LMFDB - Embedded newform 130.2.l.b.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [130,2,Mod(101,130)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(130, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("130.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	130.l (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:	$1.03805522628$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.4
Root			$1.40994 - 0.109843i$ of defining polynomial
Character	$\chi$	$=$	130.101
Dual form			130.2.l.b.121.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.300098 + 0.519785i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(0.519785 + 0.300098i) q^{6} +(1.24653 + 0.719687i) q^{7} -1.00000i q^{8} +(1.31988 - 2.28610i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.300098 + 0.519785i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(0.519785 + 0.300098i) q^{6} +(1.24653 + 0.719687i) q^{7} -1.00000i q^{8} +(1.31988 - 2.28610i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-2.40029 + 1.38581i) q^{11} +0.600196 q^{12} +(-2.76632 - 2.31246i) q^{13} +1.43937 q^{14} +(-0.519785 + 0.300098i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.25184 + 3.90029i) q^{17} -2.63977i q^{18} +(-3.75184 - 2.16612i) q^{19} +(0.866025 + 0.500000i) q^{20} +0.863906i q^{21} +(-1.38581 + 2.40029i) q^{22} +(2.21969 + 3.84461i) q^{23} +(0.519785 - 0.300098i) q^{24} -1.00000 q^{25} +(-3.55193 - 0.619491i) q^{26} +3.38496 q^{27} +(1.24653 - 0.719687i) q^{28} +(-3.93244 - 6.81119i) q^{29} +(-0.300098 + 0.519785i) q^{30} +4.16082i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.44065 - 0.831757i) q^{33} +4.50367i q^{34} +(-0.719687 + 1.24653i) q^{35} +(-1.31988 - 2.28610i) q^{36} +(0.498370 - 0.287734i) q^{37} -4.33225 q^{38} +(0.371816 - 2.13186i) q^{39} +1.00000 q^{40} +(3.65906 - 2.11256i) q^{41} +(0.431953 + 0.748164i) q^{42} +(1.30752 - 2.26469i) q^{43} +2.77162i q^{44} +(2.28610 + 1.31988i) q^{45} +(3.84461 + 2.21969i) q^{46} +12.7684i q^{47} +(0.300098 - 0.519785i) q^{48} +(-2.46410 - 4.26795i) q^{49} +(-0.866025 + 0.500000i) q^{50} -2.70308 q^{51} +(-3.38581 + 1.23947i) q^{52} +9.57123 q^{53} +(2.93146 - 1.69248i) q^{54} +(-1.38581 - 2.40029i) q^{55} +(0.719687 - 1.24653i) q^{56} -2.60020i q^{57} +(-6.81119 - 3.93244i) q^{58} +(-3.00000 - 1.73205i) q^{59} +0.600196i q^{60} +(6.25184 - 10.8285i) q^{61} +(2.08041 + 3.60338i) q^{62} +(3.29056 - 1.89980i) q^{63} -1.00000 q^{64} +(2.31246 - 2.76632i) q^{65} -1.66351 q^{66} +(4.61504 - 2.66449i) q^{67} +(2.25184 + 3.90029i) q^{68} +(-1.33225 + 2.30752i) q^{69} +1.43937i q^{70} +(5.19615 + 3.00000i) q^{71} +(-2.28610 - 1.31988i) q^{72} +1.66351i q^{73} +(0.287734 - 0.498370i) q^{74} +(-0.300098 - 0.519785i) q^{75} +(-3.75184 + 2.16612i) q^{76} -3.98940 q^{77} +(-0.743926 - 2.03215i) q^{78} +12.7288 q^{79} +(0.866025 - 0.500000i) q^{80} +(-2.94383 - 5.09886i) q^{81} +(2.11256 - 3.65906i) q^{82} +10.0469i q^{83} +(0.748164 + 0.431953i) q^{84} +(-3.90029 - 2.25184i) q^{85} -2.61504i q^{86} +(2.36023 - 4.08805i) q^{87} +(1.38581 + 2.40029i) q^{88} +(-5.15906 + 2.97859i) q^{89} +2.63977 q^{90} +(-1.78406 - 4.87345i) q^{91} +4.43937 q^{92} +(-2.16273 + 1.24865i) q^{93} +(6.38418 + 11.0577i) q^{94} +(2.16612 - 3.75184i) q^{95} -0.600196i q^{96} +(1.37380 + 0.793166i) q^{97} +(-4.26795 - 2.46410i) q^{98} +7.31643i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 4 * q^4 - 6 * q^6 - 4 * q^9	$ 8 q - 2 q^{3} + 4 q^{4} - 6 q^{6} - 4 q^{9} + 4 q^{10} - 6 q^{11} - 4 q^{12} - 2 q^{13} + 6 q^{15} - 4 q^{16} + 6 q^{17} - 6 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{24} - 8 q^{25} + 40 q^{27} + 2 q^{30} - 42 q^{33} + 4 q^{36} - 30 q^{37} - 12 q^{38} - 40 q^{39} + 8 q^{40} + 12 q^{41} - 6 q^{42} + 4 q^{43} - 12 q^{45} - 2 q^{48} + 8 q^{49} - 10 q^{52} + 60 q^{53} + 36 q^{54} + 6 q^{55} - 24 q^{59} + 26 q^{61} + 18 q^{62} + 12 q^{63} - 8 q^{64} + 6 q^{65} - 12 q^{66} + 24 q^{67} - 6 q^{68} + 12 q^{69} + 12 q^{72} + 6 q^{74} + 2 q^{75} - 6 q^{76} - 60 q^{77} - 6 q^{78} + 20 q^{79} - 28 q^{81} + 30 q^{84} - 18 q^{85} + 48 q^{87} - 6 q^{88} - 24 q^{89} - 8 q^{90} - 66 q^{91} + 24 q^{92} + 48 q^{93} + 6 q^{95} - 6 q^{97} - 48 q^{98}+O(q^{100}) $ 8 * q - 2 * q^3 + 4 * q^4 - 6 * q^6 - 4 * q^9 + 4 * q^10 - 6 * q^11 - 4 * q^12 - 2 * q^13 + 6 * q^15 - 4 * q^16 + 6 * q^17 - 6 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^24 - 8 * q^25 + 40 * q^27 + 2 * q^30 - 42 * q^33 + 4 * q^36 - 30 * q^37 - 12 * q^38 - 40 * q^39 + 8 * q^40 + 12 * q^41 - 6 * q^42 + 4 * q^43 - 12 * q^45 - 2 * q^48 + 8 * q^49 - 10 * q^52 + 60 * q^53 + 36 * q^54 + 6 * q^55 - 24 * q^59 + 26 * q^61 + 18 * q^62 + 12 * q^63 - 8 * q^64 + 6 * q^65 - 12 * q^66 + 24 * q^67 - 6 * q^68 + 12 * q^69 + 12 * q^72 + 6 * q^74 + 2 * q^75 - 6 * q^76 - 60 * q^77 - 6 * q^78 + 20 * q^79 - 28 * q^81 + 30 * q^84 - 18 * q^85 + 48 * q^87 - 6 * q^88 - 24 * q^89 - 8 * q^90 - 66 * q^91 + 24 * q^92 + 48 * q^93 + 6 * q^95 - 6 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	0.300098	+	0.519785i	0.173262	+	0.300098i	0.939558	−	0.342389i	$-0.111236\pi$
$3$	0.300098	+	0.519785i	0.173262	+	0.300098i	−0.766297	+	0.642487i	$0.777903\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	0.519785	+	0.300098i	0.212201	+	0.122514i
$7$	1.24653	+	0.719687i	0.471146	+	0.272016i	0.716719	−	0.697362i	$-0.245643\pi$
$7$	1.24653	+	0.719687i	0.471146	+	0.272016i	−0.245574	+	0.969378i	$0.578976\pi$
$8$		−	1.00000i		−	0.353553i
$9$	1.31988	−	2.28610i	0.439961	−	0.762035i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−2.40029	+	1.38581i	−0.723716	+	0.417837i	−0.816119	−	0.577884i	$-0.803879\pi$
$11$	−2.40029	+	1.38581i	−0.723716	+	0.417837i	0.0924030	+	0.995722i	$0.470545\pi$
$12$	0.600196			0.173262
$13$	−2.76632	−	2.31246i	−0.767239	−	0.641362i
$13$	−2.76632	−	2.31246i	−0.767239	−	0.641362i
$14$	1.43937			0.384689
$15$	−0.519785	+	0.300098i	−0.134208	+	0.0774849i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.25184	+	3.90029i	−0.546150	+	0.945960i	0.452383	+	0.891824i	$0.350574\pi$
$17$	−2.25184	+	3.90029i	−0.546150	+	0.945960i	−0.998534	+	0.0541365i	$0.982759\pi$
$18$		−	2.63977i		−	0.622199i
$19$	−3.75184	−	2.16612i	−0.860730	−	0.496943i	0.00352661	−	0.999994i	$-0.498877\pi$
$19$	−3.75184	−	2.16612i	−0.860730	−	0.496943i	−0.864257	+	0.503051i	$0.832211\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$			0.863906i			0.188520i
$22$	−1.38581	+	2.40029i	−0.295456	+	0.511744i
$23$	2.21969	+	3.84461i	0.462837	+	0.801657i	0.999101	−	0.0423934i	$-0.0134983\pi$
$23$	2.21969	+	3.84461i	0.462837	+	0.801657i	−0.536264	+	0.844050i	$0.680165\pi$
$24$	0.519785	−	0.300098i	0.106101	−	0.0612572i
$25$	−1.00000			−0.200000
$26$	−3.55193	−	0.619491i	−0.696591	−	0.121492i
$27$	3.38496			0.651436
$28$	1.24653	−	0.719687i	0.235573	−	0.136008i
$29$	−3.93244	−	6.81119i	−0.730236	−	1.26481i	−0.956782	−	0.290806i	$-0.906077\pi$
$29$	−3.93244	−	6.81119i	−0.730236	−	1.26481i	0.226546	−	0.974000i	$-0.427257\pi$
$30$	−0.300098	+	0.519785i	−0.0547901	+	0.0948993i
$31$			4.16082i			0.747306i	0.927569	+	0.373653i	$0.121895\pi$
$31$			4.16082i			0.747306i	−0.927569	+	0.373653i	$0.878105\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−1.44065	−	0.831757i	−0.250784	−	0.144790i
$34$			4.50367i			0.772373i
$35$	−0.719687	+	1.24653i	−0.121649	+	0.210703i
$36$	−1.31988	−	2.28610i	−0.219980	−	0.381017i
$37$	0.498370	−	0.287734i	0.0819315	−	0.0473032i	−0.458475	−	0.888708i	$-0.651604\pi$
$37$	0.498370	−	0.287734i	0.0819315	−	0.0473032i	0.540406	+	0.841404i	$0.318271\pi$
$38$	−4.33225			−0.702783
$39$	0.371816	−	2.13186i	0.0595382	−	0.341370i
$40$	1.00000			0.158114
$41$	3.65906	−	2.11256i	0.571449	−	0.329926i	−0.186279	−	0.982497i	$-0.559643\pi$
$41$	3.65906	−	2.11256i	0.571449	−	0.329926i	0.757728	+	0.652571i	$0.226309\pi$
$42$	0.431953	+	0.748164i	0.0666518	+	0.115444i
$43$	1.30752	−	2.26469i	0.199395	−	0.345362i	−0.748938	−	0.662641i	$-0.769436\pi$
$43$	1.30752	−	2.26469i	0.199395	−	0.345362i	0.948332	+	0.317279i	$0.102769\pi$
$44$			2.77162i			0.417837i
$45$	2.28610	+	1.31988i	0.340792	+	0.196756i
$46$	3.84461	+	2.21969i	0.566857	+	0.327275i
$47$			12.7684i			1.86246i	0.364436	+	0.931228i	$0.381262\pi$
$47$			12.7684i			1.86246i	−0.364436	+	0.931228i	$0.618738\pi$
$48$	0.300098	−	0.519785i	0.0433154	−	0.0750245i
$49$	−2.46410	−	4.26795i	−0.352015	−	0.609707i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	−2.70308			−0.378507
$52$	−3.38581	+	1.23947i	−0.469527	+	0.171884i
$53$	9.57123			1.31471			0.657355	−	0.753581i	$-0.271675\pi$
$53$	9.57123			1.31471			0.657355	+	0.753581i	$0.271675\pi$
$54$	2.93146	−	1.69248i	0.398922	−	0.230318i
$55$	−1.38581	−	2.40029i	−0.186863	−	0.323656i
$56$	0.719687	−	1.24653i	0.0961722	−	0.166575i
$57$		−	2.60020i		−	0.344404i
$58$	−6.81119	−	3.93244i	−0.894353	−	0.516355i
$59$	−3.00000	−	1.73205i	−0.390567	−	0.225494i	0.291839	−	0.956467i	$-0.405733\pi$
$59$	−3.00000	−	1.73205i	−0.390567	−	0.225494i	−0.682406	+	0.730974i	$0.739066\pi$
$60$			0.600196i			0.0774849i
