LMFDB - Embedded newform 2667.2.a.p.1.4

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 = [18,-6,-18,22] 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:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 11 x^{16} + 123 x^{15} - 35 x^{14} - 982 x^{13} + 988 x^{12} + 3872 x^{11} + \cdots + 16 $ x^18 - 6x^17 - 11x^16 + 123x^15 - 35x^14 - 982x^13 + 988x^12 + 3872x^11 - 5421x^10 - 7882x^9 + 13376x^8 + 7948x^7 - 15795x^6 - 3858x^5 + 8199x^4 + 1453x^3 - 1610x^2 - 380*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.40246$ 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)

$f(q)$	$=$	\(q-2.40246 q^{2} -1.00000 q^{3} +3.77179 q^{4} -0.666645 q^{5} +2.40246 q^{6} +1.00000 q^{7} -4.25666 q^{8} +1.00000 q^{9} +1.60159 q^{10} -5.05203 q^{11} -3.77179 q^{12} +5.76961 q^{13} -2.40246 q^{14} +0.666645 q^{15} +2.68284 q^{16} -0.396381 q^{17} -2.40246 q^{18} +3.56828 q^{19} -2.51445 q^{20} -1.00000 q^{21} +12.1373 q^{22} -4.24325 q^{23} +4.25666 q^{24} -4.55558 q^{25} -13.8612 q^{26} -1.00000 q^{27} +3.77179 q^{28} +0.519685 q^{29} -1.60159 q^{30} +3.84273 q^{31} +2.06791 q^{32} +5.05203 q^{33} +0.952288 q^{34} -0.666645 q^{35} +3.77179 q^{36} -7.00515 q^{37} -8.57264 q^{38} -5.76961 q^{39} +2.83768 q^{40} +3.06775 q^{41} +2.40246 q^{42} -4.79677 q^{43} -19.0552 q^{44} -0.666645 q^{45} +10.1942 q^{46} +11.2665 q^{47} -2.68284 q^{48} +1.00000 q^{49} +10.9446 q^{50} +0.396381 q^{51} +21.7618 q^{52} -1.29111 q^{53} +2.40246 q^{54} +3.36791 q^{55} -4.25666 q^{56} -3.56828 q^{57} -1.24852 q^{58} -1.96260 q^{59} +2.51445 q^{60} -9.45403 q^{61} -9.23199 q^{62} +1.00000 q^{63} -10.3337 q^{64} -3.84628 q^{65} -12.1373 q^{66} -8.88556 q^{67} -1.49507 q^{68} +4.24325 q^{69} +1.60159 q^{70} -8.51845 q^{71} -4.25666 q^{72} -6.50942 q^{73} +16.8296 q^{74} +4.55558 q^{75} +13.4588 q^{76} -5.05203 q^{77} +13.8612 q^{78} +14.8928 q^{79} -1.78850 q^{80} +1.00000 q^{81} -7.37013 q^{82} +13.6579 q^{83} -3.77179 q^{84} +0.264246 q^{85} +11.5240 q^{86} -0.519685 q^{87} +21.5047 q^{88} -12.6023 q^{89} +1.60159 q^{90} +5.76961 q^{91} -16.0047 q^{92} -3.84273 q^{93} -27.0673 q^{94} -2.37878 q^{95} -2.06791 q^{96} +9.21904 q^{97} -2.40246 q^{98} -5.05203 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{2} - 18 q^{3} + 22 q^{4} - 10 q^{5} + 6 q^{6} + 18 q^{7} - 21 q^{8} + 18 q^{9} - 4 q^{10} - 9 q^{11} - 22 q^{12} - 25 q^{13} - 6 q^{14} + 10 q^{15} + 34 q^{16} - 17 q^{17} - 6 q^{18} - 5 q^{19}+ \cdots - 9 q^{99}+O(q^{100}) $ 18 * q - 6 * q^2 - 18 * q^3 + 22 * q^4 - 10 * q^5 + 6 * q^6 + 18 * q^7 - 21 * q^8 + 18 * q^9 - 4 * q^10 - 9 * q^11 - 22 * q^12 - 25 * q^13 - 6 * q^14 + 10 * q^15 + 34 * q^16 - 17 * q^17 - 6 * q^18 - 5 * q^19 - 21 * q^20 - 18 * q^21 + 5 * q^22 - 14 * q^23 + 21 * q^24 + 28 * q^25 - 8 * q^26 - 18 * q^27 + 22 * q^28 - 17 * q^29 + 4 * q^30 + 5 * q^31 - 53 * q^32 + 9 * q^33 - 19 * q^34 - 10 * q^35 + 22 * q^36 - 15 * q^37 - 22 * q^38 + 25 * q^39 - q^40 - 17 * q^41 + 6 * q^42 + q^43 - 33 * q^44 - 10 * q^45 + 10 * q^46 - 31 * q^47 - 34 * q^48 + 18 * q^49 - 35 * q^50 + 17 * q^51 - 70 * q^52 - 35 * q^53 + 6 * q^54 + 4 * q^55 - 21 * q^56 + 5 * q^57 + 3 * q^58 - 46 * q^59 + 21 * q^60 - 5 * q^61 - 10 * q^62 + 18 * q^63 + 63 * q^64 - 12 * q^65 - 5 * q^66 + 6 * q^67 - 56 * q^68 + 14 * q^69 - 4 * q^70 - 22 * q^71 - 21 * q^72 - 16 * q^73 + 18 * q^74 - 28 * q^75 + 32 * q^76 - 9 * q^77 + 8 * q^78 + 46 * q^79 - 30 * q^80 + 18 * q^81 - 12 * q^82 - 46 * q^83 - 22 * q^84 + 4 * q^85 + 18 * q^86 + 17 * q^87 + 30 * q^88 - 42 * q^89 - 4 * q^90 - 25 * q^91 - 48 * q^92 - 5 * q^93 + 3 * q^94 - 2 * q^95 + 53 * q^96 - 35 * q^97 - 6 * q^98 - 9 * 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 $

$2$	−2.40246	−1.69879	−0.849396	−	0.527755i	$-0.823034\pi$
$2$	−2.40246	−1.69879	−0.849396	+	0.527755i	$0.823034\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.77179	1.88590
$5$	−0.666645	−0.298133	−0.149066	−	0.988827i	$-0.547627\pi$
$5$	−0.666645	−0.298133	−0.149066	+	0.988827i	$0.547627\pi$
$6$	2.40246	0.980798
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−4.25666	−1.50496
$9$	1.00000	0.333333
$10$	1.60159	0.506466
$11$	−5.05203	−1.52324	−0.761622	−	0.648022i	$-0.775597\pi$
$11$	−5.05203	−1.52324	−0.761622	+	0.648022i	$0.775597\pi$
$12$	−3.77179	−1.08882
$13$	5.76961	1.60020	0.800101	−	0.599866i	$-0.204779\pi$
$13$	5.76961	1.60020	0.800101	+	0.599866i	$0.204779\pi$
$14$	−2.40246	−0.642083
$15$	0.666645	0.172127
$16$	2.68284	0.670710
$17$	−0.396381	−0.0961366	−0.0480683	−	0.998844i	$-0.515307\pi$
$17$	−0.396381	−0.0961366	−0.0480683	+	0.998844i	$0.515307\pi$
$18$	−2.40246	−0.566264
$19$	3.56828	0.818620	0.409310	−	0.912395i	$-0.365769\pi$
$19$	3.56828	0.818620	0.409310	+	0.912395i	$0.365769\pi$
$20$	−2.51445	−0.562248
$21$	−1.00000	−0.218218
$22$	12.1373	2.58768
$23$	−4.24325	−0.884780	−0.442390	−	0.896823i	$-0.645869\pi$
$23$	−4.24325	−0.884780	−0.442390	+	0.896823i	$0.645869\pi$
$24$	4.25666	0.868886
$25$	−4.55558	−0.911117
$26$	−13.8612	−2.71841
$27$	−1.00000	−0.192450
$28$	3.77179	0.712802
$29$	0.519685	0.0965030	0.0482515	−	0.998835i	$-0.484635\pi$
$29$	0.519685	0.0965030	0.0482515	+	0.998835i	$0.484635\pi$
$30$	−1.60159	−0.292408
$31$	3.84273	0.690175	0.345087	−	0.938571i	$-0.387849\pi$
$31$	3.84273	0.690175	0.345087	+	0.938571i	$0.387849\pi$
$32$	2.06791	0.365558
$33$	5.05203	0.879445
$34$	0.952288	0.163316
$35$	−0.666645	−0.112684
$36$	3.77179	0.628632
$37$	−7.00515	−1.15164	−0.575820	−	0.817577i	$-0.695317\pi$
$37$	−7.00515	−1.15164	−0.575820	+	0.817577i	$0.695317\pi$
$38$	−8.57264	−1.39067
$39$	−5.76961	−0.923876
$40$	2.83768	0.448677
$41$	3.06775	0.479102	0.239551	−	0.970884i	$-0.423000\pi$
$41$	3.06775	0.479102	0.239551	+	0.970884i	$0.423000\pi$
$42$	2.40246	0.370707
$43$	−4.79677	−0.731501	−0.365750	−	0.930713i	$-0.619188\pi$
$43$	−4.79677	−0.731501	−0.365750	+	0.930713i	$0.619188\pi$
$44$	−19.0552	−2.87268
$45$	−0.666645	−0.0993776
