LMFDB - Embedded newform 6027.2.a.bk.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1258372982$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 19 x^{12} + 36 x^{11} + 134 x^{10} - 237 x^{9} - 438 x^{8} + 716 x^{7} + 662 x^{6} + \cdots + 16 $ x^14 - 2x^13 - 19x^12 + 36x^11 + 134x^10 - 237x^9 - 438x^8 + 716x^7 + 662x^6 - 1007x^5 - 384x^4 + 579x^3 + 44x^2 - 112*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$-2.69016$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.69016 q^{2} +1.00000 q^{3} +5.23695 q^{4} -3.40724 q^{5} +2.69016 q^{6} +8.70791 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.69016 q^{2} +1.00000 q^{3} +5.23695 q^{4} -3.40724 q^{5} +2.69016 q^{6} +8.70791 q^{8} +1.00000 q^{9} -9.16601 q^{10} -6.16208 q^{11} +5.23695 q^{12} -3.11534 q^{13} -3.40724 q^{15} +12.9518 q^{16} -2.71759 q^{17} +2.69016 q^{18} -7.15789 q^{19} -17.8435 q^{20} -16.5770 q^{22} +3.55326 q^{23} +8.70791 q^{24} +6.60927 q^{25} -8.38076 q^{26} +1.00000 q^{27} -1.79174 q^{29} -9.16601 q^{30} +6.90989 q^{31} +17.4265 q^{32} -6.16208 q^{33} -7.31075 q^{34} +5.23695 q^{36} -8.76601 q^{37} -19.2558 q^{38} -3.11534 q^{39} -29.6699 q^{40} -1.00000 q^{41} +3.02053 q^{43} -32.2705 q^{44} -3.40724 q^{45} +9.55884 q^{46} +4.99622 q^{47} +12.9518 q^{48} +17.7800 q^{50} -2.71759 q^{51} -16.3149 q^{52} -2.58012 q^{53} +2.69016 q^{54} +20.9957 q^{55} -7.15789 q^{57} -4.82007 q^{58} -9.63934 q^{59} -17.8435 q^{60} -4.52207 q^{61} +18.5887 q^{62} +20.9764 q^{64} +10.6147 q^{65} -16.5770 q^{66} -1.73848 q^{67} -14.2319 q^{68} +3.55326 q^{69} -14.2790 q^{71} +8.70791 q^{72} -0.984881 q^{73} -23.5820 q^{74} +6.60927 q^{75} -37.4855 q^{76} -8.38076 q^{78} -8.68549 q^{79} -44.1297 q^{80} +1.00000 q^{81} -2.69016 q^{82} -1.55919 q^{83} +9.25948 q^{85} +8.12570 q^{86} -1.79174 q^{87} -53.6589 q^{88} -4.47862 q^{89} -9.16601 q^{90} +18.6083 q^{92} +6.90989 q^{93} +13.4406 q^{94} +24.3886 q^{95} +17.4265 q^{96} +4.47579 q^{97} -6.16208 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 2 * q^2 + 14 * q^3 + 14 * q^4 - 10 * q^5 - 2 * q^6 - 6 * q^8 + 14 * q^9	$ 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9} - 3 q^{10} - 16 q^{11} + 14 q^{12} - 21 q^{13} - 10 q^{15} + 22 q^{16} - 12 q^{17} - 2 q^{18} - 2 q^{19} - 40 q^{20} + q^{22} - 7 q^{23} - 6 q^{24} + 22 q^{25} - 2 q^{26} + 14 q^{27} - 16 q^{29} - 3 q^{30} - 8 q^{31} - 19 q^{32} - 16 q^{33} - 33 q^{34} + 14 q^{36} + q^{37} - 32 q^{38} - 21 q^{39} + 13 q^{40} - 14 q^{41} + 14 q^{43} - 36 q^{44} - 10 q^{45} - 12 q^{46} - 12 q^{47} + 22 q^{48} - q^{50} - 12 q^{51} - 60 q^{52} - 20 q^{53} - 2 q^{54} + 11 q^{55} - 2 q^{57} + 21 q^{58} - 25 q^{59} - 40 q^{60} - 26 q^{61} + 33 q^{62} + 42 q^{64} - 8 q^{65} + q^{66} - 22 q^{67} - 15 q^{68} - 7 q^{69} - 36 q^{71} - 6 q^{72} - 31 q^{73} - 65 q^{74} + 22 q^{75} + 2 q^{76} - 2 q^{78} + 12 q^{79} - 112 q^{80} + 14 q^{81} + 2 q^{82} - 20 q^{83} + 40 q^{85} - 9 q^{86} - 16 q^{87} - 54 q^{88} - 39 q^{89} - 3 q^{90} + 63 q^{92} - 8 q^{93} - 14 q^{94} - 55 q^{95} - 19 q^{96} - 18 q^{97} - 16 q^{99}+O(q^{100}) $ 14 * q - 2 * q^2 + 14 * q^3 + 14 * q^4 - 10 * q^5 - 2 * q^6 - 6 * q^8 + 14 * q^9 - 3 * q^10 - 16 * q^11 + 14 * q^12 - 21 * q^13 - 10 * q^15 + 22 * q^16 - 12 * q^17 - 2 * q^18 - 2 * q^19 - 40 * q^20 + q^22 - 7 * q^23 - 6 * q^24 + 22 * q^25 - 2 * q^26 + 14 * q^27 - 16 * q^29 - 3 * q^30 - 8 * q^31 - 19 * q^32 - 16 * q^33 - 33 * q^34 + 14 * q^36 + q^37 - 32 * q^38 - 21 * q^39 + 13 * q^40 - 14 * q^41 + 14 * q^43 - 36 * q^44 - 10 * q^45 - 12 * q^46 - 12 * q^47 + 22 * q^48 - q^50 - 12 * q^51 - 60 * q^52 - 20 * q^53 - 2 * q^54 + 11 * q^55 - 2 * q^57 + 21 * q^58 - 25 * q^59 - 40 * q^60 - 26 * q^61 + 33 * q^62 + 42 * q^64 - 8 * q^65 + q^66 - 22 * q^67 - 15 * q^68 - 7 * q^69 - 36 * q^71 - 6 * q^72 - 31 * q^73 - 65 * q^74 + 22 * q^75 + 2 * q^76 - 2 * q^78 + 12 * q^79 - 112 * q^80 + 14 * q^81 + 2 * q^82 - 20 * q^83 + 40 * q^85 - 9 * q^86 - 16 * q^87 - 54 * q^88 - 39 * q^89 - 3 * q^90 + 63 * q^92 - 8 * q^93 - 14 * q^94 - 55 * q^95 - 19 * q^96 - 18 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.69016	1.90223	0.951115	−	0.308838i	$-0.0999401\pi$
$2$	2.69016	1.90223	0.951115	+	0.308838i	$0.0999401\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.23695	2.61848
$5$	−3.40724	−1.52376	−0.761882	−	0.647716i	$-0.775724\pi$
$5$	−3.40724	−1.52376	−0.761882	+	0.647716i	$0.775724\pi$
$6$	2.69016	1.09825
$7$	0	0
$7$	0	0
$8$	8.70791	3.07871
$9$	1.00000	0.333333
$10$	−9.16601	−2.89855
$11$	−6.16208	−1.85794	−0.928968	−	0.370159i	$-0.879303\pi$
$11$	−6.16208	−1.85794	−0.928968	+	0.370159i	$0.879303\pi$
$12$	5.23695	1.51178
$13$	−3.11534	−0.864041	−0.432020	−	0.901864i	$-0.642199\pi$
$13$	−3.11534	−0.864041	−0.432020	+	0.901864i	$0.642199\pi$
$14$	0	0
$15$	−3.40724	−0.879745
$16$	12.9518	3.23794
$17$	−2.71759	−0.659113	−0.329556	−	0.944136i	$-0.606899\pi$
$17$	−2.71759	−0.659113	−0.329556	+	0.944136i	$0.606899\pi$
$18$	2.69016	0.634076
$19$	−7.15789	−1.64213	−0.821066	−	0.570833i	$-0.806620\pi$
$19$	−7.15789	−1.64213	−0.821066	+	0.570833i	$0.806620\pi$
$20$	−17.8435	−3.98994
$21$	0	0
$22$	−16.5770	−3.53422
$23$	3.55326	0.740906	0.370453	−	0.928851i	$-0.379202\pi$
$23$	3.55326	0.740906	0.370453	+	0.928851i	$0.379202\pi$
$24$	8.70791	1.77750
$25$	6.60927	1.32185
$26$	−8.38076	−1.64360
$27$	1.00000	0.192450
$28$	0	0
$29$	−1.79174	−0.332718	−0.166359	−	0.986065i	$-0.553201\pi$
$29$	−1.79174	−0.332718	−0.166359	+	0.986065i	$0.553201\pi$
$30$	−9.16601	−1.67348
$31$	6.90989	1.24105	0.620527	−	0.784185i	$-0.286919\pi$
$31$	6.90989	1.24105	0.620527	+	0.784185i	$0.286919\pi$
$32$	17.4265	3.08059
$33$	−6.16208	−1.07268
$34$	−7.31075	−1.25378
$35$	0	0
$36$	5.23695	0.872825
$37$	−8.76601	−1.44112	−0.720562	−	0.693391i	$-0.756116\pi$
