LMFDB - Embedded newform 6027.2.a.v.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1258372982$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.981328.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 6x^{3} + 6x^{2} + 10x + 2 $ x^5 - 2x^4 - 6x^3 + 6x^2 + 10x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.92250$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.92250 q^{2} +1.00000 q^{3} +1.69602 q^{4} -2.85669 q^{5} +1.92250 q^{6} -0.584397 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.92250 q^{2} +1.00000 q^{3} +1.69602 q^{4} -2.85669 q^{5} +1.92250 q^{6} -0.584397 q^{8} +1.00000 q^{9} -5.49199 q^{10} +3.16066 q^{11} +1.69602 q^{12} -4.79597 q^{13} -2.85669 q^{15} -4.51555 q^{16} +7.60362 q^{17} +1.92250 q^{18} -7.66757 q^{19} -4.84501 q^{20} +6.07639 q^{22} +7.15956 q^{23} -0.584397 q^{24} +3.16066 q^{25} -9.22028 q^{26} +1.00000 q^{27} +4.61853 q^{29} -5.49199 q^{30} +1.05961 q^{31} -7.51237 q^{32} +3.16066 q^{33} +14.6180 q^{34} +1.69602 q^{36} -9.40940 q^{37} -14.7409 q^{38} -4.79597 q^{39} +1.66944 q^{40} -1.00000 q^{41} -9.58026 q^{43} +5.36056 q^{44} -2.85669 q^{45} +13.7643 q^{46} -9.47709 q^{47} -4.51555 q^{48} +6.07639 q^{50} +7.60362 q^{51} -8.13408 q^{52} -10.3197 q^{53} +1.92250 q^{54} -9.02903 q^{55} -7.66757 q^{57} +8.87914 q^{58} -1.88650 q^{59} -4.84501 q^{60} -10.6087 q^{61} +2.03711 q^{62} -5.41147 q^{64} +13.7006 q^{65} +6.07639 q^{66} -1.82823 q^{67} +12.8959 q^{68} +7.15956 q^{69} -4.82823 q^{71} -0.584397 q^{72} +8.67491 q^{73} -18.0896 q^{74} +3.16066 q^{75} -13.0044 q^{76} -9.22028 q^{78} -2.54613 q^{79} +12.8995 q^{80} +1.00000 q^{81} -1.92250 q^{82} +2.72718 q^{83} -21.7212 q^{85} -18.4181 q^{86} +4.61853 q^{87} -1.84708 q^{88} +3.03923 q^{89} -5.49199 q^{90} +12.1428 q^{92} +1.05961 q^{93} -18.2197 q^{94} +21.9038 q^{95} -7.51237 q^{96} -10.4869 q^{97} +3.16066 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 3 q^{2} + 5 q^{3} + 7 q^{4} - q^{5} - 3 q^{6} - 9 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 3 * q^2 + 5 * q^3 + 7 * q^4 - q^5 - 3 * q^6 - 9 * q^8 + 5 * q^9	$ 5 q - 3 q^{2} + 5 q^{3} + 7 q^{4} - q^{5} - 3 q^{6} - 9 q^{8} + 5 q^{9} - 5 q^{10} + 4 q^{11} + 7 q^{12} - 3 q^{13} - q^{15} + 3 q^{16} + 8 q^{17} - 3 q^{18} - 20 q^{19} + q^{20} + 14 q^{22} - 5 q^{23} - 9 q^{24} + 4 q^{25} - 13 q^{26} + 5 q^{27} + 9 q^{29} - 5 q^{30} - 16 q^{31} - 21 q^{32} + 4 q^{33} + 7 q^{36} - 19 q^{37} - 8 q^{38} - 3 q^{39} - 21 q^{40} - 5 q^{41} + 6 q^{43} - 24 q^{44} - q^{45} + 27 q^{46} - 9 q^{47} + 3 q^{48} + 14 q^{50} + 8 q^{51} - q^{52} - 29 q^{53} - 3 q^{54} - 32 q^{55} - 20 q^{57} - q^{58} - 28 q^{59} + q^{60} - 16 q^{61} + 8 q^{62} + 39 q^{64} + q^{65} + 14 q^{66} + 21 q^{67} + 24 q^{68} - 5 q^{69} + 6 q^{71} - 9 q^{72} + 4 q^{73} + 11 q^{74} + 4 q^{75} - 26 q^{76} - 13 q^{78} + 21 q^{79} + 25 q^{80} + 5 q^{81} + 3 q^{82} - 26 q^{83} - 20 q^{85} - 58 q^{86} + 9 q^{87} + 54 q^{88} - 12 q^{89} - 5 q^{90} + 15 q^{92} - 16 q^{93} + q^{94} + 18 q^{95} - 21 q^{96} - 37 q^{97} + 4 q^{99}+O(q^{100}) $ 5 * q - 3 * q^2 + 5 * q^3 + 7 * q^4 - q^5 - 3 * q^6 - 9 * q^8 + 5 * q^9 - 5 * q^10 + 4 * q^11 + 7 * q^12 - 3 * q^13 - q^15 + 3 * q^16 + 8 * q^17 - 3 * q^18 - 20 * q^19 + q^20 + 14 * q^22 - 5 * q^23 - 9 * q^24 + 4 * q^25 - 13 * q^26 + 5 * q^27 + 9 * q^29 - 5 * q^30 - 16 * q^31 - 21 * q^32 + 4 * q^33 + 7 * q^36 - 19 * q^37 - 8 * q^38 - 3 * q^39 - 21 * q^40 - 5 * q^41 + 6 * q^43 - 24 * q^44 - q^45 + 27 * q^46 - 9 * q^47 + 3 * q^48 + 14 * q^50 + 8 * q^51 - q^52 - 29 * q^53 - 3 * q^54 - 32 * q^55 - 20 * q^57 - q^58 - 28 * q^59 + q^60 - 16 * q^61 + 8 * q^62 + 39 * q^64 + q^65 + 14 * q^66 + 21 * q^67 + 24 * q^68 - 5 * q^69 + 6 * q^71 - 9 * q^72 + 4 * q^73 + 11 * q^74 + 4 * q^75 - 26 * q^76 - 13 * q^78 + 21 * q^79 + 25 * q^80 + 5 * q^81 + 3 * q^82 - 26 * q^83 - 20 * q^85 - 58 * q^86 + 9 * q^87 + 54 * q^88 - 12 * q^89 - 5 * q^90 + 15 * q^92 - 16 * q^93 + q^94 + 18 * q^95 - 21 * q^96 - 37 * q^97 + 4 * 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 $

$2$	1.92250	1.35942	0.679708	−	0.733483i	$-0.262107\pi$
$2$	1.92250	1.35942	0.679708	+	0.733483i	$0.262107\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.69602	0.848012
$5$	−2.85669	−1.27755	−0.638775	−	0.769394i	$-0.720558\pi$
$5$	−2.85669	−1.27755	−0.638775	+	0.769394i	$0.720558\pi$
$6$	1.92250	0.784859
$7$	0	0
$7$	0	0
$8$	−0.584397	−0.206615
$9$	1.00000	0.333333
$10$	−5.49199	−1.73672
$11$	3.16066	0.952976	0.476488	−	0.879181i	$-0.341910\pi$
$11$	3.16066	0.952976	0.476488	+	0.879181i	$0.341910\pi$
$12$	1.69602	0.489600
$13$	−4.79597	−1.33016	−0.665082	−	0.746771i	$-0.731603\pi$
$13$	−4.79597	−1.33016	−0.665082	+	0.746771i	$0.731603\pi$
$14$	0	0
$15$	−2.85669	−0.737594
$16$	−4.51555	−1.12889
$17$	7.60362	1.84415	0.922075	−	0.387012i	$-0.126493\pi$
$17$	7.60362	1.84415	0.922075	+	0.387012i	$0.126493\pi$
$18$	1.92250	0.453139
$19$	−7.66757	−1.75906	−0.879530	−	0.475843i	$-0.842143\pi$
$19$	−7.66757	−1.75906	−0.879530	+	0.475843i	$0.842143\pi$
$20$	−4.84501	−1.08338
$21$	0	0
$22$	6.07639	1.29549
$23$	7.15956	1.49287	0.746436	−	0.665458i	$-0.231764\pi$
$23$	7.15956	1.49287	0.746436	+	0.665458i	$0.231764\pi$
$24$	−0.584397	−0.119289
$25$	3.16066	0.632133
$26$	−9.22028	−1.80824
$27$	1.00000	0.192450
$28$	0	0
$29$	4.61853	0.857639	0.428820	−	0.903390i	$-0.358930\pi$
$29$	4.61853	0.857639	0.428820	+	0.903390i	$0.358930\pi$
$30$	−5.49199	−1.00270
$31$	1.05961	0.190312	0.0951560	−	0.995462i	$-0.469665\pi$
$31$	1.05961	0.190312	0.0951560	+	0.995462i	$0.469665\pi$
$32$	−7.51237	−1.32801
$33$	3.16066	0.550201
$34$	14.6180	2.50697
$35$	0	0
$36$	1.69602	0.282671
$37$	−9.40940	−1.54690	−0.773448	−	0.633860i	$-0.781470\pi$
$37$	−9.40940	−1.54690	−0.773448	+	0.633860i	$0.781470\pi$