$46$	10.1942	1.50306
$47$	11.2665	1.64339	0.821696	−	0.569926i	$-0.193028\pi$
$47$	11.2665	1.64339	0.821696	+	0.569926i	$0.193028\pi$
$48$	−2.68284	−0.387235
$49$	1.00000	0.142857
$50$	10.9446	1.54780
$51$	0.396381	0.0555045
$52$	21.7618	3.01781
$53$	−1.29111	−0.177348	−0.0886740	−	0.996061i	$-0.528263\pi$
$53$	−1.29111	−0.177348	−0.0886740	+	0.996061i	$0.528263\pi$
$54$	2.40246	0.326933
$55$	3.36791	0.454129
$56$	−4.25666	−0.568820
$57$	−3.56828	−0.472630
$58$	−1.24852	−0.163939
$59$	−1.96260	−0.255509	−0.127755	−	0.991806i	$-0.540777\pi$
$59$	−1.96260	−0.255509	−0.127755	+	0.991806i	$0.540777\pi$
$60$	2.51445	0.324614
$61$	−9.45403	−1.21046	−0.605232	−	0.796049i	$-0.706920\pi$
$61$	−9.45403	−1.21046	−0.605232	+	0.796049i	$0.706920\pi$
$62$	−9.23199	−1.17246
$63$	1.00000	0.125988
$64$	−10.3337	−1.29172
$65$	−3.84628	−0.477073
$66$	−12.1373	−1.49399
$67$	−8.88556	−1.08554	−0.542772	−	0.839880i	$-0.682625\pi$
$67$	−8.88556	−1.08554	−0.542772	+	0.839880i	$0.682625\pi$
$68$	−1.49507	−0.181304
$69$	4.24325	0.510828
$70$	1.60159	0.191426
$71$	−8.51845	−1.01095	−0.505477	−	0.862840i	$-0.668683\pi$
$71$	−8.51845	−1.01095	−0.505477	+	0.862840i	$0.668683\pi$
$72$	−4.25666	−0.501652
$73$	−6.50942	−0.761870	−0.380935	−	0.924602i	$-0.624398\pi$
$73$	−6.50942	−0.761870	−0.380935	+	0.924602i	$0.624398\pi$
$74$	16.8296	1.95640
$75$	4.55558	0.526034
$76$	13.4588	1.54383
$77$	−5.05203	−0.575732
$78$	13.8612	1.56947
$79$	14.8928	1.67557	0.837783	−	0.546004i	$-0.183852\pi$
$79$	14.8928	1.67557	0.837783	+	0.546004i	$0.183852\pi$
$80$	−1.78850	−0.199961
$81$	1.00000	0.111111
$82$	−7.37013	−0.813894
$83$	13.6579	1.49915	0.749575	−	0.661919i	$-0.230258\pi$
$83$	13.6579	1.49915	0.749575	+	0.661919i	$0.230258\pi$
$84$	−3.77179	−0.411536
$85$	0.264246	0.0286615
$86$	11.5240	1.24267
$87$	−0.519685	−0.0557161
$88$	21.5047	2.29241
$89$	−12.6023	−1.33585	−0.667923	−	0.744231i	$-0.732816\pi$
$89$	−12.6023	−1.33585	−0.667923	+	0.744231i	$0.732816\pi$
$90$	1.60159	0.168822
$91$	5.76961	0.604819
$92$	−16.0047	−1.66860
$93$	−3.84273	−0.398473
$94$	−27.0673	−2.79178
$95$	−2.37878	−0.244058
$96$	−2.06791	−0.211055
$97$	9.21904	0.936052	0.468026	−	0.883715i	$-0.344965\pi$
$97$	9.21904	0.936052	0.468026	+	0.883715i	$0.344965\pi$
$98$	−2.40246	−0.242685
$99$	−5.05203	−0.507748
$100$	−17.1827	−1.71827
$101$	5.22301	0.519709	0.259855	−	0.965648i	$-0.416325\pi$
$101$	5.22301	0.519709	0.259855	+	0.965648i	$0.416325\pi$
$102$	−0.952288	−0.0942906
$103$	−1.04722	−0.103185	−0.0515926	−	0.998668i	$-0.516430\pi$
$103$	−1.04722	−0.103185	−0.0515926	+	0.998668i	$0.516430\pi$
$104$	−24.5592	−2.40823
$105$	0.666645	0.0650579
$106$	3.10184	0.301277
$107$	15.4399	1.49263	0.746317	−	0.665590i	$-0.231820\pi$
$107$	15.4399	1.49263	0.746317	+	0.665590i	$0.231820\pi$
$108$	−3.77179	−0.362941
$109$	8.22589	0.787897	0.393949	−	0.919132i	$-0.371109\pi$
$109$	8.22589	0.787897	0.393949	+	0.919132i	$0.371109\pi$
$110$	−8.09126	−0.771471
$111$	7.00515	0.664900
$112$	2.68284	0.253505
$113$	−2.61402	−0.245906	−0.122953	−	0.992412i	$-0.539236\pi$
$113$	−2.61402	−0.245906	−0.122953	+	0.992412i	$0.539236\pi$
$114$	8.57264	0.802901
$115$	2.82875	0.263782
$116$	1.96014	0.181995
$117$	5.76961	0.533400
$118$	4.71506	0.434057
$119$	−0.396381	−0.0363362
$120$	−2.83768	−0.259044
$121$	14.5230	1.32027
$122$	22.7129	2.05633
$123$	−3.06775	−0.276609
$124$	14.4940	1.30160
$125$	6.37019	0.569767
$126$	−2.40246	−0.214028
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	20.6905	1.82880
$129$	4.79677	0.422332
$130$	9.24052	0.810447
$131$	14.8530	1.29771	0.648855	−	0.760912i	$-0.275248\pi$
$131$	14.8530	1.29771	0.648855	+	0.760912i	$0.275248\pi$
$132$	19.0552	1.65854
$133$	3.56828	0.309409
$134$	21.3472	1.84411
$135$	0.666645	0.0573757
$136$	1.68726	0.144681
$137$	−20.4969	−1.75117	−0.875583	−	0.483068i	$-0.839522\pi$
$137$	−20.4969	−1.75117	−0.875583	+	0.483068i	$0.839522\pi$
$138$	−10.1942	−0.867791
$139$	−3.53740	−0.300039	−0.150019	−	0.988683i	$-0.547934\pi$
$139$	−3.53740	−0.300039	−0.150019	+	0.988683i	$0.547934\pi$
$140$	−2.51445	−0.212510
$141$	−11.2665	−0.948813
$142$	20.4652	1.71740
$143$	−29.1482	−2.43750
$144$	2.68284	0.223570
$145$	−0.346445	−0.0287707
$146$	15.6386	1.29426
$147$	−1.00000	−0.0824786
$148$	−26.4220	−2.17187
$149$	−19.9965	−1.63817	−0.819087	−	0.573669i	$-0.805520\pi$
$149$	−19.9965	−1.63817	−0.819087	+	0.573669i	$0.805520\pi$
$150$	−10.9446	−0.893622
$151$	18.2975	1.48903	0.744516	−	0.667605i	$-0.232680\pi$
$151$	18.2975	1.48903	0.744516	+	0.667605i	$0.232680\pi$
$152$	−15.1889	−1.23199
$153$	−0.396381	−0.0320455
$154$	12.1373	0.978049
$155$	−2.56174	−0.205764
$156$	−21.7618	−1.74234
$157$	−23.8970	−1.90718	−0.953592	−	0.301100i	$-0.902646\pi$
$157$	−23.8970	−1.90718	−0.953592	+	0.301100i	$0.902646\pi$
$158$	−35.7792	−2.84644
$159$	1.29111	0.102392
$160$	−1.37856	−0.108985
$161$	−4.24325	−0.334415
$162$	−2.40246	−0.188755
$163$	−14.7857	−1.15810	−0.579051	−	0.815291i	$-0.696577\pi$
$163$	−14.7857	−1.15810	−0.579051	+	0.815291i	$0.696577\pi$
$164$	11.5709	0.903536
$165$	−3.36791	−0.262192
$166$	−32.8125	−2.54675
$167$	21.2454	1.64402	0.822010	−	0.569474i	$-0.192853\pi$
$167$	21.2454	1.64402	0.822010	+	0.569474i	$0.192853\pi$
$168$	4.25666	0.328408
$169$	20.2884	1.56064
$170$	−0.634839	−0.0486899
$171$	3.56828	0.272873
$172$	−18.0924	−1.37954
$173$	−8.03384	−0.610802	−0.305401	−	0.952224i	$-0.598790\pi$
$173$	−8.03384	−0.610802	−0.305401	+	0.952224i	$0.598790\pi$
$174$	1.24852	0.0946500
$175$	−4.55558	−0.344370
$176$	−13.5538	−1.02165
$177$	1.96260	0.147518
$178$	30.2766	2.26932
$179$	−18.5927	−1.38968	−0.694840	−	0.719164i	$-0.744525\pi$
$179$	−18.5927	−1.38968	−0.694840	+	0.719164i	$0.744525\pi$
$180$	−2.51445	−0.187416
$181$	10.8782	0.808569	0.404284	−	0.914633i	$-0.367521\pi$
$181$	10.8782	0.808569	0.404284	+	0.914633i	$0.367521\pi$
$182$	−13.8612	−1.02746
