LMFDB - Embedded newform 2541.2.a.bd.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2541,2,Mod(1,2541)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2541, 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("2541.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2541 = 3 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2541.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:	$20.2899871536$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	2541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} -2.85410 q^{5} -1.00000 q^{6} -1.00000 q^{7} -3.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} -2.85410 q^{5} -1.00000 q^{6} -1.00000 q^{7} -3.00000 q^{8} +1.00000 q^{9} -2.85410 q^{10} +1.00000 q^{12} +1.23607 q^{13} -1.00000 q^{14} +2.85410 q^{15} -1.00000 q^{16} -7.85410 q^{17} +1.00000 q^{18} -2.61803 q^{19} +2.85410 q^{20} +1.00000 q^{21} -3.09017 q^{23} +3.00000 q^{24} +3.14590 q^{25} +1.23607 q^{26} -1.00000 q^{27} +1.00000 q^{28} +2.00000 q^{29} +2.85410 q^{30} -7.32624 q^{31} +5.00000 q^{32} -7.85410 q^{34} +2.85410 q^{35} -1.00000 q^{36} -12.0902 q^{37} -2.61803 q^{38} -1.23607 q^{39} +8.56231 q^{40} +10.8541 q^{41} +1.00000 q^{42} +1.23607 q^{43} -2.85410 q^{45} -3.09017 q^{46} +2.00000 q^{47} +1.00000 q^{48} +1.00000 q^{49} +3.14590 q^{50} +7.85410 q^{51} -1.23607 q^{52} +12.1803 q^{53} -1.00000 q^{54} +3.00000 q^{56} +2.61803 q^{57} +2.00000 q^{58} +6.76393 q^{59} -2.85410 q^{60} -8.94427 q^{61} -7.32624 q^{62} -1.00000 q^{63} +7.00000 q^{64} -3.52786 q^{65} +8.00000 q^{67} +7.85410 q^{68} +3.09017 q^{69} +2.85410 q^{70} +8.94427 q^{71} -3.00000 q^{72} +5.23607 q^{73} -12.0902 q^{74} -3.14590 q^{75} +2.61803 q^{76} -1.23607 q^{78} +14.0000 q^{79} +2.85410 q^{80} +1.00000 q^{81} +10.8541 q^{82} -2.94427 q^{83} -1.00000 q^{84} +22.4164 q^{85} +1.23607 q^{86} -2.00000 q^{87} +1.09017 q^{89} -2.85410 q^{90} -1.23607 q^{91} +3.09017 q^{92} +7.32624 q^{93} +2.00000 q^{94} +7.47214 q^{95} -5.00000 q^{96} -3.52786 q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} - 2 q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + q^5 - 2 * q^6 - 2 * q^7 - 6 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} - 2 q^{7} - 6 q^{8} + 2 q^{9} + q^{10} + 2 q^{12} - 2 q^{13} - 2 q^{14} - q^{15} - 2 q^{16} - 9 q^{17} + 2 q^{18} - 3 q^{19} - q^{20} + 2 q^{21} + 5 q^{23} + 6 q^{24} + 13 q^{25} - 2 q^{26} - 2 q^{27} + 2 q^{28} + 4 q^{29} - q^{30} + q^{31} + 10 q^{32} - 9 q^{34} - q^{35} - 2 q^{36} - 13 q^{37} - 3 q^{38} + 2 q^{39} - 3 q^{40} + 15 q^{41} + 2 q^{42} - 2 q^{43} + q^{45} + 5 q^{46} + 4 q^{47} + 2 q^{48} + 2 q^{49} + 13 q^{50} + 9 q^{51} + 2 q^{52} + 2 q^{53} - 2 q^{54} + 6 q^{56} + 3 q^{57} + 4 q^{58} + 18 q^{59} + q^{60} + q^{62} - 2 q^{63} + 14 q^{64} - 16 q^{65} + 16 q^{67} + 9 q^{68} - 5 q^{69} - q^{70} - 6 q^{72} + 6 q^{73} - 13 q^{74} - 13 q^{75} + 3 q^{76} + 2 q^{78} + 28 q^{79} - q^{80} + 2 q^{81} + 15 q^{82} + 12 q^{83} - 2 q^{84} + 18 q^{85} - 2 q^{86} - 4 q^{87} - 9 q^{89} + q^{90} + 2 q^{91} - 5 q^{92} - q^{93} + 4 q^{94} + 6 q^{95} - 10 q^{96} - 16 q^{97} + 2 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + q^5 - 2 * q^6 - 2 * q^7 - 6 * q^8 + 2 * q^9 + q^10 + 2 * q^12 - 2 * q^13 - 2 * q^14 - q^15 - 2 * q^16 - 9 * q^17 + 2 * q^18 - 3 * q^19 - q^20 + 2 * q^21 + 5 * q^23 + 6 * q^24 + 13 * q^25 - 2 * q^26 - 2 * q^27 + 2 * q^28 + 4 * q^29 - q^30 + q^31 + 10 * q^32 - 9 * q^34 - q^35 - 2 * q^36 - 13 * q^37 - 3 * q^38 + 2 * q^39 - 3 * q^40 + 15 * q^41 + 2 * q^42 - 2 * q^43 + q^45 + 5 * q^46 + 4 * q^47 + 2 * q^48 + 2 * q^49 + 13 * q^50 + 9 * q^51 + 2 * q^52 + 2 * q^53 - 2 * q^54 + 6 * q^56 + 3 * q^57 + 4 * q^58 + 18 * q^59 + q^60 + q^62 - 2 * q^63 + 14 * q^64 - 16 * q^65 + 16 * q^67 + 9 * q^68 - 5 * q^69 - q^70 - 6 * q^72 + 6 * q^73 - 13 * q^74 - 13 * q^75 + 3 * q^76 + 2 * q^78 + 28 * q^79 - q^80 + 2 * q^81 + 15 * q^82 + 12 * q^83 - 2 * q^84 + 18 * q^85 - 2 * q^86 - 4 * q^87 - 9 * q^89 + q^90 + 2 * q^91 - 5 * q^92 - q^93 + 4 * q^94 + 6 * q^95 - 10 * q^96 - 16 * q^97 + 2 * q^98

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 $

$2$	1.00000	0.707107	0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000	0.707107	0.353553	+	0.935414i	$0.384973\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.00000	−0.500000
$5$	−2.85410	−1.27639	−0.638197	−	0.769873i	$-0.720319\pi$
$5$	−2.85410	−1.27639	−0.638197	+	0.769873i	$0.720319\pi$
$6$	−1.00000	−0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.00000	−1.06066
$9$	1.00000	0.333333
$10$	−2.85410	−0.902546
$11$	0	0
$11$	0	0
$12$	1.00000	0.288675
$13$	1.23607	0.342824	0.171412	−	0.985199i	$-0.445167\pi$
$13$	1.23607	0.342824	0.171412	+	0.985199i	$0.445167\pi$
$14$	−1.00000	−0.267261
$15$	2.85410	0.736926
$16$	−1.00000	−0.250000
$17$	−7.85410	−1.90490	−0.952450	−	0.304696i	$-0.901445\pi$
$17$	−7.85410	−1.90490	−0.952450	+	0.304696i	$0.901445\pi$
$18$	1.00000	0.235702
$19$	−2.61803	−0.600618	−0.300309	−	0.953842i	$-0.597090\pi$
$19$	−2.61803	−0.600618	−0.300309	+	0.953842i	$0.597090\pi$
$20$	2.85410	0.638197
$21$	1.00000	0.218218
$22$	0	0
$23$	−3.09017	−0.644345	−0.322172	−	0.946681i	$-0.604413\pi$
$23$	−3.09017	−0.644345	−0.322172	+	0.946681i	$0.604413\pi$
$24$	3.00000	0.612372
$25$	3.14590	0.629180
$26$	1.23607	0.242413
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	2.85410	0.521085
$31$	−7.32624	−1.31583	−0.657916	−	0.753092i	$-0.728562\pi$
$31$	−7.32624	−1.31583	−0.657916	+	0.753092i	$0.728562\pi$
$32$	5.00000	0.883883
$33$	0	0
$34$	−7.85410	−1.34697
$35$	2.85410	0.482431
$36$	−1.00000	−0.166667
$37$	−12.0902	−1.98761	−0.993806	−	0.111130i	$-0.964553\pi$
$37$	−12.0902	−1.98761	−0.993806	+	0.111130i	$0.964553\pi$
$38$	−2.61803	−0.424701
$39$	−1.23607	−0.197929
$40$	8.56231	1.35382
$41$	10.8541	1.69513	0.847563	−	0.530695i	$-0.178069\pi$
$41$	10.8541	1.69513	0.847563	+	0.530695i	$0.178069\pi$
$42$	1.00000	0.154303
