LMFDB - Embedded newform 122.2.c.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [122,2,Mod(13,122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(122, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("122.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 122 = 2 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	122.c (of order $3$, 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:	$0.974174904660$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 4x^{2} + 3x + 9 $ x^4 - x^3 + 4x^2 + 3x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			13.1
Root			$-0.651388 + 1.12824i$ of defining polynomial
Character	$\chi$	$=$	122.13
Dual form			122.2.c.a.47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} -1.30278 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.651388 - 1.12824i) q^{5} +(-0.651388 + 1.12824i) q^{6} +(2.15139 - 3.72631i) q^{7} -1.00000 q^{8} -1.30278 q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} -1.30278 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.651388 - 1.12824i) q^{5} +(-0.651388 + 1.12824i) q^{6} +(2.15139 - 3.72631i) q^{7} -1.00000 q^{8} -1.30278 q^{9} +(-0.651388 - 1.12824i) q^{10} +1.60555 q^{11} +(0.651388 + 1.12824i) q^{12} +(-1.15139 + 1.99426i) q^{13} +(-2.15139 - 3.72631i) q^{14} +(-0.848612 + 1.46984i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.80278 + 6.58660i) q^{17} +(-0.651388 + 1.12824i) q^{18} +(-0.348612 - 0.603814i) q^{19} -1.30278 q^{20} +(-2.80278 + 4.85455i) q^{21} +(0.802776 - 1.39045i) q^{22} +0.394449 q^{23} +1.30278 q^{24} +(1.65139 + 2.86029i) q^{25} +(1.15139 + 1.99426i) q^{26} +5.60555 q^{27} -4.30278 q^{28} +(0.348612 + 0.603814i) q^{29} +(0.848612 + 1.46984i) q^{30} +(-3.45416 - 5.98279i) q^{31} +(0.500000 + 0.866025i) q^{32} -2.09167 q^{33} +7.60555 q^{34} +(-2.80278 - 4.85455i) q^{35} +(0.651388 + 1.12824i) q^{36} -7.60555 q^{37} -0.697224 q^{38} +(1.50000 - 2.59808i) q^{39} +(-0.651388 + 1.12824i) q^{40} +10.8167 q^{41} +(2.80278 + 4.85455i) q^{42} +(-2.10555 + 3.64692i) q^{43} +(-0.802776 - 1.39045i) q^{44} +(-0.848612 + 1.46984i) q^{45} +(0.197224 - 0.341603i) q^{46} +(2.19722 + 3.80570i) q^{47} +(0.651388 - 1.12824i) q^{48} +(-5.75694 - 9.97131i) q^{49} +3.30278 q^{50} +(-4.95416 - 8.58086i) q^{51} +2.30278 q^{52} -6.60555 q^{53} +(2.80278 - 4.85455i) q^{54} +(1.04584 - 1.81144i) q^{55} +(-2.15139 + 3.72631i) q^{56} +(0.454163 + 0.786634i) q^{57} +0.697224 q^{58} +(-5.40833 + 9.36750i) q^{59} +1.69722 q^{60} +(3.60555 - 6.92820i) q^{61} -6.90833 q^{62} +(-2.80278 + 4.85455i) q^{63} +1.00000 q^{64} +(1.50000 + 2.59808i) q^{65} +(-1.04584 + 1.81144i) q^{66} +(0.545837 - 0.945417i) q^{67} +(3.80278 - 6.58660i) q^{68} -0.513878 q^{69} -5.60555 q^{70} +(-3.19722 - 5.53776i) q^{71} +1.30278 q^{72} +(1.15139 + 1.99426i) q^{73} +(-3.80278 + 6.58660i) q^{74} +(-2.15139 - 3.72631i) q^{75} +(-0.348612 + 0.603814i) q^{76} +(3.45416 - 5.98279i) q^{77} +(-1.50000 - 2.59808i) q^{78} +(7.90833 - 13.6976i) q^{79} +(0.651388 + 1.12824i) q^{80} -3.39445 q^{81} +(5.40833 - 9.36750i) q^{82} +(-1.04584 + 1.81144i) q^{83} +5.60555 q^{84} +9.90833 q^{85} +(2.10555 + 3.64692i) q^{86} +(-0.454163 - 0.786634i) q^{87} -1.60555 q^{88} +8.30278 q^{89} +(0.848612 + 1.46984i) q^{90} +(4.95416 + 8.58086i) q^{91} +(-0.197224 - 0.341603i) q^{92} +(4.50000 + 7.79423i) q^{93} +4.39445 q^{94} -0.908327 q^{95} +(-0.651388 - 1.12824i) q^{96} +(-7.10555 - 12.3072i) q^{97} -11.5139 q^{98} -2.09167 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - q^{5} + q^{6} + 5 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - q^5 + q^6 + 5 * q^7 - 4 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - q^{5} + q^{6} + 5 q^{7} - 4 q^{8} + 2 q^{9} + q^{10} - 8 q^{11} - q^{12} - q^{13} - 5 q^{14} - 7 q^{15} - 2 q^{16} + 8 q^{17} + q^{18} - 5 q^{19} + 2 q^{20} - 4 q^{21} - 4 q^{22} + 16 q^{23} - 2 q^{24} + 3 q^{25} + q^{26} + 8 q^{27} - 10 q^{28} + 5 q^{29} + 7 q^{30} - 3 q^{31} + 2 q^{32} - 30 q^{33} + 16 q^{34} - 4 q^{35} - q^{36} - 16 q^{37} - 10 q^{38} + 6 q^{39} + q^{40} + 4 q^{42} + 6 q^{43} + 4 q^{44} - 7 q^{45} + 8 q^{46} + 16 q^{47} - q^{48} - 5 q^{49} + 6 q^{50} - 9 q^{51} + 2 q^{52} - 12 q^{53} + 4 q^{54} + 15 q^{55} - 5 q^{56} - 9 q^{57} + 10 q^{58} + 14 q^{60} - 6 q^{62} - 4 q^{63} + 4 q^{64} + 6 q^{65} - 15 q^{66} + 13 q^{67} + 8 q^{68} + 34 q^{69} - 8 q^{70} - 20 q^{71} - 2 q^{72} + q^{73} - 8 q^{74} - 5 q^{75} - 5 q^{76} + 3 q^{77} - 6 q^{78} + 10 q^{79} - q^{80} - 28 q^{81} - 15 q^{83} + 8 q^{84} + 18 q^{85} - 6 q^{86} + 9 q^{87} + 8 q^{88} + 26 q^{89} + 7 q^{90} + 9 q^{91} - 8 q^{92} + 18 q^{93} + 32 q^{94} + 18 q^{95} + q^{96} - 14 q^{97} - 10 q^{98} - 30 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - q^5 + q^6 + 5 * q^7 - 4 * q^8 + 2 * q^9 + q^10 - 8 * q^11 - q^12 - q^13 - 5 * q^14 - 7 * q^15 - 2 * q^16 + 8 * q^17 + q^18 - 5 * q^19 + 2 * q^20 - 4 * q^21 - 4 * q^22 + 16 * q^23 - 2 * q^24 + 3 * q^25 + q^26 + 8 * q^27 - 10 * q^28 + 5 * q^29 + 7 * q^30 - 3 * q^31 + 2 * q^32 - 30 * q^33 + 16 * q^34 - 4 * q^35 - q^36 - 16 * q^37 - 10 * q^38 + 6 * q^39 + q^40 + 4 * q^42 + 6 * q^43 + 4 * q^44 - 7 * q^45 + 8 * q^46 + 16 * q^47 - q^48 - 5 * q^49 + 6 * q^50 - 9 * q^51 + 2 * q^52 - 12 * q^53 + 4 * q^54 + 15 * q^55 - 5 * q^56 - 9 * q^57 + 10 * q^58 + 14 * q^60 - 6 * q^62 - 4 * q^63 + 4 * q^64 + 6 * q^65 - 15 * q^66 + 13 * q^67 + 8 * q^68 + 34 * q^69 - 8 * q^70 - 20 * q^71 - 2 * q^72 + q^73 - 8 * q^74 - 5 * q^75 - 5 * q^76 + 3 * q^77 - 6 * q^78 + 10 * q^79 - q^80 - 28 * q^81 - 15 * q^83 + 8 * q^84 + 18 * q^85 - 6 * q^86 + 9 * q^87 + 8 * q^88 + 26 * q^89 + 7 * q^90 + 9 * q^91 - 8 * q^92 + 18 * q^93 + 32 * q^94 + 18 * q^95 + q^96 - 14 * q^97 - 10 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/122\mathbb{Z}\right)^\times$.

$n$	$63$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.30278			−0.752158			−0.376079	−	0.926588i	$-0.622728\pi$
$3$	−1.30278			−0.752158			−0.376079	+	0.926588i	$0.622728\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.651388	−	1.12824i	0.291309	−	0.504563i	−0.682810	−	0.730596i	$-0.739242\pi$
$5$	0.651388	−	1.12824i	0.291309	−	0.504563i	0.974120	+	0.226033i	$0.0725757\pi$
$6$	−0.651388	+	1.12824i	−0.265928	+	0.460601i
$7$	2.15139	−	3.72631i	0.813148	−	1.40841i	−0.0975019	−	0.995235i	$-0.531085\pi$
$7$	2.15139	−	3.72631i	0.813148	−	1.40841i	0.910650	−	0.413179i	$-0.135581\pi$
$8$	−1.00000			−0.353553
$9$	−1.30278			−0.434259
$10$	−0.651388	−	1.12824i	−0.205987	−	0.356780i
$11$	1.60555			0.484092			0.242046	−	0.970265i	$-0.422182\pi$
$11$	1.60555			0.484092			0.242046	+	0.970265i	$0.422182\pi$
$12$	0.651388	+	1.12824i	0.188039	+	0.325694i
$13$	−1.15139	+	1.99426i	−0.319338	+	0.553109i	−0.980350	−	0.197266i	$-0.936794\pi$
$13$	−1.15139	+	1.99426i	−0.319338	+	0.553109i	0.661012	+	0.750375i	$0.270127\pi$
$14$	−2.15139	−	3.72631i	−0.574983	−	0.995899i
$15$	−0.848612	+	1.46984i	−0.219111	+	0.379511i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.80278	+	6.58660i	0.922309	+	1.59749i	0.795834	+	0.605516i	$0.207033\pi$
$17$	3.80278	+	6.58660i	0.922309	+	1.59749i	0.126475	+	0.991970i	$0.459634\pi$
$18$	−0.651388	+	1.12824i	−0.153534	+	0.265928i
$19$	−0.348612	−	0.603814i	−0.0799771	−	0.138524i	0.823263	−	0.567661i	$-0.192151\pi$
$19$	−0.348612	−	0.603814i	−0.0799771	−	0.138524i	−0.903240	+	0.429136i	$0.858818\pi$
$20$	−1.30278			−0.291309
$21$	−2.80278	+	4.85455i	−0.611616	+	1.05935i
$22$	0.802776	−	1.39045i	0.171152	−	0.296445i
$23$	0.394449			0.0822482			0.0411241	−	0.999154i	$-0.486906\pi$
$23$	0.394449			0.0822482			0.0411241	+	0.999154i	$0.486906\pi$
$24$	1.30278			0.265928
$25$	1.65139	+	2.86029i	0.330278	+	0.572058i
$26$	1.15139	+	1.99426i	0.225806	+	0.391107i
$27$	5.60555			1.07879
$28$	−4.30278			−0.813148
$29$	0.348612	+	0.603814i	0.0647357	+	0.112125i	0.896577	−	0.442889i	$-0.146046\pi$
$29$	0.348612	+	0.603814i	0.0647357	+	0.112125i	−0.831841	+	0.555014i	$0.812713\pi$
$30$	0.848612	+	1.46984i	0.154935	+	0.268355i
$31$	−3.45416	−	5.98279i	−0.620386	−	1.07454i	−0.989414	−	0.145122i	$-0.953643\pi$
$31$	−3.45416	−	5.98279i	−0.620386	−	1.07454i	0.369028	−	0.929418i	$-0.379691\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−2.09167			−0.364114
$34$	7.60555			1.30434
$35$	−2.80278	−	4.85455i	−0.473756	−	0.820569i
$36$	0.651388	+	1.12824i	0.108565	+	0.188039i
$37$	−7.60555			−1.25034			−0.625172	−	0.780487i	$-0.714971\pi$
$37$	−7.60555			−1.25034			−0.625172	+	0.780487i	$0.714971\pi$
$38$	−0.697224			−0.113105
$39$	1.50000	−	2.59808i	0.240192	−	0.416025i
$40$	−0.651388	+	1.12824i	−0.102993	+	0.178390i
$41$	10.8167			1.68928			0.844639	−	0.535337i	$-0.179815\pi$
$41$	10.8167			1.68928			0.844639	+	0.535337i	$0.179815\pi$
$42$	2.80278	+	4.85455i	0.432478	+	0.749073i
$43$	−2.10555	+	3.64692i	−0.321094	+	0.556150i	−0.980714	−	0.195449i	$-0.937384\pi$
$43$	−2.10555	+	3.64692i	−0.321094	+	0.556150i	0.659620	+	0.751599i	$0.270717\pi$
