LMFDB - Embedded newform 140.2.g.a.111.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(111,140)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			111.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	140.111
Dual form			140.2.g.a.111.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36603 - 0.366025i) q^{2} +1.73205 q^{3} +(1.73205 + 1.00000i) q^{4} +1.00000i q^{5} +(-2.36603 - 0.633975i) q^{6} +(1.73205 + 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(0.366025 - 1.36603i) q^{10} +3.73205i q^{11} +(3.00000 + 1.73205i) q^{12} -6.46410i q^{13} +(-1.63397 - 3.36603i) q^{14} +1.73205i q^{15} +(2.00000 + 3.46410i) q^{16} -0.464102i q^{17} +6.00000 q^{19} +(-1.00000 + 1.73205i) q^{20} +(3.00000 + 3.46410i) q^{21} +(1.36603 - 5.09808i) q^{22} -5.46410i q^{23} +(-3.46410 - 3.46410i) q^{24} -1.00000 q^{25} +(-2.36603 + 8.83013i) q^{26} -5.19615 q^{27} +(1.00000 + 5.19615i) q^{28} -5.92820 q^{29} +(0.633975 - 2.36603i) q^{30} -6.00000 q^{31} +(-1.46410 - 5.46410i) q^{32} +6.46410i q^{33} +(-0.169873 + 0.633975i) q^{34} +(-2.00000 + 1.73205i) q^{35} -2.53590 q^{37} +(-8.19615 - 2.19615i) q^{38} -11.1962i q^{39} +(2.00000 - 2.00000i) q^{40} -3.46410i q^{41} +(-2.83013 - 5.83013i) q^{42} +2.00000i q^{43} +(-3.73205 + 6.46410i) q^{44} +(-2.00000 + 7.46410i) q^{46} -1.73205 q^{47} +(3.46410 + 6.00000i) q^{48} +(-1.00000 + 6.92820i) q^{49} +(1.36603 + 0.366025i) q^{50} -0.803848i q^{51} +(6.46410 - 11.1962i) q^{52} +2.00000 q^{53} +(7.09808 + 1.90192i) q^{54} -3.73205 q^{55} +(0.535898 - 7.46410i) q^{56} +10.3923 q^{57} +(8.09808 + 2.16987i) q^{58} +3.46410 q^{59} +(-1.73205 + 3.00000i) q^{60} -2.53590i q^{61} +(8.19615 + 2.19615i) q^{62} +8.00000i q^{64} +6.46410 q^{65} +(2.36603 - 8.83013i) q^{66} +3.46410i q^{67} +(0.464102 - 0.803848i) q^{68} -9.46410i q^{69} +(3.36603 - 1.63397i) q^{70} +0.535898i q^{71} +0.928203i q^{73} +(3.46410 + 0.928203i) q^{74} -1.73205 q^{75} +(10.3923 + 6.00000i) q^{76} +(-7.46410 + 6.46410i) q^{77} +(-4.09808 + 15.2942i) q^{78} -2.66025i q^{79} +(-3.46410 + 2.00000i) q^{80} -9.00000 q^{81} +(-1.26795 + 4.73205i) q^{82} +8.53590 q^{83} +(1.73205 + 9.00000i) q^{84} +0.464102 q^{85} +(0.732051 - 2.73205i) q^{86} -10.2679 q^{87} +(7.46410 - 7.46410i) q^{88} -9.46410i q^{89} +(12.9282 - 11.1962i) q^{91} +(5.46410 - 9.46410i) q^{92} -10.3923 q^{93} +(2.36603 + 0.633975i) q^{94} +6.00000i q^{95} +(-2.53590 - 9.46410i) q^{96} -7.39230i q^{97} +(3.90192 - 9.09808i) 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} - 10 q^{14} + 8 q^{16} + 24 q^{19} - 4 q^{20} + 12 q^{21} + 2 q^{22} - 4 q^{25} - 6 q^{26} + 4 q^{28} + 4 q^{29} + 6 q^{30} - 24 q^{31} + 8 q^{32}+ \cdots + 26 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 6 * q^6 - 8 * q^8 - 2 * q^10 + 12 * q^12 - 10 * q^14 + 8 * q^16 + 24 * q^19 - 4 * q^20 + 12 * q^21 + 2 * q^22 - 4 * q^25 - 6 * q^26 + 4 * 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 + 6 * 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 + 10 * 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 + 26 * 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 $

$2$	−1.36603	−	0.366025i	−0.965926	−	0.258819i
$2$	−1.36603	−	0.366025i	−0.965926	−	0.258819i
$3$	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
$6$	−2.36603	−	0.633975i	−0.965926	−	0.258819i
$7$	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
$10$	0.366025	−	1.36603i	0.115747	−	0.431975i
$11$			3.73205i			1.12526i	0.826710	+	0.562628i	$0.190210\pi$
$11$			3.73205i			1.12526i	−0.826710	+	0.562628i	$0.809790\pi$
$12$	3.00000	+	1.73205i	0.866025	+	0.500000i
$13$		−	6.46410i		−	1.79282i	−0.443227	−	0.896410i	$-0.646166\pi$
$13$		−	6.46410i		−	1.79282i	0.443227	−	0.896410i	$-0.353834\pi$
$14$	−1.63397	−	3.36603i	−0.436698	−	0.899608i
$15$			1.73205i			0.447214i
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$		−	0.464102i		−	0.112561i	−0.998415	−	0.0562806i	$-0.982076\pi$
$17$		−	0.464102i		−	0.112561i	0.998415	−	0.0562806i	$-0.0179241\pi$
$18$		0			0
$19$	6.00000			1.37649			0.688247	−	0.725476i	$-0.258380\pi$
$19$	6.00000			1.37649			0.688247	+	0.725476i	$0.258380\pi$
$20$	−1.00000	+	1.73205i	−0.223607	+	0.387298i
$21$	3.00000	+	3.46410i	0.654654	+	0.755929i
$22$	1.36603	−	5.09808i	0.291238	−	1.08691i
$23$		−	5.46410i		−	1.13934i	−0.821872	−	0.569672i	$-0.807070\pi$
$23$		−	5.46410i		−	1.13934i	0.821872	−	0.569672i	$-0.192930\pi$
$24$	−3.46410	−	3.46410i	−0.707107	−	0.707107i
$25$	−1.00000			−0.200000
$26$	−2.36603	+	8.83013i	−0.464016	+	1.73173i
$27$	−5.19615			−1.00000
$28$	1.00000	+	5.19615i	0.188982	+	0.981981i
$29$	−5.92820			−1.10084			−0.550420	−	0.834888i	$-0.685532\pi$
$29$	−5.92820			−1.10084			−0.550420	+	0.834888i	$0.685532\pi$
$30$	0.633975	−	2.36603i	0.115747	−	0.431975i
$31$	−6.00000			−1.07763			−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000			−1.07763			−0.538816	+	0.842424i	$0.681128\pi$
$32$	−1.46410	−	5.46410i	−0.258819	−	0.965926i
$33$			6.46410i			1.12526i
$34$	−0.169873	+	0.633975i	−0.0291330	+	0.108726i
$35$	−2.00000	+	1.73205i	−0.338062	+	0.292770i
$36$		0			0
$37$	−2.53590			−0.416899			−0.208450	−	0.978033i	$-0.566842\pi$
$37$	−2.53590			−0.416899			−0.208450	+	0.978033i	$0.566842\pi$
$38$	−8.19615	−	2.19615i	−1.32959	−	0.356263i
$39$		−	11.1962i		−	1.79282i
$40$	2.00000	−	2.00000i	0.316228	−	0.316228i
$41$		−	3.46410i		−	0.541002i	−0.962720	−	0.270501i	$-0.912811\pi$
$41$		−	3.46410i		−	0.541002i	0.962720	−	0.270501i	$-0.0871893\pi$
$42$	−2.83013	−	5.83013i	−0.436698	−	0.899608i
$43$			2.00000i			0.304997i	0.988304	+	0.152499i	$0.0487319\pi$
$43$			2.00000i			0.304997i	−0.988304	+	0.152499i	$0.951268\pi$
$44$	−3.73205	+	6.46410i	−0.562628	+	0.974500i
$45$		0			0
$46$	−2.00000	+	7.46410i	−0.294884	+	1.10052i
$47$	−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
$50$	1.36603	+	0.366025i	0.193185	+	0.0517638i
$51$		−	0.803848i		−	0.112561i
$52$	6.46410	−	11.1962i	0.896410	−	1.55263i
$53$	2.00000			0.274721			0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000			0.274721			0.137361	+	0.990521i	$0.456138\pi$
$54$	7.09808	+	1.90192i	0.965926	+	0.258819i
$55$	−3.73205			−0.503230
$56$	0.535898	−	7.46410i	0.0716124	−	0.997433i
$57$	10.3923			1.37649
$58$	8.09808	+	2.16987i	1.06333	+	0.284918i
$59$	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
$61$		−	2.53590i		−	0.324689i	−0.986734	−	0.162344i	$-0.948094\pi$
$61$		−	2.53590i		−	0.324689i	0.986734	−	0.162344i	$-0.0519055\pi$
$62$	8.19615	+	2.19615i	1.04091	+	0.278912i
$63$		0			0
$64$			8.00000i			1.00000i
$65$	6.46410			0.801773
$66$	2.36603	−	8.83013i	0.291238	−	1.08691i
$67$			3.46410i			0.423207i	0.977356	+	0.211604i	$0.0678686\pi$
$67$			3.46410i			0.423207i	−0.977356	+	0.211604i	$0.932131\pi$
$68$	0.464102	−	0.803848i	0.0562806	−	0.0974808i
$69$		−	9.46410i		−	1.13934i
$70$	3.36603	−	1.63397i	0.402317	−	0.195297i
$71$			0.535898i			0.0635994i	0.999494	+	0.0317997i	$0.0101239\pi$
$71$			0.535898i			0.0635994i	−0.999494	+	0.0317997i	$0.989876\pi$
$72$		0			0
$73$			0.928203i			0.108638i	0.998524	+	0.0543190i	$0.0172988\pi$
$73$			0.928203i			0.108638i	−0.998524	+	0.0543190i	$0.982701\pi$
$74$	3.46410	+	0.928203i	0.402694	+	0.107901i
$75$	−1.73205			−0.200000
$76$	10.3923	+	6.00000i	1.19208	+	0.688247i
$77$	−7.46410	+	6.46410i	−0.850613	+	0.736653i
$78$	−4.09808	+	15.2942i	−0.464016	+	1.73173i
$79$		−	2.66025i		−	0.299302i	−0.988739	−	0.149651i	$-0.952185\pi$
$79$		−	2.66025i		−	0.299302i	0.988739	−	0.149651i	$-0.0478150\pi$
$80$	−3.46410	+	2.00000i	−0.387298	+	0.223607i
$81$	−9.00000			−1.00000
