LMFDB - Embedded newform 308.2.n.a.263.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,2,Mod(219,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("308.219");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	308.n (of order $6$, degree $2$, 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:	$2.45939238226$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - x^{2} - 2x + 4 $ x^4 - x^3 - x^2 - 2*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			263.1
Root			$1.39564 + 0.228425i$ of defining polynomial
Character	$\chi$	$=$	308.263
Dual form			308.2.n.a.219.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39564 + 0.228425i) q^{2} +(-2.29129 - 1.32288i) q^{3} +(1.89564 - 0.637600i) q^{4} +(3.50000 + 1.32288i) q^{6} +(-0.500000 + 2.59808i) q^{7} +(-2.50000 + 1.32288i) q^{8} +(2.00000 + 3.46410i) q^{9} +(-1.29129 - 3.05493i) q^{11} +(-5.18693 - 1.04678i) q^{12} +2.64575i q^{13} +(0.104356 - 3.74020i) q^{14} +(3.18693 - 2.41733i) q^{16} +(4.58258 + 2.64575i) q^{17} +(-3.58258 - 4.37780i) q^{18} +(4.58258 - 5.29150i) q^{21} +(2.50000 + 3.96863i) q^{22} +(4.58258 - 2.64575i) q^{23} +(7.47822 + 0.276100i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-0.604356 - 3.69253i) q^{26} -2.64575i q^{27} +(0.708712 + 5.24383i) q^{28} -7.93725i q^{29} +(9.16515 + 5.29150i) q^{31} +(-3.89564 + 4.10170i) q^{32} +(-1.08258 + 8.70793i) q^{33} +(-7.00000 - 2.64575i) q^{34} +(6.00000 + 5.29150i) q^{36} +(4.00000 + 6.92820i) q^{37} +(3.50000 - 6.06218i) q^{39} +(-5.18693 + 8.43183i) q^{42} +2.00000 q^{43} +(-4.39564 - 4.96773i) q^{44} +(-5.79129 + 4.73930i) q^{46} +(-10.5000 + 1.32288i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(-2.50000 + 6.61438i) q^{50} +(-7.00000 - 12.1244i) q^{51} +(1.68693 + 5.01540i) q^{52} +(2.00000 - 3.46410i) q^{53} +(0.604356 + 3.69253i) q^{54} +(-2.18693 - 7.15663i) q^{56} +(1.81307 + 11.0776i) q^{58} +(2.29129 + 1.32288i) q^{59} +(-2.29129 + 1.32288i) q^{61} +(-14.0000 - 5.29150i) q^{62} +(-10.0000 + 3.46410i) q^{63} +(4.50000 - 6.61438i) q^{64} +(-0.478220 - 12.4005i) q^{66} +(2.29129 + 1.32288i) q^{67} +(10.3739 + 2.09355i) q^{68} -14.0000 q^{69} +5.29150i q^{71} +(-9.58258 - 6.01450i) q^{72} +(-9.16515 - 5.29150i) q^{73} +(-7.16515 - 8.75560i) q^{74} +(-11.4564 + 6.61438i) q^{75} +(8.58258 - 1.82740i) q^{77} +(-3.50000 + 9.26013i) q^{78} +(6.50000 + 11.2583i) q^{79} +(2.50000 - 4.33013i) q^{81} +(5.31307 - 12.9527i) q^{84} +(-2.79129 + 0.456850i) q^{86} +(-10.5000 + 18.1865i) q^{87} +(7.26951 + 5.92910i) q^{88} +(7.00000 + 12.1244i) q^{89} +(-6.87386 - 1.32288i) q^{91} +(7.00000 - 7.93725i) q^{92} +(-14.0000 - 24.2487i) q^{93} +(14.3521 - 4.24473i) q^{96} +7.00000 q^{97} +(9.66515 + 2.14123i) q^{98} +(8.00000 - 10.5830i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + 3 q^{4} + 14 q^{6} - 2 q^{7} - 10 q^{8} + 8 q^{9} + 4 q^{11} - 7 q^{12} + 5 q^{14} - q^{16} + 4 q^{18} + 10 q^{22} + 7 q^{24} + 10 q^{25} - 7 q^{26} + 12 q^{28} - 11 q^{32} + 14 q^{33} - 28 q^{34}+ \cdots + 32 q^{99}+O(q^{100}) $ 4 * q - q^2 + 3 * q^4 + 14 * q^6 - 2 * q^7 - 10 * q^8 + 8 * q^9 + 4 * q^11 - 7 * q^12 + 5 * q^14 - q^16 + 4 * q^18 + 10 * q^22 + 7 * q^24 + 10 * q^25 - 7 * q^26 + 12 * q^28 - 11 * q^32 + 14 * q^33 - 28 * q^34 + 24 * q^36 + 16 * q^37 + 14 * q^39 - 7 * q^42 + 8 * q^43 - 13 * q^44 - 14 * q^46 - 42 * q^48 - 26 * q^49 - 10 * q^50 - 28 * q^51 - 7 * q^52 + 8 * q^53 + 7 * q^54 + 5 * q^56 + 21 * q^58 - 56 * q^62 - 40 * q^63 + 18 * q^64 + 21 * q^66 + 14 * q^68 - 56 * q^69 - 20 * q^72 + 8 * q^74 + 16 * q^77 - 14 * q^78 + 26 * q^79 + 10 * q^81 + 35 * q^84 - 2 * q^86 - 42 * q^87 - 3 * q^88 + 28 * q^89 + 28 * q^92 - 56 * q^93 + 7 * q^96 + 28 * q^97 + 2 * q^98 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$

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 $

$2$	−1.39564	+	0.228425i	−0.986869	+	0.161521i
$2$	−1.39564	+	0.228425i	−0.986869	+	0.161521i
$3$	−2.29129	−	1.32288i	−1.32288	−	0.763763i	−0.338689	−	0.940898i	$-0.609984\pi$
$3$	−2.29129	−	1.32288i	−1.32288	−	0.763763i	−0.984186	+	0.177136i	$0.943317\pi$
$4$	1.89564	−	0.637600i	0.947822	−	0.318800i
$5$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$5$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$6$	3.50000	+	1.32288i	1.42887	+	0.540062i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$8$	−2.50000	+	1.32288i	−0.883883	+	0.467707i
$9$	2.00000	+	3.46410i	0.666667	+	1.15470i
$10$		0			0
$11$	−1.29129	−	3.05493i	−0.389338	−	0.921095i
$11$	−1.29129	−	3.05493i	−0.389338	−	0.921095i
$12$	−5.18693	−	1.04678i	−1.49734	−	0.302178i
$13$			2.64575i			0.733799i	0.930261	+	0.366900i	$0.119581\pi$
$13$			2.64575i			0.733799i	−0.930261	+	0.366900i	$0.880419\pi$
$14$	0.104356	−	3.74020i	0.0278903	−	0.999611i
$15$		0			0
$16$	3.18693	−	2.41733i	0.796733	−	0.604332i
$17$	4.58258	+	2.64575i	1.11144	+	0.641689i	0.939201	−	0.343367i	$-0.111567\pi$
$17$	4.58258	+	2.64575i	1.11144	+	0.641689i	0.172236	+	0.985056i	$0.444901\pi$
$18$	−3.58258	−	4.37780i	−0.844421	−	1.03186i
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$		0			0
$21$	4.58258	−	5.29150i	1.00000	−	1.15470i
$22$	2.50000	+	3.96863i	0.533002	+	0.846114i
$23$	4.58258	−	2.64575i	0.955533	−	0.551677i	0.0607377	−	0.998154i	$-0.480655\pi$
$23$	4.58258	−	2.64575i	0.955533	−	0.551677i	0.894795	+	0.446476i	$0.147321\pi$
$24$	7.47822	+	0.276100i	1.52649	+	0.0563587i
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$	−0.604356	−	3.69253i	−0.118524	−	0.724164i
$27$		−	2.64575i		−	0.509175i
$28$	0.708712	+	5.24383i	0.133934	+	0.990990i
$29$		−	7.93725i		−	1.47391i	−0.675941	−	0.736956i	$-0.736263\pi$
$29$		−	7.93725i		−	1.47391i	0.675941	−	0.736956i	$-0.263737\pi$
$30$		0			0
$31$	9.16515	+	5.29150i	1.64611	+	0.950382i	0.978598	+	0.205783i	$0.0659741\pi$
$31$	9.16515	+	5.29150i	1.64611	+	0.950382i	0.667512	+	0.744599i	$0.267359\pi$
$32$	−3.89564	+	4.10170i	−0.688659	+	0.725085i
$33$	−1.08258	+	8.70793i	−0.188452	+	1.51586i
$34$	−7.00000	−	2.64575i	−1.20049	−	0.453743i
$35$		0			0
$36$	6.00000	+	5.29150i	1.00000	+	0.881917i
$37$	4.00000	+	6.92820i	0.657596	+	1.13899i	0.981236	+	0.192809i	$0.0617599\pi$
$37$	4.00000	+	6.92820i	0.657596	+	1.13899i	−0.323640	+	0.946180i	$0.604907\pi$
$38$		0			0
$39$	3.50000	−	6.06218i	0.560449	−	0.970725i
$40$		0			0
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$	−5.18693	+	8.43183i	−0.800361	+	1.30106i
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	−4.39564	−	4.96773i	−0.662668	−	0.748913i
$45$		0			0
$46$	−5.79129	+	4.73930i	−0.853879	+	0.698772i
$47$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$47$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$48$	−10.5000	+	1.32288i	−1.51554	+	0.190941i
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	−2.50000	+	6.61438i	−0.353553	+	0.935414i
$51$	−7.00000	−	12.1244i	−0.980196	−	1.69775i
$52$	1.68693	+	5.01540i	0.233935	+	0.695511i
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	−0.695344	−	0.718677i	$-0.744748\pi$
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	0.970065	+	0.242846i	$0.0780811\pi$
$54$	0.604356	+	3.69253i	0.0822424	+	0.502489i
$55$		0			0
$56$	−2.18693	−	7.15663i	−0.292241	−	0.956345i
$57$		0			0
$58$	1.81307	+	11.0776i	0.238068	+	1.45456i
$59$	2.29129	+	1.32288i	0.298300	+	0.172224i	0.641679	−	0.766973i	$-0.278238\pi$
$59$	2.29129	+	1.32288i	0.298300	+	0.172224i	−0.343379	+	0.939197i	$0.611571\pi$
$60$		0			0
$61$	−2.29129	+	1.32288i	−0.293369	+	0.169377i	−0.639460	−	0.768824i	$-0.720842\pi$
$61$	−2.29129	+	1.32288i	−0.293369	+	0.169377i	0.346091	+	0.938201i	$0.387509\pi$
$62$	−14.0000	−	5.29150i	−1.77800	−	0.672022i
$63$	−10.0000	+	3.46410i	−1.25988	+	0.436436i
$64$	4.50000	−	6.61438i	0.562500	−	0.826797i