$37$	−8.76601	−1.44112	−0.720562	+	0.693391i	$0.756116\pi$
$38$	−19.2558	−3.12371
$39$	−3.11534	−0.498854
$40$	−29.6699	−4.69123
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	3.02053	0.460626	0.230313	−	0.973117i	$-0.426025\pi$
$43$	3.02053	0.460626	0.230313	+	0.973117i	$0.426025\pi$
$44$	−32.2705	−4.86496
$45$	−3.40724	−0.507921
$46$	9.55884	1.40937
$47$	4.99622	0.728773	0.364387	−	0.931248i	$-0.381279\pi$
$47$	4.99622	0.728773	0.364387	+	0.931248i	$0.381279\pi$
$48$	12.9518	1.86943
$49$	0	0
$50$	17.7800	2.51447
$51$	−2.71759	−0.380539
$52$	−16.3149	−2.26247
$53$	−2.58012	−0.354406	−0.177203	−	0.984174i	$-0.556705\pi$
$53$	−2.58012	−0.354406	−0.177203	+	0.984174i	$0.556705\pi$
$54$	2.69016	0.366084
$55$	20.9957	2.83106
$56$	0	0
$57$	−7.15789	−0.948085
$58$	−4.82007	−0.632906
$59$	−9.63934	−1.25494	−0.627468	−	0.778643i	$-0.715909\pi$
$59$	−9.63934	−1.25494	−0.627468	+	0.778643i	$0.715909\pi$
$60$	−17.8435	−2.30359
$61$	−4.52207	−0.578991	−0.289496	−	0.957179i	$-0.593488\pi$
$61$	−4.52207	−0.578991	−0.289496	+	0.957179i	$0.593488\pi$
$62$	18.5887	2.36077
$63$	0	0
$64$	20.9764	2.62205
$65$	10.6147	1.31659
$66$	−16.5770	−2.04048
$67$	−1.73848	−0.212390	−0.106195	−	0.994345i	$-0.533867\pi$
$67$	−1.73848	−0.212390	−0.106195	+	0.994345i	$0.533867\pi$
$68$	−14.2319	−1.72587
$69$	3.55326	0.427762
$70$	0	0
$71$	−14.2790	−1.69460	−0.847301	−	0.531113i	$-0.821774\pi$
$71$	−14.2790	−1.69460	−0.847301	+	0.531113i	$0.821774\pi$
$72$	8.70791	1.02624
$73$	−0.984881	−0.115272	−0.0576358	−	0.998338i	$-0.518356\pi$
$73$	−0.984881	−0.115272	−0.0576358	+	0.998338i	$0.518356\pi$
$74$	−23.5820	−2.74135
$75$	6.60927	0.763173
$76$	−37.4855	−4.29988
$77$	0	0
$78$	−8.38076	−0.948935
$79$	−8.68549	−0.977194	−0.488597	−	0.872510i	$-0.662491\pi$
$79$	−8.68549	−0.977194	−0.488597	+	0.872510i	$0.662491\pi$
$80$	−44.1297	−4.93386
$81$	1.00000	0.111111
$82$	−2.69016	−0.297078
$83$	−1.55919	−0.171144	−0.0855719	−	0.996332i	$-0.527272\pi$
$83$	−1.55919	−0.171144	−0.0855719	+	0.996332i	$0.527272\pi$
$84$	0	0
$85$	9.25948	1.00433
$86$	8.12570	0.876217
$87$	−1.79174	−0.192095
$88$	−53.6589	−5.72005
$89$	−4.47862	−0.474733	−0.237367	−	0.971420i	$-0.576284\pi$
$89$	−4.47862	−0.474733	−0.237367	+	0.971420i	$0.576284\pi$
$90$	−9.16601	−0.966182
$91$	0	0
$92$	18.6083	1.94005
$93$	6.90989	0.716522
$94$	13.4406	1.38629
$95$	24.3886	2.50222
$96$	17.4265	1.77858
$97$	4.47579	0.454448	0.227224	−	0.973843i	$-0.427035\pi$
$97$	4.47579	0.454448	0.227224	+	0.973843i	$0.427035\pi$
$98$	0	0
$99$	−6.16208	−0.619312
$100$	34.6124	3.46124
$101$	−3.51262	−0.349519	−0.174760	−	0.984611i	$-0.555915\pi$
$101$	−3.51262	−0.349519	−0.174760	+	0.984611i	$0.555915\pi$
$102$	−7.31075	−0.723872
$103$	−11.5411	−1.13718	−0.568588	−	0.822622i	$-0.692510\pi$
$103$	−11.5411	−1.13718	−0.568588	+	0.822622i	$0.692510\pi$
$104$	−27.1281	−2.66013
$105$	0	0
$106$	−6.94093	−0.674162
$107$	−5.39948	−0.521987	−0.260994	−	0.965341i	$-0.584050\pi$
$107$	−5.39948	−0.521987	−0.260994	+	0.965341i	$0.584050\pi$
$108$	5.23695	0.503926
$109$	18.6989	1.79103	0.895514	−	0.445032i	$-0.146808\pi$
$109$	18.6989	1.79103	0.895514	+	0.445032i	$0.146808\pi$
$110$	56.4817	5.38532
$111$	−8.76601	−0.832033
$112$	0	0
$113$	9.53967	0.897417	0.448709	−	0.893678i	$-0.351884\pi$
$113$	9.53967	0.897417	0.448709	+	0.893678i	$0.351884\pi$
$114$	−19.2558	−1.80348
$115$	−12.1068	−1.12897
$116$	−9.38326	−0.871214
$117$	−3.11534	−0.288014
$118$	−25.9314	−2.38717
$119$	0	0
$120$	−29.6699	−2.70848
$121$	26.9712	2.45193
$122$	−12.1651	−1.10137
$123$	−1.00000	−0.0901670
$124$	36.1868	3.24967
$125$	−5.48317	−0.490429
$126$	0	0
$127$	14.8639	1.31896	0.659478	−	0.751724i	$-0.270777\pi$
$127$	14.8639	1.31896	0.659478	+	0.751724i	$0.270777\pi$
$128$	21.5770	1.90715
$129$	3.02053	0.265943
$130$	28.5553	2.50446
$131$	6.15126	0.537438	0.268719	−	0.963219i	$-0.413400\pi$
$131$	6.15126	0.537438	0.268719	+	0.963219i	$0.413400\pi$
$132$	−32.2705	−2.80879
$133$	0	0
$134$	−4.67680	−0.404014
$135$	−3.40724	−0.293248
$136$	−23.6646	−2.02922
$137$	1.14084	0.0974688	0.0487344	−	0.998812i	$-0.484481\pi$
$137$	1.14084	0.0974688	0.0487344	+	0.998812i	$0.484481\pi$
$138$	9.55884	0.813702
$139$	6.86085	0.581929	0.290965	−	0.956734i	$-0.406024\pi$
$139$	6.86085	0.581929	0.290965	+	0.956734i	$0.406024\pi$
$140$	0	0
$141$	4.99622	0.420758
$142$	−38.4127	−3.22352
$143$	19.1970	1.60533
$144$	12.9518	1.07931
$145$	6.10489	0.506983
$146$	−2.64948	−0.219273
$147$	0	0
$148$	−45.9072	−3.77355
$149$	−18.1936	−1.49048	−0.745241	−	0.666796i	$-0.767665\pi$
$149$	−18.1936	−1.49048	−0.745241	+	0.666796i	$0.767665\pi$
$150$	17.7800	1.45173
$151$	−7.96692	−0.648338	−0.324169	−	0.945999i	$-0.605085\pi$
$151$	−7.96692	−0.648338	−0.324169	+	0.945999i	$0.605085\pi$
$152$	−62.3303	−5.05565
$153$	−2.71759	−0.219704
$154$	0	0
$155$	−23.5436	−1.89107
$156$	−16.3149	−1.30624
$157$	15.3395	1.22423	0.612113	−	0.790770i	$-0.290320\pi$
$157$	15.3395	1.22423	0.612113	+	0.790770i	$0.290320\pi$
$158$	−23.3653	−1.85885
$159$	−2.58012	−0.204617
$160$	−59.3761	−4.69409
$161$	0	0
$162$	2.69016	0.211359
$163$	10.0612	0.788053	0.394027	−	0.919099i	$-0.371082\pi$
$163$	10.0612	0.788053	0.394027	+	0.919099i	$0.371082\pi$
$164$	−5.23695	−0.408937
$165$	20.9957	1.63451
$166$	−4.19448	−0.325555
$167$	25.0532	1.93868	0.969338	−	0.245732i	$-0.0790283\pi$
$167$	25.0532	1.93868	0.969338	+	0.245732i	$0.0790283\pi$
$168$	0	0
$169$	−3.29464	−0.253434
$170$	24.9095	1.91047
$171$	−7.15789	−0.547377
$172$	15.8184	1.20614
$173$	3.76556	0.286291	0.143145	−	0.989702i	$-0.454278\pi$
$173$	3.76556	0.286291	0.143145	+	0.989702i	$0.454278\pi$
$174$	−4.82007	−0.365408
$175$	0	0
$176$	−79.8098	−6.01589
$177$	−9.63934	−0.724537
$178$	−12.0482	−0.903052
