LMFDB - Embedded newform 3179.2.a.bh.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3179,2,Mod(1,3179)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3179, 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("3179.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3179 = 11 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3179.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:	$25.3844428026$
Analytic rank:	$1$
Dimension:	$28$
Twist minimal:	no (minimal twist has level 187)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	3179.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.57447 q^{2} +0.262331 q^{3} +4.62792 q^{4} +1.26895 q^{5} -0.675364 q^{6} +0.195142 q^{7} -6.76552 q^{8} -2.93118 q^{9} +O(q^{10})$	\(q-2.57447 q^{2} +0.262331 q^{3} +4.62792 q^{4} +1.26895 q^{5} -0.675364 q^{6} +0.195142 q^{7} -6.76552 q^{8} -2.93118 q^{9} -3.26688 q^{10} +1.00000 q^{11} +1.21405 q^{12} -0.389335 q^{13} -0.502389 q^{14} +0.332885 q^{15} +8.16181 q^{16} +7.54626 q^{18} -2.23981 q^{19} +5.87260 q^{20} +0.0511919 q^{21} -2.57447 q^{22} -1.09189 q^{23} -1.77480 q^{24} -3.38977 q^{25} +1.00233 q^{26} -1.55593 q^{27} +0.903103 q^{28} +4.53695 q^{29} -0.857004 q^{30} -3.18014 q^{31} -7.48134 q^{32} +0.262331 q^{33} +0.247626 q^{35} -13.5653 q^{36} +5.51240 q^{37} +5.76632 q^{38} -0.102135 q^{39} -8.58510 q^{40} +9.63462 q^{41} -0.131792 q^{42} +11.7108 q^{43} +4.62792 q^{44} -3.71952 q^{45} +2.81103 q^{46} -3.65052 q^{47} +2.14109 q^{48} -6.96192 q^{49} +8.72687 q^{50} -1.80181 q^{52} -12.4525 q^{53} +4.00571 q^{54} +1.26895 q^{55} -1.32024 q^{56} -0.587570 q^{57} -11.6803 q^{58} +7.36084 q^{59} +1.54056 q^{60} -3.10273 q^{61} +8.18719 q^{62} -0.571998 q^{63} +2.93690 q^{64} -0.494047 q^{65} -0.675364 q^{66} -2.40497 q^{67} -0.286435 q^{69} -0.637506 q^{70} -9.53897 q^{71} +19.8310 q^{72} +2.52772 q^{73} -14.1915 q^{74} -0.889241 q^{75} -10.3656 q^{76} +0.195142 q^{77} +0.262943 q^{78} -13.5912 q^{79} +10.3569 q^{80} +8.38538 q^{81} -24.8041 q^{82} -7.20316 q^{83} +0.236912 q^{84} -30.1491 q^{86} +1.19018 q^{87} -6.76552 q^{88} -7.05766 q^{89} +9.57582 q^{90} -0.0759757 q^{91} -5.05316 q^{92} -0.834249 q^{93} +9.39817 q^{94} -2.84220 q^{95} -1.96259 q^{96} -16.0557 q^{97} +17.9233 q^{98} -2.93118 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 8 q^{3} + 24 q^{4} - 16 q^{5} - 16 q^{6} - 12 q^{7} + 20 q^{9}+O(q^{10}) $ 28 * q - 8 * q^3 + 24 * q^4 - 16 * q^5 - 16 * q^6 - 12 * q^7 + 20 * q^9	$ 28 q - 8 q^{3} + 24 q^{4} - 16 q^{5} - 16 q^{6} - 12 q^{7} + 20 q^{9} - 24 q^{10} + 28 q^{11} - 24 q^{12} - 16 q^{14} - 16 q^{15} + 16 q^{16} - 32 q^{20} - 8 q^{23} + 8 q^{24} + 20 q^{25} - 24 q^{26} - 32 q^{27} - 32 q^{28} - 36 q^{29} + 40 q^{30} - 56 q^{31} + 40 q^{32} - 8 q^{33} + 16 q^{35} + 40 q^{36} - 64 q^{37} - 8 q^{38} - 32 q^{39} - 72 q^{40} - 28 q^{41} + 24 q^{42} + 16 q^{43} + 24 q^{44} - 24 q^{45} - 36 q^{47} - 56 q^{48} + 16 q^{49} + 56 q^{50} - 20 q^{53} - 64 q^{54} - 16 q^{55} - 48 q^{56} - 32 q^{57} + 16 q^{58} - 28 q^{59} + 8 q^{60} - 104 q^{61} + 8 q^{62} - 28 q^{63} - 32 q^{65} - 16 q^{66} - 12 q^{67} - 32 q^{69} - 40 q^{71} + 40 q^{72} - 76 q^{73} - 24 q^{74} + 16 q^{75} - 16 q^{76} - 12 q^{77} + 24 q^{78} - 24 q^{79} - 8 q^{80} + 12 q^{81} - 56 q^{82} + 32 q^{83} - 40 q^{84} - 16 q^{86} - 8 q^{87} - 52 q^{89} - 16 q^{90} - 80 q^{91} + 56 q^{92} - 24 q^{97} - 24 q^{98} + 20 q^{99}+O(q^{100}) $ 28 * q - 8 * q^3 + 24 * q^4 - 16 * q^5 - 16 * q^6 - 12 * q^7 + 20 * q^9 - 24 * q^10 + 28 * q^11 - 24 * q^12 - 16 * q^14 - 16 * q^15 + 16 * q^16 - 32 * q^20 - 8 * q^23 + 8 * q^24 + 20 * q^25 - 24 * q^26 - 32 * q^27 - 32 * q^28 - 36 * q^29 + 40 * q^30 - 56 * q^31 + 40 * q^32 - 8 * q^33 + 16 * q^35 + 40 * q^36 - 64 * q^37 - 8 * q^38 - 32 * q^39 - 72 * q^40 - 28 * q^41 + 24 * q^42 + 16 * q^43 + 24 * q^44 - 24 * q^45 - 36 * q^47 - 56 * q^48 + 16 * q^49 + 56 * q^50 - 20 * q^53 - 64 * q^54 - 16 * q^55 - 48 * q^56 - 32 * q^57 + 16 * q^58 - 28 * q^59 + 8 * q^60 - 104 * q^61 + 8 * q^62 - 28 * q^63 - 32 * q^65 - 16 * q^66 - 12 * q^67 - 32 * q^69 - 40 * q^71 + 40 * q^72 - 76 * q^73 - 24 * q^74 + 16 * q^75 - 16 * q^76 - 12 * q^77 + 24 * q^78 - 24 * q^79 - 8 * q^80 + 12 * q^81 - 56 * q^82 + 32 * q^83 - 40 * q^84 - 16 * q^86 - 8 * q^87 - 52 * q^89 - 16 * q^90 - 80 * q^91 + 56 * q^92 - 24 * q^97 - 24 * q^98 + 20 * 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 $

$2$	−2.57447	−1.82043	−0.910214	−	0.414138i	$-0.864083\pi$
$2$	−2.57447	−1.82043	−0.910214	+	0.414138i	$0.864083\pi$
$3$	0.262331	0.151457	0.0757284	−	0.997128i	$-0.475872\pi$
$3$	0.262331	0.151457	0.0757284	+	0.997128i	$0.475872\pi$
$4$	4.62792	2.31396
$5$	1.26895	0.567492	0.283746	−	0.958900i	$-0.408423\pi$
$5$	1.26895	0.567492	0.283746	+	0.958900i	$0.408423\pi$
$6$	−0.675364	−0.275716
$7$	0.195142	0.0737568	0.0368784	−	0.999320i	$-0.488259\pi$
$7$	0.195142	0.0737568	0.0368784	+	0.999320i	$0.488259\pi$
$8$	−6.76552	−2.39197
$9$	−2.93118	−0.977061
$10$	−3.26688	−1.03308
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.21405	0.350465
$13$	−0.389335	−0.107982	−0.0539911	−	0.998541i	$-0.517194\pi$
$13$	−0.389335	−0.107982	−0.0539911	+	0.998541i	$0.517194\pi$
$14$	−0.502389	−0.134269
$15$	0.332885	0.0859505
$16$	8.16181	2.04045
$17$	0	0
$17$	0	0
$18$	7.54626	1.77867
$19$	−2.23981	−0.513847	−0.256923	−	0.966432i	$-0.582709\pi$
$19$	−2.23981	−0.513847	−0.256923	+	0.966432i	$0.582709\pi$
$20$	5.87260	1.31315
$21$	0.0511919	0.0111710
$22$	−2.57447	−0.548880
$23$	−1.09189	−0.227674	−0.113837	−	0.993499i	$-0.536314\pi$
$23$	−1.09189	−0.227674	−0.113837	+	0.993499i	$0.536314\pi$
$24$	−1.77480	−0.362280
$25$	−3.38977	−0.677953
$26$	1.00233	0.196574
$27$	−1.55593	−0.299439
$28$	0.903103	0.170670
$29$	4.53695	0.842490	0.421245	−	0.906947i	$-0.361593\pi$
$29$	4.53695	0.842490	0.421245	+	0.906947i	$0.361593\pi$
$30$	−0.857004	−0.156467
$31$	−3.18014	−0.571170	−0.285585	−	0.958353i	$-0.592188\pi$
$31$	−3.18014	−0.571170	−0.285585	+	0.958353i	$0.592188\pi$
$32$	−7.48134	−1.32253
$33$	0.262331	0.0456660