$65$		0			0
$66$	−0.478220	−	12.4005i	−0.0588648	−	1.52639i
$67$	2.29129	+	1.32288i	0.279925	+	0.161615i	0.633390	−	0.773833i	$-0.281663\pi$
$67$	2.29129	+	1.32288i	0.279925	+	0.161615i	−0.353464	+	0.935448i	$0.614996\pi$
$68$	10.3739	+	2.09355i	1.25802	+	0.253880i
$69$	−14.0000			−1.68540
$70$		0			0
$71$			5.29150i			0.627986i	0.949425	+	0.313993i	$0.101667\pi$
$71$			5.29150i			0.627986i	−0.949425	+	0.313993i	$0.898333\pi$
$72$	−9.58258	−	6.01450i	−1.12932	−	0.708816i
$73$	−9.16515	−	5.29150i	−1.07270	−	0.619324i	−0.143782	−	0.989609i	$-0.545926\pi$
$73$	−9.16515	−	5.29150i	−1.07270	−	0.619324i	−0.928918	+	0.370286i	$0.879260\pi$
$74$	−7.16515	−	8.75560i	−0.832932	−	1.01782i
$75$	−11.4564	+	6.61438i	−1.32288	+	0.763763i
$76$		0			0
$77$	8.58258	−	1.82740i	0.978075	−	0.208252i
$78$	−3.50000	+	9.26013i	−0.396297	+	1.04850i
$79$	6.50000	+	11.2583i	0.731307	+	1.26666i	0.956325	+	0.292306i	$0.0944227\pi$
$79$	6.50000	+	11.2583i	0.731307	+	1.26666i	−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$	2.50000	−	4.33013i	0.277778	−	0.481125i
$82$		0			0
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$	5.31307	−	12.9527i	0.579703	−	1.41325i
$85$		0			0
$86$	−2.79129	+	0.456850i	−0.300992	+	0.0492634i
$87$	−10.5000	+	18.1865i	−1.12572	+	1.94980i
$88$	7.26951	+	5.92910i	0.774932	+	0.632044i
$89$	7.00000	+	12.1244i	0.741999	+	1.28518i	0.951584	+	0.307389i	$0.0994552\pi$
$89$	7.00000	+	12.1244i	0.741999	+	1.28518i	−0.209585	+	0.977790i	$0.567211\pi$
$90$		0			0
$91$	−6.87386	−	1.32288i	−0.720577	−	0.138675i
$92$	7.00000	−	7.93725i	0.729800	−	0.827516i
$93$	−14.0000	−	24.2487i	−1.45173	−	2.51447i
$94$		0			0
$95$		0			0
$96$	14.3521	−	4.24473i	1.46480	−	0.433226i
$97$	7.00000			0.710742			0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000			0.710742			0.355371	+	0.934725i	$0.384354\pi$
$98$	9.66515	+	2.14123i	0.976328	+	0.216296i
$99$	8.00000	−	10.5830i	0.804030	−	1.06363i
$100$	1.97822	−	9.80238i	0.197822	−	0.980238i
$101$	6.87386	+	3.96863i	0.683975	+	0.394893i	0.801351	−	0.598194i	$-0.204115\pi$
$101$	6.87386	+	3.96863i	0.683975	+	0.394893i	−0.117376	+	0.993088i	$0.537448\pi$
$102$	12.5390	+	15.3223i	1.24155	+	1.51713i
$103$	−4.58258	+	2.64575i	−0.451535	+	0.260694i	−0.708478	−	0.705733i	$-0.750618\pi$
$103$	−4.58258	+	2.64575i	−0.451535	+	0.260694i	0.256943	+	0.966426i	$0.417285\pi$
$104$	−3.50000	−	6.61438i	−0.343203	−	0.648593i
$105$		0			0
$106$	−2.00000	+	5.29150i	−0.194257	+	0.513956i
$107$	4.00000	+	6.92820i	0.386695	+	0.669775i	0.992003	−	0.126217i	$-0.0402834\pi$
$107$	4.00000	+	6.92820i	0.386695	+	0.669775i	−0.605308	+	0.795991i	$0.706950\pi$
$108$	−1.68693	−	5.01540i	−0.162325	−	0.482607i
$109$	9.16515	+	5.29150i	0.877862	+	0.506834i	0.869953	−	0.493135i	$-0.164149\pi$
$109$	9.16515	+	5.29150i	0.877862	+	0.506834i	0.00790932	+	0.999969i	$0.497482\pi$
$110$		0			0
$111$		−	21.1660i		−	2.00899i
$112$	4.68693	+	9.48855i	0.442873	+	0.896584i
$113$	−19.0000			−1.78737			−0.893685	−	0.448695i	$-0.851889\pi$
$113$	−19.0000			−1.78737			−0.893685	+	0.448695i	$0.851889\pi$
$114$		0			0
$115$		0			0
$116$	−5.06080	−	15.0462i	−0.469883	−	1.39701i
$117$	−9.16515	+	5.29150i	−0.847319	+	0.489200i
$118$	−3.50000	−	1.32288i	−0.322201	−	0.121781i
$119$	−9.16515	+	10.5830i	−0.840168	+	0.970143i
$120$		0			0
$121$	−7.66515	+	7.88958i	−0.696832	+	0.717234i
$122$	2.89564	−	2.36965i	0.262159	−	0.214538i
$123$		0			0
$124$	20.7477	+	4.18710i	1.86320	+	0.376013i
$125$		0			0
$126$	13.1652	−	7.11890i	1.17284	−	0.634202i
$127$	5.00000			0.443678			0.221839	−	0.975083i	$-0.428794\pi$
$127$	5.00000			0.443678			0.221839	+	0.975083i	$0.428794\pi$
$128$	−4.76951	+	10.2592i	−0.421569	+	0.906796i
$129$	−4.58258	−	2.64575i	−0.403473	−	0.232945i
$130$		0			0
$131$	−7.00000	−	12.1244i	−0.611593	−	1.05931i	−0.990972	−	0.134069i	$-0.957196\pi$
$131$	−7.00000	−	12.1244i	−0.611593	−	1.05931i	0.379379	−	0.925241i	$-0.376138\pi$
$132$	3.50000	+	17.1974i	0.304636	+	1.49684i
$133$		0			0
$134$	−3.50000	−	1.32288i	−0.302354	−	0.114279i
$135$		0			0
$136$	−14.9564	−	0.552200i	−1.28250	−	0.0473508i
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	−0.922961	−	0.384893i	$-0.874238\pi$
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	0.794808	+	0.606861i	$0.207572\pi$
$138$	19.5390	−	3.19795i	1.66327	−	0.272228i
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$		0			0
$141$		0			0
$142$	−1.20871	−	7.38505i	−0.101433	−	0.619740i
$143$	8.08258	−	3.41643i	0.675899	−	0.285696i
$144$	14.7477	+	6.20520i	1.22898	+	0.517100i
$145$		0			0
$146$	14.0000	+	5.29150i	1.15865	+	0.437928i
$147$	11.4564	+	14.5516i	0.944911	+	1.20020i
$148$	12.0000	+	10.5830i	0.986394	+	0.869918i
$149$	−9.16515	+	5.29150i	−0.750838	+	0.433497i	−0.825997	−	0.563675i	$-0.809387\pi$
$149$	−9.16515	+	5.29150i	−0.750838	+	0.433497i	0.0751583	+	0.997172i	$0.476054\pi$
$150$	14.4782	−	11.8483i	1.18214	−	0.967406i
$151$	8.50000	−	14.7224i	0.691720	−	1.19809i	−0.279554	−	0.960130i	$-0.590186\pi$
$151$	8.50000	−	14.7224i	0.691720	−	1.19809i	0.971274	−	0.237964i	$-0.0764802\pi$
$152$		0			0
$153$			21.1660i			1.71117i
$154$	−11.5608	+	4.51088i	−0.931595	+	0.363497i
$155$		0			0
$156$	2.76951	−	13.7233i	0.221738	−	1.09875i
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	0.997609	−	0.0691164i	$-0.0220180\pi$
$158$	−11.6434	−	14.2279i	−0.926297	−	1.13191i
$159$	−9.16515	+	5.29150i	−0.726844	+	0.419643i
$160$		0			0
$161$	4.58258	+	13.2288i	0.361158	+	1.04257i
$162$	−2.50000	+	6.61438i	−0.196419	+	0.519675i
$163$	−2.29129	+	1.32288i	−0.179468	+	0.103616i	−0.587042	−	0.809556i	$-0.699708\pi$
$163$	−2.29129	+	1.32288i	−0.179468	+	0.103616i	0.407575	+	0.913172i	$0.366375\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−21.0000			−1.62503			−0.812514	−	0.582941i	$-0.801902\pi$
$167$	−21.0000			−1.62503			−0.812514	+	0.582941i	$0.801902\pi$
$168$	−4.45644	+	19.2909i	−0.343822	+	1.48833i
$169$	6.00000			0.461538
$170$		0			0
$171$		0			0
$172$	3.79129	−	1.27520i	0.289083	−	0.0972331i
$173$	11.4564	−	6.61438i	0.871017	−	0.502882i	0.00333090	−	0.999994i	$-0.498940\pi$
$173$	11.4564	−	6.61438i	0.871017	−	0.502882i	0.867686	+	0.497113i	$0.165606\pi$
$174$	10.5000	−	27.7804i	0.796003	−	2.10603i
$175$	10.0000	+	8.66025i	0.755929	+	0.654654i
$176$	−11.5000	−	6.61438i	−0.866845	−	0.498578i
$177$	−3.50000	−	6.06218i	−0.263076	−	0.455661i
$178$	−12.5390	−	15.3223i	−0.939839	−	1.14846i
$179$	−6.87386	−	3.96863i	−0.513777	−	0.296629i	0.220608	−	0.975363i	$-0.429196\pi$
$179$	−6.87386	−	3.96863i	−0.513777	−	0.296629i	−0.734385	+	0.678733i	$0.762529\pi$
$180$		0			0
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$	9.89564	+	0.276100i	0.733514	+	0.0204659i
$183$	7.00000			0.517455
$184$	−7.95644	+	12.6766i	−0.586556	+	0.934528i
$185$		0			0
$186$	25.0780	+	30.6446i	1.83881	+	2.24697i
$187$	2.16515	−	17.4159i	0.158332	−	1.27357i
$188$		0			0
$189$	6.87386	+	1.32288i	0.500000	+	0.0962250i
$190$		0			0
$191$	9.16515	−	5.29150i	0.663167	−	0.382880i	−0.130316	−	0.991473i	$-0.541599\pi$
$191$	9.16515	−	5.29150i	0.663167	−	0.382880i	0.793483	+	0.608593i	$0.208266\pi$
$192$	−19.0608	+	9.20250i	−1.37559	+	0.664134i
$193$	−18.3303	−	10.5830i	−1.31944	−	0.761781i	−0.335805	−	0.941932i	$-0.609008\pi$
$193$	−18.3303	−	10.5830i	−1.31944	−	0.761781i	−0.983639	+	0.180150i	$0.942342\pi$
$194$	−9.76951	+	1.59898i	−0.701410	+	0.114800i
$195$		0			0
$196$	−13.9782	−	0.780626i	−0.998444	−	0.0557590i
$197$		−	7.93725i		−	0.565506i	−0.959193	−	0.282753i	$-0.908752\pi$
$197$		−	7.93725i		−	0.565506i	0.959193	−	0.282753i	$-0.0912477\pi$
$198$	−8.74773	+	16.5975i	−0.621674	+	1.17953i
$199$	−9.16515	−	5.29150i	−0.649700	−	0.375105i	0.138641	−	0.990343i	$-0.455727\pi$
