LMFDB - Embedded newform 6027.2.a.bb.1.4

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:	$8$
Coefficient field:	8.8.7457527933.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 6x^{6} + 23x^{5} - 4x^{4} - 27x^{3} + 8x^{2} + 8x + 1 $ x^8 - 3x^7 - 6x^6 + 23x^5 - 4x^4 - 27x^3 + 8x^2 + 8*x + 1
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			1.4
Root			$-0.978012$ 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)

$f(q)$	$=$	$q-1.13860 q^{2} -1.00000 q^{3} -0.703600 q^{4} -2.27123 q^{5} +1.13860 q^{6} +3.07831 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.13860 q^{2} -1.00000 q^{3} -0.703600 q^{4} -2.27123 q^{5} +1.13860 q^{6} +3.07831 q^{8} +1.00000 q^{9} +2.58601 q^{10} +4.11356 q^{11} +0.703600 q^{12} +1.02235 q^{13} +2.27123 q^{15} -2.09775 q^{16} -1.01936 q^{17} -1.13860 q^{18} -0.361035 q^{19} +1.59804 q^{20} -4.68368 q^{22} -4.61988 q^{23} -3.07831 q^{24} +0.158481 q^{25} -1.16404 q^{26} -1.00000 q^{27} -1.50587 q^{29} -2.58601 q^{30} -3.87299 q^{31} -3.76813 q^{32} -4.11356 q^{33} +1.16064 q^{34} -0.703600 q^{36} +9.23719 q^{37} +0.411073 q^{38} -1.02235 q^{39} -6.99154 q^{40} -1.00000 q^{41} -2.19077 q^{43} -2.89430 q^{44} -2.27123 q^{45} +5.26018 q^{46} +1.32485 q^{47} +2.09775 q^{48} -0.180446 q^{50} +1.01936 q^{51} -0.719323 q^{52} +7.53796 q^{53} +1.13860 q^{54} -9.34284 q^{55} +0.361035 q^{57} +1.71458 q^{58} +1.63497 q^{59} -1.59804 q^{60} -14.8701 q^{61} +4.40977 q^{62} +8.48587 q^{64} -2.32198 q^{65} +4.68368 q^{66} +5.38619 q^{67} +0.717224 q^{68} +4.61988 q^{69} -1.61302 q^{71} +3.07831 q^{72} -2.22290 q^{73} -10.5174 q^{74} -0.158481 q^{75} +0.254024 q^{76} +1.16404 q^{78} -4.15827 q^{79} +4.76446 q^{80} +1.00000 q^{81} +1.13860 q^{82} -1.53726 q^{83} +2.31521 q^{85} +2.49440 q^{86} +1.50587 q^{87} +12.6628 q^{88} -1.06059 q^{89} +2.58601 q^{90} +3.25055 q^{92} +3.87299 q^{93} -1.50847 q^{94} +0.819993 q^{95} +3.76813 q^{96} -0.418003 q^{97} +4.11356 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 8 q^{3} + 13 q^{4} - 7 q^{5} - q^{6} + 6 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + q^2 - 8 * q^3 + 13 * q^4 - 7 * q^5 - q^6 + 6 * q^8 + 8 * q^9	$ 8 q + q^{2} - 8 q^{3} + 13 q^{4} - 7 q^{5} - q^{6} + 6 q^{8} + 8 q^{9} - 8 q^{10} + 11 q^{11} - 13 q^{12} - 10 q^{13} + 7 q^{15} - 17 q^{16} - 3 q^{17} + q^{18} - 6 q^{19} - 11 q^{20} + 15 q^{22} + 14 q^{23} - 6 q^{24} + 25 q^{25} - 24 q^{26} - 8 q^{27} + 2 q^{29} + 8 q^{30} - 16 q^{31} + 3 q^{32} - 11 q^{33} + 4 q^{34} + 13 q^{36} - 20 q^{37} - 10 q^{38} + 10 q^{39} + 3 q^{40} - 8 q^{41} + 7 q^{43} - 7 q^{45} - 5 q^{46} - 14 q^{47} + 17 q^{48} - 5 q^{50} + 3 q^{51} - 23 q^{52} + 7 q^{53} - q^{54} - 48 q^{55} + 6 q^{57} - 20 q^{58} - 22 q^{59} + 11 q^{60} + 33 q^{62} - 10 q^{64} - 14 q^{65} - 15 q^{66} + 12 q^{67} + 27 q^{68} - 14 q^{69} - 5 q^{71} + 6 q^{72} - 2 q^{73} + 6 q^{74} - 25 q^{75} - 43 q^{76} + 24 q^{78} - 15 q^{79} + 7 q^{80} + 8 q^{81} - q^{82} - 15 q^{83} - 43 q^{85} + 31 q^{86} - 2 q^{87} + 17 q^{88} - 29 q^{89} - 8 q^{90} + 19 q^{92} + 16 q^{93} - 20 q^{94} + 14 q^{95} - 3 q^{96} - 19 q^{97} + 11 q^{99}+O(q^{100}) $ 8 * q + q^2 - 8 * q^3 + 13 * q^4 - 7 * q^5 - q^6 + 6 * q^8 + 8 * q^9 - 8 * q^10 + 11 * q^11 - 13 * q^12 - 10 * q^13 + 7 * q^15 - 17 * q^16 - 3 * q^17 + q^18 - 6 * q^19 - 11 * q^20 + 15 * q^22 + 14 * q^23 - 6 * q^24 + 25 * q^25 - 24 * q^26 - 8 * q^27 + 2 * q^29 + 8 * q^30 - 16 * q^31 + 3 * q^32 - 11 * q^33 + 4 * q^34 + 13 * q^36 - 20 * q^37 - 10 * q^38 + 10 * q^39 + 3 * q^40 - 8 * q^41 + 7 * q^43 - 7 * q^45 - 5 * q^46 - 14 * q^47 + 17 * q^48 - 5 * q^50 + 3 * q^51 - 23 * q^52 + 7 * q^53 - q^54 - 48 * q^55 + 6 * q^57 - 20 * q^58 - 22 * q^59 + 11 * q^60 + 33 * q^62 - 10 * q^64 - 14 * q^65 - 15 * q^66 + 12 * q^67 + 27 * q^68 - 14 * q^69 - 5 * q^71 + 6 * q^72 - 2 * q^73 + 6 * q^74 - 25 * q^75 - 43 * q^76 + 24 * q^78 - 15 * q^79 + 7 * q^80 + 8 * q^81 - q^82 - 15 * q^83 - 43 * q^85 + 31 * q^86 - 2 * q^87 + 17 * q^88 - 29 * q^89 - 8 * q^90 + 19 * q^92 + 16 * q^93 - 20 * q^94 + 14 * q^95 - 3 * q^96 - 19 * q^97 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.13860	−0.805109	−0.402554	−	0.915396i	$-0.631878\pi$
$2$	−1.13860	−0.805109	−0.402554	+	0.915396i	$0.631878\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.703600	−0.351800
$5$	−2.27123	−1.01572	−0.507862	−	0.861438i	$-0.669564\pi$
$5$	−2.27123	−1.01572	−0.507862	+	0.861438i	$0.669564\pi$
$6$	1.13860	0.464830
$7$	0	0
$7$	0	0
$8$	3.07831	1.08835
$9$	1.00000	0.333333
$10$	2.58601	0.817769
$11$	4.11356	1.24029	0.620143	−	0.784489i	$-0.287075\pi$
$11$	4.11356	1.24029	0.620143	+	0.784489i	$0.287075\pi$
$12$	0.703600	0.203112
$13$	1.02235	0.283548	0.141774	−	0.989899i	$-0.454719\pi$
$13$	1.02235	0.283548	0.141774	+	0.989899i	$0.454719\pi$
$14$	0	0
$15$	2.27123	0.586429
$16$	−2.09775	−0.524437
$17$	−1.01936	−0.247232	−0.123616	−	0.992330i	$-0.539449\pi$
$17$	−1.01936	−0.247232	−0.123616	+	0.992330i	$0.539449\pi$
$18$	−1.13860	−0.268370
$19$	−0.361035	−0.0828271	−0.0414135	−	0.999142i	$-0.513186\pi$
$19$	−0.361035	−0.0828271	−0.0414135	+	0.999142i	$0.513186\pi$
$20$	1.59804	0.357332
$21$	0	0
$22$	−4.68368	−0.998564
$23$	−4.61988	−0.963312	−0.481656	−	0.876360i	$-0.659965\pi$
$23$	−4.61988	−0.963312	−0.481656	+	0.876360i	$0.659965\pi$
$24$	−3.07831	−0.628357
$25$	0.158481	0.0316963
$26$	−1.16404	−0.228287
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−1.50587	−0.279633	−0.139816	−	0.990177i	$-0.544651\pi$
$29$	−1.50587	−0.279633	−0.139816	+	0.990177i	$0.544651\pi$
$30$	−2.58601	−0.472139
$31$	−3.87299	−0.695610	−0.347805	−	0.937567i	$-0.613073\pi$
$31$	−3.87299	−0.695610	−0.347805	+	0.937567i	$0.613073\pi$
$32$	−3.76813	−0.666117
$33$	−4.11356	−0.716079
$34$	1.16064	0.199049
$35$	0	0
$36$	−0.703600	−0.117267
$37$	9.23719	1.51858	0.759292	−	0.650750i	$-0.225545\pi$