$179$	−17.0313	−1.27298	−0.636491	−	0.771284i	$-0.719615\pi$
$179$	−17.0313	−1.27298	−0.636491	+	0.771284i	$0.719615\pi$
$180$	−17.8435	−1.32998
$181$	−8.03112	−0.596948	−0.298474	−	0.954418i	$-0.596478\pi$
$181$	−8.03112	−0.596948	−0.298474	+	0.954418i	$0.596478\pi$
$182$	0	0
$183$	−4.52207	−0.334281
$184$	30.9415	2.28104
$185$	29.8679	2.19593
$186$	18.5887	1.36299
$187$	16.7460	1.22459
$188$	26.1650	1.90828
$189$	0	0
$190$	65.6093	4.75980
$191$	0.0253646	0.00183532	0.000917660	−	1.00000i	$-0.499708\pi$
$191$	0.0253646	0.00183532	0.000917660		1.00000i	$0.499708\pi$
$192$	20.9764	1.51384
$193$	−6.47830	−0.466319	−0.233159	−	0.972439i	$-0.574906\pi$
$193$	−6.47830	−0.466319	−0.233159	+	0.972439i	$0.574906\pi$
$194$	12.0406	0.864464
$195$	10.6147	0.760135
$196$	0	0
$197$	5.96735	0.425156	0.212578	−	0.977144i	$-0.431814\pi$
$197$	5.96735	0.425156	0.212578	+	0.977144i	$0.431814\pi$
$198$	−16.5770	−1.17807
$199$	−0.700264	−0.0496404	−0.0248202	−	0.999692i	$-0.507901\pi$
$199$	−0.700264	−0.0496404	−0.0248202	+	0.999692i	$0.507901\pi$
$200$	57.5530	4.06961
$201$	−1.73848	−0.122623
$202$	−9.44951	−0.664865
$203$	0	0
$204$	−14.2319	−0.996432
$205$	3.40724	0.237972
$206$	−31.0473	−2.16317
$207$	3.55326	0.246969
$208$	−40.3492	−2.79771
$209$	44.1075	3.05098
$210$	0	0
$211$	5.72349	0.394021	0.197010	−	0.980401i	$-0.436877\pi$
$211$	5.72349	0.394021	0.197010	+	0.980401i	$0.436877\pi$
$212$	−13.5120	−0.928005
$213$	−14.2790	−0.978379
$214$	−14.5255	−0.992940
$215$	−10.2917	−0.701886
$216$	8.70791	0.592499
$217$	0	0
$218$	50.3030	3.40695
$219$	−0.984881	−0.0665521
$220$	109.953	7.41305
$221$	8.46623	0.569500
$222$	−23.5820	−1.58272
$223$	5.28384	0.353832	0.176916	−	0.984226i	$-0.443388\pi$
$223$	5.28384	0.353832	0.176916	+	0.984226i	$0.443388\pi$
$224$	0	0
$225$	6.60927	0.440618
$226$	25.6632	1.70709
$227$	11.5976	0.769758	0.384879	−	0.922967i	$-0.374243\pi$
$227$	11.5976	0.769758	0.384879	+	0.922967i	$0.374243\pi$
$228$	−37.4855	−2.48254
$229$	13.2278	0.874119	0.437060	−	0.899433i	$-0.356020\pi$
$229$	13.2278	0.874119	0.437060	+	0.899433i	$0.356020\pi$
$230$	−32.5692	−2.14755
$231$	0	0
$232$	−15.6023	−1.02434
$233$	10.8820	0.712901	0.356451	−	0.934314i	$-0.383987\pi$
$233$	10.8820	0.712901	0.356451	+	0.934314i	$0.383987\pi$
$234$	−8.38076	−0.547868
$235$	−17.0233	−1.11048
$236$	−50.4808	−3.28602
$237$	−8.68549	−0.564183
$238$	0	0
$239$	19.8211	1.28212	0.641061	−	0.767490i	$-0.278494\pi$
$239$	19.8211	1.28212	0.641061	+	0.767490i	$0.278494\pi$
$240$	−44.1297	−2.84856
$241$	−10.6310	−0.684801	−0.342400	−	0.939554i	$-0.611240\pi$
$241$	−10.6310	−0.684801	−0.342400	+	0.939554i	$0.611240\pi$
$242$	72.5569	4.66413
$243$	1.00000	0.0641500
$244$	−23.6818	−1.51607
$245$	0	0
$246$	−2.69016	−0.171518
$247$	22.2993	1.41887
$248$	60.1707	3.82085
$249$	−1.55919	−0.0988099
$250$	−14.7506	−0.932909
$251$	−7.22243	−0.455876	−0.227938	−	0.973676i	$-0.573198\pi$
$251$	−7.22243	−0.455876	−0.227938	+	0.973676i	$0.573198\pi$
$252$	0	0
$253$	−21.8955	−1.37656
$254$	39.9862	2.50896
$255$	9.25948	0.579851
$256$	16.0927	1.00579
$257$	−22.0393	−1.37477	−0.687387	−	0.726292i	$-0.741242\pi$
$257$	−22.0393	−1.37477	−0.687387	+	0.726292i	$0.741242\pi$
$258$	8.12570	0.505884
$259$	0	0
$260$	55.5887	3.44747
$261$	−1.79174	−0.110906
$262$	16.5479	1.02233
$263$	−9.27928	−0.572185	−0.286092	−	0.958202i	$-0.592356\pi$
$263$	−9.27928	−0.572185	−0.286092	+	0.958202i	$0.592356\pi$
$264$	−53.6589	−3.30247
$265$	8.79108	0.540032
$266$	0	0
$267$	−4.47862	−0.274087
$268$	−9.10436	−0.556137
$269$	22.5924	1.37749	0.688743	−	0.725006i	$-0.258163\pi$
$269$	22.5924	1.37749	0.688743	+	0.725006i	$0.258163\pi$
$270$	−9.16601	−0.557826
$271$	−6.25846	−0.380175	−0.190087	−	0.981767i	$-0.560877\pi$
$271$	−6.25846	−0.380175	−0.190087	+	0.981767i	$0.560877\pi$
$272$	−35.1976	−2.13417
$273$	0	0
$274$	3.06905	0.185408
$275$	−40.7268	−2.45592
$276$	18.6083	1.12009
$277$	20.9071	1.25618	0.628092	−	0.778139i	$-0.283836\pi$
$277$	20.9071	1.25618	0.628092	+	0.778139i	$0.283836\pi$
$278$	18.4568	1.10696
$279$	6.90989	0.413684
$280$	0	0
$281$	−4.42179	−0.263782	−0.131891	−	0.991264i	$-0.542105\pi$
$281$	−4.42179	−0.263782	−0.131891	+	0.991264i	$0.542105\pi$
$282$	13.4406	0.800377
$283$	20.2931	1.20630	0.603150	−	0.797628i	$-0.293912\pi$
$283$	20.2931	1.20630	0.603150	+	0.797628i	$0.293912\pi$
$284$	−74.7783	−4.43728
$285$	24.3886	1.44466
$286$	51.6429	3.05371
$287$	0	0
$288$	17.4265	1.02686
$289$	−9.61469	−0.565570
$290$	16.4231	0.964399
$291$	4.47579	0.262375
$292$	−5.15777	−0.301836
$293$	−17.7507	−1.03701	−0.518503	−	0.855076i	$-0.673510\pi$
$293$	−17.7507	−1.03701	−0.518503	+	0.855076i	$0.673510\pi$
$294$	0	0
$295$	32.8435	1.91222
$296$	−76.3337	−4.43680
$297$	−6.16208	−0.357560
$298$	−48.9438	−2.83524
$299$	−11.0696	−0.640173
$300$	34.6124	1.99835
$301$	0	0
$302$	−21.4323	−1.23329
$303$	−3.51262	−0.201795
$304$	−92.7073	−5.31713
$305$	15.4078	0.882245
$306$	−7.31075	−0.417928
$307$	0.0193606	0.00110497	0.000552483	−	1.00000i	$-0.499824\pi$
$307$	0.0193606	0.00110497	0.000552483		1.00000i	$0.499824\pi$
$308$	0	0
$309$	−11.5411	−0.656549
$310$	−63.3361	−3.59725
$311$	−11.0698	−0.627713	−0.313857	−	0.949470i	$-0.601621\pi$
$311$	−11.0698	−0.627713	−0.313857	+	0.949470i	$0.601621\pi$
$312$	−27.1281	−1.53583
$313$	2.12513	0.120119	0.0600596	−	0.998195i	$-0.480871\pi$
$313$	2.12513	0.120119	0.0600596	+	0.998195i	$0.480871\pi$
$314$	41.2657	2.32876
$315$	0	0
$316$	−45.4855	−2.55876
$317$	−20.5654	−1.15507	−0.577535	−	0.816366i	$-0.695985\pi$
$317$	−20.5654	−1.15507	−0.577535	+	0.816366i	$0.695985\pi$
$318$	−6.94093	−0.389228
$319$	11.0409	0.618169
$320$	−71.4717	−3.99539
$321$	−5.39948	−0.301370
$322$	0	0
$323$	19.4522	1.08235
$324$	5.23695	0.290942
$325$	−20.5901	−1.14214
$326$	27.0662	1.49906