$61$	6.25184	−	10.8285i	0.800466	−	1.38645i	−0.118845	−	0.992913i	$-0.537919\pi$
$61$	6.25184	−	10.8285i	0.800466	−	1.38645i	0.919310	−	0.393534i	$-0.128748\pi$
$62$	2.08041	+	3.60338i	0.264212	+	0.457629i
$63$	3.29056	−	1.89980i	0.414571	−	0.239353i
$64$	−1.00000			−0.125000
$65$	2.31246	−	2.76632i	0.286826	−	0.343120i
$66$	−1.66351			−0.204764
$67$	4.61504	−	2.66449i	0.563817	−	0.325520i	−0.190859	−	0.981617i	$-0.561127\pi$
$67$	4.61504	−	2.66449i	0.563817	−	0.325520i	0.754676	+	0.656098i	$0.227794\pi$
$68$	2.25184	+	3.90029i	0.273075	+	0.472980i
$69$	−1.33225	+	2.30752i	−0.160384	+	0.277793i
$70$			1.43937i			0.172038i
$71$	5.19615	+	3.00000i	0.616670	+	0.356034i	0.775571	−	0.631260i	$-0.217462\pi$
$71$	5.19615	+	3.00000i	0.616670	+	0.356034i	−0.158901	+	0.987294i	$0.550795\pi$
$72$	−2.28610	−	1.31988i	−0.269420	−	0.155550i
$73$			1.66351i			0.194700i	0.995250	+	0.0973498i	$0.0310366\pi$
$73$			1.66351i			0.194700i	−0.995250	+	0.0973498i	$0.968963\pi$
$74$	0.287734	−	0.498370i	0.0334484	−	0.0579343i
$75$	−0.300098	−	0.519785i	−0.0346523	−	0.0600196i
$76$	−3.75184	+	2.16612i	−0.430365	+	0.248471i
$77$	−3.98940			−0.454634
$78$	−0.743926	−	2.03215i	−0.0842330	−	0.230096i
$79$	12.7288			1.43210			0.716050	−	0.698049i	$-0.245948\pi$
$79$	12.7288			1.43210			0.716050	+	0.698049i	$0.245948\pi$
$80$	0.866025	−	0.500000i	0.0968246	−	0.0559017i
$81$	−2.94383	−	5.09886i	−0.327092	−	0.566540i
$82$	2.11256	−	3.65906i	0.233293	−	0.404076i
$83$			10.0469i			1.10279i	0.834244	+	0.551396i	$0.185905\pi$
$83$			10.0469i			1.10279i	−0.834244	+	0.551396i	$0.814095\pi$
$84$	0.748164	+	0.431953i	0.0816314	+	0.0471299i
$85$	−3.90029	−	2.25184i	−0.423046	−	0.244246i
$86$		−	2.61504i		−	0.281987i
$87$	2.36023	−	4.08805i	0.253044	−	0.438285i
$88$	1.38581	+	2.40029i	0.147728	+	0.255872i
$89$	−5.15906	+	2.97859i	−0.546859	+	0.315729i	−0.747854	−	0.663863i	$-0.768916\pi$
$89$	−5.15906	+	2.97859i	−0.546859	+	0.315729i	0.200995	+	0.979592i	$0.435583\pi$
$90$	2.63977			0.278256
$91$	−1.78406	−	4.87345i	−0.187021	−	0.510876i
$92$	4.43937			0.462837
$93$	−2.16273	+	1.24865i	−0.224265	+	0.129479i
$94$	6.38418	+	11.0577i	0.658478	+	1.14052i
$95$	2.16612	−	3.75184i	0.222240	−	0.384930i
$96$		−	0.600196i		−	0.0612572i
$97$	1.37380	+	0.793166i	0.139489	+	0.0805338i	0.568120	−	0.822946i	$-0.307671\pi$
$97$	1.37380	+	0.793166i	0.139489	+	0.0805338i	−0.428632	+	0.903479i	$0.641004\pi$
$98$	−4.26795	−	2.46410i	−0.431128	−	0.248912i
$99$			7.31643i			0.735329i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	6.87676	+	11.9109i	0.684263	+	1.18518i	0.973668	+	0.227972i	$0.0732093\pi$
$101$	6.87676	+	11.9109i	0.684263	+	1.18518i	−0.289405	+	0.957207i	$0.593457\pi$
$102$	−2.34094	+	1.35154i	−0.231788	+	0.133823i
$103$	−5.73205			−0.564796			−0.282398	−	0.959297i	$-0.591130\pi$
$103$	−5.73205			−0.564796			−0.282398	+	0.959297i	$0.591130\pi$
$104$	−2.31246	+	2.76632i	−0.226756	+	0.271260i
$105$	−0.863906			−0.0843086
$106$	8.28893	−	4.78561i	0.805092	−	0.464820i
$107$	−2.33967	−	4.05242i	−0.226184	−	0.391762i	0.730490	−	0.682924i	$-0.239292\pi$
$107$	−2.33967	−	4.05242i	−0.226184	−	0.391762i	−0.956674	+	0.291161i	$0.905958\pi$
$108$	1.69248	−	2.93146i	0.162859	−	0.282080i
$109$			2.32164i			0.222373i	0.993800	+	0.111187i	$0.0354651\pi$
$109$			2.32164i			0.222373i	−0.993800	+	0.111187i	$0.964535\pi$
$110$	−2.40029	−	1.38581i	−0.228859	−	0.132132i
$111$	0.299119	+	0.172697i	0.0283912	+	0.0163916i
$112$		−	1.43937i		−	0.136008i
$113$	−3.86814	+	6.69982i	−0.363884	+	0.630266i	−0.988596	−	0.150589i	$-0.951883\pi$
$113$	−3.86814	+	6.69982i	−0.363884	+	0.630266i	0.624712	+	0.780855i	$0.285216\pi$
$114$	−1.30010	−	2.25184i	−0.121765	−	0.210904i
$115$	−3.84461	+	2.21969i	−0.358512	+	0.206987i
$116$	−7.86488			−0.730236
$117$	−8.93774	+	3.27191i	−0.826295	+	0.302489i
$118$	−3.46410			−0.318896
$119$	−5.61398	+	3.24123i	−0.514633	+	0.297123i
$120$	0.300098	+	0.519785i	0.0273951	+	0.0474496i
$121$	−1.65906	+	2.87358i	−0.150824	+	0.261234i
$122$		−	12.5037i		−	1.13203i
$123$	2.19615	+	1.26795i	0.198020	+	0.114327i
$124$	3.60338	+	2.08041i	0.323593	+	0.186826i
$125$		−	1.00000i		−	0.0894427i
$126$	1.89980	−	3.29056i	0.169248	−	0.293146i
$127$	−8.06218	−	13.9641i	−0.715403	−	1.23911i	−0.962804	−	0.270201i	$-0.912910\pi$
$127$	−8.06218	−	13.9641i	−0.715403	−	1.23911i	0.247401	−	0.968913i	$-0.420423\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	1.56953			0.138190
$130$	0.619491	−	3.55193i	0.0543330	−	0.311525i
$131$	−19.7609			−1.72651			−0.863257	−	0.504764i	$-0.831579\pi$
$131$	−19.7609			−1.72651			−0.863257	+	0.504764i	$0.831579\pi$
$132$	−1.44065	+	0.831757i	−0.125392	+	0.0723952i
$133$	−3.11786	−	5.40029i	−0.270353	−	0.468265i
$134$	2.66449	−	4.61504i	0.230177	−	0.398678i
$135$			3.38496i			0.291331i
$136$	3.90029	+	2.25184i	0.334447	+	0.193093i
$137$	−14.9517	−	8.63234i	−1.27741	−	0.737511i	−0.301036	−	0.953613i	$-0.597332\pi$
$137$	−14.9517	−	8.63234i	−1.27741	−	0.737511i	−0.976371	+	0.216102i	$0.930666\pi$
$138$			2.66449i			0.226817i
$139$	−1.47328	+	2.55180i	−0.124962	+	0.216441i	−0.921718	−	0.387860i	$-0.873214\pi$
$139$	−1.47328	+	2.55180i	−0.124962	+	0.216441i	0.796756	+	0.604301i	$0.206548\pi$
$140$	0.719687	+	1.24653i	0.0608246	+	0.105351i
$141$	−6.63680	+	3.83176i	−0.558919	+	0.322692i
$142$	6.00000			0.503509
$143$	9.84461	+	1.71699i	0.823248	+	0.143582i
$144$	−2.63977			−0.219980
$145$	6.81119	−	3.93244i	0.565639	−	0.326572i
$146$	0.831757	+	1.44065i	0.0688367	+	0.119229i
$147$	1.47894	−	2.56160i	0.121981	−	0.211278i
$148$		−	0.575468i		−	0.0473032i
$149$	−6.11871	−	3.53264i	−0.501264	−	0.289405i	0.227971	−	0.973668i	$-0.426791\pi$
$149$	−6.11871	−	3.53264i	−0.501264	−	0.289405i	−0.729235	+	0.684263i	$0.760124\pi$
$150$	−0.519785	−	0.300098i	−0.0424402	−	0.0245029i
$151$			15.8327i			1.28844i	0.764839	+	0.644222i	$0.222819\pi$
$151$			15.8327i			1.28844i	−0.764839	+	0.644222i	$0.777181\pi$
$152$	−2.16612	+	3.75184i	−0.175696	+	0.304314i
$153$	5.94432	+	10.2959i	0.480570	+	0.832371i
$154$	−3.45492	+	1.99470i	−0.278405	+	0.160737i
$155$	−4.16082			−0.334205
$156$	−1.66033	−	1.38793i	−0.132933	−	0.111123i
$157$	12.6280			1.00783			0.503913	−	0.863754i	$-0.331893\pi$
$157$	12.6280			1.00783			0.503913	+	0.863754i	$0.331893\pi$
$158$	11.0235	−	6.36440i	0.876979	−	0.506324i
$159$	2.87231	+	4.97498i	0.227789	+	0.394541i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$			6.38992i			0.503596i
$162$	−5.09886	−	2.94383i	−0.400604	−	0.231289i
$163$	−15.9076	−	9.18428i	−1.24598	−	0.719368i	−0.275677	−	0.961250i	$-0.588902\pi$
$163$	−15.9076	−	9.18428i	−1.24598	−	0.719368i	−0.970306	+	0.241882i	$0.922235\pi$
$164$		−	4.22512i		−	0.329926i
$165$	0.831757	−	1.44065i	0.0647522	−	0.112154i
$166$	5.02346	+	8.70088i	0.389896	+	0.675319i
$167$	18.7135	−	10.8043i	1.44810	−	0.836059i	0.449728	−	0.893166i	$-0.351521\pi$
$167$	18.7135	−	10.8043i	1.44810	−	0.836059i	0.998368	+	0.0571070i	$0.0181876\pi$
$168$	0.863906			0.0666518
$169$	2.30504	+	12.7940i	0.177311	+	0.984155i
$170$	−4.50367			−0.345416
$171$	−9.90396	+	5.71806i	−0.757375	+	0.437271i
$172$	−1.30752	−	2.26469i	−0.0996974	−	0.172681i
$173$	1.99470	−	3.45492i	0.151654	−	0.262673i	−0.780182	−	0.625553i	$-0.784873\pi$
$173$	1.99470	−	3.45492i	0.151654	−	0.262673i	0.931836	+	0.362880i	$0.118207\pi$
$174$		−	4.72047i		−	0.357858i
$175$	−1.24653	−	0.719687i	−0.0942291	−	0.0544032i
$176$	2.40029	+	1.38581i	0.180929	+	0.104459i
$177$		−	2.07914i		−	0.156278i
$178$	−2.97859	+	5.15906i	−0.223254	+	0.386688i
$179$	6.23996	+	10.8079i	0.466397	+	0.807823i	0.999263	−	0.0383766i	$-0.0122186\pi$
$179$	6.23996	+	10.8079i	0.466397	+	0.807823i	−0.532867	+	0.846199i	$0.678885\pi$
$180$	2.28610	−	1.31988i	0.170396	−	0.0983782i
$181$	19.4319			1.44436			0.722180	−	0.691705i	$-0.243140\pi$
$181$	19.4319			1.44436			0.722180	+	0.691705i	$0.243140\pi$
$182$	−3.98177	−	3.32850i	−0.295148	−	0.246725i
$183$	7.50465			0.554760
$184$	3.84461	−	2.21969i	0.283428	−	0.163637i
$185$	0.287734	+	0.498370i	0.0211546	+	0.0366409i
$186$	−1.24865	+	2.16273i	−0.0915557	+	0.158579i
$187$		−	12.4825i		−	0.912808i
$188$	11.0577	+	6.38418i	0.806467	+	0.465614i
$189$	4.21947	+	2.43611i	0.306921	+	0.177201i
$190$		−	4.33225i		−	0.314294i
$191$	9.16074	−	15.8669i	0.662848	−	1.14809i	−0.317016	−	0.948420i	$-0.602681\pi$
$191$	9.16074	−	15.8669i	0.662848	−	1.14809i	0.979864	−	0.199666i	$-0.0639858\pi$
$192$	−0.300098	−	0.519785i	−0.0216577	−	0.0375122i
$193$	4.10811	−	2.37182i	0.295708	−	0.170727i	−0.344805	−	0.938674i	$-0.612055\pi$
$193$	4.10811	−	2.37182i	0.295708	−	0.170727i	0.640513	+	0.767947i	$0.278722\pi$
$194$	1.58633			0.113892
$195$	2.13186	+	0.371816i	0.152665	+	0.0266263i
$196$	−4.92820			−0.352015
$197$	−9.35358	+	5.40029i	−0.666415	+	0.384755i	−0.794717	−	0.606980i	$-0.792381\pi$
$197$	−9.35358	+	5.40029i	−0.666415	+	0.384755i	0.128302	+	0.991735i	$0.459047\pi$
$198$	3.65821	+	6.33621i	0.259978	+	0.450295i
$199$	5.50367	−	9.53264i	0.390145	−	0.675751i	−0.602323	−	0.798252i	$-0.705758\pi$
