LMFDB - Embedded newform 931.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(1,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("931.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.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:	$7.43407242818$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 133)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	931.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.381966 q^{2} +0.381966 q^{3} -1.85410 q^{4} +2.23607 q^{5} -0.145898 q^{6} +1.47214 q^{8} -2.85410 q^{9} +O(q^{10})$	\(q-0.381966 q^{2} +0.381966 q^{3} -1.85410 q^{4} +2.23607 q^{5} -0.145898 q^{6} +1.47214 q^{8} -2.85410 q^{9} -0.854102 q^{10} -3.38197 q^{11} -0.708204 q^{12} -1.00000 q^{13} +0.854102 q^{15} +3.14590 q^{16} -1.85410 q^{17} +1.09017 q^{18} +1.00000 q^{19} -4.14590 q^{20} +1.29180 q^{22} -3.00000 q^{23} +0.562306 q^{24} +0.381966 q^{26} -2.23607 q^{27} -3.38197 q^{29} -0.326238 q^{30} -5.85410 q^{31} -4.14590 q^{32} -1.29180 q^{33} +0.708204 q^{34} +5.29180 q^{36} +2.70820 q^{37} -0.381966 q^{38} -0.381966 q^{39} +3.29180 q^{40} -2.61803 q^{41} -2.00000 q^{43} +6.27051 q^{44} -6.38197 q^{45} +1.14590 q^{46} +11.1803 q^{47} +1.20163 q^{48} -0.708204 q^{51} +1.85410 q^{52} -10.0902 q^{53} +0.854102 q^{54} -7.56231 q^{55} +0.381966 q^{57} +1.29180 q^{58} +12.7082 q^{59} -1.58359 q^{60} -6.70820 q^{61} +2.23607 q^{62} -4.70820 q^{64} -2.23607 q^{65} +0.493422 q^{66} -13.5623 q^{67} +3.43769 q^{68} -1.14590 q^{69} -1.47214 q^{71} -4.20163 q^{72} -10.8541 q^{73} -1.03444 q^{74} -1.85410 q^{76} +0.145898 q^{78} -10.0000 q^{79} +7.03444 q^{80} +7.70820 q^{81} +1.00000 q^{82} +1.14590 q^{83} -4.14590 q^{85} +0.763932 q^{86} -1.29180 q^{87} -4.97871 q^{88} -15.7082 q^{89} +2.43769 q^{90} +5.56231 q^{92} -2.23607 q^{93} -4.27051 q^{94} +2.23607 q^{95} -1.58359 q^{96} +12.4164 q^{97} +9.65248 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 7 q^{6} - 6 q^{8} + q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 7 * q^6 - 6 * q^8 + q^9	$ 2 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 7 q^{6} - 6 q^{8} + q^{9} + 5 q^{10} - 9 q^{11} + 12 q^{12} - 2 q^{13} - 5 q^{15} + 13 q^{16} + 3 q^{17} - 9 q^{18} + 2 q^{19} - 15 q^{20} + 16 q^{22} - 6 q^{23} - 19 q^{24} + 3 q^{26} - 9 q^{29} + 15 q^{30} - 5 q^{31} - 15 q^{32} - 16 q^{33} - 12 q^{34} + 24 q^{36} - 8 q^{37} - 3 q^{38} - 3 q^{39} + 20 q^{40} - 3 q^{41} - 4 q^{43} - 21 q^{44} - 15 q^{45} + 9 q^{46} + 27 q^{48} + 12 q^{51} - 3 q^{52} - 9 q^{53} - 5 q^{54} + 5 q^{55} + 3 q^{57} + 16 q^{58} + 12 q^{59} - 30 q^{60} + 4 q^{64} + 39 q^{66} - 7 q^{67} + 27 q^{68} - 9 q^{69} + 6 q^{71} - 33 q^{72} - 15 q^{73} + 27 q^{74} + 3 q^{76} + 7 q^{78} - 20 q^{79} - 15 q^{80} + 2 q^{81} + 2 q^{82} + 9 q^{83} - 15 q^{85} + 6 q^{86} - 16 q^{87} + 37 q^{88} - 18 q^{89} + 25 q^{90} - 9 q^{92} + 25 q^{94} - 30 q^{96} - 2 q^{97} - 12 q^{99}+O(q^{100}) $ 2 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 7 * q^6 - 6 * q^8 + q^9 + 5 * q^10 - 9 * q^11 + 12 * q^12 - 2 * q^13 - 5 * q^15 + 13 * q^16 + 3 * q^17 - 9 * q^18 + 2 * q^19 - 15 * q^20 + 16 * q^22 - 6 * q^23 - 19 * q^24 + 3 * q^26 - 9 * q^29 + 15 * q^30 - 5 * q^31 - 15 * q^32 - 16 * q^33 - 12 * q^34 + 24 * q^36 - 8 * q^37 - 3 * q^38 - 3 * q^39 + 20 * q^40 - 3 * q^41 - 4 * q^43 - 21 * q^44 - 15 * q^45 + 9 * q^46 + 27 * q^48 + 12 * q^51 - 3 * q^52 - 9 * q^53 - 5 * q^54 + 5 * q^55 + 3 * q^57 + 16 * q^58 + 12 * q^59 - 30 * q^60 + 4 * q^64 + 39 * q^66 - 7 * q^67 + 27 * q^68 - 9 * q^69 + 6 * q^71 - 33 * q^72 - 15 * q^73 + 27 * q^74 + 3 * q^76 + 7 * q^78 - 20 * q^79 - 15 * q^80 + 2 * q^81 + 2 * q^82 + 9 * q^83 - 15 * q^85 + 6 * q^86 - 16 * q^87 + 37 * q^88 - 18 * q^89 + 25 * q^90 - 9 * q^92 + 25 * q^94 - 30 * q^96 - 2 * q^97 - 12 * 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 $

$2$	−0.381966	−0.270091	−0.135045	−	0.990839i	$-0.543118\pi$
$2$	−0.381966	−0.270091	−0.135045	+	0.990839i	$0.543118\pi$
$3$	0.381966	0.220528	0.110264	−	0.993902i	$-0.464830\pi$
$3$	0.381966	0.220528	0.110264	+	0.993902i	$0.464830\pi$
$4$	−1.85410	−0.927051
$5$	2.23607	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$5$	2.23607	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$6$	−0.145898	−0.0595626
$7$	0	0
$7$	0	0
$8$	1.47214	0.520479
$9$	−2.85410	−0.951367
$10$	−0.854102	−0.270091
$11$	−3.38197	−1.01970	−0.509851	−	0.860263i	$-0.670299\pi$
$11$	−3.38197	−1.01970	−0.509851	+	0.860263i	$0.670299\pi$
$12$	−0.708204	−0.204441
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	0	0
$15$	0.854102	0.220528
$16$	3.14590	0.786475
$17$	−1.85410	−0.449686	−0.224843	−	0.974395i	$-0.572187\pi$
$17$	−1.85410	−0.449686	−0.224843	+	0.974395i	$0.572187\pi$
$18$	1.09017	0.256956
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−4.14590	−0.927051
$21$	0	0
$22$	1.29180	0.275412
$23$	−3.00000	−0.625543	−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000	−0.625543	−0.312772	+	0.949828i	$0.601257\pi$
$24$	0.562306	0.114780
$25$	0	0
$26$	0.381966	0.0749097
$27$	−2.23607	−0.430331
$28$	0	0
$29$	−3.38197	−0.628015	−0.314008	−	0.949420i	$-0.601672\pi$
$29$	−3.38197	−0.628015	−0.314008	+	0.949420i	$0.601672\pi$
$30$	−0.326238	−0.0595626
$31$	−5.85410	−1.05143	−0.525714	−	0.850661i	$-0.676202\pi$
$31$	−5.85410	−1.05143	−0.525714	+	0.850661i	$0.676202\pi$
$32$	−4.14590	−0.732898
$33$	−1.29180	−0.224873
$34$	0.708204	0.121456
$35$	0	0
$36$	5.29180	0.881966
$37$	2.70820	0.445226	0.222613	−	0.974907i	$-0.428541\pi$
$37$	2.70820	0.445226	0.222613	+	0.974907i	$0.428541\pi$
$38$	−0.381966	−0.0619631
$39$	−0.381966	−0.0611635
$40$	3.29180	0.520479
$41$	−2.61803	−0.408868	−0.204434	−	0.978880i	$-0.565535\pi$
$41$	−2.61803	−0.408868	−0.204434	+	0.978880i	$0.565535\pi$
$42$	0	0
