−14.8011	−0.485607	−0.242804	−	0.970075i	$-0.578067\pi$
$929$	−14.8011	−0.485607	−0.242804	+	0.970075i	$0.578067\pi$
$930$	5.22534	0.171346
$931$	0	0
$932$	−1.29183	−0.0423153
$933$	−13.2611	−0.434150
$934$	−54.6059	−1.78676
$935$	1.53491	0.0501970
$936$	−13.0592	−0.426853
$937$	32.9556	1.07661	0.538306	−	0.842749i	$-0.319064\pi$
$937$	32.9556	1.07661	0.538306	+	0.842749i	$0.319064\pi$
$938$	0	0
$939$	−26.2366	−0.856198
$940$	−0.140279	−0.00457540
$941$	−3.10169	−0.101112	−0.0505562	−	0.998721i	$-0.516099\pi$
$941$	−3.10169	−0.101112	−0.0505562	+	0.998721i	$0.516099\pi$
$942$	−23.3799	−0.761757
$943$	2.86954	0.0934452
$944$	−34.3535	−1.11811
$945$	0	0
$946$	−3.27851	−0.106594
$947$	−8.87354	−0.288351	−0.144176	−	0.989552i	$-0.546053\pi$
$947$	−8.87354	−0.288351	−0.144176	+	0.989552i	$0.546053\pi$
$948$	−2.55664	−0.0830358
$949$	41.6596	1.35233
$950$	38.5558	1.25092
$951$	−6.00428	−0.194702
$952$	0	0
$953$	26.6737	0.864046	0.432023	−	0.901863i	$-0.357800\pi$
$953$	26.6737	0.864046	0.432023	+	0.901863i	$0.357800\pi$
$954$	−2.49327	−0.0807225
$955$	−8.80594	−0.284953
$956$	−6.90749	−0.223404
$957$	1.04373	0.0337389
$958$	51.7266	1.67121
$959$	0	0
$960$	−7.87772	−0.254252
$961$	−11.9890	−0.386742
$962$	30.2775	0.976185
$963$	7.10706	0.229022
$964$	−4.48116	−0.144328
$965$	−22.6197	−0.728155
$966$	0	0
$967$	0.537499	0.0172848	0.00864241	−	0.999963i	$-0.497249\pi$
$967$	0.537499	0.0172848	0.00864241	+	0.999963i	$0.497249\pi$
$968$	32.5565	1.04641
$969$	−54.7907	−1.76013
$970$	11.8941	0.381896
$971$	29.9320	0.960565	0.480282	−	0.877114i	$-0.340534\pi$
$971$	29.9320	0.960565	0.480282	+	0.877114i	$0.340534\pi$
$972$	−0.241096	−0.00773314
$973$	0	0
$974$	−17.8929	−0.573325
$975$	−18.3810	−0.588664
$976$	−9.03557	−0.289222
$977$	−33.4972	−1.07167	−0.535836	−	0.844322i	$-0.680003\pi$
$977$	−33.4972	−1.07167	−0.535836	+	0.844322i	$0.680003\pi$
$978$	2.09365	0.0669476
$979$	1.37513	0.0439493
$980$	0	0
$981$	16.1938	0.517027
$982$	−34.7103	−1.10765
$983$	−41.0970	−1.31079	−0.655396	−	0.755285i	$-0.727498\pi$
$983$	−41.0970	−1.31079	−0.655396	+	0.755285i	$0.727498\pi$
$984$	−2.97222	−0.0947510
$985$	−17.3193	−0.551838
$986$	−50.6595	−1.61333
$987$	0	0
$988$	7.36136	0.234196
$989$	32.9267	1.04701
$990$	0.258185	0.00820566
$991$	12.1934	0.387335	0.193668	−	0.981067i	$-0.437962\pi$
$991$	12.1934	0.387335	0.193668	+	0.981067i	$0.437962\pi$
$992$	−5.91277	−0.187731
$993$	−20.4201	−0.648011
$994$	0	0
$995$	9.30744	0.295066
$996$	2.19457	0.0695376
$997$	−52.1158	−1.65052	−0.825262	−	0.564750i	$-0.808973\pi$
$997$	−52.1158	−1.65052	−0.825262	+	0.564750i	$0.808973\pi$
$998$	−38.3754	−1.21475
$999$	5.19593	0.164392

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.be.1.6	yes	10
7.6	odd	2		6027.2.a.bd.1.6	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bd.1.6	✓	10	7.6	odd	2