$199$	5.50367	−	9.53264i	0.390145	−	0.675751i	0.992468	+	0.122501i	$0.0390916\pi$
$200$			1.00000i			0.0707107i
$201$	2.76993	+	1.59922i	0.195375	+	0.112800i
$202$	11.9109	+	6.87676i	0.838048	+	0.483847i
$203$		−	11.3205i		−	0.794544i
$204$	−1.35154	+	2.34094i	−0.0946269	+	0.163899i
$205$	2.11256	+	3.65906i	0.147548	+	0.255560i
$206$	−4.96410	+	2.86603i	−0.345865	+	0.199685i
$207$	11.7189			0.814520
$208$	−0.619491	+	3.55193i	−0.0429540	+	0.246282i
$209$	12.0073			0.830565
$210$	−0.748164	+	0.431953i	−0.0516283	+	0.0298076i
$211$	−13.1291	−	22.7402i	−0.903843	−	1.56550i	−0.822462	−	0.568820i	$-0.807400\pi$
$211$	−13.1291	−	22.7402i	−0.903843	−	1.56550i	−0.0813811	−	0.996683i	$-0.525933\pi$
$212$	4.78561	−	8.28893i	0.328677	−	0.569286i
$213$			3.60117i			0.246748i
$214$	−4.05242	−	2.33967i	−0.277018	−	0.159936i
$215$	2.26469	+	1.30752i	0.154450	+	0.0891720i
$216$		−	3.38496i		−	0.230318i
$217$	−2.99449	+	5.18661i	−0.203279	+	0.352090i
$218$	1.16082	+	2.01060i	0.0786208	+	0.136175i
$219$	−0.864669	+	0.499217i	−0.0584289	+	0.0337340i
$220$	−2.77162			−0.186863
$221$	15.2486	−	5.58217i	1.02573	−	0.375498i
$222$	0.345393			0.0231813
$223$	−19.2294	+	11.1021i	−1.28770	+	0.743452i	−0.978243	−	0.207463i	$-0.933479\pi$
$223$	−19.2294	+	11.1021i	−1.28770	+	0.743452i	−0.309454	+	0.950915i	$0.600146\pi$
$224$	−0.719687	−	1.24653i	−0.0480861	−	0.0832876i
$225$	−1.31988	+	2.28610i	−0.0879922	+	0.152407i
$226$			7.73629i			0.514610i
$227$	1.80059	+	1.03957i	0.119509	+	0.0689986i	0.558563	−	0.829462i	$-0.311353\pi$
$227$	1.80059	+	1.03957i	0.119509	+	0.0689986i	−0.439054	+	0.898461i	$0.644686\pi$
$228$	−2.25184	−	1.30010i	−0.149131	−	0.0861011i
$229$			4.67933i			0.309219i	0.987976	+	0.154610i	$0.0494120\pi$
$229$			4.67933i			0.309219i	−0.987976	+	0.154610i	$0.950588\pi$
$230$	−2.21969	+	3.84461i	−0.146362	+	0.253506i
$231$	−1.19721	−	2.07363i	−0.0787706	−	0.136435i
$232$	−6.81119	+	3.93244i	−0.447177	+	0.258177i
$233$	0.611060			0.0400319			0.0200160	−	0.999800i	$-0.493628\pi$
$233$	0.611060			0.0400319			0.0200160	+	0.999800i	$0.493628\pi$
$234$	−6.10436	+	7.30243i	−0.399054	+	0.477375i
$235$	−12.7684			−0.832916
$236$	−3.00000	+	1.73205i	−0.195283	+	0.112747i
$237$	3.81988	+	6.61623i	0.248128	+	0.429770i
$238$	−3.24123	+	5.61398i	−0.210098	+	0.363900i
$239$		−	25.6481i		−	1.65904i	−0.558479	−	0.829518i	$-0.688615\pi$
$239$		−	25.6481i		−	1.65904i	0.558479	−	0.829518i	$-0.311385\pi$
$240$	0.519785	+	0.300098i	0.0335520	+	0.0193712i
$241$	23.4633	+	13.5466i	1.51141	+	0.872610i	0.999911	+	0.0133234i	$0.00424108\pi$
$241$	23.4633	+	13.5466i	1.51141	+	0.872610i	0.511494	+	0.859287i	$0.329092\pi$
$242$			3.31812i			0.213297i
$243$	6.84432	−	11.8547i	0.439063	−	0.760480i
$244$	−6.25184	−	10.8285i	−0.400233	−	0.693223i
$245$	4.26795	−	2.46410i	0.272669	−	0.157426i
$246$	2.53590			0.161683
$247$	5.36970	+	14.6682i	0.341666	+	0.933313i
$248$	4.16082			0.264212
$249$	−5.22223	+	3.01506i	−0.330945	+	0.191071i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	0.751836	−	1.30222i	0.0474554	−	0.0821952i	−0.841322	−	0.540534i	$-0.818222\pi$
$251$	0.751836	−	1.30222i	0.0474554	−	0.0821952i	0.888777	+	0.458339i	$0.151555\pi$
$252$		−	3.79961i		−	0.239353i
$253$	−10.6558	−	6.15213i	−0.669924	−	0.386781i
$254$	−13.9641	−	8.06218i	−0.876186	−	0.505866i
$255$		−	2.70308i		−	0.169274i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.1724	−	17.6191i	−0.634537	−	1.09905i	−0.986613	−	0.163079i	$-0.947857\pi$
$257$	−10.1724	−	17.6191i	−0.634537	−	1.09905i	0.352076	−	0.935971i	$-0.385476\pi$
$258$	1.35926	−	0.784767i	0.0846236	−	0.0488575i
$259$	0.828313			0.0514689
$260$	−1.23947	−	3.38581i	−0.0768688	−	0.209979i
$261$	−20.7614			−1.28510
$262$	−17.1134	+	9.88043i	−1.05727	+	0.610415i
$263$	8.56466	+	14.8344i	0.528119	+	0.914729i	0.999463	+	0.0327796i	$0.0104359\pi$
$263$	8.56466	+	14.8344i	0.528119	+	0.914729i	−0.471343	+	0.881950i	$0.656231\pi$
$264$	−0.831757	+	1.44065i	−0.0511911	+	0.0886656i
$265$			9.57123i			0.587956i
$266$	−5.40029	−	3.11786i	−0.331113	−	0.191168i
$267$	−3.09645	−	1.78773i	−0.189499	−	0.109408i
$268$		−	5.32899i		−	0.325520i
$269$	−9.69121	+	16.7857i	−0.590883	+	1.02344i	0.403230	+	0.915099i	$0.367887\pi$
$269$	−9.69121	+	16.7857i	−0.590883	+	1.02344i	−0.994114	+	0.108342i	$0.965446\pi$
$270$	1.69248	+	2.93146i	0.103001	+	0.178403i
$271$	−15.9098	+	9.18555i	−0.966454	+	0.557982i	−0.898153	−	0.439682i	$-0.855091\pi$
$271$	−15.9098	+	9.18555i	−0.966454	+	0.557982i	−0.0683006	+	0.997665i	$0.521758\pi$
$272$	4.50367			0.273075
$273$	1.99775	−	2.38984i	0.120909	−	0.144640i
$274$	−17.2647			−1.04300
$275$	2.40029	−	1.38581i	0.144743	−	0.0835675i
$276$	1.33225	+	2.30752i	0.0801918	+	0.138896i
$277$	−13.6171	+	23.5855i	−0.818171	+	1.41711i	0.0888576	+	0.996044i	$0.471678\pi$
$277$	−13.6171	+	23.5855i	−0.818171	+	1.41711i	−0.907028	+	0.421069i	$0.861655\pi$
$278$			2.94657i			0.176723i
$279$	9.51207	+	5.49180i	0.569473	+	0.328785i
$280$	1.24653	+	0.719687i	0.0744947	+	0.0430095i
$281$		−	30.0815i		−	1.79451i	−0.441509	−	0.897257i	$-0.645557\pi$
$281$		−	30.0815i		−	1.79451i	0.441509	−	0.897257i	$-0.354443\pi$
$282$	−3.83176	+	6.63680i	−0.228178	+	0.395216i
$283$	−12.7394	−	22.0653i	−0.757278	−	1.31164i	−0.944234	−	0.329276i	$-0.893195\pi$
$283$	−12.7394	−	22.0653i	−0.757278	−	1.31164i	0.186955	−	0.982368i	$-0.440138\pi$
$284$	5.19615	−	3.00000i	0.308335	−	0.178017i
$285$	2.60020			0.154022
$286$	9.38418	−	3.43534i	0.554898	−	0.203136i
$287$	6.08153			0.358981
$288$	−2.28610	+	1.31988i	−0.134710	+	0.0777748i
$289$	−1.64153	−	2.84321i	−0.0965604	−	0.167247i
$290$	3.93244	−	6.81119i	0.230921	−	0.399967i
$291$			0.952110i			0.0558137i
$292$	1.44065	+	0.831757i	0.0843074	+	0.0486749i
$293$	−14.3568	−	8.28893i	−0.838736	−	0.484244i	0.0180985	−	0.999836i	$-0.494239\pi$
$293$	−14.3568	−	8.28893i	−0.838736	−	0.484244i	−0.856834	+	0.515592i	$0.827572\pi$
$294$		−	2.95789i		−	0.172507i
$295$	1.73205	−	3.00000i	0.100844	−	0.174667i
$296$	−0.287734	−	0.498370i	−0.0167242	−	0.0289672i
$297$	−8.12490	+	4.69092i	−0.471455	+	0.272195i
$298$	−7.06528			−0.409280
$299$	2.75015	−	15.7684i	0.159045	−	0.911908i
$300$	−0.600196			−0.0346523
$301$	3.25973	−	1.88201i	0.187888	−	0.108477i
$302$	7.91633	+	13.7115i	0.455534	+	0.789007i
$303$	−4.12740	+	7.14887i	−0.237113	+	0.410692i
$304$			4.33225i			0.248471i
$305$	10.8285	+	6.25184i	0.620038	+	0.357979i
$306$	10.2959	+	5.94432i	0.588575	+	0.339814i
$307$			16.2722i			0.928703i	0.885651	+	0.464351i	$0.153713\pi$
$307$			16.2722i			0.928703i	−0.885651	+	0.464351i	$0.846287\pi$
$308$	−1.99470	+	3.45492i	−0.113659	+	0.196862i
$309$	−1.72018	−	2.97943i	−0.0978574	−	0.169494i
$310$	−3.60338	+	2.08041i	−0.204658	+	0.118159i
$311$	−16.1053			−0.913246			−0.456623	−	0.889660i	$-0.650941\pi$
$311$	−16.1053			−0.913246			−0.456623	+	0.889660i	$0.650941\pi$
$312$	−2.13186	−	0.371816i	−0.120693	−	0.0210499i
$313$	−10.2162			−0.577454			−0.288727	−	0.957411i	$-0.593232\pi$
$313$	−10.2162			−0.577454			−0.288727	+	0.957411i	$0.593232\pi$
$314$	10.9362	−	6.31401i	0.617165	−	0.356320i
$315$	1.89980	+	3.29056i	0.107042	+	0.185402i
$316$	6.36440	−	11.0235i	0.358025	−	0.620118i
$317$		−	0.204368i		−	0.0114785i	−0.999984	−	0.00573923i	$-0.998173\pi$
$317$		−	0.204368i		−	0.0114785i	0.999984	−	0.00573923i	$-0.00182686\pi$
$318$	4.97498	+	2.87231i	0.278983	+	0.161071i
$319$	18.8780	+	10.8992i	1.05697	+	0.610240i
$320$		−	1.00000i		−	0.0559017i
$321$	1.40426	−	2.43225i	0.0783781	−	0.135755i
$322$	3.19496	+	5.53383i	0.178048	+	0.308388i
$323$	16.8970	−	9.75551i	0.940176	−	0.542811i
$324$	−5.88766			−0.327092
$325$	2.76632	+	2.31246i	0.153448	+	0.128272i
$326$	−18.3686			−1.01734
$327$	−1.20676	+	0.696720i	−0.0667337	+	0.0385287i
$328$	−2.11256	−	3.65906i	−0.116647	−	0.202038i
$329$	−9.18922	+	15.9162i	−0.506618	+	0.877488i
$330$		−	1.66351i		−	0.0915735i
$331$	16.5110	+	9.53264i	0.907527	+	0.523961i	0.879635	−	0.475650i	$-0.157787\pi$
$331$	16.5110	+	9.53264i	0.907527	+	0.523961i	0.0278926	+	0.999611i	$0.491120\pi$
$332$	8.70088	+	5.02346i	0.477523	+	0.275698i
$333$		−	1.51910i		−	0.0832462i
$334$	10.8043	−	18.7135i	0.591183	−	1.02396i
$335$	2.66449	+	4.61504i	0.145577	+	0.252146i
$336$	0.748164	−	0.431953i	0.0408157	−	0.0235650i
$337$	19.8609			1.08189			0.540946	−	0.841057i	$-0.318066\pi$
$337$	19.8609			1.08189			0.540946	+	0.841057i	$0.318066\pi$
$338$	8.39323	+	9.92742i	0.456532	+	0.539980i
$339$	−4.64329			−0.252189
$340$	−3.90029	+	2.25184i	−0.211523	+	0.122123i
$341$	−5.76611	−	9.98719i	−0.312252	−	0.540837i
$342$	−5.71806	+	9.90396i	−0.309197	+	0.535545i
$343$		−	17.1691i		−	0.927047i
$344$	−2.26469	−	1.30752i	−0.122104	−	0.0704967i
$345$	−2.30752	−	1.33225i	−0.124233	−	0.0717257i
$346$		−	3.98940i		−	0.214471i
$347$	−8.52522	+	14.7661i	−0.457658	+	0.792686i	−0.998837	−	0.0482211i	$-0.984645\pi$
$347$	−8.52522	+	14.7661i	−0.457658	+	0.792686i	0.541179	+	0.840907i	$0.317978\pi$
$348$	−2.36023	−	4.08805i	−0.126522	−	0.219142i