$37$	9.23719	1.51858	0.759292	+	0.650750i	$0.225545\pi$
$38$	0.411073	0.0666848
$39$	−1.02235	−0.163706
$40$	−6.99154	−1.10546
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−2.19077	−0.334089	−0.167045	−	0.985949i	$-0.553422\pi$
$43$	−2.19077	−0.334089	−0.167045	+	0.985949i	$0.553422\pi$
$44$	−2.89430	−0.436332
$45$	−2.27123	−0.338575
$46$	5.26018	0.775571
$47$	1.32485	0.193249	0.0966245	−	0.995321i	$-0.469195\pi$
$47$	1.32485	0.193249	0.0966245	+	0.995321i	$0.469195\pi$
$48$	2.09775	0.302784
$49$	0	0
$50$	−0.180446	−0.0255190
$51$	1.01936	0.142739
$52$	−0.719323	−0.0997522
$53$	7.53796	1.03542	0.517709	−	0.855557i	$-0.326785\pi$
$53$	7.53796	1.03542	0.517709	+	0.855557i	$0.326785\pi$
$54$	1.13860	0.154943
$55$	−9.34284	−1.25979
$56$	0	0
$57$	0.361035	0.0478202
$58$	1.71458	0.225135
$59$	1.63497	0.212855	0.106427	−	0.994320i	$-0.466059\pi$
$59$	1.63497	0.212855	0.106427	+	0.994320i	$0.466059\pi$
$60$	−1.59804	−0.206306
$61$	−14.8701	−1.90392	−0.951961	−	0.306218i	$-0.900936\pi$
$61$	−14.8701	−1.90392	−0.951961	+	0.306218i	$0.900936\pi$
$62$	4.40977	0.560042
$63$	0	0
$64$	8.48587	1.06073
$65$	−2.32198	−0.288007
$66$	4.68368	0.576521
$67$	5.38619	0.658027	0.329014	−	0.944325i	$-0.393284\pi$
$67$	5.38619	0.658027	0.329014	+	0.944325i	$0.393284\pi$
$68$	0.717224	0.0869762
$69$	4.61988	0.556169
$70$	0	0
$71$	−1.61302	−0.191430	−0.0957149	−	0.995409i	$-0.530514\pi$
$71$	−1.61302	−0.191430	−0.0957149	+	0.995409i	$0.530514\pi$
$72$	3.07831	0.362782
$73$	−2.22290	−0.260171	−0.130086	−	0.991503i	$-0.541525\pi$
$73$	−2.22290	−0.260171	−0.130086	+	0.991503i	$0.541525\pi$
$74$	−10.5174	−1.22263
$75$	−0.158481	−0.0182999
$76$	0.254024	0.0291386
$77$	0	0
$78$	1.16404	0.131801
$79$	−4.15827	−0.467842	−0.233921	−	0.972256i	$-0.575156\pi$
$79$	−4.15827	−0.467842	−0.233921	+	0.972256i	$0.575156\pi$
$80$	4.76446	0.532683
$81$	1.00000	0.111111
$82$	1.13860	0.125737
$83$	−1.53726	−0.168736	−0.0843679	−	0.996435i	$-0.526887\pi$
$83$	−1.53726	−0.168736	−0.0843679	+	0.996435i	$0.526887\pi$
$84$	0	0
$85$	2.31521	0.251119
$86$	2.49440	0.268978
$87$	1.50587	0.161446
$88$	12.6628	1.34986
$89$	−1.06059	−0.112422	−0.0562111	−	0.998419i	$-0.517902\pi$
$89$	−1.06059	−0.112422	−0.0562111	+	0.998419i	$0.517902\pi$
$90$	2.58601	0.272590
$91$	0	0
$92$	3.25055	0.338893
$93$	3.87299	0.401611
$94$	−1.50847	−0.155586
$95$	0.819993	0.0841295
$96$	3.76813	0.384583
$97$	−0.418003	−0.0424418	−0.0212209	−	0.999775i	$-0.506755\pi$
$97$	−0.418003	−0.0424418	−0.0212209	+	0.999775i	$0.506755\pi$
$98$	0	0
$99$	4.11356	0.413428
$100$	−0.111508	−0.0111508
$101$	−3.97091	−0.395121	−0.197560	−	0.980291i	$-0.563302\pi$
$101$	−3.97091	−0.395121	−0.197560	+	0.980291i	$0.563302\pi$
$102$	−1.16064	−0.114921
$103$	10.9705	1.08096	0.540479	−	0.841358i	$-0.318243\pi$
$103$	10.9705	1.08096	0.540479	+	0.841358i	$0.318243\pi$
$104$	3.14710	0.308598
$105$	0	0
$106$	−8.58268	−0.833624
$107$	19.5498	1.88995	0.944974	−	0.327146i	$-0.106087\pi$
$107$	19.5498	1.88995	0.944974	+	0.327146i	$0.106087\pi$
$108$	0.703600	0.0677039
$109$	17.4207	1.66860	0.834299	−	0.551313i	$-0.185873\pi$
$109$	17.4207	1.66860	0.834299	+	0.551313i	$0.185873\pi$
$110$	10.6377	1.01427
$111$	−9.23719	−0.876755
$112$	0	0
$113$	−9.78704	−0.920687	−0.460344	−	0.887741i	$-0.652274\pi$
$113$	−9.78704	−0.920687	−0.460344	+	0.887741i	$0.652274\pi$
$114$	−0.411073	−0.0385005
$115$	10.4928	0.978460
$116$	1.05953	0.0983748
$117$	1.02235	0.0945160
$118$	−1.86157	−0.171371
$119$	0	0
$120$	6.99154	0.638237
$121$	5.92138	0.538307
$122$	16.9310	1.53286
$123$	1.00000	0.0901670
$124$	2.72504	0.244716
$125$	10.9962	0.983530
$126$	0	0
$127$	−16.9152	−1.50098	−0.750489	−	0.660883i	$-0.770182\pi$
$127$	−16.9152	−1.50098	−0.750489	+	0.660883i	$0.770182\pi$
$128$	−2.12572	−0.187888
$129$	2.19077	0.192887
$130$	2.64380	0.231877
$131$	20.7104	1.80948	0.904738	−	0.425969i	$-0.140067\pi$
$131$	20.7104	1.80948	0.904738	+	0.425969i	$0.140067\pi$
$132$	2.89430	0.251917
$133$	0	0
$134$	−6.13269	−0.529784
$135$	2.27123	0.195476
$136$	−3.13791	−0.269074
$137$	6.27873	0.536428	0.268214	−	0.963359i	$-0.413567\pi$
$137$	6.27873	0.536428	0.268214	+	0.963359i	$0.413567\pi$
$138$	−5.26018	−0.447776
$139$	3.27698	0.277950	0.138975	−	0.990296i	$-0.455619\pi$
$139$	3.27698	0.277950	0.138975	+	0.990296i	$0.455619\pi$
$140$	0	0
$141$	−1.32485	−0.111572
$142$	1.83657	0.154122
$143$	4.20548	0.351680
$144$	−2.09775	−0.174812
$145$	3.42017	0.284030
$146$	2.53099	0.209466
$147$	0	0
$148$	−6.49929	−0.534238
$149$	−12.5636	−1.02925	−0.514624	−	0.857416i	$-0.672068\pi$
$149$	−12.5636	−1.02925	−0.514624	+	0.857416i	$0.672068\pi$
$150$	0.180446	0.0147334
$151$	9.45156	0.769157	0.384578	−	0.923092i	$-0.374347\pi$
$151$	9.45156	0.769157	0.384578	+	0.923092i	$0.374347\pi$
$152$	−1.11138	−0.0901445
$153$	−1.01936	−0.0824106
$154$	0	0
$155$	8.79646	0.706548
$156$	0.719323	0.0575919
$157$	−11.1900	−0.893061	−0.446530	−	0.894768i	$-0.647341\pi$
$157$	−11.1900	−0.893061	−0.446530	+	0.894768i	$0.647341\pi$
$158$	4.73459	0.376664
$159$	−7.53796	−0.597799
$160$	8.55828	0.676592
$161$	0	0
$162$	−1.13860	−0.0894565
$163$	−5.24847	−0.411092	−0.205546	−	0.978647i	$-0.565897\pi$
$163$	−5.24847	−0.411092	−0.205546	+	0.978647i	$0.565897\pi$
$164$	0.703600	0.0549419
$165$	9.34284	0.727339
$166$	1.75031	0.135851
$167$	−13.1078	−1.01432	−0.507158	−	0.861853i	$-0.669304\pi$
$167$	−13.1078	−1.01432	−0.507158	+	0.861853i	$0.669304\pi$
$168$	0	0
$169$	−11.9548	−0.919601
$170$	−2.63608	−0.202178
$171$	−0.361035	−0.0276090
$172$	1.54143	0.117533
$173$	−2.61929	−0.199141	−0.0995704	−	0.995031i	$-0.531747\pi$
$173$	−2.61929	−0.199141	−0.0995704	+	0.995031i	$0.531747\pi$
$174$	−1.71458	−0.129982
$175$	0	0
$176$	−8.62921	−0.650451
$177$	−1.63497	−0.122892
$178$	1.20758	0.0905121
