LMFDB - Embedded newform 7942.2.a.z.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7942,2,Mod(1,7942)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7942, 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("7942.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7942 = 2 \cdot 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7942.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:	$63.4171892853$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	7942.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} +3.85410 q^{5} -0.618034 q^{6} -1.23607 q^{7} +1.00000 q^{8} -2.61803 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} +3.85410 q^{5} -0.618034 q^{6} -1.23607 q^{7} +1.00000 q^{8} -2.61803 q^{9} +3.85410 q^{10} +1.00000 q^{11} -0.618034 q^{12} +0.763932 q^{13} -1.23607 q^{14} -2.38197 q^{15} +1.00000 q^{16} -2.47214 q^{17} -2.61803 q^{18} +3.85410 q^{20} +0.763932 q^{21} +1.00000 q^{22} +3.85410 q^{23} -0.618034 q^{24} +9.85410 q^{25} +0.763932 q^{26} +3.47214 q^{27} -1.23607 q^{28} +1.52786 q^{29} -2.38197 q^{30} +5.09017 q^{31} +1.00000 q^{32} -0.618034 q^{33} -2.47214 q^{34} -4.76393 q^{35} -2.61803 q^{36} +7.61803 q^{37} -0.472136 q^{39} +3.85410 q^{40} +6.94427 q^{41} +0.763932 q^{42} +1.23607 q^{43} +1.00000 q^{44} -10.0902 q^{45} +3.85410 q^{46} -8.09017 q^{47} -0.618034 q^{48} -5.47214 q^{49} +9.85410 q^{50} +1.52786 q^{51} +0.763932 q^{52} -7.85410 q^{53} +3.47214 q^{54} +3.85410 q^{55} -1.23607 q^{56} +1.52786 q^{58} +1.14590 q^{59} -2.38197 q^{60} -10.9443 q^{61} +5.09017 q^{62} +3.23607 q^{63} +1.00000 q^{64} +2.94427 q^{65} -0.618034 q^{66} -10.8541 q^{67} -2.47214 q^{68} -2.38197 q^{69} -4.76393 q^{70} +10.4721 q^{71} -2.61803 q^{72} +7.70820 q^{73} +7.61803 q^{74} -6.09017 q^{75} -1.23607 q^{77} -0.472136 q^{78} +7.52786 q^{79} +3.85410 q^{80} +5.70820 q^{81} +6.94427 q^{82} +6.00000 q^{83} +0.763932 q^{84} -9.52786 q^{85} +1.23607 q^{86} -0.944272 q^{87} +1.00000 q^{88} +4.85410 q^{89} -10.0902 q^{90} -0.944272 q^{91} +3.85410 q^{92} -3.14590 q^{93} -8.09017 q^{94} -0.618034 q^{96} -7.52786 q^{97} -5.47214 q^{98} -2.61803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + q^{3} + 2 q^{4} + q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - 3 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 + q^5 + q^6 + 2 * q^7 + 2 * q^8 - 3 * q^9	$ 2 q + 2 q^{2} + q^{3} + 2 q^{4} + q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - 3 q^{9} + q^{10} + 2 q^{11} + q^{12} + 6 q^{13} + 2 q^{14} - 7 q^{15} + 2 q^{16} + 4 q^{17} - 3 q^{18} + q^{20} + 6 q^{21} + 2 q^{22} + q^{23} + q^{24} + 13 q^{25} + 6 q^{26} - 2 q^{27} + 2 q^{28} + 12 q^{29} - 7 q^{30} - q^{31} + 2 q^{32} + q^{33} + 4 q^{34} - 14 q^{35} - 3 q^{36} + 13 q^{37} + 8 q^{39} + q^{40} - 4 q^{41} + 6 q^{42} - 2 q^{43} + 2 q^{44} - 9 q^{45} + q^{46} - 5 q^{47} + q^{48} - 2 q^{49} + 13 q^{50} + 12 q^{51} + 6 q^{52} - 9 q^{53} - 2 q^{54} + q^{55} + 2 q^{56} + 12 q^{58} + 9 q^{59} - 7 q^{60} - 4 q^{61} - q^{62} + 2 q^{63} + 2 q^{64} - 12 q^{65} + q^{66} - 15 q^{67} + 4 q^{68} - 7 q^{69} - 14 q^{70} + 12 q^{71} - 3 q^{72} + 2 q^{73} + 13 q^{74} - q^{75} + 2 q^{77} + 8 q^{78} + 24 q^{79} + q^{80} - 2 q^{81} - 4 q^{82} + 12 q^{83} + 6 q^{84} - 28 q^{85} - 2 q^{86} + 16 q^{87} + 2 q^{88} + 3 q^{89} - 9 q^{90} + 16 q^{91} + q^{92} - 13 q^{93} - 5 q^{94} + q^{96} - 24 q^{97} - 2 q^{98} - 3 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 + q^5 + q^6 + 2 * q^7 + 2 * q^8 - 3 * q^9 + q^10 + 2 * q^11 + q^12 + 6 * q^13 + 2 * q^14 - 7 * q^15 + 2 * q^16 + 4 * q^17 - 3 * q^18 + q^20 + 6 * q^21 + 2 * q^22 + q^23 + q^24 + 13 * q^25 + 6 * q^26 - 2 * q^27 + 2 * q^28 + 12 * q^29 - 7 * q^30 - q^31 + 2 * q^32 + q^33 + 4 * q^34 - 14 * q^35 - 3 * q^36 + 13 * q^37 + 8 * q^39 + q^40 - 4 * q^41 + 6 * q^42 - 2 * q^43 + 2 * q^44 - 9 * q^45 + q^46 - 5 * q^47 + q^48 - 2 * q^49 + 13 * q^50 + 12 * q^51 + 6 * q^52 - 9 * q^53 - 2 * q^54 + q^55 + 2 * q^56 + 12 * q^58 + 9 * q^59 - 7 * q^60 - 4 * q^61 - q^62 + 2 * q^63 + 2 * q^64 - 12 * q^65 + q^66 - 15 * q^67 + 4 * q^68 - 7 * q^69 - 14 * q^70 + 12 * q^71 - 3 * q^72 + 2 * q^73 + 13 * q^74 - q^75 + 2 * q^77 + 8 * q^78 + 24 * q^79 + q^80 - 2 * q^81 - 4 * q^82 + 12 * q^83 + 6 * q^84 - 28 * q^85 - 2 * q^86 + 16 * q^87 + 2 * q^88 + 3 * q^89 - 9 * q^90 + 16 * q^91 + q^92 - 13 * q^93 - 5 * q^94 + q^96 - 24 * q^97 - 2 * q^98 - 3 * 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
$3$	−0.618034	−0.356822	−0.178411	−	0.983956i	$-0.557096\pi$
$3$	−0.618034	−0.356822	−0.178411	+	0.983956i	$0.557096\pi$
$4$	1.00000	0.500000
$5$	3.85410	1.72361	0.861803	−	0.507242i	$-0.169335\pi$
$5$	3.85410	1.72361	0.861803	+	0.507242i	$0.169335\pi$
$6$	−0.618034	−0.252311
$7$	−1.23607	−0.467190	−0.233595	−	0.972334i	$-0.575049\pi$
$7$	−1.23607	−0.467190	−0.233595	+	0.972334i	$0.575049\pi$
$8$	1.00000	0.353553
$9$	−2.61803	−0.872678
$10$	3.85410	1.21877
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.618034	−0.178411
$13$	0.763932	0.211877	0.105938	−	0.994373i	$-0.466215\pi$
$13$	0.763932	0.211877	0.105938	+	0.994373i	$0.466215\pi$
$14$	−1.23607	−0.330353
$15$	−2.38197	−0.615021
$16$	1.00000	0.250000
$17$	−2.47214	−0.599581	−0.299791	−	0.954005i	$-0.596917\pi$
$17$	−2.47214	−0.599581	−0.299791	+	0.954005i	$0.596917\pi$
$18$	−2.61803	−0.617077
$19$	0	0
$19$	0	0
$20$	3.85410	0.861803
$21$	0.763932	0.166704
$22$	1.00000	0.213201
$23$	3.85410	0.803636	0.401818	−	0.915720i	$-0.368378\pi$
$23$	3.85410	0.803636	0.401818	+	0.915720i	$0.368378\pi$
$24$	−0.618034	−0.126156
$25$	9.85410	1.97082
$26$	0.763932	0.149819
$27$	3.47214	0.668213
$28$	−1.23607	−0.233595
$29$	1.52786	0.283717	0.141859	−	0.989887i	$-0.454692\pi$
$29$	1.52786	0.283717	0.141859	+	0.989887i	$0.454692\pi$
$30$	−2.38197	−0.434886
$31$	5.09017	0.914222	0.457111	−	0.889410i	$-0.348884\pi$
$31$	5.09017	0.914222	0.457111	+	0.889410i	$0.348884\pi$
$32$	1.00000	0.176777
$33$	−0.618034	−0.107586
$34$	−2.47214	−0.423968
$35$	−4.76393	−0.805251
$36$	−2.61803	−0.436339