$183$	9.45403	0.698862
$184$	18.0621	1.33155
$185$	4.66995	0.343342
$186$	9.23199	0.676922
$187$	2.00253	0.146439
$188$	42.4950	3.09927
$189$	−1.00000	−0.0727393
$190$	5.71491	0.414603
$191$	19.0877	1.38114	0.690570	−	0.723266i	$-0.257360\pi$
$191$	19.0877	1.38114	0.690570	+	0.723266i	$0.257360\pi$
$192$	10.3337	0.745773
$193$	−16.5306	−1.18990	−0.594951	−	0.803762i	$-0.702828\pi$
$193$	−16.5306	−1.18990	−0.594951	+	0.803762i	$0.702828\pi$
$194$	−22.1483	−1.59016
$195$	3.84628	0.275438
$196$	3.77179	0.269414
$197$	−26.3357	−1.87634	−0.938169	−	0.346178i	$-0.887479\pi$
$197$	−26.3357	−1.87634	−0.938169	+	0.346178i	$0.887479\pi$
$198$	12.1373	0.862558
$199$	−0.679810	−0.0481905	−0.0240952	−	0.999710i	$-0.507670\pi$
$199$	−0.679810	−0.0481905	−0.0240952	+	0.999710i	$0.507670\pi$
$200$	19.3916	1.37119
$201$	8.88556	0.626739
$202$	−12.5481	−0.882878
$203$	0.519685	0.0364747
$204$	1.49507	0.104676
$205$	−2.04510	−0.142836
$206$	2.51589	0.175290
$207$	−4.24325	−0.294927
$208$	15.4789	1.07327
$209$	−18.0271	−1.24696
$210$	−1.60159	−0.110520
$211$	17.0443	1.17338	0.586688	−	0.809813i	$-0.300432\pi$
$211$	17.0443	1.17338	0.586688	+	0.809813i	$0.300432\pi$
$212$	−4.86981	−0.334460
$213$	8.51845	0.583674
$214$	−37.0938	−2.53568
$215$	3.19775	0.218084
$216$	4.25666	0.289629
$217$	3.84273	0.260862
$218$	−19.7623	−1.33847
$219$	6.50942	0.439866
$220$	12.7031	0.856441
$221$	−2.28696	−0.153838
$222$	−16.8296	−1.12953
$223$	−20.7478	−1.38938	−0.694689	−	0.719311i	$-0.744458\pi$
$223$	−20.7478	−1.38938	−0.694689	+	0.719311i	$0.744458\pi$
$224$	2.06791	0.138168
$225$	−4.55558	−0.303706
$226$	6.28006	0.417744
$227$	−10.9843	−0.729051	−0.364525	−	0.931193i	$-0.618769\pi$
$227$	−10.9843	−0.729051	−0.364525	+	0.931193i	$0.618769\pi$
$228$	−13.4588	−0.891332
$229$	−3.69557	−0.244210	−0.122105	−	0.992517i	$-0.538964\pi$
$229$	−3.69557	−0.244210	−0.122105	+	0.992517i	$0.538964\pi$
$230$	−6.79594	−0.448111
$231$	5.05203	0.332399
$232$	−2.21212	−0.145233
$233$	−27.0298	−1.77078	−0.885389	−	0.464851i	$-0.846108\pi$
$233$	−27.0298	−1.77078	−0.885389	+	0.464851i	$0.846108\pi$
$234$	−13.8612	−0.906137
$235$	−7.51078	−0.489949
$236$	−7.40253	−0.481864
$237$	−14.8928	−0.967388
$238$	0.952288	0.0617277
$239$	2.63505	0.170447	0.0852235	−	0.996362i	$-0.472840\pi$
$239$	2.63505	0.170447	0.0852235	+	0.996362i	$0.472840\pi$
$240$	1.78850	0.115447
$241$	16.8404	1.08478	0.542392	−	0.840125i	$-0.317519\pi$
$241$	16.8404	1.08478	0.542392	+	0.840125i	$0.317519\pi$
$242$	−34.8908	−2.24287
$243$	−1.00000	−0.0641500
$244$	−35.6587	−2.28281
$245$	−0.666645	−0.0425904
$246$	7.37013	0.469902
$247$	20.5876	1.30996
$248$	−16.3572	−1.03868
$249$	−13.6579	−0.865535
$250$	−15.3041	−0.967916
$251$	−22.7185	−1.43398	−0.716990	−	0.697083i	$-0.754481\pi$
$251$	−22.7185	−1.43398	−0.716990	+	0.697083i	$0.754481\pi$
$252$	3.77179	0.237601
$253$	21.4370	1.34774
$254$	−2.40246	−0.150743
$255$	−0.264246	−0.0165477
$256$	−29.0406	−1.81504
$257$	−16.8856	−1.05330	−0.526648	−	0.850084i	$-0.676551\pi$
$257$	−16.8856	−1.05330	−0.526648	+	0.850084i	$0.676551\pi$
$258$	−11.5240	−0.717455
$259$	−7.00515	−0.435279
$260$	−14.5074	−0.899710
$261$	0.519685	0.0321677
$262$	−35.6836	−2.20454
$263$	−14.4874	−0.893334	−0.446667	−	0.894700i	$-0.647389\pi$
$263$	−14.4874	−0.893334	−0.446667	+	0.894700i	$0.647389\pi$
$264$	−21.5047	−1.32353
$265$	0.860714	0.0528733
$266$	−8.57264	−0.525622
$267$	12.6023	0.771251
$268$	−33.5145	−2.04722
$269$	19.0894	1.16390	0.581952	−	0.813223i	$-0.302289\pi$
$269$	19.0894	1.16390	0.581952	+	0.813223i	$0.302289\pi$
$270$	−1.60159	−0.0974694
$271$	−12.5847	−0.764467	−0.382234	−	0.924066i	$-0.624845\pi$
$271$	−12.5847	−0.764467	−0.382234	+	0.924066i	$0.624845\pi$
$272$	−1.06343	−0.0644798
$273$	−5.76961	−0.349192
$274$	49.2428	2.97487
$275$	23.0149	1.38785
$276$	16.0047	0.963369
$277$	−23.5452	−1.41470	−0.707348	−	0.706866i	$-0.750108\pi$
$277$	−23.5452	−1.41470	−0.707348	+	0.706866i	$0.750108\pi$
$278$	8.49845	0.509703
$279$	3.84273	0.230058
$280$	2.83768	0.169584
$281$	−17.3606	−1.03565	−0.517824	−	0.855487i	$-0.673258\pi$
$281$	−17.3606	−1.03565	−0.517824	+	0.855487i	$0.673258\pi$
$282$	27.0673	1.61184
$283$	−28.0114	−1.66511	−0.832554	−	0.553945i	$-0.813122\pi$
$283$	−28.0114	−1.66511	−0.832554	+	0.553945i	$0.813122\pi$
$284$	−32.1298	−1.90655
$285$	2.37878	0.140907
$286$	70.0273	4.14080
$287$	3.06775	0.181083
$288$	2.06791	0.121853
$289$	−16.8429	−0.990758
$290$	0.832320	0.0488755
$291$	−9.21904	−0.540430
$292$	−24.5522	−1.43681
$293$	22.0696	1.28932	0.644661	−	0.764469i	$-0.276999\pi$
$293$	22.0696	1.28932	0.644661	+	0.764469i	$0.276999\pi$
$294$	2.40246	0.140114
$295$	1.30836	0.0761756
$296$	29.8185	1.73317
$297$	5.05203	0.293148
$298$	48.0406	2.78292
$299$	−24.4819	−1.41583
$300$	17.1827	0.992045
$301$	−4.79677	−0.276481
$302$	−43.9590	−2.52956
$303$	−5.22301	−0.300054
$304$	9.57313	0.549057
$305$	6.30249	0.360879
$306$	0.952288	0.0544387
$307$	−17.8522	−1.01888	−0.509439	−	0.860507i	$-0.670147\pi$
$307$	−17.8522	−1.01888	−0.509439	+	0.860507i	$0.670147\pi$
$308$	−19.0552	−1.08577
$309$	1.04722	0.0595740
$310$	6.15447	0.349550
$311$	−15.7490	−0.893045	−0.446522	−	0.894772i	$-0.647338\pi$
$311$	−15.7490	−0.893045	−0.446522	+	0.894772i	$0.647338\pi$
$312$	24.5592	1.39039
$313$	−15.8596	−0.896439	−0.448219	−	0.893924i	$-0.647942\pi$
$313$	−15.8596	−0.896439	−0.448219	+	0.893924i	$0.647942\pi$
$314$	57.4114	3.23991
$315$	−0.666645	−0.0375612
$316$	56.1724	3.15994
$317$	28.1773	1.58259	0.791296	−	0.611433i	$-0.209407\pi$
$317$	28.1773	1.58259	0.791296	+	0.611433i	$0.209407\pi$
$318$	−3.10184	−0.173943
$319$	−2.62546	−0.146998
$320$	6.88894	0.385103
$321$	−15.4399	−0.861773
$322$	10.1942	0.568102
$323$	−1.41440	−0.0786993
$324$	3.77179	0.209544
$325$	−26.2839	−1.45797
$326$	35.5219	1.96738
$327$	−8.22589	−0.454893
$328$	−13.0583	−0.721026
$329$	11.2665	0.621144
$330$	8.09126	0.445409