$179$	20.0966	1.50209	0.751044	−	0.660252i	$-0.229550\pi$
$179$	20.0966	1.50209	0.751044	+	0.660252i	$0.229550\pi$
$180$	1.59804	0.119111
$181$	13.9771	1.03891	0.519456	−	0.854497i	$-0.326135\pi$
$181$	13.9771	1.03891	0.519456	+	0.854497i	$0.326135\pi$
$182$	0	0
$183$	14.8701	1.09923
$184$	−14.2214	−1.04842
$185$	−20.9798	−1.54246
$186$	−4.40977	−0.323340
$187$	−4.19321	−0.306638
$188$	−0.932164	−0.0679850
$189$	0	0
$190$	−0.933640	−0.0677334
$191$	11.8333	0.856230	0.428115	−	0.903724i	$-0.359178\pi$
$191$	11.8333	0.856230	0.428115	+	0.903724i	$0.359178\pi$
$192$	−8.48587	−0.612415
$193$	9.09972	0.655012	0.327506	−	0.944849i	$-0.393792\pi$
$193$	9.09972	0.655012	0.327506	+	0.944849i	$0.393792\pi$
$194$	0.475937	0.0341703
$195$	2.32198	0.166281
$196$	0	0
$197$	0.846122	0.0602837	0.0301418	−	0.999546i	$-0.490404\pi$
$197$	0.846122	0.0602837	0.0301418	+	0.999546i	$0.490404\pi$
$198$	−4.68368	−0.332855
$199$	−3.86730	−0.274146	−0.137073	−	0.990561i	$-0.543769\pi$
$199$	−3.86730	−0.274146	−0.137073	+	0.990561i	$0.543769\pi$
$200$	0.487855	0.0344965
$201$	−5.38619	−0.379912
$202$	4.52126	0.318115
$203$	0	0
$204$	−0.717224	−0.0502157
$205$	2.27123	0.158630
$206$	−12.4910	−0.870288
$207$	−4.61988	−0.321104
$208$	−2.14462	−0.148703
$209$	−1.48514	−0.102729
$210$	0	0
$211$	−23.6238	−1.62633	−0.813166	−	0.582032i	$-0.802258\pi$
$211$	−23.6238	−1.62633	−0.813166	+	0.582032i	$0.802258\pi$
$212$	−5.30371	−0.364260
$213$	1.61302	0.110522
$214$	−22.2593	−1.52161
$215$	4.97574	0.339343
$216$	−3.07831	−0.209452
$217$	0	0
$218$	−19.8351	−1.34340
$219$	2.22290	0.150210
$220$	6.57362	0.443193
$221$	−1.04214	−0.0701021
$222$	10.5174	0.705883
$223$	−14.5761	−0.976089	−0.488044	−	0.872819i	$-0.662290\pi$
$223$	−14.5761	−0.976089	−0.488044	+	0.872819i	$0.662290\pi$
$224$	0	0
$225$	0.158481	0.0105654
$226$	11.1435	0.741253
$227$	−5.42919	−0.360348	−0.180174	−	0.983635i	$-0.557666\pi$
$227$	−5.42919	−0.360348	−0.180174	+	0.983635i	$0.557666\pi$
$228$	−0.254024	−0.0168232
$229$	8.50896	0.562288	0.281144	−	0.959666i	$-0.409286\pi$
$229$	8.50896	0.562288	0.281144	+	0.959666i	$0.409286\pi$
$230$	−11.9471	−0.787767
$231$	0	0
$232$	−4.63553	−0.304337
$233$	18.1099	1.18642	0.593210	−	0.805048i	$-0.297861\pi$
$233$	18.1099	1.18642	0.593210	+	0.805048i	$0.297861\pi$
$234$	−1.16404	−0.0760956
$235$	−3.00903	−0.196288
$236$	−1.15036	−0.0748823
$237$	4.15827	0.270109
$238$	0	0
$239$	2.22639	0.144013	0.0720066	−	0.997404i	$-0.477060\pi$
$239$	2.22639	0.144013	0.0720066	+	0.997404i	$0.477060\pi$
$240$	−4.76446	−0.307545
$241$	−14.2272	−0.916456	−0.458228	−	0.888835i	$-0.651516\pi$
$241$	−14.2272	−0.916456	−0.458228	+	0.888835i	$0.651516\pi$
$242$	−6.74206	−0.433396
$243$	−1.00000	−0.0641500
$244$	10.4626	0.669800
$245$	0	0
$246$	−1.13860	−0.0725942
$247$	−0.369103	−0.0234854
$248$	−11.9223	−0.757064
$249$	1.53726	0.0974197
$250$	−12.5202	−0.791848
$251$	6.81117	0.429918	0.214959	−	0.976623i	$-0.431038\pi$
$251$	6.81117	0.429918	0.214959	+	0.976623i	$0.431038\pi$
$252$	0	0
$253$	−19.0042	−1.19478
$254$	19.2595	1.20845
$255$	−2.31521	−0.144984
$256$	−14.5514	−0.909463
$257$	−4.87985	−0.304397	−0.152198	−	0.988350i	$-0.548635\pi$
$257$	−4.87985	−0.304397	−0.152198	+	0.988350i	$0.548635\pi$
$258$	−2.49440	−0.155295
$259$	0	0
$260$	1.63375	0.101321
$261$	−1.50587	−0.0932109
$262$	−23.5808	−1.45682
$263$	−16.5774	−1.02221	−0.511104	−	0.859519i	$-0.670763\pi$
$263$	−16.5774	−1.02221	−0.511104	+	0.859519i	$0.670763\pi$
$264$	−12.6628	−0.779342
$265$	−17.1204	−1.05170
$266$	0	0
$267$	1.06059	0.0649070
$268$	−3.78972	−0.231494
$269$	7.34953	0.448109	0.224054	−	0.974577i	$-0.428071\pi$
$269$	7.34953	0.448109	0.224054	+	0.974577i	$0.428071\pi$
$270$	−2.58601	−0.157380
$271$	−14.2752	−0.867158	−0.433579	−	0.901116i	$-0.642750\pi$
$271$	−14.2752	−0.867158	−0.433579	+	0.901116i	$0.642750\pi$
$272$	2.13837	0.129657
$273$	0	0
$274$	−7.14893	−0.431883
$275$	0.651923	0.0393124
$276$	−3.25055	−0.195660
$277$	−11.6467	−0.699781	−0.349891	−	0.936791i	$-0.613781\pi$
$277$	−11.6467	−0.699781	−0.349891	+	0.936791i	$0.613781\pi$
$278$	−3.73116	−0.223780
$279$	−3.87299	−0.231870
$280$	0	0
$281$	17.4871	1.04319	0.521595	−	0.853193i	$-0.325337\pi$
$281$	17.4871	1.04319	0.521595	+	0.853193i	$0.325337\pi$
$282$	1.50847	0.0898279
$283$	−15.6673	−0.931327	−0.465663	−	0.884962i	$-0.654184\pi$
$283$	−15.6673	−0.931327	−0.465663	+	0.884962i	$0.654184\pi$
$284$	1.13492	0.0673450
$285$	−0.819993	−0.0485722
$286$	−4.78835	−0.283141
$287$	0	0
$288$	−3.76813	−0.222039
$289$	−15.9609	−0.938876
$290$	−3.89419	−0.228675
$291$	0.418003	0.0245038
$292$	1.56404	0.0915282
$293$	20.8334	1.21710	0.608550	−	0.793516i	$-0.291751\pi$
$293$	20.8334	1.21710	0.608550	+	0.793516i	$0.291751\pi$
$294$	0	0
$295$	−3.71339	−0.216202
$296$	28.4349	1.65274
$297$	−4.11356	−0.238693
$298$	14.3048	0.828656
$299$	−4.72312	−0.273145
$300$	0.111508	0.00643789
$301$	0	0
$302$	−10.7615	−0.619255
$303$	3.97091	0.228123
$304$	0.757360	0.0434376
$305$	33.7734	1.93386
$306$	1.16064	0.0663495
$307$	−4.35015	−0.248276	−0.124138	−	0.992265i	$-0.539617\pi$
$307$	−4.35015	−0.248276	−0.124138	+	0.992265i	$0.539617\pi$
$308$	0	0
$309$	−10.9705	−0.624091
$310$	−10.0156	−0.568848
$311$	−17.4860	−0.991540	−0.495770	−	0.868454i	$-0.665114\pi$
$311$	−17.4860	−0.991540	−0.495770	+	0.868454i	$0.665114\pi$
$312$	−3.14710	−0.178169
$313$	−27.3870	−1.54800	−0.774001	−	0.633184i	$-0.781748\pi$
$313$	−27.3870	−1.54800	−0.774001	+	0.633184i	$0.781748\pi$
$314$	12.7409	0.719011
$315$	0	0
$316$	2.92576	0.164587
$317$	−31.8861	−1.79090	−0.895451	−	0.445161i	$-0.853147\pi$
$317$	−31.8861	−1.79090	−0.895451	+	0.445161i	$0.853147\pi$
$318$	8.58268	0.481293
$319$	−6.19448	−0.346824
$320$	−19.2734	−1.07741
$321$	−19.5498	−1.09116
$322$	0	0
$323$	0.368026	0.0204775
$324$	−0.703600	−0.0390889
$325$	0.162023	0.00898742
