LMFDB - Embedded newform 1445.2.a.q.1.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1445,2,Mod(1,1445)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1445.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1445, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1445 = 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1445.a (trivial)

Newform invariants

comment:select newform

sage:traces = [12,-4,8,12,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$11.5383830921$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 10 x^{10} + 52 x^{9} + 21 x^{8} - 232 x^{7} + 44 x^{6} + 424 x^{5} - 137 x^{4} + \cdots + 17 $ x^12 - 4x^11 - 10x^10 + 52x^9 + 21x^8 - 232x^7 + 44x^6 + 424x^5 - 137x^4 - 316x^3 + 46x^2 + 92*x + 17
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 85)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-0.747914$ of defining polynomial
Character	$\chi$	$=$	1445.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.747914 q^{2} +3.07503 q^{3} -1.44062 q^{4} -1.00000 q^{5} +2.29986 q^{6} +3.23262 q^{7} -2.57329 q^{8} +6.45581 q^{9} -0.747914 q^{10} -2.73509 q^{11} -4.42996 q^{12} +4.31833 q^{13} +2.41772 q^{14} -3.07503 q^{15} +0.956646 q^{16} +4.82839 q^{18} +1.26892 q^{19} +1.44062 q^{20} +9.94040 q^{21} -2.04561 q^{22} -0.492367 q^{23} -7.91295 q^{24} +1.00000 q^{25} +3.22974 q^{26} +10.6267 q^{27} -4.65699 q^{28} +0.444360 q^{29} -2.29986 q^{30} +5.52836 q^{31} +5.86207 q^{32} -8.41047 q^{33} -3.23262 q^{35} -9.30039 q^{36} +10.6999 q^{37} +0.949042 q^{38} +13.2790 q^{39} +2.57329 q^{40} -2.17048 q^{41} +7.43457 q^{42} -2.16182 q^{43} +3.94023 q^{44} -6.45581 q^{45} -0.368248 q^{46} -8.39597 q^{47} +2.94172 q^{48} +3.44983 q^{49} +0.747914 q^{50} -6.22109 q^{52} -1.81698 q^{53} +7.94786 q^{54} +2.73509 q^{55} -8.31847 q^{56} +3.90196 q^{57} +0.332343 q^{58} -3.01987 q^{59} +4.42996 q^{60} -12.2233 q^{61} +4.13474 q^{62} +20.8692 q^{63} +2.47104 q^{64} -4.31833 q^{65} -6.29031 q^{66} +4.21389 q^{67} -1.51404 q^{69} -2.41772 q^{70} -3.89165 q^{71} -16.6127 q^{72} -6.47062 q^{73} +8.00263 q^{74} +3.07503 q^{75} -1.82803 q^{76} -8.84149 q^{77} +9.93155 q^{78} +7.22150 q^{79} -0.956646 q^{80} +13.3100 q^{81} -1.62333 q^{82} +0.227499 q^{83} -14.3204 q^{84} -1.61686 q^{86} +1.36642 q^{87} +7.03818 q^{88} -13.3408 q^{89} -4.82839 q^{90} +13.9595 q^{91} +0.709315 q^{92} +16.9999 q^{93} -6.27946 q^{94} -1.26892 q^{95} +18.0260 q^{96} +14.8075 q^{97} +2.58018 q^{98} -17.6572 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} + 8 q^{3} + 12 q^{4} - 12 q^{5} + 8 q^{6} + 16 q^{7} - 12 q^{8} + 12 q^{9} + 4 q^{10} + 16 q^{11} + 16 q^{12} - 8 q^{13} - 16 q^{14} - 8 q^{15} + 12 q^{16} + 4 q^{18} - 12 q^{20} + 16 q^{21}+ \cdots + 56 q^{99}+O(q^{100}) $ 12 * q - 4 * q^2 + 8 * q^3 + 12 * q^4 - 12 * q^5 + 8 * q^6 + 16 * q^7 - 12 * q^8 + 12 * q^9 + 4 * q^10 + 16 * q^11 + 16 * q^12 - 8 * q^13 - 16 * q^14 - 8 * q^15 + 12 * q^16 + 4 * q^18 - 12 * q^20 + 16 * q^21 + 16 * q^22 + 16 * q^23 + 12 * q^25 + 16 * q^26 + 32 * q^27 + 40 * q^28 + 16 * q^29 - 8 * q^30 + 24 * q^31 - 28 * q^32 - 16 * q^35 + 12 * q^36 + 24 * q^37 - 24 * q^38 + 8 * q^39 + 12 * q^40 + 8 * q^41 - 16 * q^43 + 8 * q^44 - 12 * q^45 + 40 * q^46 - 32 * q^47 - 24 * q^48 + 20 * q^49 - 4 * q^50 - 24 * q^52 + 8 * q^54 - 16 * q^55 - 24 * q^56 + 32 * q^57 - 16 * q^58 + 8 * q^59 - 16 * q^60 + 24 * q^61 + 8 * q^62 + 48 * q^63 + 36 * q^64 + 8 * q^65 + 40 * q^66 - 8 * q^67 + 48 * q^69 + 16 * q^70 - 16 * q^71 + 12 * q^72 + 16 * q^73 + 8 * q^75 + 16 * q^76 + 24 * q^77 - 24 * q^78 + 40 * q^79 - 12 * q^80 + 36 * q^81 - 16 * q^82 - 40 * q^83 + 32 * q^84 - 8 * q^86 - 32 * q^87 + 48 * q^88 + 8 * q^89 - 4 * q^90 + 72 * q^91 - 8 * q^92 + 24 * q^93 - 16 * q^94 + 8 * q^96 + 32 * q^97 - 60 * q^98 + 56 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.747914	0.528855	0.264428	−	0.964406i	$-0.414817\pi$
$2$	0.747914	0.528855	0.264428	+	0.964406i	$0.414817\pi$
$3$	3.07503	1.77537	0.887684	−	0.460452i	$-0.152313\pi$
$3$	3.07503	1.77537	0.887684	+	0.460452i	$0.152313\pi$
$4$	−1.44062	−0.720312
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.29986	0.938913
$7$	3.23262	1.22182	0.610908	−	0.791702i	$-0.290805\pi$
$7$	3.23262	1.22182	0.610908	+	0.791702i	$0.290805\pi$
$8$	−2.57329	−0.909796
$9$	6.45581	2.15194
$10$	−0.747914	−0.236511
$11$	−2.73509	−0.824660	−0.412330	−	0.911035i	$-0.635285\pi$
$11$	−2.73509	−0.824660	−0.412330	+	0.911035i	$0.635285\pi$
$12$	−4.42996	−1.27882
$13$	4.31833	1.19769	0.598845	−	0.800865i	$-0.295627\pi$
$13$	4.31833	1.19769	0.598845	+	0.800865i	$0.295627\pi$
$14$	2.41772	0.646164
$15$	−3.07503	−0.793969
$16$	0.956646	0.239162
$17$	0	0
$17$	0	0
$18$	4.82839	1.13806
$19$	1.26892	0.291110	0.145555	−	0.989350i	$-0.453503\pi$
$19$	1.26892	0.291110	0.145555	+	0.989350i	$0.453503\pi$
$20$	1.44062	0.322133
$21$	9.94040	2.16917
$22$	−2.04561	−0.436126
$23$	−0.492367	−0.102666	−0.0513328	−	0.998682i	$-0.516347\pi$
$23$	−0.492367	−0.102666	−0.0513328	+	0.998682i	$0.516347\pi$
$24$	−7.91295	−1.61522
$25$	1.00000	0.200000
$26$	3.22974	0.633404
$27$	10.6267	2.04511
$28$	−4.65699	−0.880088
$29$	0.444360	0.0825156	0.0412578	−	0.999149i	$-0.486863\pi$
$29$	0.444360	0.0825156	0.0412578	+	0.999149i	$0.486863\pi$
$30$	−2.29986	−0.419895
$31$	5.52836	0.992923	0.496462	−	0.868059i	$-0.334632\pi$
$31$	5.52836	0.992923	0.496462	+	0.868059i	$0.334632\pi$
$32$	5.86207	1.03628
$33$	−8.41047	−1.46408
$34$	0	0
$35$	−3.23262	−0.546412
$36$	−9.30039	−1.55006
$37$	10.6999	1.75906	0.879529	−	0.475845i	$-0.157858\pi$
$37$	10.6999	1.75906	0.879529	+	0.475845i	$0.157858\pi$
$38$	0.949042	0.153955
$39$	13.2790	2.12634
$40$	2.57329	0.406873
$41$	−2.17048	−0.338972	−0.169486	−	0.985533i	$-0.554211\pi$
$41$	−2.17048	−0.338972	−0.169486	+	0.985533i	$0.554211\pi$
$42$	7.43457	1.14718
$43$	−2.16182	−0.329675	−0.164837	−	0.986321i	$-0.552710\pi$
$43$	−2.16182	−0.329675	−0.164837	+	0.986321i	$0.552710\pi$