$82$	−1.26795	+	4.73205i	−0.140022	+	0.522568i
$83$	8.53590			0.936937			0.468468	−	0.883480i	$-0.344806\pi$
$83$	8.53590			0.936937			0.468468	+	0.883480i	$0.344806\pi$
$84$	1.73205	+	9.00000i	0.188982	+	0.981981i
$85$	0.464102			0.0503389
$86$	0.732051	−	2.73205i	0.0789391	−	0.294605i
$87$	−10.2679			−1.10084
$88$	7.46410	−	7.46410i	0.795676	−	0.795676i
$89$		−	9.46410i		−	1.00319i	−0.865102	−	0.501596i	$-0.832746\pi$
$89$		−	9.46410i		−	1.00319i	0.865102	−	0.501596i	$-0.167254\pi$
$90$		0			0
$91$	12.9282	−	11.1962i	1.35524	−	1.17368i
$92$	5.46410	−	9.46410i	0.569672	−	0.986701i
$93$	−10.3923			−1.07763
$94$	2.36603	+	0.633975i	0.244037	+	0.0653895i
$95$			6.00000i			0.615587i
$96$	−2.53590	−	9.46410i	−0.258819	−	0.965926i
$97$		−	7.39230i		−	0.750575i	−0.926908	−	0.375287i	$-0.877544\pi$
$97$		−	7.39230i		−	0.750575i	0.926908	−	0.375287i	$-0.122456\pi$
$98$	3.90192	−	9.09808i	0.394154	−	0.919044i
$99$		0			0
$100$	−1.73205	−	1.00000i	−0.173205	−	0.100000i
$101$			8.53590i			0.849354i	0.905345	+	0.424677i	$0.139612\pi$
$101$			8.53590i			0.849354i	−0.905345	+	0.424677i	$0.860388\pi$
$102$	−0.294229	+	1.09808i	−0.0291330	+	0.108726i
$103$	−17.1962			−1.69439			−0.847194	−	0.531284i	$-0.821710\pi$
$103$	−17.1962			−1.69439			−0.847194	+	0.531284i	$0.821710\pi$
$104$	−12.9282	+	12.9282i	−1.26771	+	1.26771i
$105$	−3.46410	+	3.00000i	−0.338062	+	0.292770i
$106$	−2.73205	−	0.732051i	−0.265360	−	0.0711031i
$107$			18.3923i			1.77805i	0.457857	+	0.889026i	$0.348617\pi$
$107$			18.3923i			1.77805i	−0.457857	+	0.889026i	$0.651383\pi$
$108$	−9.00000	−	5.19615i	−0.866025	−	0.500000i
$109$	15.9282			1.52565			0.762823	−	0.646608i	$-0.223813\pi$
$109$	15.9282			1.52565			0.762823	+	0.646608i	$0.223813\pi$
$110$	5.09808	+	1.36603i	0.486082	+	0.130245i
$111$	−4.39230			−0.416899
$112$	−3.46410	+	10.0000i	−0.327327	+	0.944911i
$113$	−1.46410			−0.137731			−0.0688655	−	0.997626i	$-0.521938\pi$
$113$	−1.46410			−0.137731			−0.0688655	+	0.997626i	$0.521938\pi$
$114$	−14.1962	−	3.80385i	−1.32959	−	0.356263i
$115$	5.46410			0.509530
$116$	−10.2679	−	5.92820i	−0.953355	−	0.550420i
$117$		0			0
$118$	−4.73205	−	1.26795i	−0.435621	−	0.116724i
$119$	0.928203	−	0.803848i	0.0850883	−	0.0736886i
$120$	3.46410	−	3.46410i	0.316228	−	0.316228i
$121$	−2.92820			−0.266200
$122$	−0.928203	+	3.46410i	−0.0840356	+	0.313625i
$123$		−	6.00000i		−	0.541002i
$124$	−10.3923	−	6.00000i	−0.933257	−	0.538816i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$		−	8.53590i		−	0.757438i	−0.925512	−	0.378719i	$-0.876365\pi$
$127$		−	8.53590i		−	0.757438i	0.925512	−	0.378719i	$-0.123635\pi$
$128$	2.92820	−	10.9282i	0.258819	−	0.965926i
$129$			3.46410i			0.304997i
$130$	−8.83013	−	2.36603i	−0.774453	−	0.207514i
$131$	9.46410			0.826882			0.413441	−	0.910531i	$-0.364327\pi$
$131$	9.46410			0.826882			0.413441	+	0.910531i	$0.364327\pi$
$132$	−6.46410	+	11.1962i	−0.562628	+	0.974500i
$133$	10.3923	+	12.0000i	0.901127	+	1.04053i
$134$	1.26795	−	4.73205i	0.109534	−	0.408787i
$135$		−	5.19615i		−	0.447214i
$136$	−0.928203	+	0.928203i	−0.0795928	+	0.0795928i
$137$	−0.392305			−0.0335169			−0.0167584	−	0.999860i	$-0.505335\pi$
$137$	−0.392305			−0.0335169			−0.0167584	+	0.999860i	$0.505335\pi$
$138$	−3.46410	+	12.9282i	−0.294884	+	1.10052i
$139$	−6.92820			−0.587643			−0.293821	−	0.955860i	$-0.594927\pi$
$139$	−6.92820			−0.587643			−0.293821	+	0.955860i	$0.594927\pi$
$140$	−5.19615	+	1.00000i	−0.439155	+	0.0845154i
$141$	−3.00000			−0.252646
$142$	0.196152	−	0.732051i	0.0164607	−	0.0614323i
$143$	24.1244			2.01738
$144$		0			0
$145$		−	5.92820i		−	0.492310i
$146$	0.339746	−	1.26795i	0.0281176	−	0.104936i
$147$	−1.73205	+	12.0000i	−0.142857	+	0.989743i
$148$	−4.39230	−	2.53590i	−0.361045	−	0.208450i
$149$	16.9282			1.38681			0.693406	−	0.720547i	$-0.256109\pi$
$149$	16.9282			1.38681			0.693406	+	0.720547i	$0.256109\pi$
$150$	2.36603	+	0.633975i	0.193185	+	0.0517638i
$151$			4.80385i			0.390932i	0.980711	+	0.195466i	$0.0626219\pi$
$151$			4.80385i			0.390932i	−0.980711	+	0.195466i	$0.937378\pi$
$152$	−12.0000	−	12.0000i	−0.973329	−	0.973329i
$153$		0			0
$154$	12.5622	−	6.09808i	1.01229	−	0.491397i
$155$		−	6.00000i		−	0.481932i
$156$	11.1962	−	19.3923i	0.896410	−	1.55263i
$157$			19.8564i			1.58471i	0.610058	+	0.792357i	$0.291146\pi$
$157$			19.8564i			1.58471i	−0.610058	+	0.792357i	$0.708854\pi$
$158$	−0.973721	+	3.63397i	−0.0774650	+	0.289103i
$159$	3.46410			0.274721
$160$	5.46410	−	1.46410i	0.431975	−	0.115747i
$161$	10.9282	−	9.46410i	0.861263	−	0.745876i
$162$	12.2942	+	3.29423i	0.965926	+	0.258819i
$163$			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
$165$	−6.46410			−0.503230
$166$	−11.6603	−	3.12436i	−0.905011	−	0.242497i
$167$	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
$169$	−28.7846			−2.21420
$170$	−0.633975	−	0.169873i	−0.0486236	−	0.0130287i
$171$		0			0
$172$	−2.00000	+	3.46410i	−0.152499	+	0.264135i
$173$		−	20.3205i		−	1.54494i	−0.635051	−	0.772470i	$-0.719021\pi$
$173$		−	20.3205i		−	1.54494i	0.635051	−	0.772470i	$-0.280979\pi$
$174$	14.0263	+	3.75833i	1.06333	+	0.284918i
$175$	−1.73205	−	2.00000i	−0.130931	−	0.151186i
$176$	−12.9282	+	7.46410i	−0.974500	+	0.562628i
$177$	6.00000			0.450988
$178$	−3.46410	+	12.9282i	−0.259645	+	0.969010i
$179$			14.3923i			1.07573i	0.843031	+	0.537866i	$0.180769\pi$
$179$			14.3923i			1.07573i	−0.843031	+	0.537866i	$0.819231\pi$
$180$		0			0
$181$		−	12.9282i		−	0.960946i	−0.877010	−	0.480473i	$-0.840465\pi$
$181$		−	12.9282i		−	0.960946i	0.877010	−	0.480473i	$-0.159535\pi$
$182$	−21.7583	+	10.5622i	−1.61283	+	0.782921i
$183$		−	4.39230i		−	0.324689i
$184$	−10.9282	+	10.9282i	−0.805638	+	0.805638i
$185$		−	2.53590i		−	0.186443i
$186$	14.1962	+	3.80385i	1.04091	+	0.278912i
$187$	1.73205			0.126660
$188$	−3.00000	−	1.73205i	−0.218797	−	0.126323i
$189$	−9.00000	−	10.3923i	−0.654654	−	0.755929i
$190$	2.19615	−	8.19615i	0.159326	−	0.594611i
$191$		−	3.19615i		−	0.231265i	−0.993292	−	0.115633i	$-0.963110\pi$
$191$		−	3.19615i		−	0.231265i	0.993292	−	0.115633i	$-0.0368896\pi$
$192$			13.8564i			1.00000i
$193$	−2.53590			−0.182538			−0.0912690	−	0.995826i	$-0.529092\pi$
$193$	−2.53590			−0.182538			−0.0912690	+	0.995826i	$0.529092\pi$
$194$	−2.70577	+	10.0981i	−0.194263	+	0.725000i
$195$	11.1962			0.801773
$196$	−8.66025	+	11.0000i	−0.618590	+	0.785714i
$197$	21.3205			1.51902			0.759512	−	0.650494i	$-0.225438\pi$
$197$	21.3205			1.51902			0.759512	+	0.650494i	$0.225438\pi$
$198$		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
$202$	3.12436	−	11.6603i	0.219829	−	0.820413i
$203$	−10.2679	−	11.8564i	−0.720669	−	0.832157i
$204$	0.803848	−	1.39230i	0.0562806	−	0.0974808i
$205$	3.46410			0.241943
$206$	23.4904	+	6.29423i	1.63665	+	0.438540i
$207$		0			0
$208$	22.3923	−	12.9282i	1.55263	−	0.896410i
$209$			22.3923i			1.54891i
$210$	5.83013	−	2.83013i	0.402317	−	0.195297i
$211$		−	7.19615i		−	0.495404i	−0.968836	−	0.247702i	$-0.920325\pi$
$211$		−	7.19615i		−	0.495404i	0.968836	−	0.247702i	$-0.0796753\pi$
$212$	3.46410	+	2.00000i	0.237915	+	0.137361i
$213$			0.928203i			0.0635994i
$214$	6.73205	−	25.1244i	0.460194	−	1.71747i
$215$	−2.00000			−0.136399
$216$	10.3923	+	10.3923i	0.707107	+	0.707107i
$217$	−10.3923	−	12.0000i	−0.705476	−	0.814613i
$218$	−21.7583	−	5.83013i	−1.47366	−	0.394866i
$219$			1.60770i			0.108638i
$220$	−6.46410	−	3.73205i	−0.435810	−	0.251615i
$221$	−3.00000			−0.201802
$222$	6.00000	+	1.60770i	0.402694	+	0.107901i
$223$	−10.2679			−0.687593			−0.343796	−	0.939044i	$-0.611713\pi$
$223$	−10.2679			−0.687593			−0.343796	+	0.939044i	$0.611713\pi$