$44$	−0.802776	−	1.39045i	−0.121023	−	0.209618i
$45$	−0.848612	+	1.46984i	−0.126504	+	0.219111i
$46$	0.197224	−	0.341603i	0.0290791	−	0.0503666i
$47$	2.19722	+	3.80570i	0.320498	+	0.555119i	0.980591	−	0.196065i	$-0.0628164\pi$
$47$	2.19722	+	3.80570i	0.320498	+	0.555119i	−0.660093	+	0.751184i	$0.729483\pi$
$48$	0.651388	−	1.12824i	0.0940197	−	0.162847i
$49$	−5.75694	−	9.97131i	−0.822420	−	1.42447i
$50$	3.30278			0.467083
$51$	−4.95416	−	8.58086i	−0.693722	−	1.20156i
$52$	2.30278			0.319338
$53$	−6.60555			−0.907342			−0.453671	−	0.891169i	$-0.649886\pi$
$53$	−6.60555			−0.907342			−0.453671	+	0.891169i	$0.649886\pi$
$54$	2.80278	−	4.85455i	0.381409	−	0.660621i
$55$	1.04584	−	1.81144i	0.141021	−	0.244255i
$56$	−2.15139	+	3.72631i	−0.287491	+	0.497950i
$57$	0.454163	+	0.786634i	0.0601554	+	0.104192i
$58$	0.697224			0.0915500
$59$	−5.40833	+	9.36750i	−0.704104	+	1.21954i	0.262910	+	0.964820i	$0.415318\pi$
$59$	−5.40833	+	9.36750i	−0.704104	+	1.21954i	−0.967014	+	0.254724i	$0.918015\pi$
$60$	1.69722			0.219111
$61$	3.60555	−	6.92820i	0.461644	−	0.887066i
$61$	3.60555	−	6.92820i	0.461644	−	0.887066i
$62$	−6.90833			−0.877358
$63$	−2.80278	+	4.85455i	−0.353117	+	0.611616i
$64$	1.00000			0.125000
$65$	1.50000	+	2.59808i	0.186052	+	0.322252i
$66$	−1.04584	+	1.81144i	−0.128734	+	0.222973i
$67$	0.545837	−	0.945417i	0.0666845	−	0.115501i	−0.830755	−	0.556638i	$-0.812091\pi$
$67$	0.545837	−	0.945417i	0.0666845	−	0.115501i	0.897440	+	0.441137i	$0.145425\pi$
$68$	3.80278	−	6.58660i	0.461154	−	0.798743i
$69$	−0.513878			−0.0618637
$70$	−5.60555			−0.669992
$71$	−3.19722	−	5.53776i	−0.379441	−	0.657211i	0.611540	−	0.791213i	$-0.290550\pi$
$71$	−3.19722	−	5.53776i	−0.379441	−	0.657211i	−0.990981	+	0.134003i	$0.957217\pi$
$72$	1.30278			0.153534
$73$	1.15139	+	1.99426i	0.134760	+	0.233411i	0.925506	−	0.378734i	$-0.123640\pi$
$73$	1.15139	+	1.99426i	0.134760	+	0.233411i	−0.790746	+	0.612145i	$0.790307\pi$
$74$	−3.80278	+	6.58660i	−0.442064	+	0.765677i
$75$	−2.15139	−	3.72631i	−0.248421	−	0.430278i
$76$	−0.348612	+	0.603814i	−0.0399886	+	0.0692622i
$77$	3.45416	−	5.98279i	0.393638	−	0.681802i
$78$	−1.50000	−	2.59808i	−0.169842	−	0.294174i
$79$	7.90833	−	13.6976i	0.889756	−	1.54110i	0.0495931	−	0.998770i	$-0.484208\pi$
$79$	7.90833	−	13.6976i	0.889756	−	1.54110i	0.840163	−	0.542334i	$-0.182459\pi$
$80$	0.651388	+	1.12824i	0.0728274	+	0.126141i
$81$	−3.39445			−0.377161
$82$	5.40833	−	9.36750i	0.597250	−	1.03447i
$83$	−1.04584	+	1.81144i	−0.114795	+	0.198832i	−0.917698	−	0.397279i	$-0.869955\pi$
$83$	−1.04584	+	1.81144i	−0.114795	+	0.198832i	0.802903	+	0.596110i	$0.203288\pi$
$84$	5.60555			0.611616
$85$	9.90833			1.07471
$86$	2.10555	+	3.64692i	0.227047	+	0.393258i
$87$	−0.454163	−	0.786634i	−0.0486914	−	0.0843360i
$88$	−1.60555			−0.171152
$89$	8.30278			0.880092			0.440046	−	0.897975i	$-0.354962\pi$
$89$	8.30278			0.880092			0.440046	+	0.897975i	$0.354962\pi$
$90$	0.848612	+	1.46984i	0.0894516	+	0.154935i
$91$	4.95416	+	8.58086i	0.519337	+	0.899519i
$92$	−0.197224	−	0.341603i	−0.0205621	−	0.0356145i
$93$	4.50000	+	7.79423i	0.466628	+	0.808224i
$94$	4.39445			0.453253
$95$	−0.908327			−0.0931924
$96$	−0.651388	−	1.12824i	−0.0664820	−	0.115150i
$97$	−7.10555	−	12.3072i	−0.721459	−	1.24960i	−0.960415	−	0.278574i	$-0.910138\pi$
$97$	−7.10555	−	12.3072i	−0.721459	−	1.24960i	0.238955	−	0.971031i	$-0.423195\pi$
$98$	−11.5139			−1.16308
$99$	−2.09167			−0.210221
$100$	1.65139	−	2.86029i	0.165139	−	0.286029i
$101$	−8.30278	+	14.3808i	−0.826157	+	1.43095i	0.0748747	+	0.997193i	$0.476144\pi$
$101$	−8.30278	+	14.3808i	−0.826157	+	1.43095i	−0.901032	+	0.433753i	$0.857189\pi$
$102$	−9.90833			−0.981071
$103$	2.50000	+	4.33013i	0.246332	+	0.426660i	0.962505	−	0.271263i	$-0.0874412\pi$
$103$	2.50000	+	4.33013i	0.246332	+	0.426660i	−0.716173	+	0.697923i	$0.754108\pi$
$104$	1.15139	−	1.99426i	0.112903	−	0.195553i
$105$	3.65139	+	6.32439i	0.356339	+	0.617197i
$106$	−3.30278	+	5.72058i	−0.320794	+	0.555631i
$107$	−4.60555	+	7.97705i	−0.445235	+	0.771170i	−0.998069	−	0.0621216i	$-0.980213\pi$
$107$	−4.60555	+	7.97705i	−0.445235	+	0.771170i	0.552833	+	0.833292i	$0.313547\pi$
$108$	−2.80278	−	4.85455i	−0.269697	−	0.467129i
$109$	−6.95416	+	12.0450i	−0.666088	+	1.15370i	0.312901	+	0.949786i	$0.398699\pi$
$109$	−6.95416	+	12.0450i	−0.666088	+	1.15370i	−0.978989	+	0.203913i	$0.934634\pi$
$110$	−1.04584	−	1.81144i	−0.0997166	−	0.172714i
$111$	9.90833			0.940457
$112$	2.15139	+	3.72631i	0.203287	+	0.352103i
$113$	−9.39445			−0.883755			−0.441878	−	0.897075i	$-0.645687\pi$
$113$	−9.39445			−0.883755			−0.441878	+	0.897075i	$0.645687\pi$
$114$	0.908327			0.0850726
$115$	0.256939	−	0.445032i	0.0239597	−	0.0414994i
$116$	0.348612	−	0.603814i	0.0323678	−	0.0560627i
$117$	1.50000	−	2.59808i	0.138675	−	0.240192i
$118$	5.40833	+	9.36750i	0.497877	+	0.862348i
$119$	32.7250			2.99989
$120$	0.848612	−	1.46984i	0.0774673	−	0.134177i
$121$	−8.42221			−0.765655
$122$	−4.19722	−	6.58660i	−0.379999	−	0.596323i
$123$	−14.0917			−1.27060
$124$	−3.45416	+	5.98279i	−0.310193	+	0.537270i
$125$	10.8167			0.967471
$126$	2.80278	+	4.85455i	0.249691	+	0.432478i
$127$	−7.95416	+	13.7770i	−0.705818	+	1.22251i	0.260578	+	0.965453i	$0.416087\pi$
$127$	−7.95416	+	13.7770i	−0.705818	+	1.22251i	−0.966396	+	0.257060i	$0.917246\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	2.74306	−	4.75112i	0.241513	−	0.418313i
$130$	3.00000			0.263117
$131$	−8.81665			−0.770315			−0.385157	−	0.922851i	$-0.625853\pi$
$131$	−8.81665			−0.770315			−0.385157	+	0.922851i	$0.625853\pi$
$132$	1.04584	+	1.81144i	0.0910284	+	0.157666i
$133$	−3.00000			−0.260133
$134$	−0.545837	−	0.945417i	−0.0471531	−	0.0816716i
$135$	3.65139	−	6.32439i	0.314261	−	0.544317i
$136$	−3.80278	−	6.58660i	−0.326085	−	0.564796i
$137$	−1.69722	+	2.93968i	−0.145004	+	0.251154i	−0.929374	−	0.369139i	$-0.879653\pi$
$137$	−1.69722	+	2.93968i	−0.145004	+	0.251154i	0.784371	+	0.620292i	$0.212986\pi$
$138$	−0.256939	+	0.445032i	−0.0218721	+	0.0378836i
$139$	2.80278	+	4.85455i	0.237728	+	0.411758i	0.960062	−	0.279787i	$-0.0902639\pi$
$139$	2.80278	+	4.85455i	0.237728	+	0.411758i	−0.722334	+	0.691545i	$0.756931\pi$
$140$	−2.80278	+	4.85455i	−0.236878	+	0.410284i
$141$	−2.86249	−	4.95798i	−0.241065	−	0.417537i
$142$	−6.39445			−0.536610
$143$	−1.84861	+	3.20189i	−0.154589	+	0.267756i
$144$	0.651388	−	1.12824i	0.0542823	−	0.0940197i
$145$	0.908327			0.0754324
$146$	2.30278			0.190579
$147$	7.50000	+	12.9904i	0.618590	+	1.07143i
$148$	3.80278	+	6.58660i	0.312586	+	0.541415i
$149$	6.00000			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$150$	−4.30278			−0.351320
$151$	−7.60555	−	13.1732i	−0.618931	−	1.07202i	−0.989681	−	0.143287i	$-0.954233\pi$
$151$	−7.60555	−	13.1732i	−0.618931	−	1.07202i	0.370750	−	0.928733i	$-0.379101\pi$
$152$	0.348612	+	0.603814i	0.0282762	+	0.0489758i
$153$	−4.95416	−	8.58086i	−0.400520	−	0.693722i
$154$	−3.45416	−	5.98279i	−0.278344	−	0.482107i
$155$	−9.00000			−0.722897
$156$	−3.00000			−0.240192
$157$	2.95416	+	5.11676i	0.235768	+	0.408362i	0.959496	−	0.281724i	$-0.0909062\pi$
$157$	2.95416	+	5.11676i	0.235768	+	0.408362i	−0.723728	+	0.690086i	$0.757573\pi$
$158$	−7.90833	−	13.6976i	−0.629153	−	1.08972i
$159$	8.60555			0.682465
$160$	1.30278			0.102993
$161$	0.848612	−	1.46984i	0.0668800	−	0.115840i
$162$	−1.69722	+	2.93968i	−0.133347	+	0.230963i
$163$	0.605551			0.0474304			0.0237152	−	0.999719i	$-0.492451\pi$
$163$	0.605551			0.0474304			0.0237152	+	0.999719i	$0.492451\pi$
$164$	−5.40833	−	9.36750i	−0.422319	−	0.731479i
$165$	−1.36249	+	2.35990i	−0.106070	+	0.183718i
$166$	1.04584	+	1.81144i	0.0811727	+	0.140595i
$167$	7.30278	−	12.6488i	0.565106	−	0.978792i	−0.431934	−	0.901905i	$-0.642169\pi$
$167$	7.30278	−	12.6488i	0.565106	−	0.978792i	0.997040	−	0.0768867i	$-0.0244980\pi$
$168$	2.80278	−	4.85455i	0.216239	−	0.374537i
$169$	3.84861	+	6.66599i	0.296047	+	0.512769i
$170$	4.95416	−	8.58086i	0.379967	−	0.658122i
$171$	0.454163	+	0.786634i	0.0347307	+	0.0601554i
$172$	4.21110			0.321094
$173$	1.60555	+	2.78090i	0.122068	+	0.211428i	0.920583	−	0.390547i	$-0.127714\pi$
$173$	1.60555	+	2.78090i	0.122068	+	0.211428i	−0.798515	+	0.601975i	$0.794381\pi$
$174$	−0.908327			−0.0688601
$175$	14.2111			1.07426
$176$	−0.802776	+	1.39045i	−0.0605115	+	0.104809i
$177$	7.04584	−	12.2037i	0.529598	−	0.917290i
$178$	4.15139	−	7.19041i	0.311160	−	0.538944i
$179$	−12.6653	−	21.9369i	−0.946646	−	1.63964i	−0.752421	−	0.658683i	$-0.771114\pi$
$179$	−12.6653	−	21.9369i	−0.946646	−	1.63964i	−0.194226	−	0.980957i	$-0.562219\pi$
$180$	1.69722			0.126504
$181$	11.0597	−	19.1560i	0.822062	−	1.42385i	−0.0820819	−	0.996626i	$-0.526157\pi$
$181$	11.0597	−	19.1560i	0.822062	−	1.42385i	0.904144	−	0.427228i	$-0.140510\pi$
$182$	9.90833			0.734454
$183$	−4.69722	+	9.02589i	−0.347229	+	0.667213i
$184$	−0.394449			−0.0290791
$185$	−4.95416	+	8.58086i	−0.364237	+	0.630878i
$186$	9.00000			0.659912
$187$	6.10555	+	10.5751i	0.446482	+	0.773330i