$43$	−2.00000	−0.304997	−0.152499	−	0.988304i	$-0.548732\pi$
$43$	−2.00000	−0.304997	−0.152499	+	0.988304i	$0.548732\pi$
$44$	6.27051	0.945315
$45$	−6.38197	−0.951367
$46$	1.14590	0.168953
$47$	11.1803	1.63082	0.815410	−	0.578884i	$-0.196511\pi$
$47$	11.1803	1.63082	0.815410	+	0.578884i	$0.196511\pi$
$48$	1.20163	0.173440
$49$	0	0
$50$	0	0
$51$	−0.708204	−0.0991684
$52$	1.85410	0.257118
$53$	−10.0902	−1.38599	−0.692996	−	0.720942i	$-0.743710\pi$
$53$	−10.0902	−1.38599	−0.692996	+	0.720942i	$0.743710\pi$
$54$	0.854102	0.116229
$55$	−7.56231	−1.01970
$56$	0	0
$57$	0.381966	0.0505926
$58$	1.29180	0.169621
$59$	12.7082	1.65447	0.827234	−	0.561858i	$-0.189913\pi$
$59$	12.7082	1.65447	0.827234	+	0.561858i	$0.189913\pi$
$60$	−1.58359	−0.204441
$61$	−6.70820	−0.858898	−0.429449	−	0.903091i	$-0.641292\pi$
$61$	−6.70820	−0.858898	−0.429449	+	0.903091i	$0.641292\pi$
$62$	2.23607	0.283981
$63$	0	0
$64$	−4.70820	−0.588525
$65$	−2.23607	−0.277350
$66$	0.493422	0.0607361
$67$	−13.5623	−1.65690	−0.828450	−	0.560063i	$-0.810777\pi$
$67$	−13.5623	−1.65690	−0.828450	+	0.560063i	$0.810777\pi$
$68$	3.43769	0.416882
$69$	−1.14590	−0.137950
$70$	0	0
$71$	−1.47214	−0.174710	−0.0873552	−	0.996177i	$-0.527842\pi$
$71$	−1.47214	−0.174710	−0.0873552	+	0.996177i	$0.527842\pi$
$72$	−4.20163	−0.495166
$73$	−10.8541	−1.27038	−0.635188	−	0.772357i	$-0.719077\pi$
$73$	−10.8541	−1.27038	−0.635188	+	0.772357i	$0.719077\pi$
$74$	−1.03444	−0.120251
$75$	0	0
$76$	−1.85410	−0.212680
$77$	0	0
$78$	0.145898	0.0165197
$79$	−10.0000	−1.12509	−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000	−1.12509	−0.562544	+	0.826767i	$0.690177\pi$
$80$	7.03444	0.786475
$81$	7.70820	0.856467
$82$	1.00000	0.110432
$83$	1.14590	0.125779	0.0628893	−	0.998021i	$-0.479968\pi$
$83$	1.14590	0.125779	0.0628893	+	0.998021i	$0.479968\pi$
$84$	0	0
$85$	−4.14590	−0.449686
$86$	0.763932	0.0823769
$87$	−1.29180	−0.138495
$88$	−4.97871	−0.530733
$89$	−15.7082	−1.66507	−0.832533	−	0.553975i	$-0.813110\pi$
$89$	−15.7082	−1.66507	−0.832533	+	0.553975i	$0.813110\pi$
$90$	2.43769	0.256956
$91$	0	0
$92$	5.56231	0.579910
$93$	−2.23607	−0.231869
$94$	−4.27051	−0.440469
$95$	2.23607	0.229416
$96$	−1.58359	−0.161625
$97$	12.4164	1.26070	0.630348	−	0.776313i	$-0.282912\pi$
$97$	12.4164	1.26070	0.630348	+	0.776313i	$0.282912\pi$
$98$	0	0
$99$	9.65248	0.970110
$100$	0	0
$101$	−4.52786	−0.450539	−0.225270	−	0.974296i	$-0.572326\pi$
$101$	−4.52786	−0.450539	−0.225270	+	0.974296i	$0.572326\pi$
$102$	0.270510	0.0267845
$103$	−8.70820	−0.858045	−0.429022	−	0.903294i	$-0.641142\pi$
$103$	−8.70820	−0.858045	−0.429022	+	0.903294i	$0.641142\pi$
$104$	−1.47214	−0.144355
$105$	0	0
$106$	3.85410	0.374343
$107$	−7.47214	−0.722359	−0.361179	−	0.932496i	$-0.617626\pi$
$107$	−7.47214	−0.722359	−0.361179	+	0.932496i	$0.617626\pi$
$108$	4.14590	0.398939
$109$	16.4164	1.57241	0.786203	−	0.617968i	$-0.212044\pi$
$109$	16.4164	1.57241	0.786203	+	0.617968i	$0.212044\pi$
$110$	2.88854	0.275412
$111$	1.03444	0.0981849
$112$	0	0
$113$	−10.8541	−1.02107	−0.510534	−	0.859858i	$-0.670552\pi$
$113$	−10.8541	−1.02107	−0.510534	+	0.859858i	$0.670552\pi$
$114$	−0.145898	−0.0136646
$115$	−6.70820	−0.625543
$116$	6.27051	0.582202
$117$	2.85410	0.263862
$118$	−4.85410	−0.446856
$119$	0	0
$120$	1.25735	0.114780
$121$	0.437694	0.0397904
$122$	2.56231	0.231980
$123$	−1.00000	−0.0901670
$124$	10.8541	0.974727
$125$	−11.1803	−1.00000
$126$	0	0
$127$	19.7082	1.74882	0.874410	−	0.485187i	$-0.161249\pi$
$127$	19.7082	1.74882	0.874410	+	0.485187i	$0.161249\pi$
$128$	10.0902	0.891853
$129$	−0.763932	−0.0672605
$130$	0.854102	0.0749097
$131$	1.09017	0.0952486	0.0476243	−	0.998865i	$-0.484835\pi$
$131$	1.09017	0.0952486	0.0476243	+	0.998865i	$0.484835\pi$
$132$	2.39512	0.208469
$133$	0	0
$134$	5.18034	0.447513
$135$	−5.00000	−0.430331
$136$	−2.72949	−0.234052
$137$	7.52786	0.643149	0.321574	−	0.946884i	$-0.395788\pi$
$137$	7.52786	0.643149	0.321574	+	0.946884i	$0.395788\pi$
$138$	0.437694	0.0372590
$139$	20.7082	1.75645	0.878223	−	0.478251i	$-0.158729\pi$
$139$	20.7082	1.75645	0.878223	+	0.478251i	$0.158729\pi$
$140$	0	0
$141$	4.27051	0.359642
$142$	0.562306	0.0471877
$143$	3.38197	0.282814
$144$	−8.97871	−0.748226
$145$	−7.56231	−0.628015
$146$	4.14590	0.343117
$147$	0	0
$148$	−5.02129	−0.412747
$149$	20.8885	1.71126	0.855628	−	0.517591i	$-0.173171\pi$
$149$	20.8885	1.71126	0.855628	+	0.517591i	$0.173171\pi$
$150$	0	0
$151$	21.5623	1.75472	0.877358	−	0.479837i	$-0.159304\pi$
$151$	21.5623	1.75472	0.877358	+	0.479837i	$0.159304\pi$
$152$	1.47214	0.119406
$153$	5.29180	0.427816
$154$	0	0
$155$	−13.0902	−1.05143
$156$	0.708204	0.0567017
$157$	7.85410	0.626826	0.313413	−	0.949617i	$-0.398528\pi$
$157$	7.85410	0.626826	0.313413	+	0.949617i	$0.398528\pi$
$158$	3.81966	0.303876
$159$	−3.85410	−0.305650
$160$	−9.27051	−0.732898
$161$	0	0
$162$	−2.94427	−0.231324
$163$	−9.14590	−0.716362	−0.358181	−	0.933652i	$-0.616603\pi$
$163$	−9.14590	−0.716362	−0.358181	+	0.933652i	$0.616603\pi$
$164$	4.85410	0.379042
$165$	−2.88854	−0.224873
$166$	−0.437694	−0.0339717
$167$	−1.47214	−0.113917	−0.0569587	−	0.998377i	$-0.518140\pi$
$167$	−1.47214	−0.113917	−0.0569587	+	0.998377i	$0.518140\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	1.58359	0.121456
$171$	−2.85410	−0.218259
$172$	3.70820	0.282748
$173$	−2.18034	−0.165768	−0.0828841	−	0.996559i	$-0.526413\pi$
$173$	−2.18034	−0.165768	−0.0828841	+	0.996559i	$0.526413\pi$
$174$	0.493422	0.0374062
$175$	0	0
$176$	−10.6393	−0.801969
$177$	4.85410	0.364857
$178$	6.00000	0.449719
$179$	1.09017	0.0814831	0.0407416	−	0.999170i	$-0.487028\pi$
$179$	1.09017	0.0814831	0.0407416	+	0.999170i	$0.487028\pi$
$180$	11.8328	0.881966
$181$	21.5623	1.60271	0.801357	−	0.598187i	$-0.204112\pi$
$181$	21.5623	1.60271	0.801357	+	0.598187i	$0.204112\pi$
