LMFDB - Embedded newform 8281.2.a.ce.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8281,2,Mod(1,8281)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8281, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8281.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8281 = 7^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8281.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:	$66.1241179138$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.6995813.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 6x^{4} + 4x^{3} + 7x^{2} - x - 1 $ x^6 - x^5 - 6x^4 + 4x^3 + 7*x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.435907$ of defining polynomial
Character	$\chi$	$=$	8281.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.85816 q^{2} +2.29407 q^{3} +1.45276 q^{4} +0.197362 q^{5} -4.26275 q^{6} +1.01686 q^{8} +2.26275 q^{9} +O(q^{10})$	\(q-1.85816 q^{2} +2.29407 q^{3} +1.45276 q^{4} +0.197362 q^{5} -4.26275 q^{6} +1.01686 q^{8} +2.26275 q^{9} -0.366731 q^{10} +4.18274 q^{11} +3.33274 q^{12} +0.452762 q^{15} -4.79501 q^{16} +0.841305 q^{17} -4.20455 q^{18} -1.35175 q^{19} +0.286720 q^{20} -7.77220 q^{22} -4.11519 q^{23} +2.33274 q^{24} -4.96105 q^{25} -1.69131 q^{27} -8.23861 q^{29} -0.841305 q^{30} +1.28070 q^{31} +6.87618 q^{32} +9.59548 q^{33} -1.56328 q^{34} +3.28723 q^{36} -3.04485 q^{37} +2.51177 q^{38} +0.200689 q^{40} -5.39696 q^{41} +5.32778 q^{43} +6.07652 q^{44} +0.446581 q^{45} +7.64669 q^{46} +11.6641 q^{47} -11.0001 q^{48} +9.21843 q^{50} +1.93001 q^{51} +4.64796 q^{53} +3.14272 q^{54} +0.825514 q^{55} -3.10101 q^{57} +15.3087 q^{58} -6.05811 q^{59} +0.657756 q^{60} -11.3657 q^{61} -2.37975 q^{62} -3.18704 q^{64} -17.8300 q^{66} -13.3970 q^{67} +1.22222 q^{68} -9.44053 q^{69} +5.97040 q^{71} +2.30089 q^{72} -3.88547 q^{73} +5.65782 q^{74} -11.3810 q^{75} -1.96377 q^{76} -10.7334 q^{79} -0.946353 q^{80} -10.6682 q^{81} +10.0284 q^{82} -3.07390 q^{83} +0.166042 q^{85} -9.89987 q^{86} -18.8999 q^{87} +4.25324 q^{88} +11.9841 q^{89} -0.829819 q^{90} -5.97840 q^{92} +2.93801 q^{93} -21.6737 q^{94} -0.266785 q^{95} +15.7744 q^{96} -19.4727 q^{97} +9.46448 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - q^{3} + 4 q^{4} + q^{5} - 9 q^{6} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 2 * q^2 - q^3 + 4 * q^4 + q^5 - 9 * q^6 + 3 * q^8 - 3 * q^9	$ 6 q + 2 q^{2} - q^{3} + 4 q^{4} + q^{5} - 9 q^{6} + 3 q^{8} - 3 q^{9} - 4 q^{10} + 4 q^{11} - 5 q^{12} - 2 q^{15} - 8 q^{16} - 5 q^{17} + 3 q^{18} - q^{19} - q^{20} + 5 q^{22} + q^{23} - 11 q^{24} - 7 q^{25} - 4 q^{27} - 3 q^{29} + 5 q^{30} + 16 q^{31} + 8 q^{32} + 16 q^{33} - 16 q^{34} + 21 q^{36} - 13 q^{37} + 17 q^{38} + 5 q^{40} - 8 q^{41} + 11 q^{43} + 21 q^{44} - 7 q^{45} + 16 q^{46} - q^{47} - 21 q^{48} + 6 q^{50} + 20 q^{51} + 2 q^{53} - 18 q^{54} - 9 q^{55} - 21 q^{57} - 8 q^{58} + 13 q^{59} + 20 q^{60} + 5 q^{61} - 5 q^{62} - 15 q^{64} - 18 q^{66} - 11 q^{67} - 29 q^{68} - 23 q^{69} + 6 q^{71} + 25 q^{72} - 30 q^{73} + 3 q^{74} + 3 q^{75} - 9 q^{76} - 7 q^{79} - 7 q^{80} + 6 q^{81} - q^{82} + 27 q^{83} - q^{85} - 7 q^{86} - 16 q^{87} + 4 q^{89} - 8 q^{90} + 27 q^{92} - 7 q^{93} - 45 q^{94} + 6 q^{95} + 19 q^{96} - 35 q^{97} + 10 q^{99}+O(q^{100}) $ 6 * q + 2 * q^2 - q^3 + 4 * q^4 + q^5 - 9 * q^6 + 3 * q^8 - 3 * q^9 - 4 * q^10 + 4 * q^11 - 5 * q^12 - 2 * q^15 - 8 * q^16 - 5 * q^17 + 3 * q^18 - q^19 - q^20 + 5 * q^22 + q^23 - 11 * q^24 - 7 * q^25 - 4 * q^27 - 3 * q^29 + 5 * q^30 + 16 * q^31 + 8 * q^32 + 16 * q^33 - 16 * q^34 + 21 * q^36 - 13 * q^37 + 17 * q^38 + 5 * q^40 - 8 * q^41 + 11 * q^43 + 21 * q^44 - 7 * q^45 + 16 * q^46 - q^47 - 21 * q^48 + 6 * q^50 + 20 * q^51 + 2 * q^53 - 18 * q^54 - 9 * q^55 - 21 * q^57 - 8 * q^58 + 13 * q^59 + 20 * q^60 + 5 * q^61 - 5 * q^62 - 15 * q^64 - 18 * q^66 - 11 * q^67 - 29 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 - 30 * q^73 + 3 * q^74 + 3 * q^75 - 9 * q^76 - 7 * q^79 - 7 * q^80 + 6 * q^81 - q^82 + 27 * q^83 - q^85 - 7 * q^86 - 16 * q^87 + 4 * q^89 - 8 * q^90 + 27 * q^92 - 7 * q^93 - 45 * q^94 + 6 * q^95 + 19 * q^96 - 35 * q^97 + 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.85816	−1.31392	−0.656959	−	0.753926i	$-0.728158\pi$
$2$	−1.85816	−1.31392	−0.656959	+	0.753926i	$0.728158\pi$
$3$	2.29407	1.32448	0.662240	−	0.749291i	$-0.269606\pi$
$3$	2.29407	1.32448	0.662240	+	0.749291i	$0.269606\pi$
$4$	1.45276	0.726381
$5$	0.197362	0.0882631	0.0441315	−	0.999026i	$-0.485948\pi$
$5$	0.197362	0.0882631	0.0441315	+	0.999026i	$0.485948\pi$
$6$	−4.26275	−1.74026
$7$	0	0
$7$	0	0
$8$	1.01686	0.359513
$9$	2.26275	0.754249
$10$	−0.366731	−0.115970
$11$	4.18274	1.26114	0.630571	−	0.776131i	$-0.282821\pi$
$11$	4.18274	1.26114	0.630571	+	0.776131i	$0.282821\pi$
$12$	3.33274	0.962078
$13$	0	0
$13$	0	0
$14$	0	0
$15$	0.452762	0.116903
$16$	−4.79501	−1.19875
$17$	0.841305	0.204047	0.102023	−	0.994782i	$-0.467468\pi$
$17$	0.841305	0.204047	0.102023	+	0.994782i	$0.467468\pi$
$18$	−4.20455	−0.991022
$19$	−1.35175	−0.310113	−0.155057	−	0.987906i	$-0.549556\pi$
$19$	−1.35175	−0.310113	−0.155057	+	0.987906i	$0.549556\pi$
$20$	0.286720	0.0641126
$21$	0	0
$22$	−7.77220	−1.65704
$23$	−4.11519	−0.858077	−0.429038	−	0.903286i	$-0.641147\pi$
$23$	−4.11519	−0.858077	−0.429038	+	0.903286i	$0.641147\pi$
$24$	2.33274	0.476168
$25$	−4.96105	−0.992210
$26$	0	0
$27$	−1.69131	−0.325492
$28$	0	0
$29$	−8.23861	−1.52987	−0.764936	−	0.644106i	$-0.777230\pi$
$29$	−8.23861	−1.52987	−0.764936	+	0.644106i	$0.777230\pi$
$30$	−0.841305	−0.153601
$31$	1.28070	0.230020	0.115010	−	0.993364i	$-0.463310\pi$
$31$	1.28070	0.230020	0.115010	+	0.993364i	$0.463310\pi$
$32$	6.87618	1.21555
$33$	9.59548	1.67036
$34$	−1.56328	−0.268100
$35$	0	0
$36$	3.28723	0.547872
$37$	−3.04485	−0.500570	−0.250285	−	0.968172i	$-0.580524\pi$
$37$	−3.04485	−0.500570	−0.250285	+	0.968172i	$0.580524\pi$