$188$	2.19722	−	3.80570i	0.160249	−	0.277560i
$189$	12.0597	−	20.8880i	0.877215	−	1.51938i
$190$	−0.454163	+	0.786634i	−0.0329485	+	0.0570684i
$191$	−12.8167			−0.927381			−0.463690	−	0.885997i	$-0.653475\pi$
$191$	−12.8167			−0.927381			−0.463690	+	0.885997i	$0.653475\pi$
$192$	−1.30278			−0.0940197
$193$	−1.25694	−	2.17708i	−0.0904765	−	0.156710i	0.817235	−	0.576304i	$-0.195506\pi$
$193$	−1.25694	−	2.17708i	−0.0904765	−	0.156710i	−0.907712	+	0.419594i	$0.862172\pi$
$194$	−14.2111			−1.02030
$195$	−1.95416	−	3.38471i	−0.139941	−	0.242384i
$196$	−5.75694	+	9.97131i	−0.411210	+	0.712237i
$197$	−4.00000	−	6.92820i	−0.284988	−	0.493614i	0.687618	−	0.726073i	$-0.258656\pi$
$197$	−4.00000	−	6.92820i	−0.284988	−	0.493614i	−0.972606	+	0.232458i	$0.925323\pi$
$198$	−1.04584	+	1.81144i	−0.0743244	+	0.128734i
$199$	−3.89445	+	6.74538i	−0.276070	+	0.478168i	−0.970405	−	0.241485i	$-0.922366\pi$
$199$	−3.89445	+	6.74538i	−0.276070	+	0.478168i	0.694334	+	0.719653i	$0.255699\pi$
$200$	−1.65139	−	2.86029i	−0.116771	−	0.202253i
$201$	−0.711103	+	1.23167i	−0.0501573	+	0.0868750i
$202$	8.30278	+	14.3808i	0.584181	+	1.01183i
$203$	3.00000			0.210559
$204$	−4.95416	+	8.58086i	−0.346861	+	0.600781i
$205$	7.04584	−	12.2037i	0.492103	−	0.852347i
$206$	5.00000			0.348367
$207$	−0.513878			−0.0357170
$208$	−1.15139	−	1.99426i	−0.0798344	−	0.138277i
$209$	−0.559715	−	0.969454i	−0.0387163	−	0.0670586i
$210$	7.30278			0.503939
$211$	−23.3028			−1.60423			−0.802115	−	0.597170i	$-0.796292\pi$
$211$	−23.3028			−1.60423			−0.802115	+	0.597170i	$0.796292\pi$
$212$	3.30278	+	5.72058i	0.226836	+	0.392891i
$213$	4.16527	+	7.21445i	0.285399	+	0.494326i
$214$	4.60555	+	7.97705i	0.314829	+	0.545300i
$215$	2.74306	+	4.75112i	0.187075	+	0.324024i
$216$	−5.60555			−0.381409
$217$	−29.7250			−2.01786
$218$	6.95416	+	12.0450i	0.470995	+	0.815788i
$219$	−1.50000	−	2.59808i	−0.101361	−	0.175562i
$220$	−2.09167			−0.141021
$221$	−17.5139			−1.17811
$222$	4.95416	−	8.58086i	0.332502	−	0.575910i
$223$	−11.4542	+	19.8392i	−0.767028	+	1.32853i	0.172140	+	0.985072i	$0.444932\pi$
$223$	−11.4542	+	19.8392i	−0.767028	+	1.32853i	−0.939168	+	0.343458i	$0.888402\pi$
$224$	4.30278			0.287491
$225$	−2.15139	−	3.72631i	−0.143426	−	0.248421i
$226$	−4.69722	+	8.13583i	−0.312455	+	0.541187i
$227$	6.36249	+	11.0202i	0.422293	+	0.731433i	0.996163	−	0.0875129i	$-0.0278919\pi$
$227$	6.36249	+	11.0202i	0.422293	+	0.731433i	−0.573870	+	0.818946i	$0.694559\pi$
$228$	0.454163	−	0.786634i	0.0300777	−	0.0520961i
$229$	10.9542	−	18.9732i	0.723871	−	1.25378i	−0.235565	−	0.971859i	$-0.575694\pi$
$229$	10.9542	−	18.9732i	0.723871	−	1.25378i	0.959437	−	0.281924i	$-0.0909725\pi$
$230$	−0.256939	−	0.445032i	−0.0169421	−	0.0293445i
$231$	−4.50000	+	7.79423i	−0.296078	+	0.512823i
$232$	−0.348612	−	0.603814i	−0.0228875	−	0.0396423i
$233$	15.3944			1.00852			0.504262	−	0.863551i	$-0.331765\pi$
$233$	15.3944			1.00852			0.504262	+	0.863551i	$0.331765\pi$
$234$	−1.50000	−	2.59808i	−0.0980581	−	0.169842i
$235$	5.72498			0.373457
$236$	10.8167			0.704104
$237$	−10.3028	+	17.8449i	−0.669237	+	1.15915i
$238$	16.3625	−	28.3407i	1.06062	−	1.83705i
$239$	6.69722	−	11.5999i	0.433207	−	0.750337i	−0.563940	−	0.825816i	$-0.690715\pi$
$239$	6.69722	−	11.5999i	0.433207	−	0.750337i	0.997147	+	0.0754785i	$0.0240484\pi$
$240$	−0.848612	−	1.46984i	−0.0547777	−	0.0948777i
$241$	25.2111			1.62399			0.811995	−	0.583664i	$-0.198382\pi$
$241$	25.2111			1.62399			0.811995	+	0.583664i	$0.198382\pi$
$242$	−4.21110	+	7.29384i	−0.270700	+	0.468866i
$243$	−12.3944			−0.795104
$244$	−7.80278	+	0.341603i	−0.499522	+	0.0218689i
$245$	−15.0000			−0.958315
$246$	−7.04584	+	12.2037i	−0.449226	+	0.778082i
$247$	1.60555			0.102159
$248$	3.45416	+	5.98279i	0.219340	+	0.379907i
$249$	1.36249	−	2.35990i	0.0863443	−	0.149553i
$250$	5.40833	−	9.36750i	0.342053	−	0.592453i
$251$	13.0597	−	22.6201i	0.824322	−	1.42777i	−0.0781146	−	0.996944i	$-0.524890\pi$
$251$	13.0597	−	22.6201i	0.824322	−	1.42777i	0.902436	−	0.430823i	$-0.141777\pi$
$252$	5.60555			0.353117
$253$	0.633308			0.0398157
$254$	7.95416	+	13.7770i	0.499089	+	0.864447i
$255$	−12.9083			−0.808351
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.24306	+	2.15304i	−0.0775400	+	0.134303i	−0.902188	−	0.431343i	$-0.858040\pi$
$257$	−1.24306	+	2.15304i	−0.0775400	+	0.134303i	0.824648	+	0.565646i	$0.191373\pi$
$258$	−2.74306	−	4.75112i	−0.170776	−	0.295792i
$259$	−16.3625	+	28.3407i	−1.01672	+	1.76100i
$260$	1.50000	−	2.59808i	0.0930261	−	0.161126i
$261$	−0.454163	−	0.786634i	−0.0281120	−	0.0486914i
$262$	−4.40833	+	7.63545i	−0.272347	+	0.471719i
$263$	13.9222	+	24.1140i	0.858480	+	1.48693i	0.873379	+	0.487042i	$0.161924\pi$
$263$	13.9222	+	24.1140i	0.858480	+	1.48693i	−0.0148987	+	0.999889i	$0.504743\pi$
$264$	2.09167			0.128734
$265$	−4.30278	+	7.45263i	−0.264317	+	0.457811i
$266$	−1.50000	+	2.59808i	−0.0919709	+	0.159298i
$267$	−10.8167			−0.661968
$268$	−1.09167			−0.0666845
$269$	−9.51388	−	16.4785i	−0.580071	−	1.00471i	−0.995470	−	0.0950737i	$-0.969691\pi$
$269$	−9.51388	−	16.4785i	−0.580071	−	1.00471i	0.415399	−	0.909639i	$-0.363642\pi$
$270$	−3.65139	−	6.32439i	−0.222216	−	0.384890i
$271$	1.48612			0.0902755			0.0451377	−	0.998981i	$-0.485627\pi$
$271$	1.48612			0.0902755			0.0451377	+	0.998981i	$0.485627\pi$
$272$	−7.60555			−0.461154
$273$	−6.45416	−	11.1789i	−0.390624	−	0.676580i
$274$	1.69722	+	2.93968i	0.102533	+	0.177592i
$275$	2.65139	+	4.59234i	0.159885	+	0.276928i
$276$	0.256939	+	0.445032i	0.0154659	+	0.0267878i
$277$	−6.00000			−0.360505			−0.180253	−	0.983620i	$-0.557691\pi$
$277$	−6.00000			−0.360505			−0.180253	+	0.983620i	$0.557691\pi$
$278$	5.60555			0.336199
$279$	4.50000	+	7.79423i	0.269408	+	0.466628i
$280$	2.80278	+	4.85455i	0.167498	+	0.290115i
$281$	−3.78890			−0.226027			−0.113013	−	0.993593i	$-0.536050\pi$
$281$	−3.78890			−0.226027			−0.113013	+	0.993593i	$0.536050\pi$
$282$	−5.72498			−0.340918
$283$	−11.8625	+	20.5464i	−0.705152	+	1.22136i	0.261485	+	0.965208i	$0.415788\pi$
$283$	−11.8625	+	20.5464i	−0.705152	+	1.22136i	−0.966637	+	0.256151i	$0.917545\pi$
$284$	−3.19722	+	5.53776i	−0.189720	+	0.328605i
$285$	1.18335			0.0700954
$286$	1.84861	+	3.20189i	0.109311	+	0.189332i
$287$	23.2708	−	40.3062i	1.37363	−	2.37920i
$288$	−0.651388	−	1.12824i	−0.0383834	−	0.0664820i
$289$	−20.4222	+	35.3723i	−1.20131	+	2.08072i
$290$	0.454163	−	0.786634i	0.0266694	−	0.0461927i
$291$	9.25694	+	16.0335i	0.542651	+	0.939900i
$292$	1.15139	−	1.99426i	0.0673799	−	0.116705i
$293$	−1.80278	−	3.12250i	−0.105319	−	0.182418i	0.808549	−	0.588428i	$-0.200253\pi$
$293$	−1.80278	−	3.12250i	−0.105319	−	0.182418i	−0.913869	+	0.406010i	$0.866920\pi$
$294$	15.0000			0.874818
$295$	7.04584	+	12.2037i	0.410224	+	0.710530i
$296$	7.60555			0.442064
$297$	9.00000			0.522233
$298$	3.00000	−	5.19615i	0.173785	−	0.301005i
$299$	−0.454163	+	0.786634i	−0.0262650	+	0.0454922i
$300$	−2.15139	+	3.72631i	−0.124210	+	0.215139i
$301$	9.05971	+	15.6919i	0.522193	+	0.904465i
$302$	−15.2111			−0.875301
$303$	10.8167	−	18.7350i	0.621401	−	1.07630i
$304$	0.697224			0.0399886
$305$	−5.46804	−	8.58086i	−0.313099	−	0.491339i
$306$	−9.90833			−0.566421
$307$	13.9083	−	24.0899i	0.793790	−	1.37488i	−0.129814	−	0.991538i	$-0.541438\pi$
$307$	13.9083	−	24.0899i	0.793790	−	1.37488i	0.923605	−	0.383347i	$-0.125229\pi$
$308$	−6.90833			−0.393638
$309$	−3.25694	−	5.64118i	−0.185281	−	0.320916i
$310$	−4.50000	+	7.79423i	−0.255583	+	0.442682i
$311$	0.137510	−	0.238174i	0.00779746	−	0.0135056i	−0.862100	−	0.506738i	$-0.830851\pi$
$311$	0.137510	−	0.238174i	0.00779746	−	0.0135056i	0.869898	+	0.493232i	$0.164185\pi$
$312$	−1.50000	+	2.59808i	−0.0849208	+	0.147087i
$313$	27.0278			1.52770			0.763850	−	0.645394i	$-0.223307\pi$
$313$	27.0278			1.52770			0.763850	+	0.645394i	$0.223307\pi$
$314$	5.90833			0.333426
$315$	3.65139	+	6.32439i	0.205732	+	0.356339i
$316$	−15.8167			−0.889756
$317$	−1.04584	−	1.81144i	−0.0587400	−	0.101741i	0.835160	−	0.550007i	$-0.185375\pi$
$317$	−1.04584	−	1.81144i	−0.0587400	−	0.101741i	−0.893900	+	0.448266i	$0.852042\pi$
$318$	4.30278	−	7.45263i	0.241288	−	0.417923i
$319$	0.559715	+	0.969454i	0.0313380	+	0.0542790i
$320$	0.651388	−	1.12824i	0.0364137	−	0.0630704i
$321$	6.00000	−	10.3923i	0.334887	−	0.580042i
$322$	−0.848612	−	1.46984i	−0.0472913	−	0.0819109i
$323$	2.65139	−	4.59234i	0.147527	−	0.255525i
$324$	1.69722	+	2.93968i	0.0942902	+	0.163315i
$325$	−7.60555			−0.421880
$326$	0.302776	−	0.524423i	0.0167692	−	0.0290451i
$327$	9.05971	−	15.6919i	0.501003	−	0.867763i
$328$	−10.8167			−0.597250
$329$	18.9083			1.04245
$330$	1.36249	+	2.35990i	0.0750026	+	0.129908i
$331$	9.95416	+	17.2411i	0.547130	+	0.947657i	0.998470	+	0.0553050i	$0.0176131\pi$
$331$	9.95416	+	17.2411i	0.547130	+	0.947657i	−0.451339	+	0.892352i	$0.649054\pi$
$332$	2.09167			0.114795
$333$	9.90833			0.542973
$334$	−7.30278	−	12.6488i	−0.399590	−	0.692110i