$38$	−14.7409	−2.39129
$39$	−4.79597	−0.767970
$40$	1.66944	0.263961
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−9.58026	−1.46098	−0.730488	−	0.682925i	$-0.760707\pi$
$43$	−9.58026	−1.46098	−0.730488	+	0.682925i	$0.760707\pi$
$44$	5.36056	0.808135
$45$	−2.85669	−0.425850
$46$	13.7643	2.02943
$47$	−9.47709	−1.38238	−0.691188	−	0.722675i	$-0.742912\pi$
$47$	−9.47709	−1.38238	−0.691188	+	0.722675i	$0.742912\pi$
$48$	−4.51555	−0.651764
$49$	0	0
$50$	6.07639	0.859331
$51$	7.60362	1.06472
$52$	−8.13408	−1.12799
$53$	−10.3197	−1.41751	−0.708757	−	0.705453i	$-0.750744\pi$
$53$	−10.3197	−1.41751	−0.708757	+	0.705453i	$0.750744\pi$
$54$	1.92250	0.261620
$55$	−9.02903	−1.21747
$56$	0	0
$57$	−7.66757	−1.01559
$58$	8.87914	1.16589
$59$	−1.88650	−0.245601	−0.122801	−	0.992431i	$-0.539188\pi$
$59$	−1.88650	−0.245601	−0.122801	+	0.992431i	$0.539188\pi$
$60$	−4.84501	−0.625488
$61$	−10.6087	−1.35831	−0.679154	−	0.733996i	$-0.737653\pi$
$61$	−10.6087	−1.35831	−0.679154	+	0.733996i	$0.737653\pi$
$62$	2.03711	0.258713
$63$	0	0
$64$	−5.41147	−0.676434
$65$	13.7006	1.69935
$66$	6.07639	0.747952
$67$	−1.82823	−0.223354	−0.111677	−	0.993745i	$-0.535622\pi$
$67$	−1.82823	−0.223354	−0.111677	+	0.993745i	$0.535622\pi$
$68$	12.8959	1.56386
$69$	7.15956	0.861910
$70$	0	0
$71$	−4.82823	−0.573005	−0.286503	−	0.958079i	$-0.592493\pi$
$71$	−4.82823	−0.573005	−0.286503	+	0.958079i	$0.592493\pi$
$72$	−0.584397	−0.0688718
$73$	8.67491	1.01532	0.507661	−	0.861557i	$-0.330510\pi$
$73$	8.67491	1.01532	0.507661	+	0.861557i	$0.330510\pi$
$74$	−18.0896	−2.10287
$75$	3.16066	0.364962
$76$	−13.0044	−1.49170
$77$	0	0
$78$	−9.22028	−1.04399
$79$	−2.54613	−0.286462	−0.143231	−	0.989689i	$-0.545749\pi$
$79$	−2.54613	−0.286462	−0.143231	+	0.989689i	$0.545749\pi$
$80$	12.8995	1.44221
$81$	1.00000	0.111111
$82$	−1.92250	−0.212305
$83$	2.72718	0.299347	0.149673	−	0.988736i	$-0.452178\pi$
$83$	2.72718	0.299347	0.149673	+	0.988736i	$0.452178\pi$
$84$	0	0
$85$	−21.7212	−2.35599
$86$	−18.4181	−1.98607
$87$	4.61853	0.495158
$88$	−1.84708	−0.196900
$89$	3.03923	0.322158	0.161079	−	0.986942i	$-0.448503\pi$
$89$	3.03923	0.322158	0.161079	+	0.986942i	$0.448503\pi$
$90$	−5.49199	−0.578907
$91$	0	0
$92$	12.1428	1.26597
$93$	1.05961	0.109877
$94$	−18.2197	−1.87922
$95$	21.9038	2.24729
$96$	−7.51237	−0.766729
$97$	−10.4869	−1.06478	−0.532391	−	0.846498i	$-0.678707\pi$
$97$	−10.4869	−1.06478	−0.532391	+	0.846498i	$0.678707\pi$
$98$	0	0
$99$	3.16066	0.317659
$100$	5.36056	0.536056
$101$	9.88784	0.983877	0.491939	−	0.870630i	$-0.336288\pi$
$101$	9.88784	0.983877	0.491939	+	0.870630i	$0.336288\pi$
$102$	14.6180	1.44740
$103$	−2.58440	−0.254648	−0.127324	−	0.991861i	$-0.540639\pi$
$103$	−2.58440	−0.254648	−0.127324	+	0.991861i	$0.540639\pi$
$104$	2.80275	0.274832
$105$	0	0
$106$	−19.8396	−1.92699
$107$	−7.71525	−0.745861	−0.372931	−	0.927859i	$-0.621647\pi$
$107$	−7.71525	−0.745861	−0.372931	+	0.927859i	$0.621647\pi$
$108$	1.69602	0.163200
$109$	−7.24061	−0.693524	−0.346762	−	0.937953i	$-0.612719\pi$
$109$	−7.24061	−0.693524	−0.346762	+	0.937953i	$0.612719\pi$
$110$	−17.3584	−1.65505
$111$	−9.40940	−0.893101
$112$	0	0
$113$	−16.7292	−1.57376	−0.786878	−	0.617109i	$-0.788304\pi$
$113$	−16.7292	−1.57376	−0.786878	+	0.617109i	$0.788304\pi$
$114$	−14.7409	−1.38061
$115$	−20.4526	−1.90722
$116$	7.83313	0.727288
$117$	−4.79597	−0.443388
$118$	−3.62680	−0.333874
$119$	0	0
$120$	1.66944	0.152398
$121$	−1.01020	−0.0918365
$122$	−20.3953	−1.84651
$123$	−1.00000	−0.0901670
$124$	1.79713	0.161387
$125$	5.25441	0.469968
$126$	0	0
$127$	−6.42108	−0.569778	−0.284889	−	0.958560i	$-0.591957\pi$
$127$	−6.42108	−0.569778	−0.284889	+	0.958560i	$0.591957\pi$
$128$	4.62117	0.408458
$129$	−9.58026	−0.843495
$130$	26.3394	2.31012
$131$	14.3291	1.25194	0.625971	−	0.779847i	$-0.284703\pi$
$131$	14.3291	1.25194	0.625971	+	0.779847i	$0.284703\pi$
$132$	5.36056	0.466577
$133$	0	0
$134$	−3.51478	−0.303631
$135$	−2.85669	−0.245865
$136$	−4.44353	−0.381030
$137$	−20.2197	−1.72749	−0.863745	−	0.503930i	$-0.831887\pi$
$137$	−20.2197	−1.72749	−0.863745	+	0.503930i	$0.831887\pi$
$138$	13.7643	1.17169
$139$	5.30642	0.450085	0.225042	−	0.974349i	$-0.427748\pi$
$139$	5.30642	0.450085	0.225042	+	0.974349i	$0.427748\pi$
$140$	0	0
$141$	−9.47709	−0.798115
$142$	−9.28229	−0.778953
$143$	−15.1585	−1.26761
$144$	−4.51555	−0.376296
$145$	−13.1937	−1.09568
$146$	16.6776	1.38024
$147$	0	0
$148$	−15.9586	−1.31179
$149$	−0.808754	−0.0662557	−0.0331279	−	0.999451i	$-0.510547\pi$
$149$	−0.808754	−0.0662557	−0.0331279	+	0.999451i	$0.510547\pi$
$150$	6.07639	0.496135
$151$	15.9685	1.29950	0.649750	−	0.760148i	$-0.274874\pi$
$151$	15.9685	1.29950	0.649750	+	0.760148i	$0.274874\pi$
$152$	4.48090	0.363449
$153$	7.60362	0.614716
$154$	0	0
$155$	−3.02698	−0.243133
$156$	−8.13408	−0.651248
$157$	−19.6318	−1.56679	−0.783394	−	0.621525i	$-0.786513\pi$
$157$	−19.6318	−1.56679	−0.783394	+	0.621525i	$0.786513\pi$
$158$	−4.89495	−0.389421
$159$	−10.3197	−0.818402
$160$	21.4605	1.69660
$161$	0	0
$162$	1.92250	0.151046
$163$	−13.0721	−1.02388	−0.511941	−	0.859020i	$-0.671073\pi$
$163$	−13.0721	−1.02388	−0.511941	+	0.859020i	$0.671073\pi$
$164$	−1.69602	−0.132437
$165$	−9.02903	−0.702909
$166$	5.24301	0.406937
$167$	−17.5744	−1.35995	−0.679975	−	0.733235i	$-0.738009\pi$
$167$	−17.5744	−1.35995	−0.679975	+	0.733235i	$0.738009\pi$
$168$	0	0
$169$	10.0013	0.769334
$170$	−41.7590	−3.20277
$171$	−7.66757	−0.586353
$172$	−16.2484	−1.23893
$173$	3.47465	0.264172	0.132086	−	0.991238i	$-0.457832\pi$
$173$	3.47465	0.264172	0.132086	+	0.991238i	$0.457832\pi$
$174$	8.87914	0.673126
$175$	0	0
$176$	−14.2721	−1.07580
$177$	−1.88650	−0.141798
$178$	5.84294	0.437947
$179$	20.2559	1.51400	0.756999	−	0.653416i	$-0.226665\pi$
