LMFDB - Embedded newform 2499.2.a.bb.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2499,2,Mod(1,2499)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2499, 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("2499.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2499 = 3 \cdot 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2499.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:	$19.9546154651$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.1383597.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 7x^{3} + 14x^{2} + 7x - 15 $ x^5 - 2x^4 - 7x^3 + 14x^2 + 7x - 15
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 357)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.22966$ of defining polynomial
Character	$\chi$	$=$	2499.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.22966 q^{2} +1.00000 q^{3} -0.487931 q^{4} +2.41946 q^{5} -1.22966 q^{6} +3.05931 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.22966 q^{2} +1.00000 q^{3} -0.487931 q^{4} +2.41946 q^{5} -1.22966 q^{6} +3.05931 q^{8} +1.00000 q^{9} -2.97512 q^{10} +3.47878 q^{11} -0.487931 q^{12} -5.95098 q^{13} +2.41946 q^{15} -2.78606 q^{16} -1.00000 q^{17} -1.22966 q^{18} -7.18064 q^{19} -1.18053 q^{20} -4.27772 q^{22} -2.81020 q^{23} +3.05931 q^{24} +0.853791 q^{25} +7.31770 q^{26} +1.00000 q^{27} -3.43234 q^{29} -2.97512 q^{30} -6.27399 q^{31} -2.69271 q^{32} +3.47878 q^{33} +1.22966 q^{34} -0.487931 q^{36} -7.57150 q^{37} +8.82977 q^{38} -5.95098 q^{39} +7.40189 q^{40} +2.69271 q^{41} -9.25568 q^{43} -1.69740 q^{44} +2.41946 q^{45} +3.45560 q^{46} -8.41031 q^{47} -2.78606 q^{48} -1.04987 q^{50} -1.00000 q^{51} +2.90367 q^{52} +3.04433 q^{53} -1.22966 q^{54} +8.41676 q^{55} -7.18064 q^{57} +4.22062 q^{58} -1.31113 q^{59} -1.18053 q^{60} -9.92238 q^{61} +7.71489 q^{62} +8.88325 q^{64} -14.3982 q^{65} -4.27772 q^{66} +13.7814 q^{67} +0.487931 q^{68} -2.81020 q^{69} +1.20552 q^{71} +3.05931 q^{72} +12.3085 q^{73} +9.31039 q^{74} +0.853791 q^{75} +3.50366 q^{76} +7.31770 q^{78} -0.320283 q^{79} -6.74077 q^{80} +1.00000 q^{81} -3.31113 q^{82} +11.1337 q^{83} -2.41946 q^{85} +11.3814 q^{86} -3.43234 q^{87} +10.6427 q^{88} -11.6993 q^{89} -2.97512 q^{90} +1.37118 q^{92} -6.27399 q^{93} +10.3418 q^{94} -17.3733 q^{95} -2.69271 q^{96} -8.62561 q^{97} +3.47878 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} + 5 q^{3} + 8 q^{4} - q^{5} - 2 q^{6} + 5 q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 + 5 * q^3 + 8 * q^4 - q^5 - 2 * q^6 + 5 * q^9	$ 5 q - 2 q^{2} + 5 q^{3} + 8 q^{4} - q^{5} - 2 q^{6} + 5 q^{9} - 13 q^{10} - 11 q^{11} + 8 q^{12} - 7 q^{13} - q^{15} - 2 q^{16} - 5 q^{17} - 2 q^{18} - 9 q^{19} - 12 q^{20} + 5 q^{22} - 23 q^{23} + 14 q^{25} - 18 q^{26} + 5 q^{27} - 18 q^{29} - 13 q^{30} - 9 q^{31} + 3 q^{32} - 11 q^{33} + 2 q^{34} + 8 q^{36} - 7 q^{39} - 31 q^{40} - 3 q^{41} + 12 q^{43} - 33 q^{44} - q^{45} + 13 q^{46} - 11 q^{47} - 2 q^{48} + 24 q^{50} - 5 q^{51} - 5 q^{52} - 3 q^{53} - 2 q^{54} + 10 q^{55} - 9 q^{57} - 34 q^{58} + 14 q^{59} - 12 q^{60} - 29 q^{61} + 5 q^{62} - 8 q^{65} + 5 q^{66} + 16 q^{67} - 8 q^{68} - 23 q^{69} - 19 q^{71} - 11 q^{73} + 45 q^{74} + 14 q^{75} - 9 q^{76} - 18 q^{78} + q^{79} + 5 q^{80} + 5 q^{81} + 4 q^{82} - 5 q^{83} + q^{85} - 3 q^{86} - 18 q^{87} + 37 q^{88} - 8 q^{89} - 13 q^{90} - 48 q^{92} - 9 q^{93} + 18 q^{94} - 21 q^{95} + 3 q^{96} - 19 q^{97} - 11 q^{99}+O(q^{100}) $ 5 * q - 2 * q^2 + 5 * q^3 + 8 * q^4 - q^5 - 2 * q^6 + 5 * q^9 - 13 * q^10 - 11 * q^11 + 8 * q^12 - 7 * q^13 - q^15 - 2 * q^16 - 5 * q^17 - 2 * q^18 - 9 * q^19 - 12 * q^20 + 5 * q^22 - 23 * q^23 + 14 * q^25 - 18 * q^26 + 5 * q^27 - 18 * q^29 - 13 * q^30 - 9 * q^31 + 3 * q^32 - 11 * q^33 + 2 * q^34 + 8 * q^36 - 7 * q^39 - 31 * q^40 - 3 * q^41 + 12 * q^43 - 33 * q^44 - q^45 + 13 * q^46 - 11 * q^47 - 2 * q^48 + 24 * q^50 - 5 * q^51 - 5 * q^52 - 3 * q^53 - 2 * q^54 + 10 * q^55 - 9 * q^57 - 34 * q^58 + 14 * q^59 - 12 * q^60 - 29 * q^61 + 5 * q^62 - 8 * q^65 + 5 * q^66 + 16 * q^67 - 8 * q^68 - 23 * q^69 - 19 * q^71 - 11 * q^73 + 45 * q^74 + 14 * q^75 - 9 * q^76 - 18 * q^78 + q^79 + 5 * q^80 + 5 * q^81 + 4 * q^82 - 5 * q^83 + q^85 - 3 * q^86 - 18 * q^87 + 37 * q^88 - 8 * q^89 - 13 * q^90 - 48 * q^92 - 9 * q^93 + 18 * q^94 - 21 * 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 $

$2$	−1.22966	−0.869503	−0.434751	−	0.900551i	$-0.643164\pi$
$2$	−1.22966	−0.869503	−0.434751	+	0.900551i	$0.643164\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.487931	−0.243965
$5$	2.41946	1.08202	0.541008	−	0.841018i	$-0.318043\pi$
$5$	2.41946	1.08202	0.541008	+	0.841018i	$0.318043\pi$
$6$	−1.22966	−0.502008
$7$	0	0
$7$	0	0
$8$	3.05931	1.08163
$9$	1.00000	0.333333
$10$	−2.97512	−0.940816
$11$	3.47878	1.04889	0.524445	−	0.851444i	$-0.324273\pi$
$11$	3.47878	1.04889	0.524445	+	0.851444i	$0.324273\pi$
$12$	−0.487931	−0.140853
$13$	−5.95098	−1.65051	−0.825253	−	0.564764i	$-0.808967\pi$
$13$	−5.95098	−1.65051	−0.825253	+	0.564764i	$0.808967\pi$
$14$	0	0
$15$	2.41946	0.624702
$16$	−2.78606	−0.696516
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.22966	−0.289834
$19$	−7.18064	−1.64735	−0.823676	−	0.567060i	$-0.808081\pi$
$19$	−7.18064	−1.64735	−0.823676	+	0.567060i	$0.808081\pi$
$20$	−1.18053	−0.263974
$21$	0	0
$22$	−4.27772	−0.912013
$23$	−2.81020	−0.585968	−0.292984	−	0.956117i	$-0.594648\pi$
$23$	−2.81020	−0.585968	−0.292984	+	0.956117i	$0.594648\pi$
$24$	3.05931	0.624480
$25$	0.853791	0.170758
$26$	7.31770	1.43512
$27$	1.00000	0.192450
$28$	0	0
$29$	−3.43234	−0.637370	−0.318685	−	0.947861i	$-0.603241\pi$
$29$	−3.43234	−0.637370	−0.318685	+	0.947861i	$0.603241\pi$
$30$	−2.97512	−0.543180
$31$	−6.27399	−1.12684	−0.563421	−	0.826170i	$-0.690515\pi$
$31$	−6.27399	−1.12684	−0.563421	+	0.826170i	$0.690515\pi$
$32$	−2.69271	−0.476009
$33$	3.47878	0.605577
$34$	1.22966	0.210885
$35$	0	0