$43$	1.23607	0.188499	0.0942493	−	0.995549i	$-0.469955\pi$
$43$	1.23607	0.188499	0.0942493	+	0.995549i	$0.469955\pi$
$44$	0	0
$45$	−2.85410	−0.425464
$46$	−3.09017	−0.455621
$47$	2.00000	0.291730	0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000	0.291730	0.145865	+	0.989305i	$0.453403\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	3.14590	0.444897
$51$	7.85410	1.09979
$52$	−1.23607	−0.171412
$53$	12.1803	1.67310	0.836549	−	0.547892i	$-0.184569\pi$
$53$	12.1803	1.67310	0.836549	+	0.547892i	$0.184569\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	3.00000	0.400892
$57$	2.61803	0.346767
$58$	2.00000	0.262613
$59$	6.76393	0.880589	0.440294	−	0.897853i	$-0.354874\pi$
$59$	6.76393	0.880589	0.440294	+	0.897853i	$0.354874\pi$
$60$	−2.85410	−0.368463
$61$	−8.94427	−1.14520	−0.572598	−	0.819836i	$-0.694065\pi$
$61$	−8.94427	−1.14520	−0.572598	+	0.819836i	$0.694065\pi$
$62$	−7.32624	−0.930433
$63$	−1.00000	−0.125988
$64$	7.00000	0.875000
$65$	−3.52786	−0.437578
$66$	0	0
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	7.85410	0.952450
$69$	3.09017	0.372013
$70$	2.85410	0.341130
$71$	8.94427	1.06149	0.530745	−	0.847532i	$-0.321912\pi$
$71$	8.94427	1.06149	0.530745	+	0.847532i	$0.321912\pi$
$72$	−3.00000	−0.353553
$73$	5.23607	0.612835	0.306418	−	0.951897i	$-0.400870\pi$
$73$	5.23607	0.612835	0.306418	+	0.951897i	$0.400870\pi$
$74$	−12.0902	−1.40545
$75$	−3.14590	−0.363257
$76$	2.61803	0.300309
$77$	0	0
$78$	−1.23607	−0.139957
$79$	14.0000	1.57512	0.787562	−	0.616236i	$-0.211343\pi$
$79$	14.0000	1.57512	0.787562	+	0.616236i	$0.211343\pi$
$80$	2.85410	0.319098
$81$	1.00000	0.111111
$82$	10.8541	1.19864
$83$	−2.94427	−0.323176	−0.161588	−	0.986858i	$-0.551662\pi$
$83$	−2.94427	−0.323176	−0.161588	+	0.986858i	$0.551662\pi$
$84$	−1.00000	−0.109109
$85$	22.4164	2.43140
$86$	1.23607	0.133289
$87$	−2.00000	−0.214423
$88$	0	0
$89$	1.09017	0.115558	0.0577789	−	0.998329i	$-0.481598\pi$
$89$	1.09017	0.115558	0.0577789	+	0.998329i	$0.481598\pi$
$90$	−2.85410	−0.300849
$91$	−1.23607	−0.129575
$92$	3.09017	0.322172
$93$	7.32624	0.759695
$94$	2.00000	0.206284
$95$	7.47214	0.766625
$96$	−5.00000	−0.510310
$97$	−3.52786	−0.358200	−0.179100	−	0.983831i	$-0.557319\pi$
$97$	−3.52786	−0.358200	−0.179100	+	0.983831i	$0.557319\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	−3.14590	−0.314590
$101$	2.09017	0.207980	0.103990	−	0.994578i	$-0.466839\pi$
$101$	2.09017	0.207980	0.103990	+	0.994578i	$0.466839\pi$
$102$	7.85410	0.777672
$103$	−10.3262	−1.01747	−0.508737	−	0.860922i	$-0.669888\pi$
$103$	−10.3262	−1.01747	−0.508737	+	0.860922i	$0.669888\pi$
$104$	−3.70820	−0.363619
$105$	−2.85410	−0.278532
$106$	12.1803	1.18306
$107$	−4.90983	−0.474651	−0.237326	−	0.971430i	$-0.576271\pi$
$107$	−4.90983	−0.474651	−0.237326	+	0.971430i	$0.576271\pi$
$108$	1.00000	0.0962250
$109$	−10.5623	−1.01169	−0.505843	−	0.862626i	$-0.668818\pi$
$109$	−10.5623	−1.01169	−0.505843	+	0.862626i	$0.668818\pi$
$110$	0	0
$111$	12.0902	1.14755
$112$	1.00000	0.0944911
$113$	0.763932	0.0718647	0.0359323	−	0.999354i	$-0.488560\pi$
$113$	0.763932	0.0718647	0.0359323	+	0.999354i	$0.488560\pi$
$114$	2.61803	0.245201
$115$	8.81966	0.822438
$116$	−2.00000	−0.185695
$117$	1.23607	0.114275
$118$	6.76393	0.622670
$119$	7.85410	0.719984
$120$	−8.56231	−0.781628
$121$	0	0
$122$	−8.94427	−0.809776
$123$	−10.8541	−0.978681
$124$	7.32624	0.657916
$125$	5.29180	0.473313
$126$	−1.00000	−0.0890871
$127$	3.23607	0.287155	0.143577	−	0.989639i	$-0.454139\pi$
$127$	3.23607	0.287155	0.143577	+	0.989639i	$0.454139\pi$
$128$	−3.00000	−0.265165
$129$	−1.23607	−0.108830
$130$	−3.52786	−0.309414
$131$	−2.29180	−0.200235	−0.100118	−	0.994976i	$-0.531922\pi$
$131$	−2.29180	−0.200235	−0.100118	+	0.994976i	$0.531922\pi$
$132$	0	0
$133$	2.61803	0.227012
$134$	8.00000	0.691095
$135$	2.85410	0.245642
$136$	23.5623	2.02045
$137$	6.76393	0.577882	0.288941	−	0.957347i	$-0.406697\pi$
$137$	6.76393	0.577882	0.288941	+	0.957347i	$0.406697\pi$
$138$	3.09017	0.263053
$139$	−4.79837	−0.406993	−0.203496	−	0.979076i	$-0.565231\pi$
$139$	−4.79837	−0.406993	−0.203496	+	0.979076i	$0.565231\pi$
$140$	−2.85410	−0.241216
$141$	−2.00000	−0.168430
$142$	8.94427	0.750587
$143$	0	0
$144$	−1.00000	−0.0833333
$145$	−5.70820	−0.474041
$146$	5.23607	0.433340
$147$	−1.00000	−0.0824786
$148$	12.0902	0.993806
$149$	20.0000	1.63846	0.819232	−	0.573462i	$-0.194400\pi$
$149$	20.0000	1.63846	0.819232	+	0.573462i	$0.194400\pi$
$150$	−3.14590	−0.256861
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	7.85410	0.637052
$153$	−7.85410	−0.634967
$154$	0	0
$155$	20.9098	1.67952
$156$	1.23607	0.0989646
$157$	9.70820	0.774799	0.387400	−	0.921912i	$-0.373373\pi$
$157$	9.70820	0.774799	0.387400	+	0.921912i	$0.373373\pi$
$158$	14.0000	1.11378
$159$	−12.1803	−0.965964
$160$	−14.2705	−1.12818
$161$	3.09017	0.243540
$162$	1.00000	0.0785674
$163$	−5.41641	−0.424246	−0.212123	−	0.977243i	$-0.568038\pi$
$163$	−5.41641	−0.424246	−0.212123	+	0.977243i	$0.568038\pi$
$164$	−10.8541	−0.847563
$165$	0	0
$166$	−2.94427	−0.228520
$167$	−8.18034	−0.633014	−0.316507	−	0.948590i	$-0.602510\pi$
$167$	−8.18034	−0.633014	−0.316507	+	0.948590i	$0.602510\pi$
$168$	−3.00000	−0.231455
$169$	−11.4721	−0.882472
$170$	22.4164	1.71926
$171$	−2.61803	−0.200206
$172$	−1.23607	−0.0942493
$173$	−19.8541	−1.50948	−0.754740	−	0.656024i	$-0.772237\pi$
$173$	−19.8541	−1.50948	−0.754740	+	0.656024i	$0.772237\pi$
$174$	−2.00000	−0.151620
$175$	−3.14590	−0.237808
$176$	0	0
$177$	−6.76393	−0.508408
$178$	1.09017	0.0817117
$179$	8.38197	0.626498	0.313249	−	0.949671i	$-0.398583\pi$
$179$	8.38197	0.626498	0.313249	+	0.949671i	$0.398583\pi$
$180$	2.85410	0.212732
$181$	−18.9443	−1.40812	−0.704058	−	0.710142i	$-0.748631\pi$
$181$	−18.9443	−1.40812	−0.704058	+	0.710142i	$0.748631\pi$
$182$	−1.23607	−0.0916235
$183$	8.94427	0.661180
$184$	9.27051	0.683431
