LMFDB - Embedded newform 6027.2.a.bc.1.5

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:	$8$
Coefficient field:	8.8.7457527933.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 6x^{6} + 23x^{5} - 4x^{4} - 27x^{3} + 8x^{2} + 8x + 1 $ x^8 - 3x^7 - 6x^6 + 23x^5 - 4x^4 - 27x^3 + 8x^2 + 8*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
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			1.5
Root			$-0.169079$ 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)

$f(q)$	$=$	$q+1.62618 q^{2} +1.00000 q^{3} +0.644462 q^{4} +1.67363 q^{5} +1.62618 q^{6} -2.20435 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.62618 q^{2} +1.00000 q^{3} +0.644462 q^{4} +1.67363 q^{5} +1.62618 q^{6} -2.20435 q^{8} +1.00000 q^{9} +2.72162 q^{10} +2.72505 q^{11} +0.644462 q^{12} -2.59232 q^{13} +1.67363 q^{15} -4.87359 q^{16} +2.49455 q^{17} +1.62618 q^{18} -0.765400 q^{19} +1.07859 q^{20} +4.43142 q^{22} +1.55115 q^{23} -2.20435 q^{24} -2.19898 q^{25} -4.21557 q^{26} +1.00000 q^{27} +9.11743 q^{29} +2.72162 q^{30} +8.26914 q^{31} -3.51664 q^{32} +2.72505 q^{33} +4.05659 q^{34} +0.644462 q^{36} -3.21502 q^{37} -1.24468 q^{38} -2.59232 q^{39} -3.68926 q^{40} +1.00000 q^{41} +11.8356 q^{43} +1.75619 q^{44} +1.67363 q^{45} +2.52244 q^{46} +5.81113 q^{47} -4.87359 q^{48} -3.57593 q^{50} +2.49455 q^{51} -1.67065 q^{52} -4.59187 q^{53} +1.62618 q^{54} +4.56071 q^{55} -0.765400 q^{57} +14.8266 q^{58} -4.77304 q^{59} +1.07859 q^{60} -0.867396 q^{61} +13.4471 q^{62} +4.02849 q^{64} -4.33857 q^{65} +4.43142 q^{66} +3.89367 q^{67} +1.60764 q^{68} +1.55115 q^{69} -10.6283 q^{71} -2.20435 q^{72} +2.23945 q^{73} -5.22820 q^{74} -2.19898 q^{75} -0.493271 q^{76} -4.21557 q^{78} +8.10443 q^{79} -8.15657 q^{80} +1.00000 q^{81} +1.62618 q^{82} +8.58566 q^{83} +4.17495 q^{85} +19.2469 q^{86} +9.11743 q^{87} -6.00695 q^{88} +1.25617 q^{89} +2.72162 q^{90} +0.999655 q^{92} +8.26914 q^{93} +9.44994 q^{94} -1.28099 q^{95} -3.51664 q^{96} +8.55514 q^{97} +2.72505 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 8 q^{3} + 13 q^{4} + 7 q^{5} + q^{6} + 6 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + q^2 + 8 * q^3 + 13 * q^4 + 7 * q^5 + q^6 + 6 * q^8 + 8 * q^9	$ 8 q + q^{2} + 8 q^{3} + 13 q^{4} + 7 q^{5} + q^{6} + 6 q^{8} + 8 q^{9} + 8 q^{10} + 11 q^{11} + 13 q^{12} + 10 q^{13} + 7 q^{15} - 17 q^{16} + 3 q^{17} + q^{18} + 6 q^{19} + 11 q^{20} + 15 q^{22} + 14 q^{23} + 6 q^{24} + 25 q^{25} + 24 q^{26} + 8 q^{27} + 2 q^{29} + 8 q^{30} + 16 q^{31} + 3 q^{32} + 11 q^{33} - 4 q^{34} + 13 q^{36} - 20 q^{37} + 10 q^{38} + 10 q^{39} - 3 q^{40} + 8 q^{41} + 7 q^{43} + 7 q^{45} - 5 q^{46} + 14 q^{47} - 17 q^{48} - 5 q^{50} + 3 q^{51} + 23 q^{52} + 7 q^{53} + q^{54} + 48 q^{55} + 6 q^{57} - 20 q^{58} + 22 q^{59} + 11 q^{60} - 33 q^{62} - 10 q^{64} - 14 q^{65} + 15 q^{66} + 12 q^{67} - 27 q^{68} + 14 q^{69} - 5 q^{71} + 6 q^{72} + 2 q^{73} + 6 q^{74} + 25 q^{75} + 43 q^{76} + 24 q^{78} - 15 q^{79} - 7 q^{80} + 8 q^{81} + q^{82} + 15 q^{83} - 43 q^{85} + 31 q^{86} + 2 q^{87} + 17 q^{88} + 29 q^{89} + 8 q^{90} + 19 q^{92} + 16 q^{93} + 20 q^{94} + 14 q^{95} + 3 q^{96} + 19 q^{97} + 11 q^{99}+O(q^{100}) $ 8 * q + q^2 + 8 * q^3 + 13 * q^4 + 7 * q^5 + q^6 + 6 * q^8 + 8 * q^9 + 8 * q^10 + 11 * q^11 + 13 * q^12 + 10 * q^13 + 7 * q^15 - 17 * q^16 + 3 * q^17 + q^18 + 6 * q^19 + 11 * q^20 + 15 * q^22 + 14 * q^23 + 6 * q^24 + 25 * q^25 + 24 * q^26 + 8 * q^27 + 2 * q^29 + 8 * q^30 + 16 * q^31 + 3 * q^32 + 11 * q^33 - 4 * q^34 + 13 * q^36 - 20 * q^37 + 10 * q^38 + 10 * q^39 - 3 * q^40 + 8 * q^41 + 7 * q^43 + 7 * q^45 - 5 * q^46 + 14 * q^47 - 17 * q^48 - 5 * q^50 + 3 * q^51 + 23 * q^52 + 7 * q^53 + q^54 + 48 * q^55 + 6 * q^57 - 20 * q^58 + 22 * q^59 + 11 * q^60 - 33 * q^62 - 10 * q^64 - 14 * q^65 + 15 * q^66 + 12 * q^67 - 27 * q^68 + 14 * q^69 - 5 * q^71 + 6 * q^72 + 2 * q^73 + 6 * q^74 + 25 * q^75 + 43 * q^76 + 24 * q^78 - 15 * q^79 - 7 * q^80 + 8 * q^81 + q^82 + 15 * q^83 - 43 * q^85 + 31 * q^86 + 2 * q^87 + 17 * q^88 + 29 * q^89 + 8 * q^90 + 19 * q^92 + 16 * q^93 + 20 * q^94 + 14 * q^95 + 3 * q^96 + 19 * q^97 + 11 * 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 $

$2$	1.62618	1.14988	0.574942	−	0.818195i	$-0.305025\pi$
$2$	1.62618	1.14988	0.574942	+	0.818195i	$0.305025\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.644462	0.322231
$5$	1.67363	0.748468	0.374234	−	0.927334i	$-0.377906\pi$
$5$	1.67363	0.748468	0.374234	+	0.927334i	$0.377906\pi$
$6$	1.62618	0.663885
$7$	0	0
$7$	0	0
$8$	−2.20435	−0.779355
$9$	1.00000	0.333333
$10$	2.72162	0.860651
$11$	2.72505	0.821632	0.410816	−	0.911718i	$-0.365244\pi$
$11$	2.72505	0.821632	0.410816	+	0.911718i	$0.365244\pi$
$12$	0.644462	0.186040
$13$	−2.59232	−0.718979	−0.359490	−	0.933149i	$-0.617049\pi$
$13$	−2.59232	−0.718979	−0.359490	+	0.933149i	$0.617049\pi$
$14$	0	0
$15$	1.67363	0.432128
$16$	−4.87359	−1.21840
$17$	2.49455	0.605017	0.302509	−	0.953147i	$-0.402176\pi$
$17$	2.49455	0.605017	0.302509	+	0.953147i	$0.402176\pi$
$18$	1.62618	0.383294
$19$	−0.765400	−0.175595	−0.0877974	−	0.996138i	$-0.527983\pi$
$19$	−0.765400	−0.175595	−0.0877974	+	0.996138i	$0.527983\pi$
$20$	1.07859	0.241180
$21$	0	0
$22$	4.43142	0.944781
$23$	1.55115	0.323436	0.161718	−	0.986837i	$-0.448296\pi$
$23$	1.55115	0.323436	0.161718	+	0.986837i	$0.448296\pi$
$24$	−2.20435	−0.449961
$25$	−2.19898	−0.439795
$26$	−4.21557	−0.826742
$27$	1.00000	0.192450
$28$	0	0
$29$	9.11743	1.69306	0.846532	−	0.532338i	$-0.178687\pi$
$29$	9.11743	1.69306	0.846532	+	0.532338i	$0.178687\pi$
$30$	2.72162	0.496897
$31$	8.26914	1.48518	0.742591	−	0.669745i	$-0.233597\pi$
$31$	8.26914	1.48518	0.742591	+	0.669745i	$0.233597\pi$
$32$	−3.51664	−0.621660
$33$	2.72505	0.474370
$34$	4.05659	0.695699
$35$	0	0
$36$	0.644462	0.107410