$36$	−0.487931	−0.0813218
$37$	−7.57150	−1.24475	−0.622373	−	0.782721i	$-0.713831\pi$
$37$	−7.57150	−1.24475	−0.622373	+	0.782721i	$0.713831\pi$
$38$	8.82977	1.43238
$39$	−5.95098	−0.952920
$40$	7.40189	1.17034
$41$	2.69271	0.420531	0.210266	−	0.977644i	$-0.432567\pi$
$41$	2.69271	0.420531	0.210266	+	0.977644i	$0.432567\pi$
$42$	0	0
$43$	−9.25568	−1.41148	−0.705739	−	0.708472i	$-0.749385\pi$
$43$	−9.25568	−1.41148	−0.705739	+	0.708472i	$0.749385\pi$
$44$	−1.69740	−0.255893
$45$	2.41946	0.360672
$46$	3.45560	0.509500
$47$	−8.41031	−1.22677	−0.613385	−	0.789784i	$-0.710192\pi$
$47$	−8.41031	−1.22677	−0.613385	+	0.789784i	$0.710192\pi$
$48$	−2.78606	−0.402133
$49$	0	0
$50$	−1.04987	−0.148475
$51$	−1.00000	−0.140028
$52$	2.90367	0.402666
$53$	3.04433	0.418171	0.209086	−	0.977897i	$-0.432951\pi$
$53$	3.04433	0.418171	0.209086	+	0.977897i	$0.432951\pi$
$54$	−1.22966	−0.167336
$55$	8.41676	1.13492
$56$	0	0
$57$	−7.18064	−0.951099
$58$	4.22062	0.554195
$59$	−1.31113	−0.170694	−0.0853471	−	0.996351i	$-0.527200\pi$
$59$	−1.31113	−0.170694	−0.0853471	+	0.996351i	$0.527200\pi$
$60$	−1.18053	−0.152406
$61$	−9.92238	−1.27043	−0.635215	−	0.772335i	$-0.719089\pi$
$61$	−9.92238	−1.27043	−0.635215	+	0.772335i	$0.719089\pi$
$62$	7.71489	0.979792
$63$	0	0
$64$	8.88325	1.11041
$65$	−14.3982	−1.78587
$66$	−4.27772	−0.526551
$67$	13.7814	1.68366	0.841831	−	0.539741i	$-0.181478\pi$
$67$	13.7814	1.68366	0.841831	+	0.539741i	$0.181478\pi$
$68$	0.487931	0.0591703
$69$	−2.81020	−0.338308
$70$	0	0
$71$	1.20552	0.143069	0.0715347	−	0.997438i	$-0.477210\pi$
$71$	1.20552	0.143069	0.0715347	+	0.997438i	$0.477210\pi$
$72$	3.05931	0.360544
$73$	12.3085	1.44061	0.720303	−	0.693660i	$-0.244003\pi$
$73$	12.3085	1.44061	0.720303	+	0.693660i	$0.244003\pi$
$74$	9.31039	1.08231
$75$	0.853791	0.0985873
$76$	3.50366	0.401897
$77$	0	0
$78$	7.31770	0.828566
$79$	−0.320283	−0.0360346	−0.0180173	−	0.999838i	$-0.505735\pi$
$79$	−0.320283	−0.0360346	−0.0180173	+	0.999838i	$0.505735\pi$
$80$	−6.74077	−0.753641
$81$	1.00000	0.111111
$82$	−3.31113	−0.365653
$83$	11.1337	1.22209	0.611043	−	0.791598i	$-0.290750\pi$
$83$	11.1337	1.22209	0.611043	+	0.791598i	$0.290750\pi$
$84$	0	0
$85$	−2.41946	−0.262427
$86$	11.3814	1.22728
$87$	−3.43234	−0.367986
$88$	10.6427	1.13451
$89$	−11.6993	−1.24012	−0.620061	−	0.784554i	$-0.712892\pi$
$89$	−11.6993	−1.24012	−0.620061	+	0.784554i	$0.712892\pi$
$90$	−2.97512	−0.313605
$91$	0	0
$92$	1.37118	0.142956
$93$	−6.27399	−0.650583
$94$	10.3418	1.06668
$95$	−17.3733	−1.78246
$96$	−2.69271	−0.274824
$97$	−8.62561	−0.875798	−0.437899	−	0.899024i	$-0.644277\pi$
$97$	−8.62561	−0.875798	−0.437899	+	0.899024i	$0.644277\pi$
$98$	0	0
$99$	3.47878	0.349630
$100$	−0.416591	−0.0416591
$101$	7.73161	0.769324	0.384662	−	0.923057i	$-0.374318\pi$
$101$	7.73161	0.769324	0.384662	+	0.923057i	$0.374318\pi$
$102$	1.22966	0.121755
$103$	−7.49240	−0.738248	−0.369124	−	0.929380i	$-0.620342\pi$
$103$	−7.49240	−0.738248	−0.369124	+	0.929380i	$0.620342\pi$
$104$	−18.2059	−1.78524
$105$	0	0
$106$	−3.74350	−0.363601
$107$	1.10833	0.107147	0.0535733	−	0.998564i	$-0.482939\pi$
$107$	1.10833	0.107147	0.0535733	+	0.998564i	$0.482939\pi$
$108$	−0.487931	−0.0469511
$109$	6.27669	0.601198	0.300599	−	0.953751i	$-0.402813\pi$
$109$	6.27669	0.601198	0.300599	+	0.953751i	$0.402813\pi$
$110$	−10.3498	−0.986812
$111$	−7.57150	−0.718655
$112$	0	0
$113$	1.61373	0.151807	0.0759033	−	0.997115i	$-0.475816\pi$
$113$	1.61373	0.151807	0.0759033	+	0.997115i	$0.475816\pi$
$114$	8.82977	0.826983
$115$	−6.79917	−0.634026
$116$	1.67474	0.155496
$117$	−5.95098	−0.550168
$118$	1.61224	0.148419
$119$	0	0
$120$	7.40189	0.675697
$121$	1.10188	0.100171
$122$	12.2012	1.10464
$123$	2.69271	0.242794
$124$	3.06127	0.274910
$125$	−10.0316	−0.897253
$126$	0	0
$127$	14.7866	1.31210	0.656048	−	0.754719i	$-0.272227\pi$
$127$	14.7866	1.31210	0.656048	+	0.754719i	$0.272227\pi$
$128$	−5.53798	−0.489492
$129$	−9.25568	−0.814917
$130$	17.7049	1.55282
$131$	21.3259	1.86325	0.931626	−	0.363419i	$-0.118391\pi$
$131$	21.3259	1.86325	0.931626	+	0.363419i	$0.118391\pi$
$132$	−1.69740	−0.147740
$133$	0	0
$134$	−16.9464	−1.46395
$135$	2.41946	0.208234
$136$	−3.05931	−0.262334
$137$	2.00955	0.171688	0.0858439	−	0.996309i	$-0.472641\pi$
$137$	2.00955	0.171688	0.0858439	+	0.996309i	$0.472641\pi$
$138$	3.45560	0.294160
$139$	−8.53092	−0.723583	−0.361792	−	0.932259i	$-0.617835\pi$
$139$	−8.53092	−0.723583	−0.361792	+	0.932259i	$0.617835\pi$
$140$	0	0
$141$	−8.41031	−0.708276
$142$	−1.48239	−0.124399
$143$	−20.7021	−1.73120
$144$	−2.78606	−0.232172
$145$	−8.30442	−0.689644
$146$	−15.1354	−1.25261
$147$	0	0
$148$	3.69437	0.303675
$149$	−10.7661	−0.881996	−0.440998	−	0.897508i	$-0.645375\pi$
$149$	−10.7661	−0.881996	−0.440998	+	0.897508i	$0.645375\pi$
$150$	−1.04987	−0.0857219
$151$	−2.85763	−0.232551	−0.116275	−	0.993217i	$-0.537096\pi$
$151$	−2.85763	−0.232551	−0.116275	+	0.993217i	$0.537096\pi$
$152$	−21.9678	−1.78183
$153$	−1.00000	−0.0808452
$154$	0	0
$155$	−15.1797	−1.21926
$156$	2.90367	0.232479
$157$	−4.90022	−0.391080	−0.195540	−	0.980696i	$-0.562646\pi$
$157$	−4.90022	−0.391080	−0.195540	+	0.980696i	$0.562646\pi$
$158$	0.393840	0.0313322
$159$	3.04433	0.241431
$160$	−6.51491	−0.515049
$161$	0	0
$162$	−1.22966	−0.0966114
$163$	8.30470	0.650474	0.325237	−	0.945632i	$-0.394556\pi$
$163$	8.30470	0.650474	0.325237	+	0.945632i	$0.394556\pi$
$164$	−1.31386	−0.102595
$165$	8.41676	0.655244
$166$	−13.6907	−1.06261
$167$	10.2826	0.795694	0.397847	−	0.917452i	$-0.369757\pi$
$167$	10.2826	0.795694	0.397847	+	0.917452i	$0.369757\pi$
$168$	0	0
$169$	22.4142	1.72417
$170$	2.97512	0.228181
$171$	−7.18064	−0.549118
$172$	4.51613	0.344352
$173$	20.7809	1.57994	0.789971	−	0.613144i	$-0.210096\pi$
$173$	20.7809	1.57994	0.789971	+	0.613144i	$0.210096\pi$
$174$	4.22062	0.319964
$175$	0	0
$176$	−9.69209	−0.730568