$185$	34.5066	2.53697
$186$	7.32624	0.537186
$187$	0	0
$188$	−2.00000	−0.145865
$189$	1.00000	0.0727393
$190$	7.47214	0.542086
$191$	−18.2705	−1.32201	−0.661004	−	0.750383i	$-0.729869\pi$
$191$	−18.2705	−1.32201	−0.661004	+	0.750383i	$0.729869\pi$
$192$	−7.00000	−0.505181
$193$	−18.3820	−1.32316	−0.661581	−	0.749873i	$-0.730114\pi$
$193$	−18.3820	−1.32316	−0.661581	+	0.749873i	$0.730114\pi$
$194$	−3.52786	−0.253286
$195$	3.52786	0.252636
$196$	−1.00000	−0.0714286
$197$	−4.00000	−0.284988	−0.142494	−	0.989796i	$-0.545512\pi$
$197$	−4.00000	−0.284988	−0.142494	+	0.989796i	$0.545512\pi$
$198$	0	0
$199$	−2.61803	−0.185588	−0.0927938	−	0.995685i	$-0.529580\pi$
$199$	−2.61803	−0.185588	−0.0927938	+	0.995685i	$0.529580\pi$
$200$	−9.43769	−0.667346
$201$	−8.00000	−0.564276
$202$	2.09017	0.147064
$203$	−2.00000	−0.140372
$204$	−7.85410	−0.549897
$205$	−30.9787	−2.16365
$206$	−10.3262	−0.719463
$207$	−3.09017	−0.214782
$208$	−1.23607	−0.0857059
$209$	0	0
$210$	−2.85410	−0.196952
$211$	2.00000	0.137686	0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000	0.137686	0.0688428	+	0.997628i	$0.478069\pi$
$212$	−12.1803	−0.836549
$213$	−8.94427	−0.612851
$214$	−4.90983	−0.335629
$215$	−3.52786	−0.240598
$216$	3.00000	0.204124
$217$	7.32624	0.497337
$218$	−10.5623	−0.715370
$219$	−5.23607	−0.353821
$220$	0	0
$221$	−9.70820	−0.653044
$222$	12.0902	0.811439
$223$	20.7984	1.39276	0.696381	−	0.717672i	$-0.254792\pi$
$223$	20.7984	1.39276	0.696381	+	0.717672i	$0.254792\pi$
$224$	−5.00000	−0.334077
$225$	3.14590	0.209727
$226$	0.763932	0.0508160
$227$	−21.4164	−1.42146	−0.710728	−	0.703466i	$-0.751635\pi$
$227$	−21.4164	−1.42146	−0.710728	+	0.703466i	$0.751635\pi$
$228$	−2.61803	−0.173384
$229$	21.2361	1.40332	0.701659	−	0.712512i	$-0.252443\pi$
$229$	21.2361	1.40332	0.701659	+	0.712512i	$0.252443\pi$
$230$	8.81966	0.581551
$231$	0	0
$232$	−6.00000	−0.393919
$233$	5.70820	0.373957	0.186978	−	0.982364i	$-0.440131\pi$
$233$	5.70820	0.373957	0.186978	+	0.982364i	$0.440131\pi$
$234$	1.23607	0.0808043
$235$	−5.70820	−0.372362
$236$	−6.76393	−0.440294
$237$	−14.0000	−0.909398
$238$	7.85410	0.509106
$239$	1.56231	0.101057	0.0505286	−	0.998723i	$-0.483909\pi$
$239$	1.56231	0.101057	0.0505286	+	0.998723i	$0.483909\pi$
$240$	−2.85410	−0.184231
$241$	−4.94427	−0.318489	−0.159244	−	0.987239i	$-0.550906\pi$
$241$	−4.94427	−0.318489	−0.159244	+	0.987239i	$0.550906\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	8.94427	0.572598
$245$	−2.85410	−0.182342
$246$	−10.8541	−0.692032
$247$	−3.23607	−0.205906
$248$	21.9787	1.39565
$249$	2.94427	0.186586
$250$	5.29180	0.334683
$251$	24.1803	1.52625	0.763125	−	0.646251i	$-0.223664\pi$
$251$	24.1803	1.52625	0.763125	+	0.646251i	$0.223664\pi$
$252$	1.00000	0.0629941
$253$	0	0
$254$	3.23607	0.203049
$255$	−22.4164	−1.40377
$256$	−17.0000	−1.06250
$257$	2.61803	0.163308	0.0816542	−	0.996661i	$-0.473980\pi$
$257$	2.61803	0.163308	0.0816542	+	0.996661i	$0.473980\pi$
$258$	−1.23607	−0.0769542
$259$	12.0902	0.751247
$260$	3.52786	0.218789
$261$	2.00000	0.123797
$262$	−2.29180	−0.141588
$263$	−2.43769	−0.150315	−0.0751573	−	0.997172i	$-0.523946\pi$
$263$	−2.43769	−0.150315	−0.0751573	+	0.997172i	$0.523946\pi$
$264$	0	0
$265$	−34.7639	−2.13553
$266$	2.61803	0.160522
$267$	−1.09017	−0.0667173
$268$	−8.00000	−0.488678
$269$	27.8885	1.70039	0.850197	−	0.526464i	$-0.176483\pi$
$269$	27.8885	1.70039	0.850197	+	0.526464i	$0.176483\pi$
$270$	2.85410	0.173695
$271$	−24.0902	−1.46337	−0.731687	−	0.681641i	$-0.761267\pi$
$271$	−24.0902	−1.46337	−0.731687	+	0.681641i	$0.761267\pi$
$272$	7.85410	0.476225
$273$	1.23607	0.0748102
$274$	6.76393	0.408624
$275$	0	0
$276$	−3.09017	−0.186006
$277$	10.4377	0.627140	0.313570	−	0.949565i	$-0.398475\pi$
$277$	10.4377	0.627140	0.313570	+	0.949565i	$0.398475\pi$
$278$	−4.79837	−0.287787
$279$	−7.32624	−0.438610
$280$	−8.56231	−0.511696
$281$	−1.05573	−0.0629795	−0.0314897	−	0.999504i	$-0.510025\pi$
$281$	−1.05573	−0.0629795	−0.0314897	+	0.999504i	$0.510025\pi$
$282$	−2.00000	−0.119098
$283$	−13.4377	−0.798788	−0.399394	−	0.916779i	$-0.630779\pi$
$283$	−13.4377	−0.798788	−0.399394	+	0.916779i	$0.630779\pi$
$284$	−8.94427	−0.530745
$285$	−7.47214	−0.442611
$286$	0	0
$287$	−10.8541	−0.640697
$288$	5.00000	0.294628
$289$	44.6869	2.62864
$290$	−5.70820	−0.335197
$291$	3.52786	0.206807
$292$	−5.23607	−0.306418
$293$	−19.7984	−1.15663	−0.578317	−	0.815812i	$-0.696290\pi$
$293$	−19.7984	−1.15663	−0.578317	+	0.815812i	$0.696290\pi$
$294$	−1.00000	−0.0583212
$295$	−19.3050	−1.12398
$296$	36.2705	2.10818
$297$	0	0
$298$	20.0000	1.15857
$299$	−3.81966	−0.220897
$300$	3.14590	0.181629
$301$	−1.23607	−0.0712458
$302$	2.00000	0.115087
$303$	−2.09017	−0.120077
$304$	2.61803	0.150155
$305$	25.5279	1.46172
$306$	−7.85410	−0.448989
$307$	24.2705	1.38519	0.692596	−	0.721326i	$-0.256467\pi$
$307$	24.2705	1.38519	0.692596	+	0.721326i	$0.256467\pi$
$308$	0	0
$309$	10.3262	0.587439
$310$	20.9098	1.18760
$311$	−0.763932	−0.0433186	−0.0216593	−	0.999765i	$-0.506895\pi$
$311$	−0.763932	−0.0433186	−0.0216593	+	0.999765i	$0.506895\pi$
$312$	3.70820	0.209936
$313$	−9.81966	−0.555040	−0.277520	−	0.960720i	$-0.589512\pi$
$313$	−9.81966	−0.555040	−0.277520	+	0.960720i	$0.589512\pi$
$314$	9.70820	0.547866
$315$	2.85410	0.160810
$316$	−14.0000	−0.787562
$317$	−27.5967	−1.54999	−0.774994	−	0.631969i	$-0.782247\pi$
$317$	−27.5967	−1.54999	−0.774994	+	0.631969i	$0.782247\pi$
$318$	−12.1803	−0.683040
$319$	0	0
$320$	−19.9787	−1.11684
$321$	4.90983	0.274040
$322$	3.09017	0.172208
$323$	20.5623	1.14412
$324$	−1.00000	−0.0555556
$325$	3.88854	0.215698
$326$	−5.41641	−0.299987
$327$	10.5623	0.584097
$328$	−32.5623	−1.79795
$329$	−2.00000	−0.110264
$330$	0	0
$331$	30.3607	1.66877	0.834387	−	0.551179i	$-0.185822\pi$
$331$	30.3607	1.66877	0.834387	+	0.551179i	$0.185822\pi$
$332$	2.94427	0.161588
$333$	−12.0902	−0.662537
$334$	−8.18034	−0.447608
