LMFDB - Embedded newform 140.2.g.b.111.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [140,2,Mod(111,140)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("140.111"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(140, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-2,0,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			111.3
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	140.111
Dual form			140.2.g.b.111.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.366025 - 1.36603i) q^{2} +1.73205 q^{3} +(-1.73205 - 1.00000i) q^{4} +1.00000i q^{5} +(0.633975 - 2.36603i) q^{6} +(1.73205 - 2.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(1.36603 + 0.366025i) q^{10} -0.267949i q^{11} +(-3.00000 - 1.73205i) q^{12} +0.464102i q^{13} +(-2.09808 - 3.09808i) q^{14} +1.73205i q^{15} +(2.00000 + 3.46410i) q^{16} +6.46410i q^{17} -6.00000 q^{19} +(1.00000 - 1.73205i) q^{20} +(3.00000 - 3.46410i) q^{21} +(-0.366025 - 0.0980762i) q^{22} -1.46410i q^{23} +(-3.46410 + 3.46410i) q^{24} -1.00000 q^{25} +(0.633975 + 0.169873i) q^{26} -5.19615 q^{27} +(-5.00000 + 1.73205i) q^{28} +7.92820 q^{29} +(2.36603 + 0.633975i) q^{30} +6.00000 q^{31} +(5.46410 - 1.46410i) q^{32} -0.464102i q^{33} +(8.83013 + 2.36603i) q^{34} +(2.00000 + 1.73205i) q^{35} -9.46410 q^{37} +(-2.19615 + 8.19615i) q^{38} +0.803848i q^{39} +(-2.00000 - 2.00000i) q^{40} +3.46410i q^{41} +(-3.63397 - 5.36603i) q^{42} -2.00000i q^{43} +(-0.267949 + 0.464102i) q^{44} +(-2.00000 - 0.535898i) q^{46} -1.73205 q^{47} +(3.46410 + 6.00000i) q^{48} +(-1.00000 - 6.92820i) q^{49} +(-0.366025 + 1.36603i) q^{50} +11.1962i q^{51} +(0.464102 - 0.803848i) q^{52} +2.00000 q^{53} +(-1.90192 + 7.09808i) q^{54} +0.267949 q^{55} +(0.535898 + 7.46410i) q^{56} -10.3923 q^{57} +(2.90192 - 10.8301i) q^{58} +3.46410 q^{59} +(1.73205 - 3.00000i) q^{60} -9.46410i q^{61} +(2.19615 - 8.19615i) q^{62} -8.00000i q^{64} -0.464102 q^{65} +(-0.633975 - 0.169873i) q^{66} +3.46410i q^{67} +(6.46410 - 11.1962i) q^{68} -2.53590i q^{69} +(3.09808 - 2.09808i) q^{70} -7.46410i q^{71} -12.9282i q^{73} +(-3.46410 + 12.9282i) q^{74} -1.73205 q^{75} +(10.3923 + 6.00000i) q^{76} +(-0.535898 - 0.464102i) q^{77} +(1.09808 + 0.294229i) q^{78} -14.6603i q^{79} +(-3.46410 + 2.00000i) q^{80} -9.00000 q^{81} +(4.73205 + 1.26795i) q^{82} -15.4641 q^{83} +(-8.66025 + 3.00000i) q^{84} -6.46410 q^{85} +(-2.73205 - 0.732051i) q^{86} +13.7321 q^{87} +(0.535898 + 0.535898i) q^{88} -2.53590i q^{89} +(0.928203 + 0.803848i) q^{91} +(-1.46410 + 2.53590i) q^{92} +10.3923 q^{93} +(-0.633975 + 2.36603i) q^{94} -6.00000i q^{95} +(9.46410 - 2.53590i) q^{96} +13.3923i q^{97} +(-9.83013 - 1.16987i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 6 q^{6} - 8 q^{8} + 2 q^{10} - 12 q^{12} + 2 q^{14} + 8 q^{16} - 24 q^{19} + 4 q^{20} + 12 q^{21} + 2 q^{22} - 4 q^{25} + 6 q^{26} - 20 q^{28} + 4 q^{29} + 6 q^{30} + 24 q^{31} + 8 q^{32}+ \cdots - 22 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 + 6 * q^6 - 8 * q^8 + 2 * q^10 - 12 * q^12 + 2 * q^14 + 8 * q^16 - 24 * q^19 + 4 * q^20 + 12 * q^21 + 2 * q^22 - 4 * q^25 + 6 * q^26 - 20 * q^28 + 4 * q^29 + 6 * q^30 + 24 * q^31 + 8 * q^32 + 18 * q^34 + 8 * q^35 - 24 * q^37 + 12 * q^38 - 8 * q^40 - 18 * q^42 - 8 * q^44 - 8 * q^46 - 4 * q^49 + 2 * q^50 - 12 * q^52 + 8 * q^53 - 18 * q^54 + 8 * q^55 + 16 * q^56 + 22 * q^58 - 12 * q^62 + 12 * q^65 - 6 * q^66 + 12 * q^68 + 2 * q^70 - 16 * q^77 - 6 * q^78 - 36 * q^81 + 12 * q^82 - 48 * q^83 - 12 * q^85 - 4 * q^86 + 48 * q^87 + 16 * q^88 - 24 * q^91 + 8 * q^92 - 6 * q^94 + 24 * q^96 - 22 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.366025	−	1.36603i	0.258819	−	0.965926i
$2$	0.366025	−	1.36603i	0.258819	−	0.965926i
$3$	1.73205			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$3$	1.73205			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$4$	−1.73205	−	1.00000i	−0.866025	−	0.500000i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	0.633975	−	2.36603i	0.258819	−	0.965926i
$7$	1.73205	−	2.00000i	0.654654	−	0.755929i
$7$	1.73205	−	2.00000i	0.654654	−	0.755929i
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$		0			0
$10$	1.36603	+	0.366025i	0.431975	+	0.115747i
$11$		−	0.267949i		−	0.0807897i	−0.999184	−	0.0403949i	$-0.987138\pi$
$11$		−	0.267949i		−	0.0807897i	0.999184	−	0.0403949i	$-0.0128616\pi$
$12$	−3.00000	−	1.73205i	−0.866025	−	0.500000i
$13$			0.464102i			0.128719i	0.997927	+	0.0643593i	$0.0205004\pi$
$13$			0.464102i			0.128719i	−0.997927	+	0.0643593i	$0.979500\pi$
$14$	−2.09808	−	3.09808i	−0.560734	−	0.827996i
$15$			1.73205i			0.447214i
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$			6.46410i			1.56777i	0.620903	+	0.783887i	$0.286766\pi$
$17$			6.46410i			1.56777i	−0.620903	+	0.783887i	$0.713234\pi$
$18$		0			0
$19$	−6.00000			−1.37649			−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000			−1.37649			−0.688247	+	0.725476i	$0.741620\pi$
$20$	1.00000	−	1.73205i	0.223607	−	0.387298i
$21$	3.00000	−	3.46410i	0.654654	−	0.755929i
$22$	−0.366025	−	0.0980762i	−0.0780369	−	0.0209099i
$23$		−	1.46410i		−	0.305286i	−0.988281	−	0.152643i	$-0.951221\pi$
$23$		−	1.46410i		−	0.305286i	0.988281	−	0.152643i	$-0.0487785\pi$
$24$	−3.46410	+	3.46410i	−0.707107	+	0.707107i
$25$	−1.00000			−0.200000
$26$	0.633975	+	0.169873i	0.124333	+	0.0333148i
$27$	−5.19615			−1.00000
$28$	−5.00000	+	1.73205i	−0.944911	+	0.327327i
$29$	7.92820			1.47223			0.736115	−	0.676856i	$-0.236658\pi$
$29$	7.92820			1.47223			0.736115	+	0.676856i	$0.236658\pi$
$30$	2.36603	+	0.633975i	0.431975	+	0.115747i
$31$	6.00000			1.07763			0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000			1.07763			0.538816	+	0.842424i	$0.318872\pi$
$32$	5.46410	−	1.46410i	0.965926	−	0.258819i
$33$		−	0.464102i		−	0.0807897i
$34$	8.83013	+	2.36603i	1.51435	+	0.405770i
$35$	2.00000	+	1.73205i	0.338062	+	0.292770i
$36$		0			0
$37$	−9.46410			−1.55589			−0.777944	−	0.628333i	$-0.783737\pi$
$37$	−9.46410			−1.55589			−0.777944	+	0.628333i	$0.783737\pi$
$38$	−2.19615	+	8.19615i	−0.356263	+	1.32959i
$39$			0.803848i			0.128719i
$40$	−2.00000	−	2.00000i	−0.316228	−	0.316228i
$41$			3.46410i			0.541002i	0.962720	+	0.270501i	$0.0871893\pi$
$41$			3.46410i			0.541002i	−0.962720	+	0.270501i	$0.912811\pi$
$42$	−3.63397	−	5.36603i	−0.560734	−	0.827996i
$43$		−	2.00000i		−	0.304997i	−0.988304	−	0.152499i	$-0.951268\pi$
$43$		−	2.00000i		−	0.304997i	0.988304	−	0.152499i	$-0.0487319\pi$
$44$	−0.267949	+	0.464102i	−0.0403949	+	0.0699660i
$45$		0			0
$46$	−2.00000	−	0.535898i	−0.294884	−	0.0790139i
$47$	−1.73205			−0.252646			−0.126323	−	0.991989i	$-0.540318\pi$
$47$	−1.73205			−0.252646			−0.126323	+	0.991989i	$0.540318\pi$
$48$	3.46410	+	6.00000i	0.500000	+	0.866025i
$49$	−1.00000	−	6.92820i	−0.142857	−	0.989743i
$50$	−0.366025	+	1.36603i	−0.0517638	+	0.193185i
$51$			11.1962i			1.56777i
$52$	0.464102	−	0.803848i	0.0643593	−	0.111474i
$53$	2.00000			0.274721			0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000			0.274721			0.137361	+	0.990521i	$0.456138\pi$
$54$	−1.90192	+	7.09808i	−0.258819	+	0.965926i
$55$	0.267949			0.0361303
$56$	0.535898	+	7.46410i	0.0716124	+	0.997433i
$57$	−10.3923			−1.37649
$58$	2.90192	−	10.8301i	0.381041	−	1.42207i
$59$	3.46410			0.450988			0.225494	−	0.974245i	$-0.427600\pi$
$59$	3.46410			0.450988			0.225494	+	0.974245i	$0.427600\pi$
$60$	1.73205	−	3.00000i	0.223607	−	0.387298i
$61$		−	9.46410i		−	1.21175i	−0.795558	−	0.605877i	$-0.792822\pi$
$61$		−	9.46410i		−	1.21175i	0.795558	−	0.605877i	$-0.207178\pi$
$62$	2.19615	−	8.19615i	0.278912	−	1.04091i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	−0.464102			−0.0575647
$66$	−0.633975	−	0.169873i	−0.0780369	−	0.0209099i
$67$			3.46410i			0.423207i	0.977356	+	0.211604i	$0.0678686\pi$
$67$			3.46410i			0.423207i	−0.977356	+	0.211604i	$0.932131\pi$
$68$	6.46410	−	11.1962i	0.783887	−	1.35773i
$69$		−	2.53590i		−	0.305286i