$177$	−1.31113	−0.0985504
$178$	14.3862	1.07829
$179$	−9.01612	−0.673897	−0.336948	−	0.941523i	$-0.609395\pi$
$179$	−9.01612	−0.673897	−0.336948	+	0.941523i	$0.609395\pi$
$180$	−1.18053	−0.0879914
$181$	0.663030	0.0492826	0.0246413	−	0.999696i	$-0.492156\pi$
$181$	0.663030	0.0492826	0.0246413	+	0.999696i	$0.492156\pi$
$182$	0	0
$183$	−9.92238	−0.733483
$184$	−8.59729	−0.633801
$185$	−18.3189	−1.34684
$186$	7.71489	0.565683
$187$	−3.47878	−0.254393
$188$	4.10365	0.299289
$189$	0	0
$190$	21.3633	1.54985
$191$	−23.8474	−1.72554	−0.862768	−	0.505601i	$-0.831271\pi$
$191$	−23.8474	−1.72554	−0.862768	+	0.505601i	$0.831271\pi$
$192$	8.88325	0.641094
$193$	11.3446	0.816600	0.408300	−	0.912848i	$-0.366122\pi$
$193$	11.3446	0.816600	0.408300	+	0.912848i	$0.366122\pi$
$194$	10.6066	0.761509
$195$	−14.3982	−1.03107
$196$	0	0
$197$	−17.4455	−1.24294	−0.621470	−	0.783438i	$-0.713464\pi$
$197$	−17.4455	−1.24294	−0.621470	+	0.783438i	$0.713464\pi$
$198$	−4.27772	−0.304004
$199$	11.6550	0.826198	0.413099	−	0.910686i	$-0.364446\pi$
$199$	11.6550	0.826198	0.413099	+	0.910686i	$0.364446\pi$
$200$	2.61202	0.184697
$201$	13.7814	0.972063
$202$	−9.50727	−0.668930
$203$	0	0
$204$	0.487931	0.0341620
$205$	6.51491	0.455021
$206$	9.21312	0.641908
$207$	−2.81020	−0.195323
$208$	16.5798	1.14960
$209$	−24.9798	−1.72789
$210$	0	0
$211$	−0.420088	−0.0289200	−0.0144600	−	0.999895i	$-0.504603\pi$
$211$	−0.420088	−0.0289200	−0.0144600	+	0.999895i	$0.504603\pi$
$212$	−1.48542	−0.102019
$213$	1.20552	0.0826011
$214$	−1.36288	−0.0931643
$215$	−22.3938	−1.52724
$216$	3.05931	0.208160
$217$	0	0
$218$	−7.71821	−0.522743
$219$	12.3085	0.831734
$220$	−4.10680	−0.276880
$221$	5.95098	0.400306
$222$	9.31039	0.624872
$223$	−17.3626	−1.16269	−0.581344	−	0.813658i	$-0.697473\pi$
$223$	−17.3626	−1.16269	−0.581344	+	0.813658i	$0.697473\pi$
$224$	0	0
$225$	0.853791	0.0569194
$226$	−1.98434	−0.131996
$227$	−3.61782	−0.240123	−0.120061	−	0.992766i	$-0.538309\pi$
$227$	−3.61782	−0.240123	−0.120061	+	0.992766i	$0.538309\pi$
$228$	3.50366	0.232035
$229$	−13.9257	−0.920236	−0.460118	−	0.887858i	$-0.652193\pi$
$229$	−13.9257	−0.920236	−0.460118	+	0.887858i	$0.652193\pi$
$230$	8.36069	0.551287
$231$	0	0
$232$	−10.5006	−0.689399
$233$	23.0650	1.51104	0.755520	−	0.655125i	$-0.227384\pi$
$233$	23.0650	1.51104	0.755520	+	0.655125i	$0.227384\pi$
$234$	7.31770	0.478373
$235$	−20.3484	−1.32738
$236$	0.639739	0.0416435
$237$	−0.320283	−0.0208046
$238$	0	0
$239$	25.0229	1.61860	0.809299	−	0.587397i	$-0.199847\pi$
$239$	25.0229	1.61860	0.809299	+	0.587397i	$0.199847\pi$
$240$	−6.74077	−0.435115
$241$	16.8557	1.08577	0.542885	−	0.839807i	$-0.317332\pi$
$241$	16.8557	1.08577	0.542885	+	0.839807i	$0.317332\pi$
$242$	−1.35494	−0.0870987
$243$	1.00000	0.0641500
$244$	4.84143	0.309941
$245$	0	0
$246$	−3.31113	−0.211110
$247$	42.7319	2.71896
$248$	−19.1941	−1.21883
$249$	11.1337	0.705571
$250$	12.3355	0.780164
$251$	−14.0767	−0.888511	−0.444256	−	0.895900i	$-0.646532\pi$
$251$	−14.0767	−0.888511	−0.444256	+	0.895900i	$0.646532\pi$
$252$	0	0
$253$	−9.77606	−0.614616
$254$	−18.1825	−1.14087
$255$	−2.41946	−0.151513
$256$	−10.9567	−0.684792
$257$	5.06304	0.315824	0.157912	−	0.987453i	$-0.449524\pi$
$257$	5.06304	0.315824	0.157912	+	0.987453i	$0.449524\pi$
$258$	11.3814	0.708573
$259$	0	0
$260$	7.02531	0.435691
$261$	−3.43234	−0.212457
$262$	−26.2236	−1.62010
$263$	−25.2875	−1.55930	−0.779648	−	0.626218i	$-0.784602\pi$
$263$	−25.2875	−1.55930	−0.779648	+	0.626218i	$0.784602\pi$
$264$	10.6427	0.655011
$265$	7.36564	0.452468
$266$	0	0
$267$	−11.6993	−0.715984
$268$	−6.72435	−0.410755
$269$	−28.4411	−1.73409	−0.867043	−	0.498233i	$-0.833982\pi$
$269$	−28.4411	−1.73409	−0.867043	+	0.498233i	$0.833982\pi$
$270$	−2.97512	−0.181060
$271$	−0.507746	−0.0308434	−0.0154217	−	0.999881i	$-0.504909\pi$
$271$	−0.507746	−0.0308434	−0.0154217	+	0.999881i	$0.504909\pi$
$272$	2.78606	0.168930
$273$	0	0
$274$	−2.47107	−0.149283
$275$	2.97015	0.179107
$276$	1.37118	0.0825355
$277$	−11.1521	−0.670063	−0.335031	−	0.942207i	$-0.608747\pi$
$277$	−11.1521	−0.670063	−0.335031	+	0.942207i	$0.608747\pi$
$278$	10.4902	0.629158
$279$	−6.27399	−0.375614
$280$	0	0
$281$	9.49919	0.566674	0.283337	−	0.959020i	$-0.408558\pi$
$281$	9.49919	0.566674	0.283337	+	0.959020i	$0.408558\pi$
$282$	10.3418	0.615847
$283$	−4.96941	−0.295401	−0.147700	−	0.989032i	$-0.547187\pi$
$283$	−4.96941	−0.295401	−0.147700	+	0.989032i	$0.547187\pi$
$284$	−0.588212	−0.0349039
$285$	−17.3733	−1.02910
$286$	25.4566	1.50528
$287$	0	0
$288$	−2.69271	−0.158670
$289$	1.00000	0.0588235
$290$	10.2116	0.599647
$291$	−8.62561	−0.505642
$292$	−6.00571	−0.351458
$293$	9.41812	0.550213	0.275106	−	0.961414i	$-0.411287\pi$
$293$	9.41812	0.550213	0.275106	+	0.961414i	$0.411287\pi$
$294$	0	0
$295$	−3.17222	−0.184694
$296$	−23.1636	−1.34636
$297$	3.47878	0.201859
$298$	13.2387	0.766897
$299$	16.7235	0.967142
$300$	−0.416591	−0.0240519
$301$	0	0
$302$	3.51392	0.202203
$303$	7.73161	0.444170
$304$	20.0057	1.14741
$305$	−24.0068	−1.37463
$306$	1.22966	0.0702951
$307$	−23.4105	−1.33611	−0.668055	−	0.744112i	$-0.732873\pi$
$307$	−23.4105	−1.33611	−0.668055	+	0.744112i	$0.732873\pi$
$308$	0	0
$309$	−7.49240	−0.426228
$310$	18.6659	1.06015
$311$	−14.1327	−0.801392	−0.400696	−	0.916211i	$-0.631232\pi$
$311$	−14.1327	−0.801392	−0.400696	+	0.916211i	$0.631232\pi$
$312$	−18.2059	−1.03071
$313$	−2.55267	−0.144286	−0.0721428	−	0.997394i	$-0.522984\pi$
$313$	−2.55267	−0.144286	−0.0721428	+	0.997394i	$0.522984\pi$
$314$	6.02562	0.340045
$315$	0	0
$316$	0.156276	0.00879120
$317$	29.9490	1.68210	0.841051	−	0.540955i	$-0.181937\pi$
$317$	29.9490	1.68210	0.841051	+	0.540955i	$0.181937\pi$
$318$	−3.74350	−0.209925
$319$	−11.9403	−0.668531
$320$	21.4927	1.20148
$321$	1.10833	0.0618611
$322$	0	0
$323$	7.18064	0.399542
$324$	−0.487931	−0.0271073