$335$	−0.711103	−	1.23167i	−0.0388517	−	0.0672931i
$336$	−2.80278	−	4.85455i	−0.152904	−	0.264837i
$337$	−5.19722	−	9.00186i	−0.283111	−	0.490362i	0.689038	−	0.724725i	$-0.258033\pi$
$337$	−5.19722	−	9.00186i	−0.283111	−	0.490362i	−0.972149	+	0.234362i	$0.924700\pi$
$338$	7.69722			0.418674
$339$	12.2389			0.664724
$340$	−4.95416	−	8.58086i	−0.268677	−	0.465363i
$341$	−5.54584	−	9.60567i	−0.300324	−	0.520176i
$342$	0.908327			0.0491167
$343$	−19.4222			−1.04870
$344$	2.10555	−	3.64692i	0.113524	−	0.196629i
$345$	−0.334734	+	0.579776i	−0.0180215	+	0.0312141i
$346$	3.21110			0.172630
$347$	0.954163	+	1.65266i	0.0512222	+	0.0887194i	0.890500	−	0.454984i	$-0.150355\pi$
$347$	0.954163	+	1.65266i	0.0512222	+	0.0887194i	−0.839277	+	0.543703i	$0.817022\pi$
$348$	−0.454163	+	0.786634i	−0.0243457	+	0.0421680i
$349$	5.04584	+	8.73965i	0.270097	+	0.467822i	0.968887	−	0.247505i	$-0.0796107\pi$
$349$	5.04584	+	8.73965i	0.270097	+	0.467822i	−0.698789	+	0.715328i	$0.746277\pi$
$350$	7.10555	−	12.3072i	0.379808	−	0.657846i
$351$	−6.45416	+	11.1789i	−0.344498	+	0.596688i
$352$	0.802776	+	1.39045i	0.0427881	+	0.0741111i
$353$	−12.9083	+	22.3579i	−0.687041	+	1.18999i	0.285750	+	0.958304i	$0.407757\pi$
$353$	−12.9083	+	22.3579i	−0.687041	+	1.18999i	−0.972791	+	0.231686i	$0.925576\pi$
$354$	−7.04584	−	12.2037i	−0.374482	−	0.648622i
$355$	−8.33053			−0.442139
$356$	−4.15139	−	7.19041i	−0.220023	−	0.381091i
$357$	−42.6333			−2.25639
$358$	−25.3305			−1.33876
$359$	6.89445	−	11.9415i	0.363875	−	0.630250i	−0.624720	−	0.780849i	$-0.714787\pi$
$359$	6.89445	−	11.9415i	0.363875	−	0.630250i	0.988595	+	0.150599i	$0.0481202\pi$
$360$	0.848612	−	1.46984i	0.0447258	−	0.0774673i
$361$	9.25694	−	16.0335i	0.487207	−	0.843868i
$362$	−11.0597	−	19.1560i	−0.581286	−	1.00682i
$363$	10.9722			0.575893
$364$	4.95416	−	8.58086i	0.259669	−	0.449759i
$365$	3.00000			0.157027
$366$	5.46804	+	8.58086i	0.285819	+	0.448529i
$367$	−10.3944			−0.542586			−0.271293	−	0.962497i	$-0.587451\pi$
$367$	−10.3944			−0.542586			−0.271293	+	0.962497i	$0.587451\pi$
$368$	−0.197224	+	0.341603i	−0.0102810	+	0.0178073i
$369$	−14.0917			−0.733583
$370$	4.95416	+	8.58086i	0.257555	+	0.446098i
$371$	−14.2111	+	24.6144i	−0.737804	+	1.27791i
$372$	4.50000	−	7.79423i	0.233314	−	0.404112i
$373$	14.6653	−	25.4010i	0.759339	−	1.31521i	−0.183850	−	0.982954i	$-0.558856\pi$
$373$	14.6653	−	25.4010i	0.759339	−	1.31521i	0.943188	−	0.332259i	$-0.107811\pi$
$374$	12.2111			0.631421
$375$	−14.0917			−0.727691
$376$	−2.19722	−	3.80570i	−0.113313	−	0.196264i
$377$	−1.60555			−0.0826901
$378$	−12.0597	−	20.8880i	−0.620285	−	1.07436i
$379$	4.30278	−	7.45263i	0.221019	−	0.382816i	−0.734099	−	0.679043i	$-0.762395\pi$
$379$	4.30278	−	7.45263i	0.221019	−	0.382816i	0.955118	+	0.296227i	$0.0957285\pi$
$380$	0.454163	+	0.786634i	0.0232981	+	0.0403535i
$381$	10.3625	−	17.9484i	0.530886	−	0.919522i
$382$	−6.40833	+	11.0995i	−0.327879	+	0.567902i
$383$	−3.31665	−	5.74461i	−0.169473	−	0.293536i	0.768762	−	0.639535i	$-0.220873\pi$
$383$	−3.31665	−	5.74461i	−0.169473	−	0.293536i	−0.938235	+	0.345999i	$0.887540\pi$
$384$	−0.651388	+	1.12824i	−0.0332410	+	0.0575751i
$385$	−4.50000	−	7.79423i	−0.229341	−	0.397231i
$386$	−2.51388			−0.127953
$387$	2.74306	−	4.75112i	0.139438	−	0.241513i
$388$	−7.10555	+	12.3072i	−0.360730	+	0.624802i
$389$	26.2111			1.32896			0.664478	−	0.747308i	$-0.268654\pi$
$389$	26.2111			1.32896			0.664478	+	0.747308i	$0.268654\pi$
$390$	−3.90833			−0.197906
$391$	1.50000	+	2.59808i	0.0758583	+	0.131390i
$392$	5.75694	+	9.97131i	0.290769	+	0.503627i
$393$	11.4861			0.579398
$394$	−8.00000			−0.403034
$395$	−10.3028	−	17.8449i	−0.518389	−	0.897876i
$396$	1.04584	+	1.81144i	0.0525553	+	0.0910284i
$397$	14.0458	+	24.3281i	0.704940	+	1.22099i	0.966713	+	0.255863i	$0.0823596\pi$
$397$	14.0458	+	24.3281i	0.704940	+	1.22099i	−0.261773	+	0.965130i	$0.584307\pi$
$398$	3.89445	+	6.74538i	0.195211	+	0.338116i
$399$	3.90833			0.195661
$400$	−3.30278			−0.165139
$401$	4.36249	+	7.55605i	0.217852	+	0.377331i	0.954151	−	0.299325i	$-0.0967615\pi$
$401$	4.36249	+	7.55605i	0.217852	+	0.377331i	−0.736299	+	0.676657i	$0.763428\pi$
$402$	0.711103	+	1.23167i	0.0354666	+	0.0614299i
$403$	15.9083			0.792450
$404$	16.6056			0.826157
$405$	−2.21110	+	3.82974i	−0.109871	+	0.190301i
$406$	1.50000	−	2.59808i	0.0744438	−	0.128940i
$407$	−12.2111			−0.605282
$408$	4.95416	+	8.58086i	0.245268	+	0.424816i
$409$	2.10555	−	3.64692i	0.104113	−	0.180329i	−0.809263	−	0.587447i	$-0.800133\pi$
$409$	2.10555	−	3.64692i	0.104113	−	0.180329i	0.913375	+	0.407118i	$0.133466\pi$
$410$	−7.04584	−	12.2037i	−0.347969	−	0.602700i
$411$	2.21110	−	3.82974i	0.109066	−	0.188907i
$412$	2.50000	−	4.33013i	0.123166	−	0.213330i
$413$	23.2708	+	40.3062i	1.14508	+	1.98334i
$414$	−0.256939	+	0.445032i	−0.0126279	+	0.0218721i
$415$	1.36249	+	2.35990i	0.0668820	+	0.115843i
$416$	−2.30278			−0.112903
$417$	−3.65139	−	6.32439i	−0.178809	−	0.309707i
$418$	−1.11943			−0.0547531
$419$	−30.2111			−1.47591			−0.737954	−	0.674851i	$-0.764208\pi$
$419$	−30.2111			−1.47591			−0.737954	+	0.674851i	$0.764208\pi$
$420$	3.65139	−	6.32439i	0.178169	−	0.308599i
$421$	0.0138782	−	0.0240377i	0.000676382	−	0.00117153i	−0.865687	−	0.500586i	$-0.833118\pi$
$421$	0.0138782	−	0.0240377i	0.000676382	−	0.00117153i	0.866363	+	0.499414i	$0.166451\pi$
$422$	−11.6514	+	20.1808i	−0.567181	+	0.982386i
$423$	−2.86249	−	4.95798i	−0.139179	−	0.241065i
$424$	6.60555			0.320794
$425$	−12.5597	+	21.7541i	−0.609236	+	1.05523i
$426$	8.33053			0.403616
$427$	−18.0597	−	28.3407i	−0.873971	−	1.37150i
$428$	9.21110			0.445235
$429$	2.40833	−	4.17134i	0.116275	−	0.201394i
$430$	5.48612			0.264564
$431$	−4.45416	−	7.71484i	−0.214550	−	0.371611i	0.738584	−	0.674162i	$-0.235495\pi$
$431$	−4.45416	−	7.71484i	−0.214550	−	0.371611i	−0.953133	+	0.302551i	$0.902162\pi$
$432$	−2.80278	+	4.85455i	−0.134849	+	0.233565i
$433$	0.545837	−	0.945417i	0.0262312	−	0.0454338i	−0.852612	−	0.522545i	$-0.824983\pi$
$433$	0.545837	−	0.945417i	0.0262312	−	0.0454338i	0.878843	+	0.477111i	$0.158316\pi$
$434$	−14.8625	+	25.7426i	−0.713422	+	1.23568i
$435$	−1.18335			−0.0567371
$436$	13.9083			0.666088
$437$	−0.137510	−	0.238174i	−0.00657798	−	0.0113934i
$438$	−3.00000			−0.143346
$439$	0.591673	+	1.02481i	0.0282390	+	0.0489114i	0.879800	−	0.475345i	$-0.157677\pi$
$439$	0.591673	+	1.02481i	0.0282390	+	0.0489114i	−0.851561	+	0.524256i	$0.824343\pi$
$440$	−1.04584	+	1.81144i	−0.0498583	+	0.0863571i
$441$	7.50000	+	12.9904i	0.357143	+	0.618590i
$442$	−8.75694	+	15.1675i	−0.416525	+	0.721443i
$443$	13.0139	−	22.5407i	0.618308	−	1.07094i	−0.371486	−	0.928438i	$-0.621152\pi$
$443$	13.0139	−	22.5407i	0.618308	−	1.07094i	0.989794	−	0.142503i	$-0.0455149\pi$
$444$	−4.95416	−	8.58086i	−0.235114	−	0.407230i
$445$	5.40833	−	9.36750i	0.256379	−	0.444062i
$446$	11.4542	+	19.8392i	0.542370	+	0.939413i
$447$	−7.81665			−0.369715
$448$	2.15139	−	3.72631i	0.101644	−	0.176052i
$449$	−18.1791	+	31.4872i	−0.857927	+	1.48597i	0.0159760	+	0.999872i	$0.494914\pi$
$449$	−18.1791	+	31.4872i	−0.857927	+	1.48597i	−0.873903	+	0.486101i	$0.838419\pi$
$450$	−4.30278			−0.202835
$451$	17.3667			0.817766
$452$	4.69722	+	8.13583i	0.220939	+	0.382677i
$453$	9.90833	+	17.1617i	0.465534	+	0.806328i
$454$	12.7250			0.597213
$455$	12.9083			0.605152
$456$	−0.454163	−	0.786634i	−0.0212682	−	0.0368375i
$457$	−6.75694	−	11.7034i	−0.316076	−	0.547460i	0.663589	−	0.748097i	$-0.269032\pi$
$457$	−6.75694	−	11.7034i	−0.316076	−	0.547460i	−0.979666	+	0.200637i	$0.935699\pi$
$458$	−10.9542	−	18.9732i	−0.511854	−	0.886558i
$459$	21.3167	+	36.9215i	0.994976	+	1.72335i
$460$	−0.513878			−0.0239597
$461$	0.605551			0.0282033			0.0141017	−	0.999901i	$-0.495511\pi$
$461$	0.605551			0.0282033			0.0141017	+	0.999901i	$0.495511\pi$
$462$	4.50000	+	7.79423i	0.209359	+	0.362620i
$463$	0.197224	+	0.341603i	0.00916579	+	0.0158756i	0.870572	−	0.492041i	$-0.163749\pi$
$463$	0.197224	+	0.341603i	0.00916579	+	0.0158756i	−0.861406	+	0.507917i	$0.830416\pi$
$464$	−0.697224			−0.0323678
$465$	11.7250			0.543733
$466$	7.69722	−	13.3320i	0.356567	−	0.617592i
$467$	−0.954163	+	1.65266i	−0.0441534	+	0.0764760i	−0.887258	−	0.461274i	$-0.847392\pi$
$467$	−0.954163	+	1.65266i	−0.0441534	+	0.0764760i	0.843104	+	0.537750i	$0.180726\pi$
$468$	−3.00000			−0.138675
$469$	−2.34861	−	4.06792i	−0.108449	−	0.187839i
$470$	2.86249	−	4.95798i	0.132037	−	0.228695i
$471$	−3.84861	−	6.66599i	−0.177335	−	0.307153i
$472$	5.40833	−	9.36750i	0.248938	−	0.431174i
$473$	−3.38057	+	5.85532i	−0.155439	+	0.269228i
$474$	10.3028	+	17.8449i	0.473222	+	0.819645i
$475$	1.15139	−	1.99426i	0.0528293	−	0.0915030i
$476$	−16.3625	−	28.3407i	−0.749974	−	1.29899i
$477$	8.60555			0.394021
$478$	−6.69722	−	11.5999i	−0.306324	−	0.530569i
$479$	−29.6972			−1.35690			−0.678450	−	0.734646i	$-0.737348\pi$
$479$	−29.6972			−1.35690			−0.678450	+	0.734646i	$0.737348\pi$
$480$	−1.69722			−0.0774673