$37$	7.61803	1.25240	0.626199	−	0.779664i	$-0.284610\pi$
$37$	7.61803	1.25240	0.626199	+	0.779664i	$0.284610\pi$
$38$	0	0
$39$	−0.472136	−0.0756023
$40$	3.85410	0.609387
$41$	6.94427	1.08451	0.542257	−	0.840213i	$-0.317570\pi$
$41$	6.94427	1.08451	0.542257	+	0.840213i	$0.317570\pi$
$42$	0.763932	0.117877
$43$	1.23607	0.188499	0.0942493	−	0.995549i	$-0.469955\pi$
$43$	1.23607	0.188499	0.0942493	+	0.995549i	$0.469955\pi$
$44$	1.00000	0.150756
$45$	−10.0902	−1.50415
$46$	3.85410	0.568256
$47$	−8.09017	−1.18007	−0.590036	−	0.807377i	$-0.700887\pi$
$47$	−8.09017	−1.18007	−0.590036	+	0.807377i	$0.700887\pi$
$48$	−0.618034	−0.0892055
$49$	−5.47214	−0.781734
$50$	9.85410	1.39358
$51$	1.52786	0.213944
$52$	0.763932	0.105938
$53$	−7.85410	−1.07884	−0.539422	−	0.842036i	$-0.681357\pi$
$53$	−7.85410	−1.07884	−0.539422	+	0.842036i	$0.681357\pi$
$54$	3.47214	0.472498
$55$	3.85410	0.519687
$56$	−1.23607	−0.165177
$57$	0	0
$58$	1.52786	0.200618
$59$	1.14590	0.149183	0.0745916	−	0.997214i	$-0.476235\pi$
$59$	1.14590	0.149183	0.0745916	+	0.997214i	$0.476235\pi$
$60$	−2.38197	−0.307510
$61$	−10.9443	−1.40127	−0.700635	−	0.713520i	$-0.747100\pi$
$61$	−10.9443	−1.40127	−0.700635	+	0.713520i	$0.747100\pi$
$62$	5.09017	0.646452
$63$	3.23607	0.407706
$64$	1.00000	0.125000
$65$	2.94427	0.365192
$66$	−0.618034	−0.0760747
$67$	−10.8541	−1.32604	−0.663020	−	0.748602i	$-0.730725\pi$
$67$	−10.8541	−1.32604	−0.663020	+	0.748602i	$0.730725\pi$
$68$	−2.47214	−0.299791
$69$	−2.38197	−0.286755
$70$	−4.76393	−0.569399
$71$	10.4721	1.24281	0.621407	−	0.783488i	$-0.286561\pi$
$71$	10.4721	1.24281	0.621407	+	0.783488i	$0.286561\pi$
$72$	−2.61803	−0.308538
$73$	7.70820	0.902177	0.451089	−	0.892479i	$-0.351036\pi$
$73$	7.70820	0.902177	0.451089	+	0.892479i	$0.351036\pi$
$74$	7.61803	0.885578
$75$	−6.09017	−0.703232
$76$	0	0
$77$	−1.23607	−0.140863
$78$	−0.472136	−0.0534589
$79$	7.52786	0.846951	0.423475	−	0.905908i	$-0.360810\pi$
$79$	7.52786	0.846951	0.423475	+	0.905908i	$0.360810\pi$
$80$	3.85410	0.430902
$81$	5.70820	0.634245
$82$	6.94427	0.766867
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	0.763932	0.0833518
$85$	−9.52786	−1.03344
$86$	1.23607	0.133289
$87$	−0.944272	−0.101237
$88$	1.00000	0.106600
$89$	4.85410	0.514534	0.257267	−	0.966340i	$-0.417178\pi$
$89$	4.85410	0.514534	0.257267	+	0.966340i	$0.417178\pi$
$90$	−10.0902	−1.06360
$91$	−0.944272	−0.0989866
$92$	3.85410	0.401818
$93$	−3.14590	−0.326214
$94$	−8.09017	−0.834437
$95$	0	0
$96$	−0.618034	−0.0630778
$97$	−7.52786	−0.764339	−0.382169	−	0.924092i	$-0.624823\pi$
$97$	−7.52786	−0.764339	−0.382169	+	0.924092i	$0.624823\pi$
$98$	−5.47214	−0.552769
$99$	−2.61803	−0.263122
$100$	9.85410	0.985410
$101$	15.2361	1.51605	0.758023	−	0.652228i	$-0.226166\pi$
$101$	15.2361	1.51605	0.758023	+	0.652228i	$0.226166\pi$
$102$	1.52786	0.151281
$103$	16.9443	1.66957	0.834784	−	0.550577i	$-0.185592\pi$
$103$	16.9443	1.66957	0.834784	+	0.550577i	$0.185592\pi$
$104$	0.763932	0.0749097
$105$	2.94427	0.287332
$106$	−7.85410	−0.762858
$107$	6.00000	0.580042	0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000	0.580042	0.290021	+	0.957020i	$0.406338\pi$
$108$	3.47214	0.334106
$109$	12.1803	1.16666	0.583332	−	0.812233i	$-0.301748\pi$
$109$	12.1803	1.16666	0.583332	+	0.812233i	$0.301748\pi$
$110$	3.85410	0.367474
$111$	−4.70820	−0.446883
$112$	−1.23607	−0.116797
$113$	−9.79837	−0.921753	−0.460877	−	0.887464i	$-0.652465\pi$
$113$	−9.79837	−0.921753	−0.460877	+	0.887464i	$0.652465\pi$
$114$	0	0
$115$	14.8541	1.38515
$116$	1.52786	0.141859
$117$	−2.00000	−0.184900
$118$	1.14590	0.105488
$119$	3.05573	0.280118
$120$	−2.38197	−0.217443
$121$	1.00000	0.0909091
$122$	−10.9443	−0.990848
$123$	−4.29180	−0.386978
$124$	5.09017	0.457111
$125$	18.7082	1.67331
$126$	3.23607	0.288292
$127$	17.4164	1.54546	0.772728	−	0.634737i	$-0.218892\pi$
$127$	17.4164	1.54546	0.772728	+	0.634737i	$0.218892\pi$
$128$	1.00000	0.0883883
$129$	−0.763932	−0.0672605
$130$	2.94427	0.258230
$131$	9.41641	0.822715	0.411358	−	0.911474i	$-0.365055\pi$
$131$	9.41641	0.822715	0.411358	+	0.911474i	$0.365055\pi$
$132$	−0.618034	−0.0537930
$133$	0	0
$134$	−10.8541	−0.937652
$135$	13.3820	1.15174
$136$	−2.47214	−0.211984
$137$	7.14590	0.610515	0.305258	−	0.952270i	$-0.401257\pi$
$137$	7.14590	0.610515	0.305258	+	0.952270i	$0.401257\pi$
$138$	−2.38197	−0.202766
$139$	−13.4164	−1.13796	−0.568982	−	0.822350i	$-0.692663\pi$
$139$	−13.4164	−1.13796	−0.568982	+	0.822350i	$0.692663\pi$
$140$	−4.76393	−0.402626
$141$	5.00000	0.421076
$142$	10.4721	0.878802
$143$	0.763932	0.0638832
$144$	−2.61803	−0.218169
$145$	5.88854	0.489017
$146$	7.70820	0.637935
$147$	3.38197	0.278940
$148$	7.61803	0.626199
$149$	−23.2361	−1.90357	−0.951786	−	0.306761i	$-0.900755\pi$
$149$	−23.2361	−1.90357	−0.951786	+	0.306761i	$0.900755\pi$
$150$	−6.09017	−0.497260
$151$	−7.52786	−0.612609	−0.306304	−	0.951934i	$-0.599093\pi$
$151$	−7.52786	−0.612609	−0.306304	+	0.951934i	$0.599093\pi$
$152$	0	0
$153$	6.47214	0.523241
$154$	−1.23607	−0.0996052
$155$	19.6180	1.57576
$156$	−0.472136	−0.0378011
$157$	−4.56231	−0.364112	−0.182056	−	0.983288i	$-0.558275\pi$
$157$	−4.56231	−0.364112	−0.182056	+	0.983288i	$0.558275\pi$
$158$	7.52786	0.598885
$159$	4.85410	0.384955
$160$	3.85410	0.304694
$161$	−4.76393	−0.375450
$162$	5.70820	0.448479
$163$	9.85410	0.771833	0.385916	−	0.922534i	$-0.373885\pi$
$163$	9.85410	0.771833	0.385916	+	0.922534i	$0.373885\pi$
$164$	6.94427	0.542257
$165$	−2.38197	−0.185436
$166$	6.00000	0.465690
$167$	20.7639	1.60676	0.803381	−	0.595466i	$-0.203032\pi$
$167$	20.7639	1.60676	0.803381	+	0.595466i	$0.203032\pi$
$168$	0.763932	0.0589386
$169$	−12.4164	−0.955108
$170$	−9.52786	−0.730754
$171$	0	0
$172$	1.23607	0.0942493
$173$	10.7639	0.818367	0.409183	−	0.912452i	$-0.365814\pi$
$173$	10.7639	0.818367	0.409183	+	0.912452i	$0.365814\pi$
$174$	−0.944272	−0.0715851
$175$	−12.1803	−0.920747
$176$	1.00000	0.0753778
$177$	−0.708204	−0.0532319
$178$	4.85410	0.363830