$224$	8.39230	−	12.3923i	0.560734	−	0.827996i
$225$		0			0
$226$	2.00000	+	0.535898i	0.133038	+	0.0356474i
$227$	3.33975			0.221667			0.110833	−	0.993839i	$-0.464648\pi$
$227$	3.33975			0.221667			0.110833	+	0.993839i	$0.464648\pi$
$228$	18.0000	+	10.3923i	1.19208	+	0.688247i
$229$			15.4641i			1.02190i	0.859611	+	0.510948i	$0.170706\pi$
$229$			15.4641i			1.02190i	−0.859611	+	0.510948i	$0.829294\pi$
$230$	−7.46410	−	2.00000i	−0.492168	−	0.131876i
$231$	−12.9282	+	11.1962i	−0.850613	+	0.736653i
$232$	11.8564	+	11.8564i	0.778411	+	0.778411i
$233$	−22.9282			−1.50208			−0.751038	−	0.660259i	$-0.770447\pi$
$233$	−22.9282			−1.50208			−0.751038	+	0.660259i	$0.770447\pi$
$234$		0			0
$235$		−	1.73205i		−	0.112987i
$236$	6.00000	+	3.46410i	0.390567	+	0.225494i
$237$		−	4.60770i		−	0.299302i
$238$	−1.56218	+	0.758330i	−0.101261	+	0.0491552i
$239$			27.9808i			1.80993i	0.425491	+	0.904963i	$0.360101\pi$
$239$			27.9808i			1.80993i	−0.425491	+	0.904963i	$0.639899\pi$
$240$	−6.00000	+	3.46410i	−0.387298	+	0.223607i
$241$			4.39230i			0.282933i	0.989943	+	0.141467i	$0.0451818\pi$
$241$			4.39230i			0.282933i	−0.989943	+	0.141467i	$0.954818\pi$
$242$	4.00000	+	1.07180i	0.257130	+	0.0688977i
$243$		0			0
$244$	2.53590	−	4.39230i	0.162344	−	0.281189i
$245$	−6.92820	−	1.00000i	−0.442627	−	0.0638877i
$246$	−2.19615	+	8.19615i	−0.140022	+	0.522568i
$247$		−	38.7846i		−	2.46781i
$248$	12.0000	+	12.0000i	0.762001	+	0.762001i
$249$	14.7846			0.936937
$250$	−0.366025	+	1.36603i	−0.0231495	+	0.0863950i
$251$	1.85641			0.117175			0.0585877	−	0.998282i	$-0.481340\pi$
$251$	1.85641			0.117175			0.0585877	+	0.998282i	$0.481340\pi$
$252$		0			0
$253$	20.3923			1.28205
$254$	−3.12436	+	11.6603i	−0.196040	+	0.731629i
$255$	0.803848			0.0503389
$256$	−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	$-0.0599201\pi$
$258$	1.26795	−	4.73205i	0.0789391	−	0.294605i
$259$	−4.39230	−	5.07180i	−0.272925	−	0.315146i
$260$	11.1962	+	6.46410i	0.694356	+	0.400887i
$261$		0			0
$262$	−12.9282	−	3.46410i	−0.798707	−	0.214013i
$263$		−	4.53590i		−	0.279695i	−0.990173	−	0.139848i	$-0.955339\pi$
$263$		−	4.53590i		−	0.279695i	0.990173	−	0.139848i	$-0.0446613\pi$
$264$	12.9282	−	12.9282i	0.795676	−	0.795676i
$265$			2.00000i			0.122859i
$266$	−9.80385	−	20.1962i	−0.601112	−	1.23831i
$267$		−	16.3923i		−	1.00319i
$268$	−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	$0.880786\pi$
$270$	−1.90192	+	7.09808i	−0.115747	+	0.431975i
$271$	2.53590			0.154045			0.0770224	−	0.997029i	$-0.475459\pi$
$271$	2.53590			0.154045			0.0770224	+	0.997029i	$0.475459\pi$
$272$	1.60770	−	0.928203i	0.0974808	−	0.0562806i
$273$	22.3923	−	19.3923i	1.35524	−	1.17368i
$274$	0.535898	+	0.143594i	0.0323748	+	0.00867480i
$275$		−	3.73205i		−	0.225051i
$276$	9.46410	−	16.3923i	0.569672	−	0.986701i
$277$	−24.7846			−1.48916			−0.744581	−	0.667532i	$-0.767351\pi$
$277$	−24.7846			−1.48916			−0.744581	+	0.667532i	$0.767351\pi$
$278$	9.46410	+	2.53590i	0.567619	+	0.152093i
$279$		0			0
$280$	7.46410	+	0.535898i	0.446065	+	0.0320261i
$281$	5.92820			0.353647			0.176823	−	0.984243i	$-0.443418\pi$
$281$	5.92820			0.353647			0.176823	+	0.984243i	$0.443418\pi$
$282$	4.09808	+	1.09808i	0.244037	+	0.0653895i
$283$	−12.1244			−0.720718			−0.360359	−	0.932814i	$-0.617346\pi$
$283$	−12.1244			−0.720718			−0.360359	+	0.932814i	$0.617346\pi$
$284$	−0.535898	+	0.928203i	−0.0317997	+	0.0550787i
$285$			10.3923i			0.615587i
$286$	−32.9545	−	8.83013i	−1.94864	−	0.522136i
$287$	6.92820	−	6.00000i	0.408959	−	0.354169i
$288$		0			0
$289$	16.7846			0.987330
$290$	−2.16987	+	8.09808i	−0.127419	+	0.475535i
$291$		−	12.8038i		−	0.750575i
$292$	−0.928203	+	1.60770i	−0.0543190	+	0.0940832i
$293$			14.3205i			0.836613i	0.908306	+	0.418307i	$0.137376\pi$
$293$			14.3205i			0.836613i	−0.908306	+	0.418307i	$0.862624\pi$
$294$	6.75833	−	15.7583i	0.394154	−	0.919044i
$295$			3.46410i			0.201688i
$296$	5.07180	+	5.07180i	0.294792	+	0.294792i
$297$		−	19.3923i		−	1.12526i
$298$	−23.1244	−	6.19615i	−1.33956	−	0.358933i
$299$	−35.3205			−2.04264
$300$	−3.00000	−	1.73205i	−0.173205	−	0.100000i
$301$	−4.00000	+	3.46410i	−0.230556	+	0.199667i
$302$	1.75833	−	6.56218i	0.101181	−	0.377611i
$303$			14.7846i			0.849354i
$304$	12.0000	+	20.7846i	0.688247	+	1.19208i
$305$	2.53590			0.145205
$306$		0			0
$307$	−1.73205			−0.0988534			−0.0494267	−	0.998778i	$-0.515739\pi$
$307$	−1.73205			−0.0988534			−0.0494267	+	0.998778i	$0.515739\pi$
$308$	−19.3923	+	3.73205i	−1.10498	+	0.212653i
$309$	−29.7846			−1.69439
$310$	−2.19615	+	8.19615i	−0.124733	+	0.465510i
$311$	−19.8564			−1.12595			−0.562977	−	0.826473i	$-0.690344\pi$
$311$	−19.8564			−1.12595			−0.562977	+	0.826473i	$0.690344\pi$
$312$	−22.3923	+	22.3923i	−1.26771	+	1.26771i
$313$			24.4641i			1.38279i	0.722476	+	0.691396i	$0.243004\pi$
$313$			24.4641i			1.38279i	−0.722476	+	0.691396i	$0.756996\pi$
$314$	7.26795	−	27.1244i	0.410154	−	1.53072i
$315$		0			0
$316$	2.66025	−	4.60770i	0.149651	−	0.259203i
$317$	−16.9282			−0.950783			−0.475391	−	0.879774i	$-0.657694\pi$
$317$	−16.9282			−0.950783			−0.475391	+	0.879774i	$0.657694\pi$
$318$	−4.73205	−	1.26795i	−0.265360	−	0.0711031i
$319$		−	22.1244i		−	1.23873i
$320$	−8.00000			−0.447214
$321$			31.8564i			1.77805i
$322$	−18.3923	+	8.92820i	−1.02496	+	0.497549i
$323$		−	2.78461i		−	0.154940i
$324$	−15.5885	−	9.00000i	−0.866025	−	0.500000i
$325$			6.46410i			0.358564i
$326$	7.60770	−	28.3923i	0.421351	−	1.57250i
$327$	27.5885			1.52565
$328$	−6.92820	+	6.92820i	−0.382546	+	0.382546i
$329$	−3.00000	−	3.46410i	−0.165395	−	0.190982i
$330$	8.83013	+	2.36603i	0.486082	+	0.130245i
$331$		−	5.60770i		−	0.308227i	−0.988053	−	0.154113i	$-0.950748\pi$
$331$		−	5.60770i		−	0.308227i	0.988053	−	0.154113i	$-0.0492521\pi$
$332$	14.7846	+	8.53590i	0.811411	+	0.468468i
$333$		0			0
$334$	−7.09808	−	1.90192i	−0.388389	−	0.104069i
$335$	−3.46410			−0.189264
$336$	−6.00000	+	17.3205i	−0.327327	+	0.944911i
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	39.3205	+	10.5359i	2.13875	+	0.573077i
$339$	−2.53590			−0.137731
$340$	0.803848	+	0.464102i	0.0435948	+	0.0251694i
$341$		−	22.3923i		−	1.21261i
$342$		0			0
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$	4.00000	−	4.00000i	0.215666	−	0.215666i
$345$	9.46410			0.509530
$346$	−7.43782	+	27.7583i	−0.399860	+	1.49230i
$347$		−	14.2487i		−	0.764911i	−0.923974	−	0.382455i	$-0.875079\pi$
$347$		−	14.2487i		−	0.764911i	0.923974	−	0.382455i	$-0.124921\pi$
$348$	−17.7846	−	10.2679i	−0.953355	−	0.550420i
$349$		−	29.3205i		−	1.56949i	−0.619818	−	0.784745i	$-0.712794\pi$
$349$		−	29.3205i		−	1.56949i	0.619818	−	0.784745i	$-0.287206\pi$
$350$	1.63397	+	3.36603i	0.0873396	+	0.179922i
$351$			33.5885i			1.79282i
$352$	20.3923	−	5.46410i	1.08691	−	0.291238i
$353$		−	13.3923i		−	0.712800i	−0.934333	−	0.356400i	$-0.884004\pi$
$353$		−	13.3923i		−	0.712800i	0.934333	−	0.356400i	$-0.115996\pi$
$354$	−8.19615	−	2.19615i	−0.435621	−	0.116724i
$355$	−0.535898			−0.0284425
$356$	9.46410	−	16.3923i	0.501596	−	0.868790i
$357$	1.60770	−	1.39230i	0.0850883	−	0.0736886i
$358$	5.26795	−	19.6603i	0.278420	−	1.03908i
$359$		−	9.32051i		−	0.491918i	−0.969280	−	0.245959i	$-0.920897\pi$
$359$		−	9.32051i		−	0.491918i	0.969280	−	0.245959i	$-0.0791028\pi$
$360$		0			0
$361$	17.0000			0.894737
$362$	−4.73205	+	17.6603i	−0.248711	+	0.928202i
$363$	−5.07180			−0.266200
$364$	33.5885	−	6.46410i	1.76051	−	0.338811i
$365$	−0.928203			−0.0485844
$366$	−1.60770	+	6.00000i	−0.0840356	+	0.313625i
$367$	36.1244			1.88568			0.942838	−	0.333251i	$-0.108146\pi$