$34$	0	0
$35$	0.247626	0.0418564
$36$	−13.5653	−2.26088
$37$	5.51240	0.906233	0.453116	−	0.891451i	$-0.350312\pi$
$37$	5.51240	0.906233	0.453116	+	0.891451i	$0.350312\pi$
$38$	5.76632	0.935421
$39$	−0.102135	−0.0163546
$40$	−8.58510	−1.35742
$41$	9.63462	1.50467	0.752337	−	0.658778i	$-0.228926\pi$
$41$	9.63462	1.50467	0.752337	+	0.658778i	$0.228926\pi$
$42$	−0.131792	−0.0203360
$43$	11.7108	1.78588	0.892940	−	0.450177i	$-0.148639\pi$
$43$	11.7108	1.78588	0.892940	+	0.450177i	$0.148639\pi$
$44$	4.62792	0.697685
$45$	−3.71952	−0.554474
$46$	2.81103	0.414464
$47$	−3.65052	−0.532483	−0.266242	−	0.963906i	$-0.585782\pi$
$47$	−3.65052	−0.532483	−0.266242	+	0.963906i	$0.585782\pi$
$48$	2.14109	0.309040
$49$	−6.96192	−0.994560
$50$	8.72687	1.23417
$51$	0	0
$52$	−1.80181	−0.249866
$53$	−12.4525	−1.71049	−0.855243	−	0.518228i	$-0.826592\pi$
$53$	−12.4525	−1.71049	−0.855243	+	0.518228i	$0.826592\pi$
$54$	4.00571	0.545108
$55$	1.26895	0.171105
$56$	−1.32024	−0.176424
$57$	−0.587570	−0.0778256
$58$	−11.6803	−1.53369
$59$	7.36084	0.958299	0.479150	−	0.877733i	$-0.340945\pi$
$59$	7.36084	0.958299	0.479150	+	0.877733i	$0.340945\pi$
$60$	1.54056	0.198886
$61$	−3.10273	−0.397264	−0.198632	−	0.980074i	$-0.563650\pi$
$61$	−3.10273	−0.397264	−0.198632	+	0.980074i	$0.563650\pi$
$62$	8.18719	1.03977
$63$	−0.571998	−0.0720649
$64$	2.93690	0.367112
$65$	−0.494047	−0.0612790
$66$	−0.675364	−0.0831316
$67$	−2.40497	−0.293814	−0.146907	−	0.989150i	$-0.546932\pi$
$67$	−2.40497	−0.293814	−0.146907	+	0.989150i	$0.546932\pi$
$68$	0	0
$69$	−0.286435	−0.0344828
$70$	−0.637506	−0.0761966
$71$	−9.53897	−1.13207	−0.566034	−	0.824382i	$-0.691523\pi$
$71$	−9.53897	−1.13207	−0.566034	+	0.824382i	$0.691523\pi$
$72$	19.8310	2.33710
$73$	2.52772	0.295847	0.147924	−	0.988999i	$-0.452741\pi$
$73$	2.52772	0.295847	0.147924	+	0.988999i	$0.452741\pi$
$74$	−14.1915	−1.64973
$75$	−0.889241	−0.102681
$76$	−10.3656	−1.18902
$77$	0.195142	0.0222385
$78$	0.262943	0.0297724
$79$	−13.5912	−1.52913	−0.764563	−	0.644549i	$-0.777045\pi$
$79$	−13.5912	−1.52913	−0.764563	+	0.644549i	$0.777045\pi$
$80$	10.3569	1.15794
$81$	8.38538	0.931709
$82$	−24.8041	−2.73915
$83$	−7.20316	−0.790650	−0.395325	−	0.918541i	$-0.629368\pi$
$83$	−7.20316	−0.790650	−0.395325	+	0.918541i	$0.629368\pi$
$84$	0.236912	0.0258492
$85$	0	0
$86$	−30.1491	−3.25107
$87$	1.19018	0.127601
$88$	−6.76552	−0.721206
$89$	−7.05766	−0.748110	−0.374055	−	0.927406i	$-0.622033\pi$
$89$	−7.05766	−0.748110	−0.374055	+	0.927406i	$0.622033\pi$
$90$	9.57582	1.00938
$91$	−0.0759757	−0.00796442
$92$	−5.05316	−0.526828
$93$	−0.834249	−0.0865076
$94$	9.39817	0.969348
$95$	−2.84220	−0.291604
$96$	−1.96259	−0.200306
$97$	−16.0557	−1.63021	−0.815103	−	0.579316i	$-0.803320\pi$
$97$	−16.0557	−1.63021	−0.815103	+	0.579316i	$0.803320\pi$
$98$	17.9233	1.81053
$99$	−2.93118	−0.294595
$100$	−15.6876	−1.56876
$101$	−7.32255	−0.728621	−0.364310	−	0.931278i	$-0.618695\pi$
$101$	−7.32255	−0.728621	−0.364310	+	0.931278i	$0.618695\pi$
$102$	0	0
$103$	−6.99931	−0.689662	−0.344831	−	0.938665i	$-0.612064\pi$
$103$	−6.99931	−0.689662	−0.344831	+	0.938665i	$0.612064\pi$
$104$	2.63405	0.258290
$105$	0.0649599	0.00633944
$106$	32.0587	3.11382
$107$	10.4515	1.01039	0.505193	−	0.863006i	$-0.331421\pi$
$107$	10.4515	1.01039	0.505193	+	0.863006i	$0.331421\pi$
$108$	−7.20073	−0.692891
$109$	−14.4259	−1.38175	−0.690874	−	0.722976i	$-0.742774\pi$
$109$	−14.4259	−1.38175	−0.690874	+	0.722976i	$0.742774\pi$
$110$	−3.26688	−0.311485
$111$	1.44607	0.137255
$112$	1.59271	0.150497
$113$	14.9174	1.40331	0.701656	−	0.712516i	$-0.252444\pi$
$113$	14.9174	1.40331	0.701656	+	0.712516i	$0.252444\pi$
$114$	1.51268	0.141676
$115$	−1.38555	−0.129203
$116$	20.9966	1.94949
$117$	1.14121	0.105505
$118$	−18.9503	−1.74452
$119$	0	0
$120$	−2.25214	−0.205591
$121$	1.00000	0.0909091
$122$	7.98791	0.723191
$123$	2.52746	0.227893
$124$	−14.7174	−1.32166
$125$	−10.6462	−0.952224
$126$	1.47259	0.131189
$127$	4.17994	0.370910	0.185455	−	0.982653i	$-0.440624\pi$
$127$	4.17994	0.370910	0.185455	+	0.982653i	$0.440624\pi$
$128$	7.40170	0.654224
$129$	3.07210	0.270484
$130$	1.27191	0.111554
$131$	5.98909	0.523270	0.261635	−	0.965167i	$-0.415738\pi$
$131$	5.98909	0.523270	0.261635	+	0.965167i	$0.415738\pi$
$132$	1.21405	0.105669
$133$	−0.437081	−0.0378997
$134$	6.19153	0.534867
$135$	−1.97440	−0.169929
$136$	0	0
$137$	10.3153	0.881293	0.440647	−	0.897681i	$-0.354749\pi$
$137$	10.3153	0.881293	0.440647	+	0.897681i	$0.354749\pi$
$138$	0.737421	0.0627734
$139$	−20.3066	−1.72238	−0.861191	−	0.508282i	$-0.830281\pi$
$139$	−20.3066	−1.72238	−0.861191	+	0.508282i	$0.830281\pi$
$140$	1.14599	0.0968540
$141$	−0.957645	−0.0806482
$142$	24.5578	2.06085
$143$	−0.389335	−0.0325578
$144$	−23.9237	−1.99365
$145$	5.75716	0.478106
$146$	−6.50755	−0.538569
$147$	−1.82633	−0.150633
$148$	25.5109	2.09699
$149$	3.86695	0.316793	0.158396	−	0.987376i	$-0.449368\pi$
$149$	3.86695	0.316793	0.158396	+	0.987376i	$0.449368\pi$
$150$	2.28933	0.186923
$151$	3.12821	0.254570	0.127285	−	0.991866i	$-0.459374\pi$
$151$	3.12821	0.254570	0.127285	+	0.991866i	$0.459374\pi$
$152$	15.1534	1.22911
$153$	0	0
$154$	−0.502389	−0.0404836
$155$	−4.03544	−0.324134
$156$	−0.472671	−0.0378440
$157$	−16.7161	−1.33409	−0.667045	−	0.745017i	$-0.732441\pi$
$157$	−16.7161	−1.33409	−0.667045	+	0.745017i	$0.732441\pi$
$158$	34.9901	2.78366
$159$	−3.26668	−0.259065
$160$	−9.49344	−0.750523
$161$	−0.213073	−0.0167925
$162$	−21.5879	−1.69611
$163$	14.9594	1.17171	0.585855	−	0.810416i	$-0.300759\pi$
$163$	14.9594	1.17171	0.585855	+	0.810416i	$0.300759\pi$
$164$	44.5883	3.48176
$165$	0.332885	0.0259151
$166$	18.5444	1.43932
$167$	19.0111	1.47112	0.735561	−	0.677458i	$-0.236919\pi$
$167$	19.0111	1.47112	0.735561	+	0.677458i	$0.236919\pi$
$168$	−0.346339	−0.0267207
$169$	−12.8484	−0.988340
$170$	0	0
$171$	6.56528	0.502059
$172$	54.1966	4.13245
$173$	−5.75727	−0.437717	−0.218859	−	0.975757i	$-0.570233\pi$
$173$	−5.75727	−0.437717	−0.218859	+	0.975757i	$0.570233\pi$
$174$	−3.06409	−0.232288