$44$	3.94023	0.594012
$45$	−6.45581	−0.962375
$46$	−0.368248	−0.0542952
$47$	−8.39597	−1.22468	−0.612339	−	0.790595i	$-0.709771\pi$
$47$	−8.39597	−1.22468	−0.612339	+	0.790595i	$0.709771\pi$
$48$	2.94172	0.424600
$49$	3.44983	0.492833
$50$	0.747914	0.105771
$51$	0	0
$52$	−6.22109	−0.862710
$53$	−1.81698	−0.249581	−0.124791	−	0.992183i	$-0.539826\pi$
$53$	−1.81698	−0.249581	−0.124791	+	0.992183i	$0.539826\pi$
$54$	7.94786	1.08157
$55$	2.73509	0.368799
$56$	−8.31847	−1.11160
$57$	3.90196	0.516827
$58$	0.332343	0.0436388
$59$	−3.01987	−0.393153	−0.196577	−	0.980488i	$-0.562982\pi$
$59$	−3.01987	−0.393153	−0.196577	+	0.980488i	$0.562982\pi$
$60$	4.42996	0.571906
$61$	−12.2233	−1.56503	−0.782514	−	0.622633i	$-0.786063\pi$
$61$	−12.2233	−1.56503	−0.782514	+	0.622633i	$0.786063\pi$
$62$	4.13474	0.525113
$63$	20.8692	2.62927
$64$	2.47104	0.308880
$65$	−4.31833	−0.535623
$66$	−6.29031	−0.774284
$67$	4.21389	0.514808	0.257404	−	0.966304i	$-0.417133\pi$
$67$	4.21389	0.514808	0.257404	+	0.966304i	$0.417133\pi$
$68$	0	0
$69$	−1.51404	−0.182269
$70$	−2.41772	−0.288973
$71$	−3.89165	−0.461854	−0.230927	−	0.972971i	$-0.574176\pi$
$71$	−3.89165	−0.461854	−0.230927	+	0.972971i	$0.574176\pi$
$72$	−16.6127	−1.95782
$73$	−6.47062	−0.757329	−0.378664	−	0.925534i	$-0.623617\pi$
$73$	−6.47062	−0.757329	−0.378664	+	0.925534i	$0.623617\pi$
$74$	8.00263	0.930287
$75$	3.07503	0.355074
$76$	−1.82803	−0.209690
$77$	−8.84149	−1.00758
$78$	9.93155	1.12453
$79$	7.22150	0.812482	0.406241	−	0.913766i	$-0.366839\pi$
$79$	7.22150	0.812482	0.406241	+	0.913766i	$0.366839\pi$
$80$	−0.956646	−0.106956
$81$	13.3100	1.47889
$82$	−1.62333	−0.179267
$83$	0.227499	0.0249713	0.0124856	−	0.999922i	$-0.496026\pi$
$83$	0.227499	0.0249713	0.0124856	+	0.999922i	$0.496026\pi$
$84$	−14.3204	−1.56248
$85$	0	0
$86$	−1.61686	−0.174350
$87$	1.36642	0.146496
$88$	7.03818	0.750272
$89$	−13.3408	−1.41413	−0.707064	−	0.707150i	$-0.749981\pi$
$89$	−13.3408	−1.41413	−0.707064	+	0.707150i	$0.749981\pi$
$90$	−4.82839	−0.508957
$91$	13.9595	1.46336
$92$	0.709315	0.0739512
$93$	16.9999	1.76281
$94$	−6.27946	−0.647677
$95$	−1.26892	−0.130188
$96$	18.0260	1.83978
$97$	14.8075	1.50347	0.751734	−	0.659466i	$-0.229218\pi$
$97$	14.8075	1.50347	0.751734	+	0.659466i	$0.229218\pi$
$98$	2.58018	0.260637
$99$	−17.6572	−1.77461
$100$	−1.44062	−0.144062
$101$	0.284213	0.0282803	0.0141401	−	0.999900i	$-0.495499\pi$
$101$	0.284213	0.0282803	0.0141401	+	0.999900i	$0.495499\pi$
$102$	0	0
$103$	−14.0842	−1.38775	−0.693877	−	0.720093i	$-0.744099\pi$
$103$	−14.0842	−1.38775	−0.693877	+	0.720093i	$0.744099\pi$
$104$	−11.1123	−1.08965
$105$	−9.94040	−0.970084
$106$	−1.35894	−0.131992
$107$	18.7099	1.80875	0.904375	−	0.426738i	$-0.140337\pi$
$107$	18.7099	1.80875	0.904375	+	0.426738i	$0.140337\pi$
$108$	−15.3091	−1.47312
$109$	−3.53078	−0.338187	−0.169094	−	0.985600i	$-0.554084\pi$
$109$	−3.53078	−0.338187	−0.169094	+	0.985600i	$0.554084\pi$
$110$	2.04561	0.195041
$111$	32.9026	3.12298
$112$	3.09247	0.292211
$113$	−2.84155	−0.267310	−0.133655	−	0.991028i	$-0.542671\pi$
$113$	−2.84155	−0.267310	−0.133655	+	0.991028i	$0.542671\pi$
$114$	2.91833	0.273327
$115$	0.492367	0.0459134
$116$	−0.640156	−0.0594370
$117$	27.8783	2.57735
$118$	−2.25860	−0.207921
$119$	0	0
$120$	7.91295	0.722350
$121$	−3.51930	−0.319937
$122$	−9.14195	−0.827673
$123$	−6.67430	−0.601801
$124$	−7.96429	−0.715215
$125$	−1.00000	−0.0894427
$126$	15.6083	1.39050
$127$	5.46515	0.484954	0.242477	−	0.970157i	$-0.422040\pi$
$127$	5.46515	0.484954	0.242477	+	0.970157i	$0.422040\pi$
$128$	−9.87602	−0.872925
$129$	−6.64767	−0.585295
$130$	−3.22974	−0.283267
$131$	−9.97951	−0.871914	−0.435957	−	0.899968i	$-0.643590\pi$
$131$	−9.97951	−0.871914	−0.435957	+	0.899968i	$0.643590\pi$
$132$	12.1163	1.05459
$133$	4.10193	0.355682
$134$	3.15163	0.272259
$135$	−10.6267	−0.914601
$136$	0	0
$137$	−3.07772	−0.262947	−0.131474	−	0.991320i	$-0.541971\pi$
$137$	−3.07772	−0.262947	−0.131474	+	0.991320i	$0.541971\pi$
$138$	−1.13237	−0.0963941
$139$	−6.70991	−0.569127	−0.284564	−	0.958657i	$-0.591849\pi$
$139$	−6.70991	−0.569127	−0.284564	+	0.958657i	$0.591849\pi$
$140$	4.65699	0.393587
$141$	−25.8178	−2.17425
$142$	−2.91062	−0.244254
$143$	−11.8110	−0.987686
$144$	6.17592	0.514660
$145$	−0.444360	−0.0369021
$146$	−4.83947	−0.400517
$147$	10.6083	0.874960
$148$	−15.4146	−1.26707
$149$	−22.9914	−1.88353	−0.941764	−	0.336276i	$-0.890833\pi$
$149$	−22.9914	−1.88353	−0.941764	+	0.336276i	$0.890833\pi$
$150$	2.29986	0.187783
$151$	0.195743	0.0159294	0.00796468	−	0.999968i	$-0.497465\pi$
$151$	0.195743	0.0159294	0.00796468	+	0.999968i	$0.497465\pi$
$152$	−3.26530	−0.264850
$153$	0	0
$154$	−6.61268	−0.532865
$155$	−5.52836	−0.444049
$156$	−19.1300	−1.53163
$157$	11.8582	0.946391	0.473196	−	0.880957i	$-0.343100\pi$
$157$	11.8582	0.946391	0.473196	+	0.880957i	$0.343100\pi$
$158$	5.40106	0.429685
$159$	−5.58726	−0.443099
$160$	−5.86207	−0.463438
$161$	−1.59163	−0.125438
$162$	9.95474	0.782118
$163$	5.34472	0.418631	0.209315	−	0.977848i	$-0.432877\pi$
$163$	5.34472	0.418631	0.209315	+	0.977848i	$0.432877\pi$
$164$	3.12685	0.244166
$165$	8.41047	0.654754
$166$	0.170150	0.0132062
$167$	11.5900	0.896859	0.448429	−	0.893818i	$-0.351984\pi$
$167$	11.5900	0.896859	0.448429	+	0.893818i	$0.351984\pi$
$168$	−25.5796	−1.97351
$169$	5.64797	0.434459
$170$	0	0
$171$	8.19188	0.626449
$172$	3.11437	0.237469
$173$	11.0271	0.838373	0.419187	−	0.907900i	$-0.362315\pi$
$173$	11.0271	0.838373	0.419187	+	0.907900i	$0.362315\pi$
$174$	1.02197	0.0774750
$175$	3.23262	0.244363
$176$	−2.61651	−0.197227
$177$	−9.28618	−0.697992
$178$	−9.97781	−0.747869
$179$	−21.0731	−1.57508	−0.787539	−	0.616265i	$-0.788645\pi$
$179$	−21.0731	−1.57508	−0.787539	+	0.616265i	$0.788645\pi$
$180$	9.30039	0.693210
$181$	−22.6592	−1.68425	−0.842123	−	0.539285i	$-0.818695\pi$
$181$	−22.6592	−1.68425	−0.842123	+	0.539285i	$0.818695\pi$
$182$	10.4405	0.773903