$367$	36.1244			1.88568			0.942838	+	0.333251i	$0.108146\pi$
$368$	18.9282	−	10.9282i	0.986701	−	0.569672i
$369$		0			0
$370$	−0.928203	+	3.46410i	−0.0482550	+	0.180090i
$371$	3.46410	+	4.00000i	0.179847	+	0.207670i
$372$	−18.0000	−	10.3923i	−0.933257	−	0.538816i
$373$	−24.3923			−1.26299			−0.631493	−	0.775382i	$-0.717557\pi$
$373$	−24.3923			−1.26299			−0.631493	+	0.775382i	$0.717557\pi$
$374$	−2.36603	−	0.633975i	−0.122344	−	0.0327820i
$375$		−	1.73205i		−	0.0894427i
$376$	3.46410	+	3.46410i	0.178647	+	0.178647i
$377$			38.3205i			1.97361i
$378$	8.49038	+	17.4904i	0.436698	+	0.899608i
$379$			26.3923i			1.35568i	0.735209	+	0.677841i	$0.237084\pi$
$379$			26.3923i			1.35568i	−0.735209	+	0.677841i	$0.762916\pi$
$380$	−6.00000	+	10.3923i	−0.307794	+	0.533114i
$381$		−	14.7846i		−	0.757438i
$382$	−1.16987	+	4.36603i	−0.0598559	+	0.223385i
$383$	20.5359			1.04934			0.524668	−	0.851307i	$-0.324190\pi$
$383$	20.5359			1.04934			0.524668	+	0.851307i	$0.324190\pi$
$384$	5.07180	−	18.9282i	0.258819	−	0.965926i
$385$	−6.46410	−	7.46410i	−0.329441	−	0.380406i
$386$	3.46410	+	0.928203i	0.176318	+	0.0472443i
$387$		0			0
$388$	7.39230	−	12.8038i	0.375287	−	0.650017i
$389$	6.85641			0.347634			0.173817	−	0.984778i	$-0.444390\pi$
$389$	6.85641			0.347634			0.173817	+	0.984778i	$0.444390\pi$
$390$	−15.2942	−	4.09808i	−0.774453	−	0.207514i
$391$	−2.53590			−0.128246
$392$	15.8564	−	11.8564i	0.800869	−	0.598839i
$393$	16.3923			0.826882
$394$	−29.1244	−	7.80385i	−1.46726	−	0.393152i
$395$	2.66025			0.133852
$396$		0			0
$397$		−	5.53590i		−	0.277839i	−0.990304	−	0.138919i	$-0.955637\pi$
$397$		−	5.53590i		−	0.277839i	0.990304	−	0.138919i	$-0.0443629\pi$
$398$	4.73205	+	1.26795i	0.237196	+	0.0635566i
$399$	18.0000	+	20.7846i	0.901127	+	1.04053i
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	−23.9282			−1.19492			−0.597459	−	0.801900i	$-0.703823\pi$
$401$	−23.9282			−1.19492			−0.597459	+	0.801900i	$0.703823\pi$
$402$	2.19615	−	8.19615i	0.109534	−	0.408787i
$403$			38.7846i			1.93200i
$404$	−8.53590	+	14.7846i	−0.424677	+	0.735562i
$405$		−	9.00000i		−	0.447214i
$406$	9.68653	+	19.9545i	0.480735	+	0.990324i
$407$		−	9.46410i		−	0.469118i
$408$	−1.60770	+	1.60770i	−0.0795928	+	0.0795928i
$409$		−	31.8564i		−	1.57520i	−0.616188	−	0.787599i	$-0.711324\pi$
$409$		−	31.8564i		−	1.57520i	0.616188	−	0.787599i	$-0.288676\pi$
$410$	−4.73205	−	1.26795i	−0.233699	−	0.0626195i
$411$	−0.679492			−0.0335169
$412$	−29.7846	−	17.1962i	−1.46738	−	0.847194i
$413$	6.00000	+	6.92820i	0.295241	+	0.340915i
$414$		0			0
$415$			8.53590i			0.419011i
$416$	−35.3205	+	9.46410i	−1.73173	+	0.464016i
$417$	−12.0000			−0.587643
$418$	8.19615	−	30.5885i	0.400887	−	1.49613i
$419$	24.2487			1.18463			0.592314	−	0.805708i	$-0.298215\pi$
$419$	24.2487			1.18463			0.592314	+	0.805708i	$0.298215\pi$
$420$	−9.00000	+	1.73205i	−0.439155	+	0.0845154i
$421$	19.0000			0.926003			0.463002	−	0.886357i	$-0.346772\pi$
$421$	19.0000			0.926003			0.463002	+	0.886357i	$0.346772\pi$
$422$	−2.63397	+	9.83013i	−0.128220	+	0.478523i
$423$		0			0
$424$	−4.00000	−	4.00000i	−0.194257	−	0.194257i
$425$			0.464102i			0.0225122i
$426$	0.339746	−	1.26795i	0.0164607	−	0.0614323i
$427$	5.07180	−	4.39230i	0.245441	−	0.212559i
$428$	−18.3923	+	31.8564i	−0.889026	+	1.53984i
$429$	41.7846			2.01738
$430$	2.73205	+	0.732051i	0.131751	+	0.0353026i
$431$			17.5885i			0.847206i	0.905848	+	0.423603i	$0.139235\pi$
$431$			17.5885i			0.847206i	−0.905848	+	0.423603i	$0.860765\pi$
$432$	−10.3923	−	18.0000i	−0.500000	−	0.866025i
$433$			4.14359i			0.199128i	0.995031	+	0.0995642i	$0.0317449\pi$
$433$			4.14359i			0.199128i	−0.995031	+	0.0995642i	$0.968255\pi$
$434$	9.80385	+	20.1962i	0.470600	+	0.969446i
$435$		−	10.2679i		−	0.492310i
$436$	27.5885	+	15.9282i	1.32125	+	0.762823i
$437$		−	32.7846i		−	1.56830i
$438$	0.588457	−	2.19615i	0.0281176	−	0.104936i
$439$	15.7128			0.749932			0.374966	−	0.927039i	$-0.377654\pi$
$439$	15.7128			0.749932			0.374966	+	0.927039i	$0.377654\pi$
$440$	7.46410	+	7.46410i	0.355837	+	0.355837i
$441$		0			0
$442$	4.09808	+	1.09808i	0.194926	+	0.0522302i
$443$		−	26.0000i		−	1.23530i	−0.786454	−	0.617649i	$-0.788085\pi$
$443$		−	26.0000i		−	1.23530i	0.786454	−	0.617649i	$-0.211915\pi$
$444$	−7.60770	−	4.39230i	−0.361045	−	0.208450i
$445$	9.46410			0.448641
$446$	14.0263	+	3.75833i	0.664164	+	0.177962i
$447$	29.3205			1.38681
$448$	−16.0000	+	13.8564i	−0.755929	+	0.654654i
$449$	−1.92820			−0.0909975			−0.0454988	−	0.998964i	$-0.514488\pi$
$449$	−1.92820			−0.0909975			−0.0454988	+	0.998964i	$0.514488\pi$
$450$		0			0
$451$	12.9282			0.608765
$452$	−2.53590	−	1.46410i	−0.119279	−	0.0688655i
$453$			8.32051i			0.390932i
$454$	−4.56218	−	1.22243i	−0.214114	−	0.0573716i
$455$	11.1962	+	12.9282i	0.524884	+	0.606084i
$456$	−20.7846	−	20.7846i	−0.973329	−	0.973329i
$457$	27.4641			1.28472			0.642358	−	0.766405i	$-0.277956\pi$
$457$	27.4641			1.28472			0.642358	+	0.766405i	$0.277956\pi$
$458$	5.66025	−	21.1244i	0.264486	−	0.987076i
$459$			2.41154i			0.112561i
$460$	9.46410	+	5.46410i	0.441266	+	0.254765i
$461$			27.7128i			1.29071i	0.763881	+	0.645357i	$0.223291\pi$
$461$			27.7128i			1.29071i	−0.763881	+	0.645357i	$0.776709\pi$
$462$	21.7583	−	10.5622i	1.01229	−	0.491397i
$463$			4.39230i			0.204128i	0.994778	+	0.102064i	$0.0325446\pi$
$463$			4.39230i			0.204128i	−0.994778	+	0.102064i	$0.967455\pi$
$464$	−11.8564	−	20.5359i	−0.550420	−	0.953355i
$465$		−	10.3923i		−	0.481932i
$466$	31.3205	+	8.39230i	1.45089	+	0.388766i
$467$	−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
$470$	−0.633975	+	2.36603i	−0.0292431	+	0.109137i
$471$			34.3923i			1.58471i
$472$	−6.92820	−	6.92820i	−0.318896	−	0.318896i
$473$	−7.46410			−0.343200
$474$	−1.68653	+	6.29423i	−0.0774650	+	0.289103i
$475$	−6.00000			−0.275299
$476$	2.41154	−	0.464102i	0.110533	−	0.0212721i
$477$		0			0
$478$	10.2417	−	38.2224i	0.468443	−	1.74825i
$479$	−37.1769			−1.69866			−0.849328	−	0.527865i	$-0.822993\pi$
$479$	−37.1769			−1.69866			−0.849328	+	0.527865i	$0.822993\pi$
$480$	9.46410	−	2.53590i	0.431975	−	0.115747i
$481$			16.3923i			0.747425i
$482$	1.60770	−	6.00000i	0.0732285	−	0.273293i
$483$	18.9282	−	16.3923i	0.861263	−	0.745876i
$484$	−5.07180	−	2.92820i	−0.230536	−	0.133100i
$485$	7.39230			0.335667
$486$		0			0
$487$			28.7846i			1.30436i	0.758066	+	0.652178i	$0.226144\pi$
$487$			28.7846i			1.30436i	−0.758066	+	0.652178i	$0.773856\pi$
$488$	−5.07180	+	5.07180i	−0.229589	+	0.229589i
$489$			36.0000i			1.62798i
$490$	9.09808	+	3.90192i	0.411009	+	0.176271i
$491$		−	34.1244i		−	1.54001i	−0.638037	−	0.770005i	$-0.720254\pi$
$491$		−	34.1244i		−	1.54001i	0.638037	−	0.770005i	$-0.279746\pi$
$492$	6.00000	−	10.3923i	0.270501	−	0.468521i
$493$			2.75129i			0.123912i
$494$	−14.1962	+	52.9808i	−0.638715	+	2.38372i
$495$		0			0
$496$	−12.0000	−	20.7846i	−0.538816	−	0.933257i
$497$	−1.07180	+	0.928203i	−0.0480767	+	0.0416356i
$498$	−20.1962	−	5.41154i	−0.905011	−	0.242497i
$499$		−	5.58846i		−	0.250174i	−0.992146	−	0.125087i	$-0.960079\pi$
$499$		−	5.58846i		−	0.250174i	0.992146	−	0.125087i	$-0.0399210\pi$
$500$	1.00000	−	1.73205i	0.0447214	−	0.0774597i
$501$	9.00000			0.402090
$502$	−2.53590	−	0.679492i	−0.113183	−	0.0303272i
$503$	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
$505$	−8.53590			−0.379842
$506$	−27.8564	−	7.46410i	−1.23837	−	0.331820i
$507$	−49.8564			−2.21420
$508$	8.53590	−	14.7846i	0.378719	−	0.655961i
$509$			1.85641i			0.0822838i	0.999153	+	0.0411419i	$0.0130996\pi$
$509$			1.85641i			0.0822838i	−0.999153	+	0.0411419i	$0.986900\pi$