$175$	−0.661486	−0.0500037
$176$	8.16181	0.615219
$177$	1.93098	0.145141
$178$	18.1698	1.36188
$179$	12.5846	0.940615	0.470308	−	0.882503i	$-0.344143\pi$
$179$	12.5846	0.940615	0.470308	+	0.882503i	$0.344143\pi$
$180$	−17.2137	−1.28303
$181$	13.2955	0.988248	0.494124	−	0.869391i	$-0.335489\pi$
$181$	13.2955	0.988248	0.494124	+	0.869391i	$0.335489\pi$
$182$	0.195598	0.0144987
$183$	−0.813943	−0.0601684
$184$	7.38717	0.544589
$185$	6.99496	0.514280
$186$	2.14775	0.157481
$187$	0	0
$188$	−16.8943	−1.23214
$189$	−0.303628	−0.0220857
$190$	7.31717	0.530844
$191$	−22.4693	−1.62582	−0.812911	−	0.582388i	$-0.802118\pi$
$191$	−22.4693	−1.62582	−0.812911	+	0.582388i	$0.802118\pi$
$192$	0.770440	0.0556017
$193$	−7.94638	−0.571993	−0.285996	−	0.958231i	$-0.592325\pi$
$193$	−7.94638	−0.571993	−0.285996	+	0.958231i	$0.592325\pi$
$194$	41.3349	2.96767
$195$	−0.129604	−0.00928112
$196$	−32.2192	−2.30137
$197$	7.77974	0.554283	0.277142	−	0.960829i	$-0.410613\pi$
$197$	7.77974	0.554283	0.277142	+	0.960829i	$0.410613\pi$
$198$	7.54626	0.536289
$199$	−22.1673	−1.57140	−0.785701	−	0.618607i	$-0.787697\pi$
$199$	−22.1673	−1.57140	−0.785701	+	0.618607i	$0.787697\pi$
$200$	22.9335	1.62164
$201$	−0.630897	−0.0445001
$202$	18.8517	1.32640
$203$	0.885351	0.0621394
$204$	0	0
$205$	12.2259	0.853890
$206$	18.0195	1.25548
$207$	3.20052	0.222451
$208$	−3.17768	−0.220332
$209$	−2.23981	−0.154931
$210$	−0.167238	−0.0115405
$211$	0.938180	0.0645870	0.0322935	−	0.999478i	$-0.489719\pi$
$211$	0.938180	0.0645870	0.0322935	+	0.999478i	$0.489719\pi$
$212$	−57.6293	−3.95800
$213$	−2.50237	−0.171459
$214$	−26.9072	−1.83934
$215$	14.8604	1.01347
$216$	10.5267	0.716250
$217$	−0.620579	−0.0421277
$218$	37.1390	2.51537
$219$	0.663099	0.0448081
$220$	5.87260	0.395931
$221$	0	0
$222$	−3.72288	−0.249863
$223$	−28.3819	−1.90059	−0.950296	−	0.311348i	$-0.899219\pi$
$223$	−28.3819	−1.90059	−0.950296	+	0.311348i	$0.899219\pi$
$224$	−1.45992	−0.0975453
$225$	9.93602	0.662401
$226$	−38.4045	−2.55463
$227$	−17.8213	−1.18284	−0.591422	−	0.806362i	$-0.701433\pi$
$227$	−17.8213	−1.18284	−0.591422	+	0.806362i	$0.701433\pi$
$228$	−2.71923	−0.180085
$229$	15.3324	1.01319	0.506596	−	0.862184i	$-0.330904\pi$
$229$	15.3324	1.01319	0.506596	+	0.862184i	$0.330904\pi$
$230$	3.56706	0.235205
$231$	0.0511919	0.00336818
$232$	−30.6948	−2.01521
$233$	−21.8097	−1.42880	−0.714402	−	0.699736i	$-0.753301\pi$
$233$	−21.8097	−1.42880	−0.714402	+	0.699736i	$0.753301\pi$
$234$	−2.93802	−0.192065
$235$	−4.63233	−0.302180
$236$	34.0654	2.21747
$237$	−3.56538	−0.231597
$238$	0	0
$239$	−0.993928	−0.0642919	−0.0321459	−	0.999483i	$-0.510234\pi$
$239$	−0.993928	−0.0642919	−0.0321459	+	0.999483i	$0.510234\pi$
$240$	2.71694	0.175378
$241$	−26.1166	−1.68232	−0.841160	−	0.540786i	$-0.818127\pi$
$241$	−26.1166	−1.68232	−0.841160	+	0.540786i	$0.818127\pi$
$242$	−2.57447	−0.165494
$243$	6.86754	0.440553
$244$	−14.3592	−0.919254
$245$	−8.83433	−0.564405
$246$	−6.50688	−0.414863
$247$	0.872035	0.0554862
$248$	21.5153	1.36622
$249$	−1.88961	−0.119749
$250$	27.4084	1.73346
$251$	20.6831	1.30551	0.652754	−	0.757570i	$-0.273614\pi$
$251$	20.6831	1.30551	0.652754	+	0.757570i	$0.273614\pi$
$252$	−2.64716	−0.166755
$253$	−1.09189	−0.0686463
$254$	−10.7611	−0.675214
$255$	0	0
$256$	−24.9293	−1.55808
$257$	13.4290	0.837680	0.418840	−	0.908060i	$-0.362437\pi$
$257$	13.4290	0.837680	0.418840	+	0.908060i	$0.362437\pi$
$258$	−7.90905	−0.492396
$259$	1.07570	0.0668409
$260$	−2.28641	−0.141797
$261$	−13.2986	−0.823164
$262$	−15.4188	−0.952575
$263$	−8.87301	−0.547133	−0.273567	−	0.961853i	$-0.588203\pi$
$263$	−8.87301	−0.547133	−0.273567	+	0.961853i	$0.588203\pi$
$264$	−1.77480	−0.109232
$265$	−15.8016	−0.970686
$266$	1.12525	0.0689937
$267$	−1.85144	−0.113306
$268$	−11.1300	−0.679873
$269$	−8.02871	−0.489519	−0.244760	−	0.969584i	$-0.578709\pi$
$269$	−8.02871	−0.489519	−0.244760	+	0.969584i	$0.578709\pi$
$270$	5.08305	0.309344
$271$	3.18943	0.193744	0.0968721	−	0.995297i	$-0.469116\pi$
$271$	3.18943	0.193744	0.0968721	+	0.995297i	$0.469116\pi$
$272$	0	0
$273$	−0.0199308	−0.00120627
$274$	−26.5564	−1.60433
$275$	−3.38977	−0.204411
$276$	−1.32560	−0.0797918
$277$	6.40568	0.384880	0.192440	−	0.981309i	$-0.438360\pi$
$277$	6.40568	0.384880	0.192440	+	0.981309i	$0.438360\pi$
$278$	52.2788	3.13547
$279$	9.32156	0.558067
$280$	−1.67532	−0.100119
$281$	−12.2750	−0.732268	−0.366134	−	0.930562i	$-0.619319\pi$
$281$	−12.2750	−0.732268	−0.366134	+	0.930562i	$0.619319\pi$
$282$	2.46543	0.146814
$283$	−27.2729	−1.62120	−0.810602	−	0.585597i	$-0.800860\pi$
$283$	−27.2729	−1.62120	−0.810602	+	0.585597i	$0.800860\pi$
$284$	−44.1456	−2.61956
$285$	−0.745597	−0.0441654
$286$	1.00233	0.0592692
$287$	1.88012	0.110980
$288$	21.9292	1.29219
$289$	0	0
$290$	−14.8217	−0.870358
$291$	−4.21190	−0.246906
$292$	11.6981	0.684579
$293$	21.6665	1.26577	0.632884	−	0.774247i	$-0.281871\pi$
$293$	21.6665	1.26577	0.632884	+	0.774247i	$0.281871\pi$
$294$	4.70183	0.274216
$295$	9.34054	0.543827
$296$	−37.2942	−2.16768
$297$	−1.55593	−0.0902844
$298$	−9.95536	−0.576698
$299$	0.425109	0.0245847
$300$	−4.11533	−0.237599
$301$	2.28527	0.131721
$302$	−8.05349	−0.463427
$303$	−1.92093	−0.110355
$304$	−18.2809	−1.04848
$305$	−3.93721	−0.225444
$306$	0	0
$307$	−13.4648	−0.768479	−0.384239	−	0.923233i	$-0.625536\pi$
$307$	−13.4648	−0.768479	−0.384239	+	0.923233i	$0.625536\pi$
$308$	0.903103	0.0514591
$309$	−1.83613	−0.104454
$310$	10.3891	0.590063
$311$	−24.5185	−1.39032	−0.695159	−	0.718856i	$-0.744666\pi$
$311$	−24.5185	−1.39032	−0.695159	+	0.718856i	$0.744666\pi$
$312$	0.690994	0.0391198
$313$	8.13496	0.459815	0.229908	−	0.973212i	$-0.426158\pi$
$313$	8.13496	0.459815	0.229908	+	0.973212i	$0.426158\pi$
$314$	43.0352	2.42862
$315$	−0.725836	−0.0408962
$316$	−62.8988	−3.53834
$317$	−15.0477	−0.845161	−0.422580	−	0.906325i	$-0.638876\pi$
$317$	−15.0477	−0.845161	−0.422580	+	0.906325i	$0.638876\pi$
$318$	8.40999	0.471609
$319$	4.53695	0.254020
$320$	3.72678	0.208333
$321$	2.74176	0.153030
$322$	0.548551	0.0305696