$331$	−27.8507	−1.53081	−0.765406	−	0.643547i	$-0.777462\pi$
$331$	−27.8507	−1.53081	−0.765406	+	0.643547i	$0.777462\pi$
$332$	51.5148	2.82724
$333$	−7.00515	−0.383880
$334$	−51.0412	−2.79285
$335$	5.92352	0.323636
$336$	−2.68284	−0.146361
$337$	−7.64516	−0.416458	−0.208229	−	0.978080i	$-0.566770\pi$
$337$	−7.64516	−0.416458	−0.208229	+	0.978080i	$0.566770\pi$
$338$	−48.7419	−2.65121
$339$	2.61402	0.141974
$340$	0.996680	0.0540526
$341$	−19.4136	−1.05130
$342$	−8.57264	−0.463555
$343$	1.00000	0.0539949
$344$	20.4182	1.10088
$345$	−2.82875	−0.152295
$346$	19.3010	1.03763
$347$	22.1004	1.18641	0.593205	−	0.805052i	$-0.297863\pi$
$347$	22.1004	1.18641	0.593205	+	0.805052i	$0.297863\pi$
$348$	−1.96014	−0.105075
$349$	7.12427	0.381353	0.190677	−	0.981653i	$-0.438932\pi$
$349$	7.12427	0.381353	0.190677	+	0.981653i	$0.438932\pi$
$350$	10.9446	0.585013
$351$	−5.76961	−0.307959
$352$	−10.4471	−0.556833
$353$	−14.0285	−0.746662	−0.373331	−	0.927698i	$-0.621784\pi$
$353$	−14.0285	−0.746662	−0.373331	+	0.927698i	$0.621784\pi$
$354$	−4.71506	−0.250603
$355$	5.67878	0.301399
$356$	−47.5334	−2.51927
$357$	0.396381	0.0209787
$358$	44.6680	2.36078
$359$	6.03937	0.318746	0.159373	−	0.987218i	$-0.449053\pi$
$359$	6.03937	0.318746	0.159373	+	0.987218i	$0.449053\pi$
$360$	2.83768	0.149559
$361$	−6.26736	−0.329861
$362$	−26.1343	−1.37359
$363$	−14.5230	−0.762259
$364$	21.7618	1.14063
$365$	4.33948	0.227139
$366$	−22.7129	−1.18722
$367$	−12.6586	−0.660775	−0.330387	−	0.943845i	$-0.607179\pi$
$367$	−12.6586	−0.660775	−0.330387	+	0.943845i	$0.607179\pi$
$368$	−11.3840	−0.593431
$369$	3.06775	0.159701
$370$	−11.2194	−0.583267
$371$	−1.29111	−0.0670312
$372$	−14.4940	−0.751478
$373$	16.3249	0.845269	0.422635	−	0.906300i	$-0.361105\pi$
$373$	16.3249	0.845269	0.422635	+	0.906300i	$0.361105\pi$
$374$	−4.81099	−0.248770
$375$	−6.37019	−0.328955
$376$	−47.9577	−2.47323
$377$	2.99838	0.154424
$378$	2.40246	0.123569
$379$	16.1793	0.831074	0.415537	−	0.909576i	$-0.363594\pi$
$379$	16.1793	0.831074	0.415537	+	0.909576i	$0.363594\pi$
$380$	−8.97226	−0.460267
$381$	−1.00000	−0.0512316
$382$	−45.8574	−2.34627
$383$	−14.1963	−0.725399	−0.362699	−	0.931906i	$-0.618145\pi$
$383$	−14.1963	−0.725399	−0.362699	+	0.931906i	$0.618145\pi$
$384$	−20.6905	−1.05586
$385$	3.36791	0.171645
$386$	39.7141	2.02140
$387$	−4.79677	−0.243834
$388$	34.7723	1.76530
$389$	1.32405	0.0671318	0.0335659	−	0.999437i	$-0.489314\pi$
$389$	1.32405	0.0671318	0.0335659	+	0.999437i	$0.489314\pi$
$390$	−9.24052	−0.467912
$391$	1.68195	0.0850597
$392$	−4.25666	−0.214994
$393$	−14.8530	−0.749233
$394$	63.2702	3.18751
$395$	−9.92819	−0.499541
$396$	−19.0552	−0.957560
$397$	−33.9588	−1.70434	−0.852172	−	0.523262i	$-0.824715\pi$
$397$	−33.9588	−1.70434	−0.852172	+	0.523262i	$0.824715\pi$
$398$	1.63321	0.0818656
$399$	−3.56828	−0.178638
$400$	−12.2219	−0.611095
$401$	−3.27288	−0.163440	−0.0817198	−	0.996655i	$-0.526041\pi$
$401$	−3.27288	−0.163440	−0.0817198	+	0.996655i	$0.526041\pi$
$402$	−21.3472	−1.06470
$403$	22.1710	1.10442
$404$	19.7001	0.980118
$405$	−0.666645	−0.0331259
$406$	−1.24852	−0.0619630
$407$	35.3902	1.75423
$408$	−1.68726	−0.0835317
$409$	7.93648	0.392434	0.196217	−	0.980561i	$-0.437134\pi$
$409$	7.93648	0.392434	0.196217	+	0.980561i	$0.437134\pi$
$410$	4.91326	0.242649
$411$	20.4969	1.01104
$412$	−3.94988	−0.194597
$413$	−1.96260	−0.0965733
$414$	10.1942	0.501019
$415$	−9.10498	−0.446946
$416$	11.9310	0.584966
$417$	3.53740	0.173227
$418$	43.3092	2.11832
$419$	−21.1144	−1.03151	−0.515754	−	0.856737i	$-0.672488\pi$
$419$	−21.1144	−1.03151	−0.515754	+	0.856737i	$0.672488\pi$
$420$	2.51445	0.122693
$421$	−30.0789	−1.46596	−0.732978	−	0.680252i	$-0.761870\pi$
$421$	−30.0789	−1.46596	−0.732978	+	0.680252i	$0.761870\pi$
$422$	−40.9481	−1.99332
$423$	11.2665	0.547797
$424$	5.49582	0.266901
$425$	1.80575	0.0875916
$426$	−20.4652	−0.991542
$427$	−9.45403	−0.457513
$428$	58.2362	2.81495
$429$	29.1482	1.40729
$430$	−7.68244	−0.370480
$431$	−16.0258	−0.771938	−0.385969	−	0.922512i	$-0.626133\pi$
$431$	−16.0258	−0.771938	−0.385969	+	0.922512i	$0.626133\pi$
$432$	−2.68284	−0.129078
$433$	7.23386	0.347637	0.173819	−	0.984778i	$-0.444389\pi$
$433$	7.23386	0.347637	0.173819	+	0.984778i	$0.444389\pi$
$434$	−9.23199	−0.443150
$435$	0.346445	0.0166108
$436$	31.0264	1.48589
$437$	−15.1411	−0.724298
$438$	−15.6386	−0.747241
$439$	−10.4196	−0.497300	−0.248650	−	0.968593i	$-0.579987\pi$
$439$	−10.4196	−0.497300	−0.248650	+	0.968593i	$0.579987\pi$
$440$	−14.3360	−0.683444
$441$	1.00000	0.0476190
$442$	5.49433	0.261339
$443$	−9.43052	−0.448057	−0.224029	−	0.974583i	$-0.571921\pi$
$443$	−9.43052	−0.448057	−0.224029	+	0.974583i	$0.571921\pi$
$444$	26.4220	1.25393
$445$	8.40129	0.398259
$446$	49.8457	2.36026
$447$	19.9965	0.945800
$448$	−10.3337	−0.488223
$449$	−6.74268	−0.318207	−0.159103	−	0.987262i	$-0.550860\pi$
$449$	−6.74268	−0.318207	−0.159103	+	0.987262i	$0.550860\pi$
$450$	10.9446	0.515933
$451$	−15.4983	−0.729788
$452$	−9.85954	−0.463754
$453$	−18.2975	−0.859693
$454$	26.3892	1.23851
$455$	−3.84628	−0.180316
$456$	15.1889	0.711288
$457$	5.04899	0.236182	0.118091	−	0.993003i	$-0.462323\pi$
$457$	5.04899	0.236182	0.118091	+	0.993003i	$0.462323\pi$
$458$	8.87844	0.414862
$459$	0.396381	0.0185015
$460$	10.6694	0.497466
$461$	−12.8408	−0.598056	−0.299028	−	0.954244i	$-0.596662\pi$
$461$	−12.8408	−0.598056	−0.299028	+	0.954244i	$0.596662\pi$
$462$	−12.1373	−0.564677
$463$	−7.31274	−0.339852	−0.169926	−	0.985457i	$-0.554353\pi$
$463$	−7.31274	−0.339852	−0.169926	+	0.985457i	$0.554353\pi$
$464$	1.39423	0.0647256
$465$	2.56174	0.118798
$466$	64.9378	3.00818
$467$	−20.4933	−0.948317	−0.474159	−	0.880439i	$-0.657248\pi$
$467$	−20.4933	−0.948317	−0.474159	+	0.880439i	$0.657248\pi$
$468$	21.7618	1.00594
$469$	−8.88556	−0.410297
$470$	18.0443	0.832322
$471$	23.8970	1.10111
$472$	8.35412	0.384530
$473$	24.2334	1.11425