$510$	−1.09808	−	0.294229i	−0.0486236	−	0.0130287i
$511$	−1.85641	+	1.60770i	−0.0821226	+	0.0711202i
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$	−31.1769			−1.37649
$514$	−2.19615	+	8.19615i	−0.0968681	+	0.361517i
$515$		−	17.1962i		−	0.757753i
$516$	−3.46410	+	6.00000i	−0.152499	+	0.264135i
$517$		−	6.46410i		−	0.284291i
$518$	4.14359	+	8.53590i	0.182059	+	0.375046i
$519$		−	35.1962i		−	1.54494i
$520$	−12.9282	−	12.9282i	−0.566939	−	0.566939i
$521$		−	34.3923i		−	1.50675i	−0.657589	−	0.753377i	$-0.728424\pi$
$521$		−	34.3923i		−	1.50675i	0.657589	−	0.753377i	$-0.271576\pi$
$522$		0			0
$523$	24.2487			1.06032			0.530161	−	0.847897i	$-0.322131\pi$
$523$	24.2487			1.06032			0.530161	+	0.847897i	$0.322131\pi$
$524$	16.3923	+	9.46410i	0.716101	+	0.413441i
$525$	−3.00000	−	3.46410i	−0.130931	−	0.151186i
$526$	−1.66025	+	6.19615i	−0.0723905	+	0.270165i
$527$			2.78461i			0.121300i
$528$	−22.3923	+	12.9282i	−0.974500	+	0.562628i
$529$	−6.85641			−0.298105
$530$	0.732051	−	2.73205i	0.0317983	−	0.118673i
$531$		0			0
$532$	6.00000	+	31.1769i	0.260133	+	1.35169i
$533$	−22.3923			−0.969918
$534$	−6.00000	+	22.3923i	−0.259645	+	0.969010i
$535$	−18.3923			−0.795169
$536$	6.92820	−	6.92820i	0.299253	−	0.299253i
$537$			24.9282i			1.07573i
$538$	4.39230	−	16.3923i	0.189366	−	0.706722i
$539$	−25.8564	−	3.73205i	−1.11371	−	0.160751i
$540$	5.19615	−	9.00000i	0.223607	−	0.387298i
$541$	−33.7846			−1.45251			−0.726257	−	0.687423i	$-0.758742\pi$
$541$	−33.7846			−1.45251			−0.726257	+	0.687423i	$0.758742\pi$
$542$	−3.46410	−	0.928203i	−0.148796	−	0.0398697i
$543$		−	22.3923i		−	0.960946i
$544$	−2.53590	+	0.679492i	−0.108726	+	0.0291330i
$545$			15.9282i			0.682289i
$546$	−37.6865	+	18.2942i	−1.61283	+	0.782921i
$547$			14.5359i			0.621510i	0.950490	+	0.310755i	$0.100582\pi$
$547$			14.5359i			0.621510i	−0.950490	+	0.310755i	$0.899418\pi$
$548$	−0.679492	−	0.392305i	−0.0290265	−	0.0167584i
$549$		0			0
$550$	−1.36603	+	5.09808i	−0.0582475	+	0.217383i
$551$	−35.5692			−1.51530
$552$	−18.9282	+	18.9282i	−0.805638	+	0.805638i
$553$	5.32051	−	4.60770i	0.226251	−	0.195939i
$554$	33.8564	+	9.07180i	1.43842	+	0.385424i
$555$		−	4.39230i		−	0.186443i
$556$	−12.0000	−	6.92820i	−0.508913	−	0.293821i
$557$	5.85641			0.248144			0.124072	−	0.992273i	$-0.460405\pi$
$557$	5.85641			0.248144			0.124072	+	0.992273i	$0.460405\pi$
$558$		0			0
$559$	12.9282			0.546805
$560$	−10.0000	−	3.46410i	−0.422577	−	0.146385i
$561$	3.00000			0.126660
$562$	−8.09808	−	2.16987i	−0.341597	−	0.0915306i
$563$	−43.1769			−1.81969			−0.909845	−	0.414948i	$-0.863800\pi$
$563$	−43.1769			−1.81969			−0.909845	+	0.414948i	$0.863800\pi$
$564$	−5.19615	−	3.00000i	−0.218797	−	0.126323i
$565$		−	1.46410i		−	0.0615952i
$566$	16.5622	+	4.43782i	0.696160	+	0.186536i
$567$	−15.5885	−	18.0000i	−0.654654	−	0.755929i
$568$	1.07180	−	1.07180i	0.0449716	−	0.0449716i
$569$	20.9282			0.877356			0.438678	−	0.898644i	$-0.355447\pi$
$569$	20.9282			0.877356			0.438678	+	0.898644i	$0.355447\pi$
$570$	3.80385	−	14.1962i	0.159326	−	0.594611i
$571$		−	41.3205i		−	1.72921i	−0.502453	−	0.864605i	$-0.667569\pi$
$571$		−	41.3205i		−	1.72921i	0.502453	−	0.864605i	$-0.332431\pi$
$572$	41.7846	+	24.1244i	1.74710	+	1.00869i
$573$		−	5.53590i		−	0.231265i
$574$	−11.6603	+	5.66025i	−0.486690	+	0.236254i
$575$			5.46410i			0.227869i
$576$		0			0
$577$			1.39230i			0.0579624i	0.999580	+	0.0289812i	$0.00922630\pi$
$577$			1.39230i			0.0579624i	−0.999580	+	0.0289812i	$0.990774\pi$
$578$	−22.9282	−	6.14359i	−0.953688	−	0.255540i
$579$	−4.39230			−0.182538
$580$	5.92820	−	10.2679i	0.246155	−	0.426353i
$581$	14.7846	+	17.0718i	0.613369	+	0.708257i
$582$	−4.68653	+	17.4904i	−0.194263	+	0.725000i
$583$			7.46410i			0.309132i
$584$	1.85641	−	1.85641i	0.0768186	−	0.0768186i
$585$		0			0
$586$	5.24167	−	19.5622i	0.216531	−	0.808106i
$587$	−27.4641			−1.13356			−0.566782	−	0.823868i	$-0.691812\pi$
$587$	−27.4641			−1.13356			−0.566782	+	0.823868i	$0.691812\pi$
$588$	−15.0000	+	19.0526i	−0.618590	+	0.785714i
$589$	−36.0000			−1.48335
$590$	1.26795	−	4.73205i	0.0522006	−	0.194815i
$591$	36.9282			1.51902
$592$	−5.07180	−	8.78461i	−0.208450	−	0.361045i
$593$		−	23.5359i		−	0.966504i	−0.875481	−	0.483252i	$-0.839456\pi$
$593$		−	23.5359i		−	0.966504i	0.875481	−	0.483252i	$-0.160544\pi$
$594$	−7.09808	+	26.4904i	−0.291238	+	1.08691i
$595$	0.803848	+	0.928203i	0.0329545	+	0.0380526i
$596$	29.3205	+	16.9282i	1.20101	+	0.693406i
$597$	−6.00000			−0.245564
$598$	48.2487	+	12.9282i	1.97304	+	0.528674i
$599$			14.1244i			0.577106i	0.957464	+	0.288553i	$0.0931741\pi$
$599$			14.1244i			0.577106i	−0.957464	+	0.288553i	$0.906826\pi$
$600$	3.46410	+	3.46410i	0.141421	+	0.141421i
$601$		−	26.7846i		−	1.09257i	−0.837600	−	0.546284i	$-0.816042\pi$
$601$		−	26.7846i		−	1.09257i	0.837600	−	0.546284i	$-0.183958\pi$
$602$	6.73205	−	3.26795i	0.274378	−	0.133192i
$603$		0			0
$604$	−4.80385	+	8.32051i	−0.195466	+	0.338557i
$605$		−	2.92820i		−	0.119048i
$606$	5.41154	−	20.1962i	0.219829	−	0.820413i
$607$	−18.8038			−0.763225			−0.381612	−	0.924322i	$-0.624631\pi$
$607$	−18.8038			−0.763225			−0.381612	+	0.924322i	$0.624631\pi$
$608$	−8.78461	−	32.7846i	−0.356263	−	1.32959i
$609$	−17.7846	−	20.5359i	−0.720669	−	0.832157i
$610$	−3.46410	−	0.928203i	−0.140257	−	0.0375819i
$611$			11.1962i			0.452948i
$612$		0			0
$613$	−10.0000			−0.403896			−0.201948	−	0.979396i	$-0.564727\pi$
$613$	−10.0000			−0.403896			−0.201948	+	0.979396i	$0.564727\pi$
$614$	2.36603	+	0.633975i	0.0954850	+	0.0255851i
$615$	6.00000			0.241943
$616$	27.8564	+	2.00000i	1.12237	+	0.0805823i
$617$	−9.07180			−0.365217			−0.182608	−	0.983186i	$-0.558454\pi$
$617$	−9.07180			−0.365217			−0.182608	+	0.983186i	$0.558454\pi$
$618$	40.6865	+	10.9019i	1.63665	+	0.438540i
$619$	35.3205			1.41965			0.709826	−	0.704378i	$-0.248774\pi$
$619$	35.3205			1.41965			0.709826	+	0.704378i	$0.248774\pi$
$620$	6.00000	−	10.3923i	0.240966	−	0.417365i
$621$			28.3923i			1.13934i
$622$	27.1244	+	7.26795i	1.08759	+	0.291418i
$623$	18.9282	−	16.3923i	0.758342	−	0.656744i
$624$	38.7846	−	22.3923i	1.55263	−	0.896410i
$625$	1.00000			0.0400000
$626$	8.95448	−	33.4186i	0.357893	−	1.33568i
$627$			38.7846i			1.54891i
$628$	−19.8564	+	34.3923i	−0.792357	+	1.37240i
$629$			1.17691i			0.0469267i
$630$		0			0
$631$		−	26.9090i		−	1.07123i	−0.844463	−	0.535614i	$-0.820080\pi$
$631$		−	26.9090i		−	1.07123i	0.844463	−	0.535614i	$-0.179920\pi$
$632$	−5.32051	+	5.32051i	−0.211638	+	0.211638i
$633$		−	12.4641i		−	0.495404i
$634$	23.1244	+	6.19615i	0.918385	+	0.246081i
$635$	8.53590			0.338737
$636$	6.00000	+	3.46410i	0.237915	+	0.137361i
$637$	44.7846	+	6.46410i	1.77443	+	0.256117i
$638$	−8.09808	+	30.2224i	−0.320606	+	1.19652i
$639$		0			0
$640$	10.9282	+	2.92820i	0.431975	+	0.115747i
$641$	−4.92820			−0.194652			−0.0973262	−	0.995253i	$-0.531029\pi$
$641$	−4.92820			−0.194652			−0.0973262	+	0.995253i	$0.531029\pi$
$642$	11.6603	−	43.5167i	0.460194	−	1.71747i
$643$	−31.0526			−1.22459			−0.612297	−	0.790628i	$-0.709754\pi$
$643$	−31.0526			−1.22459			−0.612297	+	0.790628i	$0.709754\pi$
$644$	28.3923	−	5.46410i	1.11881	−	0.215316i
$645$	−3.46410			−0.136399
$646$	−1.01924	+	3.80385i	−0.0401014	+	0.149660i
$647$	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
$649$			12.9282i			0.507476i
$650$	2.36603	−	8.83013i	0.0928032	−	0.346346i
$651$	−18.0000	−	20.7846i	−0.705476	−	0.814613i
$652$	−20.7846	+	36.0000i	−0.813988	+	1.40987i
$653$	38.3923			1.50241			0.751203	−	0.660071i	$-0.229474\pi$
$653$	38.3923			1.50241			0.751203	+	0.660071i	$0.229474\pi$