$325$	−5.08089	−0.281837
$326$	−10.2120	−0.565589
$327$	6.27669	0.347102
$328$	8.23786	0.454859
$329$	0	0
$330$	−10.3498	−0.569736
$331$	−0.144985	−0.00796909	−0.00398454	−	0.999992i	$-0.501268\pi$
$331$	−0.144985	−0.00796909	−0.00398454	+	0.999992i	$0.501268\pi$
$332$	−5.43249	−0.298146
$333$	−7.57150	−0.414916
$334$	−12.6442	−0.691858
$335$	33.3435	1.82175
$336$	0	0
$337$	−3.92618	−0.213873	−0.106936	−	0.994266i	$-0.534104\pi$
$337$	−3.92618	−0.213873	−0.106936	+	0.994266i	$0.534104\pi$
$338$	−27.5619	−1.49917
$339$	1.61373	0.0876456
$340$	1.18053	0.0640232
$341$	−21.8258	−1.18193
$342$	8.82977	0.477459
$343$	0	0
$344$	−28.3160	−1.52670
$345$	−6.79917	−0.366055
$346$	−25.5535	−1.37376
$347$	−17.6109	−0.945402	−0.472701	−	0.881223i	$-0.656721\pi$
$347$	−17.6109	−0.945402	−0.472701	+	0.881223i	$0.656721\pi$
$348$	1.67474	0.0897757
$349$	−14.3609	−0.768722	−0.384361	−	0.923183i	$-0.625578\pi$
$349$	−14.3609	−0.768722	−0.384361	+	0.923183i	$0.625578\pi$
$350$	0	0
$351$	−5.95098	−0.317640
$352$	−9.36734	−0.499281
$353$	−15.1306	−0.805322	−0.402661	−	0.915349i	$-0.631915\pi$
$353$	−15.1306	−0.805322	−0.402661	+	0.915349i	$0.631915\pi$
$354$	1.61224	0.0856898
$355$	2.91672	0.154803
$356$	5.70844	0.302547
$357$	0	0
$358$	11.0868	0.585955
$359$	28.6261	1.51083	0.755415	−	0.655247i	$-0.227436\pi$
$359$	28.6261	1.51083	0.755415	+	0.655247i	$0.227436\pi$
$360$	7.40189	0.390114
$361$	32.5616	1.71377
$362$	−0.815303	−0.0428514
$363$	1.10188	0.0578336
$364$	0	0
$365$	29.7800	1.55876
$366$	12.2012	0.637765
$367$	29.0303	1.51537	0.757684	−	0.652622i	$-0.226331\pi$
$367$	29.0303	1.51537	0.757684	+	0.652622i	$0.226331\pi$
$368$	7.82940	0.408136
$369$	2.69271	0.140177
$370$	22.5261	1.17108
$371$	0	0
$372$	3.06127	0.158720
$373$	7.07936	0.366555	0.183278	−	0.983061i	$-0.441329\pi$
$373$	7.07936	0.366555	0.183278	+	0.983061i	$0.441329\pi$
$374$	4.27772	0.221196
$375$	−10.0316	−0.518029
$376$	−25.7298	−1.32691
$377$	20.4258	1.05198
$378$	0	0
$379$	−2.83980	−0.145871	−0.0729355	−	0.997337i	$-0.523237\pi$
$379$	−2.83980	−0.145871	−0.0729355	+	0.997337i	$0.523237\pi$
$380$	8.47696	0.434859
$381$	14.7866	0.757539
$382$	29.3242	1.50036
$383$	−24.8574	−1.27015	−0.635077	−	0.772449i	$-0.719032\pi$
$383$	−24.8574	−1.27015	−0.635077	+	0.772449i	$0.719032\pi$
$384$	−5.53798	−0.282609
$385$	0	0
$386$	−13.9500	−0.710036
$387$	−9.25568	−0.470493
$388$	4.20870	0.213664
$389$	12.6424	0.640993	0.320496	−	0.947250i	$-0.396150\pi$
$389$	12.6424	0.640993	0.320496	+	0.947250i	$0.396150\pi$
$390$	17.7049	0.896522
$391$	2.81020	0.142118
$392$	0	0
$393$	21.3259	1.07575
$394$	21.4521	1.08074
$395$	−0.774911	−0.0389900
$396$	−1.69740	−0.0852976
$397$	−25.3242	−1.27098	−0.635491	−	0.772108i	$-0.719202\pi$
$397$	−25.3242	−1.27098	−0.635491	+	0.772108i	$0.719202\pi$
$398$	−14.3317	−0.718381
$399$	0	0
$400$	−2.37872	−0.118936
$401$	0.0514979	0.00257168	0.00128584	−	0.999999i	$-0.499591\pi$
$401$	0.0514979	0.00257168	0.00128584	+	0.999999i	$0.499591\pi$
$402$	−16.9464	−0.845211
$403$	37.3364	1.85986
$404$	−3.77249	−0.187688
$405$	2.41946	0.120224
$406$	0	0
$407$	−26.3395	−1.30560
$408$	−3.05931	−0.151459
$409$	−18.8695	−0.933038	−0.466519	−	0.884511i	$-0.654492\pi$
$409$	−18.8695	−0.933038	−0.466519	+	0.884511i	$0.654492\pi$
$410$	−8.01114	−0.395642
$411$	2.00955	0.0991240
$412$	3.65577	0.180107
$413$	0	0
$414$	3.45560	0.169833
$415$	26.9376	1.32232
$416$	16.0243	0.785655
$417$	−8.53092	−0.417761
$418$	30.7168	1.50241
$419$	−20.3934	−0.996281	−0.498140	−	0.867096i	$-0.665984\pi$
$419$	−20.3934	−0.996281	−0.498140	+	0.867096i	$0.665984\pi$
$420$	0	0
$421$	1.70878	0.0832808	0.0416404	−	0.999133i	$-0.486742\pi$
$421$	1.70878	0.0832808	0.0416404	+	0.999133i	$0.486742\pi$
$422$	0.516566	0.0251460
$423$	−8.41031	−0.408923
$424$	9.31357	0.452307
$425$	−0.853791	−0.0414149
$426$	−1.48239	−0.0718219
$427$	0	0
$428$	−0.540790	−0.0261401
$429$	−20.7021	−0.999508
$430$	27.5368	1.32794
$431$	36.0406	1.73601	0.868006	−	0.496553i	$-0.165401\pi$
$431$	36.0406	1.73601	0.868006	+	0.496553i	$0.165401\pi$
$432$	−2.78606	−0.134044
$433$	23.2422	1.11695	0.558474	−	0.829522i	$-0.311387\pi$
$433$	23.2422	1.11695	0.558474	+	0.829522i	$0.311387\pi$
$434$	0	0
$435$	−8.30442	−0.398166
$436$	−3.06259	−0.146671
$437$	20.1791	0.965295
$438$	−15.1354	−0.723195
$439$	−23.3971	−1.11668	−0.558342	−	0.829611i	$-0.688562\pi$
$439$	−23.3971	−1.11668	−0.558342	+	0.829611i	$0.688562\pi$
$440$	25.7495	1.22756
$441$	0	0
$442$	−7.31770	−0.348067
$443$	−5.85655	−0.278253	−0.139127	−	0.990275i	$-0.544430\pi$
$443$	−5.85655	−0.278253	−0.139127	+	0.990275i	$0.544430\pi$
$444$	3.69437	0.175327
$445$	−28.3060	−1.34183
$446$	21.3502	1.01096
$447$	−10.7661	−0.509220
$448$	0	0
$449$	9.53965	0.450204	0.225102	−	0.974335i	$-0.427728\pi$
$449$	9.53965	0.450204	0.225102	+	0.974335i	$0.427728\pi$
$450$	−1.04987	−0.0494916
$451$	9.36734	0.441091
$452$	−0.787387	−0.0370355
$453$	−2.85763	−0.134263
$454$	4.44869	0.208788
$455$	0	0
$456$	−21.9678	−1.02874
$457$	−36.6180	−1.71292	−0.856458	−	0.516216i	$-0.827340\pi$
$457$	−36.6180	−1.71292	−0.856458	+	0.516216i	$0.827340\pi$
$458$	17.1239	0.800148
$459$	−1.00000	−0.0466760
$460$	3.31752	0.154680
$461$	−20.5184	−0.955638	−0.477819	−	0.878458i	$-0.658573\pi$
$461$	−20.5184	−0.955638	−0.477819	+	0.878458i	$0.658573\pi$
$462$	0	0
$463$	−32.4080	−1.50613	−0.753063	−	0.657948i	$-0.771425\pi$
$463$	−32.4080	−1.50613	−0.753063	+	0.657948i	$0.771425\pi$
$464$	9.56272	0.443938
$465$	−15.1797	−0.703941
$466$	−28.3622	−1.31385
$467$	19.4217	0.898728	0.449364	−	0.893349i	$-0.351651\pi$
$467$	19.4217	0.898728	0.449364	+	0.893349i	$0.351651\pi$
$468$	2.90367	0.134222
$469$	0	0
$470$	25.0217	1.15416
$471$	−4.90022	−0.225790
$472$	−4.01115	−0.184628
$473$	−32.1984	−1.48049
$474$	0.393840	0.0180896
$475$	−6.13077	−0.281299
$476$	0	0
$477$	3.04433	0.139390
$478$	−30.7697	−1.40738
