LMFDB - Embedded newform 2667.2.a.o.1.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2667,2,Mod(1,2667)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2667, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2667.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2667 = 3 \cdot 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2667.a (trivial)

Newform invariants

comment:select newform

sage:traces = [16,5,-16,19] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	yes
Analytic conductor:	$21.2961022191$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} - 13 x^{14} + 98 x^{13} + 9 x^{12} - 712 x^{11} + 565 x^{10} + 2282 x^{9} - 3082 x^{8} + \cdots + 4 $ x^16 - 5x^15 - 13x^14 + 98x^13 + 9x^12 - 712x^11 + 565x^10 + 2282x^9 - 3082x^8 - 2747x^7 + 5821x^6 - 158x^5 - 3341x^4 + 1002x^3 + 416x^2 - 148*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Root			$2.76723$ of defining polynomial
Character	$\chi$	$=$	2667.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.76723 q^{2} -1.00000 q^{3} +5.65757 q^{4} -3.65468 q^{5} -2.76723 q^{6} -1.00000 q^{7} +10.1213 q^{8} +1.00000 q^{9} -10.1133 q^{10} +0.555158 q^{11} -5.65757 q^{12} +1.94794 q^{13} -2.76723 q^{14} +3.65468 q^{15} +16.6929 q^{16} +6.99463 q^{17} +2.76723 q^{18} -2.93493 q^{19} -20.6766 q^{20} +1.00000 q^{21} +1.53625 q^{22} -4.18318 q^{23} -10.1213 q^{24} +8.35670 q^{25} +5.39040 q^{26} -1.00000 q^{27} -5.65757 q^{28} +8.74311 q^{29} +10.1133 q^{30} +0.936637 q^{31} +25.9505 q^{32} -0.555158 q^{33} +19.3558 q^{34} +3.65468 q^{35} +5.65757 q^{36} +2.96085 q^{37} -8.12162 q^{38} -1.94794 q^{39} -36.9902 q^{40} -0.248112 q^{41} +2.76723 q^{42} +0.630338 q^{43} +3.14084 q^{44} -3.65468 q^{45} -11.5758 q^{46} +4.41168 q^{47} -16.6929 q^{48} +1.00000 q^{49} +23.1249 q^{50} -6.99463 q^{51} +11.0206 q^{52} +7.79091 q^{53} -2.76723 q^{54} -2.02893 q^{55} -10.1213 q^{56} +2.93493 q^{57} +24.1942 q^{58} +3.50891 q^{59} +20.6766 q^{60} +0.0482375 q^{61} +2.59189 q^{62} -1.00000 q^{63} +38.4252 q^{64} -7.11910 q^{65} -1.53625 q^{66} +1.92412 q^{67} +39.5726 q^{68} +4.18318 q^{69} +10.1133 q^{70} -6.19394 q^{71} +10.1213 q^{72} +12.2682 q^{73} +8.19335 q^{74} -8.35670 q^{75} -16.6045 q^{76} -0.555158 q^{77} -5.39040 q^{78} -15.7700 q^{79} -61.0073 q^{80} +1.00000 q^{81} -0.686584 q^{82} -13.8174 q^{83} +5.65757 q^{84} -25.5632 q^{85} +1.74429 q^{86} -8.74311 q^{87} +5.61894 q^{88} +4.29172 q^{89} -10.1133 q^{90} -1.94794 q^{91} -23.6666 q^{92} -0.936637 q^{93} +12.2081 q^{94} +10.7262 q^{95} -25.9505 q^{96} +12.7904 q^{97} +2.76723 q^{98} +0.555158 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 5 q^{2} - 16 q^{3} + 19 q^{4} - q^{5} - 5 q^{6} - 16 q^{7} + 6 q^{8} + 16 q^{9} - 12 q^{10} + 11 q^{11} - 19 q^{12} + 18 q^{13} - 5 q^{14} + q^{15} + 25 q^{16} - 5 q^{17} + 5 q^{18} - 11 q^{19}+ \cdots + 11 q^{99}+O(q^{100}) $ 16 * q + 5 * q^2 - 16 * q^3 + 19 * q^4 - q^5 - 5 * q^6 - 16 * q^7 + 6 * q^8 + 16 * q^9 - 12 * q^10 + 11 * q^11 - 19 * q^12 + 18 * q^13 - 5 * q^14 + q^15 + 25 * q^16 - 5 * q^17 + 5 * q^18 - 11 * q^19 - q^20 + 16 * q^21 + q^22 + 13 * q^23 - 6 * q^24 + 33 * q^25 + 8 * q^26 - 16 * q^27 - 19 * q^28 + 24 * q^29 + 12 * q^30 - 42 * q^31 + 42 * q^32 - 11 * q^33 + 9 * q^34 + q^35 + 19 * q^36 + 40 * q^37 + 38 * q^38 - 18 * q^39 - 61 * q^40 + 9 * q^41 + 5 * q^42 + 7 * q^43 + 3 * q^44 - q^45 + 24 * q^46 + 31 * q^47 - 25 * q^48 + 16 * q^49 + 6 * q^50 + 5 * q^51 + 52 * q^52 + 66 * q^53 - 5 * q^54 - 36 * q^55 - 6 * q^56 + 11 * q^57 + 19 * q^58 - 7 * q^59 + q^60 + 6 * q^61 + 52 * q^62 - 16 * q^63 + 10 * q^64 + 51 * q^65 - q^66 + 16 * q^67 + 14 * q^68 - 13 * q^69 + 12 * q^70 + 46 * q^71 + 6 * q^72 + 39 * q^73 + 72 * q^74 - 33 * q^75 + 24 * q^76 - 11 * q^77 - 8 * q^78 + 4 * q^79 - 2 * q^80 + 16 * q^81 - 18 * q^82 + 15 * q^83 + 19 * q^84 - 4 * q^85 + 14 * q^86 - 24 * q^87 + 58 * q^88 - q^89 - 12 * q^90 - 18 * q^91 + 26 * q^92 + 42 * q^93 + 5 * q^94 + 44 * q^95 - 42 * q^96 + 41 * q^97 + 5 * q^98 + 11 * 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 $

$2$	2.76723	1.95673	0.978364	−	0.206892i	$-0.0663348\pi$
$2$	2.76723	1.95673	0.978364	+	0.206892i	$0.0663348\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.65757	2.82878
$5$	−3.65468	−1.63442	−0.817212	−	0.576338i	$-0.804481\pi$
$5$	−3.65468	−1.63442	−0.817212	+	0.576338i	$0.804481\pi$
$6$	−2.76723	−1.12972
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	10.1213	3.57843
$9$	1.00000	0.333333
$10$	−10.1133	−3.19812
$11$	0.555158	0.167386	0.0836932	−	0.996492i	$-0.473328\pi$
$11$	0.555158	0.167386	0.0836932	+	0.996492i	$0.473328\pi$
$12$	−5.65757	−1.63320
$13$	1.94794	0.540261	0.270131	−	0.962824i	$-0.412933\pi$
$13$	1.94794	0.540261	0.270131	+	0.962824i	$0.412933\pi$
$14$	−2.76723	−0.739574
$15$	3.65468	0.943635
$16$	16.6929	4.17323
$17$	6.99463	1.69645	0.848224	−	0.529638i	$-0.177672\pi$
$17$	6.99463	1.69645	0.848224	+	0.529638i	$0.177672\pi$
$18$	2.76723	0.652243
$19$	−2.93493	−0.673318	−0.336659	−	0.941627i	$-0.609297\pi$
$19$	−2.93493	−0.673318	−0.336659	+	0.941627i	$0.609297\pi$
$20$	−20.6766	−4.62343
$21$	1.00000	0.218218
$22$	1.53625	0.327530
$23$	−4.18318	−0.872253	−0.436127	−	0.899885i	$-0.643650\pi$
$23$	−4.18318	−0.872253	−0.436127	+	0.899885i	$0.643650\pi$
$24$	−10.1213	−2.06601
$25$	8.35670	1.67134
$26$	5.39040	1.05714
$27$	−1.00000	−0.192450
$28$	−5.65757	−1.06918
$29$	8.74311	1.62355	0.811777	−	0.583967i	$-0.198500\pi$
$29$	8.74311	1.62355	0.811777	+	0.583967i	$0.198500\pi$
$30$	10.1133	1.84644
$31$	0.936637	0.168225	0.0841125	−	0.996456i	$-0.473194\pi$
$31$	0.936637	0.168225	0.0841125	+	0.996456i	$0.473194\pi$
$32$	25.9505	4.58744
$33$	−0.555158	−0.0966406
$34$	19.3558	3.31949
$35$	3.65468	0.617754
$36$	5.65757	0.942928
$37$	2.96085	0.486760	0.243380	−	0.969931i	$-0.421744\pi$
$37$	2.96085	0.486760	0.243380	+	0.969931i	$0.421744\pi$
$38$	−8.12162	−1.31750
$39$	−1.94794	−0.311920
$40$	−36.9902	−5.84867