$326$	5.97589	0.330974
$327$	−17.4207	−0.963365
$328$	−3.07831	−0.169971
$329$	0	0
$330$	−10.6377	−0.585587
$331$	−16.1121	−0.885601	−0.442801	−	0.896620i	$-0.646015\pi$
$331$	−16.1121	−0.885601	−0.442801	+	0.896620i	$0.646015\pi$
$332$	1.08161	0.0593613
$333$	9.23719	0.506195
$334$	14.9245	0.816634
$335$	−12.2333	−0.668375
$336$	0	0
$337$	16.6380	0.906331	0.453166	−	0.891426i	$-0.350295\pi$
$337$	16.6380	0.906331	0.453166	+	0.891426i	$0.350295\pi$
$338$	13.6117	0.740378
$339$	9.78704	0.531559
$340$	−1.62898	−0.0883438
$341$	−15.9318	−0.862755
$342$	0.411073	0.0222283
$343$	0	0
$344$	−6.74386	−0.363605
$345$	−10.4928	−0.564914
$346$	2.98231	0.160330
$347$	25.4621	1.36688	0.683440	−	0.730007i	$-0.260483\pi$
$347$	25.4621	1.36688	0.683440	+	0.730007i	$0.260483\pi$
$348$	−1.05953	−0.0567967
$349$	15.6721	0.838911	0.419455	−	0.907776i	$-0.362221\pi$
$349$	15.6721	0.838911	0.419455	+	0.907776i	$0.362221\pi$
$350$	0	0
$351$	−1.02235	−0.0545688
$352$	−15.5004	−0.826175
$353$	−10.9229	−0.581366	−0.290683	−	0.956819i	$-0.593883\pi$
$353$	−10.9229	−0.581366	−0.290683	+	0.956819i	$0.593883\pi$
$354$	1.86157	0.0989413
$355$	3.66353	0.194440
$356$	0.746231	0.0395501
$357$	0	0
$358$	−22.8819	−1.20934
$359$	−1.37014	−0.0723134	−0.0361567	−	0.999346i	$-0.511512\pi$
$359$	−1.37014	−0.0723134	−0.0361567	+	0.999346i	$0.511512\pi$
$360$	−6.99154	−0.368487
$361$	−18.8697	−0.993140
$362$	−15.9143	−0.836437
$363$	−5.92138	−0.310792
$364$	0	0
$365$	5.04872	0.264262
$366$	−16.9310	−0.885000
$367$	−33.2866	−1.73755	−0.868774	−	0.495209i	$-0.835092\pi$
$367$	−33.2866	−1.73755	−0.868774	+	0.495209i	$0.835092\pi$
$368$	9.69135	0.505196
$369$	−1.00000	−0.0520579
$370$	23.8875	1.24185
$371$	0	0
$372$	−2.72504	−0.141287
$373$	−13.8615	−0.717719	−0.358859	−	0.933392i	$-0.616834\pi$
$373$	−13.8615	−0.717719	−0.358859	+	0.933392i	$0.616834\pi$
$374$	4.77437	0.246877
$375$	−10.9962	−0.567841
$376$	4.07829	0.210322
$377$	−1.53952	−0.0792893
$378$	0	0
$379$	1.47300	0.0756628	0.0378314	−	0.999284i	$-0.487955\pi$
$379$	1.47300	0.0756628	0.0378314	+	0.999284i	$0.487955\pi$
$380$	−0.576947	−0.0295968
$381$	16.9152	0.866590
$382$	−13.4734	−0.689359
$383$	1.29949	0.0664006	0.0332003	−	0.999449i	$-0.489430\pi$
$383$	1.29949	0.0664006	0.0332003	+	0.999449i	$0.489430\pi$
$384$	2.12572	0.108477
$385$	0	0
$386$	−10.3609	−0.527356
$387$	−2.19077	−0.111363
$388$	0.294107	0.0149310
$389$	16.8058	0.852089	0.426045	−	0.904702i	$-0.359907\pi$
$389$	16.8058	0.852089	0.426045	+	0.904702i	$0.359907\pi$
$390$	−2.64380	−0.133874
$391$	4.70934	0.238162
$392$	0	0
$393$	−20.7104	−1.04470
$394$	−0.963390	−0.0485349
$395$	9.44438	0.475198
$396$	−2.89430	−0.145444
$397$	−17.7317	−0.889930	−0.444965	−	0.895548i	$-0.646784\pi$
$397$	−17.7317	−0.889930	−0.444965	+	0.895548i	$0.646784\pi$
$398$	4.40329	0.220717
$399$	0	0
$400$	−0.332454	−0.0166227
$401$	26.9691	1.34677	0.673387	−	0.739290i	$-0.264839\pi$
$401$	26.9691	1.34677	0.673387	+	0.739290i	$0.264839\pi$
$402$	6.13269	0.305871
$403$	−3.95954	−0.197239
$404$	2.79393	0.139003
$405$	−2.27123	−0.112858
$406$	0	0
$407$	37.9977	1.88348
$408$	3.13791	0.155350
$409$	22.8930	1.13199	0.565993	−	0.824410i	$-0.308493\pi$
$409$	22.8930	1.13199	0.565993	+	0.824410i	$0.308493\pi$
$410$	−2.58601	−0.127714
$411$	−6.27873	−0.309707
$412$	−7.71886	−0.380281
$413$	0	0
$414$	5.26018	0.258524
$415$	3.49146	0.171389
$416$	−3.85233	−0.188876
$417$	−3.27698	−0.160474
$418$	1.69097	0.0827082
$419$	−38.2790	−1.87005	−0.935026	−	0.354579i	$-0.884624\pi$
$419$	−38.2790	−1.87005	−0.935026	+	0.354579i	$0.884624\pi$
$420$	0	0
$421$	−29.0730	−1.41693	−0.708465	−	0.705746i	$-0.750612\pi$
$421$	−29.0730	−1.41693	−0.708465	+	0.705746i	$0.750612\pi$
$422$	26.8980	1.30937
$423$	1.32485	0.0644164
$424$	23.2041	1.12689
$425$	−0.161550	−0.00783633
$426$	−1.83657	−0.0889823
$427$	0	0
$428$	−13.7552	−0.664884
$429$	−4.20548	−0.203043
$430$	−5.66536	−0.273208
$431$	−28.5861	−1.37694	−0.688472	−	0.725263i	$-0.741718\pi$
$431$	−28.5861	−1.37694	−0.688472	+	0.725263i	$0.741718\pi$
$432$	2.09775	0.100928
$433$	25.3115	1.21639	0.608196	−	0.793787i	$-0.291894\pi$
$433$	25.3115	1.21639	0.608196	+	0.793787i	$0.291894\pi$
$434$	0	0
$435$	−3.42017	−0.163985
$436$	−12.2572	−0.587012
$437$	1.66794	0.0797884
$438$	−2.53099	−0.120935
$439$	−11.4408	−0.546042	−0.273021	−	0.962008i	$-0.588023\pi$
$439$	−11.4408	−0.546042	−0.273021	+	0.962008i	$0.588023\pi$
$440$	−28.7601	−1.37109
$441$	0	0
$442$	1.18658	0.0564398
$443$	−28.2157	−1.34057	−0.670285	−	0.742104i	$-0.733828\pi$
$443$	−28.2157	−1.34057	−0.670285	+	0.742104i	$0.733828\pi$
$444$	6.49929	0.308442
$445$	2.40884	0.114190
$446$	16.5963	0.785858
$447$	12.5636	0.594237
$448$	0	0
$449$	37.0482	1.74841	0.874207	−	0.485553i	$-0.161382\pi$
$449$	37.0482	1.74841	0.874207	+	0.485553i	$0.161382\pi$
$450$	−0.180446	−0.00850632
$451$	−4.11356	−0.193700
$452$	6.88616	0.323898
$453$	−9.45156	−0.444073
$454$	6.18165	0.290119
$455$	0	0
$456$	1.11138	0.0520450
$457$	−3.13021	−0.146425	−0.0732126	−	0.997316i	$-0.523325\pi$
$457$	−3.13021	−0.146425	−0.0732126	+	0.997316i	$0.523325\pi$
$458$	−9.68826	−0.452703
$459$	1.01936	0.0475798
$460$	−7.38274	−0.344222
$461$	−32.8502	−1.52998	−0.764992	−	0.644040i	$-0.777257\pi$
$461$	−32.8502	−1.52998	−0.764992	+	0.644040i	$0.777257\pi$
$462$	0	0
$463$	15.8140	0.734937	0.367468	−	0.930036i	$-0.380225\pi$
$463$	15.8140	0.734937	0.367468	+	0.930036i	$0.380225\pi$
$464$	3.15893	0.146650
$465$	−8.79646	−0.407926
$466$	−20.6199	−0.955197
$467$	−36.7438	−1.70030	−0.850151	−	0.526539i	$-0.823489\pi$
$467$	−36.7438	−1.70030	−0.850151	+	0.526539i	$0.823489\pi$
$468$	−0.719323	−0.0332507
$469$	0	0
$470$	3.42607	0.158033
$471$	11.1900	0.515609
$472$	5.03294	0.231660
$473$	−9.01186	−0.414366
$474$	−4.73459	−0.217467
$475$	−0.0572173	−0.00262531