$179$	20.2559	1.51400	0.756999	+	0.653416i	$0.226665\pi$
$180$	−4.84501	−0.361126
$181$	19.3685	1.43965	0.719826	−	0.694155i	$-0.244222\pi$
$181$	19.3685	1.43965	0.719826	+	0.694155i	$0.244222\pi$
$182$	0	0
$183$	−10.6087	−0.784219
$184$	−4.18402	−0.308450
$185$	26.8797	1.97624
$186$	2.03711	0.149368
$187$	24.0325	1.75743
$188$	−16.0734	−1.17227
$189$	0	0
$190$	42.1102	3.05500
$191$	12.6516	0.915434	0.457717	−	0.889098i	$-0.348667\pi$
$191$	12.6516	0.915434	0.457717	+	0.889098i	$0.348667\pi$
$192$	−5.41147	−0.390539
$193$	−1.55651	−0.112040	−0.0560199	−	0.998430i	$-0.517841\pi$
$193$	−1.55651	−0.112040	−0.0560199	+	0.998430i	$0.517841\pi$
$194$	−20.1611	−1.44748
$195$	13.7006	0.981120
$196$	0	0
$197$	6.79544	0.484155	0.242078	−	0.970257i	$-0.422171\pi$
$197$	6.79544	0.484155	0.242078	+	0.970257i	$0.422171\pi$
$198$	6.07639	0.431830
$199$	−8.35191	−0.592051	−0.296026	−	0.955180i	$-0.595661\pi$
$199$	−8.35191	−0.592051	−0.296026	+	0.955180i	$0.595661\pi$
$200$	−1.84708	−0.130608
$201$	−1.82823	−0.128953
$202$	19.0094	1.33750
$203$	0	0
$204$	12.8959	0.902895
$205$	2.85669	0.199520
$206$	−4.96851	−0.346173
$207$	7.15956	0.497624
$208$	21.6565	1.50161
$209$	−24.2346	−1.67634
$210$	0	0
$211$	21.1650	1.45706	0.728531	−	0.685013i	$-0.240204\pi$
$211$	21.1650	1.45706	0.728531	+	0.685013i	$0.240204\pi$
$212$	−17.5024	−1.20207
$213$	−4.82823	−0.330825
$214$	−14.8326	−1.01394
$215$	27.3678	1.86647
$216$	−0.584397	−0.0397631
$217$	0	0
$218$	−13.9201	−0.942788
$219$	8.67491	0.586196
$220$	−15.3134	−1.03243
$221$	−36.4668	−2.45302
$222$	−18.0896	−1.21410
$223$	−25.2371	−1.69000	−0.845000	−	0.534766i	$-0.820400\pi$
$223$	−25.2371	−1.69000	−0.845000	+	0.534766i	$0.820400\pi$
$224$	0	0
$225$	3.16066	0.210711
$226$	−32.1621	−2.13939
$227$	7.32210	0.485985	0.242992	−	0.970028i	$-0.421871\pi$
$227$	7.32210	0.485985	0.242992	+	0.970028i	$0.421871\pi$
$228$	−13.0044	−0.861235
$229$	9.90216	0.654353	0.327177	−	0.944963i	$-0.393903\pi$
$229$	9.90216	0.654353	0.327177	+	0.944963i	$0.393903\pi$
$230$	−39.3203	−2.59270
$231$	0	0
$232$	−2.69905	−0.177201
$233$	17.7336	1.16177	0.580884	−	0.813986i	$-0.302707\pi$
$233$	17.7336	1.16177	0.580884	+	0.813986i	$0.302707\pi$
$234$	−9.22028	−0.602748
$235$	27.0731	1.76605
$236$	−3.19955	−0.208273
$237$	−2.54613	−0.165389
$238$	0	0
$239$	0.396574	0.0256523	0.0128261	−	0.999918i	$-0.495917\pi$
$239$	0.396574	0.0256523	0.0128261	+	0.999918i	$0.495917\pi$
$240$	12.8995	0.832660
$241$	−0.374499	−0.0241236	−0.0120618	−	0.999927i	$-0.503839\pi$
$241$	−0.374499	−0.0241236	−0.0120618	+	0.999927i	$0.503839\pi$
$242$	−1.94212	−0.124844
$243$	1.00000	0.0641500
$244$	−17.9926	−1.15186
$245$	0	0
$246$	−1.92250	−0.122574
$247$	36.7734	2.33984
$248$	−0.619234	−0.0393214
$249$	2.72718	0.172828
$250$	10.1016	0.638883
$251$	23.3482	1.47372	0.736861	−	0.676044i	$-0.236307\pi$
$251$	23.3482	1.47372	0.736861	+	0.676044i	$0.236307\pi$
$252$	0	0
$253$	22.6290	1.42267
$254$	−12.3445	−0.774566
$255$	−21.7212	−1.36023
$256$	19.7072	1.23170
$257$	13.8386	0.863225	0.431613	−	0.902059i	$-0.357945\pi$
$257$	13.8386	0.863225	0.431613	+	0.902059i	$0.357945\pi$
$258$	−18.4181	−1.14666
$259$	0	0
$260$	23.2365	1.44107
$261$	4.61853	0.285880
$262$	27.5478	1.70191
$263$	−27.6461	−1.70473	−0.852366	−	0.522945i	$-0.824833\pi$
$263$	−27.6461	−1.70473	−0.852366	+	0.522945i	$0.824833\pi$
$264$	−1.84708	−0.113680
$265$	29.4800	1.81094
$266$	0	0
$267$	3.03923	0.185998
$268$	−3.10072	−0.189407
$269$	6.81791	0.415695	0.207848	−	0.978161i	$-0.433354\pi$
$269$	6.81791	0.415695	0.207848	+	0.978161i	$0.433354\pi$
$270$	−5.49199	−0.334232
$271$	18.2103	1.10620	0.553098	−	0.833116i	$-0.313446\pi$
$271$	18.2103	1.10620	0.553098	+	0.833116i	$0.313446\pi$
$272$	−34.3345	−2.08184
$273$	0	0
$274$	−38.8725	−2.34838
$275$	9.98980	0.602408
$276$	12.1428	0.730910
$277$	2.58987	0.155610	0.0778051	−	0.996969i	$-0.475209\pi$
$277$	2.58987	0.155610	0.0778051	+	0.996969i	$0.475209\pi$
$278$	10.2016	0.611853
$279$	1.05961	0.0634373
$280$	0	0
$281$	−10.0200	−0.597743	−0.298872	−	0.954293i	$-0.596610\pi$
$281$	−10.0200	−0.597743	−0.298872	+	0.954293i	$0.596610\pi$
$282$	−18.2197	−1.08497
$283$	−15.7402	−0.935658	−0.467829	−	0.883819i	$-0.654964\pi$
$283$	−15.7402	−0.935658	−0.467829	+	0.883819i	$0.654964\pi$
$284$	−8.18879	−0.485915
$285$	21.9038	1.29747
$286$	−29.1422	−1.72321
$287$	0	0
$288$	−7.51237	−0.442671
$289$	40.8151	2.40089
$290$	−25.3649	−1.48948
$291$	−10.4869	−0.614753
$292$	14.7129	0.861005
$293$	−8.85383	−0.517246	−0.258623	−	0.965978i	$-0.583269\pi$
$293$	−8.85383	−0.517246	−0.258623	+	0.965978i	$0.583269\pi$
$294$	0	0
$295$	5.38914	0.313768
$296$	5.49882	0.319612
$297$	3.16066	0.183400
$298$	−1.55483	−0.0900691
$299$	−34.3370	−1.98576
$300$	5.36056	0.309492
$301$	0	0
$302$	30.6995	1.76656
$303$	9.88784	0.568042
$304$	34.6233	1.98578
$305$	30.3058	1.73531
$306$	14.6180	0.835655
$307$	−17.0233	−0.971570	−0.485785	−	0.874078i	$-0.661466\pi$
$307$	−17.0233	−0.971570	−0.485785	+	0.874078i	$0.661466\pi$
$308$	0	0
$309$	−2.58440	−0.147021
$310$	−5.81938	−0.330519
$311$	−26.9146	−1.52619	−0.763093	−	0.646289i	$-0.776320\pi$
$311$	−26.9146	−1.52619	−0.763093	+	0.646289i	$0.776320\pi$
$312$	2.80275	0.158674
$313$	−1.18880	−0.0671949	−0.0335975	−	0.999435i	$-0.510696\pi$
$313$	−1.18880	−0.0671949	−0.0335975	+	0.999435i	$0.510696\pi$
$314$	−37.7422	−2.12992
$315$	0	0
$316$	−4.31830	−0.242923
$317$	10.9471	0.614849	0.307425	−	0.951572i	$-0.400533\pi$
$317$	10.9471	0.614849	0.307425	+	0.951572i	$0.400533\pi$
$318$	−19.8396	−1.11255
$319$	14.5976	0.817310
$320$	15.4589	0.864178
$321$	−7.71525	−0.430623
$322$	0	0
$323$	−58.3013	−3.24397
$324$	1.69602	0.0942235
$325$	−15.1585	−0.840840
$326$	−25.1311	−1.39188