$179$	−0.909830	−0.0680039	−0.0340019	−	0.999422i	$-0.510825\pi$
$179$	−0.909830	−0.0680039	−0.0340019	+	0.999422i	$0.510825\pi$
$180$	−10.0902	−0.752077
$181$	−17.3262	−1.28785	−0.643925	−	0.765089i	$-0.722695\pi$
$181$	−17.3262	−1.28785	−0.643925	+	0.765089i	$0.722695\pi$
$182$	−0.944272	−0.0699941
$183$	6.76393	0.500004
$184$	3.85410	0.284128
$185$	29.3607	2.15864
$186$	−3.14590	−0.230668
$187$	−2.47214	−0.180780
$188$	−8.09017	−0.590036
$189$	−4.29180	−0.312182
$190$	0	0
$191$	−5.61803	−0.406507	−0.203253	−	0.979126i	$-0.565152\pi$
$191$	−5.61803	−0.406507	−0.203253	+	0.979126i	$0.565152\pi$
$192$	−0.618034	−0.0446028
$193$	11.8885	0.855756	0.427878	−	0.903836i	$-0.359261\pi$
$193$	11.8885	0.855756	0.427878	+	0.903836i	$0.359261\pi$
$194$	−7.52786	−0.540469
$195$	−1.81966	−0.130309
$196$	−5.47214	−0.390867
$197$	−22.4721	−1.60107	−0.800537	−	0.599284i	$-0.795452\pi$
$197$	−22.4721	−1.60107	−0.800537	+	0.599284i	$0.795452\pi$
$198$	−2.61803	−0.186056
$199$	22.3262	1.58267	0.791333	−	0.611386i	$-0.209388\pi$
$199$	22.3262	1.58267	0.791333	+	0.611386i	$0.209388\pi$
$200$	9.85410	0.696790
$201$	6.70820	0.473160
$202$	15.2361	1.07201
$203$	−1.88854	−0.132550
$204$	1.52786	0.106972
$205$	26.7639	1.86927
$206$	16.9443	1.18056
$207$	−10.0902	−0.701315
$208$	0.763932	0.0529692
$209$	0	0
$210$	2.94427	0.203174
$211$	10.9443	0.753435	0.376717	−	0.926328i	$-0.377053\pi$
$211$	10.9443	0.753435	0.376717	+	0.926328i	$0.377053\pi$
$212$	−7.85410	−0.539422
$213$	−6.47214	−0.443463
$214$	6.00000	0.410152
$215$	4.76393	0.324897
$216$	3.47214	0.236249
$217$	−6.29180	−0.427115
$218$	12.1803	0.824957
$219$	−4.76393	−0.321917
$220$	3.85410	0.259844
$221$	−1.88854	−0.127037
$222$	−4.70820	−0.315994
$223$	−10.5623	−0.707304	−0.353652	−	0.935377i	$-0.615060\pi$
$223$	−10.5623	−0.707304	−0.353652	+	0.935377i	$0.615060\pi$
$224$	−1.23607	−0.0825883
$225$	−25.7984	−1.71989
$226$	−9.79837	−0.651778
$227$	−22.3607	−1.48413	−0.742065	−	0.670328i	$-0.766154\pi$
$227$	−22.3607	−1.48413	−0.742065	+	0.670328i	$0.766154\pi$
$228$	0	0
$229$	−1.38197	−0.0913229	−0.0456614	−	0.998957i	$-0.514540\pi$
$229$	−1.38197	−0.0913229	−0.0456614	+	0.998957i	$0.514540\pi$
$230$	14.8541	0.979450
$231$	0.763932	0.0502630
$232$	1.52786	0.100309
$233$	10.4721	0.686052	0.343026	−	0.939326i	$-0.388548\pi$
$233$	10.4721	0.686052	0.343026	+	0.939326i	$0.388548\pi$
$234$	−2.00000	−0.130744
$235$	−31.1803	−2.03398
$236$	1.14590	0.0745916
$237$	−4.65248	−0.302211
$238$	3.05573	0.198073
$239$	6.29180	0.406982	0.203491	−	0.979077i	$-0.434771\pi$
$239$	6.29180	0.406982	0.203491	+	0.979077i	$0.434771\pi$
$240$	−2.38197	−0.153755
$241$	−10.0000	−0.644157	−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000	−0.644157	−0.322078	+	0.946713i	$0.604381\pi$
$242$	1.00000	0.0642824
$243$	−13.9443	−0.894525
$244$	−10.9443	−0.700635
$245$	−21.0902	−1.34740
$246$	−4.29180	−0.273635
$247$	0	0
$248$	5.09017	0.323226
$249$	−3.70820	−0.234998
$250$	18.7082	1.18321
$251$	10.8541	0.685105	0.342552	−	0.939499i	$-0.388709\pi$
$251$	10.8541	0.685105	0.342552	+	0.939499i	$0.388709\pi$
$252$	3.23607	0.203853
$253$	3.85410	0.242305
$254$	17.4164	1.09280
$255$	5.88854	0.368755
$256$	1.00000	0.0625000
$257$	9.05573	0.564881	0.282440	−	0.959285i	$-0.408856\pi$
$257$	9.05573	0.564881	0.282440	+	0.959285i	$0.408856\pi$
$258$	−0.763932	−0.0475603
$259$	−9.41641	−0.585107
$260$	2.94427	0.182596
$261$	−4.00000	−0.247594
$262$	9.41641	0.581748
$263$	24.7639	1.52701	0.763505	−	0.645802i	$-0.223477\pi$
$263$	24.7639	1.52701	0.763505	+	0.645802i	$0.223477\pi$
$264$	−0.618034	−0.0380374
$265$	−30.2705	−1.85950
$266$	0	0
$267$	−3.00000	−0.183597
$268$	−10.8541	−0.663020
$269$	0.562306	0.0342844	0.0171422	−	0.999853i	$-0.494543\pi$
$269$	0.562306	0.0342844	0.0171422	+	0.999853i	$0.494543\pi$
$270$	13.3820	0.814401
$271$	−25.2361	−1.53298	−0.766491	−	0.642255i	$-0.777999\pi$
$271$	−25.2361	−1.53298	−0.766491	+	0.642255i	$0.777999\pi$
$272$	−2.47214	−0.149895
$273$	0.583592	0.0353206
$274$	7.14590	0.431699
$275$	9.85410	0.594225
$276$	−2.38197	−0.143378
$277$	0.291796	0.0175323	0.00876616	−	0.999962i	$-0.497210\pi$
$277$	0.291796	0.0175323	0.00876616	+	0.999962i	$0.497210\pi$
$278$	−13.4164	−0.804663
$279$	−13.3262	−0.797821
$280$	−4.76393	−0.284699
$281$	6.76393	0.403502	0.201751	−	0.979437i	$-0.435337\pi$
$281$	6.76393	0.403502	0.201751	+	0.979437i	$0.435337\pi$
$282$	5.00000	0.297746
$283$	−0.944272	−0.0561311	−0.0280656	−	0.999606i	$-0.508935\pi$
$283$	−0.944272	−0.0561311	−0.0280656	+	0.999606i	$0.508935\pi$
$284$	10.4721	0.621407
$285$	0	0
$286$	0.763932	0.0451722
$287$	−8.58359	−0.506673
$288$	−2.61803	−0.154269
$289$	−10.8885	−0.640503
$290$	5.88854	0.345787
$291$	4.65248	0.272733
$292$	7.70820	0.451089
$293$	3.41641	0.199589	0.0997943	−	0.995008i	$-0.468182\pi$
$293$	3.41641	0.199589	0.0997943	+	0.995008i	$0.468182\pi$
$294$	3.38197	0.197240
$295$	4.41641	0.257133
$296$	7.61803	0.442789
$297$	3.47214	0.201474
$298$	−23.2361	−1.34603
$299$	2.94427	0.170272
$300$	−6.09017	−0.351616
$301$	−1.52786	−0.0880646
$302$	−7.52786	−0.433180
$303$	−9.41641	−0.540958
$304$	0	0
$305$	−42.1803	−2.41524
$306$	6.47214	0.369987
$307$	29.4164	1.67888	0.839442	−	0.543450i	$-0.182882\pi$
$307$	29.4164	1.67888	0.839442	+	0.543450i	$0.182882\pi$
$308$	−1.23607	−0.0704315
$309$	−10.4721	−0.595739
$310$	19.6180	1.11423
$311$	7.50658	0.425659	0.212829	−	0.977089i	$-0.431732\pi$
$311$	7.50658	0.425659	0.212829	+	0.977089i	$0.431732\pi$
$312$	−0.472136	−0.0267294
$313$	12.4721	0.704967	0.352483	−	0.935818i	$-0.385337\pi$
$313$	12.4721	0.704967	0.352483	+	0.935818i	$0.385337\pi$
$314$	−4.56231	−0.257466
$315$	12.4721	0.702725
$316$	7.52786	0.423475
$317$	−17.4164	−0.978203	−0.489101	−	0.872227i	$-0.662675\pi$
$317$	−17.4164	−0.978203	−0.489101	+	0.872227i	$0.662675\pi$
$318$	4.85410	0.272205
$319$	1.52786	0.0855440
$320$	3.85410	0.215451
$321$	−3.70820	−0.206972
$322$	−4.76393	−0.265484
$323$	0	0
$324$	5.70820	0.317122
