LMFDB - Embedded newform 3179.2.a.bh.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.40039 q^{2} -1.98044 q^{3} +3.76185 q^{4} -1.54647 q^{5} +4.75381 q^{6} -3.54271 q^{7} -4.22913 q^{8} +0.922127 q^{9} +O(q^{10})$	\(q-2.40039 q^{2} -1.98044 q^{3} +3.76185 q^{4} -1.54647 q^{5} +4.75381 q^{6} -3.54271 q^{7} -4.22913 q^{8} +0.922127 q^{9} +3.71212 q^{10} +1.00000 q^{11} -7.45011 q^{12} +4.25413 q^{13} +8.50387 q^{14} +3.06268 q^{15} +2.62783 q^{16} -2.21346 q^{18} -5.26313 q^{19} -5.81758 q^{20} +7.01611 q^{21} -2.40039 q^{22} -2.07684 q^{23} +8.37552 q^{24} -2.60844 q^{25} -10.2115 q^{26} +4.11510 q^{27} -13.3272 q^{28} -4.52834 q^{29} -7.35161 q^{30} -4.96669 q^{31} +2.15044 q^{32} -1.98044 q^{33} +5.47868 q^{35} +3.46891 q^{36} +3.82293 q^{37} +12.6335 q^{38} -8.42503 q^{39} +6.54020 q^{40} +4.88476 q^{41} -16.8414 q^{42} +8.31739 q^{43} +3.76185 q^{44} -1.42604 q^{45} +4.98521 q^{46} -0.821811 q^{47} -5.20425 q^{48} +5.55079 q^{49} +6.26127 q^{50} +16.0034 q^{52} +2.23371 q^{53} -9.87782 q^{54} -1.54647 q^{55} +14.9826 q^{56} +10.4233 q^{57} +10.8698 q^{58} +1.81700 q^{59} +11.5213 q^{60} -11.2904 q^{61} +11.9220 q^{62} -3.26683 q^{63} -10.4176 q^{64} -6.57886 q^{65} +4.75381 q^{66} +15.5881 q^{67} +4.11304 q^{69} -13.1509 q^{70} +14.5263 q^{71} -3.89979 q^{72} -14.6099 q^{73} -9.17651 q^{74} +5.16585 q^{75} -19.7991 q^{76} -3.54271 q^{77} +20.2233 q^{78} +1.80220 q^{79} -4.06385 q^{80} -10.9161 q^{81} -11.7253 q^{82} +16.7121 q^{83} +26.3936 q^{84} -19.9649 q^{86} +8.96809 q^{87} -4.22913 q^{88} -1.75856 q^{89} +3.42304 q^{90} -15.0711 q^{91} -7.81275 q^{92} +9.83622 q^{93} +1.97266 q^{94} +8.13925 q^{95} -4.25881 q^{96} -10.4058 q^{97} -13.3240 q^{98} +0.922127 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.40039	−1.69733	−0.848665	−	0.528931i	$-0.822593\pi$
$2$	−2.40039	−1.69733	−0.848665	+	0.528931i	$0.822593\pi$
$3$	−1.98044	−1.14341	−0.571703	−	0.820461i	$-0.693717\pi$
$3$	−1.98044	−1.14341	−0.571703	+	0.820461i	$0.693717\pi$
$4$	3.76185	1.88093
$5$	−1.54647	−0.691601	−0.345800	−	0.938308i	$-0.612393\pi$
$5$	−1.54647	−0.691601	−0.345800	+	0.938308i	$0.612393\pi$
$6$	4.75381	1.94074
$7$	−3.54271	−1.33902	−0.669509	−	0.742804i	$-0.733496\pi$
$7$	−3.54271	−1.33902	−0.669509	+	0.742804i	$0.733496\pi$
$8$	−4.22913	−1.49522
$9$	0.922127	0.307376
$10$	3.71212	1.17387
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−7.45011	−2.15066
$13$	4.25413	1.17988	0.589941	−	0.807446i	$-0.299151\pi$
$13$	4.25413	1.17988	0.589941	+	0.807446i	$0.299151\pi$
$14$	8.50387	2.27276
$15$	3.06268	0.790780
$16$	2.62783	0.656958
$17$	0	0
$17$	0	0
$18$	−2.21346	−0.521718
$19$	−5.26313	−1.20744	−0.603722	−	0.797195i	$-0.706316\pi$
$19$	−5.26313	−1.20744	−0.603722	+	0.797195i	$0.706316\pi$
$20$	−5.81758	−1.30085
$21$	7.01611	1.53104
$22$	−2.40039	−0.511764
$23$	−2.07684	−0.433050	−0.216525	−	0.976277i	$-0.569472\pi$
$23$	−2.07684	−0.433050	−0.216525	+	0.976277i	$0.569472\pi$
$24$	8.37552	1.70965
$25$	−2.60844	−0.521689
$26$	−10.2115	−2.00265
$27$	4.11510	0.791950
$28$	−13.3272	−2.51860
$29$	−4.52834	−0.840892	−0.420446	−	0.907318i	$-0.638126\pi$
$29$	−4.52834	−0.840892	−0.420446	+	0.907318i	$0.638126\pi$
$30$	−7.35161	−1.34221
$31$	−4.96669	−0.892044	−0.446022	−	0.895022i	$-0.647160\pi$
$31$	−4.96669	−0.892044	−0.446022	+	0.895022i	$0.647160\pi$
$32$	2.15044	0.380148
$33$	−1.98044	−0.344750
$34$	0	0
$35$	5.47868	0.926066
$36$	3.46891	0.578151
$37$	3.82293	0.628486	0.314243	−	0.949343i	$-0.398249\pi$
$37$	3.82293	0.628486	0.314243	+	0.949343i	$0.398249\pi$
$38$	12.6335	2.04943
$39$	−8.42503	−1.34908
$40$	6.54020	1.03410
$41$	4.88476	0.762871	0.381436	−	0.924395i	$-0.375430\pi$
$41$	4.88476	0.762871	0.381436	+	0.924395i	$0.375430\pi$
$42$	−16.8414	−2.59868
$43$	8.31739	1.26839	0.634195	−	0.773173i	$-0.281332\pi$
$43$	8.31739	1.26839	0.634195	+	0.773173i	$0.281332\pi$
$44$	3.76185	0.567121
$45$	−1.42604	−0.212581
$46$	4.98521	0.735029
$47$	−0.821811	−0.119873	−0.0599367	−	0.998202i	$-0.519090\pi$
$47$	−0.821811	−0.119873	−0.0599367	+	0.998202i	$0.519090\pi$
$48$	−5.20425	−0.751169
$49$	5.55079	0.792970
$50$	6.26127	0.885477
$51$	0	0
$52$	16.0034	2.21927
$53$	2.23371	0.306824	0.153412	−	0.988162i	$-0.450974\pi$
$53$	2.23371	0.306824	0.153412	+	0.988162i	$0.450974\pi$
$54$	−9.87782	−1.34420
$55$	−1.54647	−0.208525
$56$	14.9826	2.00213
$57$	10.4233	1.38060
$58$	10.8698	1.42727
$59$	1.81700	0.236553	0.118276	−	0.992981i	$-0.462263\pi$
$59$	1.81700	0.236553	0.118276	+	0.992981i	$0.462263\pi$
$60$	11.5213	1.48740
$61$	−11.2904	−1.44558	−0.722791	−	0.691067i	$-0.757141\pi$
$61$	−11.2904	−1.44558	−0.722791	+	0.691067i	$0.757141\pi$
$62$	11.9220	1.51409
$63$	−3.26683	−0.411582
$64$	−10.4176	−1.30219
$65$	−6.57886	−0.816008
$66$	4.75381	0.585154
$67$	15.5881	1.90439	0.952194	−	0.305493i	$-0.0988211\pi$
$67$	15.5881	1.90439	0.952194	+	0.305493i	$0.0988211\pi$
$68$	0	0
$69$	4.11304	0.495152
$70$	−13.1509	−1.57184
$71$	14.5263	1.72395	0.861976	−	0.506949i	$-0.169227\pi$
$71$	14.5263	1.72395	0.861976	+	0.506949i	$0.169227\pi$
$72$	−3.89979	−0.459595
$73$	−14.6099	−1.70996	−0.854979	−	0.518662i	$-0.826430\pi$
$73$	−14.6099	−1.70996	−0.854979	+	0.518662i	$0.826430\pi$
$74$	−9.17651	−1.06675
$75$	5.16585	0.596502
$76$	−19.7991	−2.27111
$77$	−3.54271	−0.403729
$78$	20.2233	2.28984
$79$	1.80220	0.202763	0.101382	−	0.994848i	$-0.467674\pi$
$79$	1.80220	0.202763	0.101382	+	0.994848i	$0.467674\pi$