$70$	3.09808	−	2.09808i	0.370291	−	0.250768i
$71$		−	7.46410i		−	0.885826i	−0.896565	−	0.442913i	$-0.853945\pi$
$71$		−	7.46410i		−	0.885826i	0.896565	−	0.442913i	$-0.146055\pi$
$72$		0			0
$73$		−	12.9282i		−	1.51313i	−0.653917	−	0.756566i	$-0.726876\pi$
$73$		−	12.9282i		−	1.51313i	0.653917	−	0.756566i	$-0.273124\pi$
$74$	−3.46410	+	12.9282i	−0.402694	+	1.50287i
$75$	−1.73205			−0.200000
$76$	10.3923	+	6.00000i	1.19208	+	0.688247i
$77$	−0.535898	−	0.464102i	−0.0610713	−	0.0528893i
$78$	1.09808	+	0.294229i	0.124333	+	0.0333148i
$79$		−	14.6603i		−	1.64941i	−0.565565	−	0.824704i	$-0.691342\pi$
$79$		−	14.6603i		−	1.64941i	0.565565	−	0.824704i	$-0.308658\pi$
$80$	−3.46410	+	2.00000i	−0.387298	+	0.223607i
$81$	−9.00000			−1.00000
$82$	4.73205	+	1.26795i	0.522568	+	0.140022i
$83$	−15.4641			−1.69741			−0.848703	−	0.528870i	$-0.822616\pi$
$83$	−15.4641			−1.69741			−0.848703	+	0.528870i	$0.822616\pi$
$84$	−8.66025	+	3.00000i	−0.944911	+	0.327327i
$85$	−6.46410			−0.701130
$86$	−2.73205	−	0.732051i	−0.294605	−	0.0789391i
$87$	13.7321			1.47223
$88$	0.535898	+	0.535898i	0.0571270	+	0.0571270i
$89$		−	2.53590i		−	0.268805i	−0.990927	−	0.134402i	$-0.957089\pi$
$89$		−	2.53590i		−	0.268805i	0.990927	−	0.134402i	$-0.0429115\pi$
$90$		0			0
$91$	0.928203	+	0.803848i	0.0973021	+	0.0842661i
$92$	−1.46410	+	2.53590i	−0.152643	+	0.264386i
$93$	10.3923			1.07763
$94$	−0.633975	+	2.36603i	−0.0653895	+	0.244037i
$95$		−	6.00000i		−	0.615587i
$96$	9.46410	−	2.53590i	0.965926	−	0.258819i
$97$			13.3923i			1.35978i	0.733313	+	0.679891i	$0.237973\pi$
$97$			13.3923i			1.35978i	−0.733313	+	0.679891i	$0.762027\pi$
$98$	−9.83013	−	1.16987i	−0.992993	−	0.118175i
$99$		0			0
$100$	1.73205	+	1.00000i	0.173205	+	0.100000i
$101$			15.4641i			1.53874i	0.638806	+	0.769368i	$0.279429\pi$
$101$			15.4641i			1.53874i	−0.638806	+	0.769368i	$0.720571\pi$
$102$	15.2942	+	4.09808i	1.51435	+	0.405770i
$103$	6.80385			0.670403			0.335202	−	0.942146i	$-0.391196\pi$
$103$	6.80385			0.670403			0.335202	+	0.942146i	$0.391196\pi$
$104$	−0.928203	−	0.928203i	−0.0910178	−	0.0910178i
$105$	3.46410	+	3.00000i	0.338062	+	0.292770i
$106$	0.732051	−	2.73205i	0.0711031	−	0.265360i
$107$			2.39230i			0.231273i	0.993292	+	0.115636i	$0.0368907\pi$
$107$			2.39230i			0.231273i	−0.993292	+	0.115636i	$0.963109\pi$
$108$	9.00000	+	5.19615i	0.866025	+	0.500000i
$109$	2.07180			0.198442			0.0992211	−	0.995065i	$-0.468365\pi$
$109$	2.07180			0.198442			0.0992211	+	0.995065i	$0.468365\pi$
$110$	0.0980762	−	0.366025i	0.00935120	−	0.0348992i
$111$	−16.3923			−1.55589
$112$	10.3923	+	2.00000i	0.981981	+	0.188982i
$113$	5.46410			0.514019			0.257010	−	0.966409i	$-0.417263\pi$
$113$	5.46410			0.514019			0.257010	+	0.966409i	$0.417263\pi$
$114$	−3.80385	+	14.1962i	−0.356263	+	1.32959i
$115$	1.46410			0.136528
$116$	−13.7321	−	7.92820i	−1.27499	−	0.736115i
$117$		0			0
$118$	1.26795	−	4.73205i	0.116724	−	0.435621i
$119$	12.9282	+	11.1962i	1.18513	+	1.02635i
$120$	−3.46410	−	3.46410i	−0.316228	−	0.316228i
$121$	10.9282			0.993473
$122$	−12.9282	−	3.46410i	−1.17046	−	0.313625i
$123$			6.00000i			0.541002i
$124$	−10.3923	−	6.00000i	−0.933257	−	0.538816i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$			15.4641i			1.37222i	0.727499	+	0.686109i	$0.240683\pi$
$127$			15.4641i			1.37222i	−0.727499	+	0.686109i	$0.759317\pi$
$128$	−10.9282	−	2.92820i	−0.965926	−	0.258819i
$129$		−	3.46410i		−	0.304997i
$130$	−0.169873	+	0.633975i	−0.0148988	+	0.0556033i
$131$	−2.53590			−0.221562			−0.110781	−	0.993845i	$-0.535335\pi$
$131$	−2.53590			−0.221562			−0.110781	+	0.993845i	$0.535335\pi$
$132$	−0.464102	+	0.803848i	−0.0403949	+	0.0699660i
$133$	−10.3923	+	12.0000i	−0.901127	+	1.04053i
$134$	4.73205	+	1.26795i	0.408787	+	0.109534i
$135$		−	5.19615i		−	0.447214i
$136$	−12.9282	−	12.9282i	−1.10858	−	1.10858i
$137$	20.3923			1.74223			0.871116	−	0.491077i	$-0.163397\pi$
$137$	20.3923			1.74223			0.871116	+	0.491077i	$0.163397\pi$
$138$	−3.46410	−	0.928203i	−0.294884	−	0.0790139i
$139$	−6.92820			−0.587643			−0.293821	−	0.955860i	$-0.594927\pi$
$139$	−6.92820			−0.587643			−0.293821	+	0.955860i	$0.594927\pi$
$140$	−1.73205	−	5.00000i	−0.146385	−	0.422577i
$141$	−3.00000			−0.252646
$142$	−10.1962	−	2.73205i	−0.855642	−	0.229269i
$143$	0.124356			0.0103991
$144$		0			0
$145$			7.92820i			0.658401i
$146$	−17.6603	−	4.73205i	−1.46157	−	0.391627i
$147$	−1.73205	−	12.0000i	−0.142857	−	0.989743i
$148$	16.3923	+	9.46410i	1.34744	+	0.777944i
$149$	3.07180			0.251651			0.125826	−	0.992052i	$-0.459842\pi$
$149$	3.07180			0.251651			0.125826	+	0.992052i	$0.459842\pi$
$150$	−0.633975	+	2.36603i	−0.0517638	+	0.193185i
$151$		−	15.1962i		−	1.23665i	−0.785924	−	0.618323i	$-0.787812\pi$
$151$		−	15.1962i		−	1.23665i	0.785924	−	0.618323i	$-0.212188\pi$
$152$	12.0000	−	12.0000i	0.973329	−	0.973329i
$153$		0			0
$154$	−0.830127	+	0.562178i	−0.0668935	+	0.0453016i
$155$			6.00000i			0.481932i
$156$	0.803848	−	1.39230i	0.0643593	−	0.111474i
$157$		−	7.85641i		−	0.627009i	−0.949587	−	0.313505i	$-0.898497\pi$
$157$		−	7.85641i		−	0.627009i	0.949587	−	0.313505i	$-0.101503\pi$
$158$	−20.0263	−	5.36603i	−1.59321	−	0.426898i
$159$	3.46410			0.274721
$160$	1.46410	+	5.46410i	0.115747	+	0.431975i
$161$	−2.92820	−	2.53590i	−0.230775	−	0.199857i
$162$	−3.29423	+	12.2942i	−0.258819	+	0.965926i
$163$			20.7846i			1.62798i	0.580881	+	0.813988i	$0.302708\pi$
$163$			20.7846i			1.62798i	−0.580881	+	0.813988i	$0.697292\pi$
$164$	3.46410	−	6.00000i	0.270501	−	0.468521i
$165$	0.464102			0.0361303
$166$	−5.66025	+	21.1244i	−0.439321	+	1.63957i
$167$	5.19615			0.402090			0.201045	−	0.979582i	$-0.435566\pi$
$167$	5.19615			0.402090			0.201045	+	0.979582i	$0.435566\pi$
$168$	0.928203	+	12.9282i	0.0716124	+	0.997433i
$169$	12.7846			0.983432
$170$	−2.36603	+	8.83013i	−0.181466	+	0.677240i
$171$		0			0
$172$	−2.00000	+	3.46410i	−0.152499	+	0.264135i
$173$			14.3205i			1.08877i	0.838836	+	0.544384i	$0.183237\pi$
$173$			14.3205i			1.08877i	−0.838836	+	0.544384i	$0.816763\pi$
$174$	5.02628	−	18.7583i	0.381041	−	1.42207i
$175$	−1.73205	+	2.00000i	−0.130931	+	0.151186i
$176$	0.928203	−	0.535898i	0.0699660	−	0.0403949i
$177$	6.00000			0.450988
$178$	−3.46410	−	0.928203i	−0.259645	−	0.0695718i
$179$			6.39230i			0.477783i	0.971046	+	0.238892i	$0.0767841\pi$
$179$			6.39230i			0.477783i	−0.971046	+	0.238892i	$0.923216\pi$
$180$		0			0
$181$			0.928203i			0.0689928i	0.999405	+	0.0344964i	$0.0109827\pi$
$181$			0.928203i			0.0689928i	−0.999405	+	0.0344964i	$0.989017\pi$
$182$	1.43782	−	0.973721i	0.106578	−	0.0721770i
$183$		−	16.3923i		−	1.21175i
$184$	2.92820	+	2.92820i	0.215870	+	0.215870i
$185$		−	9.46410i		−	0.695815i
$186$	3.80385	−	14.1962i	0.278912	−	1.04091i
$187$	1.73205			0.126660
$188$	3.00000	+	1.73205i	0.218797	+	0.126323i
$189$	−9.00000	+	10.3923i	−0.654654	+	0.755929i
$190$	−8.19615	−	2.19615i	−0.594611	−	0.159326i
$191$		−	7.19615i		−	0.520695i	−0.965515	−	0.260348i	$-0.916163\pi$
$191$		−	7.19615i		−	0.520695i	0.965515	−	0.260348i	$-0.0838372\pi$
$192$		−	13.8564i		−	1.00000i
$193$	−9.46410			−0.681241			−0.340620	−	0.940201i	$-0.610637\pi$
$193$	−9.46410			−0.681241			−0.340620	+	0.940201i	$0.610637\pi$
$194$	18.2942	+	4.90192i	1.31345	+	0.351938i
$195$	−0.803848			−0.0575647
$196$	−5.19615	+	13.0000i	−0.371154	+	0.928571i
$197$	−13.3205			−0.949047			−0.474523	−	0.880243i	$-0.657380\pi$
$197$	−13.3205			−0.949047			−0.474523	+	0.880243i	$0.657380\pi$
$198$		0			0
$199$	−3.46410			−0.245564			−0.122782	−	0.992434i	$-0.539182\pi$
$199$	−3.46410			−0.245564			−0.122782	+	0.992434i	$0.539182\pi$
$200$	2.00000	−	2.00000i	0.141421	−	0.141421i
$201$			6.00000i			0.423207i
$202$	21.1244	+	5.66025i	1.48630	+	0.398254i
$203$	13.7321	−	15.8564i	0.963801	−	1.11290i
$204$	11.1962	−	19.3923i	0.783887	−	1.35773i
$205$	−3.46410			−0.241943
$206$	2.49038	−	9.29423i	0.173513	−	0.647560i