$335$	−22.8328	−1.24749
$336$	−1.00000	−0.0545545
$337$	27.1459	1.47873	0.739366	−	0.673304i	$-0.235126\pi$
$337$	27.1459	1.47873	0.739366	+	0.673304i	$0.235126\pi$
$338$	−11.4721	−0.624002
$339$	−0.763932	−0.0414911
$340$	−22.4164	−1.21570
$341$	0	0
$342$	−2.61803	−0.141567
$343$	−1.00000	−0.0539949
$344$	−3.70820	−0.199933
$345$	−8.81966	−0.474835
$346$	−19.8541	−1.06736
$347$	12.3820	0.664699	0.332349	−	0.943156i	$-0.392159\pi$
$347$	12.3820	0.664699	0.332349	+	0.943156i	$0.392159\pi$
$348$	2.00000	0.107211
$349$	−22.7639	−1.21853	−0.609263	−	0.792968i	$-0.708534\pi$
$349$	−22.7639	−1.21853	−0.609263	+	0.792968i	$0.708534\pi$
$350$	−3.14590	−0.168155
$351$	−1.23607	−0.0659764
$352$	0	0
$353$	12.4721	0.663825	0.331912	−	0.943310i	$-0.392306\pi$
$353$	12.4721	0.663825	0.331912	+	0.943310i	$0.392306\pi$
$354$	−6.76393	−0.359499
$355$	−25.5279	−1.35488
$356$	−1.09017	−0.0577789
$357$	−7.85410	−0.415683
$358$	8.38197	0.443001
$359$	−7.03444	−0.371264	−0.185632	−	0.982619i	$-0.559433\pi$
$359$	−7.03444	−0.371264	−0.185632	+	0.982619i	$0.559433\pi$
$360$	8.56231	0.451273
$361$	−12.1459	−0.639258
$362$	−18.9443	−0.995689
$363$	0	0
$364$	1.23607	0.0647876
$365$	−14.9443	−0.782219
$366$	8.94427	0.467525
$367$	16.2705	0.849314	0.424657	−	0.905354i	$-0.360395\pi$
$367$	16.2705	0.849314	0.424657	+	0.905354i	$0.360395\pi$
$368$	3.09017	0.161086
$369$	10.8541	0.565042
$370$	34.5066	1.79391
$371$	−12.1803	−0.632372
$372$	−7.32624	−0.379848
$373$	23.3262	1.20779	0.603893	−	0.797065i	$-0.293615\pi$
$373$	23.3262	1.20779	0.603893	+	0.797065i	$0.293615\pi$
$374$	0	0
$375$	−5.29180	−0.273267
$376$	−6.00000	−0.309426
$377$	2.47214	0.127321
$378$	1.00000	0.0514344
$379$	2.47214	0.126985	0.0634925	−	0.997982i	$-0.479776\pi$
$379$	2.47214	0.126985	0.0634925	+	0.997982i	$0.479776\pi$
$380$	−7.47214	−0.383312
$381$	−3.23607	−0.165789
$382$	−18.2705	−0.934801
$383$	−13.0557	−0.667117	−0.333558	−	0.942729i	$-0.608249\pi$
$383$	−13.0557	−0.667117	−0.333558	+	0.942729i	$0.608249\pi$
$384$	3.00000	0.153093
$385$	0	0
$386$	−18.3820	−0.935617
$387$	1.23607	0.0628329
$388$	3.52786	0.179100
$389$	22.1803	1.12459	0.562294	−	0.826937i	$-0.309919\pi$
$389$	22.1803	1.12459	0.562294	+	0.826937i	$0.309919\pi$
$390$	3.52786	0.178640
$391$	24.2705	1.22741
$392$	−3.00000	−0.151523
$393$	2.29180	0.115606
$394$	−4.00000	−0.201517
$395$	−39.9574	−2.01048
$396$	0	0
$397$	14.6525	0.735387	0.367693	−	0.929947i	$-0.380148\pi$
$397$	14.6525	0.735387	0.367693	+	0.929947i	$0.380148\pi$
$398$	−2.61803	−0.131230
$399$	−2.61803	−0.131066
$400$	−3.14590	−0.157295
$401$	18.4721	0.922454	0.461227	−	0.887282i	$-0.347409\pi$
$401$	18.4721	0.922454	0.461227	+	0.887282i	$0.347409\pi$
$402$	−8.00000	−0.399004
$403$	−9.05573	−0.451098
$404$	−2.09017	−0.103990
$405$	−2.85410	−0.141821
$406$	−2.00000	−0.0992583
$407$	0	0
$408$	−23.5623	−1.16651
$409$	−28.7639	−1.42228	−0.711142	−	0.703048i	$-0.751822\pi$
$409$	−28.7639	−1.42228	−0.711142	+	0.703048i	$0.751822\pi$
$410$	−30.9787	−1.52993
$411$	−6.76393	−0.333640
$412$	10.3262	0.508737
$413$	−6.76393	−0.332831
$414$	−3.09017	−0.151874
$415$	8.40325	0.412499
$416$	6.18034	0.303016
$417$	4.79837	0.234977
$418$	0	0
$419$	14.7639	0.721265	0.360633	−	0.932708i	$-0.382561\pi$
$419$	14.7639	0.721265	0.360633	+	0.932708i	$0.382561\pi$
$420$	2.85410	0.139266
$421$	−4.32624	−0.210848	−0.105424	−	0.994427i	$-0.533620\pi$
$421$	−4.32624	−0.210848	−0.105424	+	0.994427i	$0.533620\pi$
$422$	2.00000	0.0973585
$423$	2.00000	0.0972433
$424$	−36.5410	−1.77459
$425$	−24.7082	−1.19852
$426$	−8.94427	−0.433351
$427$	8.94427	0.432844
$428$	4.90983	0.237326
$429$	0	0
$430$	−3.52786	−0.170129
$431$	2.09017	0.100680	0.0503400	−	0.998732i	$-0.483970\pi$
$431$	2.09017	0.100680	0.0503400	+	0.998732i	$0.483970\pi$
$432$	1.00000	0.0481125
$433$	−17.2361	−0.828313	−0.414156	−	0.910206i	$-0.635923\pi$
$433$	−17.2361	−0.828313	−0.414156	+	0.910206i	$0.635923\pi$
$434$	7.32624	0.351671
$435$	5.70820	0.273687
$436$	10.5623	0.505843
$437$	8.09017	0.387005
$438$	−5.23607	−0.250189
$439$	21.7984	1.04038	0.520190	−	0.854051i	$-0.325861\pi$
$439$	21.7984	1.04038	0.520190	+	0.854051i	$0.325861\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	−9.70820	−0.461772
$443$	4.90983	0.233273	0.116637	−	0.993175i	$-0.462789\pi$
$443$	4.90983	0.233273	0.116637	+	0.993175i	$0.462789\pi$
$444$	−12.0902	−0.573774
$445$	−3.11146	−0.147497
$446$	20.7984	0.984832
$447$	−20.0000	−0.945968
$448$	−7.00000	−0.330719
$449$	41.8885	1.97684	0.988421	−	0.151734i	$-0.0484858\pi$
$449$	41.8885	1.97684	0.988421	+	0.151734i	$0.0484858\pi$
$450$	3.14590	0.148299
$451$	0	0
$452$	−0.763932	−0.0359323
$453$	−2.00000	−0.0939682
$454$	−21.4164	−1.00512
$455$	3.52786	0.165389
$456$	−7.85410	−0.367802
$457$	−12.4721	−0.583422	−0.291711	−	0.956507i	$-0.594225\pi$
$457$	−12.4721	−0.583422	−0.291711	+	0.956507i	$0.594225\pi$
$458$	21.2361	0.992296
$459$	7.85410	0.366598
$460$	−8.81966	−0.411219
$461$	6.36068	0.296246	0.148123	−	0.988969i	$-0.452677\pi$
$461$	6.36068	0.296246	0.148123	+	0.988969i	$0.452677\pi$
$462$	0	0
$463$	11.4164	0.530565	0.265283	−	0.964171i	$-0.414535\pi$
$463$	11.4164	0.530565	0.265283	+	0.964171i	$0.414535\pi$
$464$	−2.00000	−0.0928477
$465$	−20.9098	−0.969670
$466$	5.70820	0.264427
$467$	19.2361	0.890139	0.445070	−	0.895496i	$-0.353179\pi$
$467$	19.2361	0.890139	0.445070	+	0.895496i	$0.353179\pi$
$468$	−1.23607	−0.0571373
$469$	−8.00000	−0.369406
$470$	−5.70820	−0.263300
$471$	−9.70820	−0.447330
$472$	−20.2918	−0.934006
$473$	0	0
$474$	−14.0000	−0.643041
$475$	−8.23607	−0.377897
$476$	−7.85410	−0.359992
$477$	12.1803	0.557699
$478$	1.56231	0.0714582
$479$	11.0557	0.505149	0.252575	−	0.967577i	$-0.418723\pi$
$479$	11.0557	0.505149	0.252575	+	0.967577i	$0.418723\pi$
$480$	14.2705	0.651357
$481$	−14.9443	−0.681400
$482$	−4.94427	−0.225205
$483$	−3.09017	−0.140608
$484$	0	0