$37$	−3.21502	−0.528546	−0.264273	−	0.964448i	$-0.585132\pi$
$37$	−3.21502	−0.528546	−0.264273	+	0.964448i	$0.585132\pi$
$38$	−1.24468	−0.201913
$39$	−2.59232	−0.415103
$40$	−3.68926	−0.583323
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	11.8356	1.80492	0.902458	−	0.430778i	$-0.141761\pi$
$43$	11.8356	1.80492	0.902458	+	0.430778i	$0.141761\pi$
$44$	1.75619	0.264755
$45$	1.67363	0.249489
$46$	2.52244	0.371914
$47$	5.81113	0.847640	0.423820	−	0.905746i	$-0.360689\pi$
$47$	5.81113	0.847640	0.423820	+	0.905746i	$0.360689\pi$
$48$	−4.87359	−0.703443
$49$	0	0
$50$	−3.57593	−0.505713
$51$	2.49455	0.349307
$52$	−1.67065	−0.231677
$53$	−4.59187	−0.630742	−0.315371	−	0.948968i	$-0.602129\pi$
$53$	−4.59187	−0.630742	−0.315371	+	0.948968i	$0.602129\pi$
$54$	1.62618	0.221295
$55$	4.56071	0.614966
$56$	0	0
$57$	−0.765400	−0.101380
$58$	14.8266	1.94682
$59$	−4.77304	−0.621397	−0.310698	−	0.950509i	$-0.600563\pi$
$59$	−4.77304	−0.621397	−0.310698	+	0.950509i	$0.600563\pi$
$60$	1.07859	0.139245
$61$	−0.867396	−0.111059	−0.0555293	−	0.998457i	$-0.517685\pi$
$61$	−0.867396	−0.111059	−0.0555293	+	0.998457i	$0.517685\pi$
$62$	13.4471	1.70779
$63$	0	0
$64$	4.02849	0.503562
$65$	−4.33857	−0.538133
$66$	4.43142	0.545470
$67$	3.89367	0.475688	0.237844	−	0.971303i	$-0.423559\pi$
$67$	3.89367	0.475688	0.237844	+	0.971303i	$0.423559\pi$
$68$	1.60764	0.194955
$69$	1.55115	0.186736
$70$	0	0
$71$	−10.6283	−1.26135	−0.630675	−	0.776047i	$-0.717222\pi$
$71$	−10.6283	−1.26135	−0.630675	+	0.776047i	$0.717222\pi$
$72$	−2.20435	−0.259785
$73$	2.23945	0.262107	0.131054	−	0.991375i	$-0.458164\pi$
$73$	2.23945	0.262107	0.131054	+	0.991375i	$0.458164\pi$
$74$	−5.22820	−0.607766
$75$	−2.19898	−0.253916
$76$	−0.493271	−0.0565821
$77$	0	0
$78$	−4.21557	−0.477320
$79$	8.10443	0.911819	0.455910	−	0.890026i	$-0.349314\pi$
$79$	8.10443	0.911819	0.455910	+	0.890026i	$0.349314\pi$
$80$	−8.15657	−0.911933
$81$	1.00000	0.111111
$82$	1.62618	0.179582
$83$	8.58566	0.942398	0.471199	−	0.882027i	$-0.343821\pi$
$83$	8.58566	0.942398	0.471199	+	0.882027i	$0.343821\pi$
$84$	0	0
$85$	4.17495	0.452836
$86$	19.2469	2.07544
$87$	9.11743	0.977491
$88$	−6.00695	−0.640343
$89$	1.25617	0.133154	0.0665770	−	0.997781i	$-0.478792\pi$
$89$	1.25617	0.133154	0.0665770	+	0.997781i	$0.478792\pi$
$90$	2.72162	0.286884
$91$	0	0
$92$	0.999655	0.104221
$93$	8.26914	0.857470
$94$	9.44994	0.974687
$95$	−1.28099	−0.131427
$96$	−3.51664	−0.358916
$97$	8.55514	0.868643	0.434322	−	0.900758i	$-0.356988\pi$
$97$	8.55514	0.868643	0.434322	+	0.900758i	$0.356988\pi$
$98$	0	0
$99$	2.72505	0.273877
$100$	−1.41716	−0.141716
$101$	1.30829	0.130179	0.0650896	−	0.997879i	$-0.479267\pi$
$101$	1.30829	0.130179	0.0650896	+	0.997879i	$0.479267\pi$
$102$	4.05659	0.401662
$103$	15.8139	1.55819	0.779097	−	0.626903i	$-0.215678\pi$
$103$	15.8139	1.55819	0.779097	+	0.626903i	$0.215678\pi$
$104$	5.71437	0.560340
$105$	0	0
$106$	−7.46721	−0.725279
$107$	6.65637	0.643495	0.321748	−	0.946825i	$-0.395730\pi$
$107$	6.65637	0.643495	0.321748	+	0.946825i	$0.395730\pi$
$108$	0.644462	0.0620134
$109$	6.62737	0.634787	0.317393	−	0.948294i	$-0.397192\pi$
$109$	6.62737	0.634787	0.317393	+	0.948294i	$0.397192\pi$
$110$	7.41653	0.707139
$111$	−3.21502	−0.305156
$112$	0	0
$113$	−17.6805	−1.66324	−0.831621	−	0.555343i	$-0.812587\pi$
$113$	−17.6805	−1.66324	−0.831621	+	0.555343i	$0.812587\pi$
$114$	−1.24468	−0.116575
$115$	2.59604	0.242082
$116$	5.87583	0.545557
$117$	−2.59232	−0.239660
$118$	−7.76182	−0.714534
$119$	0	0
$120$	−3.68926	−0.336781
$121$	−3.57412	−0.324920
$122$	−1.41054	−0.127705
$123$	1.00000	0.0901670
$124$	5.32915	0.478572
$125$	−12.0484	−1.07764
$126$	0	0
$127$	−15.6503	−1.38874	−0.694371	−	0.719617i	$-0.744317\pi$
$127$	−15.6503	−1.38874	−0.694371	+	0.719617i	$0.744317\pi$
$128$	13.5843	1.20070
$129$	11.8356	1.04207
$130$	−7.05529	−0.618790
$131$	9.62811	0.841212	0.420606	−	0.907243i	$-0.361818\pi$
$131$	9.62811	0.841212	0.420606	+	0.907243i	$0.361818\pi$
$132$	1.75619	0.152857
$133$	0	0
$134$	6.33181	0.546985
$135$	1.67363	0.144043
$136$	−5.49886	−0.471523
$137$	−3.87928	−0.331429	−0.165715	−	0.986174i	$-0.552993\pi$
$137$	−3.87928	−0.331429	−0.165715	+	0.986174i	$0.552993\pi$
$138$	2.52244	0.214725
$139$	12.8314	1.08834	0.544171	−	0.838975i	$-0.316844\pi$
$139$	12.8314	1.08834	0.544171	+	0.838975i	$0.316844\pi$
$140$	0	0
$141$	5.81113	0.489385
$142$	−17.2836	−1.45041
$143$	−7.06418	−0.590737
$144$	−4.87359	−0.406133
$145$	15.2592	1.26720
$146$	3.64174	0.301393
$147$	0	0
$148$	−2.07196	−0.170314
$149$	0.448719	0.0367605	0.0183802	−	0.999831i	$-0.494149\pi$
$149$	0.448719	0.0367605	0.0183802	+	0.999831i	$0.494149\pi$
$150$	−3.57593	−0.291973
$151$	−3.57359	−0.290815	−0.145408	−	0.989372i	$-0.546449\pi$
$151$	−3.57359	−0.290815	−0.145408	+	0.989372i	$0.546449\pi$
$152$	1.68721	0.136851
$153$	2.49455	0.201672
$154$	0	0
$155$	13.8395	1.11161
$156$	−1.67065	−0.133759
$157$	8.91606	0.711579	0.355790	−	0.934566i	$-0.384212\pi$
$157$	8.91606	0.711579	0.355790	+	0.934566i	$0.384212\pi$
$158$	13.1793	1.04849
$159$	−4.59187	−0.364159
$160$	−5.88554	−0.465293
$161$	0	0
$162$	1.62618	0.127765
$163$	−24.4870	−1.91797	−0.958984	−	0.283459i	$-0.908518\pi$
$163$	−24.4870	−1.91797	−0.958984	+	0.283459i	$0.908518\pi$
$164$	0.644462	0.0503240
$165$	4.56071	0.355051
$166$	13.9618	1.08365
$167$	0.708918	0.0548577	0.0274289	−	0.999624i	$-0.491268\pi$
$167$	0.708918	0.0548577	0.0274289	+	0.999624i	$0.491268\pi$
$168$	0	0
$169$	−6.27990	−0.483069
$170$	6.78921	0.520709
$171$	−0.765400	−0.0585316
$172$	7.62761	0.581600
$173$	2.97877	0.226472	0.113236	−	0.993568i	$-0.463878\pi$
$173$	2.97877	0.226472	0.113236	+	0.993568i	$0.463878\pi$
$174$	14.8266	1.12400
$175$	0	0
$176$	−13.2808	−1.00108
$177$	−4.77304	−0.358764
$178$	2.04276	0.153111