$38$	2.51177	0.407463
$39$	0	0
$40$	0.200689	0.0317317
$41$	−5.39696	−0.842863	−0.421431	−	0.906860i	$-0.638472\pi$
$41$	−5.39696	−0.842863	−0.421431	+	0.906860i	$0.638472\pi$
$42$	0	0
$43$	5.32778	0.812479	0.406239	−	0.913767i	$-0.366840\pi$
$43$	5.32778	0.812479	0.406239	+	0.913767i	$0.366840\pi$
$44$	6.07652	0.916070
$45$	0.446581	0.0665724
$46$	7.64669	1.12744
$47$	11.6641	1.70138	0.850690	−	0.525668i	$-0.176185\pi$
$47$	11.6641	1.70138	0.850690	+	0.525668i	$0.176185\pi$
$48$	−11.0001	−1.58772
$49$	0	0
$50$	9.21843	1.30368
$51$	1.93001	0.270256
$52$	0	0
$53$	4.64796	0.638447	0.319223	−	0.947679i	$-0.396578\pi$
$53$	4.64796	0.638447	0.319223	+	0.947679i	$0.396578\pi$
$54$	3.14272	0.427670
$55$	0.825514	0.111312
$56$	0	0
$57$	−3.10101	−0.410739
$58$	15.3087	2.01013
$59$	−6.05811	−0.788698	−0.394349	−	0.918961i	$-0.629030\pi$
$59$	−6.05811	−0.788698	−0.394349	+	0.918961i	$0.629030\pi$
$60$	0.657756	0.0849160
$61$	−11.3657	−1.45523	−0.727614	−	0.685986i	$-0.759371\pi$
$61$	−11.3657	−1.45523	−0.727614	+	0.685986i	$0.759371\pi$
$62$	−2.37975	−0.302228
$63$	0	0
$64$	−3.18704	−0.398380
$65$	0	0
$66$	−17.8300	−2.19472
$67$	−13.3970	−1.63671	−0.818354	−	0.574715i	$-0.805113\pi$
$67$	−13.3970	−1.63671	−0.818354	+	0.574715i	$0.805113\pi$
$68$	1.22222	0.148216
$69$	−9.44053	−1.13651
$70$	0	0
$71$	5.97040	0.708556	0.354278	−	0.935140i	$-0.384727\pi$
$71$	5.97040	0.708556	0.354278	+	0.935140i	$0.384727\pi$
$72$	2.30089	0.271162
$73$	−3.88547	−0.454759	−0.227380	−	0.973806i	$-0.573016\pi$
$73$	−3.88547	−0.454759	−0.227380	+	0.973806i	$0.573016\pi$
$74$	5.65782	0.657708
$75$	−11.3810	−1.31416
$76$	−1.96377	−0.225260
$77$	0	0
$78$	0	0
$79$	−10.7334	−1.20760	−0.603799	−	0.797136i	$-0.706347\pi$
$79$	−10.7334	−1.20760	−0.603799	+	0.797136i	$0.706347\pi$
$80$	−0.946353	−0.105806
$81$	−10.6682	−1.18536
$82$	10.0284	1.10745
$83$	−3.07390	−0.337404	−0.168702	−	0.985667i	$-0.553958\pi$
$83$	−3.07390	−0.337404	−0.168702	+	0.985667i	$0.553958\pi$
$84$	0	0
$85$	0.166042	0.0180098
$86$	−9.89987	−1.06753
$87$	−18.8999	−2.02629
$88$	4.25324	0.453397
$89$	11.9841	1.27032	0.635159	−	0.772382i	$-0.280935\pi$
$89$	11.9841	1.27032	0.635159	+	0.772382i	$0.280935\pi$
$90$	−0.829819	−0.0874706
$91$	0	0
$92$	−5.97840	−0.623291
$93$	2.93801	0.304658
$94$	−21.6737	−2.23547
$95$	−0.266785	−0.0273715
$96$	15.7744	1.60997
$97$	−19.4727	−1.97716	−0.988578	−	0.150709i	$-0.951844\pi$
$97$	−19.4727	−1.97716	−0.988578	+	0.150709i	$0.951844\pi$
$98$	0	0
$99$	9.46448	0.951216
$100$	−7.20722	−0.720722
$101$	−16.9339	−1.68499	−0.842495	−	0.538704i	$-0.818914\pi$
$101$	−16.9339	−1.68499	−0.842495	+	0.538704i	$0.818914\pi$
$102$	−3.58627	−0.355094
$103$	−7.23425	−0.712811	−0.356406	−	0.934331i	$-0.615998\pi$
$103$	−7.23425	−0.712811	−0.356406	+	0.934331i	$0.615998\pi$
$104$	0	0
$105$	0	0
$106$	−8.63667	−0.838867
$107$	−9.85249	−0.952477	−0.476238	−	0.879316i	$-0.658000\pi$
$107$	−9.85249	−0.952477	−0.476238	+	0.879316i	$0.658000\pi$
$108$	−2.45707	−0.236431
$109$	13.8159	1.32332	0.661662	−	0.749802i	$-0.269851\pi$
$109$	13.8159	1.32332	0.661662	+	0.749802i	$0.269851\pi$
$110$	−1.53394	−0.146255
$111$	−6.98509	−0.662995
$112$	0	0
$113$	−4.26864	−0.401560	−0.200780	−	0.979636i	$-0.564348\pi$
$113$	−4.26864	−0.401560	−0.200780	+	0.979636i	$0.564348\pi$
$114$	5.76218	0.539677
$115$	−0.812183	−0.0757365
$116$	−11.9687	−1.11127
$117$	0	0
$118$	11.2569	1.03629
$119$	0	0
$120$	0.460394	0.0420280
$121$	6.49529	0.590481
$122$	21.1193	1.91205
$123$	−12.3810	−1.11636
$124$	1.86055	0.167082
$125$	−1.96593	−0.175839
$126$	0	0
$127$	−2.19024	−0.194352	−0.0971761	−	0.995267i	$-0.530981\pi$
$127$	−2.19024	−0.194352	−0.0971761	+	0.995267i	$0.530981\pi$
$128$	−7.83033	−0.692110
$129$	12.2223	1.07611
$130$	0	0
$131$	2.27612	0.198865	0.0994326	−	0.995044i	$-0.468297\pi$
$131$	2.27612	0.198865	0.0994326	+	0.995044i	$0.468297\pi$
$132$	13.9400	1.21332
$133$	0	0
$134$	24.8938	2.15050
$135$	−0.333800	−0.0287289
$136$	0.855486	0.0733573
$137$	−13.4480	−1.14894	−0.574469	−	0.818526i	$-0.694791\pi$
$137$	−13.4480	−1.14894	−0.574469	+	0.818526i	$0.694791\pi$
$138$	17.5420	1.49328
$139$	4.04540	0.343126	0.171563	−	0.985173i	$-0.445118\pi$
$139$	4.04540	0.343126	0.171563	+	0.985173i	$0.445118\pi$
$140$	0	0
$141$	26.7582	2.25344
$142$	−11.0940	−0.930984
$143$	0	0
$144$	−10.8499	−0.904157
$145$	−1.62599	−0.135031
$146$	7.21982	0.597517
$147$	0	0
$148$	−4.42344	−0.363605
$149$	−15.3519	−1.25768	−0.628840	−	0.777535i	$-0.716470\pi$
$149$	−15.3519	−1.25768	−0.628840	+	0.777535i	$0.716470\pi$
$150$	21.1477	1.72670
$151$	−6.12108	−0.498127	−0.249063	−	0.968487i	$-0.580123\pi$
$151$	−6.12108	−0.498127	−0.249063	+	0.968487i	$0.580123\pi$
$152$	−1.37454	−0.111490
$153$	1.90366	0.153902
$154$	0	0
$155$	0.252762	0.0203023
$156$	0	0
$157$	4.53668	0.362067	0.181033	−	0.983477i	$-0.442056\pi$
$157$	4.53668	0.362067	0.181033	+	0.983477i	$0.442056\pi$
$158$	19.9443	1.58669
$159$	10.6627	0.845611
$160$	1.35710	0.107288
$161$	0	0
$162$	19.8233	1.55746
$163$	−1.82254	−0.142752	−0.0713762	−	0.997449i	$-0.522739\pi$
$163$	−1.82254	−0.142752	−0.0713762	+	0.997449i	$0.522739\pi$
$164$	−7.84049	−0.612240
$165$	1.89379	0.147431
$166$	5.71180	0.443322
$167$	10.7079	0.828606	0.414303	−	0.910139i	$-0.364025\pi$
$167$	10.7079	0.828606	0.414303	+	0.910139i	$0.364025\pi$
$168$	0	0
$169$	0	0
$170$	−0.308533	−0.0236634
$171$	−3.05867	−0.233903
$172$	7.74000	0.590169
$173$	−13.4927	−1.02583	−0.512915	−	0.858439i	$-0.671434\pi$
$173$	−13.4927	−1.02583	−0.512915	+	0.858439i	$0.671434\pi$
$174$	35.1191	2.66237
$175$	0	0
$176$	−20.0563	−1.51180
$177$	−13.8977	−1.04462
$178$	−22.2685	−1.66909
$179$	10.4692	0.782502	0.391251	−	0.920284i	$-0.372042\pi$
$179$	10.4692	0.782502	0.391251	+	0.920284i	$0.372042\pi$
$180$	0.648776	0.0483569
$181$	12.5209	0.930674	0.465337	−	0.885133i	$-0.345933\pi$