$207$		0			0
$208$	−1.60770	+	0.928203i	−0.111474	+	0.0643593i
$209$			1.60770i			0.111207i
$210$	5.36603	−	3.63397i	0.370291	−	0.250768i
$211$		−	3.19615i		−	0.220032i	−0.993930	−	0.110016i	$-0.964910\pi$
$211$		−	3.19615i		−	0.220032i	0.993930	−	0.110016i	$-0.0350902\pi$
$212$	−3.46410	−	2.00000i	−0.237915	−	0.137361i
$213$		−	12.9282i		−	0.885826i
$214$	3.26795	+	0.875644i	0.223392	+	0.0598578i
$215$	2.00000			0.136399
$216$	10.3923	−	10.3923i	0.707107	−	0.707107i
$217$	10.3923	−	12.0000i	0.705476	−	0.814613i
$218$	0.758330	−	2.83013i	0.0513606	−	0.191680i
$219$		−	22.3923i		−	1.51313i
$220$	−0.464102	−	0.267949i	−0.0312897	−	0.0180651i
$221$	−3.00000			−0.201802
$222$	−6.00000	+	22.3923i	−0.402694	+	1.50287i
$223$	13.7321			0.919566			0.459783	−	0.888031i	$-0.347927\pi$
$223$	13.7321			0.919566			0.459783	+	0.888031i	$0.347927\pi$
$224$	6.53590	−	13.4641i	0.436698	−	0.899608i
$225$		0			0
$226$	2.00000	−	7.46410i	0.133038	−	0.496505i
$227$	−20.6603			−1.37127			−0.685635	−	0.727946i	$-0.740475\pi$
$227$	−20.6603			−1.37127			−0.685635	+	0.727946i	$0.740475\pi$
$228$	18.0000	+	10.3923i	1.19208	+	0.688247i
$229$			8.53590i			0.564068i	0.959404	+	0.282034i	$0.0910091\pi$
$229$			8.53590i			0.564068i	−0.959404	+	0.282034i	$0.908991\pi$
$230$	0.535898	−	2.00000i	0.0353361	−	0.131876i
$231$	−0.928203	−	0.803848i	−0.0610713	−	0.0528893i
$232$	−15.8564	+	15.8564i	−1.04102	+	1.04102i
$233$	−9.07180			−0.594313			−0.297157	−	0.954829i	$-0.596038\pi$
$233$	−9.07180			−0.594313			−0.297157	+	0.954829i	$0.596038\pi$
$234$		0			0
$235$		−	1.73205i		−	0.112987i
$236$	−6.00000	−	3.46410i	−0.390567	−	0.225494i
$237$		−	25.3923i		−	1.64941i
$238$	20.0263	−	13.5622i	1.29811	−	0.879105i
$239$			23.9808i			1.55119i	0.631233	+	0.775593i	$0.282549\pi$
$239$			23.9808i			1.55119i	−0.631233	+	0.775593i	$0.717451\pi$
$240$	−6.00000	+	3.46410i	−0.387298	+	0.223607i
$241$		−	16.3923i		−	1.05592i	−0.849269	−	0.527961i	$-0.822957\pi$
$241$		−	16.3923i		−	1.05592i	0.849269	−	0.527961i	$-0.177043\pi$
$242$	4.00000	−	14.9282i	0.257130	−	0.959621i
$243$		0			0
$244$	−9.46410	+	16.3923i	−0.605877	+	1.04941i
$245$	6.92820	−	1.00000i	0.442627	−	0.0638877i
$246$	8.19615	+	2.19615i	0.522568	+	0.140022i
$247$		−	2.78461i		−	0.177180i
$248$	−12.0000	+	12.0000i	−0.762001	+	0.762001i
$249$	−26.7846			−1.69741
$250$	−1.36603	−	0.366025i	−0.0863950	−	0.0231495i
$251$	25.8564			1.63204			0.816021	−	0.578022i	$-0.196175\pi$
$251$	25.8564			1.63204			0.816021	+	0.578022i	$0.196175\pi$
$252$		0			0
$253$	−0.392305			−0.0246640
$254$	21.1244	+	5.66025i	1.32546	+	0.355156i
$255$	−11.1962			−0.701130
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$		−	6.00000i		−	0.374270i	−0.982334	−	0.187135i	$-0.940080\pi$
$257$		−	6.00000i		−	0.374270i	0.982334	−	0.187135i	$-0.0599201\pi$
$258$	−4.73205	−	1.26795i	−0.294605	−	0.0789391i
$259$	−16.3923	+	18.9282i	−1.01857	+	1.17614i
$260$	0.803848	+	0.464102i	0.0498525	+	0.0287824i
$261$		0			0
$262$	−0.928203	+	3.46410i	−0.0573446	+	0.214013i
$263$			11.4641i			0.706907i	0.935452	+	0.353453i	$0.114993\pi$
$263$			11.4641i			0.706907i	−0.935452	+	0.353453i	$0.885007\pi$
$264$	0.928203	+	0.928203i	0.0571270	+	0.0571270i
$265$			2.00000i			0.122859i
$266$	12.5885	+	18.5885i	0.771848	+	1.13973i
$267$		−	4.39230i		−	0.268805i
$268$	3.46410	−	6.00000i	0.211604	−	0.366508i
$269$			12.0000i			0.731653i	0.930683	+	0.365826i	$0.119214\pi$
$269$			12.0000i			0.731653i	−0.930683	+	0.365826i	$0.880786\pi$
$270$	−7.09808	−	1.90192i	−0.431975	−	0.115747i
$271$	−9.46410			−0.574903			−0.287452	−	0.957795i	$-0.592808\pi$
$271$	−9.46410			−0.574903			−0.287452	+	0.957795i	$0.592808\pi$
$272$	−22.3923	+	12.9282i	−1.35773	+	0.783887i
$273$	1.60770	+	1.39230i	0.0973021	+	0.0842661i
$274$	7.46410	−	27.8564i	0.450923	−	1.68287i
$275$			0.267949i			0.0161579i
$276$	−2.53590	+	4.39230i	−0.152643	+	0.264386i
$277$	16.7846			1.00849			0.504245	−	0.863561i	$-0.331771\pi$
$277$	16.7846			1.00849			0.504245	+	0.863561i	$0.331771\pi$
$278$	−2.53590	+	9.46410i	−0.152093	+	0.567619i
$279$		0			0
$280$	−7.46410	+	0.535898i	−0.446065	+	0.0320261i
$281$	−7.92820			−0.472957			−0.236478	−	0.971637i	$-0.575993\pi$
$281$	−7.92820			−0.472957			−0.236478	+	0.971637i	$0.575993\pi$
$282$	−1.09808	+	4.09808i	−0.0653895	+	0.244037i
$283$	−12.1244			−0.720718			−0.360359	−	0.932814i	$-0.617346\pi$
$283$	−12.1244			−0.720718			−0.360359	+	0.932814i	$0.617346\pi$
$284$	−7.46410	+	12.9282i	−0.442913	+	0.767148i
$285$		−	10.3923i		−	0.615587i
$286$	0.0455173	−	0.169873i	0.00269150	−	0.0100448i
$287$	6.92820	+	6.00000i	0.408959	+	0.354169i
$288$		0			0
$289$	−24.7846			−1.45792
$290$	10.8301	+	2.90192i	0.635967	+	0.170407i
$291$			23.1962i			1.35978i
$292$	−12.9282	+	22.3923i	−0.756566	+	1.31041i
$293$		−	20.3205i		−	1.18714i	−0.804784	−	0.593568i	$-0.797719\pi$
$293$		−	20.3205i		−	1.18714i	0.804784	−	0.593568i	$-0.202281\pi$
$294$	−17.0263	−	2.02628i	−0.992993	−	0.118175i
$295$			3.46410i			0.201688i
$296$	18.9282	−	18.9282i	1.10018	−	1.10018i
$297$			1.39230i			0.0807897i
$298$	1.12436	−	4.19615i	0.0651322	−	0.243077i
$299$	0.679492			0.0392960
$300$	3.00000	+	1.73205i	0.173205	+	0.100000i
$301$	−4.00000	−	3.46410i	−0.230556	−	0.199667i
$302$	−20.7583	−	5.56218i	−1.19451	−	0.320067i
$303$			26.7846i			1.53874i
$304$	−12.0000	−	20.7846i	−0.688247	−	1.19208i
$305$	9.46410			0.541913
$306$		0			0
$307$	−1.73205			−0.0988534			−0.0494267	−	0.998778i	$-0.515739\pi$
$307$	−1.73205			−0.0988534			−0.0494267	+	0.998778i	$0.515739\pi$
$308$	0.464102	+	1.33975i	0.0264446	+	0.0763391i
$309$	11.7846			0.670403
$310$	8.19615	+	2.19615i	0.465510	+	0.124733i
$311$	−7.85641			−0.445496			−0.222748	−	0.974876i	$-0.571503\pi$
$311$	−7.85641			−0.445496			−0.222748	+	0.974876i	$0.571503\pi$
$312$	−1.60770	−	1.60770i	−0.0910178	−	0.0910178i
$313$			17.5359i			0.991188i	0.868554	+	0.495594i	$0.165050\pi$
$313$			17.5359i			0.991188i	−0.868554	+	0.495594i	$0.834950\pi$
$314$	−10.7321	−	2.87564i	−0.605645	−	0.162282i
$315$		0			0
$316$	−14.6603	+	25.3923i	−0.824704	+	1.42843i
$317$	−3.07180			−0.172529			−0.0862646	−	0.996272i	$-0.527493\pi$
$317$	−3.07180			−0.172529			−0.0862646	+	0.996272i	$0.527493\pi$
$318$	1.26795	−	4.73205i	0.0711031	−	0.265360i
$319$		−	2.12436i		−	0.118941i
$320$	8.00000			0.447214
$321$			4.14359i			0.231273i
$322$	−4.53590	+	3.07180i	−0.252776	+	0.171185i
$323$		−	38.7846i		−	2.15803i
$324$	15.5885	+	9.00000i	0.866025	+	0.500000i
$325$		−	0.464102i		−	0.0257437i
$326$	28.3923	+	7.60770i	1.57250	+	0.421351i
$327$	3.58846			0.198442
$328$	−6.92820	−	6.92820i	−0.382546	−	0.382546i
$329$	−3.00000	+	3.46410i	−0.165395	+	0.190982i
$330$	0.169873	−	0.633975i	0.00935120	−	0.0348992i
$331$			26.3923i			1.45065i	0.688405	+	0.725326i	$0.258311\pi$
$331$			26.3923i			1.45065i	−0.688405	+	0.725326i	$0.741689\pi$
$332$	26.7846	+	15.4641i	1.47000	+	0.848703i
$333$		0			0
$334$	1.90192	−	7.09808i	0.104069	−	0.388389i
$335$	−3.46410			−0.189264
$336$	18.0000	+	3.46410i	0.981981	+	0.188982i
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	4.67949	−	17.4641i	0.254531	−	0.949922i
$339$	9.46410			0.514019
$340$	11.1962	+	6.46410i	0.607197	+	0.350565i
$341$		−	1.60770i		−	0.0870616i
$342$		0			0
$343$	−15.5885	−	10.0000i	−0.841698	−	0.539949i
$344$	4.00000	+	4.00000i	0.215666	+	0.215666i
$345$	2.53590			0.136528
$346$	19.5622	+	5.24167i	1.05167	+	0.281794i
$347$		−	34.2487i		−	1.83857i	−0.393596	−	0.919284i	$-0.628769\pi$
$347$		−	34.2487i		−	1.83857i	0.393596	−	0.919284i	$-0.371231\pi$
$348$	−23.7846	−	13.7321i	−1.27499	−	0.736115i
$349$			5.32051i			0.284800i	0.989809	+	0.142400i	$0.0454820\pi$
$349$			5.32051i			0.284800i	−0.989809	+	0.142400i	$0.954518\pi$
$350$	2.09808	+	3.09808i	0.112147	+	0.165599i
$351$		−	2.41154i		−	0.128719i
$352$	−0.392305	−	1.46410i	−0.0209099	−	0.0780369i
$353$			7.39230i			0.393453i	0.980458	+	0.196726i	$0.0630311\pi$