$182$	0	0
$183$	−2.56231	−0.189411
$184$	−4.41641	−0.325582
$185$	6.05573	0.445226
$186$	0.854102	0.0626258
$187$	6.27051	0.458545
$188$	−20.7295	−1.51185
$189$	0	0
$190$	−0.854102	−0.0619631
$191$	9.32624	0.674823	0.337411	−	0.941357i	$-0.390449\pi$
$191$	9.32624	0.674823	0.337411	+	0.941357i	$0.390449\pi$
$192$	−1.79837	−0.129786
$193$	−1.56231	−0.112457	−0.0562286	−	0.998418i	$-0.517908\pi$
$193$	−1.56231	−0.112457	−0.0562286	+	0.998418i	$0.517908\pi$
$194$	−4.74265	−0.340502
$195$	−0.854102	−0.0611635
$196$	0	0
$197$	−18.2705	−1.30172	−0.650860	−	0.759198i	$-0.725592\pi$
$197$	−18.2705	−1.30172	−0.650860	+	0.759198i	$0.725592\pi$
$198$	−3.68692	−0.262018
$199$	−3.29180	−0.233349	−0.116675	−	0.993170i	$-0.537223\pi$
$199$	−3.29180	−0.233349	−0.116675	+	0.993170i	$0.537223\pi$
$200$	0	0
$201$	−5.18034	−0.365393
$202$	1.72949	0.121687
$203$	0	0
$204$	1.31308	0.0919341
$205$	−5.85410	−0.408868
$206$	3.32624	0.231750
$207$	8.56231	0.595121
$208$	−3.14590	−0.218129
$209$	−3.38197	−0.233935
$210$	0	0
$211$	−6.56231	−0.451768	−0.225884	−	0.974154i	$-0.572527\pi$
$211$	−6.56231	−0.451768	−0.225884	+	0.974154i	$0.572527\pi$
$212$	18.7082	1.28488
$213$	−0.562306	−0.0385286
$214$	2.85410	0.195102
$215$	−4.47214	−0.304997
$216$	−3.29180	−0.223978
$217$	0	0
$218$	−6.27051	−0.424693
$219$	−4.14590	−0.280154
$220$	14.0213	0.945315
$221$	1.85410	0.124720
$222$	−0.395122	−0.0265188
$223$	26.4164	1.76897	0.884487	−	0.466565i	$-0.154509\pi$
$223$	26.4164	1.76897	0.884487	+	0.466565i	$0.154509\pi$
$224$	0	0
$225$	0	0
$226$	4.14590	0.275781
$227$	20.6180	1.36847	0.684233	−	0.729263i	$-0.260137\pi$
$227$	20.6180	1.36847	0.684233	+	0.729263i	$0.260137\pi$
$228$	−0.708204	−0.0469020
$229$	9.41641	0.622254	0.311127	−	0.950368i	$-0.399294\pi$
$229$	9.41641	0.622254	0.311127	+	0.950368i	$0.399294\pi$
$230$	2.56231	0.168953
$231$	0	0
$232$	−4.97871	−0.326869
$233$	−16.0344	−1.05045	−0.525226	−	0.850963i	$-0.676019\pi$
$233$	−16.0344	−1.05045	−0.525226	+	0.850963i	$0.676019\pi$
$234$	−1.09017	−0.0712666
$235$	25.0000	1.63082
$236$	−23.5623	−1.53378
$237$	−3.81966	−0.248114
$238$	0	0
$239$	13.4721	0.871440	0.435720	−	0.900082i	$-0.356494\pi$
$239$	13.4721	0.871440	0.435720	+	0.900082i	$0.356494\pi$
$240$	2.68692	0.173440
$241$	17.7082	1.14069	0.570343	−	0.821407i	$-0.306810\pi$
$241$	17.7082	1.14069	0.570343	+	0.821407i	$0.306810\pi$
$242$	−0.167184	−0.0107470
$243$	9.65248	0.619207
$244$	12.4377	0.796242
$245$	0	0
$246$	0.381966	0.0243533
$247$	−1.00000	−0.0636285
$248$	−8.61803	−0.547246
$249$	0.437694	0.0277377
$250$	4.27051	0.270091
$251$	−1.20163	−0.0758460	−0.0379230	−	0.999281i	$-0.512074\pi$
$251$	−1.20163	−0.0758460	−0.0379230	+	0.999281i	$0.512074\pi$
$252$	0	0
$253$	10.1459	0.637867
$254$	−7.52786	−0.472340
$255$	−1.58359	−0.0991684
$256$	5.56231	0.347644
$257$	−27.9787	−1.74526	−0.872632	−	0.488378i	$-0.837589\pi$
$257$	−27.9787	−1.74526	−0.872632	+	0.488378i	$0.837589\pi$
$258$	0.291796	0.0181664
$259$	0	0
$260$	4.14590	0.257118
$261$	9.65248	0.597473
$262$	−0.416408	−0.0257258
$263$	−3.43769	−0.211977	−0.105989	−	0.994367i	$-0.533801\pi$
$263$	−3.43769	−0.211977	−0.105989	+	0.994367i	$0.533801\pi$
$264$	−1.90170	−0.117042
$265$	−22.5623	−1.38599
$266$	0	0
$267$	−6.00000	−0.367194
$268$	25.1459	1.53603
$269$	−14.5623	−0.887879	−0.443940	−	0.896057i	$-0.646420\pi$
$269$	−14.5623	−0.887879	−0.443940	+	0.896057i	$0.646420\pi$
$270$	1.90983	0.116229
$271$	−19.2705	−1.17060	−0.585300	−	0.810817i	$-0.699023\pi$
$271$	−19.2705	−1.17060	−0.585300	+	0.810817i	$0.699023\pi$
$272$	−5.83282	−0.353666
$273$	0	0
$274$	−2.87539	−0.173709
$275$	0	0
$276$	2.12461	0.127887
$277$	−17.7082	−1.06398	−0.531991	−	0.846750i	$-0.678556\pi$
$277$	−17.7082	−1.06398	−0.531991	+	0.846750i	$0.678556\pi$
$278$	−7.90983	−0.474400
$279$	16.7082	1.00029
$280$	0	0
$281$	−8.88854	−0.530246	−0.265123	−	0.964215i	$-0.585413\pi$
$281$	−8.88854	−0.530246	−0.265123	+	0.964215i	$0.585413\pi$
$282$	−1.63119	−0.0971359
$283$	−8.56231	−0.508976	−0.254488	−	0.967076i	$-0.581907\pi$
$283$	−8.56231	−0.508976	−0.254488	+	0.967076i	$0.581907\pi$
$284$	2.72949	0.161965
$285$	0.854102	0.0505926
$286$	−1.29180	−0.0763855
$287$	0	0
$288$	11.8328	0.697255
$289$	−13.5623	−0.797783
$290$	2.88854	0.169621
$291$	4.74265	0.278019
$292$	20.1246	1.17770
$293$	12.7082	0.742421	0.371211	−	0.928549i	$-0.378943\pi$
$293$	12.7082	0.742421	0.371211	+	0.928549i	$0.378943\pi$
$294$	0	0
$295$	28.4164	1.65447
$296$	3.98684	0.231731
$297$	7.56231	0.438809
$298$	−7.97871	−0.462194
$299$	3.00000	0.173494
$300$	0	0
$301$	0	0
$302$	−8.23607	−0.473932
$303$	−1.72949	−0.0993566
$304$	3.14590	0.180430
$305$	−15.0000	−0.858898
$306$	−2.02129	−0.115549
$307$	2.43769	0.139127	0.0695633	−	0.997578i	$-0.477839\pi$
$307$	2.43769	0.139127	0.0695633	+	0.997578i	$0.477839\pi$
$308$	0	0
$309$	−3.32624	−0.189223
$310$	5.00000	0.283981
$311$	−4.90983	−0.278411	−0.139205	−	0.990264i	$-0.544455\pi$
$311$	−4.90983	−0.278411	−0.139205	+	0.990264i	$0.544455\pi$
$312$	−0.562306	−0.0318343
$313$	2.29180	0.129540	0.0647700	−	0.997900i	$-0.479369\pi$
$313$	2.29180	0.129540	0.0647700	+	0.997900i	$0.479369\pi$
$314$	−3.00000	−0.169300
$315$	0	0
$316$	18.5410	1.04301
$317$	25.4164	1.42753	0.713764	−	0.700386i	$-0.246989\pi$
$317$	25.4164	1.42753	0.713764	+	0.700386i	$0.246989\pi$
$318$	1.47214	0.0825533
$319$	11.4377	0.640388
$320$	−10.5279	−0.588525
$321$	−2.85410	−0.159300
$322$	0	0
$323$	−1.85410	−0.103165
$324$	−14.2918	−0.793989
$325$	0	0
$326$	3.49342	0.193483
$327$	6.27051	0.346760
$328$	−3.85410	−0.212807
$329$	0	0
$330$	1.10333	0.0607361
$331$	−1.43769	−0.0790228	−0.0395114	−	0.999219i	$-0.512580\pi$
$331$	−1.43769	−0.0790228	−0.0395114	+	0.999219i	$0.512580\pi$
$332$	−2.12461	−0.116603