$485$	10.0689	0.457204
$486$	−1.00000	−0.0453609
$487$	−39.2361	−1.77796	−0.888978	−	0.457950i	$-0.848584\pi$
$487$	−39.2361	−1.77796	−0.888978	+	0.457950i	$0.848584\pi$
$488$	26.8328	1.21466
$489$	5.41641	0.244938
$490$	−2.85410	−0.128935
$491$	0.326238	0.0147229	0.00736146	−	0.999973i	$-0.497657\pi$
$491$	0.326238	0.0147229	0.00736146	+	0.999973i	$0.497657\pi$
$492$	10.8541	0.489341
$493$	−15.7082	−0.707462
$494$	−3.23607	−0.145598
$495$	0	0
$496$	7.32624	0.328958
$497$	−8.94427	−0.401205
$498$	2.94427	0.131936
$499$	26.1803	1.17199	0.585996	−	0.810314i	$-0.300703\pi$
$499$	26.1803	1.17199	0.585996	+	0.810314i	$0.300703\pi$
$500$	−5.29180	−0.236656
$501$	8.18034	0.365471
$502$	24.1803	1.07922
$503$	0.583592	0.0260211	0.0130105	−	0.999915i	$-0.495858\pi$
$503$	0.583592	0.0260211	0.0130105	+	0.999915i	$0.495858\pi$
$504$	3.00000	0.133631
$505$	−5.96556	−0.265464
$506$	0	0
$507$	11.4721	0.509495
$508$	−3.23607	−0.143577
$509$	−5.90983	−0.261949	−0.130974	−	0.991386i	$-0.541811\pi$
$509$	−5.90983	−0.261949	−0.130974	+	0.991386i	$0.541811\pi$
$510$	−22.4164	−0.992615
$511$	−5.23607	−0.231630
$512$	−11.0000	−0.486136
$513$	2.61803	0.115589
$514$	2.61803	0.115477
$515$	29.4721	1.29870
$516$	1.23607	0.0544149
$517$	0	0
$518$	12.0902	0.531212
$519$	19.8541	0.871498
$520$	10.5836	0.464121
$521$	−11.6180	−0.508995	−0.254498	−	0.967073i	$-0.581910\pi$
$521$	−11.6180	−0.508995	−0.254498	+	0.967073i	$0.581910\pi$
$522$	2.00000	0.0875376
$523$	−2.90983	−0.127238	−0.0636190	−	0.997974i	$-0.520264\pi$
$523$	−2.90983	−0.127238	−0.0636190	+	0.997974i	$0.520264\pi$
$524$	2.29180	0.100118
$525$	3.14590	0.137298
$526$	−2.43769	−0.106289
$527$	57.5410	2.50653
$528$	0	0
$529$	−13.4508	−0.584820
$530$	−34.7639	−1.51005
$531$	6.76393	0.293530
$532$	−2.61803	−0.113506
$533$	13.4164	0.581129
$534$	−1.09017	−0.0471763
$535$	14.0132	0.605842
$536$	−24.0000	−1.03664
$537$	−8.38197	−0.361709
$538$	27.8885	1.20236
$539$	0	0
$540$	−2.85410	−0.122821
$541$	−16.8541	−0.724614	−0.362307	−	0.932059i	$-0.618011\pi$
$541$	−16.8541	−0.724614	−0.362307	+	0.932059i	$0.618011\pi$
$542$	−24.0902	−1.03476
$543$	18.9443	0.812977
$544$	−39.2705	−1.68371
$545$	30.1459	1.29131
$546$	1.23607	0.0528988
$547$	36.4721	1.55944	0.779718	−	0.626131i	$-0.215362\pi$
$547$	36.4721	1.55944	0.779718	+	0.626131i	$0.215362\pi$
$548$	−6.76393	−0.288941
$549$	−8.94427	−0.381732
$550$	0	0
$551$	−5.23607	−0.223064
$552$	−9.27051	−0.394579
$553$	−14.0000	−0.595341
$554$	10.4377	0.443455
$555$	−34.5066	−1.46472
$556$	4.79837	0.203496
$557$	21.4164	0.907442	0.453721	−	0.891144i	$-0.350096\pi$
$557$	21.4164	0.907442	0.453721	+	0.891144i	$0.350096\pi$
$558$	−7.32624	−0.310144
$559$	1.52786	0.0646218
$560$	−2.85410	−0.120608
$561$	0	0
$562$	−1.05573	−0.0445332
$563$	−40.3607	−1.70100	−0.850500	−	0.525975i	$-0.823700\pi$
$563$	−40.3607	−1.70100	−0.850500	+	0.525975i	$0.823700\pi$
$564$	2.00000	0.0842152
$565$	−2.18034	−0.0917276
$566$	−13.4377	−0.564828
$567$	−1.00000	−0.0419961
$568$	−26.8328	−1.12588
$569$	18.1803	0.762159	0.381080	−	0.924542i	$-0.375552\pi$
$569$	18.1803	0.762159	0.381080	+	0.924542i	$0.375552\pi$
$570$	−7.47214	−0.312973
$571$	−28.5410	−1.19440	−0.597202	−	0.802091i	$-0.703721\pi$
$571$	−28.5410	−1.19440	−0.597202	+	0.802091i	$0.703721\pi$
$572$	0	0
$573$	18.2705	0.763261
$574$	−10.8541	−0.453041
$575$	−9.72136	−0.405409
$576$	7.00000	0.291667
$577$	−14.6525	−0.609991	−0.304995	−	0.952354i	$-0.598655\pi$
$577$	−14.6525	−0.609991	−0.304995	+	0.952354i	$0.598655\pi$
$578$	44.6869	1.85873
$579$	18.3820	0.763928
$580$	5.70820	0.237020
$581$	2.94427	0.122149
$582$	3.52786	0.146235
$583$	0	0
$584$	−15.7082	−0.650010
$585$	−3.52786	−0.145859
$586$	−19.7984	−0.817863
$587$	3.88854	0.160497	0.0802487	−	0.996775i	$-0.474429\pi$
$587$	3.88854	0.160497	0.0802487	+	0.996775i	$0.474429\pi$
$588$	1.00000	0.0412393
$589$	19.1803	0.790312
$590$	−19.3050	−0.794772
$591$	4.00000	0.164538
$592$	12.0902	0.496903
$593$	−3.43769	−0.141169	−0.0705846	−	0.997506i	$-0.522486\pi$
$593$	−3.43769	−0.141169	−0.0705846	+	0.997506i	$0.522486\pi$
$594$	0	0
$595$	−22.4164	−0.918983
$596$	−20.0000	−0.819232
$597$	2.61803	0.107149
$598$	−3.81966	−0.156198
$599$	−1.56231	−0.0638341	−0.0319170	−	0.999491i	$-0.510161\pi$
$599$	−1.56231	−0.0638341	−0.0319170	+	0.999491i	$0.510161\pi$
$600$	9.43769	0.385292
$601$	−6.00000	−0.244745	−0.122373	−	0.992484i	$-0.539050\pi$
$601$	−6.00000	−0.244745	−0.122373	+	0.992484i	$0.539050\pi$
$602$	−1.23607	−0.0503784
$603$	8.00000	0.325785
$604$	−2.00000	−0.0813788
$605$	0	0
$606$	−2.09017	−0.0849073
$607$	10.3262	0.419129	0.209565	−	0.977795i	$-0.432795\pi$
$607$	10.3262	0.419129	0.209565	+	0.977795i	$0.432795\pi$
$608$	−13.0902	−0.530876
$609$	2.00000	0.0810441
$610$	25.5279	1.03359
$611$	2.47214	0.100012
$612$	7.85410	0.317483
$613$	5.85410	0.236445	0.118222	−	0.992987i	$-0.462280\pi$
$613$	5.85410	0.236445	0.118222	+	0.992987i	$0.462280\pi$
$614$	24.2705	0.979478
$615$	30.9787	1.24918
$616$	0	0
$617$	44.6525	1.79764	0.898820	−	0.438317i	$-0.144425\pi$
$617$	44.6525	1.79764	0.898820	+	0.438317i	$0.144425\pi$
$618$	10.3262	0.415382
$619$	−11.5066	−0.462488	−0.231244	−	0.972896i	$-0.574280\pi$
$619$	−11.5066	−0.462488	−0.231244	+	0.972896i	$0.574280\pi$
$620$	−20.9098	−0.839759
$621$	3.09017	0.124004
$622$	−0.763932	−0.0306309
$623$	−1.09017	−0.0436767
$624$	1.23607	0.0494823
$625$	−30.8328	−1.23331
$626$	−9.81966	−0.392473
$627$	0	0
$628$	−9.70820	−0.387400
$629$	94.9574	3.78620
$630$	2.85410	0.113710
$631$	29.8885	1.18984	0.594922	−	0.803783i	$-0.297183\pi$
$631$	29.8885	1.18984	0.594922	+	0.803783i	$0.297183\pi$
$632$	−42.0000	−1.67067
$633$	−2.00000	−0.0794929
$634$	−27.5967	−1.09601
$635$	−9.23607	−0.366522
$636$	12.1803	0.482982
$637$	1.23607	0.0489748
$638$	0	0
$639$	8.94427	0.353830
$640$	8.56231	0.338455
$641$	8.65248	0.341752	0.170876	−	0.985293i	$-0.445340\pi$