$80$	−4.06385	−0.454353
$81$	−10.9161	−1.21290
$82$	−11.7253	−1.29484
$83$	16.7121	1.83439	0.917196	−	0.398436i	$-0.130447\pi$
$83$	16.7121	1.83439	0.917196	+	0.398436i	$0.130447\pi$
$84$	26.3936	2.87978
$85$	0	0
$86$	−19.9649	−2.15288
$87$	8.96809	0.961480
$88$	−4.22913	−0.450827
$89$	−1.75856	−0.186407	−0.0932036	−	0.995647i	$-0.529711\pi$
$89$	−1.75856	−0.186407	−0.0932036	+	0.995647i	$0.529711\pi$
$90$	3.42304	0.360820
$91$	−15.0711	−1.57988
$92$	−7.81275	−0.814536
$93$	9.83622	1.01997
$94$	1.97266	0.203465
$95$	8.13925	0.835069
$96$	−4.25881	−0.434663
$97$	−10.4058	−1.05655	−0.528273	−	0.849075i	$-0.677160\pi$
$97$	−10.4058	−1.05655	−0.528273	+	0.849075i	$0.677160\pi$
$98$	−13.3240	−1.34593
$99$	0.922127	0.0926772
$100$	−9.81258	−0.981258
$101$	8.53318	0.849083	0.424542	−	0.905408i	$-0.360435\pi$
$101$	8.53318	0.849083	0.424542	+	0.905408i	$0.360435\pi$
$102$	0	0
$103$	9.63774	0.949634	0.474817	−	0.880084i	$-0.342514\pi$
$103$	9.63774	0.949634	0.474817	+	0.880084i	$0.342514\pi$
$104$	−17.9912	−1.76419
$105$	−10.8502	−1.05887
$106$	−5.36177	−0.520781
$107$	7.06136	0.682647	0.341323	−	0.939946i	$-0.389125\pi$
$107$	7.06136	0.682647	0.341323	+	0.939946i	$0.389125\pi$
$108$	15.4804	1.48960
$109$	−7.56923	−0.725001	−0.362500	−	0.931984i	$-0.618077\pi$
$109$	−7.56923	−0.725001	−0.362500	+	0.931984i	$0.618077\pi$
$110$	3.71212	0.353936
$111$	−7.57107	−0.718615
$112$	−9.30965	−0.879679
$113$	−2.46444	−0.231835	−0.115917	−	0.993259i	$-0.536981\pi$
$113$	−2.46444	−0.231835	−0.115917	+	0.993259i	$0.536981\pi$
$114$	−25.0199	−2.34333
$115$	3.21176	0.299498
$116$	−17.0350	−1.58166
$117$	3.92285	0.362667
$118$	−4.36149	−0.401508
$119$	0	0
$120$	−12.9525	−1.18239
$121$	1.00000	0.0909091
$122$	27.1012	2.45363
$123$	−9.67396	−0.872271
$124$	−18.6840	−1.67787
$125$	11.7662	1.05240
$126$	7.84165	0.698589
$127$	21.3507	1.89457	0.947286	−	0.320390i	$-0.103814\pi$
$127$	21.3507	1.89457	0.947286	+	0.320390i	$0.103814\pi$
$128$	20.7053	1.83010
$129$	−16.4721	−1.45028
$130$	15.7918	1.38503
$131$	8.61944	0.753084	0.376542	−	0.926400i	$-0.377113\pi$
$131$	8.61944	0.753084	0.376542	+	0.926400i	$0.377113\pi$
$132$	−7.45011	−0.648449
$133$	18.6457	1.61679
$134$	−37.4174	−3.23237
$135$	−6.36385	−0.547713
$136$	0	0
$137$	−8.53363	−0.729077	−0.364538	−	0.931188i	$-0.618773\pi$
$137$	−8.53363	−0.729077	−0.364538	+	0.931188i	$0.618773\pi$
$138$	−9.87289	−0.840436
$139$	18.6190	1.57924	0.789621	−	0.613595i	$-0.210277\pi$
$139$	18.6190	1.57924	0.789621	+	0.613595i	$0.210277\pi$
$140$	20.6100	1.74186
$141$	1.62754	0.137064
$142$	−34.8687	−2.92611
$143$	4.25413	0.355748
$144$	2.42319	0.201933
$145$	7.00292	0.581561
$146$	35.0694	2.90236
$147$	−10.9930	−0.906687
$148$	14.3813	1.18214
$149$	−2.39421	−0.196141	−0.0980705	−	0.995179i	$-0.531267\pi$
$149$	−2.39421	−0.196141	−0.0980705	+	0.995179i	$0.531267\pi$
$150$	−12.4000	−1.01246
$151$	1.07037	0.0871054	0.0435527	−	0.999051i	$-0.486132\pi$
$151$	1.07037	0.0871054	0.0435527	+	0.999051i	$0.486132\pi$
$152$	22.2584	1.80540
$153$	0	0
$154$	8.50387	0.685261
$155$	7.68082	0.616938
$156$	−31.6937	−2.53753
$157$	−5.83648	−0.465802	−0.232901	−	0.972500i	$-0.574822\pi$
$157$	−5.83648	−0.465802	−0.232901	+	0.972500i	$0.574822\pi$
$158$	−4.32597	−0.344156
$159$	−4.42372	−0.350824
$160$	−3.32559	−0.262911
$161$	7.35763	0.579862
$162$	26.2028	2.05868
$163$	−7.03397	−0.550943	−0.275472	−	0.961309i	$-0.588834\pi$
$163$	−7.03397	−0.550943	−0.275472	+	0.961309i	$0.588834\pi$
$164$	18.3758	1.43491
$165$	3.06268	0.238429
$166$	−40.1155	−3.11357
$167$	−5.17611	−0.400539	−0.200270	−	0.979741i	$-0.564182\pi$
$167$	−5.17611	−0.400539	−0.200270	+	0.979741i	$0.564182\pi$
$168$	−29.6720	−2.28925
$169$	5.09760	0.392123
$170$	0	0
$171$	−4.85327	−0.371139
$172$	31.2888	2.38575
$173$	17.9115	1.36179	0.680894	−	0.732382i	$-0.261591\pi$
$173$	17.9115	1.36179	0.680894	+	0.732382i	$0.261591\pi$
$174$	−21.5269	−1.63195
$175$	9.24096	0.698551
$176$	2.62783	0.198080
$177$	−3.59845	−0.270476
$178$	4.22123	0.316394
$179$	−21.7082	−1.62255	−0.811274	−	0.584666i	$-0.801226\pi$
$179$	−21.7082	−1.62255	−0.811274	+	0.584666i	$0.801226\pi$
$180$	−5.36454	−0.399849
$181$	−3.10555	−0.230834	−0.115417	−	0.993317i	$-0.536820\pi$
$181$	−3.10555	−0.230834	−0.115417	+	0.993317i	$0.536820\pi$
$182$	36.1766	2.68158
$183$	22.3598	1.65289
$184$	8.78321	0.647507
$185$	−5.91204	−0.434661
$186$	−23.6107	−1.73122
$187$	0	0
$188$	−3.09153	−0.225473
$189$	−14.5786	−1.06044
$190$	−19.5373	−1.41739
$191$	10.8201	0.782911	0.391456	−	0.920197i	$-0.371972\pi$
$191$	10.8201	0.782911	0.391456	+	0.920197i	$0.371972\pi$
$192$	20.6313	1.48894
$193$	−6.73996	−0.485153	−0.242576	−	0.970132i	$-0.577992\pi$
$193$	−6.73996	−0.485153	−0.242576	+	0.970132i	$0.577992\pi$
$194$	24.9779	1.79331
$195$	13.0290	0.933027
$196$	20.8813	1.49152
$197$	4.98840	0.355408	0.177704	−	0.984084i	$-0.443133\pi$
$197$	4.98840	0.355408	0.177704	+	0.984084i	$0.443133\pi$
$198$	−2.21346	−0.157304
$199$	14.2143	1.00763	0.503813	−	0.863813i	$-0.331930\pi$
$199$	14.2143	1.00763	0.503813	+	0.863813i	$0.331930\pi$
$200$	11.0314	0.780041
$201$	−30.8712	−2.17749
$202$	−20.4829	−1.44117
$203$	16.0426	1.12597
$204$	0	0
$205$	−7.55412	−0.527602
$206$	−23.1343	−1.61184
$207$	−1.91511	−0.133109
$208$	11.1791	0.775134
$209$	−5.26313	−0.364058
$210$	26.0446	1.79725
$211$	6.83146	0.470297	0.235148	−	0.971959i	$-0.424442\pi$
