LMFDB - Embedded newform 946.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [946,2,Mod(1,946)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(946, 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("946.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 946 = 2 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	946.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:	$7.55384803121$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	946.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.61803 q^{3} +1.00000 q^{4} -0.381966 q^{5} -2.61803 q^{6} +1.00000 q^{8} +3.85410 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.61803 q^{3} +1.00000 q^{4} -0.381966 q^{5} -2.61803 q^{6} +1.00000 q^{8} +3.85410 q^{9} -0.381966 q^{10} +1.00000 q^{11} -2.61803 q^{12} -3.23607 q^{13} +1.00000 q^{15} +1.00000 q^{16} -2.61803 q^{17} +3.85410 q^{18} -4.38197 q^{19} -0.381966 q^{20} +1.00000 q^{22} +6.09017 q^{23} -2.61803 q^{24} -4.85410 q^{25} -3.23607 q^{26} -2.23607 q^{27} +3.09017 q^{29} +1.00000 q^{30} -4.61803 q^{31} +1.00000 q^{32} -2.61803 q^{33} -2.61803 q^{34} +3.85410 q^{36} -7.85410 q^{37} -4.38197 q^{38} +8.47214 q^{39} -0.381966 q^{40} -10.0902 q^{41} -1.00000 q^{43} +1.00000 q^{44} -1.47214 q^{45} +6.09017 q^{46} -0.909830 q^{47} -2.61803 q^{48} -7.00000 q^{49} -4.85410 q^{50} +6.85410 q^{51} -3.23607 q^{52} -9.70820 q^{53} -2.23607 q^{54} -0.381966 q^{55} +11.4721 q^{57} +3.09017 q^{58} -9.70820 q^{59} +1.00000 q^{60} -13.4164 q^{61} -4.61803 q^{62} +1.00000 q^{64} +1.23607 q^{65} -2.61803 q^{66} +8.00000 q^{67} -2.61803 q^{68} -15.9443 q^{69} -10.1803 q^{71} +3.85410 q^{72} +16.1803 q^{73} -7.85410 q^{74} +12.7082 q^{75} -4.38197 q^{76} +8.47214 q^{78} +7.14590 q^{79} -0.381966 q^{80} -5.70820 q^{81} -10.0902 q^{82} +2.94427 q^{83} +1.00000 q^{85} -1.00000 q^{86} -8.09017 q^{87} +1.00000 q^{88} +6.00000 q^{89} -1.47214 q^{90} +6.09017 q^{92} +12.0902 q^{93} -0.909830 q^{94} +1.67376 q^{95} -2.61803 q^{96} +14.5623 q^{97} -7.00000 q^{98} +3.85410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{8} + q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^8 + q^9	$ 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{8} + q^{9} - 3 q^{10} + 2 q^{11} - 3 q^{12} - 2 q^{13} + 2 q^{15} + 2 q^{16} - 3 q^{17} + q^{18} - 11 q^{19} - 3 q^{20} + 2 q^{22} + q^{23} - 3 q^{24} - 3 q^{25} - 2 q^{26} - 5 q^{29} + 2 q^{30} - 7 q^{31} + 2 q^{32} - 3 q^{33} - 3 q^{34} + q^{36} - 9 q^{37} - 11 q^{38} + 8 q^{39} - 3 q^{40} - 9 q^{41} - 2 q^{43} + 2 q^{44} + 6 q^{45} + q^{46} - 13 q^{47} - 3 q^{48} - 14 q^{49} - 3 q^{50} + 7 q^{51} - 2 q^{52} - 6 q^{53} - 3 q^{55} + 14 q^{57} - 5 q^{58} - 6 q^{59} + 2 q^{60} - 7 q^{62} + 2 q^{64} - 2 q^{65} - 3 q^{66} + 16 q^{67} - 3 q^{68} - 14 q^{69} + 2 q^{71} + q^{72} + 10 q^{73} - 9 q^{74} + 12 q^{75} - 11 q^{76} + 8 q^{78} + 21 q^{79} - 3 q^{80} + 2 q^{81} - 9 q^{82} - 12 q^{83} + 2 q^{85} - 2 q^{86} - 5 q^{87} + 2 q^{88} + 12 q^{89} + 6 q^{90} + q^{92} + 13 q^{93} - 13 q^{94} + 19 q^{95} - 3 q^{96} + 9 q^{97} - 14 q^{98} + q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^8 + q^9 - 3 * q^10 + 2 * q^11 - 3 * q^12 - 2 * q^13 + 2 * q^15 + 2 * q^16 - 3 * q^17 + q^18 - 11 * q^19 - 3 * q^20 + 2 * q^22 + q^23 - 3 * q^24 - 3 * q^25 - 2 * q^26 - 5 * q^29 + 2 * q^30 - 7 * q^31 + 2 * q^32 - 3 * q^33 - 3 * q^34 + q^36 - 9 * q^37 - 11 * q^38 + 8 * q^39 - 3 * q^40 - 9 * q^41 - 2 * q^43 + 2 * q^44 + 6 * q^45 + q^46 - 13 * q^47 - 3 * q^48 - 14 * q^49 - 3 * q^50 + 7 * q^51 - 2 * q^52 - 6 * q^53 - 3 * q^55 + 14 * q^57 - 5 * q^58 - 6 * q^59 + 2 * q^60 - 7 * q^62 + 2 * q^64 - 2 * q^65 - 3 * q^66 + 16 * q^67 - 3 * q^68 - 14 * q^69 + 2 * q^71 + q^72 + 10 * q^73 - 9 * q^74 + 12 * q^75 - 11 * q^76 + 8 * q^78 + 21 * q^79 - 3 * q^80 + 2 * q^81 - 9 * q^82 - 12 * q^83 + 2 * q^85 - 2 * q^86 - 5 * q^87 + 2 * q^88 + 12 * q^89 + 6 * q^90 + q^92 + 13 * q^93 - 13 * q^94 + 19 * q^95 - 3 * q^96 + 9 * q^97 - 14 * q^98 + 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.61803	−1.51152	−0.755761	−	0.654847i	$-0.772733\pi$
$3$	−2.61803	−1.51152	−0.755761	+	0.654847i	$0.772733\pi$
$4$	1.00000	0.500000
$5$	−0.381966	−0.170820	−0.0854102	−	0.996346i	$-0.527220\pi$
$5$	−0.381966	−0.170820	−0.0854102	+	0.996346i	$0.527220\pi$
$6$	−2.61803	−1.06881
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	1.00000	0.353553
$9$	3.85410	1.28470
$10$	−0.381966	−0.120788
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.61803	−0.755761
$13$	−3.23607	−0.897524	−0.448762	−	0.893651i	$-0.648135\pi$
$13$	−3.23607	−0.897524	−0.448762	+	0.893651i	$0.648135\pi$
$14$	0	0
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−2.61803	−0.634967	−0.317483	−	0.948264i	$-0.602838\pi$
$17$	−2.61803	−0.634967	−0.317483	+	0.948264i	$0.602838\pi$
$18$	3.85410	0.908421
$19$	−4.38197	−1.00529	−0.502646	−	0.864492i	$-0.667640\pi$
$19$	−4.38197	−1.00529	−0.502646	+	0.864492i	$0.667640\pi$
$20$	−0.381966	−0.0854102
$21$	0	0
$22$	1.00000	0.213201
$23$	6.09017	1.26989	0.634944	−	0.772558i	$-0.281023\pi$
$23$	6.09017	1.26989	0.634944	+	0.772558i	$0.281023\pi$
$24$	−2.61803	−0.534404
$25$	−4.85410	−0.970820
$26$	−3.23607	−0.634645
$27$	−2.23607	−0.430331
$28$	0	0
$29$	3.09017	0.573830	0.286915	−	0.957956i	$-0.407370\pi$
$29$	3.09017	0.573830	0.286915	+	0.957956i	$0.407370\pi$
$30$	1.00000	0.182574
$31$	−4.61803	−0.829423	−0.414712	−	0.909953i	$-0.636118\pi$
$31$	−4.61803	−0.829423	−0.414712	+	0.909953i	$0.636118\pi$
$32$	1.00000	0.176777
$33$	−2.61803	−0.455741
$34$	−2.61803	−0.448989
$35$	0	0
$36$	3.85410	0.642350
$37$	−7.85410	−1.29121	−0.645603	−	0.763673i	$-0.723394\pi$
$37$	−7.85410	−1.29121	−0.645603	+	0.763673i	$0.723394\pi$
$38$	−4.38197	−0.710849
$39$	8.47214	1.35663
$40$	−0.381966	−0.0603941