$327$	18.6989	1.03405
$328$	−8.70791	−0.480814
$329$	0	0
$330$	56.4817	3.10921
$331$	−27.6456	−1.51954	−0.759769	−	0.650193i	$-0.774688\pi$
$331$	−27.6456	−1.51954	−0.759769	+	0.650193i	$0.774688\pi$
$332$	−8.16542	−0.448136
$333$	−8.76601	−0.480374
$334$	67.3971	3.68781
$335$	5.92343	0.323632
$336$	0	0
$337$	−9.41963	−0.513120	−0.256560	−	0.966528i	$-0.582589\pi$
$337$	−9.41963	−0.513120	−0.256560	+	0.966528i	$0.582589\pi$
$338$	−8.86311	−0.482089
$339$	9.53967	0.518124
$340$	48.4915	2.62982
$341$	−42.5793	−2.30580
$342$	−19.2558	−1.04124
$343$	0	0
$344$	26.3025	1.41814
$345$	−12.1068	−0.651809
$346$	10.1300	0.544590
$347$	−0.939304	−0.0504245	−0.0252123	−	0.999682i	$-0.508026\pi$
$347$	−0.939304	−0.0504245	−0.0252123	+	0.999682i	$0.508026\pi$
$348$	−9.38326	−0.502996
$349$	−3.17758	−0.170092	−0.0850461	−	0.996377i	$-0.527104\pi$
$349$	−3.17758	−0.170092	−0.0850461	+	0.996377i	$0.527104\pi$
$350$	0	0
$351$	−3.11534	−0.166285
$352$	−107.383	−5.72355
$353$	−19.4398	−1.03467	−0.517337	−	0.855782i	$-0.673077\pi$
$353$	−19.4398	−1.03467	−0.517337	+	0.855782i	$0.673077\pi$
$354$	−25.9314	−1.37824
$355$	48.6519	2.58217
$356$	−23.4543	−1.24308
$357$	0	0
$358$	−45.8170	−2.42150
$359$	−28.6801	−1.51368	−0.756839	−	0.653602i	$-0.773257\pi$
$359$	−28.6801	−1.51368	−0.756839	+	0.653602i	$0.773257\pi$
$360$	−29.6699	−1.56374
$361$	32.2353	1.69660
$362$	−21.6050	−1.13553
$363$	26.9712	1.41562
$364$	0	0
$365$	3.35572	0.175647
$366$	−12.1651	−0.635879
$367$	35.6900	1.86301	0.931503	−	0.363735i	$-0.118499\pi$
$367$	35.6900	1.86301	0.931503	+	0.363735i	$0.118499\pi$
$368$	46.0210	2.39901
$369$	−1.00000	−0.0520579
$370$	80.3493	4.17716
$371$	0	0
$372$	36.1868	1.87620
$373$	6.60288	0.341884	0.170942	−	0.985281i	$-0.445319\pi$
$373$	6.60288	0.341884	0.170942	+	0.985281i	$0.445319\pi$
$374$	45.0494	2.32945
$375$	−5.48317	−0.283150
$376$	43.5066	2.24368
$377$	5.58189	0.287482
$378$	0	0
$379$	6.60966	0.339515	0.169758	−	0.985486i	$-0.445702\pi$
$379$	6.60966	0.339515	0.169758	+	0.985486i	$0.445702\pi$
$380$	127.722	6.55200
$381$	14.8639	0.761500
$382$	0.0682349	0.00349120
$383$	−27.9782	−1.42962	−0.714809	−	0.699319i	$-0.753487\pi$
$383$	−27.9782	−1.42962	−0.714809	+	0.699319i	$0.753487\pi$
$384$	21.5770	1.10110
$385$	0	0
$386$	−17.4277	−0.887045
$387$	3.02053	0.153542
$388$	23.4395	1.18996
$389$	−23.9707	−1.21536	−0.607681	−	0.794181i	$-0.707900\pi$
$389$	−23.9707	−1.21536	−0.607681	+	0.794181i	$0.707900\pi$
$390$	28.5553	1.44595
$391$	−9.65631	−0.488341
$392$	0	0
$393$	6.15126	0.310290
$394$	16.0531	0.808745
$395$	29.5935	1.48901
$396$	−32.2705	−1.62165
$397$	−6.27159	−0.314762	−0.157381	−	0.987538i	$-0.550305\pi$
$397$	−6.27159	−0.314762	−0.157381	+	0.987538i	$0.550305\pi$
$398$	−1.88382	−0.0944274
$399$	0	0
$400$	85.6017	4.28009
$401$	2.29039	0.114376	0.0571882	−	0.998363i	$-0.481786\pi$
$401$	2.29039	0.114376	0.0571882	+	0.998363i	$0.481786\pi$
$402$	−4.67680	−0.233258
$403$	−21.5267	−1.07232
$404$	−18.3954	−0.915207
$405$	−3.40724	−0.169307
$406$	0	0
$407$	54.0168	2.67752
$408$	−23.6646	−1.17157
$409$	−6.54943	−0.323848	−0.161924	−	0.986803i	$-0.551770\pi$
$409$	−6.54943	−0.323848	−0.161924	+	0.986803i	$0.551770\pi$
$410$	9.16601	0.452677
$411$	1.14084	0.0562736
$412$	−60.4401	−2.97767
$413$	0	0
$414$	9.55884	0.469791
$415$	5.31254	0.260783
$416$	−54.2894	−2.66176
$417$	6.86085	0.335977
$418$	118.656	5.80366
$419$	−29.0673	−1.42003	−0.710016	−	0.704185i	$-0.751312\pi$
$419$	−29.0673	−1.42003	−0.710016	+	0.704185i	$0.751312\pi$
$420$	0	0
$421$	30.5913	1.49093	0.745463	−	0.666547i	$-0.232228\pi$
$421$	30.5913	1.49093	0.745463	+	0.666547i	$0.232228\pi$
$422$	15.3971	0.749518
$423$	4.99622	0.242924
$424$	−22.4674	−1.09112
$425$	−17.9613	−0.871251
$426$	−38.4127	−1.86110
$427$	0	0
$428$	−28.2768	−1.36681
$429$	19.1970	0.926839
$430$	−27.6862	−1.33515
$431$	−2.61835	−0.126121	−0.0630607	−	0.998010i	$-0.520086\pi$
$431$	−2.61835	−0.126121	−0.0630607	+	0.998010i	$0.520086\pi$
$432$	12.9518	0.623142
$433$	32.7329	1.57304	0.786520	−	0.617564i	$-0.211880\pi$
$433$	32.7329	1.57304	0.786520	+	0.617564i	$0.211880\pi$
$434$	0	0
$435$	6.10489	0.292707
$436$	97.9252	4.68977
$437$	−25.4338	−1.21667
$438$	−2.64948	−0.126597
$439$	−26.9874	−1.28804	−0.644019	−	0.765010i	$-0.722734\pi$
$439$	−26.9874	−1.28804	−0.644019	+	0.765010i	$0.722734\pi$
$440$	182.828	8.71601
$441$	0	0
$442$	22.7755	1.08332
$443$	−35.2051	−1.67264	−0.836322	−	0.548239i	$-0.815299\pi$
$443$	−35.2051	−1.67264	−0.836322	+	0.548239i	$0.815299\pi$
$444$	−45.9072	−2.17866
$445$	15.2597	0.723381
$446$	14.2144	0.673070
$447$	−18.1936	−0.860530
$448$	0	0
$449$	−5.93471	−0.280076	−0.140038	−	0.990146i	$-0.544723\pi$
$449$	−5.93471	−0.280076	−0.140038	+	0.990146i	$0.544723\pi$
$450$	17.7800	0.838156
$451$	6.16208	0.290161
$452$	49.9588	2.34987
$453$	−7.96692	−0.374318
$454$	31.1993	1.46426
$455$	0	0
$456$	−62.3303	−2.91888
$457$	−32.5841	−1.52422	−0.762109	−	0.647448i	$-0.775836\pi$
$457$	−32.5841	−1.52422	−0.762109	+	0.647448i	$0.775836\pi$
$458$	35.5849	1.66277
$459$	−2.71759	−0.126846
$460$	−63.4028	−2.95617
$461$	−33.2676	−1.54943	−0.774714	−	0.632311i	$-0.782106\pi$
$461$	−33.2676	−1.54943	−0.774714	+	0.632311i	$0.782106\pi$
$462$	0	0
$463$	8.98217	0.417437	0.208718	−	0.977976i	$-0.433071\pi$
$463$	8.98217	0.417437	0.208718	+	0.977976i	$0.433071\pi$
$464$	−23.2062	−1.07732
$465$	−23.5436	−1.09181
$466$	29.2742	1.35610
$467$	−1.61981	−0.0749559	−0.0374780	−	0.999297i	$-0.511932\pi$
$467$	−1.61981	−0.0749559	−0.0374780	+	0.999297i	$0.511932\pi$
$468$	−16.3149	−0.754157
$469$	0	0
$470$	−45.7954	−2.11238
$471$	15.3395	0.706808
$472$	−83.9386	−3.86359
$473$	−18.6127	−0.855815
$474$	−23.3653	−1.07321
$475$	−47.3084	−2.17066
$476$	0	0
$477$	−2.58012	−0.118135