$476$	0	0
$477$	7.53796	0.345139
$478$	−2.53496	−0.115946
$479$	34.6662	1.58394	0.791969	−	0.610561i	$-0.209056\pi$
$479$	34.6662	1.58394	0.791969	+	0.610561i	$0.209056\pi$
$480$	−8.55828	−0.390630
$481$	9.44361	0.430591
$482$	16.1991	0.737847
$483$	0	0
$484$	−4.16628	−0.189376
$485$	0.949381	0.0431092
$486$	1.13860	0.0516477
$487$	−24.3473	−1.10328	−0.551640	−	0.834082i	$-0.685998\pi$
$487$	−24.3473	−1.10328	−0.551640	+	0.834082i	$0.685998\pi$
$488$	−45.7748	−2.07213
$489$	5.24847	0.237344
$490$	0	0
$491$	−23.6572	−1.06764	−0.533818	−	0.845600i	$-0.679243\pi$
$491$	−23.6572	−1.06764	−0.533818	+	0.845600i	$0.679243\pi$
$492$	−0.703600	−0.0317207
$493$	1.53503	0.0691341
$494$	0.420259	0.0189083
$495$	−9.34284	−0.419929
$496$	8.12456	0.364804
$497$	0	0
$498$	−1.75031	−0.0784335
$499$	31.4749	1.40901	0.704505	−	0.709699i	$-0.251169\pi$
$499$	31.4749	1.40901	0.704505	+	0.709699i	$0.251169\pi$
$500$	−7.73692	−0.346006
$501$	13.1078	0.585615
$502$	−7.75517	−0.346130
$503$	17.3605	0.774067	0.387034	−	0.922066i	$-0.373500\pi$
$503$	17.3605	0.774067	0.387034	+	0.922066i	$0.373500\pi$
$504$	0	0
$505$	9.01885	0.401334
$506$	21.6381	0.961929
$507$	11.9548	0.530932
$508$	11.9015	0.528044
$509$	2.68874	0.119176	0.0595881	−	0.998223i	$-0.481021\pi$
$509$	2.68874	0.119176	0.0595881	+	0.998223i	$0.481021\pi$
$510$	2.63608	0.116728
$511$	0	0
$512$	20.8196	0.920105
$513$	0.361035	0.0159401
$514$	5.55618	0.245072
$515$	−24.9166	−1.09795
$516$	−1.54143	−0.0678575
$517$	5.44985	0.239684
$518$	0	0
$519$	2.61929	0.114974
$520$	−7.14778	−0.313451
$521$	39.2979	1.72167	0.860835	−	0.508884i	$-0.169942\pi$
$521$	39.2979	1.72167	0.860835	+	0.508884i	$0.169942\pi$
$522$	1.71458	0.0750449
$523$	−6.63116	−0.289961	−0.144980	−	0.989435i	$-0.546312\pi$
$523$	−6.63116	−0.289961	−0.144980	+	0.989435i	$0.546312\pi$
$524$	−14.5718	−0.636573
$525$	0	0
$526$	18.8750	0.822988
$527$	3.94799	0.171977
$528$	8.62921	0.375538
$529$	−1.65667	−0.0720292
$530$	19.4932	0.846732
$531$	1.63497	0.0709516
$532$	0	0
$533$	−1.02235	−0.0442827
$534$	−1.20758	−0.0522572
$535$	−44.4020	−1.91967
$536$	16.5803	0.716162
$537$	−20.0966	−0.867231
$538$	−8.36814	−0.360776
$539$	0	0
$540$	−1.59804	−0.0687686
$541$	32.2640	1.38714	0.693568	−	0.720391i	$-0.256038\pi$
$541$	32.2640	1.38714	0.693568	+	0.720391i	$0.256038\pi$
$542$	16.2537	0.698157
$543$	−13.9771	−0.599816
$544$	3.84109	0.164685
$545$	−39.5663	−1.69484
$546$	0	0
$547$	−7.23994	−0.309558	−0.154779	−	0.987949i	$-0.549466\pi$
$547$	−7.23994	−0.309558	−0.154779	+	0.987949i	$0.549466\pi$
$548$	−4.41771	−0.188715
$549$	−14.8701	−0.634641
$550$	−0.742277	−0.0316508
$551$	0.543671	0.0231612
$552$	14.2214	0.605304
$553$	0	0
$554$	13.2609	0.563400
$555$	20.9798	0.890542
$556$	−2.30568	−0.0977828
$557$	−0.594345	−0.0251832	−0.0125916	−	0.999921i	$-0.504008\pi$
$557$	−0.594345	−0.0251832	−0.0125916	+	0.999921i	$0.504008\pi$
$558$	4.40977	0.186681
$559$	−2.23973	−0.0947303
$560$	0	0
$561$	4.19321	0.177038
$562$	−19.9107	−0.839882
$563$	−5.25348	−0.221408	−0.110704	−	0.993853i	$-0.535310\pi$
$563$	−5.25348	−0.221408	−0.110704	+	0.993853i	$0.535310\pi$
$564$	0.932164	0.0392512
$565$	22.2286	0.935165
$566$	17.8388	0.749819
$567$	0	0
$568$	−4.96536	−0.208342
$569$	−19.6362	−0.823194	−0.411597	−	0.911366i	$-0.635029\pi$
$569$	−19.6362	−0.823194	−0.411597	+	0.911366i	$0.635029\pi$
$570$	0.933640	0.0391059
$571$	−35.2958	−1.47708	−0.738542	−	0.674207i	$-0.764485\pi$
$571$	−35.2958	−1.47708	−0.738542	+	0.674207i	$0.764485\pi$
$572$	−2.95898	−0.123721
$573$	−11.8333	−0.494345
$574$	0	0
$575$	−0.732166	−0.0305334
$576$	8.48587	0.353578
$577$	−34.3114	−1.42840	−0.714200	−	0.699941i	$-0.753210\pi$
$577$	−34.3114	−1.42840	−0.714200	+	0.699941i	$0.753210\pi$
$578$	18.1730	0.755898
$579$	−9.09972	−0.378172
$580$	−2.40643	−0.0999217
$581$	0	0
$582$	−0.475937	−0.0197282
$583$	31.0078	1.28421
$584$	−6.84278	−0.283156
$585$	−2.32198	−0.0960022
$586$	−23.7208	−0.979898
$587$	18.7338	0.773228	0.386614	−	0.922242i	$-0.373645\pi$
$587$	18.7338	0.773228	0.386614	+	0.922242i	$0.373645\pi$
$588$	0	0
$589$	1.39829	0.0576154
$590$	4.22805	0.174066
$591$	−0.846122	−0.0348048
$592$	−19.3773	−0.796401
$593$	5.35369	0.219850	0.109925	−	0.993940i	$-0.464939\pi$
$593$	5.35369	0.219850	0.109925	+	0.993940i	$0.464939\pi$
$594$	4.68368	0.192174
$595$	0	0
$596$	8.83973	0.362089
$597$	3.86730	0.158278
$598$	5.37773	0.219912
$599$	38.4103	1.56940	0.784701	−	0.619874i	$-0.212816\pi$
$599$	38.4103	1.56940	0.784701	+	0.619874i	$0.212816\pi$
$600$	−0.487855	−0.0199166
$601$	2.61417	0.106634	0.0533172	−	0.998578i	$-0.483021\pi$
$601$	2.61417	0.106634	0.0533172	+	0.998578i	$0.483021\pi$
$602$	0	0
$603$	5.38619	0.219342
$604$	−6.65011	−0.270589
$605$	−13.4488	−0.546772
$606$	−4.52126	−0.183664
$607$	34.7661	1.41111	0.705556	−	0.708654i	$-0.250697\pi$
$607$	34.7661	1.41111	0.705556	+	0.708654i	$0.250697\pi$
$608$	1.36043	0.0551726
$609$	0	0
$610$	−38.4543	−1.55697
$611$	1.35445	0.0547954
$612$	0.717224	0.0289921
$613$	−7.23499	−0.292219	−0.146109	−	0.989268i	$-0.546675\pi$
$613$	−7.23499	−0.292219	−0.146109	+	0.989268i	$0.546675\pi$
$614$	4.95306	0.199889
$615$	−2.27123	−0.0915848
$616$	0	0
$617$	3.70944	0.149337	0.0746683	−	0.997208i	$-0.476210\pi$
$617$	3.70944	0.149337	0.0746683	+	0.997208i	$0.476210\pi$
$618$	12.4910	0.502461
$619$	21.8562	0.878473	0.439237	−	0.898371i	$-0.355249\pi$
$619$	21.8562	0.878473	0.439237	+	0.898371i	$0.355249\pi$
$620$	−6.18919	−0.248564
$621$	4.61988	0.185390
$622$	19.9095	0.798298
$623$	0	0
$624$	2.14462	0.0858537
$625$	−25.7673	−1.03069
$626$	31.1827	1.24631
$627$	1.48514	0.0593107
$628$	7.87330	0.314179
$629$	−9.41605	−0.375442
$630$	0	0
$631$	21.7931	0.867569	0.433784	−	0.901017i	$-0.357178\pi$
$631$	21.7931	0.867569	0.433784	+	0.901017i	$0.357178\pi$
$632$	−12.8004	−0.509174