$641$	8.65248	0.341752	0.170876	+	0.985293i	$0.445340\pi$
$642$	4.90983	0.193776
$643$	47.9230	1.88990	0.944949	−	0.327218i	$-0.106111\pi$
$643$	47.9230	1.88990	0.944949	+	0.327218i	$0.106111\pi$
$644$	−3.09017	−0.121770
$645$	3.52786	0.138910
$646$	20.5623	0.809013
$647$	−30.3607	−1.19360	−0.596801	−	0.802389i	$-0.703562\pi$
$647$	−30.3607	−1.19360	−0.596801	+	0.802389i	$0.703562\pi$
$648$	−3.00000	−0.117851
$649$	0	0
$650$	3.88854	0.152521
$651$	−7.32624	−0.287138
$652$	5.41641	0.212123
$653$	−25.8885	−1.01310	−0.506549	−	0.862211i	$-0.669079\pi$
$653$	−25.8885	−1.01310	−0.506549	+	0.862211i	$0.669079\pi$
$654$	10.5623	0.413019
$655$	6.54102	0.255579
$656$	−10.8541	−0.423781
$657$	5.23607	0.204278
$658$	−2.00000	−0.0779681
$659$	35.0344	1.36475	0.682374	−	0.731003i	$-0.260948\pi$
$659$	35.0344	1.36475	0.682374	+	0.731003i	$0.260948\pi$
$660$	0	0
$661$	8.29180	0.322513	0.161257	−	0.986912i	$-0.448445\pi$
$661$	8.29180	0.322513	0.161257	+	0.986912i	$0.448445\pi$
$662$	30.3607	1.18000
$663$	9.70820	0.377035
$664$	8.83282	0.342780
$665$	−7.47214	−0.289757
$666$	−12.0902	−0.468485
$667$	−6.18034	−0.239304
$668$	8.18034	0.316507
$669$	−20.7984	−0.804112
$670$	−22.8328	−0.882109
$671$	0	0
$672$	5.00000	0.192879
$673$	−35.8885	−1.38340	−0.691701	−	0.722184i	$-0.743138\pi$
$673$	−35.8885	−1.38340	−0.691701	+	0.722184i	$0.743138\pi$
$674$	27.1459	1.04562
$675$	−3.14590	−0.121086
$676$	11.4721	0.441236
$677$	−23.8885	−0.918111	−0.459056	−	0.888408i	$-0.651812\pi$
$677$	−23.8885	−0.918111	−0.459056	+	0.888408i	$0.651812\pi$
$678$	−0.763932	−0.0293386
$679$	3.52786	0.135387
$680$	−67.2492	−2.57889
$681$	21.4164	0.820679
$682$	0	0
$683$	40.9230	1.56587	0.782937	−	0.622101i	$-0.213721\pi$
$683$	40.9230	1.56587	0.782937	+	0.622101i	$0.213721\pi$
$684$	2.61803	0.100103
$685$	−19.3050	−0.737604
$686$	−1.00000	−0.0381802
$687$	−21.2361	−0.810207
$688$	−1.23607	−0.0471246
$689$	15.0557	0.573578
$690$	−8.81966	−0.335759
$691$	39.9230	1.51874	0.759371	−	0.650658i	$-0.225507\pi$
$691$	39.9230	1.51874	0.759371	+	0.650658i	$0.225507\pi$
$692$	19.8541	0.754740
$693$	0	0
$694$	12.3820	0.470013
$695$	13.6950	0.519483
$696$	6.00000	0.227429
$697$	−85.2492	−3.22904
$698$	−22.7639	−0.861628
$699$	−5.70820	−0.215904
$700$	3.14590	0.118904
$701$	−24.0689	−0.909069	−0.454535	−	0.890729i	$-0.650194\pi$
$701$	−24.0689	−0.909069	−0.454535	+	0.890729i	$0.650194\pi$
$702$	−1.23607	−0.0466524
$703$	31.6525	1.19380
$704$	0	0
$705$	5.70820	0.214983
$706$	12.4721	0.469395
$707$	−2.09017	−0.0786089
$708$	6.76393	0.254204
$709$	−19.6869	−0.739358	−0.369679	−	0.929160i	$-0.620532\pi$
$709$	−19.6869	−0.739358	−0.369679	+	0.929160i	$0.620532\pi$
$710$	−25.5279	−0.958044
$711$	14.0000	0.525041
$712$	−3.27051	−0.122568
$713$	22.6393	0.847849
$714$	−7.85410	−0.293932
$715$	0	0
$716$	−8.38197	−0.313249
$717$	−1.56231	−0.0583454
$718$	−7.03444	−0.262523
$719$	4.87539	0.181821	0.0909106	−	0.995859i	$-0.471022\pi$
$719$	4.87539	0.181821	0.0909106	+	0.995859i	$0.471022\pi$
$720$	2.85410	0.106366
$721$	10.3262	0.384569
$722$	−12.1459	−0.452024
$723$	4.94427	0.183879
$724$	18.9443	0.704058
$725$	6.29180	0.233671
$726$	0	0
$727$	25.7426	0.954742	0.477371	−	0.878702i	$-0.341590\pi$
$727$	25.7426	0.954742	0.477371	+	0.878702i	$0.341590\pi$
$728$	3.70820	0.137435
$729$	1.00000	0.0370370
$730$	−14.9443	−0.553112
$731$	−9.70820	−0.359071
$732$	−8.94427	−0.330590
$733$	−31.1246	−1.14961	−0.574807	−	0.818289i	$-0.694923\pi$
$733$	−31.1246	−1.14961	−0.574807	+	0.818289i	$0.694923\pi$
$734$	16.2705	0.600555
$735$	2.85410	0.105275
$736$	−15.4508	−0.569526
$737$	0	0
$738$	10.8541	0.399545
$739$	−49.0132	−1.80298	−0.901489	−	0.432802i	$-0.857525\pi$
$739$	−49.0132	−1.80298	−0.901489	+	0.432802i	$0.857525\pi$
$740$	−34.5066	−1.26849
$741$	3.23607	0.118880
$742$	−12.1803	−0.447154
$743$	−17.3262	−0.635638	−0.317819	−	0.948151i	$-0.602950\pi$
$743$	−17.3262	−0.635638	−0.317819	+	0.948151i	$0.602950\pi$
$744$	−21.9787	−0.805779
$745$	−57.0820	−2.09132
$746$	23.3262	0.854034
$747$	−2.94427	−0.107725
$748$	0	0
$749$	4.90983	0.179401
$750$	−5.29180	−0.193229
$751$	−10.4721	−0.382134	−0.191067	−	0.981577i	$-0.561195\pi$
$751$	−10.4721	−0.382134	−0.191067	+	0.981577i	$0.561195\pi$
$752$	−2.00000	−0.0729325
$753$	−24.1803	−0.881181
$754$	2.47214	0.0900299
$755$	−5.70820	−0.207743
$756$	−1.00000	−0.0363696
$757$	0.326238	0.0118573	0.00592866	−	0.999982i	$-0.498113\pi$
$757$	0.326238	0.0118573	0.00592866	+	0.999982i	$0.498113\pi$
$758$	2.47214	0.0897920
$759$	0	0
$760$	−22.4164	−0.813129
$761$	−45.7771	−1.65942	−0.829709	−	0.558196i	$-0.811494\pi$
$761$	−45.7771	−1.65942	−0.829709	+	0.558196i	$0.811494\pi$
$762$	−3.23607	−0.117230
$763$	10.5623	0.382381
$764$	18.2705	0.661004
$765$	22.4164	0.810467
$766$	−13.0557	−0.471723
$767$	8.36068	0.301887
$768$	17.0000	0.613435
$769$	−14.5836	−0.525898	−0.262949	−	0.964810i	$-0.584695\pi$
$769$	−14.5836	−0.525898	−0.262949	+	0.964810i	$0.584695\pi$
$770$	0	0
$771$	−2.61803	−0.0942862
$772$	18.3820	0.661581
$773$	−38.9443	−1.40073	−0.700364	−	0.713786i	$-0.746979\pi$
$773$	−38.9443	−1.40073	−0.700364	+	0.713786i	$0.746979\pi$
$774$	1.23607	0.0444295
$775$	−23.0476	−0.827894
$776$	10.5836	0.379929
$777$	−12.0902	−0.433732
$778$	22.1803	0.795204
$779$	−28.4164	−1.01812
$780$	−3.52786	−0.126318
$781$	0	0
$782$	24.2705	0.867912
$783$	−2.00000	−0.0714742
$784$	−1.00000	−0.0357143
$785$	−27.7082	−0.988948
$786$	2.29180	0.0817457
$787$	−12.2705	−0.437396	−0.218698	−	0.975793i	$-0.570181\pi$
$787$	−12.2705	−0.437396	−0.218698	+	0.975793i	$0.570181\pi$
$788$	4.00000	0.142494
$789$	2.43769	0.0867842
$790$	−39.9574	−1.42162
$791$	−0.763932	−0.0271623
$792$	0	0
$793$	−11.0557	−0.392600
$794$	14.6525	0.519997
$795$	34.7639	1.23295
$796$	2.61803	0.0927938
$797$	10.2705	0.363800	0.181900	−	0.983317i	$-0.441775\pi$
$797$	10.2705	0.363800	0.181900	+	0.983317i	$0.441775\pi$