$353$			7.39230i			0.393453i	−0.980458	+	0.196726i	$0.936969\pi$
$354$	2.19615	−	8.19615i	0.116724	−	0.435621i
$355$	7.46410			0.396153
$356$	−2.53590	+	4.39230i	−0.134402	+	0.232792i
$357$	22.3923	+	19.3923i	1.18513	+	1.02635i
$358$	8.73205	+	2.33975i	0.461503	+	0.123659i
$359$		−	25.3205i		−	1.33637i	−0.743997	−	0.668183i	$-0.767072\pi$
$359$		−	25.3205i		−	1.33637i	0.743997	−	0.668183i	$-0.232928\pi$
$360$		0			0
$361$	17.0000			0.894737
$362$	1.26795	+	0.339746i	0.0666419	+	0.0178567i
$363$	18.9282			0.993473
$364$	−0.803848	−	2.32051i	−0.0421331	−	0.121628i
$365$	12.9282			0.676693
$366$	−22.3923	−	6.00000i	−1.17046	−	0.313625i
$367$	−11.8756			−0.619904			−0.309952	−	0.950752i	$-0.600313\pi$
$367$	−11.8756			−0.619904			−0.309952	+	0.950752i	$0.600313\pi$
$368$	5.07180	−	2.92820i	0.264386	−	0.152643i
$369$		0			0
$370$	−12.9282	−	3.46410i	−0.672105	−	0.180090i
$371$	3.46410	−	4.00000i	0.179847	−	0.207670i
$372$	−18.0000	−	10.3923i	−0.933257	−	0.538816i
$373$	−3.60770			−0.186799			−0.0933997	−	0.995629i	$-0.529773\pi$
$373$	−3.60770			−0.186799			−0.0933997	+	0.995629i	$0.529773\pi$
$374$	0.633975	−	2.36603i	0.0327820	−	0.122344i
$375$		−	1.73205i		−	0.0894427i
$376$	3.46410	−	3.46410i	0.178647	−	0.178647i
$377$			3.67949i			0.189503i
$378$	10.9019	+	16.0981i	0.560734	+	0.827996i
$379$		−	5.60770i		−	0.288048i	−0.989574	−	0.144024i	$-0.953996\pi$
$379$		−	5.60770i		−	0.288048i	0.989574	−	0.144024i	$-0.0460042\pi$
$380$	−6.00000	+	10.3923i	−0.307794	+	0.533114i
$381$			26.7846i			1.37222i
$382$	−9.83013	−	2.63397i	−0.502953	−	0.134766i
$383$	−27.4641			−1.40335			−0.701675	−	0.712497i	$-0.747564\pi$
$383$	−27.4641			−1.40335			−0.701675	+	0.712497i	$0.747564\pi$
$384$	−18.9282	−	5.07180i	−0.965926	−	0.258819i
$385$	0.464102	−	0.535898i	0.0236528	−	0.0273119i
$386$	−3.46410	+	12.9282i	−0.176318	+	0.658028i
$387$		0			0
$388$	13.3923	−	23.1962i	0.679891	−	1.17761i
$389$	−20.8564			−1.05746			−0.528731	−	0.848790i	$-0.677332\pi$
$389$	−20.8564			−1.05746			−0.528731	+	0.848790i	$0.677332\pi$
$390$	−0.294229	+	1.09808i	−0.0148988	+	0.0556033i
$391$	9.46410			0.478620
$392$	15.8564	+	11.8564i	0.800869	+	0.598839i
$393$	−4.39230			−0.221562
$394$	−4.87564	+	18.1962i	−0.245631	+	0.916709i
$395$	14.6603			0.737637
$396$		0			0
$397$		−	12.4641i		−	0.625555i	−0.949826	−	0.312778i	$-0.898741\pi$
$397$		−	12.4641i		−	0.625555i	0.949826	−	0.312778i	$-0.101259\pi$
$398$	−1.26795	+	4.73205i	−0.0635566	+	0.237196i
$399$	−18.0000	+	20.7846i	−0.901127	+	1.04053i
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	−10.0718			−0.502962			−0.251481	−	0.967862i	$-0.580918\pi$
$401$	−10.0718			−0.502962			−0.251481	+	0.967862i	$0.580918\pi$
$402$	8.19615	+	2.19615i	0.408787	+	0.109534i
$403$			2.78461i			0.138711i
$404$	15.4641	−	26.7846i	0.769368	−	1.33258i
$405$		−	9.00000i		−	0.447214i
$406$	−16.6340	−	24.5622i	−0.825530	−	1.21900i
$407$			2.53590i			0.125700i
$408$	−22.3923	−	22.3923i	−1.10858	−	1.10858i
$409$		−	4.14359i		−	0.204888i	−0.994739	−	0.102444i	$-0.967334\pi$
$409$		−	4.14359i		−	0.204888i	0.994739	−	0.102444i	$-0.0326662\pi$
$410$	−1.26795	+	4.73205i	−0.0626195	+	0.233699i
$411$	35.3205			1.74223
$412$	−11.7846	−	6.80385i	−0.580586	−	0.335202i
$413$	6.00000	−	6.92820i	0.295241	−	0.340915i
$414$		0			0
$415$		−	15.4641i		−	0.759103i
$416$	0.679492	+	2.53590i	0.0333148	+	0.124333i
$417$	−12.0000			−0.587643
$418$	2.19615	+	0.588457i	0.107417	+	0.0287824i
$419$	24.2487			1.18463			0.592314	−	0.805708i	$-0.298215\pi$
$419$	24.2487			1.18463			0.592314	+	0.805708i	$0.298215\pi$
$420$	−3.00000	−	8.66025i	−0.146385	−	0.422577i
$421$	19.0000			0.926003			0.463002	−	0.886357i	$-0.346772\pi$
$421$	19.0000			0.926003			0.463002	+	0.886357i	$0.346772\pi$
$422$	−4.36603	−	1.16987i	−0.212535	−	0.0569485i
$423$		0			0
$424$	−4.00000	+	4.00000i	−0.194257	+	0.194257i
$425$		−	6.46410i		−	0.313555i
$426$	−17.6603	−	4.73205i	−0.855642	−	0.229269i
$427$	−18.9282	−	16.3923i	−0.916000	−	0.793279i
$428$	2.39230	−	4.14359i	0.115636	−	0.200288i
$429$	0.215390			0.0103991
$430$	0.732051	−	2.73205i	0.0353026	−	0.131751i
$431$			13.5885i			0.654533i	0.944932	+	0.327266i	$0.106127\pi$
$431$			13.5885i			0.654533i	−0.944932	+	0.327266i	$0.893873\pi$
$432$	−10.3923	−	18.0000i	−0.500000	−	0.866025i
$433$			31.8564i			1.53092i	0.643483	+	0.765461i	$0.277489\pi$
$433$			31.8564i			1.53092i	−0.643483	+	0.765461i	$0.722511\pi$
$434$	−12.5885	−	18.5885i	−0.604265	−	0.892275i
$435$			13.7321i			0.658401i
$436$	−3.58846	−	2.07180i	−0.171856	−	0.0992211i
$437$			8.78461i			0.420225i
$438$	−30.5885	−	8.19615i	−1.46157	−	0.391627i
$439$	39.7128			1.89539			0.947695	−	0.319179i	$-0.103407\pi$
$439$	39.7128			1.89539			0.947695	+	0.319179i	$0.103407\pi$
$440$	−0.535898	+	0.535898i	−0.0255480	+	0.0255480i
$441$		0			0
$442$	−1.09808	+	4.09808i	−0.0522302	+	0.194926i
$443$			26.0000i			1.23530i	0.786454	+	0.617649i	$0.211915\pi$
$443$			26.0000i			1.23530i	−0.786454	+	0.617649i	$0.788085\pi$
$444$	28.3923	+	16.3923i	1.34744	+	0.777944i
$445$	2.53590			0.120213
$446$	5.02628	−	18.7583i	0.238001	−	0.888233i
$447$	5.32051			0.251651
$448$	−16.0000	−	13.8564i	−0.755929	−	0.654654i
$449$	11.9282			0.562927			0.281463	−	0.959572i	$-0.409180\pi$
$449$	11.9282			0.562927			0.281463	+	0.959572i	$0.409180\pi$
$450$		0			0
$451$	0.928203			0.0437074
$452$	−9.46410	−	5.46410i	−0.445154	−	0.257010i
$453$		−	26.3205i		−	1.23665i
$454$	−7.56218	+	28.2224i	−0.354911	+	1.32454i
$455$	−0.803848	+	0.928203i	−0.0376850	+	0.0435148i
$456$	20.7846	−	20.7846i	0.973329	−	0.973329i
$457$	20.5359			0.960629			0.480314	−	0.877096i	$-0.340523\pi$
$457$	20.5359			0.960629			0.480314	+	0.877096i	$0.340523\pi$
$458$	11.6603	+	3.12436i	0.544848	+	0.145992i
$459$		−	33.5885i		−	1.56777i
$460$	−2.53590	−	1.46410i	−0.118237	−	0.0682641i
$461$		−	27.7128i		−	1.29071i	−0.763881	−	0.645357i	$-0.776709\pi$
$461$		−	27.7128i		−	1.29071i	0.763881	−	0.645357i	$-0.223291\pi$
$462$	−1.43782	+	0.973721i	−0.0668935	+	0.0453016i
$463$			16.3923i			0.761815i	0.924613	+	0.380908i	$0.124388\pi$
$463$			16.3923i			0.761815i	−0.924613	+	0.380908i	$0.875612\pi$
$464$	15.8564	+	27.4641i	0.736115	+	1.27499i
$465$			10.3923i			0.481932i
$466$	−3.32051	+	12.3923i	−0.153820	+	0.574062i
$467$	−22.5167			−1.04195			−0.520973	−	0.853573i	$-0.674431\pi$
$467$	−22.5167			−1.04195			−0.520973	+	0.853573i	$0.674431\pi$
$468$		0			0
$469$	6.92820	+	6.00000i	0.319915	+	0.277054i
$470$	−2.36603	−	0.633975i	−0.109137	−	0.0292431i
$471$		−	13.6077i		−	0.627009i
$472$	−6.92820	+	6.92820i	−0.318896	+	0.318896i
$473$	−0.535898			−0.0246406
$474$	−34.6865	−	9.29423i	−1.59321	−	0.426898i
$475$	6.00000			0.275299
$476$	−11.1962	−	32.3205i	−0.513175	−	1.48141i
$477$		0			0
$478$	32.7583	+	8.77757i	1.49833	+	0.401477i
$479$	−25.1769			−1.15036			−0.575181	−	0.818026i	$-0.695068\pi$
$479$	−25.1769			−1.15036			−0.575181	+	0.818026i	$0.695068\pi$
$480$	2.53590	+	9.46410i	0.115747	+	0.431975i
$481$		−	4.39230i		−	0.200272i
$482$	−22.3923	−	6.00000i	−1.01994	−	0.273293i
$483$	−5.07180	−	4.39230i	−0.230775	−	0.199857i
$484$	−18.9282	−	10.9282i	−0.860373	−	0.496737i
$485$	−13.3923			−0.608113
$486$		0			0
$487$			12.7846i			0.579326i	0.957129	+	0.289663i	$0.0935432\pi$
$487$			12.7846i			0.579326i	−0.957129	+	0.289663i	$0.906457\pi$
$488$	18.9282	+	18.9282i	0.856840	+	0.856840i
$489$			36.0000i			1.62798i
$490$	1.16987	−	9.83013i	0.0528495	−	0.444080i
$491$			9.87564i			0.445682i	0.974855	+	0.222841i	$0.0715330\pi$
$491$			9.87564i			0.445682i	−0.974855	+	0.222841i	$0.928467\pi$
$492$	6.00000	−	10.3923i	0.270501	−	0.468521i
$493$			51.2487i			2.30813i
$494$	−3.80385	−	1.01924i	−0.171143	−	0.0458577i
$495$		0			0
$496$	12.0000	+	20.7846i	0.538816	+	0.933257i
$497$	−14.9282	−	12.9282i	−0.669621	−	0.579909i
$498$	−9.80385	+	36.5885i	−0.439321	+	1.63957i