$41$	−10.0902	−1.57582	−0.787910	−	0.615791i	$-0.788837\pi$
$41$	−10.0902	−1.57582	−0.787910	+	0.615791i	$0.788837\pi$
$42$	0	0
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.00000	0.150756
$45$	−1.47214	−0.219453
$46$	6.09017	0.897947
$47$	−0.909830	−0.132712	−0.0663562	−	0.997796i	$-0.521137\pi$
$47$	−0.909830	−0.132712	−0.0663562	+	0.997796i	$0.521137\pi$
$48$	−2.61803	−0.377881
$49$	−7.00000	−1.00000
$50$	−4.85410	−0.686474
$51$	6.85410	0.959766
$52$	−3.23607	−0.448762
$53$	−9.70820	−1.33352	−0.666762	−	0.745271i	$-0.732320\pi$
$53$	−9.70820	−1.33352	−0.666762	+	0.745271i	$0.732320\pi$
$54$	−2.23607	−0.304290
$55$	−0.381966	−0.0515043
$56$	0	0
$57$	11.4721	1.51952
$58$	3.09017	0.405759
$59$	−9.70820	−1.26390	−0.631950	−	0.775009i	$-0.717745\pi$
$59$	−9.70820	−1.26390	−0.631950	+	0.775009i	$0.717745\pi$
$60$	1.00000	0.129099
$61$	−13.4164	−1.71780	−0.858898	−	0.512148i	$-0.828850\pi$
$61$	−13.4164	−1.71780	−0.858898	+	0.512148i	$0.828850\pi$
$62$	−4.61803	−0.586491
$63$	0	0
$64$	1.00000	0.125000
$65$	1.23607	0.153315
$66$	−2.61803	−0.322258
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	−2.61803	−0.317483
$69$	−15.9443	−1.91946
$70$	0	0
$71$	−10.1803	−1.20818	−0.604092	−	0.796915i	$-0.706464\pi$
$71$	−10.1803	−1.20818	−0.604092	+	0.796915i	$0.706464\pi$
$72$	3.85410	0.454210
$73$	16.1803	1.89377	0.946883	−	0.321579i	$-0.104214\pi$
$73$	16.1803	1.89377	0.946883	+	0.321579i	$0.104214\pi$
$74$	−7.85410	−0.913021
$75$	12.7082	1.46742
$76$	−4.38197	−0.502646
$77$	0	0
$78$	8.47214	0.959280
$79$	7.14590	0.803976	0.401988	−	0.915645i	$-0.368319\pi$
$79$	7.14590	0.803976	0.401988	+	0.915645i	$0.368319\pi$
$80$	−0.381966	−0.0427051
$81$	−5.70820	−0.634245
$82$	−10.0902	−1.11427
$83$	2.94427	0.323176	0.161588	−	0.986858i	$-0.448338\pi$
$83$	2.94427	0.323176	0.161588	+	0.986858i	$0.448338\pi$
$84$	0	0
$85$	1.00000	0.108465
$86$	−1.00000	−0.107833
$87$	−8.09017	−0.867357
$88$	1.00000	0.106600
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	−1.47214	−0.155177
$91$	0	0
$92$	6.09017	0.634944
$93$	12.0902	1.25369
$94$	−0.909830	−0.0938418
$95$	1.67376	0.171724
$96$	−2.61803	−0.267202
$97$	14.5623	1.47858	0.739289	−	0.673388i	$-0.235162\pi$
$97$	14.5623	1.47858	0.739289	+	0.673388i	$0.235162\pi$
$98$	−7.00000	−0.707107
$99$	3.85410	0.387352
$100$	−4.85410	−0.485410
$101$	−1.23607	−0.122993	−0.0614967	−	0.998107i	$-0.519587\pi$
$101$	−1.23607	−0.122993	−0.0614967	+	0.998107i	$0.519587\pi$
$102$	6.85410	0.678657
$103$	10.8541	1.06949	0.534743	−	0.845015i	$-0.320408\pi$
$103$	10.8541	1.06949	0.534743	+	0.845015i	$0.320408\pi$
$104$	−3.23607	−0.317323
$105$	0	0
$106$	−9.70820	−0.942944
$107$	7.41641	0.716971	0.358486	−	0.933535i	$-0.383293\pi$
$107$	7.41641	0.716971	0.358486	+	0.933535i	$0.383293\pi$
$108$	−2.23607	−0.215166
$109$	1.70820	0.163616	0.0818081	−	0.996648i	$-0.473931\pi$
$109$	1.70820	0.163616	0.0818081	+	0.996648i	$0.473931\pi$
$110$	−0.381966	−0.0364190
$111$	20.5623	1.95169
$112$	0	0
$113$	5.23607	0.492568	0.246284	−	0.969198i	$-0.420790\pi$
$113$	5.23607	0.492568	0.246284	+	0.969198i	$0.420790\pi$
$114$	11.4721	1.07446
$115$	−2.32624	−0.216923
$116$	3.09017	0.286915
$117$	−12.4721	−1.15305
$118$	−9.70820	−0.893713
$119$	0	0
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	−13.4164	−1.21466
$123$	26.4164	2.38189
$124$	−4.61803	−0.414712
$125$	3.76393	0.336656
$126$	0	0
$127$	13.3820	1.18746	0.593729	−	0.804665i	$-0.297655\pi$
$127$	13.3820	1.18746	0.593729	+	0.804665i	$0.297655\pi$
$128$	1.00000	0.0883883
$129$	2.61803	0.230505
$130$	1.23607	0.108410
$131$	0.326238	0.0285035	0.0142518	−	0.999898i	$-0.495463\pi$
$131$	0.326238	0.0285035	0.0142518	+	0.999898i	$0.495463\pi$
$132$	−2.61803	−0.227871
$133$	0	0
$134$	8.00000	0.691095
$135$	0.854102	0.0735094
$136$	−2.61803	−0.224495
$137$	−17.8885	−1.52832	−0.764161	−	0.645026i	$-0.776847\pi$
$137$	−17.8885	−1.52832	−0.764161	+	0.645026i	$0.776847\pi$
$138$	−15.9443	−1.35727
$139$	−10.1803	−0.863485	−0.431743	−	0.901997i	$-0.642101\pi$
$139$	−10.1803	−0.863485	−0.431743	+	0.901997i	$0.642101\pi$
$140$	0	0
$141$	2.38197	0.200598
$142$	−10.1803	−0.854315
$143$	−3.23607	−0.270614
$144$	3.85410	0.321175
$145$	−1.18034	−0.0980219
$146$	16.1803	1.33909
$147$	18.3262	1.51152
$148$	−7.85410	−0.645603
$149$	−4.90983	−0.402229	−0.201114	−	0.979568i	$-0.564456\pi$
$149$	−4.90983	−0.402229	−0.201114	+	0.979568i	$0.564456\pi$
$150$	12.7082	1.03762
$151$	14.4721	1.17773	0.588863	−	0.808233i	$-0.299576\pi$
$151$	14.4721	1.17773	0.588863	+	0.808233i	$0.299576\pi$
$152$	−4.38197	−0.355424
$153$	−10.0902	−0.815742
$154$	0	0
$155$	1.76393	0.141682
$156$	8.47214	0.678314
$157$	−1.14590	−0.0914526	−0.0457263	−	0.998954i	$-0.514560\pi$
$157$	−1.14590	−0.0914526	−0.0457263	+	0.998954i	$0.514560\pi$
$158$	7.14590	0.568497
$159$	25.4164	2.01565
$160$	−0.381966	−0.0301971
$161$	0	0
$162$	−5.70820	−0.448479
$163$	−15.5066	−1.21457	−0.607284	−	0.794484i	$-0.707741\pi$
$163$	−15.5066	−1.21457	−0.607284	+	0.794484i	$0.707741\pi$
$164$	−10.0902	−0.787910
$165$	1.00000	0.0778499
$166$	2.94427	0.228520
$167$	−24.9443	−1.93025	−0.965123	−	0.261797i	$-0.915685\pi$
$167$	−24.9443	−1.93025	−0.965123	+	0.261797i	$0.915685\pi$
$168$	0	0
$169$	−2.52786	−0.194451
$170$	1.00000	0.0766965
$171$	−16.8885	−1.29150
$172$	−1.00000	−0.0762493
$173$	4.18034	0.317825	0.158913	−	0.987293i	$-0.449201\pi$
$173$	4.18034	0.317825	0.158913	+	0.987293i	$0.449201\pi$
$174$	−8.09017	−0.613314
$175$	0	0
$176$	1.00000	0.0753778
$177$	25.4164	1.91041
$178$	6.00000	0.449719
$179$	−13.6180	−1.01786	−0.508930	−	0.860808i	$-0.669959\pi$
$179$	−13.6180	−1.01786	−0.508930	+	0.860808i	$0.669959\pi$
$180$	−1.47214	−0.109727
$181$	3.41641	0.253940	0.126970	−	0.991907i	$-0.459475\pi$