$181$	12.5209	0.930674	0.465337	+	0.885133i	$0.345933\pi$
$182$	0	0
$183$	−26.0737	−1.92742
$184$	−4.18455	−0.308489
$185$	−0.600938	−0.0441819
$186$	−5.45930	−0.400295
$187$	3.51896	0.257332
$188$	16.9451	1.23585
$189$	0	0
$190$	0.495729	0.0359640
$191$	13.1137	0.948874	0.474437	−	0.880290i	$-0.342652\pi$
$191$	13.1137	0.948874	0.474437	+	0.880290i	$0.342652\pi$
$192$	−7.31129	−0.527647
$193$	−1.04157	−0.0749740	−0.0374870	−	0.999297i	$-0.511935\pi$
$193$	−1.04157	−0.0749740	−0.0374870	+	0.999297i	$0.511935\pi$
$194$	36.1835	2.59782
$195$	0	0
$196$	0	0
$197$	−1.47833	−0.105327	−0.0526635	−	0.998612i	$-0.516771\pi$
$197$	−1.47833	−0.105327	−0.0526635	+	0.998612i	$0.516771\pi$
$198$	−17.5865	−1.24982
$199$	14.0999	0.999512	0.499756	−	0.866166i	$-0.333423\pi$
$199$	14.0999	0.999512	0.499756	+	0.866166i	$0.333423\pi$
$200$	−5.04467	−0.356712
$201$	−30.7337	−2.16779
$202$	31.4660	2.21394
$203$	0	0
$204$	2.80385	0.196309
$205$	−1.06516	−0.0743937
$206$	13.4424	0.936576
$207$	−9.31164	−0.647204
$208$	0	0
$209$	−5.65402	−0.391097
$210$	0	0
$211$	26.4692	1.82222	0.911108	−	0.412167i	$-0.135228\pi$
$211$	26.4692	1.82222	0.911108	+	0.412167i	$0.135228\pi$
$212$	6.75239	0.463756
$213$	13.6965	0.938468
$214$	18.3075	1.25148
$215$	1.05150	0.0717119
$216$	−1.71981	−0.117019
$217$	0	0
$218$	−25.6722	−1.73874
$219$	−8.91352	−0.602320
$220$	1.19928	0.0808552
$221$	0	0
$222$	12.9794	0.871122
$223$	0.728048	0.0487537	0.0243769	−	0.999703i	$-0.492240\pi$
$223$	0.728048	0.0487537	0.0243769	+	0.999703i	$0.492240\pi$
$224$	0	0
$225$	−11.2256	−0.748373
$226$	7.93182	0.527617
$227$	2.85195	0.189291	0.0946454	−	0.995511i	$-0.469828\pi$
$227$	2.85195	0.189291	0.0946454	+	0.995511i	$0.469828\pi$
$228$	−4.50503	−0.298353
$229$	−3.17352	−0.209712	−0.104856	−	0.994487i	$-0.533438\pi$
$229$	−3.17352	−0.209712	−0.104856	+	0.994487i	$0.533438\pi$
$230$	1.50917	0.0995116
$231$	0	0
$232$	−8.37748	−0.550009
$233$	13.4071	0.878327	0.439163	−	0.898407i	$-0.355275\pi$
$233$	13.4071	0.878327	0.439163	+	0.898407i	$0.355275\pi$
$234$	0	0
$235$	2.30205	0.150169
$236$	−8.80099	−0.572896
$237$	−24.6231	−1.59944
$238$	0	0
$239$	15.5538	1.00609	0.503046	−	0.864259i	$-0.332212\pi$
$239$	15.5538	1.00609	0.503046	+	0.864259i	$0.332212\pi$
$240$	−2.17100	−0.140137
$241$	7.57574	0.487996	0.243998	−	0.969776i	$-0.421541\pi$
$241$	7.57574	0.487996	0.243998	+	0.969776i	$0.421541\pi$
$242$	−12.0693	−0.775844
$243$	−19.3997	−1.24449
$244$	−16.5117	−1.05705
$245$	0	0
$246$	23.0059	1.46680
$247$	0	0
$248$	1.30229	0.0826953
$249$	−7.05173	−0.446885
$250$	3.65302	0.231038
$251$	1.27476	0.0804624	0.0402312	−	0.999190i	$-0.487191\pi$
$251$	1.27476	0.0804624	0.0402312	+	0.999190i	$0.487191\pi$
$252$	0	0
$253$	−17.2128	−1.08216
$254$	4.06982	0.255363
$255$	0.380912	0.0238536
$256$	20.9241	1.30776
$257$	−8.48019	−0.528980	−0.264490	−	0.964388i	$-0.585204\pi$
$257$	−8.48019	−0.528980	−0.264490	+	0.964388i	$0.585204\pi$
$258$	−22.7110	−1.41392
$259$	0	0
$260$	0	0
$261$	−18.6419	−1.15390
$262$	−4.22939	−0.261293
$263$	12.7883	0.788560	0.394280	−	0.918990i	$-0.370994\pi$
$263$	12.7883	0.788560	0.394280	+	0.918990i	$0.370994\pi$
$264$	9.75722	0.600515
$265$	0.917333	0.0563513
$266$	0	0
$267$	27.4925	1.68251
$268$	−19.4627	−1.18887
$269$	−4.71172	−0.287278	−0.143639	−	0.989630i	$-0.545880\pi$
$269$	−4.71172	−0.287278	−0.143639	+	0.989630i	$0.545880\pi$
$270$	0.620254	0.0377475
$271$	18.0112	1.09410	0.547052	−	0.837098i	$-0.315750\pi$
$271$	18.0112	1.09410	0.547052	+	0.837098i	$0.315750\pi$
$272$	−4.03407	−0.244601
$273$	0	0
$274$	24.9885	1.50961
$275$	−20.7508	−1.25132
$276$	−13.7148	−0.825537
$277$	−26.1209	−1.56945	−0.784725	−	0.619844i	$-0.787196\pi$
$277$	−26.1209	−1.56945	−0.784725	+	0.619844i	$0.787196\pi$
$278$	−7.51700	−0.450840
$279$	2.89790	0.173493
$280$	0	0
$281$	3.66197	0.218455	0.109227	−	0.994017i	$-0.465162\pi$
$281$	3.66197	0.218455	0.109227	+	0.994017i	$0.465162\pi$
$282$	−49.7210	−2.96084
$283$	7.64527	0.454464	0.227232	−	0.973841i	$-0.427032\pi$
$283$	7.64527	0.454464	0.227232	+	0.973841i	$0.427032\pi$
$284$	8.67357	0.514682
$285$	−0.612022	−0.0362531
$286$	0	0
$287$	0	0
$288$	15.5591	0.916827
$289$	−16.2922	−0.958365
$290$	3.02135	0.177420
$291$	−44.6718	−2.61871
$292$	−5.64466	−0.330329
$293$	17.1534	1.00211	0.501056	−	0.865415i	$-0.332945\pi$
$293$	17.1534	1.00211	0.501056	+	0.865415i	$0.332945\pi$
$294$	0	0
$295$	−1.19564	−0.0696130
$296$	−3.09617	−0.179961
$297$	−7.07429	−0.410492
$298$	28.5264	1.65249
$299$	0	0
$300$	−16.5339	−0.954583
$301$	0	0
$302$	11.3740	0.654498
$303$	−38.8476	−2.23174
$304$	6.48166	0.371749
$305$	−2.24316	−0.128443
$306$	−3.53731	−0.202215
$307$	28.0696	1.60201	0.801007	−	0.598655i	$-0.204298\pi$
$307$	28.0696	1.60201	0.801007	+	0.598655i	$0.204298\pi$
$308$	0	0
$309$	−16.5959	−0.944105
$310$	−0.469672	−0.0266756
$311$	−23.5341	−1.33450	−0.667248	−	0.744836i	$-0.732528\pi$
$311$	−23.5341	−1.33450	−0.667248	+	0.744836i	$0.732528\pi$
$312$	0	0
$313$	−3.34860	−0.189274	−0.0946370	−	0.995512i	$-0.530169\pi$
$313$	−3.34860	−0.189274	−0.0946370	+	0.995512i	$0.530169\pi$
$314$	−8.42989	−0.475726
$315$	0	0
$316$	−15.5930	−0.877177
$317$	7.27834	0.408793	0.204396	−	0.978888i	$-0.434477\pi$
$317$	7.27834	0.408793	0.204396	+	0.978888i	$0.434477\pi$
$318$	−19.8131	−1.11106
$319$	−34.4600	−1.92939
$320$	−0.629002	−0.0351623
$321$	−22.6023	−1.26154
$322$	0	0
$323$	−1.13724	−0.0632775
$324$	−15.4984	−0.861021
$325$	0	0
$326$	3.38658	0.187565
$327$	31.6946	1.75272
$328$	−5.48792	−0.303020
$329$	0	0
$330$	−3.51896	−0.193712
$331$	14.3234	0.787283	0.393642	−	0.919264i	$-0.371215\pi$
$331$	14.3234	0.787283	0.393642	+	0.919264i	$0.371215\pi$
$332$	−4.46564	−0.245084
$333$	−6.88973	−0.377555
$334$	−19.8971	−1.08872
$335$	−2.64407	−0.144461
$336$	0	0
$337$	17.1802	0.935868	0.467934	−	0.883764i	$-0.344999\pi$