$479$	0.197813	0.00903833	0.00451916	−	0.999990i	$-0.498562\pi$
$479$	0.197813	0.00903833	0.00451916	+	0.999990i	$0.498562\pi$
$480$	−6.51491	−0.297364
$481$	45.0578	2.05446
$482$	−20.7268	−0.944079
$483$	0	0
$484$	−0.537640	−0.0244382
$485$	−20.8693	−0.947627
$486$	−1.22966	−0.0557786
$487$	33.2274	1.50568	0.752840	−	0.658204i	$-0.228684\pi$
$487$	33.2274	1.50568	0.752840	+	0.658204i	$0.228684\pi$
$488$	−30.3557	−1.37414
$489$	8.30470	0.375552
$490$	0	0
$491$	23.6344	1.06661	0.533303	−	0.845924i	$-0.320951\pi$
$491$	23.6344	1.06661	0.533303	+	0.845924i	$0.320951\pi$
$492$	−1.31386	−0.0592332
$493$	3.43234	0.154585
$494$	−52.5458	−2.36415
$495$	8.41676	0.378305
$496$	17.4797	0.784863
$497$	0	0
$498$	−13.6907	−0.613496
$499$	−10.7684	−0.482059	−0.241029	−	0.970518i	$-0.577485\pi$
$499$	−10.7684	−0.482059	−0.241029	+	0.970518i	$0.577485\pi$
$500$	4.89472	0.218899
$501$	10.2826	0.459394
$502$	17.3095	0.772563
$503$	34.0342	1.51751	0.758755	−	0.651376i	$-0.225808\pi$
$503$	34.0342	1.51751	0.758755	+	0.651376i	$0.225808\pi$
$504$	0	0
$505$	18.7063	0.832421
$506$	12.0213	0.534410
$507$	22.4142	0.995448
$508$	−7.21482	−0.320106
$509$	−43.2368	−1.91644	−0.958218	−	0.286040i	$-0.907661\pi$
$509$	−43.2368	−1.91644	−0.958218	+	0.286040i	$0.907661\pi$
$510$	2.97512	0.131741
$511$	0	0
$512$	24.5489	1.08492
$513$	−7.18064	−0.317033
$514$	−6.22583	−0.274610
$515$	−18.1276	−0.798796
$516$	4.51613	0.198812
$517$	−29.2576	−1.28675
$518$	0	0
$519$	20.7809	0.912180
$520$	−44.0485	−1.93166
$521$	−8.56914	−0.375421	−0.187710	−	0.982224i	$-0.560107\pi$
$521$	−8.56914	−0.375421	−0.187710	+	0.982224i	$0.560107\pi$
$522$	4.22062	0.184732
$523$	12.1574	0.531604	0.265802	−	0.964028i	$-0.414363\pi$
$523$	12.1574	0.531604	0.265802	+	0.964028i	$0.414363\pi$
$524$	−10.4056	−0.454569
$525$	0	0
$526$	31.0951	1.35581
$527$	6.27399	0.273299
$528$	−9.69209	−0.421794
$529$	−15.1028	−0.656642
$530$	−9.05725	−0.393422
$531$	−1.31113	−0.0568981
$532$	0	0
$533$	−16.0243	−0.694089
$534$	14.3862	0.622550
$535$	2.68157	0.115934
$536$	42.1616	1.82110
$537$	−9.01612	−0.389074
$538$	34.9730	1.50779
$539$	0	0
$540$	−1.18053	−0.0508019
$541$	37.7820	1.62438	0.812188	−	0.583396i	$-0.198276\pi$
$541$	37.7820	1.62438	0.812188	+	0.583396i	$0.198276\pi$
$542$	0.624356	0.0268184
$543$	0.663030	0.0284533
$544$	2.69271	0.115449
$545$	15.1862	0.650506
$546$	0	0
$547$	28.0254	1.19828	0.599140	−	0.800644i	$-0.295509\pi$
$547$	28.0254	1.19828	0.599140	+	0.800644i	$0.295509\pi$
$548$	−0.980523	−0.0418859
$549$	−9.92238	−0.423477
$550$	−3.65228	−0.155734
$551$	24.6464	1.04997
$552$	−8.59729	−0.365925
$553$	0	0
$554$	13.7133	0.582621
$555$	−18.3189	−0.777596
$556$	4.16250	0.176529
$557$	24.3772	1.03290	0.516448	−	0.856318i	$-0.327254\pi$
$557$	24.3772	1.03290	0.516448	+	0.856318i	$0.327254\pi$
$558$	7.71489	0.326597
$559$	55.0804	2.32965
$560$	0	0
$561$	−3.47878	−0.146874
$562$	−11.6808	−0.492725
$563$	32.2985	1.36122	0.680610	−	0.732646i	$-0.261715\pi$
$563$	32.2985	1.36122	0.680610	+	0.732646i	$0.261715\pi$
$564$	4.10365	0.172795
$565$	3.90435	0.164257
$566$	6.11069	0.256852
$567$	0	0
$568$	3.68808	0.154748
$569$	−6.77170	−0.283884	−0.141942	−	0.989875i	$-0.545335\pi$
$569$	−6.77170	−0.283884	−0.141942	+	0.989875i	$0.545335\pi$
$570$	21.3633	0.894809
$571$	2.73221	0.114339	0.0571697	−	0.998364i	$-0.481792\pi$
$571$	2.73221	0.114339	0.0571697	+	0.998364i	$0.481792\pi$
$572$	10.1012	0.422352
$573$	−23.8474	−0.996238
$574$	0	0
$575$	−2.39932	−0.100059
$576$	8.88325	0.370136
$577$	−34.0174	−1.41616	−0.708082	−	0.706131i	$-0.750439\pi$
$577$	−34.0174	−1.41616	−0.708082	+	0.706131i	$0.750439\pi$
$578$	−1.22966	−0.0511472
$579$	11.3446	0.471464
$580$	4.05198	0.168249
$581$	0	0
$582$	10.6066	0.439657
$583$	10.5905	0.438615
$584$	37.6557	1.55820
$585$	−14.3982	−0.595291
$586$	−11.5811	−0.478411
$587$	−10.2949	−0.424917	−0.212458	−	0.977170i	$-0.568147\pi$
$587$	−10.2949	−0.424917	−0.212458	+	0.977170i	$0.568147\pi$
$588$	0	0
$589$	45.0513	1.85631
$590$	3.90076	0.160592
$591$	−17.4455	−0.717611
$592$	21.0947	0.866986
$593$	22.0185	0.904190	0.452095	−	0.891970i	$-0.350677\pi$
$593$	22.0185	0.904190	0.452095	+	0.891970i	$0.350677\pi$
$594$	−4.27772	−0.175517
$595$	0	0
$596$	5.25312	0.215176
$597$	11.6550	0.477005
$598$	−20.5642	−0.840933
$599$	−37.9792	−1.55179	−0.775894	−	0.630863i	$-0.782701\pi$
$599$	−37.9792	−1.55179	−0.775894	+	0.630863i	$0.782701\pi$
$600$	2.61202	0.106635
$601$	11.4958	0.468923	0.234461	−	0.972125i	$-0.424667\pi$
$601$	11.4958	0.468923	0.234461	+	0.972125i	$0.424667\pi$
$602$	0	0
$603$	13.7814	0.561221
$604$	1.39433	0.0567343
$605$	2.66595	0.108386
$606$	−9.50727	−0.386207
$607$	7.15784	0.290528	0.145264	−	0.989393i	$-0.453597\pi$
$607$	7.15784	0.290528	0.145264	+	0.989393i	$0.453597\pi$
$608$	19.3354	0.784154
$609$	0	0
$610$	29.5203	1.19524
$611$	50.0496	2.02479
$612$	0.487931	0.0197234
$613$	−5.05054	−0.203989	−0.101995	−	0.994785i	$-0.532522\pi$
$613$	−5.05054	−0.203989	−0.101995	+	0.994785i	$0.532522\pi$
$614$	28.7871	1.16175
$615$	6.51491	0.262707
$616$	0	0
$617$	−5.41515	−0.218006	−0.109003	−	0.994041i	$-0.534766\pi$
$617$	−5.41515	−0.218006	−0.109003	+	0.994041i	$0.534766\pi$
$618$	9.21312	0.370606
$619$	6.16369	0.247740	0.123870	−	0.992298i	$-0.460469\pi$
$619$	6.16369	0.247740	0.123870	+	0.992298i	$0.460469\pi$
$620$	7.40663	0.297457
$621$	−2.81020	−0.112769
$622$	17.3785	0.696812
$623$	0	0
$624$	16.5798	0.663723
$625$	−28.5400	−1.14160
$626$	3.13893	0.125457
$627$	−24.9798	−0.997599
$628$	2.39097	0.0954101
$629$	7.57150	0.301895
$630$	0	0
$631$	−0.737721	−0.0293682	−0.0146841	−	0.999892i	$-0.504674\pi$
$631$	−0.737721	−0.0293682	−0.0146841	+	0.999892i	$0.504674\pi$
$632$	−0.979845	−0.0389762
$633$	−0.420088	−0.0166970
$634$	−36.8271	−1.46259
$635$	35.7755	1.41971
$636$	−1.48542	−0.0589008
$637$	0	0
$638$	14.6826	0.581289