$327$	−7.24061	−0.400406
$328$	0.584397	0.0322679
$329$	0	0
$330$	−17.3584	−0.955546
$331$	8.72158	0.479381	0.239691	−	0.970849i	$-0.422954\pi$
$331$	8.72158	0.479381	0.239691	+	0.970849i	$0.422954\pi$
$332$	4.62536	0.253849
$333$	−9.40940	−0.515632
$334$	−33.7869	−1.84874
$335$	5.22268	0.285346
$336$	0	0
$337$	27.2712	1.48556	0.742778	−	0.669538i	$-0.233508\pi$
$337$	27.2712	1.48556	0.742778	+	0.669538i	$0.233508\pi$
$338$	19.2276	1.04584
$339$	−16.7292	−0.908608
$340$	−36.8396	−1.99791
$341$	3.34908	0.181363
$342$	−14.7409	−0.797098
$343$	0	0
$344$	5.59867	0.301860
$345$	−20.4526	−1.10113
$346$	6.68002	0.359120
$347$	10.1476	0.544753	0.272377	−	0.962191i	$-0.412190\pi$
$347$	10.1476	0.544753	0.272377	+	0.962191i	$0.412190\pi$
$348$	7.83313	0.419900
$349$	−16.3540	−0.875409	−0.437704	−	0.899119i	$-0.644208\pi$
$349$	−16.3540	−0.875409	−0.437704	+	0.899119i	$0.644208\pi$
$350$	0	0
$351$	−4.79597	−0.255990
$352$	−23.7441	−1.26556
$353$	11.0231	0.586699	0.293350	−	0.956005i	$-0.405230\pi$
$353$	11.0231	0.586699	0.293350	+	0.956005i	$0.405230\pi$
$354$	−3.62680	−0.192763
$355$	13.7927	0.732043
$356$	5.15461	0.273194
$357$	0	0
$358$	38.9421	2.05815
$359$	10.1763	0.537087	0.268543	−	0.963268i	$-0.413458\pi$
$359$	10.1763	0.537087	0.268543	+	0.963268i	$0.413458\pi$
$360$	1.66944	0.0879871
$361$	39.7916	2.09429
$362$	37.2361	1.95709
$363$	−1.01020	−0.0530218
$364$	0	0
$365$	−24.7815	−1.29712
$366$	−20.3953	−1.06608
$367$	14.0024	0.730918	0.365459	−	0.930827i	$-0.380912\pi$
$367$	14.0024	0.730918	0.365459	+	0.930827i	$0.380912\pi$
$368$	−32.3294	−1.68528
$369$	−1.00000	−0.0520579
$370$	51.6764	2.68653
$371$	0	0
$372$	1.79713	0.0931767
$373$	−9.42463	−0.487989	−0.243994	−	0.969777i	$-0.578458\pi$
$373$	−9.42463	−0.487989	−0.243994	+	0.969777i	$0.578458\pi$
$374$	46.2026	2.38908
$375$	5.25441	0.271336
$376$	5.53838	0.285620
$377$	−22.1503	−1.14080
$378$	0	0
$379$	−5.91475	−0.303820	−0.151910	−	0.988394i	$-0.548542\pi$
$379$	−5.91475	−0.303820	−0.151910	+	0.988394i	$0.548542\pi$
$380$	37.1494	1.90573
$381$	−6.42108	−0.328962
$382$	24.3227	1.24446
$383$	22.3787	1.14350	0.571750	−	0.820428i	$-0.306265\pi$
$383$	22.3787	1.14350	0.571750	+	0.820428i	$0.306265\pi$
$384$	4.62117	0.235823
$385$	0	0
$386$	−2.99239	−0.152309
$387$	−9.58026	−0.486992
$388$	−17.7860	−0.902948
$389$	−1.50123	−0.0761153	−0.0380576	−	0.999276i	$-0.512117\pi$
$389$	−1.50123	−0.0761153	−0.0380576	+	0.999276i	$0.512117\pi$
$390$	26.3394	1.33375
$391$	54.4386	2.75308
$392$	0	0
$393$	14.3291	0.722809
$394$	13.0643	0.658168
$395$	7.27351	0.365970
$396$	5.36056	0.269378
$397$	−23.8203	−1.19551	−0.597754	−	0.801679i	$-0.703940\pi$
$397$	−23.8203	−1.19551	−0.597754	+	0.801679i	$0.703940\pi$
$398$	−16.0566	−0.804844
$399$	0	0
$400$	−14.2721	−0.713607
$401$	−7.15046	−0.357077	−0.178539	−	0.983933i	$-0.557137\pi$
$401$	−7.15046	−0.357077	−0.178539	+	0.983933i	$0.557137\pi$
$402$	−3.51478	−0.175301
$403$	−5.08187	−0.253146
$404$	16.7700	0.834339
$405$	−2.85669	−0.141950
$406$	0	0
$407$	−29.7400	−1.47415
$408$	−4.44353	−0.219988
$409$	−15.0739	−0.745358	−0.372679	−	0.927960i	$-0.621561\pi$
$409$	−15.0739	−0.745358	−0.372679	+	0.927960i	$0.621561\pi$
$410$	5.49199	0.271230
$411$	−20.2197	−0.997366
$412$	−4.38320	−0.215945
$413$	0	0
$414$	13.7643	0.676478
$415$	−7.79069	−0.382430
$416$	36.0291	1.76647
$417$	5.30642	0.259857
$418$	−46.5911	−2.27885
$419$	−20.6276	−1.00773	−0.503863	−	0.863784i	$-0.668088\pi$
$419$	−20.6276	−1.00773	−0.503863	+	0.863784i	$0.668088\pi$
$420$	0	0
$421$	−0.0618933	−0.00301650	−0.00150825	−	0.999999i	$-0.500480\pi$
$421$	−0.0618933	−0.00301650	−0.00150825	+	0.999999i	$0.500480\pi$
$422$	40.6899	1.98075
$423$	−9.47709	−0.460792
$424$	6.03077	0.292880
$425$	24.0325	1.16575
$426$	−9.28229	−0.449729
$427$	0	0
$428$	−13.0852	−0.632499
$429$	−15.1585	−0.731857
$430$	52.6148	2.53731
$431$	−16.2261	−0.781583	−0.390792	−	0.920479i	$-0.627799\pi$
$431$	−16.2261	−0.781583	−0.390792	+	0.920479i	$0.627799\pi$
$432$	−4.51555	−0.217255
$433$	−3.65981	−0.175879	−0.0879395	−	0.996126i	$-0.528028\pi$
$433$	−3.65981	−0.175879	−0.0879395	+	0.996126i	$0.528028\pi$
$434$	0	0
$435$	−13.1937	−0.632589
$436$	−12.2802	−0.588117
$437$	−54.8964	−2.62605
$438$	16.6776	0.796885
$439$	−20.0273	−0.955853	−0.477926	−	0.878400i	$-0.658611\pi$
$439$	−20.0273	−0.955853	−0.477926	+	0.878400i	$0.658611\pi$
$440$	5.27653	0.251549
$441$	0	0
$442$	−70.1075	−3.33467
$443$	−18.0232	−0.856308	−0.428154	−	0.903706i	$-0.640836\pi$
$443$	−18.0232	−0.856308	−0.428154	+	0.903706i	$0.640836\pi$
$444$	−15.9586	−0.757360
$445$	−8.68214	−0.411573
$446$	−48.5184	−2.29741
$447$	−0.808754	−0.0382528
$448$	0	0
$449$	−3.95365	−0.186585	−0.0932923	−	0.995639i	$-0.529739\pi$
$449$	−3.95365	−0.186585	−0.0932923	+	0.995639i	$0.529739\pi$
$450$	6.07639	0.286444
$451$	−3.16066	−0.148830
$452$	−28.3732	−1.33456
$453$	15.9685	0.750266
$454$	14.0768	0.660655
$455$	0	0
$456$	4.48090	0.209837
$457$	20.3425	0.951581	0.475790	−	0.879559i	$-0.342162\pi$
$457$	20.3425	0.951581	0.475790	+	0.879559i	$0.342162\pi$
$458$	19.0370	0.889538
$459$	7.60362	0.354907
$460$	−34.6881	−1.61734
$461$	0.537229	0.0250212	0.0125106	−	0.999922i	$-0.496018\pi$
$461$	0.537229	0.0250212	0.0125106	+	0.999922i	$0.496018\pi$
$462$	0	0
$463$	23.4591	1.09024	0.545119	−	0.838359i	$-0.316484\pi$
$463$	23.4591	1.09024	0.545119	+	0.838359i	$0.316484\pi$
$464$	−20.8552	−0.968178
$465$	−3.02698	−0.140373
$466$	34.0930	1.57933
$467$	33.4179	1.54640	0.773198	−	0.634165i	$-0.218656\pi$
$467$	33.4179	1.54640	0.773198	+	0.634165i	$0.218656\pi$
$468$	−8.13408	−0.375998
$469$	0	0
$470$	52.0481	2.40080
$471$	−19.6318	−0.904586
$472$	1.10246	0.0507450
$473$	−30.2800	−1.39228
$474$	−4.89495	−0.224833
$475$	−24.2346	−1.11196