$179$	−20.8395	−1.55762	−0.778810	−	0.627260i	$-0.784176\pi$
$179$	−20.8395	−1.55762	−0.778810	+	0.627260i	$0.784176\pi$
$180$	1.07859	0.0803932
$181$	−5.73956	−0.426618	−0.213309	−	0.976985i	$-0.568424\pi$
$181$	−5.73956	−0.426618	−0.213309	+	0.976985i	$0.568424\pi$
$182$	0	0
$183$	−0.867396	−0.0641198
$184$	−3.41927	−0.252072
$185$	−5.38074	−0.395600
$186$	13.4471	0.985991
$187$	6.79777	0.497102
$188$	3.74505	0.273136
$189$	0	0
$190$	−2.08313	−0.151126
$191$	−2.63706	−0.190811	−0.0954055	−	0.995438i	$-0.530415\pi$
$191$	−2.63706	−0.190811	−0.0954055	+	0.995438i	$0.530415\pi$
$192$	4.02849	0.290731
$193$	−0.711941	−0.0512467	−0.0256233	−	0.999672i	$-0.508157\pi$
$193$	−0.711941	−0.0512467	−0.0256233	+	0.999672i	$0.508157\pi$
$194$	13.9122	0.998838
$195$	−4.33857	−0.310691
$196$	0	0
$197$	−17.2730	−1.23065	−0.615323	−	0.788275i	$-0.710975\pi$
$197$	−17.2730	−1.23065	−0.615323	+	0.788275i	$0.710975\pi$
$198$	4.43142	0.314927
$199$	3.51338	0.249057	0.124529	−	0.992216i	$-0.460258\pi$
$199$	3.51338	0.249057	0.124529	+	0.992216i	$0.460258\pi$
$200$	4.84731	0.342757
$201$	3.89367	0.274638
$202$	2.12751	0.149691
$203$	0	0
$204$	1.60764	0.112558
$205$	1.67363	0.116891
$206$	25.7163	1.79174
$207$	1.55115	0.107812
$208$	12.6339	0.876003
$209$	−2.08575	−0.144274
$210$	0	0
$211$	2.04162	0.140551	0.0702756	−	0.997528i	$-0.477612\pi$
$211$	2.04162	0.140551	0.0702756	+	0.997528i	$0.477612\pi$
$212$	−2.95929	−0.203245
$213$	−10.6283	−0.728241
$214$	10.8244	0.739944
$215$	19.8084	1.35092
$216$	−2.20435	−0.149987
$217$	0	0
$218$	10.7773	0.729930
$219$	2.23945	0.151328
$220$	2.93920	0.198161
$221$	−6.46666	−0.434995
$222$	−5.22820	−0.350894
$223$	16.3846	1.09719	0.548597	−	0.836087i	$-0.315162\pi$
$223$	16.3846	1.09719	0.548597	+	0.836087i	$0.315162\pi$
$224$	0	0
$225$	−2.19898	−0.146598
$226$	−28.7517	−1.91253
$227$	−29.8662	−1.98229	−0.991146	−	0.132780i	$-0.957610\pi$
$227$	−29.8662	−1.98229	−0.991146	+	0.132780i	$0.957610\pi$
$228$	−0.493271	−0.0326677
$229$	−24.3750	−1.61075	−0.805374	−	0.592767i	$-0.798035\pi$
$229$	−24.3750	−1.61075	−0.805374	+	0.592767i	$0.798035\pi$
$230$	4.22163	0.278366
$231$	0	0
$232$	−20.0980	−1.31950
$233$	4.83770	0.316928	0.158464	−	0.987365i	$-0.449346\pi$
$233$	4.83770	0.316928	0.158464	+	0.987365i	$0.449346\pi$
$234$	−4.21557	−0.275581
$235$	9.72566	0.634432
$236$	−3.07604	−0.200233
$237$	8.10443	0.526439
$238$	0	0
$239$	−4.59128	−0.296985	−0.148493	−	0.988914i	$-0.547442\pi$
$239$	−4.59128	−0.296985	−0.148493	+	0.988914i	$0.547442\pi$
$240$	−8.15657	−0.526504
$241$	0.322023	0.0207433	0.0103717	−	0.999946i	$-0.496699\pi$
$241$	0.322023	0.0207433	0.0103717	+	0.999946i	$0.496699\pi$
$242$	−5.81217	−0.373620
$243$	1.00000	0.0641500
$244$	−0.559004	−0.0357866
$245$	0	0
$246$	1.62618	0.103681
$247$	1.98416	0.126249
$248$	−18.2281	−1.15748
$249$	8.58566	0.544094
$250$	−19.5929	−1.23916
$251$	−8.39485	−0.529878	−0.264939	−	0.964265i	$-0.585352\pi$
$251$	−8.39485	−0.529878	−0.264939	+	0.964265i	$0.585352\pi$
$252$	0	0
$253$	4.22695	0.265746
$254$	−25.4502	−1.59689
$255$	4.17495	0.261445
$256$	14.0336	0.877100
$257$	21.5104	1.34178	0.670892	−	0.741555i	$-0.265911\pi$
$257$	21.5104	1.34178	0.670892	+	0.741555i	$0.265911\pi$
$258$	19.2469	1.19826
$259$	0	0
$260$	−2.79604	−0.173403
$261$	9.11743	0.564354
$262$	15.6570	0.967295
$263$	15.4590	0.953240	0.476620	−	0.879109i	$-0.341862\pi$
$263$	15.4590	0.953240	0.476620	+	0.879109i	$0.341862\pi$
$264$	−6.00695	−0.369702
$265$	−7.68507	−0.472090
$266$	0	0
$267$	1.25617	0.0768765
$268$	2.50932	0.153281
$269$	21.3937	1.30440	0.652199	−	0.758048i	$-0.273847\pi$
$269$	21.3937	1.30440	0.652199	+	0.758048i	$0.273847\pi$
$270$	2.72162	0.165632
$271$	−7.41776	−0.450597	−0.225298	−	0.974290i	$-0.572336\pi$
$271$	−7.41776	−0.450597	−0.225298	+	0.974290i	$0.572336\pi$
$272$	−12.1574	−0.737152
$273$	0	0
$274$	−6.30841	−0.381105
$275$	−5.99231	−0.361350
$276$	0.999655	0.0601722
$277$	−23.9735	−1.44043	−0.720215	−	0.693751i	$-0.755957\pi$
$277$	−23.9735	−1.44043	−0.720215	+	0.693751i	$0.755957\pi$
$278$	20.8661	1.25147
$279$	8.26914	0.495061
$280$	0	0
$281$	11.7067	0.698366	0.349183	−	0.937055i	$-0.386459\pi$
$281$	11.7067	0.698366	0.349183	+	0.937055i	$0.386459\pi$
$282$	9.44994	0.562736
$283$	−13.5001	−0.802496	−0.401248	−	0.915969i	$-0.631423\pi$
$283$	−13.5001	−0.802496	−0.401248	+	0.915969i	$0.631423\pi$
$284$	−6.84955	−0.406446
$285$	−1.28099	−0.0758795
$286$	−11.4876	−0.679278
$287$	0	0
$288$	−3.51664	−0.207220
$289$	−10.7772	−0.633954
$290$	24.8141	1.45714
$291$	8.55514	0.501511
$292$	1.44324	0.0844591
$293$	−21.3767	−1.24884	−0.624419	−	0.781089i	$-0.714664\pi$
$293$	−21.3767	−1.24884	−0.624419	+	0.781089i	$0.714664\pi$
$294$	0	0
$295$	−7.98828	−0.465096
$296$	7.08703	0.411925
$297$	2.72505	0.158123
$298$	0.729698	0.0422703
$299$	−4.02106	−0.232544
$300$	−1.41716	−0.0818195
$301$	0	0
$302$	−5.81131	−0.334403
$303$	1.30829	0.0751590
$304$	3.73025	0.213944
$305$	−1.45170	−0.0831239
$306$	4.05659	0.231900
$307$	25.7934	1.47211	0.736053	−	0.676924i	$-0.236688\pi$
$307$	25.7934	1.47211	0.736053	+	0.676924i	$0.236688\pi$
$308$	0	0
$309$	15.8139	0.899624
$310$	22.5054	1.27822
$311$	4.24169	0.240524	0.120262	−	0.992742i	$-0.461626\pi$
$311$	4.24169	0.240524	0.120262	+	0.992742i	$0.461626\pi$
$312$	5.71437	0.323512
$313$	6.77432	0.382907	0.191453	−	0.981502i	$-0.438680\pi$
$313$	6.77432	0.382907	0.191453	+	0.981502i	$0.438680\pi$
$314$	14.4991	0.818233
$315$	0	0
$316$	5.22300	0.293816
$317$	33.6214	1.88836	0.944182	−	0.329423i	$-0.106854\pi$
$317$	33.6214	1.88836	0.944182	+	0.329423i	$0.106854\pi$
$318$	−7.46721	−0.418740
$319$	24.8454	1.39108
$320$	6.74219	0.376900
$321$	6.65637	0.371522
$322$	0	0
$323$	−1.90933	−0.106238
$324$	0.644462	0.0358034
$325$	5.70044	0.316203
$326$	−39.8202	−2.20544