$478$	53.3220	2.43889
$479$	32.6374	1.49124	0.745620	−	0.666371i	$-0.232153\pi$
$479$	32.6374	1.49124	0.745620	+	0.666371i	$0.232153\pi$
$480$	−59.3761	−2.71014
$481$	27.3091	1.24519
$482$	−28.5990	−1.30265
$483$	0	0
$484$	141.247	6.42032
$485$	−15.2501	−0.692471
$486$	2.69016	0.122028
$487$	−35.6551	−1.61569	−0.807844	−	0.589396i	$-0.799366\pi$
$487$	−35.6551	−1.61569	−0.807844	+	0.589396i	$0.799366\pi$
$488$	−39.3778	−1.78255
$489$	10.0612	0.454983
$490$	0	0
$491$	−30.7265	−1.38667	−0.693335	−	0.720616i	$-0.743859\pi$
$491$	−30.7265	−1.38667	−0.693335	+	0.720616i	$0.743859\pi$
$492$	−5.23695	−0.236100
$493$	4.86922	0.219299
$494$	59.9886	2.69901
$495$	20.9957	0.943685
$496$	89.4953	4.01846
$497$	0	0
$498$	−4.19448	−0.187959
$499$	−19.2668	−0.862501	−0.431251	−	0.902232i	$-0.641927\pi$
$499$	−19.2668	−0.862501	−0.431251	+	0.902232i	$0.641927\pi$
$500$	−28.7151	−1.28418
$501$	25.0532	1.11929
$502$	−19.4295	−0.867180
$503$	−29.6789	−1.32332	−0.661659	−	0.749804i	$-0.730148\pi$
$503$	−29.6789	−1.32332	−0.661659	+	0.749804i	$0.730148\pi$
$504$	0	0
$505$	11.9683	0.532584
$506$	−58.9023	−2.61853
$507$	−3.29464	−0.146320
$508$	77.8414	3.45365
$509$	−18.6264	−0.825599	−0.412799	−	0.910822i	$-0.635449\pi$
$509$	−18.6264	−0.825599	−0.412799	+	0.910822i	$0.635449\pi$
$510$	24.9095	1.10301
$511$	0	0
$512$	0.137808	0.00609032
$513$	−7.15789	−0.316028
$514$	−59.2892	−2.61513
$515$	39.3232	1.73279
$516$	15.8184	0.696365
$517$	−30.7871	−1.35402
$518$	0	0
$519$	3.76556	0.165290
$520$	92.4320	4.05341
$521$	9.20530	0.403292	0.201646	−	0.979459i	$-0.435371\pi$
$521$	9.20530	0.403292	0.201646	+	0.979459i	$0.435371\pi$
$522$	−4.82007	−0.210969
$523$	20.9820	0.917480	0.458740	−	0.888571i	$-0.348301\pi$
$523$	20.9820	0.917480	0.458740	+	0.888571i	$0.348301\pi$
$524$	32.2138	1.40727
$525$	0	0
$526$	−24.9627	−1.08843
$527$	−18.7783	−0.817994
$528$	−79.8098	−3.47328
$529$	−10.3743	−0.451058
$530$	23.6494	1.02726
$531$	−9.63934	−0.418312
$532$	0	0
$533$	3.11534	0.134940
$534$	−12.0482	−0.521377
$535$	18.3973	0.795385
$536$	−15.1386	−0.653887
$537$	−17.0313	−0.734957
$538$	60.7773	2.62029
$539$	0	0
$540$	−17.8435	−0.767864
$541$	9.69119	0.416657	0.208328	−	0.978059i	$-0.433198\pi$
$541$	9.69119	0.416657	0.208328	+	0.978059i	$0.433198\pi$
$542$	−16.8363	−0.723179
$543$	−8.03112	−0.344648
$544$	−47.3580	−2.03046
$545$	−63.7116	−2.72910
$546$	0	0
$547$	−13.5021	−0.577306	−0.288653	−	0.957434i	$-0.593207\pi$
$547$	−13.5021	−0.577306	−0.288653	+	0.957434i	$0.593207\pi$
$548$	5.97454	0.255220
$549$	−4.52207	−0.192997
$550$	−109.562	−4.67173
$551$	12.8251	0.546367
$552$	30.9415	1.31696
$553$	0	0
$554$	56.2433	2.38955
$555$	29.8679	1.26782
$556$	35.9299	1.52377
$557$	−25.6589	−1.08720	−0.543602	−	0.839343i	$-0.682940\pi$
$557$	−25.6589	−1.08720	−0.543602	+	0.839343i	$0.682940\pi$
$558$	18.5887	0.786923
$559$	−9.40998	−0.398000
$560$	0	0
$561$	16.7460	0.707017
$562$	−11.8953	−0.501774
$563$	15.6493	0.659538	0.329769	−	0.944062i	$-0.393029\pi$
$563$	15.6493	0.659538	0.329769	+	0.944062i	$0.393029\pi$
$564$	26.1650	1.10174
$565$	−32.5039	−1.36745
$566$	54.5917	2.29466
$567$	0	0
$568$	−124.340	−5.21719
$569$	20.1795	0.845968	0.422984	−	0.906137i	$-0.360983\pi$
$569$	20.1795	0.845968	0.422984	+	0.906137i	$0.360983\pi$
$570$	65.6093	2.74807
$571$	36.3684	1.52197	0.760986	−	0.648769i	$-0.224716\pi$
$571$	36.3684	1.52197	0.760986	+	0.648769i	$0.224716\pi$
$572$	100.534	4.20353
$573$	0.0253646	0.00105962
$574$	0	0
$575$	23.4845	0.979370
$576$	20.9764	0.874018
$577$	11.6347	0.484358	0.242179	−	0.970232i	$-0.422138\pi$
$577$	11.6347	0.484358	0.242179	+	0.970232i	$0.422138\pi$
$578$	−25.8650	−1.07584
$579$	−6.47830	−0.269229
$580$	31.9710	1.32752
$581$	0	0
$582$	12.0406	0.499098
$583$	15.8989	0.658465
$584$	−8.57626	−0.354888
$585$	10.6147	0.438864
$586$	−47.7521	−1.97262
$587$	16.6760	0.688291	0.344146	−	0.938916i	$-0.388169\pi$
$587$	16.6760	0.688291	0.344146	+	0.938916i	$0.388169\pi$
$588$	0	0
$589$	−49.4602	−2.03797
$590$	88.3543	3.63749
$591$	5.96735	0.245464
$592$	−113.535	−4.66627
$593$	2.82243	0.115903	0.0579516	−	0.998319i	$-0.481543\pi$
$593$	2.82243	0.115903	0.0579516	+	0.998319i	$0.481543\pi$
$594$	−16.5770	−0.680161
$595$	0	0
$596$	−95.2792	−3.90279
$597$	−0.700264	−0.0286599
$598$	−29.7790	−1.21776
$599$	8.38636	0.342658	0.171329	−	0.985214i	$-0.445194\pi$
$599$	8.38636	0.342658	0.171329	+	0.985214i	$0.445194\pi$
$600$	57.5530	2.34959
$601$	−27.8657	−1.13667	−0.568333	−	0.822799i	$-0.692411\pi$
$601$	−27.8657	−1.13667	−0.568333	+	0.822799i	$0.692411\pi$
$602$	0	0
$603$	−1.73848	−0.0707966
$604$	−41.7224	−1.69766
$605$	−91.8974	−3.73616
$606$	−9.44951	−0.383860
$607$	−28.8976	−1.17292	−0.586459	−	0.809979i	$-0.699478\pi$
$607$	−28.8976	−1.17292	−0.586459	+	0.809979i	$0.699478\pi$
$608$	−124.737	−5.05874
$609$	0	0
$610$	41.4493	1.67823
$611$	−15.5649	−0.629690
$612$	−14.2319	−0.575290
$613$	14.9001	0.601811	0.300905	−	0.953654i	$-0.402711\pi$
$613$	14.9001	0.601811	0.300905	+	0.953654i	$0.402711\pi$
$614$	0.0520830	0.00210190
$615$	3.40724	0.137393
$616$	0	0
$617$	−31.5116	−1.26861	−0.634305	−	0.773083i	$-0.718714\pi$
$617$	−31.5116	−1.26861	−0.634305	+	0.773083i	$0.718714\pi$
$618$	−31.0473	−1.24891
$619$	5.46701	0.219738	0.109869	−	0.993946i	$-0.464957\pi$
$619$	5.46701	0.219738	0.109869	+	0.993946i	$0.464957\pi$
$620$	−123.297	−4.95172
$621$	3.55326	0.142587
$622$	−29.7796	−1.19405
$623$	0	0
$624$	−40.3492	−1.61526
$625$	−14.3639	−0.574556
$626$	5.71692	0.228494
$627$	44.1075	1.76148
$628$	80.3323	3.20561
$629$	23.8224	0.949863
$630$	0	0
$631$	16.3281	0.650011	0.325005	−	0.945712i	$-0.394634\pi$
$631$	16.3281	0.650011	0.325005	+	0.945712i	$0.394634\pi$
$632$	−75.6325	−3.00850
$633$	5.72349	0.227488