$41$	−0.248112	−0.0387486	−0.0193743	−	0.999812i	$-0.506167\pi$
$41$	−0.248112	−0.0387486	−0.0193743	+	0.999812i	$0.506167\pi$
$42$	2.76723	0.426993
$43$	0.630338	0.0961257	0.0480628	−	0.998844i	$-0.484695\pi$
$43$	0.630338	0.0961257	0.0480628	+	0.998844i	$0.484695\pi$
$44$	3.14084	0.473500
$45$	−3.65468	−0.544808
$46$	−11.5758	−1.70676
$47$	4.41168	0.643509	0.321755	−	0.946823i	$-0.395727\pi$
$47$	4.41168	0.643509	0.321755	+	0.946823i	$0.395727\pi$
$48$	−16.6929	−2.40942
$49$	1.00000	0.142857
$50$	23.1249	3.27036
$51$	−6.99463	−0.979445
$52$	11.0206	1.52828
$53$	7.79091	1.07016	0.535082	−	0.844800i	$-0.320281\pi$
$53$	7.79091	1.07016	0.535082	+	0.844800i	$0.320281\pi$
$54$	−2.76723	−0.376572
$55$	−2.02893	−0.273580
$56$	−10.1213	−1.35252
$57$	2.93493	0.388740
$58$	24.1942	3.17685
$59$	3.50891	0.456822	0.228411	−	0.973565i	$-0.426647\pi$
$59$	3.50891	0.456822	0.228411	+	0.973565i	$0.426647\pi$
$60$	20.6766	2.66934
$61$	0.0482375	0.00617618	0.00308809	−	0.999995i	$-0.499017\pi$
$61$	0.0482375	0.00617618	0.00308809	+	0.999995i	$0.499017\pi$
$62$	2.59189	0.329170
$63$	−1.00000	−0.125988
$64$	38.4252	4.80315
$65$	−7.11910	−0.883015
$66$	−1.53625	−0.189099
$67$	1.92412	0.235069	0.117534	−	0.993069i	$-0.462501\pi$
$67$	1.92412	0.235069	0.117534	+	0.993069i	$0.462501\pi$
$68$	39.5726	4.79888
$69$	4.18318	0.503596
$70$	10.1133	1.20878
$71$	−6.19394	−0.735086	−0.367543	−	0.930007i	$-0.619801\pi$
$71$	−6.19394	−0.735086	−0.367543	+	0.930007i	$0.619801\pi$
$72$	10.1213	1.19281
$73$	12.2682	1.43588	0.717939	−	0.696106i	$-0.245086\pi$
$73$	12.2682	1.43588	0.717939	+	0.696106i	$0.245086\pi$
$74$	8.19335	0.952458
$75$	−8.35670	−0.964948
$76$	−16.6045	−1.90467
$77$	−0.555158	−0.0632661
$78$	−5.39040	−0.610342
$79$	−15.7700	−1.77427	−0.887133	−	0.461513i	$-0.847307\pi$
$79$	−15.7700	−1.77427	−0.887133	+	0.461513i	$0.847307\pi$
$80$	−61.0073	−6.82082
$81$	1.00000	0.111111
$82$	−0.686584	−0.0758205
$83$	−13.8174	−1.51666	−0.758328	−	0.651873i	$-0.773983\pi$
$83$	−13.8174	−1.51666	−0.758328	+	0.651873i	$0.773983\pi$
$84$	5.65757	0.617291
$85$	−25.5632	−2.77271
$86$	1.74429	0.188092
$87$	−8.74311	−0.937360
$88$	5.61894	0.598981
$89$	4.29172	0.454921	0.227461	−	0.973787i	$-0.426958\pi$
$89$	4.29172	0.454921	0.227461	+	0.973787i	$0.426958\pi$
$90$	−10.1133	−1.06604
$91$	−1.94794	−0.204200
$92$	−23.6666	−2.46742
$93$	−0.936637	−0.0971247
$94$	12.2081	1.25917
$95$	10.7262	1.10049
$96$	−25.9505	−2.64856
$97$	12.7904	1.29866	0.649332	−	0.760505i	$-0.275049\pi$
$97$	12.7904	1.29866	0.649332	+	0.760505i	$0.275049\pi$
$98$	2.76723	0.279533
$99$	0.555158	0.0557955
$100$	47.2786	4.72786
$101$	10.5712	1.05188	0.525938	−	0.850523i	$-0.323715\pi$
$101$	10.5712	1.05188	0.525938	+	0.850523i	$0.323715\pi$
$102$	−19.3558	−1.91651
$103$	−1.21519	−0.119737	−0.0598683	−	0.998206i	$-0.519068\pi$
$103$	−1.21519	−0.119737	−0.0598683	+	0.998206i	$0.519068\pi$
$104$	19.7157	1.93329
$105$	−3.65468	−0.356660
$106$	21.5592	2.09402
$107$	−9.63721	−0.931664	−0.465832	−	0.884873i	$-0.654245\pi$
$107$	−9.63721	−0.931664	−0.465832	+	0.884873i	$0.654245\pi$
$108$	−5.65757	−0.544400
$109$	13.1868	1.26306	0.631531	−	0.775351i	$-0.282427\pi$
$109$	13.1868	1.26306	0.631531	+	0.775351i	$0.282427\pi$
$110$	−5.61450	−0.535322
$111$	−2.96085	−0.281031
$112$	−16.6929	−1.57733
$113$	−20.1795	−1.89833	−0.949165	−	0.314780i	$-0.898069\pi$
$113$	−20.1795	−1.89833	−0.949165	+	0.314780i	$0.898069\pi$
$114$	8.12162	0.760659
$115$	15.2882	1.42563
$116$	49.4647	4.59268
$117$	1.94794	0.180087
$118$	9.70997	0.893875
$119$	−6.99463	−0.641197
$120$	36.9902	3.37673
$121$	−10.6918	−0.971982
$122$	0.133484	0.0120851
$123$	0.248112	0.0223715
$124$	5.29909	0.475872
$125$	−12.2677	−1.09725
$126$	−2.76723	−0.246525
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	54.4304	4.81101
$129$	−0.630338	−0.0554982
$130$	−19.7002	−1.72782
$131$	12.6295	1.10344	0.551722	−	0.834028i	$-0.313971\pi$
$131$	12.6295	1.10344	0.551722	+	0.834028i	$0.313971\pi$
$132$	−3.14084	−0.273375
$133$	2.93493	0.254490
$134$	5.32449	0.459966
$135$	3.65468	0.314545
$136$	70.7950	6.07062
$137$	−12.5440	−1.07171	−0.535854	−	0.844311i	$-0.680010\pi$
$137$	−12.5440	−1.07171	−0.535854	+	0.844311i	$0.680010\pi$
$138$	11.5758	0.985400
$139$	−21.0486	−1.78532	−0.892658	−	0.450736i	$-0.851162\pi$
$139$	−21.0486	−1.78532	−0.892658	+	0.450736i	$0.851162\pi$
$140$	20.6766	1.74749
$141$	−4.41168	−0.371530
$142$	−17.1401	−1.43836
$143$	1.08141	0.0904324
$144$	16.6929	1.39108
$145$	−31.9533	−2.65358
$146$	33.9488	2.80962
$147$	−1.00000	−0.0824786
$148$	16.7512	1.37694
$149$	15.1278	1.23932	0.619660	−	0.784871i	$-0.287271\pi$
$149$	15.1278	1.23932	0.619660	+	0.784871i	$0.287271\pi$
$150$	−23.1249	−1.88814
$151$	−3.34426	−0.272152	−0.136076	−	0.990698i	$-0.543449\pi$
$151$	−3.34426	−0.272152	−0.136076	+	0.990698i	$0.543449\pi$
$152$	−29.7053	−2.40942
$153$	6.99463	0.565483
$154$	−1.53625	−0.123795
$155$	−3.42311	−0.274951
$156$	−11.0206	−0.882354
$157$	−24.1821	−1.92994	−0.964972	−	0.262352i	$-0.915502\pi$
$157$	−24.1821	−1.92994	−0.964972	+	0.262352i	$0.915502\pi$
$158$	−43.6393	−3.47176
$159$	−7.79091	−0.617859
$160$	−94.8408	−7.49783
$161$	4.18318	0.329681
$162$	2.76723	0.217414
$163$	−1.13219	−0.0886803	−0.0443402	−	0.999016i	$-0.514119\pi$
$163$	−1.13219	−0.0886803	−0.0443402	+	0.999016i	$0.514119\pi$
$164$	−1.40371	−0.109611
$165$	2.02893	0.157952
$166$	−38.2359	−2.96768
$167$	7.51198	0.581295	0.290647	−	0.956830i	$-0.406129\pi$
$167$	7.51198	0.581295	0.290647	+	0.956830i	$0.406129\pi$
$168$	10.1213	0.780877
$169$	−9.20553	−0.708118
$170$	−70.7392	−5.42545
$171$	−2.93493	−0.224439
$172$	3.56618	0.271919
$173$	−16.2369	−1.23447	−0.617233	−	0.786781i	$-0.711746\pi$
$173$	−16.2369	−1.23447	−0.617233	+	0.786781i	$0.711746\pi$
$174$	−24.1942	−1.83416
$175$	−8.35670	−0.631707
$176$	9.26721	0.698542
$177$	−3.50891	−0.263746
$178$	11.8762	0.890157
$179$	6.60031	0.493331	0.246665	−	0.969101i	$-0.420665\pi$