$654$	−37.6865	−	10.0981i	−1.47366	−	0.394866i
$655$			9.46410i			0.369793i
$656$	12.0000	−	6.92820i	0.468521	−	0.270501i
$657$		0			0
$658$	2.83013	+	5.83013i	0.110330	+	0.227282i
$659$		−	20.8038i		−	0.810403i	−0.914227	−	0.405201i	$-0.867201\pi$
$659$		−	20.8038i		−	0.810403i	0.914227	−	0.405201i	$-0.132799\pi$
$660$	−11.1962	−	6.46410i	−0.435810	−	0.251615i
$661$			15.7128i			0.611158i	0.952167	+	0.305579i	$0.0988499\pi$
$661$			15.7128i			0.611158i	−0.952167	+	0.305579i	$0.901150\pi$
$662$	−2.05256	+	7.66025i	−0.0797750	+	0.297724i
$663$	−5.19615			−0.201802
$664$	−17.0718	−	17.0718i	−0.662514	−	0.662514i
$665$	−12.0000	+	10.3923i	−0.465340	+	0.402996i
$666$		0			0
$667$			32.3923i			1.25424i
$668$	9.00000	+	5.19615i	0.348220	+	0.201045i
$669$	−17.7846			−0.687593
$670$	4.73205	+	1.26795i	0.182815	+	0.0489852i
$671$	9.46410			0.365358
$672$	14.5359	−	21.4641i	0.560734	−	0.827996i
$673$	49.1769			1.89563			0.947815	−	0.318820i	$-0.103286\pi$
$673$	49.1769			1.89563			0.947815	+	0.318820i	$0.103286\pi$
$674$		0			0
$675$	5.19615			0.200000
$676$	−49.8564	−	28.7846i	−1.91755	−	1.10710i
$677$			4.60770i			0.177088i	0.996072	+	0.0885441i	$0.0282214\pi$
$677$			4.60770i			0.177088i	−0.996072	+	0.0885441i	$0.971779\pi$
$678$	3.46410	+	0.928203i	0.133038	+	0.0356474i
$679$	14.7846	−	12.8038i	0.567381	−	0.491367i
$680$	−0.928203	−	0.928203i	−0.0355950	−	0.0355950i
$681$	5.78461			0.221667
$682$	−8.19615	+	30.5885i	−0.313847	+	1.17129i
$683$		−	27.3205i		−	1.04539i	−0.852520	−	0.522695i	$-0.824927\pi$
$683$		−	27.3205i		−	1.04539i	0.852520	−	0.522695i	$-0.175073\pi$
$684$		0			0
$685$		−	0.392305i		−	0.0149892i
$686$	24.9545	−	7.95448i	0.952767	−	0.303704i
$687$			26.7846i			1.02190i
$688$	−6.92820	+	4.00000i	−0.264135	+	0.152499i
$689$		−	12.9282i		−	0.492525i
$690$	−12.9282	−	3.46410i	−0.492168	−	0.131876i
$691$	46.6410			1.77431			0.887154	−	0.461474i	$-0.152679\pi$
$691$	46.6410			1.77431			0.887154	+	0.461474i	$0.152679\pi$
$692$	20.3205	−	35.1962i	0.772470	−	1.33796i
$693$		0			0
$694$	−5.21539	+	19.4641i	−0.197974	+	0.738847i
$695$		−	6.92820i		−	0.262802i
$696$	20.5359	+	20.5359i	0.778411	+	0.778411i
$697$	−1.60770			−0.0608958
$698$	−10.7321	+	40.0526i	−0.406214	+	1.51601i
$699$	−39.7128			−1.50208
$700$	−1.00000	−	5.19615i	−0.0377964	−	0.196396i
$701$	3.78461			0.142943			0.0714714	−	0.997443i	$-0.477231\pi$
$701$	3.78461			0.142943			0.0714714	+	0.997443i	$0.477231\pi$
$702$	12.2942	−	45.8827i	0.464016	−	1.73173i
$703$	−15.2154			−0.573859
$704$	−29.8564			−1.12526
$705$		−	3.00000i		−	0.112987i
$706$	−4.90192	+	18.2942i	−0.184486	+	0.688512i
$707$	−17.0718	+	14.7846i	−0.642051	+	0.556032i
$708$	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	$0.370975\pi$
$710$	0.732051	+	0.196152i	0.0274734	+	0.00736147i
$711$		0			0
$712$	−18.9282	+	18.9282i	−0.709364	+	0.709364i
$713$			32.7846i			1.22779i
$714$	−2.70577	+	1.31347i	−0.101261	+	0.0491552i
$715$			24.1244i			0.902200i
$716$	−14.3923	+	24.9282i	−0.537866	+	0.931611i
$717$			48.4641i			1.80993i
$718$	−3.41154	+	12.7321i	−0.127318	+	0.475156i
$719$	45.4641			1.69552			0.847762	−	0.530376i	$-0.177949\pi$
$719$	45.4641			1.69552			0.847762	+	0.530376i	$0.177949\pi$
$720$		0			0
$721$	−29.7846	−	34.3923i	−1.10924	−	1.28084i
$722$	−23.2224	−	6.22243i	−0.864249	−	0.231575i
$723$			7.60770i			0.282933i
$724$	12.9282	−	22.3923i	0.480473	−	0.832203i
$725$	5.92820			0.220168
$726$	6.92820	+	1.85641i	0.257130	+	0.0688977i
$727$	−34.3923			−1.27554			−0.637770	−	0.770227i	$-0.720143\pi$
$727$	−34.3923			−1.27554			−0.637770	+	0.770227i	$0.720143\pi$
$728$	−48.2487	−	3.46410i	−1.78822	−	0.128388i
$729$	27.0000			1.00000
$730$	1.26795	+	0.339746i	0.0469289	+	0.0125746i
$731$	0.928203			0.0343308
$732$	4.39230	−	7.60770i	0.162344	−	0.281189i
$733$		−	18.4641i		−	0.681987i	−0.940066	−	0.340994i	$-0.889237\pi$
$733$		−	18.4641i		−	0.681987i	0.940066	−	0.340994i	$-0.110763\pi$
$734$	−49.3468	−	13.2224i	−1.82142	−	0.488049i
$735$	−12.0000	−	1.73205i	−0.442627	−	0.0638877i
$736$	−29.8564	+	8.00000i	−1.10052	+	0.294884i
$737$	−12.9282			−0.476216
$738$		0			0
$739$		−	7.73205i		−	0.284428i	−0.989836	−	0.142214i	$-0.954578\pi$
$739$		−	7.73205i		−	0.284428i	0.989836	−	0.142214i	$-0.0454221\pi$
$740$	2.53590	−	4.39230i	0.0932215	−	0.161464i
$741$		−	67.1769i		−	2.46781i
$742$	−3.26795	−	6.73205i	−0.119970	−	0.247141i
$743$			9.60770i			0.352472i	0.984348	+	0.176236i	$0.0563922\pi$
$743$			9.60770i			0.352472i	−0.984348	+	0.176236i	$0.943608\pi$
$744$	20.7846	+	20.7846i	0.762001	+	0.762001i
$745$			16.9282i			0.620201i
$746$	33.3205	+	8.92820i	1.21995	+	0.326885i
$747$		0			0
$748$	3.00000	+	1.73205i	0.109691	+	0.0633300i
$749$	−36.7846	+	31.8564i	−1.34408	+	1.16401i
$750$	−0.633975	+	2.36603i	−0.0231495	+	0.0863950i
$751$			5.58846i			0.203926i	0.994788	+	0.101963i	$0.0325123\pi$
$751$			5.58846i			0.203926i	−0.994788	+	0.101963i	$0.967488\pi$
$752$	−3.46410	−	6.00000i	−0.126323	−	0.218797i
$753$	3.21539			0.117175
$754$	14.0263	−	52.3468i	0.510807	−	1.90636i
$755$	−4.80385			−0.174830
$756$	−5.19615	−	27.0000i	−0.188982	−	0.981981i
$757$	10.1436			0.368675			0.184338	−	0.982863i	$-0.440986\pi$
$757$	10.1436			0.368675			0.184338	+	0.982863i	$0.440986\pi$
$758$	9.66025	−	36.0526i	0.350876	−	1.30949i
$759$	35.3205			1.28205
$760$	12.0000	−	12.0000i	0.435286	−	0.435286i
$761$		−	6.24871i		−	0.226516i	−0.993566	−	0.113258i	$-0.963871\pi$
$761$		−	6.24871i		−	0.226516i	0.993566	−	0.113258i	$-0.0361286\pi$
$762$	−5.41154	+	20.1962i	−0.196040	+	0.731629i
$763$	27.5885	+	31.8564i	0.998769	+	1.15328i
$764$	3.19615	−	5.53590i	0.115633	−	0.200282i
$765$		0			0
$766$	−28.0526	−	7.51666i	−1.01358	−	0.271588i
$767$		−	22.3923i		−	0.808539i
$768$	−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	$-0.105212\pi$
$770$	6.09808	+	12.5622i	0.219759	+	0.452709i
$771$		−	10.3923i		−	0.374270i
$772$	−4.39230	−	2.53590i	−0.158083	−	0.0912690i
$773$			12.4641i			0.448303i	0.974554	+	0.224151i	$0.0719610\pi$
$773$			12.4641i			0.448303i	−0.974554	+	0.224151i	$0.928039\pi$
$774$		0			0
$775$	6.00000			0.215526
$776$	−14.7846	+	14.7846i	−0.530737	+	0.530737i
$777$	−7.60770	−	8.78461i	−0.272925	−	0.315146i
$778$	−9.36603	−	2.50962i	−0.335788	−	0.0899742i
$779$		−	20.7846i		−	0.744686i
$780$	19.3923	+	11.1962i	0.694356	+	0.400887i
$781$	−2.00000			−0.0715656
$782$	3.46410	+	0.928203i	0.123876	+	0.0331925i
$783$	30.8038			1.10084
$784$	−26.0000	+	10.3923i	−0.928571	+	0.371154i
$785$	−19.8564			−0.708706
$786$	−22.3923	−	6.00000i	−0.798707	−	0.214013i
$787$	15.3397			0.546803			0.273401	−	0.961900i	$-0.411851\pi$
$787$	15.3397			0.546803			0.273401	+	0.961900i	$0.411851\pi$
$788$	36.9282	+	21.3205i	1.31551	+	0.759512i
$789$		−	7.85641i		−	0.279695i
$790$	−3.63397	−	0.973721i	−0.129291	−	0.0346434i
$791$	−2.53590	−	2.92820i	−0.0901662	−	0.104115i
$792$		0			0
$793$	−16.3923			−0.582108
$794$	−2.02628	+	7.56218i	−0.0719100	+	0.268372i
$795$			3.46410i			0.122859i
$796$	−6.00000	−	3.46410i	−0.212664	−	0.122782i
$797$		−	40.1769i		−	1.42314i	−0.702616	−	0.711570i	$-0.747985\pi$
$797$		−	40.1769i		−	1.42314i	0.702616	−	0.711570i	$-0.252015\pi$
$798$	−16.9808	−	34.9808i	−0.601112	−	1.23831i
$799$			0.803848i			0.0284381i
$800$	1.46410	+	5.46410i	0.0517638	+	0.193185i
$801$		0			0
$802$	32.6865	+	8.75833i	1.15420	+	0.309267i
$803$	−3.46410			−0.122245
$804$	−6.00000	+	10.3923i	−0.211604	+	0.366508i
$805$	9.46410	+	10.9282i	0.333566	+	0.385169i
$806$	14.1962	−	52.9808i	0.500038	−	1.86617i
$807$			20.7846i			0.731653i
$808$	17.0718	−	17.0718i	0.600584	−	0.600584i