$349$	18.3917	−	10.6185i	0.984488	−	0.568394i	0.0808657	−	0.996725i	$-0.474232\pi$
$349$	18.3917	−	10.6185i	0.984488	−	0.568394i	0.903622	+	0.428331i	$0.140898\pi$
$350$	−1.43937			−0.0769378
$351$	−9.36389	−	7.82760i	−0.499807	−	0.417806i
$352$	2.77162			0.147728
$353$	13.8710	−	8.00840i	0.738276	−	0.426244i	−0.0831659	−	0.996536i	$-0.526503\pi$
$353$	13.8710	−	8.00840i	0.738276	−	0.426244i	0.821442	+	0.570292i	$0.193170\pi$
$354$	−1.03957	−	1.80059i	−0.0552525	−	0.0957001i
$355$	−3.00000	+	5.19615i	−0.159223	+	0.275783i
$356$			5.95717i			0.315729i
$357$	−3.36949	−	1.94537i	−0.178332	−	0.102960i
$358$	10.8079	+	6.23996i	0.571217	+	0.329792i
$359$		−	24.2487i		−	1.27980i	−0.768459	−	0.639899i	$-0.778976\pi$
$359$		−	24.2487i		−	1.27980i	0.768459	−	0.639899i	$-0.221024\pi$
$360$	1.31988	−	2.28610i	0.0695639	−	0.120488i
$361$	−0.115820	−	0.200606i	−0.00609580	−	0.0105582i
$362$	16.8285	−	9.71594i	0.884486	−	0.510658i
$363$	−1.99152			−0.104528
$364$	−5.11256	−	0.891679i	−0.267971	−	0.0467367i
$365$	−1.66351			−0.0870723
$366$	6.49922	−	3.75232i	0.339720	−	0.196137i
$367$	14.8854	+	25.7822i	0.777010	+	1.34582i	0.933658	+	0.358167i	$0.116598\pi$
$367$	14.8854	+	25.7822i	0.777010	+	1.34582i	−0.156648	+	0.987655i	$0.550069\pi$
$368$	2.21969	−	3.84461i	0.115709	−	0.200414i
$369$		−	11.1533i		−	0.580619i
$370$	0.498370	+	0.287734i	0.0259090	+	0.0149586i
$371$	11.9309	+	6.88829i	0.619420	+	0.357622i
$372$			2.49731i			0.129479i
$373$	−14.1929	+	24.5828i	−0.734880	+	1.27285i	0.219896	+	0.975523i	$0.429428\pi$
$373$	−14.1929	+	24.5828i	−0.734880	+	1.27285i	−0.954776	+	0.297326i	$0.903905\pi$
$374$	−6.24123	−	10.8101i	−0.322726	−	0.558979i
$375$	0.519785	−	0.300098i	0.0268416	−	0.0154970i
$376$	12.7684			0.658478
$377$	−4.87223	+	27.9355i	−0.250932	+	1.43875i
$378$	4.87223			0.250600
$379$	−24.6070	+	14.2069i	−1.26398	+	0.729759i	−0.973842	−	0.227226i	$-0.927034\pi$
$379$	−24.6070	+	14.2069i	−1.26398	+	0.729759i	−0.290137	+	0.956985i	$0.593701\pi$
$380$	−2.16612	−	3.75184i	−0.111120	−	0.192465i
$381$	4.83888	−	8.38119i	0.247904	−	0.429382i
$382$		−	18.3215i		−	0.937409i
$383$	−8.13827	−	4.69863i	−0.415846	−	0.240089i	0.277452	−	0.960739i	$-0.410510\pi$
$383$	−8.13827	−	4.69863i	−0.415846	−	0.240089i	−0.693298	+	0.720651i	$0.743843\pi$
$384$	−0.519785	−	0.300098i	−0.0265252	−	0.0153143i
$385$		−	3.98940i		−	0.203319i
$386$	2.37182	−	4.10811i	0.120722	−	0.209097i
$387$	−3.45154	−	5.97825i	−0.175452	−	0.303891i
$388$	1.37380	−	0.793166i	0.0697443	−	0.0402669i
$389$	11.6461			0.590482			0.295241	−	0.955423i	$-0.404600\pi$
$389$	11.6461			0.590482			0.295241	+	0.955423i	$0.404600\pi$
$390$	2.03215	−	0.743926i	0.102902	−	0.0376701i
$391$	−19.9935			−1.01111
$392$	−4.26795	+	2.46410i	−0.215564	+	0.124456i
$393$	−5.93019	−	10.2714i	−0.299139	−	0.518123i
$394$	−5.40029	+	9.35358i	−0.272063	+	0.471227i
$395$			12.7288i			0.640455i
$396$	6.33621	+	3.65821i	0.318407	+	0.183832i
$397$	−0.346241	−	0.199902i	−0.0173773	−	0.0100328i	0.491286	−	0.870998i	$-0.336527\pi$
$397$	−0.346241	−	0.199902i	−0.0173773	−	0.0100328i	−0.508663	+	0.860965i	$0.669860\pi$
$398$		−	11.0073i		−	0.551748i
$399$	1.87133	−	3.24123i	0.0936835	−	0.162265i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	7.36793	−	4.25388i	0.367937	−	0.212428i	−0.304620	−	0.952474i	$-0.598529\pi$
$401$	7.36793	−	4.25388i	0.367937	−	0.212428i	0.672557	+	0.740046i	$0.265196\pi$
$402$	3.19843			0.159523
$403$	9.62174	−	11.5102i	0.479293	−	0.573362i
$404$	13.7535			0.684263
$405$	5.09886	−	2.94383i	0.253364	−	0.146280i
$406$	−5.66025	−	9.80385i	−0.280914	−	0.486557i
$407$	−0.797489	+	1.38129i	−0.0395301	+	0.0684681i
$408$			2.70308i			0.133823i
$409$	−12.1357	−	7.00657i	−0.600074	−	0.346453i	0.168997	−	0.985617i	$-0.445947\pi$
$409$	−12.1357	−	7.00657i	−0.600074	−	0.346453i	−0.769071	+	0.639164i	$0.779281\pi$
$410$	3.65906	+	2.11256i	0.180708	+	0.104332i
$411$		−	10.3622i		−	0.511129i
$412$	−2.86603	+	4.96410i	−0.141199	+	0.244564i
$413$	−2.49307	−	4.31812i	−0.122676	−	0.212481i
$414$	10.1489	−	5.85945i	0.498790	−	0.287976i
$415$	−10.0469			−0.493183
$416$	1.23947	+	3.38581i	0.0607701	+	0.166003i
$417$	−1.76852			−0.0866047
$418$	10.3987	−	6.00367i	0.508615	−	0.293649i
$419$	12.0977	+	20.9539i	0.591012	+	1.02366i	0.994096	+	0.108500i	$0.0346048\pi$
$419$	12.0977	+	20.9539i	0.591012	+	1.02366i	−0.403084	+	0.915163i	$0.632062\pi$
$420$	−0.431953	+	0.748164i	−0.0210771	+	0.0365067i
$421$			35.6392i			1.73695i	0.495735	+	0.868474i	$0.334899\pi$
$421$			35.6392i			1.73695i	−0.495735	+	0.868474i	$0.665101\pi$
$422$	−22.7402	−	13.1291i	−1.10698	−	0.639114i
$423$	29.1898	+	16.8527i	1.41926	+	0.819408i
$424$		−	9.57123i		−	0.464820i
$425$	2.25184	−	3.90029i	0.109230	−	0.189192i
$426$	1.80059	+	3.11871i	0.0872387	+	0.151102i
$427$	15.5863	−	8.99873i	0.754272	−	0.435479i
$428$	−4.67933			−0.226184
$429$	2.06188	+	5.63234i	0.0995485	+	0.271932i
$430$	2.61504			0.126108
$431$	4.29586	−	2.48022i	0.206924	−	0.119468i	−0.392957	−	0.919557i	$-0.628548\pi$
$431$	4.29586	−	2.48022i	0.206924	−	0.119468i	0.599881	+	0.800089i	$0.295215\pi$
$432$	−1.69248	−	2.93146i	−0.0814295	−	0.141040i
$433$	2.10811	−	3.65135i	0.101309	−	0.175472i	−0.810915	−	0.585164i	$-0.801030\pi$
$433$	2.10811	−	3.65135i	0.101309	−	0.175472i	0.912224	+	0.409691i	$0.134364\pi$
$434$			5.98898i			0.287480i
$435$	4.08805	+	2.36023i	0.196007	+	0.113165i
$436$	2.01060	+	1.16082i	0.0962904	+	0.0555933i
$437$		−	19.2325i		−	0.920013i
$438$	−0.499217	+	0.864669i	−0.0238535	+	0.0413155i
$439$	−7.37500	−	12.7739i	−0.351989	−	0.609664i	0.634608	−	0.772834i	$-0.281161\pi$
$439$	−7.37500	−	12.7739i	−0.351989	−	0.609664i	−0.986598	+	0.163170i	$0.947828\pi$
$440$	−2.40029	+	1.38581i	−0.114430	+	0.0660659i
$441$	−13.0093			−0.619490
$442$	10.4146	−	12.4586i	0.495370	−	0.592595i
$443$	−12.2374			−0.581417			−0.290709	−	0.956812i	$-0.593891\pi$
$443$	−12.2374			−0.581417			−0.290709	+	0.956812i	$0.593891\pi$
$444$	0.299119	−	0.172697i	0.0141956	−	0.00819582i
$445$	−2.97859	−	5.15906i	−0.141198	−	0.244563i
$446$	−11.1021	+	19.2294i	−0.525700	+	0.910539i
$447$		−	4.24055i		−	0.200571i
$448$	−1.24653	−	0.719687i	−0.0588932	−	0.0340020i
$449$	−16.5163	−	9.53569i	−0.779452	−	0.450017i	0.0567839	−	0.998386i	$-0.481915\pi$
$449$	−16.5163	−	9.53569i	−0.779452	−	0.450017i	−0.836236	+	0.548370i	$0.815249\pi$
$450$			2.63977i			0.124440i
$451$	−5.85521	+	10.1415i	−0.275711	+	0.477546i
$452$	3.86814	+	6.69982i	0.181942	+	0.315133i
$453$	−8.22957	+	4.75135i	−0.386659	+	0.223238i
$454$	2.07914			0.0975788
$455$	4.87345	−	1.78406i	0.228471	−	0.0836382i
$456$	−2.60020			−0.121765
$457$	13.9549	−	8.05688i	0.652784	−	0.376885i	−0.136738	−	0.990607i	$-0.543662\pi$
$457$	13.9549	−	8.05688i	0.652784	−	0.376885i	0.789522	+	0.613722i	$0.210329\pi$
$458$	2.33967	+	4.05242i	0.109325	+	0.189357i
$459$	−7.62238	+	13.2023i	−0.355782	+	0.616233i
$460$			4.43937i			0.206987i
$461$	4.19560	+	2.42233i	0.195408	+	0.112819i	0.594512	−	0.804087i	$-0.297345\pi$
$461$	4.19560	+	2.42233i	0.195408	+	0.112819i	−0.399104	+	0.916906i	$0.630679\pi$
$462$	−2.07363	−	1.19721i	−0.0964739	−	0.0556992i
$463$			8.23164i			0.382557i	0.981536	+	0.191278i	$0.0612633\pi$
$463$			8.23164i			0.382557i	−0.981536	+	0.191278i	$0.938737\pi$
$464$	−3.93244	+	6.81119i	−0.182559	+	0.316202i
$465$	−1.24865	−	2.16273i	−0.0579049	−	0.100294i
$466$	0.529194	−	0.305530i	0.0245144	−	0.0141534i
$467$	−33.4873			−1.54961			−0.774803	−	0.632203i	$-0.782151\pi$
$467$	−33.4873			−1.54961			−0.774803	+	0.632203i	$0.782151\pi$
$468$	−1.63531	+	9.37627i	−0.0755923	+	0.433418i
$469$	7.67040			0.354186
$470$	−11.0577	+	6.38418i	−0.510055	+	0.294480i
$471$	3.78964	+	6.56386i	0.174618	+	0.302446i
$472$	−1.73205	+	3.00000i	−0.0797241	+	0.138086i
$473$			7.24789i			0.333258i
$474$	6.61623	+	3.81988i	0.303894	+	0.175453i
$475$	3.75184	+	2.16612i	0.172146	+	0.0993886i
$476$			6.48247i			0.297123i
$477$	12.6329	−	21.8808i	0.578421	−	1.00185i
$478$	−12.8240	−	22.2119i	−0.586558	−	1.01595i
$479$	6.97448	−	4.02672i	0.318672	−	0.183985i	−0.332128	−	0.943234i	$-0.607767\pi$
$479$	6.97448	−	4.02672i	0.318672	−	0.183985i	0.650800	+	0.759249i	$0.274433\pi$
$480$	0.600196			0.0273951
$481$	−2.04402	−	0.356497i	−0.0931994	−	0.0162549i
$482$	27.0931			1.23406
$483$	−3.32138	+	1.91760i	−0.151128	+	0.0872538i
$484$	1.65906	+	2.87358i	0.0754118	+	0.130617i
$485$	−0.793166	+	1.37380i	−0.0360158	+	0.0623812i
$486$		−	13.6886i		−	0.620929i
$487$	−1.40601	−	0.811758i	−0.0637122	−	0.0367842i	0.467806	−	0.883831i	$-0.345045\pi$
$487$	−1.40601	−	0.811758i	−0.0637122	−	0.0367842i	−0.531518	+	0.847047i	$0.678378\pi$
$488$	−10.8285	−	6.25184i	−0.490183	−	0.283007i
$489$		−	11.0247i		−	0.498555i
$490$	2.46410	−	4.26795i	0.111317	−	0.192806i
$491$	5.16033	+	8.93796i	0.232883	+	0.403364i	0.958655	−	0.284570i	$-0.0918509\pi$
$491$	5.16033	+	8.93796i	0.232883	+	0.403364i	−0.725773	+	0.687935i	$0.758518\pi$
$492$	2.19615	−	1.26795i	0.0990102	−	0.0571636i
$493$	35.4209			1.59527