$633$	23.6238	0.938963
$634$	36.3054	1.44187
$635$	38.4182	1.52458
$636$	5.30371	0.210306
$637$	0	0
$638$	7.05301	0.279231
$639$	−1.61302	−0.0638099
$640$	4.82799	0.190843
$641$	−27.4415	−1.08388	−0.541938	−	0.840419i	$-0.682309\pi$
$641$	−27.4415	−1.08388	−0.541938	+	0.840419i	$0.682309\pi$
$642$	22.2593	0.878504
$643$	−0.581325	−0.0229252	−0.0114626	−	0.999934i	$-0.503649\pi$
$643$	−0.581325	−0.0229252	−0.0114626	+	0.999934i	$0.503649\pi$
$644$	0	0
$645$	−4.97574	−0.195920
$646$	−0.419032	−0.0164866
$647$	−29.9596	−1.17783	−0.588917	−	0.808194i	$-0.700445\pi$
$647$	−29.9596	−1.17783	−0.588917	+	0.808194i	$0.700445\pi$
$648$	3.07831	0.120927
$649$	6.72554	0.264001
$650$	−0.184479	−0.00723585
$651$	0	0
$652$	3.69283	0.144622
$653$	8.27365	0.323773	0.161886	−	0.986809i	$-0.448242\pi$
$653$	8.27365	0.323773	0.161886	+	0.986809i	$0.448242\pi$
$654$	19.8351	0.775614
$655$	−47.0380	−1.83793
$656$	2.09775	0.0819033
$657$	−2.22290	−0.0867237
$658$	0	0
$659$	35.3248	1.37606	0.688030	−	0.725682i	$-0.258476\pi$
$659$	35.3248	1.37606	0.688030	+	0.725682i	$0.258476\pi$
$660$	−6.57362	−0.255878
$661$	−32.2603	−1.25478	−0.627390	−	0.778705i	$-0.715877\pi$
$661$	−32.2603	−1.25478	−0.627390	+	0.778705i	$0.715877\pi$
$662$	18.3452	0.713005
$663$	1.04214	0.0404735
$664$	−4.73215	−0.183643
$665$	0	0
$666$	−10.5174	−0.407542
$667$	6.95694	0.269374
$668$	9.22268	0.356836
$669$	14.5761	0.563545
$670$	13.9287	0.538114
$671$	−61.1691	−2.36141
$672$	0	0
$673$	−5.72480	−0.220675	−0.110337	−	0.993894i	$-0.535193\pi$
$673$	−5.72480	−0.220675	−0.110337	+	0.993894i	$0.535193\pi$
$674$	−18.9440	−0.729695
$675$	−0.158481	−0.00609995
$676$	8.41140	0.323515
$677$	−51.3825	−1.97479	−0.987396	−	0.158270i	$-0.949408\pi$
$677$	−51.3825	−1.97479	−0.987396	+	0.158270i	$0.949408\pi$
$678$	−11.1435	−0.427963
$679$	0	0
$680$	7.12692	0.273305
$681$	5.42919	0.208047
$682$	18.1399	0.694611
$683$	−12.9225	−0.494465	−0.247232	−	0.968956i	$-0.579521\pi$
$683$	−12.9225	−0.494465	−0.247232	+	0.968956i	$0.579521\pi$
$684$	0.254024	0.00971286
$685$	−14.2604	−0.544863
$686$	0	0
$687$	−8.50896	−0.324637
$688$	4.59568	0.175209
$689$	7.70640	0.293591
$690$	11.9471	0.454817
$691$	−7.98422	−0.303734	−0.151867	−	0.988401i	$-0.548529\pi$
$691$	−7.98422	−0.303734	−0.151867	+	0.988401i	$0.548529\pi$
$692$	1.84293	0.0700577
$693$	0	0
$694$	−28.9911	−1.10049
$695$	−7.44278	−0.282321
$696$	4.63553	0.175709
$697$	1.01936	0.0386111
$698$	−17.8442	−0.675414
$699$	−18.1099	−0.684980
$700$	0	0
$701$	−4.14530	−0.156566	−0.0782829	−	0.996931i	$-0.524944\pi$
$701$	−4.14530	−0.156566	−0.0782829	+	0.996931i	$0.524944\pi$
$702$	1.16404	0.0439338
$703$	−3.33495	−0.125780
$704$	34.9071	1.31561
$705$	3.00903	0.113327
$706$	12.4367	0.468063
$707$	0	0
$708$	1.15036	0.0432333
$709$	22.3009	0.837527	0.418764	−	0.908095i	$-0.362464\pi$
$709$	22.3009	0.837527	0.418764	+	0.908095i	$0.362464\pi$
$710$	−4.17128	−0.156545
$711$	−4.15827	−0.155947
$712$	−3.26482	−0.122354
$713$	17.8928	0.670090
$714$	0	0
$715$	−9.55162	−0.357210
$716$	−14.1400	−0.528435
$717$	−2.22639	−0.0831461
$718$	1.56004	0.0582201
$719$	11.8846	0.443221	0.221610	−	0.975135i	$-0.428869\pi$
$719$	11.8846	0.443221	0.221610	+	0.975135i	$0.428869\pi$
$720$	4.76446	0.177561
$721$	0	0
$722$	21.4849	0.799585
$723$	14.2272	0.529116
$724$	−9.83431	−0.365489
$725$	−0.238652	−0.00886332
$726$	6.74206	0.250221
$727$	−52.7921	−1.95795	−0.978976	−	0.203977i	$-0.934613\pi$
$727$	−52.7921	−1.95795	−0.978976	+	0.203977i	$0.934613\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−5.74846	−0.212760
$731$	2.23319	0.0825975
$732$	−10.4626	−0.386709
$733$	8.77886	0.324255	0.162127	−	0.986770i	$-0.448164\pi$
$733$	8.77886	0.324255	0.162127	+	0.986770i	$0.448164\pi$
$734$	37.9000	1.39892
$735$	0	0
$736$	17.4083	0.641679
$737$	22.1564	0.816142
$738$	1.13860	0.0419123
$739$	−49.4832	−1.82027	−0.910135	−	0.414311i	$-0.864023\pi$
$739$	−49.4832	−1.82027	−0.910135	+	0.414311i	$0.864023\pi$
$740$	14.7614	0.542639
$741$	0.369103	0.0135593
$742$	0	0
$743$	26.5917	0.975554	0.487777	−	0.872968i	$-0.337808\pi$
$743$	26.5917	0.975554	0.487777	+	0.872968i	$0.337808\pi$
$744$	11.9223	0.437091
$745$	28.5348	1.04543
$746$	15.7826	0.577842
$747$	−1.53726	−0.0562453
$748$	2.95034	0.107875
$749$	0	0
$750$	12.5202	0.457174
$751$	7.81219	0.285071	0.142535	−	0.989790i	$-0.454475\pi$
$751$	7.81219	0.285071	0.142535	+	0.989790i	$0.454475\pi$
$752$	−2.77920	−0.101347
$753$	−6.81117	−0.248213
$754$	1.75289	0.0638365
$755$	−21.4666	−0.781251
$756$	0	0
$757$	29.6870	1.07899	0.539497	−	0.841988i	$-0.318614\pi$
$757$	29.6870	1.07899	0.539497	+	0.841988i	$0.318614\pi$
$758$	−1.67715	−0.0609167
$759$	19.0042	0.689808
$760$	2.52419	0.0915620
$761$	−12.7647	−0.462720	−0.231360	−	0.972868i	$-0.574317\pi$
$761$	−12.7647	−0.462720	−0.231360	+	0.972868i	$0.574317\pi$
$762$	−19.2595	−0.697699
$763$	0	0
$764$	−8.32594	−0.301222
$765$	2.31521	0.0837065
$766$	−1.47959	−0.0534597
$767$	1.67151	0.0603546
$768$	14.5514	0.525079
$769$	26.8186	0.967104	0.483552	−	0.875316i	$-0.339346\pi$
$769$	26.8186	0.967104	0.483552	+	0.875316i	$0.339346\pi$
$770$	0	0
$771$	4.87985	0.175744
$772$	−6.40257	−0.230433
$773$	19.7548	0.710531	0.355265	−	0.934766i	$-0.384391\pi$
$773$	19.7548	0.710531	0.355265	+	0.934766i	$0.384391\pi$
$774$	2.49440	0.0896594
$775$	−0.613798	−0.0220483
$776$	−1.28674	−0.0461914
$777$	0	0
$778$	−19.1350	−0.686024
$779$	0.361035	0.0129354
$780$	−1.63375	−0.0584975
$781$	−6.63524	−0.237428
$782$	−5.36203	−0.191746
$783$	1.50587	0.0538153
$784$	0	0
$785$	25.4151	0.907104
$786$	23.5808	0.841098
$787$	−38.0595	−1.35667	−0.678337	−	0.734751i	$-0.737299\pi$
$787$	−38.0595	−1.35667	−0.678337	+	0.734751i	$0.737299\pi$
$788$	−0.595331	−0.0212078
$789$	16.5774	0.590172
$790$	−10.7533	−0.382586
$791$	0	0