$327$	6.62737	0.366494
$328$	−2.20435	−0.121715
$329$	0	0
$330$	7.41653	0.408267
$331$	29.0356	1.59594	0.797970	−	0.602698i	$-0.205907\pi$
$331$	29.0356	1.59594	0.797970	+	0.602698i	$0.205907\pi$
$332$	5.53313	0.303670
$333$	−3.21502	−0.176182
$334$	1.15283	0.0630800
$335$	6.51655	0.356037
$336$	0	0
$337$	−14.5845	−0.794471	−0.397235	−	0.917717i	$-0.630030\pi$
$337$	−14.5845	−0.794471	−0.397235	+	0.917717i	$0.630030\pi$
$338$	−10.2122	−0.555473
$339$	−17.6805	−0.960274
$340$	2.69059	0.145918
$341$	22.5338	1.22027
$342$	−1.24468	−0.0673045
$343$	0	0
$344$	−26.0898	−1.40667
$345$	2.59604	0.139766
$346$	4.84402	0.260416
$347$	−19.9558	−1.07128	−0.535641	−	0.844446i	$-0.679930\pi$
$347$	−19.9558	−1.07128	−0.535641	+	0.844446i	$0.679930\pi$
$348$	5.87583	0.314978
$349$	28.9751	1.55100	0.775500	−	0.631348i	$-0.217498\pi$
$349$	28.9751	1.55100	0.775500	+	0.631348i	$0.217498\pi$
$350$	0	0
$351$	−2.59232	−0.138368
$352$	−9.58301	−0.510776
$353$	15.3168	0.815231	0.407615	−	0.913154i	$-0.366360\pi$
$353$	15.3168	0.815231	0.407615	+	0.913154i	$0.366360\pi$
$354$	−7.76182	−0.412536
$355$	−17.7878	−0.944081
$356$	0.809555	0.0429063
$357$	0	0
$358$	−33.8888	−1.79108
$359$	−21.6773	−1.14409	−0.572043	−	0.820224i	$-0.693849\pi$
$359$	−21.6773	−1.14409	−0.572043	+	0.820224i	$0.693849\pi$
$360$	−3.68926	−0.194441
$361$	−18.4142	−0.969166
$362$	−9.33355	−0.490561
$363$	−3.57412	−0.187593
$364$	0	0
$365$	3.74800	0.196179
$366$	−1.41054	−0.0737302
$367$	−14.0689	−0.734388	−0.367194	−	0.930144i	$-0.619681\pi$
$367$	−14.0689	−0.734388	−0.367194	+	0.930144i	$0.619681\pi$
$368$	−7.55966	−0.394074
$369$	1.00000	0.0520579
$370$	−8.75006	−0.454894
$371$	0	0
$372$	5.32915	0.276304
$373$	21.1728	1.09629	0.548143	−	0.836384i	$-0.315335\pi$
$373$	21.1728	1.09629	0.548143	+	0.836384i	$0.315335\pi$
$374$	11.0544	0.571609
$375$	−12.0484	−0.622176
$376$	−12.8098	−0.660613
$377$	−23.6352	−1.21728
$378$	0	0
$379$	0.272209	0.0139824	0.00699122	−	0.999976i	$-0.497775\pi$
$379$	0.272209	0.0139824	0.00699122	+	0.999976i	$0.497775\pi$
$380$	−0.825551	−0.0423499
$381$	−15.6503	−0.801790
$382$	−4.28833	−0.219410
$383$	−14.7319	−0.752767	−0.376384	−	0.926464i	$-0.622833\pi$
$383$	−14.7319	−0.752767	−0.376384	+	0.926464i	$0.622833\pi$
$384$	13.5843	0.693223
$385$	0	0
$386$	−1.15774	−0.0589277
$387$	11.8356	0.601639
$388$	5.51347	0.279904
$389$	3.29845	0.167238	0.0836189	−	0.996498i	$-0.473352\pi$
$389$	3.29845	0.167238	0.0836189	+	0.996498i	$0.473352\pi$
$390$	−7.05529	−0.357259
$391$	3.86941	0.195685
$392$	0	0
$393$	9.62811	0.485674
$394$	−28.0889	−1.41510
$395$	13.5638	0.682468
$396$	1.75619	0.0882518
$397$	−1.85602	−0.0931509	−0.0465755	−	0.998915i	$-0.514831\pi$
$397$	−1.85602	−0.0931509	−0.0465755	+	0.998915i	$0.514831\pi$
$398$	5.71340	0.286387
$399$	0	0
$400$	10.7169	0.535846
$401$	15.9025	0.794133	0.397067	−	0.917790i	$-0.370028\pi$
$401$	15.9025	0.794133	0.397067	+	0.917790i	$0.370028\pi$
$402$	6.33181	0.315802
$403$	−21.4362	−1.06781
$404$	0.843140	0.0419478
$405$	1.67363	0.0831632
$406$	0	0
$407$	−8.76108	−0.434271
$408$	−5.49886	−0.272234
$409$	4.62449	0.228666	0.114333	−	0.993442i	$-0.463527\pi$
$409$	4.62449	0.228666	0.114333	+	0.993442i	$0.463527\pi$
$410$	2.72162	0.134411
$411$	−3.87928	−0.191351
$412$	10.1915	0.502099
$413$	0	0
$414$	2.52244	0.123971
$415$	14.3692	0.705355
$416$	9.11625	0.446961
$417$	12.8314	0.628354
$418$	−3.39180	−0.165899
$419$	−28.4534	−1.39004	−0.695019	−	0.718991i	$-0.744604\pi$
$419$	−28.4534	−1.39004	−0.695019	+	0.718991i	$0.744604\pi$
$420$	0	0
$421$	−36.4418	−1.77607	−0.888033	−	0.459780i	$-0.847928\pi$
$421$	−36.4418	−1.77607	−0.888033	+	0.459780i	$0.847928\pi$
$422$	3.32005	0.161617
$423$	5.81113	0.282547
$424$	10.1221	0.491572
$425$	−5.48546	−0.266084
$426$	−17.2836	−0.837392
$427$	0	0
$428$	4.28977	0.207354
$429$	−7.06418	−0.341062
$430$	32.2120	1.55340
$431$	−7.43000	−0.357890	−0.178945	−	0.983859i	$-0.557268\pi$
$431$	−7.43000	−0.357890	−0.178945	+	0.983859i	$0.557268\pi$
$432$	−4.87359	−0.234481
$433$	−13.8996	−0.667972	−0.333986	−	0.942578i	$-0.608394\pi$
$433$	−13.8996	−0.667972	−0.333986	+	0.942578i	$0.608394\pi$
$434$	0	0
$435$	15.2592	0.731621
$436$	4.27109	0.204548
$437$	−1.18725	−0.0567937
$438$	3.64174	0.174009
$439$	9.09943	0.434292	0.217146	−	0.976139i	$-0.430325\pi$
$439$	9.09943	0.434292	0.217146	+	0.976139i	$0.430325\pi$
$440$	−10.0534	−0.479277
$441$	0	0
$442$	−10.5160	−0.500193
$443$	26.9631	1.28106	0.640529	−	0.767934i	$-0.278715\pi$
$443$	26.9631	1.28106	0.640529	+	0.767934i	$0.278715\pi$
$444$	−2.07196	−0.0983308
$445$	2.10236	0.0996615
$446$	26.6443	1.26164
$447$	0.448719	0.0212237
$448$	0	0
$449$	16.8277	0.794149	0.397074	−	0.917786i	$-0.370025\pi$
$449$	16.8277	0.794149	0.397074	+	0.917786i	$0.370025\pi$
$450$	−3.57593	−0.168571
$451$	2.72505	0.128317
$452$	−11.3944	−0.535948
$453$	−3.57359	−0.167902
$454$	−48.5679	−2.27940
$455$	0	0
$456$	1.68721	0.0790107
$457$	22.1206	1.03476	0.517379	−	0.855756i	$-0.326908\pi$
$457$	22.1206	1.03476	0.517379	+	0.855756i	$0.326908\pi$
$458$	−39.6382	−1.85217
$459$	2.49455	0.116436
$460$	1.67305	0.0780063
$461$	−35.2027	−1.63955	−0.819776	−	0.572684i	$-0.805902\pi$
$461$	−35.2027	−1.63955	−0.819776	+	0.572684i	$0.805902\pi$
$462$	0	0
$463$	−20.0710	−0.932777	−0.466389	−	0.884580i	$-0.654445\pi$
$463$	−20.0710	−0.932777	−0.466389	+	0.884580i	$0.654445\pi$
$464$	−44.4346	−2.06283
$465$	13.8395	0.641789
$466$	7.86698	0.364431
$467$	−22.8854	−1.05901	−0.529505	−	0.848307i	$-0.677622\pi$
$467$	−22.8854	−1.05901	−0.529505	+	0.848307i	$0.677622\pi$
$468$	−1.67065	−0.0772258
$469$	0	0
$470$	15.8157	0.729523
$471$	8.91606	0.410831
$472$	10.5214	0.484289
$473$	32.2526	1.48298
$474$	13.1793	0.605344
$475$	1.68309	0.0772257
$476$	0	0
$477$	−4.59187	−0.210247