$494$	11.9844	+	10.0182i	0.539203	+	0.450738i
$495$	−7.31643			−0.328849
$496$	3.60338	−	2.08041i	0.161796	−	0.0934132i
$497$	4.31812	+	7.47921i	0.193694	+	0.335488i
$498$	−3.01506	+	5.22223i	−0.135108	+	0.234014i
$499$		−	13.9807i		−	0.625860i	−0.949776	−	0.312930i	$-0.898689\pi$
$499$		−	13.9807i		−	0.625860i	0.949776	−	0.312930i	$-0.101311\pi$
$500$	−0.866025	−	0.500000i	−0.0387298	−	0.0223607i
$501$	11.2318	+	6.48467i	0.501799	+	0.289714i
$502$		−	1.50367i		−	0.0671121i
$503$	−11.8924	+	20.5983i	−0.530258	+	0.918434i	0.469119	+	0.883135i	$0.344572\pi$
$503$	−11.8924	+	20.5983i	−0.530258	+	0.918434i	−0.999377	+	0.0352988i	$0.988762\pi$
$504$	−1.89980	−	3.29056i	−0.0846240	−	0.146573i
$505$	−11.9109	+	6.87676i	−0.530028	+	0.306012i
$506$	−12.3043			−0.546991
$507$	−5.95839	+	5.03758i	−0.264622	+	0.223727i
$508$	−16.1244			−0.715403
$509$	−22.2023	+	12.8185i	−0.984102	+	0.568171i	−0.903506	−	0.428575i	$-0.859016\pi$
$509$	−22.2023	+	12.8185i	−0.984102	+	0.568171i	−0.0805958	+	0.996747i	$0.525682\pi$
$510$	−1.35154	−	2.34094i	−0.0598473	−	0.103659i
$511$	−1.19721	+	2.07363i	−0.0529614	+	0.0917319i
$512$			1.00000i			0.0441942i
$513$	−12.6998	−	7.33225i	−0.560711	−	0.323727i
$514$	−17.6191	−	10.1724i	−0.777146	−	0.448685i
$515$		−	5.73205i		−	0.252584i
$516$	0.784767	−	1.35926i	0.0345474	−	0.0598379i
$517$	−17.6945	−	30.6478i	−0.778204	−	1.34789i
$518$	0.717340	−	0.414157i	0.0315181	−	0.0181970i
$519$	2.39442			0.105103
$520$	−2.76632	−	2.31246i	−0.121311	−	0.101408i
$521$	−8.53476			−0.373915			−0.186957	−	0.982368i	$-0.559863\pi$
$521$	−8.53476			−0.373915			−0.186957	+	0.982368i	$0.559863\pi$
$522$	−17.9799	+	10.3807i	−0.786961	+	0.454352i
$523$	6.34383	+	10.9878i	0.277396	+	0.480464i	0.970737	−	0.240146i	$-0.0771952\pi$
$523$	6.34383	+	10.9878i	0.277396	+	0.480464i	−0.693341	+	0.720610i	$0.743862\pi$
$524$	−9.88043	+	17.1134i	−0.431629	+	0.747603i
$525$		−	0.863906i		−	0.0377039i
$526$	14.8344	+	8.56466i	0.646811	+	0.373437i
$527$	−16.2284	−	9.36949i	−0.706921	−	0.408141i
$528$			1.66351i			0.0723952i
$529$	1.64598	−	2.85092i	0.0715644	−	0.123953i
$530$	4.78561	+	8.28893i	0.207874	+	0.360048i
$531$	−7.91930	+	4.57221i	−0.343668	+	0.198417i
$532$	−6.23572			−0.270353
$533$	−15.0073	−	2.61742i	−0.650040	−	0.113373i
$534$	−3.57547			−0.154726
$535$	4.05242	−	2.33967i	0.175202	−	0.101153i
$536$	−2.66449	−	4.61504i	−0.115089	−	0.199339i
$537$	−3.74520	+	6.48687i	−0.161617	+	0.279929i
$538$			19.3824i			0.835635i
$539$	11.8291	+	6.82955i	0.509517	+	0.294170i
$540$	2.93146	+	1.69248i	0.126150	+	0.0728328i
$541$		−	42.0507i		−	1.80790i	−0.427636	−	0.903951i	$-0.640653\pi$
$541$		−	42.0507i		−	1.80790i	0.427636	−	0.903951i	$-0.359347\pi$
$542$	−9.18555	+	15.9098i	−0.394553	+	0.683386i
$543$	5.83146	+	10.1004i	0.250252	+	0.433449i
$544$	3.90029	−	2.25184i	0.167224	−	0.0965467i
$545$	−2.32164			−0.0994483
$546$	0.535182	−	3.06854i	0.0229037	−	0.131321i
$547$	24.6297			1.05309			0.526545	−	0.850147i	$-0.323487\pi$
$547$	24.6297			1.05309			0.526545	+	0.850147i	$0.323487\pi$
$548$	−14.9517	+	8.63234i	−0.638703	+	0.368755i
$549$	−16.5034	−	28.5847i	−0.704347	−	1.21996i
$550$	1.38581	−	2.40029i	0.0590911	−	0.102349i
$551$			34.0726i			1.45154i
$552$	2.30752	+	1.33225i	0.0982145	+	0.0567042i
$553$	15.8669	+	9.16074i	0.674728	+	0.389554i
$554$			27.2342i			1.15707i
$555$	−0.172697	+	0.299119i	−0.00733056	+	0.0126969i
$556$	1.47328	+	2.55180i	0.0624811	+	0.108221i
$557$	6.84583	−	3.95244i	0.290067	−	0.167470i	−0.347905	−	0.937530i	$-0.613107\pi$
$557$	6.84583	−	3.95244i	0.290067	−	0.167470i	0.637972	+	0.770059i	$0.279773\pi$
$558$	10.9836			0.464973
$559$	−8.85402	+	3.24126i	−0.374485	+	0.137091i
$560$	1.43937			0.0608246
$561$	6.48819	−	3.74596i	0.273932	−	0.158155i
$562$	−15.0408	−	26.0514i	−0.634456	−	1.09891i
$563$	6.63553	−	11.4931i	0.279654	−	0.484375i	−0.691645	−	0.722238i	$-0.743114\pi$
$563$	6.63553	−	11.4931i	0.279654	−	0.484375i	0.971299	+	0.237863i	$0.0764469\pi$
$564$			7.66351i			0.322692i
$565$	−6.69982	−	3.86814i	−0.281864	−	0.162734i
$566$	−22.0653	−	12.7394i	−0.927473	−	0.535477i
$567$		−	8.47454i		−	0.355897i
$568$	3.00000	−	5.19615i	0.125877	−	0.218026i
$569$	21.1323	+	36.6022i	0.885911	+	1.53444i	0.844666	+	0.535293i	$0.179799\pi$
$569$	21.1323	+	36.6022i	0.885911	+	1.53444i	0.0412443	+	0.999149i	$0.486868\pi$
$570$	2.25184	−	1.30010i	0.0943190	−	0.0544551i
$571$	1.64965			0.0690358			0.0345179	−	0.999404i	$-0.489010\pi$
$571$	1.64965			0.0690358			0.0345179	+	0.999404i	$0.489010\pi$
$572$	6.40927	−	7.66719i	0.267985	−	0.320581i
$573$	10.9965			0.459384
$574$	5.26676	−	3.04076i	0.219830	−	0.126919i
$575$	−2.21969	−	3.84461i	−0.0925673	−	0.160331i
$576$	−1.31988	+	2.28610i	−0.0549951	+	0.0952543i
$577$		−	28.4651i		−	1.18502i	−0.805564	−	0.592508i	$-0.798138\pi$
$577$		−	28.4651i		−	1.18502i	0.805564	−	0.592508i	$-0.201862\pi$
$578$	−2.84321	−	1.64153i	−0.118262	−	0.0682785i
$579$	2.46567	+	1.42355i	0.102470	+	0.0591609i
$580$		−	7.86488i		−	0.326572i
$581$	−7.23063	+	12.5238i	−0.299977	+	0.519576i
$582$	0.476055	+	0.824551i	0.0197331	+	0.0341788i
$583$	−22.9738	+	13.2639i	−0.951476	+	0.549335i
$584$	1.66351			0.0688367
$585$	−3.27191	−	8.93774i	−0.135277	−	0.369530i
$586$	−16.5779			−0.684825
$587$	19.1994	−	11.0848i	0.792445	−	0.457518i	−0.0483779	−	0.998829i	$-0.515405\pi$
$587$	19.1994	−	11.0848i	0.792445	−	0.457518i	0.840822	+	0.541311i	$0.182072\pi$
$588$	−1.47894	−	2.56160i	−0.0609906	−	0.105639i
$589$	9.01285	−	15.6107i	0.371368	−	0.643228i
$590$		−	3.46410i		−	0.142615i
$591$	−5.61398	−	3.24123i	−0.230928	−	0.133327i
$592$	−0.498370	−	0.287734i	−0.0204829	−	0.0118258i
$593$		−	9.68683i		−	0.397791i	−0.980021	−	0.198895i	$-0.936265\pi$
$593$		−	9.68683i		−	0.397791i	0.980021	−	0.198895i	$-0.0637354\pi$
$594$	−4.69092	+	8.12490i	−0.192471	+	0.333369i
$595$	−3.24123	−	5.61398i	−0.132878	−	0.230151i
$596$	−6.11871	+	3.53264i	−0.250632	+	0.144702i
$597$	6.60656			0.270388
$598$	−5.50248	−	15.0309i	−0.225013	−	0.614658i
$599$	8.33012			0.340360			0.170180	−	0.985413i	$-0.445565\pi$
$599$	8.33012			0.340360			0.170180	+	0.985413i	$0.445565\pi$
$600$	−0.519785	+	0.300098i	−0.0212201	+	0.0122514i
$601$	6.10117	+	10.5675i	0.248872	+	0.431059i	0.963213	−	0.268739i	$-0.0866068\pi$
$601$	6.10117	+	10.5675i	0.248872	+	0.431059i	−0.714341	+	0.699798i	$0.753273\pi$
$602$	1.88201	−	3.25973i	0.0767049	−	0.132857i
$603$		−	14.0673i		−	0.572864i
$604$	13.7115	+	7.91633i	0.557912	+	0.322111i
$605$	−2.87358	−	1.65906i	−0.116828	−	0.0674504i
$606$			8.25480i			0.335328i
$607$	4.91946	−	8.52075i	0.199675	−	0.345847i	−0.748748	−	0.662854i	$-0.769345\pi$
$607$	4.91946	−	8.52075i	0.199675	−	0.345847i	0.948423	+	0.317008i	$0.102678\pi$
$608$	2.16612	+	3.75184i	0.0878479	+	0.152157i
$609$	5.88423	−	3.39726i	0.238441	−	0.137664i
$610$	12.5037			0.506259
$611$	29.5263	−	35.3214i	1.19451	−	1.42895i
$612$	11.8886			0.480570
$613$	13.1737	−	7.60586i	0.532082	−	0.307198i	−0.209782	−	0.977748i	$-0.567275\pi$
$613$	13.1737	−	7.60586i	0.532082	−	0.307198i	0.741864	+	0.670551i	$0.233942\pi$
$614$	8.13609	+	14.0921i	0.328346	+	0.568712i
$615$	−1.26795	+	2.19615i	−0.0511286	+	0.0885574i
$616$			3.98940i			0.160737i
$617$	−21.1929	−	12.2357i	−0.853194	−	0.492592i	0.00853345	−	0.999964i	$-0.497284\pi$
$617$	−21.1929	−	12.2357i	−0.853194	−	0.492592i	−0.861727	+	0.507372i	$0.830617\pi$
$618$	−2.97943	−	1.72018i	−0.119850	−	0.0691956i
$619$			42.4157i			1.70483i	0.522864	+	0.852416i	$0.324864\pi$
$619$			42.4157i			1.70483i	−0.522864	+	0.852416i	$0.675136\pi$
$620$	−2.08041	+	3.60338i	−0.0835513	+	0.144715i
$621$	7.51356	+	13.0139i	0.301509	+	0.522228i
$622$	−13.9476	+	8.05264i	−0.559247	+	0.322881i
$623$	−8.57459			−0.343534
$624$	−2.03215	+	0.743926i	−0.0813511	+	0.0297809i
$625$	1.00000			0.0400000
$626$	−8.84750	+	5.10811i	−0.353617	+	0.204161i
$627$	3.60338	+	6.24123i	0.143905	+	0.249251i
$628$	6.31401	−	10.9362i	0.251957	−	0.436402i
$629$			2.59172i			0.103339i
$630$	3.29056	+	1.89980i	0.131099	+	0.0756900i
$631$	−0.0244657	−	0.0141253i	−0.000973964	−	0.000562318i	0.499513	−	0.866306i	$-0.333512\pi$
$631$	−0.0244657	−	0.0141253i	−0.000973964	−	0.000562318i	−0.500487	+	0.865744i	$0.666846\pi$
$632$		−	12.7288i		−	0.506324i
$633$	7.88002	−	13.6486i	0.313203	−	0.542483i
$634$	−0.102184	−	0.176988i	−0.00405825	−	0.00702909i
$635$	13.9641	−	8.06218i	0.554148	−	0.319938i
$636$	5.74461			0.227789
$637$	−3.05298	+	17.5046i	−0.120963	+	0.693559i
$638$	21.7985			0.863010
$639$	13.7166	−	7.91930i	0.542621	−	0.313282i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	8.10465	−	14.0377i	0.320114	−	0.554454i	−0.660397	−	0.750917i	$-0.729612\pi$
$641$	8.10465	−	14.0377i	0.320114	−	0.554454i	0.980511	+	0.196462i	$0.0629453\pi$
$642$		−	2.80852i		−	0.110843i
$643$	15.7718	+	9.10586i	0.621979	+	0.359100i	0.777639	−	0.628711i	$-0.216417\pi$
$643$	15.7718	+	9.10586i	0.621979	+	0.359100i	−0.155660	+	0.987811i	$0.549750\pi$
$644$	5.53383	+	3.19496i	0.218064	+	0.125899i
$645$			1.56953i			0.0618003i