$639$	1.20552	0.0476898
$640$	−13.3989	−0.529639
$641$	−5.56261	−0.219710	−0.109855	−	0.993948i	$-0.535039\pi$
$641$	−5.56261	−0.219710	−0.109855	+	0.993948i	$0.535039\pi$
$642$	−1.36288	−0.0537884
$643$	14.0644	0.554646	0.277323	−	0.960777i	$-0.410553\pi$
$643$	14.0644	0.554646	0.277323	+	0.960777i	$0.410553\pi$
$644$	0	0
$645$	−22.3938	−0.881754
$646$	−8.82977	−0.347403
$647$	−1.36857	−0.0538039	−0.0269020	−	0.999638i	$-0.508564\pi$
$647$	−1.36857	−0.0538039	−0.0269020	+	0.999638i	$0.508564\pi$
$648$	3.05931	0.120181
$649$	−4.56112	−0.179040
$650$	6.24778	0.245058
$651$	0	0
$652$	−4.05212	−0.158693
$653$	−6.83002	−0.267279	−0.133640	−	0.991030i	$-0.542666\pi$
$653$	−6.83002	−0.267279	−0.133640	+	0.991030i	$0.542666\pi$
$654$	−7.71821	−0.301806
$655$	51.5972	2.01607
$656$	−7.50207	−0.292906
$657$	12.3085	0.480202
$658$	0	0
$659$	8.51125	0.331551	0.165776	−	0.986163i	$-0.446987\pi$
$659$	8.51125	0.331551	0.165776	+	0.986163i	$0.446987\pi$
$660$	−4.10680	−0.159857
$661$	−8.50177	−0.330681	−0.165340	−	0.986237i	$-0.552872\pi$
$661$	−8.50177	−0.330681	−0.165340	+	0.986237i	$0.552872\pi$
$662$	0.178282	0.00692914
$663$	5.95098	0.231117
$664$	34.0616	1.32185
$665$	0	0
$666$	9.31039	0.360770
$667$	9.64557	0.373478
$668$	−5.01721	−0.194122
$669$	−17.3626	−0.671279
$670$	−41.0012	−1.58402
$671$	−34.5177	−1.33254
$672$	0	0
$673$	−39.3500	−1.51683	−0.758416	−	0.651771i	$-0.774026\pi$
$673$	−39.3500	−1.51683	−0.758416	+	0.651771i	$0.774026\pi$
$674$	4.82788	0.185963
$675$	0.853791	0.0328624
$676$	−10.9366	−0.420637
$677$	−6.00000	−0.230599	−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000	−0.230599	−0.115299	+	0.993331i	$0.536783\pi$
$678$	−1.98434	−0.0762081
$679$	0	0
$680$	−7.40189	−0.283850
$681$	−3.61782	−0.138635
$682$	26.8384	1.02769
$683$	36.5147	1.39720	0.698598	−	0.715514i	$-0.253807\pi$
$683$	36.5147	1.39720	0.698598	+	0.715514i	$0.253807\pi$
$684$	3.50366	0.133966
$685$	4.86204	0.185769
$686$	0	0
$687$	−13.9257	−0.531299
$688$	25.7869	0.983117
$689$	−18.1168	−0.690193
$690$	8.36069	0.318286
$691$	29.7648	1.13231	0.566153	−	0.824300i	$-0.308431\pi$
$691$	29.7648	1.13231	0.566153	+	0.824300i	$0.308431\pi$
$692$	−10.1396	−0.385451
$693$	0	0
$694$	21.6554	0.822029
$695$	−20.6402	−0.782929
$696$	−10.5006	−0.398025
$697$	−2.69271	−0.101994
$698$	17.6591	0.668406
$699$	23.0650	0.872400
$700$	0	0
$701$	−13.1980	−0.498480	−0.249240	−	0.968442i	$-0.580181\pi$
$701$	−13.1980	−0.498480	−0.249240	+	0.968442i	$0.580181\pi$
$702$	7.31770	0.276189
$703$	54.3682	2.05054
$704$	30.9028	1.16469
$705$	−20.3484	−0.766365
$706$	18.6056	0.700230
$707$	0	0
$708$	0.639739	0.0240429
$709$	−22.4185	−0.841944	−0.420972	−	0.907074i	$-0.638311\pi$
$709$	−22.4185	−0.841944	−0.420972	+	0.907074i	$0.638311\pi$
$710$	−3.58658	−0.134602
$711$	−0.320283	−0.0120115
$712$	−35.7918	−1.34135
$713$	17.6312	0.660293
$714$	0	0
$715$	−50.0880	−1.87318
$716$	4.39924	0.164407
$717$	25.0229	0.934498
$718$	−35.2005	−1.31367
$719$	11.8363	0.441420	0.220710	−	0.975339i	$-0.429163\pi$
$719$	11.8363	0.441420	0.220710	+	0.975339i	$0.429163\pi$
$720$	−6.74077	−0.251214
$721$	0	0
$722$	−40.0398	−1.49013
$723$	16.8557	0.626869
$724$	−0.323513	−0.0120233
$725$	−2.93050	−0.108836
$726$	−1.35494	−0.0502865
$727$	8.90070	0.330109	0.165054	−	0.986284i	$-0.447220\pi$
$727$	8.90070	0.330109	0.165054	+	0.986284i	$0.447220\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−36.6194	−1.35534
$731$	9.25568	0.342334
$732$	4.84143	0.178944
$733$	−3.76653	−0.139120	−0.0695600	−	0.997578i	$-0.522160\pi$
$733$	−3.76653	−0.139120	−0.0695600	+	0.997578i	$0.522160\pi$
$734$	−35.6974	−1.31762
$735$	0	0
$736$	7.56707	0.278926
$737$	47.9423	1.76598
$738$	−3.31113	−0.121884
$739$	−8.38640	−0.308499	−0.154249	−	0.988032i	$-0.549296\pi$
$739$	−8.38640	−0.308499	−0.154249	+	0.988032i	$0.549296\pi$
$740$	8.93837	0.328581
$741$	42.7319	1.56979
$742$	0	0
$743$	−20.0289	−0.734788	−0.367394	−	0.930065i	$-0.619750\pi$
$743$	−20.0289	−0.734788	−0.367394	+	0.930065i	$0.619750\pi$
$744$	−19.1941	−0.703691
$745$	−26.0482	−0.954333
$746$	−8.70523	−0.318721
$747$	11.1337	0.407362
$748$	1.69740	0.0620631
$749$	0	0
$750$	12.3355	0.450428
$751$	37.2282	1.35848	0.679238	−	0.733918i	$-0.262310\pi$
$751$	37.2282	1.35848	0.679238	+	0.733918i	$0.262310\pi$
$752$	23.4316	0.854464
$753$	−14.0767	−0.512982
$754$	−25.1168	−0.914701
$755$	−6.91393	−0.251624
$756$	0	0
$757$	29.9226	1.08756	0.543778	−	0.839229i	$-0.316993\pi$
$757$	29.9226	1.08756	0.543778	+	0.839229i	$0.316993\pi$
$758$	3.49200	0.126835
$759$	−9.77606	−0.354848
$760$	−53.1503	−1.92797
$761$	14.1633	0.513419	0.256710	−	0.966489i	$-0.417362\pi$
$761$	14.1633	0.513419	0.256710	+	0.966489i	$0.417362\pi$
$762$	−18.1825	−0.658682
$763$	0	0
$764$	11.6359	0.420971
$765$	−2.41946	−0.0874758
$766$	30.5662	1.10440
$767$	7.80249	0.281732
$768$	−10.9567	−0.395365
$769$	−15.2864	−0.551240	−0.275620	−	0.961267i	$-0.588883\pi$
$769$	−15.2864	−0.551240	−0.275620	+	0.961267i	$0.588883\pi$
$770$	0	0
$771$	5.06304	0.182341
$772$	−5.53536	−0.199222
$773$	−15.8769	−0.571051	−0.285525	−	0.958371i	$-0.592168\pi$
$773$	−15.8769	−0.571051	−0.285525	+	0.958371i	$0.592168\pi$
$774$	11.3814	0.409095
$775$	−5.35668	−0.192418
$776$	−26.3885	−0.947290
$777$	0	0
$778$	−15.5458	−0.557345
$779$	−19.3354	−0.692763
$780$	7.02531	0.251546
$781$	4.19375	0.150064
$782$	−3.45560	−0.123572
$783$	−3.43234	−0.122662
$784$	0	0
$785$	−11.8559	−0.423155
$786$	−26.2236	−0.935366
$787$	−36.7362	−1.30950	−0.654751	−	0.755844i	$-0.727227\pi$
$787$	−36.7362	−1.30950	−0.654751	+	0.755844i	$0.727227\pi$
$788$	8.51218	0.303234
$789$	−25.2875	−0.900260
$790$	0.952879	0.0339019
$791$	0	0
$792$	10.6427	0.378171
$793$	59.0479	2.09685
$794$	31.1402	1.10512
$795$	7.36564	0.261232
$796$	−5.68681	−0.201564
$797$	−23.1262	−0.819172	−0.409586	−	0.912272i	$-0.634327\pi$