$478$	−7.46625	−0.341498
$479$	−20.5080	−0.937036	−0.468518	−	0.883454i	$-0.655212\pi$
$479$	−20.5080	−0.937036	−0.468518	+	0.883454i	$0.655212\pi$
$480$	−5.88554	−0.268637
$481$	8.33435	0.380014
$482$	0.523668	0.0238524
$483$	0	0
$484$	−2.30339	−0.104699
$485$	14.3181	0.650152
$486$	1.62618	0.0737650
$487$	−4.07372	−0.184598	−0.0922989	−	0.995731i	$-0.529422\pi$
$487$	−4.07372	−0.184598	−0.0922989	+	0.995731i	$0.529422\pi$
$488$	1.91204	0.0865542
$489$	−24.4870	−1.10734
$490$	0	0
$491$	−6.31242	−0.284876	−0.142438	−	0.989804i	$-0.545494\pi$
$491$	−6.31242	−0.284876	−0.142438	+	0.989804i	$0.545494\pi$
$492$	0.644462	0.0290546
$493$	22.7439	1.02433
$494$	3.22660	0.145172
$495$	4.56071	0.204989
$496$	−40.3004	−1.80954
$497$	0	0
$498$	13.9618	0.625644
$499$	37.4975	1.67862	0.839310	−	0.543653i	$-0.182959\pi$
$499$	37.4975	1.67862	0.839310	+	0.543653i	$0.182959\pi$
$500$	−7.76473	−0.347249
$501$	0.708918	0.0316721
$502$	−13.6515	−0.609298
$503$	28.7997	1.28411	0.642056	−	0.766657i	$-0.278081\pi$
$503$	28.7997	1.28411	0.642056	+	0.766657i	$0.278081\pi$
$504$	0	0
$505$	2.18958	0.0974351
$506$	6.87378	0.305577
$507$	−6.27990	−0.278900
$508$	−10.0860	−0.447496
$509$	2.76539	0.122574	0.0612869	−	0.998120i	$-0.480480\pi$
$509$	2.76539	0.122574	0.0612869	+	0.998120i	$0.480480\pi$
$510$	6.78921	0.300631
$511$	0	0
$512$	−4.34752	−0.192135
$513$	−0.765400	−0.0337932
$514$	34.9798	1.54289
$515$	26.4666	1.16626
$516$	7.62761	0.335787
$517$	15.8356	0.696449
$518$	0	0
$519$	2.97877	0.130754
$520$	9.56372	0.419397
$521$	−4.05204	−0.177523	−0.0887616	−	0.996053i	$-0.528291\pi$
$521$	−4.05204	−0.177523	−0.0887616	+	0.996053i	$0.528291\pi$
$522$	14.8266	0.648942
$523$	4.28644	0.187433	0.0937165	−	0.995599i	$-0.470125\pi$
$523$	4.28644	0.187433	0.0937165	+	0.995599i	$0.470125\pi$
$524$	6.20495	0.271064
$525$	0	0
$526$	25.1391	1.09611
$527$	20.6278	0.898561
$528$	−13.2808	−0.577971
$529$	−20.5939	−0.895389
$530$	−12.4973	−0.542849
$531$	−4.77304	−0.207132
$532$	0	0
$533$	−2.59232	−0.112286
$534$	2.04276	0.0883989
$535$	11.1403	0.481636
$536$	−8.58301	−0.370730
$537$	−20.8395	−0.899292
$538$	34.7900	1.49991
$539$	0	0
$540$	1.07859	0.0464151
$541$	−41.5910	−1.78814	−0.894069	−	0.447929i	$-0.852162\pi$
$541$	−41.5910	−1.78814	−0.894069	+	0.447929i	$0.852162\pi$
$542$	−12.0626	−0.518134
$543$	−5.73956	−0.246308
$544$	−8.77244	−0.376115
$545$	11.0917	0.475118
$546$	0	0
$547$	−33.4461	−1.43005	−0.715025	−	0.699099i	$-0.753585\pi$
$547$	−33.4461	−1.43005	−0.715025	+	0.699099i	$0.753585\pi$
$548$	−2.50005	−0.106797
$549$	−0.867396	−0.0370196
$550$	−9.74458	−0.415510
$551$	−6.97847	−0.297293
$552$	−3.41927	−0.145534
$553$	0	0
$554$	−38.9853	−1.65633
$555$	−5.38074	−0.228400
$556$	8.26932	0.350697
$557$	21.7753	0.922651	0.461326	−	0.887231i	$-0.347374\pi$
$557$	21.7753	0.922651	0.461326	+	0.887231i	$0.347374\pi$
$558$	13.4471	0.569262
$559$	−30.6817	−1.29770
$560$	0	0
$561$	6.79777	0.287002
$562$	19.0373	0.803039
$563$	−41.0426	−1.72974	−0.864871	−	0.501995i	$-0.832600\pi$
$563$	−41.0426	−1.72974	−0.864871	+	0.501995i	$0.832600\pi$
$564$	3.74505	0.157695
$565$	−29.5906	−1.24488
$566$	−21.9536	−0.922777
$567$	0	0
$568$	23.4285	0.983040
$569$	12.9575	0.543206	0.271603	−	0.962409i	$-0.412446\pi$
$569$	12.9575	0.543206	0.271603	+	0.962409i	$0.412446\pi$
$570$	−2.08313	−0.0872525
$571$	36.8468	1.54199	0.770994	−	0.636842i	$-0.219760\pi$
$571$	36.8468	1.54199	0.770994	+	0.636842i	$0.219760\pi$
$572$	−4.55260	−0.190354
$573$	−2.63706	−0.110165
$574$	0	0
$575$	−3.41093	−0.142246
$576$	4.02849	0.167854
$577$	−46.7470	−1.94610	−0.973051	−	0.230589i	$-0.925935\pi$
$577$	−46.7470	−1.94610	−0.973051	+	0.230589i	$0.925935\pi$
$578$	−17.5257	−0.728973
$579$	−0.711941	−0.0295873
$580$	9.83395	0.408333
$581$	0	0
$582$	13.9122	0.576680
$583$	−12.5131	−0.518238
$584$	−4.93652	−0.204275
$585$	−4.33857	−0.179378
$586$	−34.7623	−1.43602
$587$	−23.0958	−0.953266	−0.476633	−	0.879102i	$-0.658143\pi$
$587$	−23.0958	−0.953266	−0.476633	+	0.879102i	$0.658143\pi$
$588$	0	0
$589$	−6.32920	−0.260790
$590$	−12.9904	−0.534806
$591$	−17.2730	−0.710514
$592$	15.6687	0.643980
$593$	37.8823	1.55564	0.777820	−	0.628487i	$-0.216326\pi$
$593$	37.8823	1.55564	0.777820	+	0.628487i	$0.216326\pi$
$594$	4.43142	0.181823
$595$	0	0
$596$	0.289182	0.0118454
$597$	3.51338	0.143793
$598$	−6.53897	−0.267398
$599$	−23.6611	−0.966767	−0.483384	−	0.875409i	$-0.660592\pi$
$599$	−23.6611	−0.966767	−0.483384	+	0.875409i	$0.660592\pi$
$600$	4.84731	0.197891
$601$	−47.3526	−1.93155	−0.965776	−	0.259377i	$-0.916483\pi$
$601$	−47.3526	−1.93155	−0.965776	+	0.259377i	$0.916483\pi$
$602$	0	0
$603$	3.89367	0.158563
$604$	−2.30305	−0.0937096
$605$	−5.98175	−0.243193
$606$	2.12751	0.0864241
$607$	11.0182	0.447216	0.223608	−	0.974679i	$-0.428216\pi$
$607$	11.0182	0.447216	0.223608	+	0.974679i	$0.428216\pi$
$608$	2.69164	0.109160
$609$	0	0
$610$	−2.36072	−0.0955828
$611$	−15.0643	−0.609436
$612$	1.60764	0.0649851
$613$	28.6531	1.15729	0.578643	−	0.815581i	$-0.303582\pi$
$613$	28.6531	1.15729	0.578643	+	0.815581i	$0.303582\pi$
$614$	41.9447	1.69275
$615$	1.67363	0.0674871
$616$	0	0
$617$	−19.7501	−0.795109	−0.397554	−	0.917579i	$-0.630141\pi$
$617$	−19.7501	−0.795109	−0.397554	+	0.917579i	$0.630141\pi$
$618$	25.7163	1.03446
$619$	23.5838	0.947912	0.473956	−	0.880549i	$-0.342826\pi$
$619$	23.5838	0.947912	0.473956	+	0.880549i	$0.342826\pi$
$620$	8.91900	0.358196
$621$	1.55115	0.0622454
$622$	6.89776	0.276575
$623$	0	0
$624$	12.6339	0.505760
$625$	−9.16963	−0.366785
$626$	11.0163	0.440298
$627$	−2.08575	−0.0832968
$628$	5.74606	0.229293
$629$	−8.02003	−0.319780
$630$	0	0
$631$	−9.59187	−0.381846	−0.190923	−	0.981605i	$-0.561148\pi$
$631$	−9.59187	−0.381846	−0.190923	+	0.981605i	$0.561148\pi$
$632$	−17.8650	−0.710631