$325$	7.52786	0.417571
$326$	9.85410	0.545768
$327$	−7.52786	−0.416292
$328$	6.94427	0.383433
$329$	10.0000	0.551318
$330$	−2.38197	−0.131123
$331$	−13.8541	−0.761490	−0.380745	−	0.924680i	$-0.624332\pi$
$331$	−13.8541	−0.761490	−0.380745	+	0.924680i	$0.624332\pi$
$332$	6.00000	0.329293
$333$	−19.9443	−1.09294
$334$	20.7639	1.13615
$335$	−41.8328	−2.28557
$336$	0.763932	0.0416759
$337$	31.8885	1.73708	0.868540	−	0.495619i	$-0.165059\pi$
$337$	31.8885	1.73708	0.868540	+	0.495619i	$0.165059\pi$
$338$	−12.4164	−0.675364
$339$	6.05573	0.328902
$340$	−9.52786	−0.516721
$341$	5.09017	0.275648
$342$	0	0
$343$	15.4164	0.832408
$344$	1.23607	0.0666443
$345$	−9.18034	−0.494253
$346$	10.7639	0.578673
$347$	4.94427	0.265422	0.132711	−	0.991155i	$-0.457632\pi$
$347$	4.94427	0.265422	0.132711	+	0.991155i	$0.457632\pi$
$348$	−0.944272	−0.0506183
$349$	−17.8885	−0.957552	−0.478776	−	0.877937i	$-0.658919\pi$
$349$	−17.8885	−0.957552	−0.478776	+	0.877937i	$0.658919\pi$
$350$	−12.1803	−0.651067
$351$	2.65248	0.141579
$352$	1.00000	0.0533002
$353$	−15.1459	−0.806135	−0.403067	−	0.915170i	$-0.632056\pi$
$353$	−15.1459	−0.806135	−0.403067	+	0.915170i	$0.632056\pi$
$354$	−0.708204	−0.0376406
$355$	40.3607	2.14212
$356$	4.85410	0.257267
$357$	−1.88854	−0.0999523
$358$	−0.909830	−0.0480860
$359$	−18.0000	−0.950004	−0.475002	−	0.879985i	$-0.657553\pi$
$359$	−18.0000	−0.950004	−0.475002	+	0.879985i	$0.657553\pi$
$360$	−10.0902	−0.531799
$361$	0	0
$362$	−17.3262	−0.910647
$363$	−0.618034	−0.0324384
$364$	−0.944272	−0.0494933
$365$	29.7082	1.55500
$366$	6.76393	0.353556
$367$	−33.7984	−1.76426	−0.882130	−	0.471005i	$-0.843891\pi$
$367$	−33.7984	−1.76426	−0.882130	+	0.471005i	$0.843891\pi$
$368$	3.85410	0.200909
$369$	−18.1803	−0.946431
$370$	29.3607	1.52639
$371$	9.70820	0.504025
$372$	−3.14590	−0.163107
$373$	32.6525	1.69068	0.845341	−	0.534228i	$-0.179398\pi$
$373$	32.6525	1.69068	0.845341	+	0.534228i	$0.179398\pi$
$374$	−2.47214	−0.127831
$375$	−11.5623	−0.597075
$376$	−8.09017	−0.417219
$377$	1.16718	0.0601130
$378$	−4.29180	−0.220746
$379$	−22.8328	−1.17284	−0.586421	−	0.810006i	$-0.699464\pi$
$379$	−22.8328	−1.17284	−0.586421	+	0.810006i	$0.699464\pi$
$380$	0	0
$381$	−10.7639	−0.551453
$382$	−5.61803	−0.287444
$383$	0.145898	0.00745504	0.00372752	−	0.999993i	$-0.498813\pi$
$383$	0.145898	0.00745504	0.00372752	+	0.999993i	$0.498813\pi$
$384$	−0.618034	−0.0315389
$385$	−4.76393	−0.242792
$386$	11.8885	0.605111
$387$	−3.23607	−0.164499
$388$	−7.52786	−0.382169
$389$	20.7984	1.05452	0.527260	−	0.849704i	$-0.323219\pi$
$389$	20.7984	1.05452	0.527260	+	0.849704i	$0.323219\pi$
$390$	−1.81966	−0.0921421
$391$	−9.52786	−0.481845
$392$	−5.47214	−0.276385
$393$	−5.81966	−0.293563
$394$	−22.4721	−1.13213
$395$	29.0132	1.45981
$396$	−2.61803	−0.131561
$397$	−18.6180	−0.934412	−0.467206	−	0.884148i	$-0.654739\pi$
$397$	−18.6180	−0.934412	−0.467206	+	0.884148i	$0.654739\pi$
$398$	22.3262	1.11911
$399$	0	0
$400$	9.85410	0.492705
$401$	−32.9787	−1.64688	−0.823439	−	0.567405i	$-0.807948\pi$
$401$	−32.9787	−1.64688	−0.823439	+	0.567405i	$0.807948\pi$
$402$	6.70820	0.334575
$403$	3.88854	0.193702
$404$	15.2361	0.758023
$405$	22.0000	1.09319
$406$	−1.88854	−0.0937269
$407$	7.61803	0.377612
$408$	1.52786	0.0756405
$409$	−2.29180	−0.113322	−0.0566610	−	0.998393i	$-0.518045\pi$
$409$	−2.29180	−0.113322	−0.0566610	+	0.998393i	$0.518045\pi$
$410$	26.7639	1.32178
$411$	−4.41641	−0.217845
$412$	16.9443	0.834784
$413$	−1.41641	−0.0696969
$414$	−10.0902	−0.495905
$415$	23.1246	1.13514
$416$	0.763932	0.0374548
$417$	8.29180	0.406051
$418$	0	0
$419$	−16.3262	−0.797589	−0.398794	−	0.917040i	$-0.630571\pi$
$419$	−16.3262	−0.797589	−0.398794	+	0.917040i	$0.630571\pi$
$420$	2.94427	0.143666
$421$	−22.4508	−1.09419	−0.547094	−	0.837071i	$-0.684266\pi$
$421$	−22.4508	−1.09419	−0.547094	+	0.837071i	$0.684266\pi$
$422$	10.9443	0.532759
$423$	21.1803	1.02982
$424$	−7.85410	−0.381429
$425$	−24.3607	−1.18167
$426$	−6.47214	−0.313576
$427$	13.5279	0.654659
$428$	6.00000	0.290021
$429$	−0.472136	−0.0227949
$430$	4.76393	0.229737
$431$	−19.2361	−0.926569	−0.463284	−	0.886210i	$-0.653329\pi$
$431$	−19.2361	−0.926569	−0.463284	+	0.886210i	$0.653329\pi$
$432$	3.47214	0.167053
$433$	14.7984	0.711164	0.355582	−	0.934645i	$-0.384283\pi$
$433$	14.7984	0.711164	0.355582	+	0.934645i	$0.384283\pi$
$434$	−6.29180	−0.302016
$435$	−3.63932	−0.174492
$436$	12.1803	0.583332
$437$	0	0
$438$	−4.76393	−0.227629
$439$	38.6525	1.84478	0.922391	−	0.386257i	$-0.126232\pi$
$439$	38.6525	1.84478	0.922391	+	0.386257i	$0.126232\pi$
$440$	3.85410	0.183737
$441$	14.3262	0.682202
$442$	−1.88854	−0.0898289
$443$	−18.2705	−0.868058	−0.434029	−	0.900899i	$-0.642908\pi$
$443$	−18.2705	−0.868058	−0.434029	+	0.900899i	$0.642908\pi$
$444$	−4.70820	−0.223441
$445$	18.7082	0.886854
$446$	−10.5623	−0.500140
$447$	14.3607	0.679237
$448$	−1.23607	−0.0583987
$449$	−14.5623	−0.687238	−0.343619	−	0.939109i	$-0.611653\pi$
$449$	−14.5623	−0.687238	−0.343619	+	0.939109i	$0.611653\pi$
$450$	−25.7984	−1.21615
$451$	6.94427	0.326993
$452$	−9.79837	−0.460877
$453$	4.65248	0.218592
$454$	−22.3607	−1.04944
$455$	−3.63932	−0.170614
$456$	0	0
$457$	−9.23607	−0.432045	−0.216023	−	0.976388i	$-0.569308\pi$
$457$	−9.23607	−0.432045	−0.216023	+	0.976388i	$0.569308\pi$
$458$	−1.38197	−0.0645750
$459$	−8.58359	−0.400648
$460$	14.8541	0.692576
$461$	10.6525	0.496135	0.248068	−	0.968743i	$-0.420204\pi$
$461$	10.6525	0.496135	0.248068	+	0.968743i	$0.420204\pi$
$462$	0.763932	0.0355413
$463$	30.1591	1.40161	0.700805	−	0.713353i	$-0.252824\pi$
$463$	30.1591	1.40161	0.700805	+	0.713353i	$0.252824\pi$
$464$	1.52786	0.0709293
$465$	−12.1246	−0.562265
$466$	10.4721	0.485112
$467$	−0.618034	−0.0285992	−0.0142996	−	0.999898i	$-0.504552\pi$
$467$	−0.618034	−0.0285992	−0.0142996	+	0.999898i	$0.504552\pi$
$468$	−2.00000	−0.0924500
$469$	13.4164	0.619512
$470$	−31.1803	−1.43824
$471$	2.81966	0.129923
$472$	1.14590	0.0527442
$473$	1.23607	0.0568345