$474$	35.7792	1.64339
$475$	−16.2556	−0.745858
$476$	−1.49507	−0.0685263
$477$	−1.29111	−0.0591160
$478$	−6.33058	−0.289554
$479$	42.2742	1.93156	0.965778	−	0.259371i	$-0.0835152\pi$
$479$	42.2742	1.93156	0.965778	+	0.259371i	$0.0835152\pi$
$480$	1.37856	0.0629224
$481$	−40.4170	−1.84286
$482$	−40.4583	−1.84282
$483$	4.24325	0.193075
$484$	54.7777	2.48989
$485$	−6.14583	−0.279068
$486$	2.40246	0.108978
$487$	11.3695	0.515202	0.257601	−	0.966251i	$-0.417068\pi$
$487$	11.3695	0.515202	0.257601	+	0.966251i	$0.417068\pi$
$488$	40.2426	1.82170
$489$	14.7857	0.668631
$490$	1.60159	0.0723523
$491$	−8.86723	−0.400172	−0.200086	−	0.979778i	$-0.564122\pi$
$491$	−8.86723	−0.400172	−0.200086	+	0.979778i	$0.564122\pi$
$492$	−11.5709	−0.521657
$493$	−0.205993	−0.00927747
$494$	−49.4608	−2.22534
$495$	3.36791	0.151376
$496$	10.3094	0.462907
$497$	−8.51845	−0.382105
$498$	32.8125	1.47036
$499$	4.93677	0.221000	0.110500	−	0.993876i	$-0.464755\pi$
$499$	4.93677	0.221000	0.110500	+	0.993876i	$0.464755\pi$
$500$	24.0270	1.07452
$501$	−21.2454	−0.949175
$502$	54.5802	2.43604
$503$	23.9458	1.06769	0.533846	−	0.845582i	$-0.320746\pi$
$503$	23.9458	1.06769	0.533846	+	0.845582i	$0.320746\pi$
$504$	−4.25666	−0.189607
$505$	−3.48190	−0.154942
$506$	−51.5015	−2.28952
$507$	−20.2884	−0.901038
$508$	3.77179	0.167346
$509$	−21.1558	−0.937716	−0.468858	−	0.883273i	$-0.655334\pi$
$509$	−21.1558	−0.937716	−0.468858	+	0.883273i	$0.655334\pi$
$510$	0.634839	0.0281111
$511$	−6.50942	−0.287960
$512$	28.3877	1.25457
$513$	−3.56828	−0.157543
$514$	40.5669	1.78933
$515$	0.698122	0.0307629
$516$	18.0924	0.796475
$517$	−56.9188	−2.50329
$518$	16.8296	0.739449
$519$	8.03384	0.352647
$520$	16.3723	0.717973
$521$	28.8671	1.26469	0.632346	−	0.774686i	$-0.282092\pi$
$521$	28.8671	1.26469	0.632346	+	0.774686i	$0.282092\pi$
$522$	−1.24852	−0.0546462
$523$	13.2821	0.580785	0.290393	−	0.956908i	$-0.406214\pi$
$523$	13.2821	0.580785	0.290393	+	0.956908i	$0.406214\pi$
$524$	56.0223	2.44735
$525$	4.55558	0.198822
$526$	34.8054	1.51759
$527$	−1.52319	−0.0663510
$528$	13.5538	0.589853
$529$	−4.99479	−0.217165
$530$	−2.06783	−0.0898207
$531$	−1.96260	−0.0851697
$532$	13.4588	0.583514
$533$	17.6997	0.766659
$534$	−30.2766	−1.31020
$535$	−10.2930	−0.445004
$536$	37.8228	1.63370
$537$	18.5927	0.802332
$538$	−45.8616	−1.97723
$539$	−5.05203	−0.217606
$540$	2.51445	0.108205
$541$	35.5192	1.52709	0.763545	−	0.645754i	$-0.223457\pi$
$541$	35.5192	1.52709	0.763545	+	0.645754i	$0.223457\pi$
$542$	30.2342	1.29867
$543$	−10.8782	−0.466827
$544$	−0.819679	−0.0351435
$545$	−5.48375	−0.234898
$546$	13.8612	0.593206
$547$	−1.19586	−0.0511314	−0.0255657	−	0.999673i	$-0.508139\pi$
$547$	−1.19586	−0.0511314	−0.0255657	+	0.999673i	$0.508139\pi$
$548$	−77.3100	−3.30252
$549$	−9.45403	−0.403488
$550$	−55.2924	−2.35767
$551$	1.85438	0.0789993
$552$	−18.0621	−0.768773
$553$	14.8928	0.633304
$554$	56.5664	2.40327
$555$	−4.66995	−0.198228
$556$	−13.3424	−0.565842
$557$	0.640333	0.0271318	0.0135659	−	0.999908i	$-0.495682\pi$
$557$	0.640333	0.0271318	0.0135659	+	0.999908i	$0.495682\pi$
$558$	−9.23199	−0.390821
$559$	−27.6755	−1.17055
$560$	−1.78850	−0.0755781
$561$	−2.00253	−0.0845468
$562$	41.7081	1.75935
$563$	0.399140	0.0168217	0.00841086	−	0.999965i	$-0.497323\pi$
$563$	0.399140	0.0168217	0.00841086	+	0.999965i	$0.497323\pi$
$564$	−42.4950	−1.78936
$565$	1.74262	0.0733127
$566$	67.2962	2.82867
$567$	1.00000	0.0419961
$568$	36.2601	1.52144
$569$	−10.0883	−0.422924	−0.211462	−	0.977386i	$-0.567823\pi$
$569$	−10.0883	−0.422924	−0.211462	+	0.977386i	$0.567823\pi$
$570$	−5.71491	−0.239371
$571$	5.05274	0.211451	0.105725	−	0.994395i	$-0.466284\pi$
$571$	5.05274	0.211451	0.105725	+	0.994395i	$0.466284\pi$
$572$	−109.941	−4.59687
$573$	−19.0877	−0.797401
$574$	−7.37013	−0.307623
$575$	19.3305	0.806138
$576$	−10.3337	−0.430572
$577$	−16.5648	−0.689601	−0.344800	−	0.938676i	$-0.612053\pi$
$577$	−16.5648	−0.689601	−0.344800	+	0.938676i	$0.612053\pi$
$578$	40.4643	1.68309
$579$	16.5306	0.686990
$580$	−1.30672	−0.0542586
$581$	13.6579	0.566626
$582$	22.1483	0.918078
$583$	6.52273	0.270144
$584$	27.7084	1.14658
$585$	−3.84628	−0.159024
$586$	−53.0213	−2.19029
$587$	−15.6730	−0.646896	−0.323448	−	0.946246i	$-0.604842\pi$
$587$	−15.6730	−0.646896	−0.323448	+	0.946246i	$0.604842\pi$
$588$	−3.77179	−0.155546
$589$	13.7119	0.564991
$590$	−3.14328	−0.129407
$591$	26.3357	1.08330
$592$	−18.7937	−0.772417
$593$	2.34319	0.0962235	0.0481117	−	0.998842i	$-0.484680\pi$
$593$	2.34319	0.0962235	0.0481117	+	0.998842i	$0.484680\pi$
$594$	−12.1373	−0.497998
$595$	0.264246	0.0108330
$596$	−75.4225	−3.08943
$597$	0.679810	0.0278228
$598$	58.8167	2.40519
$599$	−19.0363	−0.777802	−0.388901	−	0.921280i	$-0.627145\pi$
$599$	−19.0363	−0.777802	−0.388901	+	0.921280i	$0.627145\pi$
$600$	−19.3916	−0.791657
$601$	23.0581	0.940560	0.470280	−	0.882517i	$-0.344153\pi$
$601$	23.0581	0.940560	0.470280	+	0.882517i	$0.344153\pi$
$602$	11.5240	0.469684
$603$	−8.88556	−0.361848
$604$	69.0145	2.80816
$605$	−9.68168	−0.393616
$606$	12.5481	0.509730
$607$	16.5040	0.669878	0.334939	−	0.942240i	$-0.391284\pi$
$607$	16.5040	0.669878	0.334939	+	0.942240i	$0.391284\pi$
$608$	7.37887	0.299253
$609$	−0.519685	−0.0210587
$610$	−15.1414	−0.613059
$611$	65.0034	2.62976
$612$	−1.49507	−0.0604345
$613$	−13.9856	−0.564872	−0.282436	−	0.959286i	$-0.591142\pi$
$613$	−13.9856	−0.564872	−0.282436	+	0.959286i	$0.591142\pi$
$614$	42.8891	1.73086
$615$	2.04510	0.0824664
$616$	21.5047	0.866451
$617$	43.4723	1.75013	0.875064	−	0.484007i	$-0.160819\pi$
$617$	43.4723	1.75013	0.875064	+	0.484007i	$0.160819\pi$
$618$	−2.51589	−0.101204
$619$	40.2578	1.61810	0.809049	−	0.587741i	$-0.199983\pi$
$619$	40.2578	1.61810	0.809049	+	0.587741i	$0.199983\pi$
$620$	−9.66235	−0.388049
$621$	4.24325	0.170276
$622$	37.8363	1.51710
$623$	−12.6023	−0.504902
$624$	−15.4789	−0.619653