$633$	2.04162	0.0811473
$634$	54.6744	2.17140
$635$	−26.1928	−1.03943
$636$	−2.95929	−0.117343
$637$	0	0
$638$	40.4031	1.59957
$639$	−10.6283	−0.420450
$640$	22.7351	0.898684
$641$	−30.4344	−1.20208	−0.601042	−	0.799217i	$-0.705248\pi$
$641$	−30.4344	−1.20208	−0.601042	+	0.799217i	$0.705248\pi$
$642$	10.8244	0.427207
$643$	30.7646	1.21324	0.606619	−	0.794993i	$-0.292526\pi$
$643$	30.7646	1.21324	0.606619	+	0.794993i	$0.292526\pi$
$644$	0	0
$645$	19.8084	0.779955
$646$	−3.10491	−0.122161
$647$	−42.2810	−1.66224	−0.831120	−	0.556094i	$-0.812300\pi$
$647$	−42.2810	−1.66224	−0.831120	+	0.556094i	$0.812300\pi$
$648$	−2.20435	−0.0865950
$649$	−13.0068	−0.510560
$650$	9.26994	0.363597
$651$	0	0
$652$	−15.7809	−0.618029
$653$	−41.1413	−1.60998	−0.804992	−	0.593286i	$-0.797830\pi$
$653$	−41.1413	−1.60998	−0.804992	+	0.593286i	$0.797830\pi$
$654$	10.7773	0.421426
$655$	16.1139	0.629620
$656$	−4.87359	−0.190282
$657$	2.23945	0.0873691
$658$	0	0
$659$	8.33455	0.324668	0.162334	−	0.986736i	$-0.448098\pi$
$659$	8.33455	0.324668	0.162334	+	0.986736i	$0.448098\pi$
$660$	2.93920	0.114408
$661$	−5.15510	−0.200510	−0.100255	−	0.994962i	$-0.531966\pi$
$661$	−5.15510	−0.200510	−0.100255	+	0.994962i	$0.531966\pi$
$662$	47.2171	1.83514
$663$	−6.46666	−0.251144
$664$	−18.9258	−0.734463
$665$	0	0
$666$	−5.22820	−0.202589
$667$	14.1425	0.547598
$668$	0.456871	0.0176769
$669$	16.3846	0.633465
$670$	10.5971	0.409401
$671$	−2.36369	−0.0912494
$672$	0	0
$673$	15.0044	0.578379	0.289189	−	0.957272i	$-0.406614\pi$
$673$	15.0044	0.578379	0.289189	+	0.957272i	$0.406614\pi$
$674$	−23.7171	−0.913548
$675$	−2.19898	−0.0846386
$676$	−4.04715	−0.155660
$677$	−15.0477	−0.578332	−0.289166	−	0.957279i	$-0.593378\pi$
$677$	−15.0477	−0.578332	−0.289166	+	0.957279i	$0.593378\pi$
$678$	−28.7517	−1.10420
$679$	0	0
$680$	−9.20304	−0.352920
$681$	−29.8662	−1.14448
$682$	36.6440	1.40317
$683$	−16.4374	−0.628958	−0.314479	−	0.949264i	$-0.601830\pi$
$683$	−16.4374	−0.628958	−0.314479	+	0.949264i	$0.601830\pi$
$684$	−0.493271	−0.0188607
$685$	−6.49247	−0.248064
$686$	0	0
$687$	−24.3750	−0.929966
$688$	−57.6820	−2.19911
$689$	11.9036	0.453490
$690$	4.22163	0.160715
$691$	0.939242	0.0357304	0.0178652	−	0.999840i	$-0.494313\pi$
$691$	0.939242	0.0357304	0.0178652	+	0.999840i	$0.494313\pi$
$692$	1.91970	0.0729762
$693$	0	0
$694$	−32.4517	−1.23185
$695$	21.4749	0.814589
$696$	−20.0980	−0.761812
$697$	2.49455	0.0944878
$698$	47.1187	1.78347
$699$	4.83770	0.182979
$700$	0	0
$701$	9.38248	0.354371	0.177186	−	0.984177i	$-0.443301\pi$
$701$	9.38248	0.354371	0.177186	+	0.984177i	$0.443301\pi$
$702$	−4.21557	−0.159107
$703$	2.46078	0.0928099
$704$	10.9778	0.413742
$705$	9.72566	0.366290
$706$	24.9079	0.937420
$707$	0	0
$708$	−3.07604	−0.115605
$709$	21.5870	0.810716	0.405358	−	0.914158i	$-0.367147\pi$
$709$	21.5870	0.810716	0.405358	+	0.914158i	$0.367147\pi$
$710$	−28.9262	−1.08558
$711$	8.10443	0.303940
$712$	−2.76904	−0.103774
$713$	12.8267	0.480362
$714$	0	0
$715$	−11.8228	−0.442148
$716$	−13.4303	−0.501913
$717$	−4.59128	−0.171465
$718$	−35.2512	−1.31556
$719$	31.3926	1.17074	0.585372	−	0.810765i	$-0.300948\pi$
$719$	31.3926	1.17074	0.585372	+	0.810765i	$0.300948\pi$
$720$	−8.15657	−0.303978
$721$	0	0
$722$	−29.9447	−1.11443
$723$	0.322023	0.0119762
$724$	−3.69893	−0.137469
$725$	−20.0490	−0.744601
$726$	−5.81217	−0.215710
$727$	19.3083	0.716103	0.358052	−	0.933702i	$-0.383441\pi$
$727$	19.3083	0.716103	0.358052	+	0.933702i	$0.383441\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	6.09492	0.225583
$731$	29.5246	1.09201
$732$	−0.559004	−0.0206614
$733$	48.3152	1.78456	0.892281	−	0.451481i	$-0.149104\pi$
$733$	48.3152	1.78456	0.892281	+	0.451481i	$0.149104\pi$
$734$	−22.8785	−0.844460
$735$	0	0
$736$	−5.45483	−0.201068
$737$	10.6104	0.390841
$738$	1.62618	0.0598605
$739$	5.73102	0.210819	0.105409	−	0.994429i	$-0.466385\pi$
$739$	5.73102	0.210819	0.105409	+	0.994429i	$0.466385\pi$
$740$	−3.46768	−0.127475
$741$	1.98416	0.0728899
$742$	0	0
$743$	31.0816	1.14027	0.570136	−	0.821550i	$-0.306890\pi$
$743$	31.0816	1.14027	0.570136	+	0.821550i	$0.306890\pi$
$744$	−18.2281	−0.668274
$745$	0.750988	0.0275141
$746$	34.4308	1.26060
$747$	8.58566	0.314133
$748$	4.38090	0.160182
$749$	0	0
$750$	−19.5929	−0.715430
$751$	−34.7572	−1.26831	−0.634153	−	0.773207i	$-0.718651\pi$
$751$	−34.7572	−1.26831	−0.634153	+	0.773207i	$0.718651\pi$
$752$	−28.3211	−1.03276
$753$	−8.39485	−0.305925
$754$	−38.4352	−1.39973
$755$	−5.98086	−0.217666
$756$	0	0
$757$	−4.67741	−0.170003	−0.0850017	−	0.996381i	$-0.527090\pi$
$757$	−4.67741	−0.170003	−0.0850017	+	0.996381i	$0.527090\pi$
$758$	0.442661	0.0160782
$759$	4.22695	0.153428
$760$	2.82376	0.102428
$761$	31.7007	1.14915	0.574575	−	0.818452i	$-0.305167\pi$
$761$	31.7007	1.14915	0.574575	+	0.818452i	$0.305167\pi$
$762$	−25.4502	−0.921965
$763$	0	0
$764$	−1.69948	−0.0614852
$765$	4.17495	0.150945
$766$	−23.9568	−0.865594
$767$	12.3732	0.446771
$768$	14.0336	0.506394
$769$	−25.4093	−0.916282	−0.458141	−	0.888880i	$-0.651484\pi$
$769$	−25.4093	−0.916282	−0.458141	+	0.888880i	$0.651484\pi$
$770$	0	0
$771$	21.5104	0.774679
$772$	−0.458819	−0.0165133
$773$	39.9382	1.43648	0.718239	−	0.695797i	$-0.244948\pi$
$773$	39.9382	1.43648	0.718239	+	0.695797i	$0.244948\pi$
$774$	19.2469	0.691814
$775$	−18.1836	−0.653176
$776$	−18.8585	−0.676982
$777$	0	0
$778$	5.36387	0.192304
$779$	−0.765400	−0.0274233
$780$	−2.79604	−0.100114
$781$	−28.9627	−1.03637
$782$	6.29236	0.225014
$783$	9.11743	0.325830
$784$	0	0
$785$	14.9222	0.532595
$786$	15.6570	0.558468
$787$	−50.8086	−1.81113	−0.905565	−	0.424207i	$-0.860553\pi$
$787$	−50.8086	−1.81113	−0.905565	+	0.424207i	$0.860553\pi$
$788$	−11.1318	−0.396553
$789$	15.4590	0.550354
$790$	22.0572	0.784758
$791$	0	0
$792$	−6.00695	−0.213448