$474$	−4.65248	−0.213695
$475$	0	0
$476$	3.05573	0.140059
$477$	20.5623	0.941483
$478$	6.29180	0.287780
$479$	23.1246	1.05659	0.528295	−	0.849061i	$-0.322831\pi$
$479$	23.1246	1.05659	0.528295	+	0.849061i	$0.322831\pi$
$480$	−2.38197	−0.108721
$481$	5.81966	0.265354
$482$	−10.0000	−0.455488
$483$	2.94427	0.133969
$484$	1.00000	0.0454545
$485$	−29.0132	−1.31742
$486$	−13.9443	−0.632525
$487$	−4.14590	−0.187869	−0.0939343	−	0.995578i	$-0.529944\pi$
$487$	−4.14590	−0.187869	−0.0939343	+	0.995578i	$0.529944\pi$
$488$	−10.9443	−0.495424
$489$	−6.09017	−0.275407
$490$	−21.0902	−0.952757
$491$	5.05573	0.228162	0.114081	−	0.993471i	$-0.463608\pi$
$491$	5.05573	0.228162	0.114081	+	0.993471i	$0.463608\pi$
$492$	−4.29180	−0.193489
$493$	−3.77709	−0.170111
$494$	0	0
$495$	−10.0902	−0.453519
$496$	5.09017	0.228555
$497$	−12.9443	−0.580630
$498$	−3.70820	−0.166169
$499$	27.0344	1.21023	0.605114	−	0.796139i	$-0.293128\pi$
$499$	27.0344	1.21023	0.605114	+	0.796139i	$0.293128\pi$
$500$	18.7082	0.836656
$501$	−12.8328	−0.573328
$502$	10.8541	0.484442
$503$	9.23607	0.411816	0.205908	−	0.978571i	$-0.433985\pi$
$503$	9.23607	0.411816	0.205908	+	0.978571i	$0.433985\pi$
$504$	3.23607	0.144146
$505$	58.7214	2.61307
$506$	3.85410	0.171336
$507$	7.67376	0.340804
$508$	17.4164	0.772728
$509$	7.52786	0.333667	0.166833	−	0.985985i	$-0.446646\pi$
$509$	7.52786	0.333667	0.166833	+	0.985985i	$0.446646\pi$
$510$	5.88854	0.260749
$511$	−9.52786	−0.421488
$512$	1.00000	0.0441942
$513$	0	0
$514$	9.05573	0.399431
$515$	65.3050	2.87768
$516$	−0.763932	−0.0336302
$517$	−8.09017	−0.355805
$518$	−9.41641	−0.413733
$519$	−6.65248	−0.292011
$520$	2.94427	0.129115
$521$	26.0000	1.13908	0.569540	−	0.821963i	$-0.307121\pi$
$521$	26.0000	1.13908	0.569540	+	0.821963i	$0.307121\pi$
$522$	−4.00000	−0.175075
$523$	3.23607	0.141503	0.0707517	−	0.997494i	$-0.477460\pi$
$523$	3.23607	0.141503	0.0707517	+	0.997494i	$0.477460\pi$
$524$	9.41641	0.411358
$525$	7.52786	0.328543
$526$	24.7639	1.07976
$527$	−12.5836	−0.548150
$528$	−0.618034	−0.0268965
$529$	−8.14590	−0.354169
$530$	−30.2705	−1.31487
$531$	−3.00000	−0.130189
$532$	0	0
$533$	5.30495	0.229783
$534$	−3.00000	−0.129823
$535$	23.1246	0.999764
$536$	−10.8541	−0.468826
$537$	0.562306	0.0242653
$538$	0.562306	0.0242427
$539$	−5.47214	−0.235702
$540$	13.3820	0.575868
$541$	44.8328	1.92751	0.963757	−	0.266783i	$-0.0859607\pi$
$541$	44.8328	1.92751	0.963757	+	0.266783i	$0.0859607\pi$
$542$	−25.2361	−1.08398
$543$	10.7082	0.459533
$544$	−2.47214	−0.105992
$545$	46.9443	2.01087
$546$	0.583592	0.0249754
$547$	−19.2361	−0.822475	−0.411237	−	0.911528i	$-0.634903\pi$
$547$	−19.2361	−0.822475	−0.411237	+	0.911528i	$0.634903\pi$
$548$	7.14590	0.305258
$549$	28.6525	1.22286
$550$	9.85410	0.420180
$551$	0	0
$552$	−2.38197	−0.101383
$553$	−9.30495	−0.395687
$554$	0.291796	0.0123972
$555$	−18.1459	−0.770250
$556$	−13.4164	−0.568982
$557$	−23.8197	−1.00927	−0.504636	−	0.863332i	$-0.668373\pi$
$557$	−23.8197	−1.00927	−0.504636	+	0.863332i	$0.668373\pi$
$558$	−13.3262	−0.564145
$559$	0.944272	0.0399384
$560$	−4.76393	−0.201313
$561$	1.52786	0.0645065
$562$	6.76393	0.285319
$563$	−40.3607	−1.70100	−0.850500	−	0.525975i	$-0.823700\pi$
$563$	−40.3607	−1.70100	−0.850500	+	0.525975i	$0.823700\pi$
$564$	5.00000	0.210538
$565$	−37.7639	−1.58874
$566$	−0.944272	−0.0396907
$567$	−7.05573	−0.296313
$568$	10.4721	0.439401
$569$	−24.9443	−1.04572	−0.522859	−	0.852419i	$-0.675135\pi$
$569$	−24.9443	−1.04572	−0.522859	+	0.852419i	$0.675135\pi$
$570$	0	0
$571$	38.8328	1.62510	0.812551	−	0.582890i	$-0.198078\pi$
$571$	38.8328	1.62510	0.812551	+	0.582890i	$0.198078\pi$
$572$	0.763932	0.0319416
$573$	3.47214	0.145051
$574$	−8.58359	−0.358272
$575$	37.9787	1.58382
$576$	−2.61803	−0.109085
$577$	40.6869	1.69382	0.846909	−	0.531737i	$-0.178461\pi$
$577$	40.6869	1.69382	0.846909	+	0.531737i	$0.178461\pi$
$578$	−10.8885	−0.452904
$579$	−7.34752	−0.305353
$580$	5.88854	0.244508
$581$	−7.41641	−0.307684
$582$	4.65248	0.192851
$583$	−7.85410	−0.325284
$584$	7.70820	0.318968
$585$	−7.70820	−0.318695
$586$	3.41641	0.141131
$587$	10.4508	0.431353	0.215676	−	0.976465i	$-0.430804\pi$
$587$	10.4508	0.431353	0.215676	+	0.976465i	$0.430804\pi$
$588$	3.38197	0.139470
$589$	0	0
$590$	4.41641	0.181821
$591$	13.8885	0.571298
$592$	7.61803	0.313099
$593$	−43.5967	−1.79030	−0.895152	−	0.445761i	$-0.852933\pi$
$593$	−43.5967	−1.79030	−0.895152	+	0.445761i	$0.852933\pi$
$594$	3.47214	0.142463
$595$	11.7771	0.482814
$596$	−23.2361	−0.951786
$597$	−13.7984	−0.564730
$598$	2.94427	0.120400
$599$	−21.0344	−0.859444	−0.429722	−	0.902961i	$-0.641388\pi$
$599$	−21.0344	−0.859444	−0.429722	+	0.902961i	$0.641388\pi$
$600$	−6.09017	−0.248630
$601$	−10.0000	−0.407909	−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000	−0.407909	−0.203954	+	0.978980i	$0.565379\pi$
$602$	−1.52786	−0.0622711
$603$	28.4164	1.15721
$604$	−7.52786	−0.306304
$605$	3.85410	0.156692
$606$	−9.41641	−0.382515
$607$	−29.7771	−1.20861	−0.604307	−	0.796751i	$-0.706550\pi$
$607$	−29.7771	−1.20861	−0.604307	+	0.796751i	$0.706550\pi$
$608$	0	0
$609$	1.16718	0.0472967
$610$	−42.1803	−1.70783
$611$	−6.18034	−0.250030
$612$	6.47214	0.261621
$613$	−34.7639	−1.40410	−0.702051	−	0.712127i	$-0.747732\pi$
$613$	−34.7639	−1.40410	−0.702051	+	0.712127i	$0.747732\pi$
$614$	29.4164	1.18715
$615$	−16.5410	−0.666998
$616$	−1.23607	−0.0498026
$617$	−44.0344	−1.77276	−0.886380	−	0.462959i	$-0.846788\pi$
$617$	−44.0344	−1.77276	−0.886380	+	0.462959i	$0.846788\pi$
$618$	−10.4721	−0.421251
$619$	−47.0344	−1.89047	−0.945237	−	0.326385i	$-0.894169\pi$
$619$	−47.0344	−1.89047	−0.945237	+	0.326385i	$0.894169\pi$
$620$	19.6180	0.787879
$621$	13.3820	0.537000
$622$	7.50658	0.300986
$623$	−6.00000	−0.240385
$624$	−0.472136	−0.0189006
$625$	22.8328	0.913313
$626$	12.4721	0.498487
$627$	0	0
$628$	−4.56231	−0.182056
$629$	−18.8328	−0.750914
$630$	12.4721	0.496902
$631$	−22.9787	−0.914768	−0.457384	−	0.889269i	$-0.651214\pi$