$183$	−37.5869	−2.77850
$184$	1.26700	0.0934047
$185$	−10.6999	−0.786675
$186$	12.7145	0.932269
$187$	0	0
$188$	12.0954	0.882150
$189$	34.3521	2.49875
$190$	−0.949042	−0.0688507
$191$	−3.50162	−0.253368	−0.126684	−	0.991943i	$-0.540433\pi$
$191$	−3.50162	−0.253368	−0.126684	+	0.991943i	$0.540433\pi$
$192$	7.59851	0.548375
$193$	−12.2942	−0.884959	−0.442479	−	0.896779i	$-0.645901\pi$
$193$	−12.2942	−0.884959	−0.442479	+	0.896779i	$0.645901\pi$
$194$	11.0747	0.795117
$195$	−13.2790	−0.950928
$196$	−4.96991	−0.354993
$197$	−16.9757	−1.20947	−0.604734	−	0.796427i	$-0.706721\pi$
$197$	−16.9757	−1.20947	−0.604734	+	0.796427i	$0.706721\pi$
$198$	−13.2061	−0.938514
$199$	−11.5779	−0.820735	−0.410367	−	0.911920i	$-0.634600\pi$
$199$	−11.5779	−0.820735	−0.410367	+	0.911920i	$0.634600\pi$
$200$	−2.57329	−0.181959
$201$	12.9578	0.913975
$202$	0.212567	0.0149562
$203$	1.43645	0.100819
$204$	0	0
$205$	2.17048	0.151593
$206$	−10.5338	−0.733921
$207$	−3.17862	−0.220930
$208$	4.13111	0.286441
$209$	−3.47060	−0.240066
$210$	−7.43457	−0.513034
$211$	6.66380	0.458755	0.229378	−	0.973338i	$-0.426331\pi$
$211$	6.66380	0.458755	0.229378	+	0.973338i	$0.426331\pi$
$212$	2.61758	0.179776
$213$	−11.9669	−0.819962
$214$	13.9934	0.956567
$215$	2.16182	0.147435
$216$	−27.3456	−1.86063
$217$	17.8711	1.21317
$218$	−2.64072	−0.178852
$219$	−19.8973	−1.34454
$220$	−3.94023	−0.265650
$221$	0	0
$222$	24.6083	1.65160
$223$	−12.5928	−0.843273	−0.421637	−	0.906765i	$-0.638544\pi$
$223$	−12.5928	−0.843273	−0.421637	+	0.906765i	$0.638544\pi$
$224$	18.9499	1.26614
$225$	6.45581	0.430387
$226$	−2.12523	−0.141368
$227$	8.04265	0.533809	0.266905	−	0.963723i	$-0.413999\pi$
$227$	8.04265	0.533809	0.266905	+	0.963723i	$0.413999\pi$
$228$	−5.62126	−0.372277
$229$	−21.6295	−1.42932	−0.714658	−	0.699474i	$-0.753418\pi$
$229$	−21.6295	−1.42932	−0.714658	+	0.699474i	$0.753418\pi$
$230$	0.368248	0.0242816
$231$	−27.1879	−1.78883
$232$	−1.14347	−0.0750724
$233$	21.9506	1.43803	0.719014	−	0.694995i	$-0.244594\pi$
$233$	21.9506	1.43803	0.719014	+	0.694995i	$0.244594\pi$
$234$	20.8506	1.36304
$235$	8.39597	0.547692
$236$	4.35050	0.283193
$237$	22.2063	1.44246
$238$	0	0
$239$	5.90132	0.381725	0.190862	−	0.981617i	$-0.438872\pi$
$239$	5.90132	0.381725	0.190862	+	0.981617i	$0.438872\pi$
$240$	−2.94172	−0.189887
$241$	13.3115	0.857466	0.428733	−	0.903431i	$-0.358960\pi$
$241$	13.3115	0.857466	0.428733	+	0.903431i	$0.358960\pi$
$242$	−2.63214	−0.169200
$243$	9.04855	0.580464
$244$	17.6091	1.12731
$245$	−3.44983	−0.220402
$246$	−4.99180	−0.318266
$247$	5.47960	0.348659
$248$	−14.2261	−0.903358
$249$	0.699566	0.0443332
$250$	−0.747914	−0.0473023
$251$	3.59367	0.226831	0.113415	−	0.993548i	$-0.463821\pi$
$251$	3.59367	0.226831	0.113415	+	0.993548i	$0.463821\pi$
$252$	−30.0646	−1.89389
$253$	1.34667	0.0846641
$254$	4.08746	0.256470
$255$	0	0
$256$	−12.3285	−0.770531
$257$	24.5491	1.53133	0.765665	−	0.643239i	$-0.222410\pi$
$257$	24.5491	1.53133	0.765665	+	0.643239i	$0.222410\pi$
$258$	−4.97189	−0.309536
$259$	34.5888	2.14924
$260$	6.22109	0.385816
$261$	2.86870	0.177568
$262$	−7.46382	−0.461116
$263$	14.6401	0.902749	0.451375	−	0.892335i	$-0.350934\pi$
$263$	14.6401	0.902749	0.451375	+	0.892335i	$0.350934\pi$
$264$	21.6426	1.33201
$265$	1.81698	0.111616
$266$	3.06789	0.188104
$267$	−41.0235	−2.51060
$268$	−6.07063	−0.370823
$269$	18.7597	1.14380	0.571900	−	0.820323i	$-0.306206\pi$
$269$	18.7597	1.14380	0.571900	+	0.820323i	$0.306206\pi$
$270$	−7.94786	−0.483692
$271$	−5.76388	−0.350131	−0.175065	−	0.984557i	$-0.556014\pi$
$271$	−5.76388	−0.350131	−0.175065	+	0.984557i	$0.556014\pi$
$272$	0	0
$273$	42.9259	2.59800
$274$	−2.30187	−0.139061
$275$	−2.73509	−0.164932
$276$	2.18117	0.131291
$277$	0.123252	0.00740547	0.00370273	−	0.999993i	$-0.498821\pi$
$277$	0.123252	0.00740547	0.00370273	+	0.999993i	$0.498821\pi$
$278$	−5.01844	−0.300986
$279$	35.6900	2.13671
$280$	8.31847	0.497124
$281$	1.82363	0.108789	0.0543944	−	0.998520i	$-0.482677\pi$
$281$	1.82363	0.108789	0.0543944	+	0.998520i	$0.482677\pi$
$282$	−19.3095	−1.14987
$283$	−28.6278	−1.70174	−0.850872	−	0.525373i	$-0.823926\pi$
$283$	−28.6278	−1.70174	−0.850872	+	0.525373i	$0.823926\pi$
$284$	5.60641	0.332679
$285$	−3.90196	−0.231132
$286$	−8.83362	−0.522343
$287$	−7.01634	−0.414162
$288$	37.8444	2.23000
$289$	0	0
$290$	−0.332343	−0.0195159
$291$	45.5333	2.66921
$292$	9.32173	0.545513
$293$	−1.41607	−0.0827278	−0.0413639	−	0.999144i	$-0.513170\pi$
$293$	−1.41607	−0.0827278	−0.0413639	+	0.999144i	$0.513170\pi$
$294$	7.93412	0.462727
$295$	3.01987	0.175824
$296$	−27.5340	−1.60038
$297$	−29.0649	−1.68652
$298$	−17.1956	−0.996113
$299$	−2.12620	−0.122961
$300$	−4.42996	−0.255764
$301$	−6.98835	−0.402802
$302$	0.146399	0.00842433
$303$	0.873965	0.0502080
$304$	1.21391	0.0696222
$305$	12.2233	0.699902
$306$	0	0
$307$	−21.7364	−1.24056	−0.620281	−	0.784379i	$-0.712982\pi$
$307$	−21.7364	−1.24056	−0.620281	+	0.784379i	$0.712982\pi$
$308$	12.7373	0.725773
$309$	−43.3092	−2.46378
$310$	−4.13474	−0.234838
$311$	8.65102	0.490554	0.245277	−	0.969453i	$-0.421121\pi$
$311$	8.65102	0.490554	0.245277	+	0.969453i	$0.421121\pi$
$312$	−34.1707	−1.93454
$313$	10.2820	0.581175	0.290587	−	0.956848i	$-0.406149\pi$
$313$	10.2820	0.581175	0.290587	+	0.956848i	$0.406149\pi$
$314$	8.86896	0.500504
$315$	−20.8692	−1.17584
$316$	−10.4035	−0.585241
$317$	1.12766	0.0633359	0.0316680	−	0.999498i	$-0.489918\pi$
$317$	1.12766	0.0633359	0.0316680	+	0.999498i	$0.489918\pi$
$318$	−4.17879	−0.234335
$319$	−1.21536	−0.0680473
$320$	−2.47104	−0.138135
$321$	57.5334	3.21120
$322$	−1.19041	−0.0663387
$323$	0	0
$324$	−19.1747	−1.06526
$325$	4.31833	0.239538
$326$	3.99739	0.221395
$327$	−10.8573	−0.600407
$328$	5.58528	0.308396
$329$	−27.1410	−1.49633
$330$	6.29031	0.346270
$331$	−34.2599	−1.88310	−0.941548	−	0.336878i	$-0.890629\pi$
$331$	−34.2599	−1.88310	−0.941548	+	0.336878i	$0.890629\pi$