$809$	−5.92820			−0.208425			−0.104212	−	0.994555i	$-0.533232\pi$
$809$	−5.92820			−0.208425			−0.104212	+	0.994555i	$0.533232\pi$
$810$	−3.29423	+	12.2942i	−0.115747	+	0.431975i
$811$	42.9282			1.50741			0.753707	−	0.657211i	$-0.228264\pi$
$811$	42.9282			1.50741			0.753707	+	0.657211i	$0.228264\pi$
$812$	−5.92820	−	30.8038i	−0.208039	−	1.08100i
$813$	4.39230			0.154045
$814$	−3.46410	+	12.9282i	−0.121417	+	0.453133i
$815$	−20.7846			−0.728053
$816$	2.78461	−	1.60770i	0.0974808	−	0.0562806i
$817$			12.0000i			0.419827i
$818$	−11.6603	+	43.5167i	−0.407691	+	1.52152i
$819$		0			0
$820$	6.00000	+	3.46410i	0.209529	+	0.120972i
$821$	−13.7846			−0.481086			−0.240543	−	0.970638i	$-0.577326\pi$
$821$	−13.7846			−0.481086			−0.240543	+	0.970638i	$0.577326\pi$
$822$	0.928203	+	0.248711i	0.0323748	+	0.00867480i
$823$			24.9282i			0.868943i	0.900686	+	0.434471i	$0.143065\pi$
$823$			24.9282i			0.868943i	−0.900686	+	0.434471i	$0.856935\pi$
$824$	34.3923	+	34.3923i	1.19811	+	1.19811i
$825$		−	6.46410i		−	0.225051i
$826$	−5.66025	−	11.6603i	−0.196945	−	0.405712i
$827$			41.8564i			1.45549i	0.685848	+	0.727745i	$0.259432\pi$
$827$			41.8564i			1.45549i	−0.685848	+	0.727745i	$0.740568\pi$
$828$		0			0
$829$			48.2487i			1.67575i	0.545864	+	0.837874i	$0.316201\pi$
$829$			48.2487i			1.67575i	−0.545864	+	0.837874i	$0.683799\pi$
$830$	3.12436	−	11.6603i	0.108448	−	0.404733i
$831$	−42.9282			−1.48916
$832$	51.7128			1.79282
$833$	3.21539	+	0.464102i	0.111407	+	0.0160802i
$834$	16.3923	+	4.39230i	0.567619	+	0.152093i
$835$			5.19615i			0.179820i
$836$	−22.3923	+	38.7846i	−0.774454	+	1.34139i
$837$	31.1769			1.07763
$838$	−33.1244	−	8.87564i	−1.14426	−	0.306604i
$839$	−16.3923			−0.565925			−0.282963	−	0.959131i	$-0.591317\pi$
$839$	−16.3923			−0.565925			−0.282963	+	0.959131i	$0.591317\pi$
$840$	12.9282	+	0.928203i	0.446065	+	0.0320261i
$841$	6.14359			0.211848
$842$	−25.9545	−	6.95448i	−0.894451	−	0.239667i
$843$	10.2679			0.353647
$844$	7.19615	−	12.4641i	0.247702	−	0.429032i
$845$		−	28.7846i		−	0.990221i
$846$		0			0
$847$	−5.07180	−	5.85641i	−0.174269	−	0.201229i
$848$	4.00000	+	6.92820i	0.137361	+	0.237915i
$849$	−21.0000			−0.720718
$850$	0.169873	−	0.633975i	0.00582660	−	0.0217451i
$851$			13.8564i			0.474991i
$852$	−0.928203	+	1.60770i	−0.0317997	+	0.0550787i
$853$		−	38.7846i		−	1.32796i	−0.747750	−	0.663980i	$-0.768866\pi$
$853$		−	38.7846i		−	1.32796i	0.747750	−	0.663980i	$-0.231134\pi$
$854$	−8.53590	+	4.14359i	−0.292092	+	0.141791i
$855$		0			0
$856$	36.7846	−	36.7846i	1.25727	−	1.25727i
$857$		−	2.28719i		−	0.0781288i	−0.999237	−	0.0390644i	$-0.987562\pi$
$857$		−	2.28719i		−	0.0781288i	0.999237	−	0.0390644i	$-0.0124378\pi$
$858$	−57.0788	−	15.2942i	−1.94864	−	0.522136i
$859$	−15.7128			−0.536114			−0.268057	−	0.963403i	$-0.586382\pi$
$859$	−15.7128			−0.536114			−0.268057	+	0.963403i	$0.586382\pi$
$860$	−3.46410	−	2.00000i	−0.118125	−	0.0681994i
$861$	12.0000	−	10.3923i	0.408959	−	0.354169i
$862$	6.43782	−	24.0263i	0.219273	−	0.818338i
$863$		−	12.1436i		−	0.413373i	−0.978407	−	0.206686i	$-0.933732\pi$
$863$		−	12.1436i		−	0.413373i	0.978407	−	0.206686i	$-0.0662680\pi$
$864$	7.60770	+	28.3923i	0.258819	+	0.965926i
$865$	20.3205			0.690918
$866$	1.51666	−	5.66025i	0.0515382	−	0.192343i
$867$	29.0718			0.987330
$868$	−6.00000	−	31.1769i	−0.203653	−	1.05821i
$869$	9.92820			0.336791
$870$	−3.75833	+	14.0263i	−0.127419	+	0.475535i
$871$	22.3923			0.758734
$872$	−31.8564	−	31.8564i	−1.07879	−	1.07879i
$873$		0			0
$874$	−12.0000	+	44.7846i	−0.405906	+	1.51486i
$875$	2.00000	−	1.73205i	0.0676123	−	0.0585540i
$876$	−1.60770	+	2.78461i	−0.0543190	+	0.0940832i
$877$	2.39230			0.0807824			0.0403912	−	0.999184i	$-0.487140\pi$
$877$	2.39230			0.0807824			0.0403912	+	0.999184i	$0.487140\pi$
$878$	−21.4641	−	5.75129i	−0.724378	−	0.194097i
$879$			24.8038i			0.836613i
$880$	−7.46410	−	12.9282i	−0.251615	−	0.435810i
$881$			42.9282i			1.44629i	0.690697	+	0.723144i	$0.257304\pi$
$881$			42.9282i			1.44629i	−0.690697	+	0.723144i	$0.742696\pi$
$882$		0			0
$883$		−	44.3923i		−	1.49392i	−0.664869	−	0.746960i	$-0.731513\pi$
$883$		−	44.3923i		−	1.49392i	0.664869	−	0.746960i	$-0.268487\pi$
$884$	−5.19615	−	3.00000i	−0.174766	−	0.100901i
$885$			6.00000i			0.201688i
$886$	−9.51666	+	35.5167i	−0.319718	+	1.19321i
$887$	−15.4641			−0.519234			−0.259617	−	0.965712i	$-0.583596\pi$
$887$	−15.4641			−0.519234			−0.259617	+	0.965712i	$0.583596\pi$
$888$	8.78461	+	8.78461i	0.294792	+	0.294792i
$889$	17.0718	−	14.7846i	0.572570	−	0.495860i
$890$	−12.9282	−	3.46410i	−0.433354	−	0.116117i
$891$		−	33.5885i		−	1.12526i
$892$	−17.7846	−	10.2679i	−0.595473	−	0.343796i
$893$	−10.3923			−0.347765
$894$	−40.0526	−	10.7321i	−1.33956	−	0.358933i
$895$	−14.3923			−0.481082
$896$	26.9282	−	13.0718i	0.899608	−	0.436698i
$897$	−61.1769			−2.04264
$898$	2.63397	+	0.705771i	0.0878969	+	0.0235519i
$899$	35.5692			1.18630
$900$		0			0
$901$		−	0.928203i		−	0.0309229i
$902$	−17.6603	−	4.73205i	−0.588022	−	0.157560i
$903$	−6.92820	+	6.00000i	−0.230556	+	0.199667i
$904$	2.92820	+	2.92820i	0.0973906	+	0.0973906i
$905$	12.9282			0.429748
$906$	3.04552	−	11.3660i	0.101181	−	0.377611i
$907$		−	11.6077i		−	0.385427i	−0.981255	−	0.192714i	$-0.938271\pi$
$907$		−	11.6077i		−	0.385427i	0.981255	−	0.192714i	$-0.0617288\pi$
$908$	5.78461	+	3.33975i	0.191969	+	0.110833i
$909$		0			0
$910$	−10.5622	−	21.7583i	−0.350133	−	0.721282i
$911$			28.2487i			0.935922i	0.883749	+	0.467961i	$0.155011\pi$
$911$			28.2487i			0.935922i	−0.883749	+	0.467961i	$0.844989\pi$
$912$	20.7846	+	36.0000i	0.688247	+	1.19208i
$913$			31.8564i			1.05429i
$914$	−37.5167	−	10.0526i	−1.24094	−	0.332509i
$915$	4.39230			0.145205
$916$	−15.4641	+	26.7846i	−0.510948	+	0.884988i
$917$	16.3923	+	18.9282i	0.541322	+	0.625064i
$918$	0.882686	−	3.29423i	0.0291330	−	0.108726i
$919$		−	37.5885i		−	1.23993i	−0.784630	−	0.619964i	$-0.787147\pi$
$919$		−	37.5885i		−	1.23993i	0.784630	−	0.619964i	$-0.212853\pi$
$920$	−10.9282	−	10.9282i	−0.360292	−	0.360292i
$921$	−3.00000			−0.0988534
$922$	10.1436	−	37.8564i	0.334061	−	1.24673i
$923$	3.46410			0.114022
$924$	−33.5885	+	6.46410i	−1.10498	+	0.212653i
$925$	2.53590			0.0833798
$926$	1.60770	−	6.00000i	0.0528321	−	0.197172i
$927$		0			0
$928$	8.67949	+	32.3923i	0.284918	+	1.06333i
$929$		−	42.4974i		−	1.39430i	−0.716928	−	0.697148i	$-0.754452\pi$
$929$		−	42.4974i		−	1.39430i	0.716928	−	0.697148i	$-0.245548\pi$
$930$	−3.80385	+	14.1962i	−0.124733	+	0.465510i
$931$	−6.00000	+	41.5692i	−0.196642	+	1.36238i
$932$	−39.7128	−	22.9282i	−1.30084	−	0.751038i
$933$	−34.3923			−1.12595
$934$	30.7583	+	8.24167i	1.00644	+	0.269676i
$935$			1.73205i			0.0566441i
$936$		0			0
$937$			4.60770i			0.150527i	0.997164	+	0.0752634i	$0.0239798\pi$
$937$			4.60770i			0.150527i	−0.997164	+	0.0752634i	$0.976020\pi$
$938$	11.6603	−	5.66025i	0.380721	−	0.184814i
$939$			42.3731i			1.38279i
$940$	1.73205	−	3.00000i	0.0564933	−	0.0978492i
$941$			51.0333i			1.66364i	0.555046	+	0.831819i	$0.312700\pi$
$941$			51.0333i			1.66364i	−0.555046	+	0.831819i	$0.687300\pi$
$942$	12.5885	−	46.9808i	0.410154	−	1.53072i
$943$	−18.9282			−0.616387
$944$	6.92820	+	12.0000i	0.225494	+	0.390567i
$945$	10.3923	−	9.00000i	0.338062	−	0.292770i
$946$	10.1962	+	2.73205i	0.331506	+	0.0888266i
$947$		−	18.7846i		−	0.610418i	−0.952285	−	0.305209i	$-0.901274\pi$
$947$		−	18.7846i		−	0.610418i	0.952285	−	0.305209i	$-0.0987263\pi$
$948$	4.60770	−	7.98076i	0.149651	−	0.259203i
$949$	6.00000			0.194768
$950$	8.19615	+	2.19615i	0.265918	+	0.0712526i
$951$	−29.3205			−0.950783