$499$		−	25.5885i		−	1.14550i	−0.819731	−	0.572748i	$-0.805877\pi$
$499$		−	25.5885i		−	1.14550i	0.819731	−	0.572748i	$-0.194123\pi$
$500$	−1.00000	+	1.73205i	−0.0447214	+	0.0774597i
$501$	9.00000			0.402090
$502$	9.46410	−	35.3205i	0.422404	−	1.57643i
$503$	15.5885			0.695055			0.347527	−	0.937670i	$-0.387021\pi$
$503$	15.5885			0.695055			0.347527	+	0.937670i	$0.387021\pi$
$504$		0			0
$505$	−15.4641			−0.688143
$506$	−0.143594	+	0.535898i	−0.00638351	+	0.0238236i
$507$	22.1436			0.983432
$508$	15.4641	−	26.7846i	0.686109	−	1.18837i
$509$		−	25.8564i		−	1.14607i	−0.819533	−	0.573033i	$-0.805767\pi$
$509$		−	25.8564i		−	1.14607i	0.819533	−	0.573033i	$-0.194233\pi$
$510$	−4.09808	+	15.2942i	−0.181466	+	0.677240i
$511$	−25.8564	−	22.3923i	−1.14382	−	0.990577i
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$	31.1769			1.37649
$514$	−8.19615	−	2.19615i	−0.361517	−	0.0968681i
$515$			6.80385i			0.299813i
$516$	−3.46410	+	6.00000i	−0.152499	+	0.264135i
$517$			0.464102i			0.0204112i
$518$	19.8564	+	29.3205i	0.872440	+	1.28827i
$519$			24.8038i			1.08877i
$520$	0.928203	−	0.928203i	0.0407044	−	0.0407044i
$521$		−	13.6077i		−	0.596164i	−0.954540	−	0.298082i	$-0.903653\pi$
$521$		−	13.6077i		−	0.596164i	0.954540	−	0.298082i	$-0.0963469\pi$
$522$		0			0
$523$	24.2487			1.06032			0.530161	−	0.847897i	$-0.322131\pi$
$523$	24.2487			1.06032			0.530161	+	0.847897i	$0.322131\pi$
$524$	4.39230	+	2.53590i	0.191879	+	0.110781i
$525$	−3.00000	+	3.46410i	−0.130931	+	0.151186i
$526$	15.6603	+	4.19615i	0.682820	+	0.182961i
$527$			38.7846i			1.68948i
$528$	1.60770	−	0.928203i	0.0699660	−	0.0403949i
$529$	20.8564			0.906800
$530$	2.73205	+	0.732051i	0.118673	+	0.0317983i
$531$		0			0
$532$	30.0000	−	10.3923i	1.30066	−	0.450564i
$533$	−1.60770			−0.0696370
$534$	−6.00000	−	1.60770i	−0.259645	−	0.0695718i
$535$	−2.39230			−0.103428
$536$	−6.92820	−	6.92820i	−0.299253	−	0.299253i
$537$			11.0718i			0.477783i
$538$	16.3923	+	4.39230i	0.706722	+	0.189366i
$539$	−1.85641	+	0.267949i	−0.0799611	+	0.0115414i
$540$	−5.19615	+	9.00000i	−0.223607	+	0.387298i
$541$	7.78461			0.334687			0.167343	−	0.985899i	$-0.446481\pi$
$541$	7.78461			0.334687			0.167343	+	0.985899i	$0.446481\pi$
$542$	−3.46410	+	12.9282i	−0.148796	+	0.555314i
$543$			1.60770i			0.0689928i
$544$	9.46410	+	35.3205i	0.405770	+	1.51435i
$545$			2.07180i			0.0887460i
$546$	2.49038	−	1.68653i	0.106578	−	0.0721770i
$547$		−	21.4641i		−	0.917739i	−0.888504	−	0.458869i	$-0.848255\pi$
$547$		−	21.4641i		−	0.917739i	0.888504	−	0.458869i	$-0.151745\pi$
$548$	−35.3205	−	20.3923i	−1.50882	−	0.871116i
$549$		0			0
$550$	0.366025	+	0.0980762i	0.0156074	+	0.00418198i
$551$	−47.5692			−2.02652
$552$	5.07180	+	5.07180i	0.215870	+	0.215870i
$553$	−29.3205	−	25.3923i	−1.24683	−	1.07979i
$554$	6.14359	−	22.9282i	0.261016	−	0.974126i
$555$		−	16.3923i		−	0.695815i
$556$	12.0000	+	6.92820i	0.508913	+	0.293821i
$557$	−21.8564			−0.926086			−0.463043	−	0.886336i	$-0.653242\pi$
$557$	−21.8564			−0.926086			−0.463043	+	0.886336i	$0.653242\pi$
$558$		0			0
$559$	0.928203			0.0392588
$560$	−2.00000	+	10.3923i	−0.0845154	+	0.439155i
$561$	3.00000			0.126660
$562$	−2.90192	+	10.8301i	−0.122410	+	0.456841i
$563$	−19.1769			−0.808211			−0.404105	−	0.914712i	$-0.632417\pi$
$563$	−19.1769			−0.808211			−0.404105	+	0.914712i	$0.632417\pi$
$564$	5.19615	+	3.00000i	0.218797	+	0.126323i
$565$			5.46410i			0.229876i
$566$	−4.43782	+	16.5622i	−0.186536	+	0.696160i
$567$	−15.5885	+	18.0000i	−0.654654	+	0.755929i
$568$	14.9282	+	14.9282i	0.626373	+	0.626373i
$569$	7.07180			0.296465			0.148233	−	0.988953i	$-0.452642\pi$
$569$	7.07180			0.296465			0.148233	+	0.988953i	$0.452642\pi$
$570$	−14.1962	−	3.80385i	−0.594611	−	0.159326i
$571$			6.67949i			0.279528i	0.990185	+	0.139764i	$0.0446344\pi$
$571$			6.67949i			0.279528i	−0.990185	+	0.139764i	$0.955366\pi$
$572$	−0.215390	−	0.124356i	−0.00900592	−	0.00519957i
$573$		−	12.4641i		−	0.520695i
$574$	10.7321	−	7.26795i	0.447947	−	0.303358i
$575$			1.46410i			0.0610573i
$576$		0			0
$577$		−	19.3923i		−	0.807312i	−0.914911	−	0.403656i	$-0.867739\pi$
$577$		−	19.3923i		−	0.807312i	0.914911	−	0.403656i	$-0.132261\pi$
$578$	−9.07180	+	33.8564i	−0.377337	+	1.40824i
$579$	−16.3923			−0.681241
$580$	7.92820	−	13.7321i	0.329201	−	0.570192i
$581$	−26.7846	+	30.9282i	−1.11121	+	1.28312i
$582$	31.6865	+	8.49038i	1.31345	+	0.351938i
$583$		−	0.535898i		−	0.0221946i
$584$	25.8564	+	25.8564i	1.06995	+	1.06995i
$585$		0			0
$586$	−27.7583	−	7.43782i	−1.14669	−	0.307254i
$587$	20.5359			0.847607			0.423804	−	0.905754i	$-0.360695\pi$
$587$	20.5359			0.847607			0.423804	+	0.905754i	$0.360695\pi$
$588$	−9.00000	+	22.5167i	−0.371154	+	0.928571i
$589$	−36.0000			−1.48335
$590$	4.73205	+	1.26795i	0.194815	+	0.0522006i
$591$	−23.0718			−0.949047
$592$	−18.9282	−	32.7846i	−0.777944	−	1.34744i
$593$		−	30.4641i		−	1.25101i	−0.780220	−	0.625505i	$-0.784893\pi$
$593$		−	30.4641i		−	1.25101i	0.780220	−	0.625505i	$-0.215107\pi$
$594$	1.90192	+	0.509619i	0.0780369	+	0.0209099i
$595$	−11.1962	+	12.9282i	−0.458997	+	0.530005i
$596$	−5.32051	−	3.07180i	−0.217937	−	0.125826i
$597$	−6.00000			−0.245564
$598$	0.248711	−	0.928203i	0.0101706	−	0.0379571i
$599$			10.1244i			0.413670i	0.978376	+	0.206835i	$0.0663163\pi$
$599$			10.1244i			0.413670i	−0.978376	+	0.206835i	$0.933684\pi$
$600$	3.46410	−	3.46410i	0.141421	−	0.141421i
$601$			14.7846i			0.603077i	0.953454	+	0.301538i	$0.0975001\pi$
$601$			14.7846i			0.603077i	−0.953454	+	0.301538i	$0.902500\pi$
$602$	−6.19615	+	4.19615i	−0.252536	+	0.171022i
$603$		0			0
$604$	−15.1962	+	26.3205i	−0.618323	+	1.07097i
$605$			10.9282i			0.444295i
$606$	36.5885	+	9.80385i	1.48630	+	0.398254i
$607$	29.1962			1.18504			0.592518	−	0.805557i	$-0.298134\pi$
$607$	29.1962			1.18504			0.592518	+	0.805557i	$0.298134\pi$
$608$	−32.7846	+	8.78461i	−1.32959	+	0.356263i
$609$	23.7846	−	27.4641i	0.963801	−	1.11290i
$610$	3.46410	−	12.9282i	0.140257	−	0.523448i
$611$		−	0.803848i		−	0.0325202i
$612$		0			0
$613$	−10.0000			−0.403896			−0.201948	−	0.979396i	$-0.564727\pi$
$613$	−10.0000			−0.403896			−0.201948	+	0.979396i	$0.564727\pi$
$614$	−0.633975	+	2.36603i	−0.0255851	+	0.0954850i
$615$	−6.00000			−0.241943
$616$	2.00000	−	0.143594i	0.0805823	−	0.00578555i
$617$	−22.9282			−0.923055			−0.461527	−	0.887126i	$-0.652698\pi$
$617$	−22.9282			−0.923055			−0.461527	+	0.887126i	$0.652698\pi$
$618$	4.31347	−	16.0981i	0.173513	−	0.647560i
$619$	−0.679492			−0.0273111			−0.0136555	−	0.999907i	$-0.504347\pi$
$619$	−0.679492			−0.0273111			−0.0136555	+	0.999907i	$0.504347\pi$
$620$	6.00000	−	10.3923i	0.240966	−	0.417365i
$621$			7.60770i			0.305286i
$622$	−2.87564	+	10.7321i	−0.115303	+	0.430316i
$623$	−5.07180	−	4.39230i	−0.203197	−	0.175974i
$624$	−2.78461	+	1.60770i	−0.111474	+	0.0643593i
$625$	1.00000			0.0400000
$626$	23.9545	+	6.41858i	0.957414	+	0.256538i
$627$			2.78461i			0.111207i
$628$	−7.85641	+	13.6077i	−0.313505	+	0.543006i
$629$		−	61.1769i		−	2.43928i
$630$		0			0
$631$		−	38.9090i		−	1.54894i	−0.632610	−	0.774471i	$-0.718016\pi$
$631$		−	38.9090i		−	1.54894i	0.632610	−	0.774471i	$-0.281984\pi$
$632$	29.3205	+	29.3205i	1.16631	+	1.16631i
$633$		−	5.53590i		−	0.220032i
$634$	−1.12436	+	4.19615i	−0.0446539	+	0.166651i
$635$	−15.4641			−0.613674
$636$	−6.00000	−	3.46410i	−0.237915	−	0.137361i
$637$	3.21539	−	0.464102i	0.127398	−	0.0183884i
$638$	−2.90192	−	0.777568i	−0.114888	−	0.0307842i
$639$		0			0
$640$	2.92820	−	10.9282i	0.115747	−	0.431975i
$641$	8.92820			0.352643			0.176321	−	0.984333i	$-0.443580\pi$
$641$	8.92820			0.352643			0.176321	+	0.984333i	$0.443580\pi$
$642$	5.66025	+	1.51666i	0.223392	+	0.0598578i
$643$	−7.05256			−0.278126			−0.139063	−	0.990284i	$-0.544409\pi$
$643$	−7.05256			−0.278126			−0.139063	+	0.990284i	$0.544409\pi$
$644$	2.53590	+	7.32051i	0.0999284	+	0.288468i
$645$	3.46410			0.136399
$646$	−52.9808	−	14.1962i	−2.08450	−	0.558540i