$323$	0	0
$324$	38.8069	2.15594
$325$	1.31975	0.0732068
$326$	−38.5126	−2.13301
$327$	−3.78435	−0.209275
$328$	−65.1832	−3.59914
$329$	−0.712371	−0.0392743
$330$	−0.857004	−0.0471765
$331$	13.9159	0.764888	0.382444	−	0.923979i	$-0.375082\pi$
$331$	13.9159	0.764888	0.382444	+	0.923979i	$0.375082\pi$
$332$	−33.3357	−1.82953
$333$	−16.1578	−0.885445
$334$	−48.9436	−2.67807
$335$	−3.05178	−0.166737
$336$	0.417818	0.0227938
$337$	−10.5305	−0.573633	−0.286816	−	0.957986i	$-0.592597\pi$
$337$	−10.5305	−0.573633	−0.286816	+	0.957986i	$0.592597\pi$
$338$	33.0779	1.79920
$339$	3.91330	0.212541
$340$	0	0
$341$	−3.18014	−0.172214
$342$	−16.9021	−0.913963
$343$	−2.72456	−0.147112
$344$	−79.2295	−4.27177
$345$	−0.363472	−0.0195687
$346$	14.8220	0.796833
$347$	2.68247	0.144003	0.0720013	−	0.997405i	$-0.477061\pi$
$347$	2.68247	0.144003	0.0720013	+	0.997405i	$0.477061\pi$
$348$	5.50807	0.295264
$349$	30.8285	1.65021	0.825105	−	0.564979i	$-0.191116\pi$
$349$	30.8285	1.65021	0.825105	+	0.564979i	$0.191116\pi$
$350$	1.70298	0.0910281
$351$	0.605779	0.0323341
$352$	−7.48134	−0.398757
$353$	−13.3717	−0.711704	−0.355852	−	0.934542i	$-0.615809\pi$
$353$	−13.3717	−0.711704	−0.355852	+	0.934542i	$0.615809\pi$
$354$	−4.97125	−0.264219
$355$	−12.1045	−0.642439
$356$	−32.6623	−1.73110
$357$	0	0
$358$	−32.3987	−1.71232
$359$	28.7322	1.51643	0.758213	−	0.652007i	$-0.226073\pi$
$359$	28.7322	1.51643	0.758213	+	0.652007i	$0.226073\pi$
$360$	25.1645	1.32629
$361$	−13.9833	−0.735962
$362$	−34.2290	−1.79904
$363$	0.262331	0.0137688
$364$	−0.351610	−0.0184294
$365$	3.20755	0.167891
$366$	2.09548	0.109532
$367$	5.28484	0.275866	0.137933	−	0.990442i	$-0.455954\pi$
$367$	5.28484	0.275866	0.137933	+	0.990442i	$0.455954\pi$
$368$	−8.91176	−0.464558
$369$	−28.2408	−1.47016
$370$	−18.0083	−0.936209
$371$	−2.43001	−0.126160
$372$	−3.86084	−0.200175
$373$	16.6266	0.860895	0.430448	−	0.902616i	$-0.358356\pi$
$373$	16.6266	0.860895	0.430448	+	0.902616i	$0.358356\pi$
$374$	0	0
$375$	−2.79283	−0.144221
$376$	24.6977	1.27368
$377$	−1.76639	−0.0909739
$378$	0.781683	0.0402054
$379$	−4.85789	−0.249533	−0.124766	−	0.992186i	$-0.539818\pi$
$379$	−4.85789	−0.249533	−0.124766	+	0.992186i	$0.539818\pi$
$380$	−13.1535	−0.674759
$381$	1.09653	0.0561768
$382$	57.8466	2.95969
$383$	23.8008	1.21616	0.608081	−	0.793875i	$-0.291939\pi$
$383$	23.8008	1.21616	0.608081	+	0.793875i	$0.291939\pi$
$384$	1.94170	0.0990867
$385$	0.247626	0.0126202
$386$	20.4578	1.04127
$387$	−34.3265	−1.74491
$388$	−74.3043	−3.77223
$389$	−1.39948	−0.0709566	−0.0354783	−	0.999370i	$-0.511295\pi$
$389$	−1.39948	−0.0709566	−0.0354783	+	0.999370i	$0.511295\pi$
$390$	0.333662	0.0168956
$391$	0	0
$392$	47.1010	2.37896
$393$	1.57112	0.0792528
$394$	−20.0287	−1.00903
$395$	−17.2465	−0.867766
$396$	−13.5653	−0.681681
$397$	18.6620	0.936620	0.468310	−	0.883564i	$-0.344863\pi$
$397$	18.6620	0.936620	0.468310	+	0.883564i	$0.344863\pi$
$398$	57.0693	2.86062
$399$	−0.114660	−0.00574017
$400$	−27.6666	−1.38333
$401$	−28.1857	−1.40753	−0.703763	−	0.710435i	$-0.748498\pi$
$401$	−28.1857	−1.40753	−0.703763	+	0.710435i	$0.748498\pi$
$402$	1.62423	0.0810092
$403$	1.23814	0.0616761
$404$	−33.8882	−1.68600
$405$	10.6406	0.528737
$406$	−2.27931	−0.113120
$407$	5.51240	0.273239
$408$	0	0
$409$	1.28004	0.0632940	0.0316470	−	0.999499i	$-0.489925\pi$
$409$	1.28004	0.0632940	0.0316470	+	0.999499i	$0.489925\pi$
$410$	−31.4751	−1.55445
$411$	2.70601	0.133478
$412$	−32.3922	−1.59585
$413$	1.43641	0.0706811
$414$	−8.23965	−0.404957
$415$	−9.14045	−0.448687
$416$	2.91275	0.142809
$417$	−5.32705	−0.260867
$418$	5.76632	0.282040
$419$	15.0104	0.733305	0.366652	−	0.930358i	$-0.380504\pi$
$419$	15.0104	0.733305	0.366652	+	0.930358i	$0.380504\pi$
$420$	0.300629	0.0146692
$421$	2.48731	0.121224	0.0606120	−	0.998161i	$-0.480695\pi$
$421$	2.48731	0.121224	0.0606120	+	0.998161i	$0.480695\pi$
$422$	−2.41532	−0.117576
$423$	10.7003	0.520268
$424$	84.2477	4.09143
$425$	0	0
$426$	6.44228	0.312130
$427$	−0.605474	−0.0293010
$428$	48.3688	2.33799
$429$	−0.102135	−0.00493111
$430$	−38.2578	−1.84495
$431$	−33.4682	−1.61211	−0.806054	−	0.591842i	$-0.798401\pi$
$431$	−33.4682	−1.61211	−0.806054	+	0.591842i	$0.798401\pi$
$432$	−12.6992	−0.610992
$433$	9.24107	0.444098	0.222049	−	0.975036i	$-0.428726\pi$
$433$	9.24107	0.444098	0.222049	+	0.975036i	$0.428726\pi$
$434$	1.59767	0.0766904
$435$	1.51028	0.0724125
$436$	−66.7617	−3.19731
$437$	2.44561	0.116989
$438$	−1.70713	−0.0815700
$439$	−23.4102	−1.11731	−0.558655	−	0.829400i	$-0.688682\pi$
$439$	−23.4102	−1.11731	−0.558655	+	0.829400i	$0.688682\pi$
$440$	−8.58510	−0.409279
$441$	20.4067	0.971746
$442$	0	0
$443$	5.69673	0.270660	0.135330	−	0.990801i	$-0.456791\pi$
$443$	5.69673	0.270660	0.135330	+	0.990801i	$0.456791\pi$
$444$	6.69231	0.317603
$445$	−8.95581	−0.424546
$446$	73.0685	3.45989
$447$	1.01442	0.0479804
$448$	0.573113	0.0270770
$449$	−7.22603	−0.341018	−0.170509	−	0.985356i	$-0.554541\pi$
$449$	−7.22603	−0.341018	−0.170509	+	0.985356i	$0.554541\pi$
$450$	−25.5800	−1.20585
$451$	9.63462	0.453677
$452$	69.0366	3.24721
$453$	0.820626	0.0385564
$454$	45.8806	2.15328
$455$	−0.0964094	−0.00451974
$456$	3.97522	0.186157
$457$	−21.6683	−1.01360	−0.506800	−	0.862064i	$-0.669172\pi$
$457$	−21.6683	−1.01360	−0.506800	+	0.862064i	$0.669172\pi$
$458$	−39.4728	−1.84444
$459$	0	0
$460$	−6.41221	−0.298971
$461$	−38.2139	−1.77980	−0.889900	−	0.456155i	$-0.849226\pi$
$461$	−38.2139	−1.77980	−0.889900	+	0.456155i	$0.849226\pi$
$462$	−0.131792	−0.00613152
$463$	0.465764	0.0216459	0.0108230	−	0.999941i	$-0.496555\pi$
$463$	0.465764	0.0216459	0.0108230	+	0.999941i	$0.496555\pi$
$464$	37.0297	1.71906
$465$	−1.05862	−0.0490923
$466$	56.1486	2.60103
$467$	−7.80998	−0.361403	−0.180701	−	0.983538i	$-0.557837\pi$
$467$	−7.80998	−0.361403	−0.180701	+	0.983538i	$0.557837\pi$
$468$	5.28144	0.244135
$469$	−0.469311	−0.0216708
$470$	11.9258	0.550097
$471$	−4.38515	−0.202057
$472$	−49.7999	−2.29222
$473$	11.7108	0.538463
$474$	9.17899	0.421605
$475$	7.59241	0.348364