$625$	18.5313	0.741251
$626$	38.1020	1.52286
$627$	18.0271	0.719931
$628$	−90.1344	−3.59675
$629$	2.77671	0.110715
$630$	1.60159	0.0638087
$631$	0.191328	0.00761664	0.00380832	−	0.999993i	$-0.498788\pi$
$631$	0.191328	0.00761664	0.00380832	+	0.999993i	$0.498788\pi$
$632$	−63.3933	−2.52165
$633$	−17.0443	−0.677449
$634$	−67.6946	−2.68850
$635$	−0.666645	−0.0264550
$636$	4.86981	0.193101
$637$	5.76961	0.228600
$638$	6.30756	0.249719
$639$	−8.51845	−0.336985
$640$	−13.7932	−0.545226
$641$	16.7190	0.660361	0.330181	−	0.943918i	$-0.392890\pi$
$641$	16.7190	0.660361	0.330181	+	0.943918i	$0.392890\pi$
$642$	37.0938	1.46397
$643$	−27.9484	−1.10218	−0.551088	−	0.834447i	$-0.685787\pi$
$643$	−27.9484	−1.10218	−0.551088	+	0.834447i	$0.685787\pi$
$644$	−16.0047	−0.630673
$645$	−3.19775	−0.125911
$646$	3.39803	0.133694
$647$	−20.8215	−0.818578	−0.409289	−	0.912405i	$-0.634223\pi$
$647$	−20.8215	−0.818578	−0.409289	+	0.912405i	$0.634223\pi$
$648$	−4.25666	−0.167217
$649$	9.91512	0.389202
$650$	63.1460	2.47679
$651$	−3.84273	−0.150608
$652$	−55.7685	−2.18406
$653$	4.58740	0.179519	0.0897594	−	0.995963i	$-0.471390\pi$
$653$	4.58740	0.179519	0.0897594	+	0.995963i	$0.471390\pi$
$654$	19.7623	0.772768
$655$	−9.90167	−0.386890
$656$	8.23028	0.321338
$657$	−6.50942	−0.253957
$658$	−27.0673	−1.05519
$659$	−12.5704	−0.489674	−0.244837	−	0.969564i	$-0.578734\pi$
$659$	−12.5704	−0.489674	−0.244837	+	0.969564i	$0.578734\pi$
$660$	−12.7031	−0.494466
$661$	25.8123	1.00398	0.501991	−	0.864873i	$-0.332601\pi$
$661$	25.8123	1.00398	0.501991	+	0.864873i	$0.332601\pi$
$662$	66.9101	2.60053
$663$	2.28696	0.0888183
$664$	−58.1370	−2.25615
$665$	−2.37878	−0.0922451
$666$	16.8296	0.652133
$667$	−2.20515	−0.0853839
$668$	80.1333	3.10045
$669$	20.7478	0.802157
$670$	−14.2310	−0.549791
$671$	47.7620	1.84383
$672$	−2.06791	−0.0797712
$673$	−46.6132	−1.79681	−0.898403	−	0.439172i	$-0.855272\pi$
$673$	−46.6132	−1.79681	−0.898403	+	0.439172i	$0.855272\pi$
$674$	18.3672	0.707476
$675$	4.55558	0.175345
$676$	76.5235	2.94321
$677$	−15.3276	−0.589087	−0.294544	−	0.955638i	$-0.595168\pi$
$677$	−15.3276	−0.589087	−0.294544	+	0.955638i	$0.595168\pi$
$678$	−6.28006	−0.241184
$679$	9.21904	0.353794
$680$	−1.12480	−0.0431342
$681$	10.9843	0.420918
$682$	46.6403	1.78595
$683$	1.55964	0.0596778	0.0298389	−	0.999555i	$-0.490501\pi$
$683$	1.55964	0.0596778	0.0298389	+	0.999555i	$0.490501\pi$
$684$	13.4588	0.514611
$685$	13.6641	0.522080
$686$	−2.40246	−0.0917262
$687$	3.69557	0.140995
$688$	−12.8690	−0.490625
$689$	−7.44921	−0.283792
$690$	6.79594	0.258717
$691$	−13.6905	−0.520810	−0.260405	−	0.965499i	$-0.583856\pi$
$691$	−13.6905	−0.520810	−0.260405	+	0.965499i	$0.583856\pi$
$692$	−30.3020	−1.15191
$693$	−5.05203	−0.191911
$694$	−53.0951	−2.01546
$695$	2.35819	0.0894514
$696$	2.21212	0.0838502
$697$	−1.21600	−0.0460592
$698$	−17.1157	−0.647840
$699$	27.0298	1.02236
$700$	−17.1827	−0.649446
$701$	35.3818	1.33635	0.668176	−	0.744003i	$-0.267075\pi$
$701$	35.3818	1.33635	0.668176	+	0.744003i	$0.267075\pi$
$702$	13.8612	0.523158
$703$	−24.9964	−0.942756
$704$	52.2063	1.96760
$705$	7.51078	0.282872
$706$	33.7028	1.26842
$707$	5.22301	0.196432
$708$	7.40253	0.278204
$709$	2.44584	0.0918554	0.0459277	−	0.998945i	$-0.485376\pi$
$709$	2.44584	0.0918554	0.0459277	+	0.998945i	$0.485376\pi$
$710$	−13.6430	−0.512014
$711$	14.8928	0.558522
$712$	53.6438	2.01039
$713$	−16.3057	−0.610653
$714$	−0.952288	−0.0356385
$715$	19.4315	0.726698
$716$	−70.1277	−2.62079
$717$	−2.63505	−0.0984076
$718$	−14.5093	−0.541483
$719$	−14.0093	−0.522459	−0.261229	−	0.965277i	$-0.584128\pi$
$719$	−14.0093	−0.522459	−0.261229	+	0.965277i	$0.584128\pi$
$720$	−1.78850	−0.0666536
$721$	−1.04722	−0.0390004
$722$	15.0571	0.560366
$723$	−16.8404	−0.626301
$724$	41.0303	1.52488
$725$	−2.36747	−0.0879255
$726$	34.8908	1.29492
$727$	5.51126	0.204401	0.102201	−	0.994764i	$-0.467412\pi$
$727$	5.51126	0.204401	0.102201	+	0.994764i	$0.467412\pi$
$728$	−24.5592	−0.910226
$729$	1.00000	0.0370370
$730$	−10.4254	−0.385861
$731$	1.90135	0.0703240
$732$	35.6587	1.31798
$733$	−7.42286	−0.274170	−0.137085	−	0.990559i	$-0.543773\pi$
$733$	−7.42286	−0.274170	−0.137085	+	0.990559i	$0.543773\pi$
$734$	30.4118	1.12252
$735$	0.666645	0.0245896
$736$	−8.77465	−0.323438
$737$	44.8901	1.65355
$738$	−7.37013	−0.271298
$739$	31.5583	1.16089	0.580445	−	0.814299i	$-0.302879\pi$
$739$	31.5583	1.16089	0.580445	+	0.814299i	$0.302879\pi$
$740$	17.6141	0.647507
$741$	−20.5876	−0.756304
$742$	3.10184	0.113872
$743$	−34.9462	−1.28205	−0.641027	−	0.767519i	$-0.721491\pi$
$743$	−34.9462	−1.28205	−0.641027	+	0.767519i	$0.721491\pi$
$744$	16.3572	0.599683
$745$	13.3306	0.488394
$746$	−39.2198	−1.43594
$747$	13.6579	0.499717
$748$	7.55313	0.276170
$749$	15.4399	0.564163
$750$	15.3041	0.558826
$751$	47.6101	1.73732	0.868659	−	0.495410i	$-0.164982\pi$
$751$	47.6101	1.73732	0.868659	+	0.495410i	$0.164982\pi$
$752$	30.2263	1.10224
$753$	22.7185	0.827909
$754$	−7.20347	−0.262335
$755$	−12.1980	−0.443929
$756$	−3.77179	−0.137179
$757$	−7.55653	−0.274647	−0.137323	−	0.990526i	$-0.543850\pi$
$757$	−7.55653	−0.274647	−0.137323	+	0.990526i	$0.543850\pi$
$758$	−38.8700	−1.41182
$759$	−21.4370	−0.778115
$760$	10.1256	0.367296
$761$	−2.24334	−0.0813209	−0.0406605	−	0.999173i	$-0.512946\pi$
$761$	−2.24334	−0.0813209	−0.0406605	+	0.999173i	$0.512946\pi$
$762$	2.40246	0.0870318
$763$	8.22589	0.297797
$764$	71.9950	2.60469
$765$	0.264246	0.00955382
$766$	34.1061	1.23230
$767$	−11.3234	−0.408866
$768$	29.0406	1.04791
$769$	−31.4607	−1.13450	−0.567250	−	0.823546i	$-0.691993\pi$
$769$	−31.4607	−1.13450	−0.567250	+	0.823546i	$0.691993\pi$
$770$	−8.09126	−0.291589
$771$	16.8856	0.608121
$772$	−62.3501	−2.24403
$773$	7.68396	0.276373	0.138186	−	0.990406i	$-0.455873\pi$
$773$	7.68396	0.276373	0.138186	+	0.990406i	$0.455873\pi$
$774$	11.5240	0.414223
$775$	−17.5059	−0.628830
$776$	−39.2423	−1.40872