$211$	6.83146	0.470297	0.235148	+	0.971959i	$0.424442\pi$
$212$	8.40289	0.577113
$213$	−28.7684	−1.97118
$214$	−16.9500	−1.15868
$215$	−12.8626	−0.877219
$216$	−17.4033	−1.18414
$217$	17.5956	1.19446
$218$	18.1691	1.23056
$219$	28.9340	1.95518
$220$	−5.81758	−0.392221
$221$	0	0
$222$	18.1735	1.21973
$223$	−12.2401	−0.819660	−0.409830	−	0.912162i	$-0.634412\pi$
$223$	−12.2401	−0.819660	−0.409830	+	0.912162i	$0.634412\pi$
$224$	−7.61840	−0.509025
$225$	−2.40532	−0.160354
$226$	5.91560	0.393500
$227$	20.8281	1.38241	0.691206	−	0.722658i	$-0.257080\pi$
$227$	20.8281	1.38241	0.691206	+	0.722658i	$0.257080\pi$
$228$	39.2109	2.59680
$229$	−22.1240	−1.46199	−0.730996	−	0.682381i	$-0.760944\pi$
$229$	−22.1240	−1.46199	−0.730996	+	0.682381i	$0.760944\pi$
$230$	−7.70946	−0.508347
$231$	7.01611	0.461626
$232$	19.1509	1.25732
$233$	−18.6226	−1.22001	−0.610005	−	0.792398i	$-0.708832\pi$
$233$	−18.6226	−1.22001	−0.610005	+	0.792398i	$0.708832\pi$
$234$	−9.41634	−0.615566
$235$	1.27090	0.0829045
$236$	6.83528	0.444939
$237$	−3.56914	−0.231841
$238$	0	0
$239$	−23.8188	−1.54071	−0.770354	−	0.637617i	$-0.779920\pi$
$239$	−23.8188	−1.54071	−0.770354	+	0.637617i	$0.779920\pi$
$240$	8.04820	0.519509
$241$	2.73729	0.176325	0.0881623	−	0.996106i	$-0.471901\pi$
$241$	2.73729	0.176325	0.0881623	+	0.996106i	$0.471901\pi$
$242$	−2.40039	−0.154303
$243$	9.27328	0.594881
$244$	−42.4726	−2.71903
$245$	−8.58411	−0.548419
$246$	23.2212	1.48053
$247$	−22.3900	−1.42464
$248$	21.0048	1.33380
$249$	−33.0973	−2.09745
$250$	−28.2434	−1.78627
$251$	−10.1022	−0.637645	−0.318823	−	0.947814i	$-0.603287\pi$
$251$	−10.1022	−0.637645	−0.318823	+	0.947814i	$0.603287\pi$
$252$	−12.2893	−0.774155
$253$	−2.07684	−0.130570
$254$	−51.2500	−3.21571
$255$	0	0
$256$	−28.8655	−1.80410
$257$	3.10755	0.193844	0.0969219	−	0.995292i	$-0.469100\pi$
$257$	3.10755	0.193844	0.0969219	+	0.995292i	$0.469100\pi$
$258$	39.5393	2.46161
$259$	−13.5435	−0.841555
$260$	−24.7487	−1.53485
$261$	−4.17570	−0.258470
$262$	−20.6900	−1.27823
$263$	−11.9401	−0.736260	−0.368130	−	0.929774i	$-0.620002\pi$
$263$	−11.9401	−0.736260	−0.368130	+	0.929774i	$0.620002\pi$
$264$	8.37552	0.515477
$265$	−3.45436	−0.212199
$266$	−44.7570	−2.74423
$267$	3.48272	0.213139
$268$	58.6401	3.58202
$269$	15.7794	0.962089	0.481044	−	0.876696i	$-0.340258\pi$
$269$	15.7794	0.962089	0.481044	+	0.876696i	$0.340258\pi$
$270$	15.2757	0.929650
$271$	−29.2332	−1.77579	−0.887896	−	0.460044i	$-0.847834\pi$
$271$	−29.2332	−1.77579	−0.887896	+	0.460044i	$0.847834\pi$
$272$	0	0
$273$	29.8474	1.80645
$274$	20.4840	1.23748
$275$	−2.60844	−0.157295
$276$	15.4727	0.931345
$277$	−19.0156	−1.14254	−0.571269	−	0.820763i	$-0.693549\pi$
$277$	−19.0156	−1.14254	−0.571269	+	0.820763i	$0.693549\pi$
$278$	−44.6927	−2.68049
$279$	−4.57992	−0.274193
$280$	−23.1700	−1.38467
$281$	29.6991	1.77170	0.885850	−	0.463973i	$-0.153576\pi$
$281$	29.6991	1.77170	0.885850	+	0.463973i	$0.153576\pi$
$282$	−3.90673	−0.232643
$283$	−23.7863	−1.41395	−0.706975	−	0.707238i	$-0.749941\pi$
$283$	−23.7863	−1.41395	−0.706975	+	0.707238i	$0.749941\pi$
$284$	54.6457	3.24263
$285$	−16.1193	−0.954822
$286$	−10.2115	−0.603822
$287$	−17.3053	−1.02150
$288$	1.98298	0.116848
$289$	0	0
$290$	−16.8097	−0.987101
$291$	20.6080	1.20806
$292$	−54.9603	−3.21631
$293$	7.51115	0.438806	0.219403	−	0.975634i	$-0.429589\pi$
$293$	7.51115	0.438806	0.219403	+	0.975634i	$0.429589\pi$
$294$	26.3874	1.53895
$295$	−2.80992	−0.163600
$296$	−16.1677	−0.939727
$297$	4.11510	0.238782
$298$	5.74702	0.332916
$299$	−8.83513	−0.510949
$300$	19.4332	1.12198
$301$	−29.4661	−1.69840
$302$	−2.56930	−0.147847
$303$	−16.8994	−0.970846
$304$	−13.8306	−0.793240
$305$	17.4601	0.999765
$306$	0	0
$307$	−13.6058	−0.776525	−0.388263	−	0.921549i	$-0.626925\pi$
$307$	−13.6058	−0.776525	−0.388263	+	0.921549i	$0.626925\pi$
$308$	−13.3272	−0.759385
$309$	−19.0869	−1.08582
$310$	−18.4369	−1.04715
$311$	−15.6446	−0.887121	−0.443561	−	0.896244i	$-0.646285\pi$
$311$	−15.6446	−0.887121	−0.443561	+	0.896244i	$0.646285\pi$
$312$	35.6305	2.01718
$313$	−2.93041	−0.165636	−0.0828182	−	0.996565i	$-0.526392\pi$
$313$	−2.93041	−0.165636	−0.0828182	+	0.996565i	$0.526392\pi$
$314$	14.0098	0.790620
$315$	5.05204	0.284650
$316$	6.77961	0.381383
$317$	8.89700	0.499705	0.249853	−	0.968284i	$-0.419618\pi$
$317$	8.89700	0.499705	0.249853	+	0.968284i	$0.419618\pi$
$318$	10.6186	0.595463
$319$	−4.52834	−0.253538
$320$	16.1104	0.900599
$321$	−13.9846	−0.780542
$322$	−17.6612	−0.984217
$323$	0	0
$324$	−41.0646	−2.28137
$325$	−11.0967	−0.615531
$326$	16.8842	0.935132
$327$	14.9904	0.828969
$328$	−20.6583	−1.14066
$329$	2.91144	0.160513
$330$	−7.35161	−0.404693
$331$	4.00205	0.219972	0.109986	−	0.993933i	$-0.464919\pi$
$331$	4.00205	0.219972	0.109986	+	0.993933i	$0.464919\pi$
$332$	62.8685	3.45036
$333$	3.52523	0.193181
$334$	12.4247	0.679847
$335$	−24.1065	−1.31708
$336$	18.4372	1.00583
$337$	29.3932	1.60115	0.800575	−	0.599232i	$-0.204527\pi$
$337$	29.3932	1.60115	0.800575	+	0.599232i	$0.204527\pi$
$338$	−12.2362	−0.665563
$339$	4.88066	0.265081
$340$	0	0
$341$	−4.96669	−0.268962
$342$	11.6497	0.629945
$343$	5.13412	0.277216
$344$	−35.1753	−1.89653
$345$	−6.36068	−0.342447
$346$	−42.9946	−2.31140
$347$	2.77849	0.149157	0.0745785	−	0.997215i	$-0.476239\pi$
$347$	2.77849	0.149157	0.0745785	+	0.997215i	$0.476239\pi$
$348$	33.7366	1.80847