$476$	0	0
$477$	36.5006	1.67125
$478$	2.55884	0.117039
$479$	−34.8335	−1.59158	−0.795792	−	0.605570i	$-0.792945\pi$
$479$	−34.8335	−1.59158	−0.795792	+	0.605570i	$0.792945\pi$
$480$	−2.49042	−0.113672
$481$	−2.14617	−0.0978570
$482$	67.2366	3.06254
$483$	−0.0558956	−0.00254334
$484$	4.62792	0.210360
$485$	−20.3738	−0.925128
$486$	−17.6803	−0.801995
$487$	−4.62619	−0.209633	−0.104816	−	0.994492i	$-0.533425\pi$
$487$	−4.62619	−0.209633	−0.104816	+	0.994492i	$0.533425\pi$
$488$	20.9916	0.950245
$489$	3.92431	0.177463
$490$	22.7438	1.02746
$491$	11.3107	0.510443	0.255222	−	0.966883i	$-0.417852\pi$
$491$	11.3107	0.510443	0.255222	+	0.966883i	$0.417852\pi$
$492$	11.6969	0.527336
$493$	0	0
$494$	−2.24503	−0.101009
$495$	−3.71952	−0.167180
$496$	−25.9557	−1.16544
$497$	−1.86146	−0.0834977
$498$	4.86476	0.217995
$499$	−32.5649	−1.45781	−0.728903	−	0.684617i	$-0.759970\pi$
$499$	−32.5649	−1.45781	−0.728903	+	0.684617i	$0.759970\pi$
$500$	−49.2697	−2.20341
$501$	4.98720	0.222812
$502$	−53.2482	−2.37658
$503$	−25.3336	−1.12957	−0.564785	−	0.825238i	$-0.691041\pi$
$503$	−25.3336	−1.12957	−0.564785	+	0.825238i	$0.691041\pi$
$504$	3.86986	0.172377
$505$	−9.29195	−0.413486
$506$	2.81103	0.124966
$507$	−3.37054	−0.149691
$508$	19.3444	0.858270
$509$	−35.9402	−1.59302	−0.796510	−	0.604626i	$-0.793323\pi$
$509$	−35.9402	−1.59302	−0.796510	+	0.604626i	$0.793323\pi$
$510$	0	0
$511$	0.493265	0.0218208
$512$	49.3764	2.18215
$513$	3.48499	0.153866
$514$	−34.5727	−1.52494
$515$	−8.88177	−0.391378
$516$	14.2175	0.625888
$517$	−3.65052	−0.160550
$518$	−2.76937	−0.121679
$519$	−1.51031	−0.0662953
$520$	3.34248	0.146577
$521$	−7.18263	−0.314677	−0.157338	−	0.987545i	$-0.550291\pi$
$521$	−7.18263	−0.314677	−0.157338	+	0.987545i	$0.550291\pi$
$522$	34.2370	1.49851
$523$	−14.6695	−0.641451	−0.320726	−	0.947172i	$-0.603927\pi$
$523$	−14.6695	−0.641451	−0.320726	+	0.947172i	$0.603927\pi$
$524$	27.7170	1.21082
$525$	−0.173528	−0.00757340
$526$	22.8433	0.996017
$527$	0	0
$528$	2.14109	0.0931792
$529$	−21.8078	−0.948165
$530$	40.6809	1.76707
$531$	−21.5760	−0.936317
$532$	−2.02277	−0.0876984
$533$	−3.75110	−0.162478
$534$	4.76649	0.206266
$535$	13.2624	0.573386
$536$	16.2708	0.702793
$537$	3.30132	0.142463
$538$	20.6697	0.891134
$539$	−6.96192	−0.299871
$540$	−9.13737	−0.393210
$541$	−1.32993	−0.0571782	−0.0285891	−	0.999591i	$-0.509101\pi$
$541$	−1.32993	−0.0571782	−0.0285891	+	0.999591i	$0.509101\pi$
$542$	−8.21111	−0.352697
$543$	3.48783	0.149677
$544$	0	0
$545$	−18.3057	−0.784130
$546$	0.0513113	0.00219592
$547$	24.4070	1.04357	0.521784	−	0.853078i	$-0.325267\pi$
$547$	24.4070	1.04357	0.521784	+	0.853078i	$0.325267\pi$
$548$	47.7383	2.03928
$549$	9.09468	0.388151
$550$	8.72687	0.372115
$551$	−10.1619	−0.432911
$552$	1.93788	0.0824818
$553$	−2.65221	−0.112783
$554$	−16.4913	−0.700646
$555$	1.83499	0.0778912
$556$	−93.9773	−3.98552
$557$	36.2718	1.53688	0.768442	−	0.639920i	$-0.221032\pi$
$557$	36.2718	1.53688	0.768442	+	0.639920i	$0.221032\pi$
$558$	−23.9981	−1.01592
$559$	−4.55942	−0.192843
$560$	2.02107	0.0854059
$561$	0	0
$562$	31.6018	1.33304
$563$	8.33676	0.351353	0.175676	−	0.984448i	$-0.443789\pi$
$563$	8.33676	0.351353	0.175676	+	0.984448i	$0.443789\pi$
$564$	−4.43190	−0.186617
$565$	18.9295	0.796368
$566$	70.2133	2.95129
$567$	1.63634	0.0687199
$568$	64.5361	2.70787
$569$	−18.8342	−0.789570	−0.394785	−	0.918774i	$-0.629181\pi$
$569$	−18.8342	−0.789570	−0.394785	+	0.918774i	$0.629181\pi$
$570$	1.91952	0.0803999
$571$	0.162931	0.00681844	0.00340922	−	0.999994i	$-0.498915\pi$
$571$	0.162931	0.00681844	0.00340922	+	0.999994i	$0.498915\pi$
$572$	−1.80181	−0.0753375
$573$	−5.89439	−0.246242
$574$	−4.84032	−0.202031
$575$	3.70124	0.154352
$576$	−8.60859	−0.358691
$577$	−4.30328	−0.179148	−0.0895740	−	0.995980i	$-0.528551\pi$
$577$	−4.30328	−0.179148	−0.0895740	+	0.995980i	$0.528551\pi$
$578$	0	0
$579$	−2.08458	−0.0866322
$580$	26.6437	1.10632
$581$	−1.40564	−0.0583158
$582$	10.8434	0.449474
$583$	−12.4525	−0.515731
$584$	−17.1013	−0.707658
$585$	1.44814	0.0598733
$586$	−55.7797	−2.30424
$587$	0.280251	0.0115672	0.00578359	−	0.999983i	$-0.498159\pi$
$587$	0.280251	0.0115672	0.00578359	+	0.999983i	$0.498159\pi$
$588$	−8.45210	−0.348559
$589$	7.12289	0.293494
$590$	−24.0470	−0.989998
$591$	2.04087	0.0839500
$592$	44.9911	1.84912
$593$	21.9396	0.900952	0.450476	−	0.892788i	$-0.351254\pi$
$593$	21.9396	0.900952	0.450476	+	0.892788i	$0.351254\pi$
$594$	4.00571	0.164356
$595$	0	0
$596$	17.8959	0.733046
$597$	−5.81518	−0.238000
$598$	−1.09443	−0.0447547
$599$	−28.1990	−1.15218	−0.576090	−	0.817386i	$-0.695422\pi$
$599$	−28.1990	−1.15218	−0.576090	+	0.817386i	$0.695422\pi$
$600$	6.01617	0.245609
$601$	−25.0877	−1.02335	−0.511674	−	0.859180i	$-0.670974\pi$
$601$	−25.0877	−1.02335	−0.511674	+	0.859180i	$0.670974\pi$
$602$	−5.88337	−0.239788
$603$	7.04940	0.287074
$604$	14.4771	0.589065
$605$	1.26895	0.0515902
$606$	4.94539	0.200893
$607$	36.3753	1.47643	0.738214	−	0.674566i	$-0.235669\pi$
$607$	36.3753	1.47643	0.738214	+	0.674566i	$0.235669\pi$
$608$	16.7567	0.679575
$609$	0.232255	0.00941144
$610$	10.1363	0.410405
$611$	1.42128	0.0574987
$612$	0	0
$613$	33.9213	1.37007	0.685034	−	0.728511i	$-0.259788\pi$
$613$	33.9213	1.37007	0.685034	+	0.728511i	$0.259788\pi$
$614$	34.6649	1.39896
$615$	3.20722	0.129328
$616$	−1.32024	−0.0531939
$617$	29.9380	1.20526	0.602628	−	0.798022i	$-0.294120\pi$
$617$	29.9380	1.20526	0.602628	+	0.798022i	$0.294120\pi$
$618$	4.72708	0.190151
$619$	−14.3993	−0.578755	−0.289378	−	0.957215i	$-0.593448\pi$
$619$	−14.3993	−0.578755	−0.289378	+	0.957215i	$0.593448\pi$
$620$	−18.6757	−0.750033
$621$	1.69890	0.0681745
$622$	63.1223	2.53097
$623$	−1.37725	−0.0551782
$624$	−0.833603	−0.0333708
$625$	3.43934	0.137574
$626$	−20.9433	−0.837061
$627$	−0.587570	−0.0234653
$628$	−77.3608	−3.08703
$629$	0	0
$630$	1.86865	0.0744487
$631$	−5.85580	−0.233116	−0.116558	−	0.993184i	$-0.537186\pi$
$631$	−5.85580	−0.233116	−0.116558	+	0.993184i	$0.537186\pi$
$632$	91.9512	3.65762
$633$	0.246114	0.00978214