$337$	17.1802	0.935868	0.467934	+	0.883764i	$0.344999\pi$
$338$	0	0
$339$	−9.79255	−0.531858
$340$	0.241220	0.0130820
$341$	5.35683	0.290089
$342$	5.68351	0.307329
$343$	0	0
$344$	5.41758	0.292096
$345$	−1.86320	−0.100312
$346$	25.0716	1.34786
$347$	−7.70278	−0.413507	−0.206753	−	0.978393i	$-0.566290\pi$
$347$	−7.70278	−0.413507	−0.206753	+	0.978393i	$0.566290\pi$
$348$	−27.4571	−1.47186
$349$	−22.3701	−1.19744	−0.598721	−	0.800958i	$-0.704324\pi$
$349$	−22.3701	−1.19744	−0.598721	+	0.800958i	$0.704324\pi$
$350$	0	0
$351$	0	0
$352$	28.7613	1.53298
$353$	22.2623	1.18490	0.592451	−	0.805606i	$-0.298160\pi$
$353$	22.2623	1.18490	0.592451	+	0.805606i	$0.298160\pi$
$354$	25.8242	1.37254
$355$	1.17833	0.0625393
$356$	17.4101	0.922735
$357$	0	0
$358$	−19.4534	−1.02814
$359$	2.75842	0.145584	0.0727920	−	0.997347i	$-0.476809\pi$
$359$	2.75842	0.145584	0.0727920	+	0.997347i	$0.476809\pi$
$360$	0.454108	0.0239336
$361$	−17.1728	−0.903830
$362$	−23.2659	−1.22283
$363$	14.9006	0.782081
$364$	0	0
$365$	−0.766844	−0.0401385
$366$	48.4491	2.53248
$367$	−14.1497	−0.738609	−0.369304	−	0.929308i	$-0.620404\pi$
$367$	−14.1497	−0.738609	−0.369304	+	0.929308i	$0.620404\pi$
$368$	19.7324	1.02862
$369$	−12.2119	−0.635729
$370$	1.11664	0.0580514
$371$	0	0
$372$	4.26823	0.221298
$373$	−5.04284	−0.261109	−0.130554	−	0.991441i	$-0.541676\pi$
$373$	−5.04284	−0.261109	−0.130554	+	0.991441i	$0.541676\pi$
$374$	−6.53879	−0.338113
$375$	−4.50999	−0.232895
$376$	11.8607	0.611668
$377$	0	0
$378$	0	0
$379$	6.05964	0.311263	0.155631	−	0.987815i	$-0.450259\pi$
$379$	6.05964	0.311263	0.155631	+	0.987815i	$0.450259\pi$
$380$	−0.387575	−0.0198822
$381$	−5.02456	−0.257416
$382$	−24.3674	−1.24674
$383$	4.54105	0.232037	0.116018	−	0.993247i	$-0.462987\pi$
$383$	4.54105	0.232037	0.116018	+	0.993247i	$0.462987\pi$
$384$	−17.9633	−0.916686
$385$	0	0
$386$	1.93541	0.0985098
$387$	12.0554	0.612811
$388$	−28.2893	−1.43617
$389$	4.50765	0.228547	0.114273	−	0.993449i	$-0.463546\pi$
$389$	4.50765	0.228547	0.114273	+	0.993449i	$0.463546\pi$
$390$	0	0
$391$	−3.46213	−0.175088
$392$	0	0
$393$	5.22157	0.263393
$394$	2.74698	0.138391
$395$	−2.11836	−0.106586
$396$	13.7496	0.690945
$397$	−4.00349	−0.200929	−0.100465	−	0.994941i	$-0.532033\pi$
$397$	−4.00349	−0.200929	−0.100465	+	0.994941i	$0.532033\pi$
$398$	−26.1998	−1.31328
$399$	0	0
$400$	23.7883	1.18941
$401$	−12.6135	−0.629887	−0.314944	−	0.949110i	$-0.601986\pi$
$401$	−12.6135	−0.629887	−0.314944	+	0.949110i	$0.601986\pi$
$402$	57.1081	2.84829
$403$	0	0
$404$	−24.6010	−1.22394
$405$	−2.10550	−0.104623
$406$	0	0
$407$	−12.7358	−0.631290
$408$	1.96254	0.0971604
$409$	−20.6952	−1.02331	−0.511657	−	0.859190i	$-0.670968\pi$
$409$	−20.6952	−1.02331	−0.511657	+	0.859190i	$0.670968\pi$
$410$	1.97923	0.0977472
$411$	−30.8506	−1.52175
$412$	−10.5096	−0.517773
$413$	0	0
$414$	17.3025	0.850373
$415$	−0.606672	−0.0297803
$416$	0	0
$417$	9.28042	0.454464
$418$	10.5061	0.513869
$419$	−21.8175	−1.06586	−0.532928	−	0.846161i	$-0.678908\pi$
$419$	−21.8175	−1.06586	−0.532928	+	0.846161i	$0.678908\pi$
$420$	0	0
$421$	−9.42727	−0.459457	−0.229728	−	0.973255i	$-0.573784\pi$
$421$	−9.42727	−0.459457	−0.229728	+	0.973255i	$0.573784\pi$
$422$	−49.1841	−2.39424
$423$	26.3928	1.28326
$424$	4.72631	0.229530
$425$	−4.17376	−0.202457
$426$	−25.4503	−1.23307
$427$	0	0
$428$	−14.3133	−0.691861
$429$	0	0
$430$	−1.95386	−0.0942235
$431$	−20.4275	−0.983960	−0.491980	−	0.870607i	$-0.663727\pi$
$431$	−20.4275	−0.983960	−0.491980	+	0.870607i	$0.663727\pi$
$432$	8.10983	0.390184
$433$	26.3486	1.26623	0.633117	−	0.774056i	$-0.281775\pi$
$433$	26.3486	1.26623	0.633117	+	0.774056i	$0.281775\pi$
$434$	0	0
$435$	−3.73014	−0.178846
$436$	20.0712	0.961238
$437$	5.56272	0.266101
$438$	16.5628	0.791399
$439$	25.1310	1.19944	0.599720	−	0.800210i	$-0.295279\pi$
$439$	25.1310	1.19944	0.599720	+	0.800210i	$0.295279\pi$
$440$	0.839429	0.0400182
$441$	0	0
$442$	0	0
$443$	18.5199	0.879907	0.439953	−	0.898021i	$-0.354995\pi$
$443$	18.5199	0.879907	0.439953	+	0.898021i	$0.354995\pi$
$444$	−10.1477	−0.481587
$445$	2.36522	0.112122
$446$	−1.35283	−0.0640584
$447$	−35.2184	−1.66577
$448$	0	0
$449$	−11.6431	−0.549471	−0.274736	−	0.961520i	$-0.588590\pi$
$449$	−11.6431	−0.549471	−0.274736	+	0.961520i	$0.588590\pi$
$450$	20.8590	0.983301
$451$	−22.5740	−1.06297
$452$	−6.20132	−0.291685
$453$	−14.0422	−0.659759
$454$	−5.29939	−0.248713
$455$	0	0
$456$	−3.15328	−0.147666
$457$	−20.5184	−0.959812	−0.479906	−	0.877320i	$-0.659329\pi$
$457$	−20.5184	−0.959812	−0.479906	+	0.877320i	$0.659329\pi$
$458$	5.89691	0.275544
$459$	−1.42291	−0.0664156
$460$	−1.17991	−0.0550136
$461$	−2.04075	−0.0950473	−0.0475236	−	0.998870i	$-0.515133\pi$
$461$	−2.04075	−0.0950473	−0.0475236	+	0.998870i	$0.515133\pi$
$462$	0	0
$463$	−3.03155	−0.140888	−0.0704441	−	0.997516i	$-0.522442\pi$
$463$	−3.03155	−0.140888	−0.0704441	+	0.997516i	$0.522442\pi$
$464$	39.5042	1.83394
$465$	0.579853	0.0268900
$466$	−24.9125	−1.15405
$467$	−12.9274	−0.598210	−0.299105	−	0.954220i	$-0.596688\pi$
$467$	−12.9274	−0.598210	−0.299105	+	0.954220i	$0.596688\pi$
$468$	0	0
$469$	0	0
$470$	−4.27757	−0.197310
$471$	10.4075	0.479550
$472$	−6.16022	−0.283547
$473$	22.2847	1.02465
$474$	45.7537	2.10153
$475$	6.70611	0.307697
$476$	0	0
$477$	10.5172	0.481548
$478$	−28.9015	−1.32192
$479$	−36.5821	−1.67148	−0.835740	−	0.549126i	$-0.814961\pi$
$479$	−36.5821	−1.67148	−0.835740	+	0.549126i	$0.814961\pi$
$480$	3.11328	0.142101
$481$	0	0
$482$	−14.0769	−0.641187
$483$	0	0
$484$	9.43611	0.428914
$485$	−3.84318	−0.174510
$486$	36.0478	1.63516
$487$	−36.7496	−1.66528	−0.832642	−	0.553812i	$-0.813173\pi$
$487$	−36.7496	−1.66528	−0.832642	+	0.553812i	$0.813173\pi$
$488$	−11.5573	−0.523173
$489$	−4.18103	−0.189073
$490$	0	0
$491$	−8.19797	−0.369969	−0.184985	−	0.982741i	$-0.559224\pi$