$481$	8.75694	−	15.1675i	0.399282	−	0.691577i
$482$	12.6056	−	21.8335i	0.574167	−	0.994487i
$483$	−1.10555	+	1.91487i	−0.0503043	+	0.0871296i
$484$	4.21110	+	7.29384i	0.191414	+	0.331538i
$485$	−18.5139			−0.840672
$486$	−6.19722	+	10.7339i	−0.281112	+	0.486900i
$487$	32.5416			1.47460			0.737301	−	0.675564i	$-0.236100\pi$
$487$	32.5416			1.47460			0.737301	+	0.675564i	$0.236100\pi$
$488$	−3.60555	+	6.92820i	−0.163216	+	0.313625i
$489$	−0.788897			−0.0356752
$490$	−7.50000	+	12.9904i	−0.338815	+	0.586846i
$491$	−31.0278			−1.40026			−0.700132	−	0.714014i	$-0.746875\pi$
$491$	−31.0278			−1.40026			−0.700132	+	0.714014i	$0.746875\pi$
$492$	7.04584	+	12.2037i	0.317651	+	0.550187i
$493$	−2.65139	+	4.59234i	−0.119413	+	0.206829i
$494$	0.802776	−	1.39045i	0.0361186	−	0.0625592i
$495$	−1.36249	+	2.35990i	−0.0612394	+	0.106070i
$496$	6.90833			0.310193
$497$	−27.5139			−1.23417
$498$	−1.36249	−	2.35990i	−0.0610547	−	0.105750i
$499$	19.2389			0.861250			0.430625	−	0.902531i	$-0.358293\pi$
$499$	19.2389			0.861250			0.430625	+	0.902531i	$0.358293\pi$
$500$	−5.40833	−	9.36750i	−0.241868	−	0.418927i
$501$	−9.51388	+	16.4785i	−0.425049	+	0.736206i
$502$	−13.0597	−	22.6201i	−0.582884	−	1.00958i
$503$	−5.10555	+	8.84307i	−0.227645	+	0.394293i	−0.957110	−	0.289725i	$-0.906436\pi$
$503$	−5.10555	+	8.84307i	−0.227645	+	0.394293i	0.729465	+	0.684019i	$0.239769\pi$
$504$	2.80278	−	4.85455i	0.124846	−	0.216239i
$505$	10.8167	+	18.7350i	0.481335	+	0.833696i
$506$	0.316654	−	0.548461i	0.0140770	−	0.0243820i
$507$	−5.01388	−	8.68429i	−0.222674	−	0.385683i
$508$	15.9083			0.705818
$509$	−13.1056	+	22.6995i	−0.580893	+	1.00614i	0.414480	+	0.910058i	$0.363963\pi$
$509$	−13.1056	+	22.6995i	−0.580893	+	1.00614i	−0.995374	+	0.0960786i	$0.969370\pi$
$510$	−6.45416	+	11.1789i	−0.285795	+	0.495012i
$511$	9.90833			0.438319
$512$	−1.00000			−0.0441942
$513$	−1.95416	−	3.38471i	−0.0862784	−	0.149439i
$514$	1.24306	+	2.15304i	0.0548291	+	0.0949667i
$515$	6.51388			0.287036
$516$	−5.48612			−0.241513
$517$	3.52776	+	6.11025i	0.155151	+	0.268729i
$518$	16.3625	+	28.3407i	0.718927	+	1.24522i
$519$	−2.09167	−	3.62288i	−0.0918143	−	0.159027i
$520$	−1.50000	−	2.59808i	−0.0657794	−	0.113933i
$521$	−5.90833			−0.258849			−0.129424	−	0.991589i	$-0.541313\pi$
$521$	−5.90833			−0.258849			−0.129424	+	0.991589i	$0.541313\pi$
$522$	−0.908327			−0.0397564
$523$	−12.0139	−	20.8086i	−0.525330	−	0.909899i	−0.999565	−	0.0295001i	$-0.990608\pi$
$523$	−12.0139	−	20.8086i	−0.525330	−	0.909899i	0.474235	−	0.880399i	$-0.342725\pi$
$524$	4.40833	+	7.63545i	0.192579	+	0.333556i
$525$	−18.5139			−0.808012
$526$	27.8444			1.21407
$527$	26.2708	−	45.5024i	1.14437	−	1.98212i
$528$	1.04584	−	1.81144i	0.0455142	−	0.0788329i
$529$	−22.8444			−0.993235
$530$	4.30278	+	7.45263i	0.186901	+	0.323721i
$531$	7.04584	−	12.2037i	0.305763	−	0.529598i
$532$	1.50000	+	2.59808i	0.0650332	+	0.112641i
$533$	−12.4542	+	21.5712i	−0.539450	+	0.934354i
$534$	−5.40833	+	9.36750i	−0.234041	+	0.405371i
$535$	6.00000	+	10.3923i	0.259403	+	0.449299i
$536$	−0.545837	+	0.945417i	−0.0235765	+	0.0408358i
$537$	16.5000	+	28.5788i	0.712028	+	1.23327i
$538$	−19.0278			−0.820345
$539$	−9.24306	−	16.0095i	−0.398127	−	0.689576i
$540$	−7.30278			−0.314261
$541$	−11.2389			−0.483196			−0.241598	−	0.970376i	$-0.577672\pi$
$541$	−11.2389			−0.483196			−0.241598	+	0.970376i	$0.577672\pi$
$542$	0.743061	−	1.28702i	0.0319172	−	0.0552822i
$543$	−14.4083	+	24.9560i	−0.618320	+	1.07096i
$544$	−3.80278	+	6.58660i	−0.163043	+	0.282398i
$545$	9.05971	+	15.6919i	0.388076	+	0.672167i
$546$	−12.9083			−0.552425
$547$	0.197224	−	0.341603i	0.00843270	−	0.0146059i	−0.861778	−	0.507285i	$-0.830649\pi$
$547$	0.197224	−	0.341603i	0.00843270	−	0.0146059i	0.870211	+	0.492679i	$0.163982\pi$
$548$	3.39445			0.145004
$549$	−4.69722	+	9.02589i	−0.200473	+	0.385216i
$550$	5.30278			0.226111
$551$	0.243061	−	0.420994i	0.0103547	−	0.0179349i
$552$	0.513878			0.0218721
$553$	−34.0278	−	58.9378i	−1.44701	−	2.50629i
$554$	−3.00000	+	5.19615i	−0.127458	+	0.220763i
$555$	6.45416	−	11.1789i	0.273964	−	0.474520i
$556$	2.80278	−	4.85455i	0.118864	−	0.205879i
$557$	31.0278			1.31469			0.657344	−	0.753591i	$-0.271680\pi$
$557$	31.0278			1.31469			0.657344	+	0.753591i	$0.271680\pi$
$558$	9.00000			0.381000
$559$	−4.84861	−	8.39804i	−0.205074	−	0.355199i
$560$	5.60555			0.236878
$561$	−7.95416	−	13.7770i	−0.335825	−	0.581666i
$562$	−1.89445	+	3.28128i	−0.0799125	+	0.138413i
$563$	−10.1653	−	17.6068i	−0.428415	−	0.742036i	0.568318	−	0.822809i	$-0.307594\pi$
$563$	−10.1653	−	17.6068i	−0.428415	−	0.742036i	−0.996733	+	0.0807729i	$0.974261\pi$
$564$	−2.86249	+	4.95798i	−0.120533	+	0.208769i
$565$	−6.11943	+	10.5992i	−0.257446	+	0.445910i
$566$	11.8625	+	20.5464i	0.498618	+	0.863631i
$567$	−7.30278	+	12.6488i	−0.306688	+	0.531199i
$568$	3.19722	+	5.53776i	0.134153	+	0.232359i
$569$	24.4222			1.02383			0.511916	−	0.859035i	$-0.328936\pi$
$569$	24.4222			1.02383			0.511916	+	0.859035i	$0.328936\pi$
$570$	0.591673	−	1.02481i	0.0247825	−	0.0429245i
$571$	22.0139	−	38.1292i	0.921252	−	1.59566i	0.123772	−	0.992311i	$-0.460501\pi$
$571$	22.0139	−	38.1292i	0.921252	−	1.59566i	0.797480	−	0.603345i	$-0.206166\pi$
$572$	3.69722			0.154589
$573$	16.6972			0.697537
$574$	−23.2708	−	40.3062i	−0.971305	−	1.68235i
$575$	0.651388	+	1.12824i	0.0271647	+	0.0470507i
$576$	−1.30278			−0.0542823
$577$	−14.6056			−0.608037			−0.304019	−	0.952666i	$-0.598328\pi$
$577$	−14.6056			−0.608037			−0.304019	+	0.952666i	$0.598328\pi$
$578$	20.4222	+	35.3723i	0.849452	+	1.47129i
$579$	1.63751	+	2.83625i	0.0680526	+	0.117871i
$580$	−0.454163	−	0.786634i	−0.0188581	−	0.0326632i
$581$	4.50000	+	7.79423i	0.186691	+	0.323359i
$582$	18.5139			0.767425
$583$	−10.6056			−0.439237
$584$	−1.15139	−	1.99426i	−0.0476448	−	0.0825232i
$585$	−1.95416	−	3.38471i	−0.0807947	−	0.139941i
$586$	−3.60555			−0.148944
$587$	14.7250			0.607765			0.303882	−	0.952710i	$-0.401717\pi$
$587$	14.7250			0.607765			0.303882	+	0.952710i	$0.401717\pi$
$588$	7.50000	−	12.9904i	0.309295	−	0.535714i
$589$	−2.40833	+	4.17134i	−0.0992334	+	0.171877i
$590$	14.0917			0.580145
$591$	5.21110	+	9.02589i	0.214356	+	0.371276i
$592$	3.80278	−	6.58660i	0.156293	−	0.270708i
$593$	−8.51388	−	14.7465i	−0.349623	−	0.605565i	0.636559	−	0.771228i	$-0.280357\pi$
$593$	−8.51388	−	14.7465i	−0.349623	−	0.605565i	−0.986182	+	0.165663i	$0.947024\pi$
$594$	4.50000	−	7.79423i	0.184637	−	0.319801i
$595$	21.3167	−	36.9215i	0.873898	−	1.51364i
$596$	−3.00000	−	5.19615i	−0.122885	−	0.212843i
$597$	5.07359	−	8.78772i	0.207648	−	0.359657i
$598$	0.454163	+	0.786634i	0.0185721	+	0.0321679i
$599$	−42.4222			−1.73332			−0.866662	−	0.498895i	$-0.833739\pi$
$599$	−42.4222			−1.73332			−0.866662	+	0.498895i	$0.833739\pi$
$600$	2.15139	+	3.72631i	0.0878300	+	0.152126i
$601$	4.00000			0.163163			0.0815817	−	0.996667i	$-0.474003\pi$
$601$	4.00000			0.163163			0.0815817	+	0.996667i	$0.474003\pi$
$602$	18.1194			0.738493
$603$	−0.711103	+	1.23167i	−0.0289583	+	0.0501573i
$604$	−7.60555	+	13.1732i	−0.309465	+	0.536010i
$605$	−5.48612	+	9.50224i	−0.223043	+	0.386321i
$606$	−10.8167	−	18.7350i	−0.439397	−	0.761057i
$607$	−32.2389			−1.30853			−0.654267	−	0.756263i	$-0.727023\pi$
$607$	−32.2389			−1.30853			−0.654267	+	0.756263i	$0.727023\pi$
$608$	0.348612	−	0.603814i	0.0141381	−	0.0244879i
$609$	−3.90833			−0.158373
$610$	−10.1653	+	0.445032i	−0.411580	+	0.0180188i
$611$	−10.1194			−0.409388
$612$	−4.95416	+	8.58086i	−0.200260	+	0.346861i
$613$	−17.5416			−0.708500			−0.354250	−	0.935151i	$-0.615264\pi$
$613$	−17.5416			−0.708500			−0.354250	+	0.935151i	$0.615264\pi$
$614$	−13.9083	−	24.0899i	−0.561294	−	0.972190i
$615$	−9.17914	+	15.8987i	−0.370139	+	0.641099i
$616$	−3.45416	+	5.98279i	−0.139172	+	0.241053i
$617$	6.09167	−	10.5511i	0.245242	−	0.424771i	−0.716958	−	0.697116i	$-0.754466\pi$
$617$	6.09167	−	10.5511i	0.245242	−	0.424771i	0.962199	+	0.272346i	$0.0877994\pi$
$618$	−6.51388			−0.262027
$619$	−8.60555			−0.345886			−0.172943	−	0.984932i	$-0.555328\pi$
$619$	−8.60555			−0.345886			−0.172943	+	0.984932i	$0.555328\pi$
$620$	4.50000	+	7.79423i	0.180724	+	0.313024i
$621$	2.21110			0.0887285
$622$	−0.137510	−	0.238174i	−0.00551363	−	0.00954989i
$623$	17.8625	−	30.9387i	0.715646	−	1.23953i
$624$	1.50000	+	2.59808i	0.0600481	+	0.104006i
$625$	−1.21110	+	2.09769i	−0.0484441	+	0.0839076i
$626$	13.5139	−	23.4067i	0.540123	−	0.935521i
$627$	0.729183	+	1.26298i	0.0291208	+	0.0504386i
$628$	2.95416	−	5.11676i	0.117884	−	0.204181i
$629$	−28.9222	−	50.0947i	−1.15320	−	1.99741i
$630$	7.30278			0.290950
$631$	10.3167	−	17.8690i	0.410700	−	0.711352i	−0.584267	−	0.811562i	$-0.698618\pi$
$631$	10.3167	−	17.8690i	0.410700	−	0.711352i	0.994966	+	0.100209i	$0.0319512\pi$
$632$	−7.90833	+	13.6976i	−0.314576	+	0.544862i
$633$	30.3583			1.20663
$634$	−2.09167			−0.0830710
$635$	10.3625	+	17.9484i	0.411223	+	0.712259i
$636$	−4.30278	−	7.45263i	−0.170616	−	0.295516i