$332$	−0.327741	−0.0179871
$333$	69.0767	3.78538
$334$	8.66830	0.474309
$335$	−4.21389	−0.230229
$336$	9.50945	0.518783
$337$	13.7463	0.748806	0.374403	−	0.927266i	$-0.377848\pi$
$337$	13.7463	0.748806	0.374403	+	0.927266i	$0.377848\pi$
$338$	4.22420	0.229766
$339$	−8.73784	−0.474574
$340$	0	0
$341$	−15.1206	−0.818824
$342$	6.12683	0.331301
$343$	−11.4763	−0.619665
$344$	5.56300	0.299937
$345$	1.51404	0.0815133
$346$	8.24731	0.443378
$347$	18.8786	1.01346	0.506728	−	0.862106i	$-0.330855\pi$
$347$	18.8786	1.01346	0.506728	+	0.862106i	$0.330855\pi$
$348$	−1.96850	−0.105523
$349$	−7.04988	−0.377371	−0.188686	−	0.982038i	$-0.560423\pi$
$349$	−7.04988	−0.377371	−0.188686	+	0.982038i	$0.560423\pi$
$350$	2.41772	0.129233
$351$	45.8896	2.44941
$352$	−16.0333	−0.854577
$353$	8.60779	0.458146	0.229073	−	0.973409i	$-0.426431\pi$
$353$	8.60779	0.458146	0.229073	+	0.973409i	$0.426431\pi$
$354$	−6.94527	−0.369137
$355$	3.89165	0.206547
$356$	19.2191	1.01861
$357$	0	0
$358$	−15.7609	−0.832988
$359$	9.18100	0.484555	0.242277	−	0.970207i	$-0.422106\pi$
$359$	9.18100	0.484555	0.242277	+	0.970207i	$0.422106\pi$
$360$	16.6127	0.875565
$361$	−17.3898	−0.915255
$362$	−16.9472	−0.890723
$363$	−10.8220	−0.568005
$364$	−20.1104	−1.05407
$365$	6.47062	0.338688
$366$	−28.1118	−1.46943
$367$	6.81607	0.355796	0.177898	−	0.984049i	$-0.443070\pi$
$367$	6.81607	0.355796	0.177898	+	0.984049i	$0.443070\pi$
$368$	−0.471021	−0.0245537
$369$	−14.0122	−0.729446
$370$	−8.00263	−0.416037
$371$	−5.87360	−0.304942
$372$	−24.4904	−1.26977
$373$	−10.4647	−0.541841	−0.270920	−	0.962602i	$-0.587328\pi$
$373$	−10.4647	−0.541841	−0.270920	+	0.962602i	$0.587328\pi$
$374$	0	0
$375$	−3.07503	−0.158794
$376$	21.6053	1.11421
$377$	1.91889	0.0988281
$378$	25.6924	1.32148
$379$	25.3419	1.30173	0.650864	−	0.759195i	$-0.274407\pi$
$379$	25.3419	1.30173	0.650864	+	0.759195i	$0.274407\pi$
$380$	1.82803	0.0937761
$381$	16.8055	0.860972
$382$	−2.61891	−0.133995
$383$	7.69048	0.392965	0.196483	−	0.980507i	$-0.437048\pi$
$383$	7.69048	0.392965	0.196483	+	0.980507i	$0.437048\pi$
$384$	−30.3691	−1.54976
$385$	8.84149	0.450604
$386$	−9.19504	−0.468015
$387$	−13.9563	−0.709439
$388$	−21.3320	−1.08297
$389$	15.8379	0.803013	0.401506	−	0.915856i	$-0.368487\pi$
$389$	15.8379	0.803013	0.401506	+	0.915856i	$0.368487\pi$
$390$	−9.93155	−0.502903
$391$	0	0
$392$	−8.87742	−0.448377
$393$	−30.6873	−1.54797
$394$	−12.6964	−0.639634
$395$	−7.22150	−0.363353
$396$	25.4374	1.27828
$397$	29.1640	1.46370	0.731850	−	0.681466i	$-0.238657\pi$
$397$	29.1640	1.46370	0.731850	+	0.681466i	$0.238657\pi$
$398$	−8.65927	−0.434050
$399$	12.6135	0.631467
$400$	0.956646	0.0478323
$401$	16.3859	0.818271	0.409136	−	0.912474i	$-0.365830\pi$
$401$	16.3859	0.818271	0.409136	+	0.912474i	$0.365830\pi$
$402$	9.69135	0.483360
$403$	23.8733	1.18921
$404$	−0.409445	−0.0203706
$405$	−13.3100	−0.661379
$406$	1.07434	0.0533186
$407$	−29.2652	−1.45062
$408$	0	0
$409$	33.9971	1.68105	0.840525	−	0.541772i	$-0.182247\pi$
$409$	33.9971	1.68105	0.840525	+	0.541772i	$0.182247\pi$
$410$	1.62333	0.0801708
$411$	−9.46408	−0.466829
$412$	20.2900	0.999616
$413$	−9.76209	−0.480361
$414$	−2.37734	−0.116840
$415$	−0.227499	−0.0111675
$416$	25.3144	1.24114
$417$	−20.6332	−1.01041
$418$	−2.59571	−0.126960
$419$	−0.892935	−0.0436227	−0.0218114	−	0.999762i	$-0.506943\pi$
$419$	−0.892935	−0.0436227	−0.0218114	+	0.999762i	$0.506943\pi$
$420$	14.3204	0.698763
$421$	33.6725	1.64110	0.820550	−	0.571575i	$-0.193668\pi$
$421$	33.6725	1.64110	0.820550	+	0.571575i	$0.193668\pi$
$422$	4.98395	0.242615
$423$	−54.2027	−2.63543
$424$	4.67562	0.227068
$425$	0	0
$426$	−8.95025	−0.433641
$427$	−39.5131	−1.91218
$428$	−26.9539	−1.30286
$429$	−36.3192	−1.75351
$430$	1.61686	0.0779718
$431$	−16.2970	−0.784997	−0.392498	−	0.919753i	$-0.628389\pi$
$431$	−16.2970	−0.784997	−0.392498	+	0.919753i	$0.628389\pi$
$432$	10.1660	0.489112
$433$	−34.9947	−1.68174	−0.840869	−	0.541239i	$-0.817956\pi$
$433$	−34.9947	−1.68174	−0.840869	+	0.541239i	$0.817956\pi$
$434$	13.3660	0.641591
$435$	−1.36642	−0.0655149
$436$	5.08653	0.243600
$437$	−0.624773	−0.0298869
$438$	−14.8815	−0.711066
$439$	−22.2777	−1.06326	−0.531628	−	0.846978i	$-0.678420\pi$
$439$	−22.2777	−1.06326	−0.531628	+	0.846978i	$0.678420\pi$
$440$	−7.03818	−0.335532
$441$	22.2714	1.06054
$442$	0	0
$443$	−8.79907	−0.418056	−0.209028	−	0.977910i	$-0.567030\pi$
$443$	−8.79907	−0.418056	−0.209028	+	0.977910i	$0.567030\pi$
$444$	−47.4003	−2.24952
$445$	13.3408	0.632417
$446$	−9.41830	−0.445970
$447$	−70.6992	−3.34396
$448$	7.98792	0.377394
$449$	−8.86683	−0.418452	−0.209226	−	0.977867i	$-0.567094\pi$
$449$	−8.86683	−0.418452	−0.209226	+	0.977867i	$0.567094\pi$
$450$	4.82839	0.227612
$451$	5.93646	0.279537
$452$	4.09360	0.192547
$453$	0.601916	0.0282805
$454$	6.01521	0.282308
$455$	−13.9595	−0.654432
$456$	−10.0409	−0.470207
$457$	−18.4756	−0.864254	−0.432127	−	0.901813i	$-0.642237\pi$
$457$	−18.4756	−0.864254	−0.432127	+	0.901813i	$0.642237\pi$
$458$	−16.1770	−0.755902
$459$	0	0
$460$	−0.709315	−0.0330720
$461$	−24.5700	−1.14434	−0.572169	−	0.820136i	$-0.693898\pi$
$461$	−24.5700	−1.14434	−0.572169	+	0.820136i	$0.693898\pi$
$462$	−20.3342	−0.946032
$463$	−9.90931	−0.460525	−0.230262	−	0.973129i	$-0.573958\pi$
$463$	−9.90931	−0.460525	−0.230262	+	0.973129i	$0.573958\pi$
$464$	0.425096	0.0197346
$465$	−16.9999	−0.788351
$466$	16.4171	0.760509
$467$	−29.4041	−1.36066	−0.680329	−	0.732907i	$-0.738163\pi$
$467$	−29.4041	−1.36066	−0.680329	+	0.732907i	$0.738163\pi$
$468$	−40.1621	−1.85650
$469$	13.6219	0.629001
$470$	6.27946	0.289650
$471$	36.4645	1.68019
$472$	7.77100	0.357689
$473$	5.91277	0.271870
$474$	16.6084	0.762850
$475$	1.26892	0.0582219
$476$	0	0
$477$	−11.7301	−0.537083
$478$	4.41369	0.201877
$479$	−28.6003	−1.30678	−0.653391	−	0.757021i	$-0.726654\pi$
$479$	−28.6003	−1.30678	−0.653391	+	0.757021i	$0.726654\pi$
$480$	−18.0260	−0.822773
$481$	46.2058	2.10680