$199$	−9.16515	−	5.29150i	−0.649700	−	0.375105i	−0.788341	+	0.615238i	$0.789060\pi$
$200$	−0.521780	+	14.1325i	−0.0368954	+	0.999319i
$201$	−3.50000	−	6.06218i	−0.246871	−	0.427593i
$202$	−10.5000	−	3.96863i	−0.738777	−	0.279232i
$203$	20.6216	+	3.96863i	1.44735	+	0.278543i
$204$	−21.0000	−	18.5203i	−1.47029	−	1.29668i
$205$		0			0
$206$	5.79129	−	4.73930i	0.403498	−	0.330203i
$207$	18.3303	+	10.5830i	1.27404	+	0.735570i
$208$	6.39564	+	8.43183i	0.443458	+	0.584642i
$209$		0			0
$210$		0			0
$211$	−2.00000			−0.137686			−0.0688428	−	0.997628i	$-0.521931\pi$
$211$	−2.00000			−0.137686			−0.0688428	+	0.997628i	$0.521931\pi$
$212$	1.58258	−	7.84190i	0.108692	−	0.538584i
$213$	7.00000	−	12.1244i	0.479632	−	0.830747i
$214$	−7.16515	−	8.75560i	−0.489800	−	0.598521i
$215$		0			0
$216$	3.50000	+	6.61438i	0.238145	+	0.450051i
$217$	−18.3303	+	21.1660i	−1.24434	+	1.43684i
$218$	−14.0000	−	5.29150i	−0.948200	−	0.358386i
$219$	14.0000	+	24.2487i	0.946032	+	1.63858i
$220$		0			0
$221$	−7.00000	+	12.1244i	−0.470871	+	0.815572i
$222$	4.83485	+	29.5402i	0.324494	+	1.98261i
$223$		−	15.8745i		−	1.06304i	−0.847047	−	0.531518i	$-0.821622\pi$
$223$		−	15.8745i		−	1.06304i	0.847047	−	0.531518i	$-0.178378\pi$
$224$	−8.70871	−	12.1720i	−0.581875	−	0.813278i
$225$	20.0000			1.33333
$226$	26.5172	−	4.34008i	1.76390	−	0.288698i
$227$	7.00000	−	12.1244i	0.464606	−	0.804722i	−0.534577	−	0.845120i	$-0.679529\pi$
$227$	7.00000	−	12.1244i	0.464606	−	0.804722i	0.999184	+	0.0403978i	$0.0128625\pi$
$228$		0			0
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	0.536515	−	0.843891i	$-0.319740\pi$
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	−0.999088	+	0.0426906i	$0.986407\pi$
$230$		0			0
$231$	−22.0826	−	7.16658i	−1.45293	−	0.471526i
$232$	10.5000	+	19.8431i	0.689359	+	1.30277i
$233$	13.7477	−	7.93725i	0.900644	−	0.519987i	0.0232346	−	0.999730i	$-0.492604\pi$
$233$	13.7477	−	7.93725i	0.900644	−	0.519987i	0.877409	+	0.479743i	$0.159270\pi$
$234$	11.5826	−	9.47860i	0.757177	−	0.619636i
$235$		0			0
$236$	5.18693	+	1.04678i	0.337640	+	0.0681393i
$237$		−	34.3948i		−	2.23418i
$238$	10.3739	−	16.8637i	0.672438	−	1.09311i
$239$	19.0000			1.22901			0.614504	−	0.788914i	$-0.289356\pi$
$239$	19.0000			1.22901			0.614504	+	0.788914i	$0.289356\pi$
$240$		0			0
$241$	4.58258	+	2.64575i	0.295190	+	0.170428i	0.640280	−	0.768142i	$-0.278818\pi$
$241$	4.58258	+	2.64575i	0.295190	+	0.170428i	−0.345090	+	0.938570i	$0.612152\pi$
$242$	8.89564	−	12.7620i	0.571834	−	0.820370i
$243$	−18.3303	+	10.5830i	−1.17589	+	0.678900i
$244$	−3.50000	+	3.96863i	−0.224065	+	0.254065i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−29.9129	−	1.10440i	−1.89947	−	0.0701295i
$249$		0			0
$250$		0			0
$251$			15.8745i			1.00199i	0.865450	+	0.500995i	$0.167033\pi$
$251$			15.8745i			1.00199i	−0.865450	+	0.500995i	$0.832967\pi$
$252$	−16.7477	+	12.9427i	−1.05501	+	0.815314i
$253$	−14.0000	−	10.5830i	−0.880172	−	0.665348i
$254$	−6.97822	+	1.14213i	−0.437852	+	0.0716633i
$255$		0			0
$256$	4.31307	−	15.4077i	0.269567	−	0.962982i
$257$	3.50000	+	6.06218i	0.218324	+	0.378148i	0.954296	−	0.298864i	$-0.0966077\pi$
$257$	3.50000	+	6.06218i	0.218324	+	0.378148i	−0.735972	+	0.677012i	$0.763274\pi$
$258$	7.00000	+	2.64575i	0.435801	+	0.164717i
$259$	−20.0000	+	6.92820i	−1.24274	+	0.430498i
$260$		0			0
$261$	27.4955	−	15.8745i	1.70193	−	0.982607i
$262$	12.5390	+	15.3223i	0.774663	+	0.946615i
$263$	5.50000	−	9.52628i	0.339145	−	0.587416i	−0.645128	−	0.764075i	$-0.723196\pi$
$263$	5.50000	−	9.52628i	0.339145	−	0.587416i	0.984272	+	0.176659i	$0.0565291\pi$
$264$	−8.81307	−	23.2019i	−0.542407	−	1.42798i
$265$		0			0
$266$		0			0
$267$		−	37.0405i		−	2.26684i
$268$	5.18693	+	1.04678i	0.316842	+	0.0639420i
$269$	−14.0000	+	24.2487i	−0.853595	+	1.47847i	0.0243472	+	0.999704i	$0.492249\pi$
$269$	−14.0000	+	24.2487i	−0.853595	+	1.47847i	−0.877942	+	0.478766i	$0.841084\pi$
$270$		0			0
$271$	−3.50000	−	6.06218i	−0.212610	−	0.368251i	0.739921	−	0.672694i	$-0.234863\pi$
$271$	−3.50000	−	6.06218i	−0.212610	−	0.368251i	−0.952531	+	0.304443i	$0.901530\pi$
$272$	21.0000	−	2.64575i	1.27331	−	0.160422i
$273$	14.0000	+	12.1244i	0.847319	+	0.733799i
$274$	1.50000	−	3.96863i	0.0906183	−	0.239754i
$275$	−16.4564	−	2.04588i	−0.992361	−	0.123371i
$276$	−26.5390	+	8.92640i	−1.59746	+	0.537306i
$277$	−11.4564	−	6.61438i	−0.688351	−	0.397419i	0.114643	−	0.993407i	$-0.463428\pi$
$277$	−11.4564	−	6.61438i	−0.688351	−	0.397419i	−0.802994	+	0.595987i	$0.796761\pi$
$278$	−19.5390	+	3.19795i	−1.17187	+	0.191800i
$279$			42.3320i			2.53435i
$280$		0			0
$281$			15.8745i			0.946994i	0.880795	+	0.473497i	$0.157008\pi$
$281$			15.8745i			0.946994i	−0.880795	+	0.473497i	$0.842992\pi$
$282$		0			0
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	0.0640654	+	0.997946i	$0.479593\pi$
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	−0.896279	+	0.443491i	$0.853740\pi$
$284$	3.37386	+	10.0308i	0.200202	+	0.595219i
$285$		0			0
$286$	−10.5000	+	6.61438i	−0.620878	+	0.391116i
$287$		0			0
$288$	−22.0000	−	5.29150i	−1.29636	−	0.311805i
$289$	5.50000	+	9.52628i	0.323529	+	0.560369i
$290$		0			0
$291$	−16.0390	−	9.26013i	−0.940224	−	0.542838i
$292$	−20.7477	−	4.18710i	−1.21417	−	0.245032i
$293$			21.1660i			1.23653i	0.785969	+	0.618266i	$0.212164\pi$
$293$			21.1660i			1.23653i	−0.785969	+	0.618266i	$0.787836\pi$
$294$	−19.3131	−	17.6920i	−1.12636	−	1.03182i
$295$		0			0
$296$	−19.1652	−	12.0290i	−1.11395	−	0.699172i
$297$	−8.08258	+	3.41643i	−0.468999	+	0.198241i
$298$	11.5826	−	9.47860i	0.670961	−	0.549081i
$299$	7.00000	+	12.1244i	0.404820	+	0.701170i
$300$	−17.5000	+	19.8431i	−1.01036	+	1.14564i
$301$	−1.00000	+	5.19615i	−0.0576390	+	0.299501i
$302$	−8.50000	+	22.4889i	−0.489120	+	1.29409i
$303$	−10.5000	−	18.1865i	−0.603209	−	1.04479i
$304$		0			0
$305$		0			0
$306$	−4.83485	−	29.5402i	−0.276390	−	1.68870i
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$	15.1044	−	8.93635i	0.860651	−	0.509196i
$309$	14.0000			0.796432
$310$		0			0
$311$	−9.16515	−	5.29150i	−0.519708	−	0.300054i	0.217107	−	0.976148i	$-0.430338\pi$
$311$	−9.16515	−	5.29150i	−0.519708	−	0.300054i	−0.736815	+	0.676094i	$0.763671\pi$
$312$	−0.730493	+	19.7855i	−0.0413560	+	1.12013i
$313$	10.5000	+	18.1865i	0.593495	+	1.02796i	0.993757	+	0.111563i	$0.0355857\pi$
$313$	10.5000	+	18.1865i	0.593495	+	1.02796i	−0.400262	+	0.916401i	$0.631081\pi$
$314$	−7.00000	+	18.5203i	−0.395033	+	1.04516i
$315$		0			0
$316$	19.5000	+	17.1974i	1.09696	+	0.967428i
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	0.937892	−	0.346929i	$-0.112775\pi$
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	−0.769395	+	0.638774i	$0.779442\pi$
$318$	11.5826	−	9.47860i	0.649519	−	0.531534i
$319$	−24.2477	+	10.2493i	−1.35761	+	0.573849i
$320$		0			0
$321$		−	21.1660i		−	1.18137i
$322$	−9.41742	−	17.4159i	−0.524813	−	0.970548i
$323$		0			0
$324$	1.97822	−	9.80238i	0.109901	−	0.544577i
$325$	11.4564	+	6.61438i	0.635489	+	0.366900i
$326$	2.89564	−	2.36965i	0.160375	−	0.131243i
$327$	−14.0000	−	24.2487i	−0.774202	−	1.34096i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	20.6216	−	11.9059i	1.13347	−	0.654406i	0.188661	−	0.982042i	$-0.439585\pi$
$331$	20.6216	−	11.9059i	1.13347	−	0.654406i	0.944804	+	0.327636i	$0.106252\pi$
$332$		0			0
$333$	−16.0000	+	27.7128i	−0.876795	+	1.51865i
$334$	29.3085	−	4.79693i	1.60369	−	0.262476i
$335$		0			0
$336$	1.81307	−	27.9412i	0.0989110	−	1.52432i
$337$		−	15.8745i		−	0.864740i	−0.901696	−	0.432370i	$-0.857678\pi$
$337$		−	15.8745i		−	0.864740i	0.901696	−	0.432370i	$-0.142322\pi$
$338$	−8.37386	+	1.37055i	−0.455478	+	0.0745481i
$339$	43.5345	+	25.1346i	2.36447	+	1.36513i
$340$		0			0