$647$	10.3923			0.408564			0.204282	−	0.978912i	$-0.434514\pi$
$647$	10.3923			0.408564			0.204282	+	0.978912i	$0.434514\pi$
$648$	18.0000	−	18.0000i	0.707107	−	0.707107i
$649$		−	0.928203i		−	0.0364352i
$650$	−0.633975	−	0.169873i	−0.0248665	−	0.00666297i
$651$	18.0000	−	20.7846i	0.705476	−	0.814613i
$652$	20.7846	−	36.0000i	0.813988	−	1.40987i
$653$	17.6077			0.689042			0.344521	−	0.938779i	$-0.388041\pi$
$653$	17.6077			0.689042			0.344521	+	0.938779i	$0.388041\pi$
$654$	1.31347	−	4.90192i	0.0513606	−	0.191680i
$655$		−	2.53590i		−	0.0990857i
$656$	−12.0000	+	6.92820i	−0.468521	+	0.270501i
$657$		0			0
$658$	3.63397	+	5.36603i	0.141667	+	0.209189i
$659$			31.1962i			1.21523i	0.794232	+	0.607615i	$0.207874\pi$
$659$			31.1962i			1.21523i	−0.794232	+	0.607615i	$0.792126\pi$
$660$	−0.803848	−	0.464102i	−0.0312897	−	0.0180651i
$661$		−	39.7128i		−	1.54465i	−0.635228	−	0.772325i	$-0.719094\pi$
$661$		−	39.7128i		−	1.54465i	0.635228	−	0.772325i	$-0.280906\pi$
$662$	36.0526	+	9.66025i	1.40122	+	0.375456i
$663$	−5.19615			−0.201802
$664$	30.9282	−	30.9282i	1.20025	−	1.20025i
$665$	−12.0000	−	10.3923i	−0.465340	−	0.402996i
$666$		0			0
$667$		−	11.6077i		−	0.449452i
$668$	−9.00000	−	5.19615i	−0.348220	−	0.201045i
$669$	23.7846			0.919566
$670$	−1.26795	+	4.73205i	−0.0489852	+	0.182815i
$671$	−2.53590			−0.0978973
$672$	11.3205	−	23.3205i	0.436698	−	0.899608i
$673$	−13.1769			−0.507933			−0.253966	−	0.967213i	$-0.581735\pi$
$673$	−13.1769			−0.507933			−0.253966	+	0.967213i	$0.581735\pi$
$674$		0			0
$675$	5.19615			0.200000
$676$	−22.1436	−	12.7846i	−0.851677	−	0.491716i
$677$			25.3923i			0.975906i	0.872870	+	0.487953i	$0.162256\pi$
$677$			25.3923i			0.975906i	−0.872870	+	0.487953i	$0.837744\pi$
$678$	3.46410	−	12.9282i	0.133038	−	0.496505i
$679$	26.7846	+	23.1962i	1.02790	+	0.890187i
$680$	12.9282	−	12.9282i	0.495774	−	0.495774i
$681$	−35.7846			−1.37127
$682$	−2.19615	−	0.588457i	−0.0840950	−	0.0225332i
$683$		−	7.32051i		−	0.280111i	−0.990144	−	0.140056i	$-0.955272\pi$
$683$		−	7.32051i		−	0.280111i	0.990144	−	0.140056i	$-0.0447282\pi$
$684$		0			0
$685$			20.3923i			0.779150i
$686$	−19.3660	+	17.6340i	−0.739398	+	0.673268i
$687$			14.7846i			0.564068i
$688$	6.92820	−	4.00000i	0.264135	−	0.152499i
$689$			0.928203i			0.0353617i
$690$	0.928203	−	3.46410i	0.0353361	−	0.131876i
$691$	22.6410			0.861305			0.430652	−	0.902518i	$-0.358283\pi$
$691$	22.6410			0.861305			0.430652	+	0.902518i	$0.358283\pi$
$692$	14.3205	−	24.8038i	0.544384	−	0.942901i
$693$		0			0
$694$	−46.7846	−	12.5359i	−1.77592	−	0.475856i
$695$		−	6.92820i		−	0.262802i
$696$	−27.4641	+	27.4641i	−1.04102	+	1.04102i
$697$	−22.3923			−0.848169
$698$	7.26795	+	1.94744i	0.275096	+	0.0737117i
$699$	−15.7128			−0.594313
$700$	5.00000	−	1.73205i	0.188982	−	0.0654654i
$701$	−37.7846			−1.42711			−0.713553	−	0.700602i	$-0.752915\pi$
$701$	−37.7846			−1.42711			−0.713553	+	0.700602i	$0.752915\pi$
$702$	−3.29423	−	0.882686i	−0.124333	−	0.0333148i
$703$	56.7846			2.14167
$704$	−2.14359			−0.0807897
$705$		−	3.00000i		−	0.112987i
$706$	10.0981	+	2.70577i	0.380046	+	0.101833i
$707$	30.9282	+	26.7846i	1.16317	+	1.00734i
$708$	−10.3923	−	6.00000i	−0.390567	−	0.225494i
$709$	21.0000			0.788672			0.394336	−	0.918966i	$-0.370975\pi$
$709$	21.0000			0.788672			0.394336	+	0.918966i	$0.370975\pi$
$710$	2.73205	−	10.1962i	0.102532	−	0.382655i
$711$		0			0
$712$	5.07180	+	5.07180i	0.190074	+	0.190074i
$713$		−	8.78461i		−	0.328986i
$714$	34.6865	−	23.4904i	1.29811	−	0.879105i
$715$			0.124356i			0.00465064i
$716$	6.39230	−	11.0718i	0.238892	−	0.413772i
$717$			41.5359i			1.55119i
$718$	−34.5885	−	9.26795i	−1.29083	−	0.345877i
$719$	−38.5359			−1.43715			−0.718573	−	0.695451i	$-0.755205\pi$
$719$	−38.5359			−1.43715			−0.718573	+	0.695451i	$0.755205\pi$
$720$		0			0
$721$	11.7846	−	13.6077i	0.438882	−	0.506777i
$722$	6.22243	−	23.2224i	0.231575	−	0.864249i
$723$		−	28.3923i		−	1.05592i
$724$	0.928203	−	1.60770i	0.0344964	−	0.0597495i
$725$	−7.92820			−0.294446
$726$	6.92820	−	25.8564i	0.257130	−	0.959621i
$727$	13.6077			0.504681			0.252341	−	0.967638i	$-0.418800\pi$
$727$	13.6077			0.504681			0.252341	+	0.967638i	$0.418800\pi$
$728$	−3.46410	+	0.248711i	−0.128388	+	0.00921785i
$729$	27.0000			1.00000
$730$	4.73205	−	17.6603i	0.175141	−	0.653635i
$731$	12.9282			0.478167
$732$	−16.3923	+	28.3923i	−0.605877	+	1.04941i
$733$		−	11.5359i		−	0.426088i	−0.977043	−	0.213044i	$-0.931662\pi$
$733$		−	11.5359i		−	0.426088i	0.977043	−	0.213044i	$-0.0683378\pi$
$734$	−4.34679	+	16.2224i	−0.160443	+	0.598781i
$735$	12.0000	−	1.73205i	0.442627	−	0.0638877i
$736$	−2.14359	−	8.00000i	−0.0790139	−	0.294884i
$737$	0.928203			0.0341908
$738$		0			0
$739$			4.26795i			0.156999i	0.996914	+	0.0784995i	$0.0250129\pi$
$739$			4.26795i			0.156999i	−0.996914	+	0.0784995i	$0.974987\pi$
$740$	−9.46410	+	16.3923i	−0.347907	+	0.602593i
$741$		−	4.82309i		−	0.177180i
$742$	−4.19615	−	6.19615i	−0.154046	−	0.227468i
$743$		−	30.3923i		−	1.11499i	−0.830182	−	0.557493i	$-0.811763\pi$
$743$		−	30.3923i		−	1.11499i	0.830182	−	0.557493i	$-0.188237\pi$
$744$	−20.7846	+	20.7846i	−0.762001	+	0.762001i
$745$			3.07180i			0.112542i
$746$	−1.32051	+	4.92820i	−0.0483472	+	0.180434i
$747$		0			0
$748$	−3.00000	−	1.73205i	−0.109691	−	0.0633300i
$749$	4.78461	+	4.14359i	0.174826	+	0.151404i
$750$	−2.36603	−	0.633975i	−0.0863950	−	0.0231495i
$751$			25.5885i			0.933736i	0.884327	+	0.466868i	$0.154618\pi$
$751$			25.5885i			0.933736i	−0.884327	+	0.466868i	$0.845382\pi$
$752$	−3.46410	−	6.00000i	−0.126323	−	0.218797i
$753$	44.7846			1.63204
$754$	5.02628	+	1.34679i	0.183046	+	0.0490471i
$755$	15.1962			0.553045
$756$	25.9808	−	9.00000i	0.944911	−	0.327327i
$757$	37.8564			1.37591			0.687957	−	0.725751i	$-0.258508\pi$
$757$	37.8564			1.37591			0.687957	+	0.725751i	$0.258508\pi$
$758$	−7.66025	−	2.05256i	−0.278233	−	0.0745523i
$759$	−0.679492			−0.0246640
$760$	12.0000	+	12.0000i	0.435286	+	0.435286i
$761$			42.2487i			1.53151i	0.643130	+	0.765757i	$0.277636\pi$
$761$			42.2487i			1.53151i	−0.643130	+	0.765757i	$0.722364\pi$
$762$	36.5885	+	9.80385i	1.32546	+	0.355156i
$763$	3.58846	−	4.14359i	0.129911	−	0.150008i
$764$	−7.19615	+	12.4641i	−0.260348	+	0.450935i
$765$		0			0
$766$	−10.0526	+	37.5167i	−0.363214	+	1.35553i
$767$			1.60770i			0.0580505i
$768$	−13.8564	+	24.0000i	−0.500000	+	0.866025i
$769$		−	18.0000i		−	0.649097i	−0.945869	−	0.324548i	$-0.894788\pi$
$769$		−	18.0000i		−	0.649097i	0.945869	−	0.324548i	$-0.105212\pi$
$770$	−0.562178	−	0.830127i	−0.0202595	−	0.0299157i
$771$		−	10.3923i		−	0.374270i
$772$	16.3923	+	9.46410i	0.589972	+	0.340620i
$773$			5.53590i			0.199112i	0.995032	+	0.0995562i	$0.0317423\pi$
$773$			5.53590i			0.199112i	−0.995032	+	0.0995562i	$0.968258\pi$
$774$		0			0
$775$	−6.00000			−0.215526
$776$	−26.7846	−	26.7846i	−0.961511	−	0.961511i
$777$	−28.3923	+	32.7846i	−1.01857	+	1.17614i
$778$	−7.63397	+	28.4904i	−0.273691	+	1.02143i
$779$		−	20.7846i		−	0.744686i
$780$	1.39230	+	0.803848i	0.0498525	+	0.0287824i
$781$	−2.00000			−0.0715656
$782$	3.46410	−	12.9282i	0.123876	−	0.462312i
$783$	−41.1962			−1.47223
$784$	22.0000	−	17.3205i	0.785714	−	0.618590i
$785$	7.85641			0.280407
$786$	−1.60770	+	6.00000i	−0.0573446	+	0.214013i
$787$	−32.6603			−1.16421			−0.582106	−	0.813113i	$-0.697771\pi$
$787$	−32.6603			−1.16421			−0.582106	+	0.813113i	$0.697771\pi$
$788$	23.0718	+	13.3205i	0.821899	+	0.474523i
$789$			19.8564i			0.706907i
$790$	5.36603	−	20.0263i	0.190915	−	0.712503i
$791$	9.46410	−	10.9282i	0.336505	−	0.388562i
$792$		0			0
$793$	4.39230			0.155975
$794$	−17.0263	−	4.56218i	−0.604240	−	0.161906i
$795$			3.46410i			0.122859i
$796$	6.00000	+	3.46410i	0.212664	+	0.122782i
$797$			22.1769i			0.785547i	0.919635	+	0.392773i	$0.128484\pi$
$797$			22.1769i			0.785547i	−0.919635	+	0.392773i	$0.871516\pi$
$798$	21.8038	+	32.1962i	0.771848	+	1.13973i