$482$	9.95583	0.453476
$483$	−4.89432	−0.222699
$484$	5.06999	0.230454
$485$	−14.8075	−0.672372
$486$	6.76754	0.306982
$487$	0.617883	0.0279990	0.0139995	−	0.999902i	$-0.495544\pi$
$487$	0.617883	0.0279990	0.0139995	+	0.999902i	$0.495544\pi$
$488$	31.4540	1.42386
$489$	16.4352	0.743224
$490$	−2.58018	−0.116561
$491$	25.4667	1.14930	0.574648	−	0.818401i	$-0.305139\pi$
$491$	25.4667	1.14930	0.574648	+	0.818401i	$0.305139\pi$
$492$	9.61515	0.433485
$493$	0	0
$494$	4.09827	0.184390
$495$	17.6572	0.793631
$496$	5.28869	0.237469
$497$	−12.5802	−0.564301
$498$	0.523216	0.0234459
$499$	36.4603	1.63219	0.816093	−	0.577921i	$-0.196136\pi$
$499$	36.4603	1.63219	0.816093	+	0.577921i	$0.196136\pi$
$500$	1.44062	0.0644267
$501$	35.6395	1.59226
$502$	2.68776	0.119961
$503$	−30.1881	−1.34602	−0.673011	−	0.739632i	$-0.734999\pi$
$503$	−30.1881	−1.34602	−0.673011	+	0.739632i	$0.734999\pi$
$504$	−53.7025	−2.39210
$505$	−0.284213	−0.0126473
$506$	1.00719	0.0447751
$507$	17.3677	0.771326
$508$	−7.87323	−0.349318
$509$	40.1857	1.78120	0.890600	−	0.454787i	$-0.150285\pi$
$509$	40.1857	1.78120	0.890600	+	0.454787i	$0.150285\pi$
$510$	0	0
$511$	−20.9171	−0.925316
$512$	10.5314	0.465426
$513$	13.4844	0.595351
$514$	18.3606	0.809852
$515$	14.0842	0.620623
$516$	9.57679	0.421595
$517$	22.9637	1.00994
$518$	25.8695	1.13664
$519$	33.9086	1.48842
$520$	11.1123	0.487308
$521$	35.3560	1.54897	0.774487	−	0.632590i	$-0.218008\pi$
$521$	35.3560	1.54897	0.774487	+	0.632590i	$0.218008\pi$
$522$	2.14554	0.0939079
$523$	24.5035	1.07146	0.535732	−	0.844388i	$-0.320036\pi$
$523$	24.5035	1.07146	0.535732	+	0.844388i	$0.320036\pi$
$524$	14.3767	0.628050
$525$	9.94040	0.433835
$526$	10.9496	0.477424
$527$	0	0
$528$	−8.04585	−0.350150
$529$	−22.7576	−0.989460
$530$	1.35894	0.0590288
$531$	−19.4957	−0.846041
$532$	−5.90934	−0.256202
$533$	−9.37286	−0.405984
$534$	−30.6821	−1.32774
$535$	−18.7099	−0.808898
$536$	−10.8436	−0.468371
$537$	−64.8004	−2.79634
$538$	14.0307	0.604905
$539$	−9.43558	−0.406419
$540$	15.3091	0.658798
$541$	−25.5508	−1.09851	−0.549257	−	0.835653i	$-0.685089\pi$
$541$	−25.5508	−1.09851	−0.549257	+	0.835653i	$0.685089\pi$
$542$	−4.31089	−0.185169
$543$	−69.6778	−2.99016
$544$	0	0
$545$	3.53078	0.151242
$546$	32.1049	1.37396
$547$	−11.7618	−0.502896	−0.251448	−	0.967871i	$-0.580907\pi$
$547$	−11.7618	−0.502896	−0.251448	+	0.967871i	$0.580907\pi$
$548$	4.43384	0.189404
$549$	−78.9110	−3.36784
$550$	−2.04561	−0.0872251
$551$	0.563857	0.0240211
$552$	3.89607	0.165828
$553$	23.3444	0.992703
$554$	0.0921816	0.00391642
$555$	−32.9026	−1.39664
$556$	9.66646	0.409949
$557$	−35.6812	−1.51186	−0.755931	−	0.654651i	$-0.772816\pi$
$557$	−35.6812	−1.51186	−0.755931	+	0.654651i	$0.772816\pi$
$558$	26.6931	1.13001
$559$	−9.33546	−0.394848
$560$	−3.09247	−0.130681
$561$	0	0
$562$	1.36392	0.0575335
$563$	30.1232	1.26954	0.634771	−	0.772700i	$-0.281094\pi$
$563$	30.1232	1.26954	0.634771	+	0.772700i	$0.281094\pi$
$564$	37.1938	1.56614
$565$	2.84155	0.119545
$566$	−21.4111	−0.899976
$567$	43.0262	1.80693
$568$	10.0144	0.420193
$569$	−24.3985	−1.02284	−0.511420	−	0.859331i	$-0.670880\pi$
$569$	−24.3985	−1.02284	−0.511420	+	0.859331i	$0.670880\pi$
$570$	−2.91833	−0.122235
$571$	33.2818	1.39280	0.696399	−	0.717654i	$-0.254784\pi$
$571$	33.2818	1.39280	0.696399	+	0.717654i	$0.254784\pi$
$572$	17.0152	0.711442
$573$	−10.7676	−0.449822
$574$	−5.24762	−0.219032
$575$	−0.492367	−0.0205331
$576$	15.9525	0.664689
$577$	18.0611	0.751895	0.375947	−	0.926641i	$-0.377317\pi$
$577$	18.0611	0.751895	0.375947	+	0.926641i	$0.377317\pi$
$578$	0	0
$579$	−37.8051	−1.57113
$580$	0.640156	0.0265810
$581$	0.735418	0.0305103
$582$	34.0550	1.41163
$583$	4.96959	0.205820
$584$	16.6508	0.689015
$585$	−27.8783	−1.15263
$586$	−1.05910	−0.0437510
$587$	41.8303	1.72652	0.863261	−	0.504758i	$-0.168418\pi$
$587$	41.8303	1.72652	0.863261	+	0.504758i	$0.168418\pi$
$588$	−15.2826	−0.630244
$589$	7.01504	0.289050
$590$	2.25860	0.0929852
$591$	−52.2008	−2.14725
$592$	10.2360	0.420699
$593$	20.6659	0.848648	0.424324	−	0.905510i	$-0.360512\pi$
$593$	20.6659	0.848648	0.424324	+	0.905510i	$0.360512\pi$
$594$	−21.7381	−0.891925
$595$	0	0
$596$	33.1219	1.35673
$597$	−35.6023	−1.45711
$598$	−1.59022	−0.0650288
$599$	9.21817	0.376644	0.188322	−	0.982107i	$-0.439695\pi$
$599$	9.21817	0.376644	0.188322	+	0.982107i	$0.439695\pi$
$600$	−7.91295	−0.323045
$601$	−1.62070	−0.0661098	−0.0330549	−	0.999454i	$-0.510524\pi$
$601$	−1.62070	−0.0661098	−0.0330549	+	0.999454i	$0.510524\pi$
$602$	−5.22669	−0.213024
$603$	27.2040	1.10783
$604$	−0.281993	−0.0114741
$605$	3.51930	0.143080
$606$	0.653651	0.0265527
$607$	−25.0157	−1.01536	−0.507679	−	0.861547i	$-0.669496\pi$
$607$	−25.0157	−1.01536	−0.507679	+	0.861547i	$0.669496\pi$
$608$	7.43849	0.301671
$609$	4.41712	0.178991
$610$	9.14195	0.370147
$611$	−36.2566	−1.46678
$612$	0	0
$613$	4.83538	0.195299	0.0976495	−	0.995221i	$-0.468868\pi$
$613$	4.83538	0.195299	0.0976495	+	0.995221i	$0.468868\pi$
$614$	−16.2570	−0.656078
$615$	6.67430	0.269134
$616$	22.7517	0.916694
$617$	16.8134	0.676883	0.338441	−	0.940987i	$-0.390100\pi$
$617$	16.8134	0.676883	0.338441	+	0.940987i	$0.390100\pi$
$618$	−32.3916	−1.30298
$619$	12.7224	0.511356	0.255678	−	0.966762i	$-0.417701\pi$
$619$	12.7224	0.511356	0.255678	+	0.966762i	$0.417701\pi$
$620$	7.96429	0.319854
$621$	−5.23223	−0.209962
$622$	6.47022	0.259432
$623$	−43.1259	−1.72780
$624$	12.7033	0.508539
$625$	1.00000	0.0400000
$626$	7.69008	0.307357
$627$	−10.6722	−0.426206
$628$	−17.0833	−0.681697
$629$	0	0
$630$	−15.6083	−0.621851
$631$	4.23998	0.168791	0.0843955	−	0.996432i	$-0.473104\pi$
$631$	4.23998	0.168791	0.0843955	+	0.996432i	$0.473104\pi$
$632$	−18.5830	−0.739193
$633$	20.4914	0.814459
$634$	0.843396	0.0334955
$635$	−5.46515	−0.216878
$636$	8.04915	0.319169
$637$	14.8975	0.590261
$638$	−0.908988	−0.0359872
$639$	−25.1238	−0.993880
$640$	9.87602	0.390384