$634$	38.7398	1.53855
$635$	5.30413	0.210488
$636$	−15.1179	−0.599466
$637$	2.71052	0.107395
$638$	−11.6803	−0.462426
$639$	27.9605	1.10610
$640$	9.39239	0.371267
$641$	6.18111	0.244139	0.122070	−	0.992522i	$-0.461047\pi$
$641$	6.18111	0.244139	0.122070	+	0.992522i	$0.461047\pi$
$642$	−7.05858	−0.278580
$643$	11.5412	0.455142	0.227571	−	0.973761i	$-0.426922\pi$
$643$	11.5412	0.455142	0.227571	+	0.973761i	$0.426922\pi$
$644$	−0.986085	−0.0388572
$645$	3.89835	0.153497
$646$	0	0
$647$	28.7841	1.13162	0.565810	−	0.824535i	$-0.308563\pi$
$647$	28.7841	1.13162	0.565810	+	0.824535i	$0.308563\pi$
$648$	−56.7314	−2.22862
$649$	7.36084	0.288938
$650$	−3.39768	−0.133268
$651$	−0.162797	−0.00638052
$652$	69.2309	2.71129
$653$	−25.3064	−0.990315	−0.495158	−	0.868803i	$-0.664890\pi$
$653$	−25.3064	−0.990315	−0.495158	+	0.868803i	$0.664890\pi$
$654$	9.74271	0.380970
$655$	7.59986	0.296951
$656$	78.6359	3.07022
$657$	−7.40921	−0.289061
$658$	1.83398	0.0714960
$659$	31.9134	1.24317	0.621585	−	0.783347i	$-0.286489\pi$
$659$	31.9134	1.24317	0.621585	+	0.783347i	$0.286489\pi$
$660$	1.54056	0.0599664
$661$	−10.0744	−0.391850	−0.195925	−	0.980619i	$-0.562771\pi$
$661$	−10.0744	−0.391850	−0.195925	+	0.980619i	$0.562771\pi$
$662$	−35.8262	−1.39242
$663$	0	0
$664$	48.7331	1.89121
$665$	−0.554633	−0.0215078
$666$	41.5980	1.61189
$667$	−4.95383	−0.191813
$668$	87.9818	3.40412
$669$	−7.44545	−0.287858
$670$	7.85674	0.303532
$671$	−3.10273	−0.119780
$672$	−0.382983	−0.0147739
$673$	7.80309	0.300787	0.150393	−	0.988626i	$-0.451946\pi$
$673$	7.80309	0.300787	0.150393	+	0.988626i	$0.451946\pi$
$674$	27.1105	1.04426
$675$	5.27425	0.203006
$676$	−59.4615	−2.28698
$677$	28.2964	1.08752	0.543759	−	0.839242i	$-0.317001\pi$
$677$	28.2964	1.08752	0.543759	+	0.839242i	$0.317001\pi$
$678$	−10.0747	−0.386916
$679$	−3.13314	−0.120239
$680$	0	0
$681$	−4.67509	−0.179150
$682$	8.18719	0.313504
$683$	−41.9576	−1.60546	−0.802732	−	0.596340i	$-0.796621\pi$
$683$	−41.9576	−1.60546	−0.802732	+	0.596340i	$0.796621\pi$
$684$	30.3836	1.16175
$685$	13.0896	0.500126
$686$	7.01431	0.267808
$687$	4.02216	0.153455
$688$	95.5812	3.64400
$689$	4.84820	0.184702
$690$	0.935750	0.0356234
$691$	47.6518	1.81276	0.906379	−	0.422465i	$-0.138835\pi$
$691$	47.6518	1.81276	0.906379	+	0.422465i	$0.138835\pi$
$692$	−26.6442	−1.01286
$693$	−0.571998	−0.0217284
$694$	−6.90596	−0.262147
$695$	−25.7680	−0.977437
$696$	−8.05220	−0.305218
$697$	0	0
$698$	−79.3671	−3.00409
$699$	−5.72137	−0.216402
$700$	−3.06131	−0.115707
$701$	28.6868	1.08349	0.541743	−	0.840544i	$-0.317764\pi$
$701$	28.6868	1.08349	0.541743	+	0.840544i	$0.317764\pi$
$702$	−1.55956	−0.0588619
$703$	−12.3467	−0.465665
$704$	2.93690	0.110689
$705$	−1.21520	−0.0457672
$706$	34.4251	1.29561
$707$	−1.42894	−0.0537407
$708$	8.93640	0.335851
$709$	−19.9668	−0.749869	−0.374934	−	0.927051i	$-0.622335\pi$
$709$	−19.9668	−0.749869	−0.374934	+	0.927051i	$0.622335\pi$
$710$	31.1627	1.16951
$711$	39.8382	1.49405
$712$	47.7487	1.78946
$713$	3.47235	0.130040
$714$	0	0
$715$	−0.494047	−0.0184763
$716$	58.2404	2.17655
$717$	−0.260738	−0.00973745
$718$	−73.9703	−2.76055
$719$	44.8965	1.67436	0.837179	−	0.546928i	$-0.184203\pi$
$719$	44.8965	1.67436	0.837179	+	0.546928i	$0.184203\pi$
$720$	−30.3580	−1.13138
$721$	−1.36586	−0.0508673
$722$	35.9996	1.33977
$723$	−6.85120	−0.254799
$724$	61.5306	2.28677
$725$	−15.3792	−0.571169
$726$	−0.675364	−0.0250651
$727$	7.40307	0.274565	0.137282	−	0.990532i	$-0.456163\pi$
$727$	7.40307	0.274565	0.137282	+	0.990532i	$0.456163\pi$
$728$	0.514015	0.0190507
$729$	−23.3546	−0.864984
$730$	−8.25776	−0.305633
$731$	0	0
$732$	−3.76686	−0.139227
$733$	−17.2282	−0.636338	−0.318169	−	0.948034i	$-0.603068\pi$
$733$	−17.2282	−0.636338	−0.318169	+	0.948034i	$0.603068\pi$
$734$	−13.6057	−0.502195
$735$	−2.31752	−0.0854829
$736$	8.16876	0.301105
$737$	−2.40497	−0.0885881
$738$	72.7053	2.67632
$739$	−1.54537	−0.0568472	−0.0284236	−	0.999596i	$-0.509049\pi$
$739$	−1.54537	−0.0568472	−0.0284236	+	0.999596i	$0.509049\pi$
$740$	32.3721	1.19002
$741$	0.228762	0.00840377
$742$	6.25601	0.229665
$743$	15.2055	0.557835	0.278918	−	0.960315i	$-0.410024\pi$
$743$	15.2055	0.557835	0.278918	+	0.960315i	$0.410024\pi$
$744$	5.64412	0.206924
$745$	4.90696	0.179777
$746$	−42.8049	−1.56720
$747$	21.1138	0.772513
$748$	0	0
$749$	2.03953	0.0745229
$750$	7.19006	0.262544
$751$	17.6272	0.643227	0.321613	−	0.946871i	$-0.395775\pi$
$751$	17.6272	0.643227	0.321613	+	0.946871i	$0.395775\pi$
$752$	−29.7948	−1.08651
$753$	5.42582	0.197728
$754$	4.54754	0.165611
$755$	3.96954	0.144466
$756$	−1.40517	−0.0511054
$757$	−12.3634	−0.449357	−0.224678	−	0.974433i	$-0.572133\pi$
$757$	−12.3634	−0.449357	−0.224678	+	0.974433i	$0.572133\pi$
$758$	12.5065	0.454257
$759$	−0.286435	−0.0103969
$760$	19.2290	0.697507
$761$	18.7170	0.678491	0.339245	−	0.940698i	$-0.389828\pi$
$761$	18.7170	0.678491	0.339245	+	0.940698i	$0.389828\pi$
$762$	−2.82298	−0.102266
$763$	−2.81510	−0.101913
$764$	−103.986	−3.76209
$765$	0	0
$766$	−61.2745	−2.21394
$767$	−2.86583	−0.103479
$768$	−6.53973	−0.235982
$769$	−22.0209	−0.794094	−0.397047	−	0.917798i	$-0.629965\pi$
$769$	−22.0209	−0.794094	−0.397047	+	0.917798i	$0.629965\pi$
$770$	−0.637506	−0.0229741
$771$	3.52285	0.126872
$772$	−36.7752	−1.32357
$773$	−31.6517	−1.13843	−0.569216	−	0.822188i	$-0.692753\pi$
$773$	−31.6517	−1.13843	−0.569216	+	0.822188i	$0.692753\pi$
$774$	88.3726	3.17649
$775$	10.7799	0.387226
$776$	108.625	3.89941
$777$	0.282190	0.0101235
$778$	3.60293	0.129171
$779$	−21.5797	−0.773172
$780$	−0.599796	−0.0214761
$781$	−9.53897	−0.341331
$782$	0	0
$783$	−7.05919	−0.252275
$784$	−56.8218	−2.02935
$785$	−21.2119	−0.757085
$786$	−4.04482	−0.144274
$787$	−24.6366	−0.878199	−0.439100	−	0.898438i	$-0.644703\pi$
$787$	−24.6366	−0.878199	−0.439100	+	0.898438i	$0.644703\pi$
$788$	36.0040	1.28259
$789$	−2.32766	−0.0828671
$790$	44.4007	1.57971
$791$	2.91102	0.103504
$792$	19.8310	0.704662
$793$	1.20800	0.0428974
$794$	−48.0449	−1.70505
$795$	−4.14526	−0.147017