$798$	−2.61803	−0.0926774
$799$	−15.7082	−0.555716
$800$	15.7295	0.556121
$801$	1.09017	0.0385193
$802$	18.4721	0.652274
$803$	0	0
$804$	8.00000	0.282138
$805$	−8.81966	−0.310852
$806$	−9.05573	−0.318974
$807$	−27.8885	−0.981723
$808$	−6.27051	−0.220596
$809$	28.6525	1.00737	0.503684	−	0.863888i	$-0.331978\pi$
$809$	28.6525	1.00737	0.503684	+	0.863888i	$0.331978\pi$
$810$	−2.85410	−0.100283
$811$	16.3607	0.574501	0.287251	−	0.957855i	$-0.407259\pi$
$811$	16.3607	0.574501	0.287251	+	0.957855i	$0.407259\pi$
$812$	2.00000	0.0701862
$813$	24.0902	0.844879
$814$	0	0
$815$	15.4590	0.541504
$816$	−7.85410	−0.274949
$817$	−3.23607	−0.113216
$818$	−28.7639	−1.00571
$819$	−1.23607	−0.0431917
$820$	30.9787	1.08182
$821$	−30.3607	−1.05960	−0.529798	−	0.848124i	$-0.677732\pi$
$821$	−30.3607	−1.05960	−0.529798	+	0.848124i	$0.677732\pi$
$822$	−6.76393	−0.235919
$823$	24.4721	0.853045	0.426523	−	0.904477i	$-0.359738\pi$
$823$	24.4721	0.853045	0.426523	+	0.904477i	$0.359738\pi$
$824$	30.9787	1.07919
$825$	0	0
$826$	−6.76393	−0.235347
$827$	4.32624	0.150438	0.0752190	−	0.997167i	$-0.476034\pi$
$827$	4.32624	0.150438	0.0752190	+	0.997167i	$0.476034\pi$
$828$	3.09017	0.107391
$829$	28.9443	1.00528	0.502638	−	0.864497i	$-0.332363\pi$
$829$	28.9443	1.00528	0.502638	+	0.864497i	$0.332363\pi$
$830$	8.40325	0.291681
$831$	−10.4377	−0.362080
$832$	8.65248	0.299971
$833$	−7.85410	−0.272129
$834$	4.79837	0.166154
$835$	23.3475	0.807974
$836$	0	0
$837$	7.32624	0.253232
$838$	14.7639	0.510012
$839$	33.4164	1.15366	0.576831	−	0.816863i	$-0.304289\pi$
$839$	33.4164	1.15366	0.576831	+	0.816863i	$0.304289\pi$
$840$	8.56231	0.295428
$841$	−25.0000	−0.862069
$842$	−4.32624	−0.149092
$843$	1.05573	0.0363612
$844$	−2.00000	−0.0688428
$845$	32.7426	1.12638
$846$	2.00000	0.0687614
$847$	0	0
$848$	−12.1803	−0.418275
$849$	13.4377	0.461180
$850$	−24.7082	−0.847484
$851$	37.3607	1.28071
$852$	8.94427	0.306426
$853$	15.7082	0.537839	0.268919	−	0.963163i	$-0.413333\pi$
$853$	15.7082	0.537839	0.268919	+	0.963163i	$0.413333\pi$
$854$	8.94427	0.306067
$855$	7.47214	0.255542
$856$	14.7295	0.503444
$857$	18.9443	0.647124	0.323562	−	0.946207i	$-0.395120\pi$
$857$	18.9443	0.647124	0.323562	+	0.946207i	$0.395120\pi$
$858$	0	0
$859$	−5.88854	−0.200915	−0.100457	−	0.994941i	$-0.532031\pi$
$859$	−5.88854	−0.200915	−0.100457	+	0.994941i	$0.532031\pi$
$860$	3.52786	0.120299
$861$	10.8541	0.369907
$862$	2.09017	0.0711915
$863$	37.6869	1.28288	0.641439	−	0.767174i	$-0.278338\pi$
$863$	37.6869	1.28288	0.641439	+	0.767174i	$0.278338\pi$
$864$	−5.00000	−0.170103
$865$	56.6656	1.92669
$866$	−17.2361	−0.585705
$867$	−44.6869	−1.51765
$868$	−7.32624	−0.248669
$869$	0	0
$870$	5.70820	0.193526
$871$	9.88854	0.335061
$872$	31.6869	1.07305
$873$	−3.52786	−0.119400
$874$	8.09017	0.273654
$875$	−5.29180	−0.178895
$876$	5.23607	0.176910
$877$	46.3607	1.56549	0.782744	−	0.622343i	$-0.213819\pi$
$877$	46.3607	1.56549	0.782744	+	0.622343i	$0.213819\pi$
$878$	21.7984	0.735659
$879$	19.7984	0.667783
$880$	0	0
$881$	−33.4508	−1.12699	−0.563494	−	0.826120i	$-0.690543\pi$
$881$	−33.4508	−1.12699	−0.563494	+	0.826120i	$0.690543\pi$
$882$	1.00000	0.0336718
$883$	7.70820	0.259402	0.129701	−	0.991553i	$-0.458598\pi$
$883$	7.70820	0.259402	0.129701	+	0.991553i	$0.458598\pi$
$884$	9.70820	0.326522
$885$	19.3050	0.648929
$886$	4.90983	0.164949
$887$	46.5410	1.56269	0.781347	−	0.624097i	$-0.214533\pi$
$887$	46.5410	1.56269	0.781347	+	0.624097i	$0.214533\pi$
$888$	−36.2705	−1.21716
$889$	−3.23607	−0.108534
$890$	−3.11146	−0.104296
$891$	0	0
$892$	−20.7984	−0.696381
$893$	−5.23607	−0.175218
$894$	−20.0000	−0.668900
$895$	−23.9230	−0.799657
$896$	3.00000	0.100223
$897$	3.81966	0.127535
$898$	41.8885	1.39784
$899$	−14.6525	−0.488687
$900$	−3.14590	−0.104863
$901$	−95.6656	−3.18708
$902$	0	0
$903$	1.23607	0.0411338
$904$	−2.29180	−0.0762240
$905$	54.0689	1.79731
$906$	−2.00000	−0.0664455
$907$	−47.2361	−1.56845	−0.784224	−	0.620478i	$-0.786939\pi$
$907$	−47.2361	−1.56845	−0.784224	+	0.620478i	$0.786939\pi$
$908$	21.4164	0.710728
$909$	2.09017	0.0693266
$910$	3.52786	0.116948
$911$	−11.0557	−0.366293	−0.183146	−	0.983086i	$-0.558628\pi$
$911$	−11.0557	−0.366293	−0.183146	+	0.983086i	$0.558628\pi$
$912$	−2.61803	−0.0866918
$913$	0	0
$914$	−12.4721	−0.412542
$915$	−25.5279	−0.843925
$916$	−21.2361	−0.701659
$917$	2.29180	0.0756818
$918$	7.85410	0.259224
$919$	−7.41641	−0.244645	−0.122322	−	0.992490i	$-0.539034\pi$
$919$	−7.41641	−0.244645	−0.122322	+	0.992490i	$0.539034\pi$
$920$	−26.4590	−0.872327
$921$	−24.2705	−0.799740
$922$	6.36068	0.209478
$923$	11.0557	0.363904
$924$	0	0
$925$	−38.0344	−1.25056
$926$	11.4164	0.375166
$927$	−10.3262	−0.339158
$928$	10.0000	0.328266
$929$	−28.7984	−0.944844	−0.472422	−	0.881372i	$-0.656620\pi$
$929$	−28.7984	−0.944844	−0.472422	+	0.881372i	$0.656620\pi$
$930$	−20.9098	−0.685660
$931$	−2.61803	−0.0858026
$932$	−5.70820	−0.186978
$933$	0.763932	0.0250100
$934$	19.2361	0.629423
$935$	0	0
$936$	−3.70820	−0.121206
$937$	−11.7082	−0.382490	−0.191245	−	0.981542i	$-0.561253\pi$
$937$	−11.7082	−0.382490	−0.191245	+	0.981542i	$0.561253\pi$
$938$	−8.00000	−0.261209
$939$	9.81966	0.320452
$940$	5.70820	0.186181
$941$	11.8541	0.386433	0.193216	−	0.981156i	$-0.438108\pi$
$941$	11.8541	0.386433	0.193216	+	0.981156i	$0.438108\pi$
$942$	−9.70820	−0.316310
$943$	−33.5410	−1.09225
$944$	−6.76393	−0.220147
$945$	−2.85410	−0.0928439
$946$	0	0
$947$	−23.4377	−0.761623	−0.380811	−	0.924653i	$-0.624355\pi$
$947$	−23.4377	−0.761623	−0.380811	+	0.924653i	$0.624355\pi$
$948$	14.0000	0.454699
$949$	6.47214	0.210094
$950$	−8.23607	−0.267213
$951$	27.5967	0.894886
$952$	−23.5623	−0.763659
$953$	−4.83282	−0.156550	−0.0782751	−	0.996932i	$-0.524941\pi$
$953$	−4.83282	−0.156550	−0.0782751	+	0.996932i	$0.524941\pi$
$954$	12.1803	0.394353
$955$	52.1459	1.68740
$956$	−1.56231	−0.0505286
$957$	0	0
$958$	11.0557	0.357194