$641$	−21.2203	−0.838151	−0.419075	−	0.907951i	$-0.637646\pi$
$641$	−21.2203	−0.838151	−0.419075	+	0.907951i	$0.637646\pi$
$642$	43.0300	1.69826
$643$	8.16667	0.322062	0.161031	−	0.986949i	$-0.448518\pi$
$643$	8.16667	0.322062	0.161031	+	0.986949i	$0.448518\pi$
$644$	2.29295	0.0903548
$645$	6.64767	0.261752
$646$	0	0
$647$	23.4331	0.921249	0.460624	−	0.887595i	$-0.347626\pi$
$647$	23.4331	0.921249	0.460624	+	0.887595i	$0.347626\pi$
$648$	−34.2505	−1.34549
$649$	8.25960	0.324218
$650$	3.22974	0.126681
$651$	54.9541	2.15382
$652$	−7.69973	−0.301545
$653$	16.8073	0.657721	0.328860	−	0.944379i	$-0.393335\pi$
$653$	16.8073	0.657721	0.328860	+	0.944379i	$0.393335\pi$
$654$	−8.12029	−0.317529
$655$	9.97951	0.389932
$656$	−2.07638	−0.0810692
$657$	−41.7731	−1.62972
$658$	−20.2991	−0.791342
$659$	14.0972	0.549150	0.274575	−	0.961566i	$-0.411463\pi$
$659$	14.0972	0.549150	0.274575	+	0.961566i	$0.411463\pi$
$660$	−12.1163	−0.471627
$661$	−10.3907	−0.404152	−0.202076	−	0.979370i	$-0.564769\pi$
$661$	−10.3907	−0.404152	−0.202076	+	0.979370i	$0.564769\pi$
$662$	−25.6235	−0.995886
$663$	0	0
$664$	−0.585422	−0.0227188
$665$	−4.10193	−0.159066
$666$	51.6634	2.00192
$667$	−0.218788	−0.00847151
$668$	−16.6968	−0.646018
$669$	−38.7231	−1.49712
$670$	−3.15163	−0.121758
$671$	33.4317	1.29062
$672$	58.2714	2.24787
$673$	19.8244	0.764174	0.382087	−	0.924126i	$-0.375205\pi$
$673$	19.8244	0.764174	0.382087	+	0.924126i	$0.375205\pi$
$674$	10.2810	0.396010
$675$	10.6267	0.409022
$676$	−8.13660	−0.312946
$677$	−3.34594	−0.128595	−0.0642974	−	0.997931i	$-0.520481\pi$
$677$	−3.34594	−0.128595	−0.0642974	+	0.997931i	$0.520481\pi$
$678$	−6.53516	−0.250981
$679$	47.8669	1.83696
$680$	0	0
$681$	24.7314	0.947709
$682$	−11.3089	−0.433039
$683$	50.2828	1.92402	0.962009	−	0.273017i	$-0.0880215\pi$
$683$	50.2828	1.92402	0.962009	+	0.273017i	$0.0880215\pi$
$684$	−11.8014	−0.451239
$685$	3.07772	0.117594
$686$	−8.58333	−0.327713
$687$	−66.5113	−2.53756
$688$	−2.06810	−0.0788456
$689$	−7.84631	−0.298921
$690$	1.13237	0.0431087
$691$	38.9162	1.48044	0.740221	−	0.672364i	$-0.234721\pi$
$691$	38.9162	1.48044	0.740221	+	0.672364i	$0.234721\pi$
$692$	−15.8859	−0.603890
$693$	−57.0790	−2.16825
$694$	14.1196	0.535972
$695$	6.70991	0.254521
$696$	−3.51620	−0.133281
$697$	0	0
$698$	−5.27270	−0.199575
$699$	67.4986	2.55303
$700$	−4.65699	−0.176018
$701$	−37.5419	−1.41794	−0.708969	−	0.705239i	$-0.750840\pi$
$701$	−37.5419	−1.41794	−0.708969	+	0.705239i	$0.750840\pi$
$702$	34.3215	1.29538
$703$	13.5773	0.512079
$704$	−6.75850	−0.254721
$705$	25.8178	0.972356
$706$	6.43789	0.242293
$707$	0.918754	0.0345533
$708$	13.3779	0.502772
$709$	−13.7546	−0.516566	−0.258283	−	0.966069i	$-0.583157\pi$
$709$	−13.7546	−0.516566	−0.258283	+	0.966069i	$0.583157\pi$
$710$	2.91062	0.109234
$711$	46.6206	1.74841
$712$	34.3299	1.28657
$713$	−2.72198	−0.101939
$714$	0	0
$715$	11.8110	0.441707
$716$	30.3584	1.13455
$717$	18.1467	0.677703
$718$	6.86660	0.256259
$719$	−0.528983	−0.0197278	−0.00986388	−	0.999951i	$-0.503140\pi$
$719$	−0.528983	−0.0197278	−0.00986388	+	0.999951i	$0.503140\pi$
$720$	−6.17592	−0.230163
$721$	−45.5288	−1.69558
$722$	−13.0061	−0.484038
$723$	40.9331	1.52232
$724$	32.6434	1.21318
$725$	0.444360	0.0165031
$726$	−8.09390	−0.300393
$727$	26.7632	0.992591	0.496296	−	0.868154i	$-0.334693\pi$
$727$	26.7632	0.992591	0.496296	+	0.868154i	$0.334693\pi$
$728$	−35.9219	−1.33135
$729$	−12.1055	−0.448351
$730$	4.83947	0.179117
$731$	0	0
$732$	54.1486	2.00139
$733$	17.3486	0.640787	0.320393	−	0.947285i	$-0.396185\pi$
$733$	17.3486	0.640787	0.320393	+	0.947285i	$0.396185\pi$
$734$	5.09783	0.188164
$735$	−10.6083	−0.391294
$736$	−2.88629	−0.106390
$737$	−11.5253	−0.424542
$738$	−10.4799	−0.385772
$739$	30.2467	1.11264	0.556321	−	0.830967i	$-0.312212\pi$
$739$	30.2467	1.11264	0.556321	+	0.830967i	$0.312212\pi$
$740$	15.4146	0.566651
$741$	16.8499	0.618998
$742$	−4.39295	−0.161270
$743$	−7.18076	−0.263437	−0.131718	−	0.991287i	$-0.542049\pi$
$743$	−7.18076	−0.263437	−0.131718	+	0.991287i	$0.542049\pi$
$744$	−43.7457	−1.60379
$745$	22.9914	0.842339
$746$	−7.82669	−0.286555
$747$	1.46869	0.0537366
$748$	0	0
$749$	60.4819	2.20996
$750$	−2.29986	−0.0839790
$751$	31.2967	1.14203	0.571016	−	0.820939i	$-0.306549\pi$
$751$	31.2967	1.14203	0.571016	+	0.820939i	$0.306549\pi$
$752$	−8.03197	−0.292896
$753$	11.0506	0.402708
$754$	1.43517	0.0522658
$755$	−0.195743	−0.00712383
$756$	−49.4884	−1.79988
$757$	10.7757	0.391649	0.195824	−	0.980639i	$-0.437262\pi$
$757$	10.7757	0.391649	0.195824	+	0.980639i	$0.437262\pi$
$758$	18.9536	0.688425
$759$	4.14104	0.150310
$760$	3.26530	0.118445
$761$	33.1409	1.20136	0.600678	−	0.799491i	$-0.294898\pi$
$761$	33.1409	1.20136	0.600678	+	0.799491i	$0.294898\pi$
$762$	12.5691	0.455329
$763$	−11.4137	−0.413203
$764$	5.04452	0.182504
$765$	0	0
$766$	5.75182	0.207822
$767$	−13.0408	−0.470876
$768$	−37.9105	−1.36798
$769$	−11.4864	−0.414210	−0.207105	−	0.978319i	$-0.566404\pi$
$769$	−11.4864	−0.414210	−0.207105	+	0.978319i	$0.566404\pi$
$770$	6.61268	0.238304
$771$	75.4892	2.71868
$772$	17.7114	0.637446
$773$	−3.20903	−0.115421	−0.0577104	−	0.998333i	$-0.518380\pi$
$773$	−3.20903	−0.115421	−0.0577104	+	0.998333i	$0.518380\pi$
$774$	−10.4381	−0.375191
$775$	5.52836	0.198585
$776$	−38.1039	−1.36785
$777$	106.362	3.81570
$778$	11.8454	0.424678
$779$	−2.75416	−0.0986781
$780$	19.1300	0.684965
$781$	10.6440	0.380873
$782$	0	0
$783$	4.72208	0.168754
$784$	3.30027	0.117867
$785$	−11.8582	−0.423239
$786$	−22.9515	−0.818651
$787$	3.37029	0.120138	0.0600690	−	0.998194i	$-0.480868\pi$
$787$	3.37029	0.120138	0.0600690	+	0.998194i	$0.480868\pi$
$788$	24.4556	0.871195
$789$	45.0188	1.60271
$790$	−5.40106	−0.192161
$791$	−9.18564	−0.326604
$792$	45.4371	1.61454
$793$	−52.7841	−1.87442
$794$	21.8122	0.774085
$795$	5.58726	0.198160
$796$	16.6794	0.591185
$797$	−21.3498	−0.756247	−0.378124	−	0.925755i	$-0.623431\pi$