$341$	4.33030	−	34.8317i	0.234499	−	1.88624i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−5.00000	+	2.64575i	−0.269582	+	0.142649i
$345$		0			0
$346$	−14.4782	+	11.8483i	−0.778354	+	0.636966i
$347$	−9.00000	+	15.5885i	−0.483145	+	0.836832i	−0.999813	−	0.0193540i	$-0.993839\pi$
$347$	−9.00000	+	15.5885i	−0.483145	+	0.836832i	0.516667	+	0.856186i	$0.327172\pi$
$348$	−8.30852	+	41.1700i	−0.445384	+	2.20694i
$349$		−	10.5830i		−	0.566495i	−0.959047	−	0.283248i	$-0.908588\pi$
$349$		−	10.5830i		−	0.566495i	0.959047	−	0.283248i	$-0.0914118\pi$
$350$	−15.9347	−	9.80238i	−0.851743	−	0.523959i
$351$	7.00000			0.373632
$352$	17.5608	+	6.60443i	0.935994	+	0.352017i
$353$	−7.00000	+	12.1244i	−0.372572	+	0.645314i	−0.989960	−	0.141344i	$-0.954858\pi$
$353$	−7.00000	+	12.1244i	−0.372572	+	0.645314i	0.617388	+	0.786659i	$0.288191\pi$
$354$	6.26951	+	7.66115i	0.333221	+	0.407186i
$355$		0			0
$356$	21.0000	+	18.5203i	1.11300	+	0.981572i
$357$	35.0000	−	12.1244i	1.85240	−	0.641689i
$358$	10.5000	+	3.96863i	0.554942	+	0.209748i
$359$	−7.50000	−	12.9904i	−0.395835	−	0.685606i	0.597372	−	0.801964i	$-0.296211\pi$
$359$	−7.50000	−	12.9904i	−0.395835	−	0.685606i	−0.993207	+	0.116358i	$0.962878\pi$
$360$		0			0
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$		0			0
$363$	28.0000	−	7.93725i	1.46962	−	0.416598i
$364$	−13.8739	+	1.87508i	−0.727188	+	0.0982807i
$365$		0			0
$366$	−9.76951	+	1.59898i	−0.510660	+	0.0835798i
$367$	−13.7477	−	7.93725i	−0.717626	−	0.414321i	0.0962526	−	0.995357i	$-0.469314\pi$
$367$	−13.7477	−	7.93725i	−0.717626	−	0.414321i	−0.813878	+	0.581036i	$0.802648\pi$
$368$	8.20871	−	19.5094i	0.427909	−	1.01700i
$369$		0			0
$370$		0			0
$371$	8.00000	+	6.92820i	0.415339	+	0.359694i
$372$	−42.0000	−	37.0405i	−2.17760	−	1.92046i
$373$	20.6216	−	11.9059i	1.06775	−	0.616463i	0.140181	−	0.990126i	$-0.455232\pi$
$373$	20.6216	−	11.9059i	1.06775	−	0.616463i	0.927565	+	0.373663i	$0.121898\pi$
$374$	0.956439	+	24.8009i	0.0494563	+	1.28242i
$375$		0			0
$376$		0			0
$377$	21.0000			1.08156
$378$	−9.89564	−	0.276100i	−0.508977	−	0.0142011i
$379$			18.5203i			0.951322i	0.879629	+	0.475661i	$0.157791\pi$
$379$			18.5203i			0.951322i	−0.879629	+	0.475661i	$0.842209\pi$
$380$		0			0
$381$	−11.4564	−	6.61438i	−0.586931	−	0.338865i
$382$	−11.5826	+	9.47860i	−0.592616	+	0.484968i
$383$	13.7477	−	7.93725i	0.702476	−	0.405575i	−0.105793	−	0.994388i	$-0.533738\pi$
$383$	13.7477	−	7.93725i	0.702476	−	0.405575i	0.808269	+	0.588813i	$0.200405\pi$
$384$	24.5000	−	17.1974i	1.25026	−	0.877600i
$385$		0			0
$386$	28.0000	+	10.5830i	1.42516	+	0.538661i
$387$	4.00000	+	6.92820i	0.203331	+	0.352180i
$388$	13.2695	−	4.46320i	0.673657	−	0.226585i
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	−0.998763	−	0.0497253i	$-0.984165\pi$
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	0.542445	+	0.840091i	$0.317499\pi$
$390$		0			0
$391$	28.0000			1.41602
$392$	19.6869	−	2.10350i	0.994340	−	0.106243i
$393$			37.0405i			1.86845i
$394$	1.81307	+	11.0776i	0.0913411	+	0.558080i
$395$		0			0
$396$	8.41742	−	25.1624i	0.422991	−	1.26446i
$397$	−14.0000	−	24.2487i	−0.702640	−	1.21701i	−0.967537	−	0.252731i	$-0.918671\pi$
$397$	−14.0000	−	24.2487i	−0.702640	−	1.21701i	0.264897	−	0.964277i	$-0.414662\pi$
$398$	14.0000	+	5.29150i	0.701757	+	0.265239i
$399$		0			0
$400$	−2.50000	−	19.8431i	−0.125000	−	0.992157i
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	0.976714	+	0.214544i	$0.0688266\pi$
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	−0.302556	+	0.953131i	$0.597840\pi$
$402$	6.26951	+	7.66115i	0.312695	+	0.382104i
$403$	−14.0000	+	24.2487i	−0.697390	+	1.20791i
$404$	15.5608	+	3.14033i	0.774179	+	0.156237i
$405$		0			0
$406$	−29.6869	−	0.828301i	−1.47334	−	0.0411079i
$407$	16.0000	−	21.1660i	0.793091	−	1.04916i
$408$	33.5390	+	21.0508i	1.66043	+	1.04217i
$409$	32.0780	+	18.5203i	1.58616	+	0.915768i	0.993932	+	0.109995i	$0.0350834\pi$
$409$	32.0780	+	18.5203i	1.58616	+	0.915768i	0.592224	+	0.805773i	$0.298250\pi$
$410$		0			0
$411$	6.87386	−	3.96863i	0.339063	−	0.195758i
$412$	−7.00000	+	7.93725i	−0.344865	+	0.391040i
$413$	−4.58258	+	5.29150i	−0.225494	+	0.260378i
$414$	−28.0000	−	10.5830i	−1.37612	−	0.520126i
$415$		0			0
$416$	−10.8521	−	10.3069i	−0.532067	−	0.505338i
$417$	−32.0780	−	18.5203i	−1.57087	−	0.906941i
$418$		0			0
$419$		−	5.29150i		−	0.258507i	−0.991612	−	0.129253i	$-0.958742\pi$
$419$		−	5.29150i		−	0.258507i	0.991612	−	0.129253i	$-0.0412581\pi$
$420$		0			0
$421$	12.0000			0.584844			0.292422	−	0.956289i	$-0.405539\pi$
$421$	12.0000			0.584844			0.292422	+	0.956289i	$0.405539\pi$
$422$	2.79129	−	0.456850i	0.135878	−	0.0222391i
$423$		0			0
$424$	−0.417424	+	11.3060i	−0.0202719	+	0.549068i
$425$	22.9129	−	13.2288i	1.11144	−	0.641689i
$426$	−7.00000	+	18.5203i	−0.339151	+	0.897309i
$427$	−2.29129	−	6.61438i	−0.110883	−	0.320092i
$428$	12.0000	+	10.5830i	0.580042	+	0.511549i
$429$	−23.0390	−	2.86423i	−1.11233	−	0.138286i
$430$		0			0
$431$	1.50000	−	2.59808i	0.0722525	−	0.125145i	−0.827636	−	0.561266i	$-0.810315\pi$
$431$	1.50000	−	2.59808i	0.0722525	−	0.125145i	0.899888	+	0.436121i	$0.143648\pi$
$432$	−6.39564	−	8.43183i	−0.307711	−	0.405677i
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$	20.7477	−	33.7273i	0.995923	−	1.61896i
$435$		0			0
$436$	20.7477	+	4.18710i	0.993636	+	0.200526i
$437$		0			0
$438$	−25.0780	−	30.6446i	−1.19827	−	1.46426i
$439$	−17.5000	−	30.3109i	−0.835229	−	1.44666i	−0.893843	−	0.448379i	$-0.852001\pi$
$439$	−17.5000	−	30.3109i	−0.835229	−	1.44666i	0.0586141	−	0.998281i	$-0.481332\pi$
$440$		0			0
$441$	−4.00000	−	27.7128i	−0.190476	−	1.31966i
$442$	7.00000	−	18.5203i	0.332956	−	0.880919i
$443$	32.0780	−	18.5203i	1.52407	−	0.879924i	0.524479	−	0.851423i	$-0.324260\pi$
$443$	32.0780	−	18.5203i	1.52407	−	0.879924i	0.999594	−	0.0285009i	$-0.00907336\pi$
$444$	−13.4955	−	40.1232i	−0.640466	−	1.90416i
$445$		0			0
$446$	3.62614	+	22.1552i	0.171703	+	1.04908i
$447$	28.0000			1.32435
$448$	14.9347	+	14.9985i	0.705596	+	0.708614i
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$	−27.9129	+	4.56850i	−1.31583	+	0.215361i
$451$		0			0
$452$	−36.0172	+	12.1144i	−1.69411	+	0.569814i
$453$	−38.9519	+	22.4889i	−1.83012	+	1.05662i
$454$	−7.00000	+	18.5203i	−0.328526	+	0.869199i
$455$		0			0
$456$		0			0
$457$	4.58258	−	2.64575i	0.214364	−	0.123763i	−0.388974	−	0.921249i	$-0.627170\pi$
$457$	4.58258	−	2.64575i	0.214364	−	0.123763i	0.603338	+	0.797486i	$0.293837\pi$
$458$	12.5390	+	15.3223i	0.585910	+	0.715964i
$459$	7.00000	−	12.1244i	0.326732	−	0.565916i
$460$		0			0
$461$			7.93725i			0.369675i	0.982769	+	0.184837i	$0.0591758\pi$
$461$			7.93725i			0.369675i	−0.982769	+	0.184837i	$0.940824\pi$
$462$	32.4564	+	4.95778i	1.51001	+	0.230657i
$463$			21.1660i			0.983668i	0.870689	+	0.491834i	$0.163673\pi$
$463$			21.1660i			0.983668i	−0.870689	+	0.491834i	$0.836327\pi$
$464$	−19.1869	−	25.2955i	−0.890731	−	1.17431i
$465$		0			0
$466$	−17.3739	+	14.2179i	−0.804829	+	0.658632i
$467$	−13.7477	+	7.93725i	−0.636169	+	0.367292i	−0.783137	−	0.621849i	$-0.786382\pi$
$467$	−13.7477	+	7.93725i	−0.636169	+	0.367292i	0.146968	+	0.989141i	$0.453048\pi$
$468$	−14.0000	+	15.8745i	−0.647150	+	0.733799i
$469$	−4.58258	+	5.29150i	−0.211604	+	0.244339i
$470$		0			0
$471$	−32.0780	+	18.5203i	−1.47808	+	0.853368i
$472$	−7.47822	−	0.276100i	−0.344213	−	0.0127085i
$473$	−2.58258	−	6.10985i	−0.118747	−	0.280931i
$474$	7.85663	+	48.0028i	0.360867	+	2.20484i
$475$		0			0
$476$	−10.6261	+	25.9053i	−0.487048	+	1.18737i
$477$	16.0000			0.732590
$478$	−26.5172	+	4.34008i	−1.21287	+	0.198511i
$479$	10.5000	−	18.1865i	0.479757	−	0.830964i	−0.519973	−	0.854183i	$-0.674058\pi$
$479$	10.5000	−	18.1865i	0.479757	−	0.830964i	0.999730	+	0.0232187i	$0.00739140\pi$