$637$	26.5139			1.05052
$638$	1.11943			0.0443186
$639$	4.16527	+	7.21445i	0.164775	+	0.285399i
$640$	−0.651388	−	1.12824i	−0.0257484	−	0.0445975i
$641$	7.92221	+	13.7217i	0.312908	+	0.541973i	0.978991	−	0.203905i	$-0.0653634\pi$
$641$	7.92221	+	13.7217i	0.312908	+	0.541973i	−0.666082	+	0.745878i	$0.732030\pi$
$642$	−6.00000	−	10.3923i	−0.236801	−	0.410152i
$643$	−7.51388			−0.296318			−0.148159	−	0.988964i	$-0.547335\pi$
$643$	−7.51388			−0.296318			−0.148159	+	0.988964i	$0.547335\pi$
$644$	−1.69722			−0.0668800
$645$	−3.57359	−	6.18964i	−0.140710	−	0.243717i
$646$	−2.65139	−	4.59234i	−0.104317	−	0.180683i
$647$	6.69722			0.263295			0.131648	−	0.991297i	$-0.457973\pi$
$647$	6.69722			0.263295			0.131648	+	0.991297i	$0.457973\pi$
$648$	3.39445			0.133347
$649$	−8.68335	+	15.0400i	−0.340851	+	0.590372i
$650$	−3.80278	+	6.58660i	−0.149157	+	0.258348i
$651$	38.7250			1.51775
$652$	−0.302776	−	0.524423i	−0.0118576	−	0.0205380i
$653$	5.80278	−	10.0507i	0.227080	−	0.393314i	−0.729861	−	0.683595i	$-0.760415\pi$
$653$	5.80278	−	10.0507i	0.227080	−	0.393314i	0.956941	+	0.290281i	$0.0937487\pi$
$654$	−9.05971	−	15.6919i	−0.354263	−	0.613601i
$655$	−5.74306	+	9.94727i	−0.224400	+	0.388672i
$656$	−5.40833	+	9.36750i	−0.211160	+	0.365739i
$657$	−1.50000	−	2.59808i	−0.0585206	−	0.101361i
$658$	9.45416	−	16.3751i	0.368562	−	0.638368i
$659$	5.10555	+	8.84307i	0.198884	+	0.344477i	0.948167	−	0.317773i	$-0.102935\pi$
$659$	5.10555	+	8.84307i	0.198884	+	0.344477i	−0.749283	+	0.662250i	$0.769602\pi$
$660$	2.72498			0.106070
$661$	11.8028	+	20.4430i	0.459075	+	0.795141i	0.998912	−	0.0466284i	$-0.0148477\pi$
$661$	11.8028	+	20.4430i	0.459075	+	0.795141i	−0.539838	+	0.841769i	$0.681514\pi$
$662$	19.9083			0.773759
$663$	22.8167			0.886125
$664$	1.04584	−	1.81144i	0.0405863	−	0.0702976i
$665$	−1.95416	+	3.38471i	−0.0757792	+	0.131253i
$666$	4.95416	−	8.58086i	0.191970	−	0.332502i
$667$	0.137510	+	0.238174i	0.00532439	+	0.00922212i
$668$	−14.6056			−0.565106
$669$	14.9222	−	25.8460i	0.576926	−	0.999265i
$670$	−1.42221			−0.0549446
$671$	5.78890	−	11.1236i	0.223478	−	0.429421i
$672$	−5.60555			−0.216239
$673$	21.1056	−	36.5559i	0.813559	−	1.40913i	−0.0967986	−	0.995304i	$-0.530860\pi$
$673$	21.1056	−	36.5559i	0.813559	−	1.40913i	0.910358	−	0.413822i	$-0.135806\pi$
$674$	−10.3944			−0.400379
$675$	9.25694	+	16.0335i	0.356300	+	0.617129i
$676$	3.84861	−	6.66599i	0.148024	−	0.256384i
$677$	1.81665	−	3.14654i	0.0698197	−	0.120931i	−0.829002	−	0.559245i	$-0.811091\pi$
$677$	1.81665	−	3.14654i	0.0698197	−	0.120931i	0.898822	+	0.438314i	$0.144424\pi$
$678$	6.11943	−	10.5992i	0.235015	−	0.407058i
$679$	−61.1472			−2.34661
$680$	−9.90833			−0.379967
$681$	−8.28890	−	14.3568i	−0.317631	−	0.550153i
$682$	−11.0917			−0.424722
$683$	9.92221	+	17.1858i	0.379663	+	0.657595i	0.991013	−	0.133765i	$-0.0427067\pi$
$683$	9.92221	+	17.1858i	0.379663	+	0.657595i	−0.611350	+	0.791360i	$0.709373\pi$
$684$	0.454163	−	0.786634i	0.0173654	−	0.0300777i
$685$	2.21110	+	3.82974i	0.0844819	+	0.146327i
$686$	−9.71110	+	16.8201i	−0.370772	+	0.642195i
$687$	−14.2708	+	24.7178i	−0.544466	+	0.943042i
$688$	−2.10555	−	3.64692i	−0.0802734	−	0.139038i
$689$	7.60555	−	13.1732i	0.289748	−	0.501859i
$690$	0.334734	+	0.579776i	0.0127431	+	0.0220717i
$691$	30.4500			1.15837			0.579186	−	0.815196i	$-0.303371\pi$
$691$	30.4500			1.15837			0.579186	+	0.815196i	$0.303371\pi$
$692$	1.60555	−	2.78090i	0.0610339	−	0.105714i
$693$	−4.50000	+	7.79423i	−0.170941	+	0.296078i
$694$	1.90833			0.0724391
$695$	7.30278			0.277010
$696$	0.454163	+	0.786634i	0.0172150	+	0.0298173i
$697$	41.1333	+	71.2450i	1.55804	+	2.69860i
$698$	10.0917			0.381975
$699$	−20.0555			−0.758569
$700$	−7.10555	−	12.3072i	−0.268565	−	0.465168i
$701$	−13.3625	−	23.1445i	−0.504694	−	0.874156i	−0.999985	−	0.00542901i	$-0.998272\pi$
$701$	−13.3625	−	23.1445i	−0.504694	−	0.874156i	0.495291	−	0.868727i	$-0.335061\pi$
$702$	6.45416	+	11.1789i	0.243597	+	0.421922i
$703$	2.65139	+	4.59234i	0.0999990	+	0.173203i
$704$	1.60555			0.0605115
$705$	−7.45837			−0.280898
$706$	12.9083	+	22.3579i	0.485811	+	0.841450i
$707$	35.7250	+	61.8775i	1.34358	+	2.32714i
$708$	−14.0917			−0.529598
$709$	−31.1472			−1.16976			−0.584879	−	0.811121i	$-0.698858\pi$
$709$	−31.1472			−1.16976			−0.584879	+	0.811121i	$0.698858\pi$
$710$	−4.16527	+	7.21445i	−0.156320	+	0.270754i
$711$	−10.3028	+	17.8449i	−0.386384	+	0.669237i
$712$	−8.30278			−0.311160
$713$	−1.36249	−	2.35990i	−0.0510257	−	0.0883790i
$714$	−21.3167	+	36.9215i	−0.797756	+	1.38175i
$715$	2.40833	+	4.17134i	0.0900663	+	0.155999i
$716$	−12.6653	+	21.9369i	−0.473323	+	0.819820i
$717$	−8.72498	+	15.1121i	−0.325840	+	0.564372i
$718$	−6.89445	−	11.9415i	−0.257299	−	0.445654i
$719$	−9.55971	+	16.5579i	−0.356517	+	0.617506i	−0.987376	−	0.158391i	$-0.949369\pi$
$719$	−9.55971	+	16.5579i	−0.356517	+	0.617506i	0.630859	+	0.775897i	$0.282703\pi$
$720$	−0.848612	−	1.46984i	−0.0316259	−	0.0547777i
$721$	21.5139			0.801219
$722$	−9.25694	−	16.0335i	−0.344508	−	0.596705i
$723$	−32.8444			−1.22150
$724$	−22.1194			−0.822062
$725$	−1.15139	+	1.99426i	−0.0427615	+	0.0740650i
$726$	5.48612	−	9.50224i	0.203609	−	0.352661i
$727$	−4.66527	+	8.08048i	−0.173025	+	0.299688i	−0.939476	−	0.342615i	$-0.888688\pi$
$727$	−4.66527	+	8.08048i	−0.173025	+	0.299688i	0.766451	+	0.642303i	$0.222021\pi$
$728$	−4.95416	−	8.58086i	−0.183614	−	0.318028i
$729$	26.3305			0.975205
$730$	1.50000	−	2.59808i	0.0555175	−	0.0961591i
$731$	−32.0278			−1.18459
$732$	10.1653	−	0.445032i	0.375719	−	0.0164488i
$733$	−3.81665			−0.140971			−0.0704857	−	0.997513i	$-0.522455\pi$
$733$	−3.81665			−0.140971			−0.0704857	+	0.997513i	$0.522455\pi$
$734$	−5.19722	+	9.00186i	−0.191833	+	0.332265i
$735$	19.5416			0.720804
$736$	0.197224	+	0.341603i	0.00726979	+	0.0125916i
$737$	0.876369	−	1.51791i	0.0322815	−	0.0559131i
$738$	−7.04584	+	12.2037i	−0.259361	+	0.449226i
$739$	−4.01388	+	6.95224i	−0.147653	+	0.255742i	−0.930360	−	0.366648i	$-0.880505\pi$
$739$	−4.01388	+	6.95224i	−0.147653	+	0.255742i	0.782707	+	0.622391i	$0.213839\pi$
$740$	9.90833			0.364237
$741$	−2.09167			−0.0768395
$742$	14.2111	+	24.6144i	0.521706	+	0.903621i
$743$	7.69722			0.282384			0.141192	−	0.989982i	$-0.454907\pi$
$743$	7.69722			0.282384			0.141192	+	0.989982i	$0.454907\pi$
$744$	−4.50000	−	7.79423i	−0.164978	−	0.285750i
$745$	3.90833	−	6.76942i	0.143190	−	0.248012i
$746$	−14.6653	−	25.4010i	−0.536934	−	0.929996i
$747$	1.36249	−	2.35990i	0.0498509	−	0.0863443i
$748$	6.10555	−	10.5751i	0.223241	−	0.386665i
$749$	19.8167	+	34.3235i	0.724085	+	1.25415i
$750$	−7.04584	+	12.2037i	−0.257278	+	0.445618i
$751$	6.75694	+	11.7034i	0.246564	+	0.427062i	0.962570	−	0.271032i	$-0.0873650\pi$
$751$	6.75694	+	11.7034i	0.246564	+	0.427062i	−0.716006	+	0.698094i	$0.754032\pi$
$752$	−4.39445			−0.160249
$753$	−17.0139	+	29.4689i	−0.620020	+	1.07391i
$754$	−0.802776	+	1.39045i	−0.0292354	+	0.0506371i
$755$	−19.8167			−0.721202
$756$	−24.1194			−0.877215
$757$	−4.00000	−	6.92820i	−0.145382	−	0.251810i	0.784133	−	0.620593i	$-0.213108\pi$
$757$	−4.00000	−	6.92820i	−0.145382	−	0.251810i	−0.929516	+	0.368783i	$0.879775\pi$
$758$	−4.30278	−	7.45263i	−0.156284	−	0.270692i
$759$	−0.825058			−0.0299477
$760$	0.908327			0.0329485
$761$	−3.83473	−	6.64195i	−0.139009	−	0.240771i	0.788113	−	0.615531i	$-0.211058\pi$
$761$	−3.83473	−	6.64195i	−0.139009	−	0.240771i	−0.927122	+	0.374760i	$0.877725\pi$
$762$	−10.3625	−	17.9484i	−0.375393	−	0.650200i
$763$	29.9222	+	51.8268i	1.08326	+	1.87626i
$764$	6.40833	+	11.0995i	0.231845	+	0.401568i
$765$	−12.9083			−0.466702
$766$	−6.63331			−0.239671
$767$	−12.4542	−	21.5712i	−0.449694	−	0.778892i
$768$	0.651388	+	1.12824i	0.0235049	+	0.0407117i
$769$	−16.6056			−0.598811			−0.299406	−	0.954126i	$-0.596788\pi$
$769$	−16.6056			−0.598811			−0.299406	+	0.954126i	$0.596788\pi$
$770$	−9.00000			−0.324337
$771$	1.61943	−	2.80493i	0.0583223	−	0.101017i
$772$	−1.25694	+	2.17708i	−0.0452382	+	0.0783549i
$773$	17.7889			0.639822			0.319911	−	0.947448i	$-0.396347\pi$
$773$	17.7889			0.639822			0.319911	+	0.947448i	$0.396347\pi$
$774$	−2.74306	−	4.75112i	−0.0985973	−	0.170776i
$775$	11.4083	−	19.7598i	0.409799	−	0.709793i
$776$	7.10555	+	12.3072i	0.255074	+	0.441802i
$777$	21.3167	−	36.9215i	0.764731	−	1.32455i
$778$	13.1056	−	22.6995i	0.469857	−	0.813816i
$779$	−3.77082	−	6.53125i	−0.135104	−	0.234006i
$780$	−1.95416	+	3.38471i	−0.0699703	+	0.121192i
$781$	−5.13331	−	8.89115i	−0.183684	−	0.318150i
$782$	3.00000			0.107280
$783$	1.95416	+	3.38471i	0.0698361	+	0.120960i
$784$	11.5139			0.411210
$785$	7.69722			0.274726
$786$	5.74306	−	9.94727i	0.204848	−	0.354807i
$787$	3.61943	−	6.26904i	0.129019	−	0.223467i	−0.794278	−	0.607555i	$-0.792151\pi$
$787$	3.61943	−	6.26904i	0.129019	−	0.223467i	0.923297	+	0.384088i	$0.125484\pi$
$788$	−4.00000	+	6.92820i	−0.142494	+	0.246807i
$789$	−18.1375	−	31.4151i	−0.645712	−	1.11841i
$790$	−20.6056			−0.733113