$793$	2.24857	0.0798489
$794$	−3.01822	−0.107113
$795$	−7.68507	−0.272561
$796$	2.26424	0.0802540
$797$	47.0831	1.66777	0.833884	−	0.551939i	$-0.186112\pi$
$797$	47.0831	1.66777	0.833884	+	0.551939i	$0.186112\pi$
$798$	0	0
$799$	14.4962	0.512837
$800$	7.73301	0.273403
$801$	1.25617	0.0443847
$802$	25.8603	0.913161
$803$	6.10259	0.215356
$804$	2.50932	0.0884970
$805$	0	0
$806$	−34.8592	−1.22786
$807$	21.3937	0.753095
$808$	−2.88392	−0.101456
$809$	17.7015	0.622353	0.311176	−	0.950352i	$-0.399277\pi$
$809$	17.7015	0.622353	0.311176	+	0.950352i	$0.399277\pi$
$810$	2.72162	0.0956279
$811$	23.0207	0.808365	0.404183	−	0.914678i	$-0.367556\pi$
$811$	23.0207	0.808365	0.404183	+	0.914678i	$0.367556\pi$
$812$	0	0
$813$	−7.41776	−0.260152
$814$	−14.2471	−0.499361
$815$	−40.9821	−1.43554
$816$	−12.1574	−0.425595
$817$	−9.05898	−0.316934
$818$	7.52026	0.262940
$819$	0	0
$820$	1.07859	0.0376659
$821$	−7.63363	−0.266416	−0.133208	−	0.991088i	$-0.542528\pi$
$821$	−7.63363	−0.266416	−0.133208	+	0.991088i	$0.542528\pi$
$822$	−6.30841	−0.220031
$823$	−46.1379	−1.60827	−0.804133	−	0.594450i	$-0.797370\pi$
$823$	−46.1379	−1.60827	−0.804133	+	0.594450i	$0.797370\pi$
$824$	−34.8595	−1.21439
$825$	−5.99231	−0.208625
$826$	0	0
$827$	−8.79619	−0.305874	−0.152937	−	0.988236i	$-0.548873\pi$
$827$	−8.79619	−0.305874	−0.152937	+	0.988236i	$0.548873\pi$
$828$	0.999655	0.0347404
$829$	−18.9774	−0.659112	−0.329556	−	0.944136i	$-0.606899\pi$
$829$	−18.9774	−0.659112	−0.329556	+	0.944136i	$0.606899\pi$
$830$	23.3669	0.811076
$831$	−23.9735	−0.831633
$832$	−10.4431	−0.362050
$833$	0	0
$834$	20.8661	0.722534
$835$	1.18646	0.0410593
$836$	−1.34419	−0.0464897
$837$	8.26914	0.285823
$838$	−46.2703	−1.59838
$839$	25.8131	0.891167	0.445584	−	0.895240i	$-0.352996\pi$
$839$	25.8131	0.891167	0.445584	+	0.895240i	$0.352996\pi$
$840$	0	0
$841$	54.1274	1.86646
$842$	−59.2610	−2.04227
$843$	11.7067	0.403202
$844$	1.31575	0.0452899
$845$	−10.5102	−0.361562
$846$	9.44994	0.324896
$847$	0	0
$848$	22.3789	0.768495
$849$	−13.5001	−0.463321
$850$	−8.92034	−0.305965
$851$	−4.98697	−0.170951
$852$	−6.84955	−0.234662
$853$	−23.5448	−0.806160	−0.403080	−	0.915165i	$-0.632060\pi$
$853$	−23.5448	−0.806160	−0.403080	+	0.915165i	$0.632060\pi$
$854$	0	0
$855$	−1.28099	−0.0438090
$856$	−14.6730	−0.501511
$857$	15.4073	0.526304	0.263152	−	0.964754i	$-0.415238\pi$
$857$	15.4073	0.526304	0.263152	+	0.964754i	$0.415238\pi$
$858$	−11.4876	−0.392181
$859$	10.2841	0.350887	0.175444	−	0.984489i	$-0.443864\pi$
$859$	10.2841	0.350887	0.175444	+	0.984489i	$0.443864\pi$
$860$	12.7658	0.435309
$861$	0	0
$862$	−12.0825	−0.411532
$863$	−17.2631	−0.587644	−0.293822	−	0.955860i	$-0.594927\pi$
$863$	−17.2631	−0.587644	−0.293822	+	0.955860i	$0.594927\pi$
$864$	−3.51664	−0.119639
$865$	4.98535	0.169507
$866$	−22.6032	−0.768090
$867$	−10.7772	−0.366013
$868$	0	0
$869$	22.0849	0.749180
$870$	24.8141	0.841278
$871$	−10.0936	−0.342010
$872$	−14.6090	−0.494724
$873$	8.55514	0.289548
$874$	−1.93068	−0.0653061
$875$	0	0
$876$	1.44324	0.0487625
$877$	32.1608	1.08599	0.542997	−	0.839735i	$-0.317290\pi$
$877$	32.1608	1.08599	0.542997	+	0.839735i	$0.317290\pi$
$878$	14.7973	0.499385
$879$	−21.3767	−0.721017
$880$	−22.2270	−0.749273
$881$	−8.00714	−0.269767	−0.134884	−	0.990861i	$-0.543066\pi$
$881$	−8.00714	−0.269767	−0.134884	+	0.990861i	$0.543066\pi$
$882$	0	0
$883$	−11.9191	−0.401108	−0.200554	−	0.979683i	$-0.564274\pi$
$883$	−11.9191	−0.401108	−0.200554	+	0.979683i	$0.564274\pi$
$884$	−4.16752	−0.140169
$885$	−7.98828	−0.268523
$886$	43.8469	1.47307
$887$	−55.2315	−1.85449	−0.927247	−	0.374450i	$-0.877831\pi$
$887$	−55.2315	−1.85449	−0.927247	+	0.374450i	$0.877831\pi$
$888$	7.08703	0.237825
$889$	0	0
$890$	3.41882	0.114599
$891$	2.72505	0.0912925
$892$	10.5592	0.353550
$893$	−4.44784	−0.148841
$894$	0.729698	0.0244048
$895$	−34.8776	−1.16583
$896$	0	0
$897$	−4.02106	−0.134259
$898$	27.3649	0.913178
$899$	75.3933	2.51451
$900$	−1.41716	−0.0472385
$901$	−11.4547	−0.381610
$902$	4.43142	0.147550
$903$	0	0
$904$	38.9740	1.29626
$905$	−9.60587	−0.319310
$906$	−5.81131	−0.193068
$907$	−29.6769	−0.985405	−0.492703	−	0.870198i	$-0.663991\pi$
$907$	−29.6769	−0.985405	−0.492703	+	0.870198i	$0.663991\pi$
$908$	−19.2476	−0.638756
$909$	1.30829	0.0433931
$910$	0	0
$911$	43.6581	1.44646	0.723228	−	0.690609i	$-0.242657\pi$
$911$	43.6581	1.44646	0.723228	+	0.690609i	$0.242657\pi$
$912$	3.73025	0.123521
$913$	23.3963	0.774305
$914$	35.9721	1.18985
$915$	−1.45170	−0.0479916
$916$	−15.7088	−0.519033
$917$	0	0
$918$	4.05659	0.133887
$919$	−23.6652	−0.780642	−0.390321	−	0.920679i	$-0.627636\pi$
$919$	−23.6652	−0.780642	−0.390321	+	0.920679i	$0.627636\pi$
$920$	−5.72258	−0.188668
$921$	25.7934	0.849920
$922$	−57.2459	−1.88529
$923$	27.5520	0.906885
$924$	0	0
$925$	7.06975	0.232452
$926$	−32.6390	−1.07258
$927$	15.8139	0.519398
$928$	−32.0627	−1.05251
$929$	−41.0050	−1.34533	−0.672665	−	0.739947i	$-0.734851\pi$
$929$	−41.0050	−1.34533	−0.672665	+	0.739947i	$0.734851\pi$
$930$	22.5054	0.737983
$931$	0	0
$932$	3.11772	0.102124
$933$	4.24169	0.138867
$934$	−37.2158	−1.21774
$935$	11.3769	0.372065
$936$	5.71437	0.186780
$937$	17.7022	0.578305	0.289153	−	0.957283i	$-0.406627\pi$
$937$	17.7022	0.578305	0.289153	+	0.957283i	$0.406627\pi$
$938$	0	0
$939$	6.77432	0.221071
$940$	6.26782	0.204434
$941$	−33.0063	−1.07598	−0.537988	−	0.842953i	$-0.680815\pi$
$941$	−33.0063	−1.07598	−0.537988	+	0.842953i	$0.680815\pi$
$942$	14.4991	0.472407
$943$	1.55115	0.0505123
$944$	23.2619	0.757109
$945$	0	0
$946$	52.4486	1.70525
$947$	49.0378	1.59352	0.796758	−	0.604299i	$-0.206547\pi$
$947$	49.0378	1.59352	0.796758	+	0.604299i	$0.206547\pi$
$948$	5.22300	0.169635
$949$	−5.80535	−0.188450
$950$	2.73702	0.0888005
$951$	33.6214	1.09025