$634$	−55.3243	−2.19721
$635$	−50.6448	−2.00978
$636$	−13.5120	−0.535784
$637$	0	0
$638$	29.7016	1.17590
$639$	−14.2790	−0.564867
$640$	−73.5179	−2.90605
$641$	18.7046	0.738787	0.369393	−	0.929273i	$-0.379566\pi$
$641$	18.7046	0.738787	0.369393	+	0.929273i	$0.379566\pi$
$642$	−14.5255	−0.573274
$643$	10.5311	0.415307	0.207654	−	0.978202i	$-0.433417\pi$
$643$	10.5311	0.415307	0.207654	+	0.978202i	$0.433417\pi$
$644$	0	0
$645$	−10.2917	−0.405234
$646$	52.3295	2.05888
$647$	−11.2429	−0.442005	−0.221002	−	0.975273i	$-0.570933\pi$
$647$	−11.2429	−0.442005	−0.221002	+	0.975273i	$0.570933\pi$
$648$	8.70791	0.342079
$649$	59.3984	2.33159
$650$	−55.3907	−2.17260
$651$	0	0
$652$	52.6900	2.06350
$653$	9.58250	0.374992	0.187496	−	0.982265i	$-0.439963\pi$
$653$	9.58250	0.374992	0.187496	+	0.982265i	$0.439963\pi$
$654$	50.3030	1.96700
$655$	−20.9588	−0.818928
$656$	−12.9518	−0.505681
$657$	−0.984881	−0.0384239
$658$	0	0
$659$	−7.57775	−0.295187	−0.147594	−	0.989048i	$-0.547153\pi$
$659$	−7.57775	−0.295187	−0.147594	+	0.989048i	$0.547153\pi$
$660$	109.953	4.27993
$661$	−16.6975	−0.649457	−0.324729	−	0.945807i	$-0.605273\pi$
$661$	−16.6975	−0.649457	−0.324729	+	0.945807i	$0.605273\pi$
$662$	−74.3709	−2.89051
$663$	8.46623	0.328801
$664$	−13.5773	−0.526902
$665$	0	0
$666$	−23.5820	−0.913782
$667$	−6.36652	−0.246513
$668$	131.202	5.07638
$669$	5.28384	0.204285
$670$	15.9350	0.615622
$671$	27.8653	1.07573
$672$	0	0
$673$	30.0090	1.15676	0.578380	−	0.815767i	$-0.303685\pi$
$673$	30.0090	1.15676	0.578380	+	0.815767i	$0.303685\pi$
$674$	−25.3403	−0.976072
$675$	6.60927	0.254391
$676$	−17.2539	−0.663611
$677$	37.6766	1.44803	0.724014	−	0.689785i	$-0.242295\pi$
$677$	37.6766	1.44803	0.724014	+	0.689785i	$0.242295\pi$
$678$	25.6632	0.985591
$679$	0	0
$680$	80.6308	3.09205
$681$	11.5976	0.444420
$682$	−114.545	−4.38616
$683$	21.5536	0.824727	0.412363	−	0.911019i	$-0.364703\pi$
$683$	21.5536	0.824727	0.412363	+	0.911019i	$0.364703\pi$
$684$	−37.4855	−1.43329
$685$	−3.88712	−0.148519
$686$	0	0
$687$	13.2278	0.504673
$688$	39.1212	1.49148
$689$	8.03795	0.306222
$690$	−32.5692	−1.23989
$691$	31.7914	1.20940	0.604701	−	0.796453i	$-0.293293\pi$
$691$	31.7914	1.20940	0.604701	+	0.796453i	$0.293293\pi$
$692$	19.7201	0.749645
$693$	0	0
$694$	−2.52688	−0.0959190
$695$	−23.3765	−0.886723
$696$	−15.6023	−0.591405
$697$	2.71759	0.102936
$698$	−8.54820	−0.323554
$699$	10.8820	0.411594
$700$	0	0
$701$	−27.0893	−1.02315	−0.511574	−	0.859239i	$-0.670937\pi$
$701$	−27.0893	−1.02315	−0.511574	+	0.859239i	$0.670937\pi$
$702$	−8.38076	−0.316312
$703$	62.7461	2.36651
$704$	−129.258	−4.87161
$705$	−17.0233	−0.641135
$706$	−52.2960	−1.96819
$707$	0	0
$708$	−50.4808	−1.89718
$709$	32.4047	1.21699	0.608493	−	0.793560i	$-0.291775\pi$
$709$	32.4047	1.21699	0.608493	+	0.793560i	$0.291775\pi$
$710$	130.881	4.91188
$711$	−8.68549	−0.325731
$712$	−38.9995	−1.46157
$713$	24.5526	0.919504
$714$	0	0
$715$	−65.4087	−2.44615
$716$	−89.1923	−3.33327
$717$	19.8211	0.740234
$718$	−77.1540	−2.87936
$719$	37.4880	1.39806	0.699032	−	0.715090i	$-0.253614\pi$
$719$	37.4880	1.39806	0.699032	+	0.715090i	$0.253614\pi$
$720$	−44.1297	−1.64462
$721$	0	0
$722$	86.7182	3.22732
$723$	−10.6310	−0.395370
$724$	−42.0586	−1.56309
$725$	−11.8421	−0.439805
$726$	72.5569	2.69284
$727$	45.2143	1.67690	0.838452	−	0.544975i	$-0.183461\pi$
$727$	45.2143	1.67690	0.838452	+	0.544975i	$0.183461\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	9.02743	0.334120
$731$	−8.20857	−0.303605
$732$	−23.6818	−0.875306
$733$	−31.6823	−1.17021	−0.585106	−	0.810957i	$-0.698947\pi$
$733$	−31.6823	−1.17021	−0.585106	+	0.810957i	$0.698947\pi$
$734$	96.0119	3.54386
$735$	0	0
$736$	61.9208	2.28243
$737$	10.7127	0.394607
$738$	−2.69016	−0.0990261
$739$	11.4430	0.420937	0.210469	−	0.977601i	$-0.432501\pi$
$739$	11.4430	0.420937	0.210469	+	0.977601i	$0.432501\pi$
$740$	156.417	5.74999
$741$	22.2993	0.819184
$742$	0	0
$743$	6.82660	0.250444	0.125222	−	0.992129i	$-0.460036\pi$
$743$	6.82660	0.250444	0.125222	+	0.992129i	$0.460036\pi$
$744$	60.1707	2.20597
$745$	61.9901	2.27114
$746$	17.7628	0.650342
$747$	−1.55919	−0.0570479
$748$	87.6981	3.20656
$749$	0	0
$750$	−14.7506	−0.538615
$751$	29.9121	1.09151	0.545754	−	0.837945i	$-0.316243\pi$
$751$	29.9121	1.09151	0.545754	+	0.837945i	$0.316243\pi$
$752$	64.7099	2.35973
$753$	−7.22243	−0.263200
$754$	15.0162	0.546856
$755$	27.1452	0.987914
$756$	0	0
$757$	38.1911	1.38808	0.694039	−	0.719938i	$-0.255830\pi$
$757$	38.1911	1.38808	0.694039	+	0.719938i	$0.255830\pi$
$758$	17.7810	0.645836
$759$	−21.8955	−0.794755
$760$	212.374	7.70362
$761$	−8.15452	−0.295601	−0.147801	−	0.989017i	$-0.547219\pi$
$761$	−8.15452	−0.295601	−0.147801	+	0.989017i	$0.547219\pi$
$762$	39.9862	1.44855
$763$	0	0
$764$	0.132833	0.00480574
$765$	9.25948	0.334777
$766$	−75.2658	−2.71946
$767$	30.0298	1.08431
$768$	16.0927	0.580694
$769$	5.15883	0.186032	0.0930160	−	0.995665i	$-0.470349\pi$
$769$	5.15883	0.186032	0.0930160	+	0.995665i	$0.470349\pi$
$770$	0	0
$771$	−22.0393	−0.793726
$772$	−33.9266	−1.22104
$773$	−2.29140	−0.0824158	−0.0412079	−	0.999151i	$-0.513121\pi$
$773$	−2.29140	−0.0824158	−0.0412079	+	0.999151i	$0.513121\pi$
$774$	8.12570	0.292072
$775$	45.6693	1.64049
$776$	38.9748	1.39911
$777$	0	0
$778$	−64.4850	−2.31190
$779$	7.15789	0.256458
$780$	55.5887	1.99040
$781$	87.9882	3.14846
$782$	−25.9770	−0.928936
$783$	−1.79174	−0.0640316
$784$	0	0
$785$	−52.2654	−1.86543
$786$	16.5479	0.590242
$787$	−5.23569	−0.186632	−0.0933161	−	0.995637i	$-0.529747\pi$
$787$	−5.23569	−0.186632	−0.0933161	+	0.995637i	$0.529747\pi$
$788$	31.2507	1.11326
$789$	−9.27928	−0.330351
$790$	79.6112	2.83244
$791$	0	0
$792$	−53.6589	−1.90668
$793$	14.0878	0.500272
$794$	−16.8716	−0.598749
$795$	8.79108	0.311787