$791$	−20.2111	+	35.0067i	−0.718624	+	1.24469i
$792$	2.09167			0.0743244
$793$	9.66527	+	15.1675i	0.343224	+	0.538612i
$794$	28.0917			0.996936
$795$	5.60555	−	9.70910i	0.198808	−	0.344346i
$796$	7.78890			0.276070
$797$	22.0139	+	38.1292i	0.779772	+	1.35060i	0.932073	+	0.362270i	$0.117998\pi$
$797$	22.0139	+	38.1292i	0.779772	+	1.35060i	−0.152302	+	0.988334i	$0.548669\pi$
$798$	1.95416	−	3.38471i	0.0691766	−	0.119817i
$799$	−16.7111	+	28.9445i	−0.591196	+	1.02398i
$800$	−1.65139	+	2.86029i	−0.0583854	+	0.101126i
$801$	−10.8167			−0.382188
$802$	8.72498			0.308090
$803$	1.84861	+	3.20189i	0.0652361	+	0.112992i
$804$	1.42221			0.0501573
$805$	−1.10555	−	1.91487i	−0.0389656	−	0.0674903i
$806$	7.95416	−	13.7770i	0.280173	−	0.485275i
$807$	12.3944	+	21.4678i	0.436305	+	0.755703i
$808$	8.30278	−	14.3808i	0.292091	−	0.505916i
$809$	−2.60555	+	4.51295i	−0.0916063	+	0.158667i	−0.908187	−	0.418564i	$-0.862533\pi$
$809$	−2.60555	+	4.51295i	−0.0916063	+	0.158667i	0.816581	+	0.577231i	$0.195867\pi$
$810$	2.21110	+	3.82974i	0.0776902	+	0.134563i
$811$	11.4222	−	19.7838i	0.401088	−	0.694705i	−0.592770	−	0.805372i	$-0.701966\pi$
$811$	11.4222	−	19.7838i	0.401088	−	0.694705i	0.993857	+	0.110668i	$0.0352989\pi$
$812$	−1.50000	−	2.59808i	−0.0526397	−	0.0911746i
$813$	−1.93608			−0.0679014
$814$	−6.10555	+	10.5751i	−0.213999	+	0.370658i
$815$	0.394449	−	0.683205i	0.0138169	−	0.0239316i
$816$	9.90833			0.346861
$817$	2.93608			0.102721
$818$	−2.10555	−	3.64692i	−0.0736189	−	0.127512i
$819$	−6.45416	−	11.1789i	−0.225527	−	0.390624i
$820$	−14.0917			−0.492103
$821$	22.2111			0.775173			0.387586	−	0.921833i	$-0.373309\pi$
$821$	22.2111			0.775173			0.387586	+	0.921833i	$0.373309\pi$
$822$	−2.21110	−	3.82974i	−0.0771211	−	0.133578i
$823$	1.21110	+	2.09769i	0.0422164	+	0.0731209i	0.886362	−	0.462994i	$-0.153225\pi$
$823$	1.21110	+	2.09769i	0.0422164	+	0.0731209i	−0.844145	+	0.536115i	$0.819891\pi$
$824$	−2.50000	−	4.33013i	−0.0870916	−	0.150847i
$825$	−3.45416	−	5.98279i	−0.120259	−	0.208294i
$826$	46.5416			1.61939
$827$	−1.02776			−0.0357386			−0.0178693	−	0.999840i	$-0.505688\pi$
$827$	−1.02776			−0.0357386			−0.0178693	+	0.999840i	$0.505688\pi$
$828$	0.256939	+	0.445032i	0.00892925	+	0.0154659i
$829$	−4.00000	−	6.92820i	−0.138926	−	0.240626i	0.788165	−	0.615465i	$-0.211032\pi$
$829$	−4.00000	−	6.92820i	−0.138926	−	0.240626i	−0.927090	+	0.374838i	$0.877698\pi$
$830$	2.72498			0.0945855
$831$	7.81665			0.271157
$832$	−1.15139	+	1.99426i	−0.0399172	+	0.0691386i
$833$	43.7847	−	75.8373i	1.51705	−	2.62761i
$834$	−7.30278			−0.252874
$835$	−9.51388	−	16.4785i	−0.329241	−	0.570263i
$836$	−0.559715	+	0.969454i	−0.0193581	+	0.0335293i
$837$	−19.3625	−	33.5368i	−0.669266	−	1.15920i
$838$	−15.1056	+	26.1636i	−0.521813	+	0.903806i
$839$	−0.348612	+	0.603814i	−0.0120354	+	0.0208460i	−0.871980	−	0.489541i	$-0.837164\pi$
$839$	−0.348612	+	0.603814i	−0.0120354	+	0.0208460i	0.859945	+	0.510387i	$0.170498\pi$
$840$	−3.65139	−	6.32439i	−0.125985	−	0.218212i
$841$	14.2569	−	24.6937i	0.491619	−	0.851508i
$842$	−0.0138782	−	0.0240377i	−0.000478274	−	0.000828395i
$843$	4.93608			0.170008
$844$	11.6514	+	20.1808i	0.401057	+	0.694652i
$845$	10.0278			0.344965
$846$	−5.72498			−0.196829
$847$	−18.1194	+	31.3838i	−0.622591	+	1.07836i
$848$	3.30278	−	5.72058i	0.113418	−	0.196445i
$849$	15.4542	−	26.7674i	0.530386	−	0.918655i
$850$	12.5597	+	21.7541i	0.430795	+	0.746158i
$851$	−3.00000			−0.102839
$852$	4.16527	−	7.21445i	0.142700	−	0.247163i
$853$	−16.8806			−0.577980			−0.288990	−	0.957332i	$-0.593319\pi$
$853$	−16.8806			−0.577980			−0.288990	+	0.957332i	$0.593319\pi$
$854$	−33.5736	+	1.46984i	−1.14886	+	0.0502969i
$855$	1.18335			0.0404696
$856$	4.60555	−	7.97705i	0.157415	−	0.272650i
$857$	−52.1749			−1.78226			−0.891131	−	0.453746i	$-0.850087\pi$
$857$	−52.1749			−1.78226			−0.891131	+	0.453746i	$0.850087\pi$
$858$	−2.40833	−	4.17134i	−0.0822189	−	0.142407i
$859$	9.15139	−	15.8507i	0.312241	−	0.540818i	−0.666606	−	0.745410i	$-0.732254\pi$
$859$	9.15139	−	15.8507i	0.312241	−	0.540818i	0.978847	+	0.204592i	$0.0655869\pi$
$860$	2.74306	−	4.75112i	0.0935376	−	0.162012i
$861$	−30.3167	+	52.5100i	−1.03319	+	1.78954i
$862$	−8.90833			−0.303419
$863$	10.2750			0.349766			0.174883	−	0.984589i	$-0.444045\pi$
$863$	10.2750			0.349766			0.174883	+	0.984589i	$0.444045\pi$
$864$	2.80278	+	4.85455i	0.0953524	+	0.165155i
$865$	4.18335			0.142238
$866$	−0.545837	−	0.945417i	−0.0185483	−	0.0321266i
$867$	26.6056	−	46.0822i	0.903572	−	1.56503i
$868$	14.8625	+	25.7426i	0.504466	+	0.873760i
$869$	12.6972	−	21.9922i	0.430724	−	0.746036i
$870$	−0.591673	+	1.02481i	−0.0200596	+	0.0347442i
$871$	1.25694	+	2.17708i	0.0425898	+	0.0737676i
$872$	6.95416	−	12.0450i	0.235498	−	0.407894i
$873$	9.25694	+	16.0335i	0.313300	+	0.542651i
$874$	−0.275019			−0.00930267
$875$	23.2708	−	40.3062i	0.786697	−	1.36260i
$876$	−1.50000	+	2.59808i	−0.0506803	+	0.0877809i
$877$	−49.8444			−1.68313			−0.841563	−	0.540159i	$-0.818364\pi$
$877$	−49.8444			−1.68313			−0.841563	+	0.540159i	$0.818364\pi$
$878$	1.18335			0.0399360
$879$	2.34861	+	4.06792i	0.0792167	+	0.137207i
$880$	1.04584	+	1.81144i	0.0352551	+	0.0610637i
$881$	−31.3583			−1.05649			−0.528244	−	0.849093i	$-0.677149\pi$
$881$	−31.3583			−1.05649			−0.528244	+	0.849093i	$0.677149\pi$
$882$	15.0000			0.505076
$883$	−13.9680	−	24.1934i	−0.470062	−	0.814171i	0.529352	−	0.848402i	$-0.322435\pi$
$883$	−13.9680	−	24.1934i	−0.470062	−	0.814171i	−0.999414	+	0.0342310i	$0.989102\pi$
$884$	8.75694	+	15.1675i	0.294528	+	0.510137i
$885$	−9.17914	−	15.8987i	−0.308554	−	0.534430i
$886$	−13.0139	−	22.5407i	−0.437210	−	0.757270i
$887$	−8.39445			−0.281858			−0.140929	−	0.990020i	$-0.545009\pi$
$887$	−8.39445			−0.281858			−0.140929	+	0.990020i	$0.545009\pi$
$888$	−9.90833			−0.332502
$889$	34.2250	+	59.2794i	1.14787	+	1.98817i
$890$	−5.40833	−	9.36750i	−0.181288	−	0.313999i
$891$	−5.44996			−0.182581
$892$	22.9083			0.767028
$893$	1.53196	−	2.65343i	0.0512650	−	0.0887936i
$894$	−3.90833	+	6.76942i	−0.130714	+	0.226403i
$895$	−33.0000			−1.10307
$896$	−2.15139	−	3.72631i	−0.0718728	−	0.124487i
$897$	0.591673	−	1.02481i	0.0197554	−	0.0342173i
$898$	18.1791	+	31.4872i	0.606646	+	1.05074i
$899$	2.40833	−	4.17134i	0.0803222	−	0.139122i
$900$	−2.15139	+	3.72631i	−0.0717129	+	0.124210i
$901$	−25.1194	−	43.5081i	−0.836850	−	1.44947i
$902$	8.68335	−	15.0400i	0.289124	−	0.500777i
$903$	−11.8028	−	20.4430i	−0.392772	−	0.680301i
$904$	9.39445			0.312455
$905$	−14.4083	−	24.9560i	−0.478949	−	0.829564i
$906$	19.8167			0.658364
$907$	45.3305			1.50518			0.752588	−	0.658492i	$-0.228805\pi$
$907$	45.3305			1.50518			0.752588	+	0.658492i	$0.228805\pi$
$908$	6.36249	−	11.0202i	0.211147	−	0.365717i
$909$	10.8167	−	18.7350i	0.358766	−	0.621401i
$910$	6.45416	−	11.1789i	0.213953	−	0.370578i
$911$	11.8167	+	20.4670i	0.391503	+	0.678103i	0.992648	−	0.121037i	$-0.0386219\pi$
$911$	11.8167	+	20.4670i	0.391503	+	0.678103i	−0.601145	+	0.799140i	$0.705289\pi$
$912$	−0.908327			−0.0300777
$913$	−1.67914	+	2.90836i	−0.0555716	+	0.0962528i
$914$	−13.5139			−0.446999
$915$	7.12363	+	11.1789i	0.235500	+	0.369564i
$916$	−21.9083			−0.723871
$917$	−18.9680	+	32.8536i	−0.626380	+	1.08492i
$918$	42.6333			1.40711
$919$	12.6791	+	21.9609i	0.418246	+	0.724424i	0.995763	−	0.0919548i	$-0.0293115\pi$
$919$	12.6791	+	21.9609i	0.418246	+	0.724424i	−0.577517	+	0.816379i	$0.695978\pi$
$920$	−0.256939	+	0.445032i	−0.00847103	+	0.0146723i
$921$	−18.1194	+	31.3838i	−0.597056	+	1.03413i
$922$	0.302776	−	0.524423i	0.00997138	−	0.0172709i
$923$	14.7250			0.484679
$924$	9.00000			0.296078
$925$	−12.5597	−	21.7541i	−0.412961	−	0.715269i
$926$	0.394449			0.0129624
$927$	−3.25694	−	5.64118i	−0.106972	−	0.185281i
$928$	−0.348612	+	0.603814i	−0.0114438	+	0.0198212i
$929$	15.3028	+	26.5052i	0.502068	+	0.869607i	0.999997	+	0.00238932i	$0.000760544\pi$
$929$	15.3028	+	26.5052i	0.502068	+	0.869607i	−0.497929	+	0.867218i	$0.665906\pi$
$930$	5.86249	−	10.1541i	0.192239	−	0.332967i
$931$	−4.01388	+	6.95224i	−0.131550	+	0.227850i
$932$	−7.69722	−	13.3320i	−0.252131	−	0.436704i
$933$	−0.179144	+	0.310287i	−0.00586492	+	0.0101583i
$934$	0.954163	+	1.65266i	0.0312212	+	0.0540767i
$935$	15.9083			0.520258
$936$	−1.50000	+	2.59808i	−0.0490290	+	0.0849208i
$937$	−3.09167	+	5.35493i	−0.101001	+	0.174938i	−0.912097	−	0.409974i	$-0.865538\pi$
$937$	−3.09167	+	5.35493i	−0.101001	+	0.174938i	0.811097	+	0.584912i	$0.198871\pi$
$938$	−4.69722			−0.153370
$939$	−35.2111			−1.14907
$940$	−2.86249	−	4.95798i	−0.0933641	−	0.161711i
$941$	−23.5736	−	40.8307i	−0.768477	−	1.33104i	−0.938389	−	0.345582i	$-0.887681\pi$
$941$	−23.5736	−	40.8307i	−0.768477	−	1.33104i	0.169911	−	0.985459i	$-0.445652\pi$
$942$	−7.69722			−0.250789
$943$	4.26662			0.138940
$944$	−5.40833	−	9.36750i	−0.176026	−	0.304886i
$945$	−15.7111	−	27.2124i	−0.511082	−	0.885220i
$946$	3.38057	+	5.85532i	0.109912	+	0.190373i