$179$	6.60031	0.493331	0.246665	+	0.969101i	$0.420665\pi$
$180$	−20.6766	−1.54114
$181$	6.48777	0.482232	0.241116	−	0.970496i	$-0.422487\pi$
$181$	6.48777	0.482232	0.241116	+	0.970496i	$0.422487\pi$
$182$	−5.39040	−0.399563
$183$	−0.0482375	−0.00356582
$184$	−42.3393	−3.12130
$185$	−10.8210	−0.795573
$186$	−2.59189	−0.190047
$187$	3.88313	0.283962
$188$	24.9594	1.82035
$189$	1.00000	0.0727393
$190$	29.6819	2.15335
$191$	20.7832	1.50382	0.751908	−	0.659268i	$-0.229134\pi$
$191$	20.7832	1.50382	0.751908	+	0.659268i	$0.229134\pi$
$192$	−38.4252	−2.77310
$193$	−20.4234	−1.47011	−0.735053	−	0.678010i	$-0.762843\pi$
$193$	−20.4234	−1.47011	−0.735053	+	0.678010i	$0.762843\pi$
$194$	35.3939	2.54113
$195$	7.11910	0.509809
$196$	5.65757	0.404112
$197$	23.1445	1.64898	0.824488	−	0.565879i	$-0.191463\pi$
$197$	23.1445	1.64898	0.824488	+	0.565879i	$0.191463\pi$
$198$	1.53625	0.109177
$199$	−20.3061	−1.43946	−0.719730	−	0.694254i	$-0.755735\pi$
$199$	−20.3061	−1.43946	−0.719730	+	0.694254i	$0.755735\pi$
$200$	84.5809	5.98077
$201$	−1.92412	−0.135717
$202$	29.2530	2.05823
$203$	−8.74311	−0.613646
$204$	−39.5726	−2.77064
$205$	0.906772	0.0633317
$206$	−3.36272	−0.234292
$207$	−4.18318	−0.290751
$208$	32.5168	2.25463
$209$	−1.62935	−0.112704
$210$	−10.1133	−0.697887
$211$	−6.39849	−0.440490	−0.220245	−	0.975445i	$-0.570686\pi$
$211$	−6.39849	−0.440490	−0.220245	+	0.975445i	$0.570686\pi$
$212$	44.0776	3.02726
$213$	6.19394	0.424402
$214$	−26.6684	−1.82301
$215$	−2.30369	−0.157110
$216$	−10.1213	−0.688669
$217$	−0.936637	−0.0635831
$218$	36.4908	2.47147
$219$	−12.2682	−0.829005
$220$	−11.4788	−0.773899
$221$	13.6251	0.916525
$222$	−8.19335	−0.549902
$223$	−19.8687	−1.33051	−0.665254	−	0.746617i	$-0.731677\pi$
$223$	−19.8687	−1.33051	−0.665254	+	0.746617i	$0.731677\pi$
$224$	−25.9505	−1.73389
$225$	8.35670	0.557113
$226$	−55.8414	−3.71451
$227$	−14.6479	−0.972215	−0.486108	−	0.873899i	$-0.661584\pi$
$227$	−14.6479	−0.972215	−0.486108	+	0.873899i	$0.661584\pi$
$228$	16.6045	1.09966
$229$	−0.677012	−0.0447382	−0.0223691	−	0.999750i	$-0.507121\pi$
$229$	−0.677012	−0.0447382	−0.0223691	+	0.999750i	$0.507121\pi$
$230$	42.3060	2.78957
$231$	0.555158	0.0365267
$232$	88.4919	5.80978
$233$	−21.7935	−1.42774	−0.713870	−	0.700279i	$-0.753059\pi$
$233$	−21.7935	−1.42774	−0.713870	+	0.700279i	$0.753059\pi$
$234$	5.39040	0.352381
$235$	−16.1233	−1.05177
$236$	19.8519	1.29225
$237$	15.7700	1.02437
$238$	−19.3558	−1.25465
$239$	−10.1562	−0.656951	−0.328476	−	0.944512i	$-0.606535\pi$
$239$	−10.1562	−0.656951	−0.328476	+	0.944512i	$0.606535\pi$
$240$	61.0073	3.93800
$241$	−12.8103	−0.825185	−0.412593	−	0.910916i	$-0.635377\pi$
$241$	−12.8103	−0.825185	−0.412593	+	0.910916i	$0.635377\pi$
$242$	−29.5867	−1.90190
$243$	−1.00000	−0.0641500
$244$	0.272907	0.0174711
$245$	−3.65468	−0.233489
$246$	0.686584	0.0437750
$247$	−5.71706	−0.363768
$248$	9.48001	0.601981
$249$	13.8174	0.875642
$250$	−33.9475	−2.14703
$251$	23.8715	1.50676	0.753379	−	0.657586i	$-0.228423\pi$
$251$	23.8715	1.50676	0.753379	+	0.657586i	$0.228423\pi$
$252$	−5.65757	−0.356393
$253$	−2.32233	−0.146003
$254$	2.76723	0.173631
$255$	25.5632	1.60083
$256$	73.7710	4.61069
$257$	7.89624	0.492554	0.246277	−	0.969200i	$-0.420793\pi$
$257$	7.89624	0.492554	0.246277	+	0.969200i	$0.420793\pi$
$258$	−1.74429	−0.108595
$259$	−2.96085	−0.183978
$260$	−40.2768	−2.49786
$261$	8.74311	0.541185
$262$	34.9488	2.15914
$263$	24.4029	1.50475	0.752374	−	0.658737i	$-0.228909\pi$
$263$	24.4029	1.50475	0.752374	+	0.658737i	$0.228909\pi$
$264$	−5.61894	−0.345822
$265$	−28.4733	−1.74910
$266$	8.12162	0.497968
$267$	−4.29172	−0.262649
$268$	10.8858	0.664959
$269$	−18.5871	−1.13328	−0.566639	−	0.823966i	$-0.691756\pi$
$269$	−18.5871	−1.13328	−0.566639	+	0.823966i	$0.691756\pi$
$270$	10.1133	0.615479
$271$	−16.2454	−0.986839	−0.493419	−	0.869792i	$-0.664253\pi$
$271$	−16.2454	−0.986839	−0.493419	+	0.869792i	$0.664253\pi$
$272$	116.761	7.07967
$273$	1.94794	0.117895
$274$	−34.7122	−2.09704
$275$	4.63929	0.279760
$276$	23.6666	1.42456
$277$	0.627986	0.0377320	0.0188660	−	0.999822i	$-0.493994\pi$
$277$	0.627986	0.0377320	0.0188660	+	0.999822i	$0.493994\pi$
$278$	−58.2462	−3.49338
$279$	0.936637	0.0560750
$280$	36.9902	2.21059
$281$	−24.1453	−1.44039	−0.720195	−	0.693772i	$-0.755948\pi$
$281$	−24.1453	−1.44039	−0.720195	+	0.693772i	$0.755948\pi$
$282$	−12.2081	−0.726983
$283$	1.57053	0.0933583	0.0466791	−	0.998910i	$-0.485136\pi$
$283$	1.57053	0.0933583	0.0466791	+	0.998910i	$0.485136\pi$
$284$	−35.0426	−2.07940
$285$	−10.7262	−0.635366
$286$	2.99252	0.176951
$287$	0.248112	0.0146456
$288$	25.9505	1.52915
$289$	31.9249	1.87794
$290$	−88.4221	−5.19233
$291$	−12.7904	−0.749784
$292$	69.4079	4.06179
$293$	23.5738	1.37720	0.688599	−	0.725143i	$-0.258226\pi$
$293$	23.5738	1.37720	0.688599	+	0.725143i	$0.258226\pi$
$294$	−2.76723	−0.161388
$295$	−12.8240	−0.746640
$296$	29.9677	1.74184
$297$	−0.555158	−0.0322135
$298$	41.8622	2.42501
$299$	−8.14858	−0.471245
$300$	−47.2786	−2.72963
$301$	−0.630338	−0.0363321
$302$	−9.25434	−0.532527
$303$	−10.5712	−0.607300
$304$	−48.9925	−2.80991
$305$	−0.176293	−0.0100945
$306$	19.3558	1.10650
$307$	17.0815	0.974891	0.487446	−	0.873153i	$-0.337929\pi$
$307$	17.0815	0.974891	0.487446	+	0.873153i	$0.337929\pi$
$308$	−3.14084	−0.178966
$309$	1.21519	0.0691299
$310$	−9.47254	−0.538004
$311$	22.2805	1.26341	0.631706	−	0.775208i	$-0.282355\pi$
$311$	22.2805	1.26341	0.631706	+	0.775208i	$0.282355\pi$
$312$	−19.7157	−1.11618
$313$	−3.88085	−0.219359	−0.109679	−	0.993967i	$-0.534982\pi$
$313$	−3.88085	−0.219359	−0.109679	+	0.993967i	$0.534982\pi$
$314$	−66.9176	−3.77638
$315$	3.65468	0.205918
$316$	−89.2200	−5.01902
$317$	28.0393	1.57485	0.787423	−	0.616413i	$-0.211415\pi$
$317$	28.0393	1.57485	0.787423	+	0.616413i	$0.211415\pi$
$318$	−21.5592	−1.20898
$319$	4.85381	0.271761
$320$	−140.432	−7.85038
$321$	9.63721	0.537897