$476$	0	0
$477$	−10.3197	−0.472504
$478$	0.762416	0.0348721
$479$	4.48264	0.204817	0.102408	−	0.994742i	$-0.467345\pi$
$479$	4.48264	0.204817	0.102408	+	0.994742i	$0.467345\pi$
$480$	21.4605	0.979534
$481$	45.1272	2.05762
$482$	−0.719975	−0.0327940
$483$	0	0
$484$	−1.71332	−0.0778784
$485$	29.9578	1.36031
$486$	1.92250	0.0872066
$487$	27.1529	1.23042	0.615208	−	0.788365i	$-0.289072\pi$
$487$	27.1529	1.23042	0.615208	+	0.788365i	$0.289072\pi$
$488$	6.19970	0.280647
$489$	−13.0721	−0.591139
$490$	0	0
$491$	14.9848	0.676253	0.338126	−	0.941101i	$-0.390207\pi$
$491$	14.9848	0.676253	0.338126	+	0.941101i	$0.390207\pi$
$492$	−1.69602	−0.0764626
$493$	35.1175	1.58161
$494$	70.6971	3.18081
$495$	−9.02903	−0.405825
$496$	−4.78473	−0.214841
$497$	0	0
$498$	5.24301	0.234945
$499$	−11.5578	−0.517400	−0.258700	−	0.965958i	$-0.583294\pi$
$499$	−11.5578	−0.517400	−0.258700	+	0.965958i	$0.583294\pi$
$500$	8.91160	0.398539
$501$	−17.5744	−0.785168
$502$	44.8869	2.00340
$503$	3.95528	0.176357	0.0881786	−	0.996105i	$-0.471895\pi$
$503$	3.95528	0.176357	0.0881786	+	0.996105i	$0.471895\pi$
$504$	0	0
$505$	−28.2465	−1.25695
$506$	43.5043	1.93400
$507$	10.0013	0.444175
$508$	−10.8903	−0.483179
$509$	−30.8552	−1.36763	−0.683817	−	0.729653i	$-0.739681\pi$
$509$	−30.8552	−1.36763	−0.683817	+	0.729653i	$0.739681\pi$
$510$	−41.7590	−1.84912
$511$	0	0
$512$	28.6448	1.26593
$513$	−7.66757	−0.338531
$514$	26.6047	1.17348
$515$	7.38281	0.325326
$516$	−16.2484	−0.715294
$517$	−29.9539	−1.31737
$518$	0	0
$519$	3.47465	0.152520
$520$	−8.00658	−0.351112
$521$	18.3234	0.802763	0.401381	−	0.915911i	$-0.368530\pi$
$521$	18.3234	0.802763	0.401381	+	0.915911i	$0.368530\pi$
$522$	8.87914	0.388629
$523$	−18.6662	−0.816218	−0.408109	−	0.912933i	$-0.633812\pi$
$523$	−18.6662	−0.816218	−0.408109	+	0.912933i	$0.633812\pi$
$524$	24.3025	1.06166
$525$	0	0
$526$	−53.1498	−2.31744
$527$	8.05689	0.350964
$528$	−14.2721	−0.621115
$529$	28.2593	1.22867
$530$	56.6755	2.46183
$531$	−1.88650	−0.0818671
$532$	0	0
$533$	4.79597	0.207737
$534$	5.84294	0.252849
$535$	22.0401	0.952875
$536$	1.06841	0.0461483
$537$	20.2559	0.874107
$538$	13.1075	0.565102
$539$	0	0
$540$	−4.84501	−0.208496
$541$	−36.1966	−1.55621	−0.778106	−	0.628133i	$-0.783819\pi$
$541$	−36.1966	−1.55621	−0.778106	+	0.628133i	$0.783819\pi$
$542$	35.0093	1.50378
$543$	19.3685	0.831183
$544$	−57.1213	−2.44905
$545$	20.6841	0.886012
$546$	0	0
$547$	−4.65058	−0.198844	−0.0994222	−	0.995045i	$-0.531699\pi$
$547$	−4.65058	−0.198844	−0.0994222	+	0.995045i	$0.531699\pi$
$548$	−34.2932	−1.46493
$549$	−10.6087	−0.452769
$550$	19.2054	0.818922
$551$	−35.4129	−1.50864
$552$	−4.18402	−0.178084
$553$	0	0
$554$	4.97904	0.211539
$555$	26.8797	1.14098
$556$	8.99982	0.381677
$557$	41.5764	1.76165	0.880825	−	0.473443i	$-0.156989\pi$
$557$	41.5764	1.76165	0.880825	+	0.473443i	$0.156989\pi$
$558$	2.03711	0.0862377
$559$	45.9467	1.94334
$560$	0	0
$561$	24.0325	1.01465
$562$	−19.2635	−0.812582
$563$	−27.7070	−1.16771	−0.583855	−	0.811858i	$-0.698456\pi$
$563$	−27.7070	−1.16771	−0.583855	+	0.811858i	$0.698456\pi$
$564$	−16.0734	−0.676811
$565$	47.7902	2.01055
$566$	−30.2606	−1.27195
$567$	0	0
$568$	2.82160	0.118392
$569$	−28.3878	−1.19008	−0.595038	−	0.803697i	$-0.702863\pi$
$569$	−28.3878	−1.19008	−0.595038	+	0.803697i	$0.702863\pi$
$570$	42.1102	1.76380
$571$	−38.9877	−1.63158	−0.815792	−	0.578345i	$-0.803699\pi$
$571$	−38.9877	−1.63158	−0.815792	+	0.578345i	$0.803699\pi$
$572$	−25.7091	−1.07495
$573$	12.6516	0.528526
$574$	0	0
$575$	22.6290	0.943693
$576$	−5.41147	−0.225478
$577$	1.13914	0.0474230	0.0237115	−	0.999719i	$-0.492452\pi$
$577$	1.13914	0.0474230	0.0237115	+	0.999719i	$0.492452\pi$
$578$	78.4671	3.26380
$579$	−1.55651	−0.0646863
$580$	−22.3768	−0.929146
$581$	0	0
$582$	−20.1611	−0.835705
$583$	−32.6170	−1.35086
$584$	−5.06959	−0.209781
$585$	13.7006	0.566450
$586$	−17.0215	−0.703153
$587$	24.8747	1.02669	0.513343	−	0.858183i	$-0.328407\pi$
$587$	24.8747	1.02669	0.513343	+	0.858183i	$0.328407\pi$
$588$	0	0
$589$	−8.12464	−0.334770
$590$	10.3606	0.426541
$591$	6.79544	0.279527
$592$	42.4886	1.74627
$593$	34.9362	1.43466	0.717329	−	0.696734i	$-0.245364\pi$
$593$	34.9362	1.43466	0.717329	+	0.696734i	$0.245364\pi$
$594$	6.07639	0.249317
$595$	0	0
$596$	−1.37167	−0.0561856
$597$	−8.35191	−0.341821
$598$	−66.0131	−2.69948
$599$	−10.0846	−0.412045	−0.206023	−	0.978547i	$-0.566052\pi$
$599$	−10.0846	−0.412045	−0.206023	+	0.978547i	$0.566052\pi$
$600$	−1.84708	−0.0754068
$601$	45.4909	1.85561	0.927806	−	0.373064i	$-0.121693\pi$
$601$	45.4909	1.85561	0.927806	+	0.373064i	$0.121693\pi$
$602$	0	0
$603$	−1.82823	−0.0744513
$604$	27.0830	1.10199
$605$	2.88583	0.117326
$606$	19.0094	0.772205
$607$	−41.3501	−1.67835	−0.839174	−	0.543864i	$-0.816961\pi$
$607$	−41.3501	−1.67835	−0.839174	+	0.543864i	$0.816961\pi$
$608$	57.6016	2.33605
$609$	0	0
$610$	58.2630	2.35900
$611$	45.4518	1.83878
$612$	12.8959	0.521287
$613$	−14.8391	−0.599344	−0.299672	−	0.954042i	$-0.596877\pi$
$613$	−14.8391	−0.599344	−0.299672	+	0.954042i	$0.596877\pi$
$614$	−32.7273	−1.32077
$615$	2.85669	0.115193
$616$	0	0
$617$	25.0100	1.00687	0.503433	−	0.864034i	$-0.332070\pi$
$617$	25.0100	1.00687	0.503433	+	0.864034i	$0.332070\pi$
$618$	−4.96851	−0.199863
$619$	4.70533	0.189123	0.0945616	−	0.995519i	$-0.469855\pi$
$619$	4.70533	0.189123	0.0945616	+	0.995519i	$0.469855\pi$
$620$	−5.13383	−0.206180
$621$	7.15956	0.287303
$622$	−51.7434	−2.07472
$623$	0	0
$624$	21.6565	0.866952
$625$	−30.8135	−1.23254
$626$	−2.28547	−0.0913459
$627$	−24.2346	−0.967837
$628$	−33.2960	−1.32865
$629$	−71.5455	−2.85271
$630$	0	0
$631$	11.4581	0.456140	0.228070	−	0.973645i	$-0.426759\pi$
$631$	11.4581	0.456140	0.228070	+	0.973645i	$0.426759\pi$