$796$	−102.589	−3.63616
$797$	−13.2796	−0.470389	−0.235195	−	0.971948i	$-0.575573\pi$
$797$	−13.2796	−0.470389	−0.235195	+	0.971948i	$0.575573\pi$
$798$	0.295189	0.0104496
$799$	0	0
$800$	25.3600	0.896611
$801$	20.6873	0.730949
$802$	72.5633	2.56230
$803$	2.52772	0.0892013
$804$	−2.91974	−0.102971
$805$	−0.270379	−0.00952961
$806$	−3.18756	−0.112277
$807$	−2.10618	−0.0741410
$808$	49.5408	1.74284
$809$	14.0338	0.493403	0.246702	−	0.969091i	$-0.420653\pi$
$809$	14.0338	0.493403	0.246702	+	0.969091i	$0.420653\pi$
$810$	−27.3940	−0.962528
$811$	−1.72838	−0.0606917	−0.0303458	−	0.999539i	$-0.509661\pi$
$811$	−1.72838	−0.0606917	−0.0303458	+	0.999539i	$0.509661\pi$
$812$	4.09733	0.143788
$813$	0.836687	0.0293439
$814$	−14.1915	−0.497413
$815$	18.9827	0.664936
$816$	0	0
$817$	−26.2299	−0.917668
$818$	−3.29543	−0.115222
$819$	0.222699	0.00778172
$820$	56.5803	1.97587
$821$	2.14979	0.0750281	0.0375141	−	0.999296i	$-0.488056\pi$
$821$	2.14979	0.0750281	0.0375141	+	0.999296i	$0.488056\pi$
$822$	−6.96657	−0.242987
$823$	29.3583	1.02336	0.511682	−	0.859175i	$-0.329022\pi$
$823$	29.3583	1.02336	0.511682	+	0.859175i	$0.329022\pi$
$824$	47.3539	1.64965
$825$	−0.889241	−0.0309594
$826$	−3.69800	−0.128670
$827$	−6.03605	−0.209894	−0.104947	−	0.994478i	$-0.533467\pi$
$827$	−6.03605	−0.209894	−0.104947	+	0.994478i	$0.533467\pi$
$828$	14.8117	0.514743
$829$	−46.8982	−1.62884	−0.814420	−	0.580276i	$-0.802945\pi$
$829$	−46.8982	−1.62884	−0.814420	+	0.580276i	$0.802945\pi$
$830$	23.5319	0.816803
$831$	1.68041	0.0582927
$832$	−1.14344	−0.0396416
$833$	0	0
$834$	13.7143	0.474889
$835$	24.1241	0.834850
$836$	−10.3656	−0.358503
$837$	4.94808	0.171031
$838$	−38.6438	−1.33493
$839$	−25.9781	−0.896862	−0.448431	−	0.893817i	$-0.648017\pi$
$839$	−25.9781	−0.896862	−0.448431	+	0.893817i	$0.648017\pi$
$840$	−0.439487	−0.0151637
$841$	−8.41609	−0.290210
$842$	−6.40352	−0.220680
$843$	−3.22012	−0.110907
$844$	4.34182	0.149452
$845$	−16.3040	−0.560875
$846$	−27.5478	−0.947112
$847$	0.195142	0.00670517
$848$	−101.635	−3.49016
$849$	−7.15452	−0.245543
$850$	0	0
$851$	−6.01891	−0.206326
$852$	−11.5808	−0.396750
$853$	19.3361	0.662055	0.331027	−	0.943621i	$-0.392605\pi$
$853$	19.3361	0.662055	0.331027	+	0.943621i	$0.392605\pi$
$854$	1.55878	0.0533403
$855$	8.33101	0.284914
$856$	−70.7099	−2.41681
$857$	−42.5782	−1.45444	−0.727221	−	0.686403i	$-0.759189\pi$
$857$	−42.5782	−1.45444	−0.727221	+	0.686403i	$0.759189\pi$
$858$	0.262943	0.00897673
$859$	36.1218	1.23246	0.616230	−	0.787566i	$-0.288659\pi$
$859$	36.1218	1.23246	0.616230	+	0.787566i	$0.288659\pi$
$860$	68.7728	2.34513
$861$	0.493214	0.0168087
$862$	86.1632	2.93473
$863$	30.1763	1.02721	0.513607	−	0.858025i	$-0.328309\pi$
$863$	30.1763	1.02721	0.513607	+	0.858025i	$0.328309\pi$
$864$	11.6405	0.396016
$865$	−7.30569	−0.248401
$866$	−23.7909	−0.808448
$867$	0	0
$868$	−2.87199	−0.0974817
$869$	−13.5912	−0.461049
$870$	−3.88818	−0.131822
$871$	0.936338	0.0317266
$872$	97.5984	3.30510
$873$	47.0621	1.59281
$874$	−6.29616	−0.212971
$875$	−2.07752	−0.0702331
$876$	3.06877	0.103684
$877$	−1.09087	−0.0368362	−0.0184181	−	0.999830i	$-0.505863\pi$
$877$	−1.09087	−0.0368362	−0.0184181	+	0.999830i	$0.505863\pi$
$878$	60.2690	2.03398
$879$	5.68378	0.191709
$880$	10.3569	0.349132
$881$	−36.4350	−1.22753	−0.613764	−	0.789490i	$-0.710345\pi$
$881$	−36.4350	−1.22753	−0.613764	+	0.789490i	$0.710345\pi$
$882$	−52.5364	−1.76899
$883$	−23.7707	−0.799949	−0.399974	−	0.916526i	$-0.630981\pi$
$883$	−23.7707	−0.799949	−0.399974	+	0.916526i	$0.630981\pi$
$884$	0	0
$885$	2.45031	0.0823663
$886$	−14.6661	−0.492717
$887$	54.9368	1.84460	0.922298	−	0.386479i	$-0.126309\pi$
$887$	54.9368	1.84460	0.922298	+	0.386479i	$0.126309\pi$
$888$	−9.78343	−0.328310
$889$	0.815683	0.0273571
$890$	23.0565	0.772856
$891$	8.38538	0.280921
$892$	−131.349	−4.39789
$893$	8.17645	0.273615
$894$	−2.61160	−0.0873449
$895$	15.9692	0.533791
$896$	1.44438	0.0482535
$897$	0.111519	0.00372352
$898$	18.6032	0.620798
$899$	−14.4281	−0.481205
$900$	45.9831	1.53277
$901$	0	0
$902$	−24.8041	−0.825886
$903$	0.599497	0.0199500
$904$	−100.924	−3.35668
$905$	16.8714	0.560823
$906$	−2.11268	−0.0701891
$907$	20.1910	0.670433	0.335216	−	0.942141i	$-0.391191\pi$
$907$	20.1910	0.670433	0.335216	+	0.942141i	$0.391191\pi$
$908$	−82.4757	−2.73705
$909$	21.4637	0.711907
$910$	0.248204	0.00822787
$911$	34.0959	1.12965	0.564823	−	0.825212i	$-0.308944\pi$
$911$	34.0959	1.12965	0.564823	+	0.825212i	$0.308944\pi$
$912$	−4.79563	−0.158799
$913$	−7.20316	−0.238390
$914$	55.7845	1.84519
$915$	−1.03285	−0.0341451
$916$	70.9570	2.34449
$917$	1.16873	0.0385947
$918$	0	0
$919$	20.8562	0.687983	0.343991	−	0.938973i	$-0.388221\pi$
$919$	20.8562	0.687983	0.343991	+	0.938973i	$0.388221\pi$
$920$	9.37395	0.309050
$921$	−3.53224	−0.116391
$922$	98.3808	3.24000
$923$	3.71386	0.122243
$924$	0.236912	0.00779383
$925$	−18.6857	−0.614383
$926$	−1.19910	−0.0394048
$927$	20.5162	0.673842
$928$	−33.9424	−1.11422
$929$	−37.3706	−1.22609	−0.613045	−	0.790048i	$-0.710055\pi$
$929$	−37.3706	−1.22609	−0.613045	+	0.790048i	$0.710055\pi$
$930$	2.72539	0.0893691
$931$	15.5933	0.511051
$932$	−100.934	−3.30619
$933$	−6.43196	−0.210573
$934$	20.1066	0.657908
$935$	0	0
$936$	−7.72089	−0.252365
$937$	53.8311	1.75859	0.879293	−	0.476282i	$-0.158016\pi$
$937$	53.8311	1.75859	0.879293	+	0.476282i	$0.158016\pi$
$938$	1.20823	0.0394501
$939$	2.13405	0.0696422
$940$	−21.4380	−0.699232
$941$	1.91829	0.0625344	0.0312672	−	0.999511i	$-0.490046\pi$
$941$	1.91829	0.0625344	0.0312672	+	0.999511i	$0.490046\pi$
$942$	11.2895	0.367831
$943$	−10.5199	−0.342575
$944$	60.0777	1.95536
$945$	−0.385289	−0.0125335
$946$	−30.1491	−0.980233
$947$	12.3553	0.401494	0.200747	−	0.979643i	$-0.435663\pi$
$947$	12.3553	0.401494	0.200747	+	0.979643i	$0.435663\pi$
$948$	−16.5003	−0.535905
$949$	−0.984130	−0.0319462
$950$	−19.5465	−0.634172
$951$	−3.94747	−0.128005
$952$	0	0
$953$	−23.2373	−0.752731	−0.376366	−	0.926471i	$-0.622826\pi$
$953$	−23.2373	−0.752731	−0.376366	+	0.926471i	$0.622826\pi$