$333$	−7.72949	−0.423573
$334$	0.562306	0.0307680
$335$	−30.3262	−1.65690
$336$	0	0
$337$	11.2705	0.613944	0.306972	−	0.951719i	$-0.400684\pi$
$337$	11.2705	0.613944	0.306972	+	0.951719i	$0.400684\pi$
$338$	4.58359	0.249315
$339$	−4.14590	−0.225174
$340$	7.68692	0.416882
$341$	19.7984	1.07214
$342$	1.09017	0.0589496
$343$	0	0
$344$	−2.94427	−0.158745
$345$	−2.56231	−0.137950
$346$	0.832816	0.0447725
$347$	−9.43769	−0.506642	−0.253321	−	0.967382i	$-0.581523\pi$
$347$	−9.43769	−0.506642	−0.253321	+	0.967382i	$0.581523\pi$
$348$	2.39512	0.128392
$349$	−24.2705	−1.29917	−0.649585	−	0.760289i	$-0.725057\pi$
$349$	−24.2705	−1.29917	−0.649585	+	0.760289i	$0.725057\pi$
$350$	0	0
$351$	2.23607	0.119352
$352$	14.0213	0.747337
$353$	−9.38197	−0.499352	−0.249676	−	0.968329i	$-0.580324\pi$
$353$	−9.38197	−0.499352	−0.249676	+	0.968329i	$0.580324\pi$
$354$	−1.85410	−0.0985444
$355$	−3.29180	−0.174710
$356$	29.1246	1.54360
$357$	0	0
$358$	−0.416408	−0.0220078
$359$	−31.7426	−1.67531	−0.837656	−	0.546198i	$-0.816075\pi$
$359$	−31.7426	−1.67531	−0.837656	+	0.546198i	$0.816075\pi$
$360$	−9.39512	−0.495166
$361$	1.00000	0.0526316
$362$	−8.23607	−0.432878
$363$	0.167184	0.00877490
$364$	0	0
$365$	−24.2705	−1.27038
$366$	0.978714	0.0511582
$367$	13.0000	0.678594	0.339297	−	0.940679i	$-0.389811\pi$
$367$	13.0000	0.678594	0.339297	+	0.940679i	$0.389811\pi$
$368$	−9.43769	−0.491974
$369$	7.47214	0.388984
$370$	−2.31308	−0.120251
$371$	0	0
$372$	4.14590	0.214955
$373$	−34.2705	−1.77446	−0.887230	−	0.461328i	$-0.847373\pi$
$373$	−34.2705	−1.77446	−0.887230	+	0.461328i	$0.847373\pi$
$374$	−2.39512	−0.123849
$375$	−4.27051	−0.220528
$376$	16.4590	0.848807
$377$	3.38197	0.174180
$378$	0	0
$379$	17.2918	0.888220	0.444110	−	0.895972i	$-0.353520\pi$
$379$	17.2918	0.888220	0.444110	+	0.895972i	$0.353520\pi$
$380$	−4.14590	−0.212680
$381$	7.52786	0.385664
$382$	−3.56231	−0.182263
$383$	15.7639	0.805499	0.402750	−	0.915310i	$-0.368055\pi$
$383$	15.7639	0.805499	0.402750	+	0.915310i	$0.368055\pi$
$384$	3.85410	0.196679
$385$	0	0
$386$	0.596748	0.0303737
$387$	5.70820	0.290164
$388$	−23.0213	−1.16873
$389$	10.7984	0.547499	0.273750	−	0.961801i	$-0.411736\pi$
$389$	10.7984	0.547499	0.273750	+	0.961801i	$0.411736\pi$
$390$	0.326238	0.0165197
$391$	5.56231	0.281298
$392$	0	0
$393$	0.416408	0.0210050
$394$	6.97871	0.351583
$395$	−22.3607	−1.12509
$396$	−17.8967	−0.899342
$397$	34.5410	1.73356	0.866782	−	0.498687i	$-0.166184\pi$
$397$	34.5410	1.73356	0.866782	+	0.498687i	$0.166184\pi$
$398$	1.25735	0.0630255
$399$	0	0
$400$	0	0
$401$	−8.61803	−0.430364	−0.215182	−	0.976574i	$-0.569034\pi$
$401$	−8.61803	−0.430364	−0.215182	+	0.976574i	$0.569034\pi$
$402$	1.97871	0.0986893
$403$	5.85410	0.291614
$404$	8.39512	0.417673
$405$	17.2361	0.856467
$406$	0	0
$407$	−9.15905	−0.453997
$408$	−1.04257	−0.0516150
$409$	5.14590	0.254448	0.127224	−	0.991874i	$-0.459393\pi$
$409$	5.14590	0.254448	0.127224	+	0.991874i	$0.459393\pi$
$410$	2.23607	0.110432
$411$	2.87539	0.141832
$412$	16.1459	0.795451
$413$	0	0
$414$	−3.27051	−0.160737
$415$	2.56231	0.125779
$416$	4.14590	0.203269
$417$	7.90983	0.387346
$418$	1.29180	0.0631838
$419$	23.2918	1.13788	0.568939	−	0.822379i	$-0.307354\pi$
$419$	23.2918	1.13788	0.568939	+	0.822379i	$0.307354\pi$
$420$	0	0
$421$	−21.2918	−1.03770	−0.518849	−	0.854866i	$-0.673639\pi$
$421$	−21.2918	−1.03770	−0.518849	+	0.854866i	$0.673639\pi$
$422$	2.50658	0.122018
$423$	−31.9098	−1.55151
$424$	−14.8541	−0.721379
$425$	0	0
$426$	0.214782	0.0104062
$427$	0	0
$428$	13.8541	0.669663
$429$	1.29180	0.0623685
$430$	1.70820	0.0823769
$431$	−22.3607	−1.07708	−0.538538	−	0.842601i	$-0.681023\pi$
$431$	−22.3607	−1.07708	−0.538538	+	0.842601i	$0.681023\pi$
$432$	−7.03444	−0.338445
$433$	−31.5410	−1.51576	−0.757882	−	0.652391i	$-0.773766\pi$
$433$	−31.5410	−1.51576	−0.757882	+	0.652391i	$0.773766\pi$
$434$	0	0
$435$	−2.88854	−0.138495
$436$	−30.4377	−1.45770
$437$	−3.00000	−0.143509
$438$	1.58359	0.0756670
$439$	−8.00000	−0.381819	−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000	−0.381819	−0.190910	+	0.981608i	$0.561144\pi$
$440$	−11.1327	−0.530733
$441$	0	0
$442$	−0.708204	−0.0336858
$443$	−12.3820	−0.588285	−0.294142	−	0.955762i	$-0.595034\pi$
$443$	−12.3820	−0.588285	−0.294142	+	0.955762i	$0.595034\pi$
$444$	−1.91796	−0.0910224
$445$	−35.1246	−1.66507
$446$	−10.0902	−0.477783
$447$	7.97871	0.377380
$448$	0	0
$449$	−14.6738	−0.692498	−0.346249	−	0.938143i	$-0.612545\pi$
$449$	−14.6738	−0.692498	−0.346249	+	0.938143i	$0.612545\pi$
$450$	0	0
$451$	8.85410	0.416923
$452$	20.1246	0.946582
$453$	8.23607	0.386964
$454$	−7.87539	−0.369610
$455$	0	0
$456$	0.562306	0.0263324
$457$	24.5623	1.14898	0.574488	−	0.818513i	$-0.305201\pi$
$457$	24.5623	1.14898	0.574488	+	0.818513i	$0.305201\pi$
$458$	−3.59675	−0.168065
$459$	4.14590	0.193514
$460$	12.4377	0.579910
$461$	−34.0902	−1.58774	−0.793869	−	0.608089i	$-0.791936\pi$
$461$	−34.0902	−1.58774	−0.793869	+	0.608089i	$0.791936\pi$
$462$	0	0
$463$	30.7082	1.42713	0.713566	−	0.700588i	$-0.247079\pi$
$463$	30.7082	1.42713	0.713566	+	0.700588i	$0.247079\pi$
$464$	−10.6393	−0.493918
$465$	−5.00000	−0.231869
$466$	6.12461	0.283717
$467$	−24.9230	−1.15330	−0.576649	−	0.816992i	$-0.695640\pi$
$467$	−24.9230	−1.15330	−0.576649	+	0.816992i	$0.695640\pi$
$468$	−5.29180	−0.244613
$469$	0	0
$470$	−9.54915	−0.440469
$471$	3.00000	0.138233
$472$	18.7082	0.861115
$473$	6.76393	0.311006
$474$	1.45898	0.0670132
$475$	0	0
$476$	0	0
$477$	28.7984	1.31859
$478$	−5.14590	−0.235368
$479$	−41.4508	−1.89394	−0.946969	−	0.321325i	$-0.895872\pi$
$479$	−41.4508	−1.89394	−0.946969	+	0.321325i	$0.895872\pi$
$480$	−3.54102	−0.161625
$481$	−2.70820	−0.123483
$482$	−6.76393	−0.308089
$483$	0	0
$484$	−0.811529	−0.0368877
$485$	27.7639	1.26070