$349$	−21.4935	−1.15052	−0.575261	−	0.817970i	$-0.695100\pi$
$349$	−21.4935	−1.15052	−0.575261	+	0.817970i	$0.695100\pi$
$350$	−22.1819	−1.18567
$351$	17.5061	0.934409
$352$	2.15044	0.114619
$353$	7.63990	0.406631	0.203316	−	0.979113i	$-0.434828\pi$
$353$	7.63990	0.406631	0.203316	+	0.979113i	$0.434828\pi$
$354$	8.63766	0.459087
$355$	−22.4644	−1.19229
$356$	−6.61545	−0.350618
$357$	0	0
$358$	52.1081	2.75400
$359$	−6.70242	−0.353740	−0.176870	−	0.984234i	$-0.556597\pi$
$359$	−6.70242	−0.353740	−0.176870	+	0.984234i	$0.556597\pi$
$360$	6.03089	0.317856
$361$	8.70052	0.457922
$362$	7.45452	0.391801
$363$	−1.98044	−0.103946
$364$	−56.6954	−2.97165
$365$	22.5937	1.18261
$366$	−53.6722	−2.80549
$367$	−37.6850	−1.96714	−0.983570	−	0.180528i	$-0.942219\pi$
$367$	−37.6850	−1.96714	−0.983570	+	0.180528i	$0.942219\pi$
$368$	−5.45758	−0.284496
$369$	4.50437	0.234488
$370$	14.1912	0.737764
$371$	−7.91338	−0.410842
$372$	37.0024	1.91849
$373$	−6.79786	−0.351980	−0.175990	−	0.984392i	$-0.556313\pi$
$373$	−6.79786	−0.351980	−0.175990	+	0.984392i	$0.556313\pi$
$374$	0	0
$375$	−23.3022	−1.20332
$376$	3.47554	0.179237
$377$	−19.2641	−0.992154
$378$	34.9942	1.79991
$379$	−24.4279	−1.25477	−0.627387	−	0.778707i	$-0.715876\pi$
$379$	−24.4279	−1.25477	−0.627387	+	0.778707i	$0.715876\pi$
$380$	30.6187	1.57070
$381$	−42.2838	−2.16626
$382$	−25.9723	−1.32886
$383$	6.27522	0.320649	0.160324	−	0.987064i	$-0.448746\pi$
$383$	6.27522	0.320649	0.160324	+	0.987064i	$0.448746\pi$
$384$	−41.0055	−2.09255
$385$	5.47868	0.279219
$386$	16.1785	0.823464
$387$	7.66969	0.389872
$388$	−39.1450	−1.98728
$389$	−17.9748	−0.911361	−0.455680	−	0.890143i	$-0.650604\pi$
$389$	−17.9748	−0.911361	−0.455680	+	0.890143i	$0.650604\pi$
$390$	−31.2747	−1.58365
$391$	0	0
$392$	−23.4750	−1.18567
$393$	−17.0702	−0.861080
$394$	−11.9741	−0.603245
$395$	−2.78704	−0.140231
$396$	3.46891	0.174319
$397$	−10.9351	−0.548818	−0.274409	−	0.961613i	$-0.588482\pi$
$397$	−10.9351	−0.548818	−0.274409	+	0.961613i	$0.588482\pi$
$398$	−34.1199	−1.71027
$399$	−36.9267	−1.84865
$400$	−6.85455	−0.342728
$401$	29.5780	1.47705	0.738527	−	0.674224i	$-0.235522\pi$
$401$	29.5780	1.47705	0.738527	+	0.674224i	$0.235522\pi$
$402$	74.1029	3.69591
$403$	−21.1289	−1.05251
$404$	32.1006	1.59706
$405$	16.8813	0.838839
$406$	−38.5084	−1.91114
$407$	3.82293	0.189496
$408$	0	0
$409$	29.7932	1.47318	0.736590	−	0.676340i	$-0.236435\pi$
$409$	29.7932	1.47318	0.736590	+	0.676340i	$0.236435\pi$
$410$	18.1328	0.895515
$411$	16.9003	0.833630
$412$	36.2557	1.78619
$413$	−6.43709	−0.316749
$414$	4.59699	0.225930
$415$	−25.8447	−1.26867
$416$	9.14826	0.448530
$417$	−36.8737	−1.80571
$418$	12.6335	0.617927
$419$	−19.0060	−0.928506	−0.464253	−	0.885703i	$-0.653677\pi$
$419$	−19.0060	−0.928506	−0.464253	+	0.885703i	$0.653677\pi$
$420$	−40.8168	−1.99165
$421$	−16.8146	−0.819493	−0.409747	−	0.912199i	$-0.634383\pi$
$421$	−16.8146	−0.819493	−0.409747	+	0.912199i	$0.634383\pi$
$422$	−16.3981	−0.798248
$423$	−0.757814	−0.0368462
$424$	−9.44664	−0.458770
$425$	0	0
$426$	69.0552	3.34573
$427$	39.9984	1.93566
$428$	26.5638	1.28401
$429$	−8.42503	−0.406764
$430$	30.8751	1.48893
$431$	−18.6198	−0.896886	−0.448443	−	0.893811i	$-0.648021\pi$
$431$	−18.6198	−0.896886	−0.448443	+	0.893811i	$0.648021\pi$
$432$	10.8138	0.520278
$433$	−24.4907	−1.17695	−0.588473	−	0.808517i	$-0.700271\pi$
$433$	−24.4907	−1.17695	−0.588473	+	0.808517i	$0.700271\pi$
$434$	−42.2361	−2.02740
$435$	−13.8688	−0.664960
$436$	−28.4743	−1.36367
$437$	10.9307	0.522884
$438$	−69.4527	−3.31858
$439$	−3.42155	−0.163302	−0.0816508	−	0.996661i	$-0.526019\pi$
$439$	−3.42155	−0.163302	−0.0816508	+	0.996661i	$0.526019\pi$
$440$	6.54020	0.311792
$441$	5.11853	0.243740
$442$	0	0
$443$	1.33855	0.0635962	0.0317981	−	0.999494i	$-0.489877\pi$
$443$	1.33855	0.0635962	0.0317981	+	0.999494i	$0.489877\pi$
$444$	−28.4813	−1.35166
$445$	2.71955	0.128919
$446$	29.3811	1.39123
$447$	4.74157	0.224269
$448$	36.9064	1.74366
$449$	−35.7885	−1.68896	−0.844481	−	0.535585i	$-0.820091\pi$
$449$	−35.7885	−1.68896	−0.844481	+	0.535585i	$0.820091\pi$
$450$	5.77369	0.272174
$451$	4.88476	0.230014
$452$	−9.27086	−0.436064
$453$	−2.11980	−0.0995967
$454$	−49.9955	−2.34641
$455$	23.3070	1.09265
$456$	−44.0814	−2.06430
$457$	−17.3901	−0.813472	−0.406736	−	0.913546i	$-0.633333\pi$
$457$	−17.3901	−0.813472	−0.406736	+	0.913546i	$0.633333\pi$
$458$	53.1061	2.48148
$459$	0	0
$460$	12.0822	0.563334
$461$	33.1530	1.54409	0.772044	−	0.635569i	$-0.219234\pi$
$461$	33.1530	1.54409	0.772044	+	0.635569i	$0.219234\pi$
$462$	−16.8414	−0.783532
$463$	11.4076	0.530158	0.265079	−	0.964227i	$-0.414602\pi$
$463$	11.4076	0.530158	0.265079	+	0.964227i	$0.414602\pi$
$464$	−11.8997	−0.552431
$465$	−15.2114	−0.705411
$466$	44.7015	2.07076
$467$	−5.75869	−0.266481	−0.133240	−	0.991084i	$-0.542538\pi$
$467$	−5.75869	−0.266481	−0.133240	+	0.991084i	$0.542538\pi$
$468$	14.7572	0.682150
$469$	−55.2241	−2.55001
$470$	−3.05066	−0.140716
$471$	11.5588	0.532601
$472$	−7.68431	−0.353699
$473$	8.31739	0.382434
$474$	8.56732	0.393510
$475$	13.7286	0.629910
$476$	0	0
$477$	2.05976	0.0943101
$478$	57.1742	2.61509
$479$	−7.06735	−0.322915	−0.161458	−	0.986880i	$-0.551620\pi$
$479$	−7.06735	−0.322915	−0.161458	+	0.986880i	$0.551620\pi$
$480$	6.58611	0.300613
$481$	16.2632	0.741540
$482$	−6.57056	−0.299281
$483$	−14.5713	−0.663018
$484$	3.76185	0.170993
$485$	16.0922	0.730708
$486$	−22.2594	−1.00971