$799$		−	11.1962i		−	0.396091i
$800$	−5.46410	+	1.46410i	−0.193185	+	0.0517638i
$801$		0			0
$802$	−3.68653	+	13.7583i	−0.130176	+	0.485824i
$803$	−3.46410			−0.122245
$804$	6.00000	−	10.3923i	0.211604	−	0.366508i
$805$	2.53590	−	2.92820i	0.0893787	−	0.103206i
$806$	3.80385	+	1.01924i	0.133985	+	0.0359011i
$807$			20.7846i			0.731653i
$808$	−30.9282	−	30.9282i	−1.08805	−	1.08805i
$809$	7.92820			0.278741			0.139370	−	0.990240i	$-0.455492\pi$
$809$	7.92820			0.278741			0.139370	+	0.990240i	$0.455492\pi$
$810$	−12.2942	−	3.29423i	−0.431975	−	0.115747i
$811$	−29.0718			−1.02085			−0.510424	−	0.859923i	$-0.670512\pi$
$811$	−29.0718			−1.02085			−0.510424	+	0.859923i	$0.670512\pi$
$812$	−39.6410	+	13.7321i	−1.39113	+	0.481901i
$813$	−16.3923			−0.574903
$814$	3.46410	+	0.928203i	0.121417	+	0.0325335i
$815$	−20.7846			−0.728053
$816$	−38.7846	+	22.3923i	−1.35773	+	0.783887i
$817$			12.0000i			0.419827i
$818$	−5.66025	−	1.51666i	−0.197906	−	0.0530288i
$819$		0			0
$820$	6.00000	+	3.46410i	0.209529	+	0.120972i
$821$	27.7846			0.969690			0.484845	−	0.874600i	$-0.338876\pi$
$821$	27.7846			0.969690			0.484845	+	0.874600i	$0.338876\pi$
$822$	12.9282	−	48.2487i	0.450923	−	1.68287i
$823$		−	11.0718i		−	0.385939i	−0.981205	−	0.192969i	$-0.938188\pi$
$823$		−	11.0718i		−	0.385939i	0.981205	−	0.192969i	$-0.0618118\pi$
$824$	−13.6077	+	13.6077i	−0.474047	+	0.474047i
$825$			0.464102i			0.0161579i
$826$	−7.26795	−	10.7321i	−0.252884	−	0.373416i
$827$		−	14.1436i		−	0.491821i	−0.969293	−	0.245910i	$-0.920913\pi$
$827$		−	14.1436i		−	0.491821i	0.969293	−	0.245910i	$-0.0790869\pi$
$828$		0			0
$829$		−	0.248711i		−	0.00863810i	−0.999991	−	0.00431905i	$-0.998625\pi$
$829$		−	0.248711i		−	0.00863810i	0.999991	−	0.00431905i	$-0.00137480\pi$
$830$	−21.1244	−	5.66025i	−0.733237	−	0.196470i
$831$	29.0718			1.00849
$832$	3.71281			0.128719
$833$	44.7846	−	6.46410i	1.55169	−	0.223968i
$834$	−4.39230	+	16.3923i	−0.152093	+	0.567619i
$835$			5.19615i			0.179820i
$836$	1.60770	−	2.78461i	0.0556033	−	0.0963077i
$837$	−31.1769			−1.07763
$838$	8.87564	−	33.1244i	0.306604	−	1.14426i
$839$	−4.39230			−0.151639			−0.0758196	−	0.997122i	$-0.524157\pi$
$839$	−4.39230			−0.151639			−0.0758196	+	0.997122i	$0.524157\pi$
$840$	−12.9282	+	0.928203i	−0.446065	+	0.0320261i
$841$	33.8564			1.16746
$842$	6.95448	−	25.9545i	0.239667	−	0.894451i
$843$	−13.7321			−0.472957
$844$	−3.19615	+	5.53590i	−0.110016	+	0.190553i
$845$			12.7846i			0.439804i
$846$		0			0
$847$	18.9282	−	21.8564i	0.650381	−	0.750995i
$848$	4.00000	+	6.92820i	0.137361	+	0.237915i
$849$	−21.0000			−0.720718
$850$	−8.83013	−	2.36603i	−0.302871	−	0.0811540i
$851$			13.8564i			0.474991i
$852$	−12.9282	+	22.3923i	−0.442913	+	0.767148i
$853$			2.78461i			0.0953432i	0.998863	+	0.0476716i	$0.0151801\pi$
$853$			2.78461i			0.0953432i	−0.998863	+	0.0476716i	$0.984820\pi$
$854$	−29.3205	+	19.8564i	−1.00333	+	0.679472i
$855$		0			0
$856$	−4.78461	−	4.78461i	−0.163535	−	0.163535i
$857$		−	57.7128i		−	1.97143i	−0.168416	−	0.985716i	$-0.553865\pi$
$857$		−	57.7128i		−	1.97143i	0.168416	−	0.985716i	$-0.446135\pi$
$858$	0.0788383	−	0.294229i	0.00269150	−	0.0100448i
$859$	−39.7128			−1.35498			−0.677492	−	0.735530i	$-0.736933\pi$
$859$	−39.7128			−1.35498			−0.677492	+	0.735530i	$0.736933\pi$
$860$	−3.46410	−	2.00000i	−0.118125	−	0.0681994i
$861$	12.0000	+	10.3923i	0.408959	+	0.354169i
$862$	18.5622	+	4.97372i	0.632230	+	0.169406i
$863$			39.8564i			1.35673i	0.734726	+	0.678364i	$0.237311\pi$
$863$			39.8564i			1.35673i	−0.734726	+	0.678364i	$0.762689\pi$
$864$	−28.3923	+	7.60770i	−0.965926	+	0.258819i
$865$	−14.3205			−0.486912
$866$	43.5167	+	11.6603i	1.47876	+	0.396232i
$867$	−42.9282			−1.45792
$868$	−30.0000	+	10.3923i	−1.01827	+	0.352738i
$869$	−3.92820			−0.133255
$870$	18.7583	+	5.02628i	0.635967	+	0.170407i
$871$	−1.60770			−0.0544747
$872$	−4.14359	+	4.14359i	−0.140320	+	0.140320i
$873$		0			0
$874$	12.0000	+	3.21539i	0.405906	+	0.108762i
$875$	−2.00000	−	1.73205i	−0.0676123	−	0.0585540i
$876$	−22.3923	+	38.7846i	−0.756566	+	1.31041i
$877$	−18.3923			−0.621064			−0.310532	−	0.950563i	$-0.600507\pi$
$877$	−18.3923			−0.621064			−0.310532	+	0.950563i	$0.600507\pi$
$878$	14.5359	−	54.2487i	0.490563	−	1.83081i
$879$		−	35.1962i		−	1.18714i
$880$	0.535898	+	0.928203i	0.0180651	+	0.0312897i
$881$			29.0718i			0.979454i	0.871876	+	0.489727i	$0.162904\pi$
$881$			29.0718i			0.979454i	−0.871876	+	0.489727i	$0.837096\pi$
$882$		0			0
$883$			23.6077i			0.794462i	0.917719	+	0.397231i	$0.130029\pi$
$883$			23.6077i			0.794462i	−0.917719	+	0.397231i	$0.869971\pi$
$884$	5.19615	+	3.00000i	0.174766	+	0.100901i
$885$			6.00000i			0.201688i
$886$	35.5167	+	9.51666i	1.19321	+	0.319718i
$887$	8.53590			0.286607			0.143304	−	0.989679i	$-0.454227\pi$
$887$	8.53590			0.286607			0.143304	+	0.989679i	$0.454227\pi$
$888$	32.7846	−	32.7846i	1.10018	−	1.10018i
$889$	30.9282	+	26.7846i	1.03730	+	0.898327i
$890$	0.928203	−	3.46410i	0.0311134	−	0.116117i
$891$			2.41154i			0.0807897i
$892$	−23.7846	−	13.7321i	−0.796368	−	0.459783i
$893$	10.3923			0.347765
$894$	1.94744	−	7.26795i	0.0651322	−	0.243077i
$895$	−6.39230			−0.213671
$896$	−24.7846	+	16.7846i	−0.827996	+	0.560734i
$897$	1.17691			0.0392960
$898$	4.36603	−	16.2942i	0.145696	−	0.543745i
$899$	47.5692			1.58652
$900$		0			0
$901$			12.9282i			0.430701i
$902$	0.339746	−	1.26795i	0.0113123	−	0.0422181i
$903$	−6.92820	−	6.00000i	−0.230556	−	0.199667i
$904$	−10.9282	+	10.9282i	−0.363467	+	0.363467i
$905$	−0.928203			−0.0308545
$906$	−35.9545	−	9.63397i	−1.19451	−	0.320067i
$907$			32.3923i			1.07557i	0.843082	+	0.537784i	$0.180739\pi$
$907$			32.3923i			1.07557i	−0.843082	+	0.537784i	$0.819261\pi$
$908$	35.7846	+	20.6603i	1.18755	+	0.685635i
$909$		0			0
$910$	0.973721	+	1.43782i	0.0322785	+	0.0476633i
$911$			20.2487i			0.670870i	0.942063	+	0.335435i	$0.108883\pi$
$911$			20.2487i			0.670870i	−0.942063	+	0.335435i	$0.891117\pi$
$912$	−20.7846	−	36.0000i	−0.688247	−	1.19208i
$913$			4.14359i			0.137133i
$914$	7.51666	−	28.0526i	0.248629	−	0.927896i
$915$	16.3923			0.541913
$916$	8.53590	−	14.7846i	0.282034	−	0.488497i
$917$	−4.39230	+	5.07180i	−0.145047	+	0.167485i
$918$	−45.8827	−	12.2942i	−1.51435	−	0.405770i
$919$			6.41154i			0.211497i	0.994393	+	0.105749i	$0.0337239\pi$
$919$			6.41154i			0.211497i	−0.994393	+	0.105749i	$0.966276\pi$
$920$	−2.92820	+	2.92820i	−0.0965400	+	0.0965400i
$921$	−3.00000			−0.0988534
$922$	−37.8564	−	10.1436i	−1.24673	−	0.334061i
$923$	3.46410			0.114022
$924$	0.803848	+	2.32051i	0.0264446	+	0.0763391i
$925$	9.46410			0.311178
$926$	22.3923	+	6.00000i	0.735857	+	0.197172i
$927$		0			0
$928$	43.3205	−	11.6077i	1.42207	−	0.381041i
$929$			54.4974i			1.78800i	0.448065	+	0.894001i	$0.352113\pi$
$929$			54.4974i			1.78800i	−0.448065	+	0.894001i	$0.647887\pi$
$930$	14.1962	+	3.80385i	0.465510	+	0.124733i
$931$	6.00000	+	41.5692i	0.196642	+	1.36238i
$932$	15.7128	+	9.07180i	0.514690	+	0.297157i
$933$	−13.6077			−0.445496
$934$	−8.24167	+	30.7583i	−0.269676	+	1.00644i
$935$			1.73205i			0.0566441i
$936$		0			0
$937$			25.3923i			0.829530i	0.909928	+	0.414765i	$0.136136\pi$
$937$			25.3923i			0.829530i	−0.909928	+	0.414765i	$0.863864\pi$
$938$	10.7321	−	7.26795i	0.350414	−	0.237307i
$939$			30.3731i			0.991188i
$940$	−1.73205	+	3.00000i	−0.0564933	+	0.0978492i
$941$		−	39.0333i		−	1.27245i	−0.771504	−	0.636225i	$-0.780495\pi$
$941$		−	39.0333i		−	1.27245i	0.771504	−	0.636225i	$-0.219505\pi$
$942$	−18.5885	−	4.98076i	−0.605645	−	0.162282i
$943$	5.07180			0.165160
$944$	6.92820	+	12.0000i	0.225494	+	0.390567i
$945$	−10.3923	−	9.00000i	−0.338062	−	0.292770i
$946$	−0.196152	+	0.732051i	−0.00637747	+	0.0238010i
$947$		−	22.7846i		−	0.740400i	−0.928952	−	0.370200i	$-0.879289\pi$
$947$		−	22.7846i		−	0.740400i	0.928952	−	0.370200i	$-0.120711\pi$
$948$	−25.3923	+	43.9808i	−0.824704	+	1.42843i