$632$	1.48795	0.0591875
$633$	21.1650	0.841235
$634$	21.0458	0.835836
$635$	18.3430	0.727920
$636$	−17.5024	−0.694014
$637$	0	0
$638$	28.0640	1.11106
$639$	−4.82823	−0.191002
$640$	−13.2012	−0.521825
$641$	34.0019	1.34299	0.671497	−	0.741008i	$-0.265652\pi$
$641$	34.0019	1.34299	0.671497	+	0.741008i	$0.265652\pi$
$642$	−14.8326	−0.585396
$643$	−16.6287	−0.655773	−0.327886	−	0.944717i	$-0.606336\pi$
$643$	−16.6287	−0.655773	−0.327886	+	0.944717i	$0.606336\pi$
$644$	0	0
$645$	27.3678	1.07761
$646$	−112.084	−4.40990
$647$	0.682076	0.0268152	0.0134076	−	0.999910i	$-0.495732\pi$
$647$	0.682076	0.0268152	0.0134076	+	0.999910i	$0.495732\pi$
$648$	−0.584397	−0.0229573
$649$	−5.96259	−0.234052
$650$	−29.1422	−1.14305
$651$	0	0
$652$	−22.1705	−0.868264
$653$	−32.1200	−1.25695	−0.628476	−	0.777829i	$-0.716321\pi$
$653$	−32.1200	−1.25695	−0.628476	+	0.777829i	$0.716321\pi$
$654$	−13.9201	−0.544319
$655$	−40.9338	−1.59942
$656$	4.51555	0.176303
$657$	8.67491	0.338441
$658$	0	0
$659$	−44.9114	−1.74950	−0.874750	−	0.484574i	$-0.838975\pi$
$659$	−44.9114	−1.74950	−0.874750	+	0.484574i	$0.838975\pi$
$660$	−15.3134	−0.596075
$661$	11.4435	0.445102	0.222551	−	0.974921i	$-0.428562\pi$
$661$	11.4435	0.445102	0.222551	+	0.974921i	$0.428562\pi$
$662$	16.7673	0.651678
$663$	−36.4668	−1.41625
$664$	−1.59375	−0.0618496
$665$	0	0
$666$	−18.0896	−0.700958
$667$	33.0666	1.28034
$668$	−29.8066	−1.15325
$669$	−25.2371	−0.975723
$670$	10.0406	0.387903
$671$	−33.5306	−1.29443
$672$	0	0
$673$	−21.4686	−0.827555	−0.413778	−	0.910378i	$-0.635791\pi$
$673$	−21.4686	−0.827555	−0.413778	+	0.910378i	$0.635791\pi$
$674$	52.4290	2.01949
$675$	3.16066	0.121654
$676$	16.9625	0.652404
$677$	−23.2874	−0.895007	−0.447503	−	0.894282i	$-0.647687\pi$
$677$	−23.2874	−0.895007	−0.447503	+	0.894282i	$0.647687\pi$
$678$	−32.1621	−1.23518
$679$	0	0
$680$	12.6938	0.486784
$681$	7.32210	0.280583
$682$	6.43862	0.246547
$683$	−26.3174	−1.00701	−0.503505	−	0.863993i	$-0.667956\pi$
$683$	−26.3174	−1.00701	−0.503505	+	0.863993i	$0.667956\pi$
$684$	−13.0044	−0.497234
$685$	57.7615	2.20695
$686$	0	0
$687$	9.90216	0.377791
$688$	43.2602	1.64928
$689$	49.4928	1.88552
$690$	−39.3203	−1.49690
$691$	6.07304	0.231029	0.115515	−	0.993306i	$-0.463148\pi$
$691$	6.07304	0.231029	0.115515	+	0.993306i	$0.463148\pi$
$692$	5.89308	0.224021
$693$	0	0
$694$	19.5089	0.740546
$695$	−15.1588	−0.575006
$696$	−2.69905	−0.102307
$697$	−7.60362	−0.288008
$698$	−31.4406	−1.19004
$699$	17.7336	0.670747
$700$	0	0
$701$	3.79843	0.143465	0.0717324	−	0.997424i	$-0.477147\pi$
$701$	3.79843	0.143465	0.0717324	+	0.997424i	$0.477147\pi$
$702$	−9.22028	−0.347997
$703$	72.1472	2.72108
$704$	−17.1038	−0.644625
$705$	27.0731	1.01963
$706$	21.1919	0.797568
$707$	0	0
$708$	−3.19955	−0.120246
$709$	19.5945	0.735887	0.367944	−	0.929848i	$-0.380062\pi$
$709$	19.5945	0.735887	0.367944	+	0.929848i	$0.380062\pi$
$710$	26.5166	0.995151
$711$	−2.54613	−0.0954874
$712$	−1.77612	−0.0665628
$713$	7.58636	0.284111
$714$	0	0
$715$	43.3030	1.61944
$716$	34.3545	1.28389
$717$	0.396574	0.0148103
$718$	19.5641	0.730124
$719$	2.45838	0.0916822	0.0458411	−	0.998949i	$-0.485403\pi$
$719$	2.45838	0.0916822	0.0458411	+	0.998949i	$0.485403\pi$
$720$	12.8995	0.480737
$721$	0	0
$722$	76.4994	2.84701
$723$	−0.374499	−0.0139278
$724$	32.8495	1.22084
$725$	14.5976	0.542142
$726$	−1.94212	−0.0720787
$727$	48.1462	1.78564	0.892821	−	0.450411i	$-0.148723\pi$
$727$	48.1462	1.78564	0.892821	+	0.450411i	$0.148723\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−47.6426	−1.76333
$731$	−72.8447	−2.69426
$732$	−17.9926	−0.665027
$733$	−12.5978	−0.465309	−0.232654	−	0.972559i	$-0.574741\pi$
$733$	−12.5978	−0.465309	−0.232654	+	0.972559i	$0.574741\pi$
$734$	26.9196	0.993621
$735$	0	0
$736$	−53.7853	−1.98255
$737$	−5.77842	−0.212851
$738$	−1.92250	−0.0707684
$739$	−16.4235	−0.604148	−0.302074	−	0.953285i	$-0.597679\pi$
$739$	−16.4235	−0.604148	−0.302074	+	0.953285i	$0.597679\pi$
$740$	45.5886	1.67587
$741$	36.7734	1.35091
$742$	0	0
$743$	−33.0916	−1.21401	−0.607007	−	0.794697i	$-0.707630\pi$
$743$	−33.0916	−1.21401	−0.607007	+	0.794697i	$0.707630\pi$
$744$	−0.619234	−0.0227022
$745$	2.31036	0.0846450
$746$	−18.1189	−0.663380
$747$	2.72718	0.0997822
$748$	40.7597	1.49032
$749$	0	0
$750$	10.1016	0.368859
$751$	17.5654	0.640969	0.320484	−	0.947254i	$-0.396154\pi$
$751$	17.5654	0.640969	0.320484	+	0.947254i	$0.396154\pi$
$752$	42.7943	1.56055
$753$	23.3482	0.850854
$754$	−42.5841	−1.55082
$755$	−45.6171	−1.66017
$756$	0	0
$757$	21.5341	0.782670	0.391335	−	0.920248i	$-0.372013\pi$
$757$	21.5341	0.782670	0.391335	+	0.920248i	$0.372013\pi$
$758$	−11.3711	−0.413018
$759$	22.6290	0.821379
$760$	−12.8005	−0.464324
$761$	20.3002	0.735883	0.367941	−	0.929849i	$-0.380063\pi$
$761$	20.3002	0.735883	0.367941	+	0.929849i	$0.380063\pi$
$762$	−12.3445	−0.447196
$763$	0	0
$764$	21.4573	0.776299
$765$	−21.7212	−0.785331
$766$	43.0232	1.55449
$767$	9.04760	0.326690
$768$	19.7072	0.711121
$769$	−38.2339	−1.37875	−0.689375	−	0.724404i	$-0.742115\pi$
$769$	−38.2339	−1.37875	−0.689375	+	0.724404i	$0.742115\pi$
$770$	0	0
$771$	13.8386	0.498383
$772$	−2.63987	−0.0950111
$773$	−10.9284	−0.393066	−0.196533	−	0.980497i	$-0.562968\pi$
$773$	−10.9284	−0.393066	−0.196533	+	0.980497i	$0.562968\pi$
$774$	−18.4181	−0.662025
$775$	3.34908	0.120302
$776$	6.12850	0.220000
$777$	0	0
$778$	−2.88612	−0.103472
$779$	7.66757	0.274719
$780$	23.2365	0.832001
$781$	−15.2604	−0.546061
$782$	104.658	3.74258
$783$	4.61853	0.165053
$784$	0	0
$785$	56.0819	2.00165
$786$	27.5478	0.982598
$787$	17.0902	0.609201	0.304601	−	0.952480i	$-0.401477\pi$
$787$	17.0902	0.609201	0.304601	+	0.952480i	$0.401477\pi$
$788$	11.5252	0.410569
$789$	−27.6461	−0.984228
$790$	13.9833	0.497505