$491$	−8.19797	−0.369969	−0.184985	+	0.982741i	$0.559224\pi$
$492$	−17.9866	−0.810900
$493$	−6.93119	−0.312165
$494$	0	0
$495$	1.86793	0.0839572
$496$	−6.14096	−0.275737
$497$	0	0
$498$	13.1033	0.587171
$499$	43.2532	1.93628	0.968141	−	0.250407i	$-0.0805645\pi$
$499$	43.2532	1.93628	0.968141	+	0.250407i	$0.0805645\pi$
$500$	−2.85604	−0.127726
$501$	24.5648	1.09747
$502$	−2.36872	−0.105721
$503$	0.0181922	0.000811149 0	0.000405575	−	1.00000i	$-0.499871\pi$
$503$	0.0181922	0.000811149 0	0.000405575		1.00000i	$0.499871\pi$
$504$	0	0
$505$	−3.34212	−0.148722
$506$	31.9841	1.42187
$507$	0	0
$508$	−3.18190	−0.141174
$509$	−43.1006	−1.91040	−0.955200	−	0.295960i	$-0.904361\pi$
$509$	−43.1006	−1.91040	−0.955200	+	0.295960i	$0.904361\pi$
$510$	−0.707795	−0.0313417
$511$	0	0
$512$	−23.2197	−1.02617
$513$	2.28623	0.100939
$514$	15.7576	0.695036
$515$	−1.42777	−0.0629149
$516$	17.7561	0.781668
$517$	48.7877	2.14568
$518$	0	0
$519$	−30.9531	−1.35869
$520$	0	0
$521$	20.9540	0.918012	0.459006	−	0.888433i	$-0.348206\pi$
$521$	20.9540	0.918012	0.459006	+	0.888433i	$0.348206\pi$
$522$	34.6397	1.51614
$523$	−34.7403	−1.51909	−0.759543	−	0.650457i	$-0.774577\pi$
$523$	−34.7403	−1.51909	−0.759543	+	0.650457i	$0.774577\pi$
$524$	3.30666	0.144452
$525$	0	0
$526$	−23.7627	−1.03610
$527$	1.07746	0.0469349
$528$	−46.0104	−2.00235
$529$	−6.06520	−0.263704
$530$	−1.70455	−0.0740410
$531$	−13.7080	−0.594875
$532$	0	0
$533$	0	0
$534$	−51.0854	−2.21068
$535$	−1.94451	−0.0840685
$536$	−13.6228	−0.588417
$537$	24.0170	1.03641
$538$	8.75513	0.377460
$539$	0	0
$540$	−0.484932	−0.0208682
$541$	3.29846	0.141812	0.0709059	−	0.997483i	$-0.477411\pi$
$541$	3.29846	0.141812	0.0709059	+	0.997483i	$0.477411\pi$
$542$	−33.4678	−1.43756
$543$	28.7239	1.23266
$544$	5.78497	0.248029
$545$	2.72674	0.116801
$546$	0	0
$547$	21.9417	0.938161	0.469080	−	0.883155i	$-0.344585\pi$
$547$	21.9417	0.938161	0.469080	+	0.883155i	$0.344585\pi$
$548$	−19.5367	−0.834567
$549$	−25.7177	−1.09761
$550$	38.5583	1.64413
$551$	11.1366	0.474434
$552$	−9.59965	−0.408588
$553$	0	0
$554$	48.5368	2.06213
$555$	−1.37859	−0.0585180
$556$	5.87700	0.249240
$557$	14.2866	0.605342	0.302671	−	0.953095i	$-0.402122\pi$
$557$	14.2866	0.605342	0.302671	+	0.953095i	$0.402122\pi$
$558$	−5.38476	−0.227955
$559$	0	0
$560$	0	0
$561$	8.07273	0.340831
$562$	−6.80453	−0.287032
$563$	6.78784	0.286073	0.143037	−	0.989717i	$-0.454313\pi$
$563$	6.78784	0.286073	0.143037	+	0.989717i	$0.454313\pi$
$564$	38.8733	1.63686
$565$	−0.842468	−0.0354429
$566$	−14.2061	−0.597128
$567$	0	0
$568$	6.07103	0.254735
$569$	−17.3212	−0.726143	−0.363072	−	0.931761i	$-0.618272\pi$
$569$	−17.3212	−0.726143	−0.363072	+	0.931761i	$0.618272\pi$
$570$	1.13724	0.0476336
$571$	−13.0116	−0.544520	−0.272260	−	0.962224i	$-0.587771\pi$
$571$	−13.0116	−0.544520	−0.272260	+	0.962224i	$0.587771\pi$
$572$	0	0
$573$	30.0837	1.25676
$574$	0	0
$575$	20.4157	0.851392
$576$	−7.21147	−0.300478
$577$	0.731535	0.0304542	0.0152271	−	0.999884i	$-0.495153\pi$
$577$	0.731535	0.0304542	0.0152271	+	0.999884i	$0.495153\pi$
$578$	30.2735	1.25921
$579$	−2.38944	−0.0993017
$580$	−2.36218	−0.0980842
$581$	0	0
$582$	83.0073	3.44076
$583$	19.4412	0.805173
$584$	−3.95096	−0.163492
$585$	0	0
$586$	−31.8738	−1.31669
$587$	8.52284	0.351775	0.175888	−	0.984410i	$-0.443720\pi$
$587$	8.52284	0.351775	0.175888	+	0.984410i	$0.443720\pi$
$588$	0	0
$589$	−1.73119	−0.0713323
$590$	2.22170	0.0914657
$591$	−3.39140	−0.139503
$592$	14.6001	0.600059
$593$	31.3093	1.28572	0.642860	−	0.765984i	$-0.277748\pi$
$593$	31.3093	1.28572	0.642860	+	0.765984i	$0.277748\pi$
$594$	13.1452	0.539353
$595$	0	0
$596$	−22.3027	−0.913554
$597$	32.3460	1.32383
$598$	0	0
$599$	−0.750232	−0.0306537	−0.0153268	−	0.999883i	$-0.504879\pi$
$599$	−0.750232	−0.0306537	−0.0153268	+	0.999883i	$0.504879\pi$
$600$	−11.5728	−0.472458
$601$	−9.55305	−0.389677	−0.194838	−	0.980835i	$-0.562418\pi$
$601$	−9.55305	−0.389677	−0.194838	+	0.980835i	$0.562418\pi$
$602$	0	0
$603$	−30.3141	−1.23449
$604$	−8.89248	−0.361830
$605$	1.28193	0.0521177
$606$	72.1851	2.93232
$607$	22.2395	0.902672	0.451336	−	0.892354i	$-0.350948\pi$
$607$	22.2395	0.902672	0.451336	+	0.892354i	$0.350948\pi$
$608$	−9.29489	−0.376958
$609$	0	0
$610$	4.16815	0.168764
$611$	0	0
$612$	2.76557	0.111791
$613$	8.27987	0.334421	0.167210	−	0.985921i	$-0.446524\pi$
$613$	8.27987	0.334421	0.167210	+	0.985921i	$0.446524\pi$
$614$	−52.1578	−2.10492
$615$	−2.44354	−0.0985330
$616$	0	0
$617$	−20.3312	−0.818503	−0.409252	−	0.912422i	$-0.634210\pi$
$617$	−20.3312	−0.818503	−0.409252	+	0.912422i	$0.634210\pi$
$618$	30.8378	1.24048
$619$	−5.34097	−0.214672	−0.107336	−	0.994223i	$-0.534232\pi$
$619$	−5.34097	−0.214672	−0.107336	+	0.994223i	$0.534232\pi$
$620$	0.367203	0.0147472
$621$	6.96005	0.279297
$622$	43.7301	1.75342
$623$	0	0
$624$	0	0
$625$	24.4172	0.976690
$626$	6.22224	0.248691
$627$	−12.9707	−0.518000
$628$	6.59072	0.262998
$629$	−2.56165	−0.102140
$630$	0	0
$631$	−6.46662	−0.257432	−0.128716	−	0.991681i	$-0.541086\pi$
$631$	−6.46662	−0.257432	−0.128716	+	0.991681i	$0.541086\pi$
$632$	−10.9143	−0.434147
$633$	60.7222	2.41349
$634$	−13.5243	−0.537120
$635$	−0.432271	−0.0171541
$636$	15.4904	0.614236
$637$	0	0
$638$	64.0322	2.53506
$639$	13.5095	0.534428
$640$	−1.54541	−0.0610877
$641$	23.3289	0.921434	0.460717	−	0.887547i	$-0.347592\pi$
$641$	23.3289	0.921434	0.460717	+	0.887547i	$0.347592\pi$
$642$	41.9987	1.65756
$643$	3.58878	0.141527	0.0707637	−	0.997493i	$-0.477456\pi$
$643$	3.58878	0.141527	0.0707637	+	0.997493i	$0.477456\pi$
$644$	0	0
$645$	2.41222	0.0949810
$646$	2.11317	0.0831415
$647$	−39.6524	−1.55890	−0.779448	−	0.626467i	$-0.784500\pi$
$647$	−39.6524	−1.55890	−0.779448	+	0.626467i	$0.784500\pi$
$648$	−10.8480	−0.426151
$649$	−25.3395	−0.994661
$650$	0	0
$651$	0	0
$652$	−2.64772	−0.103693