$322$	11.5758	0.645096
$323$	−20.5287	−1.14225
$324$	5.65757	0.314309
$325$	16.2783	0.902960
$326$	−3.13304	−0.173523
$327$	−13.1868	−0.729229
$328$	−2.51123	−0.138659
$329$	−4.41168	−0.243224
$330$	5.61450	0.309068
$331$	22.4003	1.23123	0.615617	−	0.788046i	$-0.288907\pi$
$331$	22.4003	1.23123	0.615617	+	0.788046i	$0.288907\pi$
$332$	−78.1728	−4.29029
$333$	2.96085	0.162253
$334$	20.7874	1.13744
$335$	−7.03205	−0.384202
$336$	16.6929	0.910673
$337$	−8.28715	−0.451430	−0.225715	−	0.974193i	$-0.572472\pi$
$337$	−8.28715	−0.451430	−0.225715	+	0.974193i	$0.572472\pi$
$338$	−25.4738	−1.38559
$339$	20.1795	1.09600
$340$	−144.625	−7.84341
$341$	0.519981	0.0281586
$342$	−8.12162	−0.439167
$343$	−1.00000	−0.0539949
$344$	6.37986	0.343979
$345$	−15.2882	−0.823089
$346$	−44.9311	−2.41551
$347$	−12.4589	−0.668831	−0.334415	−	0.942426i	$-0.608539\pi$
$347$	−12.4589	−0.668831	−0.334415	+	0.942426i	$0.608539\pi$
$348$	−49.4647	−2.65159
$349$	21.8887	1.17168	0.585838	−	0.810428i	$-0.300765\pi$
$349$	21.8887	1.17168	0.585838	+	0.810428i	$0.300765\pi$
$350$	−23.1249	−1.23608
$351$	−1.94794	−0.103973
$352$	14.4066	0.767876
$353$	22.4787	1.19642	0.598209	−	0.801340i	$-0.295879\pi$
$353$	22.4787	1.19642	0.598209	+	0.801340i	$0.295879\pi$
$354$	−9.70997	−0.516079
$355$	22.6369	1.20144
$356$	24.2807	1.28687
$357$	6.99463	0.370195
$358$	18.2646	0.965314
$359$	3.73903	0.197339	0.0986693	−	0.995120i	$-0.468541\pi$
$359$	3.73903	0.197339	0.0986693	+	0.995120i	$0.468541\pi$
$360$	−36.9902	−1.94956
$361$	−10.3862	−0.546643
$362$	17.9532	0.943598
$363$	10.6918	0.561174
$364$	−11.0206	−0.577636
$365$	−44.8362	−2.34683
$366$	−0.133484	−0.00697733
$367$	−22.4121	−1.16990	−0.584951	−	0.811069i	$-0.698886\pi$
$367$	−22.4121	−1.16990	−0.584951	+	0.811069i	$0.698886\pi$
$368$	−69.8295	−3.64011
$369$	−0.248112	−0.0129162
$370$	−29.9441	−1.55672
$371$	−7.79091	−0.404484
$372$	−5.29909	−0.274745
$373$	−9.89929	−0.512566	−0.256283	−	0.966602i	$-0.582498\pi$
$373$	−9.89929	−0.512566	−0.256283	+	0.966602i	$0.582498\pi$
$374$	10.7455	0.555637
$375$	12.2677	0.633499
$376$	44.6520	2.30275
$377$	17.0310	0.877144
$378$	2.76723	0.142331
$379$	−14.9228	−0.766531	−0.383266	−	0.923638i	$-0.625201\pi$
$379$	−14.9228	−0.766531	−0.383266	+	0.923638i	$0.625201\pi$
$380$	60.6843	3.11304
$381$	−1.00000	−0.0512316
$382$	57.5118	2.94256
$383$	10.4734	0.535164	0.267582	−	0.963535i	$-0.413775\pi$
$383$	10.4734	0.535164	0.267582	+	0.963535i	$0.413775\pi$
$384$	−54.4304	−2.77764
$385$	2.02893	0.103404
$386$	−56.5162	−2.87660
$387$	0.630338	0.0320419
$388$	72.3623	3.67364
$389$	−20.3230	−1.03042	−0.515210	−	0.857064i	$-0.672286\pi$
$389$	−20.3230	−1.03042	−0.515210	+	0.857064i	$0.672286\pi$
$390$	19.7002	0.997558
$391$	−29.2598	−1.47973
$392$	10.1213	0.511204
$393$	−12.6295	−0.637074
$394$	64.0461	3.22660
$395$	57.6344	2.89990
$396$	3.14084	0.157833
$397$	−23.5947	−1.18418	−0.592091	−	0.805871i	$-0.701698\pi$
$397$	−23.5947	−1.18418	−0.592091	+	0.805871i	$0.701698\pi$
$398$	−56.1916	−2.81663
$399$	−2.93493	−0.146930
$400$	139.498	6.97488
$401$	−32.2761	−1.61179	−0.805896	−	0.592057i	$-0.798316\pi$
$401$	−32.2761	−1.61179	−0.805896	+	0.592057i	$0.798316\pi$
$402$	−5.32449	−0.265561
$403$	1.82451	0.0908854
$404$	59.8073	2.97553
$405$	−3.65468	−0.181603
$406$	−24.1942	−1.20074
$407$	1.64374	0.0814771
$408$	−70.7950	−3.50487
$409$	−12.1525	−0.600901	−0.300450	−	0.953797i	$-0.597137\pi$
$409$	−12.1525	−0.600901	−0.300450	+	0.953797i	$0.597137\pi$
$410$	2.50925	0.123923
$411$	12.5440	0.618751
$412$	−6.87503	−0.338709
$413$	−3.50891	−0.172662
$414$	−11.5758	−0.568921
$415$	50.4982	2.47886
$416$	50.5500	2.47842
$417$	21.0486	1.03075
$418$	−4.50878	−0.220532
$419$	18.4594	0.901802	0.450901	−	0.892574i	$-0.351103\pi$
$419$	18.4594	0.901802	0.450901	+	0.892574i	$0.351103\pi$
$420$	−20.6766	−1.00891
$421$	−6.08449	−0.296540	−0.148270	−	0.988947i	$-0.547370\pi$
$421$	−6.08449	−0.296540	−0.148270	+	0.988947i	$0.547370\pi$
$422$	−17.7061	−0.861919
$423$	4.41168	0.214503
$424$	78.8544	3.82951
$425$	58.4520	2.83534
$426$	17.1401	0.830439
$427$	−0.0482375	−0.00233438
$428$	−54.5232	−2.63548
$429$	−1.08141	−0.0522111
$430$	−6.37483	−0.307422
$431$	39.0370	1.88035	0.940174	−	0.340695i	$-0.110662\pi$
$431$	39.0370	1.88035	0.940174	+	0.340695i	$0.110662\pi$
$432$	−16.6929	−0.803138
$433$	−2.40523	−0.115588	−0.0577940	−	0.998329i	$-0.518407\pi$
$433$	−2.40523	−0.115588	−0.0577940	+	0.998329i	$0.518407\pi$
$434$	−2.59189	−0.124415
$435$	31.9533	1.53204
$436$	74.6049	3.57293
$437$	12.2773	0.587304
$438$	−33.9488	−1.62214
$439$	26.8409	1.28105	0.640523	−	0.767939i	$-0.278718\pi$
$439$	26.8409	1.28105	0.640523	+	0.767939i	$0.278718\pi$
$440$	−20.5354	−0.978988
$441$	1.00000	0.0476190
$442$	37.7039	1.79339
$443$	−31.2747	−1.48591	−0.742954	−	0.669343i	$-0.766576\pi$
$443$	−31.2747	−1.48591	−0.742954	+	0.669343i	$0.766576\pi$
$444$	−16.7512	−0.794977
$445$	−15.6849	−0.743534
$446$	−54.9814	−2.60344
$447$	−15.1278	−0.715521
$448$	−38.4252	−1.81542
$449$	32.2247	1.52078	0.760389	−	0.649468i	$-0.225008\pi$
$449$	32.2247	1.52078	0.760389	+	0.649468i	$0.225008\pi$
$450$	23.1249	1.09012
$451$	−0.137742	−0.00648599
$452$	−114.167	−5.36996
$453$	3.34426	0.157127
$454$	−40.5341	−1.90236
$455$	7.11910	0.333748
$456$	29.7053	1.39108
$457$	35.3199	1.65219	0.826097	−	0.563528i	$-0.190556\pi$
$457$	35.3199	1.65219	0.826097	+	0.563528i	$0.190556\pi$
$458$	−1.87345	−0.0875405
$459$	−6.99463	−0.326482
$460$	86.4940	4.03280
$461$	−23.2707	−1.08382	−0.541912	−	0.840435i	$-0.682299\pi$
$461$	−23.2707	−1.08382	−0.541912	+	0.840435i	$0.682299\pi$
$462$	1.53625	0.0714728
$463$	−19.8736	−0.923606	−0.461803	−	0.886982i	$-0.652797\pi$
$463$	−19.8736	−0.923606	−0.461803	+	0.886982i	$0.652797\pi$
$464$	145.948	6.77547
$465$	3.42311	0.158743
$466$	−60.3076	−2.79370
$467$	13.6216	0.630332	0.315166	−	0.949037i	$-0.397940\pi$
$467$	13.6216	0.630332	0.315166	+	0.949037i	$0.397940\pi$