$796$	−3.66725	−0.129982
$797$	36.8582	1.30558	0.652792	−	0.757537i	$-0.273598\pi$
$797$	36.8582	1.30558	0.652792	+	0.757537i	$0.273598\pi$
$798$	0	0
$799$	−13.5777	−0.480344
$800$	115.176	4.07210
$801$	−4.47862	−0.158244
$802$	6.16150	0.217570
$803$	6.06891	0.214167
$804$	−9.10436	−0.321086
$805$	0	0
$806$	−57.9102	−2.03980
$807$	22.5924	0.795292
$808$	−30.5876	−1.07607
$809$	30.4494	1.07054	0.535272	−	0.844680i	$-0.320209\pi$
$809$	30.4494	1.07054	0.535272	+	0.844680i	$0.320209\pi$
$810$	−9.16601	−0.322061
$811$	−25.5091	−0.895747	−0.447874	−	0.894097i	$-0.647819\pi$
$811$	−25.5091	−0.895747	−0.447874	+	0.894097i	$0.647819\pi$
$812$	0	0
$813$	−6.25846	−0.219494
$814$	145.314	5.09325
$815$	−34.2809	−1.20081
$816$	−35.1976	−1.23216
$817$	−21.6206	−0.756409
$818$	−17.6190	−0.616034
$819$	0	0
$820$	17.8435	0.623124
$821$	0.309981	0.0108184	0.00540921	−	0.999985i	$-0.498278\pi$
$821$	0.309981	0.0108184	0.00540921	+	0.999985i	$0.498278\pi$
$822$	3.06905	0.107045
$823$	−26.6484	−0.928904	−0.464452	−	0.885598i	$-0.653749\pi$
$823$	−26.6484	−0.928904	−0.464452	+	0.885598i	$0.653749\pi$
$824$	−100.499	−3.50104
$825$	−40.7268	−1.41793
$826$	0	0
$827$	−29.5685	−1.02820	−0.514099	−	0.857731i	$-0.671874\pi$
$827$	−29.5685	−1.02820	−0.514099	+	0.857731i	$0.671874\pi$
$828$	18.6083	0.646682
$829$	15.7905	0.548427	0.274214	−	0.961669i	$-0.411582\pi$
$829$	15.7905	0.548427	0.274214	+	0.961669i	$0.411582\pi$
$830$	14.2916	0.496068
$831$	20.9071	0.725258
$832$	−65.3488	−2.26556
$833$	0	0
$834$	18.4568	0.639105
$835$	−85.3623	−2.95408
$836$	230.989	7.98891
$837$	6.90989	0.238841
$838$	−78.1957	−2.70123
$839$	−38.4714	−1.32818	−0.664091	−	0.747652i	$-0.731181\pi$
$839$	−38.4714	−1.32818	−0.664091	+	0.747652i	$0.731181\pi$
$840$	0	0
$841$	−25.7897	−0.889299
$842$	82.2953	2.83608
$843$	−4.42179	−0.152295
$844$	29.9736	1.03173
$845$	11.2256	0.386173
$846$	13.4406	0.462098
$847$	0	0
$848$	−33.4171	−1.14755
$849$	20.2931	0.696458
$850$	−48.3187	−1.65732
$851$	−31.1479	−1.06774
$852$	−74.7783	−2.56186
$853$	−53.8643	−1.84428	−0.922140	−	0.386857i	$-0.873561\pi$
$853$	−53.8643	−1.84428	−0.922140	+	0.386857i	$0.873561\pi$
$854$	0	0
$855$	24.3886	0.834073
$856$	−47.0182	−1.60705
$857$	13.5031	0.461257	0.230628	−	0.973042i	$-0.425922\pi$
$857$	13.5031	0.461257	0.230628	+	0.973042i	$0.425922\pi$
$858$	51.6429	1.76306
$859$	−17.5376	−0.598376	−0.299188	−	0.954194i	$-0.596716\pi$
$859$	−17.5376	−0.598376	−0.299188	+	0.954194i	$0.596716\pi$
$860$	−53.8969	−1.83787
$861$	0	0
$862$	−7.04377	−0.239912
$863$	−12.3076	−0.418957	−0.209479	−	0.977813i	$-0.567177\pi$
$863$	−12.3076	−0.418957	−0.209479	+	0.977813i	$0.567177\pi$
$864$	17.4265	0.592860
$865$	−12.8302	−0.436239
$866$	88.0566	2.99228
$867$	−9.61469	−0.326532
$868$	0	0
$869$	53.5207	1.81556
$870$	16.4231	0.556796
$871$	5.41598	0.183513
$872$	162.828	5.51406
$873$	4.47579	0.151483
$874$	−68.4211	−2.31438
$875$	0	0
$876$	−5.15777	−0.174265
$877$	21.1044	0.712644	0.356322	−	0.934363i	$-0.384031\pi$
$877$	21.1044	0.712644	0.356322	+	0.934363i	$0.384031\pi$
$878$	−72.6004	−2.45014
$879$	−17.7507	−0.598715
$880$	271.931	9.16679
$881$	13.4813	0.454198	0.227099	−	0.973872i	$-0.427076\pi$
$881$	13.4813	0.454198	0.227099	+	0.973872i	$0.427076\pi$
$882$	0	0
$883$	−27.9922	−0.942012	−0.471006	−	0.882130i	$-0.656109\pi$
$883$	−27.9922	−0.942012	−0.471006	+	0.882130i	$0.656109\pi$
$884$	44.3372	1.49122
$885$	32.8435	1.10402
$886$	−94.7072	−3.18175
$887$	−10.4872	−0.352124	−0.176062	−	0.984379i	$-0.556336\pi$
$887$	−10.4872	−0.352124	−0.176062	+	0.984379i	$0.556336\pi$
$888$	−76.3337	−2.56159
$889$	0	0
$890$	41.0511	1.37604
$891$	−6.16208	−0.206437
$892$	27.6712	0.926501
$893$	−35.7624	−1.19674
$894$	−48.9438	−1.63692
$895$	58.0298	1.93972
$896$	0	0
$897$	−11.0696	−0.369604
$898$	−15.9653	−0.532769
$899$	−12.3807	−0.412921
$900$	34.6124	1.15375
$901$	7.01171	0.233594
$902$	16.5770	0.551953
$903$	0	0
$904$	83.0707	2.76289
$905$	27.3639	0.909608
$906$	−21.4323	−0.712039
$907$	−23.4770	−0.779541	−0.389770	−	0.920912i	$-0.627446\pi$
$907$	−23.4770	−0.779541	−0.389770	+	0.920912i	$0.627446\pi$
$908$	60.7359	2.01559
$909$	−3.51262	−0.116506
$910$	0	0
$911$	−9.86885	−0.326970	−0.163485	−	0.986546i	$-0.552273\pi$
$911$	−9.86885	−0.326970	−0.163485	+	0.986546i	$0.552273\pi$
$912$	−92.7073	−3.06984
$913$	9.60788	0.317974
$914$	−87.6563	−2.89941
$915$	15.4078	0.509365
$916$	69.2735	2.28886
$917$	0	0
$918$	−7.31075	−0.241291
$919$	−59.3869	−1.95899	−0.979497	−	0.201460i	$-0.935431\pi$
$919$	−59.3869	−1.95899	−0.979497	+	0.201460i	$0.935431\pi$
$920$	−105.425	−3.47576
$921$	0.0193606	0.000637953 0
$922$	−89.4952	−2.94737
$923$	44.4839	1.46421
$924$	0	0
$925$	−57.9369	−1.90495
$926$	24.1635	0.794061
$927$	−11.5411	−0.379059
$928$	−31.2237	−1.02497
$929$	51.1638	1.67863	0.839314	−	0.543647i	$-0.182957\pi$
$929$	51.1638	1.67863	0.839314	+	0.543647i	$0.182957\pi$
$930$	−63.3361	−2.07687
$931$	0	0
$932$	56.9883	1.86671
$933$	−11.0698	−0.362410
$934$	−4.35755	−0.142583
$935$	−57.0577	−1.86599
$936$	−27.1281	−0.886711
$937$	8.46933	0.276681	0.138341	−	0.990385i	$-0.455823\pi$
$937$	8.46933	0.276681	0.138341	+	0.990385i	$0.455823\pi$
$938$	0	0
$939$	2.12513	0.0693508
$940$	−89.1502	−2.90776
$941$	37.4128	1.21962	0.609812	−	0.792546i	$-0.291245\pi$
$941$	37.4128	1.21962	0.609812	+	0.792546i	$0.291245\pi$
$942$	41.2657	1.34451
$943$	−3.55326	−0.115710
$944$	−124.846	−4.06341
$945$	0	0
$946$	−50.0712	−1.62796
$947$	−24.5064	−0.796351	−0.398176	−	0.917309i	$-0.630357\pi$
$947$	−24.5064	−0.796351	−0.398176	+	0.917309i	$0.630357\pi$
$948$	−45.4855	−1.47730
$949$	3.06824	0.0995993
$950$	−127.267	−4.12909
$951$	−20.5654	−0.666880
$952$	0	0
$953$	38.4568	1.24574	0.622869	−	0.782326i	$-0.285967\pi$