$487$	16.0859	0.728920	0.364460	−	0.931219i	$-0.381254\pi$
$487$	16.0859	0.728920	0.364460	+	0.931219i	$0.381254\pi$
$488$	47.7483	2.16147
$489$	13.9303	0.629951
$490$	20.6052	0.930847
$491$	36.0180	1.62547	0.812734	−	0.582634i	$-0.197978\pi$
$491$	36.0180	1.62547	0.812734	+	0.582634i	$0.197978\pi$
$492$	−36.3920	−1.64068
$493$	0	0
$494$	53.7447	2.41809
$495$	−1.42604	−0.0640956
$496$	−13.0516	−0.586036
$497$	−51.4624	−2.30840
$498$	79.4462	3.56007
$499$	25.2752	1.13147	0.565736	−	0.824587i	$-0.308592\pi$
$499$	25.2752	1.13147	0.565736	+	0.824587i	$0.308592\pi$
$500$	44.2627	1.97949
$501$	10.2510	0.457979
$502$	24.2492	1.08229
$503$	−5.61582	−0.250397	−0.125198	−	0.992132i	$-0.539957\pi$
$503$	−5.61582	−0.250397	−0.125198	+	0.992132i	$0.539957\pi$
$504$	13.8158	0.615406
$505$	−13.1963	−0.587226
$506$	4.98521	0.221620
$507$	−10.0955	−0.448356
$508$	80.3183	3.56355
$509$	−40.7415	−1.80584	−0.902918	−	0.429813i	$-0.858579\pi$
$509$	−40.7415	−1.80584	−0.902918	+	0.429813i	$0.858579\pi$
$510$	0	0
$511$	51.7586	2.28967
$512$	27.8779	1.23204
$513$	−21.6583	−0.956236
$514$	−7.45932	−0.329017
$515$	−14.9044	−0.656768
$516$	−61.9655	−2.72788
$517$	−0.821811	−0.0361432
$518$	32.5097	1.42840
$519$	−35.4726	−1.55708
$520$	27.8229	1.22011
$521$	−6.02738	−0.264064	−0.132032	−	0.991245i	$-0.542150\pi$
$521$	−6.02738	−0.264064	−0.132032	+	0.991245i	$0.542150\pi$
$522$	10.0233	0.438708
$523$	9.87471	0.431791	0.215895	−	0.976416i	$-0.430733\pi$
$523$	9.87471	0.431791	0.215895	+	0.976416i	$0.430733\pi$
$524$	32.4251	1.41650
$525$	−18.3011	−0.798727
$526$	28.6609	1.24968
$527$	0	0
$528$	−5.20425	−0.226486
$529$	−18.6867	−0.812467
$530$	8.29179	0.360172
$531$	1.67550	0.0727106
$532$	70.1425	3.04106
$533$	20.7804	0.900099
$534$	−8.35987	−0.361767
$535$	−10.9201	−0.472119
$536$	−65.9240	−2.84748
$537$	42.9917	1.85523
$538$	−37.8767	−1.63298
$539$	5.55079	0.239090
$540$	−23.9399	−1.03021
$541$	19.7963	0.851110	0.425555	−	0.904932i	$-0.360079\pi$
$541$	19.7963	0.851110	0.425555	+	0.904932i	$0.360079\pi$
$542$	70.1710	3.01410
$543$	6.15034	0.263936
$544$	0	0
$545$	11.7056	0.501411
$546$	−71.6454	−3.06614
$547$	3.14858	0.134624	0.0673119	−	0.997732i	$-0.478558\pi$
$547$	3.14858	0.134624	0.0673119	+	0.997732i	$0.478558\pi$
$548$	−32.1023	−1.37134
$549$	−10.4111	−0.444336
$550$	6.26127	0.266981
$551$	23.8332	1.01533
$552$	−17.3946	−0.740362
$553$	−6.38467	−0.271504
$554$	45.6449	1.93926
$555$	11.7084	0.496994
$556$	70.0419	2.97044
$557$	4.35315	0.184449	0.0922245	−	0.995738i	$-0.470602\pi$
$557$	4.35315	0.184449	0.0922245	+	0.995738i	$0.470602\pi$
$558$	10.9936	0.465395
$559$	35.3832	1.49655
$560$	14.3971	0.608386
$561$	0	0
$562$	−71.2893	−3.00716
$563$	−17.3001	−0.729112	−0.364556	−	0.931181i	$-0.618779\pi$
$563$	−17.3001	−0.729112	−0.364556	+	0.931181i	$0.618779\pi$
$564$	6.12258	0.257807
$565$	3.81117	0.160337
$566$	57.0964	2.39994
$567$	38.6724	1.62409
$568$	−61.4335	−2.57769
$569$	29.5341	1.23813	0.619067	−	0.785338i	$-0.287511\pi$
$569$	29.5341	1.23813	0.619067	+	0.785338i	$0.287511\pi$
$570$	38.6924	1.62065
$571$	13.8263	0.578614	0.289307	−	0.957236i	$-0.406575\pi$
$571$	13.8263	0.578614	0.289307	+	0.957236i	$0.406575\pi$
$572$	16.0034	0.669136
$573$	−21.4284	−0.895185
$574$	41.5394	1.73382
$575$	5.41731	0.225917
$576$	−9.60631	−0.400263
$577$	−9.31419	−0.387755	−0.193878	−	0.981026i	$-0.562106\pi$
$577$	−9.31419	−0.387755	−0.193878	+	0.981026i	$0.562106\pi$
$578$	0	0
$579$	13.3481	0.554726
$580$	26.3440	1.09387
$581$	−59.2061	−2.45628
$582$	−49.4671	−2.05048
$583$	2.23371	0.0925108
$584$	61.7871	2.55677
$585$	−6.06655	−0.250821
$586$	−18.0297	−0.744799
$587$	7.12868	0.294232	0.147116	−	0.989119i	$-0.453001\pi$
$587$	7.12868	0.294232	0.147116	+	0.989119i	$0.453001\pi$
$588$	−41.3540	−1.70541
$589$	26.1403	1.07709
$590$	6.74490	0.277683
$591$	−9.87920	−0.406376
$592$	10.0460	0.412889
$593$	−17.0526	−0.700268	−0.350134	−	0.936700i	$-0.613864\pi$
$593$	−17.0526	−0.700268	−0.350134	+	0.936700i	$0.613864\pi$
$594$	−9.87782	−0.405292
$595$	0	0
$596$	−9.00665	−0.368927
$597$	−28.1506	−1.15213
$598$	21.2077	0.867248
$599$	−9.66080	−0.394730	−0.197365	−	0.980330i	$-0.563238\pi$
$599$	−9.66080	−0.394730	−0.197365	+	0.980330i	$0.563238\pi$
$600$	−21.8471	−0.891902
$601$	16.7076	0.681519	0.340759	−	0.940151i	$-0.389316\pi$
$601$	16.7076	0.681519	0.340759	+	0.940151i	$0.389316\pi$
$602$	70.7300	2.88274
$603$	14.3742	0.585363
$604$	4.02657	0.163839
$605$	−1.54647	−0.0628728
$606$	40.5651	1.64785
$607$	29.7638	1.20808	0.604038	−	0.796955i	$-0.293557\pi$
$607$	29.7638	1.20808	0.604038	+	0.796955i	$0.293557\pi$
$608$	−11.3181	−0.459008
$609$	−31.7713	−1.28744
$610$	−41.9111	−1.69693
$611$	−3.49609	−0.141437
$612$	0	0
$613$	−30.7618	−1.24246	−0.621229	−	0.783629i	$-0.713366\pi$
$613$	−30.7618	−1.24246	−0.621229	+	0.783629i	$0.713366\pi$
$614$	32.6592	1.31802
$615$	14.9604	0.603263
$616$	14.9826	0.603665
$617$	−4.28739	−0.172604	−0.0863019	−	0.996269i	$-0.527505\pi$
$617$	−4.28739	−0.172604	−0.0863019	+	0.996269i	$0.527505\pi$
$618$	45.8160	1.84299
$619$	−15.3564	−0.617227	−0.308613	−	0.951188i	$-0.599865\pi$
$619$	−15.3564	−0.617227	−0.308613	+	0.951188i	$0.599865\pi$
$620$	28.8941	1.16042
$621$	−8.54638	−0.342954
$622$	37.5530	1.50574
$623$	6.23007	0.249603
$624$	−22.1396	−0.886292
$625$	−5.15381	−0.206152
$626$	7.03411	0.281139
$627$	10.4233	0.416266
$628$	−21.9560	−0.876140