$181$	3.41641	0.253940	0.126970	+	0.991907i	$0.459475\pi$
$182$	0	0
$183$	35.1246	2.59649
$184$	6.09017	0.448973
$185$	3.00000	0.220564
$186$	12.0902	0.886494
$187$	−2.61803	−0.191450
$188$	−0.909830	−0.0663562
$189$	0	0
$190$	1.67376	0.121427
$191$	14.9443	1.08133	0.540665	−	0.841238i	$-0.318173\pi$
$191$	14.9443	1.08133	0.540665	+	0.841238i	$0.318173\pi$
$192$	−2.61803	−0.188940
$193$	−1.32624	−0.0954647	−0.0477323	−	0.998860i	$-0.515199\pi$
$193$	−1.32624	−0.0954647	−0.0477323	+	0.998860i	$0.515199\pi$
$194$	14.5623	1.04551
$195$	−3.23607	−0.231740
$196$	−7.00000	−0.500000
$197$	−9.52786	−0.678832	−0.339416	−	0.940636i	$-0.610229\pi$
$197$	−9.52786	−0.678832	−0.339416	+	0.940636i	$0.610229\pi$
$198$	3.85410	0.273899
$199$	8.00000	0.567105	0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000	0.567105	0.283552	+	0.958957i	$0.408487\pi$
$200$	−4.85410	−0.343237
$201$	−20.9443	−1.47730
$202$	−1.23607	−0.0869694
$203$	0	0
$204$	6.85410	0.479883
$205$	3.85410	0.269182
$206$	10.8541	0.756241
$207$	23.4721	1.63143
$208$	−3.23607	−0.224381
$209$	−4.38197	−0.303107
$210$	0	0
$211$	13.8541	0.953756	0.476878	−	0.878970i	$-0.341768\pi$
$211$	13.8541	0.953756	0.476878	+	0.878970i	$0.341768\pi$
$212$	−9.70820	−0.666762
$213$	26.6525	1.82620
$214$	7.41641	0.506975
$215$	0.381966	0.0260499
$216$	−2.23607	−0.152145
$217$	0	0
$218$	1.70820	0.115694
$219$	−42.3607	−2.86247
$220$	−0.381966	−0.0257521
$221$	8.47214	0.569898
$222$	20.5623	1.38005
$223$	15.7082	1.05190	0.525950	−	0.850516i	$-0.323710\pi$
$223$	15.7082	1.05190	0.525950	+	0.850516i	$0.323710\pi$
$224$	0	0
$225$	−18.7082	−1.24721
$226$	5.23607	0.348298
$227$	8.38197	0.556331	0.278165	−	0.960533i	$-0.410274\pi$
$227$	8.38197	0.556331	0.278165	+	0.960533i	$0.410274\pi$
$228$	11.4721	0.759761
$229$	−8.47214	−0.559855	−0.279927	−	0.960021i	$-0.590310\pi$
$229$	−8.47214	−0.559855	−0.279927	+	0.960021i	$0.590310\pi$
$230$	−2.32624	−0.153388
$231$	0	0
$232$	3.09017	0.202880
$233$	16.1803	1.06001	0.530005	−	0.847995i	$-0.322190\pi$
$233$	16.1803	1.06001	0.530005	+	0.847995i	$0.322190\pi$
$234$	−12.4721	−0.815329
$235$	0.347524	0.0226700
$236$	−9.70820	−0.631950
$237$	−18.7082	−1.21523
$238$	0	0
$239$	−21.9787	−1.42168	−0.710842	−	0.703351i	$-0.751686\pi$
$239$	−21.9787	−1.42168	−0.710842	+	0.703351i	$0.751686\pi$
$240$	1.00000	0.0645497
$241$	9.41641	0.606564	0.303282	−	0.952901i	$-0.401918\pi$
$241$	9.41641	0.606564	0.303282	+	0.952901i	$0.401918\pi$
$242$	1.00000	0.0642824
$243$	21.6525	1.38901
$244$	−13.4164	−0.858898
$245$	2.67376	0.170820
$246$	26.4164	1.68425
$247$	14.1803	0.902273
$248$	−4.61803	−0.293245
$249$	−7.70820	−0.488488
$250$	3.76393	0.238052
$251$	3.70820	0.234060	0.117030	−	0.993128i	$-0.462663\pi$
$251$	3.70820	0.234060	0.117030	+	0.993128i	$0.462663\pi$
$252$	0	0
$253$	6.09017	0.382886
$254$	13.3820	0.839659
$255$	−2.61803	−0.163948
$256$	1.00000	0.0625000
$257$	21.8885	1.36537	0.682685	−	0.730713i	$-0.260812\pi$
$257$	21.8885	1.36537	0.682685	+	0.730713i	$0.260812\pi$
$258$	2.61803	0.162992
$259$	0	0
$260$	1.23607	0.0766577
$261$	11.9098	0.737200
$262$	0.326238	0.0201550
$263$	−0.652476	−0.0402334	−0.0201167	−	0.999798i	$-0.506404\pi$
$263$	−0.652476	−0.0402334	−0.0201167	+	0.999798i	$0.506404\pi$
$264$	−2.61803	−0.161129
$265$	3.70820	0.227793
$266$	0	0
$267$	−15.7082	−0.961326
$268$	8.00000	0.488678
$269$	−22.4721	−1.37015	−0.685075	−	0.728472i	$-0.740231\pi$
$269$	−22.4721	−1.37015	−0.685075	+	0.728472i	$0.740231\pi$
$270$	0.854102	0.0519790
$271$	20.0902	1.22039	0.610195	−	0.792251i	$-0.291091\pi$
$271$	20.0902	1.22039	0.610195	+	0.792251i	$0.291091\pi$
$272$	−2.61803	−0.158742
$273$	0	0
$274$	−17.8885	−1.08069
$275$	−4.85410	−0.292713
$276$	−15.9443	−0.959732
$277$	−14.5623	−0.874964	−0.437482	−	0.899227i	$-0.644130\pi$
$277$	−14.5623	−0.874964	−0.437482	+	0.899227i	$0.644130\pi$
$278$	−10.1803	−0.610576
$279$	−17.7984	−1.06556
$280$	0	0
$281$	0.798374	0.0476270	0.0238135	−	0.999716i	$-0.492419\pi$
$281$	0.798374	0.0476270	0.0238135	+	0.999716i	$0.492419\pi$
$282$	2.38197	0.141844
$283$	−21.4164	−1.27307	−0.636537	−	0.771246i	$-0.719634\pi$
$283$	−21.4164	−1.27307	−0.636537	+	0.771246i	$0.719634\pi$
$284$	−10.1803	−0.604092
$285$	−4.38197	−0.259565
$286$	−3.23607	−0.191353
$287$	0	0
$288$	3.85410	0.227105
$289$	−10.1459	−0.596818
$290$	−1.18034	−0.0693119
$291$	−38.1246	−2.23490
$292$	16.1803	0.946883
$293$	9.52786	0.556624	0.278312	−	0.960491i	$-0.410225\pi$
$293$	9.52786	0.556624	0.278312	+	0.960491i	$0.410225\pi$
$294$	18.3262	1.06881
$295$	3.70820	0.215900
$296$	−7.85410	−0.456510
$297$	−2.23607	−0.129750
$298$	−4.90983	−0.284419
$299$	−19.7082	−1.13975
$300$	12.7082	0.733708
$301$	0	0
$302$	14.4721	0.832778
$303$	3.23607	0.185907
$304$	−4.38197	−0.251323
$305$	5.12461	0.293434
$306$	−10.0902	−0.576817
$307$	−20.0000	−1.14146	−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000	−1.14146	−0.570730	+	0.821138i	$0.693340\pi$
$308$	0	0
$309$	−28.4164	−1.61655
$310$	1.76393	0.100185
$311$	−25.5279	−1.44755	−0.723776	−	0.690035i	$-0.757595\pi$
$311$	−25.5279	−1.44755	−0.723776	+	0.690035i	$0.757595\pi$
$312$	8.47214	0.479640
$313$	−12.9443	−0.731654	−0.365827	−	0.930683i	$-0.619214\pi$
$313$	−12.9443	−0.731654	−0.365827	+	0.930683i	$0.619214\pi$
$314$	−1.14590	−0.0646668
$315$	0	0
$316$	7.14590	0.401988
$317$	−26.8328	−1.50708	−0.753541	−	0.657401i	$-0.771656\pi$
$317$	−26.8328	−1.50708	−0.753541	+	0.657401i	$0.771656\pi$
$318$	25.4164	1.42528
$319$	3.09017	0.173016
$320$	−0.381966	−0.0213525
$321$	−19.4164	−1.08372
$322$	0	0
$323$	11.4721	0.638327
$324$	−5.70820	−0.317122
$325$	15.7082	0.871334
$326$	−15.5066	−0.858830
$327$	−4.47214	−0.247310
$328$	−10.0902	−0.557136
$329$	0	0
$330$	1.00000	0.0550482
$331$	16.0000	0.879440	0.439720	−	0.898135i	$-0.355078\pi$