$953$	38.4568	1.24574	0.622869	+	0.782326i	$0.285967\pi$
$954$	−6.94093	−0.224721
$955$	−0.0864233	−0.00279659
$956$	103.802	3.35721
$957$	11.0409	0.356900
$958$	87.7997	2.83668
$959$	0	0
$960$	−71.4717	−2.30674
$961$	16.7466	0.540213
$962$	73.4659	2.36863
$963$	−5.39948	−0.173996
$964$	−55.6739	−1.79313
$965$	22.0731	0.710559
$966$	0	0
$967$	39.5442	1.27166	0.635828	−	0.771831i	$-0.280659\pi$
$967$	39.5442	1.27166	0.635828	+	0.771831i	$0.280659\pi$
$968$	234.863	7.54879
$969$	19.4522	0.624895
$970$	−41.0251	−1.31724
$971$	−19.2833	−0.618831	−0.309416	−	0.950927i	$-0.600133\pi$
$971$	−19.2833	−0.618831	−0.309416	+	0.950927i	$0.600133\pi$
$972$	5.23695	0.167975
$973$	0	0
$974$	−95.9180	−3.07341
$975$	−20.5901	−0.659412
$976$	−58.5687	−1.87474
$977$	56.6543	1.81253	0.906266	−	0.422707i	$-0.138920\pi$
$977$	56.6543	1.81253	0.906266	+	0.422707i	$0.138920\pi$
$978$	27.0662	0.865481
$979$	27.5976	0.882024
$980$	0	0
$981$	18.6989	0.597010
$982$	−82.6593	−2.63776
$983$	−25.1899	−0.803434	−0.401717	−	0.915764i	$-0.631587\pi$
$983$	−25.1899	−0.803434	−0.401717	+	0.915764i	$0.631587\pi$
$984$	−8.70791	−0.277598
$985$	−20.3322	−0.647837
$986$	13.0990	0.417156
$987$	0	0
$988$	116.780	3.71527
$989$	10.7327	0.341281
$990$	56.4817	1.79511
$991$	−31.5924	−1.00357	−0.501783	−	0.864994i	$-0.667322\pi$
$991$	−31.5924	−1.00357	−0.501783	+	0.864994i	$0.667322\pi$
$992$	120.415	3.82318
$993$	−27.6456	−0.877305
$994$	0	0
$995$	2.38597	0.0756402
$996$	−8.16542	−0.258731
$997$	−49.0226	−1.55256	−0.776280	−	0.630388i	$-0.782896\pi$
$997$	−49.0226	−1.55256	−0.776280	+	0.630388i	$0.782896\pi$
$998$	−51.8308	−1.64067
$999$	−8.76601	−0.277344

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bk.1.14		14
7.3	odd	6		861.2.i.g.247.1	✓	28
7.5	odd	6		861.2.i.g.739.1	yes	28
7.6	odd	2		6027.2.a.bj.1.14		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.g.247.1	✓	28	7.3	odd	6
861.2.i.g.739.1	yes	28	7.5	odd	6
6027.2.a.bj.1.14		14	7.6	odd	2
6027.2.a.bk.1.14		14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.69016 q^{2} +1.00000 q^{3} +5.23695 q^{4} -3.40724 q^{5} +2.69016 q^{6} +8.70791 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.69016 q^{2} +1.00000 q^{3} +5.23695 q^{4} -3.40724 q^{5} +2.69016 q^{6} +8.70791 q^{8} +1.00000 q^{9} -9.16601 q^{10} -6.16208 q^{11} +5.23695 q^{12} -3.11534 q^{13} -3.40724 q^{15} +12.9518 q^{16} -2.71759 q^{17} +2.69016 q^{18} -7.15789 q^{19} -17.8435 q^{20} -16.5770 q^{22} +3.55326 q^{23} +8.70791 q^{24} +6.60927 q^{25} -8.38076 q^{26} +1.00000 q^{27} -1.79174 q^{29} -9.16601 q^{30} +6.90989 q^{31} +17.4265 q^{32} -6.16208 q^{33} -7.31075 q^{34} +5.23695 q^{36} -8.76601 q^{37} -19.2558 q^{38} -3.11534 q^{39} -29.6699 q^{40} -1.00000 q^{41} +3.02053 q^{43} -32.2705 q^{44} -3.40724 q^{45} +9.55884 q^{46} +4.99622 q^{47} +12.9518 q^{48} +17.7800 q^{50} -2.71759 q^{51} -16.3149 q^{52} -2.58012 q^{53} +2.69016 q^{54} +20.9957 q^{55} -7.15789 q^{57} -4.82007 q^{58} -9.63934 q^{59} -17.8435 q^{60} -4.52207 q^{61} +18.5887 q^{62} +20.9764 q^{64} +10.6147 q^{65} -16.5770 q^{66} -1.73848 q^{67} -14.2319 q^{68} +3.55326 q^{69} -14.2790 q^{71} +8.70791 q^{72} -0.984881 q^{73} -23.5820 q^{74} +6.60927 q^{75} -37.4855 q^{76} -8.38076 q^{78} -8.68549 q^{79} -44.1297 q^{80} +1.00000 q^{81} -2.69016 q^{82} -1.55919 q^{83} +9.25948 q^{85} +8.12570 q^{86} -1.79174 q^{87} -53.6589 q^{88} -4.47862 q^{89} -9.16601 q^{90} +18.6083 q^{92} +6.90989 q^{93} +13.4406 q^{94} +24.3886 q^{95} +17.4265 q^{96} +4.47579 q^{97} -6.16208 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 2 * q^2 + 14 * q^3 + 14 * q^4 - 10 * q^5 - 2 * q^6 - 6 * q^8 + 14 * q^9	\( 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9} - 3 q^{10} - 16 q^{11} + 14 q^{12} - 21 q^{13} - 10 q^{15} + 22 q^{16} - 12 q^{17} - 2 q^{18} - 2 q^{19} - 40 q^{20} + q^{22} - 7 q^{23} - 6 q^{24} + 22 q^{25} - 2 q^{26} + 14 q^{27} - 16 q^{29} - 3 q^{30} - 8 q^{31} - 19 q^{32} - 16 q^{33} - 33 q^{34} + 14 q^{36} + q^{37} - 32 q^{38} - 21 q^{39} + 13 q^{40} - 14 q^{41} + 14 q^{43} - 36 q^{44} - 10 q^{45} - 12 q^{46} - 12 q^{47} + 22 q^{48} - q^{50} - 12 q^{51} - 60 q^{52} - 20 q^{53} - 2 q^{54} + 11 q^{55} - 2 q^{57} + 21 q^{58} - 25 q^{59} - 40 q^{60} - 26 q^{61} + 33 q^{62} + 42 q^{64} - 8 q^{65} + q^{66} - 22 q^{67} - 15 q^{68} - 7 q^{69} - 36 q^{71} - 6 q^{72} - 31 q^{73} - 65 q^{74} + 22 q^{75} + 2 q^{76} - 2 q^{78} + 12 q^{79} - 112 q^{80} + 14 q^{81} + 2 q^{82} - 20 q^{83} + 40 q^{85} - 9 q^{86} - 16 q^{87} - 54 q^{88} - 39 q^{89} - 3 q^{90} + 63 q^{92} - 8 q^{93} - 14 q^{94} - 55 q^{95} - 19 q^{96} - 18 q^{97} - 16 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 + 14 * q^3 + 14 * q^4 - 10 * q^5 - 2 * q^6 - 6 * q^8 + 14 * q^9 - 3 * q^10 - 16 * q^11 + 14 * q^12 - 21 * q^13 - 10 * q^15 + 22 * q^16 - 12 * q^17 - 2 * q^18 - 2 * q^19 - 40 * q^20 + q^22 - 7 * q^23 - 6 * q^24 + 22 * q^25 - 2 * q^26 + 14 * q^27 - 16 * q^29 - 3 * q^30 - 8 * q^31 - 19 * q^32 - 16 * q^33 - 33 * q^34 + 14 * q^36 + q^37 - 32 * q^38 - 21 * q^39 + 13 * q^40 - 14 * q^41 + 14 * q^43 - 36 * q^44 - 10 * q^45 - 12 * q^46 - 12 * q^47 + 22 * q^48 - q^50 - 12 * q^51 - 60 * q^52 - 20 * q^53 - 2 * q^54 + 11 * q^55 - 2 * q^57 + 21 * q^58 - 25 * q^59 - 40 * q^60 - 26 * q^61 + 33 * q^62 + 42 * q^64 - 8 * q^65 + q^66 - 22 * q^67 - 15 * q^68 - 7 * q^69 - 36 * q^71 - 6 * q^72 - 31 * q^73 - 65 * q^74 + 22 * q^75 + 2 * q^76 - 2 * q^78 + 12 * q^79 - 112 * q^80 + 14 * q^81 + 2 * q^82 - 20 * q^83 + 40 * q^85 - 9 * q^86 - 16 * q^87 - 54 * q^88 - 39 * q^89 - 3 * q^90 + 63 * q^92 - 8 * q^93 - 14 * q^94 - 55 * q^95 - 19 * q^96 - 18 * q^97 - 16 * q^99

Introduction

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Modular forms

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