$653$	18.1355	0.709699	0.354849	−	0.934923i	$-0.384532\pi$
$653$	18.1355	0.709699	0.354849	+	0.934923i	$0.384532\pi$
$654$	−58.8938	−2.30293
$655$	0.449219	0.0175525
$656$	25.8784	1.01038
$657$	−8.79183	−0.343002
$658$	0	0
$659$	13.4810	0.525147	0.262573	−	0.964912i	$-0.415429\pi$
$659$	13.4810	0.525147	0.262573	+	0.964912i	$0.415429\pi$
$660$	2.75122	0.107091
$661$	−10.3122	−0.401099	−0.200549	−	0.979684i	$-0.564273\pi$
$661$	−10.3122	−0.401099	−0.200549	+	0.979684i	$0.564273\pi$
$662$	−26.6151	−1.03443
$663$	0	0
$664$	−3.12571	−0.121301
$665$	0	0
$666$	12.8022	0.496076
$667$	33.9035	1.31275
$668$	15.5561	0.601884
$669$	1.67019	0.0645733
$670$	4.91310	0.189810
$671$	−47.5397	−1.83525
$672$	0	0
$673$	−9.23056	−0.355812	−0.177906	−	0.984048i	$-0.556932\pi$
$673$	−9.23056	−0.355812	−0.177906	+	0.984048i	$0.556932\pi$
$674$	−31.9237	−1.22965
$675$	8.39066	0.322956
$676$	0	0
$677$	−21.0934	−0.810687	−0.405343	−	0.914165i	$-0.632848\pi$
$677$	−21.0934	−0.810687	−0.405343	+	0.914165i	$0.632848\pi$
$678$	18.1961	0.698818
$679$	0	0
$680$	0.168841	0.00647474
$681$	6.54258	0.250712
$682$	−9.95385	−0.381153
$683$	38.2212	1.46249	0.731246	−	0.682113i	$-0.238939\pi$
$683$	38.2212	1.46249	0.731246	+	0.682113i	$0.238939\pi$
$684$	−4.44353	−0.169902
$685$	−2.65412	−0.101409
$686$	0	0
$687$	−7.28027	−0.277760
$688$	−25.5467	−0.973960
$689$	0	0
$690$	3.46213	0.131801
$691$	26.2322	0.997920	0.498960	−	0.866625i	$-0.333715\pi$
$691$	26.2322	0.997920	0.498960	+	0.866625i	$0.333715\pi$
$692$	−19.6017	−0.745144
$693$	0	0
$694$	14.3130	0.543314
$695$	0.798409	0.0302854
$696$	−19.2185	−0.728476
$697$	−4.54049	−0.171983
$698$	41.5672	1.57334
$699$	30.7567	1.16333
$700$	0	0
$701$	−46.7346	−1.76514	−0.882570	−	0.470180i	$-0.844189\pi$
$701$	−46.7346	−1.76514	−0.882570	+	0.470180i	$0.844189\pi$
$702$	0	0
$703$	4.11588	0.155233
$704$	−13.3306	−0.502414
$705$	5.28105	0.198896
$706$	−41.3669	−1.55687
$707$	0	0
$708$	−20.1901	−0.758789
$709$	47.4464	1.78189	0.890944	−	0.454113i	$-0.150044\pi$
$709$	47.4464	1.78189	0.890944	+	0.454113i	$0.150044\pi$
$710$	−2.18953	−0.0821715
$711$	−24.2869	−0.910830
$712$	12.1861	0.456695
$713$	−5.27032	−0.197375
$714$	0	0
$715$	0	0
$716$	15.2092	0.568395
$717$	35.6815	1.33255
$718$	−5.12560	−0.191286
$719$	−49.2380	−1.83627	−0.918133	−	0.396273i	$-0.870304\pi$
$719$	−49.2380	−1.83627	−0.918133	+	0.396273i	$0.870304\pi$
$720$	−2.14136	−0.0798037
$721$	0	0
$722$	31.9098	1.18756
$723$	17.3793	0.646342
$724$	18.1900	0.676024
$725$	40.8722	1.51795
$726$	−27.6878	−1.02759
$727$	−32.0495	−1.18865	−0.594325	−	0.804225i	$-0.702581\pi$
$727$	−32.0495	−1.18865	−0.594325	+	0.804225i	$0.702581\pi$
$728$	0	0
$729$	−12.4996	−0.462947
$730$	1.42492	0.0527387
$731$	4.48229	0.165783
$732$	−37.8789	−1.40004
$733$	−28.2010	−1.04163	−0.520813	−	0.853670i	$-0.674371\pi$
$733$	−28.2010	−1.04163	−0.520813	+	0.853670i	$0.674371\pi$
$734$	26.2924	0.970472
$735$	0	0
$736$	−28.2968	−1.04303
$737$	−56.0362	−2.06412
$738$	22.6918	0.835295
$739$	42.5370	1.56475	0.782375	−	0.622808i	$-0.214008\pi$
$739$	42.5370	1.56475	0.782375	+	0.622808i	$0.214008\pi$
$740$	−0.873021	−0.0320929
$741$	0	0
$742$	0	0
$743$	−15.9142	−0.583836	−0.291918	−	0.956443i	$-0.594294\pi$
$743$	−15.9142	−0.583836	−0.291918	+	0.956443i	$0.594294\pi$
$744$	2.98753	0.109528
$745$	−3.02989	−0.111007
$746$	9.37042	0.343075
$747$	−6.95546	−0.254487
$748$	5.11221	0.186921
$749$	0	0
$750$	8.38028	0.306005
$751$	18.1996	0.664114	0.332057	−	0.943259i	$-0.392257\pi$
$751$	18.1996	0.664114	0.332057	+	0.943259i	$0.392257\pi$
$752$	−55.9293	−2.03953
$753$	2.92440	0.106571
$754$	0	0
$755$	−1.20807	−0.0439662
$756$	0	0
$757$	−44.9004	−1.63193	−0.815967	−	0.578099i	$-0.803795\pi$
$757$	−44.9004	−1.63193	−0.815967	+	0.578099i	$0.803795\pi$
$758$	−11.2598	−0.408974
$759$	−39.4872	−1.43330
$760$	−0.271282	−0.00984042
$761$	26.4888	0.960217	0.480108	−	0.877209i	$-0.340597\pi$
$761$	26.4888	0.960217	0.480108	+	0.877209i	$0.340597\pi$
$762$	9.33644	0.338223
$763$	0	0
$764$	19.0511	0.689244
$765$	0.375711	0.0135839
$766$	−8.43800	−0.304877
$767$	0	0
$768$	48.0013	1.73210
$769$	−13.9625	−0.503502	−0.251751	−	0.967792i	$-0.581006\pi$
$769$	−13.9625	−0.503502	−0.251751	+	0.967792i	$0.581006\pi$
$770$	0	0
$771$	−19.4541	−0.700623
$772$	−1.51316	−0.0544597
$773$	−12.8113	−0.460790	−0.230395	−	0.973097i	$-0.574002\pi$
$773$	−12.8113	−0.460790	−0.230395	+	0.973097i	$0.574002\pi$
$774$	−22.4009	−0.805184
$775$	−6.35361	−0.228228
$776$	−19.8010	−0.710813
$777$	0	0
$778$	−8.37594	−0.300292
$779$	7.29534	0.261383
$780$	0	0
$781$	24.9726	0.893590
$782$	6.43320	0.230051
$783$	13.9340	0.497961
$784$	0	0
$785$	0.895370	0.0319571
$786$	−9.70251	−0.346077
$787$	27.3199	0.973848	0.486924	−	0.873444i	$-0.338119\pi$
$787$	27.3199	0.973848	0.486924	+	0.873444i	$0.338119\pi$
$788$	−2.14767	−0.0765075
$789$	29.3372	1.04443
$790$	3.93626	0.140046
$791$	0	0
$792$	9.62401	0.341974
$793$	0	0
$794$	7.43912	0.264005
$795$	2.10442	0.0746362
$796$	20.4837	0.726027
$797$	−29.4003	−1.04141	−0.520707	−	0.853736i	$-0.674332\pi$
$797$	−29.4003	−1.04141	−0.520707	+	0.853736i	$0.674332\pi$
$798$	0	0
$799$	9.81305	0.347161
$800$	−34.1131	−1.20608
$801$	27.1171	0.958136
$802$	23.4379	0.827621
$803$	−16.2519	−0.573517
$804$	−44.6487	−1.57464
$805$	0	0
$806$	0	0
$807$	−10.8090	−0.380495
$808$	−17.2194	−0.605775
$809$	−6.01233	−0.211382	−0.105691	−	0.994399i	$-0.533706\pi$
$809$	−6.01233	−0.211382	−0.105691	+	0.994399i	$0.533706\pi$
$810$	3.91236	0.137466
$811$	−8.44807	−0.296652	−0.148326	−	0.988939i	$-0.547388\pi$
$811$	−8.44807	−0.296652	−0.148326	+	0.988939i	$0.547388\pi$
$812$	0	0
$813$	41.3190	1.44912
$814$	23.6652	0.829464
$815$	−0.359701	−0.0125998
$816$	−9.25442	−0.323969
$817$	−7.20184	−0.251960
$818$	38.4551	1.34455
$819$	0	0
$820$	−1.54742	−0.0540382
$821$	34.2635	1.19581	0.597903	−	0.801569i	$-0.296001\pi$