$629$	0	0
$630$	−12.1268	−0.483145
$631$	−10.3768	−0.413094	−0.206547	−	0.978437i	$-0.566223\pi$
$631$	−10.3768	−0.413094	−0.206547	+	0.978437i	$0.566223\pi$
$632$	−7.62173	−0.303176
$633$	−13.5293	−0.537740
$634$	−21.3562	−0.848164
$635$	−33.0182	−1.31029
$636$	−16.6414	−0.659874
$637$	23.6138	0.935612
$638$	10.8698	0.430338
$639$	13.3951	0.529901
$640$	−32.0200	−1.26570
$641$	1.48379	0.0586063	0.0293032	−	0.999571i	$-0.490671\pi$
$641$	1.48379	0.0586063	0.0293032	+	0.999571i	$0.490671\pi$
$642$	33.5683	1.32484
$643$	7.02830	0.277169	0.138585	−	0.990351i	$-0.455745\pi$
$643$	7.02830	0.277169	0.138585	+	0.990351i	$0.455745\pi$
$644$	27.6783	1.09068
$645$	25.4735	1.00302
$646$	0	0
$647$	−23.1964	−0.911946	−0.455973	−	0.889994i	$-0.650709\pi$
$647$	−23.1964	−0.911946	−0.455973	+	0.889994i	$0.650709\pi$
$648$	46.1654	1.81355
$649$	1.81700	0.0713234
$650$	26.6362	1.04476
$651$	−34.8469	−1.36576
$652$	−26.4608	−1.03628
$653$	15.0865	0.590382	0.295191	−	0.955438i	$-0.404617\pi$
$653$	15.0865	0.590382	0.295191	+	0.955438i	$0.404617\pi$
$654$	−35.9827	−1.40703
$655$	−13.3297	−0.520833
$656$	12.8363	0.501175
$657$	−13.4722	−0.525600
$658$	−6.98857	−0.272443
$659$	−21.6863	−0.844779	−0.422390	−	0.906414i	$-0.638809\pi$
$659$	−21.6863	−0.844779	−0.422390	+	0.906414i	$0.638809\pi$
$660$	11.5213	0.448468
$661$	21.1802	0.823815	0.411907	−	0.911226i	$-0.364863\pi$
$661$	21.1802	0.823815	0.411907	+	0.911226i	$0.364863\pi$
$662$	−9.60646	−0.373366
$663$	0	0
$664$	−70.6776	−2.74282
$665$	−28.8350	−1.11817
$666$	−8.46191	−0.327892
$667$	9.40462	0.364148
$668$	−19.4718	−0.753385
$669$	24.2408	0.937204
$670$	57.8648	2.23551
$671$	−11.2904	−0.435859
$672$	15.0877	0.582022
$673$	2.31538	0.0892514	0.0446257	−	0.999004i	$-0.485790\pi$
$673$	2.31538	0.0892514	0.0446257	+	0.999004i	$0.485790\pi$
$674$	−70.5550	−2.71768
$675$	−10.7340	−0.413152
$676$	19.1764	0.737555
$677$	1.66733	0.0640809	0.0320404	−	0.999487i	$-0.489799\pi$
$677$	1.66733	0.0640809	0.0320404	+	0.999487i	$0.489799\pi$
$678$	−11.7155	−0.449930
$679$	36.8646	1.41473
$680$	0	0
$681$	−41.2488	−1.58066
$682$	11.9220	0.456516
$683$	−19.0953	−0.730662	−0.365331	−	0.930878i	$-0.619044\pi$
$683$	−19.0953	−0.730662	−0.365331	+	0.930878i	$0.619044\pi$
$684$	−18.2573	−0.698085
$685$	13.1970	0.504230
$686$	−12.3239	−0.470527
$687$	43.8151	1.67165
$688$	21.8567	0.833279
$689$	9.50249	0.362016
$690$	15.2681	0.581246
$691$	−25.5219	−0.970898	−0.485449	−	0.874265i	$-0.661344\pi$
$691$	−25.5219	−0.970898	−0.485449	+	0.874265i	$0.661344\pi$
$692$	67.3806	2.56142
$693$	−3.26683	−0.124097
$694$	−6.66945	−0.253169
$695$	−28.7936	−1.09220
$696$	−37.9272	−1.43763
$697$	0	0
$698$	51.5928	1.95281
$699$	36.8809	1.39496
$700$	34.7631	1.31392
$701$	−28.3803	−1.07191	−0.535955	−	0.844247i	$-0.680048\pi$
$701$	−28.3803	−1.07191	−0.535955	+	0.844247i	$0.680048\pi$
$702$	−42.0215	−1.58600
$703$	−20.1206	−0.758862
$704$	−10.4176	−0.392626
$705$	−2.51694	−0.0947935
$706$	−18.3387	−0.690187
$707$	−30.2306	−1.13694
$708$	−13.5368	−0.508745
$709$	−10.8901	−0.408985	−0.204492	−	0.978868i	$-0.565554\pi$
$709$	−10.8901	−0.408985	−0.204492	+	0.978868i	$0.565554\pi$
$710$	53.9232	2.02370
$711$	1.66186	0.0623245
$712$	7.43718	0.278720
$713$	10.3150	0.386300
$714$	0	0
$715$	−6.57886	−0.246036
$716$	−81.6631	−3.05189
$717$	47.1715	1.76165
$718$	16.0884	0.600413
$719$	19.2995	0.719750	0.359875	−	0.933001i	$-0.382819\pi$
$719$	19.2995	0.719750	0.359875	+	0.933001i	$0.382819\pi$
$720$	−3.74739	−0.139657
$721$	−34.1437	−1.27158
$722$	−20.8846	−0.777244
$723$	−5.42104	−0.201610
$724$	−11.6826	−0.434181
$725$	11.8119	0.438684
$726$	4.75381	0.176430
$727$	−18.6357	−0.691158	−0.345579	−	0.938390i	$-0.612318\pi$
$727$	−18.6357	−0.691158	−0.345579	+	0.938390i	$0.612318\pi$
$728$	63.7378	2.36228
$729$	14.3831	0.532706
$730$	−54.2336	−2.00728
$731$	0	0
$732$	84.1144	3.10896
$733$	2.28825	0.0845185	0.0422592	−	0.999107i	$-0.486544\pi$
$733$	2.28825	0.0845185	0.0422592	+	0.999107i	$0.486544\pi$
$734$	90.4585	3.33888
$735$	17.0003	0.627065
$736$	−4.46612	−0.164623
$737$	15.5881	0.574195
$738$	−10.8122	−0.398003
$739$	−2.89271	−0.106410	−0.0532050	−	0.998584i	$-0.516944\pi$
$739$	−2.89271	−0.106410	−0.0532050	+	0.998584i	$0.516944\pi$
$740$	−22.2402	−0.817566
$741$	44.3420	1.62894
$742$	18.9952	0.697335
$743$	25.5858	0.938654	0.469327	−	0.883025i	$-0.344497\pi$
$743$	25.5858	0.938654	0.469327	+	0.883025i	$0.344497\pi$
$744$	−41.5986	−1.52508
$745$	3.70256	0.135651
$746$	16.3175	0.597426
$747$	15.4107	0.563847
$748$	0	0
$749$	−25.0163	−0.914077
$750$	55.9343	2.04243
$751$	9.88931	0.360866	0.180433	−	0.983587i	$-0.442250\pi$
$751$	9.88931	0.360866	0.180433	+	0.983587i	$0.442250\pi$
$752$	−2.15958	−0.0787518
$753$	20.0068	0.729087
$754$	46.2414	1.68401
$755$	−1.65529	−0.0602421
$756$	−54.8425	−1.99460
$757$	28.8410	1.04824	0.524121	−	0.851644i	$-0.324394\pi$
$757$	28.8410	1.04824	0.524121	+	0.851644i	$0.324394\pi$
$758$	58.6363	2.12977
$759$	4.11304	0.149294
$760$	−34.4219	−1.24861
$761$	−33.6168	−1.21861	−0.609304	−	0.792936i	$-0.708551\pi$
$761$	−33.6168	−1.21861	−0.609304	+	0.792936i	$0.708551\pi$
$762$	101.497	3.67686
$763$	26.8156	0.970789
$764$	40.7034	1.47260
$765$	0	0
$766$	−15.0630	−0.544247
$767$	7.72974	0.279105
$768$	57.1663	2.06281
$769$	6.70627	0.241834	0.120917	−	0.992663i	$-0.461416\pi$
$769$	6.70627	0.241834	0.120917	+	0.992663i	$0.461416\pi$