$952$	−3.46410	−	0.248711i	−0.112272	−	0.00806078i
$953$	−13.3205			−0.431494			−0.215747	−	0.976449i	$-0.569219\pi$
$953$	−13.3205			−0.431494			−0.215747	+	0.976449i	$0.569219\pi$
$954$		0			0
$955$	3.19615			0.103425
$956$	−27.9808	+	48.4641i	−0.904963	+	1.56744i
$957$		−	38.3205i		−	1.23873i
$958$	50.7846	+	13.6077i	1.64078	+	0.439645i
$959$	−0.679492	−	0.784610i	−0.0219419	−	0.0253364i
$960$	−13.8564			−0.447214
$961$	5.00000			0.161290
$962$	6.00000	−	22.3923i	0.193448	−	0.721957i
$963$		0			0
$964$	−4.39230	+	7.60770i	−0.141467	+	0.245027i
$965$		−	2.53590i		−	0.0816335i
$966$	−31.8564	+	15.4641i	−1.02496	+	0.497549i
$967$		−	31.1769i		−	1.00258i	−0.865279	−	0.501291i	$-0.832859\pi$
$967$		−	31.1769i		−	1.00258i	0.865279	−	0.501291i	$-0.167141\pi$
$968$	5.85641	+	5.85641i	0.188232	+	0.188232i
$969$		−	4.82309i		−	0.154940i
$970$	−10.0981	−	2.70577i	−0.324230	−	0.0868771i
$971$	−26.7846			−0.859559			−0.429780	−	0.902934i	$-0.641409\pi$
$971$	−26.7846			−0.859559			−0.429780	+	0.902934i	$0.641409\pi$
$972$		0			0
$973$	−12.0000	−	13.8564i	−0.384702	−	0.444216i
$974$	10.5359	−	39.3205i	0.337592	−	1.25991i
$975$			11.1962i			0.358564i
$976$	8.78461	−	5.07180i	0.281189	−	0.162344i
$977$	44.2487			1.41564			0.707821	−	0.706392i	$-0.249678\pi$
$977$	44.2487			1.41564			0.707821	+	0.706392i	$0.249678\pi$
$978$	13.1769	−	49.1769i	0.421351	−	1.57250i
$979$	35.3205			1.12885
$980$	−11.0000	−	8.66025i	−0.351382	−	0.276642i
$981$		0			0
$982$	−12.4904	+	46.6147i	−0.398584	+	1.48754i
$983$	3.58846			0.114454			0.0572270	−	0.998361i	$-0.481774\pi$
$983$	3.58846			0.114454			0.0572270	+	0.998361i	$0.481774\pi$
$984$	−12.0000	+	12.0000i	−0.382546	+	0.382546i
$985$			21.3205i			0.679328i
$986$	1.00704	−	3.75833i	0.0320707	−	0.119690i
$987$	−5.19615	−	6.00000i	−0.165395	−	0.190982i
$988$	38.7846	−	67.1769i	1.23390	−	2.13718i
$989$	10.9282			0.347497
$990$		0			0
$991$		−	15.1769i		−	0.482111i	−0.970511	−	0.241055i	$-0.922506\pi$
$991$		−	15.1769i		−	0.482111i	0.970511	−	0.241055i	$-0.0774935\pi$
$992$	8.78461	+	32.7846i	0.278912	+	1.04091i
$993$		−	9.71281i		−	0.308227i
$994$	1.80385	−	0.875644i	0.0572146	−	0.0277738i
$995$		−	3.46410i		−	0.109819i
$996$	25.6077	+	14.7846i	0.811411	+	0.468468i
$997$		−	12.4641i		−	0.394742i	−0.980329	−	0.197371i	$-0.936760\pi$
$997$		−	12.4641i		−	0.394742i	0.980329	−	0.197371i	$-0.0632404\pi$
$998$	−2.04552	+	7.63397i	−0.0647497	+	0.241649i
$999$	13.1769			0.416899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.g.a.111.1	✓	4
3.2	odd	2		1260.2.c.a.811.4		4
4.3	odd	2		140.2.g.b.111.2	yes	4
5.2	odd	4		700.2.c.b.699.3		4
5.3	odd	4		700.2.c.e.699.2		4
5.4	even	2		700.2.g.f.251.4		4
7.2	even	3		980.2.o.a.31.2		4
7.3	odd	6		980.2.o.d.411.1		4
7.4	even	3		980.2.o.c.411.1		4
7.5	odd	6		980.2.o.b.31.2		4
7.6	odd	2		140.2.g.b.111.1	yes	4
8.3	odd	2		2240.2.k.b.1791.3		4
8.5	even	2		2240.2.k.a.1791.1		4
12.11	even	2		1260.2.c.b.811.3		4
20.3	even	4		700.2.c.c.699.4		4
20.7	even	4		700.2.c.f.699.1		4
20.19	odd	2		700.2.g.g.251.3		4
21.20	even	2		1260.2.c.b.811.4		4
28.3	even	6		980.2.o.a.411.2		4
28.11	odd	6		980.2.o.b.411.2		4
28.19	even	6		980.2.o.c.31.2		4
28.23	odd	6		980.2.o.d.31.2		4
28.27	even	2	inner	140.2.g.a.111.2	yes	4
35.13	even	4		700.2.c.f.699.2		4
35.27	even	4		700.2.c.c.699.3		4
35.34	odd	2		700.2.g.g.251.4		4
56.13	odd	2		2240.2.k.b.1791.4		4
56.27	even	2		2240.2.k.a.1791.2		4
84.83	odd	2		1260.2.c.a.811.3		4
140.27	odd	4		700.2.c.e.699.1		4
140.83	odd	4		700.2.c.b.699.4		4
140.139	even	2		700.2.g.f.251.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.g.a.111.1	✓	4	1.1	even	1	trivial
140.2.g.a.111.2	yes	4	28.27	even	2	inner
140.2.g.b.111.1	yes	4	7.6	odd	2
140.2.g.b.111.2	yes	4	4.3	odd	2
700.2.c.b.699.3		4	5.2	odd	4
700.2.c.b.699.4		4	140.83	odd	4
700.2.c.c.699.3		4	35.27	even	4
700.2.c.c.699.4		4	20.3	even	4
700.2.c.e.699.1		4	140.27	odd	4
700.2.c.e.699.2		4	5.3	odd	4
700.2.c.f.699.1		4	20.7	even	4
700.2.c.f.699.2		4	35.13	even	4
700.2.g.f.251.3		4	140.139	even	2
700.2.g.f.251.4		4	5.4	even	2
700.2.g.g.251.3		4	20.19	odd	2
700.2.g.g.251.4		4	35.34	odd	2
980.2.o.a.31.2		4	7.2	even	3
980.2.o.a.411.2		4	28.3	even	6
980.2.o.b.31.2		4	7.5	odd	6
980.2.o.b.411.2		4	28.11	odd	6
980.2.o.c.31.2		4	28.19	even	6
980.2.o.c.411.1		4	7.4	even	3
980.2.o.d.31.2		4	28.23	odd	6
980.2.o.d.411.1		4	7.3	odd	6
1260.2.c.a.811.3		4	84.83	odd	2
1260.2.c.a.811.4		4	3.2	odd	2
1260.2.c.b.811.3		4	12.11	even	2
1260.2.c.b.811.4		4	21.20	even	2
2240.2.k.a.1791.1		4	8.5	even	2
2240.2.k.a.1791.2		4	56.27	even	2
2240.2.k.b.1791.3		4	8.3	odd	2
2240.2.k.b.1791.4		4	56.13	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 $\F_{q}$

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+(-1.36603 - 0.366025i) q^{2} +1.73205 q^{3} +(1.73205 + 1.00000i) q^{4} +1.00000i q^{5} +(-2.36603 - 0.633975i) q^{6} +(1.73205 + 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(0.366025 - 1.36603i) q^{10} +3.73205i q^{11} +(3.00000 + 1.73205i) q^{12} -6.46410i q^{13} +(-1.63397 - 3.36603i) q^{14} +1.73205i q^{15} +(2.00000 + 3.46410i) q^{16} -0.464102i q^{17} +6.00000 q^{19} +(-1.00000 + 1.73205i) q^{20} +(3.00000 + 3.46410i) q^{21} +(1.36603 - 5.09808i) q^{22} -5.46410i q^{23} +(-3.46410 - 3.46410i) q^{24} -1.00000 q^{25} +(-2.36603 + 8.83013i) q^{26} -5.19615 q^{27} +(1.00000 + 5.19615i) q^{28} -5.92820 q^{29} +(0.633975 - 2.36603i) q^{30} -6.00000 q^{31} +(-1.46410 - 5.46410i) q^{32} +6.46410i q^{33} +(-0.169873 + 0.633975i) q^{34} +(-2.00000 + 1.73205i) q^{35} -2.53590 q^{37} +(-8.19615 - 2.19615i) q^{38} -11.1962i q^{39} +(2.00000 - 2.00000i) q^{40} -3.46410i q^{41} +(-2.83013 - 5.83013i) q^{42} +2.00000i q^{43} +(-3.73205 + 6.46410i) q^{44} +(-2.00000 + 7.46410i) q^{46} -1.73205 q^{47} +(3.46410 + 6.00000i) q^{48} +(-1.00000 + 6.92820i) q^{49} +(1.36603 + 0.366025i) q^{50} -0.803848i q^{51} +(6.46410 - 11.1962i) q^{52} +2.00000 q^{53} +(7.09808 + 1.90192i) q^{54} -3.73205 q^{55} +(0.535898 - 7.46410i) q^{56} +10.3923 q^{57} +(8.09808 + 2.16987i) q^{58} +3.46410 q^{59} +(-1.73205 + 3.00000i) q^{60} -2.53590i q^{61} +(8.19615 + 2.19615i) q^{62} +8.00000i q^{64} +6.46410 q^{65} +(2.36603 - 8.83013i) q^{66} +3.46410i q^{67} +(0.464102 - 0.803848i) q^{68} -9.46410i q^{69} +(3.36603 - 1.63397i) q^{70} +0.535898i q^{71} +0.928203i q^{73} +(3.46410 + 0.928203i) q^{74} -1.73205 q^{75} +(10.3923 + 6.00000i) q^{76} +(-7.46410 + 6.46410i) q^{77} +(-4.09808 + 15.2942i) q^{78} -2.66025i q^{79} +(-3.46410 + 2.00000i) q^{80} -9.00000 q^{81} +(-1.26795 + 4.73205i) q^{82} +8.53590 q^{83} +(1.73205 + 9.00000i) q^{84} +0.464102 q^{85} +(0.732051 - 2.73205i) q^{86} -10.2679 q^{87} +(7.46410 - 7.46410i) q^{88} -9.46410i q^{89} +(12.9282 - 11.1962i) q^{91} +(5.46410 - 9.46410i) q^{92} -10.3923 q^{93} +(2.36603 + 0.633975i) q^{94} +6.00000i q^{95} +(-2.53590 - 9.46410i) q^{96} -7.39230i q^{97} +(3.90192 - 9.09808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 6 q^{6} - 8 q^{8} - 2 q^{10} + 12 q^{12} - 10 q^{14} + 8 q^{16} + 24 q^{19} - 4 q^{20} + 12 q^{21} + 2 q^{22} - 4 q^{25} - 6 q^{26} + 4 q^{28} + 4 q^{29} + 6 q^{30} - 24 q^{31} + 8 q^{32}+ \cdots + 26 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 6 * q^6 - 8 * q^8 - 2 * q^10 + 12 * q^12 - 10 * q^14 + 8 * q^16 + 24 * q^19 - 4 * q^20 + 12 * q^21 + 2 * q^22 - 4 * q^25 - 6 * q^26 + 4 * 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 + 6 * 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 + 10 * 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 + 26 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more