$777$	7.00515	0.251308
$778$	−3.18096	−0.114043
$779$	10.9466	0.392202
$780$	14.5074	0.519448
$781$	43.0354	1.53993
$782$	−4.04080	−0.144499
$783$	−0.519685	−0.0185720
$784$	2.68284	0.0958157
$785$	15.9308	0.568595
$786$	35.6836	1.27279
$787$	−4.63829	−0.165337	−0.0826686	−	0.996577i	$-0.526344\pi$
$787$	−4.63829	−0.165337	−0.0826686	+	0.996577i	$0.526344\pi$
$788$	−99.3326	−3.53858
$789$	14.4874	0.515767
$790$	23.8520	0.848617
$791$	−2.61402	−0.0929438
$792$	21.5047	0.764138
$793$	−54.5461	−1.93699
$794$	81.5845	2.89533
$795$	−0.860714	−0.0305264
$796$	−2.56410	−0.0908823
$797$	50.7223	1.79668	0.898338	−	0.439304i	$-0.144775\pi$
$797$	50.7223	1.79668	0.898338	+	0.439304i	$0.144775\pi$
$798$	8.57264	0.303468
$799$	−4.46584	−0.157990
$800$	−9.42052	−0.333066
$801$	−12.6023	−0.445282
$802$	7.86294	0.277650
$803$	32.8858	1.16051
$804$	33.5145	1.18197
$805$	2.82875	0.0997002
$806$	−53.2650	−1.87618
$807$	−19.0894	−0.671980
$808$	−22.2326	−0.782139
$809$	−8.25319	−0.290167	−0.145083	−	0.989419i	$-0.546345\pi$
$809$	−8.25319	−0.290167	−0.145083	+	0.989419i	$0.546345\pi$
$810$	1.60159	0.0562740
$811$	−42.5309	−1.49346	−0.746731	−	0.665127i	$-0.768378\pi$
$811$	−42.5309	−1.49346	−0.746731	+	0.665127i	$0.768378\pi$
$812$	1.96014	0.0687876
$813$	12.5847	0.441366
$814$	−85.0234	−2.98007
$815$	9.85679	0.345268
$816$	1.06343	0.0372274
$817$	−17.1162	−0.598821
$818$	−19.0670	−0.666664
$819$	5.76961	0.201606
$820$	−7.71369	−0.269374
$821$	34.7449	1.21260	0.606302	−	0.795235i	$-0.292652\pi$
$821$	34.7449	1.21260	0.606302	+	0.795235i	$0.292652\pi$
$822$	−49.2428	−1.71754
$823$	6.45981	0.225175	0.112587	−	0.993642i	$-0.464086\pi$
$823$	6.45981	0.225175	0.112587	+	0.993642i	$0.464086\pi$
$824$	4.45764	0.155289
$825$	−23.0149	−0.801277
$826$	4.71506	0.164058
$827$	−32.2022	−1.11978	−0.559889	−	0.828567i	$-0.689156\pi$
$827$	−32.2022	−1.11978	−0.559889	+	0.828567i	$0.689156\pi$
$828$	−16.0047	−0.556201
$829$	17.8107	0.618593	0.309296	−	0.950966i	$-0.399906\pi$
$829$	17.8107	0.618593	0.309296	+	0.950966i	$0.399906\pi$
$830$	21.8743	0.759269
$831$	23.5452	0.816775
$832$	−59.6216	−2.06701
$833$	−0.396381	−0.0137338
$834$	−8.49845	−0.294277
$835$	−14.1632	−0.490136
$836$	−67.9943	−2.35163
$837$	−3.84273	−0.132824
$838$	50.7265	1.75232
$839$	11.6047	0.400639	0.200319	−	0.979731i	$-0.435802\pi$
$839$	11.6047	0.400639	0.200319	+	0.979731i	$0.435802\pi$
$840$	−2.83768	−0.0979093
$841$	−28.7299	−0.990687
$842$	72.2633	2.49036
$843$	17.3606	0.597931
$844$	64.2875	2.21287
$845$	−13.5251	−0.465279
$846$	−27.0673	−0.930594
$847$	14.5230	0.499016
$848$	−3.46385	−0.118949
$849$	28.0114	0.961350
$850$	−4.33823	−0.148800
$851$	29.7246	1.01895
$852$	32.1298	1.10075
$853$	34.3397	1.17577	0.587884	−	0.808945i	$-0.299961\pi$
$853$	34.3397	1.17577	0.587884	+	0.808945i	$0.299961\pi$
$854$	22.7129	0.777219
$855$	−2.37878	−0.0813525
$856$	−65.7225	−2.24635
$857$	14.3054	0.488664	0.244332	−	0.969692i	$-0.421431\pi$
$857$	14.3054	0.488664	0.244332	+	0.969692i	$0.421431\pi$
$858$	−70.0273	−2.39069
$859$	−49.4636	−1.68768	−0.843838	−	0.536597i	$-0.819709\pi$
$859$	−49.4636	−1.68768	−0.843838	+	0.536597i	$0.819709\pi$
$860$	12.0612	0.411285
$861$	−3.06775	−0.104549
$862$	38.5014	1.31136
$863$	−39.0263	−1.32847	−0.664235	−	0.747524i	$-0.731243\pi$
$863$	−39.0263	−1.32847	−0.664235	+	0.747524i	$0.731243\pi$
$864$	−2.06791	−0.0703516
$865$	5.35572	0.182100
$866$	−17.3790	−0.590564
$867$	16.8429	0.572014
$868$	14.4940	0.491958
$869$	−75.2386	−2.55229
$870$	−0.832320	−0.0282183
$871$	−51.2662	−1.73709
$872$	−35.0148	−1.18575
$873$	9.21904	0.312017
$874$	36.3759	1.23043
$875$	6.37019	0.215352
$876$	24.5522	0.829542
$877$	−32.8794	−1.11026	−0.555129	−	0.831764i	$-0.687331\pi$
$877$	−32.8794	−1.11026	−0.555129	+	0.831764i	$0.687331\pi$
$878$	25.0326	0.844809
$879$	−22.0696	−0.744390
$880$	9.03557	0.304589
$881$	−23.5044	−0.791884	−0.395942	−	0.918275i	$-0.629582\pi$
$881$	−23.5044	−0.791884	−0.395942	+	0.918275i	$0.629582\pi$
$882$	−2.40246	−0.0808949
$883$	3.78292	0.127305	0.0636527	−	0.997972i	$-0.479725\pi$
$883$	3.78292	0.127305	0.0636527	+	0.997972i	$0.479725\pi$
$884$	−8.62596	−0.290122
$885$	−1.30836	−0.0439800
$886$	22.6564	0.761156
$887$	16.0603	0.539253	0.269627	−	0.962965i	$-0.413100\pi$
$887$	16.0603	0.539253	0.269627	+	0.962965i	$0.413100\pi$
$888$	−29.8185	−1.00064
$889$	1.00000	0.0335389
$890$	−20.1837	−0.676560
$891$	−5.05203	−0.169249
$892$	−78.2565	−2.62022
$893$	40.2021	1.34531
$894$	−48.0406	−1.60672
$895$	12.3947	0.414309
$896$	20.6905	0.691222
$897$	24.4819	0.817427
$898$	16.1990	0.540567
$899$	1.99701	0.0666040
$900$	−17.1827	−0.572757
$901$	0.511773	0.0170496
$902$	37.2341	1.23976
$903$	4.79677	0.159627
$904$	11.1270	0.370078
$905$	−7.25189	−0.241061
$906$	43.9590	1.46044
$907$	−3.13873	−0.104220	−0.0521099	−	0.998641i	$-0.516595\pi$
$907$	−3.13873	−0.104220	−0.0521099	+	0.998641i	$0.516595\pi$
$908$	−41.4304	−1.37491
$909$	5.22301	0.173236
$910$	9.24052	0.306320
$911$	5.56286	0.184306	0.0921530	−	0.995745i	$-0.470625\pi$
$911$	5.56286	0.184306	0.0921530	+	0.995745i	$0.470625\pi$
$912$	−9.57313	−0.316998
$913$	−69.0001	−2.28357
$914$	−12.1300	−0.401224
$915$	−6.30249	−0.208354
$916$	−13.9389	−0.460555
$917$	14.8530	0.490488
$918$	−0.952288	−0.0314302
$919$	−55.9312	−1.84500	−0.922501	−	0.385995i	$-0.873858\pi$
$919$	−55.9312	−1.84500	−0.922501	+	0.385995i	$0.873858\pi$
$920$	−12.0410	−0.396980
$921$	17.8522	0.588249
$922$	30.8494	1.01597
$923$	−49.1481	−1.61773
$924$	19.0552	0.626870
$925$	31.9126	1.04928
$926$	17.5685	0.577338
$927$	−1.04722	−0.0343951
$928$	1.07466	0.0352774
$929$	15.0146	0.492612	0.246306	−	0.969192i	$-0.420783\pi$
$929$	15.0146	0.492612	0.246306	+	0.969192i	$0.420783\pi$
$930$	−6.15447	−0.201813
$931$	3.56828	0.116946
$932$	−101.951	−3.33950
$933$	15.7490	0.515600
$934$	49.2343	1.61099
$935$	−1.33498	−0.0436584
$936$	−24.5592	−0.802744