$646$	9.75551	−	16.8970i	0.383825	−	0.664805i
$647$	−3.56139	−	6.16852i	−0.140013	−	0.242509i	0.787488	−	0.616330i	$-0.211381\pi$
$647$	−3.56139	−	6.16852i	−0.140013	−	0.242509i	−0.927501	+	0.373820i	$0.878048\pi$
$648$	−5.09886	+	2.94383i	−0.200302	+	0.115644i
$649$	9.60117			0.376879
$650$	3.55193	+	0.619491i	0.139318	+	0.0242984i
$651$	−3.59456			−0.140882
$652$	−15.9076	+	9.18428i	−0.622991	+	0.359684i
$653$	8.03546	+	13.9178i	0.314452	+	0.544647i	0.979321	−	0.202313i	$-0.0648459\pi$
$653$	8.03546	+	13.9178i	0.314452	+	0.544647i	−0.664869	+	0.746960i	$0.731513\pi$
$654$	−0.696720	+	1.20676i	−0.0272439	+	0.0471879i
$655$		−	19.7609i		−	0.772121i
$656$	−3.65906	−	2.11256i	−0.142862	−	0.0824816i
$657$	3.80297	+	2.19564i	0.148368	+	0.0856602i
$658$			18.3784i			0.716466i
$659$	−22.5988	+	39.1423i	−0.880326	+	1.52477i	−0.0293473	+	0.999569i	$0.509343\pi$
$659$	−22.5988	+	39.1423i	−0.880326	+	1.52477i	−0.850979	+	0.525200i	$0.823990\pi$
$660$	−0.831757	−	1.44065i	−0.0323761	−	0.0560771i
$661$	−7.63354	+	4.40723i	−0.296910	+	0.171421i	−0.641054	−	0.767496i	$-0.721503\pi$
$661$	−7.63354	+	4.40723i	−0.296910	+	0.171421i	0.344144	+	0.938917i	$0.388169\pi$
$662$	19.0653			0.740993
$663$	7.47759	+	6.25078i	0.290406	+	0.242760i
$664$	10.0469			0.389896
$665$	5.40029	−	3.11786i	0.209414	−	0.120905i
$666$	−0.759550	−	1.31558i	−0.0294320	−	0.0509777i
$667$	17.4576	−	30.2374i	0.675960	−	1.17080i
$668$		−	21.6085i		−	0.836059i
$669$	−11.5414	−	6.66344i	−0.446217	−	0.257623i
$670$	4.61504	+	2.66449i	0.178294	+	0.102938i
$671$			34.6554i			1.33786i
$672$	0.431953	−	0.748164i	0.0166629	−	0.0288611i
$673$	20.7199	+	35.8879i	0.798693	+	1.38338i	0.920468	+	0.390819i	$0.127808\pi$
$673$	20.7199	+	35.8879i	0.798693	+	1.38338i	−0.121775	+	0.992558i	$0.538859\pi$
$674$	17.2001	−	9.93045i	0.662521	−	0.382507i
$675$	−3.38496			−0.130287
$676$	12.2325	+	4.40078i	0.470479	+	0.169261i
$677$	−18.8510			−0.724504			−0.362252	−	0.932080i	$-0.617992\pi$
$677$	−18.8510			−0.724504			−0.362252	+	0.932080i	$0.617992\pi$
$678$	−4.02121	+	2.32164i	−0.154433	+	0.0891622i
$679$	1.14166	+	1.97742i	0.0438130	+	0.0758863i
$680$	−2.25184	+	3.90029i	−0.0863540	+	0.149569i
$681$			1.24789i			0.0478193i
$682$	−9.98719	−	5.76611i	−0.382429	−	0.220796i
$683$	19.6297	+	11.3332i	0.751110	+	0.433654i	0.826095	−	0.563531i	$-0.190557\pi$
$683$	19.6297	+	11.3332i	0.751110	+	0.433654i	−0.0749846	+	0.997185i	$0.523891\pi$
$684$			11.4361i			0.437271i
$685$	8.63234	−	14.9517i	0.329825	−	0.571274i
$686$	−8.58457	−	14.8689i	−0.327760	−	0.567698i
$687$	−2.43225	+	1.40426i	−0.0927960	+	0.0535758i
$688$	−2.61504			−0.0996974
$689$	−26.4771	−	22.1331i	−1.00870	−	0.843204i
$690$	−2.66449			−0.101436
$691$	27.5736	−	15.9196i	1.04895	−	0.605612i	0.126595	−	0.991954i	$-0.459595\pi$
$691$	27.5736	−	15.9196i	1.04895	−	0.605612i	0.922355	+	0.386343i	$0.126262\pi$
$692$	−1.99470	−	3.45492i	−0.0758271	−	0.131336i
$693$	−5.26554	+	9.12018i	−0.200021	+	0.346447i
$694$			17.0504i			0.647226i
$695$	−2.55180	−	1.47328i	−0.0967954	−	0.0558848i
$696$	−4.08805	−	2.36023i	−0.154957	−	0.0894645i
$697$			19.0285i			0.720758i
$698$	10.6185	−	18.3917i	0.401915	−	0.696138i
$699$	0.183378	+	0.317620i	0.00693599	+	0.0120135i
$700$	−1.24653	+	0.719687i	−0.0471146	+	0.0272016i
$701$	0.611060			0.0230794			0.0115397	−	0.999933i	$-0.496327\pi$
$701$	0.611060			0.0230794			0.0115397	+	0.999933i	$0.496327\pi$
$702$	−12.0232	−	2.09695i	−0.453785	−	0.0791444i
$703$	−2.49307			−0.0940279
$704$	2.40029	−	1.38581i	0.0904645	−	0.0522297i
$705$	−3.83176	−	6.63680i	−0.144312	−	0.249956i
$706$	8.00840	−	13.8710i	0.301400	−	0.522040i
$707$			19.7965i			0.744522i
$708$	−1.80059	−	1.03957i	−0.0676702	−	0.0390694i
$709$	11.2274	+	6.48212i	0.421653	+	0.243441i	0.695784	−	0.718251i	$-0.255057\pi$
$709$	11.2274	+	6.48212i	0.421653	+	0.243441i	−0.274131	+	0.961692i	$0.588390\pi$
$710$			6.00000i			0.225176i
$711$	16.8005	−	29.0993i	0.630068	−	1.09131i
$712$	2.97859	+	5.15906i	0.111627	+	0.193344i
$713$	−15.9967	+	9.23572i	−0.599083	+	0.345881i
$714$	−3.89075			−0.145608
$715$	−1.71699	+	9.84461i	−0.0642119	+	0.368168i
$716$	12.4799			0.466397
$717$	13.3315	−	7.69694i	0.497873	−	0.287447i
$718$	−12.1244	−	21.0000i	−0.452477	−	0.783713i
$719$	17.8616	−	30.9372i	0.666126	−	1.15376i	−0.312853	−	0.949802i	$-0.601285\pi$
$719$	17.8616	−	30.9372i	0.666126	−	1.15376i	0.978979	−	0.203963i	$-0.0653821\pi$
$720$		−	2.63977i		−	0.0983782i
$721$	−7.14520	−	4.12528i	−0.266101	−	0.153634i
$722$	−0.200606	−	0.115820i	−0.00746580	−	0.00431038i
$723$			16.2612i			0.604759i
$724$	9.71594	−	16.8285i	0.361090	−	0.625426i
$725$	3.93244	+	6.81119i	0.146047	+	0.252961i
$726$	−1.72471	+	0.995761i	−0.0640099	+	0.0369562i
$727$	−51.7313			−1.91861			−0.959304	−	0.282375i	$-0.908878\pi$
$727$	−51.7313			−1.91861			−0.959304	+	0.282375i	$0.908878\pi$
$728$	−4.87345	+	1.78406i	−0.180622	+	0.0661218i
$729$	−9.44711			−0.349893
$730$	−1.44065	+	0.831757i	−0.0533207	+	0.0307847i
$731$	5.88863	+	10.1994i	0.217799	+	0.377239i
$732$	3.75232	−	6.49922i	0.138690	−	0.240218i
$733$		−	26.4319i		−	0.976284i	−0.872764	−	0.488142i	$-0.837675\pi$
$733$		−	26.4319i		−	0.976284i	0.872764	−	0.488142i	$-0.162325\pi$
$734$	25.7822	+	14.8854i	0.951639	+	0.549429i
$735$	2.56160	+	1.47894i	0.0944862	+	0.0545516i
$736$		−	4.43937i		−	0.163637i
$737$	−7.38496	+	12.7911i	−0.272029	+	0.471167i
$738$	−5.57666	−	9.65906i	−0.205280	−	0.355555i
$739$	−23.7380	+	13.7051i	−0.873215	+	0.504151i	−0.868415	−	0.495837i	$-0.834861\pi$
$739$	−23.7380	+	13.7051i	−0.873215	+	0.504151i	−0.00480000	+	0.999988i	$0.501528\pi$
$740$	0.575468			0.0211546
$741$	−6.01285	+	7.19297i	−0.220888	+	0.264240i
$742$	13.7766			0.505754
$743$	−36.5306	+	21.0909i	−1.34018	+	0.773751i	−0.986833	−	0.161742i	$-0.948289\pi$
$743$	−36.5306	+	21.0909i	−1.34018	+	0.773751i	−0.353344	+	0.935494i	$0.614955\pi$
$744$	1.24865	+	2.16273i	0.0457779	+	0.0792896i
$745$	3.53264	−	6.11871i	0.129426	−	0.224172i
$746$			28.3858i			1.03928i
$747$	22.9683	+	13.2607i	0.840365	+	0.485185i
$748$	−10.8101	−	6.24123i	−0.395258	−	0.228202i
$749$		−	6.73531i		−	0.246103i
$750$	0.300098	−	0.519785i	0.0109580	−	0.0189799i
$751$	9.66351	+	16.7377i	0.352627	+	0.610767i	0.986709	−	0.162498i	$-0.0519552\pi$
$751$	9.66351	+	16.7377i	0.352627	+	0.610767i	−0.634082	+	0.773266i	$0.718622\pi$
$752$	11.0577	−	6.38418i	0.403234	−	0.232807i
$753$	0.902497			0.0328888
$754$	9.74830	+	26.6290i	0.355012	+	0.969771i
$755$	−15.8327			−0.576209
$756$	4.21947	−	2.43611i	0.153461	−	0.0886006i
$757$	10.1513	+	17.5825i	0.368955	+	0.639048i	0.989402	−	0.145200i	$-0.0463824\pi$
$757$	10.1513	+	17.5825i	0.368955	+	0.639048i	−0.620448	+	0.784248i	$0.713049\pi$
$758$	−14.2069	+	24.6070i	−0.516017	+	0.893768i
$759$		−	7.38496i		−	0.268057i
$760$	−3.75184	−	2.16612i	−0.136093	−	0.0785735i
$761$	−38.3386	−	22.1348i	−1.38977	−	0.802386i	−0.396484	−	0.918042i	$-0.629770\pi$
$761$	−38.3386	−	22.1348i	−1.38977	−	0.802386i	−0.993289	+	0.115656i	$0.963103\pi$
$762$		−	9.67777i		−	0.350589i
$763$	−1.67086	+	2.89401i	−0.0604891	+	0.104770i
$764$	−9.16074	−	15.8669i	−0.331424	−	0.574043i
$765$	−10.2959	+	5.94432i	−0.372248	+	0.214917i
$766$	−9.39726			−0.339537
$767$	4.29366	+	11.7288i	0.155035	+	0.423502i
$768$	−0.600196			−0.0216577
$769$	3.23903	−	1.87005i	0.116802	−	0.0674359i	−0.440461	−	0.897772i	$-0.645185\pi$
$769$	3.23903	−	1.87005i	0.116802	−	0.0674359i	0.557263	+	0.830336i	$0.311852\pi$
$770$	−1.99470	−	3.45492i	−0.0718840	−	0.124507i
$771$	6.10543	−	10.5749i	0.219882	−	0.380846i
$772$		−	4.74363i		−	0.170727i
$773$	3.88057	+	2.24045i	0.139575	+	0.0805834i	0.568161	−	0.822917i	$-0.307655\pi$
$773$	3.88057	+	2.24045i	0.139575	+	0.0805834i	−0.428587	+	0.903501i	$0.640988\pi$
$774$	−5.97825	−	3.45154i	−0.214884	−	0.124063i
$775$		−	4.16082i		−	0.149461i
$776$	0.793166	−	1.37380i	0.0284730	−	0.0493167i
$777$	0.248575	+	0.430545i	0.00891758	+	0.0154457i
$778$	10.0858	−	5.82306i	0.361595	−	0.208767i
$779$	−18.3043			−0.655818
$780$	1.38793	−	1.66033i	0.0496959	−	0.0594494i
$781$	−16.6297			−0.595058
$782$	−17.3149	+	9.99674i	−0.619178	+	0.357483i
$783$	−13.3112	−	23.0556i	−0.475702	−	0.823941i
$784$	−2.46410	+	4.26795i	−0.0880036	+	0.152427i
$785$			12.6280i			0.450714i
$786$	−10.2714	−	5.93019i	−0.366368	−	0.211523i
$787$	−27.7963	−	16.0482i	−0.990830	−	0.572056i	−0.0853077	−	0.996355i	$-0.527187\pi$
$787$	−27.7963	−	16.0482i	−0.990830	−	0.572056i	−0.905522	+	0.424299i	$0.860521\pi$
$788$			10.8006i			0.384755i
$789$	−5.14047	+	8.90355i	−0.183006	+	0.316975i
$790$	6.36440	+	11.0235i	0.226435	+	0.392197i
$791$	−9.64355	+	5.56771i	−0.342885	+	0.197965i
$792$	7.31643			0.259978
$793$	−42.3351	+	15.4979i	−1.50336	+	0.550348i
$794$	−0.399804			−0.0141885
$795$	−4.97498	+	2.87231i	−0.176444	+	0.101870i
$796$	−5.50367	−	9.53264i	−0.195072	−	0.337875i
$797$	11.1083	−	19.2402i	0.393477	−	0.681522i	−0.599429	−	0.800428i	$-0.704605\pi$
$797$	11.1083	−	19.2402i	0.393477	−	0.681522i	0.992905	+	0.118906i	$0.0379388\pi$