$791$	0	0
$792$	−1.84708	−0.0656332
$793$	50.8791	1.80677
$794$	−45.7947	−1.62519
$795$	29.4800	1.04555
$796$	−14.1650	−0.502066
$797$	27.0085	0.956690	0.478345	−	0.878172i	$-0.341237\pi$
$797$	27.0085	0.956690	0.478345	+	0.878172i	$0.341237\pi$
$798$	0	0
$799$	−72.0602	−2.54931
$800$	−23.7441	−0.839481
$801$	3.03923	0.107386
$802$	−13.7468	−0.485416
$803$	27.4185	0.967577
$804$	−3.10072	−0.109354
$805$	0	0
$806$	−9.76991	−0.344131
$807$	6.81791	0.240002
$808$	−5.77842	−0.203284
$809$	−25.6569	−0.902047	−0.451023	−	0.892512i	$-0.648941\pi$
$809$	−25.6569	−0.902047	−0.451023	+	0.892512i	$0.648941\pi$
$810$	−5.49199	−0.192969
$811$	−42.5589	−1.49445	−0.747223	−	0.664573i	$-0.768613\pi$
$811$	−42.5589	−1.49445	−0.747223	+	0.664573i	$0.768613\pi$
$812$	0	0
$813$	18.2103	0.638662
$814$	−57.1752	−2.00399
$815$	37.3428	1.30806
$816$	−34.3345	−1.20195
$817$	73.4573	2.56995
$818$	−28.9797	−1.01325
$819$	0	0
$820$	4.84501	0.169195
$821$	22.0355	0.769043	0.384522	−	0.923116i	$-0.374366\pi$
$821$	22.0355	0.769043	0.384522	+	0.923116i	$0.374366\pi$
$822$	−38.8725	−1.35584
$823$	2.79804	0.0975336	0.0487668	−	0.998810i	$-0.484471\pi$
$823$	2.79804	0.0975336	0.0487668	+	0.998810i	$0.484471\pi$
$824$	1.51031	0.0526142
$825$	9.98980	0.347800
$826$	0	0
$827$	−44.1212	−1.53424	−0.767122	−	0.641502i	$-0.778312\pi$
$827$	−44.1212	−1.53424	−0.767122	+	0.641502i	$0.778312\pi$
$828$	12.1428	0.421991
$829$	−36.1269	−1.25474	−0.627370	−	0.778721i	$-0.715869\pi$
$829$	−36.1269	−1.25474	−0.627370	+	0.778721i	$0.715869\pi$
$830$	−14.9776	−0.519882
$831$	2.58987	0.0898416
$832$	25.9533	0.899767
$833$	0	0
$834$	10.2016	0.353253
$835$	50.2047	1.73740
$836$	−41.1024	−1.42156
$837$	1.05961	0.0366255
$838$	−39.6567	−1.36992
$839$	−12.2317	−0.422284	−0.211142	−	0.977455i	$-0.567718\pi$
$839$	−12.2317	−0.422284	−0.211142	+	0.977455i	$0.567718\pi$
$840$	0	0
$841$	−7.66920	−0.264455
$842$	−0.118990	−0.00410067
$843$	−10.0200	−0.345107
$844$	35.8964	1.23560
$845$	−28.5707	−0.982862
$846$	−18.2197	−0.626408
$847$	0	0
$848$	46.5989	1.60021
$849$	−15.7402	−0.540203
$850$	46.2026	1.58474
$851$	−67.3672	−2.30932
$852$	−8.18879	−0.280543
$853$	−25.6706	−0.878945	−0.439473	−	0.898256i	$-0.644835\pi$
$853$	−25.6706	−0.878945	−0.439473	+	0.898256i	$0.644835\pi$
$854$	0	0
$855$	21.9038	0.749095
$856$	4.50876	0.154106
$857$	37.4207	1.27827	0.639134	−	0.769095i	$-0.279293\pi$
$857$	37.4207	1.27827	0.639134	+	0.769095i	$0.279293\pi$
$858$	−29.1422	−0.994898
$859$	38.8672	1.32613	0.663067	−	0.748560i	$-0.269255\pi$
$859$	38.8672	1.32613	0.663067	+	0.748560i	$0.269255\pi$
$860$	46.4165	1.58279
$861$	0	0
$862$	−31.1947	−1.06250
$863$	3.26563	0.111163	0.0555817	−	0.998454i	$-0.482299\pi$
$863$	3.26563	0.111163	0.0555817	+	0.998454i	$0.482299\pi$
$864$	−7.51237	−0.255576
$865$	−9.92598	−0.337493
$866$	−7.03599	−0.239093
$867$	40.8151	1.38615
$868$	0	0
$869$	−8.04747	−0.272992
$870$	−25.3649	−0.859952
$871$	8.76814	0.297097
$872$	4.23138	0.143293
$873$	−10.4869	−0.354928
$874$	−105.539	−3.56990
$875$	0	0
$876$	14.7129	0.497101
$877$	−13.4468	−0.454065	−0.227032	−	0.973887i	$-0.572902\pi$
$877$	−13.4468	−0.454065	−0.227032	+	0.973887i	$0.572902\pi$
$878$	−38.5027	−1.29940
$879$	−8.85383	−0.298632
$880$	40.7711	1.37439
$881$	−37.6633	−1.26891	−0.634455	−	0.772960i	$-0.718775\pi$
$881$	−37.6633	−1.26891	−0.634455	+	0.772960i	$0.718775\pi$
$882$	0	0
$883$	31.4383	1.05798	0.528992	−	0.848627i	$-0.322570\pi$
$883$	31.4383	1.05798	0.528992	+	0.848627i	$0.322570\pi$
$884$	−61.8485	−2.08019
$885$	5.38914	0.181154
$886$	−34.6497	−1.16408
$887$	27.6030	0.926817	0.463408	−	0.886145i	$-0.346626\pi$
$887$	27.6030	0.926817	0.463408	+	0.886145i	$0.346626\pi$
$888$	5.49882	0.184528
$889$	0	0
$890$	−16.6914	−0.559498
$891$	3.16066	0.105886
$892$	−42.8027	−1.43314
$893$	72.6662	2.43168
$894$	−1.55483	−0.0520014
$895$	−57.8648	−1.93421
$896$	0	0
$897$	−34.3370	−1.14648
$898$	−7.60092	−0.253646
$899$	4.89385	0.163219
$900$	5.36056	0.178685
$901$	−78.4667	−2.61411
$902$	−6.07639	−0.202322
$903$	0	0
$904$	9.77652	0.325162
$905$	−55.3298	−1.83923
$906$	30.6995	1.01992
$907$	34.5959	1.14874	0.574370	−	0.818596i	$-0.305247\pi$
$907$	34.5959	1.14874	0.574370	+	0.818596i	$0.305247\pi$
$908$	12.4184	0.412121
$909$	9.88784	0.327959
$910$	0	0
$911$	−42.7849	−1.41753	−0.708764	−	0.705445i	$-0.750747\pi$
$911$	−42.7849	−1.41753	−0.708764	+	0.705445i	$0.750747\pi$
$912$	34.6233	1.14649
$913$	8.61969	0.285270
$914$	39.1085	1.29359
$915$	30.3058	1.00188
$916$	16.7943	0.554899
$917$	0	0
$918$	14.6180	0.482466
$919$	−3.73410	−0.123176	−0.0615882	−	0.998102i	$-0.519617\pi$
$919$	−3.73410	−0.123176	−0.0615882	+	0.998102i	$0.519617\pi$
$920$	11.9524	0.394060
$921$	−17.0233	−0.560936
$922$	1.03282	0.0340143
$923$	23.1561	0.762191
$924$	0	0
$925$	−29.7400	−0.977844
$926$	45.1003	1.48209
$927$	−2.58440	−0.0848827
$928$	−34.6961	−1.13896
$929$	15.5961	0.511692	0.255846	−	0.966718i	$-0.417646\pi$
$929$	15.5961	0.511692	0.255846	+	0.966718i	$0.417646\pi$
$930$	−5.81938	−0.190825
$931$	0	0
$932$	30.0766	0.985193
$933$	−26.9146	−0.881144
$934$	64.2460	2.10219
$935$	−68.6533	−2.24520
$936$	2.80275	0.0916107
$937$	46.1410	1.50736	0.753681	−	0.657241i	$-0.228277\pi$
$937$	46.1410	1.50736	0.753681	+	0.657241i	$0.228277\pi$
$938$	0	0
$939$	−1.18880	−0.0387950
$940$	45.9166	1.49763
$941$	14.9196	0.486365	0.243182	−	0.969981i	$-0.421809\pi$
$941$	14.9196	0.486365	0.243182	+	0.969981i	$0.421809\pi$
$942$	−37.7422	−1.22971
$943$	−7.15956	−0.233147
$944$	8.51859	0.277256
$945$	0	0
$946$	−58.2134	−1.89268
$947$	33.0103	1.07269	0.536346	−	0.843998i	$-0.319804\pi$
$947$	33.0103	1.07269	0.536346	+	0.843998i	$0.319804\pi$
$948$	−4.31830	−0.140252
$949$	−41.6046	−1.35054
$950$	−46.5911	−1.51162