$468$	11.0206	0.509427
$469$	−1.92412	−0.0888477
$470$	−44.6168	−2.05802
$471$	24.1821	1.11425
$472$	35.5149	1.63470
$473$	0.349937	0.0160901
$474$	43.6393	2.00442
$475$	−24.5263	−1.12534
$476$	−39.5726	−1.81381
$477$	7.79091	0.356721
$478$	−28.1046	−1.28548
$479$	−8.95421	−0.409128	−0.204564	−	0.978853i	$-0.565578\pi$
$479$	−8.95421	−0.409128	−0.204564	+	0.978853i	$0.565578\pi$
$480$	94.8408	4.32887
$481$	5.76755	0.262978
$482$	−35.4491	−1.61466
$483$	−4.18318	−0.190341
$484$	−60.4896	−2.74953
$485$	−46.7447	−2.12257
$486$	−2.76723	−0.125524
$487$	24.5758	1.11364	0.556818	−	0.830635i	$-0.312022\pi$
$487$	24.5758	1.11364	0.556818	+	0.830635i	$0.312022\pi$
$488$	0.488227	0.0221010
$489$	1.13219	0.0511996
$490$	−10.1133	−0.456874
$491$	5.65703	0.255298	0.127649	−	0.991819i	$-0.459257\pi$
$491$	5.65703	0.255298	0.127649	+	0.991819i	$0.459257\pi$
$492$	1.40371	0.0632842
$493$	61.1549	2.75428
$494$	−15.8204	−0.711794
$495$	−2.02893	−0.0911934
$496$	15.6352	0.702042
$497$	6.19394	0.277836
$498$	38.2359	1.71339
$499$	20.5463	0.919778	0.459889	−	0.887976i	$-0.347889\pi$
$499$	20.5463	0.919778	0.459889	+	0.887976i	$0.347889\pi$
$500$	−69.4051	−3.10389
$501$	−7.51198	−0.335611
$502$	66.0581	2.94832
$503$	21.5279	0.959881	0.479941	−	0.877301i	$-0.340658\pi$
$503$	21.5279	0.959881	0.479941	+	0.877301i	$0.340658\pi$
$504$	−10.1213	−0.450840
$505$	−38.6344	−1.71921
$506$	−6.42641	−0.285689
$507$	9.20553	0.408832
$508$	5.65757	0.251014
$509$	−16.2431	−0.719963	−0.359982	−	0.932959i	$-0.617217\pi$
$509$	−16.2431	−0.719963	−0.359982	+	0.932959i	$0.617217\pi$
$510$	70.7392	3.13238
$511$	−12.2682	−0.542711
$512$	95.2806	4.21085
$513$	2.93493	0.129580
$514$	21.8507	0.963793
$515$	4.44114	0.195700
$516$	−3.56618	−0.156992
$517$	2.44918	0.107715
$518$	−8.19335	−0.359995
$519$	16.2369	0.712719
$520$	−72.0547	−3.15981
$521$	−9.68875	−0.424472	−0.212236	−	0.977218i	$-0.568074\pi$
$521$	−9.68875	−0.424472	−0.212236	+	0.977218i	$0.568074\pi$
$522$	24.1942	1.05895
$523$	39.2356	1.71565	0.857827	−	0.513938i	$-0.171814\pi$
$523$	39.2356	1.71565	0.857827	+	0.513938i	$0.171814\pi$
$524$	71.4523	3.12141
$525$	8.35670	0.364716
$526$	67.5285	2.94438
$527$	6.55143	0.285385
$528$	−9.26721	−0.403303
$529$	−5.50100	−0.239174
$530$	−78.7922	−3.42251
$531$	3.50891	0.152274
$532$	16.6045	0.719898
$533$	−0.483308	−0.0209344
$534$	−11.8762	−0.513932
$535$	35.2209	1.52273
$536$	19.4747	0.841178
$537$	−6.60031	−0.284825
$538$	−51.4349	−2.21752
$539$	0.555158	0.0239123
$540$	20.6766	0.889779
$541$	−3.27381	−0.140752	−0.0703761	−	0.997521i	$-0.522420\pi$
$541$	−3.27381	−0.140752	−0.0703761	+	0.997521i	$0.522420\pi$
$542$	−44.9548	−1.93097
$543$	−6.48777	−0.278417
$544$	181.514	7.78236
$545$	−48.1934	−2.06438
$546$	5.39040	0.230688
$547$	9.89249	0.422972	0.211486	−	0.977381i	$-0.432170\pi$
$547$	9.89249	0.422972	0.211486	+	0.977381i	$0.432170\pi$
$548$	−70.9686	−3.03163
$549$	0.0482375	0.00205873
$550$	12.8380	0.547413
$551$	−25.6604	−1.09317
$552$	42.3393	1.80208
$553$	15.7700	0.670610
$554$	1.73778	0.0738312
$555$	10.8210	0.459324
$556$	−119.084	−5.05027
$557$	43.2458	1.83238	0.916191	−	0.400741i	$-0.131247\pi$
$557$	43.2458	1.83238	0.916191	+	0.400741i	$0.131247\pi$
$558$	2.59189	0.109723
$559$	1.22786	0.0519330
$560$	61.0073	2.57803
$561$	−3.88313	−0.163946
$562$	−66.8157	−2.81845
$563$	−32.6266	−1.37505	−0.687523	−	0.726163i	$-0.741302\pi$
$563$	−32.6266	−1.37505	−0.687523	+	0.726163i	$0.741302\pi$
$564$	−24.9594	−1.05098
$565$	73.7497	3.10267
$566$	4.34602	0.182677
$567$	−1.00000	−0.0419961
$568$	−62.6909	−2.63045
$569$	−19.9702	−0.837194	−0.418597	−	0.908172i	$-0.637478\pi$
$569$	−19.9702	−0.837194	−0.418597	+	0.908172i	$0.637478\pi$
$570$	−29.6819	−1.24324
$571$	1.89515	0.0793095	0.0396548	−	0.999213i	$-0.487374\pi$
$571$	1.89515	0.0793095	0.0396548	+	0.999213i	$0.487374\pi$
$572$	6.11817	0.255814
$573$	−20.7832	−0.868229
$574$	0.686584	0.0286575
$575$	−34.9576	−1.45783
$576$	38.4252	1.60105
$577$	−42.2561	−1.75914	−0.879572	−	0.475766i	$-0.842171\pi$
$577$	−42.2561	−1.75914	−0.879572	+	0.475766i	$0.842171\pi$
$578$	88.3436	3.67461
$579$	20.4234	0.848766
$580$	−180.778	−7.50639
$581$	13.8174	0.573242
$582$	−35.3939	−1.46712
$583$	4.32518	0.179131
$584$	124.170	5.13819
$585$	−7.11910	−0.294338
$586$	65.2342	2.69480
$587$	21.6495	0.893570	0.446785	−	0.894641i	$-0.352569\pi$
$587$	21.6495	0.893570	0.446785	+	0.894641i	$0.352569\pi$
$588$	−5.65757	−0.233314
$589$	−2.74896	−0.113269
$590$	−35.4869	−1.46097
$591$	−23.1445	−0.952037
$592$	49.4252	2.03136
$593$	6.30725	0.259008	0.129504	−	0.991579i	$-0.458662\pi$
$593$	6.30725	0.259008	0.129504	+	0.991579i	$0.458662\pi$
$594$	−1.53625	−0.0630331
$595$	25.5632	1.04799
$596$	85.5866	3.50577
$597$	20.3061	0.831073
$598$	−22.5490	−0.922097
$599$	14.2600	0.582646	0.291323	−	0.956625i	$-0.405905\pi$
$599$	14.2600	0.582646	0.291323	+	0.956625i	$0.405905\pi$
$600$	−84.5809	−3.45300
$601$	12.9645	0.528834	0.264417	−	0.964408i	$-0.414821\pi$
$601$	12.9645	0.528834	0.264417	+	0.964408i	$0.414821\pi$
$602$	−1.74429	−0.0710920
$603$	1.92412	0.0783563
$604$	−18.9204	−0.769859
$605$	39.0751	1.58863
$606$	−29.2530	−1.18832
$607$	8.86616	0.359866	0.179933	−	0.983679i	$-0.442412\pi$
$607$	8.86616	0.359866	0.179933	+	0.983679i	$0.442412\pi$
$608$	−76.1628	−3.08881
$609$	8.74311	0.354289
$610$	−0.487842	−0.0197522
$611$	8.59368	0.347663
$612$	39.5726	1.59963
$613$	−28.1476	−1.13687	−0.568436	−	0.822728i	$-0.692451\pi$
$613$	−28.1476	−1.13687	−0.568436	+	0.822728i	$0.692451\pi$
$614$	47.2684	1.90760
$615$	−0.906772	−0.0365646
$616$	−5.61894	−0.226393
$617$	−31.2917	−1.25976	−0.629878	−	0.776694i	$-0.716895\pi$
$617$	−31.2917	−1.25976	−0.629878	+	0.776694i	$0.716895\pi$
$618$	3.36272	0.135268
$619$	−15.0630	−0.605433	−0.302717	−	0.953081i	$-0.597894\pi$
$619$	−15.0630	−0.605433	−0.302717	+	0.953081i	$0.597894\pi$
$620$	−19.3665	−0.777776
$621$	4.18318	0.167865