$331$	16.0000	0.879440	0.439720	+	0.898135i	$0.355078\pi$
$332$	2.94427	0.161588
$333$	−30.2705	−1.65881
$334$	−24.9443	−1.36489
$335$	−3.05573	−0.166952
$336$	0	0
$337$	−27.2705	−1.48552	−0.742760	−	0.669558i	$-0.766484\pi$
$337$	−27.2705	−1.48552	−0.742760	+	0.669558i	$0.766484\pi$
$338$	−2.52786	−0.137498
$339$	−13.7082	−0.744527
$340$	1.00000	0.0542326
$341$	−4.61803	−0.250081
$342$	−16.8885	−0.913228
$343$	0	0
$344$	−1.00000	−0.0539164
$345$	6.09017	0.327884
$346$	4.18034	0.224736
$347$	−9.32624	−0.500659	−0.250329	−	0.968161i	$-0.580539\pi$
$347$	−9.32624	−0.500659	−0.250329	+	0.968161i	$0.580539\pi$
$348$	−8.09017	−0.433679
$349$	32.0344	1.71476	0.857382	−	0.514680i	$-0.172089\pi$
$349$	32.0344	1.71476	0.857382	+	0.514680i	$0.172089\pi$
$350$	0	0
$351$	7.23607	0.386233
$352$	1.00000	0.0533002
$353$	16.4721	0.876723	0.438362	−	0.898799i	$-0.355559\pi$
$353$	16.4721	0.876723	0.438362	+	0.898799i	$0.355559\pi$
$354$	25.4164	1.35087
$355$	3.88854	0.206382
$356$	6.00000	0.317999
$357$	0	0
$358$	−13.6180	−0.719735
$359$	9.09017	0.479761	0.239880	−	0.970802i	$-0.422892\pi$
$359$	9.09017	0.479761	0.239880	+	0.970802i	$0.422892\pi$
$360$	−1.47214	−0.0775884
$361$	0.201626	0.0106119
$362$	3.41641	0.179562
$363$	−2.61803	−0.137411
$364$	0	0
$365$	−6.18034	−0.323494
$366$	35.1246	1.83599
$367$	−9.56231	−0.499148	−0.249574	−	0.968356i	$-0.580291\pi$
$367$	−9.56231	−0.499148	−0.249574	+	0.968356i	$0.580291\pi$
$368$	6.09017	0.317472
$369$	−38.8885	−2.02446
$370$	3.00000	0.155963
$371$	0	0
$372$	12.0902	0.626846
$373$	25.9787	1.34513	0.672563	−	0.740040i	$-0.265193\pi$
$373$	25.9787	1.34513	0.672563	+	0.740040i	$0.265193\pi$
$374$	−2.61803	−0.135375
$375$	−9.85410	−0.508864
$376$	−0.909830	−0.0469209
$377$	−10.0000	−0.515026
$378$	0	0
$379$	29.1246	1.49603	0.748015	−	0.663681i	$-0.231007\pi$
$379$	29.1246	1.49603	0.748015	+	0.663681i	$0.231007\pi$
$380$	1.67376	0.0858622
$381$	−35.0344	−1.79487
$382$	14.9443	0.764615
$383$	38.3607	1.96014	0.980070	−	0.198654i	$-0.0636572\pi$
$383$	38.3607	1.96014	0.980070	+	0.198654i	$0.0636572\pi$
$384$	−2.61803	−0.133601
$385$	0	0
$386$	−1.32624	−0.0675037
$387$	−3.85410	−0.195915
$388$	14.5623	0.739289
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	−3.23607	−0.163865
$391$	−15.9443	−0.806336
$392$	−7.00000	−0.353553
$393$	−0.854102	−0.0430837
$394$	−9.52786	−0.480007
$395$	−2.72949	−0.137336
$396$	3.85410	0.193676
$397$	−13.0557	−0.655248	−0.327624	−	0.944808i	$-0.606248\pi$
$397$	−13.0557	−0.655248	−0.327624	+	0.944808i	$0.606248\pi$
$398$	8.00000	0.401004
$399$	0	0
$400$	−4.85410	−0.242705
$401$	14.5066	0.724424	0.362212	−	0.932096i	$-0.382022\pi$
$401$	14.5066	0.724424	0.362212	+	0.932096i	$0.382022\pi$
$402$	−20.9443	−1.04461
$403$	14.9443	0.744427
$404$	−1.23607	−0.0614967
$405$	2.18034	0.108342
$406$	0	0
$407$	−7.85410	−0.389313
$408$	6.85410	0.339329
$409$	15.4164	0.762292	0.381146	−	0.924515i	$-0.375529\pi$
$409$	15.4164	0.762292	0.381146	+	0.924515i	$0.375529\pi$
$410$	3.85410	0.190341
$411$	46.8328	2.31009
$412$	10.8541	0.534743
$413$	0	0
$414$	23.4721	1.15359
$415$	−1.12461	−0.0552050
$416$	−3.23607	−0.158661
$417$	26.6525	1.30518
$418$	−4.38197	−0.214329
$419$	−7.05573	−0.344695	−0.172347	−	0.985036i	$-0.555135\pi$
$419$	−7.05573	−0.344695	−0.172347	+	0.985036i	$0.555135\pi$
$420$	0	0
$421$	−15.6180	−0.761176	−0.380588	−	0.924745i	$-0.624278\pi$
$421$	−15.6180	−0.761176	−0.380588	+	0.924745i	$0.624278\pi$
$422$	13.8541	0.674407
$423$	−3.50658	−0.170496
$424$	−9.70820	−0.471472
$425$	12.7082	0.616438
$426$	26.6525	1.29132
$427$	0	0
$428$	7.41641	0.358486
$429$	8.47214	0.409039
$430$	0.381966	0.0184200
$431$	−12.5066	−0.602421	−0.301210	−	0.953558i	$-0.597391\pi$
$431$	−12.5066	−0.602421	−0.301210	+	0.953558i	$0.597391\pi$
$432$	−2.23607	−0.107583
$433$	−21.7082	−1.04323	−0.521615	−	0.853181i	$-0.674670\pi$
$433$	−21.7082	−1.04323	−0.521615	+	0.853181i	$0.674670\pi$
$434$	0	0
$435$	3.09017	0.148162
$436$	1.70820	0.0818081
$437$	−26.6869	−1.27661
$438$	−42.3607	−2.02407
$439$	−38.9787	−1.86035	−0.930176	−	0.367113i	$-0.880346\pi$
$439$	−38.9787	−1.86035	−0.930176	+	0.367113i	$0.880346\pi$
$440$	−0.381966	−0.0182095
$441$	−26.9787	−1.28470
$442$	8.47214	0.402978
$443$	33.7082	1.60153	0.800763	−	0.598982i	$-0.204428\pi$
$443$	33.7082	1.60153	0.800763	+	0.598982i	$0.204428\pi$
$444$	20.5623	0.975844
$445$	−2.29180	−0.108642
$446$	15.7082	0.743805
$447$	12.8541	0.607978
$448$	0	0
$449$	14.8328	0.700004	0.350002	−	0.936749i	$-0.386181\pi$
$449$	14.8328	0.700004	0.350002	+	0.936749i	$0.386181\pi$
$450$	−18.7082	−0.881913
$451$	−10.0902	−0.475128
$452$	5.23607	0.246284
$453$	−37.8885	−1.78016
$454$	8.38197	0.393385
$455$	0	0
$456$	11.4721	0.537232
$457$	17.5279	0.819919	0.409959	−	0.912104i	$-0.365543\pi$
$457$	17.5279	0.819919	0.409959	+	0.912104i	$0.365543\pi$
$458$	−8.47214	−0.395877
$459$	5.85410	0.273246
$460$	−2.32624	−0.108461
$461$	2.76393	0.128729	0.0643646	−	0.997926i	$-0.479498\pi$
$461$	2.76393	0.128729	0.0643646	+	0.997926i	$0.479498\pi$
$462$	0	0
$463$	−8.00000	−0.371792	−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000	−0.371792	−0.185896	+	0.982569i	$0.559519\pi$
$464$	3.09017	0.143458
$465$	−4.61803	−0.214156
$466$	16.1803	0.749540
$467$	4.50658	0.208540	0.104270	−	0.994549i	$-0.466749\pi$
$467$	4.50658	0.208540	0.104270	+	0.994549i	$0.466749\pi$
$468$	−12.4721	−0.576525
$469$	0	0
$470$	0.347524	0.0160301
$471$	3.00000	0.138233
$472$	−9.70820	−0.446856
$473$	−1.00000	−0.0459800
$474$	−18.7082	−0.859296
$475$	21.2705	0.975958
$476$	0	0
$477$	−37.4164	−1.71318
$478$	−21.9787	−1.00528
$479$	2.56231	0.117075	0.0585374	−	0.998285i	$-0.481356\pi$
$479$	2.56231	0.117075	0.0585374	+	0.998285i	$0.481356\pi$