$951$	10.9471	0.354983
$952$	0	0
$953$	0.806546	0.0261266	0.0130633	−	0.999915i	$-0.495842\pi$
$953$	0.806546	0.0261266	0.0130633	+	0.999915i	$0.495842\pi$
$954$	−19.8396	−0.642330
$955$	−36.1415	−1.16951
$956$	0.672600	0.0217534
$957$	14.5976	0.471874
$958$	8.61789	0.278431
$959$	0	0
$960$	15.4589	0.498933
$961$	−29.8772	−0.963781
$962$	86.7573	2.79717
$963$	−7.71525	−0.248620
$964$	−0.635159	−0.0204571
$965$	4.44646	0.143137
$966$	0	0
$967$	−0.0532427	−0.00171217	−0.000856086	−	1.00000i	$-0.500273\pi$
$967$	−0.0532427	−0.00171217	−0.000856086		1.00000i	$0.500273\pi$
$968$	0.590358	0.0189748
$969$	−58.3013	−1.87291
$970$	57.5940	1.84923
$971$	−18.8722	−0.605639	−0.302820	−	0.953048i	$-0.597928\pi$
$971$	−18.8722	−0.605639	−0.302820	+	0.953048i	$0.597928\pi$
$972$	1.69602	0.0544000
$973$	0	0
$974$	52.2016	1.67265
$975$	−15.1585	−0.485459
$976$	47.9042	1.53338
$977$	19.9282	0.637560	0.318780	−	0.947829i	$-0.396727\pi$
$977$	19.9282	0.637560	0.318780	+	0.947829i	$0.396727\pi$
$978$	−25.1311	−0.803604
$979$	9.60599	0.307009
$980$	0	0
$981$	−7.24061	−0.231175
$982$	28.8083	0.919309
$983$	−17.8633	−0.569750	−0.284875	−	0.958565i	$-0.591952\pi$
$983$	−17.8633	−0.569750	−0.284875	+	0.958565i	$0.591952\pi$
$984$	0.584397	0.0186299
$985$	−19.4124	−0.618532
$986$	67.5136	2.15007
$987$	0	0
$988$	62.3686	1.98421
$989$	−68.5905	−2.18105
$990$	−17.3584	−0.551685
$991$	5.58787	0.177505	0.0887523	−	0.996054i	$-0.471712\pi$
$991$	5.58787	0.177505	0.0887523	+	0.996054i	$0.471712\pi$
$992$	−7.96020	−0.252737
$993$	8.72158	0.276771
$994$	0	0
$995$	23.8588	0.756375
$996$	4.62536	0.146560
$997$	−9.97420	−0.315886	−0.157943	−	0.987448i	$-0.550486\pi$
$997$	−9.97420	−0.315886	−0.157943	+	0.987448i	$0.550486\pi$
$998$	−22.2200	−0.703362
$999$	−9.40940	−0.297700

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.v.1.5		5
7.6	odd	2		861.2.a.j.1.5	✓	5
21.20	even	2		2583.2.a.s.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.a.j.1.5	✓	5	7.6	odd	2
2583.2.a.s.1.1		5	21.20	even	2
6027.2.a.v.1.5		5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.92250 q^{2} +1.00000 q^{3} +1.69602 q^{4} -2.85669 q^{5} +1.92250 q^{6} -0.584397 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.92250 q^{2} +1.00000 q^{3} +1.69602 q^{4} -2.85669 q^{5} +1.92250 q^{6} -0.584397 q^{8} +1.00000 q^{9} -5.49199 q^{10} +3.16066 q^{11} +1.69602 q^{12} -4.79597 q^{13} -2.85669 q^{15} -4.51555 q^{16} +7.60362 q^{17} +1.92250 q^{18} -7.66757 q^{19} -4.84501 q^{20} +6.07639 q^{22} +7.15956 q^{23} -0.584397 q^{24} +3.16066 q^{25} -9.22028 q^{26} +1.00000 q^{27} +4.61853 q^{29} -5.49199 q^{30} +1.05961 q^{31} -7.51237 q^{32} +3.16066 q^{33} +14.6180 q^{34} +1.69602 q^{36} -9.40940 q^{37} -14.7409 q^{38} -4.79597 q^{39} +1.66944 q^{40} -1.00000 q^{41} -9.58026 q^{43} +5.36056 q^{44} -2.85669 q^{45} +13.7643 q^{46} -9.47709 q^{47} -4.51555 q^{48} +6.07639 q^{50} +7.60362 q^{51} -8.13408 q^{52} -10.3197 q^{53} +1.92250 q^{54} -9.02903 q^{55} -7.66757 q^{57} +8.87914 q^{58} -1.88650 q^{59} -4.84501 q^{60} -10.6087 q^{61} +2.03711 q^{62} -5.41147 q^{64} +13.7006 q^{65} +6.07639 q^{66} -1.82823 q^{67} +12.8959 q^{68} +7.15956 q^{69} -4.82823 q^{71} -0.584397 q^{72} +8.67491 q^{73} -18.0896 q^{74} +3.16066 q^{75} -13.0044 q^{76} -9.22028 q^{78} -2.54613 q^{79} +12.8995 q^{80} +1.00000 q^{81} -1.92250 q^{82} +2.72718 q^{83} -21.7212 q^{85} -18.4181 q^{86} +4.61853 q^{87} -1.84708 q^{88} +3.03923 q^{89} -5.49199 q^{90} +12.1428 q^{92} +1.05961 q^{93} -18.2197 q^{94} +21.9038 q^{95} -7.51237 q^{96} -10.4869 q^{97} +3.16066 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 3 q^{2} + 5 q^{3} + 7 q^{4} - q^{5} - 3 q^{6} - 9 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 3 * q^2 + 5 * q^3 + 7 * q^4 - q^5 - 3 * q^6 - 9 * q^8 + 5 * q^9	\( 5 q - 3 q^{2} + 5 q^{3} + 7 q^{4} - q^{5} - 3 q^{6} - 9 q^{8} + 5 q^{9} - 5 q^{10} + 4 q^{11} + 7 q^{12} - 3 q^{13} - q^{15} + 3 q^{16} + 8 q^{17} - 3 q^{18} - 20 q^{19} + q^{20} + 14 q^{22} - 5 q^{23} - 9 q^{24} + 4 q^{25} - 13 q^{26} + 5 q^{27} + 9 q^{29} - 5 q^{30} - 16 q^{31} - 21 q^{32} + 4 q^{33} + 7 q^{36} - 19 q^{37} - 8 q^{38} - 3 q^{39} - 21 q^{40} - 5 q^{41} + 6 q^{43} - 24 q^{44} - q^{45} + 27 q^{46} - 9 q^{47} + 3 q^{48} + 14 q^{50} + 8 q^{51} - q^{52} - 29 q^{53} - 3 q^{54} - 32 q^{55} - 20 q^{57} - q^{58} - 28 q^{59} + q^{60} - 16 q^{61} + 8 q^{62} + 39 q^{64} + q^{65} + 14 q^{66} + 21 q^{67} + 24 q^{68} - 5 q^{69} + 6 q^{71} - 9 q^{72} + 4 q^{73} + 11 q^{74} + 4 q^{75} - 26 q^{76} - 13 q^{78} + 21 q^{79} + 25 q^{80} + 5 q^{81} + 3 q^{82} - 26 q^{83} - 20 q^{85} - 58 q^{86} + 9 q^{87} + 54 q^{88} - 12 q^{89} - 5 q^{90} + 15 q^{92} - 16 q^{93} + q^{94} + 18 q^{95} - 21 q^{96} - 37 q^{97} + 4 q^{99}+O(q^{100}) \) 5 * q - 3 * q^2 + 5 * q^3 + 7 * q^4 - q^5 - 3 * q^6 - 9 * q^8 + 5 * q^9 - 5 * q^10 + 4 * q^11 + 7 * q^12 - 3 * q^13 - q^15 + 3 * q^16 + 8 * q^17 - 3 * q^18 - 20 * q^19 + q^20 + 14 * q^22 - 5 * q^23 - 9 * q^24 + 4 * q^25 - 13 * q^26 + 5 * q^27 + 9 * q^29 - 5 * q^30 - 16 * q^31 - 21 * q^32 + 4 * q^33 + 7 * q^36 - 19 * q^37 - 8 * q^38 - 3 * q^39 - 21 * q^40 - 5 * q^41 + 6 * q^43 - 24 * q^44 - q^45 + 27 * q^46 - 9 * q^47 + 3 * q^48 + 14 * q^50 + 8 * q^51 - q^52 - 29 * q^53 - 3 * q^54 - 32 * q^55 - 20 * q^57 - q^58 - 28 * q^59 + q^60 - 16 * q^61 + 8 * q^62 + 39 * q^64 + q^65 + 14 * q^66 + 21 * q^67 + 24 * q^68 - 5 * q^69 + 6 * q^71 - 9 * q^72 + 4 * q^73 + 11 * q^74 + 4 * q^75 - 26 * q^76 - 13 * q^78 + 21 * q^79 + 25 * q^80 + 5 * q^81 + 3 * q^82 - 26 * q^83 - 20 * q^85 - 58 * q^86 + 9 * q^87 + 54 * q^88 - 12 * q^89 - 5 * q^90 + 15 * q^92 - 16 * q^93 + q^94 + 18 * q^95 - 21 * q^96 - 37 * q^97 + 4 * q^99

Introduction

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