$952$	0	0
$953$	−20.5062	−0.664260	−0.332130	−	0.943234i	$-0.607767\pi$
$953$	−20.5062	−0.664260	−0.332130	+	0.943234i	$0.607767\pi$
$954$	−7.46721	−0.241760
$955$	−4.41345	−0.142816
$956$	−2.95891	−0.0956979
$957$	24.8454	0.803138
$958$	−33.3498	−1.07748
$959$	0	0
$960$	6.74219	0.217603
$961$	37.3787	1.20577
$962$	13.5532	0.436971
$963$	6.65637	0.214498
$964$	0.207532	0.00668415
$965$	−1.19152	−0.0383565
$966$	0	0
$967$	−50.9026	−1.63692	−0.818459	−	0.574566i	$-0.805171\pi$
$967$	−50.9026	−1.63692	−0.818459	+	0.574566i	$0.805171\pi$
$968$	7.87861	0.253228
$969$	−1.90933	−0.0613365
$970$	23.2838	0.747599
$971$	−5.25431	−0.168619	−0.0843095	−	0.996440i	$-0.526868\pi$
$971$	−5.25431	−0.168619	−0.0843095	+	0.996440i	$0.526868\pi$
$972$	0.644462	0.0206711
$973$	0	0
$974$	−6.62460	−0.212266
$975$	5.70044	0.182560
$976$	4.22734	0.135314
$977$	6.91693	0.221292	0.110646	−	0.993860i	$-0.464708\pi$
$977$	6.91693	0.221292	0.110646	+	0.993860i	$0.464708\pi$
$978$	−39.8202	−1.27331
$979$	3.42313	0.109404
$980$	0	0
$981$	6.62737	0.211596
$982$	−10.2651	−0.327574
$983$	30.1743	0.962410	0.481205	−	0.876608i	$-0.340199\pi$
$983$	30.1743	0.962410	0.481205	+	0.876608i	$0.340199\pi$
$984$	−2.20435	−0.0702721
$985$	−28.9085	−0.921100
$986$	36.9856	1.17786
$987$	0	0
$988$	1.27871	0.0406813
$989$	18.3588	0.583775
$990$	7.41653	0.235713
$991$	−4.07409	−0.129418	−0.0647089	−	0.997904i	$-0.520612\pi$
$991$	−4.07409	−0.129418	−0.0647089	+	0.997904i	$0.520612\pi$
$992$	−29.0796	−0.923279
$993$	29.0356	0.921416
$994$	0	0
$995$	5.88009	0.186411
$996$	5.53313	0.175324
$997$	32.1123	1.01701	0.508503	−	0.861060i	$-0.330199\pi$
$997$	32.1123	1.01701	0.508503	+	0.861060i	$0.330199\pi$
$998$	60.9778	1.93022
$999$	−3.21502	−0.101719

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bc.1.5		8
7.3	odd	6		861.2.i.d.247.4	✓	16
7.5	odd	6		861.2.i.d.739.4	yes	16
7.6	odd	2		6027.2.a.bb.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.d.247.4	✓	16	7.3	odd	6
861.2.i.d.739.4	yes	16	7.5	odd	6
6027.2.a.bb.1.5		8	7.6	odd	2
6027.2.a.bc.1.5		8	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)

\(f(q)\)	\(=\)	\(q+1.62618 q^{2} +1.00000 q^{3} +0.644462 q^{4} +1.67363 q^{5} +1.62618 q^{6} -2.20435 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.62618 q^{2} +1.00000 q^{3} +0.644462 q^{4} +1.67363 q^{5} +1.62618 q^{6} -2.20435 q^{8} +1.00000 q^{9} +2.72162 q^{10} +2.72505 q^{11} +0.644462 q^{12} -2.59232 q^{13} +1.67363 q^{15} -4.87359 q^{16} +2.49455 q^{17} +1.62618 q^{18} -0.765400 q^{19} +1.07859 q^{20} +4.43142 q^{22} +1.55115 q^{23} -2.20435 q^{24} -2.19898 q^{25} -4.21557 q^{26} +1.00000 q^{27} +9.11743 q^{29} +2.72162 q^{30} +8.26914 q^{31} -3.51664 q^{32} +2.72505 q^{33} +4.05659 q^{34} +0.644462 q^{36} -3.21502 q^{37} -1.24468 q^{38} -2.59232 q^{39} -3.68926 q^{40} +1.00000 q^{41} +11.8356 q^{43} +1.75619 q^{44} +1.67363 q^{45} +2.52244 q^{46} +5.81113 q^{47} -4.87359 q^{48} -3.57593 q^{50} +2.49455 q^{51} -1.67065 q^{52} -4.59187 q^{53} +1.62618 q^{54} +4.56071 q^{55} -0.765400 q^{57} +14.8266 q^{58} -4.77304 q^{59} +1.07859 q^{60} -0.867396 q^{61} +13.4471 q^{62} +4.02849 q^{64} -4.33857 q^{65} +4.43142 q^{66} +3.89367 q^{67} +1.60764 q^{68} +1.55115 q^{69} -10.6283 q^{71} -2.20435 q^{72} +2.23945 q^{73} -5.22820 q^{74} -2.19898 q^{75} -0.493271 q^{76} -4.21557 q^{78} +8.10443 q^{79} -8.15657 q^{80} +1.00000 q^{81} +1.62618 q^{82} +8.58566 q^{83} +4.17495 q^{85} +19.2469 q^{86} +9.11743 q^{87} -6.00695 q^{88} +1.25617 q^{89} +2.72162 q^{90} +0.999655 q^{92} +8.26914 q^{93} +9.44994 q^{94} -1.28099 q^{95} -3.51664 q^{96} +8.55514 q^{97} +2.72505 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 8 q^{3} + 13 q^{4} + 7 q^{5} + q^{6} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + q^2 + 8 * q^3 + 13 * q^4 + 7 * q^5 + q^6 + 6 * q^8 + 8 * q^9	\( 8 q + q^{2} + 8 q^{3} + 13 q^{4} + 7 q^{5} + q^{6} + 6 q^{8} + 8 q^{9} + 8 q^{10} + 11 q^{11} + 13 q^{12} + 10 q^{13} + 7 q^{15} - 17 q^{16} + 3 q^{17} + q^{18} + 6 q^{19} + 11 q^{20} + 15 q^{22} + 14 q^{23} + 6 q^{24} + 25 q^{25} + 24 q^{26} + 8 q^{27} + 2 q^{29} + 8 q^{30} + 16 q^{31} + 3 q^{32} + 11 q^{33} - 4 q^{34} + 13 q^{36} - 20 q^{37} + 10 q^{38} + 10 q^{39} - 3 q^{40} + 8 q^{41} + 7 q^{43} + 7 q^{45} - 5 q^{46} + 14 q^{47} - 17 q^{48} - 5 q^{50} + 3 q^{51} + 23 q^{52} + 7 q^{53} + q^{54} + 48 q^{55} + 6 q^{57} - 20 q^{58} + 22 q^{59} + 11 q^{60} - 33 q^{62} - 10 q^{64} - 14 q^{65} + 15 q^{66} + 12 q^{67} - 27 q^{68} + 14 q^{69} - 5 q^{71} + 6 q^{72} + 2 q^{73} + 6 q^{74} + 25 q^{75} + 43 q^{76} + 24 q^{78} - 15 q^{79} - 7 q^{80} + 8 q^{81} + q^{82} + 15 q^{83} - 43 q^{85} + 31 q^{86} + 2 q^{87} + 17 q^{88} + 29 q^{89} + 8 q^{90} + 19 q^{92} + 16 q^{93} + 20 q^{94} + 14 q^{95} + 3 q^{96} + 19 q^{97} + 11 q^{99}+O(q^{100}) \) 8 * q + q^2 + 8 * q^3 + 13 * q^4 + 7 * q^5 + q^6 + 6 * q^8 + 8 * q^9 + 8 * q^10 + 11 * q^11 + 13 * q^12 + 10 * q^13 + 7 * q^15 - 17 * q^16 + 3 * q^17 + q^18 + 6 * q^19 + 11 * q^20 + 15 * q^22 + 14 * q^23 + 6 * q^24 + 25 * q^25 + 24 * q^26 + 8 * q^27 + 2 * q^29 + 8 * q^30 + 16 * q^31 + 3 * q^32 + 11 * q^33 - 4 * q^34 + 13 * q^36 - 20 * q^37 + 10 * q^38 + 10 * q^39 - 3 * q^40 + 8 * q^41 + 7 * q^43 + 7 * q^45 - 5 * q^46 + 14 * q^47 - 17 * q^48 - 5 * q^50 + 3 * q^51 + 23 * q^52 + 7 * q^53 + q^54 + 48 * q^55 + 6 * q^57 - 20 * q^58 + 22 * q^59 + 11 * q^60 - 33 * q^62 - 10 * q^64 - 14 * q^65 + 15 * q^66 + 12 * q^67 - 27 * q^68 + 14 * q^69 - 5 * q^71 + 6 * q^72 + 2 * q^73 + 6 * q^74 + 25 * q^75 + 43 * q^76 + 24 * q^78 - 15 * q^79 - 7 * q^80 + 8 * q^81 + q^82 + 15 * q^83 - 43 * q^85 + 31 * q^86 + 2 * q^87 + 17 * q^88 + 29 * q^89 + 8 * q^90 + 19 * q^92 + 16 * q^93 + 20 * q^94 + 14 * q^95 + 3 * q^96 + 19 * q^97 + 11 * q^99

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