$480$	1.00000	0.0456435
$481$	25.4164	1.15889
$482$	9.41641	0.428906
$483$	0	0
$484$	1.00000	0.0454545
$485$	−5.56231	−0.252571
$486$	21.6525	0.982176
$487$	12.5623	0.569252	0.284626	−	0.958639i	$-0.408131\pi$
$487$	12.5623	0.569252	0.284626	+	0.958639i	$0.408131\pi$
$488$	−13.4164	−0.607332
$489$	40.5967	1.83585
$490$	2.67376	0.120788
$491$	−16.7426	−0.755585	−0.377793	−	0.925890i	$-0.623317\pi$
$491$	−16.7426	−0.755585	−0.377793	+	0.925890i	$0.623317\pi$
$492$	26.4164	1.19094
$493$	−8.09017	−0.364363
$494$	14.1803	0.638004
$495$	−1.47214	−0.0661676
$496$	−4.61803	−0.207356
$497$	0	0
$498$	−7.70820	−0.345413
$499$	−39.8541	−1.78411	−0.892057	−	0.451922i	$-0.850738\pi$
$499$	−39.8541	−1.78411	−0.892057	+	0.451922i	$0.850738\pi$
$500$	3.76393	0.168328
$501$	65.3050	2.91761
$502$	3.70820	0.165505
$503$	−13.4164	−0.598208	−0.299104	−	0.954221i	$-0.596688\pi$
$503$	−13.4164	−0.598208	−0.299104	+	0.954221i	$0.596688\pi$
$504$	0	0
$505$	0.472136	0.0210098
$506$	6.09017	0.270741
$507$	6.61803	0.293917
$508$	13.3820	0.593729
$509$	9.70820	0.430309	0.215154	−	0.976580i	$-0.430975\pi$
$509$	9.70820	0.430309	0.215154	+	0.976580i	$0.430975\pi$
$510$	−2.61803	−0.115928
$511$	0	0
$512$	1.00000	0.0441942
$513$	9.79837	0.432609
$514$	21.8885	0.965462
$515$	−4.14590	−0.182690
$516$	2.61803	0.115253
$517$	−0.909830	−0.0400143
$518$	0	0
$519$	−10.9443	−0.480400
$520$	1.23607	0.0542052
$521$	−6.36068	−0.278666	−0.139333	−	0.990246i	$-0.544496\pi$
$521$	−6.36068	−0.278666	−0.139333	+	0.990246i	$0.544496\pi$
$522$	11.9098	0.521279
$523$	29.2705	1.27991	0.639955	−	0.768412i	$-0.278953\pi$
$523$	29.2705	1.27991	0.639955	+	0.768412i	$0.278953\pi$
$524$	0.326238	0.0142518
$525$	0	0
$526$	−0.652476	−0.0284493
$527$	12.0902	0.526656
$528$	−2.61803	−0.113935
$529$	14.0902	0.612616
$530$	3.70820	0.161074
$531$	−37.4164	−1.62373
$532$	0	0
$533$	32.6525	1.41434
$534$	−15.7082	−0.679760
$535$	−2.83282	−0.122473
$536$	8.00000	0.345547
$537$	35.6525	1.53852
$538$	−22.4721	−0.968843
$539$	−7.00000	−0.301511
$540$	0.854102	0.0367547
$541$	31.1246	1.33815	0.669076	−	0.743194i	$-0.266690\pi$
$541$	31.1246	1.33815	0.669076	+	0.743194i	$0.266690\pi$
$542$	20.0902	0.862947
$543$	−8.94427	−0.383835
$544$	−2.61803	−0.112247
$545$	−0.652476	−0.0279490
$546$	0	0
$547$	−13.8885	−0.593831	−0.296916	−	0.954904i	$-0.595958\pi$
$547$	−13.8885	−0.593831	−0.296916	+	0.954904i	$0.595958\pi$
$548$	−17.8885	−0.764161
$549$	−51.7082	−2.20685
$550$	−4.85410	−0.206980
$551$	−13.5410	−0.576867
$552$	−15.9443	−0.678633
$553$	0	0
$554$	−14.5623	−0.618693
$555$	−7.85410	−0.333388
$556$	−10.1803	−0.431743
$557$	−0.111456	−0.00472255	−0.00236127	−	0.999997i	$-0.500752\pi$
$557$	−0.111456	−0.00472255	−0.00236127	+	0.999997i	$0.500752\pi$
$558$	−17.7984	−0.753465
$559$	3.23607	0.136871
$560$	0	0
$561$	6.85410	0.289380
$562$	0.798374	0.0336774
$563$	−30.0000	−1.26435	−0.632175	−	0.774826i	$-0.717837\pi$
$563$	−30.0000	−1.26435	−0.632175	+	0.774826i	$0.717837\pi$
$564$	2.38197	0.100299
$565$	−2.00000	−0.0841406
$566$	−21.4164	−0.900199
$567$	0	0
$568$	−10.1803	−0.427158
$569$	−19.5279	−0.818651	−0.409325	−	0.912389i	$-0.634236\pi$
$569$	−19.5279	−0.818651	−0.409325	+	0.912389i	$0.634236\pi$
$570$	−4.38197	−0.183540
$571$	39.7426	1.66318	0.831589	−	0.555392i	$-0.187432\pi$
$571$	39.7426	1.66318	0.831589	+	0.555392i	$0.187432\pi$
$572$	−3.23607	−0.135307
$573$	−39.1246	−1.63445
$574$	0	0
$575$	−29.5623	−1.23283
$576$	3.85410	0.160588
$577$	−24.8328	−1.03380	−0.516902	−	0.856045i	$-0.672915\pi$
$577$	−24.8328	−1.03380	−0.516902	+	0.856045i	$0.672915\pi$
$578$	−10.1459	−0.422014
$579$	3.47214	0.144297
$580$	−1.18034	−0.0490109
$581$	0	0
$582$	−38.1246	−1.58032
$583$	−9.70820	−0.402073
$584$	16.1803	0.669547
$585$	4.76393	0.196964
$586$	9.52786	0.393592
$587$	24.3607	1.00547	0.502736	−	0.864440i	$-0.332327\pi$
$587$	24.3607	1.00547	0.502736	+	0.864440i	$0.332327\pi$
$588$	18.3262	0.755761
$589$	20.2361	0.833813
$590$	3.70820	0.152664
$591$	24.9443	1.02607
$592$	−7.85410	−0.322802
$593$	−39.7082	−1.63062	−0.815310	−	0.579024i	$-0.803434\pi$
$593$	−39.7082	−1.63062	−0.815310	+	0.579024i	$0.803434\pi$
$594$	−2.23607	−0.0917470
$595$	0	0
$596$	−4.90983	−0.201114
$597$	−20.9443	−0.857192
$598$	−19.7082	−0.805928
$599$	26.7984	1.09495	0.547476	−	0.836821i	$-0.315589\pi$
$599$	26.7984	1.09495	0.547476	+	0.836821i	$0.315589\pi$
$600$	12.7082	0.518810
$601$	10.6525	0.434524	0.217262	−	0.976113i	$-0.430287\pi$
$601$	10.6525	0.434524	0.217262	+	0.976113i	$0.430287\pi$
$602$	0	0
$603$	30.8328	1.25561
$604$	14.4721	0.588863
$605$	−0.381966	−0.0155291
$606$	3.23607	0.131456
$607$	27.4164	1.11280	0.556399	−	0.830915i	$-0.312183\pi$
$607$	27.4164	1.11280	0.556399	+	0.830915i	$0.312183\pi$
$608$	−4.38197	−0.177712
$609$	0	0
$610$	5.12461	0.207489
$611$	2.94427	0.119112
$612$	−10.0902	−0.407871
$613$	−2.76393	−0.111634	−0.0558171	−	0.998441i	$-0.517776\pi$
$613$	−2.76393	−0.111634	−0.0558171	+	0.998441i	$0.517776\pi$
$614$	−20.0000	−0.807134
$615$	−10.0902	−0.406875
$616$	0	0
$617$	−36.4508	−1.46746	−0.733728	−	0.679443i	$-0.762221\pi$
$617$	−36.4508	−1.46746	−0.733728	+	0.679443i	$0.762221\pi$
$618$	−28.4164	−1.14308
$619$	−39.4164	−1.58428	−0.792140	−	0.610340i	$-0.791033\pi$
$619$	−39.4164	−1.58428	−0.792140	+	0.610340i	$0.791033\pi$
$620$	1.76393	0.0708412
$621$	−13.6180	−0.546473
$622$	−25.5279	−1.02357
$623$	0	0
$624$	8.47214	0.339157
$625$	22.8328	0.913313
$626$	−12.9443	−0.517357
$627$	11.4721	0.458153
$628$	−1.14590	−0.0457263
$629$	20.5623	0.819873
$630$	0	0
$631$	23.3050	0.927755	0.463878	−	0.885899i	$-0.346458\pi$
$631$	23.3050	0.927755	0.463878	+	0.885899i	$0.346458\pi$
$632$	7.14590	0.284249
$633$	−36.2705	−1.44162
$634$	−26.8328	−1.06567
$635$	−5.11146	−0.202842