$797$	−21.3498	−0.756247	−0.378124	+	0.925755i	$0.623431\pi$
$798$	9.43385	0.333955
$799$	0	0
$800$	5.86207	0.207256
$801$	−86.1259	−3.04311
$802$	12.2552	0.432747
$803$	17.6977	0.624538
$804$	−18.6674	−0.658347
$805$	1.59163	0.0560977
$806$	17.8552	0.628922
$807$	57.6867	2.03067
$808$	−0.731364	−0.0257293
$809$	2.72968	0.0959705	0.0479852	−	0.998848i	$-0.484720\pi$
$809$	2.72968	0.0959705	0.0479852	+	0.998848i	$0.484720\pi$
$810$	−9.95474	−0.349774
$811$	37.3353	1.31102	0.655510	−	0.755187i	$-0.272454\pi$
$811$	37.3353	1.31102	0.655510	+	0.755187i	$0.272454\pi$
$812$	−2.06938	−0.0726211
$813$	−17.7241	−0.621611
$814$	−21.8879	−0.767170
$815$	−5.34472	−0.187217
$816$	0	0
$817$	−2.74317	−0.0959715
$818$	25.4269	0.889032
$819$	90.1199	3.14905
$820$	−3.12685	−0.109194
$821$	−42.2293	−1.47381	−0.736906	−	0.675995i	$-0.763714\pi$
$821$	−42.2293	−1.47381	−0.736906	+	0.675995i	$0.763714\pi$
$822$	−7.07832	−0.246885
$823$	20.7606	0.723668	0.361834	−	0.932243i	$-0.382151\pi$
$823$	20.7606	0.723668	0.361834	+	0.932243i	$0.382151\pi$
$824$	36.2427	1.26257
$825$	−8.41047	−0.292815
$826$	−7.30120	−0.254041
$827$	11.5073	0.400149	0.200075	−	0.979781i	$-0.435881\pi$
$827$	11.5073	0.400149	0.200075	+	0.979781i	$0.435881\pi$
$828$	4.57920	0.159138
$829$	−11.7508	−0.408121	−0.204060	−	0.978958i	$-0.565414\pi$
$829$	−11.7508	−0.408121	−0.204060	+	0.978958i	$0.565414\pi$
$830$	−0.170150	−0.00590599
$831$	0.379002	0.0131474
$832$	10.6708	0.369942
$833$	0	0
$834$	−15.4318	−0.534361
$835$	−11.5900	−0.401087
$836$	4.99983	0.172923
$837$	58.7483	2.03064
$838$	−0.667839	−0.0230701
$839$	−36.5993	−1.26355	−0.631775	−	0.775152i	$-0.717673\pi$
$839$	−36.5993	−1.26355	−0.631775	+	0.775152i	$0.717673\pi$
$840$	25.5796	0.882578
$841$	−28.8025	−0.993191
$842$	25.1842	0.867904
$843$	5.60772	0.193140
$844$	−9.60003	−0.330447
$845$	−5.64797	−0.194296
$846$	−40.5390	−1.39376
$847$	−11.3766	−0.390903
$848$	−1.73821	−0.0596902
$849$	−88.0312	−3.02122
$850$	0	0
$851$	−5.26829	−0.180595
$852$	17.2399	0.590628
$853$	38.0771	1.30374	0.651868	−	0.758332i	$-0.273986\pi$
$853$	38.0771	1.30374	0.651868	+	0.758332i	$0.273986\pi$
$854$	−29.5524	−1.01126
$855$	−8.19188	−0.280157
$856$	−48.1459	−1.64559
$857$	−20.2277	−0.690965	−0.345482	−	0.938425i	$-0.612285\pi$
$857$	−20.2277	−0.690965	−0.345482	+	0.938425i	$0.612285\pi$
$858$	−27.1636	−0.927351
$859$	−2.60725	−0.0889581	−0.0444790	−	0.999010i	$-0.514163\pi$
$859$	−2.60725	−0.0889581	−0.0444790	+	0.999010i	$0.514163\pi$
$860$	−3.11437	−0.106199
$861$	−21.5755	−0.735290
$862$	−12.1887	−0.415150
$863$	11.2563	0.383169	0.191584	−	0.981476i	$-0.438637\pi$
$863$	11.2563	0.383169	0.191584	+	0.981476i	$0.438637\pi$
$864$	62.2945	2.11930
$865$	−11.0271	−0.374932
$866$	−26.1730	−0.889396
$867$	0	0
$868$	−25.7455	−0.873860
$869$	−19.7514	−0.670021
$870$	−1.02197	−0.0346479
$871$	18.1970	0.616580
$872$	9.08573	0.307682
$873$	95.5940	3.23537
$874$	−0.467276	−0.0158059
$875$	−3.23262	−0.109282
$876$	28.6646	0.968487
$877$	6.00107	0.202642	0.101321	−	0.994854i	$-0.467693\pi$
$877$	6.00107	0.202642	0.101321	+	0.994854i	$0.467693\pi$
$878$	−16.6618	−0.562309
$879$	−4.35446	−0.146872
$880$	2.61651	0.0882025
$881$	−34.3314	−1.15665	−0.578327	−	0.815805i	$-0.696294\pi$
$881$	−34.3314	−1.15665	−0.578327	+	0.815805i	$0.696294\pi$
$882$	16.6571	0.560874
$883$	11.8244	0.397921	0.198961	−	0.980007i	$-0.436243\pi$
$883$	11.8244	0.397921	0.198961	+	0.980007i	$0.436243\pi$
$884$	0	0
$885$	9.28618	0.312152
$886$	−6.58095	−0.221091
$887$	−24.2352	−0.813738	−0.406869	−	0.913487i	$-0.633379\pi$
$887$	−24.2352	−0.813738	−0.406869	+	0.913487i	$0.633379\pi$
$888$	−84.6680	−2.84127
$889$	17.6668	0.592524
$890$	9.97781	0.334457
$891$	−36.4040	−1.21958
$892$	18.1414	0.607420
$893$	−10.6538	−0.356515
$894$	−52.8769	−1.76847
$895$	21.0731	0.704396
$896$	−31.9254	−1.06655
$897$	−6.53813	−0.218302
$898$	−6.63163	−0.221300
$899$	2.45659	0.0819317
$900$	−9.30039	−0.310013
$901$	0	0
$902$	4.43996	0.147835
$903$	−21.4894	−0.715122
$904$	7.31213	0.243198
$905$	22.6592	0.753218
$906$	0.450182	0.0149563
$907$	−44.7796	−1.48688	−0.743441	−	0.668802i	$-0.766808\pi$
$907$	−44.7796	−1.48688	−0.743441	+	0.668802i	$0.766808\pi$
$908$	−11.5864	−0.384509
$909$	1.83483	0.0608574
$910$	−10.4405	−0.346100
$911$	−9.94858	−0.329611	−0.164806	−	0.986326i	$-0.552700\pi$
$911$	−9.94858	−0.329611	−0.164806	+	0.986326i	$0.552700\pi$
$912$	3.73279	0.123605
$913$	−0.622230	−0.0205928
$914$	−13.8182	−0.457066
$915$	37.5869	1.24258
$916$	31.1600	1.02955
$917$	−32.2600	−1.06532
$918$	0	0
$919$	−33.3601	−1.10045	−0.550224	−	0.835017i	$-0.685458\pi$
$919$	−33.3601	−1.10045	−0.550224	+	0.835017i	$0.685458\pi$
$920$	−1.26700	−0.0417719
$921$	−66.8401	−2.20246
$922$	−18.3762	−0.605189
$923$	−16.8054	−0.553158
$924$	39.1675	1.28852
$925$	10.6999	0.351812
$926$	−7.41132	−0.243551
$927$	−90.9247	−2.98636
$928$	2.60487	0.0855091
$929$	24.8961	0.816813	0.408407	−	0.912800i	$-0.366085\pi$
$929$	24.8961	0.816813	0.408407	+	0.912800i	$0.366085\pi$
$930$	−12.7145	−0.416923
$931$	4.37755	0.143468
$932$	−31.6225	−1.03583
$933$	26.6021	0.870915
$934$	−21.9917	−0.719592
$935$	0	0
$936$	−71.7390	−2.34486
$937$	31.2460	1.02076	0.510381	−	0.859948i	$-0.329504\pi$
$937$	31.2460	1.02076	0.510381	+	0.859948i	$0.329504\pi$
$938$	10.1880	0.332650
$939$	31.6176	1.03180
$940$	−12.0954	−0.394510
$941$	−1.73372	−0.0565177	−0.0282589	−	0.999601i	$-0.508996\pi$
$941$	−1.73372	−0.0565177	−0.0282589	+	0.999601i	$0.508996\pi$
$942$	27.2723	0.888579
$943$	1.06867	0.0348008
$944$	−2.88895	−0.0940272
$945$	−34.3521	−1.11747
$946$	4.42225	0.143780
$947$	−10.8513	−0.352619	−0.176309	−	0.984335i	$-0.556416\pi$
$947$	−10.8513	−0.352619	−0.176309	+	0.984335i	$0.556416\pi$
$948$	−31.9910	−1.03902
$949$	−27.9423	−0.907044
$950$	0.949042	0.0307910
$951$	3.46760	0.112445
$952$	0	0
$953$	−16.9007	−0.547466	−0.273733	−	0.961806i	$-0.588258\pi$
$953$	−16.9007	−0.547466	−0.273733	+	0.961806i	$0.588258\pi$