$954$	−93.9699	−3.04239
$955$	−28.5124	−0.922640
$956$	−4.59982	−0.148769
$957$	1.19018	0.0384731
$958$	89.6780	2.89736
$959$	2.01294	0.0650014
$960$	0.977649	0.0315535
$961$	−20.8867	−0.673765
$962$	5.52526	0.178142
$963$	−30.6353	−0.987208
$964$	−120.866	−3.89282
$965$	−10.0836	−0.324601
$966$	0.143902	0.00462997
$967$	−9.51420	−0.305956	−0.152978	−	0.988230i	$-0.548886\pi$
$967$	−9.51420	−0.305956	−0.152978	+	0.988230i	$0.548886\pi$
$968$	−6.76552	−0.217452
$969$	0	0
$970$	52.4519	1.68413
$971$	16.7351	0.537054	0.268527	−	0.963272i	$-0.413463\pi$
$971$	16.7351	0.537054	0.268527	+	0.963272i	$0.413463\pi$
$972$	31.7824	1.01942
$973$	−3.96267	−0.127037
$974$	11.9100	0.381621
$975$	0.346213	0.0110877
$976$	−25.3239	−0.810599
$977$	3.78884	0.121216	0.0606078	−	0.998162i	$-0.480696\pi$
$977$	3.78884	0.121216	0.0606078	+	0.998162i	$0.480696\pi$
$978$	−10.1030	−0.323060
$979$	−7.05766	−0.225564
$980$	−40.8846	−1.30601
$981$	42.2848	1.35005
$982$	−29.1190	−0.929226
$983$	17.9970	0.574014	0.287007	−	0.957928i	$-0.407340\pi$
$983$	17.9970	0.574014	0.287007	+	0.957928i	$0.407340\pi$
$984$	−17.0996	−0.545114
$985$	9.87210	0.314551
$986$	0	0
$987$	−0.186877	−0.00594836
$988$	4.03571	0.128393
$989$	−12.7868	−0.406598
$990$	9.57582	0.304340
$991$	15.2551	0.484593	0.242296	−	0.970202i	$-0.422099\pi$
$991$	15.2551	0.484593	0.242296	+	0.970202i	$0.422099\pi$
$992$	23.7917	0.755387
$993$	3.65058	0.115848
$994$	4.79227	0.152002
$995$	−28.1293	−0.891757
$996$	−8.74498	−0.277095
$997$	−11.7235	−0.371287	−0.185644	−	0.982617i	$-0.559437\pi$
$997$	−11.7235	−0.371287	−0.185644	+	0.982617i	$0.559437\pi$
$998$	83.8376	2.65383
$999$	−8.57692	−0.271362

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3179.2.a.bh.1.1		28
17.5	odd	16		187.2.h.a.144.14	yes	56
17.7	odd	16		187.2.h.a.100.14	✓	56
17.16	even	2		3179.2.a.bi.1.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.h.a.100.14	✓	56	17.7	odd	16
187.2.h.a.144.14	yes	56	17.5	odd	16
3179.2.a.bh.1.1		28	1.1	even	1	trivial
3179.2.a.bi.1.1		28	17.16	even	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:	\( N \)	\(=\)	\( 3179 = 11 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3179.a (trivial)

\(f(q)\)	\(=\)	\(q-2.57447 q^{2} +0.262331 q^{3} +4.62792 q^{4} +1.26895 q^{5} -0.675364 q^{6} +0.195142 q^{7} -6.76552 q^{8} -2.93118 q^{9} +O(q^{10})\)	\(q-2.57447 q^{2} +0.262331 q^{3} +4.62792 q^{4} +1.26895 q^{5} -0.675364 q^{6} +0.195142 q^{7} -6.76552 q^{8} -2.93118 q^{9} -3.26688 q^{10} +1.00000 q^{11} +1.21405 q^{12} -0.389335 q^{13} -0.502389 q^{14} +0.332885 q^{15} +8.16181 q^{16} +7.54626 q^{18} -2.23981 q^{19} +5.87260 q^{20} +0.0511919 q^{21} -2.57447 q^{22} -1.09189 q^{23} -1.77480 q^{24} -3.38977 q^{25} +1.00233 q^{26} -1.55593 q^{27} +0.903103 q^{28} +4.53695 q^{29} -0.857004 q^{30} -3.18014 q^{31} -7.48134 q^{32} +0.262331 q^{33} +0.247626 q^{35} -13.5653 q^{36} +5.51240 q^{37} +5.76632 q^{38} -0.102135 q^{39} -8.58510 q^{40} +9.63462 q^{41} -0.131792 q^{42} +11.7108 q^{43} +4.62792 q^{44} -3.71952 q^{45} +2.81103 q^{46} -3.65052 q^{47} +2.14109 q^{48} -6.96192 q^{49} +8.72687 q^{50} -1.80181 q^{52} -12.4525 q^{53} +4.00571 q^{54} +1.26895 q^{55} -1.32024 q^{56} -0.587570 q^{57} -11.6803 q^{58} +7.36084 q^{59} +1.54056 q^{60} -3.10273 q^{61} +8.18719 q^{62} -0.571998 q^{63} +2.93690 q^{64} -0.494047 q^{65} -0.675364 q^{66} -2.40497 q^{67} -0.286435 q^{69} -0.637506 q^{70} -9.53897 q^{71} +19.8310 q^{72} +2.52772 q^{73} -14.1915 q^{74} -0.889241 q^{75} -10.3656 q^{76} +0.195142 q^{77} +0.262943 q^{78} -13.5912 q^{79} +10.3569 q^{80} +8.38538 q^{81} -24.8041 q^{82} -7.20316 q^{83} +0.236912 q^{84} -30.1491 q^{86} +1.19018 q^{87} -6.76552 q^{88} -7.05766 q^{89} +9.57582 q^{90} -0.0759757 q^{91} -5.05316 q^{92} -0.834249 q^{93} +9.39817 q^{94} -2.84220 q^{95} -1.96259 q^{96} -16.0557 q^{97} +17.9233 q^{98} -2.93118 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 8 q^{3} + 24 q^{4} - 16 q^{5} - 16 q^{6} - 12 q^{7} + 20 q^{9}+O(q^{10}) \) 28 * q - 8 * q^3 + 24 * q^4 - 16 * q^5 - 16 * q^6 - 12 * q^7 + 20 * q^9	\( 28 q - 8 q^{3} + 24 q^{4} - 16 q^{5} - 16 q^{6} - 12 q^{7} + 20 q^{9} - 24 q^{10} + 28 q^{11} - 24 q^{12} - 16 q^{14} - 16 q^{15} + 16 q^{16} - 32 q^{20} - 8 q^{23} + 8 q^{24} + 20 q^{25} - 24 q^{26} - 32 q^{27} - 32 q^{28} - 36 q^{29} + 40 q^{30} - 56 q^{31} + 40 q^{32} - 8 q^{33} + 16 q^{35} + 40 q^{36} - 64 q^{37} - 8 q^{38} - 32 q^{39} - 72 q^{40} - 28 q^{41} + 24 q^{42} + 16 q^{43} + 24 q^{44} - 24 q^{45} - 36 q^{47} - 56 q^{48} + 16 q^{49} + 56 q^{50} - 20 q^{53} - 64 q^{54} - 16 q^{55} - 48 q^{56} - 32 q^{57} + 16 q^{58} - 28 q^{59} + 8 q^{60} - 104 q^{61} + 8 q^{62} - 28 q^{63} - 32 q^{65} - 16 q^{66} - 12 q^{67} - 32 q^{69} - 40 q^{71} + 40 q^{72} - 76 q^{73} - 24 q^{74} + 16 q^{75} - 16 q^{76} - 12 q^{77} + 24 q^{78} - 24 q^{79} - 8 q^{80} + 12 q^{81} - 56 q^{82} + 32 q^{83} - 40 q^{84} - 16 q^{86} - 8 q^{87} - 52 q^{89} - 16 q^{90} - 80 q^{91} + 56 q^{92} - 24 q^{97} - 24 q^{98} + 20 q^{99}+O(q^{100}) \) 28 * q - 8 * q^3 + 24 * q^4 - 16 * q^5 - 16 * q^6 - 12 * q^7 + 20 * q^9 - 24 * q^10 + 28 * q^11 - 24 * q^12 - 16 * q^14 - 16 * q^15 + 16 * q^16 - 32 * q^20 - 8 * q^23 + 8 * q^24 + 20 * q^25 - 24 * q^26 - 32 * q^27 - 32 * q^28 - 36 * q^29 + 40 * q^30 - 56 * q^31 + 40 * q^32 - 8 * q^33 + 16 * q^35 + 40 * q^36 - 64 * q^37 - 8 * q^38 - 32 * q^39 - 72 * q^40 - 28 * q^41 + 24 * q^42 + 16 * q^43 + 24 * q^44 - 24 * q^45 - 36 * q^47 - 56 * q^48 + 16 * q^49 + 56 * q^50 - 20 * q^53 - 64 * q^54 - 16 * q^55 - 48 * q^56 - 32 * q^57 + 16 * q^58 - 28 * q^59 + 8 * q^60 - 104 * q^61 + 8 * q^62 - 28 * q^63 - 32 * q^65 - 16 * q^66 - 12 * q^67 - 32 * q^69 - 40 * q^71 + 40 * q^72 - 76 * q^73 - 24 * q^74 + 16 * q^75 - 16 * q^76 - 12 * q^77 + 24 * q^78 - 24 * q^79 - 8 * q^80 + 12 * q^81 - 56 * q^82 + 32 * q^83 - 40 * q^84 - 16 * q^86 - 8 * q^87 - 52 * q^89 - 16 * q^90 - 80 * q^91 + 56 * q^92 - 24 * q^97 - 24 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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