$636$	25.4164	1.00783
$637$	22.6525	0.897524
$638$	3.09017	0.122341
$639$	−39.2361	−1.55215
$640$	−0.381966	−0.0150985
$641$	−0.875388	−0.0345758	−0.0172879	−	0.999851i	$-0.505503\pi$
$641$	−0.875388	−0.0345758	−0.0172879	+	0.999851i	$0.505503\pi$
$642$	−19.4164	−0.766304
$643$	−7.23607	−0.285363	−0.142681	−	0.989769i	$-0.545572\pi$
$643$	−7.23607	−0.285363	−0.142681	+	0.989769i	$0.545572\pi$
$644$	0	0
$645$	−1.00000	−0.0393750
$646$	11.4721	0.451365
$647$	−17.8885	−0.703271	−0.351636	−	0.936137i	$-0.614374\pi$
$647$	−17.8885	−0.703271	−0.351636	+	0.936137i	$0.614374\pi$
$648$	−5.70820	−0.224239
$649$	−9.70820	−0.381080
$650$	15.7082	0.616126
$651$	0	0
$652$	−15.5066	−0.607284
$653$	−8.56231	−0.335069	−0.167534	−	0.985866i	$-0.553581\pi$
$653$	−8.56231	−0.335069	−0.167534	+	0.985866i	$0.553581\pi$
$654$	−4.47214	−0.174874
$655$	−0.124612	−0.00486899
$656$	−10.0902	−0.393955
$657$	62.3607	2.43292
$658$	0	0
$659$	−12.1803	−0.474479	−0.237239	−	0.971451i	$-0.576243\pi$
$659$	−12.1803	−0.474479	−0.237239	+	0.971451i	$0.576243\pi$
$660$	1.00000	0.0389249
$661$	28.9443	1.12580	0.562901	−	0.826524i	$-0.309685\pi$
$661$	28.9443	1.12580	0.562901	+	0.826524i	$0.309685\pi$
$662$	16.0000	0.621858
$663$	−22.1803	−0.861413
$664$	2.94427	0.114260
$665$	0	0
$666$	−30.2705	−1.17296
$667$	18.8197	0.728700
$668$	−24.9443	−0.965123
$669$	−41.1246	−1.58997
$670$	−3.05573	−0.118053
$671$	−13.4164	−0.517935
$672$	0	0
$673$	6.94427	0.267682	0.133841	−	0.991003i	$-0.457269\pi$
$673$	6.94427	0.267682	0.133841	+	0.991003i	$0.457269\pi$
$674$	−27.2705	−1.05042
$675$	10.8541	0.417775
$676$	−2.52786	−0.0972255
$677$	12.6738	0.487092	0.243546	−	0.969889i	$-0.421689\pi$
$677$	12.6738	0.487092	0.243546	+	0.969889i	$0.421689\pi$
$678$	−13.7082	−0.526460
$679$	0	0
$680$	1.00000	0.0383482
$681$	−21.9443	−0.840906
$682$	−4.61803	−0.176834
$683$	−3.34752	−0.128089	−0.0640447	−	0.997947i	$-0.520400\pi$
$683$	−3.34752	−0.128089	−0.0640447	+	0.997947i	$0.520400\pi$
$684$	−16.8885	−0.645750
$685$	6.83282	0.261068
$686$	0	0
$687$	22.1803	0.846233
$688$	−1.00000	−0.0381246
$689$	31.4164	1.19687
$690$	6.09017	0.231849
$691$	−14.4721	−0.550546	−0.275273	−	0.961366i	$-0.588768\pi$
$691$	−14.4721	−0.550546	−0.275273	+	0.961366i	$0.588768\pi$
$692$	4.18034	0.158913
$693$	0	0
$694$	−9.32624	−0.354019
$695$	3.88854	0.147501
$696$	−8.09017	−0.306657
$697$	26.4164	1.00059
$698$	32.0344	1.21252
$699$	−42.3607	−1.60223
$700$	0	0
$701$	−8.18034	−0.308967	−0.154484	−	0.987995i	$-0.549371\pi$
$701$	−8.18034	−0.308967	−0.154484	+	0.987995i	$0.549371\pi$
$702$	7.23607	0.273108
$703$	34.4164	1.29804
$704$	1.00000	0.0376889
$705$	−0.909830	−0.0342662
$706$	16.4721	0.619937
$707$	0	0
$708$	25.4164	0.955207
$709$	−45.0132	−1.69050	−0.845252	−	0.534367i	$-0.820550\pi$
$709$	−45.0132	−1.69050	−0.845252	+	0.534367i	$0.820550\pi$
$710$	3.88854	0.145934
$711$	27.5410	1.03287
$712$	6.00000	0.224860
$713$	−28.1246	−1.05327
$714$	0	0
$715$	1.23607	0.0462263
$716$	−13.6180	−0.508930
$717$	57.5410	2.14891
$718$	9.09017	0.339242
$719$	−47.4508	−1.76962	−0.884809	−	0.465954i	$-0.845711\pi$
$719$	−47.4508	−1.76962	−0.884809	+	0.465954i	$0.845711\pi$
$720$	−1.47214	−0.0548633
$721$	0	0
$722$	0.201626	0.00750375
$723$	−24.6525	−0.916835
$724$	3.41641	0.126970
$725$	−15.0000	−0.557086
$726$	−2.61803	−0.0971644
$727$	−25.4164	−0.942642	−0.471321	−	0.881962i	$-0.656223\pi$
$727$	−25.4164	−0.942642	−0.471321	+	0.881962i	$0.656223\pi$
$728$	0	0
$729$	−39.5623	−1.46527
$730$	−6.18034	−0.228745
$731$	2.61803	0.0968315
$732$	35.1246	1.29824
$733$	22.1459	0.817977	0.408989	−	0.912539i	$-0.365882\pi$
$733$	22.1459	0.817977	0.408989	+	0.912539i	$0.365882\pi$
$734$	−9.56231	−0.352951
$735$	−7.00000	−0.258199
$736$	6.09017	0.224487
$737$	8.00000	0.294684
$738$	−38.8885	−1.43151
$739$	−35.0902	−1.29081	−0.645406	−	0.763839i	$-0.723312\pi$
$739$	−35.0902	−1.29081	−0.645406	+	0.763839i	$0.723312\pi$
$740$	3.00000	0.110282
$741$	−37.1246	−1.36381
$742$	0	0
$743$	−2.83282	−0.103926	−0.0519630	−	0.998649i	$-0.516548\pi$
$743$	−2.83282	−0.103926	−0.0519630	+	0.998649i	$0.516548\pi$
$744$	12.0902	0.443247
$745$	1.87539	0.0687089
$746$	25.9787	0.951148
$747$	11.3475	0.415184
$748$	−2.61803	−0.0957248
$749$	0	0
$750$	−9.85410	−0.359821
$751$	−1.70820	−0.0623332	−0.0311666	−	0.999514i	$-0.509922\pi$
$751$	−1.70820	−0.0623332	−0.0311666	+	0.999514i	$0.509922\pi$
$752$	−0.909830	−0.0331781
$753$	−9.70820	−0.353787
$754$	−10.0000	−0.364179
$755$	−5.52786	−0.201180
$756$	0	0
$757$	−38.1033	−1.38489	−0.692444	−	0.721471i	$-0.743466\pi$
$757$	−38.1033	−1.38489	−0.692444	+	0.721471i	$0.743466\pi$
$758$	29.1246	1.05785
$759$	−15.9443	−0.578740
$760$	1.67376	0.0607137
$761$	39.2361	1.42231	0.711153	−	0.703037i	$-0.248173\pi$
$761$	39.2361	1.42231	0.711153	+	0.703037i	$0.248173\pi$
$762$	−35.0344	−1.26916
$763$	0	0
$764$	14.9443	0.540665
$765$	3.85410	0.139345
$766$	38.3607	1.38603
$767$	31.4164	1.13438
$768$	−2.61803	−0.0944702
$769$	25.6738	0.925820	0.462910	−	0.886405i	$-0.346805\pi$
$769$	25.6738	0.925820	0.462910	+	0.886405i	$0.346805\pi$
$770$	0	0
$771$	−57.3050	−2.06379
$772$	−1.32624	−0.0477323
$773$	−25.6738	−0.923421	−0.461711	−	0.887031i	$-0.652764\pi$
$773$	−25.6738	−0.923421	−0.461711	+	0.887031i	$0.652764\pi$
$774$	−3.85410	−0.138533
$775$	22.4164	0.805221
$776$	14.5623	0.522756
$777$	0	0
$778$	−6.00000	−0.215110
$779$	44.2148	1.58416
$780$	−3.23607	−0.115870
$781$	−10.1803	−0.364281
$782$	−15.9443	−0.570166
$783$	−6.90983	−0.246937
$784$	−7.00000	−0.250000
$785$	0.437694	0.0156220
$786$	−0.854102	−0.0304648
$787$	23.1246	0.824303	0.412152	−	0.911115i	$-0.364777\pi$
$787$	23.1246	0.824303	0.412152	+	0.911115i	$0.364777\pi$
$788$	−9.52786	−0.339416
$789$	1.70820	0.0608137
$790$	−2.72949	−0.0971109