$622$	61.6553	2.47215
$623$	−4.29172	−0.171944
$624$	−32.5168	−1.30171
$625$	3.05091	0.122036
$626$	−10.7392	−0.429225
$627$	1.62935	0.0650699
$628$	−136.812	−5.45939
$629$	20.7101	0.825764
$630$	10.1133	0.402925
$631$	−19.6368	−0.781729	−0.390864	−	0.920448i	$-0.627824\pi$
$631$	−19.6368	−0.781729	−0.390864	+	0.920448i	$0.627824\pi$
$632$	−159.614	−6.34909
$633$	6.39849	0.254317
$634$	77.5913	3.08154
$635$	−3.65468	−0.145032
$636$	−44.0776	−1.74779
$637$	1.94794	0.0771802
$638$	13.4316	0.531762
$639$	−6.19394	−0.245029
$640$	−198.926	−7.86323
$641$	−20.2180	−0.798562	−0.399281	−	0.916829i	$-0.630740\pi$
$641$	−20.2180	−0.798562	−0.399281	+	0.916829i	$0.630740\pi$
$642$	26.6684	1.05252
$643$	−41.3314	−1.62995	−0.814975	−	0.579496i	$-0.803249\pi$
$643$	−41.3314	−1.62995	−0.814975	+	0.579496i	$0.803249\pi$
$644$	23.6666	0.932595
$645$	2.30369	0.0907075
$646$	−56.8077	−2.23507
$647$	14.2815	0.561462	0.280731	−	0.959786i	$-0.409423\pi$
$647$	14.2815	0.561462	0.280731	+	0.959786i	$0.409423\pi$
$648$	10.1213	0.397603
$649$	1.94800	0.0764657
$650$	45.0459	1.76685
$651$	0.936637	0.0367097
$652$	−6.40546	−0.250857
$653$	19.3064	0.755517	0.377758	−	0.925904i	$-0.376695\pi$
$653$	19.3064	0.755517	0.377758	+	0.925904i	$0.376695\pi$
$654$	−36.4908	−1.42690
$655$	−46.1568	−1.80350
$656$	−4.14172	−0.161707
$657$	12.2682	0.478626
$658$	−12.2081	−0.475922
$659$	−5.14897	−0.200576	−0.100288	−	0.994958i	$-0.531976\pi$
$659$	−5.14897	−0.200576	−0.100288	+	0.994958i	$0.531976\pi$
$660$	11.4788	0.446811
$661$	25.0695	0.975090	0.487545	−	0.873098i	$-0.337892\pi$
$661$	25.0695	0.975090	0.487545	+	0.873098i	$0.337892\pi$
$662$	61.9869	2.40919
$663$	−13.6251	−0.529156
$664$	−139.850	−5.42725
$665$	−10.7262	−0.415945
$666$	8.19335	0.317486
$667$	−36.5740	−1.41615
$668$	42.4995	1.64436
$669$	19.8687	0.768169
$670$	−19.4593	−0.751779
$671$	0.0267794	0.00103381
$672$	25.9505	1.00106
$673$	4.32081	0.166555	0.0832774	−	0.996526i	$-0.473461\pi$
$673$	4.32081	0.166555	0.0832774	+	0.996526i	$0.473461\pi$
$674$	−22.9325	−0.883325
$675$	−8.35670	−0.321649
$676$	−52.0809	−2.00311
$677$	29.7713	1.14420	0.572102	−	0.820182i	$-0.306128\pi$
$677$	29.7713	1.14420	0.572102	+	0.820182i	$0.306128\pi$
$678$	55.8414	2.14458
$679$	−12.7904	−0.490849
$680$	−258.733	−9.92196
$681$	14.6479	0.561309
$682$	1.43891	0.0550987
$683$	47.0408	1.79996	0.899982	−	0.435926i	$-0.143579\pi$
$683$	47.0408	1.79996	0.899982	+	0.435926i	$0.143579\pi$
$684$	−16.6045	−0.634890
$685$	45.8444	1.75163
$686$	−2.76723	−0.105653
$687$	0.677012	0.0258296
$688$	10.5222	0.401155
$689$	15.1762	0.578168
$690$	−42.3060	−1.61056
$691$	−45.5994	−1.73468	−0.867341	−	0.497714i	$-0.834173\pi$
$691$	−45.5994	−1.73468	−0.867341	+	0.497714i	$0.834173\pi$
$692$	−91.8611	−3.49203
$693$	−0.555158	−0.0210887
$694$	−34.4768	−1.30872
$695$	76.9258	2.91796
$696$	−88.4919	−3.35428
$697$	−1.73545	−0.0657350
$698$	60.5712	2.29265
$699$	21.7935	0.824306
$700$	−47.2786	−1.78696
$701$	−36.8277	−1.39096	−0.695482	−	0.718543i	$-0.744809\pi$
$701$	−36.8277	−1.39096	−0.695482	+	0.718543i	$0.744809\pi$
$702$	−5.39040	−0.203447
$703$	−8.68987	−0.327745
$704$	21.3320	0.803982
$705$	16.1233	0.607238
$706$	62.2037	2.34107
$707$	−10.5712	−0.397571
$708$	−19.8519	−0.746080
$709$	−44.4738	−1.67025	−0.835124	−	0.550062i	$-0.814604\pi$
$709$	−44.4738	−1.67025	−0.835124	+	0.550062i	$0.814604\pi$
$710$	62.6415	2.35089
$711$	−15.7700	−0.591422
$712$	43.4379	1.62790
$713$	−3.91812	−0.146735
$714$	19.3558	0.724371
$715$	−3.95222	−0.147805
$716$	37.3417	1.39553
$717$	10.1562	0.379291
$718$	10.3468	0.386138
$719$	−40.3684	−1.50549	−0.752745	−	0.658313i	$-0.771270\pi$
$719$	−40.3684	−1.50549	−0.752745	+	0.658313i	$0.771270\pi$
$720$	−61.0073	−2.27361
$721$	1.21519	0.0452562
$722$	−28.7410	−1.06963
$723$	12.8103	0.476421
$724$	36.7050	1.36413
$725$	73.0635	2.71351
$726$	29.5867	1.09806
$727$	−13.3192	−0.493983	−0.246992	−	0.969018i	$-0.579442\pi$
$727$	−13.3192	−0.493983	−0.246992	+	0.969018i	$0.579442\pi$
$728$	−19.7157	−0.730714
$729$	1.00000	0.0370370
$730$	−124.072	−4.59211
$731$	4.40899	0.163072
$732$	−0.272907	−0.0100869
$733$	4.42067	0.163281	0.0816407	−	0.996662i	$-0.473984\pi$
$733$	4.42067	0.163281	0.0816407	+	0.996662i	$0.473984\pi$
$734$	−62.0194	−2.28918
$735$	3.65468	0.134805
$736$	−108.556	−4.00141
$737$	1.06819	0.0393473
$738$	−0.686584	−0.0252735
$739$	−8.20650	−0.301881	−0.150940	−	0.988543i	$-0.548230\pi$
$739$	−8.20650	−0.301881	−0.150940	+	0.988543i	$0.548230\pi$
$740$	−61.2203	−2.25050
$741$	5.71706	0.210021
$742$	−21.5592	−0.791465
$743$	−9.58619	−0.351683	−0.175842	−	0.984418i	$-0.556265\pi$
$743$	−9.58619	−0.351683	−0.175842	+	0.984418i	$0.556265\pi$
$744$	−9.48001	−0.347554
$745$	−55.2874	−2.02557
$746$	−27.3936	−1.00295
$747$	−13.8174	−0.505552
$748$	21.9690	0.803268
$749$	9.63721	0.352136
$750$	33.9475	1.23959
$751$	12.9709	0.473315	0.236657	−	0.971593i	$-0.423948\pi$
$751$	12.9709	0.473315	0.236657	+	0.971593i	$0.423948\pi$
$752$	73.6438	2.68551
$753$	−23.8715	−0.869927
$754$	47.1288	1.71633
$755$	12.2222	0.444812
$756$	5.65757	0.205764
$757$	−2.09572	−0.0761704	−0.0380852	−	0.999274i	$-0.512126\pi$
$757$	−2.09572	−0.0761704	−0.0380852	+	0.999274i	$0.512126\pi$
$758$	−41.2948	−1.49989
$759$	2.32233	0.0842951
$760$	108.564	3.93802
$761$	−33.6016	−1.21806	−0.609028	−	0.793149i	$-0.708440\pi$
$761$	−33.6016	−1.21806	−0.609028	+	0.793149i	$0.708440\pi$
$762$	−2.76723	−0.100246
$763$	−13.1868	−0.477393
$764$	117.582	4.25397
$765$	−25.5632	−0.924238
$766$	28.9822	1.04717
$767$	6.83515	0.246803
$768$	−73.7710	−2.66198
$769$	26.8826	0.969410	0.484705	−	0.874678i	$-0.338927\pi$
$769$	26.8826	0.969410	0.484705	+	0.874678i	$0.338927\pi$
$770$	5.61450	0.202333
$771$	−7.89624	−0.284376
$772$	−115.547	−4.15861
$773$	−23.9492	−0.861392	−0.430696	−	0.902497i	$-0.641732\pi$
$773$	−23.9492	−0.861392	−0.430696	+	0.902497i	$0.641732\pi$
$774$	1.74429	0.0626973
$775$	7.82719	0.281161