$797$	−23.1262	−0.819172	−0.409586	+	0.912272i	$0.634327\pi$
$798$	0	0
$799$	8.41031	0.297535
$800$	−2.29901	−0.0812824
$801$	−11.6993	−0.413374
$802$	−0.0633250	−0.00223608
$803$	42.8187	1.51104
$804$	−6.72435	−0.237150
$805$	0	0
$806$	−45.9112	−1.61715
$807$	−28.4411	−1.00118
$808$	23.6534	0.832125
$809$	−54.5268	−1.91706	−0.958530	−	0.284992i	$-0.908009\pi$
$809$	−54.5268	−1.91706	−0.958530	+	0.284992i	$0.908009\pi$
$810$	−2.97512	−0.104535
$811$	−18.5864	−0.652656	−0.326328	−	0.945257i	$-0.605811\pi$
$811$	−18.5864	−0.652656	−0.326328	+	0.945257i	$0.605811\pi$
$812$	0	0
$813$	−0.507746	−0.0178074
$814$	32.3887	1.13522
$815$	20.0929	0.703824
$816$	2.78606	0.0975317
$817$	66.4618	2.32520
$818$	23.2031	0.811279
$819$	0	0
$820$	−3.17883	−0.111009
$821$	19.6707	0.686513	0.343257	−	0.939242i	$-0.388470\pi$
$821$	19.6707	0.686513	0.343257	+	0.939242i	$0.388470\pi$
$822$	−2.47107	−0.0861886
$823$	−1.16844	−0.0407293	−0.0203646	−	0.999793i	$-0.506483\pi$
$823$	−1.16844	−0.0407293	−0.0203646	+	0.999793i	$0.506483\pi$
$824$	−22.9216	−0.798512
$825$	2.97015	0.103407
$826$	0	0
$827$	−19.4510	−0.676377	−0.338189	−	0.941078i	$-0.609814\pi$
$827$	−19.4510	−0.676377	−0.338189	+	0.941078i	$0.609814\pi$
$828$	1.37118	0.0476519
$829$	23.1381	0.803619	0.401809	−	0.915723i	$-0.368381\pi$
$829$	23.1381	0.803619	0.401809	+	0.915723i	$0.368381\pi$
$830$	−33.1242	−1.14976
$831$	−11.1521	−0.386861
$832$	−52.8641	−1.83273
$833$	0	0
$834$	10.4902	0.363244
$835$	24.8784	0.860954
$836$	12.1884	0.421546
$837$	−6.27399	−0.216861
$838$	25.0769	0.866269
$839$	13.5536	0.467922	0.233961	−	0.972246i	$-0.424831\pi$
$839$	13.5536	0.467922	0.233961	+	0.972246i	$0.424831\pi$
$840$	0	0
$841$	−17.2190	−0.593760
$842$	−2.10122	−0.0724129
$843$	9.49919	0.327169
$844$	0.204974	0.00705548
$845$	54.2302	1.86558
$846$	10.3418	0.355560
$847$	0	0
$848$	−8.48170	−0.291263
$849$	−4.96941	−0.170550
$850$	1.04987	0.0360104
$851$	21.2774	0.729381
$852$	−0.588212	−0.0201518
$853$	25.8370	0.884641	0.442320	−	0.896857i	$-0.354155\pi$
$853$	25.8370	0.884641	0.442320	+	0.896857i	$0.354155\pi$
$854$	0	0
$855$	−17.3733	−0.594154
$856$	3.39074	0.115893
$857$	−2.60226	−0.0888915	−0.0444458	−	0.999012i	$-0.514152\pi$
$857$	−2.60226	−0.0888915	−0.0444458	+	0.999012i	$0.514152\pi$
$858$	25.4566	0.869075
$859$	−6.03528	−0.205921	−0.102961	−	0.994685i	$-0.532832\pi$
$859$	−6.03528	−0.205921	−0.102961	+	0.994685i	$0.532832\pi$
$860$	10.9266	0.372594
$861$	0	0
$862$	−44.3177	−1.50947
$863$	−40.0350	−1.36281	−0.681403	−	0.731908i	$-0.738630\pi$
$863$	−40.0350	−1.36281	−0.681403	+	0.731908i	$0.738630\pi$
$864$	−2.69271	−0.0916079
$865$	50.2786	1.70952
$866$	−28.5800	−0.971189
$867$	1.00000	0.0339618
$868$	0	0
$869$	−1.11419	−0.0377964
$870$	10.2116	0.346207
$871$	−82.0127	−2.77889
$872$	19.2024	0.650275
$873$	−8.62561	−0.291933
$874$	−24.8134	−0.839327
$875$	0	0
$876$	−6.00571	−0.202914
$877$	−40.8243	−1.37854	−0.689270	−	0.724505i	$-0.742069\pi$
$877$	−40.8243	−1.37854	−0.689270	+	0.724505i	$0.742069\pi$
$878$	28.7705	0.970959
$879$	9.41812	0.317665
$880$	−23.4496	−0.790487
$881$	9.86270	0.332283	0.166141	−	0.986102i	$-0.446869\pi$
$881$	9.86270	0.332283	0.166141	+	0.986102i	$0.446869\pi$
$882$	0	0
$883$	−15.2724	−0.513957	−0.256979	−	0.966417i	$-0.582727\pi$
$883$	−15.2724	−0.513957	−0.256979	+	0.966417i	$0.582727\pi$
$884$	−2.90367	−0.0976608
$885$	−3.17222	−0.106633
$886$	7.20158	0.241942
$887$	9.18636	0.308448	0.154224	−	0.988036i	$-0.450712\pi$
$887$	9.18636	0.308448	0.154224	+	0.988036i	$0.450712\pi$
$888$	−23.1636	−0.777319
$889$	0	0
$890$	34.8068	1.16673
$891$	3.47878	0.116543
$892$	8.47177	0.283656
$893$	60.3914	2.02092
$894$	13.2387	0.442768
$895$	−21.8142	−0.729167
$896$	0	0
$897$	16.7235	0.558380
$898$	−11.7305	−0.391453
$899$	21.5345	0.718215
$900$	−0.416591	−0.0138864
$901$	−3.04433	−0.101421
$902$	−11.5187	−0.383530
$903$	0	0
$904$	4.93690	0.164199
$905$	1.60418	0.0533246
$906$	3.51392	0.116742
$907$	−11.5257	−0.382705	−0.191353	−	0.981521i	$-0.561287\pi$
$907$	−11.5257	−0.382705	−0.191353	+	0.981521i	$0.561287\pi$
$908$	1.76524	0.0585817
$909$	7.73161	0.256441
$910$	0	0
$911$	47.5409	1.57510	0.787550	−	0.616251i	$-0.211349\pi$
$911$	47.5409	1.57510	0.787550	+	0.616251i	$0.211349\pi$
$912$	20.0057	0.662456
$913$	38.7317	1.28183
$914$	45.0277	1.48939
$915$	−24.0068	−0.793640
$916$	6.79478	0.224506
$917$	0	0
$918$	1.22966	0.0405849
$919$	−13.7040	−0.452053	−0.226027	−	0.974121i	$-0.572574\pi$
$919$	−13.7040	−0.452053	−0.226027	+	0.974121i	$0.572574\pi$
$920$	−20.8008	−0.685782
$921$	−23.4105	−0.771403
$922$	25.2307	0.830930
$923$	−7.17405	−0.236137
$924$	0	0
$925$	−6.46448	−0.212551
$926$	39.8509	1.30958
$927$	−7.49240	−0.246083
$928$	9.24231	0.303394
$929$	−46.3641	−1.52116	−0.760579	−	0.649246i	$-0.775085\pi$
$929$	−46.3641	−1.52116	−0.760579	+	0.649246i	$0.775085\pi$
$930$	18.6659	0.612078
$931$	0	0
$932$	−11.2541	−0.368642
$933$	−14.1327	−0.462684
$934$	−23.8821	−0.781446
$935$	−8.41676	−0.275258
$936$	−18.2059	−0.595079
$937$	−21.0492	−0.687646	−0.343823	−	0.939034i	$-0.611722\pi$
$937$	−21.0492	−0.687646	−0.343823	+	0.939034i	$0.611722\pi$
$938$	0	0
$939$	−2.55267	−0.0833034
$940$	9.92861	0.323836
$941$	−41.6738	−1.35853	−0.679263	−	0.733895i	$-0.737700\pi$
$941$	−41.6738	−1.35853	−0.679263	+	0.733895i	$0.737700\pi$
$942$	6.02562	0.196325
$943$	−7.56707	−0.246418
$944$	3.65288	0.118891
$945$	0	0
$946$	39.5932	1.28729
$947$	2.62137	0.0851829	0.0425915	−	0.999093i	$-0.486439\pi$
$947$	2.62137	0.0851829	0.0425915	+	0.999093i	$0.486439\pi$
$948$	0.156276	0.00507560
$949$	−73.2479	−2.37773
$950$	7.53878	0.244590
$951$	29.9490	0.971163
$952$	0	0
$953$	7.65023	0.247815	0.123908	−	0.992294i	$-0.460457\pi$
$953$	7.65023	0.247815	0.123908	+	0.992294i	$0.460457\pi$
$954$	−3.74350	−0.121200
$955$	−57.6978	−1.86706
$956$	−12.2094	−0.394882
$957$	−11.9403	−0.385977