$937$	6.36422	0.207910	0.103955	−	0.994582i	$-0.466850\pi$
$937$	6.36422	0.207910	0.103955	+	0.994582i	$0.466850\pi$
$938$	21.3472	0.697010
$939$	15.8596	0.517559
$940$	−28.3291	−0.923994
$941$	−40.4525	−1.31871	−0.659357	−	0.751830i	$-0.729171\pi$
$941$	−40.4525	−1.31871	−0.659357	+	0.751830i	$0.729171\pi$
$942$	−57.4114	−1.87056
$943$	−13.0172	−0.423899
$944$	−5.26535	−0.171372
$945$	0.666645	0.0216860
$946$	−58.2197	−1.89289
$947$	−48.6835	−1.58200	−0.791000	−	0.611816i	$-0.790439\pi$
$947$	−48.6835	−1.58200	−0.791000	+	0.611816i	$0.790439\pi$
$948$	−56.1724	−1.82439
$949$	−37.5568	−1.21915
$950$	39.0534	1.26706
$951$	−28.1773	−0.913710
$952$	1.68726	0.0546844
$953$	2.87131	0.0930110	0.0465055	−	0.998918i	$-0.485191\pi$
$953$	2.87131	0.0930110	0.0465055	+	0.998918i	$0.485191\pi$
$954$	3.10184	0.100426
$955$	−12.7247	−0.411763
$956$	9.93885	0.321445
$957$	2.62546	0.0848691
$958$	−101.562	−3.28131
$959$	−20.4969	−0.661878
$960$	−6.88894	−0.222340
$961$	−16.2334	−0.523659
$962$	97.1000	3.13063
$963$	15.4399	0.497545
$964$	63.5185	2.04579
$965$	11.0201	0.354749
$966$	−10.1942	−0.327994
$967$	45.1711	1.45261	0.726303	−	0.687375i	$-0.241237\pi$
$967$	45.1711	1.45261	0.726303	+	0.687375i	$0.241237\pi$
$968$	−61.8193	−1.98695
$969$	1.41440	0.0454371
$970$	14.7651	0.474079
$971$	−30.5373	−0.979990	−0.489995	−	0.871725i	$-0.663001\pi$
$971$	−30.5373	−0.979990	−0.489995	+	0.871725i	$0.663001\pi$
$972$	−3.77179	−0.120980
$973$	−3.53740	−0.113404
$974$	−27.3147	−0.875221
$975$	26.2839	0.841759
$976$	−25.3637	−0.811871
$977$	−51.3484	−1.64278	−0.821391	−	0.570365i	$-0.806802\pi$
$977$	−51.3484	−1.64278	−0.821391	+	0.570365i	$0.806802\pi$
$978$	−35.5219	−1.13587
$979$	63.6674	2.03482
$980$	−2.51445	−0.0803211
$981$	8.22589	0.262632
$982$	21.3031	0.679810
$983$	17.9373	0.572111	0.286055	−	0.958213i	$-0.407656\pi$
$983$	17.9373	0.572111	0.286055	+	0.958213i	$0.407656\pi$
$984$	13.0583	0.416285
$985$	17.5565	0.559398
$986$	0.494890	0.0157605
$987$	−11.2665	−0.358618
$988$	77.6521	2.47044
$989$	20.3539	0.647217
$990$	−8.09126	−0.257157
$991$	1.31878	0.0418924	0.0209462	−	0.999781i	$-0.493332\pi$
$991$	1.31878	0.0418924	0.0209462	+	0.999781i	$0.493332\pi$
$992$	7.94641	0.252299
$993$	27.8507	0.883815
$994$	20.4652	0.649116
$995$	0.453193	0.0143672
$996$	−51.5148	−1.63231
$997$	−4.64514	−0.147113	−0.0735565	−	0.997291i	$-0.523435\pi$
$997$	−4.64514	−0.147113	−0.0735565	+	0.997291i	$0.523435\pi$
$998$	−11.8604	−0.375433
$999$	7.00515	0.221633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.p.1.4	✓	18
3.2	odd	2		8001.2.a.u.1.15		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.p.1.4	✓	18	1.1	even	1	trivial
8001.2.a.u.1.15		18	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)

\(f(q)\)	\(=\)	\(q-2.40246 q^{2} -1.00000 q^{3} +3.77179 q^{4} -0.666645 q^{5} +2.40246 q^{6} +1.00000 q^{7} -4.25666 q^{8} +1.00000 q^{9} +1.60159 q^{10} -5.05203 q^{11} -3.77179 q^{12} +5.76961 q^{13} -2.40246 q^{14} +0.666645 q^{15} +2.68284 q^{16} -0.396381 q^{17} -2.40246 q^{18} +3.56828 q^{19} -2.51445 q^{20} -1.00000 q^{21} +12.1373 q^{22} -4.24325 q^{23} +4.25666 q^{24} -4.55558 q^{25} -13.8612 q^{26} -1.00000 q^{27} +3.77179 q^{28} +0.519685 q^{29} -1.60159 q^{30} +3.84273 q^{31} +2.06791 q^{32} +5.05203 q^{33} +0.952288 q^{34} -0.666645 q^{35} +3.77179 q^{36} -7.00515 q^{37} -8.57264 q^{38} -5.76961 q^{39} +2.83768 q^{40} +3.06775 q^{41} +2.40246 q^{42} -4.79677 q^{43} -19.0552 q^{44} -0.666645 q^{45} +10.1942 q^{46} +11.2665 q^{47} -2.68284 q^{48} +1.00000 q^{49} +10.9446 q^{50} +0.396381 q^{51} +21.7618 q^{52} -1.29111 q^{53} +2.40246 q^{54} +3.36791 q^{55} -4.25666 q^{56} -3.56828 q^{57} -1.24852 q^{58} -1.96260 q^{59} +2.51445 q^{60} -9.45403 q^{61} -9.23199 q^{62} +1.00000 q^{63} -10.3337 q^{64} -3.84628 q^{65} -12.1373 q^{66} -8.88556 q^{67} -1.49507 q^{68} +4.24325 q^{69} +1.60159 q^{70} -8.51845 q^{71} -4.25666 q^{72} -6.50942 q^{73} +16.8296 q^{74} +4.55558 q^{75} +13.4588 q^{76} -5.05203 q^{77} +13.8612 q^{78} +14.8928 q^{79} -1.78850 q^{80} +1.00000 q^{81} -7.37013 q^{82} +13.6579 q^{83} -3.77179 q^{84} +0.264246 q^{85} +11.5240 q^{86} -0.519685 q^{87} +21.5047 q^{88} -12.6023 q^{89} +1.60159 q^{90} +5.76961 q^{91} -16.0047 q^{92} -3.84273 q^{93} -27.0673 q^{94} -2.37878 q^{95} -2.06791 q^{96} +9.21904 q^{97} -2.40246 q^{98} -5.05203 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{2} - 18 q^{3} + 22 q^{4} - 10 q^{5} + 6 q^{6} + 18 q^{7} - 21 q^{8} + 18 q^{9} - 4 q^{10} - 9 q^{11} - 22 q^{12} - 25 q^{13} - 6 q^{14} + 10 q^{15} + 34 q^{16} - 17 q^{17} - 6 q^{18} - 5 q^{19}+ \cdots - 9 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 - 18 * q^3 + 22 * q^4 - 10 * q^5 + 6 * q^6 + 18 * q^7 - 21 * q^8 + 18 * q^9 - 4 * q^10 - 9 * q^11 - 22 * q^12 - 25 * q^13 - 6 * q^14 + 10 * q^15 + 34 * q^16 - 17 * q^17 - 6 * q^18 - 5 * q^19 - 21 * q^20 - 18 * q^21 + 5 * q^22 - 14 * q^23 + 21 * q^24 + 28 * q^25 - 8 * q^26 - 18 * q^27 + 22 * q^28 - 17 * q^29 + 4 * q^30 + 5 * q^31 - 53 * q^32 + 9 * q^33 - 19 * q^34 - 10 * q^35 + 22 * q^36 - 15 * q^37 - 22 * q^38 + 25 * q^39 - q^40 - 17 * q^41 + 6 * q^42 + q^43 - 33 * q^44 - 10 * q^45 + 10 * q^46 - 31 * q^47 - 34 * q^48 + 18 * q^49 - 35 * q^50 + 17 * q^51 - 70 * q^52 - 35 * q^53 + 6 * q^54 + 4 * q^55 - 21 * q^56 + 5 * q^57 + 3 * q^58 - 46 * q^59 + 21 * q^60 - 5 * q^61 - 10 * q^62 + 18 * q^63 + 63 * q^64 - 12 * q^65 - 5 * q^66 + 6 * q^67 - 56 * q^68 + 14 * q^69 - 4 * q^70 - 22 * q^71 - 21 * q^72 - 16 * q^73 + 18 * q^74 - 28 * q^75 + 32 * q^76 - 9 * q^77 + 8 * q^78 + 46 * q^79 - 30 * q^80 + 18 * q^81 - 12 * q^82 - 46 * q^83 - 22 * q^84 + 4 * q^85 + 18 * q^86 + 17 * q^87 + 30 * q^88 - 42 * q^89 - 4 * q^90 - 25 * q^91 - 48 * q^92 - 5 * q^93 + 3 * q^94 - 2 * q^95 + 53 * q^96 - 35 * q^97 - 6 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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