$776$	129.455	4.64718
$777$	2.96085	0.106220
$778$	−56.2386	−2.01625
$779$	0.728191	0.0260902
$780$	40.2768	1.44214
$781$	−3.43861	−0.123043
$782$	−80.9687	−2.89543
$783$	−8.74311	−0.312453
$784$	16.6929	0.596176
$785$	88.3780	3.15435
$786$	−34.9488	−1.24658
$787$	−14.0942	−0.502405	−0.251203	−	0.967934i	$-0.580826\pi$
$787$	−14.0942	−0.502405	−0.251203	+	0.967934i	$0.580826\pi$
$788$	130.941	4.66460
$789$	−24.4029	−0.868766
$790$	159.488	5.67432
$791$	20.1795	0.717501
$792$	5.61894	0.199660
$793$	0.0939637	0.00333675
$794$	−65.2919	−2.31712
$795$	28.4733	1.00984
$796$	−114.883	−4.07192
$797$	−8.70735	−0.308430	−0.154215	−	0.988037i	$-0.549285\pi$
$797$	−8.70735	−0.308430	−0.154215	+	0.988037i	$0.549285\pi$
$798$	−8.12162	−0.287502
$799$	30.8581	1.09168
$800$	216.861	7.66718
$801$	4.29172	0.151640
$802$	−89.3155	−3.15384
$803$	6.81076	0.240347
$804$	−10.8858	−0.383914
$805$	−15.2882	−0.538838
$806$	5.04885	0.177838
$807$	18.5871	0.654298
$808$	106.995	3.76406
$809$	22.8454	0.803200	0.401600	−	0.915815i	$-0.368454\pi$
$809$	22.8454	0.803200	0.401600	+	0.915815i	$0.368454\pi$
$810$	−10.1133	−0.355347
$811$	−18.2254	−0.639981	−0.319990	−	0.947421i	$-0.603680\pi$
$811$	−18.2254	−0.639981	−0.319990	+	0.947421i	$0.603680\pi$
$812$	−49.4647	−1.73587
$813$	16.2454	0.569752
$814$	4.54860	0.159428
$815$	4.13781	0.144941
$816$	−116.761	−4.08745
$817$	−1.85000	−0.0647232
$818$	−33.6287	−1.17580
$819$	−1.94794	−0.0680665
$820$	5.13012	0.179152
$821$	−18.9953	−0.662940	−0.331470	−	0.943466i	$-0.607545\pi$
$821$	−18.9953	−0.662940	−0.331470	+	0.943466i	$0.607545\pi$
$822$	34.7122	1.21073
$823$	36.8392	1.28413	0.642067	−	0.766648i	$-0.278077\pi$
$823$	36.8392	1.28413	0.642067	+	0.766648i	$0.278077\pi$
$824$	−12.2994	−0.428469
$825$	−4.63929	−0.161519
$826$	−9.70997	−0.337853
$827$	−3.56729	−0.124047	−0.0620234	−	0.998075i	$-0.519755\pi$
$827$	−3.56729	−0.124047	−0.0620234	+	0.998075i	$0.519755\pi$
$828$	−23.6666	−0.822472
$829$	30.7868	1.06927	0.534636	−	0.845083i	$-0.320449\pi$
$829$	30.7868	1.06927	0.534636	+	0.845083i	$0.320449\pi$
$830$	139.740	4.85045
$831$	−0.627986	−0.0217846
$832$	74.8499	2.59495
$833$	6.99463	0.242350
$834$	58.2462	2.01690
$835$	−27.4539	−0.950082
$836$	−9.21814	−0.318816
$837$	−0.936637	−0.0323749
$838$	51.0815	1.76458
$839$	−12.1456	−0.419311	−0.209656	−	0.977775i	$-0.567234\pi$
$839$	−12.1456	−0.419311	−0.209656	+	0.977775i	$0.567234\pi$
$840$	−36.9902	−1.27628
$841$	47.4420	1.63593
$842$	−16.8372	−0.580248
$843$	24.1453	0.831610
$844$	−36.1999	−1.24605
$845$	33.6433	1.15736
$846$	12.2081	0.419724
$847$	10.6918	0.367375
$848$	130.053	4.46604
$849$	−1.57053	−0.0539004
$850$	161.750	5.54799
$851$	−12.3858	−0.424579
$852$	35.0426	1.20054
$853$	17.8567	0.611402	0.305701	−	0.952128i	$-0.401109\pi$
$853$	17.8567	0.611402	0.305701	+	0.952128i	$0.401109\pi$
$854$	−0.133484	−0.00456774
$855$	10.7262	0.366829
$856$	−97.5414	−3.33390
$857$	−6.09791	−0.208301	−0.104150	−	0.994562i	$-0.533212\pi$
$857$	−6.09791	−0.208301	−0.104150	+	0.994562i	$0.533212\pi$
$858$	−2.99252	−0.102163
$859$	32.1385	1.09655	0.548276	−	0.836297i	$-0.315284\pi$
$859$	32.1385	1.09655	0.548276	+	0.836297i	$0.315284\pi$
$860$	−13.0333	−0.444430
$861$	−0.248112	−0.00845565
$862$	108.024	3.67933
$863$	−17.6484	−0.600760	−0.300380	−	0.953820i	$-0.597114\pi$
$863$	−17.6484	−0.600760	−0.300380	+	0.953820i	$0.597114\pi$
$864$	−25.9505	−0.882854
$865$	59.3405	2.01764
$866$	−6.65583	−0.226174
$867$	−31.9249	−1.08423
$868$	−5.29909	−0.179863
$869$	−8.75486	−0.296988
$870$	88.4221	2.99779
$871$	3.74807	0.126999
$872$	133.467	4.51978
$873$	12.7904	0.432888
$874$	33.9742	1.14919
$875$	12.2677	0.414723
$876$	−69.4079	−2.34507
$877$	4.16997	0.140810	0.0704050	−	0.997518i	$-0.477571\pi$
$877$	4.16997	0.140810	0.0704050	+	0.997518i	$0.477571\pi$
$878$	74.2750	2.50666
$879$	−23.5738	−0.795125
$880$	−33.8687	−1.14171
$881$	−19.7775	−0.666322	−0.333161	−	0.942870i	$-0.608115\pi$
$881$	−19.7775	−0.666322	−0.333161	+	0.942870i	$0.608115\pi$
$882$	2.76723	0.0931775
$883$	−1.45909	−0.0491022	−0.0245511	−	0.999699i	$-0.507816\pi$
$883$	−1.45909	−0.0491022	−0.0245511	+	0.999699i	$0.507816\pi$
$884$	77.0850	2.59265
$885$	12.8240	0.431073
$886$	−86.5444	−2.90752
$887$	38.1475	1.28087	0.640435	−	0.768013i	$-0.278754\pi$
$887$	38.1475	1.28087	0.640435	+	0.768013i	$0.278754\pi$
$888$	−29.9677	−1.00565
$889$	−1.00000	−0.0335389
$890$	−43.4036	−1.45489
$891$	0.555158	0.0185985
$892$	−112.409	−3.76372
$893$	−12.9479	−0.433286
$894$	−41.8622	−1.40008
$895$	−24.1220	−0.806311
$896$	−54.4304	−1.81839
$897$	8.14858	0.272073
$898$	89.1732	2.97575
$899$	8.18912	0.273122
$900$	47.2786	1.57595
$901$	54.4946	1.81548
$902$	−0.381163	−0.0126913
$903$	0.630338	0.0209763
$904$	−204.244	−6.79304
$905$	−23.7107	−0.788172
$906$	9.25434	0.307455
$907$	−40.0841	−1.33097	−0.665485	−	0.746411i	$-0.731775\pi$
$907$	−40.0841	−1.33097	−0.665485	+	0.746411i	$0.731775\pi$
$908$	−82.8715	−2.75019
$909$	10.5712	0.350625
$910$	19.7002	0.653055
$911$	−6.62158	−0.219383	−0.109691	−	0.993966i	$-0.534986\pi$
$911$	−6.62158	−0.219383	−0.109691	+	0.993966i	$0.534986\pi$
$912$	48.9925	1.62230
$913$	−7.67083	−0.253868
$914$	97.7382	3.23289
$915$	0.176293	0.00582806
$916$	−3.83024	−0.126555
$917$	−12.6295	−0.417063
$918$	−19.3558	−0.638835
$919$	−42.7740	−1.41098	−0.705492	−	0.708718i	$-0.749274\pi$
$919$	−42.7740	−1.41098	−0.705492	+	0.708718i	$0.749274\pi$
$920$	154.737	5.10152
$921$	−17.0815	−0.562854
$922$	−64.3954	−2.12075
$923$	−12.0654	−0.397138
$924$	3.14084	0.103326
$925$	24.7429	0.813542
$926$	−54.9949	−1.80725
$927$	−1.21519	−0.0399122
$928$	226.888	7.44797
$929$	21.4514	0.703798	0.351899	−	0.936038i	$-0.385536\pi$
$929$	21.4514	0.703798	0.351899	+	0.936038i	$0.385536\pi$
$930$	9.47254	0.310617
$931$	−2.93493	−0.0961883
$932$	−123.298	−4.03876
$933$	−22.2805	−0.729431
$934$	37.6941	1.23339
$935$	−14.1916	−0.464115
$936$	19.7157	0.644429