$480$		0			0
$481$	−18.3303	+	10.5830i	−0.835790	+	0.482544i
$482$	−7.00000	−	2.64575i	−0.318841	−	0.120511i
$483$	7.00000	−	36.3731i	0.318511	−	1.65503i
$484$	−9.50000	+	19.8431i	−0.431818	+	0.901961i
$485$		0			0
$486$	23.1652	−	18.9572i	1.05079	−	0.859916i
$487$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$487$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$488$	3.97822	−	6.33828i	0.180086	−	0.286920i
$489$	7.00000			0.316551
$490$		0			0
$491$	−26.0000			−1.17336			−0.586682	−	0.809818i	$-0.699566\pi$
$491$	−26.0000			−1.17336			−0.586682	+	0.809818i	$0.699566\pi$
$492$		0			0
$493$	21.0000	−	36.3731i	0.945792	−	1.63816i
$494$		0			0
$495$		0			0
$496$	42.0000	−	5.29150i	1.88586	−	0.237595i
$497$	−13.7477	−	2.64575i	−0.616670	−	0.118678i
$498$		0			0
$499$	−22.9129	+	13.2288i	−1.02572	+	0.592200i	−0.915756	−	0.401735i	$-0.868407\pi$
$499$	−22.9129	+	13.2288i	−1.02572	+	0.592200i	−0.109965	+	0.993935i	$0.535074\pi$
$500$		0			0
$501$	48.1170	+	27.7804i	2.14971	+	1.24114i
$502$	−3.62614	−	22.1552i	−0.161842	−	0.988833i
$503$	−7.00000			−0.312115			−0.156057	−	0.987748i	$-0.549878\pi$
$503$	−7.00000			−0.312115			−0.156057	+	0.987748i	$0.549878\pi$
$504$	20.4174	−	21.8890i	0.909464	−	0.975014i
$505$		0			0
$506$	21.9564	+	11.5722i	0.976083	+	0.514445i
$507$	−13.7477	−	7.93725i	−0.610558	−	0.352506i
$508$	9.47822	−	3.18800i	0.420528	−	0.141445i
$509$	7.00000	+	12.1244i	0.310270	+	0.537403i	0.978421	−	0.206623i	$-0.0662474\pi$
$509$	7.00000	+	12.1244i	0.310270	+	0.537403i	−0.668151	+	0.744026i	$0.732914\pi$
$510$		0			0
$511$	18.3303	−	21.1660i	0.810885	−	0.936329i
$512$	−2.50000	+	22.4889i	−0.110485	+	0.993878i
$513$		0			0
$514$	−6.26951	−	7.66115i	−0.276536	−	0.337919i
$515$		0			0
$516$	−10.3739	−	2.09355i	−0.456684	−	0.0921634i
$517$		0			0
$518$	26.3303	−	14.2378i	1.15689	−	0.625573i
$519$	−35.0000			−1.53633
$520$		0			0
$521$	21.0000	−	36.3731i	0.920027	−	1.59353i	0.120656	−	0.992694i	$-0.461500\pi$
$521$	21.0000	−	36.3731i	0.920027	−	1.59353i	0.799370	−	0.600839i	$-0.205167\pi$
$522$	−34.7477	+	28.4358i	−1.52087	+	1.24460i
$523$	7.00000	+	12.1244i	0.306089	+	0.530161i	0.977503	−	0.210921i	$-0.0676463\pi$
$523$	7.00000	+	12.1244i	0.306089	+	0.530161i	−0.671414	+	0.741082i	$0.734313\pi$
$524$	−21.0000	−	18.5203i	−0.917389	−	0.809061i
$525$	−11.4564	−	33.0719i	−0.500000	−	1.44338i
$526$	−5.50000	+	14.5516i	−0.239811	+	0.634481i
$527$	28.0000	+	48.4974i	1.21970	+	2.11258i
$528$	17.5998	+	30.3685i	0.765933	+	1.32162i
$529$	2.50000	−	4.33013i	0.108696	−	0.188266i
$530$		0			0
$531$			10.5830i			0.459263i
$532$		0			0
$533$		0			0
$534$	8.46099	+	51.6954i	0.366143	+	2.23708i
$535$		0			0
$536$	−7.47822	−	0.276100i	−0.323010	−	0.0119257i
$537$	10.5000	+	18.1865i	0.453108	+	0.784807i
$538$	14.0000	−	37.0405i	0.603583	−	1.59693i
$539$	0.456439	+	23.2119i	0.0196602	+	0.999807i
$540$		0			0
$541$	−20.6216	+	11.9059i	−0.886591	+	0.511874i	−0.872826	−	0.488031i	$-0.837715\pi$
$541$	−20.6216	+	11.9059i	−0.886591	+	0.511874i	−0.0137654	+	0.999905i	$0.504382\pi$
$542$	6.26951	+	7.66115i	0.269298	+	0.329075i
$543$		0			0
$544$	−28.7042	+	8.48945i	−1.23068	+	0.363982i
$545$		0			0
$546$	−22.3085	−	13.7233i	−0.954717	−	0.587304i
$547$	−2.00000			−0.0855138			−0.0427569	−	0.999086i	$-0.513614\pi$
$547$	−2.00000			−0.0855138			−0.0427569	+	0.999086i	$0.513614\pi$
$548$	−1.18693	+	5.88143i	−0.0507032	+	0.251242i
$549$	−9.16515	−	5.29150i	−0.391159	−	0.225836i
$550$	23.4347	−	0.903750i	0.999257	−	0.0385360i
$551$		0			0
$552$	35.0000	−	18.5203i	1.48970	−	0.788275i
$553$	−32.5000	+	11.2583i	−1.38204	+	0.478753i
$554$	17.5000	+	6.61438i	0.743504	+	0.281018i
$555$		0			0
$556$	26.5390	−	8.92640i	1.12550	−	0.378564i
$557$	9.16515	+	5.29150i	0.388340	+	0.224208i	0.681441	−	0.731873i	$-0.261354\pi$
$557$	9.16515	+	5.29150i	0.388340	+	0.224208i	−0.293101	+	0.956082i	$0.594687\pi$
$558$	−9.66970	−	59.0804i	−0.409351	−	2.50107i
$559$			5.29150i			0.223807i
$560$		0			0
$561$	−28.0000	+	37.0405i	−1.18216	+	1.56385i
$562$	−3.62614	−	22.1552i	−0.152959	−	0.934559i
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$		0			0
$565$		0			0
$566$	14.0000	−	37.0405i	0.588464	−	1.55693i
$567$	10.0000	+	8.66025i	0.419961	+	0.363696i
$568$	−7.00000	−	13.2288i	−0.293713	−	0.555066i
$569$	−27.4955	+	15.8745i	−1.15267	+	0.665494i	−0.949536	−	0.313657i	$-0.898446\pi$
$569$	−27.4955	+	15.8745i	−1.15267	+	0.665494i	−0.203133	+	0.979151i	$0.565112\pi$
$570$		0			0
$571$	9.00000	−	15.5885i	0.376638	−	0.652357i	−0.613933	−	0.789359i	$-0.710413\pi$
$571$	9.00000	−	15.5885i	0.376638	−	0.652357i	0.990571	+	0.137002i	$0.0437466\pi$
$572$	13.1434	−	11.6298i	0.549552	−	0.486266i
$573$	−28.0000			−1.16972
$574$		0			0
$575$		−	26.4575i		−	1.10335i
$576$	31.9129	+	2.35970i	1.32970	+	0.0983209i
$577$	−17.5000	+	30.3109i	−0.728535	+	1.26186i	0.228968	+	0.973434i	$0.426465\pi$
$577$	−17.5000	+	30.3109i	−0.728535	+	1.26186i	−0.957503	+	0.288425i	$0.906868\pi$
$578$	−9.85208	−	12.0390i	−0.409793	−	0.500755i
$579$	28.0000	+	48.4974i	1.16364	+	2.01548i
$580$		0			0
$581$		0			0
$582$	24.5000	+	9.26013i	1.01556	+	0.383845i
$583$	−13.1652	−	1.63670i	−0.545245	−	0.0677852i
$584$	29.9129	+	1.10440i	1.23780	+	0.0457004i
$585$		0			0
$586$	−4.83485	−	29.5402i	−0.199726	−	1.22029i
$587$			7.93725i			0.327606i	0.986493	+	0.163803i	$0.0523761\pi$
$587$			7.93725i			0.327606i	−0.986493	+	0.163803i	$0.947624\pi$
$588$	30.9955	+	20.2801i	1.27823	+	0.836337i
$589$		0			0
$590$		0			0
$591$	−10.5000	+	18.1865i	−0.431912	+	0.748094i
$592$	29.4955	+	12.4104i	1.21226	+	0.510065i
$593$	13.7477	−	7.93725i	0.564551	−	0.325944i	−0.190419	−	0.981703i	$-0.560985\pi$
$593$	13.7477	−	7.93725i	0.564551	−	0.325944i	0.754970	+	0.655759i	$0.227651\pi$
$594$	10.5000	−	6.61438i	0.430820	−	0.271391i
$595$		0			0
$596$	−14.0000	+	15.8745i	−0.573462	+	0.650245i
$597$	14.0000	+	24.2487i	0.572982	+	0.992434i
$598$	−12.5390	−	15.3223i	−0.512758	−	0.626576i
$599$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$599$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$600$	19.8911	−	31.6914i	0.812051	−	1.29380i
$601$		−	42.3320i		−	1.72676i	−0.504555	−	0.863380i	$-0.668343\pi$
$601$		−	42.3320i		−	1.72676i	0.504555	−	0.863380i	$-0.331657\pi$
$602$	0.208712	−	7.48040i	0.00850647	−	0.304878i
$603$			10.5830i			0.430973i
$604$	6.72595	−	33.3281i	0.273675	−	1.35610i
$605$		0			0
$606$	18.8085	+	22.9835i	0.764044	+	0.933639i
$607$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$607$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$608$		0			0
$609$	−42.0000	−	36.3731i	−1.70193	−	1.47391i
$610$		0			0
$611$		0			0
$612$	13.4955	+	40.1232i	0.545521	+	1.62189i
$613$	36.6606	+	21.1660i	1.48071	+	0.854887i	0.999761	−	0.0218626i	$-0.00695964\pi$
$613$	36.6606	+	21.1660i	1.48071	+	0.854887i	0.480947	+	0.876750i	$0.340293\pi$
$614$	39.0780	−	6.39590i	1.57706	−	0.258118i
$615$		0			0
$616$	−19.0390	+	15.9222i	−0.767104	+	0.641523i
$617$	−23.0000			−0.925945			−0.462973	−	0.886373i	$-0.653217\pi$
$617$	−23.0000			−0.925945			−0.462973	+	0.886373i	$0.653217\pi$
$618$	−19.5390	+	3.19795i	−0.785974	+	0.128640i
$619$	−4.58258	−	2.64575i	−0.184189	−	0.106342i	0.405070	−	0.914286i	$-0.367247\pi$
$619$	−4.58258	−	2.64575i	−0.184189	−	0.106342i	−0.589259	+	0.807944i	$0.700580\pi$
$620$		0			0
$621$	−7.00000	−	12.1244i	−0.280900	−	0.486534i
$622$	14.0000	+	5.29150i	0.561349	+	0.212170i
$623$	−35.0000	+	12.1244i	−1.40225	+	0.485752i
$624$	−3.50000	−	27.7804i	−0.140112	−	1.11211i
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	−18.8085	−	22.9835i	−0.751740	−	0.918604i
$627$		0			0
$628$	5.53901	−	27.4467i	0.221031	−	1.09524i
$629$			42.3320i			1.68789i
$630$		0			0