$958$	−0.243244	−0.00785885
$959$	0	0
$960$	21.4927	0.693673
$961$	8.36299	0.269774
$962$	−55.4059	−1.78636
$963$	1.10833	0.0357155
$964$	−8.22440	−0.264890
$965$	27.4477	0.883574
$966$	0	0
$967$	−17.0958	−0.549764	−0.274882	−	0.961478i	$-0.588639\pi$
$967$	−17.0958	−0.549764	−0.274882	+	0.961478i	$0.588639\pi$
$968$	3.37099	0.108348
$969$	7.18064	0.230675
$970$	25.6622	0.823964
$971$	50.1539	1.60951	0.804757	−	0.593604i	$-0.202295\pi$
$971$	50.1539	1.60951	0.804757	+	0.593604i	$0.202295\pi$
$972$	−0.487931	−0.0156504
$973$	0	0
$974$	−40.8585	−1.30919
$975$	−5.08089	−0.162719
$976$	27.6444	0.884874
$977$	32.8914	1.05229	0.526145	−	0.850395i	$-0.323637\pi$
$977$	32.8914	1.05229	0.526145	+	0.850395i	$0.323637\pi$
$978$	−10.2120	−0.326543
$979$	−40.6992	−1.30075
$980$	0	0
$981$	6.27669	0.200399
$982$	−29.0623	−0.927416
$983$	4.89448	0.156110	0.0780548	−	0.996949i	$-0.475129\pi$
$983$	4.89448	0.156110	0.0780548	+	0.996949i	$0.475129\pi$
$984$	8.23786	0.262613
$985$	−42.2087	−1.34488
$986$	−4.22062	−0.134412
$987$	0	0
$988$	−20.8502	−0.663333
$989$	26.0103	0.827080
$990$	−10.3498	−0.328937
$991$	−17.3632	−0.551562	−0.275781	−	0.961221i	$-0.588936\pi$
$991$	−17.3632	−0.551562	−0.275781	+	0.961221i	$0.588936\pi$
$992$	16.8941	0.536387
$993$	−0.144985	−0.00460095
$994$	0	0
$995$	28.1987	0.893959
$996$	−5.43249	−0.172135
$997$	40.8148	1.29262	0.646309	−	0.763076i	$-0.276312\pi$
$997$	40.8148	1.29262	0.646309	+	0.763076i	$0.276312\pi$
$998$	13.2415	0.419151
$999$	−7.57150	−0.239552

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2499.2.a.bb.1.3		5
3.2	odd	2		7497.2.a.bw.1.3		5
7.3	odd	6		357.2.i.f.205.3	✓	10
7.5	odd	6		357.2.i.f.256.3	yes	10
7.6	odd	2		2499.2.a.ba.1.3		5
21.5	even	6		1071.2.i.g.613.3		10
21.17	even	6		1071.2.i.g.919.3		10
21.20	even	2		7497.2.a.bv.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.i.f.205.3	✓	10	7.3	odd	6
357.2.i.f.256.3	yes	10	7.5	odd	6
1071.2.i.g.613.3		10	21.5	even	6
1071.2.i.g.919.3		10	21.17	even	6
2499.2.a.ba.1.3		5	7.6	odd	2
2499.2.a.bb.1.3		5	1.1	even	1	trivial
7497.2.a.bv.1.3		5	21.20	even	2
7497.2.a.bw.1.3		5	3.2	odd	2

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:	\( N \)	\(=\)	\( 2499 = 3 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2499.a (trivial)

\(f(q)\)	\(=\)	\(q-1.22966 q^{2} +1.00000 q^{3} -0.487931 q^{4} +2.41946 q^{5} -1.22966 q^{6} +3.05931 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.22966 q^{2} +1.00000 q^{3} -0.487931 q^{4} +2.41946 q^{5} -1.22966 q^{6} +3.05931 q^{8} +1.00000 q^{9} -2.97512 q^{10} +3.47878 q^{11} -0.487931 q^{12} -5.95098 q^{13} +2.41946 q^{15} -2.78606 q^{16} -1.00000 q^{17} -1.22966 q^{18} -7.18064 q^{19} -1.18053 q^{20} -4.27772 q^{22} -2.81020 q^{23} +3.05931 q^{24} +0.853791 q^{25} +7.31770 q^{26} +1.00000 q^{27} -3.43234 q^{29} -2.97512 q^{30} -6.27399 q^{31} -2.69271 q^{32} +3.47878 q^{33} +1.22966 q^{34} -0.487931 q^{36} -7.57150 q^{37} +8.82977 q^{38} -5.95098 q^{39} +7.40189 q^{40} +2.69271 q^{41} -9.25568 q^{43} -1.69740 q^{44} +2.41946 q^{45} +3.45560 q^{46} -8.41031 q^{47} -2.78606 q^{48} -1.04987 q^{50} -1.00000 q^{51} +2.90367 q^{52} +3.04433 q^{53} -1.22966 q^{54} +8.41676 q^{55} -7.18064 q^{57} +4.22062 q^{58} -1.31113 q^{59} -1.18053 q^{60} -9.92238 q^{61} +7.71489 q^{62} +8.88325 q^{64} -14.3982 q^{65} -4.27772 q^{66} +13.7814 q^{67} +0.487931 q^{68} -2.81020 q^{69} +1.20552 q^{71} +3.05931 q^{72} +12.3085 q^{73} +9.31039 q^{74} +0.853791 q^{75} +3.50366 q^{76} +7.31770 q^{78} -0.320283 q^{79} -6.74077 q^{80} +1.00000 q^{81} -3.31113 q^{82} +11.1337 q^{83} -2.41946 q^{85} +11.3814 q^{86} -3.43234 q^{87} +10.6427 q^{88} -11.6993 q^{89} -2.97512 q^{90} +1.37118 q^{92} -6.27399 q^{93} +10.3418 q^{94} -17.3733 q^{95} -2.69271 q^{96} -8.62561 q^{97} +3.47878 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} + 5 q^{3} + 8 q^{4} - q^{5} - 2 q^{6} + 5 q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 + 5 * q^3 + 8 * q^4 - q^5 - 2 * q^6 + 5 * q^9	\( 5 q - 2 q^{2} + 5 q^{3} + 8 q^{4} - q^{5} - 2 q^{6} + 5 q^{9} - 13 q^{10} - 11 q^{11} + 8 q^{12} - 7 q^{13} - q^{15} - 2 q^{16} - 5 q^{17} - 2 q^{18} - 9 q^{19} - 12 q^{20} + 5 q^{22} - 23 q^{23} + 14 q^{25} - 18 q^{26} + 5 q^{27} - 18 q^{29} - 13 q^{30} - 9 q^{31} + 3 q^{32} - 11 q^{33} + 2 q^{34} + 8 q^{36} - 7 q^{39} - 31 q^{40} - 3 q^{41} + 12 q^{43} - 33 q^{44} - q^{45} + 13 q^{46} - 11 q^{47} - 2 q^{48} + 24 q^{50} - 5 q^{51} - 5 q^{52} - 3 q^{53} - 2 q^{54} + 10 q^{55} - 9 q^{57} - 34 q^{58} + 14 q^{59} - 12 q^{60} - 29 q^{61} + 5 q^{62} - 8 q^{65} + 5 q^{66} + 16 q^{67} - 8 q^{68} - 23 q^{69} - 19 q^{71} - 11 q^{73} + 45 q^{74} + 14 q^{75} - 9 q^{76} - 18 q^{78} + q^{79} + 5 q^{80} + 5 q^{81} + 4 q^{82} - 5 q^{83} + q^{85} - 3 q^{86} - 18 q^{87} + 37 q^{88} - 8 q^{89} - 13 q^{90} - 48 q^{92} - 9 q^{93} + 18 q^{94} - 21 q^{95} + 3 q^{96} - 19 q^{97} - 11 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 + 5 * q^3 + 8 * q^4 - q^5 - 2 * q^6 + 5 * q^9 - 13 * q^10 - 11 * q^11 + 8 * q^12 - 7 * q^13 - q^15 - 2 * q^16 - 5 * q^17 - 2 * q^18 - 9 * q^19 - 12 * q^20 + 5 * q^22 - 23 * q^23 + 14 * q^25 - 18 * q^26 + 5 * q^27 - 18 * q^29 - 13 * q^30 - 9 * q^31 + 3 * q^32 - 11 * q^33 + 2 * q^34 + 8 * q^36 - 7 * q^39 - 31 * q^40 - 3 * q^41 + 12 * q^43 - 33 * q^44 - q^45 + 13 * q^46 - 11 * q^47 - 2 * q^48 + 24 * q^50 - 5 * q^51 - 5 * q^52 - 3 * q^53 - 2 * q^54 + 10 * q^55 - 9 * q^57 - 34 * q^58 + 14 * q^59 - 12 * q^60 - 29 * q^61 + 5 * q^62 - 8 * q^65 + 5 * q^66 + 16 * q^67 - 8 * q^68 - 23 * q^69 - 19 * q^71 - 11 * q^73 + 45 * q^74 + 14 * q^75 - 9 * q^76 - 18 * q^78 + q^79 + 5 * q^80 + 5 * q^81 + 4 * q^82 - 5 * q^83 + q^85 - 3 * q^86 - 18 * q^87 + 37 * q^88 - 8 * q^89 - 13 * q^90 - 48 * q^92 - 9 * q^93 + 18 * q^94 - 21 * q^95 + 3 * q^96 - 19 * q^97 - 11 * q^99

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