$791$	0	0
$792$	3.85410	0.136950
$793$	43.4164	1.54176
$794$	−13.0557	−0.463330
$795$	−9.70820	−0.344315
$796$	8.00000	0.283552
$797$	19.8885	0.704488	0.352244	−	0.935908i	$-0.385419\pi$
$797$	19.8885	0.704488	0.352244	+	0.935908i	$0.385419\pi$
$798$	0	0
$799$	2.38197	0.0842679
$800$	−4.85410	−0.171618
$801$	23.1246	0.817068
$802$	14.5066	0.512245
$803$	16.1803	0.570992
$804$	−20.9443	−0.738648
$805$	0	0
$806$	14.9443	0.526390
$807$	58.8328	2.07101
$808$	−1.23607	−0.0434847
$809$	12.2148	0.429449	0.214724	−	0.976675i	$-0.431115\pi$
$809$	12.2148	0.429449	0.214724	+	0.976675i	$0.431115\pi$
$810$	2.18034	0.0766093
$811$	2.85410	0.100221	0.0501105	−	0.998744i	$-0.484043\pi$
$811$	2.85410	0.100221	0.0501105	+	0.998744i	$0.484043\pi$
$812$	0	0
$813$	−52.5967	−1.84465
$814$	−7.85410	−0.275286
$815$	5.92299	0.207473
$816$	6.85410	0.239942
$817$	4.38197	0.153306
$818$	15.4164	0.539022
$819$	0	0
$820$	3.85410	0.134591
$821$	−9.59675	−0.334929	−0.167464	−	0.985878i	$-0.553558\pi$
$821$	−9.59675	−0.334929	−0.167464	+	0.985878i	$0.553558\pi$
$822$	46.8328	1.63348
$823$	42.4721	1.48049	0.740243	−	0.672340i	$-0.234711\pi$
$823$	42.4721	1.48049	0.740243	+	0.672340i	$0.234711\pi$
$824$	10.8541	0.378121
$825$	12.7082	0.442443
$826$	0	0
$827$	−18.9443	−0.658757	−0.329378	−	0.944198i	$-0.606839\pi$
$827$	−18.9443	−0.658757	−0.329378	+	0.944198i	$0.606839\pi$
$828$	23.4721	0.815713
$829$	−18.9787	−0.659158	−0.329579	−	0.944128i	$-0.606907\pi$
$829$	−18.9787	−0.659158	−0.329579	+	0.944128i	$0.606907\pi$
$830$	−1.12461	−0.0390358
$831$	38.1246	1.32253
$832$	−3.23607	−0.112190
$833$	18.3262	0.634967
$834$	26.6525	0.922900
$835$	9.52786	0.329725
$836$	−4.38197	−0.151553
$837$	10.3262	0.356927
$838$	−7.05573	−0.243736
$839$	−20.4721	−0.706777	−0.353388	−	0.935477i	$-0.614971\pi$
$839$	−20.4721	−0.706777	−0.353388	+	0.935477i	$0.614971\pi$
$840$	0	0
$841$	−19.4508	−0.670719
$842$	−15.6180	−0.538233
$843$	−2.09017	−0.0719893
$844$	13.8541	0.476878
$845$	0.965558	0.0332162
$846$	−3.50658	−0.120559
$847$	0	0
$848$	−9.70820	−0.333381
$849$	56.0689	1.92428
$850$	12.7082	0.435888
$851$	−47.8328	−1.63969
$852$	26.6525	0.913099
$853$	43.5967	1.49272	0.746362	−	0.665540i	$-0.231799\pi$
$853$	43.5967	1.49272	0.746362	+	0.665540i	$0.231799\pi$
$854$	0	0
$855$	6.45085	0.220614
$856$	7.41641	0.253488
$857$	29.5066	1.00793	0.503963	−	0.863725i	$-0.331875\pi$
$857$	29.5066	1.00793	0.503963	+	0.863725i	$0.331875\pi$
$858$	8.47214	0.289234
$859$	−18.7426	−0.639491	−0.319745	−	0.947503i	$-0.603597\pi$
$859$	−18.7426	−0.639491	−0.319745	+	0.947503i	$0.603597\pi$
$860$	0.381966	0.0130249
$861$	0	0
$862$	−12.5066	−0.425976
$863$	−15.3050	−0.520987	−0.260493	−	0.965476i	$-0.583885\pi$
$863$	−15.3050	−0.520987	−0.260493	+	0.965476i	$0.583885\pi$
$864$	−2.23607	−0.0760726
$865$	−1.59675	−0.0542911
$866$	−21.7082	−0.737675
$867$	26.5623	0.902103
$868$	0	0
$869$	7.14590	0.242408
$870$	3.09017	0.104767
$871$	−25.8885	−0.877200
$872$	1.70820	0.0578471
$873$	56.1246	1.89953
$874$	−26.6869	−0.902698
$875$	0	0
$876$	−42.3607	−1.43123
$877$	41.1246	1.38868	0.694340	−	0.719647i	$-0.255697\pi$
$877$	41.1246	1.38868	0.694340	+	0.719647i	$0.255697\pi$
$878$	−38.9787	−1.31547
$879$	−24.9443	−0.841349
$880$	−0.381966	−0.0128761
$881$	−31.6738	−1.06712	−0.533558	−	0.845763i	$-0.679145\pi$
$881$	−31.6738	−1.06712	−0.533558	+	0.845763i	$0.679145\pi$
$882$	−26.9787	−0.908421
$883$	8.47214	0.285110	0.142555	−	0.989787i	$-0.454468\pi$
$883$	8.47214	0.285110	0.142555	+	0.989787i	$0.454468\pi$
$884$	8.47214	0.284949
$885$	−9.70820	−0.326338
$886$	33.7082	1.13245
$887$	−1.41641	−0.0475583	−0.0237792	−	0.999717i	$-0.507570\pi$
$887$	−1.41641	−0.0475583	−0.0237792	+	0.999717i	$0.507570\pi$
$888$	20.5623	0.690026
$889$	0	0
$890$	−2.29180	−0.0768212
$891$	−5.70820	−0.191232
$892$	15.7082	0.525950
$893$	3.98684	0.133415
$894$	12.8541	0.429905
$895$	5.20163	0.173871
$896$	0	0
$897$	51.5967	1.72277
$898$	14.8328	0.494977
$899$	−14.2705	−0.475948
$900$	−18.7082	−0.623607
$901$	25.4164	0.846743
$902$	−10.0902	−0.335966
$903$	0	0
$904$	5.23607	0.174149
$905$	−1.30495	−0.0433781
$906$	−37.8885	−1.25876
$907$	−5.05573	−0.167873	−0.0839363	−	0.996471i	$-0.526749\pi$
$907$	−5.05573	−0.167873	−0.0839363	+	0.996471i	$0.526749\pi$
$908$	8.38197	0.278165
$909$	−4.76393	−0.158010
$910$	0	0
$911$	−54.0689	−1.79138	−0.895691	−	0.444677i	$-0.853318\pi$
$911$	−54.0689	−1.79138	−0.895691	+	0.444677i	$0.853318\pi$
$912$	11.4721	0.379880
$913$	2.94427	0.0974412
$914$	17.5279	0.579770
$915$	−13.4164	−0.443533
$916$	−8.47214	−0.279927
$917$	0	0
$918$	5.85410	0.193214
$919$	59.2705	1.95515	0.977577	−	0.210579i	$-0.0675349\pi$
$919$	59.2705	1.95515	0.977577	+	0.210579i	$0.0675349\pi$
$920$	−2.32624	−0.0766938
$921$	52.3607	1.72534
$922$	2.76393	0.0910253
$923$	32.9443	1.08437
$924$	0	0
$925$	38.1246	1.25353
$926$	−8.00000	−0.262896
$927$	41.8328	1.37397
$928$	3.09017	0.101440
$929$	2.06888	0.0678779	0.0339389	−	0.999424i	$-0.489195\pi$
$929$	2.06888	0.0678779	0.0339389	+	0.999424i	$0.489195\pi$
$930$	−4.61803	−0.151431
$931$	30.6738	1.00529
$932$	16.1803	0.530005
$933$	66.8328	2.18801
$934$	4.50658	0.147460
$935$	1.00000	0.0327035
$936$	−12.4721	−0.407665
$937$	−20.8328	−0.680578	−0.340289	−	0.940321i	$-0.610525\pi$
$937$	−20.8328	−0.680578	−0.340289	+	0.940321i	$0.610525\pi$
$938$	0	0
$939$	33.8885	1.10591
$940$	0.347524	0.0113350
$941$	36.5410	1.19120	0.595602	−	0.803280i	$-0.296914\pi$
$941$	36.5410	1.19120	0.595602	+	0.803280i	$0.296914\pi$
$942$	3.00000	0.0977453
$943$	−61.4508	−2.00111
$944$	−9.70820	−0.315975
$945$	0	0
$946$	−1.00000	−0.0325128
$947$	−24.6525	−0.801098	−0.400549	−	0.916275i	$-0.631181\pi$
$947$	−24.6525	−0.801098	−0.400549	+	0.916275i	$0.631181\pi$
$948$	−18.7082	−0.607614