$631$	−22.9787	−0.914768	−0.457384	+	0.889269i	$0.651214\pi$
$632$	7.52786	0.299442
$633$	−6.76393	−0.268842
$634$	−17.4164	−0.691694
$635$	67.1246	2.66376
$636$	4.85410	0.192478
$637$	−4.18034	−0.165631
$638$	1.52786	0.0604887
$639$	−27.4164	−1.08458
$640$	3.85410	0.152347
$641$	40.9787	1.61856	0.809281	−	0.587422i	$-0.199857\pi$
$641$	40.9787	1.61856	0.809281	+	0.587422i	$0.199857\pi$
$642$	−3.70820	−0.146351
$643$	−34.8541	−1.37451	−0.687256	−	0.726415i	$-0.741185\pi$
$643$	−34.8541	−1.37451	−0.687256	+	0.726415i	$0.741185\pi$
$644$	−4.76393	−0.187725
$645$	−2.94427	−0.115931
$646$	0	0
$647$	−30.7426	−1.20862	−0.604309	−	0.796750i	$-0.706551\pi$
$647$	−30.7426	−1.20862	−0.604309	+	0.796750i	$0.706551\pi$
$648$	5.70820	0.224239
$649$	1.14590	0.0449804
$650$	7.52786	0.295267
$651$	3.88854	0.152404
$652$	9.85410	0.385916
$653$	−44.3820	−1.73680	−0.868400	−	0.495864i	$-0.834851\pi$
$653$	−44.3820	−1.73680	−0.868400	+	0.495864i	$0.834851\pi$
$654$	−7.52786	−0.294363
$655$	36.2918	1.41804
$656$	6.94427	0.271128
$657$	−20.1803	−0.787310
$658$	10.0000	0.389841
$659$	−25.8885	−1.00847	−0.504237	−	0.863565i	$-0.668226\pi$
$659$	−25.8885	−1.00847	−0.504237	+	0.863565i	$0.668226\pi$
$660$	−2.38197	−0.0927179
$661$	4.79837	0.186635	0.0933176	−	0.995636i	$-0.470253\pi$
$661$	4.79837	0.186635	0.0933176	+	0.995636i	$0.470253\pi$
$662$	−13.8541	−0.538455
$663$	1.16718	0.0453297
$664$	6.00000	0.232845
$665$	0	0
$666$	−19.9443	−0.772825
$667$	5.88854	0.228005
$668$	20.7639	0.803381
$669$	6.52786	0.252382
$670$	−41.8328	−1.61614
$671$	−10.9443	−0.422499
$672$	0.763932	0.0294693
$673$	5.88854	0.226987	0.113493	−	0.993539i	$-0.463796\pi$
$673$	5.88854	0.226987	0.113493	+	0.993539i	$0.463796\pi$
$674$	31.8885	1.22830
$675$	34.2148	1.31693
$676$	−12.4164	−0.477554
$677$	28.8328	1.10814	0.554068	−	0.832472i	$-0.313075\pi$
$677$	28.8328	1.10814	0.554068	+	0.832472i	$0.313075\pi$
$678$	6.05573	0.232569
$679$	9.30495	0.357091
$680$	−9.52786	−0.365377
$681$	13.8197	0.529571
$682$	5.09017	0.194913
$683$	−25.9230	−0.991915	−0.495958	−	0.868347i	$-0.665183\pi$
$683$	−25.9230	−0.991915	−0.495958	+	0.868347i	$0.665183\pi$
$684$	0	0
$685$	27.5410	1.05229
$686$	15.4164	0.588601
$687$	0.854102	0.0325860
$688$	1.23607	0.0471246
$689$	−6.00000	−0.228582
$690$	−9.18034	−0.349490
$691$	28.6180	1.08868	0.544341	−	0.838864i	$-0.316780\pi$
$691$	28.6180	1.08868	0.544341	+	0.838864i	$0.316780\pi$
$692$	10.7639	0.409183
$693$	3.23607	0.122928
$694$	4.94427	0.187682
$695$	−51.7082	−1.96140
$696$	−0.944272	−0.0357925
$697$	−17.1672	−0.650253
$698$	−17.8885	−0.677091
$699$	−6.47214	−0.244799
$700$	−12.1803	−0.460374
$701$	5.34752	0.201973	0.100987	−	0.994888i	$-0.467800\pi$
$701$	5.34752	0.201973	0.100987	+	0.994888i	$0.467800\pi$
$702$	2.65248	0.100111
$703$	0	0
$704$	1.00000	0.0376889
$705$	19.2705	0.725769
$706$	−15.1459	−0.570023
$707$	−18.8328	−0.708281
$708$	−0.708204	−0.0266159
$709$	36.8328	1.38329	0.691643	−	0.722240i	$-0.256887\pi$
$709$	36.8328	1.38329	0.691643	+	0.722240i	$0.256887\pi$
$710$	40.3607	1.51471
$711$	−19.7082	−0.739115
$712$	4.85410	0.181915
$713$	19.6180	0.734701
$714$	−1.88854	−0.0706770
$715$	2.94427	0.110110
$716$	−0.909830	−0.0340019
$717$	−3.88854	−0.145220
$718$	−18.0000	−0.671754
$719$	25.9787	0.968843	0.484421	−	0.874835i	$-0.339030\pi$
$719$	25.9787	0.968843	0.484421	+	0.874835i	$0.339030\pi$
$720$	−10.0902	−0.376038
$721$	−20.9443	−0.780005
$722$	0	0
$723$	6.18034	0.229849
$724$	−17.3262	−0.643925
$725$	15.0557	0.559156
$726$	−0.618034	−0.0229374
$727$	50.1591	1.86030	0.930148	−	0.367184i	$-0.119678\pi$
$727$	50.1591	1.86030	0.930148	+	0.367184i	$0.119678\pi$
$728$	−0.944272	−0.0349970
$729$	−8.50658	−0.315058
$730$	29.7082	1.09955
$731$	−3.05573	−0.113020
$732$	6.76393	0.250002
$733$	−40.0689	−1.47998	−0.739989	−	0.672619i	$-0.765169\pi$
$733$	−40.0689	−1.47998	−0.739989	+	0.672619i	$0.765169\pi$
$734$	−33.7984	−1.24752
$735$	13.0344	0.480783
$736$	3.85410	0.142064
$737$	−10.8541	−0.399816
$738$	−18.1803	−0.669228
$739$	38.1803	1.40449	0.702243	−	0.711937i	$-0.252182\pi$
$739$	38.1803	1.40449	0.702243	+	0.711937i	$0.252182\pi$
$740$	29.3607	1.07932
$741$	0	0
$742$	9.70820	0.356399
$743$	1.81966	0.0667569	0.0333784	−	0.999443i	$-0.489373\pi$
$743$	1.81966	0.0667569	0.0333784	+	0.999443i	$0.489373\pi$
$744$	−3.14590	−0.115334
$745$	−89.5542	−3.28101
$746$	32.6525	1.19549
$747$	−15.7082	−0.574733
$748$	−2.47214	−0.0903902
$749$	−7.41641	−0.270990
$750$	−11.5623	−0.422196
$751$	−13.6738	−0.498963	−0.249481	−	0.968380i	$-0.580260\pi$
$751$	−13.6738	−0.498963	−0.249481	+	0.968380i	$0.580260\pi$
$752$	−8.09017	−0.295018
$753$	−6.70820	−0.244461
$754$	1.16718	0.0425063
$755$	−29.0132	−1.05590
$756$	−4.29180	−0.156091
$757$	−50.9443	−1.85160	−0.925801	−	0.378012i	$-0.876608\pi$
$757$	−50.9443	−1.85160	−0.925801	+	0.378012i	$0.876608\pi$
$758$	−22.8328	−0.829325
$759$	−2.38197	−0.0864599
$760$	0	0
$761$	−11.0557	−0.400770	−0.200385	−	0.979717i	$-0.564219\pi$
$761$	−11.0557	−0.400770	−0.200385	+	0.979717i	$0.564219\pi$
$762$	−10.7639	−0.389936
$763$	−15.0557	−0.545054
$764$	−5.61803	−0.203253
$765$	24.9443	0.901862
$766$	0.145898	0.00527151
$767$	0.875388	0.0316084
$768$	−0.618034	−0.0223014
$769$	0.360680	0.0130064	0.00650322	−	0.999979i	$-0.497930\pi$
$769$	0.360680	0.0130064	0.00650322	+	0.999979i	$0.497930\pi$
$770$	−4.76393	−0.171680
$771$	−5.59675	−0.201562
$772$	11.8885	0.427878
$773$	30.6738	1.10326	0.551629	−	0.834089i	$-0.314006\pi$
$773$	30.6738	1.10326	0.551629	+	0.834089i	$0.314006\pi$
$774$	−3.23607	−0.116318
$775$	50.1591	1.80177
$776$	−7.52786	−0.270235
$777$	5.81966	0.208779
$778$	20.7984	0.745658
$779$	0	0
$780$	−1.81966	−0.0651543
$781$	10.4721	0.374722
$782$	−9.52786	−0.340716
$783$	5.30495	0.189584
$784$	−5.47214	−0.195433
$785$	−17.5836	−0.627585
$786$	−5.81966	−0.207580
$787$	−33.5967	−1.19759	−0.598797	−	0.800901i	$-0.704355\pi$
$787$	−33.5967	−1.19759	−0.598797	+	0.800901i	$0.704355\pi$
$788$	−22.4721	−0.800537