$798$		−	3.74265i		−	0.132488i
$799$	−49.8004	−	28.7522i	−1.76181	−	1.01718i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$			15.7255i			0.555634i
$802$	4.25388	−	7.36793i	0.150210	−	0.260171i
$803$	−2.30532	−	3.99292i	−0.0813528	−	0.140907i
$804$	2.76993	−	1.59922i	0.0976877	−	0.0564000i
$805$	−6.38992			−0.225215
$806$	2.57759	−	14.7790i	0.0907918	−	0.520567i
$807$	−11.6332			−0.409510
$808$	11.9109	−	6.87676i	0.419024	−	0.241924i
$809$	5.27410	+	9.13501i	0.185427	+	0.321170i	0.943720	−	0.330744i	$-0.107300\pi$
$809$	5.27410	+	9.13501i	0.185427	+	0.321170i	−0.758293	+	0.651914i	$0.773966\pi$
$810$	2.94383	−	5.09886i	0.103436	−	0.179156i
$811$		−	41.6434i		−	1.46230i	−0.682218	−	0.731149i	$-0.738984\pi$
$811$		−	41.6434i		−	1.46230i	0.682218	−	0.731149i	$-0.261016\pi$
$812$	−9.80385	−	5.66025i	−0.344048	−	0.198636i
$813$	−9.54902	−	5.51313i	−0.334899	−	0.193354i
$814$			1.59498i			0.0559040i
$815$	9.18428	−	15.9076i	0.321711	−	0.557220i
$816$	1.35154	+	2.34094i	0.0473134	+	0.0819493i
$817$	−9.81119	+	5.66449i	−0.343250	+	0.198176i
$818$	−14.0131			−0.489958
$819$	−13.4960	−	2.35382i	−0.471587	−	0.0822493i
$820$	4.22512			0.147548
$821$	20.1160	−	11.6140i	0.702053	−	0.405331i	−0.106058	−	0.994360i	$-0.533823\pi$
$821$	20.1160	−	11.6140i	0.702053	−	0.405331i	0.808112	+	0.589029i	$0.200490\pi$
$822$	−5.18110	−	8.97392i	−0.180711	−	0.313001i
$823$	−0.499427	+	0.865033i	−0.0174089	+	0.0301531i	−0.874599	−	0.484848i	$-0.838875\pi$
$823$	−0.499427	+	0.865033i	−0.0174089	+	0.0301531i	0.857190	+	0.515001i	$0.172208\pi$
$824$			5.73205i			0.199685i
$825$	1.44065	+	0.831757i	0.0501569	+	0.0289581i
$826$	−4.31812	−	2.49307i	−0.150247	−	0.0867449i
$827$			29.8030i			1.03635i	0.855274	+	0.518175i	$0.173389\pi$
$827$			29.8030i			1.03635i	−0.855274	+	0.518175i	$0.826611\pi$
$828$	5.85945	−	10.1489i	0.203630	−	0.352698i
$829$	11.8508	+	20.5261i	0.411594	+	0.712902i	0.995064	−	0.0992329i	$-0.0316389\pi$
$829$	11.8508	+	20.5261i	0.411594	+	0.712902i	−0.583470	+	0.812134i	$0.698306\pi$
$830$	−8.70088	+	5.02346i	−0.302012	+	0.174367i
$831$	−16.3458			−0.567030
$832$	2.76632	+	2.31246i	0.0959049	+	0.0801702i
$833$	22.1950			0.769011
$834$	−1.53158	+	0.884259i	−0.0530343	+	0.0306194i
$835$	10.8043	+	18.7135i	0.373897	+	0.647608i
$836$	6.00367	−	10.3987i	0.207641	−	0.359645i
$837$			14.0842i			0.486822i
$838$	20.9539	+	12.0977i	0.723839	+	0.417909i
$839$	−21.2991	−	12.2971i	−0.735327	−	0.424541i	0.0850406	−	0.996377i	$-0.472898\pi$
$839$	−21.2991	−	12.2971i	−0.735327	−	0.424541i	−0.820368	+	0.571836i	$0.806231\pi$
$840$			0.863906i			0.0298076i
$841$	−16.4282	+	28.4545i	−0.566490	+	0.981189i
$842$	17.8196	+	30.8644i	0.614104	+	1.06366i
$843$	15.6359	−	9.02740i	0.538530	−	0.310920i
$844$	−26.2582			−0.903843
$845$	−12.7940	+	2.30504i	−0.440127	+	0.0792958i
$846$	33.7055			1.15882
$847$	−4.13615	+	2.38801i	−0.142120	+	0.0820529i
$848$	−4.78561	−	8.28893i	−0.164339	−	0.284643i
$849$	7.64613	−	13.2435i	0.262414	−	0.454515i
$850$		−	4.50367i		−	0.154475i
$851$	2.21245	+	1.27736i	0.0758418	+	0.0437873i
$852$	3.11871	+	1.80059i	0.106845	+	0.0616871i
$853$			41.7449i			1.42932i	0.699473	+	0.714659i	$0.253418\pi$
$853$			41.7449i			1.42932i	−0.699473	+	0.714659i	$0.746582\pi$
$854$	8.99873	−	15.5863i	0.307930	−	0.533351i
$855$	−5.71806	−	9.90396i	−0.195553	−	0.338708i
$856$	−4.05242	+	2.33967i	−0.138509	+	0.0799682i
$857$	18.7543			0.640636			0.320318	−	0.947310i	$-0.396210\pi$
$857$	18.7543			0.640636			0.320318	+	0.947310i	$0.396210\pi$
$858$	4.60181	+	3.84681i	0.157103	+	0.131328i
$859$	13.8357			0.472066			0.236033	−	0.971745i	$-0.424153\pi$
$859$	13.8357			0.472066			0.236033	+	0.971745i	$0.424153\pi$
$860$	2.26469	−	1.30752i	0.0772252	−	0.0445860i
$861$	1.82505	+	3.16108i	0.0621976	+	0.107729i
$862$	2.48022	−	4.29586i	0.0844765	−	0.146318i
$863$			8.00891i			0.272626i	0.990666	+	0.136313i	$0.0435253\pi$
$863$			8.00891i			0.272626i	−0.990666	+	0.136313i	$0.956475\pi$
$864$	−2.93146	−	1.69248i	−0.0997304	−	0.0575794i
$865$	3.45492	+	1.99470i	0.117471	+	0.0678218i
$866$		−	4.21621i		−	0.143273i
$867$	0.985237	−	1.70648i	0.0334604	−	0.0579551i
$868$	2.99449	+	5.18661i	0.101640	+	0.176045i
$869$	−30.5528	+	17.6397i	−1.03643	+	0.598385i
$870$	4.72047			0.160039
$871$	−18.9282	−	3.30126i	−0.641358	−	0.111859i
$872$	2.32164			0.0786208
$873$	3.62652	−	2.09377i	0.122739	−	0.0708635i
$874$	−9.61623	−	16.6558i	−0.325274	−	0.563391i
$875$	0.719687	−	1.24653i	0.0243299	−	0.0421405i
$876$			0.998434i			0.0337340i
$877$	32.5033	+	18.7658i	1.09756	+	0.633677i	0.935579	−	0.353117i	$-0.114878\pi$
$877$	32.5033	+	18.7658i	1.09756	+	0.633677i	0.161981	+	0.986794i	$0.448212\pi$
$878$	−12.7739	−	7.37500i	−0.431097	−	0.248894i
$879$		−	9.94996i		−	0.335604i
$880$	−1.38581	+	2.40029i	−0.0467156	+	0.0809139i
$881$	6.05808	+	10.4929i	0.204102	+	0.353515i	0.949846	−	0.312717i	$-0.101239\pi$
$881$	6.05808	+	10.4929i	0.204102	+	0.353515i	−0.745744	+	0.666232i	$0.767906\pi$
$882$	−11.2664	+	6.50465i	−0.379359	+	0.219023i
$883$	44.4026			1.49427			0.747133	−	0.664675i	$-0.231430\pi$
$883$	44.4026			1.49427			0.747133	+	0.664675i	$0.231430\pi$
$884$	2.78998	−	15.9967i	0.0938373	−	0.538029i
$885$	2.07914			0.0698895
$886$	−10.5979	+	6.11871i	−0.356044	+	0.205562i
$887$	3.25714	+	5.64153i	0.109364	+	0.189424i	0.915513	−	0.402289i	$-0.131785\pi$
$887$	3.25714	+	5.64153i	0.109364	+	0.189424i	−0.806149	+	0.591713i	$0.798452\pi$
$888$	0.172697	−	0.299119i	0.00579532	−	0.0100378i
$889$		−	23.2090i		−	0.778404i
$890$	−5.15906	−	2.97859i	−0.172932	−	0.0998424i
$891$	14.1321	+	8.15917i	0.473443	+	0.273343i
$892$			22.2042i			0.743452i
$893$	27.6578	−	47.9048i	0.925534	−	1.60307i
$894$	−2.12027	−	3.67242i	−0.0709126	−	0.122824i
$895$	−10.8079	+	6.23996i	−0.361269	+	0.208579i
$896$	−1.43937			−0.0480861
$897$	9.02147	−	3.30256i	0.301218	−	0.110269i
$898$	−19.0714			−0.636420
$899$	28.3401	−	16.3622i	0.945197	−	0.545710i
$900$	1.31988	+	2.28610i	0.0439961	+	0.0762035i
$901$	−21.5528	+	37.3306i	−0.718029	+	1.24366i
$902$			11.7104i			0.389915i
$903$	1.95648	+	1.12957i	0.0651075	+	0.0375898i
$904$	6.69982	+	3.86814i	0.222833	+	0.128653i
$905$			19.4319i			0.645937i
$906$	−4.75135	+	8.22957i	−0.157853	+	0.273409i
$907$	−2.96883	−	5.14216i	−0.0985784	−	0.170743i	0.812518	−	0.582936i	$-0.198096\pi$
$907$	−2.96883	−	5.14216i	−0.0985784	−	0.170743i	−0.911096	+	0.412193i	$0.864763\pi$
$908$	1.80059	−	1.03957i	0.0597546	−	0.0344993i
$909$	36.3061			1.20420
$910$	3.32850	−	3.98177i	0.110339	−	0.131994i
$911$	48.7860			1.61635			0.808177	−	0.588940i	$-0.200455\pi$
$911$	48.7860			1.61635			0.808177	+	0.588940i	$0.200455\pi$
$912$	−2.25184	+	1.30010i	−0.0745657	+	0.0430505i
$913$	−13.9231	−	24.1155i	−0.460788	−	0.798108i
$914$	8.05688	−	13.9549i	0.266498	−	0.461588i
$915$			7.50465i			0.248096i
$916$	4.05242	+	2.33967i	0.133896	+	0.0773048i
$917$	−24.6326	−	14.2216i	−0.813440	−	0.469640i
$918$			15.2448i			0.503152i
$919$	14.8564	−	25.7321i	0.490068	−	0.848822i	−0.509867	−	0.860253i	$-0.670305\pi$
$919$	14.8564	−	25.7321i	0.490068	−	0.848822i	0.999935	+	0.0114312i	$0.00363874\pi$
$920$	2.21969	+	3.84461i	0.0731809	+	0.126753i
$921$	−8.45803	+	4.88325i	−0.278702	+	0.160909i
$922$	4.84466			0.159550
$923$	−7.43683	−	20.3149i	−0.244786	−	0.668672i
$924$	−2.39442			−0.0787706
$925$	−0.498370	+	0.287734i	−0.0163863	+	0.00946063i
$926$	4.11582	+	7.12881i	0.135254	+	0.234267i
$927$	−7.56563	+	13.1041i	−0.248488	+	0.430394i
$928$			7.86488i			0.258177i
$929$	15.6012	+	9.00734i	0.511858	+	0.295521i	0.733597	−	0.679585i	$-0.237840\pi$
$929$	15.6012	+	9.00734i	0.511858	+	0.295521i	−0.221739	+	0.975106i	$0.571173\pi$
$930$	−2.16273	−	1.24865i	−0.0709188	−	0.0409450i
$931$			21.3502i			0.699724i
$932$	0.305530	−	0.529194i	0.0100080	−	0.0173343i
$933$	−4.83316	−	8.37128i	−0.158231	−	0.274063i
$934$	−29.0008	+	16.7436i	−0.948936	+	0.547868i
$935$	12.4825			0.408220
$936$	3.27191	+	8.93774i	0.106946	+	0.292139i
$937$	28.9796			0.946723			0.473361	−	0.880868i	$-0.343040\pi$
$937$	28.9796			0.946723			0.473361	+	0.880868i	$0.343040\pi$
$938$	6.64276	−	3.83520i	0.216894	−	0.125224i
$939$	−3.06586	−	5.31023i	−0.100051	−	0.173293i
$940$	−6.38418	+	11.0577i	−0.208229	+	0.360663i
$941$		−	4.61504i		−	0.150446i	−0.997167	−	0.0752230i	$-0.976033\pi$
$941$		−	4.61504i		−	0.150446i	0.997167	−	0.0752230i	$-0.0239669\pi$
$942$	6.56386	+	3.78964i	0.213862	+	0.123473i
$943$	16.2439	+	9.37844i	0.528975	+	0.305404i
$944$			3.46410i			0.112747i
$945$	−2.43611	+	4.21947i	−0.0792468	+	0.137259i
$946$	3.62395	+	6.27686i	0.117825	+	0.204078i
$947$	9.18041	−	5.30031i	0.298323	−	0.172237i	−0.343366	−	0.939202i	$-0.611567\pi$
$947$	9.18041	−	5.30031i	0.298323	−	0.172237i	0.641689	+	0.766965i	$0.278234\pi$
$948$	7.63977			0.248128
$949$	3.84681	−	4.60181i	0.124873	−	0.149381i
$950$	4.33225			0.140557
$951$	0.106227	−	0.0613304i	0.00344466	−	0.00198878i
$952$	3.24123	+	5.61398i	0.105049	+	0.181950i
$953$	14.3705	−	24.8905i	0.465508	−	0.806283i	−0.533717	−	0.845663i	$-0.679205\pi$