$949$	−52.3607	−1.69970
$950$	21.2705	0.690106
$951$	70.2492	2.27799
$952$	0	0
$953$	−47.3050	−1.53236	−0.766179	−	0.642627i	$-0.777844\pi$
$953$	−47.3050	−1.53236	−0.766179	+	0.642627i	$0.777844\pi$
$954$	−37.4164	−1.21140
$955$	−5.70820	−0.184713
$956$	−21.9787	−0.710842
$957$	−8.09017	−0.261518
$958$	2.56231	0.0827843
$959$	0	0
$960$	1.00000	0.0322749
$961$	−9.67376	−0.312057
$962$	25.4164	0.819458
$963$	28.5836	0.921093
$964$	9.41641	0.303282
$965$	0.506578	0.0163073
$966$	0	0
$967$	−26.1591	−0.841218	−0.420609	−	0.907242i	$-0.638184\pi$
$967$	−26.1591	−0.841218	−0.420609	+	0.907242i	$0.638184\pi$
$968$	1.00000	0.0321412
$969$	−30.0344	−0.964845
$970$	−5.56231	−0.178595
$971$	−47.1246	−1.51230	−0.756150	−	0.654398i	$-0.772922\pi$
$971$	−47.1246	−1.51230	−0.756150	+	0.654398i	$0.772922\pi$
$972$	21.6525	0.694503
$973$	0	0
$974$	12.5623	0.402522
$975$	−41.1246	−1.31704
$976$	−13.4164	−0.429449
$977$	42.2148	1.35057	0.675285	−	0.737557i	$-0.264021\pi$
$977$	42.2148	1.35057	0.675285	+	0.737557i	$0.264021\pi$
$978$	40.5967	1.29814
$979$	6.00000	0.191761
$980$	2.67376	0.0854102
$981$	6.58359	0.210198
$982$	−16.7426	−0.534279
$983$	23.2361	0.741115	0.370558	−	0.928809i	$-0.379167\pi$
$983$	23.2361	0.741115	0.370558	+	0.928809i	$0.379167\pi$
$984$	26.4164	0.842124
$985$	3.63932	0.115958
$986$	−8.09017	−0.257643
$987$	0	0
$988$	14.1803	0.451137
$989$	−6.09017	−0.193656
$990$	−1.47214	−0.0467876
$991$	15.5279	0.493259	0.246629	−	0.969110i	$-0.420677\pi$
$991$	15.5279	0.493259	0.246629	+	0.969110i	$0.420677\pi$
$992$	−4.61803	−0.146623
$993$	−41.8885	−1.32929
$994$	0	0
$995$	−3.05573	−0.0968731
$996$	−7.70820	−0.244244
$997$	17.5623	0.556204	0.278102	−	0.960552i	$-0.410295\pi$
$997$	17.5623	0.556204	0.278102	+	0.960552i	$0.410295\pi$
$998$	−39.8541	−1.26156
$999$	17.5623	0.555647

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	946.2.a.f.1.1	✓	2
3.2	odd	2		8514.2.a.o.1.1		2
4.3	odd	2		7568.2.a.u.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
946.2.a.f.1.1	✓	2	1.1	even	1	trivial
7568.2.a.u.1.2		2	4.3	odd	2
8514.2.a.o.1.1		2	3.2	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:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	946.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.61803 q^{3} +1.00000 q^{4} -0.381966 q^{5} -2.61803 q^{6} +1.00000 q^{8} +3.85410 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.61803 q^{3} +1.00000 q^{4} -0.381966 q^{5} -2.61803 q^{6} +1.00000 q^{8} +3.85410 q^{9} -0.381966 q^{10} +1.00000 q^{11} -2.61803 q^{12} -3.23607 q^{13} +1.00000 q^{15} +1.00000 q^{16} -2.61803 q^{17} +3.85410 q^{18} -4.38197 q^{19} -0.381966 q^{20} +1.00000 q^{22} +6.09017 q^{23} -2.61803 q^{24} -4.85410 q^{25} -3.23607 q^{26} -2.23607 q^{27} +3.09017 q^{29} +1.00000 q^{30} -4.61803 q^{31} +1.00000 q^{32} -2.61803 q^{33} -2.61803 q^{34} +3.85410 q^{36} -7.85410 q^{37} -4.38197 q^{38} +8.47214 q^{39} -0.381966 q^{40} -10.0902 q^{41} -1.00000 q^{43} +1.00000 q^{44} -1.47214 q^{45} +6.09017 q^{46} -0.909830 q^{47} -2.61803 q^{48} -7.00000 q^{49} -4.85410 q^{50} +6.85410 q^{51} -3.23607 q^{52} -9.70820 q^{53} -2.23607 q^{54} -0.381966 q^{55} +11.4721 q^{57} +3.09017 q^{58} -9.70820 q^{59} +1.00000 q^{60} -13.4164 q^{61} -4.61803 q^{62} +1.00000 q^{64} +1.23607 q^{65} -2.61803 q^{66} +8.00000 q^{67} -2.61803 q^{68} -15.9443 q^{69} -10.1803 q^{71} +3.85410 q^{72} +16.1803 q^{73} -7.85410 q^{74} +12.7082 q^{75} -4.38197 q^{76} +8.47214 q^{78} +7.14590 q^{79} -0.381966 q^{80} -5.70820 q^{81} -10.0902 q^{82} +2.94427 q^{83} +1.00000 q^{85} -1.00000 q^{86} -8.09017 q^{87} +1.00000 q^{88} +6.00000 q^{89} -1.47214 q^{90} +6.09017 q^{92} +12.0902 q^{93} -0.909830 q^{94} +1.67376 q^{95} -2.61803 q^{96} +14.5623 q^{97} -7.00000 q^{98} +3.85410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{8} + q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^8 + q^9	\( 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{8} + q^{9} - 3 q^{10} + 2 q^{11} - 3 q^{12} - 2 q^{13} + 2 q^{15} + 2 q^{16} - 3 q^{17} + q^{18} - 11 q^{19} - 3 q^{20} + 2 q^{22} + q^{23} - 3 q^{24} - 3 q^{25} - 2 q^{26} - 5 q^{29} + 2 q^{30} - 7 q^{31} + 2 q^{32} - 3 q^{33} - 3 q^{34} + q^{36} - 9 q^{37} - 11 q^{38} + 8 q^{39} - 3 q^{40} - 9 q^{41} - 2 q^{43} + 2 q^{44} + 6 q^{45} + q^{46} - 13 q^{47} - 3 q^{48} - 14 q^{49} - 3 q^{50} + 7 q^{51} - 2 q^{52} - 6 q^{53} - 3 q^{55} + 14 q^{57} - 5 q^{58} - 6 q^{59} + 2 q^{60} - 7 q^{62} + 2 q^{64} - 2 q^{65} - 3 q^{66} + 16 q^{67} - 3 q^{68} - 14 q^{69} + 2 q^{71} + q^{72} + 10 q^{73} - 9 q^{74} + 12 q^{75} - 11 q^{76} + 8 q^{78} + 21 q^{79} - 3 q^{80} + 2 q^{81} - 9 q^{82} - 12 q^{83} + 2 q^{85} - 2 q^{86} - 5 q^{87} + 2 q^{88} + 12 q^{89} + 6 q^{90} + q^{92} + 13 q^{93} - 13 q^{94} + 19 q^{95} - 3 q^{96} + 9 q^{97} - 14 q^{98} + q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^8 + q^9 - 3 * q^10 + 2 * q^11 - 3 * q^12 - 2 * q^13 + 2 * q^15 + 2 * q^16 - 3 * q^17 + q^18 - 11 * q^19 - 3 * q^20 + 2 * q^22 + q^23 - 3 * q^24 - 3 * q^25 - 2 * q^26 - 5 * q^29 + 2 * q^30 - 7 * q^31 + 2 * q^32 - 3 * q^33 - 3 * q^34 + q^36 - 9 * q^37 - 11 * q^38 + 8 * q^39 - 3 * q^40 - 9 * q^41 - 2 * q^43 + 2 * q^44 + 6 * q^45 + q^46 - 13 * q^47 - 3 * q^48 - 14 * q^49 - 3 * q^50 + 7 * q^51 - 2 * q^52 - 6 * q^53 - 3 * q^55 + 14 * q^57 - 5 * q^58 - 6 * q^59 + 2 * q^60 - 7 * q^62 + 2 * q^64 - 2 * q^65 - 3 * q^66 + 16 * q^67 - 3 * q^68 - 14 * q^69 + 2 * q^71 + q^72 + 10 * q^73 - 9 * q^74 + 12 * q^75 - 11 * q^76 + 8 * q^78 + 21 * q^79 - 3 * q^80 + 2 * q^81 - 9 * q^82 - 12 * q^83 + 2 * q^85 - 2 * q^86 - 5 * q^87 + 2 * q^88 + 12 * q^89 + 6 * q^90 + q^92 + 13 * q^93 - 13 * q^94 + 19 * q^95 - 3 * q^96 + 9 * q^97 - 14 * q^98 + q^99

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