$792$	12.6628	0.449953
$793$	−15.2024	−0.539853
$794$	20.1893	0.716490
$795$	17.1204	0.607199
$796$	2.72103	0.0964444
$797$	−42.5173	−1.50604	−0.753019	−	0.657998i	$-0.771403\pi$
$797$	−42.5173	−1.50604	−0.753019	+	0.657998i	$0.771403\pi$
$798$	0	0
$799$	−1.35050	−0.0477773
$800$	−0.597179	−0.0211135
$801$	−1.06059	−0.0374741
$802$	−30.7069	−1.08430
$803$	−9.14405	−0.322687
$804$	3.78972	0.133653
$805$	0	0
$806$	4.50832	0.158799
$807$	−7.34953	−0.258716
$808$	−12.2237	−0.430028
$809$	−38.2867	−1.34609	−0.673044	−	0.739603i	$-0.735013\pi$
$809$	−38.2867	−1.34609	−0.673044	+	0.739603i	$0.735013\pi$
$810$	2.58601	0.0908632
$811$	35.9502	1.26238	0.631191	−	0.775628i	$-0.282566\pi$
$811$	35.9502	1.26238	0.631191	+	0.775628i	$0.282566\pi$
$812$	0	0
$813$	14.2752	0.500654
$814$	−43.2640	−1.51640
$815$	11.9205	0.417556
$816$	−2.13837	−0.0748578
$817$	0.790944	0.0276716
$818$	−26.0659	−0.911372
$819$	0	0
$820$	−1.59804	−0.0558059
$821$	−18.3527	−0.640514	−0.320257	−	0.947331i	$-0.603769\pi$
$821$	−18.3527	−0.640514	−0.320257	+	0.947331i	$0.603769\pi$
$822$	7.14893	0.249348
$823$	−41.0862	−1.43218	−0.716088	−	0.698010i	$-0.754069\pi$
$823$	−41.0862	−1.43218	−0.716088	+	0.698010i	$0.754069\pi$
$824$	33.7706	1.17646
$825$	−0.651923	−0.0226970
$826$	0	0
$827$	23.0152	0.800316	0.400158	−	0.916446i	$-0.368955\pi$
$827$	23.0152	0.800316	0.400158	+	0.916446i	$0.368955\pi$
$828$	3.25055	0.112964
$829$	−24.1424	−0.838499	−0.419249	−	0.907871i	$-0.637707\pi$
$829$	−24.1424	−0.838499	−0.419249	+	0.907871i	$0.637707\pi$
$830$	−3.97536	−0.137987
$831$	11.6467	0.404019
$832$	8.67550	0.300769
$833$	0	0
$834$	3.73116	0.129199
$835$	29.7709	1.03027
$836$	1.04494	0.0361401
$837$	3.87299	0.133870
$838$	43.5843	1.50559
$839$	15.6154	0.539105	0.269552	−	0.962986i	$-0.413124\pi$
$839$	15.6154	0.539105	0.269552	+	0.962986i	$0.413124\pi$
$840$	0	0
$841$	−26.7324	−0.921806
$842$	33.1024	1.14078
$843$	−17.4871	−0.602286
$844$	16.6217	0.572144
$845$	27.1521	0.934061
$846$	−1.50847	−0.0518622
$847$	0	0
$848$	−15.8127	−0.543011
$849$	15.6673	0.537702
$850$	0.183940	0.00630910
$851$	−42.6747	−1.46287
$852$	−1.13492	−0.0388817
$853$	16.3069	0.558338	0.279169	−	0.960242i	$-0.409941\pi$
$853$	16.3069	0.558338	0.279169	+	0.960242i	$0.409941\pi$
$854$	0	0
$855$	0.819993	0.0280432
$856$	60.1802	2.05692
$857$	−10.4701	−0.357653	−0.178827	−	0.983881i	$-0.557230\pi$
$857$	−10.4701	−0.357653	−0.178827	+	0.983881i	$0.557230\pi$
$858$	4.78835	0.163471
$859$	−29.4060	−1.00332	−0.501659	−	0.865065i	$-0.667277\pi$
$859$	−29.4060	−1.00332	−0.501659	+	0.865065i	$0.667277\pi$
$860$	−3.50093	−0.119381
$861$	0	0
$862$	32.5480	1.10859
$863$	−11.8231	−0.402463	−0.201231	−	0.979544i	$-0.564494\pi$
$863$	−11.8231	−0.402463	−0.201231	+	0.979544i	$0.564494\pi$
$864$	3.76813	0.128194
$865$	5.94900	0.202272
$866$	−28.8195	−0.979327
$867$	15.9609	0.542061
$868$	0	0
$869$	−17.1053	−0.580257
$870$	3.89419	0.132026
$871$	5.50655	0.186582
$872$	53.6262	1.81601
$873$	−0.418003	−0.0141473
$874$	−1.89911	−0.0642383
$875$	0	0
$876$	−1.56404	−0.0528439
$877$	−35.9145	−1.21275	−0.606373	−	0.795181i	$-0.707376\pi$
$877$	−35.9145	−1.21275	−0.606373	+	0.795181i	$0.707376\pi$
$878$	13.0265	0.439623
$879$	−20.8334	−0.702693
$880$	19.5989	0.660679
$881$	−41.3275	−1.39236	−0.696180	−	0.717868i	$-0.745118\pi$
$881$	−41.3275	−1.39236	−0.696180	+	0.717868i	$0.745118\pi$
$882$	0	0
$883$	−29.3608	−0.988068	−0.494034	−	0.869443i	$-0.664478\pi$
$883$	−29.3608	−0.988068	−0.494034	+	0.869443i	$0.664478\pi$
$884$	0.733251	0.0246619
$885$	3.71339	0.124824
$886$	32.1263	1.07930
$887$	25.4418	0.854253	0.427126	−	0.904192i	$-0.359526\pi$
$887$	25.4418	0.854253	0.427126	+	0.904192i	$0.359526\pi$
$888$	−28.4349	−0.954213
$889$	0	0
$890$	−2.74270	−0.0919354
$891$	4.11356	0.137809
$892$	10.2558	0.343388
$893$	−0.478317	−0.0160063
$894$	−14.3048	−0.478425
$895$	−45.6439	−1.52571
$896$	0	0
$897$	4.72312	0.157700
$898$	−42.1830	−1.40766
$899$	5.83222	0.194515
$900$	−0.111508	−0.00371692
$901$	−7.68391	−0.255988
$902$	4.68368	0.155950
$903$	0	0
$904$	−30.1275	−1.00203
$905$	−31.7453	−1.05525
$906$	10.7615	0.357527
$907$	−21.3485	−0.708864	−0.354432	−	0.935082i	$-0.615326\pi$
$907$	−21.3485	−0.708864	−0.354432	+	0.935082i	$0.615326\pi$
$908$	3.81998	0.126770
$909$	−3.97091	−0.131707
$910$	0	0
$911$	−27.8400	−0.922381	−0.461190	−	0.887301i	$-0.652577\pi$
$911$	−27.8400	−0.922381	−0.461190	+	0.887301i	$0.652577\pi$
$912$	−0.757360	−0.0250787
$913$	−6.32360	−0.209281
$914$	3.56405	0.117888
$915$	−33.7734	−1.11652
$916$	−5.98690	−0.197813
$917$	0	0
$918$	−1.16064	−0.0383069
$919$	−0.843163	−0.0278134	−0.0139067	−	0.999903i	$-0.504427\pi$
$919$	−0.843163	−0.0278134	−0.0139067	+	0.999903i	$0.504427\pi$
$920$	32.3001	1.06490
$921$	4.35015	0.143342
$922$	37.4030	1.23180
$923$	−1.64906	−0.0542795
$924$	0	0
$925$	1.46392	0.0481335
$926$	−18.0057	−0.591704
$927$	10.9705	0.360319
$928$	5.67431	0.186268
$929$	3.50232	0.114907	0.0574537	−	0.998348i	$-0.481702\pi$
$929$	3.50232	0.114907	0.0574537	+	0.998348i	$0.481702\pi$
$930$	10.0156	0.328425
$931$	0	0
$932$	−12.7421	−0.417382
$933$	17.4860	0.572466
$934$	41.8364	1.36893
$935$	9.52375	0.311460
$936$	3.14710	0.102866
$937$	31.5255	1.02989	0.514946	−	0.857222i	$-0.327812\pi$
$937$	31.5255	1.02989	0.514946	+	0.857222i	$0.327812\pi$
$938$	0	0
$939$	27.3870	0.893740
$940$	2.11716	0.0690540
$941$	−38.5977	−1.25825	−0.629124	−	0.777305i	$-0.716586\pi$
$941$	−38.5977	−1.25825	−0.629124	+	0.777305i	$0.716586\pi$
$942$	−12.7409	−0.415121
$943$	4.61988	0.150444
$944$	−3.42975	−0.111629
$945$	0	0
$946$	10.2609	0.333610
$947$	−23.0815	−0.750047	−0.375023	−	0.927015i	$-0.622365\pi$
$947$	−23.0815	−0.750047	−0.375023	+	0.927015i	$0.622365\pi$
$948$	−2.92576	−0.0950242
$949$	−2.27258	−0.0737710
$950$	0.0651474	0.00211366
$951$	31.8861	1.03398