$789$	−15.3050	−0.544871
$790$	29.0132	1.03224
$791$	12.1115	0.430634
$792$	−2.61803	−0.0930278
$793$	−8.36068	−0.296896
$794$	−18.6180	−0.660729
$795$	18.7082	0.663512
$796$	22.3262	0.791333
$797$	−21.0902	−0.747052	−0.373526	−	0.927620i	$-0.621851\pi$
$797$	−21.0902	−0.747052	−0.373526	+	0.927620i	$0.621851\pi$
$798$	0	0
$799$	20.0000	0.707549
$800$	9.85410	0.348395
$801$	−12.7082	−0.449022
$802$	−32.9787	−1.16452
$803$	7.70820	0.272017
$804$	6.70820	0.236580
$805$	−18.3607	−0.647129
$806$	3.88854	0.136968
$807$	−0.347524	−0.0122334
$808$	15.2361	0.536003
$809$	−40.9443	−1.43952	−0.719762	−	0.694221i	$-0.755749\pi$
$809$	−40.9443	−1.43952	−0.719762	+	0.694221i	$0.755749\pi$
$810$	22.0000	0.773001
$811$	−17.8885	−0.628152	−0.314076	−	0.949398i	$-0.601695\pi$
$811$	−17.8885	−0.628152	−0.314076	+	0.949398i	$0.601695\pi$
$812$	−1.88854	−0.0662749
$813$	15.5967	0.547002
$814$	7.61803	0.267012
$815$	37.9787	1.33034
$816$	1.52786	0.0534859
$817$	0	0
$818$	−2.29180	−0.0801308
$819$	2.47214	0.0863834
$820$	26.7639	0.934637
$821$	−0.763932	−0.0266614	−0.0133307	−	0.999911i	$-0.504243\pi$
$821$	−0.763932	−0.0266614	−0.0133307	+	0.999911i	$0.504243\pi$
$822$	−4.41641	−0.154040
$823$	−27.8541	−0.970933	−0.485466	−	0.874255i	$-0.661350\pi$
$823$	−27.8541	−0.970933	−0.485466	+	0.874255i	$0.661350\pi$
$824$	16.9443	0.590282
$825$	−6.09017	−0.212033
$826$	−1.41641	−0.0492831
$827$	−21.3475	−0.742326	−0.371163	−	0.928568i	$-0.621041\pi$
$827$	−21.3475	−0.742326	−0.371163	+	0.928568i	$0.621041\pi$
$828$	−10.0902	−0.350658
$829$	39.3050	1.36512	0.682559	−	0.730831i	$-0.260867\pi$
$829$	39.3050	1.36512	0.682559	+	0.730831i	$0.260867\pi$
$830$	23.1246	0.802667
$831$	−0.180340	−0.00625592
$832$	0.763932	0.0264846
$833$	13.5279	0.468713
$834$	8.29180	0.287121
$835$	80.0263	2.76942
$836$	0	0
$837$	17.6738	0.610895
$838$	−16.3262	−0.563981
$839$	−33.4508	−1.15485	−0.577426	−	0.816443i	$-0.695943\pi$
$839$	−33.4508	−1.15485	−0.577426	+	0.816443i	$0.695943\pi$
$840$	2.94427	0.101587
$841$	−26.6656	−0.919505
$842$	−22.4508	−0.773707
$843$	−4.18034	−0.143979
$844$	10.9443	0.376717
$845$	−47.8541	−1.64623
$846$	21.1803	0.728195
$847$	−1.23607	−0.0424718
$848$	−7.85410	−0.269711
$849$	0.583592	0.0200288
$850$	−24.3607	−0.835564
$851$	29.3607	1.00647
$852$	−6.47214	−0.221732
$853$	16.8328	0.576345	0.288172	−	0.957579i	$-0.406952\pi$
$853$	16.8328	0.576345	0.288172	+	0.957579i	$0.406952\pi$
$854$	13.5279	0.462914
$855$	0	0
$856$	6.00000	0.205076
$857$	12.5410	0.428393	0.214197	−	0.976791i	$-0.431287\pi$
$857$	12.5410	0.428393	0.214197	+	0.976791i	$0.431287\pi$
$858$	−0.472136	−0.0161185
$859$	−16.0344	−0.547088	−0.273544	−	0.961859i	$-0.588196\pi$
$859$	−16.0344	−0.547088	−0.273544	+	0.961859i	$0.588196\pi$
$860$	4.76393	0.162449
$861$	5.30495	0.180792
$862$	−19.2361	−0.655183
$863$	48.5066	1.65118	0.825592	−	0.564268i	$-0.190842\pi$
$863$	48.5066	1.65118	0.825592	+	0.564268i	$0.190842\pi$
$864$	3.47214	0.118124
$865$	41.4853	1.41054
$866$	14.7984	0.502869
$867$	6.72949	0.228545
$868$	−6.29180	−0.213557
$869$	7.52786	0.255365
$870$	−3.63932	−0.123385
$871$	−8.29180	−0.280957
$872$	12.1803	0.412478
$873$	19.7082	0.667022
$874$	0	0
$875$	−23.1246	−0.781755
$876$	−4.76393	−0.160958
$877$	−49.3050	−1.66491	−0.832455	−	0.554093i	$-0.813065\pi$
$877$	−49.3050	−1.66491	−0.832455	+	0.554093i	$0.813065\pi$
$878$	38.6525	1.30446
$879$	−2.11146	−0.0712176
$880$	3.85410	0.129922
$881$	−18.0000	−0.606435	−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000	−0.606435	−0.303218	+	0.952921i	$0.598061\pi$
$882$	14.3262	0.482390
$883$	31.3820	1.05609	0.528044	−	0.849217i	$-0.322926\pi$
$883$	31.3820	1.05609	0.528044	+	0.849217i	$0.322926\pi$
$884$	−1.88854	−0.0635186
$885$	−2.72949	−0.0917508
$886$	−18.2705	−0.613810
$887$	11.7082	0.393123	0.196562	−	0.980491i	$-0.437022\pi$
$887$	11.7082	0.393123	0.196562	+	0.980491i	$0.437022\pi$
$888$	−4.70820	−0.157997
$889$	−21.5279	−0.722021
$890$	18.7082	0.627100
$891$	5.70820	0.191232
$892$	−10.5623	−0.353652
$893$	0	0
$894$	14.3607	0.480293
$895$	−3.50658	−0.117212
$896$	−1.23607	−0.0412941
$897$	−1.81966	−0.0607567
$898$	−14.5623	−0.485950
$899$	7.77709	0.259380
$900$	−25.7984	−0.859946
$901$	19.4164	0.646854
$902$	6.94427	0.231219
$903$	0.944272	0.0314234
$904$	−9.79837	−0.325889
$905$	−66.7771	−2.21975
$906$	4.65248	0.154568
$907$	33.5623	1.11442	0.557209	−	0.830372i	$-0.311872\pi$
$907$	33.5623	1.11442	0.557209	+	0.830372i	$0.311872\pi$
$908$	−22.3607	−0.742065
$909$	−39.8885	−1.32302
$910$	−3.63932	−0.120642
$911$	18.6180	0.616843	0.308421	−	0.951250i	$-0.400199\pi$
$911$	18.6180	0.616843	0.308421	+	0.951250i	$0.400199\pi$
$912$	0	0
$913$	6.00000	0.198571
$914$	−9.23607	−0.305502
$915$	26.0689	0.861811
$916$	−1.38197	−0.0456614
$917$	−11.6393	−0.384364
$918$	−8.58359	−0.283301
$919$	27.0132	0.891082	0.445541	−	0.895262i	$-0.353011\pi$
$919$	27.0132	0.891082	0.445541	+	0.895262i	$0.353011\pi$
$920$	14.8541	0.489725
$921$	−18.1803	−0.599063
$922$	10.6525	0.350821
$923$	8.00000	0.263323
$924$	0.763932	0.0251315
$925$	75.0689	2.46825
$926$	30.1591	0.991088
$927$	−44.3607	−1.45700
$928$	1.52786	0.0501546
$929$	−49.3394	−1.61877	−0.809386	−	0.587276i	$-0.800200\pi$
$929$	−49.3394	−1.61877	−0.809386	+	0.587276i	$0.800200\pi$
$930$	−12.1246	−0.397582
$931$	0	0
$932$	10.4721	0.343026
$933$	−4.63932	−0.151885
$934$	−0.618034	−0.0202227
$935$	−9.52786	−0.311594
$936$	−2.00000	−0.0653720
$937$	−12.1803	−0.397914	−0.198957	−	0.980008i	$-0.563755\pi$
$937$	−12.1803	−0.397914	−0.198957	+	0.980008i	$0.563755\pi$
$938$	13.4164	0.438061
$939$	−7.70820	−0.251548
$940$	−31.1803	−1.01699
$941$	−33.4164	−1.08934	−0.544672	−	0.838649i	$-0.683346\pi$
$941$	−33.4164	−1.08934	−0.544672	+	0.838649i	$0.683346\pi$
$942$	2.81966	0.0918695
$943$	26.7639	0.871554
$944$	1.14590	0.0372958
$945$	−16.5410	−0.538079
$946$	1.23607	0.0401880
$947$	−1.16718	−0.0379284	−0.0189642	−	0.999820i	$-0.506037\pi$
$947$	−1.16718	−0.0379284	−0.0189642	+	0.999820i	$0.506037\pi$