$770$	−13.1509	−0.473927
$771$	−6.15431	−0.221642
$772$	−25.3547	−0.912537
$773$	16.8964	0.607722	0.303861	−	0.952716i	$-0.401724\pi$
$773$	16.8964	0.607722	0.303861	+	0.952716i	$0.401724\pi$
$774$	−18.4102	−0.661741
$775$	12.9553	0.465369
$776$	44.0073	1.57977
$777$	26.8221	0.962238
$778$	43.1466	1.54688
$779$	−25.7091	−0.921125
$780$	49.0133	1.75496
$781$	14.5263	0.519791
$782$	0	0
$783$	−18.6346	−0.665944
$784$	14.5866	0.520948
$785$	9.02592	0.322149
$786$	40.9752	1.46154
$787$	−38.5837	−1.37536	−0.687681	−	0.726013i	$-0.741371\pi$
$787$	−38.5837	−1.37536	−0.687681	+	0.726013i	$0.741371\pi$
$788$	18.7656	0.668497
$789$	23.6467	0.841843
$790$	6.68997	0.238019
$791$	8.73079	0.310431
$792$	−3.89979	−0.138573
$793$	−48.0306	−1.70562
$794$	26.2485	0.931525
$795$	6.84113	0.242630
$796$	53.4722	1.89527
$797$	−22.3104	−0.790275	−0.395138	−	0.918622i	$-0.629303\pi$
$797$	−22.3104	−0.790275	−0.395138	+	0.918622i	$0.629303\pi$
$798$	88.6383	3.13776
$799$	0	0
$800$	−5.60931	−0.198319
$801$	−1.62162	−0.0572970
$802$	−70.9986	−2.50705
$803$	−14.6099	−0.515572
$804$	−116.133	−4.09570
$805$	−11.3783	−0.401033
$806$	50.7176	1.78645
$807$	−31.2502	−1.10006
$808$	−36.0879	−1.26957
$809$	26.9861	0.948779	0.474390	−	0.880315i	$-0.342669\pi$
$809$	26.9861	0.948779	0.474390	+	0.880315i	$0.342669\pi$
$810$	−40.5217	−1.42379
$811$	45.4115	1.59461	0.797306	−	0.603575i	$-0.206258\pi$
$811$	45.4115	1.59461	0.797306	+	0.603575i	$0.206258\pi$
$812$	60.3499	2.11787
$813$	57.8945	2.03045
$814$	−9.17651	−0.321637
$815$	10.8778	0.381033
$816$	0	0
$817$	−43.7755	−1.53151
$818$	−71.5152	−2.50047
$819$	−13.8975	−0.485618
$820$	−28.4175	−0.992381
$821$	−5.14534	−0.179574	−0.0897868	−	0.995961i	$-0.528619\pi$
$821$	−5.14534	−0.179574	−0.0897868	+	0.995961i	$0.528619\pi$
$822$	−40.5672	−1.41495
$823$	24.7390	0.862348	0.431174	−	0.902269i	$-0.358100\pi$
$823$	24.7390	0.862348	0.431174	+	0.902269i	$0.358100\pi$
$824$	−40.7592	−1.41991
$825$	5.16585	0.179852
$826$	15.4515	0.537627
$827$	32.5824	1.13300	0.566500	−	0.824061i	$-0.308297\pi$
$827$	32.5824	1.13300	0.566500	+	0.824061i	$0.308297\pi$
$828$	−7.20435	−0.250368
$829$	−5.51888	−0.191679	−0.0958393	−	0.995397i	$-0.530553\pi$
$829$	−5.51888	−0.191679	−0.0958393	+	0.995397i	$0.530553\pi$
$830$	62.0373	2.15334
$831$	37.6592	1.30638
$832$	−44.3176	−1.53644
$833$	0	0
$834$	88.5111	3.06489
$835$	8.00468	0.277013
$836$	−19.7991	−0.684767
$837$	−20.4384	−0.706455
$838$	45.6218	1.57598
$839$	−13.1816	−0.455079	−0.227540	−	0.973769i	$-0.573068\pi$
$839$	−13.1816	−0.455079	−0.227540	+	0.973769i	$0.573068\pi$
$840$	45.8868	1.58324
$841$	−8.49414	−0.292901
$842$	40.3615	1.39095
$843$	−58.8171	−2.02577
$844$	25.6989	0.884594
$845$	−7.88327	−0.271193
$846$	1.81905	0.0625401
$847$	−3.54271	−0.121729
$848$	5.86981	0.201570
$849$	47.1073	1.61672
$850$	0	0
$851$	−7.93961	−0.272166
$852$	−108.222	−3.70764
$853$	−11.2378	−0.384776	−0.192388	−	0.981319i	$-0.561623\pi$
$853$	−11.2378	−0.384776	−0.192388	+	0.981319i	$0.561623\pi$
$854$	−96.0117	−3.28545
$855$	7.50542	0.256680
$856$	−29.8634	−1.02071
$857$	45.2264	1.54490	0.772452	−	0.635073i	$-0.219030\pi$
$857$	45.2264	1.54490	0.772452	+	0.635073i	$0.219030\pi$
$858$	20.2233	0.690413
$859$	4.39071	0.149809	0.0749045	−	0.997191i	$-0.476135\pi$
$859$	4.39071	0.149809	0.0749045	+	0.997191i	$0.476135\pi$
$860$	−48.3871	−1.64998
$861$	34.2720	1.16799
$862$	44.6948	1.52231
$863$	−3.89363	−0.132541	−0.0662704	−	0.997802i	$-0.521110\pi$
$863$	−3.89363	−0.132541	−0.0662704	+	0.997802i	$0.521110\pi$
$864$	8.84928	0.301059
$865$	−27.6996	−0.941814
$866$	58.7870	1.99766
$867$	0	0
$868$	66.1919	2.24670
$869$	1.80220	0.0611354
$870$	33.2906	1.12866
$871$	66.3138	2.24696
$872$	32.0112	1.08404
$873$	−9.59544	−0.324756
$874$	−26.2378	−0.887507
$875$	−41.6842	−1.40918
$876$	108.845	3.67754
$877$	−15.9496	−0.538580	−0.269290	−	0.963059i	$-0.586789\pi$
$877$	−15.9496	−0.538580	−0.269290	+	0.963059i	$0.586789\pi$
$878$	8.21304	0.277177
$879$	−14.8754	−0.501733
$880$	−4.06385	−0.136992
$881$	−29.1600	−0.982424	−0.491212	−	0.871040i	$-0.663446\pi$
$881$	−29.1600	−0.982424	−0.491212	+	0.871040i	$0.663446\pi$
$882$	−12.2865	−0.413707
$883$	−43.6727	−1.46970	−0.734852	−	0.678228i	$-0.762748\pi$
$883$	−43.6727	−1.46970	−0.734852	+	0.678228i	$0.762748\pi$
$884$	0	0
$885$	5.56487	0.187061
$886$	−3.21303	−0.107944
$887$	−15.9946	−0.537046	−0.268523	−	0.963273i	$-0.586536\pi$
$887$	−15.9946	−0.537046	−0.268523	+	0.963273i	$0.586536\pi$
$888$	32.0190	1.07449
$889$	−75.6395	−2.53687
$890$	−6.52798	−0.218818
$891$	−10.9161	−0.365702
$892$	−46.0456	−1.54172
$893$	4.32530	0.144740
$894$	−11.3816	−0.380658
$895$	33.5710	1.12216
$896$	−73.3528	−2.45054
$897$	17.4974	0.584221
$898$	85.9061	2.86673
$899$	22.4909	0.750113
$900$	−9.04844	−0.301615
$901$	0	0
$902$	−11.7253	−0.390410
$903$	58.3557	1.94196
$904$	10.4224	0.346645
$905$	4.80263	0.159645
$906$	5.08833	0.169048
$907$	35.8315	1.18976	0.594882	−	0.803813i	$-0.297199\pi$
$907$	35.8315	1.18976	0.594882	+	0.803813i	$0.297199\pi$
$908$	78.3524	2.60021
$909$	7.86867	0.260987
$910$	−55.9458	−1.85459
$911$	−7.34288	−0.243281	−0.121640	−	0.992574i	$-0.538815\pi$
$911$	−7.34288	−0.243281	−0.121640	+	0.992574i	$0.538815\pi$
$912$	27.3907	0.906995
$913$	16.7121	0.553090
$914$	41.7428	1.38073
$915$	−34.5787	−1.14314
$916$	−83.2271	−2.74990
$917$	−30.5362	−1.00839
$918$	0	0