$486$	−3.68692	−0.167242
$487$	9.58359	0.434274	0.217137	−	0.976141i	$-0.430328\pi$
$487$	9.58359	0.434274	0.217137	+	0.976141i	$0.430328\pi$
$488$	−9.87539	−0.447038
$489$	−3.49342	−0.157978
$490$	0	0
$491$	−10.4721	−0.472601	−0.236300	−	0.971680i	$-0.575935\pi$
$491$	−10.4721	−0.472601	−0.236300	+	0.971680i	$0.575935\pi$
$492$	1.85410	0.0835894
$493$	6.27051	0.282410
$494$	0.381966	0.0171855
$495$	21.5836	0.970110
$496$	−18.4164	−0.826921
$497$	0	0
$498$	−0.167184	−0.00749171
$499$	3.14590	0.140830	0.0704149	−	0.997518i	$-0.477568\pi$
$499$	3.14590	0.140830	0.0704149	+	0.997518i	$0.477568\pi$
$500$	20.7295	0.927051
$501$	−0.562306	−0.0251220
$502$	0.458980	0.0204853
$503$	−17.8885	−0.797611	−0.398805	−	0.917036i	$-0.630575\pi$
$503$	−17.8885	−0.797611	−0.398805	+	0.917036i	$0.630575\pi$
$504$	0	0
$505$	−10.1246	−0.450539
$506$	−3.87539	−0.172282
$507$	−4.58359	−0.203564
$508$	−36.5410	−1.62125
$509$	−30.0000	−1.32973	−0.664863	−	0.746965i	$-0.731510\pi$
$509$	−30.0000	−1.32973	−0.664863	+	0.746965i	$0.731510\pi$
$510$	0.604878	0.0267845
$511$	0	0
$512$	−22.3050	−0.985749
$513$	−2.23607	−0.0987248
$514$	10.6869	0.471380
$515$	−19.4721	−0.858045
$516$	1.41641	0.0623539
$517$	−37.8115	−1.66295
$518$	0	0
$519$	−0.832816	−0.0365566
$520$	−3.29180	−0.144355
$521$	32.2361	1.41229	0.706144	−	0.708068i	$-0.250433\pi$
$521$	32.2361	1.41229	0.706144	+	0.708068i	$0.250433\pi$
$522$	−3.68692	−0.161372
$523$	−13.5836	−0.593969	−0.296985	−	0.954882i	$-0.595981\pi$
$523$	−13.5836	−0.593969	−0.296985	+	0.954882i	$0.595981\pi$
$524$	−2.02129	−0.0883003
$525$	0	0
$526$	1.31308	0.0572531
$527$	10.8541	0.472812
$528$	−4.06386	−0.176857
$529$	−14.0000	−0.608696
$530$	8.61803	0.374343
$531$	−36.2705	−1.57401
$532$	0	0
$533$	2.61803	0.113400
$534$	2.29180	0.0991757
$535$	−16.7082	−0.722359
$536$	−19.9656	−0.862381
$537$	0.416408	0.0179693
$538$	5.56231	0.239808
$539$	0	0
$540$	9.27051	0.398939
$541$	13.4164	0.576816	0.288408	−	0.957508i	$-0.406874\pi$
$541$	13.4164	0.576816	0.288408	+	0.957508i	$0.406874\pi$
$542$	7.36068	0.316168
$543$	8.23607	0.353444
$544$	7.68692	0.329574
$545$	36.7082	1.57241
$546$	0	0
$547$	16.2705	0.695677	0.347838	−	0.937555i	$-0.386916\pi$
$547$	16.2705	0.695677	0.347838	+	0.937555i	$0.386916\pi$
$548$	−13.9574	−0.596232
$549$	19.1459	0.817127
$550$	0	0
$551$	−3.38197	−0.144077
$552$	−1.68692	−0.0718000
$553$	0	0
$554$	6.76393	0.287372
$555$	2.31308	0.0981849
$556$	−38.3951	−1.62832
$557$	−18.3262	−0.776508	−0.388254	−	0.921552i	$-0.626922\pi$
$557$	−18.3262	−0.776508	−0.388254	+	0.921552i	$0.626922\pi$
$558$	−6.38197	−0.270170
$559$	2.00000	0.0845910
$560$	0	0
$561$	2.39512	0.101122
$562$	3.39512	0.143215
$563$	17.1803	0.724065	0.362032	−	0.932165i	$-0.382083\pi$
$563$	17.1803	0.724065	0.362032	+	0.932165i	$0.382083\pi$
$564$	−7.91796	−0.333406
$565$	−24.2705	−1.02107
$566$	3.27051	0.137470
$567$	0	0
$568$	−2.16718	−0.0909330
$569$	−24.5967	−1.03115	−0.515575	−	0.856845i	$-0.672422\pi$
$569$	−24.5967	−1.03115	−0.515575	+	0.856845i	$0.672422\pi$
$570$	−0.326238	−0.0136646
$571$	−16.1246	−0.674794	−0.337397	−	0.941362i	$-0.609546\pi$
$571$	−16.1246	−0.674794	−0.337397	+	0.941362i	$0.609546\pi$
$572$	−6.27051	−0.262183
$573$	3.56231	0.148817
$574$	0	0
$575$	0	0
$576$	13.4377	0.559904
$577$	−20.8541	−0.868168	−0.434084	−	0.900872i	$-0.642928\pi$
$577$	−20.8541	−0.868168	−0.434084	+	0.900872i	$0.642928\pi$
$578$	5.18034	0.215474
$579$	−0.596748	−0.0248000
$580$	14.0213	0.582202
$581$	0	0
$582$	−1.81153	−0.0750903
$583$	34.1246	1.41330
$584$	−15.9787	−0.661204
$585$	6.38197	0.263862
$586$	−4.85410	−0.200521
$587$	−38.9443	−1.60740	−0.803701	−	0.595033i	$-0.797139\pi$
$587$	−38.9443	−1.60740	−0.803701	+	0.595033i	$0.797139\pi$
$588$	0	0
$589$	−5.85410	−0.241214
$590$	−10.8541	−0.446856
$591$	−6.97871	−0.287066
$592$	8.51973	0.350159
$593$	15.0000	0.615976	0.307988	−	0.951390i	$-0.400344\pi$
$593$	15.0000	0.615976	0.307988	+	0.951390i	$0.400344\pi$
$594$	−2.88854	−0.118518
$595$	0	0
$596$	−38.7295	−1.58642
$597$	−1.25735	−0.0514601
$598$	−1.14590	−0.0468593
$599$	−4.09017	−0.167120	−0.0835599	−	0.996503i	$-0.526629\pi$
$599$	−4.09017	−0.167120	−0.0835599	+	0.996503i	$0.526629\pi$
$600$	0	0
$601$	14.5623	0.594009	0.297004	−	0.954876i	$-0.404012\pi$
$601$	14.5623	0.594009	0.297004	+	0.954876i	$0.404012\pi$
$602$	0	0
$603$	38.7082	1.57632
$604$	−39.9787	−1.62671
$605$	0.978714	0.0397904
$606$	0.660606	0.0268353
$607$	40.1246	1.62861	0.814304	−	0.580439i	$-0.197119\pi$
$607$	40.1246	1.62861	0.814304	+	0.580439i	$0.197119\pi$
$608$	−4.14590	−0.168138
$609$	0	0
$610$	5.72949	0.231980
$611$	−11.1803	−0.452308
$612$	−9.81153	−0.396608
$613$	13.6869	0.552809	0.276405	−	0.961041i	$-0.410857\pi$
$613$	13.6869	0.552809	0.276405	+	0.961041i	$0.410857\pi$
$614$	−0.931116	−0.0375768
$615$	−2.23607	−0.0901670
$616$	0	0
$617$	24.2148	0.974850	0.487425	−	0.873165i	$-0.337936\pi$
$617$	24.2148	0.974850	0.487425	+	0.873165i	$0.337936\pi$
$618$	1.27051	0.0511074
$619$	−13.4377	−0.540107	−0.270053	−	0.962845i	$-0.587041\pi$
$619$	−13.4377	−0.540107	−0.270053	+	0.962845i	$0.587041\pi$
$620$	24.2705	0.974727
$621$	6.70820	0.269191
$622$	1.87539	0.0751962
$623$	0	0
$624$	−1.20163	−0.0481035
$625$	−25.0000	−1.00000
$626$	−0.875388	−0.0349875
$627$	−1.29180	−0.0515894
$628$	−14.5623	−0.581099
$629$	−5.02129	−0.200212
$630$	0	0
$631$	−1.29180	−0.0514256	−0.0257128	−	0.999669i	$-0.508186\pi$
$631$	−1.29180	−0.0514256	−0.0257128	+	0.999669i	$0.508186\pi$
$632$	−14.7214	−0.585584
$633$	−2.50658	−0.0996275
$634$	−9.70820	−0.385562
$635$	44.0689	1.74882
$636$	7.14590	0.283353
$637$	0	0
$638$	−4.36881	−0.172963
$639$	4.20163	0.166214
$640$	22.5623	0.891853
$641$	−40.6869	−1.60704	−0.803518	−	0.595280i	$-0.797041\pi$