$631$			26.4575i			1.05326i	0.850096	+	0.526628i	$0.176544\pi$
$631$			26.4575i			1.05326i	−0.850096	+	0.526628i	$0.823456\pi$
$632$	−31.1434	−	19.5471i	−1.23882	−	0.777543i
$633$	4.58258	+	2.64575i	0.182141	+	0.105159i
$634$	−5.37386	−	6.56670i	−0.213423	−	0.260797i
$635$		0			0
$636$	−14.0000	+	15.8745i	−0.555136	+	0.629465i
$637$	6.87386	−	17.1974i	0.272352	−	0.681385i
$638$	31.5000	−	19.8431i	1.24710	−	0.785597i
$639$	−18.3303	+	10.5830i	−0.725136	+	0.418657i
$640$		0			0
$641$	5.50000	−	9.52628i	0.217237	−	0.376265i	−0.736725	−	0.676192i	$-0.763629\pi$
$641$	5.50000	−	9.52628i	0.217237	−	0.376265i	0.953962	+	0.299927i	$0.0969622\pi$
$642$	4.83485	+	29.5402i	0.190816	+	1.16586i
$643$		−	18.5203i		−	0.730368i	−0.930935	−	0.365184i	$-0.881006\pi$
$643$		−	18.5203i		−	0.730368i	0.930935	−	0.365184i	$-0.118994\pi$
$644$	17.1216	+	22.1552i	0.674685	+	0.873036i
$645$		0			0
$646$		0			0
$647$	−27.4955	−	15.8745i	−1.08096	−	0.624091i	−0.149803	−	0.988716i	$-0.547864\pi$
$647$	−27.4955	−	15.8745i	−1.08096	−	0.624091i	−0.931155	+	0.364625i	$0.881197\pi$
$648$	−0.521780	+	14.1325i	−0.0204975	+	0.555177i
$649$	1.08258	−	8.70793i	0.0424948	−	0.341816i
$650$	−17.5000	−	6.61438i	−0.686406	−	0.259437i
$651$	70.0000	−	24.2487i	2.74352	−	0.950382i
$652$	−3.50000	+	3.96863i	−0.137071	+	0.155423i
$653$	−4.00000	−	6.92820i	−0.156532	−	0.271122i	0.777084	−	0.629397i	$-0.216698\pi$
$653$	−4.00000	−	6.92820i	−0.156532	−	0.271122i	−0.933616	+	0.358276i	$0.883365\pi$
$654$	25.0780	+	30.6446i	0.980629	+	1.19830i
$655$		0			0
$656$		0			0
$657$		−	42.3320i		−	1.65153i
$658$		0			0
$659$	−26.0000			−1.01282			−0.506408	−	0.862294i	$-0.669027\pi$
$659$	−26.0000			−1.01282			−0.506408	+	0.862294i	$0.669027\pi$
$660$		0			0
$661$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$661$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$662$	−26.0608	+	21.3269i	−1.01288	+	0.828892i
$663$	32.0780	−	18.5203i	1.24581	−	0.719267i
$664$		0			0
$665$		0			0
$666$	16.0000	−	42.3320i	0.619987	−	1.64033i
$667$	−21.0000	−	36.3731i	−0.813123	−	1.40837i
$668$	−39.8085	+	13.3896i	−1.54024	+	0.518059i
$669$	−21.0000	+	36.3731i	−0.811907	+	1.40626i
$670$		0			0
$671$	7.00000	+	5.29150i	0.270232	+	0.204276i
$672$	3.85208	+	39.4102i	0.148597	+	1.52028i
$673$		−	31.7490i		−	1.22383i	−0.790922	−	0.611917i	$-0.790399\pi$
$673$		−	31.7490i		−	1.22383i	0.790922	−	0.611917i	$-0.209601\pi$
$674$	3.62614	+	22.1552i	0.139674	+	0.853385i
$675$	−11.4564	−	6.61438i	−0.440959	−	0.254588i
$676$	11.3739	−	3.82560i	0.437456	−	0.147139i
$677$	−27.4955	+	15.8745i	−1.05674	+	0.610107i	−0.924528	−	0.381115i	$-0.875540\pi$
$677$	−27.4955	+	15.8745i	−1.05674	+	0.610107i	−0.132209	+	0.991222i	$0.542207\pi$
$678$	−66.5000	−	25.1346i	−2.55392	−	0.965290i
$679$	−3.50000	+	18.1865i	−0.134318	+	0.697935i
$680$		0			0
$681$	−32.0780	+	18.5203i	−1.22923	+	0.709698i
$682$	1.91288	+	49.6018i	0.0732479	+	1.89935i
$683$	−20.6216	−	11.9059i	−0.789063	−	0.455566i	0.0505694	−	0.998721i	$-0.483896\pi$
$683$	−20.6216	−	11.9059i	−0.789063	−	0.455566i	−0.839633	+	0.543155i	$0.817230\pi$
$684$		0			0
$685$		0			0
$686$	−10.3956	+	24.0402i	−0.396908	+	0.917859i
$687$			37.0405i			1.41318i
$688$	6.37386	−	4.83465i	0.243001	−	0.184319i
$689$	9.16515	+	5.29150i	0.349164	+	0.201590i
$690$		0			0
$691$	2.29129	−	1.32288i	0.0871647	−	0.0503246i	−0.455784	−	0.890090i	$-0.650641\pi$
$691$	2.29129	−	1.32288i	0.0871647	−	0.0503246i	0.542949	+	0.839766i	$0.317308\pi$
$692$	17.5000	−	19.8431i	0.665250	−	0.754323i
$693$	23.4955	+	26.0761i	0.892519	+	0.990550i
$694$	9.00000	−	23.8118i	0.341635	−	0.903882i
$695$		0			0
$696$	2.19148	−	59.3565i	0.0830677	−	2.24990i
$697$		0			0
$698$	2.41742	+	14.7701i	0.0915009	+	0.559057i
$699$	−42.0000			−1.58859
$700$	24.4782	+	10.0408i	0.925190	+	0.379505i
$701$		−	34.3948i		−	1.29907i	−0.760331	−	0.649536i	$-0.774963\pi$
$701$		−	34.3948i		−	1.29907i	0.760331	−	0.649536i	$-0.225037\pi$
$702$	−9.76951	+	1.59898i	−0.368726	+	0.0603495i
$703$		0			0
$704$	−26.0172	−	5.20610i	−0.980561	−	0.196212i
$705$		0			0
$706$	7.00000	−	18.5203i	0.263448	−	0.697019i
$707$	−13.7477	+	15.8745i	−0.517036	+	0.597022i
$708$	−10.5000	−	9.26013i	−0.394614	−	0.348017i
$709$	−4.00000	−	6.92820i	−0.150223	−	0.260194i	0.781086	−	0.624423i	$-0.214666\pi$
$709$	−4.00000	−	6.92820i	−0.150223	−	0.260194i	−0.931309	+	0.364229i	$0.881333\pi$
$710$		0			0
$711$	−26.0000	+	45.0333i	−0.975076	+	1.68888i
$712$	−33.5390	−	21.0508i	−1.25693	−	0.788911i
$713$	56.0000			2.09722
$714$	−46.0780	+	24.9162i	−1.72443	+	0.932464i
$715$		0			0
$716$	−15.5608	−	3.14033i	−0.581534	−	0.117360i
$717$	−43.5345	−	25.1346i	−1.62582	−	0.938670i
$718$	13.4347	+	16.4168i	0.501377	+	0.612668i
$719$	27.4955	−	15.8745i	1.02541	−	0.592019i	0.109742	−	0.993960i	$-0.464998\pi$
$719$	27.4955	−	15.8745i	1.02541	−	0.592019i	0.915666	+	0.401941i	$0.131664\pi$
$720$		0			0
$721$	−4.58258	−	13.2288i	−0.170664	−	0.492665i
$722$	−9.50000	+	25.1346i	−0.353553	+	0.935414i
$723$	−7.00000	−	12.1244i	−0.260333	−	0.450910i
$724$		0			0
$725$	−34.3693	−	19.8431i	−1.27644	−	0.736956i
$726$	−37.2650	+	17.4735i	−1.38303	+	0.648502i
$727$			21.1660i			0.785004i	0.919751	+	0.392502i	$0.128390\pi$
$727$			21.1660i			0.785004i	−0.919751	+	0.392502i	$0.871610\pi$
$728$	18.9347	−	5.78608i	0.701765	−	0.214446i
$729$	41.0000			1.51852
$730$		0			0
$731$	9.16515	+	5.29150i	0.338985	+	0.195713i
$732$	13.2695	−	4.46320i	0.490455	−	0.164965i
$733$	−11.4564	+	6.61438i	−0.423153	+	0.244308i	−0.696426	−	0.717629i	$-0.745227\pi$
$733$	−11.4564	+	6.61438i	−0.423153	+	0.244308i	0.273272	+	0.961937i	$0.411894\pi$
$734$	21.0000	+	7.93725i	0.775124	+	0.292969i
$735$		0			0
$736$	−7.00000	+	29.1033i	−0.258023	+	1.07276i
$737$	1.08258	−	8.70793i	0.0398772	−	0.320761i
$738$		0			0
$739$	23.0000	−	39.8372i	0.846069	−	1.46543i	−0.0386212	−	0.999254i	$-0.512297\pi$
$739$	23.0000	−	39.8372i	0.846069	−	1.46543i	0.884690	−	0.466180i	$-0.154370\pi$
$740$		0			0
$741$		0			0
$742$	−12.7477	−	7.84190i	−0.467984	−	0.287885i
$743$	12.0000			0.440237			0.220119	−	0.975473i	$-0.429356\pi$
$743$	12.0000			0.440237			0.220119	+	0.975473i	$0.429356\pi$
$744$	67.0780	+	42.1015i	2.45920	+	1.54352i
$745$		0			0
$746$	−26.0608	+	21.3269i	−0.954154	+	0.780832i
$747$		0			0
$748$	−7.00000	−	34.3948i	−0.255945	−	1.25760i
$749$	−20.0000	+	6.92820i	−0.730784	+	0.253151i
$750$		0			0
$751$	−41.2432	+	23.8118i	−1.50499	+	0.868904i	−0.505002	+	0.863118i	$0.668508\pi$
$751$	−41.2432	+	23.8118i	−1.50499	+	0.868904i	−0.999983	+	0.00578524i	$0.998158\pi$
$752$		0			0
$753$	21.0000	−	36.3731i	0.765283	−	1.32551i
$754$	−29.3085	+	4.79693i	−1.06735	+	0.174694i
$755$		0			0
$756$	13.8739	−	1.87508i	0.504588	−	0.0681959i
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	−4.23049	−	25.8477i	−0.153658	−	0.938830i
$759$	18.0780	+	42.7690i	0.656191	+	1.55242i
$760$		0			0
$761$	13.7477	−	7.93725i	0.498355	−	0.287725i	−0.229679	−	0.973266i	$-0.573768\pi$
$761$	13.7477	−	7.93725i	0.498355	−	0.287725i	0.728034	+	0.685541i	$0.240434\pi$
$762$	17.5000	+	6.61438i	0.633958	+	0.239614i
$763$	−18.3303	+	21.1660i	−0.663602	+	0.766261i
$764$	14.0000	−	15.8745i	0.506502	−	0.574320i
$765$		0			0
$766$	−17.3739	+	14.2179i	−0.627743	+	0.513714i
$767$	−3.50000	+	6.06218i	−0.126378	+	0.218893i
$768$	−30.2650	+	29.5978i	−1.09209	+	1.06802i
$769$			47.6235i			1.71735i	0.512522	+	0.858674i	$0.328711\pi$
$769$			47.6235i			1.71735i	−0.512522	+	0.858674i	$0.671289\pi$
$770$		0			0
$771$		−	18.5203i		−	0.666991i
$772$	−41.4955	−	8.37420i	−1.49345	−	0.301394i
$773$	7.00000	−	12.1244i	0.251773	−	0.436083i	−0.712241	−	0.701935i	$-0.752320\pi$
$773$	7.00000	−	12.1244i	0.251773	−	0.436083i	0.964014	+	0.265852i	$0.0856532\pi$