$919$	−4.79334	−0.158118	−0.0790589	−	0.996870i	$-0.525192\pi$
$919$	−4.79334	−0.158118	−0.0790589	+	0.996870i	$0.525192\pi$
$920$	−13.5829	−0.447816
$921$	26.9455	0.887883
$922$	−79.5799	−2.62083
$923$	61.7967	2.03406
$924$	26.3936	0.868285
$925$	−9.97190	−0.327874
$926$	−27.3828	−0.899853
$927$	8.88721	0.291894
$928$	−9.73794	−0.319663
$929$	−22.6314	−0.742513	−0.371256	−	0.928530i	$-0.621073\pi$
$929$	−22.6314	−0.742513	−0.371256	+	0.928530i	$0.621073\pi$
$930$	36.5132	1.19731
$931$	−29.2145	−0.957468
$932$	−70.0556	−2.29475
$933$	30.9830	1.01434
$934$	13.8231	0.452305
$935$	0	0
$936$	−16.5902	−0.542268
$937$	−11.0630	−0.361412	−0.180706	−	0.983537i	$-0.557838\pi$
$937$	−11.0630	−0.361412	−0.180706	+	0.983537i	$0.557838\pi$
$938$	132.559	4.32821
$939$	5.80348	0.189389
$940$	4.78095	0.155937
$941$	−23.6759	−0.771814	−0.385907	−	0.922538i	$-0.626111\pi$
$941$	−23.6759	−0.771814	−0.385907	+	0.922538i	$0.626111\pi$
$942$	−27.7455	−0.903999
$943$	−10.1448	−0.330362
$944$	4.77476	0.155405
$945$	22.5453	0.733398
$946$	−19.9649	−0.649116
$947$	18.1918	0.591154	0.295577	−	0.955319i	$-0.404488\pi$
$947$	18.1918	0.591154	0.295577	+	0.955319i	$0.404488\pi$
$948$	−13.4266	−0.436075
$949$	−62.1524	−2.01755
$950$	−32.9539	−1.06916
$951$	−17.6199	−0.571366
$952$	0	0
$953$	26.5803	0.861020	0.430510	−	0.902586i	$-0.358334\pi$
$953$	26.5803	0.861020	0.430510	+	0.902586i	$0.358334\pi$
$954$	−4.94423	−0.160075
$955$	−16.7328	−0.541462
$956$	−89.6027	−2.89796
$957$	8.96809	0.289897
$958$	16.9644	0.548094
$959$	30.2322	0.976247
$960$	−31.9056	−1.02975
$961$	−6.33196	−0.204257
$962$	−39.0381	−1.25864
$963$	6.51146	0.209829
$964$	10.2973	0.331654
$965$	10.4231	0.335532
$966$	34.9768	1.12536
$967$	−29.8071	−0.958533	−0.479266	−	0.877670i	$-0.659097\pi$
$967$	−29.8071	−0.958533	−0.479266	+	0.877670i	$0.659097\pi$
$968$	−4.22913	−0.135929
$969$	0	0
$970$	−38.6274	−1.24025
$971$	10.6586	0.342052	0.171026	−	0.985266i	$-0.445292\pi$
$971$	10.6586	0.342052	0.171026	+	0.985266i	$0.445292\pi$
$972$	34.8847	1.11893
$973$	−65.9616	−2.11463
$974$	−38.6123	−1.23722
$975$	21.9762	0.703802
$976$	−29.6692	−0.949686
$977$	−7.35465	−0.235296	−0.117648	−	0.993055i	$-0.537535\pi$
$977$	−7.35465	−0.235296	−0.117648	+	0.993055i	$0.537535\pi$
$978$	−33.4382	−1.06923
$979$	−1.75856	−0.0562039
$980$	−32.2922	−1.03154
$981$	−6.97979	−0.222847
$982$	−86.4571	−2.75896
$983$	−21.6516	−0.690577	−0.345289	−	0.938497i	$-0.612219\pi$
$983$	−21.6516	−0.690577	−0.345289	+	0.938497i	$0.612219\pi$
$984$	40.9124	1.30424
$985$	−7.71438	−0.245801
$986$	0	0
$987$	−5.76592	−0.183531
$988$	−84.2280	−2.67965
$989$	−17.2739	−0.549277
$990$	3.42304	0.108791
$991$	43.7032	1.38828	0.694138	−	0.719842i	$-0.255786\pi$
$991$	43.7032	1.38828	0.694138	+	0.719842i	$0.255786\pi$
$992$	−10.6806	−0.339109
$993$	−7.92580	−0.251518
$994$	123.530	3.91812
$995$	−21.9820	−0.696875
$996$	−124.507	−3.94516
$997$	40.8062	1.29234	0.646172	−	0.763192i	$-0.276369\pi$
$997$	40.8062	1.29234	0.646172	+	0.763192i	$0.276369\pi$
$998$	−60.6701	−1.92048
$999$	15.7317	0.497730

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3179.2.a.bh.1.3		28
17.3	odd	16		187.2.h.a.111.2	✓	56
17.6	odd	16		187.2.h.a.155.2	yes	56
17.16	even	2		3179.2.a.bi.1.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.h.a.111.2	✓	56	17.3	odd	16
187.2.h.a.155.2	yes	56	17.6	odd	16
3179.2.a.bh.1.3		28	1.1	even	1	trivial
3179.2.a.bi.1.3		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)

\(f(q)\)	\(=\)	\(q-2.40039 q^{2} -1.98044 q^{3} +3.76185 q^{4} -1.54647 q^{5} +4.75381 q^{6} -3.54271 q^{7} -4.22913 q^{8} +0.922127 q^{9} +O(q^{10})\)	\(q-2.40039 q^{2} -1.98044 q^{3} +3.76185 q^{4} -1.54647 q^{5} +4.75381 q^{6} -3.54271 q^{7} -4.22913 q^{8} +0.922127 q^{9} +3.71212 q^{10} +1.00000 q^{11} -7.45011 q^{12} +4.25413 q^{13} +8.50387 q^{14} +3.06268 q^{15} +2.62783 q^{16} -2.21346 q^{18} -5.26313 q^{19} -5.81758 q^{20} +7.01611 q^{21} -2.40039 q^{22} -2.07684 q^{23} +8.37552 q^{24} -2.60844 q^{25} -10.2115 q^{26} +4.11510 q^{27} -13.3272 q^{28} -4.52834 q^{29} -7.35161 q^{30} -4.96669 q^{31} +2.15044 q^{32} -1.98044 q^{33} +5.47868 q^{35} +3.46891 q^{36} +3.82293 q^{37} +12.6335 q^{38} -8.42503 q^{39} +6.54020 q^{40} +4.88476 q^{41} -16.8414 q^{42} +8.31739 q^{43} +3.76185 q^{44} -1.42604 q^{45} +4.98521 q^{46} -0.821811 q^{47} -5.20425 q^{48} +5.55079 q^{49} +6.26127 q^{50} +16.0034 q^{52} +2.23371 q^{53} -9.87782 q^{54} -1.54647 q^{55} +14.9826 q^{56} +10.4233 q^{57} +10.8698 q^{58} +1.81700 q^{59} +11.5213 q^{60} -11.2904 q^{61} +11.9220 q^{62} -3.26683 q^{63} -10.4176 q^{64} -6.57886 q^{65} +4.75381 q^{66} +15.5881 q^{67} +4.11304 q^{69} -13.1509 q^{70} +14.5263 q^{71} -3.89979 q^{72} -14.6099 q^{73} -9.17651 q^{74} +5.16585 q^{75} -19.7991 q^{76} -3.54271 q^{77} +20.2233 q^{78} +1.80220 q^{79} -4.06385 q^{80} -10.9161 q^{81} -11.7253 q^{82} +16.7121 q^{83} +26.3936 q^{84} -19.9649 q^{86} +8.96809 q^{87} -4.22913 q^{88} -1.75856 q^{89} +3.42304 q^{90} -15.0711 q^{91} -7.81275 q^{92} +9.83622 q^{93} +1.97266 q^{94} +8.13925 q^{95} -4.25881 q^{96} -10.4058 q^{97} -13.3240 q^{98} +0.922127 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 8 q^{3} + 24 q^{4} - 16 q^{5} - 16 q^{6} - 12 q^{7} + 20 q^{9}+O(q^{10}) \) 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

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Database

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