$937$	35.3709	1.15552	0.577758	−	0.816208i	$-0.303928\pi$
$937$	35.3709	1.15552	0.577758	+	0.816208i	$0.303928\pi$
$938$	−5.32449	−0.173851
$939$	3.88085	0.126647
$940$	−91.2185	−2.97522
$941$	−23.7917	−0.775586	−0.387793	−	0.921746i	$-0.626762\pi$
$941$	−23.7917	−0.775586	−0.387793	+	0.921746i	$0.626762\pi$
$942$	66.9176	2.18029
$943$	1.03790	0.0337986
$944$	58.5740	1.90642
$945$	−3.65468	−0.118887
$946$	0.968357	0.0314840
$947$	−25.7666	−0.837303	−0.418651	−	0.908147i	$-0.637497\pi$
$947$	−25.7666	−0.837303	−0.418651	+	0.908147i	$0.637497\pi$
$948$	89.2200	2.89773
$949$	23.8976	0.775749
$950$	−67.8699	−2.20199
$951$	−28.0393	−0.909238
$952$	−70.7950	−2.29448
$953$	−3.23924	−0.104929	−0.0524646	−	0.998623i	$-0.516708\pi$
$953$	−3.23924	−0.104929	−0.0524646	+	0.998623i	$0.516708\pi$
$954$	21.5592	0.698006
$955$	−75.9558	−2.45787
$956$	−57.4595	−1.85837
$957$	−4.85381	−0.156901
$958$	−24.7784	−0.800553
$959$	12.5440	0.405068
$960$	140.432	4.53242
$961$	−30.1227	−0.971700
$962$	15.9601	0.514576
$963$	−9.63721	−0.310555
$964$	−72.4752	−2.33427
$965$	74.6409	2.40278
$966$	−11.5758	−0.372446
$967$	−55.7057	−1.79138	−0.895688	−	0.444683i	$-0.853316\pi$
$967$	−55.7057	−1.79138	−0.895688	+	0.444683i	$0.853316\pi$
$968$	−108.215	−3.47817
$969$	20.5287	0.659478
$970$	−129.353	−4.15328
$971$	−22.6780	−0.727773	−0.363886	−	0.931443i	$-0.618550\pi$
$971$	−22.6780	−0.727773	−0.363886	+	0.931443i	$0.618550\pi$
$972$	−5.65757	−0.181467
$973$	21.0486	0.674786
$974$	68.0069	2.17908
$975$	−16.2783	−0.521324
$976$	0.805225	0.0257746
$977$	31.1235	0.995731	0.497865	−	0.867254i	$-0.334117\pi$
$977$	31.1235	0.995731	0.497865	+	0.867254i	$0.334117\pi$
$978$	3.13304	0.100184
$979$	2.38258	0.0761476
$980$	−20.6766	−0.660490
$981$	13.1868	0.421021
$982$	15.6543	0.499549
$983$	−41.0026	−1.30778	−0.653890	−	0.756590i	$-0.726864\pi$
$983$	−41.0026	−1.30778	−0.653890	+	0.756590i	$0.726864\pi$
$984$	2.51123	0.0800550
$985$	−84.5857	−2.69513
$986$	169.230	5.38937
$987$	4.41168	0.140425
$988$	−32.3446	−1.02902
$989$	−2.63682	−0.0838460
$990$	−5.61450	−0.178441
$991$	−54.0876	−1.71815	−0.859074	−	0.511852i	$-0.828960\pi$
$991$	−54.0876	−1.71815	−0.859074	+	0.511852i	$0.828960\pi$
$992$	24.3062	0.771723
$993$	−22.4003	−0.710853
$994$	17.1401	0.543650
$995$	74.2123	2.35269
$996$	78.1728	2.47700
$997$	50.5374	1.60054	0.800268	−	0.599643i	$-0.204691\pi$
$997$	50.5374	1.60054	0.800268	+	0.599643i	$0.204691\pi$
$998$	56.8563	1.79975
$999$	−2.96085	−0.0936771

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.o.1.16	✓	16
3.2	odd	2		8001.2.a.r.1.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.o.1.16	✓	16	1.1	even	1	trivial
8001.2.a.r.1.1		16	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2667 = 3 \cdot 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2667.a (trivial)

\(f(q)\)	\(=\)	\(q+2.76723 q^{2} -1.00000 q^{3} +5.65757 q^{4} -3.65468 q^{5} -2.76723 q^{6} -1.00000 q^{7} +10.1213 q^{8} +1.00000 q^{9} -10.1133 q^{10} +0.555158 q^{11} -5.65757 q^{12} +1.94794 q^{13} -2.76723 q^{14} +3.65468 q^{15} +16.6929 q^{16} +6.99463 q^{17} +2.76723 q^{18} -2.93493 q^{19} -20.6766 q^{20} +1.00000 q^{21} +1.53625 q^{22} -4.18318 q^{23} -10.1213 q^{24} +8.35670 q^{25} +5.39040 q^{26} -1.00000 q^{27} -5.65757 q^{28} +8.74311 q^{29} +10.1133 q^{30} +0.936637 q^{31} +25.9505 q^{32} -0.555158 q^{33} +19.3558 q^{34} +3.65468 q^{35} +5.65757 q^{36} +2.96085 q^{37} -8.12162 q^{38} -1.94794 q^{39} -36.9902 q^{40} -0.248112 q^{41} +2.76723 q^{42} +0.630338 q^{43} +3.14084 q^{44} -3.65468 q^{45} -11.5758 q^{46} +4.41168 q^{47} -16.6929 q^{48} +1.00000 q^{49} +23.1249 q^{50} -6.99463 q^{51} +11.0206 q^{52} +7.79091 q^{53} -2.76723 q^{54} -2.02893 q^{55} -10.1213 q^{56} +2.93493 q^{57} +24.1942 q^{58} +3.50891 q^{59} +20.6766 q^{60} +0.0482375 q^{61} +2.59189 q^{62} -1.00000 q^{63} +38.4252 q^{64} -7.11910 q^{65} -1.53625 q^{66} +1.92412 q^{67} +39.5726 q^{68} +4.18318 q^{69} +10.1133 q^{70} -6.19394 q^{71} +10.1213 q^{72} +12.2682 q^{73} +8.19335 q^{74} -8.35670 q^{75} -16.6045 q^{76} -0.555158 q^{77} -5.39040 q^{78} -15.7700 q^{79} -61.0073 q^{80} +1.00000 q^{81} -0.686584 q^{82} -13.8174 q^{83} +5.65757 q^{84} -25.5632 q^{85} +1.74429 q^{86} -8.74311 q^{87} +5.61894 q^{88} +4.29172 q^{89} -10.1133 q^{90} -1.94794 q^{91} -23.6666 q^{92} -0.936637 q^{93} +12.2081 q^{94} +10.7262 q^{95} -25.9505 q^{96} +12.7904 q^{97} +2.76723 q^{98} +0.555158 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{2} - 16 q^{3} + 19 q^{4} - q^{5} - 5 q^{6} - 16 q^{7} + 6 q^{8} + 16 q^{9} - 12 q^{10} + 11 q^{11} - 19 q^{12} + 18 q^{13} - 5 q^{14} + q^{15} + 25 q^{16} - 5 q^{17} + 5 q^{18} - 11 q^{19}+ \cdots + 11 q^{99}+O(q^{100}) \) 16 * q + 5 * q^2 - 16 * q^3 + 19 * q^4 - q^5 - 5 * q^6 - 16 * q^7 + 6 * q^8 + 16 * q^9 - 12 * q^10 + 11 * q^11 - 19 * q^12 + 18 * q^13 - 5 * q^14 + q^15 + 25 * q^16 - 5 * q^17 + 5 * q^18 - 11 * q^19 - q^20 + 16 * q^21 + q^22 + 13 * q^23 - 6 * q^24 + 33 * q^25 + 8 * q^26 - 16 * q^27 - 19 * q^28 + 24 * q^29 + 12 * q^30 - 42 * q^31 + 42 * q^32 - 11 * q^33 + 9 * q^34 + q^35 + 19 * q^36 + 40 * q^37 + 38 * q^38 - 18 * q^39 - 61 * q^40 + 9 * q^41 + 5 * q^42 + 7 * q^43 + 3 * q^44 - q^45 + 24 * q^46 + 31 * q^47 - 25 * q^48 + 16 * q^49 + 6 * q^50 + 5 * q^51 + 52 * q^52 + 66 * q^53 - 5 * q^54 - 36 * q^55 - 6 * q^56 + 11 * q^57 + 19 * q^58 - 7 * q^59 + q^60 + 6 * q^61 + 52 * q^62 - 16 * q^63 + 10 * q^64 + 51 * q^65 - q^66 + 16 * q^67 + 14 * q^68 - 13 * q^69 + 12 * q^70 + 46 * q^71 + 6 * q^72 + 39 * q^73 + 72 * q^74 - 33 * q^75 + 24 * q^76 - 11 * q^77 - 8 * q^78 + 4 * q^79 - 2 * q^80 + 16 * q^81 - 18 * q^82 + 15 * q^83 + 19 * q^84 - 4 * q^85 + 14 * q^86 - 24 * q^87 + 58 * q^88 - q^89 - 12 * q^90 - 18 * q^91 + 26 * q^92 + 42 * q^93 + 5 * q^94 + 44 * q^95 - 42 * q^96 + 41 * q^97 + 5 * q^98 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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