$641$	−40.6869	−1.60704	−0.803518	+	0.595280i	$0.797041\pi$
$642$	1.09017	0.0430256
$643$	48.4164	1.90936	0.954678	−	0.297639i	$-0.0961993\pi$
$643$	48.4164	1.90936	0.954678	+	0.297639i	$0.0961993\pi$
$644$	0	0
$645$	−1.70820	−0.0672605
$646$	0.708204	0.0278639
$647$	17.0689	0.671047	0.335524	−	0.942032i	$-0.391087\pi$
$647$	17.0689	0.671047	0.335524	+	0.942032i	$0.391087\pi$
$648$	11.3475	0.445773
$649$	−42.9787	−1.68706
$650$	0	0
$651$	0	0
$652$	16.9574	0.664104
$653$	−18.5967	−0.727747	−0.363873	−	0.931448i	$-0.618546\pi$
$653$	−18.5967	−0.727747	−0.363873	+	0.931448i	$0.618546\pi$
$654$	−2.39512	−0.0936567
$655$	2.43769	0.0952486
$656$	−8.23607	−0.321564
$657$	30.9787	1.20859
$658$	0	0
$659$	26.5066	1.03255	0.516275	−	0.856423i	$-0.327318\pi$
$659$	26.5066	1.03255	0.516275	+	0.856423i	$0.327318\pi$
$660$	5.35565	0.208469
$661$	16.8328	0.654721	0.327360	−	0.944900i	$-0.393841\pi$
$661$	16.8328	0.654721	0.327360	+	0.944900i	$0.393841\pi$
$662$	0.549150	0.0213433
$663$	0.708204	0.0275044
$664$	1.68692	0.0654651
$665$	0	0
$666$	2.95240	0.114403
$667$	10.1459	0.392851
$668$	2.72949	0.105607
$669$	10.0902	0.390109
$670$	11.5836	0.447513
$671$	22.6869	0.875819
$672$	0	0
$673$	−18.2705	−0.704276	−0.352138	−	0.935948i	$-0.614545\pi$
$673$	−18.2705	−0.704276	−0.352138	+	0.935948i	$0.614545\pi$
$674$	−4.30495	−0.165821
$675$	0	0
$676$	22.2492	0.855739
$677$	34.7426	1.33527	0.667634	−	0.744489i	$-0.267307\pi$
$677$	34.7426	1.33527	0.667634	+	0.744489i	$0.267307\pi$
$678$	1.58359	0.0608175
$679$	0	0
$680$	−6.10333	−0.234052
$681$	7.87539	0.301786
$682$	−7.56231	−0.289576
$683$	−28.5279	−1.09159	−0.545794	−	0.837919i	$-0.683772\pi$
$683$	−28.5279	−1.09159	−0.545794	+	0.837919i	$0.683772\pi$
$684$	5.29180	0.202337
$685$	16.8328	0.643149
$686$	0	0
$687$	3.59675	0.137224
$688$	−6.29180	−0.239872
$689$	10.0902	0.384405
$690$	0.978714	0.0372590
$691$	18.2918	0.695853	0.347926	−	0.937522i	$-0.386886\pi$
$691$	18.2918	0.695853	0.347926	+	0.937522i	$0.386886\pi$
$692$	4.04257	0.153676
$693$	0	0
$694$	3.60488	0.136839
$695$	46.3050	1.75645
$696$	−1.90170	−0.0720837
$697$	4.85410	0.183862
$698$	9.27051	0.350894
$699$	−6.12461	−0.231654
$700$	0	0
$701$	−37.5279	−1.41741	−0.708704	−	0.705506i	$-0.750720\pi$
$701$	−37.5279	−1.41741	−0.708704	+	0.705506i	$0.750720\pi$
$702$	−0.854102	−0.0322360
$703$	2.70820	0.102142
$704$	15.9230	0.600120
$705$	9.54915	0.359642
$706$	3.58359	0.134870
$707$	0	0
$708$	−9.00000	−0.338241
$709$	11.2918	0.424072	0.212036	−	0.977262i	$-0.431991\pi$
$709$	11.2918	0.424072	0.212036	+	0.977262i	$0.431991\pi$
$710$	1.25735	0.0471877
$711$	28.5410	1.07037
$712$	−23.1246	−0.866631
$713$	17.5623	0.657714
$714$	0	0
$715$	7.56231	0.282814
$716$	−2.02129	−0.0755390
$717$	5.14590	0.192177
$718$	12.1246	0.452486
$719$	−5.88854	−0.219606	−0.109803	−	0.993953i	$-0.535022\pi$
$719$	−5.88854	−0.219606	−0.109803	+	0.993953i	$0.535022\pi$
$720$	−20.0770	−0.748226
$721$	0	0
$722$	−0.381966	−0.0142153
$723$	6.76393	0.251553
$724$	−39.9787	−1.48580
$725$	0	0
$726$	−0.0638587	−0.00237002
$727$	−43.0000	−1.59478	−0.797391	−	0.603463i	$-0.793787\pi$
$727$	−43.0000	−1.59478	−0.797391	+	0.603463i	$0.793787\pi$
$728$	0	0
$729$	−19.4377	−0.719915
$730$	9.27051	0.343117
$731$	3.70820	0.137153
$732$	4.75078	0.175594
$733$	22.8328	0.843349	0.421675	−	0.906747i	$-0.361442\pi$
$733$	22.8328	0.843349	0.421675	+	0.906747i	$0.361442\pi$
$734$	−4.96556	−0.183282
$735$	0	0
$736$	12.4377	0.458459
$737$	45.8673	1.68954
$738$	−2.85410	−0.105061
$739$	22.4164	0.824601	0.412300	−	0.911048i	$-0.364725\pi$
$739$	22.4164	0.824601	0.412300	+	0.911048i	$0.364725\pi$
$740$	−11.2279	−0.412747
$741$	−0.381966	−0.0140319
$742$	0	0
$743$	14.8885	0.546208	0.273104	−	0.961985i	$-0.411950\pi$
$743$	14.8885	0.546208	0.273104	+	0.961985i	$0.411950\pi$
$744$	−3.29180	−0.120683
$745$	46.7082	1.71126
$746$	13.0902	0.479265
$747$	−3.27051	−0.119662
$748$	−11.6262	−0.425095
$749$	0	0
$750$	1.63119	0.0595626
$751$	28.8541	1.05290	0.526451	−	0.850206i	$-0.323523\pi$
$751$	28.8541	1.05290	0.526451	+	0.850206i	$0.323523\pi$
$752$	35.1722	1.28260
$753$	−0.458980	−0.0167262
$754$	−1.29180	−0.0470444
$755$	48.2148	1.75472
$756$	0	0
$757$	5.41641	0.196863	0.0984313	−	0.995144i	$-0.468618\pi$
$757$	5.41641	0.196863	0.0984313	+	0.995144i	$0.468618\pi$
$758$	−6.60488	−0.239900
$759$	3.87539	0.140668
$760$	3.29180	0.119406
$761$	−41.1803	−1.49279	−0.746393	−	0.665505i	$-0.768216\pi$
$761$	−41.1803	−1.49279	−0.746393	+	0.665505i	$0.768216\pi$
$762$	−2.87539	−0.104164
$763$	0	0
$764$	−17.2918	−0.625595
$765$	11.8328	0.427816
$766$	−6.02129	−0.217558
$767$	−12.7082	−0.458867
$768$	2.12461	0.0766653
$769$	−10.8328	−0.390641	−0.195321	−	0.980739i	$-0.562575\pi$
$769$	−10.8328	−0.390641	−0.195321	+	0.980739i	$0.562575\pi$
$770$	0	0
$771$	−10.6869	−0.384880
$772$	2.89667	0.104254
$773$	5.34752	0.192337	0.0961685	−	0.995365i	$-0.469341\pi$
$773$	5.34752	0.192337	0.0961685	+	0.995365i	$0.469341\pi$
$774$	−2.18034	−0.0783707
$775$	0	0
$776$	18.2786	0.656165
$777$	0	0
$778$	−4.12461	−0.147874
$779$	−2.61803	−0.0938008
$780$	1.58359	0.0567017
$781$	4.97871	0.178152
$782$	−2.12461	−0.0759760
$783$	7.56231	0.270255
$784$	0	0
$785$	17.5623	0.626826
$786$	−0.159054	−0.00567326
$787$	−15.4164	−0.549536	−0.274768	−	0.961511i	$-0.588601\pi$
$787$	−15.4164	−0.549536	−0.274768	+	0.961511i	$0.588601\pi$
$788$	33.8754	1.20676
$789$	−1.31308	−0.0467470
$790$	8.54102	0.303876
$791$	0	0
$792$	14.2098	0.504922
$793$	6.70820	0.238215
$794$	−13.1935	−0.468220
$795$	−8.61803	−0.305650
$796$	6.10333	0.216327
$797$	−46.6869	−1.65374	−0.826868	−	0.562396i	$-0.809880\pi$
$797$	−46.6869	−1.65374	−0.826868	+	0.562396i	$0.809880\pi$
$798$	0	0
$799$	−20.7295	−0.733357
$800$	0	0
$801$	44.8328	1.58409
$802$	3.29180	0.116237