$948$	−4.65248	−0.151105
$949$	5.88854	0.191150
$950$	0	0
$951$	10.7639	0.349044
$952$	3.05573	0.0990367
$953$	27.4164	0.888105	0.444052	−	0.896001i	$-0.353540\pi$
$953$	27.4164	0.888105	0.444052	+	0.896001i	$0.353540\pi$
$954$	20.5623	0.665729
$955$	−21.6525	−0.700658
$956$	6.29180	0.203491
$957$	−0.944272	−0.0305240
$958$	23.1246	0.747122
$959$	−8.83282	−0.285226
$960$	−2.38197	−0.0768776
$961$	−5.09017	−0.164199
$962$	5.81966	0.187633
$963$	−15.7082	−0.506190
$964$	−10.0000	−0.322078
$965$	45.8197	1.47499
$966$	2.94427	0.0947304
$967$	37.9574	1.22063	0.610314	−	0.792159i	$-0.291043\pi$
$967$	37.9574	1.22063	0.610314	+	0.792159i	$0.291043\pi$
$968$	1.00000	0.0321412
$969$	0	0
$970$	−29.0132	−0.931556
$971$	2.27051	0.0728641	0.0364321	−	0.999336i	$-0.488401\pi$
$971$	2.27051	0.0728641	0.0364321	+	0.999336i	$0.488401\pi$
$972$	−13.9443	−0.447263
$973$	16.5836	0.531646
$974$	−4.14590	−0.132843
$975$	−4.65248	−0.148998
$976$	−10.9443	−0.350318
$977$	−8.85410	−0.283268	−0.141634	−	0.989919i	$-0.545236\pi$
$977$	−8.85410	−0.283268	−0.141634	+	0.989919i	$0.545236\pi$
$978$	−6.09017	−0.194742
$979$	4.85410	0.155138
$980$	−21.0902	−0.673701
$981$	−31.8885	−1.01812
$982$	5.05573	0.161335
$983$	16.6312	0.530453	0.265226	−	0.964186i	$-0.414553\pi$
$983$	16.6312	0.530453	0.265226	+	0.964186i	$0.414553\pi$
$984$	−4.29180	−0.136817
$985$	−86.6099	−2.75962
$986$	−3.77709	−0.120287
$987$	−6.18034	−0.196722
$988$	0	0
$989$	4.76393	0.151484
$990$	−10.0902	−0.320687
$991$	−34.3262	−1.09041	−0.545204	−	0.838303i	$-0.683548\pi$
$991$	−34.3262	−1.09041	−0.545204	+	0.838303i	$0.683548\pi$
$992$	5.09017	0.161613
$993$	8.56231	0.271717
$994$	−12.9443	−0.410567
$995$	86.0476	2.72789
$996$	−3.70820	−0.117499
$997$	32.0689	1.01563	0.507816	−	0.861466i	$-0.330453\pi$
$997$	32.0689	1.01563	0.507816	+	0.861466i	$0.330453\pi$
$998$	27.0344	0.855760
$999$	26.4508	0.836868

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.z.1.1	yes	2
19.18	odd	2		7942.2.a.u.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7942.2.a.u.1.2	✓	2	19.18	odd	2
7942.2.a.z.1.1	yes	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7942.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} +3.85410 q^{5} -0.618034 q^{6} -1.23607 q^{7} +1.00000 q^{8} -2.61803 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} +3.85410 q^{5} -0.618034 q^{6} -1.23607 q^{7} +1.00000 q^{8} -2.61803 q^{9} +3.85410 q^{10} +1.00000 q^{11} -0.618034 q^{12} +0.763932 q^{13} -1.23607 q^{14} -2.38197 q^{15} +1.00000 q^{16} -2.47214 q^{17} -2.61803 q^{18} +3.85410 q^{20} +0.763932 q^{21} +1.00000 q^{22} +3.85410 q^{23} -0.618034 q^{24} +9.85410 q^{25} +0.763932 q^{26} +3.47214 q^{27} -1.23607 q^{28} +1.52786 q^{29} -2.38197 q^{30} +5.09017 q^{31} +1.00000 q^{32} -0.618034 q^{33} -2.47214 q^{34} -4.76393 q^{35} -2.61803 q^{36} +7.61803 q^{37} -0.472136 q^{39} +3.85410 q^{40} +6.94427 q^{41} +0.763932 q^{42} +1.23607 q^{43} +1.00000 q^{44} -10.0902 q^{45} +3.85410 q^{46} -8.09017 q^{47} -0.618034 q^{48} -5.47214 q^{49} +9.85410 q^{50} +1.52786 q^{51} +0.763932 q^{52} -7.85410 q^{53} +3.47214 q^{54} +3.85410 q^{55} -1.23607 q^{56} +1.52786 q^{58} +1.14590 q^{59} -2.38197 q^{60} -10.9443 q^{61} +5.09017 q^{62} +3.23607 q^{63} +1.00000 q^{64} +2.94427 q^{65} -0.618034 q^{66} -10.8541 q^{67} -2.47214 q^{68} -2.38197 q^{69} -4.76393 q^{70} +10.4721 q^{71} -2.61803 q^{72} +7.70820 q^{73} +7.61803 q^{74} -6.09017 q^{75} -1.23607 q^{77} -0.472136 q^{78} +7.52786 q^{79} +3.85410 q^{80} +5.70820 q^{81} +6.94427 q^{82} +6.00000 q^{83} +0.763932 q^{84} -9.52786 q^{85} +1.23607 q^{86} -0.944272 q^{87} +1.00000 q^{88} +4.85410 q^{89} -10.0902 q^{90} -0.944272 q^{91} +3.85410 q^{92} -3.14590 q^{93} -8.09017 q^{94} -0.618034 q^{96} -7.52786 q^{97} -5.47214 q^{98} -2.61803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 + q^5 + q^6 + 2 * q^7 + 2 * q^8 - 3 * q^9	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - 3 q^{9} + q^{10} + 2 q^{11} + q^{12} + 6 q^{13} + 2 q^{14} - 7 q^{15} + 2 q^{16} + 4 q^{17} - 3 q^{18} + q^{20} + 6 q^{21} + 2 q^{22} + q^{23} + q^{24} + 13 q^{25} + 6 q^{26} - 2 q^{27} + 2 q^{28} + 12 q^{29} - 7 q^{30} - q^{31} + 2 q^{32} + q^{33} + 4 q^{34} - 14 q^{35} - 3 q^{36} + 13 q^{37} + 8 q^{39} + q^{40} - 4 q^{41} + 6 q^{42} - 2 q^{43} + 2 q^{44} - 9 q^{45} + q^{46} - 5 q^{47} + q^{48} - 2 q^{49} + 13 q^{50} + 12 q^{51} + 6 q^{52} - 9 q^{53} - 2 q^{54} + q^{55} + 2 q^{56} + 12 q^{58} + 9 q^{59} - 7 q^{60} - 4 q^{61} - q^{62} + 2 q^{63} + 2 q^{64} - 12 q^{65} + q^{66} - 15 q^{67} + 4 q^{68} - 7 q^{69} - 14 q^{70} + 12 q^{71} - 3 q^{72} + 2 q^{73} + 13 q^{74} - q^{75} + 2 q^{77} + 8 q^{78} + 24 q^{79} + q^{80} - 2 q^{81} - 4 q^{82} + 12 q^{83} + 6 q^{84} - 28 q^{85} - 2 q^{86} + 16 q^{87} + 2 q^{88} + 3 q^{89} - 9 q^{90} + 16 q^{91} + q^{92} - 13 q^{93} - 5 q^{94} + q^{96} - 24 q^{97} - 2 q^{98} - 3 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 + q^5 + q^6 + 2 * q^7 + 2 * q^8 - 3 * q^9 + q^10 + 2 * q^11 + q^12 + 6 * q^13 + 2 * q^14 - 7 * q^15 + 2 * q^16 + 4 * q^17 - 3 * q^18 + q^20 + 6 * q^21 + 2 * q^22 + q^23 + q^24 + 13 * q^25 + 6 * q^26 - 2 * q^27 + 2 * q^28 + 12 * q^29 - 7 * q^30 - q^31 + 2 * q^32 + q^33 + 4 * q^34 - 14 * q^35 - 3 * q^36 + 13 * q^37 + 8 * q^39 + q^40 - 4 * q^41 + 6 * q^42 - 2 * q^43 + 2 * q^44 - 9 * q^45 + q^46 - 5 * q^47 + q^48 - 2 * q^49 + 13 * q^50 + 12 * q^51 + 6 * q^52 - 9 * q^53 - 2 * q^54 + q^55 + 2 * q^56 + 12 * q^58 + 9 * q^59 - 7 * q^60 - 4 * q^61 - q^62 + 2 * q^63 + 2 * q^64 - 12 * q^65 + q^66 - 15 * q^67 + 4 * q^68 - 7 * q^69 - 14 * q^70 + 12 * q^71 - 3 * q^72 + 2 * q^73 + 13 * q^74 - q^75 + 2 * q^77 + 8 * q^78 + 24 * q^79 + q^80 - 2 * q^81 - 4 * q^82 + 12 * q^83 + 6 * q^84 - 28 * q^85 - 2 * q^86 + 16 * q^87 + 2 * q^88 + 3 * q^89 - 9 * q^90 + 16 * q^91 + q^92 - 13 * q^93 - 5 * q^94 + q^96 - 24 * q^97 - 2 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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