$947$	−7.75694	−	13.4354i	−0.252067	−	0.436592i	0.712028	−	0.702151i	$-0.247777\pi$
$947$	−7.75694	−	13.4354i	−0.252067	−	0.436592i	−0.964095	+	0.265559i	$0.914444\pi$
$948$	20.6056			0.669237
$949$	−5.30278			−0.172135
$950$	−1.15139	−	1.99426i	−0.0373560	−	0.0647024i
$951$	1.36249	+	2.35990i	0.0441818	+	0.0765251i
$952$	−32.7250			−1.06062
$953$	21.5139			0.696903			0.348451	−	0.937327i	$-0.386708\pi$
$953$	21.5139			0.696903			0.348451	+	0.937327i	$0.386708\pi$
$954$	4.30278	−	7.45263i	0.139308	−	0.241288i
$955$	−8.34861	+	14.4602i	−0.270155	+	0.467922i
$956$	−13.3944			−0.433207
$957$	−0.729183	−	1.26298i	−0.0235711	−	0.0408264i
$958$	−14.8486	+	25.7186i	−0.479737	+	0.830929i
$959$	7.30278	+	12.6488i	0.235819	+	0.408450i
$960$	−0.848612	+	1.46984i	−0.0273888	+	0.0474389i
$961$	−8.36249	+	14.4843i	−0.269758	+	0.467234i
$962$	−8.75694	−	15.1675i	−0.282335	−	0.489019i
$963$	6.00000	−	10.3923i	0.193347	−	0.334887i
$964$	−12.6056	−	21.8335i	−0.405997	−	0.703208i
$965$	−3.27502			−0.105427
$966$	1.10555	+	1.91487i	0.0355705	+	0.0616100i
$967$	−15.0639			−0.484423			−0.242211	−	0.970223i	$-0.577873\pi$
$967$	−15.0639			−0.484423			−0.242211	+	0.970223i	$0.577873\pi$
$968$	8.42221			0.270700
$969$	−3.45416	+	5.98279i	−0.110964	+	0.192195i
$970$	−9.25694	+	16.0335i	−0.297222	+	0.514804i
$971$	10.1653	−	17.6068i	0.326219	−	0.565028i	−0.655539	−	0.755161i	$-0.727559\pi$
$971$	10.1653	−	17.6068i	0.326219	−	0.565028i	0.981758	+	0.190133i	$0.0608920\pi$
$972$	6.19722	+	10.7339i	0.198776	+	0.344290i
$973$	24.1194			0.773233
$974$	16.2708	−	28.1819i	0.521351	−	0.903006i
$975$	9.90833			0.317320
$976$	4.19722	+	6.58660i	0.134350	+	0.210832i
$977$	−26.9361			−0.861762			−0.430881	−	0.902409i	$-0.641797\pi$
$977$	−26.9361			−0.861762			−0.430881	+	0.902409i	$0.641797\pi$
$978$	−0.394449	+	0.683205i	−0.0126131	+	0.0218465i
$979$	13.3305			0.426046
$980$	7.50000	+	12.9904i	0.239579	+	0.414963i
$981$	9.05971	−	15.6919i	0.289254	−	0.501003i
$982$	−15.5139	+	26.8708i	−0.495068	+	0.857482i
$983$	2.72498	−	4.71981i	0.0869134	−	0.150538i	−0.819292	−	0.573377i	$-0.805633\pi$
$983$	2.72498	−	4.71981i	0.0869134	−	0.150538i	0.906205	+	0.422839i	$0.138966\pi$
$984$	14.0917			0.449226
$985$	−10.4222			−0.332079
$986$	2.65139	+	4.59234i	0.0844374	+	0.146250i
$987$	−24.6333			−0.784087
$988$	−0.802776	−	1.39045i	−0.0255397	−	0.0442360i
$989$	−0.830532	+	1.43852i	−0.0264094	+	0.0457424i
$990$	1.36249	+	2.35990i	0.0433028	+	0.0750026i
$991$	3.01388	−	5.22019i	0.0957390	−	0.165825i	−0.814178	−	0.580616i	$-0.802812\pi$
$991$	3.01388	−	5.22019i	0.0957390	−	0.165825i	0.909917	+	0.414791i	$0.136145\pi$
$992$	3.45416	−	5.98279i	0.109670	−	0.189954i
$993$	−12.9680	−	22.4613i	−0.411528	−	0.712788i
$994$	−13.7569	+	23.8277i	−0.436344	+	0.755769i
$995$	5.07359	+	8.78772i	0.160844	+	0.278589i
$996$	−2.72498			−0.0863443
$997$	25.0597	−	43.4047i	0.793649	−	1.37464i	−0.130044	−	0.991508i	$-0.541512\pi$
$997$	25.0597	−	43.4047i	0.793649	−	1.37464i	0.923693	−	0.383132i	$-0.125155\pi$
$998$	9.61943	−	16.6613i	0.304498	−	0.527406i
$999$	−42.6333			−1.34886

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	122.2.c.a.13.1	✓	4
3.2	odd	2		1098.2.f.c.379.1		4
4.3	odd	2		976.2.i.c.257.2		4
61.13	even	3		7442.2.a.e.1.1		2
61.47	even	3	inner	122.2.c.a.47.1	yes	4
61.48	even	6		7442.2.a.h.1.1		2
183.47	odd	6		1098.2.f.c.901.1		4
244.47	odd	6		976.2.i.c.657.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
122.2.c.a.13.1	✓	4	1.1	even	1	trivial
122.2.c.a.47.1	yes	4	61.47	even	3	inner
976.2.i.c.257.2		4	4.3	odd	2
976.2.i.c.657.2		4	244.47	odd	6
1098.2.f.c.379.1		4	3.2	odd	2
1098.2.f.c.901.1		4	183.47	odd	6
7442.2.a.e.1.1		2	61.13	even	3
7442.2.a.h.1.1		2	61.48	even	6

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:	\( N \)	\(=\)	\( 122 = 2 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	122.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} -1.30278 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.651388 - 1.12824i) q^{5} +(-0.651388 + 1.12824i) q^{6} +(2.15139 - 3.72631i) q^{7} -1.00000 q^{8} -1.30278 q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} -1.30278 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.651388 - 1.12824i) q^{5} +(-0.651388 + 1.12824i) q^{6} +(2.15139 - 3.72631i) q^{7} -1.00000 q^{8} -1.30278 q^{9} +(-0.651388 - 1.12824i) q^{10} +1.60555 q^{11} +(0.651388 + 1.12824i) q^{12} +(-1.15139 + 1.99426i) q^{13} +(-2.15139 - 3.72631i) q^{14} +(-0.848612 + 1.46984i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.80278 + 6.58660i) q^{17} +(-0.651388 + 1.12824i) q^{18} +(-0.348612 - 0.603814i) q^{19} -1.30278 q^{20} +(-2.80278 + 4.85455i) q^{21} +(0.802776 - 1.39045i) q^{22} +0.394449 q^{23} +1.30278 q^{24} +(1.65139 + 2.86029i) q^{25} +(1.15139 + 1.99426i) q^{26} +5.60555 q^{27} -4.30278 q^{28} +(0.348612 + 0.603814i) q^{29} +(0.848612 + 1.46984i) q^{30} +(-3.45416 - 5.98279i) q^{31} +(0.500000 + 0.866025i) q^{32} -2.09167 q^{33} +7.60555 q^{34} +(-2.80278 - 4.85455i) q^{35} +(0.651388 + 1.12824i) q^{36} -7.60555 q^{37} -0.697224 q^{38} +(1.50000 - 2.59808i) q^{39} +(-0.651388 + 1.12824i) q^{40} +10.8167 q^{41} +(2.80278 + 4.85455i) q^{42} +(-2.10555 + 3.64692i) q^{43} +(-0.802776 - 1.39045i) q^{44} +(-0.848612 + 1.46984i) q^{45} +(0.197224 - 0.341603i) q^{46} +(2.19722 + 3.80570i) q^{47} +(0.651388 - 1.12824i) q^{48} +(-5.75694 - 9.97131i) q^{49} +3.30278 q^{50} +(-4.95416 - 8.58086i) q^{51} +2.30278 q^{52} -6.60555 q^{53} +(2.80278 - 4.85455i) q^{54} +(1.04584 - 1.81144i) q^{55} +(-2.15139 + 3.72631i) q^{56} +(0.454163 + 0.786634i) q^{57} +0.697224 q^{58} +(-5.40833 + 9.36750i) q^{59} +1.69722 q^{60} +(3.60555 - 6.92820i) q^{61} -6.90833 q^{62} +(-2.80278 + 4.85455i) q^{63} +1.00000 q^{64} +(1.50000 + 2.59808i) q^{65} +(-1.04584 + 1.81144i) q^{66} +(0.545837 - 0.945417i) q^{67} +(3.80278 - 6.58660i) q^{68} -0.513878 q^{69} -5.60555 q^{70} +(-3.19722 - 5.53776i) q^{71} +1.30278 q^{72} +(1.15139 + 1.99426i) q^{73} +(-3.80278 + 6.58660i) q^{74} +(-2.15139 - 3.72631i) q^{75} +(-0.348612 + 0.603814i) q^{76} +(3.45416 - 5.98279i) q^{77} +(-1.50000 - 2.59808i) q^{78} +(7.90833 - 13.6976i) q^{79} +(0.651388 + 1.12824i) q^{80} -3.39445 q^{81} +(5.40833 - 9.36750i) q^{82} +(-1.04584 + 1.81144i) q^{83} +5.60555 q^{84} +9.90833 q^{85} +(2.10555 + 3.64692i) q^{86} +(-0.454163 - 0.786634i) q^{87} -1.60555 q^{88} +8.30278 q^{89} +(0.848612 + 1.46984i) q^{90} +(4.95416 + 8.58086i) q^{91} +(-0.197224 - 0.341603i) q^{92} +(4.50000 + 7.79423i) q^{93} +4.39445 q^{94} -0.908327 q^{95} +(-0.651388 - 1.12824i) q^{96} +(-7.10555 - 12.3072i) q^{97} -11.5139 q^{98} -2.09167 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - q^{5} + q^{6} + 5 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - q^5 + q^6 + 5 * q^7 - 4 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - q^{5} + q^{6} + 5 q^{7} - 4 q^{8} + 2 q^{9} + q^{10} - 8 q^{11} - q^{12} - q^{13} - 5 q^{14} - 7 q^{15} - 2 q^{16} + 8 q^{17} + q^{18} - 5 q^{19} + 2 q^{20} - 4 q^{21} - 4 q^{22} + 16 q^{23} - 2 q^{24} + 3 q^{25} + q^{26} + 8 q^{27} - 10 q^{28} + 5 q^{29} + 7 q^{30} - 3 q^{31} + 2 q^{32} - 30 q^{33} + 16 q^{34} - 4 q^{35} - q^{36} - 16 q^{37} - 10 q^{38} + 6 q^{39} + q^{40} + 4 q^{42} + 6 q^{43} + 4 q^{44} - 7 q^{45} + 8 q^{46} + 16 q^{47} - q^{48} - 5 q^{49} + 6 q^{50} - 9 q^{51} + 2 q^{52} - 12 q^{53} + 4 q^{54} + 15 q^{55} - 5 q^{56} - 9 q^{57} + 10 q^{58} + 14 q^{60} - 6 q^{62} - 4 q^{63} + 4 q^{64} + 6 q^{65} - 15 q^{66} + 13 q^{67} + 8 q^{68} + 34 q^{69} - 8 q^{70} - 20 q^{71} - 2 q^{72} + q^{73} - 8 q^{74} - 5 q^{75} - 5 q^{76} + 3 q^{77} - 6 q^{78} + 10 q^{79} - q^{80} - 28 q^{81} - 15 q^{83} + 8 q^{84} + 18 q^{85} - 6 q^{86} + 9 q^{87} + 8 q^{88} + 26 q^{89} + 7 q^{90} + 9 q^{91} - 8 q^{92} + 18 q^{93} + 32 q^{94} + 18 q^{95} + q^{96} - 14 q^{97} - 10 q^{98} - 30 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - q^5 + q^6 + 5 * q^7 - 4 * q^8 + 2 * q^9 + q^10 - 8 * q^11 - q^12 - q^13 - 5 * q^14 - 7 * q^15 - 2 * q^16 + 8 * q^17 + q^18 - 5 * q^19 + 2 * q^20 - 4 * q^21 - 4 * q^22 + 16 * q^23 - 2 * q^24 + 3 * q^25 + q^26 + 8 * q^27 - 10 * q^28 + 5 * q^29 + 7 * q^30 - 3 * q^31 + 2 * q^32 - 30 * q^33 + 16 * q^34 - 4 * q^35 - q^36 - 16 * q^37 - 10 * q^38 + 6 * q^39 + q^40 + 4 * q^42 + 6 * q^43 + 4 * q^44 - 7 * q^45 + 8 * q^46 + 16 * q^47 - q^48 - 5 * q^49 + 6 * q^50 - 9 * q^51 + 2 * q^52 - 12 * q^53 + 4 * q^54 + 15 * q^55 - 5 * q^56 - 9 * q^57 + 10 * q^58 + 14 * q^60 - 6 * q^62 - 4 * q^63 + 4 * q^64 + 6 * q^65 - 15 * q^66 + 13 * q^67 + 8 * q^68 + 34 * q^69 - 8 * q^70 - 20 * q^71 - 2 * q^72 + q^73 - 8 * q^74 - 5 * q^75 - 5 * q^76 + 3 * q^77 - 6 * q^78 + 10 * q^79 - q^80 - 28 * q^81 - 15 * q^83 + 8 * q^84 + 18 * q^85 - 6 * q^86 + 9 * q^87 + 8 * q^88 + 26 * q^89 + 7 * q^90 + 9 * q^91 - 8 * q^92 + 18 * q^93 + 32 * q^94 + 18 * q^95 + q^96 - 14 * q^97 - 10 * q^98 - 30 * q^99

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