$953$	14.3705	−	24.8905i	0.465508	−	0.806283i	0.999224	+	0.0393806i	$0.0125385\pi$
$954$		−	25.2658i		−	0.818010i
$955$	15.8669	+	9.16074i	0.513440	+	0.296435i
$956$	−22.2119	−	12.8240i	−0.718384	−	0.414759i
$957$			13.0833i			0.422925i
$958$	4.02672	−	6.97448i	0.130097	−	0.225335i
$959$	−12.4252	−	21.5210i	−0.401230	−	0.694950i
$960$	0.519785	−	0.300098i	0.0167760	−	0.00968562i
$961$	13.6876			0.441534
$962$	−1.94842	+	0.713276i	−0.0628197	+	0.0229969i
$963$	−12.3523			−0.398049
$964$	23.4633	−	13.5466i	0.755703	−	0.436305i
$965$	2.37182	+	4.10811i	0.0763515	+	0.132245i
$966$	−1.91760	+	3.32138i	−0.0616978	+	0.106864i
$967$			8.08648i			0.260044i	0.991511	+	0.130022i	$0.0415047\pi$
$967$			8.08648i			0.260044i	−0.991511	+	0.130022i	$0.958495\pi$
$968$	2.87358	+	1.65906i	0.0923603	+	0.0533242i
$969$	10.1415	+	5.85521i	0.325793	+	0.188097i
$970$			1.58633i			0.0509341i
$971$	−0.302790	+	0.524448i	−0.00971701	+	0.0168304i	−0.870843	−	0.491561i	$-0.836426\pi$
$971$	−0.302790	+	0.524448i	−0.00971701	+	0.0168304i	0.861126	+	0.508392i	$0.169760\pi$
$972$	−6.84432	−	11.8547i	−0.219532	−	0.380240i
$973$	−3.67300	+	2.12061i	−0.117751	+	0.0679835i
$974$	−1.62352			−0.0520208
$975$	−0.371816	+	2.13186i	−0.0119076	+	0.0682740i
$976$	−12.5037			−0.400233
$977$	42.4727	−	24.5216i	1.35882	−	0.784516i	0.369356	−	0.929288i	$-0.379578\pi$
$977$	42.4727	−	24.5216i	1.35882	−	0.784516i	0.989465	+	0.144772i	$0.0462448\pi$
$978$	−5.51236	−	9.54769i	−0.176266	−	0.305302i
$979$	8.25551	−	14.2990i	0.263847	−	0.456997i
$980$		−	4.92820i		−	0.157426i
$981$	5.30752	+	3.06430i	0.169456	+	0.0978355i
$982$	8.93796	+	5.16033i	0.285222	+	0.164673i
$983$		−	30.7684i		−	0.981358i	−0.871340	−	0.490679i	$-0.836749\pi$
$983$		−	30.7684i		−	0.981358i	0.871340	−	0.490679i	$-0.163251\pi$
$984$	1.26795	−	2.19615i	0.0404207	−	0.0700108i
$985$	−5.40029	−	9.35358i	−0.172068	−	0.298030i
$986$	30.6754	−	17.7104i	0.976902	−	0.564015i
$987$	−11.0307			−0.351110
$988$	15.3879	+	2.68379i	0.489553	+	0.0853827i
$989$	11.6091			0.369149
$990$	−6.33621	+	3.65821i	−0.201378	+	0.116266i
$991$	−7.74435	−	13.4136i	−0.246007	−	0.426097i	0.716407	−	0.697683i	$-0.245785\pi$
$991$	−7.74435	−	13.4136i	−0.246007	−	0.426097i	−0.962414	+	0.271585i	$0.912452\pi$
$992$	2.08041	−	3.60338i	0.0660531	−	0.114407i
$993$			11.4429i			0.363129i
$994$	7.47921	+	4.31812i	0.237226	+	0.136962i
$995$	9.53264	+	5.50367i	0.302205	+	0.174478i
$996$			6.03011i			0.191071i
$997$	3.91111	−	6.77423i	0.123866	−	0.214542i	−0.797423	−	0.603421i	$-0.793804\pi$
$997$	3.91111	−	6.77423i	0.123866	−	0.214542i	0.921289	+	0.388878i	$0.127137\pi$
$998$	−6.99033	−	12.1076i	−0.221275	−	0.383260i
$999$	1.68696	−	0.973969i	0.0533731	−	0.0308150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.2.l.b.101.4	✓	8
3.2	odd	2		1170.2.bs.g.361.2		8
4.3	odd	2		1040.2.da.d.881.2		8
5.2	odd	4		650.2.n.e.49.3		8
5.3	odd	4		650.2.n.d.49.2		8
5.4	even	2		650.2.m.c.101.1		8
13.2	odd	12		1690.2.a.u.1.2		4
13.3	even	3		1690.2.d.k.1351.6		8
13.4	even	6	inner	130.2.l.b.121.4	yes	8
13.5	odd	4		1690.2.e.s.991.3		8
13.6	odd	12		1690.2.e.s.191.3		8
13.7	odd	12		1690.2.e.t.191.3		8
13.8	odd	4		1690.2.e.t.991.3		8
13.9	even	3		1690.2.l.j.1161.2		8
13.10	even	6		1690.2.d.k.1351.2		8
13.11	odd	12		1690.2.a.t.1.2		4
13.12	even	2		1690.2.l.j.361.2		8
39.17	odd	6		1170.2.bs.g.901.2		8
52.43	odd	6		1040.2.da.d.641.2		8
65.4	even	6		650.2.m.c.251.1		8
65.17	odd	12		650.2.n.d.199.2		8
65.24	odd	12		8450.2.a.cm.1.3		4
65.43	odd	12		650.2.n.e.199.3		8
65.54	odd	12		8450.2.a.ci.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.b.101.4	✓	8	1.1	even	1	trivial
130.2.l.b.121.4	yes	8	13.4	even	6	inner
650.2.m.c.101.1		8	5.4	even	2
650.2.m.c.251.1		8	65.4	even	6
650.2.n.d.49.2		8	5.3	odd	4
650.2.n.d.199.2		8	65.17	odd	12
650.2.n.e.49.3		8	5.2	odd	4
650.2.n.e.199.3		8	65.43	odd	12
1040.2.da.d.641.2		8	52.43	odd	6
1040.2.da.d.881.2		8	4.3	odd	2
1170.2.bs.g.361.2		8	3.2	odd	2
1170.2.bs.g.901.2		8	39.17	odd	6
1690.2.a.t.1.2		4	13.11	odd	12
1690.2.a.u.1.2		4	13.2	odd	12
1690.2.d.k.1351.2		8	13.10	even	6
1690.2.d.k.1351.6		8	13.3	even	3
1690.2.e.s.191.3		8	13.6	odd	12
1690.2.e.s.991.3		8	13.5	odd	4
1690.2.e.t.191.3		8	13.7	odd	12
1690.2.e.t.991.3		8	13.8	odd	4
1690.2.l.j.361.2		8	13.12	even	2
1690.2.l.j.1161.2		8	13.9	even	3
8450.2.a.ci.1.3		4	65.54	odd	12
8450.2.a.cm.1.3		4	65.24	odd	12

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:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	130.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.300098 + 0.519785i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(0.519785 + 0.300098i) q^{6} +(1.24653 + 0.719687i) q^{7} -1.00000i q^{8} +(1.31988 - 2.28610i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.300098 + 0.519785i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(0.519785 + 0.300098i) q^{6} +(1.24653 + 0.719687i) q^{7} -1.00000i q^{8} +(1.31988 - 2.28610i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-2.40029 + 1.38581i) q^{11} +0.600196 q^{12} +(-2.76632 - 2.31246i) q^{13} +1.43937 q^{14} +(-0.519785 + 0.300098i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.25184 + 3.90029i) q^{17} -2.63977i q^{18} +(-3.75184 - 2.16612i) q^{19} +(0.866025 + 0.500000i) q^{20} +0.863906i q^{21} +(-1.38581 + 2.40029i) q^{22} +(2.21969 + 3.84461i) q^{23} +(0.519785 - 0.300098i) q^{24} -1.00000 q^{25} +(-3.55193 - 0.619491i) q^{26} +3.38496 q^{27} +(1.24653 - 0.719687i) q^{28} +(-3.93244 - 6.81119i) q^{29} +(-0.300098 + 0.519785i) q^{30} +4.16082i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.44065 - 0.831757i) q^{33} +4.50367i q^{34} +(-0.719687 + 1.24653i) q^{35} +(-1.31988 - 2.28610i) q^{36} +(0.498370 - 0.287734i) q^{37} -4.33225 q^{38} +(0.371816 - 2.13186i) q^{39} +1.00000 q^{40} +(3.65906 - 2.11256i) q^{41} +(0.431953 + 0.748164i) q^{42} +(1.30752 - 2.26469i) q^{43} +2.77162i q^{44} +(2.28610 + 1.31988i) q^{45} +(3.84461 + 2.21969i) q^{46} +12.7684i q^{47} +(0.300098 - 0.519785i) q^{48} +(-2.46410 - 4.26795i) q^{49} +(-0.866025 + 0.500000i) q^{50} -2.70308 q^{51} +(-3.38581 + 1.23947i) q^{52} +9.57123 q^{53} +(2.93146 - 1.69248i) q^{54} +(-1.38581 - 2.40029i) q^{55} +(0.719687 - 1.24653i) q^{56} -2.60020i q^{57} +(-6.81119 - 3.93244i) q^{58} +(-3.00000 - 1.73205i) q^{59} +0.600196i q^{60} +(6.25184 - 10.8285i) q^{61} +(2.08041 + 3.60338i) q^{62} +(3.29056 - 1.89980i) q^{63} -1.00000 q^{64} +(2.31246 - 2.76632i) q^{65} -1.66351 q^{66} +(4.61504 - 2.66449i) q^{67} +(2.25184 + 3.90029i) q^{68} +(-1.33225 + 2.30752i) q^{69} +1.43937i q^{70} +(5.19615 + 3.00000i) q^{71} +(-2.28610 - 1.31988i) q^{72} +1.66351i q^{73} +(0.287734 - 0.498370i) q^{74} +(-0.300098 - 0.519785i) q^{75} +(-3.75184 + 2.16612i) q^{76} -3.98940 q^{77} +(-0.743926 - 2.03215i) q^{78} +12.7288 q^{79} +(0.866025 - 0.500000i) q^{80} +(-2.94383 - 5.09886i) q^{81} +(2.11256 - 3.65906i) q^{82} +10.0469i q^{83} +(0.748164 + 0.431953i) q^{84} +(-3.90029 - 2.25184i) q^{85} -2.61504i q^{86} +(2.36023 - 4.08805i) q^{87} +(1.38581 + 2.40029i) q^{88} +(-5.15906 + 2.97859i) q^{89} +2.63977 q^{90} +(-1.78406 - 4.87345i) q^{91} +4.43937 q^{92} +(-2.16273 + 1.24865i) q^{93} +(6.38418 + 11.0577i) q^{94} +(2.16612 - 3.75184i) q^{95} -0.600196i q^{96} +(1.37380 + 0.793166i) q^{97} +(-4.26795 - 2.46410i) q^{98} +7.31643i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 4 * q^4 - 6 * q^6 - 4 * q^9	\( 8 q - 2 q^{3} + 4 q^{4} - 6 q^{6} - 4 q^{9} + 4 q^{10} - 6 q^{11} - 4 q^{12} - 2 q^{13} + 6 q^{15} - 4 q^{16} + 6 q^{17} - 6 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{24} - 8 q^{25} + 40 q^{27} + 2 q^{30} - 42 q^{33} + 4 q^{36} - 30 q^{37} - 12 q^{38} - 40 q^{39} + 8 q^{40} + 12 q^{41} - 6 q^{42} + 4 q^{43} - 12 q^{45} - 2 q^{48} + 8 q^{49} - 10 q^{52} + 60 q^{53} + 36 q^{54} + 6 q^{55} - 24 q^{59} + 26 q^{61} + 18 q^{62} + 12 q^{63} - 8 q^{64} + 6 q^{65} - 12 q^{66} + 24 q^{67} - 6 q^{68} + 12 q^{69} + 12 q^{72} + 6 q^{74} + 2 q^{75} - 6 q^{76} - 60 q^{77} - 6 q^{78} + 20 q^{79} - 28 q^{81} + 30 q^{84} - 18 q^{85} + 48 q^{87} - 6 q^{88} - 24 q^{89} - 8 q^{90} - 66 q^{91} + 24 q^{92} + 48 q^{93} + 6 q^{95} - 6 q^{97} - 48 q^{98}+O(q^{100}) \) 8 * q - 2 * q^3 + 4 * q^4 - 6 * q^6 - 4 * q^9 + 4 * q^10 - 6 * q^11 - 4 * q^12 - 2 * q^13 + 6 * q^15 - 4 * q^16 + 6 * q^17 - 6 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^24 - 8 * q^25 + 40 * q^27 + 2 * q^30 - 42 * q^33 + 4 * q^36 - 30 * q^37 - 12 * q^38 - 40 * q^39 + 8 * q^40 + 12 * q^41 - 6 * q^42 + 4 * q^43 - 12 * q^45 - 2 * q^48 + 8 * q^49 - 10 * q^52 + 60 * q^53 + 36 * q^54 + 6 * q^55 - 24 * q^59 + 26 * q^61 + 18 * q^62 + 12 * q^63 - 8 * q^64 + 6 * q^65 - 12 * q^66 + 24 * q^67 - 6 * q^68 + 12 * q^69 + 12 * q^72 + 6 * q^74 + 2 * q^75 - 6 * q^76 - 60 * q^77 - 6 * q^78 + 20 * q^79 - 28 * q^81 + 30 * q^84 - 18 * q^85 + 48 * q^87 - 6 * q^88 - 24 * q^89 - 8 * q^90 - 66 * q^91 + 24 * q^92 + 48 * q^93 + 6 * q^95 - 6 * q^97 - 48 * q^98

Introduction

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