6027.2.a.be.1.6	yes	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q+1.32624 q^{2} +1.00000 q^{3} -0.241096 q^{4} -0.903630 q^{5} +1.32624 q^{6} -2.97222 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.32624 q^{2} +1.00000 q^{3} -0.241096 q^{4} -0.903630 q^{5} +1.32624 q^{6} -2.97222 q^{8} +1.00000 q^{9} -1.19843 q^{10} -0.215437 q^{11} -0.241096 q^{12} +4.39375 q^{13} -0.903630 q^{15} -3.45968 q^{16} +7.88448 q^{17} +1.32624 q^{18} -6.94919 q^{19} +0.217861 q^{20} -0.285720 q^{22} +2.86954 q^{23} -2.97222 q^{24} -4.18345 q^{25} +5.82715 q^{26} +1.00000 q^{27} -4.84470 q^{29} -1.19843 q^{30} -4.36016 q^{31} +1.35609 q^{32} -0.215437 q^{33} +10.4567 q^{34} -0.241096 q^{36} +5.19593 q^{37} -9.21627 q^{38} +4.39375 q^{39} +2.68579 q^{40} +1.00000 q^{41} +11.4746 q^{43} +0.0519408 q^{44} -0.903630 q^{45} +3.80570 q^{46} -0.643892 q^{47} -3.45968 q^{48} -5.54825 q^{50} +7.88448 q^{51} -1.05931 q^{52} -1.87995 q^{53} +1.32624 q^{54} +0.194675 q^{55} -6.94919 q^{57} -6.42523 q^{58} +9.92968 q^{59} +0.217861 q^{60} +2.61168 q^{61} -5.78261 q^{62} +8.71786 q^{64} -3.97032 q^{65} -0.285720 q^{66} +13.5451 q^{67} -1.90091 q^{68} +2.86954 q^{69} +0.978400 q^{71} -2.97222 q^{72} +9.48157 q^{73} +6.89104 q^{74} -4.18345 q^{75} +1.67542 q^{76} +5.82715 q^{78} +10.6043 q^{79} +3.12627 q^{80} +1.00000 q^{81} +1.32624 q^{82} -9.10249 q^{83} -7.12465 q^{85} +15.2180 q^{86} -4.84470 q^{87} +0.640326 q^{88} -6.38298 q^{89} -1.19843 q^{90} -0.691834 q^{92} -4.36016 q^{93} -0.853954 q^{94} +6.27950 q^{95} +1.35609 q^{96} -9.92473 q^{97} -0.215437 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 10 q^{3} + 18 q^{4} + 6 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 + 10 * q^3 + 18 * q^4 + 6 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9	\( 10 q + 4 q^{2} + 10 q^{3} + 18 q^{4} + 6 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9} + 2 q^{10} - 2 q^{11} + 18 q^{12} + 6 q^{15} + 14 q^{16} + 8 q^{17} + 4 q^{18} + 6 q^{19} + 20 q^{20} + 2 q^{22} + 12 q^{24} + 10 q^{25} + 16 q^{26} + 10 q^{27} + 16 q^{29} + 2 q^{30} + 2 q^{31} + 38 q^{32} - 2 q^{33} - 4 q^{34} + 18 q^{36} + 24 q^{37} - 26 q^{38} + 40 q^{40} + 10 q^{41} + 8 q^{43} - 8 q^{44} + 6 q^{45} + 4 q^{46} - 8 q^{47} + 14 q^{48} + 44 q^{50} + 8 q^{51} - 30 q^{52} + 24 q^{53} + 4 q^{54} + 6 q^{57} - 14 q^{58} + 6 q^{59} + 20 q^{60} - 14 q^{61} - 2 q^{62} + 86 q^{64} + 28 q^{65} + 2 q^{66} + 26 q^{67} - 6 q^{68} + 14 q^{71} + 12 q^{72} - 36 q^{73} + 18 q^{74} + 10 q^{75} - 32 q^{76} + 16 q^{78} + 20 q^{79} + 70 q^{80} + 10 q^{81} + 4 q^{82} + 40 q^{83} + 24 q^{85} - 36 q^{86} + 16 q^{87} + 14 q^{88} + 2 q^{89} + 2 q^{90} + 8 q^{92} + 2 q^{93} - 54 q^{94} - 24 q^{95} + 38 q^{96} + 16 q^{97} - 2 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + 10 * q^3 + 18 * q^4 + 6 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9 + 2 * q^10 - 2 * q^11 + 18 * q^12 + 6 * q^15 + 14 * q^16 + 8 * q^17 + 4 * q^18 + 6 * q^19 + 20 * q^20 + 2 * q^22 + 12 * q^24 + 10 * q^25 + 16 * q^26 + 10 * q^27 + 16 * q^29 + 2 * q^30 + 2 * q^31 + 38 * q^32 - 2 * q^33 - 4 * q^34 + 18 * q^36 + 24 * q^37 - 26 * q^38 + 40 * q^40 + 10 * q^41 + 8 * q^43 - 8 * q^44 + 6 * q^45 + 4 * q^46 - 8 * q^47 + 14 * q^48 + 44 * q^50 + 8 * q^51 - 30 * q^52 + 24 * q^53 + 4 * q^54 + 6 * q^57 - 14 * q^58 + 6 * q^59 + 20 * q^60 - 14 * q^61 - 2 * q^62 + 86 * q^64 + 28 * q^65 + 2 * q^66 + 26 * q^67 - 6 * q^68 + 14 * q^71 + 12 * q^72 - 36 * q^73 + 18 * q^74 + 10 * q^75 - 32 * q^76 + 16 * q^78 + 20 * q^79 + 70 * q^80 + 10 * q^81 + 4 * q^82 + 40 * q^83 + 24 * q^85 - 36 * q^86 + 16 * q^87 + 14 * q^88 + 2 * q^89 + 2 * q^90 + 8 * q^92 + 2 * q^93 - 54 * q^94 - 24 * q^95 + 38 * q^96 + 16 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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