$774$	−7.16515	−	8.75560i	−0.257546	−	0.314714i
$775$	45.8258	−	26.4575i	1.64611	−	0.950382i
$776$	−17.5000	+	9.26013i	−0.628213	+	0.332419i
$777$	54.9909	+	10.5830i	1.97279	+	0.379663i
$778$	9.00000	−	23.8118i	0.322666	−	0.853693i
$779$		0			0
$780$		0			0
$781$	16.1652	−	6.83285i	0.578435	−	0.244499i
$782$	−39.0780	+	6.39590i	−1.39743	+	0.228717i
$783$	−21.0000			−0.750479
$784$	−26.9955	+	7.43273i	−0.964123	+	0.265455i
$785$		0			0
$786$	−8.46099	−	51.6954i	−0.301793	−	1.84391i
$787$	7.00000	−	12.1244i	0.249523	−	0.432187i	−0.713871	−	0.700278i	$-0.753059\pi$
$787$	7.00000	−	12.1244i	0.249523	−	0.432187i	0.963394	+	0.268091i	$0.0863928\pi$
$788$	−5.06080	−	15.0462i	−0.180283	−	0.535999i
$789$	−25.2042	+	14.5516i	−0.897292	+	0.518052i
$790$		0			0
$791$	9.50000	−	49.3634i	0.337781	−	1.75516i
$792$	−6.00000	+	37.0405i	−0.213201	+	1.31618i
$793$	−3.50000	−	6.06218i	−0.124289	−	0.215274i
$794$	25.0780	+	30.6446i	0.889986	+	1.08754i
$795$		0			0
$796$	−20.7477	−	4.18710i	−0.735384	−	0.148408i
$797$	14.0000			0.495905			0.247953	−	0.968772i	$-0.420242\pi$
$797$	14.0000			0.495905			0.247953	+	0.968772i	$0.420242\pi$
$798$		0			0
$799$		0			0
$800$	8.02178	+	27.1229i	0.283613	+	0.958939i
$801$	−28.0000	+	48.4974i	−0.989331	+	1.71357i
$802$	−24.1824	−	29.5502i	−0.853910	−	1.04345i
$803$	−4.33030	+	34.8317i	−0.152813	+	1.22918i
$804$	−10.5000	−	9.26013i	−0.370306	−	0.326580i
$805$		0			0
$806$	14.0000	−	37.0405i	0.493129	−	1.30470i
$807$	64.1561	−	37.0405i	2.25840	−	1.30389i
$808$	−22.4347	−	0.828301i	−0.789249	−	0.0291395i
$809$	27.4955	+	15.8745i	0.966689	+	0.558118i	0.898225	−	0.439536i	$-0.144857\pi$
$809$	27.4955	+	15.8745i	0.966689	+	0.558118i	0.0684635	+	0.997654i	$0.478190\pi$
$810$		0			0
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$	41.6216	−	5.62523i	1.46063	−	0.197407i
$813$			18.5203i			0.649534i
$814$	−17.4955	+	33.1950i	−0.613215	+	1.16348i
$815$		0			0
$816$	−51.6170	−	21.7182i	−1.80696	−	0.760289i
$817$		0			0
$818$	−49.0000	−	18.5203i	−1.71324	−	0.647546i
$819$	−9.16515	−	26.4575i	−0.320256	−	0.924500i
$820$		0			0
$821$	−29.7867	+	17.1974i	−1.03956	+	0.600193i	−0.919710	−	0.392599i	$-0.871576\pi$
$821$	−29.7867	+	17.1974i	−1.03956	+	0.600193i	−0.119855	+	0.992791i	$0.538243\pi$
$822$	−8.68693	+	7.10895i	−0.302992	+	0.247953i
$823$	9.16515	+	5.29150i	0.319477	+	0.184450i	0.651159	−	0.758941i	$-0.274283\pi$
$823$	9.16515	+	5.29150i	0.319477	+	0.184450i	−0.331682	+	0.943391i	$0.607616\pi$
$824$	7.95644	−	12.6766i	0.277176	−	0.441609i
$825$	35.0000	+	26.4575i	1.21854	+	0.921132i
$826$	5.18693	−	8.43183i	0.180476	−	0.293381i
$827$	−26.0000			−0.904109			−0.452054	−	0.891990i	$-0.649309\pi$
$827$	−26.0000			−0.904109			−0.452054	+	0.891990i	$0.649309\pi$
$828$	41.4955	+	8.37420i	1.44207	+	0.291024i
$829$	−21.0000	+	36.3731i	−0.729360	+	1.26329i	0.227794	+	0.973709i	$0.426849\pi$
$829$	−21.0000	+	36.3731i	−0.729360	+	1.26329i	−0.957154	+	0.289579i	$0.906485\pi$
$830$		0			0
$831$	17.5000	+	30.3109i	0.607068	+	1.05147i
$832$	17.5000	+	11.9059i	0.606703	+	0.412762i
$833$	−22.9129	−	29.1033i	−0.793884	−	1.00837i
$834$	49.0000	+	18.5203i	1.69673	+	0.641304i
$835$		0			0
$836$		0			0
$837$	14.0000	−	24.2487i	0.483911	−	0.838158i
$838$	1.20871	+	7.38505i	0.0417543	+	0.255112i
$839$		0			0		1.00000			$0$
$839$		0			0		−1.00000			$\pi$
$840$		0			0
$841$	−34.0000			−1.17241
$842$	−16.7477	+	2.74110i	−0.577165	+	0.0944646i
$843$	21.0000	−	36.3731i	0.723278	−	1.25275i
$844$	−3.79129	+	1.27520i	−0.130502	+	0.0438942i
$845$		0			0
$846$		0			0
$847$	−16.6652	−	23.8594i	−0.572621	−	0.819820i
$848$	−2.00000	−	15.8745i	−0.0686803	−	0.545133i
$849$	64.1561	−	37.0405i	2.20183	−	1.27123i
$850$	−28.9564	+	23.6965i	−0.993198	+	0.812784i
$851$	36.6606	+	21.1660i	1.25671	+	0.725561i
$852$	5.53901	−	27.4467i	0.189764	−	0.940307i
$853$		0			0		1.00000			$0$
$853$		0			0		−1.00000			$\pi$
$854$	4.70871	+	8.70793i	0.161129	+	0.297979i
$855$		0			0
$856$	−19.1652	−	12.0290i	−0.655051	−	0.411143i
$857$	−18.3303	−	10.5830i	−0.626151	−	0.361509i	0.153109	−	0.988209i	$-0.451072\pi$
$857$	−18.3303	−	10.5830i	−0.626151	−	0.361509i	−0.779260	+	0.626701i	$0.784405\pi$
$858$	32.8085	−	1.26525i	1.12006	−	0.0431949i
$859$	16.0390	−	9.26013i	0.547244	−	0.315952i	−0.200766	−	0.979639i	$-0.564343\pi$
$859$	16.0390	−	9.26013i	0.547244	−	0.315952i	0.748010	+	0.663688i	$0.231010\pi$
$860$		0			0
$861$		0			0
$862$	−1.50000	+	3.96863i	−0.0510902	+	0.135172i
$863$	−13.7477	+	7.93725i	−0.467978	+	0.270187i	−0.715393	−	0.698722i	$-0.753752\pi$
$863$	−13.7477	+	7.93725i	−0.467978	+	0.270187i	0.247415	+	0.968910i	$0.420419\pi$
$864$	10.8521	+	10.3069i	0.369195	+	0.350648i
$865$		0			0
$866$	19.5390	−	3.19795i	0.663963	−	0.108671i
$867$		−	29.1033i		−	0.988399i
$868$	−21.2523	+	51.8106i	−0.721349	+	1.75857i
$869$	26.0000	−	34.3948i	0.881990	−	1.16676i
$870$		0			0
$871$	−3.50000	+	6.06218i	−0.118593	+	0.205409i
$872$	−29.9129	−	1.10440i	−1.01298	−	0.0373997i
$873$	14.0000	+	24.2487i	0.473828	+	0.820695i
$874$		0			0
$875$		0			0
$876$	42.0000	+	37.0405i	1.41905	+	1.25148i
$877$	11.4564	−	6.61438i	0.386856	−	0.223352i	−0.293941	−	0.955824i	$-0.594967\pi$
$877$	11.4564	−	6.61438i	0.386856	−	0.223352i	0.680797	+	0.732472i	$0.261633\pi$
$878$	31.3475	+	38.3058i	1.05793	+	1.29276i
$879$	28.0000	−	48.4974i	0.944417	−	1.63578i
$880$		0			0
$881$	7.00000			0.235836			0.117918	−	0.993023i	$-0.462378\pi$
$881$	7.00000			0.235836			0.117918	+	0.993023i	$0.462378\pi$
$882$	11.9129	+	37.7635i	0.401127	+	1.27156i
$883$			34.3948i			1.15748i	0.815514	+	0.578738i	$0.196455\pi$
$883$			34.3948i			1.15748i	−0.815514	+	0.578738i	$0.803545\pi$
$884$	−5.53901	+	27.4467i	−0.186297	+	0.923131i
$885$		0			0
$886$	−40.5390	+	33.1751i	−1.36193	+	1.11454i
$887$	24.5000	+	42.4352i	0.822629	+	1.42484i	0.903718	+	0.428129i	$0.140827\pi$
$887$	24.5000	+	42.4352i	0.822629	+	1.42484i	−0.0810881	+	0.996707i	$0.525840\pi$
$888$	28.0000	+	52.9150i	0.939618	+	1.77571i
$889$	−2.50000	+	12.9904i	−0.0838473	+	0.435683i
$890$		0			0
$891$	−16.4564	−	2.04588i	−0.551311	−	0.0685394i
$892$	−10.1216	−	30.0924i	−0.338896	−	1.00757i
$893$		0			0
$894$	−39.0780	+	6.39590i	−1.30696	+	0.213911i
$895$		0			0
$896$	−24.2695	−	17.5212i	−0.810787	−	0.585341i
$897$		−	37.0405i		−	1.23675i
$898$	41.8693	−	6.85275i	1.39720	−	0.228679i
$899$	42.0000	−	72.7461i	1.40078	−	2.42622i
$900$	37.9129	−	12.7520i	1.26376	−	0.425067i
$901$	18.3303	−	10.5830i	0.610671	−	0.352571i
$902$		0			0
$903$	9.16515	−	10.5830i	0.304997	−	0.352180i
$904$	47.5000	−	25.1346i	1.57983	−	0.835966i
$905$		0			0
$906$	49.2259	−	40.2841i	1.63542	−	1.33835i
$907$	4.58258	+	2.64575i	0.152162	+	0.0878507i	0.574148	−	0.818752i	$-0.305333\pi$
$907$	4.58258	+	2.64575i	0.152162	+	0.0878507i	−0.421986	+	0.906602i	$0.638667\pi$
$908$	5.53901	−	27.4467i	0.183819	−	0.910850i
$909$			31.7490i			1.05305i
$910$		0			0
$911$			15.8745i			0.525946i	0.964803	+	0.262973i	$0.0847030\pi$
$911$			15.8745i			0.525946i	−0.964803	+	0.262973i	$0.915297\pi$
$912$		0			0
$913$		0			0
$914$	−5.79129	+	4.73930i	−0.191559	+	0.156762i
$915$		0			0
$916$	−21.0000	−	18.5203i	−0.693860	−	0.611927i
$917$	35.0000	−	12.1244i	1.15580	−	0.400381i
$918$	−7.00000	+	18.5203i	−0.231034	+	0.611260i
$919$	4.00000	+	6.92820i	0.131948	+	0.228540i	0.924427	−	0.381358i	$-0.124544\pi$
$919$	4.00000	+	6.92820i	0.131948	+	0.228540i	−0.792480	+	0.609898i	$0.791210\pi$
$920$		0			0
$921$	64.1561	+	37.0405i	2.11401	+	1.22053i
$922$	−1.81307	−	11.0776i	−0.0597102	−	0.364821i
$923$	−14.0000			−0.460816
$924$	−46.4301	+	0.494575i	−1.52744	+	0.0162703i
$925$	40.0000			1.31519
$926$	−4.83485	−	29.5402i	−0.158883	−	0.970752i
$927$	−18.3303	−	10.5830i	−0.602046	−	0.347591i