$954$	−8.77308	−0.284039
$955$	3.50162	0.113310
$956$	−8.50159	−0.274961
$957$	−3.73728	−0.120809
$958$	−21.3906	−0.691098
$959$	−9.94910	−0.321273
$960$	−7.59851	−0.245241
$961$	−0.437196	−0.0141031
$962$	34.5580	1.11419
$963$	120.787	3.89231
$964$	−19.1768	−0.617643
$965$	12.2942	0.395765
$966$	−3.66053	−0.117776
$967$	31.2356	1.00447	0.502234	−	0.864732i	$-0.332511\pi$
$967$	31.2356	1.00447	0.502234	+	0.864732i	$0.332511\pi$
$968$	9.05619	0.291077
$969$	0	0
$970$	−11.0747	−0.355587
$971$	17.3888	0.558033	0.279016	−	0.960286i	$-0.409992\pi$
$971$	17.3888	0.558033	0.279016	+	0.960286i	$0.409992\pi$
$972$	−13.0356	−0.418116
$973$	−21.6906	−0.695368
$974$	0.462124	0.0148074
$975$	13.2790	0.425268
$976$	−11.6933	−0.374294
$977$	−9.17338	−0.293482	−0.146741	−	0.989175i	$-0.546878\pi$
$977$	−9.17338	−0.293482	−0.146741	+	0.989175i	$0.546878\pi$
$978$	12.2921	0.393058
$979$	36.4884	1.16617
$980$	4.96991	0.158758
$981$	−22.7940	−0.727757
$982$	19.0469	0.607811
$983$	−37.2969	−1.18959	−0.594793	−	0.803879i	$-0.702766\pi$
$983$	−37.2969	−1.18959	−0.594793	+	0.803879i	$0.702766\pi$
$984$	17.1749	0.547516
$985$	16.9757	0.540891
$986$	0	0
$987$	−83.4593	−2.65654
$988$	−7.89405	−0.251143
$989$	1.06441	0.0338463
$990$	13.2061	0.419716
$991$	−35.0682	−1.11398	−0.556990	−	0.830519i	$-0.688044\pi$
$991$	−35.0682	−1.11398	−0.556990	+	0.830519i	$0.688044\pi$
$992$	32.4077	1.02894
$993$	−105.350	−3.34319
$994$	−9.40894	−0.298433
$995$	11.5779	0.367044
$996$	−1.00781	−0.0319338
$997$	−37.3576	−1.18313	−0.591563	−	0.806259i	$-0.701489\pi$
$997$	−37.3576	−1.18313	−0.591563	+	0.806259i	$0.701489\pi$
$998$	27.2692	0.863190
$999$	113.705	3.59747

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1445.2.a.q.1.9		12
5.4	even	2		7225.2.a.bq.1.4		12
17.4	even	4		1445.2.d.j.866.8		24
17.10	odd	16		85.2.l.a.66.2	✓	24
17.12	odd	16		85.2.l.a.76.2	yes	24
17.13	even	4		1445.2.d.j.866.7		24
17.16	even	2		1445.2.a.p.1.9		12
51.29	even	16		765.2.be.b.586.5		24
51.44	even	16		765.2.be.b.406.5		24
85.12	even	16		425.2.n.f.399.2		24
85.27	even	16		425.2.n.c.49.5		24
85.29	odd	16		425.2.m.b.76.5		24
85.44	odd	16		425.2.m.b.151.5		24
85.63	even	16		425.2.n.c.399.5		24
85.78	even	16		425.2.n.f.49.2		24
85.84	even	2		7225.2.a.bs.1.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.66.2	✓	24	17.10	odd	16
85.2.l.a.76.2	yes	24	17.12	odd	16
425.2.m.b.76.5		24	85.29	odd	16
425.2.m.b.151.5		24	85.44	odd	16
425.2.n.c.49.5		24	85.27	even	16
425.2.n.c.399.5		24	85.63	even	16
425.2.n.f.49.2		24	85.78	even	16
425.2.n.f.399.2		24	85.12	even	16
765.2.be.b.406.5		24	51.44	even	16
765.2.be.b.586.5		24	51.29	even	16
1445.2.a.p.1.9		12	17.16	even	2
1445.2.a.q.1.9		12	1.1	even	1	trivial
1445.2.d.j.866.7		24	17.13	even	4
1445.2.d.j.866.8		24	17.4	even	4
7225.2.a.bq.1.4		12	5.4	even	2
7225.2.a.bs.1.4		12	85.84	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1445.a (trivial)

\(f(q)\)	\(=\)	\(q+0.747914 q^{2} +3.07503 q^{3} -1.44062 q^{4} -1.00000 q^{5} +2.29986 q^{6} +3.23262 q^{7} -2.57329 q^{8} +6.45581 q^{9} -0.747914 q^{10} -2.73509 q^{11} -4.42996 q^{12} +4.31833 q^{13} +2.41772 q^{14} -3.07503 q^{15} +0.956646 q^{16} +4.82839 q^{18} +1.26892 q^{19} +1.44062 q^{20} +9.94040 q^{21} -2.04561 q^{22} -0.492367 q^{23} -7.91295 q^{24} +1.00000 q^{25} +3.22974 q^{26} +10.6267 q^{27} -4.65699 q^{28} +0.444360 q^{29} -2.29986 q^{30} +5.52836 q^{31} +5.86207 q^{32} -8.41047 q^{33} -3.23262 q^{35} -9.30039 q^{36} +10.6999 q^{37} +0.949042 q^{38} +13.2790 q^{39} +2.57329 q^{40} -2.17048 q^{41} +7.43457 q^{42} -2.16182 q^{43} +3.94023 q^{44} -6.45581 q^{45} -0.368248 q^{46} -8.39597 q^{47} +2.94172 q^{48} +3.44983 q^{49} +0.747914 q^{50} -6.22109 q^{52} -1.81698 q^{53} +7.94786 q^{54} +2.73509 q^{55} -8.31847 q^{56} +3.90196 q^{57} +0.332343 q^{58} -3.01987 q^{59} +4.42996 q^{60} -12.2233 q^{61} +4.13474 q^{62} +20.8692 q^{63} +2.47104 q^{64} -4.31833 q^{65} -6.29031 q^{66} +4.21389 q^{67} -1.51404 q^{69} -2.41772 q^{70} -3.89165 q^{71} -16.6127 q^{72} -6.47062 q^{73} +8.00263 q^{74} +3.07503 q^{75} -1.82803 q^{76} -8.84149 q^{77} +9.93155 q^{78} +7.22150 q^{79} -0.956646 q^{80} +13.3100 q^{81} -1.62333 q^{82} +0.227499 q^{83} -14.3204 q^{84} -1.61686 q^{86} +1.36642 q^{87} +7.03818 q^{88} -13.3408 q^{89} -4.82839 q^{90} +13.9595 q^{91} +0.709315 q^{92} +16.9999 q^{93} -6.27946 q^{94} -1.26892 q^{95} +18.0260 q^{96} +14.8075 q^{97} +2.58018 q^{98} -17.6572 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + 8 q^{3} + 12 q^{4} - 12 q^{5} + 8 q^{6} + 16 q^{7} - 12 q^{8} + 12 q^{9} + 4 q^{10} + 16 q^{11} + 16 q^{12} - 8 q^{13} - 16 q^{14} - 8 q^{15} + 12 q^{16} + 4 q^{18} - 12 q^{20} + 16 q^{21}+ \cdots + 56 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 + 8 * q^3 + 12 * q^4 - 12 * q^5 + 8 * q^6 + 16 * q^7 - 12 * q^8 + 12 * q^9 + 4 * q^10 + 16 * q^11 + 16 * q^12 - 8 * q^13 - 16 * q^14 - 8 * q^15 + 12 * q^16 + 4 * q^18 - 12 * q^20 + 16 * q^21 + 16 * q^22 + 16 * q^23 + 12 * q^25 + 16 * q^26 + 32 * q^27 + 40 * q^28 + 16 * q^29 - 8 * q^30 + 24 * q^31 - 28 * q^32 - 16 * q^35 + 12 * q^36 + 24 * q^37 - 24 * q^38 + 8 * q^39 + 12 * q^40 + 8 * q^41 - 16 * q^43 + 8 * q^44 - 12 * q^45 + 40 * q^46 - 32 * q^47 - 24 * q^48 + 20 * q^49 - 4 * q^50 - 24 * q^52 + 8 * q^54 - 16 * q^55 - 24 * q^56 + 32 * q^57 - 16 * q^58 + 8 * q^59 - 16 * q^60 + 24 * q^61 + 8 * q^62 + 48 * q^63 + 36 * q^64 + 8 * q^65 + 40 * q^66 - 8 * q^67 + 48 * q^69 + 16 * q^70 - 16 * q^71 + 12 * q^72 + 16 * q^73 + 8 * q^75 + 16 * q^76 + 24 * q^77 - 24 * q^78 + 40 * q^79 - 12 * q^80 + 36 * q^81 - 16 * q^82 - 40 * q^83 + 32 * q^84 - 8 * q^86 - 32 * q^87 + 48 * q^88 + 8 * q^89 - 4 * q^90 + 72 * q^91 - 8 * q^92 + 24 * q^93 - 16 * q^94 + 8 * q^96 + 32 * q^97 - 60 * q^98 + 56 * q^99

Introduction

L-functions

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Groups

Database

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