$803$	36.7082	1.29540
$804$	9.60488	0.338738
$805$	0	0
$806$	−2.23607	−0.0787621
$807$	−5.56231	−0.195802
$808$	−6.66563	−0.234496
$809$	54.4853	1.91560	0.957800	−	0.287434i	$-0.0928022\pi$
$809$	54.4853	1.91560	0.957800	+	0.287434i	$0.0928022\pi$
$810$	−6.58359	−0.231324
$811$	44.2492	1.55380	0.776900	−	0.629624i	$-0.216791\pi$
$811$	44.2492	1.55380	0.776900	+	0.629624i	$0.216791\pi$
$812$	0	0
$813$	−7.36068	−0.258150
$814$	3.49845	0.122621
$815$	−20.4508	−0.716362
$816$	−2.22794	−0.0779934
$817$	−2.00000	−0.0699711
$818$	−1.96556	−0.0687241
$819$	0	0
$820$	10.8541	0.379042
$821$	−31.4164	−1.09644	−0.548220	−	0.836334i	$-0.684694\pi$
$821$	−31.4164	−1.09644	−0.548220	+	0.836334i	$0.684694\pi$
$822$	−1.09830	−0.0383076
$823$	−13.1246	−0.457495	−0.228748	−	0.973486i	$-0.573463\pi$
$823$	−13.1246	−0.457495	−0.228748	+	0.973486i	$0.573463\pi$
$824$	−12.8197	−0.446594
$825$	0	0
$826$	0	0
$827$	12.0557	0.419219	0.209609	−	0.977785i	$-0.432781\pi$
$827$	12.0557	0.419219	0.209609	+	0.977785i	$0.432781\pi$
$828$	−15.8754	−0.551708
$829$	−46.8328	−1.62657	−0.813285	−	0.581865i	$-0.802323\pi$
$829$	−46.8328	−1.62657	−0.813285	+	0.581865i	$0.802323\pi$
$830$	−0.978714	−0.0339717
$831$	−6.76393	−0.234638
$832$	4.70820	0.163228
$833$	0	0
$834$	−3.02129	−0.104619
$835$	−3.29180	−0.113917
$836$	6.27051	0.216870
$837$	13.0902	0.452462
$838$	−8.89667	−0.307331
$839$	−16.3607	−0.564833	−0.282417	−	0.959292i	$-0.591136\pi$
$839$	−16.3607	−0.564833	−0.282417	+	0.959292i	$0.591136\pi$
$840$	0	0
$841$	−17.5623	−0.605597
$842$	8.13274	0.280273
$843$	−3.39512	−0.116934
$844$	12.1672	0.418812
$845$	−26.8328	−0.923077
$846$	12.1885	0.419048
$847$	0	0
$848$	−31.7426	−1.09005
$849$	−3.27051	−0.112244
$850$	0	0
$851$	−8.12461	−0.278508
$852$	1.04257	0.0357179
$853$	−16.5623	−0.567083	−0.283541	−	0.958960i	$-0.591509\pi$
$853$	−16.5623	−0.567083	−0.283541	+	0.958960i	$0.591509\pi$
$854$	0	0
$855$	−6.38197	−0.218259
$856$	−11.0000	−0.375972
$857$	54.8673	1.87423	0.937115	−	0.349021i	$-0.113486\pi$
$857$	54.8673	1.87423	0.937115	+	0.349021i	$0.113486\pi$
$858$	−0.493422	−0.0168452
$859$	−24.4377	−0.833803	−0.416902	−	0.908952i	$-0.636884\pi$
$859$	−24.4377	−0.833803	−0.416902	+	0.908952i	$0.636884\pi$
$860$	8.29180	0.282748
$861$	0	0
$862$	8.54102	0.290908
$863$	18.3820	0.625729	0.312865	−	0.949798i	$-0.398711\pi$
$863$	18.3820	0.625729	0.312865	+	0.949798i	$0.398711\pi$
$864$	9.27051	0.315389
$865$	−4.87539	−0.165768
$866$	12.0476	0.409394
$867$	−5.18034	−0.175934
$868$	0	0
$869$	33.8197	1.14725
$870$	1.10333	0.0374062
$871$	13.5623	0.459541
$872$	24.1672	0.818404
$873$	−35.4377	−1.19938
$874$	1.14590	0.0387606
$875$	0	0
$876$	7.68692	0.259717
$877$	16.8754	0.569841	0.284921	−	0.958551i	$-0.408033\pi$
$877$	16.8754	0.569841	0.284921	+	0.958551i	$0.408033\pi$
$878$	3.05573	0.103126
$879$	4.85410	0.163725
$880$	−23.7902	−0.801969
$881$	−51.1033	−1.72171	−0.860857	−	0.508846i	$-0.830072\pi$
$881$	−51.1033	−1.72171	−0.860857	+	0.508846i	$0.830072\pi$
$882$	0	0
$883$	−51.8328	−1.74431	−0.872157	−	0.489227i	$-0.837279\pi$
$883$	−51.8328	−1.74431	−0.872157	+	0.489227i	$0.837279\pi$
$884$	−3.43769	−0.115622
$885$	10.8541	0.364857
$886$	4.72949	0.158890
$887$	1.58359	0.0531718	0.0265859	−	0.999647i	$-0.491536\pi$
$887$	1.58359	0.0531718	0.0265859	+	0.999647i	$0.491536\pi$
$888$	1.52284	0.0511031
$889$	0	0
$890$	13.4164	0.449719
$891$	−26.0689	−0.873340
$892$	−48.9787	−1.63993
$893$	11.1803	0.374136
$894$	−3.04760	−0.101927
$895$	2.43769	0.0814831
$896$	0	0
$897$	1.14590	0.0382604
$898$	5.60488	0.187037
$899$	19.7984	0.660313
$900$	0	0
$901$	18.7082	0.623261
$902$	−3.38197	−0.112607
$903$	0	0
$904$	−15.9787	−0.531444
$905$	48.2148	1.60271
$906$	−3.14590	−0.104515
$907$	−26.1246	−0.867453	−0.433727	−	0.901044i	$-0.642802\pi$
$907$	−26.1246	−0.867453	−0.433727	+	0.901044i	$0.642802\pi$
$908$	−38.2279	−1.26864
$909$	12.9230	0.428628
$910$	0	0
$911$	−9.05573	−0.300030	−0.150015	−	0.988684i	$-0.547932\pi$
$911$	−9.05573	−0.300030	−0.150015	+	0.988684i	$0.547932\pi$
$912$	1.20163	0.0397898
$913$	−3.87539	−0.128257
$914$	−9.38197	−0.310328
$915$	−5.72949	−0.189411
$916$	−17.4590	−0.576861
$917$	0	0
$918$	−1.58359	−0.0522663
$919$	−44.7082	−1.47479	−0.737394	−	0.675463i	$-0.763944\pi$
$919$	−44.7082	−1.47479	−0.737394	+	0.675463i	$0.763944\pi$
$920$	−9.87539	−0.325582
$921$	0.931116	0.0306813
$922$	13.0213	0.428833
$923$	1.47214	0.0484559
$924$	0	0
$925$	0	0
$926$	−11.7295	−0.385455
$927$	24.8541	0.816316
$928$	14.0213	0.460271
$929$	−39.3262	−1.29025	−0.645126	−	0.764076i	$-0.723195\pi$
$929$	−39.3262	−1.29025	−0.645126	+	0.764076i	$0.723195\pi$
$930$	1.90983	0.0626258
$931$	0	0
$932$	29.7295	0.973822
$933$	−1.87539	−0.0613975
$934$	9.51973	0.311495
$935$	14.0213	0.458545
$936$	4.20163	0.137334
$937$	32.9787	1.07737	0.538684	−	0.842508i	$-0.318922\pi$
$937$	32.9787	1.07737	0.538684	+	0.842508i	$0.318922\pi$
$938$	0	0
$939$	0.875388	0.0285672
$940$	−46.3525	−1.51185
$941$	−13.6393	−0.444629	−0.222315	−	0.974975i	$-0.571361\pi$
$941$	−13.6393	−0.444629	−0.222315	+	0.974975i	$0.571361\pi$
$942$	−1.14590	−0.0373354
$943$	7.85410	0.255765
$944$	39.9787	1.30120
$945$	0	0
$946$	−2.58359	−0.0839998
$947$	25.7984	0.838335	0.419167	−	0.907909i	$-0.362322\pi$
$947$	25.7984	0.838335	0.419167	+	0.907909i	$0.362322\pi$
$948$	7.08204	0.230014
$949$	10.8541	0.352339
$950$	0	0
$951$	9.70820	0.314810
$952$	0	0
$953$	−31.7426	−1.02825	−0.514123	−	0.857717i	$-0.671882\pi$
$953$	−31.7426	−1.02825	−0.514123	+	0.857717i	$0.671882\pi$
$954$	−11.0000	−0.356138
$955$	20.8541	0.674823
$956$	−24.9787	−0.807869
$957$	4.36881	0.141224
$958$	15.8328	0.511535
$959$	0	0
$960$	−4.02129	−0.129786
$961$	3.27051	0.105500
$962$	1.03444	0.0333517
$963$	21.3262	0.687228