$928$	32.5562	+	30.9207i	1.06871	+	1.01502i
$929$	−17.5000	−	30.3109i	−0.574156	−	0.994468i	−0.996133	−	0.0878612i	$-0.971997\pi$
$929$	−17.5000	−	30.3109i	−0.574156	−	0.994468i	0.421976	−	0.906607i	$-0.361337\pi$
$930$		0			0
$931$		0			0
$932$	21.0000	−	23.8118i	0.687878	−	0.779980i
$933$	14.0000	+	24.2487i	0.458339	+	0.793867i
$934$	17.3739	−	14.2179i	0.568490	−	0.465224i
$935$		0			0
$936$	15.9129	−	25.3531i	0.520129	−	0.828692i
$937$		−	26.4575i		−	0.864329i	−0.901795	−	0.432165i	$-0.857750\pi$
$937$		−	26.4575i		−	0.864329i	0.901795	−	0.432165i	$-0.142250\pi$
$938$	5.18693	−	8.43183i	0.169359	−	0.275309i
$939$		−	55.5608i		−	1.81316i
$940$		0			0
$941$	−48.1170	−	27.7804i	−1.56857	−	0.905615i	−0.996336	−	0.0855250i	$-0.972743\pi$
$941$	−48.1170	−	27.7804i	−1.56857	−	0.905615i	−0.572235	−	0.820090i	$-0.693923\pi$
$942$	40.5390	−	33.1751i	1.32083	−	1.08090i
$943$		0			0
$944$	10.5000	−	1.32288i	0.341746	−	0.0430559i
$945$		0			0
$946$	5.00000	+	7.93725i	0.162564	+	0.258062i
$947$	13.7477	−	7.93725i	0.446741	−	0.257926i	−0.259712	−	0.965686i	$-0.583628\pi$
$947$	13.7477	−	7.93725i	0.446741	−	0.257926i	0.706453	+	0.707760i	$0.250294\pi$
$948$	−21.9301	−	65.2002i	−0.712257	−	2.11761i
$949$	14.0000	−	24.2487i	0.454459	−	0.787146i
$950$		0			0
$951$		−	15.8745i		−	0.514766i
$952$	8.91288	−	38.5819i	0.288868	−	1.25045i
$953$			15.8745i			0.514226i	0.966381	+	0.257113i	$0.0827712\pi$
$953$			15.8745i			0.514226i	−0.966381	+	0.257113i	$0.917229\pi$
$954$	−22.3303	+	3.65480i	−0.722970	+	0.118329i
$955$		0			0
$956$	36.0172	−	12.1144i	1.16488	−	0.391808i
$957$	69.1170	+	8.59268i	2.23424	+	0.277762i
$958$	−10.5000	+	27.7804i	−0.339240	+	0.897544i
$959$	−6.00000	−	5.19615i	−0.193750	−	0.167793i
$960$		0			0
$961$	40.5000	+	70.1481i	1.30645	+	2.26284i
$962$	23.1652	−	18.9572i	0.746874	−	0.611205i
$963$	−16.0000	+	27.7128i	−0.515593	+	0.893033i
$964$	10.3739	+	2.09355i	0.334120	+	0.0674287i
$965$		0			0
$966$	−1.46099	+	52.3628i	−0.0470064	+	1.68475i
$967$	16.0000			0.514525			0.257263	−	0.966342i	$-0.417179\pi$
$967$	16.0000			0.514525			0.257263	+	0.966342i	$0.417179\pi$
$968$	8.72595	−	29.8640i	0.280463	−	0.959865i
$969$		0			0
$970$		0			0
$971$	−25.2042	+	14.5516i	−0.808840	+	0.466984i	−0.846553	−	0.532305i	$-0.821326\pi$
$971$	−25.2042	+	14.5516i	−0.808840	+	0.466984i	0.0377128	+	0.999289i	$0.487993\pi$
$972$	−28.0000	+	31.7490i	−0.898100	+	1.01835i
$973$	−7.00000	+	36.3731i	−0.224410	+	1.16607i
$974$		0			0
$975$	−17.5000	−	30.3109i	−0.560449	−	0.970725i
$976$	−4.10436	+	9.75470i	−0.131377	+	0.312240i
$977$	19.0000	−	32.9090i	0.607864	−	1.05285i	−0.383728	−	0.923446i	$-0.625360\pi$
$977$	19.0000	−	32.9090i	0.607864	−	1.05285i	0.991592	−	0.129405i	$-0.0413067\pi$
$978$	−9.76951	+	1.59898i	−0.312394	+	0.0511296i
$979$	28.0000	−	37.0405i	0.894884	−	1.18382i
$980$		0			0
$981$			42.3320i			1.35156i
$982$	36.2867	−	5.93905i	1.15796	−	0.189523i
$983$	−41.2432	−	23.8118i	−1.31545	−	0.759477i	−0.332460	−	0.943117i	$-0.607879\pi$
$983$	−41.2432	−	23.8118i	−1.31545	−	0.759477i	−0.982994	+	0.183640i	$0.941212\pi$
$984$		0			0
$985$		0			0
$986$	−21.0000	+	55.5608i	−0.668776	+	1.76942i
$987$		0			0
$988$		0			0
$989$	9.16515	−	5.29150i	0.291435	−	0.168260i
$990$		0			0
$991$	18.3303	+	10.5830i	0.582281	+	0.336180i	0.762039	−	0.647531i	$-0.224198\pi$
$991$	18.3303	+	10.5830i	0.582281	+	0.336180i	−0.179758	+	0.983711i	$0.557532\pi$
$992$	−57.4083	+	16.9789i	−1.82272	+	0.539081i
$993$	−63.0000			−1.99924
$994$	19.7913	+	0.552200i	0.627742	+	0.0175147i
$995$		0			0
$996$		0			0
$997$	45.8258	+	26.4575i	1.45132	+	0.837918i	0.998556	−	0.0537146i	$-0.0171061\pi$
$997$	45.8258	+	26.4575i	1.45132	+	0.837918i	0.452760	+	0.891632i	$0.350439\pi$
$998$	28.9564	−	23.6965i	0.916600	−	0.750100i
$999$	18.3303	−	10.5830i	0.579945	−	0.334831i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.2.n.a.263.1	yes	4
4.3	odd	2		308.2.n.b.263.1	yes	4
7.2	even	3	inner	308.2.n.a.219.2	yes	4
11.10	odd	2		308.2.n.b.263.2	yes	4
28.23	odd	6		308.2.n.b.219.2	yes	4
44.43	even	2	inner	308.2.n.a.263.2	yes	4
77.65	odd	6		308.2.n.b.219.1	yes	4
308.219	even	6	inner	308.2.n.a.219.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.n.a.219.1	✓	4	308.219	even	6	inner
308.2.n.a.219.2	yes	4	7.2	even	3	inner
308.2.n.a.263.1	yes	4	1.1	even	1	trivial
308.2.n.a.263.2	yes	4	44.43	even	2	inner
308.2.n.b.219.1	yes	4	77.65	odd	6
308.2.n.b.219.2	yes	4	28.23	odd	6
308.2.n.b.263.1	yes	4	4.3	odd	2
308.2.n.b.263.2	yes	4	11.10	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:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39564 + 0.228425i) q^{2} +(-2.29129 - 1.32288i) q^{3} +(1.89564 - 0.637600i) q^{4} +(3.50000 + 1.32288i) q^{6} +(-0.500000 + 2.59808i) q^{7} +(-2.50000 + 1.32288i) q^{8} +(2.00000 + 3.46410i) q^{9} +(-1.29129 - 3.05493i) q^{11} +(-5.18693 - 1.04678i) q^{12} +2.64575i q^{13} +(0.104356 - 3.74020i) q^{14} +(3.18693 - 2.41733i) q^{16} +(4.58258 + 2.64575i) q^{17} +(-3.58258 - 4.37780i) q^{18} +(4.58258 - 5.29150i) q^{21} +(2.50000 + 3.96863i) q^{22} +(4.58258 - 2.64575i) q^{23} +(7.47822 + 0.276100i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-0.604356 - 3.69253i) q^{26} -2.64575i q^{27} +(0.708712 + 5.24383i) q^{28} -7.93725i q^{29} +(9.16515 + 5.29150i) q^{31} +(-3.89564 + 4.10170i) q^{32} +(-1.08258 + 8.70793i) q^{33} +(-7.00000 - 2.64575i) q^{34} +(6.00000 + 5.29150i) q^{36} +(4.00000 + 6.92820i) q^{37} +(3.50000 - 6.06218i) q^{39} +(-5.18693 + 8.43183i) q^{42} +2.00000 q^{43} +(-4.39564 - 4.96773i) q^{44} +(-5.79129 + 4.73930i) q^{46} +(-10.5000 + 1.32288i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(-2.50000 + 6.61438i) q^{50} +(-7.00000 - 12.1244i) q^{51} +(1.68693 + 5.01540i) q^{52} +(2.00000 - 3.46410i) q^{53} +(0.604356 + 3.69253i) q^{54} +(-2.18693 - 7.15663i) q^{56} +(1.81307 + 11.0776i) q^{58} +(2.29129 + 1.32288i) q^{59} +(-2.29129 + 1.32288i) q^{61} +(-14.0000 - 5.29150i) q^{62} +(-10.0000 + 3.46410i) q^{63} +(4.50000 - 6.61438i) q^{64} +(-0.478220 - 12.4005i) q^{66} +(2.29129 + 1.32288i) q^{67} +(10.3739 + 2.09355i) q^{68} -14.0000 q^{69} +5.29150i q^{71} +(-9.58258 - 6.01450i) q^{72} +(-9.16515 - 5.29150i) q^{73} +(-7.16515 - 8.75560i) q^{74} +(-11.4564 + 6.61438i) q^{75} +(8.58258 - 1.82740i) q^{77} +(-3.50000 + 9.26013i) q^{78} +(6.50000 + 11.2583i) q^{79} +(2.50000 - 4.33013i) q^{81} +(5.31307 - 12.9527i) q^{84} +(-2.79129 + 0.456850i) q^{86} +(-10.5000 + 18.1865i) q^{87} +(7.26951 + 5.92910i) q^{88} +(7.00000 + 12.1244i) q^{89} +(-6.87386 - 1.32288i) q^{91} +(7.00000 - 7.93725i) q^{92} +(-14.0000 - 24.2487i) q^{93} +(14.3521 - 4.24473i) q^{96} +7.00000 q^{97} +(9.66515 + 2.14123i) q^{98} +(8.00000 - 10.5830i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + 3 q^{4} + 14 q^{6} - 2 q^{7} - 10 q^{8} + 8 q^{9} + 4 q^{11} - 7 q^{12} + 5 q^{14} - q^{16} + 4 q^{18} + 10 q^{22} + 7 q^{24} + 10 q^{25} - 7 q^{26} + 12 q^{28} - 11 q^{32} + 14 q^{33} - 28 q^{34}+ \cdots + 32 q^{99}+O(q^{100}) \) 4 * q - q^2 + 3 * q^4 + 14 * q^6 - 2 * q^7 - 10 * q^8 + 8 * q^9 + 4 * q^11 - 7 * q^12 + 5 * q^14 - q^16 + 4 * q^18 + 10 * q^22 + 7 * q^24 + 10 * q^25 - 7 * q^26 + 12 * q^28 - 11 * q^32 + 14 * q^33 - 28 * q^34 + 24 * q^36 + 16 * q^37 + 14 * q^39 - 7 * q^42 + 8 * q^43 - 13 * q^44 - 14 * q^46 - 42 * q^48 - 26 * q^49 - 10 * q^50 - 28 * q^51 - 7 * q^52 + 8 * q^53 + 7 * q^54 + 5 * q^56 + 21 * q^58 - 56 * q^62 - 40 * q^63 + 18 * q^64 + 21 * q^66 + 14 * q^68 - 56 * q^69 - 20 * q^72 + 8 * q^74 + 16 * q^77 - 14 * q^78 + 26 * q^79 + 10 * q^81 + 35 * q^84 - 2 * q^86 - 42 * q^87 - 3 * q^88 + 28 * q^89 + 28 * q^92 - 56 * q^93 + 7 * q^96 + 28 * q^97 + 2 * q^98 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more