$952$	0	0
$953$	−0.506172	−0.0163965	−0.00819826	−	0.999966i	$-0.502610\pi$
$953$	−0.506172	−0.0163965	−0.00819826	+	0.999966i	$0.502610\pi$
$954$	−8.58268	−0.277875
$955$	−26.8762	−0.869694
$956$	−1.56649	−0.0506638
$957$	6.19448	0.200239
$958$	−39.4707	−1.27524
$959$	0	0
$960$	19.2734	0.622045
$961$	−15.9999	−0.516127
$962$	−10.7524	−0.346673
$963$	19.5498	0.629983
$964$	10.0103	0.322409
$965$	−20.6676	−0.665312
$966$	0	0
$967$	−48.6196	−1.56350	−0.781750	−	0.623592i	$-0.785673\pi$
$967$	−48.6196	−1.56350	−0.781750	+	0.623592i	$0.785673\pi$
$968$	18.2278	0.585864
$969$	−0.368026	−0.0118227
$970$	−1.08096	−0.0347076
$971$	3.29543	0.105755	0.0528777	−	0.998601i	$-0.483161\pi$
$971$	3.29543	0.105755	0.0528777	+	0.998601i	$0.483161\pi$
$972$	0.703600	0.0225680
$973$	0	0
$974$	27.7217	0.888260
$975$	−0.162023	−0.00518889
$976$	31.1937	0.998487
$977$	−3.50798	−0.112230	−0.0561151	−	0.998424i	$-0.517871\pi$
$977$	−3.50798	−0.112230	−0.0561151	+	0.998424i	$0.517871\pi$
$978$	−5.97589	−0.191088
$979$	−4.36280	−0.139436
$980$	0	0
$981$	17.4207	0.556199
$982$	26.9360	0.859562
$983$	22.3364	0.712422	0.356211	−	0.934406i	$-0.384068\pi$
$983$	22.3364	0.712422	0.356211	+	0.934406i	$0.384068\pi$
$984$	3.07831	0.0981328
$985$	−1.92174	−0.0612316
$986$	−1.74777	−0.0556605
$987$	0	0
$988$	0.259701	0.00826218
$989$	10.1211	0.321832
$990$	10.6377	0.338089
$991$	53.4713	1.69857	0.849286	−	0.527933i	$-0.177033\pi$
$991$	53.4713	1.69857	0.849286	+	0.527933i	$0.177033\pi$
$992$	14.5939	0.463358
$993$	16.1121	0.511302
$994$	0	0
$995$	8.78352	0.278456
$996$	−1.08161	−0.0342723
$997$	−41.4921	−1.31407	−0.657033	−	0.753862i	$-0.728189\pi$
$997$	−41.4921	−1.31407	−0.657033	+	0.753862i	$0.728189\pi$
$998$	−35.8372	−1.13441
$999$	−9.23719	−0.292252

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bb.1.4		8
7.2	even	3		861.2.i.d.739.5	yes	16
7.4	even	3		861.2.i.d.247.5	✓	16
7.6	odd	2		6027.2.a.bc.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.d.247.5	✓	16	7.4	even	3
861.2.i.d.739.5	yes	16	7.2	even	3
6027.2.a.bb.1.4		8	1.1	even	1	trivial
6027.2.a.bc.1.4		8	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.13860 q^{2} -1.00000 q^{3} -0.703600 q^{4} -2.27123 q^{5} +1.13860 q^{6} +3.07831 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.13860 q^{2} -1.00000 q^{3} -0.703600 q^{4} -2.27123 q^{5} +1.13860 q^{6} +3.07831 q^{8} +1.00000 q^{9} +2.58601 q^{10} +4.11356 q^{11} +0.703600 q^{12} +1.02235 q^{13} +2.27123 q^{15} -2.09775 q^{16} -1.01936 q^{17} -1.13860 q^{18} -0.361035 q^{19} +1.59804 q^{20} -4.68368 q^{22} -4.61988 q^{23} -3.07831 q^{24} +0.158481 q^{25} -1.16404 q^{26} -1.00000 q^{27} -1.50587 q^{29} -2.58601 q^{30} -3.87299 q^{31} -3.76813 q^{32} -4.11356 q^{33} +1.16064 q^{34} -0.703600 q^{36} +9.23719 q^{37} +0.411073 q^{38} -1.02235 q^{39} -6.99154 q^{40} -1.00000 q^{41} -2.19077 q^{43} -2.89430 q^{44} -2.27123 q^{45} +5.26018 q^{46} +1.32485 q^{47} +2.09775 q^{48} -0.180446 q^{50} +1.01936 q^{51} -0.719323 q^{52} +7.53796 q^{53} +1.13860 q^{54} -9.34284 q^{55} +0.361035 q^{57} +1.71458 q^{58} +1.63497 q^{59} -1.59804 q^{60} -14.8701 q^{61} +4.40977 q^{62} +8.48587 q^{64} -2.32198 q^{65} +4.68368 q^{66} +5.38619 q^{67} +0.717224 q^{68} +4.61988 q^{69} -1.61302 q^{71} +3.07831 q^{72} -2.22290 q^{73} -10.5174 q^{74} -0.158481 q^{75} +0.254024 q^{76} +1.16404 q^{78} -4.15827 q^{79} +4.76446 q^{80} +1.00000 q^{81} +1.13860 q^{82} -1.53726 q^{83} +2.31521 q^{85} +2.49440 q^{86} +1.50587 q^{87} +12.6628 q^{88} -1.06059 q^{89} +2.58601 q^{90} +3.25055 q^{92} +3.87299 q^{93} -1.50847 q^{94} +0.819993 q^{95} +3.76813 q^{96} -0.418003 q^{97} +4.11356 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 8 q^{3} + 13 q^{4} - 7 q^{5} - q^{6} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + q^2 - 8 * q^3 + 13 * q^4 - 7 * q^5 - q^6 + 6 * q^8 + 8 * q^9	\( 8 q + q^{2} - 8 q^{3} + 13 q^{4} - 7 q^{5} - q^{6} + 6 q^{8} + 8 q^{9} - 8 q^{10} + 11 q^{11} - 13 q^{12} - 10 q^{13} + 7 q^{15} - 17 q^{16} - 3 q^{17} + q^{18} - 6 q^{19} - 11 q^{20} + 15 q^{22} + 14 q^{23} - 6 q^{24} + 25 q^{25} - 24 q^{26} - 8 q^{27} + 2 q^{29} + 8 q^{30} - 16 q^{31} + 3 q^{32} - 11 q^{33} + 4 q^{34} + 13 q^{36} - 20 q^{37} - 10 q^{38} + 10 q^{39} + 3 q^{40} - 8 q^{41} + 7 q^{43} - 7 q^{45} - 5 q^{46} - 14 q^{47} + 17 q^{48} - 5 q^{50} + 3 q^{51} - 23 q^{52} + 7 q^{53} - q^{54} - 48 q^{55} + 6 q^{57} - 20 q^{58} - 22 q^{59} + 11 q^{60} + 33 q^{62} - 10 q^{64} - 14 q^{65} - 15 q^{66} + 12 q^{67} + 27 q^{68} - 14 q^{69} - 5 q^{71} + 6 q^{72} - 2 q^{73} + 6 q^{74} - 25 q^{75} - 43 q^{76} + 24 q^{78} - 15 q^{79} + 7 q^{80} + 8 q^{81} - q^{82} - 15 q^{83} - 43 q^{85} + 31 q^{86} - 2 q^{87} + 17 q^{88} - 29 q^{89} - 8 q^{90} + 19 q^{92} + 16 q^{93} - 20 q^{94} + 14 q^{95} - 3 q^{96} - 19 q^{97} + 11 q^{99}+O(q^{100}) \) 8 * q + q^2 - 8 * q^3 + 13 * q^4 - 7 * q^5 - q^6 + 6 * q^8 + 8 * q^9 - 8 * q^10 + 11 * q^11 - 13 * q^12 - 10 * q^13 + 7 * q^15 - 17 * q^16 - 3 * q^17 + q^18 - 6 * q^19 - 11 * q^20 + 15 * q^22 + 14 * q^23 - 6 * q^24 + 25 * q^25 - 24 * q^26 - 8 * q^27 + 2 * q^29 + 8 * q^30 - 16 * q^31 + 3 * q^32 - 11 * q^33 + 4 * q^34 + 13 * q^36 - 20 * q^37 - 10 * q^38 + 10 * q^39 + 3 * q^40 - 8 * q^41 + 7 * q^43 - 7 * q^45 - 5 * q^46 - 14 * q^47 + 17 * q^48 - 5 * q^50 + 3 * q^51 - 23 * q^52 + 7 * q^53 - q^54 - 48 * q^55 + 6 * q^57 - 20 * q^58 - 22 * q^59 + 11 * q^60 + 33 * q^62 - 10 * q^64 - 14 * q^65 - 15 * q^66 + 12 * q^67 + 27 * q^68 - 14 * q^69 - 5 * q^71 + 6 * q^72 - 2 * q^73 + 6 * q^74 - 25 * q^75 - 43 * q^76 + 24 * q^78 - 15 * q^79 + 7 * q^80 + 8 * q^81 - q^82 - 15 * q^83 - 43 * q^85 + 31 * q^86 - 2 * q^87 + 17 * q^88 - 29 * q^89 - 8 * q^90 + 19 * q^92 + 16 * q^93 - 20 * q^94 + 14 * q^95 - 3 * q^96 - 19 * q^97 + 11 * q^99

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