$959$	−6.76393	−0.218419
$960$	19.9787	0.644810
$961$	22.6738	0.731412
$962$	−14.9443	−0.481823
$963$	−4.90983	−0.158217
$964$	4.94427	0.159244
$965$	52.4640	1.68888
$966$	−3.09017	−0.0994246
$967$	−49.3050	−1.58554	−0.792770	−	0.609521i	$-0.791362\pi$
$967$	−49.3050	−1.58554	−0.792770	+	0.609521i	$0.791362\pi$
$968$	0	0
$969$	−20.5623	−0.660556
$970$	10.0689	0.323292
$971$	42.0689	1.35005	0.675027	−	0.737793i	$-0.264132\pi$
$971$	42.0689	1.35005	0.675027	+	0.737793i	$0.264132\pi$
$972$	1.00000	0.0320750
$973$	4.79837	0.153829
$974$	−39.2361	−1.25720
$975$	−3.88854	−0.124533
$976$	8.94427	0.286299
$977$	−26.5836	−0.850484	−0.425242	−	0.905080i	$-0.639811\pi$
$977$	−26.5836	−0.850484	−0.425242	+	0.905080i	$0.639811\pi$
$978$	5.41641	0.173198
$979$	0	0
$980$	2.85410	0.0911709
$981$	−10.5623	−0.337228
$982$	0.326238	0.0104107
$983$	48.4721	1.54602	0.773011	−	0.634393i	$-0.218750\pi$
$983$	48.4721	1.54602	0.773011	+	0.634393i	$0.218750\pi$
$984$	32.5623	1.03805
$985$	11.4164	0.363757
$986$	−15.7082	−0.500251
$987$	2.00000	0.0636607
$988$	3.23607	0.102953
$989$	−3.81966	−0.121458
$990$	0	0
$991$	18.6525	0.592515	0.296258	−	0.955108i	$-0.404261\pi$
$991$	18.6525	0.592515	0.296258	+	0.955108i	$0.404261\pi$
$992$	−36.6312	−1.16304
$993$	−30.3607	−0.963467
$994$	−8.94427	−0.283695
$995$	7.47214	0.236883
$996$	−2.94427	−0.0932928
$997$	52.5410	1.66399	0.831995	−	0.554783i	$-0.187199\pi$
$997$	52.5410	1.66399	0.831995	+	0.554783i	$0.187199\pi$
$998$	26.1803	0.828724
$999$	12.0902	0.382516

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2541.2.a.bd.1.1		2
3.2	odd	2		7623.2.a.w.1.2		2
11.2	odd	10		231.2.j.c.169.1	✓	4
11.6	odd	10		231.2.j.c.190.1	yes	4
11.10	odd	2		2541.2.a.n.1.1		2
33.2	even	10		693.2.m.c.631.1		4
33.17	even	10		693.2.m.c.190.1		4
33.32	even	2		7623.2.a.bu.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.c.169.1	✓	4	11.2	odd	10
231.2.j.c.190.1	yes	4	11.6	odd	10
693.2.m.c.190.1		4	33.17	even	10
693.2.m.c.631.1		4	33.2	even	10
2541.2.a.n.1.1		2	11.10	odd	2
2541.2.a.bd.1.1		2	1.1	even	1	trivial
7623.2.a.w.1.2		2	3.2	odd	2
7623.2.a.bu.1.2		2	33.32	even	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:	\( N \)	\(=\)	\( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2541.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} -2.85410 q^{5} -1.00000 q^{6} -1.00000 q^{7} -3.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} -2.85410 q^{5} -1.00000 q^{6} -1.00000 q^{7} -3.00000 q^{8} +1.00000 q^{9} -2.85410 q^{10} +1.00000 q^{12} +1.23607 q^{13} -1.00000 q^{14} +2.85410 q^{15} -1.00000 q^{16} -7.85410 q^{17} +1.00000 q^{18} -2.61803 q^{19} +2.85410 q^{20} +1.00000 q^{21} -3.09017 q^{23} +3.00000 q^{24} +3.14590 q^{25} +1.23607 q^{26} -1.00000 q^{27} +1.00000 q^{28} +2.00000 q^{29} +2.85410 q^{30} -7.32624 q^{31} +5.00000 q^{32} -7.85410 q^{34} +2.85410 q^{35} -1.00000 q^{36} -12.0902 q^{37} -2.61803 q^{38} -1.23607 q^{39} +8.56231 q^{40} +10.8541 q^{41} +1.00000 q^{42} +1.23607 q^{43} -2.85410 q^{45} -3.09017 q^{46} +2.00000 q^{47} +1.00000 q^{48} +1.00000 q^{49} +3.14590 q^{50} +7.85410 q^{51} -1.23607 q^{52} +12.1803 q^{53} -1.00000 q^{54} +3.00000 q^{56} +2.61803 q^{57} +2.00000 q^{58} +6.76393 q^{59} -2.85410 q^{60} -8.94427 q^{61} -7.32624 q^{62} -1.00000 q^{63} +7.00000 q^{64} -3.52786 q^{65} +8.00000 q^{67} +7.85410 q^{68} +3.09017 q^{69} +2.85410 q^{70} +8.94427 q^{71} -3.00000 q^{72} +5.23607 q^{73} -12.0902 q^{74} -3.14590 q^{75} +2.61803 q^{76} -1.23607 q^{78} +14.0000 q^{79} +2.85410 q^{80} +1.00000 q^{81} +10.8541 q^{82} -2.94427 q^{83} -1.00000 q^{84} +22.4164 q^{85} +1.23607 q^{86} -2.00000 q^{87} +1.09017 q^{89} -2.85410 q^{90} -1.23607 q^{91} +3.09017 q^{92} +7.32624 q^{93} +2.00000 q^{94} +7.47214 q^{95} -5.00000 q^{96} -3.52786 q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} - 2 q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + q^5 - 2 * q^6 - 2 * q^7 - 6 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} - 2 q^{7} - 6 q^{8} + 2 q^{9} + q^{10} + 2 q^{12} - 2 q^{13} - 2 q^{14} - q^{15} - 2 q^{16} - 9 q^{17} + 2 q^{18} - 3 q^{19} - q^{20} + 2 q^{21} + 5 q^{23} + 6 q^{24} + 13 q^{25} - 2 q^{26} - 2 q^{27} + 2 q^{28} + 4 q^{29} - q^{30} + q^{31} + 10 q^{32} - 9 q^{34} - q^{35} - 2 q^{36} - 13 q^{37} - 3 q^{38} + 2 q^{39} - 3 q^{40} + 15 q^{41} + 2 q^{42} - 2 q^{43} + q^{45} + 5 q^{46} + 4 q^{47} + 2 q^{48} + 2 q^{49} + 13 q^{50} + 9 q^{51} + 2 q^{52} + 2 q^{53} - 2 q^{54} + 6 q^{56} + 3 q^{57} + 4 q^{58} + 18 q^{59} + q^{60} + q^{62} - 2 q^{63} + 14 q^{64} - 16 q^{65} + 16 q^{67} + 9 q^{68} - 5 q^{69} - q^{70} - 6 q^{72} + 6 q^{73} - 13 q^{74} - 13 q^{75} + 3 q^{76} + 2 q^{78} + 28 q^{79} - q^{80} + 2 q^{81} + 15 q^{82} + 12 q^{83} - 2 q^{84} + 18 q^{85} - 2 q^{86} - 4 q^{87} - 9 q^{89} + q^{90} + 2 q^{91} - 5 q^{92} - q^{93} + 4 q^{94} + 6 q^{95} - 10 q^{96} - 16 q^{97} + 2 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + q^5 - 2 * q^6 - 2 * q^7 - 6 * q^8 + 2 * q^9 + q^10 + 2 * q^12 - 2 * q^13 - 2 * q^14 - q^15 - 2 * q^16 - 9 * q^17 + 2 * q^18 - 3 * q^19 - q^20 + 2 * q^21 + 5 * q^23 + 6 * q^24 + 13 * q^25 - 2 * q^26 - 2 * q^27 + 2 * q^28 + 4 * q^29 - q^30 + q^31 + 10 * q^32 - 9 * q^34 - q^35 - 2 * q^36 - 13 * q^37 - 3 * q^38 + 2 * q^39 - 3 * q^40 + 15 * q^41 + 2 * q^42 - 2 * q^43 + q^45 + 5 * q^46 + 4 * q^47 + 2 * q^48 + 2 * q^49 + 13 * q^50 + 9 * q^51 + 2 * q^52 + 2 * q^53 - 2 * q^54 + 6 * q^56 + 3 * q^57 + 4 * q^58 + 18 * q^59 + q^60 + q^62 - 2 * q^63 + 14 * q^64 - 16 * q^65 + 16 * q^67 + 9 * q^68 - 5 * q^69 - q^70 - 6 * q^72 + 6 * q^73 - 13 * q^74 - 13 * q^75 + 3 * q^76 + 2 * q^78 + 28 * q^79 - q^80 + 2 * q^81 + 15 * q^82 + 12 * q^83 - 2 * q^84 + 18 * q^85 - 2 * q^86 - 4 * q^87 - 9 * q^89 + q^90 + 2 * q^91 - 5 * q^92 - q^93 + 4 * q^94 + 6 * q^95 - 10 * q^96 - 16 * q^97 + 2 * q^98

Introduction

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