$949$	6.00000			0.194768
$950$	2.19615	−	8.19615i	0.0712526	−	0.265918i
$951$	−5.32051			−0.172529
$952$	−48.2487	+	3.46410i	−1.56375	+	0.112272i
$953$	21.3205			0.690639			0.345320	−	0.938485i	$-0.387771\pi$
$953$	21.3205			0.690639			0.345320	+	0.938485i	$0.387771\pi$
$954$		0			0
$955$	7.19615			0.232862
$956$	23.9808	−	41.5359i	0.775593	−	1.34337i
$957$		−	3.67949i		−	0.118941i
$958$	−9.21539	+	34.3923i	−0.297736	+	1.11116i
$959$	35.3205	−	40.7846i	1.14056	−	1.31700i
$960$	13.8564			0.447214
$961$	5.00000			0.161290
$962$	−6.00000	−	1.60770i	−0.193448	−	0.0518342i
$963$		0			0
$964$	−16.3923	+	28.3923i	−0.527961	+	0.914455i
$965$		−	9.46410i		−	0.304660i
$966$	−7.85641	+	5.32051i	−0.252776	+	0.171185i
$967$		−	31.1769i		−	1.00258i	−0.865279	−	0.501291i	$-0.832859\pi$
$967$		−	31.1769i		−	1.00258i	0.865279	−	0.501291i	$-0.167141\pi$
$968$	−21.8564	+	21.8564i	−0.702492	+	0.702492i
$969$		−	67.1769i		−	2.15803i
$970$	−4.90192	+	18.2942i	−0.157391	+	0.587392i
$971$	−14.7846			−0.474461			−0.237230	−	0.971453i	$-0.576240\pi$
$971$	−14.7846			−0.474461			−0.237230	+	0.971453i	$0.576240\pi$
$972$		0			0
$973$	−12.0000	+	13.8564i	−0.384702	+	0.444216i
$974$	17.4641	+	4.67949i	0.559586	+	0.149941i
$975$		−	0.803848i		−	0.0257437i
$976$	32.7846	−	18.9282i	1.04941	−	0.605877i
$977$	−4.24871			−0.135928			−0.0679642	−	0.997688i	$-0.521650\pi$
$977$	−4.24871			−0.135928			−0.0679642	+	0.997688i	$0.521650\pi$
$978$	49.1769	+	13.1769i	1.57250	+	0.421351i
$979$	−0.679492			−0.0217167
$980$	−13.0000	−	5.19615i	−0.415270	−	0.165985i
$981$		0			0
$982$	13.4904	+	3.61474i	0.430495	+	0.115351i
$983$	27.5885			0.879935			0.439968	−	0.898014i	$-0.354990\pi$
$983$	27.5885			0.879935			0.439968	+	0.898014i	$0.354990\pi$
$984$	−12.0000	−	12.0000i	−0.382546	−	0.382546i
$985$		−	13.3205i		−	0.424427i
$986$	70.0070	+	18.7583i	2.22948	+	0.597387i
$987$	−5.19615	+	6.00000i	−0.165395	+	0.190982i
$988$	−2.78461	+	4.82309i	−0.0885902	+	0.153443i
$989$	−2.92820			−0.0931114
$990$		0			0
$991$		−	47.1769i		−	1.49862i	−0.662217	−	0.749312i	$-0.730384\pi$
$991$		−	47.1769i		−	1.49862i	0.662217	−	0.749312i	$-0.269616\pi$
$992$	32.7846	−	8.78461i	1.04091	−	0.278912i
$993$			45.7128i			1.45065i
$994$	−23.1244	+	15.6603i	−0.733460	+	0.496713i
$995$		−	3.46410i		−	0.109819i
$996$	46.3923	+	26.7846i	1.47000	+	0.848703i
$997$		−	5.53590i		−	0.175324i	−0.996150	−	0.0876618i	$-0.972061\pi$
$997$		−	5.53590i		−	0.175324i	0.996150	−	0.0876618i	$-0.0279395\pi$
$998$	−34.9545	−	9.36603i	−1.10646	−	0.296476i
$999$	49.1769			1.55589

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.g.b.111.3	yes	4
3.2	odd	2		1260.2.c.b.811.2		4
4.3	odd	2		140.2.g.a.111.4	yes	4
5.2	odd	4		700.2.c.f.699.4		4
5.3	odd	4		700.2.c.c.699.1		4
5.4	even	2		700.2.g.g.251.2		4
7.2	even	3		980.2.o.b.31.1		4
7.3	odd	6		980.2.o.c.411.2		4
7.4	even	3		980.2.o.d.411.2		4
7.5	odd	6		980.2.o.a.31.1		4
7.6	odd	2		140.2.g.a.111.3	✓	4
8.3	odd	2		2240.2.k.a.1791.3		4
8.5	even	2		2240.2.k.b.1791.1		4
12.11	even	2		1260.2.c.a.811.1		4
20.3	even	4		700.2.c.e.699.3		4
20.7	even	4		700.2.c.b.699.2		4
20.19	odd	2		700.2.g.f.251.1		4
21.20	even	2		1260.2.c.a.811.2		4
28.3	even	6		980.2.o.b.411.1		4
28.11	odd	6		980.2.o.a.411.1		4
28.19	even	6		980.2.o.d.31.1		4
28.23	odd	6		980.2.o.c.31.1		4
28.27	even	2	inner	140.2.g.b.111.4	yes	4
35.13	even	4		700.2.c.b.699.1		4
35.27	even	4		700.2.c.e.699.4		4
35.34	odd	2		700.2.g.f.251.2		4
56.13	odd	2		2240.2.k.a.1791.4		4
56.27	even	2		2240.2.k.b.1791.2		4
84.83	odd	2		1260.2.c.b.811.1		4
140.27	odd	4		700.2.c.c.699.2		4
140.83	odd	4		700.2.c.f.699.3		4
140.139	even	2		700.2.g.g.251.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.g.a.111.3	✓	4	7.6	odd	2
140.2.g.a.111.4	yes	4	4.3	odd	2
140.2.g.b.111.3	yes	4	1.1	even	1	trivial
140.2.g.b.111.4	yes	4	28.27	even	2	inner
700.2.c.b.699.1		4	35.13	even	4
700.2.c.b.699.2		4	20.7	even	4
700.2.c.c.699.1		4	5.3	odd	4
700.2.c.c.699.2		4	140.27	odd	4
700.2.c.e.699.3		4	20.3	even	4
700.2.c.e.699.4		4	35.27	even	4
700.2.c.f.699.3		4	140.83	odd	4
700.2.c.f.699.4		4	5.2	odd	4
700.2.g.f.251.1		4	20.19	odd	2
700.2.g.f.251.2		4	35.34	odd	2
700.2.g.g.251.1		4	140.139	even	2
700.2.g.g.251.2		4	5.4	even	2
980.2.o.a.31.1		4	7.5	odd	6
980.2.o.a.411.1		4	28.11	odd	6
980.2.o.b.31.1		4	7.2	even	3
980.2.o.b.411.1		4	28.3	even	6
980.2.o.c.31.1		4	28.23	odd	6
980.2.o.c.411.2		4	7.3	odd	6
980.2.o.d.31.1		4	28.19	even	6
980.2.o.d.411.2		4	7.4	even	3
1260.2.c.a.811.1		4	12.11	even	2
1260.2.c.a.811.2		4	21.20	even	2
1260.2.c.b.811.1		4	84.83	odd	2
1260.2.c.b.811.2		4	3.2	odd	2
2240.2.k.a.1791.3		4	8.3	odd	2
2240.2.k.a.1791.4		4	56.13	odd	2
2240.2.k.b.1791.1		4	8.5	even	2
2240.2.k.b.1791.2		4	56.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 - 1.36603i) q^{2} +1.73205 q^{3} +(-1.73205 - 1.00000i) q^{4} +1.00000i q^{5} +(0.633975 - 2.36603i) q^{6} +(1.73205 - 2.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(1.36603 + 0.366025i) q^{10} -0.267949i q^{11} +(-3.00000 - 1.73205i) q^{12} +0.464102i q^{13} +(-2.09808 - 3.09808i) q^{14} +1.73205i q^{15} +(2.00000 + 3.46410i) q^{16} +6.46410i q^{17} -6.00000 q^{19} +(1.00000 - 1.73205i) q^{20} +(3.00000 - 3.46410i) q^{21} +(-0.366025 - 0.0980762i) q^{22} -1.46410i q^{23} +(-3.46410 + 3.46410i) q^{24} -1.00000 q^{25} +(0.633975 + 0.169873i) q^{26} -5.19615 q^{27} +(-5.00000 + 1.73205i) q^{28} +7.92820 q^{29} +(2.36603 + 0.633975i) q^{30} +6.00000 q^{31} +(5.46410 - 1.46410i) q^{32} -0.464102i q^{33} +(8.83013 + 2.36603i) q^{34} +(2.00000 + 1.73205i) q^{35} -9.46410 q^{37} +(-2.19615 + 8.19615i) q^{38} +0.803848i q^{39} +(-2.00000 - 2.00000i) q^{40} +3.46410i q^{41} +(-3.63397 - 5.36603i) q^{42} -2.00000i q^{43} +(-0.267949 + 0.464102i) q^{44} +(-2.00000 - 0.535898i) q^{46} -1.73205 q^{47} +(3.46410 + 6.00000i) q^{48} +(-1.00000 - 6.92820i) q^{49} +(-0.366025 + 1.36603i) q^{50} +11.1962i q^{51} +(0.464102 - 0.803848i) q^{52} +2.00000 q^{53} +(-1.90192 + 7.09808i) q^{54} +0.267949 q^{55} +(0.535898 + 7.46410i) q^{56} -10.3923 q^{57} +(2.90192 - 10.8301i) q^{58} +3.46410 q^{59} +(1.73205 - 3.00000i) q^{60} -9.46410i q^{61} +(2.19615 - 8.19615i) q^{62} -8.00000i q^{64} -0.464102 q^{65} +(-0.633975 - 0.169873i) q^{66} +3.46410i q^{67} +(6.46410 - 11.1962i) q^{68} -2.53590i q^{69} +(3.09808 - 2.09808i) q^{70} -7.46410i q^{71} -12.9282i q^{73} +(-3.46410 + 12.9282i) q^{74} -1.73205 q^{75} +(10.3923 + 6.00000i) q^{76} +(-0.535898 - 0.464102i) q^{77} +(1.09808 + 0.294229i) q^{78} -14.6603i q^{79} +(-3.46410 + 2.00000i) q^{80} -9.00000 q^{81} +(4.73205 + 1.26795i) q^{82} -15.4641 q^{83} +(-8.66025 + 3.00000i) q^{84} -6.46410 q^{85} +(-2.73205 - 0.732051i) q^{86} +13.7321 q^{87} +(0.535898 + 0.535898i) q^{88} -2.53590i q^{89} +(0.928203 + 0.803848i) q^{91} +(-1.46410 + 2.53590i) q^{92} +10.3923 q^{93} +(-0.633975 + 2.36603i) q^{94} -6.00000i q^{95} +(9.46410 - 2.53590i) q^{96} +13.3923i q^{97} +(-9.83013 - 1.16987i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 6 q^{6} - 8 q^{8} + 2 q^{10} - 12 q^{12} + 2 q^{14} + 8 q^{16} - 24 q^{19} + 4 q^{20} + 12 q^{21} + 2 q^{22} - 4 q^{25} + 6 q^{26} - 20 q^{28} + 4 q^{29} + 6 q^{30} + 24 q^{31} + 8 q^{32}+ \cdots - 22 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 6 * q^6 - 8 * q^8 + 2 * q^10 - 12 * q^12 + 2 * q^14 + 8 * q^16 - 24 * q^19 + 4 * q^20 + 12 * q^21 + 2 * q^22 - 4 * q^25 + 6 * q^26 - 20 * q^28 + 4 * q^29 + 6 * q^30 + 24 * q^31 + 8 * q^32 + 18 * q^34 + 8 * q^35 - 24 * q^37 + 12 * q^38 - 8 * q^40 - 18 * q^42 - 8 * q^44 - 8 * q^46 - 4 * q^49 + 2 * q^50 - 12 * q^52 + 8 * q^53 - 18 * q^54 + 8 * q^55 + 16 * q^56 + 22 * q^58 - 12 * q^62 + 12 * q^65 - 6 * q^66 + 12 * q^68 + 2 * q^70 - 16 * q^77 - 6 * q^78 - 36 * q^81 + 12 * q^82 - 48 * q^83 - 12 * q^85 - 4 * q^86 + 48 * q^87 + 16 * q^88 - 24 * q^91 + 8 * q^92 - 6 * q^94 + 24 * q^96 - 22 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more