$964$	−32.8328	−1.05747
$965$	−3.49342	−0.112457
$966$	0	0
$967$	−20.1459	−0.647848	−0.323924	−	0.946083i	$-0.605002\pi$
$967$	−20.1459	−0.647848	−0.323924	+	0.946083i	$0.605002\pi$
$968$	0.644345	0.0207100
$969$	−0.708204	−0.0227508
$970$	−10.6049	−0.340502
$971$	29.1803	0.936442	0.468221	−	0.883611i	$-0.344895\pi$
$971$	29.1803	0.936442	0.468221	+	0.883611i	$0.344895\pi$
$972$	−17.8967	−0.574036
$973$	0	0
$974$	−3.66061	−0.117293
$975$	0	0
$976$	−21.1033	−0.675501
$977$	−3.81966	−0.122202	−0.0611009	−	0.998132i	$-0.519461\pi$
$977$	−3.81966	−0.122202	−0.0611009	+	0.998132i	$0.519461\pi$
$978$	1.33437	0.0426684
$979$	53.1246	1.69787
$980$	0	0
$981$	−46.8541	−1.49594
$982$	4.00000	0.127645
$983$	47.0689	1.50126	0.750632	−	0.660720i	$-0.229749\pi$
$983$	47.0689	1.50126	0.750632	+	0.660720i	$0.229749\pi$
$984$	−1.47214	−0.0469300
$985$	−40.8541	−1.30172
$986$	−2.39512	−0.0762762
$987$	0	0
$988$	1.85410	0.0589868
$989$	6.00000	0.190789
$990$	−8.24420	−0.262018
$991$	−18.8754	−0.599596	−0.299798	−	0.954003i	$-0.596919\pi$
$991$	−18.8754	−0.599596	−0.299798	+	0.954003i	$0.596919\pi$
$992$	24.2705	0.770589
$993$	−0.549150	−0.0174268
$994$	0	0
$995$	−7.36068	−0.233349
$996$	−0.811529	−0.0257143
$997$	30.8541	0.977159	0.488580	−	0.872519i	$-0.337515\pi$
$997$	30.8541	0.977159	0.488580	+	0.872519i	$0.337515\pi$
$998$	−1.20163	−0.0380368
$999$	−6.05573	−0.191595

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.a.d.1.2		2
3.2	odd	2		8379.2.a.bn.1.1		2
7.2	even	3		931.2.f.j.704.1		4
7.3	odd	6		931.2.f.k.324.1		4
7.4	even	3		931.2.f.j.324.1		4
7.5	odd	6		931.2.f.k.704.1		4
7.6	odd	2		133.2.a.a.1.2	✓	2
21.20	even	2		1197.2.a.j.1.1		2
28.27	even	2		2128.2.a.o.1.1		2
35.34	odd	2		3325.2.a.q.1.1		2
56.13	odd	2		8512.2.a.be.1.1		2
56.27	even	2		8512.2.a.j.1.2		2
133.132	even	2		2527.2.a.e.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.a.a.1.2	✓	2	7.6	odd	2
931.2.a.d.1.2		2	1.1	even	1	trivial
931.2.f.j.324.1		4	7.4	even	3
931.2.f.j.704.1		4	7.2	even	3
931.2.f.k.324.1		4	7.3	odd	6
931.2.f.k.704.1		4	7.5	odd	6
1197.2.a.j.1.1		2	21.20	even	2
2128.2.a.o.1.1		2	28.27	even	2
2527.2.a.e.1.1		2	133.132	even	2
3325.2.a.q.1.1		2	35.34	odd	2
8379.2.a.bn.1.1		2	3.2	odd	2
8512.2.a.j.1.2		2	56.27	even	2
8512.2.a.be.1.1		2	56.13	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:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.a (trivial)

\(f(q)\)	\(=\)	\(q-0.381966 q^{2} +0.381966 q^{3} -1.85410 q^{4} +2.23607 q^{5} -0.145898 q^{6} +1.47214 q^{8} -2.85410 q^{9} +O(q^{10})\)	\(q-0.381966 q^{2} +0.381966 q^{3} -1.85410 q^{4} +2.23607 q^{5} -0.145898 q^{6} +1.47214 q^{8} -2.85410 q^{9} -0.854102 q^{10} -3.38197 q^{11} -0.708204 q^{12} -1.00000 q^{13} +0.854102 q^{15} +3.14590 q^{16} -1.85410 q^{17} +1.09017 q^{18} +1.00000 q^{19} -4.14590 q^{20} +1.29180 q^{22} -3.00000 q^{23} +0.562306 q^{24} +0.381966 q^{26} -2.23607 q^{27} -3.38197 q^{29} -0.326238 q^{30} -5.85410 q^{31} -4.14590 q^{32} -1.29180 q^{33} +0.708204 q^{34} +5.29180 q^{36} +2.70820 q^{37} -0.381966 q^{38} -0.381966 q^{39} +3.29180 q^{40} -2.61803 q^{41} -2.00000 q^{43} +6.27051 q^{44} -6.38197 q^{45} +1.14590 q^{46} +11.1803 q^{47} +1.20163 q^{48} -0.708204 q^{51} +1.85410 q^{52} -10.0902 q^{53} +0.854102 q^{54} -7.56231 q^{55} +0.381966 q^{57} +1.29180 q^{58} +12.7082 q^{59} -1.58359 q^{60} -6.70820 q^{61} +2.23607 q^{62} -4.70820 q^{64} -2.23607 q^{65} +0.493422 q^{66} -13.5623 q^{67} +3.43769 q^{68} -1.14590 q^{69} -1.47214 q^{71} -4.20163 q^{72} -10.8541 q^{73} -1.03444 q^{74} -1.85410 q^{76} +0.145898 q^{78} -10.0000 q^{79} +7.03444 q^{80} +7.70820 q^{81} +1.00000 q^{82} +1.14590 q^{83} -4.14590 q^{85} +0.763932 q^{86} -1.29180 q^{87} -4.97871 q^{88} -15.7082 q^{89} +2.43769 q^{90} +5.56231 q^{92} -2.23607 q^{93} -4.27051 q^{94} +2.23607 q^{95} -1.58359 q^{96} +12.4164 q^{97} +9.65248 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 7 q^{6} - 6 q^{8} + q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 7 * q^6 - 6 * q^8 + q^9	\( 2 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 7 q^{6} - 6 q^{8} + q^{9} + 5 q^{10} - 9 q^{11} + 12 q^{12} - 2 q^{13} - 5 q^{15} + 13 q^{16} + 3 q^{17} - 9 q^{18} + 2 q^{19} - 15 q^{20} + 16 q^{22} - 6 q^{23} - 19 q^{24} + 3 q^{26} - 9 q^{29} + 15 q^{30} - 5 q^{31} - 15 q^{32} - 16 q^{33} - 12 q^{34} + 24 q^{36} - 8 q^{37} - 3 q^{38} - 3 q^{39} + 20 q^{40} - 3 q^{41} - 4 q^{43} - 21 q^{44} - 15 q^{45} + 9 q^{46} + 27 q^{48} + 12 q^{51} - 3 q^{52} - 9 q^{53} - 5 q^{54} + 5 q^{55} + 3 q^{57} + 16 q^{58} + 12 q^{59} - 30 q^{60} + 4 q^{64} + 39 q^{66} - 7 q^{67} + 27 q^{68} - 9 q^{69} + 6 q^{71} - 33 q^{72} - 15 q^{73} + 27 q^{74} + 3 q^{76} + 7 q^{78} - 20 q^{79} - 15 q^{80} + 2 q^{81} + 2 q^{82} + 9 q^{83} - 15 q^{85} + 6 q^{86} - 16 q^{87} + 37 q^{88} - 18 q^{89} + 25 q^{90} - 9 q^{92} + 25 q^{94} - 30 q^{96} - 2 q^{97} - 12 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 7 * q^6 - 6 * q^8 + q^9 + 5 * q^10 - 9 * q^11 + 12 * q^12 - 2 * q^13 - 5 * q^15 + 13 * q^16 + 3 * q^17 - 9 * q^18 + 2 * q^19 - 15 * q^20 + 16 * q^22 - 6 * q^23 - 19 * q^24 + 3 * q^26 - 9 * q^29 + 15 * q^30 - 5 * q^31 - 15 * q^32 - 16 * q^33 - 12 * q^34 + 24 * q^36 - 8 * q^37 - 3 * q^38 - 3 * q^39 + 20 * q^40 - 3 * q^41 - 4 * q^43 - 21 * q^44 - 15 * q^45 + 9 * q^46 + 27 * q^48 + 12 * q^51 - 3 * q^52 - 9 * q^53 - 5 * q^54 + 5 * q^55 + 3 * q^57 + 16 * q^58 + 12 * q^59 - 30 * q^60 + 4 * q^64 + 39 * q^66 - 7 * q^67 + 27 * q^68 - 9 * q^69 + 6 * q^71 - 33 * q^72 - 15 * q^73 + 27 * q^74 + 3 * q^76 + 7 * q^78 - 20 * q^79 - 15 * q^80 + 2 * q^81 + 2 * q^82 + 9 * q^83 - 15 * q^85 + 6 * q^86 - 16 * q^87 + 37 * q^88 - 18 * q^89 + 25 * q^90 - 9 * q^92 + 25 * q^94 - 30 * q^96 - 2 * q^97 - 12 * q^99

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