$821$	34.2635	1.19581	0.597903	+	0.801569i	$0.296001\pi$
$822$	57.3253	1.99945
$823$	−6.23732	−0.217419	−0.108710	−	0.994074i	$-0.534672\pi$
$823$	−6.23732	−0.217419	−0.108710	+	0.994074i	$0.534672\pi$
$824$	−7.35618	−0.256265
$825$	−47.6037	−1.65735
$826$	0	0
$827$	−19.5232	−0.678889	−0.339445	−	0.940626i	$-0.610239\pi$
$827$	−19.5232	−0.678889	−0.339445	+	0.940626i	$0.610239\pi$
$828$	−13.5276	−0.470117
$829$	32.6766	1.13491	0.567453	−	0.823406i	$-0.307929\pi$
$829$	32.6766	1.13491	0.567453	+	0.823406i	$0.307929\pi$
$830$	1.12729	0.0391289
$831$	−59.9230	−2.07871
$832$	0	0
$833$	0	0
$834$	−17.2445	−0.597128
$835$	2.11334	0.0731353
$836$	−8.21395	−0.284085
$837$	−2.16606	−0.0748698
$838$	40.5405	1.40045
$839$	−24.7427	−0.854212	−0.427106	−	0.904202i	$-0.640467\pi$
$839$	−24.7427	−0.854212	−0.427106	+	0.904202i	$0.640467\pi$
$840$	0	0
$841$	38.8748	1.34051
$842$	17.5174	0.603689
$843$	8.40080	0.289339
$844$	38.4535	1.32362
$845$	0	0
$846$	−49.0422	−1.68610
$847$	0	0
$848$	−22.2870	−0.765339
$849$	17.5388	0.601929
$850$	7.75551	0.266012
$851$	12.5301	0.429528
$852$	19.8978	0.681686
$853$	−18.2245	−0.623994	−0.311997	−	0.950083i	$-0.600998\pi$
$853$	−18.2245	−0.623994	−0.311997	+	0.950083i	$0.600998\pi$
$854$	0	0
$855$	−0.603667	−0.0206450
$856$	−10.0186	−0.342427
$857$	2.54679	0.0869967	0.0434984	−	0.999053i	$-0.486150\pi$
$857$	2.54679	0.0869967	0.0434984	+	0.999053i	$0.486150\pi$
$858$	0	0
$859$	54.0090	1.84276	0.921382	−	0.388657i	$-0.127061\pi$
$859$	54.0090	1.84276	0.921382	+	0.388657i	$0.127061\pi$
$860$	1.52758	0.0520902
$861$	0	0
$862$	37.9577	1.29284
$863$	−1.24309	−0.0423153	−0.0211576	−	0.999776i	$-0.506735\pi$
$863$	−1.24309	−0.0423153	−0.0211576	+	0.999776i	$0.506735\pi$
$864$	−11.6297	−0.395652
$865$	−2.66295	−0.0905429
$866$	−48.9600	−1.66373
$867$	−37.3754	−1.26934
$868$	0	0
$869$	−44.8949	−1.52295
$870$	6.93119	0.234989
$871$	0	0
$872$	14.0488	0.475752
$873$	−44.0619	−1.49127
$874$	−10.3364	−0.349635
$875$	0	0
$876$	−12.9492	−0.437514
$877$	−0.802661	−0.0271039	−0.0135520	−	0.999908i	$-0.504314\pi$
$877$	−0.802661	−0.0271039	−0.0135520	+	0.999908i	$0.504314\pi$
$878$	−46.6975	−1.57597
$879$	39.3511	1.32728
$880$	−3.95835	−0.133436
$881$	−37.0636	−1.24870	−0.624352	−	0.781143i	$-0.714637\pi$
$881$	−37.0636	−1.24870	−0.624352	+	0.781143i	$0.714637\pi$
$882$	0	0
$883$	−22.8671	−0.769539	−0.384770	−	0.923013i	$-0.625719\pi$
$883$	−22.8671	−0.769539	−0.384770	+	0.923013i	$0.625719\pi$
$884$	0	0
$885$	−2.74288	−0.0922010
$886$	−34.4130	−1.15613
$887$	−49.2573	−1.65390	−0.826950	−	0.562276i	$-0.809926\pi$
$887$	−49.2573	−1.65390	−0.826950	+	0.562276i	$0.809926\pi$
$888$	−7.10283	−0.238355
$889$	0	0
$890$	−4.39496	−0.147319
$891$	−44.6223	−1.49490
$892$	1.05768	0.0354138
$893$	−15.7669	−0.527620
$894$	65.4414	2.18869
$895$	2.06622	0.0690661
$896$	0	0
$897$	0	0
$898$	21.6347	0.721961
$899$	−10.5512	−0.351902
$900$	−16.3081	−0.543604
$901$	3.91036	0.130273
$902$	41.9462	1.39666
$903$	0	0
$904$	−4.34059	−0.144366
$905$	2.47116	0.0821442
$906$	26.0926	0.866870
$907$	−5.00455	−0.166173	−0.0830867	−	0.996542i	$-0.526478\pi$
$907$	−5.00455	−0.166173	−0.0830867	+	0.996542i	$0.526478\pi$
$908$	4.14321	0.137497
$909$	−38.3172	−1.27090
$910$	0	0
$911$	49.0582	1.62537	0.812685	−	0.582703i	$-0.198005\pi$
$911$	49.0582	1.62537	0.812685	+	0.582703i	$0.198005\pi$
$912$	14.8694	0.492374
$913$	−12.8573	−0.425515
$914$	38.1266	1.26111
$915$	−5.14596	−0.170120
$916$	−4.61037	−0.152331
$917$	0	0
$918$	2.64399	0.0872646
$919$	29.6056	0.976598	0.488299	−	0.872676i	$-0.337618\pi$
$919$	29.6056	0.976598	0.488299	+	0.872676i	$0.337618\pi$
$920$	−0.825873	−0.0272282
$921$	64.3935	2.12184
$922$	3.79205	0.124884
$923$	0	0
$924$	0	0
$925$	15.1056	0.496670
$926$	5.63311	0.185116
$927$	−16.3693	−0.537637
$928$	−56.6502	−1.85963
$929$	−16.8305	−0.552191	−0.276095	−	0.961130i	$-0.589041\pi$
$929$	−16.8305	−0.552191	−0.276095	+	0.961130i	$0.589041\pi$
$930$	−1.07746	−0.0353313
$931$	0	0
$932$	19.4773	0.638000
$933$	−53.9888	−1.76751
$934$	24.0212	0.785998
$935$	0.694510	0.0227129
$936$	0	0
$937$	44.0131	1.43784	0.718922	−	0.695091i	$-0.244636\pi$
$937$	44.0131	1.43784	0.718922	+	0.695091i	$0.244636\pi$
$938$	0	0
$939$	−7.68191	−0.250690
$940$	3.34433	0.109080
$941$	−53.0675	−1.72995	−0.864976	−	0.501814i	$-0.832666\pi$
$941$	−53.0675	−1.72995	−0.864976	+	0.501814i	$0.832666\pi$
$942$	−19.3387	−0.630090
$943$	22.2095	0.723241
$944$	29.0487	0.945453
$945$	0	0
$946$	−41.4086	−1.34631
$947$	27.8817	0.906034	0.453017	−	0.891502i	$-0.350348\pi$
$947$	27.8817	0.906034	0.453017	+	0.891502i	$0.350348\pi$
$948$	−35.7715	−1.16180
$949$	0	0
$950$	−12.4610	−0.404289
$951$	16.6970	0.541438
$952$	0	0
$953$	−36.3568	−1.17771	−0.588856	−	0.808238i	$-0.700421\pi$
$953$	−36.3568	−1.17771	−0.588856	+	0.808238i	$0.700421\pi$
$954$	−19.5426	−0.632715
$955$	2.58815	0.0837505
$956$	22.5960	0.730807
$957$	−79.0535	−2.55544
$958$	67.9754	2.19619
$959$	0	0
$960$	−1.44297	−0.0465718
$961$	−29.3598	−0.947091
$962$	0	0
$963$	−22.2937	−0.718405
$964$	11.0057	0.354471
$965$	−0.205567	−0.00661744
$966$	0	0
$967$	15.2681	0.490988	0.245494	−	0.969398i	$-0.421050\pi$
$967$	15.2681	0.490988	0.245494	+	0.969398i	$0.421050\pi$
$968$	6.60477	0.212285
$969$	−2.60890	−0.0838099
$970$	7.14125	0.229292
$971$	−36.8920	−1.18392	−0.591961	−	0.805967i	$-0.701646\pi$
$971$	−36.8920	−1.18392	−0.591961	+	0.805967i	$0.701646\pi$
$972$	−28.1831	−0.903975
$973$	0	0
$974$	68.2867	2.18805
$975$	0	0
$976$	54.4986	1.74446
$977$	0.443914	0.0142021	0.00710104	−	0.999975i	$-0.497740\pi$
$977$	0.443914	0.0142021	0.00710104	+	0.999975i	$0.497740\pi$
$978$	7.76904	0.248426
$979$	50.1265	1.60205
$980$	0	0
$981$	31.2619	0.998117
$982$	15.2332	0.486109
$983$	−45.5603	−1.45315	−0.726575	−	0.687088i	$-0.758889\pi$
$983$	−45.5603	−1.45315	−0.726575	+	0.687088i	$0.758889\pi$
$984$	−12.5897	−0.401344
$985$	−0.291767	−0.00929648
$986$	12.8793	0.410160
$987$	0	0
$988$	0	0
$989$	−21.9248	−0.697169
$990$	−3.47092	−0.110313
$991$	53.6295	1.70360	0.851799	−	0.523869i	$-0.175512\pi$
$991$	53.6295	1.70360	0.851799	+	0.523869i	$0.175512\pi$
$992$	8.80632	0.279601
$993$	32.8588	1.04274
$994$	0	0
$995$	2.78278	0.0882200
$996$	−10.2445	−0.324609
$997$	29.0852	0.921139	0.460569	−	0.887624i	$-0.347645\pi$
$997$	29.0852	0.921139	0.460569	+	0.887624i	$0.347645\pi$
$998$	−80.3715	−2.54412
$999$	5.14977	0.162932

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8281.2.a.ce.1.1		6
7.2	even	3		1183.2.e.g.508.6		12
7.4	even	3		1183.2.e.g.170.6		12
7.6	odd	2		8281.2.a.cf.1.1		6
13.4	even	6		637.2.f.k.393.1		12
13.10	even	6		637.2.f.k.295.1		12
13.12	even	2		8281.2.a.bz.1.6		6
91.4	even	6		91.2.h.b.16.6	yes	12
91.10	odd	6		637.2.g.l.373.1		12
91.17	odd	6		637.2.h.l.471.6		12
91.23	even	6		91.2.h.b.74.6	yes	12
91.25	even	6		1183.2.e.h.170.1		12
91.30	even	6		91.2.g.b.81.1	yes	12
91.51	even	6		1183.2.e.h.508.1		12
91.62	odd	6		637.2.f.j.295.1		12
91.69	odd	6		637.2.f.j.393.1		12
91.75	odd	6		637.2.h.l.165.6		12
91.82	odd	6		637.2.g.l.263.1		12
91.88	even	6		91.2.g.b.9.1	✓	12
91.90	odd	2		8281.2.a.ca.1.6		6
273.23	odd	6		819.2.s.d.802.1		12
273.95	odd	6		819.2.s.d.289.1		12
273.179	odd	6		819.2.n.d.100.6		12
273.212	odd	6		819.2.n.d.172.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.1	✓	12	91.88	even	6
91.2.g.b.81.1	yes	12	91.30	even	6
91.2.h.b.16.6	yes	12	91.4	even	6
91.2.h.b.74.6	yes	12	91.23	even	6
637.2.f.j.295.1		12	91.62	odd	6
637.2.f.j.393.1		12	91.69	odd	6
637.2.f.k.295.1		12	13.10	even	6
637.2.f.k.393.1		12	13.4	even	6
637.2.g.l.263.1		12	91.82	odd	6
637.2.g.l.373.1		12	91.10	odd	6
637.2.h.l.165.6		12	91.75	odd	6
637.2.h.l.471.6		12	91.17	odd	6
819.2.n.d.100.6		12	273.179	odd	6
819.2.n.d.172.6		12	273.212	odd	6
819.2.s.d.289.1		12	273.95	odd	6
819.2.s.d.802.1		12	273.23	odd	6
1183.2.e.g.170.6		12	7.4	even	3
1183.2.e.g.508.6		12	7.2	even	3
1183.2.e.h.170.1		12	91.25	even	6
1183.2.e.h.508.1		12	91.51	even	6
8281.2.a.bz.1.6		6	13.12	even	2
8281.2.a.ca.1.6		6	91.90	odd	2
8281.2.a.ce.1.1		6	1.1	even	1	trivial
8281.2.a.cf.1.1		6	7.6	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:	\( N \)	\(=\)	\( 8281 = 7^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8281.a (trivial)

\(f(q)\)	\(=\)	\(q-1.85816 q^{2} +2.29407 q^{3} +1.45276 q^{4} +0.197362 q^{5} -4.26275 q^{6} +1.01686 q^{8} +2.26275 q^{9} +O(q^{10})\)	\(q-1.85816 q^{2} +2.29407 q^{3} +1.45276 q^{4} +0.197362 q^{5} -4.26275 q^{6} +1.01686 q^{8} +2.26275 q^{9} -0.366731 q^{10} +4.18274 q^{11} +3.33274 q^{12} +0.452762 q^{15} -4.79501 q^{16} +0.841305 q^{17} -4.20455 q^{18} -1.35175 q^{19} +0.286720 q^{20} -7.77220 q^{22} -4.11519 q^{23} +2.33274 q^{24} -4.96105 q^{25} -1.69131 q^{27} -8.23861 q^{29} -0.841305 q^{30} +1.28070 q^{31} +6.87618 q^{32} +9.59548 q^{33} -1.56328 q^{34} +3.28723 q^{36} -3.04485 q^{37} +2.51177 q^{38} +0.200689 q^{40} -5.39696 q^{41} +5.32778 q^{43} +6.07652 q^{44} +0.446581 q^{45} +7.64669 q^{46} +11.6641 q^{47} -11.0001 q^{48} +9.21843 q^{50} +1.93001 q^{51} +4.64796 q^{53} +3.14272 q^{54} +0.825514 q^{55} -3.10101 q^{57} +15.3087 q^{58} -6.05811 q^{59} +0.657756 q^{60} -11.3657 q^{61} -2.37975 q^{62} -3.18704 q^{64} -17.8300 q^{66} -13.3970 q^{67} +1.22222 q^{68} -9.44053 q^{69} +5.97040 q^{71} +2.30089 q^{72} -3.88547 q^{73} +5.65782 q^{74} -11.3810 q^{75} -1.96377 q^{76} -10.7334 q^{79} -0.946353 q^{80} -10.6682 q^{81} +10.0284 q^{82} -3.07390 q^{83} +0.166042 q^{85} -9.89987 q^{86} -18.8999 q^{87} +4.25324 q^{88} +11.9841 q^{89} -0.829819 q^{90} -5.97840 q^{92} +2.93801 q^{93} -21.6737 q^{94} -0.266785 q^{95} +15.7744 q^{96} -19.4727 q^{97} +9.46448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - q^{3} + 4 q^{4} + q^{5} - 9 q^{6} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 2 * q^2 - q^3 + 4 * q^4 + q^5 - 9 * q^6 + 3 * q^8 - 3 * q^9	\( 6 q + 2 q^{2} - q^{3} + 4 q^{4} + q^{5} - 9 q^{6} + 3 q^{8} - 3 q^{9} - 4 q^{10} + 4 q^{11} - 5 q^{12} - 2 q^{15} - 8 q^{16} - 5 q^{17} + 3 q^{18} - q^{19} - q^{20} + 5 q^{22} + q^{23} - 11 q^{24} - 7 q^{25} - 4 q^{27} - 3 q^{29} + 5 q^{30} + 16 q^{31} + 8 q^{32} + 16 q^{33} - 16 q^{34} + 21 q^{36} - 13 q^{37} + 17 q^{38} + 5 q^{40} - 8 q^{41} + 11 q^{43} + 21 q^{44} - 7 q^{45} + 16 q^{46} - q^{47} - 21 q^{48} + 6 q^{50} + 20 q^{51} + 2 q^{53} - 18 q^{54} - 9 q^{55} - 21 q^{57} - 8 q^{58} + 13 q^{59} + 20 q^{60} + 5 q^{61} - 5 q^{62} - 15 q^{64} - 18 q^{66} - 11 q^{67} - 29 q^{68} - 23 q^{69} + 6 q^{71} + 25 q^{72} - 30 q^{73} + 3 q^{74} + 3 q^{75} - 9 q^{76} - 7 q^{79} - 7 q^{80} + 6 q^{81} - q^{82} + 27 q^{83} - q^{85} - 7 q^{86} - 16 q^{87} + 4 q^{89} - 8 q^{90} + 27 q^{92} - 7 q^{93} - 45 q^{94} + 6 q^{95} + 19 q^{96} - 35 q^{97} + 10 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 - q^3 + 4 * q^4 + q^5 - 9 * q^6 + 3 * q^8 - 3 * q^9 - 4 * q^10 + 4 * q^11 - 5 * q^12 - 2 * q^15 - 8 * q^16 - 5 * q^17 + 3 * q^18 - q^19 - q^20 + 5 * q^22 + q^23 - 11 * q^24 - 7 * q^25 - 4 * q^27 - 3 * q^29 + 5 * q^30 + 16 * q^31 + 8 * q^32 + 16 * q^33 - 16 * q^34 + 21 * q^36 - 13 * q^37 + 17 * q^38 + 5 * q^40 - 8 * q^41 + 11 * q^43 + 21 * q^44 - 7 * q^45 + 16 * q^46 - q^47 - 21 * q^48 + 6 * q^50 + 20 * q^51 + 2 * q^53 - 18 * q^54 - 9 * q^55 - 21 * q^57 - 8 * q^58 + 13 * q^59 + 20 * q^60 + 5 * q^61 - 5 * q^62 - 15 * q^64 - 18 * q^66 - 11 * q^67 - 29 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 - 30 * q^73 + 3 * q^74 + 3 * q^75 - 9 * q^76 - 7 * q^79 - 7 * q^80 + 6 * q^81 - q^82 + 27 * q^83 - q^85 - 7 * q^86 - 16 * q^87 + 4 * q^89 - 8 * q^90 + 27 * q^92 - 7 * q^93 - 45 * q^94 + 6 * q^95 + 19 * q^96 - 35 * q^97 + 10 * q^99

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